Metrics for 2sin (example 3.3)

analyze40.0ms (0.3%)

Memory

28.1MiB live, 64.8MiB 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)

sample5.8s (40.1%)

Memory

-151.0MiB live, 6 608.1MiB allocated

Samples

2.9s	25 882×	0	invalid
613.0ms	2 761×	1	valid
585.0ms	5 495×	0	valid

Precisions

Click to see histograms. Total time spent on operations: 3.0s

const: 895.0ms (29.4% of total)

ival-sin: 549.0ms (18% of total)

ival-add: 293.0ms (9.6% of total)

ival-mult: 275.0ms (9% of total)

ival-<=: 222.0ms (7.3% of total)

ival-fabs: 204.0ms (6.7% of total)

ival-<: 176.0ms (5.8% of total)

ival-sub: 171.0ms (5.6% of total)

adjust: 105.0ms (3.4% of total)

ival-and: 102.0ms (3.3% of total)

exact: 42.0ms (1.4% of total)

ival-assert: 14.0ms (0.5% of total)

Bogosity

preprocess28.0ms (0.2%)

Memory

1.8MiB live, 48.1MiB allocated

Algorithm

1×	egg-herbie

Rules

102×	`sub-neg`
80×	`lower-fma.f64`
80×	`lower-fma.f32`
68×	`cancel-sign-sub-inv`
64×	`associate--r+`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	18	39
1	38	35
2	86	35
3	169	35
4	310	35
5	367	35
6	445	35
7	482	35
8	491	35
0	6	7
0	10	7
1	13	7
2	18	7
3	24	7
4	32	7
5	47	7
6	80	7
7	107	7
8	151	7
9	166	7
10	174	7
0	174	7

Stop Event

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

Calls

Call 1

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

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

explain82.0ms (0.6%)

Memory

2.5MiB live, 160.3MiB allocated

FPErrors

Click to see full error table

Ground Truth	Overpredictions	Example	Underpredictions	Example	Subexpression
224	6	(-2.882811203987059e-129 1.5955952455467284e-131)	4	(-1.076107965451668e-175 1.4867591914498493e-177)	`(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))`
3	0	-	0	-	`(sin.f64 (+.f64 x eps))`
0	0	-	0	-	`eps`
0	0	-	0	-	`(+.f64 x eps)`
0	0	-	0	-	`(sin.f64 x)`
0	0	-	0	-	`x`

Explanations

Click to see full explanations table

Operator	Subexpression	Explanation	Count
`-.f64`	`(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))`	cancellation	226	9
`sin.f64`	`(sin.f64 (+.f64 x eps))`	sensitivity	2	0
`sin.f64`	`(sin.f64 (+.f64 x eps))`	cancellation	1	0

Confusion

	Predicted +	Predicted -
+	223	5
-	6	22

Precision

0.9737991266375546

Recall

0.9780701754385965

Confusion?

	Predicted +	Predicted Maybe	Predicted -
+	223	5	0
-	6	4	18

Precision?

0.957983193277311

Recall?

1.0

Freqs

test

number	freq
0	27
1	229

Total Confusion?

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

Precision?

1.0

Recall?

1.0

Samples

18.0ms	342×	0	valid
17.0ms	170×	1	valid

Compiler

Compiled 58 to 28 computations (51.7% saved)

Precisions

Click to see histograms. Total time spent on operations: 20.0ms

ival-sin: 10.0ms (50% of total)

adjust: 3.0ms (15% of total)

ival-sub: 3.0ms (15% of total)

ival-add: 3.0ms (15% of total)

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

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

eval0.0ms (0%)

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

prune1.0ms (0%)

Memory

1.4MiB live, 1.4MiB allocated

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	62.4%	(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))

Compiler

Compiled 9 to 6 computations (33.3% saved)

simplify9.0ms (0.1%)

Memory

11.4MiB live, 11.4MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 4 expressions of interest:

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

Rules

80×	`lower-fma.f64`
80×	`lower-fma.f32`
48×	`lower-*.f64`
48×	`lower-*.f32`
36×	`lower-+.f32`

Iterations

Useful iterations: 0 (0.0ms)

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

Stop Event

1×	iter limit
1×	saturated
1×	iter limit

Calls

Call 1

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

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

localize50.0ms (0.3%)

Memory

-9.9MiB live, 29.0MiB allocated

Localize:

Found 4 expressions of interest:

New	Metric	Score	Program
✓	accuracy	100.0%	(+.f64 x eps)
✓	accuracy	100.0%	(sin.f64 x)
✓	accuracy	99.8%	(sin.f64 (+.f64 x eps))
✓	accuracy	62.6%	(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))

Samples

35.0ms	85×	1	valid
8.0ms	171×	0	valid

Compiler

Compiled 20 to 8 computations (60% saved)

Precisions

Click to see histograms. Total time spent on operations: 36.0ms

adjust: 28.0ms (78.6% of total)

ival-sin: 4.0ms (11.2% of total)

ival-add: 2.0ms (5.6% of total)

ival-sub: 1.0ms (2.8% of total)

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

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

series4.0ms (0%)

Memory

5.5MiB live, 5.5MiB allocated

Counts

4 → 84

Calls

Call 1

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

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

Calls

21 calls:

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

simplify345.0ms (2.4%)

Memory

-24.6MiB live, 491.9MiB allocated

Algorithm

1×	egg-herbie

Rules

16 678×	`lower-fma.f64`
16 678×	`lower-fma.f32`
4 132×	`lower-*.f64`
4 132×	`lower-*.f32`
2 614×	`lower-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	107	496
1	314	496
2	775	489
3	2836	489
4	6173	489
0	8126	458

Stop Event

1×	iter limit
1×	node limit

Counts

84 → 77

Calls

Call 1

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

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

rewrite432.0ms (3%)

Memory

13.2MiB live, 391.7MiB allocated

Algorithm

1×	batch-egg-rewrite

Rules

4 986×	`lower-fma.f64`
4 986×	`lower-fma.f32`
4 676×	`lower-*.f64`
4 676×	`lower-*.f32`
2 176×	`lower-/.f64`

Iterations

Useful iterations: 0 (0.0ms)

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

Stop Event

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

Counts

4 → 214

Calls

Call 1

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

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

eval69.0ms (0.5%)

Memory: 2.7MiB live, 44.4MiB allocated
Compiler: Compiled 7 823 to 844 computations (89.2% saved)

prune70.0ms (0.5%)

Memory

-10.0MiB live, 67.1MiB allocated

Pruning

12 alts after pruning (11 fresh and 1 done)

	Pruned	Kept	Total
New	280	11	291
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	280	12	292

Accuracy

100.0%

Counts

292 → 12

Alt Table

Click to see full alt table

Status	Accuracy	Program
	99.7%	(fma.f64 (sin.f64 eps) (cos.f64 x) (-.f64 (*.f64 (sin.f64 x) (cos.f64 eps)) (sin.f64 x)))
▶	7.2%	(/.f64 (/.f64 (-.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 (+.f64 x eps) #s(literal 2 binary64))) (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal -1/2 binary64) (cos.f64 (+.f64 x x)))))) #s(literal 2 binary64)) (.f64 (sin.f64 (.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64))) (cos.f64 (*.f64 (+.f64 eps #s(literal 0 binary64)) #s(literal 1/2 binary64)))))
	8.7%	(/.f64 (-.f64 (.f64 (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal -1/2 binary64) (cos.f64 (+.f64 x x)))) (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 #s(literal 2 binary64) eps))))) (pow.f64 (-.f64 (.f64 (cos.f64 x) (sin.f64 eps)) (sin.f64 x)) #s(literal 2 binary64))) (-.f64 (.f64 (sin.f64 x) (cos.f64 eps)) (-.f64 (*.f64 (cos.f64 x) (sin.f64 eps)) (sin.f64 x))))
	9.1%	(/.f64 (+.f64 (pow.f64 (.f64 (sin.f64 x) (cos.f64 eps)) #s(literal 3 binary64)) (pow.f64 (-.f64 (.f64 (cos.f64 x) (sin.f64 eps)) (sin.f64 x)) #s(literal 3 binary64))) (fma.f64 (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal -1/2 binary64) (cos.f64 (+.f64 x x)))) (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 #s(literal 2 binary64) eps)))) (-.f64 (pow.f64 (-.f64 (.f64 (cos.f64 x) (sin.f64 eps)) (sin.f64 x)) #s(literal 2 binary64)) (.f64 (.f64 (sin.f64 x) (cos.f64 eps)) (-.f64 (*.f64 (cos.f64 x) (sin.f64 eps)) (sin.f64 x))))))
	36.5%	(-.f64 (/.f64 (*.f64 (sin.f64 (+.f64 x eps)) (sin.f64 (-.f64 x eps))) (sin.f64 (-.f64 x eps))) (sin.f64 x))
✓	62.4%	(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
▶	61.0%	(-.f64 (sin.f64 (+.f64 x eps)) #s(approx (sin x) (fma.f64 #s(literal -1/6 binary64) (.f64 x (.f64 x x)) x)))
▶	99.8%	(.f64 (.f64 (sin.f64 (.f64 (+.f64 eps #s(literal 0 binary64)) #s(literal 1/2 binary64))) (cos.f64 (.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)))) #s(literal 2 binary64))
▶	61.2%	#s(approx (- (sin (+ x eps)) (sin x)) (-.f64 (fma.f64 (fma.f64 x (.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64)) (sin.f64 eps) (.f64 x (cos.f64 eps))) x))
	99.0%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 eps (fma.f64 eps (.f64 #s(literal -1/2 binary64) (sin.f64 x)) (cos.f64 x))))
	98.7%	#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 eps (cos.f64 x)))
▶	97.5%	#s(approx (- (sin (+ x eps)) (sin x)) (sin.f64 eps))

Compiler

Compiled 521 to 296 computations (43.2% saved)

simplify462.0ms (3.2%)

Memory

-7.9MiB live, 227.1MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 18 expressions of interest:

New	Metric	Score	Program
✓	cost-diff	192	(fma.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 (+.f64 x eps) #s(literal 2 binary64))) (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal -1/2 binary64) (cos.f64 (+.f64 x x)))))
✓	cost-diff	256	(-.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 (+.f64 x eps) #s(literal 2 binary64))) (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal -1/2 binary64) (cos.f64 (+.f64 x x))))))
✓	cost-diff	320	(*.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64))
✓	cost-diff	704	(/.f64 (-.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 (+.f64 x eps) #s(literal 2 binary64))) (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal -1/2 binary64) (cos.f64 (+.f64 x x)))))) #s(literal 2 binary64))
✓	cost-diff	0	(fma.f64 x (*.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64))
✓	cost-diff	0	(fma.f64 (fma.f64 x (.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64)) (sin.f64 eps) (.f64 x (cos.f64 eps)))
✓	cost-diff	0	(-.f64 (fma.f64 (fma.f64 x (.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64)) (sin.f64 eps) (.f64 x (cos.f64 eps))) x)
✓	cost-diff	0	#s(approx (- (sin (+ x eps)) (sin x)) (-.f64 (fma.f64 (fma.f64 x (.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64)) (sin.f64 eps) (.f64 x (cos.f64 eps))) x))
✓	cost-diff	0	#s(approx (sin x) (fma.f64 #s(literal -1/6 binary64) (.f64 x (.f64 x x)) x))
✓	cost-diff	0	(+.f64 x eps)
✓	cost-diff	0	(sin.f64 (+.f64 x eps))
✓	cost-diff	0	(-.f64 (sin.f64 (+.f64 x eps)) #s(approx (sin x) (fma.f64 #s(literal -1/6 binary64) (.f64 x (.f64 x x)) x)))
✓	cost-diff	0	(sin.f64 eps)
✓	cost-diff	0	#s(approx (- (sin (+ x eps)) (sin x)) (sin.f64 eps))
✓	cost-diff	0	(.f64 (sin.f64 (.f64 (+.f64 eps #s(literal 0 binary64)) #s(literal 1/2 binary64))) (cos.f64 (*.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64))))
✓	cost-diff	0	(.f64 (.f64 (sin.f64 (.f64 (+.f64 eps #s(literal 0 binary64)) #s(literal 1/2 binary64))) (cos.f64 (.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)))) #s(literal 2 binary64))
✓	cost-diff	192	(+.f64 eps #s(literal 0 binary64))
✓	cost-diff	320	(*.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64))

Rules

9 758×	`lower-fma.f32`
9 748×	`lower-fma.f64`
3 902×	`lower-*.f32`
3 880×	`lower-*.f64`
1 964×	`lower--.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	49	379
0	88	351
1	145	351
2	279	342
3	667	328
4	1955	323
5	7204	323
0	8191	310

Stop Event

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

Calls

Call 1

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

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

localize366.0ms (2.5%)

Memory

22.6MiB live, 537.8MiB allocated

Localize:

Found 18 expressions of interest:

New	Metric	Score	Program
✓	accuracy	99.8%	(sin.f64 (*.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)))
✓	accuracy	54.9%	(-.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 (+.f64 x eps) #s(literal 2 binary64))) (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal -1/2 binary64) (cos.f64 (+.f64 x x))))))
✓	accuracy	54.4%	(+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 (+.f64 x x))))
✓	accuracy	53.6%	(/.f64 (/.f64 (-.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 (+.f64 x eps) #s(literal 2 binary64))) (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal -1/2 binary64) (cos.f64 (+.f64 x x)))))) #s(literal 2 binary64)) (.f64 (sin.f64 (.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64))) (cos.f64 (*.f64 (+.f64 eps #s(literal 0 binary64)) #s(literal 1/2 binary64)))))
✓	accuracy	100.0%	(fma.f64 (fma.f64 x (.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64)) (sin.f64 eps) (.f64 x (cos.f64 eps)))
✓	accuracy	100.0%	(*.f64 x (cos.f64 eps))
✓	accuracy	97.6%	#s(approx (- (sin (+ x eps)) (sin x)) (-.f64 (fma.f64 (fma.f64 x (.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64)) (sin.f64 eps) (.f64 x (cos.f64 eps))) x))
✓	accuracy	62.6%	(-.f64 (fma.f64 (fma.f64 x (.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64)) (sin.f64 eps) (.f64 x (cos.f64 eps))) x)
✓	accuracy	99.9%	(.f64 x (.f64 x x))
✓	accuracy	99.8%	(sin.f64 (+.f64 x eps))
✓	accuracy	97.8%	#s(approx (sin x) (fma.f64 #s(literal -1/6 binary64) (.f64 x (.f64 x x)) x))
✓	accuracy	62.6%	(-.f64 (sin.f64 (+.f64 x eps)) #s(approx (sin x) (fma.f64 #s(literal -1/6 binary64) (.f64 x (.f64 x x)) x)))
✓	accuracy	100.0%	(sin.f64 eps)
✓	accuracy	97.5%	#s(approx (- (sin (+ x eps)) (sin x)) (sin.f64 eps))
✓	accuracy	100.0%	(.f64 (.f64 (sin.f64 (.f64 (+.f64 eps #s(literal 0 binary64)) #s(literal 1/2 binary64))) (cos.f64 (.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)))) #s(literal 2 binary64))
✓	accuracy	100.0%	(sin.f64 (*.f64 (+.f64 eps #s(literal 0 binary64)) #s(literal 1/2 binary64)))
✓	accuracy	100.0%	(.f64 (sin.f64 (.f64 (+.f64 eps #s(literal 0 binary64)) #s(literal 1/2 binary64))) (cos.f64 (*.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64))))
✓	accuracy	99.9%	(cos.f64 (*.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)))

Samples

167.0ms	146×	2	valid
67.0ms	35×	3	valid
52.0ms	70×	1	valid
2.0ms	5×	0	valid

Compiler

Compiled 364 to 50 computations (86.3% saved)

Precisions

Click to see histograms. Total time spent on operations: 232.0ms

ival-cos: 97.0ms (41.8% of total)

adjust: 54.0ms (23.3% of total)

ival-mult: 31.0ms (13.4% of total)

ival-add: 16.0ms (6.9% of total)

ival-sin: 13.0ms (5.6% of total)

ival-div: 9.0ms (3.9% of total)

ival-sub: 8.0ms (3.4% of total)

const: 4.0ms (1.7% of total)

exact: 1.0ms (0.4% of total)

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

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

series58.0ms (0.4%)

Memory

12.3MiB live, 50.1MiB allocated

Counts

24 → 492

Calls

Call 1

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

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

Calls

123 calls:

Time	Variable		Point	Expression
6.0ms	x	@	inf	(- (+ (* (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) x)
3.0ms	x	@	inf	(/ (- 1/2 (+ (* 1/2 (cos (* (+ x eps) 2))) (+ 1/2 (* -1/2 (cos (+ x x)))))) 2)
2.0ms	x	@	0	(/ (/ (- 1/2 (+ (* 1/2 (cos (* (+ x eps) 2))) (+ 1/2 (* -1/2 (cos (+ x x)))))) 2) (* (sin (* (+ (* x 2) eps) 1/2)) (cos (* (+ eps 0) 1/2))))
2.0ms	x	@	inf	(/ (/ (- 1/2 (+ (* 1/2 (cos (* (+ x eps) 2))) (+ 1/2 (* -1/2 (cos (+ x x)))))) 2) (* (sin (* (+ (* x 2) eps) 1/2)) (cos (* (+ eps 0) 1/2))))
1.0ms	eps	@	0	(/ (/ (- 1/2 (+ (* 1/2 (cos (* (+ x eps) 2))) (+ 1/2 (* -1/2 (cos (+ x x)))))) 2) (* (sin (* (+ (* x 2) eps) 1/2)) (cos (* (+ eps 0) 1/2))))

simplify342.0ms (2.4%)

Memory

-30.3MiB live, 482.2MiB allocated

Algorithm

1×	egg-herbie

Rules

11 892×	`lower-fma.f64`
11 892×	`lower-fma.f32`
5 916×	`lower-*.f64`
5 916×	`lower-*.f32`
3 278×	`lower-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	629	6443
1	2043	5926
2	6093	5775
0	8199	5322

Stop Event

1×	iter limit
1×	node limit

Counts

492 → 467

Calls

Call 1

Inputs
(* 1/2 eps)
(+ x (* 1/2 eps))
(+ x (* 1/2 eps))
(+ x (* 1/2 eps))
x
(* x (+ 1 (* 1/2 (/ eps x))))
(* x (+ 1 (* 1/2 (/ eps x))))
(* x (+ 1 (* 1/2 (/ eps x))))
x
(* -1 (* x (- (* -1/2 (/ eps x)) 1)))
(* -1 (* x (- (* -1/2 (/ eps x)) 1)))
(* -1 (* x (- (* -1/2 (/ eps x)) 1)))
x
(+ x (* 1/2 eps))
(+ x (* 1/2 eps))
(+ x (* 1/2 eps))
(* 1/2 eps)
(* eps (+ 1/2 (/ x eps)))
(* eps (+ 1/2 (/ x eps)))
(* eps (+ 1/2 (/ x 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
eps
eps
eps
eps
eps
eps
eps
eps
(* eps (cos x))
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* 2 (* eps (+ (* -1/16 (cos x)) (* -1/48 (cos x)))))))))
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* eps (+ (* 1/24 (* eps (sin x))) (* 2 (+ (* -1/16 (cos x)) (* -1/48 (cos x))))))))))
(* 2 (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))))
(* 2 (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))))
(* 2 (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))))
(* 2 (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))))
(* 2 (* (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps))))
(* 2 (* (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps))))
(* 2 (* (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps))))
(* 2 (* (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps))))
(* 2 (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))
(+ (* -2 (* x (pow (sin (* 1/2 eps)) 2))) (* 2 (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))))
(+ (* 2 (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) (* x (+ (* -2 (pow (sin (* 1/2 eps)) 2)) (* -1 (* x (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))))))
(+ (* 2 (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) (* x (+ (* -2 (pow (sin (* 1/2 eps)) 2)) (* x (+ (* -1 (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) (* 1/3 (* x (pow (sin (* 1/2 eps)) 2))))))))
(* 2 (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))))
(* 2 (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))))
(* 2 (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))))
(* 2 (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))))
(* 2 (* (cos (* 1/2 (- eps (* -2 x)))) (sin (* 1/2 eps))))
(* 2 (* (cos (* 1/2 (- eps (* -2 x)))) (sin (* 1/2 eps))))
(* 2 (* (cos (* 1/2 (- eps (* -2 x)))) (sin (* 1/2 eps))))
(* 2 (* (cos (* 1/2 (- eps (* -2 x)))) (sin (* 1/2 eps))))
(* 1/2 (* eps (cos x)))
(* eps (+ (* -1/4 (* eps (sin x))) (* 1/2 (cos x))))
(* eps (+ (* 1/2 (cos x)) (* eps (+ (* -1/4 (sin x)) (* eps (+ (* -1/16 (cos x)) (* -1/48 (cos x))))))))
(* eps (+ (* 1/2 (cos x)) (* eps (+ (* -1/4 (sin x)) (* eps (+ (* -1/16 (cos x)) (+ (* -1/48 (cos x)) (* 1/48 (* eps (sin x))))))))))
(* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps)))
(* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps)))
(* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps)))
(* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps)))
(* (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps)))
(* (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps)))
(* (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps)))
(* (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps)))
(* (cos (* 1/2 eps)) (sin (* 1/2 eps)))
(+ (* -1 (* x (pow (sin (* 1/2 eps)) 2))) (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))
(+ (* x (+ (* -1 (pow (sin (* 1/2 eps)) 2)) (* -1/2 (* x (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))))) (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))
(+ (* x (+ (* -1 (pow (sin (* 1/2 eps)) 2)) (* x (+ (* -1/2 (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) (* 1/6 (* x (pow (sin (* 1/2 eps)) 2))))))) (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))
(* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps)))
(* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps)))
(* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps)))
(* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps)))
(* (cos (* 1/2 (- eps (* -2 x)))) (sin (* 1/2 eps)))
(* (cos (* 1/2 (- eps (* -2 x)))) (sin (* 1/2 eps)))
(* (cos (* 1/2 (- eps (* -2 x)))) (sin (* 1/2 eps)))
(* (cos (* 1/2 (- eps (* -2 x)))) (sin (* 1/2 eps)))
(sin eps)
(+ (sin eps) (* x (- (cos eps) 1)))
(+ (sin eps) (* x (- (+ (cos eps) (* -1/2 (* x (sin eps)))) 1)))
(+ (sin eps) (* x (- (+ (cos eps) (* x (+ (* -1/2 (sin eps)) (* x (+ 1/6 (* -1/6 (cos eps))))))) 1)))
(- (sin (+ eps x)) (sin x))
(- (sin (+ eps x)) (sin x))
(- (sin (+ eps x)) (sin x))
(- (sin (+ eps x)) (sin x))
(- (sin (- eps (* -1 x))) (sin x))
(- (sin (- eps (* -1 x))) (sin x))
(- (sin (- eps (* -1 x))) (sin x))
(- (sin (- eps (* -1 x))) (sin x))
(* eps (cos x))
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x)))))))
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* eps (+ (* -1/6 (cos x)) (* 1/24 (* eps (sin x)))))))))
(- (sin (+ eps x)) (sin x))
(- (sin (+ eps x)) (sin x))
(- (sin (+ eps x)) (sin x))
(- (sin (+ eps x)) (sin x))
(- (sin (- x (* -1 eps))) (sin x))
(- (sin (- x (* -1 eps))) (sin x))
(- (sin (- x (* -1 eps))) (sin x))
(- (sin (- x (* -1 eps))) (sin x))
eps
(* eps (+ 1 (* -1/6 (pow eps 2))))
(* eps (+ 1 (* (pow eps 2) (- (* 1/120 (pow eps 2)) 1/6))))
(* eps (+ 1 (* (pow eps 2) (- (* (pow eps 2) (+ 1/120 (* -1/5040 (pow eps 2)))) 1/6))))
(sin eps)
(sin eps)
(sin eps)
(sin eps)
(sin eps)
(sin eps)
(sin eps)
(sin eps)
(sin eps)
(+ (sin eps) (* x (- (cos eps) 1)))
(+ (sin eps) (* x (- (+ (cos eps) (* -1/2 (* x (sin eps)))) 1)))
(+ (sin eps) (* x (- (+ (cos eps) (* x (+ (* -1/2 (sin eps)) (* x (+ 1/6 (* -1/6 (cos eps))))))) 1)))
(- (sin (+ eps x)) (sin x))
(- (sin (+ eps x)) (sin x))
(- (sin (+ eps x)) (sin x))
(- (sin (+ eps x)) (sin x))
(- (sin (- eps (* -1 x))) (sin x))
(- (sin (- eps (* -1 x))) (sin x))
(- (sin (- eps (* -1 x))) (sin x))
(- (sin (- eps (* -1 x))) (sin x))
(* eps (cos x))
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x)))))))
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* eps (+ (* -1/6 (cos x)) (* 1/24 (* eps (sin x)))))))))
(- (sin (+ eps x)) (sin x))
(- (sin (+ eps x)) (sin x))
(- (sin (+ eps x)) (sin x))
(- (sin (+ eps x)) (sin x))
(- (sin (- x (* -1 eps))) (sin x))
(- (sin (- x (* -1 eps))) (sin x))
(- (sin (- x (* -1 eps))) (sin x))
(- (sin (- x (* -1 eps))) (sin x))
(sin eps)
(+ (sin eps) (* x (cos eps)))
(+ (sin eps) (* x (+ (cos eps) (* -1/2 (* x (sin eps))))))
(+ (sin eps) (* x (+ (cos eps) (* x (+ (* -1/2 (sin eps)) (* -1/6 (* x (cos eps))))))))
(sin (+ eps x))
(sin (+ eps x))
(sin (+ eps x))
(sin (+ eps x))
(sin (- eps (* -1 x)))
(sin (- eps (* -1 x)))
(sin (- eps (* -1 x)))
(sin (- eps (* -1 x)))
(sin x)
(+ (sin x) (* eps (cos x)))
(+ (sin x) (* eps (+ (cos x) (* -1/2 (* eps (sin x))))))
(+ (sin x) (* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x))))))))
(sin (+ eps x))
(sin (+ eps x))
(sin (+ eps x))
(sin (+ eps x))
(sin (- x (* -1 eps)))
(sin (- x (* -1 eps)))
(sin (- x (* -1 eps)))
(sin (- x (* -1 eps)))
eps
(+ eps x)
(+ eps x)
(+ eps x)
x
(* x (+ 1 (/ eps x)))
(* x (+ 1 (/ eps x)))
(* x (+ 1 (/ eps x)))
x
(* -1 (* x (- (* -1 (/ eps x)) 1)))
(* -1 (* x (- (* -1 (/ eps x)) 1)))
(* -1 (* x (- (* -1 (/ eps x)) 1)))
x
(+ eps x)
(+ eps x)
(+ eps x)
eps
(* eps (+ 1 (/ x eps)))
(* eps (+ 1 (/ x eps)))
(* eps (+ 1 (/ x eps)))
eps
(* -1 (* eps (- (* -1 (/ x eps)) 1)))
(* -1 (* eps (- (* -1 (/ x eps)) 1)))
(* -1 (* eps (- (* -1 (/ x eps)) 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))))
(sin x)
(sin x)
(sin x)
(sin x)
(sin x)
(sin x)
(sin x)
(sin x)
(sin eps)
(+ (sin eps) (* x (- (cos eps) 1)))
(+ (sin eps) (* x (- (+ (cos eps) (* -1/2 (* x (sin eps)))) 1)))
(+ (sin eps) (* x (- (+ (cos eps) (* x (+ (* -1/2 (sin eps)) (* x (+ 1/6 (* -1/6 (cos eps))))))) 1)))
(- (sin (+ eps x)) (sin x))
(- (sin (+ eps x)) (sin x))
(- (sin (+ eps x)) (sin x))
(- (sin (+ eps x)) (sin x))
(- (sin (- eps (* -1 x))) (sin x))
(- (sin (- eps (* -1 x))) (sin x))
(- (sin (- eps (* -1 x))) (sin x))
(- (sin (- eps (* -1 x))) (sin x))
(* eps (cos x))
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x)))))))
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* eps (+ (* -1/6 (cos x)) (* 1/24 (* eps (sin x)))))))))
(- (sin (+ eps x)) (sin x))
(- (sin (+ eps x)) (sin x))
(- (sin (+ eps x)) (sin x))
(- (sin (+ eps x)) (sin x))
(- (sin (- x (* -1 eps))) (sin x))
(- (sin (- x (* -1 eps))) (sin x))
(- (sin (- x (* -1 eps))) (sin x))
(- (sin (- x (* -1 eps))) (sin x))
(sin eps)
(+ (sin eps) (* x (- (cos eps) 1)))
(+ (sin eps) (* x (- (+ (cos eps) (* -1/2 (* x (sin eps)))) 1)))
(+ (sin eps) (* x (- (+ (cos eps) (* -1/2 (* x (sin eps)))) 1)))
(* -1/2 (* (pow x 2) (sin eps)))
(* (pow x 2) (- (+ (* -1/2 (sin eps)) (/ (cos eps) x)) (/ 1 x)))
(* (pow x 2) (- (+ (* -1/2 (sin eps)) (+ (/ (cos eps) x) (/ (sin eps) (pow x 2)))) (/ 1 x)))
(* (pow x 2) (- (+ (* -1/2 (sin eps)) (+ (/ (cos eps) x) (/ (sin eps) (pow x 2)))) (/ 1 x)))
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(* -1/2 (/ (+ (* -1/2 (cos (* 2 x))) (* 1/2 (cos (* 2 (+ eps x))))) (* (cos (* 1/2 eps)) (sin (* 1/2 (+ eps (* 2 x)))))))
(* -1/2 (/ (+ (* -1/2 (cos (* 2 x))) (* 1/2 (cos (* 2 (- x (* -1 eps)))))) (* (cos (* 1/2 eps)) (sin (* 1/2 (- (* 2 x) (* -1 eps)))))))
(* -1/2 (/ (+ (* -1/2 (cos (* 2 x))) (* 1/2 (cos (* 2 (- x (* -1 eps)))))) (* (cos (* 1/2 eps)) (sin (* 1/2 (- (* 2 x) (* -1 eps)))))))
(* -1/2 (/ (+ (* -1/2 (cos (* 2 x))) (* 1/2 (cos (* 2 (- x (* -1 eps)))))) (* (cos (* 1/2 eps)) (sin (* 1/2 (- (* 2 x) (* -1 eps)))))))
(* -1/2 (/ (+ (* -1/2 (cos (* 2 x))) (* 1/2 (cos (* 2 (- x (* -1 eps)))))) (* (cos (* 1/2 eps)) (sin (* 1/2 (- (* 2 x) (* -1 eps)))))))
(pow x 2)
(* (pow x 2) (+ 1 (* -1/3 (pow x 2))))
(* (pow x 2) (+ 1 (* (pow x 2) (- (* 2/45 (pow x 2)) 1/3))))
(* (pow x 2) (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 2/45 (* -1/315 (pow x 2)))) 1/3))))
(+ 1/2 (* -1/2 (cos (* 2 x))))
(+ 1/2 (* -1/2 (cos (* 2 x))))
(+ 1/2 (* -1/2 (cos (* 2 x))))
(+ 1/2 (* -1/2 (cos (* 2 x))))
(+ 1/2 (* -1/2 (cos (neg (* -2 x)))))
(+ 1/2 (* -1/2 (cos (neg (* -2 x)))))
(+ 1/2 (* -1/2 (cos (neg (* -2 x)))))
(+ 1/2 (* -1/2 (cos (neg (* -2 x)))))
(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)))))))))
(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))))
(sin (* 1/2 (- eps (* -2 x))))
(sin (* 1/2 (- eps (* -2 x))))
(sin (* 1/2 (- eps (* -2 x))))
(sin x)
(+ (sin x) (* 1/2 (* eps (cos x))))
(+ (sin x) (* eps (+ (* -1/8 (* eps (sin x))) (* 1/2 (cos x)))))
(+ (sin x) (* eps (+ (* 1/2 (cos x)) (* eps (+ (* -1/8 (sin x)) (* -1/48 (* eps (cos x))))))))
(sin (* 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 (- (* 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))))

Outputs
(* 1/2 eps)
(*.f64 #s(literal 1/2 binary64) eps)
(+ 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)
x
(* x (+ 1 (* 1/2 (/ eps x))))
(fma.f64 #s(literal 1/2 binary64) (/.f64 (*.f64 eps x) x) x)
(* x (+ 1 (* 1/2 (/ eps x))))
(fma.f64 #s(literal 1/2 binary64) (/.f64 (*.f64 eps x) x) x)
(* x (+ 1 (* 1/2 (/ eps x))))
(fma.f64 #s(literal 1/2 binary64) (/.f64 (*.f64 eps x) x) x)
x
(* -1 (* x (- (* -1/2 (/ eps x)) 1)))
(fma.f64 (/.f64 (*.f64 #s(literal -1/2 binary64) eps) x) (neg.f64 x) x)
(* -1 (* x (- (* -1/2 (/ eps x)) 1)))
(fma.f64 (/.f64 (*.f64 #s(literal -1/2 binary64) eps) x) (neg.f64 x) x)
(* -1 (* x (- (* -1/2 (/ eps x)) 1)))
(fma.f64 (/.f64 (*.f64 #s(literal -1/2 binary64) eps) x) (neg.f64 x) 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)
(* 1/2 eps)
(*.f64 #s(literal 1/2 binary64) eps)
(* eps (+ 1/2 (/ x eps)))
(*.f64 eps (+.f64 #s(literal 1/2 binary64) (/.f64 x eps)))
(* eps (+ 1/2 (/ x eps)))
(*.f64 eps (+.f64 #s(literal 1/2 binary64) (/.f64 x eps)))
(* eps (+ 1/2 (/ x eps)))
(*.f64 eps (+.f64 #s(literal 1/2 binary64) (/.f64 x eps)))
(* 1/2 eps)
(*.f64 #s(literal 1/2 binary64) eps)
(* -1 (* eps (- (* -1 (/ x eps)) 1/2)))
(*.f64 (-.f64 #s(literal -1/2 binary64) (/.f64 x eps)) (neg.f64 eps))
(* -1 (* eps (- (* -1 (/ x eps)) 1/2)))
(*.f64 (-.f64 #s(literal -1/2 binary64) (/.f64 x eps)) (neg.f64 eps))
(* -1 (* eps (- (* -1 (/ x eps)) 1/2)))
(*.f64 (-.f64 #s(literal -1/2 binary64) (/.f64 x eps)) (neg.f64 eps))
eps
eps
eps
eps
eps
eps
eps
eps
eps
eps
eps
eps
(* eps (cos x))
(*.f64 eps (cos.f64 x))
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(.f64 eps (fma.f64 #s(literal -1/2 binary64) (.f64 eps (sin.f64 x)) (cos.f64 x)))
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* 2 (* eps (+ (* -1/16 (cos x)) (* -1/48 (cos x)))))))))
(.f64 eps (fma.f64 eps (fma.f64 eps (.f64 (cos.f64 x) #s(literal -1/6 binary64)) (*.f64 #s(literal -1/2 binary64) (sin.f64 x))) (cos.f64 x)))
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* eps (+ (* 1/24 (* eps (sin x))) (* 2 (+ (* -1/16 (cos x)) (* -1/48 (cos x))))))))))
(.f64 eps (fma.f64 eps (fma.f64 eps (fma.f64 eps (.f64 (sin.f64 x) #s(literal 1/24 binary64)) (.f64 (cos.f64 x) #s(literal -1/6 binary64))) (.f64 #s(literal -1/2 binary64) (sin.f64 x))) (cos.f64 x)))
(* 2 (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))))
(.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (*.f64 (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) #s(literal 2 binary64)))
(* 2 (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))))
(.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (*.f64 (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) #s(literal 2 binary64)))
(* 2 (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))))
(.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (*.f64 (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) #s(literal 2 binary64)))
(* 2 (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))))
(.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (*.f64 (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) #s(literal 2 binary64)))
(* 2 (* (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps))))
(.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (*.f64 (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) #s(literal 2 binary64)))
(* 2 (* (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps))))
(.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (*.f64 (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) #s(literal 2 binary64)))
(* 2 (* (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps))))
(.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (*.f64 (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) #s(literal 2 binary64)))
(* 2 (* (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps))))
(.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (*.f64 (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) #s(literal 2 binary64)))
(* 2 (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))
(.f64 #s(literal 2 binary64) (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (cos.f64 (.f64 #s(literal 1/2 binary64) eps))))
(+ (* -2 (* x (pow (sin (* 1/2 eps)) 2))) (* 2 (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))))
(fma.f64 x (.f64 #s(literal -2 binary64) (pow.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) #s(literal 2 binary64))) (.f64 #s(literal 2 binary64) (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (cos.f64 (.f64 #s(literal 1/2 binary64) eps)))))
(+ (* 2 (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) (* x (+ (* -2 (pow (sin (* 1/2 eps)) 2)) (* -1 (* x (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))))))
(fma.f64 x (-.f64 (.f64 #s(literal -2 binary64) (pow.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) #s(literal 2 binary64))) (.f64 x (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (cos.f64 (.f64 #s(literal 1/2 binary64) eps))))) (.f64 #s(literal 2 binary64) (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (cos.f64 (.f64 #s(literal 1/2 binary64) eps)))))
(+ (* 2 (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) (* x (+ (* -2 (pow (sin (* 1/2 eps)) 2)) (* x (+ (* -1 (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) (* 1/3 (* x (pow (sin (* 1/2 eps)) 2))))))))
(fma.f64 x (fma.f64 x (fma.f64 (pow.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) #s(literal 2 binary64)) (.f64 x #s(literal 1/3 binary64)) (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (neg.f64 (cos.f64 (.f64 #s(literal 1/2 binary64) eps))))) (.f64 #s(literal -2 binary64) (pow.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) #s(literal 2 binary64)))) (.f64 #s(literal 2 binary64) (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (cos.f64 (*.f64 #s(literal 1/2 binary64) eps)))))
(* 2 (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))))
(.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (*.f64 (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) #s(literal 2 binary64)))
(* 2 (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))))
(.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (*.f64 (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) #s(literal 2 binary64)))
(* 2 (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))))
(.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (*.f64 (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) #s(literal 2 binary64)))
(* 2 (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))))
(.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (*.f64 (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) #s(literal 2 binary64)))
(* 2 (* (cos (* 1/2 (- eps (* -2 x)))) (sin (* 1/2 eps))))
(.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (*.f64 (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) #s(literal 2 binary64)))
(* 2 (* (cos (* 1/2 (- eps (* -2 x)))) (sin (* 1/2 eps))))
(.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (*.f64 (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) #s(literal 2 binary64)))
(* 2 (* (cos (* 1/2 (- eps (* -2 x)))) (sin (* 1/2 eps))))
(.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (*.f64 (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) #s(literal 2 binary64)))
(* 2 (* (cos (* 1/2 (- eps (* -2 x)))) (sin (* 1/2 eps))))
(.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (*.f64 (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) #s(literal 2 binary64)))
(* 1/2 (* eps (cos x)))
(.f64 eps (.f64 #s(literal 1/2 binary64) (cos.f64 x)))
(* eps (+ (* -1/4 (* eps (sin x))) (* 1/2 (cos x))))
(.f64 eps (fma.f64 #s(literal 1/2 binary64) (cos.f64 x) (.f64 (*.f64 eps (sin.f64 x)) #s(literal -1/4 binary64))))
(* eps (+ (* 1/2 (cos x)) (* eps (+ (* -1/4 (sin x)) (* eps (+ (* -1/16 (cos x)) (* -1/48 (cos x))))))))
(.f64 eps (fma.f64 #s(literal 1/2 binary64) (cos.f64 x) (.f64 eps (fma.f64 eps (.f64 (cos.f64 x) #s(literal -1/12 binary64)) (.f64 (sin.f64 x) #s(literal -1/4 binary64))))))
(* eps (+ (* 1/2 (cos x)) (* eps (+ (* -1/4 (sin x)) (* eps (+ (* -1/16 (cos x)) (+ (* -1/48 (cos x)) (* 1/48 (* eps (sin x))))))))))
(.f64 eps (fma.f64 eps (fma.f64 eps (fma.f64 (.f64 eps (sin.f64 x)) #s(literal 1/48 binary64) (.f64 (cos.f64 x) #s(literal -1/12 binary64))) (.f64 (sin.f64 x) #s(literal -1/4 binary64))) (*.f64 #s(literal 1/2 binary64) (cos.f64 x))))
(* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps)))
(.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)))
(* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps)))
(.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)))
(* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps)))
(.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)))
(* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps)))
(.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)))
(* (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps)))
(.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)))
(* (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps)))
(.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)))
(* (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps)))
(.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)))
(* (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps)))
(.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)))
(* (cos (* 1/2 eps)) (sin (* 1/2 eps)))
(.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (cos.f64 (*.f64 #s(literal 1/2 binary64) eps)))
(+ (* -1 (* x (pow (sin (* 1/2 eps)) 2))) (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))
(-.f64 (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (cos.f64 (.f64 #s(literal 1/2 binary64) eps))) (.f64 x (pow.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) #s(literal 2 binary64))))
(+ (* x (+ (* -1 (pow (sin (* 1/2 eps)) 2)) (* -1/2 (* x (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))))) (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))
(fma.f64 x (-.f64 (.f64 (.f64 (cos.f64 (.f64 #s(literal 1/2 binary64) eps)) (.f64 x #s(literal -1/2 binary64))) (sin.f64 (.f64 #s(literal 1/2 binary64) eps))) (pow.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) #s(literal 2 binary64))) (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (cos.f64 (*.f64 #s(literal 1/2 binary64) eps))))
(+ (* x (+ (* -1 (pow (sin (* 1/2 eps)) 2)) (* x (+ (* -1/2 (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) (* 1/6 (* x (pow (sin (* 1/2 eps)) 2))))))) (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))
(fma.f64 x (fma.f64 x (fma.f64 x (.f64 (pow.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) #s(literal 2 binary64)) #s(literal 1/6 binary64)) (.f64 #s(literal -1/2 binary64) (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (cos.f64 (.f64 #s(literal 1/2 binary64) eps))))) (neg.f64 (pow.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) #s(literal 2 binary64)))) (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (cos.f64 (.f64 #s(literal 1/2 binary64) eps))))
(* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps)))
(.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)))
(* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps)))
(.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)))
(* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps)))
(.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)))
(* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps)))
(.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)))
(* (cos (* 1/2 (- eps (* -2 x)))) (sin (* 1/2 eps)))
(.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)))
(* (cos (* 1/2 (- eps (* -2 x)))) (sin (* 1/2 eps)))
(.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)))
(* (cos (* 1/2 (- eps (* -2 x)))) (sin (* 1/2 eps)))
(.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)))
(* (cos (* 1/2 (- eps (* -2 x)))) (sin (* 1/2 eps)))
(.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)))
(sin eps)
(sin.f64 eps)
(+ (sin eps) (* x (- (cos eps) 1)))
(fma.f64 x (+.f64 #s(literal -1 binary64) (cos.f64 eps)) (sin.f64 eps))
(+ (sin eps) (* x (- (+ (cos eps) (* -1/2 (* x (sin eps)))) 1)))
(fma.f64 x (fma.f64 x (*.f64 #s(literal -1/2 binary64) (sin.f64 eps)) (+.f64 #s(literal -1 binary64) (cos.f64 eps))) (sin.f64 eps))
(+ (sin eps) (* x (- (+ (cos eps) (* x (+ (* -1/2 (sin eps)) (* x (+ 1/6 (* -1/6 (cos eps))))))) 1)))
(fma.f64 x (+.f64 (cos.f64 eps) (fma.f64 x (fma.f64 x (fma.f64 (cos.f64 eps) #s(literal -1/6 binary64) #s(literal 1/6 binary64)) (*.f64 #s(literal -1/2 binary64) (sin.f64 eps))) #s(literal -1 binary64))) (sin.f64 eps))
(- (sin (+ eps x)) (sin x))
(-.f64 (sin.f64 (+.f64 eps x)) (sin.f64 x))
(- (sin (+ eps x)) (sin x))
(-.f64 (sin.f64 (+.f64 eps x)) (sin.f64 x))
(- (sin (+ eps x)) (sin x))
(-.f64 (sin.f64 (+.f64 eps x)) (sin.f64 x))
(- (sin (+ eps x)) (sin x))
(-.f64 (sin.f64 (+.f64 eps x)) (sin.f64 x))
(- (sin (- eps (* -1 x))) (sin x))
(-.f64 (sin.f64 (+.f64 eps x)) (sin.f64 x))
(- (sin (- eps (* -1 x))) (sin x))
(-.f64 (sin.f64 (+.f64 eps x)) (sin.f64 x))
(- (sin (- eps (* -1 x))) (sin x))
(-.f64 (sin.f64 (+.f64 eps x)) (sin.f64 x))
(- (sin (- eps (* -1 x))) (sin x))
(-.f64 (sin.f64 (+.f64 eps x)) (sin.f64 x))
(* eps (cos x))
(*.f64 eps (cos.f64 x))
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(.f64 eps (fma.f64 #s(literal -1/2 binary64) (.f64 eps (sin.f64 x)) (cos.f64 x)))
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x)))))))
(.f64 eps (fma.f64 eps (fma.f64 eps (.f64 (cos.f64 x) #s(literal -1/6 binary64)) (*.f64 #s(literal -1/2 binary64) (sin.f64 x))) (cos.f64 x)))
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* eps (+ (* -1/6 (cos x)) (* 1/24 (* eps (sin x)))))))))
(.f64 eps (fma.f64 eps (fma.f64 eps (fma.f64 eps (.f64 (sin.f64 x) #s(literal 1/24 binary64)) (.f64 (cos.f64 x) #s(literal -1/6 binary64))) (.f64 #s(literal -1/2 binary64) (sin.f64 x))) (cos.f64 x)))
(- (sin (+ eps x)) (sin x))
(-.f64 (sin.f64 (+.f64 eps x)) (sin.f64 x))
(- (sin (+ eps x)) (sin x))
(-.f64 (sin.f64 (+.f64 eps x)) (sin.f64 x))
(- (sin (+ eps x)) (sin x))
(-.f64 (sin.f64 (+.f64 eps x)) (sin.f64 x))
(- (sin (+ eps x)) (sin x))
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(.f64 (.f64 x x) (fma.f64 (.f64 x x) (fma.f64 (.f64 x x) (fma.f64 (*.f64 x x) #s(literal -1/315 binary64) #s(literal 2/45 binary64)) #s(literal -1/3 binary64)) #s(literal 1 binary64)))
(+ 1/2 (* -1/2 (cos (* 2 x))))
(fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 x #s(literal 2 binary64))) #s(literal 1/2 binary64))
(+ 1/2 (* -1/2 (cos (* 2 x))))
(fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 x #s(literal 2 binary64))) #s(literal 1/2 binary64))
(+ 1/2 (* -1/2 (cos (* 2 x))))
(fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 x #s(literal 2 binary64))) #s(literal 1/2 binary64))
(+ 1/2 (* -1/2 (cos (* 2 x))))
(fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 x #s(literal 2 binary64))) #s(literal 1/2 binary64))
(+ 1/2 (* -1/2 (cos (neg (* -2 x)))))
(fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 x #s(literal 2 binary64))) #s(literal 1/2 binary64))
(+ 1/2 (* -1/2 (cos (neg (* -2 x)))))
(fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 x #s(literal 2 binary64))) #s(literal 1/2 binary64))
(+ 1/2 (* -1/2 (cos (neg (* -2 x)))))
(fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 x #s(literal 2 binary64))) #s(literal 1/2 binary64))
(+ 1/2 (* -1/2 (cos (neg (* -2 x)))))
(fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 x #s(literal 2 binary64))) #s(literal 1/2 binary64))
(sin (* 1/2 eps))
(sin.f64 (*.f64 #s(literal 1/2 binary64) eps))
(+ (sin (* 1/2 eps)) (* x (cos (* 1/2 eps))))
(fma.f64 x (cos.f64 (.f64 #s(literal 1/2 binary64) eps)) (sin.f64 (.f64 #s(literal 1/2 binary64) eps)))
(+ (sin (* 1/2 eps)) (* x (+ (cos (* 1/2 eps)) (* -1/2 (* x (sin (* 1/2 eps)))))))
(fma.f64 x (fma.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (.f64 x #s(literal -1/2 binary64)) (cos.f64 (.f64 #s(literal 1/2 binary64) eps))) (sin.f64 (.f64 #s(literal 1/2 binary64) eps)))
(+ (sin (* 1/2 eps)) (* x (+ (cos (* 1/2 eps)) (* x (+ (* -1/2 (sin (* 1/2 eps))) (* -1/6 (* x (cos (* 1/2 eps)))))))))
(fma.f64 x (fma.f64 x (fma.f64 #s(literal -1/2 binary64) (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (.f64 (cos.f64 (.f64 #s(literal 1/2 binary64) eps)) (.f64 x #s(literal -1/6 binary64)))) (cos.f64 (.f64 #s(literal 1/2 binary64) eps))) (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))
(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))
(sin x)
(sin.f64 x)
(+ (sin x) (* 1/2 (* eps (cos x))))
(fma.f64 #s(literal 1/2 binary64) (*.f64 eps (cos.f64 x)) (sin.f64 x))
(+ (sin x) (* eps (+ (* -1/8 (* eps (sin x))) (* 1/2 (cos x)))))
(fma.f64 eps (fma.f64 #s(literal 1/2 binary64) (cos.f64 x) (.f64 eps (.f64 (sin.f64 x) #s(literal -1/8 binary64)))) (sin.f64 x))
(+ (sin x) (* eps (+ (* 1/2 (cos x)) (* eps (+ (* -1/8 (sin x)) (* -1/48 (* eps (cos x))))))))
(fma.f64 eps (fma.f64 eps (fma.f64 eps (.f64 (cos.f64 x) #s(literal -1/48 binary64)) (.f64 (sin.f64 x) #s(literal -1/8 binary64))) (*.f64 #s(literal 1/2 binary64) (cos.f64 x))) (sin.f64 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))
(sin (* 1/2 (+ eps (* 2 x))))
(sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x))
(sin (* 1/2 (- (* 2 x) (* -1 eps))))
(sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x))
(sin (* 1/2 (- (* 2 x) (* -1 eps))))
(sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x))
(sin (* 1/2 (- (* 2 x) (* -1 eps))))
(sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x))
(sin (* 1/2 (- (* 2 x) (* -1 eps))))
(sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x))

rewrite140.0ms (1%)

