Metrics for 2cos (problem 3.3.5)

start0.0ms (0%)

Memory: 0.1MiB live, 0.1MiB allocated

analyze54.0ms (0.3%)

Memory

-21.9MiB live, 63.3MiB allocated

Algorithm

1×

Search

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

Compiler

Compiled 27 to 19 computations (29.6% saved)

sample9.0s (55.5%)

Memory

-51.6MiB live, 9 853.9MiB allocated

Samples

3.3s	5 639×	2	valid
3.3s	25 708×	0	invalid
533.0ms	2 478×	1	valid
17.0ms	139×	0	valid

Precisions

Click to see histograms. Total time spent on operations: 5.4s

ival-cos: 2.8s (52% of total)

const: 617.0ms (11.4% of total)

adjust: 407.0ms (7.5% of total)

ival-sub: 315.0ms (5.8% of total)

ival-<=: 290.0ms (5.4% of total)

ival-mult: 231.0ms (4.3% of total)

ival-add: 226.0ms (4.2% of total)

ival-fabs: 205.0ms (3.8% of total)

ival-<: 158.0ms (2.9% of total)

ival-and: 100.0ms (1.8% of total)

exact: 43.0ms (0.8% of total)

ival-assert: 11.0ms (0.2% of total)

Bogosity

explain334.0ms (2.1%)

Memory

29.1MiB live, 338.4MiB allocated

FPErrors

Click to see full error table

Ground Truth	Example	Example	Subexpression
145	-	-	`(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))`
2	-	-	`(cos.f64 (+.f64 x eps))`
0	-	-	`eps`
0	-	-	`(+.f64 x eps)`
0	-	-	`(cos.f64 x)`
0	-	-	`x`

Explanations

Click to see full explanations table

Operator	Subexpression	Explanation	Count
`-.f64`	`(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))`	cancellation	145	0
`cos.f64`	`(cos.f64 (+.f64 x eps))`	sensitivity	2	0

Confusion

	Predicted +	Predicted -
+	147	0
-	0	109

Precision

1.0

Recall

1.0

Confusion?

	Predicted +	Predicted Maybe	Predicted -
+	147	0	0
-	0	0	109

Precision?

1.0

Recall?

1.0

Freqs

test

number	freq
0	109
1	147

Total Confusion?

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

Precision?

1.0

Recall?

1.0

Samples

171.0ms	318×	2	valid
63.0ms	180×	1	valid
1.0ms	14×	0	valid

Compiler

Compiled 65 to 28 computations (56.9% saved)

Precisions

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

ival-cos: 142.0ms (84% of total)

adjust: 17.0ms (10.1% of total)

ival-sub: 6.0ms (3.6% of total)

ival-add: 3.0ms (1.8% of total)

ival-true: 1.0ms (0.6% of total)

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

preprocess31.0ms (0.2%)

Memory

-5.8MiB live, 32.3MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	18	41
1	38	37
2	81	35
3	151	35
4	277	35
5	374	35
6	460	35
7	498	35
8	550	35
9	566	35
10	574	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	110	7
8	159	7
9	175	7
10	183	7
0	183	7

Stop Event

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

Calls

Call 1

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

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

Compiler

Compiled 7 to 6 computations (14.3% saved)

eval0.0ms (0%)

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

prune0.0ms (0%)

Memory

1.3MiB live, 1.3MiB allocated

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	48.5%	(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))

Compiler

Compiled 7 to 6 computations (14.3% saved)

simplify6.0ms (0%)

Memory

11.2MiB live, 11.2MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 4 expressions of interest:

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	18
0	10	18
1	13	18
2	18	18
3	24	18
4	32	18
5	47	18
6	80	18
7	110	18
8	159	18
9	175	18
10	183	18
0	183	18

Stop Event

1×	iter limit
1×	saturated
1×	iter limit

Calls

Call 1

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

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

localize105.0ms (0.6%)

Memory

-13.4MiB live, 81.9MiB allocated

Localize:

Found 4 expressions of interest:

New	Metric	Score
accuracy	0	(+.f64 x eps)
accuracy	0	(cos.f64 x)
accuracy	0.07106138553059821	(cos.f64 (+.f64 x eps))
accuracy	32.84906024895874	(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))

Samples

66.0ms	159×	2	valid
30.0ms	90×	1	valid
1.0ms	7×	0	valid

Compiler

Compiled 38 to 14 computations (63.2% saved)

Precisions

Click to see histograms. Total time spent on operations: 84.0ms

ival-cos: 71.0ms (84.5% of total)

adjust: 9.0ms (10.7% of total)

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

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

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

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

series5.0ms (0%)

Memory

5.9MiB live, 5.9MiB allocated

Counts

4 → 84

Calls

Call 1

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

Outputs
#s(alt (* -1 (* eps (sin x))) (taylor 0 eps) (#s(alt (-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x)) (patch (-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x)) #<representation binary64>) () ())) ())
#s(alt (* eps (- (* -1/2 (* eps (cos x))) (sin x))) (taylor 0 eps) (#s(alt (-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x)) (patch (-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x)) #<representation binary64>) () ())) ())
#s(alt (* eps (- (* eps (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x))))) (sin x))) (taylor 0 eps) (#s(alt (-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x)) (patch (-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x)) #<representation binary64>) () ())) ())
#s(alt (* eps (- (* eps (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x)))))) (sin x))) (taylor 0 eps) (#s(alt (-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x)) (patch (-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x)) #<representation binary64>) () ())) ())
#s(alt (cos x) (taylor 0 eps) (#s(alt (cos.f64 (+.f64 x eps)) (patch (cos.f64 (+.f64 x eps)) #<representation binary64>) () ())) ())
#s(alt (+ (cos x) (* -1 (* eps (sin x)))) (taylor 0 eps) (#s(alt (cos.f64 (+.f64 x eps)) (patch (cos.f64 (+.f64 x eps)) #<representation binary64>) () ())) ())
#s(alt (+ (cos x) (* eps (- (* -1/2 (* eps (cos x))) (sin x)))) (taylor 0 eps) (#s(alt (cos.f64 (+.f64 x eps)) (patch (cos.f64 (+.f64 x eps)) #<representation binary64>) () ())) ())
#s(alt (+ (cos x) (* eps (- (* eps (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x))))) (sin x)))) (taylor 0 eps) (#s(alt (cos.f64 (+.f64 x eps)) (patch (cos.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 (- (cos (+ eps x)) (cos x)) (taylor inf eps) (#s(alt (-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x)) (patch (-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x)) #<representation binary64>) () ())) ())
#s(alt (- (cos (+ eps x)) (cos x)) (taylor inf eps) (#s(alt (-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x)) (patch (-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x)) #<representation binary64>) () ())) ())
#s(alt (- (cos (+ eps x)) (cos x)) (taylor inf eps) (#s(alt (-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x)) (patch (-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x)) #<representation binary64>) () ())) ())
#s(alt (- (cos (+ eps x)) (cos x)) (taylor inf eps) (#s(alt (-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x)) (patch (-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x)) #<representation binary64>) () ())) ())
#s(alt (cos (+ eps x)) (taylor inf eps) (#s(alt (cos.f64 (+.f64 x eps)) (patch (cos.f64 (+.f64 x eps)) #<representation binary64>) () ())) ())
#s(alt (cos (+ eps x)) (taylor inf eps) (#s(alt (cos.f64 (+.f64 x eps)) (patch (cos.f64 (+.f64 x eps)) #<representation binary64>) () ())) ())
#s(alt (cos (+ eps x)) (taylor inf eps) (#s(alt (cos.f64 (+.f64 x eps)) (patch (cos.f64 (+.f64 x eps)) #<representation binary64>) () ())) ())
#s(alt (cos (+ eps x)) (taylor inf eps) (#s(alt (cos.f64 (+.f64 x eps)) (patch (cos.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 (- (cos (- x (* -1 eps))) (cos x)) (taylor -inf eps) (#s(alt (-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x)) (patch (-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x)) #<representation binary64>) () ())) ())
#s(alt (- (cos (- x (* -1 eps))) (cos x)) (taylor -inf eps) (#s(alt (-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x)) (patch (-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x)) #<representation binary64>) () ())) ())
#s(alt (- (cos (- x (* -1 eps))) (cos x)) (taylor -inf eps) (#s(alt (-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x)) (patch (-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x)) #<representation binary64>) () ())) ())
#s(alt (- (cos (- x (* -1 eps))) (cos x)) (taylor -inf eps) (#s(alt (-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x)) (patch (-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x)) #<representation binary64>) () ())) ())
#s(alt (cos (- x (* -1 eps))) (taylor -inf eps) (#s(alt (cos.f64 (+.f64 x eps)) (patch (cos.f64 (+.f64 x eps)) #<representation binary64>) () ())) ())
#s(alt (cos (- x (* -1 eps))) (taylor -inf eps) (#s(alt (cos.f64 (+.f64 x eps)) (patch (cos.f64 (+.f64 x eps)) #<representation binary64>) () ())) ())
#s(alt (cos (- x (* -1 eps))) (taylor -inf eps) (#s(alt (cos.f64 (+.f64 x eps)) (patch (cos.f64 (+.f64 x eps)) #<representation binary64>) () ())) ())
#s(alt (cos (- x (* -1 eps))) (taylor -inf eps) (#s(alt (cos.f64 (+.f64 x eps)) (patch (cos.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 (- (cos eps) 1) (taylor 0 x) (#s(alt (-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x)) (patch (-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x)) #<representation binary64>) () ())) ())
#s(alt (- (+ (cos eps) (* -1 (* x (sin eps)))) 1) (taylor 0 x) (#s(alt (-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x)) (patch (-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x)) #<representation binary64>) () ())) ())
#s(alt (- (+ (cos eps) (* x (- (* x (+ 1/2 (* -1/2 (cos eps)))) (sin eps)))) 1) (taylor 0 x) (#s(alt (-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x)) (patch (-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x)) #<representation binary64>) () ())) ())
#s(alt (- (+ (cos eps) (* x (- (* x (+ 1/2 (+ (* -1/2 (cos eps)) (* 1/6 (* x (sin eps)))))) (sin eps)))) 1) (taylor 0 x) (#s(alt (-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x)) (patch (-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x)) #<representation binary64>) () ())) ())
#s(alt (cos eps) (taylor 0 x) (#s(alt (cos.f64 (+.f64 x eps)) (patch (cos.f64 (+.f64 x eps)) #<representation binary64>) () ())) ())
#s(alt (+ (cos eps) (* -1 (* x (sin eps)))) (taylor 0 x) (#s(alt (cos.f64 (+.f64 x eps)) (patch (cos.f64 (+.f64 x eps)) #<representation binary64>) () ())) ())
#s(alt (+ (cos eps) (* x (- (* -1/2 (* x (cos eps))) (sin eps)))) (taylor 0 x) (#s(alt (cos.f64 (+.f64 x eps)) (patch (cos.f64 (+.f64 x eps)) #<representation binary64>) () ())) ())
#s(alt (+ (cos eps) (* x (- (* x (+ (* -1/2 (cos eps)) (* 1/6 (* x (sin eps))))) (sin eps)))) (taylor 0 x) (#s(alt (cos.f64 (+.f64 x eps)) (patch (cos.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 1 (taylor 0 x) (#s(alt (cos.f64 x) (patch (cos.f64 x) #<representation binary64>) () ())) ())
#s(alt (+ 1 (* -1/2 (pow x 2))) (taylor 0 x) (#s(alt (cos.f64 x) (patch (cos.f64 x) #<representation binary64>) () ())) ())
#s(alt (+ 1 (* (pow x 2) (- (* 1/24 (pow x 2)) 1/2))) (taylor 0 x) (#s(alt (cos.f64 x) (patch (cos.f64 x) #<representation binary64>) () ())) ())
#s(alt (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))) 1/2))) (taylor 0 x) (#s(alt (cos.f64 x) (patch (cos.f64 x) #<representation binary64>) () ())) ())
#s(alt (- (cos (+ eps x)) (cos x)) (taylor inf x) (#s(alt (-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x)) (patch (-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x)) #<representation binary64>) () ())) ())
#s(alt (- (cos (+ eps x)) (cos x)) (taylor inf x) (#s(alt (-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x)) (patch (-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x)) #<representation binary64>) () ())) ())
#s(alt (- (cos (+ eps x)) (cos x)) (taylor inf x) (#s(alt (-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x)) (patch (-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x)) #<representation binary64>) () ())) ())
#s(alt (- (cos (+ eps x)) (cos x)) (taylor inf x) (#s(alt (-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x)) (patch (-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x)) #<representation binary64>) () ())) ())
#s(alt (cos (+ eps x)) (taylor inf x) (#s(alt (cos.f64 (+.f64 x eps)) (patch (cos.f64 (+.f64 x eps)) #<representation binary64>) () ())) ())
#s(alt (cos (+ eps x)) (taylor inf x) (#s(alt (cos.f64 (+.f64 x eps)) (patch (cos.f64 (+.f64 x eps)) #<representation binary64>) () ())) ())
#s(alt (cos (+ eps x)) (taylor inf x) (#s(alt (cos.f64 (+.f64 x eps)) (patch (cos.f64 (+.f64 x eps)) #<representation binary64>) () ())) ())
#s(alt (cos (+ eps x)) (taylor inf x) (#s(alt (cos.f64 (+.f64 x eps)) (patch (cos.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 (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>) () ())) ())
#s(alt (- (cos (- eps (* -1 x))) (cos x)) (taylor -inf x) (#s(alt (-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x)) (patch (-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x)) #<representation binary64>) () ())) ())
#s(alt (- (cos (- eps (* -1 x))) (cos x)) (taylor -inf x) (#s(alt (-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x)) (patch (-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x)) #<representation binary64>) () ())) ())
#s(alt (- (cos (- eps (* -1 x))) (cos x)) (taylor -inf x) (#s(alt (-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x)) (patch (-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x)) #<representation binary64>) () ())) ())
#s(alt (- (cos (- eps (* -1 x))) (cos x)) (taylor -inf x) (#s(alt (-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x)) (patch (-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x)) #<representation binary64>) () ())) ())
#s(alt (cos (- eps (* -1 x))) (taylor -inf x) (#s(alt (cos.f64 (+.f64 x eps)) (patch (cos.f64 (+.f64 x eps)) #<representation binary64>) () ())) ())
#s(alt (cos (- eps (* -1 x))) (taylor -inf x) (#s(alt (cos.f64 (+.f64 x eps)) (patch (cos.f64 (+.f64 x eps)) #<representation binary64>) () ())) ())
#s(alt (cos (- eps (* -1 x))) (taylor -inf x) (#s(alt (cos.f64 (+.f64 x eps)) (patch (cos.f64 (+.f64 x eps)) #<representation binary64>) () ())) ())
#s(alt (cos (- eps (* -1 x))) (taylor -inf x) (#s(alt (cos.f64 (+.f64 x eps)) (patch (cos.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 (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
1.0ms	eps	@	inf	((- (cos (+ x eps)) (cos x)) (cos (+ x eps)) (+ x eps) (cos x))
1.0ms	x	@	0	((- (cos (+ x eps)) (cos x)) (cos (+ x eps)) (+ x eps) (cos x))
1.0ms	eps	@	0	((- (cos (+ x eps)) (cos x)) (cos (+ x eps)) (+ x eps) (cos x))
1.0ms	eps	@	-inf	((- (cos (+ x eps)) (cos x)) (cos (+ x eps)) (+ x eps) (cos x))
0.0ms	x	@	-inf	((- (cos (+ x eps)) (cos x)) (cos (+ x eps)) (+ x eps) (cos x))

simplify221.0ms (1.4%)

Memory

-6.5MiB live, 173.0MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	105	498
1	277	495
2	626	495
3	2434	494
0	8369	474

Stop Event

1×	iter limit
1×	node limit

Counts

84 → 78

Calls

Call 1

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

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

rewrite177.0ms (1.1%)

Memory

1.1MiB live, 168.0MiB allocated

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	16
0	10	16
1	54	16
2	385	16
3	4790	16
0	8343	16

Stop Event

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

Counts

4 → 228

Calls

Call 1

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

Outputs
#<batchref>
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eval62.0ms (0.4%)

Memory: 9.4MiB live, 47.1MiB allocated
Compiler: Compiled 6 943 to 891 computations (87.2% saved)

prune60.0ms (0.4%)

Memory

-3.1MiB live, 41.0MiB allocated

Pruning

13 alts after pruning (12 fresh and 1 done)

	Pruned	Kept	Total
New	294	12	306
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	294	13	307

Accuracy

99.8%

Counts

307 → 13

Alt Table

Click to see full alt table

Status	Accuracy	Program
	48.7%	(-.f64 (fma.f64 (sin.f64 x) (neg.f64 (sin.f64 eps)) (*.f64 (cos.f64 eps) (cos.f64 x))) (cos.f64 x))
	48.7%	(-.f64 (*.f64 (cos.f64 eps) (cos.f64 x)) (fma.f64 (sin.f64 eps) (sin.f64 x) (cos.f64 x)))
✓	48.5%	(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))
	47.4%	(-.f64 (cos.f64 (+.f64 x eps)) #s(approx (cos x) (fma.f64 (fma.f64 (fma.f64 #s(literal -1/720 binary64) (.f64 x x) #s(literal 1/24 binary64)) (.f64 x x) #s(literal -1/2 binary64)) (*.f64 x x) #s(literal 1 binary64))))
▶	47.2%	(-.f64 (cos.f64 (+.f64 x eps)) #s(approx (cos x) (fma.f64 (fma.f64 (.f64 x x) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) (.f64 x x) #s(literal 1 binary64))))
	46.9%	(-.f64 (cos.f64 (+.f64 x eps)) #s(approx (cos x) (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64))))
	46.3%	(-.f64 (cos.f64 (+.f64 x eps)) #s(approx (cos x) #s(literal 1 binary64)))
▶	46.6%	(-.f64 #s(approx (cos (+ x eps)) (cos.f64 eps)) (cos.f64 x))
▶	99.7%	(.f64 (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps))) (sin.f64 (.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 0 binary64) eps)))) #s(literal -2 binary64))
▶	46.3%	#s(approx (- (cos (+ x eps)) (cos x)) (-.f64 (cos.f64 eps) #s(literal 1 binary64)))
	99.1%	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 (-.f64 (.f64 (fma.f64 (fma.f64 #s(literal 1/6 binary64) (sin.f64 x) (.f64 #s(literal 1/24 binary64) (.f64 (cos.f64 x) eps))) eps (*.f64 (cos.f64 x) #s(literal -1/2 binary64))) eps) (sin.f64 x)) eps))
	98.5%	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 (-.f64 (.f64 (*.f64 (cos.f64 x) #s(literal -1/2 binary64)) eps) (sin.f64 x)) eps))
▶	75.2%	#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (neg.f64 (sin.f64 x)) eps))

Compiler

Compiled 315 to 246 computations (21.9% saved)

simplify576.0ms (3.5%)

Memory

-1.4MiB live, 170.2MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 19 expressions of interest:

New	Metric	Score
cost-diff	0	(cos.f64 x)
cost-diff	0	(cos.f64 eps)
cost-diff	0	#s(approx (cos (+ x eps)) (cos.f64 eps))
cost-diff	0	(-.f64 #s(approx (cos (+ x eps)) (cos.f64 eps)) (cos.f64 x))
cost-diff	0	#s(approx (cos x) (fma.f64 (fma.f64 (.f64 x x) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) (.f64 x x) #s(literal 1 binary64)))
cost-diff	0	(+.f64 x eps)
cost-diff	0	(cos.f64 (+.f64 x eps))
cost-diff	0	(-.f64 (cos.f64 (+.f64 x eps)) #s(approx (cos x) (fma.f64 (fma.f64 (.f64 x x) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) (.f64 x x) #s(literal 1 binary64))))
cost-diff	0	(sin.f64 x)
cost-diff	0	(neg.f64 (sin.f64 x))
cost-diff	0	(*.f64 (neg.f64 (sin.f64 x)) eps)
cost-diff	0	#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (neg.f64 (sin.f64 x)) eps))
cost-diff	0	(cos.f64 eps)
cost-diff	0	(-.f64 (cos.f64 eps) #s(literal 1 binary64))
cost-diff	0	#s(approx (- (cos (+ x eps)) (cos x)) (-.f64 (cos.f64 eps) #s(literal 1 binary64)))
cost-diff	0	(.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps))) (sin.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 0 binary64) eps))))
cost-diff	0	(.f64 (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps))) (sin.f64 (.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 0 binary64) eps)))) #s(literal -2 binary64))
cost-diff	192	(+.f64 #s(literal 0 binary64) eps)
cost-diff	320	(*.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	38	200
0	64	190
1	109	190
2	190	186
3	295	186
4	674	186
5	1337	186
6	1561	186
7	1844	186
8	2318	186
9	3353	186
10	4802	186
11	5403	186
12	5708	186
13	5741	186
14	5765	186
15	5778	186
16	6049	186
17	6159	186
18	6227	186
19	6267	186
20	6291	186
21	6311	186
22	6319	186
23	6319	186
24	6825	186
25	7033	186
26	7033	186
27	7033	186
28	7033	186
29	7033	186
30	7033	186
31	7033	186
0	12821	182

Stop Event

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

Calls

Call 1

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

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

localize275.0ms (1.7%)

Memory

0.4MiB live, 158.3MiB allocated

Localize:

Found 19 expressions of interest:

New	Metric	Score
accuracy	0	(cos.f64 x)
accuracy	0	(cos.f64 eps)
accuracy	1.9172297504219822	#s(approx (cos (+ x eps)) (cos.f64 eps))
accuracy	32.84906024895874	(-.f64 #s(approx (cos (+ x eps)) (cos.f64 eps)) (cos.f64 x))
accuracy	0.02768540172363414	(fma.f64 (*.f64 x x) #s(literal 1/24 binary64) #s(literal -1/2 binary64))
accuracy	0.07106138553059821	(cos.f64 (+.f64 x eps))
accuracy	1.1239978216842443	#s(approx (cos x) (fma.f64 (fma.f64 (.f64 x x) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) (.f64 x x) #s(literal 1 binary64)))
accuracy	32.84906024895874	(-.f64 (cos.f64 (+.f64 x eps)) #s(approx (cos x) (fma.f64 (fma.f64 (.f64 x x) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) (.f64 x x) #s(literal 1 binary64))))
accuracy	0	(*.f64 (neg.f64 (sin.f64 x)) eps)
accuracy	0	(sin.f64 x)
accuracy	0	(neg.f64 (sin.f64 x))
accuracy	15.856391180419081	#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (neg.f64 (sin.f64 x)) eps))
accuracy	0	(cos.f64 eps)
accuracy	32.554681003050774	(-.f64 (cos.f64 eps) #s(literal 1 binary64))
accuracy	33.32883884922006	#s(approx (- (cos (+ x eps)) (cos x)) (-.f64 (cos.f64 eps) #s(literal 1 binary64)))
accuracy	0	(sin.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 0 binary64) eps)))
accuracy	0.01953125	(.f64 (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps))) (sin.f64 (.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 0 binary64) eps)))) #s(literal -2 binary64))
accuracy	0.0921260934066794	(sin.f64 (*.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps)))
accuracy	0.109375	(.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps))) (sin.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 0 binary64) eps))))

Samples

178.0ms	159×	2	valid
35.0ms	90×	1	valid
2.0ms	6×	0	valid
2.0ms	1×	3	valid

Compiler

Compiled 343 to 68 computations (80.2% saved)

Precisions

Click to see histograms. Total time spent on operations: 167.0ms

ival-cos: 97.0ms (58% of total)

adjust: 26.0ms (15.5% of total)

ival-mult: 22.0ms (13.1% of total)

ival-sub: 6.0ms (3.6% of total)

ival-sin: 6.0ms (3.6% of total)

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

const: 4.0ms (2.4% of total)

exact: 1.0ms (0.6% of total)

ival-neg: 1.0ms (0.6% of total)

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

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

series55.0ms (0.3%)

Memory

-26.3MiB live, 44.3MiB allocated

Counts

21 → 396

Calls

Call 1

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

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

Calls

6 calls:

Time	Variable		Point	Expression
18.0ms	eps	@	inf	((* 1/2 (+ (* 2 x) eps)) (+ 0 eps) (* (* (sin (* 1/2 (+ (* 2 x) eps))) (sin (* 1/2 (+ 0 eps)))) -2) (* (sin (* 1/2 (+ (* 2 x) eps))) (sin (* 1/2 (+ 0 eps)))) (- (cos (+ x eps)) (cos x)) (- (cos eps) 1) (cos eps) (- (cos (+ x eps)) (cos x)) (* (neg (sin x)) eps) (neg (sin x)) (sin x) (- (cos (+ x eps)) (cos x)) (cos (+ x eps)) (+ x eps) (cos x) (- (cos (+ x eps)) (cos x)) (cos (+ x eps)) (cos x) (sin (* 1/2 (+ (* 2 x) eps))) (sin (* 1/2 (+ 0 eps))) (+ (* (* x x) 1/24) -1/2))
3.0ms	eps	@	0	((* 1/2 (+ (* 2 x) eps)) (+ 0 eps) (* (* (sin (* 1/2 (+ (* 2 x) eps))) (sin (* 1/2 (+ 0 eps)))) -2) (* (sin (* 1/2 (+ (* 2 x) eps))) (sin (* 1/2 (+ 0 eps)))) (- (cos (+ x eps)) (cos x)) (- (cos eps) 1) (cos eps) (- (cos (+ x eps)) (cos x)) (* (neg (sin x)) eps) (neg (sin x)) (sin x) (- (cos (+ x eps)) (cos x)) (cos (+ x eps)) (+ x eps) (cos x) (- (cos (+ x eps)) (cos x)) (cos (+ x eps)) (cos x) (sin (* 1/2 (+ (* 2 x) eps))) (sin (* 1/2 (+ 0 eps))) (+ (* (* x x) 1/24) -1/2))
3.0ms	eps	@	-inf	((* 1/2 (+ (* 2 x) eps)) (+ 0 eps) (* (* (sin (* 1/2 (+ (* 2 x) eps))) (sin (* 1/2 (+ 0 eps)))) -2) (* (sin (* 1/2 (+ (* 2 x) eps))) (sin (* 1/2 (+ 0 eps)))) (- (cos (+ x eps)) (cos x)) (- (cos eps) 1) (cos eps) (- (cos (+ x eps)) (cos x)) (* (neg (sin x)) eps) (neg (sin x)) (sin x) (- (cos (+ x eps)) (cos x)) (cos (+ x eps)) (+ x eps) (cos x) (- (cos (+ x eps)) (cos x)) (cos (+ x eps)) (cos x) (sin (* 1/2 (+ (* 2 x) eps))) (sin (* 1/2 (+ 0 eps))) (+ (* (* x x) 1/24) -1/2))
3.0ms	x	@	inf	((* 1/2 (+ (* 2 x) eps)) (+ 0 eps) (* (* (sin (* 1/2 (+ (* 2 x) eps))) (sin (* 1/2 (+ 0 eps)))) -2) (* (sin (* 1/2 (+ (* 2 x) eps))) (sin (* 1/2 (+ 0 eps)))) (- (cos (+ x eps)) (cos x)) (- (cos eps) 1) (cos eps) (- (cos (+ x eps)) (cos x)) (* (neg (sin x)) eps) (neg (sin x)) (sin x) (- (cos (+ x eps)) (cos x)) (cos (+ x eps)) (+ x eps) (cos x) (- (cos (+ x eps)) (cos x)) (cos (+ x eps)) (cos x) (sin (* 1/2 (+ (* 2 x) eps))) (sin (* 1/2 (+ 0 eps))) (+ (* (* x x) 1/24) -1/2))
2.0ms	x	@	-inf	((* 1/2 (+ (* 2 x) eps)) (+ 0 eps) (* (* (sin (* 1/2 (+ (* 2 x) eps))) (sin (* 1/2 (+ 0 eps)))) -2) (* (sin (* 1/2 (+ (* 2 x) eps))) (sin (* 1/2 (+ 0 eps)))) (- (cos (+ x eps)) (cos x)) (- (cos eps) 1) (cos eps) (- (cos (+ x eps)) (cos x)) (* (neg (sin x)) eps) (neg (sin x)) (sin x) (- (cos (+ x eps)) (cos x)) (cos (+ x eps)) (+ x eps) (cos x) (- (cos (+ x eps)) (cos x)) (cos (+ x eps)) (cos x) (sin (* 1/2 (+ (* 2 x) eps))) (sin (* 1/2 (+ 0 eps))) (+ (* (* x x) 1/24) -1/2))

simplify183.0ms (1.1%)

Memory

26.1MiB live, 301.9MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	335	3170
1	1002	3025
2	2640	2989
3	6133	2989
0	8160	2793

Stop Event

1×	iter limit
1×	node limit

Counts

396 → 374

Calls

Call 1

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

Outputs
x
(+ x (* 1/2 eps))
(fma.f64 eps #s(literal 1/2 binary64) x)
(+ x (* 1/2 eps))
(fma.f64 eps #s(literal 1/2 binary64) x)
(+ x (* 1/2 eps))
(fma.f64 eps #s(literal 1/2 binary64) x)
eps
eps
eps
eps
(* -1 (* eps (sin x)))
(*.f64 (neg.f64 eps) (sin.f64 x))
(* eps (+ (* -1 (sin x)) (* -1/2 (* eps (cos x)))))
(.f64 (fma.f64 (.f64 #s(literal -1/2 binary64) eps) (cos.f64 x) (neg.f64 (sin.f64 x))) eps)
(* eps (+ (* -1 (sin x)) (* eps (+ (* -2 (* eps (+ (* -1/16 (sin x)) (* -1/48 (sin x))))) (* -1/2 (cos x))))))
(.f64 (fma.f64 (fma.f64 #s(literal 1/6 binary64) (.f64 (sin.f64 x) eps) (*.f64 (cos.f64 x) #s(literal -1/2 binary64))) eps (neg.f64 (sin.f64 x))) eps)
(* eps (+ (* -1 (sin x)) (* eps (+ (* -1/2 (cos x)) (* eps (+ (* -2 (+ (* -1/16 (sin x)) (* -1/48 (sin x)))) (* 1/24 (* eps (cos x)))))))))
(.f64 (fma.f64 (fma.f64 (cos.f64 x) (fma.f64 (.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) (.f64 (.f64 #s(literal 1/6 binary64) (sin.f64 x)) eps)) eps (neg.f64 (sin.f64 x))) eps)
(* 1/2 (* eps (sin x)))
(.f64 (.f64 (sin.f64 x) #s(literal 1/2 binary64)) eps)
(* eps (+ (* 1/4 (* eps (cos x))) (* 1/2 (sin x))))
(.f64 (fma.f64 (.f64 #s(literal 1/4 binary64) (cos.f64 x)) eps (*.f64 (sin.f64 x) #s(literal 1/2 binary64))) eps)
(* eps (+ (* 1/2 (sin x)) (* eps (+ (* 1/4 (cos x)) (* eps (+ (* -1/16 (sin x)) (* -1/48 (sin x))))))))
(.f64 (fma.f64 (fma.f64 #s(literal 1/4 binary64) (cos.f64 x) (.f64 (.f64 #s(literal -1/12 binary64) (sin.f64 x)) eps)) eps (.f64 (sin.f64 x) #s(literal 1/2 binary64))) eps)
(* eps (+ (* 1/2 (sin x)) (* eps (+ (* 1/4 (cos x)) (* eps (+ (* -1/16 (sin x)) (+ (* -1/48 (sin x)) (* -1/48 (* eps (cos x))))))))))
(.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -1/12 binary64) (sin.f64 x) (.f64 #s(literal -1/48 binary64) (.f64 (cos.f64 x) eps))) eps (.f64 #s(literal 1/4 binary64) (cos.f64 x))) eps (*.f64 (sin.f64 x) #s(literal 1/2 binary64))) eps)
(* -1 (* eps (sin x)))
(*.f64 (neg.f64 eps) (sin.f64 x))
(* eps (- (* -1/2 (* eps (cos x))) (sin x)))
(.f64 (fma.f64 (.f64 #s(literal -1/2 binary64) eps) (cos.f64 x) (neg.f64 (sin.f64 x))) eps)
(* eps (- (* eps (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x))))) (sin x)))
(.f64 (fma.f64 (fma.f64 #s(literal 1/6 binary64) (.f64 (sin.f64 x) eps) (*.f64 (cos.f64 x) #s(literal -1/2 binary64))) eps (neg.f64 (sin.f64 x))) eps)
(* eps (- (* eps (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x)))))) (sin x)))
(.f64 (fma.f64 (fma.f64 (cos.f64 x) (fma.f64 (.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) (.f64 (.f64 #s(literal 1/6 binary64) (sin.f64 x)) eps)) eps (neg.f64 (sin.f64 x))) eps)
(* -1/2 (pow eps 2))
(.f64 (.f64 eps eps) #s(literal -1/2 binary64))
(* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2))
(.f64 (.f64 (fma.f64 (*.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) eps) eps)
(* (pow eps 2) (- (* (pow eps 2) (+ 1/24 (* -1/720 (pow eps 2)))) 1/2))
(.f64 (.f64 (fma.f64 (fma.f64 #s(literal -1/720 binary64) (.f64 eps eps) #s(literal 1/24 binary64)) (.f64 eps eps) #s(literal -1/2 binary64)) eps) eps)
(* (pow eps 2) (- (* (pow eps 2) (+ 1/24 (* (pow eps 2) (- (* 1/40320 (pow eps 2)) 1/720)))) 1/2))
(.f64 (.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 1/40320 binary64) (.f64 eps eps) #s(literal -1/720 binary64)) (.f64 eps eps) #s(literal 1/24 binary64)) (*.f64 eps eps) #s(literal -1/2 binary64)) eps) eps)
1
#s(literal 1 binary64)
(+ 1 (* -1/2 (pow eps 2)))
(fma.f64 (*.f64 eps eps) #s(literal -1/2 binary64) #s(literal 1 binary64))
(+ 1 (* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2)))
(fma.f64 (fma.f64 (.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) (.f64 eps eps) #s(literal 1 binary64))
(+ 1 (* (pow eps 2) (- (* (pow eps 2) (+ 1/24 (* -1/720 (pow eps 2)))) 1/2)))
(fma.f64 (fma.f64 (fma.f64 #s(literal -1/720 binary64) (.f64 eps eps) #s(literal 1/24 binary64)) (.f64 eps eps) #s(literal -1/2 binary64)) (*.f64 eps eps) #s(literal 1 binary64))
(* -1 (* eps (sin x)))
(*.f64 (neg.f64 eps) (sin.f64 x))
(* eps (- (* -1/2 (* eps (cos x))) (sin x)))
(.f64 (fma.f64 (.f64 #s(literal -1/2 binary64) eps) (cos.f64 x) (neg.f64 (sin.f64 x))) eps)
(* eps (- (* eps (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x))))) (sin x)))
(.f64 (fma.f64 (fma.f64 #s(literal 1/6 binary64) (.f64 (sin.f64 x) eps) (*.f64 (cos.f64 x) #s(literal -1/2 binary64))) eps (neg.f64 (sin.f64 x))) eps)
(* eps (- (* eps (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x)))))) (sin x)))
(.f64 (fma.f64 (fma.f64 (cos.f64 x) (fma.f64 (.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) (.f64 (.f64 #s(literal 1/6 binary64) (sin.f64 x)) eps)) eps (neg.f64 (sin.f64 x))) eps)
(* -1 (* eps (sin x)))
(*.f64 (neg.f64 eps) (sin.f64 x))
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(* -1 (* eps (sin x)))
(*.f64 (neg.f64 eps) (sin.f64 x))
(* -1 (* eps (sin x)))
(*.f64 (neg.f64 eps) (sin.f64 x))
(* -1 (* eps (sin x)))
(*.f64 (neg.f64 eps) (sin.f64 x))
(* -1 (sin x))
(neg.f64 (sin.f64 x))
(* -1 (sin x))
(neg.f64 (sin.f64 x))
(* -1 (sin x))
(neg.f64 (sin.f64 x))
(* -1 (sin x))
(neg.f64 (sin.f64 x))
(sin x)
(sin.f64 x)
(sin x)
(sin.f64 x)
(sin x)
(sin.f64 x)
(sin x)
(sin.f64 x)
(- (cos (- eps (* -1 x))) (cos x))
(-.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x))
(- (cos (- eps (* -1 x))) (cos x))
(-.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x))
(- (cos (- eps (* -1 x))) (cos x))
(-.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x))
(- (cos (- eps (* -1 x))) (cos x))
(-.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x))
(cos (- eps (* -1 x)))
(cos.f64 (+.f64 eps x))
(cos (- eps (* -1 x)))
(cos.f64 (+.f64 eps x))
(cos (- eps (* -1 x)))
(cos.f64 (+.f64 eps x))
(cos (- eps (* -1 x)))
(cos.f64 (+.f64 eps x))
x
(* -1 (* x (- (* -1 (/ eps x)) 1)))
(+.f64 eps x)
(* -1 (* x (- (* -1 (/ eps x)) 1)))
(+.f64 eps x)
(* -1 (* x (- (* -1 (/ eps x)) 1)))
(+.f64 eps x)
(cos x)
(cos.f64 x)
(cos x)
(cos.f64 x)
(cos x)
(cos.f64 x)
(cos x)
(cos.f64 x)
(- (cos (- eps (* -1 x))) (cos x))
(-.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x))
(- (cos (- eps (* -1 x))) (cos x))
(-.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x))
(- (cos (- eps (* -1 x))) (cos x))
(-.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x))
(- (cos (- eps (* -1 x))) (cos x))
(-.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x))
(cos (- eps (* -1 x)))
(cos.f64 (+.f64 eps x))
(cos (- eps (* -1 x)))
(cos.f64 (+.f64 eps x))
(cos (- eps (* -1 x)))
(cos.f64 (+.f64 eps x))
(cos (- eps (* -1 x)))
(cos.f64 (+.f64 eps x))
(cos x)
(cos.f64 x)
(cos x)
(cos.f64 x)
(cos x)
(cos.f64 x)
(cos x)
(cos.f64 x)
(sin (* 1/2 (- eps (* -2 x))))
(sin.f64 (fma.f64 eps #s(literal 1/2 binary64) x))
(sin (* 1/2 (- eps (* -2 x))))
(sin.f64 (fma.f64 eps #s(literal 1/2 binary64) x))
(sin (* 1/2 (- eps (* -2 x))))
(sin.f64 (fma.f64 eps #s(literal 1/2 binary64) x))
(sin (* 1/2 (- eps (* -2 x))))
(sin.f64 (fma.f64 eps #s(literal 1/2 binary64) x))
(* 1/24 (pow x 2))
(.f64 (.f64 x x) #s(literal 1/24 binary64))
(* (pow x 2) (- 1/24 (* 1/2 (/ 1 (pow x 2)))))
(.f64 (.f64 (-.f64 #s(literal 1/24 binary64) (/.f64 #s(literal 1/2 binary64) (*.f64 x x))) x) x)
(* (pow x 2) (- 1/24 (* 1/2 (/ 1 (pow x 2)))))
(.f64 (.f64 (-.f64 #s(literal 1/24 binary64) (/.f64 #s(literal 1/2 binary64) (*.f64 x x))) x) x)
(* (pow x 2) (- 1/24 (* 1/2 (/ 1 (pow x 2)))))
(.f64 (.f64 (-.f64 #s(literal 1/24 binary64) (/.f64 #s(literal 1/2 binary64) (*.f64 x x))) x) x)

rewrite227.0ms (1.4%)

Memory

0.8MiB live, 385.5MiB allocated

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	38	158
0	64	150
1	230	150
2	1677	150
0	8288	150

Stop Event

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

Counts

21 → 370

Calls

Call 1

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

Outputs
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eval93.0ms (0.6%)

Memory: 9.9MiB live, 245.9MiB allocated
Compiler: Compiled 14 420 to 1 899 computations (86.8% saved)

prune115.0ms (0.7%)

Memory

-24.9MiB live, 125.2MiB allocated

Pruning

32 alts after pruning (29 fresh and 3 done)

	Pruned	Kept	Total
New	739	26	765
Fresh	4	3	7
Picked	3	2	5
Done	0	1	1
Total	746	32	778

