Metrics for 2sin (example 3.3)

start0.0ms (0%)

Memory: 0.1MiB live, 0.1MiB allocated

analyze42.0ms (0.3%)

Memory

-6.5MiB live, 78.4MiB 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)

sample6.3s (44.2%)

Memory

139.0MiB live, 7 194.1MiB allocated

Samples

3.4s	26 399×	0	invalid
656.0ms	5 520×	0	valid
507.0ms	2 736×	1	valid

Precisions

Click to see histograms. Total time spent on operations: 3.4s

const: 882.0ms (25.6% of total)

ival-sin: 729.0ms (21.1% of total)

ival-<=: 311.0ms (9% of total)

ival-mult: 310.0ms (9% of total)

ival-fabs: 286.0ms (8.3% of total)

ival-<: 265.0ms (7.7% of total)

ival-add: 237.0ms (6.9% of total)

ival-sub: 196.0ms (5.7% of total)

ival-and: 101.0ms (2.9% of total)

adjust: 74.0ms (2.1% of total)

exact: 44.0ms (1.3% of total)

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

Bogosity

explain202.0ms (1.4%)

Memory

-1.3MiB live, 76.1MiB allocated

FPErrors

Click to see full error table

Ground Truth	Overpredictions	Example	Underpredictions	Example	Subexpression
217	1	(-5.260965472320147e-258 1.5846438986147005e-260)	1	(-2.820818594153094e-54 5.371383043721107e-56)	`(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))`
5	0	-	1	(93.5228927064356 0.05326189858433034)	`(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	217	4
`sin.f64`	`(sin.f64 (+.f64 x eps))`	sensitivity	4	1

Confusion

	Predicted +	Predicted -
+	217	3
-	1	35

Precision

0.9954128440366973

Recall

0.9863636363636363

Confusion?

	Predicted +	Predicted Maybe	Predicted -
+	217	2	1
-	1	3	32

Precision?

0.9820627802690582

Recall?

0.9954545454545455

Freqs

test

number	freq
0	38
1	215
2	3

Total Confusion?

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

Precision?

1.0

Recall?

1.0

Samples

66.0ms	326×	0	valid
17.0ms	180×	1	valid
3.0ms	4×	3	valid
0.0ms	2×	2	valid

Compiler

Compiled 49 to 22 computations (55.1% saved)

Precisions

Click to see histograms. Total time spent on operations: 22.0ms

ival-sin: 11.0ms (50.8% of total)

adjust: 4.0ms (18.5% of total)

ival-add: 3.0ms (13.8% of total)

ival-sub: 3.0ms (13.8% of total)

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

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

preprocess24.0ms (0.2%)

Memory

18.3MiB live, 18.3MiB 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))

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

0.8MiB live, 0.8MiB allocated

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	62.8%	(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))

Compiler

Compiled 9 to 6 computations (33.3% saved)

simplify72.0ms (0.5%)

Memory

-18.1MiB live, 20.2MiB 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))
(sin.f64 (+.f64 x eps))
(+.f64 x eps)
x
eps
(sin.f64 x)

localize27.0ms (0.2%)

Memory

-10.8MiB live, 34.0MiB allocated

Localize:

Found 4 expressions of interest:

New	Metric	Score
accuracy	0	(+.f64 x eps)
accuracy	0	(sin.f64 x)
accuracy	0.14057965590938684	(sin.f64 (+.f64 x eps))
accuracy	23.630841062339364	(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))

Samples

10.0ms	163×	0	valid
9.0ms	90×	1	valid
1.0ms	2×	3	valid
0.0ms	1×	2	valid

Compiler

Compiled 20 to 8 computations (60% saved)

Precisions

Click to see histograms. Total time spent on operations: 13.0ms

ival-sin: 6.0ms (46.4% of total)

ival-sub: 3.0ms (23.2% of total)

adjust: 2.0ms (15.5% of total)

ival-add: 2.0ms (15.5% of total)

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

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

series5.0ms (0%)

Memory

7.3MiB live, 7.3MiB 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	(- (sin (+ x eps)) (sin x))
0.0ms	x	@	inf	(+ x eps)

simplify229.0ms (1.6%)

Memory

32.4MiB live, 298.5MiB allocated

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

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

Stop Event

1×	iter limit
1×	node limit

Counts

84 → 77

Calls

Call 1

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

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

rewrite310.0ms (2.2%)

Memory

-14.3MiB live, 386.3MiB 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
(exp.f64 (*.f64 (log.f64 (/.f64 #s(literal 1 binary64) (-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)))) #s(literal -1 binary64)))
(+.f64 (sin.f64 (+.f64 x eps)) (sin.f64 (neg.f64 x)))
(+.f64 (.f64 (sin.f64 x) (cos.f64 eps)) (-.f64 (.f64 (cos.f64 x) (sin.f64 eps)) (sin.f64 x)))
(+.f64 (*.f64 (cos.f64 x) (sin.f64 eps)) (fma.f64 (sin.f64 x) (cos.f64 eps) (sin.f64 (neg.f64 x))))
(+.f64 (.f64 (cos.f64 x) (sin.f64 eps)) (-.f64 (.f64 (sin.f64 x) (cos.f64 eps)) (sin.f64 x)))
(+.f64 (sin.f64 (neg.f64 x)) (sin.f64 (+.f64 x eps)))
(+.f64 (/.f64 (pow.f64 (sin.f64 (+.f64 x eps)) #s(literal 3 binary64)) (-.f64 (fma.f64 (sin.f64 x) (+.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) #s(literal 1/2 binary64)) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 (+.f64 x eps) #s(literal 2 binary64)))))) (neg.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (-.f64 (fma.f64 (sin.f64 x) (+.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) #s(literal 1/2 binary64)) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 (+.f64 x eps) #s(literal 2 binary64))))))))
(+.f64 (/.f64 (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal -1/2 binary64) (cos.f64 (.f64 (+.f64 x eps) #s(literal 2 binary64))))) (+.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))) (neg.f64 (/.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 (+.f64 x x)))) (+.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)))))
(+.f64 (-.f64 (.f64 (cos.f64 x) (sin.f64 eps)) (sin.f64 x)) (.f64 (sin.f64 x) (cos.f64 eps)))
(+.f64 (+.f64 (sin.f64 (neg.f64 x)) (.f64 (sin.f64 x) (cos.f64 eps))) (.f64 (cos.f64 x) (sin.f64 eps)))
(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
(-.f64 (/.f64 (pow.f64 (sin.f64 (+.f64 x eps)) #s(literal 3 binary64)) (-.f64 (fma.f64 (sin.f64 x) (+.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) #s(literal 1/2 binary64)) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 (+.f64 x eps) #s(literal 2 binary64)))))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (-.f64 (fma.f64 (sin.f64 x) (+.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) #s(literal 1/2 binary64)) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 (+.f64 x eps) #s(literal 2 binary64)))))))
(-.f64 (/.f64 (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal -1/2 binary64) (cos.f64 (.f64 (+.f64 x eps) #s(literal 2 binary64))))) (+.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))) (/.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 (+.f64 x x)))) (+.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))))
(-.f64 #s(literal 0 binary64) (-.f64 (sin.f64 x) (sin.f64 (+.f64 x eps))))
(-.f64 (+.f64 (sin.f64 (+.f64 x eps)) #s(literal 0 binary64)) (sin.f64 x))
(fma.f64 (sin.f64 (+.f64 x eps)) (/.f64 (sin.f64 (+.f64 x eps)) (+.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))) (neg.f64 (/.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 (+.f64 x x)))) (+.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)))))
(fma.f64 (sin.f64 (+.f64 x eps)) (/.f64 (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal -1/2 binary64) (cos.f64 (.f64 (+.f64 x eps) #s(literal 2 binary64))))) (-.f64 (fma.f64 (sin.f64 x) (+.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) #s(literal 1/2 binary64)) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 (+.f64 x eps) #s(literal 2 binary64)))))) (neg.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (-.f64 (fma.f64 (sin.f64 x) (+.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) #s(literal 1/2 binary64)) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 (+.f64 x eps) #s(literal 2 binary64))))))))
(fma.f64 (sin.f64 x) (cos.f64 eps) (-.f64 (*.f64 (cos.f64 x) (sin.f64 eps)) (sin.f64 x)))
(fma.f64 (sin.f64 x) #s(literal -1 binary64) (sin.f64 (+.f64 x eps)))
(fma.f64 (cos.f64 eps) (sin.f64 x) (-.f64 (*.f64 (cos.f64 x) (sin.f64 eps)) (sin.f64 x)))
(fma.f64 (cos.f64 x) (sin.f64 eps) (fma.f64 (sin.f64 x) (cos.f64 eps) (sin.f64 (neg.f64 x))))
(fma.f64 (cos.f64 x) (sin.f64 eps) (-.f64 (*.f64 (sin.f64 x) (cos.f64 eps)) (sin.f64 x)))
(fma.f64 (sin.f64 eps) (cos.f64 x) (fma.f64 (sin.f64 x) (cos.f64 eps) (sin.f64 (neg.f64 x))))
(fma.f64 (sin.f64 eps) (cos.f64 x) (-.f64 (*.f64 (sin.f64 x) (cos.f64 eps)) (sin.f64 x)))
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(/.f64 (-.f64 (.f64 (/.f64 (.f64 x x) (-.f64 x eps)) (/.f64 (.f64 x x) (-.f64 x eps))) (.f64 (/.f64 (.f64 eps eps) (-.f64 x eps)) (/.f64 (.f64 eps eps) (-.f64 x eps)))) (fma.f64 x (/.f64 x (-.f64 x eps)) (/.f64 (*.f64 eps eps) (-.f64 x eps))))
(/.f64 (.f64 (fma.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x))) (.f64 (.f64 eps (.f64 eps eps)) (.f64 (.f64 eps (.f64 eps eps)) (.f64 eps (.f64 eps eps))))) (/.f64 #s(literal 1 binary64) (fma.f64 x x (.f64 eps (-.f64 eps x))))) (fma.f64 (.f64 eps (.f64 eps eps)) (-.f64 (.f64 eps (.f64 eps eps)) (.f64 x (.f64 x x))) (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x)))))
(/.f64 (.f64 (.f64 (fma.f64 x (.f64 x x) (.f64 eps (.f64 eps eps))) (.f64 (fma.f64 x x (.f64 eps (+.f64 x eps))) (-.f64 x eps))) (/.f64 #s(literal 1 binary64) (fma.f64 x x (.f64 eps (-.f64 eps x))))) (.f64 (fma.f64 x x (.f64 eps (+.f64 x eps))) (-.f64 x eps)))
(/.f64 (.f64 (.f64 (fma.f64 x (.f64 x x) (.f64 eps (.f64 eps eps))) (.f64 (fma.f64 x x (.f64 eps (+.f64 x eps))) (-.f64 x eps))) (/.f64 #s(literal 1 binary64) (-.f64 x eps))) (fma.f64 (.f64 eps eps) (fma.f64 x x (.f64 eps eps)) (.f64 (.f64 x x) (.f64 x x))))
(/.f64 (.f64 (.f64 (fma.f64 x x (.f64 eps eps)) (.f64 (+.f64 x eps) (-.f64 x eps))) (/.f64 #s(literal 1 binary64) (-.f64 x eps))) (fma.f64 x x (*.f64 eps eps)))
(pow.f64 (/.f64 #s(literal 1 binary64) (+.f64 x eps)) #s(literal -1 binary64))
(pow.f64 (/.f64 (/.f64 #s(literal 1 binary64) (+.f64 x eps)) #s(literal 1 binary64)) #s(literal -1 binary64))
(pow.f64 (/.f64 (-.f64 eps x) (*.f64 (+.f64 x eps) (-.f64 eps x))) #s(literal -1 binary64))
(.f64 (+.f64 x eps) (.f64 (-.f64 x eps) (/.f64 #s(literal 1 binary64) (-.f64 x eps))))
(*.f64 (+.f64 x eps) (/.f64 (-.f64 x eps) (-.f64 x eps)))
(.f64 (fma.f64 x (.f64 x x) (.f64 eps (.f64 eps eps))) (/.f64 #s(literal 1 binary64) (fma.f64 x x (*.f64 eps (-.f64 eps x)))))
(.f64 (fma.f64 x x (.f64 eps (-.f64 eps x))) (.f64 (+.f64 x eps) (/.f64 #s(literal 1 binary64) (fma.f64 x x (.f64 eps (-.f64 eps x))))))
(.f64 (fma.f64 x x (.f64 eps (-.f64 eps x))) (/.f64 (+.f64 x eps) (fma.f64 x x (*.f64 eps (-.f64 eps x)))))
(.f64 (.f64 (+.f64 x eps) (-.f64 x eps)) (/.f64 #s(literal 1 binary64) (-.f64 x eps)))
(.f64 (neg.f64 (fma.f64 x (.f64 x x) (.f64 eps (.f64 eps eps)))) (/.f64 #s(literal 1 binary64) (neg.f64 (fma.f64 x x (*.f64 eps (-.f64 eps x))))))
(.f64 (neg.f64 (.f64 (+.f64 x eps) (-.f64 x eps))) (/.f64 #s(literal 1 binary64) (neg.f64 (-.f64 x eps))))
(*.f64 #s(literal 1 binary64) (+.f64 x eps))
(.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x x (.f64 eps (-.f64 eps x)))) (fma.f64 x (.f64 x x) (.f64 eps (*.f64 eps eps))))
(.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x x (.f64 eps (-.f64 eps x)))) (pow.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x (.f64 x x) (.f64 eps (*.f64 eps eps)))) #s(literal -1 binary64)))
(.f64 (/.f64 #s(literal 1 binary64) (-.f64 x eps)) (.f64 (+.f64 x eps) (-.f64 x eps)))
(.f64 (/.f64 #s(literal 1 binary64) (-.f64 x eps)) (pow.f64 (/.f64 #s(literal 1 binary64) (.f64 (+.f64 x eps) (-.f64 x eps))) #s(literal -1 binary64)))
(.f64 (.f64 (+.f64 x eps) (-.f64 eps x)) (/.f64 #s(literal 1 binary64) (-.f64 eps x)))
(.f64 (/.f64 (.f64 (+.f64 x eps) (-.f64 x eps)) (*.f64 (+.f64 x eps) (-.f64 x eps))) (+.f64 x eps))
(.f64 (/.f64 (fma.f64 x (.f64 x x) (.f64 eps (.f64 eps eps))) (fma.f64 (.f64 eps (.f64 eps eps)) (.f64 (.f64 (-.f64 eps x) (-.f64 eps x)) (-.f64 eps x)) (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x))))) (fma.f64 x (.f64 x (.f64 x x)) (.f64 (.f64 eps (-.f64 eps x)) (-.f64 (.f64 eps (-.f64 eps x)) (*.f64 x x)))))
(.f64 (/.f64 (fma.f64 x (.f64 x x) (.f64 eps (.f64 eps eps))) (.f64 (fma.f64 x x (.f64 eps (-.f64 eps x))) (-.f64 (.f64 x x) (.f64 eps (-.f64 eps x))))) (-.f64 (.f64 x x) (.f64 eps (-.f64 eps x))))
(.f64 (/.f64 (.f64 (+.f64 x eps) (-.f64 x eps)) (.f64 (fma.f64 x x (.f64 eps (+.f64 x eps))) (-.f64 x eps))) (fma.f64 x x (*.f64 eps (+.f64 x eps))))
(.f64 (pow.f64 (/.f64 (-.f64 x eps) (.f64 (fma.f64 x (.f64 x x) (.f64 eps (.f64 eps eps))) (.f64 (fma.f64 x x (.f64 eps (+.f64 x eps))) (-.f64 x eps)))) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (fma.f64 (.f64 eps eps) (fma.f64 x x (.f64 eps eps)) (.f64 (.f64 x x) (.f64 x x)))))
(.f64 (pow.f64 (/.f64 (-.f64 x eps) (.f64 (fma.f64 x x (.f64 eps eps)) (.f64 (+.f64 x eps) (-.f64 x eps)))) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (fma.f64 x x (*.f64 eps eps))))
(.f64 (pow.f64 (/.f64 (fma.f64 x x (.f64 eps (-.f64 eps x))) (fma.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x))) (.f64 (.f64 eps (.f64 eps eps)) (.f64 (.f64 eps (.f64 eps eps)) (.f64 eps (.f64 eps eps)))))) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (fma.f64 (.f64 eps (.f64 eps eps)) (-.f64 (.f64 eps (.f64 eps eps)) (.f64 x (.f64 x x))) (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x))))))
(.f64 (pow.f64 (/.f64 (fma.f64 x x (.f64 eps (-.f64 eps x))) (.f64 (fma.f64 x (.f64 x x) (.f64 eps (.f64 eps eps))) (.f64 (fma.f64 x x (.f64 eps (+.f64 x eps))) (-.f64 x eps)))) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (.f64 (fma.f64 x x (.f64 eps (+.f64 x eps))) (-.f64 x eps))))
(exp.f64 (*.f64 (log.f64 (sin.f64 x)) #s(literal 1 binary64)))
(sin.f64 x)
(pow.f64 (sin.f64 x) #s(literal 1 binary64))

eval37.0ms (0.3%)

Memory: 2.2MiB live, 75.0MiB allocated
Compiler: Compiled 7 823 to 844 computations (89.2% saved)

prune50.0ms (0.4%)

Memory

17.5MiB live, 99.7MiB allocated

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	284	7	291
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	284	8	292

Accuracy

100.0%

Counts

292 → 8

Alt Table

Click to see full alt table

Status	Accuracy	Program
	99.7%	(fma.f64 (sin.f64 eps) (cos.f64 x) (fma.f64 (sin.f64 x) (cos.f64 eps) (sin.f64 (neg.f64 x))))
✓	62.8%	(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
▶	61.4%	(-.f64 (sin.f64 (+.f64 x eps)) #s(approx (sin x) (fma.f64 #s(literal -1/6 binary64) (.f64 x (.f64 x x)) x)))
▶	99.8%	(.f64 (.f64 (sin.f64 (.f64 (+.f64 eps #s(literal 0 binary64)) #s(literal 1/2 binary64))) (cos.f64 (.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)))) #s(literal 2 binary64))
	99.4%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 eps (fma.f64 (fma.f64 eps (.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64)) (cos.f64 x) (.f64 (.f64 eps (sin.f64 x)) (fma.f64 eps (*.f64 eps #s(literal 1/24 binary64)) #s(literal -1/2 binary64))))))
▶	99.0%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 eps (fma.f64 eps (.f64 #s(literal -1/2 binary64) (sin.f64 x)) (cos.f64 x))))
▶	98.6%	#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 eps (cos.f64 x)))
▶	97.5%	#s(approx (- (sin (+ x eps)) (sin x)) (sin.f64 eps))

Compiler

Compiled 207 to 132 computations (36.2% saved)

simplify248.0ms (1.8%)

Memory

-8.2MiB live, 192.3MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 17 expressions of interest:

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

Rules

7 458×	`lower-fma.f32`
7 452×	`lower-fma.f64`
4 886×	`lower-*.f32`
4 868×	`lower-*.f64`
1 562×	`neg-mul-1`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	36	199
0	61	181
1	96	181
2	183	181
3	308	177
4	389	177
5	589	177
6	1706	177
7	2044	177
8	2175	177
9	2211	177
10	2309	177
11	2473	177
12	3211	177
13	3461	177
14	3741	177
15	3982	177
16	4392	177
17	6268	177
18	7985	177
0	8050	173

Stop Event

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

Calls

Call 1

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

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

localize126.0ms (0.9%)

Memory

-10.8MiB live, 185.4MiB allocated

Localize:

Found 17 expressions of interest:

New	Metric	Score
accuracy	0	(cos.f64 x)
accuracy	0.0078125	(fma.f64 eps (*.f64 #s(literal -1/2 binary64) (sin.f64 x)) (cos.f64 x))
accuracy	0.015625	(.f64 eps (fma.f64 eps (.f64 #s(literal -1/2 binary64) (sin.f64 x)) (cos.f64 x)))
accuracy	0.6075516331400427	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 eps (fma.f64 eps (.f64 #s(literal -1/2 binary64) (sin.f64 x)) (cos.f64 x))))
accuracy	0.11328125	(.f64 x (.f64 x x))
accuracy	0.14057965590938684	(sin.f64 (+.f64 x eps))
accuracy	1.3029342354348852	#s(approx (sin x) (fma.f64 #s(literal -1/6 binary64) (.f64 x (.f64 x x)) x))
accuracy	23.630841062339364	(-.f64 (sin.f64 (+.f64 x eps)) #s(approx (sin x) (fma.f64 #s(literal -1/6 binary64) (.f64 x (.f64 x x)) x)))
accuracy	0	(cos.f64 x)
accuracy	0.01171875	(*.f64 eps (cos.f64 x))
accuracy	0.9119086677164644	#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 eps (cos.f64 x)))
accuracy	0	(sin.f64 eps)
accuracy	1.6038462998568086	#s(approx (- (sin (+ x eps)) (sin x)) (sin.f64 eps))
accuracy	0	(.f64 (.f64 (sin.f64 (.f64 (+.f64 eps #s(literal 0 binary64)) #s(literal 1/2 binary64))) (cos.f64 (.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)))) #s(literal 2 binary64))
accuracy	0	(sin.f64 (*.f64 (+.f64 eps #s(literal 0 binary64)) #s(literal 1/2 binary64)))
accuracy	0.0078125	(.f64 (sin.f64 (.f64 (+.f64 eps #s(literal 0 binary64)) #s(literal 1/2 binary64))) (cos.f64 (*.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64))))
accuracy	0.12433519012083698	(cos.f64 (*.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)))

Samples

40.0ms	163×	0	valid
40.0ms	90×	1	valid
2.0ms	2×	3	valid
0.0ms	1×	2	valid

Compiler

Compiled 172 to 33 computations (80.8% saved)

Precisions

Click to see histograms. Total time spent on operations: 62.0ms

ival-mult: 28.0ms (44.9% of total)

adjust: 9.0ms (14.4% of total)

ival-sin: 9.0ms (14.4% of total)

ival-add: 6.0ms (9.6% of total)

ival-cos: 5.0ms (8% of total)

const: 4.0ms (6.4% of total)

ival-sub: 2.0ms (3.2% of total)

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

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

exact: 0.0ms (0% of total)

series34.0ms (0.2%)