Memory

48.1MiB live, 199.3MiB allocated

Algorithm

1×	batch-egg-rewrite

Rules

1 378×	`lower-fma.f32`
1 370×	`lower-fma.f64`
1 262×	`lower-*.f32`
1 244×	`lower-*.f64`
1 034×	`lower-/.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	49	268
0	88	249
1	324	207
0	2827	201

Stop Event

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

Counts

24 → 371

Calls

Call 1

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

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

eval159.0ms (1.1%)

Memory: -17.2MiB live, 253.9MiB allocated
Compiler: Compiled 26 497 to 2 295 computations (91.3% saved)

prune112.0ms (0.8%)

Memory

24.2MiB live, 226.4MiB allocated

Pruning

21 alts after pruning (20 fresh and 1 done)

	Pruned	Kept	Total
New	961	16	977
Fresh	2	4	6
Picked	5	0	5
Done	0	1	1
Total	968	21	989

Accuracy

100.0%

Counts

989 → 21

Alt Table

Click to see full alt table

Status	Accuracy	Program
	62.6%	(fma.f64 (sin.f64 x) (cos.f64 eps) (fma.f64 (sin.f64 eps) (cos.f64 x) (neg.f64 (sin.f64 x))))
	99.7%	(fma.f64 (sin.f64 eps) (cos.f64 x) (-.f64 (*.f64 (sin.f64 x) (cos.f64 eps)) (sin.f64 x)))
	7.2%	(/.f64 (/.f64 (-.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 (+.f64 x eps) #s(literal 2 binary64))) (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal -1/2 binary64) (cos.f64 (+.f64 x x)))))) #s(literal 2 binary64)) (.f64 (sin.f64 #s(approx ( (+ (* x 2) eps) 1/2) (.f64 eps (+.f64 #s(literal 1/2 binary64) (/.f64 x eps))))) (cos.f64 (.f64 (+.f64 eps #s(literal 0 binary64)) #s(literal 1/2 binary64)))))
	9.1%	(/.f64 (+.f64 (pow.f64 (.f64 (sin.f64 x) (cos.f64 eps)) #s(literal 3 binary64)) (pow.f64 (-.f64 (.f64 (cos.f64 x) (sin.f64 eps)) (sin.f64 x)) #s(literal 3 binary64))) (fma.f64 (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal -1/2 binary64) (cos.f64 (+.f64 x x)))) (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 #s(literal 2 binary64) eps)))) (-.f64 (pow.f64 (-.f64 (.f64 (cos.f64 x) (sin.f64 eps)) (sin.f64 x)) #s(literal 2 binary64)) (.f64 (.f64 (sin.f64 x) (cos.f64 eps)) (-.f64 (*.f64 (cos.f64 x) (sin.f64 eps)) (sin.f64 x))))))
	36.5%	(-.f64 (/.f64 (*.f64 (sin.f64 (+.f64 x eps)) (sin.f64 (-.f64 x eps))) (sin.f64 (-.f64 x eps))) (sin.f64 x))
✓	62.4%	(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
▶	21.5%	(.f64 (.f64 (sin.f64 (.f64 (fma.f64 (fma.f64 x (.f64 x x) (.f64 eps (.f64 eps eps))) (/.f64 #s(literal 1 binary64) (fma.f64 x x (.f64 eps (-.f64 eps x)))) (neg.f64 x)) #s(literal 1/2 binary64))) (cos.f64 (.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)))) #s(literal 2 binary64))
	99.4%	(.f64 (.f64 #s(approx (sin (* (+ eps 0) 1/2)) (.f64 eps (fma.f64 (.f64 eps eps) (fma.f64 eps (.f64 eps #s(literal 1/3840 binary64)) #s(literal -1/48 binary64)) #s(literal 1/2 binary64)))) (cos.f64 (.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)))) #s(literal 2 binary64))
	99.5%	(.f64 (.f64 #s(approx (sin (* (+ eps 0) 1/2)) (.f64 eps (fma.f64 eps (.f64 eps (fma.f64 (.f64 eps eps) (fma.f64 (.f64 eps eps) #s(literal -1/645120 binary64) #s(literal 1/3840 binary64)) #s(literal -1/48 binary64))) #s(literal 1/2 binary64)))) (cos.f64 (*.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)))) #s(literal 2 binary64))
	99.2%	(.f64 (.f64 #s(approx (sin (* (+ eps 0) 1/2)) (.f64 eps (fma.f64 eps (.f64 eps #s(literal -1/48 binary64)) #s(literal 1/2 binary64)))) (cos.f64 (*.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)))) #s(literal 2 binary64))
▶	99.1%	(.f64 (.f64 #s(approx (sin (* (+ eps 0) 1/2)) (.f64 #s(literal 1/2 binary64) eps)) (cos.f64 (.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)))) #s(literal 2 binary64))
▶	99.8%	(.f64 #s(approx ( (sin (* (+ eps 0) 1/2)) (cos (* (+ (* x 2) eps) 1/2))) (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)))) #s(literal 2 binary64))
	7.3%	#s(approx (/ (/ (- 1/2 (+ (* 1/2 (cos (* (+ x eps) 2))) (+ 1/2 (* -1/2 (cos (+ x x)))))) 2) (* (sin (* (+ (* x 2) eps) 1/2)) (cos (* (+ eps 0) 1/2)))) (/.f64 (fma.f64 #s(literal -1/4 binary64) (cos.f64 (.f64 #s(literal 2 binary64) (+.f64 eps x))) (.f64 (cos.f64 (.f64 x #s(literal 2 binary64))) #s(literal 1/4 binary64))) (.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) eps)) (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x)))))
▶	5.5%	#s(approx (/ (/ (- 1/2 (+ (* 1/2 (cos (* (+ x eps) 2))) (+ 1/2 (* -1/2 (cos (+ x x)))))) 2) (* (sin (* (+ (* x 2) eps) 1/2)) (cos (* (+ eps 0) 1/2)))) #s(literal 0 binary64))
▶	61.0%	#s(approx (- (sin (+ x eps)) (sin x)) (-.f64 #s(approx (+ (* (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) (fma.f64 eps (fma.f64 x (*.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64)) x)) x))
	98.7%	#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 eps (cos.f64 x)))
	97.6%	#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (- (+ (* (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) x) (fma.f64 eps (fma.f64 #s(literal -1/2 binary64) (.f64 x (+.f64 eps x)) (.f64 eps (.f64 eps (fma.f64 (.f64 x x) #s(literal 1/12 binary64) #s(literal -1/6 binary64))))) eps)))
	97.5%	#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (- (+ (* (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) x) (fma.f64 eps (.f64 x (.f64 x #s(literal -1/2 binary64))) eps)))
	97.5%	#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (- (+ (* (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) x) (fma.f64 #s(literal -1/2 binary64) (.f64 (.f64 x (+.f64 eps x)) eps) eps)))
	97.5%	#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (sin eps) (fma.f64 (.f64 eps eps) (.f64 (fma.f64 eps (*.f64 eps #s(literal 1/120 binary64)) #s(literal -1/6 binary64)) eps) eps)))
	97.5%	#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (sin eps) (fma.f64 eps (.f64 eps (.f64 eps #s(literal -1/6 binary64))) eps)))

Compiler

Compiled 871 to 498 computations (42.8% saved)

simplify297.0ms (2.1%)

Memory

-33.5MiB live, 337.2MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 17 expressions of interest:

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

Rules

10 094×	`lower-fma.f32`
10 080×	`lower-fma.f64`
3 578×	`lower-*.f32`
3 550×	`lower-*.f64`
2 346×	`lower-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	75	514
0	109	476
1	188	466
2	396	462
3	1064	444
4	2820	442
0	8196	436

Stop Event

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

Calls

Call 1

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

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

localize459.0ms (3.2%)

Memory

3.2MiB live, 469.1MiB allocated

Localize:

Found 17 expressions of interest:

New	Metric	Score	Program
✓	accuracy	99.9%	(cos.f64 (*.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)))
✓	accuracy	99.8%	(/.f64 #s(literal 1 binary64) (fma.f64 x x (*.f64 eps (-.f64 eps x))))
✓	accuracy	99.8%	(*.f64 eps (-.f64 eps x))
✓	accuracy	22.7%	(fma.f64 (fma.f64 x (.f64 x x) (.f64 eps (.f64 eps eps))) (/.f64 #s(literal 1 binary64) (fma.f64 x x (.f64 eps (-.f64 eps x)))) (neg.f64 x))
✓	accuracy	100.0%	(*.f64 #s(literal 1/2 binary64) eps)
✓	accuracy	100.0%	(.f64 #s(approx (sin ( (+ eps 0) 1/2)) (.f64 #s(literal 1/2 binary64) eps)) (cos.f64 (.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64))))
✓	accuracy	99.9%	(cos.f64 (*.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)))
✓	accuracy	99.1%	#s(approx (sin (* (+ eps 0) 1/2)) (*.f64 #s(literal 1/2 binary64) eps))
✓	accuracy	100.0%	(fma.f64 eps (fma.f64 x (*.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64)) x)
✓	accuracy	99.0%	#s(approx (+ (* (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) (fma.f64 eps (fma.f64 x (*.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64)) x))
✓	accuracy	97.6%	#s(approx (- (sin (+ x eps)) (sin x)) (-.f64 #s(approx (+ (* (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) (fma.f64 eps (fma.f64 x (*.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64)) x)) x))
✓	accuracy	62.6%	(-.f64 #s(approx (+ (* (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) (fma.f64 eps (fma.f64 x (*.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64)) x)) x)
✓	accuracy	5.5%	#s(approx (/ (/ (- 1/2 (+ (* 1/2 (cos (* (+ x eps) 2))) (+ 1/2 (* -1/2 (cos (+ x x)))))) 2) (* (sin (* (+ (* x 2) eps) 1/2)) (cos (* (+ eps 0) 1/2)))) #s(literal 0 binary64))
✓	accuracy	100.0%	(sin.f64 (*.f64 #s(literal 1/2 binary64) eps))
✓	accuracy	100.0%	#s(approx (* (sin (* (+ eps 0) 1/2)) (cos (* (+ (* x 2) eps) 1/2))) (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x))))
✓	accuracy	100.0%	(.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)))
✓	accuracy	99.9%	(cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x))

Samples

221.0ms	145×	2	valid
67.0ms	35×	3	valid
57.0ms	71×	1	valid
3.0ms	5×	0	valid

Compiler

Compiled 472 to 68 computations (85.6% saved)

Precisions

Click to see histograms. Total time spent on operations: 294.0ms

ival-cos: 90.0ms (30.6% of total)

adjust: 82.0ms (27.9% of total)

ival-mult: 59.0ms (20.1% of total)

ival-add: 26.0ms (8.8% of total)

ival-sin: 16.0ms (5.4% of total)

ival-div: 12.0ms (4.1% of total)

ival-sub: 8.0ms (2.7% of total)

exact: 1.0ms (0.3% of total)

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

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

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

series54.0ms (0.4%)

Memory

36.8MiB live, 74.0MiB allocated

Counts

21 → 468

Calls

Call 1

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

Outputs
#s(alt (* eps (cos x)) (taylor 0 eps) (#s(alt (.f64 #s(approx ( (sin (* (+ eps 0) 1/2)) (cos (* (+ (* x 2) eps) 1/2))) (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)))) #s(literal 2 binary64)) (patch (.f64 #s(approx ( (sin (* (+ eps 0) 1/2)) (cos (* (+ (* x 2) eps) 1/2))) (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)))) #s(literal 2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* eps (+ (cos x) (* -1/2 (* eps (sin x))))) (taylor 0 eps) (#s(alt (.f64 #s(approx ( (sin (* (+ eps 0) 1/2)) (cos (* (+ (* x 2) eps) 1/2))) (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)))) #s(literal 2 binary64)) (patch (.f64 #s(approx ( (sin (* (+ eps 0) 1/2)) (cos (* (+ (* x 2) eps) 1/2))) (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)))) #s(literal 2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* 2 (* eps (+ (* -1/16 (cos x)) (* -1/48 (cos x))))))))) (taylor 0 eps) (#s(alt (.f64 #s(approx ( (sin (* (+ eps 0) 1/2)) (cos (* (+ (* x 2) eps) 1/2))) (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)))) #s(literal 2 binary64)) (patch (.f64 #s(approx ( (sin (* (+ eps 0) 1/2)) (cos (* (+ (* x 2) eps) 1/2))) (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)))) #s(literal 2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* eps (+ (* 1/24 (* eps (sin x))) (* 2 (+ (* -1/16 (cos x)) (* -1/48 (cos x)))))))))) (taylor 0 eps) (#s(alt (.f64 #s(approx ( (sin (* (+ eps 0) 1/2)) (cos (* (+ (* x 2) eps) 1/2))) (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)))) #s(literal 2 binary64)) (patch (.f64 #s(approx ( (sin (* (+ eps 0) 1/2)) (cos (* (+ (* x 2) eps) 1/2))) (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)))) #s(literal 2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* 2 (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps)))) (taylor inf eps) (#s(alt (.f64 #s(approx ( (sin (* (+ eps 0) 1/2)) (cos (* (+ (* x 2) eps) 1/2))) (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)))) #s(literal 2 binary64)) (patch (.f64 #s(approx ( (sin (* (+ eps 0) 1/2)) (cos (* (+ (* x 2) eps) 1/2))) (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)))) #s(literal 2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* 2 (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps)))) (taylor inf eps) (#s(alt (.f64 #s(approx ( (sin (* (+ eps 0) 1/2)) (cos (* (+ (* x 2) eps) 1/2))) (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)))) #s(literal 2 binary64)) (patch (.f64 #s(approx ( (sin (* (+ eps 0) 1/2)) (cos (* (+ (* x 2) eps) 1/2))) (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)))) #s(literal 2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* 2 (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps)))) (taylor inf eps) (#s(alt (.f64 #s(approx ( (sin (* (+ eps 0) 1/2)) (cos (* (+ (* x 2) eps) 1/2))) (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)))) #s(literal 2 binary64)) (patch (.f64 #s(approx ( (sin (* (+ eps 0) 1/2)) (cos (* (+ (* x 2) eps) 1/2))) (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)))) #s(literal 2 binary64)) #<representation binary64>) () ())) ())
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#s(alt (+ (cos x) (* eps (- (* eps (+ (* -1/8 (cos x)) (* 1/48 (* eps (sin x))))) (* 1/2 (sin x))))) (taylor 0 eps) (#s(alt (cos.f64 (.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64))) (patch (cos.f64 (.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64))) #<representation binary64>) () ())) ())
#s(alt (cos (* 1/2 (+ eps (* 2 x)))) (taylor inf eps) (#s(alt (cos.f64 (.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64))) (patch (cos.f64 (.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64))) #<representation binary64>) () ())) ())
#s(alt (cos (* 1/2 (+ eps (* 2 x)))) (taylor inf eps) (#s(alt (cos.f64 (.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64))) (patch (cos.f64 (.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64))) #<representation binary64>) () ())) ())
#s(alt (cos (* 1/2 (+ eps (* 2 x)))) (taylor inf eps) (#s(alt (cos.f64 (.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64))) (patch (cos.f64 (.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64))) #<representation binary64>) () ())) ())
#s(alt (cos (* 1/2 (+ eps (* 2 x)))) (taylor inf eps) (#s(alt (cos.f64 (.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64))) (patch (cos.f64 (.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64))) #<representation binary64>) () ())) ())
#s(alt (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (taylor -inf eps) (#s(alt (cos.f64 (.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64))) (patch (cos.f64 (.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64))) #<representation binary64>) () ())) ())
#s(alt (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (taylor -inf eps) (#s(alt (cos.f64 (.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64))) (patch (cos.f64 (.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64))) #<representation binary64>) () ())) ())
#s(alt (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (taylor -inf eps) (#s(alt (cos.f64 (.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64))) (patch (cos.f64 (.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64))) #<representation binary64>) () ())) ())
#s(alt (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (taylor -inf eps) (#s(alt (cos.f64 (.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64))) (patch (cos.f64 (.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64))) #<representation binary64>) () ())) ())
#s(alt (* 1/2 eps) (taylor 0 eps) (#s(alt (.f64 #s(literal 1/2 binary64) eps) (patch (.f64 #s(literal 1/2 binary64) eps) #<representation binary64>) () ())) ())
#s(alt (* 1/2 eps) (taylor 0 eps) (#s(alt (.f64 #s(literal 1/2 binary64) eps) (patch (.f64 #s(literal 1/2 binary64) eps) #<representation binary64>) () ())) ())
#s(alt (* 1/2 eps) (taylor 0 eps) (#s(alt (.f64 #s(literal 1/2 binary64) eps) (patch (.f64 #s(literal 1/2 binary64) eps) #<representation binary64>) () ())) ())
#s(alt (* 1/2 eps) (taylor 0 eps) (#s(alt (.f64 #s(literal 1/2 binary64) eps) (patch (.f64 #s(literal 1/2 binary64) eps) #<representation binary64>) () ())) ())
#s(alt (* 1/2 eps) (taylor inf eps) (#s(alt (.f64 #s(literal 1/2 binary64) eps) (patch (.f64 #s(literal 1/2 binary64) eps) #<representation binary64>) () ())) ())
#s(alt (* 1/2 eps) (taylor inf eps) (#s(alt (.f64 #s(literal 1/2 binary64) eps) (patch (.f64 #s(literal 1/2 binary64) eps) #<representation binary64>) () ())) ())
#s(alt (* 1/2 eps) (taylor inf eps) (#s(alt (.f64 #s(literal 1/2 binary64) eps) (patch (.f64 #s(literal 1/2 binary64) eps) #<representation binary64>) () ())) ())
#s(alt (* 1/2 eps) (taylor inf eps) (#s(alt (.f64 #s(literal 1/2 binary64) eps) (patch (.f64 #s(literal 1/2 binary64) eps) #<representation binary64>) () ())) ())
#s(alt (* 1/2 eps) (taylor -inf eps) (#s(alt (.f64 #s(literal 1/2 binary64) eps) (patch (.f64 #s(literal 1/2 binary64) eps) #<representation binary64>) () ())) ())
#s(alt (* 1/2 eps) (taylor -inf eps) (#s(alt (.f64 #s(literal 1/2 binary64) eps) (patch (.f64 #s(literal 1/2 binary64) eps) #<representation binary64>) () ())) ())
#s(alt (* 1/2 eps) (taylor -inf eps) (#s(alt (.f64 #s(literal 1/2 binary64) eps) (patch (.f64 #s(literal 1/2 binary64) eps) #<representation binary64>) () ())) ())
#s(alt (* 1/2 eps) (taylor -inf eps) (#s(alt (.f64 #s(literal 1/2 binary64) eps) (patch (.f64 #s(literal 1/2 binary64) eps) #<representation binary64>) () ())) ())
#s(alt (* -1 (* eps x)) (taylor 0 eps) (#s(alt (.f64 eps (-.f64 eps x)) (patch (.f64 eps (-.f64 eps x)) #<representation binary64>) () ())) ())
#s(alt (* eps (+ eps (* -1 x))) (taylor 0 eps) (#s(alt (.f64 eps (-.f64 eps x)) (patch (.f64 eps (-.f64 eps x)) #<representation binary64>) () ())) ())
#s(alt (* eps (+ eps (* -1 x))) (taylor 0 eps) (#s(alt (.f64 eps (-.f64 eps x)) (patch (.f64 eps (-.f64 eps x)) #<representation binary64>) () ())) ())
#s(alt (* eps (+ eps (* -1 x))) (taylor 0 eps) (#s(alt (.f64 eps (-.f64 eps x)) (patch (.f64 eps (-.f64 eps x)) #<representation binary64>) () ())) ())
#s(alt (pow eps 2) (taylor inf eps) (#s(alt (.f64 eps (-.f64 eps x)) (patch (.f64 eps (-.f64 eps x)) #<representation binary64>) () ())) ())
#s(alt (* (pow eps 2) (+ 1 (* -1 (/ x eps)))) (taylor inf eps) (#s(alt (.f64 eps (-.f64 eps x)) (patch (.f64 eps (-.f64 eps x)) #<representation binary64>) () ())) ())
#s(alt (* (pow eps 2) (+ 1 (* -1 (/ x eps)))) (taylor inf eps) (#s(alt (.f64 eps (-.f64 eps x)) (patch (.f64 eps (-.f64 eps x)) #<representation binary64>) () ())) ())
#s(alt (* (pow eps 2) (+ 1 (* -1 (/ x eps)))) (taylor inf eps) (#s(alt (.f64 eps (-.f64 eps x)) (patch (.f64 eps (-.f64 eps x)) #<representation binary64>) () ())) ())
#s(alt (pow eps 2) (taylor -inf eps) (#s(alt (.f64 eps (-.f64 eps x)) (patch (.f64 eps (-.f64 eps x)) #<representation binary64>) () ())) ())
#s(alt (* (pow eps 2) (+ 1 (* -1 (/ x eps)))) (taylor -inf eps) (#s(alt (.f64 eps (-.f64 eps x)) (patch (.f64 eps (-.f64 eps x)) #<representation binary64>) () ())) ())
#s(alt (* (pow eps 2) (+ 1 (* -1 (/ x eps)))) (taylor -inf eps) (#s(alt (.f64 eps (-.f64 eps x)) (patch (.f64 eps (-.f64 eps x)) #<representation binary64>) () ())) ())
#s(alt (* (pow eps 2) (+ 1 (* -1 (/ x eps)))) (taylor -inf eps) (#s(alt (.f64 eps (-.f64 eps x)) (patch (.f64 eps (-.f64 eps x)) #<representation binary64>) () ())) ())
#s(alt (pow eps 2) (taylor 0 x) (#s(alt (.f64 eps (-.f64 eps x)) (patch (.f64 eps (-.f64 eps x)) #<representation binary64>) () ())) ())
#s(alt (+ (* -1 (* eps x)) (pow eps 2)) (taylor 0 x) (#s(alt (.f64 eps (-.f64 eps x)) (patch (.f64 eps (-.f64 eps x)) #<representation binary64>) () ())) ())
#s(alt (+ (* -1 (* eps x)) (pow eps 2)) (taylor 0 x) (#s(alt (.f64 eps (-.f64 eps x)) (patch (.f64 eps (-.f64 eps x)) #<representation binary64>) () ())) ())
#s(alt (+ (* -1 (* eps x)) (pow eps 2)) (taylor 0 x) (#s(alt (.f64 eps (-.f64 eps x)) (patch (.f64 eps (-.f64 eps x)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* eps x)) (taylor inf x) (#s(alt (.f64 eps (-.f64 eps x)) (patch (.f64 eps (-.f64 eps x)) #<representation binary64>) () ())) ())
#s(alt (* x (+ (* -1 eps) (/ (pow eps 2) x))) (taylor inf x) (#s(alt (.f64 eps (-.f64 eps x)) (patch (.f64 eps (-.f64 eps x)) #<representation binary64>) () ())) ())
#s(alt (* x (+ (* -1 eps) (/ (pow eps 2) x))) (taylor inf x) (#s(alt (.f64 eps (-.f64 eps x)) (patch (.f64 eps (-.f64 eps x)) #<representation binary64>) () ())) ())
#s(alt (* x (+ (* -1 eps) (/ (pow eps 2) x))) (taylor inf x) (#s(alt (.f64 eps (-.f64 eps x)) (patch (.f64 eps (-.f64 eps x)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* eps x)) (taylor -inf x) (#s(alt (.f64 eps (-.f64 eps x)) (patch (.f64 eps (-.f64 eps x)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (+ eps (* -1 (/ (pow eps 2) x))))) (taylor -inf x) (#s(alt (.f64 eps (-.f64 eps x)) (patch (.f64 eps (-.f64 eps x)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (+ eps (* -1 (/ (pow eps 2) x))))) (taylor -inf x) (#s(alt (.f64 eps (-.f64 eps x)) (patch (.f64 eps (-.f64 eps x)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (+ eps (* -1 (/ (pow eps 2) x))))) (taylor -inf x) (#s(alt (.f64 eps (-.f64 eps x)) (patch (.f64 eps (-.f64 eps x)) #<representation binary64>) () ())) ())
#s(alt (/ 1 (pow eps 2)) (taylor 0 x) (#s(alt (/.f64 #s(literal 1 binary64) (fma.f64 x x (.f64 eps (-.f64 eps x)))) (patch (/.f64 #s(literal 1 binary64) (fma.f64 x x (.f64 eps (-.f64 eps x)))) #<representation binary64>) () ())) ())
#s(alt (+ (/ 1 (pow eps 2)) (/ x (pow eps 3))) (taylor 0 x) (#s(alt (/.f64 #s(literal 1 binary64) (fma.f64 x x (.f64 eps (-.f64 eps x)))) (patch (/.f64 #s(literal 1 binary64) (fma.f64 x x (.f64 eps (-.f64 eps x)))) #<representation binary64>) () ())) ())
#s(alt (+ (* x (+ (* -1 (/ (pow x 2) (pow eps 5))) (/ 1 (pow eps 3)))) (/ 1 (pow eps 2))) (taylor 0 x) (#s(alt (/.f64 #s(literal 1 binary64) (fma.f64 x x (.f64 eps (-.f64 eps x)))) (patch (/.f64 #s(literal 1 binary64) (fma.f64 x x (.f64 eps (-.f64 eps x)))) #<representation binary64>) () ())) ())
#s(alt (+ (* x (+ (* (pow x 2) (- (* -1 (/ x (pow eps 6))) (/ 1 (pow eps 5)))) (/ 1 (pow eps 3)))) (/ 1 (pow eps 2))) (taylor 0 x) (#s(alt (/.f64 #s(literal 1 binary64) (fma.f64 x x (.f64 eps (-.f64 eps x)))) (patch (/.f64 #s(literal 1 binary64) (fma.f64 x x (.f64 eps (-.f64 eps x)))) #<representation binary64>) () ())) ())
#s(alt (/ 1 (pow x 2)) (taylor inf x) (#s(alt (/.f64 #s(literal 1 binary64) (fma.f64 x x (.f64 eps (-.f64 eps x)))) (patch (/.f64 #s(literal 1 binary64) (fma.f64 x x (.f64 eps (-.f64 eps x)))) #<representation binary64>) () ())) ())
#s(alt (/ (+ 1 (/ eps x)) (pow x 2)) (taylor inf x) (#s(alt (/.f64 #s(literal 1 binary64) (fma.f64 x x (.f64 eps (-.f64 eps x)))) (patch (/.f64 #s(literal 1 binary64) (fma.f64 x x (.f64 eps (-.f64 eps x)))) #<representation binary64>) () ())) ())
#s(alt (/ (- (+ 1 (* -1 (/ (+ (* -1 (pow eps 2)) (pow eps 2)) (pow x 2)))) (* -1 (/ eps x))) (pow x 2)) (taylor inf x) (#s(alt (/.f64 #s(literal 1 binary64) (fma.f64 x x (.f64 eps (-.f64 eps x)))) (patch (/.f64 #s(literal 1 binary64) (fma.f64 x x (.f64 eps (-.f64 eps x)))) #<representation binary64>) () ())) ())
#s(alt (/ (- (+ 1 (* -1 (/ (+ (* eps (+ (* -1 (pow eps 2)) (pow eps 2))) (pow eps 3)) (pow x 3)))) (+ (* -1 (/ eps x)) (+ (* -1 (/ (pow eps 2) (pow x 2))) (/ (pow eps 2) (pow x 2))))) (pow x 2)) (taylor inf x) (#s(alt (/.f64 #s(literal 1 binary64) (fma.f64 x x (.f64 eps (-.f64 eps x)))) (patch (/.f64 #s(literal 1 binary64) (fma.f64 x x (.f64 eps (-.f64 eps x)))) #<representation binary64>) () ())) ())
#s(alt (/ 1 (pow x 2)) (taylor -inf x) (#s(alt (/.f64 #s(literal 1 binary64) (fma.f64 x x (.f64 eps (-.f64 eps x)))) (patch (/.f64 #s(literal 1 binary64) (fma.f64 x x (.f64 eps (-.f64 eps x)))) #<representation binary64>) () ())) ())
#s(alt (/ (+ 1 (/ eps x)) (pow x 2)) (taylor -inf x) (#s(alt (/.f64 #s(literal 1 binary64) (fma.f64 x x (.f64 eps (-.f64 eps x)))) (patch (/.f64 #s(literal 1 binary64) (fma.f64 x x (.f64 eps (-.f64 eps x)))) #<representation binary64>) () ())) ())
#s(alt (/ (+ 1 (* -1 (/ (- (+ (* -1 (/ (pow eps 2) x)) (/ (pow eps 2) x)) eps) x))) (pow x 2)) (taylor -inf x) (#s(alt (/.f64 #s(literal 1 binary64) (fma.f64 x x (.f64 eps (-.f64 eps x)))) (patch (/.f64 #s(literal 1 binary64) (fma.f64 x x (.f64 eps (-.f64 eps x)))) #<representation binary64>) () ())) ())
#s(alt (/ (+ 1 (* -1 (/ (- (* -1 (/ (- (+ (* -1 (/ (* eps (+ (* -1 (pow eps 2)) (pow eps 2))) x)) (* -1 (/ (pow eps 3) x))) (+ (* -1 (pow eps 2)) (pow eps 2))) x)) eps) x))) (pow x 2)) (taylor -inf x) (#s(alt (/.f64 #s(literal 1 binary64) (fma.f64 x x (.f64 eps (-.f64 eps x)))) (patch (/.f64 #s(literal 1 binary64) (fma.f64 x x (.f64 eps (-.f64 eps x)))) #<representation binary64>) () ())) ())
#s(alt (/ 1 (pow x 2)) (taylor 0 eps) (#s(alt (/.f64 #s(literal 1 binary64) (fma.f64 x x (.f64 eps (-.f64 eps x)))) (patch (/.f64 #s(literal 1 binary64) (fma.f64 x x (.f64 eps (-.f64 eps x)))) #<representation binary64>) () ())) ())
#s(alt (+ (/ 1 (pow x 2)) (/ eps (pow x 3))) (taylor 0 eps) (#s(alt (/.f64 #s(literal 1 binary64) (fma.f64 x x (.f64 eps (-.f64 eps x)))) (patch (/.f64 #s(literal 1 binary64) (fma.f64 x x (.f64 eps (-.f64 eps x)))) #<representation binary64>) () ())) ())
#s(alt (+ (* eps (+ (* -1 (/ (pow eps 2) (pow x 5))) (/ 1 (pow x 3)))) (/ 1 (pow x 2))) (taylor 0 eps) (#s(alt (/.f64 #s(literal 1 binary64) (fma.f64 x x (.f64 eps (-.f64 eps x)))) (patch (/.f64 #s(literal 1 binary64) (fma.f64 x x (.f64 eps (-.f64 eps x)))) #<representation binary64>) () ())) ())
#s(alt (+ (* eps (+ (* (pow eps 2) (- (* -1 (/ eps (pow x 6))) (/ 1 (pow x 5)))) (/ 1 (pow x 3)))) (/ 1 (pow x 2))) (taylor 0 eps) (#s(alt (/.f64 #s(literal 1 binary64) (fma.f64 x x (.f64 eps (-.f64 eps x)))) (patch (/.f64 #s(literal 1 binary64) (fma.f64 x x (.f64 eps (-.f64 eps x)))) #<representation binary64>) () ())) ())
#s(alt (/ 1 (pow eps 2)) (taylor inf eps) (#s(alt (/.f64 #s(literal 1 binary64) (fma.f64 x x (.f64 eps (-.f64 eps x)))) (patch (/.f64 #s(literal 1 binary64) (fma.f64 x x (.f64 eps (-.f64 eps x)))) #<representation binary64>) () ())) ())
#s(alt (/ (+ 1 (/ x eps)) (pow eps 2)) (taylor inf eps) (#s(alt (/.f64 #s(literal 1 binary64) (fma.f64 x x (.f64 eps (-.f64 eps x)))) (patch (/.f64 #s(literal 1 binary64) (fma.f64 x x (.f64 eps (-.f64 eps x)))) #<representation binary64>) () ())) ())
#s(alt (/ (- (+ 1 (* -1 (/ (+ (* -1 (pow x 2)) (pow x 2)) (pow eps 2)))) (* -1 (/ x eps))) (pow eps 2)) (taylor inf eps) (#s(alt (/.f64 #s(literal 1 binary64) (fma.f64 x x (.f64 eps (-.f64 eps x)))) (patch (/.f64 #s(literal 1 binary64) (fma.f64 x x (.f64 eps (-.f64 eps x)))) #<representation binary64>) () ())) ())
#s(alt (/ (- (+ 1 (* -1 (/ (+ (* x (+ (* -1 (pow x 2)) (pow x 2))) (pow x 3)) (pow eps 3)))) (+ (* -1 (/ x eps)) (+ (* -1 (/ (pow x 2) (pow eps 2))) (/ (pow x 2) (pow eps 2))))) (pow eps 2)) (taylor inf eps) (#s(alt (/.f64 #s(literal 1 binary64) (fma.f64 x x (.f64 eps (-.f64 eps x)))) (patch (/.f64 #s(literal 1 binary64) (fma.f64 x x (.f64 eps (-.f64 eps x)))) #<representation binary64>) () ())) ())
#s(alt (/ 1 (pow eps 2)) (taylor -inf eps) (#s(alt (/.f64 #s(literal 1 binary64) (fma.f64 x x (.f64 eps (-.f64 eps x)))) (patch (/.f64 #s(literal 1 binary64) (fma.f64 x x (.f64 eps (-.f64 eps x)))) #<representation binary64>) () ())) ())
#s(alt (/ (+ 1 (/ x eps)) (pow eps 2)) (taylor -inf eps) (#s(alt (/.f64 #s(literal 1 binary64) (fma.f64 x x (.f64 eps (-.f64 eps x)))) (patch (/.f64 #s(literal 1 binary64) (fma.f64 x x (.f64 eps (-.f64 eps x)))) #<representation binary64>) () ())) ())
#s(alt (/ (+ 1 (* -1 (/ (- (+ (* -1 (/ (pow x 2) eps)) (/ (pow x 2) eps)) x) eps))) (pow eps 2)) (taylor -inf eps) (#s(alt (/.f64 #s(literal 1 binary64) (fma.f64 x x (.f64 eps (-.f64 eps x)))) (patch (/.f64 #s(literal 1 binary64) (fma.f64 x x (.f64 eps (-.f64 eps x)))) #<representation binary64>) () ())) ())
#s(alt (/ (+ 1 (* -1 (/ (- (* -1 (/ (- (+ (* -1 (/ (* x (+ (* -1 (pow x 2)) (pow x 2))) eps)) (* -1 (/ (pow x 3) eps))) (+ (* -1 (pow x 2)) (pow x 2))) eps)) x) eps))) (pow eps 2)) (taylor -inf eps) (#s(alt (/.f64 #s(literal 1 binary64) (fma.f64 x x (.f64 eps (-.f64 eps x)))) (patch (/.f64 #s(literal 1 binary64) (fma.f64 x x (.f64 eps (-.f64 eps x)))) #<representation binary64>) () ())) ())

Calls

117 calls:

Time	Variable		Point	Expression
8.0ms	x	@	0	(+ (* (+ (* x (* x x)) (* eps (* eps eps))) (/ 1 (+ (* x x) (* eps (- eps x))))) (neg x))
3.0ms	x	@	inf	(* (* (sin (* (+ (* (+ (* x (* x x)) (* eps (* eps eps))) (/ 1 (+ (* x x) (* eps (- eps x))))) (neg x)) 1/2)) (cos (* (+ (* x 2) eps) 1/2))) 2)
3.0ms	x	@	inf	(cos (+ (* 1/2 eps) x))
3.0ms	eps	@	0	(+ (* (+ (* x (* x x)) (* eps (* eps eps))) (/ 1 (+ (* x x) (* eps (- eps x))))) (neg x))
2.0ms	x	@	-inf	(* (* (sin (* (+ (* (+ (* x (* x x)) (* eps (* eps eps))) (/ 1 (+ (* x x) (* eps (- eps x))))) (neg x)) 1/2)) (cos (* (+ (* x 2) eps) 1/2))) 2)

simplify367.0ms (2.5%)

Memory

-4.7MiB live, 436.8MiB allocated

Algorithm

1×	egg-herbie

Rules

9 540×	`lower-fma.f64`
9 540×	`lower-fma.f32`
4 848×	`lower-*.f64`
4 848×	`lower-*.f32`
3 126×	`lower-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	780	8306
1	2550	7133
0	8863	6630

Stop Event

1×	iter limit
1×	node limit

Counts

468 → 450

Calls

Call 1

Inputs
(* eps (cos x))
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* 2 (* eps (+ (* -1/16 (cos x)) (* -1/48 (cos x)))))))))
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* eps (+ (* 1/24 (* eps (sin x))) (* 2 (+ (* -1/16 (cos x)) (* -1/48 (cos x))))))))))
(* 2 (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))))
(* 2 (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))))
(* 2 (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))))
(* 2 (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))))
(* 2 (* (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps))))
(* 2 (* (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps))))
(* 2 (* (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps))))
(* 2 (* (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps))))
(* 2 (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))
(+ (* -2 (* x (pow (sin (* 1/2 eps)) 2))) (* 2 (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))))
(+ (* 2 (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) (* x (+ (* -2 (pow (sin (* 1/2 eps)) 2)) (* -1 (* x (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))))))
(+ (* 2 (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) (* x (+ (* -2 (pow (sin (* 1/2 eps)) 2)) (* x (+ (* -1 (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) (* 1/3 (* x (pow (sin (* 1/2 eps)) 2))))))))
(* 2 (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))))
(* 2 (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))))
(* 2 (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))))
(* 2 (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))))
(* 2 (* (cos (* 1/2 (- eps (* -2 x)))) (sin (* 1/2 eps))))
(* 2 (* (cos (* 1/2 (- eps (* -2 x)))) (sin (* 1/2 eps))))
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x
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(* 1/2 eps)
(* 1/2 eps)
(* 1/2 eps)
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(* 1/2 eps)
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(* 1/2 eps)
(* 1/2 eps)
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(* eps (+ eps (* -1 x)))
(pow eps 2)
(* (pow eps 2) (+ 1 (* -1 (/ x eps))))
(* (pow eps 2) (+ 1 (* -1 (/ x eps))))
(* (pow eps 2) (+ 1 (* -1 (/ x eps))))
(pow eps 2)
(* (pow eps 2) (+ 1 (* -1 (/ x eps))))
(* (pow eps 2) (+ 1 (* -1 (/ x eps))))
(* (pow eps 2) (+ 1 (* -1 (/ x eps))))
(pow eps 2)
(+ (* -1 (* eps x)) (pow eps 2))
(+ (* -1 (* eps x)) (pow eps 2))
(+ (* -1 (* eps x)) (pow eps 2))
(* -1 (* eps x))
(* x (+ (* -1 eps) (/ (pow eps 2) x)))
(* x (+ (* -1 eps) (/ (pow eps 2) x)))
(* x (+ (* -1 eps) (/ (pow eps 2) x)))
(* -1 (* eps x))
(* -1 (* x (+ eps (* -1 (/ (pow eps 2) x)))))
(* -1 (* x (+ eps (* -1 (/ (pow eps 2) x)))))
(* -1 (* x (+ eps (* -1 (/ (pow eps 2) x)))))
(/ 1 (pow eps 2))
(+ (/ 1 (pow eps 2)) (/ x (pow eps 3)))
(+ (* x (+ (* -1 (/ (pow x 2) (pow eps 5))) (/ 1 (pow eps 3)))) (/ 1 (pow eps 2)))
(+ (* x (+ (* (pow x 2) (- (* -1 (/ x (pow eps 6))) (/ 1 (pow eps 5)))) (/ 1 (pow eps 3)))) (/ 1 (pow eps 2)))
(/ 1 (pow x 2))
(/ (+ 1 (/ eps x)) (pow x 2))
(/ (- (+ 1 (* -1 (/ (+ (* -1 (pow eps 2)) (pow eps 2)) (pow x 2)))) (* -1 (/ eps x))) (pow x 2))
(/ (- (+ 1 (* -1 (/ (+ (* eps (+ (* -1 (pow eps 2)) (pow eps 2))) (pow eps 3)) (pow x 3)))) (+ (* -1 (/ eps x)) (+ (* -1 (/ (pow eps 2) (pow x 2))) (/ (pow eps 2) (pow x 2))))) (pow x 2))
(/ 1 (pow x 2))
(/ (+ 1 (/ eps x)) (pow x 2))
(/ (+ 1 (* -1 (/ (- (+ (* -1 (/ (pow eps 2) x)) (/ (pow eps 2) x)) eps) x))) (pow x 2))
(/ (+ 1 (* -1 (/ (- (* -1 (/ (- (+ (* -1 (/ (* eps (+ (* -1 (pow eps 2)) (pow eps 2))) x)) (* -1 (/ (pow eps 3) x))) (+ (* -1 (pow eps 2)) (pow eps 2))) x)) eps) x))) (pow x 2))
(/ 1 (pow x 2))
(+ (/ 1 (pow x 2)) (/ eps (pow x 3)))
(+ (* eps (+ (* -1 (/ (pow eps 2) (pow x 5))) (/ 1 (pow x 3)))) (/ 1 (pow x 2)))
(+ (* eps (+ (* (pow eps 2) (- (* -1 (/ eps (pow x 6))) (/ 1 (pow x 5)))) (/ 1 (pow x 3)))) (/ 1 (pow x 2)))
(/ 1 (pow eps 2))
(/ (+ 1 (/ x eps)) (pow eps 2))
(/ (- (+ 1 (* -1 (/ (+ (* -1 (pow x 2)) (pow x 2)) (pow eps 2)))) (* -1 (/ x eps))) (pow eps 2))
(/ (- (+ 1 (* -1 (/ (+ (* x (+ (* -1 (pow x 2)) (pow x 2))) (pow x 3)) (pow eps 3)))) (+ (* -1 (/ x eps)) (+ (* -1 (/ (pow x 2) (pow eps 2))) (/ (pow x 2) (pow eps 2))))) (pow eps 2))
(/ 1 (pow eps 2))
(/ (+ 1 (/ x eps)) (pow eps 2))
(/ (+ 1 (* -1 (/ (- (+ (* -1 (/ (pow x 2) eps)) (/ (pow x 2) eps)) x) eps))) (pow eps 2))
(/ (+ 1 (* -1 (/ (- (* -1 (/ (- (+ (* -1 (/ (* x (+ (* -1 (pow x 2)) (pow x 2))) eps)) (* -1 (/ (pow x 3) eps))) (+ (* -1 (pow x 2)) (pow x 2))) eps)) x) eps))) (pow eps 2))