Accuracy

100.0%

Counts

778 → 32

Alt Table

Click to see full alt table

Status	Accuracy	Program
	48.7%	(-.f64 (fma.f64 (sin.f64 x) (neg.f64 (sin.f64 eps)) (*.f64 (cos.f64 eps) (cos.f64 x))) (cos.f64 x))
	48.7%	(-.f64 (*.f64 (cos.f64 eps) (cos.f64 x)) (fma.f64 (sin.f64 eps) (sin.f64 x) (cos.f64 x)))
✓	48.5%	(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))
✓	47.2%	(-.f64 (cos.f64 (+.f64 x eps)) #s(approx (cos x) (fma.f64 (fma.f64 (.f64 x x) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) (.f64 x x) #s(literal 1 binary64))))
	46.9%	(-.f64 (cos.f64 (+.f64 x eps)) #s(approx (cos x) (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64))))
	46.6%	(-.f64 #s(approx (cos (+ x eps)) #s(approx (cos eps) (fma.f64 (*.f64 eps eps) #s(literal -1/2 binary64) #s(literal 1 binary64)))) (cos.f64 x))
	46.6%	(-.f64 #s(approx (cos (+ x eps)) #s(approx (cos eps) #s(literal 1 binary64))) (cos.f64 x))
	99.5%	(.f64 (.f64 (sin.f64 (/.f64 (.f64 (fma.f64 #s(literal 4 binary64) (.f64 x x) (.f64 (neg.f64 eps) eps)) #s(literal 1/2 binary64)) (fma.f64 x #s(literal 2 binary64) (neg.f64 eps)))) (sin.f64 (.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 0 binary64) eps)))) #s(literal -2 binary64))
	41.8%	(.f64 (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps))) (sin.f64 (.f64 #s(literal 1/2 binary64) (/.f64 (pow.f64 eps #s(literal 3 binary64)) (*.f64 eps eps))))) #s(literal -2 binary64))
	99.1%	(.f64 (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps))) (sin.f64 (.f64 #s(literal 1/2 binary64) (/.f64 (*.f64 eps eps) (-.f64 eps #s(literal 0 binary64)))))) #s(literal -2 binary64))
	99.6%	(.f64 (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps))) (sin.f64 (.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1 binary64) (pow.f64 eps #s(literal -1 binary64)))))) #s(literal -2 binary64))
	98.9%	(.f64 (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps))) (sin.f64 (.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1 binary64) (/.f64 (neg.f64 eps) (neg.f64 (*.f64 eps eps))))))) #s(literal -2 binary64))
	98.9%	(.f64 (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps))) (sin.f64 (.f64 #s(literal 1/2 binary64) (.f64 (neg.f64 (.f64 eps eps)) (pow.f64 (neg.f64 eps) #s(literal -1 binary64)))))) #s(literal -2 binary64))
▶	99.5%	(.f64 (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps))) #s(approx (sin ( 1/2 (+ 0 eps))) (.f64 (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))
	99.3%	(.f64 (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps))) #s(approx (sin ( 1/2 (+ 0 eps))) (.f64 (fma.f64 (fma.f64 #s(literal 1/3840 binary64) (.f64 eps eps) #s(literal -1/48 binary64)) (*.f64 eps eps) #s(literal 1/2 binary64)) eps))) #s(literal -2 binary64))
	99.1%	(.f64 (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps))) #s(approx (sin ( 1/2 (+ 0 eps))) (.f64 (fma.f64 (.f64 eps eps) #s(literal -1/48 binary64) #s(literal 1/2 binary64)) eps))) #s(literal -2 binary64))
	98.5%	(.f64 (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps))) #s(approx (sin ( 1/2 (+ 0 eps))) (*.f64 eps #s(literal 1/2 binary64)))) #s(literal -2 binary64))
▶	99.7%	(.f64 #s(approx ( (sin (* 1/2 (+ (* 2 x) eps))) (sin (* 1/2 (+ 0 eps)))) (.f64 (sin.f64 (fma.f64 eps #s(literal 1/2 binary64) x)) (sin.f64 (.f64 eps #s(literal 1/2 binary64))))) #s(literal -2 binary64))
▶	46.3%	#s(approx (- (cos (+ x eps)) (cos x)) (-.f64 #s(approx (cos eps) #s(literal 1 binary64)) #s(literal 1 binary64)))
▶	99.1%	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 (fma.f64 (fma.f64 (cos.f64 x) (fma.f64 (.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) (.f64 (.f64 #s(literal 1/6 binary64) (sin.f64 x)) eps)) eps (neg.f64 (sin.f64 x))) eps))
	98.5%	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 (fma.f64 (.f64 #s(literal -1/2 binary64) eps) (cos.f64 x) (neg.f64 (sin.f64 x))) eps))
	67.2%	#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (/.f64 (pow.f64 eps #s(literal 3 binary64)) eps) (/.f64 (neg.f64 (sin.f64 x)) eps)))
✓	75.2%	#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (neg.f64 (sin.f64 x)) eps))
▶	75.0%	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (neg (sin x)) (.f64 (fma.f64 (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)) (*.f64 x x) #s(literal -1 binary64)) x)) eps))
	74.9%	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (neg (sin x)) (.f64 (fma.f64 (fma.f64 #s(literal -1/120 binary64) (.f64 x x) #s(literal 1/6 binary64)) (.f64 x x) #s(literal -1 binary64)) x)) eps))
	74.8%	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (neg (sin x)) (.f64 (fma.f64 (*.f64 x x) #s(literal 1/6 binary64) #s(literal -1 binary64)) x)) eps))
	74.6%	#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 #s(approx (neg (sin x)) (neg.f64 x)) eps))
	47.9%	#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (- (cos eps) 1) (.f64 (.f64 eps eps) #s(literal -1/2 binary64))))
	74.9%	#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg (sin x)) eps) (.f64 (fma.f64 (.f64 eps (fma.f64 #s(literal -1/120 binary64) (.f64 x x) #s(literal 1/6 binary64))) (.f64 x x) (neg.f64 eps)) x)))
	74.8%	#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg (sin x)) eps) (.f64 (.f64 eps (fma.f64 (*.f64 x x) #s(literal 1/6 binary64) #s(literal -1 binary64))) x)))
	98.0%	#s(approx (* (* (sin (* 1/2 (+ (* 2 x) eps))) (sin (* 1/2 (+ 0 eps)))) -2) (fma.f64 (fma.f64 (.f64 (cos.f64 (.f64 eps #s(literal 1/2 binary64))) (sin.f64 (.f64 eps #s(literal 1/2 binary64)))) (+.f64 #s(literal -2 binary64) (.f64 x (.f64 #s(literal 1/3 binary64) x))) (.f64 (pow.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) #s(literal 2 binary64)) x)) x (.f64 (pow.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) #s(literal 2 binary64)) #s(literal -2 binary64))))
	97.0%	#s(approx (* (* (sin (* 1/2 (+ (* 2 x) eps))) (sin (* 1/2 (+ 0 eps)))) -2) (fma.f64 (pow.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) #s(literal 2 binary64)) (fma.f64 x x #s(literal -2 binary64)) (.f64 (.f64 (.f64 #s(literal -2 binary64) x) (cos.f64 (.f64 eps #s(literal 1/2 binary64)))) (sin.f64 (.f64 eps #s(literal 1/2 binary64))))))

Compiler

Compiled 1 012 to 766 computations (24.3% saved)

simplify331.0ms (2%)

Memory

14.9MiB live, 174.5MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 19 expressions of interest:

New	Metric	Score
cost-diff	0	(fma.f64 (cos.f64 x) (fma.f64 (.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) (.f64 (*.f64 #s(literal 1/6 binary64) (sin.f64 x)) eps))
cost-diff	0	(fma.f64 (fma.f64 (cos.f64 x) (fma.f64 (.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) (.f64 (*.f64 #s(literal 1/6 binary64) (sin.f64 x)) eps)) eps (neg.f64 (sin.f64 x)))
cost-diff	0	(.f64 (fma.f64 (fma.f64 (cos.f64 x) (fma.f64 (.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) (.f64 (.f64 #s(literal 1/6 binary64) (sin.f64 x)) eps)) eps (neg.f64 (sin.f64 x))) eps)
cost-diff	0	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 (fma.f64 (fma.f64 (cos.f64 x) (fma.f64 (.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) (.f64 (.f64 #s(literal 1/6 binary64) (sin.f64 x)) eps)) eps (neg.f64 (sin.f64 x))) eps))
cost-diff	0	(sin.f64 (*.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps)))
cost-diff	0	(.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps))) #s(approx (sin (* 1/2 (+ 0 eps))) (.f64 (fma.f64 (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 (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps))) #s(approx (sin ( 1/2 (+ 0 eps))) (.f64 (fma.f64 (fma.f64 (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	320	(*.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps))
cost-diff	0	(fma.f64 (fma.f64 (fma.f64 #s(literal 1/5040 binary64) (.f64 x x) #s(literal -1/120 binary64)) (.f64 x x) #s(literal 1/6 binary64)) (*.f64 x x) #s(literal -1 binary64))
cost-diff	0	#s(approx (neg (sin x)) (.f64 (fma.f64 (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)) (.f64 x x) #s(literal -1 binary64)) x))
cost-diff	0	(.f64 #s(approx (neg (sin x)) (.f64 (fma.f64 (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)) (*.f64 x x) #s(literal -1 binary64)) x)) eps)
cost-diff	0	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (neg (sin x)) (.f64 (fma.f64 (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)) (*.f64 x x) #s(literal -1 binary64)) x)) eps))
cost-diff	0	#s(approx (cos eps) #s(literal 1 binary64))
cost-diff	0	(-.f64 #s(approx (cos eps) #s(literal 1 binary64)) #s(literal 1 binary64))
cost-diff	0	#s(approx (- (cos (+ x eps)) (cos x)) (-.f64 #s(approx (cos eps) #s(literal 1 binary64)) #s(literal 1 binary64)))
cost-diff	0	(sin.f64 (fma.f64 eps #s(literal 1/2 binary64) x))
cost-diff	0	(.f64 (sin.f64 (fma.f64 eps #s(literal 1/2 binary64) x)) (sin.f64 (.f64 eps #s(literal 1/2 binary64))))
cost-diff	0	#s(approx (* (sin (* 1/2 (+ (* 2 x) eps))) (sin (* 1/2 (+ 0 eps)))) (.f64 (sin.f64 (fma.f64 eps #s(literal 1/2 binary64) x)) (sin.f64 (.f64 eps #s(literal 1/2 binary64)))))
cost-diff	0	(.f64 #s(approx ( (sin (* 1/2 (+ (* 2 x) eps))) (sin (* 1/2 (+ 0 eps)))) (.f64 (sin.f64 (fma.f64 eps #s(literal 1/2 binary64) x)) (sin.f64 (.f64 eps #s(literal 1/2 binary64))))) #s(literal -2 binary64))

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	70	535
0	111	521
1	191	521
2	441	513
3	1211	509
4	3493	509
5	4680	509
6	6905	509
0	8186	509

Stop Event

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

Calls

Call 1

Inputs
(.f64 #s(approx ( (sin (* 1/2 (+ (* 2 x) eps))) (sin (* 1/2 (+ 0 eps)))) (.f64 (sin.f64 (fma.f64 eps #s(literal 1/2 binary64) x)) (sin.f64 (.f64 eps #s(literal 1/2 binary64))))) #s(literal -2 binary64))
#s(approx (* (sin (* 1/2 (+ (* 2 x) eps))) (sin (* 1/2 (+ 0 eps)))) (.f64 (sin.f64 (fma.f64 eps #s(literal 1/2 binary64) x)) (sin.f64 (.f64 eps #s(literal 1/2 binary64)))))
(.f64 (sin.f64 (fma.f64 eps #s(literal 1/2 binary64) x)) (sin.f64 (.f64 eps #s(literal 1/2 binary64))))
(sin.f64 (fma.f64 eps #s(literal 1/2 binary64) x))
(fma.f64 eps #s(literal 1/2 binary64) x)
eps
#s(literal 1/2 binary64)
x
(sin.f64 (*.f64 eps #s(literal 1/2 binary64)))
(*.f64 eps #s(literal 1/2 binary64))
#s(literal -2 binary64)
#s(approx (- (cos (+ x eps)) (cos x)) (-.f64 #s(approx (cos eps) #s(literal 1 binary64)) #s(literal 1 binary64)))
(-.f64 #s(approx (cos eps) #s(literal 1 binary64)) #s(literal 1 binary64))
#s(approx (cos eps) #s(literal 1 binary64))
#s(literal 1 binary64)
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (neg (sin x)) (.f64 (fma.f64 (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)) (*.f64 x x) #s(literal -1 binary64)) x)) eps))
(.f64 #s(approx (neg (sin x)) (.f64 (fma.f64 (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)) (*.f64 x x) #s(literal -1 binary64)) x)) eps)
#s(approx (neg (sin x)) (.f64 (fma.f64 (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)) (.f64 x x) #s(literal -1 binary64)) x))
(.f64 (fma.f64 (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)) (.f64 x x) #s(literal -1 binary64)) x)
(fma.f64 (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)) (*.f64 x x) #s(literal -1 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))
(fma.f64 #s(literal 1/5040 binary64) (*.f64 x x) #s(literal -1/120 binary64))
#s(literal 1/5040 binary64)
(*.f64 x x)
x
#s(literal -1/120 binary64)
#s(literal 1/6 binary64)
#s(literal -1 binary64)
eps
(.f64 (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps))) #s(approx (sin ( 1/2 (+ 0 eps))) (.f64 (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 (sin.f64 (.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps))) #s(approx (sin (* 1/2 (+ 0 eps))) (.f64 (fma.f64 (fma.f64 (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)))
(sin.f64 (*.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps)))
(*.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps))
#s(literal 1/2 binary64)
(fma.f64 #s(literal 2 binary64) x eps)
#s(literal 2 binary64)
x
eps
#s(approx (sin (* 1/2 (+ 0 eps))) (.f64 (fma.f64 (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)
#s(literal 1/3840 binary64)
#s(literal -1/48 binary64)
#s(literal -2 binary64)
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 (fma.f64 (fma.f64 (cos.f64 x) (fma.f64 (.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) (.f64 (.f64 #s(literal 1/6 binary64) (sin.f64 x)) eps)) eps (neg.f64 (sin.f64 x))) eps))
(.f64 (fma.f64 (fma.f64 (cos.f64 x) (fma.f64 (.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) (.f64 (.f64 #s(literal 1/6 binary64) (sin.f64 x)) eps)) eps (neg.f64 (sin.f64 x))) eps)
(fma.f64 (fma.f64 (cos.f64 x) (fma.f64 (.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) (.f64 (*.f64 #s(literal 1/6 binary64) (sin.f64 x)) eps)) eps (neg.f64 (sin.f64 x)))
(fma.f64 (cos.f64 x) (fma.f64 (.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) (.f64 (*.f64 #s(literal 1/6 binary64) (sin.f64 x)) eps))
(cos.f64 x)
x
(fma.f64 (*.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64))
(*.f64 eps eps)
eps
#s(literal 1/24 binary64)
#s(literal -1/2 binary64)
(.f64 (.f64 #s(literal 1/6 binary64) (sin.f64 x)) eps)
(*.f64 #s(literal 1/6 binary64) (sin.f64 x))
#s(literal 1/6 binary64)
(sin.f64 x)
(neg.f64 (sin.f64 x))

Outputs
(.f64 #s(approx ( (sin (* 1/2 (+ (* 2 x) eps))) (sin (* 1/2 (+ 0 eps)))) (.f64 (sin.f64 (fma.f64 eps #s(literal 1/2 binary64) x)) (sin.f64 (.f64 eps #s(literal 1/2 binary64))))) #s(literal -2 binary64))
(.f64 #s(literal -2 binary64) #s(approx ( (sin (* 1/2 (+ (* 2 x) eps))) (sin (* 1/2 (+ 0 eps)))) (.f64 (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) (sin.f64 (.f64 #s(literal 1/2 binary64) eps)))))
#s(approx (* (sin (* 1/2 (+ (* 2 x) eps))) (sin (* 1/2 (+ 0 eps)))) (.f64 (sin.f64 (fma.f64 eps #s(literal 1/2 binary64) x)) (sin.f64 (.f64 eps #s(literal 1/2 binary64)))))
#s(approx (* (sin (* 1/2 (+ (* 2 x) eps))) (sin (* 1/2 (+ 0 eps)))) (.f64 (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) (sin.f64 (.f64 #s(literal 1/2 binary64) eps))))
(.f64 (sin.f64 (fma.f64 eps #s(literal 1/2 binary64) x)) (sin.f64 (.f64 eps #s(literal 1/2 binary64))))
(.f64 (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) (sin.f64 (.f64 #s(literal 1/2 binary64) eps)))
(sin.f64 (fma.f64 eps #s(literal 1/2 binary64) x))
(sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x))
(fma.f64 eps #s(literal 1/2 binary64) x)
(fma.f64 #s(literal 1/2 binary64) eps x)
eps
#s(literal 1/2 binary64)
x
(sin.f64 (*.f64 eps #s(literal 1/2 binary64)))
(sin.f64 (*.f64 #s(literal 1/2 binary64) eps))
(*.f64 eps #s(literal 1/2 binary64))
(*.f64 #s(literal 1/2 binary64) eps)
#s(literal -2 binary64)
#s(approx (- (cos (+ x eps)) (cos x)) (-.f64 #s(approx (cos eps) #s(literal 1 binary64)) #s(literal 1 binary64)))
(-.f64 #s(approx (cos eps) #s(literal 1 binary64)) #s(literal 1 binary64))
#s(approx (cos eps) #s(literal 1 binary64))
#s(literal 1 binary64)
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (neg (sin x)) (.f64 (fma.f64 (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)) (*.f64 x x) #s(literal -1 binary64)) x)) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (neg (sin x)) (fma.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 (fma.f64 (.f64 x x) #s(literal 1/5040 binary64) #s(literal -1/120 binary64)) (*.f64 x x) #s(literal 1/6 binary64)) (neg.f64 x))) eps))
(.f64 #s(approx (neg (sin x)) (.f64 (fma.f64 (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)) (*.f64 x x) #s(literal -1 binary64)) x)) eps)
(.f64 #s(approx (neg (sin x)) (fma.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 (fma.f64 (.f64 x x) #s(literal 1/5040 binary64) #s(literal -1/120 binary64)) (*.f64 x x) #s(literal 1/6 binary64)) (neg.f64 x))) eps)
#s(approx (neg (sin x)) (.f64 (fma.f64 (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)) (.f64 x x) #s(literal -1 binary64)) x))
#s(approx (neg (sin x)) (fma.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 (fma.f64 (.f64 x x) #s(literal 1/5040 binary64) #s(literal -1/120 binary64)) (.f64 x x) #s(literal 1/6 binary64)) (neg.f64 x)))
(.f64 (fma.f64 (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)) (.f64 x x) #s(literal -1 binary64)) x)
(fma.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 (fma.f64 (.f64 x x) #s(literal 1/5040 binary64) #s(literal -1/120 binary64)) (.f64 x x) #s(literal 1/6 binary64)) (neg.f64 x))
(fma.f64 (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)) (*.f64 x x) #s(literal -1 binary64))
(fma.f64 (fma.f64 (fma.f64 (.f64 x x) #s(literal 1/5040 binary64) #s(literal -1/120 binary64)) (.f64 x x) #s(literal 1/6 binary64)) (*.f64 x x) #s(literal -1 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))
(fma.f64 (fma.f64 (.f64 x x) #s(literal 1/5040 binary64) #s(literal -1/120 binary64)) (.f64 x x) #s(literal 1/6 binary64))
(fma.f64 #s(literal 1/5040 binary64) (*.f64 x x) #s(literal -1/120 binary64))
(fma.f64 (*.f64 x x) #s(literal 1/5040 binary64) #s(literal -1/120 binary64))
#s(literal 1/5040 binary64)
(*.f64 x x)
x
#s(literal -1/120 binary64)
#s(literal 1/6 binary64)
#s(literal -1 binary64)
eps
(.f64 (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps))) #s(approx (sin ( 1/2 (+ 0 eps))) (.f64 (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 (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) #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 (sin.f64 (.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps))) #s(approx (sin (* 1/2 (+ 0 eps))) (.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -1/645120 binary64) (.f64 eps eps) #s(literal 1/3840 binary64)) (.f64 eps eps) #s(literal -1/48 binary64)) (.f64 eps eps) #s(literal 1/2 binary64)) eps)))
(.f64 #s(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)) (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x)))
(sin.f64 (*.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps)))
(sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x))
(*.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps))
(fma.f64 #s(literal 1/2 binary64) eps x)
#s(literal 1/2 binary64)
(fma.f64 #s(literal 2 binary64) x eps)
#s(literal 2 binary64)
x
eps
#s(approx (sin (* 1/2 (+ 0 eps))) (.f64 (fma.f64 (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)
#s(literal 1/3840 binary64)
#s(literal -1/48 binary64)
#s(literal -2 binary64)
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 (fma.f64 (fma.f64 (cos.f64 x) (fma.f64 (.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) (.f64 (.f64 #s(literal 1/6 binary64) (sin.f64 x)) eps)) eps (neg.f64 (sin.f64 x))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 1/24 binary64) (.f64 eps eps) #s(literal -1/2 binary64)) (cos.f64 x) (.f64 (.f64 (sin.f64 x) #s(literal 1/6 binary64)) eps)) eps (neg.f64 (sin.f64 x))) eps))
(.f64 (fma.f64 (fma.f64 (cos.f64 x) (fma.f64 (.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) (.f64 (.f64 #s(literal 1/6 binary64) (sin.f64 x)) eps)) eps (neg.f64 (sin.f64 x))) eps)
(.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 1/24 binary64) (.f64 eps eps) #s(literal -1/2 binary64)) (cos.f64 x) (.f64 (.f64 (sin.f64 x) #s(literal 1/6 binary64)) eps)) eps (neg.f64 (sin.f64 x))) eps)
(fma.f64 (fma.f64 (cos.f64 x) (fma.f64 (.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) (.f64 (*.f64 #s(literal 1/6 binary64) (sin.f64 x)) eps)) eps (neg.f64 (sin.f64 x)))
(fma.f64 (fma.f64 (fma.f64 #s(literal 1/24 binary64) (.f64 eps eps) #s(literal -1/2 binary64)) (cos.f64 x) (.f64 (*.f64 (sin.f64 x) #s(literal 1/6 binary64)) eps)) eps (neg.f64 (sin.f64 x)))
(fma.f64 (cos.f64 x) (fma.f64 (.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) (.f64 (*.f64 #s(literal 1/6 binary64) (sin.f64 x)) eps))
(fma.f64 (fma.f64 #s(literal 1/24 binary64) (.f64 eps eps) #s(literal -1/2 binary64)) (cos.f64 x) (.f64 (*.f64 (sin.f64 x) #s(literal 1/6 binary64)) eps))
(cos.f64 x)
x
(fma.f64 (*.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64))
(fma.f64 #s(literal 1/24 binary64) (*.f64 eps eps) #s(literal -1/2 binary64))
(*.f64 eps eps)
eps
#s(literal 1/24 binary64)
#s(literal -1/2 binary64)
(.f64 (.f64 #s(literal 1/6 binary64) (sin.f64 x)) eps)
(.f64 (.f64 (sin.f64 x) #s(literal 1/6 binary64)) eps)
(*.f64 #s(literal 1/6 binary64) (sin.f64 x))
(*.f64 (sin.f64 x) #s(literal 1/6 binary64))
#s(literal 1/6 binary64)
(sin.f64 x)
(neg.f64 (sin.f64 x))

localize828.0ms (5.1%)

Memory

-12.2MiB live, 541.4MiB allocated

Localize:

Found 19 expressions of interest:

New	Metric	Score
accuracy	0.109375	(.f64 (fma.f64 (fma.f64 (cos.f64 x) (fma.f64 (.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) (.f64 (.f64 #s(literal 1/6 binary64) (sin.f64 x)) eps)) eps (neg.f64 (sin.f64 x))) eps)
accuracy	0.1171875	(.f64 (.f64 #s(literal 1/6 binary64) (sin.f64 x)) eps)
accuracy	0.3125	(*.f64 #s(literal 1/6 binary64) (sin.f64 x))
accuracy	0.46038007253661184	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 (fma.f64 (fma.f64 (cos.f64 x) (fma.f64 (.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) (.f64 (.f64 #s(literal 1/6 binary64) (sin.f64 x)) eps)) eps (neg.f64 (sin.f64 x))) eps))
accuracy	0.01953125	(.f64 (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps))) #s(approx (sin ( 1/2 (+ 0 eps))) (.f64 (fma.f64 (fma.f64 (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	0.0921260934066794	(sin.f64 (*.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps)))
accuracy	0.109375	(.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps))) #s(approx (sin (* 1/2 (+ 0 eps))) (.f64 (fma.f64 (fma.f64 (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	0.15012321344468227	#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))
accuracy	0.015625	(fma.f64 (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)) (*.f64 x x) #s(literal -1 binary64))
accuracy	0.02734375	(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))
accuracy	0.8947319202701678	#s(approx (neg (sin x)) (.f64 (fma.f64 (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)) (.f64 x x) #s(literal -1 binary64)) x))
accuracy	15.856391180419081	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (neg (sin x)) (.f64 (fma.f64 (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)) (*.f64 x x) #s(literal -1 binary64)) x)) eps))
accuracy	0.9160777511437491	#s(approx (cos eps) #s(literal 1 binary64))
accuracy	32.554681003050774	(-.f64 #s(approx (cos eps) #s(literal 1 binary64)) #s(literal 1 binary64))
accuracy	33.32883884922006	#s(approx (- (cos (+ x eps)) (cos x)) (-.f64 #s(approx (cos eps) #s(literal 1 binary64)) #s(literal 1 binary64)))
accuracy	0	#s(approx (* (sin (* 1/2 (+ (* 2 x) eps))) (sin (* 1/2 (+ 0 eps)))) (.f64 (sin.f64 (fma.f64 eps #s(literal 1/2 binary64) x)) (sin.f64 (.f64 eps #s(literal 1/2 binary64)))))
accuracy	0.01953125	(.f64 #s(approx ( (sin (* 1/2 (+ (* 2 x) eps))) (sin (* 1/2 (+ 0 eps)))) (.f64 (sin.f64 (fma.f64 eps #s(literal 1/2 binary64) x)) (sin.f64 (.f64 eps #s(literal 1/2 binary64))))) #s(literal -2 binary64))
accuracy	0.0921260934066794	(sin.f64 (fma.f64 eps #s(literal 1/2 binary64) x))
accuracy	0.109375	(.f64 (sin.f64 (fma.f64 eps #s(literal 1/2 binary64) x)) (sin.f64 (.f64 eps #s(literal 1/2 binary64))))

Samples

420.0ms	158×	2	valid
303.0ms	90×	1	valid
6.0ms	2×	3	valid
4.0ms	6×	0	valid

Compiler

Compiled 851 to 120 computations (85.9% saved)

Precisions

Click to see histograms. Total time spent on operations: 587.0ms

ival-mult: 168.0ms (28.6% of total)

ival-cos: 142.0ms (24.2% of total)

const: 118.0ms (20.1% of total)

ival-add: 57.0ms (9.7% of total)

adjust: 50.0ms (8.5% of total)

ival-sin: 41.0ms (7% of total)

ival-sub: 7.0ms (1.2% of total)

ival-neg: 2.0ms (0.3% of total)

exact: 1.0ms (0.2% of total)

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

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

series63.0ms (0.4%)

Memory

22.6MiB live, 104.1MiB allocated

Counts

23 → 468

Calls

Call 1

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

Outputs
#s(alt (* -1 (* eps (sin x))) (taylor 0 eps) (#s(alt (.f64 #s(approx ( (sin (* 1/2 (+ (* 2 x) eps))) (sin (* 1/2 (+ 0 eps)))) (.f64 (sin.f64 (fma.f64 eps #s(literal 1/2 binary64) x)) (sin.f64 (.f64 eps #s(literal 1/2 binary64))))) #s(literal -2 binary64)) (patch (.f64 #s(approx ( (sin (* 1/2 (+ (* 2 x) eps))) (sin (* 1/2 (+ 0 eps)))) (.f64 (sin.f64 (fma.f64 eps #s(literal 1/2 binary64) x)) (sin.f64 (.f64 eps #s(literal 1/2 binary64))))) #s(literal -2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* eps (+ (* -1 (sin x)) (* -1/2 (* eps (cos x))))) (taylor 0 eps) (#s(alt (.f64 #s(approx ( (sin (* 1/2 (+ (* 2 x) eps))) (sin (* 1/2 (+ 0 eps)))) (.f64 (sin.f64 (fma.f64 eps #s(literal 1/2 binary64) x)) (sin.f64 (.f64 eps #s(literal 1/2 binary64))))) #s(literal -2 binary64)) (patch (.f64 #s(approx ( (sin (* 1/2 (+ (* 2 x) eps))) (sin (* 1/2 (+ 0 eps)))) (.f64 (sin.f64 (fma.f64 eps #s(literal 1/2 binary64) x)) (sin.f64 (.f64 eps #s(literal 1/2 binary64))))) #s(literal -2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* eps (+ (* -1 (sin x)) (* eps (+ (* -2 (* eps (+ (* -1/16 (sin x)) (* -1/48 (sin x))))) (* -1/2 (cos x)))))) (taylor 0 eps) (#s(alt (.f64 #s(approx ( (sin (* 1/2 (+ (* 2 x) eps))) (sin (* 1/2 (+ 0 eps)))) (.f64 (sin.f64 (fma.f64 eps #s(literal 1/2 binary64) x)) (sin.f64 (.f64 eps #s(literal 1/2 binary64))))) #s(literal -2 binary64)) (patch (.f64 #s(approx ( (sin (* 1/2 (+ (* 2 x) eps))) (sin (* 1/2 (+ 0 eps)))) (.f64 (sin.f64 (fma.f64 eps #s(literal 1/2 binary64) x)) (sin.f64 (.f64 eps #s(literal 1/2 binary64))))) #s(literal -2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* eps (+ (* -1 (sin x)) (* eps (+ (* -1/2 (cos x)) (* eps (+ (* -2 (+ (* -1/16 (sin x)) (* -1/48 (sin x)))) (* 1/24 (* eps (cos x))))))))) (taylor 0 eps) (#s(alt (.f64 #s(approx ( (sin (* 1/2 (+ (* 2 x) eps))) (sin (* 1/2 (+ 0 eps)))) (.f64 (sin.f64 (fma.f64 eps #s(literal 1/2 binary64) x)) (sin.f64 (.f64 eps #s(literal 1/2 binary64))))) #s(literal -2 binary64)) (patch (.f64 #s(approx ( (sin (* 1/2 (+ (* 2 x) eps))) (sin (* 1/2 (+ 0 eps)))) (.f64 (sin.f64 (fma.f64 eps #s(literal 1/2 binary64) x)) (sin.f64 (.f64 eps #s(literal 1/2 binary64))))) #s(literal -2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* 1/2 (* eps (sin x))) (taylor 0 eps) (#s(alt #s(approx (* (sin (* 1/2 (+ (* 2 x) eps))) (sin (* 1/2 (+ 0 eps)))) (.f64 (sin.f64 (fma.f64 eps #s(literal 1/2 binary64) x)) (sin.f64 (.f64 eps #s(literal 1/2 binary64))))) (patch #s(approx (* (sin (* 1/2 (+ (* 2 x) eps))) (sin (* 1/2 (+ 0 eps)))) (.f64 (sin.f64 (fma.f64 eps #s(literal 1/2 binary64) x)) (sin.f64 (.f64 eps #s(literal 1/2 binary64))))) #<representation binary64>) () ())) ())
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#s(alt (* eps (- (* eps (+ (* 1/6 (* eps (sin x))) (* (cos x) (- (* 1/24 (pow eps 2)) 1/2)))) (sin x))) (taylor -inf x) (#s(alt (.f64 (fma.f64 (fma.f64 (cos.f64 x) (fma.f64 (.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) (.f64 (.f64 #s(literal 1/6 binary64) (sin.f64 x)) eps)) eps (neg.f64 (sin.f64 x))) eps) (patch (.f64 (fma.f64 (fma.f64 (cos.f64 x) (fma.f64 (.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) (.f64 (.f64 #s(literal 1/6 binary64) (sin.f64 x)) eps)) eps (neg.f64 (sin.f64 x))) eps) #<representation binary64>) () ())) ())
#s(alt (* eps (- (* eps (+ (* 1/6 (* eps (sin x))) (* (cos x) (- (* 1/24 (pow eps 2)) 1/2)))) (sin x))) (taylor -inf x) (#s(alt (.f64 (fma.f64 (fma.f64 (cos.f64 x) (fma.f64 (.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) (.f64 (.f64 #s(literal 1/6 binary64) (sin.f64 x)) eps)) eps (neg.f64 (sin.f64 x))) eps) (patch (.f64 (fma.f64 (fma.f64 (cos.f64 x) (fma.f64 (.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) (.f64 (.f64 #s(literal 1/6 binary64) (sin.f64 x)) eps)) eps (neg.f64 (sin.f64 x))) eps) #<representation binary64>) () ())) ())
#s(alt (* eps (- (* eps (+ (* 1/6 (* eps (sin x))) (* (cos x) (- (* 1/24 (pow eps 2)) 1/2)))) (sin x))) (taylor -inf x) (#s(alt (.f64 (fma.f64 (fma.f64 (cos.f64 x) (fma.f64 (.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) (.f64 (.f64 #s(literal 1/6 binary64) (sin.f64 x)) eps)) eps (neg.f64 (sin.f64 x))) eps) (patch (.f64 (fma.f64 (fma.f64 (cos.f64 x) (fma.f64 (.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) (.f64 (.f64 #s(literal 1/6 binary64) (sin.f64 x)) eps)) eps (neg.f64 (sin.f64 x))) eps) #<representation binary64>) () ())) ())
#s(alt (* eps (- (* eps (+ (* 1/6 (* eps (sin x))) (* (cos x) (- (* 1/24 (pow eps 2)) 1/2)))) (sin x))) (taylor -inf x) (#s(alt (.f64 (fma.f64 (fma.f64 (cos.f64 x) (fma.f64 (.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) (.f64 (.f64 #s(literal 1/6 binary64) (sin.f64 x)) eps)) eps (neg.f64 (sin.f64 x))) eps) (patch (.f64 (fma.f64 (fma.f64 (cos.f64 x) (fma.f64 (.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) (.f64 (.f64 #s(literal 1/6 binary64) (sin.f64 x)) eps)) eps (neg.f64 (sin.f64 x))) eps) #<representation binary64>) () ())) ())
#s(alt (- (* eps (+ (* 1/6 (* eps (sin x))) (* (cos x) (- (* 1/24 (pow eps 2)) 1/2)))) (sin x)) (taylor -inf x) (#s(alt (fma.f64 (fma.f64 (cos.f64 x) (fma.f64 (.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) (.f64 (.f64 #s(literal 1/6 binary64) (sin.f64 x)) eps)) eps (neg.f64 (sin.f64 x))) (patch (fma.f64 (fma.f64 (cos.f64 x) (fma.f64 (.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) (.f64 (.f64 #s(literal 1/6 binary64) (sin.f64 x)) eps)) eps (neg.f64 (sin.f64 x))) #<representation binary64>) () ())) ())
#s(alt (- (* eps (+ (* 1/6 (* eps (sin x))) (* (cos x) (- (* 1/24 (pow eps 2)) 1/2)))) (sin x)) (taylor -inf x) (#s(alt (fma.f64 (fma.f64 (cos.f64 x) (fma.f64 (.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) (.f64 (.f64 #s(literal 1/6 binary64) (sin.f64 x)) eps)) eps (neg.f64 (sin.f64 x))) (patch (fma.f64 (fma.f64 (cos.f64 x) (fma.f64 (.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) (.f64 (.f64 #s(literal 1/6 binary64) (sin.f64 x)) eps)) eps (neg.f64 (sin.f64 x))) #<representation binary64>) () ())) ())
#s(alt (- (* eps (+ (* 1/6 (* eps (sin x))) (* (cos x) (- (* 1/24 (pow eps 2)) 1/2)))) (sin x)) (taylor -inf x) (#s(alt (fma.f64 (fma.f64 (cos.f64 x) (fma.f64 (.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) (.f64 (.f64 #s(literal 1/6 binary64) (sin.f64 x)) eps)) eps (neg.f64 (sin.f64 x))) (patch (fma.f64 (fma.f64 (cos.f64 x) (fma.f64 (.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) (.f64 (.f64 #s(literal 1/6 binary64) (sin.f64 x)) eps)) eps (neg.f64 (sin.f64 x))) #<representation binary64>) () ())) ())
#s(alt (- (* eps (+ (* 1/6 (* eps (sin x))) (* (cos x) (- (* 1/24 (pow eps 2)) 1/2)))) (sin x)) (taylor -inf x) (#s(alt (fma.f64 (fma.f64 (cos.f64 x) (fma.f64 (.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) (.f64 (.f64 #s(literal 1/6 binary64) (sin.f64 x)) eps)) eps (neg.f64 (sin.f64 x))) (patch (fma.f64 (fma.f64 (cos.f64 x) (fma.f64 (.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) (.f64 (.f64 #s(literal 1/6 binary64) (sin.f64 x)) eps)) eps (neg.f64 (sin.f64 x))) #<representation binary64>) () ())) ())
#s(alt (+ (* 1/6 (* eps (sin x))) (* (cos x) (- (* 1/24 (pow eps 2)) 1/2))) (taylor -inf x) (#s(alt (fma.f64 (cos.f64 x) (fma.f64 (.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) (.f64 (.f64 #s(literal 1/6 binary64) (sin.f64 x)) eps)) (patch (fma.f64 (cos.f64 x) (fma.f64 (.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) (.f64 (.f64 #s(literal 1/6 binary64) (sin.f64 x)) eps)) #<representation binary64>) () ())) ())
#s(alt (+ (* 1/6 (* eps (sin x))) (* (cos x) (- (* 1/24 (pow eps 2)) 1/2))) (taylor -inf x) (#s(alt (fma.f64 (cos.f64 x) (fma.f64 (.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) (.f64 (.f64 #s(literal 1/6 binary64) (sin.f64 x)) eps)) (patch (fma.f64 (cos.f64 x) (fma.f64 (.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) (.f64 (.f64 #s(literal 1/6 binary64) (sin.f64 x)) eps)) #<representation binary64>) () ())) ())
#s(alt (+ (* 1/6 (* eps (sin x))) (* (cos x) (- (* 1/24 (pow eps 2)) 1/2))) (taylor -inf x) (#s(alt (fma.f64 (cos.f64 x) (fma.f64 (.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) (.f64 (.f64 #s(literal 1/6 binary64) (sin.f64 x)) eps)) (patch (fma.f64 (cos.f64 x) (fma.f64 (.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) (.f64 (.f64 #s(literal 1/6 binary64) (sin.f64 x)) eps)) #<representation binary64>) () ())) ())
#s(alt (+ (* 1/6 (* eps (sin x))) (* (cos x) (- (* 1/24 (pow eps 2)) 1/2))) (taylor -inf x) (#s(alt (fma.f64 (cos.f64 x) (fma.f64 (.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) (.f64 (.f64 #s(literal 1/6 binary64) (sin.f64 x)) eps)) (patch (fma.f64 (cos.f64 x) (fma.f64 (.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) (.f64 (.f64 #s(literal 1/6 binary64) (sin.f64 x)) eps)) #<representation binary64>) () ())) ())
#s(alt (* 1/5040 (pow x 4)) (taylor -inf x) (#s(alt (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)) (patch (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)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 4) (- 1/5040 (* 1/120 (/ 1 (pow x 2))))) (taylor -inf x) (#s(alt (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)) (patch (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)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 4) (- (+ 1/5040 (/ 1/6 (pow x 4))) (* 1/120 (/ 1 (pow x 2))))) (taylor -inf x) (#s(alt (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)) (patch (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)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 4) (- (+ 1/5040 (/ 1/6 (pow x 4))) (* 1/120 (/ 1 (pow x 2))))) (taylor -inf x) (#s(alt (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)) (patch (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)) #<representation binary64>) () ())) ())
#s(alt (* 1/6 (sin x)) (taylor -inf x) (#s(alt (.f64 #s(literal 1/6 binary64) (sin.f64 x)) (patch (.f64 #s(literal 1/6 binary64) (sin.f64 x)) #<representation binary64>) () ())) ())
#s(alt (* 1/6 (sin x)) (taylor -inf x) (#s(alt (.f64 #s(literal 1/6 binary64) (sin.f64 x)) (patch (.f64 #s(literal 1/6 binary64) (sin.f64 x)) #<representation binary64>) () ())) ())
#s(alt (* 1/6 (sin x)) (taylor -inf x) (#s(alt (.f64 #s(literal 1/6 binary64) (sin.f64 x)) (patch (.f64 #s(literal 1/6 binary64) (sin.f64 x)) #<representation binary64>) () ())) ())
#s(alt (* 1/6 (sin x)) (taylor -inf x) (#s(alt (.f64 #s(literal 1/6 binary64) (sin.f64 x)) (patch (.f64 #s(literal 1/6 binary64) (sin.f64 x)) #<representation binary64>) () ())) ())
#s(alt (* 1/6 (* eps (sin x))) (taylor -inf x) (#s(alt (.f64 (.f64 #s(literal 1/6 binary64) (sin.f64 x)) eps) (patch (.f64 (.f64 #s(literal 1/6 binary64) (sin.f64 x)) eps) #<representation binary64>) () ())) ())
#s(alt (* 1/6 (* eps (sin x))) (taylor -inf x) (#s(alt (.f64 (.f64 #s(literal 1/6 binary64) (sin.f64 x)) eps) (patch (.f64 (.f64 #s(literal 1/6 binary64) (sin.f64 x)) eps) #<representation binary64>) () ())) ())
#s(alt (* 1/6 (* eps (sin x))) (taylor -inf x) (#s(alt (.f64 (.f64 #s(literal 1/6 binary64) (sin.f64 x)) eps) (patch (.f64 (.f64 #s(literal 1/6 binary64) (sin.f64 x)) eps) #<representation binary64>) () ())) ())
#s(alt (* 1/6 (* eps (sin x))) (taylor -inf x) (#s(alt (.f64 (.f64 #s(literal 1/6 binary64) (sin.f64 x)) eps) (patch (.f64 (.f64 #s(literal 1/6 binary64) (sin.f64 x)) eps) #<representation binary64>) () ())) ())

Calls

6 calls:

Time	Variable		Point	Expression
11.0ms	eps	@	-inf	((* (* (sin (* 1/2 (+ (* 2 x) eps))) (sin (* 1/2 (+ 0 eps)))) -2) (* (sin (* 1/2 (+ (* 2 x) eps))) (sin (* 1/2 (+ 0 eps)))) (* (sin (+ (* eps 1/2) x)) (sin (* eps 1/2))) (sin (+ (* eps 1/2) x)) (- (cos (+ x eps)) (cos x)) (- (cos eps) 1) (cos eps) (- (cos (+ x eps)) (cos x)) (* (neg (sin x)) eps) (neg (sin x)) (+ (* (+ (* (+ (* 1/5040 (* x x)) -1/120) (* x x)) 1/6) (* x x)) -1) (* 1/2 (+ (* 2 x) eps)) (* (* (sin (* 1/2 (+ (* 2 x) eps))) (sin (* 1/2 (+ 0 eps)))) -2) (* (sin (* 1/2 (+ (* 2 x) eps))) (sin (* 1/2 (+ 0 eps)))) (sin (* 1/2 (+ (* 2 x) eps))) (- (cos (+ x eps)) (cos x)) (* (+ (* (+ (* (cos x) (+ (* (* eps eps) 1/24) -1/2)) (* (* 1/6 (sin x)) eps)) eps) (neg (sin x))) eps) (+ (* (+ (* (cos x) (+ (* (* eps eps) 1/24) -1/2)) (* (* 1/6 (sin x)) eps)) eps) (neg (sin x))) (+ (* (cos x) (+ (* (* eps eps) 1/24) -1/2)) (* (* 1/6 (sin x)) eps)) (+ (* (+ (* 1/5040 (* x x)) -1/120) (* x x)) 1/6) (sin (* 1/2 (+ 0 eps))) (* 1/6 (sin x)) (* (* 1/6 (sin x)) eps))
4.0ms	x	@	inf	((* (* (sin (* 1/2 (+ (* 2 x) eps))) (sin (* 1/2 (+ 0 eps)))) -2) (* (sin (* 1/2 (+ (* 2 x) eps))) (sin (* 1/2 (+ 0 eps)))) (* (sin (+ (* eps 1/2) x)) (sin (* eps 1/2))) (sin (+ (* eps 1/2) x)) (- (cos (+ x eps)) (cos x)) (- (cos eps) 1) (cos eps) (- (cos (+ x eps)) (cos x)) (* (neg (sin x)) eps) (neg (sin x)) (+ (* (+ (* (+ (* 1/5040 (* x x)) -1/120) (* x x)) 1/6) (* x x)) -1) (* 1/2 (+ (* 2 x) eps)) (* (* (sin (* 1/2 (+ (* 2 x) eps))) (sin (* 1/2 (+ 0 eps)))) -2) (* (sin (* 1/2 (+ (* 2 x) eps))) (sin (* 1/2 (+ 0 eps)))) (sin (* 1/2 (+ (* 2 x) eps))) (- (cos (+ x eps)) (cos x)) (* (+ (* (+ (* (cos x) (+ (* (* eps eps) 1/24) -1/2)) (* (* 1/6 (sin x)) eps)) eps) (neg (sin x))) eps) (+ (* (+ (* (cos x) (+ (* (* eps eps) 1/24) -1/2)) (* (* 1/6 (sin x)) eps)) eps) (neg (sin x))) (+ (* (cos x) (+ (* (* eps eps) 1/24) -1/2)) (* (* 1/6 (sin x)) eps)) (+ (* (+ (* 1/5040 (* x x)) -1/120) (* x x)) 1/6) (sin (* 1/2 (+ 0 eps))) (* 1/6 (sin x)) (* (* 1/6 (sin x)) eps))
4.0ms	x	@	-inf	((* (* (sin (* 1/2 (+ (* 2 x) eps))) (sin (* 1/2 (+ 0 eps)))) -2) (* (sin (* 1/2 (+ (* 2 x) eps))) (sin (* 1/2 (+ 0 eps)))) (* (sin (+ (* eps 1/2) x)) (sin (* eps 1/2))) (sin (+ (* eps 1/2) x)) (- (cos (+ x eps)) (cos x)) (- (cos eps) 1) (cos eps) (- (cos (+ x eps)) (cos x)) (* (neg (sin x)) eps) (neg (sin x)) (+ (* (+ (* (+ (* 1/5040 (* x x)) -1/120) (* x x)) 1/6) (* x x)) -1) (* 1/2 (+ (* 2 x) eps)) (* (* (sin (* 1/2 (+ (* 2 x) eps))) (sin (* 1/2 (+ 0 eps)))) -2) (* (sin (* 1/2 (+ (* 2 x) eps))) (sin (* 1/2 (+ 0 eps)))) (sin (* 1/2 (+ (* 2 x) eps))) (- (cos (+ x eps)) (cos x)) (* (+ (* (+ (* (cos x) (+ (* (* eps eps) 1/24) -1/2)) (* (* 1/6 (sin x)) eps)) eps) (neg (sin x))) eps) (+ (* (+ (* (cos x) (+ (* (* eps eps) 1/24) -1/2)) (* (* 1/6 (sin x)) eps)) eps) (neg (sin x))) (+ (* (cos x) (+ (* (* eps eps) 1/24) -1/2)) (* (* 1/6 (sin x)) eps)) (+ (* (+ (* 1/5040 (* x x)) -1/120) (* x x)) 1/6) (sin (* 1/2 (+ 0 eps))) (* 1/6 (sin x)) (* (* 1/6 (sin x)) eps))
4.0ms	eps	@	0	((* (* (sin (* 1/2 (+ (* 2 x) eps))) (sin (* 1/2 (+ 0 eps)))) -2) (* (sin (* 1/2 (+ (* 2 x) eps))) (sin (* 1/2 (+ 0 eps)))) (* (sin (+ (* eps 1/2) x)) (sin (* eps 1/2))) (sin (+ (* eps 1/2) x)) (- (cos (+ x eps)) (cos x)) (- (cos eps) 1) (cos eps) (- (cos (+ x eps)) (cos x)) (* (neg (sin x)) eps) (neg (sin x)) (+ (* (+ (* (+ (* 1/5040 (* x x)) -1/120) (* x x)) 1/6) (* x x)) -1) (* 1/2 (+ (* 2 x) eps)) (* (* (sin (* 1/2 (+ (* 2 x) eps))) (sin (* 1/2 (+ 0 eps)))) -2) (* (sin (* 1/2 (+ (* 2 x) eps))) (sin (* 1/2 (+ 0 eps)))) (sin (* 1/2 (+ (* 2 x) eps))) (- (cos (+ x eps)) (cos x)) (* (+ (* (+ (* (cos x) (+ (* (* eps eps) 1/24) -1/2)) (* (* 1/6 (sin x)) eps)) eps) (neg (sin x))) eps) (+ (* (+ (* (cos x) (+ (* (* eps eps) 1/24) -1/2)) (* (* 1/6 (sin x)) eps)) eps) (neg (sin x))) (+ (* (cos x) (+ (* (* eps eps) 1/24) -1/2)) (* (* 1/6 (sin x)) eps)) (+ (* (+ (* 1/5040 (* x x)) -1/120) (* x x)) 1/6) (sin (* 1/2 (+ 0 eps))) (* 1/6 (sin x)) (* (* 1/6 (sin x)) eps))
3.0ms	eps	@	inf	((* (* (sin (* 1/2 (+ (* 2 x) eps))) (sin (* 1/2 (+ 0 eps)))) -2) (* (sin (* 1/2 (+ (* 2 x) eps))) (sin (* 1/2 (+ 0 eps)))) (* (sin (+ (* eps 1/2) x)) (sin (* eps 1/2))) (sin (+ (* eps 1/2) x)) (- (cos (+ x eps)) (cos x)) (- (cos eps) 1) (cos eps) (- (cos (+ x eps)) (cos x)) (* (neg (sin x)) eps) (neg (sin x)) (+ (* (+ (* (+ (* 1/5040 (* x x)) -1/120) (* x x)) 1/6) (* x x)) -1) (* 1/2 (+ (* 2 x) eps)) (* (* (sin (* 1/2 (+ (* 2 x) eps))) (sin (* 1/2 (+ 0 eps)))) -2) (* (sin (* 1/2 (+ (* 2 x) eps))) (sin (* 1/2 (+ 0 eps)))) (sin (* 1/2 (+ (* 2 x) eps))) (- (cos (+ x eps)) (cos x)) (* (+ (* (+ (* (cos x) (+ (* (* eps eps) 1/24) -1/2)) (* (* 1/6 (sin x)) eps)) eps) (neg (sin x))) eps) (+ (* (+ (* (cos x) (+ (* (* eps eps) 1/24) -1/2)) (* (* 1/6 (sin x)) eps)) eps) (neg (sin x))) (+ (* (cos x) (+ (* (* eps eps) 1/24) -1/2)) (* (* 1/6 (sin x)) eps)) (+ (* (+ (* 1/5040 (* x x)) -1/120) (* x x)) 1/6) (sin (* 1/2 (+ 0 eps))) (* 1/6 (sin x)) (* (* 1/6 (sin x)) eps))

simplify287.0ms (1.8%)

Memory

-9.7MiB live, 308.8MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	479	5739
1	1482	5387
2	4323	5298
0	8075	4902

Stop Event

1×	iter limit
1×	node limit

Counts

468 → 465

Calls

Call 1

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

Outputs
(* -1 (* eps (sin x)))
(*.f64 (neg.f64 eps) (sin.f64 x))
(* eps (+ (* -1 (sin x)) (* -1/2 (* eps (cos x)))))
(.f64 (fma.f64 (.f64 #s(literal -1/2 binary64) eps) (cos.f64 x) (neg.f64 (sin.f64 x))) eps)
(* eps (+ (* -1 (sin x)) (* eps (+ (* -2 (* eps (+ (* -1/16 (sin x)) (* -1/48 (sin x))))) (* -1/2 (cos x))))))
(.f64 (fma.f64 (fma.f64 #s(literal 1/6 binary64) (.f64 (sin.f64 x) eps) (*.f64 (cos.f64 x) #s(literal -1/2 binary64))) eps (neg.f64 (sin.f64 x))) eps)
(* eps (+ (* -1 (sin x)) (* eps (+ (* -1/2 (cos x)) (* eps (+ (* -2 (+ (* -1/16 (sin x)) (* -1/48 (sin x)))) (* 1/24 (* eps (cos x)))))))))
(.f64 (fma.f64 (fma.f64 (fma.f64 (.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) (cos.f64 x) (.f64 #s(literal 1/6 binary64) (.f64 (sin.f64 x) eps))) eps (neg.f64 (sin.f64 x))) eps)
(* 1/2 (* eps (sin x)))
(.f64 (.f64 #s(literal 1/2 binary64) (sin.f64 x)) eps)
(* eps (+ (* 1/4 (* eps (cos x))) (* 1/2 (sin x))))
(.f64 (fma.f64 (.f64 #s(literal 1/4 binary64) (cos.f64 x)) eps (*.f64 #s(literal 1/2 binary64) (sin.f64 x))) eps)
(* eps (+ (* 1/2 (sin x)) (* eps (+ (* 1/4 (cos x)) (* eps (+ (* -1/16 (sin x)) (* -1/48 (sin x))))))))
(.f64 (fma.f64 (fma.f64 #s(literal 1/4 binary64) (cos.f64 x) (.f64 (.f64 #s(literal -1/12 binary64) (sin.f64 x)) eps)) eps (.f64 #s(literal 1/2 binary64) (sin.f64 x))) eps)
(* eps (+ (* 1/2 (sin x)) (* eps (+ (* 1/4 (cos x)) (* eps (+ (* -1/16 (sin x)) (+ (* -1/48 (sin x)) (* -1/48 (* eps (cos x))))))))))
(.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -1/12 binary64) (sin.f64 x) (.f64 #s(literal -1/48 binary64) (.f64 (cos.f64 x) eps))) eps (.f64 #s(literal 1/4 binary64) (cos.f64 x))) eps (*.f64 #s(literal 1/2 binary64) (sin.f64 x))) eps)
(* 1/2 (* eps (sin x)))
(.f64 (.f64 #s(literal 1/2 binary64) (sin.f64 x)) eps)
(* eps (+ (* 1/4 (* eps (cos x))) (* 1/2 (sin x))))
(.f64 (fma.f64 (.f64 #s(literal 1/4 binary64) (cos.f64 x)) eps (*.f64 #s(literal 1/2 binary64) (sin.f64 x))) eps)
(* eps (+ (* 1/2 (sin x)) (* eps (+ (* 1/4 (cos x)) (* eps (+ (* -1/16 (sin x)) (* -1/48 (sin x))))))))
(.f64 (fma.f64 (fma.f64 #s(literal 1/4 binary64) (cos.f64 x) (.f64 (.f64 #s(literal -1/12 binary64) (sin.f64 x)) eps)) eps (.f64 #s(literal 1/2 binary64) (sin.f64 x))) eps)
(* eps (+ (* 1/2 (sin x)) (* eps (+ (* 1/4 (cos x)) (* eps (+ (* -1/16 (sin x)) (+ (* -1/48 (sin x)) (* -1/48 (* eps (cos x))))))))))
(.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -1/12 binary64) (sin.f64 x) (.f64 #s(literal -1/48 binary64) (.f64 (cos.f64 x) eps))) eps (.f64 #s(literal 1/4 binary64) (cos.f64 x))) eps (*.f64 #s(literal 1/2 binary64) (sin.f64 x))) eps)
(sin x)
(sin.f64 x)
(+ (sin x) (* 1/2 (* eps (cos x))))
(fma.f64 (*.f64 #s(literal 1/2 binary64) (cos.f64 x)) eps (sin.f64 x))
(+ (sin x) (* eps (+ (* -1/8 (* eps (sin x))) (* 1/2 (cos x)))))
(fma.f64 (fma.f64 (.f64 #s(literal -1/8 binary64) (sin.f64 x)) eps (.f64 #s(literal 1/2 binary64) (cos.f64 x))) eps (sin.f64 x))
(+ (sin x) (* eps (+ (* 1/2 (cos x)) (* eps (+ (* -1/8 (sin x)) (* -1/48 (* eps (cos x))))))))
(fma.f64 (fma.f64 (.f64 #s(literal -1/8 binary64) eps) (sin.f64 x) (.f64 (cos.f64 x) (fma.f64 (*.f64 eps eps) #s(literal -1/48 binary64) #s(literal 1/2 binary64)))) eps (sin.f64 x))
(* -1 (* eps (sin x)))
(*.f64 (neg.f64 eps) (sin.f64 x))
(* eps (- (* -1/2 (* eps (cos x))) (sin x)))
(.f64 (fma.f64 (.f64 #s(literal -1/2 binary64) eps) (cos.f64 x) (neg.f64 (sin.f64 x))) eps)
(* eps (- (* eps (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x))))) (sin x)))
(.f64 (fma.f64 (fma.f64 #s(literal 1/6 binary64) (.f64 (sin.f64 x) eps) (*.f64 (cos.f64 x) #s(literal -1/2 binary64))) eps (neg.f64 (sin.f64 x))) eps)
(* eps (- (* eps (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x)))))) (sin x)))
(.f64 (fma.f64 (fma.f64 (fma.f64 (.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) (cos.f64 x) (.f64 #s(literal 1/6 binary64) (.f64 (sin.f64 x) eps))) eps (neg.f64 (sin.f64 x))) eps)
(* -1/2 (pow eps 2))
(.f64 (.f64 eps eps) #s(literal -1/2 binary64))
(* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2))
(.f64 (.f64 (fma.f64 (*.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) eps) eps)
(* (pow eps 2) (- (* (pow eps 2) (+ 1/24 (* -1/720 (pow eps 2)))) 1/2))
(.f64 (.f64 (fma.f64 (fma.f64 #s(literal -1/720 binary64) (.f64 eps eps) #s(literal 1/24 binary64)) (.f64 eps eps) #s(literal -1/2 binary64)) eps) eps)
(* (pow eps 2) (- (* (pow eps 2) (+ 1/24 (* (pow eps 2) (- (* 1/40320 (pow eps 2)) 1/720)))) 1/2))
(.f64 (.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 1/40320 binary64) (.f64 eps eps) #s(literal -1/720 binary64)) (.f64 eps eps) #s(literal 1/24 binary64)) (*.f64 eps eps) #s(literal -1/2 binary64)) eps) eps)
1
#s(literal 1 binary64)
(+ 1 (* -1/2 (pow eps 2)))
(fma.f64 (*.f64 eps eps) #s(literal -1/2 binary64) #s(literal 1 binary64))
(+ 1 (* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2)))
(fma.f64 (fma.f64 (.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) (.f64 eps eps) #s(literal 1 binary64))
(+ 1 (* (pow eps 2) (- (* (pow eps 2) (+ 1/24 (* -1/720 (pow eps 2)))) 1/2)))
(fma.f64 (fma.f64 (fma.f64 #s(literal -1/720 binary64) (.f64 eps eps) #s(literal 1/24 binary64)) (.f64 eps eps) #s(literal -1/2 binary64)) (*.f64 eps eps) #s(literal 1 binary64))
(* -1 (* eps (sin x)))
(*.f64 (neg.f64 eps) (sin.f64 x))
(* eps (- (* -1/2 (* eps (cos x))) (sin x)))
(.f64 (fma.f64 (.f64 #s(literal -1/2 binary64) eps) (cos.f64 x) (neg.f64 (sin.f64 x))) eps)
(* eps (- (* eps (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x))))) (sin x)))
(.f64 (fma.f64 (fma.f64 #s(literal 1/6 binary64) (.f64 (sin.f64 x) eps) (*.f64 (cos.f64 x) #s(literal -1/2 binary64))) eps (neg.f64 (sin.f64 x))) eps)
(* eps (- (* eps (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x)))))) (sin x)))
(.f64 (fma.f64 (fma.f64 (fma.f64 (.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) (cos.f64 x) (.f64 #s(literal 1/6 binary64) (.f64 (sin.f64 x) eps))) eps (neg.f64 (sin.f64 x))) eps)
(* -1 (* eps (sin x)))
(*.f64 (neg.f64 eps) (sin.f64 x))
(* -1 (* eps (sin x)))
(*.f64 (neg.f64 eps) (sin.f64 x))
(* -1 (* eps (sin x)))
(*.f64 (neg.f64 eps) (sin.f64 x))
(* -1 (* eps (sin x)))
(*.f64 (neg.f64 eps) (sin.f64 x))
x
(+ x (* 1/2 eps))
(fma.f64 #s(literal 1/2 binary64) eps x)
(+ x (* 1/2 eps))
(fma.f64 #s(literal 1/2 binary64) eps x)
(+ x (* 1/2 eps))
(fma.f64 #s(literal 1/2 binary64) eps x)
(* -1 (* eps (sin x)))
(*.f64 (neg.f64 eps) (sin.f64 x))
(* eps (+ (* -1 (sin x)) (* -1/2 (* eps (cos x)))))
(.f64 (fma.f64 (.f64 #s(literal -1/2 binary64) eps) (cos.f64 x) (neg.f64 (sin.f64 x))) eps)
(* eps (+ (* -1 (sin x)) (* eps (+ (* -2 (* eps (+ (* -1/16 (sin x)) (* -1/48 (sin x))))) (* -1/2 (cos x))))))
(.f64 (fma.f64 (fma.f64 #s(literal 1/6 binary64) (.f64 (sin.f64 x) eps) (*.f64 (cos.f64 x) #s(literal -1/2 binary64))) eps (neg.f64 (sin.f64 x))) eps)
(* eps (+ (* -1 (sin x)) (* eps (+ (* -1/2 (cos x)) (* eps (+ (* -2 (+ (* -1/16 (sin x)) (* -1/48 (sin x)))) (* 1/24 (* eps (cos x)))))))))
(.f64 (fma.f64 (fma.f64 (fma.f64 (.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) (cos.f64 x) (.f64 #s(literal 1/6 binary64) (.f64 (sin.f64 x) eps))) eps (neg.f64 (sin.f64 x))) eps)
(* 1/2 (* eps (sin x)))
(.f64 (.f64 #s(literal 1/2 binary64) (sin.f64 x)) eps)
(* eps (+ (* 1/4 (* eps (cos x))) (* 1/2 (sin x))))
(.f64 (fma.f64 (.f64 #s(literal 1/4 binary64) (cos.f64 x)) eps (*.f64 #s(literal 1/2 binary64) (sin.f64 x))) eps)
(* eps (+ (* 1/2 (sin x)) (* eps (+ (* 1/4 (cos x)) (* eps (+ (* -1/16 (sin x)) (* -1/48 (sin x))))))))
(.f64 (fma.f64 (fma.f64 #s(literal 1/4 binary64) (cos.f64 x) (.f64 (.f64 #s(literal -1/12 binary64) (sin.f64 x)) eps)) eps (.f64 #s(literal 1/2 binary64) (sin.f64 x))) eps)
(* eps (+ (* 1/2 (sin x)) (* eps (+ (* 1/4 (cos x)) (* eps (+ (* -1/16 (sin x)) (+ (* -1/48 (sin x)) (* -1/48 (* eps (cos x))))))))))
(.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -1/12 binary64) (sin.f64 x) (.f64 #s(literal -1/48 binary64) (.f64 (cos.f64 x) eps))) eps (.f64 #s(literal 1/4 binary64) (cos.f64 x))) eps (*.f64 #s(literal 1/2 binary64) (sin.f64 x))) eps)
(sin x)
(sin.f64 x)
(+ (sin x) (* 1/2 (* eps (cos x))))
(fma.f64 (*.f64 #s(literal 1/2 binary64) (cos.f64 x)) eps (sin.f64 x))
(+ (sin x) (* eps (+ (* -1/8 (* eps (sin x))) (* 1/2 (cos x)))))
(fma.f64 (fma.f64 (.f64 #s(literal -1/8 binary64) (sin.f64 x)) eps (.f64 #s(literal 1/2 binary64) (cos.f64 x))) eps (sin.f64 x))
(+ (sin x) (* eps (+ (* 1/2 (cos x)) (* eps (+ (* -1/8 (sin x)) (* -1/48 (* eps (cos x))))))))
(fma.f64 (fma.f64 (.f64 #s(literal -1/8 binary64) eps) (sin.f64 x) (.f64 (cos.f64 x) (fma.f64 (*.f64 eps eps) #s(literal -1/48 binary64) #s(literal 1/2 binary64)))) eps (sin.f64 x))
(* -1 (* eps (sin x)))
(*.f64 (neg.f64 eps) (sin.f64 x))
(* eps (- (* -1/2 (* eps (cos x))) (sin x)))
(.f64 (fma.f64 (.f64 #s(literal -1/2 binary64) eps) (cos.f64 x) (neg.f64 (sin.f64 x))) eps)
(* eps (- (* eps (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x))))) (sin x)))
(.f64 (fma.f64 (fma.f64 #s(literal 1/6 binary64) (.f64 (sin.f64 x) eps) (*.f64 (cos.f64 x) #s(literal -1/2 binary64))) eps (neg.f64 (sin.f64 x))) eps)
(* eps (- (* eps (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x)))))) (sin x)))
(.f64 (fma.f64 (fma.f64 (fma.f64 (.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) (cos.f64 x) (.f64 #s(literal 1/6 binary64) (.f64 (sin.f64 x) eps))) eps (neg.f64 (sin.f64 x))) eps)
(* -1 (* eps (sin x)))
(*.f64 (neg.f64 eps) (sin.f64 x))
(* eps (+ (* -1 (sin x)) (* -1/2 (* eps (cos x)))))
(.f64 (fma.f64 (.f64 #s(literal -1/2 binary64) eps) (cos.f64 x) (neg.f64 (sin.f64 x))) eps)
(* eps (+ (* -1 (sin x)) (* eps (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x)))))))
(.f64 (fma.f64 (fma.f64 #s(literal 1/6 binary64) (.f64 (sin.f64 x) eps) (*.f64 (cos.f64 x) #s(literal -1/2 binary64))) eps (neg.f64 (sin.f64 x))) eps)
(* eps (+ (* -1 (sin x)) (* eps (+ (* -1/2 (cos x)) (* eps (+ (* 1/24 (* eps (cos x))) (* 1/6 (sin x))))))))
(.f64 (fma.f64 (fma.f64 (fma.f64 (.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) (cos.f64 x) (.f64 #s(literal 1/6 binary64) (.f64 (sin.f64 x) eps))) eps (neg.f64 (sin.f64 x))) eps)
(* -1 (sin x))
(neg.f64 (sin.f64 x))
(- (* -1/2 (* eps (cos x))) (sin x))
(fma.f64 (*.f64 #s(literal -1/2 binary64) eps) (cos.f64 x) (neg.f64 (sin.f64 x)))
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(fma.f64 (fma.f64 (.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) (cos.f64 x) (.f64 #s(literal 1/6 binary64) (*.f64 (sin.f64 x) eps)))
(+ (* 1/6 (* eps (sin x))) (* (cos x) (- (* 1/24 (pow eps 2)) 1/2)))
(fma.f64 (fma.f64 (.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) (cos.f64 x) (.f64 #s(literal 1/6 binary64) (*.f64 (sin.f64 x) eps)))
(* 1/5040 (pow x 4))
(*.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 1/5040 binary64))
(* (pow x 4) (- 1/5040 (* 1/120 (/ 1 (pow x 2)))))
(.f64 (pow.f64 x #s(literal 4 binary64)) (-.f64 #s(literal 1/5040 binary64) (/.f64 #s(literal 1/120 binary64) (.f64 x x))))
(* (pow x 4) (- (+ 1/5040 (/ 1/6 (pow x 4))) (* 1/120 (/ 1 (pow x 2)))))
(.f64 (-.f64 (+.f64 (/.f64 #s(literal 1/6 binary64) (pow.f64 x #s(literal 4 binary64))) #s(literal 1/5040 binary64)) (/.f64 #s(literal 1/120 binary64) (.f64 x x))) (pow.f64 x #s(literal 4 binary64)))
(* (pow x 4) (- (+ 1/5040 (/ 1/6 (pow x 4))) (* 1/120 (/ 1 (pow x 2)))))
(.f64 (-.f64 (+.f64 (/.f64 #s(literal 1/6 binary64) (pow.f64 x #s(literal 4 binary64))) #s(literal 1/5040 binary64)) (/.f64 #s(literal 1/120 binary64) (.f64 x x))) (pow.f64 x #s(literal 4 binary64)))
(* 1/6 (sin x))
(*.f64 #s(literal 1/6 binary64) (sin.f64 x))
(* 1/6 (sin x))
(*.f64 #s(literal 1/6 binary64) (sin.f64 x))
(* 1/6 (sin x))
(*.f64 #s(literal 1/6 binary64) (sin.f64 x))
(* 1/6 (sin x))
(*.f64 #s(literal 1/6 binary64) (sin.f64 x))
(* 1/6 (* eps (sin x)))
(.f64 #s(literal 1/6 binary64) (.f64 (sin.f64 x) eps))
(* 1/6 (* eps (sin x)))
(.f64 #s(literal 1/6 binary64) (.f64 (sin.f64 x) eps))
(* 1/6 (* eps (sin x)))
(.f64 #s(literal 1/6 binary64) (.f64 (sin.f64 x) eps))
(* 1/6 (* eps (sin x)))
(.f64 #s(literal 1/6 binary64) (.f64 (sin.f64 x) eps))
(* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (- eps (* -2 x))))))
(.f64 (.f64 #s(literal -2 binary64) (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x))) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)))
(* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (- eps (* -2 x))))))
(.f64 (.f64 #s(literal -2 binary64) (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x))) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)))
(* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (- eps (* -2 x))))))
(.f64 (.f64 #s(literal -2 binary64) (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x))) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)))
(* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (- eps (* -2 x))))))
(.f64 (.f64 #s(literal -2 binary64) (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x))) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)))
(* (sin (* 1/2 eps)) (sin (* 1/2 (- eps (* -2 x)))))
(.f64 (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) (sin.f64 (.f64 #s(literal 1/2 binary64) eps)))
(* (sin (* 1/2 eps)) (sin (* 1/2 (- eps (* -2 x)))))
(.f64 (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) (sin.f64 (.f64 #s(literal 1/2 binary64) eps)))
(* (sin (* 1/2 eps)) (sin (* 1/2 (- eps (* -2 x)))))
(.f64 (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) (sin.f64 (.f64 #s(literal 1/2 binary64) eps)))
(* (sin (* 1/2 eps)) (sin (* 1/2 (- eps (* -2 x)))))
(.f64 (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) (sin.f64 (.f64 #s(literal 1/2 binary64) eps)))
(* (sin (* 1/2 eps)) (sin (- (* 1/2 eps) (* -1 x))))
(.f64 (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) (sin.f64 (.f64 #s(literal 1/2 binary64) eps)))
(* (sin (* 1/2 eps)) (sin (- (* 1/2 eps) (* -1 x))))
(.f64 (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) (sin.f64 (.f64 #s(literal 1/2 binary64) eps)))
(* (sin (* 1/2 eps)) (sin (- (* 1/2 eps) (* -1 x))))
(.f64 (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) (sin.f64 (.f64 #s(literal 1/2 binary64) eps)))
(* (sin (* 1/2 eps)) (sin (- (* 1/2 eps) (* -1 x))))
(.f64 (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) (sin.f64 (.f64 #s(literal 1/2 binary64) eps)))
(sin (- (* 1/2 eps) (* -1 x)))
(sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x))
(sin (- (* 1/2 eps) (* -1 x)))
(sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x))
(sin (- (* 1/2 eps) (* -1 x)))
(sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x))
(sin (- (* 1/2 eps) (* -1 x)))
(sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x))
(- (cos (- eps (* -1 x))) (cos x))
(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))
(- (cos (- eps (* -1 x))) (cos x))
(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))
(- (cos (- eps (* -1 x))) (cos x))
(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))
(- (cos (- eps (* -1 x))) (cos x))
(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))
(- (cos (- eps (* -1 x))) (cos x))
(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))
(- (cos (- eps (* -1 x))) (cos x))
(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))
(- (cos (- eps (* -1 x))) (cos x))
(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))
(- (cos (- eps (* -1 x))) (cos x))
(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))
(* -1 (* eps (sin x)))
(*.f64 (neg.f64 eps) (sin.f64 x))
(* -1 (* eps (sin x)))
(*.f64 (neg.f64 eps) (sin.f64 x))
(* -1 (* eps (sin x)))
(*.f64 (neg.f64 eps) (sin.f64 x))
(* -1 (* eps (sin x)))
(*.f64 (neg.f64 eps) (sin.f64 x))
(* -1 (sin x))
(neg.f64 (sin.f64 x))
(* -1 (sin x))
(neg.f64 (sin.f64 x))
(* -1 (sin x))
(neg.f64 (sin.f64 x))
(* -1 (sin x))
(neg.f64 (sin.f64 x))
(* 1/5040 (pow x 6))
(*.f64 (pow.f64 x #s(literal 6 binary64)) #s(literal 1/5040 binary64))
(* (pow x 6) (- 1/5040 (* 1/120 (/ 1 (pow x 2)))))
(.f64 (-.f64 #s(literal 1/5040 binary64) (/.f64 #s(literal 1/120 binary64) (.f64 x x))) (pow.f64 x #s(literal 6 binary64)))
(* (pow x 6) (- (+ 1/5040 (/ 1/6 (pow x 4))) (* 1/120 (/ 1 (pow x 2)))))
(.f64 (-.f64 (+.f64 (/.f64 #s(literal 1/6 binary64) (pow.f64 x #s(literal 4 binary64))) #s(literal 1/5040 binary64)) (/.f64 #s(literal 1/120 binary64) (.f64 x x))) (pow.f64 x #s(literal 6 binary64)))
(* (pow x 6) (- (+ 1/5040 (/ 1/6 (pow x 4))) (+ (* 1/120 (/ 1 (pow x 2))) (/ 1 (pow x 6)))))
(.f64 (-.f64 (-.f64 (+.f64 (/.f64 #s(literal 1/6 binary64) (pow.f64 x #s(literal 4 binary64))) #s(literal 1/5040 binary64)) (/.f64 #s(literal 1/120 binary64) (.f64 x x))) (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 6 binary64)))) (pow.f64 x #s(literal 6 binary64)))
x
(* -1 (* x (- (* -1/2 (/ eps x)) 1)))
(fma.f64 (*.f64 (/.f64 eps x) #s(literal 1/2 binary64)) x x)
(* -1 (* x (- (* -1/2 (/ eps x)) 1)))
(fma.f64 (*.f64 (/.f64 eps x) #s(literal 1/2 binary64)) x x)
(* -1 (* x (- (* -1/2 (/ eps x)) 1)))
(fma.f64 (*.f64 (/.f64 eps x) #s(literal 1/2 binary64)) x x)
(* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (- eps (* -2 x))))))
(.f64 (.f64 #s(literal -2 binary64) (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x))) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)))
(* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (- eps (* -2 x))))))
(.f64 (.f64 #s(literal -2 binary64) (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x))) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)))
(* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (- eps (* -2 x))))))
(.f64 (.f64 #s(literal -2 binary64) (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x))) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)))
(* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (- eps (* -2 x))))))
(.f64 (.f64 #s(literal -2 binary64) (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x))) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)))
(* (sin (* 1/2 eps)) (sin (* 1/2 (- eps (* -2 x)))))
(.f64 (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) (sin.f64 (.f64 #s(literal 1/2 binary64) eps)))
(* (sin (* 1/2 eps)) (sin (* 1/2 (- eps (* -2 x)))))
(.f64 (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) (sin.f64 (.f64 #s(literal 1/2 binary64) eps)))
(* (sin (* 1/2 eps)) (sin (* 1/2 (- eps (* -2 x)))))
(.f64 (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) (sin.f64 (.f64 #s(literal 1/2 binary64) eps)))
(* (sin (* 1/2 eps)) (sin (* 1/2 (- eps (* -2 x)))))
(.f64 (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) (sin.f64 (.f64 #s(literal 1/2 binary64) eps)))
(sin (* 1/2 (- eps (* -2 x))))
(sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x))
(sin (* 1/2 (- eps (* -2 x))))
(sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x))
(sin (* 1/2 (- eps (* -2 x))))
(sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x))
(sin (* 1/2 (- eps (* -2 x))))
(sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x))
(- (cos (- eps (* -1 x))) (cos x))
(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))
(- (cos (- eps (* -1 x))) (cos x))
(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))
(- (cos (- eps (* -1 x))) (cos x))
(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))
(- (cos (- eps (* -1 x))) (cos x))
(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))
(* eps (- (* eps (+ (* 1/6 (* eps (sin x))) (* (cos x) (- (* 1/24 (pow eps 2)) 1/2)))) (sin x)))
(.f64 (fma.f64 (fma.f64 (fma.f64 (.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) (cos.f64 x) (.f64 #s(literal 1/6 binary64) (.f64 (sin.f64 x) eps))) eps (neg.f64 (sin.f64 x))) eps)
(* eps (- (* eps (+ (* 1/6 (* eps (sin x))) (* (cos x) (- (* 1/24 (pow eps 2)) 1/2)))) (sin x)))
(.f64 (fma.f64 (fma.f64 (fma.f64 (.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) (cos.f64 x) (.f64 #s(literal 1/6 binary64) (.f64 (sin.f64 x) eps))) eps (neg.f64 (sin.f64 x))) eps)
(* eps (- (* eps (+ (* 1/6 (* eps (sin x))) (* (cos x) (- (* 1/24 (pow eps 2)) 1/2)))) (sin x)))
(.f64 (fma.f64 (fma.f64 (fma.f64 (.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) (cos.f64 x) (.f64 #s(literal 1/6 binary64) (.f64 (sin.f64 x) eps))) eps (neg.f64 (sin.f64 x))) eps)
(* eps (- (* eps (+ (* 1/6 (* eps (sin x))) (* (cos x) (- (* 1/24 (pow eps 2)) 1/2)))) (sin x)))
(.f64 (fma.f64 (fma.f64 (fma.f64 (.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) (cos.f64 x) (.f64 #s(literal 1/6 binary64) (.f64 (sin.f64 x) eps))) eps (neg.f64 (sin.f64 x))) eps)
(- (* eps (+ (* 1/6 (* eps (sin x))) (* (cos x) (- (* 1/24 (pow eps 2)) 1/2)))) (sin x))
(fma.f64 (fma.f64 (fma.f64 (.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) (cos.f64 x) (.f64 #s(literal 1/6 binary64) (*.f64 (sin.f64 x) eps))) eps (neg.f64 (sin.f64 x)))
(- (* eps (+ (* 1/6 (* eps (sin x))) (* (cos x) (- (* 1/24 (pow eps 2)) 1/2)))) (sin x))
(fma.f64 (fma.f64 (fma.f64 (.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) (cos.f64 x) (.f64 #s(literal 1/6 binary64) (*.f64 (sin.f64 x) eps))) eps (neg.f64 (sin.f64 x)))
(- (* eps (+ (* 1/6 (* eps (sin x))) (* (cos x) (- (* 1/24 (pow eps 2)) 1/2)))) (sin x))
(fma.f64 (fma.f64 (fma.f64 (.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) (cos.f64 x) (.f64 #s(literal 1/6 binary64) (*.f64 (sin.f64 x) eps))) eps (neg.f64 (sin.f64 x)))
(- (* eps (+ (* 1/6 (* eps (sin x))) (* (cos x) (- (* 1/24 (pow eps 2)) 1/2)))) (sin x))
(fma.f64 (fma.f64 (fma.f64 (.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) (cos.f64 x) (.f64 #s(literal 1/6 binary64) (*.f64 (sin.f64 x) eps))) eps (neg.f64 (sin.f64 x)))
(+ (* 1/6 (* eps (sin x))) (* (cos x) (- (* 1/24 (pow eps 2)) 1/2)))
(fma.f64 (fma.f64 (.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) (cos.f64 x) (.f64 #s(literal 1/6 binary64) (*.f64 (sin.f64 x) eps)))
(+ (* 1/6 (* eps (sin x))) (* (cos x) (- (* 1/24 (pow eps 2)) 1/2)))
(fma.f64 (fma.f64 (.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) (cos.f64 x) (.f64 #s(literal 1/6 binary64) (*.f64 (sin.f64 x) eps)))
(+ (* 1/6 (* eps (sin x))) (* (cos x) (- (* 1/24 (pow eps 2)) 1/2)))
(fma.f64 (fma.f64 (.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) (cos.f64 x) (.f64 #s(literal 1/6 binary64) (*.f64 (sin.f64 x) eps)))
(+ (* 1/6 (* eps (sin x))) (* (cos x) (- (* 1/24 (pow eps 2)) 1/2)))
(fma.f64 (fma.f64 (.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) (cos.f64 x) (.f64 #s(literal 1/6 binary64) (*.f64 (sin.f64 x) eps)))
(* 1/5040 (pow x 4))
(*.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 1/5040 binary64))
(* (pow x 4) (- 1/5040 (* 1/120 (/ 1 (pow x 2)))))
(.f64 (pow.f64 x #s(literal 4 binary64)) (-.f64 #s(literal 1/5040 binary64) (/.f64 #s(literal 1/120 binary64) (.f64 x x))))
(* (pow x 4) (- (+ 1/5040 (/ 1/6 (pow x 4))) (* 1/120 (/ 1 (pow x 2)))))
(.f64 (-.f64 (+.f64 (/.f64 #s(literal 1/6 binary64) (pow.f64 x #s(literal 4 binary64))) #s(literal 1/5040 binary64)) (/.f64 #s(literal 1/120 binary64) (.f64 x x))) (pow.f64 x #s(literal 4 binary64)))
(* (pow x 4) (- (+ 1/5040 (/ 1/6 (pow x 4))) (* 1/120 (/ 1 (pow x 2)))))
(.f64 (-.f64 (+.f64 (/.f64 #s(literal 1/6 binary64) (pow.f64 x #s(literal 4 binary64))) #s(literal 1/5040 binary64)) (/.f64 #s(literal 1/120 binary64) (.f64 x x))) (pow.f64 x #s(literal 4 binary64)))
(* 1/6 (sin x))
(*.f64 #s(literal 1/6 binary64) (sin.f64 x))
(* 1/6 (sin x))
(*.f64 #s(literal 1/6 binary64) (sin.f64 x))
(* 1/6 (sin x))
(*.f64 #s(literal 1/6 binary64) (sin.f64 x))
(* 1/6 (sin x))
(*.f64 #s(literal 1/6 binary64) (sin.f64 x))
(* 1/6 (* eps (sin x)))
(.f64 #s(literal 1/6 binary64) (.f64 (sin.f64 x) eps))
(* 1/6 (* eps (sin x)))
(.f64 #s(literal 1/6 binary64) (.f64 (sin.f64 x) eps))
(* 1/6 (* eps (sin x)))
(.f64 #s(literal 1/6 binary64) (.f64 (sin.f64 x) eps))
(* 1/6 (* eps (sin x)))
(.f64 #s(literal 1/6 binary64) (.f64 (sin.f64 x) eps))

rewrite195.0ms (1.2%)

Memory

2.3MiB live, 353.7MiB allocated

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	70	399
0	111	389
1	407	389
2	3262	389
0	8362	389

Stop Event

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

Counts

23 → 380

Calls

Call 1

Inputs
(.f64 #s(approx ( (sin (* 1/2 (+ (* 2 x) eps))) (sin (* 1/2 (+ 0 eps)))) (.f64 (sin.f64 (fma.f64 eps #s(literal 1/2 binary64) x)) (sin.f64 (.f64 eps #s(literal 1/2 binary64))))) #s(literal -2 binary64))
#s(approx (* (sin (* 1/2 (+ (* 2 x) eps))) (sin (* 1/2 (+ 0 eps)))) (.f64 (sin.f64 (fma.f64 eps #s(literal 1/2 binary64) x)) (sin.f64 (.f64 eps #s(literal 1/2 binary64)))))
(.f64 (sin.f64 (fma.f64 eps #s(literal 1/2 binary64) x)) (sin.f64 (.f64 eps #s(literal 1/2 binary64))))
(sin.f64 (fma.f64 eps #s(literal 1/2 binary64) x))
#s(approx (- (cos (+ x eps)) (cos x)) (-.f64 #s(approx (cos eps) #s(literal 1 binary64)) #s(literal 1 binary64)))
(-.f64 #s(approx (cos eps) #s(literal 1 binary64)) #s(literal 1 binary64))
#s(approx (cos eps) #s(literal 1 binary64))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (neg (sin x)) (.f64 (fma.f64 (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)) (*.f64 x x) #s(literal -1 binary64)) x)) eps))
(.f64 #s(approx (neg (sin x)) (.f64 (fma.f64 (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)) (*.f64 x x) #s(literal -1 binary64)) x)) eps)
#s(approx (neg (sin x)) (.f64 (fma.f64 (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)) (.f64 x x) #s(literal -1 binary64)) x))
(fma.f64 (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)) (*.f64 x x) #s(literal -1 binary64))
(*.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps))
(.f64 (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps))) #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 (sin.f64 (.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps))) #s(approx (sin (* 1/2 (+ 0 eps))) (.f64 (fma.f64 (fma.f64 (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)))
(sin.f64 (*.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps)))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 (fma.f64 (fma.f64 (cos.f64 x) (fma.f64 (.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) (.f64 (.f64 #s(literal 1/6 binary64) (sin.f64 x)) eps)) eps (neg.f64 (sin.f64 x))) eps))
(.f64 (fma.f64 (fma.f64 (cos.f64 x) (fma.f64 (.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) (.f64 (.f64 #s(literal 1/6 binary64) (sin.f64 x)) eps)) eps (neg.f64 (sin.f64 x))) eps)
(fma.f64 (fma.f64 (cos.f64 x) (fma.f64 (.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) (.f64 (*.f64 #s(literal 1/6 binary64) (sin.f64 x)) eps)) eps (neg.f64 (sin.f64 x)))
(fma.f64 (cos.f64 x) (fma.f64 (.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) (.f64 (*.f64 #s(literal 1/6 binary64) (sin.f64 x)) eps))
(fma.f64 (fma.f64 #s(literal 1/5040 binary64) (.f64 x x) #s(literal -1/120 binary64)) (.f64 x x) #s(literal 1/6 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 #s(literal 1/6 binary64) (sin.f64 x))
(.f64 (.f64 #s(literal 1/6 binary64) (sin.f64 x)) eps)

Outputs
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eval115.0ms (0.7%)

Memory: -4.2MiB live, 271.8MiB allocated
Compiler: Compiled 26 234 to 2 625 computations (90% saved)

prune60.0ms (0.4%)

Memory

-3.9MiB live, 206.1MiB allocated

Pruning

32 alts after pruning (26 fresh and 6 done)

	Pruned	Kept	Total
New	835	10	845
Fresh	8	16	24
Picked	1	4	5
Done	1	2	3
Total	845	32	877