Memory

0.1MiB live, 46.2MiB allocated

Counts

20 → 396

Calls

Call 1

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

Outputs
#s(alt (* 1/2 eps) (taylor 0 x) (#s(alt (.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)) (patch (.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt (+ x (* 1/2 eps)) (taylor 0 x) (#s(alt (.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)) (patch (.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt (+ x (* 1/2 eps)) (taylor 0 x) (#s(alt (.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)) (patch (.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt (+ x (* 1/2 eps)) (taylor 0 x) (#s(alt (.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)) (patch (.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt x (taylor inf x) (#s(alt (.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)) (patch (.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1 (* 1/2 (/ eps x)))) (taylor inf x) (#s(alt (.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)) (patch (.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1 (* 1/2 (/ eps x)))) (taylor inf x) (#s(alt (.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)) (patch (.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1 (* 1/2 (/ eps x)))) (taylor inf x) (#s(alt (.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)) (patch (.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt x (taylor -inf x) (#s(alt (.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)) (patch (.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (- (* -1/2 (/ eps x)) 1))) (taylor -inf x) (#s(alt (.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)) (patch (.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (- (* -1/2 (/ eps x)) 1))) (taylor -inf x) (#s(alt (.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)) (patch (.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (- (* -1/2 (/ eps x)) 1))) (taylor -inf x) (#s(alt (.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)) (patch (.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt x (taylor 0 eps) (#s(alt (.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)) (patch (.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt (+ x (* 1/2 eps)) (taylor 0 eps) (#s(alt (.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)) (patch (.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt (+ x (* 1/2 eps)) (taylor 0 eps) (#s(alt (.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)) (patch (.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt (+ x (* 1/2 eps)) (taylor 0 eps) (#s(alt (.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)) (patch (.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* 1/2 eps) (taylor inf eps) (#s(alt (.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)) (patch (.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* eps (+ 1/2 (/ x eps))) (taylor inf eps) (#s(alt (.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)) (patch (.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* eps (+ 1/2 (/ x eps))) (taylor inf eps) (#s(alt (.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)) (patch (.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* eps (+ 1/2 (/ x eps))) (taylor inf eps) (#s(alt (.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)) (patch (.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* 1/2 eps) (taylor -inf eps) (#s(alt (.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)) (patch (.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* eps (- (* -1 (/ x eps)) 1/2))) (taylor -inf eps) (#s(alt (.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)) (patch (.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* eps (- (* -1 (/ x eps)) 1/2))) (taylor -inf eps) (#s(alt (.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)) (patch (.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* eps (- (* -1 (/ x eps)) 1/2))) (taylor -inf eps) (#s(alt (.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)) (patch (.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt eps (taylor 0 eps) (#s(alt (+.f64 eps #s(literal 0 binary64)) (patch (+.f64 eps #s(literal 0 binary64)) #<representation binary64>) () ())) ())
#s(alt eps (taylor 0 eps) (#s(alt (+.f64 eps #s(literal 0 binary64)) (patch (+.f64 eps #s(literal 0 binary64)) #<representation binary64>) () ())) ())
#s(alt eps (taylor 0 eps) (#s(alt (+.f64 eps #s(literal 0 binary64)) (patch (+.f64 eps #s(literal 0 binary64)) #<representation binary64>) () ())) ())
#s(alt eps (taylor 0 eps) (#s(alt (+.f64 eps #s(literal 0 binary64)) (patch (+.f64 eps #s(literal 0 binary64)) #<representation binary64>) () ())) ())
#s(alt eps (taylor inf eps) (#s(alt (+.f64 eps #s(literal 0 binary64)) (patch (+.f64 eps #s(literal 0 binary64)) #<representation binary64>) () ())) ())
#s(alt eps (taylor inf eps) (#s(alt (+.f64 eps #s(literal 0 binary64)) (patch (+.f64 eps #s(literal 0 binary64)) #<representation binary64>) () ())) ())
#s(alt eps (taylor inf eps) (#s(alt (+.f64 eps #s(literal 0 binary64)) (patch (+.f64 eps #s(literal 0 binary64)) #<representation binary64>) () ())) ())
#s(alt eps (taylor inf eps) (#s(alt (+.f64 eps #s(literal 0 binary64)) (patch (+.f64 eps #s(literal 0 binary64)) #<representation binary64>) () ())) ())
#s(alt eps (taylor -inf eps) (#s(alt (+.f64 eps #s(literal 0 binary64)) (patch (+.f64 eps #s(literal 0 binary64)) #<representation binary64>) () ())) ())
#s(alt eps (taylor -inf eps) (#s(alt (+.f64 eps #s(literal 0 binary64)) (patch (+.f64 eps #s(literal 0 binary64)) #<representation binary64>) () ())) ())
#s(alt eps (taylor -inf eps) (#s(alt (+.f64 eps #s(literal 0 binary64)) (patch (+.f64 eps #s(literal 0 binary64)) #<representation binary64>) () ())) ())
#s(alt eps (taylor -inf eps) (#s(alt (+.f64 eps #s(literal 0 binary64)) (patch (+.f64 eps #s(literal 0 binary64)) #<representation binary64>) () ())) ())
#s(alt (* eps (cos x)) (taylor 0 eps) (#s(alt (.f64 (.f64 (sin.f64 (.f64 (+.f64 eps #s(literal 0 binary64)) #s(literal 1/2 binary64))) (cos.f64 (.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)))) #s(literal 2 binary64)) (patch (.f64 (.f64 (sin.f64 (.f64 (+.f64 eps #s(literal 0 binary64)) #s(literal 1/2 binary64))) (cos.f64 (.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)))) #s(literal 2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* eps (+ (cos x) (* -1/2 (* eps (sin x))))) (taylor 0 eps) (#s(alt (.f64 (.f64 (sin.f64 (.f64 (+.f64 eps #s(literal 0 binary64)) #s(literal 1/2 binary64))) (cos.f64 (.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)))) #s(literal 2 binary64)) (patch (.f64 (.f64 (sin.f64 (.f64 (+.f64 eps #s(literal 0 binary64)) #s(literal 1/2 binary64))) (cos.f64 (.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)))) #s(literal 2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* 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 (+.f64 eps #s(literal 0 binary64)) #s(literal 1/2 binary64))) (cos.f64 (.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)))) #s(literal 2 binary64)) (patch (.f64 (.f64 (sin.f64 (.f64 (+.f64 eps #s(literal 0 binary64)) #s(literal 1/2 binary64))) (cos.f64 (.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)))) #s(literal 2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* 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 (+.f64 eps #s(literal 0 binary64)) #s(literal 1/2 binary64))) (cos.f64 (.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)))) #s(literal 2 binary64)) (patch (.f64 (.f64 (sin.f64 (.f64 (+.f64 eps #s(literal 0 binary64)) #s(literal 1/2 binary64))) (cos.f64 (.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)))) #s(literal 2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* 2 (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps)))) (taylor inf eps) (#s(alt (.f64 (.f64 (sin.f64 (.f64 (+.f64 eps #s(literal 0 binary64)) #s(literal 1/2 binary64))) (cos.f64 (.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)))) #s(literal 2 binary64)) (patch (.f64 (.f64 (sin.f64 (.f64 (+.f64 eps #s(literal 0 binary64)) #s(literal 1/2 binary64))) (cos.f64 (.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)))) #s(literal 2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* 2 (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps)))) (taylor inf eps) (#s(alt (.f64 (.f64 (sin.f64 (.f64 (+.f64 eps #s(literal 0 binary64)) #s(literal 1/2 binary64))) (cos.f64 (.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)))) #s(literal 2 binary64)) (patch (.f64 (.f64 (sin.f64 (.f64 (+.f64 eps #s(literal 0 binary64)) #s(literal 1/2 binary64))) (cos.f64 (.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)))) #s(literal 2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* 2 (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps)))) (taylor inf eps) (#s(alt (.f64 (.f64 (sin.f64 (.f64 (+.f64 eps #s(literal 0 binary64)) #s(literal 1/2 binary64))) (cos.f64 (.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)))) #s(literal 2 binary64)) (patch (.f64 (.f64 (sin.f64 (.f64 (+.f64 eps #s(literal 0 binary64)) #s(literal 1/2 binary64))) (cos.f64 (.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)))) #s(literal 2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* 2 (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps)))) (taylor inf eps) (#s(alt (.f64 (.f64 (sin.f64 (.f64 (+.f64 eps #s(literal 0 binary64)) #s(literal 1/2 binary64))) (cos.f64 (.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)))) #s(literal 2 binary64)) (patch (.f64 (.f64 (sin.f64 (.f64 (+.f64 eps #s(literal 0 binary64)) #s(literal 1/2 binary64))) (cos.f64 (.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)))) #s(literal 2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* 2 (* (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps)))) (taylor -inf eps) (#s(alt (.f64 (.f64 (sin.f64 (.f64 (+.f64 eps #s(literal 0 binary64)) #s(literal 1/2 binary64))) (cos.f64 (.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)))) #s(literal 2 binary64)) (patch (.f64 (.f64 (sin.f64 (.f64 (+.f64 eps #s(literal 0 binary64)) #s(literal 1/2 binary64))) (cos.f64 (.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)))) #s(literal 2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* 2 (* (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps)))) (taylor -inf eps) (#s(alt (.f64 (.f64 (sin.f64 (.f64 (+.f64 eps #s(literal 0 binary64)) #s(literal 1/2 binary64))) (cos.f64 (.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)))) #s(literal 2 binary64)) (patch (.f64 (.f64 (sin.f64 (.f64 (+.f64 eps #s(literal 0 binary64)) #s(literal 1/2 binary64))) (cos.f64 (.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)))) #s(literal 2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* 2 (* (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps)))) (taylor -inf eps) (#s(alt (.f64 (.f64 (sin.f64 (.f64 (+.f64 eps #s(literal 0 binary64)) #s(literal 1/2 binary64))) (cos.f64 (.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)))) #s(literal 2 binary64)) (patch (.f64 (.f64 (sin.f64 (.f64 (+.f64 eps #s(literal 0 binary64)) #s(literal 1/2 binary64))) (cos.f64 (.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)))) #s(literal 2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* 2 (* (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps)))) (taylor -inf eps) (#s(alt (.f64 (.f64 (sin.f64 (.f64 (+.f64 eps #s(literal 0 binary64)) #s(literal 1/2 binary64))) (cos.f64 (.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)))) #s(literal 2 binary64)) (patch (.f64 (.f64 (sin.f64 (.f64 (+.f64 eps #s(literal 0 binary64)) #s(literal 1/2 binary64))) (cos.f64 (.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)))) #s(literal 2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* 2 (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) (taylor 0 x) (#s(alt (.f64 (.f64 (sin.f64 (.f64 (+.f64 eps #s(literal 0 binary64)) #s(literal 1/2 binary64))) (cos.f64 (.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)))) #s(literal 2 binary64)) (patch (.f64 (.f64 (sin.f64 (.f64 (+.f64 eps #s(literal 0 binary64)) #s(literal 1/2 binary64))) (cos.f64 (.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)))) #s(literal 2 binary64)) #<representation binary64>) () ())) ())
#s(alt (+ (* -2 (* x (pow (sin (* 1/2 eps)) 2))) (* 2 (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))) (taylor 0 x) (#s(alt (.f64 (.f64 (sin.f64 (.f64 (+.f64 eps #s(literal 0 binary64)) #s(literal 1/2 binary64))) (cos.f64 (.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)))) #s(literal 2 binary64)) (patch (.f64 (.f64 (sin.f64 (.f64 (+.f64 eps #s(literal 0 binary64)) #s(literal 1/2 binary64))) (cos.f64 (.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)))) #s(literal 2 binary64)) #<representation binary64>) () ())) ())
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#s(alt (+ 1 (* x (+ (* -1/2 eps) (* x (- (* 1/12 (* eps x)) 1/2))))) (taylor 0 x) (#s(alt (fma.f64 eps (.f64 #s(literal -1/2 binary64) (sin.f64 x)) (cos.f64 x)) (patch (fma.f64 eps (.f64 #s(literal -1/2 binary64) (sin.f64 x)) (cos.f64 x)) #<representation binary64>) () ())) ())
#s(alt (+ (cos x) (* -1/2 (* eps (sin x)))) (taylor inf x) (#s(alt (fma.f64 eps (.f64 #s(literal -1/2 binary64) (sin.f64 x)) (cos.f64 x)) (patch (fma.f64 eps (.f64 #s(literal -1/2 binary64) (sin.f64 x)) (cos.f64 x)) #<representation binary64>) () ())) ())
#s(alt (+ (cos x) (* -1/2 (* eps (sin x)))) (taylor inf x) (#s(alt (fma.f64 eps (.f64 #s(literal -1/2 binary64) (sin.f64 x)) (cos.f64 x)) (patch (fma.f64 eps (.f64 #s(literal -1/2 binary64) (sin.f64 x)) (cos.f64 x)) #<representation binary64>) () ())) ())
#s(alt (+ (cos x) (* -1/2 (* eps (sin x)))) (taylor inf x) (#s(alt (fma.f64 eps (.f64 #s(literal -1/2 binary64) (sin.f64 x)) (cos.f64 x)) (patch (fma.f64 eps (.f64 #s(literal -1/2 binary64) (sin.f64 x)) (cos.f64 x)) #<representation binary64>) () ())) ())
#s(alt (+ (cos x) (* -1/2 (* eps (sin x)))) (taylor inf x) (#s(alt (fma.f64 eps (.f64 #s(literal -1/2 binary64) (sin.f64 x)) (cos.f64 x)) (patch (fma.f64 eps (.f64 #s(literal -1/2 binary64) (sin.f64 x)) (cos.f64 x)) #<representation binary64>) () ())) ())
#s(alt (+ (cos x) (* -1/2 (* eps (sin x)))) (taylor -inf x) (#s(alt (fma.f64 eps (.f64 #s(literal -1/2 binary64) (sin.f64 x)) (cos.f64 x)) (patch (fma.f64 eps (.f64 #s(literal -1/2 binary64) (sin.f64 x)) (cos.f64 x)) #<representation binary64>) () ())) ())
#s(alt (+ (cos x) (* -1/2 (* eps (sin x)))) (taylor -inf x) (#s(alt (fma.f64 eps (.f64 #s(literal -1/2 binary64) (sin.f64 x)) (cos.f64 x)) (patch (fma.f64 eps (.f64 #s(literal -1/2 binary64) (sin.f64 x)) (cos.f64 x)) #<representation binary64>) () ())) ())
#s(alt (+ (cos x) (* -1/2 (* eps (sin x)))) (taylor -inf x) (#s(alt (fma.f64 eps (.f64 #s(literal -1/2 binary64) (sin.f64 x)) (cos.f64 x)) (patch (fma.f64 eps (.f64 #s(literal -1/2 binary64) (sin.f64 x)) (cos.f64 x)) #<representation binary64>) () ())) ())
#s(alt (+ (cos x) (* -1/2 (* eps (sin x)))) (taylor -inf x) (#s(alt (fma.f64 eps (.f64 #s(literal -1/2 binary64) (sin.f64 x)) (cos.f64 x)) (patch (fma.f64 eps (.f64 #s(literal -1/2 binary64) (sin.f64 x)) (cos.f64 x)) #<representation binary64>) () ())) ())
#s(alt (* -1/2 x) (taylor 0 x) (#s(alt (.f64 #s(literal -1/2 binary64) (sin.f64 x)) (patch (.f64 #s(literal -1/2 binary64) (sin.f64 x)) #<representation binary64>) () ())) ())
#s(alt (* x (- (* 1/12 (pow x 2)) 1/2)) (taylor 0 x) (#s(alt (.f64 #s(literal -1/2 binary64) (sin.f64 x)) (patch (.f64 #s(literal -1/2 binary64) (sin.f64 x)) #<representation binary64>) () ())) ())
#s(alt (* x (- (* (pow x 2) (+ 1/12 (* -1/240 (pow x 2)))) 1/2)) (taylor 0 x) (#s(alt (.f64 #s(literal -1/2 binary64) (sin.f64 x)) (patch (.f64 #s(literal -1/2 binary64) (sin.f64 x)) #<representation binary64>) () ())) ())
#s(alt (* x (- (* (pow x 2) (+ 1/12 (* (pow x 2) (- (* 1/10080 (pow x 2)) 1/240)))) 1/2)) (taylor 0 x) (#s(alt (.f64 #s(literal -1/2 binary64) (sin.f64 x)) (patch (.f64 #s(literal -1/2 binary64) (sin.f64 x)) #<representation binary64>) () ())) ())
#s(alt (* -1/2 (sin x)) (taylor inf x) (#s(alt (.f64 #s(literal -1/2 binary64) (sin.f64 x)) (patch (.f64 #s(literal -1/2 binary64) (sin.f64 x)) #<representation binary64>) () ())) ())
#s(alt (* -1/2 (sin x)) (taylor inf x) (#s(alt (.f64 #s(literal -1/2 binary64) (sin.f64 x)) (patch (.f64 #s(literal -1/2 binary64) (sin.f64 x)) #<representation binary64>) () ())) ())
#s(alt (* -1/2 (sin x)) (taylor inf x) (#s(alt (.f64 #s(literal -1/2 binary64) (sin.f64 x)) (patch (.f64 #s(literal -1/2 binary64) (sin.f64 x)) #<representation binary64>) () ())) ())
#s(alt (* -1/2 (sin x)) (taylor inf x) (#s(alt (.f64 #s(literal -1/2 binary64) (sin.f64 x)) (patch (.f64 #s(literal -1/2 binary64) (sin.f64 x)) #<representation binary64>) () ())) ())
#s(alt (* -1/2 (sin x)) (taylor -inf x) (#s(alt (.f64 #s(literal -1/2 binary64) (sin.f64 x)) (patch (.f64 #s(literal -1/2 binary64) (sin.f64 x)) #<representation binary64>) () ())) ())
#s(alt (* -1/2 (sin x)) (taylor -inf x) (#s(alt (.f64 #s(literal -1/2 binary64) (sin.f64 x)) (patch (.f64 #s(literal -1/2 binary64) (sin.f64 x)) #<representation binary64>) () ())) ())
#s(alt (* -1/2 (sin x)) (taylor -inf x) (#s(alt (.f64 #s(literal -1/2 binary64) (sin.f64 x)) (patch (.f64 #s(literal -1/2 binary64) (sin.f64 x)) #<representation binary64>) () ())) ())
#s(alt (* -1/2 (sin x)) (taylor -inf x) (#s(alt (.f64 #s(literal -1/2 binary64) (sin.f64 x)) (patch (.f64 #s(literal -1/2 binary64) (sin.f64 x)) #<representation binary64>) () ())) ())
#s(alt (cos (* 1/2 eps)) (taylor 0 x) (#s(alt (cos.f64 (.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64))) (patch (cos.f64 (.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64))) #<representation binary64>) () ())) ())
#s(alt (+ (cos (* 1/2 eps)) (* -1 (* x (sin (* 1/2 eps))))) (taylor 0 x) (#s(alt (cos.f64 (.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64))) (patch (cos.f64 (.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64))) #<representation binary64>) () ())) ())
#s(alt (+ (cos (* 1/2 eps)) (* x (- (* -1/2 (* x (cos (* 1/2 eps)))) (sin (* 1/2 eps))))) (taylor 0 x) (#s(alt (cos.f64 (.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64))) (patch (cos.f64 (.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64))) #<representation binary64>) () ())) ())
#s(alt (+ (cos (* 1/2 eps)) (* x (- (* x (+ (* -1/2 (cos (* 1/2 eps))) (* 1/6 (* x (sin (* 1/2 eps)))))) (sin (* 1/2 eps))))) (taylor 0 x) (#s(alt (cos.f64 (.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64))) (patch (cos.f64 (.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64))) #<representation binary64>) () ())) ())
#s(alt (cos (* 1/2 (+ eps (* 2 x)))) (taylor inf x) (#s(alt (cos.f64 (.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64))) (patch (cos.f64 (.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64))) #<representation binary64>) () ())) ())
#s(alt (cos (* 1/2 (+ eps (* 2 x)))) (taylor inf x) (#s(alt (cos.f64 (.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64))) (patch (cos.f64 (.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64))) #<representation binary64>) () ())) ())
#s(alt (cos (* 1/2 (+ eps (* 2 x)))) (taylor inf x) (#s(alt (cos.f64 (.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64))) (patch (cos.f64 (.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64))) #<representation binary64>) () ())) ())
#s(alt (cos (* 1/2 (+ eps (* 2 x)))) (taylor inf x) (#s(alt (cos.f64 (.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64))) (patch (cos.f64 (.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64))) #<representation binary64>) () ())) ())
#s(alt (cos (* 1/2 (- eps (* -2 x)))) (taylor -inf x) (#s(alt (cos.f64 (.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64))) (patch (cos.f64 (.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64))) #<representation binary64>) () ())) ())
#s(alt (cos (* 1/2 (- eps (* -2 x)))) (taylor -inf x) (#s(alt (cos.f64 (.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64))) (patch (cos.f64 (.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64))) #<representation binary64>) () ())) ())
#s(alt (cos (* 1/2 (- eps (* -2 x)))) (taylor -inf x) (#s(alt (cos.f64 (.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64))) (patch (cos.f64 (.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64))) #<representation binary64>) () ())) ())
#s(alt (cos (* 1/2 (- eps (* -2 x)))) (taylor -inf x) (#s(alt (cos.f64 (.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64))) (patch (cos.f64 (.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64))) #<representation binary64>) () ())) ())
#s(alt (cos x) (taylor 0 eps) (#s(alt (cos.f64 (.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64))) (patch (cos.f64 (.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64))) #<representation binary64>) () ())) ())
#s(alt (+ (cos x) (* -1/2 (* eps (sin x)))) (taylor 0 eps) (#s(alt (cos.f64 (.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64))) (patch (cos.f64 (.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64))) #<representation binary64>) () ())) ())
#s(alt (+ (cos x) (* eps (- (* -1/8 (* eps (cos x))) (* 1/2 (sin x))))) (taylor 0 eps) (#s(alt (cos.f64 (.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64))) (patch (cos.f64 (.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64))) #<representation binary64>) () ())) ())
#s(alt (+ (cos x) (* eps (- (* eps (+ (* -1/8 (cos x)) (* 1/48 (* eps (sin x))))) (* 1/2 (sin x))))) (taylor 0 eps) (#s(alt (cos.f64 (.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64))) (patch (cos.f64 (.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64))) #<representation binary64>) () ())) ())
#s(alt (cos (* 1/2 (+ eps (* 2 x)))) (taylor inf eps) (#s(alt (cos.f64 (.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64))) (patch (cos.f64 (.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64))) #<representation binary64>) () ())) ())
#s(alt (cos (* 1/2 (+ eps (* 2 x)))) (taylor inf eps) (#s(alt (cos.f64 (.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64))) (patch (cos.f64 (.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64))) #<representation binary64>) () ())) ())
#s(alt (cos (* 1/2 (+ eps (* 2 x)))) (taylor inf eps) (#s(alt (cos.f64 (.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64))) (patch (cos.f64 (.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64))) #<representation binary64>) () ())) ())
#s(alt (cos (* 1/2 (+ eps (* 2 x)))) (taylor inf eps) (#s(alt (cos.f64 (.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64))) (patch (cos.f64 (.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64))) #<representation binary64>) () ())) ())
#s(alt (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (taylor -inf eps) (#s(alt (cos.f64 (.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64))) (patch (cos.f64 (.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64))) #<representation binary64>) () ())) ())
#s(alt (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (taylor -inf eps) (#s(alt (cos.f64 (.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64))) (patch (cos.f64 (.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64))) #<representation binary64>) () ())) ())
#s(alt (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (taylor -inf eps) (#s(alt (cos.f64 (.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64))) (patch (cos.f64 (.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64))) #<representation binary64>) () ())) ())
#s(alt (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (taylor -inf eps) (#s(alt (cos.f64 (.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64))) (patch (cos.f64 (.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64))) #<representation binary64>) () ())) ())
#s(alt (* 1/2 eps) (taylor 0 eps) (#s(alt (sin.f64 (.f64 (+.f64 eps #s(literal 0 binary64)) #s(literal 1/2 binary64))) (patch (sin.f64 (.f64 (+.f64 eps #s(literal 0 binary64)) #s(literal 1/2 binary64))) #<representation binary64>) () ())) ())
#s(alt (* eps (+ 1/2 (* -1/48 (pow eps 2)))) (taylor 0 eps) (#s(alt (sin.f64 (.f64 (+.f64 eps #s(literal 0 binary64)) #s(literal 1/2 binary64))) (patch (sin.f64 (.f64 (+.f64 eps #s(literal 0 binary64)) #s(literal 1/2 binary64))) #<representation binary64>) () ())) ())
#s(alt (* eps (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48)))) (taylor 0 eps) (#s(alt (sin.f64 (.f64 (+.f64 eps #s(literal 0 binary64)) #s(literal 1/2 binary64))) (patch (sin.f64 (.f64 (+.f64 eps #s(literal 0 binary64)) #s(literal 1/2 binary64))) #<representation binary64>) () ())) ())
#s(alt (* eps (+ 1/2 (* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48)))) (taylor 0 eps) (#s(alt (sin.f64 (.f64 (+.f64 eps #s(literal 0 binary64)) #s(literal 1/2 binary64))) (patch (sin.f64 (.f64 (+.f64 eps #s(literal 0 binary64)) #s(literal 1/2 binary64))) #<representation binary64>) () ())) ())
#s(alt (sin (* 1/2 eps)) (taylor inf eps) (#s(alt (sin.f64 (.f64 (+.f64 eps #s(literal 0 binary64)) #s(literal 1/2 binary64))) (patch (sin.f64 (.f64 (+.f64 eps #s(literal 0 binary64)) #s(literal 1/2 binary64))) #<representation binary64>) () ())) ())
#s(alt (sin (* 1/2 eps)) (taylor inf eps) (#s(alt (sin.f64 (.f64 (+.f64 eps #s(literal 0 binary64)) #s(literal 1/2 binary64))) (patch (sin.f64 (.f64 (+.f64 eps #s(literal 0 binary64)) #s(literal 1/2 binary64))) #<representation binary64>) () ())) ())
#s(alt (sin (* 1/2 eps)) (taylor inf eps) (#s(alt (sin.f64 (.f64 (+.f64 eps #s(literal 0 binary64)) #s(literal 1/2 binary64))) (patch (sin.f64 (.f64 (+.f64 eps #s(literal 0 binary64)) #s(literal 1/2 binary64))) #<representation binary64>) () ())) ())
#s(alt (sin (* 1/2 eps)) (taylor inf eps) (#s(alt (sin.f64 (.f64 (+.f64 eps #s(literal 0 binary64)) #s(literal 1/2 binary64))) (patch (sin.f64 (.f64 (+.f64 eps #s(literal 0 binary64)) #s(literal 1/2 binary64))) #<representation binary64>) () ())) ())
#s(alt (sin (* 1/2 eps)) (taylor -inf eps) (#s(alt (sin.f64 (.f64 (+.f64 eps #s(literal 0 binary64)) #s(literal 1/2 binary64))) (patch (sin.f64 (.f64 (+.f64 eps #s(literal 0 binary64)) #s(literal 1/2 binary64))) #<representation binary64>) () ())) ())
#s(alt (sin (* 1/2 eps)) (taylor -inf eps) (#s(alt (sin.f64 (.f64 (+.f64 eps #s(literal 0 binary64)) #s(literal 1/2 binary64))) (patch (sin.f64 (.f64 (+.f64 eps #s(literal 0 binary64)) #s(literal 1/2 binary64))) #<representation binary64>) () ())) ())
#s(alt (sin (* 1/2 eps)) (taylor -inf eps) (#s(alt (sin.f64 (.f64 (+.f64 eps #s(literal 0 binary64)) #s(literal 1/2 binary64))) (patch (sin.f64 (.f64 (+.f64 eps #s(literal 0 binary64)) #s(literal 1/2 binary64))) #<representation binary64>) () ())) ())
#s(alt (sin (* 1/2 eps)) (taylor -inf eps) (#s(alt (sin.f64 (.f64 (+.f64 eps #s(literal 0 binary64)) #s(literal 1/2 binary64))) (patch (sin.f64 (.f64 (+.f64 eps #s(literal 0 binary64)) #s(literal 1/2 binary64))) #<representation binary64>) () ())) ())
#s(alt (pow x 3) (taylor 0 x) (#s(alt (.f64 x (.f64 x x)) (patch (.f64 x (.f64 x x)) #<representation binary64>) () ())) ())
#s(alt (pow x 3) (taylor 0 x) (#s(alt (.f64 x (.f64 x x)) (patch (.f64 x (.f64 x x)) #<representation binary64>) () ())) ())
#s(alt (pow x 3) (taylor 0 x) (#s(alt (.f64 x (.f64 x x)) (patch (.f64 x (.f64 x x)) #<representation binary64>) () ())) ())
#s(alt (pow x 3) (taylor 0 x) (#s(alt (.f64 x (.f64 x x)) (patch (.f64 x (.f64 x x)) #<representation binary64>) () ())) ())
#s(alt (pow x 3) (taylor inf x) (#s(alt (.f64 x (.f64 x x)) (patch (.f64 x (.f64 x x)) #<representation binary64>) () ())) ())
#s(alt (pow x 3) (taylor inf x) (#s(alt (.f64 x (.f64 x x)) (patch (.f64 x (.f64 x x)) #<representation binary64>) () ())) ())
#s(alt (pow x 3) (taylor inf x) (#s(alt (.f64 x (.f64 x x)) (patch (.f64 x (.f64 x x)) #<representation binary64>) () ())) ())
#s(alt (pow x 3) (taylor inf x) (#s(alt (.f64 x (.f64 x x)) (patch (.f64 x (.f64 x x)) #<representation binary64>) () ())) ())
#s(alt (pow x 3) (taylor -inf x) (#s(alt (.f64 x (.f64 x x)) (patch (.f64 x (.f64 x x)) #<representation binary64>) () ())) ())
#s(alt (pow x 3) (taylor -inf x) (#s(alt (.f64 x (.f64 x x)) (patch (.f64 x (.f64 x x)) #<representation binary64>) () ())) ())
#s(alt (pow x 3) (taylor -inf x) (#s(alt (.f64 x (.f64 x x)) (patch (.f64 x (.f64 x x)) #<representation binary64>) () ())) ())
#s(alt (pow x 3) (taylor -inf x) (#s(alt (.f64 x (.f64 x x)) (patch (.f64 x (.f64 x x)) #<representation binary64>) () ())) ())

Calls

99 calls:

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

simplify293.0ms (2.1%)

Memory

18.9MiB live, 328.2MiB allocated

Algorithm

1×	egg-herbie

Rules

13 684×	`lower-fma.f64`
13 684×	`lower-fma.f32`
6 158×	`lower-*.f64`
6 158×	`lower-*.f32`
3 622×	`lower-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	359	3341
1	1096	3209
2	2826	3169
3	6529	3169
0	8151	2921

Stop Event

1×	iter limit
1×	node limit

Counts

396 → 371

Calls

Call 1

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

Outputs
(* 1/2 eps)
(*.f64 #s(literal 1/2 binary64) eps)
(+ x (* 1/2 eps))
(fma.f64 #s(literal 1/2 binary64) eps x)
(+ x (* 1/2 eps))
(fma.f64 #s(literal 1/2 binary64) eps x)
(+ x (* 1/2 eps))
(fma.f64 #s(literal 1/2 binary64) eps x)
x
(* x (+ 1 (* 1/2 (/ eps x))))
(fma.f64 #s(literal 1/2 binary64) (/.f64 (*.f64 eps x) x) x)
(* x (+ 1 (* 1/2 (/ eps x))))
(fma.f64 #s(literal 1/2 binary64) (/.f64 (*.f64 eps x) x) x)
(* x (+ 1 (* 1/2 (/ eps x))))
(fma.f64 #s(literal 1/2 binary64) (/.f64 (*.f64 eps x) x) x)
x
(* -1 (* x (- (* -1/2 (/ eps x)) 1)))
(fma.f64 (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x) (neg.f64 x) x)
(* -1 (* x (- (* -1/2 (/ eps x)) 1)))
(fma.f64 (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x) (neg.f64 x) x)
(* -1 (* x (- (* -1/2 (/ eps x)) 1)))
(fma.f64 (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x) (neg.f64 x) x)
x
(+ x (* 1/2 eps))
(fma.f64 #s(literal 1/2 binary64) eps x)
(+ x (* 1/2 eps))
(fma.f64 #s(literal 1/2 binary64) eps x)
(+ x (* 1/2 eps))
(fma.f64 #s(literal 1/2 binary64) eps x)
(* 1/2 eps)
(*.f64 #s(literal 1/2 binary64) eps)
(* eps (+ 1/2 (/ x eps)))
(*.f64 eps (+.f64 #s(literal 1/2 binary64) (/.f64 x eps)))
(* eps (+ 1/2 (/ x eps)))
(*.f64 eps (+.f64 #s(literal 1/2 binary64) (/.f64 x eps)))
(* eps (+ 1/2 (/ x eps)))
(*.f64 eps (+.f64 #s(literal 1/2 binary64) (/.f64 x eps)))
(* 1/2 eps)
(*.f64 #s(literal 1/2 binary64) eps)
(* -1 (* eps (- (* -1 (/ x eps)) 1/2)))
(*.f64 eps (+.f64 #s(literal 1/2 binary64) (/.f64 x eps)))
(* -1 (* eps (- (* -1 (/ x eps)) 1/2)))
(*.f64 eps (+.f64 #s(literal 1/2 binary64) (/.f64 x eps)))
(* -1 (* eps (- (* -1 (/ x eps)) 1/2)))
(*.f64 eps (+.f64 #s(literal 1/2 binary64) (/.f64 x eps)))
eps
eps
eps
eps
eps
eps
eps
eps
eps
eps
eps
eps
(* eps (cos x))
(*.f64 eps (cos.f64 x))
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(.f64 eps (fma.f64 eps (.f64 #s(literal -1/2 binary64) (sin.f64 x)) (cos.f64 x)))
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* 2 (* eps (+ (* -1/16 (cos x)) (* -1/48 (cos x)))))))))
(.f64 eps (fma.f64 eps (.f64 #s(literal -1/2 binary64) (sin.f64 x)) (.f64 (fma.f64 #s(literal -1/6 binary64) (.f64 eps eps) #s(literal 1 binary64)) (cos.f64 x))))
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* eps (+ (* 1/24 (* eps (sin x))) (* 2 (+ (* -1/16 (cos x)) (* -1/48 (cos x))))))))))
(.f64 eps (fma.f64 eps (fma.f64 eps (.f64 (cos.f64 x) #s(literal -1/6 binary64)) (.f64 (sin.f64 x) (fma.f64 eps (.f64 eps #s(literal 1/24 binary64)) #s(literal -1/2 binary64)))) (cos.f64 x)))
(* 2 (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))))
(.f64 (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) (.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) #s(literal 2 binary64)))
(* 2 (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))))
(.f64 (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) (.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) #s(literal 2 binary64)))
(* 2 (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))))
(.f64 (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) (.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) #s(literal 2 binary64)))
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1
#s(literal 1 binary64)
(+ 1 (* -1/2 (pow x 2)))
(fma.f64 x (*.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64))
(+ 1 (* (pow x 2) (- (* 1/24 (pow x 2)) 1/2)))
(fma.f64 (.f64 x x) (fma.f64 #s(literal 1/24 binary64) (.f64 x x) #s(literal -1/2 binary64)) #s(literal 1 binary64))
(+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))) 1/2)))
(fma.f64 (.f64 x x) (fma.f64 x (.f64 x (fma.f64 (*.f64 x x) #s(literal -1/720 binary64) #s(literal 1/24 binary64))) #s(literal -1/2 binary64)) #s(literal 1 binary64))
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(cos x)
(cos.f64 x)
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(cos.f64 x)
(cos x)
(cos.f64 x)
(cos x)
(cos.f64 x)
(cos x)
(cos.f64 x)
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(sin.f64 eps)
(+ (sin eps) (* x (- (cos eps) 1)))
(fma.f64 x (+.f64 #s(literal -1 binary64) (cos.f64 eps)) (sin.f64 eps))
(+ (sin eps) (* x (- (+ (cos eps) (* -1/2 (* x (sin eps)))) 1)))
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(+ (sin eps) (* x (- (+ (cos eps) (* x (+ (* -1/2 (sin eps)) (* x (+ 1/6 (* -1/6 (cos eps))))))) 1)))
(fma.f64 x (+.f64 #s(literal -1 binary64) (fma.f64 x (.f64 #s(literal -1/2 binary64) (sin.f64 eps)) (fma.f64 x (.f64 x #s(literal 1/6 binary64)) (.f64 (fma.f64 x (.f64 x #s(literal -1/6 binary64)) #s(literal 1 binary64)) (cos.f64 eps))))) (sin.f64 eps))
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(- (sin (- eps (* -1 x))) (sin x))
(-.f64 (sin.f64 (+.f64 eps x)) (sin.f64 x))
(* eps (cos x))
(*.f64 eps (cos.f64 x))
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(.f64 eps (fma.f64 eps (.f64 #s(literal -1/2 binary64) (sin.f64 x)) (cos.f64 x)))
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x)))))))
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(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* eps (+ (* -1/6 (cos x)) (* 1/24 (* eps (sin x)))))))))
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(- (sin (+ eps x)) (sin x))
(-.f64 (sin.f64 (+.f64 eps x)) (sin.f64 x))
(- (sin (+ eps x)) (sin x))
(-.f64 (sin.f64 (+.f64 eps x)) (sin.f64 x))
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(- (sin (- x (* -1 eps))) (sin x))
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(- (sin (- x (* -1 eps))) (sin x))
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(- (sin (- x (* -1 eps))) (sin x))
(-.f64 (sin.f64 (+.f64 eps x)) (sin.f64 x))
(sin eps)
(sin.f64 eps)
(+ (sin eps) (* x (cos eps)))
(fma.f64 x (cos.f64 eps) (sin.f64 eps))
(+ (sin eps) (* x (+ (cos eps) (* -1/2 (* x (sin eps))))))
(fma.f64 (fma.f64 x (.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64)) (sin.f64 eps) (.f64 x (cos.f64 eps)))
(+ (sin eps) (* x (+ (cos eps) (* x (+ (* -1/2 (sin eps)) (* -1/6 (* x (cos eps))))))))
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(sin (+ eps x))
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(sin (+ eps x))
(sin.f64 (+.f64 eps x))
(sin (+ eps x))
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(sin (- eps (* -1 x)))
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(sin (- eps (* -1 x)))
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(sin (- eps (* -1 x)))
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(sin (- eps (* -1 x)))
(sin.f64 (+.f64 eps x))
(sin x)
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(+ (sin x) (* eps (cos x)))
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(+ (sin x) (* eps (+ (cos x) (* -1/2 (* eps (sin x))))))
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(+ (sin x) (* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x))))))))
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(sin (+ eps x))
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(sin (+ eps x))
(sin.f64 (+.f64 eps x))
(sin (+ eps x))
(sin.f64 (+.f64 eps x))
(sin (- x (* -1 eps)))
(sin.f64 (+.f64 eps x))
(sin (- x (* -1 eps)))
(sin.f64 (+.f64 eps x))
(sin (- x (* -1 eps)))
(sin.f64 (+.f64 eps x))
(sin (- x (* -1 eps)))
(sin.f64 (+.f64 eps x))
eps
(+ eps x)
(+.f64 eps x)
(+ eps x)
(+.f64 eps x)
(+ eps x)
(+.f64 eps x)
x
(* x (+ 1 (/ eps x)))
(fma.f64 eps (/.f64 x x) x)
(* x (+ 1 (/ eps x)))
(fma.f64 eps (/.f64 x x) x)
(* x (+ 1 (/ eps x)))
(fma.f64 eps (/.f64 x x) x)
x
(* -1 (* x (- (* -1 (/ eps x)) 1)))
(fma.f64 eps (/.f64 x x) x)
(* -1 (* x (- (* -1 (/ eps x)) 1)))
(fma.f64 eps (/.f64 x x) x)
(* -1 (* x (- (* -1 (/ eps x)) 1)))
(fma.f64 eps (/.f64 x x) x)
x
(+ eps x)
(+.f64 eps x)
(+ eps x)
(+.f64 eps x)
(+ eps x)
(+.f64 eps x)
eps
(* eps (+ 1 (/ x eps)))
(fma.f64 x (/.f64 eps eps) eps)
(* eps (+ 1 (/ x eps)))
(fma.f64 x (/.f64 eps eps) eps)
(* eps (+ 1 (/ x eps)))
(fma.f64 x (/.f64 eps eps) eps)
eps
(* -1 (* eps (- (* -1 (/ x eps)) 1)))
(fma.f64 x (/.f64 eps eps) eps)
(* -1 (* eps (- (* -1 (/ x eps)) 1)))
(fma.f64 x (/.f64 eps eps) eps)
(* -1 (* eps (- (* -1 (/ x eps)) 1)))
(fma.f64 x (/.f64 eps eps) eps)
x
(* x (+ 1 (* -1/6 (pow x 2))))
(fma.f64 x (.f64 #s(literal -1/6 binary64) (.f64 x x)) x)
(* x (+ 1 (* (pow x 2) (- (* 1/120 (pow x 2)) 1/6))))
(fma.f64 (fma.f64 x (.f64 x #s(literal 1/120 binary64)) #s(literal -1/6 binary64)) (.f64 x (*.f64 x x)) x)
(* x (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/120 (* -1/5040 (pow x 2)))) 1/6))))
(fma.f64 x (.f64 (.f64 (fma.f64 (.f64 x x) (fma.f64 x (.f64 x #s(literal -1/5040 binary64)) #s(literal 1/120 binary64)) #s(literal -1/6 binary64)) x) x) x)
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(sin x)
(sin.f64 x)
(sin x)
(sin.f64 x)
(sin eps)
(sin.f64 eps)
(+ (sin eps) (* x (- (cos eps) 1)))
(fma.f64 x (+.f64 #s(literal -1 binary64) (cos.f64 eps)) (sin.f64 eps))
(+ (sin eps) (* x (- (+ (cos eps) (* -1/2 (* x (sin eps)))) 1)))
(+.f64 (fma.f64 (fma.f64 x (.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64)) (sin.f64 eps) (.f64 x (cos.f64 eps))) (neg.f64 x))
(+ (sin eps) (* x (- (+ (cos eps) (* x (+ (* -1/2 (sin eps)) (* x (+ 1/6 (* -1/6 (cos eps))))))) 1)))
(fma.f64 x (+.f64 #s(literal -1 binary64) (fma.f64 x (.f64 #s(literal -1/2 binary64) (sin.f64 eps)) (fma.f64 x (.f64 x #s(literal 1/6 binary64)) (.f64 (fma.f64 x (.f64 x #s(literal -1/6 binary64)) #s(literal 1 binary64)) (cos.f64 eps))))) (sin.f64 eps))
(- (sin (+ eps x)) (sin x))
(-.f64 (sin.f64 (+.f64 eps x)) (sin.f64 x))
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(-.f64 (sin.f64 (+.f64 eps x)) (sin.f64 x))
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(-.f64 (sin.f64 (+.f64 eps x)) (sin.f64 x))
(- (sin (- eps (* -1 x))) (sin x))
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(- (sin (- eps (* -1 x))) (sin x))
(-.f64 (sin.f64 (+.f64 eps x)) (sin.f64 x))
(- (sin (- eps (* -1 x))) (sin x))
(-.f64 (sin.f64 (+.f64 eps x)) (sin.f64 x))
(* eps (cos x))
(*.f64 eps (cos.f64 x))
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(.f64 eps (fma.f64 eps (.f64 #s(literal -1/2 binary64) (sin.f64 x)) (cos.f64 x)))
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x)))))))
(.f64 eps (fma.f64 eps (.f64 #s(literal -1/2 binary64) (sin.f64 x)) (.f64 (fma.f64 #s(literal -1/6 binary64) (.f64 eps eps) #s(literal 1 binary64)) (cos.f64 x))))
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* eps (+ (* -1/6 (cos x)) (* 1/24 (* eps (sin x)))))))))
(.f64 eps (fma.f64 eps (fma.f64 eps (.f64 (cos.f64 x) #s(literal -1/6 binary64)) (.f64 (sin.f64 x) (fma.f64 eps (.f64 eps #s(literal 1/24 binary64)) #s(literal -1/2 binary64)))) (cos.f64 x)))
(- (sin (+ eps x)) (sin x))
(-.f64 (sin.f64 (+.f64 eps x)) (sin.f64 x))
(- (sin (+ eps x)) (sin x))
(-.f64 (sin.f64 (+.f64 eps x)) (sin.f64 x))
(- (sin (+ eps x)) (sin x))
(-.f64 (sin.f64 (+.f64 eps x)) (sin.f64 x))
(- (sin (+ eps x)) (sin x))
(-.f64 (sin.f64 (+.f64 eps x)) (sin.f64 x))
(- (sin (- x (* -1 eps))) (sin x))
(-.f64 (sin.f64 (+.f64 eps x)) (sin.f64 x))
(- (sin (- x (* -1 eps))) (sin x))
(-.f64 (sin.f64 (+.f64 eps x)) (sin.f64 x))
(- (sin (- x (* -1 eps))) (sin x))
(-.f64 (sin.f64 (+.f64 eps x)) (sin.f64 x))
(- (sin (- x (* -1 eps))) (sin x))
(-.f64 (sin.f64 (+.f64 eps x)) (sin.f64 x))
(* eps (cos x))
(*.f64 eps (cos.f64 x))
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(.f64 eps (fma.f64 eps (.f64 #s(literal -1/2 binary64) (sin.f64 x)) (cos.f64 x)))
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(.f64 eps (fma.f64 eps (.f64 #s(literal -1/2 binary64) (sin.f64 x)) (cos.f64 x)))
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(.f64 eps (fma.f64 eps (.f64 #s(literal -1/2 binary64) (sin.f64 x)) (cos.f64 x)))
(* -1/2 (* (pow eps 2) (sin x)))
(.f64 #s(literal -1/2 binary64) (.f64 eps (*.f64 eps (sin.f64 x))))
(* (pow eps 2) (+ (* -1/2 (sin x)) (/ (cos x) eps)))
(.f64 eps (.f64 eps (fma.f64 #s(literal -1/2 binary64) (sin.f64 x) (/.f64 (cos.f64 x) eps))))
(* (pow eps 2) (+ (* -1/2 (sin x)) (/ (cos x) eps)))
(.f64 eps (.f64 eps (fma.f64 #s(literal -1/2 binary64) (sin.f64 x) (/.f64 (cos.f64 x) eps))))
(* (pow eps 2) (+ (* -1/2 (sin x)) (/ (cos x) eps)))
(.f64 eps (.f64 eps (fma.f64 #s(literal -1/2 binary64) (sin.f64 x) (/.f64 (cos.f64 x) eps))))
(* -1/2 (* (pow eps 2) (sin x)))
(.f64 #s(literal -1/2 binary64) (.f64 eps (*.f64 eps (sin.f64 x))))
(* (pow eps 2) (+ (* -1/2 (sin x)) (/ (cos x) eps)))
(.f64 eps (.f64 eps (fma.f64 #s(literal -1/2 binary64) (sin.f64 x) (/.f64 (cos.f64 x) eps))))
(* (pow eps 2) (+ (* -1/2 (sin x)) (/ (cos x) eps)))
(.f64 eps (.f64 eps (fma.f64 #s(literal -1/2 binary64) (sin.f64 x) (/.f64 (cos.f64 x) eps))))
(* (pow eps 2) (+ (* -1/2 (sin x)) (/ (cos x) eps)))
(.f64 eps (.f64 eps (fma.f64 #s(literal -1/2 binary64) (sin.f64 x) (/.f64 (cos.f64 x) eps))))
eps
(+ eps (* -1/2 (* (pow eps 2) x)))
(fma.f64 x (.f64 eps (.f64 eps #s(literal -1/2 binary64))) eps)
(+ eps (* x (+ (* -1/2 (* eps x)) (* -1/2 (pow eps 2)))))
(fma.f64 x (.f64 eps (.f64 #s(literal -1/2 binary64) (+.f64 eps x))) eps)
(+ eps (* x (+ (* -1/2 (pow eps 2)) (* x (+ (* -1/2 eps) (* 1/12 (* (pow eps 2) x)))))))
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(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(.f64 eps (fma.f64 eps (.f64 #s(literal -1/2 binary64) (sin.f64 x)) (cos.f64 x)))
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(.f64 eps (fma.f64 eps (.f64 #s(literal -1/2 binary64) (sin.f64 x)) (cos.f64 x)))
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(.f64 eps (fma.f64 eps (.f64 #s(literal -1/2 binary64) (sin.f64 x)) (cos.f64 x)))
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(.f64 eps (fma.f64 eps (.f64 #s(literal -1/2 binary64) (sin.f64 x)) (cos.f64 x)))
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(.f64 eps (fma.f64 eps (.f64 #s(literal -1/2 binary64) (sin.f64 x)) (cos.f64 x)))
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(.f64 eps (fma.f64 eps (.f64 #s(literal -1/2 binary64) (sin.f64 x)) (cos.f64 x)))
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(.f64 eps (fma.f64 eps (.f64 #s(literal -1/2 binary64) (sin.f64 x)) (cos.f64 x)))
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(.f64 eps (fma.f64 eps (.f64 #s(literal -1/2 binary64) (sin.f64 x)) (cos.f64 x)))
(cos x)
(cos.f64 x)
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(fma.f64 eps (*.f64 #s(literal -1/2 binary64) (sin.f64 x)) (cos.f64 x))
(* -1/2 (* eps (sin x)))
(.f64 eps (.f64 #s(literal -1/2 binary64) (sin.f64 x)))
(* eps (+ (* -1/2 (sin x)) (/ (cos x) eps)))
(*.f64 eps (fma.f64 #s(literal -1/2 binary64) (sin.f64 x) (/.f64 (cos.f64 x) eps)))
(* eps (+ (* -1/2 (sin x)) (/ (cos x) eps)))
(*.f64 eps (fma.f64 #s(literal -1/2 binary64) (sin.f64 x) (/.f64 (cos.f64 x) eps)))
(* eps (+ (* -1/2 (sin x)) (/ (cos x) eps)))
(*.f64 eps (fma.f64 #s(literal -1/2 binary64) (sin.f64 x) (/.f64 (cos.f64 x) eps)))
(* -1/2 (* eps (sin x)))
(.f64 eps (.f64 #s(literal -1/2 binary64) (sin.f64 x)))
(* -1 (* eps (+ (* -1 (/ (cos x) eps)) (* 1/2 (sin x)))))
(*.f64 eps (fma.f64 #s(literal -1/2 binary64) (sin.f64 x) (/.f64 (cos.f64 x) eps)))
(* -1 (* eps (+ (* -1 (/ (cos x) eps)) (* 1/2 (sin x)))))
(*.f64 eps (fma.f64 #s(literal -1/2 binary64) (sin.f64 x) (/.f64 (cos.f64 x) eps)))
(* -1 (* eps (+ (* -1 (/ (cos x) eps)) (* 1/2 (sin x)))))
(*.f64 eps (fma.f64 #s(literal -1/2 binary64) (sin.f64 x) (/.f64 (cos.f64 x) eps)))
1
#s(literal 1 binary64)
(+ 1 (* -1/2 (* eps x)))
(fma.f64 eps (*.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64))
(+ 1 (* x (+ (* -1/2 eps) (* -1/2 x))))
(fma.f64 (*.f64 x #s(literal -1/2 binary64)) (+.f64 eps x) #s(literal 1 binary64))
(+ 1 (* x (+ (* -1/2 eps) (* x (- (* 1/12 (* eps x)) 1/2)))))
(fma.f64 x (fma.f64 eps #s(literal -1/2 binary64) (.f64 x (fma.f64 (.f64 eps x) #s(literal 1/12 binary64) #s(literal -1/2 binary64)))) #s(literal 1 binary64))
(+ (cos x) (* -1/2 (* eps (sin x))))
(fma.f64 eps (*.f64 #s(literal -1/2 binary64) (sin.f64 x)) (cos.f64 x))
(+ (cos x) (* -1/2 (* eps (sin x))))
(fma.f64 eps (*.f64 #s(literal -1/2 binary64) (sin.f64 x)) (cos.f64 x))
(+ (cos x) (* -1/2 (* eps (sin x))))
(fma.f64 eps (*.f64 #s(literal -1/2 binary64) (sin.f64 x)) (cos.f64 x))
(+ (cos x) (* -1/2 (* eps (sin x))))
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(fma.f64 eps (*.f64 #s(literal -1/2 binary64) (sin.f64 x)) (cos.f64 x))
(+ (cos x) (* -1/2 (* eps (sin x))))
(fma.f64 eps (*.f64 #s(literal -1/2 binary64) (sin.f64 x)) (cos.f64 x))
(+ (cos x) (* -1/2 (* eps (sin x))))
(fma.f64 eps (*.f64 #s(literal -1/2 binary64) (sin.f64 x)) (cos.f64 x))
(+ (cos x) (* -1/2 (* eps (sin x))))
(fma.f64 eps (*.f64 #s(literal -1/2 binary64) (sin.f64 x)) (cos.f64 x))
(* -1/2 x)
(*.f64 x #s(literal -1/2 binary64))
(* x (- (* 1/12 (pow x 2)) 1/2))
(.f64 x (fma.f64 (.f64 x x) #s(literal 1/12 binary64) #s(literal -1/2 binary64)))
(* x (- (* (pow x 2) (+ 1/12 (* -1/240 (pow x 2)))) 1/2))
(.f64 x (fma.f64 (.f64 x x) (fma.f64 (*.f64 x x) #s(literal -1/240 binary64) #s(literal 1/12 binary64)) #s(literal -1/2 binary64)))
(* x (- (* (pow x 2) (+ 1/12 (* (pow x 2) (- (* 1/10080 (pow x 2)) 1/240)))) 1/2))
(.f64 x (fma.f64 (.f64 x x) (fma.f64 (.f64 x x) (fma.f64 (.f64 x x) #s(literal 1/10080 binary64) #s(literal -1/240 binary64)) #s(literal 1/12 binary64)) #s(literal -1/2 binary64)))
(* -1/2 (sin x))
(*.f64 #s(literal -1/2 binary64) (sin.f64 x))
(* -1/2 (sin x))
(*.f64 #s(literal -1/2 binary64) (sin.f64 x))
(* -1/2 (sin x))
(*.f64 #s(literal -1/2 binary64) (sin.f64 x))
(* -1/2 (sin x))
(*.f64 #s(literal -1/2 binary64) (sin.f64 x))
(* -1/2 (sin x))
(*.f64 #s(literal -1/2 binary64) (sin.f64 x))
(* -1/2 (sin x))
(*.f64 #s(literal -1/2 binary64) (sin.f64 x))
(* -1/2 (sin x))
(*.f64 #s(literal -1/2 binary64) (sin.f64 x))
(* -1/2 (sin x))
(*.f64 #s(literal -1/2 binary64) (sin.f64 x))
(cos (* 1/2 eps))
(cos.f64 (*.f64 #s(literal 1/2 binary64) eps))
(+ (cos (* 1/2 eps)) (* -1 (* x (sin (* 1/2 eps)))))
(fma.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (neg.f64 x) (cos.f64 (.f64 #s(literal 1/2 binary64) eps)))
(+ (cos (* 1/2 eps)) (* x (- (* -1/2 (* x (cos (* 1/2 eps)))) (sin (* 1/2 eps)))))
(fma.f64 x (-.f64 (.f64 (cos.f64 (.f64 #s(literal 1/2 binary64) eps)) (.f64 x #s(literal -1/2 binary64))) (sin.f64 (.f64 #s(literal 1/2 binary64) eps))) (cos.f64 (*.f64 #s(literal 1/2 binary64) eps)))
(+ (cos (* 1/2 eps)) (* x (- (* x (+ (* -1/2 (cos (* 1/2 eps))) (* 1/6 (* x (sin (* 1/2 eps)))))) (sin (* 1/2 eps)))))
(fma.f64 x (fma.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (fma.f64 x (.f64 x #s(literal 1/6 binary64)) #s(literal -1 binary64)) (.f64 (cos.f64 (.f64 #s(literal 1/2 binary64) eps)) (.f64 x #s(literal -1/2 binary64)))) (cos.f64 (.f64 #s(literal 1/2 binary64) eps)))
(cos (* 1/2 (+ eps (* 2 x))))
(cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x))
(cos (* 1/2 (+ eps (* 2 x))))
(cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x))
(cos (* 1/2 (+ eps (* 2 x))))
(cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x))
(cos (* 1/2 (+ eps (* 2 x))))
(cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x))
(cos (* 1/2 (- eps (* -2 x))))
(cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x))
(cos (* 1/2 (- eps (* -2 x))))
(cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x))
(cos (* 1/2 (- eps (* -2 x))))
(cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x))
(cos (* 1/2 (- eps (* -2 x))))
(cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x))
(cos x)
(cos.f64 x)
(+ (cos x) (* -1/2 (* eps (sin x))))
(fma.f64 eps (*.f64 #s(literal -1/2 binary64) (sin.f64 x)) (cos.f64 x))
(+ (cos x) (* eps (- (* -1/8 (* eps (cos x))) (* 1/2 (sin x)))))
(fma.f64 eps (fma.f64 eps (.f64 (cos.f64 x) #s(literal -1/8 binary64)) (.f64 #s(literal -1/2 binary64) (sin.f64 x))) (cos.f64 x))
(+ (cos x) (* eps (- (* eps (+ (* -1/8 (cos x)) (* 1/48 (* eps (sin x))))) (* 1/2 (sin x)))))
(fma.f64 eps (fma.f64 (sin.f64 x) (fma.f64 eps (.f64 eps #s(literal 1/48 binary64)) #s(literal -1/2 binary64)) (.f64 eps (*.f64 (cos.f64 x) #s(literal -1/8 binary64)))) (cos.f64 x))
(cos (* 1/2 (+ eps (* 2 x))))
(cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x))
(cos (* 1/2 (+ eps (* 2 x))))
(cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x))
(cos (* 1/2 (+ eps (* 2 x))))
(cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x))
(cos (* 1/2 (+ eps (* 2 x))))
(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))
(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))
(* 1/2 eps)
(*.f64 #s(literal 1/2 binary64) eps)
(* eps (+ 1/2 (* -1/48 (pow eps 2))))
(.f64 eps (fma.f64 eps (.f64 eps #s(literal -1/48 binary64)) #s(literal 1/2 binary64)))
(* eps (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48))))
(.f64 eps (fma.f64 eps (.f64 eps (fma.f64 (*.f64 eps eps) #s(literal 1/3840 binary64) #s(literal -1/48 binary64))) #s(literal 1/2 binary64)))
(* eps (+ 1/2 (* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48))))
(.f64 eps (fma.f64 (.f64 eps eps) (fma.f64 eps (.f64 eps (fma.f64 (.f64 eps eps) #s(literal -1/645120 binary64) #s(literal 1/3840 binary64))) #s(literal -1/48 binary64)) #s(literal 1/2 binary64)))
(sin (* 1/2 eps))
(sin.f64 (*.f64 #s(literal 1/2 binary64) eps))
(sin (* 1/2 eps))
(sin.f64 (*.f64 #s(literal 1/2 binary64) eps))
(sin (* 1/2 eps))
(sin.f64 (*.f64 #s(literal 1/2 binary64) eps))
(sin (* 1/2 eps))
(sin.f64 (*.f64 #s(literal 1/2 binary64) eps))
(sin (* 1/2 eps))
(sin.f64 (*.f64 #s(literal 1/2 binary64) eps))
(sin (* 1/2 eps))
(sin.f64 (*.f64 #s(literal 1/2 binary64) eps))
(sin (* 1/2 eps))
(sin.f64 (*.f64 #s(literal 1/2 binary64) eps))
(sin (* 1/2 eps))
(sin.f64 (*.f64 #s(literal 1/2 binary64) eps))
(pow x 3)
(.f64 x (.f64 x x))
(pow x 3)
(.f64 x (.f64 x x))
(pow x 3)
(.f64 x (.f64 x x))
(pow x 3)
(.f64 x (.f64 x x))
(pow x 3)
(.f64 x (.f64 x x))
(pow x 3)
(.f64 x (.f64 x x))
(pow x 3)
(.f64 x (.f64 x x))
(pow x 3)
(.f64 x (.f64 x x))
(pow x 3)
(.f64 x (.f64 x x))
(pow x 3)
(.f64 x (.f64 x x))
(pow x 3)
(.f64 x (.f64 x x))
(pow x 3)
(.f64 x (.f64 x x))

