Metrics for 2sin (example 3.3)

start0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated

analyze39.0ms (0.3%)

Memory

27.7MiB live, 27.7MiB 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)

sample6.4s (41.5%)

Memory

-195.3MiB live, 6 910.1MiB allocated

Samples

3.7s	26 194×	0	invalid
694.0ms	5 470×	0	valid
622.0ms	2 786×	1	valid

Precisions

Click to see histograms. Total time spent on operations: 3.5s

const: 743.0ms (21.4% of total)

ival-sin: 647.0ms (18.6% of total)

ival-sub: 421.0ms (12.1% of total)

ival-fabs: 353.0ms (10.1% of total)

ival-mult: 316.0ms (9.1% of total)

ival-<=: 315.0ms (9.1% of total)

ival-add: 260.0ms (7.5% of total)

ival-<: 191.0ms (5.5% of total)

ival-and: 103.0ms (3% of total)

adjust: 70.0ms (2% of total)

exact: 46.0ms (1.3% of total)

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

Bogosity

explain91.0ms (0.6%)

Memory

16.9MiB live, 92.3MiB allocated

FPErrors

Click to see full error table

Ground Truth	Overpredictions	Example	Underpredictions	Example	Subexpression
218	2	(2.3794404783451385e-103 2.258794647997274e-105)	2	(-2.2077112374028354e-243 6.6877552078313866e-245)	`(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))`
4	0	-	0	-	`(sin.f64 (+.f64 x eps))`
0	0	-	0	-	`eps`
0	0	-	0	-	`(+.f64 x eps)`
0	0	-	0	-	`(sin.f64 x)`
0	0	-	0	-	`x`

Explanations

Click to see full explanations table

Operator	Subexpression	Explanation	Count
`-.f64`	`(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))`	cancellation	218	6
`sin.f64`	`(sin.f64 (+.f64 x eps))`	sensitivity	4	2

Confusion

	Predicted +	Predicted -
+	216	2
-	2	36

Precision

0.9908256880733946

Recall

0.9908256880733946

Confusion?

	Predicted +	Predicted Maybe	Predicted -
+	216	2	0
-	2	5	31

Precision?

0.9688888888888889

Recall?

1.0

Freqs

test

number	freq
0	38
1	214
2	4

Total Confusion?

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

Precision?

1.0

Recall?

1.0

Samples

17.0ms	170×	1	valid
16.0ms	338×	0	valid
4.0ms	2×	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: 23.0ms

ival-sin: 13.0ms (56.8% of total)

adjust: 3.0ms (13.1% of total)

ival-add: 3.0ms (13.1% of total)

ival-sub: 3.0ms (13.1% of total)

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

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

preprocess27.0ms (0.2%)

Memory

-19.8MiB live, 17.2MiB 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: 0.4MiB live, 0.4MiB 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
▶	62.9%	(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))

Compiler

Compiled 9 to 6 computations (33.3% saved)

simplify7.0ms (0%)

Memory

7.2MiB live, 7.2MiB 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)

localize37.0ms (0.2%)

Memory

-14.4MiB live, 27.3MiB allocated

Localize:

Found 4 expressions of interest:

New	Metric	Score
accuracy	0	(+.f64 x eps)
accuracy	0	(sin.f64 x)
accuracy	0.19074756896139175	(sin.f64 (+.f64 x eps))
accuracy	23.57645487103795	(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))

Samples

20.0ms	169×	0	valid
8.0ms	85×	1	valid
2.0ms	1×	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: 12.0ms

ival-sin: 6.0ms (48.2% of total)

ival-add: 3.0ms (24.1% of total)

adjust: 2.0ms (16.1% of total)

ival-sub: 1.0ms (8% of total)

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

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

series4.0ms (0%)

Memory

6.0MiB live, 6.0MiB 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	eps	@	0	(- (sin (+ x eps)) (sin x))
0.0ms	x	@	0	(- (sin (+ x eps)) (sin x))
0.0ms	x	@	-inf	(- (sin (+ x eps)) (sin x))
0.0ms	x	@	inf	(+ x eps)

simplify261.0ms (1.7%)

Memory

22.2MiB live, 248.9MiB allocated

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

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

Stop Event

1×	iter limit
1×	node limit

Counts

84 → 77

Calls

Call 1

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

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

rewrite261.0ms (1.7%)

Memory

10.7MiB live, 321.8MiB allocated

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

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

Stop Event

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

Counts

4 → 214

Calls

Call 1

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

Outputs
(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))

eval38.0ms (0.2%)

Memory: -16.8MiB live, 66.3MiB allocated
Compiler: Compiled 7 823 to 844 computations (89.2% saved)

prune50.0ms (0.3%)

Memory

-6.4MiB live, 108.8MiB allocated

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	282	9	291
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	282	10	292

Accuracy

99.9%

Counts

292 → 10

Alt Table

Click to see full alt table

Status	Accuracy	Program
	2.3%	(fma.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)) (-.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))))))))
▶	99.5%	(fma.f64 (sin.f64 eps) (cos.f64 x) (fma.f64 (sin.f64 x) (cos.f64 eps) (sin.f64 (neg.f64 x))))
✓	62.9%	(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
▶	61.2%	(-.f64 (sin.f64 (+.f64 x eps)) #s(approx (sin x) (fma.f64 #s(literal -1/6 binary64) (.f64 x (.f64 x x)) x)))
▶	99.6%	(.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))
	99.5%	#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))))))
▶	99.3%	#s(approx (- (sin (+ x eps)) (sin 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)))))
	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))))
	98.4%	#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 eps (cos.f64 x)))
▶	96.4%	#s(approx (- (sin (+ x eps)) (sin x)) (sin.f64 eps))

Compiler

Compiled 375 to 202 computations (46.1% saved)

simplify570.0ms (3.7%)

Memory

9.6MiB live, 411.8MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 18 expressions of interest:

New	Metric	Score
cost-diff	0	(cos.f64 x)
cost-diff	0	(sin.f64 eps)
cost-diff	0	(fma.f64 (sin.f64 eps) (cos.f64 x) (fma.f64 (sin.f64 x) (cos.f64 eps) (sin.f64 (neg.f64 x))))
cost-diff	6400	(fma.f64 (sin.f64 x) (cos.f64 eps) (sin.f64 (neg.f64 x)))
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)) (.f64 (fma.f64 eps (*.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64)) (cos.f64 x)))
cost-diff	0	(.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))))
cost-diff	0	#s(approx (- (sin (+ x eps)) (sin 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)))))
cost-diff	0	#s(approx (sin x) (fma.f64 #s(literal -1/6 binary64) (.f64 x (.f64 x x)) x))
cost-diff	0	(+.f64 x eps)
cost-diff	0	(sin.f64 (+.f64 x eps))
cost-diff	0	(-.f64 (sin.f64 (+.f64 x eps)) #s(approx (sin x) (fma.f64 #s(literal -1/6 binary64) (.f64 x (.f64 x x)) x)))
cost-diff	0	(sin.f64 eps)
cost-diff	0	#s(approx (- (sin (+ x eps)) (sin x)) (sin.f64 eps))
cost-diff	0	(.f64 (sin.f64 (.f64 (+.f64 eps #s(literal 0 binary64)) #s(literal 1/2 binary64))) (cos.f64 (*.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64))))
cost-diff	0	(.f64 (.f64 (sin.f64 (.f64 (+.f64 eps #s(literal 0 binary64)) #s(literal 1/2 binary64))) (cos.f64 (.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)))) #s(literal 2 binary64))
cost-diff	192	(+.f64 eps #s(literal 0 binary64))
cost-diff	320	(*.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64))

Rules

29 248×	`lower-fma.f32`
29 236×	`lower-fma.f64`
4 168×	`lower-*.f32`
4 148×	`lower-*.f64`
3 392×	`lower-+.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	43	256
0	78	238
1	129	238
2	262	236
3	507	232
4	968	232
5	1420	232
6	1981	232
7	2328	232
8	2720	232
9	3805	232
10	5353	232
11	5932	232
12	6199	232
13	6228	232
14	6245	232
15	6343	232
16	6493	232
17	6525	232
18	6537	232
19	6547	232
20	6555	232
21	6559	232
22	6559	232
23	7879	232
0	8471	225

Stop Event

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

Calls

Call 1

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

localize331.0ms (2.1%)

Memory

-34.6MiB live, 285.2MiB allocated

Localize:

Found 18 expressions of interest:

New	Metric	Score
accuracy	0	(cos.f64 x)
accuracy	0	(cos.f64 eps)
accuracy	0.015625	(fma.f64 (sin.f64 eps) (cos.f64 x) (fma.f64 (sin.f64 x) (cos.f64 eps) (sin.f64 (neg.f64 x))))
accuracy	23.12686517226103	(fma.f64 (sin.f64 x) (cos.f64 eps) (sin.f64 (neg.f64 x)))
accuracy	0.01171875	(.f64 (fma.f64 eps (.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64)) (cos.f64 x))
accuracy	0.01953125	(.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))))
accuracy	0.34765625	(*.f64 eps #s(literal -1/6 binary64))
accuracy	0.447769100952185	#s(approx (- (sin (+ x eps)) (sin 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)))))
accuracy	0.09765625	(.f64 x (.f64 x x))
accuracy	0.19074756896139175	(sin.f64 (+.f64 x eps))
accuracy	1.8312047479638287	#s(approx (sin x) (fma.f64 #s(literal -1/6 binary64) (.f64 x (.f64 x x)) x))
accuracy	23.57645487103795	(-.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	(sin.f64 eps)
accuracy	2.32577376567232	#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	0.0234375	(.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	0.2232612867848975	(cos.f64 (*.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)))

Samples

176.0ms	228×	1	valid
17.0ms	19×	2	valid
5.0ms	1×	3	valid
3.0ms	8×	0	valid

Compiler

Compiled 234 to 44 computations (81.2% saved)

Precisions

Click to see histograms. Total time spent on operations: 118.0ms

ival-mult: 31.0ms (26.2% of total)

ival-sin: 26.0ms (22% of total)

adjust: 22.0ms (18.6% of total)

ival-add: 20.0ms (16.9% of total)

ival-cos: 11.0ms (9.3% of total)

const: 4.0ms (3.4% of total)

ival-sub: 2.0ms (1.7% of total)

exact: 1.0ms (0.8% of total)

ival-neg: 1.0ms (0.8% of total)

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

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

series41.0ms (0.3%)

Memory

12.4MiB live, 48.2MiB allocated

Counts

23 → 444

Calls

Call 1

Inputs
#s(alt (.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)) (patch (.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)) #<representation binary64>) () ())
#s(alt (+.f64 eps #s(literal 0 binary64)) (patch (+.f64 eps #s(literal 0 binary64)) #<representation binary64>) () ())
#s(alt (.f64 (.f64 (sin.f64 (.f64 (+.f64 eps #s(literal 0 binary64)) #s(literal 1/2 binary64))) (cos.f64 (.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)))) #s(literal 2 binary64)) (patch (.f64 (.f64 (sin.f64 (.f64 (+.f64 eps #s(literal 0 binary64)) #s(literal 1/2 binary64))) (cos.f64 (.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)))) #s(literal 2 binary64)) #<representation binary64>) () ())
#s(alt (.f64 (sin.f64 (.f64 (+.f64 eps #s(literal 0 binary64)) #s(literal 1/2 binary64))) (cos.f64 (.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)))) (patch (.f64 (sin.f64 (.f64 (+.f64 eps #s(literal 0 binary64)) #s(literal 1/2 binary64))) (cos.f64 (.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)))) #<representation binary64>) () ())
#s(alt #s(approx (- (sin (+ x eps)) (sin x)) (sin.f64 eps)) (patch #s(approx (- (sin (+ x eps)) (sin x)) (sin.f64 eps)) #<representation binary64>) () ())
#s(alt (sin.f64 eps) (patch (sin.f64 eps) #<representation binary64>) () ())
#s(alt (-.f64 (sin.f64 (+.f64 x eps)) #s(approx (sin x) (fma.f64 #s(literal -1/6 binary64) (.f64 x (.f64 x x)) x))) (patch (-.f64 (sin.f64 (+.f64 x eps)) #s(approx (sin x) (fma.f64 #s(literal -1/6 binary64) (.f64 x (.f64 x x)) x))) #<representation binary64>) () ())
#s(alt (sin.f64 (+.f64 x eps)) (patch (sin.f64 (+.f64 x eps)) #<representation binary64>) () ())
#s(alt (+.f64 x eps) (patch (+.f64 x eps) #<representation binary64>) () ())
#s(alt #s(approx (sin x) (fma.f64 #s(literal -1/6 binary64) (.f64 x (.f64 x x)) x)) (patch #s(approx (sin x) (fma.f64 #s(literal -1/6 binary64) (.f64 x (.f64 x x)) x)) #<representation binary64>) () ())
#s(alt #s(approx (- (sin (+ x eps)) (sin x)) (.f64 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))))) (patch #s(approx (- (sin (+ x eps)) (sin 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))))) #<representation binary64>) () ())
#s(alt (.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)))) (patch (.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)))) #<representation binary64>) () ())
#s(alt (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))) (patch (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))) #<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 (fma.f64 (sin.f64 x) (cos.f64 eps) (sin.f64 (neg.f64 x))) (patch (fma.f64 (sin.f64 x) (cos.f64 eps) (sin.f64 (neg.f64 x))) #<representation binary64>) () ())
#s(alt (fma.f64 (sin.f64 eps) (cos.f64 x) (fma.f64 (sin.f64 x) (cos.f64 eps) (sin.f64 (neg.f64 x)))) (patch (fma.f64 (sin.f64 eps) (cos.f64 x) (fma.f64 (sin.f64 x) (cos.f64 eps) (sin.f64 (neg.f64 x)))) #<representation binary64>) () ())
#s(alt (cos.f64 x) (patch (cos.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>) () ())
#s(alt (.f64 eps #s(literal -1/6 binary64)) (patch (.f64 eps #s(literal -1/6 binary64)) #<representation binary64>) () ())
#s(alt (.f64 (fma.f64 eps (.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64)) (cos.f64 x)) (patch (.f64 (fma.f64 eps (.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64)) (cos.f64 x)) #<representation binary64>) () ())
#s(alt (cos.f64 eps) (patch (cos.f64 eps) #<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>) () ())) ())
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#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>) () ())) ())
#s(alt (* -1/6 eps) (taylor 0 eps) (#s(alt (.f64 eps #s(literal -1/6 binary64)) (patch (.f64 eps #s(literal -1/6 binary64)) #<representation binary64>) () ())) ())
#s(alt (* -1/6 eps) (taylor 0 eps) (#s(alt (.f64 eps #s(literal -1/6 binary64)) (patch (.f64 eps #s(literal -1/6 binary64)) #<representation binary64>) () ())) ())
#s(alt (* -1/6 eps) (taylor 0 eps) (#s(alt (.f64 eps #s(literal -1/6 binary64)) (patch (.f64 eps #s(literal -1/6 binary64)) #<representation binary64>) () ())) ())
#s(alt (* -1/6 eps) (taylor 0 eps) (#s(alt (.f64 eps #s(literal -1/6 binary64)) (patch (.f64 eps #s(literal -1/6 binary64)) #<representation binary64>) () ())) ())
#s(alt (* -1/6 eps) (taylor inf eps) (#s(alt (.f64 eps #s(literal -1/6 binary64)) (patch (.f64 eps #s(literal -1/6 binary64)) #<representation binary64>) () ())) ())
#s(alt (* -1/6 eps) (taylor inf eps) (#s(alt (.f64 eps #s(literal -1/6 binary64)) (patch (.f64 eps #s(literal -1/6 binary64)) #<representation binary64>) () ())) ())
#s(alt (* -1/6 eps) (taylor inf eps) (#s(alt (.f64 eps #s(literal -1/6 binary64)) (patch (.f64 eps #s(literal -1/6 binary64)) #<representation binary64>) () ())) ())
#s(alt (* -1/6 eps) (taylor inf eps) (#s(alt (.f64 eps #s(literal -1/6 binary64)) (patch (.f64 eps #s(literal -1/6 binary64)) #<representation binary64>) () ())) ())
#s(alt (* -1/6 eps) (taylor -inf eps) (#s(alt (.f64 eps #s(literal -1/6 binary64)) (patch (.f64 eps #s(literal -1/6 binary64)) #<representation binary64>) () ())) ())
#s(alt (* -1/6 eps) (taylor -inf eps) (#s(alt (.f64 eps #s(literal -1/6 binary64)) (patch (.f64 eps #s(literal -1/6 binary64)) #<representation binary64>) () ())) ())
#s(alt (* -1/6 eps) (taylor -inf eps) (#s(alt (.f64 eps #s(literal -1/6 binary64)) (patch (.f64 eps #s(literal -1/6 binary64)) #<representation binary64>) () ())) ())
#s(alt (* -1/6 eps) (taylor -inf eps) (#s(alt (.f64 eps #s(literal -1/6 binary64)) (patch (.f64 eps #s(literal -1/6 binary64)) #<representation binary64>) () ())) ())
#s(alt (cos x) (taylor 0 eps) (#s(alt (.f64 (fma.f64 eps (.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64)) (cos.f64 x)) (patch (.f64 (fma.f64 eps (.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64)) (cos.f64 x)) #<representation binary64>) () ())) ())
#s(alt (+ (cos x) (* -1/6 (* (pow eps 2) (cos x)))) (taylor 0 eps) (#s(alt (.f64 (fma.f64 eps (.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64)) (cos.f64 x)) (patch (.f64 (fma.f64 eps (.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64)) (cos.f64 x)) #<representation binary64>) () ())) ())
#s(alt (+ (cos x) (* -1/6 (* (pow eps 2) (cos x)))) (taylor 0 eps) (#s(alt (.f64 (fma.f64 eps (.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64)) (cos.f64 x)) (patch (.f64 (fma.f64 eps (.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64)) (cos.f64 x)) #<representation binary64>) () ())) ())
#s(alt (+ (cos x) (* -1/6 (* (pow eps 2) (cos x)))) (taylor 0 eps) (#s(alt (.f64 (fma.f64 eps (.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64)) (cos.f64 x)) (patch (.f64 (fma.f64 eps (.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64)) (cos.f64 x)) #<representation binary64>) () ())) ())
#s(alt (* -1/6 (* (pow eps 2) (cos x))) (taylor inf eps) (#s(alt (.f64 (fma.f64 eps (.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64)) (cos.f64 x)) (patch (.f64 (fma.f64 eps (.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64)) (cos.f64 x)) #<representation binary64>) () ())) ())
#s(alt (* (pow eps 2) (+ (* -1/6 (cos x)) (/ (cos x) (pow eps 2)))) (taylor inf eps) (#s(alt (.f64 (fma.f64 eps (.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64)) (cos.f64 x)) (patch (.f64 (fma.f64 eps (.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64)) (cos.f64 x)) #<representation binary64>) () ())) ())
#s(alt (* (pow eps 2) (+ (* -1/6 (cos x)) (/ (cos x) (pow eps 2)))) (taylor inf eps) (#s(alt (.f64 (fma.f64 eps (.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64)) (cos.f64 x)) (patch (.f64 (fma.f64 eps (.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64)) (cos.f64 x)) #<representation binary64>) () ())) ())
#s(alt (* (pow eps 2) (+ (* -1/6 (cos x)) (/ (cos x) (pow eps 2)))) (taylor inf eps) (#s(alt (.f64 (fma.f64 eps (.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64)) (cos.f64 x)) (patch (.f64 (fma.f64 eps (.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64)) (cos.f64 x)) #<representation binary64>) () ())) ())
#s(alt (* -1/6 (* (pow eps 2) (cos x))) (taylor -inf eps) (#s(alt (.f64 (fma.f64 eps (.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64)) (cos.f64 x)) (patch (.f64 (fma.f64 eps (.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64)) (cos.f64 x)) #<representation binary64>) () ())) ())
#s(alt (* (pow eps 2) (+ (* -1/6 (cos x)) (/ (cos x) (pow eps 2)))) (taylor -inf eps) (#s(alt (.f64 (fma.f64 eps (.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64)) (cos.f64 x)) (patch (.f64 (fma.f64 eps (.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64)) (cos.f64 x)) #<representation binary64>) () ())) ())
#s(alt (* (pow eps 2) (+ (* -1/6 (cos x)) (/ (cos x) (pow eps 2)))) (taylor -inf eps) (#s(alt (.f64 (fma.f64 eps (.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64)) (cos.f64 x)) (patch (.f64 (fma.f64 eps (.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64)) (cos.f64 x)) #<representation binary64>) () ())) ())
#s(alt (* (pow eps 2) (+ (* -1/6 (cos x)) (/ (cos x) (pow eps 2)))) (taylor -inf eps) (#s(alt (.f64 (fma.f64 eps (.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64)) (cos.f64 x)) (patch (.f64 (fma.f64 eps (.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64)) (cos.f64 x)) #<representation binary64>) () ())) ())
#s(alt (+ 1 (* -1/6 (pow eps 2))) (taylor 0 x) (#s(alt (.f64 (fma.f64 eps (.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64)) (cos.f64 x)) (patch (.f64 (fma.f64 eps (.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64)) (cos.f64 x)) #<representation binary64>) () ())) ())
#s(alt (+ 1 (+ (* -1/2 (* (pow x 2) (+ 1 (* -1/6 (pow eps 2))))) (* -1/6 (pow eps 2)))) (taylor 0 x) (#s(alt (.f64 (fma.f64 eps (.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64)) (cos.f64 x)) (patch (.f64 (fma.f64 eps (.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64)) (cos.f64 x)) #<representation binary64>) () ())) ())
#s(alt (+ 1 (+ (* -1/6 (pow eps 2)) (* (pow x 2) (+ (* -1/2 (+ 1 (* -1/6 (pow eps 2)))) (* 1/24 (* (pow x 2) (+ 1 (* -1/6 (pow eps 2))))))))) (taylor 0 x) (#s(alt (.f64 (fma.f64 eps (.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64)) (cos.f64 x)) (patch (.f64 (fma.f64 eps (.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64)) (cos.f64 x)) #<representation binary64>) () ())) ())
#s(alt (+ 1 (+ (* -1/6 (pow eps 2)) (* (pow x 2) (+ (* -1/2 (+ 1 (* -1/6 (pow eps 2)))) (* (pow x 2) (+ (* -1/720 (* (pow x 2) (+ 1 (* -1/6 (pow eps 2))))) (* 1/24 (+ 1 (* -1/6 (pow eps 2)))))))))) (taylor 0 x) (#s(alt (.f64 (fma.f64 eps (.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64)) (cos.f64 x)) (patch (.f64 (fma.f64 eps (.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64)) (cos.f64 x)) #<representation binary64>) () ())) ())
#s(alt (* (cos x) (+ 1 (* -1/6 (pow eps 2)))) (taylor inf x) (#s(alt (.f64 (fma.f64 eps (.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64)) (cos.f64 x)) (patch (.f64 (fma.f64 eps (.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64)) (cos.f64 x)) #<representation binary64>) () ())) ())
#s(alt (* (cos x) (+ 1 (* -1/6 (pow eps 2)))) (taylor inf x) (#s(alt (.f64 (fma.f64 eps (.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64)) (cos.f64 x)) (patch (.f64 (fma.f64 eps (.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64)) (cos.f64 x)) #<representation binary64>) () ())) ())
#s(alt (* (cos x) (+ 1 (* -1/6 (pow eps 2)))) (taylor inf x) (#s(alt (.f64 (fma.f64 eps (.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64)) (cos.f64 x)) (patch (.f64 (fma.f64 eps (.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64)) (cos.f64 x)) #<representation binary64>) () ())) ())
#s(alt (* (cos x) (+ 1 (* -1/6 (pow eps 2)))) (taylor inf x) (#s(alt (.f64 (fma.f64 eps (.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64)) (cos.f64 x)) (patch (.f64 (fma.f64 eps (.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64)) (cos.f64 x)) #<representation binary64>) () ())) ())
#s(alt (* (cos x) (+ 1 (* -1/6 (pow eps 2)))) (taylor -inf x) (#s(alt (.f64 (fma.f64 eps (.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64)) (cos.f64 x)) (patch (.f64 (fma.f64 eps (.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64)) (cos.f64 x)) #<representation binary64>) () ())) ())
#s(alt (* (cos x) (+ 1 (* -1/6 (pow eps 2)))) (taylor -inf x) (#s(alt (.f64 (fma.f64 eps (.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64)) (cos.f64 x)) (patch (.f64 (fma.f64 eps (.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64)) (cos.f64 x)) #<representation binary64>) () ())) ())
#s(alt (* (cos x) (+ 1 (* -1/6 (pow eps 2)))) (taylor -inf x) (#s(alt (.f64 (fma.f64 eps (.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64)) (cos.f64 x)) (patch (.f64 (fma.f64 eps (.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64)) (cos.f64 x)) #<representation binary64>) () ())) ())
#s(alt (* (cos x) (+ 1 (* -1/6 (pow eps 2)))) (taylor -inf x) (#s(alt (.f64 (fma.f64 eps (.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64)) (cos.f64 x)) (patch (.f64 (fma.f64 eps (.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64)) (cos.f64 x)) #<representation binary64>) () ())) ())
#s(alt 1 (taylor 0 eps) (#s(alt (cos.f64 eps) (patch (cos.f64 eps) #<representation binary64>) () ())) ())
#s(alt (+ 1 (* -1/2 (pow eps 2))) (taylor 0 eps) (#s(alt (cos.f64 eps) (patch (cos.f64 eps) #<representation binary64>) () ())) ())
#s(alt (+ 1 (* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2))) (taylor 0 eps) (#s(alt (cos.f64 eps) (patch (cos.f64 eps) #<representation binary64>) () ())) ())
#s(alt (+ 1 (* (pow eps 2) (- (* (pow eps 2) (+ 1/24 (* -1/720 (pow eps 2)))) 1/2))) (taylor 0 eps) (#s(alt (cos.f64 eps) (patch (cos.f64 eps) #<representation binary64>) () ())) ())
#s(alt (cos eps) (taylor inf eps) (#s(alt (cos.f64 eps) (patch (cos.f64 eps) #<representation binary64>) () ())) ())
#s(alt (cos eps) (taylor inf eps) (#s(alt (cos.f64 eps) (patch (cos.f64 eps) #<representation binary64>) () ())) ())
#s(alt (cos eps) (taylor inf eps) (#s(alt (cos.f64 eps) (patch (cos.f64 eps) #<representation binary64>) () ())) ())
#s(alt (cos eps) (taylor inf eps) (#s(alt (cos.f64 eps) (patch (cos.f64 eps) #<representation binary64>) () ())) ())
#s(alt (cos eps) (taylor -inf eps) (#s(alt (cos.f64 eps) (patch (cos.f64 eps) #<representation binary64>) () ())) ())
#s(alt (cos eps) (taylor -inf eps) (#s(alt (cos.f64 eps) (patch (cos.f64 eps) #<representation binary64>) () ())) ())
#s(alt (cos eps) (taylor -inf eps) (#s(alt (cos.f64 eps) (patch (cos.f64 eps) #<representation binary64>) () ())) ())
#s(alt (cos eps) (taylor -inf eps) (#s(alt (cos.f64 eps) (patch (cos.f64 eps) #<representation binary64>) () ())) ())

Calls

111 calls:

Time	Variable		Point	Expression
4.0ms	x	@	inf	(+ (* (sin eps) (cos x)) (+ (* (sin x) (cos eps)) (sin (neg x))))
2.0ms	eps	@	inf	(+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x)))
1.0ms	x	@	inf	(* eps (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (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)

simplify330.0ms (2.1%)

Memory

0.8MiB live, 376.0MiB allocated

Algorithm

1×	egg-herbie

Rules

14 218×	`lower-fma.f64`
14 218×	`lower-fma.f32`
7 102×	`lower-*.f64`
7 102×	`lower-*.f32`
4 240×	`lower-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	471	4424
1	1463	4173
2	4278	4141
0	8553	3792

