Metrics for 2sin (example 3.3)

start0.0ms (0%)

Memory: 0.1MiB live, 0.1MiB allocated

analyze46.0ms (0.4%)

Memory

-10.0MiB live, 68.5MiB allocated

Algorithm

1×

Search

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

Compiler

Compiled 27 to 19 computations (29.6% saved)

sample6.5s (52%)

Memory

-117.1MiB live, 6 838.9MiB allocated

Samples

3.3s	26 025×	0	invalid
951.0ms	5 495×	0	valid
455.0ms	2 761×	1	valid

Precisions

Click to see histograms. Total time spent on operations: 3.1s

ival-sin: 689.0ms (22.2% of total)

const: 671.0ms (21.6% of total)

ival-fabs: 385.0ms (12.4% of total)

ival-add: 305.0ms (9.8% of total)

ival-<=: 265.0ms (8.5% of total)

ival-mult: 237.0ms (7.6% of total)

ival-sub: 164.0ms (5.3% of total)

ival-<: 160.0ms (5.1% of total)

ival-and: 104.0ms (3.3% of total)

adjust: 71.0ms (2.3% of total)

exact: 45.0ms (1.4% of total)

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

Bogosity

explain103.0ms (0.8%)

Memory

-56.5MiB live, 150.8MiB allocated

FPErrors

Click to see full error table

Ground Truth	Overpredictions	Example	Underpredictions	Example	Subexpression
221	1	(4.7051946720034294e-281 2.413098295469309e-283)	3	(-2.570792754780557e-38 4.171590678617577e-40)	`(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))`
2	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	219	5
`sin.f64`	`(sin.f64 (+.f64 x eps))`	sensitivity	2	1

Confusion

	Predicted +	Predicted -
+	219	3
-	1	33

Precision

0.9954545454545455

Recall

0.9864864864864865

Confusion?

	Predicted +	Predicted Maybe	Predicted -
+	219	3	0
-	1	2	31

Precision?

0.9866666666666667

Recall?

1.0

Freqs

test

number	freq
0	36
1	219
2	1

Total Confusion?

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

Precision?

1.0

Recall?

1.0

Samples

18.0ms	372×	0	valid
13.0ms	138×	1	valid
1.0ms	2×	3	valid

Compiler

Compiled 47 to 22 computations (53.2% saved)

Precisions

Click to see histograms. Total time spent on operations: 18.0ms

ival-sin: 9.0ms (50.7% of total)

adjust: 3.0ms (16.9% of total)

ival-add: 3.0ms (16.9% of total)

ival-sub: 3.0ms (16.9% of total)

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

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

preprocess24.0ms (0.2%)

Memory

-10.9MiB live, 31.0MiB 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))
(-.f64 (sin.f64 (+.f64 eps x)) (sin.f64 x))

Compiler

Compiled 7 to 6 computations (14.3% saved)

eval0.0ms (0%)

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

prune0.0ms (0%)

Memory

1.2MiB live, 1.2MiB allocated

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	65.5%	(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))

Compiler

Compiled 7 to 6 computations (14.3% saved)

simplify6.0ms (0.1%)

Memory

10.8MiB live, 10.8MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 4 expressions of interest:

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

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

localize23.0ms (0.2%)

Memory

4.5MiB live, 43.4MiB allocated

Localize:

Found 4 expressions of interest:

New	Metric	Score
accuracy	0	(+.f64 x eps)
accuracy	0	(sin.f64 x)
accuracy	0.09797445325152507	(sin.f64 (+.f64 x eps))
accuracy	21.954237914132744	(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))

Samples

10.0ms	186×	0	valid
7.0ms	69×	1	valid
0.0ms	1×	3	valid

Compiler

Compiled 20 to 8 computations (60% saved)

Precisions

Click to see histograms. Total time spent on operations: 11.0ms

ival-sin: 6.0ms (55.5% of total)

ival-add: 2.0ms (18.5% of total)

adjust: 1.0ms (9.2% of total)

ival-sub: 1.0ms (9.2% of total)

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

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

series6.0ms (0%)

Memory

-29.5MiB live, 9.5MiB 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 (* eps (cos x)) (taylor 0 eps) (#s(alt (-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) (patch (-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) #<representation binary64>) () ())) ())
#s(alt (* eps (+ (cos x) (* -1/2 (* eps (sin x))))) (taylor 0 eps) (#s(alt (-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) (patch (-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) #<representation binary64>) () ())) ())
#s(alt (* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x))))))) (taylor 0 eps) (#s(alt (-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) (patch (-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) #<representation binary64>) () ())) ())
#s(alt (* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* eps (+ (* -1/6 (cos x)) (* 1/24 (* eps (sin x))))))))) (taylor 0 eps) (#s(alt (-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) (patch (-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) #<representation binary64>) () ())) ())
#s(alt (sin x) (taylor 0 eps) (#s(alt (sin.f64 (+.f64 x eps)) (patch (sin.f64 (+.f64 x eps)) #<representation binary64>) () ())) ())
#s(alt (+ (sin x) (* eps (cos x))) (taylor 0 eps) (#s(alt (sin.f64 (+.f64 x eps)) (patch (sin.f64 (+.f64 x eps)) #<representation binary64>) () ())) ())
#s(alt (+ (sin x) (* eps (+ (cos x) (* -1/2 (* eps (sin x)))))) (taylor 0 eps) (#s(alt (sin.f64 (+.f64 x eps)) (patch (sin.f64 (+.f64 x eps)) #<representation binary64>) () ())) ())
#s(alt (+ (sin x) (* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x)))))))) (taylor 0 eps) (#s(alt (sin.f64 (+.f64 x eps)) (patch (sin.f64 (+.f64 x eps)) #<representation binary64>) () ())) ())
#s(alt x (taylor 0 eps) (#s(alt (+.f64 x eps) (patch (+.f64 x eps) #<representation binary64>) () ())) ())
#s(alt (+ eps x) (taylor 0 eps) (#s(alt (+.f64 x eps) (patch (+.f64 x eps) #<representation binary64>) () ())) ())
#s(alt (+ eps x) (taylor 0 eps) (#s(alt (+.f64 x eps) (patch (+.f64 x eps) #<representation binary64>) () ())) ())
#s(alt (+ eps x) (taylor 0 eps) (#s(alt (+.f64 x eps) (patch (+.f64 x eps) #<representation binary64>) () ())) ())
#s(alt (- (sin (+ eps x)) (sin x)) (taylor inf eps) (#s(alt (-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) (patch (-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) #<representation binary64>) () ())) ())
#s(alt (- (sin (+ eps x)) (sin x)) (taylor inf eps) (#s(alt (-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) (patch (-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) #<representation binary64>) () ())) ())
#s(alt (- (sin (+ eps x)) (sin x)) (taylor inf eps) (#s(alt (-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) (patch (-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) #<representation binary64>) () ())) ())
#s(alt (- (sin (+ eps x)) (sin x)) (taylor inf eps) (#s(alt (-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) (patch (-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) #<representation binary64>) () ())) ())
#s(alt (sin (+ eps x)) (taylor inf eps) (#s(alt (sin.f64 (+.f64 x eps)) (patch (sin.f64 (+.f64 x eps)) #<representation binary64>) () ())) ())
#s(alt (sin (+ eps x)) (taylor inf eps) (#s(alt (sin.f64 (+.f64 x eps)) (patch (sin.f64 (+.f64 x eps)) #<representation binary64>) () ())) ())
#s(alt (sin (+ eps x)) (taylor inf eps) (#s(alt (sin.f64 (+.f64 x eps)) (patch (sin.f64 (+.f64 x eps)) #<representation binary64>) () ())) ())
#s(alt (sin (+ eps x)) (taylor inf eps) (#s(alt (sin.f64 (+.f64 x eps)) (patch (sin.f64 (+.f64 x eps)) #<representation binary64>) () ())) ())
#s(alt eps (taylor inf eps) (#s(alt (+.f64 x eps) (patch (+.f64 x eps) #<representation binary64>) () ())) ())
#s(alt (* eps (+ 1 (/ x eps))) (taylor inf eps) (#s(alt (+.f64 x eps) (patch (+.f64 x eps) #<representation binary64>) () ())) ())
#s(alt (* eps (+ 1 (/ x eps))) (taylor inf eps) (#s(alt (+.f64 x eps) (patch (+.f64 x eps) #<representation binary64>) () ())) ())
#s(alt (* eps (+ 1 (/ x eps))) (taylor inf eps) (#s(alt (+.f64 x eps) (patch (+.f64 x eps) #<representation binary64>) () ())) ())
#s(alt (- (sin (- x (* -1 eps))) (sin x)) (taylor -inf eps) (#s(alt (-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) (patch (-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) #<representation binary64>) () ())) ())
#s(alt (- (sin (- x (* -1 eps))) (sin x)) (taylor -inf eps) (#s(alt (-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) (patch (-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) #<representation binary64>) () ())) ())
#s(alt (- (sin (- x (* -1 eps))) (sin x)) (taylor -inf eps) (#s(alt (-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) (patch (-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) #<representation binary64>) () ())) ())
#s(alt (- (sin (- x (* -1 eps))) (sin x)) (taylor -inf eps) (#s(alt (-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) (patch (-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) #<representation binary64>) () ())) ())
#s(alt (sin (- x (* -1 eps))) (taylor -inf eps) (#s(alt (sin.f64 (+.f64 x eps)) (patch (sin.f64 (+.f64 x eps)) #<representation binary64>) () ())) ())
#s(alt (sin (- x (* -1 eps))) (taylor -inf eps) (#s(alt (sin.f64 (+.f64 x eps)) (patch (sin.f64 (+.f64 x eps)) #<representation binary64>) () ())) ())
#s(alt (sin (- x (* -1 eps))) (taylor -inf eps) (#s(alt (sin.f64 (+.f64 x eps)) (patch (sin.f64 (+.f64 x eps)) #<representation binary64>) () ())) ())
#s(alt (sin (- x (* -1 eps))) (taylor -inf eps) (#s(alt (sin.f64 (+.f64 x eps)) (patch (sin.f64 (+.f64 x eps)) #<representation binary64>) () ())) ())
#s(alt eps (taylor -inf eps) (#s(alt (+.f64 x eps) (patch (+.f64 x eps) #<representation binary64>) () ())) ())
#s(alt (* -1 (* eps (- (* -1 (/ x eps)) 1))) (taylor -inf eps) (#s(alt (+.f64 x eps) (patch (+.f64 x eps) #<representation binary64>) () ())) ())
#s(alt (* -1 (* eps (- (* -1 (/ x eps)) 1))) (taylor -inf eps) (#s(alt (+.f64 x eps) (patch (+.f64 x eps) #<representation binary64>) () ())) ())
#s(alt (* -1 (* eps (- (* -1 (/ x eps)) 1))) (taylor -inf eps) (#s(alt (+.f64 x eps) (patch (+.f64 x eps) #<representation binary64>) () ())) ())
#s(alt (sin eps) (taylor 0 x) (#s(alt (-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) (patch (-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) #<representation binary64>) () ())) ())
#s(alt (+ (sin eps) (* x (- (cos eps) 1))) (taylor 0 x) (#s(alt (-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) (patch (-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) #<representation binary64>) () ())) ())
#s(alt (+ (sin eps) (* x (- (+ (cos eps) (* -1/2 (* x (sin eps)))) 1))) (taylor 0 x) (#s(alt (-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) (patch (-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) #<representation binary64>) () ())) ())
#s(alt (+ (sin eps) (* x (- (+ (cos eps) (* x (+ (* -1/2 (sin eps)) (* x (+ 1/6 (* -1/6 (cos eps))))))) 1))) (taylor 0 x) (#s(alt (-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) (patch (-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) #<representation binary64>) () ())) ())
#s(alt (sin eps) (taylor 0 x) (#s(alt (sin.f64 (+.f64 x eps)) (patch (sin.f64 (+.f64 x eps)) #<representation binary64>) () ())) ())
#s(alt (+ (sin eps) (* x (cos eps))) (taylor 0 x) (#s(alt (sin.f64 (+.f64 x eps)) (patch (sin.f64 (+.f64 x eps)) #<representation binary64>) () ())) ())
#s(alt (+ (sin eps) (* x (+ (cos eps) (* -1/2 (* x (sin eps)))))) (taylor 0 x) (#s(alt (sin.f64 (+.f64 x eps)) (patch (sin.f64 (+.f64 x eps)) #<representation binary64>) () ())) ())
#s(alt (+ (sin eps) (* x (+ (cos eps) (* x (+ (* -1/2 (sin eps)) (* -1/6 (* x (cos eps)))))))) (taylor 0 x) (#s(alt (sin.f64 (+.f64 x eps)) (patch (sin.f64 (+.f64 x eps)) #<representation binary64>) () ())) ())
#s(alt eps (taylor 0 x) (#s(alt (+.f64 x eps) (patch (+.f64 x eps) #<representation binary64>) () ())) ())
#s(alt (+ eps x) (taylor 0 x) (#s(alt (+.f64 x eps) (patch (+.f64 x eps) #<representation binary64>) () ())) ())
#s(alt (+ eps x) (taylor 0 x) (#s(alt (+.f64 x eps) (patch (+.f64 x eps) #<representation binary64>) () ())) ())
#s(alt (+ eps x) (taylor 0 x) (#s(alt (+.f64 x eps) (patch (+.f64 x eps) #<representation binary64>) () ())) ())
#s(alt x (taylor 0 x) (#s(alt (sin.f64 x) (patch (sin.f64 x) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1 (* -1/6 (pow x 2)))) (taylor 0 x) (#s(alt (sin.f64 x) (patch (sin.f64 x) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1 (* (pow x 2) (- (* 1/120 (pow x 2)) 1/6)))) (taylor 0 x) (#s(alt (sin.f64 x) (patch (sin.f64 x) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/120 (* -1/5040 (pow x 2)))) 1/6)))) (taylor 0 x) (#s(alt (sin.f64 x) (patch (sin.f64 x) #<representation binary64>) () ())) ())
#s(alt (- (sin (+ eps x)) (sin x)) (taylor inf x) (#s(alt (-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) (patch (-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) #<representation binary64>) () ())) ())
#s(alt (- (sin (+ eps x)) (sin x)) (taylor inf x) (#s(alt (-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) (patch (-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) #<representation binary64>) () ())) ())
#s(alt (- (sin (+ eps x)) (sin x)) (taylor inf x) (#s(alt (-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) (patch (-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) #<representation binary64>) () ())) ())
#s(alt (- (sin (+ eps x)) (sin x)) (taylor inf x) (#s(alt (-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) (patch (-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) #<representation binary64>) () ())) ())
#s(alt (sin (+ eps x)) (taylor inf x) (#s(alt (sin.f64 (+.f64 x eps)) (patch (sin.f64 (+.f64 x eps)) #<representation binary64>) () ())) ())
#s(alt (sin (+ eps x)) (taylor inf x) (#s(alt (sin.f64 (+.f64 x eps)) (patch (sin.f64 (+.f64 x eps)) #<representation binary64>) () ())) ())
#s(alt (sin (+ eps x)) (taylor inf x) (#s(alt (sin.f64 (+.f64 x eps)) (patch (sin.f64 (+.f64 x eps)) #<representation binary64>) () ())) ())
#s(alt (sin (+ eps x)) (taylor inf x) (#s(alt (sin.f64 (+.f64 x eps)) (patch (sin.f64 (+.f64 x eps)) #<representation binary64>) () ())) ())
#s(alt x (taylor inf x) (#s(alt (+.f64 x eps) (patch (+.f64 x eps) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1 (/ eps x))) (taylor inf x) (#s(alt (+.f64 x eps) (patch (+.f64 x eps) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1 (/ eps x))) (taylor inf x) (#s(alt (+.f64 x eps) (patch (+.f64 x eps) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1 (/ eps x))) (taylor inf x) (#s(alt (+.f64 x eps) (patch (+.f64 x eps) #<representation binary64>) () ())) ())
#s(alt (sin x) (taylor inf x) (#s(alt (sin.f64 x) (patch (sin.f64 x) #<representation binary64>) () ())) ())
#s(alt (sin x) (taylor inf x) (#s(alt (sin.f64 x) (patch (sin.f64 x) #<representation binary64>) () ())) ())
#s(alt (sin x) (taylor inf x) (#s(alt (sin.f64 x) (patch (sin.f64 x) #<representation binary64>) () ())) ())
#s(alt (sin x) (taylor inf x) (#s(alt (sin.f64 x) (patch (sin.f64 x) #<representation binary64>) () ())) ())
#s(alt (- (sin (- eps (* -1 x))) (sin x)) (taylor -inf x) (#s(alt (-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) (patch (-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) #<representation binary64>) () ())) ())
#s(alt (- (sin (- eps (* -1 x))) (sin x)) (taylor -inf x) (#s(alt (-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) (patch (-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) #<representation binary64>) () ())) ())
#s(alt (- (sin (- eps (* -1 x))) (sin x)) (taylor -inf x) (#s(alt (-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) (patch (-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) #<representation binary64>) () ())) ())
#s(alt (- (sin (- eps (* -1 x))) (sin x)) (taylor -inf x) (#s(alt (-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) (patch (-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) #<representation binary64>) () ())) ())
#s(alt (sin (- eps (* -1 x))) (taylor -inf x) (#s(alt (sin.f64 (+.f64 x eps)) (patch (sin.f64 (+.f64 x eps)) #<representation binary64>) () ())) ())
#s(alt (sin (- eps (* -1 x))) (taylor -inf x) (#s(alt (sin.f64 (+.f64 x eps)) (patch (sin.f64 (+.f64 x eps)) #<representation binary64>) () ())) ())
#s(alt (sin (- eps (* -1 x))) (taylor -inf x) (#s(alt (sin.f64 (+.f64 x eps)) (patch (sin.f64 (+.f64 x eps)) #<representation binary64>) () ())) ())
#s(alt (sin (- eps (* -1 x))) (taylor -inf x) (#s(alt (sin.f64 (+.f64 x eps)) (patch (sin.f64 (+.f64 x eps)) #<representation binary64>) () ())) ())
#s(alt x (taylor -inf x) (#s(alt (+.f64 x eps) (patch (+.f64 x eps) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (- (* -1 (/ eps x)) 1))) (taylor -inf x) (#s(alt (+.f64 x eps) (patch (+.f64 x eps) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (- (* -1 (/ eps x)) 1))) (taylor -inf x) (#s(alt (+.f64 x eps) (patch (+.f64 x eps) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (- (* -1 (/ eps x)) 1))) (taylor -inf x) (#s(alt (+.f64 x eps) (patch (+.f64 x eps) #<representation binary64>) () ())) ())
#s(alt (sin x) (taylor -inf x) (#s(alt (sin.f64 x) (patch (sin.f64 x) #<representation binary64>) () ())) ())
#s(alt (sin x) (taylor -inf x) (#s(alt (sin.f64 x) (patch (sin.f64 x) #<representation binary64>) () ())) ())
#s(alt (sin x) (taylor -inf x) (#s(alt (sin.f64 x) (patch (sin.f64 x) #<representation binary64>) () ())) ())
#s(alt (sin x) (taylor -inf x) (#s(alt (sin.f64 x) (patch (sin.f64 x) #<representation binary64>) () ())) ())

Calls

6 calls:

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

simplify142.0ms (1.1%)

Memory

22.1MiB live, 176.0MiB 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	2829	489
4	6198	489
0	8141	458

Stop Event

1×	iter limit
1×	node limit

Counts

84 → 77

Calls

Call 1

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

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

rewrite176.0ms (1.4%)