rewrite266.0ms (1.9%)

Memory

3.6MiB live, 381.1MiB allocated

Rules

6 010×	`lower-fma.f32`
6 004×	`lower-fma.f64`
4 252×	`lower-/.f64`
4 252×	`lower-/.f32`
4 168×	`lower-*.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	36	161
0	61	147
1	189	147
2	1458	147
0	8241	147

Stop Event

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

Counts

20 → 625

Calls

Call 1

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

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

eval117.0ms (0.8%)

Memory: 16.3MiB live, 207.7MiB allocated
Compiler: Compiled 24 311 to 2 223 computations (90.9% saved)

prune161.0ms (1.1%)

Memory

-11.7MiB live, 248.4MiB allocated

Pruning

24 alts after pruning (20 fresh and 4 done)

	Pruned	Kept	Total
New	991	18	1 009
Fresh	0	2	2
Picked	2	3	5
Done	0	1	1
Total	993	24	1 017

Accuracy

100.0%

Counts

1 017 → 24

Alt Table

Click to see full alt table

Status	Accuracy	Program
	99.7%	(fma.f64 (sin.f64 eps) (cos.f64 x) (fma.f64 (sin.f64 x) (cos.f64 eps) (sin.f64 (neg.f64 x))))
✓	62.8%	(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
✓	61.4%	(-.f64 (sin.f64 (+.f64 x eps)) #s(approx (sin x) (fma.f64 #s(literal -1/6 binary64) (.f64 x (.f64 x x)) x)))
	50.0%	(.f64 (.f64 (sin.f64 (.f64 (/.f64 (.f64 eps eps) eps) #s(literal 1/2 binary64))) (cos.f64 (*.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)))) #s(literal 2 binary64))
▶	100.0%	(.f64 (.f64 (sin.f64 (.f64 (+.f64 eps #s(literal 0 binary64)) #s(literal 1/2 binary64))) (-.f64 (.f64 (cos.f64 (.f64 (.f64 x #s(literal 2 binary64)) #s(literal 1/2 binary64))) (cos.f64 (.f64 eps #s(literal 1/2 binary64)))) (.f64 (sin.f64 (.f64 (.f64 x #s(literal 2 binary64)) #s(literal 1/2 binary64))) (sin.f64 (*.f64 eps #s(literal 1/2 binary64)))))) #s(literal 2 binary64))
	99.8%	(.f64 (.f64 #s(approx (sin (* (+ eps 0) 1/2)) (.f64 eps (fma.f64 (.f64 eps eps) (fma.f64 eps (.f64 eps (fma.f64 (.f64 eps eps) #s(literal -1/645120 binary64) #s(literal 1/3840 binary64))) #s(literal -1/48 binary64)) #s(literal 1/2 binary64)))) (cos.f64 (*.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)))) #s(literal 2 binary64))
	99.7%	(.f64 (.f64 #s(approx (sin (* (+ eps 0) 1/2)) (.f64 eps (fma.f64 eps (.f64 eps (fma.f64 (.f64 eps eps) #s(literal 1/3840 binary64) #s(literal -1/48 binary64))) #s(literal 1/2 binary64)))) (cos.f64 (.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)))) #s(literal 2 binary64))
▶	99.5%	(.f64 (.f64 #s(approx (sin (* (+ eps 0) 1/2)) (.f64 eps (fma.f64 eps (.f64 eps #s(literal -1/48 binary64)) #s(literal 1/2 binary64)))) (cos.f64 (*.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)))) #s(literal 2 binary64))
	99.1%	(.f64 (.f64 #s(approx (sin (* (+ eps 0) 1/2)) (.f64 #s(literal 1/2 binary64) eps)) (cos.f64 (.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)))) #s(literal 2 binary64))
	99.8%	(.f64 #s(approx ( (sin (* (+ eps 0) 1/2)) (cos (* (+ (* x 2) eps) 1/2))) (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)))) #s(literal 2 binary64))
	48.6%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (/.f64 (cos.f64 x) eps) (.f64 eps eps)))
	99.4%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 eps (fma.f64 (fma.f64 eps (.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64)) (cos.f64 x) (.f64 (.f64 eps (sin.f64 x)) (fma.f64 eps (*.f64 eps #s(literal 1/24 binary64)) #s(literal -1/2 binary64))))))
✓	99.0%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 eps (fma.f64 eps (.f64 #s(literal -1/2 binary64) (sin.f64 x)) (cos.f64 x))))
	97.5%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 eps (fma.f64 eps (.f64 #s(literal -1/2 binary64) (sin.f64 x)) #s(approx (cos x) #s(literal 1 binary64)))))
▶	98.4%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 eps (fma.f64 eps #s(approx ( -1/2 (sin x)) (*.f64 x #s(literal -1/2 binary64))) (cos.f64 x))))
✓	98.6%	#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 eps (cos.f64 x)))
	97.8%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 eps #s(approx (+ ( eps (* -1/2 (sin x))) (cos x)) (fma.f64 (*.f64 x #s(literal -1/2 binary64)) (+.f64 eps x) #s(literal 1 binary64)))))
	97.4%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 eps #s(approx (+ ( eps (* -1/2 (sin x))) (cos x)) (fma.f64 eps (*.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64)))))
▶	97.5%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 eps #s(approx (+ ( eps (* -1/2 (sin x))) (cos x)) #s(literal 1 binary64))))
	97.8%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 eps #s(approx (cos x) (fma.f64 (.f64 x x) (fma.f64 x (.f64 x (fma.f64 (.f64 x x) #s(literal -1/720 binary64) #s(literal 1/24 binary64))) #s(literal -1/2 binary64)) #s(literal 1 binary64)))))
	97.9%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 eps #s(approx (cos x) (fma.f64 (.f64 x x) (fma.f64 #s(literal 1/24 binary64) (*.f64 x x) #s(literal -1/2 binary64)) #s(literal 1 binary64)))))
▶	97.8%	#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* eps (+ (* eps (* -1/2 (sin x))) (cos x))) (fma.f64 x (.f64 eps (.f64 #s(literal -1/2 binary64) (+.f64 eps x))) eps)))
	97.7%	#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* eps (cos x)) (fma.f64 eps (.f64 x (.f64 x #s(literal -1/2 binary64))) eps)))
	97.5%	#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (sin eps) (fma.f64 eps (.f64 #s(literal -1/6 binary64) (.f64 eps eps)) eps)))

Compiler

Compiled 745 to 439 computations (41.1% saved)

simplify235.0ms (1.7%)

Memory

-19.4MiB live, 255.0MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 19 expressions of interest:

New	Metric	Score
cost-diff	0	#s(approx (sin (* (+ eps 0) 1/2)) (.f64 eps (fma.f64 eps (.f64 eps #s(literal -1/48 binary64)) #s(literal 1/2 binary64))))
cost-diff	0	(.f64 #s(approx (sin ( (+ eps 0) 1/2)) (.f64 eps (fma.f64 eps (.f64 eps #s(literal -1/48 binary64)) #s(literal 1/2 binary64)))) (cos.f64 (*.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64))))
cost-diff	0	(.f64 (.f64 #s(approx (sin (* (+ eps 0) 1/2)) (.f64 eps (fma.f64 eps (.f64 eps #s(literal -1/48 binary64)) #s(literal 1/2 binary64)))) (cos.f64 (*.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)))) #s(literal 2 binary64))
cost-diff	320	(*.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64))
cost-diff	0	#s(approx (* -1/2 (sin x)) (*.f64 x #s(literal -1/2 binary64)))
cost-diff	0	(fma.f64 eps #s(approx (* -1/2 (sin x)) (*.f64 x #s(literal -1/2 binary64))) (cos.f64 x))
cost-diff	0	(.f64 eps (fma.f64 eps #s(approx ( -1/2 (sin x)) (*.f64 x #s(literal -1/2 binary64))) (cos.f64 x)))
cost-diff	0	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 eps (fma.f64 eps #s(approx ( -1/2 (sin x)) (*.f64 x #s(literal -1/2 binary64))) (cos.f64 x))))
cost-diff	0	(.f64 eps (.f64 #s(literal -1/2 binary64) (+.f64 eps x)))
cost-diff	0	(fma.f64 x (.f64 eps (.f64 #s(literal -1/2 binary64) (+.f64 eps x))) eps)
cost-diff	0	#s(approx (* eps (+ (* eps (* -1/2 (sin x))) (cos x))) (fma.f64 x (.f64 eps (.f64 #s(literal -1/2 binary64) (+.f64 eps x))) eps))
cost-diff	0	#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* eps (+ (* eps (* -1/2 (sin x))) (cos x))) (fma.f64 x (.f64 eps (.f64 #s(literal -1/2 binary64) (+.f64 eps x))) eps)))
cost-diff	0	#s(approx (+ (* eps (* -1/2 (sin x))) (cos x)) #s(literal 1 binary64))
cost-diff	0	(.f64 eps #s(approx (+ ( eps (* -1/2 (sin x))) (cos x)) #s(literal 1 binary64)))
cost-diff	0	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 eps #s(approx (+ ( eps (* -1/2 (sin x))) (cos x)) #s(literal 1 binary64))))
cost-diff	0	(.f64 (sin.f64 (.f64 (+.f64 eps #s(literal 0 binary64)) #s(literal 1/2 binary64))) (-.f64 (.f64 (cos.f64 (.f64 (.f64 x #s(literal 2 binary64)) #s(literal 1/2 binary64))) (cos.f64 (.f64 eps #s(literal 1/2 binary64)))) (.f64 (sin.f64 (.f64 (.f64 x #s(literal 2 binary64)) #s(literal 1/2 binary64))) (sin.f64 (.f64 eps #s(literal 1/2 binary64))))))
cost-diff	0	(.f64 (.f64 (sin.f64 (.f64 (+.f64 eps #s(literal 0 binary64)) #s(literal 1/2 binary64))) (-.f64 (.f64 (cos.f64 (.f64 (.f64 x #s(literal 2 binary64)) #s(literal 1/2 binary64))) (cos.f64 (.f64 eps #s(literal 1/2 binary64)))) (.f64 (sin.f64 (.f64 (.f64 x #s(literal 2 binary64)) #s(literal 1/2 binary64))) (sin.f64 (*.f64 eps #s(literal 1/2 binary64)))))) #s(literal 2 binary64))
cost-diff	192	(+.f64 eps #s(literal 0 binary64))
cost-diff	640	(.f64 (.f64 x #s(literal 2 binary64)) #s(literal 1/2 binary64))

Rules

14 632×	`lower-fma.f32`
14 624×	`lower-fma.f64`
5 666×	`lower-*.f32`
5 632×	`lower-*.f64`
2 268×	`lower-+.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	59	450
0	94	422
1	168	386
2	423	386
3	1072	386
4	2343	386
5	3324	386
6	4145	386
7	6415	386
0	8367	377

Stop Event

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

Calls

Call 1

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

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

localize206.0ms (1.5%)

Memory

7.0MiB live, 250.4MiB allocated

Localize:

Found 19 expressions of interest:

New	Metric	Score
accuracy	0.0078125	(.f64 eps (fma.f64 eps (.f64 eps #s(literal -1/48 binary64)) #s(literal 1/2 binary64)))
accuracy	0.12433519012083698	(cos.f64 (*.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)))
accuracy	0.2995093154419517	#s(approx (sin (* (+ eps 0) 1/2)) (.f64 eps (fma.f64 eps (.f64 eps #s(literal -1/48 binary64)) #s(literal 1/2 binary64))))
accuracy	0.33203125	(*.f64 eps #s(literal -1/48 binary64))
accuracy	0.0078125	(fma.f64 eps #s(approx (* -1/2 (sin x)) (*.f64 x #s(literal -1/2 binary64))) (cos.f64 x))
accuracy	0.015625	(.f64 eps (fma.f64 eps #s(approx ( -1/2 (sin x)) (*.f64 x #s(literal -1/2 binary64))) (cos.f64 x)))
accuracy	0.6075516331400427	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 eps (fma.f64 eps #s(approx ( -1/2 (sin x)) (*.f64 x #s(literal -1/2 binary64))) (cos.f64 x))))
accuracy	1.7240835547500155	#s(approx (* -1/2 (sin x)) (*.f64 x #s(literal -1/2 binary64)))
accuracy	0.015625	(fma.f64 x (.f64 eps (.f64 #s(literal -1/2 binary64) (+.f64 eps x))) eps)
accuracy	0.109375	(.f64 eps (.f64 #s(literal -1/2 binary64) (+.f64 eps x)))
accuracy	0.6075516331400427	#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* eps (+ (* eps (* -1/2 (sin x))) (cos x))) (fma.f64 x (.f64 eps (.f64 #s(literal -1/2 binary64) (+.f64 eps x))) eps)))
accuracy	1.3953416245767343	#s(approx (* eps (+ (* eps (* -1/2 (sin x))) (cos x))) (fma.f64 x (.f64 eps (.f64 #s(literal -1/2 binary64) (+.f64 eps x))) eps))
accuracy	0.015625	(.f64 eps #s(approx (+ ( eps (* -1/2 (sin x))) (cos x)) #s(literal 1 binary64)))
accuracy	0.6075516331400427	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 eps #s(approx (+ ( eps (* -1/2 (sin x))) (cos x)) #s(literal 1 binary64))))
accuracy	1.618046024877226	#s(approx (+ (* eps (* -1/2 (sin x))) (cos x)) #s(literal 1 binary64))
accuracy	0.0078125	(.f64 (sin.f64 (.f64 (+.f64 eps #s(literal 0 binary64)) #s(literal 1/2 binary64))) (-.f64 (.f64 (cos.f64 (.f64 (.f64 x #s(literal 2 binary64)) #s(literal 1/2 binary64))) (cos.f64 (.f64 eps #s(literal 1/2 binary64)))) (.f64 (sin.f64 (.f64 (.f64 x #s(literal 2 binary64)) #s(literal 1/2 binary64))) (sin.f64 (.f64 eps #s(literal 1/2 binary64))))))
accuracy	0.0078125	(.f64 (sin.f64 (.f64 (.f64 x #s(literal 2 binary64)) #s(literal 1/2 binary64))) (sin.f64 (.f64 eps #s(literal 1/2 binary64))))
accuracy	0.01171875	(-.f64 (.f64 (cos.f64 (.f64 (.f64 x #s(literal 2 binary64)) #s(literal 1/2 binary64))) (cos.f64 (.f64 eps #s(literal 1/2 binary64)))) (.f64 (sin.f64 (.f64 (.f64 x #s(literal 2 binary64)) #s(literal 1/2 binary64))) (sin.f64 (.f64 eps #s(literal 1/2 binary64)))))
accuracy	0.01171875	(.f64 (cos.f64 (.f64 (.f64 x #s(literal 2 binary64)) #s(literal 1/2 binary64))) (cos.f64 (.f64 eps #s(literal 1/2 binary64))))

Samples

65.0ms	90×	1	valid
51.0ms	166×	0	valid

Compiler

Compiled 356 to 49 computations (86.2% saved)

Precisions

Click to see histograms. Total time spent on operations: 89.0ms

ival-mult: 46.0ms (51.6% of total)

ival-cos: 11.0ms (12.3% of total)

ival-sin: 9.0ms (10.1% of total)

ival-add: 8.0ms (9% of total)

adjust: 7.0ms (7.9% of total)

const: 4.0ms (4.5% of total)

ival-sub: 3.0ms (3.4% of total)

exact: 1.0ms (1.1% of total)

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

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

series47.0ms (0.3%)

Memory

17.2MiB live, 54.4MiB allocated

Counts

25 → 528

Calls

Call 1

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

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

Calls

132 calls:

Time	Variable		Point	Expression
5.0ms	eps	@	inf	(* eps (+ (* eps (* eps -1/48)) 1/2))
1.0ms	x	@	inf	(* (* (sin (* (+ eps 0) 1/2)) (- (* (cos (* (* x 2) 1/2)) (cos (* eps 1/2))) (* (sin (* (* x 2) 1/2)) (sin (* eps 1/2))))) 2)
1.0ms	eps	@	-inf	(* (* (sin (* (+ eps 0) 1/2)) (- (* (cos (* (* x 2) 1/2)) (cos (* eps 1/2))) (* (sin (* (* x 2) 1/2)) (sin (* eps 1/2))))) 2)
1.0ms	eps	@	inf	(* (* (sin (* (+ eps 0) 1/2)) (- (* (cos (* (* x 2) 1/2)) (cos (* eps 1/2))) (* (sin (* (* x 2) 1/2)) (sin (* eps 1/2))))) 2)
1.0ms	x	@	-inf	(* (* (sin (* (+ eps 0) 1/2)) (- (* (cos (* (* x 2) 1/2)) (cos (* eps 1/2))) (* (sin (* (* x 2) 1/2)) (sin (* eps 1/2))))) 2)

simplify371.0ms (2.6%)

Memory

-0.6MiB live, 355.2MiB allocated

Algorithm

1×	egg-herbie

Rules

15 396×	`lower-fma.f64`
15 396×	`lower-fma.f32`
6 820×	`lower-*.f64`
6 820×	`lower-*.f32`
4 048×	`lower-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	403	5847
1	1287	5642
2	3612	5577
0	8071	5228