Stop Event

1×	iter limit
1×	node limit

Counts

444 → 421

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

Outputs
(* 1/2 eps)
(*.f64 #s(literal 1/2 binary64) eps)
(+ x (* 1/2 eps))
(fma.f64 #s(literal 1/2 binary64) eps x)
(+ x (* 1/2 eps))
(fma.f64 #s(literal 1/2 binary64) eps x)
(+ x (* 1/2 eps))
(fma.f64 #s(literal 1/2 binary64) eps x)
x
(* x (+ 1 (* 1/2 (/ eps x))))
(fma.f64 #s(literal 1/2 binary64) (/.f64 (*.f64 eps x) x) x)
(* x (+ 1 (* 1/2 (/ eps x))))
(fma.f64 #s(literal 1/2 binary64) (/.f64 (*.f64 eps x) x) x)
(* x (+ 1 (* 1/2 (/ eps x))))
(fma.f64 #s(literal 1/2 binary64) (/.f64 (*.f64 eps x) x) x)
x
(* -1 (* x (- (* -1/2 (/ eps x)) 1)))
(fma.f64 (/.f64 (*.f64 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 (cos.f64 x) (fma.f64 #s(literal -1/6 binary64) (.f64 eps eps) #s(literal 1 binary64)) (.f64 eps (.f64 #s(literal -1/2 binary64) (sin.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)))
(* 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 (- (* 2 x) (* -1 eps)))) (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 (- (* 2 x) (* -1 eps)))) (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 (- (* 2 x) (* -1 eps)))) (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 (- (* 2 x) (* -1 eps)))) (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)) (sin (* 1/2 eps))))
(.f64 #s(literal 2 binary64) (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (cos.f64 (.f64 #s(literal 1/2 binary64) eps))))
(+ (* -2 (* x (pow (sin (* 1/2 eps)) 2))) (* 2 (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))))
(fma.f64 x (.f64 #s(literal -2 binary64) (pow.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) #s(literal 2 binary64))) (.f64 #s(literal 2 binary64) (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (cos.f64 (.f64 #s(literal 1/2 binary64) eps)))))
(+ (* 2 (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) (* x (+ (* -2 (pow (sin (* 1/2 eps)) 2)) (* -1 (* x (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))))))
(fma.f64 x (-.f64 (.f64 #s(literal -2 binary64) (pow.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) #s(literal 2 binary64))) (.f64 x (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (cos.f64 (.f64 #s(literal 1/2 binary64) eps))))) (.f64 #s(literal 2 binary64) (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (cos.f64 (.f64 #s(literal 1/2 binary64) eps)))))
(+ (* 2 (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) (* x (+ (* -2 (pow (sin (* 1/2 eps)) 2)) (* x (+ (* -1 (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) (* 1/3 (* x (pow (sin (* 1/2 eps)) 2))))))))
(fma.f64 x (fma.f64 x (fma.f64 (pow.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) #s(literal 2 binary64)) (.f64 x #s(literal 1/3 binary64)) (.f64 (cos.f64 (.f64 #s(literal 1/2 binary64) eps)) (neg.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps))))) (.f64 #s(literal -2 binary64) (pow.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) #s(literal 2 binary64)))) (.f64 #s(literal 2 binary64) (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (cos.f64 (*.f64 #s(literal 1/2 binary64) eps)))))
(* 2 (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))))
(.f64 (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)))
(* 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)))
(* 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)))
(* 1/2 (* eps (cos x)))
(.f64 eps (.f64 #s(literal 1/2 binary64) (cos.f64 x)))
(* eps (+ (* -1/4 (* eps (sin x))) (* 1/2 (cos x))))
(.f64 eps (fma.f64 #s(literal 1/2 binary64) (cos.f64 x) (.f64 (*.f64 eps (sin.f64 x)) #s(literal -1/4 binary64))))
(* eps (+ (* 1/2 (cos x)) (* eps (+ (* -1/4 (sin x)) (* eps (+ (* -1/16 (cos x)) (* -1/48 (cos x))))))))
(.f64 eps (fma.f64 eps (fma.f64 eps (.f64 (cos.f64 x) #s(literal -1/12 binary64)) (.f64 (sin.f64 x) #s(literal -1/4 binary64))) (.f64 #s(literal 1/2 binary64) (cos.f64 x))))
(* eps (+ (* 1/2 (cos x)) (* eps (+ (* -1/4 (sin x)) (* eps (+ (* -1/16 (cos x)) (+ (* -1/48 (cos x)) (* 1/48 (* eps (sin x))))))))))
(.f64 eps (fma.f64 eps (fma.f64 eps (fma.f64 (.f64 eps (sin.f64 x)) #s(literal 1/48 binary64) (.f64 (cos.f64 x) #s(literal -1/12 binary64))) (.f64 (sin.f64 x) #s(literal -1/4 binary64))) (*.f64 #s(literal 1/2 binary64) (cos.f64 x))))
(* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps)))
(.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)))
(* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps)))
(.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)))
(* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps)))
(.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)))
(* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps)))
(.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)))
(* (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps)))
(.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)))
(* (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps)))
(.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)))
(* (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps)))
(.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)))
(* (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps)))
(.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)))
(* (cos (* 1/2 eps)) (sin (* 1/2 eps)))
(.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (cos.f64 (*.f64 #s(literal 1/2 binary64) eps)))
(+ (* -1 (* x (pow (sin (* 1/2 eps)) 2))) (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))
(-.f64 (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (cos.f64 (.f64 #s(literal 1/2 binary64) eps))) (.f64 x (pow.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) #s(literal 2 binary64))))
(+ (* x (+ (* -1 (pow (sin (* 1/2 eps)) 2)) (* -1/2 (* x (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))))) (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))
(fma.f64 x (-.f64 (.f64 (.f64 (.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))) (pow.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) #s(literal 2 binary64))) (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (cos.f64 (*.f64 #s(literal 1/2 binary64) eps))))
(+ (* x (+ (* -1 (pow (sin (* 1/2 eps)) 2)) (* x (+ (* -1/2 (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) (* 1/6 (* x (pow (sin (* 1/2 eps)) 2))))))) (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))
(fma.f64 x (fma.f64 x (fma.f64 #s(literal -1/2 binary64) (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (cos.f64 (.f64 #s(literal 1/2 binary64) eps))) (.f64 (pow.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) #s(literal 2 binary64)) (.f64 x #s(literal 1/6 binary64)))) (neg.f64 (pow.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) #s(literal 2 binary64)))) (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (cos.f64 (.f64 #s(literal 1/2 binary64) eps))))
(* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps)))
(.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)))
(* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps)))
(.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)))
(* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps)))
(.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)))
(* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps)))
(.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)))
(* (cos (* 1/2 (- eps (* -2 x)))) (sin (* 1/2 eps)))
(.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)))
(* (cos (* 1/2 (- eps (* -2 x)))) (sin (* 1/2 eps)))
(.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)))
(* (cos (* 1/2 (- eps (* -2 x)))) (sin (* 1/2 eps)))
(.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)))
(* (cos (* 1/2 (- eps (* -2 x)))) (sin (* 1/2 eps)))
(.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)))
(sin eps)
(sin.f64 eps)
(+ (sin eps) (* x (- (cos eps) 1)))
(fma.f64 x (+.f64 #s(literal -1 binary64) (cos.f64 eps)) (sin.f64 eps))
(+ (sin eps) (* x (- (+ (cos eps) (* -1/2 (* x (sin eps)))) 1)))
(fma.f64 x (+.f64 #s(literal -1 binary64) (fma.f64 x (*.f64 #s(literal -1/2 binary64) (sin.f64 eps)) (cos.f64 eps))) (sin.f64 eps))
(+ (sin eps) (* x (- (+ (cos eps) (* x (+ (* -1/2 (sin eps)) (* x (+ 1/6 (* -1/6 (cos eps))))))) 1)))
(fma.f64 x (fma.f64 x (fma.f64 x (fma.f64 (cos.f64 eps) #s(literal -1/6 binary64) #s(literal 1/6 binary64)) (*.f64 #s(literal -1/2 binary64) (sin.f64 eps))) (+.f64 #s(literal -1 binary64) (cos.f64 eps))) (sin.f64 eps))
(- (sin (+ eps x)) (sin x))
(-.f64 (sin.f64 (+.f64 eps x)) (sin.f64 x))
(- (sin (+ eps x)) (sin x))
(-.f64 (sin.f64 (+.f64 eps x)) (sin.f64 x))
(- (sin (+ eps x)) (sin x))
(-.f64 (sin.f64 (+.f64 eps x)) (sin.f64 x))
(- (sin (+ eps x)) (sin x))
(-.f64 (sin.f64 (+.f64 eps x)) (sin.f64 x))
(- (sin (- eps (* -1 x))) (sin x))
(-.f64 (sin.f64 (+.f64 eps x)) (sin.f64 x))
(- (sin (- eps (* -1 x))) (sin x))
(-.f64 (sin.f64 (+.f64 eps x)) (sin.f64 x))
(- (sin (- eps (* -1 x))) (sin x))
(-.f64 (sin.f64 (+.f64 eps x)) (sin.f64 x))
(- (sin (- eps (* -1 x))) (sin x))
(-.f64 (sin.f64 (+.f64 eps x)) (sin.f64 x))
(* eps (cos x))
(*.f64 eps (cos.f64 x))
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(.f64 eps (fma.f64 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 (cos.f64 x) (fma.f64 #s(literal -1/6 binary64) (.f64 eps eps) #s(literal 1 binary64)) (.f64 eps (.f64 #s(literal -1/2 binary64) (sin.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
(* eps (+ 1 (* -1/6 (pow eps 2))))
(fma.f64 eps (.f64 #s(literal -1/6 binary64) (.f64 eps eps)) eps)
(* eps (+ 1 (* (pow eps 2) (- (* 1/120 (pow eps 2)) 1/6))))
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(* -1/6 (* (pow eps 2) (cos x)))
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(* (pow eps 2) (+ (* -1/2 (/ (sin x) eps)) (* -1/6 (cos x))))
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(cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x))
(cos (* 1/2 (- (* 2 x) (* -1 eps))))
(cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x))
(* 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))
(* -1/6 eps)
(*.f64 eps #s(literal -1/6 binary64))
(* -1/6 eps)
(*.f64 eps #s(literal -1/6 binary64))
(* -1/6 eps)
(*.f64 eps #s(literal -1/6 binary64))
(* -1/6 eps)
(*.f64 eps #s(literal -1/6 binary64))
(* -1/6 eps)
(*.f64 eps #s(literal -1/6 binary64))
(* -1/6 eps)
(*.f64 eps #s(literal -1/6 binary64))
(* -1/6 eps)
(*.f64 eps #s(literal -1/6 binary64))
(* -1/6 eps)
(*.f64 eps #s(literal -1/6 binary64))
(* -1/6 eps)
(*.f64 eps #s(literal -1/6 binary64))
(* -1/6 eps)
(*.f64 eps #s(literal -1/6 binary64))
(* -1/6 eps)
(*.f64 eps #s(literal -1/6 binary64))
(* -1/6 eps)
(*.f64 eps #s(literal -1/6 binary64))
(cos x)
(cos.f64 x)
(+ (cos x) (* -1/6 (* (pow eps 2) (cos x))))
(.f64 (cos.f64 x) (fma.f64 #s(literal -1/6 binary64) (.f64 eps eps) #s(literal 1 binary64)))
(+ (cos x) (* -1/6 (* (pow eps 2) (cos x))))
(.f64 (cos.f64 x) (fma.f64 #s(literal -1/6 binary64) (.f64 eps eps) #s(literal 1 binary64)))
(+ (cos x) (* -1/6 (* (pow eps 2) (cos x))))
(.f64 (cos.f64 x) (fma.f64 #s(literal -1/6 binary64) (.f64 eps eps) #s(literal 1 binary64)))
(* -1/6 (* (pow eps 2) (cos x)))
(.f64 (cos.f64 x) (.f64 #s(literal -1/6 binary64) (*.f64 eps eps)))
(* (pow eps 2) (+ (* -1/6 (cos x)) (/ (cos x) (pow eps 2))))
(.f64 (.f64 eps eps) (fma.f64 (cos.f64 x) #s(literal -1/6 binary64) (/.f64 (cos.f64 x) (*.f64 eps eps))))
(* (pow eps 2) (+ (* -1/6 (cos x)) (/ (cos x) (pow eps 2))))
(.f64 (.f64 eps eps) (fma.f64 (cos.f64 x) #s(literal -1/6 binary64) (/.f64 (cos.f64 x) (*.f64 eps eps))))
(* (pow eps 2) (+ (* -1/6 (cos x)) (/ (cos x) (pow eps 2))))
(.f64 (.f64 eps eps) (fma.f64 (cos.f64 x) #s(literal -1/6 binary64) (/.f64 (cos.f64 x) (*.f64 eps eps))))
(* -1/6 (* (pow eps 2) (cos x)))
(.f64 (cos.f64 x) (.f64 #s(literal -1/6 binary64) (*.f64 eps eps)))
(* (pow eps 2) (+ (* -1/6 (cos x)) (/ (cos x) (pow eps 2))))
(.f64 (.f64 eps eps) (fma.f64 (cos.f64 x) #s(literal -1/6 binary64) (/.f64 (cos.f64 x) (*.f64 eps eps))))
(* (pow eps 2) (+ (* -1/6 (cos x)) (/ (cos x) (pow eps 2))))
(.f64 (.f64 eps eps) (fma.f64 (cos.f64 x) #s(literal -1/6 binary64) (/.f64 (cos.f64 x) (*.f64 eps eps))))
(* (pow eps 2) (+ (* -1/6 (cos x)) (/ (cos x) (pow eps 2))))
(.f64 (.f64 eps eps) (fma.f64 (cos.f64 x) #s(literal -1/6 binary64) (/.f64 (cos.f64 x) (*.f64 eps eps))))
(+ 1 (* -1/6 (pow eps 2)))
(fma.f64 #s(literal -1/6 binary64) (*.f64 eps eps) #s(literal 1 binary64))
(+ 1 (+ (* -1/2 (* (pow x 2) (+ 1 (* -1/6 (pow eps 2))))) (* -1/6 (pow eps 2))))
(fma.f64 eps (.f64 eps #s(literal -1/6 binary64)) (fma.f64 (.f64 x x) (fma.f64 (*.f64 eps eps) #s(literal 1/12 binary64) #s(literal -1/2 binary64)) #s(literal 1 binary64)))
(+ 1 (+ (* -1/6 (pow eps 2)) (* (pow x 2) (+ (* -1/2 (+ 1 (* -1/6 (pow eps 2)))) (* 1/24 (* (pow x 2) (+ 1 (* -1/6 (pow eps 2)))))))))
(fma.f64 (.f64 x x) (.f64 (fma.f64 #s(literal -1/6 binary64) (.f64 eps eps) #s(literal 1 binary64)) (fma.f64 #s(literal 1/24 binary64) (.f64 x x) #s(literal -1/2 binary64))) (fma.f64 #s(literal -1/6 binary64) (*.f64 eps eps) #s(literal 1 binary64)))
(+ 1 (+ (* -1/6 (pow eps 2)) (* (pow x 2) (+ (* -1/2 (+ 1 (* -1/6 (pow eps 2)))) (* (pow x 2) (+ (* -1/720 (* (pow x 2) (+ 1 (* -1/6 (pow eps 2))))) (* 1/24 (+ 1 (* -1/6 (pow eps 2))))))))))
(fma.f64 eps (.f64 eps #s(literal -1/6 binary64)) (fma.f64 x (.f64 x (fma.f64 (.f64 x x) (.f64 (fma.f64 #s(literal -1/6 binary64) (.f64 eps eps) #s(literal 1 binary64)) (fma.f64 (.f64 x x) #s(literal -1/720 binary64) #s(literal 1/24 binary64))) (fma.f64 (*.f64 eps eps) #s(literal 1/12 binary64) #s(literal -1/2 binary64)))) #s(literal 1 binary64)))
(* (cos x) (+ 1 (* -1/6 (pow eps 2))))
(.f64 (cos.f64 x) (fma.f64 #s(literal -1/6 binary64) (.f64 eps eps) #s(literal 1 binary64)))
(* (cos x) (+ 1 (* -1/6 (pow eps 2))))
(.f64 (cos.f64 x) (fma.f64 #s(literal -1/6 binary64) (.f64 eps eps) #s(literal 1 binary64)))
(* (cos x) (+ 1 (* -1/6 (pow eps 2))))
(.f64 (cos.f64 x) (fma.f64 #s(literal -1/6 binary64) (.f64 eps eps) #s(literal 1 binary64)))
(* (cos x) (+ 1 (* -1/6 (pow eps 2))))
(.f64 (cos.f64 x) (fma.f64 #s(literal -1/6 binary64) (.f64 eps eps) #s(literal 1 binary64)))
(* (cos x) (+ 1 (* -1/6 (pow eps 2))))
(.f64 (cos.f64 x) (fma.f64 #s(literal -1/6 binary64) (.f64 eps eps) #s(literal 1 binary64)))
(* (cos x) (+ 1 (* -1/6 (pow eps 2))))
(.f64 (cos.f64 x) (fma.f64 #s(literal -1/6 binary64) (.f64 eps eps) #s(literal 1 binary64)))
(* (cos x) (+ 1 (* -1/6 (pow eps 2))))
(.f64 (cos.f64 x) (fma.f64 #s(literal -1/6 binary64) (.f64 eps eps) #s(literal 1 binary64)))
(* (cos x) (+ 1 (* -1/6 (pow eps 2))))
(.f64 (cos.f64 x) (fma.f64 #s(literal -1/6 binary64) (.f64 eps eps) #s(literal 1 binary64)))
1
#s(literal 1 binary64)
(+ 1 (* -1/2 (pow eps 2)))
(fma.f64 eps (*.f64 eps #s(literal -1/2 binary64)) #s(literal 1 binary64))
(+ 1 (* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2)))
(fma.f64 eps (.f64 eps (fma.f64 eps (.f64 eps #s(literal 1/24 binary64)) #s(literal -1/2 binary64))) #s(literal 1 binary64))
(+ 1 (* (pow eps 2) (- (* (pow eps 2) (+ 1/24 (* -1/720 (pow eps 2)))) 1/2)))
(fma.f64 eps (.f64 eps (fma.f64 (.f64 eps eps) (fma.f64 eps (*.f64 eps #s(literal -1/720 binary64)) #s(literal 1/24 binary64)) #s(literal -1/2 binary64))) #s(literal 1 binary64))
(cos eps)
(cos.f64 eps)
(cos eps)
(cos.f64 eps)
(cos eps)
(cos.f64 eps)
(cos eps)
(cos.f64 eps)
(cos eps)
(cos.f64 eps)
(cos eps)
(cos.f64 eps)
(cos eps)
(cos.f64 eps)
(cos eps)
(cos.f64 eps)

rewrite333.0ms (2.2%)

Memory

-2.2MiB live, 411.9MiB allocated

Rules

4 696×	`lower-*.f32`
4 676×	`lower-*.f64`
4 068×	`lower-/.f64`
4 068×	`lower-/.f32`
3 484×	`lower-fma.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	43	201
0	78	181
1	264	181
2	2190	181
0	8427	181

Stop Event

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

Counts

23 → 550

Calls

Call 1

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

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)))
(/.f64 (.f64 #s(literal 1/2 binary64) (fma.f64 eps (.f64 eps eps) (.f64 (.f64 x (.f64 x x)) #s(literal 8 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 (*.f64 x #s(literal 2 binary64)) eps))
(/.f64 (.f64 (fma.f64 eps (.f64 eps eps) (.f64 (.f64 x (.f64 x x)) #s(literal 8 binary64))) #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)) (-.f64 (*.f64 x #s(literal 2 binary64)) eps))
(/.f64 (neg.f64 (.f64 #s(literal 1/2 binary64) (fma.f64 eps (.f64 eps eps) (.f64 (.f64 x (.f64 x x)) #s(literal 8 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 #s(literal 1/2 binary64) (-.f64 (.f64 (.f64 x x) #s(literal 4 binary64)) (.f64 eps eps)))) (neg.f64 (-.f64 (*.f64 x #s(literal 2 binary64)) eps)))
(/.f64 (neg.f64 (.f64 (fma.f64 eps (.f64 eps eps) (.f64 (.f64 x (.f64 x x)) #s(literal 8 binary64))) #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 (-.f64 (*.f64 x #s(literal 2 binary64)) eps)))
(*.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))
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 #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 (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 (-.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 (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 (.f64 eps (.f64 eps eps)) #s(literal 0 binary64))) (neg.f64 (*.f64 eps 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 (.f64 #s(literal 2 binary64) (+.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) (-.f64 eps (fma.f64 x #s(literal 2 binary64) eps)))) (sin.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 eps (fma.f64 x #s(literal 2 binary64) eps)))))) #s(literal 2 binary64))
(/.f64 (.f64 (+.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) (-.f64 eps (fma.f64 x #s(literal 2 binary64) eps)))) (sin.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 eps (fma.f64 x #s(literal 2 binary64) eps))))) #s(literal 2 binary64)) #s(literal 2 binary64))
(/.f64 (neg.f64 (.f64 #s(literal 2 binary64) (+.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) (-.f64 eps (fma.f64 x #s(literal 2 binary64) eps)))) (sin.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 eps (fma.f64 x #s(literal 2 binary64) eps))))))) #s(literal -2 binary64))
(/.f64 (neg.f64 (.f64 (+.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) (-.f64 eps (fma.f64 x #s(literal 2 binary64) eps)))) (sin.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 eps (fma.f64 x #s(literal 2 binary64) eps))))) #s(literal 2 binary64))) #s(literal -2 binary64))
(.f64 #s(literal 2 binary64) (.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (cos.f64 (.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)))))
(.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (.f64 #s(literal 2 binary64) (cos.f64 (.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)))))
(.f64 (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))) #s(literal 2 binary64)))
(.f64 (.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (cos.f64 (.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)))) #s(literal 2 binary64))
(.f64 (.f64 #s(literal 2 binary64) (cos.f64 (.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)))) (sin.f64 (.f64 eps #s(literal 1/2 binary64))))
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(.f64 x (.f64 x x))
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(/.f64 (neg.f64 (.f64 (.f64 eps (.f64 eps eps)) #s(literal -1/6 binary64))) (neg.f64 (.f64 eps eps)))
(*.f64 eps #s(literal -1/6 binary64))
(*.f64 #s(literal -1/6 binary64) eps)
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(fma.f64 #s(literal 1 binary64) (cos.f64 x) (.f64 (.f64 eps (*.f64 eps #s(literal -1/6 binary64))) (cos.f64 x)))
(fma.f64 (cos.f64 x) #s(literal 1 binary64) (.f64 (cos.f64 x) (.f64 eps (*.f64 eps #s(literal -1/6 binary64)))))
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(cos.f64 eps)
(-.f64 (.f64 (cos.f64 eps) #s(literal 1 binary64)) (.f64 (sin.f64 eps) #s(literal 0 binary64)))
(-.f64 (.f64 #s(literal 1 binary64) (cos.f64 eps)) (.f64 #s(literal 0 binary64) (sin.f64 eps)))
(fma.f64 (cos.f64 eps) #s(literal 1 binary64) (*.f64 (sin.f64 eps) #s(literal 0 binary64)))
(fma.f64 (cos.f64 eps) (cos.f64 (/.f64 #s(literal 0 binary64) eps)) (*.f64 (sin.f64 eps) (sin.f64 (/.f64 #s(literal 0 binary64) eps))))

eval127.0ms (0.8%)

Memory: 9.4MiB live, 234.0MiB allocated
Compiler: Compiled 29 047 to 2 286 computations (92.1% saved)

prune150.0ms (1%)

Memory

3.6MiB live, 299.4MiB allocated

Pruning

23 alts after pruning (20 fresh and 3 done)

	Pruned	Kept	Total
New	985	17	1 002
Fresh	1	3	4
Picked	3	2	5
Done	0	1	1
Total	989	23	1 012

Accuracy

100.0%

Counts

1 012 → 23

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	99.5%	(fma.f64 (sin.f64 eps) (cos.f64 x) (fma.f64 (sin.f64 x) (cos.f64 eps) (sin.f64 (neg.f64 x))))
▶	99.7%	(fma.f64 (sin.f64 eps) (cos.f64 x) #s(approx (+ (* (sin x) (cos eps)) (sin (neg x))) (fma.f64 (.f64 eps eps) (fma.f64 (.f64 eps eps) (.f64 (sin.f64 x) (fma.f64 eps (.f64 eps #s(literal -1/720 binary64)) #s(literal 1/24 binary64))) (*.f64 #s(literal -1/2 binary64) (sin.f64 x))) #s(literal 0 binary64))))
	99.6%	(fma.f64 (sin.f64 eps) (cos.f64 x) #s(approx (+ (* (sin x) (cos eps)) (sin (neg x))) (fma.f64 (.f64 eps eps) (.f64 (sin.f64 x) (fma.f64 eps (*.f64 eps #s(literal 1/24 binary64)) #s(literal -1/2 binary64))) #s(literal 0 binary64))))
✓	62.9%	(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
	38.7%	(.f64 (.f64 (sin.f64 (.f64 (.f64 (.f64 eps (.f64 eps eps)) (/.f64 #s(literal 1 binary64) (.f64 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))
	57.6%	(.f64 (.f64 (sin.f64 (.f64 (.f64 (.f64 eps eps) (/.f64 #s(literal 1 binary64) 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))
	99.5%	(.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))
	99.4%	(.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))
	99.3%	(.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))
▶	98.9%	(.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))
	99.6%	(.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))
	38.6%	#s(approx (- (sin (+ x eps)) (sin x)) (/.f64 (fma.f64 (.f64 (.f64 (fma.f64 eps (.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64)) (cos.f64 x)) (.f64 eps eps)) eps (.f64 eps (.f64 (.f64 eps (.f64 #s(literal -1/2 binary64) (sin.f64 x))) (.f64 eps eps)))) (.f64 eps eps)))
	99.5%	#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))))))
✓	99.3%	#s(approx (- (sin (+ x eps)) (sin 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)))))
▶	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))))
	98.4%	#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 eps (cos.f64 x)))
	97.1%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 eps #s(approx (+ ( eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x))) (fma.f64 x (fma.f64 x (fma.f64 eps (.f64 x #s(literal 1/12 binary64)) (fma.f64 (.f64 eps eps) #s(literal 1/12 binary64) #s(literal -1/2 binary64))) (.f64 eps #s(literal -1/2 binary64))) (fma.f64 #s(literal -1/6 binary64) (.f64 eps eps) #s(literal 1 binary64))))))
	96.4%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 eps #s(approx (+ ( eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x))) (fma.f64 eps (.f64 x #s(literal -1/2 binary64)) (fma.f64 #s(literal -1/6 binary64) (.f64 eps eps) #s(literal 1 binary64))))))
▶	97.1%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 eps #s(approx (+ ( eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x))) (fma.f64 eps (.f64 eps #s(literal -1/6 binary64)) (fma.f64 x (fma.f64 x (fma.f64 (.f64 eps eps) #s(literal 1/12 binary64) #s(literal -1/2 binary64)) (*.f64 eps #s(literal -1/2 binary64))) #s(literal 1 binary64))))))
	96.4%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 eps #s(approx (+ ( eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x))) (fma.f64 #s(literal -1/6 binary64) (*.f64 eps eps) #s(literal 1 binary64)))))
	97.1%	#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* eps (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x)))) (fma.f64 eps (fma.f64 #s(literal -1/6 binary64) (.f64 eps eps) #s(literal 1 binary64)) (.f64 (.f64 x #s(literal -1/2 binary64)) (.f64 eps (fma.f64 x (fma.f64 #s(literal -1/6 binary64) (*.f64 eps eps) #s(literal 1 binary64)) eps))))))
	96.4%	#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* eps (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x)))) (fma.f64 eps (fma.f64 #s(literal -1/6 binary64) (.f64 eps eps) #s(literal 1 binary64)) (.f64 x (.f64 #s(literal -1/2 binary64) (.f64 eps eps))))))
▶	5.3%	#s(approx (+ (* (sin eps) (cos x)) (+ (* (sin x) (cos eps)) (sin (neg x)))) #s(literal 0 binary64))