Outputs
(* eps (cos x))
(*.f64 eps (cos.f64 x))
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(.f64 eps (fma.f64 eps (.f64 #s(literal -1/2 binary64) (sin.f64 x)) (cos.f64 x)))
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* 2 (* eps (+ (* -1/16 (cos x)) (* -1/48 (cos x)))))))))
(.f64 eps (fma.f64 eps (fma.f64 #s(literal -1/2 binary64) (sin.f64 x) (.f64 (*.f64 eps (cos.f64 x)) #s(literal -1/6 binary64))) (cos.f64 x)))
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* eps (+ (* 1/24 (* eps (sin x))) (* 2 (+ (* -1/16 (cos x)) (* -1/48 (cos x))))))))))
(.f64 eps (fma.f64 eps (fma.f64 eps (fma.f64 eps (.f64 (sin.f64 x) #s(literal 1/24 binary64)) (.f64 (cos.f64 x) #s(literal -1/6 binary64))) (.f64 #s(literal -1/2 binary64) (sin.f64 x))) (cos.f64 x)))
(* 2 (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))))
(.f64 (cos.f64 (fma.f64 eps #s(literal 1/2 binary64) x)) (.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) #s(literal 2 binary64)))
(* 2 (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))))
(.f64 (cos.f64 (fma.f64 eps #s(literal 1/2 binary64) x)) (.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) #s(literal 2 binary64)))
(* 2 (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))))
(.f64 (cos.f64 (fma.f64 eps #s(literal 1/2 binary64) x)) (.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) #s(literal 2 binary64)))
(* 2 (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))))
(.f64 (cos.f64 (fma.f64 eps #s(literal 1/2 binary64) x)) (.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) #s(literal 2 binary64)))
(* 2 (* (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps))))
(.f64 (cos.f64 (fma.f64 eps #s(literal 1/2 binary64) x)) (.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) #s(literal 2 binary64)))
(* 2 (* (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps))))
(.f64 (cos.f64 (fma.f64 eps #s(literal 1/2 binary64) x)) (.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) #s(literal 2 binary64)))
(* 2 (* (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps))))
(.f64 (cos.f64 (fma.f64 eps #s(literal 1/2 binary64) x)) (.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) #s(literal 2 binary64)))
(* 2 (* (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps))))
(.f64 (cos.f64 (fma.f64 eps #s(literal 1/2 binary64) x)) (.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) #s(literal 2 binary64)))
(* 2 (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))
(.f64 (cos.f64 (.f64 eps #s(literal 1/2 binary64))) (.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) #s(literal 2 binary64)))
(+ (* -2 (* x (pow (sin (* 1/2 eps)) 2))) (* 2 (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))))
(fma.f64 x (.f64 #s(literal -2 binary64) (pow.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) #s(literal 2 binary64))) (.f64 (cos.f64 (.f64 eps #s(literal 1/2 binary64))) (.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) #s(literal 2 binary64))))
(+ (* 2 (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) (* x (+ (* -2 (pow (sin (* 1/2 eps)) 2)) (* -1 (* x (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))))))
(fma.f64 x (-.f64 (.f64 #s(literal -2 binary64) (pow.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) #s(literal 2 binary64))) (.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (.f64 x (cos.f64 (.f64 eps #s(literal 1/2 binary64)))))) (.f64 (cos.f64 (.f64 eps #s(literal 1/2 binary64))) (.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) #s(literal 2 binary64))))
(+ (* 2 (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) (* x (+ (* -2 (pow (sin (* 1/2 eps)) 2)) (* x (+ (* -1 (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) (* 1/3 (* x (pow (sin (* 1/2 eps)) 2))))))))
(fma.f64 x (fma.f64 x (fma.f64 (pow.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) #s(literal 2 binary64)) (.f64 x #s(literal 1/3 binary64)) (.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (neg.f64 (cos.f64 (.f64 eps #s(literal 1/2 binary64)))))) (.f64 #s(literal -2 binary64) (pow.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) #s(literal 2 binary64)))) (.f64 (cos.f64 (.f64 eps #s(literal 1/2 binary64))) (.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) #s(literal 2 binary64))))
(* 2 (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))))
(.f64 (cos.f64 (fma.f64 eps #s(literal 1/2 binary64) x)) (.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) #s(literal 2 binary64)))
(* 2 (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))))
(.f64 (cos.f64 (fma.f64 eps #s(literal 1/2 binary64) x)) (.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) #s(literal 2 binary64)))
(* 2 (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))))
(.f64 (cos.f64 (fma.f64 eps #s(literal 1/2 binary64) x)) (.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) #s(literal 2 binary64)))
(* 2 (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))))
(.f64 (cos.f64 (fma.f64 eps #s(literal 1/2 binary64) x)) (.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) #s(literal 2 binary64)))
(* 2 (* (cos (* 1/2 (- eps (* -2 x)))) (sin (* 1/2 eps))))
(.f64 (cos.f64 (fma.f64 eps #s(literal 1/2 binary64) x)) (.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) #s(literal 2 binary64)))
(* 2 (* (cos (* 1/2 (- eps (* -2 x)))) (sin (* 1/2 eps))))
(.f64 (cos.f64 (fma.f64 eps #s(literal 1/2 binary64) x)) (.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) #s(literal 2 binary64)))
(* 2 (* (cos (* 1/2 (- eps (* -2 x)))) (sin (* 1/2 eps))))
(.f64 (cos.f64 (fma.f64 eps #s(literal 1/2 binary64) x)) (.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) #s(literal 2 binary64)))
(* 2 (* (cos (* 1/2 (- eps (* -2 x)))) (sin (* 1/2 eps))))
(.f64 (cos.f64 (fma.f64 eps #s(literal 1/2 binary64) x)) (.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) #s(literal 2 binary64)))
(* 1/2 (* eps (cos x)))
(.f64 eps (.f64 (cos.f64 x) #s(literal 1/2 binary64)))
(* eps (+ (* -1/4 (* eps (sin x))) (* 1/2 (cos x))))
(.f64 eps (fma.f64 eps (.f64 (sin.f64 x) #s(literal -1/4 binary64)) (*.f64 (cos.f64 x) #s(literal 1/2 binary64))))
(* eps (+ (* 1/2 (cos x)) (* eps (+ (* -1/4 (sin x)) (* eps (+ (* -1/16 (cos x)) (* -1/48 (cos x))))))))
(.f64 eps (fma.f64 eps (fma.f64 eps (.f64 (cos.f64 x) #s(literal -1/12 binary64)) (.f64 (sin.f64 x) #s(literal -1/4 binary64))) (.f64 (cos.f64 x) #s(literal 1/2 binary64))))
(* eps (+ (* 1/2 (cos x)) (* eps (+ (* -1/4 (sin x)) (* eps (+ (* -1/16 (cos x)) (+ (* -1/48 (cos x)) (* 1/48 (* eps (sin x))))))))))
(.f64 eps (fma.f64 eps (fma.f64 eps (fma.f64 eps (.f64 (sin.f64 x) #s(literal 1/48 binary64)) (.f64 (cos.f64 x) #s(literal -1/12 binary64))) (.f64 (sin.f64 x) #s(literal -1/4 binary64))) (*.f64 (cos.f64 x) #s(literal 1/2 binary64))))
(* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps)))
(.f64 (cos.f64 (fma.f64 eps #s(literal 1/2 binary64) x)) (sin.f64 (.f64 eps #s(literal 1/2 binary64))))
(* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps)))
(.f64 (cos.f64 (fma.f64 eps #s(literal 1/2 binary64) x)) (sin.f64 (.f64 eps #s(literal 1/2 binary64))))
(* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps)))
(.f64 (cos.f64 (fma.f64 eps #s(literal 1/2 binary64) x)) (sin.f64 (.f64 eps #s(literal 1/2 binary64))))
(* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps)))
(.f64 (cos.f64 (fma.f64 eps #s(literal 1/2 binary64) x)) (sin.f64 (.f64 eps #s(literal 1/2 binary64))))
(* (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps)))
(.f64 (cos.f64 (fma.f64 eps #s(literal 1/2 binary64) x)) (sin.f64 (.f64 eps #s(literal 1/2 binary64))))
(* (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps)))
(.f64 (cos.f64 (fma.f64 eps #s(literal 1/2 binary64) x)) (sin.f64 (.f64 eps #s(literal 1/2 binary64))))
(* (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps)))
(.f64 (cos.f64 (fma.f64 eps #s(literal 1/2 binary64) x)) (sin.f64 (.f64 eps #s(literal 1/2 binary64))))
(* (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps)))
(.f64 (cos.f64 (fma.f64 eps #s(literal 1/2 binary64) x)) (sin.f64 (.f64 eps #s(literal 1/2 binary64))))
(* (cos (* 1/2 eps)) (sin (* 1/2 eps)))
(.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (cos.f64 (*.f64 eps #s(literal 1/2 binary64))))
(+ (* -1 (* x (pow (sin (* 1/2 eps)) 2))) (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))
(-.f64 (.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (cos.f64 (.f64 eps #s(literal 1/2 binary64)))) (.f64 x (pow.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) #s(literal 2 binary64))))
(+ (* x (+ (* -1 (pow (sin (* 1/2 eps)) 2)) (* -1/2 (* x (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))))) (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))
(fma.f64 x (-.f64 (.f64 (.f64 (cos.f64 (.f64 eps #s(literal 1/2 binary64))) (.f64 x #s(literal -1/2 binary64))) (sin.f64 (.f64 eps #s(literal 1/2 binary64)))) (pow.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) #s(literal 2 binary64))) (.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (cos.f64 (*.f64 eps #s(literal 1/2 binary64)))))
(+ (* x (+ (* -1 (pow (sin (* 1/2 eps)) 2)) (* x (+ (* -1/2 (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) (* 1/6 (* x (pow (sin (* 1/2 eps)) 2))))))) (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))
(fma.f64 x (fma.f64 x (fma.f64 (pow.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) #s(literal 2 binary64)) (.f64 x #s(literal 1/6 binary64)) (.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (.f64 #s(literal -1/2 binary64) (cos.f64 (.f64 eps #s(literal 1/2 binary64)))))) (neg.f64 (pow.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) #s(literal 2 binary64)))) (.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (cos.f64 (.f64 eps #s(literal 1/2 binary64)))))
(* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps)))
(.f64 (cos.f64 (fma.f64 eps #s(literal 1/2 binary64) x)) (sin.f64 (.f64 eps #s(literal 1/2 binary64))))
(* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps)))
(.f64 (cos.f64 (fma.f64 eps #s(literal 1/2 binary64) x)) (sin.f64 (.f64 eps #s(literal 1/2 binary64))))
(* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps)))
(.f64 (cos.f64 (fma.f64 eps #s(literal 1/2 binary64) x)) (sin.f64 (.f64 eps #s(literal 1/2 binary64))))
(* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps)))
(.f64 (cos.f64 (fma.f64 eps #s(literal 1/2 binary64) x)) (sin.f64 (.f64 eps #s(literal 1/2 binary64))))
(* (cos (* 1/2 (- eps (* -2 x)))) (sin (* 1/2 eps)))
(.f64 (cos.f64 (fma.f64 eps #s(literal 1/2 binary64) x)) (sin.f64 (.f64 eps #s(literal 1/2 binary64))))
(* (cos (* 1/2 (- eps (* -2 x)))) (sin (* 1/2 eps)))
(.f64 (cos.f64 (fma.f64 eps #s(literal 1/2 binary64) x)) (sin.f64 (.f64 eps #s(literal 1/2 binary64))))
(* (cos (* 1/2 (- eps (* -2 x)))) (sin (* 1/2 eps)))
(.f64 (cos.f64 (fma.f64 eps #s(literal 1/2 binary64) x)) (sin.f64 (.f64 eps #s(literal 1/2 binary64))))
(* (cos (* 1/2 (- eps (* -2 x)))) (sin (* 1/2 eps)))
(.f64 (cos.f64 (fma.f64 eps #s(literal 1/2 binary64) x)) (sin.f64 (.f64 eps #s(literal 1/2 binary64))))
(* 1/2 (* eps (cos x)))
(.f64 eps (.f64 (cos.f64 x) #s(literal 1/2 binary64)))
(* eps (+ (* -1/4 (* eps (sin x))) (* 1/2 (cos x))))
(.f64 eps (fma.f64 eps (.f64 (sin.f64 x) #s(literal -1/4 binary64)) (*.f64 (cos.f64 x) #s(literal 1/2 binary64))))
(* eps (+ (* 1/2 (cos x)) (* eps (+ (* -1/4 (sin x)) (* eps (+ (* -1/16 (cos x)) (* -1/48 (cos x))))))))
(.f64 eps (fma.f64 eps (fma.f64 eps (.f64 (cos.f64 x) #s(literal -1/12 binary64)) (.f64 (sin.f64 x) #s(literal -1/4 binary64))) (.f64 (cos.f64 x) #s(literal 1/2 binary64))))
(* eps (+ (* 1/2 (cos x)) (* eps (+ (* -1/4 (sin x)) (* eps (+ (* -1/16 (cos x)) (+ (* -1/48 (cos x)) (* 1/48 (* eps (sin x))))))))))
(.f64 eps (fma.f64 eps (fma.f64 eps (fma.f64 eps (.f64 (sin.f64 x) #s(literal 1/48 binary64)) (.f64 (cos.f64 x) #s(literal -1/12 binary64))) (.f64 (sin.f64 x) #s(literal -1/4 binary64))) (*.f64 (cos.f64 x) #s(literal 1/2 binary64))))
(* (cos (+ x (* 1/2 eps))) (sin (* 1/2 eps)))
(.f64 (cos.f64 (fma.f64 eps #s(literal 1/2 binary64) x)) (sin.f64 (.f64 eps #s(literal 1/2 binary64))))
(* (cos (+ x (* 1/2 eps))) (sin (* 1/2 eps)))
(.f64 (cos.f64 (fma.f64 eps #s(literal 1/2 binary64) x)) (sin.f64 (.f64 eps #s(literal 1/2 binary64))))
(* (cos (+ x (* 1/2 eps))) (sin (* 1/2 eps)))
(.f64 (cos.f64 (fma.f64 eps #s(literal 1/2 binary64) x)) (sin.f64 (.f64 eps #s(literal 1/2 binary64))))
(* (cos (+ x (* 1/2 eps))) (sin (* 1/2 eps)))
(.f64 (cos.f64 (fma.f64 eps #s(literal 1/2 binary64) x)) (sin.f64 (.f64 eps #s(literal 1/2 binary64))))
(* (cos (- x (* -1/2 eps))) (sin (* 1/2 eps)))
(.f64 (cos.f64 (fma.f64 eps #s(literal 1/2 binary64) x)) (sin.f64 (.f64 eps #s(literal 1/2 binary64))))
(* (cos (- x (* -1/2 eps))) (sin (* 1/2 eps)))
(.f64 (cos.f64 (fma.f64 eps #s(literal 1/2 binary64) x)) (sin.f64 (.f64 eps #s(literal 1/2 binary64))))
(* (cos (- x (* -1/2 eps))) (sin (* 1/2 eps)))
(.f64 (cos.f64 (fma.f64 eps #s(literal 1/2 binary64) x)) (sin.f64 (.f64 eps #s(literal 1/2 binary64))))
(* (cos (- x (* -1/2 eps))) (sin (* 1/2 eps)))
(.f64 (cos.f64 (fma.f64 eps #s(literal 1/2 binary64) x)) (sin.f64 (.f64 eps #s(literal 1/2 binary64))))
(* (cos (* 1/2 eps)) (sin (* 1/2 eps)))
(.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (cos.f64 (*.f64 eps #s(literal 1/2 binary64))))
(+ (* -1 (* x (pow (sin (* 1/2 eps)) 2))) (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))
(-.f64 (.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (cos.f64 (.f64 eps #s(literal 1/2 binary64)))) (.f64 x (pow.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) #s(literal 2 binary64))))
(+ (* x (+ (* -1 (pow (sin (* 1/2 eps)) 2)) (* -1/2 (* x (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))))) (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))
(fma.f64 x (-.f64 (.f64 (.f64 (cos.f64 (.f64 eps #s(literal 1/2 binary64))) (.f64 x #s(literal -1/2 binary64))) (sin.f64 (.f64 eps #s(literal 1/2 binary64)))) (pow.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) #s(literal 2 binary64))) (.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (cos.f64 (*.f64 eps #s(literal 1/2 binary64)))))
(+ (* x (+ (* -1 (pow (sin (* 1/2 eps)) 2)) (* x (+ (* -1/2 (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) (* 1/6 (* x (pow (sin (* 1/2 eps)) 2))))))) (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))
(fma.f64 x (fma.f64 x (fma.f64 (pow.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) #s(literal 2 binary64)) (.f64 x #s(literal 1/6 binary64)) (.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (.f64 #s(literal -1/2 binary64) (cos.f64 (.f64 eps #s(literal 1/2 binary64)))))) (neg.f64 (pow.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) #s(literal 2 binary64)))) (.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (cos.f64 (.f64 eps #s(literal 1/2 binary64)))))
(* (cos (+ x (* 1/2 eps))) (sin (* 1/2 eps)))
(.f64 (cos.f64 (fma.f64 eps #s(literal 1/2 binary64) x)) (sin.f64 (.f64 eps #s(literal 1/2 binary64))))
(* (cos (+ x (* 1/2 eps))) (sin (* 1/2 eps)))
(.f64 (cos.f64 (fma.f64 eps #s(literal 1/2 binary64) x)) (sin.f64 (.f64 eps #s(literal 1/2 binary64))))
(* (cos (+ x (* 1/2 eps))) (sin (* 1/2 eps)))
(.f64 (cos.f64 (fma.f64 eps #s(literal 1/2 binary64) x)) (sin.f64 (.f64 eps #s(literal 1/2 binary64))))
(* (cos (+ x (* 1/2 eps))) (sin (* 1/2 eps)))
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(* (cos (- (* 1/2 eps) (* -1 x))) (sin (* 1/2 eps)))
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(.f64 eps (.f64 eps (-.f64 #s(literal 1 binary64) (/.f64 x eps))))
(* (pow eps 2) (+ 1 (* -1 (/ x eps))))
(.f64 eps (.f64 eps (-.f64 #s(literal 1 binary64) (/.f64 x eps))))
(* (pow eps 2) (+ 1 (* -1 (/ x eps))))
(.f64 eps (.f64 eps (-.f64 #s(literal 1 binary64) (/.f64 x eps))))
(pow eps 2)
(*.f64 eps eps)
(* (pow eps 2) (+ 1 (* -1 (/ x eps))))
(.f64 eps (.f64 eps (-.f64 #s(literal 1 binary64) (/.f64 x eps))))
(* (pow eps 2) (+ 1 (* -1 (/ x eps))))
(.f64 eps (.f64 eps (-.f64 #s(literal 1 binary64) (/.f64 x eps))))
(* (pow eps 2) (+ 1 (* -1 (/ x eps))))
(.f64 eps (.f64 eps (-.f64 #s(literal 1 binary64) (/.f64 x eps))))
(pow eps 2)
(*.f64 eps eps)
(+ (* -1 (* eps x)) (pow eps 2))
(*.f64 eps (-.f64 eps x))
(+ (* -1 (* eps x)) (pow eps 2))
(*.f64 eps (-.f64 eps x))
(+ (* -1 (* eps x)) (pow eps 2))
(*.f64 eps (-.f64 eps x))
(* -1 (* eps x))
(*.f64 eps (neg.f64 x))
(* x (+ (* -1 eps) (/ (pow eps 2) x)))
(*.f64 x (fma.f64 eps (/.f64 eps x) (neg.f64 eps)))
(* x (+ (* -1 eps) (/ (pow eps 2) x)))
(*.f64 x (fma.f64 eps (/.f64 eps x) (neg.f64 eps)))
(* x (+ (* -1 eps) (/ (pow eps 2) x)))
(*.f64 x (fma.f64 eps (/.f64 eps x) (neg.f64 eps)))
(* -1 (* eps x))
(*.f64 eps (neg.f64 x))
(* -1 (* x (+ eps (* -1 (/ (pow eps 2) x)))))
(neg.f64 (.f64 x (-.f64 eps (/.f64 (.f64 eps eps) x))))
(* -1 (* x (+ eps (* -1 (/ (pow eps 2) x)))))
(neg.f64 (.f64 x (-.f64 eps (/.f64 (.f64 eps eps) x))))
(* -1 (* x (+ eps (* -1 (/ (pow eps 2) x)))))
(neg.f64 (.f64 x (-.f64 eps (/.f64 (.f64 eps eps) x))))
(/ 1 (pow eps 2))
(/.f64 #s(literal 1 binary64) (*.f64 eps eps))
(+ (/ 1 (pow eps 2)) (/ x (pow eps 3)))
(+.f64 (/.f64 #s(literal 1 binary64) (.f64 eps eps)) (/.f64 x (.f64 eps (*.f64 eps eps))))
(+ (* x (+ (* -1 (/ (pow x 2) (pow eps 5))) (/ 1 (pow eps 3)))) (/ 1 (pow eps 2)))
(fma.f64 x (-.f64 (/.f64 #s(literal 1 binary64) (.f64 eps (.f64 eps eps))) (/.f64 (.f64 x x) (pow.f64 eps #s(literal 5 binary64)))) (/.f64 #s(literal 1 binary64) (.f64 eps eps)))
(+ (* x (+ (* (pow x 2) (- (* -1 (/ x (pow eps 6))) (/ 1 (pow eps 5)))) (/ 1 (pow eps 3)))) (/ 1 (pow eps 2)))
(fma.f64 x (fma.f64 (.f64 x x) (+.f64 (/.f64 (neg.f64 x) (pow.f64 eps #s(literal 6 binary64))) (/.f64 #s(literal -1 binary64) (pow.f64 eps #s(literal 5 binary64)))) (/.f64 #s(literal 1 binary64) (.f64 eps (.f64 eps eps)))) (/.f64 #s(literal 1 binary64) (.f64 eps eps)))
(/ 1 (pow x 2))
(/.f64 #s(literal 1 binary64) (*.f64 x x))
(/ (+ 1 (/ eps x)) (pow x 2))
(/.f64 (+.f64 #s(literal 1 binary64) (/.f64 eps x)) (*.f64 x x))
(/ (- (+ 1 (* -1 (/ (+ (* -1 (pow eps 2)) (pow eps 2)) (pow x 2)))) (* -1 (/ eps x))) (pow x 2))
(/.f64 (+.f64 #s(literal 1 binary64) (/.f64 eps x)) (*.f64 x x))
(/ (- (+ 1 (* -1 (/ (+ (* eps (+ (* -1 (pow eps 2)) (pow eps 2))) (pow eps 3)) (pow x 3)))) (+ (* -1 (/ eps x)) (+ (* -1 (/ (pow eps 2) (pow x 2))) (/ (pow eps 2) (pow x 2))))) (pow x 2))
(/.f64 (+.f64 (/.f64 eps x) (-.f64 #s(literal 1 binary64) (/.f64 (fma.f64 eps (.f64 eps eps) #s(literal 0 binary64)) (.f64 x (.f64 x x))))) (.f64 x x))
(/ 1 (pow x 2))
(/.f64 #s(literal 1 binary64) (*.f64 x x))
(/ (+ 1 (/ eps x)) (pow x 2))
(/.f64 (+.f64 #s(literal 1 binary64) (/.f64 eps x)) (*.f64 x x))
(/ (+ 1 (* -1 (/ (- (+ (* -1 (/ (pow eps 2) x)) (/ (pow eps 2) x)) eps) x))) (pow x 2))
(/.f64 (+.f64 #s(literal 1 binary64) (/.f64 eps x)) (*.f64 x x))
(/ (+ 1 (* -1 (/ (- (* -1 (/ (- (+ (* -1 (/ (* eps (+ (* -1 (pow eps 2)) (pow eps 2))) x)) (* -1 (/ (pow eps 3) x))) (+ (* -1 (pow eps 2)) (pow eps 2))) x)) eps) x))) (pow x 2))
(/.f64 (-.f64 #s(literal 1 binary64) (/.f64 (-.f64 (/.f64 (/.f64 (.f64 eps (.f64 eps (neg.f64 eps))) x) (neg.f64 x)) eps) x)) (*.f64 x x))
(/ 1 (pow x 2))
(/.f64 #s(literal 1 binary64) (*.f64 x x))
(+ (/ 1 (pow x 2)) (/ eps (pow x 3)))
(+.f64 (/.f64 #s(literal 1 binary64) (.f64 x x)) (/.f64 eps (.f64 x (*.f64 x x))))
(+ (* eps (+ (* -1 (/ (pow eps 2) (pow x 5))) (/ 1 (pow x 3)))) (/ 1 (pow x 2)))
(fma.f64 eps (-.f64 (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x x))) (/.f64 (.f64 eps eps) (pow.f64 x #s(literal 5 binary64)))) (/.f64 #s(literal 1 binary64) (.f64 x x)))
(+ (* eps (+ (* (pow eps 2) (- (* -1 (/ eps (pow x 6))) (/ 1 (pow x 5)))) (/ 1 (pow x 3)))) (/ 1 (pow x 2)))
(fma.f64 eps (fma.f64 (.f64 eps eps) (+.f64 (/.f64 (neg.f64 eps) (pow.f64 x #s(literal 6 binary64))) (/.f64 #s(literal -1 binary64) (pow.f64 x #s(literal 5 binary64)))) (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x x)))) (/.f64 #s(literal 1 binary64) (.f64 x x)))
(/ 1 (pow eps 2))
(/.f64 #s(literal 1 binary64) (*.f64 eps eps))
(/ (+ 1 (/ x eps)) (pow eps 2))
(/.f64 (+.f64 #s(literal 1 binary64) (/.f64 x eps)) (*.f64 eps eps))
(/ (- (+ 1 (* -1 (/ (+ (* -1 (pow x 2)) (pow x 2)) (pow eps 2)))) (* -1 (/ x eps))) (pow eps 2))
(/.f64 (+.f64 #s(literal 1 binary64) (/.f64 x eps)) (*.f64 eps eps))
(/ (- (+ 1 (* -1 (/ (+ (* x (+ (* -1 (pow x 2)) (pow x 2))) (pow x 3)) (pow eps 3)))) (+ (* -1 (/ x eps)) (+ (* -1 (/ (pow x 2) (pow eps 2))) (/ (pow x 2) (pow eps 2))))) (pow eps 2))
(/.f64 (+.f64 (/.f64 x eps) (-.f64 #s(literal 1 binary64) (/.f64 (fma.f64 x (.f64 x x) #s(literal 0 binary64)) (.f64 eps (.f64 eps eps))))) (.f64 eps eps))
(/ 1 (pow eps 2))
(/.f64 #s(literal 1 binary64) (*.f64 eps eps))
(/ (+ 1 (/ x eps)) (pow eps 2))
(/.f64 (+.f64 #s(literal 1 binary64) (/.f64 x eps)) (*.f64 eps eps))
(/ (+ 1 (* -1 (/ (- (+ (* -1 (/ (pow x 2) eps)) (/ (pow x 2) eps)) x) eps))) (pow eps 2))
(/.f64 (+.f64 #s(literal 1 binary64) (/.f64 x eps)) (*.f64 eps eps))
(/ (+ 1 (* -1 (/ (- (* -1 (/ (- (+ (* -1 (/ (* x (+ (* -1 (pow x 2)) (pow x 2))) eps)) (* -1 (/ (pow x 3) eps))) (+ (* -1 (pow x 2)) (pow x 2))) eps)) x) eps))) (pow eps 2))
(/.f64 (-.f64 #s(literal 1 binary64) (/.f64 (-.f64 (/.f64 (neg.f64 (.f64 x (/.f64 (.f64 x x) eps))) (neg.f64 eps)) x) eps)) (*.f64 eps eps))

rewrite193.0ms (1.3%)

Memory

-21.6MiB live, 209.4MiB allocated

Algorithm

1×	batch-egg-rewrite

Rules

2 564×	`lower-fma.f32`
2 552×	`lower-fma.f64`
1 852×	`lower-*.f32`
1 826×	`lower-*.f64`
1 386×	`lower-/.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	75	374
0	109	309
1	437	255
0	3980	251

Stop Event

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

Counts

21 → 309

Calls

Call 1

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

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

eval112.0ms (0.8%)

Memory: 9.6MiB live, 209.4MiB allocated
Compiler: Compiled 22 346 to 2 192 computations (90.2% saved)

prune120.0ms (0.8%)

Memory

22.5MiB live, 258.6MiB allocated

Pruning

25 alts after pruning (21 fresh and 4 done)

	Pruned	Kept	Total
New	857	12	869
Fresh	6	9	15
Picked	2	3	5
Done	0	1	1
Total	865	25	890

Accuracy

100.0%

Counts

890 → 25

Alt Table

Click to see full alt table

Status	Accuracy	Program
	62.6%	(fma.f64 (sin.f64 x) (cos.f64 eps) (fma.f64 (sin.f64 eps) (cos.f64 x) (neg.f64 (sin.f64 x))))
	99.7%	(fma.f64 (sin.f64 eps) (cos.f64 x) (-.f64 (*.f64 (sin.f64 x) (cos.f64 eps)) (sin.f64 x)))
	7.2%	(/.f64 (/.f64 (-.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 (+.f64 x eps) #s(literal 2 binary64))) (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal -1/2 binary64) (cos.f64 (+.f64 x x)))))) #s(literal 2 binary64)) (.f64 (sin.f64 #s(approx ( (+ (* x 2) eps) 1/2) (.f64 eps (+.f64 #s(literal 1/2 binary64) (/.f64 x eps))))) (cos.f64 (.f64 (+.f64 eps #s(literal 0 binary64)) #s(literal 1/2 binary64)))))
✓	62.4%	(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
	21.5%	(.f64 (.f64 (sin.f64 (.f64 (fma.f64 (fma.f64 x (.f64 x x) (.f64 eps (.f64 eps eps))) (/.f64 #s(literal 1 binary64) (fma.f64 x x (.f64 eps (-.f64 eps x)))) (neg.f64 x)) #s(literal 1/2 binary64))) (cos.f64 #s(approx ( (+ (* x 2) eps) 1/2) (fma.f64 eps #s(literal 1/2 binary64) x)))) #s(literal 2 binary64))
	21.5%	(.f64 (.f64 (sin.f64 (.f64 (fma.f64 (fma.f64 eps (.f64 eps eps) (.f64 x (.f64 x x))) (/.f64 #s(literal 1 binary64) (fma.f64 eps (-.f64 eps x) (.f64 x x))) (neg.f64 x)) #s(literal 1/2 binary64))) (cos.f64 (.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)))) #s(literal 2 binary64))
	10.0%	(.f64 (.f64 (sin.f64 (.f64 (fma.f64 (/.f64 (fma.f64 eps (.f64 eps eps) (.f64 x (.f64 x x))) (fma.f64 x (.f64 (.f64 x x) (.f64 x (.f64 x x))) (.f64 (.f64 eps (-.f64 eps x)) (.f64 (-.f64 eps x) (.f64 eps (.f64 eps (-.f64 eps x))))))) (fma.f64 (.f64 eps (-.f64 eps x)) (-.f64 (.f64 eps (-.f64 eps x)) (.f64 x x)) (.f64 x (.f64 x (.f64 x x)))) (neg.f64 x)) #s(literal 1/2 binary64))) (cos.f64 (.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)))) #s(literal 2 binary64))
	99.1%	(.f64 (.f64 #s(approx (sin (* (+ eps 0) 1/2)) (.f64 #s(literal 1/2 binary64) eps)) (cos.f64 #s(approx ( (+ (* x 2) eps) 1/2) (fma.f64 eps #s(literal 1/2 binary64) x)))) #s(literal 2 binary64))
	99.1%	(.f64 (.f64 #s(approx (sin (* (+ eps 0) 1/2)) (.f64 #s(literal 1/2 binary64) eps)) (cos.f64 #s(approx ( (+ (* x 2) eps) 1/2) (*.f64 eps (+.f64 #s(literal 1/2 binary64) (/.f64 x eps)))))) #s(literal 2 binary64))
▶	100.0%	(.f64 #s(approx ( (sin (* (+ eps 0) 1/2)) (cos (* (+ (* x 2) eps) 1/2))) (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (/.f64 (-.f64 (pow.f64 (.f64 (cos.f64 (.f64 eps #s(literal 1/2 binary64))) (cos.f64 x)) #s(literal 3 binary64)) (pow.f64 (.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (sin.f64 x)) #s(literal 3 binary64))) (fma.f64 (.f64 (cos.f64 (.f64 eps #s(literal 1/2 binary64))) (cos.f64 x)) (.f64 (cos.f64 (.f64 eps #s(literal 1/2 binary64))) (cos.f64 x)) (fma.f64 (.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (sin.f64 x)) (.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (sin.f64 x)) (.f64 (.f64 (cos.f64 (.f64 eps #s(literal 1/2 binary64))) (cos.f64 x)) (.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) (sin.f64 x)))))))) #s(literal 2 binary64))
	100.0%	(.f64 #s(approx ( (sin (* (+ eps 0) 1/2)) (cos (* (+ (* x 2) eps) 1/2))) (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (-.f64 (.f64 (cos.f64 (.f64 eps #s(literal 1/2 binary64))) (cos.f64 x)) (.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (sin.f64 x))))) #s(literal 2 binary64))
✓	99.8%	(.f64 #s(approx ( (sin (* (+ eps 0) 1/2)) (cos (* (+ (* x 2) eps) 1/2))) (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)))) #s(literal 2 binary64))
	99.5%	(.f64 #s(approx ( (sin (* (+ eps 0) 1/2)) (cos (* (+ (* x 2) eps) 1/2))) (.f64 #s(approx (sin ( 1/2 eps)) (.f64 eps (fma.f64 (.f64 eps eps) (fma.f64 (.f64 eps eps) (fma.f64 (.f64 eps eps) #s(literal -1/645120 binary64) #s(literal 1/3840 binary64)) #s(literal -1/48 binary64)) #s(literal 1/2 binary64)))) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)))) #s(literal 2 binary64))
▶	99.4%	(.f64 #s(approx ( (sin (* (+ eps 0) 1/2)) (cos (* (+ (* x 2) eps) 1/2))) (.f64 #s(approx (sin ( 1/2 eps)) (.f64 eps (fma.f64 eps (.f64 eps (fma.f64 (*.f64 eps eps) #s(literal 1/3840 binary64) #s(literal -1/48 binary64))) #s(literal 1/2 binary64)))) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)))) #s(literal 2 binary64))
	99.2%	(.f64 #s(approx ( (sin (* (+ eps 0) 1/2)) (cos (* (+ (* x 2) eps) 1/2))) (.f64 #s(approx (sin ( 1/2 eps)) (.f64 eps (fma.f64 eps (.f64 eps #s(literal -1/48 binary64)) #s(literal 1/2 binary64)))) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)))) #s(literal 2 binary64))
▶	7.3%	#s(approx (/ (/ (- 1/2 (+ (* 1/2 (cos (* (+ x eps) 2))) (+ 1/2 (* -1/2 (cos (+ x x)))))) 2) (* (sin (* (+ (* x 2) eps) 1/2)) (cos (* (+ eps 0) 1/2)))) (/.f64 (fma.f64 #s(literal -1/4 binary64) (cos.f64 (.f64 #s(literal 2 binary64) (+.f64 eps x))) (.f64 (cos.f64 (.f64 x #s(literal 2 binary64))) #s(literal 1/4 binary64))) (.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) eps)) (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x)))))
✓	5.5%	#s(approx (/ (/ (- 1/2 (+ (* 1/2 (cos (* (+ x eps) 2))) (+ 1/2 (* -1/2 (cos (+ x x)))))) 2) (* (sin (* (+ (* x 2) eps) 1/2)) (cos (* (+ eps 0) 1/2)))) #s(literal 0 binary64))
▶	34.1%	#s(approx (- (sin (+ x eps)) (sin x)) (/.f64 #s(literal 1 binary64) (/.f64 (+.f64 x #s(approx (+ (* (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) (fma.f64 eps (fma.f64 #s(literal -1/2 binary64) (.f64 x x) #s(literal 1 binary64)) x))) (.f64 (+.f64 x #s(approx (+ (* (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) (fma.f64 eps (fma.f64 #s(literal -1/2 binary64) (.f64 x x) #s(literal 1 binary64)) x))) (-.f64 #s(approx (+ ( (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) (fma.f64 eps (fma.f64 #s(literal -1/2 binary64) (*.f64 x x) #s(literal 1 binary64)) x)) x)))))
✓	61.0%	#s(approx (- (sin (+ x eps)) (sin x)) (-.f64 #s(approx (+ (* (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) (fma.f64 eps (fma.f64 x (*.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64)) x)) x))
▶	61.2%	#s(approx (- (sin (+ x eps)) (sin x)) (-.f64 #s(approx (+ (* (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) #s(approx (+ (* eps (+ (* x (* x -1/2)) 1)) x) (+.f64 eps x))) x))
	98.7%	#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 eps (cos.f64 x)))
	97.6%	#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (- (+ (* (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) x) (fma.f64 eps (fma.f64 #s(literal -1/2 binary64) (.f64 x (+.f64 eps x)) (.f64 eps (.f64 eps (fma.f64 (.f64 x x) #s(literal 1/12 binary64) #s(literal -1/6 binary64))))) eps)))
	97.5%	#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (- (+ (* (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) x) (fma.f64 eps (.f64 x (.f64 x #s(literal -1/2 binary64))) eps)))
	97.5%	#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (- (+ (* (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) x) (fma.f64 #s(literal -1/2 binary64) (.f64 (.f64 x (+.f64 eps x)) eps) eps)))
	97.5%	#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (sin eps) (fma.f64 eps (.f64 eps (.f64 eps #s(literal -1/6 binary64))) eps)))

Compiler

Compiled 1 205 to 599 computations (50.3% saved)

simplify314.0ms (2.2%)

Memory

-18.8MiB live, 461.3MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 20 expressions of interest:

New	Metric	Score	Program
✓	cost-diff	0	(fma.f64 #s(literal -1/4 binary64) (cos.f64 (.f64 #s(literal 2 binary64) (+.f64 eps x))) (.f64 (cos.f64 (*.f64 x #s(literal 2 binary64))) #s(literal 1/4 binary64)))
✓	cost-diff	0	#s(approx (/ (/ (- 1/2 (+ (* 1/2 (cos (* (+ x eps) 2))) (+ 1/2 (* -1/2 (cos (+ x x)))))) 2) (* (sin (* (+ (* x 2) eps) 1/2)) (cos (* (+ eps 0) 1/2)))) (/.f64 (fma.f64 #s(literal -1/4 binary64) (cos.f64 (.f64 #s(literal 2 binary64) (+.f64 eps x))) (.f64 (cos.f64 (.f64 x #s(literal 2 binary64))) #s(literal 1/4 binary64))) (.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) eps)) (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x)))))
✓	cost-diff	128	(*.f64 x #s(literal 2 binary64))
✓	cost-diff	192	(/.f64 (fma.f64 #s(literal -1/4 binary64) (cos.f64 (.f64 #s(literal 2 binary64) (+.f64 eps x))) (.f64 (cos.f64 (.f64 x #s(literal 2 binary64))) #s(literal 1/4 binary64))) (.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) eps)) (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x))))
✓	cost-diff	0	#s(approx (sin (* 1/2 eps)) (.f64 eps (fma.f64 eps (.f64 eps (fma.f64 (*.f64 eps eps) #s(literal 1/3840 binary64) #s(literal -1/48 binary64))) #s(literal 1/2 binary64))))
✓	cost-diff	0	(.f64 #s(approx (sin ( 1/2 eps)) (.f64 eps (fma.f64 eps (.f64 eps (fma.f64 (*.f64 eps eps) #s(literal 1/3840 binary64) #s(literal -1/48 binary64))) #s(literal 1/2 binary64)))) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)))
✓	cost-diff	0	#s(approx (* (sin (* (+ eps 0) 1/2)) (cos (* (+ (* x 2) eps) 1/2))) (.f64 #s(approx (sin ( 1/2 eps)) (.f64 eps (fma.f64 eps (.f64 eps (fma.f64 (*.f64 eps eps) #s(literal 1/3840 binary64) #s(literal -1/48 binary64))) #s(literal 1/2 binary64)))) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x))))
✓	cost-diff	0	(.f64 #s(approx ( (sin (* (+ eps 0) 1/2)) (cos (* (+ (* x 2) eps) 1/2))) (.f64 #s(approx (sin ( 1/2 eps)) (.f64 eps (fma.f64 eps (.f64 eps (fma.f64 (*.f64 eps eps) #s(literal 1/3840 binary64) #s(literal -1/48 binary64))) #s(literal 1/2 binary64)))) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)))) #s(literal 2 binary64))
✓	cost-diff	0	(+.f64 x #s(approx (+ (* (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) (fma.f64 eps (fma.f64 #s(literal -1/2 binary64) (*.f64 x x) #s(literal 1 binary64)) x)))
✓	cost-diff	0	#s(approx (- (sin (+ x eps)) (sin x)) (/.f64 #s(literal 1 binary64) (/.f64 (+.f64 x #s(approx (+ (* (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) (fma.f64 eps (fma.f64 #s(literal -1/2 binary64) (.f64 x x) #s(literal 1 binary64)) x))) (.f64 (+.f64 x #s(approx (+ (* (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) (fma.f64 eps (fma.f64 #s(literal -1/2 binary64) (.f64 x x) #s(literal 1 binary64)) x))) (-.f64 #s(approx (+ ( (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) (fma.f64 eps (fma.f64 #s(literal -1/2 binary64) (*.f64 x x) #s(literal 1 binary64)) x)) x)))))
✓	cost-diff	1408	(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 x #s(approx (+ (* (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) (fma.f64 eps (fma.f64 #s(literal -1/2 binary64) (.f64 x x) #s(literal 1 binary64)) x))) (.f64 (+.f64 x #s(approx (+ (* (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) (fma.f64 eps (fma.f64 #s(literal -1/2 binary64) (.f64 x x) #s(literal 1 binary64)) x))) (-.f64 #s(approx (+ ( (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) (fma.f64 eps (fma.f64 #s(literal -1/2 binary64) (*.f64 x x) #s(literal 1 binary64)) x)) x))))
✓	cost-diff	2880	(/.f64 (+.f64 x #s(approx (+ (* (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) (fma.f64 eps (fma.f64 #s(literal -1/2 binary64) (.f64 x x) #s(literal 1 binary64)) x))) (.f64 (+.f64 x #s(approx (+ (* (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) (fma.f64 eps (fma.f64 #s(literal -1/2 binary64) (.f64 x x) #s(literal 1 binary64)) x))) (-.f64 #s(approx (+ ( (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) (fma.f64 eps (fma.f64 #s(literal -1/2 binary64) (*.f64 x x) #s(literal 1 binary64)) x)) x)))
✓	cost-diff	0	#s(approx (+ (* eps (+ (* x (* x -1/2)) 1)) x) (+.f64 eps x))
✓	cost-diff	0	#s(approx (+ (* (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) #s(approx (+ (* eps (+ (* x (* x -1/2)) 1)) x) (+.f64 eps x)))
✓	cost-diff	0	(-.f64 #s(approx (+ (* (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) #s(approx (+ (* eps (+ (* x (* x -1/2)) 1)) x) (+.f64 eps x))) x)
✓	cost-diff	0	#s(approx (- (sin (+ x eps)) (sin x)) (-.f64 #s(approx (+ (* (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) #s(approx (+ (* eps (+ (* x (* x -1/2)) 1)) x) (+.f64 eps x))) x))
✓	cost-diff	0	(.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (/.f64 (-.f64 (pow.f64 (.f64 (cos.f64 (.f64 eps #s(literal 1/2 binary64))) (cos.f64 x)) #s(literal 3 binary64)) (pow.f64 (.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (sin.f64 x)) #s(literal 3 binary64))) (fma.f64 (.f64 (cos.f64 (.f64 eps #s(literal 1/2 binary64))) (cos.f64 x)) (.f64 (cos.f64 (.f64 eps #s(literal 1/2 binary64))) (cos.f64 x)) (fma.f64 (.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (sin.f64 x)) (.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (sin.f64 x)) (.f64 (.f64 (cos.f64 (.f64 eps #s(literal 1/2 binary64))) (cos.f64 x)) (.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) (sin.f64 x)))))))
✓	cost-diff	0	#s(approx (* (sin (* (+ eps 0) 1/2)) (cos (* (+ (* x 2) eps) 1/2))) (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (/.f64 (-.f64 (pow.f64 (.f64 (cos.f64 (.f64 eps #s(literal 1/2 binary64))) (cos.f64 x)) #s(literal 3 binary64)) (pow.f64 (.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (sin.f64 x)) #s(literal 3 binary64))) (fma.f64 (.f64 (cos.f64 (.f64 eps #s(literal 1/2 binary64))) (cos.f64 x)) (.f64 (cos.f64 (.f64 eps #s(literal 1/2 binary64))) (cos.f64 x)) (fma.f64 (.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (sin.f64 x)) (.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (sin.f64 x)) (.f64 (.f64 (cos.f64 (.f64 eps #s(literal 1/2 binary64))) (cos.f64 x)) (.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) (sin.f64 x))))))))
✓	cost-diff	0	(.f64 #s(approx ( (sin (* (+ eps 0) 1/2)) (cos (* (+ (* x 2) eps) 1/2))) (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (/.f64 (-.f64 (pow.f64 (.f64 (cos.f64 (.f64 eps #s(literal 1/2 binary64))) (cos.f64 x)) #s(literal 3 binary64)) (pow.f64 (.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (sin.f64 x)) #s(literal 3 binary64))) (fma.f64 (.f64 (cos.f64 (.f64 eps #s(literal 1/2 binary64))) (cos.f64 x)) (.f64 (cos.f64 (.f64 eps #s(literal 1/2 binary64))) (cos.f64 x)) (fma.f64 (.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (sin.f64 x)) (.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (sin.f64 x)) (.f64 (.f64 (cos.f64 (.f64 eps #s(literal 1/2 binary64))) (cos.f64 x)) (.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) (sin.f64 x)))))))) #s(literal 2 binary64))
✓	cost-diff	13760	(fma.f64 (.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (sin.f64 x)) (.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (sin.f64 x)) (.f64 (.f64 (cos.f64 (.f64 eps #s(literal 1/2 binary64))) (cos.f64 x)) (.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) (sin.f64 x))))

Rules

7 324×	`lower-fma.f32`
7 308×	`lower-fma.f64`
4 990×	`lower-*.f32`
4 954×	`lower-*.f64`
1 666×	`lower-/.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	106	1360
0	160	1349
1	320	1135
2	736	1121
3	2181	1097
4	4817	1094
0	8266	1066