Stop Event

1×	iter limit
1×	node limit

Counts

528 → 497

Calls

Call 1

Inputs
x
x
x
x
x
x
x
x
x
x
x
x
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 (* (sin (* 1/2 eps)) (- (* (cos x) (cos (* 1/2 eps))) (* (sin x) (sin (* 1/2 eps))))))
(* 2 (* (sin (* 1/2 eps)) (- (* (cos x) (cos (* 1/2 eps))) (* (sin x) (sin (* 1/2 eps))))))
(* 2 (* (sin (* 1/2 eps)) (- (* (cos x) (cos (* 1/2 eps))) (* (sin x) (sin (* 1/2 eps))))))
(* 2 (* (sin (* 1/2 eps)) (- (* (cos x) (cos (* 1/2 eps))) (* (sin x) (sin (* 1/2 eps))))))
(* 2 (* (sin (* 1/2 eps)) (- (* (cos x) (cos (* 1/2 eps))) (* (sin x) (sin (* 1/2 eps))))))
(* 2 (* (sin (* 1/2 eps)) (- (* (cos x) (cos (* 1/2 eps))) (* (sin x) (sin (* 1/2 eps))))))
(* 2 (* (sin (* 1/2 eps)) (- (* (cos x) (cos (* 1/2 eps))) (* (sin x) (sin (* 1/2 eps))))))
(* 2 (* (sin (* 1/2 eps)) (- (* (cos x) (cos (* 1/2 eps))) (* (sin x) (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 (* (sin (* 1/2 eps)) (- (* (cos x) (cos (* 1/2 eps))) (* (sin x) (sin (* 1/2 eps))))))
(* 2 (* (sin (* 1/2 eps)) (- (* (cos x) (cos (* 1/2 eps))) (* (sin x) (sin (* 1/2 eps))))))
(* 2 (* (sin (* 1/2 eps)) (- (* (cos x) (cos (* 1/2 eps))) (* (sin x) (sin (* 1/2 eps))))))
(* 2 (* (sin (* 1/2 eps)) (- (* (cos x) (cos (* 1/2 eps))) (* (sin x) (sin (* 1/2 eps))))))
(* 2 (* (sin (* 1/2 eps)) (- (* (cos x) (cos (* 1/2 eps))) (* (sin x) (sin (* 1/2 eps))))))
(* 2 (* (sin (* 1/2 eps)) (- (* (cos x) (cos (* 1/2 eps))) (* (sin x) (sin (* 1/2 eps))))))
(* 2 (* (sin (* 1/2 eps)) (- (* (cos x) (cos (* 1/2 eps))) (* (sin x) (sin (* 1/2 eps))))))
(* 2 (* (sin (* 1/2 eps)) (- (* (cos x) (cos (* 1/2 eps))) (* (sin x) (sin (* 1/2 eps))))))
(* 1/2 (* eps (cos x)))
(* eps (+ (* -1/4 (* eps (sin x))) (* 1/2 (cos x))))
(* eps (+ (* 1/2 (cos x)) (* eps (+ (* -1/4 (sin x)) (* eps (+ (* -1/16 (cos x)) (* -1/48 (cos x))))))))
(* eps (+ (* 1/2 (cos x)) (* eps (+ (* -1/4 (sin x)) (* eps (+ (* -1/16 (cos x)) (+ (* -1/48 (cos x)) (* 1/48 (* eps (sin x))))))))))
(* (sin (* 1/2 eps)) (- (* (cos x) (cos (* 1/2 eps))) (* (sin x) (sin (* 1/2 eps)))))
(* (sin (* 1/2 eps)) (- (* (cos x) (cos (* 1/2 eps))) (* (sin x) (sin (* 1/2 eps)))))
(* (sin (* 1/2 eps)) (- (* (cos x) (cos (* 1/2 eps))) (* (sin x) (sin (* 1/2 eps)))))
(* (sin (* 1/2 eps)) (- (* (cos x) (cos (* 1/2 eps))) (* (sin x) (sin (* 1/2 eps)))))
(* (sin (* 1/2 eps)) (- (* (cos x) (cos (* 1/2 eps))) (* (sin x) (sin (* 1/2 eps)))))
(* (sin (* 1/2 eps)) (- (* (cos x) (cos (* 1/2 eps))) (* (sin x) (sin (* 1/2 eps)))))
(* (sin (* 1/2 eps)) (- (* (cos x) (cos (* 1/2 eps))) (* (sin x) (sin (* 1/2 eps)))))
(* (sin (* 1/2 eps)) (- (* (cos x) (cos (* 1/2 eps))) (* (sin x) (sin (* 1/2 eps)))))
(* (cos (* 1/2 eps)) (sin (* 1/2 eps)))
(+ (* -1 (* x (pow (sin (* 1/2 eps)) 2))) (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))
(+ (* x (+ (* -1 (pow (sin (* 1/2 eps)) 2)) (* -1/2 (* x (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))))) (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))
(+ (* x (+ (* -1 (pow (sin (* 1/2 eps)) 2)) (* x (+ (* -1/2 (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) (* 1/6 (* x (pow (sin (* 1/2 eps)) 2))))))) (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))
(* (sin (* 1/2 eps)) (- (* (cos x) (cos (* 1/2 eps))) (* (sin x) (sin (* 1/2 eps)))))
(* (sin (* 1/2 eps)) (- (* (cos x) (cos (* 1/2 eps))) (* (sin x) (sin (* 1/2 eps)))))
(* (sin (* 1/2 eps)) (- (* (cos x) (cos (* 1/2 eps))) (* (sin x) (sin (* 1/2 eps)))))
(* (sin (* 1/2 eps)) (- (* (cos x) (cos (* 1/2 eps))) (* (sin x) (sin (* 1/2 eps)))))
(* (sin (* 1/2 eps)) (- (* (cos x) (cos (* 1/2 eps))) (* (sin x) (sin (* 1/2 eps)))))
(* (sin (* 1/2 eps)) (- (* (cos x) (cos (* 1/2 eps))) (* (sin x) (sin (* 1/2 eps)))))
(* (sin (* 1/2 eps)) (- (* (cos x) (cos (* 1/2 eps))) (* (sin x) (sin (* 1/2 eps)))))
(* (sin (* 1/2 eps)) (- (* (cos x) (cos (* 1/2 eps))) (* (sin x) (sin (* 1/2 eps)))))
(sin eps)
(+ (sin eps) (* x (- (cos eps) 1)))
(+ (sin eps) (* x (- (+ (cos eps) (* -1/2 (* x (sin eps)))) 1)))
(+ (sin eps) (* x (- (+ (cos eps) (* x (+ (* -1/2 (sin eps)) (* x (+ 1/6 (* -1/6 (cos eps))))))) 1)))
(- (sin (+ eps x)) (sin x))
(- (sin (+ eps x)) (sin x))
(- (sin (+ eps x)) (sin x))
(- (sin (+ eps x)) (sin x))
(- (sin (- eps (* -1 x))) (sin x))
(- (sin (- eps (* -1 x))) (sin x))
(- (sin (- eps (* -1 x))) (sin x))
(- (sin (- eps (* -1 x))) (sin x))
(* eps (cos x))
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x)))))))
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* eps (+ (* -1/6 (cos x)) (* 1/24 (* eps (sin x)))))))))
(- (sin (+ eps x)) (sin x))
(- (sin (+ eps x)) (sin x))
(- (sin (+ eps x)) (sin x))
(- (sin (+ eps x)) (sin x))
(- (sin (- x (* -1 eps))) (sin x))
(- (sin (- x (* -1 eps))) (sin x))
(- (sin (- x (* -1 eps))) (sin x))
(- (sin (- x (* -1 eps))) (sin x))
(* eps (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)))
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)))))
(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)))))
(+ (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))))
(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 (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)))
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
(+ eps (* -1/2 (* (pow eps 2) x)))
(+ eps (* x (+ (* -1/2 (* eps x)) (* -1/2 (pow eps 2)))))
(+ eps (* x (+ (* -1/2 (* eps x)) (* -1/2 (pow eps 2)))))
(* -1/2 (* eps (pow x 2)))
(* (pow x 2) (+ (* -1/2 eps) (* -1/2 (/ (pow eps 2) x))))
(* (pow x 2) (+ (* -1/2 eps) (+ (* -1/2 (/ (pow eps 2) x)) (/ eps (pow x 2)))))
(* (pow x 2) (+ (* -1/2 eps) (+ (* -1/2 (/ (pow eps 2) x)) (/ eps (pow x 2)))))
(* -1/2 (* eps (pow x 2)))
(* (pow x 2) (+ (* -1/2 eps) (* -1/2 (/ (pow eps 2) x))))
(* (pow x 2) (+ (* -1 (/ (+ (* -1 (/ eps x)) (* 1/2 (pow eps 2))) x)) (* -1/2 eps)))
(* (pow x 2) (+ (* -1 (/ (+ (* -1 (/ eps x)) (* 1/2 (pow eps 2))) x)) (* -1/2 eps)))
(* eps (+ 1 (* -1/2 (pow x 2))))
(* eps (+ 1 (+ (* -1/2 (* eps x)) (* -1/2 (pow x 2)))))
(* eps (+ 1 (+ (* -1/2 (* eps x)) (* -1/2 (pow x 2)))))
(* eps (+ 1 (+ (* -1/2 (* eps x)) (* -1/2 (pow x 2)))))
(* -1/2 (* (pow eps 2) x))
(* (pow eps 2) (+ (* -1/2 x) (+ (* -1/2 (/ (pow x 2) eps)) (/ 1 eps))))
(* (pow eps 2) (+ (* -1/2 x) (+ (* -1/2 (/ (pow x 2) eps)) (/ 1 eps))))
(* (pow eps 2) (+ (* -1/2 x) (+ (* -1/2 (/ (pow x 2) eps)) (/ 1 eps))))
(* -1/2 (* (pow eps 2) x))
(* (pow eps 2) (+ (* -1 (/ (- (* 1/2 (pow x 2)) 1) eps)) (* -1/2 x)))
(* (pow eps 2) (+ (* -1 (/ (- (* 1/2 (pow x 2)) 1) eps)) (* -1/2 x)))
(* (pow eps 2) (+ (* -1 (/ (- (* 1/2 (pow x 2)) 1) eps)) (* -1/2 x)))
(* -1/2 (* eps x))
(* eps (+ (* -1/2 eps) (* -1/2 x)))
(* eps (+ (* -1/2 eps) (* -1/2 x)))
(* eps (+ (* -1/2 eps) (* -1/2 x)))
(* -1/2 (pow eps 2))
(* (pow eps 2) (- (* -1/2 (/ x eps)) 1/2))
(* (pow eps 2) (- (* -1/2 (/ x eps)) 1/2))
(* (pow eps 2) (- (* -1/2 (/ x eps)) 1/2))
(* -1/2 (pow eps 2))
(* (pow eps 2) (- (* -1/2 (/ x eps)) 1/2))
(* (pow eps 2) (- (* -1/2 (/ x eps)) 1/2))
(* (pow eps 2) (- (* -1/2 (/ x eps)) 1/2))
(* -1/2 (pow eps 2))
(+ (* -1/2 (* eps x)) (* -1/2 (pow eps 2)))
(+ (* -1/2 (* eps x)) (* -1/2 (pow eps 2)))
(+ (* -1/2 (* eps x)) (* -1/2 (pow eps 2)))
(* -1/2 (* eps x))
(* x (+ (* -1/2 eps) (* -1/2 (/ (pow eps 2) x))))
(* x (+ (* -1/2 eps) (* -1/2 (/ (pow eps 2) x))))
(* x (+ (* -1/2 eps) (* -1/2 (/ (pow eps 2) x))))
(* -1/2 (* eps x))
(* -1 (* x (+ (* 1/2 eps) (* 1/2 (/ (pow eps 2) x)))))
(* -1 (* x (+ (* 1/2 eps) (* 1/2 (/ (pow eps 2) x)))))
(* -1 (* x (+ (* 1/2 eps) (* 1/2 (/ (pow eps 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 (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)))
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)))))
(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)))))
(+ (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))))
(* -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))))
(* 1/2 (* eps (cos x)))
(* eps (+ (* -1/4 (* eps (sin x))) (* 1/2 (cos x))))
(* eps (+ (* 1/2 (cos x)) (* eps (+ (* -1/4 (sin x)) (* eps (+ (* -1/16 (cos x)) (* -1/48 (cos x))))))))
(* eps (+ (* 1/2 (cos x)) (* eps (+ (* -1/4 (sin x)) (* eps (+ (* -1/16 (cos x)) (+ (* -1/48 (cos x)) (* 1/48 (* eps (sin x))))))))))
(* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps)))
(* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps)))
(* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps)))
(* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps)))
(* (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps)))
(* (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps)))
(* (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps)))
(* (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps)))
(* (cos (* 1/2 eps)) (sin (* 1/2 eps)))
(+ (* -1 (* x (pow (sin (* 1/2 eps)) 2))) (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))
(+ (* x (+ (* -1 (pow (sin (* 1/2 eps)) 2)) (* -1/2 (* x (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))))) (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))
(+ (* x (+ (* -1 (pow (sin (* 1/2 eps)) 2)) (* x (+ (* -1/2 (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) (* 1/6 (* x (pow (sin (* 1/2 eps)) 2))))))) (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))
(* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps)))
(* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps)))
(* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps)))
(* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps)))
(* (cos (* 1/2 (- eps (* -2 x)))) (sin (* 1/2 eps)))
(* (cos (* 1/2 (- eps (* -2 x)))) (sin (* 1/2 eps)))
(* (cos (* 1/2 (- eps (* -2 x)))) (sin (* 1/2 eps)))
(* (cos (* 1/2 (- eps (* -2 x)))) (sin (* 1/2 eps)))
(* 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))
(cos (* 1/2 eps))
(+ (cos (* 1/2 eps)) (* -1/2 (* (pow x 2) (cos (* 1/2 eps)))))
(+ (cos (* 1/2 eps)) (* (pow x 2) (+ (* -1/2 (cos (* 1/2 eps))) (* 1/24 (* (pow x 2) (cos (* 1/2 eps)))))))
(+ (cos (* 1/2 eps)) (* (pow x 2) (+ (* -1/2 (cos (* 1/2 eps))) (* (pow x 2) (+ (* -1/720 (* (pow x 2) (cos (* 1/2 eps)))) (* 1/24 (cos (* 1/2 eps))))))))
(* (cos x) (cos (* 1/2 eps)))
(* (cos x) (cos (* 1/2 eps)))
(* (cos x) (cos (* 1/2 eps)))
(* (cos x) (cos (* 1/2 eps)))
(* (cos x) (cos (* 1/2 eps)))
(* (cos x) (cos (* 1/2 eps)))
(* (cos x) (cos (* 1/2 eps)))
(* (cos x) (cos (* 1/2 eps)))
(cos x)
(+ (cos x) (* -1/8 (* (pow eps 2) (cos x))))
(+ (cos x) (* (pow eps 2) (+ (* -1/8 (cos x)) (* 1/384 (* (pow eps 2) (cos x))))))
(+ (cos x) (* (pow eps 2) (+ (* -1/8 (cos x)) (* (pow eps 2) (+ (* -1/46080 (* (pow eps 2) (cos x))) (* 1/384 (cos x)))))))
(* (cos x) (cos (* 1/2 eps)))
(* (cos x) (cos (* 1/2 eps)))
(* (cos x) (cos (* 1/2 eps)))
(* (cos x) (cos (* 1/2 eps)))
(* (cos x) (cos (* 1/2 eps)))
(* (cos x) (cos (* 1/2 eps)))
(* (cos x) (cos (* 1/2 eps)))
(* (cos x) (cos (* 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) (cos (* 1/2 eps))) (* (sin x) (sin (* 1/2 eps))))
(- (* (cos x) (cos (* 1/2 eps))) (* (sin x) (sin (* 1/2 eps))))
(- (* (cos x) (cos (* 1/2 eps))) (* (sin x) (sin (* 1/2 eps))))
(- (* (cos x) (cos (* 1/2 eps))) (* (sin x) (sin (* 1/2 eps))))
(- (* (cos x) (cos (* 1/2 eps))) (* (sin x) (sin (* 1/2 eps))))
(- (* (cos x) (cos (* 1/2 eps))) (* (sin x) (sin (* 1/2 eps))))
(- (* (cos x) (cos (* 1/2 eps))) (* (sin x) (sin (* 1/2 eps))))
(- (* (cos x) (cos (* 1/2 eps))) (* (sin x) (sin (* 1/2 eps))))
(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) (cos (* 1/2 eps))) (* (sin x) (sin (* 1/2 eps))))
(- (* (cos x) (cos (* 1/2 eps))) (* (sin x) (sin (* 1/2 eps))))
(- (* (cos x) (cos (* 1/2 eps))) (* (sin x) (sin (* 1/2 eps))))
(- (* (cos x) (cos (* 1/2 eps))) (* (sin x) (sin (* 1/2 eps))))
(- (* (cos x) (cos (* 1/2 eps))) (* (sin x) (sin (* 1/2 eps))))
(- (* (cos x) (cos (* 1/2 eps))) (* (sin x) (sin (* 1/2 eps))))
(- (* (cos x) (cos (* 1/2 eps))) (* (sin x) (sin (* 1/2 eps))))
(- (* (cos x) (cos (* 1/2 eps))) (* (sin x) (sin (* 1/2 eps))))
(* x (sin (* 1/2 eps)))
(* x (+ (sin (* 1/2 eps)) (* -1/6 (* (pow x 2) (sin (* 1/2 eps))))))
(* x (+ (sin (* 1/2 eps)) (* (pow x 2) (+ (* -1/6 (sin (* 1/2 eps))) (* 1/120 (* (pow x 2) (sin (* 1/2 eps))))))))
(* x (+ (sin (* 1/2 eps)) (* (pow x 2) (+ (* -1/6 (sin (* 1/2 eps))) (* (pow x 2) (+ (* -1/5040 (* (pow x 2) (sin (* 1/2 eps)))) (* 1/120 (sin (* 1/2 eps)))))))))
(* (sin x) (sin (* 1/2 eps)))
(* (sin x) (sin (* 1/2 eps)))
(* (sin x) (sin (* 1/2 eps)))
(* (sin x) (sin (* 1/2 eps)))
(* (sin x) (sin (* 1/2 eps)))
(* (sin x) (sin (* 1/2 eps)))
(* (sin x) (sin (* 1/2 eps)))
(* (sin x) (sin (* 1/2 eps)))
(* 1/2 (* eps (sin x)))
(* eps (+ (* -1/48 (* (pow eps 2) (sin x))) (* 1/2 (sin x))))
(* eps (+ (* 1/2 (sin x)) (* (pow eps 2) (+ (* -1/48 (sin x)) (* 1/3840 (* (pow eps 2) (sin x)))))))
(* eps (+ (* 1/2 (sin x)) (* (pow eps 2) (+ (* -1/48 (sin x)) (* (pow eps 2) (+ (* -1/645120 (* (pow eps 2) (sin x))) (* 1/3840 (sin x))))))))
(* (sin x) (sin (* 1/2 eps)))
(* (sin x) (sin (* 1/2 eps)))
(* (sin x) (sin (* 1/2 eps)))
(* (sin x) (sin (* 1/2 eps)))
(* (sin x) (sin (* 1/2 eps)))
(* (sin x) (sin (* 1/2 eps)))
(* (sin x) (sin (* 1/2 eps)))
(* (sin x) (sin (* 1/2 eps)))
(* -1/48 eps)
(* -1/48 eps)
(* -1/48 eps)
(* -1/48 eps)
(* -1/48 eps)
(* -1/48 eps)
(* -1/48 eps)
(* -1/48 eps)
(* -1/48 eps)
(* -1/48 eps)
(* -1/48 eps)
(* -1/48 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 (* 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 (* -1/48 (pow eps 2))))
(* eps (+ 1/2 (* -1/48 (pow eps 2))))
(* -1/48 (pow eps 3))
(* (pow eps 3) (- (* 1/2 (/ 1 (pow eps 2))) 1/48))
(* (pow eps 3) (- (* 1/2 (/ 1 (pow eps 2))) 1/48))
(* (pow eps 3) (- (* 1/2 (/ 1 (pow eps 2))) 1/48))
(* -1/48 (pow eps 3))
(* -1 (* (pow eps 3) (- 1/48 (* 1/2 (/ 1 (pow eps 2))))))
(* -1 (* (pow eps 3) (- 1/48 (* 1/2 (/ 1 (pow eps 2))))))
(* -1 (* (pow eps 3) (- 1/48 (* 1/2 (/ 1 (pow eps 2))))))

Outputs
x
x
x
x
x
x
x
x
x
x
x
x
eps
eps
eps
eps
eps
eps
eps
eps
eps
eps
eps
eps
(* eps (cos x))
(*.f64 eps (cos.f64 x))
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(.f64 eps (fma.f64 eps (.f64 #s(literal -1/2 binary64) (sin.f64 x)) (cos.f64 x)))
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* 2 (* eps (+ (* -1/16 (cos x)) (* -1/48 (cos x)))))))))
(.f64 eps (fma.f64 eps (.f64 #s(literal -1/2 binary64) (sin.f64 x)) (.f64 (fma.f64 eps (.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64)) (cos.f64 x))))
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* eps (+ (* 1/24 (* eps (sin x))) (* 2 (+ (* -1/16 (cos x)) (* -1/48 (cos x))))))))))
(.f64 eps (fma.f64 eps (fma.f64 eps (.f64 (cos.f64 x) #s(literal -1/6 binary64)) (.f64 (sin.f64 x) (fma.f64 eps (.f64 eps #s(literal 1/24 binary64)) #s(literal -1/2 binary64)))) (cos.f64 x)))
(* 2 (* (sin (* 1/2 eps)) (- (* (cos x) (cos (* 1/2 eps))) (* (sin x) (sin (* 1/2 eps))))))
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(* 2 (* (sin (* 1/2 eps)) (- (* (cos x) (cos (* 1/2 eps))) (* (sin x) (sin (* 1/2 eps))))))
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(* 2 (* (sin (* 1/2 eps)) (- (* (cos x) (cos (* 1/2 eps))) (* (sin x) (sin (* 1/2 eps))))))
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(* 2 (* (sin (* 1/2 eps)) (- (* (cos x) (cos (* 1/2 eps))) (* (sin x) (sin (* 1/2 eps))))))
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(* 2 (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))
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(.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (fma.f64 #s(literal 2 binary64) (cos.f64 (.f64 eps #s(literal 1/2 binary64))) (.f64 (.f64 x #s(literal -2 binary64)) (sin.f64 (.f64 eps #s(literal 1/2 binary64))))))
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(* 1/2 (* eps (cos x)))
(.f64 eps (.f64 (cos.f64 x) #s(literal 1/2 binary64)))
(* eps (+ (* -1/4 (* eps (sin x))) (* 1/2 (cos x))))
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(* eps (+ (* 1/2 (cos x)) (* eps (+ (* -1/4 (sin x)) (* eps (+ (* -1/16 (cos x)) (* -1/48 (cos x))))))))
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(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
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(sin (* 1/2 eps))
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(cos (* 1/2 eps))
(cos.f64 (*.f64 eps #s(literal 1/2 binary64)))
(+ (cos (* 1/2 eps)) (* -1/2 (* (pow x 2) (cos (* 1/2 eps)))))
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(* (cos x) (cos (* 1/2 eps)))
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(* x (sin (* 1/2 eps)))
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(.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (fma.f64 x (.f64 #s(literal -1/6 binary64) (.f64 x x)) x))
(* x (+ (sin (* 1/2 eps)) (* (pow x 2) (+ (* -1/6 (sin (* 1/2 eps))) (* 1/120 (* (pow x 2) (sin (* 1/2 eps))))))))
(.f64 x (.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (+.f64 (fma.f64 #s(literal -1/6 binary64) (.f64 x x) #s(literal 1 binary64)) (.f64 (.f64 x x) (.f64 (.f64 x x) #s(literal 1/120 binary64))))))
(* x (+ (sin (* 1/2 eps)) (* (pow x 2) (+ (* -1/6 (sin (* 1/2 eps))) (* (pow x 2) (+ (* -1/5040 (* (pow x 2) (sin (* 1/2 eps)))) (* 1/120 (sin (* 1/2 eps)))))))))
(.f64 x (fma.f64 (.f64 x x) (.f64 (.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (.f64 x x)) (fma.f64 (.f64 x x) #s(literal -1/5040 binary64) #s(literal 1/120 binary64))) (.f64 (fma.f64 #s(literal -1/6 binary64) (.f64 x x) #s(literal 1 binary64)) (sin.f64 (.f64 eps #s(literal 1/2 binary64))))))
(* (sin x) (sin (* 1/2 eps)))
(.f64 (sin.f64 x) (sin.f64 (.f64 eps #s(literal 1/2 binary64))))
(* (sin x) (sin (* 1/2 eps)))
(.f64 (sin.f64 x) (sin.f64 (.f64 eps #s(literal 1/2 binary64))))
(* (sin x) (sin (* 1/2 eps)))
(.f64 (sin.f64 x) (sin.f64 (.f64 eps #s(literal 1/2 binary64))))
(* (sin x) (sin (* 1/2 eps)))
(.f64 (sin.f64 x) (sin.f64 (.f64 eps #s(literal 1/2 binary64))))
(* (sin x) (sin (* 1/2 eps)))
(.f64 (sin.f64 x) (sin.f64 (.f64 eps #s(literal 1/2 binary64))))
(* (sin x) (sin (* 1/2 eps)))
(.f64 (sin.f64 x) (sin.f64 (.f64 eps #s(literal 1/2 binary64))))
(* (sin x) (sin (* 1/2 eps)))
(.f64 (sin.f64 x) (sin.f64 (.f64 eps #s(literal 1/2 binary64))))
(* (sin x) (sin (* 1/2 eps)))
(.f64 (sin.f64 x) (sin.f64 (.f64 eps #s(literal 1/2 binary64))))
(* 1/2 (* eps (sin x)))
(.f64 eps (.f64 (sin.f64 x) #s(literal 1/2 binary64)))
(* eps (+ (* -1/48 (* (pow eps 2) (sin x))) (* 1/2 (sin x))))
(.f64 (sin.f64 x) (.f64 eps (fma.f64 eps (*.f64 eps #s(literal -1/48 binary64)) #s(literal 1/2 binary64))))
(* eps (+ (* 1/2 (sin x)) (* (pow eps 2) (+ (* -1/48 (sin x)) (* 1/3840 (* (pow eps 2) (sin x)))))))
(.f64 eps (fma.f64 (sin.f64 x) #s(literal 1/2 binary64) (.f64 (.f64 eps (.f64 eps (sin.f64 x))) (fma.f64 eps (*.f64 eps #s(literal 1/3840 binary64)) #s(literal -1/48 binary64)))))
(* eps (+ (* 1/2 (sin x)) (* (pow eps 2) (+ (* -1/48 (sin x)) (* (pow eps 2) (+ (* -1/645120 (* (pow eps 2) (sin x))) (* 1/3840 (sin x))))))))
(.f64 eps (fma.f64 (sin.f64 x) (fma.f64 eps (.f64 eps #s(literal -1/48 binary64)) #s(literal 1/2 binary64)) (.f64 (.f64 eps eps) (.f64 (.f64 eps (.f64 eps (sin.f64 x))) (fma.f64 (.f64 eps eps) #s(literal -1/645120 binary64) #s(literal 1/3840 binary64))))))
(* (sin x) (sin (* 1/2 eps)))
(.f64 (sin.f64 x) (sin.f64 (.f64 eps #s(literal 1/2 binary64))))
(* (sin x) (sin (* 1/2 eps)))
(.f64 (sin.f64 x) (sin.f64 (.f64 eps #s(literal 1/2 binary64))))
(* (sin x) (sin (* 1/2 eps)))
(.f64 (sin.f64 x) (sin.f64 (.f64 eps #s(literal 1/2 binary64))))
(* (sin x) (sin (* 1/2 eps)))
(.f64 (sin.f64 x) (sin.f64 (.f64 eps #s(literal 1/2 binary64))))
(* (sin x) (sin (* 1/2 eps)))
(.f64 (sin.f64 x) (sin.f64 (.f64 eps #s(literal 1/2 binary64))))
(* (sin x) (sin (* 1/2 eps)))
(.f64 (sin.f64 x) (sin.f64 (.f64 eps #s(literal 1/2 binary64))))
(* (sin x) (sin (* 1/2 eps)))
(.f64 (sin.f64 x) (sin.f64 (.f64 eps #s(literal 1/2 binary64))))
(* (sin x) (sin (* 1/2 eps)))
(.f64 (sin.f64 x) (sin.f64 (.f64 eps #s(literal 1/2 binary64))))
(* -1/48 eps)
(*.f64 eps #s(literal -1/48 binary64))
(* -1/48 eps)
(*.f64 eps #s(literal -1/48 binary64))
(* -1/48 eps)
(*.f64 eps #s(literal -1/48 binary64))
(* -1/48 eps)
(*.f64 eps #s(literal -1/48 binary64))
(* -1/48 eps)
(*.f64 eps #s(literal -1/48 binary64))
(* -1/48 eps)
(*.f64 eps #s(literal -1/48 binary64))
(* -1/48 eps)
(*.f64 eps #s(literal -1/48 binary64))
(* -1/48 eps)
(*.f64 eps #s(literal -1/48 binary64))
(* -1/48 eps)
(*.f64 eps #s(literal -1/48 binary64))
(* -1/48 eps)
(*.f64 eps #s(literal -1/48 binary64))
(* -1/48 eps)
(*.f64 eps #s(literal -1/48 binary64))
(* -1/48 eps)
(*.f64 eps #s(literal -1/48 binary64))
(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 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (neg.f64 x) (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 (fma.f64 x (.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64)) (cos.f64 (.f64 eps #s(literal 1/2 binary64))) (.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (neg.f64 x)))
(+ (cos (* 1/2 eps)) (* x (- (* x (+ (* -1/2 (cos (* 1/2 eps))) (* 1/6 (* x (sin (* 1/2 eps)))))) (sin (* 1/2 eps)))))
(fma.f64 x (fma.f64 x (.f64 #s(literal -1/2 binary64) (cos.f64 (.f64 eps #s(literal 1/2 binary64)))) (.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (fma.f64 x (.f64 x #s(literal 1/6 binary64)) #s(literal -1 binary64)))) (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 eps (*.f64 #s(literal -1/2 binary64) (sin.f64 x)) (cos.f64 x))
(+ (cos x) (* eps (- (* -1/8 (* eps (cos x))) (* 1/2 (sin x)))))
(fma.f64 (fma.f64 (.f64 eps eps) #s(literal -1/8 binary64) #s(literal 1 binary64)) (cos.f64 x) (.f64 eps (*.f64 #s(literal -1/2 binary64) (sin.f64 x))))
(+ (cos x) (* eps (- (* eps (+ (* -1/8 (cos x)) (* 1/48 (* eps (sin x))))) (* 1/2 (sin x)))))
(fma.f64 eps (fma.f64 (cos.f64 x) (.f64 eps #s(literal -1/8 binary64)) (.f64 (sin.f64 x) (fma.f64 eps (*.f64 eps #s(literal 1/48 binary64)) #s(literal -1/2 binary64)))) (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 eps (fma.f64 eps (.f64 eps #s(literal -1/48 binary64)) #s(literal 1/2 binary64)))
(* eps (+ 1/2 (* -1/48 (pow eps 2))))
(.f64 eps (fma.f64 eps (.f64 eps #s(literal -1/48 binary64)) #s(literal 1/2 binary64)))
(* eps (+ 1/2 (* -1/48 (pow eps 2))))
(.f64 eps (fma.f64 eps (.f64 eps #s(literal -1/48 binary64)) #s(literal 1/2 binary64)))
(* -1/48 (pow eps 3))
(.f64 eps (.f64 #s(literal -1/48 binary64) (*.f64 eps eps)))
(* (pow eps 3) (- (* 1/2 (/ 1 (pow eps 2))) 1/48))
(.f64 (.f64 eps eps) (.f64 eps (+.f64 #s(literal -1/48 binary64) (/.f64 #s(literal 1/2 binary64) (.f64 eps eps)))))
(* (pow eps 3) (- (* 1/2 (/ 1 (pow eps 2))) 1/48))
(.f64 (.f64 eps eps) (.f64 eps (+.f64 #s(literal -1/48 binary64) (/.f64 #s(literal 1/2 binary64) (.f64 eps eps)))))
(* (pow eps 3) (- (* 1/2 (/ 1 (pow eps 2))) 1/48))
(.f64 (.f64 eps eps) (.f64 eps (+.f64 #s(literal -1/48 binary64) (/.f64 #s(literal 1/2 binary64) (.f64 eps eps)))))
(* -1/48 (pow eps 3))
(.f64 eps (.f64 #s(literal -1/48 binary64) (*.f64 eps eps)))
(* -1 (* (pow eps 3) (- 1/48 (* 1/2 (/ 1 (pow eps 2))))))
(.f64 (.f64 eps eps) (.f64 eps (+.f64 #s(literal -1/48 binary64) (/.f64 #s(literal 1/2 binary64) (.f64 eps eps)))))
(* -1 (* (pow eps 3) (- 1/48 (* 1/2 (/ 1 (pow eps 2))))))
(.f64 (.f64 eps eps) (.f64 eps (+.f64 #s(literal -1/48 binary64) (/.f64 #s(literal 1/2 binary64) (.f64 eps eps)))))
(* -1 (* (pow eps 3) (- 1/48 (* 1/2 (/ 1 (pow eps 2))))))
(.f64 (.f64 eps eps) (.f64 eps (+.f64 #s(literal -1/48 binary64) (/.f64 #s(literal 1/2 binary64) (.f64 eps eps)))))

rewrite299.0ms (2.1%)

Memory

13.7MiB live, 362.7MiB allocated

Rules

4 386×	`lower-*.f32`
4 352×	`lower-*.f64`
4 064×	`lower-/.f64`
4 064×	`lower-/.f32`
3 664×	`lower-fma.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	59	372
0	94	354
1	300	293
2	2522	293
0	8384	281

Stop Event

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

Counts

25 → 565

Calls

Call 1

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

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

eval199.0ms (1.4%)

Memory: -15.5MiB live, 257.7MiB allocated
Compiler: Compiled 28 043 to 2 355 computations (91.6% saved)

prune203.0ms (1.4%)

Memory

-4.9MiB live, 327.5MiB allocated

Pruning

31 alts after pruning (24 fresh and 7 done)

	Pruned	Kept	Total
New	1 054	15	1 069
Fresh	6	9	15
Picked	2	3	5
Done	0	4	4
Total	1 062	31	1 093

Accuracy

100.0%

Counts

1 093 → 31

Alt Table

Click to see full alt table

Status	Accuracy	Program
	99.7%	(fma.f64 (sin.f64 eps) (cos.f64 x) (fma.f64 (sin.f64 x) (cos.f64 eps) (sin.f64 (neg.f64 x))))
✓	62.8%	(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
✓	61.4%	(-.f64 (sin.f64 (+.f64 x eps)) #s(approx (sin x) (fma.f64 #s(literal -1/6 binary64) (.f64 x (.f64 x x)) x)))
	50.0%	(.f64 (.f64 (sin.f64 (.f64 (/.f64 (.f64 eps eps) eps) #s(literal 1/2 binary64))) (cos.f64 (*.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)))) #s(literal 2 binary64))
	99.7%	(.f64 (.f64 (sin.f64 (.f64 (+.f64 eps #s(literal 0 binary64)) #s(literal 1/2 binary64))) (-.f64 #s(approx ( (cos (* (* x 2) 1/2)) (cos (* eps 1/2))) (.f64 (cos.f64 x) (+.f64 (fma.f64 (.f64 eps eps) #s(literal -1/8 binary64) #s(literal 1 binary64)) (.f64 (.f64 eps eps) (.f64 (.f64 eps eps) #s(literal 1/384 binary64)))))) (.f64 (sin.f64 (.f64 (.f64 x #s(literal 2 binary64)) #s(literal 1/2 binary64))) (sin.f64 (.f64 eps #s(literal 1/2 binary64)))))) #s(literal 2 binary64))
	99.5%	(.f64 (.f64 (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) #s(approx (sin (* (+ eps 0) 1/2)) (.f64 eps (fma.f64 eps (.f64 eps #s(literal -1/48 binary64)) #s(literal 1/2 binary64))))) #s(literal 2 binary64))
	99.5%	(.f64 (.f64 #s(approx (sin (* (+ eps 0) 1/2)) (fma.f64 (.f64 eps (.f64 eps eps)) #s(literal -1/48 binary64) (.f64 #s(literal 1/2 binary64) eps))) (cos.f64 (.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)))) #s(literal 2 binary64))
	49.6%	(.f64 (.f64 #s(approx (sin (* (+ eps 0) 1/2)) (/.f64 (.f64 (fma.f64 eps (.f64 eps #s(literal -1/48 binary64)) #s(literal 1/2 binary64)) (.f64 eps eps)) eps)) (cos.f64 (.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)))) #s(literal 2 binary64))
▶	99.8%	(.f64 (.f64 #s(approx (sin (* (+ eps 0) 1/2)) (.f64 eps (fma.f64 (.f64 eps eps) (fma.f64 (.f64 eps eps) (fma.f64 (.f64 eps eps) #s(literal -1/645120 binary64) #s(literal 1/3840 binary64)) #s(literal -1/48 binary64)) #s(literal 1/2 binary64)))) (cos.f64 (*.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)))) #s(literal 2 binary64))
	99.7%	(.f64 (.f64 #s(approx (sin (* (+ eps 0) 1/2)) (.f64 eps (fma.f64 (.f64 eps eps) (fma.f64 eps (.f64 eps #s(literal 1/3840 binary64)) #s(literal -1/48 binary64)) #s(literal 1/2 binary64)))) (cos.f64 (.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)))) #s(literal 2 binary64))
	99.4%	(.f64 (.f64 #s(approx (sin (* (+ eps 0) 1/2)) (.f64 eps (fma.f64 eps (.f64 eps #s(literal -1/48 binary64)) #s(literal 1/2 binary64)))) (cos.f64 #s(approx (* (+ (* x 2) eps) 1/2) (*.f64 eps (+.f64 #s(literal 1/2 binary64) (/.f64 x eps)))))) #s(literal 2 binary64))
▶	99.1%	(.f64 (.f64 #s(approx (sin (* (+ eps 0) 1/2)) (.f64 eps #s(literal 1/2 binary64))) (cos.f64 (.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)))) #s(literal 2 binary64))
▶	100.0%	(.f64 #s(approx ( (sin (* (+ eps 0) 1/2)) (- (* (cos (* (* x 2) 1/2)) (cos (* eps 1/2))) (* (sin (* (* x 2) 1/2)) (sin (* eps 1/2))))) (.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (-.f64 (.f64 (cos.f64 x) (cos.f64 (.f64 eps #s(literal 1/2 binary64)))) (.f64 (sin.f64 x) (sin.f64 (.f64 eps #s(literal 1/2 binary64))))))) #s(literal 2 binary64))
	98.4%	#s(approx (- (sin (+ x eps)) (sin x)) (fma.f64 (cos.f64 x) eps (.f64 #s(approx ( -1/2 (sin x)) (.f64 x #s(literal -1/2 binary64))) (.f64 eps eps))))
	48.6%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (/.f64 (cos.f64 x) eps) (.f64 eps eps)))
	99.4%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 eps (fma.f64 (fma.f64 eps (.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64)) (cos.f64 x) (.f64 (.f64 eps (sin.f64 x)) (fma.f64 eps (*.f64 eps #s(literal 1/24 binary64)) #s(literal -1/2 binary64))))))
✓	99.0%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 eps (fma.f64 eps (.f64 #s(literal -1/2 binary64) (sin.f64 x)) (cos.f64 x))))
	97.5%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 eps (fma.f64 eps (.f64 #s(literal -1/2 binary64) (sin.f64 x)) #s(approx (cos x) #s(literal 1 binary64)))))
✓	98.4%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 eps (fma.f64 eps #s(approx ( -1/2 (sin x)) (*.f64 x #s(literal -1/2 binary64))) (cos.f64 x))))
✓	98.6%	#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 eps (cos.f64 x)))
	97.8%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 eps #s(approx (+ ( eps (* -1/2 (sin x))) (cos x)) (fma.f64 (*.f64 x #s(literal -1/2 binary64)) (+.f64 eps x) #s(literal 1 binary64)))))
	97.4%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 eps #s(approx (+ ( eps (* -1/2 (sin x))) (cos x)) (fma.f64 x (*.f64 eps #s(literal -1/2 binary64)) #s(literal 1 binary64)))))
✓	97.5%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 eps #s(approx (+ ( eps (* -1/2 (sin x))) (cos x)) #s(literal 1 binary64))))
▶	97.8%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 eps #s(approx (cos x) (fma.f64 (.f64 x x) (fma.f64 x (.f64 x (fma.f64 (.f64 x x) #s(literal -1/720 binary64) #s(literal 1/24 binary64))) #s(literal -1/2 binary64)) #s(literal 1 binary64)))))
	97.9%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 eps #s(approx (cos x) (fma.f64 (.f64 x x) (fma.f64 #s(literal 1/24 binary64) (*.f64 x x) #s(literal -1/2 binary64)) #s(literal 1 binary64)))))
✓	97.8%	#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* eps (+ (* eps (* -1/2 (sin x))) (cos x))) (fma.f64 x (.f64 eps (.f64 #s(literal -1/2 binary64) (+.f64 eps x))) eps)))
	97.7%	#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* eps (+ (* eps (* -1/2 (sin x))) (cos x))) (fma.f64 x #s(approx (* eps (* -1/2 (+ eps x))) (.f64 x (.f64 eps #s(literal -1/2 binary64)))) eps)))
	47.8%	#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* eps (+ (* eps (* -1/2 (sin x))) (cos x))) (.f64 (.f64 (fma.f64 x (.f64 eps (.f64 (+.f64 x eps) #s(literal -1/2 binary64))) eps) (fma.f64 x (.f64 eps (.f64 (+.f64 x eps) #s(literal -1/2 binary64))) (neg.f64 eps))) (/.f64 #s(literal 1 binary64) (fma.f64 x (.f64 eps (.f64 (+.f64 x eps) #s(literal -1/2 binary64))) (neg.f64 eps))))))
	47.8%	#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* eps (+ (* eps (* -1/2 (sin x))) (cos x))) #s(approx (+ (* x (* eps (* -1/2 (+ eps x)))) eps) (.f64 (.f64 eps eps) (-.f64 (.f64 x #s(literal -1/2 binary64)) (/.f64 (fma.f64 x (.f64 x #s(literal 1/2 binary64)) #s(literal -1 binary64)) eps))))))
▶	5.1%	#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* eps (+ (* eps (* -1/2 (sin x))) (cos x))) #s(approx (+ (* x (* eps (* -1/2 (+ eps x)))) eps) (.f64 x (.f64 x (*.f64 eps #s(literal -1/2 binary64)))))))
	97.5%	#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (sin eps) (fma.f64 eps (.f64 #s(literal -1/6 binary64) (.f64 eps eps)) eps)))

Compiler

Compiled 1 065 to 603 computations (43.4% saved)

simplify212.0ms (1.5%)

Memory

27.0MiB live, 292.3MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 20 expressions of interest:

New	Metric	Score
cost-diff	0	#s(approx (sin (* (+ eps 0) 1/2)) (.f64 eps (fma.f64 (.f64 eps eps) (fma.f64 (.f64 eps eps) (fma.f64 (.f64 eps eps) #s(literal -1/645120 binary64) #s(literal 1/3840 binary64)) #s(literal -1/48 binary64)) #s(literal 1/2 binary64))))
cost-diff	0	(.f64 #s(approx (sin ( (+ eps 0) 1/2)) (.f64 eps (fma.f64 (.f64 eps eps) (fma.f64 (.f64 eps eps) (fma.f64 (.f64 eps eps) #s(literal -1/645120 binary64) #s(literal 1/3840 binary64)) #s(literal -1/48 binary64)) #s(literal 1/2 binary64)))) (cos.f64 (*.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64))))
cost-diff	0	(.f64 (.f64 #s(approx (sin (* (+ eps 0) 1/2)) (.f64 eps (fma.f64 (.f64 eps eps) (fma.f64 (.f64 eps eps) (fma.f64 (.f64 eps eps) #s(literal -1/645120 binary64) #s(literal 1/3840 binary64)) #s(literal -1/48 binary64)) #s(literal 1/2 binary64)))) (cos.f64 (*.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)))) #s(literal 2 binary64))
cost-diff	320	(*.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64))
cost-diff	0	#s(approx (sin (* (+ eps 0) 1/2)) (*.f64 eps #s(literal 1/2 binary64)))
cost-diff	0	(.f64 #s(approx (sin ( (+ eps 0) 1/2)) (.f64 eps #s(literal 1/2 binary64))) (cos.f64 (.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64))))
cost-diff	0	(.f64 (.f64 #s(approx (sin (* (+ eps 0) 1/2)) (.f64 eps #s(literal 1/2 binary64))) (cos.f64 (.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)))) #s(literal 2 binary64))
cost-diff	320	(*.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64))
cost-diff	0	(fma.f64 (.f64 x x) (fma.f64 x (.f64 x (fma.f64 (*.f64 x x) #s(literal -1/720 binary64) #s(literal 1/24 binary64))) #s(literal -1/2 binary64)) #s(literal 1 binary64))
cost-diff	0	#s(approx (cos x) (fma.f64 (.f64 x x) (fma.f64 x (.f64 x (fma.f64 (*.f64 x x) #s(literal -1/720 binary64) #s(literal 1/24 binary64))) #s(literal -1/2 binary64)) #s(literal 1 binary64)))
cost-diff	0	(.f64 eps #s(approx (cos x) (fma.f64 (.f64 x x) (fma.f64 x (.f64 x (fma.f64 (.f64 x x) #s(literal -1/720 binary64) #s(literal 1/24 binary64))) #s(literal -1/2 binary64)) #s(literal 1 binary64))))
cost-diff	0	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 eps #s(approx (cos x) (fma.f64 (.f64 x x) (fma.f64 x (.f64 x (fma.f64 (.f64 x x) #s(literal -1/720 binary64) #s(literal 1/24 binary64))) #s(literal -1/2 binary64)) #s(literal 1 binary64)))))
cost-diff	0	(.f64 x (.f64 x (*.f64 eps #s(literal -1/2 binary64))))
cost-diff	0	#s(approx (+ (* x (* eps (* -1/2 (+ eps x)))) eps) (.f64 x (.f64 x (*.f64 eps #s(literal -1/2 binary64)))))
cost-diff	0	#s(approx (* eps (+ (* eps (* -1/2 (sin x))) (cos x))) #s(approx (+ (* x (* eps (* -1/2 (+ eps x)))) eps) (.f64 x (.f64 x (*.f64 eps #s(literal -1/2 binary64))))))
cost-diff	0	#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* eps (+ (* eps (* -1/2 (sin x))) (cos x))) #s(approx (+ (* x (* eps (* -1/2 (+ eps x)))) eps) (.f64 x (.f64 x (*.f64 eps #s(literal -1/2 binary64)))))))
cost-diff	0	(sin.f64 (*.f64 eps #s(literal 1/2 binary64)))
cost-diff	0	(.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (-.f64 (.f64 (cos.f64 x) (cos.f64 (.f64 eps #s(literal 1/2 binary64)))) (.f64 (sin.f64 x) (sin.f64 (.f64 eps #s(literal 1/2 binary64))))))
cost-diff	0	#s(approx (* (sin (* (+ eps 0) 1/2)) (- (* (cos (* (* x 2) 1/2)) (cos (* eps 1/2))) (* (sin (* (* x 2) 1/2)) (sin (* eps 1/2))))) (.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (-.f64 (.f64 (cos.f64 x) (cos.f64 (.f64 eps #s(literal 1/2 binary64)))) (.f64 (sin.f64 x) (sin.f64 (.f64 eps #s(literal 1/2 binary64)))))))
cost-diff	0	(.f64 #s(approx ( (sin (* (+ eps 0) 1/2)) (- (* (cos (* (* x 2) 1/2)) (cos (* eps 1/2))) (* (sin (* (* x 2) 1/2)) (sin (* eps 1/2))))) (.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (-.f64 (.f64 (cos.f64 x) (cos.f64 (.f64 eps #s(literal 1/2 binary64)))) (.f64 (sin.f64 x) (sin.f64 (.f64 eps #s(literal 1/2 binary64))))))) #s(literal 2 binary64))

Rules

12 718×	`lower-fma.f32`
12 704×	`lower-fma.f64`
3 740×	`lower-*.f32`
3 704×	`lower-*.f64`
2 490×	`lower-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	79	641
0	119	621
1	241	601
2	645	601
3	2212	601
4	2768	601
5	3025	601
6	3358	601
7	4135	601
8	6473	601
0	8196	588

Stop Event

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

Calls

Call 1

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

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

localize327.0ms (2.3%)

Memory

-26.2MiB live, 353.1MiB allocated

Localize:

Found 20 expressions of interest:

New	Metric	Score
accuracy	0.01171875	(fma.f64 (.f64 eps eps) (fma.f64 (.f64 eps eps) #s(literal -1/645120 binary64) #s(literal 1/3840 binary64)) #s(literal -1/48 binary64))
accuracy	0.01171875	(.f64 eps (fma.f64 (.f64 eps eps) (fma.f64 (.f64 eps eps) (fma.f64 (.f64 eps eps) #s(literal -1/645120 binary64) #s(literal 1/3840 binary64)) #s(literal -1/48 binary64)) #s(literal 1/2 binary64)))
accuracy	0.06740076172875197	#s(approx (sin (* (+ eps 0) 1/2)) (.f64 eps (fma.f64 (.f64 eps eps) (fma.f64 (.f64 eps eps) (fma.f64 (.f64 eps eps) #s(literal -1/645120 binary64) #s(literal 1/3840 binary64)) #s(literal -1/48 binary64)) #s(literal 1/2 binary64))))
accuracy	0.124335190120837	(cos.f64 (*.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)))
accuracy	0	(*.f64 eps #s(literal 1/2 binary64))
accuracy	0.0078125	(.f64 #s(approx (sin ( (+ eps 0) 1/2)) (.f64 eps #s(literal 1/2 binary64))) (cos.f64 (.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64))))
accuracy	0.124335190120837	(cos.f64 (*.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)))
accuracy	0.5669531085279471	#s(approx (sin (* (+ eps 0) 1/2)) (*.f64 eps #s(literal 1/2 binary64)))
accuracy	0.01953125	(fma.f64 (*.f64 x x) #s(literal -1/720 binary64) #s(literal 1/24 binary64))
accuracy	0.28125	(.f64 x (fma.f64 (.f64 x x) #s(literal -1/720 binary64) #s(literal 1/24 binary64)))
accuracy	0.9119086677164644	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 eps #s(approx (cos x) (fma.f64 (.f64 x x) (fma.f64 x (.f64 x (fma.f64 (.f64 x x) #s(literal -1/720 binary64) #s(literal 1/24 binary64))) #s(literal -1/2 binary64)) #s(literal 1 binary64)))))
accuracy	1.287051638549886	#s(approx (cos x) (fma.f64 (.f64 x x) (fma.f64 x (.f64 x (fma.f64 (*.f64 x x) #s(literal -1/720 binary64) #s(literal 1/24 binary64))) #s(literal -1/2 binary64)) #s(literal 1 binary64)))
accuracy	0.0703125	(.f64 x (.f64 x (*.f64 eps #s(literal -1/2 binary64))))
accuracy	0.6075516331400427	#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* eps (+ (* eps (* -1/2 (sin x))) (cos x))) #s(approx (+ (* x (* eps (* -1/2 (+ eps x)))) eps) (.f64 x (.f64 x (*.f64 eps #s(literal -1/2 binary64)))))))
accuracy	1.3953416245767343	#s(approx (* eps (+ (* eps (* -1/2 (sin x))) (cos x))) #s(approx (+ (* x (* eps (* -1/2 (+ eps x)))) eps) (.f64 x (.f64 x (*.f64 eps #s(literal -1/2 binary64))))))
accuracy	60.29803535734107	#s(approx (+ (* x (* eps (* -1/2 (+ eps x)))) eps) (.f64 x (.f64 x (*.f64 eps #s(literal -1/2 binary64)))))
accuracy	0.0078125	(.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (-.f64 (.f64 (cos.f64 x) (cos.f64 (.f64 eps #s(literal 1/2 binary64)))) (.f64 (sin.f64 x) (sin.f64 (.f64 eps #s(literal 1/2 binary64))))))
accuracy	0.0078125	(.f64 (sin.f64 x) (sin.f64 (.f64 eps #s(literal 1/2 binary64))))
accuracy	0.01171875	(-.f64 (.f64 (cos.f64 x) (cos.f64 (.f64 eps #s(literal 1/2 binary64)))) (.f64 (sin.f64 x) (sin.f64 (.f64 eps #s(literal 1/2 binary64)))))
accuracy	0.01171875	(.f64 (cos.f64 x) (cos.f64 (.f64 eps #s(literal 1/2 binary64))))

Samples

135.0ms	90×	1	valid
91.0ms	166×	0	valid

Compiler

Compiled 442 to 72 computations (83.7% saved)

Precisions

Click to see histograms. Total time spent on operations: 159.0ms

ival-mult: 57.0ms (35.9% of total)

ival-add: 51.0ms (32.1% of total)

const: 17.0ms (10.7% of total)

adjust: 11.0ms (6.9% of total)

ival-sin: 9.0ms (5.7% of total)

ival-cos: 9.0ms (5.7% of total)

ival-sub: 4.0ms (2.5% of total)

exact: 1.0ms (0.6% of total)

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

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

series55.0ms (0.4%)

Memory

6.1MiB live, 42.8MiB allocated

Counts

28 → 552

Calls

Call 1

Inputs
#s(alt (.f64 #s(approx ( (sin (* (+ eps 0) 1/2)) (- (* (cos (* (* x 2) 1/2)) (cos (* eps 1/2))) (* (sin (* (* x 2) 1/2)) (sin (* eps 1/2))))) (.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (-.f64 (.f64 (cos.f64 x) (cos.f64 (.f64 eps #s(literal 1/2 binary64)))) (.f64 (sin.f64 x) (sin.f64 (.f64 eps #s(literal 1/2 binary64))))))) #s(literal 2 binary64)) (patch (.f64 #s(approx ( (sin (* (+ eps 0) 1/2)) (- (* (cos (* (* x 2) 1/2)) (cos (* eps 1/2))) (* (sin (* (* x 2) 1/2)) (sin (* eps 1/2))))) (.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (-.f64 (.f64 (cos.f64 x) (cos.f64 (.f64 eps #s(literal 1/2 binary64)))) (.f64 (sin.f64 x) (sin.f64 (.f64 eps #s(literal 1/2 binary64))))))) #s(literal 2 binary64)) #<representation binary64>) () ())
#s(alt #s(approx (* (sin (* (+ eps 0) 1/2)) (- (* (cos (* (* x 2) 1/2)) (cos (* eps 1/2))) (* (sin (* (* x 2) 1/2)) (sin (* eps 1/2))))) (.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (-.f64 (.f64 (cos.f64 x) (cos.f64 (.f64 eps #s(literal 1/2 binary64)))) (.f64 (sin.f64 x) (sin.f64 (.f64 eps #s(literal 1/2 binary64))))))) (patch #s(approx (* (sin (* (+ eps 0) 1/2)) (- (* (cos (* (* x 2) 1/2)) (cos (* eps 1/2))) (* (sin (* (* x 2) 1/2)) (sin (* eps 1/2))))) (.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (-.f64 (.f64 (cos.f64 x) (cos.f64 (.f64 eps #s(literal 1/2 binary64)))) (.f64 (sin.f64 x) (sin.f64 (.f64 eps #s(literal 1/2 binary64))))))) #<representation binary64>) () ())
#s(alt (.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (-.f64 (.f64 (cos.f64 x) (cos.f64 (.f64 eps #s(literal 1/2 binary64)))) (.f64 (sin.f64 x) (sin.f64 (.f64 eps #s(literal 1/2 binary64)))))) (patch (.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (-.f64 (.f64 (cos.f64 x) (cos.f64 (.f64 eps #s(literal 1/2 binary64)))) (.f64 (sin.f64 x) (sin.f64 (.f64 eps #s(literal 1/2 binary64)))))) #<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 #s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* eps (+ (* eps (* -1/2 (sin x))) (cos x))) #s(approx (+ (* x (* eps (* -1/2 (+ eps x)))) eps) (.f64 x (.f64 x (.f64 eps #s(literal -1/2 binary64))))))) (patch #s(approx (- (sin (+ x eps)) (sin x)) #s(approx ( eps (+ (* eps (* -1/2 (sin x))) (cos x))) #s(approx (+ (* x (* eps (* -1/2 (+ eps x)))) eps) (.f64 x (.f64 x (*.f64 eps #s(literal -1/2 binary64))))))) #<representation binary64>) () ())
#s(alt #s(approx (* eps (+ (* eps (* -1/2 (sin x))) (cos x))) #s(approx (+ (* x (* eps (* -1/2 (+ eps x)))) eps) (.f64 x (.f64 x (.f64 eps #s(literal -1/2 binary64)))))) (patch #s(approx ( eps (+ (* eps (* -1/2 (sin x))) (cos x))) #s(approx (+ (* x (* eps (* -1/2 (+ eps x)))) eps) (.f64 x (.f64 x (*.f64 eps #s(literal -1/2 binary64)))))) #<representation binary64>) () ())
#s(alt #s(approx (+ (* x (* eps (* -1/2 (+ eps x)))) eps) (.f64 x (.f64 x (.f64 eps #s(literal -1/2 binary64))))) (patch #s(approx (+ ( x (* eps (* -1/2 (+ eps x)))) eps) (.f64 x (.f64 x (*.f64 eps #s(literal -1/2 binary64))))) #<representation binary64>) () ())
#s(alt (.f64 x (.f64 x (.f64 eps #s(literal -1/2 binary64)))) (patch (.f64 x (.f64 x (.f64 eps #s(literal -1/2 binary64)))) #<representation binary64>) () ())
#s(alt #s(approx (- (sin (+ x eps)) (sin x)) (.f64 eps #s(approx (cos x) (fma.f64 (.f64 x x) (fma.f64 x (.f64 x (fma.f64 (.f64 x x) #s(literal -1/720 binary64) #s(literal 1/24 binary64))) #s(literal -1/2 binary64)) #s(literal 1 binary64))))) (patch #s(approx (- (sin (+ x eps)) (sin x)) (.f64 eps #s(approx (cos x) (fma.f64 (.f64 x x) (fma.f64 x (.f64 x (fma.f64 (.f64 x x) #s(literal -1/720 binary64) #s(literal 1/24 binary64))) #s(literal -1/2 binary64)) #s(literal 1 binary64))))) #<representation binary64>) () ())
#s(alt (.f64 eps #s(approx (cos x) (fma.f64 (.f64 x x) (fma.f64 x (.f64 x (fma.f64 (.f64 x x) #s(literal -1/720 binary64) #s(literal 1/24 binary64))) #s(literal -1/2 binary64)) #s(literal 1 binary64)))) (patch (.f64 eps #s(approx (cos x) (fma.f64 (.f64 x x) (fma.f64 x (.f64 x (fma.f64 (.f64 x x) #s(literal -1/720 binary64) #s(literal 1/24 binary64))) #s(literal -1/2 binary64)) #s(literal 1 binary64)))) #<representation binary64>) () ())
#s(alt #s(approx (cos x) (fma.f64 (.f64 x x) (fma.f64 x (.f64 x (fma.f64 (.f64 x x) #s(literal -1/720 binary64) #s(literal 1/24 binary64))) #s(literal -1/2 binary64)) #s(literal 1 binary64))) (patch #s(approx (cos x) (fma.f64 (.f64 x x) (fma.f64 x (.f64 x (fma.f64 (.f64 x x) #s(literal -1/720 binary64) #s(literal 1/24 binary64))) #s(literal -1/2 binary64)) #s(literal 1 binary64))) #<representation binary64>) () ())
#s(alt (fma.f64 (.f64 x x) (fma.f64 x (.f64 x (fma.f64 (.f64 x x) #s(literal -1/720 binary64) #s(literal 1/24 binary64))) #s(literal -1/2 binary64)) #s(literal 1 binary64)) (patch (fma.f64 (.f64 x x) (fma.f64 x (.f64 x (fma.f64 (.f64 x x) #s(literal -1/720 binary64) #s(literal 1/24 binary64))) #s(literal -1/2 binary64)) #s(literal 1 binary64)) #<representation binary64>) () ())
#s(alt (.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)) (patch (.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)) #<representation binary64>) () ())
#s(alt (.f64 (.f64 #s(approx (sin (* (+ eps 0) 1/2)) (.f64 eps #s(literal 1/2 binary64))) (cos.f64 (.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)))) #s(literal 2 binary64)) (patch (.f64 (.f64 #s(approx (sin (* (+ eps 0) 1/2)) (.f64 eps #s(literal 1/2 binary64))) (cos.f64 (.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)))) #s(literal 2 binary64)) #<representation binary64>) () ())
#s(alt (.f64 #s(approx (sin ( (+ eps 0) 1/2)) (.f64 eps #s(literal 1/2 binary64))) (cos.f64 (.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)))) (patch (.f64 #s(approx (sin ( (+ eps 0) 1/2)) (.f64 eps #s(literal 1/2 binary64))) (cos.f64 (.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)))) #<representation binary64>) () ())
#s(alt #s(approx (sin (* (+ eps 0) 1/2)) (.f64 eps #s(literal 1/2 binary64))) (patch #s(approx (sin ( (+ eps 0) 1/2)) (*.f64 eps #s(literal 1/2 binary64))) #<representation binary64>) () ())
#s(alt (.f64 (.f64 #s(approx (sin (* (+ eps 0) 1/2)) (.f64 eps (fma.f64 (.f64 eps eps) (fma.f64 (.f64 eps eps) (fma.f64 (.f64 eps eps) #s(literal -1/645120 binary64) #s(literal 1/3840 binary64)) #s(literal -1/48 binary64)) #s(literal 1/2 binary64)))) (cos.f64 (.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)))) #s(literal 2 binary64)) (patch (.f64 (.f64 #s(approx (sin ( (+ eps 0) 1/2)) (.f64 eps (fma.f64 (.f64 eps eps) (fma.f64 (.f64 eps eps) (fma.f64 (.f64 eps eps) #s(literal -1/645120 binary64) #s(literal 1/3840 binary64)) #s(literal -1/48 binary64)) #s(literal 1/2 binary64)))) (cos.f64 (*.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)))) #s(literal 2 binary64)) #<representation binary64>) () ())
#s(alt (.f64 #s(approx (sin ( (+ eps 0) 1/2)) (.f64 eps (fma.f64 (.f64 eps eps) (fma.f64 (.f64 eps eps) (fma.f64 (.f64 eps eps) #s(literal -1/645120 binary64) #s(literal 1/3840 binary64)) #s(literal -1/48 binary64)) #s(literal 1/2 binary64)))) (cos.f64 (.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)))) (patch (.f64 #s(approx (sin (* (+ eps 0) 1/2)) (.f64 eps (fma.f64 (.f64 eps eps) (fma.f64 (.f64 eps eps) (fma.f64 (.f64 eps eps) #s(literal -1/645120 binary64) #s(literal 1/3840 binary64)) #s(literal -1/48 binary64)) #s(literal 1/2 binary64)))) (cos.f64 (*.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)))) #<representation binary64>) () ())
#s(alt #s(approx (sin (* (+ eps 0) 1/2)) (.f64 eps (fma.f64 (.f64 eps eps) (fma.f64 (.f64 eps eps) (fma.f64 (.f64 eps eps) #s(literal -1/645120 binary64) #s(literal 1/3840 binary64)) #s(literal -1/48 binary64)) #s(literal 1/2 binary64)))) (patch #s(approx (sin (* (+ eps 0) 1/2)) (.f64 eps (fma.f64 (.f64 eps eps) (fma.f64 (.f64 eps eps) (fma.f64 (.f64 eps eps) #s(literal -1/645120 binary64) #s(literal 1/3840 binary64)) #s(literal -1/48 binary64)) #s(literal 1/2 binary64)))) #<representation binary64>) () ())
#s(alt (.f64 (cos.f64 x) (cos.f64 (.f64 eps #s(literal 1/2 binary64)))) (patch (.f64 (cos.f64 x) (cos.f64 (.f64 eps #s(literal 1/2 binary64)))) #<representation binary64>) () ())
#s(alt (-.f64 (.f64 (cos.f64 x) (cos.f64 (.f64 eps #s(literal 1/2 binary64)))) (.f64 (sin.f64 x) (sin.f64 (.f64 eps #s(literal 1/2 binary64))))) (patch (-.f64 (.f64 (cos.f64 x) (cos.f64 (.f64 eps #s(literal 1/2 binary64)))) (.f64 (sin.f64 x) (sin.f64 (.f64 eps #s(literal 1/2 binary64))))) #<representation binary64>) () ())
#s(alt (.f64 (sin.f64 x) (sin.f64 (.f64 eps #s(literal 1/2 binary64)))) (patch (.f64 (sin.f64 x) (sin.f64 (.f64 eps #s(literal 1/2 binary64)))) #<representation binary64>) () ())
#s(alt (.f64 x (fma.f64 (.f64 x x) #s(literal -1/720 binary64) #s(literal 1/24 binary64))) (patch (.f64 x (fma.f64 (.f64 x x) #s(literal -1/720 binary64) #s(literal 1/24 binary64))) #<representation binary64>) () ())
#s(alt (fma.f64 (.f64 x x) #s(literal -1/720 binary64) #s(literal 1/24 binary64)) (patch (fma.f64 (.f64 x x) #s(literal -1/720 binary64) #s(literal 1/24 binary64)) #<representation binary64>) () ())
#s(alt (cos.f64 (.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64))) (patch (cos.f64 (.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64))) #<representation binary64>) () ())
#s(alt (.f64 eps #s(literal 1/2 binary64)) (patch (.f64 eps #s(literal 1/2 binary64)) #<representation binary64>) () ())
#s(alt (.f64 eps (fma.f64 (.f64 eps eps) (fma.f64 (.f64 eps eps) (fma.f64 (.f64 eps eps) #s(literal -1/645120 binary64) #s(literal 1/3840 binary64)) #s(literal -1/48 binary64)) #s(literal 1/2 binary64))) (patch (.f64 eps (fma.f64 (.f64 eps eps) (fma.f64 (.f64 eps eps) (fma.f64 (.f64 eps eps) #s(literal -1/645120 binary64) #s(literal 1/3840 binary64)) #s(literal -1/48 binary64)) #s(literal 1/2 binary64))) #<representation binary64>) () ())
#s(alt (fma.f64 (.f64 eps eps) (fma.f64 (.f64 eps eps) #s(literal -1/645120 binary64) #s(literal 1/3840 binary64)) #s(literal -1/48 binary64)) (patch (fma.f64 (.f64 eps eps) (fma.f64 (.f64 eps eps) #s(literal -1/645120 binary64) #s(literal 1/3840 binary64)) #s(literal -1/48 binary64)) #<representation binary64>) () ())

Outputs
#s(alt (* eps (cos x)) (taylor 0 eps) (#s(alt (.f64 #s(approx ( (sin (* (+ eps 0) 1/2)) (- (* (cos (* (* x 2) 1/2)) (cos (* eps 1/2))) (* (sin (* (* x 2) 1/2)) (sin (* eps 1/2))))) (.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (-.f64 (.f64 (cos.f64 x) (cos.f64 (.f64 eps #s(literal 1/2 binary64)))) (.f64 (sin.f64 x) (sin.f64 (.f64 eps #s(literal 1/2 binary64))))))) #s(literal 2 binary64)) (patch (.f64 #s(approx ( (sin (* (+ eps 0) 1/2)) (- (* (cos (* (* x 2) 1/2)) (cos (* eps 1/2))) (* (sin (* (* x 2) 1/2)) (sin (* eps 1/2))))) (.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (-.f64 (.f64 (cos.f64 x) (cos.f64 (.f64 eps #s(literal 1/2 binary64)))) (.f64 (sin.f64 x) (sin.f64 (.f64 eps #s(literal 1/2 binary64))))))) #s(literal 2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* eps (+ (cos x) (* -1/2 (* eps (sin x))))) (taylor 0 eps) (#s(alt (.f64 #s(approx ( (sin (* (+ eps 0) 1/2)) (- (* (cos (* (* x 2) 1/2)) (cos (* eps 1/2))) (* (sin (* (* x 2) 1/2)) (sin (* eps 1/2))))) (.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (-.f64 (.f64 (cos.f64 x) (cos.f64 (.f64 eps #s(literal 1/2 binary64)))) (.f64 (sin.f64 x) (sin.f64 (.f64 eps #s(literal 1/2 binary64))))))) #s(literal 2 binary64)) (patch (.f64 #s(approx ( (sin (* (+ eps 0) 1/2)) (- (* (cos (* (* x 2) 1/2)) (cos (* eps 1/2))) (* (sin (* (* x 2) 1/2)) (sin (* eps 1/2))))) (.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (-.f64 (.f64 (cos.f64 x) (cos.f64 (.f64 eps #s(literal 1/2 binary64)))) (.f64 (sin.f64 x) (sin.f64 (.f64 eps #s(literal 1/2 binary64))))))) #s(literal 2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* 2 (* eps (+ (* -1/16 (cos x)) (* -1/48 (cos x))))))))) (taylor 0 eps) (#s(alt (.f64 #s(approx ( (sin (* (+ eps 0) 1/2)) (- (* (cos (* (* x 2) 1/2)) (cos (* eps 1/2))) (* (sin (* (* x 2) 1/2)) (sin (* eps 1/2))))) (.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (-.f64 (.f64 (cos.f64 x) (cos.f64 (.f64 eps #s(literal 1/2 binary64)))) (.f64 (sin.f64 x) (sin.f64 (.f64 eps #s(literal 1/2 binary64))))))) #s(literal 2 binary64)) (patch (.f64 #s(approx ( (sin (* (+ eps 0) 1/2)) (- (* (cos (* (* x 2) 1/2)) (cos (* eps 1/2))) (* (sin (* (* x 2) 1/2)) (sin (* eps 1/2))))) (.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (-.f64 (.f64 (cos.f64 x) (cos.f64 (.f64 eps #s(literal 1/2 binary64)))) (.f64 (sin.f64 x) (sin.f64 (.f64 eps #s(literal 1/2 binary64))))))) #s(literal 2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* eps (+ (* 1/24 (* eps (sin x))) (* 2 (+ (* -1/16 (cos x)) (* -1/48 (cos x)))))))))) (taylor 0 eps) (#s(alt (.f64 #s(approx ( (sin (* (+ eps 0) 1/2)) (- (* (cos (* (* x 2) 1/2)) (cos (* eps 1/2))) (* (sin (* (* x 2) 1/2)) (sin (* eps 1/2))))) (.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (-.f64 (.f64 (cos.f64 x) (cos.f64 (.f64 eps #s(literal 1/2 binary64)))) (.f64 (sin.f64 x) (sin.f64 (.f64 eps #s(literal 1/2 binary64))))))) #s(literal 2 binary64)) (patch (.f64 #s(approx ( (sin (* (+ eps 0) 1/2)) (- (* (cos (* (* x 2) 1/2)) (cos (* eps 1/2))) (* (sin (* (* x 2) 1/2)) (sin (* eps 1/2))))) (.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (-.f64 (.f64 (cos.f64 x) (cos.f64 (.f64 eps #s(literal 1/2 binary64)))) (.f64 (sin.f64 x) (sin.f64 (.f64 eps #s(literal 1/2 binary64))))))) #s(literal 2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* 2 (* (sin (* 1/2 eps)) (- (* (cos x) (cos (* 1/2 eps))) (* (sin x) (sin (* 1/2 eps)))))) (taylor inf eps) (#s(alt (.f64 #s(approx ( (sin (* (+ eps 0) 1/2)) (- (* (cos (* (* x 2) 1/2)) (cos (* eps 1/2))) (* (sin (* (* x 2) 1/2)) (sin (* eps 1/2))))) (.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (-.f64 (.f64 (cos.f64 x) (cos.f64 (.f64 eps #s(literal 1/2 binary64)))) (.f64 (sin.f64 x) (sin.f64 (.f64 eps #s(literal 1/2 binary64))))))) #s(literal 2 binary64)) (patch (.f64 #s(approx ( (sin (* (+ eps 0) 1/2)) (- (* (cos (* (* x 2) 1/2)) (cos (* eps 1/2))) (* (sin (* (* x 2) 1/2)) (sin (* eps 1/2))))) (.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (-.f64 (.f64 (cos.f64 x) (cos.f64 (.f64 eps #s(literal 1/2 binary64)))) (.f64 (sin.f64 x) (sin.f64 (.f64 eps #s(literal 1/2 binary64))))))) #s(literal 2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* 2 (* (sin (* 1/2 eps)) (- (* (cos x) (cos (* 1/2 eps))) (* (sin x) (sin (* 1/2 eps)))))) (taylor inf eps) (#s(alt (.f64 #s(approx ( (sin (* (+ eps 0) 1/2)) (- (* (cos (* (* x 2) 1/2)) (cos (* eps 1/2))) (* (sin (* (* x 2) 1/2)) (sin (* eps 1/2))))) (.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (-.f64 (.f64 (cos.f64 x) (cos.f64 (.f64 eps #s(literal 1/2 binary64)))) (.f64 (sin.f64 x) (sin.f64 (.f64 eps #s(literal 1/2 binary64))))))) #s(literal 2 binary64)) (patch (.f64 #s(approx ( (sin (* (+ eps 0) 1/2)) (- (* (cos (* (* x 2) 1/2)) (cos (* eps 1/2))) (* (sin (* (* x 2) 1/2)) (sin (* eps 1/2))))) (.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (-.f64 (.f64 (cos.f64 x) (cos.f64 (.f64 eps #s(literal 1/2 binary64)))) (.f64 (sin.f64 x) (sin.f64 (.f64 eps #s(literal 1/2 binary64))))))) #s(literal 2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* 2 (* (sin (* 1/2 eps)) (- (* (cos x) (cos (* 1/2 eps))) (* (sin x) (sin (* 1/2 eps)))))) (taylor inf eps) (#s(alt (.f64 #s(approx ( (sin (* (+ eps 0) 1/2)) (- (* (cos (* (* x 2) 1/2)) (cos (* eps 1/2))) (* (sin (* (* x 2) 1/2)) (sin (* eps 1/2))))) (.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (-.f64 (.f64 (cos.f64 x) (cos.f64 (.f64 eps #s(literal 1/2 binary64)))) (.f64 (sin.f64 x) (sin.f64 (.f64 eps #s(literal 1/2 binary64))))))) #s(literal 2 binary64)) (patch (.f64 #s(approx ( (sin (* (+ eps 0) 1/2)) (- (* (cos (* (* x 2) 1/2)) (cos (* eps 1/2))) (* (sin (* (* x 2) 1/2)) (sin (* eps 1/2))))) (.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (-.f64 (.f64 (cos.f64 x) (cos.f64 (.f64 eps #s(literal 1/2 binary64)))) (.f64 (sin.f64 x) (sin.f64 (.f64 eps #s(literal 1/2 binary64))))))) #s(literal 2 binary64)) #<representation binary64>) () ())) ())
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#s(alt (* (pow eps 7) (- (* 1/3840 (/ 1 (pow eps 2))) 1/645120)) (taylor inf eps) (#s(alt (.f64 eps (fma.f64 (.f64 eps eps) (fma.f64 (.f64 eps eps) (fma.f64 (.f64 eps eps) #s(literal -1/645120 binary64) #s(literal 1/3840 binary64)) #s(literal -1/48 binary64)) #s(literal 1/2 binary64))) (patch (.f64 eps (fma.f64 (.f64 eps eps) (fma.f64 (.f64 eps eps) (fma.f64 (.f64 eps eps) #s(literal -1/645120 binary64) #s(literal 1/3840 binary64)) #s(literal -1/48 binary64)) #s(literal 1/2 binary64))) #<representation binary64>) () ())) ())
#s(alt (* (pow eps 7) (- (* 1/3840 (/ 1 (pow eps 2))) (+ 1/645120 (/ 1/48 (pow eps 4))))) (taylor inf eps) (#s(alt (.f64 eps (fma.f64 (.f64 eps eps) (fma.f64 (.f64 eps eps) (fma.f64 (.f64 eps eps) #s(literal -1/645120 binary64) #s(literal 1/3840 binary64)) #s(literal -1/48 binary64)) #s(literal 1/2 binary64))) (patch (.f64 eps (fma.f64 (.f64 eps eps) (fma.f64 (.f64 eps eps) (fma.f64 (.f64 eps eps) #s(literal -1/645120 binary64) #s(literal 1/3840 binary64)) #s(literal -1/48 binary64)) #s(literal 1/2 binary64))) #<representation binary64>) () ())) ())
#s(alt (* (pow eps 7) (- (+ (* 1/3840 (/ 1 (pow eps 2))) (* 1/2 (/ 1 (pow eps 6)))) (+ 1/645120 (/ 1/48 (pow eps 4))))) (taylor inf eps) (#s(alt (.f64 eps (fma.f64 (.f64 eps eps) (fma.f64 (.f64 eps eps) (fma.f64 (.f64 eps eps) #s(literal -1/645120 binary64) #s(literal 1/3840 binary64)) #s(literal -1/48 binary64)) #s(literal 1/2 binary64))) (patch (.f64 eps (fma.f64 (.f64 eps eps) (fma.f64 (.f64 eps eps) (fma.f64 (.f64 eps eps) #s(literal -1/645120 binary64) #s(literal 1/3840 binary64)) #s(literal -1/48 binary64)) #s(literal 1/2 binary64))) #<representation binary64>) () ())) ())
#s(alt (* -1/645120 (pow eps 7)) (taylor -inf eps) (#s(alt (.f64 eps (fma.f64 (.f64 eps eps) (fma.f64 (.f64 eps eps) (fma.f64 (.f64 eps eps) #s(literal -1/645120 binary64) #s(literal 1/3840 binary64)) #s(literal -1/48 binary64)) #s(literal 1/2 binary64))) (patch (.f64 eps (fma.f64 (.f64 eps eps) (fma.f64 (.f64 eps eps) (fma.f64 (.f64 eps eps) #s(literal -1/645120 binary64) #s(literal 1/3840 binary64)) #s(literal -1/48 binary64)) #s(literal 1/2 binary64))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* (pow eps 7) (- 1/645120 (* 1/3840 (/ 1 (pow eps 2)))))) (taylor -inf eps) (#s(alt (.f64 eps (fma.f64 (.f64 eps eps) (fma.f64 (.f64 eps eps) (fma.f64 (.f64 eps eps) #s(literal -1/645120 binary64) #s(literal 1/3840 binary64)) #s(literal -1/48 binary64)) #s(literal 1/2 binary64))) (patch (.f64 eps (fma.f64 (.f64 eps eps) (fma.f64 (.f64 eps eps) (fma.f64 (.f64 eps eps) #s(literal -1/645120 binary64) #s(literal 1/3840 binary64)) #s(literal -1/48 binary64)) #s(literal 1/2 binary64))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* (pow eps 7) (- (+ 1/645120 (/ 1/48 (pow eps 4))) (* 1/3840 (/ 1 (pow eps 2)))))) (taylor -inf eps) (#s(alt (.f64 eps (fma.f64 (.f64 eps eps) (fma.f64 (.f64 eps eps) (fma.f64 (.f64 eps eps) #s(literal -1/645120 binary64) #s(literal 1/3840 binary64)) #s(literal -1/48 binary64)) #s(literal 1/2 binary64))) (patch (.f64 eps (fma.f64 (.f64 eps eps) (fma.f64 (.f64 eps eps) (fma.f64 (.f64 eps eps) #s(literal -1/645120 binary64) #s(literal 1/3840 binary64)) #s(literal -1/48 binary64)) #s(literal 1/2 binary64))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* (pow eps 7) (- (+ 1/645120 (/ 1/48 (pow eps 4))) (+ (* 1/3840 (/ 1 (pow eps 2))) (* 1/2 (/ 1 (pow eps 6))))))) (taylor -inf eps) (#s(alt (.f64 eps (fma.f64 (.f64 eps eps) (fma.f64 (.f64 eps eps) (fma.f64 (.f64 eps eps) #s(literal -1/645120 binary64) #s(literal 1/3840 binary64)) #s(literal -1/48 binary64)) #s(literal 1/2 binary64))) (patch (.f64 eps (fma.f64 (.f64 eps eps) (fma.f64 (.f64 eps eps) (fma.f64 (.f64 eps eps) #s(literal -1/645120 binary64) #s(literal 1/3840 binary64)) #s(literal -1/48 binary64)) #s(literal 1/2 binary64))) #<representation binary64>) () ())) ())
#s(alt -1/48 (taylor 0 eps) (#s(alt (fma.f64 (.f64 eps eps) (fma.f64 (.f64 eps eps) #s(literal -1/645120 binary64) #s(literal 1/3840 binary64)) #s(literal -1/48 binary64)) (patch (fma.f64 (.f64 eps eps) (fma.f64 (.f64 eps eps) #s(literal -1/645120 binary64) #s(literal 1/3840 binary64)) #s(literal -1/48 binary64)) #<representation binary64>) () ())) ())
#s(alt (- (* 1/3840 (pow eps 2)) 1/48) (taylor 0 eps) (#s(alt (fma.f64 (.f64 eps eps) (fma.f64 (.f64 eps eps) #s(literal -1/645120 binary64) #s(literal 1/3840 binary64)) #s(literal -1/48 binary64)) (patch (fma.f64 (.f64 eps eps) (fma.f64 (.f64 eps eps) #s(literal -1/645120 binary64) #s(literal 1/3840 binary64)) #s(literal -1/48 binary64)) #<representation binary64>) () ())) ())
#s(alt (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48) (taylor 0 eps) (#s(alt (fma.f64 (.f64 eps eps) (fma.f64 (.f64 eps eps) #s(literal -1/645120 binary64) #s(literal 1/3840 binary64)) #s(literal -1/48 binary64)) (patch (fma.f64 (.f64 eps eps) (fma.f64 (.f64 eps eps) #s(literal -1/645120 binary64) #s(literal 1/3840 binary64)) #s(literal -1/48 binary64)) #<representation binary64>) () ())) ())
#s(alt (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48) (taylor 0 eps) (#s(alt (fma.f64 (.f64 eps eps) (fma.f64 (.f64 eps eps) #s(literal -1/645120 binary64) #s(literal 1/3840 binary64)) #s(literal -1/48 binary64)) (patch (fma.f64 (.f64 eps eps) (fma.f64 (.f64 eps eps) #s(literal -1/645120 binary64) #s(literal 1/3840 binary64)) #s(literal -1/48 binary64)) #<representation binary64>) () ())) ())
#s(alt (* -1/645120 (pow eps 4)) (taylor inf eps) (#s(alt (fma.f64 (.f64 eps eps) (fma.f64 (.f64 eps eps) #s(literal -1/645120 binary64) #s(literal 1/3840 binary64)) #s(literal -1/48 binary64)) (patch (fma.f64 (.f64 eps eps) (fma.f64 (.f64 eps eps) #s(literal -1/645120 binary64) #s(literal 1/3840 binary64)) #s(literal -1/48 binary64)) #<representation binary64>) () ())) ())
#s(alt (* (pow eps 4) (- (* 1/3840 (/ 1 (pow eps 2))) 1/645120)) (taylor inf eps) (#s(alt (fma.f64 (.f64 eps eps) (fma.f64 (.f64 eps eps) #s(literal -1/645120 binary64) #s(literal 1/3840 binary64)) #s(literal -1/48 binary64)) (patch (fma.f64 (.f64 eps eps) (fma.f64 (.f64 eps eps) #s(literal -1/645120 binary64) #s(literal 1/3840 binary64)) #s(literal -1/48 binary64)) #<representation binary64>) () ())) ())
#s(alt (* (pow eps 4) (- (* 1/3840 (/ 1 (pow eps 2))) (+ 1/645120 (/ 1/48 (pow eps 4))))) (taylor inf eps) (#s(alt (fma.f64 (.f64 eps eps) (fma.f64 (.f64 eps eps) #s(literal -1/645120 binary64) #s(literal 1/3840 binary64)) #s(literal -1/48 binary64)) (patch (fma.f64 (.f64 eps eps) (fma.f64 (.f64 eps eps) #s(literal -1/645120 binary64) #s(literal 1/3840 binary64)) #s(literal -1/48 binary64)) #<representation binary64>) () ())) ())
#s(alt (* (pow eps 4) (- (* 1/3840 (/ 1 (pow eps 2))) (+ 1/645120 (/ 1/48 (pow eps 4))))) (taylor inf eps) (#s(alt (fma.f64 (.f64 eps eps) (fma.f64 (.f64 eps eps) #s(literal -1/645120 binary64) #s(literal 1/3840 binary64)) #s(literal -1/48 binary64)) (patch (fma.f64 (.f64 eps eps) (fma.f64 (.f64 eps eps) #s(literal -1/645120 binary64) #s(literal 1/3840 binary64)) #s(literal -1/48 binary64)) #<representation binary64>) () ())) ())
#s(alt (* -1/645120 (pow eps 4)) (taylor -inf eps) (#s(alt (fma.f64 (.f64 eps eps) (fma.f64 (.f64 eps eps) #s(literal -1/645120 binary64) #s(literal 1/3840 binary64)) #s(literal -1/48 binary64)) (patch (fma.f64 (.f64 eps eps) (fma.f64 (.f64 eps eps) #s(literal -1/645120 binary64) #s(literal 1/3840 binary64)) #s(literal -1/48 binary64)) #<representation binary64>) () ())) ())
#s(alt (* (pow eps 4) (- (* 1/3840 (/ 1 (pow eps 2))) 1/645120)) (taylor -inf eps) (#s(alt (fma.f64 (.f64 eps eps) (fma.f64 (.f64 eps eps) #s(literal -1/645120 binary64) #s(literal 1/3840 binary64)) #s(literal -1/48 binary64)) (patch (fma.f64 (.f64 eps eps) (fma.f64 (.f64 eps eps) #s(literal -1/645120 binary64) #s(literal 1/3840 binary64)) #s(literal -1/48 binary64)) #<representation binary64>) () ())) ())
#s(alt (* (pow eps 4) (- (* 1/3840 (/ 1 (pow eps 2))) (+ 1/645120 (/ 1/48 (pow eps 4))))) (taylor -inf eps) (#s(alt (fma.f64 (.f64 eps eps) (fma.f64 (.f64 eps eps) #s(literal -1/645120 binary64) #s(literal 1/3840 binary64)) #s(literal -1/48 binary64)) (patch (fma.f64 (.f64 eps eps) (fma.f64 (.f64 eps eps) #s(literal -1/645120 binary64) #s(literal 1/3840 binary64)) #s(literal -1/48 binary64)) #<representation binary64>) () ())) ())
#s(alt (* (pow eps 4) (- (* 1/3840 (/ 1 (pow eps 2))) (+ 1/645120 (/ 1/48 (pow eps 4))))) (taylor -inf eps) (#s(alt (fma.f64 (.f64 eps eps) (fma.f64 (.f64 eps eps) #s(literal -1/645120 binary64) #s(literal 1/3840 binary64)) #s(literal -1/48 binary64)) (patch (fma.f64 (.f64 eps eps) (fma.f64 (.f64 eps eps) #s(literal -1/645120 binary64) #s(literal 1/3840 binary64)) #s(literal -1/48 binary64)) #<representation binary64>) () ())) ())