Compiler

Compiled 888 to 521 computations (41.3% saved)

simplify267.0ms (1.7%)

Memory

-7.9MiB live, 300.9MiB 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 (* (+ eps 0) 1/2)) (*.f64 #s(literal 1/2 binary64) eps))
cost-diff	0	(.f64 #s(approx (sin ( (+ eps 0) 1/2)) (.f64 #s(literal 1/2 binary64) eps)) (cos.f64 (.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64))))
cost-diff	0	(.f64 (.f64 #s(approx (sin (* (+ eps 0) 1/2)) (.f64 #s(literal 1/2 binary64) eps)) (cos.f64 (.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)))) #s(literal 2 binary64))
cost-diff	320	(*.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64))
cost-diff	0	#s(approx (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x))) (fma.f64 eps (.f64 eps #s(literal -1/6 binary64)) (fma.f64 x (fma.f64 x (fma.f64 (.f64 eps eps) #s(literal 1/12 binary64) #s(literal -1/2 binary64)) (*.f64 eps #s(literal -1/2 binary64))) #s(literal 1 binary64))))
cost-diff	0	(.f64 eps #s(approx (+ ( eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x))) (fma.f64 eps (.f64 eps #s(literal -1/6 binary64)) (fma.f64 x (fma.f64 x (fma.f64 (.f64 eps eps) #s(literal 1/12 binary64) #s(literal -1/2 binary64)) (*.f64 eps #s(literal -1/2 binary64))) #s(literal 1 binary64)))))
cost-diff	0	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 eps #s(approx (+ ( eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x))) (fma.f64 eps (.f64 eps #s(literal -1/6 binary64)) (fma.f64 x (fma.f64 x (fma.f64 (.f64 eps eps) #s(literal 1/12 binary64) #s(literal -1/2 binary64)) (*.f64 eps #s(literal -1/2 binary64))) #s(literal 1 binary64))))))
cost-diff	192	(fma.f64 eps (.f64 eps #s(literal -1/6 binary64)) (fma.f64 x (fma.f64 x (fma.f64 (.f64 eps eps) #s(literal 1/12 binary64) #s(literal -1/2 binary64)) (*.f64 eps #s(literal -1/2 binary64))) #s(literal 1 binary64)))
cost-diff	0	#s(approx (+ (* (sin eps) (cos x)) (+ (* (sin x) (cos eps)) (sin (neg x)))) #s(literal 0 binary64))
cost-diff	0	(sin.f64 eps)
cost-diff	0	(fma.f64 (sin.f64 eps) (cos.f64 x) #s(approx (+ (* (sin x) (cos eps)) (sin (neg x))) (fma.f64 (.f64 eps eps) (fma.f64 (.f64 eps eps) (.f64 (sin.f64 x) (fma.f64 eps (.f64 eps #s(literal -1/720 binary64)) #s(literal 1/24 binary64))) (*.f64 #s(literal -1/2 binary64) (sin.f64 x))) #s(literal 0 binary64))))
cost-diff	64	(fma.f64 (.f64 eps eps) (fma.f64 (.f64 eps eps) (.f64 (sin.f64 x) (fma.f64 eps (.f64 eps #s(literal -1/720 binary64)) #s(literal 1/24 binary64))) (*.f64 #s(literal -1/2 binary64) (sin.f64 x))) #s(literal 0 binary64))
cost-diff	6720	(fma.f64 (.f64 eps eps) (.f64 (sin.f64 x) (fma.f64 eps (.f64 eps #s(literal -1/720 binary64)) #s(literal 1/24 binary64))) (.f64 #s(literal -1/2 binary64) (sin.f64 x)))

Rules

10 540×	`lower-fma.f32`
10 520×	`lower-fma.f64`
3 430×	`lower-*.f32`
3 406×	`lower-*.f64`
2 608×	`lower-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	66	470
0	104	461
1	198	458
2	508	447
3	1433	440
4	2836	440
5	3221	440
6	3500	440
7	3712	440
8	4342	440
9	7610	440
0	8425	421

Stop Event

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

Calls

Call 1

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

localize342.0ms (2.2%)

Memory

4.3MiB live, 443.3MiB allocated

Localize:

Found 17 expressions of interest:

New	Metric	Score
accuracy	0	(cos.f64 x)
accuracy	0.00390625	(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	0.638556655459079	#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	(*.f64 #s(literal 1/2 binary64) eps)
accuracy	0.0234375	(.f64 #s(approx (sin ( (+ eps 0) 1/2)) (.f64 #s(literal 1/2 binary64) eps)) (cos.f64 (.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64))))
accuracy	0.2232612867848975	(cos.f64 (*.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)))
accuracy	0.5981804633793378	#s(approx (sin (* (+ eps 0) 1/2)) (*.f64 #s(literal 1/2 binary64) eps))
accuracy	0.03515625	(fma.f64 x (fma.f64 (.f64 eps eps) #s(literal 1/12 binary64) #s(literal -1/2 binary64)) (.f64 eps #s(literal -1/2 binary64)))
accuracy	0.34765625	(*.f64 eps #s(literal -1/6 binary64))
accuracy	0.447769100952185	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 eps #s(approx (+ ( eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x))) (fma.f64 eps (.f64 eps #s(literal -1/6 binary64)) (fma.f64 x (fma.f64 x (fma.f64 (.f64 eps eps) #s(literal 1/12 binary64) #s(literal -1/2 binary64)) (*.f64 eps #s(literal -1/2 binary64))) #s(literal 1 binary64))))))
accuracy	1.8720939710084297	#s(approx (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x))) (fma.f64 eps (.f64 eps #s(literal -1/6 binary64)) (fma.f64 x (fma.f64 x (fma.f64 (.f64 eps eps) #s(literal 1/12 binary64) #s(literal -1/2 binary64)) (*.f64 eps #s(literal -1/2 binary64))) #s(literal 1 binary64))))
accuracy	60.60863487303139	#s(approx (+ (* (sin eps) (cos x)) (+ (* (sin x) (cos eps)) (sin (neg x)))) #s(literal 0 binary64))
accuracy	0.12109375	(fma.f64 (.f64 eps eps) (fma.f64 (.f64 eps eps) (.f64 (sin.f64 x) (fma.f64 eps (.f64 eps #s(literal -1/720 binary64)) #s(literal 1/24 binary64))) (*.f64 #s(literal -1/2 binary64) (sin.f64 x))) #s(literal 0 binary64))
accuracy	0.1611416223852303	#s(approx (+ (* (sin x) (cos eps)) (sin (neg x))) (fma.f64 (.f64 eps eps) (fma.f64 (.f64 eps eps) (.f64 (sin.f64 x) (fma.f64 eps (.f64 eps #s(literal -1/720 binary64)) #s(literal 1/24 binary64))) (*.f64 #s(literal -1/2 binary64) (sin.f64 x))) #s(literal 0 binary64)))
accuracy	0.20703125	(*.f64 eps #s(literal -1/720 binary64))
accuracy	0.33984375	(.f64 (sin.f64 x) (fma.f64 eps (.f64 eps #s(literal -1/720 binary64)) #s(literal 1/24 binary64)))

Samples

226.0ms	228×	1	valid
28.0ms	19×	2	valid
4.0ms	1×	3	valid
4.0ms	8×	0	valid

Compiler

Compiled 346 to 63 computations (81.8% saved)

Precisions

Click to see histograms. Total time spent on operations: 213.0ms

ival-mult: 85.0ms (39.8% of total)

adjust: 32.0ms (15% of total)

ival-add: 30.0ms (14.1% of total)

ival-sin: 26.0ms (12.2% of total)

const: 22.0ms (10.3% of total)

ival-cos: 15.0ms (7% of total)

ival-sub: 2.0ms (0.9% of total)

exact: 1.0ms (0.5% of total)

ival-neg: 1.0ms (0.5% of total)

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

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

series46.0ms (0.3%)

Memory

7.5MiB live, 82.9MiB allocated

Counts

25 → 516

Calls

Call 1

Inputs
#s(alt (fma.f64 (.f64 eps eps) (.f64 (sin.f64 x) (fma.f64 eps (.f64 eps #s(literal -1/720 binary64)) #s(literal 1/24 binary64))) (.f64 #s(literal -1/2 binary64) (sin.f64 x))) (patch (fma.f64 (.f64 eps eps) (.f64 (sin.f64 x) (fma.f64 eps (.f64 eps #s(literal -1/720 binary64)) #s(literal 1/24 binary64))) (.f64 #s(literal -1/2 binary64) (sin.f64 x))) #<representation binary64>) () ())
#s(alt (fma.f64 (.f64 eps eps) (fma.f64 (.f64 eps eps) (.f64 (sin.f64 x) (fma.f64 eps (.f64 eps #s(literal -1/720 binary64)) #s(literal 1/24 binary64))) (.f64 #s(literal -1/2 binary64) (sin.f64 x))) #s(literal 0 binary64)) (patch (fma.f64 (.f64 eps eps) (fma.f64 (.f64 eps eps) (.f64 (sin.f64 x) (fma.f64 eps (.f64 eps #s(literal -1/720 binary64)) #s(literal 1/24 binary64))) (.f64 #s(literal -1/2 binary64) (sin.f64 x))) #s(literal 0 binary64)) #<representation binary64>) () ())
#s(alt (fma.f64 (sin.f64 eps) (cos.f64 x) #s(approx (+ (* (sin x) (cos eps)) (sin (neg x))) (fma.f64 (.f64 eps eps) (fma.f64 (.f64 eps eps) (.f64 (sin.f64 x) (fma.f64 eps (.f64 eps #s(literal -1/720 binary64)) #s(literal 1/24 binary64))) (.f64 #s(literal -1/2 binary64) (sin.f64 x))) #s(literal 0 binary64)))) (patch (fma.f64 (sin.f64 eps) (cos.f64 x) #s(approx (+ ( (sin x) (cos eps)) (sin (neg x))) (fma.f64 (.f64 eps eps) (fma.f64 (.f64 eps eps) (.f64 (sin.f64 x) (fma.f64 eps (.f64 eps #s(literal -1/720 binary64)) #s(literal 1/24 binary64))) (*.f64 #s(literal -1/2 binary64) (sin.f64 x))) #s(literal 0 binary64)))) #<representation binary64>) () ())
#s(alt (sin.f64 eps) (patch (sin.f64 eps) #<representation binary64>) () ())
#s(alt #s(approx (+ (* (sin eps) (cos x)) (+ (* (sin x) (cos eps)) (sin (neg x)))) #s(literal 0 binary64)) (patch #s(approx (+ (* (sin eps) (cos x)) (+ (* (sin x) (cos eps)) (sin (neg x)))) #s(literal 0 binary64)) #<representation binary64>) () ())
#s(alt (fma.f64 eps (.f64 eps #s(literal -1/6 binary64)) (fma.f64 x (fma.f64 x (fma.f64 (.f64 eps eps) #s(literal 1/12 binary64) #s(literal -1/2 binary64)) (.f64 eps #s(literal -1/2 binary64))) #s(literal 1 binary64))) (patch (fma.f64 eps (.f64 eps #s(literal -1/6 binary64)) (fma.f64 x (fma.f64 x (fma.f64 (.f64 eps eps) #s(literal 1/12 binary64) #s(literal -1/2 binary64)) (.f64 eps #s(literal -1/2 binary64))) #s(literal 1 binary64))) #<representation binary64>) () ())
#s(alt #s(approx (- (sin (+ x eps)) (sin x)) (.f64 eps #s(approx (+ ( eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x))) (fma.f64 eps (.f64 eps #s(literal -1/6 binary64)) (fma.f64 x (fma.f64 x (fma.f64 (.f64 eps eps) #s(literal 1/12 binary64) #s(literal -1/2 binary64)) (.f64 eps #s(literal -1/2 binary64))) #s(literal 1 binary64)))))) (patch #s(approx (- (sin (+ x eps)) (sin x)) (.f64 eps #s(approx (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x))) (fma.f64 eps (.f64 eps #s(literal -1/6 binary64)) (fma.f64 x (fma.f64 x (fma.f64 (.f64 eps eps) #s(literal 1/12 binary64) #s(literal -1/2 binary64)) (*.f64 eps #s(literal -1/2 binary64))) #s(literal 1 binary64)))))) #<representation binary64>) () ())
#s(alt (.f64 eps #s(approx (+ ( eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x))) (fma.f64 eps (.f64 eps #s(literal -1/6 binary64)) (fma.f64 x (fma.f64 x (fma.f64 (.f64 eps eps) #s(literal 1/12 binary64) #s(literal -1/2 binary64)) (.f64 eps #s(literal -1/2 binary64))) #s(literal 1 binary64))))) (patch (.f64 eps #s(approx (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x))) (fma.f64 eps (.f64 eps #s(literal -1/6 binary64)) (fma.f64 x (fma.f64 x (fma.f64 (.f64 eps eps) #s(literal 1/12 binary64) #s(literal -1/2 binary64)) (*.f64 eps #s(literal -1/2 binary64))) #s(literal 1 binary64))))) #<representation binary64>) () ())
#s(alt #s(approx (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x))) (fma.f64 eps (.f64 eps #s(literal -1/6 binary64)) (fma.f64 x (fma.f64 x (fma.f64 (.f64 eps eps) #s(literal 1/12 binary64) #s(literal -1/2 binary64)) (.f64 eps #s(literal -1/2 binary64))) #s(literal 1 binary64)))) (patch #s(approx (+ ( eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x))) (fma.f64 eps (.f64 eps #s(literal -1/6 binary64)) (fma.f64 x (fma.f64 x (fma.f64 (.f64 eps eps) #s(literal 1/12 binary64) #s(literal -1/2 binary64)) (*.f64 eps #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 #s(literal 1/2 binary64) eps)) (cos.f64 (.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)))) #s(literal 2 binary64)) (patch (.f64 (.f64 #s(approx (sin (* (+ eps 0) 1/2)) (.f64 #s(literal 1/2 binary64) eps)) (cos.f64 (.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)))) #s(literal 2 binary64)) #<representation binary64>) () ())
#s(alt (.f64 #s(approx (sin ( (+ eps 0) 1/2)) (.f64 #s(literal 1/2 binary64) eps)) (cos.f64 (.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)))) (patch (.f64 #s(approx (sin ( (+ eps 0) 1/2)) (.f64 #s(literal 1/2 binary64) eps)) (cos.f64 (.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)))) #<representation binary64>) () ())
#s(alt #s(approx (sin (* (+ eps 0) 1/2)) (.f64 #s(literal 1/2 binary64) eps)) (patch #s(approx (sin ( (+ eps 0) 1/2)) (*.f64 #s(literal 1/2 binary64) eps)) #<representation binary64>) () ())
#s(alt #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 (.f64 (sin.f64 x) (fma.f64 eps (.f64 eps #s(literal -1/720 binary64)) #s(literal 1/24 binary64))) (patch (.f64 (sin.f64 x) (fma.f64 eps (.f64 eps #s(literal -1/720 binary64)) #s(literal 1/24 binary64))) #<representation binary64>) () ())
#s(alt (.f64 eps #s(literal -1/720 binary64)) (patch (.f64 eps #s(literal -1/720 binary64)) #<representation binary64>) () ())
#s(alt #s(approx (+ (* (sin x) (cos eps)) (sin (neg x))) (fma.f64 (.f64 eps eps) (fma.f64 (.f64 eps eps) (.f64 (sin.f64 x) (fma.f64 eps (.f64 eps #s(literal -1/720 binary64)) #s(literal 1/24 binary64))) (.f64 #s(literal -1/2 binary64) (sin.f64 x))) #s(literal 0 binary64))) (patch #s(approx (+ ( (sin x) (cos eps)) (sin (neg x))) (fma.f64 (.f64 eps eps) (fma.f64 (.f64 eps eps) (.f64 (sin.f64 x) (fma.f64 eps (.f64 eps #s(literal -1/720 binary64)) #s(literal 1/24 binary64))) (*.f64 #s(literal -1/2 binary64) (sin.f64 x))) #s(literal 0 binary64))) #<representation binary64>) () ())
#s(alt (.f64 eps #s(literal -1/6 binary64)) (patch (.f64 eps #s(literal -1/6 binary64)) #<representation binary64>) () ())
#s(alt (fma.f64 x (fma.f64 (.f64 eps eps) #s(literal 1/12 binary64) #s(literal -1/2 binary64)) (.f64 eps #s(literal -1/2 binary64))) (patch (fma.f64 x (fma.f64 (.f64 eps eps) #s(literal 1/12 binary64) #s(literal -1/2 binary64)) (.f64 eps #s(literal -1/2 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 #s(literal 1/2 binary64) eps) (patch (.f64 #s(literal 1/2 binary64) eps) #<representation binary64>) () ())
#s(alt (cos.f64 x) (patch (cos.f64 x) #<representation binary64>) () ())

Outputs
#s(alt (* -1/2 (sin x)) (taylor 0 eps) (#s(alt (fma.f64 (.f64 eps eps) (.f64 (sin.f64 x) (fma.f64 eps (.f64 eps #s(literal -1/720 binary64)) #s(literal 1/24 binary64))) (.f64 #s(literal -1/2 binary64) (sin.f64 x))) (patch (fma.f64 (.f64 eps eps) (.f64 (sin.f64 x) (fma.f64 eps (.f64 eps #s(literal -1/720 binary64)) #s(literal 1/24 binary64))) (.f64 #s(literal -1/2 binary64) (sin.f64 x))) #<representation binary64>) () ())) ())
#s(alt (+ (* -1/2 (sin x)) (* 1/24 (* (pow eps 2) (sin x)))) (taylor 0 eps) (#s(alt (fma.f64 (.f64 eps eps) (.f64 (sin.f64 x) (fma.f64 eps (.f64 eps #s(literal -1/720 binary64)) #s(literal 1/24 binary64))) (.f64 #s(literal -1/2 binary64) (sin.f64 x))) (patch (fma.f64 (.f64 eps eps) (.f64 (sin.f64 x) (fma.f64 eps (.f64 eps #s(literal -1/720 binary64)) #s(literal 1/24 binary64))) (.f64 #s(literal -1/2 binary64) (sin.f64 x))) #<representation binary64>) () ())) ())
#s(alt (+ (* -1/2 (sin x)) (* (pow eps 2) (+ (* -1/720 (* (pow eps 2) (sin x))) (* 1/24 (sin x))))) (taylor 0 eps) (#s(alt (fma.f64 (.f64 eps eps) (.f64 (sin.f64 x) (fma.f64 eps (.f64 eps #s(literal -1/720 binary64)) #s(literal 1/24 binary64))) (.f64 #s(literal -1/2 binary64) (sin.f64 x))) (patch (fma.f64 (.f64 eps eps) (.f64 (sin.f64 x) (fma.f64 eps (.f64 eps #s(literal -1/720 binary64)) #s(literal 1/24 binary64))) (.f64 #s(literal -1/2 binary64) (sin.f64 x))) #<representation binary64>) () ())) ())
#s(alt (+ (* -1/2 (sin x)) (* (pow eps 2) (+ (* -1/720 (* (pow eps 2) (sin x))) (* 1/24 (sin x))))) (taylor 0 eps) (#s(alt (fma.f64 (.f64 eps eps) (.f64 (sin.f64 x) (fma.f64 eps (.f64 eps #s(literal -1/720 binary64)) #s(literal 1/24 binary64))) (.f64 #s(literal -1/2 binary64) (sin.f64 x))) (patch (fma.f64 (.f64 eps eps) (.f64 (sin.f64 x) (fma.f64 eps (.f64 eps #s(literal -1/720 binary64)) #s(literal 1/24 binary64))) (.f64 #s(literal -1/2 binary64) (sin.f64 x))) #<representation binary64>) () ())) ())
#s(alt (* -1/720 (* (pow eps 4) (sin x))) (taylor inf eps) (#s(alt (fma.f64 (.f64 eps eps) (.f64 (sin.f64 x) (fma.f64 eps (.f64 eps #s(literal -1/720 binary64)) #s(literal 1/24 binary64))) (.f64 #s(literal -1/2 binary64) (sin.f64 x))) (patch (fma.f64 (.f64 eps eps) (.f64 (sin.f64 x) (fma.f64 eps (.f64 eps #s(literal -1/720 binary64)) #s(literal 1/24 binary64))) (.f64 #s(literal -1/2 binary64) (sin.f64 x))) #<representation binary64>) () ())) ())
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#s(alt (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (taylor -inf eps) (#s(alt (cos.f64 (.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64))) (patch (cos.f64 (.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64))) #<representation binary64>) () ())) ())
#s(alt (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (taylor -inf eps) (#s(alt (cos.f64 (.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64))) (patch (cos.f64 (.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64))) #<representation binary64>) () ())) ())
#s(alt (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (taylor -inf eps) (#s(alt (cos.f64 (.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64))) (patch (cos.f64 (.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64))) #<representation binary64>) () ())) ())
#s(alt (* 1/2 eps) (taylor 0 eps) (#s(alt (.f64 #s(literal 1/2 binary64) eps) (patch (.f64 #s(literal 1/2 binary64) eps) #<representation binary64>) () ())) ())
#s(alt (* 1/2 eps) (taylor 0 eps) (#s(alt (.f64 #s(literal 1/2 binary64) eps) (patch (.f64 #s(literal 1/2 binary64) eps) #<representation binary64>) () ())) ())
#s(alt (* 1/2 eps) (taylor 0 eps) (#s(alt (.f64 #s(literal 1/2 binary64) eps) (patch (.f64 #s(literal 1/2 binary64) eps) #<representation binary64>) () ())) ())
#s(alt (* 1/2 eps) (taylor 0 eps) (#s(alt (.f64 #s(literal 1/2 binary64) eps) (patch (.f64 #s(literal 1/2 binary64) eps) #<representation binary64>) () ())) ())
#s(alt (* 1/2 eps) (taylor inf eps) (#s(alt (.f64 #s(literal 1/2 binary64) eps) (patch (.f64 #s(literal 1/2 binary64) eps) #<representation binary64>) () ())) ())
#s(alt (* 1/2 eps) (taylor inf eps) (#s(alt (.f64 #s(literal 1/2 binary64) eps) (patch (.f64 #s(literal 1/2 binary64) eps) #<representation binary64>) () ())) ())
#s(alt (* 1/2 eps) (taylor inf eps) (#s(alt (.f64 #s(literal 1/2 binary64) eps) (patch (.f64 #s(literal 1/2 binary64) eps) #<representation binary64>) () ())) ())
#s(alt (* 1/2 eps) (taylor inf eps) (#s(alt (.f64 #s(literal 1/2 binary64) eps) (patch (.f64 #s(literal 1/2 binary64) eps) #<representation binary64>) () ())) ())
#s(alt (* 1/2 eps) (taylor -inf eps) (#s(alt (.f64 #s(literal 1/2 binary64) eps) (patch (.f64 #s(literal 1/2 binary64) eps) #<representation binary64>) () ())) ())
#s(alt (* 1/2 eps) (taylor -inf eps) (#s(alt (.f64 #s(literal 1/2 binary64) eps) (patch (.f64 #s(literal 1/2 binary64) eps) #<representation binary64>) () ())) ())
#s(alt (* 1/2 eps) (taylor -inf eps) (#s(alt (.f64 #s(literal 1/2 binary64) eps) (patch (.f64 #s(literal 1/2 binary64) eps) #<representation binary64>) () ())) ())
#s(alt (* 1/2 eps) (taylor -inf eps) (#s(alt (.f64 #s(literal 1/2 binary64) eps) (patch (.f64 #s(literal 1/2 binary64) eps) #<representation binary64>) () ())) ())
#s(alt 1 (taylor 0 x) (#s(alt (cos.f64 x) (patch (cos.f64 x) #<representation binary64>) () ())) ())
#s(alt (+ 1 (* -1/2 (pow x 2))) (taylor 0 x) (#s(alt (cos.f64 x) (patch (cos.f64 x) #<representation binary64>) () ())) ())
#s(alt (+ 1 (* (pow x 2) (- (* 1/24 (pow x 2)) 1/2))) (taylor 0 x) (#s(alt (cos.f64 x) (patch (cos.f64 x) #<representation binary64>) () ())) ())
#s(alt (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))) 1/2))) (taylor 0 x) (#s(alt (cos.f64 x) (patch (cos.f64 x) #<representation binary64>) () ())) ())
#s(alt (cos x) (taylor inf x) (#s(alt (cos.f64 x) (patch (cos.f64 x) #<representation binary64>) () ())) ())
#s(alt (cos x) (taylor inf x) (#s(alt (cos.f64 x) (patch (cos.f64 x) #<representation binary64>) () ())) ())
#s(alt (cos x) (taylor inf x) (#s(alt (cos.f64 x) (patch (cos.f64 x) #<representation binary64>) () ())) ())
#s(alt (cos x) (taylor inf x) (#s(alt (cos.f64 x) (patch (cos.f64 x) #<representation binary64>) () ())) ())
#s(alt (cos x) (taylor -inf x) (#s(alt (cos.f64 x) (patch (cos.f64 x) #<representation binary64>) () ())) ())
#s(alt (cos x) (taylor -inf x) (#s(alt (cos.f64 x) (patch (cos.f64 x) #<representation binary64>) () ())) ())
#s(alt (cos x) (taylor -inf x) (#s(alt (cos.f64 x) (patch (cos.f64 x) #<representation binary64>) () ())) ())
#s(alt (cos x) (taylor -inf x) (#s(alt (cos.f64 x) (patch (cos.f64 x) #<representation binary64>) () ())) ())

Calls

129 calls:

Time	Variable		Point	Expression
5.0ms	eps	@	-inf	(* eps (+ (* eps (* -1/2 (sin x))) (cos x)))
2.0ms	x	@	inf	(* eps (+ (* eps (* -1/2 (sin x))) (cos x)))
1.0ms	x	@	0	(+ (* (* eps eps) (+ (* (* eps eps) (* (sin x) (+ (* eps (* eps -1/720)) 1/24))) (* -1/2 (sin x)))) 0)
1.0ms	x	@	inf	(+ (* (* eps eps) (* (sin x) (+ (* eps (* eps -1/720)) 1/24))) (* -1/2 (sin x)))
1.0ms	x	@	0	(+ (* (* eps eps) (* (sin x) (+ (* eps (* eps -1/720)) 1/24))) (* -1/2 (sin x)))

simplify424.0ms (2.8%)

Memory

28.4MiB live, 334.4MiB allocated

Algorithm

1×	egg-herbie

Rules

11 910×	`lower-fma.f64`
11 910×	`lower-fma.f32`
7 208×	`lower-*.f64`
7 208×	`lower-*.f32`
3 080×	`lower-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	601	6606
1	1920	6337
2	6056	6282
0	8283	5716