Stop Event

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

Calls

Call 1

Inputs
(.f64 #s(approx ( (sin (* (+ eps 0) 1/2)) (cos (* (+ (* x 2) eps) 1/2))) (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (/.f64 (-.f64 (pow.f64 (.f64 (cos.f64 (.f64 eps #s(literal 1/2 binary64))) (cos.f64 x)) #s(literal 3 binary64)) (pow.f64 (.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (sin.f64 x)) #s(literal 3 binary64))) (fma.f64 (.f64 (cos.f64 (.f64 eps #s(literal 1/2 binary64))) (cos.f64 x)) (.f64 (cos.f64 (.f64 eps #s(literal 1/2 binary64))) (cos.f64 x)) (fma.f64 (.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (sin.f64 x)) (.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (sin.f64 x)) (.f64 (.f64 (cos.f64 (.f64 eps #s(literal 1/2 binary64))) (cos.f64 x)) (.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) (sin.f64 x)))))))) #s(literal 2 binary64))
#s(approx (* (sin (* (+ eps 0) 1/2)) (cos (* (+ (* x 2) eps) 1/2))) (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (/.f64 (-.f64 (pow.f64 (.f64 (cos.f64 (.f64 eps #s(literal 1/2 binary64))) (cos.f64 x)) #s(literal 3 binary64)) (pow.f64 (.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (sin.f64 x)) #s(literal 3 binary64))) (fma.f64 (.f64 (cos.f64 (.f64 eps #s(literal 1/2 binary64))) (cos.f64 x)) (.f64 (cos.f64 (.f64 eps #s(literal 1/2 binary64))) (cos.f64 x)) (fma.f64 (.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (sin.f64 x)) (.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (sin.f64 x)) (.f64 (.f64 (cos.f64 (.f64 eps #s(literal 1/2 binary64))) (cos.f64 x)) (.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) (sin.f64 x))))))))
(.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (/.f64 (-.f64 (pow.f64 (.f64 (cos.f64 (.f64 eps #s(literal 1/2 binary64))) (cos.f64 x)) #s(literal 3 binary64)) (pow.f64 (.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (sin.f64 x)) #s(literal 3 binary64))) (fma.f64 (.f64 (cos.f64 (.f64 eps #s(literal 1/2 binary64))) (cos.f64 x)) (.f64 (cos.f64 (.f64 eps #s(literal 1/2 binary64))) (cos.f64 x)) (fma.f64 (.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (sin.f64 x)) (.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (sin.f64 x)) (.f64 (.f64 (cos.f64 (.f64 eps #s(literal 1/2 binary64))) (cos.f64 x)) (.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) (sin.f64 x)))))))
(sin.f64 (*.f64 #s(literal 1/2 binary64) eps))
(*.f64 #s(literal 1/2 binary64) eps)
#s(literal 1/2 binary64)
eps
(/.f64 (-.f64 (pow.f64 (.f64 (cos.f64 (.f64 eps #s(literal 1/2 binary64))) (cos.f64 x)) #s(literal 3 binary64)) (pow.f64 (.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (sin.f64 x)) #s(literal 3 binary64))) (fma.f64 (.f64 (cos.f64 (.f64 eps #s(literal 1/2 binary64))) (cos.f64 x)) (.f64 (cos.f64 (.f64 eps #s(literal 1/2 binary64))) (cos.f64 x)) (fma.f64 (.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (sin.f64 x)) (.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (sin.f64 x)) (.f64 (.f64 (cos.f64 (.f64 eps #s(literal 1/2 binary64))) (cos.f64 x)) (.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) (sin.f64 x))))))
(-.f64 (pow.f64 (.f64 (cos.f64 (.f64 eps #s(literal 1/2 binary64))) (cos.f64 x)) #s(literal 3 binary64)) (pow.f64 (.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (sin.f64 x)) #s(literal 3 binary64)))
(pow.f64 (.f64 (cos.f64 (.f64 eps #s(literal 1/2 binary64))) (cos.f64 x)) #s(literal 3 binary64))
(.f64 (cos.f64 (.f64 eps #s(literal 1/2 binary64))) (cos.f64 x))
(cos.f64 (*.f64 eps #s(literal 1/2 binary64)))
(*.f64 eps #s(literal 1/2 binary64))
(cos.f64 x)
x
#s(literal 3 binary64)
(pow.f64 (.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (sin.f64 x)) #s(literal 3 binary64))
(.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (sin.f64 x))
(sin.f64 (*.f64 eps #s(literal 1/2 binary64)))
(sin.f64 x)
(fma.f64 (.f64 (cos.f64 (.f64 eps #s(literal 1/2 binary64))) (cos.f64 x)) (.f64 (cos.f64 (.f64 eps #s(literal 1/2 binary64))) (cos.f64 x)) (fma.f64 (.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (sin.f64 x)) (.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (sin.f64 x)) (.f64 (.f64 (cos.f64 (.f64 eps #s(literal 1/2 binary64))) (cos.f64 x)) (.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) (sin.f64 x)))))
(fma.f64 (.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (sin.f64 x)) (.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (sin.f64 x)) (.f64 (.f64 (cos.f64 (.f64 eps #s(literal 1/2 binary64))) (cos.f64 x)) (.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) (sin.f64 x))))
(.f64 (.f64 (cos.f64 (.f64 eps #s(literal 1/2 binary64))) (cos.f64 x)) (.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) (sin.f64 x)))
#s(literal 2 binary64)
#s(approx (- (sin (+ x eps)) (sin x)) (-.f64 #s(approx (+ (* (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) #s(approx (+ (* eps (+ (* x (* x -1/2)) 1)) x) (+.f64 eps x))) x))
(-.f64 #s(approx (+ (* (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) #s(approx (+ (* eps (+ (* x (* x -1/2)) 1)) x) (+.f64 eps x))) x)
#s(approx (+ (* (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) #s(approx (+ (* eps (+ (* x (* x -1/2)) 1)) x) (+.f64 eps x)))
#s(approx (+ (* eps (+ (* x (* x -1/2)) 1)) x) (+.f64 eps x))
(+.f64 eps x)
eps
x
#s(approx (- (sin (+ x eps)) (sin x)) (/.f64 #s(literal 1 binary64) (/.f64 (+.f64 x #s(approx (+ (* (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) (fma.f64 eps (fma.f64 #s(literal -1/2 binary64) (.f64 x x) #s(literal 1 binary64)) x))) (.f64 (+.f64 x #s(approx (+ (* (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) (fma.f64 eps (fma.f64 #s(literal -1/2 binary64) (.f64 x x) #s(literal 1 binary64)) x))) (-.f64 #s(approx (+ ( (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) (fma.f64 eps (fma.f64 #s(literal -1/2 binary64) (*.f64 x x) #s(literal 1 binary64)) x)) x)))))
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 x #s(approx (+ (* (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) (fma.f64 eps (fma.f64 #s(literal -1/2 binary64) (.f64 x x) #s(literal 1 binary64)) x))) (.f64 (+.f64 x #s(approx (+ (* (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) (fma.f64 eps (fma.f64 #s(literal -1/2 binary64) (.f64 x x) #s(literal 1 binary64)) x))) (-.f64 #s(approx (+ ( (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) (fma.f64 eps (fma.f64 #s(literal -1/2 binary64) (*.f64 x x) #s(literal 1 binary64)) x)) x))))
#s(literal 1 binary64)
(/.f64 (+.f64 x #s(approx (+ (* (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) (fma.f64 eps (fma.f64 #s(literal -1/2 binary64) (.f64 x x) #s(literal 1 binary64)) x))) (.f64 (+.f64 x #s(approx (+ (* (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) (fma.f64 eps (fma.f64 #s(literal -1/2 binary64) (.f64 x x) #s(literal 1 binary64)) x))) (-.f64 #s(approx (+ ( (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) (fma.f64 eps (fma.f64 #s(literal -1/2 binary64) (*.f64 x x) #s(literal 1 binary64)) x)) x)))
(+.f64 x #s(approx (+ (* (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) (fma.f64 eps (fma.f64 #s(literal -1/2 binary64) (*.f64 x x) #s(literal 1 binary64)) x)))
x
#s(approx (+ (* (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) (fma.f64 eps (fma.f64 #s(literal -1/2 binary64) (*.f64 x x) #s(literal 1 binary64)) x))
(fma.f64 eps (fma.f64 #s(literal -1/2 binary64) (*.f64 x x) #s(literal 1 binary64)) x)
eps
(fma.f64 #s(literal -1/2 binary64) (*.f64 x x) #s(literal 1 binary64))
#s(literal -1/2 binary64)
(*.f64 x x)
(.f64 (+.f64 x #s(approx (+ ( (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) (fma.f64 eps (fma.f64 #s(literal -1/2 binary64) (.f64 x x) #s(literal 1 binary64)) x))) (-.f64 #s(approx (+ ( (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) (fma.f64 eps (fma.f64 #s(literal -1/2 binary64) (*.f64 x x) #s(literal 1 binary64)) x)) x))
(-.f64 #s(approx (+ (* (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) (fma.f64 eps (fma.f64 #s(literal -1/2 binary64) (*.f64 x x) #s(literal 1 binary64)) x)) x)
(.f64 #s(approx ( (sin (* (+ eps 0) 1/2)) (cos (* (+ (* x 2) eps) 1/2))) (.f64 #s(approx (sin ( 1/2 eps)) (.f64 eps (fma.f64 eps (.f64 eps (fma.f64 (*.f64 eps eps) #s(literal 1/3840 binary64) #s(literal -1/48 binary64))) #s(literal 1/2 binary64)))) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)))) #s(literal 2 binary64))
#s(approx (* (sin (* (+ eps 0) 1/2)) (cos (* (+ (* x 2) eps) 1/2))) (.f64 #s(approx (sin ( 1/2 eps)) (.f64 eps (fma.f64 eps (.f64 eps (fma.f64 (*.f64 eps eps) #s(literal 1/3840 binary64) #s(literal -1/48 binary64))) #s(literal 1/2 binary64)))) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x))))
(.f64 #s(approx (sin ( 1/2 eps)) (.f64 eps (fma.f64 eps (.f64 eps (fma.f64 (*.f64 eps eps) #s(literal 1/3840 binary64) #s(literal -1/48 binary64))) #s(literal 1/2 binary64)))) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)))
#s(approx (sin (* 1/2 eps)) (.f64 eps (fma.f64 eps (.f64 eps (fma.f64 (*.f64 eps eps) #s(literal 1/3840 binary64) #s(literal -1/48 binary64))) #s(literal 1/2 binary64))))
(.f64 eps (fma.f64 eps (.f64 eps (fma.f64 (*.f64 eps eps) #s(literal 1/3840 binary64) #s(literal -1/48 binary64))) #s(literal 1/2 binary64)))
eps
(fma.f64 eps (.f64 eps (fma.f64 (.f64 eps eps) #s(literal 1/3840 binary64) #s(literal -1/48 binary64))) #s(literal 1/2 binary64))
(.f64 eps (fma.f64 (.f64 eps eps) #s(literal 1/3840 binary64) #s(literal -1/48 binary64)))
(fma.f64 (*.f64 eps eps) #s(literal 1/3840 binary64) #s(literal -1/48 binary64))
(*.f64 eps eps)
#s(literal 1/3840 binary64)
#s(literal -1/48 binary64)
#s(literal 1/2 binary64)
(cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x))
(fma.f64 #s(literal 1/2 binary64) eps x)
x
#s(literal 2 binary64)
#s(approx (/ (/ (- 1/2 (+ (* 1/2 (cos (* (+ x eps) 2))) (+ 1/2 (* -1/2 (cos (+ x x)))))) 2) (* (sin (* (+ (* x 2) eps) 1/2)) (cos (* (+ eps 0) 1/2)))) (/.f64 (fma.f64 #s(literal -1/4 binary64) (cos.f64 (.f64 #s(literal 2 binary64) (+.f64 eps x))) (.f64 (cos.f64 (.f64 x #s(literal 2 binary64))) #s(literal 1/4 binary64))) (.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) eps)) (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x)))))
(/.f64 (fma.f64 #s(literal -1/4 binary64) (cos.f64 (.f64 #s(literal 2 binary64) (+.f64 eps x))) (.f64 (cos.f64 (.f64 x #s(literal 2 binary64))) #s(literal 1/4 binary64))) (.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) eps)) (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x))))
(fma.f64 #s(literal -1/4 binary64) (cos.f64 (.f64 #s(literal 2 binary64) (+.f64 eps x))) (.f64 (cos.f64 (*.f64 x #s(literal 2 binary64))) #s(literal 1/4 binary64)))
#s(literal -1/4 binary64)
(cos.f64 (*.f64 #s(literal 2 binary64) (+.f64 eps x)))
(*.f64 #s(literal 2 binary64) (+.f64 eps x))
#s(literal 2 binary64)
(+.f64 eps x)
eps
x
(.f64 (cos.f64 (.f64 x #s(literal 2 binary64))) #s(literal 1/4 binary64))
(cos.f64 (*.f64 x #s(literal 2 binary64)))
(*.f64 x #s(literal 2 binary64))
#s(literal 1/4 binary64)
(.f64 (cos.f64 (.f64 #s(literal 1/2 binary64) eps)) (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x)))
(cos.f64 (*.f64 #s(literal 1/2 binary64) eps))
(*.f64 #s(literal 1/2 binary64) eps)
#s(literal 1/2 binary64)
(sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x))
(fma.f64 #s(literal 1/2 binary64) eps x)

Outputs
(.f64 #s(approx ( (sin (* (+ eps 0) 1/2)) (cos (* (+ (* x 2) eps) 1/2))) (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (/.f64 (-.f64 (pow.f64 (.f64 (cos.f64 (.f64 eps #s(literal 1/2 binary64))) (cos.f64 x)) #s(literal 3 binary64)) (pow.f64 (.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (sin.f64 x)) #s(literal 3 binary64))) (fma.f64 (.f64 (cos.f64 (.f64 eps #s(literal 1/2 binary64))) (cos.f64 x)) (.f64 (cos.f64 (.f64 eps #s(literal 1/2 binary64))) (cos.f64 x)) (fma.f64 (.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (sin.f64 x)) (.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (sin.f64 x)) (.f64 (.f64 (cos.f64 (.f64 eps #s(literal 1/2 binary64))) (cos.f64 x)) (.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) (sin.f64 x)))))))) #s(literal 2 binary64))
(.f64 #s(literal 2 binary64) #s(approx ( (sin (* (+ eps 0) 1/2)) (cos (* (+ (* x 2) eps) 1/2))) (/.f64 (.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (-.f64 (pow.f64 (.f64 (cos.f64 (.f64 eps #s(literal 1/2 binary64))) (cos.f64 x)) #s(literal 3 binary64)) (pow.f64 (.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (sin.f64 x)) #s(literal 3 binary64)))) (fma.f64 (cos.f64 (.f64 eps #s(literal 1/2 binary64))) (.f64 (cos.f64 x) (fma.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (sin.f64 x) (.f64 (cos.f64 (.f64 eps #s(literal 1/2 binary64))) (cos.f64 x)))) (.f64 (.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (sin.f64 (.f64 eps #s(literal 1/2 binary64)))) (.f64 (sin.f64 x) (sin.f64 x)))))))
#s(approx (* (sin (* (+ eps 0) 1/2)) (cos (* (+ (* x 2) eps) 1/2))) (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (/.f64 (-.f64 (pow.f64 (.f64 (cos.f64 (.f64 eps #s(literal 1/2 binary64))) (cos.f64 x)) #s(literal 3 binary64)) (pow.f64 (.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (sin.f64 x)) #s(literal 3 binary64))) (fma.f64 (.f64 (cos.f64 (.f64 eps #s(literal 1/2 binary64))) (cos.f64 x)) (.f64 (cos.f64 (.f64 eps #s(literal 1/2 binary64))) (cos.f64 x)) (fma.f64 (.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (sin.f64 x)) (.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (sin.f64 x)) (.f64 (.f64 (cos.f64 (.f64 eps #s(literal 1/2 binary64))) (cos.f64 x)) (.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) (sin.f64 x))))))))
#s(approx (* (sin (* (+ eps 0) 1/2)) (cos (* (+ (* x 2) eps) 1/2))) (/.f64 (.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (-.f64 (pow.f64 (.f64 (cos.f64 (.f64 eps #s(literal 1/2 binary64))) (cos.f64 x)) #s(literal 3 binary64)) (pow.f64 (.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (sin.f64 x)) #s(literal 3 binary64)))) (fma.f64 (cos.f64 (.f64 eps #s(literal 1/2 binary64))) (.f64 (cos.f64 x) (fma.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (sin.f64 x) (.f64 (cos.f64 (.f64 eps #s(literal 1/2 binary64))) (cos.f64 x)))) (.f64 (.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (sin.f64 (.f64 eps #s(literal 1/2 binary64)))) (.f64 (sin.f64 x) (sin.f64 x))))))
(.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (/.f64 (-.f64 (pow.f64 (.f64 (cos.f64 (.f64 eps #s(literal 1/2 binary64))) (cos.f64 x)) #s(literal 3 binary64)) (pow.f64 (.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (sin.f64 x)) #s(literal 3 binary64))) (fma.f64 (.f64 (cos.f64 (.f64 eps #s(literal 1/2 binary64))) (cos.f64 x)) (.f64 (cos.f64 (.f64 eps #s(literal 1/2 binary64))) (cos.f64 x)) (fma.f64 (.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (sin.f64 x)) (.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (sin.f64 x)) (.f64 (.f64 (cos.f64 (.f64 eps #s(literal 1/2 binary64))) (cos.f64 x)) (.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) (sin.f64 x)))))))
(/.f64 (.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (-.f64 (pow.f64 (.f64 (cos.f64 (.f64 eps #s(literal 1/2 binary64))) (cos.f64 x)) #s(literal 3 binary64)) (pow.f64 (.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (sin.f64 x)) #s(literal 3 binary64)))) (fma.f64 (cos.f64 (.f64 eps #s(literal 1/2 binary64))) (.f64 (cos.f64 x) (fma.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (sin.f64 x) (.f64 (cos.f64 (.f64 eps #s(literal 1/2 binary64))) (cos.f64 x)))) (.f64 (.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (sin.f64 (.f64 eps #s(literal 1/2 binary64)))) (.f64 (sin.f64 x) (sin.f64 x)))))
(sin.f64 (*.f64 #s(literal 1/2 binary64) eps))
(sin.f64 (*.f64 eps #s(literal 1/2 binary64)))
(*.f64 #s(literal 1/2 binary64) eps)
(*.f64 eps #s(literal 1/2 binary64))
#s(literal 1/2 binary64)
eps
(/.f64 (-.f64 (pow.f64 (.f64 (cos.f64 (.f64 eps #s(literal 1/2 binary64))) (cos.f64 x)) #s(literal 3 binary64)) (pow.f64 (.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (sin.f64 x)) #s(literal 3 binary64))) (fma.f64 (.f64 (cos.f64 (.f64 eps #s(literal 1/2 binary64))) (cos.f64 x)) (.f64 (cos.f64 (.f64 eps #s(literal 1/2 binary64))) (cos.f64 x)) (fma.f64 (.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (sin.f64 x)) (.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (sin.f64 x)) (.f64 (.f64 (cos.f64 (.f64 eps #s(literal 1/2 binary64))) (cos.f64 x)) (.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) (sin.f64 x))))))
(/.f64 (-.f64 (pow.f64 (.f64 (cos.f64 (.f64 eps #s(literal 1/2 binary64))) (cos.f64 x)) #s(literal 3 binary64)) (pow.f64 (.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (sin.f64 x)) #s(literal 3 binary64))) (fma.f64 (cos.f64 (.f64 eps #s(literal 1/2 binary64))) (.f64 (cos.f64 x) (fma.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (sin.f64 x) (.f64 (cos.f64 (.f64 eps #s(literal 1/2 binary64))) (cos.f64 x)))) (.f64 (.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (sin.f64 (.f64 eps #s(literal 1/2 binary64)))) (.f64 (sin.f64 x) (sin.f64 x)))))
(-.f64 (pow.f64 (.f64 (cos.f64 (.f64 eps #s(literal 1/2 binary64))) (cos.f64 x)) #s(literal 3 binary64)) (pow.f64 (.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (sin.f64 x)) #s(literal 3 binary64)))
(pow.f64 (.f64 (cos.f64 (.f64 eps #s(literal 1/2 binary64))) (cos.f64 x)) #s(literal 3 binary64))
(.f64 (cos.f64 (.f64 eps #s(literal 1/2 binary64))) (cos.f64 x))
(cos.f64 (*.f64 eps #s(literal 1/2 binary64)))
(*.f64 eps #s(literal 1/2 binary64))
(cos.f64 x)
x
#s(literal 3 binary64)
(pow.f64 (.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (sin.f64 x)) #s(literal 3 binary64))
(.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (sin.f64 x))
(sin.f64 (*.f64 eps #s(literal 1/2 binary64)))
(sin.f64 x)
(fma.f64 (.f64 (cos.f64 (.f64 eps #s(literal 1/2 binary64))) (cos.f64 x)) (.f64 (cos.f64 (.f64 eps #s(literal 1/2 binary64))) (cos.f64 x)) (fma.f64 (.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (sin.f64 x)) (.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (sin.f64 x)) (.f64 (.f64 (cos.f64 (.f64 eps #s(literal 1/2 binary64))) (cos.f64 x)) (.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) (sin.f64 x)))))
(fma.f64 (cos.f64 (.f64 eps #s(literal 1/2 binary64))) (.f64 (cos.f64 x) (fma.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (sin.f64 x) (.f64 (cos.f64 (.f64 eps #s(literal 1/2 binary64))) (cos.f64 x)))) (.f64 (.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (sin.f64 (.f64 eps #s(literal 1/2 binary64)))) (.f64 (sin.f64 x) (sin.f64 x))))
(fma.f64 (.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (sin.f64 x)) (.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (sin.f64 x)) (.f64 (.f64 (cos.f64 (.f64 eps #s(literal 1/2 binary64))) (cos.f64 x)) (.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) (sin.f64 x))))
(.f64 (sin.f64 x) (.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (fma.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (sin.f64 x) (.f64 (cos.f64 (.f64 eps #s(literal 1/2 binary64))) (cos.f64 x)))))
(.f64 (.f64 (cos.f64 (.f64 eps #s(literal 1/2 binary64))) (cos.f64 x)) (.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) (sin.f64 x)))
(.f64 (cos.f64 (.f64 eps #s(literal 1/2 binary64))) (.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (*.f64 (cos.f64 x) (sin.f64 x))))
#s(literal 2 binary64)
#s(approx (- (sin (+ x eps)) (sin x)) (-.f64 #s(approx (+ (* (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) #s(approx (+ (* eps (+ (* x (* x -1/2)) 1)) x) (+.f64 eps x))) x))
(-.f64 #s(approx (+ (* (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) #s(approx (+ (* eps (+ (* x (* x -1/2)) 1)) x) (+.f64 eps x))) x)
#s(approx (+ (* (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) #s(approx (+ (* eps (+ (* x (* x -1/2)) 1)) x) (+.f64 eps x)))
#s(approx (+ (* eps (+ (* x (* x -1/2)) 1)) x) (+.f64 eps x))
(+.f64 eps x)
eps
x
#s(approx (- (sin (+ x eps)) (sin x)) (/.f64 #s(literal 1 binary64) (/.f64 (+.f64 x #s(approx (+ (* (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) (fma.f64 eps (fma.f64 #s(literal -1/2 binary64) (.f64 x x) #s(literal 1 binary64)) x))) (.f64 (+.f64 x #s(approx (+ (* (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) (fma.f64 eps (fma.f64 #s(literal -1/2 binary64) (.f64 x x) #s(literal 1 binary64)) x))) (-.f64 #s(approx (+ ( (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) (fma.f64 eps (fma.f64 #s(literal -1/2 binary64) (*.f64 x x) #s(literal 1 binary64)) x)) x)))))
#s(approx (- (sin (+ x eps)) (sin x)) (-.f64 #s(approx (+ (* (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) (fma.f64 eps (fma.f64 x (*.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64)) x)) x))
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 x #s(approx (+ (* (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) (fma.f64 eps (fma.f64 #s(literal -1/2 binary64) (.f64 x x) #s(literal 1 binary64)) x))) (.f64 (+.f64 x #s(approx (+ (* (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) (fma.f64 eps (fma.f64 #s(literal -1/2 binary64) (.f64 x x) #s(literal 1 binary64)) x))) (-.f64 #s(approx (+ ( (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) (fma.f64 eps (fma.f64 #s(literal -1/2 binary64) (*.f64 x x) #s(literal 1 binary64)) x)) x))))
(-.f64 #s(approx (+ (* (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) (fma.f64 eps (fma.f64 x (*.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64)) x)) x)
#s(literal 1 binary64)
(/.f64 (+.f64 x #s(approx (+ (* (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) (fma.f64 eps (fma.f64 #s(literal -1/2 binary64) (.f64 x x) #s(literal 1 binary64)) x))) (.f64 (+.f64 x #s(approx (+ (* (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) (fma.f64 eps (fma.f64 #s(literal -1/2 binary64) (.f64 x x) #s(literal 1 binary64)) x))) (-.f64 #s(approx (+ ( (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) (fma.f64 eps (fma.f64 #s(literal -1/2 binary64) (*.f64 x x) #s(literal 1 binary64)) x)) x)))
(/.f64 #s(literal 1 binary64) (-.f64 #s(approx (+ (* (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) (fma.f64 eps (fma.f64 x (*.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64)) x)) x))
(+.f64 x #s(approx (+ (* (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) (fma.f64 eps (fma.f64 #s(literal -1/2 binary64) (*.f64 x x) #s(literal 1 binary64)) x)))
(+.f64 x #s(approx (+ (* (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) (fma.f64 eps (fma.f64 x (*.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64)) x)))
x
#s(approx (+ (* (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) (fma.f64 eps (fma.f64 #s(literal -1/2 binary64) (*.f64 x x) #s(literal 1 binary64)) x))
#s(approx (+ (* (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) (fma.f64 eps (fma.f64 x (*.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64)) x))
(fma.f64 eps (fma.f64 #s(literal -1/2 binary64) (*.f64 x x) #s(literal 1 binary64)) x)
(fma.f64 eps (fma.f64 x (*.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64)) x)
eps
(fma.f64 #s(literal -1/2 binary64) (*.f64 x x) #s(literal 1 binary64))
(fma.f64 x (*.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64))
#s(literal -1/2 binary64)
(*.f64 x x)
(.f64 (+.f64 x #s(approx (+ ( (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) (fma.f64 eps (fma.f64 #s(literal -1/2 binary64) (.f64 x x) #s(literal 1 binary64)) x))) (-.f64 #s(approx (+ ( (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) (fma.f64 eps (fma.f64 #s(literal -1/2 binary64) (*.f64 x x) #s(literal 1 binary64)) x)) x))
(.f64 (+.f64 x #s(approx (+ ( (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) (fma.f64 eps (fma.f64 x (.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64)) x))) (-.f64 #s(approx (+ ( (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) (fma.f64 eps (fma.f64 x (*.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64)) x)) x))
(-.f64 #s(approx (+ (* (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) (fma.f64 eps (fma.f64 #s(literal -1/2 binary64) (*.f64 x x) #s(literal 1 binary64)) x)) x)
(-.f64 #s(approx (+ (* (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) (fma.f64 eps (fma.f64 x (*.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64)) x)) x)
(.f64 #s(approx ( (sin (* (+ eps 0) 1/2)) (cos (* (+ (* x 2) eps) 1/2))) (.f64 #s(approx (sin ( 1/2 eps)) (.f64 eps (fma.f64 eps (.f64 eps (fma.f64 (*.f64 eps eps) #s(literal 1/3840 binary64) #s(literal -1/48 binary64))) #s(literal 1/2 binary64)))) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)))) #s(literal 2 binary64))
(.f64 #s(literal 2 binary64) #s(approx ( (sin (* (+ eps 0) 1/2)) (cos (* (+ (* x 2) eps) 1/2))) (.f64 #s(approx (sin ( 1/2 eps)) (.f64 eps (fma.f64 (.f64 eps eps) (fma.f64 (*.f64 eps eps) #s(literal 1/3840 binary64) #s(literal -1/48 binary64)) #s(literal 1/2 binary64)))) (cos.f64 (fma.f64 eps #s(literal 1/2 binary64) x)))))
#s(approx (* (sin (* (+ eps 0) 1/2)) (cos (* (+ (* x 2) eps) 1/2))) (.f64 #s(approx (sin ( 1/2 eps)) (.f64 eps (fma.f64 eps (.f64 eps (fma.f64 (*.f64 eps eps) #s(literal 1/3840 binary64) #s(literal -1/48 binary64))) #s(literal 1/2 binary64)))) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x))))
#s(approx (* (sin (* (+ eps 0) 1/2)) (cos (* (+ (* x 2) eps) 1/2))) (.f64 #s(approx (sin ( 1/2 eps)) (.f64 eps (fma.f64 (.f64 eps eps) (fma.f64 (*.f64 eps eps) #s(literal 1/3840 binary64) #s(literal -1/48 binary64)) #s(literal 1/2 binary64)))) (cos.f64 (fma.f64 eps #s(literal 1/2 binary64) x))))
(.f64 #s(approx (sin ( 1/2 eps)) (.f64 eps (fma.f64 eps (.f64 eps (fma.f64 (*.f64 eps eps) #s(literal 1/3840 binary64) #s(literal -1/48 binary64))) #s(literal 1/2 binary64)))) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)))
(.f64 #s(approx (sin ( 1/2 eps)) (.f64 eps (fma.f64 (.f64 eps eps) (fma.f64 (*.f64 eps eps) #s(literal 1/3840 binary64) #s(literal -1/48 binary64)) #s(literal 1/2 binary64)))) (cos.f64 (fma.f64 eps #s(literal 1/2 binary64) x)))
#s(approx (sin (* 1/2 eps)) (.f64 eps (fma.f64 eps (.f64 eps (fma.f64 (*.f64 eps eps) #s(literal 1/3840 binary64) #s(literal -1/48 binary64))) #s(literal 1/2 binary64))))
#s(approx (sin (* 1/2 eps)) (.f64 eps (fma.f64 (.f64 eps eps) (fma.f64 (*.f64 eps eps) #s(literal 1/3840 binary64) #s(literal -1/48 binary64)) #s(literal 1/2 binary64))))
(.f64 eps (fma.f64 eps (.f64 eps (fma.f64 (*.f64 eps eps) #s(literal 1/3840 binary64) #s(literal -1/48 binary64))) #s(literal 1/2 binary64)))
(.f64 eps (fma.f64 (.f64 eps eps) (fma.f64 (*.f64 eps eps) #s(literal 1/3840 binary64) #s(literal -1/48 binary64)) #s(literal 1/2 binary64)))
eps
(fma.f64 eps (.f64 eps (fma.f64 (.f64 eps eps) #s(literal 1/3840 binary64) #s(literal -1/48 binary64))) #s(literal 1/2 binary64))
(fma.f64 (.f64 eps eps) (fma.f64 (.f64 eps eps) #s(literal 1/3840 binary64) #s(literal -1/48 binary64)) #s(literal 1/2 binary64))
(.f64 eps (fma.f64 (.f64 eps eps) #s(literal 1/3840 binary64) #s(literal -1/48 binary64)))
(fma.f64 (*.f64 eps eps) #s(literal 1/3840 binary64) #s(literal -1/48 binary64))
(*.f64 eps eps)
#s(literal 1/3840 binary64)
#s(literal -1/48 binary64)
#s(literal 1/2 binary64)
(cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x))
(cos.f64 (fma.f64 eps #s(literal 1/2 binary64) x))
(fma.f64 #s(literal 1/2 binary64) eps x)
(fma.f64 eps #s(literal 1/2 binary64) x)
x
#s(literal 2 binary64)
#s(approx (/ (/ (- 1/2 (+ (* 1/2 (cos (* (+ x eps) 2))) (+ 1/2 (* -1/2 (cos (+ x x)))))) 2) (* (sin (* (+ (* x 2) eps) 1/2)) (cos (* (+ eps 0) 1/2)))) (/.f64 (fma.f64 #s(literal -1/4 binary64) (cos.f64 (.f64 #s(literal 2 binary64) (+.f64 eps x))) (.f64 (cos.f64 (.f64 x #s(literal 2 binary64))) #s(literal 1/4 binary64))) (.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) eps)) (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x)))))
#s(approx (/ (/ (- 1/2 (+ (* 1/2 (cos (* (+ x eps) 2))) (+ 1/2 (* -1/2 (cos (+ x x)))))) 2) (* (sin (* (+ (* x 2) eps) 1/2)) (cos (* (+ eps 0) 1/2)))) (.f64 #s(literal -1/4 binary64) (/.f64 (-.f64 (cos.f64 (.f64 #s(literal 2 binary64) (+.f64 eps x))) (cos.f64 (+.f64 x x))) (.f64 (cos.f64 (.f64 eps #s(literal 1/2 binary64))) (sin.f64 (fma.f64 eps #s(literal 1/2 binary64) x))))))
(/.f64 (fma.f64 #s(literal -1/4 binary64) (cos.f64 (.f64 #s(literal 2 binary64) (+.f64 eps x))) (.f64 (cos.f64 (.f64 x #s(literal 2 binary64))) #s(literal 1/4 binary64))) (.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) eps)) (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x))))
(.f64 #s(literal -1/4 binary64) (/.f64 (-.f64 (cos.f64 (.f64 #s(literal 2 binary64) (+.f64 eps x))) (cos.f64 (+.f64 x x))) (.f64 (cos.f64 (.f64 eps #s(literal 1/2 binary64))) (sin.f64 (fma.f64 eps #s(literal 1/2 binary64) x)))))
(fma.f64 #s(literal -1/4 binary64) (cos.f64 (.f64 #s(literal 2 binary64) (+.f64 eps x))) (.f64 (cos.f64 (*.f64 x #s(literal 2 binary64))) #s(literal 1/4 binary64)))
(fma.f64 #s(literal -1/4 binary64) (cos.f64 (.f64 #s(literal 2 binary64) (+.f64 eps x))) (.f64 (cos.f64 (+.f64 x x)) #s(literal 1/4 binary64)))
#s(literal -1/4 binary64)
(cos.f64 (*.f64 #s(literal 2 binary64) (+.f64 eps x)))
(*.f64 #s(literal 2 binary64) (+.f64 eps x))
#s(literal 2 binary64)
(+.f64 eps x)
eps
x
(.f64 (cos.f64 (.f64 x #s(literal 2 binary64))) #s(literal 1/4 binary64))
(*.f64 (cos.f64 (+.f64 x x)) #s(literal 1/4 binary64))
(cos.f64 (*.f64 x #s(literal 2 binary64)))
(cos.f64 (+.f64 x x))
(*.f64 x #s(literal 2 binary64))
(+.f64 x x)
#s(literal 1/4 binary64)
(.f64 (cos.f64 (.f64 #s(literal 1/2 binary64) eps)) (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x)))
(.f64 (cos.f64 (.f64 eps #s(literal 1/2 binary64))) (sin.f64 (fma.f64 eps #s(literal 1/2 binary64) x)))
(cos.f64 (*.f64 #s(literal 1/2 binary64) eps))
(cos.f64 (*.f64 eps #s(literal 1/2 binary64)))
(*.f64 #s(literal 1/2 binary64) eps)
(*.f64 eps #s(literal 1/2 binary64))
#s(literal 1/2 binary64)
(sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x))
(sin.f64 (fma.f64 eps #s(literal 1/2 binary64) x))
(fma.f64 #s(literal 1/2 binary64) eps x)
(fma.f64 eps #s(literal 1/2 binary64) x)

localize753.0ms (5.2%)

Memory

-3.5MiB live, 952.8MiB allocated

Localize:

Found 20 expressions of interest:

New	Metric	Score	Program
✓	accuracy	99.9%	(cos.f64 (*.f64 #s(literal 2 binary64) (+.f64 eps x)))
✓	accuracy	99.8%	(sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x))
✓	accuracy	54.9%	(fma.f64 #s(literal -1/4 binary64) (cos.f64 (.f64 #s(literal 2 binary64) (+.f64 eps x))) (.f64 (cos.f64 (*.f64 x #s(literal 2 binary64))) #s(literal 1/4 binary64)))
✓	accuracy	53.6%	(/.f64 (fma.f64 #s(literal -1/4 binary64) (cos.f64 (.f64 #s(literal 2 binary64) (+.f64 eps x))) (.f64 (cos.f64 (.f64 x #s(literal 2 binary64))) #s(literal 1/4 binary64))) (.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) eps)) (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x))))
✓	accuracy	100.0%	(.f64 #s(approx (sin ( 1/2 eps)) (.f64 eps (fma.f64 eps (.f64 eps (fma.f64 (*.f64 eps eps) #s(literal 1/3840 binary64) #s(literal -1/48 binary64))) #s(literal 1/2 binary64)))) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)))
✓	accuracy	99.9%	(cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x))
✓	accuracy	99.5%	(.f64 eps (fma.f64 (.f64 eps eps) #s(literal 1/3840 binary64) #s(literal -1/48 binary64)))
✓	accuracy	99.5%	#s(approx (sin (* 1/2 eps)) (.f64 eps (fma.f64 eps (.f64 eps (fma.f64 (*.f64 eps eps) #s(literal 1/3840 binary64) #s(literal -1/48 binary64))) #s(literal 1/2 binary64))))
✓	accuracy	99.0%	#s(approx (+ (* (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) (fma.f64 eps (fma.f64 #s(literal -1/2 binary64) (*.f64 x x) #s(literal 1 binary64)) x))
✓	accuracy	97.6%	#s(approx (- (sin (+ x eps)) (sin x)) (/.f64 #s(literal 1 binary64) (/.f64 (+.f64 x #s(approx (+ (* (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) (fma.f64 eps (fma.f64 #s(literal -1/2 binary64) (.f64 x x) #s(literal 1 binary64)) x))) (.f64 (+.f64 x #s(approx (+ (* (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) (fma.f64 eps (fma.f64 #s(literal -1/2 binary64) (.f64 x x) #s(literal 1 binary64)) x))) (-.f64 #s(approx (+ ( (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) (fma.f64 eps (fma.f64 #s(literal -1/2 binary64) (*.f64 x x) #s(literal 1 binary64)) x)) x)))))
✓	accuracy	62.6%	(-.f64 #s(approx (+ (* (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) (fma.f64 eps (fma.f64 #s(literal -1/2 binary64) (*.f64 x x) #s(literal 1 binary64)) x)) x)
✓	accuracy	53.6%	(/.f64 (+.f64 x #s(approx (+ (* (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) (fma.f64 eps (fma.f64 #s(literal -1/2 binary64) (.f64 x x) #s(literal 1 binary64)) x))) (.f64 (+.f64 x #s(approx (+ (* (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) (fma.f64 eps (fma.f64 #s(literal -1/2 binary64) (.f64 x x) #s(literal 1 binary64)) x))) (-.f64 #s(approx (+ ( (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) (fma.f64 eps (fma.f64 #s(literal -1/2 binary64) (*.f64 x x) #s(literal 1 binary64)) x)) x)))
✓	accuracy	99.0%	#s(approx (+ (* (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) #s(approx (+ (* eps (+ (* x (* x -1/2)) 1)) x) (+.f64 eps x)))
✓	accuracy	98.4%	#s(approx (+ (* eps (+ (* x (* x -1/2)) 1)) x) (+.f64 eps x))
✓	accuracy	97.6%	#s(approx (- (sin (+ x eps)) (sin x)) (-.f64 #s(approx (+ (* (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) #s(approx (+ (* eps (+ (* x (* x -1/2)) 1)) x) (+.f64 eps x))) x))
✓	accuracy	62.6%	(-.f64 #s(approx (+ (* (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) #s(approx (+ (* eps (+ (* x (* x -1/2)) 1)) x) (+.f64 eps x))) x)
✓	accuracy	100.0%	(/.f64 (-.f64 (pow.f64 (.f64 (cos.f64 (.f64 eps #s(literal 1/2 binary64))) (cos.f64 x)) #s(literal 3 binary64)) (pow.f64 (.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (sin.f64 x)) #s(literal 3 binary64))) (fma.f64 (.f64 (cos.f64 (.f64 eps #s(literal 1/2 binary64))) (cos.f64 x)) (.f64 (cos.f64 (.f64 eps #s(literal 1/2 binary64))) (cos.f64 x)) (fma.f64 (.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (sin.f64 x)) (.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (sin.f64 x)) (.f64 (.f64 (cos.f64 (.f64 eps #s(literal 1/2 binary64))) (cos.f64 x)) (.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) (sin.f64 x))))))
✓	accuracy	100.0%	(fma.f64 (.f64 (cos.f64 (.f64 eps #s(literal 1/2 binary64))) (cos.f64 x)) (.f64 (cos.f64 (.f64 eps #s(literal 1/2 binary64))) (cos.f64 x)) (fma.f64 (.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (sin.f64 x)) (.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (sin.f64 x)) (.f64 (.f64 (cos.f64 (.f64 eps #s(literal 1/2 binary64))) (cos.f64 x)) (.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) (sin.f64 x)))))
✓	accuracy	99.9%	(pow.f64 (.f64 (cos.f64 (.f64 eps #s(literal 1/2 binary64))) (cos.f64 x)) #s(literal 3 binary64))
✓	accuracy	99.9%	(pow.f64 (.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (sin.f64 x)) #s(literal 3 binary64))

Samples

370.0ms	146×	2	valid
118.0ms	36×	3	valid
96.0ms	69×	1	valid
4.0ms	5×	0	valid

Compiler

Compiled 875 to 100 computations (88.6% saved)

Precisions

Click to see histograms. Total time spent on operations: 509.0ms

ival-cos: 201.0ms (39.5% of total)

adjust: 108.0ms (21.2% of total)

ival-mult: 84.0ms (16.5% of total)

ival-add: 43.0ms (8.4% of total)

ival-div: 21.0ms (4.1% of total)

ival-sin: 19.0ms (3.7% of total)

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

const: 10.0ms (2% of total)

ival-sub: 9.0ms (1.8% of total)

exact: 1.0ms (0.2% of total)

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

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

series129.0ms (0.9%)