Memory

-1.1MiB live, 189.8MiB allocated

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
(*.f64 (pow.f64 (/.f64 (fma.f64 (+.f64 (sin.f64 x) (sin.f64 (+.f64 eps x))) (sin.f64 x) (pow.f64 (sin.f64 (+.f64 eps x)) #s(literal 2 binary64))) (-.f64 (pow.f64 (sin.f64 (+.f64 eps x)) #s(literal 6 binary64)) (pow.f64 (sin.f64 x) #s(literal 6 binary64)))) #s(literal -1 binary64)) (pow.f64 (-.f64 (pow.f64 (sin.f64 (+.f64 eps x)) #s(literal 3 binary64)) (pow.f64 (sin.f64 x) #s(literal 3 binary64))) #s(literal -1 binary64)))
(.f64 (pow.f64 (/.f64 (fma.f64 (+.f64 (sin.f64 x) (sin.f64 (+.f64 eps x))) (sin.f64 x) (pow.f64 (sin.f64 (+.f64 eps x)) #s(literal 2 binary64))) (-.f64 (pow.f64 (sin.f64 (+.f64 eps x)) #s(literal 9 binary64)) (pow.f64 (sin.f64 x) #s(literal 9 binary64)))) #s(literal -1 binary64)) (pow.f64 (+.f64 (pow.f64 (sin.f64 (+.f64 eps x)) #s(literal 6 binary64)) (+.f64 (pow.f64 (.f64 (sin.f64 x) (sin.f64 (+.f64 eps x))) #s(literal 3 binary64)) (pow.f64 (sin.f64 x) #s(literal 6 binary64)))) #s(literal -1 binary64)))
(*.f64 (pow.f64 (/.f64 (+.f64 (sin.f64 x) (sin.f64 (+.f64 eps x))) (-.f64 (pow.f64 (sin.f64 (+.f64 eps x)) #s(literal 4 binary64)) (pow.f64 (sin.f64 x) #s(literal 4 binary64)))) #s(literal -1 binary64)) (pow.f64 (fma.f64 (sin.f64 x) (sin.f64 x) (pow.f64 (sin.f64 (+.f64 eps x)) #s(literal 2 binary64))) #s(literal -1 binary64)))
(.f64 (pow.f64 (/.f64 (+.f64 (sin.f64 x) (sin.f64 (+.f64 eps x))) (-.f64 (pow.f64 (sin.f64 (+.f64 eps x)) #s(literal 6 binary64)) (pow.f64 (sin.f64 x) #s(literal 6 binary64)))) #s(literal -1 binary64)) (pow.f64 (+.f64 (+.f64 (pow.f64 (.f64 (sin.f64 x) (sin.f64 (+.f64 eps x))) #s(literal 2 binary64)) (pow.f64 (sin.f64 x) #s(literal 4 binary64))) (pow.f64 (sin.f64 (+.f64 eps x)) #s(literal 4 binary64))) #s(literal -1 binary64)))
(.f64 (pow.f64 (/.f64 #s(literal 2 binary64) (+.f64 (sin.f64 x) (sin.f64 (+.f64 eps x)))) #s(literal -1 binary64)) (pow.f64 (/.f64 (.f64 (cos.f64 (/.f64 (+.f64 #s(literal 0 binary64) eps) #s(literal -2 binary64))) (sin.f64 (*.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps)))) (-.f64 (sin.f64 (+.f64 eps x)) (sin.f64 x))) #s(literal -1 binary64)))
(.f64 (/.f64 (-.f64 (pow.f64 (sin.f64 (+.f64 eps x)) #s(literal 3 binary64)) (pow.f64 (sin.f64 x) #s(literal 3 binary64))) (-.f64 (pow.f64 (sin.f64 (+.f64 eps x)) #s(literal 4 binary64)) (pow.f64 (.f64 (+.f64 (sin.f64 x) (sin.f64 (+.f64 eps x))) (sin.f64 x)) #s(literal 2 binary64)))) (-.f64 (pow.f64 (sin.f64 (+.f64 eps x)) #s(literal 2 binary64)) (*.f64 (+.f64 (sin.f64 x) (sin.f64 (+.f64 eps x))) (sin.f64 x))))
(.f64 (/.f64 (-.f64 (pow.f64 (sin.f64 (+.f64 eps x)) #s(literal 3 binary64)) (pow.f64 (sin.f64 x) #s(literal 3 binary64))) (+.f64 (pow.f64 (.f64 (+.f64 (sin.f64 x) (sin.f64 (+.f64 eps x))) (sin.f64 x)) #s(literal 3 binary64)) (pow.f64 (sin.f64 (+.f64 eps x)) #s(literal 6 binary64)))) (fma.f64 (.f64 (+.f64 (sin.f64 x) (sin.f64 (+.f64 eps x))) (sin.f64 x)) (-.f64 (.f64 (+.f64 (sin.f64 x) (sin.f64 (+.f64 eps x))) (sin.f64 x)) (pow.f64 (sin.f64 (+.f64 eps x)) #s(literal 2 binary64))) (pow.f64 (sin.f64 (+.f64 eps x)) #s(literal 4 binary64))))
(*.f64 (/.f64 (-.f64 (pow.f64 (sin.f64 (+.f64 eps x)) #s(literal 2 binary64)) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (-.f64 (pow.f64 (sin.f64 (+.f64 eps x)) #s(literal 2 binary64)) (pow.f64 (sin.f64 x) #s(literal 2 binary64)))) (-.f64 (sin.f64 (+.f64 eps x)) (sin.f64 x)))
(*.f64 (/.f64 (-.f64 (pow.f64 (sin.f64 (+.f64 eps x)) #s(literal 2 binary64)) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (-.f64 (pow.f64 (sin.f64 (+.f64 eps x)) #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 eps x))) (pow.f64 (sin.f64 (+.f64 eps x)) #s(literal 2 binary64))))
(.f64 (.f64 #s(literal 2 binary64) (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64)))) (sin.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 0 binary64) eps))))
(.f64 (/.f64 (+.f64 (sin.f64 x) (sin.f64 (+.f64 eps x))) #s(literal 2 binary64)) (/.f64 (-.f64 (sin.f64 (+.f64 eps x)) (sin.f64 x)) (.f64 (cos.f64 (/.f64 (+.f64 #s(literal 0 binary64) eps) #s(literal -2 binary64))) (sin.f64 (*.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps))))))
(.f64 (.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 0 binary64) eps))) #s(literal 2 binary64)) (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64))))
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(sin.f64 (+.f64 eps x))
(-.f64 (.f64 (sin.f64 (/.f64 (.f64 eps eps) (-.f64 eps x))) (cos.f64 (/.f64 (.f64 x x) (-.f64 eps x)))) (.f64 (cos.f64 (/.f64 (.f64 eps eps) (-.f64 eps x))) (sin.f64 (/.f64 (.f64 x x) (-.f64 eps x)))))
(-.f64 (/.f64 (pow.f64 (.f64 (cos.f64 eps) (sin.f64 x)) #s(literal 2 binary64)) (sin.f64 (-.f64 x eps))) (/.f64 (pow.f64 (.f64 (sin.f64 eps) (cos.f64 x)) #s(literal 2 binary64)) (sin.f64 (-.f64 x eps))))
(-.f64 (.f64 (sin.f64 (.f64 x (/.f64 x (-.f64 x eps)))) (cos.f64 (.f64 eps (/.f64 eps (-.f64 x eps))))) (.f64 (cos.f64 (.f64 x (/.f64 x (-.f64 x eps)))) (sin.f64 (.f64 eps (/.f64 eps (-.f64 x eps))))))
(+.f64 (.f64 (sin.f64 (.f64 x (/.f64 x (-.f64 x eps)))) (cos.f64 (neg.f64 (.f64 eps (/.f64 eps (-.f64 x eps)))))) (.f64 (cos.f64 (.f64 x (/.f64 x (-.f64 x eps)))) (sin.f64 (neg.f64 (.f64 eps (/.f64 eps (-.f64 x eps)))))))
(+.f64 (.f64 (sin.f64 eps) (cos.f64 x)) (.f64 (cos.f64 eps) (sin.f64 x)))
(+.f64 (.f64 (cos.f64 eps) (sin.f64 x)) (.f64 (sin.f64 eps) (cos.f64 x)))
(exp.f64 (*.f64 (log.f64 (sin.f64 (+.f64 eps x))) #s(literal 1 binary64)))
(.f64 (pow.f64 (/.f64 (fma.f64 (-.f64 eps x) eps (.f64 x x)) (-.f64 (pow.f64 x #s(literal 6 binary64)) (pow.f64 eps #s(literal 6 binary64)))) #s(literal -1 binary64)) (pow.f64 (-.f64 (pow.f64 x #s(literal 3 binary64)) (pow.f64 eps #s(literal 3 binary64))) #s(literal -1 binary64)))
(.f64 (pow.f64 (/.f64 (fma.f64 (-.f64 eps x) eps (.f64 x x)) (+.f64 (pow.f64 eps #s(literal 9 binary64)) (pow.f64 x #s(literal 9 binary64)))) #s(literal -1 binary64)) (pow.f64 (-.f64 (+.f64 (pow.f64 x #s(literal 6 binary64)) (pow.f64 eps #s(literal 6 binary64))) (pow.f64 (*.f64 eps x) #s(literal 3 binary64))) #s(literal -1 binary64)))
(.f64 (pow.f64 (/.f64 (-.f64 x eps) (-.f64 (pow.f64 x #s(literal 4 binary64)) (pow.f64 eps #s(literal 4 binary64)))) #s(literal -1 binary64)) (pow.f64 (fma.f64 eps eps (.f64 x x)) #s(literal -1 binary64)))
(.f64 (pow.f64 (/.f64 (-.f64 x eps) (-.f64 (pow.f64 x #s(literal 6 binary64)) (pow.f64 eps #s(literal 6 binary64)))) #s(literal -1 binary64)) (pow.f64 (fma.f64 (.f64 eps eps) (fma.f64 eps eps (*.f64 x x)) (pow.f64 x #s(literal 4 binary64))) #s(literal -1 binary64)))
(.f64 (/.f64 (.f64 (-.f64 x eps) (+.f64 eps x)) (-.f64 (pow.f64 x #s(literal 3 binary64)) (pow.f64 eps #s(literal 3 binary64)))) (fma.f64 eps (+.f64 eps x) (*.f64 x x)))
(.f64 (/.f64 (+.f64 (pow.f64 eps #s(literal 3 binary64)) (pow.f64 x #s(literal 3 binary64))) (-.f64 (pow.f64 x #s(literal 4 binary64)) (pow.f64 (.f64 (-.f64 eps x) eps) #s(literal 2 binary64)))) (-.f64 (.f64 x x) (.f64 (-.f64 eps x) eps)))
(.f64 (/.f64 (+.f64 (pow.f64 eps #s(literal 3 binary64)) (pow.f64 x #s(literal 3 binary64))) (+.f64 (pow.f64 (.f64 (-.f64 eps x) eps) #s(literal 3 binary64)) (pow.f64 x #s(literal 6 binary64)))) (fma.f64 (.f64 (-.f64 eps x) eps) (-.f64 (.f64 (-.f64 eps x) eps) (*.f64 x x)) (pow.f64 x #s(literal 4 binary64))))
(.f64 (/.f64 (.f64 (-.f64 x eps) (+.f64 eps x)) (*.f64 (-.f64 x eps) (+.f64 eps x))) (+.f64 eps x))
(.f64 (.f64 (+.f64 eps x) (-.f64 eps x)) (pow.f64 (-.f64 eps x) #s(literal -1 binary64)))
(.f64 (pow.f64 (-.f64 x eps) #s(literal -1 binary64)) (pow.f64 (pow.f64 (.f64 (-.f64 x eps) (+.f64 eps x)) #s(literal -1 binary64)) #s(literal -1 binary64)))
(.f64 (pow.f64 (-.f64 x eps) #s(literal -1 binary64)) (.f64 (-.f64 x eps) (+.f64 eps x)))
(.f64 (pow.f64 (fma.f64 (-.f64 eps x) eps (.f64 x x)) #s(literal -1 binary64)) (pow.f64 (pow.f64 (+.f64 (pow.f64 eps #s(literal 3 binary64)) (pow.f64 x #s(literal 3 binary64))) #s(literal -1 binary64)) #s(literal -1 binary64)))
(.f64 (pow.f64 (fma.f64 (-.f64 eps x) eps (.f64 x x)) #s(literal -1 binary64)) (+.f64 (pow.f64 eps #s(literal 3 binary64)) (pow.f64 x #s(literal 3 binary64))))
(*.f64 #s(literal 1 binary64) (+.f64 eps x))
(.f64 (neg.f64 (.f64 (-.f64 x eps) (+.f64 eps x))) (pow.f64 (neg.f64 (-.f64 x eps)) #s(literal -1 binary64)))
(.f64 (neg.f64 (+.f64 (pow.f64 eps #s(literal 3 binary64)) (pow.f64 x #s(literal 3 binary64)))) (pow.f64 (neg.f64 (fma.f64 (-.f64 eps x) eps (.f64 x x))) #s(literal -1 binary64)))
(.f64 (.f64 (-.f64 x eps) (+.f64 eps x)) (pow.f64 (-.f64 x eps) #s(literal -1 binary64)))
(.f64 (fma.f64 (-.f64 eps x) eps (.f64 x x)) (/.f64 (+.f64 eps x) (fma.f64 (-.f64 eps x) eps (*.f64 x x))))
(.f64 (fma.f64 (-.f64 eps x) eps (.f64 x x)) (.f64 (+.f64 eps x) (pow.f64 (fma.f64 (-.f64 eps x) eps (.f64 x x)) #s(literal -1 binary64))))
(.f64 (+.f64 (pow.f64 eps #s(literal 3 binary64)) (pow.f64 x #s(literal 3 binary64))) (pow.f64 (fma.f64 (-.f64 eps x) eps (.f64 x x)) #s(literal -1 binary64)))
(*.f64 (+.f64 eps x) (/.f64 (-.f64 x eps) (-.f64 x eps)))
(.f64 (+.f64 eps x) (.f64 (-.f64 x eps) (pow.f64 (-.f64 x eps) #s(literal -1 binary64))))
(pow.f64 (/.f64 (-.f64 eps x) (*.f64 (+.f64 eps x) (-.f64 eps x))) #s(literal -1 binary64))
(pow.f64 (/.f64 (pow.f64 (+.f64 eps x) #s(literal -1 binary64)) #s(literal 1 binary64)) #s(literal -1 binary64))
(pow.f64 (pow.f64 (+.f64 eps x) #s(literal -1 binary64)) #s(literal -1 binary64))
(/.f64 (.f64 (-.f64 (pow.f64 x #s(literal 4 binary64)) (pow.f64 eps #s(literal 4 binary64))) (pow.f64 (-.f64 x eps) #s(literal -1 binary64))) (fma.f64 eps eps (.f64 x x)))
(/.f64 (.f64 (-.f64 (pow.f64 x #s(literal 6 binary64)) (pow.f64 eps #s(literal 6 binary64))) (pow.f64 (-.f64 x eps) #s(literal -1 binary64))) (fma.f64 (.f64 eps eps) (fma.f64 eps eps (*.f64 x x)) (pow.f64 x #s(literal 4 binary64))))
(/.f64 (.f64 (-.f64 (pow.f64 x #s(literal 6 binary64)) (pow.f64 eps #s(literal 6 binary64))) (pow.f64 (fma.f64 (-.f64 eps x) eps (.f64 x x)) #s(literal -1 binary64))) (-.f64 (pow.f64 x #s(literal 3 binary64)) (pow.f64 eps #s(literal 3 binary64))))
(/.f64 (.f64 (+.f64 (pow.f64 eps #s(literal 9 binary64)) (pow.f64 x #s(literal 9 binary64))) (pow.f64 (fma.f64 (-.f64 eps x) eps (.f64 x x)) #s(literal -1 binary64))) (-.f64 (+.f64 (pow.f64 x #s(literal 6 binary64)) (pow.f64 eps #s(literal 6 binary64))) (pow.f64 (*.f64 eps x) #s(literal 3 binary64))))
(/.f64 (-.f64 (pow.f64 (.f64 x (/.f64 x (-.f64 x eps))) #s(literal 2 binary64)) (pow.f64 (.f64 eps (/.f64 eps (-.f64 x eps))) #s(literal 2 binary64))) (fma.f64 x (/.f64 x (-.f64 x eps)) (*.f64 eps (/.f64 eps (-.f64 x eps)))))
(/.f64 (-.f64 (.f64 (pow.f64 x #s(literal 6 binary64)) (pow.f64 (-.f64 x eps) #s(literal -3 binary64))) (.f64 (pow.f64 eps #s(literal 6 binary64)) (pow.f64 (-.f64 x eps) #s(literal -3 binary64)))) (+.f64 (pow.f64 (.f64 x (/.f64 x (-.f64 x eps))) #s(literal 2 binary64)) (+.f64 (pow.f64 (.f64 eps (/.f64 eps (-.f64 x eps))) #s(literal 2 binary64)) (.f64 (.f64 x (/.f64 x (-.f64 x eps))) (*.f64 eps (/.f64 eps (-.f64 x eps)))))))
(/.f64 (neg.f64 (*.f64 (+.f64 eps x) (-.f64 eps x))) (neg.f64 (-.f64 eps x)))
(/.f64 (neg.f64 (neg.f64 (*.f64 (-.f64 x eps) (+.f64 eps x)))) (neg.f64 (neg.f64 (-.f64 x eps))))
(/.f64 (neg.f64 (neg.f64 (+.f64 (pow.f64 eps #s(literal 3 binary64)) (pow.f64 x #s(literal 3 binary64))))) (neg.f64 (neg.f64 (fma.f64 (-.f64 eps x) eps (*.f64 x x)))))
(/.f64 (.f64 (-.f64 (pow.f64 x #s(literal 4 binary64)) (pow.f64 eps #s(literal 4 binary64))) #s(literal 1 binary64)) (.f64 (fma.f64 eps eps (*.f64 x x)) (-.f64 x eps)))
(/.f64 (.f64 (-.f64 (pow.f64 x #s(literal 6 binary64)) (pow.f64 eps #s(literal 6 binary64))) #s(literal 1 binary64)) (.f64 (fma.f64 (.f64 eps eps) (fma.f64 eps eps (.f64 x x)) (pow.f64 x #s(literal 4 binary64))) (-.f64 x eps)))
(/.f64 (.f64 (-.f64 (pow.f64 x #s(literal 6 binary64)) (pow.f64 eps #s(literal 6 binary64))) #s(literal 1 binary64)) (.f64 (-.f64 (pow.f64 x #s(literal 3 binary64)) (pow.f64 eps #s(literal 3 binary64))) (fma.f64 (-.f64 eps x) eps (*.f64 x x))))
(/.f64 (.f64 (+.f64 (pow.f64 eps #s(literal 9 binary64)) (pow.f64 x #s(literal 9 binary64))) #s(literal 1 binary64)) (.f64 (-.f64 (+.f64 (pow.f64 x #s(literal 6 binary64)) (pow.f64 eps #s(literal 6 binary64))) (pow.f64 (.f64 eps x) #s(literal 3 binary64))) (fma.f64 (-.f64 eps x) eps (.f64 x x))))
(/.f64 (.f64 (+.f64 (pow.f64 eps #s(literal 3 binary64)) (pow.f64 x #s(literal 3 binary64))) #s(literal 1 binary64)) (fma.f64 (-.f64 eps x) eps (.f64 x x)))
(/.f64 (-.f64 (.f64 (.f64 x x) (-.f64 x eps)) (.f64 (-.f64 x eps) (.f64 eps eps))) (pow.f64 (-.f64 x eps) #s(literal 2 binary64)))
(/.f64 (-.f64 (pow.f64 x #s(literal 4 binary64)) (pow.f64 eps #s(literal 4 binary64))) (.f64 (-.f64 x eps) (fma.f64 eps eps (.f64 x x))))
(/.f64 (*.f64 (+.f64 eps x) (-.f64 eps x)) (-.f64 eps x))
(/.f64 (-.f64 (pow.f64 x #s(literal 6 binary64)) (pow.f64 eps #s(literal 6 binary64))) (.f64 (-.f64 x eps) (fma.f64 (.f64 eps eps) (fma.f64 eps eps (*.f64 x x)) (pow.f64 x #s(literal 4 binary64)))))
(/.f64 (-.f64 (pow.f64 x #s(literal 6 binary64)) (pow.f64 eps #s(literal 6 binary64))) (.f64 (fma.f64 (-.f64 eps x) eps (.f64 x x)) (-.f64 (pow.f64 x #s(literal 3 binary64)) (pow.f64 eps #s(literal 3 binary64)))))
(/.f64 #s(literal -1 binary64) (neg.f64 (pow.f64 (+.f64 eps x) #s(literal -1 binary64))))
(/.f64 #s(literal 1 binary64) (/.f64 (-.f64 eps x) (*.f64 (+.f64 eps x) (-.f64 eps x))))
(/.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (+.f64 eps x) #s(literal -1 binary64)) #s(literal 1 binary64)))
(/.f64 #s(literal 1 binary64) (pow.f64 (+.f64 eps x) #s(literal -1 binary64)))
(/.f64 (+.f64 (pow.f64 eps #s(literal 9 binary64)) (pow.f64 x #s(literal 9 binary64))) (.f64 (fma.f64 (-.f64 eps x) eps (.f64 x x)) (-.f64 (+.f64 (pow.f64 x #s(literal 6 binary64)) (pow.f64 eps #s(literal 6 binary64))) (pow.f64 (*.f64 eps x) #s(literal 3 binary64)))))
(/.f64 (neg.f64 (*.f64 (-.f64 x eps) (+.f64 eps x))) (neg.f64 (-.f64 x eps)))
(/.f64 (neg.f64 (+.f64 (pow.f64 eps #s(literal 3 binary64)) (pow.f64 x #s(literal 3 binary64)))) (neg.f64 (fma.f64 (-.f64 eps x) eps (*.f64 x x))))
(/.f64 (*.f64 (-.f64 x eps) (+.f64 eps x)) (-.f64 x eps))
(/.f64 (+.f64 (pow.f64 eps #s(literal 3 binary64)) (pow.f64 x #s(literal 3 binary64))) (fma.f64 (-.f64 eps x) eps (*.f64 x x)))
(neg.f64 (/.f64 (neg.f64 (*.f64 (-.f64 x eps) (+.f64 eps x))) (-.f64 x eps)))
(neg.f64 (/.f64 (neg.f64 (+.f64 (pow.f64 eps #s(literal 3 binary64)) (pow.f64 x #s(literal 3 binary64)))) (fma.f64 (-.f64 eps x) eps (*.f64 x x))))
(neg.f64 (/.f64 (*.f64 (-.f64 x eps) (+.f64 eps x)) (neg.f64 (-.f64 x eps))))
(neg.f64 (/.f64 (+.f64 (pow.f64 eps #s(literal 3 binary64)) (pow.f64 x #s(literal 3 binary64))) (neg.f64 (fma.f64 (-.f64 eps x) eps (*.f64 x x)))))
(fma.f64 (/.f64 (.f64 x x) (-.f64 (pow.f64 x #s(literal 3 binary64)) (pow.f64 eps #s(literal 3 binary64)))) (fma.f64 eps (+.f64 eps x) (.f64 x x)) (neg.f64 (*.f64 eps (/.f64 eps (-.f64 x eps)))))
(fma.f64 (/.f64 (.f64 x x) (.f64 (-.f64 x eps) (+.f64 eps x))) (+.f64 eps x) (neg.f64 (*.f64 eps (/.f64 eps (-.f64 x eps)))))
(fma.f64 (.f64 x x) (pow.f64 (-.f64 x eps) #s(literal -1 binary64)) (neg.f64 (.f64 eps (/.f64 eps (-.f64 x eps)))))
(fma.f64 x (/.f64 x (-.f64 x eps)) (neg.f64 (*.f64 eps (/.f64 eps (-.f64 x eps)))))
(-.f64 (/.f64 (.f64 eps eps) (-.f64 eps x)) (/.f64 (.f64 x x) (-.f64 eps x)))
(-.f64 (.f64 x (/.f64 x (-.f64 x eps))) (.f64 eps (/.f64 eps (-.f64 x eps))))
(+.f64 (.f64 x (/.f64 x (-.f64 x eps))) (neg.f64 (.f64 eps (/.f64 eps (-.f64 x eps)))))
(+.f64 eps x)
(+.f64 x eps)
(exp.f64 (*.f64 (log.f64 (pow.f64 (+.f64 eps x) #s(literal -1 binary64))) #s(literal -1 binary64)))
(pow.f64 (sin.f64 x) #s(literal 1 binary64))
(sin.f64 x)
(exp.f64 (*.f64 (log.f64 (sin.f64 x)) #s(literal 1 binary64)))

eval52.0ms (0.4%)

Memory: 13.6MiB live, 105.7MiB allocated
Compiler: Compiled 6 625 to 852 computations (87.1% saved)

prune10.0ms (0.1%)

Memory

-16.9MiB live, 21.4MiB allocated

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	283	8	291
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	283	9	292

Accuracy

100.0%

Counts

292 → 9

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	65.7%	(fma.f64 (sin.f64 x) (cos.f64 eps) (fma.f64 (sin.f64 eps) (cos.f64 x) (neg.f64 (sin.f64 x))))
✓	65.5%	(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
▶	7.9%	(-.f64 #s(approx (sin (+ x eps)) (sin.f64 eps)) (sin.f64 x))
▶	99.9%	(.f64 (.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 0 binary64) eps))) #s(literal 2 binary64)) (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64))))
▶	98.9%	#s(approx (- (sin (+ x eps)) (sin x)) (fma.f64 (fma.f64 (*.f64 (sin.f64 eps) x) #s(literal -1/2 binary64) (-.f64 (cos.f64 eps) #s(literal 1 binary64))) x (sin.f64 eps)))
	99.6%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 (fma.f64 #s(literal -1/6 binary64) (.f64 (cos.f64 x) eps) (*.f64 (sin.f64 x) #s(literal -1/2 binary64))) eps (cos.f64 x)) eps))
	99.5%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 (.f64 (sin.f64 x) #s(literal -1/2 binary64)) eps (cos.f64 x)) eps))
	99.2%	#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (cos.f64 x) eps))
▶	98.5%	#s(approx (- (sin (+ x eps)) (sin x)) (sin.f64 eps))

Compiler

Compiled 179 to 146 computations (18.4% saved)

simplify175.0ms (1.4%)

Memory

-0.9MiB live, 110.2MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 18 expressions of interest:

New	Metric	Score
cost-diff	0	(fma.f64 (sin.f64 eps) (cos.f64 x) (neg.f64 (sin.f64 x)))
cost-diff	0	(cos.f64 eps)
cost-diff	0	(sin.f64 x)
cost-diff	6400	(fma.f64 (sin.f64 x) (cos.f64 eps) (fma.f64 (sin.f64 eps) (cos.f64 x) (neg.f64 (sin.f64 x))))
cost-diff	0	(*.f64 (sin.f64 eps) x)
cost-diff	0	(fma.f64 (*.f64 (sin.f64 eps) x) #s(literal -1/2 binary64) (-.f64 (cos.f64 eps) #s(literal 1 binary64)))
cost-diff	0	(fma.f64 (fma.f64 (*.f64 (sin.f64 eps) x) #s(literal -1/2 binary64) (-.f64 (cos.f64 eps) #s(literal 1 binary64))) x (sin.f64 eps))
cost-diff	0	#s(approx (- (sin (+ x eps)) (sin x)) (fma.f64 (fma.f64 (*.f64 (sin.f64 eps) x) #s(literal -1/2 binary64) (-.f64 (cos.f64 eps) #s(literal 1 binary64))) x (sin.f64 eps)))
cost-diff	0	(sin.f64 x)
cost-diff	0	(sin.f64 eps)
cost-diff	0	#s(approx (sin (+ x eps)) (sin.f64 eps))
cost-diff	0	(-.f64 #s(approx (sin (+ x eps)) (sin.f64 eps)) (sin.f64 x))
cost-diff	0	(sin.f64 eps)
cost-diff	0	#s(approx (- (sin (+ x eps)) (sin x)) (sin.f64 eps))
cost-diff	0	(.f64 (.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 0 binary64) eps))) #s(literal 2 binary64)) (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64))))
cost-diff	128	(cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64)))
cost-diff	192	(+.f64 #s(literal 0 binary64) eps)
cost-diff	576	(/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64))

Rules

7 854×	`lower-fma.f32`
7 844×	`lower-fma.f64`
2 966×	`lower-*.f32`
2 958×	`lower-*.f64`
1 298×	`lower--.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	35	193
0	60	183
1	101	183
2	168	183
3	304	183
4	603	183
5	1064	183
6	1586	183
7	2462	183
8	2727	183
9	2807	180
10	2878	180
11	3116	180
12	4614	180
13	6833	180
0	8069	177

Stop Event

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

Calls

Call 1

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

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

localize220.0ms (1.8%)

Memory

14.9MiB live, 211.1MiB allocated

Localize:

Found 18 expressions of interest:

New	Metric	Score
accuracy	0	(cos.f64 x)
accuracy	0	(cos.f64 eps)
accuracy	0.0078125	(fma.f64 (sin.f64 eps) (cos.f64 x) (neg.f64 (sin.f64 x)))
accuracy	21.961791491472216	(fma.f64 (sin.f64 x) (cos.f64 eps) (fma.f64 (sin.f64 eps) (cos.f64 x) (neg.f64 (sin.f64 x))))
accuracy	0.00390625	(*.f64 (sin.f64 eps) x)
accuracy	0.12109375	(fma.f64 (*.f64 (sin.f64 eps) x) #s(literal -1/2 binary64) (-.f64 (cos.f64 eps) #s(literal 1 binary64)))
accuracy	0.7098673144904891	#s(approx (- (sin (+ x eps)) (sin x)) (fma.f64 (fma.f64 (*.f64 (sin.f64 eps) x) #s(literal -1/2 binary64) (-.f64 (cos.f64 eps) #s(literal 1 binary64))) x (sin.f64 eps)))
accuracy	27.566437143252585	(-.f64 (cos.f64 eps) #s(literal 1 binary64))
accuracy	0	(sin.f64 x)
accuracy	0	(sin.f64 eps)
accuracy	21.954237914132744	(-.f64 #s(approx (sin (+ x eps)) (sin.f64 eps)) (sin.f64 x))
accuracy	58.63201613428731	#s(approx (sin (+ x eps)) (sin.f64 eps))
accuracy	0	(sin.f64 eps)
accuracy	0.984543643185955	#s(approx (- (sin (+ x eps)) (sin x)) (sin.f64 eps))
accuracy	0.00390625	(.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 0 binary64) eps))) #s(literal 2 binary64))
accuracy	0.00390625	(sin.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 0 binary64) eps)))
accuracy	0.01171875	(.f64 (.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 0 binary64) eps))) #s(literal 2 binary64)) (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64))))
accuracy	0.08925386872974028	(cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64)))

Samples

183.0ms	249×	1	valid
7.0ms	4×	3	valid
1.0ms	3×	0	valid

Compiler

Compiled 181 to 37 computations (79.6% saved)

Precisions

Click to see histograms. Total time spent on operations: 162.0ms

ival-cos: 51.0ms (31.6% of total)

adjust: 44.0ms (27.2% of total)

ival-sin: 23.0ms (14.2% of total)

ival-mult: 20.0ms (12.4% of total)

ival-add: 15.0ms (9.3% of total)

ival-sub: 5.0ms (3.1% of total)

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

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

exact: 1.0ms (0.6% of total)

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

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

series36.0ms (0.3%)