Stop Event

1×	iter limit
1×	node limit

Counts

516 → 511

Calls

Call 1

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

Outputs
(* -1/2 (sin x))
(*.f64 #s(literal -1/2 binary64) (sin.f64 x))
(+ (* -1/2 (sin x)) (* 1/24 (* (pow eps 2) (sin x))))
(.f64 (sin.f64 x) (fma.f64 #s(literal 1/24 binary64) (.f64 eps eps) #s(literal -1/2 binary64)))
(+ (* -1/2 (sin x)) (* (pow eps 2) (+ (* -1/720 (* (pow eps 2) (sin x))) (* 1/24 (sin x)))))
(fma.f64 #s(literal -1/2 binary64) (sin.f64 x) (.f64 (sin.f64 x) (.f64 eps (.f64 eps (fma.f64 (.f64 eps eps) #s(literal -1/720 binary64) #s(literal 1/24 binary64))))))
(+ (* -1/2 (sin x)) (* (pow eps 2) (+ (* -1/720 (* (pow eps 2) (sin x))) (* 1/24 (sin x)))))
(fma.f64 #s(literal -1/2 binary64) (sin.f64 x) (.f64 (sin.f64 x) (.f64 eps (.f64 eps (fma.f64 (.f64 eps eps) #s(literal -1/720 binary64) #s(literal 1/24 binary64))))))
(* -1/720 (* (pow eps 4) (sin x)))
(.f64 (sin.f64 x) (.f64 eps (.f64 eps (.f64 (*.f64 eps eps) #s(literal -1/720 binary64)))))
(* (pow eps 4) (+ (* -1/720 (sin x)) (* 1/24 (/ (sin x) (pow eps 2)))))
(.f64 (.f64 (.f64 eps eps) (.f64 eps eps)) (fma.f64 (sin.f64 x) #s(literal -1/720 binary64) (/.f64 (.f64 (sin.f64 x) #s(literal 1/24 binary64)) (.f64 eps eps))))
(* (pow eps 4) (+ (* -1/2 (/ (sin x) (pow eps 4))) (+ (* -1/720 (sin x)) (* 1/24 (/ (sin x) (pow eps 2))))))
(.f64 (.f64 (.f64 eps eps) (.f64 eps eps)) (fma.f64 #s(literal -1/2 binary64) (/.f64 (sin.f64 x) (.f64 (.f64 eps eps) (.f64 eps eps))) (fma.f64 (sin.f64 x) #s(literal -1/720 binary64) (/.f64 (.f64 (sin.f64 x) #s(literal 1/24 binary64)) (*.f64 eps eps)))))
(* (pow eps 4) (+ (* -1/2 (/ (sin x) (pow eps 4))) (+ (* -1/720 (sin x)) (* 1/24 (/ (sin x) (pow eps 2))))))
(.f64 (.f64 (.f64 eps eps) (.f64 eps eps)) (fma.f64 #s(literal -1/2 binary64) (/.f64 (sin.f64 x) (.f64 (.f64 eps eps) (.f64 eps eps))) (fma.f64 (sin.f64 x) #s(literal -1/720 binary64) (/.f64 (.f64 (sin.f64 x) #s(literal 1/24 binary64)) (*.f64 eps eps)))))
(* -1/720 (* (pow eps 4) (sin x)))
(.f64 (sin.f64 x) (.f64 eps (.f64 eps (.f64 (*.f64 eps eps) #s(literal -1/720 binary64)))))
(* (pow eps 4) (+ (* -1/720 (sin x)) (* 1/24 (/ (sin x) (pow eps 2)))))
(.f64 (.f64 (.f64 eps eps) (.f64 eps eps)) (fma.f64 (sin.f64 x) #s(literal -1/720 binary64) (/.f64 (.f64 (sin.f64 x) #s(literal 1/24 binary64)) (.f64 eps eps))))
(* (pow eps 4) (+ (* -1/2 (/ (sin x) (pow eps 4))) (+ (* -1/720 (sin x)) (* 1/24 (/ (sin x) (pow eps 2))))))
(.f64 (.f64 (.f64 eps eps) (.f64 eps eps)) (fma.f64 #s(literal -1/2 binary64) (/.f64 (sin.f64 x) (.f64 (.f64 eps eps) (.f64 eps eps))) (fma.f64 (sin.f64 x) #s(literal -1/720 binary64) (/.f64 (.f64 (sin.f64 x) #s(literal 1/24 binary64)) (*.f64 eps eps)))))
(* (pow eps 4) (+ (* -1/2 (/ (sin x) (pow eps 4))) (+ (* -1/720 (sin x)) (* 1/24 (/ (sin x) (pow eps 2))))))
(.f64 (.f64 (.f64 eps eps) (.f64 eps eps)) (fma.f64 #s(literal -1/2 binary64) (/.f64 (sin.f64 x) (.f64 (.f64 eps eps) (.f64 eps eps))) (fma.f64 (sin.f64 x) #s(literal -1/720 binary64) (/.f64 (.f64 (sin.f64 x) #s(literal 1/24 binary64)) (*.f64 eps eps)))))
(* x (- (* (pow eps 2) (+ 1/24 (* -1/720 (pow eps 2)))) 1/2))
(.f64 x (fma.f64 eps (.f64 eps (fma.f64 (*.f64 eps eps) #s(literal -1/720 binary64) #s(literal 1/24 binary64))) #s(literal -1/2 binary64)))
(* x (- (+ (* (pow eps 2) (+ 1/24 (* -1/720 (pow eps 2)))) (* (pow x 2) (+ 1/12 (* -1/6 (* (pow eps 2) (+ 1/24 (* -1/720 (pow eps 2)))))))) 1/2))
(.f64 x (fma.f64 x (.f64 x (fma.f64 (.f64 eps eps) (fma.f64 (.f64 eps eps) #s(literal 1/4320 binary64) #s(literal -1/144 binary64)) #s(literal 1/12 binary64))) (fma.f64 eps (.f64 eps (fma.f64 (.f64 eps eps) #s(literal -1/720 binary64) #s(literal 1/24 binary64))) #s(literal -1/2 binary64))))
(* x (- (+ (* (pow eps 2) (+ 1/24 (* -1/720 (pow eps 2)))) (* (pow x 2) (+ 1/12 (+ (* -1/6 (* (pow eps 2) (+ 1/24 (* -1/720 (pow eps 2))))) (* (pow x 2) (- (* 1/120 (* (pow eps 2) (+ 1/24 (* -1/720 (pow eps 2))))) 1/240)))))) 1/2))
(.f64 x (fma.f64 eps (.f64 eps (fma.f64 (.f64 eps eps) #s(literal -1/720 binary64) #s(literal 1/24 binary64))) (fma.f64 (.f64 x x) (fma.f64 (.f64 x x) (fma.f64 (.f64 eps eps) (fma.f64 (.f64 eps eps) #s(literal -1/86400 binary64) #s(literal 1/2880 binary64)) #s(literal -1/240 binary64)) (fma.f64 (.f64 eps eps) (fma.f64 (*.f64 eps eps) #s(literal 1/4320 binary64) #s(literal -1/144 binary64)) #s(literal 1/12 binary64))) #s(literal -1/2 binary64))))
(* x (- (+ (* (pow eps 2) (+ 1/24 (* -1/720 (pow eps 2)))) (* (pow x 2) (+ 1/12 (+ (* -1/6 (* (pow eps 2) (+ 1/24 (* -1/720 (pow eps 2))))) (* (pow x 2) (- (+ (* 1/120 (* (pow eps 2) (+ 1/24 (* -1/720 (pow eps 2))))) (* (pow x 2) (+ 1/10080 (* -1/5040 (* (pow eps 2) (+ 1/24 (* -1/720 (pow eps 2)))))))) 1/240)))))) 1/2))
(.f64 x (fma.f64 (.f64 x x) (fma.f64 (.f64 x x) (fma.f64 (.f64 x x) (fma.f64 (.f64 eps eps) (.f64 #s(literal -1/5040 binary64) (fma.f64 (.f64 eps eps) #s(literal -1/720 binary64) #s(literal 1/24 binary64))) #s(literal 1/10080 binary64)) (fma.f64 (.f64 eps eps) (fma.f64 (.f64 eps eps) #s(literal -1/86400 binary64) #s(literal 1/2880 binary64)) #s(literal -1/240 binary64))) (fma.f64 (.f64 eps eps) (fma.f64 (.f64 eps eps) #s(literal 1/4320 binary64) #s(literal -1/144 binary64)) #s(literal 1/12 binary64))) (fma.f64 eps (.f64 eps (fma.f64 (*.f64 eps eps) #s(literal -1/720 binary64) #s(literal 1/24 binary64))) #s(literal -1/2 binary64))))
(+ (* -1/2 (sin x)) (* (pow eps 2) (* (sin x) (+ 1/24 (* -1/720 (pow eps 2))))))
(fma.f64 #s(literal -1/2 binary64) (sin.f64 x) (.f64 (sin.f64 x) (.f64 eps (.f64 eps (fma.f64 (.f64 eps eps) #s(literal -1/720 binary64) #s(literal 1/24 binary64))))))
(+ (* -1/2 (sin x)) (* (pow eps 2) (* (sin x) (+ 1/24 (* -1/720 (pow eps 2))))))
(fma.f64 #s(literal -1/2 binary64) (sin.f64 x) (.f64 (sin.f64 x) (.f64 eps (.f64 eps (fma.f64 (.f64 eps eps) #s(literal -1/720 binary64) #s(literal 1/24 binary64))))))
(+ (* -1/2 (sin x)) (* (pow eps 2) (* (sin x) (+ 1/24 (* -1/720 (pow eps 2))))))
(fma.f64 #s(literal -1/2 binary64) (sin.f64 x) (.f64 (sin.f64 x) (.f64 eps (.f64 eps (fma.f64 (.f64 eps eps) #s(literal -1/720 binary64) #s(literal 1/24 binary64))))))
(+ (* -1/2 (sin x)) (* (pow eps 2) (* (sin x) (+ 1/24 (* -1/720 (pow eps 2))))))
(fma.f64 #s(literal -1/2 binary64) (sin.f64 x) (.f64 (sin.f64 x) (.f64 eps (.f64 eps (fma.f64 (.f64 eps eps) #s(literal -1/720 binary64) #s(literal 1/24 binary64))))))
(+ (* -1/2 (sin x)) (* (pow eps 2) (* (sin x) (+ 1/24 (* -1/720 (pow eps 2))))))
(fma.f64 #s(literal -1/2 binary64) (sin.f64 x) (.f64 (sin.f64 x) (.f64 eps (.f64 eps (fma.f64 (.f64 eps eps) #s(literal -1/720 binary64) #s(literal 1/24 binary64))))))
(+ (* -1/2 (sin x)) (* (pow eps 2) (* (sin x) (+ 1/24 (* -1/720 (pow eps 2))))))
(fma.f64 #s(literal -1/2 binary64) (sin.f64 x) (.f64 (sin.f64 x) (.f64 eps (.f64 eps (fma.f64 (.f64 eps eps) #s(literal -1/720 binary64) #s(literal 1/24 binary64))))))
(+ (* -1/2 (sin x)) (* (pow eps 2) (* (sin x) (+ 1/24 (* -1/720 (pow eps 2))))))
(fma.f64 #s(literal -1/2 binary64) (sin.f64 x) (.f64 (sin.f64 x) (.f64 eps (.f64 eps (fma.f64 (.f64 eps eps) #s(literal -1/720 binary64) #s(literal 1/24 binary64))))))
(+ (* -1/2 (sin x)) (* (pow eps 2) (* (sin x) (+ 1/24 (* -1/720 (pow eps 2))))))
(fma.f64 #s(literal -1/2 binary64) (sin.f64 x) (.f64 (sin.f64 x) (.f64 eps (.f64 eps (fma.f64 (.f64 eps eps) #s(literal -1/720 binary64) #s(literal 1/24 binary64))))))
(* -1/2 (* (pow eps 2) (sin x)))
(.f64 eps (.f64 #s(literal -1/2 binary64) (*.f64 (sin.f64 x) eps)))
(* (pow eps 2) (+ (* -1/2 (sin x)) (* 1/24 (* (pow eps 2) (sin x)))))
(.f64 (.f64 eps eps) (.f64 (sin.f64 x) (fma.f64 #s(literal 1/24 binary64) (.f64 eps eps) #s(literal -1/2 binary64))))
(* (pow eps 2) (+ (* -1/2 (sin x)) (* (pow eps 2) (+ (* -1/720 (* (pow eps 2) (sin x))) (* 1/24 (sin x))))))
(.f64 (.f64 eps eps) (fma.f64 #s(literal -1/2 binary64) (sin.f64 x) (.f64 (sin.f64 x) (.f64 eps (.f64 eps (fma.f64 (.f64 eps eps) #s(literal -1/720 binary64) #s(literal 1/24 binary64)))))))
(* (pow eps 2) (+ (* -1/2 (sin x)) (* (pow eps 2) (+ (* -1/720 (* (pow eps 2) (sin x))) (* 1/24 (sin x))))))
(.f64 (.f64 eps eps) (fma.f64 #s(literal -1/2 binary64) (sin.f64 x) (.f64 (sin.f64 x) (.f64 eps (.f64 eps (fma.f64 (.f64 eps eps) #s(literal -1/720 binary64) #s(literal 1/24 binary64)))))))
(* -1/720 (* (pow eps 6) (sin x)))
(.f64 (sin.f64 x) (.f64 #s(literal -1/720 binary64) (pow.f64 eps #s(literal 6 binary64))))
(* (pow eps 6) (+ (* -1/720 (sin x)) (* 1/24 (/ (sin x) (pow eps 2)))))
(.f64 (fma.f64 (sin.f64 x) #s(literal -1/720 binary64) (/.f64 (.f64 (sin.f64 x) #s(literal 1/24 binary64)) (*.f64 eps eps))) (pow.f64 eps #s(literal 6 binary64)))
(* (pow eps 6) (+ (* -1/2 (/ (sin x) (pow eps 4))) (+ (* -1/720 (sin x)) (* 1/24 (/ (sin x) (pow eps 2))))))
(.f64 (fma.f64 #s(literal -1/2 binary64) (/.f64 (sin.f64 x) (.f64 (.f64 eps eps) (.f64 eps eps))) (fma.f64 (sin.f64 x) #s(literal -1/720 binary64) (/.f64 (.f64 (sin.f64 x) #s(literal 1/24 binary64)) (.f64 eps eps)))) (pow.f64 eps #s(literal 6 binary64)))
(* (pow eps 6) (+ (* -1/2 (/ (sin x) (pow eps 4))) (+ (* -1/720 (sin x)) (* 1/24 (/ (sin x) (pow eps 2))))))
(.f64 (fma.f64 #s(literal -1/2 binary64) (/.f64 (sin.f64 x) (.f64 (.f64 eps eps) (.f64 eps eps))) (fma.f64 (sin.f64 x) #s(literal -1/720 binary64) (/.f64 (.f64 (sin.f64 x) #s(literal 1/24 binary64)) (.f64 eps eps)))) (pow.f64 eps #s(literal 6 binary64)))
(* -1/720 (* (pow eps 6) (sin x)))
(.f64 (sin.f64 x) (.f64 #s(literal -1/720 binary64) (pow.f64 eps #s(literal 6 binary64))))
(* (pow eps 6) (+ (* -1/720 (sin x)) (* 1/24 (/ (sin x) (pow eps 2)))))
(.f64 (fma.f64 (sin.f64 x) #s(literal -1/720 binary64) (/.f64 (.f64 (sin.f64 x) #s(literal 1/24 binary64)) (*.f64 eps eps))) (pow.f64 eps #s(literal 6 binary64)))
(* (pow eps 6) (+ (* -1/2 (/ (sin x) (pow eps 4))) (+ (* -1/720 (sin x)) (* 1/24 (/ (sin x) (pow eps 2))))))
(.f64 (fma.f64 #s(literal -1/2 binary64) (/.f64 (sin.f64 x) (.f64 (.f64 eps eps) (.f64 eps eps))) (fma.f64 (sin.f64 x) #s(literal -1/720 binary64) (/.f64 (.f64 (sin.f64 x) #s(literal 1/24 binary64)) (.f64 eps eps)))) (pow.f64 eps #s(literal 6 binary64)))
(* (pow eps 6) (+ (* -1/2 (/ (sin x) (pow eps 4))) (+ (* -1/720 (sin x)) (* 1/24 (/ (sin x) (pow eps 2))))))
(.f64 (fma.f64 #s(literal -1/2 binary64) (/.f64 (sin.f64 x) (.f64 (.f64 eps eps) (.f64 eps eps))) (fma.f64 (sin.f64 x) #s(literal -1/720 binary64) (/.f64 (.f64 (sin.f64 x) #s(literal 1/24 binary64)) (.f64 eps eps)))) (pow.f64 eps #s(literal 6 binary64)))
(* (pow eps 2) (* x (- (* (pow eps 2) (+ 1/24 (* -1/720 (pow eps 2)))) 1/2)))
(.f64 eps (.f64 eps (.f64 x (fma.f64 eps (.f64 eps (fma.f64 (*.f64 eps eps) #s(literal -1/720 binary64) #s(literal 1/24 binary64))) #s(literal -1/2 binary64)))))
(* x (+ (* (pow eps 2) (* (pow x 2) (+ 1/12 (* -1/6 (* (pow eps 2) (+ 1/24 (* -1/720 (pow eps 2)))))))) (* (pow eps 2) (- (* (pow eps 2) (+ 1/24 (* -1/720 (pow eps 2)))) 1/2))))
(.f64 (.f64 x (.f64 eps eps)) (fma.f64 x (.f64 x (fma.f64 (.f64 eps eps) (fma.f64 (.f64 eps eps) #s(literal 1/4320 binary64) #s(literal -1/144 binary64)) #s(literal 1/12 binary64))) (fma.f64 eps (.f64 eps (fma.f64 (.f64 eps eps) #s(literal -1/720 binary64) #s(literal 1/24 binary64))) #s(literal -1/2 binary64))))
(* x (+ (* (pow eps 2) (- (* (pow eps 2) (+ 1/24 (* -1/720 (pow eps 2)))) 1/2)) (* (pow x 2) (+ (* (pow eps 2) (* (pow x 2) (- (* 1/120 (* (pow eps 2) (+ 1/24 (* -1/720 (pow eps 2))))) 1/240))) (* (pow eps 2) (+ 1/12 (* -1/6 (* (pow eps 2) (+ 1/24 (* -1/720 (pow eps 2)))))))))))
(.f64 x (fma.f64 eps (.f64 eps (fma.f64 eps (.f64 eps (fma.f64 (.f64 eps eps) #s(literal -1/720 binary64) #s(literal 1/24 binary64))) #s(literal -1/2 binary64))) (.f64 (.f64 (.f64 x (.f64 eps eps)) x) (fma.f64 (.f64 x x) (fma.f64 (.f64 eps eps) (fma.f64 (.f64 eps eps) #s(literal -1/86400 binary64) #s(literal 1/2880 binary64)) #s(literal -1/240 binary64)) (fma.f64 (.f64 eps eps) (fma.f64 (*.f64 eps eps) #s(literal 1/4320 binary64) #s(literal -1/144 binary64)) #s(literal 1/12 binary64))))))
(* x (+ (* (pow eps 2) (- (* (pow eps 2) (+ 1/24 (* -1/720 (pow eps 2)))) 1/2)) (* (pow x 2) (+ (* (pow eps 2) (+ 1/12 (* -1/6 (* (pow eps 2) (+ 1/24 (* -1/720 (pow eps 2))))))) (* (pow x 2) (+ (* (pow eps 2) (* (pow x 2) (+ 1/10080 (* -1/5040 (* (pow eps 2) (+ 1/24 (* -1/720 (pow eps 2)))))))) (* (pow eps 2) (- (* 1/120 (* (pow eps 2) (+ 1/24 (* -1/720 (pow eps 2))))) 1/240))))))))
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(* (pow eps 2) (+ (* -1/2 (sin x)) (* (pow eps 2) (* (sin x) (+ 1/24 (* -1/720 (pow eps 2)))))))
(.f64 (.f64 eps eps) (fma.f64 #s(literal -1/2 binary64) (sin.f64 x) (.f64 (sin.f64 x) (.f64 eps (.f64 eps (fma.f64 (.f64 eps eps) #s(literal -1/720 binary64) #s(literal 1/24 binary64)))))))
(* (pow eps 2) (+ (* -1/2 (sin x)) (* (pow eps 2) (* (sin x) (+ 1/24 (* -1/720 (pow eps 2)))))))
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(* (pow eps 2) (+ (* -1/2 (sin x)) (* (pow eps 2) (* (sin x) (+ 1/24 (* -1/720 (pow eps 2)))))))
(.f64 (.f64 eps eps) (fma.f64 #s(literal -1/2 binary64) (sin.f64 x) (.f64 (sin.f64 x) (.f64 eps (.f64 eps (fma.f64 (.f64 eps eps) #s(literal -1/720 binary64) #s(literal 1/24 binary64)))))))
(* (pow eps 2) (+ (* -1/2 (sin x)) (* (pow eps 2) (* (sin x) (+ 1/24 (* -1/720 (pow eps 2)))))))
(.f64 (.f64 eps eps) (fma.f64 #s(literal -1/2 binary64) (sin.f64 x) (.f64 (sin.f64 x) (.f64 eps (.f64 eps (fma.f64 (.f64 eps eps) #s(literal -1/720 binary64) #s(literal 1/24 binary64)))))))
(* (pow eps 2) (+ (* -1/2 (sin x)) (* (pow eps 2) (* (sin x) (+ 1/24 (* -1/720 (pow eps 2)))))))
(.f64 (.f64 eps eps) (fma.f64 #s(literal -1/2 binary64) (sin.f64 x) (.f64 (sin.f64 x) (.f64 eps (.f64 eps (fma.f64 (.f64 eps eps) #s(literal -1/720 binary64) #s(literal 1/24 binary64)))))))
(* (pow eps 2) (+ (* -1/2 (sin x)) (* (pow eps 2) (* (sin x) (+ 1/24 (* -1/720 (pow eps 2)))))))
(.f64 (.f64 eps eps) (fma.f64 #s(literal -1/2 binary64) (sin.f64 x) (.f64 (sin.f64 x) (.f64 eps (.f64 eps (fma.f64 (.f64 eps eps) #s(literal -1/720 binary64) #s(literal 1/24 binary64)))))))
(* (pow eps 2) (+ (* -1/2 (sin x)) (* (pow eps 2) (* (sin x) (+ 1/24 (* -1/720 (pow eps 2)))))))
(.f64 (.f64 eps eps) (fma.f64 #s(literal -1/2 binary64) (sin.f64 x) (.f64 (sin.f64 x) (.f64 eps (.f64 eps (fma.f64 (.f64 eps eps) #s(literal -1/720 binary64) #s(literal 1/24 binary64)))))))
(* (pow eps 2) (+ (* -1/2 (sin x)) (* (pow eps 2) (* (sin x) (+ 1/24 (* -1/720 (pow eps 2)))))))
(.f64 (.f64 eps eps) (fma.f64 #s(literal -1/2 binary64) (sin.f64 x) (.f64 (sin.f64 x) (.f64 eps (.f64 eps (fma.f64 (.f64 eps eps) #s(literal -1/720 binary64) #s(literal 1/24 binary64)))))))
(+ (sin x) (sin (neg x)))
#s(literal 0 binary64)
(+ (sin x) (+ (sin (neg x)) (* eps (cos x))))
(fma.f64 eps (cos.f64 x) #s(literal 0 binary64))
(+ (sin x) (+ (sin (neg x)) (* eps (+ (cos x) (* -1/2 (* eps (sin x)))))))
(fma.f64 eps (fma.f64 #s(literal -1/2 binary64) (*.f64 (sin.f64 x) eps) (cos.f64 x)) #s(literal 0 binary64))
(+ (sin x) (+ (sin (neg x)) (* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x)))))))))
(fma.f64 eps (fma.f64 (cos.f64 x) (fma.f64 eps (.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64)) (.f64 #s(literal -1/2 binary64) (*.f64 (sin.f64 x) eps))) #s(literal 0 binary64))
(+ (sin (neg x)) (+ (* (cos eps) (sin x)) (* (cos x) (sin eps))))
(-.f64 (fma.f64 (sin.f64 x) (cos.f64 eps) (*.f64 (cos.f64 x) (sin.f64 eps))) (sin.f64 x))
(+ (sin (neg x)) (+ (* (cos eps) (sin x)) (* (cos x) (sin eps))))
(-.f64 (fma.f64 (sin.f64 x) (cos.f64 eps) (*.f64 (cos.f64 x) (sin.f64 eps))) (sin.f64 x))
(+ (sin (neg x)) (+ (* (cos eps) (sin x)) (* (cos x) (sin eps))))
(-.f64 (fma.f64 (sin.f64 x) (cos.f64 eps) (*.f64 (cos.f64 x) (sin.f64 eps))) (sin.f64 x))
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(-.f64 (fma.f64 (sin.f64 x) (cos.f64 eps) (*.f64 (cos.f64 x) (sin.f64 eps))) (sin.f64 x))
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(sin eps)
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(-.f64 (fma.f64 (sin.f64 x) (cos.f64 eps) (*.f64 (cos.f64 x) (sin.f64 eps))) (sin.f64 x))
eps
(* eps (+ 1 (* -1/6 (pow eps 2))))
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(* eps (+ 1 (* (pow eps 2) (- (* 1/120 (pow eps 2)) 1/6))))
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(* eps (+ 1 (* (pow eps 2) (- (* (pow eps 2) (+ 1/120 (* -1/5040 (pow eps 2)))) 1/6))))
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(sin eps)
(sin.f64 eps)
(sin eps)
(sin.f64 eps)
(sin eps)
(sin.f64 eps)
(sin eps)
(sin.f64 eps)
(sin eps)
(sin.f64 eps)
(sin eps)
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(sin eps)
(sin.f64 eps)
(sin eps)
(sin.f64 eps)
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#s(literal 0 binary64)
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(+ (sin x) (+ (sin (neg x)) (* eps (+ (cos x) (* -1/2 (* eps (sin x)))))))
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(sin eps)
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(+ (sin eps) (* x (- (cos eps) 1)))
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(+ (sin eps) (* x (- (+ (cos eps) (* -1/2 (* x (sin eps)))) 1)))
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(-.f64 (fma.f64 (sin.f64 x) (cos.f64 eps) (*.f64 (cos.f64 x) (sin.f64 eps))) (sin.f64 x))
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(-.f64 (fma.f64 (sin.f64 x) (cos.f64 eps) (*.f64 (cos.f64 x) (sin.f64 eps))) (sin.f64 x))
(+ 1 (* -1/2 (pow x 2)))
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(+ 1 (+ (* -1/2 (* eps x)) (* -1/2 (pow x 2))))
(fma.f64 (*.f64 #s(literal -1/2 binary64) x) (+.f64 x eps) #s(literal 1 binary64))
(+ 1 (+ (* -1/2 (pow x 2)) (* eps (+ (* -1/2 x) (* eps (- (* 1/12 (pow x 2)) 1/6))))))
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(+ 1 (+ (* -1/2 (pow x 2)) (* eps (+ (* -1/2 x) (* eps (- (* 1/12 (pow x 2)) 1/6))))))
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(* (pow eps 2) (- (* 1/12 (pow x 2)) 1/6))
(.f64 eps (.f64 eps (fma.f64 (*.f64 x x) #s(literal 1/12 binary64) #s(literal -1/6 binary64))))
(* (pow eps 2) (- (+ (* -1/2 (/ x eps)) (* 1/12 (pow x 2))) 1/6))
(.f64 (.f64 eps eps) (fma.f64 #s(literal -1/2 binary64) (/.f64 x eps) (fma.f64 (*.f64 x x) #s(literal 1/12 binary64) #s(literal -1/6 binary64))))
(* (pow eps 2) (- (+ (* -1/2 (/ x eps)) (+ (* -1/2 (/ (pow x 2) (pow eps 2))) (+ (* 1/12 (pow x 2)) (/ 1 (pow eps 2))))) 1/6))
(.f64 (.f64 eps eps) (fma.f64 #s(literal -1/2 binary64) (+.f64 (/.f64 x eps) (/.f64 (.f64 x x) (.f64 eps eps))) (+.f64 (fma.f64 x (.f64 x #s(literal 1/12 binary64)) (/.f64 #s(literal 1 binary64) (.f64 eps eps))) #s(literal -1/6 binary64))))
(* (pow eps 2) (- (+ (* -1/2 (/ x eps)) (+ (* -1/2 (/ (pow x 2) (pow eps 2))) (+ (* 1/12 (pow x 2)) (/ 1 (pow eps 2))))) 1/6))
(.f64 (.f64 eps eps) (fma.f64 #s(literal -1/2 binary64) (+.f64 (/.f64 x eps) (/.f64 (.f64 x x) (.f64 eps eps))) (+.f64 (fma.f64 x (.f64 x #s(literal 1/12 binary64)) (/.f64 #s(literal 1 binary64) (.f64 eps eps))) #s(literal -1/6 binary64))))
(* (pow eps 2) (- (* 1/12 (pow x 2)) 1/6))
(.f64 eps (.f64 eps (fma.f64 (*.f64 x x) #s(literal 1/12 binary64) #s(literal -1/6 binary64))))
(* (pow eps 2) (- (+ (* -1/2 (/ x eps)) (* 1/12 (pow x 2))) 1/6))
(.f64 (.f64 eps eps) (fma.f64 #s(literal -1/2 binary64) (/.f64 x eps) (fma.f64 (*.f64 x x) #s(literal 1/12 binary64) #s(literal -1/6 binary64))))
(* (pow eps 2) (- (+ (* -1 (/ (+ (* -1 (/ (+ 1 (* -1/2 (pow x 2))) eps)) (* 1/2 x)) eps)) (* 1/12 (pow x 2))) 1/6))
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(* (pow eps 2) (- (+ (* -1 (/ (+ (* -1 (/ (+ 1 (* -1/2 (pow x 2))) eps)) (* 1/2 x)) eps)) (* 1/12 (pow x 2))) 1/6))
(.f64 (.f64 eps eps) (-.f64 (fma.f64 (.f64 x x) #s(literal 1/12 binary64) #s(literal -1/6 binary64)) (/.f64 (-.f64 (.f64 x #s(literal 1/2 binary64)) (/.f64 (fma.f64 #s(literal -1/2 binary64) (*.f64 x x) #s(literal 1 binary64)) eps)) eps)))
(+ 1 (* -1/6 (pow eps 2)))
(fma.f64 eps (*.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64))
(+ 1 (+ (* -1/2 (* eps x)) (* -1/6 (pow eps 2))))
(fma.f64 #s(literal -1/2 binary64) (.f64 x eps) (fma.f64 eps (.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64)))
(+ 1 (+ (* -1/6 (pow eps 2)) (* x (+ (* -1/2 eps) (* x (- (* 1/12 (pow eps 2)) 1/2))))))
(fma.f64 x (fma.f64 x (fma.f64 eps (.f64 eps #s(literal 1/12 binary64)) #s(literal -1/2 binary64)) (.f64 #s(literal -1/2 binary64) eps)) (fma.f64 eps (*.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64)))
(+ 1 (+ (* -1/6 (pow eps 2)) (* x (+ (* -1/2 eps) (* x (- (* 1/12 (pow eps 2)) 1/2))))))
(fma.f64 x (fma.f64 x (fma.f64 eps (.f64 eps #s(literal 1/12 binary64)) #s(literal -1/2 binary64)) (.f64 #s(literal -1/2 binary64) eps)) (fma.f64 eps (*.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64)))
(* (pow x 2) (- (* 1/12 (pow eps 2)) 1/2))
(.f64 (.f64 x x) (fma.f64 eps (*.f64 eps #s(literal 1/12 binary64)) #s(literal -1/2 binary64)))
(* (pow x 2) (- (+ (* -1/2 (/ eps x)) (* 1/12 (pow eps 2))) 1/2))
(.f64 (.f64 x x) (fma.f64 #s(literal -1/2 binary64) (/.f64 eps x) (fma.f64 eps (*.f64 eps #s(literal 1/12 binary64)) #s(literal -1/2 binary64))))
(* (pow x 2) (- (+ (* -1/2 (/ eps x)) (+ (* -1/6 (/ (pow eps 2) (pow x 2))) (+ (* 1/12 (pow eps 2)) (/ 1 (pow x 2))))) 1/2))
(.f64 (.f64 x x) (+.f64 (fma.f64 (.f64 eps eps) (/.f64 #s(literal -1/6 binary64) (.f64 x x)) (fma.f64 eps (.f64 eps #s(literal 1/12 binary64)) (/.f64 #s(literal 1 binary64) (.f64 x x)))) (fma.f64 #s(literal -1/2 binary64) (/.f64 eps x) #s(literal -1/2 binary64))))
(* (pow x 2) (- (+ (* -1/2 (/ eps x)) (+ (* -1/6 (/ (pow eps 2) (pow x 2))) (+ (* 1/12 (pow eps 2)) (/ 1 (pow x 2))))) 1/2))
(.f64 (.f64 x x) (+.f64 (fma.f64 (.f64 eps eps) (/.f64 #s(literal -1/6 binary64) (.f64 x x)) (fma.f64 eps (.f64 eps #s(literal 1/12 binary64)) (/.f64 #s(literal 1 binary64) (.f64 x x)))) (fma.f64 #s(literal -1/2 binary64) (/.f64 eps x) #s(literal -1/2 binary64))))
(* (pow x 2) (- (* 1/12 (pow eps 2)) 1/2))
(.f64 (.f64 x x) (fma.f64 eps (*.f64 eps #s(literal 1/12 binary64)) #s(literal -1/2 binary64)))
(* (pow x 2) (- (+ (* -1/2 (/ eps x)) (* 1/12 (pow eps 2))) 1/2))
(.f64 (.f64 x x) (fma.f64 #s(literal -1/2 binary64) (/.f64 eps x) (fma.f64 eps (*.f64 eps #s(literal 1/12 binary64)) #s(literal -1/2 binary64))))
(* (pow x 2) (- (+ (* -1 (/ (+ (* -1 (/ (+ 1 (* -1/6 (pow eps 2))) x)) (* 1/2 eps)) x)) (* 1/12 (pow eps 2))) 1/2))
(.f64 (.f64 x x) (-.f64 (fma.f64 eps (.f64 eps #s(literal 1/12 binary64)) #s(literal -1/2 binary64)) (/.f64 (-.f64 (.f64 eps #s(literal 1/2 binary64)) (/.f64 (fma.f64 eps (*.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64)) x)) x)))
(* (pow x 2) (- (+ (* -1 (/ (+ (* -1 (/ (+ 1 (* -1/6 (pow eps 2))) x)) (* 1/2 eps)) x)) (* 1/12 (pow eps 2))) 1/2))
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(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)))
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(+ (sin eps) (* x (- (+ (cos eps) (* x (+ (* -1/2 (sin eps)) (* x (+ 1/6 (* -1/6 (cos eps))))))) 1)))
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(- (sin (+ eps x)) (sin x))
(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
(- (sin (+ eps x)) (sin x))
(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
(- (sin (+ eps x)) (sin x))
(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
(- (sin (+ eps x)) (sin x))
(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
(- (sin (- eps (* -1 x))) (sin x))
(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
(- (sin (- eps (* -1 x))) (sin x))
(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
(- (sin (- eps (* -1 x))) (sin x))
(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
(- (sin (- eps (* -1 x))) (sin x))
(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
(* eps (cos x))
(*.f64 eps (cos.f64 x))
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(.f64 eps (fma.f64 #s(literal -1/2 binary64) (.f64 (sin.f64 x) eps) (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))
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(- (sin (+ eps x)) (sin x))
(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
(- (sin (+ eps x)) (sin x))
(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
(- (sin (+ eps x)) (sin x))
(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
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(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
(- (sin (- x (* -1 eps))) (sin x))
(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
(- (sin (- x (* -1 eps))) (sin x))
(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
(- (sin (- x (* -1 eps))) (sin x))
(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
(* eps (cos x))
(*.f64 eps (cos.f64 x))
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
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(* 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)) (* -1/6 (* eps (cos x)))))))
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(*.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
#s(literal 1 binary64)
(+ 1 (* -1/2 (pow x 2)))
(fma.f64 #s(literal -1/2 binary64) (*.f64 x x) #s(literal 1 binary64))
(+ 1 (* (pow x 2) (- (* 1/24 (pow x 2)) 1/2)))
(fma.f64 x (.f64 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 x (*.f64 x #s(literal -1/720 binary64)) #s(literal 1/24 binary64))) #s(literal -1/2 binary64)) #s(literal 1 binary64))
(cos x)
(cos.f64 x)
(cos x)
(cos.f64 x)
(cos x)
(cos.f64 x)
(cos x)
(cos.f64 x)
(cos x)
(cos.f64 x)
(cos x)
(cos.f64 x)
(cos x)
(cos.f64 x)
(cos x)
(cos.f64 x)

