Metrics for 2sin (example 3.3)

start0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated

analyze50.0ms (0.4%)

Memory

-9.9MiB live, 44.4MiB 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)

sample6.6s (52%)

Memory

-159.8MiB live, 6 969.6MiB allocated

Samples

3.9s	26 447×	0	invalid
666.0ms	5 423×	0	valid
602.0ms	2 833×	1	valid

Precisions

Click to see histograms. Total time spent on operations: 3.8s

const: 854.0ms (22.4% of total)

ival-sin: 685.0ms (18% of total)

ival-sub: 574.0ms (15.1% of total)

ival-<=: 352.0ms (9.2% of total)

ival-fabs: 313.0ms (8.2% of total)

ival-add: 278.0ms (7.3% of total)

ival-<: 274.0ms (7.2% of total)

ival-mult: 226.0ms (5.9% of total)

ival-and: 102.0ms (2.7% of total)

adjust: 90.0ms (2.4% of total)

exact: 49.0ms (1.3% of total)

ival-assert: 14.0ms (0.4% of total)

Bogosity

explain90.0ms (0.7%)

Memory

10.5MiB live, 99.4MiB allocated

FPErrors

Click to see full error table

Ground Truth	Overpredictions	Example	Underpredictions	Example	Subexpression
220	3	(-1.416919849175757e-287 1.3021226862724824e-289)	4	(2.1834476938807615e-101 2.357669797071679e-103)	`(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))`
1	0	-	1	(32.20894738896712 8.664518947479058e-9)	`(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

Confusion

	Predicted +	Predicted -
+	216	4
-	3	33

Precision

0.9863013698630136

Recall

0.9818181818181818

Confusion?

	Predicted +	Predicted Maybe	Predicted -
+	216	3	1
-	3	2	31

Precision?

0.9776785714285714

Recall?

0.9954545454545455

Freqs

test

number	freq
0	37
1	219

Total Confusion?

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

Precision?

1.0

Recall?

1.0

Samples

17.0ms	346×	0	valid
16.0ms	162×	1	valid
1.0ms	4×	3	valid

Compiler

Compiled 49 to 22 computations (55.1% saved)

Precisions

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

ival-sin: 10.0ms (50.1% of total)

adjust: 3.0ms (15% of total)

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

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

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

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

preprocess24.0ms (0.2%)

Memory

-10.8MiB live, 26.0MiB 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 9 to 6 computations (33.3% saved)

eval0.0ms (0%)

Memory: 0.3MiB live, 0.3MiB allocated
Compiler: Compiled 2 to 2 computations (0% saved)

prune1.0ms (0%)

Memory

0.9MiB live, 0.9MiB allocated

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	62.5%	(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))

Compiler

Compiled 9 to 6 computations (33.3% saved)

simplify7.0ms (0.1%)

Memory

5.9MiB live, 5.9MiB 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)

localize26.0ms (0.2%)

Memory

-10.5MiB live, 27.6MiB allocated

Localize:

Found 4 expressions of interest:

New	Metric	Score
accuracy	0	(+.f64 x eps)
accuracy	0	(sin.f64 x)
accuracy	0.04331040172363414	(sin.f64 (+.f64 x eps))
accuracy	23.938343398647625	(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))

Samples

10.0ms	173×	0	valid
8.0ms	81×	1	valid
1.0ms	2×	3	valid

Compiler

Compiled 20 to 8 computations (60% saved)

Precisions

Click to see histograms. Total time spent on operations: 10.0ms

ival-sin: 5.0ms (51% of total)

adjust: 2.0ms (20.4% of total)

ival-add: 2.0ms (20.4% of total)

ival-sub: 1.0ms (10.2% of total)

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

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

series4.0ms (0%)

Memory

5.4MiB live, 5.4MiB allocated

Counts

4 → 84

Calls

Call 1

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

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

Calls

21 calls:

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

simplify158.0ms (1.3%)

Memory

6.2MiB live, 158.2MiB allocated

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

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

Stop Event

1×	iter limit
1×	node limit

Counts

84 → 77

Calls

Call 1

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

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

rewrite216.0ms (1.7%)

Memory

-6.9MiB live, 192.0MiB 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 #s(literal 1 binary64) (cos.f64 (.f64 #s(literal 2 binary64) (+.f64 eps x)))) #s(literal 1/2 binary64) (*.f64 (+.f64 (sin.f64 x) (sin.f64 (+.f64 eps x))) (sin.f64 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)) (/.f64 #s(literal 1 binary64) (-.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 (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 #s(literal 2 binary64) (+.f64 eps x)))) #s(literal 1/2 binary64) (.f64 (+.f64 (sin.f64 x) (sin.f64 (+.f64 eps x))) (sin.f64 x))) (-.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)) (/.f64 #s(literal 1 binary64) (+.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))))))
(.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)) (/.f64 #s(literal 1 binary64) (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 x x))) #s(literal 1/2 binary64) (.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) (+.f64 eps x)))) #s(literal 1/2 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)) (/.f64 #s(literal 1 binary64) (fma.f64 (.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 x x))) #s(literal 1/2 binary64)) (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 x x))) #s(literal 1/2 binary64) (.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 #s(literal 2 binary64) (+.f64 eps x)))) #s(literal 1/2 binary64))) (pow.f64 (sin.f64 (+.f64 eps x)) #s(literal 4 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 #s(literal 1/2 binary64) (+.f64 #s(literal 0 binary64) eps))) (sin.f64 (.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps)))) (-.f64 (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 #s(literal 1/2 binary64) (fma.f64 (cos.f64 (.f64 #s(literal 2 binary64) (+.f64 eps x))) #s(literal 1/2 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)) (.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 #s(literal 2 binary64) (+.f64 eps x)))) #s(literal 1/2 binary64))) (pow.f64 (sin.f64 (+.f64 eps x)) #s(literal 4 binary64))))
(.f64 (/.f64 (-.f64 #s(literal 1/2 binary64) (fma.f64 (cos.f64 (.f64 #s(literal 2 binary64) (+.f64 eps x))) #s(literal 1/2 binary64) (.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 x x))) #s(literal 1/2 binary64)))) (-.f64 #s(literal 1/2 binary64) (fma.f64 (cos.f64 (.f64 #s(literal 2 binary64) (+.f64 eps x))) #s(literal 1/2 binary64) (*.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 x x))) #s(literal 1/2 binary64))))) (-.f64 (sin.f64 (+.f64 eps x)) (sin.f64 x)))
(.f64 (/.f64 (-.f64 #s(literal 1/2 binary64) (fma.f64 (cos.f64 (.f64 #s(literal 2 binary64) (+.f64 eps x))) #s(literal 1/2 binary64) (.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 x x))) #s(literal 1/2 binary64)))) (-.f64 (pow.f64 (sin.f64 (+.f64 eps x)) #s(literal 3 binary64)) (pow.f64 (sin.f64 x) #s(literal 3 binary64)))) (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 #s(literal 2 binary64) (+.f64 eps x)))) #s(literal 1/2 binary64) (*.f64 (sin.f64 x) (-.f64 (sin.f64 x) (sin.f64 (+.f64 eps x))))))
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(/.f64 (.f64 (.f64 (fma.f64 (.f64 eps eps) eps (.f64 (.f64 x x) x)) (.f64 (fma.f64 eps (+.f64 eps x) (.f64 x x)) (-.f64 x eps))) #s(literal 1 binary64)) (.f64 (fma.f64 (.f64 eps eps) (fma.f64 eps eps (.f64 x x)) (.f64 (.f64 x x) (*.f64 x x))) (-.f64 x eps)))
(/.f64 (.f64 (.f64 (fma.f64 (.f64 eps eps) eps (.f64 (.f64 x x) x)) (.f64 (fma.f64 eps (+.f64 eps x) (.f64 x x)) (-.f64 x eps))) #s(literal 1 binary64)) (.f64 (.f64 (fma.f64 eps (+.f64 eps x) (.f64 x x)) (-.f64 x eps)) (fma.f64 (-.f64 eps x) eps (*.f64 x x))))
(/.f64 (.f64 (fma.f64 (.f64 (.f64 (.f64 eps eps) eps) (.f64 (.f64 eps eps) eps)) (.f64 (.f64 eps eps) eps) (.f64 (.f64 (.f64 (.f64 x x) x) (.f64 (.f64 x x) x)) (.f64 (.f64 x x) x))) #s(literal 1 binary64)) (.f64 (fma.f64 (.f64 (.f64 eps eps) eps) (-.f64 (.f64 (.f64 eps eps) eps) (.f64 (.f64 x x) x)) (.f64 (.f64 (.f64 x x) x) (.f64 (.f64 x x) x))) (fma.f64 (-.f64 eps x) eps (*.f64 x x))))
(/.f64 (.f64 (fma.f64 (.f64 eps eps) eps (.f64 (.f64 x x) x)) #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))) (*.f64 (-.f64 x eps) (-.f64 x eps)))
(/.f64 (.f64 (fma.f64 eps eps (.f64 x x)) (.f64 (-.f64 x eps) (+.f64 eps x))) (.f64 (-.f64 x eps) (fma.f64 eps eps (*.f64 x x))))
(/.f64 (*.f64 (+.f64 eps x) (-.f64 eps x)) (-.f64 eps x))
(/.f64 (.f64 (fma.f64 (.f64 eps eps) eps (.f64 (.f64 x x) x)) (.f64 (fma.f64 eps (+.f64 eps x) (.f64 x x)) (-.f64 x eps))) (.f64 (-.f64 x eps) (fma.f64 (.f64 eps eps) (fma.f64 eps eps (.f64 x x)) (.f64 (.f64 x x) (.f64 x x)))))
(/.f64 (.f64 (fma.f64 (.f64 eps eps) eps (.f64 (.f64 x x) x)) (.f64 (fma.f64 eps (+.f64 eps x) (.f64 x x)) (-.f64 x eps))) (.f64 (fma.f64 (-.f64 eps x) eps (.f64 x x)) (.f64 (fma.f64 eps (+.f64 eps x) (.f64 x x)) (-.f64 x eps))))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 #s(literal 1 binary64) (+.f64 eps x))))
(/.f64 #s(literal 1 binary64) (/.f64 (-.f64 eps x) (*.f64 (+.f64 eps x) (-.f64 eps x))))
(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 #s(literal 1 binary64) (+.f64 eps x)) #s(literal 1 binary64)))
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (+.f64 eps x)))
(/.f64 (fma.f64 (.f64 (.f64 (.f64 eps eps) eps) (.f64 (.f64 eps eps) eps)) (.f64 (.f64 eps eps) eps) (.f64 (.f64 (.f64 (.f64 x x) x) (.f64 (.f64 x x) x)) (.f64 (.f64 x x) x))) (.f64 (fma.f64 (-.f64 eps x) eps (.f64 x x)) (fma.f64 (.f64 (.f64 eps eps) eps) (-.f64 (.f64 (.f64 eps eps) eps) (.f64 (.f64 x x) x)) (.f64 (.f64 (.f64 x x) x) (.f64 (.f64 x x) x)))))
(/.f64 (neg.f64 (*.f64 (-.f64 x eps) (+.f64 eps x))) (neg.f64 (-.f64 x eps)))
(/.f64 (neg.f64 (fma.f64 (.f64 eps eps) eps (.f64 (.f64 x x) x))) (neg.f64 (fma.f64 (-.f64 eps x) eps (.f64 x x))))
(/.f64 (*.f64 (-.f64 x eps) (+.f64 eps x)) (-.f64 x eps))
(/.f64 (fma.f64 (.f64 eps eps) eps (.f64 (.f64 x x) x)) (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 (fma.f64 (.f64 eps eps) eps (.f64 (.f64 x x) x))) (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 (fma.f64 (.f64 eps eps) eps (.f64 (.f64 x x) x)) (neg.f64 (fma.f64 (-.f64 eps x) eps (.f64 x x)))))
(fma.f64 (/.f64 (.f64 x x) (.f64 (fma.f64 eps (+.f64 eps x) (.f64 x x)) (-.f64 x eps))) (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) (/.f64 #s(literal 1 binary64) (-.f64 x eps)) (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 (/.f64 #s(literal 1 binary64) (+.f64 eps x))) #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)))

eval51.0ms (0.4%)

Memory: -8.0MiB live, 72.7MiB allocated
Compiler: Compiled 7 823 to 838 computations (89.3% saved)

prune42.0ms (0.3%)

Memory

33.3MiB live, 70.8MiB allocated

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	285	6	291
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	285	7	292

Accuracy

100.0%

Counts

292 → 7

Alt Table

Click to see full alt table

Status	Accuracy	Program
	62.6%	(fma.f64 (sin.f64 x) (cos.f64 eps) (fma.f64 (sin.f64 eps) (cos.f64 x) (neg.f64 (sin.f64 x))))
✓	62.5%	(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
▶	61.8%	(-.f64 (sin.f64 (+.f64 x eps)) #s(approx (sin x) (.f64 (fma.f64 (fma.f64 #s(literal 1/120 binary64) (.f64 x x) #s(literal -1/6 binary64)) (*.f64 x x) #s(literal 1 binary64)) x)))
▶	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 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps))))
▶	99.7%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 (.f64 (sin.f64 x) #s(literal -1/2 binary64)) eps (cos.f64 x)) eps))
▶	99.3%	#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (cos.f64 x) eps))
▶	98.1%	#s(approx (- (sin (+ x eps)) (sin x)) (sin.f64 eps))

Compiler

Compiled 167 to 104 computations (37.7% saved)

simplify207.0ms (1.6%)

Memory

-38.1MiB live, 50.3MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 17 expressions of interest:

New	Metric	Score
cost-diff	0	(*.f64 (sin.f64 x) #s(literal -1/2 binary64))
cost-diff	0	(fma.f64 (*.f64 (sin.f64 x) #s(literal -1/2 binary64)) eps (cos.f64 x))
cost-diff	0	(.f64 (fma.f64 (.f64 (sin.f64 x) #s(literal -1/2 binary64)) eps (cos.f64 x)) eps)
cost-diff	0	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 (.f64 (sin.f64 x) #s(literal -1/2 binary64)) eps (cos.f64 x)) eps))
cost-diff	0	#s(approx (sin x) (.f64 (fma.f64 (fma.f64 #s(literal 1/120 binary64) (.f64 x x) #s(literal -1/6 binary64)) (*.f64 x x) #s(literal 1 binary64)) x))
cost-diff	0	(+.f64 x eps)
cost-diff	0	(sin.f64 (+.f64 x eps))
cost-diff	0	(-.f64 (sin.f64 (+.f64 x eps)) #s(approx (sin x) (.f64 (fma.f64 (fma.f64 #s(literal 1/120 binary64) (.f64 x x) #s(literal -1/6 binary64)) (*.f64 x x) #s(literal 1 binary64)) x)))
cost-diff	0	(cos.f64 x)
cost-diff	0	(*.f64 (cos.f64 x) eps)
cost-diff	0	#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (cos.f64 x) eps))
cost-diff	0	(sin.f64 eps)
cost-diff	0	#s(approx (- (sin (+ x eps)) (sin x)) (sin.f64 eps))
cost-diff	0	(.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 0 binary64) eps))) #s(literal 2 binary64))
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 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps))))
cost-diff	192	(+.f64 #s(literal 0 binary64) eps)
cost-diff	320	(*.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps))

Rules

7 748×	`lower-fma.f32`
7 740×	`lower-fma.f64`
3 990×	`lower-*.f32`
3 972×	`lower-*.f64`
1 424×	`lower-+.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	39	222
0	66	212
1	110	212
2	213	209
3	388	206
4	985	206
5	2109	206
6	2281	206
7	2329	206
8	2385	206
9	2421	206
10	2533	206
11	2952	206
12	3129	206
13	3280	206
14	3521	206
15	3749	206
16	4189	206
17	5954	206
18	7227	206
19	7835	206
0	8002	200

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

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

localize150.0ms (1.2%)

Memory

5.0MiB live, 163.5MiB allocated

Localize:

Found 17 expressions of interest:

New	Metric	Score
accuracy	0	(sin.f64 x)
accuracy	0	(cos.f64 x)
accuracy	0.00390625	(.f64 (fma.f64 (.f64 (sin.f64 x) #s(literal -1/2 binary64)) eps (cos.f64 x)) eps)
accuracy	0.1809942524239391	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 (.f64 (sin.f64 x) #s(literal -1/2 binary64)) eps (cos.f64 x)) eps))
accuracy	0.01171875	(fma.f64 (fma.f64 #s(literal 1/120 binary64) (.f64 x x) #s(literal -1/6 binary64)) (.f64 x x) #s(literal 1 binary64))
accuracy	0.04331040172363414	(sin.f64 (+.f64 x eps))
accuracy	0.8047176853293299	#s(approx (sin x) (.f64 (fma.f64 (fma.f64 #s(literal 1/120 binary64) (.f64 x x) #s(literal -1/6 binary64)) (*.f64 x x) #s(literal 1 binary64)) x))
accuracy	23.938343398647625	(-.f64 (sin.f64 (+.f64 x eps)) #s(approx (sin x) (.f64 (fma.f64 (fma.f64 #s(literal 1/120 binary64) (.f64 x x) #s(literal -1/6 binary64)) (*.f64 x x) #s(literal 1 binary64)) x)))
accuracy	0	(cos.f64 x)
accuracy	0.00390625	(*.f64 (cos.f64 x) eps)
accuracy	0.45925062897182506	#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (cos.f64 x) eps))
accuracy	0	(sin.f64 eps)
accuracy	1.2471092528947976	#s(approx (- (sin (+ x eps)) (sin x)) (sin.f64 eps))
accuracy	0	(sin.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 0 binary64) eps)))
accuracy	0.00390625	(.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 0 binary64) eps))) #s(literal 2 binary64))
accuracy	0.0078125	(.f64 (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 0 binary64) eps))) #s(literal 2 binary64)) (cos.f64 (.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps))))
accuracy	0.0464165744115697	(cos.f64 (*.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps)))

Samples

62.0ms	173×	0	valid
39.0ms	81×	1	valid
2.0ms	2×	3	valid

Compiler

Compiled 188 to 37 computations (80.3% saved)

Precisions

Click to see histograms. Total time spent on operations: 80.0ms

ival-sin: 28.0ms (34.8% of total)

ival-mult: 24.0ms (29.9% of total)

ival-add: 8.0ms (10% of total)

const: 7.0ms (8.7% of total)

adjust: 6.0ms (7.5% of total)

ival-cos: 4.0ms (5% of total)

ival-sub: 1.0ms (1.2% of total)

exact: 1.0ms (1.2% of total)

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

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

series34.0ms (0.3%)

Memory

15.9MiB live, 51.5MiB allocated

Counts

21 → 396

Calls

Call 1

Inputs
#s(alt (.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps)) (patch (.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps)) #<representation binary64>) () ())
#s(alt (+.f64 #s(literal 0 binary64) eps) (patch (+.f64 #s(literal 0 binary64) eps) #<representation binary64>) () ())
#s(alt (.f64 (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 0 binary64) eps))) #s(literal 2 binary64)) (cos.f64 (.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps)))) (patch (.f64 (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 0 binary64) eps))) #s(literal 2 binary64)) (cos.f64 (.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x 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 #s(approx (- (sin (+ x eps)) (sin x)) (sin.f64 eps)) (patch #s(approx (- (sin (+ x eps)) (sin x)) (sin.f64 eps)) #<representation binary64>) () ())
#s(alt (sin.f64 eps) (patch (sin.f64 eps) #<representation binary64>) () ())
#s(alt #s(approx (- (sin (+ x eps)) (sin x)) (.f64 (cos.f64 x) eps)) (patch #s(approx (- (sin (+ x eps)) (sin x)) (.f64 (cos.f64 x) eps)) #<representation binary64>) () ())
#s(alt (.f64 (cos.f64 x) eps) (patch (.f64 (cos.f64 x) eps) #<representation binary64>) () ())
#s(alt (cos.f64 x) (patch (cos.f64 x) #<representation binary64>) () ())
#s(alt (-.f64 (sin.f64 (+.f64 x eps)) #s(approx (sin x) (.f64 (fma.f64 (fma.f64 #s(literal 1/120 binary64) (.f64 x x) #s(literal -1/6 binary64)) (.f64 x x) #s(literal 1 binary64)) x))) (patch (-.f64 (sin.f64 (+.f64 x eps)) #s(approx (sin x) (.f64 (fma.f64 (fma.f64 #s(literal 1/120 binary64) (.f64 x x) #s(literal -1/6 binary64)) (.f64 x x) #s(literal 1 binary64)) x))) #<representation binary64>) () ())
#s(alt (sin.f64 (+.f64 x eps)) (patch (sin.f64 (+.f64 x eps)) #<representation binary64>) () ())
#s(alt (+.f64 x eps) (patch (+.f64 x eps) #<representation binary64>) () ())
#s(alt #s(approx (sin x) (.f64 (fma.f64 (fma.f64 #s(literal 1/120 binary64) (.f64 x x) #s(literal -1/6 binary64)) (.f64 x x) #s(literal 1 binary64)) x)) (patch #s(approx (sin x) (.f64 (fma.f64 (fma.f64 #s(literal 1/120 binary64) (.f64 x x) #s(literal -1/6 binary64)) (.f64 x x) #s(literal 1 binary64)) x)) #<representation binary64>) () ())
#s(alt #s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 (.f64 (sin.f64 x) #s(literal -1/2 binary64)) eps (cos.f64 x)) eps)) (patch #s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 (.f64 (sin.f64 x) #s(literal -1/2 binary64)) eps (cos.f64 x)) eps)) #<representation binary64>) () ())
#s(alt (.f64 (fma.f64 (.f64 (sin.f64 x) #s(literal -1/2 binary64)) eps (cos.f64 x)) eps) (patch (.f64 (fma.f64 (.f64 (sin.f64 x) #s(literal -1/2 binary64)) eps (cos.f64 x)) eps) #<representation binary64>) () ())
#s(alt (fma.f64 (.f64 (sin.f64 x) #s(literal -1/2 binary64)) eps (cos.f64 x)) (patch (fma.f64 (.f64 (sin.f64 x) #s(literal -1/2 binary64)) eps (cos.f64 x)) #<representation binary64>) () ())
#s(alt (.f64 (sin.f64 x) #s(literal -1/2 binary64)) (patch (.f64 (sin.f64 x) #s(literal -1/2 binary64)) #<representation binary64>) () ())
#s(alt (cos.f64 (.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps))) (patch (cos.f64 (.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps))) #<representation binary64>) () ())
#s(alt (sin.f64 (.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 0 binary64) eps))) (patch (sin.f64 (.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 0 binary64) eps))) #<representation binary64>) () ())
#s(alt (fma.f64 (fma.f64 #s(literal 1/120 binary64) (.f64 x x) #s(literal -1/6 binary64)) (.f64 x x) #s(literal 1 binary64)) (patch (fma.f64 (fma.f64 #s(literal 1/120 binary64) (.f64 x x) #s(literal -1/6 binary64)) (.f64 x x) #s(literal 1 binary64)) #<representation binary64>) () ())
#s(alt (sin.f64 x) (patch (sin.f64 x) #<representation binary64>) () ())

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

Calls

99 calls:

Time	Variable		Point	Expression
4.0ms	eps	@	0	(cos (* 1/2 (+ (* 2 x) eps)))
3.0ms	eps	@	0	(* (+ (* (* (sin x) -1/2) eps) (cos x)) eps)
1.0ms	x	@	0	(* (* (sin (* 1/2 (+ 0 eps))) 2) (cos (* 1/2 (+ (* 2 x) eps))))
1.0ms	x	@	inf	(* (* (sin (* 1/2 (+ 0 eps))) 2) (cos (* 1/2 (+ (* 2 x) eps))))
1.0ms	x	@	-inf	(* (+ (* (* (sin x) -1/2) eps) (cos x)) eps)

simplify185.0ms (1.5%)

Memory

27.0MiB live, 250.4MiB allocated

Algorithm

1×	egg-herbie

Rules

15 424×	`lower-fma.f64`
15 424×	`lower-fma.f32`
5 974×	`lower-*.f64`
5 974×	`lower-*.f32`
3 538×	`lower-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	355	3129
1	1054	3038
2	2674	2990
3	6284	2974
0	8391	2742

Stop Event

1×	iter limit
1×	node limit

Counts

396 → 369

Calls

Call 1

Inputs
(* 1/2 eps)
(+ x (* 1/2 eps))
(+ x (* 1/2 eps))
(+ x (* 1/2 eps))
x
(* x (+ 1 (* 1/2 (/ eps x))))
(* x (+ 1 (* 1/2 (/ eps x))))
(* x (+ 1 (* 1/2 (/ eps x))))
x
(* -1 (* x (- (* -1/2 (/ eps x)) 1)))
(* -1 (* x (- (* -1/2 (/ eps x)) 1)))
(* -1 (* x (- (* -1/2 (/ eps x)) 1)))
x
(+ x (* 1/2 eps))
(+ x (* 1/2 eps))
(+ x (* 1/2 eps))
(* 1/2 eps)
(* eps (+ 1/2 (/ x eps)))
(* eps (+ 1/2 (/ x eps)))
(* eps (+ 1/2 (/ x eps)))
(* 1/2 eps)
(* -1 (* eps (- (* -1 (/ x eps)) 1/2)))
(* -1 (* eps (- (* -1 (/ x eps)) 1/2)))
(* -1 (* eps (- (* -1 (/ x eps)) 1/2)))
eps
eps
eps
eps
eps
eps
eps
eps
eps
eps
eps
eps
(* eps (cos x))
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* 2 (* eps (+ (* -1/16 (cos x)) (* -1/48 (cos x)))))))))
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* eps (+ (* 1/24 (* eps (sin x))) (* 2 (+ (* -1/16 (cos x)) (* -1/48 (cos x))))))))))
(* 2 (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))))
(* 2 (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))))
(* 2 (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))))
(* 2 (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))))
(* 2 (* (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps))))
(* 2 (* (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps))))
(* 2 (* (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps))))
(* 2 (* (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps))))
(* 2 (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))
(+ (* -2 (* x (pow (sin (* 1/2 eps)) 2))) (* 2 (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))))
(+ (* 2 (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) (* x (+ (* -2 (pow (sin (* 1/2 eps)) 2)) (* -1 (* x (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))))))
(+ (* 2 (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) (* x (+ (* -2 (pow (sin (* 1/2 eps)) 2)) (* x (+ (* -1 (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) (* 1/3 (* x (pow (sin (* 1/2 eps)) 2))))))))
(* 2 (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))))
(* 2 (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))))
(* 2 (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))))
(* 2 (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))))
(* 2 (* (cos (* 1/2 (- eps (* -2 x)))) (sin (* 1/2 eps))))
(* 2 (* (cos (* 1/2 (- eps (* -2 x)))) (sin (* 1/2 eps))))
(* 2 (* (cos (* 1/2 (- eps (* -2 x)))) (sin (* 1/2 eps))))
(* 2 (* (cos (* 1/2 (- eps (* -2 x)))) (sin (* 1/2 eps))))
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))))
(* 2 (sin (* 1/2 eps)))
(* 2 (sin (* 1/2 eps)))
(* 2 (sin (* 1/2 eps)))
(* 2 (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 eps)
(+ (sin eps) (* x (- (cos eps) 1)))
(+ (sin eps) (* x (- (+ (cos eps) (* -1/2 (* x (sin eps)))) 1)))
(+ (sin eps) (* x (- (+ (cos eps) (* x (+ (* -1/2 (sin eps)) (* x (+ 1/6 (* -1/6 (cos eps))))))) 1)))
(- (sin (+ eps x)) (sin x))
(- (sin (+ eps x)) (sin x))
(- (sin (+ eps x)) (sin x))
(- (sin (+ eps x)) (sin x))
(- (sin (- eps (* -1 x))) (sin x))
(- (sin (- eps (* -1 x))) (sin x))
(- (sin (- eps (* -1 x))) (sin x))
(- (sin (- eps (* -1 x))) (sin x))
(* eps (cos x))
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x)))))))
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* eps (+ (* -1/6 (cos x)) (* 1/24 (* eps (sin x)))))))))
(- (sin (+ eps x)) (sin x))
(- (sin (+ eps x)) (sin x))
(- (sin (+ eps x)) (sin x))
(- (sin (+ eps x)) (sin x))
(- (sin (- x (* -1 eps))) (sin x))
(- (sin (- x (* -1 eps))) (sin x))
(- (sin (- x (* -1 eps))) (sin x))
(- (sin (- x (* -1 eps))) (sin x))
eps
(* eps (+ 1 (* -1/6 (pow eps 2))))
(* eps (+ 1 (* (pow eps 2) (- (* 1/120 (pow eps 2)) 1/6))))
(* eps (+ 1 (* (pow eps 2) (- (* (pow eps 2) (+ 1/120 (* -1/5040 (pow eps 2)))) 1/6))))
(sin eps)
(sin eps)
(sin eps)
(sin eps)
(sin eps)
(sin eps)
(sin eps)
(sin eps)
(sin eps)
(+ (sin eps) (* x (- (cos eps) 1)))
(+ (sin eps) (* x (- (+ (cos eps) (* -1/2 (* x (sin eps)))) 1)))
(+ (sin eps) (* x (- (+ (cos eps) (* x (+ (* -1/2 (sin eps)) (* x (+ 1/6 (* -1/6 (cos eps))))))) 1)))
(- (sin (+ eps x)) (sin x))
(- (sin (+ eps x)) (sin x))
(- (sin (+ eps x)) (sin x))
(- (sin (+ eps x)) (sin x))
(- (sin (- eps (* -1 x))) (sin x))
(- (sin (- eps (* -1 x))) (sin x))
(- (sin (- eps (* -1 x))) (sin x))
(- (sin (- eps (* -1 x))) (sin x))
(* eps (cos x))
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x)))))))
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* eps (+ (* -1/6 (cos x)) (* 1/24 (* eps (sin x)))))))))
(- (sin (+ eps x)) (sin x))
(- (sin (+ eps x)) (sin x))
(- (sin (+ eps x)) (sin x))
(- (sin (+ eps x)) (sin x))
(- (sin (- x (* -1 eps))) (sin x))
(- (sin (- x (* -1 eps))) (sin x))
(- (sin (- x (* -1 eps))) (sin x))
(- (sin (- x (* -1 eps))) (sin x))
eps
(+ eps (* -1/2 (* eps (pow x 2))))
(+ eps (* (pow x 2) (+ (* -1/2 eps) (* 1/24 (* eps (pow x 2))))))
(+ eps (* (pow x 2) (+ (* -1/2 eps) (* (pow x 2) (+ (* -1/720 (* eps (pow x 2))) (* 1/24 eps))))))
(* eps (cos x))
(* eps (cos x))
(* eps (cos x))
(* eps (cos x))
(* eps (cos x))
(* eps (cos x))
(* eps (cos x))
(* eps (cos x))
(* eps (cos x))
(* eps (cos x))
(* eps (cos x))
(* eps (cos x))
(* eps (cos x))
(* eps (cos x))
(* eps (cos x))
(* eps (cos x))
(* eps (cos x))
(* eps (cos x))
(* eps (cos x))
(* eps (cos x))
1
(+ 1 (* -1/2 (pow x 2)))
(+ 1 (* (pow x 2) (- (* 1/24 (pow x 2)) 1/2)))
(+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))) 1/2)))
(cos x)
(cos x)
(cos x)
(cos x)
(cos x)
(cos x)
(cos x)
(cos x)
(sin eps)
(+ (sin eps) (* x (- (cos eps) 1)))
(+ (sin eps) (* x (- (+ (cos eps) (* -1/2 (* x (sin eps)))) 1)))
(+ (sin eps) (* x (- (+ (cos eps) (* x (+ (* -1/2 (sin eps)) (* x (+ 1/6 (* -1/6 (cos eps))))))) 1)))
(- (sin (+ eps x)) (sin x))
(- (sin (+ eps x)) (sin x))
(- (sin (+ eps x)) (sin x))
(- (sin (+ eps x)) (sin x))
(- (sin (- eps (* -1 x))) (sin x))
(- (sin (- eps (* -1 x))) (sin x))
(- (sin (- eps (* -1 x))) (sin x))
(- (sin (- eps (* -1 x))) (sin x))
(* eps (cos x))
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x)))))))
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* eps (+ (* -1/6 (cos x)) (* 1/24 (* eps (sin x)))))))))
(- (sin (+ eps x)) (sin x))
(- (sin (+ eps x)) (sin x))
(- (sin (+ eps x)) (sin x))
(- (sin (+ eps x)) (sin x))
(- (sin (- x (* -1 eps))) (sin x))
(- (sin (- x (* -1 eps))) (sin x))
(- (sin (- x (* -1 eps))) (sin x))
(- (sin (- x (* -1 eps))) (sin x))
(sin eps)
(+ (sin eps) (* x (cos eps)))
(+ (sin eps) (* x (+ (cos eps) (* -1/2 (* x (sin eps))))))
(+ (sin eps) (* x (+ (cos eps) (* x (+ (* -1/2 (sin eps)) (* -1/6 (* x (cos eps))))))))
(sin (+ eps x))
(sin (+ eps x))
(sin (+ eps x))
(sin (+ eps x))
(sin (- eps (* -1 x)))
(sin (- eps (* -1 x)))
(sin (- eps (* -1 x)))
(sin (- eps (* -1 x)))
(sin x)
(+ (sin x) (* eps (cos x)))
(+ (sin x) (* eps (+ (cos x) (* -1/2 (* eps (sin x))))))
(+ (sin x) (* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x))))))))
(sin (+ eps x))
(sin (+ eps x))
(sin (+ eps x))
(sin (+ eps x))
(sin (- x (* -1 eps)))
(sin (- x (* -1 eps)))
(sin (- x (* -1 eps)))
(sin (- x (* -1 eps)))
eps
(+ eps x)
(+ eps x)
(+ eps x)
x
(* x (+ 1 (/ eps x)))
(* x (+ 1 (/ eps x)))
(* x (+ 1 (/ eps x)))
x
(* -1 (* x (- (* -1 (/ eps x)) 1)))
(* -1 (* x (- (* -1 (/ eps x)) 1)))
(* -1 (* x (- (* -1 (/ eps x)) 1)))
x
(+ eps x)
(+ eps x)
(+ eps x)
eps
(* eps (+ 1 (/ x eps)))
(* eps (+ 1 (/ x eps)))
(* eps (+ 1 (/ x eps)))
eps
(* -1 (* eps (- (* -1 (/ x eps)) 1)))
(* -1 (* eps (- (* -1 (/ x eps)) 1)))
(* -1 (* eps (- (* -1 (/ x eps)) 1)))
x
(* x (+ 1 (* -1/6 (pow x 2))))
(* x (+ 1 (* (pow x 2) (- (* 1/120 (pow x 2)) 1/6))))
(* x (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/120 (* -1/5040 (pow x 2)))) 1/6))))
(sin x)
(sin x)
(sin x)
(sin x)
(sin x)
(sin x)
(sin x)
(sin x)
(sin eps)
(+ (sin eps) (* x (- (cos eps) 1)))
(+ (sin eps) (* x (- (+ (cos eps) (* -1/2 (* x (sin eps)))) 1)))
(+ (sin eps) (* x (- (+ (cos eps) (* x (+ (* -1/2 (sin eps)) (* x (+ 1/6 (* -1/6 (cos eps))))))) 1)))
(- (sin (+ eps x)) (sin x))
(- (sin (+ eps x)) (sin x))
(- (sin (+ eps x)) (sin x))
(- (sin (+ eps x)) (sin x))
(- (sin (- eps (* -1 x))) (sin x))
(- (sin (- eps (* -1 x))) (sin x))
(- (sin (- eps (* -1 x))) (sin x))
(- (sin (- eps (* -1 x))) (sin x))
(* eps (cos x))
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x)))))))
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* eps (+ (* -1/6 (cos x)) (* 1/24 (* eps (sin x)))))))))
(- (sin (+ eps x)) (sin x))
(- (sin (+ eps x)) (sin x))
(- (sin (+ eps x)) (sin x))
(- (sin (+ eps x)) (sin x))
(- (sin (- x (* -1 eps))) (sin x))
(- (sin (- x (* -1 eps))) (sin x))
(- (sin (- x (* -1 eps))) (sin x))
(- (sin (- x (* -1 eps))) (sin x))
eps
(+ eps (* -1/2 (* (pow eps 2) x)))
(+ eps (* x (+ (* -1/2 (* eps x)) (* -1/2 (pow eps 2)))))
(+ eps (* x (+ (* -1/2 (pow eps 2)) (* x (+ (* -1/2 eps) (* 1/12 (* (pow eps 2) x)))))))
(* eps (+ (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)))))
(* 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)))))
(* 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)))))
(* -1/2 (* (pow eps 2) (sin x)))
(* (pow eps 2) (+ (* -1/2 (sin x)) (/ (cos x) eps)))
(* (pow eps 2) (+ (* -1/2 (sin x)) (/ (cos x) eps)))
(* (pow eps 2) (+ (* -1/2 (sin x)) (/ (cos x) eps)))
(* -1/2 (* (pow eps 2) (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
(+ 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)))))
(+ (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))))
(+ (cos x) (* -1/2 (* eps (sin x))))
(+ (cos x) (* -1/2 (* eps (sin x))))
(+ (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))))
(* -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)))
(* -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)))))
(* -1/2 x)
(* x (- (* 1/12 (pow x 2)) 1/2))
(* x (- (* (pow x 2) (+ 1/12 (* -1/240 (pow x 2)))) 1/2))
(* x (- (* (pow x 2) (+ 1/12 (* (pow x 2) (- (* 1/10080 (pow x 2)) 1/240)))) 1/2))
(* -1/2 (sin x))
(* -1/2 (sin x))
(* -1/2 (sin x))
(* -1/2 (sin x))
(* -1/2 (sin x))
(* -1/2 (sin x))
(* -1/2 (sin x))
(* -1/2 (sin x))
(cos (* 1/2 eps))
(+ (cos (* 1/2 eps)) (* -1 (* x (sin (* 1/2 eps)))))
(+ (cos (* 1/2 eps)) (* x (- (* -1/2 (* x (cos (* 1/2 eps)))) (sin (* 1/2 eps)))))
(+ (cos (* 1/2 eps)) (* x (- (* x (+ (* -1/2 (cos (* 1/2 eps))) (* 1/6 (* x (sin (* 1/2 eps)))))) (sin (* 1/2 eps)))))
(cos (* 1/2 (+ eps (* 2 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))))
(cos (* 1/2 (- eps (* -2 x))))
(cos (* 1/2 (- eps (* -2 x))))
(cos (* 1/2 (- eps (* -2 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)))))
(cos (* 1/2 (+ eps (* 2 x))))
(cos (* 1/2 (+ eps (* 2 x))))
(cos (* 1/2 (+ eps (* 2 x))))
(cos (* 1/2 (+ eps (* 2 x))))
(cos (* 1/2 (- (* 2 x) (* -1 eps))))
(cos (* 1/2 (- (* 2 x) (* -1 eps))))
(cos (* 1/2 (- (* 2 x) (* -1 eps))))
(cos (* 1/2 (- (* 2 x) (* -1 eps))))
(* 1/2 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))))
(sin (* 1/2 eps))
(sin (* 1/2 eps))
(sin (* 1/2 eps))
(sin (* 1/2 eps))
(sin (* 1/2 eps))
(sin (* 1/2 eps))
(sin (* 1/2 eps))
(sin (* 1/2 eps))
1
(+ 1 (* -1/6 (pow x 2)))
(+ 1 (* (pow x 2) (- (* 1/120 (pow x 2)) 1/6)))
(+ 1 (* (pow x 2) (- (* 1/120 (pow x 2)) 1/6)))
(* 1/120 (pow x 4))
(* (pow x 4) (- 1/120 (* 1/6 (/ 1 (pow x 2)))))
(* (pow x 4) (- (+ 1/120 (/ 1 (pow x 4))) (* 1/6 (/ 1 (pow x 2)))))
(* (pow x 4) (- (+ 1/120 (/ 1 (pow x 4))) (* 1/6 (/ 1 (pow x 2)))))
(* 1/120 (pow x 4))
(* (pow x 4) (- 1/120 (* 1/6 (/ 1 (pow x 2)))))
(* (pow x 4) (- (+ 1/120 (/ 1 (pow x 4))) (* 1/6 (/ 1 (pow x 2)))))
(* (pow x 4) (- (+ 1/120 (/ 1 (pow x 4))) (* 1/6 (/ 1 (pow x 2)))))
x
(* x (+ 1 (* -1/6 (pow x 2))))
(* x (+ 1 (* (pow x 2) (- (* 1/120 (pow x 2)) 1/6))))
(* x (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/120 (* -1/5040 (pow x 2)))) 1/6))))
(sin x)
(sin x)
(sin x)
(sin x)
(sin x)
(sin x)
(sin x)
(sin x)