Accuracy

100.0%

Counts

877 → 32

Alt Table

Click to see full alt table

Status	Accuracy	Program
	48.7%	(-.f64 (fma.f64 (sin.f64 x) (neg.f64 (sin.f64 eps)) (*.f64 (cos.f64 eps) (cos.f64 x))) (cos.f64 x))
	48.7%	(-.f64 (*.f64 (cos.f64 eps) (cos.f64 x)) (fma.f64 (sin.f64 eps) (sin.f64 x) (cos.f64 x)))
✓	48.5%	(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))
	46.6%	(-.f64 #s(approx (cos (+ x eps)) #s(approx (cos eps) (fma.f64 (*.f64 eps eps) #s(literal -1/2 binary64) #s(literal 1 binary64)))) (cos.f64 x))
	46.6%	(-.f64 #s(approx (cos (+ x eps)) #s(approx (cos eps) #s(literal 1 binary64))) (cos.f64 x))
▶	99.6%	(.f64 (.f64 (fma.f64 (sin.f64 (.f64 #s(literal 1 binary64) x)) (cos.f64 (.f64 #s(literal 1/2 binary64) eps)) (.f64 (cos.f64 (.f64 #s(literal 1 binary64) x)) (sin.f64 (.f64 #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(literal -2 binary64))
▶	99.4%	(.f64 (.f64 (sin.f64 (/.f64 (.f64 (fma.f64 #s(literal 4 binary64) (.f64 x x) (.f64 (neg.f64 eps) eps)) #s(literal 1/2 binary64)) (fma.f64 #s(literal 2 binary64) x (neg.f64 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(literal -2 binary64))
	41.8%	(.f64 (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps))) (sin.f64 (.f64 #s(literal 1/2 binary64) (/.f64 (pow.f64 eps #s(literal 3 binary64)) (*.f64 eps eps))))) #s(literal -2 binary64))
	98.9%	(.f64 (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps))) (sin.f64 (.f64 #s(literal 1/2 binary64) (.f64 (neg.f64 (.f64 eps eps)) (pow.f64 (neg.f64 eps) #s(literal -1 binary64)))))) #s(literal -2 binary64))
	99.3%	(.f64 (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps))) #s(approx (sin ( 1/2 (+ 0 eps))) (.f64 (fma.f64 (fma.f64 #s(literal 1/3840 binary64) (.f64 eps eps) #s(literal -1/48 binary64)) (*.f64 eps eps) #s(literal 1/2 binary64)) eps))) #s(literal -2 binary64))
	99.1%	(.f64 (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps))) #s(approx (sin ( 1/2 (+ 0 eps))) (.f64 (fma.f64 (.f64 eps eps) #s(literal -1/48 binary64) #s(literal 1/2 binary64)) eps))) #s(literal -2 binary64))
	98.5%	(.f64 (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps))) #s(approx (sin ( 1/2 (+ 0 eps))) (*.f64 eps #s(literal 1/2 binary64)))) #s(literal -2 binary64))
	99.5%	(.f64 (.f64 (sin.f64 #s(approx (* 1/2 (+ (* 2 x) eps)) (fma.f64 #s(literal 1/2 binary64) eps x))) #s(approx (sin (* 1/2 (+ 0 eps))) (.f64 (fma.f64 (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))
	99.4%	(.f64 (.f64 (sin.f64 #s(approx (* 1/2 (+ (* 2 x) eps)) (.f64 (+.f64 (/.f64 x 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(literal -2 binary64))
✓	99.7%	(.f64 #s(approx ( (sin (* 1/2 (+ (* 2 x) eps))) (sin (* 1/2 (+ 0 eps)))) (.f64 (sin.f64 (fma.f64 eps #s(literal 1/2 binary64) x)) (sin.f64 (.f64 eps #s(literal 1/2 binary64))))) #s(literal -2 binary64))
	99.3%	#s(approx (- (cos (+ x eps)) (cos x)) (fma.f64 (neg.f64 (sin.f64 x)) eps (.f64 (.f64 (fma.f64 (fma.f64 #s(literal 1/24 binary64) (.f64 eps eps) #s(literal -1/2 binary64)) (cos.f64 x) (.f64 (*.f64 (sin.f64 x) #s(literal 1/6 binary64)) eps)) eps) eps)))
✓	46.3%	#s(approx (- (cos (+ x eps)) (cos x)) (-.f64 #s(approx (cos eps) #s(literal 1 binary64)) #s(literal 1 binary64)))
✓	99.1%	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 (fma.f64 (fma.f64 (cos.f64 x) (fma.f64 (.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) (.f64 (.f64 #s(literal 1/6 binary64) (sin.f64 x)) eps)) eps (neg.f64 (sin.f64 x))) eps))
▶	98.1%	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 (fma.f64 #s(approx (+ ( (cos x) (+ (* (* eps eps) 1/24) -1/2)) (* (* 1/6 (sin x)) eps)) (fma.f64 (*.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64))) eps (neg.f64 (sin.f64 x))) eps))
	67.2%	#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (/.f64 (pow.f64 eps #s(literal 3 binary64)) eps) (/.f64 (neg.f64 (sin.f64 x)) eps)))
✓	75.2%	#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (neg.f64 (sin.f64 x)) eps))
	97.9%	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (+ ( (+ (* (cos x) (+ (* (* eps eps) 1/24) -1/2)) (* (* 1/6 (sin x)) eps)) eps) (neg (sin x))) (fma.f64 (fma.f64 (fma.f64 (.f64 (fma.f64 (.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) eps) #s(literal -1/2 binary64) (.f64 (fma.f64 #s(literal -1/36 binary64) (.f64 eps eps) #s(literal 1/6 binary64)) x)) x (fma.f64 (.f64 #s(literal 1/6 binary64) eps) eps #s(literal -1 binary64))) x (.f64 (fma.f64 (*.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) eps))) eps))
▶	97.0%	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (+ ( (+ (* (cos x) (+ (* (* eps eps) 1/24) -1/2)) (* (* 1/6 (sin x)) eps)) eps) (neg (sin x))) (fma.f64 (fma.f64 (.f64 #s(literal 1/6 binary64) eps) eps #s(literal -1 binary64)) x (.f64 (fma.f64 (*.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) eps))) eps))
✓	75.0%	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (neg (sin x)) (.f64 (fma.f64 (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)) (*.f64 x x) #s(literal -1 binary64)) x)) eps))
	74.9%	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (neg (sin x)) (.f64 (fma.f64 (fma.f64 #s(literal -1/120 binary64) (.f64 x x) #s(literal 1/6 binary64)) (.f64 x x) #s(literal -1 binary64)) x)) eps))
	75.0%	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (neg (sin x)) (.f64 (fma.f64 (.f64 (fma.f64 (fma.f64 (.f64 x x) #s(literal 1/5040 binary64) #s(literal -1/120 binary64)) (*.f64 x x) #s(literal 1/6 binary64)) x) x #s(literal -1 binary64)) x)) eps))
	74.8%	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (neg (sin x)) (.f64 (fma.f64 (*.f64 x x) #s(literal 1/6 binary64) #s(literal -1 binary64)) x)) eps))
▶	74.6%	#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 #s(approx (neg (sin x)) (neg.f64 x)) eps))
	47.9%	#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (- (cos eps) 1) (.f64 (.f64 eps eps) #s(literal -1/2 binary64))))
	97.8%	#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (+ (* (+ (* (cos x) (+ (* (* eps eps) 1/24) -1/2)) (* (* 1/6 (sin x)) eps)) eps) (neg (sin x))) eps) (fma.f64 (.f64 (fma.f64 (.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) eps) eps (.f64 (fma.f64 (fma.f64 (.f64 eps (fma.f64 #s(literal -1/36 binary64) (.f64 eps eps) #s(literal 1/6 binary64))) x (.f64 (.f64 (fma.f64 (.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) #s(literal -1/2 binary64)) (.f64 eps eps))) x (.f64 (fma.f64 (*.f64 #s(literal 1/6 binary64) eps) eps #s(literal -1 binary64)) eps)) x))))
	74.9%	#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg (sin x)) eps) (.f64 (fma.f64 (.f64 eps (fma.f64 #s(literal -1/120 binary64) (.f64 x x) #s(literal 1/6 binary64))) (.f64 x x) (neg.f64 eps)) x)))
	74.8%	#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg (sin x)) eps) (.f64 (.f64 eps (fma.f64 (*.f64 x x) #s(literal 1/6 binary64) #s(literal -1 binary64))) x)))

Compiler

Compiled 1 144 to 799 computations (30.2% saved)

simplify137.0ms (0.8%)

Memory

-3.1MiB live, 192.9MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 20 expressions of interest:

New	Metric	Score
cost-diff	0	(.f64 (sin.f64 (/.f64 (.f64 (fma.f64 #s(literal 4 binary64) (.f64 x x) (.f64 (neg.f64 eps) eps)) #s(literal 1/2 binary64)) (fma.f64 #s(literal 2 binary64) x (neg.f64 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)))
cost-diff	0	(.f64 (.f64 (sin.f64 (/.f64 (.f64 (fma.f64 #s(literal 4 binary64) (.f64 x x) (.f64 (neg.f64 eps) eps)) #s(literal 1/2 binary64)) (fma.f64 #s(literal 2 binary64) x (neg.f64 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(literal -2 binary64))
cost-diff	128	(.f64 (fma.f64 #s(literal 4 binary64) (.f64 x x) (*.f64 (neg.f64 eps) eps)) #s(literal 1/2 binary64))
cost-diff	128	(/.f64 (.f64 (fma.f64 #s(literal 4 binary64) (.f64 x x) (*.f64 (neg.f64 eps) eps)) #s(literal 1/2 binary64)) (fma.f64 #s(literal 2 binary64) x (neg.f64 eps)))
cost-diff	0	#s(approx (+ (* (cos x) (+ (* (* eps eps) 1/24) -1/2)) (* (* 1/6 (sin x)) eps)) (fma.f64 (*.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)))
cost-diff	0	(fma.f64 #s(approx (+ (* (cos x) (+ (* (* eps eps) 1/24) -1/2)) (* (* 1/6 (sin x)) eps)) (fma.f64 (*.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64))) eps (neg.f64 (sin.f64 x)))
cost-diff	0	(.f64 (fma.f64 #s(approx (+ ( (cos x) (+ (* (* eps eps) 1/24) -1/2)) (* (* 1/6 (sin x)) eps)) (fma.f64 (*.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64))) eps (neg.f64 (sin.f64 x))) eps)
cost-diff	0	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 (fma.f64 #s(approx (+ ( (cos x) (+ (* (* eps eps) 1/24) -1/2)) (* (* 1/6 (sin x)) eps)) (fma.f64 (*.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64))) eps (neg.f64 (sin.f64 x))) eps))
cost-diff	0	#s(approx (+ (* (+ (* (cos x) (+ (* (* eps eps) 1/24) -1/2)) (* (* 1/6 (sin x)) eps)) eps) (neg (sin x))) (fma.f64 (fma.f64 (.f64 #s(literal 1/6 binary64) eps) eps #s(literal -1 binary64)) x (.f64 (fma.f64 (*.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) eps)))
cost-diff	0	(.f64 #s(approx (+ ( (+ (* (cos x) (+ (* (* eps eps) 1/24) -1/2)) (* (* 1/6 (sin x)) eps)) eps) (neg (sin x))) (fma.f64 (fma.f64 (.f64 #s(literal 1/6 binary64) eps) eps #s(literal -1 binary64)) x (.f64 (fma.f64 (*.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) eps))) eps)
cost-diff	0	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (+ ( (+ (* (cos x) (+ (* (* eps eps) 1/24) -1/2)) (* (* 1/6 (sin x)) eps)) eps) (neg (sin x))) (fma.f64 (fma.f64 (.f64 #s(literal 1/6 binary64) eps) eps #s(literal -1 binary64)) x (.f64 (fma.f64 (*.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) eps))) eps))
cost-diff	512	(fma.f64 (fma.f64 (.f64 #s(literal 1/6 binary64) eps) eps #s(literal -1 binary64)) x (.f64 (fma.f64 (*.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) eps))
cost-diff	0	(neg.f64 x)
cost-diff	0	#s(approx (neg (sin x)) (neg.f64 x))
cost-diff	0	(*.f64 #s(approx (neg (sin x)) (neg.f64 x)) eps)
cost-diff	0	#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 #s(approx (neg (sin x)) (neg.f64 x)) eps))
cost-diff	0	(fma.f64 (sin.f64 (.f64 #s(literal 1 binary64) x)) (cos.f64 (.f64 #s(literal 1/2 binary64) eps)) (.f64 (cos.f64 (.f64 #s(literal 1 binary64) x)) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps))))
cost-diff	0	(.f64 (fma.f64 (sin.f64 (.f64 #s(literal 1 binary64) x)) (cos.f64 (.f64 #s(literal 1/2 binary64) eps)) (.f64 (cos.f64 (.f64 #s(literal 1 binary64) x)) (sin.f64 (.f64 #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)))
cost-diff	0	(.f64 (.f64 (fma.f64 (sin.f64 (.f64 #s(literal 1 binary64) x)) (cos.f64 (.f64 #s(literal 1/2 binary64) eps)) (.f64 (cos.f64 (.f64 #s(literal 1 binary64) x)) (sin.f64 (.f64 #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(literal -2 binary64))
cost-diff	320	(*.f64 #s(literal 1 binary64) x)

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	77	821
0	126	786
1	218	786
2	538	786
3	1462	786
4	3089	786
5	4538	782
6	6967	782
0	8383	758

Stop Event

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

Calls

Call 1

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

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

localize410.0ms (2.5%)

Memory

1.6MiB live, 841.9MiB allocated

Localize:

Found 20 expressions of interest:

New	Metric	Score
accuracy	0.109375	(.f64 (sin.f64 (/.f64 (.f64 (fma.f64 #s(literal 4 binary64) (.f64 x x) (.f64 (neg.f64 eps) eps)) #s(literal 1/2 binary64)) (fma.f64 #s(literal 2 binary64) x (neg.f64 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)))
accuracy	0.12013627930532605	(fma.f64 #s(literal 4 binary64) (.f64 x x) (.f64 (neg.f64 eps) eps))
accuracy	0.15012321344468227	#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))
accuracy	24.988243661079075	(/.f64 (.f64 (fma.f64 #s(literal 4 binary64) (.f64 x x) (*.f64 (neg.f64 eps) eps)) #s(literal 1/2 binary64)) (fma.f64 #s(literal 2 binary64) x (neg.f64 eps)))
accuracy	0.01953125	(fma.f64 #s(approx (+ (* (cos x) (+ (* (* eps eps) 1/24) -1/2)) (* (* 1/6 (sin x)) eps)) (fma.f64 (*.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64))) eps (neg.f64 (sin.f64 x)))
accuracy	0.109375	(.f64 (fma.f64 #s(approx (+ ( (cos x) (+ (* (* eps eps) 1/24) -1/2)) (* (* 1/6 (sin x)) eps)) (fma.f64 (*.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64))) eps (neg.f64 (sin.f64 x))) eps)
accuracy	0.46038007253661184	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 (fma.f64 #s(approx (+ ( (cos x) (+ (* (* eps eps) 1/24) -1/2)) (* (* 1/6 (sin x)) eps)) (fma.f64 (*.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64))) eps (neg.f64 (sin.f64 x))) eps))
accuracy	1.9215567538907166	#s(approx (+ (* (cos x) (+ (* (* eps eps) 1/24) -1/2)) (* (* 1/6 (sin x)) eps)) (fma.f64 (*.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)))
accuracy	0.109375	(.f64 #s(approx (+ ( (+ (* (cos x) (+ (* (* eps eps) 1/24) -1/2)) (* (* 1/6 (sin x)) eps)) eps) (neg (sin x))) (fma.f64 (fma.f64 (.f64 #s(literal 1/6 binary64) eps) eps #s(literal -1 binary64)) x (.f64 (fma.f64 (*.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) eps))) eps)
accuracy	0.29296875	(*.f64 #s(literal 1/6 binary64) eps)
accuracy	0.46038007253661184	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (+ ( (+ (* (cos x) (+ (* (* eps eps) 1/24) -1/2)) (* (* 1/6 (sin x)) eps)) eps) (neg (sin x))) (fma.f64 (fma.f64 (.f64 #s(literal 1/6 binary64) eps) eps #s(literal -1 binary64)) x (.f64 (fma.f64 (*.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) eps))) eps))
accuracy	1.8053969294999332	#s(approx (+ (* (+ (* (cos x) (+ (* (* eps eps) 1/24) -1/2)) (* (* 1/6 (sin x)) eps)) eps) (neg (sin x))) (fma.f64 (fma.f64 (.f64 #s(literal 1/6 binary64) eps) eps #s(literal -1 binary64)) x (.f64 (fma.f64 (*.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) eps)))
accuracy	0	(*.f64 #s(approx (neg (sin x)) (neg.f64 x)) eps)
accuracy	0	(neg.f64 x)
accuracy	1.8372299474159495	#s(approx (neg (sin x)) (neg.f64 x))
accuracy	15.856391180419081	#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 #s(approx (neg (sin x)) (neg.f64 x)) eps))
accuracy	0.01953125	(.f64 (.f64 (fma.f64 (sin.f64 (.f64 #s(literal 1 binary64) x)) (cos.f64 (.f64 #s(literal 1/2 binary64) eps)) (.f64 (cos.f64 (.f64 #s(literal 1 binary64) x)) (sin.f64 (.f64 #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(literal -2 binary64))
accuracy	0.0234375	(fma.f64 (sin.f64 (.f64 #s(literal 1 binary64) x)) (cos.f64 (.f64 #s(literal 1/2 binary64) eps)) (.f64 (cos.f64 (.f64 #s(literal 1 binary64) x)) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps))))
accuracy	0.109375	(.f64 (fma.f64 (sin.f64 (.f64 #s(literal 1 binary64) x)) (cos.f64 (.f64 #s(literal 1/2 binary64) eps)) (.f64 (cos.f64 (.f64 #s(literal 1 binary64) x)) (sin.f64 (.f64 #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)))
accuracy	0.15012321344468227	#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))

Samples

222.0ms	155×	2	valid
108.0ms	93×	1	valid
8.0ms	2×	3	valid
3.0ms	6×	0	valid

Compiler

Compiled 1 237 to 132 computations (89.3% saved)

Precisions

Click to see histograms. Total time spent on operations: 277.0ms

ival-mult: 89.0ms (32.2% of total)

ival-cos: 57.0ms (20.6% of total)

adjust: 49.0ms (17.7% of total)

ival-add: 28.0ms (10.1% of total)

const: 22.0ms (8% of total)

ival-sin: 20.0ms (7.2% of total)

ival-neg: 4.0ms (1.4% of total)

ival-div: 3.0ms (1.1% of total)

ival-sub: 3.0ms (1.1% of total)

exact: 1.0ms (0.4% of total)

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

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

series65.0ms (0.4%)

Memory

6.8MiB live, 86.1MiB allocated

Counts

23 → 492

Calls

Call 1

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

Outputs
#s(alt (* -1 (* eps (sin x))) (taylor 0 eps) (#s(alt (.f64 (.f64 (fma.f64 (sin.f64 (.f64 #s(literal 1 binary64) x)) (cos.f64 (.f64 #s(literal 1/2 binary64) eps)) (.f64 (cos.f64 (.f64 #s(literal 1 binary64) x)) (sin.f64 (.f64 #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(literal -2 binary64)) (patch (.f64 (.f64 (fma.f64 (sin.f64 (.f64 #s(literal 1 binary64) x)) (cos.f64 (.f64 #s(literal 1/2 binary64) eps)) (.f64 (cos.f64 (.f64 #s(literal 1 binary64) x)) (sin.f64 (.f64 #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(literal -2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* eps (+ (* -1 (sin x)) (* -1/2 (* eps (cos x))))) (taylor 0 eps) (#s(alt (.f64 (.f64 (fma.f64 (sin.f64 (.f64 #s(literal 1 binary64) x)) (cos.f64 (.f64 #s(literal 1/2 binary64) eps)) (.f64 (cos.f64 (.f64 #s(literal 1 binary64) x)) (sin.f64 (.f64 #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(literal -2 binary64)) (patch (.f64 (.f64 (fma.f64 (sin.f64 (.f64 #s(literal 1 binary64) x)) (cos.f64 (.f64 #s(literal 1/2 binary64) eps)) (.f64 (cos.f64 (.f64 #s(literal 1 binary64) x)) (sin.f64 (.f64 #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(literal -2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* eps (+ (* -1 (sin x)) (* eps (+ (* -2 (* eps (+ (* -1/16 (sin x)) (* -1/48 (sin x))))) (* -1/2 (cos x)))))) (taylor 0 eps) (#s(alt (.f64 (.f64 (fma.f64 (sin.f64 (.f64 #s(literal 1 binary64) x)) (cos.f64 (.f64 #s(literal 1/2 binary64) eps)) (.f64 (cos.f64 (.f64 #s(literal 1 binary64) x)) (sin.f64 (.f64 #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(literal -2 binary64)) (patch (.f64 (.f64 (fma.f64 (sin.f64 (.f64 #s(literal 1 binary64) x)) (cos.f64 (.f64 #s(literal 1/2 binary64) eps)) (.f64 (cos.f64 (.f64 #s(literal 1 binary64) x)) (sin.f64 (.f64 #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(literal -2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* eps (+ (* -1 (sin x)) (* eps (+ (* -1/2 (cos x)) (* eps (+ (* -2 (+ (* -1/16 (sin x)) (* -1/48 (sin x)))) (* 1/24 (* eps (cos x))))))))) (taylor 0 eps) (#s(alt (.f64 (.f64 (fma.f64 (sin.f64 (.f64 #s(literal 1 binary64) x)) (cos.f64 (.f64 #s(literal 1/2 binary64) eps)) (.f64 (cos.f64 (.f64 #s(literal 1 binary64) x)) (sin.f64 (.f64 #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(literal -2 binary64)) (patch (.f64 (.f64 (fma.f64 (sin.f64 (.f64 #s(literal 1 binary64) x)) (cos.f64 (.f64 #s(literal 1/2 binary64) eps)) (.f64 (cos.f64 (.f64 #s(literal 1 binary64) x)) (sin.f64 (.f64 #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(literal -2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* 1/2 (* eps (sin x))) (taylor 0 eps) (#s(alt (.f64 (fma.f64 (sin.f64 (.f64 #s(literal 1 binary64) x)) (cos.f64 (.f64 #s(literal 1/2 binary64) eps)) (.f64 (cos.f64 (.f64 #s(literal 1 binary64) x)) (sin.f64 (.f64 #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))) (patch (.f64 (fma.f64 (sin.f64 (.f64 #s(literal 1 binary64) x)) (cos.f64 (.f64 #s(literal 1/2 binary64) eps)) (.f64 (cos.f64 (.f64 #s(literal 1 binary64) x)) (sin.f64 (.f64 #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))) #<representation binary64>) () ())) ())
#s(alt (* eps (+ (* 1/4 (* eps (cos x))) (* 1/2 (sin x)))) (taylor 0 eps) (#s(alt (.f64 (fma.f64 (sin.f64 (.f64 #s(literal 1 binary64) x)) (cos.f64 (.f64 #s(literal 1/2 binary64) eps)) (.f64 (cos.f64 (.f64 #s(literal 1 binary64) x)) (sin.f64 (.f64 #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))) (patch (.f64 (fma.f64 (sin.f64 (.f64 #s(literal 1 binary64) x)) (cos.f64 (.f64 #s(literal 1/2 binary64) eps)) (.f64 (cos.f64 (.f64 #s(literal 1 binary64) x)) (sin.f64 (.f64 #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))) #<representation binary64>) () ())) ())
#s(alt (* eps (+ (* 1/2 (sin x)) (* eps (+ (* 1/4 (cos x)) (* eps (+ (* -1/16 (sin x)) (* -1/48 (sin x)))))))) (taylor 0 eps) (#s(alt (.f64 (fma.f64 (sin.f64 (.f64 #s(literal 1 binary64) x)) (cos.f64 (.f64 #s(literal 1/2 binary64) eps)) (.f64 (cos.f64 (.f64 #s(literal 1 binary64) x)) (sin.f64 (.f64 #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))) (patch (.f64 (fma.f64 (sin.f64 (.f64 #s(literal 1 binary64) x)) (cos.f64 (.f64 #s(literal 1/2 binary64) eps)) (.f64 (cos.f64 (.f64 #s(literal 1 binary64) x)) (sin.f64 (.f64 #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))) #<representation binary64>) () ())) ())
#s(alt (* eps (+ (* 1/2 (sin x)) (* eps (+ (* 1/4 (cos x)) (* eps (+ (* -1/16 (sin x)) (+ (* -1/48 (sin x)) (* -1/48 (* eps (cos x)))))))))) (taylor 0 eps) (#s(alt (.f64 (fma.f64 (sin.f64 (.f64 #s(literal 1 binary64) x)) (cos.f64 (.f64 #s(literal 1/2 binary64) eps)) (.f64 (cos.f64 (.f64 #s(literal 1 binary64) x)) (sin.f64 (.f64 #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))) (patch (.f64 (fma.f64 (sin.f64 (.f64 #s(literal 1 binary64) x)) (cos.f64 (.f64 #s(literal 1/2 binary64) eps)) (.f64 (cos.f64 (.f64 #s(literal 1 binary64) x)) (sin.f64 (.f64 #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))) #<representation binary64>) () ())) ())
#s(alt (sin x) (taylor 0 eps) (#s(alt (fma.f64 (sin.f64 (.f64 #s(literal 1 binary64) x)) (cos.f64 (.f64 #s(literal 1/2 binary64) eps)) (.f64 (cos.f64 (.f64 #s(literal 1 binary64) x)) (sin.f64 (.f64 #s(literal 1/2 binary64) eps)))) (patch (fma.f64 (sin.f64 (.f64 #s(literal 1 binary64) x)) (cos.f64 (.f64 #s(literal 1/2 binary64) eps)) (.f64 (cos.f64 (.f64 #s(literal 1 binary64) x)) (sin.f64 (.f64 #s(literal 1/2 binary64) eps)))) #<representation binary64>) () ())) ())
#s(alt (+ (sin x) (* 1/2 (* eps (cos x)))) (taylor 0 eps) (#s(alt (fma.f64 (sin.f64 (.f64 #s(literal 1 binary64) x)) (cos.f64 (.f64 #s(literal 1/2 binary64) eps)) (.f64 (cos.f64 (.f64 #s(literal 1 binary64) x)) (sin.f64 (.f64 #s(literal 1/2 binary64) eps)))) (patch (fma.f64 (sin.f64 (.f64 #s(literal 1 binary64) x)) (cos.f64 (.f64 #s(literal 1/2 binary64) eps)) (.f64 (cos.f64 (.f64 #s(literal 1 binary64) x)) (sin.f64 (.f64 #s(literal 1/2 binary64) eps)))) #<representation binary64>) () ())) ())
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#s(alt (* -2 (* (sin (* -1/2 (/ (+ (* -1 (pow eps 2)) (* 4 (pow x 2))) (+ eps (* -2 x))))) (sin (* 1/2 eps)))) (taylor -inf x) (#s(alt (.f64 (.f64 (sin.f64 (/.f64 (.f64 (fma.f64 #s(literal 4 binary64) (.f64 x x) (.f64 (neg.f64 eps) eps)) #s(literal 1/2 binary64)) (fma.f64 #s(literal 2 binary64) x (neg.f64 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(literal -2 binary64)) (patch (.f64 (.f64 (sin.f64 (/.f64 (.f64 (fma.f64 #s(literal 4 binary64) (.f64 x x) (.f64 (neg.f64 eps) eps)) #s(literal 1/2 binary64)) (fma.f64 #s(literal 2 binary64) x (neg.f64 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(literal -2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* -2 (* (sin (* -1/2 (/ (+ (* -1 (pow eps 2)) (* 4 (pow x 2))) (+ eps (* -2 x))))) (sin (* 1/2 eps)))) (taylor -inf x) (#s(alt (.f64 (.f64 (sin.f64 (/.f64 (.f64 (fma.f64 #s(literal 4 binary64) (.f64 x x) (.f64 (neg.f64 eps) eps)) #s(literal 1/2 binary64)) (fma.f64 #s(literal 2 binary64) x (neg.f64 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(literal -2 binary64)) (patch (.f64 (.f64 (sin.f64 (/.f64 (.f64 (fma.f64 #s(literal 4 binary64) (.f64 x x) (.f64 (neg.f64 eps) eps)) #s(literal 1/2 binary64)) (fma.f64 #s(literal 2 binary64) x (neg.f64 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(literal -2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* (sin (* -1/2 (/ (+ (* -1 (pow eps 2)) (* 4 (pow x 2))) (+ eps (* -2 x))))) (sin (* 1/2 eps))) (taylor -inf x) (#s(alt (.f64 (sin.f64 (/.f64 (.f64 (fma.f64 #s(literal 4 binary64) (.f64 x x) (.f64 (neg.f64 eps) eps)) #s(literal 1/2 binary64)) (fma.f64 #s(literal 2 binary64) x (neg.f64 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))) (patch (.f64 (sin.f64 (/.f64 (.f64 (fma.f64 #s(literal 4 binary64) (.f64 x x) (.f64 (neg.f64 eps) eps)) #s(literal 1/2 binary64)) (fma.f64 #s(literal 2 binary64) x (neg.f64 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))) #<representation binary64>) () ())) ())
#s(alt (* (sin (* -1/2 (/ (+ (* -1 (pow eps 2)) (* 4 (pow x 2))) (+ eps (* -2 x))))) (sin (* 1/2 eps))) (taylor -inf x) (#s(alt (.f64 (sin.f64 (/.f64 (.f64 (fma.f64 #s(literal 4 binary64) (.f64 x x) (.f64 (neg.f64 eps) eps)) #s(literal 1/2 binary64)) (fma.f64 #s(literal 2 binary64) x (neg.f64 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))) (patch (.f64 (sin.f64 (/.f64 (.f64 (fma.f64 #s(literal 4 binary64) (.f64 x x) (.f64 (neg.f64 eps) eps)) #s(literal 1/2 binary64)) (fma.f64 #s(literal 2 binary64) x (neg.f64 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))) #<representation binary64>) () ())) ())
#s(alt (* (sin (* -1/2 (/ (+ (* -1 (pow eps 2)) (* 4 (pow x 2))) (+ eps (* -2 x))))) (sin (* 1/2 eps))) (taylor -inf x) (#s(alt (.f64 (sin.f64 (/.f64 (.f64 (fma.f64 #s(literal 4 binary64) (.f64 x x) (.f64 (neg.f64 eps) eps)) #s(literal 1/2 binary64)) (fma.f64 #s(literal 2 binary64) x (neg.f64 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))) (patch (.f64 (sin.f64 (/.f64 (.f64 (fma.f64 #s(literal 4 binary64) (.f64 x x) (.f64 (neg.f64 eps) eps)) #s(literal 1/2 binary64)) (fma.f64 #s(literal 2 binary64) x (neg.f64 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))) #<representation binary64>) () ())) ())
#s(alt (* (sin (* -1/2 (/ (+ (* -1 (pow eps 2)) (* 4 (pow x 2))) (+ eps (* -2 x))))) (sin (* 1/2 eps))) (taylor -inf x) (#s(alt (.f64 (sin.f64 (/.f64 (.f64 (fma.f64 #s(literal 4 binary64) (.f64 x x) (.f64 (neg.f64 eps) eps)) #s(literal 1/2 binary64)) (fma.f64 #s(literal 2 binary64) x (neg.f64 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))) (patch (.f64 (sin.f64 (/.f64 (.f64 (fma.f64 #s(literal 4 binary64) (.f64 x x) (.f64 (neg.f64 eps) eps)) #s(literal 1/2 binary64)) (fma.f64 #s(literal 2 binary64) x (neg.f64 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))) #<representation binary64>) () ())) ())
#s(alt (* 4 (pow x 2)) (taylor -inf x) (#s(alt (fma.f64 #s(literal 4 binary64) (.f64 x x) (.f64 (neg.f64 eps) eps)) (patch (fma.f64 #s(literal 4 binary64) (.f64 x x) (.f64 (neg.f64 eps) eps)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (+ 4 (* -1 (/ (pow eps 2) (pow x 2))))) (taylor -inf x) (#s(alt (fma.f64 #s(literal 4 binary64) (.f64 x x) (.f64 (neg.f64 eps) eps)) (patch (fma.f64 #s(literal 4 binary64) (.f64 x x) (.f64 (neg.f64 eps) eps)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (+ 4 (* -1 (/ (pow eps 2) (pow x 2))))) (taylor -inf x) (#s(alt (fma.f64 #s(literal 4 binary64) (.f64 x x) (.f64 (neg.f64 eps) eps)) (patch (fma.f64 #s(literal 4 binary64) (.f64 x x) (.f64 (neg.f64 eps) eps)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (+ 4 (* -1 (/ (pow eps 2) (pow x 2))))) (taylor -inf x) (#s(alt (fma.f64 #s(literal 4 binary64) (.f64 x x) (.f64 (neg.f64 eps) eps)) (patch (fma.f64 #s(literal 4 binary64) (.f64 x x) (.f64 (neg.f64 eps) eps)) #<representation binary64>) () ())) ())

Calls

6 calls:

Time	Variable		Point	Expression
9.0ms	eps	@	-inf	((* 1 x) (* (* (+ (* (sin (* 1 x)) (cos (* 1/2 eps))) (* (cos (* 1 x)) (sin (* 1/2 eps)))) (sin (* 1/2 (+ 0 eps)))) -2) (* (+ (* (sin (* 1 x)) (cos (* 1/2 eps))) (* (cos (* 1 x)) (sin (* 1/2 eps)))) (sin (* 1/2 (+ 0 eps)))) (+ (* (sin (* 1 x)) (cos (* 1/2 eps))) (* (cos (* 1 x)) (sin (* 1/2 eps)))) (- (cos (+ x eps)) (cos x)) (* (neg (sin x)) eps) (neg (sin x)) (neg x) (+ (* (+ (* (* 1/6 eps) eps) -1) x) (* (+ (* (* eps eps) 1/24) -1/2) eps)) (- (cos (+ x eps)) (cos x)) (* (+ (* (+ (* (cos x) (+ (* (* eps eps) 1/24) -1/2)) (* (* 1/6 (sin x)) eps)) eps) (neg (sin x))) eps) (+ (* (+ (* (cos x) (+ (* (* eps eps) 1/24) -1/2)) (* (* 1/6 (sin x)) eps)) eps) (neg (sin x))) (- (cos (+ x eps)) (cos x)) (* (+ (* (+ (* (cos x) (+ (* (* eps eps) 1/24) -1/2)) (* (* 1/6 (sin x)) eps)) eps) (neg (sin x))) eps) (+ (* (+ (* (cos x) (+ (* (* eps eps) 1/24) -1/2)) (* (* 1/6 (sin x)) eps)) eps) (neg (sin x))) (+ (* (cos x) (+ (* (* eps eps) 1/24) -1/2)) (* (* 1/6 (sin x)) eps)) (/ (* (+ (* 4 (* x x)) (* (neg eps) eps)) 1/2) (+ (* 2 x) (neg eps))) (* (+ (* 4 (* x x)) (* (neg eps) eps)) 1/2) (* (* (sin (/ (* (+ (* 4 (* x x)) (* (neg eps) eps)) 1/2) (+ (* 2 x) (neg eps)))) (sin (* 1/2 (+ 0 eps)))) -2) (* (sin (/ (* (+ (* 4 (* x x)) (* (neg eps) eps)) 1/2) (+ (* 2 x) (neg eps)))) (sin (* 1/2 (+ 0 eps)))) (sin (* 1/2 (+ 0 eps))) (* 1/6 eps) (+ (* 4 (* x x)) (* (neg eps) eps)))
7.0ms	x	@	0	((* 1 x) (* (* (+ (* (sin (* 1 x)) (cos (* 1/2 eps))) (* (cos (* 1 x)) (sin (* 1/2 eps)))) (sin (* 1/2 (+ 0 eps)))) -2) (* (+ (* (sin (* 1 x)) (cos (* 1/2 eps))) (* (cos (* 1 x)) (sin (* 1/2 eps)))) (sin (* 1/2 (+ 0 eps)))) (+ (* (sin (* 1 x)) (cos (* 1/2 eps))) (* (cos (* 1 x)) (sin (* 1/2 eps)))) (- (cos (+ x eps)) (cos x)) (* (neg (sin x)) eps) (neg (sin x)) (neg x) (+ (* (+ (* (* 1/6 eps) eps) -1) x) (* (+ (* (* eps eps) 1/24) -1/2) eps)) (- (cos (+ x eps)) (cos x)) (* (+ (* (+ (* (cos x) (+ (* (* eps eps) 1/24) -1/2)) (* (* 1/6 (sin x)) eps)) eps) (neg (sin x))) eps) (+ (* (+ (* (cos x) (+ (* (* eps eps) 1/24) -1/2)) (* (* 1/6 (sin x)) eps)) eps) (neg (sin x))) (- (cos (+ x eps)) (cos x)) (* (+ (* (+ (* (cos x) (+ (* (* eps eps) 1/24) -1/2)) (* (* 1/6 (sin x)) eps)) eps) (neg (sin x))) eps) (+ (* (+ (* (cos x) (+ (* (* eps eps) 1/24) -1/2)) (* (* 1/6 (sin x)) eps)) eps) (neg (sin x))) (+ (* (cos x) (+ (* (* eps eps) 1/24) -1/2)) (* (* 1/6 (sin x)) eps)) (/ (* (+ (* 4 (* x x)) (* (neg eps) eps)) 1/2) (+ (* 2 x) (neg eps))) (* (+ (* 4 (* x x)) (* (neg eps) eps)) 1/2) (* (* (sin (/ (* (+ (* 4 (* x x)) (* (neg eps) eps)) 1/2) (+ (* 2 x) (neg eps)))) (sin (* 1/2 (+ 0 eps)))) -2) (* (sin (/ (* (+ (* 4 (* x x)) (* (neg eps) eps)) 1/2) (+ (* 2 x) (neg eps)))) (sin (* 1/2 (+ 0 eps)))) (sin (* 1/2 (+ 0 eps))) (* 1/6 eps) (+ (* 4 (* x x)) (* (neg eps) eps)))
6.0ms	x	@	inf	((* 1 x) (* (* (+ (* (sin (* 1 x)) (cos (* 1/2 eps))) (* (cos (* 1 x)) (sin (* 1/2 eps)))) (sin (* 1/2 (+ 0 eps)))) -2) (* (+ (* (sin (* 1 x)) (cos (* 1/2 eps))) (* (cos (* 1 x)) (sin (* 1/2 eps)))) (sin (* 1/2 (+ 0 eps)))) (+ (* (sin (* 1 x)) (cos (* 1/2 eps))) (* (cos (* 1 x)) (sin (* 1/2 eps)))) (- (cos (+ x eps)) (cos x)) (* (neg (sin x)) eps) (neg (sin x)) (neg x) (+ (* (+ (* (* 1/6 eps) eps) -1) x) (* (+ (* (* eps eps) 1/24) -1/2) eps)) (- (cos (+ x eps)) (cos x)) (* (+ (* (+ (* (cos x) (+ (* (* eps eps) 1/24) -1/2)) (* (* 1/6 (sin x)) eps)) eps) (neg (sin x))) eps) (+ (* (+ (* (cos x) (+ (* (* eps eps) 1/24) -1/2)) (* (* 1/6 (sin x)) eps)) eps) (neg (sin x))) (- (cos (+ x eps)) (cos x)) (* (+ (* (+ (* (cos x) (+ (* (* eps eps) 1/24) -1/2)) (* (* 1/6 (sin x)) eps)) eps) (neg (sin x))) eps) (+ (* (+ (* (cos x) (+ (* (* eps eps) 1/24) -1/2)) (* (* 1/6 (sin x)) eps)) eps) (neg (sin x))) (+ (* (cos x) (+ (* (* eps eps) 1/24) -1/2)) (* (* 1/6 (sin x)) eps)) (/ (* (+ (* 4 (* x x)) (* (neg eps) eps)) 1/2) (+ (* 2 x) (neg eps))) (* (+ (* 4 (* x x)) (* (neg eps) eps)) 1/2) (* (* (sin (/ (* (+ (* 4 (* x x)) (* (neg eps) eps)) 1/2) (+ (* 2 x) (neg eps)))) (sin (* 1/2 (+ 0 eps)))) -2) (* (sin (/ (* (+ (* 4 (* x x)) (* (neg eps) eps)) 1/2) (+ (* 2 x) (neg eps)))) (sin (* 1/2 (+ 0 eps)))) (sin (* 1/2 (+ 0 eps))) (* 1/6 eps) (+ (* 4 (* x x)) (* (neg eps) eps)))
6.0ms	x	@	-inf	((* 1 x) (* (* (+ (* (sin (* 1 x)) (cos (* 1/2 eps))) (* (cos (* 1 x)) (sin (* 1/2 eps)))) (sin (* 1/2 (+ 0 eps)))) -2) (* (+ (* (sin (* 1 x)) (cos (* 1/2 eps))) (* (cos (* 1 x)) (sin (* 1/2 eps)))) (sin (* 1/2 (+ 0 eps)))) (+ (* (sin (* 1 x)) (cos (* 1/2 eps))) (* (cos (* 1 x)) (sin (* 1/2 eps)))) (- (cos (+ x eps)) (cos x)) (* (neg (sin x)) eps) (neg (sin x)) (neg x) (+ (* (+ (* (* 1/6 eps) eps) -1) x) (* (+ (* (* eps eps) 1/24) -1/2) eps)) (- (cos (+ x eps)) (cos x)) (* (+ (* (+ (* (cos x) (+ (* (* eps eps) 1/24) -1/2)) (* (* 1/6 (sin x)) eps)) eps) (neg (sin x))) eps) (+ (* (+ (* (cos x) (+ (* (* eps eps) 1/24) -1/2)) (* (* 1/6 (sin x)) eps)) eps) (neg (sin x))) (- (cos (+ x eps)) (cos x)) (* (+ (* (+ (* (cos x) (+ (* (* eps eps) 1/24) -1/2)) (* (* 1/6 (sin x)) eps)) eps) (neg (sin x))) eps) (+ (* (+ (* (cos x) (+ (* (* eps eps) 1/24) -1/2)) (* (* 1/6 (sin x)) eps)) eps) (neg (sin x))) (+ (* (cos x) (+ (* (* eps eps) 1/24) -1/2)) (* (* 1/6 (sin x)) eps)) (/ (* (+ (* 4 (* x x)) (* (neg eps) eps)) 1/2) (+ (* 2 x) (neg eps))) (* (+ (* 4 (* x x)) (* (neg eps) eps)) 1/2) (* (* (sin (/ (* (+ (* 4 (* x x)) (* (neg eps) eps)) 1/2) (+ (* 2 x) (neg eps)))) (sin (* 1/2 (+ 0 eps)))) -2) (* (sin (/ (* (+ (* 4 (* x x)) (* (neg eps) eps)) 1/2) (+ (* 2 x) (neg eps)))) (sin (* 1/2 (+ 0 eps)))) (sin (* 1/2 (+ 0 eps))) (* 1/6 eps) (+ (* 4 (* x x)) (* (neg eps) eps)))
5.0ms	eps	@	inf	((* 1 x) (* (* (+ (* (sin (* 1 x)) (cos (* 1/2 eps))) (* (cos (* 1 x)) (sin (* 1/2 eps)))) (sin (* 1/2 (+ 0 eps)))) -2) (* (+ (* (sin (* 1 x)) (cos (* 1/2 eps))) (* (cos (* 1 x)) (sin (* 1/2 eps)))) (sin (* 1/2 (+ 0 eps)))) (+ (* (sin (* 1 x)) (cos (* 1/2 eps))) (* (cos (* 1 x)) (sin (* 1/2 eps)))) (- (cos (+ x eps)) (cos x)) (* (neg (sin x)) eps) (neg (sin x)) (neg x) (+ (* (+ (* (* 1/6 eps) eps) -1) x) (* (+ (* (* eps eps) 1/24) -1/2) eps)) (- (cos (+ x eps)) (cos x)) (* (+ (* (+ (* (cos x) (+ (* (* eps eps) 1/24) -1/2)) (* (* 1/6 (sin x)) eps)) eps) (neg (sin x))) eps) (+ (* (+ (* (cos x) (+ (* (* eps eps) 1/24) -1/2)) (* (* 1/6 (sin x)) eps)) eps) (neg (sin x))) (- (cos (+ x eps)) (cos x)) (* (+ (* (+ (* (cos x) (+ (* (* eps eps) 1/24) -1/2)) (* (* 1/6 (sin x)) eps)) eps) (neg (sin x))) eps) (+ (* (+ (* (cos x) (+ (* (* eps eps) 1/24) -1/2)) (* (* 1/6 (sin x)) eps)) eps) (neg (sin x))) (+ (* (cos x) (+ (* (* eps eps) 1/24) -1/2)) (* (* 1/6 (sin x)) eps)) (/ (* (+ (* 4 (* x x)) (* (neg eps) eps)) 1/2) (+ (* 2 x) (neg eps))) (* (+ (* 4 (* x x)) (* (neg eps) eps)) 1/2) (* (* (sin (/ (* (+ (* 4 (* x x)) (* (neg eps) eps)) 1/2) (+ (* 2 x) (neg eps)))) (sin (* 1/2 (+ 0 eps)))) -2) (* (sin (/ (* (+ (* 4 (* x x)) (* (neg eps) eps)) 1/2) (+ (* 2 x) (neg eps)))) (sin (* 1/2 (+ 0 eps)))) (sin (* 1/2 (+ 0 eps))) (* 1/6 eps) (+ (* 4 (* x x)) (* (neg eps) eps)))

simplify178.0ms (1.1%)

Memory

21.3MiB live, 217.3MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	485	7113
1	1509	6913
2	4486	6814
0	8613	6389