Memory

13.5MiB live, 50.3MiB allocated

Counts

20 → 384

Calls

Call 1

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

Outputs
#s(alt (* -1 x) (taylor 0 eps) (#s(alt (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64)) (patch (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64)) #<representation binary64>) () ())) ())
#s(alt (+ (* -1 x) (* -1/2 eps)) (taylor 0 eps) (#s(alt (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64)) (patch (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64)) #<representation binary64>) () ())) ())
#s(alt (+ (* -1 x) (* -1/2 eps)) (taylor 0 eps) (#s(alt (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64)) (patch (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64)) #<representation binary64>) () ())) ())
#s(alt (+ (* -1 x) (* -1/2 eps)) (taylor 0 eps) (#s(alt (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64)) (patch (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64)) #<representation binary64>) () ())) ())
#s(alt eps (taylor 0 eps) (#s(alt (+.f64 #s(literal 0 binary64) eps) (patch (+.f64 #s(literal 0 binary64) eps) #<representation binary64>) () ())) ())
#s(alt eps (taylor 0 eps) (#s(alt (+.f64 #s(literal 0 binary64) eps) (patch (+.f64 #s(literal 0 binary64) eps) #<representation binary64>) () ())) ())
#s(alt eps (taylor 0 eps) (#s(alt (+.f64 #s(literal 0 binary64) eps) (patch (+.f64 #s(literal 0 binary64) eps) #<representation binary64>) () ())) ())
#s(alt eps (taylor 0 eps) (#s(alt (+.f64 #s(literal 0 binary64) eps) (patch (+.f64 #s(literal 0 binary64) eps) #<representation binary64>) () ())) ())
#s(alt (cos (* -1 x)) (taylor 0 eps) (#s(alt (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64))) (patch (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64))) #<representation binary64>) () ())) ())
#s(alt (+ (cos (* -1 x)) (* 1/2 (* eps (sin (* -1 x))))) (taylor 0 eps) (#s(alt (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64))) (patch (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64))) #<representation binary64>) () ())) ())
#s(alt (+ (cos (* -1 x)) (* eps (- (* -1/8 (* eps (cos (* -1 x)))) (* -1/2 (sin (* -1 x)))))) (taylor 0 eps) (#s(alt (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64))) (patch (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64))) #<representation binary64>) () ())) ())
#s(alt (+ (cos (* -1 x)) (* eps (- (* eps (+ (* -1/8 (cos (* -1 x))) (* -1/48 (* eps (sin (* -1 x)))))) (* -1/2 (sin (* -1 x)))))) (taylor 0 eps) (#s(alt (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64))) (patch (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64))) #<representation binary64>) () ())) ())
#s(alt (* eps (cos (* -1 x))) (taylor 0 eps) (#s(alt (.f64 (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 0 binary64) eps))) #s(literal 2 binary64)) (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64)))) (patch (.f64 (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 0 binary64) eps))) #s(literal 2 binary64)) (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64)))) #<representation binary64>) () ())) ())
#s(alt (* eps (+ (cos (* -1 x)) (* 1/2 (* eps (sin (* -1 x)))))) (taylor 0 eps) (#s(alt (.f64 (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 0 binary64) eps))) #s(literal 2 binary64)) (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64)))) (patch (.f64 (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 0 binary64) eps))) #s(literal 2 binary64)) (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64)))) #<representation binary64>) () ())) ())
#s(alt (* eps (+ (cos (* -1 x)) (* eps (+ (* 1/2 (sin (* -1 x))) (* 2 (* eps (+ (* -1/16 (cos (* -1 x))) (* -1/48 (cos (* -1 x)))))))))) (taylor 0 eps) (#s(alt (.f64 (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 0 binary64) eps))) #s(literal 2 binary64)) (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64)))) (patch (.f64 (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 0 binary64) eps))) #s(literal 2 binary64)) (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64)))) #<representation binary64>) () ())) ())
#s(alt (* eps (+ (cos (* -1 x)) (* eps (+ (* 1/2 (sin (* -1 x))) (* eps (+ (* -1/24 (* eps (sin (* -1 x)))) (* 2 (+ (* -1/16 (cos (* -1 x))) (* -1/48 (cos (* -1 x))))))))))) (taylor 0 eps) (#s(alt (.f64 (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 0 binary64) eps))) #s(literal 2 binary64)) (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64)))) (patch (.f64 (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 0 binary64) eps))) #s(literal 2 binary64)) (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64)))) #<representation binary64>) () ())) ())
#s(alt (* eps (cos x)) (taylor 0 eps) (#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 (* eps (+ (cos x) (* -1/2 (* eps (sin x))))) (taylor 0 eps) (#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 (* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x))))))) (taylor 0 eps) (#s(alt #s(approx (- (sin (+ x eps)) (sin x)) (sin.f64 eps)) (patch #s(approx (- (sin (+ x eps)) (sin x)) (sin.f64 eps)) #<representation binary64>) () ())) ())
#s(alt (* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* eps (+ (* -1/6 (cos x)) (* 1/24 (* eps (sin x))))))))) (taylor 0 eps) (#s(alt #s(approx (- (sin (+ x eps)) (sin x)) (sin.f64 eps)) (patch #s(approx (- (sin (+ x eps)) (sin x)) (sin.f64 eps)) #<representation binary64>) () ())) ())
#s(alt eps (taylor 0 eps) (#s(alt (sin.f64 eps) (patch (sin.f64 eps) #<representation binary64>) () ())) ())
#s(alt (* eps (+ 1 (* -1/6 (pow eps 2)))) (taylor 0 eps) (#s(alt (sin.f64 eps) (patch (sin.f64 eps) #<representation binary64>) () ())) ())
#s(alt (* eps (+ 1 (* (pow eps 2) (- (* 1/120 (pow eps 2)) 1/6)))) (taylor 0 eps) (#s(alt (sin.f64 eps) (patch (sin.f64 eps) #<representation binary64>) () ())) ())
#s(alt (* eps (+ 1 (* (pow eps 2) (- (* (pow eps 2) (+ 1/120 (* -1/5040 (pow eps 2)))) 1/6)))) (taylor 0 eps) (#s(alt (sin.f64 eps) (patch (sin.f64 eps) #<representation binary64>) () ())) ())
#s(alt (* eps (cos x)) (taylor 0 eps) (#s(alt (-.f64 #s(approx (sin (+ x eps)) (sin.f64 eps)) (sin.f64 x)) (patch (-.f64 #s(approx (sin (+ x eps)) (sin.f64 eps)) (sin.f64 x)) #<representation binary64>) () ())) ())
#s(alt (* eps (+ (cos x) (* -1/2 (* eps (sin x))))) (taylor 0 eps) (#s(alt (-.f64 #s(approx (sin (+ x eps)) (sin.f64 eps)) (sin.f64 x)) (patch (-.f64 #s(approx (sin (+ x eps)) (sin.f64 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 #s(approx (sin (+ x eps)) (sin.f64 eps)) (sin.f64 x)) (patch (-.f64 #s(approx (sin (+ x eps)) (sin.f64 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 #s(approx (sin (+ x eps)) (sin.f64 eps)) (sin.f64 x)) (patch (-.f64 #s(approx (sin (+ x eps)) (sin.f64 eps)) (sin.f64 x)) #<representation binary64>) () ())) ())
#s(alt (sin x) (taylor 0 eps) (#s(alt #s(approx (sin (+ x eps)) (sin.f64 eps)) (patch #s(approx (sin (+ x eps)) (sin.f64 eps)) #<representation binary64>) () ())) ())
#s(alt (+ (sin x) (* eps (cos x))) (taylor 0 eps) (#s(alt #s(approx (sin (+ x eps)) (sin.f64 eps)) (patch #s(approx (sin (+ x eps)) (sin.f64 eps)) #<representation binary64>) () ())) ())
#s(alt (+ (sin x) (* eps (+ (cos x) (* -1/2 (* eps (sin x)))))) (taylor 0 eps) (#s(alt #s(approx (sin (+ x eps)) (sin.f64 eps)) (patch #s(approx (sin (+ x eps)) (sin.f64 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 #s(approx (sin (+ x eps)) (sin.f64 eps)) (patch #s(approx (sin (+ x eps)) (sin.f64 eps)) #<representation binary64>) () ())) ())
#s(alt (* eps (cos x)) (taylor 0 eps) (#s(alt #s(approx (- (sin (+ x eps)) (sin x)) (fma.f64 (fma.f64 (.f64 (sin.f64 eps) x) #s(literal -1/2 binary64) (-.f64 (cos.f64 eps) #s(literal 1 binary64))) x (sin.f64 eps))) (patch #s(approx (- (sin (+ x eps)) (sin x)) (fma.f64 (fma.f64 (.f64 (sin.f64 eps) x) #s(literal -1/2 binary64) (-.f64 (cos.f64 eps) #s(literal 1 binary64))) x (sin.f64 eps))) #<representation binary64>) () ())) ())
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#s(alt (- (sin (- eps (* -1 x))) (sin x)) (taylor -inf x) (#s(alt #s(approx (- (sin (+ x eps)) (sin x)) (fma.f64 (fma.f64 (.f64 (sin.f64 eps) x) #s(literal -1/2 binary64) (-.f64 (cos.f64 eps) #s(literal 1 binary64))) x (sin.f64 eps))) (patch #s(approx (- (sin (+ x eps)) (sin x)) (fma.f64 (fma.f64 (.f64 (sin.f64 eps) x) #s(literal -1/2 binary64) (-.f64 (cos.f64 eps) #s(literal 1 binary64))) x (sin.f64 eps))) #<representation binary64>) () ())) ())
#s(alt (- (sin (- eps (* -1 x))) (sin x)) (taylor -inf x) (#s(alt #s(approx (- (sin (+ x eps)) (sin x)) (fma.f64 (fma.f64 (.f64 (sin.f64 eps) x) #s(literal -1/2 binary64) (-.f64 (cos.f64 eps) #s(literal 1 binary64))) x (sin.f64 eps))) (patch #s(approx (- (sin (+ x eps)) (sin x)) (fma.f64 (fma.f64 (.f64 (sin.f64 eps) x) #s(literal -1/2 binary64) (-.f64 (cos.f64 eps) #s(literal 1 binary64))) x (sin.f64 eps))) #<representation binary64>) () ())) ())
#s(alt (- (sin (- eps (* -1 x))) (sin x)) (taylor -inf x) (#s(alt #s(approx (- (sin (+ x eps)) (sin x)) (fma.f64 (fma.f64 (.f64 (sin.f64 eps) x) #s(literal -1/2 binary64) (-.f64 (cos.f64 eps) #s(literal 1 binary64))) x (sin.f64 eps))) (patch #s(approx (- (sin (+ x eps)) (sin x)) (fma.f64 (fma.f64 (.f64 (sin.f64 eps) x) #s(literal -1/2 binary64) (-.f64 (cos.f64 eps) #s(literal 1 binary64))) x (sin.f64 eps))) #<representation binary64>) () ())) ())
#s(alt (* -1/2 (* (pow x 2) (sin eps))) (taylor -inf x) (#s(alt (fma.f64 (fma.f64 (.f64 (sin.f64 eps) x) #s(literal -1/2 binary64) (-.f64 (cos.f64 eps) #s(literal 1 binary64))) x (sin.f64 eps)) (patch (fma.f64 (fma.f64 (.f64 (sin.f64 eps) x) #s(literal -1/2 binary64) (-.f64 (cos.f64 eps) #s(literal 1 binary64))) x (sin.f64 eps)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (- (+ (* -1/2 (sin eps)) (/ (cos eps) x)) (/ 1 x))) (taylor -inf x) (#s(alt (fma.f64 (fma.f64 (.f64 (sin.f64 eps) x) #s(literal -1/2 binary64) (-.f64 (cos.f64 eps) #s(literal 1 binary64))) x (sin.f64 eps)) (patch (fma.f64 (fma.f64 (.f64 (sin.f64 eps) x) #s(literal -1/2 binary64) (-.f64 (cos.f64 eps) #s(literal 1 binary64))) x (sin.f64 eps)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (+ (* -1 (/ (+ (* -1 (- (cos eps) 1)) (* -1 (/ (sin eps) x))) x)) (* -1/2 (sin eps)))) (taylor -inf x) (#s(alt (fma.f64 (fma.f64 (.f64 (sin.f64 eps) x) #s(literal -1/2 binary64) (-.f64 (cos.f64 eps) #s(literal 1 binary64))) x (sin.f64 eps)) (patch (fma.f64 (fma.f64 (.f64 (sin.f64 eps) x) #s(literal -1/2 binary64) (-.f64 (cos.f64 eps) #s(literal 1 binary64))) x (sin.f64 eps)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (+ (* -1 (/ (+ (* -1 (- (cos eps) 1)) (* -1 (/ (sin eps) x))) x)) (* -1/2 (sin eps)))) (taylor -inf x) (#s(alt (fma.f64 (fma.f64 (.f64 (sin.f64 eps) x) #s(literal -1/2 binary64) (-.f64 (cos.f64 eps) #s(literal 1 binary64))) x (sin.f64 eps)) (patch (fma.f64 (fma.f64 (.f64 (sin.f64 eps) x) #s(literal -1/2 binary64) (-.f64 (cos.f64 eps) #s(literal 1 binary64))) x (sin.f64 eps)) #<representation binary64>) () ())) ())
#s(alt (* -1/2 (* x (sin eps))) (taylor -inf x) (#s(alt (fma.f64 (.f64 (sin.f64 eps) x) #s(literal -1/2 binary64) (-.f64 (cos.f64 eps) #s(literal 1 binary64))) (patch (fma.f64 (.f64 (sin.f64 eps) x) #s(literal -1/2 binary64) (-.f64 (cos.f64 eps) #s(literal 1 binary64))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (+ (* -1 (/ (- (cos eps) 1) x)) (* 1/2 (sin eps))))) (taylor -inf x) (#s(alt (fma.f64 (.f64 (sin.f64 eps) x) #s(literal -1/2 binary64) (-.f64 (cos.f64 eps) #s(literal 1 binary64))) (patch (fma.f64 (.f64 (sin.f64 eps) x) #s(literal -1/2 binary64) (-.f64 (cos.f64 eps) #s(literal 1 binary64))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (+ (* -1 (/ (- (cos eps) 1) x)) (* 1/2 (sin eps))))) (taylor -inf x) (#s(alt (fma.f64 (.f64 (sin.f64 eps) x) #s(literal -1/2 binary64) (-.f64 (cos.f64 eps) #s(literal 1 binary64))) (patch (fma.f64 (.f64 (sin.f64 eps) x) #s(literal -1/2 binary64) (-.f64 (cos.f64 eps) #s(literal 1 binary64))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (+ (* -1 (/ (- (cos eps) 1) x)) (* 1/2 (sin eps))))) (taylor -inf x) (#s(alt (fma.f64 (.f64 (sin.f64 eps) x) #s(literal -1/2 binary64) (-.f64 (cos.f64 eps) #s(literal 1 binary64))) (patch (fma.f64 (.f64 (sin.f64 eps) x) #s(literal -1/2 binary64) (-.f64 (cos.f64 eps) #s(literal 1 binary64))) #<representation binary64>) () ())) ())
#s(alt (* x (sin eps)) (taylor -inf x) (#s(alt (.f64 (sin.f64 eps) x) (patch (.f64 (sin.f64 eps) x) #<representation binary64>) () ())) ())
#s(alt (* x (sin eps)) (taylor -inf x) (#s(alt (.f64 (sin.f64 eps) x) (patch (.f64 (sin.f64 eps) x) #<representation binary64>) () ())) ())
#s(alt (* x (sin eps)) (taylor -inf x) (#s(alt (.f64 (sin.f64 eps) x) (patch (.f64 (sin.f64 eps) x) #<representation binary64>) () ())) ())
#s(alt (* x (sin eps)) (taylor -inf x) (#s(alt (.f64 (sin.f64 eps) x) (patch (.f64 (sin.f64 eps) x) #<representation binary64>) () ())) ())
#s(alt (- (+ (* (cos eps) (sin x)) (* (cos x) (sin eps))) (sin x)) (taylor -inf x) (#s(alt (fma.f64 (sin.f64 x) (cos.f64 eps) (fma.f64 (sin.f64 eps) (cos.f64 x) (neg.f64 (sin.f64 x)))) (patch (fma.f64 (sin.f64 x) (cos.f64 eps) (fma.f64 (sin.f64 eps) (cos.f64 x) (neg.f64 (sin.f64 x)))) #<representation binary64>) () ())) ())
#s(alt (- (+ (* (cos eps) (sin x)) (* (cos x) (sin eps))) (sin x)) (taylor -inf x) (#s(alt (fma.f64 (sin.f64 x) (cos.f64 eps) (fma.f64 (sin.f64 eps) (cos.f64 x) (neg.f64 (sin.f64 x)))) (patch (fma.f64 (sin.f64 x) (cos.f64 eps) (fma.f64 (sin.f64 eps) (cos.f64 x) (neg.f64 (sin.f64 x)))) #<representation binary64>) () ())) ())
#s(alt (- (+ (* (cos eps) (sin x)) (* (cos x) (sin eps))) (sin x)) (taylor -inf x) (#s(alt (fma.f64 (sin.f64 x) (cos.f64 eps) (fma.f64 (sin.f64 eps) (cos.f64 x) (neg.f64 (sin.f64 x)))) (patch (fma.f64 (sin.f64 x) (cos.f64 eps) (fma.f64 (sin.f64 eps) (cos.f64 x) (neg.f64 (sin.f64 x)))) #<representation binary64>) () ())) ())
#s(alt (- (+ (* (cos eps) (sin x)) (* (cos x) (sin eps))) (sin x)) (taylor -inf x) (#s(alt (fma.f64 (sin.f64 x) (cos.f64 eps) (fma.f64 (sin.f64 eps) (cos.f64 x) (neg.f64 (sin.f64 x)))) (patch (fma.f64 (sin.f64 x) (cos.f64 eps) (fma.f64 (sin.f64 eps) (cos.f64 x) (neg.f64 (sin.f64 x)))) #<representation binary64>) () ())) ())
#s(alt (- (* (cos x) (sin eps)) (sin x)) (taylor -inf x) (#s(alt (fma.f64 (sin.f64 eps) (cos.f64 x) (neg.f64 (sin.f64 x))) (patch (fma.f64 (sin.f64 eps) (cos.f64 x) (neg.f64 (sin.f64 x))) #<representation binary64>) () ())) ())
#s(alt (- (* (cos x) (sin eps)) (sin x)) (taylor -inf x) (#s(alt (fma.f64 (sin.f64 eps) (cos.f64 x) (neg.f64 (sin.f64 x))) (patch (fma.f64 (sin.f64 eps) (cos.f64 x) (neg.f64 (sin.f64 x))) #<representation binary64>) () ())) ())
#s(alt (- (* (cos x) (sin eps)) (sin x)) (taylor -inf x) (#s(alt (fma.f64 (sin.f64 eps) (cos.f64 x) (neg.f64 (sin.f64 x))) (patch (fma.f64 (sin.f64 eps) (cos.f64 x) (neg.f64 (sin.f64 x))) #<representation binary64>) () ())) ())
#s(alt (- (* (cos x) (sin eps)) (sin x)) (taylor -inf x) (#s(alt (fma.f64 (sin.f64 eps) (cos.f64 x) (neg.f64 (sin.f64 x))) (patch (fma.f64 (sin.f64 eps) (cos.f64 x) (neg.f64 (sin.f64 x))) #<representation binary64>) () ())) ())
#s(alt (cos x) (taylor -inf x) (#s(alt (cos.f64 x) (patch (cos.f64 x) #<representation binary64>) () ())) ())
#s(alt (cos x) (taylor -inf x) (#s(alt (cos.f64 x) (patch (cos.f64 x) #<representation binary64>) () ())) ())
#s(alt (cos x) (taylor -inf x) (#s(alt (cos.f64 x) (patch (cos.f64 x) #<representation binary64>) () ())) ())
#s(alt (cos x) (taylor -inf x) (#s(alt (cos.f64 x) (patch (cos.f64 x) #<representation binary64>) () ())) ())

Calls

6 calls:

Time	Variable		Point	Expression
8.0ms	x	@	inf	((/ (+ (* 2 x) eps) -2) (+ 0 eps) (cos (/ (+ (* 2 x) eps) -2)) (* (* (sin (* 1/2 (+ 0 eps))) 2) (cos (/ (+ (* 2 x) eps) -2))) (- (sin (+ x eps)) (sin x)) (sin eps) (- (sin (+ x eps)) (sin x)) (sin (+ x eps)) (sin x) (- (sin (+ x eps)) (sin x)) (+ (* (+ (* (* (sin eps) x) -1/2) (- (cos eps) 1)) x) (sin eps)) (+ (* (* (sin eps) x) -1/2) (- (cos eps) 1)) (* (sin eps) x) (+ (* (sin x) (cos eps)) (+ (* (sin eps) (cos x)) (neg (sin x)))) (cos eps) (+ (* (sin eps) (cos x)) (neg (sin x))) (sin (* 1/2 (+ 0 eps))) (* (sin (* 1/2 (+ 0 eps))) 2) (- (cos eps) 1) (cos x))
4.0ms	eps	@	inf	((/ (+ (* 2 x) eps) -2) (+ 0 eps) (cos (/ (+ (* 2 x) eps) -2)) (* (* (sin (* 1/2 (+ 0 eps))) 2) (cos (/ (+ (* 2 x) eps) -2))) (- (sin (+ x eps)) (sin x)) (sin eps) (- (sin (+ x eps)) (sin x)) (sin (+ x eps)) (sin x) (- (sin (+ x eps)) (sin x)) (+ (* (+ (* (* (sin eps) x) -1/2) (- (cos eps) 1)) x) (sin eps)) (+ (* (* (sin eps) x) -1/2) (- (cos eps) 1)) (* (sin eps) x) (+ (* (sin x) (cos eps)) (+ (* (sin eps) (cos x)) (neg (sin x)))) (cos eps) (+ (* (sin eps) (cos x)) (neg (sin x))) (sin (* 1/2 (+ 0 eps))) (* (sin (* 1/2 (+ 0 eps))) 2) (- (cos eps) 1) (cos x))
3.0ms	x	@	-inf	((/ (+ (* 2 x) eps) -2) (+ 0 eps) (cos (/ (+ (* 2 x) eps) -2)) (* (* (sin (* 1/2 (+ 0 eps))) 2) (cos (/ (+ (* 2 x) eps) -2))) (- (sin (+ x eps)) (sin x)) (sin eps) (- (sin (+ x eps)) (sin x)) (sin (+ x eps)) (sin x) (- (sin (+ x eps)) (sin x)) (+ (* (+ (* (* (sin eps) x) -1/2) (- (cos eps) 1)) x) (sin eps)) (+ (* (* (sin eps) x) -1/2) (- (cos eps) 1)) (* (sin eps) x) (+ (* (sin x) (cos eps)) (+ (* (sin eps) (cos x)) (neg (sin x)))) (cos eps) (+ (* (sin eps) (cos x)) (neg (sin x))) (sin (* 1/2 (+ 0 eps))) (* (sin (* 1/2 (+ 0 eps))) 2) (- (cos eps) 1) (cos x))
3.0ms	eps	@	-inf	((/ (+ (* 2 x) eps) -2) (+ 0 eps) (cos (/ (+ (* 2 x) eps) -2)) (* (* (sin (* 1/2 (+ 0 eps))) 2) (cos (/ (+ (* 2 x) eps) -2))) (- (sin (+ x eps)) (sin x)) (sin eps) (- (sin (+ x eps)) (sin x)) (sin (+ x eps)) (sin x) (- (sin (+ x eps)) (sin x)) (+ (* (+ (* (* (sin eps) x) -1/2) (- (cos eps) 1)) x) (sin eps)) (+ (* (* (sin eps) x) -1/2) (- (cos eps) 1)) (* (sin eps) x) (+ (* (sin x) (cos eps)) (+ (* (sin eps) (cos x)) (neg (sin x)))) (cos eps) (+ (* (sin eps) (cos x)) (neg (sin x))) (sin (* 1/2 (+ 0 eps))) (* (sin (* 1/2 (+ 0 eps))) 2) (- (cos eps) 1) (cos x))
3.0ms	eps	@	0	((/ (+ (* 2 x) eps) -2) (+ 0 eps) (cos (/ (+ (* 2 x) eps) -2)) (* (* (sin (* 1/2 (+ 0 eps))) 2) (cos (/ (+ (* 2 x) eps) -2))) (- (sin (+ x eps)) (sin x)) (sin eps) (- (sin (+ x eps)) (sin x)) (sin (+ x eps)) (sin x) (- (sin (+ x eps)) (sin x)) (+ (* (+ (* (* (sin eps) x) -1/2) (- (cos eps) 1)) x) (sin eps)) (+ (* (* (sin eps) x) -1/2) (- (cos eps) 1)) (* (sin eps) x) (+ (* (sin x) (cos eps)) (+ (* (sin eps) (cos x)) (neg (sin x)))) (cos eps) (+ (* (sin eps) (cos x)) (neg (sin x))) (sin (* 1/2 (+ 0 eps))) (* (sin (* 1/2 (+ 0 eps))) 2) (- (cos eps) 1) (cos x))

simplify181.0ms (1.5%)

Memory

-2.3MiB live, 203.4MiB allocated

Algorithm

1×	egg-herbie

Rules

12 518×	`lower-fma.f64`
12 518×	`lower-fma.f32`
5 710×	`lower-*.f64`
5 710×	`lower-*.f32`
4 312×	`lower-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	408	3554
1	1222	3395
2	3320	3315
3	7919	3315
0	8305	3097

Stop Event

1×	iter limit
1×	node limit

Counts

384 → 369

Calls

Call 1

Inputs
(* -1 x)
(+ (* -1 x) (* -1/2 eps))
(+ (* -1 x) (* -1/2 eps))
(+ (* -1 x) (* -1/2 eps))
eps
eps
eps
eps
(cos (* -1 x))
(+ (cos (* -1 x)) (* 1/2 (* eps (sin (* -1 x)))))
(+ (cos (* -1 x)) (* eps (- (* -1/8 (* eps (cos (* -1 x)))) (* -1/2 (sin (* -1 x))))))
(+ (cos (* -1 x)) (* eps (- (* eps (+ (* -1/8 (cos (* -1 x))) (* -1/48 (* eps (sin (* -1 x)))))) (* -1/2 (sin (* -1 x))))))
(* eps (cos (* -1 x)))
(* eps (+ (cos (* -1 x)) (* 1/2 (* eps (sin (* -1 x))))))
(* eps (+ (cos (* -1 x)) (* eps (+ (* 1/2 (sin (* -1 x))) (* 2 (* eps (+ (* -1/16 (cos (* -1 x))) (* -1/48 (cos (* -1 x))))))))))
(* eps (+ (cos (* -1 x)) (* eps (+ (* 1/2 (sin (* -1 x))) (* eps (+ (* -1/24 (* eps (sin (* -1 x)))) (* 2 (+ (* -1/16 (cos (* -1 x))) (* -1/48 (cos (* -1 x)))))))))))
(* eps (cos x))
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x)))))))
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* eps (+ (* -1/6 (cos x)) (* 1/24 (* eps (sin x)))))))))
eps
(* eps (+ 1 (* -1/6 (pow eps 2))))
(* eps (+ 1 (* (pow eps 2) (- (* 1/120 (pow eps 2)) 1/6))))
(* eps (+ 1 (* (pow eps 2) (- (* (pow eps 2) (+ 1/120 (* -1/5040 (pow eps 2)))) 1/6))))
(* eps (cos x))
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x)))))))
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* eps (+ (* -1/6 (cos x)) (* 1/24 (* eps (sin x)))))))))
(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))))))))
(* eps (cos x))
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x)))))))
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* eps (+ (* -1/6 (cos x)) (* 1/24 (* eps (sin x)))))))))
(* eps (+ 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) (* eps (- (* 1/12 (pow x 2)) 1/6)))))))
(* eps (+ 1 (+ (* -1/2 (pow x 2)) (* eps (+ (* -1/2 x) (* eps (- (+ (* 1/24 (* eps x)) (* 1/12 (pow x 2))) 1/6)))))))
(* -1/2 (* eps x))
(* eps (+ (* -1/2 eps) (* -1/2 x)))
(* eps (+ (* -1/2 x) (* eps (- (* 1/12 (* eps x)) 1/2))))
(* eps (+ (* -1/2 x) (* eps (- (* eps (+ (* 1/24 eps) (* 1/12 x))) 1/2))))
(* eps x)
(* eps (+ x (* -1/6 (* (pow eps 2) x))))
(* eps (+ x (* (pow eps 2) (+ (* -1/6 x) (* 1/120 (* (pow eps 2) x))))))
(* eps (+ x (* (pow eps 2) (+ (* -1/6 x) (* (pow eps 2) (+ (* -1/5040 (* (pow eps 2) x)) (* 1/120 x)))))))
(* eps (cos x))
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x)))))))
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* eps (+ (* -1/6 (cos x)) (* 1/24 (* eps (sin x)))))))))
1
(+ 1 (* -1/2 (pow eps 2)))
(+ 1 (* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2)))
(+ 1 (* (pow eps 2) (- (* (pow eps 2) (+ 1/24 (* -1/720 (pow eps 2)))) 1/2)))
(* -1 (sin x))
(- (* eps (cos x)) (sin x))
(- (* eps (+ (cos x) (* -1/6 (* (pow eps 2) (cos x))))) (sin x))
(- (* eps (+ (cos x) (* (pow eps 2) (+ (* -1/6 (cos x)) (* 1/120 (* (pow eps 2) (cos x))))))) (sin x))
(* 1/2 eps)
(* eps (+ 1/2 (* -1/48 (pow eps 2))))
(* eps (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48))))
(* eps (+ 1/2 (* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48))))
eps
(* eps (+ 1 (* -1/24 (pow eps 2))))
(* eps (+ 1 (* (pow eps 2) (- (* 1/1920 (pow eps 2)) 1/24))))
(* eps (+ 1 (* (pow eps 2) (- (* (pow eps 2) (+ 1/1920 (* -1/322560 (pow eps 2)))) 1/24))))
(* -1/2 (pow eps 2))
(* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2))
(* (pow eps 2) (- (* (pow eps 2) (+ 1/24 (* -1/720 (pow eps 2)))) 1/2))
(* (pow eps 2) (- (* (pow eps 2) (+ 1/24 (* (pow eps 2) (- (* 1/40320 (pow eps 2)) 1/720)))) 1/2))
(* -1/2 eps)
(* eps (- (* -1 (/ x eps)) 1/2))
(* eps (- (* -1 (/ x eps)) 1/2))
(* eps (- (* -1 (/ x eps)) 1/2))
eps
eps
eps
eps
(cos (* -1/2 (+ eps (* 2 x))))
(cos (* -1/2 (+ eps (* 2 x))))
(cos (* -1/2 (+ eps (* 2 x))))
(cos (* -1/2 (+ eps (* 2 x))))
(* 2 (* (cos (* -1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))))
(* 2 (* (cos (* -1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))))
(* 2 (* (cos (* -1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))))
(* 2 (* (cos (* -1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))))
(- (sin (+ eps x)) (sin x))
(- (sin (+ eps x)) (sin x))
(- (sin (+ eps x)) (sin x))
(- (sin (+ eps x)) (sin x))
(sin eps)
(sin eps)
(sin eps)
(sin eps)
(- (sin (+ eps x)) (sin x))
(- (sin (+ eps x)) (sin x))
(- (sin (+ eps x)) (sin x))
(- (sin (+ eps x)) (sin x))
(sin (+ eps x))
(sin (+ eps x))
(sin (+ eps x))
(sin (+ eps x))
(- (sin (+ eps x)) (sin x))
(- (sin (+ eps x)) (sin x))
(- (sin (+ eps x)) (sin x))
(- (sin (+ eps x)) (sin x))
(+ (sin eps) (* x (- (+ (cos eps) (* -1/2 (* x (sin eps)))) 1)))
(+ (sin eps) (* x (- (+ (cos eps) (* -1/2 (* x (sin eps)))) 1)))
(+ (sin eps) (* x (- (+ (cos eps) (* -1/2 (* x (sin eps)))) 1)))
(+ (sin eps) (* x (- (+ (cos eps) (* -1/2 (* x (sin eps)))) 1)))
(- (+ (cos eps) (* -1/2 (* x (sin eps)))) 1)
(- (+ (cos eps) (* -1/2 (* x (sin eps)))) 1)
(- (+ (cos eps) (* -1/2 (* x (sin eps)))) 1)
(- (+ (cos eps) (* -1/2 (* x (sin eps)))) 1)
(* x (sin eps))
(* x (sin eps))
(* x (sin eps))
(* x (sin eps))
(- (+ (* (cos eps) (sin x)) (* (cos x) (sin eps))) (sin x))
(- (+ (* (cos eps) (sin x)) (* (cos x) (sin eps))) (sin x))
(- (+ (* (cos eps) (sin x)) (* (cos x) (sin eps))) (sin x))
(- (+ (* (cos eps) (sin x)) (* (cos x) (sin eps))) (sin x))
(cos eps)
(cos eps)
(cos eps)
(cos eps)
(- (* (cos x) (sin eps)) (sin x))
(- (* (cos x) (sin eps)) (sin x))
(- (* (cos x) (sin eps)) (sin x))
(- (* (cos x) (sin eps)) (sin x))
(sin (* 1/2 eps))
(sin (* 1/2 eps))
(sin (* 1/2 eps))
(sin (* 1/2 eps))
(* 2 (sin (* 1/2 eps)))
(* 2 (sin (* 1/2 eps)))
(* 2 (sin (* 1/2 eps)))
(* 2 (sin (* 1/2 eps)))
(- (cos eps) 1)
(- (cos eps) 1)
(- (cos eps) 1)
(- (cos eps) 1)
(* -1/2 eps)
(* -1 (* eps (+ 1/2 (/ x eps))))
(* -1 (* eps (+ 1/2 (/ x eps))))
(* -1 (* eps (+ 1/2 (/ x eps))))
eps
eps
eps
eps
(cos (* -1/2 (- (* 2 x) (* -1 eps))))
(cos (* -1/2 (- (* 2 x) (* -1 eps))))
(cos (* -1/2 (- (* 2 x) (* -1 eps))))
(cos (* -1/2 (- (* 2 x) (* -1 eps))))
(* 2 (* (cos (* -1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps))))
(* 2 (* (cos (* -1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps))))
(* 2 (* (cos (* -1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps))))
(* 2 (* (cos (* -1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps))))
(- (sin (- x (* -1 eps))) (sin x))
(- (sin (- x (* -1 eps))) (sin x))
(- (sin (- x (* -1 eps))) (sin x))
(- (sin (- x (* -1 eps))) (sin x))
(sin eps)
(sin eps)
(sin eps)
(sin eps)
(- (sin (- x (* -1 eps))) (sin x))
(- (sin (- x (* -1 eps))) (sin x))
(- (sin (- x (* -1 eps))) (sin x))
(- (sin (- x (* -1 eps))) (sin x))
(sin (- x (* -1 eps)))
(sin (- x (* -1 eps)))
(sin (- x (* -1 eps)))
(sin (- x (* -1 eps)))
(- (sin (- x (* -1 eps))) (sin x))
(- (sin (- x (* -1 eps))) (sin x))
(- (sin (- x (* -1 eps))) (sin x))
(- (sin (- x (* -1 eps))) (sin x))
(+ (sin eps) (* x (- (+ (cos eps) (* -1/2 (* x (sin eps)))) 1)))
(+ (sin eps) (* x (- (+ (cos eps) (* -1/2 (* x (sin eps)))) 1)))
(+ (sin eps) (* x (- (+ (cos eps) (* -1/2 (* x (sin eps)))) 1)))
(+ (sin eps) (* x (- (+ (cos eps) (* -1/2 (* x (sin eps)))) 1)))
(- (+ (cos eps) (* -1/2 (* x (sin eps)))) 1)
(- (+ (cos eps) (* -1/2 (* x (sin eps)))) 1)
(- (+ (cos eps) (* -1/2 (* x (sin eps)))) 1)
(- (+ (cos eps) (* -1/2 (* x (sin eps)))) 1)
(* x (sin eps))
(* x (sin eps))
(* x (sin eps))
(* x (sin eps))
(- (+ (* (cos eps) (sin x)) (* (cos x) (sin eps))) (sin x))
(- (+ (* (cos eps) (sin x)) (* (cos x) (sin eps))) (sin x))
(- (+ (* (cos eps) (sin x)) (* (cos x) (sin eps))) (sin x))
(- (+ (* (cos eps) (sin x)) (* (cos x) (sin eps))) (sin x))
(cos eps)
(cos eps)
(cos eps)
(cos eps)
(- (* (cos x) (sin eps)) (sin x))
(- (* (cos x) (sin eps)) (sin x))
(- (* (cos x) (sin eps)) (sin x))
(- (* (cos x) (sin eps)) (sin x))
(sin (* 1/2 eps))
(sin (* 1/2 eps))
(sin (* 1/2 eps))
(sin (* 1/2 eps))
(* 2 (sin (* 1/2 eps)))
(* 2 (sin (* 1/2 eps)))
(* 2 (sin (* 1/2 eps)))
(* 2 (sin (* 1/2 eps)))
(- (cos eps) 1)
(- (cos eps) 1)
(- (cos eps) 1)
(- (cos eps) 1)
(* -1/2 eps)
(+ (* -1 x) (* -1/2 eps))
(+ (* -1 x) (* -1/2 eps))
(+ (* -1 x) (* -1/2 eps))
(cos (* -1/2 eps))
(+ (cos (* -1/2 eps)) (* x (sin (* -1/2 eps))))
(+ (cos (* -1/2 eps)) (* x (- (* -1/2 (* x (cos (* -1/2 eps)))) (* -1 (sin (* -1/2 eps))))))
(+ (cos (* -1/2 eps)) (* x (- (* x (+ (* -1/2 (cos (* -1/2 eps))) (* -1/6 (* x (sin (* -1/2 eps)))))) (* -1 (sin (* -1/2 eps))))))
(* 2 (* (cos (* -1/2 eps)) (sin (* 1/2 eps))))
(+ (* 2 (* x (* (sin (* -1/2 eps)) (sin (* 1/2 eps))))) (* 2 (* (cos (* -1/2 eps)) (sin (* 1/2 eps)))))
(+ (* 2 (* (cos (* -1/2 eps)) (sin (* 1/2 eps)))) (* x (+ (* -1 (* x (* (cos (* -1/2 eps)) (sin (* 1/2 eps))))) (* 2 (* (sin (* -1/2 eps)) (sin (* 1/2 eps)))))))
(+ (* 2 (* (cos (* -1/2 eps)) (sin (* 1/2 eps)))) (* x (+ (* 2 (* (sin (* -1/2 eps)) (sin (* 1/2 eps)))) (* x (+ (* -1 (* (cos (* -1/2 eps)) (sin (* 1/2 eps)))) (* -1/3 (* x (* (sin (* -1/2 eps)) (sin (* 1/2 eps))))))))))
(sin eps)
(+ (sin eps) (* x (- (cos eps) 1)))
(+ (sin eps) (* x (- (+ (cos eps) (* -1/2 (* x (sin eps)))) 1)))
(+ (sin eps) (* x (- (+ (cos eps) (* x (+ (* -1/2 (sin eps)) (* x (+ 1/6 (* -1/6 (cos eps))))))) 1)))
(sin eps)
(+ (sin eps) (* x (- (cos eps) 1)))
(+ (sin eps) (* x (- (+ (cos eps) (* -1/2 (* x (sin eps)))) 1)))
(+ (sin eps) (* x (- (+ (cos eps) (* x (+ (* -1/2 (sin eps)) (* x (+ 1/6 (* -1/6 (cos eps))))))) 1)))
(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))))))))
x
(* x (+ 1 (* -1/6 (pow x 2))))
(* x (+ 1 (* (pow x 2) (- (* 1/120 (pow x 2)) 1/6))))
(* x (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/120 (* -1/5040 (pow x 2)))) 1/6))))
(sin eps)
(+ (sin eps) (* x (- (cos eps) 1)))
(+ (sin eps) (* x (- (+ (cos eps) (* -1/2 (* x (sin eps)))) 1)))
(+ (sin eps) (* x (- (+ (cos eps) (* x (+ (* -1/2 (sin eps)) (* x (+ 1/6 (* -1/6 (cos eps))))))) 1)))
(sin eps)
(+ (sin eps) (* x (- (cos eps) 1)))
(+ (sin eps) (* x (- (+ (cos eps) (* -1/2 (* x (sin eps)))) 1)))
(+ (sin eps) (* x (- (+ (cos eps) (* -1/2 (* x (sin eps)))) 1)))
(- (cos eps) 1)
(- (+ (cos eps) (* -1/2 (* x (sin eps)))) 1)
(- (+ (cos eps) (* -1/2 (* x (sin eps)))) 1)
(- (+ (cos eps) (* -1/2 (* x (sin eps)))) 1)
(* x (sin eps))
(* x (sin eps))
(* x (sin eps))
(* x (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)
(+ (sin eps) (* -1 x))
(+ (sin eps) (* x (- (* -1/2 (* x (sin eps))) 1)))
(+ (sin eps) (* x (- (* x (+ (* -1/2 (sin eps)) (* 1/6 x))) 1)))
1
(+ 1 (* -1/2 (pow x 2)))
(+ 1 (* (pow x 2) (- (* 1/24 (pow x 2)) 1/2)))
(+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))) 1/2)))
(* -1 x)
(* x (- (* -1/2 (/ eps x)) 1))
(* x (- (* -1/2 (/ eps x)) 1))
(* x (- (* -1/2 (/ eps x)) 1))
(cos (* -1/2 (+ eps (* 2 x))))
(cos (* -1/2 (+ eps (* 2 x))))
(cos (* -1/2 (+ eps (* 2 x))))
(cos (* -1/2 (+ eps (* 2 x))))
(* 2 (* (cos (* -1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))))
(* 2 (* (cos (* -1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))))
(* 2 (* (cos (* -1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))))
(* 2 (* (cos (* -1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))))
(- (sin (+ eps x)) (sin x))
(- (sin (+ eps x)) (sin x))
(- (sin (+ eps x)) (sin x))
(- (sin (+ eps x)) (sin x))
(- (sin (+ eps x)) (sin x))
(- (sin (+ eps x)) (sin x))
(- (sin (+ eps x)) (sin x))
(- (sin (+ eps x)) (sin x))
(sin (+ eps x))
(sin (+ eps x))
(sin (+ eps x))
(sin (+ eps x))
(sin x)
(sin x)
(sin x)
(sin x)
(- (sin (+ eps x)) (sin x))
(- (sin (+ eps x)) (sin x))
(- (sin (+ eps x)) (sin x))
(- (sin (+ eps x)) (sin x))
(* -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 (* x (sin eps)))
(* x (- (+ (* -1/2 (sin eps)) (/ (cos eps) x)) (/ 1 x)))
(* x (- (+ (* -1/2 (sin eps)) (/ (cos eps) x)) (/ 1 x)))
(* x (- (+ (* -1/2 (sin eps)) (/ (cos eps) x)) (/ 1 x)))
(* x (sin eps))
(* x (sin eps))
(* x (sin eps))
(* x (sin eps))
(- (+ (* (cos eps) (sin x)) (* (cos x) (sin eps))) (sin x))
(- (+ (* (cos eps) (sin x)) (* (cos x) (sin eps))) (sin x))
(- (+ (* (cos eps) (sin x)) (* (cos x) (sin eps))) (sin x))
(- (+ (* (cos eps) (sin x)) (* (cos x) (sin eps))) (sin x))
(- (* (cos x) (sin eps)) (sin x))
(- (* (cos x) (sin eps)) (sin x))
(- (* (cos x) (sin eps)) (sin x))
(- (* (cos x) (sin eps)) (sin x))
(cos x)
(cos x)
(cos x)
(cos x)
(* -1 x)
(* -1 (* x (+ 1 (* 1/2 (/ eps x)))))
(* -1 (* x (+ 1 (* 1/2 (/ eps x)))))
(* -1 (* x (+ 1 (* 1/2 (/ eps x)))))
(cos (* -1/2 (- eps (* -2 x))))
(cos (* -1/2 (- eps (* -2 x))))
(cos (* -1/2 (- eps (* -2 x))))
(cos (* -1/2 (- eps (* -2 x))))
(* 2 (* (cos (* -1/2 (- eps (* -2 x)))) (sin (* 1/2 eps))))
(* 2 (* (cos (* -1/2 (- eps (* -2 x)))) (sin (* 1/2 eps))))
(* 2 (* (cos (* -1/2 (- eps (* -2 x)))) (sin (* 1/2 eps))))
(* 2 (* (cos (* -1/2 (- eps (* -2 x)))) (sin (* 1/2 eps))))
(- (sin (- eps (* -1 x))) (sin x))
(- (sin (- eps (* -1 x))) (sin x))
(- (sin (- eps (* -1 x))) (sin x))
(- (sin (- eps (* -1 x))) (sin x))
(- (sin (- eps (* -1 x))) (sin x))
(- (sin (- eps (* -1 x))) (sin x))
(- (sin (- eps (* -1 x))) (sin x))
(- (sin (- eps (* -1 x))) (sin x))
(sin (- eps (* -1 x)))
(sin (- eps (* -1 x)))
(sin (- eps (* -1 x)))
(sin (- eps (* -1 x)))
(sin x)
(sin x)
(sin x)
(sin x)
(- (sin (- eps (* -1 x))) (sin x))
(- (sin (- eps (* -1 x))) (sin x))
(- (sin (- eps (* -1 x))) (sin x))
(- (sin (- eps (* -1 x))) (sin x))
(* -1/2 (* (pow x 2) (sin eps)))
(* (pow x 2) (- (+ (* -1/2 (sin eps)) (/ (cos eps) x)) (/ 1 x)))
(* (pow x 2) (+ (* -1 (/ (+ (* -1 (- (cos eps) 1)) (* -1 (/ (sin eps) x))) x)) (* -1/2 (sin eps))))
(* (pow x 2) (+ (* -1 (/ (+ (* -1 (- (cos eps) 1)) (* -1 (/ (sin eps) x))) x)) (* -1/2 (sin eps))))
(* -1/2 (* x (sin eps)))
(* -1 (* x (+ (* -1 (/ (- (cos eps) 1) x)) (* 1/2 (sin eps)))))
(* -1 (* x (+ (* -1 (/ (- (cos eps) 1) x)) (* 1/2 (sin eps)))))
(* -1 (* x (+ (* -1 (/ (- (cos eps) 1) x)) (* 1/2 (sin eps)))))
(* x (sin eps))
(* x (sin eps))
(* x (sin eps))
(* x (sin eps))
(- (+ (* (cos eps) (sin x)) (* (cos x) (sin eps))) (sin x))
(- (+ (* (cos eps) (sin x)) (* (cos x) (sin eps))) (sin x))
(- (+ (* (cos eps) (sin x)) (* (cos x) (sin eps))) (sin x))
(- (+ (* (cos eps) (sin x)) (* (cos x) (sin eps))) (sin x))
(- (* (cos x) (sin eps)) (sin x))
(- (* (cos x) (sin eps)) (sin x))
(- (* (cos x) (sin eps)) (sin x))
(- (* (cos x) (sin eps)) (sin x))
(cos x)
(cos x)
(cos x)
(cos x)