Outputs
(* 1/2 eps)
(*.f64 eps #s(literal 1/2 binary64))
(+ x (* 1/2 eps))
(fma.f64 eps #s(literal 1/2 binary64) x)
(+ x (* 1/2 eps))
(fma.f64 eps #s(literal 1/2 binary64) x)
(+ x (* 1/2 eps))
(fma.f64 eps #s(literal 1/2 binary64) x)
x
(* x (+ 1 (* 1/2 (/ eps x))))
(fma.f64 eps #s(literal 1/2 binary64) x)
(* x (+ 1 (* 1/2 (/ eps x))))
(fma.f64 eps #s(literal 1/2 binary64) x)
(* x (+ 1 (* 1/2 (/ eps x))))
(fma.f64 eps #s(literal 1/2 binary64) x)
x
(* -1 (* x (- (* -1/2 (/ eps x)) 1)))
(fma.f64 eps #s(literal 1/2 binary64) x)
(* -1 (* x (- (* -1/2 (/ eps x)) 1)))
(fma.f64 eps #s(literal 1/2 binary64) x)
(* -1 (* x (- (* -1/2 (/ eps x)) 1)))
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(+ (cos (* 1/2 eps)) (* -1 (* x (sin (* 1/2 eps)))))
(fma.f64 (neg.f64 x) (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (cos.f64 (.f64 eps #s(literal 1/2 binary64))))
(+ (cos (* 1/2 eps)) (* x (- (* -1/2 (* x (cos (* 1/2 eps)))) (sin (* 1/2 eps)))))
(fma.f64 (-.f64 (.f64 (.f64 #s(literal -1/2 binary64) x) (cos.f64 (.f64 eps #s(literal 1/2 binary64)))) (sin.f64 (.f64 eps #s(literal 1/2 binary64)))) x (cos.f64 (*.f64 eps #s(literal 1/2 binary64))))
(+ (cos (* 1/2 eps)) (* x (- (* x (+ (* -1/2 (cos (* 1/2 eps))) (* 1/6 (* x (sin (* 1/2 eps)))))) (sin (* 1/2 eps)))))
(fma.f64 (fma.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (fma.f64 x (.f64 #s(literal 1/6 binary64) x) #s(literal -1 binary64)) (.f64 (.f64 #s(literal -1/2 binary64) x) (cos.f64 (.f64 eps #s(literal 1/2 binary64))))) x (cos.f64 (.f64 eps #s(literal 1/2 binary64))))
(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))
(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))
(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 (sin.f64 x) (fma.f64 eps (.f64 #s(literal 1/48 binary64) eps) #s(literal -1/2 binary64)) (.f64 #s(literal -1/8 binary64) (*.f64 (cos.f64 x) eps))) eps (cos.f64 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))
(cos (* 1/2 (- (* 2 x) (* -1 eps))))
(cos.f64 (fma.f64 eps #s(literal 1/2 binary64) x))
(cos (* 1/2 (- (* 2 x) (* -1 eps))))
(cos.f64 (fma.f64 eps #s(literal 1/2 binary64) x))
(cos (* 1/2 (- (* 2 x) (* -1 eps))))
(cos.f64 (fma.f64 eps #s(literal 1/2 binary64) x))
(cos (* 1/2 (- (* 2 x) (* -1 eps))))
(cos.f64 (fma.f64 eps #s(literal 1/2 binary64) x))
(* 1/2 eps)
(*.f64 eps #s(literal 1/2 binary64))
(* eps (+ 1/2 (* -1/48 (pow eps 2))))
(.f64 (fma.f64 (.f64 eps eps) #s(literal -1/48 binary64) #s(literal 1/2 binary64)) eps)
(* eps (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48))))
(.f64 (fma.f64 (fma.f64 #s(literal 1/3840 binary64) (.f64 eps eps) #s(literal -1/48 binary64)) (*.f64 eps eps) #s(literal 1/2 binary64)) eps)
(* eps (+ 1/2 (* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48))))
(.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -1/645120 binary64) (.f64 eps eps) #s(literal 1/3840 binary64)) (.f64 eps eps) #s(literal -1/48 binary64)) (.f64 eps eps) #s(literal 1/2 binary64)) eps)
(sin (* 1/2 eps))
(sin.f64 (*.f64 eps #s(literal 1/2 binary64)))
(sin (* 1/2 eps))
(sin.f64 (*.f64 eps #s(literal 1/2 binary64)))
(sin (* 1/2 eps))
(sin.f64 (*.f64 eps #s(literal 1/2 binary64)))
(sin (* 1/2 eps))
(sin.f64 (*.f64 eps #s(literal 1/2 binary64)))
(sin (* 1/2 eps))
(sin.f64 (*.f64 eps #s(literal 1/2 binary64)))
(sin (* 1/2 eps))
(sin.f64 (*.f64 eps #s(literal 1/2 binary64)))
(sin (* 1/2 eps))
(sin.f64 (*.f64 eps #s(literal 1/2 binary64)))
(sin (* 1/2 eps))
(sin.f64 (*.f64 eps #s(literal 1/2 binary64)))
1
#s(literal 1 binary64)
(+ 1 (* -1/6 (pow x 2)))
(fma.f64 (*.f64 x x) #s(literal -1/6 binary64) #s(literal 1 binary64))
(+ 1 (* (pow x 2) (- (* 1/120 (pow x 2)) 1/6)))
(fma.f64 (fma.f64 (.f64 x x) #s(literal 1/120 binary64) #s(literal -1/6 binary64)) (.f64 x x) #s(literal 1 binary64))
(+ 1 (* (pow x 2) (- (* 1/120 (pow x 2)) 1/6)))
(fma.f64 (fma.f64 (.f64 x x) #s(literal 1/120 binary64) #s(literal -1/6 binary64)) (.f64 x x) #s(literal 1 binary64))
(* 1/120 (pow x 4))
(.f64 (.f64 (.f64 x x) (.f64 x x)) #s(literal 1/120 binary64))
(* (pow x 4) (- 1/120 (* 1/6 (/ 1 (pow x 2)))))
(.f64 (-.f64 #s(literal 1/120 binary64) (/.f64 #s(literal 1/6 binary64) (.f64 x x))) (.f64 (.f64 x x) (*.f64 x x)))
(* (pow x 4) (- (+ 1/120 (/ 1 (pow x 4))) (* 1/6 (/ 1 (pow x 2)))))
(+.f64 #s(literal 1 binary64) (.f64 (-.f64 #s(literal 1/120 binary64) (/.f64 #s(literal 1/6 binary64) (.f64 x x))) (.f64 (.f64 x x) (*.f64 x x))))
(* (pow x 4) (- (+ 1/120 (/ 1 (pow x 4))) (* 1/6 (/ 1 (pow x 2)))))
(+.f64 #s(literal 1 binary64) (.f64 (-.f64 #s(literal 1/120 binary64) (/.f64 #s(literal 1/6 binary64) (.f64 x x))) (.f64 (.f64 x x) (*.f64 x x))))
(* 1/120 (pow x 4))
(.f64 (.f64 (.f64 x x) (.f64 x x)) #s(literal 1/120 binary64))
(* (pow x 4) (- 1/120 (* 1/6 (/ 1 (pow x 2)))))
(.f64 (-.f64 #s(literal 1/120 binary64) (/.f64 #s(literal 1/6 binary64) (.f64 x x))) (.f64 (.f64 x x) (*.f64 x x)))
(* (pow x 4) (- (+ 1/120 (/ 1 (pow x 4))) (* 1/6 (/ 1 (pow x 2)))))
(+.f64 #s(literal 1 binary64) (.f64 (-.f64 #s(literal 1/120 binary64) (/.f64 #s(literal 1/6 binary64) (.f64 x x))) (.f64 (.f64 x x) (*.f64 x x))))
(* (pow x 4) (- (+ 1/120 (/ 1 (pow x 4))) (* 1/6 (/ 1 (pow x 2)))))
(+.f64 #s(literal 1 binary64) (.f64 (-.f64 #s(literal 1/120 binary64) (/.f64 #s(literal 1/6 binary64) (.f64 x x))) (.f64 (.f64 x x) (*.f64 x x))))
x
(* x (+ 1 (* -1/6 (pow x 2))))
(.f64 (fma.f64 (.f64 x x) #s(literal -1/6 binary64) #s(literal 1 binary64)) x)
(* x (+ 1 (* (pow x 2) (- (* 1/120 (pow x 2)) 1/6))))
(.f64 (fma.f64 (fma.f64 (.f64 x x) #s(literal 1/120 binary64) #s(literal -1/6 binary64)) (*.f64 x x) #s(literal 1 binary64)) x)
(* x (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/120 (* -1/5040 (pow x 2)))) 1/6))))
(.f64 (fma.f64 (fma.f64 (fma.f64 (.f64 x x) #s(literal -1/5040 binary64) #s(literal 1/120 binary64)) (.f64 x x) #s(literal -1/6 binary64)) (.f64 x x) #s(literal 1 binary64)) x)
(sin x)
(sin.f64 x)
(sin x)
(sin.f64 x)
(sin x)
(sin.f64 x)
(sin x)
(sin.f64 x)
(sin x)
(sin.f64 x)
(sin x)
(sin.f64 x)
(sin x)
(sin.f64 x)
(sin x)
(sin.f64 x)

rewrite218.0ms (1.7%)

Memory

-20.6MiB live, 235.3MiB allocated

Rules

5 936×	`lower-fma.f32`
5 928×	`lower-fma.f64`
4 136×	`lower-/.f64`
4 136×	`lower-/.f32`
3 884×	`lower-*.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	39	173
0	66	165
1	215	165
2	1601	165
0	8346	165

Stop Event

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

Counts

21 → 545

Calls

Call 1

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

Outputs
(.f64 (.f64 (fma.f64 #s(literal 4 binary64) (.f64 x x) (.f64 (neg.f64 eps) eps)) #s(literal 1/2 binary64)) (/.f64 #s(literal 1 binary64) (fma.f64 x #s(literal 2 binary64) (neg.f64 eps))))
(.f64 (.f64 (fma.f64 #s(literal 8 binary64) (.f64 (.f64 x x) x) (.f64 (.f64 eps eps) eps)) #s(literal 1/2 binary64)) (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal 4 binary64) (.f64 x x) (.f64 eps (-.f64 eps (*.f64 x #s(literal 2 binary64)))))))
(.f64 (.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 4 binary64) (.f64 x x) (.f64 (neg.f64 eps) eps))) (/.f64 #s(literal 1 binary64) (fma.f64 x #s(literal 2 binary64) (neg.f64 eps))))
(.f64 (.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 8 binary64) (.f64 (.f64 x x) x) (.f64 (.f64 eps eps) eps))) (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal 4 binary64) (.f64 x x) (.f64 eps (-.f64 eps (*.f64 x #s(literal 2 binary64)))))))
(.f64 (-.f64 (.f64 (.f64 #s(literal 1 binary64) x) (.f64 #s(literal 1 binary64) x)) (.f64 (.f64 eps #s(literal 1/2 binary64)) (.f64 eps #s(literal 1/2 binary64)))) (/.f64 #s(literal 1 binary64) (-.f64 (.f64 #s(literal 1 binary64) x) (*.f64 eps #s(literal 1/2 binary64)))))
(.f64 (fma.f64 (.f64 (.f64 x x) x) #s(literal 1 binary64) (.f64 #s(literal 1/8 binary64) (.f64 (.f64 eps eps) eps))) (/.f64 #s(literal 1 binary64) (fma.f64 (.f64 #s(literal 1 binary64) x) (.f64 #s(literal 1 binary64) x) (-.f64 (.f64 (.f64 eps #s(literal 1/2 binary64)) (.f64 eps #s(literal 1/2 binary64))) (.f64 (.f64 #s(literal 1 binary64) x) (.f64 eps #s(literal 1/2 binary64)))))))
(*.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64))
(*.f64 #s(literal 1/2 binary64) (fma.f64 x #s(literal 2 binary64) eps))
(/.f64 (+.f64 (pow.f64 (fma.f64 #s(literal 1 binary64) x #s(literal 0 binary64)) #s(literal 3 binary64)) (.f64 #s(literal 1/8 binary64) (.f64 (.f64 eps eps) eps))) (fma.f64 (fma.f64 #s(literal 1 binary64) x #s(literal 0 binary64)) (fma.f64 #s(literal 1 binary64) x #s(literal 0 binary64)) (-.f64 (.f64 (.f64 eps #s(literal 1/2 binary64)) (.f64 eps #s(literal 1/2 binary64))) (.f64 (fma.f64 #s(literal 1 binary64) x #s(literal 0 binary64)) (.f64 eps #s(literal 1/2 binary64))))))
(/.f64 (fma.f64 #s(literal 1/8 binary64) (.f64 (.f64 eps eps) eps) (.f64 (.f64 (.f64 x x) x) #s(literal 1 binary64))) (fma.f64 (.f64 eps #s(literal 1/2 binary64)) (.f64 eps #s(literal 1/2 binary64)) (-.f64 (.f64 (.f64 #s(literal 1 binary64) x) (.f64 #s(literal 1 binary64) x)) (.f64 (.f64 eps #s(literal 1/2 binary64)) (*.f64 #s(literal 1 binary64) x)))))
(/.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) (.f64 (.f64 x x) x) (.f64 (.f64 eps eps) eps)) #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 (.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 4 binary64) (.f64 x x) (*.f64 (neg.f64 eps) eps)))) (neg.f64 (fma.f64 x #s(literal 2 binary64) (neg.f64 eps))))
(/.f64 (neg.f64 (.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 8 binary64) (.f64 (.f64 x x) x) (.f64 (.f64 eps eps) eps)))) (neg.f64 (fma.f64 #s(literal 4 binary64) (.f64 x x) (.f64 eps (-.f64 eps (.f64 x #s(literal 2 binary64)))))))
(/.f64 (neg.f64 (-.f64 (.f64 (.f64 #s(literal 1 binary64) x) (.f64 #s(literal 1 binary64) x)) (.f64 (.f64 eps #s(literal 1/2 binary64)) (.f64 eps #s(literal 1/2 binary64))))) (neg.f64 (-.f64 (.f64 #s(literal 1 binary64) x) (.f64 eps #s(literal 1/2 binary64)))))
(/.f64 (neg.f64 (fma.f64 (.f64 (.f64 x x) x) #s(literal 1 binary64) (.f64 #s(literal 1/8 binary64) (.f64 (.f64 eps eps) eps)))) (neg.f64 (fma.f64 (.f64 #s(literal 1 binary64) x) (.f64 #s(literal 1 binary64) x) (-.f64 (.f64 (.f64 eps #s(literal 1/2 binary64)) (.f64 eps #s(literal 1/2 binary64))) (.f64 (.f64 #s(literal 1 binary64) x) (*.f64 eps #s(literal 1/2 binary64)))))))
(/.f64 (.f64 (fma.f64 #s(literal 4 binary64) (.f64 x x) (*.f64 (neg.f64 eps) eps)) #s(literal 1/2 binary64)) (fma.f64 x #s(literal 2 binary64) (neg.f64 eps)))
(/.f64 (.f64 (fma.f64 #s(literal 8 binary64) (.f64 (.f64 x x) x) (.f64 (.f64 eps eps) eps)) #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 (.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 4 binary64) (.f64 x x) (*.f64 (neg.f64 eps) eps))) (fma.f64 x #s(literal 2 binary64) (neg.f64 eps)))
(/.f64 (.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 8 binary64) (.f64 (.f64 x x) x) (.f64 (.f64 eps eps) eps))) (fma.f64 #s(literal 4 binary64) (.f64 x x) (.f64 eps (-.f64 eps (.f64 x #s(literal 2 binary64))))))
(/.f64 (-.f64 (.f64 (.f64 #s(literal 1 binary64) x) (.f64 #s(literal 1 binary64) x)) (.f64 (.f64 eps #s(literal 1/2 binary64)) (.f64 eps #s(literal 1/2 binary64)))) (-.f64 (.f64 #s(literal 1 binary64) x) (.f64 eps #s(literal 1/2 binary64))))
(/.f64 (fma.f64 (.f64 (.f64 x x) x) #s(literal 1 binary64) (.f64 #s(literal 1/8 binary64) (.f64 (.f64 eps eps) eps))) (fma.f64 (.f64 #s(literal 1 binary64) x) (.f64 #s(literal 1 binary64) x) (-.f64 (.f64 (.f64 eps #s(literal 1/2 binary64)) (.f64 eps #s(literal 1/2 binary64))) (.f64 (.f64 #s(literal 1 binary64) x) (*.f64 eps #s(literal 1/2 binary64))))))
(/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 x #s(literal 2 binary64) (neg.f64 eps)) (.f64 (fma.f64 #s(literal 4 binary64) (.f64 x x) (*.f64 (neg.f64 eps) eps)) #s(literal 1/2 binary64))))
(/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 #s(literal 4 binary64) (.f64 x x) (.f64 eps (-.f64 eps (.f64 x #s(literal 2 binary64))))) (.f64 (fma.f64 #s(literal 8 binary64) (.f64 (.f64 x x) x) (.f64 (.f64 eps eps) eps)) #s(literal 1/2 binary64))))
(/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 x #s(literal 2 binary64) (neg.f64 eps)) (.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 4 binary64) (.f64 x x) (*.f64 (neg.f64 eps) eps)))))
(/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 #s(literal 4 binary64) (.f64 x x) (.f64 eps (-.f64 eps (.f64 x #s(literal 2 binary64))))) (.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 8 binary64) (.f64 (.f64 x x) x) (.f64 (.f64 eps eps) eps)))))
(/.f64 #s(literal 1 binary64) (/.f64 (-.f64 (.f64 #s(literal 1 binary64) x) (.f64 eps #s(literal 1/2 binary64))) (-.f64 (.f64 (.f64 #s(literal 1 binary64) x) (.f64 #s(literal 1 binary64) x)) (.f64 (.f64 eps #s(literal 1/2 binary64)) (.f64 eps #s(literal 1/2 binary64))))))
(/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 (.f64 #s(literal 1 binary64) x) (.f64 #s(literal 1 binary64) x) (-.f64 (.f64 (.f64 eps #s(literal 1/2 binary64)) (.f64 eps #s(literal 1/2 binary64))) (.f64 (.f64 #s(literal 1 binary64) x) (.f64 eps #s(literal 1/2 binary64))))) (fma.f64 (.f64 (.f64 x x) x) #s(literal 1 binary64) (.f64 #s(literal 1/8 binary64) (.f64 (*.f64 eps eps) eps)))))
(/.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1 binary64) (fma.f64 x #s(literal 2 binary64) eps)))
(fma.f64 (/.f64 #s(literal 1/2 binary64) eps) (/.f64 (.f64 (.f64 eps eps) eps) eps) (*.f64 #s(literal 1 binary64) x))
(fma.f64 (/.f64 (.f64 (.f64 eps eps) eps) eps) (/.f64 #s(literal 1/2 binary64) eps) (*.f64 #s(literal 1 binary64) x))
(fma.f64 (.f64 (neg.f64 (.f64 eps eps)) #s(literal 1/2 binary64)) (/.f64 #s(literal 1 binary64) (neg.f64 eps)) (*.f64 #s(literal 1 binary64) x))
(fma.f64 (.f64 (.f64 (.f64 eps eps) eps) #s(literal 1/2 binary64)) (/.f64 #s(literal 1 binary64) (.f64 eps eps)) (*.f64 #s(literal 1 binary64) x))
(fma.f64 (.f64 #s(literal 1/2 binary64) (neg.f64 (.f64 eps eps))) (/.f64 #s(literal 1 binary64) (neg.f64 eps)) (*.f64 #s(literal 1 binary64) x))
(fma.f64 (.f64 #s(literal 1/2 binary64) (.f64 (.f64 eps eps) eps)) (/.f64 #s(literal 1 binary64) (.f64 eps eps)) (*.f64 #s(literal 1 binary64) x))
(fma.f64 (.f64 #s(literal 1/2 binary64) x) #s(literal 2 binary64) (.f64 eps #s(literal 1/2 binary64)))
(fma.f64 (-.f64 #s(literal 0 binary64) (.f64 (.f64 eps #s(literal 1/2 binary64)) (.f64 eps #s(literal 1/2 binary64)))) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 0 binary64) (.f64 eps #s(literal 1/2 binary64)))) (*.f64 #s(literal 1 binary64) x))
(fma.f64 (+.f64 #s(literal 0 binary64) (.f64 #s(literal 1/8 binary64) (.f64 (.f64 eps eps) eps))) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 0 binary64) (-.f64 (.f64 (.f64 eps #s(literal 1/2 binary64)) (.f64 eps #s(literal 1/2 binary64))) (.f64 #s(literal 0 binary64) (.f64 eps #s(literal 1/2 binary64)))))) (*.f64 #s(literal 1 binary64) x))
(fma.f64 (.f64 x #s(literal 2 binary64)) #s(literal 1/2 binary64) (.f64 eps #s(literal 1/2 binary64)))
(fma.f64 #s(literal 1 binary64) x (*.f64 eps #s(literal 1/2 binary64)))
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(/.f64 (neg.f64 (fma.f64 (.f64 (.f64 (fma.f64 (.f64 x x) #s(literal 1/120 binary64) #s(literal -1/6 binary64)) x) (.f64 (fma.f64 (.f64 x x) #s(literal 1/120 binary64) #s(literal -1/6 binary64)) x)) (.f64 x x) #s(literal -1 binary64))) (neg.f64 (fma.f64 (fma.f64 (.f64 x x) #s(literal 1/120 binary64) #s(literal -1/6 binary64)) (.f64 x x) #s(literal -1 binary64))))
(/.f64 (neg.f64 (fma.f64 (.f64 (.f64 (.f64 (fma.f64 (.f64 x x) #s(literal 1/120 binary64) #s(literal -1/6 binary64)) x) (.f64 (fma.f64 (.f64 x x) #s(literal 1/120 binary64) #s(literal -1/6 binary64)) x)) (.f64 (fma.f64 (.f64 x x) #s(literal 1/120 binary64) #s(literal -1/6 binary64)) x)) (.f64 (.f64 x x) x) #s(literal 1 binary64))) (neg.f64 (+.f64 #s(literal 1 binary64) (-.f64 (.f64 (.f64 (.f64 (fma.f64 (.f64 x x) #s(literal 1/120 binary64) #s(literal -1/6 binary64)) x) (.f64 (fma.f64 (.f64 x x) #s(literal 1/120 binary64) #s(literal -1/6 binary64)) x)) (.f64 x x)) (.f64 (.f64 (fma.f64 (.f64 x x) #s(literal 1/120 binary64) #s(literal -1/6 binary64)) x) x)))))
(/.f64 (neg.f64 (fma.f64 (.f64 (.f64 (.f64 (fma.f64 (.f64 x x) #s(literal 1/120 binary64) #s(literal -1/6 binary64)) x) (.f64 (fma.f64 (.f64 x x) #s(literal 1/120 binary64) #s(literal -1/6 binary64)) x)) (.f64 (fma.f64 (.f64 x x) #s(literal 1/120 binary64) #s(literal -1/6 binary64)) x)) (.f64 (.f64 x x) x) #s(literal 1 binary64))) (neg.f64 (fma.f64 (.f64 (.f64 (fma.f64 (.f64 x x) #s(literal 1/120 binary64) #s(literal -1/6 binary64)) x) (.f64 (fma.f64 (.f64 x x) #s(literal 1/120 binary64) #s(literal -1/6 binary64)) x)) (.f64 x x) (-.f64 #s(literal 1 binary64) (.f64 (.f64 (fma.f64 (*.f64 x x) #s(literal 1/120 binary64) #s(literal -1/6 binary64)) x) x)))))
(/.f64 (fma.f64 (.f64 (.f64 (fma.f64 (.f64 x x) #s(literal 1/120 binary64) #s(literal -1/6 binary64)) x) (.f64 (fma.f64 (.f64 x x) #s(literal 1/120 binary64) #s(literal -1/6 binary64)) x)) (.f64 x x) #s(literal -1 binary64)) (fma.f64 (fma.f64 (.f64 x x) #s(literal 1/120 binary64) #s(literal -1/6 binary64)) (.f64 x x) #s(literal -1 binary64)))
(/.f64 (fma.f64 (.f64 (.f64 (.f64 (fma.f64 (.f64 x x) #s(literal 1/120 binary64) #s(literal -1/6 binary64)) x) (.f64 (fma.f64 (.f64 x x) #s(literal 1/120 binary64) #s(literal -1/6 binary64)) x)) (.f64 (fma.f64 (.f64 x x) #s(literal 1/120 binary64) #s(literal -1/6 binary64)) x)) (.f64 (.f64 x x) x) #s(literal 1 binary64)) (+.f64 #s(literal 1 binary64) (-.f64 (.f64 (.f64 (.f64 (fma.f64 (.f64 x x) #s(literal 1/120 binary64) #s(literal -1/6 binary64)) x) (.f64 (fma.f64 (.f64 x x) #s(literal 1/120 binary64) #s(literal -1/6 binary64)) x)) (.f64 x x)) (.f64 (.f64 (fma.f64 (.f64 x x) #s(literal 1/120 binary64) #s(literal -1/6 binary64)) x) x))))
(/.f64 (fma.f64 (.f64 (.f64 (.f64 (fma.f64 (.f64 x x) #s(literal 1/120 binary64) #s(literal -1/6 binary64)) x) (.f64 (fma.f64 (.f64 x x) #s(literal 1/120 binary64) #s(literal -1/6 binary64)) x)) (.f64 (fma.f64 (.f64 x x) #s(literal 1/120 binary64) #s(literal -1/6 binary64)) x)) (.f64 (.f64 x x) x) #s(literal 1 binary64)) (fma.f64 (.f64 (.f64 (fma.f64 (.f64 x x) #s(literal 1/120 binary64) #s(literal -1/6 binary64)) x) (.f64 (fma.f64 (.f64 x x) #s(literal 1/120 binary64) #s(literal -1/6 binary64)) x)) (.f64 x x) (-.f64 #s(literal 1 binary64) (.f64 (.f64 (fma.f64 (*.f64 x x) #s(literal 1/120 binary64) #s(literal -1/6 binary64)) x) x))))
(/.f64 #s(literal 1 binary64) (/.f64 (-.f64 #s(literal 1 binary64) (.f64 (.f64 (fma.f64 (.f64 x x) #s(literal 1/120 binary64) #s(literal -1/6 binary64)) x) x)) (-.f64 #s(literal 1 binary64) (.f64 (.f64 (.f64 (fma.f64 (.f64 x x) #s(literal 1/120 binary64) #s(literal -1/6 binary64)) x) (.f64 (fma.f64 (.f64 x x) #s(literal 1/120 binary64) #s(literal -1/6 binary64)) x)) (.f64 x x)))))
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 #s(literal 1 binary64) (-.f64 (.f64 (.f64 (.f64 (fma.f64 (.f64 x x) #s(literal 1/120 binary64) #s(literal -1/6 binary64)) x) (.f64 (fma.f64 (.f64 x x) #s(literal 1/120 binary64) #s(literal -1/6 binary64)) x)) (.f64 x x)) (.f64 (.f64 (fma.f64 (.f64 x x) #s(literal 1/120 binary64) #s(literal -1/6 binary64)) x) x))) (fma.f64 (.f64 (.f64 (.f64 (fma.f64 (.f64 x x) #s(literal 1/120 binary64) #s(literal -1/6 binary64)) x) (.f64 (fma.f64 (.f64 x x) #s(literal 1/120 binary64) #s(literal -1/6 binary64)) x)) (.f64 (fma.f64 (.f64 x x) #s(literal 1/120 binary64) #s(literal -1/6 binary64)) x)) (.f64 (.f64 x x) x) #s(literal 1 binary64))))
(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (fma.f64 (.f64 x x) #s(literal 1/120 binary64) #s(literal -1/6 binary64)) (.f64 x x) #s(literal 1 binary64))) #s(literal 1 binary64)))
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (fma.f64 (fma.f64 (.f64 x x) #s(literal 1/120 binary64) #s(literal -1/6 binary64)) (.f64 x x) #s(literal 1 binary64))))
(fma.f64 (.f64 (fma.f64 #s(literal 1/14400 binary64) (.f64 (.f64 x x) (.f64 x x)) #s(literal -1/36 binary64)) (.f64 x x)) (/.f64 #s(literal 1 binary64) (fma.f64 (.f64 x x) #s(literal 1/120 binary64) #s(literal 1/6 binary64))) #s(literal 1 binary64))
(fma.f64 (.f64 (fma.f64 (.f64 #s(literal 1/1728000 binary64) (.f64 (.f64 x x) x)) (.f64 (.f64 x x) x) #s(literal -1/216 binary64)) (.f64 x x)) (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/14400 binary64) (.f64 (.f64 x x) (.f64 x x)) (-.f64 #s(literal 1/36 binary64) (.f64 (.f64 x x) #s(literal -1/720 binary64))))) #s(literal 1 binary64))
(fma.f64 (.f64 (.f64 x x) (fma.f64 #s(literal 1/14400 binary64) (.f64 (.f64 x x) (.f64 x x)) #s(literal -1/36 binary64))) (/.f64 #s(literal 1 binary64) (fma.f64 (.f64 x x) #s(literal 1/120 binary64) #s(literal 1/6 binary64))) #s(literal 1 binary64))
(fma.f64 (.f64 (.f64 x x) (fma.f64 (.f64 #s(literal 1/1728000 binary64) (.f64 (.f64 x x) x)) (.f64 (.f64 x x) x) #s(literal -1/216 binary64))) (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/14400 binary64) (.f64 (.f64 x x) (.f64 x x)) (-.f64 #s(literal 1/36 binary64) (.f64 (.f64 x x) #s(literal -1/720 binary64))))) #s(literal 1 binary64))
(fma.f64 (.f64 (fma.f64 (.f64 x x) #s(literal 1/120 binary64) #s(literal -1/6 binary64)) x) (*.f64 #s(literal 1 binary64) x) #s(literal 1 binary64))
(fma.f64 (.f64 (fma.f64 (.f64 x x) #s(literal 1/120 binary64) #s(literal -1/6 binary64)) x) x #s(literal 1 binary64))
(fma.f64 (.f64 (.f64 (.f64 (fma.f64 (.f64 x x) #s(literal 1/120 binary64) #s(literal -1/6 binary64)) x) (.f64 (fma.f64 (.f64 x x) #s(literal 1/120 binary64) #s(literal -1/6 binary64)) x)) (.f64 x x)) (/.f64 #s(literal 1 binary64) (fma.f64 (fma.f64 (.f64 x x) #s(literal 1/120 binary64) #s(literal -1/6 binary64)) (.f64 x x) #s(literal -1 binary64))) (neg.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (fma.f64 (.f64 x x) #s(literal 1/120 binary64) #s(literal -1/6 binary64)) (*.f64 x x) #s(literal -1 binary64)))))
(fma.f64 (.f64 (.f64 (fma.f64 (*.f64 x x) #s(literal 1/120 binary64) #s(literal -1/6 binary64)) x) x) #s(literal 1 binary64) #s(literal 1 binary64))
(fma.f64 #s(literal 1 binary64) (.f64 (.f64 (fma.f64 (*.f64 x x) #s(literal 1/120 binary64) #s(literal -1/6 binary64)) x) x) #s(literal 1 binary64))
(fma.f64 (fma.f64 (.f64 x x) #s(literal 1/120 binary64) #s(literal -1/6 binary64)) (.f64 (*.f64 x x) #s(literal 1 binary64)) #s(literal 1 binary64))
(fma.f64 (fma.f64 (.f64 x x) #s(literal 1/120 binary64) #s(literal -1/6 binary64)) (.f64 x x) #s(literal 1 binary64))
(fma.f64 (.f64 x x) (.f64 (fma.f64 (*.f64 x x) #s(literal 1/120 binary64) #s(literal -1/6 binary64)) #s(literal 1 binary64)) #s(literal 1 binary64))
(fma.f64 (.f64 x x) (fma.f64 (.f64 x x) #s(literal 1/120 binary64) #s(literal -1/6 binary64)) #s(literal 1 binary64))
(fma.f64 x (.f64 (fma.f64 (.f64 x x) #s(literal 1/120 binary64) #s(literal -1/6 binary64)) x) #s(literal 1 binary64))
(-.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (.f64 (.f64 (fma.f64 (.f64 x x) #s(literal 1/120 binary64) #s(literal -1/6 binary64)) x) x))) (/.f64 (.f64 (.f64 (.f64 (fma.f64 (.f64 x x) #s(literal 1/120 binary64) #s(literal -1/6 binary64)) x) (.f64 (fma.f64 (.f64 x x) #s(literal 1/120 binary64) #s(literal -1/6 binary64)) x)) (.f64 x x)) (-.f64 #s(literal 1 binary64) (.f64 (.f64 (fma.f64 (*.f64 x x) #s(literal 1/120 binary64) #s(literal -1/6 binary64)) x) x))))
(-.f64 (/.f64 (.f64 (.f64 (.f64 (fma.f64 (.f64 x x) #s(literal 1/120 binary64) #s(literal -1/6 binary64)) x) (.f64 (fma.f64 (.f64 x x) #s(literal 1/120 binary64) #s(literal -1/6 binary64)) x)) (.f64 x x)) (fma.f64 (fma.f64 (.f64 x x) #s(literal 1/120 binary64) #s(literal -1/6 binary64)) (.f64 x x) #s(literal -1 binary64))) (/.f64 #s(literal 1 binary64) (fma.f64 (fma.f64 (.f64 x x) #s(literal 1/120 binary64) #s(literal -1/6 binary64)) (*.f64 x x) #s(literal -1 binary64))))
(+.f64 (/.f64 (.f64 (.f64 (.f64 (fma.f64 (.f64 x x) #s(literal 1/120 binary64) #s(literal -1/6 binary64)) x) (.f64 (fma.f64 (.f64 x x) #s(literal 1/120 binary64) #s(literal -1/6 binary64)) x)) (.f64 x x)) (fma.f64 (fma.f64 (.f64 x x) #s(literal 1/120 binary64) #s(literal -1/6 binary64)) (.f64 x x) #s(literal -1 binary64))) (neg.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (fma.f64 (.f64 x x) #s(literal 1/120 binary64) #s(literal -1/6 binary64)) (*.f64 x x) #s(literal -1 binary64)))))
(+.f64 (.f64 (.f64 (fma.f64 (*.f64 x x) #s(literal 1/120 binary64) #s(literal -1/6 binary64)) x) x) #s(literal 1 binary64))
(+.f64 #s(literal 1 binary64) (.f64 (.f64 (fma.f64 (*.f64 x x) #s(literal 1/120 binary64) #s(literal -1/6 binary64)) x) x))
(sin.f64 x)

eval117.0ms (0.9%)

Memory: -6.8MiB live, 183.6MiB allocated
Compiler: Compiled 25 335 to 2 009 computations (92.1% saved)

prune115.0ms (0.9%)

Memory

26.1MiB live, 188.4MiB allocated

Pruning

19 alts after pruning (16 fresh and 3 done)

	Pruned	Kept	Total
New	911	16	927
Fresh	1	0	1
Picked	3	2	5
Done	0	1	1
Total	915	19	934