Stop Event

1×	iter limit
1×	node limit

Counts

492 → 477

Calls

Call 1

Inputs
(* -1 (* eps (sin x)))
(* eps (+ (* -1 (sin x)) (* -1/2 (* eps (cos x)))))
(* eps (+ (* -1 (sin x)) (* eps (+ (* -2 (* eps (+ (* -1/16 (sin x)) (* -1/48 (sin x))))) (* -1/2 (cos x))))))
(* eps (+ (* -1 (sin x)) (* eps (+ (* -1/2 (cos x)) (* eps (+ (* -2 (+ (* -1/16 (sin x)) (* -1/48 (sin x)))) (* 1/24 (* eps (cos x)))))))))
(* 1/2 (* eps (sin x)))
(* eps (+ (* 1/4 (* eps (cos x))) (* 1/2 (sin x))))
(* eps (+ (* 1/2 (sin x)) (* eps (+ (* 1/4 (cos x)) (* eps (+ (* -1/16 (sin x)) (* -1/48 (sin x))))))))
(* eps (+ (* 1/2 (sin x)) (* eps (+ (* 1/4 (cos x)) (* eps (+ (* -1/16 (sin x)) (+ (* -1/48 (sin x)) (* -1/48 (* eps (cos x))))))))))
(sin x)
(+ (sin x) (* 1/2 (* eps (cos x))))
(+ (sin x) (* eps (+ (* -1/8 (* eps (sin x))) (* 1/2 (cos x)))))
(+ (sin x) (* eps (+ (* 1/2 (cos x)) (* eps (+ (* -1/8 (sin x)) (* -1/48 (* eps (cos x))))))))
(* -1 (* eps (sin x)))
(* eps (- (* -1/2 (* eps (cos x))) (sin x)))
(* eps (- (* eps (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x))))) (sin x)))
(* eps (- (* eps (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x)))))) (sin x)))
(* -1 (* eps (sin x)))
(* -1 (* eps (sin x)))
(* -1 (* eps (sin x)))
(* -1 (* eps (sin x)))
(* -1 x)
(+ (* -1 x) (* -1/2 eps))
(+ (* -1 x) (* eps (- (* 1/6 (* eps x)) 1/2)))
(+ (* -1 x) (* eps (- (* eps (+ (* 1/24 eps) (* 1/6 x))) 1/2)))
(* -1 (* eps (sin x)))
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(* eps (- (* eps (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x))))) (sin x)))
(* eps (- (* eps (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x)))))) (sin x)))
(* -1 (* eps (sin x)))
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(* eps (+ (* -1 (sin x)) (* eps (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x)))))))
(* eps (+ (* -1 (sin x)) (* eps (+ (* -1/2 (cos x)) (* eps (+ (* 1/24 (* eps (cos x))) (* 1/6 (sin x))))))))
(* -1 (sin x))
(- (* -1/2 (* eps (cos x))) (sin x))
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(- (* eps (+ (* -1/2 (cos x)) (* eps (+ (* 1/24 (* eps (cos x))) (* 1/6 (sin x)))))) (sin x))
(* -1 (* eps (sin x)))
(* eps (- (* -1/2 (* eps (cos x))) (sin x)))
(* eps (- (* eps (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x))))) (sin x)))
(* eps (- (* eps (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x)))))) (sin x)))
(* -1 (* eps (sin x)))
(* eps (+ (* -1 (sin x)) (* -1/2 (* eps (cos x)))))
(* eps (+ (* -1 (sin x)) (* eps (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x)))))))
(* eps (+ (* -1 (sin x)) (* eps (+ (* -1/2 (cos x)) (* eps (+ (* 1/24 (* eps (cos x))) (* 1/6 (sin x))))))))
(* -1 (sin x))
(- (* -1/2 (* eps (cos x))) (sin x))
(- (* eps (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x))))) (sin x))
(- (* eps (+ (* -1/2 (cos x)) (* eps (+ (* 1/24 (* eps (cos x))) (* 1/6 (sin x)))))) (sin x))
(* -1/2 (cos x))
(+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x))))
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(+ (* -1/2 (cos x)) (* eps (+ (* 1/24 (* eps (cos x))) (* 1/6 (sin x)))))
x
(+ x (* 1/2 eps))
(+ x (* 1/2 eps))
(+ x (* 1/2 eps))
(* 2 (pow x 2))
(+ (* -1/2 (pow eps 2)) (* 2 (pow x 2)))
(+ (* -1/2 (pow eps 2)) (* 2 (pow x 2)))
(+ (* -1/2 (pow eps 2)) (* 2 (pow x 2)))
(* -1 (* eps (sin x)))
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(* eps (+ (* -1 (sin x)) (* eps (+ (* -2 (* eps (+ (* -1/16 (sin x)) (* -1/48 (sin x))))) (* -1/2 (cos x))))))
(* eps (+ (* -1 (sin x)) (* eps (+ (* -1/2 (cos x)) (* eps (+ (* -2 (+ (* -1/16 (sin x)) (* -1/48 (sin x)))) (* 1/24 (* eps (cos x)))))))))
(* 1/2 (* eps (sin x)))
(* eps (+ (* 1/4 (* eps (cos x))) (* 1/2 (sin x))))
(* eps (+ (* 1/2 (sin x)) (* eps (+ (* 1/4 (cos x)) (* eps (+ (* -1/16 (sin x)) (* -1/48 (sin x))))))))
(* eps (+ (* 1/2 (sin x)) (* eps (+ (* 1/4 (cos x)) (* eps (+ (* -1/16 (sin x)) (+ (* -1/48 (sin x)) (* -1/48 (* eps (cos x))))))))))
(* 1/2 eps)
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(* 1/6 eps)
(* 1/6 eps)
(* 1/6 eps)
(* 1/6 eps)
(* 4 (pow x 2))
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(+ (* -1 (pow eps 2)) (* 4 (pow x 2)))
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(* -2 (* (sin (* 1/2 eps)) (+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x)))))
(* -2 (* (sin (* 1/2 eps)) (+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x)))))
(* -2 (* (sin (* 1/2 eps)) (+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x)))))
(* (sin (* 1/2 eps)) (+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x))))
(* (sin (* 1/2 eps)) (+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x))))
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(* (sin (* 1/2 eps)) (+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x))))
(+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x)))
(+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x)))
(+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x)))
(+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x)))
(- (cos (+ eps x)) (cos x))
(- (cos (+ eps x)) (cos x))
(- (cos (+ eps x)) (cos x))
(- (cos (+ eps x)) (cos x))
(* -1 (* eps (sin x)))
(* -1 (* eps (sin x)))
(* -1 (* eps (sin x)))
(* -1 (* eps (sin x)))
(* 1/24 (pow eps 3))
(* (pow eps 3) (+ 1/24 (* 1/6 (/ x eps))))
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(- (cos (+ eps x)) (cos x))
(- (cos (+ eps x)) (cos x))
(- (cos (+ eps x)) (cos x))
(- (cos (+ eps x)) (cos x))
(* 1/24 (* (pow eps 4) (cos x)))
(* (pow eps 4) (+ (* 1/24 (cos x)) (* 1/6 (/ (sin x) eps))))
(* (pow eps 4) (+ (* -1/2 (/ (cos x) (pow eps 2))) (+ (* 1/24 (cos x)) (* 1/6 (/ (sin x) eps)))))
(* (pow eps 4) (+ (* -1 (/ (sin x) (pow eps 3))) (+ (* -1/2 (/ (cos x) (pow eps 2))) (+ (* 1/24 (cos x)) (* 1/6 (/ (sin x) eps))))))
(* 1/24 (* (pow eps 3) (cos x)))
(* (pow eps 3) (+ (* 1/24 (cos x)) (* 1/6 (/ (sin x) eps))))
(* (pow eps 3) (+ (* -1/2 (/ (cos x) (pow eps 2))) (+ (* 1/24 (cos x)) (* 1/6 (/ (sin x) eps)))))
(* (pow eps 3) (+ (* -1 (/ (sin x) (pow eps 3))) (+ (* -1/2 (/ (cos x) (pow eps 2))) (+ (* 1/24 (cos x)) (* 1/6 (/ (sin x) eps))))))
(- (cos (+ eps x)) (cos x))
(- (cos (+ eps x)) (cos x))
(- (cos (+ eps x)) (cos x))
(- (cos (+ eps x)) (cos x))
(* 1/24 (* (pow eps 4) (cos x)))
(* (pow eps 4) (+ (* 1/24 (cos x)) (* 1/6 (/ (sin x) eps))))
(* (pow eps 4) (+ (* -1/2 (/ (cos x) (pow eps 2))) (+ (* 1/24 (cos x)) (* 1/6 (/ (sin x) eps)))))
(* (pow eps 4) (+ (* -1 (/ (sin x) (pow eps 3))) (+ (* -1/2 (/ (cos x) (pow eps 2))) (+ (* 1/24 (cos x)) (* 1/6 (/ (sin x) eps))))))
(* 1/24 (* (pow eps 3) (cos x)))
(* (pow eps 3) (+ (* 1/24 (cos x)) (* 1/6 (/ (sin x) eps))))
(* (pow eps 3) (+ (* -1/2 (/ (cos x) (pow eps 2))) (+ (* 1/24 (cos x)) (* 1/6 (/ (sin x) eps)))))
(* (pow eps 3) (+ (* -1 (/ (sin x) (pow eps 3))) (+ (* -1/2 (/ (cos x) (pow eps 2))) (+ (* 1/24 (cos x)) (* 1/6 (/ (sin x) eps))))))
(* 1/24 (* (pow eps 2) (cos x)))
(* (pow eps 2) (+ (* 1/24 (cos x)) (* 1/6 (/ (sin x) eps))))
(* (pow eps 2) (+ (* -1/2 (/ (cos x) (pow eps 2))) (+ (* 1/24 (cos x)) (* 1/6 (/ (sin x) eps)))))
(* (pow eps 2) (+ (* -1/2 (/ (cos x) (pow eps 2))) (+ (* 1/24 (cos x)) (* 1/6 (/ (sin x) eps)))))
(* 1/2 eps)
(* eps (+ 1/2 (/ x eps)))
(* eps (+ 1/2 (/ x eps)))
(* eps (+ 1/2 (/ x eps)))
(* -1/2 (pow eps 2))
(* (pow eps 2) (- (* 2 (/ (pow x 2) (pow eps 2))) 1/2))
(* (pow eps 2) (- (* 2 (/ (pow x 2) (pow eps 2))) 1/2))
(* (pow eps 2) (- (* 2 (/ (pow x 2) (pow eps 2))) 1/2))
(* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (/ (- (* 4 (pow x 2)) (pow eps 2)) (- (* 2 x) eps))))))
(* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (/ (- (* 4 (pow x 2)) (pow eps 2)) (- (* 2 x) eps))))))
(* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (/ (- (* 4 (pow x 2)) (pow eps 2)) (- (* 2 x) eps))))))
(* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (/ (- (* 4 (pow x 2)) (pow eps 2)) (- (* 2 x) eps))))))
(* (sin (* 1/2 eps)) (sin (* 1/2 (/ (- (* 4 (pow x 2)) (pow eps 2)) (- (* 2 x) eps)))))
(* (sin (* 1/2 eps)) (sin (* 1/2 (/ (- (* 4 (pow x 2)) (pow eps 2)) (- (* 2 x) eps)))))
(* (sin (* 1/2 eps)) (sin (* 1/2 (/ (- (* 4 (pow x 2)) (pow eps 2)) (- (* 2 x) eps)))))
(* (sin (* 1/2 eps)) (sin (* 1/2 (/ (- (* 4 (pow x 2)) (pow eps 2)) (- (* 2 x) eps)))))
(sin (* 1/2 eps))
(sin (* 1/2 eps))
(sin (* 1/2 eps))
(sin (* 1/2 eps))
(* 1/6 eps)
(* 1/6 eps)
(* 1/6 eps)
(* 1/6 eps)
(* -1 (pow eps 2))
(* (pow eps 2) (- (* 4 (/ (pow x 2) (pow eps 2))) 1))
(* (pow eps 2) (- (* 4 (/ (pow x 2) (pow eps 2))) 1))
(* (pow eps 2) (- (* 4 (/ (pow x 2) (pow eps 2))) 1))
(* -2 (* (sin (* 1/2 eps)) (+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x)))))
(* -2 (* (sin (* 1/2 eps)) (+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x)))))
(* -2 (* (sin (* 1/2 eps)) (+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x)))))
(* -2 (* (sin (* 1/2 eps)) (+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x)))))
(* (sin (* 1/2 eps)) (+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x))))
(* (sin (* 1/2 eps)) (+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x))))
(* (sin (* 1/2 eps)) (+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x))))
(* (sin (* 1/2 eps)) (+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x))))
(+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x)))
(+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x)))
(+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x)))
(+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x)))
(- (cos (- x (* -1 eps))) (cos x))
(- (cos (- x (* -1 eps))) (cos x))
(- (cos (- x (* -1 eps))) (cos x))
(- (cos (- x (* -1 eps))) (cos x))
(* -1 (* eps (sin x)))
(* -1 (* eps (sin x)))
(* -1 (* eps (sin x)))
(* -1 (* eps (sin x)))
(* 1/24 (pow eps 3))
(* -1 (* (pow eps 3) (- (* -1/6 (/ x eps)) 1/24)))
(* -1 (* (pow eps 3) (- (* -1 (/ (- (* 1/6 x) (* 1/2 (/ 1 eps))) eps)) 1/24)))
(* -1 (* (pow eps 3) (- (* -1 (/ (+ (* -1 (/ (+ 1/2 (/ x eps)) eps)) (* 1/6 x)) eps)) 1/24)))
(- (cos (- x (* -1 eps))) (cos x))
(- (cos (- x (* -1 eps))) (cos x))
(- (cos (- x (* -1 eps))) (cos x))
(- (cos (- x (* -1 eps))) (cos x))
(* 1/24 (* (pow eps 4) (cos x)))
(* (pow eps 4) (+ (* 1/24 (cos x)) (* 1/6 (/ (sin x) eps))))
(* (pow eps 4) (+ (* -1 (/ (+ (* -1/6 (sin x)) (* 1/2 (/ (cos x) eps))) eps)) (* 1/24 (cos x))))
(* (pow eps 4) (+ (* -1 (/ (+ (* -1 (/ (+ (* -1 (/ (sin x) eps)) (* -1/2 (cos x))) eps)) (* -1/6 (sin x))) eps)) (* 1/24 (cos x))))
(* 1/24 (* (pow eps 3) (cos x)))
(* -1 (* (pow eps 3) (+ (* -1/6 (/ (sin x) eps)) (* -1/24 (cos x)))))
(* -1 (* (pow eps 3) (+ (* -1 (/ (+ (* -1/2 (/ (cos x) eps)) (* 1/6 (sin x))) eps)) (* -1/24 (cos x)))))
(* -1 (* (pow eps 3) (+ (* -1 (/ (+ (* -1 (/ (+ (* 1/2 (cos x)) (/ (sin x) eps)) eps)) (* 1/6 (sin x))) eps)) (* -1/24 (cos x)))))
(- (cos (- x (* -1 eps))) (cos x))
(- (cos (- x (* -1 eps))) (cos x))
(- (cos (- x (* -1 eps))) (cos x))
(- (cos (- x (* -1 eps))) (cos x))
(* 1/24 (* (pow eps 4) (cos x)))
(* (pow eps 4) (+ (* 1/24 (cos x)) (* 1/6 (/ (sin x) eps))))
(* (pow eps 4) (+ (* -1 (/ (+ (* -1/6 (sin x)) (* 1/2 (/ (cos x) eps))) eps)) (* 1/24 (cos x))))
(* (pow eps 4) (+ (* -1 (/ (+ (* -1 (/ (+ (* -1 (/ (sin x) eps)) (* -1/2 (cos x))) eps)) (* -1/6 (sin x))) eps)) (* 1/24 (cos x))))
(* 1/24 (* (pow eps 3) (cos x)))
(* -1 (* (pow eps 3) (+ (* -1/6 (/ (sin x) eps)) (* -1/24 (cos x)))))
(* -1 (* (pow eps 3) (+ (* -1 (/ (+ (* -1/2 (/ (cos x) eps)) (* 1/6 (sin x))) eps)) (* -1/24 (cos x)))))
(* -1 (* (pow eps 3) (+ (* -1 (/ (+ (* -1 (/ (+ (* 1/2 (cos x)) (/ (sin x) eps)) eps)) (* 1/6 (sin x))) eps)) (* -1/24 (cos x)))))
(* 1/24 (* (pow eps 2) (cos x)))
(* (pow eps 2) (+ (* 1/24 (cos x)) (* 1/6 (/ (sin x) eps))))
(* (pow eps 2) (+ (* -1 (/ (+ (* -1/6 (sin x)) (* 1/2 (/ (cos x) eps))) eps)) (* 1/24 (cos x))))
(* (pow eps 2) (+ (* -1 (/ (+ (* -1/6 (sin x)) (* 1/2 (/ (cos x) eps))) eps)) (* 1/24 (cos x))))
(* 1/2 eps)
(* -1 (* eps (- (* -1 (/ x eps)) 1/2)))
(* -1 (* eps (- (* -1 (/ x eps)) 1/2)))
(* -1 (* eps (- (* -1 (/ x eps)) 1/2)))
(* -1/2 (pow eps 2))
(* (pow eps 2) (- (* 2 (/ (pow x 2) (pow eps 2))) 1/2))
(* (pow eps 2) (- (* 2 (/ (pow x 2) (pow eps 2))) 1/2))
(* (pow eps 2) (- (* 2 (/ (pow x 2) (pow eps 2))) 1/2))
(* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (/ (- (* 4 (pow x 2)) (pow eps 2)) (+ (* -1 eps) (* 2 x)))))))
(* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (/ (- (* 4 (pow x 2)) (pow eps 2)) (+ (* -1 eps) (* 2 x)))))))
(* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (/ (- (* 4 (pow x 2)) (pow eps 2)) (+ (* -1 eps) (* 2 x)))))))
(* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (/ (- (* 4 (pow x 2)) (pow eps 2)) (+ (* -1 eps) (* 2 x)))))))
(* (sin (* 1/2 eps)) (sin (* 1/2 (/ (- (* 4 (pow x 2)) (pow eps 2)) (+ (* -1 eps) (* 2 x))))))
(* (sin (* 1/2 eps)) (sin (* 1/2 (/ (- (* 4 (pow x 2)) (pow eps 2)) (+ (* -1 eps) (* 2 x))))))
(* (sin (* 1/2 eps)) (sin (* 1/2 (/ (- (* 4 (pow x 2)) (pow eps 2)) (+ (* -1 eps) (* 2 x))))))
(* (sin (* 1/2 eps)) (sin (* 1/2 (/ (- (* 4 (pow x 2)) (pow eps 2)) (+ (* -1 eps) (* 2 x))))))
(sin (* 1/2 eps))
(sin (* 1/2 eps))
(sin (* 1/2 eps))
(sin (* 1/2 eps))
(* 1/6 eps)
(* 1/6 eps)
(* 1/6 eps)
(* 1/6 eps)
(* -1 (pow eps 2))
(* (pow eps 2) (- (* 4 (/ (pow x 2) (pow eps 2))) 1))
(* (pow eps 2) (- (* 4 (/ (pow x 2) (pow eps 2))) 1))
(* (pow eps 2) (- (* 4 (/ (pow x 2) (pow eps 2))) 1))
x
x
x
x
(* -2 (pow (sin (* 1/2 eps)) 2))
(+ (* -2 (* x (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))) (* -2 (pow (sin (* 1/2 eps)) 2)))
(+ (* -2 (pow (sin (* 1/2 eps)) 2)) (* x (+ (* -2 (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) (* x (pow (sin (* 1/2 eps)) 2)))))
(+ (* -2 (pow (sin (* 1/2 eps)) 2)) (* x (+ (* -2 (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) (* x (+ (* 1/3 (* x (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))) (pow (sin (* 1/2 eps)) 2))))))
(pow (sin (* 1/2 eps)) 2)
(+ (* x (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) (pow (sin (* 1/2 eps)) 2))
(+ (* x (+ (* -1/2 (* x (pow (sin (* 1/2 eps)) 2))) (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))) (pow (sin (* 1/2 eps)) 2))
(+ (* x (+ (* x (+ (* -1/2 (pow (sin (* 1/2 eps)) 2)) (* -1/6 (* x (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))))) (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))) (pow (sin (* 1/2 eps)) 2))
(sin (* 1/2 eps))
(+ (sin (* 1/2 eps)) (* x (cos (* 1/2 eps))))
(+ (sin (* 1/2 eps)) (* x (+ (cos (* 1/2 eps)) (* -1/2 (* x (sin (* 1/2 eps)))))))
(+ (sin (* 1/2 eps)) (* x (+ (cos (* 1/2 eps)) (* x (+ (* -1/2 (sin (* 1/2 eps))) (* -1/6 (* x (cos (* 1/2 eps)))))))))
(- (cos eps) 1)
(- (+ (cos eps) (* -1 (* x (sin eps)))) 1)
(- (+ (cos eps) (* x (- (* x (+ 1/2 (* -1/2 (cos eps)))) (sin eps)))) 1)
(- (+ (cos eps) (* x (- (* x (+ 1/2 (+ (* -1/2 (cos eps)) (* 1/6 (* x (sin eps)))))) (sin eps)))) 1)
(* -1 (* eps x))
(* x (+ (* -1 eps) (* 1/6 (* eps (pow x 2)))))
(* x (+ (* -1 eps) (* (pow x 2) (+ (* -1/120 (* eps (pow x 2))) (* 1/6 eps)))))
(* x (+ (* -1 eps) (* (pow x 2) (+ (* 1/6 eps) (* (pow x 2) (+ (* -1/120 eps) (* 1/5040 (* eps (pow x 2)))))))))
(* -1 x)
(* x (- (* 1/6 (pow x 2)) 1))
(* x (- (* (pow x 2) (+ 1/6 (* -1/120 (pow x 2)))) 1))
(* x (- (* (pow x 2) (+ 1/6 (* (pow x 2) (- (* 1/5040 (pow x 2)) 1/120)))) 1))
(* -1 x)
(* -1 x)
(* -1 x)
(* -1 x)
(* eps (- (* 1/24 (pow eps 2)) 1/2))
(+ (* eps (- (* 1/24 (pow eps 2)) 1/2)) (* x (- (* 1/6 (pow eps 2)) 1)))
(+ (* eps (- (* 1/24 (pow eps 2)) 1/2)) (* x (- (* 1/6 (pow eps 2)) 1)))
(+ (* eps (- (* 1/24 (pow eps 2)) 1/2)) (* x (- (* 1/6 (pow eps 2)) 1)))
(- (cos eps) 1)
(- (+ (cos eps) (* -1 (* x (sin eps)))) 1)
(- (+ (cos eps) (* x (- (* x (+ 1/2 (* -1/2 (cos eps)))) (sin eps)))) 1)
(- (+ (cos eps) (* x (- (* x (+ 1/2 (+ (* -1/2 (cos eps)) (* 1/6 (* x (sin eps)))))) (sin eps)))) 1)
(* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2))
(+ (* eps (* x (- (* 1/6 (pow eps 2)) 1))) (* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2)))
(+ (* x (+ (* -1/2 (* (pow eps 2) (* x (- (* 1/24 (pow eps 2)) 1/2)))) (* eps (- (* 1/6 (pow eps 2)) 1)))) (* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2)))
(+ (* x (+ (* eps (- (* 1/6 (pow eps 2)) 1)) (* x (+ (* -1/2 (* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2))) (* eps (* x (+ 1/6 (* -1/36 (pow eps 2))))))))) (* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2)))
(* eps (- (* 1/24 (pow eps 2)) 1/2))
(+ (* eps (- (* 1/24 (pow eps 2)) 1/2)) (* x (- (* 1/6 (pow eps 2)) 1)))
(+ (* eps (- (* 1/24 (pow eps 2)) 1/2)) (* x (- (+ (* -1/2 (* eps (* x (- (* 1/24 (pow eps 2)) 1/2)))) (* 1/6 (pow eps 2))) 1)))
(+ (* eps (- (* 1/24 (pow eps 2)) 1/2)) (* x (- (+ (* 1/6 (pow eps 2)) (* x (+ (* -1/2 (* eps (- (* 1/24 (pow eps 2)) 1/2))) (* x (+ 1/6 (* -1/36 (pow eps 2))))))) 1)))
(- (cos eps) 1)
(- (+ (cos eps) (* -1 (* x (sin eps)))) 1)
(- (+ (cos eps) (* x (- (* x (+ 1/2 (* -1/2 (cos eps)))) (sin eps)))) 1)
(- (+ (cos eps) (* x (- (* x (+ 1/2 (+ (* -1/2 (cos eps)) (* 1/6 (* x (sin eps)))))) (sin eps)))) 1)
(* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2))
(+ (* eps (* x (- (* 1/6 (pow eps 2)) 1))) (* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2)))
(+ (* x (+ (* -1/2 (* (pow eps 2) (* x (- (* 1/24 (pow eps 2)) 1/2)))) (* eps (- (* 1/6 (pow eps 2)) 1)))) (* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2)))
(+ (* x (+ (* eps (- (* 1/6 (pow eps 2)) 1)) (* x (+ (* -1/2 (* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2))) (* eps (* x (+ 1/6 (* -1/36 (pow eps 2))))))))) (* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2)))
(* eps (- (* 1/24 (pow eps 2)) 1/2))
(+ (* eps (- (* 1/24 (pow eps 2)) 1/2)) (* x (- (* 1/6 (pow eps 2)) 1)))
(+ (* eps (- (* 1/24 (pow eps 2)) 1/2)) (* x (- (+ (* -1/2 (* eps (* x (- (* 1/24 (pow eps 2)) 1/2)))) (* 1/6 (pow eps 2))) 1)))
(+ (* eps (- (* 1/24 (pow eps 2)) 1/2)) (* x (- (+ (* 1/6 (pow eps 2)) (* x (+ (* -1/2 (* eps (- (* 1/24 (pow eps 2)) 1/2))) (* x (+ 1/6 (* -1/36 (pow eps 2))))))) 1)))
(- (* 1/24 (pow eps 2)) 1/2)
(- (+ (* 1/24 (pow eps 2)) (* 1/6 (* eps x))) 1/2)
(- (+ (* 1/24 (pow eps 2)) (* x (+ (* -1/2 (* x (- (* 1/24 (pow eps 2)) 1/2))) (* 1/6 eps)))) 1/2)
(- (+ (* 1/24 (pow eps 2)) (* x (+ (* 1/6 eps) (* x (+ (* -1/2 (- (* 1/24 (pow eps 2)) 1/2)) (* -1/36 (* eps x))))))) 1/2)
(* 1/2 eps)
(+ x (* 1/2 eps))
(+ x (* 1/2 eps))
(+ x (* 1/2 eps))
(* -1/2 (pow eps 2))
(+ (* -1/2 (pow eps 2)) (* 2 (pow x 2)))
(+ (* -1/2 (pow eps 2)) (* 2 (pow x 2)))
(+ (* -1/2 (pow eps 2)) (* 2 (pow x 2)))
(* -2 (pow (sin (* 1/2 eps)) 2))
(+ (* -2 (* x (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))) (* -2 (pow (sin (* 1/2 eps)) 2)))
(+ (* -2 (pow (sin (* 1/2 eps)) 2)) (* x (+ (* -2 (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) (* x (pow (sin (* 1/2 eps)) 2)))))
(+ (* -2 (pow (sin (* 1/2 eps)) 2)) (* x (+ (* -2 (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) (* x (+ (* 1/3 (* x (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))) (pow (sin (* 1/2 eps)) 2))))))
(pow (sin (* 1/2 eps)) 2)
(+ (* x (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) (pow (sin (* 1/2 eps)) 2))
(+ (* x (+ (* -1/2 (* x (pow (sin (* 1/2 eps)) 2))) (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))) (pow (sin (* 1/2 eps)) 2))
(+ (* x (+ (* x (+ (* -1/2 (pow (sin (* 1/2 eps)) 2)) (* -1/6 (* x (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))))) (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))) (pow (sin (* 1/2 eps)) 2))
(* -1 (pow eps 2))
(+ (* -1 (pow eps 2)) (* 4 (pow x 2)))
(+ (* -1 (pow eps 2)) (* 4 (pow x 2)))
(+ (* -1 (pow eps 2)) (* 4 (pow x 2)))
x
x
x
x
(* -2 (* (sin (* 1/2 eps)) (+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x)))))
(* -2 (* (sin (* 1/2 eps)) (+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x)))))
(* -2 (* (sin (* 1/2 eps)) (+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x)))))
(* -2 (* (sin (* 1/2 eps)) (+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x)))))
(* (sin (* 1/2 eps)) (+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x))))
(* (sin (* 1/2 eps)) (+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x))))
(* (sin (* 1/2 eps)) (+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x))))
(* (sin (* 1/2 eps)) (+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x))))
(+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x)))
(+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x)))
(+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x)))
(+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x)))
(- (cos (+ eps x)) (cos x))
(- (cos (+ eps x)) (cos x))
(- (cos (+ eps x)) (cos x))
(- (cos (+ eps x)) (cos x))
(* -1 (* eps (sin x)))
(* -1 (* eps (sin x)))
(* -1 (* eps (sin x)))
(* -1 (* eps (sin x)))
(* -1 (sin x))
(* -1 (sin x))
(* -1 (sin x))
(* -1 (sin x))
(* -1 x)
(* -1 x)
(* -1 x)
(* -1 x)
(* x (- (* 1/6 (pow eps 2)) 1))
(* x (- (+ (* 1/6 (pow eps 2)) (/ (* eps (- (* 1/24 (pow eps 2)) 1/2)) x)) 1))
(* x (- (+ (* 1/6 (pow eps 2)) (/ (* eps (- (* 1/24 (pow eps 2)) 1/2)) x)) 1))
(* x (- (+ (* 1/6 (pow eps 2)) (/ (* eps (- (* 1/24 (pow eps 2)) 1/2)) x)) 1))
(- (cos (+ eps x)) (cos x))
(- (cos (+ eps x)) (cos x))
(- (cos (+ eps x)) (cos x))
(- (cos (+ eps x)) (cos x))
(* eps (- (* eps (+ (* 1/6 (* eps (sin x))) (* (cos x) (- (* 1/24 (pow eps 2)) 1/2)))) (sin x)))
(* eps (- (* eps (+ (* 1/6 (* eps (sin x))) (* (cos x) (- (* 1/24 (pow eps 2)) 1/2)))) (sin x)))
(* eps (- (* eps (+ (* 1/6 (* eps (sin x))) (* (cos x) (- (* 1/24 (pow eps 2)) 1/2)))) (sin x)))
(* eps (- (* eps (+ (* 1/6 (* eps (sin x))) (* (cos x) (- (* 1/24 (pow eps 2)) 1/2)))) (sin x)))
(- (* eps (+ (* 1/6 (* eps (sin x))) (* (cos x) (- (* 1/24 (pow eps 2)) 1/2)))) (sin x))
(- (* eps (+ (* 1/6 (* eps (sin x))) (* (cos x) (- (* 1/24 (pow eps 2)) 1/2)))) (sin x))
(- (* eps (+ (* 1/6 (* eps (sin x))) (* (cos x) (- (* 1/24 (pow eps 2)) 1/2)))) (sin x))
(- (* eps (+ (* 1/6 (* eps (sin x))) (* (cos x) (- (* 1/24 (pow eps 2)) 1/2)))) (sin x))
(- (cos (+ eps x)) (cos x))
(- (cos (+ eps x)) (cos x))
(- (cos (+ eps x)) (cos x))
(- (cos (+ eps x)) (cos x))
(* eps (- (* eps (+ (* 1/6 (* eps (sin x))) (* (cos x) (- (* 1/24 (pow eps 2)) 1/2)))) (sin x)))
(* eps (- (* eps (+ (* 1/6 (* eps (sin x))) (* (cos x) (- (* 1/24 (pow eps 2)) 1/2)))) (sin x)))
(* eps (- (* eps (+ (* 1/6 (* eps (sin x))) (* (cos x) (- (* 1/24 (pow eps 2)) 1/2)))) (sin x)))
(* eps (- (* eps (+ (* 1/6 (* eps (sin x))) (* (cos x) (- (* 1/24 (pow eps 2)) 1/2)))) (sin x)))
(- (* eps (+ (* 1/6 (* eps (sin x))) (* (cos x) (- (* 1/24 (pow eps 2)) 1/2)))) (sin x))
(- (* eps (+ (* 1/6 (* eps (sin x))) (* (cos x) (- (* 1/24 (pow eps 2)) 1/2)))) (sin x))
(- (* eps (+ (* 1/6 (* eps (sin x))) (* (cos x) (- (* 1/24 (pow eps 2)) 1/2)))) (sin x))
(- (* eps (+ (* 1/6 (* eps (sin x))) (* (cos x) (- (* 1/24 (pow eps 2)) 1/2)))) (sin x))
(+ (* 1/6 (* eps (sin x))) (* (cos x) (- (* 1/24 (pow eps 2)) 1/2)))
(+ (* 1/6 (* eps (sin x))) (* (cos x) (- (* 1/24 (pow eps 2)) 1/2)))
(+ (* 1/6 (* eps (sin x))) (* (cos x) (- (* 1/24 (pow eps 2)) 1/2)))
(+ (* 1/6 (* eps (sin x))) (* (cos x) (- (* 1/24 (pow eps 2)) 1/2)))
x
(* x (+ 1 (* 1/2 (/ eps x))))
(* x (+ 1 (* 1/2 (/ eps x))))
(* x (+ 1 (* 1/2 (/ eps x))))
(* 2 (pow x 2))
(* (pow x 2) (+ 2 (* -1/2 (/ (pow eps 2) (pow x 2)))))
(* (pow x 2) (+ 2 (* -1/2 (/ (pow eps 2) (pow x 2)))))
(* (pow x 2) (+ 2 (* -1/2 (/ (pow eps 2) (pow x 2)))))
(* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (/ (+ (* -1 (pow eps 2)) (* 4 (pow x 2))) (- (* 2 x) eps))))))
(* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (/ (+ (* -1 (pow eps 2)) (* 4 (pow x 2))) (- (* 2 x) eps))))))
(* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (/ (+ (* -1 (pow eps 2)) (* 4 (pow x 2))) (- (* 2 x) eps))))))
(* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (/ (+ (* -1 (pow eps 2)) (* 4 (pow x 2))) (- (* 2 x) eps))))))
(* (sin (* 1/2 eps)) (sin (* 1/2 (/ (+ (* -1 (pow eps 2)) (* 4 (pow x 2))) (- (* 2 x) eps)))))
(* (sin (* 1/2 eps)) (sin (* 1/2 (/ (+ (* -1 (pow eps 2)) (* 4 (pow x 2))) (- (* 2 x) eps)))))
(* (sin (* 1/2 eps)) (sin (* 1/2 (/ (+ (* -1 (pow eps 2)) (* 4 (pow x 2))) (- (* 2 x) eps)))))
(* (sin (* 1/2 eps)) (sin (* 1/2 (/ (+ (* -1 (pow eps 2)) (* 4 (pow x 2))) (- (* 2 x) eps)))))
(* 4 (pow x 2))
(* (pow x 2) (+ 4 (* -1 (/ (pow eps 2) (pow x 2)))))
(* (pow x 2) (+ 4 (* -1 (/ (pow eps 2) (pow x 2)))))
(* (pow x 2) (+ 4 (* -1 (/ (pow eps 2) (pow x 2)))))
x
x
x
x
(* -2 (* (sin (* 1/2 eps)) (+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x)))))
(* -2 (* (sin (* 1/2 eps)) (+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x)))))
(* -2 (* (sin (* 1/2 eps)) (+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x)))))
(* -2 (* (sin (* 1/2 eps)) (+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x)))))
(* (sin (* 1/2 eps)) (+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x))))
(* (sin (* 1/2 eps)) (+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x))))
(* (sin (* 1/2 eps)) (+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x))))
(* (sin (* 1/2 eps)) (+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x))))
(+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x)))
(+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x)))
(+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x)))
(+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x)))
(- (cos (- eps (* -1 x))) (cos x))
(- (cos (- eps (* -1 x))) (cos x))
(- (cos (- eps (* -1 x))) (cos x))
(- (cos (- eps (* -1 x))) (cos x))
(* -1 (* eps (sin x)))
(* -1 (* eps (sin x)))
(* -1 (* eps (sin x)))
(* -1 (* eps (sin x)))
(* -1 (sin x))
(* -1 (sin x))
(* -1 (sin x))
(* -1 (sin x))
(* -1 x)
(* -1 x)
(* -1 x)
(* -1 x)
(* x (- (* 1/6 (pow eps 2)) 1))
(* -1 (* x (+ (* -1 (- (* 1/6 (pow eps 2)) 1)) (* -1 (/ (* eps (- (* 1/24 (pow eps 2)) 1/2)) x)))))
(* -1 (* x (+ (* -1 (- (* 1/6 (pow eps 2)) 1)) (* -1 (/ (* eps (- (* 1/24 (pow eps 2)) 1/2)) x)))))
(* -1 (* x (+ (* -1 (- (* 1/6 (pow eps 2)) 1)) (* -1 (/ (* eps (- (* 1/24 (pow eps 2)) 1/2)) x)))))
(- (cos (- eps (* -1 x))) (cos x))
(- (cos (- eps (* -1 x))) (cos x))
(- (cos (- eps (* -1 x))) (cos x))
(- (cos (- eps (* -1 x))) (cos x))
(* eps (- (* eps (+ (* 1/6 (* eps (sin x))) (* (cos x) (- (* 1/24 (pow eps 2)) 1/2)))) (sin x)))
(* eps (- (* eps (+ (* 1/6 (* eps (sin x))) (* (cos x) (- (* 1/24 (pow eps 2)) 1/2)))) (sin x)))
(* eps (- (* eps (+ (* 1/6 (* eps (sin x))) (* (cos x) (- (* 1/24 (pow eps 2)) 1/2)))) (sin x)))
(* eps (- (* eps (+ (* 1/6 (* eps (sin x))) (* (cos x) (- (* 1/24 (pow eps 2)) 1/2)))) (sin x)))
(- (* eps (+ (* 1/6 (* eps (sin x))) (* (cos x) (- (* 1/24 (pow eps 2)) 1/2)))) (sin x))
(- (* eps (+ (* 1/6 (* eps (sin x))) (* (cos x) (- (* 1/24 (pow eps 2)) 1/2)))) (sin x))
(- (* eps (+ (* 1/6 (* eps (sin x))) (* (cos x) (- (* 1/24 (pow eps 2)) 1/2)))) (sin x))
(- (* eps (+ (* 1/6 (* eps (sin x))) (* (cos x) (- (* 1/24 (pow eps 2)) 1/2)))) (sin x))
(- (cos (- eps (* -1 x))) (cos x))
(- (cos (- eps (* -1 x))) (cos x))
(- (cos (- eps (* -1 x))) (cos x))
(- (cos (- eps (* -1 x))) (cos x))
(* eps (- (* eps (+ (* 1/6 (* eps (sin x))) (* (cos x) (- (* 1/24 (pow eps 2)) 1/2)))) (sin x)))
(* eps (- (* eps (+ (* 1/6 (* eps (sin x))) (* (cos x) (- (* 1/24 (pow eps 2)) 1/2)))) (sin x)))
(* eps (- (* eps (+ (* 1/6 (* eps (sin x))) (* (cos x) (- (* 1/24 (pow eps 2)) 1/2)))) (sin x)))
(* eps (- (* eps (+ (* 1/6 (* eps (sin x))) (* (cos x) (- (* 1/24 (pow eps 2)) 1/2)))) (sin x)))
(- (* eps (+ (* 1/6 (* eps (sin x))) (* (cos x) (- (* 1/24 (pow eps 2)) 1/2)))) (sin x))
(- (* eps (+ (* 1/6 (* eps (sin x))) (* (cos x) (- (* 1/24 (pow eps 2)) 1/2)))) (sin x))
(- (* eps (+ (* 1/6 (* eps (sin x))) (* (cos x) (- (* 1/24 (pow eps 2)) 1/2)))) (sin x))
(- (* eps (+ (* 1/6 (* eps (sin x))) (* (cos x) (- (* 1/24 (pow eps 2)) 1/2)))) (sin x))
(+ (* 1/6 (* eps (sin x))) (* (cos x) (- (* 1/24 (pow eps 2)) 1/2)))
(+ (* 1/6 (* eps (sin x))) (* (cos x) (- (* 1/24 (pow eps 2)) 1/2)))
(+ (* 1/6 (* eps (sin x))) (* (cos x) (- (* 1/24 (pow eps 2)) 1/2)))
(+ (* 1/6 (* eps (sin x))) (* (cos x) (- (* 1/24 (pow eps 2)) 1/2)))
x
(* -1 (* x (- (* -1/2 (/ eps x)) 1)))
(* -1 (* x (- (* -1/2 (/ eps x)) 1)))
(* -1 (* x (- (* -1/2 (/ eps x)) 1)))
(* 2 (pow x 2))
(* (pow x 2) (+ 2 (* -1/2 (/ (pow eps 2) (pow x 2)))))
(* (pow x 2) (+ 2 (* -1/2 (/ (pow eps 2) (pow x 2)))))
(* (pow x 2) (+ 2 (* -1/2 (/ (pow eps 2) (pow x 2)))))
(* -2 (* (sin (* -1/2 (/ (+ (* -1 (pow eps 2)) (* 4 (pow x 2))) (+ eps (* -2 x))))) (sin (* 1/2 eps))))
(* -2 (* (sin (* -1/2 (/ (+ (* -1 (pow eps 2)) (* 4 (pow x 2))) (+ eps (* -2 x))))) (sin (* 1/2 eps))))
(* -2 (* (sin (* -1/2 (/ (+ (* -1 (pow eps 2)) (* 4 (pow x 2))) (+ eps (* -2 x))))) (sin (* 1/2 eps))))
(* -2 (* (sin (* -1/2 (/ (+ (* -1 (pow eps 2)) (* 4 (pow x 2))) (+ eps (* -2 x))))) (sin (* 1/2 eps))))
(* (sin (* -1/2 (/ (+ (* -1 (pow eps 2)) (* 4 (pow x 2))) (+ eps (* -2 x))))) (sin (* 1/2 eps)))
(* (sin (* -1/2 (/ (+ (* -1 (pow eps 2)) (* 4 (pow x 2))) (+ eps (* -2 x))))) (sin (* 1/2 eps)))
(* (sin (* -1/2 (/ (+ (* -1 (pow eps 2)) (* 4 (pow x 2))) (+ eps (* -2 x))))) (sin (* 1/2 eps)))
(* (sin (* -1/2 (/ (+ (* -1 (pow eps 2)) (* 4 (pow x 2))) (+ eps (* -2 x))))) (sin (* 1/2 eps)))
(* 4 (pow x 2))
(* (pow x 2) (+ 4 (* -1 (/ (pow eps 2) (pow x 2)))))
(* (pow x 2) (+ 4 (* -1 (/ (pow eps 2) (pow x 2)))))
(* (pow x 2) (+ 4 (* -1 (/ (pow eps 2) (pow x 2)))))