rewrite483.0ms (3.1%)

Memory

-16.2MiB live, 315.7MiB allocated

Rules

6 810×	`lower-*.f32`
6 786×	`lower-*.f64`
6 222×	`lower-fma.f32`
6 202×	`lower-fma.f64`
3 434×	`lower-/.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	66	401
0	104	392
1	412	382
2	3741	382
0	9987	376

Stop Event

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

Counts

25 → 606

Calls

Call 1

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

Outputs
(+.f64 (.f64 (sin.f64 x) #s(literal -1/2 binary64)) (.f64 (fma.f64 (.f64 eps eps) #s(literal -1/720 binary64) #s(literal 1/24 binary64)) (.f64 eps (*.f64 eps (sin.f64 x)))))
(+.f64 (.f64 (fma.f64 (.f64 eps eps) #s(literal -1/720 binary64) #s(literal 1/24 binary64)) (.f64 eps (.f64 eps (sin.f64 x)))) (*.f64 (sin.f64 x) #s(literal -1/2 binary64)))
(-.f64 (/.f64 (pow.f64 (.f64 (fma.f64 (.f64 eps eps) #s(literal -1/720 binary64) #s(literal 1/24 binary64)) (.f64 eps (.f64 eps (sin.f64 x)))) #s(literal 2 binary64)) (fma.f64 eps (.f64 (.f64 eps (sin.f64 x)) (fma.f64 (.f64 eps eps) #s(literal -1/720 binary64) #s(literal 1/24 binary64))) (.f64 #s(literal 1/2 binary64) (sin.f64 x)))) (/.f64 (.f64 #s(literal 1/4 binary64) (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x))))) (fma.f64 eps (.f64 (.f64 eps (sin.f64 x)) (fma.f64 (.f64 eps eps) #s(literal -1/720 binary64) #s(literal 1/24 binary64))) (.f64 #s(literal 1/2 binary64) (sin.f64 x)))))
(fma.f64 eps (.f64 (.f64 eps (sin.f64 x)) (fma.f64 (.f64 eps eps) #s(literal -1/720 binary64) #s(literal 1/24 binary64))) (.f64 (sin.f64 x) #s(literal -1/2 binary64)))
(fma.f64 (.f64 eps eps) (.f64 (sin.f64 x) (fma.f64 (.f64 eps eps) #s(literal -1/720 binary64) #s(literal 1/24 binary64))) (.f64 (sin.f64 x) #s(literal -1/2 binary64)))
(fma.f64 (sin.f64 x) #s(literal -1/2 binary64) (.f64 (fma.f64 (.f64 eps eps) #s(literal -1/720 binary64) #s(literal 1/24 binary64)) (.f64 eps (.f64 eps (sin.f64 x)))))
(fma.f64 (sin.f64 x) (.f64 (fma.f64 (.f64 eps eps) #s(literal -1/720 binary64) #s(literal 1/24 binary64)) (.f64 eps eps)) (.f64 (sin.f64 x) #s(literal -1/2 binary64)))
(fma.f64 (fma.f64 (.f64 eps eps) #s(literal -1/720 binary64) #s(literal 1/24 binary64)) (.f64 eps (.f64 eps (sin.f64 x))) (.f64 (sin.f64 x) #s(literal -1/2 binary64)))
(fma.f64 (.f64 (sin.f64 x) (fma.f64 (.f64 eps eps) #s(literal -1/720 binary64) #s(literal 1/24 binary64))) (.f64 eps eps) (.f64 (sin.f64 x) #s(literal -1/2 binary64)))
(fma.f64 #s(literal -1/2 binary64) (sin.f64 x) (.f64 (fma.f64 (.f64 eps eps) #s(literal -1/720 binary64) #s(literal 1/24 binary64)) (.f64 eps (.f64 eps (sin.f64 x)))))
(fma.f64 (.f64 eps (.f64 eps (sin.f64 x))) (fma.f64 (.f64 eps eps) #s(literal -1/720 binary64) #s(literal 1/24 binary64)) (.f64 (sin.f64 x) #s(literal -1/2 binary64)))
(fma.f64 (.f64 (.f64 eps (sin.f64 x)) (fma.f64 (.f64 eps eps) #s(literal -1/720 binary64) #s(literal 1/24 binary64))) eps (.f64 (sin.f64 x) #s(literal -1/2 binary64)))
(fma.f64 (.f64 (.f64 eps eps) (fma.f64 (.f64 eps eps) #s(literal -1/720 binary64) #s(literal 1/24 binary64))) (sin.f64 x) (.f64 (sin.f64 x) #s(literal -1/2 binary64)))
(/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 (.f64 (sin.f64 x) #s(literal -1/2 binary64)) (-.f64 (.f64 (sin.f64 x) #s(literal -1/2 binary64)) (.f64 (fma.f64 (.f64 eps eps) #s(literal -1/720 binary64) #s(literal 1/24 binary64)) (.f64 eps (.f64 eps (sin.f64 x))))) (pow.f64 (.f64 (fma.f64 (.f64 eps eps) #s(literal -1/720 binary64) #s(literal 1/24 binary64)) (.f64 eps (.f64 eps (sin.f64 x)))) #s(literal 2 binary64))) (fma.f64 #s(literal -1/8 binary64) (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (.f64 (fma.f64 (.f64 eps eps) #s(literal -1/720 binary64) #s(literal 1/24 binary64)) (.f64 eps (.f64 eps (sin.f64 x)))) #s(literal 3 binary64)))))
(/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 eps (.f64 (.f64 eps (sin.f64 x)) (fma.f64 (.f64 eps eps) #s(literal -1/720 binary64) #s(literal 1/24 binary64))) (.f64 #s(literal 1/2 binary64) (sin.f64 x))) (-.f64 (pow.f64 (.f64 (fma.f64 (.f64 eps eps) #s(literal -1/720 binary64) #s(literal 1/24 binary64)) (.f64 eps (.f64 eps (sin.f64 x)))) #s(literal 2 binary64)) (.f64 #s(literal 1/4 binary64) (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x))))))))
(/.f64 (fma.f64 #s(literal -1/8 binary64) (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (.f64 (fma.f64 (.f64 eps eps) #s(literal -1/720 binary64) #s(literal 1/24 binary64)) (.f64 eps (.f64 eps (sin.f64 x)))) #s(literal 3 binary64))) (fma.f64 (.f64 (sin.f64 x) #s(literal -1/2 binary64)) (-.f64 (.f64 (sin.f64 x) #s(literal -1/2 binary64)) (.f64 (fma.f64 (.f64 eps eps) #s(literal -1/720 binary64) #s(literal 1/24 binary64)) (.f64 eps (.f64 eps (sin.f64 x))))) (pow.f64 (.f64 (fma.f64 (.f64 eps eps) #s(literal -1/720 binary64) #s(literal 1/24 binary64)) (.f64 eps (.f64 eps (sin.f64 x)))) #s(literal 2 binary64))))
(/.f64 (fma.f64 #s(literal -1/8 binary64) (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (.f64 (fma.f64 (.f64 eps eps) #s(literal -1/720 binary64) #s(literal 1/24 binary64)) (.f64 eps (.f64 eps (sin.f64 x)))) #s(literal 3 binary64))) (fma.f64 #s(literal 1/4 binary64) (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x)))) (-.f64 (pow.f64 (.f64 (fma.f64 (.f64 eps eps) #s(literal -1/720 binary64) #s(literal 1/24 binary64)) (.f64 eps (.f64 eps (sin.f64 x)))) #s(literal 2 binary64)) (.f64 (.f64 eps eps) (.f64 (.f64 (sin.f64 x) (fma.f64 (.f64 eps eps) #s(literal -1/720 binary64) #s(literal 1/24 binary64))) (*.f64 (sin.f64 x) #s(literal -1/2 binary64)))))))
(/.f64 (-.f64 (pow.f64 (.f64 (fma.f64 (.f64 eps eps) #s(literal -1/720 binary64) #s(literal 1/24 binary64)) (.f64 eps (.f64 eps (sin.f64 x)))) #s(literal 2 binary64)) (.f64 #s(literal 1/4 binary64) (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x)))))) (fma.f64 eps (.f64 (.f64 eps (sin.f64 x)) (fma.f64 (.f64 eps eps) #s(literal -1/720 binary64) #s(literal 1/24 binary64))) (.f64 #s(literal 1/2 binary64) (sin.f64 x))))
(/.f64 (neg.f64 (fma.f64 #s(literal -1/8 binary64) (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (.f64 (fma.f64 (.f64 eps eps) #s(literal -1/720 binary64) #s(literal 1/24 binary64)) (.f64 eps (.f64 eps (sin.f64 x)))) #s(literal 3 binary64)))) (neg.f64 (fma.f64 (.f64 (sin.f64 x) #s(literal -1/2 binary64)) (-.f64 (.f64 (sin.f64 x) #s(literal -1/2 binary64)) (.f64 (fma.f64 (.f64 eps eps) #s(literal -1/720 binary64) #s(literal 1/24 binary64)) (.f64 eps (.f64 eps (sin.f64 x))))) (pow.f64 (.f64 (fma.f64 (.f64 eps eps) #s(literal -1/720 binary64) #s(literal 1/24 binary64)) (.f64 eps (.f64 eps (sin.f64 x)))) #s(literal 2 binary64)))))
(/.f64 (neg.f64 (-.f64 (pow.f64 (.f64 (fma.f64 (.f64 eps eps) #s(literal -1/720 binary64) #s(literal 1/24 binary64)) (.f64 eps (.f64 eps (sin.f64 x)))) #s(literal 2 binary64)) (.f64 #s(literal 1/4 binary64) (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x))))))) (neg.f64 (fma.f64 eps (.f64 (.f64 eps (sin.f64 x)) (fma.f64 (.f64 eps eps) #s(literal -1/720 binary64) #s(literal 1/24 binary64))) (.f64 #s(literal 1/2 binary64) (sin.f64 x)))))
(/.f64 (-.f64 (.f64 #s(literal 1/4 binary64) (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x))))) (pow.f64 (.f64 (fma.f64 (.f64 eps eps) #s(literal -1/720 binary64) #s(literal 1/24 binary64)) (.f64 eps (.f64 eps (sin.f64 x)))) #s(literal 2 binary64))) (-.f64 (.f64 (sin.f64 x) #s(literal -1/2 binary64)) (.f64 (fma.f64 (.f64 eps eps) #s(literal -1/720 binary64) #s(literal 1/24 binary64)) (.f64 eps (*.f64 eps (sin.f64 x))))))
(pow.f64 (/.f64 (fma.f64 (.f64 (sin.f64 x) #s(literal -1/2 binary64)) (-.f64 (.f64 (sin.f64 x) #s(literal -1/2 binary64)) (.f64 (fma.f64 (.f64 eps eps) #s(literal -1/720 binary64) #s(literal 1/24 binary64)) (.f64 eps (.f64 eps (sin.f64 x))))) (pow.f64 (.f64 (fma.f64 (.f64 eps eps) #s(literal -1/720 binary64) #s(literal 1/24 binary64)) (.f64 eps (.f64 eps (sin.f64 x)))) #s(literal 2 binary64))) (fma.f64 #s(literal -1/8 binary64) (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (.f64 (fma.f64 (.f64 eps eps) #s(literal -1/720 binary64) #s(literal 1/24 binary64)) (.f64 eps (.f64 eps (sin.f64 x)))) #s(literal 3 binary64)))) #s(literal -1 binary64))
(pow.f64 (/.f64 (fma.f64 eps (.f64 (.f64 eps (sin.f64 x)) (fma.f64 (.f64 eps eps) #s(literal -1/720 binary64) #s(literal 1/24 binary64))) (.f64 #s(literal 1/2 binary64) (sin.f64 x))) (-.f64 (pow.f64 (.f64 (fma.f64 (.f64 eps eps) #s(literal -1/720 binary64) #s(literal 1/24 binary64)) (.f64 eps (.f64 eps (sin.f64 x)))) #s(literal 2 binary64)) (.f64 #s(literal 1/4 binary64) (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x))))))) #s(literal -1 binary64))
(.f64 (fma.f64 #s(literal -1/8 binary64) (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (.f64 (fma.f64 (.f64 eps eps) #s(literal -1/720 binary64) #s(literal 1/24 binary64)) (.f64 eps (.f64 eps (sin.f64 x)))) #s(literal 3 binary64))) (/.f64 #s(literal 1 binary64) (fma.f64 (.f64 (sin.f64 x) #s(literal -1/2 binary64)) (-.f64 (.f64 (sin.f64 x) #s(literal -1/2 binary64)) (.f64 (fma.f64 (.f64 eps eps) #s(literal -1/720 binary64) #s(literal 1/24 binary64)) (.f64 eps (.f64 eps (sin.f64 x))))) (pow.f64 (.f64 (fma.f64 (.f64 eps eps) #s(literal -1/720 binary64) #s(literal 1/24 binary64)) (.f64 eps (*.f64 eps (sin.f64 x)))) #s(literal 2 binary64)))))
(.f64 (-.f64 (pow.f64 (.f64 (fma.f64 (.f64 eps eps) #s(literal -1/720 binary64) #s(literal 1/24 binary64)) (.f64 eps (.f64 eps (sin.f64 x)))) #s(literal 2 binary64)) (.f64 #s(literal 1/4 binary64) (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x)))))) (/.f64 #s(literal 1 binary64) (fma.f64 eps (.f64 (.f64 eps (sin.f64 x)) (fma.f64 (.f64 eps eps) #s(literal -1/720 binary64) #s(literal 1/24 binary64))) (*.f64 #s(literal 1/2 binary64) (sin.f64 x)))))
(+.f64 #s(literal 0 binary64) (.f64 eps (.f64 eps (fma.f64 eps (.f64 (.f64 eps (sin.f64 x)) (fma.f64 (.f64 eps eps) #s(literal -1/720 binary64) #s(literal 1/24 binary64))) (.f64 (sin.f64 x) #s(literal -1/2 binary64))))))
(+.f64 (.f64 eps (.f64 eps (fma.f64 eps (.f64 (.f64 eps (sin.f64 x)) (fma.f64 (.f64 eps eps) #s(literal -1/720 binary64) #s(literal 1/24 binary64))) (.f64 (sin.f64 x) #s(literal -1/2 binary64))))) #s(literal 0 binary64))
(+.f64 (.f64 eps (.f64 #s(literal -1/2 binary64) (.f64 eps (sin.f64 x)))) (.f64 (.f64 eps eps) (.f64 (fma.f64 (.f64 eps eps) #s(literal -1/720 binary64) #s(literal 1/24 binary64)) (.f64 eps (*.f64 eps (sin.f64 x))))))
(+.f64 (.f64 (.f64 eps eps) (.f64 (fma.f64 (.f64 eps eps) #s(literal -1/720 binary64) #s(literal 1/24 binary64)) (.f64 eps (.f64 eps (sin.f64 x))))) (.f64 eps (.f64 #s(literal -1/2 binary64) (*.f64 eps (sin.f64 x)))))
(+.f64 (.f64 (.f64 eps eps) (.f64 (fma.f64 (.f64 eps eps) #s(literal -1/720 binary64) #s(literal 1/24 binary64)) (.f64 eps (.f64 eps (sin.f64 x))))) (fma.f64 eps (.f64 #s(literal -1/2 binary64) (.f64 eps (sin.f64 x))) #s(literal 0 binary64)))
(+.f64 (.f64 (.f64 eps eps) (.f64 (fma.f64 (.f64 eps eps) #s(literal -1/720 binary64) #s(literal 1/24 binary64)) (.f64 eps (.f64 eps (sin.f64 x))))) (-.f64 (.f64 eps (.f64 #s(literal -1/2 binary64) (*.f64 eps (sin.f64 x)))) #s(literal 0 binary64)))
(+.f64 (+.f64 #s(literal 0 binary64) (.f64 (.f64 eps eps) (.f64 (fma.f64 (.f64 eps eps) #s(literal -1/720 binary64) #s(literal 1/24 binary64)) (.f64 eps (.f64 eps (sin.f64 x)))))) (.f64 eps (.f64 #s(literal -1/2 binary64) (*.f64 eps (sin.f64 x)))))
(-.f64 (.f64 eps (.f64 eps (fma.f64 eps (.f64 (.f64 eps (sin.f64 x)) (fma.f64 (.f64 eps eps) #s(literal -1/720 binary64) #s(literal 1/24 binary64))) (.f64 (sin.f64 x) #s(literal -1/2 binary64))))) #s(literal 0 binary64))
(-.f64 (.f64 eps (.f64 eps (fma.f64 eps (.f64 (.f64 eps (sin.f64 x)) (fma.f64 (.f64 eps eps) #s(literal -1/720 binary64) #s(literal 1/24 binary64))) (.f64 (sin.f64 x) #s(literal -1/2 binary64))))) (/.f64 #s(literal 0 binary64) (.f64 eps (.f64 eps (fma.f64 eps (.f64 (.f64 eps (sin.f64 x)) (fma.f64 (.f64 eps eps) #s(literal -1/720 binary64) #s(literal 1/24 binary64))) (.f64 (sin.f64 x) #s(literal -1/2 binary64)))))))
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(/.f64 (fma.f64 (.f64 x (fma.f64 (.f64 (.f64 eps (.f64 eps eps)) eps) #s(literal 1/144 binary64) #s(literal -1/4 binary64))) (.f64 eps eps) (.f64 (fma.f64 (.f64 eps eps) #s(literal 1/12 binary64) #s(literal 1/2 binary64)) (.f64 (.f64 eps (.f64 eps eps)) #s(literal -1/2 binary64)))) (.f64 (fma.f64 (.f64 eps eps) #s(literal 1/12 binary64) #s(literal 1/2 binary64)) (*.f64 eps eps)))
(/.f64 (fma.f64 (.f64 (fma.f64 (.f64 eps (.f64 eps eps)) (.f64 (.f64 eps (.f64 eps eps)) #s(literal 1/1728 binary64)) #s(literal -1/8 binary64)) x) eps (.f64 (-.f64 (fma.f64 (.f64 (.f64 eps (.f64 eps eps)) eps) #s(literal 1/144 binary64) #s(literal 1/4 binary64)) (.f64 (.f64 eps eps) #s(literal -1/24 binary64))) (.f64 (.f64 eps eps) #s(literal -1/2 binary64)))) (.f64 (-.f64 (fma.f64 (.f64 (.f64 eps (.f64 eps eps)) eps) #s(literal 1/144 binary64) #s(literal 1/4 binary64)) (.f64 (.f64 eps eps) #s(literal -1/24 binary64))) eps))
(/.f64 (fma.f64 (.f64 (fma.f64 (.f64 eps (.f64 eps eps)) (.f64 (.f64 eps (.f64 eps eps)) #s(literal 1/1728 binary64)) #s(literal -1/8 binary64)) x) eps (.f64 (-.f64 (fma.f64 (.f64 (.f64 eps (.f64 eps eps)) eps) #s(literal 1/144 binary64) #s(literal 1/4 binary64)) (.f64 (.f64 eps eps) #s(literal -1/24 binary64))) (.f64 #s(literal -1/2 binary64) (.f64 eps eps)))) (.f64 (-.f64 (fma.f64 (.f64 (.f64 eps (.f64 eps eps)) eps) #s(literal 1/144 binary64) #s(literal 1/4 binary64)) (.f64 (.f64 eps eps) #s(literal -1/24 binary64))) eps))
(/.f64 (fma.f64 (.f64 (fma.f64 (.f64 eps (.f64 eps eps)) (.f64 (.f64 eps (.f64 eps eps)) #s(literal 1/1728 binary64)) #s(literal -1/8 binary64)) x) (.f64 eps eps) (.f64 (-.f64 (fma.f64 (.f64 (.f64 eps (.f64 eps eps)) eps) #s(literal 1/144 binary64) #s(literal 1/4 binary64)) (.f64 (.f64 eps eps) #s(literal -1/24 binary64))) (.f64 #s(literal -1/2 binary64) (.f64 eps (.f64 eps eps))))) (.f64 (-.f64 (fma.f64 (.f64 (.f64 eps (.f64 eps eps)) eps) #s(literal 1/144 binary64) #s(literal 1/4 binary64)) (.f64 (.f64 eps eps) #s(literal -1/24 binary64))) (*.f64 eps eps)))
(/.f64 (fma.f64 (.f64 (fma.f64 (.f64 eps (.f64 eps eps)) (.f64 (.f64 eps (.f64 eps eps)) #s(literal 1/1728 binary64)) #s(literal -1/8 binary64)) x) (.f64 eps eps) (.f64 (-.f64 (fma.f64 (.f64 (.f64 eps (.f64 eps eps)) eps) #s(literal 1/144 binary64) #s(literal 1/4 binary64)) (.f64 (.f64 eps eps) #s(literal -1/24 binary64))) (.f64 (.f64 eps (.f64 eps eps)) #s(literal -1/2 binary64)))) (.f64 (-.f64 (fma.f64 (.f64 (.f64 eps (.f64 eps eps)) eps) #s(literal 1/144 binary64) #s(literal 1/4 binary64)) (.f64 (.f64 eps eps) #s(literal -1/24 binary64))) (*.f64 eps eps)))
(/.f64 (fma.f64 (.f64 (fma.f64 (.f64 (.f64 eps (.f64 eps eps)) eps) #s(literal 1/144 binary64) #s(literal -1/4 binary64)) x) eps (.f64 (fma.f64 (.f64 eps eps) #s(literal 1/12 binary64) #s(literal 1/2 binary64)) (.f64 (.f64 eps eps) #s(literal -1/2 binary64)))) (.f64 (fma.f64 (.f64 eps eps) #s(literal 1/12 binary64) #s(literal 1/2 binary64)) eps))
(/.f64 (fma.f64 (.f64 (fma.f64 (.f64 (.f64 eps (.f64 eps eps)) eps) #s(literal 1/144 binary64) #s(literal -1/4 binary64)) x) eps (.f64 (fma.f64 (.f64 eps eps) #s(literal 1/12 binary64) #s(literal 1/2 binary64)) (.f64 #s(literal -1/2 binary64) (.f64 eps eps)))) (.f64 (fma.f64 (.f64 eps eps) #s(literal 1/12 binary64) #s(literal 1/2 binary64)) eps))
(/.f64 (fma.f64 (.f64 (fma.f64 (.f64 (.f64 eps (.f64 eps eps)) eps) #s(literal 1/144 binary64) #s(literal -1/4 binary64)) x) (.f64 eps eps) (.f64 (fma.f64 (.f64 eps eps) #s(literal 1/12 binary64) #s(literal 1/2 binary64)) (.f64 #s(literal -1/2 binary64) (.f64 eps (.f64 eps eps))))) (.f64 (fma.f64 (.f64 eps eps) #s(literal 1/12 binary64) #s(literal 1/2 binary64)) (*.f64 eps eps)))
(/.f64 (fma.f64 (.f64 (fma.f64 (.f64 (.f64 eps (.f64 eps eps)) eps) #s(literal 1/144 binary64) #s(literal -1/4 binary64)) x) (.f64 eps eps) (.f64 (fma.f64 (.f64 eps eps) #s(literal 1/12 binary64) #s(literal 1/2 binary64)) (.f64 (.f64 eps (.f64 eps eps)) #s(literal -1/2 binary64)))) (.f64 (fma.f64 (.f64 eps eps) #s(literal 1/12 binary64) #s(literal 1/2 binary64)) (*.f64 eps eps)))
(pow.f64 (/.f64 (fma.f64 (.f64 eps #s(literal -1/2 binary64)) (-.f64 (.f64 eps #s(literal -1/2 binary64)) (.f64 x (fma.f64 eps (.f64 eps #s(literal 1/12 binary64)) #s(literal -1/2 binary64)))) (.f64 (fma.f64 eps (.f64 eps #s(literal 1/12 binary64)) #s(literal -1/2 binary64)) (.f64 (fma.f64 eps (.f64 eps #s(literal 1/12 binary64)) #s(literal -1/2 binary64)) (.f64 x x)))) (fma.f64 (.f64 x (fma.f64 eps (.f64 eps #s(literal 1/12 binary64)) #s(literal -1/2 binary64))) (.f64 (fma.f64 eps (.f64 eps #s(literal 1/12 binary64)) #s(literal -1/2 binary64)) (.f64 (fma.f64 eps (.f64 eps #s(literal 1/12 binary64)) #s(literal -1/2 binary64)) (.f64 x x))) (.f64 #s(literal -1/8 binary64) (.f64 eps (*.f64 eps eps))))) #s(literal -1 binary64))
(pow.f64 (/.f64 (fma.f64 x (fma.f64 eps (.f64 eps #s(literal 1/12 binary64)) #s(literal -1/2 binary64)) (.f64 eps #s(literal 1/2 binary64))) (.f64 (fma.f64 x (fma.f64 eps (.f64 eps #s(literal 1/12 binary64)) #s(literal -1/2 binary64)) (.f64 eps #s(literal -1/2 binary64))) (fma.f64 x (fma.f64 eps (.f64 eps #s(literal 1/12 binary64)) #s(literal -1/2 binary64)) (*.f64 eps #s(literal 1/2 binary64))))) #s(literal -1 binary64))
(.f64 (fma.f64 (.f64 x (fma.f64 eps (.f64 eps #s(literal 1/12 binary64)) #s(literal -1/2 binary64))) (.f64 (fma.f64 eps (.f64 eps #s(literal 1/12 binary64)) #s(literal -1/2 binary64)) (.f64 (fma.f64 eps (.f64 eps #s(literal 1/12 binary64)) #s(literal -1/2 binary64)) (.f64 x x))) (.f64 #s(literal -1/8 binary64) (.f64 eps (.f64 eps eps)))) (/.f64 #s(literal 1 binary64) (fma.f64 (.f64 eps #s(literal -1/2 binary64)) (-.f64 (.f64 eps #s(literal -1/2 binary64)) (.f64 x (fma.f64 eps (.f64 eps #s(literal 1/12 binary64)) #s(literal -1/2 binary64)))) (.f64 (fma.f64 eps (.f64 eps #s(literal 1/12 binary64)) #s(literal -1/2 binary64)) (.f64 (fma.f64 eps (.f64 eps #s(literal 1/12 binary64)) #s(literal -1/2 binary64)) (.f64 x x))))))
(.f64 (.f64 (fma.f64 x (fma.f64 eps (.f64 eps #s(literal 1/12 binary64)) #s(literal -1/2 binary64)) (.f64 eps #s(literal -1/2 binary64))) (fma.f64 x (fma.f64 eps (.f64 eps #s(literal 1/12 binary64)) #s(literal -1/2 binary64)) (.f64 eps #s(literal 1/2 binary64)))) (/.f64 #s(literal 1 binary64) (fma.f64 x (fma.f64 eps (.f64 eps #s(literal 1/12 binary64)) #s(literal -1/2 binary64)) (.f64 eps #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 #s(literal 0 binary64) (*.f64 eps #s(literal 1/2 binary64)))
(+.f64 (*.f64 eps #s(literal 1/2 binary64)) #s(literal 0 binary64))
(fma.f64 eps #s(literal 1/2 binary64) #s(literal 0 binary64))
(fma.f64 #s(literal 1/2 binary64) eps #s(literal 0 binary64))
(/.f64 (.f64 #s(literal 1/2 binary64) (.f64 eps (.f64 eps eps))) (.f64 eps eps))
(/.f64 (.f64 #s(literal 1/2 binary64) (.f64 eps eps)) eps)
(/.f64 (.f64 (.f64 eps (.f64 eps eps)) #s(literal 1/2 binary64)) (.f64 eps eps))
(/.f64 (.f64 (.f64 eps eps) #s(literal 1/2 binary64)) eps)
(*.f64 eps #s(literal 1/2 binary64))
(*.f64 #s(literal 1/2 binary64) eps)
(cos.f64 x)