Outputs
(* -1 x)
(neg.f64 x)
(+ (* -1 x) (* -1/2 eps))
(fma.f64 eps #s(literal -1/2 binary64) (neg.f64 x))
(+ (* -1 x) (* -1/2 eps))
(fma.f64 eps #s(literal -1/2 binary64) (neg.f64 x))
(+ (* -1 x) (* -1/2 eps))
(fma.f64 eps #s(literal -1/2 binary64) (neg.f64 x))
eps
eps
eps
eps
(cos (* -1 x))
(cos.f64 x)
(+ (cos (* -1 x)) (* 1/2 (* eps (sin (* -1 x)))))
(fma.f64 (*.f64 (sin.f64 x) eps) #s(literal -1/2 binary64) (cos.f64 x))
(+ (cos (* -1 x)) (* eps (- (* -1/8 (* eps (cos (* -1 x)))) (* -1/2 (sin (* -1 x))))))
(fma.f64 (fma.f64 (sin.f64 x) #s(literal -1/2 binary64) (.f64 (.f64 (cos.f64 x) #s(literal -1/8 binary64)) eps)) eps (cos.f64 x))
(+ (cos (* -1 x)) (* eps (- (* eps (+ (* -1/8 (cos (* -1 x))) (* -1/48 (* eps (sin (* -1 x)))))) (* -1/2 (sin (* -1 x))))))
(fma.f64 (fma.f64 (neg.f64 (sin.f64 x)) (fma.f64 (.f64 eps eps) #s(literal -1/48 binary64) #s(literal 1/2 binary64)) (.f64 (*.f64 (cos.f64 x) #s(literal -1/8 binary64)) eps)) eps (cos.f64 x))
(* eps (cos (* -1 x)))
(*.f64 (cos.f64 x) eps)
(* eps (+ (cos (* -1 x)) (* 1/2 (* eps (sin (* -1 x))))))
(.f64 (fma.f64 (.f64 (sin.f64 x) eps) #s(literal -1/2 binary64) (cos.f64 x)) eps)
(* eps (+ (cos (* -1 x)) (* eps (+ (* 1/2 (sin (* -1 x))) (* 2 (* eps (+ (* -1/16 (cos (* -1 x))) (* -1/48 (cos (* -1 x))))))))))
(.f64 (fma.f64 (fma.f64 (.f64 #s(literal -1/6 binary64) eps) (cos.f64 x) (*.f64 (sin.f64 x) #s(literal -1/2 binary64))) eps (cos.f64 x)) eps)
(* eps (+ (cos (* -1 x)) (* eps (+ (* 1/2 (sin (* -1 x))) (* eps (+ (* -1/24 (* eps (sin (* -1 x)))) (* 2 (+ (* -1/16 (cos (* -1 x))) (* -1/48 (cos (* -1 x)))))))))))
(.f64 (fma.f64 (fma.f64 (neg.f64 (sin.f64 x)) (+.f64 #s(literal 1/2 binary64) (.f64 (.f64 eps eps) #s(literal -1/24 binary64))) (.f64 (*.f64 #s(literal -1/6 binary64) (cos.f64 x)) eps)) eps (cos.f64 x)) eps)
(* eps (cos x))
(*.f64 (cos.f64 x) eps)
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(.f64 (fma.f64 (.f64 (sin.f64 x) eps) #s(literal -1/2 binary64) (cos.f64 x)) eps)
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x)))))))
(.f64 (fma.f64 (fma.f64 (.f64 #s(literal -1/6 binary64) eps) (cos.f64 x) (*.f64 (sin.f64 x) #s(literal -1/2 binary64))) eps (cos.f64 x)) eps)
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* eps (+ (* -1/6 (cos x)) (* 1/24 (* eps (sin x)))))))))
(.f64 (fma.f64 (fma.f64 (sin.f64 x) (fma.f64 (.f64 #s(literal 1/24 binary64) eps) eps #s(literal -1/2 binary64)) (.f64 (.f64 #s(literal -1/6 binary64) (cos.f64 x)) eps)) eps (cos.f64 x)) eps)
eps
(* eps (+ 1 (* -1/6 (pow eps 2))))
(fma.f64 (pow.f64 eps #s(literal 3 binary64)) #s(literal -1/6 binary64) eps)
(* eps (+ 1 (* (pow eps 2) (- (* 1/120 (pow eps 2)) 1/6))))
(fma.f64 (pow.f64 eps #s(literal 3 binary64)) (fma.f64 #s(literal 1/120 binary64) (*.f64 eps eps) #s(literal -1/6 binary64)) eps)
(* eps (+ 1 (* (pow eps 2) (- (* (pow eps 2) (+ 1/120 (* -1/5040 (pow eps 2)))) 1/6))))
(fma.f64 (pow.f64 eps #s(literal 3 binary64)) (fma.f64 (fma.f64 #s(literal -1/5040 binary64) (.f64 eps eps) #s(literal 1/120 binary64)) (.f64 eps eps) #s(literal -1/6 binary64)) eps)
(* eps (cos x))
(*.f64 (cos.f64 x) eps)
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(.f64 (fma.f64 (.f64 (sin.f64 x) eps) #s(literal -1/2 binary64) (cos.f64 x)) eps)
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x)))))))
(.f64 (fma.f64 (fma.f64 (.f64 #s(literal -1/6 binary64) eps) (cos.f64 x) (*.f64 (sin.f64 x) #s(literal -1/2 binary64))) eps (cos.f64 x)) eps)
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* eps (+ (* -1/6 (cos x)) (* 1/24 (* eps (sin x)))))))))
(.f64 (fma.f64 (fma.f64 (sin.f64 x) (fma.f64 (.f64 #s(literal 1/24 binary64) eps) eps #s(literal -1/2 binary64)) (.f64 (.f64 #s(literal -1/6 binary64) (cos.f64 x)) eps)) eps (cos.f64 x)) eps)
(sin x)
(sin.f64 x)
(+ (sin x) (* eps (cos x)))
(fma.f64 (cos.f64 x) eps (sin.f64 x))
(+ (sin x) (* eps (+ (cos x) (* -1/2 (* eps (sin x))))))
(fma.f64 (fma.f64 (*.f64 (sin.f64 x) eps) #s(literal -1/2 binary64) (cos.f64 x)) eps (sin.f64 x))
(+ (sin x) (* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x))))))))
(fma.f64 (fma.f64 (fma.f64 (.f64 #s(literal -1/6 binary64) eps) (cos.f64 x) (.f64 (sin.f64 x) #s(literal -1/2 binary64))) eps (cos.f64 x)) eps (sin.f64 x))
(* eps (cos x))
(*.f64 (cos.f64 x) eps)
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(.f64 (fma.f64 (.f64 (sin.f64 x) eps) #s(literal -1/2 binary64) (cos.f64 x)) eps)
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x)))))))
(.f64 (fma.f64 (fma.f64 (.f64 #s(literal -1/6 binary64) eps) (cos.f64 x) (*.f64 (sin.f64 x) #s(literal -1/2 binary64))) eps (cos.f64 x)) eps)
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* eps (+ (* -1/6 (cos x)) (* 1/24 (* eps (sin x)))))))))
(.f64 (fma.f64 (fma.f64 (sin.f64 x) (fma.f64 (.f64 #s(literal 1/24 binary64) eps) eps #s(literal -1/2 binary64)) (.f64 (.f64 #s(literal -1/6 binary64) (cos.f64 x)) eps)) eps (cos.f64 x)) eps)
(* eps (+ 1 (* -1/2 (pow x 2))))
(.f64 (fma.f64 (.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64)) eps)
(* eps (+ 1 (+ (* -1/2 (* eps x)) (* -1/2 (pow x 2)))))
(.f64 (fma.f64 (.f64 x (+.f64 eps x)) #s(literal -1/2 binary64) #s(literal 1 binary64)) eps)
(* eps (+ 1 (+ (* -1/2 (pow x 2)) (* eps (+ (* -1/2 x) (* eps (- (* 1/12 (pow x 2)) 1/6)))))))
(.f64 (fma.f64 (.f64 x (+.f64 eps x)) #s(literal -1/2 binary64) (fma.f64 (.f64 (fma.f64 #s(literal 1/12 binary64) (.f64 x x) #s(literal -1/6 binary64)) eps) eps #s(literal 1 binary64))) eps)
(* eps (+ 1 (+ (* -1/2 (pow x 2)) (* eps (+ (* -1/2 x) (* eps (- (+ (* 1/24 (* eps x)) (* 1/12 (pow x 2))) 1/6)))))))
(.f64 (fma.f64 (.f64 (fma.f64 x (fma.f64 #s(literal 1/12 binary64) x (.f64 #s(literal 1/24 binary64) eps)) #s(literal -1/6 binary64)) eps) eps (fma.f64 (.f64 x (+.f64 eps x)) #s(literal -1/2 binary64) #s(literal 1 binary64))) eps)
(* -1/2 (* eps x))
(.f64 (.f64 #s(literal -1/2 binary64) x) eps)
(* eps (+ (* -1/2 eps) (* -1/2 x)))
(.f64 #s(literal -1/2 binary64) (.f64 (+.f64 eps x) eps))
(* eps (+ (* -1/2 x) (* eps (- (* 1/12 (* eps x)) 1/2))))
(.f64 (fma.f64 (fma.f64 #s(literal 1/12 binary64) (.f64 eps x) #s(literal -1/2 binary64)) eps (*.f64 #s(literal -1/2 binary64) x)) eps)
(* eps (+ (* -1/2 x) (* eps (- (* eps (+ (* 1/24 eps) (* 1/12 x))) 1/2))))
(.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 1/12 binary64) x (.f64 #s(literal 1/24 binary64) eps)) eps #s(literal -1/2 binary64)) eps (*.f64 #s(literal -1/2 binary64) x)) eps)
(* eps x)
(*.f64 eps x)
(* eps (+ x (* -1/6 (* (pow eps 2) x))))
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(cos.f64 (fma.f64 eps #s(literal -1/2 binary64) (neg.f64 x)))
(cos (* -1/2 (- eps (* -2 x))))
(cos.f64 (fma.f64 eps #s(literal -1/2 binary64) (neg.f64 x)))
(* 2 (* (cos (* -1/2 (- eps (* -2 x)))) (sin (* 1/2 eps))))
(.f64 (cos.f64 (fma.f64 eps #s(literal -1/2 binary64) (neg.f64 x))) (.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) #s(literal 2 binary64)))
(* 2 (* (cos (* -1/2 (- eps (* -2 x)))) (sin (* 1/2 eps))))
(.f64 (cos.f64 (fma.f64 eps #s(literal -1/2 binary64) (neg.f64 x))) (.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) #s(literal 2 binary64)))
(* 2 (* (cos (* -1/2 (- eps (* -2 x)))) (sin (* 1/2 eps))))
(.f64 (cos.f64 (fma.f64 eps #s(literal -1/2 binary64) (neg.f64 x))) (.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) #s(literal 2 binary64)))
(* 2 (* (cos (* -1/2 (- eps (* -2 x)))) (sin (* 1/2 eps))))
(.f64 (cos.f64 (fma.f64 eps #s(literal -1/2 binary64) (neg.f64 x))) (.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) #s(literal 2 binary64)))
(- (sin (- eps (* -1 x))) (sin x))
(-.f64 (sin.f64 (+.f64 eps x)) (sin.f64 x))
(- (sin (- eps (* -1 x))) (sin x))
(-.f64 (sin.f64 (+.f64 eps x)) (sin.f64 x))
(- (sin (- eps (* -1 x))) (sin x))
(-.f64 (sin.f64 (+.f64 eps x)) (sin.f64 x))
(- (sin (- eps (* -1 x))) (sin x))
(-.f64 (sin.f64 (+.f64 eps x)) (sin.f64 x))
(- (sin (- eps (* -1 x))) (sin x))
(-.f64 (sin.f64 (+.f64 eps x)) (sin.f64 x))
(- (sin (- eps (* -1 x))) (sin x))
(-.f64 (sin.f64 (+.f64 eps x)) (sin.f64 x))
(- (sin (- eps (* -1 x))) (sin x))
(-.f64 (sin.f64 (+.f64 eps x)) (sin.f64 x))
(- (sin (- eps (* -1 x))) (sin x))
(-.f64 (sin.f64 (+.f64 eps x)) (sin.f64 x))
(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)
(sin.f64 x)
(sin x)
(sin.f64 x)
(sin 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))
(* -1/2 (* (pow x 2) (sin eps)))
(.f64 (.f64 (*.f64 (sin.f64 eps) #s(literal -1/2 binary64)) x) x)
(* (pow x 2) (- (+ (* -1/2 (sin eps)) (/ (cos eps) x)) (/ 1 x)))
(.f64 (.f64 (fma.f64 (sin.f64 eps) #s(literal -1/2 binary64) (/.f64 (-.f64 (cos.f64 eps) #s(literal 1 binary64)) x)) x) x)
(* (pow x 2) (+ (* -1 (/ (+ (* -1 (- (cos eps) 1)) (* -1 (/ (sin eps) x))) x)) (* -1/2 (sin eps))))
(.f64 (.f64 (fma.f64 (sin.f64 eps) #s(literal -1/2 binary64) (/.f64 (-.f64 (cos.f64 eps) (-.f64 #s(literal 1 binary64) (/.f64 (sin.f64 eps) x))) x)) x) x)
(* (pow x 2) (+ (* -1 (/ (+ (* -1 (- (cos eps) 1)) (* -1 (/ (sin eps) x))) x)) (* -1/2 (sin eps))))
(.f64 (.f64 (fma.f64 (sin.f64 eps) #s(literal -1/2 binary64) (/.f64 (-.f64 (cos.f64 eps) (-.f64 #s(literal 1 binary64) (/.f64 (sin.f64 eps) x))) x)) x) x)
(* -1/2 (* x (sin eps)))
(.f64 (.f64 (sin.f64 eps) #s(literal -1/2 binary64)) x)
(* -1 (* x (+ (* -1 (/ (- (cos eps) 1) x)) (* 1/2 (sin eps)))))
(*.f64 (fma.f64 (sin.f64 eps) #s(literal -1/2 binary64) (/.f64 (-.f64 (cos.f64 eps) #s(literal 1 binary64)) x)) x)
(* -1 (* x (+ (* -1 (/ (- (cos eps) 1) x)) (* 1/2 (sin eps)))))
(*.f64 (fma.f64 (sin.f64 eps) #s(literal -1/2 binary64) (/.f64 (-.f64 (cos.f64 eps) #s(literal 1 binary64)) x)) x)
(* -1 (* x (+ (* -1 (/ (- (cos eps) 1) x)) (* 1/2 (sin eps)))))
(*.f64 (fma.f64 (sin.f64 eps) #s(literal -1/2 binary64) (/.f64 (-.f64 (cos.f64 eps) #s(literal 1 binary64)) x)) x)
(* x (sin eps))
(*.f64 (sin.f64 eps) x)
(* x (sin eps))
(*.f64 (sin.f64 eps) x)
(* x (sin eps))
(*.f64 (sin.f64 eps) x)
(* x (sin eps))
(*.f64 (sin.f64 eps) x)
(- (+ (* (cos eps) (sin x)) (* (cos x) (sin eps))) (sin x))
(fma.f64 (sin.f64 x) (-.f64 (cos.f64 eps) #s(literal 1 binary64)) (*.f64 (sin.f64 eps) (cos.f64 x)))
(- (+ (* (cos eps) (sin x)) (* (cos x) (sin eps))) (sin x))
(fma.f64 (sin.f64 x) (-.f64 (cos.f64 eps) #s(literal 1 binary64)) (*.f64 (sin.f64 eps) (cos.f64 x)))
(- (+ (* (cos eps) (sin x)) (* (cos x) (sin eps))) (sin x))
(fma.f64 (sin.f64 x) (-.f64 (cos.f64 eps) #s(literal 1 binary64)) (*.f64 (sin.f64 eps) (cos.f64 x)))
(- (+ (* (cos eps) (sin x)) (* (cos x) (sin eps))) (sin x))
(fma.f64 (sin.f64 x) (-.f64 (cos.f64 eps) #s(literal 1 binary64)) (*.f64 (sin.f64 eps) (cos.f64 x)))
(- (* (cos x) (sin eps)) (sin x))
(fma.f64 (sin.f64 eps) (cos.f64 x) (neg.f64 (sin.f64 x)))
(- (* (cos x) (sin eps)) (sin x))
(fma.f64 (sin.f64 eps) (cos.f64 x) (neg.f64 (sin.f64 x)))
(- (* (cos x) (sin eps)) (sin x))
(fma.f64 (sin.f64 eps) (cos.f64 x) (neg.f64 (sin.f64 x)))
(- (* (cos x) (sin eps)) (sin x))
(fma.f64 (sin.f64 eps) (cos.f64 x) (neg.f64 (sin.f64 x)))
(cos x)
(cos.f64 x)
(cos x)
(cos.f64 x)
(cos x)
(cos.f64 x)
(cos x)
(cos.f64 x)

rewrite167.0ms (1.3%)

Memory

-3.6MiB live, 189.8MiB allocated

Rules

4 500×	`lower-/.f32`
4 498×	`lower-/.f64`
4 234×	`lower-*.f32`
4 226×	`lower-*.f64`
3 116×	`lower-fma.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	35	156
0	60	142
1	241	142
2	1948	142
0	8307	142

Stop Event

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

Counts

20 → 429

Calls

Call 1

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

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

eval111.0ms (0.9%)

Memory: 19.1MiB live, 175.8MiB allocated
Compiler: Compiled 21 813 to 2 258 computations (89.6% saved)

prune25.0ms (0.2%)

Memory

-6.0MiB live, 69.9MiB allocated

Pruning

15 alts after pruning (11 fresh and 4 done)

	Pruned	Kept	Total
New	901	10	911
Fresh	2	1	3
Picked	2	3	5
Done	0	1	1
Total	905	15	920

Accuracy

100.0%

Counts

920 → 15

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	65.7%	(fma.f64 (sin.f64 x) (cos.f64 eps) (fma.f64 (sin.f64 eps) (cos.f64 x) (neg.f64 (sin.f64 x))))
✓	65.5%	(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
✓	7.9%	(-.f64 #s(approx (sin (+ x eps)) (sin.f64 eps)) (sin.f64 x))
▶	99.5%	(.f64 (.f64 #s(approx (sin (* 1/2 (+ 0 eps))) (.f64 (fma.f64 (.f64 eps eps) #s(literal -1/48 binary64) #s(literal 1/2 binary64)) eps)) #s(literal 2 binary64)) (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64))))
	99.5%	(.f64 (.f64 #s(approx (sin (* 1/2 (+ 0 eps))) (*.f64 #s(literal 1/2 binary64) eps)) #s(literal 2 binary64)) (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64))))
▶	98.8%	#s(approx (- (sin (+ x eps)) (sin x)) (fma.f64 #s(approx (+ (* (* (sin eps) x) -1/2) (- (cos eps) 1)) (.f64 (.f64 #s(literal -1/2 binary64) x) eps)) x (sin.f64 eps)))
	99.6%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 (fma.f64 (.f64 #s(literal -1/6 binary64) eps) (cos.f64 x) (*.f64 (sin.f64 x) #s(literal -1/2 binary64))) eps (cos.f64 x)) eps))
	99.5%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 (.f64 (sin.f64 x) eps) #s(literal -1/2 binary64) (cos.f64 x)) eps))
	99.2%	#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (cos.f64 x) eps))
✓	98.5%	#s(approx (- (sin (+ x eps)) (sin x)) (sin.f64 eps))
▶	98.8%	#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (+ (* (+ (* (* (sin eps) x) -1/2) (- (cos eps) 1)) x) (sin eps)) (.f64 (fma.f64 (.f64 x (+.f64 eps x)) #s(literal -1/2 binary64) (fma.f64 (.f64 (fma.f64 #s(literal 1/12 binary64) (.f64 x x) #s(literal -1/6 binary64)) eps) eps #s(literal 1 binary64))) eps)))
	98.9%	#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (+ (* (+ (* (* (sin eps) x) -1/2) (- (cos eps) 1)) x) (sin eps)) (.f64 (fma.f64 (.f64 x (+.f64 eps x)) #s(literal -1/2 binary64) #s(literal 1 binary64)) eps)))
▶	98.8%	#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (+ (* (+ (* (* (sin eps) x) -1/2) (- (cos eps) 1)) x) (sin eps)) (.f64 (fma.f64 (.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64)) eps)))
	99.7%	#s(approx (+ (* (sin x) (cos eps)) (+ (* (sin eps) (cos x)) (neg (sin x)))) (fma.f64 (sin.f64 x) (-.f64 (cos.f64 eps) #s(literal 1 binary64)) (*.f64 (sin.f64 eps) (cos.f64 x))))
▶	99.9%	#s(approx (* (* (sin (* 1/2 (+ 0 eps))) 2) (cos (/ (+ (* 2 x) eps) -2))) (.f64 (cos.f64 (fma.f64 eps #s(literal -1/2 binary64) (neg.f64 x))) (.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) #s(literal 2 binary64))))

Compiler

Compiled 325 to 267 computations (17.8% saved)

simplify161.0ms (1.3%)

Memory

-3.4MiB live, 78.3MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 20 expressions of interest:

New	Metric	Score
cost-diff	0	(.f64 #s(approx (sin ( 1/2 (+ 0 eps))) (.f64 (fma.f64 (.f64 eps eps) #s(literal -1/48 binary64) #s(literal 1/2 binary64)) eps)) #s(literal 2 binary64))
cost-diff	0	(.f64 (.f64 #s(approx (sin (* 1/2 (+ 0 eps))) (.f64 (fma.f64 (.f64 eps eps) #s(literal -1/48 binary64) #s(literal 1/2 binary64)) eps)) #s(literal 2 binary64)) (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64))))
cost-diff	128	(cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64)))
cost-diff	576	(/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64))
cost-diff	0	(.f64 (.f64 #s(literal -1/2 binary64) x) eps)
cost-diff	0	#s(approx (+ (* (* (sin eps) x) -1/2) (- (cos eps) 1)) (.f64 (.f64 #s(literal -1/2 binary64) x) eps))
cost-diff	0	(fma.f64 #s(approx (+ (* (* (sin eps) x) -1/2) (- (cos eps) 1)) (.f64 (.f64 #s(literal -1/2 binary64) x) eps)) x (sin.f64 eps))
cost-diff	0	#s(approx (- (sin (+ x eps)) (sin x)) (fma.f64 #s(approx (+ (* (* (sin eps) x) -1/2) (- (cos eps) 1)) (.f64 (.f64 #s(literal -1/2 binary64) x) eps)) x (sin.f64 eps)))
cost-diff	0	(fma.f64 (.f64 x (+.f64 eps x)) #s(literal -1/2 binary64) (fma.f64 (.f64 (fma.f64 #s(literal 1/12 binary64) (*.f64 x x) #s(literal -1/6 binary64)) eps) eps #s(literal 1 binary64)))
cost-diff	0	(.f64 (fma.f64 (.f64 x (+.f64 eps x)) #s(literal -1/2 binary64) (fma.f64 (.f64 (fma.f64 #s(literal 1/12 binary64) (.f64 x x) #s(literal -1/6 binary64)) eps) eps #s(literal 1 binary64))) eps)
cost-diff	0	#s(approx (+ (* (+ (* (* (sin eps) x) -1/2) (- (cos eps) 1)) x) (sin eps)) (.f64 (fma.f64 (.f64 x (+.f64 eps x)) #s(literal -1/2 binary64) (fma.f64 (.f64 (fma.f64 #s(literal 1/12 binary64) (.f64 x x) #s(literal -1/6 binary64)) eps) eps #s(literal 1 binary64))) eps))
cost-diff	0	#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (+ (* (+ (* (* (sin eps) x) -1/2) (- (cos eps) 1)) x) (sin eps)) (.f64 (fma.f64 (.f64 x (+.f64 eps x)) #s(literal -1/2 binary64) (fma.f64 (.f64 (fma.f64 #s(literal 1/12 binary64) (.f64 x x) #s(literal -1/6 binary64)) eps) eps #s(literal 1 binary64))) eps)))
cost-diff	0	(fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64))
cost-diff	0	(.f64 (fma.f64 (.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64)) eps)
cost-diff	0	#s(approx (+ (* (+ (* (* (sin eps) x) -1/2) (- (cos eps) 1)) x) (sin eps)) (.f64 (fma.f64 (.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64)) eps))
cost-diff	0	#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (+ (* (+ (* (* (sin eps) x) -1/2) (- (cos eps) 1)) x) (sin eps)) (.f64 (fma.f64 (.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64)) eps)))
cost-diff	0	(fma.f64 eps #s(literal -1/2 binary64) (neg.f64 x))
cost-diff	0	(.f64 (cos.f64 (fma.f64 eps #s(literal -1/2 binary64) (neg.f64 x))) (.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) #s(literal 2 binary64)))
cost-diff	0	#s(approx (* (* (sin (* 1/2 (+ 0 eps))) 2) (cos (/ (+ (* 2 x) eps) -2))) (.f64 (cos.f64 (fma.f64 eps #s(literal -1/2 binary64) (neg.f64 x))) (.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) #s(literal 2 binary64))))
cost-diff	128	(cos.f64 (fma.f64 eps #s(literal -1/2 binary64) (neg.f64 x)))

Rules

12 442×	`lower-fma.f32`
12 426×	`lower-fma.f64`
3 284×	`lower-*.f32`
3 256×	`lower-*.f64`
2 260×	`lower-+.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	69	492
0	105	482
1	184	482
2	365	482
3	850	482
4	1913	482
5	2738	482
6	3408	482
7	4833	482
8	6584	480
9	7873	480
0	8034	463

Stop Event

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

Calls

Call 1

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

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

localize401.0ms (3.2%)

Memory

-1.1MiB live, 231.4MiB allocated

Localize:

Found 20 expressions of interest:

New	Metric	Score
accuracy	0.0078125	(.f64 (fma.f64 (.f64 eps eps) #s(literal -1/48 binary64) #s(literal 1/2 binary64)) eps)
accuracy	0.01171875	(.f64 (.f64 #s(approx (sin (* 1/2 (+ 0 eps))) (.f64 (fma.f64 (.f64 eps eps) #s(literal -1/48 binary64) #s(literal 1/2 binary64)) eps)) #s(literal 2 binary64)) (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64))))
accuracy	0.08925386872974028	(cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64)))
accuracy	0.2461120916758713	#s(approx (sin (* 1/2 (+ 0 eps))) (.f64 (fma.f64 (.f64 eps eps) #s(literal -1/48 binary64) #s(literal 1/2 binary64)) eps))
accuracy	0	(*.f64 #s(literal -1/2 binary64) x)
accuracy	0	(sin.f64 eps)
accuracy	0.7098673144904891	#s(approx (- (sin (+ x eps)) (sin x)) (fma.f64 #s(approx (+ (* (* (sin eps) x) -1/2) (- (cos eps) 1)) (.f64 (.f64 #s(literal -1/2 binary64) x) eps)) x (sin.f64 eps)))
accuracy	12.739737755540691	#s(approx (+ (* (* (sin eps) x) -1/2) (- (cos eps) 1)) (.f64 (.f64 #s(literal -1/2 binary64) x) eps))
accuracy	0.0859375	(*.f64 x (+.f64 eps x))
accuracy	0.24623485261033592	#s(approx (+ (* (+ (* (* (sin eps) x) -1/2) (- (cos eps) 1)) x) (sin eps)) (.f64 (fma.f64 (.f64 x (+.f64 eps x)) #s(literal -1/2 binary64) (fma.f64 (.f64 (fma.f64 #s(literal 1/12 binary64) (.f64 x x) #s(literal -1/6 binary64)) eps) eps #s(literal 1 binary64))) eps))
accuracy	0.37109375	(.f64 (fma.f64 #s(literal 1/12 binary64) (.f64 x x) #s(literal -1/6 binary64)) eps)
accuracy	0.7098673144904891	#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (+ (* (+ (* (* (sin eps) x) -1/2) (- (cos eps) 1)) x) (sin eps)) (.f64 (fma.f64 (.f64 x (+.f64 eps x)) #s(literal -1/2 binary64) (fma.f64 (.f64 (fma.f64 #s(literal 1/12 binary64) (.f64 x x) #s(literal -1/6 binary64)) eps) eps #s(literal 1 binary64))) eps)))
accuracy	0	(*.f64 x x)
accuracy	0.0078125	(.f64 (fma.f64 (.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64)) eps)
accuracy	0.44968963782770377	#s(approx (+ (* (+ (* (* (sin eps) x) -1/2) (- (cos eps) 1)) x) (sin eps)) (.f64 (fma.f64 (.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64)) eps))
accuracy	0.7098673144904891	#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (+ (* (+ (* (* (sin eps) x) -1/2) (- (cos eps) 1)) x) (sin eps)) (.f64 (fma.f64 (.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64)) eps)))
accuracy	0.00390625	(.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) #s(literal 2 binary64))
accuracy	0.00390625	(sin.f64 (*.f64 #s(literal 1/2 binary64) eps))
accuracy	0.01171875	(.f64 (cos.f64 (fma.f64 eps #s(literal -1/2 binary64) (neg.f64 x))) (.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) #s(literal 2 binary64)))
accuracy	0.08925386872974028	(cos.f64 (fma.f64 eps #s(literal -1/2 binary64) (neg.f64 x)))

Samples

314.0ms	251×	1	valid
2.0ms	4×	0	valid
2.0ms	1×	3	valid

Compiler

Compiled 348 to 62 computations (82.2% saved)

Precisions

Click to see histograms. Total time spent on operations: 242.0ms

ival-mult: 77.0ms (31.8% of total)

ival-cos: 52.0ms (21.5% of total)

ival-sin: 47.0ms (19.4% of total)

adjust: 28.0ms (11.6% of total)

ival-add: 18.0ms (7.4% of total)

const: 12.0ms (5% of total)

ival-sub: 5.0ms (2.1% of total)

ival-div: 2.0ms (0.8% of total)

exact: 1.0ms (0.4% of total)

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

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

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

series74.0ms (0.6%)

Memory

9.0MiB live, 54.3MiB allocated

Counts

29 → 588

Calls

Call 1

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

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

Calls

6 calls:

Time	Variable		Point	Expression
24.0ms	x	@	-inf	((cos (+ (* eps -1/2) (neg x))) (* (* (sin (* 1/2 (+ 0 eps))) 2) (cos (/ (+ (* 2 x) eps) -2))) (* (cos (+ (* eps -1/2) (neg x))) (* (sin (* 1/2 eps)) 2)) (+ (* eps -1/2) (neg x)) (- (sin (+ x eps)) (sin x)) (+ (* (+ (* (* (sin eps) x) -1/2) (- (cos eps) 1)) x) (sin eps)) (* (+ (* (* x x) -1/2) 1) eps) (+ (* (* x x) -1/2) 1) (- (sin (+ x eps)) (sin x)) (+ (* (+ (* (* (sin eps) x) -1/2) (- (cos eps) 1)) x) (sin eps)) (* (+ (* (* x (+ eps x)) -1/2) (+ (* (* (+ (* 1/12 (* x x)) -1/6) eps) eps) 1)) eps) (+ (* (* x (+ eps x)) -1/2) (+ (* (* (+ (* 1/12 (* x x)) -1/6) eps) eps) 1)) (- (sin (+ x eps)) (sin x)) (+ (* (+ (* (* (sin eps) x) -1/2) (- (cos eps) 1)) x) (sin eps)) (+ (* (* (sin eps) x) -1/2) (- (cos eps) 1)) (* (* -1/2 x) eps) (/ (+ (* 2 x) eps) -2) (cos (/ (+ (* 2 x) eps) -2)) (* (* (sin (* 1/2 (+ 0 eps))) 2) (cos (/ (+ (* 2 x) eps) -2))) (* (sin (* 1/2 (+ 0 eps))) 2) (sin (* 1/2 eps)) (* (sin (* 1/2 eps)) 2) (* x x) (* (+ (* 1/12 (* x x)) -1/6) eps) (* x (+ eps x)) (sin eps) (* -1/2 x) (sin (* 1/2 (+ 0 eps))) (* (+ (* (* eps eps) -1/48) 1/2) eps))
7.0ms	x	@	0	((cos (+ (* eps -1/2) (neg x))) (* (* (sin (* 1/2 (+ 0 eps))) 2) (cos (/ (+ (* 2 x) eps) -2))) (* (cos (+ (* eps -1/2) (neg x))) (* (sin (* 1/2 eps)) 2)) (+ (* eps -1/2) (neg x)) (- (sin (+ x eps)) (sin x)) (+ (* (+ (* (* (sin eps) x) -1/2) (- (cos eps) 1)) x) (sin eps)) (* (+ (* (* x x) -1/2) 1) eps) (+ (* (* x x) -1/2) 1) (- (sin (+ x eps)) (sin x)) (+ (* (+ (* (* (sin eps) x) -1/2) (- (cos eps) 1)) x) (sin eps)) (* (+ (* (* x (+ eps x)) -1/2) (+ (* (* (+ (* 1/12 (* x x)) -1/6) eps) eps) 1)) eps) (+ (* (* x (+ eps x)) -1/2) (+ (* (* (+ (* 1/12 (* x x)) -1/6) eps) eps) 1)) (- (sin (+ x eps)) (sin x)) (+ (* (+ (* (* (sin eps) x) -1/2) (- (cos eps) 1)) x) (sin eps)) (+ (* (* (sin eps) x) -1/2) (- (cos eps) 1)) (* (* -1/2 x) eps) (/ (+ (* 2 x) eps) -2) (cos (/ (+ (* 2 x) eps) -2)) (* (* (sin (* 1/2 (+ 0 eps))) 2) (cos (/ (+ (* 2 x) eps) -2))) (* (sin (* 1/2 (+ 0 eps))) 2) (sin (* 1/2 eps)) (* (sin (* 1/2 eps)) 2) (* x x) (* (+ (* 1/12 (* x x)) -1/6) eps) (* x (+ eps x)) (sin eps) (* -1/2 x) (sin (* 1/2 (+ 0 eps))) (* (+ (* (* eps eps) -1/48) 1/2) eps))
5.0ms	eps	@	inf	((cos (+ (* eps -1/2) (neg x))) (* (* (sin (* 1/2 (+ 0 eps))) 2) (cos (/ (+ (* 2 x) eps) -2))) (* (cos (+ (* eps -1/2) (neg x))) (* (sin (* 1/2 eps)) 2)) (+ (* eps -1/2) (neg x)) (- (sin (+ x eps)) (sin x)) (+ (* (+ (* (* (sin eps) x) -1/2) (- (cos eps) 1)) x) (sin eps)) (* (+ (* (* x x) -1/2) 1) eps) (+ (* (* x x) -1/2) 1) (- (sin (+ x eps)) (sin x)) (+ (* (+ (* (* (sin eps) x) -1/2) (- (cos eps) 1)) x) (sin eps)) (* (+ (* (* x (+ eps x)) -1/2) (+ (* (* (+ (* 1/12 (* x x)) -1/6) eps) eps) 1)) eps) (+ (* (* x (+ eps x)) -1/2) (+ (* (* (+ (* 1/12 (* x x)) -1/6) eps) eps) 1)) (- (sin (+ x eps)) (sin x)) (+ (* (+ (* (* (sin eps) x) -1/2) (- (cos eps) 1)) x) (sin eps)) (+ (* (* (sin eps) x) -1/2) (- (cos eps) 1)) (* (* -1/2 x) eps) (/ (+ (* 2 x) eps) -2) (cos (/ (+ (* 2 x) eps) -2)) (* (* (sin (* 1/2 (+ 0 eps))) 2) (cos (/ (+ (* 2 x) eps) -2))) (* (sin (* 1/2 (+ 0 eps))) 2) (sin (* 1/2 eps)) (* (sin (* 1/2 eps)) 2) (* x x) (* (+ (* 1/12 (* x x)) -1/6) eps) (* x (+ eps x)) (sin eps) (* -1/2 x) (sin (* 1/2 (+ 0 eps))) (* (+ (* (* eps eps) -1/48) 1/2) eps))
5.0ms	eps	@	-inf	((cos (+ (* eps -1/2) (neg x))) (* (* (sin (* 1/2 (+ 0 eps))) 2) (cos (/ (+ (* 2 x) eps) -2))) (* (cos (+ (* eps -1/2) (neg x))) (* (sin (* 1/2 eps)) 2)) (+ (* eps -1/2) (neg x)) (- (sin (+ x eps)) (sin x)) (+ (* (+ (* (* (sin eps) x) -1/2) (- (cos eps) 1)) x) (sin eps)) (* (+ (* (* x x) -1/2) 1) eps) (+ (* (* x x) -1/2) 1) (- (sin (+ x eps)) (sin x)) (+ (* (+ (* (* (sin eps) x) -1/2) (- (cos eps) 1)) x) (sin eps)) (* (+ (* (* x (+ eps x)) -1/2) (+ (* (* (+ (* 1/12 (* x x)) -1/6) eps) eps) 1)) eps) (+ (* (* x (+ eps x)) -1/2) (+ (* (* (+ (* 1/12 (* x x)) -1/6) eps) eps) 1)) (- (sin (+ x eps)) (sin x)) (+ (* (+ (* (* (sin eps) x) -1/2) (- (cos eps) 1)) x) (sin eps)) (+ (* (* (sin eps) x) -1/2) (- (cos eps) 1)) (* (* -1/2 x) eps) (/ (+ (* 2 x) eps) -2) (cos (/ (+ (* 2 x) eps) -2)) (* (* (sin (* 1/2 (+ 0 eps))) 2) (cos (/ (+ (* 2 x) eps) -2))) (* (sin (* 1/2 (+ 0 eps))) 2) (sin (* 1/2 eps)) (* (sin (* 1/2 eps)) 2) (* x x) (* (+ (* 1/12 (* x x)) -1/6) eps) (* x (+ eps x)) (sin eps) (* -1/2 x) (sin (* 1/2 (+ 0 eps))) (* (+ (* (* eps eps) -1/48) 1/2) eps))
4.0ms	x	@	inf	((cos (+ (* eps -1/2) (neg x))) (* (* (sin (* 1/2 (+ 0 eps))) 2) (cos (/ (+ (* 2 x) eps) -2))) (* (cos (+ (* eps -1/2) (neg x))) (* (sin (* 1/2 eps)) 2)) (+ (* eps -1/2) (neg x)) (- (sin (+ x eps)) (sin x)) (+ (* (+ (* (* (sin eps) x) -1/2) (- (cos eps) 1)) x) (sin eps)) (* (+ (* (* x x) -1/2) 1) eps) (+ (* (* x x) -1/2) 1) (- (sin (+ x eps)) (sin x)) (+ (* (+ (* (* (sin eps) x) -1/2) (- (cos eps) 1)) x) (sin eps)) (* (+ (* (* x (+ eps x)) -1/2) (+ (* (* (+ (* 1/12 (* x x)) -1/6) eps) eps) 1)) eps) (+ (* (* x (+ eps x)) -1/2) (+ (* (* (+ (* 1/12 (* x x)) -1/6) eps) eps) 1)) (- (sin (+ x eps)) (sin x)) (+ (* (+ (* (* (sin eps) x) -1/2) (- (cos eps) 1)) x) (sin eps)) (+ (* (* (sin eps) x) -1/2) (- (cos eps) 1)) (* (* -1/2 x) eps) (/ (+ (* 2 x) eps) -2) (cos (/ (+ (* 2 x) eps) -2)) (* (* (sin (* 1/2 (+ 0 eps))) 2) (cos (/ (+ (* 2 x) eps) -2))) (* (sin (* 1/2 (+ 0 eps))) 2) (sin (* 1/2 eps)) (* (sin (* 1/2 eps)) 2) (* x x) (* (+ (* 1/12 (* x x)) -1/6) eps) (* x (+ eps x)) (sin eps) (* -1/2 x) (sin (* 1/2 (+ 0 eps))) (* (+ (* (* eps eps) -1/48) 1/2) eps))

simplify213.0ms (1.7%)

Memory

4.3MiB live, 113.9MiB allocated

Algorithm

1×	egg-herbie

Rules

11 690×	`lower-fma.f64`
11 690×	`lower-fma.f32`
7 108×	`lower-*.f64`
7 108×	`lower-*.f32`
3 786×	`lower-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	481	6562
1	1501	6287
2	3898	6240
0	8436	5720

Stop Event

1×	iter limit
1×	node limit

Counts

588 → 584

Calls

Call 1

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

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

rewrite295.0ms (2.4%)

Memory

-13.7MiB live, 138.6MiB allocated

Rules

5 374×	`lower-*.f32`
5 346×	`lower-*.f64`
4 726×	`lower-fma.f32`
4 710×	`lower-fma.f64`
3 508×	`lower-/.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	69	427
0	105	419
1	381	419
2	3046	419
0	8807	408