Memory

38.0MiB live, 113.4MiB allocated

Counts

30 → 684

Calls

Call 1

Inputs
#s(alt (fma.f64 (.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (sin.f64 x)) (.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (sin.f64 x)) (.f64 (.f64 (cos.f64 (.f64 eps #s(literal 1/2 binary64))) (cos.f64 x)) (.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (sin.f64 x)))) (patch (fma.f64 (.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (sin.f64 x)) (.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (sin.f64 x)) (.f64 (.f64 (cos.f64 (.f64 eps #s(literal 1/2 binary64))) (cos.f64 x)) (.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (sin.f64 x)))) #<representation binary64>) () ())
#s(alt (.f64 #s(approx ( (sin (* (+ eps 0) 1/2)) (cos (* (+ (* x 2) eps) 1/2))) (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (/.f64 (-.f64 (pow.f64 (.f64 (cos.f64 (.f64 eps #s(literal 1/2 binary64))) (cos.f64 x)) #s(literal 3 binary64)) (pow.f64 (.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (sin.f64 x)) #s(literal 3 binary64))) (fma.f64 (.f64 (cos.f64 (.f64 eps #s(literal 1/2 binary64))) (cos.f64 x)) (.f64 (cos.f64 (.f64 eps #s(literal 1/2 binary64))) (cos.f64 x)) (fma.f64 (.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (sin.f64 x)) (.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (sin.f64 x)) (.f64 (.f64 (cos.f64 (.f64 eps #s(literal 1/2 binary64))) (cos.f64 x)) (.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (sin.f64 x)))))))) #s(literal 2 binary64)) (patch (.f64 #s(approx (* (sin (* (+ eps 0) 1/2)) (cos (* (+ (* x 2) eps) 1/2))) (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (/.f64 (-.f64 (pow.f64 (.f64 (cos.f64 (.f64 eps #s(literal 1/2 binary64))) (cos.f64 x)) #s(literal 3 binary64)) (pow.f64 (.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (sin.f64 x)) #s(literal 3 binary64))) (fma.f64 (.f64 (cos.f64 (.f64 eps #s(literal 1/2 binary64))) (cos.f64 x)) (.f64 (cos.f64 (.f64 eps #s(literal 1/2 binary64))) (cos.f64 x)) (fma.f64 (.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (sin.f64 x)) (.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (sin.f64 x)) (.f64 (.f64 (cos.f64 (.f64 eps #s(literal 1/2 binary64))) (cos.f64 x)) (.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) (sin.f64 x)))))))) #s(literal 2 binary64)) #<representation binary64>) () ())
#s(alt #s(approx (* (sin (* (+ eps 0) 1/2)) (cos (* (+ (* x 2) eps) 1/2))) (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (/.f64 (-.f64 (pow.f64 (.f64 (cos.f64 (.f64 eps #s(literal 1/2 binary64))) (cos.f64 x)) #s(literal 3 binary64)) (pow.f64 (.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (sin.f64 x)) #s(literal 3 binary64))) (fma.f64 (.f64 (cos.f64 (.f64 eps #s(literal 1/2 binary64))) (cos.f64 x)) (.f64 (cos.f64 (.f64 eps #s(literal 1/2 binary64))) (cos.f64 x)) (fma.f64 (.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (sin.f64 x)) (.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (sin.f64 x)) (.f64 (.f64 (cos.f64 (.f64 eps #s(literal 1/2 binary64))) (cos.f64 x)) (.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (sin.f64 x)))))))) (patch #s(approx ( (sin (* (+ eps 0) 1/2)) (cos (* (+ (* x 2) eps) 1/2))) (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (/.f64 (-.f64 (pow.f64 (.f64 (cos.f64 (.f64 eps #s(literal 1/2 binary64))) (cos.f64 x)) #s(literal 3 binary64)) (pow.f64 (.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (sin.f64 x)) #s(literal 3 binary64))) (fma.f64 (.f64 (cos.f64 (.f64 eps #s(literal 1/2 binary64))) (cos.f64 x)) (.f64 (cos.f64 (.f64 eps #s(literal 1/2 binary64))) (cos.f64 x)) (fma.f64 (.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (sin.f64 x)) (.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (sin.f64 x)) (.f64 (.f64 (cos.f64 (.f64 eps #s(literal 1/2 binary64))) (cos.f64 x)) (.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) (sin.f64 x)))))))) #<representation binary64>) () ())
#s(alt (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (/.f64 (-.f64 (pow.f64 (.f64 (cos.f64 (.f64 eps #s(literal 1/2 binary64))) (cos.f64 x)) #s(literal 3 binary64)) (pow.f64 (.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (sin.f64 x)) #s(literal 3 binary64))) (fma.f64 (.f64 (cos.f64 (.f64 eps #s(literal 1/2 binary64))) (cos.f64 x)) (.f64 (cos.f64 (.f64 eps #s(literal 1/2 binary64))) (cos.f64 x)) (fma.f64 (.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (sin.f64 x)) (.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (sin.f64 x)) (.f64 (.f64 (cos.f64 (.f64 eps #s(literal 1/2 binary64))) (cos.f64 x)) (.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (sin.f64 x))))))) (patch (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (/.f64 (-.f64 (pow.f64 (.f64 (cos.f64 (.f64 eps #s(literal 1/2 binary64))) (cos.f64 x)) #s(literal 3 binary64)) (pow.f64 (.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (sin.f64 x)) #s(literal 3 binary64))) (fma.f64 (.f64 (cos.f64 (.f64 eps #s(literal 1/2 binary64))) (cos.f64 x)) (.f64 (cos.f64 (.f64 eps #s(literal 1/2 binary64))) (cos.f64 x)) (fma.f64 (.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (sin.f64 x)) (.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (sin.f64 x)) (.f64 (.f64 (cos.f64 (.f64 eps #s(literal 1/2 binary64))) (cos.f64 x)) (.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (sin.f64 x))))))) #<representation binary64>) () ())
#s(alt #s(approx (- (sin (+ x eps)) (sin x)) (-.f64 #s(approx (+ (* (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) #s(approx (+ (* eps (+ (* x (* x -1/2)) 1)) x) (+.f64 eps x))) x)) (patch #s(approx (- (sin (+ x eps)) (sin x)) (-.f64 #s(approx (+ (* (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) #s(approx (+ (* eps (+ (* x (* x -1/2)) 1)) x) (+.f64 eps x))) x)) #<representation binary64>) () ())
#s(alt (-.f64 #s(approx (+ (* (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) #s(approx (+ (* eps (+ (* x (* x -1/2)) 1)) x) (+.f64 eps x))) x) (patch (-.f64 #s(approx (+ (* (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) #s(approx (+ (* eps (+ (* x (* x -1/2)) 1)) x) (+.f64 eps x))) x) #<representation binary64>) () ())
#s(alt #s(approx (+ (* (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) #s(approx (+ (* eps (+ (* x (* x -1/2)) 1)) x) (+.f64 eps x))) (patch #s(approx (+ (* (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) #s(approx (+ (* eps (+ (* x (* x -1/2)) 1)) x) (+.f64 eps x))) #<representation binary64>) () ())
#s(alt #s(approx (+ (* eps (+ (* x (* x -1/2)) 1)) x) (+.f64 eps x)) (patch #s(approx (+ (* eps (+ (* x (* x -1/2)) 1)) x) (+.f64 eps x)) #<representation binary64>) () ())
#s(alt (/.f64 (+.f64 x #s(approx (+ (* (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) (fma.f64 eps (fma.f64 #s(literal -1/2 binary64) (.f64 x x) #s(literal 1 binary64)) x))) (.f64 (+.f64 x #s(approx (+ (* (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) (fma.f64 eps (fma.f64 #s(literal -1/2 binary64) (.f64 x x) #s(literal 1 binary64)) x))) (-.f64 #s(approx (+ ( (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) (fma.f64 eps (fma.f64 #s(literal -1/2 binary64) (.f64 x x) #s(literal 1 binary64)) x)) x))) (patch (/.f64 (+.f64 x #s(approx (+ ( (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) (fma.f64 eps (fma.f64 #s(literal -1/2 binary64) (.f64 x x) #s(literal 1 binary64)) x))) (.f64 (+.f64 x #s(approx (+ (* (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) (fma.f64 eps (fma.f64 #s(literal -1/2 binary64) (.f64 x x) #s(literal 1 binary64)) x))) (-.f64 #s(approx (+ ( (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) (fma.f64 eps (fma.f64 #s(literal -1/2 binary64) (*.f64 x x) #s(literal 1 binary64)) x)) x))) #<representation binary64>) () ())
#s(alt (/.f64 #s(literal 1 binary64) (/.f64 (+.f64 x #s(approx (+ (* (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) (fma.f64 eps (fma.f64 #s(literal -1/2 binary64) (.f64 x x) #s(literal 1 binary64)) x))) (.f64 (+.f64 x #s(approx (+ (* (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) (fma.f64 eps (fma.f64 #s(literal -1/2 binary64) (.f64 x x) #s(literal 1 binary64)) x))) (-.f64 #s(approx (+ ( (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) (fma.f64 eps (fma.f64 #s(literal -1/2 binary64) (.f64 x x) #s(literal 1 binary64)) x)) x)))) (patch (/.f64 #s(literal 1 binary64) (/.f64 (+.f64 x #s(approx (+ ( (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) (fma.f64 eps (fma.f64 #s(literal -1/2 binary64) (.f64 x x) #s(literal 1 binary64)) x))) (.f64 (+.f64 x #s(approx (+ (* (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) (fma.f64 eps (fma.f64 #s(literal -1/2 binary64) (.f64 x x) #s(literal 1 binary64)) x))) (-.f64 #s(approx (+ ( (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) (fma.f64 eps (fma.f64 #s(literal -1/2 binary64) (*.f64 x x) #s(literal 1 binary64)) x)) x)))) #<representation binary64>) () ())
#s(alt #s(approx (- (sin (+ x eps)) (sin x)) (/.f64 #s(literal 1 binary64) (/.f64 (+.f64 x #s(approx (+ (* (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) (fma.f64 eps (fma.f64 #s(literal -1/2 binary64) (.f64 x x) #s(literal 1 binary64)) x))) (.f64 (+.f64 x #s(approx (+ (* (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) (fma.f64 eps (fma.f64 #s(literal -1/2 binary64) (.f64 x x) #s(literal 1 binary64)) x))) (-.f64 #s(approx (+ ( (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) (fma.f64 eps (fma.f64 #s(literal -1/2 binary64) (.f64 x x) #s(literal 1 binary64)) x)) x))))) (patch #s(approx (- (sin (+ x eps)) (sin x)) (/.f64 #s(literal 1 binary64) (/.f64 (+.f64 x #s(approx (+ ( (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) (fma.f64 eps (fma.f64 #s(literal -1/2 binary64) (.f64 x x) #s(literal 1 binary64)) x))) (.f64 (+.f64 x #s(approx (+ (* (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) (fma.f64 eps (fma.f64 #s(literal -1/2 binary64) (.f64 x x) #s(literal 1 binary64)) x))) (-.f64 #s(approx (+ ( (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) (fma.f64 eps (fma.f64 #s(literal -1/2 binary64) (*.f64 x x) #s(literal 1 binary64)) x)) x))))) #<representation binary64>) () ())
#s(alt (+.f64 x #s(approx (+ (* (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) (fma.f64 eps (fma.f64 #s(literal -1/2 binary64) (.f64 x x) #s(literal 1 binary64)) x))) (patch (+.f64 x #s(approx (+ ( (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) (fma.f64 eps (fma.f64 #s(literal -1/2 binary64) (*.f64 x x) #s(literal 1 binary64)) x))) #<representation binary64>) () ())
#s(alt (.f64 #s(approx ( (sin (* (+ eps 0) 1/2)) (cos (* (+ (* x 2) eps) 1/2))) (.f64 #s(approx (sin ( 1/2 eps)) (.f64 eps (fma.f64 eps (.f64 eps (fma.f64 (.f64 eps eps) #s(literal 1/3840 binary64) #s(literal -1/48 binary64))) #s(literal 1/2 binary64)))) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)))) #s(literal 2 binary64)) (patch (.f64 #s(approx (* (sin (* (+ eps 0) 1/2)) (cos (* (+ (* x 2) eps) 1/2))) (.f64 #s(approx (sin ( 1/2 eps)) (.f64 eps (fma.f64 eps (.f64 eps (fma.f64 (*.f64 eps eps) #s(literal 1/3840 binary64) #s(literal -1/48 binary64))) #s(literal 1/2 binary64)))) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)))) #s(literal 2 binary64)) #<representation binary64>) () ())
#s(alt #s(approx (* (sin (* (+ eps 0) 1/2)) (cos (* (+ (* x 2) eps) 1/2))) (.f64 #s(approx (sin ( 1/2 eps)) (.f64 eps (fma.f64 eps (.f64 eps (fma.f64 (.f64 eps eps) #s(literal 1/3840 binary64) #s(literal -1/48 binary64))) #s(literal 1/2 binary64)))) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)))) (patch #s(approx ( (sin (* (+ eps 0) 1/2)) (cos (* (+ (* x 2) eps) 1/2))) (.f64 #s(approx (sin ( 1/2 eps)) (.f64 eps (fma.f64 eps (.f64 eps (fma.f64 (*.f64 eps eps) #s(literal 1/3840 binary64) #s(literal -1/48 binary64))) #s(literal 1/2 binary64)))) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)))) #<representation binary64>) () ())
#s(alt (.f64 #s(approx (sin ( 1/2 eps)) (.f64 eps (fma.f64 eps (.f64 eps (fma.f64 (.f64 eps eps) #s(literal 1/3840 binary64) #s(literal -1/48 binary64))) #s(literal 1/2 binary64)))) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x))) (patch (.f64 #s(approx (sin (* 1/2 eps)) (.f64 eps (fma.f64 eps (.f64 eps (fma.f64 (*.f64 eps eps) #s(literal 1/3840 binary64) #s(literal -1/48 binary64))) #s(literal 1/2 binary64)))) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x))) #<representation binary64>) () ())
#s(alt #s(approx (sin (* 1/2 eps)) (.f64 eps (fma.f64 eps (.f64 eps (fma.f64 (.f64 eps eps) #s(literal 1/3840 binary64) #s(literal -1/48 binary64))) #s(literal 1/2 binary64)))) (patch #s(approx (sin ( 1/2 eps)) (.f64 eps (fma.f64 eps (.f64 eps (fma.f64 (*.f64 eps eps) #s(literal 1/3840 binary64) #s(literal -1/48 binary64))) #s(literal 1/2 binary64)))) #<representation binary64>) () ())
#s(alt (/.f64 (fma.f64 #s(literal -1/4 binary64) (cos.f64 (.f64 #s(literal 2 binary64) (+.f64 eps x))) (.f64 (cos.f64 (.f64 x #s(literal 2 binary64))) #s(literal 1/4 binary64))) (.f64 (cos.f64 (.f64 #s(literal 1/2 binary64) eps)) (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x)))) (patch (/.f64 (fma.f64 #s(literal -1/4 binary64) (cos.f64 (.f64 #s(literal 2 binary64) (+.f64 eps x))) (.f64 (cos.f64 (.f64 x #s(literal 2 binary64))) #s(literal 1/4 binary64))) (.f64 (cos.f64 (.f64 #s(literal 1/2 binary64) eps)) (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x)))) #<representation binary64>) () ())
#s(alt (.f64 x #s(literal 2 binary64)) (patch (.f64 x #s(literal 2 binary64)) #<representation binary64>) () ())
#s(alt #s(approx (/ (/ (- 1/2 (+ (* 1/2 (cos (* (+ x eps) 2))) (+ 1/2 (* -1/2 (cos (+ x x)))))) 2) (* (sin (* (+ (* x 2) eps) 1/2)) (cos (* (+ eps 0) 1/2)))) (/.f64 (fma.f64 #s(literal -1/4 binary64) (cos.f64 (.f64 #s(literal 2 binary64) (+.f64 eps x))) (.f64 (cos.f64 (.f64 x #s(literal 2 binary64))) #s(literal 1/4 binary64))) (.f64 (cos.f64 (.f64 #s(literal 1/2 binary64) eps)) (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x))))) (patch #s(approx (/ (/ (- 1/2 (+ ( 1/2 (cos (* (+ x eps) 2))) (+ 1/2 (* -1/2 (cos (+ x x)))))) 2) (* (sin (* (+ (* x 2) eps) 1/2)) (cos (* (+ eps 0) 1/2)))) (/.f64 (fma.f64 #s(literal -1/4 binary64) (cos.f64 (.f64 #s(literal 2 binary64) (+.f64 eps x))) (.f64 (cos.f64 (.f64 x #s(literal 2 binary64))) #s(literal 1/4 binary64))) (.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) eps)) (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x))))) #<representation binary64>) () ())
#s(alt (fma.f64 #s(literal -1/4 binary64) (cos.f64 (.f64 #s(literal 2 binary64) (+.f64 eps x))) (.f64 (cos.f64 (.f64 x #s(literal 2 binary64))) #s(literal 1/4 binary64))) (patch (fma.f64 #s(literal -1/4 binary64) (cos.f64 (.f64 #s(literal 2 binary64) (+.f64 eps x))) (.f64 (cos.f64 (.f64 x #s(literal 2 binary64))) #s(literal 1/4 binary64))) #<representation binary64>) () ())
#s(alt (pow.f64 (.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (sin.f64 x)) #s(literal 3 binary64)) (patch (pow.f64 (.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (sin.f64 x)) #s(literal 3 binary64)) #<representation binary64>) () ())
#s(alt (pow.f64 (.f64 (cos.f64 (.f64 eps #s(literal 1/2 binary64))) (cos.f64 x)) #s(literal 3 binary64)) (patch (pow.f64 (.f64 (cos.f64 (.f64 eps #s(literal 1/2 binary64))) (cos.f64 x)) #s(literal 3 binary64)) #<representation binary64>) () ())
#s(alt (fma.f64 (.f64 (cos.f64 (.f64 eps #s(literal 1/2 binary64))) (cos.f64 x)) (.f64 (cos.f64 (.f64 eps #s(literal 1/2 binary64))) (cos.f64 x)) (fma.f64 (.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (sin.f64 x)) (.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (sin.f64 x)) (.f64 (.f64 (cos.f64 (.f64 eps #s(literal 1/2 binary64))) (cos.f64 x)) (.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (sin.f64 x))))) (patch (fma.f64 (.f64 (cos.f64 (.f64 eps #s(literal 1/2 binary64))) (cos.f64 x)) (.f64 (cos.f64 (.f64 eps #s(literal 1/2 binary64))) (cos.f64 x)) (fma.f64 (.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (sin.f64 x)) (.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (sin.f64 x)) (.f64 (.f64 (cos.f64 (.f64 eps #s(literal 1/2 binary64))) (cos.f64 x)) (.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (sin.f64 x))))) #<representation binary64>) () ())
#s(alt (/.f64 (-.f64 (pow.f64 (.f64 (cos.f64 (.f64 eps #s(literal 1/2 binary64))) (cos.f64 x)) #s(literal 3 binary64)) (pow.f64 (.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (sin.f64 x)) #s(literal 3 binary64))) (fma.f64 (.f64 (cos.f64 (.f64 eps #s(literal 1/2 binary64))) (cos.f64 x)) (.f64 (cos.f64 (.f64 eps #s(literal 1/2 binary64))) (cos.f64 x)) (fma.f64 (.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (sin.f64 x)) (.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (sin.f64 x)) (.f64 (.f64 (cos.f64 (.f64 eps #s(literal 1/2 binary64))) (cos.f64 x)) (.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (sin.f64 x)))))) (patch (/.f64 (-.f64 (pow.f64 (.f64 (cos.f64 (.f64 eps #s(literal 1/2 binary64))) (cos.f64 x)) #s(literal 3 binary64)) (pow.f64 (.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (sin.f64 x)) #s(literal 3 binary64))) (fma.f64 (.f64 (cos.f64 (.f64 eps #s(literal 1/2 binary64))) (cos.f64 x)) (.f64 (cos.f64 (.f64 eps #s(literal 1/2 binary64))) (cos.f64 x)) (fma.f64 (.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (sin.f64 x)) (.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (sin.f64 x)) (.f64 (.f64 (cos.f64 (.f64 eps #s(literal 1/2 binary64))) (cos.f64 x)) (.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (sin.f64 x)))))) #<representation binary64>) () ())
#s(alt (-.f64 #s(approx (+ (* (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) (fma.f64 eps (fma.f64 #s(literal -1/2 binary64) (.f64 x x) #s(literal 1 binary64)) x)) x) (patch (-.f64 #s(approx (+ ( (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) (fma.f64 eps (fma.f64 #s(literal -1/2 binary64) (*.f64 x x) #s(literal 1 binary64)) x)) x) #<representation binary64>) () ())
#s(alt #s(approx (+ (* (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) (fma.f64 eps (fma.f64 #s(literal -1/2 binary64) (.f64 x x) #s(literal 1 binary64)) x)) (patch #s(approx (+ ( (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) (fma.f64 eps (fma.f64 #s(literal -1/2 binary64) (*.f64 x x) #s(literal 1 binary64)) x)) #<representation binary64>) () ())
#s(alt (.f64 eps (fma.f64 (.f64 eps eps) #s(literal 1/3840 binary64) #s(literal -1/48 binary64))) (patch (.f64 eps (fma.f64 (.f64 eps eps) #s(literal 1/3840 binary64) #s(literal -1/48 binary64))) #<representation binary64>) () ())
#s(alt (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) (patch (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) #<representation binary64>) () ())
#s(alt (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) (patch (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) #<representation binary64>) () ())
#s(alt (cos.f64 (.f64 #s(literal 2 binary64) (+.f64 eps x))) (patch (cos.f64 (.f64 #s(literal 2 binary64) (+.f64 eps x))) #<representation binary64>) () ())

Outputs
#s(alt (* 1/2 (* eps (* (cos x) (sin x)))) (taylor 0 eps) (#s(alt (fma.f64 (.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (sin.f64 x)) (.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (sin.f64 x)) (.f64 (.f64 (cos.f64 (.f64 eps #s(literal 1/2 binary64))) (cos.f64 x)) (.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (sin.f64 x)))) (patch (fma.f64 (.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (sin.f64 x)) (.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (sin.f64 x)) (.f64 (.f64 (cos.f64 (.f64 eps #s(literal 1/2 binary64))) (cos.f64 x)) (.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (sin.f64 x)))) #<representation binary64>) () ())) ())
#s(alt (* eps (+ (* 1/4 (* eps (pow (sin x) 2))) (* 1/2 (* (cos x) (sin x))))) (taylor 0 eps) (#s(alt (fma.f64 (.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (sin.f64 x)) (.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (sin.f64 x)) (.f64 (.f64 (cos.f64 (.f64 eps #s(literal 1/2 binary64))) (cos.f64 x)) (.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (sin.f64 x)))) (patch (fma.f64 (.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (sin.f64 x)) (.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (sin.f64 x)) (.f64 (.f64 (cos.f64 (.f64 eps #s(literal 1/2 binary64))) (cos.f64 x)) (.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (sin.f64 x)))) #<representation binary64>) () ())) ())
#s(alt (* eps (+ (* 1/2 (* (cos x) (sin x))) (* eps (+ (* 1/4 (pow (sin x) 2)) (* eps (* (cos x) (+ (* -1/16 (sin x)) (* -1/48 (sin x))))))))) (taylor 0 eps) (#s(alt (fma.f64 (.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (sin.f64 x)) (.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (sin.f64 x)) (.f64 (.f64 (cos.f64 (.f64 eps #s(literal 1/2 binary64))) (cos.f64 x)) (.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (sin.f64 x)))) (patch (fma.f64 (.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (sin.f64 x)) (.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (sin.f64 x)) (.f64 (.f64 (cos.f64 (.f64 eps #s(literal 1/2 binary64))) (cos.f64 x)) (.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (sin.f64 x)))) #<representation binary64>) () ())) ())
#s(alt (* eps (+ (* 1/2 (* (cos x) (sin x))) (* eps (+ (* 1/4 (pow (sin x) 2)) (* eps (+ (* -1/48 (* eps (pow (sin x) 2))) (* (cos x) (+ (* -1/16 (sin x)) (* -1/48 (sin x)))))))))) (taylor 0 eps) (#s(alt (fma.f64 (.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (sin.f64 x)) (.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (sin.f64 x)) (.f64 (.f64 (cos.f64 (.f64 eps #s(literal 1/2 binary64))) (cos.f64 x)) (.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (sin.f64 x)))) (patch (fma.f64 (.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (sin.f64 x)) (.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (sin.f64 x)) (.f64 (.f64 (cos.f64 (.f64 eps #s(literal 1/2 binary64))) (cos.f64 x)) (.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (sin.f64 x)))) #<representation binary64>) () ())) ())
#s(alt (+ (* (cos x) (* (cos (* 1/2 eps)) (* (sin x) (sin (* 1/2 eps))))) (* (pow (sin x) 2) (pow (sin (* 1/2 eps)) 2))) (taylor inf eps) (#s(alt (fma.f64 (.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (sin.f64 x)) (.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (sin.f64 x)) (.f64 (.f64 (cos.f64 (.f64 eps #s(literal 1/2 binary64))) (cos.f64 x)) (.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (sin.f64 x)))) (patch (fma.f64 (.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (sin.f64 x)) (.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (sin.f64 x)) (.f64 (.f64 (cos.f64 (.f64 eps #s(literal 1/2 binary64))) (cos.f64 x)) (.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (sin.f64 x)))) #<representation binary64>) () ())) ())
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#s(alt (cos (- (* 1/2 eps) (* -1 x))) (taylor -inf x) (#s(alt (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) (patch (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) #<representation binary64>) () ())) ())
#s(alt (cos (- (* 1/2 eps) (* -1 x))) (taylor -inf x) (#s(alt (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) (patch (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) #<representation binary64>) () ())) ())
#s(alt (sin x) (taylor 0 eps) (#s(alt (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) (patch (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) #<representation binary64>) () ())) ())
#s(alt (+ (sin x) (* 1/2 (* eps (cos x)))) (taylor 0 eps) (#s(alt (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) (patch (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) #<representation binary64>) () ())) ())
#s(alt (+ (sin x) (* eps (+ (* -1/8 (* eps (sin x))) (* 1/2 (cos x))))) (taylor 0 eps) (#s(alt (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) (patch (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) #<representation binary64>) () ())) ())
#s(alt (+ (sin x) (* eps (+ (* 1/2 (cos x)) (* eps (+ (* -1/8 (sin x)) (* -1/48 (* eps (cos x)))))))) (taylor 0 eps) (#s(alt (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) (patch (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) #<representation binary64>) () ())) ())
#s(alt (sin (+ x (* 1/2 eps))) (taylor inf eps) (#s(alt (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) (patch (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) #<representation binary64>) () ())) ())
#s(alt (sin (+ x (* 1/2 eps))) (taylor inf eps) (#s(alt (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) (patch (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) #<representation binary64>) () ())) ())
#s(alt (sin (+ x (* 1/2 eps))) (taylor inf eps) (#s(alt (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) (patch (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) #<representation binary64>) () ())) ())
#s(alt (sin (+ x (* 1/2 eps))) (taylor inf eps) (#s(alt (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) (patch (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) #<representation binary64>) () ())) ())
#s(alt (sin (- x (* -1/2 eps))) (taylor -inf eps) (#s(alt (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) (patch (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) #<representation binary64>) () ())) ())
#s(alt (sin (- x (* -1/2 eps))) (taylor -inf eps) (#s(alt (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) (patch (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) #<representation binary64>) () ())) ())
#s(alt (sin (- x (* -1/2 eps))) (taylor -inf eps) (#s(alt (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) (patch (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) #<representation binary64>) () ())) ())
#s(alt (sin (- x (* -1/2 eps))) (taylor -inf eps) (#s(alt (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) (patch (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) #<representation binary64>) () ())) ())
#s(alt (sin (* 1/2 eps)) (taylor 0 x) (#s(alt (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) (patch (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) #<representation binary64>) () ())) ())
#s(alt (+ (sin (* 1/2 eps)) (* x (cos (* 1/2 eps)))) (taylor 0 x) (#s(alt (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) (patch (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) #<representation binary64>) () ())) ())
#s(alt (+ (sin (* 1/2 eps)) (* x (+ (cos (* 1/2 eps)) (* -1/2 (* x (sin (* 1/2 eps))))))) (taylor 0 x) (#s(alt (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) (patch (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) #<representation binary64>) () ())) ())
#s(alt (+ (sin (* 1/2 eps)) (* x (+ (cos (* 1/2 eps)) (* x (+ (* -1/2 (sin (* 1/2 eps))) (* -1/6 (* x (cos (* 1/2 eps))))))))) (taylor 0 x) (#s(alt (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) (patch (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) #<representation binary64>) () ())) ())
#s(alt (sin (+ x (* 1/2 eps))) (taylor inf x) (#s(alt (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) (patch (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) #<representation binary64>) () ())) ())
#s(alt (sin (+ x (* 1/2 eps))) (taylor inf x) (#s(alt (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) (patch (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) #<representation binary64>) () ())) ())
#s(alt (sin (+ x (* 1/2 eps))) (taylor inf x) (#s(alt (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) (patch (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) #<representation binary64>) () ())) ())
#s(alt (sin (+ x (* 1/2 eps))) (taylor inf x) (#s(alt (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) (patch (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) #<representation binary64>) () ())) ())
#s(alt (sin (- (* 1/2 eps) (* -1 x))) (taylor -inf x) (#s(alt (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) (patch (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) #<representation binary64>) () ())) ())
#s(alt (sin (- (* 1/2 eps) (* -1 x))) (taylor -inf x) (#s(alt (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) (patch (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) #<representation binary64>) () ())) ())
#s(alt (sin (- (* 1/2 eps) (* -1 x))) (taylor -inf x) (#s(alt (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) (patch (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) #<representation binary64>) () ())) ())
#s(alt (sin (- (* 1/2 eps) (* -1 x))) (taylor -inf x) (#s(alt (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) (patch (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) #<representation binary64>) () ())) ())
#s(alt (cos (* 2 x)) (taylor 0 eps) (#s(alt (cos.f64 (.f64 #s(literal 2 binary64) (+.f64 eps x))) (patch (cos.f64 (.f64 #s(literal 2 binary64) (+.f64 eps x))) #<representation binary64>) () ())) ())
#s(alt (+ (cos (* 2 x)) (* -2 (* eps (sin (* 2 x))))) (taylor 0 eps) (#s(alt (cos.f64 (.f64 #s(literal 2 binary64) (+.f64 eps x))) (patch (cos.f64 (.f64 #s(literal 2 binary64) (+.f64 eps x))) #<representation binary64>) () ())) ())
#s(alt (+ (cos (* 2 x)) (* eps (- (* -2 (* eps (cos (* 2 x)))) (* 2 (sin (* 2 x)))))) (taylor 0 eps) (#s(alt (cos.f64 (.f64 #s(literal 2 binary64) (+.f64 eps x))) (patch (cos.f64 (.f64 #s(literal 2 binary64) (+.f64 eps x))) #<representation binary64>) () ())) ())
#s(alt (+ (cos (* 2 x)) (* eps (- (* eps (+ (* -2 (cos (* 2 x))) (* 4/3 (* eps (sin (* 2 x)))))) (* 2 (sin (* 2 x)))))) (taylor 0 eps) (#s(alt (cos.f64 (.f64 #s(literal 2 binary64) (+.f64 eps x))) (patch (cos.f64 (.f64 #s(literal 2 binary64) (+.f64 eps x))) #<representation binary64>) () ())) ())
#s(alt (cos (* 2 (+ eps x))) (taylor inf eps) (#s(alt (cos.f64 (.f64 #s(literal 2 binary64) (+.f64 eps x))) (patch (cos.f64 (.f64 #s(literal 2 binary64) (+.f64 eps x))) #<representation binary64>) () ())) ())
#s(alt (cos (* 2 (+ eps x))) (taylor inf eps) (#s(alt (cos.f64 (.f64 #s(literal 2 binary64) (+.f64 eps x))) (patch (cos.f64 (.f64 #s(literal 2 binary64) (+.f64 eps x))) #<representation binary64>) () ())) ())
#s(alt (cos (* 2 (+ eps x))) (taylor inf eps) (#s(alt (cos.f64 (.f64 #s(literal 2 binary64) (+.f64 eps x))) (patch (cos.f64 (.f64 #s(literal 2 binary64) (+.f64 eps x))) #<representation binary64>) () ())) ())
#s(alt (cos (* 2 (+ eps x))) (taylor inf eps) (#s(alt (cos.f64 (.f64 #s(literal 2 binary64) (+.f64 eps x))) (patch (cos.f64 (.f64 #s(literal 2 binary64) (+.f64 eps x))) #<representation binary64>) () ())) ())
#s(alt (cos (* 2 (- x (* -1 eps)))) (taylor -inf eps) (#s(alt (cos.f64 (.f64 #s(literal 2 binary64) (+.f64 eps x))) (patch (cos.f64 (.f64 #s(literal 2 binary64) (+.f64 eps x))) #<representation binary64>) () ())) ())
#s(alt (cos (* 2 (- x (* -1 eps)))) (taylor -inf eps) (#s(alt (cos.f64 (.f64 #s(literal 2 binary64) (+.f64 eps x))) (patch (cos.f64 (.f64 #s(literal 2 binary64) (+.f64 eps x))) #<representation binary64>) () ())) ())
#s(alt (cos (* 2 (- x (* -1 eps)))) (taylor -inf eps) (#s(alt (cos.f64 (.f64 #s(literal 2 binary64) (+.f64 eps x))) (patch (cos.f64 (.f64 #s(literal 2 binary64) (+.f64 eps x))) #<representation binary64>) () ())) ())
#s(alt (cos (* 2 (- x (* -1 eps)))) (taylor -inf eps) (#s(alt (cos.f64 (.f64 #s(literal 2 binary64) (+.f64 eps x))) (patch (cos.f64 (.f64 #s(literal 2 binary64) (+.f64 eps x))) #<representation binary64>) () ())) ())
#s(alt (cos (* 2 eps)) (taylor 0 x) (#s(alt (cos.f64 (.f64 #s(literal 2 binary64) (+.f64 eps x))) (patch (cos.f64 (.f64 #s(literal 2 binary64) (+.f64 eps x))) #<representation binary64>) () ())) ())
#s(alt (+ (cos (* 2 eps)) (* -2 (* x (sin (* 2 eps))))) (taylor 0 x) (#s(alt (cos.f64 (.f64 #s(literal 2 binary64) (+.f64 eps x))) (patch (cos.f64 (.f64 #s(literal 2 binary64) (+.f64 eps x))) #<representation binary64>) () ())) ())
#s(alt (+ (cos (* 2 eps)) (* x (- (* -2 (* x (cos (* 2 eps)))) (* 2 (sin (* 2 eps)))))) (taylor 0 x) (#s(alt (cos.f64 (.f64 #s(literal 2 binary64) (+.f64 eps x))) (patch (cos.f64 (.f64 #s(literal 2 binary64) (+.f64 eps x))) #<representation binary64>) () ())) ())
#s(alt (+ (cos (* 2 eps)) (* x (- (* x (+ (* -2 (cos (* 2 eps))) (* 4/3 (* x (sin (* 2 eps)))))) (* 2 (sin (* 2 eps)))))) (taylor 0 x) (#s(alt (cos.f64 (.f64 #s(literal 2 binary64) (+.f64 eps x))) (patch (cos.f64 (.f64 #s(literal 2 binary64) (+.f64 eps x))) #<representation binary64>) () ())) ())
#s(alt (cos (* 2 (+ eps x))) (taylor inf x) (#s(alt (cos.f64 (.f64 #s(literal 2 binary64) (+.f64 eps x))) (patch (cos.f64 (.f64 #s(literal 2 binary64) (+.f64 eps x))) #<representation binary64>) () ())) ())
#s(alt (cos (* 2 (+ eps x))) (taylor inf x) (#s(alt (cos.f64 (.f64 #s(literal 2 binary64) (+.f64 eps x))) (patch (cos.f64 (.f64 #s(literal 2 binary64) (+.f64 eps x))) #<representation binary64>) () ())) ())
#s(alt (cos (* 2 (+ eps x))) (taylor inf x) (#s(alt (cos.f64 (.f64 #s(literal 2 binary64) (+.f64 eps x))) (patch (cos.f64 (.f64 #s(literal 2 binary64) (+.f64 eps x))) #<representation binary64>) () ())) ())
#s(alt (cos (* 2 (+ eps x))) (taylor inf x) (#s(alt (cos.f64 (.f64 #s(literal 2 binary64) (+.f64 eps x))) (patch (cos.f64 (.f64 #s(literal 2 binary64) (+.f64 eps x))) #<representation binary64>) () ())) ())
#s(alt (cos (* 2 (- eps (* -1 x)))) (taylor -inf x) (#s(alt (cos.f64 (.f64 #s(literal 2 binary64) (+.f64 eps x))) (patch (cos.f64 (.f64 #s(literal 2 binary64) (+.f64 eps x))) #<representation binary64>) () ())) ())
#s(alt (cos (* 2 (- eps (* -1 x)))) (taylor -inf x) (#s(alt (cos.f64 (.f64 #s(literal 2 binary64) (+.f64 eps x))) (patch (cos.f64 (.f64 #s(literal 2 binary64) (+.f64 eps x))) #<representation binary64>) () ())) ())
#s(alt (cos (* 2 (- eps (* -1 x)))) (taylor -inf x) (#s(alt (cos.f64 (.f64 #s(literal 2 binary64) (+.f64 eps x))) (patch (cos.f64 (.f64 #s(literal 2 binary64) (+.f64 eps x))) #<representation binary64>) () ())) ())
#s(alt (cos (* 2 (- eps (* -1 x)))) (taylor -inf x) (#s(alt (cos.f64 (.f64 #s(literal 2 binary64) (+.f64 eps x))) (patch (cos.f64 (.f64 #s(literal 2 binary64) (+.f64 eps x))) #<representation binary64>) () ())) ())

Calls

171 calls:

Time	Variable		Point	Expression
17.0ms	eps	@	0	(/ (- (pow (* (cos (* eps 1/2)) (cos x)) 3) (pow (* (sin (* eps 1/2)) (sin x)) 3)) (+ (* (* (cos (* eps 1/2)) (cos x)) (* (cos (* eps 1/2)) (cos x))) (+ (* (* (sin (* eps 1/2)) (sin x)) (* (sin (* eps 1/2)) (sin x))) (* (* (cos (* eps 1/2)) (cos x)) (* (sin (* eps 1/2)) (sin x))))))
14.0ms	x	@	-inf	(* (sin (* 1/2 eps)) (/ (- (pow (* (cos (* eps 1/2)) (cos x)) 3) (pow (* (sin (* eps 1/2)) (sin x)) 3)) (+ (* (* (cos (* eps 1/2)) (cos x)) (* (cos (* eps 1/2)) (cos x))) (+ (* (* (sin (* eps 1/2)) (sin x)) (* (sin (* eps 1/2)) (sin x))) (* (* (cos (* eps 1/2)) (cos x)) (* (sin (* eps 1/2)) (sin x)))))))
6.0ms	x	@	inf	(* (sin (* 1/2 eps)) (/ (- (pow (* (cos (* eps 1/2)) (cos x)) 3) (pow (* (sin (* eps 1/2)) (sin x)) 3)) (+ (* (* (cos (* eps 1/2)) (cos x)) (* (cos (* eps 1/2)) (cos x))) (+ (* (* (sin (* eps 1/2)) (sin x)) (* (sin (* eps 1/2)) (sin x))) (* (* (cos (* eps 1/2)) (cos x)) (* (sin (* eps 1/2)) (sin x)))))))
4.0ms	eps	@	inf	(* (sin (* 1/2 eps)) (/ (- (pow (* (cos (* eps 1/2)) (cos x)) 3) (pow (* (sin (* eps 1/2)) (sin x)) 3)) (+ (* (* (cos (* eps 1/2)) (cos x)) (* (cos (* eps 1/2)) (cos x))) (+ (* (* (sin (* eps 1/2)) (sin x)) (* (sin (* eps 1/2)) (sin x))) (* (* (cos (* eps 1/2)) (cos x)) (* (sin (* eps 1/2)) (sin x)))))))
3.0ms	eps	@	-inf	(* (sin (* 1/2 eps)) (/ (- (pow (* (cos (* eps 1/2)) (cos x)) 3) (pow (* (sin (* eps 1/2)) (sin x)) 3)) (+ (* (* (cos (* eps 1/2)) (cos x)) (* (cos (* eps 1/2)) (cos x))) (+ (* (* (sin (* eps 1/2)) (sin x)) (* (sin (* eps 1/2)) (sin x))) (* (* (cos (* eps 1/2)) (cos x)) (* (sin (* eps 1/2)) (sin x)))))))

simplify426.0ms (3%)

Memory

-11.0MiB live, 583.5MiB allocated

Algorithm

1×	egg-herbie

Rules

9 040×	`lower-fma.f64`
9 040×	`lower-fma.f32`
6 660×	`lower-+.f64`
6 660×	`lower-+.f32`
5 730×	`lower-*.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	1099	15148
1	3483	14627
0	8116	13742

Stop Event

1×	iter limit
1×	node limit

Counts

684 → 680

Calls

Call 1

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

Outputs
(* 1/2 (* eps (* (cos x) (sin x))))
(.f64 #s(literal 1/2 binary64) (.f64 (*.f64 eps (cos.f64 x)) (sin.f64 x)))
(* eps (+ (* 1/4 (* eps (pow (sin x) 2))) (* 1/2 (* (cos x) (sin x)))))
(.f64 eps (fma.f64 (.f64 #s(literal 1/2 binary64) (cos.f64 x)) (sin.f64 x) (.f64 (.f64 #s(literal 1/4 binary64) eps) (pow.f64 (sin.f64 x) #s(literal 2 binary64)))))
(* eps (+ (* 1/2 (* (cos x) (sin x))) (* eps (+ (* 1/4 (pow (sin x) 2)) (* eps (* (cos x) (+ (* -1/16 (sin x)) (* -1/48 (sin x)))))))))
(.f64 eps (fma.f64 eps (fma.f64 eps (.f64 (cos.f64 x) (.f64 (sin.f64 x) #s(literal -1/12 binary64))) (.f64 #s(literal 1/4 binary64) (pow.f64 (sin.f64 x) #s(literal 2 binary64)))) (.f64 (.f64 #s(literal 1/2 binary64) (cos.f64 x)) (sin.f64 x))))
(* eps (+ (* 1/2 (* (cos x) (sin x))) (* eps (+ (* 1/4 (pow (sin x) 2)) (* eps (+ (* -1/48 (* eps (pow (sin x) 2))) (* (cos x) (+ (* -1/16 (sin x)) (* -1/48 (sin x))))))))))
(.f64 eps (fma.f64 eps (fma.f64 eps (fma.f64 (cos.f64 x) (.f64 (sin.f64 x) #s(literal -1/12 binary64)) (.f64 (.f64 eps #s(literal -1/48 binary64)) (pow.f64 (sin.f64 x) #s(literal 2 binary64)))) (.f64 #s(literal 1/4 binary64) (pow.f64 (sin.f64 x) #s(literal 2 binary64)))) (.f64 (*.f64 #s(literal 1/2 binary64) (cos.f64 x)) (sin.f64 x))))
(+ (* (cos x) (* (cos (* 1/2 eps)) (* (sin x) (sin (* 1/2 eps))))) (* (pow (sin x) 2) (pow (sin (* 1/2 eps)) 2)))
(fma.f64 (cos.f64 x) (.f64 (cos.f64 (.f64 #s(literal 1/2 binary64) eps)) (.f64 (sin.f64 x) (sin.f64 (.f64 #s(literal 1/2 binary64) eps)))) (.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) #s(literal 2 binary64))))
(+ (* (cos x) (* (cos (* 1/2 eps)) (* (sin x) (sin (* 1/2 eps))))) (* (pow (sin x) 2) (pow (sin (* 1/2 eps)) 2)))
(fma.f64 (cos.f64 x) (.f64 (cos.f64 (.f64 #s(literal 1/2 binary64) eps)) (.f64 (sin.f64 x) (sin.f64 (.f64 #s(literal 1/2 binary64) eps)))) (.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) #s(literal 2 binary64))))
(+ (* (cos x) (* (cos (* 1/2 eps)) (* (sin x) (sin (* 1/2 eps))))) (* (pow (sin x) 2) (pow (sin (* 1/2 eps)) 2)))
(fma.f64 (cos.f64 x) (.f64 (cos.f64 (.f64 #s(literal 1/2 binary64) eps)) (.f64 (sin.f64 x) (sin.f64 (.f64 #s(literal 1/2 binary64) eps)))) (.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) #s(literal 2 binary64))))
(+ (* (cos x) (* (cos (* 1/2 eps)) (* (sin x) (sin (* 1/2 eps))))) (* (pow (sin x) 2) (pow (sin (* 1/2 eps)) 2)))
(fma.f64 (cos.f64 x) (.f64 (cos.f64 (.f64 #s(literal 1/2 binary64) eps)) (.f64 (sin.f64 x) (sin.f64 (.f64 #s(literal 1/2 binary64) eps)))) (.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) #s(literal 2 binary64))))
(+ (* (cos x) (* (cos (* 1/2 eps)) (* (sin x) (sin (* 1/2 eps))))) (* (pow (sin x) 2) (pow (sin (* 1/2 eps)) 2)))
(fma.f64 (cos.f64 x) (.f64 (cos.f64 (.f64 #s(literal 1/2 binary64) eps)) (.f64 (sin.f64 x) (sin.f64 (.f64 #s(literal 1/2 binary64) eps)))) (.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) #s(literal 2 binary64))))
(+ (* (cos x) (* (cos (* 1/2 eps)) (* (sin x) (sin (* 1/2 eps))))) (* (pow (sin x) 2) (pow (sin (* 1/2 eps)) 2)))
(fma.f64 (cos.f64 x) (.f64 (cos.f64 (.f64 #s(literal 1/2 binary64) eps)) (.f64 (sin.f64 x) (sin.f64 (.f64 #s(literal 1/2 binary64) eps)))) (.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) #s(literal 2 binary64))))
(+ (* (cos x) (* (cos (* 1/2 eps)) (* (sin x) (sin (* 1/2 eps))))) (* (pow (sin x) 2) (pow (sin (* 1/2 eps)) 2)))
(fma.f64 (cos.f64 x) (.f64 (cos.f64 (.f64 #s(literal 1/2 binary64) eps)) (.f64 (sin.f64 x) (sin.f64 (.f64 #s(literal 1/2 binary64) eps)))) (.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) #s(literal 2 binary64))))
(+ (* (cos x) (* (cos (* 1/2 eps)) (* (sin x) (sin (* 1/2 eps))))) (* (pow (sin x) 2) (pow (sin (* 1/2 eps)) 2)))
(fma.f64 (cos.f64 x) (.f64 (cos.f64 (.f64 #s(literal 1/2 binary64) eps)) (.f64 (sin.f64 x) (sin.f64 (.f64 #s(literal 1/2 binary64) eps)))) (.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) #s(literal 2 binary64))))
(* x (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))
(.f64 x (.f64 (cos.f64 (.f64 #s(literal 1/2 binary64) eps)) (sin.f64 (.f64 #s(literal 1/2 binary64) eps))))
(* x (+ (* x (pow (sin (* 1/2 eps)) 2)) (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))))
(.f64 x (fma.f64 x (pow.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) #s(literal 2 binary64)) (.f64 (cos.f64 (.f64 #s(literal 1/2 binary64) eps)) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)))))
(* x (+ (* x (+ (* x (+ (* -1/2 (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) (* -1/6 (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))))) (pow (sin (* 1/2 eps)) 2))) (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))))
(.f64 x (fma.f64 x (fma.f64 x (.f64 (.f64 (cos.f64 (.f64 #s(literal 1/2 binary64) eps)) (sin.f64 (.f64 #s(literal 1/2 binary64) eps))) #s(literal -2/3 binary64)) (pow.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) #s(literal 2 binary64))) (.f64 (cos.f64 (.f64 #s(literal 1/2 binary64) eps)) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)))))
(* x (+ (* x (+ (* x (+ (* -1/2 (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) (+ (* -1/3 (* x (pow (sin (* 1/2 eps)) 2))) (* -1/6 (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))))) (pow (sin (* 1/2 eps)) 2))) (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))))
(.f64 x (fma.f64 x (fma.f64 x (fma.f64 (.f64 (cos.f64 (.f64 #s(literal 1/2 binary64) eps)) (sin.f64 (.f64 #s(literal 1/2 binary64) eps))) #s(literal -2/3 binary64) (.f64 (.f64 #s(literal -1/3 binary64) x) (pow.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) #s(literal 2 binary64)))) (pow.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) #s(literal 2 binary64))) (.f64 (cos.f64 (.f64 #s(literal 1/2 binary64) eps)) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)))))
(+ (* (cos x) (* (cos (* 1/2 eps)) (* (sin x) (sin (* 1/2 eps))))) (* (pow (sin x) 2) (pow (sin (* 1/2 eps)) 2)))
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(* -1/2 (* (pow x 2) (sin eps)))
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(* (pow x 2) (+ (* -1 (/ (+ 1 (* -1 (cos eps))) x)) (* -1/2 (sin eps))))
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(* eps (+ 1 (* -1/2 (pow x 2))))
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(* eps (+ 1 (+ (* -1/2 (* eps x)) (* -1/2 (pow x 2)))))
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(* eps (+ 1 (+ (* -1/2 (pow x 2)) (* eps (+ (* -1/2 x) (* -1/6 (* eps (+ 1 (* -1/2 (pow x 2))))))))))
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(* -1/2 (* (pow x 2) (sin eps)))
(.f64 (.f64 #s(literal -1/2 binary64) (*.f64 x x)) (sin.f64 eps))
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x
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(+ x (* eps (+ 1 (+ (* -1/2 (pow x 2)) (* eps (+ (* -1/2 x) (* -1/6 (* eps (+ 1 (* -1/2 (pow x 2)))))))))))
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(* 1/3840 (pow eps 3))
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(cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x))
(cos (- x (* -1/2 eps)))
(cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x))
(cos (- x (* -1/2 eps)))
(cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x))
(cos (- x (* -1/2 eps)))
(cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x))
(cos (* 1/2 eps))
(cos.f64 (*.f64 #s(literal 1/2 binary64) eps))
(+ (cos (* 1/2 eps)) (* -1 (* x (sin (* 1/2 eps)))))
(fma.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (neg.f64 x) (cos.f64 (.f64 #s(literal 1/2 binary64) eps)))
(+ (cos (* 1/2 eps)) (* x (- (* -1/2 (* x (cos (* 1/2 eps)))) (sin (* 1/2 eps)))))
(fma.f64 x (-.f64 (.f64 (.f64 x #s(literal -1/2 binary64)) (cos.f64 (.f64 #s(literal 1/2 binary64) eps))) (sin.f64 (.f64 #s(literal 1/2 binary64) eps))) (cos.f64 (*.f64 #s(literal 1/2 binary64) eps)))
(+ (cos (* 1/2 eps)) (* x (- (* x (+ (* -1/2 (cos (* 1/2 eps))) (* 1/6 (* x (sin (* 1/2 eps)))))) (sin (* 1/2 eps)))))
(fma.f64 x (fma.f64 x (fma.f64 (cos.f64 (.f64 #s(literal 1/2 binary64) eps)) #s(literal -1/2 binary64) (.f64 (.f64 #s(literal 1/6 binary64) x) (sin.f64 (.f64 #s(literal 1/2 binary64) eps)))) (neg.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)))) (cos.f64 (.f64 #s(literal 1/2 binary64) eps)))
(cos (+ x (* 1/2 eps)))
(cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x))
(cos (+ x (* 1/2 eps)))
(cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x))
(cos (+ x (* 1/2 eps)))
(cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x))
(cos (+ x (* 1/2 eps)))
(cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x))
(cos (- (* 1/2 eps) (* -1 x)))
(cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x))
(cos (- (* 1/2 eps) (* -1 x)))
(cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x))
(cos (- (* 1/2 eps) (* -1 x)))
(cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x))
(cos (- (* 1/2 eps) (* -1 x)))
(cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x))
(sin x)
(sin.f64 x)
(+ (sin x) (* 1/2 (* eps (cos x))))
(fma.f64 #s(literal 1/2 binary64) (*.f64 eps (cos.f64 x)) (sin.f64 x))
(+ (sin x) (* eps (+ (* -1/8 (* eps (sin x))) (* 1/2 (cos x)))))
(fma.f64 eps (fma.f64 #s(literal 1/2 binary64) (cos.f64 x) (.f64 (.f64 eps (sin.f64 x)) #s(literal -1/8 binary64))) (sin.f64 x))
(+ (sin x) (* eps (+ (* 1/2 (cos x)) (* eps (+ (* -1/8 (sin x)) (* -1/48 (* eps (cos x))))))))
(fma.f64 eps (fma.f64 #s(literal 1/2 binary64) (cos.f64 x) (.f64 eps (fma.f64 (sin.f64 x) #s(literal -1/8 binary64) (.f64 #s(literal -1/48 binary64) (*.f64 eps (cos.f64 x)))))) (sin.f64 x))
(sin (+ x (* 1/2 eps)))
(sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x))
(sin (+ x (* 1/2 eps)))
(sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x))
(sin (+ x (* 1/2 eps)))
(sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x))
(sin (+ x (* 1/2 eps)))
(sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x))
(sin (- x (* -1/2 eps)))
(sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x))
(sin (- x (* -1/2 eps)))
(sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x))
(sin (- x (* -1/2 eps)))
(sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x))
(sin (- x (* -1/2 eps)))
(sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x))
(sin (* 1/2 eps))
(sin.f64 (*.f64 #s(literal 1/2 binary64) eps))
(+ (sin (* 1/2 eps)) (* x (cos (* 1/2 eps))))
(fma.f64 x (cos.f64 (.f64 #s(literal 1/2 binary64) eps)) (sin.f64 (.f64 #s(literal 1/2 binary64) eps)))
(+ (sin (* 1/2 eps)) (* x (+ (cos (* 1/2 eps)) (* -1/2 (* x (sin (* 1/2 eps)))))))
(fma.f64 x (fma.f64 (.f64 x #s(literal -1/2 binary64)) (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (cos.f64 (.f64 #s(literal 1/2 binary64) eps))) (sin.f64 (.f64 #s(literal 1/2 binary64) eps)))
(+ (sin (* 1/2 eps)) (* x (+ (cos (* 1/2 eps)) (* x (+ (* -1/2 (sin (* 1/2 eps))) (* -1/6 (* x (cos (* 1/2 eps)))))))))
(fma.f64 x (fma.f64 x (fma.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) #s(literal -1/2 binary64) (.f64 (.f64 #s(literal -1/6 binary64) x) (cos.f64 (.f64 #s(literal 1/2 binary64) eps)))) (cos.f64 (.f64 #s(literal 1/2 binary64) eps))) (sin.f64 (.f64 #s(literal 1/2 binary64) eps)))
(sin (+ x (* 1/2 eps)))
(sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x))
(sin (+ x (* 1/2 eps)))
(sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x))
(sin (+ x (* 1/2 eps)))
(sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x))
(sin (+ x (* 1/2 eps)))
(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))
(sin (- (* 1/2 eps) (* -1 x)))
(sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x))
(cos (* 2 x))
(cos.f64 (*.f64 x #s(literal 2 binary64)))
(+ (cos (* 2 x)) (* -2 (* eps (sin (* 2 x)))))
(fma.f64 (.f64 #s(literal -2 binary64) eps) (sin.f64 (.f64 x #s(literal 2 binary64))) (cos.f64 (*.f64 x #s(literal 2 binary64))))
(+ (cos (* 2 x)) (* eps (- (* -2 (* eps (cos (* 2 x)))) (* 2 (sin (* 2 x))))))
(fma.f64 eps (.f64 #s(literal -2 binary64) (fma.f64 eps (cos.f64 (.f64 x #s(literal 2 binary64))) (sin.f64 (.f64 x #s(literal 2 binary64))))) (cos.f64 (.f64 x #s(literal 2 binary64))))
(+ (cos (* 2 x)) (* eps (- (* eps (+ (* -2 (cos (* 2 x))) (* 4/3 (* eps (sin (* 2 x)))))) (* 2 (sin (* 2 x))))))
(fma.f64 eps (fma.f64 eps (fma.f64 #s(literal -2 binary64) (cos.f64 (.f64 x #s(literal 2 binary64))) (.f64 (.f64 #s(literal 4/3 binary64) eps) (sin.f64 (.f64 x #s(literal 2 binary64))))) (.f64 #s(literal -2 binary64) (sin.f64 (.f64 x #s(literal 2 binary64))))) (cos.f64 (*.f64 x #s(literal 2 binary64))))
(cos (* 2 (+ eps x)))
(cos.f64 (*.f64 #s(literal 2 binary64) (+.f64 eps x)))
(cos (* 2 (+ eps x)))
(cos.f64 (*.f64 #s(literal 2 binary64) (+.f64 eps x)))
(cos (* 2 (+ eps x)))
(cos.f64 (*.f64 #s(literal 2 binary64) (+.f64 eps x)))
(cos (* 2 (+ eps x)))
(cos.f64 (*.f64 #s(literal 2 binary64) (+.f64 eps x)))
(cos (* 2 (- x (* -1 eps))))
(cos.f64 (*.f64 #s(literal 2 binary64) (+.f64 eps x)))
(cos (* 2 (- x (* -1 eps))))
(cos.f64 (*.f64 #s(literal 2 binary64) (+.f64 eps x)))
(cos (* 2 (- x (* -1 eps))))
(cos.f64 (*.f64 #s(literal 2 binary64) (+.f64 eps x)))
(cos (* 2 (- x (* -1 eps))))
(cos.f64 (*.f64 #s(literal 2 binary64) (+.f64 eps x)))
(cos (* 2 eps))
(cos.f64 (*.f64 eps #s(literal 2 binary64)))
(+ (cos (* 2 eps)) (* -2 (* x (sin (* 2 eps)))))
(fma.f64 (.f64 x #s(literal -2 binary64)) (sin.f64 (.f64 eps #s(literal 2 binary64))) (cos.f64 (*.f64 eps #s(literal 2 binary64))))
(+ (cos (* 2 eps)) (* x (- (* -2 (* x (cos (* 2 eps)))) (* 2 (sin (* 2 eps))))))
(fma.f64 x (.f64 #s(literal -2 binary64) (fma.f64 x (cos.f64 (.f64 eps #s(literal 2 binary64))) (sin.f64 (.f64 eps #s(literal 2 binary64))))) (cos.f64 (.f64 eps #s(literal 2 binary64))))
(+ (cos (* 2 eps)) (* x (- (* x (+ (* -2 (cos (* 2 eps))) (* 4/3 (* x (sin (* 2 eps)))))) (* 2 (sin (* 2 eps))))))
(fma.f64 x (fma.f64 x (fma.f64 #s(literal -2 binary64) (cos.f64 (.f64 eps #s(literal 2 binary64))) (.f64 (.f64 #s(literal 4/3 binary64) x) (sin.f64 (.f64 eps #s(literal 2 binary64))))) (.f64 #s(literal -2 binary64) (sin.f64 (.f64 eps #s(literal 2 binary64))))) (cos.f64 (*.f64 eps #s(literal 2 binary64))))
(cos (* 2 (+ eps x)))
(cos.f64 (*.f64 #s(literal 2 binary64) (+.f64 eps x)))
(cos (* 2 (+ eps x)))
(cos.f64 (*.f64 #s(literal 2 binary64) (+.f64 eps x)))
(cos (* 2 (+ eps x)))
(cos.f64 (*.f64 #s(literal 2 binary64) (+.f64 eps x)))
(cos (* 2 (+ eps x)))
(cos.f64 (*.f64 #s(literal 2 binary64) (+.f64 eps x)))
(cos (* 2 (- eps (* -1 x))))
(cos.f64 (*.f64 #s(literal 2 binary64) (+.f64 eps x)))
(cos (* 2 (- eps (* -1 x))))
(cos.f64 (*.f64 #s(literal 2 binary64) (+.f64 eps x)))
(cos (* 2 (- eps (* -1 x))))
(cos.f64 (*.f64 #s(literal 2 binary64) (+.f64 eps x)))
(cos (* 2 (- eps (* -1 x))))
(cos.f64 (*.f64 #s(literal 2 binary64) (+.f64 eps x)))

rewrite308.0ms (2.1%)