eval244.0ms (1.6%)

Memory: -12.6MiB live, 183.8MiB allocated
Compiler: Compiled 48 714 to 2 904 computations (94% saved)

prune261.0ms (1.7%)

Memory

-2.2MiB live, 287.0MiB allocated

Pruning

33 alts after pruning (28 fresh and 5 done)

	Pruned	Kept	Total
New	1 125	19	1 144
Fresh	6	9	15
Picked	3	2	5
Done	0	3	3
Total	1 134	33	1 167

Accuracy

100.0%

Counts

1 167 → 33

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	99.5%	(fma.f64 (sin.f64 eps) (cos.f64 x) (fma.f64 (sin.f64 x) (cos.f64 eps) (sin.f64 (neg.f64 x))))
	99.6%	(fma.f64 (sin.f64 eps) (cos.f64 x) #s(approx (+ (* (sin x) (cos eps)) (sin (neg x))) #s(approx (+ (* (* eps eps) (+ (* (* eps eps) (* (sin x) (+ (* eps (* eps -1/720)) 1/24))) (* -1/2 (sin x)))) 0) (.f64 (.f64 eps eps) (.f64 (sin.f64 x) (fma.f64 #s(literal 1/24 binary64) (.f64 eps eps) #s(literal -1/2 binary64)))))))
▶	99.7%	(fma.f64 #s(approx (sin eps) (fma.f64 eps (.f64 eps (.f64 eps (fma.f64 (.f64 eps eps) #s(literal 1/120 binary64) #s(literal -1/6 binary64)))) eps)) (cos.f64 x) #s(approx (+ ( (sin x) (cos eps)) (sin (neg x))) (fma.f64 (.f64 eps eps) (fma.f64 (.f64 eps eps) (.f64 (sin.f64 x) (fma.f64 eps (.f64 eps #s(literal -1/720 binary64)) #s(literal 1/24 binary64))) (*.f64 #s(literal -1/2 binary64) (sin.f64 x))) #s(literal 0 binary64))))
✓	62.9%	(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
	38.7%	(.f64 (.f64 (sin.f64 (.f64 (.f64 (.f64 eps (.f64 eps eps)) (/.f64 #s(literal 1 binary64) (.f64 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))
	57.6%	(.f64 (.f64 (sin.f64 (.f64 (.f64 (.f64 eps eps) (/.f64 #s(literal 1 binary64) 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))
	99.5%	(.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))
	99.4%	(.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))
▶	99.3%	(.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))
	98.9%	(.f64 (.f64 #s(approx (sin (* (+ eps 0) 1/2)) (.f64 #s(literal 1/2 binary64) eps)) (cos.f64 #s(approx ( (+ (* x 2) eps) 1/2) (fma.f64 eps #s(literal 1/2 binary64) x)))) #s(literal 2 binary64))
	99.6%	(.f64 #s(approx ( (sin (* (+ eps 0) 1/2)) (cos (* (+ (* x 2) eps) 1/2))) (.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (cos.f64 (fma.f64 eps #s(literal 1/2 binary64) x)))) #s(literal 2 binary64))
	38.3%	#s(approx (- (sin (+ x eps)) (sin x)) (/.f64 (fma.f64 (.f64 (.f64 eps eps) (.f64 #s(literal -1/2 binary64) (.f64 eps (sin.f64 x)))) eps (.f64 eps (.f64 (.f64 eps eps) (cos.f64 x)))) (.f64 eps eps)))
	36.4%	#s(approx (- (sin (+ x eps)) (sin x)) (/.f64 (.f64 (.f64 eps (.f64 eps eps)) #s(approx (+ ( eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x))) (fma.f64 x (fma.f64 x (fma.f64 eps (.f64 eps #s(literal 1/12 binary64)) #s(literal -1/2 binary64)) (.f64 eps #s(literal -1/2 binary64))) (fma.f64 (.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64))))) (.f64 eps eps)))
	99.5%	#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))))))
✓	99.3%	#s(approx (- (sin (+ x eps)) (sin 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)))))
✓	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))))
	98.1%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 eps (fma.f64 eps #s(approx ( -1/2 (sin x)) (*.f64 #s(literal -1/2 binary64) x)) (cos.f64 x))))
	98.4%	#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 eps (cos.f64 x)))
▶	96.4%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 eps #s(approx (+ ( eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x))) (fma.f64 eps (.f64 x #s(literal -1/2 binary64)) (fma.f64 #s(literal -1/6 binary64) (.f64 eps eps) #s(literal 1 binary64))))))
	97.1%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 eps #s(approx (+ ( eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x))) (fma.f64 eps (.f64 eps #s(literal -1/6 binary64)) (fma.f64 x (fma.f64 eps #s(literal -1/2 binary64) (.f64 x (fma.f64 eps (*.f64 eps #s(literal 1/12 binary64)) #s(literal -1/2 binary64)))) #s(literal 1 binary64))))))
	97.0%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 eps #s(approx (+ ( eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x))) (fma.f64 eps (.f64 eps #s(literal -1/6 binary64)) (fma.f64 x #s(approx (+ ( x (+ (* (* eps eps) 1/12) -1/2)) (* eps -1/2)) (.f64 x (fma.f64 eps (.f64 eps #s(literal 1/12 binary64)) #s(literal -1/2 binary64)))) #s(literal 1 binary64))))))
	97.1%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 eps #s(approx (+ ( eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x))) (fma.f64 eps (.f64 eps #s(literal -1/6 binary64)) (fma.f64 x #s(approx (+ ( x (+ (* (* eps eps) 1/12) -1/2)) (* eps -1/2)) (*.f64 #s(literal -1/2 binary64) (+.f64 x eps))) #s(literal 1 binary64))))))
	96.4%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 eps #s(approx (+ ( eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x))) (fma.f64 eps (*.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64)))))
	97.0%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 eps #s(approx (+ ( eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x))) #s(approx (+ (* eps (* eps -1/6)) (+ (* x (+ (* x (+ (* (* eps eps) 1/12) -1/2)) (* eps -1/2))) 1)) (fma.f64 #s(literal -1/2 binary64) (*.f64 x x) #s(literal 1 binary64))))))
▶	97.1%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 eps #s(approx (+ ( eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x))) #s(approx (+ (* eps (* eps -1/6)) (+ (* x (+ (* x (+ (* (* eps eps) 1/12) -1/2)) (* eps -1/2))) 1)) (+.f64 (fma.f64 (.f64 #s(literal -1/2 binary64) x) (+.f64 x eps) #s(literal 1 binary64)) (.f64 eps (.f64 eps (fma.f64 (.f64 x x) #s(literal 1/12 binary64) #s(literal -1/6 binary64)))))))))
	5.0%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 eps #s(approx (+ ( eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x))) #s(approx (+ (* eps (* eps -1/6)) (+ (* x (+ (* x (+ (* (* eps eps) 1/12) -1/2)) (* eps -1/2))) 1)) (.f64 (.f64 x x) (fma.f64 eps (*.f64 eps #s(literal 1/12 binary64)) #s(literal -1/2 binary64)))))))
	5.7%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 eps #s(approx (+ ( eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x))) #s(approx (+ (* eps (* eps -1/6)) (+ (* x (+ (* x (+ (* (* eps eps) 1/12) -1/2)) (* eps -1/2))) 1)) (.f64 (.f64 eps eps) (fma.f64 #s(literal -1/2 binary64) (/.f64 x eps) (fma.f64 (*.f64 x x) #s(literal 1/12 binary64) #s(literal -1/6 binary64))))))))
	97.1%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 eps #s(approx (+ ( eps (* -1/2 (sin x))) (cos x)) (fma.f64 x (fma.f64 x (fma.f64 x (.f64 eps #s(literal 1/12 binary64)) #s(literal -1/2 binary64)) (.f64 #s(literal -1/2 binary64) eps)) #s(literal 1 binary64)))))
	96.4%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 eps #s(approx (+ ( eps (* -1/2 (sin x))) (cos x)) (fma.f64 #s(literal -1/2 binary64) (*.f64 x eps) #s(literal 1 binary64)))))
▶	96.4%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 eps #s(approx (+ ( eps (* -1/2 (sin x))) (cos x)) #s(literal 1 binary64))))
	96.4%	#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* eps (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x)))) (fma.f64 eps (fma.f64 #s(literal -1/6 binary64) (.f64 eps eps) #s(literal 1 binary64)) (.f64 x (.f64 #s(literal -1/2 binary64) (.f64 eps eps))))))
	97.1%	#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* eps (+ (* eps (* -1/2 (sin x))) (cos x))) (fma.f64 #s(literal -1/2 binary64) (.f64 (.f64 eps (+.f64 x eps)) x) eps)))
✓	5.3%	#s(approx (+ (* (sin eps) (cos x)) (+ (* (sin x) (cos eps)) (sin (neg x)))) #s(literal 0 binary64))

Compiler

Compiled 1 205 to 688 computations (42.9% saved)

simplify226.0ms (1.5%)

Memory

23.1MiB live, 257.5MiB 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 (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x))) #s(approx (+ (* eps (* eps -1/6)) (+ (* x (+ (* x (+ (* (* eps eps) 1/12) -1/2)) (* eps -1/2))) 1)) (+.f64 (fma.f64 (.f64 #s(literal -1/2 binary64) x) (+.f64 x eps) #s(literal 1 binary64)) (.f64 eps (.f64 eps (fma.f64 (.f64 x x) #s(literal 1/12 binary64) #s(literal -1/6 binary64)))))))
cost-diff	0	(.f64 eps #s(approx (+ ( eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x))) #s(approx (+ (* eps (* eps -1/6)) (+ (* x (+ (* x (+ (* (* eps eps) 1/12) -1/2)) (* eps -1/2))) 1)) (+.f64 (fma.f64 (.f64 #s(literal -1/2 binary64) x) (+.f64 x eps) #s(literal 1 binary64)) (.f64 eps (.f64 eps (fma.f64 (.f64 x x) #s(literal 1/12 binary64) #s(literal -1/6 binary64))))))))
cost-diff	0	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 eps #s(approx (+ ( eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x))) #s(approx (+ (* eps (* eps -1/6)) (+ (* x (+ (* x (+ (* (* eps eps) 1/12) -1/2)) (* eps -1/2))) 1)) (+.f64 (fma.f64 (.f64 #s(literal -1/2 binary64) x) (+.f64 x eps) #s(literal 1 binary64)) (.f64 eps (.f64 eps (fma.f64 (.f64 x x) #s(literal 1/12 binary64) #s(literal -1/6 binary64)))))))))
cost-diff	128	(+.f64 (fma.f64 (.f64 #s(literal -1/2 binary64) x) (+.f64 x eps) #s(literal 1 binary64)) (.f64 eps (.f64 eps (fma.f64 (.f64 x x) #s(literal 1/12 binary64) #s(literal -1/6 binary64)))))
cost-diff	0	#s(approx (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x))) (fma.f64 eps (.f64 x #s(literal -1/2 binary64)) (fma.f64 #s(literal -1/6 binary64) (.f64 eps eps) #s(literal 1 binary64))))
cost-diff	0	(.f64 eps #s(approx (+ ( eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x))) (fma.f64 eps (.f64 x #s(literal -1/2 binary64)) (fma.f64 #s(literal -1/6 binary64) (.f64 eps eps) #s(literal 1 binary64)))))
cost-diff	0	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 eps #s(approx (+ ( eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x))) (fma.f64 eps (.f64 x #s(literal -1/2 binary64)) (fma.f64 #s(literal -1/6 binary64) (.f64 eps eps) #s(literal 1 binary64))))))
cost-diff	320	(fma.f64 eps (.f64 x #s(literal -1/2 binary64)) (fma.f64 #s(literal -1/6 binary64) (.f64 eps eps) #s(literal 1 binary64)))
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	#s(approx (sin eps) (fma.f64 eps (.f64 eps (.f64 eps (fma.f64 (*.f64 eps eps) #s(literal 1/120 binary64) #s(literal -1/6 binary64)))) eps))
cost-diff	0	(fma.f64 #s(approx (sin eps) (fma.f64 eps (.f64 eps (.f64 eps (fma.f64 (.f64 eps eps) #s(literal 1/120 binary64) #s(literal -1/6 binary64)))) eps)) (cos.f64 x) #s(approx (+ ( (sin x) (cos eps)) (sin (neg x))) (fma.f64 (.f64 eps eps) (fma.f64 (.f64 eps eps) (.f64 (sin.f64 x) (fma.f64 eps (.f64 eps #s(literal -1/720 binary64)) #s(literal 1/24 binary64))) (*.f64 #s(literal -1/2 binary64) (sin.f64 x))) #s(literal 0 binary64))))
cost-diff	64	(fma.f64 (.f64 eps eps) (fma.f64 (.f64 eps eps) (.f64 (sin.f64 x) (fma.f64 eps (.f64 eps #s(literal -1/720 binary64)) #s(literal 1/24 binary64))) (*.f64 #s(literal -1/2 binary64) (sin.f64 x))) #s(literal 0 binary64))
cost-diff	6720	(fma.f64 (.f64 eps eps) (.f64 (sin.f64 x) (fma.f64 eps (.f64 eps #s(literal -1/720 binary64)) #s(literal 1/24 binary64))) (.f64 #s(literal -1/2 binary64) (sin.f64 x)))

Rules

10 434×	`lower-fma.f32`
10 410×	`lower-fma.f64`
3 394×	`lower-*.f32`
3 356×	`lower-*.f64`
2 712×	`lower-+.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	90	792
0	140	781
1	290	774
2	767	746
3	2136	742
4	3439	742
5	3701	742
6	3899	742
7	4055	742
8	4636	742
9	7667	742
0	8028	699

Stop Event

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

Calls

Call 1

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

localize439.0ms (2.9%)

Memory

19.3MiB live, 764.8MiB allocated

Localize:

Found 19 expressions of interest:

New	Metric	Score
accuracy	0.0234375	(.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))))
accuracy	0.2232612867848975	(cos.f64 (*.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)))
accuracy	0.25503658697986015	#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	0.34375	(*.f64 eps #s(literal -1/48 binary64))
accuracy	0.15234375	(.f64 eps (.f64 eps (fma.f64 (*.f64 x x) #s(literal 1/12 binary64) #s(literal -1/6 binary64))))
accuracy	0.33984375	(.f64 eps (fma.f64 (.f64 x x) #s(literal 1/12 binary64) #s(literal -1/6 binary64)))
accuracy	0.447769100952185	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 eps #s(approx (+ ( eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x))) #s(approx (+ (* eps (* eps -1/6)) (+ (* x (+ (* x (+ (* (* eps eps) 1/12) -1/2)) (* eps -1/2))) 1)) (+.f64 (fma.f64 (.f64 #s(literal -1/2 binary64) x) (+.f64 x eps) #s(literal 1 binary64)) (.f64 eps (.f64 eps (fma.f64 (.f64 x x) #s(literal 1/12 binary64) #s(literal -1/6 binary64)))))))))
accuracy	1.8720939710084297	#s(approx (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x))) #s(approx (+ (* eps (* eps -1/6)) (+ (* x (+ (* x (+ (* (* eps eps) 1/12) -1/2)) (* eps -1/2))) 1)) (+.f64 (fma.f64 (.f64 #s(literal -1/2 binary64) x) (+.f64 x eps) #s(literal 1 binary64)) (.f64 eps (.f64 eps (fma.f64 (.f64 x x) #s(literal 1/12 binary64) #s(literal -1/6 binary64)))))))
accuracy	0	(*.f64 eps eps)
accuracy	0.01953125	(.f64 eps #s(approx (+ ( eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x))) (fma.f64 eps (.f64 x #s(literal -1/2 binary64)) (fma.f64 #s(literal -1/6 binary64) (.f64 eps eps) #s(literal 1 binary64)))))
accuracy	0.447769100952185	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 eps #s(approx (+ ( eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x))) (fma.f64 eps (.f64 x #s(literal -1/2 binary64)) (fma.f64 #s(literal -1/6 binary64) (.f64 eps eps) #s(literal 1 binary64))))))
accuracy	2.346944144933273	#s(approx (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x))) (fma.f64 eps (.f64 x #s(literal -1/2 binary64)) (fma.f64 #s(literal -1/6 binary64) (.f64 eps eps) #s(literal 1 binary64))))
accuracy	0.015625	(.f64 eps #s(approx (+ ( eps (* -1/2 (sin x))) (cos x)) #s(literal 1 binary64)))
accuracy	0.638556655459079	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 eps #s(approx (+ ( eps (* -1/2 (sin x))) (cos x)) #s(literal 1 binary64))))
accuracy	2.342405291456133	#s(approx (+ (* eps (* -1/2 (sin x))) (cos x)) #s(literal 1 binary64))
accuracy	0.1712372109291372	#s(approx (sin eps) (fma.f64 eps (.f64 eps (.f64 eps (fma.f64 (*.f64 eps eps) #s(literal 1/120 binary64) #s(literal -1/6 binary64)))) eps))
accuracy	0.20703125	(*.f64 eps #s(literal -1/720 binary64))
accuracy	0.33984375	(.f64 (sin.f64 x) (fma.f64 eps (.f64 eps #s(literal -1/720 binary64)) #s(literal 1/24 binary64)))
accuracy	0.34765625	(.f64 eps (fma.f64 (.f64 eps eps) #s(literal 1/120 binary64) #s(literal -1/6 binary64)))

Samples

279.0ms	230×	1	valid
28.0ms	18×	2	valid
5.0ms	8×	0	valid

Compiler

Compiled 476 to 88 computations (81.5% saved)

Precisions

Click to see histograms. Total time spent on operations: 261.0ms

ival-mult: 86.0ms (33% of total)

ival-add: 68.0ms (26.1% of total)

adjust: 43.0ms (16.5% of total)

const: 27.0ms (10.4% of total)

ival-sin: 23.0ms (8.8% of total)

ival-cos: 11.0ms (4.2% of total)

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

exact: 1.0ms (0.4% of total)

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

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

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

series44.0ms (0.3%)