Stop Event

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

Counts

29 → 415

Calls

Call 1

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

Outputs
(/.f64 (-.f64 (.f64 (+.f64 (cos.f64 (fma.f64 #s(literal -1/2 binary64) eps (neg.f64 x))) (cos.f64 (fma.f64 #s(literal -1/2 binary64) eps (.f64 #s(literal 1 binary64) x)))) #s(literal 2 binary64)) (.f64 #s(literal 2 binary64) (-.f64 (cos.f64 (fma.f64 #s(literal -1/2 binary64) eps (.f64 #s(literal 1 binary64) x))) (cos.f64 (fma.f64 #s(literal -1/2 binary64) eps (neg.f64 x)))))) #s(literal 4 binary64))
(/.f64 (-.f64 (+.f64 (cos.f64 (fma.f64 #s(literal -1/2 binary64) eps (neg.f64 x))) (cos.f64 (fma.f64 #s(literal -1/2 binary64) eps (.f64 #s(literal 1 binary64) x)))) (-.f64 (cos.f64 (fma.f64 #s(literal -1/2 binary64) eps (.f64 #s(literal 1 binary64) x))) (cos.f64 (fma.f64 #s(literal -1/2 binary64) eps (neg.f64 x))))) #s(literal 2 binary64))
(/.f64 (-.f64 (pow.f64 (.f64 (cos.f64 (.f64 #s(literal -1/2 binary64) eps)) (cos.f64 x)) #s(literal 2 binary64)) (pow.f64 (.f64 (neg.f64 (sin.f64 x)) (sin.f64 (.f64 #s(literal -1/2 binary64) eps))) #s(literal 2 binary64))) (cos.f64 (fma.f64 #s(literal -1/2 binary64) eps (*.f64 #s(literal 1 binary64) x))))
(/.f64 (-.f64 (pow.f64 (.f64 (cos.f64 (.f64 #s(literal -1/2 binary64) eps)) (cos.f64 x)) #s(literal 3 binary64)) (pow.f64 (.f64 (neg.f64 (sin.f64 x)) (sin.f64 (.f64 #s(literal -1/2 binary64) eps))) #s(literal 3 binary64))) (+.f64 (pow.f64 (.f64 (cos.f64 (.f64 #s(literal -1/2 binary64) eps)) (cos.f64 x)) #s(literal 2 binary64)) (+.f64 (pow.f64 (.f64 (neg.f64 (sin.f64 x)) (sin.f64 (.f64 #s(literal -1/2 binary64) eps))) #s(literal 2 binary64)) (.f64 (.f64 (cos.f64 (.f64 #s(literal -1/2 binary64) eps)) (cos.f64 x)) (.f64 (neg.f64 (sin.f64 x)) (sin.f64 (*.f64 #s(literal -1/2 binary64) eps)))))))
(fma.f64 (cos.f64 (/.f64 (.f64 #s(literal 1/4 binary64) (.f64 eps eps)) (fma.f64 #s(literal -1/2 binary64) eps (.f64 #s(literal 1 binary64) x)))) (cos.f64 (/.f64 (.f64 x x) (fma.f64 #s(literal -1/2 binary64) eps (.f64 #s(literal 1 binary64) x)))) (.f64 (sin.f64 (/.f64 (.f64 #s(literal 1/4 binary64) (.f64 eps eps)) (fma.f64 #s(literal -1/2 binary64) eps (.f64 #s(literal 1 binary64) x)))) (sin.f64 (/.f64 (.f64 x x) (fma.f64 #s(literal -1/2 binary64) eps (*.f64 #s(literal 1 binary64) x))))))
(fma.f64 (cos.f64 (.f64 #s(literal -1/2 binary64) eps)) (cos.f64 x) (.f64 (neg.f64 (sin.f64 (*.f64 #s(literal -1/2 binary64) eps))) (neg.f64 (sin.f64 x))))
(fma.f64 (cos.f64 (.f64 #s(literal -1/2 binary64) eps)) (cos.f64 x) (neg.f64 (.f64 (neg.f64 (sin.f64 x)) (sin.f64 (*.f64 #s(literal -1/2 binary64) eps)))))
(fma.f64 (cos.f64 (.f64 #s(literal -1/2 binary64) eps)) (cos.f64 x) (.f64 (sin.f64 (*.f64 #s(literal -1/2 binary64) eps)) (sin.f64 x)))
(fma.f64 (cos.f64 x) (cos.f64 (.f64 #s(literal -1/2 binary64) eps)) (.f64 (neg.f64 (sin.f64 (*.f64 #s(literal -1/2 binary64) eps))) (neg.f64 (sin.f64 x))))
(fma.f64 (cos.f64 x) (cos.f64 (.f64 #s(literal -1/2 binary64) eps)) (neg.f64 (.f64 (neg.f64 (sin.f64 x)) (sin.f64 (*.f64 #s(literal -1/2 binary64) eps)))))
(fma.f64 (cos.f64 x) (cos.f64 (.f64 #s(literal -1/2 binary64) eps)) (.f64 (sin.f64 (*.f64 #s(literal -1/2 binary64) eps)) (sin.f64 x)))
(fma.f64 #s(literal 1 binary64) (cos.f64 (-.f64 x (.f64 #s(literal -1/2 binary64) eps))) (.f64 #s(literal 0 binary64) (sin.f64 (-.f64 x (*.f64 #s(literal -1/2 binary64) eps)))))
(-.f64 (.f64 (cos.f64 (.f64 #s(literal -1/2 binary64) eps)) (cos.f64 x)) (.f64 (neg.f64 (sin.f64 x)) (sin.f64 (.f64 #s(literal -1/2 binary64) eps))))
(cos.f64 (fma.f64 #s(literal -1/2 binary64) eps (neg.f64 x)))
(+.f64 (.f64 (cos.f64 (/.f64 (.f64 #s(literal 1/4 binary64) (.f64 eps eps)) (fma.f64 #s(literal -1/2 binary64) eps (.f64 #s(literal 1 binary64) x)))) (cos.f64 (/.f64 (.f64 x x) (fma.f64 #s(literal -1/2 binary64) eps (.f64 #s(literal 1 binary64) x))))) (.f64 (sin.f64 (/.f64 (.f64 #s(literal 1/4 binary64) (.f64 eps eps)) (fma.f64 #s(literal -1/2 binary64) eps (.f64 #s(literal 1 binary64) x)))) (sin.f64 (/.f64 (.f64 x x) (fma.f64 #s(literal -1/2 binary64) eps (.f64 #s(literal 1 binary64) x))))))
(+.f64 (.f64 #s(literal 1 binary64) (cos.f64 (-.f64 x (.f64 #s(literal -1/2 binary64) eps)))) (.f64 #s(literal 0 binary64) (sin.f64 (-.f64 x (.f64 #s(literal -1/2 binary64) eps)))))
(+.f64 (.f64 (cos.f64 (.f64 #s(literal -1/2 binary64) eps)) (cos.f64 x)) (.f64 (neg.f64 (sin.f64 (.f64 #s(literal -1/2 binary64) eps))) (neg.f64 (sin.f64 x))))
(+.f64 (.f64 (cos.f64 (.f64 #s(literal -1/2 binary64) eps)) (cos.f64 x)) (neg.f64 (.f64 (neg.f64 (sin.f64 x)) (sin.f64 (.f64 #s(literal -1/2 binary64) eps)))))
(+.f64 (.f64 (cos.f64 (.f64 #s(literal -1/2 binary64) eps)) (cos.f64 x)) (.f64 (sin.f64 (.f64 #s(literal -1/2 binary64) eps)) (sin.f64 x)))
#s(approx (* (* (sin (* 1/2 (+ 0 eps))) 2) (cos (/ (+ (* 2 x) eps) -2))) (.f64 (.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) #s(literal 2 binary64)) (cos.f64 (fma.f64 #s(literal -1/2 binary64) eps (neg.f64 x)))))
(.f64 (.f64 (cos.f64 (fma.f64 #s(literal -1/2 binary64) eps (neg.f64 x))) #s(literal 2 binary64)) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)))
(.f64 (.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (cos.f64 (fma.f64 #s(literal -1/2 binary64) eps (neg.f64 x)))) #s(literal 2 binary64))
(.f64 (.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) #s(literal 2 binary64)) (cos.f64 (fma.f64 #s(literal -1/2 binary64) eps (neg.f64 x))))
(.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (*.f64 #s(literal 2 binary64) (cos.f64 (fma.f64 #s(literal -1/2 binary64) eps (neg.f64 x)))))
(.f64 #s(literal 2 binary64) (.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (cos.f64 (fma.f64 #s(literal -1/2 binary64) eps (neg.f64 x)))))
(.f64 (cos.f64 (fma.f64 #s(literal -1/2 binary64) eps (neg.f64 x))) (.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) #s(literal 2 binary64)))
(.f64 (fma.f64 #s(literal 1/4 binary64) (.f64 eps eps) (.f64 x (neg.f64 x))) (pow.f64 (fma.f64 #s(literal -1/2 binary64) eps (.f64 #s(literal 1 binary64) x)) #s(literal -1 binary64)))
(.f64 (fma.f64 #s(literal -1/8 binary64) (pow.f64 eps #s(literal 3 binary64)) (pow.f64 x #s(literal 3 binary64))) (pow.f64 (fma.f64 #s(literal 1/4 binary64) (.f64 eps eps) (.f64 (neg.f64 x) (-.f64 (neg.f64 x) (.f64 #s(literal -1/2 binary64) eps)))) #s(literal -1 binary64)))
(pow.f64 (/.f64 (fma.f64 #s(literal -1/2 binary64) eps (.f64 #s(literal 1 binary64) x)) (fma.f64 #s(literal 1/4 binary64) (.f64 eps eps) (*.f64 x (neg.f64 x)))) #s(literal -1 binary64))
(pow.f64 (/.f64 (fma.f64 #s(literal 1/4 binary64) (.f64 eps eps) (.f64 (neg.f64 x) (-.f64 (neg.f64 x) (*.f64 #s(literal -1/2 binary64) eps)))) (fma.f64 #s(literal -1/8 binary64) (pow.f64 eps #s(literal 3 binary64)) (pow.f64 x #s(literal 3 binary64)))) #s(literal -1 binary64))
(/.f64 (-.f64 (.f64 (.f64 #s(literal 1/4 binary64) (.f64 eps eps)) (fma.f64 #s(literal -1/2 binary64) eps (.f64 #s(literal 1 binary64) x))) (.f64 (fma.f64 #s(literal -1/2 binary64) eps (.f64 #s(literal 1 binary64) x)) (.f64 x x))) (.f64 (fma.f64 #s(literal -1/2 binary64) eps (.f64 #s(literal 1 binary64) x)) (fma.f64 #s(literal -1/2 binary64) eps (.f64 #s(literal 1 binary64) x))))
(/.f64 (fma.f64 (.f64 (neg.f64 (.f64 eps eps)) #s(literal -1/2 binary64)) (+.f64 #s(literal 0 binary64) x) (.f64 (neg.f64 eps) (-.f64 #s(literal 0 binary64) (.f64 x x)))) (*.f64 (neg.f64 eps) (+.f64 #s(literal 0 binary64) x)))
(/.f64 (fma.f64 (.f64 (neg.f64 (.f64 eps eps)) #s(literal -1/2 binary64)) (+.f64 #s(literal 0 binary64) (fma.f64 x x (.f64 #s(literal 0 binary64) x))) (.f64 (neg.f64 eps) (-.f64 #s(literal 0 binary64) (pow.f64 x #s(literal 3 binary64))))) (.f64 (neg.f64 eps) (+.f64 #s(literal 0 binary64) (fma.f64 x x (.f64 #s(literal 0 binary64) x)))))
(/.f64 (fma.f64 (.f64 (pow.f64 eps #s(literal 3 binary64)) #s(literal -1/2 binary64)) (+.f64 #s(literal 0 binary64) x) (.f64 (.f64 eps eps) (-.f64 #s(literal 0 binary64) (.f64 x x)))) (.f64 (.f64 eps eps) (+.f64 #s(literal 0 binary64) x)))
(/.f64 (fma.f64 (.f64 (pow.f64 eps #s(literal 3 binary64)) #s(literal -1/2 binary64)) (+.f64 #s(literal 0 binary64) (fma.f64 x x (.f64 #s(literal 0 binary64) x))) (.f64 (.f64 eps eps) (-.f64 #s(literal 0 binary64) (pow.f64 x #s(literal 3 binary64))))) (.f64 (.f64 eps eps) (+.f64 #s(literal 0 binary64) (fma.f64 x x (*.f64 #s(literal 0 binary64) x)))))
(/.f64 (fma.f64 (.f64 #s(literal -1/2 binary64) (neg.f64 (.f64 eps eps))) (+.f64 #s(literal 0 binary64) x) (.f64 (neg.f64 eps) (-.f64 #s(literal 0 binary64) (.f64 x x)))) (*.f64 (neg.f64 eps) (+.f64 #s(literal 0 binary64) x)))
(/.f64 (fma.f64 (.f64 #s(literal -1/2 binary64) (neg.f64 (.f64 eps eps))) (+.f64 #s(literal 0 binary64) (fma.f64 x x (.f64 #s(literal 0 binary64) x))) (.f64 (neg.f64 eps) (-.f64 #s(literal 0 binary64) (pow.f64 x #s(literal 3 binary64))))) (.f64 (neg.f64 eps) (+.f64 #s(literal 0 binary64) (fma.f64 x x (.f64 #s(literal 0 binary64) x)))))
(/.f64 (fma.f64 (.f64 #s(literal -1/2 binary64) (pow.f64 eps #s(literal 3 binary64))) (+.f64 #s(literal 0 binary64) x) (.f64 (.f64 eps eps) (-.f64 #s(literal 0 binary64) (.f64 x x)))) (.f64 (.f64 eps eps) (+.f64 #s(literal 0 binary64) x)))
(/.f64 (fma.f64 (.f64 #s(literal -1/2 binary64) (pow.f64 eps #s(literal 3 binary64))) (+.f64 #s(literal 0 binary64) (fma.f64 x x (.f64 #s(literal 0 binary64) x))) (.f64 (.f64 eps eps) (-.f64 #s(literal 0 binary64) (pow.f64 x #s(literal 3 binary64))))) (.f64 (.f64 eps eps) (+.f64 #s(literal 0 binary64) (fma.f64 x x (*.f64 #s(literal 0 binary64) x)))))
(/.f64 (fma.f64 (-.f64 #s(literal 0 binary64) (.f64 x x)) (neg.f64 eps) (.f64 (+.f64 #s(literal 0 binary64) x) (.f64 (neg.f64 (.f64 eps eps)) #s(literal -1/2 binary64)))) (*.f64 (+.f64 #s(literal 0 binary64) x) (neg.f64 eps)))
(/.f64 (fma.f64 (-.f64 #s(literal 0 binary64) (.f64 x x)) (.f64 eps eps) (.f64 (+.f64 #s(literal 0 binary64) x) (.f64 (pow.f64 eps #s(literal 3 binary64)) #s(literal -1/2 binary64)))) (.f64 (+.f64 #s(literal 0 binary64) x) (.f64 eps eps)))
(/.f64 (fma.f64 (-.f64 #s(literal 0 binary64) (.f64 x x)) (neg.f64 eps) (.f64 (+.f64 #s(literal 0 binary64) x) (.f64 #s(literal -1/2 binary64) (neg.f64 (.f64 eps eps))))) (*.f64 (+.f64 #s(literal 0 binary64) x) (neg.f64 eps)))
(/.f64 (fma.f64 (-.f64 #s(literal 0 binary64) (.f64 x x)) (.f64 eps eps) (.f64 (+.f64 #s(literal 0 binary64) x) (.f64 #s(literal -1/2 binary64) (pow.f64 eps #s(literal 3 binary64))))) (.f64 (+.f64 #s(literal 0 binary64) x) (.f64 eps eps)))
(/.f64 (fma.f64 (-.f64 #s(literal 0 binary64) (pow.f64 x #s(literal 3 binary64))) (neg.f64 eps) (.f64 (+.f64 #s(literal 0 binary64) (fma.f64 x x (.f64 #s(literal 0 binary64) x))) (.f64 (neg.f64 (.f64 eps eps)) #s(literal -1/2 binary64)))) (.f64 (+.f64 #s(literal 0 binary64) (fma.f64 x x (.f64 #s(literal 0 binary64) x))) (neg.f64 eps)))
(/.f64 (fma.f64 (-.f64 #s(literal 0 binary64) (pow.f64 x #s(literal 3 binary64))) (.f64 eps eps) (.f64 (+.f64 #s(literal 0 binary64) (fma.f64 x x (.f64 #s(literal 0 binary64) x))) (.f64 (pow.f64 eps #s(literal 3 binary64)) #s(literal -1/2 binary64)))) (.f64 (+.f64 #s(literal 0 binary64) (fma.f64 x x (.f64 #s(literal 0 binary64) x))) (*.f64 eps eps)))
(/.f64 (fma.f64 (-.f64 #s(literal 0 binary64) (pow.f64 x #s(literal 3 binary64))) (neg.f64 eps) (.f64 (+.f64 #s(literal 0 binary64) (fma.f64 x x (.f64 #s(literal 0 binary64) x))) (.f64 #s(literal -1/2 binary64) (neg.f64 (.f64 eps eps))))) (.f64 (+.f64 #s(literal 0 binary64) (fma.f64 x x (.f64 #s(literal 0 binary64) x))) (neg.f64 eps)))
(/.f64 (fma.f64 (-.f64 #s(literal 0 binary64) (pow.f64 x #s(literal 3 binary64))) (.f64 eps eps) (.f64 (+.f64 #s(literal 0 binary64) (fma.f64 x x (.f64 #s(literal 0 binary64) x))) (.f64 #s(literal -1/2 binary64) (pow.f64 eps #s(literal 3 binary64))))) (.f64 (+.f64 #s(literal 0 binary64) (fma.f64 x x (.f64 #s(literal 0 binary64) x))) (*.f64 eps eps)))
(/.f64 (-.f64 (.f64 x x) (.f64 #s(literal 1/4 binary64) (.f64 eps eps))) (-.f64 (neg.f64 x) (.f64 #s(literal -1/2 binary64) eps)))
(/.f64 (-.f64 (pow.f64 (.f64 #s(literal -1/2 binary64) eps) #s(literal 3 binary64)) (pow.f64 x #s(literal 3 binary64))) (fma.f64 #s(literal 1/4 binary64) (.f64 eps eps) (fma.f64 x x (.f64 (.f64 x #s(literal -1/2 binary64)) eps))))
(/.f64 (neg.f64 (fma.f64 #s(literal 1/4 binary64) (.f64 eps eps) (.f64 x (neg.f64 x)))) (neg.f64 (fma.f64 #s(literal -1/2 binary64) eps (*.f64 #s(literal 1 binary64) x))))
(/.f64 (neg.f64 (fma.f64 #s(literal -1/8 binary64) (pow.f64 eps #s(literal 3 binary64)) (pow.f64 x #s(literal 3 binary64)))) (neg.f64 (fma.f64 #s(literal 1/4 binary64) (.f64 eps eps) (.f64 (neg.f64 x) (-.f64 (neg.f64 x) (*.f64 #s(literal -1/2 binary64) eps))))))
(/.f64 (fma.f64 #s(literal 1/4 binary64) (.f64 eps eps) (.f64 x (neg.f64 x))) (fma.f64 #s(literal -1/2 binary64) eps x))
(/.f64 (fma.f64 #s(literal 1/4 binary64) (.f64 eps eps) (.f64 x (neg.f64 x))) (fma.f64 #s(literal -1/2 binary64) eps (*.f64 #s(literal 1 binary64) x)))
(/.f64 (fma.f64 #s(literal -1/8 binary64) (pow.f64 eps #s(literal 3 binary64)) (pow.f64 x #s(literal 3 binary64))) (fma.f64 x x (-.f64 (.f64 #s(literal 1/4 binary64) (.f64 eps eps)) (.f64 (.f64 #s(literal -1/2 binary64) eps) (neg.f64 x)))))
(/.f64 (fma.f64 #s(literal -1/8 binary64) (pow.f64 eps #s(literal 3 binary64)) (pow.f64 x #s(literal 3 binary64))) (fma.f64 #s(literal 1/4 binary64) (.f64 eps eps) (.f64 (neg.f64 x) (-.f64 (neg.f64 x) (*.f64 #s(literal -1/2 binary64) eps)))))
(/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 #s(literal -1/2 binary64) eps (.f64 #s(literal 1 binary64) x)) (fma.f64 #s(literal 1/4 binary64) (.f64 eps eps) (*.f64 x (neg.f64 x)))))
(/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 #s(literal 1/4 binary64) (.f64 eps eps) (.f64 (neg.f64 x) (-.f64 (neg.f64 x) (*.f64 #s(literal -1/2 binary64) eps)))) (fma.f64 #s(literal -1/8 binary64) (pow.f64 eps #s(literal 3 binary64)) (pow.f64 x #s(literal 3 binary64)))))
(fma.f64 #s(literal -1 binary64) x (*.f64 #s(literal -1/2 binary64) eps))
(fma.f64 x #s(literal -1 binary64) (*.f64 #s(literal -1/2 binary64) eps))
(fma.f64 #s(literal -1/2 binary64) eps (neg.f64 x))
(fma.f64 eps #s(literal -1/2 binary64) (neg.f64 x))
(-.f64 (/.f64 (.f64 #s(literal 1/4 binary64) (.f64 eps eps)) (fma.f64 #s(literal -1/2 binary64) eps (.f64 #s(literal 1 binary64) x))) (/.f64 (.f64 x x) (fma.f64 #s(literal -1/2 binary64) eps (*.f64 #s(literal 1 binary64) x))))
(-.f64 (*.f64 #s(literal -1/2 binary64) eps) x)
(-.f64 #s(literal 0 binary64) (-.f64 x (*.f64 #s(literal -1/2 binary64) eps)))
(+.f64 (*.f64 #s(literal -1/2 binary64) eps) (neg.f64 x))
(+.f64 (neg.f64 x) (*.f64 #s(literal -1/2 binary64) eps))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (+ (* (+ (* (* (sin eps) x) -1/2) (- (cos eps) 1)) x) (sin eps)) (.f64 (fma.f64 (.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64)) eps)))
#s(approx (+ (* (+ (* (* (sin eps) x) -1/2) (- (cos eps) 1)) x) (sin eps)) (.f64 (fma.f64 (.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64)) eps))
(.f64 (fma.f64 (.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64)) eps)
(.f64 eps (fma.f64 (.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64)))
(/.f64 (.f64 (fma.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 1/4 binary64) #s(literal -1 binary64)) eps) (fma.f64 (.f64 x #s(literal -1/2 binary64)) x #s(literal -1 binary64)))
(/.f64 (.f64 (fma.f64 #s(literal -1/8 binary64) (pow.f64 x #s(literal 6 binary64)) #s(literal 1 binary64)) eps) (fma.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 1/4 binary64) (-.f64 #s(literal 1 binary64) (.f64 (*.f64 x #s(literal -1/2 binary64)) x))))
(/.f64 (.f64 (neg.f64 (.f64 eps eps)) (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64))) (neg.f64 eps))
(/.f64 (.f64 (pow.f64 eps #s(literal 3 binary64)) (fma.f64 (.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64))) (*.f64 eps eps))
(/.f64 (.f64 (fma.f64 (.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64)) (neg.f64 (*.f64 eps eps))) (neg.f64 eps))
(/.f64 (.f64 (fma.f64 (.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64)) (pow.f64 eps #s(literal 3 binary64))) (*.f64 eps eps))
(/.f64 (.f64 eps (fma.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 1/4 binary64) #s(literal -1 binary64))) (fma.f64 (.f64 x #s(literal -1/2 binary64)) x #s(literal -1 binary64)))
(/.f64 (.f64 eps (fma.f64 #s(literal -1/8 binary64) (pow.f64 x #s(literal 6 binary64)) #s(literal 1 binary64))) (fma.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 1/4 binary64) (-.f64 #s(literal 1 binary64) (.f64 (*.f64 x #s(literal -1/2 binary64)) x))))
(/.f64 (.f64 (fma.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 1/4 binary64) #s(literal -1 binary64)) (neg.f64 (.f64 eps eps))) (.f64 (fma.f64 (.f64 x #s(literal -1/2 binary64)) x #s(literal -1 binary64)) (neg.f64 eps)))
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(/.f64 (.f64 (neg.f64 (.f64 eps eps)) (fma.f64 #s(literal 1/2304 binary64) (pow.f64 eps #s(literal 4 binary64)) #s(literal -1/4 binary64))) (.f64 (neg.f64 eps) (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal -1/2 binary64))))
(/.f64 (.f64 (neg.f64 (.f64 eps eps)) (fma.f64 #s(literal -1/110592 binary64) (pow.f64 eps #s(literal 6 binary64)) #s(literal 1/8 binary64))) (.f64 (neg.f64 eps) (fma.f64 #s(literal 1/2304 binary64) (pow.f64 eps #s(literal 4 binary64)) (-.f64 #s(literal 1/4 binary64) (.f64 (*.f64 eps eps) #s(literal -1/96 binary64))))))
(/.f64 (.f64 (pow.f64 eps #s(literal 3 binary64)) (fma.f64 #s(literal 1/2304 binary64) (pow.f64 eps #s(literal 4 binary64)) #s(literal -1/4 binary64))) (.f64 (.f64 eps eps) (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal -1/2 binary64))))
(/.f64 (.f64 (pow.f64 eps #s(literal 3 binary64)) (fma.f64 #s(literal -1/110592 binary64) (pow.f64 eps #s(literal 6 binary64)) #s(literal 1/8 binary64))) (.f64 (.f64 eps eps) (fma.f64 #s(literal 1/2304 binary64) (pow.f64 eps #s(literal 4 binary64)) (-.f64 #s(literal 1/4 binary64) (.f64 (*.f64 eps eps) #s(literal -1/96 binary64))))))
(fma.f64 (.f64 #s(literal -1/48 binary64) (.f64 eps eps)) eps (*.f64 #s(literal 1/2 binary64) eps))
(fma.f64 (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal 1/2 binary64)) #s(literal 0 binary64) (.f64 (fma.f64 #s(literal -1/48 binary64) (*.f64 eps eps) #s(literal 1/2 binary64)) eps))
(fma.f64 (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal 1/2 binary64)) eps (.f64 #s(literal 0 binary64) (fma.f64 #s(literal -1/48 binary64) (*.f64 eps eps) #s(literal 1/2 binary64))))
(fma.f64 (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal 1/2 binary64)) eps (.f64 (fma.f64 #s(literal -1/48 binary64) (*.f64 eps eps) #s(literal 1/2 binary64)) #s(literal 0 binary64)))
(fma.f64 #s(literal 0 binary64) (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal 1/2 binary64)) (.f64 (fma.f64 #s(literal -1/48 binary64) (*.f64 eps eps) #s(literal 1/2 binary64)) eps))
(fma.f64 #s(literal 1/2 binary64) eps (.f64 (.f64 #s(literal -1/48 binary64) (*.f64 eps eps)) eps))
(fma.f64 #s(literal 1/2 binary64) eps (.f64 eps (.f64 #s(literal -1/48 binary64) (*.f64 eps eps))))
(fma.f64 eps (.f64 #s(literal -1/48 binary64) (.f64 eps eps)) (*.f64 #s(literal 1/2 binary64) eps))
(fma.f64 eps (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal 1/2 binary64)) (.f64 #s(literal 0 binary64) (fma.f64 #s(literal -1/48 binary64) (*.f64 eps eps) #s(literal 1/2 binary64))))
(fma.f64 eps (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal 1/2 binary64)) (.f64 (fma.f64 #s(literal -1/48 binary64) (*.f64 eps eps) #s(literal 1/2 binary64)) #s(literal 0 binary64)))
(fma.f64 eps #s(literal 1/2 binary64) (.f64 (.f64 #s(literal -1/48 binary64) (*.f64 eps eps)) eps))
(fma.f64 eps #s(literal 1/2 binary64) (.f64 eps (.f64 #s(literal -1/48 binary64) (*.f64 eps eps))))
(+.f64 (.f64 #s(literal 0 binary64) (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal 1/2 binary64))) (.f64 (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal 1/2 binary64)) eps))
(+.f64 (.f64 (.f64 #s(literal -1/48 binary64) (.f64 eps eps)) eps) (.f64 #s(literal 1/2 binary64) eps))
(+.f64 (.f64 (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal 1/2 binary64)) #s(literal 0 binary64)) (.f64 (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal 1/2 binary64)) eps))
(+.f64 (.f64 eps (.f64 #s(literal -1/48 binary64) (.f64 eps eps))) (.f64 #s(literal 1/2 binary64) eps))
(+.f64 (.f64 (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal 1/2 binary64)) eps) (.f64 #s(literal 0 binary64) (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal 1/2 binary64))))
(+.f64 (.f64 (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal 1/2 binary64)) eps) (.f64 (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal 1/2 binary64)) #s(literal 0 binary64)))
(+.f64 (.f64 #s(literal 1/2 binary64) eps) (.f64 (.f64 #s(literal -1/48 binary64) (.f64 eps eps)) eps))
(+.f64 (.f64 #s(literal 1/2 binary64) eps) (.f64 eps (.f64 #s(literal -1/48 binary64) (.f64 eps eps))))

eval198.0ms (1.6%)

Memory: 38.2MiB live, 196.8MiB allocated
Compiler: Compiled 21 342 to 2 769 computations (87% saved)

prune143.0ms (1.1%)

Memory

-48.2MiB live, 93.3MiB allocated

Pruning

21 alts after pruning (17 fresh and 4 done)

	Pruned	Kept	Total
New	1 013	13	1 026
Fresh	2	4	6
Picked	4	1	5
Done	1	3	4
Total	1 020	21	1 041

Accuracy

100.0%

Counts

1 041 → 21

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	65.7%	(fma.f64 (sin.f64 x) (cos.f64 eps) (fma.f64 (sin.f64 eps) (cos.f64 x) (neg.f64 (sin.f64 x))))
✓	65.5%	(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
✓	7.9%	(-.f64 #s(approx (sin (+ x eps)) (sin.f64 eps)) (sin.f64 x))
	99.5%	(.f64 (.f64 #s(approx (sin (* 1/2 (+ 0 eps))) (.f64 (fma.f64 (.f64 eps eps) #s(literal -1/48 binary64) #s(literal 1/2 binary64)) eps)) #s(literal 2 binary64)) #s(approx (cos (/ (+ (* 2 x) eps) -2)) (fma.f64 (*.f64 (sin.f64 x) eps) #s(literal -1/2 binary64) (cos.f64 x))))
	99.5%	(.f64 (.f64 #s(approx (sin (* 1/2 (+ 0 eps))) (.f64 (fma.f64 (.f64 eps eps) #s(literal -1/48 binary64) #s(literal 1/2 binary64)) eps)) #s(literal 2 binary64)) #s(approx (cos (/ (+ (* 2 x) eps) -2)) (cos.f64 (fma.f64 eps #s(literal 1/2 binary64) x))))
	99.6%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 (fma.f64 (.f64 #s(literal -1/6 binary64) eps) (cos.f64 x) (*.f64 (sin.f64 x) #s(literal -1/2 binary64))) eps (cos.f64 x)) eps))
▶	99.5%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 (.f64 (sin.f64 x) eps) #s(literal -1/2 binary64) (cos.f64 x)) eps))
	99.2%	#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (cos.f64 x) eps))
▶	98.8%	#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (+ (* (+ (* (* (sin eps) x) -1/2) (- (cos eps) 1)) x) (sin eps)) (fma.f64 (.f64 (.f64 x #s(literal -1/2 binary64)) x) eps (*.f64 #s(literal 1 binary64) eps))))
	98.9%	#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (+ (* (+ (* (* (sin eps) x) -1/2) (- (cos eps) 1)) x) (sin eps)) (.f64 (fma.f64 (.f64 (+.f64 eps x) x) #s(literal -1/2 binary64) #s(literal 1 binary64)) eps)))
	98.9%	#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (+ (* (+ (* (* (sin eps) x) -1/2) (- (cos eps) 1)) x) (sin eps)) (.f64 (fma.f64 (.f64 x (+.f64 eps x)) #s(literal -1/2 binary64) (fma.f64 #s(approx (* (+ (* 1/12 (* x x)) -1/6) eps) (*.f64 #s(literal -1/6 binary64) eps)) eps #s(literal 1 binary64))) eps)))
✓	98.8%	#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (+ (* (+ (* (* (sin eps) x) -1/2) (- (cos eps) 1)) x) (sin eps)) (.f64 (fma.f64 (.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64)) eps)))
	98.8%	#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (+ (* (+ (* (* (sin eps) x) -1/2) (- (cos eps) 1)) x) (sin eps)) (.f64 (fma.f64 #s(approx ( x (+ eps x)) (.f64 x x)) #s(literal -1/2 binary64) (fma.f64 (.f64 (fma.f64 #s(literal 1/12 binary64) (*.f64 x x) #s(literal -1/6 binary64)) eps) eps #s(literal 1 binary64))) eps)))
	98.5%	#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (+ (* (+ (* (* (sin eps) x) -1/2) (- (cos eps) 1)) x) (sin eps)) (.f64 #s(approx (+ ( (* x (+ eps x)) -1/2) (+ (* (* (+ (* 1/12 (* x x)) -1/6) eps) eps) 1)) (fma.f64 (*.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64))) eps)))
	98.5%	#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (+ (* (+ (* (* (sin eps) x) -1/2) (- (cos eps) 1)) x) (sin eps)) (.f64 #s(approx (+ ( (* x (+ eps x)) -1/2) (+ (* (* (+ (* 1/12 (* x x)) -1/6) eps) eps) 1)) (fma.f64 (.f64 #s(literal -1/2 binary64) x) eps (fma.f64 (.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64)))) eps)))
▶	5.8%	#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (+ (* (+ (* (* (sin eps) x) -1/2) (- (cos eps) 1)) x) (sin eps)) (.f64 #s(approx (+ ( (* x (+ eps x)) -1/2) (+ (* (* (+ (* 1/12 (* x x)) -1/6) eps) eps) 1)) (.f64 (.f64 (fma.f64 (/.f64 x eps) #s(literal -1/2 binary64) (fma.f64 #s(literal 1/12 binary64) (*.f64 x x) #s(literal -1/6 binary64))) eps) eps)) eps)))
	5.4%	#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (+ (* (+ (* (* (sin eps) x) -1/2) (- (cos eps) 1)) x) (sin eps)) (.f64 #s(approx (+ ( (* x x) -1/2) 1) (.f64 (.f64 x x) #s(literal -1/2 binary64))) eps)))
▶	98.5%	#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (+ (* (+ (* (* (sin eps) x) -1/2) (- (cos eps) 1)) x) (sin eps)) (.f64 #s(approx (+ ( (* x x) -1/2) 1) #s(literal 1 binary64)) eps)))
	99.7%	#s(approx (+ (* (sin x) (cos eps)) (+ (* (sin eps) (cos x)) (neg (sin x)))) (fma.f64 (sin.f64 x) (-.f64 (cos.f64 eps) #s(literal 1 binary64)) (*.f64 (sin.f64 eps) (cos.f64 x))))
▶	99.9%	#s(approx (* (* (sin (* 1/2 (+ 0 eps))) 2) (cos (/ (+ (* 2 x) eps) -2))) (.f64 (cos.f64 (fma.f64 eps #s(literal 1/2 binary64) x)) (.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) #s(literal 2 binary64))))
	99.5%	#s(approx (* (* (sin (* 1/2 (+ 0 eps))) 2) (cos (/ (+ (* 2 x) eps) -2))) (.f64 (cos.f64 (fma.f64 eps #s(literal -1/2 binary64) (neg.f64 x))) (.f64 #s(approx (sin (* 1/2 eps)) (*.f64 eps #s(literal 1/2 binary64))) #s(literal 2 binary64))))

Compiler

Compiled 512 to 420 computations (18% saved)

simplify138.0ms (1.1%)

Memory

28.0MiB live, 145.9MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 20 expressions of interest:

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

Rules

12 212×	`lower-fma.f32`
12 202×	`lower-fma.f64`
3 650×	`lower-*.f32`
3 624×	`lower-*.f64`
1 396×	`lower-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	76	536
0	102	526
1	188	526
2	478	526
3	1309	526
4	2446	520
5	3538	520
6	4582	520
7	6939	520
0	8179	487

Stop Event

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

Calls

Call 1

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

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

localize192.0ms (1.5%)

Memory

0.9MiB live, 276.6MiB allocated

Localize:

Found 20 expressions of interest:

New	Metric	Score
accuracy	0.00390625	(fma.f64 (*.f64 (sin.f64 x) eps) #s(literal -1/2 binary64) (cos.f64 x))
accuracy	0.00390625	(.f64 (fma.f64 (.f64 (sin.f64 x) eps) #s(literal -1/2 binary64) (cos.f64 x)) eps)
accuracy	0.00390625	(*.f64 (sin.f64 x) eps)
accuracy	0.2845845292356662	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 (.f64 (sin.f64 x) eps) #s(literal -1/2 binary64) (cos.f64 x)) eps))
accuracy	0.27734375	(.f64 (fma.f64 (/.f64 x eps) #s(literal -1/2 binary64) (fma.f64 #s(literal 1/12 binary64) (.f64 x x) #s(literal -1/6 binary64))) eps)
accuracy	0.34765625	(fma.f64 (/.f64 x eps) #s(literal -1/2 binary64) (fma.f64 #s(literal 1/12 binary64) (*.f64 x x) #s(literal -1/6 binary64)))
accuracy	0.7098673144904891	#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (+ (* (+ (* (* (sin eps) x) -1/2) (- (cos eps) 1)) x) (sin eps)) (.f64 #s(approx (+ ( (* x (+ eps x)) -1/2) (+ (* (* (+ (* 1/12 (* x x)) -1/6) eps) eps) 1)) (.f64 (.f64 (fma.f64 (/.f64 x eps) #s(literal -1/2 binary64) (fma.f64 #s(literal 1/12 binary64) (*.f64 x x) #s(literal -1/6 binary64))) eps) eps)) eps)))
accuracy	61.756760326251154	#s(approx (+ (* (* x (+ eps x)) -1/2) (+ (* (* (+ (* 1/12 (* x x)) -1/6) eps) eps) 1)) (.f64 (.f64 (fma.f64 (/.f64 x eps) #s(literal -1/2 binary64) (fma.f64 #s(literal 1/12 binary64) (*.f64 x x) #s(literal -1/6 binary64))) eps) eps))
accuracy	0	(*.f64 #s(literal 1 binary64) eps)
accuracy	0.00390625	(fma.f64 (.f64 (.f64 x #s(literal -1/2 binary64)) x) eps (*.f64 #s(literal 1 binary64) eps))
accuracy	0.44968963782770377	#s(approx (+ (* (+ (* (* (sin eps) x) -1/2) (- (cos eps) 1)) x) (sin eps)) (fma.f64 (.f64 (.f64 x #s(literal -1/2 binary64)) x) eps (*.f64 #s(literal 1 binary64) eps)))
accuracy	0.7098673144904891	#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (+ (* (+ (* (* (sin eps) x) -1/2) (- (cos eps) 1)) x) (sin eps)) (fma.f64 (.f64 (.f64 x #s(literal -1/2 binary64)) x) eps (*.f64 #s(literal 1 binary64) eps))))
accuracy	0.0078125	(.f64 #s(approx (+ ( (* x x) -1/2) 1) #s(literal 1 binary64)) eps)
accuracy	0.44968963782770377	#s(approx (+ (* (+ (* (* (sin eps) x) -1/2) (- (cos eps) 1)) x) (sin eps)) (.f64 #s(approx (+ ( (* x x) -1/2) 1) #s(literal 1 binary64)) eps))
accuracy	0.7098673144904891	#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (+ (* (+ (* (* (sin eps) x) -1/2) (- (cos eps) 1)) x) (sin eps)) (.f64 #s(approx (+ ( (* x x) -1/2) 1) #s(literal 1 binary64)) eps)))
accuracy	1.0324008928616741	#s(approx (+ (* (* x x) -1/2) 1) #s(literal 1 binary64))
accuracy	0.00390625	(.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) #s(literal 2 binary64))
accuracy	0.00390625	(sin.f64 (*.f64 eps #s(literal 1/2 binary64)))
accuracy	0.01171875	(.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)))
accuracy	0.08925386872974028	(cos.f64 (fma.f64 eps #s(literal 1/2 binary64) x))