Accuracy

100.0%

Counts

934 → 19

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	62.5%	(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
	55.7%	(.f64 (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) (.f64 (.f64 eps eps) (/.f64 #s(literal 1 binary64) eps)))) #s(literal 2 binary64)) (cos.f64 (.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps))))
	99.6%	(.f64 (.f64 #s(approx (sin (* 1/2 (+ 0 eps))) (.f64 eps #s(literal 1/2 binary64))) #s(literal 2 binary64)) (cos.f64 (.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps))))
	99.9%	(.f64 #s(approx ( (sin (* 1/2 (+ 0 eps))) 2) (.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -1/322560 binary64) (.f64 eps eps) #s(literal 1/1920 binary64)) (.f64 eps eps) #s(literal -1/24 binary64)) (.f64 eps eps) #s(literal 1 binary64)) eps)) (cos.f64 (*.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps))))
▶	99.8%	(.f64 #s(approx ( (sin (* 1/2 (+ 0 eps))) 2) (.f64 (fma.f64 (fma.f64 #s(literal 1/1920 binary64) (.f64 eps eps) #s(literal -1/24 binary64)) (.f64 eps eps) #s(literal 1 binary64)) eps)) (cos.f64 (.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps))))
	99.7%	(.f64 #s(approx ( (sin (* 1/2 (+ 0 eps))) 2) (.f64 (fma.f64 (.f64 eps eps) #s(literal -1/24 binary64) #s(literal 1 binary64)) eps)) (cos.f64 (*.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps))))
	99.0%	#s(approx (- (sin (+ x eps)) (sin x)) (/.f64 (cos.f64 x) (/.f64 #s(literal 1 binary64) eps)))
✓	99.7%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 (.f64 (sin.f64 x) #s(literal -1/2 binary64)) eps (cos.f64 x)) eps))
▶	99.3%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 #s(approx ( (sin x) -1/2) (*.f64 #s(literal -1/2 binary64) x)) eps (cos.f64 x)) eps))
✓	99.3%	#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (cos.f64 x) eps))
	98.6%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (* (sin x) -1/2) eps) (cos x)) (fma.f64 (fma.f64 (fma.f64 #s(literal 1/12 binary64) (.f64 x eps) #s(literal -1/2 binary64)) x (.f64 #s(literal -1/2 binary64) eps)) x #s(literal 1 binary64))) eps))
	98.6%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (* (sin x) -1/2) eps) (cos x)) (fma.f64 (*.f64 (+.f64 x eps) #s(literal -1/2 binary64)) x #s(literal 1 binary64))) eps))
	98.1%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (* (sin x) -1/2) eps) (cos x)) (fma.f64 (*.f64 x eps) #s(literal -1/2 binary64) #s(literal 1 binary64))) eps))
▶	98.1%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (* (sin x) -1/2) eps) (cos x)) #s(literal 1 binary64)) eps))
	98.8%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (cos x) (fma.f64 (fma.f64 (fma.f64 #s(literal -1/720 binary64) (.f64 x x) #s(literal 1/24 binary64)) (.f64 x x) #s(literal -1/2 binary64)) (.f64 x x) #s(literal 1 binary64))) eps))
▶	98.6%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (cos x) (fma.f64 (fma.f64 (.f64 x x) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) (*.f64 x x) #s(literal 1 binary64))) eps))
	98.8%	#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (cos x) eps) (fma.f64 (fma.f64 (.f64 eps (fma.f64 #s(literal -1/720 binary64) (.f64 x x) #s(literal 1/24 binary64))) (.f64 x x) (.f64 #s(literal -1/2 binary64) eps)) (*.f64 x x) eps)))
	98.5%	#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (cos x) eps) (fma.f64 (.f64 #s(literal -1/2 binary64) x) (.f64 x eps) eps)))
▶	99.9%	#s(approx (* (* (sin (* 1/2 (+ 0 eps))) 2) (cos (* 1/2 (+ (* 2 x) eps)))) (.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)))))

Compiler

Compiled 579 to 338 computations (41.6% saved)

simplify213.0ms (1.7%)

Memory

-22.9MiB live, 124.9MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 19 expressions of interest:

New	Metric	Score
cost-diff	0	(.f64 (fma.f64 (fma.f64 #s(literal 1/1920 binary64) (.f64 eps eps) #s(literal -1/24 binary64)) (*.f64 eps eps) #s(literal 1 binary64)) eps)
cost-diff	0	#s(approx (* (sin (* 1/2 (+ 0 eps))) 2) (.f64 (fma.f64 (fma.f64 #s(literal 1/1920 binary64) (.f64 eps eps) #s(literal -1/24 binary64)) (*.f64 eps eps) #s(literal 1 binary64)) eps))
cost-diff	0	(.f64 #s(approx ( (sin (* 1/2 (+ 0 eps))) 2) (.f64 (fma.f64 (fma.f64 #s(literal 1/1920 binary64) (.f64 eps eps) #s(literal -1/24 binary64)) (.f64 eps eps) #s(literal 1 binary64)) eps)) (cos.f64 (.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps))))
cost-diff	320	(*.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps))
cost-diff	0	#s(approx (* (sin x) -1/2) (*.f64 #s(literal -1/2 binary64) x))
cost-diff	0	(fma.f64 #s(approx (* (sin x) -1/2) (*.f64 #s(literal -1/2 binary64) x)) eps (cos.f64 x))
cost-diff	0	(.f64 (fma.f64 #s(approx ( (sin x) -1/2) (*.f64 #s(literal -1/2 binary64) x)) eps (cos.f64 x)) eps)
cost-diff	0	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 #s(approx ( (sin x) -1/2) (*.f64 #s(literal -1/2 binary64) x)) eps (cos.f64 x)) eps))
cost-diff	0	(fma.f64 (fma.f64 (.f64 x x) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) (.f64 x x) #s(literal 1 binary64))
cost-diff	0	#s(approx (cos x) (fma.f64 (fma.f64 (.f64 x x) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) (.f64 x x) #s(literal 1 binary64)))
cost-diff	0	(.f64 #s(approx (cos x) (fma.f64 (fma.f64 (.f64 x x) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) (*.f64 x x) #s(literal 1 binary64))) eps)
cost-diff	0	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (cos x) (fma.f64 (fma.f64 (.f64 x x) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) (*.f64 x x) #s(literal 1 binary64))) eps))
cost-diff	0	#s(approx (+ (* (* (sin x) -1/2) eps) (cos x)) #s(literal 1 binary64))
cost-diff	0	(.f64 #s(approx (+ ( (* (sin x) -1/2) eps) (cos x)) #s(literal 1 binary64)) eps)
cost-diff	0	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (* (sin x) -1/2) eps) (cos x)) #s(literal 1 binary64)) eps))
cost-diff	0	(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)) #s(literal 2 binary64))
cost-diff	0	(.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))))
cost-diff	0	#s(approx (* (* (sin (* 1/2 (+ 0 eps))) 2) (cos (* 1/2 (+ (* 2 x) eps)))) (.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)))))

Rules

7 006×	`lower-fma.f32`
6 992×	`lower-fma.f64`
4 148×	`lower-*.f32`
4 124×	`lower-*.f64`
1 334×	`unsub-neg`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	58	367
0	86	357
1	145	357
2	321	353
3	632	350
4	1299	350
5	2030	350
6	2150	350
7	2314	350
8	2600	350
9	3305	350
10	4748	350
11	6073	350
12	6385	350
13	6608	350
14	6769	350
15	6878	350
16	7477	350
0	8198	344

Stop Event

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

Calls

Call 1

Inputs
#s(approx (* (* (sin (* 1/2 (+ 0 eps))) 2) (cos (* 1/2 (+ (* 2 x) eps)))) (.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 (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 (cos.f64 (fma.f64 eps #s(literal 1/2 binary64) x)) #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
#s(literal 2 binary64)
(sin.f64 (*.f64 eps #s(literal 1/2 binary64)))
(*.f64 eps #s(literal 1/2 binary64))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (* (sin x) -1/2) eps) (cos x)) #s(literal 1 binary64)) eps))
(.f64 #s(approx (+ ( (* (sin x) -1/2) eps) (cos x)) #s(literal 1 binary64)) eps)
#s(approx (+ (* (* (sin x) -1/2) eps) (cos x)) #s(literal 1 binary64))
#s(literal 1 binary64)
eps
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (cos x) (fma.f64 (fma.f64 (.f64 x x) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) (*.f64 x x) #s(literal 1 binary64))) eps))
(.f64 #s(approx (cos x) (fma.f64 (fma.f64 (.f64 x x) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) (*.f64 x x) #s(literal 1 binary64))) eps)
#s(approx (cos x) (fma.f64 (fma.f64 (.f64 x x) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) (.f64 x x) #s(literal 1 binary64)))
(fma.f64 (fma.f64 (.f64 x x) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) (.f64 x x) #s(literal 1 binary64))
(fma.f64 (*.f64 x x) #s(literal 1/24 binary64) #s(literal -1/2 binary64))
(*.f64 x x)
x
#s(literal 1/24 binary64)
#s(literal -1/2 binary64)
#s(literal 1 binary64)
eps
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 #s(approx ( (sin x) -1/2) (*.f64 #s(literal -1/2 binary64) x)) eps (cos.f64 x)) eps))
(.f64 (fma.f64 #s(approx ( (sin x) -1/2) (*.f64 #s(literal -1/2 binary64) x)) eps (cos.f64 x)) eps)
(fma.f64 #s(approx (* (sin x) -1/2) (*.f64 #s(literal -1/2 binary64) x)) eps (cos.f64 x))
#s(approx (* (sin x) -1/2) (*.f64 #s(literal -1/2 binary64) x))
(*.f64 #s(literal -1/2 binary64) x)
#s(literal -1/2 binary64)
x
eps
(cos.f64 x)
(.f64 #s(approx ( (sin (* 1/2 (+ 0 eps))) 2) (.f64 (fma.f64 (fma.f64 #s(literal 1/1920 binary64) (.f64 eps eps) #s(literal -1/24 binary64)) (.f64 eps eps) #s(literal 1 binary64)) eps)) (cos.f64 (.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps))))
#s(approx (* (sin (* 1/2 (+ 0 eps))) 2) (.f64 (fma.f64 (fma.f64 #s(literal 1/1920 binary64) (.f64 eps eps) #s(literal -1/24 binary64)) (*.f64 eps eps) #s(literal 1 binary64)) eps))
(.f64 (fma.f64 (fma.f64 #s(literal 1/1920 binary64) (.f64 eps eps) #s(literal -1/24 binary64)) (*.f64 eps eps) #s(literal 1 binary64)) eps)
(fma.f64 (fma.f64 #s(literal 1/1920 binary64) (.f64 eps eps) #s(literal -1/24 binary64)) (.f64 eps eps) #s(literal 1 binary64))
(fma.f64 #s(literal 1/1920 binary64) (*.f64 eps eps) #s(literal -1/24 binary64))
#s(literal 1/1920 binary64)
(*.f64 eps eps)
eps
#s(literal -1/24 binary64)
#s(literal 1 binary64)
(cos.f64 (*.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps)))
(*.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps))
#s(literal 1/2 binary64)
(fma.f64 #s(literal 2 binary64) x eps)
#s(literal 2 binary64)
x

Outputs
#s(approx (* (* (sin (* 1/2 (+ 0 eps))) 2) (cos (* 1/2 (+ (* 2 x) eps)))) (.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)))))
#s(approx (* (* (sin (* 1/2 (+ 0 eps))) 2) (cos (* 1/2 (+ (* 2 x) eps)))) (.f64 (cos.f64 (fma.f64 eps #s(literal 1/2 binary64) x)) (.f64 #s(literal -2 binary64) (sin.f64 (*.f64 #s(literal -1/2 binary64) eps)))))
(.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 (cos.f64 (fma.f64 eps #s(literal 1/2 binary64) x)) (.f64 #s(literal -2 binary64) (sin.f64 (*.f64 #s(literal -1/2 binary64) eps))))
(*.f64 (cos.f64 (fma.f64 eps #s(literal 1/2 binary64) x)) #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
#s(literal 2 binary64)
(sin.f64 (*.f64 eps #s(literal 1/2 binary64)))
(*.f64 eps #s(literal 1/2 binary64))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (* (sin x) -1/2) eps) (cos x)) #s(literal 1 binary64)) eps))
(.f64 #s(approx (+ ( (* (sin x) -1/2) eps) (cos x)) #s(literal 1 binary64)) eps)
#s(approx (+ (* (* (sin x) -1/2) eps) (cos x)) #s(literal 1 binary64))
#s(literal 1 binary64)
eps
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (cos x) (fma.f64 (fma.f64 (.f64 x x) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) (*.f64 x x) #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (cos x) (fma.f64 (fma.f64 #s(literal 1/24 binary64) (.f64 x x) #s(literal -1/2 binary64)) (*.f64 x x) #s(literal 1 binary64))) eps))
(.f64 #s(approx (cos x) (fma.f64 (fma.f64 (.f64 x x) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) (*.f64 x x) #s(literal 1 binary64))) eps)
(.f64 #s(approx (cos x) (fma.f64 (fma.f64 #s(literal 1/24 binary64) (.f64 x x) #s(literal -1/2 binary64)) (*.f64 x x) #s(literal 1 binary64))) eps)
#s(approx (cos x) (fma.f64 (fma.f64 (.f64 x x) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) (.f64 x x) #s(literal 1 binary64)))
#s(approx (cos x) (fma.f64 (fma.f64 #s(literal 1/24 binary64) (.f64 x x) #s(literal -1/2 binary64)) (.f64 x x) #s(literal 1 binary64)))
(fma.f64 (fma.f64 (.f64 x x) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) (.f64 x x) #s(literal 1 binary64))
(fma.f64 (fma.f64 #s(literal 1/24 binary64) (.f64 x x) #s(literal -1/2 binary64)) (.f64 x x) #s(literal 1 binary64))
(fma.f64 (*.f64 x x) #s(literal 1/24 binary64) #s(literal -1/2 binary64))
(fma.f64 #s(literal 1/24 binary64) (*.f64 x x) #s(literal -1/2 binary64))
(*.f64 x x)
x
#s(literal 1/24 binary64)
#s(literal -1/2 binary64)
#s(literal 1 binary64)
eps
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 #s(approx ( (sin x) -1/2) (*.f64 #s(literal -1/2 binary64) x)) eps (cos.f64 x)) eps))
(.f64 (fma.f64 #s(approx ( (sin x) -1/2) (*.f64 #s(literal -1/2 binary64) x)) eps (cos.f64 x)) eps)
(fma.f64 #s(approx (* (sin x) -1/2) (*.f64 #s(literal -1/2 binary64) x)) eps (cos.f64 x))
#s(approx (* (sin x) -1/2) (*.f64 #s(literal -1/2 binary64) x))
(*.f64 #s(literal -1/2 binary64) x)
#s(literal -1/2 binary64)
x
eps
(cos.f64 x)
(.f64 #s(approx ( (sin (* 1/2 (+ 0 eps))) 2) (.f64 (fma.f64 (fma.f64 #s(literal 1/1920 binary64) (.f64 eps eps) #s(literal -1/24 binary64)) (.f64 eps eps) #s(literal 1 binary64)) eps)) (cos.f64 (.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps))))
(.f64 (cos.f64 (fma.f64 eps #s(literal 1/2 binary64) x)) #s(approx ( (sin (* 1/2 (+ 0 eps))) 2) (.f64 (fma.f64 (fma.f64 (.f64 eps eps) #s(literal 1/1920 binary64) #s(literal -1/24 binary64)) (*.f64 eps eps) #s(literal 1 binary64)) eps)))
#s(approx (* (sin (* 1/2 (+ 0 eps))) 2) (.f64 (fma.f64 (fma.f64 #s(literal 1/1920 binary64) (.f64 eps eps) #s(literal -1/24 binary64)) (*.f64 eps eps) #s(literal 1 binary64)) eps))
#s(approx (* (sin (* 1/2 (+ 0 eps))) 2) (.f64 (fma.f64 (fma.f64 (.f64 eps eps) #s(literal 1/1920 binary64) #s(literal -1/24 binary64)) (*.f64 eps eps) #s(literal 1 binary64)) eps))
(.f64 (fma.f64 (fma.f64 #s(literal 1/1920 binary64) (.f64 eps eps) #s(literal -1/24 binary64)) (*.f64 eps eps) #s(literal 1 binary64)) eps)
(.f64 (fma.f64 (fma.f64 (.f64 eps eps) #s(literal 1/1920 binary64) #s(literal -1/24 binary64)) (*.f64 eps eps) #s(literal 1 binary64)) eps)
(fma.f64 (fma.f64 #s(literal 1/1920 binary64) (.f64 eps eps) #s(literal -1/24 binary64)) (.f64 eps eps) #s(literal 1 binary64))
(fma.f64 (fma.f64 (.f64 eps eps) #s(literal 1/1920 binary64) #s(literal -1/24 binary64)) (.f64 eps eps) #s(literal 1 binary64))
(fma.f64 #s(literal 1/1920 binary64) (*.f64 eps eps) #s(literal -1/24 binary64))
(fma.f64 (*.f64 eps eps) #s(literal 1/1920 binary64) #s(literal -1/24 binary64))
#s(literal 1/1920 binary64)
(*.f64 eps eps)
eps
#s(literal -1/24 binary64)
#s(literal 1 binary64)
(cos.f64 (*.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps)))
(cos.f64 (fma.f64 eps #s(literal 1/2 binary64) x))
(*.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps))
(fma.f64 eps #s(literal 1/2 binary64) x)
#s(literal 1/2 binary64)
(fma.f64 #s(literal 2 binary64) x eps)
(fma.f64 x #s(literal 2 binary64) eps)
#s(literal 2 binary64)
x

localize244.0ms (1.9%)

Memory

-23.0MiB live, 197.0MiB allocated

Localize:

Found 19 expressions of interest:

New	Metric	Score
accuracy	0.00390625	(.f64 (fma.f64 (fma.f64 #s(literal 1/1920 binary64) (.f64 eps eps) #s(literal -1/24 binary64)) (*.f64 eps eps) #s(literal 1 binary64)) eps)
accuracy	0.0078125	(.f64 #s(approx ( (sin (* 1/2 (+ 0 eps))) 2) (.f64 (fma.f64 (fma.f64 #s(literal 1/1920 binary64) (.f64 eps eps) #s(literal -1/24 binary64)) (.f64 eps eps) #s(literal 1 binary64)) eps)) (cos.f64 (.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps))))
accuracy	0.0464165744115697	(cos.f64 (*.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps)))
accuracy	0.08117142671031594	#s(approx (* (sin (* 1/2 (+ 0 eps))) 2) (.f64 (fma.f64 (fma.f64 #s(literal 1/1920 binary64) (.f64 eps eps) #s(literal -1/24 binary64)) (*.f64 eps eps) #s(literal 1 binary64)) eps))
accuracy	0	(cos.f64 x)
accuracy	0.00390625	(.f64 (fma.f64 #s(approx ( (sin x) -1/2) (*.f64 #s(literal -1/2 binary64) x)) eps (cos.f64 x)) eps)
accuracy	0.1809942524239391	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 #s(approx ( (sin x) -1/2) (*.f64 #s(literal -1/2 binary64) x)) eps (cos.f64 x)) eps))
accuracy	1.2191317641267825	#s(approx (* (sin x) -1/2) (*.f64 #s(literal -1/2 binary64) x))
accuracy	0.0078125	(fma.f64 (fma.f64 (.f64 x x) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) (.f64 x x) #s(literal 1 binary64))
accuracy	0.015625	(fma.f64 (*.f64 x x) #s(literal 1/24 binary64) #s(literal -1/2 binary64))
accuracy	0.45925062897182506	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (cos x) (fma.f64 (fma.f64 (.f64 x x) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) (*.f64 x x) #s(literal 1 binary64))) eps))
accuracy	0.8214398162726576	#s(approx (cos x) (fma.f64 (fma.f64 (.f64 x x) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) (.f64 x x) #s(literal 1 binary64)))
accuracy	0.00390625	(.f64 #s(approx (+ ( (* (sin x) -1/2) eps) (cos x)) #s(literal 1 binary64)) eps)
accuracy	0.1809942524239391	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (* (sin x) -1/2) eps) (cos x)) #s(literal 1 binary64)) eps))
accuracy	1.257665500246664	#s(approx (+ (* (* (sin x) -1/2) eps) (cos x)) #s(literal 1 binary64))
accuracy	0	(sin.f64 (*.f64 eps #s(literal 1/2 binary64)))
accuracy	0	#s(approx (* (* (sin (* 1/2 (+ 0 eps))) 2) (cos (* 1/2 (+ (* 2 x) eps)))) (.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)))))
accuracy	0.01171875	(.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))))
accuracy	0.0464165744115697	(cos.f64 (fma.f64 eps #s(literal 1/2 binary64) x))

Samples

87.0ms	175×	0	valid
47.0ms	81×	1	valid

Compiler

Compiled 261 to 49 computations (81.2% saved)

Precisions

Click to see histograms. Total time spent on operations: 106.0ms

ival-mult: 62.0ms (58.7% of total)

ival-add: 12.0ms (11.4% of total)

const: 10.0ms (9.5% of total)

adjust: 7.0ms (6.6% of total)

ival-sin: 7.0ms (6.6% of total)

ival-cos: 5.0ms (4.7% of total)

ival-sub: 1.0ms (0.9% of total)

exact: 1.0ms (0.9% of total)

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

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

series30.0ms (0.2%)

Memory

-5.6MiB live, 47.0MiB allocated

Counts

23 → 456

Calls

Call 1

Inputs
#s(alt #s(approx (* (* (sin (* 1/2 (+ 0 eps))) 2) (cos (* 1/2 (+ (* 2 x) eps)))) (.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))))) (patch #s(approx ( (* (sin (* 1/2 (+ 0 eps))) 2) (cos (* 1/2 (+ (* 2 x) eps)))) (.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))))) #<representation binary64>) () ())
#s(alt (.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)))) (patch (.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)))) #<representation binary64>) () ())
#s(alt (.f64 (cos.f64 (fma.f64 eps #s(literal 1/2 binary64) x)) #s(literal 2 binary64)) (patch (.f64 (cos.f64 (fma.f64 eps #s(literal 1/2 binary64) x)) #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 #s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (* (sin x) -1/2) eps) (cos x)) #s(literal 1 binary64)) eps)) (patch #s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (* (sin x) -1/2) eps) (cos x)) #s(literal 1 binary64)) eps)) #<representation binary64>) () ())
#s(alt (.f64 #s(approx (+ ( (* (sin x) -1/2) eps) (cos x)) #s(literal 1 binary64)) eps) (patch (.f64 #s(approx (+ ( (* (sin x) -1/2) eps) (cos x)) #s(literal 1 binary64)) eps) #<representation binary64>) () ())
#s(alt #s(approx (+ (* (* (sin x) -1/2) eps) (cos x)) #s(literal 1 binary64)) (patch #s(approx (+ (* (* (sin x) -1/2) eps) (cos x)) #s(literal 1 binary64)) #<representation binary64>) () ())
#s(alt #s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (cos x) (fma.f64 (fma.f64 (.f64 x x) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) (.f64 x x) #s(literal 1 binary64))) eps)) (patch #s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (cos x) (fma.f64 (fma.f64 (.f64 x x) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) (.f64 x x) #s(literal 1 binary64))) eps)) #<representation binary64>) () ())
#s(alt (.f64 #s(approx (cos x) (fma.f64 (fma.f64 (.f64 x x) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) (.f64 x x) #s(literal 1 binary64))) eps) (patch (.f64 #s(approx (cos x) (fma.f64 (fma.f64 (.f64 x x) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) (.f64 x x) #s(literal 1 binary64))) eps) #<representation binary64>) () ())
#s(alt #s(approx (cos x) (fma.f64 (fma.f64 (.f64 x x) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) (.f64 x x) #s(literal 1 binary64))) (patch #s(approx (cos x) (fma.f64 (fma.f64 (.f64 x x) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) (.f64 x x) #s(literal 1 binary64))) #<representation binary64>) () ())
#s(alt (fma.f64 (fma.f64 (.f64 x x) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) (.f64 x x) #s(literal 1 binary64)) (patch (fma.f64 (fma.f64 (.f64 x x) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) (.f64 x x) #s(literal 1 binary64)) #<representation binary64>) () ())
#s(alt #s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 #s(approx ( (sin x) -1/2) (.f64 #s(literal -1/2 binary64) x)) eps (cos.f64 x)) eps)) (patch #s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 #s(approx (* (sin x) -1/2) (*.f64 #s(literal -1/2 binary64) x)) eps (cos.f64 x)) eps)) #<representation binary64>) () ())
#s(alt (.f64 (fma.f64 #s(approx ( (sin x) -1/2) (.f64 #s(literal -1/2 binary64) x)) eps (cos.f64 x)) eps) (patch (.f64 (fma.f64 #s(approx (* (sin x) -1/2) (*.f64 #s(literal -1/2 binary64) x)) eps (cos.f64 x)) eps) #<representation binary64>) () ())
#s(alt (fma.f64 #s(approx (* (sin x) -1/2) (.f64 #s(literal -1/2 binary64) x)) eps (cos.f64 x)) (patch (fma.f64 #s(approx ( (sin x) -1/2) (*.f64 #s(literal -1/2 binary64) x)) eps (cos.f64 x)) #<representation binary64>) () ())
#s(alt #s(approx (* (sin x) -1/2) (.f64 #s(literal -1/2 binary64) x)) (patch #s(approx ( (sin x) -1/2) (*.f64 #s(literal -1/2 binary64) x)) #<representation binary64>) () ())
#s(alt (.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps)) (patch (.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps)) #<representation binary64>) () ())
#s(alt (.f64 #s(approx ( (sin (* 1/2 (+ 0 eps))) 2) (.f64 (fma.f64 (fma.f64 #s(literal 1/1920 binary64) (.f64 eps eps) #s(literal -1/24 binary64)) (.f64 eps eps) #s(literal 1 binary64)) eps)) (cos.f64 (.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps)))) (patch (.f64 #s(approx ( (sin (* 1/2 (+ 0 eps))) 2) (.f64 (fma.f64 (fma.f64 #s(literal 1/1920 binary64) (.f64 eps eps) #s(literal -1/24 binary64)) (.f64 eps eps) #s(literal 1 binary64)) eps)) (cos.f64 (.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps)))) #<representation binary64>) () ())
#s(alt #s(approx (* (sin (* 1/2 (+ 0 eps))) 2) (.f64 (fma.f64 (fma.f64 #s(literal 1/1920 binary64) (.f64 eps eps) #s(literal -1/24 binary64)) (.f64 eps eps) #s(literal 1 binary64)) eps)) (patch #s(approx ( (sin (* 1/2 (+ 0 eps))) 2) (.f64 (fma.f64 (fma.f64 #s(literal 1/1920 binary64) (.f64 eps eps) #s(literal -1/24 binary64)) (*.f64 eps eps) #s(literal 1 binary64)) eps)) #<representation binary64>) () ())
#s(alt (.f64 (fma.f64 (fma.f64 #s(literal 1/1920 binary64) (.f64 eps eps) #s(literal -1/24 binary64)) (.f64 eps eps) #s(literal 1 binary64)) eps) (patch (.f64 (fma.f64 (fma.f64 #s(literal 1/1920 binary64) (.f64 eps eps) #s(literal -1/24 binary64)) (.f64 eps eps) #s(literal 1 binary64)) 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 (fma.f64 (.f64 x x) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) (patch (fma.f64 (.f64 x x) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) #<representation binary64>) () ())
#s(alt (cos.f64 x) (patch (cos.f64 x) #<representation binary64>) () ())
#s(alt (cos.f64 (.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps))) (patch (cos.f64 (.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps))) #<representation binary64>) () ())

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

Calls

114 calls:

Time	Variable		Point	Expression
1.0ms	eps	@	inf	(* (* (cos (+ (* eps 1/2) x)) 2) (sin (* eps 1/2)))
1.0ms	eps	@	-inf	(* (* (cos (+ (* eps 1/2) x)) 2) (sin (* eps 1/2)))
1.0ms	x	@	-inf	(* (* (cos (+ (* eps 1/2) x)) 2) (sin (* eps 1/2)))
1.0ms	eps	@	inf	(* (+ (* (+ (* 1/1920 (* eps eps)) -1/24) (* eps eps)) 1) eps)
1.0ms	x	@	inf	(* (* (cos (+ (* eps 1/2) x)) 2) (sin (* eps 1/2)))

simplify178.0ms (1.4%)

Memory

20.5MiB live, 244.6MiB allocated

Algorithm

1×	egg-herbie

Rules

12 790×	`lower-fma.f64`
12 790×	`lower-fma.f32`
5 648×	`lower-*.f64`
5 648×	`lower-*.f32`
3 556×	`lower-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	362	4559
1	1062	4418
2	2636	4349
3	6128	4318
0	8164	3960