Memory

12.5MiB live, 497.6MiB allocated

Algorithm

1×	batch-egg-rewrite

Rules

3 718×	`lower-fma.f32`
3 702×	`lower-fma.f64`
3 258×	`lower-*.f32`
3 224×	`lower-*.f64`
2 158×	`lower-/.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	106	1115
0	160	1119
1	697	595
0	5737	584

Stop Event

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

Counts

30 → 503

Calls

Call 1

Inputs
(fma.f64 (.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (sin.f64 x)) (.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (sin.f64 x)) (.f64 (.f64 (cos.f64 (.f64 eps #s(literal 1/2 binary64))) (cos.f64 x)) (.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) (sin.f64 x))))
(.f64 #s(approx ( (sin (* (+ eps 0) 1/2)) (cos (* (+ (* x 2) eps) 1/2))) (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (/.f64 (-.f64 (pow.f64 (.f64 (cos.f64 (.f64 eps #s(literal 1/2 binary64))) (cos.f64 x)) #s(literal 3 binary64)) (pow.f64 (.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (sin.f64 x)) #s(literal 3 binary64))) (fma.f64 (.f64 (cos.f64 (.f64 eps #s(literal 1/2 binary64))) (cos.f64 x)) (.f64 (cos.f64 (.f64 eps #s(literal 1/2 binary64))) (cos.f64 x)) (fma.f64 (.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (sin.f64 x)) (.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (sin.f64 x)) (.f64 (.f64 (cos.f64 (.f64 eps #s(literal 1/2 binary64))) (cos.f64 x)) (.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) (sin.f64 x)))))))) #s(literal 2 binary64))
#s(approx (* (sin (* (+ eps 0) 1/2)) (cos (* (+ (* x 2) eps) 1/2))) (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (/.f64 (-.f64 (pow.f64 (.f64 (cos.f64 (.f64 eps #s(literal 1/2 binary64))) (cos.f64 x)) #s(literal 3 binary64)) (pow.f64 (.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (sin.f64 x)) #s(literal 3 binary64))) (fma.f64 (.f64 (cos.f64 (.f64 eps #s(literal 1/2 binary64))) (cos.f64 x)) (.f64 (cos.f64 (.f64 eps #s(literal 1/2 binary64))) (cos.f64 x)) (fma.f64 (.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (sin.f64 x)) (.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (sin.f64 x)) (.f64 (.f64 (cos.f64 (.f64 eps #s(literal 1/2 binary64))) (cos.f64 x)) (.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) (sin.f64 x))))))))
(.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (/.f64 (-.f64 (pow.f64 (.f64 (cos.f64 (.f64 eps #s(literal 1/2 binary64))) (cos.f64 x)) #s(literal 3 binary64)) (pow.f64 (.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (sin.f64 x)) #s(literal 3 binary64))) (fma.f64 (.f64 (cos.f64 (.f64 eps #s(literal 1/2 binary64))) (cos.f64 x)) (.f64 (cos.f64 (.f64 eps #s(literal 1/2 binary64))) (cos.f64 x)) (fma.f64 (.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (sin.f64 x)) (.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (sin.f64 x)) (.f64 (.f64 (cos.f64 (.f64 eps #s(literal 1/2 binary64))) (cos.f64 x)) (.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) (sin.f64 x)))))))
#s(approx (- (sin (+ x eps)) (sin x)) (-.f64 #s(approx (+ (* (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) #s(approx (+ (* eps (+ (* x (* x -1/2)) 1)) x) (+.f64 eps x))) x))
(-.f64 #s(approx (+ (* (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) #s(approx (+ (* eps (+ (* x (* x -1/2)) 1)) x) (+.f64 eps x))) x)
#s(approx (+ (* (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) #s(approx (+ (* eps (+ (* x (* x -1/2)) 1)) x) (+.f64 eps x)))
#s(approx (+ (* eps (+ (* x (* x -1/2)) 1)) x) (+.f64 eps x))
(/.f64 (+.f64 x #s(approx (+ (* (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) (fma.f64 eps (fma.f64 #s(literal -1/2 binary64) (.f64 x x) #s(literal 1 binary64)) x))) (.f64 (+.f64 x #s(approx (+ (* (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) (fma.f64 eps (fma.f64 #s(literal -1/2 binary64) (.f64 x x) #s(literal 1 binary64)) x))) (-.f64 #s(approx (+ ( (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) (fma.f64 eps (fma.f64 #s(literal -1/2 binary64) (*.f64 x x) #s(literal 1 binary64)) x)) x)))
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 x #s(approx (+ (* (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) (fma.f64 eps (fma.f64 #s(literal -1/2 binary64) (.f64 x x) #s(literal 1 binary64)) x))) (.f64 (+.f64 x #s(approx (+ (* (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) (fma.f64 eps (fma.f64 #s(literal -1/2 binary64) (.f64 x x) #s(literal 1 binary64)) x))) (-.f64 #s(approx (+ ( (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) (fma.f64 eps (fma.f64 #s(literal -1/2 binary64) (*.f64 x x) #s(literal 1 binary64)) x)) x))))
#s(approx (- (sin (+ x eps)) (sin x)) (/.f64 #s(literal 1 binary64) (/.f64 (+.f64 x #s(approx (+ (* (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) (fma.f64 eps (fma.f64 #s(literal -1/2 binary64) (.f64 x x) #s(literal 1 binary64)) x))) (.f64 (+.f64 x #s(approx (+ (* (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) (fma.f64 eps (fma.f64 #s(literal -1/2 binary64) (.f64 x x) #s(literal 1 binary64)) x))) (-.f64 #s(approx (+ ( (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) (fma.f64 eps (fma.f64 #s(literal -1/2 binary64) (*.f64 x x) #s(literal 1 binary64)) x)) x)))))
(+.f64 x #s(approx (+ (* (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) (fma.f64 eps (fma.f64 #s(literal -1/2 binary64) (*.f64 x x) #s(literal 1 binary64)) x)))
(.f64 #s(approx ( (sin (* (+ eps 0) 1/2)) (cos (* (+ (* x 2) eps) 1/2))) (.f64 #s(approx (sin ( 1/2 eps)) (.f64 eps (fma.f64 eps (.f64 eps (fma.f64 (*.f64 eps eps) #s(literal 1/3840 binary64) #s(literal -1/48 binary64))) #s(literal 1/2 binary64)))) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)))) #s(literal 2 binary64))
#s(approx (* (sin (* (+ eps 0) 1/2)) (cos (* (+ (* x 2) eps) 1/2))) (.f64 #s(approx (sin ( 1/2 eps)) (.f64 eps (fma.f64 eps (.f64 eps (fma.f64 (*.f64 eps eps) #s(literal 1/3840 binary64) #s(literal -1/48 binary64))) #s(literal 1/2 binary64)))) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x))))
(.f64 #s(approx (sin ( 1/2 eps)) (.f64 eps (fma.f64 eps (.f64 eps (fma.f64 (*.f64 eps eps) #s(literal 1/3840 binary64) #s(literal -1/48 binary64))) #s(literal 1/2 binary64)))) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)))
#s(approx (sin (* 1/2 eps)) (.f64 eps (fma.f64 eps (.f64 eps (fma.f64 (*.f64 eps eps) #s(literal 1/3840 binary64) #s(literal -1/48 binary64))) #s(literal 1/2 binary64))))
(/.f64 (fma.f64 #s(literal -1/4 binary64) (cos.f64 (.f64 #s(literal 2 binary64) (+.f64 eps x))) (.f64 (cos.f64 (.f64 x #s(literal 2 binary64))) #s(literal 1/4 binary64))) (.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) eps)) (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x))))
(*.f64 x #s(literal 2 binary64))
#s(approx (/ (/ (- 1/2 (+ (* 1/2 (cos (* (+ x eps) 2))) (+ 1/2 (* -1/2 (cos (+ x x)))))) 2) (* (sin (* (+ (* x 2) eps) 1/2)) (cos (* (+ eps 0) 1/2)))) (/.f64 (fma.f64 #s(literal -1/4 binary64) (cos.f64 (.f64 #s(literal 2 binary64) (+.f64 eps x))) (.f64 (cos.f64 (.f64 x #s(literal 2 binary64))) #s(literal 1/4 binary64))) (.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) eps)) (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x)))))
(fma.f64 #s(literal -1/4 binary64) (cos.f64 (.f64 #s(literal 2 binary64) (+.f64 eps x))) (.f64 (cos.f64 (*.f64 x #s(literal 2 binary64))) #s(literal 1/4 binary64)))
(pow.f64 (.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (sin.f64 x)) #s(literal 3 binary64))
(pow.f64 (.f64 (cos.f64 (.f64 eps #s(literal 1/2 binary64))) (cos.f64 x)) #s(literal 3 binary64))
(fma.f64 (.f64 (cos.f64 (.f64 eps #s(literal 1/2 binary64))) (cos.f64 x)) (.f64 (cos.f64 (.f64 eps #s(literal 1/2 binary64))) (cos.f64 x)) (fma.f64 (.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (sin.f64 x)) (.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (sin.f64 x)) (.f64 (.f64 (cos.f64 (.f64 eps #s(literal 1/2 binary64))) (cos.f64 x)) (.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) (sin.f64 x)))))
(/.f64 (-.f64 (pow.f64 (.f64 (cos.f64 (.f64 eps #s(literal 1/2 binary64))) (cos.f64 x)) #s(literal 3 binary64)) (pow.f64 (.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (sin.f64 x)) #s(literal 3 binary64))) (fma.f64 (.f64 (cos.f64 (.f64 eps #s(literal 1/2 binary64))) (cos.f64 x)) (.f64 (cos.f64 (.f64 eps #s(literal 1/2 binary64))) (cos.f64 x)) (fma.f64 (.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (sin.f64 x)) (.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (sin.f64 x)) (.f64 (.f64 (cos.f64 (.f64 eps #s(literal 1/2 binary64))) (cos.f64 x)) (.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) (sin.f64 x))))))
(-.f64 #s(approx (+ (* (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) (fma.f64 eps (fma.f64 #s(literal -1/2 binary64) (*.f64 x x) #s(literal 1 binary64)) x)) x)
#s(approx (+ (* (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) (fma.f64 eps (fma.f64 #s(literal -1/2 binary64) (*.f64 x x) #s(literal 1 binary64)) x))
(.f64 eps (fma.f64 (.f64 eps eps) #s(literal 1/3840 binary64) #s(literal -1/48 binary64)))
(cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x))
(sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x))
(cos.f64 (*.f64 #s(literal 2 binary64) (+.f64 eps x)))

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

eval217.0ms (1.5%)

Memory: -21.7MiB live, 369.1MiB allocated
Compiler: Compiled 59 572 to 3 231 computations (94.6% saved)

prune181.0ms (1.3%)

Memory

5.7MiB live, 321.8MiB allocated

Pruning

33 alts after pruning (26 fresh and 7 done)

	Pruned	Kept	Total
New	1 256	12	1 268
Fresh	2	14	16
Picked	2	3	5
Done	0	4	4
Total	1 260	33	1 293

Accuracy

100.0%

Counts

1 293 → 33

Alt Table

Click to see full alt table

Status	Accuracy	Program
	62.6%	(fma.f64 (sin.f64 x) (cos.f64 eps) (fma.f64 (sin.f64 eps) (cos.f64 x) (neg.f64 (sin.f64 x))))
	99.7%	(fma.f64 (sin.f64 eps) (cos.f64 x) (-.f64 (*.f64 (sin.f64 x) (cos.f64 eps)) (sin.f64 x)))
	7.2%	(/.f64 (/.f64 (-.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 (+.f64 x eps) #s(literal 2 binary64))) (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal -1/2 binary64) (cos.f64 (+.f64 x x)))))) #s(literal 2 binary64)) (.f64 (sin.f64 #s(approx ( (+ (* x 2) eps) 1/2) (.f64 eps (+.f64 #s(literal 1/2 binary64) (/.f64 x eps))))) (cos.f64 (.f64 (+.f64 eps #s(literal 0 binary64)) #s(literal 1/2 binary64)))))
✓	62.4%	(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
	21.5%	(.f64 (.f64 (sin.f64 (.f64 (fma.f64 (fma.f64 x (.f64 x x) (.f64 eps (.f64 eps eps))) (/.f64 #s(literal 1 binary64) (fma.f64 x x (.f64 eps (-.f64 eps x)))) (neg.f64 x)) #s(literal 1/2 binary64))) (cos.f64 #s(approx ( (+ (* x 2) eps) 1/2) (fma.f64 eps #s(literal 1/2 binary64) x)))) #s(literal 2 binary64))
	21.5%	(.f64 (.f64 (sin.f64 (.f64 (fma.f64 (fma.f64 eps (.f64 eps eps) (.f64 x (.f64 x x))) (/.f64 #s(literal 1 binary64) (fma.f64 eps (-.f64 eps x) (.f64 x x))) (neg.f64 x)) #s(literal 1/2 binary64))) (cos.f64 (.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)))) #s(literal 2 binary64))
	10.0%	(.f64 (.f64 (sin.f64 (.f64 (fma.f64 (/.f64 (fma.f64 eps (.f64 eps eps) (.f64 x (.f64 x x))) (fma.f64 x (.f64 (.f64 x x) (.f64 x (.f64 x x))) (.f64 (.f64 eps (-.f64 eps x)) (.f64 (-.f64 eps x) (.f64 eps (.f64 eps (-.f64 eps x))))))) (fma.f64 (.f64 eps (-.f64 eps x)) (-.f64 (.f64 eps (-.f64 eps x)) (.f64 x x)) (.f64 x (.f64 x (.f64 x x)))) (neg.f64 x)) #s(literal 1/2 binary64))) (cos.f64 (.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)))) #s(literal 2 binary64))
	99.1%	(.f64 (.f64 #s(approx (sin (* (+ eps 0) 1/2)) (.f64 #s(literal 1/2 binary64) eps)) (cos.f64 #s(approx ( (+ (* x 2) eps) 1/2) (fma.f64 eps #s(literal 1/2 binary64) x)))) #s(literal 2 binary64))
	99.1%	(.f64 (.f64 #s(approx (sin (* (+ eps 0) 1/2)) (.f64 #s(literal 1/2 binary64) eps)) (cos.f64 #s(approx ( (+ (* x 2) eps) 1/2) (*.f64 eps (+.f64 #s(literal 1/2 binary64) (/.f64 x eps)))))) #s(literal 2 binary64))
	99.8%	(.f64 #s(approx ( (sin (* (+ eps 0) 1/2)) (cos (* (+ (* x 2) eps) 1/2))) (/.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) (/.f64 #s(literal 1 binary64) (cos.f64 (fma.f64 eps #s(literal 1/2 binary64) x))))) #s(literal 2 binary64))
	100.0%	(.f64 #s(approx ( (sin (* (+ eps 0) 1/2)) (cos (* (+ (* x 2) eps) 1/2))) (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (-.f64 (.f64 (cos.f64 (.f64 eps #s(literal 1/2 binary64))) (cos.f64 x)) (.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (sin.f64 x))))) #s(literal 2 binary64))
✓	99.8%	(.f64 #s(approx ( (sin (* (+ eps 0) 1/2)) (cos (* (+ (* x 2) eps) 1/2))) (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)))) #s(literal 2 binary64))
	99.5%	(.f64 #s(approx ( (sin (* (+ eps 0) 1/2)) (cos (* (+ (* x 2) eps) 1/2))) (.f64 #s(approx (sin ( 1/2 eps)) (.f64 eps (fma.f64 (.f64 eps eps) (fma.f64 (.f64 eps eps) (fma.f64 (.f64 eps eps) #s(literal -1/645120 binary64) #s(literal 1/3840 binary64)) #s(literal -1/48 binary64)) #s(literal 1/2 binary64)))) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)))) #s(literal 2 binary64))
	99.5%	(.f64 #s(approx ( (sin (* (+ eps 0) 1/2)) (cos (* (+ (* x 2) eps) 1/2))) (.f64 #s(approx (sin ( 1/2 eps)) (.f64 eps (fma.f64 eps (.f64 eps (fma.f64 (.f64 eps eps) #s(literal 1/3840 binary64) #s(literal -1/48 binary64))) #s(literal 1/2 binary64)))) (.f64 (fma.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (.f64 (sin.f64 x) (cos.f64 (-.f64 (.f64 eps #s(literal 1/2 binary64)) x))) (.f64 (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 #s(literal 0 binary64)))) (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 #s(literal 2 binary64) (.f64 eps #s(literal 1/2 binary64)))))))) (.f64 (cos.f64 (fma.f64 eps #s(literal 1/2 binary64) x)) (/.f64 #s(literal 1 binary64) (fma.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (.f64 (sin.f64 x) (cos.f64 (-.f64 (.f64 eps #s(literal 1/2 binary64)) x))) (.f64 (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 #s(literal 0 binary64)))) (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 #s(literal 2 binary64) (*.f64 eps #s(literal 1/2 binary64))))))))))))) #s(literal 2 binary64))
✓	99.4%	(.f64 #s(approx ( (sin (* (+ eps 0) 1/2)) (cos (* (+ (* x 2) eps) 1/2))) (.f64 #s(approx (sin ( 1/2 eps)) (.f64 eps (fma.f64 eps (.f64 eps (fma.f64 (*.f64 eps eps) #s(literal 1/3840 binary64) #s(literal -1/48 binary64))) #s(literal 1/2 binary64)))) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)))) #s(literal 2 binary64))
	99.2%	(.f64 #s(approx ( (sin (* (+ eps 0) 1/2)) (cos (* (+ (* x 2) eps) 1/2))) (.f64 #s(approx (sin ( 1/2 eps)) (.f64 eps (fma.f64 eps (.f64 eps #s(literal -1/48 binary64)) #s(literal 1/2 binary64)))) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)))) #s(literal 2 binary64))
✓	7.3%	#s(approx (/ (/ (- 1/2 (+ (* 1/2 (cos (* (+ x eps) 2))) (+ 1/2 (* -1/2 (cos (+ x x)))))) 2) (* (sin (* (+ (* x 2) eps) 1/2)) (cos (* (+ eps 0) 1/2)))) (/.f64 (fma.f64 #s(literal -1/4 binary64) (cos.f64 (.f64 #s(literal 2 binary64) (+.f64 eps x))) (.f64 (cos.f64 (.f64 x #s(literal 2 binary64))) #s(literal 1/4 binary64))) (.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) eps)) (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x)))))
✓	5.5%	#s(approx (/ (/ (- 1/2 (+ (* 1/2 (cos (* (+ x eps) 2))) (+ 1/2 (* -1/2 (cos (+ x x)))))) 2) (* (sin (* (+ (* x 2) eps) 1/2)) (cos (* (+ eps 0) 1/2)))) #s(literal 0 binary64))
	20.3%	#s(approx (- (sin (+ x eps)) (sin x)) (/.f64 (fma.f64 #s(approx (+ (* (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) #s(approx (+ (* eps (+ (* x (* x -1/2)) 1)) x) (+.f64 eps x))) (.f64 #s(approx (+ ( (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) #s(approx (+ (* eps (+ (* x (* x -1/2)) 1)) x) (+.f64 eps x))) #s(approx (+ (* (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) #s(approx (+ (* eps (+ (* x (* x -1/2)) 1)) x) (+.f64 eps x)))) (neg.f64 (.f64 x (.f64 x x)))) (fma.f64 x (+.f64 x #s(approx (+ (* (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) #s(approx (+ (* eps (+ (* x (* x -1/2)) 1)) x) (+.f64 eps x)))) (.f64 #s(approx (+ ( (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) #s(approx (+ (* eps (+ (* x (* x -1/2)) 1)) x) (+.f64 eps x))) #s(approx (+ (* (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) #s(approx (+ (* eps (+ (* x (* x -1/2)) 1)) x) (+.f64 eps x)))))))
	34.0%	#s(approx (- (sin (+ x eps)) (sin x)) (/.f64 (-.f64 (.f64 #s(approx (+ ( (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) (fma.f64 eps (fma.f64 #s(literal -1/2 binary64) (.f64 x x) #s(literal 1 binary64)) x)) #s(approx (+ ( (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) (fma.f64 eps (fma.f64 #s(literal -1/2 binary64) (.f64 x x) #s(literal 1 binary64)) x))) (.f64 (neg.f64 x) (neg.f64 x))) (-.f64 #s(approx (+ (* (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) (fma.f64 eps (fma.f64 #s(literal -1/2 binary64) (*.f64 x x) #s(literal 1 binary64)) x)) (neg.f64 x))))
	34.2%	#s(approx (- (sin (+ x eps)) (sin x)) (/.f64 (-.f64 (.f64 #s(approx (+ ( (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) #s(approx (+ (* eps (+ (* x (* x -1/2)) 1)) x) (+.f64 eps x))) #s(approx (+ (* (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) #s(approx (+ (* eps (+ (* x (* x -1/2)) 1)) x) (+.f64 eps x)))) (.f64 (neg.f64 x) (neg.f64 x))) (-.f64 #s(approx (+ ( (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) #s(approx (+ (* eps (+ (* x (* x -1/2)) 1)) x) (+.f64 eps x))) (neg.f64 x))))
	23.5%	#s(approx (- (sin (+ x eps)) (sin x)) (/.f64 #s(literal 1 binary64) (/.f64 (+.f64 x #s(approx (+ (* (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) (fma.f64 eps (fma.f64 #s(literal -1/2 binary64) (.f64 x x) #s(literal 1 binary64)) x))) (.f64 #s(approx (+ x (+ (* (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps)))) (.f64 x #s(literal 2 binary64))) (-.f64 #s(approx (+ ( (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) (fma.f64 eps (fma.f64 #s(literal -1/2 binary64) (*.f64 x x) #s(literal 1 binary64)) x)) x)))))
	34.3%	#s(approx (- (sin (+ x eps)) (sin x)) (/.f64 #s(literal 1 binary64) (/.f64 (+.f64 x #s(approx (+ (* (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) #s(approx (+ (* eps (+ (* x (* x -1/2)) 1)) x) (+.f64 eps x)))) (.f64 (+.f64 x #s(approx (+ ( (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) #s(approx (+ (* eps (+ (* x (* x -1/2)) 1)) x) (+.f64 eps x)))) (-.f64 #s(approx (+ (* (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) #s(approx (+ (* eps (+ (* x (* x -1/2)) 1)) x) (+.f64 eps x))) x)))))
	23.5%	#s(approx (- (sin (+ x eps)) (sin x)) (/.f64 #s(literal 1 binary64) (/.f64 #s(approx (+ x (+ (* (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps)))) (.f64 x #s(literal 2 binary64))) (.f64 (+.f64 x #s(approx (+ (* (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) (fma.f64 eps (fma.f64 #s(literal -1/2 binary64) (.f64 x x) #s(literal 1 binary64)) x))) (-.f64 #s(approx (+ ( (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) (fma.f64 eps (fma.f64 #s(literal -1/2 binary64) (*.f64 x x) #s(literal 1 binary64)) x)) x)))))
	61.0%	#s(approx (- (sin (+ x eps)) (sin x)) (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (-.f64 #s(approx (+ (* (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) (fma.f64 eps (fma.f64 #s(literal -1/2 binary64) (*.f64 x x) #s(literal 1 binary64)) x)) x))))
✓	61.0%	#s(approx (- (sin (+ x eps)) (sin x)) (-.f64 #s(approx (+ (* (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) (fma.f64 eps (fma.f64 x (*.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64)) x)) x))
✓	61.2%	#s(approx (- (sin (+ x eps)) (sin x)) (-.f64 #s(approx (+ (* (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) #s(approx (+ (* eps (+ (* x (* x -1/2)) 1)) x) (+.f64 eps x))) x))
	34.3%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (.f64 (+.f64 x #s(approx (+ (* (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) #s(approx (+ (* eps (+ (* x (* x -1/2)) 1)) x) (+.f64 eps x)))) (-.f64 #s(approx (+ (* (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) #s(approx (+ (* eps (+ (* x (* x -1/2)) 1)) x) (+.f64 eps x))) x)) (/.f64 #s(literal 1 binary64) (+.f64 x #s(approx (+ (* (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) #s(approx (+ (* eps (+ (* x (* x -1/2)) 1)) x) (+.f64 eps x)))))))
	98.7%	#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 eps (cos.f64 x)))
	97.5%	#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (/ 1 (/ (+ x (+ (* (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps)))) (* (+ x (+ (* (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps)))) (- (+ (* (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) x)))) (fma.f64 eps (.f64 #s(literal -1/2 binary64) (.f64 x (+.f64 eps x))) eps)))
	97.5%	#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (/ 1 (/ (+ x (+ (* (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps)))) (* (+ x (+ (* (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps)))) (- (+ (* (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) x)))) (fma.f64 eps (.f64 #s(literal -1/2 binary64) (.f64 x x)) eps)))
	97.6%	#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (- (+ (* (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) x) (fma.f64 eps (fma.f64 #s(literal -1/2 binary64) (.f64 x (+.f64 eps x)) (.f64 eps (.f64 eps (fma.f64 (.f64 x x) #s(literal 1/12 binary64) #s(literal -1/6 binary64))))) eps)))
	97.5%	#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (sin eps) (fma.f64 eps (.f64 eps (.f64 eps #s(literal -1/6 binary64))) eps)))

Compiler

Compiled 2 183 to 693 computations (68.3% saved)

regimes44.0ms (0.3%)

Memory

22.9MiB live, 60.7MiB allocated

Counts

52 → 1

Calls

Call 1

Inputs
#s(approx (/ (/ (- 1/2 (+ (* 1/2 (cos (* (+ x eps) 2))) (+ 1/2 (* -1/2 (cos (+ x x)))))) 2) (* (sin (* (+ (* x 2) eps) 1/2)) (cos (* (+ eps 0) 1/2)))) #s(literal 0 binary64))
#s(approx (- (sin (+ x eps)) (sin x)) (-.f64 #s(approx (+ (* (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) #s(approx (+ (* eps (+ (* x (* x -1/2)) 1)) x) (+.f64 eps x))) x))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (sin eps) (fma.f64 eps (.f64 eps (.f64 eps #s(literal -1/6 binary64))) eps)))
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#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (/ 1 (/ (+ x (+ (* (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps)))) (* (+ x (+ (* (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps)))) (- (+ (* (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) x)))) (fma.f64 eps (.f64 #s(literal -1/2 binary64) (.f64 x x)) eps)))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (- (+ (* (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) x) (fma.f64 #s(literal -1/2 binary64) (.f64 (.f64 x (+.f64 eps x)) eps) eps)))
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#s(approx (- (sin (+ x eps)) (sin x)) (-.f64 #s(approx (+ (* (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) (fma.f64 eps (fma.f64 x (*.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64)) x)) x))
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#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (- (+ (* (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) x) (fma.f64 eps (fma.f64 #s(literal -1/2 binary64) (.f64 x (+.f64 eps x)) (.f64 eps (.f64 eps (fma.f64 (.f64 x x) #s(literal 1/12 binary64) #s(literal -1/6 binary64))))) eps)))
#s(approx (- (sin (+ x eps)) (sin x)) (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (-.f64 #s(approx (+ (* (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) (fma.f64 eps (fma.f64 #s(literal -1/2 binary64) (*.f64 x x) #s(literal 1 binary64)) x)) x))))
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#s(approx (- (sin (+ x eps)) (sin x)) (/.f64 #s(literal 1 binary64) (/.f64 #s(approx (+ x (+ (* (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps)))) (.f64 x #s(literal 2 binary64))) (.f64 (+.f64 x #s(approx (+ (* (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) (fma.f64 eps (fma.f64 #s(literal -1/2 binary64) (.f64 x x) #s(literal 1 binary64)) x))) (-.f64 #s(approx (+ ( (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) (fma.f64 eps (fma.f64 #s(literal -1/2 binary64) (*.f64 x x) #s(literal 1 binary64)) x)) x)))))
#s(approx (- (sin (+ x eps)) (sin x)) (/.f64 #s(literal 1 binary64) (/.f64 (+.f64 x #s(approx (+ (* (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) (fma.f64 eps (fma.f64 #s(literal -1/2 binary64) (.f64 x x) #s(literal 1 binary64)) x))) (.f64 #s(approx (+ x (+ (* (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps)))) (.f64 x #s(literal 2 binary64))) (-.f64 #s(approx (+ ( (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) (fma.f64 eps (fma.f64 #s(literal -1/2 binary64) (*.f64 x x) #s(literal 1 binary64)) x)) x)))))
#s(approx (- (sin (+ x eps)) (sin x)) (/.f64 (-.f64 (.f64 #s(approx (+ ( (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) (fma.f64 eps (fma.f64 #s(literal -1/2 binary64) (.f64 x x) #s(literal 1 binary64)) x)) #s(approx (+ ( (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) (fma.f64 eps (fma.f64 #s(literal -1/2 binary64) (.f64 x x) #s(literal 1 binary64)) x))) (.f64 (neg.f64 x) (neg.f64 x))) (-.f64 #s(approx (+ (* (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) (fma.f64 eps (fma.f64 #s(literal -1/2 binary64) (*.f64 x x) #s(literal 1 binary64)) x)) (neg.f64 x))))
#s(approx (- (sin (+ x eps)) (sin x)) (/.f64 #s(literal 1 binary64) (/.f64 (+.f64 x #s(approx (+ (* (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) (fma.f64 eps (fma.f64 #s(literal -1/2 binary64) (.f64 x x) #s(literal 1 binary64)) x))) (.f64 (+.f64 x #s(approx (+ (* (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) (fma.f64 eps (fma.f64 #s(literal -1/2 binary64) (.f64 x x) #s(literal 1 binary64)) x))) (-.f64 #s(approx (+ ( (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) (fma.f64 eps (fma.f64 #s(literal -1/2 binary64) (*.f64 x x) #s(literal 1 binary64)) x)) x)))))
#s(approx (- (sin (+ x eps)) (sin x)) (sin.f64 eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 eps (cos.f64 x)))
(.f64 (.f64 #s(approx (sin (* (+ eps 0) 1/2)) (.f64 #s(literal 1/2 binary64) eps)) (cos.f64 #s(approx ( (+ (* x 2) eps) 1/2) (fma.f64 eps #s(literal 1/2 binary64) x)))) #s(literal 2 binary64))
(-.f64 (sin.f64 (+.f64 x eps)) #s(approx (sin x) (fma.f64 #s(literal -1/6 binary64) (.f64 x (.f64 x x)) x)))
(.f64 (.f64 #s(approx (sin (* (+ eps 0) 1/2)) (.f64 #s(literal 1/2 binary64) eps)) (cos.f64 (.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)))) #s(literal 2 binary64))
(.f64 #s(approx ( (sin (* (+ eps 0) 1/2)) (cos (* (+ (* x 2) eps) 1/2))) (.f64 #s(approx (sin ( 1/2 eps)) (.f64 eps (fma.f64 eps (.f64 eps #s(literal -1/48 binary64)) #s(literal 1/2 binary64)))) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)))) #s(literal 2 binary64))
(.f64 (.f64 #s(approx (sin (* (+ eps 0) 1/2)) (.f64 #s(literal 1/2 binary64) eps)) (cos.f64 #s(approx ( (+ (* x 2) eps) 1/2) (*.f64 eps (+.f64 #s(literal 1/2 binary64) (/.f64 x eps)))))) #s(literal 2 binary64))
(.f64 (.f64 #s(approx (sin (* (+ eps 0) 1/2)) (.f64 eps (fma.f64 eps (.f64 eps #s(literal -1/48 binary64)) #s(literal 1/2 binary64)))) (cos.f64 (*.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)))) #s(literal 2 binary64))
(.f64 #s(approx ( (sin (* (+ eps 0) 1/2)) (cos (* (+ (* x 2) eps) 1/2))) (.f64 #s(approx (sin ( 1/2 eps)) (.f64 eps (fma.f64 eps (.f64 eps (fma.f64 (*.f64 eps eps) #s(literal 1/3840 binary64) #s(literal -1/48 binary64))) #s(literal 1/2 binary64)))) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)))) #s(literal 2 binary64))
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(.f64 #s(approx ( (sin (* (+ eps 0) 1/2)) (cos (* (+ (* x 2) eps) 1/2))) (.f64 #s(approx (sin ( 1/2 eps)) (.f64 eps (fma.f64 (.f64 eps eps) (fma.f64 (.f64 eps eps) (fma.f64 (.f64 eps eps) #s(literal -1/645120 binary64) #s(literal 1/3840 binary64)) #s(literal -1/48 binary64)) #s(literal 1/2 binary64)))) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)))) #s(literal 2 binary64))
(.f64 (.f64 #s(approx (sin (* (+ eps 0) 1/2)) (.f64 eps (fma.f64 eps (.f64 eps (fma.f64 (.f64 eps eps) (fma.f64 (.f64 eps eps) #s(literal -1/645120 binary64) #s(literal 1/3840 binary64)) #s(literal -1/48 binary64))) #s(literal 1/2 binary64)))) (cos.f64 (*.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)))) #s(literal 2 binary64))
(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 eps (fma.f64 eps (.f64 #s(literal -1/2 binary64) (sin.f64 x)) (cos.f64 x))))
(.f64 #s(approx ( (sin (* (+ eps 0) 1/2)) (cos (* (+ (* x 2) eps) 1/2))) (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)))) #s(literal 2 binary64))
#s(approx (- (sin (+ x eps)) (sin x)) (-.f64 (fma.f64 (fma.f64 x (.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64)) (sin.f64 eps) (.f64 x (cos.f64 eps))) x))
(.f64 (.f64 (sin.f64 (.f64 (+.f64 eps #s(literal 0 binary64)) #s(literal 1/2 binary64))) (cos.f64 (.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)))) #s(literal 2 binary64))
(.f64 #s(approx ( (sin (* (+ eps 0) 1/2)) (cos (* (+ (* x 2) eps) 1/2))) (/.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) (/.f64 #s(literal 1 binary64) (cos.f64 (fma.f64 eps #s(literal 1/2 binary64) x))))) #s(literal 2 binary64))
(.f64 (.f64 (sin.f64 (.f64 (fma.f64 (fma.f64 x (.f64 x x) (.f64 eps (.f64 eps eps))) (/.f64 #s(literal 1 binary64) (fma.f64 x x (.f64 eps (-.f64 eps x)))) (neg.f64 x)) #s(literal 1/2 binary64))) (cos.f64 #s(approx ( (+ (* x 2) eps) 1/2) (fma.f64 eps #s(literal 1/2 binary64) x)))) #s(literal 2 binary64))
(.f64 (.f64 (sin.f64 (.f64 (fma.f64 (fma.f64 eps (.f64 eps eps) (.f64 x (.f64 x x))) (/.f64 #s(literal 1 binary64) (fma.f64 eps (-.f64 eps x) (.f64 x x))) (neg.f64 x)) #s(literal 1/2 binary64))) (cos.f64 (.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)))) #s(literal 2 binary64))
(.f64 (.f64 (sin.f64 (.f64 (fma.f64 (fma.f64 x (.f64 x x) (.f64 eps (.f64 eps eps))) (/.f64 #s(literal 1 binary64) (fma.f64 x x (.f64 eps (-.f64 eps x)))) (neg.f64 x)) #s(literal 1/2 binary64))) (cos.f64 (.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)))) #s(literal 2 binary64))
(.f64 (.f64 (sin.f64 (.f64 (fma.f64 (/.f64 (fma.f64 eps (.f64 eps eps) (.f64 x (.f64 x x))) (fma.f64 x (.f64 (.f64 x x) (.f64 x (.f64 x x))) (.f64 (.f64 eps (-.f64 eps x)) (.f64 (-.f64 eps x) (.f64 eps (.f64 eps (-.f64 eps x))))))) (fma.f64 (.f64 eps (-.f64 eps x)) (-.f64 (.f64 eps (-.f64 eps x)) (.f64 x x)) (.f64 x (.f64 x (.f64 x x)))) (neg.f64 x)) #s(literal 1/2 binary64))) (cos.f64 (.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)))) #s(literal 2 binary64))
(-.f64 (/.f64 (*.f64 (sin.f64 (+.f64 x eps)) (sin.f64 (-.f64 x eps))) (sin.f64 (-.f64 x eps))) (sin.f64 x))
#s(approx (/ (/ (- 1/2 (+ (* 1/2 (cos (* (+ x eps) 2))) (+ 1/2 (* -1/2 (cos (+ x x)))))) 2) (* (sin (* (+ (* x 2) eps) 1/2)) (cos (* (+ eps 0) 1/2)))) (/.f64 (fma.f64 #s(literal -1/4 binary64) (cos.f64 (.f64 #s(literal 2 binary64) (+.f64 eps x))) (.f64 (cos.f64 (.f64 x #s(literal 2 binary64))) #s(literal 1/4 binary64))) (.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) eps)) (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x)))))
(/.f64 (/.f64 (-.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 (+.f64 x eps) #s(literal 2 binary64))) (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal -1/2 binary64) (cos.f64 (+.f64 x x)))))) #s(literal 2 binary64)) (.f64 (sin.f64 (.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64))) (cos.f64 (*.f64 (+.f64 eps #s(literal 0 binary64)) #s(literal 1/2 binary64)))))
(/.f64 (/.f64 (-.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 (+.f64 x eps) #s(literal 2 binary64))) (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal -1/2 binary64) (cos.f64 (+.f64 x x)))))) #s(literal 2 binary64)) (.f64 (sin.f64 #s(approx ( (+ (* x 2) eps) 1/2) (.f64 eps (+.f64 #s(literal 1/2 binary64) (/.f64 x eps))))) (cos.f64 (.f64 (+.f64 eps #s(literal 0 binary64)) #s(literal 1/2 binary64)))))
(fma.f64 (sin.f64 eps) (cos.f64 x) (-.f64 (*.f64 (sin.f64 x) (cos.f64 eps)) (sin.f64 x)))
(fma.f64 (sin.f64 x) (cos.f64 eps) (fma.f64 (sin.f64 eps) (cos.f64 x) (neg.f64 (sin.f64 x))))
(.f64 #s(approx ( (sin (* (+ eps 0) 1/2)) (cos (* (+ (* x 2) eps) 1/2))) (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (-.f64 (.f64 (cos.f64 (.f64 eps #s(literal 1/2 binary64))) (cos.f64 x)) (.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (sin.f64 x))))) #s(literal 2 binary64))
(/.f64 (-.f64 (.f64 (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal -1/2 binary64) (cos.f64 (+.f64 x x)))) (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 #s(literal 2 binary64) eps))))) (pow.f64 (-.f64 (.f64 (cos.f64 x) (sin.f64 eps)) (sin.f64 x)) #s(literal 2 binary64))) (-.f64 (.f64 (sin.f64 x) (cos.f64 eps)) (-.f64 (*.f64 (cos.f64 x) (sin.f64 eps)) (sin.f64 x))))
(.f64 #s(approx ( (sin (* (+ eps 0) 1/2)) (cos (* (+ (* x 2) eps) 1/2))) (.f64 #s(approx (sin ( 1/2 eps)) (.f64 eps (fma.f64 eps (.f64 eps (fma.f64 (.f64 eps eps) #s(literal 1/3840 binary64) #s(literal -1/48 binary64))) #s(literal 1/2 binary64)))) (.f64 (fma.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (.f64 (sin.f64 x) (cos.f64 (-.f64 (.f64 eps #s(literal 1/2 binary64)) x))) (.f64 (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 #s(literal 0 binary64)))) (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 #s(literal 2 binary64) (.f64 eps #s(literal 1/2 binary64)))))))) (.f64 (cos.f64 (fma.f64 eps #s(literal 1/2 binary64) x)) (/.f64 #s(literal 1 binary64) (fma.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (.f64 (sin.f64 x) (cos.f64 (-.f64 (.f64 eps #s(literal 1/2 binary64)) x))) (.f64 (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 #s(literal 0 binary64)))) (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 #s(literal 2 binary64) (*.f64 eps #s(literal 1/2 binary64))))))))))))) #s(literal 2 binary64))
(/.f64 (+.f64 (pow.f64 (.f64 (sin.f64 x) (cos.f64 eps)) #s(literal 3 binary64)) (pow.f64 (-.f64 (.f64 (cos.f64 x) (sin.f64 eps)) (sin.f64 x)) #s(literal 3 binary64))) (fma.f64 (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal -1/2 binary64) (cos.f64 (+.f64 x x)))) (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 #s(literal 2 binary64) eps)))) (-.f64 (pow.f64 (-.f64 (.f64 (cos.f64 x) (sin.f64 eps)) (sin.f64 x)) #s(literal 2 binary64)) (.f64 (.f64 (sin.f64 x) (cos.f64 eps)) (-.f64 (*.f64 (cos.f64 x) (sin.f64 eps)) (sin.f64 x))))))
(.f64 #s(approx ( (sin (* (+ eps 0) 1/2)) (cos (* (+ (* x 2) eps) 1/2))) (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (/.f64 (-.f64 (pow.f64 (.f64 (cos.f64 (.f64 eps #s(literal 1/2 binary64))) (cos.f64 x)) #s(literal 3 binary64)) (pow.f64 (.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (sin.f64 x)) #s(literal 3 binary64))) (fma.f64 (.f64 (cos.f64 (.f64 eps #s(literal 1/2 binary64))) (cos.f64 x)) (.f64 (cos.f64 (.f64 eps #s(literal 1/2 binary64))) (cos.f64 x)) (fma.f64 (.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (sin.f64 x)) (.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (sin.f64 x)) (.f64 (.f64 (cos.f64 (.f64 eps #s(literal 1/2 binary64))) (cos.f64 x)) (.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) (sin.f64 x)))))))) #s(literal 2 binary64))

Outputs

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

Calls

3 calls:

14.0ms	eps
13.0ms	(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
13.0ms	x

Results

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

Compiler

Compiled 15 to 10 computations (33.3% saved)

regimes44.0ms (0.3%)