Outputs
(* -1 (* eps (sin x)))
(*.f64 (neg.f64 eps) (sin.f64 x))
(* eps (+ (* -1 (sin x)) (* -1/2 (* eps (cos x)))))
(.f64 (fma.f64 (.f64 #s(literal -1/2 binary64) eps) (cos.f64 x) (neg.f64 (sin.f64 x))) eps)
(* eps (+ (* -1 (sin x)) (* eps (+ (* -2 (* eps (+ (* -1/16 (sin x)) (* -1/48 (sin x))))) (* -1/2 (cos x))))))
(.f64 (fma.f64 (fma.f64 #s(literal 1/6 binary64) (.f64 (sin.f64 x) eps) (*.f64 (cos.f64 x) #s(literal -1/2 binary64))) eps (neg.f64 (sin.f64 x))) eps)
(* eps (+ (* -1 (sin x)) (* eps (+ (* -1/2 (cos x)) (* eps (+ (* -2 (+ (* -1/16 (sin x)) (* -1/48 (sin x)))) (* 1/24 (* eps (cos x)))))))))
(.f64 (fma.f64 (fma.f64 (fma.f64 (.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) (cos.f64 x) (.f64 #s(literal 1/6 binary64) (.f64 (sin.f64 x) eps))) eps (neg.f64 (sin.f64 x))) eps)
(* 1/2 (* eps (sin x)))
(.f64 (.f64 #s(literal 1/2 binary64) (sin.f64 x)) eps)
(* eps (+ (* 1/4 (* eps (cos x))) (* 1/2 (sin x))))
(.f64 (fma.f64 (.f64 #s(literal 1/4 binary64) (cos.f64 x)) eps (*.f64 #s(literal 1/2 binary64) (sin.f64 x))) eps)
(* eps (+ (* 1/2 (sin x)) (* eps (+ (* 1/4 (cos x)) (* eps (+ (* -1/16 (sin x)) (* -1/48 (sin x))))))))
(.f64 (fma.f64 (fma.f64 #s(literal 1/4 binary64) (cos.f64 x) (.f64 (.f64 #s(literal -1/12 binary64) (sin.f64 x)) eps)) eps (.f64 #s(literal 1/2 binary64) (sin.f64 x))) eps)
(* eps (+ (* 1/2 (sin x)) (* eps (+ (* 1/4 (cos x)) (* eps (+ (* -1/16 (sin x)) (+ (* -1/48 (sin x)) (* -1/48 (* eps (cos x))))))))))
(.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -1/12 binary64) (sin.f64 x) (.f64 #s(literal -1/48 binary64) (.f64 (cos.f64 x) eps))) eps (.f64 #s(literal 1/4 binary64) (cos.f64 x))) eps (*.f64 #s(literal 1/2 binary64) (sin.f64 x))) eps)
(sin x)
(sin.f64 x)
(+ (sin x) (* 1/2 (* eps (cos x))))
(fma.f64 (*.f64 #s(literal 1/2 binary64) (cos.f64 x)) eps (sin.f64 x))
(+ (sin x) (* eps (+ (* -1/8 (* eps (sin x))) (* 1/2 (cos x)))))
(fma.f64 (fma.f64 (.f64 #s(literal -1/8 binary64) (sin.f64 x)) eps (.f64 #s(literal 1/2 binary64) (cos.f64 x))) eps (sin.f64 x))
(+ (sin x) (* eps (+ (* 1/2 (cos x)) (* eps (+ (* -1/8 (sin x)) (* -1/48 (* eps (cos x))))))))
(fma.f64 (fma.f64 (.f64 #s(literal -1/8 binary64) eps) (sin.f64 x) (.f64 (cos.f64 x) (fma.f64 (*.f64 eps eps) #s(literal -1/48 binary64) #s(literal 1/2 binary64)))) eps (sin.f64 x))
(* -1 (* eps (sin x)))
(*.f64 (neg.f64 eps) (sin.f64 x))
(* eps (- (* -1/2 (* eps (cos x))) (sin x)))
(.f64 (fma.f64 (.f64 #s(literal -1/2 binary64) eps) (cos.f64 x) (neg.f64 (sin.f64 x))) eps)
(* eps (- (* eps (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x))))) (sin x)))
(.f64 (fma.f64 (fma.f64 #s(literal 1/6 binary64) (.f64 (sin.f64 x) eps) (*.f64 (cos.f64 x) #s(literal -1/2 binary64))) eps (neg.f64 (sin.f64 x))) eps)
(* eps (- (* eps (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x)))))) (sin x)))
(.f64 (fma.f64 (fma.f64 (fma.f64 (.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) (cos.f64 x) (.f64 #s(literal 1/6 binary64) (.f64 (sin.f64 x) eps))) eps (neg.f64 (sin.f64 x))) eps)
(* -1 (* eps (sin x)))
(*.f64 (neg.f64 eps) (sin.f64 x))
(* -1 (* eps (sin x)))
(*.f64 (neg.f64 eps) (sin.f64 x))
(* -1 (* eps (sin x)))
(*.f64 (neg.f64 eps) (sin.f64 x))
(* -1 (* eps (sin x)))
(*.f64 (neg.f64 eps) (sin.f64 x))
(* -1 x)
(neg.f64 x)
(+ (* -1 x) (* -1/2 eps))
(fma.f64 #s(literal -1/2 binary64) eps (neg.f64 x))
(+ (* -1 x) (* eps (- (* 1/6 (* eps x)) 1/2)))
(fma.f64 (fma.f64 (*.f64 x eps) #s(literal 1/6 binary64) #s(literal -1/2 binary64)) eps (neg.f64 x))
(+ (* -1 x) (* eps (- (* eps (+ (* 1/24 eps) (* 1/6 x))) 1/2)))
(fma.f64 (fma.f64 (fma.f64 #s(literal 1/6 binary64) x (*.f64 #s(literal 1/24 binary64) eps)) eps #s(literal -1/2 binary64)) eps (neg.f64 x))
(* -1 (* eps (sin x)))
(*.f64 (neg.f64 eps) (sin.f64 x))
(* eps (- (* -1/2 (* eps (cos x))) (sin x)))
(.f64 (fma.f64 (.f64 #s(literal -1/2 binary64) eps) (cos.f64 x) (neg.f64 (sin.f64 x))) eps)
(* eps (- (* eps (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x))))) (sin x)))
(.f64 (fma.f64 (fma.f64 #s(literal 1/6 binary64) (.f64 (sin.f64 x) eps) (*.f64 (cos.f64 x) #s(literal -1/2 binary64))) eps (neg.f64 (sin.f64 x))) eps)
(* eps (- (* eps (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x)))))) (sin x)))
(.f64 (fma.f64 (fma.f64 (fma.f64 (.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) (cos.f64 x) (.f64 #s(literal 1/6 binary64) (.f64 (sin.f64 x) eps))) eps (neg.f64 (sin.f64 x))) eps)
(* -1 (* eps (sin x)))
(*.f64 (neg.f64 eps) (sin.f64 x))
(* eps (+ (* -1 (sin x)) (* -1/2 (* eps (cos x)))))
(.f64 (fma.f64 (.f64 #s(literal -1/2 binary64) eps) (cos.f64 x) (neg.f64 (sin.f64 x))) eps)
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(fma.f64 (fma.f64 (.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) (cos.f64 x) (.f64 #s(literal 1/6 binary64) (*.f64 (sin.f64 x) eps)))
(+ (* 1/6 (* eps (sin x))) (* (cos x) (- (* 1/24 (pow eps 2)) 1/2)))
(fma.f64 (fma.f64 (.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) (cos.f64 x) (.f64 #s(literal 1/6 binary64) (*.f64 (sin.f64 x) eps)))
x
(* -1 (* x (- (* -1/2 (/ eps x)) 1)))
(fma.f64 (*.f64 (/.f64 eps x) #s(literal -1/2 binary64)) (neg.f64 x) x)
(* -1 (* x (- (* -1/2 (/ eps x)) 1)))
(fma.f64 (*.f64 (/.f64 eps x) #s(literal -1/2 binary64)) (neg.f64 x) x)
(* -1 (* x (- (* -1/2 (/ eps x)) 1)))
(fma.f64 (*.f64 (/.f64 eps x) #s(literal -1/2 binary64)) (neg.f64 x) x)
(* 2 (pow x 2))
(.f64 (.f64 x x) #s(literal 2 binary64))
(* (pow x 2) (+ 2 (* -1/2 (/ (pow eps 2) (pow x 2)))))
(.f64 (fma.f64 (/.f64 (.f64 eps eps) x) (/.f64 #s(literal -1/2 binary64) x) #s(literal 2 binary64)) (*.f64 x x))
(* (pow x 2) (+ 2 (* -1/2 (/ (pow eps 2) (pow x 2)))))
(.f64 (fma.f64 (/.f64 (.f64 eps eps) x) (/.f64 #s(literal -1/2 binary64) x) #s(literal 2 binary64)) (*.f64 x x))
(* (pow x 2) (+ 2 (* -1/2 (/ (pow eps 2) (pow x 2)))))
(.f64 (fma.f64 (/.f64 (.f64 eps eps) x) (/.f64 #s(literal -1/2 binary64) x) #s(literal 2 binary64)) (*.f64 x x))
(* -2 (* (sin (* -1/2 (/ (+ (* -1 (pow eps 2)) (* 4 (pow x 2))) (+ eps (* -2 x))))) (sin (* 1/2 eps))))
(.f64 (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) #s(literal -2 binary64)) (sin.f64 (.f64 (/.f64 (fma.f64 (.f64 #s(literal 4 binary64) x) x (.f64 (neg.f64 eps) eps)) (fma.f64 #s(literal -2 binary64) x eps)) #s(literal -1/2 binary64))))
(* -2 (* (sin (* -1/2 (/ (+ (* -1 (pow eps 2)) (* 4 (pow x 2))) (+ eps (* -2 x))))) (sin (* 1/2 eps))))
(.f64 (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) #s(literal -2 binary64)) (sin.f64 (.f64 (/.f64 (fma.f64 (.f64 #s(literal 4 binary64) x) x (.f64 (neg.f64 eps) eps)) (fma.f64 #s(literal -2 binary64) x eps)) #s(literal -1/2 binary64))))
(* -2 (* (sin (* -1/2 (/ (+ (* -1 (pow eps 2)) (* 4 (pow x 2))) (+ eps (* -2 x))))) (sin (* 1/2 eps))))
(.f64 (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) #s(literal -2 binary64)) (sin.f64 (.f64 (/.f64 (fma.f64 (.f64 #s(literal 4 binary64) x) x (.f64 (neg.f64 eps) eps)) (fma.f64 #s(literal -2 binary64) x eps)) #s(literal -1/2 binary64))))
(* -2 (* (sin (* -1/2 (/ (+ (* -1 (pow eps 2)) (* 4 (pow x 2))) (+ eps (* -2 x))))) (sin (* 1/2 eps))))
(.f64 (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) #s(literal -2 binary64)) (sin.f64 (.f64 (/.f64 (fma.f64 (.f64 #s(literal 4 binary64) x) x (.f64 (neg.f64 eps) eps)) (fma.f64 #s(literal -2 binary64) x eps)) #s(literal -1/2 binary64))))
(* (sin (* -1/2 (/ (+ (* -1 (pow eps 2)) (* 4 (pow x 2))) (+ eps (* -2 x))))) (sin (* 1/2 eps)))
(.f64 (sin.f64 (.f64 (/.f64 (fma.f64 (.f64 #s(literal 4 binary64) x) x (.f64 (neg.f64 eps) eps)) (fma.f64 #s(literal -2 binary64) x eps)) #s(literal -1/2 binary64))) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)))
(* (sin (* -1/2 (/ (+ (* -1 (pow eps 2)) (* 4 (pow x 2))) (+ eps (* -2 x))))) (sin (* 1/2 eps)))
(.f64 (sin.f64 (.f64 (/.f64 (fma.f64 (.f64 #s(literal 4 binary64) x) x (.f64 (neg.f64 eps) eps)) (fma.f64 #s(literal -2 binary64) x eps)) #s(literal -1/2 binary64))) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)))
(* (sin (* -1/2 (/ (+ (* -1 (pow eps 2)) (* 4 (pow x 2))) (+ eps (* -2 x))))) (sin (* 1/2 eps)))
(.f64 (sin.f64 (.f64 (/.f64 (fma.f64 (.f64 #s(literal 4 binary64) x) x (.f64 (neg.f64 eps) eps)) (fma.f64 #s(literal -2 binary64) x eps)) #s(literal -1/2 binary64))) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)))
(* (sin (* -1/2 (/ (+ (* -1 (pow eps 2)) (* 4 (pow x 2))) (+ eps (* -2 x))))) (sin (* 1/2 eps)))
(.f64 (sin.f64 (.f64 (/.f64 (fma.f64 (.f64 #s(literal 4 binary64) x) x (.f64 (neg.f64 eps) eps)) (fma.f64 #s(literal -2 binary64) x eps)) #s(literal -1/2 binary64))) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)))
(* 4 (pow x 2))
(.f64 #s(literal 4 binary64) (.f64 x x))
(* (pow x 2) (+ 4 (* -1 (/ (pow eps 2) (pow x 2)))))
(.f64 (fma.f64 (/.f64 (neg.f64 eps) x) (/.f64 eps x) #s(literal 4 binary64)) (.f64 x x))
(* (pow x 2) (+ 4 (* -1 (/ (pow eps 2) (pow x 2)))))
(.f64 (fma.f64 (/.f64 (neg.f64 eps) x) (/.f64 eps x) #s(literal 4 binary64)) (.f64 x x))
(* (pow x 2) (+ 4 (* -1 (/ (pow eps 2) (pow x 2)))))
(.f64 (fma.f64 (/.f64 (neg.f64 eps) x) (/.f64 eps x) #s(literal 4 binary64)) (.f64 x x))

rewrite160.0ms (1%)

Memory

-3.5MiB live, 116.2MiB allocated

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	77	562
0	126	535
1	429	481
2	3615	476
0	9003	466

Stop Event

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

Counts

23 → 460

Calls

Call 1

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

Outputs
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eval135.0ms (0.8%)

Memory: -17.8MiB live, 136.2MiB allocated
Compiler: Compiled 30 732 to 2 986 computations (90.3% saved)

prune52.0ms (0.3%)

Memory

-13.1MiB live, 115.0MiB allocated

Pruning

38 alts after pruning (30 fresh and 8 done)

	Pruned	Kept	Total
New	940	15	955
Fresh	6	15	21
Picked	3	2	5
Done	0	6	6
Total	949	38	987

Accuracy

100.0%

Counts

987 → 38

Alt Table

Click to see full alt table

Status	Accuracy	Program
	48.7%	(-.f64 (fma.f64 (sin.f64 x) (neg.f64 (sin.f64 eps)) (*.f64 (cos.f64 eps) (cos.f64 x))) (cos.f64 x))
	48.7%	(-.f64 (*.f64 (cos.f64 eps) (cos.f64 x)) (fma.f64 (sin.f64 eps) (sin.f64 x) (cos.f64 x)))
✓	48.5%	(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))
	46.6%	(-.f64 #s(approx (cos (+ x eps)) #s(approx (cos eps) (fma.f64 (*.f64 eps eps) #s(literal -1/2 binary64) #s(literal 1 binary64)))) (cos.f64 x))
	46.6%	(-.f64 #s(approx (cos (+ x eps)) #s(approx (cos eps) #s(literal 1 binary64))) (cos.f64 x))
	99.6%	(.f64 (.f64 (fma.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (cos.f64 x) (.f64 (sin.f64 x) (cos.f64 (.f64 eps #s(literal 1/2 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))) #s(literal -2 binary64))
	99.5%	(.f64 (.f64 (sin.f64 (fma.f64 eps #s(literal 1/2 binary64) x)) #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(literal -2 binary64))
	99.5%	(.f64 (.f64 (sin.f64 (/.f64 (.f64 #s(approx (+ ( 4 (* x x)) (* (neg eps) eps)) (fma.f64 (.f64 #s(literal 4 binary64) x) x (.f64 (neg.f64 eps) eps))) #s(literal 1/2 binary64)) (fma.f64 #s(literal 2 binary64) x (neg.f64 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(literal -2 binary64))
	99.4%	(.f64 (.f64 (sin.f64 (/.f64 #s(approx (* (+ (* 4 (* x x)) (* (neg eps) eps)) 1/2) (fma.f64 (.f64 eps eps) #s(literal -1/2 binary64) (.f64 (.f64 x x) #s(literal 2 binary64)))) (fma.f64 #s(literal 2 binary64) x (neg.f64 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(literal -2 binary64))
	99.3%	(.f64 (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps))) #s(approx (sin ( 1/2 (+ 0 eps))) (.f64 (fma.f64 (fma.f64 #s(literal 1/3840 binary64) (.f64 eps eps) #s(literal -1/48 binary64)) (*.f64 eps eps) #s(literal 1/2 binary64)) eps))) #s(literal -2 binary64))
	99.1%	(.f64 (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps))) #s(approx (sin ( 1/2 (+ 0 eps))) (.f64 (fma.f64 (.f64 eps eps) #s(literal -1/48 binary64) #s(literal 1/2 binary64)) eps))) #s(literal -2 binary64))
	98.5%	(.f64 (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps))) #s(approx (sin ( 1/2 (+ 0 eps))) (*.f64 eps #s(literal 1/2 binary64)))) #s(literal -2 binary64))
	99.4%	(.f64 (.f64 (sin.f64 #s(approx (/ (* (+ (* 4 (* x x)) (* (neg eps) eps)) 1/2) (+ (* 2 x) (neg eps))) (.f64 (+.f64 (/.f64 x 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(literal -2 binary64))
✓	99.7%	(.f64 #s(approx ( (sin (* 1/2 (+ (* 2 x) eps))) (sin (* 1/2 (+ 0 eps)))) (.f64 (sin.f64 (fma.f64 eps #s(literal 1/2 binary64) x)) (sin.f64 (.f64 eps #s(literal 1/2 binary64))))) #s(literal -2 binary64))
	98.0%	#s(approx (- (cos (+ x eps)) (cos x)) (fma.f64 (.f64 #s(approx (+ ( (cos x) (+ (* (* eps eps) 1/24) -1/2)) (* (* 1/6 (sin x)) eps)) (fma.f64 #s(literal 1/24 binary64) (.f64 eps eps) #s(literal -1/2 binary64))) eps) eps (.f64 (neg.f64 (sin.f64 x)) eps)))
	99.3%	#s(approx (- (cos (+ x eps)) (cos x)) (fma.f64 (neg.f64 (sin.f64 x)) eps (.f64 (.f64 (fma.f64 (fma.f64 #s(literal 1/24 binary64) (.f64 eps eps) #s(literal -1/2 binary64)) (cos.f64 x) (.f64 (*.f64 (sin.f64 x) #s(literal 1/6 binary64)) eps)) eps) eps)))
	82.0%	#s(approx (- (cos (+ x eps)) (cos x)) (/.f64 (.f64 (.f64 eps eps) #s(approx (+ (* (+ (* (cos x) (+ (* (* eps eps) 1/24) -1/2)) (* (* 1/6 (sin x)) eps)) eps) (neg (sin x))) (fma.f64 (fma.f64 #s(literal 1/24 binary64) (.f64 eps eps) #s(literal -1/2 binary64)) eps (.f64 (fma.f64 (*.f64 #s(literal 1/6 binary64) eps) eps #s(literal -1 binary64)) x)))) eps))
✓	46.3%	#s(approx (- (cos (+ x eps)) (cos x)) (-.f64 #s(approx (cos eps) #s(literal 1 binary64)) #s(literal 1 binary64)))
✓	99.1%	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 (fma.f64 (fma.f64 (cos.f64 x) (fma.f64 (.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) (.f64 (.f64 #s(literal 1/6 binary64) (sin.f64 x)) eps)) eps (neg.f64 (sin.f64 x))) eps))
✓	98.1%	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 (fma.f64 #s(approx (+ ( (cos x) (+ (* (* eps eps) 1/24) -1/2)) (* (* 1/6 (sin x)) eps)) (fma.f64 (*.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64))) eps (neg.f64 (sin.f64 x))) eps))
✓	75.2%	#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (neg.f64 (sin.f64 x)) eps))
	97.9%	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (+ ( (+ (* (cos x) (+ (* (* eps eps) 1/24) -1/2)) (* (* 1/6 (sin x)) eps)) eps) (neg (sin x))) (fma.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -1/36 binary64) (.f64 eps eps) #s(literal 1/6 binary64)) x (.f64 (.f64 (fma.f64 (.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) eps) #s(literal -1/2 binary64))) x (fma.f64 (.f64 #s(literal 1/6 binary64) eps) eps #s(literal -1 binary64))) x (.f64 (fma.f64 (*.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) eps))) eps))
	73.8%	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (+ ( (+ (* (cos x) (+ (* (* eps eps) 1/24) -1/2)) (* (* 1/6 (sin x)) eps)) eps) (neg (sin x))) (fma.f64 (fma.f64 (.f64 #s(literal 1/6 binary64) eps) eps #s(literal -1 binary64)) x (.f64 (neg.f64 (fma.f64 #s(literal 1/24 binary64) (*.f64 eps eps) #s(literal -1/2 binary64))) eps))) eps))
	97.0%	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (+ ( (+ (* (cos x) (+ (* (* eps eps) 1/24) -1/2)) (* (* 1/6 (sin x)) eps)) eps) (neg (sin x))) #s(approx (+ (* (+ (* (* 1/6 eps) eps) -1) x) (* (+ (* (* eps eps) 1/24) -1/2) eps)) (fma.f64 (fma.f64 (*.f64 x eps) #s(literal 1/6 binary64) #s(literal -1/2 binary64)) eps (neg.f64 x)))) eps))
	97.0%	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (+ ( (+ (* (cos x) (+ (* (* eps eps) 1/24) -1/2)) (* (* 1/6 (sin x)) eps)) eps) (neg (sin x))) #s(approx (+ (* (+ (* (* 1/6 eps) eps) -1) x) (* (+ (* (* eps eps) 1/24) -1/2) eps)) (fma.f64 #s(literal -1/2 binary64) eps (neg.f64 x)))) eps))
	74.6%	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (+ ( (+ (* (cos x) (+ (* (* eps eps) 1/24) -1/2)) (* (* 1/6 (sin x)) eps)) eps) (neg (sin x))) #s(approx (+ (* (+ (* (* 1/6 eps) eps) -1) x) (* (+ (* (* eps eps) 1/24) -1/2) eps)) (.f64 (fma.f64 (.f64 #s(literal 1/6 binary64) eps) eps #s(literal -1 binary64)) x))) eps))
	97.0%	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (+ ( (+ (* (cos x) (+ (* (* eps eps) 1/24) -1/2)) (* (* 1/6 (sin x)) eps)) eps) (neg (sin x))) #s(approx (+ (* (+ (* (* 1/6 eps) eps) -1) x) (* (+ (* (* eps eps) 1/24) -1/2) eps)) (.f64 (fma.f64 eps (fma.f64 #s(literal 1/6 binary64) eps (/.f64 (fma.f64 (.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) x)) #s(literal -1 binary64)) x))) eps))
	46.7%	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (+ ( (+ (* (cos x) (+ (* (* eps eps) 1/24) -1/2)) (* (* 1/6 (sin x)) eps)) eps) (neg (sin x))) #s(approx (+ (* (+ (* (* 1/6 eps) eps) -1) x) (* (+ (* (* eps eps) 1/24) -1/2) eps)) (*.f64 (pow.f64 eps #s(literal 3 binary64)) #s(literal 1/24 binary64)))) eps))
✓	75.0%	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (neg (sin x)) (.f64 (fma.f64 (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)) (*.f64 x x) #s(literal -1 binary64)) x)) eps))
	74.9%	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (neg (sin x)) (.f64 (fma.f64 (fma.f64 #s(literal -1/120 binary64) (.f64 x x) #s(literal 1/6 binary64)) (.f64 x x) #s(literal -1 binary64)) x)) eps))
	75.0%	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (neg (sin x)) (.f64 (fma.f64 (.f64 (fma.f64 (fma.f64 (.f64 x x) #s(literal 1/5040 binary64) #s(literal -1/120 binary64)) (*.f64 x x) #s(literal 1/6 binary64)) x) x #s(literal -1 binary64)) x)) eps))
	74.8%	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (neg (sin x)) (.f64 (fma.f64 (*.f64 x x) #s(literal 1/6 binary64) #s(literal -1 binary64)) x)) eps))
✓	74.6%	#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 #s(approx (neg (sin x)) (neg.f64 x)) eps))
	47.9%	#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (- (cos eps) 1) (.f64 (.f64 eps eps) #s(literal -1/2 binary64))))
	98.0%	#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (+ (* (+ (* (cos x) (+ (* (* eps eps) 1/24) -1/2)) (* (* 1/6 (sin x)) eps)) eps) (neg (sin x))) eps) (fma.f64 (fma.f64 (fma.f64 (.f64 (fma.f64 #s(literal -1/36 binary64) (.f64 eps eps) #s(literal 1/6 binary64)) x) eps (.f64 (.f64 (.f64 (fma.f64 (.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) eps) eps) #s(literal -1/2 binary64))) x (.f64 (fma.f64 (.f64 #s(literal 1/6 binary64) eps) eps #s(literal -1 binary64)) eps)) x (.f64 (.f64 (fma.f64 (*.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) eps) eps))))
	97.8%	#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (+ (* (+ (* (cos x) (+ (* (* eps eps) 1/24) -1/2)) (* (* 1/6 (sin x)) eps)) eps) (neg (sin x))) eps) (fma.f64 (.f64 (fma.f64 (.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) eps) eps (.f64 (fma.f64 (fma.f64 (.f64 eps (fma.f64 #s(literal -1/36 binary64) (.f64 eps eps) #s(literal 1/6 binary64))) x (.f64 (.f64 (fma.f64 (.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) #s(literal -1/2 binary64)) (.f64 eps eps))) x (.f64 (fma.f64 (*.f64 #s(literal 1/6 binary64) eps) eps #s(literal -1 binary64)) eps)) x))))
	74.9%	#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg (sin x)) eps) (.f64 (fma.f64 (.f64 eps (fma.f64 #s(literal -1/120 binary64) (.f64 x x) #s(literal 1/6 binary64))) (.f64 x x) (neg.f64 eps)) x)))
	74.8%	#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg (sin x)) eps) (.f64 (.f64 eps (fma.f64 (*.f64 x x) #s(literal 1/6 binary64) #s(literal -1 binary64))) x)))

Compiler

Compiled 2 061 to 900 computations (56.3% saved)

regimes47.0ms (0.3%)

Memory

22.4MiB live, 22.4MiB allocated

Counts

64 → 1

Calls

Call 1

Inputs
#s(approx (- (cos (+ x eps)) (cos x)) (-.f64 #s(approx (cos eps) #s(literal 1 binary64)) #s(literal 1 binary64)))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 #s(approx (neg (sin x)) (neg.f64 x)) eps))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (- (cos eps) 1) (.f64 (.f64 eps eps) #s(literal -1/2 binary64))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (+ ( (+ (* (cos x) (+ (* (* eps eps) 1/24) -1/2)) (* (* 1/6 (sin x)) eps)) eps) (neg (sin x))) #s(approx (+ (* (+ (* (* 1/6 eps) eps) -1) x) (* (+ (* (* eps eps) 1/24) -1/2) eps)) (fma.f64 #s(literal -1/2 binary64) eps (neg.f64 x)))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg (sin x)) eps) (.f64 (.f64 eps (fma.f64 (*.f64 x x) #s(literal 1/6 binary64) #s(literal -1 binary64))) x)))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (neg (sin x)) (.f64 (fma.f64 (*.f64 x x) #s(literal 1/6 binary64) #s(literal -1 binary64)) x)) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (+ ( (+ (* (cos x) (+ (* (* eps eps) 1/24) -1/2)) (* (* 1/6 (sin x)) eps)) eps) (neg (sin x))) #s(approx (+ (* (+ (* (* 1/6 eps) eps) -1) x) (* (+ (* (* eps eps) 1/24) -1/2) eps)) (.f64 (fma.f64 (.f64 #s(literal 1/6 binary64) eps) eps #s(literal -1 binary64)) x))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (+ ( (+ (* (cos x) (+ (* (* eps eps) 1/24) -1/2)) (* (* 1/6 (sin x)) eps)) eps) (neg (sin x))) #s(approx (+ (* (+ (* (* 1/6 eps) eps) -1) x) (* (+ (* (* eps eps) 1/24) -1/2) eps)) (fma.f64 (fma.f64 (*.f64 x eps) #s(literal 1/6 binary64) #s(literal -1/2 binary64)) eps (neg.f64 x)))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (neg (sin x)) (.f64 (fma.f64 (fma.f64 #s(literal -1/120 binary64) (.f64 x x) #s(literal 1/6 binary64)) (.f64 x x) #s(literal -1 binary64)) x)) eps))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg (sin x)) eps) (.f64 (fma.f64 (.f64 eps (fma.f64 #s(literal -1/120 binary64) (.f64 x x) #s(literal 1/6 binary64))) (.f64 x x) (neg.f64 eps)) x)))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (+ ( (+ (* (cos x) (+ (* (* eps eps) 1/24) -1/2)) (* (* 1/6 (sin x)) eps)) eps) (neg (sin x))) (fma.f64 (fma.f64 (.f64 #s(literal 1/6 binary64) eps) eps #s(literal -1 binary64)) x (.f64 (fma.f64 (*.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) eps))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (+ ( (+ (* (cos x) (+ (* (* eps eps) 1/24) -1/2)) (* (* 1/6 (sin x)) eps)) eps) (neg (sin x))) (fma.f64 (fma.f64 (.f64 #s(literal 1/6 binary64) eps) eps #s(literal -1 binary64)) x (.f64 (neg.f64 (fma.f64 #s(literal 1/24 binary64) (*.f64 eps eps) #s(literal -1/2 binary64))) eps))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (neg (sin x)) (.f64 (fma.f64 (.f64 (fma.f64 (fma.f64 (.f64 x x) #s(literal 1/5040 binary64) #s(literal -1/120 binary64)) (*.f64 x x) #s(literal 1/6 binary64)) x) x #s(literal -1 binary64)) x)) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (neg (sin x)) (.f64 (fma.f64 (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)) (*.f64 x x) #s(literal -1 binary64)) x)) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (+ ( (+ (* (cos x) (+ (* (* eps eps) 1/24) -1/2)) (* (* 1/6 (sin x)) eps)) eps) (neg (sin x))) #s(approx (+ (* (+ (* (* 1/6 eps) eps) -1) x) (* (+ (* (* eps eps) 1/24) -1/2) eps)) (.f64 (fma.f64 eps (fma.f64 #s(literal 1/6 binary64) eps (/.f64 (fma.f64 (.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) x)) #s(literal -1 binary64)) x))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (/.f64 (.f64 (.f64 eps eps) #s(approx (+ (* (+ (* (cos x) (+ (* (* eps eps) 1/24) -1/2)) (* (* 1/6 (sin x)) eps)) eps) (neg (sin x))) (fma.f64 (fma.f64 #s(literal 1/24 binary64) (.f64 eps eps) #s(literal -1/2 binary64)) eps (.f64 (fma.f64 (*.f64 #s(literal 1/6 binary64) eps) eps #s(literal -1 binary64)) x)))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (+ ( (+ (* (cos x) (+ (* (* eps eps) 1/24) -1/2)) (* (* 1/6 (sin x)) eps)) eps) (neg (sin x))) (fma.f64 (fma.f64 (fma.f64 (.f64 (fma.f64 (.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) eps) #s(literal -1/2 binary64) (.f64 (fma.f64 #s(literal -1/36 binary64) (.f64 eps eps) #s(literal 1/6 binary64)) x)) x (fma.f64 (.f64 #s(literal 1/6 binary64) eps) eps #s(literal -1 binary64))) x (.f64 (fma.f64 (*.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) eps))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (+ ( (+ (* (cos x) (+ (* (* eps eps) 1/24) -1/2)) (* (* 1/6 (sin x)) eps)) eps) (neg (sin x))) (fma.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -1/36 binary64) (.f64 eps eps) #s(literal 1/6 binary64)) x (.f64 (.f64 (fma.f64 (.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) eps) #s(literal -1/2 binary64))) x (fma.f64 (.f64 #s(literal 1/6 binary64) eps) eps #s(literal -1 binary64))) x (.f64 (fma.f64 (*.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) eps))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (+ (* (+ (* (cos x) (+ (* (* eps eps) 1/24) -1/2)) (* (* 1/6 (sin x)) eps)) eps) (neg (sin x))) eps) (fma.f64 (.f64 (fma.f64 (.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) eps) eps (.f64 (fma.f64 (fma.f64 (.f64 eps (fma.f64 #s(literal -1/36 binary64) (.f64 eps eps) #s(literal 1/6 binary64))) x (.f64 (.f64 (fma.f64 (.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) #s(literal -1/2 binary64)) (.f64 eps eps))) x (.f64 (fma.f64 (*.f64 #s(literal 1/6 binary64) eps) eps #s(literal -1 binary64)) eps)) x))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (+ (* (+ (* (cos x) (+ (* (* eps eps) 1/24) -1/2)) (* (* 1/6 (sin x)) eps)) eps) (neg (sin x))) eps) (fma.f64 (fma.f64 (fma.f64 (.f64 (fma.f64 #s(literal -1/36 binary64) (.f64 eps eps) #s(literal 1/6 binary64)) x) eps (.f64 (.f64 (.f64 (fma.f64 (.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) eps) eps) #s(literal -1/2 binary64))) x (.f64 (fma.f64 (.f64 #s(literal 1/6 binary64) eps) eps #s(literal -1 binary64)) eps)) x (.f64 (.f64 (fma.f64 (*.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) eps) eps))))
#s(approx (- (cos (+ x eps)) (cos x)) (-.f64 (cos.f64 eps) #s(literal 1 binary64)))
(-.f64 #s(approx (cos (+ x eps)) #s(approx (cos eps) #s(literal 1 binary64))) (cos.f64 x))
(-.f64 (cos.f64 (+.f64 x eps)) #s(approx (cos x) #s(literal 1 binary64)))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (neg.f64 (sin.f64 x)) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (+ ( (+ (* (cos x) (+ (* (* eps eps) 1/24) -1/2)) (* (* 1/6 (sin x)) eps)) eps) (neg (sin x))) #s(approx (+ (* (+ (* (* 1/6 eps) eps) -1) x) (* (+ (* (* eps eps) 1/24) -1/2) eps)) (*.f64 (pow.f64 eps #s(literal 3 binary64)) #s(literal 1/24 binary64)))) eps))
(-.f64 #s(approx (cos (+ x eps)) #s(approx (cos eps) (fma.f64 (*.f64 eps eps) #s(literal -1/2 binary64) #s(literal 1 binary64)))) (cos.f64 x))
(-.f64 (cos.f64 (+.f64 x eps)) #s(approx (cos x) (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 (fma.f64 #s(approx (+ ( (cos x) (+ (* (* eps eps) 1/24) -1/2)) (* (* 1/6 (sin x)) eps)) (fma.f64 (*.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64))) eps (neg.f64 (sin.f64 x))) eps))
(.f64 (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps))) #s(approx (sin ( 1/2 (+ 0 eps))) (*.f64 eps #s(literal 1/2 binary64)))) #s(literal -2 binary64))
(-.f64 (cos.f64 (+.f64 x eps)) #s(approx (cos x) (fma.f64 (fma.f64 (.f64 x x) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) (.f64 x x) #s(literal 1 binary64))))
#s(approx (- (cos (+ x eps)) (cos x)) (fma.f64 (.f64 #s(approx (+ ( (cos x) (+ (* (* eps eps) 1/24) -1/2)) (* (* 1/6 (sin x)) eps)) (fma.f64 #s(literal 1/24 binary64) (.f64 eps eps) #s(literal -1/2 binary64))) eps) eps (.f64 (neg.f64 (sin.f64 x)) eps)))
(.f64 (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps))) #s(approx (sin ( 1/2 (+ 0 eps))) (.f64 (fma.f64 (.f64 eps eps) #s(literal -1/48 binary64) #s(literal 1/2 binary64)) eps))) #s(literal -2 binary64))
(-.f64 (cos.f64 (+.f64 x eps)) #s(approx (cos x) (fma.f64 (fma.f64 (fma.f64 #s(literal -1/720 binary64) (.f64 x x) #s(literal 1/24 binary64)) (.f64 x x) #s(literal -1/2 binary64)) (*.f64 x x) #s(literal 1 binary64))))
(.f64 (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps))) #s(approx (sin ( 1/2 (+ 0 eps))) (.f64 (fma.f64 (fma.f64 #s(literal 1/3840 binary64) (.f64 eps eps) #s(literal -1/48 binary64)) (*.f64 eps eps) #s(literal 1/2 binary64)) eps))) #s(literal -2 binary64))
(.f64 (.f64 (sin.f64 #s(approx (* 1/2 (+ (* 2 x) eps)) (fma.f64 #s(literal 1/2 binary64) eps x))) #s(approx (sin (* 1/2 (+ 0 eps))) (.f64 (fma.f64 (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 (sin.f64 (fma.f64 eps #s(literal 1/2 binary64) x)) #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(literal -2 binary64))
(.f64 (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps))) #s(approx (sin ( 1/2 (+ 0 eps))) (.f64 (fma.f64 (fma.f64 (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 (sin.f64 #s(approx (* 1/2 (+ (* 2 x) eps)) (.f64 (+.f64 (/.f64 x 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(literal -2 binary64))
(.f64 (.f64 (sin.f64 #s(approx (/ (* (+ (* 4 (* x x)) (* (neg eps) eps)) 1/2) (+ (* 2 x) (neg eps))) (.f64 (+.f64 (/.f64 x 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(literal -2 binary64))
(.f64 (.f64 (sin.f64 (/.f64 #s(approx (* (+ (* 4 (* x x)) (* (neg eps) eps)) 1/2) (fma.f64 (.f64 eps eps) #s(literal -1/2 binary64) (.f64 (.f64 x x) #s(literal 2 binary64)))) (fma.f64 #s(literal 2 binary64) x (neg.f64 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(literal -2 binary64))
(.f64 (.f64 (sin.f64 (/.f64 (.f64 #s(approx (+ ( 4 (* x x)) (* (neg eps) eps)) (fma.f64 (.f64 #s(literal 4 binary64) x) x (.f64 (neg.f64 eps) eps))) #s(literal 1/2 binary64)) (fma.f64 #s(literal 2 binary64) x (neg.f64 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(literal -2 binary64))
(.f64 (.f64 (sin.f64 (/.f64 (.f64 (fma.f64 #s(literal 4 binary64) (.f64 x x) (.f64 (neg.f64 eps) eps)) #s(literal 1/2 binary64)) (fma.f64 #s(literal 2 binary64) x (neg.f64 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(literal -2 binary64))
(-.f64 #s(approx (cos (+ x eps)) (cos.f64 eps)) (cos.f64 x))
(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 (-.f64 (.f64 (*.f64 (cos.f64 x) #s(literal -1/2 binary64)) eps) (sin.f64 x)) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 (fma.f64 (.f64 #s(literal -1/2 binary64) eps) (cos.f64 x) (neg.f64 (sin.f64 x))) eps))
(.f64 #s(approx ( (sin (* 1/2 (+ (* 2 x) eps))) (sin (* 1/2 (+ 0 eps)))) (.f64 (sin.f64 (fma.f64 eps #s(literal 1/2 binary64) x)) (sin.f64 (.f64 eps #s(literal 1/2 binary64))))) #s(literal -2 binary64))
(.f64 (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps))) (sin.f64 (.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 0 binary64) eps)))) #s(literal -2 binary64))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (/.f64 (pow.f64 eps #s(literal 3 binary64)) eps) (/.f64 (neg.f64 (sin.f64 x)) eps)))
(.f64 (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps))) (sin.f64 (.f64 #s(literal 1/2 binary64) (/.f64 (*.f64 eps eps) (-.f64 eps #s(literal 0 binary64)))))) #s(literal -2 binary64))
(.f64 (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps))) (sin.f64 (.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1 binary64) (/.f64 (neg.f64 eps) (neg.f64 (*.f64 eps eps))))))) #s(literal -2 binary64))
(.f64 (.f64 (sin.f64 (/.f64 (.f64 (fma.f64 #s(literal 4 binary64) (.f64 x x) (.f64 (neg.f64 eps) eps)) #s(literal 1/2 binary64)) (fma.f64 x #s(literal 2 binary64) (neg.f64 eps)))) (sin.f64 (.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 0 binary64) eps)))) #s(literal -2 binary64))
(.f64 (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps))) (sin.f64 (.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1 binary64) (pow.f64 eps #s(literal -1 binary64)))))) #s(literal -2 binary64))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 (fma.f64 (fma.f64 (cos.f64 x) (fma.f64 (.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) (.f64 (.f64 #s(literal 1/6 binary64) (sin.f64 x)) eps)) eps (neg.f64 (sin.f64 x))) eps))
(.f64 (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps))) (sin.f64 (.f64 #s(literal 1/2 binary64) (.f64 (neg.f64 (.f64 eps eps)) (pow.f64 (neg.f64 eps) #s(literal -1 binary64)))))) #s(literal -2 binary64))
(.f64 (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps))) (sin.f64 (.f64 #s(literal 1/2 binary64) (/.f64 (pow.f64 eps #s(literal 3 binary64)) (*.f64 eps eps))))) #s(literal -2 binary64))
#s(approx (- (cos (+ x eps)) (cos x)) (fma.f64 (neg.f64 (sin.f64 x)) eps (.f64 (.f64 (fma.f64 (fma.f64 #s(literal 1/24 binary64) (.f64 eps eps) #s(literal -1/2 binary64)) (cos.f64 x) (.f64 (*.f64 (sin.f64 x) #s(literal 1/6 binary64)) eps)) eps) eps)))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 (-.f64 (.f64 (fma.f64 (fma.f64 #s(literal 1/6 binary64) (sin.f64 x) (.f64 #s(literal 1/24 binary64) (.f64 (cos.f64 x) eps))) eps (*.f64 (cos.f64 x) #s(literal -1/2 binary64))) eps) (sin.f64 x)) eps))
#s(approx (* (* (sin (* 1/2 (+ (* 2 x) eps))) (sin (* 1/2 (+ 0 eps)))) -2) (fma.f64 (pow.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) #s(literal 2 binary64)) (fma.f64 x x #s(literal -2 binary64)) (.f64 (.f64 (.f64 #s(literal -2 binary64) x) (cos.f64 (.f64 eps #s(literal 1/2 binary64)))) (sin.f64 (.f64 eps #s(literal 1/2 binary64))))))
(.f64 (.f64 (fma.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (cos.f64 x) (.f64 (sin.f64 x) (cos.f64 (.f64 eps #s(literal 1/2 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))) #s(literal -2 binary64))
(.f64 (.f64 (fma.f64 (sin.f64 (.f64 #s(literal 1 binary64) x)) (cos.f64 (.f64 #s(literal 1/2 binary64) eps)) (.f64 (cos.f64 (.f64 #s(literal 1 binary64) x)) (sin.f64 (.f64 #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(literal -2 binary64))
(-.f64 (*.f64 (cos.f64 eps) (cos.f64 x)) (fma.f64 (sin.f64 eps) (sin.f64 x) (cos.f64 x)))
(-.f64 (fma.f64 (sin.f64 x) (neg.f64 (sin.f64 eps)) (*.f64 (cos.f64 eps) (cos.f64 x))) (cos.f64 x))
#s(approx (* (* (sin (* 1/2 (+ (* 2 x) eps))) (sin (* 1/2 (+ 0 eps)))) -2) (fma.f64 (fma.f64 (.f64 (cos.f64 (.f64 eps #s(literal 1/2 binary64))) (sin.f64 (.f64 eps #s(literal 1/2 binary64)))) (+.f64 #s(literal -2 binary64) (.f64 x (.f64 #s(literal 1/3 binary64) x))) (.f64 (pow.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) #s(literal 2 binary64)) x)) x (.f64 (pow.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) #s(literal 2 binary64)) #s(literal -2 binary64))))