Stop Event

1×	iter limit
1×	node limit

Counts

456 → 448

Calls

Call 1

Inputs
(* eps (cos x))
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* 2 (* eps (+ (* -1/16 (cos x)) (* -1/48 (cos x)))))))))
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* eps (+ (* 1/24 (* eps (sin x))) (* 2 (+ (* -1/16 (cos x)) (* -1/48 (cos x))))))))))
(* 2 (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))))
(* 2 (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))))
(* 2 (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))))
(* 2 (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))))
(* 2 (* (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps))))
(* 2 (* (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps))))
(* 2 (* (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps))))
(* 2 (* (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps))))
(* 2 (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))
(+ (* -2 (* x (pow (sin (* 1/2 eps)) 2))) (* 2 (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))))
(+ (* 2 (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) (* x (+ (* -2 (pow (sin (* 1/2 eps)) 2)) (* -1 (* x (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))))))
(+ (* 2 (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) (* x (+ (* -2 (pow (sin (* 1/2 eps)) 2)) (* x (+ (* -1 (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) (* 1/3 (* x (pow (sin (* 1/2 eps)) 2))))))))
(* 2 (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))))
(* 2 (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))))
(* 2 (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))))
(* 2 (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))))
(* 2 (* (cos (* 1/2 (- eps (* -2 x)))) (sin (* 1/2 eps))))
(* 2 (* (cos (* 1/2 (- eps (* -2 x)))) (sin (* 1/2 eps))))
(* 2 (* (cos (* 1/2 (- eps (* -2 x)))) (sin (* 1/2 eps))))
(* 2 (* (cos (* 1/2 (- eps (* -2 x)))) (sin (* 1/2 eps))))
(* eps (cos x))
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* 2 (* eps (+ (* -1/16 (cos x)) (* -1/48 (cos x)))))))))
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* eps (+ (* 1/24 (* eps (sin x))) (* 2 (+ (* -1/16 (cos x)) (* -1/48 (cos x))))))))))
(* 2 (* (cos (+ 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))))
(* 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))))
(* 2 (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))
(+ (* -2 (* x (pow (sin (* 1/2 eps)) 2))) (* 2 (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))))
(+ (* 2 (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) (* x (+ (* -2 (pow (sin (* 1/2 eps)) 2)) (* -1 (* x (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))))))
(+ (* 2 (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) (* x (+ (* -2 (pow (sin (* 1/2 eps)) 2)) (* x (+ (* -1 (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) (* 1/3 (* x (pow (sin (* 1/2 eps)) 2))))))))
(* 2 (* (cos (+ 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))))
(* 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))))
(* 2 (cos x))
(+ (* -1 (* eps (sin x))) (* 2 (cos x)))
(+ (* 2 (cos x)) (* eps (+ (* -1 (sin x)) (* -1/4 (* eps (cos x))))))
(+ (* 2 (cos x)) (* eps (+ (* -1 (sin x)) (* eps (+ (* -1/4 (cos x)) (* 1/24 (* eps (sin x))))))))
(* 2 (cos (+ x (* 1/2 eps))))
(* 2 (cos (+ x (* 1/2 eps))))
(* 2 (cos (+ x (* 1/2 eps))))
(* 2 (cos (+ x (* 1/2 eps))))
(* 2 (cos (- x (* -1/2 eps))))
(* 2 (cos (- x (* -1/2 eps))))
(* 2 (cos (- x (* -1/2 eps))))
(* 2 (cos (- x (* -1/2 eps))))
(* 2 (cos (* 1/2 eps)))
(+ (* -2 (* x (sin (* 1/2 eps)))) (* 2 (cos (* 1/2 eps))))
(+ (* 2 (cos (* 1/2 eps))) (* x (+ (* -2 (sin (* 1/2 eps))) (* -1 (* x (cos (* 1/2 eps)))))))
(+ (* 2 (cos (* 1/2 eps))) (* x (+ (* -2 (sin (* 1/2 eps))) (* x (+ (* -1 (cos (* 1/2 eps))) (* 1/3 (* x (sin (* 1/2 eps)))))))))
(* 2 (cos (+ x (* 1/2 eps))))
(* 2 (cos (+ x (* 1/2 eps))))
(* 2 (cos (+ x (* 1/2 eps))))
(* 2 (cos (+ x (* 1/2 eps))))
(* 2 (cos (- (* 1/2 eps) (* -1 x))))
(* 2 (cos (- (* 1/2 eps) (* -1 x))))
(* 2 (cos (- (* 1/2 eps) (* -1 x))))
(* 2 (cos (- (* 1/2 eps) (* -1 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)))))
(cos (+ x (* 1/2 eps)))
(cos (+ x (* 1/2 eps)))
(cos (+ x (* 1/2 eps)))
(cos (+ x (* 1/2 eps)))
(cos (- x (* -1/2 eps)))
(cos (- x (* -1/2 eps)))
(cos (- x (* -1/2 eps)))
(cos (- x (* -1/2 eps)))
(cos (* 1/2 eps))
(+ (cos (* 1/2 eps)) (* -1 (* x (sin (* 1/2 eps)))))
(+ (cos (* 1/2 eps)) (* x (- (* -1/2 (* x (cos (* 1/2 eps)))) (sin (* 1/2 eps)))))
(+ (cos (* 1/2 eps)) (* x (- (* x (+ (* -1/2 (cos (* 1/2 eps))) (* 1/6 (* x (sin (* 1/2 eps)))))) (sin (* 1/2 eps)))))
(cos (+ x (* 1/2 eps)))
(cos (+ x (* 1/2 eps)))
(cos (+ x (* 1/2 eps)))
(cos (+ x (* 1/2 eps)))
(cos (- (* 1/2 eps) (* -1 x)))
(cos (- (* 1/2 eps) (* -1 x)))
(cos (- (* 1/2 eps) (* -1 x)))
(cos (- (* 1/2 eps) (* -1 x)))
(sin eps)
(+ (sin eps) (* x (- (cos eps) 1)))
(+ (sin eps) (* x (- (+ (cos eps) (* -1/2 (* x (sin eps)))) 1)))
(+ (sin eps) (* x (- (+ (cos eps) (* x (+ (* -1/2 (sin eps)) (* x (+ 1/6 (* -1/6 (cos eps))))))) 1)))
(- (sin (+ eps x)) (sin x))
(- (sin (+ eps x)) (sin x))
(- (sin (+ eps x)) (sin x))
(- (sin (+ eps x)) (sin x))
(- (sin (- eps (* -1 x))) (sin x))
(- (sin (- eps (* -1 x))) (sin x))
(- (sin (- eps (* -1 x))) (sin x))
(- (sin (- eps (* -1 x))) (sin x))
(* eps (cos x))
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x)))))))
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* eps (+ (* -1/6 (cos x)) (* 1/24 (* eps (sin x)))))))))
(- (sin (+ eps x)) (sin x))
(- (sin (+ eps x)) (sin x))
(- (sin (+ eps x)) (sin x))
(- (sin (+ eps x)) (sin x))
(- (sin (- x (* -1 eps))) (sin x))
(- (sin (- x (* -1 eps))) (sin x))
(- (sin (- x (* -1 eps))) (sin x))
(- (sin (- x (* -1 eps))) (sin x))
eps
(+ eps (* -1/2 (* (pow eps 2) x)))
(+ eps (* x (+ (* -1/2 (* eps x)) (* -1/2 (pow eps 2)))))
(+ eps (* x (+ (* -1/2 (pow eps 2)) (* x (+ (* -1/2 eps) (* 1/12 (* (pow eps 2) x)))))))
(* eps (+ (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)))))
(* 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)))))
(* 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)))))
(* -1/2 (* (pow eps 2) (sin x)))
(* (pow eps 2) (+ (* -1/2 (sin x)) (/ (cos x) eps)))
(* (pow eps 2) (+ (* -1/2 (sin x)) (/ (cos x) eps)))
(* (pow eps 2) (+ (* -1/2 (sin x)) (/ (cos x) eps)))
(* -1/2 (* (pow eps 2) (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
(+ 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)))))
(+ (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))))
(+ (cos x) (* -1/2 (* eps (sin x))))
(+ (cos x) (* -1/2 (* eps (sin x))))
(+ (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))))
(* -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)))
(* -1/2 (* eps (sin x)))
(* -1 (* eps (+ (* -1 (/ (cos x) eps)) (* 1/2 (sin x)))))
(* -1 (* eps (+ (* -1 (/ (cos x) eps)) (* 1/2 (sin x)))))
(* -1 (* eps (+ (* -1 (/ (cos x) eps)) (* 1/2 (sin x)))))
(sin eps)
(+ (sin eps) (* x (- (cos eps) 1)))
(+ (sin eps) (* x (- (+ (cos eps) (* -1/2 (* x (sin eps)))) 1)))
(+ (sin eps) (* x (- (+ (cos eps) (* x (+ (* -1/2 (sin eps)) (* x (+ 1/6 (* -1/6 (cos eps))))))) 1)))
(- (sin (+ eps x)) (sin x))
(- (sin (+ eps x)) (sin x))
(- (sin (+ eps x)) (sin x))
(- (sin (+ eps x)) (sin x))
(- (sin (- eps (* -1 x))) (sin x))
(- (sin (- eps (* -1 x))) (sin x))
(- (sin (- eps (* -1 x))) (sin x))
(- (sin (- eps (* -1 x))) (sin x))
(* eps (cos x))
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x)))))))
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* eps (+ (* -1/6 (cos x)) (* 1/24 (* eps (sin x)))))))))
(- (sin (+ eps x)) (sin x))
(- (sin (+ eps x)) (sin x))
(- (sin (+ eps x)) (sin x))
(- (sin (+ eps x)) (sin x))
(- (sin (- x (* -1 eps))) (sin x))
(- (sin (- x (* -1 eps))) (sin x))
(- (sin (- x (* -1 eps))) (sin x))
(- (sin (- x (* -1 eps))) (sin x))
eps
(+ eps (* -1/2 (* eps (pow x 2))))
(+ eps (* (pow x 2) (+ (* -1/2 eps) (* 1/24 (* eps (pow x 2))))))
(+ eps (* (pow x 2) (+ (* -1/2 eps) (* (pow x 2) (+ (* -1/720 (* eps (pow x 2))) (* 1/24 eps))))))
(* eps (cos x))
(* eps (cos x))
(* eps (cos x))
(* eps (cos x))
(* eps (cos x))
(* eps (cos x))
(* eps (cos x))
(* eps (cos x))
(* eps (cos x))
(* eps (cos x))
(* eps (cos x))
(* eps (cos x))
(* eps (cos x))
(* eps (cos x))
(* eps (cos x))
(* eps (cos x))
(* eps (cos x))
(* eps (cos x))
(* eps (cos x))
(* eps (cos x))
1
(+ 1 (* -1/2 (pow x 2)))
(+ 1 (* (pow x 2) (- (* 1/24 (pow x 2)) 1/2)))
(+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))) 1/2)))
(cos x)
(cos x)
(cos x)
(cos x)
(cos x)
(cos x)
(cos x)
(cos x)
1
(+ 1 (* -1/2 (pow x 2)))
(+ 1 (* (pow x 2) (- (* 1/24 (pow x 2)) 1/2)))
(+ 1 (* (pow x 2) (- (* 1/24 (pow x 2)) 1/2)))
(* 1/24 (pow x 4))
(* (pow x 4) (- 1/24 (* 1/2 (/ 1 (pow x 2)))))
(* (pow x 4) (- (+ 1/24 (/ 1 (pow x 4))) (* 1/2 (/ 1 (pow x 2)))))
(* (pow x 4) (- (+ 1/24 (/ 1 (pow x 4))) (* 1/2 (/ 1 (pow x 2)))))
(* 1/24 (pow x 4))
(* (pow x 4) (- 1/24 (* 1/2 (/ 1 (pow x 2)))))
(* (pow x 4) (- (+ 1/24 (/ 1 (pow x 4))) (* 1/2 (/ 1 (pow x 2)))))
(* (pow x 4) (- (+ 1/24 (/ 1 (pow x 4))) (* 1/2 (/ 1 (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 x)) (sin x))
(- (sin (+ eps x)) (sin x))
(- (sin (+ eps x)) (sin x))
(- (sin (+ eps x)) (sin x))
(- (sin (- eps (* -1 x))) (sin x))
(- (sin (- eps (* -1 x))) (sin x))
(- (sin (- eps (* -1 x))) (sin x))
(- (sin (- eps (* -1 x))) (sin x))
(* eps (cos x))
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x)))))))
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* eps (+ (* -1/6 (cos x)) (* 1/24 (* eps (sin x)))))))))
(- (sin (+ eps x)) (sin x))
(- (sin (+ eps x)) (sin x))
(- (sin (+ eps x)) (sin x))
(- (sin (+ eps x)) (sin x))
(- (sin (- x (* -1 eps))) (sin x))
(- (sin (- x (* -1 eps))) (sin x))
(- (sin (- x (* -1 eps))) (sin x))
(- (sin (- x (* -1 eps))) (sin x))
eps
(+ eps (* -1/2 (* (pow eps 2) x)))
(+ eps (* x (+ (* -1/2 (* eps x)) (* -1/2 (pow eps 2)))))
(+ eps (* x (+ (* -1/2 (pow eps 2)) (* x (+ (* -1/2 eps) (* 1/12 (* (pow eps 2) x)))))))
(* eps (+ (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)))))
(* 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)))))
(* 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)))))
(* -1/2 (* (pow eps 2) (sin x)))
(* (pow eps 2) (+ (* -1/2 (sin x)) (/ (cos x) eps)))
(* (pow eps 2) (+ (* -1/2 (sin x)) (/ (cos x) eps)))
(* (pow eps 2) (+ (* -1/2 (sin x)) (/ (cos x) eps)))
(* -1/2 (* (pow eps 2) (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
(+ 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)))))
(+ (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))))
(+ (cos x) (* -1/2 (* eps (sin x))))
(+ (cos x) (* -1/2 (* eps (sin x))))
(+ (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))))
(* -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)))
(* -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)))))
(* -1/2 x)
(* x (- (* 1/12 (pow x 2)) 1/2))
(* x (- (* (pow x 2) (+ 1/12 (* -1/240 (pow x 2)))) 1/2))
(* x (- (* (pow x 2) (+ 1/12 (* (pow x 2) (- (* 1/10080 (pow x 2)) 1/240)))) 1/2))
(* -1/2 (sin x))
(* -1/2 (sin x))
(* -1/2 (sin x))
(* -1/2 (sin x))
(* -1/2 (sin x))
(* -1/2 (sin x))
(* -1/2 (sin x))
(* -1/2 (sin x))
(* 1/2 eps)
(+ x (* 1/2 eps))
(+ x (* 1/2 eps))
(+ x (* 1/2 eps))
x
(* x (+ 1 (* 1/2 (/ eps x))))
(* x (+ 1 (* 1/2 (/ eps x))))
(* x (+ 1 (* 1/2 (/ eps x))))
x
(* -1 (* x (- (* -1/2 (/ eps x)) 1)))
(* -1 (* x (- (* -1/2 (/ eps x)) 1)))
(* -1 (* x (- (* -1/2 (/ eps x)) 1)))
x
(+ x (* 1/2 eps))
(+ x (* 1/2 eps))
(+ x (* 1/2 eps))
(* 1/2 eps)
(* eps (+ 1/2 (/ x eps)))
(* eps (+ 1/2 (/ x eps)))
(* eps (+ 1/2 (/ x eps)))
(* 1/2 eps)
(* -1 (* eps (- (* -1 (/ x eps)) 1/2)))
(* -1 (* eps (- (* -1 (/ x eps)) 1/2)))
(* -1 (* eps (- (* -1 (/ x eps)) 1/2)))
(* eps (cos x))
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* 2 (* eps (+ (* -1/16 (cos x)) (* -1/48 (cos x)))))))))
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* eps (+ (* 1/24 (* eps (sin x))) (* 2 (+ (* -1/16 (cos x)) (* -1/48 (cos x))))))))))
(* 2 (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))))
(* 2 (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))))
(* 2 (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))))
(* 2 (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))))
(* 2 (* (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps))))
(* 2 (* (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps))))
(* 2 (* (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps))))
(* 2 (* (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps))))
(* 2 (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))
(+ (* -2 (* x (pow (sin (* 1/2 eps)) 2))) (* 2 (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))))
(+ (* 2 (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) (* x (+ (* -2 (pow (sin (* 1/2 eps)) 2)) (* -1 (* x (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))))))
(+ (* 2 (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) (* x (+ (* -2 (pow (sin (* 1/2 eps)) 2)) (* x (+ (* -1 (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) (* 1/3 (* x (pow (sin (* 1/2 eps)) 2))))))))
(* 2 (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))))
(* 2 (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))))
(* 2 (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))))
(* 2 (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))))
(* 2 (* (cos (* 1/2 (- eps (* -2 x)))) (sin (* 1/2 eps))))
(* 2 (* (cos (* 1/2 (- eps (* -2 x)))) (sin (* 1/2 eps))))
(* 2 (* (cos (* 1/2 (- eps (* -2 x)))) (sin (* 1/2 eps))))
(* 2 (* (cos (* 1/2 (- eps (* -2 x)))) (sin (* 1/2 eps))))
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))))
(* 2 (sin (* 1/2 eps)))
(* 2 (sin (* 1/2 eps)))
(* 2 (sin (* 1/2 eps)))
(* 2 (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
(* eps (+ 1 (* -1/24 (pow eps 2))))
(* eps (+ 1 (* (pow eps 2) (- (* 1/1920 (pow eps 2)) 1/24))))
(* eps (+ 1 (* (pow eps 2) (- (* 1/1920 (pow eps 2)) 1/24))))
(* 1/1920 (pow eps 5))
(* (pow eps 5) (- 1/1920 (* 1/24 (/ 1 (pow eps 2)))))
(* (pow eps 5) (- (+ 1/1920 (/ 1 (pow eps 4))) (* 1/24 (/ 1 (pow eps 2)))))
(* (pow eps 5) (- (+ 1/1920 (/ 1 (pow eps 4))) (* 1/24 (/ 1 (pow eps 2)))))
(* 1/1920 (pow eps 5))
(* -1 (* (pow eps 5) (- (* 1/24 (/ 1 (pow eps 2))) 1/1920)))
(* -1 (* (pow eps 5) (- (* 1/24 (/ 1 (pow eps 2))) (+ 1/1920 (/ 1 (pow eps 4))))))
(* -1 (* (pow eps 5) (- (* 1/24 (/ 1 (pow eps 2))) (+ 1/1920 (/ 1 (pow eps 4))))))
(* 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))))
(sin (* 1/2 eps))
(sin (* 1/2 eps))
(sin (* 1/2 eps))
(sin (* 1/2 eps))
(sin (* 1/2 eps))
(sin (* 1/2 eps))
(sin (* 1/2 eps))
(sin (* 1/2 eps))
-1/2
(- (* 1/24 (pow x 2)) 1/2)
(- (* 1/24 (pow x 2)) 1/2)
(- (* 1/24 (pow x 2)) 1/2)
(* 1/24 (pow x 2))
(* (pow x 2) (- 1/24 (* 1/2 (/ 1 (pow x 2)))))
(* (pow x 2) (- 1/24 (* 1/2 (/ 1 (pow x 2)))))
(* (pow x 2) (- 1/24 (* 1/2 (/ 1 (pow x 2)))))
(* 1/24 (pow x 2))
(* (pow x 2) (- 1/24 (* 1/2 (/ 1 (pow x 2)))))
(* (pow x 2) (- 1/24 (* 1/2 (/ 1 (pow x 2)))))
(* (pow x 2) (- 1/24 (* 1/2 (/ 1 (pow x 2)))))
1
(+ 1 (* -1/2 (pow x 2)))
(+ 1 (* (pow x 2) (- (* 1/24 (pow x 2)) 1/2)))
(+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))) 1/2)))
(cos x)
(cos x)
(cos x)
(cos x)
(cos x)
(cos x)
(cos x)
(cos x)
(cos (* 1/2 eps))
(+ (cos (* 1/2 eps)) (* -1 (* x (sin (* 1/2 eps)))))
(+ (cos (* 1/2 eps)) (* x (- (* -1/2 (* x (cos (* 1/2 eps)))) (sin (* 1/2 eps)))))
(+ (cos (* 1/2 eps)) (* x (- (* x (+ (* -1/2 (cos (* 1/2 eps))) (* 1/6 (* x (sin (* 1/2 eps)))))) (sin (* 1/2 eps)))))
(cos (* 1/2 (+ eps (* 2 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))))
(cos (* 1/2 (- eps (* -2 x))))
(cos (* 1/2 (- eps (* -2 x))))
(cos (* 1/2 (- eps (* -2 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)))))
(cos (* 1/2 (+ eps (* 2 x))))
(cos (* 1/2 (+ eps (* 2 x))))
(cos (* 1/2 (+ eps (* 2 x))))
(cos (* 1/2 (+ eps (* 2 x))))
(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))))

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

rewrite218.0ms (1.7%)

Memory

-5.9MiB live, 315.3MiB allocated

Rules

5 758×	`lower-fma.f32`
5 744×	`lower-fma.f64`
4 336×	`lower-*.f32`
4 312×	`lower-*.f64`
3 692×	`lower-/.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	58	309
0	86	303
1	289	303
2	2253	303
0	8602	300

Stop Event

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

Counts

23 → 388

Calls

Call 1

Inputs
#s(approx (* (* (sin (* 1/2 (+ 0 eps))) 2) (cos (* 1/2 (+ (* 2 x) eps)))) (.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 (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 (cos.f64 (fma.f64 eps #s(literal 1/2 binary64) x)) #s(literal 2 binary64))
(cos.f64 (fma.f64 eps #s(literal 1/2 binary64) x))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (* (sin x) -1/2) eps) (cos x)) #s(literal 1 binary64)) eps))
(.f64 #s(approx (+ ( (* (sin x) -1/2) eps) (cos x)) #s(literal 1 binary64)) eps)
#s(approx (+ (* (* (sin x) -1/2) eps) (cos x)) #s(literal 1 binary64))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (cos x) (fma.f64 (fma.f64 (.f64 x x) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) (*.f64 x x) #s(literal 1 binary64))) eps))
(.f64 #s(approx (cos x) (fma.f64 (fma.f64 (.f64 x x) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) (*.f64 x x) #s(literal 1 binary64))) eps)
#s(approx (cos x) (fma.f64 (fma.f64 (.f64 x x) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) (.f64 x x) #s(literal 1 binary64)))
(fma.f64 (fma.f64 (.f64 x x) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) (.f64 x x) #s(literal 1 binary64))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 #s(approx ( (sin x) -1/2) (*.f64 #s(literal -1/2 binary64) x)) eps (cos.f64 x)) eps))
(.f64 (fma.f64 #s(approx ( (sin x) -1/2) (*.f64 #s(literal -1/2 binary64) x)) eps (cos.f64 x)) eps)
(fma.f64 #s(approx (* (sin x) -1/2) (*.f64 #s(literal -1/2 binary64) x)) eps (cos.f64 x))
#s(approx (* (sin x) -1/2) (*.f64 #s(literal -1/2 binary64) x))
(*.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps))
(.f64 #s(approx ( (sin (* 1/2 (+ 0 eps))) 2) (.f64 (fma.f64 (fma.f64 #s(literal 1/1920 binary64) (.f64 eps eps) #s(literal -1/24 binary64)) (.f64 eps eps) #s(literal 1 binary64)) eps)) (cos.f64 (.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps))))
#s(approx (* (sin (* 1/2 (+ 0 eps))) 2) (.f64 (fma.f64 (fma.f64 #s(literal 1/1920 binary64) (.f64 eps eps) #s(literal -1/24 binary64)) (*.f64 eps eps) #s(literal 1 binary64)) eps))
(.f64 (fma.f64 (fma.f64 #s(literal 1/1920 binary64) (.f64 eps eps) #s(literal -1/24 binary64)) (*.f64 eps eps) #s(literal 1 binary64)) eps)
(sin.f64 (*.f64 eps #s(literal 1/2 binary64)))
(fma.f64 (*.f64 x x) #s(literal 1/24 binary64) #s(literal -1/2 binary64))
(cos.f64 x)
(cos.f64 (*.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps)))

Outputs
#s(approx (* (* (sin (* 1/2 (+ 0 eps))) 2) (cos (* 1/2 (+ (* 2 x) eps)))) (.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (*.f64 (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))) (cos.f64 (fma.f64 eps #s(literal 1/2 binary64) x))) #s(literal 2 binary64))
(.f64 (.f64 (cos.f64 (fma.f64 eps #s(literal 1/2 binary64) x)) (sin.f64 (*.f64 eps #s(literal 1/2 binary64)))) #s(literal 2 binary64))
(.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (*.f64 (cos.f64 (fma.f64 eps #s(literal 1/2 binary64) x)) #s(literal 2 binary64)))
(.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 (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)))
(.f64 #s(literal 2 binary64) (.f64 (cos.f64 (fma.f64 eps #s(literal 1/2 binary64) x)) (sin.f64 (*.f64 eps #s(literal 1/2 binary64)))))
(*.f64 (cos.f64 (fma.f64 eps #s(literal 1/2 binary64) x)) #s(literal 2 binary64))
(*.f64 #s(literal 2 binary64) (cos.f64 (fma.f64 eps #s(literal 1/2 binary64) 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 (neg.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64)))) (sin.f64 x)) #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 (.f64 (.f64 (neg.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64)))) (sin.f64 x)) (.f64 (neg.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64)))) (sin.f64 x))) (.f64 (.f64 (cos.f64 (.f64 eps #s(literal 1/2 binary64))) (cos.f64 x)) (.f64 (neg.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64)))) (sin.f64 x))))))
(/.f64 (+.f64 (pow.f64 (.f64 (cos.f64 (.f64 eps #s(literal 1/2 binary64))) (cos.f64 x)) #s(literal 3 binary64)) (pow.f64 (neg.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 (.f64 (neg.f64 (.f64 (sin.f64 x) (sin.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 eps #s(literal 1/2 binary64))) (cos.f64 x)) (neg.f64 (.f64 (sin.f64 x) (sin.f64 (.f64 eps #s(literal 1/2 binary64)))))))))
(/.f64 (neg.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)))) (neg.f64 (cos.f64 (-.f64 (*.f64 eps #s(literal 1/2 binary64)) x))))
(/.f64 (neg.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)))) (neg.f64 (+.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)))))))))
(/.f64 (-.f64 (.f64 (+.f64 (cos.f64 (fma.f64 eps #s(literal 1/2 binary64) x)) (cos.f64 (-.f64 (.f64 eps #s(literal 1/2 binary64)) x))) #s(literal 2 binary64)) (.f64 #s(literal 2 binary64) (-.f64 (cos.f64 (-.f64 (.f64 eps #s(literal 1/2 binary64)) x)) (cos.f64 (fma.f64 eps #s(literal 1/2 binary64) x))))) #s(literal 4 binary64))
(/.f64 (-.f64 (+.f64 (cos.f64 (fma.f64 eps #s(literal 1/2 binary64) x)) (cos.f64 (-.f64 (.f64 eps #s(literal 1/2 binary64)) x))) (-.f64 (cos.f64 (-.f64 (.f64 eps #s(literal 1/2 binary64)) 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 (-.f64 (*.f64 eps #s(literal 1/2 binary64)) 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)) (-.f64 (.f64 eps #s(literal 1/2 binary64)) x))) (cos.f64 (/.f64 (.f64 x x) (-.f64 (.f64 eps #s(literal 1/2 binary64)) x))) (.f64 (sin.f64 (/.f64 (.f64 #s(literal 1/4 binary64) (.f64 eps eps)) (-.f64 (.f64 eps #s(literal 1/2 binary64)) x))) (sin.f64 (/.f64 (.f64 x x) (-.f64 (*.f64 eps #s(literal 1/2 binary64)) 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 (pow.f64 (.f64 (cos.f64 (.f64 eps #s(literal 1/2 binary64))) (cos.f64 x)) #s(literal 2 binary64)) (cos.f64 (-.f64 (.f64 eps #s(literal 1/2 binary64)) x))) (/.f64 (pow.f64 (.f64 (sin.f64 x) (sin.f64 (.f64 eps #s(literal 1/2 binary64)))) #s(literal 2 binary64)) (cos.f64 (-.f64 (.f64 eps #s(literal 1/2 binary64)) x))))
(-.f64 (/.f64 (pow.f64 (.f64 (cos.f64 (.f64 eps #s(literal 1/2 binary64))) (cos.f64 x)) #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)))))))) (/.f64 (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)))))))))
(-.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))))
(-.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)))))
(cos.f64 (fma.f64 eps #s(literal 1/2 binary64) x))
(+.f64 (.f64 (cos.f64 (/.f64 (.f64 #s(literal 1/4 binary64) (.f64 eps eps)) (-.f64 (.f64 eps #s(literal 1/2 binary64)) x))) (cos.f64 (/.f64 (.f64 x x) (-.f64 (.f64 eps #s(literal 1/2 binary64)) x)))) (.f64 (sin.f64 (/.f64 (.f64 #s(literal 1/4 binary64) (.f64 eps eps)) (-.f64 (.f64 eps #s(literal 1/2 binary64)) x))) (sin.f64 (/.f64 (.f64 x x) (-.f64 (.f64 eps #s(literal 1/2 binary64)) x)))))
(+.f64 (.f64 (cos.f64 (.f64 eps #s(literal 1/2 binary64))) (cos.f64 x)) (.f64 (neg.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64)))) (sin.f64 x)))
(+.f64 (.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))))))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (* (sin x) -1/2) eps) (cos x)) #s(literal 1 binary64)) eps))
(.f64 (/.f64 #s(approx (+ ( (* (sin x) -1/2) eps) (cos x)) #s(literal 1 binary64)) eps) (/.f64 (.f64 (.f64 eps eps) eps) (-.f64 eps #s(literal 0 binary64))))
(.f64 (/.f64 #s(approx (+ ( (* (sin x) -1/2) eps) (cos x)) #s(literal 1 binary64)) eps) (/.f64 (.f64 (.f64 eps eps) eps) eps))
(.f64 (/.f64 (.f64 (.f64 eps eps) eps) eps) (/.f64 #s(approx (+ ( (* (sin x) -1/2) eps) (cos x)) #s(literal 1 binary64)) (-.f64 eps #s(literal 0 binary64))))
(.f64 (/.f64 (.f64 (.f64 eps eps) eps) eps) (/.f64 #s(approx (+ ( (* (sin x) -1/2) eps) (cos x)) #s(literal 1 binary64)) eps))
(.f64 #s(approx (+ ( (* (sin x) -1/2) eps) (cos x)) #s(literal 1 binary64)) eps)
(.f64 eps #s(approx (+ ( (* (sin x) -1/2) eps) (cos x)) #s(literal 1 binary64)))
(/.f64 (+.f64 (pow.f64 (.f64 #s(literal 0 binary64) #s(approx (+ ( (* (sin x) -1/2) eps) (cos x)) #s(literal 1 binary64))) #s(literal 3 binary64)) (pow.f64 (.f64 #s(approx (+ ( (* (sin x) -1/2) eps) (cos x)) #s(literal 1 binary64)) eps) #s(literal 3 binary64))) (fma.f64 (.f64 #s(literal 0 binary64) #s(approx (+ ( (* (sin x) -1/2) eps) (cos x)) #s(literal 1 binary64))) (.f64 #s(literal 0 binary64) #s(approx (+ ( (* (sin x) -1/2) eps) (cos x)) #s(literal 1 binary64))) (-.f64 (.f64 (.f64 #s(approx (+ (* (* (sin x) -1/2) eps) (cos x)) #s(literal 1 binary64)) eps) (.f64 #s(approx (+ ( (* (sin x) -1/2) eps) (cos x)) #s(literal 1 binary64)) eps)) (.f64 (.f64 #s(literal 0 binary64) #s(approx (+ (* (* (sin x) -1/2) eps) (cos x)) #s(literal 1 binary64))) (.f64 #s(approx (+ ( (* (sin x) -1/2) eps) (cos x)) #s(literal 1 binary64)) eps)))))
(/.f64 (+.f64 (pow.f64 (.f64 #s(approx (+ ( (* (sin x) -1/2) eps) (cos x)) #s(literal 1 binary64)) #s(literal 0 binary64)) #s(literal 3 binary64)) (pow.f64 (.f64 #s(approx (+ ( (* (sin x) -1/2) eps) (cos x)) #s(literal 1 binary64)) eps) #s(literal 3 binary64))) (fma.f64 (.f64 #s(approx (+ ( (* (sin x) -1/2) eps) (cos x)) #s(literal 1 binary64)) #s(literal 0 binary64)) (.f64 #s(approx (+ ( (* (sin x) -1/2) eps) (cos x)) #s(literal 1 binary64)) #s(literal 0 binary64)) (-.f64 (.f64 (.f64 #s(approx (+ (* (* (sin x) -1/2) eps) (cos x)) #s(literal 1 binary64)) eps) (.f64 #s(approx (+ ( (* (sin x) -1/2) eps) (cos x)) #s(literal 1 binary64)) eps)) (.f64 (.f64 #s(approx (+ (* (* (sin x) -1/2) eps) (cos x)) #s(literal 1 binary64)) #s(literal 0 binary64)) (.f64 #s(approx (+ ( (* (sin x) -1/2) eps) (cos x)) #s(literal 1 binary64)) eps)))))
(/.f64 (+.f64 (pow.f64 (.f64 #s(approx (+ ( (* (sin x) -1/2) eps) (cos x)) #s(literal 1 binary64)) eps) #s(literal 3 binary64)) (pow.f64 (.f64 #s(literal 0 binary64) #s(approx (+ ( (* (sin x) -1/2) eps) (cos x)) #s(literal 1 binary64))) #s(literal 3 binary64))) (fma.f64 (.f64 #s(approx (+ ( (* (sin x) -1/2) eps) (cos x)) #s(literal 1 binary64)) eps) (.f64 #s(approx (+ ( (* (sin x) -1/2) eps) (cos x)) #s(literal 1 binary64)) eps) (-.f64 (.f64 (.f64 #s(literal 0 binary64) #s(approx (+ (* (* (sin x) -1/2) eps) (cos x)) #s(literal 1 binary64))) (.f64 #s(literal 0 binary64) #s(approx (+ ( (* (sin x) -1/2) eps) (cos x)) #s(literal 1 binary64)))) (.f64 (.f64 #s(approx (+ (* (* (sin x) -1/2) eps) (cos x)) #s(literal 1 binary64)) eps) (.f64 #s(literal 0 binary64) #s(approx (+ ( (* (sin x) -1/2) eps) (cos x)) #s(literal 1 binary64)))))))
(/.f64 (+.f64 (pow.f64 (.f64 #s(approx (+ ( (* (sin x) -1/2) eps) (cos x)) #s(literal 1 binary64)) eps) #s(literal 3 binary64)) (pow.f64 (.f64 #s(approx (+ ( (* (sin x) -1/2) eps) (cos x)) #s(literal 1 binary64)) #s(literal 0 binary64)) #s(literal 3 binary64))) (fma.f64 (.f64 #s(approx (+ ( (* (sin x) -1/2) eps) (cos x)) #s(literal 1 binary64)) eps) (.f64 #s(approx (+ ( (* (sin x) -1/2) eps) (cos x)) #s(literal 1 binary64)) eps) (-.f64 (.f64 (.f64 #s(approx (+ (* (* (sin x) -1/2) eps) (cos x)) #s(literal 1 binary64)) #s(literal 0 binary64)) (.f64 #s(approx (+ ( (* (sin x) -1/2) eps) (cos x)) #s(literal 1 binary64)) #s(literal 0 binary64))) (.f64 (.f64 #s(approx (+ (* (* (sin x) -1/2) eps) (cos x)) #s(literal 1 binary64)) eps) (.f64 #s(approx (+ ( (* (sin x) -1/2) eps) (cos x)) #s(literal 1 binary64)) #s(literal 0 binary64))))))
(/.f64 (neg.f64 (.f64 (neg.f64 (.f64 eps eps)) #s(approx (+ (* (* (sin x) -1/2) eps) (cos x)) #s(literal 1 binary64)))) (neg.f64 (neg.f64 eps)))
(/.f64 (neg.f64 (.f64 (.f64 (.f64 eps eps) eps) #s(approx (+ ( (* (sin x) -1/2) eps) (cos x)) #s(literal 1 binary64)))) (neg.f64 (*.f64 eps eps)))
(/.f64 (neg.f64 (.f64 #s(approx (+ ( (* (sin x) -1/2) eps) (cos x)) #s(literal 1 binary64)) (neg.f64 (*.f64 eps eps)))) (neg.f64 (neg.f64 eps)))
(/.f64 (neg.f64 (.f64 #s(approx (+ ( (* (sin x) -1/2) eps) (cos x)) #s(literal 1 binary64)) (.f64 (.f64 eps eps) eps))) (neg.f64 (*.f64 eps eps)))
(/.f64 (.f64 (neg.f64 (.f64 eps eps)) #s(approx (+ (* (* (sin x) -1/2) eps) (cos x)) #s(literal 1 binary64))) (neg.f64 eps))
(/.f64 (.f64 (.f64 (.f64 eps eps) eps) #s(approx (+ ( (* (sin x) -1/2) eps) (cos x)) #s(literal 1 binary64))) (*.f64 eps eps))
(/.f64 (.f64 #s(approx (+ ( (* (sin x) -1/2) eps) (cos x)) #s(literal 1 binary64)) (neg.f64 (*.f64 eps eps))) (neg.f64 eps))
(/.f64 (.f64 #s(approx (+ ( (* (sin x) -1/2) eps) (cos x)) #s(literal 1 binary64)) (.f64 (.f64 eps eps) eps)) (*.f64 eps eps))
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(fma.f64 (/.f64 #s(approx (+ (* (* (sin x) -1/2) eps) (cos x)) #s(literal 1 binary64)) eps) (/.f64 (.f64 (.f64 eps eps) eps) (-.f64 eps #s(literal 0 binary64))) (.f64 #s(approx (+ ( (* (sin x) -1/2) eps) (cos x)) #s(literal 1 binary64)) #s(literal 0 binary64)))
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(fma.f64 (*.f64 #s(literal 1/24 binary64) x) x #s(literal -1/2 binary64))
(fma.f64 #s(literal 1/24 binary64) (*.f64 x x) #s(literal -1/2 binary64))
(fma.f64 (*.f64 x x) #s(literal 1/24 binary64) #s(literal -1/2 binary64))
(fma.f64 x (*.f64 #s(literal 1/24 binary64) x) #s(literal -1/2 binary64))
(-.f64 (/.f64 #s(literal 1/4 binary64) (-.f64 #s(literal -1/2 binary64) (.f64 #s(literal 1/24 binary64) (.f64 x x)))) (/.f64 (.f64 (.f64 (.f64 x x) (.f64 x x)) #s(literal 1/576 binary64)) (-.f64 #s(literal -1/2 binary64) (.f64 #s(literal 1/24 binary64) (.f64 x x)))))
(-.f64 (/.f64 (.f64 (.f64 (.f64 x x) (.f64 x x)) #s(literal 1/576 binary64)) (fma.f64 #s(literal 1/24 binary64) (.f64 x x) #s(literal 1/2 binary64))) (/.f64 #s(literal 1/4 binary64) (fma.f64 #s(literal 1/24 binary64) (.f64 x x) #s(literal 1/2 binary64))))
(+.f64 (.f64 #s(literal 1/24 binary64) (.f64 x x)) #s(literal -1/2 binary64))
(+.f64 #s(literal -1/2 binary64) (.f64 #s(literal 1/24 binary64) (.f64 x x)))
(cos.f64 x)
(-.f64 (.f64 (cos.f64 (fma.f64 #s(literal 1 binary64) x #s(literal 0 binary64))) (cos.f64 (.f64 eps #s(literal 1/2 binary64)))) (.f64 (sin.f64 (fma.f64 #s(literal 1 binary64) x #s(literal 0 binary64))) (sin.f64 (.f64 eps #s(literal 1/2 binary64)))))
(-.f64 (.f64 (cos.f64 (.f64 eps #s(literal 1/2 binary64))) (cos.f64 (.f64 #s(literal 1 binary64) x))) (.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (sin.f64 (.f64 #s(literal 1 binary64) x))))
(-.f64 (.f64 (cos.f64 (.f64 #s(literal 1 binary64) x)) (cos.f64 (.f64 eps #s(literal 1/2 binary64)))) (.f64 (sin.f64 (.f64 #s(literal 1 binary64) x)) (sin.f64 (.f64 eps #s(literal 1/2 binary64)))))
(cos.f64 (*.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)))

eval97.0ms (0.8%)

Memory: 23.9MiB live, 218.7MiB allocated
Compiler: Compiled 20 594 to 1 509 computations (92.7% saved)

prune137.0ms (1.1%)

Memory

-19.3MiB live, 223.6MiB allocated

Pruning

19 alts after pruning (13 fresh and 6 done)

	Pruned	Kept	Total
New	831	5	836
Fresh	3	8	11
Picked	2	3	5
Done	0	3	3
Total	836	19	855

Accuracy

100.0%

Counts

855 → 19

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	62.5%	(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
	55.7%	(.f64 (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) (.f64 (.f64 eps eps) (/.f64 #s(literal 1 binary64) eps)))) #s(literal 2 binary64)) (cos.f64 (.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps))))
▶	99.9%	(.f64 #s(approx ( (sin (* 1/2 (+ 0 eps))) 2) (.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -1/322560 binary64) (.f64 eps eps) #s(literal 1/1920 binary64)) (.f64 eps eps) #s(literal -1/24 binary64)) (.f64 eps eps) #s(literal 1 binary64)) eps)) (cos.f64 (*.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps))))
	99.8%	(.f64 #s(approx ( (sin (* 1/2 (+ 0 eps))) 2) (.f64 (fma.f64 (fma.f64 #s(literal 1/1920 binary64) (.f64 eps eps) #s(literal -1/24 binary64)) (.f64 eps eps) #s(literal 1 binary64)) eps)) (cos.f64 #s(approx ( 1/2 (+ (* 2 x) eps)) (fma.f64 #s(literal 1/2 binary64) eps x))))
▶	99.7%	(.f64 #s(approx ( (sin (* 1/2 (+ 0 eps))) 2) (.f64 (fma.f64 (.f64 eps eps) #s(literal -1/24 binary64) #s(literal 1 binary64)) eps)) (cos.f64 (*.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps))))
	99.3%	#s(approx (- (sin (+ x eps)) (sin x)) (fma.f64 (cos.f64 x) eps (.f64 (.f64 #s(approx (* (sin x) -1/2) (*.f64 #s(literal -1/2 binary64) x)) eps) eps)))
✓	99.7%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 (.f64 (sin.f64 x) #s(literal -1/2 binary64)) eps (cos.f64 x)) eps))
	98.7%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 #s(approx ( (sin x) -1/2) (.f64 #s(literal -1/2 binary64) x)) eps #s(approx (cos x) (fma.f64 (fma.f64 (.f64 x x) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) (*.f64 x x) #s(literal 1 binary64)))) eps))
	98.1%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 #s(approx ( (sin x) -1/2) (*.f64 #s(literal -1/2 binary64) x)) eps #s(approx (cos x) #s(literal 1 binary64))) eps))
✓	99.3%	#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (cos.f64 x) eps))
▶	98.6%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (* (sin x) -1/2) eps) (cos x)) (fma.f64 (fma.f64 (fma.f64 #s(literal 1/12 binary64) (.f64 x eps) #s(literal -1/2 binary64)) x (.f64 #s(literal -1/2 binary64) eps)) x #s(literal 1 binary64))) eps))
	98.6%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (* (sin x) -1/2) eps) (cos x)) (fma.f64 (*.f64 (+.f64 x eps) #s(literal -1/2 binary64)) x #s(literal 1 binary64))) eps))
✓	98.1%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (* (sin x) -1/2) eps) (cos x)) #s(literal 1 binary64)) eps))
	98.8%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (cos x) (fma.f64 (fma.f64 (fma.f64 #s(literal -1/720 binary64) (.f64 x x) #s(literal 1/24 binary64)) (.f64 x x) #s(literal -1/2 binary64)) (.f64 x x) #s(literal 1 binary64))) eps))
✓	98.6%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (cos x) (fma.f64 (fma.f64 (.f64 x x) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) (*.f64 x x) #s(literal 1 binary64))) eps))
▶	98.8%	#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (cos x) eps) (fma.f64 (fma.f64 (.f64 eps (fma.f64 #s(literal -1/720 binary64) (.f64 x x) #s(literal 1/24 binary64))) (.f64 x x) (.f64 #s(literal -1/2 binary64) eps)) (*.f64 x x) eps)))
▶	98.5%	#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (cos x) eps) (fma.f64 (.f64 #s(literal -1/2 binary64) x) (.f64 x eps) eps)))
✓	99.9%	#s(approx (* (* (sin (* 1/2 (+ 0 eps))) 2) (cos (* 1/2 (+ (* 2 x) eps)))) (.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)))))
	99.6%	#s(approx (* (* (sin (* 1/2 (+ 0 eps))) 2) (cos (* 1/2 (+ (* 2 x) eps)))) (.f64 (.f64 (cos.f64 (fma.f64 eps #s(literal 1/2 binary64) x)) #s(literal 2 binary64)) #s(approx (sin (* eps 1/2)) (*.f64 #s(literal 1/2 binary64) eps))))

Compiler

Compiled 570 to 321 computations (43.7% saved)

simplify189.0ms (1.5%)

Memory

17.4MiB live, 178.0MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 20 expressions of interest:

New	Metric	Score
cost-diff	0	(.f64 (fma.f64 (.f64 eps eps) #s(literal -1/24 binary64) #s(literal 1 binary64)) eps)
cost-diff	0	#s(approx (* (sin (* 1/2 (+ 0 eps))) 2) (.f64 (fma.f64 (.f64 eps eps) #s(literal -1/24 binary64) #s(literal 1 binary64)) eps))
cost-diff	0	(.f64 #s(approx ( (sin (* 1/2 (+ 0 eps))) 2) (.f64 (fma.f64 (.f64 eps eps) #s(literal -1/24 binary64) #s(literal 1 binary64)) eps)) (cos.f64 (*.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps))))
cost-diff	320	(*.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps))
cost-diff	0	(fma.f64 (fma.f64 (.f64 eps (fma.f64 #s(literal -1/720 binary64) (.f64 x x) #s(literal 1/24 binary64))) (.f64 x x) (.f64 #s(literal -1/2 binary64) eps)) (*.f64 x x) eps)
cost-diff	0	#s(approx (* (cos x) eps) (fma.f64 (fma.f64 (.f64 eps (fma.f64 #s(literal -1/720 binary64) (.f64 x x) #s(literal 1/24 binary64))) (.f64 x x) (.f64 #s(literal -1/2 binary64) eps)) (*.f64 x x) eps))
cost-diff	0	#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (cos x) eps) (fma.f64 (fma.f64 (.f64 eps (fma.f64 #s(literal -1/720 binary64) (.f64 x x) #s(literal 1/24 binary64))) (.f64 x x) (.f64 #s(literal -1/2 binary64) eps)) (*.f64 x x) eps)))
cost-diff	320	(fma.f64 (.f64 eps (fma.f64 #s(literal -1/720 binary64) (.f64 x x) #s(literal 1/24 binary64))) (.f64 x x) (.f64 #s(literal -1/2 binary64) eps))
cost-diff	0	(fma.f64 (fma.f64 (fma.f64 #s(literal 1/12 binary64) (.f64 x eps) #s(literal -1/2 binary64)) x (.f64 #s(literal -1/2 binary64) eps)) x #s(literal 1 binary64))
cost-diff	0	#s(approx (+ (* (* (sin x) -1/2) eps) (cos x)) (fma.f64 (fma.f64 (fma.f64 #s(literal 1/12 binary64) (.f64 x eps) #s(literal -1/2 binary64)) x (.f64 #s(literal -1/2 binary64) eps)) x #s(literal 1 binary64)))
cost-diff	0	(.f64 #s(approx (+ ( (* (sin x) -1/2) eps) (cos x)) (fma.f64 (fma.f64 (fma.f64 #s(literal 1/12 binary64) (.f64 x eps) #s(literal -1/2 binary64)) x (.f64 #s(literal -1/2 binary64) eps)) x #s(literal 1 binary64))) eps)
cost-diff	0	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (* (sin x) -1/2) eps) (cos x)) (fma.f64 (fma.f64 (fma.f64 #s(literal 1/12 binary64) (.f64 x eps) #s(literal -1/2 binary64)) x (.f64 #s(literal -1/2 binary64) eps)) x #s(literal 1 binary64))) eps))
cost-diff	0	(*.f64 #s(literal -1/2 binary64) x)
cost-diff	0	(fma.f64 (.f64 #s(literal -1/2 binary64) x) (.f64 x eps) eps)
cost-diff	0	#s(approx (* (cos x) eps) (fma.f64 (.f64 #s(literal -1/2 binary64) x) (.f64 x eps) eps))
cost-diff	0	#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (cos x) eps) (fma.f64 (.f64 #s(literal -1/2 binary64) x) (.f64 x eps) eps)))
cost-diff	0	(.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -1/322560 binary64) (.f64 eps eps) #s(literal 1/1920 binary64)) (.f64 eps eps) #s(literal -1/24 binary64)) (.f64 eps eps) #s(literal 1 binary64)) eps)
cost-diff	0	#s(approx (* (sin (* 1/2 (+ 0 eps))) 2) (.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -1/322560 binary64) (.f64 eps eps) #s(literal 1/1920 binary64)) (.f64 eps eps) #s(literal -1/24 binary64)) (.f64 eps eps) #s(literal 1 binary64)) eps))
cost-diff	0	(.f64 #s(approx ( (sin (* 1/2 (+ 0 eps))) 2) (.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -1/322560 binary64) (.f64 eps eps) #s(literal 1/1920 binary64)) (.f64 eps eps) #s(literal -1/24 binary64)) (.f64 eps eps) #s(literal 1 binary64)) eps)) (cos.f64 (*.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps))))
cost-diff	320	(*.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps))

Rules

13 034×	`lower-fma.f32`
13 010×	`lower-fma.f64`
4 878×	`lower-*.f32`
4 854×	`lower-*.f64`
2 196×	`lower-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	59	518
0	96	510
1	181	506
2	495	500
3	1248	494
4	3513	494
5	4122	494
6	4914	494
7	5497	494
8	7302	494
0	8146	475

Stop Event

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

Calls

Call 1

Inputs
(.f64 #s(approx ( (sin (* 1/2 (+ 0 eps))) 2) (.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -1/322560 binary64) (.f64 eps eps) #s(literal 1/1920 binary64)) (.f64 eps eps) #s(literal -1/24 binary64)) (.f64 eps eps) #s(literal 1 binary64)) eps)) (cos.f64 (*.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps))))
#s(approx (* (sin (* 1/2 (+ 0 eps))) 2) (.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -1/322560 binary64) (.f64 eps eps) #s(literal 1/1920 binary64)) (.f64 eps eps) #s(literal -1/24 binary64)) (.f64 eps eps) #s(literal 1 binary64)) eps))
(.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -1/322560 binary64) (.f64 eps eps) #s(literal 1/1920 binary64)) (.f64 eps eps) #s(literal -1/24 binary64)) (.f64 eps eps) #s(literal 1 binary64)) eps)
(fma.f64 (fma.f64 (fma.f64 #s(literal -1/322560 binary64) (.f64 eps eps) #s(literal 1/1920 binary64)) (.f64 eps eps) #s(literal -1/24 binary64)) (*.f64 eps eps) #s(literal 1 binary64))
(fma.f64 (fma.f64 #s(literal -1/322560 binary64) (.f64 eps eps) #s(literal 1/1920 binary64)) (.f64 eps eps) #s(literal -1/24 binary64))
(fma.f64 #s(literal -1/322560 binary64) (*.f64 eps eps) #s(literal 1/1920 binary64))
#s(literal -1/322560 binary64)
(*.f64 eps eps)
eps
#s(literal 1/1920 binary64)
#s(literal -1/24 binary64)
#s(literal 1 binary64)
(cos.f64 (*.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps)))
(*.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps))
#s(literal 1/2 binary64)
(fma.f64 #s(literal 2 binary64) x eps)
#s(literal 2 binary64)
x
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (cos x) eps) (fma.f64 (.f64 #s(literal -1/2 binary64) x) (.f64 x eps) eps)))
#s(approx (* (cos x) eps) (fma.f64 (.f64 #s(literal -1/2 binary64) x) (.f64 x eps) eps))
(fma.f64 (.f64 #s(literal -1/2 binary64) x) (.f64 x eps) eps)
(*.f64 #s(literal -1/2 binary64) x)
#s(literal -1/2 binary64)
x
(*.f64 x eps)
eps
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (* (sin x) -1/2) eps) (cos x)) (fma.f64 (fma.f64 (fma.f64 #s(literal 1/12 binary64) (.f64 x eps) #s(literal -1/2 binary64)) x (.f64 #s(literal -1/2 binary64) eps)) x #s(literal 1 binary64))) eps))
(.f64 #s(approx (+ ( (* (sin x) -1/2) eps) (cos x)) (fma.f64 (fma.f64 (fma.f64 #s(literal 1/12 binary64) (.f64 x eps) #s(literal -1/2 binary64)) x (.f64 #s(literal -1/2 binary64) eps)) x #s(literal 1 binary64))) eps)
#s(approx (+ (* (* (sin x) -1/2) eps) (cos x)) (fma.f64 (fma.f64 (fma.f64 #s(literal 1/12 binary64) (.f64 x eps) #s(literal -1/2 binary64)) x (.f64 #s(literal -1/2 binary64) eps)) x #s(literal 1 binary64)))
(fma.f64 (fma.f64 (fma.f64 #s(literal 1/12 binary64) (.f64 x eps) #s(literal -1/2 binary64)) x (.f64 #s(literal -1/2 binary64) eps)) x #s(literal 1 binary64))
(fma.f64 (fma.f64 #s(literal 1/12 binary64) (.f64 x eps) #s(literal -1/2 binary64)) x (.f64 #s(literal -1/2 binary64) eps))
(fma.f64 #s(literal 1/12 binary64) (*.f64 x eps) #s(literal -1/2 binary64))
#s(literal 1/12 binary64)
(*.f64 x eps)
x
eps
#s(literal -1/2 binary64)
(*.f64 #s(literal -1/2 binary64) eps)
#s(literal 1 binary64)
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (cos x) eps) (fma.f64 (fma.f64 (.f64 eps (fma.f64 #s(literal -1/720 binary64) (.f64 x x) #s(literal 1/24 binary64))) (.f64 x x) (.f64 #s(literal -1/2 binary64) eps)) (*.f64 x x) eps)))
#s(approx (* (cos x) eps) (fma.f64 (fma.f64 (.f64 eps (fma.f64 #s(literal -1/720 binary64) (.f64 x x) #s(literal 1/24 binary64))) (.f64 x x) (.f64 #s(literal -1/2 binary64) eps)) (*.f64 x x) eps))
(fma.f64 (fma.f64 (.f64 eps (fma.f64 #s(literal -1/720 binary64) (.f64 x x) #s(literal 1/24 binary64))) (.f64 x x) (.f64 #s(literal -1/2 binary64) eps)) (*.f64 x x) eps)
(fma.f64 (.f64 eps (fma.f64 #s(literal -1/720 binary64) (.f64 x x) #s(literal 1/24 binary64))) (.f64 x x) (.f64 #s(literal -1/2 binary64) eps))
(.f64 eps (fma.f64 #s(literal -1/720 binary64) (.f64 x x) #s(literal 1/24 binary64)))
eps
(fma.f64 #s(literal -1/720 binary64) (*.f64 x x) #s(literal 1/24 binary64))
#s(literal -1/720 binary64)
(*.f64 x x)
x
#s(literal 1/24 binary64)
(*.f64 #s(literal -1/2 binary64) eps)
#s(literal -1/2 binary64)
(.f64 #s(approx ( (sin (* 1/2 (+ 0 eps))) 2) (.f64 (fma.f64 (.f64 eps eps) #s(literal -1/24 binary64) #s(literal 1 binary64)) eps)) (cos.f64 (*.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps))))
#s(approx (* (sin (* 1/2 (+ 0 eps))) 2) (.f64 (fma.f64 (.f64 eps eps) #s(literal -1/24 binary64) #s(literal 1 binary64)) eps))
(.f64 (fma.f64 (.f64 eps eps) #s(literal -1/24 binary64) #s(literal 1 binary64)) eps)
(fma.f64 (*.f64 eps eps) #s(literal -1/24 binary64) #s(literal 1 binary64))
(*.f64 eps eps)
eps
#s(literal -1/24 binary64)
#s(literal 1 binary64)
(cos.f64 (*.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps)))
(*.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps))
#s(literal 1/2 binary64)
(fma.f64 #s(literal 2 binary64) x eps)
#s(literal 2 binary64)
x

Outputs
(.f64 #s(approx ( (sin (* 1/2 (+ 0 eps))) 2) (.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -1/322560 binary64) (.f64 eps eps) #s(literal 1/1920 binary64)) (.f64 eps eps) #s(literal -1/24 binary64)) (.f64 eps eps) #s(literal 1 binary64)) eps)) (cos.f64 (*.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps))))
(.f64 (cos.f64 (fma.f64 eps #s(literal 1/2 binary64) x)) #s(approx ( (sin (* 1/2 (+ 0 eps))) 2) (.f64 (fma.f64 (fma.f64 (fma.f64 (.f64 eps eps) #s(literal -1/322560 binary64) #s(literal 1/1920 binary64)) (.f64 eps eps) #s(literal -1/24 binary64)) (.f64 eps eps) #s(literal 1 binary64)) eps)))
#s(approx (* (sin (* 1/2 (+ 0 eps))) 2) (.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -1/322560 binary64) (.f64 eps eps) #s(literal 1/1920 binary64)) (.f64 eps eps) #s(literal -1/24 binary64)) (.f64 eps eps) #s(literal 1 binary64)) eps))
#s(approx (* (sin (* 1/2 (+ 0 eps))) 2) (.f64 (fma.f64 (fma.f64 (fma.f64 (.f64 eps eps) #s(literal -1/322560 binary64) #s(literal 1/1920 binary64)) (.f64 eps eps) #s(literal -1/24 binary64)) (.f64 eps eps) #s(literal 1 binary64)) eps))
(.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -1/322560 binary64) (.f64 eps eps) #s(literal 1/1920 binary64)) (.f64 eps eps) #s(literal -1/24 binary64)) (.f64 eps eps) #s(literal 1 binary64)) eps)
(.f64 (fma.f64 (fma.f64 (fma.f64 (.f64 eps eps) #s(literal -1/322560 binary64) #s(literal 1/1920 binary64)) (.f64 eps eps) #s(literal -1/24 binary64)) (.f64 eps eps) #s(literal 1 binary64)) eps)
(fma.f64 (fma.f64 (fma.f64 #s(literal -1/322560 binary64) (.f64 eps eps) #s(literal 1/1920 binary64)) (.f64 eps eps) #s(literal -1/24 binary64)) (*.f64 eps eps) #s(literal 1 binary64))
(fma.f64 (fma.f64 (fma.f64 (.f64 eps eps) #s(literal -1/322560 binary64) #s(literal 1/1920 binary64)) (.f64 eps eps) #s(literal -1/24 binary64)) (*.f64 eps eps) #s(literal 1 binary64))
(fma.f64 (fma.f64 #s(literal -1/322560 binary64) (.f64 eps eps) #s(literal 1/1920 binary64)) (.f64 eps eps) #s(literal -1/24 binary64))
(fma.f64 (fma.f64 (.f64 eps eps) #s(literal -1/322560 binary64) #s(literal 1/1920 binary64)) (.f64 eps eps) #s(literal -1/24 binary64))
(fma.f64 #s(literal -1/322560 binary64) (*.f64 eps eps) #s(literal 1/1920 binary64))
(fma.f64 (*.f64 eps eps) #s(literal -1/322560 binary64) #s(literal 1/1920 binary64))
#s(literal -1/322560 binary64)
(*.f64 eps eps)
eps
#s(literal 1/1920 binary64)
#s(literal -1/24 binary64)
#s(literal 1 binary64)
(cos.f64 (*.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps)))
(cos.f64 (fma.f64 eps #s(literal 1/2 binary64) x))
(*.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps))
(fma.f64 eps #s(literal 1/2 binary64) x)
#s(literal 1/2 binary64)
(fma.f64 #s(literal 2 binary64) x eps)
(fma.f64 x #s(literal 2 binary64) eps)
#s(literal 2 binary64)
x
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (cos x) eps) (fma.f64 (.f64 #s(literal -1/2 binary64) x) (.f64 x eps) eps)))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (cos x) eps) (fma.f64 (.f64 x eps) (.f64 #s(literal -1/2 binary64) x) eps)))
#s(approx (* (cos x) eps) (fma.f64 (.f64 #s(literal -1/2 binary64) x) (.f64 x eps) eps))
#s(approx (* (cos x) eps) (fma.f64 (.f64 x eps) (.f64 #s(literal -1/2 binary64) x) eps))
(fma.f64 (.f64 #s(literal -1/2 binary64) x) (.f64 x eps) eps)
(fma.f64 (.f64 x eps) (.f64 #s(literal -1/2 binary64) x) eps)
(*.f64 #s(literal -1/2 binary64) x)
#s(literal -1/2 binary64)
x
(*.f64 x eps)
eps
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (* (sin x) -1/2) eps) (cos x)) (fma.f64 (fma.f64 (fma.f64 #s(literal 1/12 binary64) (.f64 x eps) #s(literal -1/2 binary64)) x (.f64 #s(literal -1/2 binary64) eps)) x #s(literal 1 binary64))) eps))
(.f64 #s(approx (+ ( (* (sin x) -1/2) eps) (cos x)) (fma.f64 (fma.f64 (fma.f64 #s(literal 1/12 binary64) (.f64 x eps) #s(literal -1/2 binary64)) x (.f64 #s(literal -1/2 binary64) eps)) x #s(literal 1 binary64))) eps)
#s(approx (+ (* (* (sin x) -1/2) eps) (cos x)) (fma.f64 (fma.f64 (fma.f64 #s(literal 1/12 binary64) (.f64 x eps) #s(literal -1/2 binary64)) x (.f64 #s(literal -1/2 binary64) eps)) x #s(literal 1 binary64)))
(fma.f64 (fma.f64 (fma.f64 #s(literal 1/12 binary64) (.f64 x eps) #s(literal -1/2 binary64)) x (.f64 #s(literal -1/2 binary64) eps)) x #s(literal 1 binary64))
(fma.f64 (fma.f64 #s(literal 1/12 binary64) (.f64 x eps) #s(literal -1/2 binary64)) x (.f64 #s(literal -1/2 binary64) eps))
(fma.f64 #s(literal 1/12 binary64) (*.f64 x eps) #s(literal -1/2 binary64))
#s(literal 1/12 binary64)
(*.f64 x eps)
x
eps
#s(literal -1/2 binary64)
(*.f64 #s(literal -1/2 binary64) eps)
#s(literal 1 binary64)
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (cos x) eps) (fma.f64 (fma.f64 (.f64 eps (fma.f64 #s(literal -1/720 binary64) (.f64 x x) #s(literal 1/24 binary64))) (.f64 x x) (.f64 #s(literal -1/2 binary64) eps)) (*.f64 x x) eps)))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (cos x) eps) (.f64 (fma.f64 (.f64 (fma.f64 (fma.f64 (.f64 x x) #s(literal -1/720 binary64) #s(literal 1/24 binary64)) (.f64 x x) #s(literal -1/2 binary64)) x) x #s(literal 1 binary64)) eps)))
#s(approx (* (cos x) eps) (fma.f64 (fma.f64 (.f64 eps (fma.f64 #s(literal -1/720 binary64) (.f64 x x) #s(literal 1/24 binary64))) (.f64 x x) (.f64 #s(literal -1/2 binary64) eps)) (*.f64 x x) eps))
#s(approx (* (cos x) eps) (.f64 (fma.f64 (.f64 (fma.f64 (fma.f64 (.f64 x x) #s(literal -1/720 binary64) #s(literal 1/24 binary64)) (.f64 x x) #s(literal -1/2 binary64)) x) x #s(literal 1 binary64)) eps))
(fma.f64 (fma.f64 (.f64 eps (fma.f64 #s(literal -1/720 binary64) (.f64 x x) #s(literal 1/24 binary64))) (.f64 x x) (.f64 #s(literal -1/2 binary64) eps)) (*.f64 x x) eps)
(.f64 (fma.f64 (.f64 (fma.f64 (fma.f64 (.f64 x x) #s(literal -1/720 binary64) #s(literal 1/24 binary64)) (.f64 x x) #s(literal -1/2 binary64)) x) x #s(literal 1 binary64)) eps)
(fma.f64 (.f64 eps (fma.f64 #s(literal -1/720 binary64) (.f64 x x) #s(literal 1/24 binary64))) (.f64 x x) (.f64 #s(literal -1/2 binary64) eps))
(.f64 (fma.f64 (fma.f64 (.f64 x x) #s(literal -1/720 binary64) #s(literal 1/24 binary64)) (*.f64 x x) #s(literal -1/2 binary64)) eps)
(.f64 eps (fma.f64 #s(literal -1/720 binary64) (.f64 x x) #s(literal 1/24 binary64)))
(.f64 (fma.f64 (.f64 x x) #s(literal -1/720 binary64) #s(literal 1/24 binary64)) eps)
eps
(fma.f64 #s(literal -1/720 binary64) (*.f64 x x) #s(literal 1/24 binary64))
(fma.f64 (*.f64 x x) #s(literal -1/720 binary64) #s(literal 1/24 binary64))
#s(literal -1/720 binary64)
(*.f64 x x)
x
#s(literal 1/24 binary64)
(*.f64 #s(literal -1/2 binary64) eps)
#s(literal -1/2 binary64)
(.f64 #s(approx ( (sin (* 1/2 (+ 0 eps))) 2) (.f64 (fma.f64 (.f64 eps eps) #s(literal -1/24 binary64) #s(literal 1 binary64)) eps)) (cos.f64 (*.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps))))
(.f64 #s(approx ( (sin (* 1/2 (+ 0 eps))) 2) (.f64 (fma.f64 #s(literal -1/24 binary64) (.f64 eps eps) #s(literal 1 binary64)) eps)) (cos.f64 (fma.f64 eps #s(literal 1/2 binary64) x)))
#s(approx (* (sin (* 1/2 (+ 0 eps))) 2) (.f64 (fma.f64 (.f64 eps eps) #s(literal -1/24 binary64) #s(literal 1 binary64)) eps))
#s(approx (* (sin (* 1/2 (+ 0 eps))) 2) (.f64 (fma.f64 #s(literal -1/24 binary64) (.f64 eps eps) #s(literal 1 binary64)) eps))
(.f64 (fma.f64 (.f64 eps eps) #s(literal -1/24 binary64) #s(literal 1 binary64)) eps)
(.f64 (fma.f64 #s(literal -1/24 binary64) (.f64 eps eps) #s(literal 1 binary64)) eps)
(fma.f64 (*.f64 eps eps) #s(literal -1/24 binary64) #s(literal 1 binary64))
(fma.f64 #s(literal -1/24 binary64) (*.f64 eps eps) #s(literal 1 binary64))
(*.f64 eps eps)
eps
#s(literal -1/24 binary64)
#s(literal 1 binary64)
(cos.f64 (*.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps)))
(cos.f64 (fma.f64 eps #s(literal 1/2 binary64) x))
(*.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps))
(fma.f64 eps #s(literal 1/2 binary64) x)
#s(literal 1/2 binary64)
(fma.f64 #s(literal 2 binary64) x eps)
(fma.f64 x #s(literal 2 binary64) eps)
#s(literal 2 binary64)
x

localize317.0ms (2.5%)

Memory

-12.4MiB live, 186.0MiB allocated

Localize:

Found 20 expressions of interest:

New	Metric	Score
accuracy	0.00390625	(.f64 (fma.f64 (.f64 eps eps) #s(literal -1/24 binary64) #s(literal 1 binary64)) eps)
accuracy	0.0078125	(.f64 #s(approx ( (sin (* 1/2 (+ 0 eps))) 2) (.f64 (fma.f64 (.f64 eps eps) #s(literal -1/24 binary64) #s(literal 1 binary64)) eps)) (cos.f64 (*.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps))))
accuracy	0.0464165744115697	(cos.f64 (*.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps)))
accuracy	0.1278156975370348	#s(approx (* (sin (* 1/2 (+ 0 eps))) 2) (.f64 (fma.f64 (.f64 eps eps) #s(literal -1/24 binary64) #s(literal 1 binary64)) eps))
accuracy	0.01171875	(fma.f64 #s(literal -1/720 binary64) (*.f64 x x) #s(literal 1/24 binary64))
accuracy	0.3046875	(.f64 eps (fma.f64 #s(literal -1/720 binary64) (.f64 x x) #s(literal 1/24 binary64)))
accuracy	0.45925062897182506	#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (cos x) eps) (fma.f64 (fma.f64 (.f64 eps (fma.f64 #s(literal -1/720 binary64) (.f64 x x) #s(literal 1/24 binary64))) (.f64 x x) (.f64 #s(literal -1/2 binary64) eps)) (*.f64 x x) eps)))
accuracy	0.7323134152972174	#s(approx (* (cos x) eps) (fma.f64 (fma.f64 (.f64 eps (fma.f64 #s(literal -1/720 binary64) (.f64 x x) #s(literal 1/24 binary64))) (.f64 x x) (.f64 #s(literal -1/2 binary64) eps)) (*.f64 x x) eps))
accuracy	0.00390625	(.f64 #s(approx (+ ( (* (sin x) -1/2) eps) (cos x)) (fma.f64 (fma.f64 (fma.f64 #s(literal 1/12 binary64) (.f64 x eps) #s(literal -1/2 binary64)) x (.f64 #s(literal -1/2 binary64) eps)) x #s(literal 1 binary64))) eps)
accuracy	0.01953125	(fma.f64 (fma.f64 #s(literal 1/12 binary64) (.f64 x eps) #s(literal -1/2 binary64)) x (.f64 #s(literal -1/2 binary64) eps))
accuracy	0.1809942524239391	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (* (sin x) -1/2) eps) (cos x)) (fma.f64 (fma.f64 (fma.f64 #s(literal 1/12 binary64) (.f64 x eps) #s(literal -1/2 binary64)) x (.f64 #s(literal -1/2 binary64) eps)) x #s(literal 1 binary64))) eps))
accuracy	0.915514254007739	#s(approx (+ (* (* (sin x) -1/2) eps) (cos x)) (fma.f64 (fma.f64 (fma.f64 #s(literal 1/12 binary64) (.f64 x eps) #s(literal -1/2 binary64)) x (.f64 #s(literal -1/2 binary64) eps)) x #s(literal 1 binary64)))
accuracy	0	(*.f64 #s(literal -1/2 binary64) x)
accuracy	0.0078125	(fma.f64 (.f64 #s(literal -1/2 binary64) x) (.f64 x eps) eps)
accuracy	0.45925062897182506	#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (cos x) eps) (fma.f64 (.f64 #s(literal -1/2 binary64) x) (.f64 x eps) eps)))
accuracy	0.9088469829361734	#s(approx (* (cos x) eps) (fma.f64 (.f64 #s(literal -1/2 binary64) x) (.f64 x eps) eps))
accuracy	0.00390625	(.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -1/322560 binary64) (.f64 eps eps) #s(literal 1/1920 binary64)) (.f64 eps eps) #s(literal -1/24 binary64)) (.f64 eps eps) #s(literal 1 binary64)) eps)
accuracy	0.0078125	(.f64 #s(approx ( (sin (* 1/2 (+ 0 eps))) 2) (.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -1/322560 binary64) (.f64 eps eps) #s(literal 1/1920 binary64)) (.f64 eps eps) #s(literal -1/24 binary64)) (.f64 eps eps) #s(literal 1 binary64)) eps)) (cos.f64 (*.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps))))
accuracy	0.03150816090022567	#s(approx (* (sin (* 1/2 (+ 0 eps))) 2) (.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -1/322560 binary64) (.f64 eps eps) #s(literal 1/1920 binary64)) (.f64 eps eps) #s(literal -1/24 binary64)) (.f64 eps eps) #s(literal 1 binary64)) eps))
accuracy	0.0464165744115697	(cos.f64 (*.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps)))

Samples

107.0ms	171×	0	valid
92.0ms	81×	1	valid
4.0ms	3×	3	valid
1.0ms	1×	2	valid

Compiler

Compiled 370 to 64 computations (82.7% saved)

Precisions

Click to see histograms. Total time spent on operations: 172.0ms

ival-mult: 56.0ms (32.5% of total)

ival-add: 45.0ms (26.2% of total)

adjust: 38.0ms (22.1% of total)

const: 21.0ms (12.2% of total)

ival-sin: 6.0ms (3.5% of total)

ival-cos: 4.0ms (2.3% of total)

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

exact: 1.0ms (0.6% of total)

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

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

series53.0ms (0.4%)

Memory

3.8MiB live, 40.6MiB allocated

Counts

23 → 480

Calls

Call 1

Inputs
#s(alt (.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps)) (patch (.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps)) #<representation binary64>) () ())
#s(alt (.f64 #s(approx ( (sin (* 1/2 (+ 0 eps))) 2) (.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -1/322560 binary64) (.f64 eps eps) #s(literal 1/1920 binary64)) (.f64 eps eps) #s(literal -1/24 binary64)) (.f64 eps eps) #s(literal 1 binary64)) eps)) (cos.f64 (.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps)))) (patch (.f64 #s(approx (* (sin (* 1/2 (+ 0 eps))) 2) (.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -1/322560 binary64) (.f64 eps eps) #s(literal 1/1920 binary64)) (.f64 eps eps) #s(literal -1/24 binary64)) (.f64 eps eps) #s(literal 1 binary64)) eps)) (cos.f64 (*.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps)))) #<representation binary64>) () ())
#s(alt #s(approx (* (sin (* 1/2 (+ 0 eps))) 2) (.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -1/322560 binary64) (.f64 eps eps) #s(literal 1/1920 binary64)) (.f64 eps eps) #s(literal -1/24 binary64)) (.f64 eps eps) #s(literal 1 binary64)) eps)) (patch #s(approx (* (sin (* 1/2 (+ 0 eps))) 2) (.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -1/322560 binary64) (.f64 eps eps) #s(literal 1/1920 binary64)) (.f64 eps eps) #s(literal -1/24 binary64)) (.f64 eps eps) #s(literal 1 binary64)) eps)) #<representation binary64>) () ())
#s(alt (.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -1/322560 binary64) (.f64 eps eps) #s(literal 1/1920 binary64)) (.f64 eps eps) #s(literal -1/24 binary64)) (.f64 eps eps) #s(literal 1 binary64)) eps) (patch (.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -1/322560 binary64) (.f64 eps eps) #s(literal 1/1920 binary64)) (.f64 eps eps) #s(literal -1/24 binary64)) (.f64 eps eps) #s(literal 1 binary64)) eps) #<representation binary64>) () ())
#s(alt #s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (cos x) eps) (fma.f64 (.f64 #s(literal -1/2 binary64) x) (.f64 x eps) eps))) (patch #s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (cos x) eps) (fma.f64 (.f64 #s(literal -1/2 binary64) x) (.f64 x eps) eps))) #<representation binary64>) () ())
#s(alt #s(approx (* (cos x) eps) (fma.f64 (.f64 #s(literal -1/2 binary64) x) (.f64 x eps) eps)) (patch #s(approx (* (cos x) eps) (fma.f64 (.f64 #s(literal -1/2 binary64) x) (.f64 x eps) eps)) #<representation binary64>) () ())
#s(alt (fma.f64 (.f64 #s(literal -1/2 binary64) x) (.f64 x eps) eps) (patch (fma.f64 (.f64 #s(literal -1/2 binary64) x) (.f64 x eps) 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 (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (* (sin x) -1/2) eps) (cos x)) (fma.f64 (fma.f64 (fma.f64 #s(literal 1/12 binary64) (.f64 x eps) #s(literal -1/2 binary64)) x (.f64 #s(literal -1/2 binary64) eps)) x #s(literal 1 binary64))) eps)) (patch #s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (* (sin x) -1/2) eps) (cos x)) (fma.f64 (fma.f64 (fma.f64 #s(literal 1/12 binary64) (.f64 x eps) #s(literal -1/2 binary64)) x (.f64 #s(literal -1/2 binary64) eps)) x #s(literal 1 binary64))) eps)) #<representation binary64>) () ())
#s(alt (.f64 #s(approx (+ ( (* (sin x) -1/2) eps) (cos x)) (fma.f64 (fma.f64 (fma.f64 #s(literal 1/12 binary64) (.f64 x eps) #s(literal -1/2 binary64)) x (.f64 #s(literal -1/2 binary64) eps)) x #s(literal 1 binary64))) eps) (patch (.f64 #s(approx (+ ( (* (sin x) -1/2) eps) (cos x)) (fma.f64 (fma.f64 (fma.f64 #s(literal 1/12 binary64) (.f64 x eps) #s(literal -1/2 binary64)) x (.f64 #s(literal -1/2 binary64) eps)) x #s(literal 1 binary64))) eps) #<representation binary64>) () ())
#s(alt #s(approx (+ (* (* (sin x) -1/2) eps) (cos x)) (fma.f64 (fma.f64 (fma.f64 #s(literal 1/12 binary64) (.f64 x eps) #s(literal -1/2 binary64)) x (.f64 #s(literal -1/2 binary64) eps)) x #s(literal 1 binary64))) (patch #s(approx (+ (* (* (sin x) -1/2) eps) (cos x)) (fma.f64 (fma.f64 (fma.f64 #s(literal 1/12 binary64) (.f64 x eps) #s(literal -1/2 binary64)) x (.f64 #s(literal -1/2 binary64) eps)) x #s(literal 1 binary64))) #<representation binary64>) () ())
#s(alt (fma.f64 (fma.f64 (fma.f64 #s(literal 1/12 binary64) (.f64 x eps) #s(literal -1/2 binary64)) x (.f64 #s(literal -1/2 binary64) eps)) x #s(literal 1 binary64)) (patch (fma.f64 (fma.f64 (fma.f64 #s(literal 1/12 binary64) (.f64 x eps) #s(literal -1/2 binary64)) x (.f64 #s(literal -1/2 binary64) eps)) x #s(literal 1 binary64)) #<representation binary64>) () ())
#s(alt (fma.f64 (.f64 eps (fma.f64 #s(literal -1/720 binary64) (.f64 x x) #s(literal 1/24 binary64))) (.f64 x x) (.f64 #s(literal -1/2 binary64) eps)) (patch (fma.f64 (.f64 eps (fma.f64 #s(literal -1/720 binary64) (.f64 x x) #s(literal 1/24 binary64))) (.f64 x x) (.f64 #s(literal -1/2 binary64) eps)) #<representation binary64>) () ())
#s(alt #s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (cos x) eps) (fma.f64 (fma.f64 (.f64 eps (fma.f64 #s(literal -1/720 binary64) (.f64 x x) #s(literal 1/24 binary64))) (.f64 x x) (.f64 #s(literal -1/2 binary64) eps)) (.f64 x x) eps))) (patch #s(approx (- (sin (+ x eps)) (sin x)) #s(approx ( (cos x) eps) (fma.f64 (fma.f64 (.f64 eps (fma.f64 #s(literal -1/720 binary64) (.f64 x x) #s(literal 1/24 binary64))) (.f64 x x) (.f64 #s(literal -1/2 binary64) eps)) (*.f64 x x) eps))) #<representation binary64>) () ())
#s(alt #s(approx (* (cos x) eps) (fma.f64 (fma.f64 (.f64 eps (fma.f64 #s(literal -1/720 binary64) (.f64 x x) #s(literal 1/24 binary64))) (.f64 x x) (.f64 #s(literal -1/2 binary64) eps)) (.f64 x x) eps)) (patch #s(approx ( (cos x) eps) (fma.f64 (fma.f64 (.f64 eps (fma.f64 #s(literal -1/720 binary64) (.f64 x x) #s(literal 1/24 binary64))) (.f64 x x) (.f64 #s(literal -1/2 binary64) eps)) (*.f64 x x) eps)) #<representation binary64>) () ())
#s(alt (fma.f64 (fma.f64 (.f64 eps (fma.f64 #s(literal -1/720 binary64) (.f64 x x) #s(literal 1/24 binary64))) (.f64 x x) (.f64 #s(literal -1/2 binary64) eps)) (.f64 x x) eps) (patch (fma.f64 (fma.f64 (.f64 eps (fma.f64 #s(literal -1/720 binary64) (.f64 x x) #s(literal 1/24 binary64))) (.f64 x x) (.f64 #s(literal -1/2 binary64) eps)) (.f64 x x) eps) #<representation binary64>) () ())
#s(alt (.f64 #s(approx ( (sin (* 1/2 (+ 0 eps))) 2) (.f64 (fma.f64 (.f64 eps eps) #s(literal -1/24 binary64) #s(literal 1 binary64)) eps)) (cos.f64 (.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps)))) (patch (.f64 #s(approx (* (sin (* 1/2 (+ 0 eps))) 2) (.f64 (fma.f64 (.f64 eps eps) #s(literal -1/24 binary64) #s(literal 1 binary64)) eps)) (cos.f64 (*.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps)))) #<representation binary64>) () ())
#s(alt #s(approx (* (sin (* 1/2 (+ 0 eps))) 2) (.f64 (fma.f64 (.f64 eps eps) #s(literal -1/24 binary64) #s(literal 1 binary64)) eps)) (patch #s(approx (* (sin (* 1/2 (+ 0 eps))) 2) (.f64 (fma.f64 (.f64 eps eps) #s(literal -1/24 binary64) #s(literal 1 binary64)) eps)) #<representation binary64>) () ())
#s(alt (.f64 (fma.f64 (.f64 eps eps) #s(literal -1/24 binary64) #s(literal 1 binary64)) eps) (patch (.f64 (fma.f64 (.f64 eps eps) #s(literal -1/24 binary64) #s(literal 1 binary64)) eps) #<representation binary64>) () ())
#s(alt (cos.f64 (.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps))) (patch (cos.f64 (.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps))) #<representation binary64>) () ())
#s(alt (fma.f64 (fma.f64 #s(literal 1/12 binary64) (.f64 x eps) #s(literal -1/2 binary64)) x (.f64 #s(literal -1/2 binary64) eps)) (patch (fma.f64 (fma.f64 #s(literal 1/12 binary64) (.f64 x eps) #s(literal -1/2 binary64)) x (.f64 #s(literal -1/2 binary64) eps)) #<representation binary64>) () ())
#s(alt (.f64 eps (fma.f64 #s(literal -1/720 binary64) (.f64 x x) #s(literal 1/24 binary64))) (patch (.f64 eps (fma.f64 #s(literal -1/720 binary64) (.f64 x x) #s(literal 1/24 binary64))) #<representation binary64>) () ())
#s(alt (fma.f64 #s(literal -1/720 binary64) (.f64 x x) #s(literal 1/24 binary64)) (patch (fma.f64 #s(literal -1/720 binary64) (.f64 x x) #s(literal 1/24 binary64)) #<representation binary64>) () ())