Samples

91.0ms	187×	0	valid
62.0ms	68×	1	valid
1.0ms	1×	3	valid

Compiler

Compiled 318 to 68 computations (78.6% saved)

Precisions

Click to see histograms. Total time spent on operations: 124.0ms

ival-mult: 55.0ms (44.5% of total)

ival-cos: 19.0ms (15.4% of total)

ival-add: 18.0ms (14.6% of total)

adjust: 9.0ms (7.3% of total)

ival-sin: 8.0ms (6.5% of total)

const: 7.0ms (5.7% of total)

ival-div: 4.0ms (3.2% of total)

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

exact: 1.0ms (0.8% of total)

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

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

series57.0ms (0.5%)

Memory

8.3MiB live, 84.7MiB allocated

Counts

24 → 528

Calls

Call 1

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

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

Calls

6 calls:

Time	Variable		Point	Expression
11.0ms	eps	@	0	((* (* (sin (* 1/2 (+ 0 eps))) 2) (cos (/ (+ (* 2 x) eps) -2))) (* (cos (+ (* eps 1/2) x)) (* (sin (* eps 1/2)) 2)) (cos (+ (* eps 1/2) x)) (+ (* eps 1/2) x) (- (sin (+ x eps)) (sin x)) (+ (* (+ (* (* (sin eps) x) -1/2) (- (cos eps) 1)) x) (sin eps)) (* (+ (* (* x x) -1/2) 1) eps) (+ (* (* x x) -1/2) 1) (* 1 eps) (- (sin (+ x eps)) (sin x)) (+ (* (+ (* (* (sin eps) x) -1/2) (- (cos eps) 1)) x) (sin eps)) (+ (* (* (* x -1/2) x) eps) (* 1 eps)) (+ (* (/ x eps) -1/2) (+ (* 1/12 (* x x)) -1/6)) (- (sin (+ x eps)) (sin x)) (+ (* (+ (* (* (sin eps) x) -1/2) (- (cos eps) 1)) x) (sin eps)) (* (+ (* (* x (+ eps x)) -1/2) (+ (* (* (+ (* 1/12 (* x x)) -1/6) eps) eps) 1)) eps) (- (sin (+ x eps)) (sin x)) (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (+ (* (* (sin x) eps) -1/2) (cos x)) (* (sin x) eps) (sin (* eps 1/2)) (* (sin (* eps 1/2)) 2) (+ (* (* x (+ eps x)) -1/2) (+ (* (* (+ (* 1/12 (* x x)) -1/6) eps) eps) 1)) (* (+ (* (/ x eps) -1/2) (+ (* 1/12 (* x x)) -1/6)) eps))
6.0ms	x	@	-inf	((* (* (sin (* 1/2 (+ 0 eps))) 2) (cos (/ (+ (* 2 x) eps) -2))) (* (cos (+ (* eps 1/2) x)) (* (sin (* eps 1/2)) 2)) (cos (+ (* eps 1/2) x)) (+ (* eps 1/2) x) (- (sin (+ x eps)) (sin x)) (+ (* (+ (* (* (sin eps) x) -1/2) (- (cos eps) 1)) x) (sin eps)) (* (+ (* (* x x) -1/2) 1) eps) (+ (* (* x x) -1/2) 1) (* 1 eps) (- (sin (+ x eps)) (sin x)) (+ (* (+ (* (* (sin eps) x) -1/2) (- (cos eps) 1)) x) (sin eps)) (+ (* (* (* x -1/2) x) eps) (* 1 eps)) (+ (* (/ x eps) -1/2) (+ (* 1/12 (* x x)) -1/6)) (- (sin (+ x eps)) (sin x)) (+ (* (+ (* (* (sin eps) x) -1/2) (- (cos eps) 1)) x) (sin eps)) (* (+ (* (* x (+ eps x)) -1/2) (+ (* (* (+ (* 1/12 (* x x)) -1/6) eps) eps) 1)) eps) (- (sin (+ x eps)) (sin x)) (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (+ (* (* (sin x) eps) -1/2) (cos x)) (* (sin x) eps) (sin (* eps 1/2)) (* (sin (* eps 1/2)) 2) (+ (* (* x (+ eps x)) -1/2) (+ (* (* (+ (* 1/12 (* x x)) -1/6) eps) eps) 1)) (* (+ (* (/ x eps) -1/2) (+ (* 1/12 (* x x)) -1/6)) eps))
5.0ms	eps	@	-inf	((* (* (sin (* 1/2 (+ 0 eps))) 2) (cos (/ (+ (* 2 x) eps) -2))) (* (cos (+ (* eps 1/2) x)) (* (sin (* eps 1/2)) 2)) (cos (+ (* eps 1/2) x)) (+ (* eps 1/2) x) (- (sin (+ x eps)) (sin x)) (+ (* (+ (* (* (sin eps) x) -1/2) (- (cos eps) 1)) x) (sin eps)) (* (+ (* (* x x) -1/2) 1) eps) (+ (* (* x x) -1/2) 1) (* 1 eps) (- (sin (+ x eps)) (sin x)) (+ (* (+ (* (* (sin eps) x) -1/2) (- (cos eps) 1)) x) (sin eps)) (+ (* (* (* x -1/2) x) eps) (* 1 eps)) (+ (* (/ x eps) -1/2) (+ (* 1/12 (* x x)) -1/6)) (- (sin (+ x eps)) (sin x)) (+ (* (+ (* (* (sin eps) x) -1/2) (- (cos eps) 1)) x) (sin eps)) (* (+ (* (* x (+ eps x)) -1/2) (+ (* (* (+ (* 1/12 (* x x)) -1/6) eps) eps) 1)) eps) (- (sin (+ x eps)) (sin x)) (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (+ (* (* (sin x) eps) -1/2) (cos x)) (* (sin x) eps) (sin (* eps 1/2)) (* (sin (* eps 1/2)) 2) (+ (* (* x (+ eps x)) -1/2) (+ (* (* (+ (* 1/12 (* x x)) -1/6) eps) eps) 1)) (* (+ (* (/ x eps) -1/2) (+ (* 1/12 (* x x)) -1/6)) eps))
5.0ms	eps	@	inf	((* (* (sin (* 1/2 (+ 0 eps))) 2) (cos (/ (+ (* 2 x) eps) -2))) (* (cos (+ (* eps 1/2) x)) (* (sin (* eps 1/2)) 2)) (cos (+ (* eps 1/2) x)) (+ (* eps 1/2) x) (- (sin (+ x eps)) (sin x)) (+ (* (+ (* (* (sin eps) x) -1/2) (- (cos eps) 1)) x) (sin eps)) (* (+ (* (* x x) -1/2) 1) eps) (+ (* (* x x) -1/2) 1) (* 1 eps) (- (sin (+ x eps)) (sin x)) (+ (* (+ (* (* (sin eps) x) -1/2) (- (cos eps) 1)) x) (sin eps)) (+ (* (* (* x -1/2) x) eps) (* 1 eps)) (+ (* (/ x eps) -1/2) (+ (* 1/12 (* x x)) -1/6)) (- (sin (+ x eps)) (sin x)) (+ (* (+ (* (* (sin eps) x) -1/2) (- (cos eps) 1)) x) (sin eps)) (* (+ (* (* x (+ eps x)) -1/2) (+ (* (* (+ (* 1/12 (* x x)) -1/6) eps) eps) 1)) eps) (- (sin (+ x eps)) (sin x)) (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (+ (* (* (sin x) eps) -1/2) (cos x)) (* (sin x) eps) (sin (* eps 1/2)) (* (sin (* eps 1/2)) 2) (+ (* (* x (+ eps x)) -1/2) (+ (* (* (+ (* 1/12 (* x x)) -1/6) eps) eps) 1)) (* (+ (* (/ x eps) -1/2) (+ (* 1/12 (* x x)) -1/6)) eps))
4.0ms	x	@	inf	((* (* (sin (* 1/2 (+ 0 eps))) 2) (cos (/ (+ (* 2 x) eps) -2))) (* (cos (+ (* eps 1/2) x)) (* (sin (* eps 1/2)) 2)) (cos (+ (* eps 1/2) x)) (+ (* eps 1/2) x) (- (sin (+ x eps)) (sin x)) (+ (* (+ (* (* (sin eps) x) -1/2) (- (cos eps) 1)) x) (sin eps)) (* (+ (* (* x x) -1/2) 1) eps) (+ (* (* x x) -1/2) 1) (* 1 eps) (- (sin (+ x eps)) (sin x)) (+ (* (+ (* (* (sin eps) x) -1/2) (- (cos eps) 1)) x) (sin eps)) (+ (* (* (* x -1/2) x) eps) (* 1 eps)) (+ (* (/ x eps) -1/2) (+ (* 1/12 (* x x)) -1/6)) (- (sin (+ x eps)) (sin x)) (+ (* (+ (* (* (sin eps) x) -1/2) (- (cos eps) 1)) x) (sin eps)) (* (+ (* (* x (+ eps x)) -1/2) (+ (* (* (+ (* 1/12 (* x x)) -1/6) eps) eps) 1)) eps) (- (sin (+ x eps)) (sin x)) (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (+ (* (* (sin x) eps) -1/2) (cos x)) (* (sin x) eps) (sin (* eps 1/2)) (* (sin (* eps 1/2)) 2) (+ (* (* x (+ eps x)) -1/2) (+ (* (* (+ (* 1/12 (* x x)) -1/6) eps) eps) 1)) (* (+ (* (/ x eps) -1/2) (+ (* 1/12 (* x x)) -1/6)) eps))

simplify215.0ms (1.7%)

Memory

-5.2MiB live, 242.1MiB allocated

Algorithm

1×	egg-herbie

Rules

10 650×	`lower-fma.f64`
10 650×	`lower-fma.f32`
6 856×	`lower-*.f64`
6 856×	`lower-*.f32`
3 032×	`lower-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	509	6253
1	1565	5994
2	4439	5968
0	8274	5462

Stop Event

1×	iter limit
1×	node limit

Counts

528 → 509

Calls

Call 1

Inputs
(* eps (cos (* -1 x)))
(* eps (+ (cos (* -1 x)) (* 1/2 (* eps (sin (* -1 x))))))
(* eps (+ (cos (* -1 x)) (* eps (+ (* 1/2 (sin (* -1 x))) (* 2 (* eps (+ (* -1/16 (cos (* -1 x))) (* -1/48 (cos (* -1 x))))))))))
(* eps (+ (cos (* -1 x)) (* eps (+ (* 1/2 (sin (* -1 x))) (* eps (+ (* -1/24 (* eps (sin (* -1 x)))) (* 2 (+ (* -1/16 (cos (* -1 x))) (* -1/48 (cos (* -1 x)))))))))))
(* eps (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))))))))))
(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)))))
x
(+ x (* 1/2 eps))
(+ x (* 1/2 eps))
(+ x (* 1/2 eps))
(* eps (cos x))
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x)))))))
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* eps (+ (* -1/6 (cos x)) (* 1/24 (* eps (sin x)))))))))
(* eps (+ 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) (* eps (- (* 1/12 (pow x 2)) 1/6)))))))
(* eps (+ 1 (+ (* -1/2 (pow x 2)) (* eps (+ (* -1/2 x) (* eps (- (+ (* 1/24 (* eps x)) (* 1/12 (pow x 2))) 1/6)))))))
(* eps (+ 1 (* -1/2 (pow x 2))))
(* eps (+ 1 (* -1/2 (pow x 2))))
(* eps (+ 1 (* -1/2 (pow x 2))))
(* eps (+ 1 (* -1/2 (pow x 2))))
eps
eps
eps
eps
(* eps (cos x))
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x)))))))
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* eps (+ (* -1/6 (cos x)) (* 1/24 (* eps (sin x)))))))))
(* eps (+ 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) (* eps (- (* 1/12 (pow x 2)) 1/6)))))))
(* eps (+ 1 (+ (* -1/2 (pow x 2)) (* eps (+ (* -1/2 x) (* eps (- (+ (* 1/24 (* eps x)) (* 1/12 (pow x 2))) 1/6)))))))
(* eps (+ 1 (* -1/2 (pow x 2))))
(* eps (+ 1 (* -1/2 (pow x 2))))
(* eps (+ 1 (* -1/2 (pow x 2))))
(* eps (+ 1 (* -1/2 (pow x 2))))
(* -1/2 (/ x eps))
(/ (+ (* -1/2 x) (* eps (- (* 1/12 (pow x 2)) 1/6))) eps)
(/ (+ (* -1/2 x) (* eps (- (* 1/12 (pow x 2)) 1/6))) eps)
(/ (+ (* -1/2 x) (* eps (- (* 1/12 (pow x 2)) 1/6))) eps)
(* eps (cos x))
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x)))))))
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* eps (+ (* -1/6 (cos x)) (* 1/24 (* eps (sin x)))))))))
(* eps (+ 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) (* eps (- (* 1/12 (pow x 2)) 1/6)))))))
(* eps (+ 1 (+ (* -1/2 (pow x 2)) (* eps (+ (* -1/2 x) (* eps (- (+ (* 1/24 (* eps x)) (* 1/12 (pow x 2))) 1/6)))))))
(* 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) (* eps (- (* 1/12 (pow x 2)) 1/6)))))))
(* eps (+ 1 (+ (* -1/2 (pow x 2)) (* eps (+ (* -1/2 x) (* eps (- (* 1/12 (pow x 2)) 1/6)))))))
(* eps (cos x))
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x)))))))
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* eps (+ (* -1/6 (cos x)) (* 1/24 (* eps (sin x)))))))))
(* eps (cos x))
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(cos x)
(+ (cos x) (* -1/2 (* eps (sin x))))
(+ (cos x) (* -1/2 (* eps (sin x))))
(+ (cos x) (* -1/2 (* eps (sin x))))
(* eps (sin x))
(* eps (sin x))
(* eps (sin x))
(* eps (sin x))
(* 1/2 eps)
(* eps (+ 1/2 (* -1/48 (pow eps 2))))
(* eps (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48))))
(* eps (+ 1/2 (* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48))))
eps
(* eps (+ 1 (* -1/24 (pow eps 2))))
(* eps (+ 1 (* (pow eps 2) (- (* 1/1920 (pow eps 2)) 1/24))))
(* eps (+ 1 (* (pow eps 2) (- (* (pow eps 2) (+ 1/1920 (* -1/322560 (pow eps 2)))) 1/24))))
(+ 1 (* -1/2 (pow x 2)))
(+ 1 (+ (* -1/2 (* eps x)) (* -1/2 (pow x 2))))
(+ 1 (+ (* -1/2 (pow x 2)) (* eps (+ (* -1/2 x) (* eps (- (* 1/12 (pow x 2)) 1/6))))))
(+ 1 (+ (* -1/2 (pow x 2)) (* eps (+ (* -1/2 x) (* eps (- (* 1/12 (pow x 2)) 1/6))))))
(* -1/2 x)
(+ (* -1/2 x) (* eps (- (* 1/12 (pow x 2)) 1/6)))
(+ (* -1/2 x) (* eps (- (* 1/12 (pow x 2)) 1/6)))
(+ (* -1/2 x) (* eps (- (* 1/12 (pow x 2)) 1/6)))
(* 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 (+ x (* 1/2 eps))) (sin (* 1/2 eps))))
(* 2 (* (cos (+ x (* 1/2 eps))) (sin (* 1/2 eps))))
(* 2 (* (cos (+ x (* 1/2 eps))) (sin (* 1/2 eps))))
(* 2 (* (cos (+ x (* 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)))
(* 1/2 eps)
(* eps (+ 1/2 (/ x eps)))
(* eps (+ 1/2 (/ x eps)))
(* eps (+ 1/2 (/ x eps)))
(- (sin (+ eps x)) (sin x))
(- (sin (+ eps x)) (sin x))
(- (sin (+ eps x)) (sin x))
(- (sin (+ eps x)) (sin x))
(+ (sin eps) (* x (- (+ (cos eps) (* -1/2 (* x (sin eps)))) 1)))
(+ (sin eps) (* x (- (+ (cos eps) (* -1/2 (* x (sin eps)))) 1)))
(+ (sin eps) (* x (- (+ (cos eps) (* -1/2 (* x (sin eps)))) 1)))
(+ (sin eps) (* x (- (+ (cos eps) (* -1/2 (* x (sin eps)))) 1)))
(* eps (+ 1 (* -1/2 (pow x 2))))
(* eps (+ 1 (* -1/2 (pow x 2))))
(* eps (+ 1 (* -1/2 (pow x 2))))
(* eps (+ 1 (* -1/2 (pow x 2))))
eps
eps
eps
eps
(- (sin (+ eps x)) (sin x))
(- (sin (+ eps x)) (sin x))
(- (sin (+ eps x)) (sin x))
(- (sin (+ eps x)) (sin x))
(+ (sin eps) (* x (- (+ (cos eps) (* -1/2 (* x (sin eps)))) 1)))
(+ (sin eps) (* x (- (+ (cos eps) (* -1/2 (* x (sin eps)))) 1)))
(+ (sin eps) (* x (- (+ (cos eps) (* -1/2 (* x (sin eps)))) 1)))
(+ (sin eps) (* x (- (+ (cos eps) (* -1/2 (* x (sin eps)))) 1)))
(* eps (+ 1 (* -1/2 (pow x 2))))
(* eps (+ 1 (* -1/2 (pow x 2))))
(* eps (+ 1 (* -1/2 (pow x 2))))
(* eps (+ 1 (* -1/2 (pow x 2))))
(- (* 1/12 (pow x 2)) 1/6)
(- (+ (* -1/2 (/ x eps)) (* 1/12 (pow x 2))) 1/6)
(- (+ (* -1/2 (/ x eps)) (* 1/12 (pow x 2))) 1/6)
(- (+ (* -1/2 (/ x eps)) (* 1/12 (pow x 2))) 1/6)
(- (sin (+ eps x)) (sin x))
(- (sin (+ eps x)) (sin x))
(- (sin (+ eps x)) (sin x))
(- (sin (+ eps x)) (sin x))
(+ (sin eps) (* x (- (+ (cos eps) (* -1/2 (* x (sin eps)))) 1)))
(+ (sin eps) (* x (- (+ (cos eps) (* -1/2 (* x (sin eps)))) 1)))
(+ (sin eps) (* x (- (+ (cos eps) (* -1/2 (* x (sin eps)))) 1)))
(+ (sin eps) (* x (- (+ (cos eps) (* -1/2 (* x (sin eps)))) 1)))
(* (pow eps 3) (- (* 1/12 (pow x 2)) 1/6))
(* (pow eps 3) (- (+ (* -1/2 (/ x eps)) (* 1/12 (pow x 2))) 1/6))
(* (pow eps 3) (- (+ (* -1/2 (/ x eps)) (+ (* -1/2 (/ (pow x 2) (pow eps 2))) (+ (* 1/12 (pow x 2)) (/ 1 (pow eps 2))))) 1/6))
(* (pow eps 3) (- (+ (* -1/2 (/ x eps)) (+ (* -1/2 (/ (pow x 2) (pow eps 2))) (+ (* 1/12 (pow x 2)) (/ 1 (pow eps 2))))) 1/6))
(- (sin (+ eps x)) (sin x))
(- (sin (+ eps x)) (sin x))
(- (sin (+ eps x)) (sin x))
(- (sin (+ eps x)) (sin x))
(* -1/2 (* (pow eps 2) (sin x)))
(* (pow eps 2) (+ (* -1/2 (sin x)) (/ (cos x) eps)))
(* (pow eps 2) (+ (* -1/2 (sin x)) (/ (cos x) eps)))
(* (pow eps 2) (+ (* -1/2 (sin x)) (/ (cos x) eps)))
(* -1/2 (* eps (sin x)))
(* eps (+ (* -1/2 (sin x)) (/ (cos x) eps)))
(* eps (+ (* -1/2 (sin x)) (/ (cos x) eps)))
(* eps (+ (* -1/2 (sin x)) (/ (cos x) eps)))
(* eps (sin x))
(* eps (sin x))
(* eps (sin x))
(* eps (sin x))
(sin (* 1/2 eps))
(sin (* 1/2 eps))
(sin (* 1/2 eps))
(sin (* 1/2 eps))
(* 2 (sin (* 1/2 eps)))
(* 2 (sin (* 1/2 eps)))
(* 2 (sin (* 1/2 eps)))
(* 2 (sin (* 1/2 eps)))
(* (pow eps 2) (- (* 1/12 (pow x 2)) 1/6))
(* (pow eps 2) (- (+ (* -1/2 (/ x eps)) (* 1/12 (pow x 2))) 1/6))
(* (pow eps 2) (- (+ (* -1/2 (/ x eps)) (+ (* -1/2 (/ (pow x 2) (pow eps 2))) (+ (* 1/12 (pow x 2)) (/ 1 (pow eps 2))))) 1/6))
(* (pow eps 2) (- (+ (* -1/2 (/ x eps)) (+ (* -1/2 (/ (pow x 2) (pow eps 2))) (+ (* 1/12 (pow x 2)) (/ 1 (pow eps 2))))) 1/6))
(* eps (- (* 1/12 (pow x 2)) 1/6))
(* eps (- (+ (* -1/2 (/ x eps)) (* 1/12 (pow x 2))) 1/6))
(* eps (- (+ (* -1/2 (/ x eps)) (* 1/12 (pow x 2))) 1/6))
(* eps (- (+ (* -1/2 (/ x eps)) (* 1/12 (pow x 2))) 1/6))
(* 2 (* (cos (* -1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps))))
(* 2 (* (cos (* -1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps))))
(* 2 (* (cos (* -1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps))))
(* 2 (* (cos (* -1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps))))
(* 2 (* (cos (- x (* -1/2 eps))) (sin (* 1/2 eps))))
(* 2 (* (cos (- x (* -1/2 eps))) (sin (* 1/2 eps))))
(* 2 (* (cos (- x (* -1/2 eps))) (sin (* 1/2 eps))))
(* 2 (* (cos (- x (* -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)))
(* 1/2 eps)
(* -1 (* eps (- (* -1 (/ x eps)) 1/2)))
(* -1 (* eps (- (* -1 (/ x eps)) 1/2)))
(* -1 (* eps (- (* -1 (/ x eps)) 1/2)))
(- (sin (- x (* -1 eps))) (sin x))
(- (sin (- x (* -1 eps))) (sin x))
(- (sin (- x (* -1 eps))) (sin x))
(- (sin (- x (* -1 eps))) (sin x))
(+ (sin eps) (* x (- (+ (cos eps) (* -1/2 (* x (sin eps)))) 1)))
(+ (sin eps) (* x (- (+ (cos eps) (* -1/2 (* x (sin eps)))) 1)))
(+ (sin eps) (* x (- (+ (cos eps) (* -1/2 (* x (sin eps)))) 1)))
(+ (sin eps) (* x (- (+ (cos eps) (* -1/2 (* x (sin eps)))) 1)))
(* eps (+ 1 (* -1/2 (pow x 2))))
(* eps (+ 1 (* -1/2 (pow x 2))))
(* eps (+ 1 (* -1/2 (pow x 2))))
(* eps (+ 1 (* -1/2 (pow x 2))))
eps
eps
eps
eps
(- (sin (- x (* -1 eps))) (sin x))
(- (sin (- x (* -1 eps))) (sin x))
(- (sin (- x (* -1 eps))) (sin x))
(- (sin (- x (* -1 eps))) (sin x))
(+ (sin eps) (* x (- (+ (cos eps) (* -1/2 (* x (sin eps)))) 1)))
(+ (sin eps) (* x (- (+ (cos eps) (* -1/2 (* x (sin 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 (* eps (- (* 1/2 (pow x 2)) 1)))
(* -1 (* eps (- (* 1/2 (pow x 2)) 1)))
(* -1 (* eps (- (* 1/2 (pow x 2)) 1)))
(* -1 (* eps (- (* 1/2 (pow x 2)) 1)))
(- (* 1/12 (pow x 2)) 1/6)
(- (+ (* -1/2 (/ x eps)) (* 1/12 (pow x 2))) 1/6)
(- (+ (* -1/2 (/ x eps)) (* 1/12 (pow x 2))) 1/6)
(- (+ (* -1/2 (/ x eps)) (* 1/12 (pow x 2))) 1/6)
(- (sin (- x (* -1 eps))) (sin x))
(- (sin (- x (* -1 eps))) (sin x))
(- (sin (- x (* -1 eps))) (sin x))
(- (sin (- x (* -1 eps))) (sin x))
(+ (sin eps) (* x (- (+ (cos eps) (* -1/2 (* x (sin eps)))) 1)))
(+ (sin eps) (* x (- (+ (cos eps) (* -1/2 (* x (sin eps)))) 1)))
(+ (sin eps) (* x (- (+ (cos eps) (* -1/2 (* x (sin eps)))) 1)))
(+ (sin eps) (* x (- (+ (cos eps) (* -1/2 (* x (sin eps)))) 1)))
(* (pow eps 3) (- (* 1/12 (pow x 2)) 1/6))
(* -1 (* (pow eps 3) (+ (* -1 (- (* 1/12 (pow x 2)) 1/6)) (* 1/2 (/ x eps)))))
(* -1 (* (pow eps 3) (+ (* -1 (- (* 1/12 (pow x 2)) 1/6)) (* -1 (/ (+ (* -1/2 x) (+ (* -1/2 (/ (pow x 2) eps)) (/ 1 eps))) eps)))))
(* -1 (* (pow eps 3) (+ (* -1 (- (* 1/12 (pow x 2)) 1/6)) (* -1 (/ (+ (* -1/2 x) (+ (* -1/2 (/ (pow x 2) eps)) (/ 1 eps))) eps)))))
(- (sin (- x (* -1 eps))) (sin x))
(- (sin (- x (* -1 eps))) (sin x))
(- (sin (- x (* -1 eps))) (sin x))
(- (sin (- x (* -1 eps))) (sin x))
(* -1/2 (* (pow eps 2) (sin x)))
(* (pow eps 2) (+ (* -1/2 (sin x)) (/ (cos x) eps)))
(* (pow eps 2) (+ (* -1/2 (sin x)) (/ (cos x) eps)))
(* (pow eps 2) (+ (* -1/2 (sin x)) (/ (cos x) eps)))
(* -1/2 (* eps (sin x)))
(* -1 (* eps (+ (* -1 (/ (cos x) eps)) (* 1/2 (sin x)))))
(* -1 (* eps (+ (* -1 (/ (cos x) eps)) (* 1/2 (sin x)))))
(* -1 (* eps (+ (* -1 (/ (cos x) eps)) (* 1/2 (sin x)))))
(* eps (sin x))
(* eps (sin x))
(* eps (sin x))
(* eps (sin x))
(sin (* 1/2 eps))
(sin (* 1/2 eps))
(sin (* 1/2 eps))
(sin (* 1/2 eps))
(* 2 (sin (* 1/2 eps)))
(* 2 (sin (* 1/2 eps)))
(* 2 (sin (* 1/2 eps)))
(* 2 (sin (* 1/2 eps)))
(* (pow eps 2) (- (* 1/12 (pow x 2)) 1/6))
(* (pow eps 2) (- (+ (* -1/2 (/ x eps)) (* 1/12 (pow x 2))) 1/6))
(* (pow eps 2) (- (+ (* -1 (/ (+ (* -1 (/ (+ 1 (* -1/2 (pow x 2))) eps)) (* 1/2 x)) eps)) (* 1/12 (pow x 2))) 1/6))
(* (pow eps 2) (- (+ (* -1 (/ (+ (* -1 (/ (+ 1 (* -1/2 (pow x 2))) eps)) (* 1/2 x)) eps)) (* 1/12 (pow x 2))) 1/6))
(* eps (- (* 1/12 (pow x 2)) 1/6))
(* -1 (* eps (+ (* -1 (- (* 1/12 (pow x 2)) 1/6)) (* 1/2 (/ x eps)))))
(* -1 (* eps (+ (* -1 (- (* 1/12 (pow x 2)) 1/6)) (* 1/2 (/ x eps)))))
(* -1 (* eps (+ (* -1 (- (* 1/12 (pow x 2)) 1/6)) (* 1/2 (/ x eps)))))
(* 2 (* (cos (* -1/2 eps)) (sin (* 1/2 eps))))
(+ (* 2 (* x (* (sin (* -1/2 eps)) (sin (* 1/2 eps))))) (* 2 (* (cos (* -1/2 eps)) (sin (* 1/2 eps)))))
(+ (* 2 (* (cos (* -1/2 eps)) (sin (* 1/2 eps)))) (* x (+ (* -1 (* x (* (cos (* -1/2 eps)) (sin (* 1/2 eps))))) (* 2 (* (sin (* -1/2 eps)) (sin (* 1/2 eps)))))))
(+ (* 2 (* (cos (* -1/2 eps)) (sin (* 1/2 eps)))) (* x (+ (* 2 (* (sin (* -1/2 eps)) (sin (* 1/2 eps)))) (* x (+ (* -1 (* (cos (* -1/2 eps)) (sin (* 1/2 eps)))) (* -1/3 (* x (* (sin (* -1/2 eps)) (sin (* 1/2 eps))))))))))
(* 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))))))))
(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)))))
(* 1/2 eps)
(+ x (* 1/2 eps))
(+ x (* 1/2 eps))
(+ x (* 1/2 eps))
(sin eps)
(+ (sin eps) (* x (- (cos eps) 1)))
(+ (sin eps) (* x (- (+ (cos eps) (* -1/2 (* x (sin eps)))) 1)))
(+ (sin eps) (* x (- (+ (cos eps) (* x (+ (* -1/2 (sin eps)) (* x (+ 1/6 (* -1/6 (cos eps))))))) 1)))
(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)))
eps
(+ eps (* -1/2 (* eps (pow x 2))))
(+ eps (* -1/2 (* eps (pow x 2))))
(+ eps (* -1/2 (* eps (pow x 2))))
1
(+ 1 (* -1/2 (pow x 2)))
(+ 1 (* -1/2 (pow x 2)))
(+ 1 (* -1/2 (pow x 2)))
(sin eps)
(+ (sin eps) (* x (- (cos eps) 1)))
(+ (sin eps) (* x (- (+ (cos eps) (* -1/2 (* x (sin eps)))) 1)))
(+ (sin eps) (* x (- (+ (cos eps) (* x (+ (* -1/2 (sin eps)) (* x (+ 1/6 (* -1/6 (cos eps))))))) 1)))
(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)))
eps
(+ eps (* -1/2 (* eps (pow x 2))))
(+ eps (* -1/2 (* eps (pow x 2))))
(+ eps (* -1/2 (* eps (pow x 2))))
-1/6
(- (* -1/2 (/ x eps)) 1/6)
(- (* x (- (* 1/12 x) (* 1/2 (/ 1 eps)))) 1/6)
(- (* x (- (* 1/12 x) (* 1/2 (/ 1 eps)))) 1/6)
(sin eps)
(+ (sin eps) (* x (- (cos eps) 1)))
(+ (sin eps) (* x (- (+ (cos eps) (* -1/2 (* x (sin eps)))) 1)))
(+ (sin eps) (* x (- (+ (cos eps) (* x (+ (* -1/2 (sin eps)) (* x (+ 1/6 (* -1/6 (cos eps))))))) 1)))
(sin eps)
(+ (sin eps) (* x (- (cos eps) 1)))
(+ (sin eps) (* x (- (+ (cos eps) (* -1/2 (* x (sin eps)))) 1)))
(+ (sin eps) (* x (- (+ (cos eps) (* -1/2 (* x (sin eps)))) 1)))
(* eps (+ 1 (* -1/6 (pow eps 2))))
(+ (* -1/2 (* (pow eps 2) x)) (* eps (+ 1 (* -1/6 (pow eps 2)))))
(+ (* eps (+ 1 (* -1/6 (pow eps 2)))) (* x (+ (* -1/2 (pow eps 2)) (* eps (* x (- (* 1/12 (pow eps 2)) 1/2))))))
(+ (* eps (+ 1 (* -1/6 (pow eps 2)))) (* x (+ (* -1/2 (pow eps 2)) (* eps (* x (- (* 1/12 (pow eps 2)) 1/2))))))
(sin eps)
(+ (sin eps) (* x (- (cos eps) 1)))
(+ (sin eps) (* x (- (+ (cos eps) (* -1/2 (* x (sin eps)))) 1)))
(+ (sin eps) (* x (- (+ (cos eps) (* x (+ (* -1/2 (sin eps)) (* x (+ 1/6 (* -1/6 (cos eps))))))) 1)))
eps
(+ eps (* -1/2 (* (pow eps 2) x)))
(+ eps (* x (+ (* -1/2 (* eps x)) (* -1/2 (pow eps 2)))))
(+ eps (* x (+ (* -1/2 (pow eps 2)) (* x (+ (* -1/2 eps) (* 1/12 (* (pow eps 2) x)))))))
1
(+ 1 (* -1/2 (* eps x)))
(+ 1 (* x (+ (* -1/2 eps) (* -1/2 x))))
(+ 1 (* x (+ (* -1/2 eps) (* x (- (* 1/12 (* eps x)) 1/2)))))
(* eps x)
(* x (+ eps (* -1/6 (* eps (pow x 2)))))
(* x (+ eps (* (pow x 2) (+ (* -1/6 eps) (* 1/120 (* eps (pow x 2)))))))
(* x (+ eps (* (pow x 2) (+ (* -1/6 eps) (* (pow x 2) (+ (* -1/5040 (* eps (pow x 2))) (* 1/120 eps)))))))
(+ 1 (* -1/6 (pow eps 2)))
(+ 1 (+ (* -1/2 (* eps x)) (* -1/6 (pow eps 2))))
(+ 1 (+ (* -1/6 (pow eps 2)) (* x (+ (* -1/2 eps) (* x (- (* 1/12 (pow eps 2)) 1/2))))))
(+ 1 (+ (* -1/6 (pow eps 2)) (* x (+ (* -1/2 eps) (* x (- (* 1/12 (pow eps 2)) 1/2))))))
(* -1/6 eps)
(+ (* -1/2 x) (* -1/6 eps))
(+ (* -1/6 eps) (* x (- (* 1/12 (* eps x)) 1/2)))
(+ (* -1/6 eps) (* x (- (* 1/12 (* eps x)) 1/2)))
(* 2 (* (cos (* -1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))))
(* 2 (* (cos (* -1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))))
(* 2 (* (cos (* -1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))))
(* 2 (* (cos (* -1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))))
(* 2 (* (cos (+ x (* 1/2 eps))) (sin (* 1/2 eps))))
(* 2 (* (cos (+ x (* 1/2 eps))) (sin (* 1/2 eps))))
(* 2 (* (cos (+ x (* 1/2 eps))) (sin (* 1/2 eps))))
(* 2 (* (cos (+ x (* 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)))
x
(* x (+ 1 (* 1/2 (/ eps x))))
(* x (+ 1 (* 1/2 (/ eps x))))
(* x (+ 1 (* 1/2 (/ eps x))))
(- (sin (+ eps x)) (sin x))
(- (sin (+ eps x)) (sin x))
(- (sin (+ eps x)) (sin x))
(- (sin (+ eps x)) (sin x))
(* -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 (* eps (pow x 2)))
(* (pow x 2) (+ (* -1/2 eps) (/ eps (pow x 2))))
(* (pow x 2) (+ (* -1/2 eps) (/ eps (pow x 2))))
(* (pow x 2) (+ (* -1/2 eps) (/ eps (pow x 2))))
(* -1/2 (pow x 2))
(* (pow x 2) (- (/ 1 (pow x 2)) 1/2))
(* (pow x 2) (- (/ 1 (pow x 2)) 1/2))
(* (pow x 2) (- (/ 1 (pow x 2)) 1/2))
(- (sin (+ eps x)) (sin x))
(- (sin (+ eps x)) (sin x))
(- (sin (+ eps x)) (sin x))
(- (sin (+ eps x)) (sin x))
(* -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 (* eps (pow x 2)))
(* (pow x 2) (+ (* -1/2 eps) (/ eps (pow x 2))))
(* (pow x 2) (+ (* -1/2 eps) (/ eps (pow x 2))))
(* (pow x 2) (+ (* -1/2 eps) (/ eps (pow x 2))))
(* 1/12 (pow x 2))
(* (pow x 2) (- 1/12 (* 1/2 (/ 1 (* eps x)))))
(* (pow x 2) (+ 1/12 (* -1 (/ (+ (* 1/2 (/ 1 eps)) (* 1/6 (/ 1 x))) x))))
(* (pow x 2) (+ 1/12 (* -1 (/ (+ (* 1/2 (/ 1 eps)) (* 1/6 (/ 1 x))) x))))
(- (sin (+ eps x)) (sin x))
(- (sin (+ eps x)) (sin x))
(- (sin (+ eps x)) (sin x))
(- (sin (+ eps x)) (sin x))
(* -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)))
(* eps (* (pow x 2) (- (* 1/12 (pow eps 2)) 1/2)))
(* (pow x 2) (+ (* -1/2 (/ (pow eps 2) x)) (* eps (- (* 1/12 (pow eps 2)) 1/2))))
(* (pow x 2) (+ (* -1/2 (/ (pow eps 2) x)) (+ (* eps (- (* 1/12 (pow eps 2)) 1/2)) (/ (* eps (+ 1 (* -1/6 (pow eps 2)))) (pow x 2)))))
(* (pow x 2) (+ (* -1/2 (/ (pow eps 2) x)) (+ (* eps (- (* 1/12 (pow eps 2)) 1/2)) (/ (* eps (+ 1 (* -1/6 (pow eps 2)))) (pow x 2)))))
(- (sin (+ eps x)) (sin x))
(- (sin (+ eps x)) (sin x))
(- (sin (+ eps x)) (sin x))
(- (sin (+ eps x)) (sin x))
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(+ (cos x) (* -1/2 (* eps (sin x))))
(+ (cos x) (* -1/2 (* eps (sin x))))
(+ (cos x) (* -1/2 (* eps (sin x))))
(+ (cos x) (* -1/2 (* eps (sin x))))
(* eps (sin x))
(* eps (sin x))
(* eps (sin x))
(* eps (sin x))
(* (pow x 2) (- (* 1/12 (pow eps 2)) 1/2))
(* (pow x 2) (- (+ (* -1/2 (/ eps x)) (* 1/12 (pow eps 2))) 1/2))
(* (pow x 2) (- (+ (* -1/2 (/ eps x)) (+ (* -1/6 (/ (pow eps 2) (pow x 2))) (+ (* 1/12 (pow eps 2)) (/ 1 (pow x 2))))) 1/2))
(* (pow x 2) (- (+ (* -1/2 (/ eps x)) (+ (* -1/6 (/ (pow eps 2) (pow x 2))) (+ (* 1/12 (pow eps 2)) (/ 1 (pow x 2))))) 1/2))
(* 1/12 (* eps (pow x 2)))
(* (pow x 2) (- (* 1/12 eps) (* 1/2 (/ 1 x))))
(* (pow x 2) (- (+ (* -1/6 (/ eps (pow x 2))) (* 1/12 eps)) (* 1/2 (/ 1 x))))
(* (pow x 2) (- (+ (* -1/6 (/ eps (pow x 2))) (* 1/12 eps)) (* 1/2 (/ 1 x))))
(* 2 (* (cos (* -1/2 (- eps (* -2 x)))) (sin (* 1/2 eps))))
(* 2 (* (cos (* -1/2 (- eps (* -2 x)))) (sin (* 1/2 eps))))
(* 2 (* (cos (* -1/2 (- eps (* -2 x)))) (sin (* 1/2 eps))))
(* 2 (* (cos (* -1/2 (- eps (* -2 x)))) (sin (* 1/2 eps))))
(* 2 (* (cos (- (* 1/2 eps) (* -1 x))) (sin (* 1/2 eps))))
(* 2 (* (cos (- (* 1/2 eps) (* -1 x))) (sin (* 1/2 eps))))
(* 2 (* (cos (- (* 1/2 eps) (* -1 x))) (sin (* 1/2 eps))))
(* 2 (* (cos (- (* 1/2 eps) (* -1 x))) (sin (* 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)))
x
(* -1 (* x (- (* -1/2 (/ eps x)) 1)))
(* -1 (* x (- (* -1/2 (/ eps x)) 1)))
(* -1 (* x (- (* -1/2 (/ eps x)) 1)))
(- (sin (- eps (* -1 x))) (sin x))
(- (sin (- eps (* -1 x))) (sin x))
(- (sin (- eps (* -1 x))) (sin x))
(- (sin (- eps (* -1 x))) (sin x))
(* -1/2 (* (pow x 2) (sin eps)))
(* (pow x 2) (- (+ (* -1/2 (sin eps)) (/ (cos eps) x)) (/ 1 x)))
(* (pow x 2) (+ (* -1 (/ (+ (* -1 (- (cos eps) 1)) (* -1 (/ (sin eps) x))) x)) (* -1/2 (sin eps))))
(* (pow x 2) (+ (* -1 (/ (+ (* -1 (- (cos eps) 1)) (* -1 (/ (sin eps) x))) x)) (* -1/2 (sin eps))))
(* -1/2 (* eps (pow x 2)))
(* (pow x 2) (+ (* -1/2 eps) (/ eps (pow x 2))))
(* (pow x 2) (+ (* -1/2 eps) (/ eps (pow x 2))))
(* (pow x 2) (+ (* -1/2 eps) (/ eps (pow x 2))))
(* -1/2 (pow x 2))
(* (pow x 2) (- (/ 1 (pow x 2)) 1/2))
(* (pow x 2) (- (/ 1 (pow x 2)) 1/2))
(* (pow x 2) (- (/ 1 (pow x 2)) 1/2))
(- (sin (- eps (* -1 x))) (sin x))
(- (sin (- eps (* -1 x))) (sin x))
(- (sin (- eps (* -1 x))) (sin x))
(- (sin (- eps (* -1 x))) (sin x))
(* -1/2 (* (pow x 2) (sin eps)))
(* (pow x 2) (- (+ (* -1/2 (sin eps)) (/ (cos eps) x)) (/ 1 x)))
(* (pow x 2) (+ (* -1 (/ (+ (* -1 (- (cos eps) 1)) (* -1 (/ (sin eps) x))) x)) (* -1/2 (sin eps))))
(* (pow x 2) (+ (* -1 (/ (+ (* -1 (- (cos eps) 1)) (* -1 (/ (sin eps) x))) x)) (* -1/2 (sin eps))))
(* -1/2 (* eps (pow x 2)))
(* (pow x 2) (+ (* -1/2 eps) (/ eps (pow x 2))))
(* (pow x 2) (+ (* -1/2 eps) (/ eps (pow x 2))))
(* (pow x 2) (+ (* -1/2 eps) (/ eps (pow x 2))))
(* 1/12 (pow x 2))
(* (pow x 2) (- 1/12 (* 1/2 (/ 1 (* eps x)))))
(* (pow x 2) (+ 1/12 (* -1 (/ (+ (* 1/2 (/ 1 eps)) (* 1/6 (/ 1 x))) x))))
(* (pow x 2) (+ 1/12 (* -1 (/ (+ (* 1/2 (/ 1 eps)) (* 1/6 (/ 1 x))) x))))
(- (sin (- eps (* -1 x))) (sin x))
(- (sin (- eps (* -1 x))) (sin x))
(- (sin (- eps (* -1 x))) (sin x))
(- (sin (- eps (* -1 x))) (sin x))
(* -1/2 (* (pow x 2) (sin eps)))
(* (pow x 2) (- (+ (* -1/2 (sin eps)) (/ (cos eps) x)) (/ 1 x)))
(* (pow x 2) (+ (* -1 (/ (+ (* -1 (- (cos eps) 1)) (* -1 (/ (sin eps) x))) x)) (* -1/2 (sin eps))))
(* (pow x 2) (+ (* -1 (/ (+ (* -1 (- (cos eps) 1)) (* -1 (/ (sin eps) x))) x)) (* -1/2 (sin eps))))
(* eps (* (pow x 2) (- (* 1/12 (pow eps 2)) 1/2)))
(* (pow x 2) (+ (* -1/2 (/ (pow eps 2) x)) (* eps (- (* 1/12 (pow eps 2)) 1/2))))
(* (pow x 2) (+ (* -1 (/ (+ (* -1 (/ (* eps (+ 1 (* -1/6 (pow eps 2)))) x)) (* 1/2 (pow eps 2))) x)) (* eps (- (* 1/12 (pow eps 2)) 1/2))))
(* (pow x 2) (+ (* -1 (/ (+ (* -1 (/ (* eps (+ 1 (* -1/6 (pow eps 2)))) x)) (* 1/2 (pow eps 2))) x)) (* eps (- (* 1/12 (pow eps 2)) 1/2))))
(- (sin (- eps (* -1 x))) (sin x))
(- (sin (- eps (* -1 x))) (sin x))
(- (sin (- eps (* -1 x))) (sin x))
(- (sin (- eps (* -1 x))) (sin x))
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(+ (cos x) (* -1/2 (* eps (sin x))))
(+ (cos x) (* -1/2 (* eps (sin x))))
(+ (cos x) (* -1/2 (* eps (sin x))))
(+ (cos x) (* -1/2 (* eps (sin x))))
(* eps (sin x))
(* eps (sin x))
(* eps (sin x))
(* eps (sin x))
(* (pow x 2) (- (* 1/12 (pow eps 2)) 1/2))
(* (pow x 2) (- (+ (* -1/2 (/ eps x)) (* 1/12 (pow eps 2))) 1/2))
(* (pow x 2) (- (+ (* -1 (/ (+ (* -1 (/ (+ 1 (* -1/6 (pow eps 2))) x)) (* 1/2 eps)) x)) (* 1/12 (pow eps 2))) 1/2))
(* (pow x 2) (- (+ (* -1 (/ (+ (* -1 (/ (+ 1 (* -1/6 (pow eps 2))) x)) (* 1/2 eps)) x)) (* 1/12 (pow eps 2))) 1/2))
(* 1/12 (* eps (pow x 2)))
(* (pow x 2) (- (* 1/12 eps) (* 1/2 (/ 1 x))))
(* (pow x 2) (+ (* -1 (/ (+ 1/2 (* 1/6 (/ eps x))) x)) (* 1/12 eps)))
(* (pow x 2) (+ (* -1 (/ (+ 1/2 (* 1/6 (/ eps x))) x)) (* 1/12 eps)))