Calls

138 calls:

Time	Variable		Point	Expression
1.0ms	eps	@	0	(* x (* x (* eps -1/2)))
1.0ms	x	@	0	(+ (* (* x x) (+ (* x (* x (+ (* (* x x) -1/720) 1/24))) -1/2)) 1)
1.0ms	eps	@	inf	(* x (* x (* eps -1/2)))
1.0ms	x	@	0	(* x (* x (* eps -1/2)))
0.0ms	x	@	inf	(+ (* (* x x) (+ (* x (* x (+ (* (* x x) -1/720) 1/24))) -1/2)) 1)

simplify287.0ms (2%)

Memory

39.1MiB live, 380.4MiB allocated

Algorithm

1×	egg-herbie

Rules

13 688×	`lower-fma.f64`
13 688×	`lower-fma.f32`
6 624×	`lower-*.f64`
6 624×	`lower-*.f32`
4 568×	`lower-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	431	6704
1	1337	6435
2	3766	6333
0	8118	5991

Stop Event

1×	iter limit
1×	node limit

Counts

552 → 546

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 (* (sin (* 1/2 eps)) (- (* (cos x) (cos (* 1/2 eps))) (* (sin x) (sin (* 1/2 eps))))))
(* 2 (* (sin (* 1/2 eps)) (- (* (cos x) (cos (* 1/2 eps))) (* (sin x) (sin (* 1/2 eps))))))
(* 2 (* (sin (* 1/2 eps)) (- (* (cos x) (cos (* 1/2 eps))) (* (sin x) (sin (* 1/2 eps))))))
(* 2 (* (sin (* 1/2 eps)) (- (* (cos x) (cos (* 1/2 eps))) (* (sin x) (sin (* 1/2 eps))))))
(* 2 (* (sin (* 1/2 eps)) (- (* (cos x) (cos (* 1/2 eps))) (* (sin x) (sin (* 1/2 eps))))))
(* 2 (* (sin (* 1/2 eps)) (- (* (cos x) (cos (* 1/2 eps))) (* (sin x) (sin (* 1/2 eps))))))
(* 2 (* (sin (* 1/2 eps)) (- (* (cos x) (cos (* 1/2 eps))) (* (sin x) (sin (* 1/2 eps))))))
(* 2 (* (sin (* 1/2 eps)) (- (* (cos x) (cos (* 1/2 eps))) (* (sin x) (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 (* (sin (* 1/2 eps)) (- (* (cos x) (cos (* 1/2 eps))) (* (sin x) (sin (* 1/2 eps))))))
(* 2 (* (sin (* 1/2 eps)) (- (* (cos x) (cos (* 1/2 eps))) (* (sin x) (sin (* 1/2 eps))))))
(* 2 (* (sin (* 1/2 eps)) (- (* (cos x) (cos (* 1/2 eps))) (* (sin x) (sin (* 1/2 eps))))))
(* 2 (* (sin (* 1/2 eps)) (- (* (cos x) (cos (* 1/2 eps))) (* (sin x) (sin (* 1/2 eps))))))
(* 2 (* (sin (* 1/2 eps)) (- (* (cos x) (cos (* 1/2 eps))) (* (sin x) (sin (* 1/2 eps))))))
(* 2 (* (sin (* 1/2 eps)) (- (* (cos x) (cos (* 1/2 eps))) (* (sin x) (sin (* 1/2 eps))))))
(* 2 (* (sin (* 1/2 eps)) (- (* (cos x) (cos (* 1/2 eps))) (* (sin x) (sin (* 1/2 eps))))))
(* 2 (* (sin (* 1/2 eps)) (- (* (cos x) (cos (* 1/2 eps))) (* (sin x) (sin (* 1/2 eps))))))
(* 1/2 (* eps (cos x)))
(* eps (+ (* -1/4 (* eps (sin x))) (* 1/2 (cos x))))
(* eps (+ (* 1/2 (cos x)) (* eps (+ (* -1/4 (sin x)) (* eps (+ (* -1/16 (cos x)) (* -1/48 (cos x))))))))
(* eps (+ (* 1/2 (cos x)) (* eps (+ (* -1/4 (sin x)) (* eps (+ (* -1/16 (cos x)) (+ (* -1/48 (cos x)) (* 1/48 (* eps (sin x))))))))))
(* (sin (* 1/2 eps)) (- (* (cos x) (cos (* 1/2 eps))) (* (sin x) (sin (* 1/2 eps)))))
(* (sin (* 1/2 eps)) (- (* (cos x) (cos (* 1/2 eps))) (* (sin x) (sin (* 1/2 eps)))))
(* (sin (* 1/2 eps)) (- (* (cos x) (cos (* 1/2 eps))) (* (sin x) (sin (* 1/2 eps)))))
(* (sin (* 1/2 eps)) (- (* (cos x) (cos (* 1/2 eps))) (* (sin x) (sin (* 1/2 eps)))))
(* (sin (* 1/2 eps)) (- (* (cos x) (cos (* 1/2 eps))) (* (sin x) (sin (* 1/2 eps)))))
(* (sin (* 1/2 eps)) (- (* (cos x) (cos (* 1/2 eps))) (* (sin x) (sin (* 1/2 eps)))))
(* (sin (* 1/2 eps)) (- (* (cos x) (cos (* 1/2 eps))) (* (sin x) (sin (* 1/2 eps)))))
(* (sin (* 1/2 eps)) (- (* (cos x) (cos (* 1/2 eps))) (* (sin x) (sin (* 1/2 eps)))))
(* (cos (* 1/2 eps)) (sin (* 1/2 eps)))
(+ (* -1 (* x (pow (sin (* 1/2 eps)) 2))) (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))
(+ (* x (+ (* -1 (pow (sin (* 1/2 eps)) 2)) (* -1/2 (* x (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))))) (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))
(+ (* x (+ (* -1 (pow (sin (* 1/2 eps)) 2)) (* x (+ (* -1/2 (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) (* 1/6 (* x (pow (sin (* 1/2 eps)) 2))))))) (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))
(* (sin (* 1/2 eps)) (- (* (cos x) (cos (* 1/2 eps))) (* (sin x) (sin (* 1/2 eps)))))
(* (sin (* 1/2 eps)) (- (* (cos x) (cos (* 1/2 eps))) (* (sin x) (sin (* 1/2 eps)))))
(* (sin (* 1/2 eps)) (- (* (cos x) (cos (* 1/2 eps))) (* (sin x) (sin (* 1/2 eps)))))
(* (sin (* 1/2 eps)) (- (* (cos x) (cos (* 1/2 eps))) (* (sin x) (sin (* 1/2 eps)))))
(* (sin (* 1/2 eps)) (- (* (cos x) (cos (* 1/2 eps))) (* (sin x) (sin (* 1/2 eps)))))
(* (sin (* 1/2 eps)) (- (* (cos x) (cos (* 1/2 eps))) (* (sin x) (sin (* 1/2 eps)))))
(* (sin (* 1/2 eps)) (- (* (cos x) (cos (* 1/2 eps))) (* (sin x) (sin (* 1/2 eps)))))
(* (sin (* 1/2 eps)) (- (* (cos x) (cos (* 1/2 eps))) (* (sin x) (sin (* 1/2 eps)))))
(* 1/2 (* eps (cos x)))
(* eps (+ (* -1/4 (* eps (sin x))) (* 1/2 (cos x))))
(* eps (+ (* 1/2 (cos x)) (* eps (+ (* -1/4 (sin x)) (* eps (+ (* -1/16 (cos x)) (* -1/48 (cos x))))))))
(* eps (+ (* 1/2 (cos x)) (* eps (+ (* -1/4 (sin x)) (* eps (+ (* -1/16 (cos x)) (+ (* -1/48 (cos x)) (* 1/48 (* eps (sin x))))))))))
(* (sin (* 1/2 eps)) (- (* (cos x) (cos (* 1/2 eps))) (* (sin x) (sin (* 1/2 eps)))))
(* (sin (* 1/2 eps)) (- (* (cos x) (cos (* 1/2 eps))) (* (sin x) (sin (* 1/2 eps)))))
(* (sin (* 1/2 eps)) (- (* (cos x) (cos (* 1/2 eps))) (* (sin x) (sin (* 1/2 eps)))))
(* (sin (* 1/2 eps)) (- (* (cos x) (cos (* 1/2 eps))) (* (sin x) (sin (* 1/2 eps)))))
(* (sin (* 1/2 eps)) (- (* (cos x) (cos (* 1/2 eps))) (* (sin x) (sin (* 1/2 eps)))))
(* (sin (* 1/2 eps)) (- (* (cos x) (cos (* 1/2 eps))) (* (sin x) (sin (* 1/2 eps)))))
(* (sin (* 1/2 eps)) (- (* (cos x) (cos (* 1/2 eps))) (* (sin x) (sin (* 1/2 eps)))))
(* (sin (* 1/2 eps)) (- (* (cos x) (cos (* 1/2 eps))) (* (sin x) (sin (* 1/2 eps)))))
(* (cos (* 1/2 eps)) (sin (* 1/2 eps)))
(+ (* -1 (* x (pow (sin (* 1/2 eps)) 2))) (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))
(+ (* x (+ (* -1 (pow (sin (* 1/2 eps)) 2)) (* -1/2 (* x (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))))) (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))
(+ (* x (+ (* -1 (pow (sin (* 1/2 eps)) 2)) (* x (+ (* -1/2 (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) (* 1/6 (* x (pow (sin (* 1/2 eps)) 2))))))) (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))
(* (sin (* 1/2 eps)) (- (* (cos x) (cos (* 1/2 eps))) (* (sin x) (sin (* 1/2 eps)))))
(* (sin (* 1/2 eps)) (- (* (cos x) (cos (* 1/2 eps))) (* (sin x) (sin (* 1/2 eps)))))
(* (sin (* 1/2 eps)) (- (* (cos x) (cos (* 1/2 eps))) (* (sin x) (sin (* 1/2 eps)))))
(* (sin (* 1/2 eps)) (- (* (cos x) (cos (* 1/2 eps))) (* (sin x) (sin (* 1/2 eps)))))
(* (sin (* 1/2 eps)) (- (* (cos x) (cos (* 1/2 eps))) (* (sin x) (sin (* 1/2 eps)))))
(* (sin (* 1/2 eps)) (- (* (cos x) (cos (* 1/2 eps))) (* (sin x) (sin (* 1/2 eps)))))
(* (sin (* 1/2 eps)) (- (* (cos x) (cos (* 1/2 eps))) (* (sin x) (sin (* 1/2 eps)))))
(* (sin (* 1/2 eps)) (- (* (cos x) (cos (* 1/2 eps))) (* (sin x) (sin (* 1/2 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))
(sin eps)
(+ (sin eps) (* x (- (cos eps) 1)))
(+ (sin eps) (* x (- (+ (cos eps) (* -1/2 (* x (sin eps)))) 1)))
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(+ (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) (cos (* 1/2 eps))) (* (sin x) (sin (* 1/2 eps))))
(- (* (cos x) (cos (* 1/2 eps))) (* (sin x) (sin (* 1/2 eps))))
(- (* (cos x) (cos (* 1/2 eps))) (* (sin x) (sin (* 1/2 eps))))
(- (* (cos x) (cos (* 1/2 eps))) (* (sin x) (sin (* 1/2 eps))))
(- (* (cos x) (cos (* 1/2 eps))) (* (sin x) (sin (* 1/2 eps))))
(- (* (cos x) (cos (* 1/2 eps))) (* (sin x) (sin (* 1/2 eps))))
(- (* (cos x) (cos (* 1/2 eps))) (* (sin x) (sin (* 1/2 eps))))
(- (* (cos x) (cos (* 1/2 eps))) (* (sin x) (sin (* 1/2 eps))))
(* x (sin (* 1/2 eps)))
(* x (+ (sin (* 1/2 eps)) (* -1/6 (* (pow x 2) (sin (* 1/2 eps))))))
(* x (+ (sin (* 1/2 eps)) (* (pow x 2) (+ (* -1/6 (sin (* 1/2 eps))) (* 1/120 (* (pow x 2) (sin (* 1/2 eps))))))))
(* x (+ (sin (* 1/2 eps)) (* (pow x 2) (+ (* -1/6 (sin (* 1/2 eps))) (* (pow x 2) (+ (* -1/5040 (* (pow x 2) (sin (* 1/2 eps)))) (* 1/120 (sin (* 1/2 eps)))))))))
(* (sin x) (sin (* 1/2 eps)))
(* (sin x) (sin (* 1/2 eps)))
(* (sin x) (sin (* 1/2 eps)))
(* (sin x) (sin (* 1/2 eps)))
(* (sin x) (sin (* 1/2 eps)))
(* (sin x) (sin (* 1/2 eps)))
(* (sin x) (sin (* 1/2 eps)))
(* (sin x) (sin (* 1/2 eps)))
(* 1/2 (* eps (sin x)))
(* eps (+ (* -1/48 (* (pow eps 2) (sin x))) (* 1/2 (sin x))))
(* eps (+ (* 1/2 (sin x)) (* (pow eps 2) (+ (* -1/48 (sin x)) (* 1/3840 (* (pow eps 2) (sin x)))))))
(* eps (+ (* 1/2 (sin x)) (* (pow eps 2) (+ (* -1/48 (sin x)) (* (pow eps 2) (+ (* -1/645120 (* (pow eps 2) (sin x))) (* 1/3840 (sin x))))))))
(* (sin x) (sin (* 1/2 eps)))
(* (sin x) (sin (* 1/2 eps)))
(* (sin x) (sin (* 1/2 eps)))
(* (sin x) (sin (* 1/2 eps)))
(* (sin x) (sin (* 1/2 eps)))
(* (sin x) (sin (* 1/2 eps)))
(* (sin x) (sin (* 1/2 eps)))
(* (sin x) (sin (* 1/2 eps)))
(* 1/24 x)
(* x (+ 1/24 (* -1/720 (pow x 2))))
(* x (+ 1/24 (* -1/720 (pow x 2))))
(* x (+ 1/24 (* -1/720 (pow x 2))))
(* -1/720 (pow x 3))
(* (pow x 3) (- (* 1/24 (/ 1 (pow x 2))) 1/720))
(* (pow x 3) (- (* 1/24 (/ 1 (pow x 2))) 1/720))
(* (pow x 3) (- (* 1/24 (/ 1 (pow x 2))) 1/720))
(* -1/720 (pow x 3))
(* -1 (* (pow x 3) (- 1/720 (* 1/24 (/ 1 (pow x 2))))))
(* -1 (* (pow x 3) (- 1/720 (* 1/24 (/ 1 (pow x 2))))))
(* -1 (* (pow x 3) (- 1/720 (* 1/24 (/ 1 (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))
(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 eps)
(* 1/2 eps)
(* 1/2 eps)
(* 1/2 eps)
(* 1/2 eps)
(* 1/2 eps)
(* 1/2 eps)
(* 1/2 eps)
(* 1/2 eps)
(* 1/2 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))))
(* -1/645120 (pow eps 7))
(* (pow eps 7) (- (* 1/3840 (/ 1 (pow eps 2))) 1/645120))
(* (pow eps 7) (- (* 1/3840 (/ 1 (pow eps 2))) (+ 1/645120 (/ 1/48 (pow eps 4)))))
(* (pow eps 7) (- (+ (* 1/3840 (/ 1 (pow eps 2))) (* 1/2 (/ 1 (pow eps 6)))) (+ 1/645120 (/ 1/48 (pow eps 4)))))
(* -1/645120 (pow eps 7))
(* -1 (* (pow eps 7) (- 1/645120 (* 1/3840 (/ 1 (pow eps 2))))))
(* -1 (* (pow eps 7) (- (+ 1/645120 (/ 1/48 (pow eps 4))) (* 1/3840 (/ 1 (pow eps 2))))))
(* -1 (* (pow eps 7) (- (+ 1/645120 (/ 1/48 (pow eps 4))) (+ (* 1/3840 (/ 1 (pow eps 2))) (* 1/2 (/ 1 (pow eps 6)))))))
-1/48
(- (* 1/3840 (pow eps 2)) 1/48)
(- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48)
(- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48)
(* -1/645120 (pow eps 4))
(* (pow eps 4) (- (* 1/3840 (/ 1 (pow eps 2))) 1/645120))
(* (pow eps 4) (- (* 1/3840 (/ 1 (pow eps 2))) (+ 1/645120 (/ 1/48 (pow eps 4)))))
(* (pow eps 4) (- (* 1/3840 (/ 1 (pow eps 2))) (+ 1/645120 (/ 1/48 (pow eps 4)))))
(* -1/645120 (pow eps 4))
(* (pow eps 4) (- (* 1/3840 (/ 1 (pow eps 2))) 1/645120))
(* (pow eps 4) (- (* 1/3840 (/ 1 (pow eps 2))) (+ 1/645120 (/ 1/48 (pow eps 4)))))
(* (pow eps 4) (- (* 1/3840 (/ 1 (pow eps 2))) (+ 1/645120 (/ 1/48 (pow eps 4)))))