Outputs

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

Calls

3 calls:

16.0ms	x
16.0ms	eps
13.0ms	(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))

Results

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

Compiler

Compiled 9 to 10 computations (-11.1% saved)

regimes36.0ms (0.2%)

Memory

-21.7MiB live, 17.4MiB allocated

Counts

46 → 1

Calls

Call 1

Inputs
#s(approx (- (cos (+ x eps)) (cos x)) (-.f64 #s(approx (cos eps) #s(literal 1 binary64)) #s(literal 1 binary64)))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 #s(approx (neg (sin x)) (neg.f64 x)) eps))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (- (cos eps) 1) (.f64 (.f64 eps eps) #s(literal -1/2 binary64))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (+ ( (+ (* (cos x) (+ (* (* eps eps) 1/24) -1/2)) (* (* 1/6 (sin x)) eps)) eps) (neg (sin x))) #s(approx (+ (* (+ (* (* 1/6 eps) eps) -1) x) (* (+ (* (* eps eps) 1/24) -1/2) eps)) (fma.f64 #s(literal -1/2 binary64) eps (neg.f64 x)))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg (sin x)) eps) (.f64 (.f64 eps (fma.f64 (*.f64 x x) #s(literal 1/6 binary64) #s(literal -1 binary64))) x)))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (neg (sin x)) (.f64 (fma.f64 (*.f64 x x) #s(literal 1/6 binary64) #s(literal -1 binary64)) x)) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (+ ( (+ (* (cos x) (+ (* (* eps eps) 1/24) -1/2)) (* (* 1/6 (sin x)) eps)) eps) (neg (sin x))) #s(approx (+ (* (+ (* (* 1/6 eps) eps) -1) x) (* (+ (* (* eps eps) 1/24) -1/2) eps)) (.f64 (fma.f64 (.f64 #s(literal 1/6 binary64) eps) eps #s(literal -1 binary64)) x))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (+ ( (+ (* (cos x) (+ (* (* eps eps) 1/24) -1/2)) (* (* 1/6 (sin x)) eps)) eps) (neg (sin x))) #s(approx (+ (* (+ (* (* 1/6 eps) eps) -1) x) (* (+ (* (* eps eps) 1/24) -1/2) eps)) (fma.f64 (fma.f64 (*.f64 x eps) #s(literal 1/6 binary64) #s(literal -1/2 binary64)) eps (neg.f64 x)))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (neg (sin x)) (.f64 (fma.f64 (fma.f64 #s(literal -1/120 binary64) (.f64 x x) #s(literal 1/6 binary64)) (.f64 x x) #s(literal -1 binary64)) x)) eps))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg (sin x)) eps) (.f64 (fma.f64 (.f64 eps (fma.f64 #s(literal -1/120 binary64) (.f64 x x) #s(literal 1/6 binary64))) (.f64 x x) (neg.f64 eps)) x)))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (+ ( (+ (* (cos x) (+ (* (* eps eps) 1/24) -1/2)) (* (* 1/6 (sin x)) eps)) eps) (neg (sin x))) (fma.f64 (fma.f64 (.f64 #s(literal 1/6 binary64) eps) eps #s(literal -1 binary64)) x (.f64 (fma.f64 (*.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) eps))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (+ ( (+ (* (cos x) (+ (* (* eps eps) 1/24) -1/2)) (* (* 1/6 (sin x)) eps)) eps) (neg (sin x))) (fma.f64 (fma.f64 (.f64 #s(literal 1/6 binary64) eps) eps #s(literal -1 binary64)) x (.f64 (neg.f64 (fma.f64 #s(literal 1/24 binary64) (*.f64 eps eps) #s(literal -1/2 binary64))) eps))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (neg (sin x)) (.f64 (fma.f64 (.f64 (fma.f64 (fma.f64 (.f64 x x) #s(literal 1/5040 binary64) #s(literal -1/120 binary64)) (*.f64 x x) #s(literal 1/6 binary64)) x) x #s(literal -1 binary64)) x)) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (neg (sin x)) (.f64 (fma.f64 (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)) (*.f64 x x) #s(literal -1 binary64)) x)) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (+ ( (+ (* (cos x) (+ (* (* eps eps) 1/24) -1/2)) (* (* 1/6 (sin x)) eps)) eps) (neg (sin x))) #s(approx (+ (* (+ (* (* 1/6 eps) eps) -1) x) (* (+ (* (* eps eps) 1/24) -1/2) eps)) (.f64 (fma.f64 eps (fma.f64 #s(literal 1/6 binary64) eps (/.f64 (fma.f64 (.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) x)) #s(literal -1 binary64)) x))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (/.f64 (.f64 (.f64 eps eps) #s(approx (+ (* (+ (* (cos x) (+ (* (* eps eps) 1/24) -1/2)) (* (* 1/6 (sin x)) eps)) eps) (neg (sin x))) (fma.f64 (fma.f64 #s(literal 1/24 binary64) (.f64 eps eps) #s(literal -1/2 binary64)) eps (.f64 (fma.f64 (*.f64 #s(literal 1/6 binary64) eps) eps #s(literal -1 binary64)) x)))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (+ ( (+ (* (cos x) (+ (* (* eps eps) 1/24) -1/2)) (* (* 1/6 (sin x)) eps)) eps) (neg (sin x))) (fma.f64 (fma.f64 (fma.f64 (.f64 (fma.f64 (.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) eps) #s(literal -1/2 binary64) (.f64 (fma.f64 #s(literal -1/36 binary64) (.f64 eps eps) #s(literal 1/6 binary64)) x)) x (fma.f64 (.f64 #s(literal 1/6 binary64) eps) eps #s(literal -1 binary64))) x (.f64 (fma.f64 (*.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) eps))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (+ ( (+ (* (cos x) (+ (* (* eps eps) 1/24) -1/2)) (* (* 1/6 (sin x)) eps)) eps) (neg (sin x))) (fma.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -1/36 binary64) (.f64 eps eps) #s(literal 1/6 binary64)) x (.f64 (.f64 (fma.f64 (.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) eps) #s(literal -1/2 binary64))) x (fma.f64 (.f64 #s(literal 1/6 binary64) eps) eps #s(literal -1 binary64))) x (.f64 (fma.f64 (*.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) eps))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (+ (* (+ (* (cos x) (+ (* (* eps eps) 1/24) -1/2)) (* (* 1/6 (sin x)) eps)) eps) (neg (sin x))) eps) (fma.f64 (.f64 (fma.f64 (.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) eps) eps (.f64 (fma.f64 (fma.f64 (.f64 eps (fma.f64 #s(literal -1/36 binary64) (.f64 eps eps) #s(literal 1/6 binary64))) x (.f64 (.f64 (fma.f64 (.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) #s(literal -1/2 binary64)) (.f64 eps eps))) x (.f64 (fma.f64 (*.f64 #s(literal 1/6 binary64) eps) eps #s(literal -1 binary64)) eps)) x))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (+ (* (+ (* (cos x) (+ (* (* eps eps) 1/24) -1/2)) (* (* 1/6 (sin x)) eps)) eps) (neg (sin x))) eps) (fma.f64 (fma.f64 (fma.f64 (.f64 (fma.f64 #s(literal -1/36 binary64) (.f64 eps eps) #s(literal 1/6 binary64)) x) eps (.f64 (.f64 (.f64 (fma.f64 (.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) eps) eps) #s(literal -1/2 binary64))) x (.f64 (fma.f64 (.f64 #s(literal 1/6 binary64) eps) eps #s(literal -1 binary64)) eps)) x (.f64 (.f64 (fma.f64 (*.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) eps) eps))))
#s(approx (- (cos (+ x eps)) (cos x)) (-.f64 (cos.f64 eps) #s(literal 1 binary64)))
(-.f64 #s(approx (cos (+ x eps)) #s(approx (cos eps) #s(literal 1 binary64))) (cos.f64 x))
(-.f64 (cos.f64 (+.f64 x eps)) #s(approx (cos x) #s(literal 1 binary64)))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (neg.f64 (sin.f64 x)) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (+ ( (+ (* (cos x) (+ (* (* eps eps) 1/24) -1/2)) (* (* 1/6 (sin x)) eps)) eps) (neg (sin x))) #s(approx (+ (* (+ (* (* 1/6 eps) eps) -1) x) (* (+ (* (* eps eps) 1/24) -1/2) eps)) (*.f64 (pow.f64 eps #s(literal 3 binary64)) #s(literal 1/24 binary64)))) eps))
(-.f64 #s(approx (cos (+ x eps)) #s(approx (cos eps) (fma.f64 (*.f64 eps eps) #s(literal -1/2 binary64) #s(literal 1 binary64)))) (cos.f64 x))
(-.f64 (cos.f64 (+.f64 x eps)) #s(approx (cos x) (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 (fma.f64 #s(approx (+ ( (cos x) (+ (* (* eps eps) 1/24) -1/2)) (* (* 1/6 (sin x)) eps)) (fma.f64 (*.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64))) eps (neg.f64 (sin.f64 x))) eps))
(.f64 (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps))) #s(approx (sin ( 1/2 (+ 0 eps))) (*.f64 eps #s(literal 1/2 binary64)))) #s(literal -2 binary64))
(-.f64 (cos.f64 (+.f64 x eps)) #s(approx (cos x) (fma.f64 (fma.f64 (.f64 x x) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) (.f64 x x) #s(literal 1 binary64))))
#s(approx (- (cos (+ x eps)) (cos x)) (fma.f64 (.f64 #s(approx (+ ( (cos x) (+ (* (* eps eps) 1/24) -1/2)) (* (* 1/6 (sin x)) eps)) (fma.f64 #s(literal 1/24 binary64) (.f64 eps eps) #s(literal -1/2 binary64))) eps) eps (.f64 (neg.f64 (sin.f64 x)) eps)))
(.f64 (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps))) #s(approx (sin ( 1/2 (+ 0 eps))) (.f64 (fma.f64 (.f64 eps eps) #s(literal -1/48 binary64) #s(literal 1/2 binary64)) eps))) #s(literal -2 binary64))
(-.f64 (cos.f64 (+.f64 x eps)) #s(approx (cos x) (fma.f64 (fma.f64 (fma.f64 #s(literal -1/720 binary64) (.f64 x x) #s(literal 1/24 binary64)) (.f64 x x) #s(literal -1/2 binary64)) (*.f64 x x) #s(literal 1 binary64))))
(.f64 (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps))) #s(approx (sin ( 1/2 (+ 0 eps))) (.f64 (fma.f64 (fma.f64 #s(literal 1/3840 binary64) (.f64 eps eps) #s(literal -1/48 binary64)) (*.f64 eps eps) #s(literal 1/2 binary64)) eps))) #s(literal -2 binary64))
(.f64 (.f64 (sin.f64 #s(approx (* 1/2 (+ (* 2 x) eps)) (fma.f64 #s(literal 1/2 binary64) eps x))) #s(approx (sin (* 1/2 (+ 0 eps))) (.f64 (fma.f64 (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 (sin.f64 (fma.f64 eps #s(literal 1/2 binary64) x)) #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(literal -2 binary64))
(.f64 (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps))) #s(approx (sin ( 1/2 (+ 0 eps))) (.f64 (fma.f64 (fma.f64 (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 (sin.f64 #s(approx (* 1/2 (+ (* 2 x) eps)) (.f64 (+.f64 (/.f64 x 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(literal -2 binary64))
(.f64 (.f64 (sin.f64 #s(approx (/ (* (+ (* 4 (* x x)) (* (neg eps) eps)) 1/2) (+ (* 2 x) (neg eps))) (.f64 (+.f64 (/.f64 x 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(literal -2 binary64))
(.f64 (.f64 (sin.f64 (/.f64 #s(approx (* (+ (* 4 (* x x)) (* (neg eps) eps)) 1/2) (fma.f64 (.f64 eps eps) #s(literal -1/2 binary64) (.f64 (.f64 x x) #s(literal 2 binary64)))) (fma.f64 #s(literal 2 binary64) x (neg.f64 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(literal -2 binary64))
(.f64 (.f64 (sin.f64 (/.f64 (.f64 #s(approx (+ ( 4 (* x x)) (* (neg eps) eps)) (fma.f64 (.f64 #s(literal 4 binary64) x) x (.f64 (neg.f64 eps) eps))) #s(literal 1/2 binary64)) (fma.f64 #s(literal 2 binary64) x (neg.f64 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(literal -2 binary64))
(.f64 (.f64 (sin.f64 (/.f64 (.f64 (fma.f64 #s(literal 4 binary64) (.f64 x x) (.f64 (neg.f64 eps) eps)) #s(literal 1/2 binary64)) (fma.f64 #s(literal 2 binary64) x (neg.f64 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(literal -2 binary64))
(-.f64 #s(approx (cos (+ x eps)) (cos.f64 eps)) (cos.f64 x))
(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 (-.f64 (.f64 (*.f64 (cos.f64 x) #s(literal -1/2 binary64)) eps) (sin.f64 x)) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 (fma.f64 (.f64 #s(literal -1/2 binary64) eps) (cos.f64 x) (neg.f64 (sin.f64 x))) eps))

Outputs

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

Calls

3 calls:

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

Results

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

Compiler

Compiled 9 to 10 computations (-11.1% saved)

regimes26.0ms (0.2%)

Memory

13.7MiB live, 13.7MiB allocated

Counts

34 → 1

Calls

Call 1

Inputs
#s(approx (- (cos (+ x eps)) (cos x)) (-.f64 #s(approx (cos eps) #s(literal 1 binary64)) #s(literal 1 binary64)))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 #s(approx (neg (sin x)) (neg.f64 x)) eps))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (- (cos eps) 1) (.f64 (.f64 eps eps) #s(literal -1/2 binary64))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (+ ( (+ (* (cos x) (+ (* (* eps eps) 1/24) -1/2)) (* (* 1/6 (sin x)) eps)) eps) (neg (sin x))) #s(approx (+ (* (+ (* (* 1/6 eps) eps) -1) x) (* (+ (* (* eps eps) 1/24) -1/2) eps)) (fma.f64 #s(literal -1/2 binary64) eps (neg.f64 x)))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg (sin x)) eps) (.f64 (.f64 eps (fma.f64 (*.f64 x x) #s(literal 1/6 binary64) #s(literal -1 binary64))) x)))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (neg (sin x)) (.f64 (fma.f64 (*.f64 x x) #s(literal 1/6 binary64) #s(literal -1 binary64)) x)) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (+ ( (+ (* (cos x) (+ (* (* eps eps) 1/24) -1/2)) (* (* 1/6 (sin x)) eps)) eps) (neg (sin x))) #s(approx (+ (* (+ (* (* 1/6 eps) eps) -1) x) (* (+ (* (* eps eps) 1/24) -1/2) eps)) (.f64 (fma.f64 (.f64 #s(literal 1/6 binary64) eps) eps #s(literal -1 binary64)) x))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (+ ( (+ (* (cos x) (+ (* (* eps eps) 1/24) -1/2)) (* (* 1/6 (sin x)) eps)) eps) (neg (sin x))) #s(approx (+ (* (+ (* (* 1/6 eps) eps) -1) x) (* (+ (* (* eps eps) 1/24) -1/2) eps)) (fma.f64 (fma.f64 (*.f64 x eps) #s(literal 1/6 binary64) #s(literal -1/2 binary64)) eps (neg.f64 x)))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (neg (sin x)) (.f64 (fma.f64 (fma.f64 #s(literal -1/120 binary64) (.f64 x x) #s(literal 1/6 binary64)) (.f64 x x) #s(literal -1 binary64)) x)) eps))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg (sin x)) eps) (.f64 (fma.f64 (.f64 eps (fma.f64 #s(literal -1/120 binary64) (.f64 x x) #s(literal 1/6 binary64))) (.f64 x x) (neg.f64 eps)) x)))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (+ ( (+ (* (cos x) (+ (* (* eps eps) 1/24) -1/2)) (* (* 1/6 (sin x)) eps)) eps) (neg (sin x))) (fma.f64 (fma.f64 (.f64 #s(literal 1/6 binary64) eps) eps #s(literal -1 binary64)) x (.f64 (fma.f64 (*.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) eps))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (+ ( (+ (* (cos x) (+ (* (* eps eps) 1/24) -1/2)) (* (* 1/6 (sin x)) eps)) eps) (neg (sin x))) (fma.f64 (fma.f64 (.f64 #s(literal 1/6 binary64) eps) eps #s(literal -1 binary64)) x (.f64 (neg.f64 (fma.f64 #s(literal 1/24 binary64) (*.f64 eps eps) #s(literal -1/2 binary64))) eps))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (neg (sin x)) (.f64 (fma.f64 (.f64 (fma.f64 (fma.f64 (.f64 x x) #s(literal 1/5040 binary64) #s(literal -1/120 binary64)) (*.f64 x x) #s(literal 1/6 binary64)) x) x #s(literal -1 binary64)) x)) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (neg (sin x)) (.f64 (fma.f64 (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)) (*.f64 x x) #s(literal -1 binary64)) x)) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (+ ( (+ (* (cos x) (+ (* (* eps eps) 1/24) -1/2)) (* (* 1/6 (sin x)) eps)) eps) (neg (sin x))) #s(approx (+ (* (+ (* (* 1/6 eps) eps) -1) x) (* (+ (* (* eps eps) 1/24) -1/2) eps)) (.f64 (fma.f64 eps (fma.f64 #s(literal 1/6 binary64) eps (/.f64 (fma.f64 (.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) x)) #s(literal -1 binary64)) x))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (/.f64 (.f64 (.f64 eps eps) #s(approx (+ (* (+ (* (cos x) (+ (* (* eps eps) 1/24) -1/2)) (* (* 1/6 (sin x)) eps)) eps) (neg (sin x))) (fma.f64 (fma.f64 #s(literal 1/24 binary64) (.f64 eps eps) #s(literal -1/2 binary64)) eps (.f64 (fma.f64 (*.f64 #s(literal 1/6 binary64) eps) eps #s(literal -1 binary64)) x)))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (+ ( (+ (* (cos x) (+ (* (* eps eps) 1/24) -1/2)) (* (* 1/6 (sin x)) eps)) eps) (neg (sin x))) (fma.f64 (fma.f64 (fma.f64 (.f64 (fma.f64 (.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) eps) #s(literal -1/2 binary64) (.f64 (fma.f64 #s(literal -1/36 binary64) (.f64 eps eps) #s(literal 1/6 binary64)) x)) x (fma.f64 (.f64 #s(literal 1/6 binary64) eps) eps #s(literal -1 binary64))) x (.f64 (fma.f64 (*.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) eps))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (+ ( (+ (* (cos x) (+ (* (* eps eps) 1/24) -1/2)) (* (* 1/6 (sin x)) eps)) eps) (neg (sin x))) (fma.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -1/36 binary64) (.f64 eps eps) #s(literal 1/6 binary64)) x (.f64 (.f64 (fma.f64 (.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) eps) #s(literal -1/2 binary64))) x (fma.f64 (.f64 #s(literal 1/6 binary64) eps) eps #s(literal -1 binary64))) x (.f64 (fma.f64 (*.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) eps))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (+ (* (+ (* (cos x) (+ (* (* eps eps) 1/24) -1/2)) (* (* 1/6 (sin x)) eps)) eps) (neg (sin x))) eps) (fma.f64 (.f64 (fma.f64 (.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) eps) eps (.f64 (fma.f64 (fma.f64 (.f64 eps (fma.f64 #s(literal -1/36 binary64) (.f64 eps eps) #s(literal 1/6 binary64))) x (.f64 (.f64 (fma.f64 (.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) #s(literal -1/2 binary64)) (.f64 eps eps))) x (.f64 (fma.f64 (*.f64 #s(literal 1/6 binary64) eps) eps #s(literal -1 binary64)) eps)) x))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (+ (* (+ (* (cos x) (+ (* (* eps eps) 1/24) -1/2)) (* (* 1/6 (sin x)) eps)) eps) (neg (sin x))) eps) (fma.f64 (fma.f64 (fma.f64 (.f64 (fma.f64 #s(literal -1/36 binary64) (.f64 eps eps) #s(literal 1/6 binary64)) x) eps (.f64 (.f64 (.f64 (fma.f64 (.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) eps) eps) #s(literal -1/2 binary64))) x (.f64 (fma.f64 (.f64 #s(literal 1/6 binary64) eps) eps #s(literal -1 binary64)) eps)) x (.f64 (.f64 (fma.f64 (*.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) eps) eps))))
#s(approx (- (cos (+ x eps)) (cos x)) (-.f64 (cos.f64 eps) #s(literal 1 binary64)))
(-.f64 #s(approx (cos (+ x eps)) #s(approx (cos eps) #s(literal 1 binary64))) (cos.f64 x))
(-.f64 (cos.f64 (+.f64 x eps)) #s(approx (cos x) #s(literal 1 binary64)))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (neg.f64 (sin.f64 x)) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (+ ( (+ (* (cos x) (+ (* (* eps eps) 1/24) -1/2)) (* (* 1/6 (sin x)) eps)) eps) (neg (sin x))) #s(approx (+ (* (+ (* (* 1/6 eps) eps) -1) x) (* (+ (* (* eps eps) 1/24) -1/2) eps)) (*.f64 (pow.f64 eps #s(literal 3 binary64)) #s(literal 1/24 binary64)))) eps))
(-.f64 #s(approx (cos (+ x eps)) #s(approx (cos eps) (fma.f64 (*.f64 eps eps) #s(literal -1/2 binary64) #s(literal 1 binary64)))) (cos.f64 x))
(-.f64 (cos.f64 (+.f64 x eps)) #s(approx (cos x) (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 (fma.f64 #s(approx (+ ( (cos x) (+ (* (* eps eps) 1/24) -1/2)) (* (* 1/6 (sin x)) eps)) (fma.f64 (*.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64))) eps (neg.f64 (sin.f64 x))) eps))
(.f64 (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps))) #s(approx (sin ( 1/2 (+ 0 eps))) (*.f64 eps #s(literal 1/2 binary64)))) #s(literal -2 binary64))
(-.f64 (cos.f64 (+.f64 x eps)) #s(approx (cos x) (fma.f64 (fma.f64 (.f64 x x) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) (.f64 x x) #s(literal 1 binary64))))
#s(approx (- (cos (+ x eps)) (cos x)) (fma.f64 (.f64 #s(approx (+ ( (cos x) (+ (* (* eps eps) 1/24) -1/2)) (* (* 1/6 (sin x)) eps)) (fma.f64 #s(literal 1/24 binary64) (.f64 eps eps) #s(literal -1/2 binary64))) eps) eps (.f64 (neg.f64 (sin.f64 x)) eps)))
(.f64 (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps))) #s(approx (sin ( 1/2 (+ 0 eps))) (.f64 (fma.f64 (.f64 eps eps) #s(literal -1/48 binary64) #s(literal 1/2 binary64)) eps))) #s(literal -2 binary64))
(-.f64 (cos.f64 (+.f64 x eps)) #s(approx (cos x) (fma.f64 (fma.f64 (fma.f64 #s(literal -1/720 binary64) (.f64 x x) #s(literal 1/24 binary64)) (.f64 x x) #s(literal -1/2 binary64)) (*.f64 x x) #s(literal 1 binary64))))
(.f64 (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps))) #s(approx (sin ( 1/2 (+ 0 eps))) (.f64 (fma.f64 (fma.f64 #s(literal 1/3840 binary64) (.f64 eps eps) #s(literal -1/48 binary64)) (*.f64 eps eps) #s(literal 1/2 binary64)) eps))) #s(literal -2 binary64))

Outputs

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

Calls

3 calls:

9.0ms	eps
9.0ms	x
7.0ms	(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))

Results

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

Compiler

Compiled 9 to 10 computations (-11.1% saved)

regimes25.0ms (0.2%)

Memory

13.7MiB live, 13.7MiB allocated

Counts

33 → 1

Calls

Call 1

Inputs
#s(approx (- (cos (+ x eps)) (cos x)) (-.f64 #s(approx (cos eps) #s(literal 1 binary64)) #s(literal 1 binary64)))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 #s(approx (neg (sin x)) (neg.f64 x)) eps))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (- (cos eps) 1) (.f64 (.f64 eps eps) #s(literal -1/2 binary64))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (+ ( (+ (* (cos x) (+ (* (* eps eps) 1/24) -1/2)) (* (* 1/6 (sin x)) eps)) eps) (neg (sin x))) #s(approx (+ (* (+ (* (* 1/6 eps) eps) -1) x) (* (+ (* (* eps eps) 1/24) -1/2) eps)) (fma.f64 #s(literal -1/2 binary64) eps (neg.f64 x)))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg (sin x)) eps) (.f64 (.f64 eps (fma.f64 (*.f64 x x) #s(literal 1/6 binary64) #s(literal -1 binary64))) x)))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (neg (sin x)) (.f64 (fma.f64 (*.f64 x x) #s(literal 1/6 binary64) #s(literal -1 binary64)) x)) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (+ ( (+ (* (cos x) (+ (* (* eps eps) 1/24) -1/2)) (* (* 1/6 (sin x)) eps)) eps) (neg (sin x))) #s(approx (+ (* (+ (* (* 1/6 eps) eps) -1) x) (* (+ (* (* eps eps) 1/24) -1/2) eps)) (.f64 (fma.f64 (.f64 #s(literal 1/6 binary64) eps) eps #s(literal -1 binary64)) x))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (+ ( (+ (* (cos x) (+ (* (* eps eps) 1/24) -1/2)) (* (* 1/6 (sin x)) eps)) eps) (neg (sin x))) #s(approx (+ (* (+ (* (* 1/6 eps) eps) -1) x) (* (+ (* (* eps eps) 1/24) -1/2) eps)) (fma.f64 (fma.f64 (*.f64 x eps) #s(literal 1/6 binary64) #s(literal -1/2 binary64)) eps (neg.f64 x)))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (neg (sin x)) (.f64 (fma.f64 (fma.f64 #s(literal -1/120 binary64) (.f64 x x) #s(literal 1/6 binary64)) (.f64 x x) #s(literal -1 binary64)) x)) eps))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg (sin x)) eps) (.f64 (fma.f64 (.f64 eps (fma.f64 #s(literal -1/120 binary64) (.f64 x x) #s(literal 1/6 binary64))) (.f64 x x) (neg.f64 eps)) x)))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (+ ( (+ (* (cos x) (+ (* (* eps eps) 1/24) -1/2)) (* (* 1/6 (sin x)) eps)) eps) (neg (sin x))) (fma.f64 (fma.f64 (.f64 #s(literal 1/6 binary64) eps) eps #s(literal -1 binary64)) x (.f64 (fma.f64 (*.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) eps))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (+ ( (+ (* (cos x) (+ (* (* eps eps) 1/24) -1/2)) (* (* 1/6 (sin x)) eps)) eps) (neg (sin x))) (fma.f64 (fma.f64 (.f64 #s(literal 1/6 binary64) eps) eps #s(literal -1 binary64)) x (.f64 (neg.f64 (fma.f64 #s(literal 1/24 binary64) (*.f64 eps eps) #s(literal -1/2 binary64))) eps))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (neg (sin x)) (.f64 (fma.f64 (.f64 (fma.f64 (fma.f64 (.f64 x x) #s(literal 1/5040 binary64) #s(literal -1/120 binary64)) (*.f64 x x) #s(literal 1/6 binary64)) x) x #s(literal -1 binary64)) x)) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (neg (sin x)) (.f64 (fma.f64 (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)) (*.f64 x x) #s(literal -1 binary64)) x)) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (+ ( (+ (* (cos x) (+ (* (* eps eps) 1/24) -1/2)) (* (* 1/6 (sin x)) eps)) eps) (neg (sin x))) #s(approx (+ (* (+ (* (* 1/6 eps) eps) -1) x) (* (+ (* (* eps eps) 1/24) -1/2) eps)) (.f64 (fma.f64 eps (fma.f64 #s(literal 1/6 binary64) eps (/.f64 (fma.f64 (.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) x)) #s(literal -1 binary64)) x))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (/.f64 (.f64 (.f64 eps eps) #s(approx (+ (* (+ (* (cos x) (+ (* (* eps eps) 1/24) -1/2)) (* (* 1/6 (sin x)) eps)) eps) (neg (sin x))) (fma.f64 (fma.f64 #s(literal 1/24 binary64) (.f64 eps eps) #s(literal -1/2 binary64)) eps (.f64 (fma.f64 (*.f64 #s(literal 1/6 binary64) eps) eps #s(literal -1 binary64)) x)))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (+ ( (+ (* (cos x) (+ (* (* eps eps) 1/24) -1/2)) (* (* 1/6 (sin x)) eps)) eps) (neg (sin x))) (fma.f64 (fma.f64 (fma.f64 (.f64 (fma.f64 (.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) eps) #s(literal -1/2 binary64) (.f64 (fma.f64 #s(literal -1/36 binary64) (.f64 eps eps) #s(literal 1/6 binary64)) x)) x (fma.f64 (.f64 #s(literal 1/6 binary64) eps) eps #s(literal -1 binary64))) x (.f64 (fma.f64 (*.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) eps))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (+ ( (+ (* (cos x) (+ (* (* eps eps) 1/24) -1/2)) (* (* 1/6 (sin x)) eps)) eps) (neg (sin x))) (fma.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -1/36 binary64) (.f64 eps eps) #s(literal 1/6 binary64)) x (.f64 (.f64 (fma.f64 (.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) eps) #s(literal -1/2 binary64))) x (fma.f64 (.f64 #s(literal 1/6 binary64) eps) eps #s(literal -1 binary64))) x (.f64 (fma.f64 (*.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) eps))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (+ (* (+ (* (cos x) (+ (* (* eps eps) 1/24) -1/2)) (* (* 1/6 (sin x)) eps)) eps) (neg (sin x))) eps) (fma.f64 (.f64 (fma.f64 (.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) eps) eps (.f64 (fma.f64 (fma.f64 (.f64 eps (fma.f64 #s(literal -1/36 binary64) (.f64 eps eps) #s(literal 1/6 binary64))) x (.f64 (.f64 (fma.f64 (.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) #s(literal -1/2 binary64)) (.f64 eps eps))) x (.f64 (fma.f64 (*.f64 #s(literal 1/6 binary64) eps) eps #s(literal -1 binary64)) eps)) x))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (+ (* (+ (* (cos x) (+ (* (* eps eps) 1/24) -1/2)) (* (* 1/6 (sin x)) eps)) eps) (neg (sin x))) eps) (fma.f64 (fma.f64 (fma.f64 (.f64 (fma.f64 #s(literal -1/36 binary64) (.f64 eps eps) #s(literal 1/6 binary64)) x) eps (.f64 (.f64 (.f64 (fma.f64 (.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) eps) eps) #s(literal -1/2 binary64))) x (.f64 (fma.f64 (.f64 #s(literal 1/6 binary64) eps) eps #s(literal -1 binary64)) eps)) x (.f64 (.f64 (fma.f64 (*.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) eps) eps))))
#s(approx (- (cos (+ x eps)) (cos x)) (-.f64 (cos.f64 eps) #s(literal 1 binary64)))
(-.f64 #s(approx (cos (+ x eps)) #s(approx (cos eps) #s(literal 1 binary64))) (cos.f64 x))
(-.f64 (cos.f64 (+.f64 x eps)) #s(approx (cos x) #s(literal 1 binary64)))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (neg.f64 (sin.f64 x)) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (+ ( (+ (* (cos x) (+ (* (* eps eps) 1/24) -1/2)) (* (* 1/6 (sin x)) eps)) eps) (neg (sin x))) #s(approx (+ (* (+ (* (* 1/6 eps) eps) -1) x) (* (+ (* (* eps eps) 1/24) -1/2) eps)) (*.f64 (pow.f64 eps #s(literal 3 binary64)) #s(literal 1/24 binary64)))) eps))
(-.f64 #s(approx (cos (+ x eps)) #s(approx (cos eps) (fma.f64 (*.f64 eps eps) #s(literal -1/2 binary64) #s(literal 1 binary64)))) (cos.f64 x))
(-.f64 (cos.f64 (+.f64 x eps)) #s(approx (cos x) (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 (fma.f64 #s(approx (+ ( (cos x) (+ (* (* eps eps) 1/24) -1/2)) (* (* 1/6 (sin x)) eps)) (fma.f64 (*.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64))) eps (neg.f64 (sin.f64 x))) eps))
(.f64 (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps))) #s(approx (sin ( 1/2 (+ 0 eps))) (*.f64 eps #s(literal 1/2 binary64)))) #s(literal -2 binary64))
(-.f64 (cos.f64 (+.f64 x eps)) #s(approx (cos x) (fma.f64 (fma.f64 (.f64 x x) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) (.f64 x x) #s(literal 1 binary64))))
#s(approx (- (cos (+ x eps)) (cos x)) (fma.f64 (.f64 #s(approx (+ ( (cos x) (+ (* (* eps eps) 1/24) -1/2)) (* (* 1/6 (sin x)) eps)) (fma.f64 #s(literal 1/24 binary64) (.f64 eps eps) #s(literal -1/2 binary64))) eps) eps (.f64 (neg.f64 (sin.f64 x)) eps)))
(.f64 (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps))) #s(approx (sin ( 1/2 (+ 0 eps))) (.f64 (fma.f64 (.f64 eps eps) #s(literal -1/48 binary64) #s(literal 1/2 binary64)) eps))) #s(literal -2 binary64))
(-.f64 (cos.f64 (+.f64 x eps)) #s(approx (cos x) (fma.f64 (fma.f64 (fma.f64 #s(literal -1/720 binary64) (.f64 x x) #s(literal 1/24 binary64)) (.f64 x x) #s(literal -1/2 binary64)) (*.f64 x x) #s(literal 1 binary64))))

Outputs

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

Calls

3 calls:

9.0ms	eps
9.0ms	x
7.0ms	(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))

Results

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

Compiler

Compiled 9 to 10 computations (-11.1% saved)

regimes25.0ms (0.2%)

Memory

-26.4MiB live, 13.1MiB allocated

Counts

31 → 1

Calls

Call 1

Inputs
#s(approx (- (cos (+ x eps)) (cos x)) (-.f64 #s(approx (cos eps) #s(literal 1 binary64)) #s(literal 1 binary64)))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 #s(approx (neg (sin x)) (neg.f64 x)) eps))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (- (cos eps) 1) (.f64 (.f64 eps eps) #s(literal -1/2 binary64))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (+ ( (+ (* (cos x) (+ (* (* eps eps) 1/24) -1/2)) (* (* 1/6 (sin x)) eps)) eps) (neg (sin x))) #s(approx (+ (* (+ (* (* 1/6 eps) eps) -1) x) (* (+ (* (* eps eps) 1/24) -1/2) eps)) (fma.f64 #s(literal -1/2 binary64) eps (neg.f64 x)))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg (sin x)) eps) (.f64 (.f64 eps (fma.f64 (*.f64 x x) #s(literal 1/6 binary64) #s(literal -1 binary64))) x)))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (neg (sin x)) (.f64 (fma.f64 (*.f64 x x) #s(literal 1/6 binary64) #s(literal -1 binary64)) x)) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (+ ( (+ (* (cos x) (+ (* (* eps eps) 1/24) -1/2)) (* (* 1/6 (sin x)) eps)) eps) (neg (sin x))) #s(approx (+ (* (+ (* (* 1/6 eps) eps) -1) x) (* (+ (* (* eps eps) 1/24) -1/2) eps)) (.f64 (fma.f64 (.f64 #s(literal 1/6 binary64) eps) eps #s(literal -1 binary64)) x))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (+ ( (+ (* (cos x) (+ (* (* eps eps) 1/24) -1/2)) (* (* 1/6 (sin x)) eps)) eps) (neg (sin x))) #s(approx (+ (* (+ (* (* 1/6 eps) eps) -1) x) (* (+ (* (* eps eps) 1/24) -1/2) eps)) (fma.f64 (fma.f64 (*.f64 x eps) #s(literal 1/6 binary64) #s(literal -1/2 binary64)) eps (neg.f64 x)))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (neg (sin x)) (.f64 (fma.f64 (fma.f64 #s(literal -1/120 binary64) (.f64 x x) #s(literal 1/6 binary64)) (.f64 x x) #s(literal -1 binary64)) x)) eps))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg (sin x)) eps) (.f64 (fma.f64 (.f64 eps (fma.f64 #s(literal -1/120 binary64) (.f64 x x) #s(literal 1/6 binary64))) (.f64 x x) (neg.f64 eps)) x)))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (+ ( (+ (* (cos x) (+ (* (* eps eps) 1/24) -1/2)) (* (* 1/6 (sin x)) eps)) eps) (neg (sin x))) (fma.f64 (fma.f64 (.f64 #s(literal 1/6 binary64) eps) eps #s(literal -1 binary64)) x (.f64 (fma.f64 (*.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) eps))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (+ ( (+ (* (cos x) (+ (* (* eps eps) 1/24) -1/2)) (* (* 1/6 (sin x)) eps)) eps) (neg (sin x))) (fma.f64 (fma.f64 (.f64 #s(literal 1/6 binary64) eps) eps #s(literal -1 binary64)) x (.f64 (neg.f64 (fma.f64 #s(literal 1/24 binary64) (*.f64 eps eps) #s(literal -1/2 binary64))) eps))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (neg (sin x)) (.f64 (fma.f64 (.f64 (fma.f64 (fma.f64 (.f64 x x) #s(literal 1/5040 binary64) #s(literal -1/120 binary64)) (*.f64 x x) #s(literal 1/6 binary64)) x) x #s(literal -1 binary64)) x)) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (neg (sin x)) (.f64 (fma.f64 (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)) (*.f64 x x) #s(literal -1 binary64)) x)) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (+ ( (+ (* (cos x) (+ (* (* eps eps) 1/24) -1/2)) (* (* 1/6 (sin x)) eps)) eps) (neg (sin x))) #s(approx (+ (* (+ (* (* 1/6 eps) eps) -1) x) (* (+ (* (* eps eps) 1/24) -1/2) eps)) (.f64 (fma.f64 eps (fma.f64 #s(literal 1/6 binary64) eps (/.f64 (fma.f64 (.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) x)) #s(literal -1 binary64)) x))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (/.f64 (.f64 (.f64 eps eps) #s(approx (+ (* (+ (* (cos x) (+ (* (* eps eps) 1/24) -1/2)) (* (* 1/6 (sin x)) eps)) eps) (neg (sin x))) (fma.f64 (fma.f64 #s(literal 1/24 binary64) (.f64 eps eps) #s(literal -1/2 binary64)) eps (.f64 (fma.f64 (*.f64 #s(literal 1/6 binary64) eps) eps #s(literal -1 binary64)) x)))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (+ ( (+ (* (cos x) (+ (* (* eps eps) 1/24) -1/2)) (* (* 1/6 (sin x)) eps)) eps) (neg (sin x))) (fma.f64 (fma.f64 (fma.f64 (.f64 (fma.f64 (.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) eps) #s(literal -1/2 binary64) (.f64 (fma.f64 #s(literal -1/36 binary64) (.f64 eps eps) #s(literal 1/6 binary64)) x)) x (fma.f64 (.f64 #s(literal 1/6 binary64) eps) eps #s(literal -1 binary64))) x (.f64 (fma.f64 (*.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) eps))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (+ ( (+ (* (cos x) (+ (* (* eps eps) 1/24) -1/2)) (* (* 1/6 (sin x)) eps)) eps) (neg (sin x))) (fma.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -1/36 binary64) (.f64 eps eps) #s(literal 1/6 binary64)) x (.f64 (.f64 (fma.f64 (.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) eps) #s(literal -1/2 binary64))) x (fma.f64 (.f64 #s(literal 1/6 binary64) eps) eps #s(literal -1 binary64))) x (.f64 (fma.f64 (*.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) eps))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (+ (* (+ (* (cos x) (+ (* (* eps eps) 1/24) -1/2)) (* (* 1/6 (sin x)) eps)) eps) (neg (sin x))) eps) (fma.f64 (.f64 (fma.f64 (.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) eps) eps (.f64 (fma.f64 (fma.f64 (.f64 eps (fma.f64 #s(literal -1/36 binary64) (.f64 eps eps) #s(literal 1/6 binary64))) x (.f64 (.f64 (fma.f64 (.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) #s(literal -1/2 binary64)) (.f64 eps eps))) x (.f64 (fma.f64 (*.f64 #s(literal 1/6 binary64) eps) eps #s(literal -1 binary64)) eps)) x))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (+ (* (+ (* (cos x) (+ (* (* eps eps) 1/24) -1/2)) (* (* 1/6 (sin x)) eps)) eps) (neg (sin x))) eps) (fma.f64 (fma.f64 (fma.f64 (.f64 (fma.f64 #s(literal -1/36 binary64) (.f64 eps eps) #s(literal 1/6 binary64)) x) eps (.f64 (.f64 (.f64 (fma.f64 (.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) eps) eps) #s(literal -1/2 binary64))) x (.f64 (fma.f64 (.f64 #s(literal 1/6 binary64) eps) eps #s(literal -1 binary64)) eps)) x (.f64 (.f64 (fma.f64 (*.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) eps) eps))))
#s(approx (- (cos (+ x eps)) (cos x)) (-.f64 (cos.f64 eps) #s(literal 1 binary64)))
(-.f64 #s(approx (cos (+ x eps)) #s(approx (cos eps) #s(literal 1 binary64))) (cos.f64 x))
(-.f64 (cos.f64 (+.f64 x eps)) #s(approx (cos x) #s(literal 1 binary64)))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (neg.f64 (sin.f64 x)) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (+ ( (+ (* (cos x) (+ (* (* eps eps) 1/24) -1/2)) (* (* 1/6 (sin x)) eps)) eps) (neg (sin x))) #s(approx (+ (* (+ (* (* 1/6 eps) eps) -1) x) (* (+ (* (* eps eps) 1/24) -1/2) eps)) (*.f64 (pow.f64 eps #s(literal 3 binary64)) #s(literal 1/24 binary64)))) eps))
(-.f64 #s(approx (cos (+ x eps)) #s(approx (cos eps) (fma.f64 (*.f64 eps eps) #s(literal -1/2 binary64) #s(literal 1 binary64)))) (cos.f64 x))
(-.f64 (cos.f64 (+.f64 x eps)) #s(approx (cos x) (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 (fma.f64 #s(approx (+ ( (cos x) (+ (* (* eps eps) 1/24) -1/2)) (* (* 1/6 (sin x)) eps)) (fma.f64 (*.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64))) eps (neg.f64 (sin.f64 x))) eps))
(.f64 (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps))) #s(approx (sin ( 1/2 (+ 0 eps))) (*.f64 eps #s(literal 1/2 binary64)))) #s(literal -2 binary64))
(-.f64 (cos.f64 (+.f64 x eps)) #s(approx (cos x) (fma.f64 (fma.f64 (.f64 x x) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) (.f64 x x) #s(literal 1 binary64))))
#s(approx (- (cos (+ x eps)) (cos x)) (fma.f64 (.f64 #s(approx (+ ( (cos x) (+ (* (* eps eps) 1/24) -1/2)) (* (* 1/6 (sin x)) eps)) (fma.f64 #s(literal 1/24 binary64) (.f64 eps eps) #s(literal -1/2 binary64))) eps) eps (.f64 (neg.f64 (sin.f64 x)) eps)))

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

Calls

3 calls:

9.0ms	x
8.0ms	eps
6.0ms	(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))

Results

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

Compiler

Compiled 9 to 10 computations (-11.1% saved)

regimes22.0ms (0.1%)

Memory

12.1MiB live, 12.1MiB allocated

Counts

28 → 1

Calls

Call 1

Inputs
#s(approx (- (cos (+ x eps)) (cos x)) (-.f64 #s(approx (cos eps) #s(literal 1 binary64)) #s(literal 1 binary64)))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 #s(approx (neg (sin x)) (neg.f64 x)) eps))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (- (cos eps) 1) (.f64 (.f64 eps eps) #s(literal -1/2 binary64))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (+ ( (+ (* (cos x) (+ (* (* eps eps) 1/24) -1/2)) (* (* 1/6 (sin x)) eps)) eps) (neg (sin x))) #s(approx (+ (* (+ (* (* 1/6 eps) eps) -1) x) (* (+ (* (* eps eps) 1/24) -1/2) eps)) (fma.f64 #s(literal -1/2 binary64) eps (neg.f64 x)))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg (sin x)) eps) (.f64 (.f64 eps (fma.f64 (*.f64 x x) #s(literal 1/6 binary64) #s(literal -1 binary64))) x)))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (neg (sin x)) (.f64 (fma.f64 (*.f64 x x) #s(literal 1/6 binary64) #s(literal -1 binary64)) x)) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (+ ( (+ (* (cos x) (+ (* (* eps eps) 1/24) -1/2)) (* (* 1/6 (sin x)) eps)) eps) (neg (sin x))) #s(approx (+ (* (+ (* (* 1/6 eps) eps) -1) x) (* (+ (* (* eps eps) 1/24) -1/2) eps)) (.f64 (fma.f64 (.f64 #s(literal 1/6 binary64) eps) eps #s(literal -1 binary64)) x))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (+ ( (+ (* (cos x) (+ (* (* eps eps) 1/24) -1/2)) (* (* 1/6 (sin x)) eps)) eps) (neg (sin x))) #s(approx (+ (* (+ (* (* 1/6 eps) eps) -1) x) (* (+ (* (* eps eps) 1/24) -1/2) eps)) (fma.f64 (fma.f64 (*.f64 x eps) #s(literal 1/6 binary64) #s(literal -1/2 binary64)) eps (neg.f64 x)))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (neg (sin x)) (.f64 (fma.f64 (fma.f64 #s(literal -1/120 binary64) (.f64 x x) #s(literal 1/6 binary64)) (.f64 x x) #s(literal -1 binary64)) x)) eps))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg (sin x)) eps) (.f64 (fma.f64 (.f64 eps (fma.f64 #s(literal -1/120 binary64) (.f64 x x) #s(literal 1/6 binary64))) (.f64 x x) (neg.f64 eps)) x)))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (+ ( (+ (* (cos x) (+ (* (* eps eps) 1/24) -1/2)) (* (* 1/6 (sin x)) eps)) eps) (neg (sin x))) (fma.f64 (fma.f64 (.f64 #s(literal 1/6 binary64) eps) eps #s(literal -1 binary64)) x (.f64 (fma.f64 (*.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) eps))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (+ ( (+ (* (cos x) (+ (* (* eps eps) 1/24) -1/2)) (* (* 1/6 (sin x)) eps)) eps) (neg (sin x))) (fma.f64 (fma.f64 (.f64 #s(literal 1/6 binary64) eps) eps #s(literal -1 binary64)) x (.f64 (neg.f64 (fma.f64 #s(literal 1/24 binary64) (*.f64 eps eps) #s(literal -1/2 binary64))) eps))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (neg (sin x)) (.f64 (fma.f64 (.f64 (fma.f64 (fma.f64 (.f64 x x) #s(literal 1/5040 binary64) #s(literal -1/120 binary64)) (*.f64 x x) #s(literal 1/6 binary64)) x) x #s(literal -1 binary64)) x)) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (neg (sin x)) (.f64 (fma.f64 (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)) (*.f64 x x) #s(literal -1 binary64)) x)) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (+ ( (+ (* (cos x) (+ (* (* eps eps) 1/24) -1/2)) (* (* 1/6 (sin x)) eps)) eps) (neg (sin x))) #s(approx (+ (* (+ (* (* 1/6 eps) eps) -1) x) (* (+ (* (* eps eps) 1/24) -1/2) eps)) (.f64 (fma.f64 eps (fma.f64 #s(literal 1/6 binary64) eps (/.f64 (fma.f64 (.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) x)) #s(literal -1 binary64)) x))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (/.f64 (.f64 (.f64 eps eps) #s(approx (+ (* (+ (* (cos x) (+ (* (* eps eps) 1/24) -1/2)) (* (* 1/6 (sin x)) eps)) eps) (neg (sin x))) (fma.f64 (fma.f64 #s(literal 1/24 binary64) (.f64 eps eps) #s(literal -1/2 binary64)) eps (.f64 (fma.f64 (*.f64 #s(literal 1/6 binary64) eps) eps #s(literal -1 binary64)) x)))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (+ ( (+ (* (cos x) (+ (* (* eps eps) 1/24) -1/2)) (* (* 1/6 (sin x)) eps)) eps) (neg (sin x))) (fma.f64 (fma.f64 (fma.f64 (.f64 (fma.f64 (.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) eps) #s(literal -1/2 binary64) (.f64 (fma.f64 #s(literal -1/36 binary64) (.f64 eps eps) #s(literal 1/6 binary64)) x)) x (fma.f64 (.f64 #s(literal 1/6 binary64) eps) eps #s(literal -1 binary64))) x (.f64 (fma.f64 (*.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) eps))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (+ ( (+ (* (cos x) (+ (* (* eps eps) 1/24) -1/2)) (* (* 1/6 (sin x)) eps)) eps) (neg (sin x))) (fma.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -1/36 binary64) (.f64 eps eps) #s(literal 1/6 binary64)) x (.f64 (.f64 (fma.f64 (.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) eps) #s(literal -1/2 binary64))) x (fma.f64 (.f64 #s(literal 1/6 binary64) eps) eps #s(literal -1 binary64))) x (.f64 (fma.f64 (*.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) eps))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (+ (* (+ (* (cos x) (+ (* (* eps eps) 1/24) -1/2)) (* (* 1/6 (sin x)) eps)) eps) (neg (sin x))) eps) (fma.f64 (.f64 (fma.f64 (.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) eps) eps (.f64 (fma.f64 (fma.f64 (.f64 eps (fma.f64 #s(literal -1/36 binary64) (.f64 eps eps) #s(literal 1/6 binary64))) x (.f64 (.f64 (fma.f64 (.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) #s(literal -1/2 binary64)) (.f64 eps eps))) x (.f64 (fma.f64 (*.f64 #s(literal 1/6 binary64) eps) eps #s(literal -1 binary64)) eps)) x))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (+ (* (+ (* (cos x) (+ (* (* eps eps) 1/24) -1/2)) (* (* 1/6 (sin x)) eps)) eps) (neg (sin x))) eps) (fma.f64 (fma.f64 (fma.f64 (.f64 (fma.f64 #s(literal -1/36 binary64) (.f64 eps eps) #s(literal 1/6 binary64)) x) eps (.f64 (.f64 (.f64 (fma.f64 (.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) eps) eps) #s(literal -1/2 binary64))) x (.f64 (fma.f64 (.f64 #s(literal 1/6 binary64) eps) eps #s(literal -1 binary64)) eps)) x (.f64 (.f64 (fma.f64 (*.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) eps) eps))))
#s(approx (- (cos (+ x eps)) (cos x)) (-.f64 (cos.f64 eps) #s(literal 1 binary64)))
(-.f64 #s(approx (cos (+ x eps)) #s(approx (cos eps) #s(literal 1 binary64))) (cos.f64 x))
(-.f64 (cos.f64 (+.f64 x eps)) #s(approx (cos x) #s(literal 1 binary64)))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (neg.f64 (sin.f64 x)) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (+ ( (+ (* (cos x) (+ (* (* eps eps) 1/24) -1/2)) (* (* 1/6 (sin x)) eps)) eps) (neg (sin x))) #s(approx (+ (* (+ (* (* 1/6 eps) eps) -1) x) (* (+ (* (* eps eps) 1/24) -1/2) eps)) (*.f64 (pow.f64 eps #s(literal 3 binary64)) #s(literal 1/24 binary64)))) eps))
(-.f64 #s(approx (cos (+ x eps)) #s(approx (cos eps) (fma.f64 (*.f64 eps eps) #s(literal -1/2 binary64) #s(literal 1 binary64)))) (cos.f64 x))
(-.f64 (cos.f64 (+.f64 x eps)) #s(approx (cos x) (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 (fma.f64 #s(approx (+ ( (cos x) (+ (* (* eps eps) 1/24) -1/2)) (* (* 1/6 (sin x)) eps)) (fma.f64 (*.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64))) eps (neg.f64 (sin.f64 x))) eps))

Outputs

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

Calls

3 calls:

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

Results

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

Compiler

Compiled 9 to 10 computations (-11.1% saved)

regimes21.0ms (0.1%)

Memory

11.9MiB live, 11.9MiB allocated

Counts

27 → 1

Calls

Call 1

Inputs
#s(approx (- (cos (+ x eps)) (cos x)) (-.f64 #s(approx (cos eps) #s(literal 1 binary64)) #s(literal 1 binary64)))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 #s(approx (neg (sin x)) (neg.f64 x)) eps))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (- (cos eps) 1) (.f64 (.f64 eps eps) #s(literal -1/2 binary64))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (+ ( (+ (* (cos x) (+ (* (* eps eps) 1/24) -1/2)) (* (* 1/6 (sin x)) eps)) eps) (neg (sin x))) #s(approx (+ (* (+ (* (* 1/6 eps) eps) -1) x) (* (+ (* (* eps eps) 1/24) -1/2) eps)) (fma.f64 #s(literal -1/2 binary64) eps (neg.f64 x)))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg (sin x)) eps) (.f64 (.f64 eps (fma.f64 (*.f64 x x) #s(literal 1/6 binary64) #s(literal -1 binary64))) x)))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (neg (sin x)) (.f64 (fma.f64 (*.f64 x x) #s(literal 1/6 binary64) #s(literal -1 binary64)) x)) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (+ ( (+ (* (cos x) (+ (* (* eps eps) 1/24) -1/2)) (* (* 1/6 (sin x)) eps)) eps) (neg (sin x))) #s(approx (+ (* (+ (* (* 1/6 eps) eps) -1) x) (* (+ (* (* eps eps) 1/24) -1/2) eps)) (.f64 (fma.f64 (.f64 #s(literal 1/6 binary64) eps) eps #s(literal -1 binary64)) x))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (+ ( (+ (* (cos x) (+ (* (* eps eps) 1/24) -1/2)) (* (* 1/6 (sin x)) eps)) eps) (neg (sin x))) #s(approx (+ (* (+ (* (* 1/6 eps) eps) -1) x) (* (+ (* (* eps eps) 1/24) -1/2) eps)) (fma.f64 (fma.f64 (*.f64 x eps) #s(literal 1/6 binary64) #s(literal -1/2 binary64)) eps (neg.f64 x)))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (neg (sin x)) (.f64 (fma.f64 (fma.f64 #s(literal -1/120 binary64) (.f64 x x) #s(literal 1/6 binary64)) (.f64 x x) #s(literal -1 binary64)) x)) eps))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg (sin x)) eps) (.f64 (fma.f64 (.f64 eps (fma.f64 #s(literal -1/120 binary64) (.f64 x x) #s(literal 1/6 binary64))) (.f64 x x) (neg.f64 eps)) x)))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (+ ( (+ (* (cos x) (+ (* (* eps eps) 1/24) -1/2)) (* (* 1/6 (sin x)) eps)) eps) (neg (sin x))) (fma.f64 (fma.f64 (.f64 #s(literal 1/6 binary64) eps) eps #s(literal -1 binary64)) x (.f64 (fma.f64 (*.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) eps))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (+ ( (+ (* (cos x) (+ (* (* eps eps) 1/24) -1/2)) (* (* 1/6 (sin x)) eps)) eps) (neg (sin x))) (fma.f64 (fma.f64 (.f64 #s(literal 1/6 binary64) eps) eps #s(literal -1 binary64)) x (.f64 (neg.f64 (fma.f64 #s(literal 1/24 binary64) (*.f64 eps eps) #s(literal -1/2 binary64))) eps))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (neg (sin x)) (.f64 (fma.f64 (.f64 (fma.f64 (fma.f64 (.f64 x x) #s(literal 1/5040 binary64) #s(literal -1/120 binary64)) (*.f64 x x) #s(literal 1/6 binary64)) x) x #s(literal -1 binary64)) x)) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (neg (sin x)) (.f64 (fma.f64 (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)) (*.f64 x x) #s(literal -1 binary64)) x)) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (+ ( (+ (* (cos x) (+ (* (* eps eps) 1/24) -1/2)) (* (* 1/6 (sin x)) eps)) eps) (neg (sin x))) #s(approx (+ (* (+ (* (* 1/6 eps) eps) -1) x) (* (+ (* (* eps eps) 1/24) -1/2) eps)) (.f64 (fma.f64 eps (fma.f64 #s(literal 1/6 binary64) eps (/.f64 (fma.f64 (.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) x)) #s(literal -1 binary64)) x))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (/.f64 (.f64 (.f64 eps eps) #s(approx (+ (* (+ (* (cos x) (+ (* (* eps eps) 1/24) -1/2)) (* (* 1/6 (sin x)) eps)) eps) (neg (sin x))) (fma.f64 (fma.f64 #s(literal 1/24 binary64) (.f64 eps eps) #s(literal -1/2 binary64)) eps (.f64 (fma.f64 (*.f64 #s(literal 1/6 binary64) eps) eps #s(literal -1 binary64)) x)))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (+ ( (+ (* (cos x) (+ (* (* eps eps) 1/24) -1/2)) (* (* 1/6 (sin x)) eps)) eps) (neg (sin x))) (fma.f64 (fma.f64 (fma.f64 (.f64 (fma.f64 (.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) eps) #s(literal -1/2 binary64) (.f64 (fma.f64 #s(literal -1/36 binary64) (.f64 eps eps) #s(literal 1/6 binary64)) x)) x (fma.f64 (.f64 #s(literal 1/6 binary64) eps) eps #s(literal -1 binary64))) x (.f64 (fma.f64 (*.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) eps))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (+ ( (+ (* (cos x) (+ (* (* eps eps) 1/24) -1/2)) (* (* 1/6 (sin x)) eps)) eps) (neg (sin x))) (fma.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -1/36 binary64) (.f64 eps eps) #s(literal 1/6 binary64)) x (.f64 (.f64 (fma.f64 (.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) eps) #s(literal -1/2 binary64))) x (fma.f64 (.f64 #s(literal 1/6 binary64) eps) eps #s(literal -1 binary64))) x (.f64 (fma.f64 (*.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) eps))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (+ (* (+ (* (cos x) (+ (* (* eps eps) 1/24) -1/2)) (* (* 1/6 (sin x)) eps)) eps) (neg (sin x))) eps) (fma.f64 (.f64 (fma.f64 (.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) eps) eps (.f64 (fma.f64 (fma.f64 (.f64 eps (fma.f64 #s(literal -1/36 binary64) (.f64 eps eps) #s(literal 1/6 binary64))) x (.f64 (.f64 (fma.f64 (.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) #s(literal -1/2 binary64)) (.f64 eps eps))) x (.f64 (fma.f64 (*.f64 #s(literal 1/6 binary64) eps) eps #s(literal -1 binary64)) eps)) x))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (+ (* (+ (* (cos x) (+ (* (* eps eps) 1/24) -1/2)) (* (* 1/6 (sin x)) eps)) eps) (neg (sin x))) eps) (fma.f64 (fma.f64 (fma.f64 (.f64 (fma.f64 #s(literal -1/36 binary64) (.f64 eps eps) #s(literal 1/6 binary64)) x) eps (.f64 (.f64 (.f64 (fma.f64 (.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) eps) eps) #s(literal -1/2 binary64))) x (.f64 (fma.f64 (.f64 #s(literal 1/6 binary64) eps) eps #s(literal -1 binary64)) eps)) x (.f64 (.f64 (fma.f64 (*.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) eps) eps))))
#s(approx (- (cos (+ x eps)) (cos x)) (-.f64 (cos.f64 eps) #s(literal 1 binary64)))
(-.f64 #s(approx (cos (+ x eps)) #s(approx (cos eps) #s(literal 1 binary64))) (cos.f64 x))
(-.f64 (cos.f64 (+.f64 x eps)) #s(approx (cos x) #s(literal 1 binary64)))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (neg.f64 (sin.f64 x)) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (+ ( (+ (* (cos x) (+ (* (* eps eps) 1/24) -1/2)) (* (* 1/6 (sin x)) eps)) eps) (neg (sin x))) #s(approx (+ (* (+ (* (* 1/6 eps) eps) -1) x) (* (+ (* (* eps eps) 1/24) -1/2) eps)) (*.f64 (pow.f64 eps #s(literal 3 binary64)) #s(literal 1/24 binary64)))) eps))
(-.f64 #s(approx (cos (+ x eps)) #s(approx (cos eps) (fma.f64 (*.f64 eps eps) #s(literal -1/2 binary64) #s(literal 1 binary64)))) (cos.f64 x))
(-.f64 (cos.f64 (+.f64 x eps)) #s(approx (cos x) (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64))))

Outputs

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

Calls

3 calls:

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

Results

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

Compiler

Compiled 9 to 10 computations (-11.1% saved)

regimes16.0ms (0.1%)

Memory

9.5MiB live, 9.5MiB allocated

Counts

19 → 1

Calls

Call 1

Inputs
#s(approx (- (cos (+ x eps)) (cos x)) (-.f64 #s(approx (cos eps) #s(literal 1 binary64)) #s(literal 1 binary64)))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 #s(approx (neg (sin x)) (neg.f64 x)) eps))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (- (cos eps) 1) (.f64 (.f64 eps eps) #s(literal -1/2 binary64))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (+ ( (+ (* (cos x) (+ (* (* eps eps) 1/24) -1/2)) (* (* 1/6 (sin x)) eps)) eps) (neg (sin x))) #s(approx (+ (* (+ (* (* 1/6 eps) eps) -1) x) (* (+ (* (* eps eps) 1/24) -1/2) eps)) (fma.f64 #s(literal -1/2 binary64) eps (neg.f64 x)))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg (sin x)) eps) (.f64 (.f64 eps (fma.f64 (*.f64 x x) #s(literal 1/6 binary64) #s(literal -1 binary64))) x)))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (neg (sin x)) (.f64 (fma.f64 (*.f64 x x) #s(literal 1/6 binary64) #s(literal -1 binary64)) x)) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (+ ( (+ (* (cos x) (+ (* (* eps eps) 1/24) -1/2)) (* (* 1/6 (sin x)) eps)) eps) (neg (sin x))) #s(approx (+ (* (+ (* (* 1/6 eps) eps) -1) x) (* (+ (* (* eps eps) 1/24) -1/2) eps)) (.f64 (fma.f64 (.f64 #s(literal 1/6 binary64) eps) eps #s(literal -1 binary64)) x))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (+ ( (+ (* (cos x) (+ (* (* eps eps) 1/24) -1/2)) (* (* 1/6 (sin x)) eps)) eps) (neg (sin x))) #s(approx (+ (* (+ (* (* 1/6 eps) eps) -1) x) (* (+ (* (* eps eps) 1/24) -1/2) eps)) (fma.f64 (fma.f64 (*.f64 x eps) #s(literal 1/6 binary64) #s(literal -1/2 binary64)) eps (neg.f64 x)))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (neg (sin x)) (.f64 (fma.f64 (fma.f64 #s(literal -1/120 binary64) (.f64 x x) #s(literal 1/6 binary64)) (.f64 x x) #s(literal -1 binary64)) x)) eps))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg (sin x)) eps) (.f64 (fma.f64 (.f64 eps (fma.f64 #s(literal -1/120 binary64) (.f64 x x) #s(literal 1/6 binary64))) (.f64 x x) (neg.f64 eps)) x)))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (+ ( (+ (* (cos x) (+ (* (* eps eps) 1/24) -1/2)) (* (* 1/6 (sin x)) eps)) eps) (neg (sin x))) (fma.f64 (fma.f64 (.f64 #s(literal 1/6 binary64) eps) eps #s(literal -1 binary64)) x (.f64 (fma.f64 (*.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) eps))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (+ ( (+ (* (cos x) (+ (* (* eps eps) 1/24) -1/2)) (* (* 1/6 (sin x)) eps)) eps) (neg (sin x))) (fma.f64 (fma.f64 (.f64 #s(literal 1/6 binary64) eps) eps #s(literal -1 binary64)) x (.f64 (neg.f64 (fma.f64 #s(literal 1/24 binary64) (*.f64 eps eps) #s(literal -1/2 binary64))) eps))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (neg (sin x)) (.f64 (fma.f64 (.f64 (fma.f64 (fma.f64 (.f64 x x) #s(literal 1/5040 binary64) #s(literal -1/120 binary64)) (*.f64 x x) #s(literal 1/6 binary64)) x) x #s(literal -1 binary64)) x)) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (neg (sin x)) (.f64 (fma.f64 (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)) (*.f64 x x) #s(literal -1 binary64)) x)) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (+ ( (+ (* (cos x) (+ (* (* eps eps) 1/24) -1/2)) (* (* 1/6 (sin x)) eps)) eps) (neg (sin x))) #s(approx (+ (* (+ (* (* 1/6 eps) eps) -1) x) (* (+ (* (* eps eps) 1/24) -1/2) eps)) (.f64 (fma.f64 eps (fma.f64 #s(literal 1/6 binary64) eps (/.f64 (fma.f64 (.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) x)) #s(literal -1 binary64)) x))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (/.f64 (.f64 (.f64 eps eps) #s(approx (+ (* (+ (* (cos x) (+ (* (* eps eps) 1/24) -1/2)) (* (* 1/6 (sin x)) eps)) eps) (neg (sin x))) (fma.f64 (fma.f64 #s(literal 1/24 binary64) (.f64 eps eps) #s(literal -1/2 binary64)) eps (.f64 (fma.f64 (*.f64 #s(literal 1/6 binary64) eps) eps #s(literal -1 binary64)) x)))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (+ ( (+ (* (cos x) (+ (* (* eps eps) 1/24) -1/2)) (* (* 1/6 (sin x)) eps)) eps) (neg (sin x))) (fma.f64 (fma.f64 (fma.f64 (.f64 (fma.f64 (.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) eps) #s(literal -1/2 binary64) (.f64 (fma.f64 #s(literal -1/36 binary64) (.f64 eps eps) #s(literal 1/6 binary64)) x)) x (fma.f64 (.f64 #s(literal 1/6 binary64) eps) eps #s(literal -1 binary64))) x (.f64 (fma.f64 (*.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) eps))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (+ ( (+ (* (cos x) (+ (* (* eps eps) 1/24) -1/2)) (* (* 1/6 (sin x)) eps)) eps) (neg (sin x))) (fma.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -1/36 binary64) (.f64 eps eps) #s(literal 1/6 binary64)) x (.f64 (.f64 (fma.f64 (.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) eps) #s(literal -1/2 binary64))) x (fma.f64 (.f64 #s(literal 1/6 binary64) eps) eps #s(literal -1 binary64))) x (.f64 (fma.f64 (*.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) eps))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (+ (* (+ (* (cos x) (+ (* (* eps eps) 1/24) -1/2)) (* (* 1/6 (sin x)) eps)) eps) (neg (sin x))) eps) (fma.f64 (.f64 (fma.f64 (.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) eps) eps (.f64 (fma.f64 (fma.f64 (.f64 eps (fma.f64 #s(literal -1/36 binary64) (.f64 eps eps) #s(literal 1/6 binary64))) x (.f64 (.f64 (fma.f64 (.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) #s(literal -1/2 binary64)) (.f64 eps eps))) x (.f64 (fma.f64 (*.f64 #s(literal 1/6 binary64) eps) eps #s(literal -1 binary64)) eps)) x))))

Outputs

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

Calls

3 calls:

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

Results

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

Compiler

Compiled 9 to 10 computations (-11.1% saved)

regimes14.0ms (0.1%)

Memory

-31.0MiB live, 8.6MiB allocated

Counts

16 → 1

Calls

Call 1

Inputs
#s(approx (- (cos (+ x eps)) (cos x)) (-.f64 #s(approx (cos eps) #s(literal 1 binary64)) #s(literal 1 binary64)))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 #s(approx (neg (sin x)) (neg.f64 x)) eps))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (- (cos eps) 1) (.f64 (.f64 eps eps) #s(literal -1/2 binary64))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (+ ( (+ (* (cos x) (+ (* (* eps eps) 1/24) -1/2)) (* (* 1/6 (sin x)) eps)) eps) (neg (sin x))) #s(approx (+ (* (+ (* (* 1/6 eps) eps) -1) x) (* (+ (* (* eps eps) 1/24) -1/2) eps)) (fma.f64 #s(literal -1/2 binary64) eps (neg.f64 x)))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg (sin x)) eps) (.f64 (.f64 eps (fma.f64 (*.f64 x x) #s(literal 1/6 binary64) #s(literal -1 binary64))) x)))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (neg (sin x)) (.f64 (fma.f64 (*.f64 x x) #s(literal 1/6 binary64) #s(literal -1 binary64)) x)) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (+ ( (+ (* (cos x) (+ (* (* eps eps) 1/24) -1/2)) (* (* 1/6 (sin x)) eps)) eps) (neg (sin x))) #s(approx (+ (* (+ (* (* 1/6 eps) eps) -1) x) (* (+ (* (* eps eps) 1/24) -1/2) eps)) (.f64 (fma.f64 (.f64 #s(literal 1/6 binary64) eps) eps #s(literal -1 binary64)) x))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (+ ( (+ (* (cos x) (+ (* (* eps eps) 1/24) -1/2)) (* (* 1/6 (sin x)) eps)) eps) (neg (sin x))) #s(approx (+ (* (+ (* (* 1/6 eps) eps) -1) x) (* (+ (* (* eps eps) 1/24) -1/2) eps)) (fma.f64 (fma.f64 (*.f64 x eps) #s(literal 1/6 binary64) #s(literal -1/2 binary64)) eps (neg.f64 x)))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (neg (sin x)) (.f64 (fma.f64 (fma.f64 #s(literal -1/120 binary64) (.f64 x x) #s(literal 1/6 binary64)) (.f64 x x) #s(literal -1 binary64)) x)) eps))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg (sin x)) eps) (.f64 (fma.f64 (.f64 eps (fma.f64 #s(literal -1/120 binary64) (.f64 x x) #s(literal 1/6 binary64))) (.f64 x x) (neg.f64 eps)) x)))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (+ ( (+ (* (cos x) (+ (* (* eps eps) 1/24) -1/2)) (* (* 1/6 (sin x)) eps)) eps) (neg (sin x))) (fma.f64 (fma.f64 (.f64 #s(literal 1/6 binary64) eps) eps #s(literal -1 binary64)) x (.f64 (fma.f64 (*.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) eps))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (+ ( (+ (* (cos x) (+ (* (* eps eps) 1/24) -1/2)) (* (* 1/6 (sin x)) eps)) eps) (neg (sin x))) (fma.f64 (fma.f64 (.f64 #s(literal 1/6 binary64) eps) eps #s(literal -1 binary64)) x (.f64 (neg.f64 (fma.f64 #s(literal 1/24 binary64) (*.f64 eps eps) #s(literal -1/2 binary64))) eps))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (neg (sin x)) (.f64 (fma.f64 (.f64 (fma.f64 (fma.f64 (.f64 x x) #s(literal 1/5040 binary64) #s(literal -1/120 binary64)) (*.f64 x x) #s(literal 1/6 binary64)) x) x #s(literal -1 binary64)) x)) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (neg (sin x)) (.f64 (fma.f64 (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)) (*.f64 x x) #s(literal -1 binary64)) x)) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (+ ( (+ (* (cos x) (+ (* (* eps eps) 1/24) -1/2)) (* (* 1/6 (sin x)) eps)) eps) (neg (sin x))) #s(approx (+ (* (+ (* (* 1/6 eps) eps) -1) x) (* (+ (* (* eps eps) 1/24) -1/2) eps)) (.f64 (fma.f64 eps (fma.f64 #s(literal 1/6 binary64) eps (/.f64 (fma.f64 (.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) x)) #s(literal -1 binary64)) x))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (/.f64 (.f64 (.f64 eps eps) #s(approx (+ (* (+ (* (cos x) (+ (* (* eps eps) 1/24) -1/2)) (* (* 1/6 (sin x)) eps)) eps) (neg (sin x))) (fma.f64 (fma.f64 #s(literal 1/24 binary64) (.f64 eps eps) #s(literal -1/2 binary64)) eps (.f64 (fma.f64 (*.f64 #s(literal 1/6 binary64) eps) eps #s(literal -1 binary64)) x)))) eps))

Outputs

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

Calls

3 calls:

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

Results

Accuracy	Segments	Branch
97.0%	1	`x`
97.0%	1	`eps`
97.0%	1	`(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))`

Compiler

Compiled 9 to 10 computations (-11.1% saved)

regimes8.0ms (0%)

Memory

6.2MiB live, 6.2MiB allocated

Counts

7 → 1

Calls

Call 1

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

Outputs

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

Calls

3 calls:

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

Results

Accuracy	Segments	Branch
97.0%	1	`x`
97.0%	1	`eps`
97.0%	1	`(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))`

Compiler

Compiled 9 to 10 computations (-11.1% saved)

regimes5.0ms (0%)

Memory

4.7MiB live, 4.7MiB allocated

Counts

3 → 1

Calls

Call 1

Inputs

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

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

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

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

Calls

3 calls:

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

Results

Accuracy	Segments	Branch
74.6%	1	`x`
74.6%	1	`eps`
74.6%	1	`(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))`

Compiler

Compiled 9 to 10 computations (-11.1% saved)

regimes4.0ms (0%)

Memory

4.1MiB live, 4.1MiB allocated

Accuracy

Total -0.0b remaining (-0%)

Threshold costs -0b (-0%)

Counts

1 → 1

Calls

Call 1

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

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

Calls

3 calls:

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

Results

Accuracy	Segments	Branch
46.3%	1	`x`
46.3%	1	`(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))`
46.3%	1	`eps`

Compiler

Compiled 9 to 10 computations (-11.1% saved)

simplify119.0ms (0.7%)

Memory

10.5MiB live, 10.5MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 5 (0.0ms)

Iter	Nodes	Cost
0	126	470
1	212	470
2	378	470
3	859	466
4	1743	466
5	3355	462
6	5294	462
7	6299	462
8	6985	462
9	7266	462
10	7362	462
11	7463	462

Stop Event

1×	node limit

Calls

Call 1

Inputs
(.f64 #s(approx ( (sin (* 1/2 (+ (* 2 x) eps))) (sin (* 1/2 (+ 0 eps)))) (.f64 (sin.f64 (fma.f64 eps #s(literal 1/2 binary64) x)) (sin.f64 (.f64 eps #s(literal 1/2 binary64))))) #s(literal -2 binary64))
(.f64 (.f64 (sin.f64 #s(approx (* 1/2 (+ (* 2 x) eps)) (fma.f64 #s(literal 1/2 binary64) eps x))) #s(approx (sin (* 1/2 (+ 0 eps))) (.f64 (fma.f64 (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 (sin.f64 (.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps))) #s(approx (sin ( 1/2 (+ 0 eps))) (.f64 (fma.f64 (fma.f64 #s(literal 1/3840 binary64) (.f64 eps eps) #s(literal -1/48 binary64)) (*.f64 eps eps) #s(literal 1/2 binary64)) eps))) #s(literal -2 binary64))
(.f64 (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps))) #s(approx (sin ( 1/2 (+ 0 eps))) (.f64 (fma.f64 (.f64 eps eps) #s(literal -1/48 binary64) #s(literal 1/2 binary64)) eps))) #s(literal -2 binary64))
(.f64 (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps))) #s(approx (sin ( 1/2 (+ 0 eps))) (*.f64 eps #s(literal 1/2 binary64)))) #s(literal -2 binary64))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 (fma.f64 #s(approx (+ ( (cos x) (+ (* (* eps eps) 1/24) -1/2)) (* (* 1/6 (sin x)) eps)) (fma.f64 (*.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64))) eps (neg.f64 (sin.f64 x))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (+ (* (+ (* (cos x) (+ (* (* eps eps) 1/24) -1/2)) (* (* 1/6 (sin x)) eps)) eps) (neg (sin x))) eps) (fma.f64 (fma.f64 (fma.f64 (.f64 (fma.f64 #s(literal -1/36 binary64) (.f64 eps eps) #s(literal 1/6 binary64)) x) eps (.f64 (.f64 (.f64 (fma.f64 (.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) eps) eps) #s(literal -1/2 binary64))) x (.f64 (fma.f64 (.f64 #s(literal 1/6 binary64) eps) eps #s(literal -1 binary64)) eps)) x (.f64 (.f64 (fma.f64 (*.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) eps) eps))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (+ ( (+ (* (cos x) (+ (* (* eps eps) 1/24) -1/2)) (* (* 1/6 (sin x)) eps)) eps) (neg (sin x))) (fma.f64 (fma.f64 (fma.f64 (.f64 (fma.f64 (.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) eps) #s(literal -1/2 binary64) (.f64 (fma.f64 #s(literal -1/36 binary64) (.f64 eps eps) #s(literal 1/6 binary64)) x)) x (fma.f64 (.f64 #s(literal 1/6 binary64) eps) eps #s(literal -1 binary64))) x (.f64 (fma.f64 (*.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) eps))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (+ ( (+ (* (cos x) (+ (* (* eps eps) 1/24) -1/2)) (* (* 1/6 (sin x)) eps)) eps) (neg (sin x))) #s(approx (+ (* (+ (* (* 1/6 eps) eps) -1) x) (* (+ (* (* eps eps) 1/24) -1/2) eps)) (fma.f64 (fma.f64 (*.f64 x eps) #s(literal 1/6 binary64) #s(literal -1/2 binary64)) eps (neg.f64 x)))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (+ ( (+ (* (cos x) (+ (* (* eps eps) 1/24) -1/2)) (* (* 1/6 (sin x)) eps)) eps) (neg (sin x))) #s(approx (+ (* (+ (* (* 1/6 eps) eps) -1) x) (* (+ (* (* eps eps) 1/24) -1/2) eps)) (fma.f64 #s(literal -1/2 binary64) eps (neg.f64 x)))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 #s(approx (neg (sin x)) (neg.f64 x)) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (-.f64 #s(approx (cos eps) #s(literal 1 binary64)) #s(literal 1 binary64)))

Outputs
(.f64 #s(approx ( (sin (* 1/2 (+ (* 2 x) eps))) (sin (* 1/2 (+ 0 eps)))) (.f64 (sin.f64 (fma.f64 eps #s(literal 1/2 binary64) x)) (sin.f64 (.f64 eps #s(literal 1/2 binary64))))) #s(literal -2 binary64))
(.f64 #s(literal -2 binary64) #s(approx ( (sin (* 1/2 (+ (* 2 x) eps))) (sin (* 1/2 (+ 0 eps)))) (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (sin.f64 (fma.f64 eps #s(literal 1/2 binary64) x)))))
(.f64 (.f64 (sin.f64 #s(approx (* 1/2 (+ (* 2 x) eps)) (fma.f64 #s(literal 1/2 binary64) eps x))) #s(approx (sin (* 1/2 (+ 0 eps))) (.f64 (fma.f64 (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 (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)) (sin.f64 #s(approx (* 1/2 (+ (* 2 x) eps)) (fma.f64 #s(literal 1/2 binary64) eps x)))) #s(literal -2 binary64))
(.f64 (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps))) #s(approx (sin ( 1/2 (+ 0 eps))) (.f64 (fma.f64 (fma.f64 #s(literal 1/3840 binary64) (.f64 eps eps) #s(literal -1/48 binary64)) (*.f64 eps eps) #s(literal 1/2 binary64)) eps))) #s(literal -2 binary64))
(.f64 (.f64 #s(approx (sin (* 1/2 (+ 0 eps))) (.f64 (fma.f64 (fma.f64 #s(literal 1/3840 binary64) (.f64 eps eps) #s(literal -1/48 binary64)) (.f64 eps eps) #s(literal 1/2 binary64)) eps)) (sin.f64 (.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal 1/2 binary64)))) #s(literal -2 binary64))
(.f64 (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps))) #s(approx (sin ( 1/2 (+ 0 eps))) (.f64 (fma.f64 (.f64 eps eps) #s(literal -1/48 binary64) #s(literal 1/2 binary64)) eps))) #s(literal -2 binary64))
(.f64 (.f64 #s(approx (sin (* 1/2 (+ 0 eps))) (.f64 (fma.f64 (.f64 eps eps) #s(literal -1/48 binary64) #s(literal 1/2 binary64)) eps)) (sin.f64 (*.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal 1/2 binary64)))) #s(literal -2 binary64))
(.f64 (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps))) #s(approx (sin ( 1/2 (+ 0 eps))) (*.f64 eps #s(literal 1/2 binary64)))) #s(literal -2 binary64))
(.f64 (.f64 #s(approx (sin (* 1/2 (+ 0 eps))) (.f64 #s(literal 1/2 binary64) eps)) (sin.f64 (.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal 1/2 binary64)))) #s(literal -2 binary64))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 (fma.f64 #s(approx (+ ( (cos x) (+ (* (* eps eps) 1/24) -1/2)) (* (* 1/6 (sin x)) eps)) (fma.f64 (*.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64))) eps (neg.f64 (sin.f64 x))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (+ (* (+ (* (cos x) (+ (* (* eps eps) 1/24) -1/2)) (* (* 1/6 (sin x)) eps)) eps) (neg (sin x))) eps) (fma.f64 (fma.f64 (fma.f64 (.f64 (fma.f64 #s(literal -1/36 binary64) (.f64 eps eps) #s(literal 1/6 binary64)) x) eps (.f64 (.f64 (.f64 (fma.f64 (.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) eps) eps) #s(literal -1/2 binary64))) x (.f64 (fma.f64 (.f64 #s(literal 1/6 binary64) eps) eps #s(literal -1 binary64)) eps)) x (.f64 (.f64 (fma.f64 (*.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) eps) eps))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (+ ( (+ (* (cos x) (+ (* (* eps eps) 1/24) -1/2)) (* (* 1/6 (sin x)) eps)) eps) (neg (sin x))) (fma.f64 (fma.f64 (fma.f64 (.f64 (fma.f64 (.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) eps) #s(literal -1/2 binary64) (.f64 (fma.f64 #s(literal -1/36 binary64) (.f64 eps eps) #s(literal 1/6 binary64)) x)) x (fma.f64 (.f64 #s(literal 1/6 binary64) eps) eps #s(literal -1 binary64))) x (.f64 (fma.f64 (*.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) eps))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (+ ( (+ (* (cos x) (+ (* (* eps eps) 1/24) -1/2)) (* (* 1/6 (sin x)) eps)) eps) (neg (sin x))) #s(approx (+ (* (+ (* (* 1/6 eps) eps) -1) x) (* (+ (* (* eps eps) 1/24) -1/2) eps)) (fma.f64 (fma.f64 (*.f64 x eps) #s(literal 1/6 binary64) #s(literal -1/2 binary64)) eps (neg.f64 x)))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (+ ( (+ (* (cos x) (+ (* (* eps eps) 1/24) -1/2)) (* (* 1/6 (sin x)) eps)) eps) (neg (sin x))) #s(approx (+ (* (+ (* (* 1/6 eps) eps) -1) x) (* (+ (* (* eps eps) 1/24) -1/2) eps)) (fma.f64 #s(literal -1/2 binary64) eps (neg.f64 x)))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 #s(approx (neg (sin x)) (neg.f64 x)) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (-.f64 #s(approx (cos eps) #s(literal 1 binary64)) #s(literal 1 binary64)))

soundness1.2s (7.4%)

Memory

-29.3MiB live, 17.6MiB allocated

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	16
0	10	16
1	54	16
2	385	16
3	4790	16
0	8343	16
0	105	498
1	277	495
2	626	495
3	2434	494
0	8369	474
0	335	3170
1	1002	3025
2	2640	2989
3	6133	2989
0	8160	2793
0	485	7113
1	1509	6913
2	4486	6814
0	8613	6389
0	479	5739
1	1482	5387
2	4323	5298
0	8075	4902

Stop Event

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

Compiler

Compiled 424 to 268 computations (36.8% saved)

preprocess72.0ms (0.4%)

Memory: 22.9MiB live, 61.9MiB allocated
Compiler: Compiled 518 to 230 computations (55.6% saved)

end0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated

Iter	Nodes	Cost
0	18	41
1	38	37
2	81	35
3	151	35
4	277	35
5	374	35
6	460	35
7	498	35
8	550	35
9	566	35
10	574	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	110	7
8	159	7
9	175	7
10	183	7
0	183	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	110	18
8	159	18
9	175	18
10	183	18
0	183	18

Iter	Nodes	Cost
0	18	41
1	38	37
2	81	35
3	151	35
4	277	35
5	374	35
6	460	35
7	498	35
8	550	35
9	566	35
10	574	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	110	7
8	159	7
9	175	7
10	183	7
0	183	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	110	18
8	159	18
9	175	18
10	183	18
0	183	18

start0.0ms (0%)

analyze54.0ms (0.3%)

sample9.0s (55.5%)

explain334.0ms (2.1%)

preprocess31.0ms (0.2%)

eval0.0ms (0%)

prune0.0ms (0%)

simplify6.0ms (0%)

localize105.0ms (0.6%)

series5.0ms (0%)

simplify221.0ms (1.4%)

rewrite177.0ms (1.1%)

eval62.0ms (0.4%)

prune60.0ms (0.4%)

simplify576.0ms (3.5%)

localize275.0ms (1.7%)

series55.0ms (0.3%)

simplify183.0ms (1.1%)

rewrite227.0ms (1.4%)

eval93.0ms (0.6%)

prune115.0ms (0.7%)

simplify331.0ms (2%)

localize828.0ms (5.1%)

series63.0ms (0.4%)

simplify287.0ms (1.8%)

rewrite195.0ms (1.2%)

eval115.0ms (0.7%)

prune60.0ms (0.4%)

simplify137.0ms (0.8%)

localize410.0ms (2.5%)

series65.0ms (0.4%)

simplify178.0ms (1.1%)

rewrite160.0ms (1%)

eval135.0ms (0.8%)

prune52.0ms (0.3%)

regimes47.0ms (0.3%)

regimes36.0ms (0.2%)

regimes26.0ms (0.2%)

regimes25.0ms (0.2%)

regimes25.0ms (0.2%)

regimes22.0ms (0.1%)

regimes21.0ms (0.1%)

regimes16.0ms (0.1%)

regimes14.0ms (0.1%)

regimes8.0ms (0%)

regimes5.0ms (0%)

regimes4.0ms (0%)

simplify119.0ms (0.7%)

soundness1.2s (7.4%)

preprocess72.0ms (0.4%)

end0.0ms (0%)

Profiling

Iter	Nodes	Cost
0	18	41
1	38	37
2	81	35
3	151	35
4	277	35
5	374	35
6	460	35
7	498	35
8	550	35
9	566	35
10	574	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	110	7
8	159	7
9	175	7
10	183	7
0	183	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	110	18
8	159	18
9	175	18
10	183	18
0	183	18