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

rewrite240.0ms (1.9%)

Memory

-20.3MiB live, 332.1MiB allocated

Rules

6 722×	`lower-*.f32`
6 696×	`lower-*.f64`
6 532×	`lower-fma.f32`
6 522×	`lower-fma.f64`
3 740×	`lower-/.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	76	476
0	102	466
1	400	466
2	3491	466
0	9952	441

Stop Event

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

Counts

24 → 593

Calls

Call 1

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

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

eval174.0ms (1.4%)

Memory: 33.2MiB live, 383.2MiB allocated
Compiler: Compiled 24 839 to 4 108 computations (83.5% saved)

prune44.0ms (0.4%)

Memory

-32.9MiB live, 127.1MiB allocated

Pruning

20 alts after pruning (14 fresh and 6 done)

	Pruned	Kept	Total
New	1 095	7	1 102
Fresh	5	7	12
Picked	2	3	5
Done	1	3	4
Total	1 103	20	1 123

Accuracy

100.0%

Counts

1 123 → 20

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	65.7%	(fma.f64 (sin.f64 x) (cos.f64 eps) (fma.f64 (sin.f64 eps) (cos.f64 x) (neg.f64 (sin.f64 x))))
✓	65.5%	(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
✓	7.9%	(-.f64 #s(approx (sin (+ x eps)) (sin.f64 eps)) (sin.f64 x))
	99.5%	(.f64 (.f64 #s(approx (sin (* 1/2 (+ 0 eps))) (.f64 (fma.f64 (.f64 eps eps) #s(literal -1/48 binary64) #s(literal 1/2 binary64)) eps)) #s(literal 2 binary64)) #s(approx (cos (/ (+ (* 2 x) eps) -2)) (fma.f64 (*.f64 (sin.f64 x) eps) #s(literal -1/2 binary64) (cos.f64 x))))
	99.5%	(.f64 (.f64 #s(approx (sin (* 1/2 (+ 0 eps))) (.f64 (fma.f64 (.f64 eps eps) #s(literal -1/48 binary64) #s(literal 1/2 binary64)) eps)) #s(literal 2 binary64)) #s(approx (cos (/ (+ (* 2 x) eps) -2)) (cos.f64 (fma.f64 eps #s(literal 1/2 binary64) x))))
	99.6%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 (fma.f64 (.f64 #s(literal -1/6 binary64) eps) (cos.f64 x) (*.f64 (sin.f64 x) #s(literal -1/2 binary64))) eps (cos.f64 x)) eps))
✓	99.5%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 (.f64 (sin.f64 x) eps) #s(literal -1/2 binary64) (cos.f64 x)) eps))
	99.2%	#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (cos.f64 x) eps))
	98.9%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (* (sin x) eps) -1/2) (cos x)) (fma.f64 (*.f64 x (+.f64 x eps)) #s(literal -1/2 binary64) #s(literal 1 binary64))) eps))
	98.5%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (* (sin x) eps) -1/2) (cos x)) (fma.f64 (*.f64 #s(literal -1/2 binary64) eps) x #s(literal 1 binary64))) eps))
	98.8%	#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (+ (* (+ (* (* (sin eps) x) -1/2) (- (cos eps) 1)) x) (sin eps)) (fma.f64 (.f64 (.f64 x x) #s(literal -1/2 binary64)) eps eps)))
	98.9%	#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (+ (* (+ (* (* (sin eps) x) -1/2) (- (cos eps) 1)) x) (sin eps)) (.f64 (fma.f64 (.f64 x (+.f64 eps x)) #s(literal -1/2 binary64) (fma.f64 #s(approx (* (+ (* 1/12 (* x x)) -1/6) eps) (*.f64 #s(literal -1/6 binary64) eps)) eps #s(literal 1 binary64))) eps)))
	98.5%	#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (+ (* (+ (* (* (sin eps) x) -1/2) (- (cos eps) 1)) x) (sin eps)) (.f64 #s(approx (+ ( (* x (+ eps x)) -1/2) (+ (* (* (+ (* 1/12 (* x x)) -1/6) eps) eps) 1)) (fma.f64 (*.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64))) eps)))
	5.4%	#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (+ (* (+ (* (* (sin eps) x) -1/2) (- (cos eps) 1)) x) (sin eps)) (.f64 #s(approx (+ ( (* x (+ eps x)) -1/2) (+ (* (* (+ (* 1/12 (* x x)) -1/6) eps) eps) 1)) (.f64 (.f64 #s(approx (+ (* (/ x eps) -1/2) (+ (* 1/12 (* x x)) -1/6)) #s(literal -1/6 binary64)) eps) eps)) eps)))
	5.8%	#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (+ (* (+ (* (* (sin eps) x) -1/2) (- (cos eps) 1)) x) (sin eps)) (.f64 #s(approx (+ ( (* x (+ eps x)) -1/2) (+ (* (* (+ (* 1/12 (* x x)) -1/6) eps) eps) 1)) (.f64 #s(approx ( (+ (* (/ x eps) -1/2) (+ (* 1/12 (* x x)) -1/6)) eps) (fma.f64 #s(literal -1/6 binary64) eps (*.f64 #s(literal -1/2 binary64) x))) eps)) eps)))
	5.8%	#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (+ (* (+ (* (* (sin eps) x) -1/2) (- (cos eps) 1)) x) (sin eps)) (.f64 #s(approx (+ ( (* x (+ eps x)) -1/2) (+ (* (* (+ (* 1/12 (* x x)) -1/6) eps) eps) 1)) (.f64 #s(approx ( (+ (* (/ x eps) -1/2) (+ (* 1/12 (* x x)) -1/6)) eps) (*.f64 #s(literal -1/2 binary64) x)) eps)) eps)))
✓	98.5%	#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (+ (* (+ (* (* (sin eps) x) -1/2) (- (cos eps) 1)) x) (sin eps)) (.f64 #s(approx (+ ( (* x x) -1/2) 1) #s(literal 1 binary64)) eps)))
	99.7%	#s(approx (+ (* (sin x) (cos eps)) (+ (* (sin eps) (cos x)) (neg (sin x)))) (fma.f64 (sin.f64 x) (-.f64 (cos.f64 eps) #s(literal 1 binary64)) (*.f64 (sin.f64 eps) (cos.f64 x))))
✓	99.9%	#s(approx (* (* (sin (* 1/2 (+ 0 eps))) 2) (cos (/ (+ (* 2 x) eps) -2))) (.f64 (cos.f64 (fma.f64 eps #s(literal 1/2 binary64) x)) (.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) #s(literal 2 binary64))))
	99.5%	#s(approx (* (* (sin (* 1/2 (+ 0 eps))) 2) (cos (/ (+ (* 2 x) eps) -2))) (.f64 (cos.f64 (fma.f64 eps #s(literal 1/2 binary64) x)) (.f64 #s(approx (sin (* eps 1/2)) (*.f64 #s(literal 1/2 binary64) eps)) #s(literal 2 binary64))))

Compiler

Compiled 749 to 401 computations (46.5% saved)

regimes40.0ms (0.3%)

Memory

2.7MiB live, 80.3MiB allocated

Counts

39 → 1

Calls

Call 1

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

Outputs

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

Calls

3 calls:

12.0ms	eps
11.0ms	(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
10.0ms	x

Results

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

Compiler

Compiled 9 to 10 computations (-11.1% saved)

regimes28.0ms (0.2%)

Memory

33.0MiB live, 70.7MiB allocated

Counts

30 → 1

Calls

Call 1

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

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

Calls

3 calls:

10.0ms	eps
8.0ms	x
8.0ms	(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))

Results

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

Compiler

Compiled 9 to 10 computations (-11.1% saved)

regimes28.0ms (0.2%)

Memory

-15.4MiB live, 60.7MiB allocated

Counts

28 → 1

Calls

Call 1

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

Outputs

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

Calls

3 calls:

9.0ms	(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
9.0ms	x
8.0ms	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 9 to 10 computations (-11.1% saved)

regimes34.0ms (0.3%)

Memory

-3.9MiB live, 42.5MiB allocated

Counts

21 → 1

Calls

Call 1

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

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

Calls

3 calls:

20.0ms	x
6.0ms	(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
6.0ms	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 9 to 10 computations (-11.1% saved)

regimes20.0ms (0.2%)

Memory

1.2MiB live, 39.1MiB allocated

Counts

19 → 1

Calls

Call 1

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

Outputs

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

Calls

3 calls:

8.0ms	eps
6.0ms	(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
6.0ms	x

Results

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

Compiler

Compiled 9 to 10 computations (-11.1% saved)

regimes18.0ms (0.1%)

Memory

3.3MiB live, 39.5MiB allocated

Counts

14 → 1

Calls

Call 1

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

Outputs

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

Calls

3 calls:

8.0ms	x
4.0ms	(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
4.0ms	eps

Results

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

Compiler

Compiled 9 to 10 computations (-11.1% saved)

regimes15.0ms (0.1%)

Memory

-3.8MiB live, 30.4MiB allocated

Counts

8 → 1

Calls

Call 1

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

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

Calls

3 calls:

8.0ms	x
3.0ms	(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
3.0ms	eps

Results

Accuracy	Segments	Branch
98.8%	1	`x`
98.8%	1	`eps`
98.8%	1	`(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))`

Compiler

Compiled 9 to 10 computations (-11.1% saved)

regimes8.0ms (0.1%)

Memory

20.6MiB live, 20.6MiB allocated

Counts

6 → 1

Calls

Call 1

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

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

Calls

3 calls:

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

Results

Accuracy	Segments	Branch
98.8%	1	`x`
98.8%	1	`eps`
98.8%	1	`(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))`

Compiler

Compiled 9 to 10 computations (-11.1% saved)

regimes298.0ms (2.4%)

Memory

-196.5MiB live, 20.2MiB allocated

Counts

5 → 1

Calls

Call 1

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

Outputs

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

Calls

3 calls:

293.0ms	x
2.0ms	(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
2.0ms	eps

Results

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

Compiler

Compiled 9 to 10 computations (-11.1% saved)

regimes7.0ms (0.1%)

Memory

17.1MiB live, 17.1MiB allocated

Accuracy

Total -59.6b remaining (-6053.3%)

Threshold costs -59.6b (-6053.3%)

Counts

4 → 1

Calls

Call 1

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

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

Calls

3 calls:

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

Results

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

Compiler

Compiled 9 to 10 computations (-11.1% saved)

simplify26.0ms (0.2%)

Memory

-22.8MiB live, 61.0MiB allocated

Algorithm

1×	egg-herbie

Rules

32×	`-commutative-binary64-.f64`
2×	`1-exp-binary32-exp.f32`
2×	`1-exp-binary64-exp.f64`
2×	`+-commutative-binary64-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	97	336
1	116	336

Stop Event

1×

saturated

Calls

Call 1

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

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

soundness1.3s (10.8%)

Memory

21.4MiB live, 893.9MiB allocated

Rules

16 678×	`lower-fma.f64`
16 678×	`lower-fma.f32`
12 518×	`lower-fma.f64`
12 518×	`lower-fma.f32`
11 690×	`lower-fma.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	509	6253
1	1565	5994
2	4439	5968
0	8274	5462
0	76	476
0	102	466
1	400	466
2	3491	466
0	9952	441
0	6	16
0	10	16
1	53	16
2	380	16
3	4766	16
0	8210	16
0	69	427
0	105	419
1	381	419
2	3046	419
0	8807	408
0	107	496
1	314	496
2	775	489
3	2829	489
4	6198	489
0	8141	458
0	481	6562
1	1501	6287
2	3898	6240
0	8436	5720
0	408	3554
1	1222	3395
2	3320	3315
3	7919	3315
0	8305	3097

Stop Event

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

Compiler

Compiled 248 to 193 computations (22.2% saved)

preprocess63.0ms (0.5%)

Memory: 13.1MiB live, 127.7MiB allocated
Compiler: Compiled 262 to 154 computations (41.2% 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

start0.0ms (0%)

analyze46.0ms (0.4%)

sample6.5s (52%)

explain103.0ms (0.8%)

preprocess24.0ms (0.2%)

eval0.0ms (0%)

prune0.0ms (0%)

simplify6.0ms (0.1%)

localize23.0ms (0.2%)

series6.0ms (0%)

simplify142.0ms (1.1%)

rewrite176.0ms (1.4%)

eval52.0ms (0.4%)

prune10.0ms (0.1%)

simplify175.0ms (1.4%)

localize220.0ms (1.8%)

series36.0ms (0.3%)

simplify181.0ms (1.5%)

rewrite167.0ms (1.3%)

eval111.0ms (0.9%)

prune25.0ms (0.2%)

simplify161.0ms (1.3%)

localize401.0ms (3.2%)

series74.0ms (0.6%)

simplify213.0ms (1.7%)

rewrite295.0ms (2.4%)

eval198.0ms (1.6%)

prune143.0ms (1.1%)

simplify138.0ms (1.1%)

localize192.0ms (1.5%)

series57.0ms (0.5%)

simplify215.0ms (1.7%)

rewrite240.0ms (1.9%)

eval174.0ms (1.4%)

prune44.0ms (0.4%)

regimes40.0ms (0.3%)

regimes28.0ms (0.2%)

regimes28.0ms (0.2%)

regimes34.0ms (0.3%)

regimes20.0ms (0.2%)

regimes18.0ms (0.1%)

regimes15.0ms (0.1%)

regimes8.0ms (0.1%)

regimes298.0ms (2.4%)

regimes7.0ms (0.1%)

simplify26.0ms (0.2%)

soundness1.3s (10.8%)

preprocess63.0ms (0.5%)

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