Outputs
(* eps (cos x))
(*.f64 eps (cos.f64 x))
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(.f64 eps (fma.f64 eps (.f64 #s(literal -1/2 binary64) (sin.f64 x)) (cos.f64 x)))
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* 2 (* eps (+ (* -1/16 (cos x)) (* -1/48 (cos x)))))))))
(.f64 eps (fma.f64 eps (.f64 #s(literal -1/2 binary64) (sin.f64 x)) (.f64 (fma.f64 eps (.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64)) (cos.f64 x))))
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* eps (+ (* 1/24 (* eps (sin x))) (* 2 (+ (* -1/16 (cos x)) (* -1/48 (cos x))))))))))
(.f64 eps (fma.f64 eps (fma.f64 (cos.f64 x) (.f64 eps #s(literal -1/6 binary64)) (.f64 (sin.f64 x) (fma.f64 eps (.f64 eps #s(literal 1/24 binary64)) #s(literal -1/2 binary64)))) (cos.f64 x)))
(* 2 (* (sin (* 1/2 eps)) (- (* (cos x) (cos (* 1/2 eps))) (* (sin x) (sin (* 1/2 eps))))))
(.f64 (-.f64 (.f64 (cos.f64 x) (cos.f64 (.f64 eps #s(literal 1/2 binary64)))) (.f64 (sin.f64 x) (sin.f64 (.f64 eps #s(literal 1/2 binary64))))) (.f64 #s(literal 2 binary64) (sin.f64 (*.f64 eps #s(literal 1/2 binary64)))))
(* 2 (* (sin (* 1/2 eps)) (- (* (cos x) (cos (* 1/2 eps))) (* (sin x) (sin (* 1/2 eps))))))
(.f64 (-.f64 (.f64 (cos.f64 x) (cos.f64 (.f64 eps #s(literal 1/2 binary64)))) (.f64 (sin.f64 x) (sin.f64 (.f64 eps #s(literal 1/2 binary64))))) (.f64 #s(literal 2 binary64) (sin.f64 (*.f64 eps #s(literal 1/2 binary64)))))
(* 2 (* (sin (* 1/2 eps)) (- (* (cos x) (cos (* 1/2 eps))) (* (sin x) (sin (* 1/2 eps))))))
(.f64 (-.f64 (.f64 (cos.f64 x) (cos.f64 (.f64 eps #s(literal 1/2 binary64)))) (.f64 (sin.f64 x) (sin.f64 (.f64 eps #s(literal 1/2 binary64))))) (.f64 #s(literal 2 binary64) (sin.f64 (*.f64 eps #s(literal 1/2 binary64)))))
(* 2 (* (sin (* 1/2 eps)) (- (* (cos x) (cos (* 1/2 eps))) (* (sin x) (sin (* 1/2 eps))))))
(.f64 (-.f64 (.f64 (cos.f64 x) (cos.f64 (.f64 eps #s(literal 1/2 binary64)))) (.f64 (sin.f64 x) (sin.f64 (.f64 eps #s(literal 1/2 binary64))))) (.f64 #s(literal 2 binary64) (sin.f64 (*.f64 eps #s(literal 1/2 binary64)))))
(* 2 (* (sin (* 1/2 eps)) (- (* (cos x) (cos (* 1/2 eps))) (* (sin x) (sin (* 1/2 eps))))))
(.f64 (-.f64 (.f64 (cos.f64 x) (cos.f64 (.f64 eps #s(literal 1/2 binary64)))) (.f64 (sin.f64 x) (sin.f64 (.f64 eps #s(literal 1/2 binary64))))) (.f64 #s(literal 2 binary64) (sin.f64 (*.f64 eps #s(literal 1/2 binary64)))))
(* 2 (* (sin (* 1/2 eps)) (- (* (cos x) (cos (* 1/2 eps))) (* (sin x) (sin (* 1/2 eps))))))
(.f64 (-.f64 (.f64 (cos.f64 x) (cos.f64 (.f64 eps #s(literal 1/2 binary64)))) (.f64 (sin.f64 x) (sin.f64 (.f64 eps #s(literal 1/2 binary64))))) (.f64 #s(literal 2 binary64) (sin.f64 (*.f64 eps #s(literal 1/2 binary64)))))
(* 2 (* (sin (* 1/2 eps)) (- (* (cos x) (cos (* 1/2 eps))) (* (sin x) (sin (* 1/2 eps))))))
(.f64 (-.f64 (.f64 (cos.f64 x) (cos.f64 (.f64 eps #s(literal 1/2 binary64)))) (.f64 (sin.f64 x) (sin.f64 (.f64 eps #s(literal 1/2 binary64))))) (.f64 #s(literal 2 binary64) (sin.f64 (*.f64 eps #s(literal 1/2 binary64)))))
(* 2 (* (sin (* 1/2 eps)) (- (* (cos x) (cos (* 1/2 eps))) (* (sin x) (sin (* 1/2 eps))))))
(.f64 (-.f64 (.f64 (cos.f64 x) (cos.f64 (.f64 eps #s(literal 1/2 binary64)))) (.f64 (sin.f64 x) (sin.f64 (.f64 eps #s(literal 1/2 binary64))))) (.f64 #s(literal 2 binary64) (sin.f64 (*.f64 eps #s(literal 1/2 binary64)))))
(* 2 (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))
(.f64 #s(literal 2 binary64) (.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (cos.f64 (.f64 eps #s(literal 1/2 binary64)))))
(+ (* -2 (* x (pow (sin (* 1/2 eps)) 2))) (* 2 (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))))
(.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (fma.f64 #s(literal 2 binary64) (cos.f64 (.f64 eps #s(literal 1/2 binary64))) (.f64 (.f64 x #s(literal -2 binary64)) (sin.f64 (.f64 eps #s(literal 1/2 binary64))))))
(+ (* 2 (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) (* x (+ (* -2 (pow (sin (* 1/2 eps)) 2)) (* -1 (* x (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))))))
(fma.f64 x (.f64 #s(literal -2 binary64) (pow.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))) (cos.f64 (.f64 eps #s(literal 1/2 binary64)))) (fma.f64 x (neg.f64 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 x (fma.f64 x (neg.f64 (.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (cos.f64 (.f64 eps #s(literal 1/2 binary64))))) (.f64 (pow.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) #s(literal 2 binary64)) (fma.f64 x (.f64 x #s(literal 1/3 binary64)) #s(literal -2 binary64)))) (.f64 #s(literal 2 binary64) (.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (cos.f64 (.f64 eps #s(literal 1/2 binary64))))))
(* 2 (* (sin (* 1/2 eps)) (- (* (cos x) (cos (* 1/2 eps))) (* (sin x) (sin (* 1/2 eps))))))
(.f64 (-.f64 (.f64 (cos.f64 x) (cos.f64 (.f64 eps #s(literal 1/2 binary64)))) (.f64 (sin.f64 x) (sin.f64 (.f64 eps #s(literal 1/2 binary64))))) (.f64 #s(literal 2 binary64) (sin.f64 (*.f64 eps #s(literal 1/2 binary64)))))
(* 2 (* (sin (* 1/2 eps)) (- (* (cos x) (cos (* 1/2 eps))) (* (sin x) (sin (* 1/2 eps))))))
(.f64 (-.f64 (.f64 (cos.f64 x) (cos.f64 (.f64 eps #s(literal 1/2 binary64)))) (.f64 (sin.f64 x) (sin.f64 (.f64 eps #s(literal 1/2 binary64))))) (.f64 #s(literal 2 binary64) (sin.f64 (*.f64 eps #s(literal 1/2 binary64)))))
(* 2 (* (sin (* 1/2 eps)) (- (* (cos x) (cos (* 1/2 eps))) (* (sin x) (sin (* 1/2 eps))))))
(.f64 (-.f64 (.f64 (cos.f64 x) (cos.f64 (.f64 eps #s(literal 1/2 binary64)))) (.f64 (sin.f64 x) (sin.f64 (.f64 eps #s(literal 1/2 binary64))))) (.f64 #s(literal 2 binary64) (sin.f64 (*.f64 eps #s(literal 1/2 binary64)))))
(* 2 (* (sin (* 1/2 eps)) (- (* (cos x) (cos (* 1/2 eps))) (* (sin x) (sin (* 1/2 eps))))))
(.f64 (-.f64 (.f64 (cos.f64 x) (cos.f64 (.f64 eps #s(literal 1/2 binary64)))) (.f64 (sin.f64 x) (sin.f64 (.f64 eps #s(literal 1/2 binary64))))) (.f64 #s(literal 2 binary64) (sin.f64 (*.f64 eps #s(literal 1/2 binary64)))))
(* 2 (* (sin (* 1/2 eps)) (- (* (cos x) (cos (* 1/2 eps))) (* (sin x) (sin (* 1/2 eps))))))
(.f64 (-.f64 (.f64 (cos.f64 x) (cos.f64 (.f64 eps #s(literal 1/2 binary64)))) (.f64 (sin.f64 x) (sin.f64 (.f64 eps #s(literal 1/2 binary64))))) (.f64 #s(literal 2 binary64) (sin.f64 (*.f64 eps #s(literal 1/2 binary64)))))
(* 2 (* (sin (* 1/2 eps)) (- (* (cos x) (cos (* 1/2 eps))) (* (sin x) (sin (* 1/2 eps))))))
(.f64 (-.f64 (.f64 (cos.f64 x) (cos.f64 (.f64 eps #s(literal 1/2 binary64)))) (.f64 (sin.f64 x) (sin.f64 (.f64 eps #s(literal 1/2 binary64))))) (.f64 #s(literal 2 binary64) (sin.f64 (*.f64 eps #s(literal 1/2 binary64)))))
(* 2 (* (sin (* 1/2 eps)) (- (* (cos x) (cos (* 1/2 eps))) (* (sin x) (sin (* 1/2 eps))))))
(.f64 (-.f64 (.f64 (cos.f64 x) (cos.f64 (.f64 eps #s(literal 1/2 binary64)))) (.f64 (sin.f64 x) (sin.f64 (.f64 eps #s(literal 1/2 binary64))))) (.f64 #s(literal 2 binary64) (sin.f64 (*.f64 eps #s(literal 1/2 binary64)))))
(* 2 (* (sin (* 1/2 eps)) (- (* (cos x) (cos (* 1/2 eps))) (* (sin x) (sin (* 1/2 eps))))))
(.f64 (-.f64 (.f64 (cos.f64 x) (cos.f64 (.f64 eps #s(literal 1/2 binary64)))) (.f64 (sin.f64 x) (sin.f64 (.f64 eps #s(literal 1/2 binary64))))) (.f64 #s(literal 2 binary64) (sin.f64 (*.f64 eps #s(literal 1/2 binary64)))))
(* 1/2 (* eps (cos x)))
(.f64 eps (.f64 (cos.f64 x) #s(literal 1/2 binary64)))
(* eps (+ (* -1/4 (* eps (sin x))) (* 1/2 (cos x))))
(.f64 eps (fma.f64 eps (.f64 (sin.f64 x) #s(literal -1/4 binary64)) (*.f64 (cos.f64 x) #s(literal 1/2 binary64))))
(* eps (+ (* 1/2 (cos x)) (* eps (+ (* -1/4 (sin x)) (* eps (+ (* -1/16 (cos x)) (* -1/48 (cos x))))))))
(.f64 eps (fma.f64 eps (fma.f64 eps (.f64 (cos.f64 x) #s(literal -1/12 binary64)) (.f64 (sin.f64 x) #s(literal -1/4 binary64))) (.f64 (cos.f64 x) #s(literal 1/2 binary64))))
(* eps (+ (* 1/2 (cos x)) (* eps (+ (* -1/4 (sin x)) (* eps (+ (* -1/16 (cos x)) (+ (* -1/48 (cos x)) (* 1/48 (* eps (sin x))))))))))
(.f64 eps (fma.f64 eps (fma.f64 eps (fma.f64 (cos.f64 x) #s(literal -1/12 binary64) (.f64 (.f64 eps (sin.f64 x)) #s(literal 1/48 binary64))) (.f64 (sin.f64 x) #s(literal -1/4 binary64))) (*.f64 (cos.f64 x) #s(literal 1/2 binary64))))
(* (sin (* 1/2 eps)) (- (* (cos x) (cos (* 1/2 eps))) (* (sin x) (sin (* 1/2 eps)))))
(.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (-.f64 (.f64 (cos.f64 x) (cos.f64 (.f64 eps #s(literal 1/2 binary64)))) (.f64 (sin.f64 x) (sin.f64 (.f64 eps #s(literal 1/2 binary64))))))
(* (sin (* 1/2 eps)) (- (* (cos x) (cos (* 1/2 eps))) (* (sin x) (sin (* 1/2 eps)))))
(.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (-.f64 (.f64 (cos.f64 x) (cos.f64 (.f64 eps #s(literal 1/2 binary64)))) (.f64 (sin.f64 x) (sin.f64 (.f64 eps #s(literal 1/2 binary64))))))
(* (sin (* 1/2 eps)) (- (* (cos x) (cos (* 1/2 eps))) (* (sin x) (sin (* 1/2 eps)))))
(.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (-.f64 (.f64 (cos.f64 x) (cos.f64 (.f64 eps #s(literal 1/2 binary64)))) (.f64 (sin.f64 x) (sin.f64 (.f64 eps #s(literal 1/2 binary64))))))
(* (sin (* 1/2 eps)) (- (* (cos x) (cos (* 1/2 eps))) (* (sin x) (sin (* 1/2 eps)))))
(.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (-.f64 (.f64 (cos.f64 x) (cos.f64 (.f64 eps #s(literal 1/2 binary64)))) (.f64 (sin.f64 x) (sin.f64 (.f64 eps #s(literal 1/2 binary64))))))
(* (sin (* 1/2 eps)) (- (* (cos x) (cos (* 1/2 eps))) (* (sin x) (sin (* 1/2 eps)))))
(.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (-.f64 (.f64 (cos.f64 x) (cos.f64 (.f64 eps #s(literal 1/2 binary64)))) (.f64 (sin.f64 x) (sin.f64 (.f64 eps #s(literal 1/2 binary64))))))
(* (sin (* 1/2 eps)) (- (* (cos x) (cos (* 1/2 eps))) (* (sin x) (sin (* 1/2 eps)))))
(.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (-.f64 (.f64 (cos.f64 x) (cos.f64 (.f64 eps #s(literal 1/2 binary64)))) (.f64 (sin.f64 x) (sin.f64 (.f64 eps #s(literal 1/2 binary64))))))
(* (sin (* 1/2 eps)) (- (* (cos x) (cos (* 1/2 eps))) (* (sin x) (sin (* 1/2 eps)))))
(.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (-.f64 (.f64 (cos.f64 x) (cos.f64 (.f64 eps #s(literal 1/2 binary64)))) (.f64 (sin.f64 x) (sin.f64 (.f64 eps #s(literal 1/2 binary64))))))
(* (sin (* 1/2 eps)) (- (* (cos x) (cos (* 1/2 eps))) (* (sin x) (sin (* 1/2 eps)))))
(.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (-.f64 (.f64 (cos.f64 x) (cos.f64 (.f64 eps #s(literal 1/2 binary64)))) (.f64 (sin.f64 x) (sin.f64 (.f64 eps #s(literal 1/2 binary64))))))
(* (cos (* 1/2 eps)) (sin (* 1/2 eps)))
(.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (cos.f64 (*.f64 eps #s(literal 1/2 binary64))))
(+ (* -1 (* x (pow (sin (* 1/2 eps)) 2))) (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))
(.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (fma.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (neg.f64 x) (cos.f64 (.f64 eps #s(literal 1/2 binary64)))))
(+ (* x (+ (* -1 (pow (sin (* 1/2 eps)) 2)) (* -1/2 (* x (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))))) (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))
(fma.f64 x (neg.f64 (pow.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) #s(literal 2 binary64))) (.f64 (fma.f64 x (.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64)) (.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (cos.f64 (.f64 eps #s(literal 1/2 binary64))))))
(+ (* x (+ (* -1 (pow (sin (* 1/2 eps)) 2)) (* x (+ (* -1/2 (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) (* 1/6 (* x (pow (sin (* 1/2 eps)) 2))))))) (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))
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(.f64 (+.f64 #s(literal -1/720 binary64) (/.f64 #s(literal 1/24 binary64) (.f64 x x))) (.f64 x (.f64 x x)))
(* -1 (* (pow x 3) (- 1/720 (* 1/24 (/ 1 (pow x 2))))))
(.f64 (+.f64 #s(literal -1/720 binary64) (/.f64 #s(literal 1/24 binary64) (.f64 x x))) (.f64 x (.f64 x x)))
(* -1 (* (pow x 3) (- 1/720 (* 1/24 (/ 1 (pow x 2))))))
(.f64 (+.f64 #s(literal -1/720 binary64) (/.f64 #s(literal 1/24 binary64) (.f64 x x))) (.f64 x (.f64 x x)))
1/24
#s(literal 1/24 binary64)
(+ 1/24 (* -1/720 (pow x 2)))
(fma.f64 (*.f64 x x) #s(literal -1/720 binary64) #s(literal 1/24 binary64))
(+ 1/24 (* -1/720 (pow x 2)))
(fma.f64 (*.f64 x x) #s(literal -1/720 binary64) #s(literal 1/24 binary64))
(+ 1/24 (* -1/720 (pow x 2)))
(fma.f64 (*.f64 x x) #s(literal -1/720 binary64) #s(literal 1/24 binary64))
(* -1/720 (pow x 2))
(.f64 (.f64 x x) #s(literal -1/720 binary64))
(* (pow x 2) (- (* 1/24 (/ 1 (pow x 2))) 1/720))
(.f64 (.f64 x x) (+.f64 #s(literal -1/720 binary64) (/.f64 #s(literal 1/24 binary64) (*.f64 x x))))
(* (pow x 2) (- (* 1/24 (/ 1 (pow x 2))) 1/720))
(.f64 (.f64 x x) (+.f64 #s(literal -1/720 binary64) (/.f64 #s(literal 1/24 binary64) (*.f64 x x))))
(* (pow x 2) (- (* 1/24 (/ 1 (pow x 2))) 1/720))
(.f64 (.f64 x x) (+.f64 #s(literal -1/720 binary64) (/.f64 #s(literal 1/24 binary64) (*.f64 x x))))
(* -1/720 (pow x 2))
(.f64 (.f64 x x) #s(literal -1/720 binary64))
(* (pow x 2) (- (* 1/24 (/ 1 (pow x 2))) 1/720))
(.f64 (.f64 x x) (+.f64 #s(literal -1/720 binary64) (/.f64 #s(literal 1/24 binary64) (*.f64 x x))))
(* (pow x 2) (- (* 1/24 (/ 1 (pow x 2))) 1/720))
(.f64 (.f64 x x) (+.f64 #s(literal -1/720 binary64) (/.f64 #s(literal 1/24 binary64) (*.f64 x x))))
(* (pow x 2) (- (* 1/24 (/ 1 (pow x 2))) 1/720))
(.f64 (.f64 x x) (+.f64 #s(literal -1/720 binary64) (/.f64 #s(literal 1/24 binary64) (*.f64 x x))))
(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 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (neg.f64 x) (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 (fma.f64 x (.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64)) (cos.f64 (.f64 eps #s(literal 1/2 binary64))) (.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (neg.f64 x)))
(+ (cos (* 1/2 eps)) (* x (- (* x (+ (* -1/2 (cos (* 1/2 eps))) (* 1/6 (* x (sin (* 1/2 eps)))))) (sin (* 1/2 eps)))))
(fma.f64 x (fma.f64 (cos.f64 (.f64 eps #s(literal 1/2 binary64))) (.f64 x #s(literal -1/2 binary64)) (.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (fma.f64 x (.f64 x #s(literal 1/6 binary64)) #s(literal -1 binary64)))) (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 eps (*.f64 #s(literal -1/2 binary64) (sin.f64 x)) (cos.f64 x))
(+ (cos x) (* eps (- (* -1/8 (* eps (cos x))) (* 1/2 (sin x)))))
(fma.f64 (fma.f64 (.f64 eps eps) #s(literal -1/8 binary64) #s(literal 1 binary64)) (cos.f64 x) (.f64 eps (*.f64 #s(literal -1/2 binary64) (sin.f64 x))))
(+ (cos x) (* eps (- (* eps (+ (* -1/8 (cos x)) (* 1/48 (* eps (sin x))))) (* 1/2 (sin x)))))
(fma.f64 eps (fma.f64 eps (.f64 (cos.f64 x) #s(literal -1/8 binary64)) (.f64 (sin.f64 x) (fma.f64 eps (*.f64 eps #s(literal 1/48 binary64)) #s(literal -1/2 binary64)))) (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))
(* 1/2 eps)
(*.f64 eps #s(literal 1/2 binary64))
(* 1/2 eps)
(*.f64 eps #s(literal 1/2 binary64))
(* 1/2 eps)
(*.f64 eps #s(literal 1/2 binary64))
(* 1/2 eps)
(*.f64 eps #s(literal 1/2 binary64))
(* 1/2 eps)
(*.f64 eps #s(literal 1/2 binary64))
(* 1/2 eps)
(*.f64 eps #s(literal 1/2 binary64))
(* 1/2 eps)
(*.f64 eps #s(literal 1/2 binary64))
(* 1/2 eps)
(*.f64 eps #s(literal 1/2 binary64))
(* 1/2 eps)
(*.f64 eps #s(literal 1/2 binary64))
(* 1/2 eps)
(*.f64 eps #s(literal 1/2 binary64))
(* 1/2 eps)
(*.f64 eps #s(literal 1/2 binary64))
(* 1/2 eps)
(*.f64 eps #s(literal 1/2 binary64))
(* eps (+ 1/2 (* -1/48 (pow eps 2))))
(.f64 eps (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal 1/2 binary64)))
(* eps (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48))))
(.f64 eps (fma.f64 (.f64 eps eps) (fma.f64 (*.f64 eps eps) #s(literal 1/3840 binary64) #s(literal -1/48 binary64)) #s(literal 1/2 binary64)))
(* eps (+ 1/2 (* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48))))
(.f64 eps (fma.f64 (.f64 eps eps) (fma.f64 (.f64 eps eps) (fma.f64 (.f64 eps eps) #s(literal -1/645120 binary64) #s(literal 1/3840 binary64)) #s(literal -1/48 binary64)) #s(literal 1/2 binary64)))
(* -1/645120 (pow eps 7))
(*.f64 #s(literal -1/645120 binary64) (pow.f64 eps #s(literal 7 binary64)))
(* (pow eps 7) (- (* 1/3840 (/ 1 (pow eps 2))) 1/645120))
(.f64 (pow.f64 eps #s(literal 7 binary64)) (+.f64 #s(literal -1/645120 binary64) (/.f64 #s(literal 1/3840 binary64) (.f64 eps eps))))
(* (pow eps 7) (- (* 1/3840 (/ 1 (pow eps 2))) (+ 1/645120 (/ 1/48 (pow eps 4)))))
(.f64 (pow.f64 eps #s(literal 7 binary64)) (+.f64 #s(literal -1/645120 binary64) (+.f64 (/.f64 #s(literal -1/48 binary64) (.f64 (.f64 eps eps) (.f64 eps eps))) (/.f64 #s(literal 1/3840 binary64) (*.f64 eps eps)))))
(* (pow eps 7) (- (+ (* 1/3840 (/ 1 (pow eps 2))) (* 1/2 (/ 1 (pow eps 6)))) (+ 1/645120 (/ 1/48 (pow eps 4)))))
(.f64 (pow.f64 eps #s(literal 7 binary64)) (+.f64 (+.f64 #s(literal -1/645120 binary64) (+.f64 (/.f64 #s(literal -1/48 binary64) (.f64 (.f64 eps eps) (.f64 eps eps))) (/.f64 #s(literal 1/3840 binary64) (*.f64 eps eps)))) (/.f64 #s(literal 1/2 binary64) (pow.f64 eps #s(literal 6 binary64)))))
(* -1/645120 (pow eps 7))
(*.f64 #s(literal -1/645120 binary64) (pow.f64 eps #s(literal 7 binary64)))
(* -1 (* (pow eps 7) (- 1/645120 (* 1/3840 (/ 1 (pow eps 2))))))
(.f64 (pow.f64 eps #s(literal 7 binary64)) (+.f64 #s(literal -1/645120 binary64) (/.f64 #s(literal 1/3840 binary64) (.f64 eps eps))))
(* -1 (* (pow eps 7) (- (+ 1/645120 (/ 1/48 (pow eps 4))) (* 1/3840 (/ 1 (pow eps 2))))))
(.f64 (pow.f64 eps #s(literal 7 binary64)) (+.f64 #s(literal -1/645120 binary64) (+.f64 (/.f64 #s(literal -1/48 binary64) (.f64 (.f64 eps eps) (.f64 eps eps))) (/.f64 #s(literal 1/3840 binary64) (*.f64 eps eps)))))
(* -1 (* (pow eps 7) (- (+ 1/645120 (/ 1/48 (pow eps 4))) (+ (* 1/3840 (/ 1 (pow eps 2))) (* 1/2 (/ 1 (pow eps 6)))))))
(.f64 (pow.f64 eps #s(literal 7 binary64)) (+.f64 (+.f64 #s(literal -1/645120 binary64) (+.f64 (/.f64 #s(literal -1/48 binary64) (.f64 (.f64 eps eps) (.f64 eps eps))) (/.f64 #s(literal 1/3840 binary64) (*.f64 eps eps)))) (neg.f64 (/.f64 #s(literal -1/2 binary64) (pow.f64 eps #s(literal 6 binary64))))))
-1/48
#s(literal -1/48 binary64)
(- (* 1/3840 (pow eps 2)) 1/48)
(fma.f64 (*.f64 eps eps) #s(literal 1/3840 binary64) #s(literal -1/48 binary64))
(- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48)
(fma.f64 (.f64 eps eps) (fma.f64 (.f64 eps eps) #s(literal -1/645120 binary64) #s(literal 1/3840 binary64)) #s(literal -1/48 binary64))
(- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48)
(fma.f64 (.f64 eps eps) (fma.f64 (.f64 eps eps) #s(literal -1/645120 binary64) #s(literal 1/3840 binary64)) #s(literal -1/48 binary64))
(* -1/645120 (pow eps 4))
(.f64 (.f64 eps eps) (.f64 (.f64 eps eps) #s(literal -1/645120 binary64)))
(* (pow eps 4) (- (* 1/3840 (/ 1 (pow eps 2))) 1/645120))
(.f64 (+.f64 #s(literal -1/645120 binary64) (/.f64 #s(literal 1/3840 binary64) (.f64 eps eps))) (.f64 (.f64 eps eps) (*.f64 eps eps)))
(* (pow eps 4) (- (* 1/3840 (/ 1 (pow eps 2))) (+ 1/645120 (/ 1/48 (pow eps 4)))))
(.f64 (.f64 (.f64 eps eps) (.f64 eps eps)) (+.f64 #s(literal -1/645120 binary64) (+.f64 (/.f64 #s(literal -1/48 binary64) (.f64 (.f64 eps eps) (.f64 eps eps))) (/.f64 #s(literal 1/3840 binary64) (.f64 eps eps)))))
(* (pow eps 4) (- (* 1/3840 (/ 1 (pow eps 2))) (+ 1/645120 (/ 1/48 (pow eps 4)))))
(.f64 (.f64 (.f64 eps eps) (.f64 eps eps)) (+.f64 #s(literal -1/645120 binary64) (+.f64 (/.f64 #s(literal -1/48 binary64) (.f64 (.f64 eps eps) (.f64 eps eps))) (/.f64 #s(literal 1/3840 binary64) (.f64 eps eps)))))
(* -1/645120 (pow eps 4))
(.f64 (.f64 eps eps) (.f64 (.f64 eps eps) #s(literal -1/645120 binary64)))
(* (pow eps 4) (- (* 1/3840 (/ 1 (pow eps 2))) 1/645120))
(.f64 (+.f64 #s(literal -1/645120 binary64) (/.f64 #s(literal 1/3840 binary64) (.f64 eps eps))) (.f64 (.f64 eps eps) (*.f64 eps eps)))
(* (pow eps 4) (- (* 1/3840 (/ 1 (pow eps 2))) (+ 1/645120 (/ 1/48 (pow eps 4)))))
(.f64 (.f64 (.f64 eps eps) (.f64 eps eps)) (+.f64 #s(literal -1/645120 binary64) (+.f64 (/.f64 #s(literal -1/48 binary64) (.f64 (.f64 eps eps) (.f64 eps eps))) (/.f64 #s(literal 1/3840 binary64) (.f64 eps eps)))))
(* (pow eps 4) (- (* 1/3840 (/ 1 (pow eps 2))) (+ 1/645120 (/ 1/48 (pow eps 4)))))
(.f64 (.f64 (.f64 eps eps) (.f64 eps eps)) (+.f64 #s(literal -1/645120 binary64) (+.f64 (/.f64 #s(literal -1/48 binary64) (.f64 (.f64 eps eps) (.f64 eps eps))) (/.f64 #s(literal 1/3840 binary64) (.f64 eps eps)))))

rewrite331.0ms (2.3%)

Memory

-13.6MiB live, 419.6MiB allocated

Rules

5 400×	`lower-*.f32`
5 364×	`lower-*.f64`
4 936×	`lower-fma.f32`
4 922×	`lower-fma.f64`
2 694×	`lower-/.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	79	538
0	119	526
1	450	446
2	3865	446
0	8648	429

Stop Event

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

Counts

28 → 367

Calls

Call 1

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

Outputs
(.f64 #s(literal 2 binary64) #s(approx ( (sin (* (+ eps 0) 1/2)) (- (* (cos (* (* x 2) 1/2)) (cos (* eps 1/2))) (* (sin (* (* x 2) 1/2)) (sin (* eps 1/2))))) (.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (cos.f64 (fma.f64 eps #s(literal 1/2 binary64) x)))))
(.f64 #s(approx ( (sin (* (+ eps 0) 1/2)) (- (* (cos (* (* x 2) 1/2)) (cos (* eps 1/2))) (* (sin (* (* x 2) 1/2)) (sin (* eps 1/2))))) (.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (cos.f64 (fma.f64 eps #s(literal 1/2 binary64) x)))) #s(literal 2 binary64))
#s(approx (* (sin (* (+ eps 0) 1/2)) (- (* (cos (* (* x 2) 1/2)) (cos (* eps 1/2))) (* (sin (* (* x 2) 1/2)) (sin (* eps 1/2))))) (.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (cos.f64 (fma.f64 eps #s(literal 1/2 binary64) x))))
(+.f64 (.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (.f64 (cos.f64 x) (cos.f64 (.f64 eps #s(literal 1/2 binary64))))) (.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (neg.f64 (sin.f64 x)))))
(+.f64 (.f64 (.f64 (cos.f64 x) (cos.f64 (.f64 eps #s(literal 1/2 binary64)))) (sin.f64 (.f64 eps #s(literal 1/2 binary64)))) (.f64 (.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (neg.f64 (sin.f64 x))) (sin.f64 (.f64 eps #s(literal 1/2 binary64)))))
(fma.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (.f64 (cos.f64 x) (cos.f64 (.f64 eps #s(literal 1/2 binary64)))) (.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) (neg.f64 (sin.f64 x)))))
(fma.f64 (.f64 (cos.f64 x) (cos.f64 (.f64 eps #s(literal 1/2 binary64)))) (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (.f64 (.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (neg.f64 (sin.f64 x))) (sin.f64 (*.f64 eps #s(literal 1/2 binary64)))))
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(/.f64 (fma.f64 (.f64 eps (.f64 eps eps)) (.f64 (.f64 eps (fma.f64 eps (.f64 eps #s(literal -1/645120 binary64)) #s(literal 1/3840 binary64))) (.f64 (.f64 eps (fma.f64 eps (.f64 eps #s(literal -1/645120 binary64)) #s(literal 1/3840 binary64))) (.f64 eps (fma.f64 eps (.f64 eps #s(literal -1/645120 binary64)) #s(literal 1/3840 binary64))))) #s(literal -1/110592 binary64)) (+.f64 #s(literal 1/2304 binary64) (-.f64 (.f64 (.f64 eps eps) (.f64 (.f64 eps (fma.f64 eps (.f64 eps #s(literal -1/645120 binary64)) #s(literal 1/3840 binary64))) (.f64 eps (fma.f64 eps (.f64 eps #s(literal -1/645120 binary64)) #s(literal 1/3840 binary64))))) (.f64 eps (.f64 (.f64 eps (fma.f64 eps (*.f64 eps #s(literal -1/645120 binary64)) #s(literal 1/3840 binary64))) #s(literal -1/48 binary64))))))
(/.f64 (fma.f64 (.f64 eps eps) (.f64 (.f64 eps (fma.f64 eps (.f64 eps #s(literal -1/645120 binary64)) #s(literal 1/3840 binary64))) (.f64 eps (fma.f64 eps (.f64 eps #s(literal -1/645120 binary64)) #s(literal 1/3840 binary64)))) #s(literal -1/2304 binary64)) (fma.f64 eps (.f64 eps (fma.f64 eps (.f64 eps #s(literal -1/645120 binary64)) #s(literal 1/3840 binary64))) #s(literal 1/48 binary64)))
(/.f64 (neg.f64 (fma.f64 (.f64 eps (.f64 eps eps)) (.f64 (.f64 eps (fma.f64 eps (.f64 eps #s(literal -1/645120 binary64)) #s(literal 1/3840 binary64))) (.f64 (.f64 eps (fma.f64 eps (.f64 eps #s(literal -1/645120 binary64)) #s(literal 1/3840 binary64))) (.f64 eps (fma.f64 eps (.f64 eps #s(literal -1/645120 binary64)) #s(literal 1/3840 binary64))))) #s(literal -1/110592 binary64))) (neg.f64 (-.f64 (fma.f64 (.f64 eps eps) (.f64 (.f64 eps (fma.f64 eps (.f64 eps #s(literal -1/645120 binary64)) #s(literal 1/3840 binary64))) (.f64 eps (fma.f64 eps (.f64 eps #s(literal -1/645120 binary64)) #s(literal 1/3840 binary64)))) #s(literal 1/2304 binary64)) (.f64 eps (.f64 (.f64 eps (fma.f64 eps (.f64 eps #s(literal -1/645120 binary64)) #s(literal 1/3840 binary64))) #s(literal -1/48 binary64))))))
(/.f64 (neg.f64 (fma.f64 (.f64 eps eps) (.f64 (.f64 eps (fma.f64 eps (.f64 eps #s(literal -1/645120 binary64)) #s(literal 1/3840 binary64))) (.f64 eps (fma.f64 eps (.f64 eps #s(literal -1/645120 binary64)) #s(literal 1/3840 binary64)))) #s(literal -1/2304 binary64))) (neg.f64 (fma.f64 eps (.f64 eps (fma.f64 eps (.f64 eps #s(literal -1/645120 binary64)) #s(literal 1/3840 binary64))) #s(literal 1/48 binary64))))
(/.f64 (-.f64 #s(literal 1/2304 binary64) (.f64 (.f64 eps eps) (.f64 (.f64 eps (fma.f64 eps (.f64 eps #s(literal -1/645120 binary64)) #s(literal 1/3840 binary64))) (.f64 eps (fma.f64 eps (.f64 eps #s(literal -1/645120 binary64)) #s(literal 1/3840 binary64)))))) (-.f64 #s(literal -1/48 binary64) (.f64 eps (.f64 eps (fma.f64 eps (.f64 eps #s(literal -1/645120 binary64)) #s(literal 1/3840 binary64))))))
(pow.f64 (/.f64 (-.f64 (fma.f64 (.f64 eps eps) (.f64 (.f64 eps (fma.f64 eps (.f64 eps #s(literal -1/645120 binary64)) #s(literal 1/3840 binary64))) (.f64 eps (fma.f64 eps (.f64 eps #s(literal -1/645120 binary64)) #s(literal 1/3840 binary64)))) #s(literal 1/2304 binary64)) (.f64 eps (.f64 (.f64 eps (fma.f64 eps (.f64 eps #s(literal -1/645120 binary64)) #s(literal 1/3840 binary64))) #s(literal -1/48 binary64)))) (fma.f64 (.f64 eps (.f64 eps eps)) (.f64 (.f64 eps (fma.f64 eps (.f64 eps #s(literal -1/645120 binary64)) #s(literal 1/3840 binary64))) (.f64 (.f64 eps (fma.f64 eps (.f64 eps #s(literal -1/645120 binary64)) #s(literal 1/3840 binary64))) (.f64 eps (fma.f64 eps (.f64 eps #s(literal -1/645120 binary64)) #s(literal 1/3840 binary64))))) #s(literal -1/110592 binary64))) #s(literal -1 binary64))
(pow.f64 (/.f64 (fma.f64 eps (.f64 eps (fma.f64 eps (.f64 eps #s(literal -1/645120 binary64)) #s(literal 1/3840 binary64))) #s(literal 1/48 binary64)) (fma.f64 (.f64 eps eps) (.f64 (.f64 eps (fma.f64 eps (.f64 eps #s(literal -1/645120 binary64)) #s(literal 1/3840 binary64))) (.f64 eps (fma.f64 eps (.f64 eps #s(literal -1/645120 binary64)) #s(literal 1/3840 binary64)))) #s(literal -1/2304 binary64))) #s(literal -1 binary64))
(.f64 (fma.f64 (.f64 eps (.f64 eps eps)) (.f64 (.f64 eps (fma.f64 eps (.f64 eps #s(literal -1/645120 binary64)) #s(literal 1/3840 binary64))) (.f64 (.f64 eps (fma.f64 eps (.f64 eps #s(literal -1/645120 binary64)) #s(literal 1/3840 binary64))) (.f64 eps (fma.f64 eps (.f64 eps #s(literal -1/645120 binary64)) #s(literal 1/3840 binary64))))) #s(literal -1/110592 binary64)) (/.f64 #s(literal 1 binary64) (-.f64 (fma.f64 (.f64 eps eps) (.f64 (.f64 eps (fma.f64 eps (.f64 eps #s(literal -1/645120 binary64)) #s(literal 1/3840 binary64))) (.f64 eps (fma.f64 eps (.f64 eps #s(literal -1/645120 binary64)) #s(literal 1/3840 binary64)))) #s(literal 1/2304 binary64)) (.f64 eps (.f64 (.f64 eps (fma.f64 eps (*.f64 eps #s(literal -1/645120 binary64)) #s(literal 1/3840 binary64))) #s(literal -1/48 binary64))))))
(.f64 (fma.f64 (.f64 eps eps) (.f64 (.f64 eps (fma.f64 eps (.f64 eps #s(literal -1/645120 binary64)) #s(literal 1/3840 binary64))) (.f64 eps (fma.f64 eps (.f64 eps #s(literal -1/645120 binary64)) #s(literal 1/3840 binary64)))) #s(literal -1/2304 binary64)) (/.f64 #s(literal 1 binary64) (fma.f64 eps (.f64 eps (fma.f64 eps (*.f64 eps #s(literal -1/645120 binary64)) #s(literal 1/3840 binary64))) #s(literal 1/48 binary64))))

eval202.0ms (1.4%)

Memory: 2.3MiB live, 285.4MiB allocated
Compiler: Compiled 29 921 to 2 117 computations (92.9% saved)

prune236.0ms (1.7%)

Memory

-8.5MiB live, 467.6MiB allocated

Pruning

31 alts after pruning (23 fresh and 8 done)

	Pruned	Kept	Total
New	1 094	10	1 104
Fresh	6	13	19
Picked	4	1	5
Done	0	7	7
Total	1 104	31	1 135

Accuracy

100.0%

Counts

1 135 → 31

Alt Table

Click to see full alt table

Status	Accuracy	Program
	99.7%	(fma.f64 (sin.f64 eps) (cos.f64 x) (fma.f64 (sin.f64 x) (cos.f64 eps) (sin.f64 (neg.f64 x))))
✓	62.8%	(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
✓	61.4%	(-.f64 (sin.f64 (+.f64 x eps)) #s(approx (sin x) (fma.f64 #s(literal -1/6 binary64) (.f64 x (.f64 x x)) x)))
	99.8%	(.f64 (.f64 (cos.f64 (fma.f64 eps #s(literal 1/2 binary64) x)) #s(approx (sin (* (+ eps 0) 1/2)) (.f64 eps (fma.f64 eps (.f64 eps (fma.f64 eps (.f64 eps (fma.f64 eps (.f64 eps #s(literal -1/645120 binary64)) #s(literal 1/3840 binary64))) #s(literal -1/48 binary64))) #s(literal 1/2 binary64))))) #s(literal 2 binary64))
	99.1%	(.f64 (.f64 (cos.f64 (fma.f64 eps #s(literal 1/2 binary64) x)) #s(approx (sin (* (+ eps 0) 1/2)) (*.f64 eps #s(literal 1/2 binary64)))) #s(literal 2 binary64))
	99.5%	(.f64 (.f64 (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) #s(approx (sin (* (+ eps 0) 1/2)) (.f64 eps (fma.f64 eps (.f64 eps #s(literal -1/48 binary64)) #s(literal 1/2 binary64))))) #s(literal 2 binary64))
	99.5%	(.f64 (.f64 #s(approx (sin (* (+ eps 0) 1/2)) (fma.f64 (.f64 eps (.f64 eps eps)) #s(literal -1/48 binary64) (.f64 #s(literal 1/2 binary64) eps))) (cos.f64 (.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)))) #s(literal 2 binary64))
	17.8%	(.f64 (.f64 #s(approx (sin (* (+ eps 0) 1/2)) (/.f64 (fma.f64 (.f64 (.f64 eps (.f64 eps (fma.f64 eps (.f64 eps (fma.f64 eps (.f64 eps #s(literal -1/645120 binary64)) #s(literal 1/3840 binary64))) #s(literal -1/48 binary64)))) (.f64 eps (.f64 eps eps))) (.f64 eps eps) (.f64 (.f64 eps eps) (.f64 (.f64 eps (.f64 eps eps)) #s(literal 1/2 binary64)))) (.f64 (.f64 eps (.f64 eps eps)) eps))) (cos.f64 (*.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)))) #s(literal 2 binary64))
	49.9%	(.f64 (.f64 #s(approx (sin (* (+ eps 0) 1/2)) (/.f64 (.f64 (fma.f64 eps (.f64 eps (fma.f64 eps (.f64 eps (fma.f64 eps (.f64 eps #s(literal -1/645120 binary64)) #s(literal 1/3840 binary64))) #s(literal -1/48 binary64))) #s(literal 1/2 binary64)) (.f64 eps eps)) eps)) (cos.f64 (.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)))) #s(literal 2 binary64))
	49.6%	(.f64 (.f64 #s(approx (sin (* (+ eps 0) 1/2)) (/.f64 (.f64 (fma.f64 eps (.f64 eps #s(literal -1/48 binary64)) #s(literal 1/2 binary64)) (.f64 eps eps)) eps)) (cos.f64 (.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)))) #s(literal 2 binary64))
	99.9%	(.f64 (.f64 #s(approx (sin (* (+ eps 0) 1/2)) (.f64 eps (fma.f64 (.f64 eps eps) (fma.f64 (.f64 eps eps) (fma.f64 (.f64 eps eps) #s(literal -1/645120 binary64) #s(literal 1/3840 binary64)) #s(literal -1/48 binary64)) #s(literal 1/2 binary64)))) (fma.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (neg.f64 (sin.f64 x)) (.f64 (cos.f64 x) (cos.f64 (*.f64 eps #s(literal 1/2 binary64)))))) #s(literal 2 binary64))
	99.7%	(.f64 (.f64 #s(approx (sin (* (+ eps 0) 1/2)) (.f64 eps (fma.f64 (.f64 eps eps) (fma.f64 (.f64 eps eps) (fma.f64 (.f64 eps eps) #s(literal -1/645120 binary64) #s(literal 1/3840 binary64)) #s(literal -1/48 binary64)) #s(literal 1/2 binary64)))) (cos.f64 #s(approx (* (+ (* x 2) eps) 1/2) (*.f64 eps (+.f64 #s(literal 1/2 binary64) (/.f64 x eps)))))) #s(literal 2 binary64))
	99.7%	(.f64 (.f64 #s(approx (sin (* (+ eps 0) 1/2)) (.f64 eps (fma.f64 (.f64 eps eps) (fma.f64 (.f64 eps eps) #s(literal 1/3840 binary64) #s(literal -1/48 binary64)) #s(literal 1/2 binary64)))) (cos.f64 (.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)))) #s(literal 2 binary64))
	99.4%	(.f64 (.f64 #s(approx (sin (* (+ eps 0) 1/2)) (.f64 eps (fma.f64 eps (.f64 eps #s(literal -1/48 binary64)) #s(literal 1/2 binary64)))) (cos.f64 #s(approx (* (+ (* x 2) eps) 1/2) (*.f64 eps (+.f64 #s(literal 1/2 binary64) (/.f64 x eps)))))) #s(literal 2 binary64))
	99.8%	(.f64 #s(approx ( (sin (* (+ eps 0) 1/2)) (- (* (cos (* (* x 2) 1/2)) (cos (* eps 1/2))) (* (sin (* (* x 2) 1/2)) (sin (* eps 1/2))))) (.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (-.f64 (.f64 (cos.f64 x) (cos.f64 (.f64 eps #s(literal 1/2 binary64)))) (.f64 (sin.f64 x) #s(approx (sin ( eps 1/2)) (.f64 eps (fma.f64 (.f64 eps eps) (fma.f64 (*.f64 eps eps) #s(literal 1/3840 binary64) #s(literal -1/48 binary64)) #s(literal 1/2 binary64)))))))) #s(literal 2 binary64))
	99.4%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 eps (fma.f64 (fma.f64 eps (.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64)) (cos.f64 x) (.f64 (.f64 eps (sin.f64 x)) (fma.f64 eps (*.f64 eps #s(literal 1/24 binary64)) #s(literal -1/2 binary64))))))
✓	99.0%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 eps (fma.f64 eps (.f64 #s(literal -1/2 binary64) (sin.f64 x)) (cos.f64 x))))
	97.5%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 eps (fma.f64 eps (.f64 #s(literal -1/2 binary64) (sin.f64 x)) #s(approx (cos x) #s(literal 1 binary64)))))
✓	98.4%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 eps (fma.f64 eps #s(approx ( -1/2 (sin x)) (*.f64 x #s(literal -1/2 binary64))) (cos.f64 x))))
✓	98.6%	#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 eps (cos.f64 x)))
	97.8%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 eps #s(approx (+ ( eps (* -1/2 (sin x))) (cos x)) (fma.f64 (*.f64 x #s(literal -1/2 binary64)) (+.f64 eps x) #s(literal 1 binary64)))))
	97.4%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 eps #s(approx (+ ( eps (* -1/2 (sin x))) (cos x)) (fma.f64 x (*.f64 eps #s(literal -1/2 binary64)) #s(literal 1 binary64)))))
✓	97.5%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 eps #s(approx (+ ( eps (* -1/2 (sin x))) (cos x)) #s(literal 1 binary64))))
✓	97.8%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 eps #s(approx (cos x) (fma.f64 (.f64 x x) (fma.f64 x (.f64 x (fma.f64 (.f64 x x) #s(literal -1/720 binary64) #s(literal 1/24 binary64))) #s(literal -1/2 binary64)) #s(literal 1 binary64)))))
	97.9%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 eps #s(approx (cos x) (fma.f64 (.f64 x x) (fma.f64 x (.f64 x #s(approx (+ ( (* x x) -1/720) 1/24) #s(literal 1/24 binary64))) #s(literal -1/2 binary64)) #s(literal 1 binary64)))))
✓	97.8%	#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* eps (+ (* eps (* -1/2 (sin x))) (cos x))) (fma.f64 x (.f64 eps (.f64 #s(literal -1/2 binary64) (+.f64 eps x))) eps)))
	97.7%	#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* eps (+ (* eps (* -1/2 (sin x))) (cos x))) (fma.f64 x #s(approx (* eps (* -1/2 (+ eps x))) (.f64 x (.f64 eps #s(literal -1/2 binary64)))) eps)))
	47.8%	#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* eps (+ (* eps (* -1/2 (sin x))) (cos x))) (.f64 (.f64 (fma.f64 x (.f64 eps (.f64 (+.f64 x eps) #s(literal -1/2 binary64))) eps) (fma.f64 x (.f64 eps (.f64 (+.f64 x eps) #s(literal -1/2 binary64))) (neg.f64 eps))) (/.f64 #s(literal 1 binary64) (fma.f64 x (.f64 eps (.f64 (+.f64 x eps) #s(literal -1/2 binary64))) (neg.f64 eps))))))
	5.1%	#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* eps (+ (* eps (* -1/2 (sin x))) (cos x))) #s(approx (+ (* x (* eps (* -1/2 (+ eps x)))) eps) (.f64 (.f64 (*.f64 x x) eps) #s(literal -1/2 binary64)))))
	47.8%	#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* eps (+ (* eps (* -1/2 (sin x))) (cos x))) #s(approx (+ (* x (* eps (* -1/2 (+ eps x)))) eps) (.f64 (.f64 eps eps) (-.f64 (.f64 x #s(literal -1/2 binary64)) (/.f64 (fma.f64 x (.f64 x #s(literal 1/2 binary64)) #s(literal -1 binary64)) eps))))))
	97.5%	#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (sin eps) (fma.f64 eps (.f64 #s(literal -1/6 binary64) (.f64 eps eps)) eps)))

Compiler

Compiled 1 614 to 595 computations (63.1% saved)

regimes63.0ms (0.4%)