Memory

-11.9MiB live, 104.7MiB allocated

Counts

27 → 576

Calls

Call 1

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

Outputs
#s(alt (* -1/2 (sin x)) (taylor 0 eps) (#s(alt (fma.f64 (.f64 eps eps) (.f64 (sin.f64 x) (fma.f64 eps (.f64 eps #s(literal -1/720 binary64)) #s(literal 1/24 binary64))) (.f64 #s(literal -1/2 binary64) (sin.f64 x))) (patch (fma.f64 (.f64 eps eps) (.f64 (sin.f64 x) (fma.f64 eps (.f64 eps #s(literal -1/720 binary64)) #s(literal 1/24 binary64))) (.f64 #s(literal -1/2 binary64) (sin.f64 x))) #<representation binary64>) () ())) ())
#s(alt (+ (* -1/2 (sin x)) (* 1/24 (* (pow eps 2) (sin x)))) (taylor 0 eps) (#s(alt (fma.f64 (.f64 eps eps) (.f64 (sin.f64 x) (fma.f64 eps (.f64 eps #s(literal -1/720 binary64)) #s(literal 1/24 binary64))) (.f64 #s(literal -1/2 binary64) (sin.f64 x))) (patch (fma.f64 (.f64 eps eps) (.f64 (sin.f64 x) (fma.f64 eps (.f64 eps #s(literal -1/720 binary64)) #s(literal 1/24 binary64))) (.f64 #s(literal -1/2 binary64) (sin.f64 x))) #<representation binary64>) () ())) ())
#s(alt (+ (* -1/2 (sin x)) (* (pow eps 2) (+ (* -1/720 (* (pow eps 2) (sin x))) (* 1/24 (sin x))))) (taylor 0 eps) (#s(alt (fma.f64 (.f64 eps eps) (.f64 (sin.f64 x) (fma.f64 eps (.f64 eps #s(literal -1/720 binary64)) #s(literal 1/24 binary64))) (.f64 #s(literal -1/2 binary64) (sin.f64 x))) (patch (fma.f64 (.f64 eps eps) (.f64 (sin.f64 x) (fma.f64 eps (.f64 eps #s(literal -1/720 binary64)) #s(literal 1/24 binary64))) (.f64 #s(literal -1/2 binary64) (sin.f64 x))) #<representation binary64>) () ())) ())
#s(alt (+ (* -1/2 (sin x)) (* (pow eps 2) (+ (* -1/720 (* (pow eps 2) (sin x))) (* 1/24 (sin x))))) (taylor 0 eps) (#s(alt (fma.f64 (.f64 eps eps) (.f64 (sin.f64 x) (fma.f64 eps (.f64 eps #s(literal -1/720 binary64)) #s(literal 1/24 binary64))) (.f64 #s(literal -1/2 binary64) (sin.f64 x))) (patch (fma.f64 (.f64 eps eps) (.f64 (sin.f64 x) (fma.f64 eps (.f64 eps #s(literal -1/720 binary64)) #s(literal 1/24 binary64))) (.f64 #s(literal -1/2 binary64) (sin.f64 x))) #<representation binary64>) () ())) ())
#s(alt (* -1/720 (* (pow eps 4) (sin x))) (taylor inf eps) (#s(alt (fma.f64 (.f64 eps eps) (.f64 (sin.f64 x) (fma.f64 eps (.f64 eps #s(literal -1/720 binary64)) #s(literal 1/24 binary64))) (.f64 #s(literal -1/2 binary64) (sin.f64 x))) (patch (fma.f64 (.f64 eps eps) (.f64 (sin.f64 x) (fma.f64 eps (.f64 eps #s(literal -1/720 binary64)) #s(literal 1/24 binary64))) (.f64 #s(literal -1/2 binary64) (sin.f64 x))) #<representation binary64>) () ())) ())
#s(alt (* (pow eps 4) (+ (* -1/720 (sin x)) (* 1/24 (/ (sin x) (pow eps 2))))) (taylor inf eps) (#s(alt (fma.f64 (.f64 eps eps) (.f64 (sin.f64 x) (fma.f64 eps (.f64 eps #s(literal -1/720 binary64)) #s(literal 1/24 binary64))) (.f64 #s(literal -1/2 binary64) (sin.f64 x))) (patch (fma.f64 (.f64 eps eps) (.f64 (sin.f64 x) (fma.f64 eps (.f64 eps #s(literal -1/720 binary64)) #s(literal 1/24 binary64))) (.f64 #s(literal -1/2 binary64) (sin.f64 x))) #<representation binary64>) () ())) ())
#s(alt (* (pow eps 4) (+ (* -1/2 (/ (sin x) (pow eps 4))) (+ (* -1/720 (sin x)) (* 1/24 (/ (sin x) (pow eps 2)))))) (taylor inf eps) (#s(alt (fma.f64 (.f64 eps eps) (.f64 (sin.f64 x) (fma.f64 eps (.f64 eps #s(literal -1/720 binary64)) #s(literal 1/24 binary64))) (.f64 #s(literal -1/2 binary64) (sin.f64 x))) (patch (fma.f64 (.f64 eps eps) (.f64 (sin.f64 x) (fma.f64 eps (.f64 eps #s(literal -1/720 binary64)) #s(literal 1/24 binary64))) (.f64 #s(literal -1/2 binary64) (sin.f64 x))) #<representation binary64>) () ())) ())
#s(alt (* (pow eps 4) (+ (* -1/2 (/ (sin x) (pow eps 4))) (+ (* -1/720 (sin x)) (* 1/24 (/ (sin x) (pow eps 2)))))) (taylor inf eps) (#s(alt (fma.f64 (.f64 eps eps) (.f64 (sin.f64 x) (fma.f64 eps (.f64 eps #s(literal -1/720 binary64)) #s(literal 1/24 binary64))) (.f64 #s(literal -1/2 binary64) (sin.f64 x))) (patch (fma.f64 (.f64 eps eps) (.f64 (sin.f64 x) (fma.f64 eps (.f64 eps #s(literal -1/720 binary64)) #s(literal 1/24 binary64))) (.f64 #s(literal -1/2 binary64) (sin.f64 x))) #<representation binary64>) () ())) ())
#s(alt (* -1/720 (* (pow eps 4) (sin x))) (taylor -inf eps) (#s(alt (fma.f64 (.f64 eps eps) (.f64 (sin.f64 x) (fma.f64 eps (.f64 eps #s(literal -1/720 binary64)) #s(literal 1/24 binary64))) (.f64 #s(literal -1/2 binary64) (sin.f64 x))) (patch (fma.f64 (.f64 eps eps) (.f64 (sin.f64 x) (fma.f64 eps (.f64 eps #s(literal -1/720 binary64)) #s(literal 1/24 binary64))) (.f64 #s(literal -1/2 binary64) (sin.f64 x))) #<representation binary64>) () ())) ())
#s(alt (* (pow eps 4) (+ (* -1/720 (sin x)) (* 1/24 (/ (sin x) (pow eps 2))))) (taylor -inf eps) (#s(alt (fma.f64 (.f64 eps eps) (.f64 (sin.f64 x) (fma.f64 eps (.f64 eps #s(literal -1/720 binary64)) #s(literal 1/24 binary64))) (.f64 #s(literal -1/2 binary64) (sin.f64 x))) (patch (fma.f64 (.f64 eps eps) (.f64 (sin.f64 x) (fma.f64 eps (.f64 eps #s(literal -1/720 binary64)) #s(literal 1/24 binary64))) (.f64 #s(literal -1/2 binary64) (sin.f64 x))) #<representation binary64>) () ())) ())
#s(alt (* (pow eps 4) (+ (* -1/2 (/ (sin x) (pow eps 4))) (+ (* -1/720 (sin x)) (* 1/24 (/ (sin x) (pow eps 2)))))) (taylor -inf eps) (#s(alt (fma.f64 (.f64 eps eps) (.f64 (sin.f64 x) (fma.f64 eps (.f64 eps #s(literal -1/720 binary64)) #s(literal 1/24 binary64))) (.f64 #s(literal -1/2 binary64) (sin.f64 x))) (patch (fma.f64 (.f64 eps eps) (.f64 (sin.f64 x) (fma.f64 eps (.f64 eps #s(literal -1/720 binary64)) #s(literal 1/24 binary64))) (.f64 #s(literal -1/2 binary64) (sin.f64 x))) #<representation binary64>) () ())) ())
#s(alt (* (pow eps 4) (+ (* -1/2 (/ (sin x) (pow eps 4))) (+ (* -1/720 (sin x)) (* 1/24 (/ (sin x) (pow eps 2)))))) (taylor -inf eps) (#s(alt (fma.f64 (.f64 eps eps) (.f64 (sin.f64 x) (fma.f64 eps (.f64 eps #s(literal -1/720 binary64)) #s(literal 1/24 binary64))) (.f64 #s(literal -1/2 binary64) (sin.f64 x))) (patch (fma.f64 (.f64 eps eps) (.f64 (sin.f64 x) (fma.f64 eps (.f64 eps #s(literal -1/720 binary64)) #s(literal 1/24 binary64))) (.f64 #s(literal -1/2 binary64) (sin.f64 x))) #<representation binary64>) () ())) ())
#s(alt (* x (- (* (pow eps 2) (+ 1/24 (* -1/720 (pow eps 2)))) 1/2)) (taylor 0 x) (#s(alt (fma.f64 (.f64 eps eps) (.f64 (sin.f64 x) (fma.f64 eps (.f64 eps #s(literal -1/720 binary64)) #s(literal 1/24 binary64))) (.f64 #s(literal -1/2 binary64) (sin.f64 x))) (patch (fma.f64 (.f64 eps eps) (.f64 (sin.f64 x) (fma.f64 eps (.f64 eps #s(literal -1/720 binary64)) #s(literal 1/24 binary64))) (.f64 #s(literal -1/2 binary64) (sin.f64 x))) #<representation binary64>) () ())) ())
#s(alt (* x (- (+ (* (pow eps 2) (+ 1/24 (* -1/720 (pow eps 2)))) (* (pow x 2) (+ 1/12 (* -1/6 (* (pow eps 2) (+ 1/24 (* -1/720 (pow eps 2)))))))) 1/2)) (taylor 0 x) (#s(alt (fma.f64 (.f64 eps eps) (.f64 (sin.f64 x) (fma.f64 eps (.f64 eps #s(literal -1/720 binary64)) #s(literal 1/24 binary64))) (.f64 #s(literal -1/2 binary64) (sin.f64 x))) (patch (fma.f64 (.f64 eps eps) (.f64 (sin.f64 x) (fma.f64 eps (.f64 eps #s(literal -1/720 binary64)) #s(literal 1/24 binary64))) (.f64 #s(literal -1/2 binary64) (sin.f64 x))) #<representation binary64>) () ())) ())
#s(alt (* x (- (+ (* (pow eps 2) (+ 1/24 (* -1/720 (pow eps 2)))) (* (pow x 2) (+ 1/12 (+ (* -1/6 (* (pow eps 2) (+ 1/24 (* -1/720 (pow eps 2))))) (* (pow x 2) (- (* 1/120 (* (pow eps 2) (+ 1/24 (* -1/720 (pow eps 2))))) 1/240)))))) 1/2)) (taylor 0 x) (#s(alt (fma.f64 (.f64 eps eps) (.f64 (sin.f64 x) (fma.f64 eps (.f64 eps #s(literal -1/720 binary64)) #s(literal 1/24 binary64))) (.f64 #s(literal -1/2 binary64) (sin.f64 x))) (patch (fma.f64 (.f64 eps eps) (.f64 (sin.f64 x) (fma.f64 eps (.f64 eps #s(literal -1/720 binary64)) #s(literal 1/24 binary64))) (.f64 #s(literal -1/2 binary64) (sin.f64 x))) #<representation binary64>) () ())) ())
#s(alt (* x (- (+ (* (pow eps 2) (+ 1/24 (* -1/720 (pow eps 2)))) (* (pow x 2) (+ 1/12 (+ (* -1/6 (* (pow eps 2) (+ 1/24 (* -1/720 (pow eps 2))))) (* (pow x 2) (- (+ (* 1/120 (* (pow eps 2) (+ 1/24 (* -1/720 (pow eps 2))))) (* (pow x 2) (+ 1/10080 (* -1/5040 (* (pow eps 2) (+ 1/24 (* -1/720 (pow eps 2)))))))) 1/240)))))) 1/2)) (taylor 0 x) (#s(alt (fma.f64 (.f64 eps eps) (.f64 (sin.f64 x) (fma.f64 eps (.f64 eps #s(literal -1/720 binary64)) #s(literal 1/24 binary64))) (.f64 #s(literal -1/2 binary64) (sin.f64 x))) (patch (fma.f64 (.f64 eps eps) (.f64 (sin.f64 x) (fma.f64 eps (.f64 eps #s(literal -1/720 binary64)) #s(literal 1/24 binary64))) (.f64 #s(literal -1/2 binary64) (sin.f64 x))) #<representation binary64>) () ())) ())
#s(alt (+ (* -1/2 (sin x)) (* (pow eps 2) (* (sin x) (+ 1/24 (* -1/720 (pow eps 2)))))) (taylor inf x) (#s(alt (fma.f64 (.f64 eps eps) (.f64 (sin.f64 x) (fma.f64 eps (.f64 eps #s(literal -1/720 binary64)) #s(literal 1/24 binary64))) (.f64 #s(literal -1/2 binary64) (sin.f64 x))) (patch (fma.f64 (.f64 eps eps) (.f64 (sin.f64 x) (fma.f64 eps (.f64 eps #s(literal -1/720 binary64)) #s(literal 1/24 binary64))) (.f64 #s(literal -1/2 binary64) (sin.f64 x))) #<representation binary64>) () ())) ())
#s(alt (+ (* -1/2 (sin x)) (* (pow eps 2) (* (sin x) (+ 1/24 (* -1/720 (pow eps 2)))))) (taylor inf x) (#s(alt (fma.f64 (.f64 eps eps) (.f64 (sin.f64 x) (fma.f64 eps (.f64 eps #s(literal -1/720 binary64)) #s(literal 1/24 binary64))) (.f64 #s(literal -1/2 binary64) (sin.f64 x))) (patch (fma.f64 (.f64 eps eps) (.f64 (sin.f64 x) (fma.f64 eps (.f64 eps #s(literal -1/720 binary64)) #s(literal 1/24 binary64))) (.f64 #s(literal -1/2 binary64) (sin.f64 x))) #<representation binary64>) () ())) ())
#s(alt (+ (* -1/2 (sin x)) (* (pow eps 2) (* (sin x) (+ 1/24 (* -1/720 (pow eps 2)))))) (taylor inf x) (#s(alt (fma.f64 (.f64 eps eps) (.f64 (sin.f64 x) (fma.f64 eps (.f64 eps #s(literal -1/720 binary64)) #s(literal 1/24 binary64))) (.f64 #s(literal -1/2 binary64) (sin.f64 x))) (patch (fma.f64 (.f64 eps eps) (.f64 (sin.f64 x) (fma.f64 eps (.f64 eps #s(literal -1/720 binary64)) #s(literal 1/24 binary64))) (.f64 #s(literal -1/2 binary64) (sin.f64 x))) #<representation binary64>) () ())) ())
#s(alt (+ (* -1/2 (sin x)) (* (pow eps 2) (* (sin x) (+ 1/24 (* -1/720 (pow eps 2)))))) (taylor inf x) (#s(alt (fma.f64 (.f64 eps eps) (.f64 (sin.f64 x) (fma.f64 eps (.f64 eps #s(literal -1/720 binary64)) #s(literal 1/24 binary64))) (.f64 #s(literal -1/2 binary64) (sin.f64 x))) (patch (fma.f64 (.f64 eps eps) (.f64 (sin.f64 x) (fma.f64 eps (.f64 eps #s(literal -1/720 binary64)) #s(literal 1/24 binary64))) (.f64 #s(literal -1/2 binary64) (sin.f64 x))) #<representation binary64>) () ())) ())
#s(alt (+ (* -1/2 (sin x)) (* (pow eps 2) (* (sin x) (+ 1/24 (* -1/720 (pow eps 2)))))) (taylor -inf x) (#s(alt (fma.f64 (.f64 eps eps) (.f64 (sin.f64 x) (fma.f64 eps (.f64 eps #s(literal -1/720 binary64)) #s(literal 1/24 binary64))) (.f64 #s(literal -1/2 binary64) (sin.f64 x))) (patch (fma.f64 (.f64 eps eps) (.f64 (sin.f64 x) (fma.f64 eps (.f64 eps #s(literal -1/720 binary64)) #s(literal 1/24 binary64))) (.f64 #s(literal -1/2 binary64) (sin.f64 x))) #<representation binary64>) () ())) ())
#s(alt (+ (* -1/2 (sin x)) (* (pow eps 2) (* (sin x) (+ 1/24 (* -1/720 (pow eps 2)))))) (taylor -inf x) (#s(alt (fma.f64 (.f64 eps eps) (.f64 (sin.f64 x) (fma.f64 eps (.f64 eps #s(literal -1/720 binary64)) #s(literal 1/24 binary64))) (.f64 #s(literal -1/2 binary64) (sin.f64 x))) (patch (fma.f64 (.f64 eps eps) (.f64 (sin.f64 x) (fma.f64 eps (.f64 eps #s(literal -1/720 binary64)) #s(literal 1/24 binary64))) (.f64 #s(literal -1/2 binary64) (sin.f64 x))) #<representation binary64>) () ())) ())
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#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>) () ())) ())

Calls

144 calls:

Time	Variable		Point	Expression
2.0ms	x	@	inf	(+ (* eps (* -1/2 (sin x))) (cos x))
1.0ms	eps	@	0	(* eps (+ (* (* x x) 1/12) -1/6))
0.0ms	eps	@	inf	(+ (+ (* (* -1/2 x) (+ x eps)) 1) (* eps (* eps (+ (* (* x x) 1/12) -1/6))))
0.0ms	eps	@	inf	(* eps (+ (* (* eps eps) 1/120) -1/6))
0.0ms	x	@	inf	(+ (+ (* (* -1/2 x) (+ x eps)) 1) (* eps (* eps (+ (* (* x x) 1/12) -1/6))))

simplify283.0ms (1.8%)

Memory

7.0MiB live, 446.3MiB allocated

Algorithm

1×	egg-herbie

Rules

11 964×	`lower-fma.f64`
11 964×	`lower-fma.f32`
7 892×	`lower-*.f64`
7 892×	`lower-*.f32`
2 724×	`lower-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	563	7456
1	1823	7215
2	5700	7184
0	8813	6541

Stop Event

1×	iter limit
1×	node limit

Counts

576 → 571

Calls

Call 1

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

Outputs
(* -1/2 (sin x))
(*.f64 #s(literal -1/2 binary64) (sin.f64 x))
(+ (* -1/2 (sin x)) (* 1/24 (* (pow eps 2) (sin x))))
(.f64 (sin.f64 x) (fma.f64 #s(literal 1/24 binary64) (.f64 eps eps) #s(literal -1/2 binary64)))
(+ (* -1/2 (sin x)) (* (pow eps 2) (+ (* -1/720 (* (pow eps 2) (sin x))) (* 1/24 (sin x)))))
(fma.f64 (sin.f64 x) (.f64 eps (.f64 eps (fma.f64 (.f64 eps eps) #s(literal -1/720 binary64) #s(literal 1/24 binary64)))) (.f64 #s(literal -1/2 binary64) (sin.f64 x)))
(+ (* -1/2 (sin x)) (* (pow eps 2) (+ (* -1/720 (* (pow eps 2) (sin x))) (* 1/24 (sin x)))))
(fma.f64 (sin.f64 x) (.f64 eps (.f64 eps (fma.f64 (.f64 eps eps) #s(literal -1/720 binary64) #s(literal 1/24 binary64)))) (.f64 #s(literal -1/2 binary64) (sin.f64 x)))
(* -1/720 (* (pow eps 4) (sin x)))
(.f64 (sin.f64 x) (.f64 eps (.f64 eps (.f64 (*.f64 eps eps) #s(literal -1/720 binary64)))))
(* (pow eps 4) (+ (* -1/720 (sin x)) (* 1/24 (/ (sin x) (pow eps 2)))))
(.f64 (.f64 (.f64 eps eps) (.f64 eps eps)) (fma.f64 (sin.f64 x) #s(literal -1/720 binary64) (/.f64 (.f64 (sin.f64 x) #s(literal 1/24 binary64)) (.f64 eps eps))))
(* (pow eps 4) (+ (* -1/2 (/ (sin x) (pow eps 4))) (+ (* -1/720 (sin x)) (* 1/24 (/ (sin x) (pow eps 2))))))
(.f64 (.f64 (.f64 eps eps) (.f64 eps eps)) (fma.f64 #s(literal -1/2 binary64) (/.f64 (sin.f64 x) (.f64 (.f64 eps eps) (.f64 eps eps))) (fma.f64 (sin.f64 x) #s(literal -1/720 binary64) (/.f64 (.f64 (sin.f64 x) #s(literal 1/24 binary64)) (*.f64 eps eps)))))
(* (pow eps 4) (+ (* -1/2 (/ (sin x) (pow eps 4))) (+ (* -1/720 (sin x)) (* 1/24 (/ (sin x) (pow eps 2))))))
(.f64 (.f64 (.f64 eps eps) (.f64 eps eps)) (fma.f64 #s(literal -1/2 binary64) (/.f64 (sin.f64 x) (.f64 (.f64 eps eps) (.f64 eps eps))) (fma.f64 (sin.f64 x) #s(literal -1/720 binary64) (/.f64 (.f64 (sin.f64 x) #s(literal 1/24 binary64)) (*.f64 eps eps)))))
(* -1/720 (* (pow eps 4) (sin x)))
(.f64 (sin.f64 x) (.f64 eps (.f64 eps (.f64 (*.f64 eps eps) #s(literal -1/720 binary64)))))
(* (pow eps 4) (+ (* -1/720 (sin x)) (* 1/24 (/ (sin x) (pow eps 2)))))
(.f64 (.f64 (.f64 eps eps) (.f64 eps eps)) (fma.f64 (sin.f64 x) #s(literal -1/720 binary64) (/.f64 (.f64 (sin.f64 x) #s(literal 1/24 binary64)) (.f64 eps eps))))
(* (pow eps 4) (+ (* -1/2 (/ (sin x) (pow eps 4))) (+ (* -1/720 (sin x)) (* 1/24 (/ (sin x) (pow eps 2))))))
(.f64 (.f64 (.f64 eps eps) (.f64 eps eps)) (fma.f64 #s(literal -1/2 binary64) (/.f64 (sin.f64 x) (.f64 (.f64 eps eps) (.f64 eps eps))) (fma.f64 (sin.f64 x) #s(literal -1/720 binary64) (/.f64 (.f64 (sin.f64 x) #s(literal 1/24 binary64)) (*.f64 eps eps)))))
(* (pow eps 4) (+ (* -1/2 (/ (sin x) (pow eps 4))) (+ (* -1/720 (sin x)) (* 1/24 (/ (sin x) (pow eps 2))))))
(.f64 (.f64 (.f64 eps eps) (.f64 eps eps)) (fma.f64 #s(literal -1/2 binary64) (/.f64 (sin.f64 x) (.f64 (.f64 eps eps) (.f64 eps eps))) (fma.f64 (sin.f64 x) #s(literal -1/720 binary64) (/.f64 (.f64 (sin.f64 x) #s(literal 1/24 binary64)) (*.f64 eps eps)))))
(* x (- (* (pow eps 2) (+ 1/24 (* -1/720 (pow eps 2)))) 1/2))
(.f64 x (fma.f64 eps (.f64 eps (fma.f64 (*.f64 eps eps) #s(literal -1/720 binary64) #s(literal 1/24 binary64))) #s(literal -1/2 binary64)))
(* x (- (+ (* (pow eps 2) (+ 1/24 (* -1/720 (pow eps 2)))) (* (pow x 2) (+ 1/12 (* -1/6 (* (pow eps 2) (+ 1/24 (* -1/720 (pow eps 2)))))))) 1/2))
(.f64 x (fma.f64 eps (.f64 eps (fma.f64 (.f64 eps eps) #s(literal -1/720 binary64) #s(literal 1/24 binary64))) (fma.f64 (.f64 x x) (fma.f64 (.f64 eps eps) (fma.f64 (.f64 eps eps) #s(literal 1/4320 binary64) #s(literal -1/144 binary64)) #s(literal 1/12 binary64)) #s(literal -1/2 binary64))))
(* x (- (+ (* (pow eps 2) (+ 1/24 (* -1/720 (pow eps 2)))) (* (pow x 2) (+ 1/12 (+ (* -1/6 (* (pow eps 2) (+ 1/24 (* -1/720 (pow eps 2))))) (* (pow x 2) (- (* 1/120 (* (pow eps 2) (+ 1/24 (* -1/720 (pow eps 2))))) 1/240)))))) 1/2))
(.f64 x (fma.f64 eps (.f64 eps (fma.f64 (.f64 eps eps) #s(literal -1/720 binary64) #s(literal 1/24 binary64))) (fma.f64 (.f64 x x) (fma.f64 (.f64 eps eps) (fma.f64 (.f64 eps eps) #s(literal 1/4320 binary64) #s(literal -1/144 binary64)) (fma.f64 (.f64 x x) (fma.f64 (.f64 eps eps) (fma.f64 (*.f64 eps eps) #s(literal -1/86400 binary64) #s(literal 1/2880 binary64)) #s(literal -1/240 binary64)) #s(literal 1/12 binary64))) #s(literal -1/2 binary64))))
(* x (- (+ (* (pow eps 2) (+ 1/24 (* -1/720 (pow eps 2)))) (* (pow x 2) (+ 1/12 (+ (* -1/6 (* (pow eps 2) (+ 1/24 (* -1/720 (pow eps 2))))) (* (pow x 2) (- (+ (* 1/120 (* (pow eps 2) (+ 1/24 (* -1/720 (pow eps 2))))) (* (pow x 2) (+ 1/10080 (* -1/5040 (* (pow eps 2) (+ 1/24 (* -1/720 (pow eps 2)))))))) 1/240)))))) 1/2))
(.f64 x (fma.f64 (.f64 x x) (fma.f64 (.f64 x x) (fma.f64 (.f64 eps eps) (fma.f64 (.f64 eps eps) #s(literal -1/86400 binary64) #s(literal 1/2880 binary64)) (fma.f64 (.f64 x x) (fma.f64 (.f64 eps eps) (.f64 #s(literal -1/5040 binary64) (fma.f64 (.f64 eps eps) #s(literal -1/720 binary64) #s(literal 1/24 binary64))) #s(literal 1/10080 binary64)) #s(literal -1/240 binary64))) (fma.f64 (.f64 eps eps) (fma.f64 (.f64 eps eps) #s(literal 1/4320 binary64) #s(literal -1/144 binary64)) #s(literal 1/12 binary64))) (fma.f64 eps (.f64 eps (fma.f64 (*.f64 eps eps) #s(literal -1/720 binary64) #s(literal 1/24 binary64))) #s(literal -1/2 binary64))))
(+ (* -1/2 (sin x)) (* (pow eps 2) (* (sin x) (+ 1/24 (* -1/720 (pow eps 2))))))
(fma.f64 (sin.f64 x) (.f64 eps (.f64 eps (fma.f64 (.f64 eps eps) #s(literal -1/720 binary64) #s(literal 1/24 binary64)))) (.f64 #s(literal -1/2 binary64) (sin.f64 x)))
(+ (* -1/2 (sin x)) (* (pow eps 2) (* (sin x) (+ 1/24 (* -1/720 (pow eps 2))))))
(fma.f64 (sin.f64 x) (.f64 eps (.f64 eps (fma.f64 (.f64 eps eps) #s(literal -1/720 binary64) #s(literal 1/24 binary64)))) (.f64 #s(literal -1/2 binary64) (sin.f64 x)))
(+ (* -1/2 (sin x)) (* (pow eps 2) (* (sin x) (+ 1/24 (* -1/720 (pow eps 2))))))
(fma.f64 (sin.f64 x) (.f64 eps (.f64 eps (fma.f64 (.f64 eps eps) #s(literal -1/720 binary64) #s(literal 1/24 binary64)))) (.f64 #s(literal -1/2 binary64) (sin.f64 x)))
(+ (* -1/2 (sin x)) (* (pow eps 2) (* (sin x) (+ 1/24 (* -1/720 (pow eps 2))))))
(fma.f64 (sin.f64 x) (.f64 eps (.f64 eps (fma.f64 (.f64 eps eps) #s(literal -1/720 binary64) #s(literal 1/24 binary64)))) (.f64 #s(literal -1/2 binary64) (sin.f64 x)))
(+ (* -1/2 (sin x)) (* (pow eps 2) (* (sin x) (+ 1/24 (* -1/720 (pow eps 2))))))
(fma.f64 (sin.f64 x) (.f64 eps (.f64 eps (fma.f64 (.f64 eps eps) #s(literal -1/720 binary64) #s(literal 1/24 binary64)))) (.f64 #s(literal -1/2 binary64) (sin.f64 x)))
(+ (* -1/2 (sin x)) (* (pow eps 2) (* (sin x) (+ 1/24 (* -1/720 (pow eps 2))))))
(fma.f64 (sin.f64 x) (.f64 eps (.f64 eps (fma.f64 (.f64 eps eps) #s(literal -1/720 binary64) #s(literal 1/24 binary64)))) (.f64 #s(literal -1/2 binary64) (sin.f64 x)))
(+ (* -1/2 (sin x)) (* (pow eps 2) (* (sin x) (+ 1/24 (* -1/720 (pow eps 2))))))
(fma.f64 (sin.f64 x) (.f64 eps (.f64 eps (fma.f64 (.f64 eps eps) #s(literal -1/720 binary64) #s(literal 1/24 binary64)))) (.f64 #s(literal -1/2 binary64) (sin.f64 x)))
(+ (* -1/2 (sin x)) (* (pow eps 2) (* (sin x) (+ 1/24 (* -1/720 (pow eps 2))))))
(fma.f64 (sin.f64 x) (.f64 eps (.f64 eps (fma.f64 (.f64 eps eps) #s(literal -1/720 binary64) #s(literal 1/24 binary64)))) (.f64 #s(literal -1/2 binary64) (sin.f64 x)))
(* -1/2 (* (pow eps 2) (sin x)))
(.f64 #s(literal -1/2 binary64) (.f64 eps (*.f64 (sin.f64 x) eps)))
(* (pow eps 2) (+ (* -1/2 (sin x)) (* 1/24 (* (pow eps 2) (sin x)))))
(.f64 (.f64 eps eps) (.f64 (sin.f64 x) (fma.f64 #s(literal 1/24 binary64) (.f64 eps eps) #s(literal -1/2 binary64))))
(* (pow eps 2) (+ (* -1/2 (sin x)) (* (pow eps 2) (+ (* -1/720 (* (pow eps 2) (sin x))) (* 1/24 (sin x))))))
(.f64 (.f64 eps eps) (fma.f64 (sin.f64 x) (.f64 eps (.f64 eps (fma.f64 (.f64 eps eps) #s(literal -1/720 binary64) #s(literal 1/24 binary64)))) (.f64 #s(literal -1/2 binary64) (sin.f64 x))))
(* (pow eps 2) (+ (* -1/2 (sin x)) (* (pow eps 2) (+ (* -1/720 (* (pow eps 2) (sin x))) (* 1/24 (sin x))))))
(.f64 (.f64 eps eps) (fma.f64 (sin.f64 x) (.f64 eps (.f64 eps (fma.f64 (.f64 eps eps) #s(literal -1/720 binary64) #s(literal 1/24 binary64)))) (.f64 #s(literal -1/2 binary64) (sin.f64 x))))
(* -1/720 (* (pow eps 6) (sin x)))
(.f64 (sin.f64 x) (.f64 #s(literal -1/720 binary64) (pow.f64 eps #s(literal 6 binary64))))
(* (pow eps 6) (+ (* -1/720 (sin x)) (* 1/24 (/ (sin x) (pow eps 2)))))
(.f64 (fma.f64 (sin.f64 x) #s(literal -1/720 binary64) (/.f64 (.f64 (sin.f64 x) #s(literal 1/24 binary64)) (*.f64 eps eps))) (pow.f64 eps #s(literal 6 binary64)))
(* (pow eps 6) (+ (* -1/2 (/ (sin x) (pow eps 4))) (+ (* -1/720 (sin x)) (* 1/24 (/ (sin x) (pow eps 2))))))
(.f64 (fma.f64 #s(literal -1/2 binary64) (/.f64 (sin.f64 x) (.f64 (.f64 eps eps) (.f64 eps eps))) (fma.f64 (sin.f64 x) #s(literal -1/720 binary64) (/.f64 (.f64 (sin.f64 x) #s(literal 1/24 binary64)) (.f64 eps eps)))) (pow.f64 eps #s(literal 6 binary64)))
(* (pow eps 6) (+ (* -1/2 (/ (sin x) (pow eps 4))) (+ (* -1/720 (sin x)) (* 1/24 (/ (sin x) (pow eps 2))))))
(.f64 (fma.f64 #s(literal -1/2 binary64) (/.f64 (sin.f64 x) (.f64 (.f64 eps eps) (.f64 eps eps))) (fma.f64 (sin.f64 x) #s(literal -1/720 binary64) (/.f64 (.f64 (sin.f64 x) #s(literal 1/24 binary64)) (.f64 eps eps)))) (pow.f64 eps #s(literal 6 binary64)))
(* -1/720 (* (pow eps 6) (sin x)))
(.f64 (sin.f64 x) (.f64 #s(literal -1/720 binary64) (pow.f64 eps #s(literal 6 binary64))))
(* (pow eps 6) (+ (* -1/720 (sin x)) (* 1/24 (/ (sin x) (pow eps 2)))))
(.f64 (fma.f64 (sin.f64 x) #s(literal -1/720 binary64) (/.f64 (.f64 (sin.f64 x) #s(literal 1/24 binary64)) (*.f64 eps eps))) (pow.f64 eps #s(literal 6 binary64)))
(* (pow eps 6) (+ (* -1/2 (/ (sin x) (pow eps 4))) (+ (* -1/720 (sin x)) (* 1/24 (/ (sin x) (pow eps 2))))))
(.f64 (fma.f64 #s(literal -1/2 binary64) (/.f64 (sin.f64 x) (.f64 (.f64 eps eps) (.f64 eps eps))) (fma.f64 (sin.f64 x) #s(literal -1/720 binary64) (/.f64 (.f64 (sin.f64 x) #s(literal 1/24 binary64)) (.f64 eps eps)))) (pow.f64 eps #s(literal 6 binary64)))
(* (pow eps 6) (+ (* -1/2 (/ (sin x) (pow eps 4))) (+ (* -1/720 (sin x)) (* 1/24 (/ (sin x) (pow eps 2))))))
(.f64 (fma.f64 #s(literal -1/2 binary64) (/.f64 (sin.f64 x) (.f64 (.f64 eps eps) (.f64 eps eps))) (fma.f64 (sin.f64 x) #s(literal -1/720 binary64) (/.f64 (.f64 (sin.f64 x) #s(literal 1/24 binary64)) (.f64 eps eps)))) (pow.f64 eps #s(literal 6 binary64)))
(* (pow eps 2) (* x (- (* (pow eps 2) (+ 1/24 (* -1/720 (pow eps 2)))) 1/2)))
(.f64 (.f64 eps eps) (.f64 x (fma.f64 eps (.f64 eps (fma.f64 (*.f64 eps eps) #s(literal -1/720 binary64) #s(literal 1/24 binary64))) #s(literal -1/2 binary64))))
(* x (+ (* (pow eps 2) (* (pow x 2) (+ 1/12 (* -1/6 (* (pow eps 2) (+ 1/24 (* -1/720 (pow eps 2)))))))) (* (pow eps 2) (- (* (pow eps 2) (+ 1/24 (* -1/720 (pow eps 2)))) 1/2))))
(.f64 (.f64 x (.f64 eps eps)) (fma.f64 eps (.f64 eps (fma.f64 (.f64 eps eps) #s(literal -1/720 binary64) #s(literal 1/24 binary64))) (fma.f64 (.f64 x x) (fma.f64 (.f64 eps eps) (fma.f64 (.f64 eps eps) #s(literal 1/4320 binary64) #s(literal -1/144 binary64)) #s(literal 1/12 binary64)) #s(literal -1/2 binary64))))
(* x (+ (* (pow eps 2) (- (* (pow eps 2) (+ 1/24 (* -1/720 (pow eps 2)))) 1/2)) (* (pow x 2) (+ (* (pow eps 2) (* (pow x 2) (- (* 1/120 (* (pow eps 2) (+ 1/24 (* -1/720 (pow eps 2))))) 1/240))) (* (pow eps 2) (+ 1/12 (* -1/6 (* (pow eps 2) (+ 1/24 (* -1/720 (pow eps 2)))))))))))
(.f64 x (fma.f64 eps (.f64 eps (fma.f64 eps (.f64 eps (fma.f64 (.f64 eps eps) #s(literal -1/720 binary64) #s(literal 1/24 binary64))) #s(literal -1/2 binary64))) (.f64 (.f64 eps eps) (.f64 (.f64 x x) (fma.f64 (.f64 eps eps) (fma.f64 (.f64 eps eps) #s(literal 1/4320 binary64) #s(literal -1/144 binary64)) (fma.f64 (.f64 x x) (fma.f64 (.f64 eps eps) (fma.f64 (*.f64 eps eps) #s(literal -1/86400 binary64) #s(literal 1/2880 binary64)) #s(literal -1/240 binary64)) #s(literal 1/12 binary64)))))))
(* x (+ (* (pow eps 2) (- (* (pow eps 2) (+ 1/24 (* -1/720 (pow eps 2)))) 1/2)) (* (pow x 2) (+ (* (pow eps 2) (+ 1/12 (* -1/6 (* (pow eps 2) (+ 1/24 (* -1/720 (pow eps 2))))))) (* (pow x 2) (+ (* (pow eps 2) (* (pow x 2) (+ 1/10080 (* -1/5040 (* (pow eps 2) (+ 1/24 (* -1/720 (pow eps 2)))))))) (* (pow eps 2) (- (* 1/120 (* (pow eps 2) (+ 1/24 (* -1/720 (pow eps 2))))) 1/240))))))))
(.f64 x (fma.f64 (.f64 x x) (fma.f64 (.f64 eps (.f64 x (.f64 x eps))) (fma.f64 (.f64 eps eps) (fma.f64 (.f64 eps eps) #s(literal -1/86400 binary64) #s(literal 1/2880 binary64)) (fma.f64 (.f64 x x) (fma.f64 (.f64 eps eps) (.f64 #s(literal -1/5040 binary64) (fma.f64 (.f64 eps eps) #s(literal -1/720 binary64) #s(literal 1/24 binary64))) #s(literal 1/10080 binary64)) #s(literal -1/240 binary64))) (.f64 (.f64 eps eps) (fma.f64 (.f64 eps eps) (fma.f64 (.f64 eps eps) #s(literal 1/4320 binary64) #s(literal -1/144 binary64)) #s(literal 1/12 binary64)))) (.f64 (.f64 eps eps) (fma.f64 eps (.f64 eps (fma.f64 (*.f64 eps eps) #s(literal -1/720 binary64) #s(literal 1/24 binary64))) #s(literal -1/2 binary64)))))
(* (pow eps 2) (+ (* -1/2 (sin x)) (* (pow eps 2) (* (sin x) (+ 1/24 (* -1/720 (pow eps 2)))))))
(.f64 (.f64 eps eps) (fma.f64 (sin.f64 x) (.f64 eps (.f64 eps (fma.f64 (.f64 eps eps) #s(literal -1/720 binary64) #s(literal 1/24 binary64)))) (.f64 #s(literal -1/2 binary64) (sin.f64 x))))
(* (pow eps 2) (+ (* -1/2 (sin x)) (* (pow eps 2) (* (sin x) (+ 1/24 (* -1/720 (pow eps 2)))))))
(.f64 (.f64 eps eps) (fma.f64 (sin.f64 x) (.f64 eps (.f64 eps (fma.f64 (.f64 eps eps) #s(literal -1/720 binary64) #s(literal 1/24 binary64)))) (.f64 #s(literal -1/2 binary64) (sin.f64 x))))
(* (pow eps 2) (+ (* -1/2 (sin x)) (* (pow eps 2) (* (sin x) (+ 1/24 (* -1/720 (pow eps 2)))))))
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(cos (* 1/2 (- (* 2 x) (* -1 eps))))
(cos.f64 (fma.f64 eps #s(literal 1/2 binary64) x))