Memory

-14.1MiB live, 62.9MiB allocated

Counts

51 → 1

Calls

Call 1

Inputs
#s(approx (/ (/ (- 1/2 (+ (* 1/2 (cos (* (+ x eps) 2))) (+ 1/2 (* -1/2 (cos (+ x x)))))) 2) (* (sin (* (+ (* x 2) eps) 1/2)) (cos (* (+ eps 0) 1/2)))) #s(literal 0 binary64))
#s(approx (- (sin (+ x eps)) (sin x)) (-.f64 #s(approx (+ (* (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) #s(approx (+ (* eps (+ (* x (* x -1/2)) 1)) x) (+.f64 eps x))) x))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (sin eps) (fma.f64 eps (.f64 eps (.f64 eps #s(literal -1/6 binary64))) eps)))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (- (+ (* (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) x) (fma.f64 eps (.f64 x (.f64 x #s(literal -1/2 binary64))) eps)))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (/ 1 (/ (+ x (+ (* (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps)))) (* (+ x (+ (* (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps)))) (- (+ (* (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) x)))) (fma.f64 eps (.f64 #s(literal -1/2 binary64) (.f64 x x)) eps)))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (- (+ (* (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) x) (fma.f64 #s(literal -1/2 binary64) (.f64 (.f64 x (+.f64 eps x)) eps) eps)))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (/ 1 (/ (+ x (+ (* (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps)))) (* (+ x (+ (* (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps)))) (- (+ (* (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) x)))) (fma.f64 eps (.f64 #s(literal -1/2 binary64) (.f64 x (+.f64 eps x))) eps)))
#s(approx (- (sin (+ x eps)) (sin x)) (-.f64 #s(approx (+ (* (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) (fma.f64 eps (fma.f64 x (*.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64)) x)) x))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (sin eps) (fma.f64 (.f64 eps eps) (.f64 (fma.f64 eps (*.f64 eps #s(literal 1/120 binary64)) #s(literal -1/6 binary64)) eps) eps)))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (.f64 (+.f64 x #s(approx (+ (* (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) #s(approx (+ (* eps (+ (* x (* x -1/2)) 1)) x) (+.f64 eps x)))) (-.f64 #s(approx (+ (* (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) #s(approx (+ (* eps (+ (* x (* x -1/2)) 1)) x) (+.f64 eps x))) x)) (/.f64 #s(literal 1 binary64) (+.f64 x #s(approx (+ (* (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) #s(approx (+ (* eps (+ (* x (* x -1/2)) 1)) x) (+.f64 eps x)))))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (- (+ (* (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) x) (fma.f64 eps (fma.f64 #s(literal -1/2 binary64) (.f64 x (+.f64 eps x)) (.f64 eps (.f64 eps (fma.f64 (.f64 x x) #s(literal 1/12 binary64) #s(literal -1/6 binary64))))) eps)))
#s(approx (- (sin (+ x eps)) (sin x)) (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (-.f64 #s(approx (+ (* (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) (fma.f64 eps (fma.f64 #s(literal -1/2 binary64) (*.f64 x x) #s(literal 1 binary64)) x)) x))))
#s(approx (- (sin (+ x eps)) (sin x)) (/.f64 (-.f64 (.f64 #s(approx (+ ( (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) #s(approx (+ (* eps (+ (* x (* x -1/2)) 1)) x) (+.f64 eps x))) #s(approx (+ (* (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) #s(approx (+ (* eps (+ (* x (* x -1/2)) 1)) x) (+.f64 eps x)))) (.f64 (neg.f64 x) (neg.f64 x))) (-.f64 #s(approx (+ ( (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) #s(approx (+ (* eps (+ (* x (* x -1/2)) 1)) x) (+.f64 eps x))) (neg.f64 x))))
#s(approx (- (sin (+ x eps)) (sin x)) (/.f64 #s(literal 1 binary64) (/.f64 (+.f64 x #s(approx (+ (* (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) #s(approx (+ (* eps (+ (* x (* x -1/2)) 1)) x) (+.f64 eps x)))) (.f64 (+.f64 x #s(approx (+ ( (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) #s(approx (+ (* eps (+ (* x (* x -1/2)) 1)) x) (+.f64 eps x)))) (-.f64 #s(approx (+ (* (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) #s(approx (+ (* eps (+ (* x (* x -1/2)) 1)) x) (+.f64 eps x))) x)))))
#s(approx (- (sin (+ x eps)) (sin x)) (/.f64 (fma.f64 #s(approx (+ (* (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) #s(approx (+ (* eps (+ (* x (* x -1/2)) 1)) x) (+.f64 eps x))) (.f64 #s(approx (+ ( (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) #s(approx (+ (* eps (+ (* x (* x -1/2)) 1)) x) (+.f64 eps x))) #s(approx (+ (* (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) #s(approx (+ (* eps (+ (* x (* x -1/2)) 1)) x) (+.f64 eps x)))) (neg.f64 (.f64 x (.f64 x x)))) (fma.f64 x (+.f64 x #s(approx (+ (* (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) #s(approx (+ (* eps (+ (* x (* x -1/2)) 1)) x) (+.f64 eps x)))) (.f64 #s(approx (+ ( (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) #s(approx (+ (* eps (+ (* x (* x -1/2)) 1)) x) (+.f64 eps x))) #s(approx (+ (* (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) #s(approx (+ (* eps (+ (* x (* x -1/2)) 1)) x) (+.f64 eps x)))))))
#s(approx (- (sin (+ x eps)) (sin x)) (/.f64 #s(literal 1 binary64) (/.f64 #s(approx (+ x (+ (* (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps)))) (.f64 x #s(literal 2 binary64))) (.f64 (+.f64 x #s(approx (+ (* (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) (fma.f64 eps (fma.f64 #s(literal -1/2 binary64) (.f64 x x) #s(literal 1 binary64)) x))) (-.f64 #s(approx (+ ( (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) (fma.f64 eps (fma.f64 #s(literal -1/2 binary64) (*.f64 x x) #s(literal 1 binary64)) x)) x)))))
#s(approx (- (sin (+ x eps)) (sin x)) (/.f64 #s(literal 1 binary64) (/.f64 (+.f64 x #s(approx (+ (* (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) (fma.f64 eps (fma.f64 #s(literal -1/2 binary64) (.f64 x x) #s(literal 1 binary64)) x))) (.f64 #s(approx (+ x (+ (* (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps)))) (.f64 x #s(literal 2 binary64))) (-.f64 #s(approx (+ ( (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) (fma.f64 eps (fma.f64 #s(literal -1/2 binary64) (*.f64 x x) #s(literal 1 binary64)) x)) x)))))
#s(approx (- (sin (+ x eps)) (sin x)) (/.f64 (-.f64 (.f64 #s(approx (+ ( (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) (fma.f64 eps (fma.f64 #s(literal -1/2 binary64) (.f64 x x) #s(literal 1 binary64)) x)) #s(approx (+ ( (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) (fma.f64 eps (fma.f64 #s(literal -1/2 binary64) (.f64 x x) #s(literal 1 binary64)) x))) (.f64 (neg.f64 x) (neg.f64 x))) (-.f64 #s(approx (+ (* (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) (fma.f64 eps (fma.f64 #s(literal -1/2 binary64) (*.f64 x x) #s(literal 1 binary64)) x)) (neg.f64 x))))
#s(approx (- (sin (+ x eps)) (sin x)) (/.f64 #s(literal 1 binary64) (/.f64 (+.f64 x #s(approx (+ (* (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) (fma.f64 eps (fma.f64 #s(literal -1/2 binary64) (.f64 x x) #s(literal 1 binary64)) x))) (.f64 (+.f64 x #s(approx (+ (* (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) (fma.f64 eps (fma.f64 #s(literal -1/2 binary64) (.f64 x x) #s(literal 1 binary64)) x))) (-.f64 #s(approx (+ ( (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) (fma.f64 eps (fma.f64 #s(literal -1/2 binary64) (*.f64 x x) #s(literal 1 binary64)) x)) x)))))
#s(approx (- (sin (+ x eps)) (sin x)) (sin.f64 eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 eps (cos.f64 x)))
(.f64 (.f64 #s(approx (sin (* (+ eps 0) 1/2)) (.f64 #s(literal 1/2 binary64) eps)) (cos.f64 #s(approx ( (+ (* x 2) eps) 1/2) (fma.f64 eps #s(literal 1/2 binary64) x)))) #s(literal 2 binary64))
(-.f64 (sin.f64 (+.f64 x eps)) #s(approx (sin x) (fma.f64 #s(literal -1/6 binary64) (.f64 x (.f64 x x)) x)))
(.f64 (.f64 #s(approx (sin (* (+ eps 0) 1/2)) (.f64 #s(literal 1/2 binary64) eps)) (cos.f64 (.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)))) #s(literal 2 binary64))
(.f64 #s(approx ( (sin (* (+ eps 0) 1/2)) (cos (* (+ (* x 2) eps) 1/2))) (.f64 #s(approx (sin ( 1/2 eps)) (.f64 eps (fma.f64 eps (.f64 eps #s(literal -1/48 binary64)) #s(literal 1/2 binary64)))) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)))) #s(literal 2 binary64))
(.f64 (.f64 #s(approx (sin (* (+ eps 0) 1/2)) (.f64 #s(literal 1/2 binary64) eps)) (cos.f64 #s(approx ( (+ (* x 2) eps) 1/2) (*.f64 eps (+.f64 #s(literal 1/2 binary64) (/.f64 x eps)))))) #s(literal 2 binary64))
(.f64 (.f64 #s(approx (sin (* (+ eps 0) 1/2)) (.f64 eps (fma.f64 eps (.f64 eps #s(literal -1/48 binary64)) #s(literal 1/2 binary64)))) (cos.f64 (*.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)))) #s(literal 2 binary64))
(.f64 #s(approx ( (sin (* (+ eps 0) 1/2)) (cos (* (+ (* x 2) eps) 1/2))) (.f64 #s(approx (sin ( 1/2 eps)) (.f64 eps (fma.f64 eps (.f64 eps (fma.f64 (*.f64 eps eps) #s(literal 1/3840 binary64) #s(literal -1/48 binary64))) #s(literal 1/2 binary64)))) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)))) #s(literal 2 binary64))
(.f64 (.f64 #s(approx (sin (* (+ eps 0) 1/2)) (.f64 eps (fma.f64 (.f64 eps eps) (fma.f64 eps (.f64 eps #s(literal 1/3840 binary64)) #s(literal -1/48 binary64)) #s(literal 1/2 binary64)))) (cos.f64 (.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)))) #s(literal 2 binary64))
(.f64 #s(approx ( (sin (* (+ eps 0) 1/2)) (cos (* (+ (* x 2) eps) 1/2))) (.f64 #s(approx (sin ( 1/2 eps)) (.f64 eps (fma.f64 (.f64 eps eps) (fma.f64 (.f64 eps eps) (fma.f64 (.f64 eps eps) #s(literal -1/645120 binary64) #s(literal 1/3840 binary64)) #s(literal -1/48 binary64)) #s(literal 1/2 binary64)))) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)))) #s(literal 2 binary64))
(.f64 (.f64 #s(approx (sin (* (+ eps 0) 1/2)) (.f64 eps (fma.f64 eps (.f64 eps (fma.f64 (.f64 eps eps) (fma.f64 (.f64 eps eps) #s(literal -1/645120 binary64) #s(literal 1/3840 binary64)) #s(literal -1/48 binary64))) #s(literal 1/2 binary64)))) (cos.f64 (*.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)))) #s(literal 2 binary64))
(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 eps (fma.f64 eps (.f64 #s(literal -1/2 binary64) (sin.f64 x)) (cos.f64 x))))
(.f64 #s(approx ( (sin (* (+ eps 0) 1/2)) (cos (* (+ (* x 2) eps) 1/2))) (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)))) #s(literal 2 binary64))
#s(approx (- (sin (+ x eps)) (sin x)) (-.f64 (fma.f64 (fma.f64 x (.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64)) (sin.f64 eps) (.f64 x (cos.f64 eps))) x))
(.f64 (.f64 (sin.f64 (.f64 (+.f64 eps #s(literal 0 binary64)) #s(literal 1/2 binary64))) (cos.f64 (.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)))) #s(literal 2 binary64))
(.f64 #s(approx ( (sin (* (+ eps 0) 1/2)) (cos (* (+ (* x 2) eps) 1/2))) (/.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) (/.f64 #s(literal 1 binary64) (cos.f64 (fma.f64 eps #s(literal 1/2 binary64) x))))) #s(literal 2 binary64))
(.f64 (.f64 (sin.f64 (.f64 (fma.f64 (fma.f64 x (.f64 x x) (.f64 eps (.f64 eps eps))) (/.f64 #s(literal 1 binary64) (fma.f64 x x (.f64 eps (-.f64 eps x)))) (neg.f64 x)) #s(literal 1/2 binary64))) (cos.f64 #s(approx ( (+ (* x 2) eps) 1/2) (fma.f64 eps #s(literal 1/2 binary64) x)))) #s(literal 2 binary64))
(.f64 (.f64 (sin.f64 (.f64 (fma.f64 (fma.f64 eps (.f64 eps eps) (.f64 x (.f64 x x))) (/.f64 #s(literal 1 binary64) (fma.f64 eps (-.f64 eps x) (.f64 x x))) (neg.f64 x)) #s(literal 1/2 binary64))) (cos.f64 (.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)))) #s(literal 2 binary64))
(.f64 (.f64 (sin.f64 (.f64 (fma.f64 (fma.f64 x (.f64 x x) (.f64 eps (.f64 eps eps))) (/.f64 #s(literal 1 binary64) (fma.f64 x x (.f64 eps (-.f64 eps x)))) (neg.f64 x)) #s(literal 1/2 binary64))) (cos.f64 (.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)))) #s(literal 2 binary64))
(.f64 (.f64 (sin.f64 (.f64 (fma.f64 (/.f64 (fma.f64 eps (.f64 eps eps) (.f64 x (.f64 x x))) (fma.f64 x (.f64 (.f64 x x) (.f64 x (.f64 x x))) (.f64 (.f64 eps (-.f64 eps x)) (.f64 (-.f64 eps x) (.f64 eps (.f64 eps (-.f64 eps x))))))) (fma.f64 (.f64 eps (-.f64 eps x)) (-.f64 (.f64 eps (-.f64 eps x)) (.f64 x x)) (.f64 x (.f64 x (.f64 x x)))) (neg.f64 x)) #s(literal 1/2 binary64))) (cos.f64 (.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)))) #s(literal 2 binary64))
(-.f64 (/.f64 (*.f64 (sin.f64 (+.f64 x eps)) (sin.f64 (-.f64 x eps))) (sin.f64 (-.f64 x eps))) (sin.f64 x))
#s(approx (/ (/ (- 1/2 (+ (* 1/2 (cos (* (+ x eps) 2))) (+ 1/2 (* -1/2 (cos (+ x x)))))) 2) (* (sin (* (+ (* x 2) eps) 1/2)) (cos (* (+ eps 0) 1/2)))) (/.f64 (fma.f64 #s(literal -1/4 binary64) (cos.f64 (.f64 #s(literal 2 binary64) (+.f64 eps x))) (.f64 (cos.f64 (.f64 x #s(literal 2 binary64))) #s(literal 1/4 binary64))) (.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) eps)) (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x)))))
(/.f64 (/.f64 (-.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 (+.f64 x eps) #s(literal 2 binary64))) (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal -1/2 binary64) (cos.f64 (+.f64 x x)))))) #s(literal 2 binary64)) (.f64 (sin.f64 (.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64))) (cos.f64 (*.f64 (+.f64 eps #s(literal 0 binary64)) #s(literal 1/2 binary64)))))
(/.f64 (/.f64 (-.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 (+.f64 x eps) #s(literal 2 binary64))) (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal -1/2 binary64) (cos.f64 (+.f64 x x)))))) #s(literal 2 binary64)) (.f64 (sin.f64 #s(approx ( (+ (* x 2) eps) 1/2) (.f64 eps (+.f64 #s(literal 1/2 binary64) (/.f64 x eps))))) (cos.f64 (.f64 (+.f64 eps #s(literal 0 binary64)) #s(literal 1/2 binary64)))))
(fma.f64 (sin.f64 eps) (cos.f64 x) (-.f64 (*.f64 (sin.f64 x) (cos.f64 eps)) (sin.f64 x)))
(fma.f64 (sin.f64 x) (cos.f64 eps) (fma.f64 (sin.f64 eps) (cos.f64 x) (neg.f64 (sin.f64 x))))
(.f64 #s(approx ( (sin (* (+ eps 0) 1/2)) (cos (* (+ (* x 2) eps) 1/2))) (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (-.f64 (.f64 (cos.f64 (.f64 eps #s(literal 1/2 binary64))) (cos.f64 x)) (.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (sin.f64 x))))) #s(literal 2 binary64))
(/.f64 (-.f64 (.f64 (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal -1/2 binary64) (cos.f64 (+.f64 x x)))) (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 #s(literal 2 binary64) eps))))) (pow.f64 (-.f64 (.f64 (cos.f64 x) (sin.f64 eps)) (sin.f64 x)) #s(literal 2 binary64))) (-.f64 (.f64 (sin.f64 x) (cos.f64 eps)) (-.f64 (*.f64 (cos.f64 x) (sin.f64 eps)) (sin.f64 x))))
(.f64 #s(approx ( (sin (* (+ eps 0) 1/2)) (cos (* (+ (* x 2) eps) 1/2))) (.f64 #s(approx (sin ( 1/2 eps)) (.f64 eps (fma.f64 eps (.f64 eps (fma.f64 (.f64 eps eps) #s(literal 1/3840 binary64) #s(literal -1/48 binary64))) #s(literal 1/2 binary64)))) (.f64 (fma.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (.f64 (sin.f64 x) (cos.f64 (-.f64 (.f64 eps #s(literal 1/2 binary64)) x))) (.f64 (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 #s(literal 0 binary64)))) (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 #s(literal 2 binary64) (.f64 eps #s(literal 1/2 binary64)))))))) (.f64 (cos.f64 (fma.f64 eps #s(literal 1/2 binary64) x)) (/.f64 #s(literal 1 binary64) (fma.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (.f64 (sin.f64 x) (cos.f64 (-.f64 (.f64 eps #s(literal 1/2 binary64)) x))) (.f64 (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 #s(literal 0 binary64)))) (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 #s(literal 2 binary64) (*.f64 eps #s(literal 1/2 binary64))))))))))))) #s(literal 2 binary64))
(/.f64 (+.f64 (pow.f64 (.f64 (sin.f64 x) (cos.f64 eps)) #s(literal 3 binary64)) (pow.f64 (-.f64 (.f64 (cos.f64 x) (sin.f64 eps)) (sin.f64 x)) #s(literal 3 binary64))) (fma.f64 (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal -1/2 binary64) (cos.f64 (+.f64 x x)))) (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 #s(literal 2 binary64) eps)))) (-.f64 (pow.f64 (-.f64 (.f64 (cos.f64 x) (sin.f64 eps)) (sin.f64 x)) #s(literal 2 binary64)) (.f64 (.f64 (sin.f64 x) (cos.f64 eps)) (-.f64 (*.f64 (cos.f64 x) (sin.f64 eps)) (sin.f64 x))))))

Outputs

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

Calls

3 calls:

14.0ms	(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
14.0ms	x
13.0ms	eps

Results

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

Compiler

Compiled 15 to 10 computations (33.3% saved)

regimes50.0ms (0.3%)

Memory

0.1MiB live, 63.8MiB allocated

Counts

47 → 1

Calls

Call 1

Inputs
#s(approx (/ (/ (- 1/2 (+ (* 1/2 (cos (* (+ x eps) 2))) (+ 1/2 (* -1/2 (cos (+ x x)))))) 2) (* (sin (* (+ (* x 2) eps) 1/2)) (cos (* (+ eps 0) 1/2)))) #s(literal 0 binary64))
#s(approx (- (sin (+ x eps)) (sin x)) (-.f64 #s(approx (+ (* (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) #s(approx (+ (* eps (+ (* x (* x -1/2)) 1)) x) (+.f64 eps x))) x))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (sin eps) (fma.f64 eps (.f64 eps (.f64 eps #s(literal -1/6 binary64))) eps)))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (- (+ (* (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) x) (fma.f64 eps (.f64 x (.f64 x #s(literal -1/2 binary64))) eps)))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (/ 1 (/ (+ x (+ (* (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps)))) (* (+ x (+ (* (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps)))) (- (+ (* (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) x)))) (fma.f64 eps (.f64 #s(literal -1/2 binary64) (.f64 x x)) eps)))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (- (+ (* (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) x) (fma.f64 #s(literal -1/2 binary64) (.f64 (.f64 x (+.f64 eps x)) eps) eps)))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (/ 1 (/ (+ x (+ (* (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps)))) (* (+ x (+ (* (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps)))) (- (+ (* (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) x)))) (fma.f64 eps (.f64 #s(literal -1/2 binary64) (.f64 x (+.f64 eps x))) eps)))
#s(approx (- (sin (+ x eps)) (sin x)) (-.f64 #s(approx (+ (* (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) (fma.f64 eps (fma.f64 x (*.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64)) x)) x))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (sin eps) (fma.f64 (.f64 eps eps) (.f64 (fma.f64 eps (*.f64 eps #s(literal 1/120 binary64)) #s(literal -1/6 binary64)) eps) eps)))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (.f64 (+.f64 x #s(approx (+ (* (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) #s(approx (+ (* eps (+ (* x (* x -1/2)) 1)) x) (+.f64 eps x)))) (-.f64 #s(approx (+ (* (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) #s(approx (+ (* eps (+ (* x (* x -1/2)) 1)) x) (+.f64 eps x))) x)) (/.f64 #s(literal 1 binary64) (+.f64 x #s(approx (+ (* (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) #s(approx (+ (* eps (+ (* x (* x -1/2)) 1)) x) (+.f64 eps x)))))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (- (+ (* (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) x) (fma.f64 eps (fma.f64 #s(literal -1/2 binary64) (.f64 x (+.f64 eps x)) (.f64 eps (.f64 eps (fma.f64 (.f64 x x) #s(literal 1/12 binary64) #s(literal -1/6 binary64))))) eps)))
#s(approx (- (sin (+ x eps)) (sin x)) (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (-.f64 #s(approx (+ (* (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) (fma.f64 eps (fma.f64 #s(literal -1/2 binary64) (*.f64 x x) #s(literal 1 binary64)) x)) x))))
#s(approx (- (sin (+ x eps)) (sin x)) (/.f64 (-.f64 (.f64 #s(approx (+ ( (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) #s(approx (+ (* eps (+ (* x (* x -1/2)) 1)) x) (+.f64 eps x))) #s(approx (+ (* (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) #s(approx (+ (* eps (+ (* x (* x -1/2)) 1)) x) (+.f64 eps x)))) (.f64 (neg.f64 x) (neg.f64 x))) (-.f64 #s(approx (+ ( (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) #s(approx (+ (* eps (+ (* x (* x -1/2)) 1)) x) (+.f64 eps x))) (neg.f64 x))))
#s(approx (- (sin (+ x eps)) (sin x)) (/.f64 #s(literal 1 binary64) (/.f64 (+.f64 x #s(approx (+ (* (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) #s(approx (+ (* eps (+ (* x (* x -1/2)) 1)) x) (+.f64 eps x)))) (.f64 (+.f64 x #s(approx (+ ( (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) #s(approx (+ (* eps (+ (* x (* x -1/2)) 1)) x) (+.f64 eps x)))) (-.f64 #s(approx (+ (* (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) #s(approx (+ (* eps (+ (* x (* x -1/2)) 1)) x) (+.f64 eps x))) x)))))
#s(approx (- (sin (+ x eps)) (sin x)) (/.f64 (fma.f64 #s(approx (+ (* (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) #s(approx (+ (* eps (+ (* x (* x -1/2)) 1)) x) (+.f64 eps x))) (.f64 #s(approx (+ ( (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) #s(approx (+ (* eps (+ (* x (* x -1/2)) 1)) x) (+.f64 eps x))) #s(approx (+ (* (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) #s(approx (+ (* eps (+ (* x (* x -1/2)) 1)) x) (+.f64 eps x)))) (neg.f64 (.f64 x (.f64 x x)))) (fma.f64 x (+.f64 x #s(approx (+ (* (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) #s(approx (+ (* eps (+ (* x (* x -1/2)) 1)) x) (+.f64 eps x)))) (.f64 #s(approx (+ ( (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) #s(approx (+ (* eps (+ (* x (* x -1/2)) 1)) x) (+.f64 eps x))) #s(approx (+ (* (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) #s(approx (+ (* eps (+ (* x (* x -1/2)) 1)) x) (+.f64 eps x)))))))
#s(approx (- (sin (+ x eps)) (sin x)) (/.f64 #s(literal 1 binary64) (/.f64 #s(approx (+ x (+ (* (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps)))) (.f64 x #s(literal 2 binary64))) (.f64 (+.f64 x #s(approx (+ (* (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) (fma.f64 eps (fma.f64 #s(literal -1/2 binary64) (.f64 x x) #s(literal 1 binary64)) x))) (-.f64 #s(approx (+ ( (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) (fma.f64 eps (fma.f64 #s(literal -1/2 binary64) (*.f64 x x) #s(literal 1 binary64)) x)) x)))))
#s(approx (- (sin (+ x eps)) (sin x)) (/.f64 #s(literal 1 binary64) (/.f64 (+.f64 x #s(approx (+ (* (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) (fma.f64 eps (fma.f64 #s(literal -1/2 binary64) (.f64 x x) #s(literal 1 binary64)) x))) (.f64 #s(approx (+ x (+ (* (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps)))) (.f64 x #s(literal 2 binary64))) (-.f64 #s(approx (+ ( (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) (fma.f64 eps (fma.f64 #s(literal -1/2 binary64) (*.f64 x x) #s(literal 1 binary64)) x)) x)))))
#s(approx (- (sin (+ x eps)) (sin x)) (/.f64 (-.f64 (.f64 #s(approx (+ ( (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) (fma.f64 eps (fma.f64 #s(literal -1/2 binary64) (.f64 x x) #s(literal 1 binary64)) x)) #s(approx (+ ( (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) (fma.f64 eps (fma.f64 #s(literal -1/2 binary64) (.f64 x x) #s(literal 1 binary64)) x))) (.f64 (neg.f64 x) (neg.f64 x))) (-.f64 #s(approx (+ (* (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) (fma.f64 eps (fma.f64 #s(literal -1/2 binary64) (*.f64 x x) #s(literal 1 binary64)) x)) (neg.f64 x))))
#s(approx (- (sin (+ x eps)) (sin x)) (/.f64 #s(literal 1 binary64) (/.f64 (+.f64 x #s(approx (+ (* (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) (fma.f64 eps (fma.f64 #s(literal -1/2 binary64) (.f64 x x) #s(literal 1 binary64)) x))) (.f64 (+.f64 x #s(approx (+ (* (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) (fma.f64 eps (fma.f64 #s(literal -1/2 binary64) (.f64 x x) #s(literal 1 binary64)) x))) (-.f64 #s(approx (+ ( (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) (fma.f64 eps (fma.f64 #s(literal -1/2 binary64) (*.f64 x x) #s(literal 1 binary64)) x)) x)))))
#s(approx (- (sin (+ x eps)) (sin x)) (sin.f64 eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 eps (cos.f64 x)))
(.f64 (.f64 #s(approx (sin (* (+ eps 0) 1/2)) (.f64 #s(literal 1/2 binary64) eps)) (cos.f64 #s(approx ( (+ (* x 2) eps) 1/2) (fma.f64 eps #s(literal 1/2 binary64) x)))) #s(literal 2 binary64))
(-.f64 (sin.f64 (+.f64 x eps)) #s(approx (sin x) (fma.f64 #s(literal -1/6 binary64) (.f64 x (.f64 x x)) x)))
(.f64 (.f64 #s(approx (sin (* (+ eps 0) 1/2)) (.f64 #s(literal 1/2 binary64) eps)) (cos.f64 (.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)))) #s(literal 2 binary64))
(.f64 #s(approx ( (sin (* (+ eps 0) 1/2)) (cos (* (+ (* x 2) eps) 1/2))) (.f64 #s(approx (sin ( 1/2 eps)) (.f64 eps (fma.f64 eps (.f64 eps #s(literal -1/48 binary64)) #s(literal 1/2 binary64)))) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)))) #s(literal 2 binary64))
(.f64 (.f64 #s(approx (sin (* (+ eps 0) 1/2)) (.f64 #s(literal 1/2 binary64) eps)) (cos.f64 #s(approx ( (+ (* x 2) eps) 1/2) (*.f64 eps (+.f64 #s(literal 1/2 binary64) (/.f64 x eps)))))) #s(literal 2 binary64))
(.f64 (.f64 #s(approx (sin (* (+ eps 0) 1/2)) (.f64 eps (fma.f64 eps (.f64 eps #s(literal -1/48 binary64)) #s(literal 1/2 binary64)))) (cos.f64 (*.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)))) #s(literal 2 binary64))
(.f64 #s(approx ( (sin (* (+ eps 0) 1/2)) (cos (* (+ (* x 2) eps) 1/2))) (.f64 #s(approx (sin ( 1/2 eps)) (.f64 eps (fma.f64 eps (.f64 eps (fma.f64 (*.f64 eps eps) #s(literal 1/3840 binary64) #s(literal -1/48 binary64))) #s(literal 1/2 binary64)))) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)))) #s(literal 2 binary64))
(.f64 (.f64 #s(approx (sin (* (+ eps 0) 1/2)) (.f64 eps (fma.f64 (.f64 eps eps) (fma.f64 eps (.f64 eps #s(literal 1/3840 binary64)) #s(literal -1/48 binary64)) #s(literal 1/2 binary64)))) (cos.f64 (.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)))) #s(literal 2 binary64))
(.f64 #s(approx ( (sin (* (+ eps 0) 1/2)) (cos (* (+ (* x 2) eps) 1/2))) (.f64 #s(approx (sin ( 1/2 eps)) (.f64 eps (fma.f64 (.f64 eps eps) (fma.f64 (.f64 eps eps) (fma.f64 (.f64 eps eps) #s(literal -1/645120 binary64) #s(literal 1/3840 binary64)) #s(literal -1/48 binary64)) #s(literal 1/2 binary64)))) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)))) #s(literal 2 binary64))
(.f64 (.f64 #s(approx (sin (* (+ eps 0) 1/2)) (.f64 eps (fma.f64 eps (.f64 eps (fma.f64 (.f64 eps eps) (fma.f64 (.f64 eps eps) #s(literal -1/645120 binary64) #s(literal 1/3840 binary64)) #s(literal -1/48 binary64))) #s(literal 1/2 binary64)))) (cos.f64 (*.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)))) #s(literal 2 binary64))
(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 eps (fma.f64 eps (.f64 #s(literal -1/2 binary64) (sin.f64 x)) (cos.f64 x))))
(.f64 #s(approx ( (sin (* (+ eps 0) 1/2)) (cos (* (+ (* x 2) eps) 1/2))) (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)))) #s(literal 2 binary64))
#s(approx (- (sin (+ x eps)) (sin x)) (-.f64 (fma.f64 (fma.f64 x (.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64)) (sin.f64 eps) (.f64 x (cos.f64 eps))) x))
(.f64 (.f64 (sin.f64 (.f64 (+.f64 eps #s(literal 0 binary64)) #s(literal 1/2 binary64))) (cos.f64 (.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)))) #s(literal 2 binary64))
(.f64 #s(approx ( (sin (* (+ eps 0) 1/2)) (cos (* (+ (* x 2) eps) 1/2))) (/.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) (/.f64 #s(literal 1 binary64) (cos.f64 (fma.f64 eps #s(literal 1/2 binary64) x))))) #s(literal 2 binary64))
(.f64 (.f64 (sin.f64 (.f64 (fma.f64 (fma.f64 x (.f64 x x) (.f64 eps (.f64 eps eps))) (/.f64 #s(literal 1 binary64) (fma.f64 x x (.f64 eps (-.f64 eps x)))) (neg.f64 x)) #s(literal 1/2 binary64))) (cos.f64 #s(approx ( (+ (* x 2) eps) 1/2) (fma.f64 eps #s(literal 1/2 binary64) x)))) #s(literal 2 binary64))
(.f64 (.f64 (sin.f64 (.f64 (fma.f64 (fma.f64 eps (.f64 eps eps) (.f64 x (.f64 x x))) (/.f64 #s(literal 1 binary64) (fma.f64 eps (-.f64 eps x) (.f64 x x))) (neg.f64 x)) #s(literal 1/2 binary64))) (cos.f64 (.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)))) #s(literal 2 binary64))
(.f64 (.f64 (sin.f64 (.f64 (fma.f64 (fma.f64 x (.f64 x x) (.f64 eps (.f64 eps eps))) (/.f64 #s(literal 1 binary64) (fma.f64 x x (.f64 eps (-.f64 eps x)))) (neg.f64 x)) #s(literal 1/2 binary64))) (cos.f64 (.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)))) #s(literal 2 binary64))
(.f64 (.f64 (sin.f64 (.f64 (fma.f64 (/.f64 (fma.f64 eps (.f64 eps eps) (.f64 x (.f64 x x))) (fma.f64 x (.f64 (.f64 x x) (.f64 x (.f64 x x))) (.f64 (.f64 eps (-.f64 eps x)) (.f64 (-.f64 eps x) (.f64 eps (.f64 eps (-.f64 eps x))))))) (fma.f64 (.f64 eps (-.f64 eps x)) (-.f64 (.f64 eps (-.f64 eps x)) (.f64 x x)) (.f64 x (.f64 x (.f64 x x)))) (neg.f64 x)) #s(literal 1/2 binary64))) (cos.f64 (.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)))) #s(literal 2 binary64))
(-.f64 (/.f64 (*.f64 (sin.f64 (+.f64 x eps)) (sin.f64 (-.f64 x eps))) (sin.f64 (-.f64 x eps))) (sin.f64 x))
#s(approx (/ (/ (- 1/2 (+ (* 1/2 (cos (* (+ x eps) 2))) (+ 1/2 (* -1/2 (cos (+ x x)))))) 2) (* (sin (* (+ (* x 2) eps) 1/2)) (cos (* (+ eps 0) 1/2)))) (/.f64 (fma.f64 #s(literal -1/4 binary64) (cos.f64 (.f64 #s(literal 2 binary64) (+.f64 eps x))) (.f64 (cos.f64 (.f64 x #s(literal 2 binary64))) #s(literal 1/4 binary64))) (.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) eps)) (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x)))))
(/.f64 (/.f64 (-.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 (+.f64 x eps) #s(literal 2 binary64))) (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal -1/2 binary64) (cos.f64 (+.f64 x x)))))) #s(literal 2 binary64)) (.f64 (sin.f64 (.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64))) (cos.f64 (*.f64 (+.f64 eps #s(literal 0 binary64)) #s(literal 1/2 binary64)))))
(/.f64 (/.f64 (-.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 (+.f64 x eps) #s(literal 2 binary64))) (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal -1/2 binary64) (cos.f64 (+.f64 x x)))))) #s(literal 2 binary64)) (.f64 (sin.f64 #s(approx ( (+ (* x 2) eps) 1/2) (.f64 eps (+.f64 #s(literal 1/2 binary64) (/.f64 x eps))))) (cos.f64 (.f64 (+.f64 eps #s(literal 0 binary64)) #s(literal 1/2 binary64)))))
(fma.f64 (sin.f64 eps) (cos.f64 x) (-.f64 (*.f64 (sin.f64 x) (cos.f64 eps)) (sin.f64 x)))
(fma.f64 (sin.f64 x) (cos.f64 eps) (fma.f64 (sin.f64 eps) (cos.f64 x) (neg.f64 (sin.f64 x))))

Outputs

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

Calls

3 calls:

23.0ms	eps
12.0ms	(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
12.0ms	x

Results

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

Compiler

Compiled 15 to 10 computations (33.3% saved)

regimes42.0ms (0.3%)

Memory

-9.1MiB live, 28.5MiB allocated

Counts

33 → 1

Calls

Call 1

Inputs
#s(approx (/ (/ (- 1/2 (+ (* 1/2 (cos (* (+ x eps) 2))) (+ 1/2 (* -1/2 (cos (+ x x)))))) 2) (* (sin (* (+ (* x 2) eps) 1/2)) (cos (* (+ eps 0) 1/2)))) #s(literal 0 binary64))
#s(approx (- (sin (+ x eps)) (sin x)) (-.f64 #s(approx (+ (* (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) #s(approx (+ (* eps (+ (* x (* x -1/2)) 1)) x) (+.f64 eps x))) x))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (sin eps) (fma.f64 eps (.f64 eps (.f64 eps #s(literal -1/6 binary64))) eps)))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (- (+ (* (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) x) (fma.f64 eps (.f64 x (.f64 x #s(literal -1/2 binary64))) eps)))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (/ 1 (/ (+ x (+ (* (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps)))) (* (+ x (+ (* (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps)))) (- (+ (* (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) x)))) (fma.f64 eps (.f64 #s(literal -1/2 binary64) (.f64 x x)) eps)))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (- (+ (* (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) x) (fma.f64 #s(literal -1/2 binary64) (.f64 (.f64 x (+.f64 eps x)) eps) eps)))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (/ 1 (/ (+ x (+ (* (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps)))) (* (+ x (+ (* (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps)))) (- (+ (* (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) x)))) (fma.f64 eps (.f64 #s(literal -1/2 binary64) (.f64 x (+.f64 eps x))) eps)))
#s(approx (- (sin (+ x eps)) (sin x)) (-.f64 #s(approx (+ (* (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) (fma.f64 eps (fma.f64 x (*.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64)) x)) x))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (sin eps) (fma.f64 (.f64 eps eps) (.f64 (fma.f64 eps (*.f64 eps #s(literal 1/120 binary64)) #s(literal -1/6 binary64)) eps) eps)))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (.f64 (+.f64 x #s(approx (+ (* (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) #s(approx (+ (* eps (+ (* x (* x -1/2)) 1)) x) (+.f64 eps x)))) (-.f64 #s(approx (+ (* (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) #s(approx (+ (* eps (+ (* x (* x -1/2)) 1)) x) (+.f64 eps x))) x)) (/.f64 #s(literal 1 binary64) (+.f64 x #s(approx (+ (* (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) #s(approx (+ (* eps (+ (* x (* x -1/2)) 1)) x) (+.f64 eps x)))))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (- (+ (* (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) x) (fma.f64 eps (fma.f64 #s(literal -1/2 binary64) (.f64 x (+.f64 eps x)) (.f64 eps (.f64 eps (fma.f64 (.f64 x x) #s(literal 1/12 binary64) #s(literal -1/6 binary64))))) eps)))
#s(approx (- (sin (+ x eps)) (sin x)) (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (-.f64 #s(approx (+ (* (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) (fma.f64 eps (fma.f64 #s(literal -1/2 binary64) (*.f64 x x) #s(literal 1 binary64)) x)) x))))
#s(approx (- (sin (+ x eps)) (sin x)) (/.f64 (-.f64 (.f64 #s(approx (+ ( (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) #s(approx (+ (* eps (+ (* x (* x -1/2)) 1)) x) (+.f64 eps x))) #s(approx (+ (* (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) #s(approx (+ (* eps (+ (* x (* x -1/2)) 1)) x) (+.f64 eps x)))) (.f64 (neg.f64 x) (neg.f64 x))) (-.f64 #s(approx (+ ( (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) #s(approx (+ (* eps (+ (* x (* x -1/2)) 1)) x) (+.f64 eps x))) (neg.f64 x))))
#s(approx (- (sin (+ x eps)) (sin x)) (/.f64 #s(literal 1 binary64) (/.f64 (+.f64 x #s(approx (+ (* (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) #s(approx (+ (* eps (+ (* x (* x -1/2)) 1)) x) (+.f64 eps x)))) (.f64 (+.f64 x #s(approx (+ ( (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) #s(approx (+ (* eps (+ (* x (* x -1/2)) 1)) x) (+.f64 eps x)))) (-.f64 #s(approx (+ (* (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) #s(approx (+ (* eps (+ (* x (* x -1/2)) 1)) x) (+.f64 eps x))) x)))))
#s(approx (- (sin (+ x eps)) (sin x)) (/.f64 (fma.f64 #s(approx (+ (* (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) #s(approx (+ (* eps (+ (* x (* x -1/2)) 1)) x) (+.f64 eps x))) (.f64 #s(approx (+ ( (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) #s(approx (+ (* eps (+ (* x (* x -1/2)) 1)) x) (+.f64 eps x))) #s(approx (+ (* (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) #s(approx (+ (* eps (+ (* x (* x -1/2)) 1)) x) (+.f64 eps x)))) (neg.f64 (.f64 x (.f64 x x)))) (fma.f64 x (+.f64 x #s(approx (+ (* (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) #s(approx (+ (* eps (+ (* x (* x -1/2)) 1)) x) (+.f64 eps x)))) (.f64 #s(approx (+ ( (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) #s(approx (+ (* eps (+ (* x (* x -1/2)) 1)) x) (+.f64 eps x))) #s(approx (+ (* (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) #s(approx (+ (* eps (+ (* x (* x -1/2)) 1)) x) (+.f64 eps x)))))))
#s(approx (- (sin (+ x eps)) (sin x)) (/.f64 #s(literal 1 binary64) (/.f64 #s(approx (+ x (+ (* (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps)))) (.f64 x #s(literal 2 binary64))) (.f64 (+.f64 x #s(approx (+ (* (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) (fma.f64 eps (fma.f64 #s(literal -1/2 binary64) (.f64 x x) #s(literal 1 binary64)) x))) (-.f64 #s(approx (+ ( (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) (fma.f64 eps (fma.f64 #s(literal -1/2 binary64) (*.f64 x x) #s(literal 1 binary64)) x)) x)))))
#s(approx (- (sin (+ x eps)) (sin x)) (/.f64 #s(literal 1 binary64) (/.f64 (+.f64 x #s(approx (+ (* (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) (fma.f64 eps (fma.f64 #s(literal -1/2 binary64) (.f64 x x) #s(literal 1 binary64)) x))) (.f64 #s(approx (+ x (+ (* (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps)))) (.f64 x #s(literal 2 binary64))) (-.f64 #s(approx (+ ( (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) (fma.f64 eps (fma.f64 #s(literal -1/2 binary64) (*.f64 x x) #s(literal 1 binary64)) x)) x)))))
#s(approx (- (sin (+ x eps)) (sin x)) (/.f64 (-.f64 (.f64 #s(approx (+ ( (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) (fma.f64 eps (fma.f64 #s(literal -1/2 binary64) (.f64 x x) #s(literal 1 binary64)) x)) #s(approx (+ ( (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) (fma.f64 eps (fma.f64 #s(literal -1/2 binary64) (.f64 x x) #s(literal 1 binary64)) x))) (.f64 (neg.f64 x) (neg.f64 x))) (-.f64 #s(approx (+ (* (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) (fma.f64 eps (fma.f64 #s(literal -1/2 binary64) (*.f64 x x) #s(literal 1 binary64)) x)) (neg.f64 x))))
#s(approx (- (sin (+ x eps)) (sin x)) (/.f64 #s(literal 1 binary64) (/.f64 (+.f64 x #s(approx (+ (* (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) (fma.f64 eps (fma.f64 #s(literal -1/2 binary64) (.f64 x x) #s(literal 1 binary64)) x))) (.f64 (+.f64 x #s(approx (+ (* (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) (fma.f64 eps (fma.f64 #s(literal -1/2 binary64) (.f64 x x) #s(literal 1 binary64)) x))) (-.f64 #s(approx (+ ( (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) (fma.f64 eps (fma.f64 #s(literal -1/2 binary64) (*.f64 x x) #s(literal 1 binary64)) x)) x)))))
#s(approx (- (sin (+ x eps)) (sin x)) (sin.f64 eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 eps (cos.f64 x)))
(.f64 (.f64 #s(approx (sin (* (+ eps 0) 1/2)) (.f64 #s(literal 1/2 binary64) eps)) (cos.f64 #s(approx ( (+ (* x 2) eps) 1/2) (fma.f64 eps #s(literal 1/2 binary64) x)))) #s(literal 2 binary64))
(-.f64 (sin.f64 (+.f64 x eps)) #s(approx (sin x) (fma.f64 #s(literal -1/6 binary64) (.f64 x (.f64 x x)) x)))
(.f64 (.f64 #s(approx (sin (* (+ eps 0) 1/2)) (.f64 #s(literal 1/2 binary64) eps)) (cos.f64 (.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)))) #s(literal 2 binary64))
(.f64 #s(approx ( (sin (* (+ eps 0) 1/2)) (cos (* (+ (* x 2) eps) 1/2))) (.f64 #s(approx (sin ( 1/2 eps)) (.f64 eps (fma.f64 eps (.f64 eps #s(literal -1/48 binary64)) #s(literal 1/2 binary64)))) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)))) #s(literal 2 binary64))
(.f64 (.f64 #s(approx (sin (* (+ eps 0) 1/2)) (.f64 #s(literal 1/2 binary64) eps)) (cos.f64 #s(approx ( (+ (* x 2) eps) 1/2) (*.f64 eps (+.f64 #s(literal 1/2 binary64) (/.f64 x eps)))))) #s(literal 2 binary64))
(.f64 (.f64 #s(approx (sin (* (+ eps 0) 1/2)) (.f64 eps (fma.f64 eps (.f64 eps #s(literal -1/48 binary64)) #s(literal 1/2 binary64)))) (cos.f64 (*.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)))) #s(literal 2 binary64))
(.f64 #s(approx ( (sin (* (+ eps 0) 1/2)) (cos (* (+ (* x 2) eps) 1/2))) (.f64 #s(approx (sin ( 1/2 eps)) (.f64 eps (fma.f64 eps (.f64 eps (fma.f64 (*.f64 eps eps) #s(literal 1/3840 binary64) #s(literal -1/48 binary64))) #s(literal 1/2 binary64)))) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)))) #s(literal 2 binary64))
(.f64 (.f64 #s(approx (sin (* (+ eps 0) 1/2)) (.f64 eps (fma.f64 (.f64 eps eps) (fma.f64 eps (.f64 eps #s(literal 1/3840 binary64)) #s(literal -1/48 binary64)) #s(literal 1/2 binary64)))) (cos.f64 (.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)))) #s(literal 2 binary64))
(.f64 #s(approx ( (sin (* (+ eps 0) 1/2)) (cos (* (+ (* x 2) eps) 1/2))) (.f64 #s(approx (sin ( 1/2 eps)) (.f64 eps (fma.f64 (.f64 eps eps) (fma.f64 (.f64 eps eps) (fma.f64 (.f64 eps eps) #s(literal -1/645120 binary64) #s(literal 1/3840 binary64)) #s(literal -1/48 binary64)) #s(literal 1/2 binary64)))) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)))) #s(literal 2 binary64))
(.f64 (.f64 #s(approx (sin (* (+ eps 0) 1/2)) (.f64 eps (fma.f64 eps (.f64 eps (fma.f64 (.f64 eps eps) (fma.f64 (.f64 eps eps) #s(literal -1/645120 binary64) #s(literal 1/3840 binary64)) #s(literal -1/48 binary64))) #s(literal 1/2 binary64)))) (cos.f64 (*.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)))) #s(literal 2 binary64))
(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 eps (fma.f64 eps (.f64 #s(literal -1/2 binary64) (sin.f64 x)) (cos.f64 x))))

Outputs

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

Calls

3 calls:

23.0ms	(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
9.0ms	x
9.0ms	eps

Results

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

Compiler

Compiled 15 to 10 computations (33.3% saved)

regimes43.0ms (0.3%)