Outputs
#s(alt (* 1/2 eps) (taylor 0 x) (#s(alt (.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps)) (patch (.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps)) #<representation binary64>) () ())) ())
#s(alt (+ x (* 1/2 eps)) (taylor 0 x) (#s(alt (.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps)) (patch (.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps)) #<representation binary64>) () ())) ())
#s(alt (+ x (* 1/2 eps)) (taylor 0 x) (#s(alt (.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps)) (patch (.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps)) #<representation binary64>) () ())) ())
#s(alt (+ x (* 1/2 eps)) (taylor 0 x) (#s(alt (.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps)) (patch (.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps)) #<representation binary64>) () ())) ())
#s(alt x (taylor inf x) (#s(alt (.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps)) (patch (.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps)) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1 (* 1/2 (/ eps x)))) (taylor inf x) (#s(alt (.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps)) (patch (.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps)) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1 (* 1/2 (/ eps x)))) (taylor inf x) (#s(alt (.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps)) (patch (.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps)) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1 (* 1/2 (/ eps x)))) (taylor inf x) (#s(alt (.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps)) (patch (.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps)) #<representation binary64>) () ())) ())
#s(alt x (taylor -inf x) (#s(alt (.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps)) (patch (.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (- (* -1/2 (/ eps x)) 1))) (taylor -inf x) (#s(alt (.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps)) (patch (.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (- (* -1/2 (/ eps x)) 1))) (taylor -inf x) (#s(alt (.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps)) (patch (.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (- (* -1/2 (/ eps x)) 1))) (taylor -inf x) (#s(alt (.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps)) (patch (.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps)) #<representation binary64>) () ())) ())
#s(alt x (taylor 0 eps) (#s(alt (.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps)) (patch (.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps)) #<representation binary64>) () ())) ())
#s(alt (+ x (* 1/2 eps)) (taylor 0 eps) (#s(alt (.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps)) (patch (.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps)) #<representation binary64>) () ())) ())
#s(alt (+ x (* 1/2 eps)) (taylor 0 eps) (#s(alt (.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps)) (patch (.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps)) #<representation binary64>) () ())) ())
#s(alt (+ x (* 1/2 eps)) (taylor 0 eps) (#s(alt (.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps)) (patch (.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps)) #<representation binary64>) () ())) ())
#s(alt (* 1/2 eps) (taylor inf eps) (#s(alt (.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps)) (patch (.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps)) #<representation binary64>) () ())) ())
#s(alt (* eps (+ 1/2 (/ x eps))) (taylor inf eps) (#s(alt (.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps)) (patch (.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps)) #<representation binary64>) () ())) ())
#s(alt (* eps (+ 1/2 (/ x eps))) (taylor inf eps) (#s(alt (.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps)) (patch (.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps)) #<representation binary64>) () ())) ())
#s(alt (* eps (+ 1/2 (/ x eps))) (taylor inf eps) (#s(alt (.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps)) (patch (.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps)) #<representation binary64>) () ())) ())
#s(alt (* 1/2 eps) (taylor -inf eps) (#s(alt (.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps)) (patch (.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* eps (- (* -1 (/ x eps)) 1/2))) (taylor -inf eps) (#s(alt (.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps)) (patch (.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* eps (- (* -1 (/ x eps)) 1/2))) (taylor -inf eps) (#s(alt (.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps)) (patch (.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* eps (- (* -1 (/ x eps)) 1/2))) (taylor -inf eps) (#s(alt (.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps)) (patch (.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps)) #<representation binary64>) () ())) ())
#s(alt (* eps (cos x)) (taylor 0 eps) (#s(alt (.f64 #s(approx ( (sin (* 1/2 (+ 0 eps))) 2) (.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -1/322560 binary64) (.f64 eps eps) #s(literal 1/1920 binary64)) (.f64 eps eps) #s(literal -1/24 binary64)) (.f64 eps eps) #s(literal 1 binary64)) eps)) (cos.f64 (.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps)))) (patch (.f64 #s(approx (* (sin (* 1/2 (+ 0 eps))) 2) (.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -1/322560 binary64) (.f64 eps eps) #s(literal 1/1920 binary64)) (.f64 eps eps) #s(literal -1/24 binary64)) (.f64 eps eps) #s(literal 1 binary64)) eps)) (cos.f64 (*.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps)))) #<representation binary64>) () ())) ())
#s(alt (* eps (+ (cos x) (* -1/2 (* eps (sin x))))) (taylor 0 eps) (#s(alt (.f64 #s(approx ( (sin (* 1/2 (+ 0 eps))) 2) (.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -1/322560 binary64) (.f64 eps eps) #s(literal 1/1920 binary64)) (.f64 eps eps) #s(literal -1/24 binary64)) (.f64 eps eps) #s(literal 1 binary64)) eps)) (cos.f64 (.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps)))) (patch (.f64 #s(approx (* (sin (* 1/2 (+ 0 eps))) 2) (.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -1/322560 binary64) (.f64 eps eps) #s(literal 1/1920 binary64)) (.f64 eps eps) #s(literal -1/24 binary64)) (.f64 eps eps) #s(literal 1 binary64)) eps)) (cos.f64 (*.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps)))) #<representation binary64>) () ())) ())
#s(alt (* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* 2 (* eps (+ (* -1/16 (cos x)) (* -1/48 (cos x))))))))) (taylor 0 eps) (#s(alt (.f64 #s(approx ( (sin (* 1/2 (+ 0 eps))) 2) (.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -1/322560 binary64) (.f64 eps eps) #s(literal 1/1920 binary64)) (.f64 eps eps) #s(literal -1/24 binary64)) (.f64 eps eps) #s(literal 1 binary64)) eps)) (cos.f64 (.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps)))) (patch (.f64 #s(approx (* (sin (* 1/2 (+ 0 eps))) 2) (.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -1/322560 binary64) (.f64 eps eps) #s(literal 1/1920 binary64)) (.f64 eps eps) #s(literal -1/24 binary64)) (.f64 eps eps) #s(literal 1 binary64)) eps)) (cos.f64 (*.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps)))) #<representation binary64>) () ())) ())
#s(alt (* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* eps (+ (* 1/24 (* eps (sin x))) (* 2 (+ (* -1/16 (cos x)) (* -1/48 (cos x)))))))))) (taylor 0 eps) (#s(alt (.f64 #s(approx ( (sin (* 1/2 (+ 0 eps))) 2) (.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -1/322560 binary64) (.f64 eps eps) #s(literal 1/1920 binary64)) (.f64 eps eps) #s(literal -1/24 binary64)) (.f64 eps eps) #s(literal 1 binary64)) eps)) (cos.f64 (.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps)))) (patch (.f64 #s(approx (* (sin (* 1/2 (+ 0 eps))) 2) (.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -1/322560 binary64) (.f64 eps eps) #s(literal 1/1920 binary64)) (.f64 eps eps) #s(literal -1/24 binary64)) (.f64 eps eps) #s(literal 1 binary64)) eps)) (cos.f64 (*.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps)))) #<representation binary64>) () ())) ())
#s(alt (* 2 (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps)))) (taylor inf eps) (#s(alt (.f64 #s(approx ( (sin (* 1/2 (+ 0 eps))) 2) (.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -1/322560 binary64) (.f64 eps eps) #s(literal 1/1920 binary64)) (.f64 eps eps) #s(literal -1/24 binary64)) (.f64 eps eps) #s(literal 1 binary64)) eps)) (cos.f64 (.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps)))) (patch (.f64 #s(approx (* (sin (* 1/2 (+ 0 eps))) 2) (.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -1/322560 binary64) (.f64 eps eps) #s(literal 1/1920 binary64)) (.f64 eps eps) #s(literal -1/24 binary64)) (.f64 eps eps) #s(literal 1 binary64)) eps)) (cos.f64 (*.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps)))) #<representation binary64>) () ())) ())
#s(alt (* 2 (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps)))) (taylor inf eps) (#s(alt (.f64 #s(approx ( (sin (* 1/2 (+ 0 eps))) 2) (.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -1/322560 binary64) (.f64 eps eps) #s(literal 1/1920 binary64)) (.f64 eps eps) #s(literal -1/24 binary64)) (.f64 eps eps) #s(literal 1 binary64)) eps)) (cos.f64 (.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps)))) (patch (.f64 #s(approx (* (sin (* 1/2 (+ 0 eps))) 2) (.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -1/322560 binary64) (.f64 eps eps) #s(literal 1/1920 binary64)) (.f64 eps eps) #s(literal -1/24 binary64)) (.f64 eps eps) #s(literal 1 binary64)) eps)) (cos.f64 (*.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps)))) #<representation binary64>) () ())) ())
#s(alt (* 2 (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps)))) (taylor inf eps) (#s(alt (.f64 #s(approx ( (sin (* 1/2 (+ 0 eps))) 2) (.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -1/322560 binary64) (.f64 eps eps) #s(literal 1/1920 binary64)) (.f64 eps eps) #s(literal -1/24 binary64)) (.f64 eps eps) #s(literal 1 binary64)) eps)) (cos.f64 (.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps)))) (patch (.f64 #s(approx (* (sin (* 1/2 (+ 0 eps))) 2) (.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -1/322560 binary64) (.f64 eps eps) #s(literal 1/1920 binary64)) (.f64 eps eps) #s(literal -1/24 binary64)) (.f64 eps eps) #s(literal 1 binary64)) eps)) (cos.f64 (*.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps)))) #<representation binary64>) () ())) ())
#s(alt (* 2 (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps)))) (taylor inf eps) (#s(alt (.f64 #s(approx ( (sin (* 1/2 (+ 0 eps))) 2) (.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -1/322560 binary64) (.f64 eps eps) #s(literal 1/1920 binary64)) (.f64 eps eps) #s(literal -1/24 binary64)) (.f64 eps eps) #s(literal 1 binary64)) eps)) (cos.f64 (.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps)))) (patch (.f64 #s(approx (* (sin (* 1/2 (+ 0 eps))) 2) (.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -1/322560 binary64) (.f64 eps eps) #s(literal 1/1920 binary64)) (.f64 eps eps) #s(literal -1/24 binary64)) (.f64 eps eps) #s(literal 1 binary64)) eps)) (cos.f64 (*.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps)))) #<representation binary64>) () ())) ())
#s(alt (* 2 (* (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps)))) (taylor -inf eps) (#s(alt (.f64 #s(approx ( (sin (* 1/2 (+ 0 eps))) 2) (.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -1/322560 binary64) (.f64 eps eps) #s(literal 1/1920 binary64)) (.f64 eps eps) #s(literal -1/24 binary64)) (.f64 eps eps) #s(literal 1 binary64)) eps)) (cos.f64 (.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps)))) (patch (.f64 #s(approx (* (sin (* 1/2 (+ 0 eps))) 2) (.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -1/322560 binary64) (.f64 eps eps) #s(literal 1/1920 binary64)) (.f64 eps eps) #s(literal -1/24 binary64)) (.f64 eps eps) #s(literal 1 binary64)) eps)) (cos.f64 (*.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps)))) #<representation binary64>) () ())) ())
#s(alt (* 2 (* (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps)))) (taylor -inf eps) (#s(alt (.f64 #s(approx ( (sin (* 1/2 (+ 0 eps))) 2) (.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -1/322560 binary64) (.f64 eps eps) #s(literal 1/1920 binary64)) (.f64 eps eps) #s(literal -1/24 binary64)) (.f64 eps eps) #s(literal 1 binary64)) eps)) (cos.f64 (.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps)))) (patch (.f64 #s(approx (* (sin (* 1/2 (+ 0 eps))) 2) (.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -1/322560 binary64) (.f64 eps eps) #s(literal 1/1920 binary64)) (.f64 eps eps) #s(literal -1/24 binary64)) (.f64 eps eps) #s(literal 1 binary64)) eps)) (cos.f64 (*.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps)))) #<representation binary64>) () ())) ())
#s(alt (* 2 (* (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps)))) (taylor -inf eps) (#s(alt (.f64 #s(approx ( (sin (* 1/2 (+ 0 eps))) 2) (.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -1/322560 binary64) (.f64 eps eps) #s(literal 1/1920 binary64)) (.f64 eps eps) #s(literal -1/24 binary64)) (.f64 eps eps) #s(literal 1 binary64)) eps)) (cos.f64 (.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps)))) (patch (.f64 #s(approx (* (sin (* 1/2 (+ 0 eps))) 2) (.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -1/322560 binary64) (.f64 eps eps) #s(literal 1/1920 binary64)) (.f64 eps eps) #s(literal -1/24 binary64)) (.f64 eps eps) #s(literal 1 binary64)) eps)) (cos.f64 (*.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps)))) #<representation binary64>) () ())) ())
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#s(alt (* eps (+ 1/24 (* -1/720 (pow x 2)))) (taylor -inf eps) (#s(alt (.f64 eps (fma.f64 #s(literal -1/720 binary64) (.f64 x x) #s(literal 1/24 binary64))) (patch (.f64 eps (fma.f64 #s(literal -1/720 binary64) (.f64 x x) #s(literal 1/24 binary64))) #<representation binary64>) () ())) ())
#s(alt (* eps (+ 1/24 (* -1/720 (pow x 2)))) (taylor -inf eps) (#s(alt (.f64 eps (fma.f64 #s(literal -1/720 binary64) (.f64 x x) #s(literal 1/24 binary64))) (patch (.f64 eps (fma.f64 #s(literal -1/720 binary64) (.f64 x x) #s(literal 1/24 binary64))) #<representation binary64>) () ())) ())
#s(alt (* eps (+ 1/24 (* -1/720 (pow x 2)))) (taylor -inf eps) (#s(alt (.f64 eps (fma.f64 #s(literal -1/720 binary64) (.f64 x x) #s(literal 1/24 binary64))) (patch (.f64 eps (fma.f64 #s(literal -1/720 binary64) (.f64 x x) #s(literal 1/24 binary64))) #<representation binary64>) () ())) ())
#s(alt (* 1/24 eps) (taylor 0 x) (#s(alt (.f64 eps (fma.f64 #s(literal -1/720 binary64) (.f64 x x) #s(literal 1/24 binary64))) (patch (.f64 eps (fma.f64 #s(literal -1/720 binary64) (.f64 x x) #s(literal 1/24 binary64))) #<representation binary64>) () ())) ())
#s(alt (+ (* -1/720 (* eps (pow x 2))) (* 1/24 eps)) (taylor 0 x) (#s(alt (.f64 eps (fma.f64 #s(literal -1/720 binary64) (.f64 x x) #s(literal 1/24 binary64))) (patch (.f64 eps (fma.f64 #s(literal -1/720 binary64) (.f64 x x) #s(literal 1/24 binary64))) #<representation binary64>) () ())) ())
#s(alt (+ (* -1/720 (* eps (pow x 2))) (* 1/24 eps)) (taylor 0 x) (#s(alt (.f64 eps (fma.f64 #s(literal -1/720 binary64) (.f64 x x) #s(literal 1/24 binary64))) (patch (.f64 eps (fma.f64 #s(literal -1/720 binary64) (.f64 x x) #s(literal 1/24 binary64))) #<representation binary64>) () ())) ())
#s(alt (+ (* -1/720 (* eps (pow x 2))) (* 1/24 eps)) (taylor 0 x) (#s(alt (.f64 eps (fma.f64 #s(literal -1/720 binary64) (.f64 x x) #s(literal 1/24 binary64))) (patch (.f64 eps (fma.f64 #s(literal -1/720 binary64) (.f64 x x) #s(literal 1/24 binary64))) #<representation binary64>) () ())) ())
#s(alt (* -1/720 (* eps (pow x 2))) (taylor inf x) (#s(alt (.f64 eps (fma.f64 #s(literal -1/720 binary64) (.f64 x x) #s(literal 1/24 binary64))) (patch (.f64 eps (fma.f64 #s(literal -1/720 binary64) (.f64 x x) #s(literal 1/24 binary64))) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (+ (* -1/720 eps) (* 1/24 (/ eps (pow x 2))))) (taylor inf x) (#s(alt (.f64 eps (fma.f64 #s(literal -1/720 binary64) (.f64 x x) #s(literal 1/24 binary64))) (patch (.f64 eps (fma.f64 #s(literal -1/720 binary64) (.f64 x x) #s(literal 1/24 binary64))) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (+ (* -1/720 eps) (* 1/24 (/ eps (pow x 2))))) (taylor inf x) (#s(alt (.f64 eps (fma.f64 #s(literal -1/720 binary64) (.f64 x x) #s(literal 1/24 binary64))) (patch (.f64 eps (fma.f64 #s(literal -1/720 binary64) (.f64 x x) #s(literal 1/24 binary64))) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (+ (* -1/720 eps) (* 1/24 (/ eps (pow x 2))))) (taylor inf x) (#s(alt (.f64 eps (fma.f64 #s(literal -1/720 binary64) (.f64 x x) #s(literal 1/24 binary64))) (patch (.f64 eps (fma.f64 #s(literal -1/720 binary64) (.f64 x x) #s(literal 1/24 binary64))) #<representation binary64>) () ())) ())
#s(alt (* -1/720 (* eps (pow x 2))) (taylor -inf x) (#s(alt (.f64 eps (fma.f64 #s(literal -1/720 binary64) (.f64 x x) #s(literal 1/24 binary64))) (patch (.f64 eps (fma.f64 #s(literal -1/720 binary64) (.f64 x x) #s(literal 1/24 binary64))) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (+ (* -1/720 eps) (* 1/24 (/ eps (pow x 2))))) (taylor -inf x) (#s(alt (.f64 eps (fma.f64 #s(literal -1/720 binary64) (.f64 x x) #s(literal 1/24 binary64))) (patch (.f64 eps (fma.f64 #s(literal -1/720 binary64) (.f64 x x) #s(literal 1/24 binary64))) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (+ (* -1/720 eps) (* 1/24 (/ eps (pow x 2))))) (taylor -inf x) (#s(alt (.f64 eps (fma.f64 #s(literal -1/720 binary64) (.f64 x x) #s(literal 1/24 binary64))) (patch (.f64 eps (fma.f64 #s(literal -1/720 binary64) (.f64 x x) #s(literal 1/24 binary64))) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (+ (* -1/720 eps) (* 1/24 (/ eps (pow x 2))))) (taylor -inf x) (#s(alt (.f64 eps (fma.f64 #s(literal -1/720 binary64) (.f64 x x) #s(literal 1/24 binary64))) (patch (.f64 eps (fma.f64 #s(literal -1/720 binary64) (.f64 x x) #s(literal 1/24 binary64))) #<representation binary64>) () ())) ())
#s(alt 1/24 (taylor 0 x) (#s(alt (fma.f64 #s(literal -1/720 binary64) (.f64 x x) #s(literal 1/24 binary64)) (patch (fma.f64 #s(literal -1/720 binary64) (.f64 x x) #s(literal 1/24 binary64)) #<representation binary64>) () ())) ())
#s(alt (+ 1/24 (* -1/720 (pow x 2))) (taylor 0 x) (#s(alt (fma.f64 #s(literal -1/720 binary64) (.f64 x x) #s(literal 1/24 binary64)) (patch (fma.f64 #s(literal -1/720 binary64) (.f64 x x) #s(literal 1/24 binary64)) #<representation binary64>) () ())) ())
#s(alt (+ 1/24 (* -1/720 (pow x 2))) (taylor 0 x) (#s(alt (fma.f64 #s(literal -1/720 binary64) (.f64 x x) #s(literal 1/24 binary64)) (patch (fma.f64 #s(literal -1/720 binary64) (.f64 x x) #s(literal 1/24 binary64)) #<representation binary64>) () ())) ())
#s(alt (+ 1/24 (* -1/720 (pow x 2))) (taylor 0 x) (#s(alt (fma.f64 #s(literal -1/720 binary64) (.f64 x x) #s(literal 1/24 binary64)) (patch (fma.f64 #s(literal -1/720 binary64) (.f64 x x) #s(literal 1/24 binary64)) #<representation binary64>) () ())) ())
#s(alt (* -1/720 (pow x 2)) (taylor inf x) (#s(alt (fma.f64 #s(literal -1/720 binary64) (.f64 x x) #s(literal 1/24 binary64)) (patch (fma.f64 #s(literal -1/720 binary64) (.f64 x x) #s(literal 1/24 binary64)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (- (* 1/24 (/ 1 (pow x 2))) 1/720)) (taylor inf x) (#s(alt (fma.f64 #s(literal -1/720 binary64) (.f64 x x) #s(literal 1/24 binary64)) (patch (fma.f64 #s(literal -1/720 binary64) (.f64 x x) #s(literal 1/24 binary64)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (- (* 1/24 (/ 1 (pow x 2))) 1/720)) (taylor inf x) (#s(alt (fma.f64 #s(literal -1/720 binary64) (.f64 x x) #s(literal 1/24 binary64)) (patch (fma.f64 #s(literal -1/720 binary64) (.f64 x x) #s(literal 1/24 binary64)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (- (* 1/24 (/ 1 (pow x 2))) 1/720)) (taylor inf x) (#s(alt (fma.f64 #s(literal -1/720 binary64) (.f64 x x) #s(literal 1/24 binary64)) (patch (fma.f64 #s(literal -1/720 binary64) (.f64 x x) #s(literal 1/24 binary64)) #<representation binary64>) () ())) ())
#s(alt (* -1/720 (pow x 2)) (taylor -inf x) (#s(alt (fma.f64 #s(literal -1/720 binary64) (.f64 x x) #s(literal 1/24 binary64)) (patch (fma.f64 #s(literal -1/720 binary64) (.f64 x x) #s(literal 1/24 binary64)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (- (* 1/24 (/ 1 (pow x 2))) 1/720)) (taylor -inf x) (#s(alt (fma.f64 #s(literal -1/720 binary64) (.f64 x x) #s(literal 1/24 binary64)) (patch (fma.f64 #s(literal -1/720 binary64) (.f64 x x) #s(literal 1/24 binary64)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (- (* 1/24 (/ 1 (pow x 2))) 1/720)) (taylor -inf x) (#s(alt (fma.f64 #s(literal -1/720 binary64) (.f64 x x) #s(literal 1/24 binary64)) (patch (fma.f64 #s(literal -1/720 binary64) (.f64 x x) #s(literal 1/24 binary64)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (- (* 1/24 (/ 1 (pow x 2))) 1/720)) (taylor -inf x) (#s(alt (fma.f64 #s(literal -1/720 binary64) (.f64 x x) #s(literal 1/24 binary64)) (patch (fma.f64 #s(literal -1/720 binary64) (.f64 x x) #s(literal 1/24 binary64)) #<representation binary64>) () ())) ())

Calls

120 calls:

Time	Variable		Point	Expression
5.0ms	eps	@	-inf	(+ (* (+ (* (+ (* 1/12 (* x eps)) -1/2) x) (* -1/2 eps)) x) 1)
1.0ms	eps	@	0	(+ (* (* eps (+ (* -1/720 (* x x)) 1/24)) (* x x)) (* -1/2 eps))
1.0ms	eps	@	0	(+ (* (* -1/2 x) (* x eps)) eps)
1.0ms	x	@	-inf	(+ (* (+ (* (+ (* 1/12 (* x eps)) -1/2) x) (* -1/2 eps)) x) 1)
1.0ms	eps	@	inf	(+ (* (+ (* (+ (* 1/12 (* x eps)) -1/2) x) (* -1/2 eps)) x) 1)

simplify236.0ms (1.9%)

Memory

0.8MiB live, 149.3MiB allocated

Algorithm

1×	egg-herbie

Rules

13 214×	`lower-fma.f64`
13 214×	`lower-fma.f32`
6 790×	`lower-*.f64`
6 790×	`lower-*.f32`
4 032×	`lower-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	412	5221
1	1267	5028
2	3712	4916
0	8390	4512

Stop Event

1×	iter limit
1×	node limit

Counts

480 → 468

Calls

Call 1

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

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

rewrite300.0ms (2.4%)

Memory

31.5MiB live, 186.9MiB allocated

Rules

5 308×	`lower-fma.f32`
5 284×	`lower-fma.f64`
5 210×	`lower-*.f32`
5 186×	`lower-*.f64`
3 240×	`lower-/.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	59	404
0	96	396
1	379	392
2	3329	392
0	8626	385

Stop Event

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

Counts

23 → 497

Calls

Call 1

Inputs
(*.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps))
(.f64 #s(approx ( (sin (* 1/2 (+ 0 eps))) 2) (.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -1/322560 binary64) (.f64 eps eps) #s(literal 1/1920 binary64)) (.f64 eps eps) #s(literal -1/24 binary64)) (.f64 eps eps) #s(literal 1 binary64)) eps)) (cos.f64 (*.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps))))
#s(approx (* (sin (* 1/2 (+ 0 eps))) 2) (.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -1/322560 binary64) (.f64 eps eps) #s(literal 1/1920 binary64)) (.f64 eps eps) #s(literal -1/24 binary64)) (.f64 eps eps) #s(literal 1 binary64)) eps))
(.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -1/322560 binary64) (.f64 eps eps) #s(literal 1/1920 binary64)) (.f64 eps eps) #s(literal -1/24 binary64)) (.f64 eps eps) #s(literal 1 binary64)) eps)
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (cos x) eps) (fma.f64 (.f64 #s(literal -1/2 binary64) x) (.f64 x eps) eps)))
#s(approx (* (cos x) eps) (fma.f64 (.f64 #s(literal -1/2 binary64) x) (.f64 x eps) eps))
(fma.f64 (.f64 #s(literal -1/2 binary64) x) (.f64 x eps) eps)
(*.f64 #s(literal -1/2 binary64) x)
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (* (sin x) -1/2) eps) (cos x)) (fma.f64 (fma.f64 (fma.f64 #s(literal 1/12 binary64) (.f64 x eps) #s(literal -1/2 binary64)) x (.f64 #s(literal -1/2 binary64) eps)) x #s(literal 1 binary64))) eps))
(.f64 #s(approx (+ ( (* (sin x) -1/2) eps) (cos x)) (fma.f64 (fma.f64 (fma.f64 #s(literal 1/12 binary64) (.f64 x eps) #s(literal -1/2 binary64)) x (.f64 #s(literal -1/2 binary64) eps)) x #s(literal 1 binary64))) eps)
#s(approx (+ (* (* (sin x) -1/2) eps) (cos x)) (fma.f64 (fma.f64 (fma.f64 #s(literal 1/12 binary64) (.f64 x eps) #s(literal -1/2 binary64)) x (.f64 #s(literal -1/2 binary64) eps)) x #s(literal 1 binary64)))
(fma.f64 (fma.f64 (fma.f64 #s(literal 1/12 binary64) (.f64 x eps) #s(literal -1/2 binary64)) x (.f64 #s(literal -1/2 binary64) eps)) x #s(literal 1 binary64))
(fma.f64 (.f64 eps (fma.f64 #s(literal -1/720 binary64) (.f64 x x) #s(literal 1/24 binary64))) (.f64 x x) (.f64 #s(literal -1/2 binary64) eps))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (cos x) eps) (fma.f64 (fma.f64 (.f64 eps (fma.f64 #s(literal -1/720 binary64) (.f64 x x) #s(literal 1/24 binary64))) (.f64 x x) (.f64 #s(literal -1/2 binary64) eps)) (*.f64 x x) eps)))
#s(approx (* (cos x) eps) (fma.f64 (fma.f64 (.f64 eps (fma.f64 #s(literal -1/720 binary64) (.f64 x x) #s(literal 1/24 binary64))) (.f64 x x) (.f64 #s(literal -1/2 binary64) eps)) (*.f64 x x) eps))
(fma.f64 (fma.f64 (.f64 eps (fma.f64 #s(literal -1/720 binary64) (.f64 x x) #s(literal 1/24 binary64))) (.f64 x x) (.f64 #s(literal -1/2 binary64) eps)) (*.f64 x x) eps)
(.f64 #s(approx ( (sin (* 1/2 (+ 0 eps))) 2) (.f64 (fma.f64 (.f64 eps eps) #s(literal -1/24 binary64) #s(literal 1 binary64)) eps)) (cos.f64 (*.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps))))
#s(approx (* (sin (* 1/2 (+ 0 eps))) 2) (.f64 (fma.f64 (.f64 eps eps) #s(literal -1/24 binary64) #s(literal 1 binary64)) eps))
(.f64 (fma.f64 (.f64 eps eps) #s(literal -1/24 binary64) #s(literal 1 binary64)) eps)
(cos.f64 (*.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps)))
(fma.f64 (fma.f64 #s(literal 1/12 binary64) (.f64 x eps) #s(literal -1/2 binary64)) x (.f64 #s(literal -1/2 binary64) eps))
(.f64 eps (fma.f64 #s(literal -1/720 binary64) (.f64 x x) #s(literal 1/24 binary64)))
(fma.f64 #s(literal -1/720 binary64) (*.f64 x x) #s(literal 1/24 binary64))