Memory

3.1MiB live, 79.6MiB allocated

Counts

51 → 1

Calls

Call 1

Inputs
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 eps #s(approx (+ ( eps (* -1/2 (sin x))) (cos x)) #s(literal 1 binary64))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* eps (+ (* eps (* -1/2 (sin x))) (cos x))) #s(approx (+ (* x (* eps (* -1/2 (+ eps x)))) eps) (.f64 x (.f64 x (*.f64 eps #s(literal -1/2 binary64)))))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* eps (+ (* eps (* -1/2 (sin x))) (cos x))) #s(approx (+ (* x (* eps (* -1/2 (+ eps x)))) eps) (.f64 (.f64 (*.f64 x x) eps) #s(literal -1/2 binary64)))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (sin eps) (fma.f64 eps (.f64 #s(literal -1/6 binary64) (.f64 eps eps)) eps)))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* eps (cos x)) (fma.f64 eps (.f64 x (.f64 x #s(literal -1/2 binary64))) eps)))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* eps (+ (* eps (* -1/2 (sin x))) (cos x))) (fma.f64 x #s(approx (* eps (* -1/2 (+ eps x))) (.f64 x (.f64 eps #s(literal -1/2 binary64)))) eps)))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 eps #s(approx (+ ( eps (* -1/2 (sin x))) (cos x)) (fma.f64 eps (*.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64)))))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 eps #s(approx (+ ( eps (* -1/2 (sin x))) (cos x)) (fma.f64 x (*.f64 eps #s(literal -1/2 binary64)) #s(literal 1 binary64)))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* eps (+ (* eps (* -1/2 (sin x))) (cos x))) (fma.f64 x (.f64 eps (.f64 #s(literal -1/2 binary64) (+.f64 eps x))) eps)))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 eps #s(approx (+ ( eps (* -1/2 (sin x))) (cos x)) (fma.f64 (*.f64 x #s(literal -1/2 binary64)) (+.f64 eps x) #s(literal 1 binary64)))))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 eps #s(approx (cos x) (fma.f64 (.f64 x x) (fma.f64 #s(literal 1/24 binary64) (*.f64 x x) #s(literal -1/2 binary64)) #s(literal 1 binary64)))))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 eps #s(approx (cos x) (fma.f64 (.f64 x x) (fma.f64 x (.f64 x #s(approx (+ ( (* x x) -1/720) 1/24) #s(literal 1/24 binary64))) #s(literal -1/2 binary64)) #s(literal 1 binary64)))))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 eps #s(approx (cos x) (fma.f64 (.f64 x x) (fma.f64 x (.f64 x (fma.f64 (.f64 x x) #s(literal -1/720 binary64) #s(literal 1/24 binary64))) #s(literal -1/2 binary64)) #s(literal 1 binary64)))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* eps (+ (* eps (* -1/2 (sin x))) (cos x))) #s(approx (+ (* x (* eps (* -1/2 (+ eps x)))) eps) (.f64 (.f64 eps eps) (-.f64 (.f64 x #s(literal -1/2 binary64)) (/.f64 (fma.f64 x (.f64 x #s(literal 1/2 binary64)) #s(literal -1 binary64)) eps))))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* eps (+ (* eps (* -1/2 (sin x))) (cos x))) (.f64 (.f64 (fma.f64 x (.f64 eps (.f64 (+.f64 x eps) #s(literal -1/2 binary64))) eps) (fma.f64 x (.f64 eps (.f64 (+.f64 x eps) #s(literal -1/2 binary64))) (neg.f64 eps))) (/.f64 #s(literal 1 binary64) (fma.f64 x (.f64 eps (.f64 (+.f64 x eps) #s(literal -1/2 binary64))) (neg.f64 eps))))))
#s(approx (- (sin (+ x eps)) (sin x)) (sin.f64 eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 eps (cos.f64 x)))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 eps (fma.f64 eps #s(approx ( -1/2 (sin x)) (*.f64 x #s(literal -1/2 binary64))) (cos.f64 x))))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 eps (fma.f64 eps (.f64 #s(literal -1/2 binary64) (sin.f64 x)) #s(approx (cos x) #s(literal 1 binary64)))))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (/.f64 (cos.f64 x) eps) (.f64 eps eps)))
#s(approx (- (sin (+ x eps)) (sin x)) (fma.f64 (cos.f64 x) eps (.f64 #s(approx ( -1/2 (sin x)) (.f64 x #s(literal -1/2 binary64))) (.f64 eps eps))))
(.f64 (.f64 (cos.f64 (fma.f64 eps #s(literal 1/2 binary64) x)) #s(approx (sin (* (+ eps 0) 1/2)) (*.f64 eps #s(literal 1/2 binary64)))) #s(literal 2 binary64))
(-.f64 (sin.f64 (+.f64 x eps)) #s(approx (sin x) (fma.f64 #s(literal -1/6 binary64) (.f64 x (.f64 x x)) x)))
(.f64 (.f64 #s(approx (sin (* (+ eps 0) 1/2)) (.f64 #s(literal 1/2 binary64) eps)) (cos.f64 (.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)))) #s(literal 2 binary64))
(.f64 (.f64 #s(approx (sin (* (+ eps 0) 1/2)) (.f64 eps #s(literal 1/2 binary64))) (cos.f64 (.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)))) #s(literal 2 binary64))
(.f64 (.f64 (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) #s(approx (sin (* (+ eps 0) 1/2)) (.f64 eps (fma.f64 eps (.f64 eps #s(literal -1/48 binary64)) #s(literal 1/2 binary64))))) #s(literal 2 binary64))
(.f64 (.f64 #s(approx (sin (* (+ eps 0) 1/2)) (.f64 eps (fma.f64 eps (.f64 eps #s(literal -1/48 binary64)) #s(literal 1/2 binary64)))) (cos.f64 (*.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)))) #s(literal 2 binary64))
(.f64 (.f64 #s(approx (sin (* (+ eps 0) 1/2)) (fma.f64 (.f64 eps (.f64 eps eps)) #s(literal -1/48 binary64) (.f64 #s(literal 1/2 binary64) eps))) (cos.f64 (.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)))) #s(literal 2 binary64))
(.f64 (.f64 #s(approx (sin (* (+ eps 0) 1/2)) (.f64 eps (fma.f64 eps (.f64 eps #s(literal -1/48 binary64)) #s(literal 1/2 binary64)))) (cos.f64 #s(approx (* (+ (* x 2) eps) 1/2) (*.f64 eps (+.f64 #s(literal 1/2 binary64) (/.f64 x eps)))))) #s(literal 2 binary64))
(.f64 (.f64 #s(approx (sin (* (+ eps 0) 1/2)) (.f64 eps (fma.f64 eps (.f64 eps (fma.f64 (.f64 eps eps) #s(literal 1/3840 binary64) #s(literal -1/48 binary64))) #s(literal 1/2 binary64)))) (cos.f64 (.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)))) #s(literal 2 binary64))
(.f64 (.f64 #s(approx (sin (* (+ eps 0) 1/2)) (.f64 eps (fma.f64 (.f64 eps eps) (fma.f64 eps (.f64 eps #s(literal 1/3840 binary64)) #s(literal -1/48 binary64)) #s(literal 1/2 binary64)))) (cos.f64 (.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)))) #s(literal 2 binary64))
(.f64 (.f64 #s(approx (sin (* (+ eps 0) 1/2)) (.f64 eps (fma.f64 (.f64 eps eps) (fma.f64 (.f64 eps eps) #s(literal 1/3840 binary64) #s(literal -1/48 binary64)) #s(literal 1/2 binary64)))) (cos.f64 (.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)))) #s(literal 2 binary64))
(.f64 (.f64 #s(approx (sin (* (+ eps 0) 1/2)) (/.f64 (.f64 (fma.f64 eps (.f64 eps #s(literal -1/48 binary64)) #s(literal 1/2 binary64)) (.f64 eps eps)) eps)) (cos.f64 (.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)))) #s(literal 2 binary64))
(.f64 (.f64 (cos.f64 (fma.f64 eps #s(literal 1/2 binary64) x)) #s(approx (sin (* (+ eps 0) 1/2)) (.f64 eps (fma.f64 eps (.f64 eps (fma.f64 eps (.f64 eps (fma.f64 eps (.f64 eps #s(literal -1/645120 binary64)) #s(literal 1/3840 binary64))) #s(literal -1/48 binary64))) #s(literal 1/2 binary64))))) #s(literal 2 binary64))
(.f64 (.f64 #s(approx (sin (* (+ eps 0) 1/2)) (.f64 eps (fma.f64 (.f64 eps eps) (fma.f64 eps (.f64 eps (fma.f64 (.f64 eps eps) #s(literal -1/645120 binary64) #s(literal 1/3840 binary64))) #s(literal -1/48 binary64)) #s(literal 1/2 binary64)))) (cos.f64 (*.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)))) #s(literal 2 binary64))
(.f64 (.f64 #s(approx (sin (* (+ eps 0) 1/2)) (.f64 eps (fma.f64 (.f64 eps eps) (fma.f64 (.f64 eps eps) (fma.f64 (.f64 eps eps) #s(literal -1/645120 binary64) #s(literal 1/3840 binary64)) #s(literal -1/48 binary64)) #s(literal 1/2 binary64)))) (cos.f64 (*.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)))) #s(literal 2 binary64))
(.f64 (.f64 #s(approx (sin (* (+ eps 0) 1/2)) (.f64 eps (fma.f64 (.f64 eps eps) (fma.f64 (.f64 eps eps) (fma.f64 (.f64 eps eps) #s(literal -1/645120 binary64) #s(literal 1/3840 binary64)) #s(literal -1/48 binary64)) #s(literal 1/2 binary64)))) (cos.f64 #s(approx (* (+ (* x 2) eps) 1/2) (*.f64 eps (+.f64 #s(literal 1/2 binary64) (/.f64 x eps)))))) #s(literal 2 binary64))
(.f64 (.f64 #s(approx (sin (* (+ eps 0) 1/2)) (/.f64 (.f64 (fma.f64 eps (.f64 eps (fma.f64 eps (.f64 eps (fma.f64 eps (.f64 eps #s(literal -1/645120 binary64)) #s(literal 1/3840 binary64))) #s(literal -1/48 binary64))) #s(literal 1/2 binary64)) (.f64 eps eps)) eps)) (cos.f64 (.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)))) #s(literal 2 binary64))
(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 eps (fma.f64 eps (.f64 #s(literal -1/2 binary64) (sin.f64 x)) (cos.f64 x))))
(.f64 #s(approx ( (sin (* (+ eps 0) 1/2)) (cos (* (+ (* x 2) eps) 1/2))) (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)))) #s(literal 2 binary64))
(.f64 (.f64 (sin.f64 (.f64 (+.f64 eps #s(literal 0 binary64)) #s(literal 1/2 binary64))) (cos.f64 (.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)))) #s(literal 2 binary64))
(.f64 (.f64 #s(approx (sin (* (+ eps 0) 1/2)) (/.f64 (fma.f64 (.f64 (.f64 eps (.f64 eps (fma.f64 eps (.f64 eps (fma.f64 eps (.f64 eps #s(literal -1/645120 binary64)) #s(literal 1/3840 binary64))) #s(literal -1/48 binary64)))) (.f64 eps (.f64 eps eps))) (.f64 eps eps) (.f64 (.f64 eps eps) (.f64 (.f64 eps (.f64 eps eps)) #s(literal 1/2 binary64)))) (.f64 (.f64 eps (.f64 eps eps)) eps))) (cos.f64 (*.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)))) #s(literal 2 binary64))
(.f64 (.f64 (sin.f64 (.f64 (/.f64 (.f64 eps eps) eps) #s(literal 1/2 binary64))) (cos.f64 (*.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)))) #s(literal 2 binary64))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 eps (fma.f64 (fma.f64 eps (.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64)) (cos.f64 x) (.f64 (.f64 eps (sin.f64 x)) (fma.f64 eps (*.f64 eps #s(literal 1/24 binary64)) #s(literal -1/2 binary64))))))
(.f64 #s(approx ( (sin (* (+ eps 0) 1/2)) (- (* (cos (* (* x 2) 1/2)) (cos (* eps 1/2))) (* (sin (* (* x 2) 1/2)) (sin (* eps 1/2))))) (.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (-.f64 (.f64 (cos.f64 x) (cos.f64 (.f64 eps #s(literal 1/2 binary64)))) (.f64 (sin.f64 x) #s(approx (sin ( eps 1/2)) (.f64 eps (fma.f64 (.f64 eps eps) (fma.f64 (*.f64 eps eps) #s(literal 1/3840 binary64) #s(literal -1/48 binary64)) #s(literal 1/2 binary64)))))))) #s(literal 2 binary64))
(.f64 (.f64 #s(approx (sin (* (+ eps 0) 1/2)) (.f64 eps (fma.f64 (.f64 eps eps) (fma.f64 (.f64 eps eps) (fma.f64 (.f64 eps eps) #s(literal -1/645120 binary64) #s(literal 1/3840 binary64)) #s(literal -1/48 binary64)) #s(literal 1/2 binary64)))) (fma.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (neg.f64 (sin.f64 x)) (.f64 (cos.f64 x) (cos.f64 (*.f64 eps #s(literal 1/2 binary64)))))) #s(literal 2 binary64))
(.f64 (.f64 (sin.f64 (.f64 (+.f64 eps #s(literal 0 binary64)) #s(literal 1/2 binary64))) (-.f64 #s(approx ( (cos (* (* x 2) 1/2)) (cos (* eps 1/2))) (.f64 (cos.f64 x) (+.f64 (fma.f64 (.f64 eps eps) #s(literal -1/8 binary64) #s(literal 1 binary64)) (.f64 (.f64 eps eps) (.f64 (.f64 eps eps) #s(literal 1/384 binary64)))))) (.f64 (sin.f64 (.f64 (.f64 x #s(literal 2 binary64)) #s(literal 1/2 binary64))) (sin.f64 (.f64 eps #s(literal 1/2 binary64)))))) #s(literal 2 binary64))
(fma.f64 (sin.f64 eps) (cos.f64 x) (fma.f64 (sin.f64 x) (cos.f64 eps) (sin.f64 (neg.f64 x))))
(.f64 #s(approx ( (sin (* (+ eps 0) 1/2)) (- (* (cos (* (* x 2) 1/2)) (cos (* eps 1/2))) (* (sin (* (* x 2) 1/2)) (sin (* eps 1/2))))) (.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (-.f64 (.f64 (cos.f64 x) (cos.f64 (.f64 eps #s(literal 1/2 binary64)))) (.f64 (sin.f64 x) (sin.f64 (.f64 eps #s(literal 1/2 binary64))))))) #s(literal 2 binary64))
(.f64 (.f64 (sin.f64 (.f64 (+.f64 eps #s(literal 0 binary64)) #s(literal 1/2 binary64))) (-.f64 (.f64 (cos.f64 (.f64 (.f64 x #s(literal 2 binary64)) #s(literal 1/2 binary64))) (cos.f64 (.f64 eps #s(literal 1/2 binary64)))) (.f64 (sin.f64 (.f64 (.f64 x #s(literal 2 binary64)) #s(literal 1/2 binary64))) (sin.f64 (*.f64 eps #s(literal 1/2 binary64)))))) #s(literal 2 binary64))

Outputs

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

Calls

3 calls:

32.0ms	x
15.0ms	eps
13.0ms	(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))

Results

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

Compiler

Compiled 15 to 10 computations (33.3% saved)

regimes43.0ms (0.3%)

Memory

27.4MiB live, 64.7MiB allocated

Counts

49 → 1

Calls

Call 1

Inputs
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 eps #s(approx (+ ( eps (* -1/2 (sin x))) (cos x)) #s(literal 1 binary64))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* eps (+ (* eps (* -1/2 (sin x))) (cos x))) #s(approx (+ (* x (* eps (* -1/2 (+ eps x)))) eps) (.f64 x (.f64 x (*.f64 eps #s(literal -1/2 binary64)))))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* eps (+ (* eps (* -1/2 (sin x))) (cos x))) #s(approx (+ (* x (* eps (* -1/2 (+ eps x)))) eps) (.f64 (.f64 (*.f64 x x) eps) #s(literal -1/2 binary64)))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (sin eps) (fma.f64 eps (.f64 #s(literal -1/6 binary64) (.f64 eps eps)) eps)))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* eps (cos x)) (fma.f64 eps (.f64 x (.f64 x #s(literal -1/2 binary64))) eps)))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* eps (+ (* eps (* -1/2 (sin x))) (cos x))) (fma.f64 x #s(approx (* eps (* -1/2 (+ eps x))) (.f64 x (.f64 eps #s(literal -1/2 binary64)))) eps)))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 eps #s(approx (+ ( eps (* -1/2 (sin x))) (cos x)) (fma.f64 eps (*.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64)))))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 eps #s(approx (+ ( eps (* -1/2 (sin x))) (cos x)) (fma.f64 x (*.f64 eps #s(literal -1/2 binary64)) #s(literal 1 binary64)))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* eps (+ (* eps (* -1/2 (sin x))) (cos x))) (fma.f64 x (.f64 eps (.f64 #s(literal -1/2 binary64) (+.f64 eps x))) eps)))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 eps #s(approx (+ ( eps (* -1/2 (sin x))) (cos x)) (fma.f64 (*.f64 x #s(literal -1/2 binary64)) (+.f64 eps x) #s(literal 1 binary64)))))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 eps #s(approx (cos x) (fma.f64 (.f64 x x) (fma.f64 #s(literal 1/24 binary64) (*.f64 x x) #s(literal -1/2 binary64)) #s(literal 1 binary64)))))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 eps #s(approx (cos x) (fma.f64 (.f64 x x) (fma.f64 x (.f64 x #s(approx (+ ( (* x x) -1/720) 1/24) #s(literal 1/24 binary64))) #s(literal -1/2 binary64)) #s(literal 1 binary64)))))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 eps #s(approx (cos x) (fma.f64 (.f64 x x) (fma.f64 x (.f64 x (fma.f64 (.f64 x x) #s(literal -1/720 binary64) #s(literal 1/24 binary64))) #s(literal -1/2 binary64)) #s(literal 1 binary64)))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* eps (+ (* eps (* -1/2 (sin x))) (cos x))) #s(approx (+ (* x (* eps (* -1/2 (+ eps x)))) eps) (.f64 (.f64 eps eps) (-.f64 (.f64 x #s(literal -1/2 binary64)) (/.f64 (fma.f64 x (.f64 x #s(literal 1/2 binary64)) #s(literal -1 binary64)) eps))))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* eps (+ (* eps (* -1/2 (sin x))) (cos x))) (.f64 (.f64 (fma.f64 x (.f64 eps (.f64 (+.f64 x eps) #s(literal -1/2 binary64))) eps) (fma.f64 x (.f64 eps (.f64 (+.f64 x eps) #s(literal -1/2 binary64))) (neg.f64 eps))) (/.f64 #s(literal 1 binary64) (fma.f64 x (.f64 eps (.f64 (+.f64 x eps) #s(literal -1/2 binary64))) (neg.f64 eps))))))
#s(approx (- (sin (+ x eps)) (sin x)) (sin.f64 eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 eps (cos.f64 x)))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 eps (fma.f64 eps #s(approx ( -1/2 (sin x)) (*.f64 x #s(literal -1/2 binary64))) (cos.f64 x))))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 eps (fma.f64 eps (.f64 #s(literal -1/2 binary64) (sin.f64 x)) #s(approx (cos x) #s(literal 1 binary64)))))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (/.f64 (cos.f64 x) eps) (.f64 eps eps)))
#s(approx (- (sin (+ x eps)) (sin x)) (fma.f64 (cos.f64 x) eps (.f64 #s(approx ( -1/2 (sin x)) (.f64 x #s(literal -1/2 binary64))) (.f64 eps eps))))
(.f64 (.f64 (cos.f64 (fma.f64 eps #s(literal 1/2 binary64) x)) #s(approx (sin (* (+ eps 0) 1/2)) (*.f64 eps #s(literal 1/2 binary64)))) #s(literal 2 binary64))
(-.f64 (sin.f64 (+.f64 x eps)) #s(approx (sin x) (fma.f64 #s(literal -1/6 binary64) (.f64 x (.f64 x x)) x)))
(.f64 (.f64 #s(approx (sin (* (+ eps 0) 1/2)) (.f64 #s(literal 1/2 binary64) eps)) (cos.f64 (.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)))) #s(literal 2 binary64))
(.f64 (.f64 #s(approx (sin (* (+ eps 0) 1/2)) (.f64 eps #s(literal 1/2 binary64))) (cos.f64 (.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)))) #s(literal 2 binary64))
(.f64 (.f64 (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) #s(approx (sin (* (+ eps 0) 1/2)) (.f64 eps (fma.f64 eps (.f64 eps #s(literal -1/48 binary64)) #s(literal 1/2 binary64))))) #s(literal 2 binary64))
(.f64 (.f64 #s(approx (sin (* (+ eps 0) 1/2)) (.f64 eps (fma.f64 eps (.f64 eps #s(literal -1/48 binary64)) #s(literal 1/2 binary64)))) (cos.f64 (*.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)))) #s(literal 2 binary64))
(.f64 (.f64 #s(approx (sin (* (+ eps 0) 1/2)) (fma.f64 (.f64 eps (.f64 eps eps)) #s(literal -1/48 binary64) (.f64 #s(literal 1/2 binary64) eps))) (cos.f64 (.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)))) #s(literal 2 binary64))
(.f64 (.f64 #s(approx (sin (* (+ eps 0) 1/2)) (.f64 eps (fma.f64 eps (.f64 eps #s(literal -1/48 binary64)) #s(literal 1/2 binary64)))) (cos.f64 #s(approx (* (+ (* x 2) eps) 1/2) (*.f64 eps (+.f64 #s(literal 1/2 binary64) (/.f64 x eps)))))) #s(literal 2 binary64))
(.f64 (.f64 #s(approx (sin (* (+ eps 0) 1/2)) (.f64 eps (fma.f64 eps (.f64 eps (fma.f64 (.f64 eps eps) #s(literal 1/3840 binary64) #s(literal -1/48 binary64))) #s(literal 1/2 binary64)))) (cos.f64 (.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)))) #s(literal 2 binary64))
(.f64 (.f64 #s(approx (sin (* (+ eps 0) 1/2)) (.f64 eps (fma.f64 (.f64 eps eps) (fma.f64 eps (.f64 eps #s(literal 1/3840 binary64)) #s(literal -1/48 binary64)) #s(literal 1/2 binary64)))) (cos.f64 (.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)))) #s(literal 2 binary64))
(.f64 (.f64 #s(approx (sin (* (+ eps 0) 1/2)) (.f64 eps (fma.f64 (.f64 eps eps) (fma.f64 (.f64 eps eps) #s(literal 1/3840 binary64) #s(literal -1/48 binary64)) #s(literal 1/2 binary64)))) (cos.f64 (.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)))) #s(literal 2 binary64))
(.f64 (.f64 #s(approx (sin (* (+ eps 0) 1/2)) (/.f64 (.f64 (fma.f64 eps (.f64 eps #s(literal -1/48 binary64)) #s(literal 1/2 binary64)) (.f64 eps eps)) eps)) (cos.f64 (.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)))) #s(literal 2 binary64))
(.f64 (.f64 (cos.f64 (fma.f64 eps #s(literal 1/2 binary64) x)) #s(approx (sin (* (+ eps 0) 1/2)) (.f64 eps (fma.f64 eps (.f64 eps (fma.f64 eps (.f64 eps (fma.f64 eps (.f64 eps #s(literal -1/645120 binary64)) #s(literal 1/3840 binary64))) #s(literal -1/48 binary64))) #s(literal 1/2 binary64))))) #s(literal 2 binary64))
(.f64 (.f64 #s(approx (sin (* (+ eps 0) 1/2)) (.f64 eps (fma.f64 (.f64 eps eps) (fma.f64 eps (.f64 eps (fma.f64 (.f64 eps eps) #s(literal -1/645120 binary64) #s(literal 1/3840 binary64))) #s(literal -1/48 binary64)) #s(literal 1/2 binary64)))) (cos.f64 (*.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)))) #s(literal 2 binary64))
(.f64 (.f64 #s(approx (sin (* (+ eps 0) 1/2)) (.f64 eps (fma.f64 (.f64 eps eps) (fma.f64 (.f64 eps eps) (fma.f64 (.f64 eps eps) #s(literal -1/645120 binary64) #s(literal 1/3840 binary64)) #s(literal -1/48 binary64)) #s(literal 1/2 binary64)))) (cos.f64 (*.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)))) #s(literal 2 binary64))
(.f64 (.f64 #s(approx (sin (* (+ eps 0) 1/2)) (.f64 eps (fma.f64 (.f64 eps eps) (fma.f64 (.f64 eps eps) (fma.f64 (.f64 eps eps) #s(literal -1/645120 binary64) #s(literal 1/3840 binary64)) #s(literal -1/48 binary64)) #s(literal 1/2 binary64)))) (cos.f64 #s(approx (* (+ (* x 2) eps) 1/2) (*.f64 eps (+.f64 #s(literal 1/2 binary64) (/.f64 x eps)))))) #s(literal 2 binary64))
(.f64 (.f64 #s(approx (sin (* (+ eps 0) 1/2)) (/.f64 (.f64 (fma.f64 eps (.f64 eps (fma.f64 eps (.f64 eps (fma.f64 eps (.f64 eps #s(literal -1/645120 binary64)) #s(literal 1/3840 binary64))) #s(literal -1/48 binary64))) #s(literal 1/2 binary64)) (.f64 eps eps)) eps)) (cos.f64 (.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)))) #s(literal 2 binary64))
(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 eps (fma.f64 eps (.f64 #s(literal -1/2 binary64) (sin.f64 x)) (cos.f64 x))))
(.f64 #s(approx ( (sin (* (+ eps 0) 1/2)) (cos (* (+ (* x 2) eps) 1/2))) (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)))) #s(literal 2 binary64))
(.f64 (.f64 (sin.f64 (.f64 (+.f64 eps #s(literal 0 binary64)) #s(literal 1/2 binary64))) (cos.f64 (.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)))) #s(literal 2 binary64))
(.f64 (.f64 #s(approx (sin (* (+ eps 0) 1/2)) (/.f64 (fma.f64 (.f64 (.f64 eps (.f64 eps (fma.f64 eps (.f64 eps (fma.f64 eps (.f64 eps #s(literal -1/645120 binary64)) #s(literal 1/3840 binary64))) #s(literal -1/48 binary64)))) (.f64 eps (.f64 eps eps))) (.f64 eps eps) (.f64 (.f64 eps eps) (.f64 (.f64 eps (.f64 eps eps)) #s(literal 1/2 binary64)))) (.f64 (.f64 eps (.f64 eps eps)) eps))) (cos.f64 (*.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)))) #s(literal 2 binary64))
(.f64 (.f64 (sin.f64 (.f64 (/.f64 (.f64 eps eps) eps) #s(literal 1/2 binary64))) (cos.f64 (*.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)))) #s(literal 2 binary64))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 eps (fma.f64 (fma.f64 eps (.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64)) (cos.f64 x) (.f64 (.f64 eps (sin.f64 x)) (fma.f64 eps (*.f64 eps #s(literal 1/24 binary64)) #s(literal -1/2 binary64))))))
(.f64 #s(approx ( (sin (* (+ eps 0) 1/2)) (- (* (cos (* (* x 2) 1/2)) (cos (* eps 1/2))) (* (sin (* (* x 2) 1/2)) (sin (* eps 1/2))))) (.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (-.f64 (.f64 (cos.f64 x) (cos.f64 (.f64 eps #s(literal 1/2 binary64)))) (.f64 (sin.f64 x) #s(approx (sin ( eps 1/2)) (.f64 eps (fma.f64 (.f64 eps eps) (fma.f64 (*.f64 eps eps) #s(literal 1/3840 binary64) #s(literal -1/48 binary64)) #s(literal 1/2 binary64)))))))) #s(literal 2 binary64))
(.f64 (.f64 #s(approx (sin (* (+ eps 0) 1/2)) (.f64 eps (fma.f64 (.f64 eps eps) (fma.f64 (.f64 eps eps) (fma.f64 (.f64 eps eps) #s(literal -1/645120 binary64) #s(literal 1/3840 binary64)) #s(literal -1/48 binary64)) #s(literal 1/2 binary64)))) (fma.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (neg.f64 (sin.f64 x)) (.f64 (cos.f64 x) (cos.f64 (*.f64 eps #s(literal 1/2 binary64)))))) #s(literal 2 binary64))
(.f64 (.f64 (sin.f64 (.f64 (+.f64 eps #s(literal 0 binary64)) #s(literal 1/2 binary64))) (-.f64 #s(approx ( (cos (* (* x 2) 1/2)) (cos (* eps 1/2))) (.f64 (cos.f64 x) (+.f64 (fma.f64 (.f64 eps eps) #s(literal -1/8 binary64) #s(literal 1 binary64)) (.f64 (.f64 eps eps) (.f64 (.f64 eps eps) #s(literal 1/384 binary64)))))) (.f64 (sin.f64 (.f64 (.f64 x #s(literal 2 binary64)) #s(literal 1/2 binary64))) (sin.f64 (.f64 eps #s(literal 1/2 binary64)))))) #s(literal 2 binary64))
(fma.f64 (sin.f64 eps) (cos.f64 x) (fma.f64 (sin.f64 x) (cos.f64 eps) (sin.f64 (neg.f64 x))))

Outputs

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

Calls

3 calls:

15.0ms	eps
13.0ms	x
13.0ms	(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 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)

regimes48.0ms (0.3%)

Memory

-8.2MiB live, 76.9MiB allocated

Counts

46 → 1

Calls

Call 1

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

Outputs

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

Calls

3 calls:

19.0ms	(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
15.0ms	x
12.0ms	eps

Results

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

Compiler

Compiled 15 to 10 computations (33.3% saved)

regimes40.0ms (0.3%)

Memory

-9.6MiB live, 67.6MiB allocated

Counts

45 → 1

Calls

Call 1

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

Outputs

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

Calls

3 calls:

13.0ms	(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
13.0ms	x
12.0ms	eps

Results

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

Compiler

Compiled 15 to 10 computations (33.3% saved)

regimes36.0ms (0.3%)

Memory

15.1MiB live, 62.9MiB allocated

Counts

40 → 1

Calls

Call 1

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

Outputs

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

Calls

3 calls:

13.0ms	eps
11.0ms	x
11.0ms	(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 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)

regimes29.0ms (0.2%)

Memory

-2.1MiB live, 37.1MiB allocated

Counts

33 → 1

Calls

Call 1

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

Outputs

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

Calls

3 calls:

10.0ms	(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
9.0ms	x
9.0ms	eps

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)

regimes27.0ms (0.2%)

Memory

-32.4MiB live, 45.8MiB allocated

Counts

29 → 1

Calls

Call 1

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

Outputs

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

Calls

3 calls:

9.0ms	(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
8.0ms	eps
8.0ms	x

Results

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

Compiler

Compiled 15 to 10 computations (33.3% saved)

regimes24.0ms (0.2%)

Memory

34.6MiB live, 34.6MiB allocated

Counts

27 → 1

Calls

Call 1

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

Outputs

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

Calls

3 calls:

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

Results

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

Compiler

Compiled 15 to 10 computations (33.3% saved)

regimes24.0ms (0.2%)

Memory

-6.9MiB live, 33.4MiB allocated

Counts

25 → 1

Calls

Call 1

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

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

Calls

3 calls:

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

Results

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

Compiler

Compiled 15 to 10 computations (33.3% saved)

regimes20.0ms (0.1%)

Memory

-11.3MiB live, 27.9MiB allocated

Counts

21 → 1

Calls

Call 1

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

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

Calls

3 calls:

7.0ms	eps
6.0ms	x
6.0ms	(-.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)

regimes15.0ms (0.1%)

Memory

21.1MiB live, 21.1MiB allocated

Counts

16 → 1

Calls

Call 1

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

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

Calls

3 calls:

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

Results

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

Compiler

Compiled 15 to 10 computations (33.3% saved)

regimes12.0ms (0.1%)

Memory

-21.7MiB live, 17.3MiB allocated

Counts

10 → 1

Calls

Call 1

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

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

Calls

3 calls:

5.0ms	(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
3.0ms	x
3.0ms	eps

Results

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

Compiler

Compiled 15 to 10 computations (33.3% saved)

regimes9.0ms (0.1%)

Memory

18.2MiB live, 18.2MiB allocated

Counts

8 → 1

Calls

Call 1

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

Outputs
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* eps (cos x)) (fma.f64 eps (.f64 x (.f64 x #s(literal -1/2 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
97.7%	1	`x`
97.7%	1	`eps`
97.7%	1	`(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))`

Compiler

Compiled 15 to 10 computations (33.3% saved)

regimes7.0ms (0.1%)

Memory

-29.2MiB live, 9.6MiB allocated

Counts

4 → 1

Calls

Call 1

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

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

Calls

3 calls:

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

Results

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

Compiler

Compiled 15 to 10 computations (33.3% saved)

regimes6.0ms (0%)

Memory

19.0MiB live, 19.0MiB allocated

Accuracy

Total -59.2b remaining (-3684.6%)

Threshold costs -59.2b (-3684.6%)

Counts

3 → 1

Calls

Call 1

Inputs

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

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

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

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

Calls

3 calls:

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

Results

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

Compiler

Compiled 15 to 10 computations (33.3% saved)

simplify17.0ms (0.1%)

Memory

-20.6MiB live, 20.2MiB allocated

Algorithm

1×	egg-herbie

Rules

94×	`*-commutative_binary64`
16×	`+-commutative_binary64`
14×	`sub-neg_binary64`
10×	`neg-sub0_binary64`
10×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	139	449
1	197	449
2	215	449
3	224	449
4	230	449
5	232	449

Stop Event

1×

saturated

Calls

Call 1

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

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

soundness1.9s (13.2%)

Memory

1.1MiB live, 1 005.8MiB allocated

Rules

16 678×	`lower-fma.f64`
16 678×	`lower-fma.f32`
15 396×	`lower-fma.f64`
15 396×	`lower-fma.f32`
13 688×	`lower-fma.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	16
0	10	16
1	53	16
2	380	16
3	4766	16
0	8210	16
0	403	5847
1	1287	5642
2	3612	5577
0	8071	5228
0	431	6704
1	1337	6435
2	3766	6333
0	8118	5991
0	107	496
1	314	496
2	775	489
3	2836	489
4	6173	489
0	8126	458
0	59	372
0	94	354
1	300	293
2	2522	293
0	8384	281
0	79	538
0	119	526
1	450	446
2	3865	446
0	8648	429
0	359	3341
1	1096	3209
2	2826	3169
3	6529	3169
0	8151	2921
0	36	161
0	61	147
1	189	147
2	1458	147
0	8241	147

Stop Event

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

Compiler

Compiled 796 to 427 computations (46.4% saved)

preprocess158.0ms (1.1%)

Memory: 17.8MiB live, 213.1MiB allocated
Compiler: Compiled 644 to 250 computations (61.2% saved)

end0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated

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

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

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

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

start0.0ms (0%)

analyze42.0ms (0.3%)

sample6.3s (44.2%)

explain202.0ms (1.4%)

preprocess24.0ms (0.2%)

eval0.0ms (0%)

prune1.0ms (0%)

simplify72.0ms (0.5%)

localize27.0ms (0.2%)

series5.0ms (0%)

simplify229.0ms (1.6%)

rewrite310.0ms (2.2%)

eval37.0ms (0.3%)

prune50.0ms (0.4%)

simplify248.0ms (1.8%)

localize126.0ms (0.9%)

series34.0ms (0.2%)

simplify293.0ms (2.1%)

rewrite266.0ms (1.9%)

eval117.0ms (0.8%)

prune161.0ms (1.1%)

simplify235.0ms (1.7%)

localize206.0ms (1.5%)

series47.0ms (0.3%)

simplify371.0ms (2.6%)

rewrite299.0ms (2.1%)

eval199.0ms (1.4%)

prune203.0ms (1.4%)

simplify212.0ms (1.5%)

localize327.0ms (2.3%)

series55.0ms (0.4%)

simplify287.0ms (2%)

rewrite331.0ms (2.3%)

eval202.0ms (1.4%)

prune236.0ms (1.7%)

regimes63.0ms (0.4%)

regimes43.0ms (0.3%)

regimes48.0ms (0.3%)

regimes40.0ms (0.3%)

regimes36.0ms (0.3%)

regimes29.0ms (0.2%)

regimes27.0ms (0.2%)

regimes24.0ms (0.2%)

regimes24.0ms (0.2%)

regimes20.0ms (0.1%)

regimes15.0ms (0.1%)

regimes12.0ms (0.1%)

regimes9.0ms (0.1%)

regimes7.0ms (0.1%)

regimes6.0ms (0%)

simplify17.0ms (0.1%)

soundness1.9s (13.2%)

preprocess158.0ms (1.1%)

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