Memory

-14.2MiB live, 24.6MiB allocated

Counts

29 → 1

Calls

Call 1

Inputs
#s(approx (/ (/ (- 1/2 (+ (* 1/2 (cos (* (+ x eps) 2))) (+ 1/2 (* -1/2 (cos (+ x x)))))) 2) (* (sin (* (+ (* x 2) eps) 1/2)) (cos (* (+ eps 0) 1/2)))) #s(literal 0 binary64))
#s(approx (- (sin (+ x eps)) (sin x)) (-.f64 #s(approx (+ (* (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) #s(approx (+ (* eps (+ (* x (* x -1/2)) 1)) x) (+.f64 eps x))) x))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (sin eps) (fma.f64 eps (.f64 eps (.f64 eps #s(literal -1/6 binary64))) eps)))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (- (+ (* (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) x) (fma.f64 eps (.f64 x (.f64 x #s(literal -1/2 binary64))) eps)))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (/ 1 (/ (+ x (+ (* (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps)))) (* (+ x (+ (* (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps)))) (- (+ (* (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) x)))) (fma.f64 eps (.f64 #s(literal -1/2 binary64) (.f64 x x)) eps)))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (- (+ (* (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) x) (fma.f64 #s(literal -1/2 binary64) (.f64 (.f64 x (+.f64 eps x)) eps) eps)))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (/ 1 (/ (+ x (+ (* (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps)))) (* (+ x (+ (* (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps)))) (- (+ (* (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) x)))) (fma.f64 eps (.f64 #s(literal -1/2 binary64) (.f64 x (+.f64 eps x))) eps)))
#s(approx (- (sin (+ x eps)) (sin x)) (-.f64 #s(approx (+ (* (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) (fma.f64 eps (fma.f64 x (*.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64)) x)) x))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (sin eps) (fma.f64 (.f64 eps eps) (.f64 (fma.f64 eps (*.f64 eps #s(literal 1/120 binary64)) #s(literal -1/6 binary64)) eps) eps)))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (.f64 (+.f64 x #s(approx (+ (* (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) #s(approx (+ (* eps (+ (* x (* x -1/2)) 1)) x) (+.f64 eps x)))) (-.f64 #s(approx (+ (* (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) #s(approx (+ (* eps (+ (* x (* x -1/2)) 1)) x) (+.f64 eps x))) x)) (/.f64 #s(literal 1 binary64) (+.f64 x #s(approx (+ (* (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) #s(approx (+ (* eps (+ (* x (* x -1/2)) 1)) x) (+.f64 eps x)))))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (- (+ (* (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) x) (fma.f64 eps (fma.f64 #s(literal -1/2 binary64) (.f64 x (+.f64 eps x)) (.f64 eps (.f64 eps (fma.f64 (.f64 x x) #s(literal 1/12 binary64) #s(literal -1/6 binary64))))) eps)))
#s(approx (- (sin (+ x eps)) (sin x)) (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (-.f64 #s(approx (+ (* (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) (fma.f64 eps (fma.f64 #s(literal -1/2 binary64) (*.f64 x x) #s(literal 1 binary64)) x)) x))))
#s(approx (- (sin (+ x eps)) (sin x)) (/.f64 (-.f64 (.f64 #s(approx (+ ( (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) #s(approx (+ (* eps (+ (* x (* x -1/2)) 1)) x) (+.f64 eps x))) #s(approx (+ (* (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) #s(approx (+ (* eps (+ (* x (* x -1/2)) 1)) x) (+.f64 eps x)))) (.f64 (neg.f64 x) (neg.f64 x))) (-.f64 #s(approx (+ ( (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) #s(approx (+ (* eps (+ (* x (* x -1/2)) 1)) x) (+.f64 eps x))) (neg.f64 x))))
#s(approx (- (sin (+ x eps)) (sin x)) (/.f64 #s(literal 1 binary64) (/.f64 (+.f64 x #s(approx (+ (* (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) #s(approx (+ (* eps (+ (* x (* x -1/2)) 1)) x) (+.f64 eps x)))) (.f64 (+.f64 x #s(approx (+ ( (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) #s(approx (+ (* eps (+ (* x (* x -1/2)) 1)) x) (+.f64 eps x)))) (-.f64 #s(approx (+ (* (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) #s(approx (+ (* eps (+ (* x (* x -1/2)) 1)) x) (+.f64 eps x))) x)))))
#s(approx (- (sin (+ x eps)) (sin x)) (/.f64 (fma.f64 #s(approx (+ (* (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) #s(approx (+ (* eps (+ (* x (* x -1/2)) 1)) x) (+.f64 eps x))) (.f64 #s(approx (+ ( (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) #s(approx (+ (* eps (+ (* x (* x -1/2)) 1)) x) (+.f64 eps x))) #s(approx (+ (* (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) #s(approx (+ (* eps (+ (* x (* x -1/2)) 1)) x) (+.f64 eps x)))) (neg.f64 (.f64 x (.f64 x x)))) (fma.f64 x (+.f64 x #s(approx (+ (* (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) #s(approx (+ (* eps (+ (* x (* x -1/2)) 1)) x) (+.f64 eps x)))) (.f64 #s(approx (+ ( (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) #s(approx (+ (* eps (+ (* x (* x -1/2)) 1)) x) (+.f64 eps x))) #s(approx (+ (* (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) #s(approx (+ (* eps (+ (* x (* x -1/2)) 1)) x) (+.f64 eps x)))))))
#s(approx (- (sin (+ x eps)) (sin x)) (/.f64 #s(literal 1 binary64) (/.f64 #s(approx (+ x (+ (* (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps)))) (.f64 x #s(literal 2 binary64))) (.f64 (+.f64 x #s(approx (+ (* (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) (fma.f64 eps (fma.f64 #s(literal -1/2 binary64) (.f64 x x) #s(literal 1 binary64)) x))) (-.f64 #s(approx (+ ( (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) (fma.f64 eps (fma.f64 #s(literal -1/2 binary64) (*.f64 x x) #s(literal 1 binary64)) x)) x)))))
#s(approx (- (sin (+ x eps)) (sin x)) (/.f64 #s(literal 1 binary64) (/.f64 (+.f64 x #s(approx (+ (* (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) (fma.f64 eps (fma.f64 #s(literal -1/2 binary64) (.f64 x x) #s(literal 1 binary64)) x))) (.f64 #s(approx (+ x (+ (* (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps)))) (.f64 x #s(literal 2 binary64))) (-.f64 #s(approx (+ ( (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) (fma.f64 eps (fma.f64 #s(literal -1/2 binary64) (*.f64 x x) #s(literal 1 binary64)) x)) x)))))
#s(approx (- (sin (+ x eps)) (sin x)) (/.f64 (-.f64 (.f64 #s(approx (+ ( (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) (fma.f64 eps (fma.f64 #s(literal -1/2 binary64) (.f64 x x) #s(literal 1 binary64)) x)) #s(approx (+ ( (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) (fma.f64 eps (fma.f64 #s(literal -1/2 binary64) (.f64 x x) #s(literal 1 binary64)) x))) (.f64 (neg.f64 x) (neg.f64 x))) (-.f64 #s(approx (+ (* (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) (fma.f64 eps (fma.f64 #s(literal -1/2 binary64) (*.f64 x x) #s(literal 1 binary64)) x)) (neg.f64 x))))
#s(approx (- (sin (+ x eps)) (sin x)) (/.f64 #s(literal 1 binary64) (/.f64 (+.f64 x #s(approx (+ (* (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) (fma.f64 eps (fma.f64 #s(literal -1/2 binary64) (.f64 x x) #s(literal 1 binary64)) x))) (.f64 (+.f64 x #s(approx (+ (* (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) (fma.f64 eps (fma.f64 #s(literal -1/2 binary64) (.f64 x x) #s(literal 1 binary64)) x))) (-.f64 #s(approx (+ ( (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) (fma.f64 eps (fma.f64 #s(literal -1/2 binary64) (*.f64 x x) #s(literal 1 binary64)) x)) x)))))
#s(approx (- (sin (+ x eps)) (sin x)) (sin.f64 eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 eps (cos.f64 x)))
(.f64 (.f64 #s(approx (sin (* (+ eps 0) 1/2)) (.f64 #s(literal 1/2 binary64) eps)) (cos.f64 #s(approx ( (+ (* x 2) eps) 1/2) (fma.f64 eps #s(literal 1/2 binary64) x)))) #s(literal 2 binary64))
(-.f64 (sin.f64 (+.f64 x eps)) #s(approx (sin x) (fma.f64 #s(literal -1/6 binary64) (.f64 x (.f64 x x)) x)))
(.f64 (.f64 #s(approx (sin (* (+ eps 0) 1/2)) (.f64 #s(literal 1/2 binary64) eps)) (cos.f64 (.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)))) #s(literal 2 binary64))
(.f64 #s(approx ( (sin (* (+ eps 0) 1/2)) (cos (* (+ (* x 2) eps) 1/2))) (.f64 #s(approx (sin ( 1/2 eps)) (.f64 eps (fma.f64 eps (.f64 eps #s(literal -1/48 binary64)) #s(literal 1/2 binary64)))) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)))) #s(literal 2 binary64))
(.f64 (.f64 #s(approx (sin (* (+ eps 0) 1/2)) (.f64 #s(literal 1/2 binary64) eps)) (cos.f64 #s(approx ( (+ (* x 2) eps) 1/2) (*.f64 eps (+.f64 #s(literal 1/2 binary64) (/.f64 x eps)))))) #s(literal 2 binary64))
(.f64 (.f64 #s(approx (sin (* (+ eps 0) 1/2)) (.f64 eps (fma.f64 eps (.f64 eps #s(literal -1/48 binary64)) #s(literal 1/2 binary64)))) (cos.f64 (*.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)))) #s(literal 2 binary64))
(.f64 #s(approx ( (sin (* (+ eps 0) 1/2)) (cos (* (+ (* x 2) eps) 1/2))) (.f64 #s(approx (sin ( 1/2 eps)) (.f64 eps (fma.f64 eps (.f64 eps (fma.f64 (*.f64 eps eps) #s(literal 1/3840 binary64) #s(literal -1/48 binary64))) #s(literal 1/2 binary64)))) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)))) #s(literal 2 binary64))
(.f64 (.f64 #s(approx (sin (* (+ eps 0) 1/2)) (.f64 eps (fma.f64 (.f64 eps eps) (fma.f64 eps (.f64 eps #s(literal 1/3840 binary64)) #s(literal -1/48 binary64)) #s(literal 1/2 binary64)))) (cos.f64 (.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)))) #s(literal 2 binary64))

Outputs

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

Calls

3 calls:

26.0ms	x
8.0ms	(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
8.0ms	eps

Results

Accuracy	Segments	Branch
99.4%	1	`x`
99.4%	1	`eps`
99.4%	1	`(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))`

Compiler

Compiled 15 to 10 computations (33.3% saved)

regimes24.0ms (0.2%)

Memory

16.7MiB live, 16.7MiB allocated

Counts

27 → 1

Calls

Call 1

Inputs
#s(approx (/ (/ (- 1/2 (+ (* 1/2 (cos (* (+ x eps) 2))) (+ 1/2 (* -1/2 (cos (+ x x)))))) 2) (* (sin (* (+ (* x 2) eps) 1/2)) (cos (* (+ eps 0) 1/2)))) #s(literal 0 binary64))
#s(approx (- (sin (+ x eps)) (sin x)) (-.f64 #s(approx (+ (* (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) #s(approx (+ (* eps (+ (* x (* x -1/2)) 1)) x) (+.f64 eps x))) x))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (sin eps) (fma.f64 eps (.f64 eps (.f64 eps #s(literal -1/6 binary64))) eps)))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (- (+ (* (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) x) (fma.f64 eps (.f64 x (.f64 x #s(literal -1/2 binary64))) eps)))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (/ 1 (/ (+ x (+ (* (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps)))) (* (+ x (+ (* (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps)))) (- (+ (* (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) x)))) (fma.f64 eps (.f64 #s(literal -1/2 binary64) (.f64 x x)) eps)))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (- (+ (* (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) x) (fma.f64 #s(literal -1/2 binary64) (.f64 (.f64 x (+.f64 eps x)) eps) eps)))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (/ 1 (/ (+ x (+ (* (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps)))) (* (+ x (+ (* (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps)))) (- (+ (* (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) x)))) (fma.f64 eps (.f64 #s(literal -1/2 binary64) (.f64 x (+.f64 eps x))) eps)))
#s(approx (- (sin (+ x eps)) (sin x)) (-.f64 #s(approx (+ (* (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) (fma.f64 eps (fma.f64 x (*.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64)) x)) x))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (sin eps) (fma.f64 (.f64 eps eps) (.f64 (fma.f64 eps (*.f64 eps #s(literal 1/120 binary64)) #s(literal -1/6 binary64)) eps) eps)))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (.f64 (+.f64 x #s(approx (+ (* (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) #s(approx (+ (* eps (+ (* x (* x -1/2)) 1)) x) (+.f64 eps x)))) (-.f64 #s(approx (+ (* (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) #s(approx (+ (* eps (+ (* x (* x -1/2)) 1)) x) (+.f64 eps x))) x)) (/.f64 #s(literal 1 binary64) (+.f64 x #s(approx (+ (* (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) #s(approx (+ (* eps (+ (* x (* x -1/2)) 1)) x) (+.f64 eps x)))))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (- (+ (* (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) x) (fma.f64 eps (fma.f64 #s(literal -1/2 binary64) (.f64 x (+.f64 eps x)) (.f64 eps (.f64 eps (fma.f64 (.f64 x x) #s(literal 1/12 binary64) #s(literal -1/6 binary64))))) eps)))
#s(approx (- (sin (+ x eps)) (sin x)) (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (-.f64 #s(approx (+ (* (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) (fma.f64 eps (fma.f64 #s(literal -1/2 binary64) (*.f64 x x) #s(literal 1 binary64)) x)) x))))
#s(approx (- (sin (+ x eps)) (sin x)) (/.f64 (-.f64 (.f64 #s(approx (+ ( (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) #s(approx (+ (* eps (+ (* x (* x -1/2)) 1)) x) (+.f64 eps x))) #s(approx (+ (* (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) #s(approx (+ (* eps (+ (* x (* x -1/2)) 1)) x) (+.f64 eps x)))) (.f64 (neg.f64 x) (neg.f64 x))) (-.f64 #s(approx (+ ( (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) #s(approx (+ (* eps (+ (* x (* x -1/2)) 1)) x) (+.f64 eps x))) (neg.f64 x))))
#s(approx (- (sin (+ x eps)) (sin x)) (/.f64 #s(literal 1 binary64) (/.f64 (+.f64 x #s(approx (+ (* (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) #s(approx (+ (* eps (+ (* x (* x -1/2)) 1)) x) (+.f64 eps x)))) (.f64 (+.f64 x #s(approx (+ ( (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) #s(approx (+ (* eps (+ (* x (* x -1/2)) 1)) x) (+.f64 eps x)))) (-.f64 #s(approx (+ (* (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) #s(approx (+ (* eps (+ (* x (* x -1/2)) 1)) x) (+.f64 eps x))) x)))))
#s(approx (- (sin (+ x eps)) (sin x)) (/.f64 (fma.f64 #s(approx (+ (* (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) #s(approx (+ (* eps (+ (* x (* x -1/2)) 1)) x) (+.f64 eps x))) (.f64 #s(approx (+ ( (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) #s(approx (+ (* eps (+ (* x (* x -1/2)) 1)) x) (+.f64 eps x))) #s(approx (+ (* (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) #s(approx (+ (* eps (+ (* x (* x -1/2)) 1)) x) (+.f64 eps x)))) (neg.f64 (.f64 x (.f64 x x)))) (fma.f64 x (+.f64 x #s(approx (+ (* (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) #s(approx (+ (* eps (+ (* x (* x -1/2)) 1)) x) (+.f64 eps x)))) (.f64 #s(approx (+ ( (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) #s(approx (+ (* eps (+ (* x (* x -1/2)) 1)) x) (+.f64 eps x))) #s(approx (+ (* (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) #s(approx (+ (* eps (+ (* x (* x -1/2)) 1)) x) (+.f64 eps x)))))))
#s(approx (- (sin (+ x eps)) (sin x)) (/.f64 #s(literal 1 binary64) (/.f64 #s(approx (+ x (+ (* (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps)))) (.f64 x #s(literal 2 binary64))) (.f64 (+.f64 x #s(approx (+ (* (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) (fma.f64 eps (fma.f64 #s(literal -1/2 binary64) (.f64 x x) #s(literal 1 binary64)) x))) (-.f64 #s(approx (+ ( (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) (fma.f64 eps (fma.f64 #s(literal -1/2 binary64) (*.f64 x x) #s(literal 1 binary64)) x)) x)))))
#s(approx (- (sin (+ x eps)) (sin x)) (/.f64 #s(literal 1 binary64) (/.f64 (+.f64 x #s(approx (+ (* (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) (fma.f64 eps (fma.f64 #s(literal -1/2 binary64) (.f64 x x) #s(literal 1 binary64)) x))) (.f64 #s(approx (+ x (+ (* (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps)))) (.f64 x #s(literal 2 binary64))) (-.f64 #s(approx (+ ( (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) (fma.f64 eps (fma.f64 #s(literal -1/2 binary64) (*.f64 x x) #s(literal 1 binary64)) x)) x)))))
#s(approx (- (sin (+ x eps)) (sin x)) (/.f64 (-.f64 (.f64 #s(approx (+ ( (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) (fma.f64 eps (fma.f64 #s(literal -1/2 binary64) (.f64 x x) #s(literal 1 binary64)) x)) #s(approx (+ ( (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) (fma.f64 eps (fma.f64 #s(literal -1/2 binary64) (.f64 x x) #s(literal 1 binary64)) x))) (.f64 (neg.f64 x) (neg.f64 x))) (-.f64 #s(approx (+ (* (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) (fma.f64 eps (fma.f64 #s(literal -1/2 binary64) (*.f64 x x) #s(literal 1 binary64)) x)) (neg.f64 x))))
#s(approx (- (sin (+ x eps)) (sin x)) (/.f64 #s(literal 1 binary64) (/.f64 (+.f64 x #s(approx (+ (* (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) (fma.f64 eps (fma.f64 #s(literal -1/2 binary64) (.f64 x x) #s(literal 1 binary64)) x))) (.f64 (+.f64 x #s(approx (+ (* (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) (fma.f64 eps (fma.f64 #s(literal -1/2 binary64) (.f64 x x) #s(literal 1 binary64)) x))) (-.f64 #s(approx (+ ( (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) (fma.f64 eps (fma.f64 #s(literal -1/2 binary64) (*.f64 x x) #s(literal 1 binary64)) x)) x)))))
#s(approx (- (sin (+ x eps)) (sin x)) (sin.f64 eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 eps (cos.f64 x)))
(.f64 (.f64 #s(approx (sin (* (+ eps 0) 1/2)) (.f64 #s(literal 1/2 binary64) eps)) (cos.f64 #s(approx ( (+ (* x 2) eps) 1/2) (fma.f64 eps #s(literal 1/2 binary64) x)))) #s(literal 2 binary64))
(-.f64 (sin.f64 (+.f64 x eps)) #s(approx (sin x) (fma.f64 #s(literal -1/6 binary64) (.f64 x (.f64 x x)) x)))
(.f64 (.f64 #s(approx (sin (* (+ eps 0) 1/2)) (.f64 #s(literal 1/2 binary64) eps)) (cos.f64 (.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)))) #s(literal 2 binary64))
(.f64 #s(approx ( (sin (* (+ eps 0) 1/2)) (cos (* (+ (* x 2) eps) 1/2))) (.f64 #s(approx (sin ( 1/2 eps)) (.f64 eps (fma.f64 eps (.f64 eps #s(literal -1/48 binary64)) #s(literal 1/2 binary64)))) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)))) #s(literal 2 binary64))
(.f64 (.f64 #s(approx (sin (* (+ eps 0) 1/2)) (.f64 #s(literal 1/2 binary64) eps)) (cos.f64 #s(approx ( (+ (* x 2) eps) 1/2) (*.f64 eps (+.f64 #s(literal 1/2 binary64) (/.f64 x eps)))))) #s(literal 2 binary64))
(.f64 (.f64 #s(approx (sin (* (+ eps 0) 1/2)) (.f64 eps (fma.f64 eps (.f64 eps #s(literal -1/48 binary64)) #s(literal 1/2 binary64)))) (cos.f64 (*.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)))) #s(literal 2 binary64))

Outputs

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

Calls

3 calls:

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

Results

Accuracy	Segments	Branch
99.2%	1	`x`
99.2%	1	`eps`
99.2%	1	`(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))`

Compiler

Compiled 15 to 10 computations (33.3% saved)

regimes22.0ms (0.2%)

Memory

14.2MiB live, 14.2MiB allocated

Counts

24 → 1

Calls

Call 1

Inputs
#s(approx (/ (/ (- 1/2 (+ (* 1/2 (cos (* (+ x eps) 2))) (+ 1/2 (* -1/2 (cos (+ x x)))))) 2) (* (sin (* (+ (* x 2) eps) 1/2)) (cos (* (+ eps 0) 1/2)))) #s(literal 0 binary64))
#s(approx (- (sin (+ x eps)) (sin x)) (-.f64 #s(approx (+ (* (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) #s(approx (+ (* eps (+ (* x (* x -1/2)) 1)) x) (+.f64 eps x))) x))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (sin eps) (fma.f64 eps (.f64 eps (.f64 eps #s(literal -1/6 binary64))) eps)))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (- (+ (* (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) x) (fma.f64 eps (.f64 x (.f64 x #s(literal -1/2 binary64))) eps)))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (/ 1 (/ (+ x (+ (* (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps)))) (* (+ x (+ (* (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps)))) (- (+ (* (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) x)))) (fma.f64 eps (.f64 #s(literal -1/2 binary64) (.f64 x x)) eps)))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (- (+ (* (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) x) (fma.f64 #s(literal -1/2 binary64) (.f64 (.f64 x (+.f64 eps x)) eps) eps)))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (/ 1 (/ (+ x (+ (* (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps)))) (* (+ x (+ (* (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps)))) (- (+ (* (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) x)))) (fma.f64 eps (.f64 #s(literal -1/2 binary64) (.f64 x (+.f64 eps x))) eps)))
#s(approx (- (sin (+ x eps)) (sin x)) (-.f64 #s(approx (+ (* (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) (fma.f64 eps (fma.f64 x (*.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64)) x)) x))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (sin eps) (fma.f64 (.f64 eps eps) (.f64 (fma.f64 eps (*.f64 eps #s(literal 1/120 binary64)) #s(literal -1/6 binary64)) eps) eps)))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (.f64 (+.f64 x #s(approx (+ (* (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) #s(approx (+ (* eps (+ (* x (* x -1/2)) 1)) x) (+.f64 eps x)))) (-.f64 #s(approx (+ (* (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) #s(approx (+ (* eps (+ (* x (* x -1/2)) 1)) x) (+.f64 eps x))) x)) (/.f64 #s(literal 1 binary64) (+.f64 x #s(approx (+ (* (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) #s(approx (+ (* eps (+ (* x (* x -1/2)) 1)) x) (+.f64 eps x)))))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (- (+ (* (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) x) (fma.f64 eps (fma.f64 #s(literal -1/2 binary64) (.f64 x (+.f64 eps x)) (.f64 eps (.f64 eps (fma.f64 (.f64 x x) #s(literal 1/12 binary64) #s(literal -1/6 binary64))))) eps)))
#s(approx (- (sin (+ x eps)) (sin x)) (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (-.f64 #s(approx (+ (* (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) (fma.f64 eps (fma.f64 #s(literal -1/2 binary64) (*.f64 x x) #s(literal 1 binary64)) x)) x))))
#s(approx (- (sin (+ x eps)) (sin x)) (/.f64 (-.f64 (.f64 #s(approx (+ ( (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) #s(approx (+ (* eps (+ (* x (* x -1/2)) 1)) x) (+.f64 eps x))) #s(approx (+ (* (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) #s(approx (+ (* eps (+ (* x (* x -1/2)) 1)) x) (+.f64 eps x)))) (.f64 (neg.f64 x) (neg.f64 x))) (-.f64 #s(approx (+ ( (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) #s(approx (+ (* eps (+ (* x (* x -1/2)) 1)) x) (+.f64 eps x))) (neg.f64 x))))
#s(approx (- (sin (+ x eps)) (sin x)) (/.f64 #s(literal 1 binary64) (/.f64 (+.f64 x #s(approx (+ (* (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) #s(approx (+ (* eps (+ (* x (* x -1/2)) 1)) x) (+.f64 eps x)))) (.f64 (+.f64 x #s(approx (+ ( (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) #s(approx (+ (* eps (+ (* x (* x -1/2)) 1)) x) (+.f64 eps x)))) (-.f64 #s(approx (+ (* (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) #s(approx (+ (* eps (+ (* x (* x -1/2)) 1)) x) (+.f64 eps x))) x)))))
#s(approx (- (sin (+ x eps)) (sin x)) (/.f64 (fma.f64 #s(approx (+ (* (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) #s(approx (+ (* eps (+ (* x (* x -1/2)) 1)) x) (+.f64 eps x))) (.f64 #s(approx (+ ( (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) #s(approx (+ (* eps (+ (* x (* x -1/2)) 1)) x) (+.f64 eps x))) #s(approx (+ (* (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) #s(approx (+ (* eps (+ (* x (* x -1/2)) 1)) x) (+.f64 eps x)))) (neg.f64 (.f64 x (.f64 x x)))) (fma.f64 x (+.f64 x #s(approx (+ (* (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) #s(approx (+ (* eps (+ (* x (* x -1/2)) 1)) x) (+.f64 eps x)))) (.f64 #s(approx (+ ( (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) #s(approx (+ (* eps (+ (* x (* x -1/2)) 1)) x) (+.f64 eps x))) #s(approx (+ (* (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) #s(approx (+ (* eps (+ (* x (* x -1/2)) 1)) x) (+.f64 eps x)))))))
#s(approx (- (sin (+ x eps)) (sin x)) (/.f64 #s(literal 1 binary64) (/.f64 #s(approx (+ x (+ (* (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps)))) (.f64 x #s(literal 2 binary64))) (.f64 (+.f64 x #s(approx (+ (* (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) (fma.f64 eps (fma.f64 #s(literal -1/2 binary64) (.f64 x x) #s(literal 1 binary64)) x))) (-.f64 #s(approx (+ ( (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) (fma.f64 eps (fma.f64 #s(literal -1/2 binary64) (*.f64 x x) #s(literal 1 binary64)) x)) x)))))
#s(approx (- (sin (+ x eps)) (sin x)) (/.f64 #s(literal 1 binary64) (/.f64 (+.f64 x #s(approx (+ (* (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) (fma.f64 eps (fma.f64 #s(literal -1/2 binary64) (.f64 x x) #s(literal 1 binary64)) x))) (.f64 #s(approx (+ x (+ (* (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps)))) (.f64 x #s(literal 2 binary64))) (-.f64 #s(approx (+ ( (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) (fma.f64 eps (fma.f64 #s(literal -1/2 binary64) (*.f64 x x) #s(literal 1 binary64)) x)) x)))))
#s(approx (- (sin (+ x eps)) (sin x)) (/.f64 (-.f64 (.f64 #s(approx (+ ( (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) (fma.f64 eps (fma.f64 #s(literal -1/2 binary64) (.f64 x x) #s(literal 1 binary64)) x)) #s(approx (+ ( (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) (fma.f64 eps (fma.f64 #s(literal -1/2 binary64) (.f64 x x) #s(literal 1 binary64)) x))) (.f64 (neg.f64 x) (neg.f64 x))) (-.f64 #s(approx (+ (* (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) (fma.f64 eps (fma.f64 #s(literal -1/2 binary64) (*.f64 x x) #s(literal 1 binary64)) x)) (neg.f64 x))))
#s(approx (- (sin (+ x eps)) (sin x)) (/.f64 #s(literal 1 binary64) (/.f64 (+.f64 x #s(approx (+ (* (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) (fma.f64 eps (fma.f64 #s(literal -1/2 binary64) (.f64 x x) #s(literal 1 binary64)) x))) (.f64 (+.f64 x #s(approx (+ (* (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) (fma.f64 eps (fma.f64 #s(literal -1/2 binary64) (.f64 x x) #s(literal 1 binary64)) x))) (-.f64 #s(approx (+ ( (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) (fma.f64 eps (fma.f64 #s(literal -1/2 binary64) (*.f64 x x) #s(literal 1 binary64)) x)) x)))))
#s(approx (- (sin (+ x eps)) (sin x)) (sin.f64 eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 eps (cos.f64 x)))
(.f64 (.f64 #s(approx (sin (* (+ eps 0) 1/2)) (.f64 #s(literal 1/2 binary64) eps)) (cos.f64 #s(approx ( (+ (* x 2) eps) 1/2) (fma.f64 eps #s(literal 1/2 binary64) x)))) #s(literal 2 binary64))
(-.f64 (sin.f64 (+.f64 x eps)) #s(approx (sin x) (fma.f64 #s(literal -1/6 binary64) (.f64 x (.f64 x x)) x)))
(.f64 (.f64 #s(approx (sin (* (+ eps 0) 1/2)) (.f64 #s(literal 1/2 binary64) eps)) (cos.f64 (.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)))) #s(literal 2 binary64))

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

Calls

3 calls:

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

Results

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

Compiler

Compiled 15 to 10 computations (33.3% saved)

regimes51.0ms (0.4%)

Memory

-19.6MiB live, 19.6MiB allocated

Counts

21 → 1

Calls

Call 1

Inputs
#s(approx (/ (/ (- 1/2 (+ (* 1/2 (cos (* (+ x eps) 2))) (+ 1/2 (* -1/2 (cos (+ x x)))))) 2) (* (sin (* (+ (* x 2) eps) 1/2)) (cos (* (+ eps 0) 1/2)))) #s(literal 0 binary64))
#s(approx (- (sin (+ x eps)) (sin x)) (-.f64 #s(approx (+ (* (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) #s(approx (+ (* eps (+ (* x (* x -1/2)) 1)) x) (+.f64 eps x))) x))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (sin eps) (fma.f64 eps (.f64 eps (.f64 eps #s(literal -1/6 binary64))) eps)))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (- (+ (* (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) x) (fma.f64 eps (.f64 x (.f64 x #s(literal -1/2 binary64))) eps)))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (/ 1 (/ (+ x (+ (* (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps)))) (* (+ x (+ (* (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps)))) (- (+ (* (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) x)))) (fma.f64 eps (.f64 #s(literal -1/2 binary64) (.f64 x x)) eps)))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (- (+ (* (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) x) (fma.f64 #s(literal -1/2 binary64) (.f64 (.f64 x (+.f64 eps x)) eps) eps)))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (/ 1 (/ (+ x (+ (* (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps)))) (* (+ x (+ (* (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps)))) (- (+ (* (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) x)))) (fma.f64 eps (.f64 #s(literal -1/2 binary64) (.f64 x (+.f64 eps x))) eps)))
#s(approx (- (sin (+ x eps)) (sin x)) (-.f64 #s(approx (+ (* (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) (fma.f64 eps (fma.f64 x (*.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64)) x)) x))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (sin eps) (fma.f64 (.f64 eps eps) (.f64 (fma.f64 eps (*.f64 eps #s(literal 1/120 binary64)) #s(literal -1/6 binary64)) eps) eps)))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (.f64 (+.f64 x #s(approx (+ (* (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) #s(approx (+ (* eps (+ (* x (* x -1/2)) 1)) x) (+.f64 eps x)))) (-.f64 #s(approx (+ (* (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) #s(approx (+ (* eps (+ (* x (* x -1/2)) 1)) x) (+.f64 eps x))) x)) (/.f64 #s(literal 1 binary64) (+.f64 x #s(approx (+ (* (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) #s(approx (+ (* eps (+ (* x (* x -1/2)) 1)) x) (+.f64 eps x)))))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (- (+ (* (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) x) (fma.f64 eps (fma.f64 #s(literal -1/2 binary64) (.f64 x (+.f64 eps x)) (.f64 eps (.f64 eps (fma.f64 (.f64 x x) #s(literal 1/12 binary64) #s(literal -1/6 binary64))))) eps)))
#s(approx (- (sin (+ x eps)) (sin x)) (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (-.f64 #s(approx (+ (* (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) (fma.f64 eps (fma.f64 #s(literal -1/2 binary64) (*.f64 x x) #s(literal 1 binary64)) x)) x))))
#s(approx (- (sin (+ x eps)) (sin x)) (/.f64 (-.f64 (.f64 #s(approx (+ ( (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) #s(approx (+ (* eps (+ (* x (* x -1/2)) 1)) x) (+.f64 eps x))) #s(approx (+ (* (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) #s(approx (+ (* eps (+ (* x (* x -1/2)) 1)) x) (+.f64 eps x)))) (.f64 (neg.f64 x) (neg.f64 x))) (-.f64 #s(approx (+ ( (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) #s(approx (+ (* eps (+ (* x (* x -1/2)) 1)) x) (+.f64 eps x))) (neg.f64 x))))
#s(approx (- (sin (+ x eps)) (sin x)) (/.f64 #s(literal 1 binary64) (/.f64 (+.f64 x #s(approx (+ (* (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) #s(approx (+ (* eps (+ (* x (* x -1/2)) 1)) x) (+.f64 eps x)))) (.f64 (+.f64 x #s(approx (+ ( (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) #s(approx (+ (* eps (+ (* x (* x -1/2)) 1)) x) (+.f64 eps x)))) (-.f64 #s(approx (+ (* (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) #s(approx (+ (* eps (+ (* x (* x -1/2)) 1)) x) (+.f64 eps x))) x)))))
#s(approx (- (sin (+ x eps)) (sin x)) (/.f64 (fma.f64 #s(approx (+ (* (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) #s(approx (+ (* eps (+ (* x (* x -1/2)) 1)) x) (+.f64 eps x))) (.f64 #s(approx (+ ( (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) #s(approx (+ (* eps (+ (* x (* x -1/2)) 1)) x) (+.f64 eps x))) #s(approx (+ (* (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) #s(approx (+ (* eps (+ (* x (* x -1/2)) 1)) x) (+.f64 eps x)))) (neg.f64 (.f64 x (.f64 x x)))) (fma.f64 x (+.f64 x #s(approx (+ (* (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) #s(approx (+ (* eps (+ (* x (* x -1/2)) 1)) x) (+.f64 eps x)))) (.f64 #s(approx (+ ( (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) #s(approx (+ (* eps (+ (* x (* x -1/2)) 1)) x) (+.f64 eps x))) #s(approx (+ (* (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) #s(approx (+ (* eps (+ (* x (* x -1/2)) 1)) x) (+.f64 eps x)))))))
#s(approx (- (sin (+ x eps)) (sin x)) (/.f64 #s(literal 1 binary64) (/.f64 #s(approx (+ x (+ (* (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps)))) (.f64 x #s(literal 2 binary64))) (.f64 (+.f64 x #s(approx (+ (* (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) (fma.f64 eps (fma.f64 #s(literal -1/2 binary64) (.f64 x x) #s(literal 1 binary64)) x))) (-.f64 #s(approx (+ ( (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) (fma.f64 eps (fma.f64 #s(literal -1/2 binary64) (*.f64 x x) #s(literal 1 binary64)) x)) x)))))
#s(approx (- (sin (+ x eps)) (sin x)) (/.f64 #s(literal 1 binary64) (/.f64 (+.f64 x #s(approx (+ (* (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) (fma.f64 eps (fma.f64 #s(literal -1/2 binary64) (.f64 x x) #s(literal 1 binary64)) x))) (.f64 #s(approx (+ x (+ (* (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps)))) (.f64 x #s(literal 2 binary64))) (-.f64 #s(approx (+ ( (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) (fma.f64 eps (fma.f64 #s(literal -1/2 binary64) (*.f64 x x) #s(literal 1 binary64)) x)) x)))))
#s(approx (- (sin (+ x eps)) (sin x)) (/.f64 (-.f64 (.f64 #s(approx (+ ( (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) (fma.f64 eps (fma.f64 #s(literal -1/2 binary64) (.f64 x x) #s(literal 1 binary64)) x)) #s(approx (+ ( (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) (fma.f64 eps (fma.f64 #s(literal -1/2 binary64) (.f64 x x) #s(literal 1 binary64)) x))) (.f64 (neg.f64 x) (neg.f64 x))) (-.f64 #s(approx (+ (* (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) (fma.f64 eps (fma.f64 #s(literal -1/2 binary64) (*.f64 x x) #s(literal 1 binary64)) x)) (neg.f64 x))))
#s(approx (- (sin (+ x eps)) (sin x)) (/.f64 #s(literal 1 binary64) (/.f64 (+.f64 x #s(approx (+ (* (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) (fma.f64 eps (fma.f64 #s(literal -1/2 binary64) (.f64 x x) #s(literal 1 binary64)) x))) (.f64 (+.f64 x #s(approx (+ (* (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) (fma.f64 eps (fma.f64 #s(literal -1/2 binary64) (.f64 x x) #s(literal 1 binary64)) x))) (-.f64 #s(approx (+ ( (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) (fma.f64 eps (fma.f64 #s(literal -1/2 binary64) (*.f64 x x) #s(literal 1 binary64)) x)) x)))))
#s(approx (- (sin (+ x eps)) (sin x)) (sin.f64 eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 eps (cos.f64 x)))

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

Calls

3 calls:

38.0ms	(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
6.0ms	x
6.0ms	eps

Results

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

Compiler

Compiled 15 to 10 computations (33.3% saved)

regimes22.0ms (0.2%)

Memory

-16.1MiB live, 25.0MiB allocated

Counts

20 → 1

Calls

Call 1

Inputs
#s(approx (/ (/ (- 1/2 (+ (* 1/2 (cos (* (+ x eps) 2))) (+ 1/2 (* -1/2 (cos (+ x x)))))) 2) (* (sin (* (+ (* x 2) eps) 1/2)) (cos (* (+ eps 0) 1/2)))) #s(literal 0 binary64))
#s(approx (- (sin (+ x eps)) (sin x)) (-.f64 #s(approx (+ (* (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) #s(approx (+ (* eps (+ (* x (* x -1/2)) 1)) x) (+.f64 eps x))) x))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (sin eps) (fma.f64 eps (.f64 eps (.f64 eps #s(literal -1/6 binary64))) eps)))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (- (+ (* (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) x) (fma.f64 eps (.f64 x (.f64 x #s(literal -1/2 binary64))) eps)))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (/ 1 (/ (+ x (+ (* (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps)))) (* (+ x (+ (* (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps)))) (- (+ (* (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) x)))) (fma.f64 eps (.f64 #s(literal -1/2 binary64) (.f64 x x)) eps)))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (- (+ (* (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) x) (fma.f64 #s(literal -1/2 binary64) (.f64 (.f64 x (+.f64 eps x)) eps) eps)))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (/ 1 (/ (+ x (+ (* (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps)))) (* (+ x (+ (* (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps)))) (- (+ (* (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) x)))) (fma.f64 eps (.f64 #s(literal -1/2 binary64) (.f64 x (+.f64 eps x))) eps)))
#s(approx (- (sin (+ x eps)) (sin x)) (-.f64 #s(approx (+ (* (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) (fma.f64 eps (fma.f64 x (*.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64)) x)) x))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (sin eps) (fma.f64 (.f64 eps eps) (.f64 (fma.f64 eps (*.f64 eps #s(literal 1/120 binary64)) #s(literal -1/6 binary64)) eps) eps)))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (.f64 (+.f64 x #s(approx (+ (* (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) #s(approx (+ (* eps (+ (* x (* x -1/2)) 1)) x) (+.f64 eps x)))) (-.f64 #s(approx (+ (* (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) #s(approx (+ (* eps (+ (* x (* x -1/2)) 1)) x) (+.f64 eps x))) x)) (/.f64 #s(literal 1 binary64) (+.f64 x #s(approx (+ (* (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) #s(approx (+ (* eps (+ (* x (* x -1/2)) 1)) x) (+.f64 eps x)))))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (- (+ (* (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) x) (fma.f64 eps (fma.f64 #s(literal -1/2 binary64) (.f64 x (+.f64 eps x)) (.f64 eps (.f64 eps (fma.f64 (.f64 x x) #s(literal 1/12 binary64) #s(literal -1/6 binary64))))) eps)))
#s(approx (- (sin (+ x eps)) (sin x)) (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (-.f64 #s(approx (+ (* (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) (fma.f64 eps (fma.f64 #s(literal -1/2 binary64) (*.f64 x x) #s(literal 1 binary64)) x)) x))))
#s(approx (- (sin (+ x eps)) (sin x)) (/.f64 (-.f64 (.f64 #s(approx (+ ( (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) #s(approx (+ (* eps (+ (* x (* x -1/2)) 1)) x) (+.f64 eps x))) #s(approx (+ (* (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) #s(approx (+ (* eps (+ (* x (* x -1/2)) 1)) x) (+.f64 eps x)))) (.f64 (neg.f64 x) (neg.f64 x))) (-.f64 #s(approx (+ ( (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) #s(approx (+ (* eps (+ (* x (* x -1/2)) 1)) x) (+.f64 eps x))) (neg.f64 x))))
#s(approx (- (sin (+ x eps)) (sin x)) (/.f64 #s(literal 1 binary64) (/.f64 (+.f64 x #s(approx (+ (* (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) #s(approx (+ (* eps (+ (* x (* x -1/2)) 1)) x) (+.f64 eps x)))) (.f64 (+.f64 x #s(approx (+ ( (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) #s(approx (+ (* eps (+ (* x (* x -1/2)) 1)) x) (+.f64 eps x)))) (-.f64 #s(approx (+ (* (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) #s(approx (+ (* eps (+ (* x (* x -1/2)) 1)) x) (+.f64 eps x))) x)))))
#s(approx (- (sin (+ x eps)) (sin x)) (/.f64 (fma.f64 #s(approx (+ (* (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) #s(approx (+ (* eps (+ (* x (* x -1/2)) 1)) x) (+.f64 eps x))) (.f64 #s(approx (+ ( (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) #s(approx (+ (* eps (+ (* x (* x -1/2)) 1)) x) (+.f64 eps x))) #s(approx (+ (* (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) #s(approx (+ (* eps (+ (* x (* x -1/2)) 1)) x) (+.f64 eps x)))) (neg.f64 (.f64 x (.f64 x x)))) (fma.f64 x (+.f64 x #s(approx (+ (* (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) #s(approx (+ (* eps (+ (* x (* x -1/2)) 1)) x) (+.f64 eps x)))) (.f64 #s(approx (+ ( (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) #s(approx (+ (* eps (+ (* x (* x -1/2)) 1)) x) (+.f64 eps x))) #s(approx (+ (* (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) #s(approx (+ (* eps (+ (* x (* x -1/2)) 1)) x) (+.f64 eps x)))))))
#s(approx (- (sin (+ x eps)) (sin x)) (/.f64 #s(literal 1 binary64) (/.f64 #s(approx (+ x (+ (* (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps)))) (.f64 x #s(literal 2 binary64))) (.f64 (+.f64 x #s(approx (+ (* (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) (fma.f64 eps (fma.f64 #s(literal -1/2 binary64) (.f64 x x) #s(literal 1 binary64)) x))) (-.f64 #s(approx (+ ( (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) (fma.f64 eps (fma.f64 #s(literal -1/2 binary64) (*.f64 x x) #s(literal 1 binary64)) x)) x)))))
#s(approx (- (sin (+ x eps)) (sin x)) (/.f64 #s(literal 1 binary64) (/.f64 (+.f64 x #s(approx (+ (* (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) (fma.f64 eps (fma.f64 #s(literal -1/2 binary64) (.f64 x x) #s(literal 1 binary64)) x))) (.f64 #s(approx (+ x (+ (* (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps)))) (.f64 x #s(literal 2 binary64))) (-.f64 #s(approx (+ ( (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) (fma.f64 eps (fma.f64 #s(literal -1/2 binary64) (*.f64 x x) #s(literal 1 binary64)) x)) x)))))
#s(approx (- (sin (+ x eps)) (sin x)) (/.f64 (-.f64 (.f64 #s(approx (+ ( (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) (fma.f64 eps (fma.f64 #s(literal -1/2 binary64) (.f64 x x) #s(literal 1 binary64)) x)) #s(approx (+ ( (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) (fma.f64 eps (fma.f64 #s(literal -1/2 binary64) (.f64 x x) #s(literal 1 binary64)) x))) (.f64 (neg.f64 x) (neg.f64 x))) (-.f64 #s(approx (+ (* (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) (fma.f64 eps (fma.f64 #s(literal -1/2 binary64) (*.f64 x x) #s(literal 1 binary64)) x)) (neg.f64 x))))
#s(approx (- (sin (+ x eps)) (sin x)) (/.f64 #s(literal 1 binary64) (/.f64 (+.f64 x #s(approx (+ (* (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) (fma.f64 eps (fma.f64 #s(literal -1/2 binary64) (.f64 x x) #s(literal 1 binary64)) x))) (.f64 (+.f64 x #s(approx (+ (* (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) (fma.f64 eps (fma.f64 #s(literal -1/2 binary64) (.f64 x x) #s(literal 1 binary64)) x))) (-.f64 #s(approx (+ ( (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) (fma.f64 eps (fma.f64 #s(literal -1/2 binary64) (*.f64 x x) #s(literal 1 binary64)) x)) x)))))
#s(approx (- (sin (+ x eps)) (sin x)) (sin.f64 eps))

Outputs

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

Calls

3 calls:

9.0ms	x
6.0ms	(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
6.0ms	eps

Results

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

Compiler

Compiled 15 to 10 computations (33.3% saved)

regimes11.0ms (0.1%)

Memory

15.8MiB live, 15.8MiB allocated

Counts

10 → 1

Calls

Call 1

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

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

Calls

3 calls:

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

Results

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

Compiler

Compiled 15 to 10 computations (33.3% saved)

regimes8.0ms (0.1%)

Memory

11.5MiB live, 11.5MiB allocated

Counts

5 → 1

Calls

Call 1

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

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

Calls

3 calls:

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

Results

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

Compiler

Compiled 15 to 10 computations (33.3% saved)

regimes8.0ms (0.1%)

Memory

-28.0MiB live, 10.7MiB allocated

Counts

3 → 1

Calls

Call 1

Inputs

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

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

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

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

Calls

3 calls:

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

Results

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

Compiler

Compiled 15 to 10 computations (33.3% saved)

regimes5.0ms (0%)

Memory

10.3MiB live, 10.3MiB allocated

Counts

2 → 1

Calls

Call 1

Inputs

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

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

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

Calls

3 calls:

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

Results

Accuracy	Segments	Branch
61.2%	1	`eps`
61.2%	1	`(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))`
61.2%	1	`x`

Compiler

Compiled 15 to 10 computations (33.3% saved)

regimes4.0ms (0%)

Memory

8.7MiB live, 8.7MiB allocated

Accuracy

Total -0.0b remaining (-0%)

Threshold costs -0b (-0%)

Counts

1 → 1

Calls

Call 1

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

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

Calls

3 calls:

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

Results

Accuracy	Segments	Branch
5.5%	1	`x`
5.5%	1	`(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))`
5.5%	1	`eps`

Compiler

Compiled 15 to 10 computations (33.3% saved)

simplify13.0ms (0.1%)

Memory

16.3MiB live, 16.3MiB allocated

Algorithm

1×	egg-herbie

Rules

74×	`*-commutative_binary64`
18×	`+-commutative_binary64`
16×	`sub-neg_binary64`
10×	`neg-sub0_binary64`
10×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	141	533
1	188	533
2	205	533
3	215	533
4	221	533
5	222	533

Stop Event

1×

saturated

Calls

Call 1

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

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

soundness1.4s (9.8%)

Memory

4.5MiB live, 831.6MiB allocated

Rules

16 678×	`lower-fma.f64`
16 678×	`lower-fma.f32`
11 892×	`lower-fma.f64`
11 892×	`lower-fma.f32`
9 540×	`lower-fma.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	16
0	10	16
1	53	16
2	380	16
3	4766	16
0	8210	16
0	75	374
0	109	309
1	437	255
0	3980	251
0	629	6443
1	2043	5926
2	6093	5775
0	8199	5322
0	107	496
1	314	496
2	775	489
3	2836	489
4	6173	489
0	8126	458
0	780	8306
1	2550	7133
0	8863	6630

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

Compiler

Compiled 477 to 232 computations (51.4% saved)

preprocess132.0ms (0.9%)

Memory: -0.4MiB live, 196.3MiB allocated
Compiler: Compiled 636 to 228 computations (64.2% saved)

end0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated

Iter	Nodes	Cost
0	18	39
1	38	35
2	86	35
3	169	35
4	310	35
5	367	35
6	445	35
7	482	35
8	491	35
0	6	7
0	10	7
1	13	7
2	18	7
3	24	7
4	32	7
5	47	7
6	80	7
7	107	7
8	151	7
9	166	7
10	174	7
0	174	7

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

Iter	Nodes	Cost
0	18	39
1	38	35
2	86	35
3	169	35
4	310	35
5	367	35
6	445	35
7	482	35
8	491	35
0	6	7
0	10	7
1	13	7
2	18	7
3	24	7
4	32	7
5	47	7
6	80	7
7	107	7
8	151	7
9	166	7
10	174	7
0	174	7

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

analyze40.0ms (0.3%)

sample5.8s (40.1%)

preprocess28.0ms (0.2%)

explain82.0ms (0.6%)

eval0.0ms (0%)

prune1.0ms (0%)

simplify9.0ms (0.1%)

localize50.0ms (0.3%)

series4.0ms (0%)

simplify345.0ms (2.4%)

rewrite432.0ms (3%)

eval69.0ms (0.5%)

prune70.0ms (0.5%)

simplify462.0ms (3.2%)

localize366.0ms (2.5%)

series58.0ms (0.4%)

simplify342.0ms (2.4%)

rewrite140.0ms (1%)

eval159.0ms (1.1%)

prune112.0ms (0.8%)

simplify297.0ms (2.1%)

localize459.0ms (3.2%)

series54.0ms (0.4%)

simplify367.0ms (2.5%)

rewrite193.0ms (1.3%)

eval112.0ms (0.8%)

prune120.0ms (0.8%)

simplify314.0ms (2.2%)

localize753.0ms (5.2%)

series129.0ms (0.9%)

simplify426.0ms (3%)

rewrite308.0ms (2.1%)

eval217.0ms (1.5%)

prune181.0ms (1.3%)

regimes44.0ms (0.3%)

regimes44.0ms (0.3%)

regimes50.0ms (0.3%)

regimes42.0ms (0.3%)

regimes43.0ms (0.3%)

regimes24.0ms (0.2%)

regimes22.0ms (0.2%)

regimes51.0ms (0.4%)

regimes22.0ms (0.2%)

regimes11.0ms (0.1%)

regimes8.0ms (0.1%)

regimes8.0ms (0.1%)

regimes5.0ms (0%)

regimes4.0ms (0%)

simplify13.0ms (0.1%)

soundness1.4s (9.8%)

preprocess132.0ms (0.9%)

end0.0ms (0%)

Profiling

Iter	Nodes	Cost
0	18	39
1	38	35
2	86	35
3	169	35
4	310	35
5	367	35
6	445	35
7	482	35
8	491	35
0	6	7
0	10	7
1	13	7
2	18	7
3	24	7
4	32	7
5	47	7
6	80	7
7	107	7
8	151	7
9	166	7
10	174	7
0	174	7

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