Outputs
(*.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64))
(*.f64 #s(literal 1/2 binary64) (fma.f64 x #s(literal 2 binary64) eps))
(/.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) (.f64 (.f64 x x) x) (.f64 (.f64 eps eps) eps)) #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 (.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 4 binary64) (.f64 x x) (*.f64 (neg.f64 eps) eps))) (fma.f64 x #s(literal 2 binary64) (neg.f64 eps)))
(/.f64 (.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 8 binary64) (.f64 (.f64 x x) x) (.f64 (.f64 eps eps) eps))) (fma.f64 #s(literal 4 binary64) (.f64 x x) (.f64 eps (-.f64 eps (.f64 x #s(literal 2 binary64))))))
(/.f64 (-.f64 (.f64 (.f64 #s(literal 1 binary64) x) (.f64 #s(literal 1 binary64) x)) (.f64 (.f64 eps #s(literal 1/2 binary64)) (.f64 eps #s(literal 1/2 binary64)))) (-.f64 (.f64 #s(literal 1 binary64) x) (.f64 eps #s(literal 1/2 binary64))))
(/.f64 (fma.f64 (.f64 (.f64 x x) x) #s(literal 1 binary64) (.f64 #s(literal 1/8 binary64) (.f64 (.f64 eps eps) eps))) (fma.f64 (.f64 #s(literal 1 binary64) x) (.f64 #s(literal 1 binary64) x) (-.f64 (.f64 (.f64 eps #s(literal 1/2 binary64)) (.f64 eps #s(literal 1/2 binary64))) (.f64 (.f64 #s(literal 1 binary64) x) (*.f64 eps #s(literal 1/2 binary64))))))
(fma.f64 (.f64 #s(literal 1/2 binary64) x) #s(literal 2 binary64) (.f64 eps #s(literal 1/2 binary64)))
(fma.f64 (.f64 x #s(literal 2 binary64)) #s(literal 1/2 binary64) (.f64 eps #s(literal 1/2 binary64)))
(fma.f64 #s(literal 1 binary64) x (*.f64 eps #s(literal 1/2 binary64)))
(fma.f64 eps #s(literal 1/2 binary64) (*.f64 #s(literal 1 binary64) x))
(fma.f64 x #s(literal 1 binary64) (*.f64 eps #s(literal 1/2 binary64)))
(fma.f64 #s(literal 2 binary64) (.f64 x #s(literal 1/2 binary64)) (.f64 eps #s(literal 1/2 binary64)))
(fma.f64 #s(literal 1/2 binary64) (.f64 x #s(literal 2 binary64)) (.f64 eps #s(literal 1/2 binary64)))
(fma.f64 #s(literal 1/2 binary64) eps (*.f64 #s(literal 1 binary64) x))
(+.f64 (fma.f64 #s(literal 1 binary64) x #s(literal 0 binary64)) (*.f64 eps #s(literal 1/2 binary64)))
(+.f64 (.f64 #s(literal 1 binary64) x) (.f64 eps #s(literal 1/2 binary64)))
(+.f64 (.f64 eps #s(literal 1/2 binary64)) (.f64 #s(literal 1 binary64) x))
(.f64 (cos.f64 (.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64))) #s(approx (* (sin (* 1/2 (+ 0 eps))) 2) (.f64 (fma.f64 (fma.f64 (fma.f64 (.f64 eps eps) #s(literal -1/322560 binary64) #s(literal 1/1920 binary64)) (.f64 eps eps) #s(literal -1/24 binary64)) (.f64 eps eps) #s(literal 1 binary64)) eps)))
(.f64 #s(approx ( (sin (* 1/2 (+ 0 eps))) 2) (.f64 (fma.f64 (fma.f64 (fma.f64 (.f64 eps eps) #s(literal -1/322560 binary64) #s(literal 1/1920 binary64)) (.f64 eps eps) #s(literal -1/24 binary64)) (.f64 eps eps) #s(literal 1 binary64)) eps)) (cos.f64 (*.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64))))
#s(approx (* (sin (* 1/2 (+ 0 eps))) 2) (.f64 (fma.f64 (fma.f64 (fma.f64 (.f64 eps eps) #s(literal -1/322560 binary64) #s(literal 1/1920 binary64)) (.f64 eps eps) #s(literal -1/24 binary64)) (.f64 eps eps) #s(literal 1 binary64)) eps))
(.f64 (fma.f64 (fma.f64 (fma.f64 (.f64 eps eps) #s(literal -1/322560 binary64) #s(literal 1/1920 binary64)) (.f64 eps eps) #s(literal -1/24 binary64)) (.f64 eps eps) #s(literal 1 binary64)) eps)
(.f64 eps (fma.f64 (fma.f64 (fma.f64 (.f64 eps eps) #s(literal -1/322560 binary64) #s(literal 1/1920 binary64)) (.f64 eps eps) #s(literal -1/24 binary64)) (.f64 eps eps) #s(literal 1 binary64)))
(/.f64 (.f64 (fma.f64 (.f64 (.f64 (fma.f64 (fma.f64 (.f64 eps eps) #s(literal -1/322560 binary64) #s(literal 1/1920 binary64)) (.f64 eps eps) #s(literal -1/24 binary64)) eps) (.f64 (fma.f64 (fma.f64 (.f64 eps eps) #s(literal -1/322560 binary64) #s(literal 1/1920 binary64)) (.f64 eps eps) #s(literal -1/24 binary64)) eps)) (.f64 eps eps) #s(literal -1 binary64)) eps) (fma.f64 (fma.f64 (fma.f64 (.f64 eps eps) #s(literal -1/322560 binary64) #s(literal 1/1920 binary64)) (.f64 eps eps) #s(literal -1/24 binary64)) (.f64 eps eps) #s(literal -1 binary64)))
(/.f64 (.f64 (fma.f64 (.f64 (.f64 (.f64 (fma.f64 (fma.f64 (.f64 eps eps) #s(literal -1/322560 binary64) #s(literal 1/1920 binary64)) (.f64 eps eps) #s(literal -1/24 binary64)) eps) (.f64 (fma.f64 (fma.f64 (.f64 eps eps) #s(literal -1/322560 binary64) #s(literal 1/1920 binary64)) (.f64 eps eps) #s(literal -1/24 binary64)) eps)) (.f64 (fma.f64 (fma.f64 (.f64 eps eps) #s(literal -1/322560 binary64) #s(literal 1/1920 binary64)) (.f64 eps eps) #s(literal -1/24 binary64)) eps)) (.f64 (.f64 eps eps) eps) #s(literal 1 binary64)) eps) (fma.f64 (.f64 (.f64 (fma.f64 (fma.f64 (.f64 eps eps) #s(literal -1/322560 binary64) #s(literal 1/1920 binary64)) (.f64 eps eps) #s(literal -1/24 binary64)) eps) (.f64 (fma.f64 (fma.f64 (.f64 eps eps) #s(literal -1/322560 binary64) #s(literal 1/1920 binary64)) (.f64 eps eps) #s(literal -1/24 binary64)) eps)) (.f64 eps eps) (-.f64 #s(literal 1 binary64) (.f64 (.f64 (fma.f64 (fma.f64 (.f64 eps eps) #s(literal -1/322560 binary64) #s(literal 1/1920 binary64)) (.f64 eps eps) #s(literal -1/24 binary64)) eps) eps))))
(/.f64 (.f64 (neg.f64 (.f64 eps eps)) (fma.f64 (fma.f64 (fma.f64 (.f64 eps eps) #s(literal -1/322560 binary64) #s(literal 1/1920 binary64)) (.f64 eps eps) #s(literal -1/24 binary64)) (*.f64 eps eps) #s(literal 1 binary64))) (neg.f64 eps))
(/.f64 (.f64 (.f64 (.f64 eps eps) eps) (fma.f64 (fma.f64 (fma.f64 (.f64 eps eps) #s(literal -1/322560 binary64) #s(literal 1/1920 binary64)) (.f64 eps eps) #s(literal -1/24 binary64)) (.f64 eps eps) #s(literal 1 binary64))) (*.f64 eps eps))
(/.f64 (.f64 (fma.f64 (fma.f64 (fma.f64 (.f64 eps eps) #s(literal -1/322560 binary64) #s(literal 1/1920 binary64)) (.f64 eps eps) #s(literal -1/24 binary64)) (.f64 eps eps) #s(literal 1 binary64)) (neg.f64 (*.f64 eps eps))) (neg.f64 eps))
(/.f64 (.f64 (fma.f64 (fma.f64 (fma.f64 (.f64 eps eps) #s(literal -1/322560 binary64) #s(literal 1/1920 binary64)) (.f64 eps eps) #s(literal -1/24 binary64)) (.f64 eps eps) #s(literal 1 binary64)) (.f64 (.f64 eps eps) eps)) (*.f64 eps eps))
(/.f64 (.f64 eps (fma.f64 (.f64 (.f64 (fma.f64 (fma.f64 (.f64 eps eps) #s(literal -1/322560 binary64) #s(literal 1/1920 binary64)) (.f64 eps eps) #s(literal -1/24 binary64)) eps) (.f64 (fma.f64 (fma.f64 (.f64 eps eps) #s(literal -1/322560 binary64) #s(literal 1/1920 binary64)) (.f64 eps eps) #s(literal -1/24 binary64)) eps)) (.f64 eps eps) #s(literal -1 binary64))) (fma.f64 (fma.f64 (fma.f64 (.f64 eps eps) #s(literal -1/322560 binary64) #s(literal 1/1920 binary64)) (.f64 eps eps) #s(literal -1/24 binary64)) (.f64 eps eps) #s(literal -1 binary64)))
(/.f64 (.f64 eps (fma.f64 (.f64 (.f64 (.f64 (fma.f64 (fma.f64 (.f64 eps eps) #s(literal -1/322560 binary64) #s(literal 1/1920 binary64)) (.f64 eps eps) #s(literal -1/24 binary64)) eps) (.f64 (fma.f64 (fma.f64 (.f64 eps eps) #s(literal -1/322560 binary64) #s(literal 1/1920 binary64)) (.f64 eps eps) #s(literal -1/24 binary64)) eps)) (.f64 (fma.f64 (fma.f64 (.f64 eps eps) #s(literal -1/322560 binary64) #s(literal 1/1920 binary64)) (.f64 eps eps) #s(literal -1/24 binary64)) eps)) (.f64 (.f64 eps eps) eps) #s(literal 1 binary64))) (fma.f64 (.f64 (.f64 (fma.f64 (fma.f64 (.f64 eps eps) #s(literal -1/322560 binary64) #s(literal 1/1920 binary64)) (.f64 eps eps) #s(literal -1/24 binary64)) eps) (.f64 (fma.f64 (fma.f64 (.f64 eps eps) #s(literal -1/322560 binary64) #s(literal 1/1920 binary64)) (.f64 eps eps) #s(literal -1/24 binary64)) eps)) (.f64 eps eps) (-.f64 #s(literal 1 binary64) (.f64 (.f64 (fma.f64 (fma.f64 (.f64 eps eps) #s(literal -1/322560 binary64) #s(literal 1/1920 binary64)) (.f64 eps eps) #s(literal -1/24 binary64)) eps) eps))))
(/.f64 (.f64 (fma.f64 (.f64 (.f64 (fma.f64 (fma.f64 (.f64 eps eps) #s(literal -1/322560 binary64) #s(literal 1/1920 binary64)) (.f64 eps eps) #s(literal -1/24 binary64)) eps) (.f64 (fma.f64 (fma.f64 (.f64 eps eps) #s(literal -1/322560 binary64) #s(literal 1/1920 binary64)) (.f64 eps eps) #s(literal -1/24 binary64)) eps)) (.f64 eps eps) #s(literal -1 binary64)) (neg.f64 (.f64 eps eps))) (.f64 (fma.f64 (fma.f64 (fma.f64 (.f64 eps eps) #s(literal -1/322560 binary64) #s(literal 1/1920 binary64)) (.f64 eps eps) #s(literal -1/24 binary64)) (.f64 eps eps) #s(literal -1 binary64)) (neg.f64 eps)))
(/.f64 (.f64 (fma.f64 (.f64 (.f64 (fma.f64 (fma.f64 (.f64 eps eps) #s(literal -1/322560 binary64) #s(literal 1/1920 binary64)) (.f64 eps eps) #s(literal -1/24 binary64)) eps) (.f64 (fma.f64 (fma.f64 (.f64 eps eps) #s(literal -1/322560 binary64) #s(literal 1/1920 binary64)) (.f64 eps eps) #s(literal -1/24 binary64)) eps)) (.f64 eps eps) #s(literal -1 binary64)) (.f64 (.f64 eps eps) eps)) (.f64 (fma.f64 (fma.f64 (fma.f64 (.f64 eps eps) #s(literal -1/322560 binary64) #s(literal 1/1920 binary64)) (.f64 eps eps) #s(literal -1/24 binary64)) (.f64 eps eps) #s(literal -1 binary64)) (.f64 eps eps)))
(/.f64 (.f64 (fma.f64 (.f64 (.f64 (.f64 (fma.f64 (fma.f64 (.f64 eps eps) #s(literal -1/322560 binary64) #s(literal 1/1920 binary64)) (.f64 eps eps) #s(literal -1/24 binary64)) eps) (.f64 (fma.f64 (fma.f64 (.f64 eps eps) #s(literal -1/322560 binary64) #s(literal 1/1920 binary64)) (.f64 eps eps) #s(literal -1/24 binary64)) eps)) (.f64 (fma.f64 (fma.f64 (.f64 eps eps) #s(literal -1/322560 binary64) #s(literal 1/1920 binary64)) (.f64 eps eps) #s(literal -1/24 binary64)) eps)) (.f64 (.f64 eps eps) eps) #s(literal 1 binary64)) (neg.f64 (.f64 eps eps))) (.f64 (fma.f64 (.f64 (.f64 (fma.f64 (fma.f64 (.f64 eps eps) #s(literal -1/322560 binary64) #s(literal 1/1920 binary64)) (.f64 eps eps) #s(literal -1/24 binary64)) eps) (.f64 (fma.f64 (fma.f64 (.f64 eps eps) #s(literal -1/322560 binary64) #s(literal 1/1920 binary64)) (.f64 eps eps) #s(literal -1/24 binary64)) eps)) (.f64 eps eps) (-.f64 #s(literal 1 binary64) (.f64 (.f64 (fma.f64 (fma.f64 (.f64 eps eps) #s(literal -1/322560 binary64) #s(literal 1/1920 binary64)) (.f64 eps eps) #s(literal -1/24 binary64)) eps) eps))) (neg.f64 eps)))
(/.f64 (.f64 (fma.f64 (.f64 (.f64 (.f64 (fma.f64 (fma.f64 (.f64 eps eps) #s(literal -1/322560 binary64) #s(literal 1/1920 binary64)) (.f64 eps eps) #s(literal -1/24 binary64)) eps) (.f64 (fma.f64 (fma.f64 (.f64 eps eps) #s(literal -1/322560 binary64) #s(literal 1/1920 binary64)) (.f64 eps eps) #s(literal -1/24 binary64)) eps)) (.f64 (fma.f64 (fma.f64 (.f64 eps eps) #s(literal -1/322560 binary64) #s(literal 1/1920 binary64)) (.f64 eps eps) #s(literal -1/24 binary64)) eps)) (.f64 (.f64 eps eps) eps) #s(literal 1 binary64)) (.f64 (.f64 eps eps) eps)) (.f64 (fma.f64 (.f64 (.f64 (fma.f64 (fma.f64 (.f64 eps eps) #s(literal -1/322560 binary64) #s(literal 1/1920 binary64)) (.f64 eps eps) #s(literal -1/24 binary64)) eps) (.f64 (fma.f64 (fma.f64 (.f64 eps eps) #s(literal -1/322560 binary64) #s(literal 1/1920 binary64)) (.f64 eps eps) #s(literal -1/24 binary64)) eps)) (.f64 eps eps) (-.f64 #s(literal 1 binary64) (.f64 (.f64 (fma.f64 (fma.f64 (.f64 eps eps) #s(literal -1/322560 binary64) #s(literal 1/1920 binary64)) (.f64 eps eps) #s(literal -1/24 binary64)) eps) eps))) (.f64 eps eps)))
(/.f64 (.f64 (neg.f64 (.f64 eps eps)) (fma.f64 (.f64 (.f64 (fma.f64 (fma.f64 (.f64 eps eps) #s(literal -1/322560 binary64) #s(literal 1/1920 binary64)) (.f64 eps eps) #s(literal -1/24 binary64)) eps) (.f64 (fma.f64 (fma.f64 (.f64 eps eps) #s(literal -1/322560 binary64) #s(literal 1/1920 binary64)) (.f64 eps eps) #s(literal -1/24 binary64)) eps)) (.f64 eps eps) #s(literal -1 binary64))) (.f64 (neg.f64 eps) (fma.f64 (fma.f64 (fma.f64 (.f64 eps eps) #s(literal -1/322560 binary64) #s(literal 1/1920 binary64)) (.f64 eps eps) #s(literal -1/24 binary64)) (.f64 eps eps) #s(literal -1 binary64))))
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(fma.f64 (fma.f64 (.f64 x x) #s(literal -1/720 binary64) #s(literal 1/24 binary64)) eps (.f64 #s(literal 0 binary64) (fma.f64 (*.f64 x x) #s(literal -1/720 binary64) #s(literal 1/24 binary64))))
(fma.f64 (fma.f64 (.f64 x x) #s(literal -1/720 binary64) #s(literal 1/24 binary64)) eps (.f64 (fma.f64 (*.f64 x x) #s(literal -1/720 binary64) #s(literal 1/24 binary64)) #s(literal 0 binary64)))
(fma.f64 #s(literal 1/24 binary64) eps (.f64 (.f64 (*.f64 x x) #s(literal -1/720 binary64)) eps))
(fma.f64 (.f64 x x) (.f64 #s(literal -1/720 binary64) eps) (*.f64 #s(literal 1/24 binary64) eps))
(fma.f64 #s(literal -1/720 binary64) (.f64 (.f64 x x) eps) (*.f64 #s(literal 1/24 binary64) eps))
(fma.f64 #s(literal 0 binary64) (fma.f64 (.f64 x x) #s(literal -1/720 binary64) #s(literal 1/24 binary64)) (.f64 (fma.f64 (*.f64 x x) #s(literal -1/720 binary64) #s(literal 1/24 binary64)) eps))
(fma.f64 eps (.f64 (.f64 x x) #s(literal -1/720 binary64)) (*.f64 #s(literal 1/24 binary64) eps))
(fma.f64 eps (fma.f64 (.f64 x x) #s(literal -1/720 binary64) #s(literal 1/24 binary64)) (.f64 #s(literal 0 binary64) (fma.f64 (*.f64 x x) #s(literal -1/720 binary64) #s(literal 1/24 binary64))))
(fma.f64 eps (fma.f64 (.f64 x x) #s(literal -1/720 binary64) #s(literal 1/24 binary64)) (.f64 (fma.f64 (*.f64 x x) #s(literal -1/720 binary64) #s(literal 1/24 binary64)) #s(literal 0 binary64)))
(fma.f64 eps #s(literal 1/24 binary64) (.f64 (.f64 (*.f64 x x) #s(literal -1/720 binary64)) eps))
(+.f64 (.f64 #s(literal 0 binary64) (fma.f64 (.f64 x x) #s(literal -1/720 binary64) #s(literal 1/24 binary64))) (.f64 (fma.f64 (.f64 x x) #s(literal -1/720 binary64) #s(literal 1/24 binary64)) eps))
(+.f64 (.f64 (fma.f64 (.f64 x x) #s(literal -1/720 binary64) #s(literal 1/24 binary64)) #s(literal 0 binary64)) (.f64 (fma.f64 (.f64 x x) #s(literal -1/720 binary64) #s(literal 1/24 binary64)) eps))
(+.f64 (.f64 (.f64 (.f64 x x) #s(literal -1/720 binary64)) eps) (.f64 #s(literal 1/24 binary64) eps))
(+.f64 (.f64 #s(literal 1/24 binary64) eps) (.f64 (.f64 (.f64 x x) #s(literal -1/720 binary64)) eps))
(+.f64 (.f64 (fma.f64 (.f64 x x) #s(literal -1/720 binary64) #s(literal 1/24 binary64)) eps) (.f64 #s(literal 0 binary64) (fma.f64 (.f64 x x) #s(literal -1/720 binary64) #s(literal 1/24 binary64))))
(+.f64 (.f64 (fma.f64 (.f64 x x) #s(literal -1/720 binary64) #s(literal 1/24 binary64)) eps) (.f64 (fma.f64 (.f64 x x) #s(literal -1/720 binary64) #s(literal 1/24 binary64)) #s(literal 0 binary64)))
(.f64 (fma.f64 #s(literal 1/518400 binary64) (.f64 (.f64 x x) (.f64 x x)) #s(literal -1/576 binary64)) (/.f64 #s(literal 1 binary64) (fma.f64 (*.f64 x x) #s(literal -1/720 binary64) #s(literal -1/24 binary64))))
(.f64 (fma.f64 (.f64 #s(literal -1/373248000 binary64) (.f64 (.f64 x x) x)) (.f64 (.f64 x x) x) #s(literal 1/13824 binary64)) (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/518400 binary64) (.f64 (.f64 x x) (.f64 x x)) (-.f64 #s(literal 1/576 binary64) (.f64 (*.f64 x x) #s(literal -1/17280 binary64))))))
(pow.f64 (/.f64 (fma.f64 (.f64 x x) #s(literal -1/720 binary64) #s(literal -1/24 binary64)) (fma.f64 #s(literal 1/518400 binary64) (.f64 (.f64 x x) (.f64 x x)) #s(literal -1/576 binary64))) #s(literal -1 binary64))
(pow.f64 (/.f64 (fma.f64 #s(literal 1/518400 binary64) (.f64 (.f64 x x) (.f64 x x)) (-.f64 #s(literal 1/576 binary64) (.f64 (.f64 x x) #s(literal -1/17280 binary64)))) (fma.f64 (.f64 #s(literal -1/373248000 binary64) (.f64 (.f64 x x) x)) (.f64 (.f64 x x) x) #s(literal 1/13824 binary64))) #s(literal -1 binary64))
(/.f64 (-.f64 (.f64 (.f64 #s(literal 1/518400 binary64) (.f64 (.f64 x x) (.f64 x x))) (fma.f64 (.f64 x x) #s(literal -1/720 binary64) #s(literal -1/24 binary64))) (.f64 (fma.f64 (.f64 x x) #s(literal -1/720 binary64) #s(literal -1/24 binary64)) #s(literal 1/576 binary64))) (.f64 (fma.f64 (.f64 x x) #s(literal -1/720 binary64) #s(literal -1/24 binary64)) (fma.f64 (*.f64 x x) #s(literal -1/720 binary64) #s(literal -1/24 binary64))))
(/.f64 (-.f64 #s(literal 1/576 binary64) (.f64 #s(literal 1/518400 binary64) (.f64 (.f64 x x) (.f64 x x)))) (-.f64 #s(literal 1/24 binary64) (.f64 (.f64 x x) #s(literal -1/720 binary64))))
(/.f64 (neg.f64 (fma.f64 #s(literal 1/518400 binary64) (.f64 (.f64 x x) (.f64 x x)) #s(literal -1/576 binary64))) (neg.f64 (fma.f64 (.f64 x x) #s(literal -1/720 binary64) #s(literal -1/24 binary64))))
(/.f64 (neg.f64 (fma.f64 (.f64 #s(literal -1/373248000 binary64) (.f64 (.f64 x x) x)) (.f64 (.f64 x x) x) #s(literal 1/13824 binary64))) (neg.f64 (fma.f64 #s(literal 1/518400 binary64) (.f64 (.f64 x x) (.f64 x x)) (-.f64 #s(literal 1/576 binary64) (.f64 (.f64 x x) #s(literal -1/17280 binary64))))))
(/.f64 (fma.f64 #s(literal 1/518400 binary64) (.f64 (.f64 x x) (.f64 x x)) #s(literal -1/576 binary64)) (fma.f64 (.f64 x x) #s(literal -1/720 binary64) #s(literal -1/24 binary64)))
(/.f64 (fma.f64 (.f64 #s(literal -1/373248000 binary64) (.f64 (.f64 x x) x)) (.f64 (.f64 x x) x) #s(literal 1/13824 binary64)) (+.f64 #s(literal 1/576 binary64) (-.f64 (.f64 #s(literal 1/518400 binary64) (.f64 (.f64 x x) (.f64 x x))) (.f64 (*.f64 x x) #s(literal -1/17280 binary64)))))
(/.f64 (fma.f64 (.f64 #s(literal -1/373248000 binary64) (.f64 (.f64 x x) x)) (.f64 (.f64 x x) x) #s(literal 1/13824 binary64)) (fma.f64 #s(literal 1/518400 binary64) (.f64 (.f64 x x) (.f64 x x)) (-.f64 #s(literal 1/576 binary64) (.f64 (.f64 x x) #s(literal -1/17280 binary64)))))
(/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 (.f64 x x) #s(literal -1/720 binary64) #s(literal -1/24 binary64)) (fma.f64 #s(literal 1/518400 binary64) (.f64 (.f64 x x) (.f64 x x)) #s(literal -1/576 binary64))))
(/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 #s(literal 1/518400 binary64) (.f64 (.f64 x x) (.f64 x x)) (-.f64 #s(literal 1/576 binary64) (.f64 (.f64 x x) #s(literal -1/17280 binary64)))) (fma.f64 (.f64 #s(literal -1/373248000 binary64) (.f64 (.f64 x x) x)) (.f64 (.f64 x x) x) #s(literal 1/13824 binary64))))
(fma.f64 (*.f64 #s(literal -1/720 binary64) x) x #s(literal 1/24 binary64))
(fma.f64 (*.f64 x x) #s(literal -1/720 binary64) #s(literal 1/24 binary64))
(fma.f64 #s(literal -1/720 binary64) (*.f64 x x) #s(literal 1/24 binary64))
(fma.f64 x (*.f64 #s(literal -1/720 binary64) x) #s(literal 1/24 binary64))
(-.f64 (/.f64 (.f64 #s(literal 1/518400 binary64) (.f64 (.f64 x x) (.f64 x x))) (fma.f64 (.f64 x x) #s(literal -1/720 binary64) #s(literal -1/24 binary64))) (/.f64 #s(literal 1/576 binary64) (fma.f64 (.f64 x x) #s(literal -1/720 binary64) #s(literal -1/24 binary64))))
(+.f64 (.f64 (.f64 x x) #s(literal -1/720 binary64)) #s(literal 1/24 binary64))
(+.f64 #s(literal 1/24 binary64) (.f64 (.f64 x x) #s(literal -1/720 binary64)))

eval264.0ms (2.1%)

Memory: -14.5MiB live, 196.1MiB allocated
Compiler: Compiled 33 681 to 2 075 computations (93.8% saved)

prune241.0ms (1.9%)

Memory

-0.2MiB live, 277.3MiB allocated

Pruning

25 alts after pruning (16 fresh and 9 done)

	Pruned	Kept	Total
New	1 025	8	1 033
Fresh	0	8	8
Picked	2	3	5
Done	0	6	6
Total	1 027	25	1 052

Accuracy

100.0%

Counts

1 052 → 25

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	62.5%	(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
	55.7%	(.f64 (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) (.f64 (.f64 eps eps) (/.f64 #s(literal 1 binary64) eps)))) #s(literal 2 binary64)) (cos.f64 (.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps))))
	99.9%	(.f64 #s(approx ( (sin (* 1/2 (+ 0 eps))) 2) (.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -1/322560 binary64) (.f64 eps eps) #s(literal 1/1920 binary64)) (.f64 eps eps) #s(literal -1/24 binary64)) (.f64 eps eps) #s(literal 1 binary64)) eps)) (cos.f64 #s(approx (* 1/2 (+ (* 2 x) eps)) (fma.f64 eps #s(literal 1/2 binary64) x))))
	99.8%	(.f64 #s(approx ( (sin (* 1/2 (+ 0 eps))) 2) (.f64 (fma.f64 (fma.f64 #s(literal 1/1920 binary64) (.f64 eps eps) #s(literal -1/24 binary64)) (.f64 eps eps) #s(literal 1 binary64)) eps)) (cos.f64 #s(approx ( 1/2 (+ (* 2 x) eps)) (fma.f64 #s(literal 1/2 binary64) eps x))))
	99.7%	(.f64 #s(approx ( (sin (* 1/2 (+ 0 eps))) 2) (.f64 (fma.f64 (.f64 eps eps) #s(literal -1/24 binary64) #s(literal 1 binary64)) eps)) (cos.f64 #s(approx (* 1/2 (+ (* 2 x) eps)) (fma.f64 eps #s(literal 1/2 binary64) x))))
	99.3%	#s(approx (- (sin (+ x eps)) (sin x)) (fma.f64 (cos.f64 x) eps (.f64 (.f64 #s(approx (* (sin x) -1/2) (*.f64 #s(literal -1/2 binary64) x)) eps) eps)))
✓	99.7%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 (.f64 (sin.f64 x) #s(literal -1/2 binary64)) eps (cos.f64 x)) eps))
	98.7%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 #s(approx ( (sin x) -1/2) (.f64 #s(literal -1/2 binary64) x)) eps #s(approx (cos x) (fma.f64 (fma.f64 (.f64 x x) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) (*.f64 x x) #s(literal 1 binary64)))) eps))
	98.1%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 #s(approx ( (sin x) -1/2) (*.f64 #s(literal -1/2 binary64) x)) eps #s(approx (cos x) #s(literal 1 binary64))) eps))
✓	99.3%	#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (cos.f64 x) eps))
✓	98.6%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (* (sin x) -1/2) eps) (cos x)) (fma.f64 (fma.f64 (fma.f64 #s(literal 1/12 binary64) (.f64 x eps) #s(literal -1/2 binary64)) x (.f64 #s(literal -1/2 binary64) eps)) x #s(literal 1 binary64))) eps))
	98.6%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (* (sin x) -1/2) eps) (cos x)) (fma.f64 (*.f64 (+.f64 x eps) #s(literal -1/2 binary64)) x #s(literal 1 binary64))) eps))
	98.5%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (* (sin x) -1/2) eps) (cos x)) (fma.f64 #s(approx (+ (* (+ (* 1/12 (* x eps)) -1/2) x) (* -1/2 eps)) (.f64 (fma.f64 #s(literal 1/12 binary64) eps (/.f64 #s(literal -1/2 binary64) x)) (.f64 x x))) x #s(literal 1 binary64))) eps))
✓	98.1%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (* (sin x) -1/2) eps) (cos x)) #s(literal 1 binary64)) eps))
	98.8%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (cos x) (fma.f64 (fma.f64 (fma.f64 #s(literal -1/720 binary64) (.f64 x x) #s(literal 1/24 binary64)) (.f64 x x) #s(literal -1/2 binary64)) (.f64 x x) #s(literal 1 binary64))) eps))
✓	98.6%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (cos x) (fma.f64 (fma.f64 (.f64 x x) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) (*.f64 x x) #s(literal 1 binary64))) eps))
	98.8%	#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (cos x) eps) (fma.f64 (fma.f64 (/.f64 (.f64 (fma.f64 (.f64 x x) #s(literal -1/720 binary64) #s(literal 1/24 binary64)) (neg.f64 (.f64 eps eps))) (neg.f64 eps)) (.f64 x x) (.f64 #s(literal -1/2 binary64) eps)) (.f64 x x) eps)))
✓	98.8%	#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (cos x) eps) (fma.f64 (fma.f64 (.f64 eps (fma.f64 #s(literal -1/720 binary64) (.f64 x x) #s(literal 1/24 binary64))) (.f64 x x) (.f64 #s(literal -1/2 binary64) eps)) (*.f64 x x) eps)))
	98.8%	#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (cos x) eps) (fma.f64 (fma.f64 (.f64 eps (/.f64 (fma.f64 #s(literal 1/518400 binary64) (.f64 (.f64 x x) (.f64 x x)) #s(literal -1/576 binary64)) (fma.f64 (.f64 x x) #s(literal -1/720 binary64) #s(literal -1/24 binary64)))) (.f64 x x) (.f64 #s(literal -1/2 binary64) eps)) (.f64 x x) eps)))
	98.5%	#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (cos x) eps) (fma.f64 (.f64 (.f64 x x) eps) #s(literal -1/2 binary64) eps)))
✓	98.5%	#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (cos x) eps) (fma.f64 (.f64 #s(literal -1/2 binary64) x) (.f64 x eps) eps)))
	98.1%	#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (cos x) eps) (fma.f64 #s(approx (+ (* (* eps (+ (* -1/720 (* x x)) 1/24)) (* x x)) (* -1/2 eps)) (.f64 (.f64 (.f64 #s(literal -1/720 binary64) (.f64 (.f64 x x) eps)) x) x)) (.f64 x x) eps)))
	5.1%	#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (cos x) eps) #s(approx (+ (* (* -1/2 x) (* x eps)) eps) (.f64 (.f64 (*.f64 x eps) #s(literal -1/2 binary64)) x))))
✓	99.9%	#s(approx (* (* (sin (* 1/2 (+ 0 eps))) 2) (cos (* 1/2 (+ (* 2 x) eps)))) (.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)))))
	99.6%	#s(approx (* (* (sin (* 1/2 (+ 0 eps))) 2) (cos (* 1/2 (+ (* 2 x) eps)))) (.f64 (.f64 (cos.f64 (fma.f64 eps #s(literal 1/2 binary64) x)) #s(literal 2 binary64)) #s(approx (sin (* eps 1/2)) (*.f64 #s(literal 1/2 binary64) eps))))

Compiler

Compiled 1 005 to 379 computations (62.3% saved)

regimes48.0ms (0.4%)

Memory

8.9MiB live, 48.8MiB allocated

Counts

36 → 1

Calls

Call 1

Inputs
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (* (sin x) -1/2) eps) (cos x)) #s(literal 1 binary64)) eps))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (cos x) eps) #s(approx (+ (* (* -1/2 x) (* x eps)) eps) (.f64 (.f64 (*.f64 x eps) #s(literal -1/2 binary64)) x))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (cos x) eps) (fma.f64 (.f64 #s(literal -1/2 binary64) x) (.f64 x eps) eps)))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (cos x) eps) (fma.f64 (.f64 (.f64 x x) eps) #s(literal -1/2 binary64) eps)))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (* (sin x) -1/2) eps) (cos x)) (fma.f64 (*.f64 x eps) #s(literal -1/2 binary64) #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 #s(approx ( (sin x) -1/2) (*.f64 #s(literal -1/2 binary64) x)) eps #s(approx (cos x) #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (* (sin x) -1/2) eps) (cos x)) (fma.f64 (*.f64 (+.f64 x eps) #s(literal -1/2 binary64)) x #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (cos x) (fma.f64 (fma.f64 (.f64 x x) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) (*.f64 x x) #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (* (sin x) -1/2) eps) (cos x)) (fma.f64 (fma.f64 (fma.f64 #s(literal 1/12 binary64) (.f64 x eps) #s(literal -1/2 binary64)) x (.f64 #s(literal -1/2 binary64) eps)) x #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (cos x) eps) (fma.f64 #s(approx (+ (* (* eps (+ (* -1/720 (* x x)) 1/24)) (* x x)) (* -1/2 eps)) (.f64 (.f64 (.f64 #s(literal -1/720 binary64) (.f64 (.f64 x x) eps)) x) x)) (.f64 x x) eps)))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (cos x) (fma.f64 (fma.f64 (fma.f64 #s(literal -1/720 binary64) (.f64 x x) #s(literal 1/24 binary64)) (.f64 x x) #s(literal -1/2 binary64)) (.f64 x x) #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (* (sin x) -1/2) eps) (cos x)) (fma.f64 #s(approx (+ (* (+ (* 1/12 (* x eps)) -1/2) x) (* -1/2 eps)) (.f64 (fma.f64 #s(literal 1/12 binary64) eps (/.f64 #s(literal -1/2 binary64) x)) (.f64 x x))) x #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 #s(approx ( (sin x) -1/2) (.f64 #s(literal -1/2 binary64) x)) eps #s(approx (cos x) (fma.f64 (fma.f64 (.f64 x x) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) (*.f64 x x) #s(literal 1 binary64)))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (cos x) eps) (fma.f64 (fma.f64 (.f64 eps (fma.f64 #s(literal -1/720 binary64) (.f64 x x) #s(literal 1/24 binary64))) (.f64 x x) (.f64 #s(literal -1/2 binary64) eps)) (*.f64 x x) eps)))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (cos x) eps) (fma.f64 (fma.f64 (/.f64 (.f64 (fma.f64 (.f64 x x) #s(literal -1/720 binary64) #s(literal 1/24 binary64)) (neg.f64 (.f64 eps eps))) (neg.f64 eps)) (.f64 x x) (.f64 #s(literal -1/2 binary64) eps)) (.f64 x x) eps)))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (cos x) eps) (fma.f64 (fma.f64 (.f64 eps (/.f64 (fma.f64 #s(literal 1/518400 binary64) (.f64 (.f64 x x) (.f64 x x)) #s(literal -1/576 binary64)) (fma.f64 (.f64 x x) #s(literal -1/720 binary64) #s(literal -1/24 binary64)))) (.f64 x x) (.f64 #s(literal -1/2 binary64) eps)) (.f64 x x) eps)))
#s(approx (- (sin (+ x eps)) (sin x)) (sin.f64 eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (cos.f64 x) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 #s(approx ( (sin x) -1/2) (*.f64 #s(literal -1/2 binary64) x)) eps (cos.f64 x)) eps))
#s(approx (* (* (sin (* 1/2 (+ 0 eps))) 2) (cos (* 1/2 (+ (* 2 x) eps)))) (.f64 (.f64 (cos.f64 (fma.f64 eps #s(literal 1/2 binary64) x)) #s(literal 2 binary64)) #s(approx (sin (* eps 1/2)) (*.f64 #s(literal 1/2 binary64) eps))))
#s(approx (- (sin (+ x eps)) (sin x)) (fma.f64 (cos.f64 x) eps (.f64 (.f64 #s(approx (* (sin x) -1/2) (*.f64 #s(literal -1/2 binary64) x)) eps) eps)))
#s(approx (- (sin (+ x eps)) (sin x)) (/.f64 (cos.f64 x) (/.f64 #s(literal 1 binary64) eps)))
(.f64 (.f64 #s(approx (sin (* 1/2 (+ 0 eps))) (.f64 eps #s(literal 1/2 binary64))) #s(literal 2 binary64)) (cos.f64 (.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps))))
(.f64 #s(approx ( (sin (* 1/2 (+ 0 eps))) 2) (.f64 (fma.f64 (.f64 eps eps) #s(literal -1/24 binary64) #s(literal 1 binary64)) eps)) (cos.f64 #s(approx (* 1/2 (+ (* 2 x) eps)) (fma.f64 eps #s(literal 1/2 binary64) x))))
(.f64 #s(approx ( (sin (* 1/2 (+ 0 eps))) 2) (.f64 (fma.f64 (.f64 eps eps) #s(literal -1/24 binary64) #s(literal 1 binary64)) eps)) (cos.f64 (*.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps))))
(-.f64 (sin.f64 (+.f64 x eps)) #s(approx (sin x) (.f64 (fma.f64 (fma.f64 #s(literal 1/120 binary64) (.f64 x x) #s(literal -1/6 binary64)) (*.f64 x x) #s(literal 1 binary64)) x)))
(.f64 #s(approx ( (sin (* 1/2 (+ 0 eps))) 2) (.f64 (fma.f64 (fma.f64 #s(literal 1/1920 binary64) (.f64 eps eps) #s(literal -1/24 binary64)) (.f64 eps eps) #s(literal 1 binary64)) eps)) (cos.f64 #s(approx ( 1/2 (+ (* 2 x) eps)) (fma.f64 #s(literal 1/2 binary64) eps x))))
(.f64 #s(approx ( (sin (* 1/2 (+ 0 eps))) 2) (.f64 (fma.f64 (fma.f64 #s(literal 1/1920 binary64) (.f64 eps eps) #s(literal -1/24 binary64)) (.f64 eps eps) #s(literal 1 binary64)) eps)) (cos.f64 (.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps))))
(.f64 #s(approx ( (sin (* 1/2 (+ 0 eps))) 2) (.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -1/322560 binary64) (.f64 eps eps) #s(literal 1/1920 binary64)) (.f64 eps eps) #s(literal -1/24 binary64)) (.f64 eps eps) #s(literal 1 binary64)) eps)) (cos.f64 #s(approx (* 1/2 (+ (* 2 x) eps)) (fma.f64 eps #s(literal 1/2 binary64) x))))
(.f64 #s(approx ( (sin (* 1/2 (+ 0 eps))) 2) (.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -1/322560 binary64) (.f64 eps eps) #s(literal 1/1920 binary64)) (.f64 eps eps) #s(literal -1/24 binary64)) (.f64 eps eps) #s(literal 1 binary64)) eps)) (cos.f64 (*.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps))))
(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 (.f64 (sin.f64 x) #s(literal -1/2 binary64)) eps (cos.f64 x)) eps))
#s(approx (* (* (sin (* 1/2 (+ 0 eps))) 2) (cos (* 1/2 (+ (* 2 x) eps)))) (.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 #s(literal 1/2 binary64) (+.f64 #s(literal 0 binary64) eps))) #s(literal 2 binary64)) (cos.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 (.f64 eps eps) (/.f64 #s(literal 1 binary64) eps)))) #s(literal 2 binary64)) (cos.f64 (.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps))))
(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 (* 1/2 (+ (* 2 x) eps)))) (*.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)))))

Calls

3 calls:

28.0ms	eps
9.0ms	(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
9.0ms	x

Results

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

Compiler

Compiled 15 to 10 computations (33.3% saved)

regimes38.0ms (0.3%)

Memory

9.3MiB live, 48.8MiB allocated

Counts

32 → 1

Calls

Call 1

Inputs
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (* (sin x) -1/2) eps) (cos x)) #s(literal 1 binary64)) eps))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (cos x) eps) #s(approx (+ (* (* -1/2 x) (* x eps)) eps) (.f64 (.f64 (*.f64 x eps) #s(literal -1/2 binary64)) x))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (cos x) eps) (fma.f64 (.f64 #s(literal -1/2 binary64) x) (.f64 x eps) eps)))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (cos x) eps) (fma.f64 (.f64 (.f64 x x) eps) #s(literal -1/2 binary64) eps)))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (* (sin x) -1/2) eps) (cos x)) (fma.f64 (*.f64 x eps) #s(literal -1/2 binary64) #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 #s(approx ( (sin x) -1/2) (*.f64 #s(literal -1/2 binary64) x)) eps #s(approx (cos x) #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (* (sin x) -1/2) eps) (cos x)) (fma.f64 (*.f64 (+.f64 x eps) #s(literal -1/2 binary64)) x #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (cos x) (fma.f64 (fma.f64 (.f64 x x) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) (*.f64 x x) #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (* (sin x) -1/2) eps) (cos x)) (fma.f64 (fma.f64 (fma.f64 #s(literal 1/12 binary64) (.f64 x eps) #s(literal -1/2 binary64)) x (.f64 #s(literal -1/2 binary64) eps)) x #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (cos x) eps) (fma.f64 #s(approx (+ (* (* eps (+ (* -1/720 (* x x)) 1/24)) (* x x)) (* -1/2 eps)) (.f64 (.f64 (.f64 #s(literal -1/720 binary64) (.f64 (.f64 x x) eps)) x) x)) (.f64 x x) eps)))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (cos x) (fma.f64 (fma.f64 (fma.f64 #s(literal -1/720 binary64) (.f64 x x) #s(literal 1/24 binary64)) (.f64 x x) #s(literal -1/2 binary64)) (.f64 x x) #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (* (sin x) -1/2) eps) (cos x)) (fma.f64 #s(approx (+ (* (+ (* 1/12 (* x eps)) -1/2) x) (* -1/2 eps)) (.f64 (fma.f64 #s(literal 1/12 binary64) eps (/.f64 #s(literal -1/2 binary64) x)) (.f64 x x))) x #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 #s(approx ( (sin x) -1/2) (.f64 #s(literal -1/2 binary64) x)) eps #s(approx (cos x) (fma.f64 (fma.f64 (.f64 x x) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) (*.f64 x x) #s(literal 1 binary64)))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (cos x) eps) (fma.f64 (fma.f64 (.f64 eps (fma.f64 #s(literal -1/720 binary64) (.f64 x x) #s(literal 1/24 binary64))) (.f64 x x) (.f64 #s(literal -1/2 binary64) eps)) (*.f64 x x) eps)))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (cos x) eps) (fma.f64 (fma.f64 (/.f64 (.f64 (fma.f64 (.f64 x x) #s(literal -1/720 binary64) #s(literal 1/24 binary64)) (neg.f64 (.f64 eps eps))) (neg.f64 eps)) (.f64 x x) (.f64 #s(literal -1/2 binary64) eps)) (.f64 x x) eps)))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (cos x) eps) (fma.f64 (fma.f64 (.f64 eps (/.f64 (fma.f64 #s(literal 1/518400 binary64) (.f64 (.f64 x x) (.f64 x x)) #s(literal -1/576 binary64)) (fma.f64 (.f64 x x) #s(literal -1/720 binary64) #s(literal -1/24 binary64)))) (.f64 x x) (.f64 #s(literal -1/2 binary64) eps)) (.f64 x x) eps)))
#s(approx (- (sin (+ x eps)) (sin x)) (sin.f64 eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (cos.f64 x) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 #s(approx ( (sin x) -1/2) (*.f64 #s(literal -1/2 binary64) x)) eps (cos.f64 x)) eps))
#s(approx (* (* (sin (* 1/2 (+ 0 eps))) 2) (cos (* 1/2 (+ (* 2 x) eps)))) (.f64 (.f64 (cos.f64 (fma.f64 eps #s(literal 1/2 binary64) x)) #s(literal 2 binary64)) #s(approx (sin (* eps 1/2)) (*.f64 #s(literal 1/2 binary64) eps))))
#s(approx (- (sin (+ x eps)) (sin x)) (fma.f64 (cos.f64 x) eps (.f64 (.f64 #s(approx (* (sin x) -1/2) (*.f64 #s(literal -1/2 binary64) x)) eps) eps)))
#s(approx (- (sin (+ x eps)) (sin x)) (/.f64 (cos.f64 x) (/.f64 #s(literal 1 binary64) eps)))
(.f64 (.f64 #s(approx (sin (* 1/2 (+ 0 eps))) (.f64 eps #s(literal 1/2 binary64))) #s(literal 2 binary64)) (cos.f64 (.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps))))
(.f64 #s(approx ( (sin (* 1/2 (+ 0 eps))) 2) (.f64 (fma.f64 (.f64 eps eps) #s(literal -1/24 binary64) #s(literal 1 binary64)) eps)) (cos.f64 #s(approx (* 1/2 (+ (* 2 x) eps)) (fma.f64 eps #s(literal 1/2 binary64) x))))
(.f64 #s(approx ( (sin (* 1/2 (+ 0 eps))) 2) (.f64 (fma.f64 (.f64 eps eps) #s(literal -1/24 binary64) #s(literal 1 binary64)) eps)) (cos.f64 (*.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps))))
(-.f64 (sin.f64 (+.f64 x eps)) #s(approx (sin x) (.f64 (fma.f64 (fma.f64 #s(literal 1/120 binary64) (.f64 x x) #s(literal -1/6 binary64)) (*.f64 x x) #s(literal 1 binary64)) x)))
(.f64 #s(approx ( (sin (* 1/2 (+ 0 eps))) 2) (.f64 (fma.f64 (fma.f64 #s(literal 1/1920 binary64) (.f64 eps eps) #s(literal -1/24 binary64)) (.f64 eps eps) #s(literal 1 binary64)) eps)) (cos.f64 #s(approx ( 1/2 (+ (* 2 x) eps)) (fma.f64 #s(literal 1/2 binary64) eps x))))
(.f64 #s(approx ( (sin (* 1/2 (+ 0 eps))) 2) (.f64 (fma.f64 (fma.f64 #s(literal 1/1920 binary64) (.f64 eps eps) #s(literal -1/24 binary64)) (.f64 eps eps) #s(literal 1 binary64)) eps)) (cos.f64 (.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps))))
(.f64 #s(approx ( (sin (* 1/2 (+ 0 eps))) 2) (.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -1/322560 binary64) (.f64 eps eps) #s(literal 1/1920 binary64)) (.f64 eps eps) #s(literal -1/24 binary64)) (.f64 eps eps) #s(literal 1 binary64)) eps)) (cos.f64 #s(approx (* 1/2 (+ (* 2 x) eps)) (fma.f64 eps #s(literal 1/2 binary64) x))))
(.f64 #s(approx ( (sin (* 1/2 (+ 0 eps))) 2) (.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -1/322560 binary64) (.f64 eps eps) #s(literal 1/1920 binary64)) (.f64 eps eps) #s(literal -1/24 binary64)) (.f64 eps eps) #s(literal 1 binary64)) eps)) (cos.f64 (*.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps))))
(-.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))

Outputs

(*.f64 #s(approx (* (sin (* 1/2 (+ 0 eps))) 2) (*.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -1/322560 binary64) (*.f64 eps eps) #s(literal 1/1920 binary64)) (*.f64 eps eps) #s(literal -1/24 binary64)) (*.f64 eps eps) #s(literal 1 binary64)) eps)) (cos.f64 #s(approx (* 1/2 (+ (* 2 x) eps)) (fma.f64 eps #s(literal 1/2 binary64) x))))

Calls

3 calls:

20.0ms	eps
8.0ms	(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
8.0ms	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 15 to 10 computations (33.3% saved)

regimes25.0ms (0.2%)

Memory

-21.1MiB live, 57.6MiB allocated

Counts

28 → 1

Calls

Call 1

Inputs
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (* (sin x) -1/2) eps) (cos x)) #s(literal 1 binary64)) eps))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (cos x) eps) #s(approx (+ (* (* -1/2 x) (* x eps)) eps) (.f64 (.f64 (*.f64 x eps) #s(literal -1/2 binary64)) x))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (cos x) eps) (fma.f64 (.f64 #s(literal -1/2 binary64) x) (.f64 x eps) eps)))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (cos x) eps) (fma.f64 (.f64 (.f64 x x) eps) #s(literal -1/2 binary64) eps)))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (* (sin x) -1/2) eps) (cos x)) (fma.f64 (*.f64 x eps) #s(literal -1/2 binary64) #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 #s(approx ( (sin x) -1/2) (*.f64 #s(literal -1/2 binary64) x)) eps #s(approx (cos x) #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (* (sin x) -1/2) eps) (cos x)) (fma.f64 (*.f64 (+.f64 x eps) #s(literal -1/2 binary64)) x #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (cos x) (fma.f64 (fma.f64 (.f64 x x) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) (*.f64 x x) #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (* (sin x) -1/2) eps) (cos x)) (fma.f64 (fma.f64 (fma.f64 #s(literal 1/12 binary64) (.f64 x eps) #s(literal -1/2 binary64)) x (.f64 #s(literal -1/2 binary64) eps)) x #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (cos x) eps) (fma.f64 #s(approx (+ (* (* eps (+ (* -1/720 (* x x)) 1/24)) (* x x)) (* -1/2 eps)) (.f64 (.f64 (.f64 #s(literal -1/720 binary64) (.f64 (.f64 x x) eps)) x) x)) (.f64 x x) eps)))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (cos x) (fma.f64 (fma.f64 (fma.f64 #s(literal -1/720 binary64) (.f64 x x) #s(literal 1/24 binary64)) (.f64 x x) #s(literal -1/2 binary64)) (.f64 x x) #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (* (sin x) -1/2) eps) (cos x)) (fma.f64 #s(approx (+ (* (+ (* 1/12 (* x eps)) -1/2) x) (* -1/2 eps)) (.f64 (fma.f64 #s(literal 1/12 binary64) eps (/.f64 #s(literal -1/2 binary64) x)) (.f64 x x))) x #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 #s(approx ( (sin x) -1/2) (.f64 #s(literal -1/2 binary64) x)) eps #s(approx (cos x) (fma.f64 (fma.f64 (.f64 x x) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) (*.f64 x x) #s(literal 1 binary64)))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (cos x) eps) (fma.f64 (fma.f64 (.f64 eps (fma.f64 #s(literal -1/720 binary64) (.f64 x x) #s(literal 1/24 binary64))) (.f64 x x) (.f64 #s(literal -1/2 binary64) eps)) (*.f64 x x) eps)))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (cos x) eps) (fma.f64 (fma.f64 (/.f64 (.f64 (fma.f64 (.f64 x x) #s(literal -1/720 binary64) #s(literal 1/24 binary64)) (neg.f64 (.f64 eps eps))) (neg.f64 eps)) (.f64 x x) (.f64 #s(literal -1/2 binary64) eps)) (.f64 x x) eps)))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (cos x) eps) (fma.f64 (fma.f64 (.f64 eps (/.f64 (fma.f64 #s(literal 1/518400 binary64) (.f64 (.f64 x x) (.f64 x x)) #s(literal -1/576 binary64)) (fma.f64 (.f64 x x) #s(literal -1/720 binary64) #s(literal -1/24 binary64)))) (.f64 x x) (.f64 #s(literal -1/2 binary64) eps)) (.f64 x x) eps)))
#s(approx (- (sin (+ x eps)) (sin x)) (sin.f64 eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (cos.f64 x) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 #s(approx ( (sin x) -1/2) (*.f64 #s(literal -1/2 binary64) x)) eps (cos.f64 x)) eps))
#s(approx (* (* (sin (* 1/2 (+ 0 eps))) 2) (cos (* 1/2 (+ (* 2 x) eps)))) (.f64 (.f64 (cos.f64 (fma.f64 eps #s(literal 1/2 binary64) x)) #s(literal 2 binary64)) #s(approx (sin (* eps 1/2)) (*.f64 #s(literal 1/2 binary64) eps))))
#s(approx (- (sin (+ x eps)) (sin x)) (fma.f64 (cos.f64 x) eps (.f64 (.f64 #s(approx (* (sin x) -1/2) (*.f64 #s(literal -1/2 binary64) x)) eps) eps)))
#s(approx (- (sin (+ x eps)) (sin x)) (/.f64 (cos.f64 x) (/.f64 #s(literal 1 binary64) eps)))
(.f64 (.f64 #s(approx (sin (* 1/2 (+ 0 eps))) (.f64 eps #s(literal 1/2 binary64))) #s(literal 2 binary64)) (cos.f64 (.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps))))
(.f64 #s(approx ( (sin (* 1/2 (+ 0 eps))) 2) (.f64 (fma.f64 (.f64 eps eps) #s(literal -1/24 binary64) #s(literal 1 binary64)) eps)) (cos.f64 #s(approx (* 1/2 (+ (* 2 x) eps)) (fma.f64 eps #s(literal 1/2 binary64) x))))
(.f64 #s(approx ( (sin (* 1/2 (+ 0 eps))) 2) (.f64 (fma.f64 (.f64 eps eps) #s(literal -1/24 binary64) #s(literal 1 binary64)) eps)) (cos.f64 (*.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps))))
(-.f64 (sin.f64 (+.f64 x eps)) #s(approx (sin x) (.f64 (fma.f64 (fma.f64 #s(literal 1/120 binary64) (.f64 x x) #s(literal -1/6 binary64)) (*.f64 x x) #s(literal 1 binary64)) x)))
(.f64 #s(approx ( (sin (* 1/2 (+ 0 eps))) 2) (.f64 (fma.f64 (fma.f64 #s(literal 1/1920 binary64) (.f64 eps eps) #s(literal -1/24 binary64)) (.f64 eps eps) #s(literal 1 binary64)) eps)) (cos.f64 #s(approx ( 1/2 (+ (* 2 x) eps)) (fma.f64 #s(literal 1/2 binary64) eps x))))
(.f64 #s(approx ( (sin (* 1/2 (+ 0 eps))) 2) (.f64 (fma.f64 (fma.f64 #s(literal 1/1920 binary64) (.f64 eps eps) #s(literal -1/24 binary64)) (.f64 eps eps) #s(literal 1 binary64)) eps)) (cos.f64 (.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps))))

Outputs

(*.f64 #s(approx (* (sin (* 1/2 (+ 0 eps))) 2) (*.f64 (fma.f64 (fma.f64 #s(literal 1/1920 binary64) (*.f64 eps eps) #s(literal -1/24 binary64)) (*.f64 eps eps) #s(literal 1 binary64)) eps)) (cos.f64 #s(approx (* 1/2 (+ (* 2 x) eps)) (fma.f64 #s(literal 1/2 binary64) eps x))))

Calls

3 calls:

8.0ms	eps
7.0ms	(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
7.0ms	x

Results

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

Compiler

Compiled 15 to 10 computations (33.3% saved)

regimes102.0ms (0.8%)

Memory

-24.7MiB live, 29.4MiB allocated

Counts

26 → 1

Calls

Call 1

Inputs
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (* (sin x) -1/2) eps) (cos x)) #s(literal 1 binary64)) eps))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (cos x) eps) #s(approx (+ (* (* -1/2 x) (* x eps)) eps) (.f64 (.f64 (*.f64 x eps) #s(literal -1/2 binary64)) x))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (cos x) eps) (fma.f64 (.f64 #s(literal -1/2 binary64) x) (.f64 x eps) eps)))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (cos x) eps) (fma.f64 (.f64 (.f64 x x) eps) #s(literal -1/2 binary64) eps)))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (* (sin x) -1/2) eps) (cos x)) (fma.f64 (*.f64 x eps) #s(literal -1/2 binary64) #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 #s(approx ( (sin x) -1/2) (*.f64 #s(literal -1/2 binary64) x)) eps #s(approx (cos x) #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (* (sin x) -1/2) eps) (cos x)) (fma.f64 (*.f64 (+.f64 x eps) #s(literal -1/2 binary64)) x #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (cos x) (fma.f64 (fma.f64 (.f64 x x) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) (*.f64 x x) #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (* (sin x) -1/2) eps) (cos x)) (fma.f64 (fma.f64 (fma.f64 #s(literal 1/12 binary64) (.f64 x eps) #s(literal -1/2 binary64)) x (.f64 #s(literal -1/2 binary64) eps)) x #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (cos x) eps) (fma.f64 #s(approx (+ (* (* eps (+ (* -1/720 (* x x)) 1/24)) (* x x)) (* -1/2 eps)) (.f64 (.f64 (.f64 #s(literal -1/720 binary64) (.f64 (.f64 x x) eps)) x) x)) (.f64 x x) eps)))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (cos x) (fma.f64 (fma.f64 (fma.f64 #s(literal -1/720 binary64) (.f64 x x) #s(literal 1/24 binary64)) (.f64 x x) #s(literal -1/2 binary64)) (.f64 x x) #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (* (sin x) -1/2) eps) (cos x)) (fma.f64 #s(approx (+ (* (+ (* 1/12 (* x eps)) -1/2) x) (* -1/2 eps)) (.f64 (fma.f64 #s(literal 1/12 binary64) eps (/.f64 #s(literal -1/2 binary64) x)) (.f64 x x))) x #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 #s(approx ( (sin x) -1/2) (.f64 #s(literal -1/2 binary64) x)) eps #s(approx (cos x) (fma.f64 (fma.f64 (.f64 x x) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) (*.f64 x x) #s(literal 1 binary64)))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (cos x) eps) (fma.f64 (fma.f64 (.f64 eps (fma.f64 #s(literal -1/720 binary64) (.f64 x x) #s(literal 1/24 binary64))) (.f64 x x) (.f64 #s(literal -1/2 binary64) eps)) (*.f64 x x) eps)))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (cos x) eps) (fma.f64 (fma.f64 (/.f64 (.f64 (fma.f64 (.f64 x x) #s(literal -1/720 binary64) #s(literal 1/24 binary64)) (neg.f64 (.f64 eps eps))) (neg.f64 eps)) (.f64 x x) (.f64 #s(literal -1/2 binary64) eps)) (.f64 x x) eps)))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (cos x) eps) (fma.f64 (fma.f64 (.f64 eps (/.f64 (fma.f64 #s(literal 1/518400 binary64) (.f64 (.f64 x x) (.f64 x x)) #s(literal -1/576 binary64)) (fma.f64 (.f64 x x) #s(literal -1/720 binary64) #s(literal -1/24 binary64)))) (.f64 x x) (.f64 #s(literal -1/2 binary64) eps)) (.f64 x x) eps)))
#s(approx (- (sin (+ x eps)) (sin x)) (sin.f64 eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (cos.f64 x) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 #s(approx ( (sin x) -1/2) (*.f64 #s(literal -1/2 binary64) x)) eps (cos.f64 x)) eps))
#s(approx (* (* (sin (* 1/2 (+ 0 eps))) 2) (cos (* 1/2 (+ (* 2 x) eps)))) (.f64 (.f64 (cos.f64 (fma.f64 eps #s(literal 1/2 binary64) x)) #s(literal 2 binary64)) #s(approx (sin (* eps 1/2)) (*.f64 #s(literal 1/2 binary64) eps))))
#s(approx (- (sin (+ x eps)) (sin x)) (fma.f64 (cos.f64 x) eps (.f64 (.f64 #s(approx (* (sin x) -1/2) (*.f64 #s(literal -1/2 binary64) x)) eps) eps)))
#s(approx (- (sin (+ x eps)) (sin x)) (/.f64 (cos.f64 x) (/.f64 #s(literal 1 binary64) eps)))
(.f64 (.f64 #s(approx (sin (* 1/2 (+ 0 eps))) (.f64 eps #s(literal 1/2 binary64))) #s(literal 2 binary64)) (cos.f64 (.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps))))
(.f64 #s(approx ( (sin (* 1/2 (+ 0 eps))) 2) (.f64 (fma.f64 (.f64 eps eps) #s(literal -1/24 binary64) #s(literal 1 binary64)) eps)) (cos.f64 #s(approx (* 1/2 (+ (* 2 x) eps)) (fma.f64 eps #s(literal 1/2 binary64) x))))
(.f64 #s(approx ( (sin (* 1/2 (+ 0 eps))) 2) (.f64 (fma.f64 (.f64 eps eps) #s(literal -1/24 binary64) #s(literal 1 binary64)) eps)) (cos.f64 (*.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps))))
(-.f64 (sin.f64 (+.f64 x eps)) #s(approx (sin x) (.f64 (fma.f64 (fma.f64 #s(literal 1/120 binary64) (.f64 x x) #s(literal -1/6 binary64)) (*.f64 x x) #s(literal 1 binary64)) x)))

Outputs

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

Calls

3 calls:

87.0ms	eps
7.0ms	(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
7.0ms	x

Results

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

Compiler

Compiled 15 to 10 computations (33.3% saved)

regimes20.0ms (0.2%)

Memory

12.8MiB live, 12.8MiB allocated

Counts

23 → 1

Calls

Call 1

Inputs
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (* (sin x) -1/2) eps) (cos x)) #s(literal 1 binary64)) eps))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (cos x) eps) #s(approx (+ (* (* -1/2 x) (* x eps)) eps) (.f64 (.f64 (*.f64 x eps) #s(literal -1/2 binary64)) x))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (cos x) eps) (fma.f64 (.f64 #s(literal -1/2 binary64) x) (.f64 x eps) eps)))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (cos x) eps) (fma.f64 (.f64 (.f64 x x) eps) #s(literal -1/2 binary64) eps)))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (* (sin x) -1/2) eps) (cos x)) (fma.f64 (*.f64 x eps) #s(literal -1/2 binary64) #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 #s(approx ( (sin x) -1/2) (*.f64 #s(literal -1/2 binary64) x)) eps #s(approx (cos x) #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (* (sin x) -1/2) eps) (cos x)) (fma.f64 (*.f64 (+.f64 x eps) #s(literal -1/2 binary64)) x #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (cos x) (fma.f64 (fma.f64 (.f64 x x) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) (*.f64 x x) #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (* (sin x) -1/2) eps) (cos x)) (fma.f64 (fma.f64 (fma.f64 #s(literal 1/12 binary64) (.f64 x eps) #s(literal -1/2 binary64)) x (.f64 #s(literal -1/2 binary64) eps)) x #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (cos x) eps) (fma.f64 #s(approx (+ (* (* eps (+ (* -1/720 (* x x)) 1/24)) (* x x)) (* -1/2 eps)) (.f64 (.f64 (.f64 #s(literal -1/720 binary64) (.f64 (.f64 x x) eps)) x) x)) (.f64 x x) eps)))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (cos x) (fma.f64 (fma.f64 (fma.f64 #s(literal -1/720 binary64) (.f64 x x) #s(literal 1/24 binary64)) (.f64 x x) #s(literal -1/2 binary64)) (.f64 x x) #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (* (sin x) -1/2) eps) (cos x)) (fma.f64 #s(approx (+ (* (+ (* 1/12 (* x eps)) -1/2) x) (* -1/2 eps)) (.f64 (fma.f64 #s(literal 1/12 binary64) eps (/.f64 #s(literal -1/2 binary64) x)) (.f64 x x))) x #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 #s(approx ( (sin x) -1/2) (.f64 #s(literal -1/2 binary64) x)) eps #s(approx (cos x) (fma.f64 (fma.f64 (.f64 x x) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) (*.f64 x x) #s(literal 1 binary64)))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (cos x) eps) (fma.f64 (fma.f64 (.f64 eps (fma.f64 #s(literal -1/720 binary64) (.f64 x x) #s(literal 1/24 binary64))) (.f64 x x) (.f64 #s(literal -1/2 binary64) eps)) (*.f64 x x) eps)))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (cos x) eps) (fma.f64 (fma.f64 (/.f64 (.f64 (fma.f64 (.f64 x x) #s(literal -1/720 binary64) #s(literal 1/24 binary64)) (neg.f64 (.f64 eps eps))) (neg.f64 eps)) (.f64 x x) (.f64 #s(literal -1/2 binary64) eps)) (.f64 x x) eps)))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (cos x) eps) (fma.f64 (fma.f64 (.f64 eps (/.f64 (fma.f64 #s(literal 1/518400 binary64) (.f64 (.f64 x x) (.f64 x x)) #s(literal -1/576 binary64)) (fma.f64 (.f64 x x) #s(literal -1/720 binary64) #s(literal -1/24 binary64)))) (.f64 x x) (.f64 #s(literal -1/2 binary64) eps)) (.f64 x x) eps)))
#s(approx (- (sin (+ x eps)) (sin x)) (sin.f64 eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (cos.f64 x) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 #s(approx ( (sin x) -1/2) (*.f64 #s(literal -1/2 binary64) x)) eps (cos.f64 x)) eps))
#s(approx (* (* (sin (* 1/2 (+ 0 eps))) 2) (cos (* 1/2 (+ (* 2 x) eps)))) (.f64 (.f64 (cos.f64 (fma.f64 eps #s(literal 1/2 binary64) x)) #s(literal 2 binary64)) #s(approx (sin (* eps 1/2)) (*.f64 #s(literal 1/2 binary64) eps))))
#s(approx (- (sin (+ x eps)) (sin x)) (fma.f64 (cos.f64 x) eps (.f64 (.f64 #s(approx (* (sin x) -1/2) (*.f64 #s(literal -1/2 binary64) x)) eps) eps)))
#s(approx (- (sin (+ x eps)) (sin x)) (/.f64 (cos.f64 x) (/.f64 #s(literal 1 binary64) eps)))
(.f64 (.f64 #s(approx (sin (* 1/2 (+ 0 eps))) (.f64 eps #s(literal 1/2 binary64))) #s(literal 2 binary64)) (cos.f64 (.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps))))

Outputs

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

Calls

3 calls:

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

Results

Accuracy	Segments	Branch
99.6%	1	`x`
99.6%	1	`eps`
99.6%	1	`(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))`

Compiler

Compiled 15 to 10 computations (33.3% saved)

regimes19.0ms (0.1%)

Memory

-8.1MiB live, 30.2MiB allocated

Counts

19 → 1

Calls

Call 1

Inputs
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (* (sin x) -1/2) eps) (cos x)) #s(literal 1 binary64)) eps))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (cos x) eps) #s(approx (+ (* (* -1/2 x) (* x eps)) eps) (.f64 (.f64 (*.f64 x eps) #s(literal -1/2 binary64)) x))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (cos x) eps) (fma.f64 (.f64 #s(literal -1/2 binary64) x) (.f64 x eps) eps)))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (cos x) eps) (fma.f64 (.f64 (.f64 x x) eps) #s(literal -1/2 binary64) eps)))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (* (sin x) -1/2) eps) (cos x)) (fma.f64 (*.f64 x eps) #s(literal -1/2 binary64) #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 #s(approx ( (sin x) -1/2) (*.f64 #s(literal -1/2 binary64) x)) eps #s(approx (cos x) #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (* (sin x) -1/2) eps) (cos x)) (fma.f64 (*.f64 (+.f64 x eps) #s(literal -1/2 binary64)) x #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (cos x) (fma.f64 (fma.f64 (.f64 x x) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) (*.f64 x x) #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (* (sin x) -1/2) eps) (cos x)) (fma.f64 (fma.f64 (fma.f64 #s(literal 1/12 binary64) (.f64 x eps) #s(literal -1/2 binary64)) x (.f64 #s(literal -1/2 binary64) eps)) x #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (cos x) eps) (fma.f64 #s(approx (+ (* (* eps (+ (* -1/720 (* x x)) 1/24)) (* x x)) (* -1/2 eps)) (.f64 (.f64 (.f64 #s(literal -1/720 binary64) (.f64 (.f64 x x) eps)) x) x)) (.f64 x x) eps)))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (cos x) (fma.f64 (fma.f64 (fma.f64 #s(literal -1/720 binary64) (.f64 x x) #s(literal 1/24 binary64)) (.f64 x x) #s(literal -1/2 binary64)) (.f64 x x) #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (* (sin x) -1/2) eps) (cos x)) (fma.f64 #s(approx (+ (* (+ (* 1/12 (* x eps)) -1/2) x) (* -1/2 eps)) (.f64 (fma.f64 #s(literal 1/12 binary64) eps (/.f64 #s(literal -1/2 binary64) x)) (.f64 x x))) x #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 #s(approx ( (sin x) -1/2) (.f64 #s(literal -1/2 binary64) x)) eps #s(approx (cos x) (fma.f64 (fma.f64 (.f64 x x) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) (*.f64 x x) #s(literal 1 binary64)))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (cos x) eps) (fma.f64 (fma.f64 (.f64 eps (fma.f64 #s(literal -1/720 binary64) (.f64 x x) #s(literal 1/24 binary64))) (.f64 x x) (.f64 #s(literal -1/2 binary64) eps)) (*.f64 x x) eps)))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (cos x) eps) (fma.f64 (fma.f64 (/.f64 (.f64 (fma.f64 (.f64 x x) #s(literal -1/720 binary64) #s(literal 1/24 binary64)) (neg.f64 (.f64 eps eps))) (neg.f64 eps)) (.f64 x x) (.f64 #s(literal -1/2 binary64) eps)) (.f64 x x) eps)))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (cos x) eps) (fma.f64 (fma.f64 (.f64 eps (/.f64 (fma.f64 #s(literal 1/518400 binary64) (.f64 (.f64 x x) (.f64 x x)) #s(literal -1/576 binary64)) (fma.f64 (.f64 x x) #s(literal -1/720 binary64) #s(literal -1/24 binary64)))) (.f64 x x) (.f64 #s(literal -1/2 binary64) eps)) (.f64 x x) eps)))
#s(approx (- (sin (+ x eps)) (sin x)) (sin.f64 eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (cos.f64 x) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 #s(approx ( (sin x) -1/2) (*.f64 #s(literal -1/2 binary64) x)) eps (cos.f64 x)) eps))

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

Calls

3 calls:

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

Results

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

Compiler

Compiled 15 to 10 computations (33.3% saved)

regimes18.0ms (0.1%)

Memory

-6.1MiB live, 31.2MiB allocated

Counts

17 → 1

Calls

Call 1

Inputs
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (* (sin x) -1/2) eps) (cos x)) #s(literal 1 binary64)) eps))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (cos x) eps) #s(approx (+ (* (* -1/2 x) (* x eps)) eps) (.f64 (.f64 (*.f64 x eps) #s(literal -1/2 binary64)) x))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (cos x) eps) (fma.f64 (.f64 #s(literal -1/2 binary64) x) (.f64 x eps) eps)))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (cos x) eps) (fma.f64 (.f64 (.f64 x x) eps) #s(literal -1/2 binary64) eps)))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (* (sin x) -1/2) eps) (cos x)) (fma.f64 (*.f64 x eps) #s(literal -1/2 binary64) #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 #s(approx ( (sin x) -1/2) (*.f64 #s(literal -1/2 binary64) x)) eps #s(approx (cos x) #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (* (sin x) -1/2) eps) (cos x)) (fma.f64 (*.f64 (+.f64 x eps) #s(literal -1/2 binary64)) x #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (cos x) (fma.f64 (fma.f64 (.f64 x x) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) (*.f64 x x) #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (* (sin x) -1/2) eps) (cos x)) (fma.f64 (fma.f64 (fma.f64 #s(literal 1/12 binary64) (.f64 x eps) #s(literal -1/2 binary64)) x (.f64 #s(literal -1/2 binary64) eps)) x #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (cos x) eps) (fma.f64 #s(approx (+ (* (* eps (+ (* -1/720 (* x x)) 1/24)) (* x x)) (* -1/2 eps)) (.f64 (.f64 (.f64 #s(literal -1/720 binary64) (.f64 (.f64 x x) eps)) x) x)) (.f64 x x) eps)))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (cos x) (fma.f64 (fma.f64 (fma.f64 #s(literal -1/720 binary64) (.f64 x x) #s(literal 1/24 binary64)) (.f64 x x) #s(literal -1/2 binary64)) (.f64 x x) #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (* (sin x) -1/2) eps) (cos x)) (fma.f64 #s(approx (+ (* (+ (* 1/12 (* x eps)) -1/2) x) (* -1/2 eps)) (.f64 (fma.f64 #s(literal 1/12 binary64) eps (/.f64 #s(literal -1/2 binary64) x)) (.f64 x x))) x #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 #s(approx ( (sin x) -1/2) (.f64 #s(literal -1/2 binary64) x)) eps #s(approx (cos x) (fma.f64 (fma.f64 (.f64 x x) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) (*.f64 x x) #s(literal 1 binary64)))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (cos x) eps) (fma.f64 (fma.f64 (.f64 eps (fma.f64 #s(literal -1/720 binary64) (.f64 x x) #s(literal 1/24 binary64))) (.f64 x x) (.f64 #s(literal -1/2 binary64) eps)) (*.f64 x x) eps)))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (cos x) eps) (fma.f64 (fma.f64 (/.f64 (.f64 (fma.f64 (.f64 x x) #s(literal -1/720 binary64) #s(literal 1/24 binary64)) (neg.f64 (.f64 eps eps))) (neg.f64 eps)) (.f64 x x) (.f64 #s(literal -1/2 binary64) eps)) (.f64 x x) eps)))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (cos x) eps) (fma.f64 (fma.f64 (.f64 eps (/.f64 (fma.f64 #s(literal 1/518400 binary64) (.f64 (.f64 x x) (.f64 x x)) #s(literal -1/576 binary64)) (fma.f64 (.f64 x x) #s(literal -1/720 binary64) #s(literal -1/24 binary64)))) (.f64 x x) (.f64 #s(literal -1/2 binary64) eps)) (.f64 x x) eps)))
#s(approx (- (sin (+ x eps)) (sin x)) (sin.f64 eps))

Outputs

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

Calls

3 calls:

5.0ms	(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
5.0ms	x
5.0ms	eps

Results

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

Compiler

Compiled 15 to 10 computations (33.3% saved)

regimes11.0ms (0.1%)

Memory

21.2MiB live, 21.2MiB allocated

Counts

10 → 1

Calls

Call 1

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

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

Calls

3 calls:

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

Results

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

Compiler

Compiled 15 to 10 computations (33.3% saved)

regimes10.0ms (0.1%)

Memory

-17.7MiB live, 20.9MiB allocated

Counts

7 → 1

Calls

Call 1

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

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

Calls

3 calls:

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

Results

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

Compiler

Compiled 15 to 10 computations (33.3% saved)

regimes8.0ms (0.1%)

Memory

20.7MiB live, 20.7MiB allocated

Counts

6 → 1

Calls

Call 1

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

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

Calls

3 calls:

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

Results

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

Compiler

Compiled 15 to 10 computations (33.3% saved)

regimes5.0ms (0%)

Memory

12.2MiB live, 12.2MiB allocated

Accuracy

Total -59.5b remaining (-4774.1%)

Threshold costs -59.5b (-4774.1%)

Counts

2 → 1

Calls

Call 1

Inputs

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

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

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

Calls

3 calls:

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

Results

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

Compiler

Compiled 15 to 10 computations (33.3% saved)

simplify10.0ms (0.1%)

Memory

-28.8MiB live, 14.5MiB allocated

Algorithm

1×	egg-herbie

Rules

36×	`*-commutative_binary64`
2×	`+-commutative_binary64`
2×	`1-exp_binary64`
2×	`1-exp_binary32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	93	307
1	114	307

Stop Event

1×

saturated

Calls

Call 1

Inputs
#s(approx (* (* (sin (* 1/2 (+ 0 eps))) 2) (cos (* 1/2 (+ (* 2 x) eps)))) (.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 #s(approx ( (sin (* 1/2 (+ 0 eps))) 2) (.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -1/322560 binary64) (.f64 eps eps) #s(literal 1/1920 binary64)) (.f64 eps eps) #s(literal -1/24 binary64)) (.f64 eps eps) #s(literal 1 binary64)) eps)) (cos.f64 #s(approx (* 1/2 (+ (* 2 x) eps)) (fma.f64 eps #s(literal 1/2 binary64) x))))
(.f64 #s(approx ( (sin (* 1/2 (+ 0 eps))) 2) (.f64 (fma.f64 (fma.f64 #s(literal 1/1920 binary64) (.f64 eps eps) #s(literal -1/24 binary64)) (.f64 eps eps) #s(literal 1 binary64)) eps)) (cos.f64 #s(approx ( 1/2 (+ (* 2 x) eps)) (fma.f64 #s(literal 1/2 binary64) eps x))))
(.f64 #s(approx ( (sin (* 1/2 (+ 0 eps))) 2) (.f64 (fma.f64 (.f64 eps eps) #s(literal -1/24 binary64) #s(literal 1 binary64)) eps)) (cos.f64 #s(approx (* 1/2 (+ (* 2 x) eps)) (fma.f64 eps #s(literal 1/2 binary64) x))))
#s(approx (* (* (sin (* 1/2 (+ 0 eps))) 2) (cos (* 1/2 (+ (* 2 x) eps)))) (.f64 (.f64 (cos.f64 (fma.f64 eps #s(literal 1/2 binary64) x)) #s(literal 2 binary64)) #s(approx (sin (* eps 1/2)) (*.f64 #s(literal 1/2 binary64) eps))))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (cos.f64 x) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (cos x) (fma.f64 (fma.f64 (fma.f64 #s(literal -1/720 binary64) (.f64 x x) #s(literal 1/24 binary64)) (.f64 x x) #s(literal -1/2 binary64)) (.f64 x x) #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (cos x) (fma.f64 (fma.f64 (.f64 x x) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) (*.f64 x x) #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (* (sin x) -1/2) eps) (cos x)) (fma.f64 (*.f64 (+.f64 x eps) #s(literal -1/2 binary64)) x #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (cos x) eps) (fma.f64 (.f64 #s(literal -1/2 binary64) x) (.f64 x eps) eps)))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (* (sin x) -1/2) eps) (cos x)) #s(literal 1 binary64)) eps))

Outputs
#s(approx (* (* (sin (* 1/2 (+ 0 eps))) 2) (cos (* 1/2 (+ (* 2 x) eps)))) (.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)))))
#s(approx (* (* (sin (* 1/2 (+ 0 eps))) 2) (cos (* 1/2 (+ (* 2 x) eps)))) (.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (*.f64 (cos.f64 (fma.f64 eps #s(literal 1/2 binary64) x)) #s(literal 2 binary64))))
(.f64 #s(approx ( (sin (* 1/2 (+ 0 eps))) 2) (.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -1/322560 binary64) (.f64 eps eps) #s(literal 1/1920 binary64)) (.f64 eps eps) #s(literal -1/24 binary64)) (.f64 eps eps) #s(literal 1 binary64)) eps)) (cos.f64 #s(approx (* 1/2 (+ (* 2 x) eps)) (fma.f64 eps #s(literal 1/2 binary64) x))))
(.f64 (cos.f64 #s(approx ( 1/2 (+ (* 2 x) eps)) (fma.f64 eps #s(literal 1/2 binary64) x))) #s(approx (* (sin (* 1/2 (+ 0 eps))) 2) (.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -1/322560 binary64) (.f64 eps eps) #s(literal 1/1920 binary64)) (.f64 eps eps) #s(literal -1/24 binary64)) (.f64 eps eps) #s(literal 1 binary64)) eps)))
(.f64 #s(approx ( (sin (* 1/2 (+ 0 eps))) 2) (.f64 (fma.f64 (fma.f64 #s(literal 1/1920 binary64) (.f64 eps eps) #s(literal -1/24 binary64)) (.f64 eps eps) #s(literal 1 binary64)) eps)) (cos.f64 #s(approx ( 1/2 (+ (* 2 x) eps)) (fma.f64 #s(literal 1/2 binary64) eps x))))
(.f64 (cos.f64 #s(approx ( 1/2 (+ (* 2 x) eps)) (fma.f64 #s(literal 1/2 binary64) eps x))) #s(approx (* (sin (* 1/2 (+ 0 eps))) 2) (.f64 (fma.f64 (fma.f64 #s(literal 1/1920 binary64) (.f64 eps eps) #s(literal -1/24 binary64)) (*.f64 eps eps) #s(literal 1 binary64)) eps)))
(.f64 #s(approx ( (sin (* 1/2 (+ 0 eps))) 2) (.f64 (fma.f64 (.f64 eps eps) #s(literal -1/24 binary64) #s(literal 1 binary64)) eps)) (cos.f64 #s(approx (* 1/2 (+ (* 2 x) eps)) (fma.f64 eps #s(literal 1/2 binary64) x))))
#s(approx (* (* (sin (* 1/2 (+ 0 eps))) 2) (cos (* 1/2 (+ (* 2 x) eps)))) (.f64 (.f64 (cos.f64 (fma.f64 eps #s(literal 1/2 binary64) x)) #s(literal 2 binary64)) #s(approx (sin (* eps 1/2)) (*.f64 #s(literal 1/2 binary64) eps))))
#s(approx (* (* (sin (* 1/2 (+ 0 eps))) 2) (cos (* 1/2 (+ (* 2 x) eps)))) (.f64 #s(approx (sin ( eps 1/2)) (.f64 eps #s(literal 1/2 binary64))) (.f64 (cos.f64 (fma.f64 eps #s(literal 1/2 binary64) x)) #s(literal 2 binary64))))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (cos.f64 x) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (cos x) (fma.f64 (fma.f64 (fma.f64 #s(literal -1/720 binary64) (.f64 x x) #s(literal 1/24 binary64)) (.f64 x x) #s(literal -1/2 binary64)) (.f64 x x) #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (cos x) (fma.f64 (fma.f64 (.f64 x x) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) (*.f64 x x) #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (* (sin x) -1/2) eps) (cos x)) (fma.f64 (*.f64 (+.f64 x eps) #s(literal -1/2 binary64)) x #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (cos x) eps) (fma.f64 (.f64 #s(literal -1/2 binary64) x) (.f64 x eps) eps)))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (* (sin x) -1/2) eps) (cos x)) #s(literal 1 binary64)) eps))

soundness1.2s (9.6%)

Memory

35.4MiB live, 1 059.7MiB allocated

Rules

16 678×	`lower-fma.f64`
16 678×	`lower-fma.f32`
15 424×	`lower-fma.f64`
15 424×	`lower-fma.f32`
13 214×	`lower-fma.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	412	5221
1	1267	5028
2	3712	4916
0	8390	4512
0	6	16
0	10	16
1	53	16
2	380	16
3	4766	16
0	8210	16
0	107	496
1	314	496
2	775	489
3	2836	489
4	6173	489
0	8126	458
0	362	4559
1	1062	4418
2	2636	4349
3	6128	4318
0	8164	3960
0	355	3129
1	1054	3038
2	2674	2990
3	6284	2974
0	8391	2742

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

Compiler

Compiled 406 to 215 computations (47% saved)

preprocess126.0ms (1%)

Memory: -12.2MiB live, 306.5MiB allocated
Compiler: Compiled 428 to 180 computations (57.9% saved)

end0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated

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

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

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

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

start0.0ms (0%)

analyze50.0ms (0.4%)

sample6.6s (52%)

explain90.0ms (0.7%)

preprocess24.0ms (0.2%)

eval0.0ms (0%)

prune1.0ms (0%)

simplify7.0ms (0.1%)

localize26.0ms (0.2%)

series4.0ms (0%)

simplify158.0ms (1.3%)

rewrite216.0ms (1.7%)

eval51.0ms (0.4%)

prune42.0ms (0.3%)

simplify207.0ms (1.6%)

localize150.0ms (1.2%)

series34.0ms (0.3%)

simplify185.0ms (1.5%)

rewrite218.0ms (1.7%)

eval117.0ms (0.9%)

prune115.0ms (0.9%)

simplify213.0ms (1.7%)

localize244.0ms (1.9%)

series30.0ms (0.2%)

simplify178.0ms (1.4%)

rewrite218.0ms (1.7%)

eval97.0ms (0.8%)

prune137.0ms (1.1%)

simplify189.0ms (1.5%)

localize317.0ms (2.5%)

series53.0ms (0.4%)

simplify236.0ms (1.9%)

rewrite300.0ms (2.4%)

eval264.0ms (2.1%)

prune241.0ms (1.9%)

regimes48.0ms (0.4%)

regimes38.0ms (0.3%)

regimes25.0ms (0.2%)

regimes102.0ms (0.8%)

regimes20.0ms (0.2%)

regimes19.0ms (0.1%)

regimes18.0ms (0.1%)

regimes11.0ms (0.1%)

regimes10.0ms (0.1%)

regimes8.0ms (0.1%)

regimes5.0ms (0%)

simplify10.0ms (0.1%)

soundness1.2s (9.6%)

preprocess126.0ms (1%)

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