rewrite561.0ms (3.6%)

Memory

-182.5MiB live, 353.4MiB allocated

Rules

6 698×	`lower-fma.f32`
6 674×	`lower-fma.f64`
5 300×	`lower-*.f32`
5 262×	`lower-*.f64`
1 988×	`lower-pow.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	90	595
0	140	581
1	582	575
2	5179	575
0	8180	543

Stop Event

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

Counts

27 → 480

Calls

Call 1

Inputs
(fma.f64 (.f64 eps eps) (.f64 (sin.f64 x) (fma.f64 eps (.f64 eps #s(literal -1/720 binary64)) #s(literal 1/24 binary64))) (.f64 #s(literal -1/2 binary64) (sin.f64 x)))
(fma.f64 (.f64 eps eps) (fma.f64 (.f64 eps eps) (.f64 (sin.f64 x) (fma.f64 eps (.f64 eps #s(literal -1/720 binary64)) #s(literal 1/24 binary64))) (*.f64 #s(literal -1/2 binary64) (sin.f64 x))) #s(literal 0 binary64))
(fma.f64 #s(approx (sin eps) (fma.f64 eps (.f64 eps (.f64 eps (fma.f64 (.f64 eps eps) #s(literal 1/120 binary64) #s(literal -1/6 binary64)))) eps)) (cos.f64 x) #s(approx (+ ( (sin x) (cos eps)) (sin (neg x))) (fma.f64 (.f64 eps eps) (fma.f64 (.f64 eps eps) (.f64 (sin.f64 x) (fma.f64 eps (.f64 eps #s(literal -1/720 binary64)) #s(literal 1/24 binary64))) (*.f64 #s(literal -1/2 binary64) (sin.f64 x))) #s(literal 0 binary64))))
#s(approx (sin eps) (fma.f64 eps (.f64 eps (.f64 eps (fma.f64 (*.f64 eps eps) #s(literal 1/120 binary64) #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))))
(.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))
(fma.f64 eps (.f64 x #s(literal -1/2 binary64)) (fma.f64 #s(literal -1/6 binary64) (.f64 eps eps) #s(literal 1 binary64)))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 eps #s(approx (+ ( eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x))) (fma.f64 eps (.f64 x #s(literal -1/2 binary64)) (fma.f64 #s(literal -1/6 binary64) (.f64 eps eps) #s(literal 1 binary64))))))
(.f64 eps #s(approx (+ ( eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x))) (fma.f64 eps (.f64 x #s(literal -1/2 binary64)) (fma.f64 #s(literal -1/6 binary64) (.f64 eps eps) #s(literal 1 binary64)))))
#s(approx (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x))) (fma.f64 eps (.f64 x #s(literal -1/2 binary64)) (fma.f64 #s(literal -1/6 binary64) (.f64 eps eps) #s(literal 1 binary64))))
(+.f64 (fma.f64 (.f64 #s(literal -1/2 binary64) x) (+.f64 x eps) #s(literal 1 binary64)) (.f64 eps (.f64 eps (fma.f64 (.f64 x x) #s(literal 1/12 binary64) #s(literal -1/6 binary64)))))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 eps #s(approx (+ ( eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x))) #s(approx (+ (* eps (* eps -1/6)) (+ (* x (+ (* x (+ (* (* eps eps) 1/12) -1/2)) (* eps -1/2))) 1)) (+.f64 (fma.f64 (.f64 #s(literal -1/2 binary64) x) (+.f64 x eps) #s(literal 1 binary64)) (.f64 eps (.f64 eps (fma.f64 (.f64 x x) #s(literal 1/12 binary64) #s(literal -1/6 binary64)))))))))
(.f64 eps #s(approx (+ ( eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x))) #s(approx (+ (* eps (* eps -1/6)) (+ (* x (+ (* x (+ (* (* eps eps) 1/12) -1/2)) (* eps -1/2))) 1)) (+.f64 (fma.f64 (.f64 #s(literal -1/2 binary64) x) (+.f64 x eps) #s(literal 1 binary64)) (.f64 eps (.f64 eps (fma.f64 (.f64 x x) #s(literal 1/12 binary64) #s(literal -1/6 binary64))))))))
#s(approx (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x))) #s(approx (+ (* eps (* eps -1/6)) (+ (* x (+ (* x (+ (* (* eps eps) 1/12) -1/2)) (* eps -1/2))) 1)) (+.f64 (fma.f64 (.f64 #s(literal -1/2 binary64) x) (+.f64 x eps) #s(literal 1 binary64)) (.f64 eps (.f64 eps (fma.f64 (.f64 x x) #s(literal 1/12 binary64) #s(literal -1/6 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 eps (fma.f64 (.f64 eps eps) #s(literal 1/120 binary64) #s(literal -1/6 binary64)))
(.f64 (sin.f64 x) (fma.f64 eps (.f64 eps #s(literal -1/720 binary64)) #s(literal 1/24 binary64)))
(*.f64 eps #s(literal -1/720 binary64))
(*.f64 eps eps)
(.f64 eps (fma.f64 (.f64 x x) #s(literal 1/12 binary64) #s(literal -1/6 binary64)))
(.f64 eps (.f64 eps (fma.f64 (*.f64 x x) #s(literal 1/12 binary64) #s(literal -1/6 binary64))))
(*.f64 eps #s(literal -1/48 binary64))
(cos.f64 (*.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)))

Outputs
(+.f64 (.f64 (sin.f64 x) #s(literal -1/2 binary64)) (.f64 (.f64 eps eps) (.f64 (sin.f64 x) (fma.f64 eps (*.f64 eps #s(literal -1/720 binary64)) #s(literal 1/24 binary64)))))
(+.f64 (.f64 (.f64 eps eps) (.f64 (sin.f64 x) (fma.f64 eps (.f64 eps #s(literal -1/720 binary64)) #s(literal 1/24 binary64)))) (*.f64 (sin.f64 x) #s(literal -1/2 binary64)))
(-.f64 (/.f64 (pow.f64 (.f64 (.f64 eps eps) (.f64 (sin.f64 x) (fma.f64 eps (.f64 eps #s(literal -1/720 binary64)) #s(literal 1/24 binary64)))) #s(literal 2 binary64)) (fma.f64 eps (.f64 (.f64 eps (sin.f64 x)) (fma.f64 eps (.f64 eps #s(literal -1/720 binary64)) #s(literal 1/24 binary64))) (.f64 #s(literal 1/2 binary64) (sin.f64 x)))) (/.f64 (.f64 #s(literal 1/4 binary64) (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x))))) (fma.f64 eps (.f64 (.f64 eps (sin.f64 x)) (fma.f64 eps (.f64 eps #s(literal -1/720 binary64)) #s(literal 1/24 binary64))) (.f64 #s(literal 1/2 binary64) (sin.f64 x)))))
(fma.f64 eps (.f64 (.f64 eps (sin.f64 x)) (fma.f64 eps (.f64 eps #s(literal -1/720 binary64)) #s(literal 1/24 binary64))) (.f64 (sin.f64 x) #s(literal -1/2 binary64)))
(fma.f64 (.f64 eps eps) (.f64 (sin.f64 x) (fma.f64 eps (.f64 eps #s(literal -1/720 binary64)) #s(literal 1/24 binary64))) (.f64 (sin.f64 x) #s(literal -1/2 binary64)))
(fma.f64 (sin.f64 x) #s(literal -1/2 binary64) (.f64 (.f64 eps eps) (.f64 (sin.f64 x) (fma.f64 eps (.f64 eps #s(literal -1/720 binary64)) #s(literal 1/24 binary64)))))
(fma.f64 (sin.f64 x) (.f64 (fma.f64 eps (.f64 eps #s(literal -1/720 binary64)) #s(literal 1/24 binary64)) (.f64 eps eps)) (.f64 (sin.f64 x) #s(literal -1/2 binary64)))
(fma.f64 (fma.f64 eps (.f64 eps #s(literal -1/720 binary64)) #s(literal 1/24 binary64)) (.f64 eps (.f64 eps (sin.f64 x))) (.f64 (sin.f64 x) #s(literal -1/2 binary64)))
(fma.f64 (.f64 (sin.f64 x) (fma.f64 eps (.f64 eps #s(literal -1/720 binary64)) #s(literal 1/24 binary64))) (.f64 eps eps) (.f64 (sin.f64 x) #s(literal -1/2 binary64)))
(fma.f64 #s(literal -1/2 binary64) (sin.f64 x) (.f64 (.f64 eps eps) (.f64 (sin.f64 x) (fma.f64 eps (.f64 eps #s(literal -1/720 binary64)) #s(literal 1/24 binary64)))))
(fma.f64 (.f64 eps (.f64 eps (sin.f64 x))) (fma.f64 eps (.f64 eps #s(literal -1/720 binary64)) #s(literal 1/24 binary64)) (.f64 (sin.f64 x) #s(literal -1/2 binary64)))
(fma.f64 (.f64 (.f64 eps (sin.f64 x)) (fma.f64 eps (.f64 eps #s(literal -1/720 binary64)) #s(literal 1/24 binary64))) eps (.f64 (sin.f64 x) #s(literal -1/2 binary64)))
(fma.f64 (.f64 (.f64 eps eps) (fma.f64 eps (.f64 eps #s(literal -1/720 binary64)) #s(literal 1/24 binary64))) (sin.f64 x) (.f64 (sin.f64 x) #s(literal -1/2 binary64)))
(/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 (.f64 (sin.f64 x) #s(literal -1/2 binary64)) (-.f64 (.f64 (sin.f64 x) #s(literal -1/2 binary64)) (.f64 (.f64 eps eps) (.f64 (sin.f64 x) (fma.f64 eps (.f64 eps #s(literal -1/720 binary64)) #s(literal 1/24 binary64))))) (pow.f64 (.f64 (.f64 eps eps) (.f64 (sin.f64 x) (fma.f64 eps (.f64 eps #s(literal -1/720 binary64)) #s(literal 1/24 binary64)))) #s(literal 2 binary64))) (fma.f64 #s(literal -1/8 binary64) (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (.f64 (.f64 eps eps) (.f64 (sin.f64 x) (fma.f64 eps (.f64 eps #s(literal -1/720 binary64)) #s(literal 1/24 binary64)))) #s(literal 3 binary64)))))
(/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 eps (.f64 (.f64 eps (sin.f64 x)) (fma.f64 eps (.f64 eps #s(literal -1/720 binary64)) #s(literal 1/24 binary64))) (.f64 #s(literal 1/2 binary64) (sin.f64 x))) (-.f64 (pow.f64 (.f64 (.f64 eps eps) (.f64 (sin.f64 x) (fma.f64 eps (.f64 eps #s(literal -1/720 binary64)) #s(literal 1/24 binary64)))) #s(literal 2 binary64)) (.f64 #s(literal 1/4 binary64) (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x))))))))
(/.f64 (fma.f64 #s(literal -1/8 binary64) (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (.f64 (.f64 eps eps) (.f64 (sin.f64 x) (fma.f64 eps (.f64 eps #s(literal -1/720 binary64)) #s(literal 1/24 binary64)))) #s(literal 3 binary64))) (fma.f64 (.f64 (sin.f64 x) #s(literal -1/2 binary64)) (-.f64 (.f64 (sin.f64 x) #s(literal -1/2 binary64)) (.f64 (.f64 eps eps) (.f64 (sin.f64 x) (fma.f64 eps (.f64 eps #s(literal -1/720 binary64)) #s(literal 1/24 binary64))))) (pow.f64 (.f64 (.f64 eps eps) (.f64 (sin.f64 x) (fma.f64 eps (.f64 eps #s(literal -1/720 binary64)) #s(literal 1/24 binary64)))) #s(literal 2 binary64))))
(/.f64 (fma.f64 #s(literal -1/8 binary64) (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (.f64 (.f64 eps eps) (.f64 (sin.f64 x) (fma.f64 eps (.f64 eps #s(literal -1/720 binary64)) #s(literal 1/24 binary64)))) #s(literal 3 binary64))) (fma.f64 #s(literal 1/4 binary64) (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x)))) (-.f64 (pow.f64 (.f64 (.f64 eps eps) (.f64 (sin.f64 x) (fma.f64 eps (.f64 eps #s(literal -1/720 binary64)) #s(literal 1/24 binary64)))) #s(literal 2 binary64)) (.f64 (.f64 (sin.f64 x) (fma.f64 eps (.f64 eps #s(literal -1/720 binary64)) #s(literal 1/24 binary64))) (.f64 (.f64 eps eps) (*.f64 (sin.f64 x) #s(literal -1/2 binary64)))))))
(/.f64 (-.f64 (pow.f64 (.f64 (.f64 eps eps) (.f64 (sin.f64 x) (fma.f64 eps (.f64 eps #s(literal -1/720 binary64)) #s(literal 1/24 binary64)))) #s(literal 2 binary64)) (.f64 #s(literal 1/4 binary64) (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x)))))) (fma.f64 eps (.f64 (.f64 eps (sin.f64 x)) (fma.f64 eps (.f64 eps #s(literal -1/720 binary64)) #s(literal 1/24 binary64))) (.f64 #s(literal 1/2 binary64) (sin.f64 x))))
(/.f64 (neg.f64 (fma.f64 #s(literal -1/8 binary64) (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (.f64 (.f64 eps eps) (.f64 (sin.f64 x) (fma.f64 eps (.f64 eps #s(literal -1/720 binary64)) #s(literal 1/24 binary64)))) #s(literal 3 binary64)))) (neg.f64 (fma.f64 (.f64 (sin.f64 x) #s(literal -1/2 binary64)) (-.f64 (.f64 (sin.f64 x) #s(literal -1/2 binary64)) (.f64 (.f64 eps eps) (.f64 (sin.f64 x) (fma.f64 eps (.f64 eps #s(literal -1/720 binary64)) #s(literal 1/24 binary64))))) (pow.f64 (.f64 (.f64 eps eps) (.f64 (sin.f64 x) (fma.f64 eps (.f64 eps #s(literal -1/720 binary64)) #s(literal 1/24 binary64)))) #s(literal 2 binary64)))))
(/.f64 (neg.f64 (-.f64 (pow.f64 (.f64 (.f64 eps eps) (.f64 (sin.f64 x) (fma.f64 eps (.f64 eps #s(literal -1/720 binary64)) #s(literal 1/24 binary64)))) #s(literal 2 binary64)) (.f64 #s(literal 1/4 binary64) (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x))))))) (neg.f64 (fma.f64 eps (.f64 (.f64 eps (sin.f64 x)) (fma.f64 eps (.f64 eps #s(literal -1/720 binary64)) #s(literal 1/24 binary64))) (.f64 #s(literal 1/2 binary64) (sin.f64 x)))))
(/.f64 (-.f64 (.f64 #s(literal 1/4 binary64) (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x))))) (pow.f64 (.f64 (.f64 eps eps) (.f64 (sin.f64 x) (fma.f64 eps (.f64 eps #s(literal -1/720 binary64)) #s(literal 1/24 binary64)))) #s(literal 2 binary64))) (-.f64 (.f64 (sin.f64 x) #s(literal -1/2 binary64)) (.f64 (.f64 eps eps) (.f64 (sin.f64 x) (fma.f64 eps (*.f64 eps #s(literal -1/720 binary64)) #s(literal 1/24 binary64))))))
(pow.f64 (/.f64 (fma.f64 (.f64 (sin.f64 x) #s(literal -1/2 binary64)) (-.f64 (.f64 (sin.f64 x) #s(literal -1/2 binary64)) (.f64 (.f64 eps eps) (.f64 (sin.f64 x) (fma.f64 eps (.f64 eps #s(literal -1/720 binary64)) #s(literal 1/24 binary64))))) (pow.f64 (.f64 (.f64 eps eps) (.f64 (sin.f64 x) (fma.f64 eps (.f64 eps #s(literal -1/720 binary64)) #s(literal 1/24 binary64)))) #s(literal 2 binary64))) (fma.f64 #s(literal -1/8 binary64) (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (.f64 (.f64 eps eps) (.f64 (sin.f64 x) (fma.f64 eps (.f64 eps #s(literal -1/720 binary64)) #s(literal 1/24 binary64)))) #s(literal 3 binary64)))) #s(literal -1 binary64))
(pow.f64 (/.f64 (fma.f64 eps (.f64 (.f64 eps (sin.f64 x)) (fma.f64 eps (.f64 eps #s(literal -1/720 binary64)) #s(literal 1/24 binary64))) (.f64 #s(literal 1/2 binary64) (sin.f64 x))) (-.f64 (pow.f64 (.f64 (.f64 eps eps) (.f64 (sin.f64 x) (fma.f64 eps (.f64 eps #s(literal -1/720 binary64)) #s(literal 1/24 binary64)))) #s(literal 2 binary64)) (.f64 #s(literal 1/4 binary64) (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x))))))) #s(literal -1 binary64))
(.f64 (fma.f64 #s(literal -1/8 binary64) (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (.f64 (.f64 eps eps) (.f64 (sin.f64 x) (fma.f64 eps (.f64 eps #s(literal -1/720 binary64)) #s(literal 1/24 binary64)))) #s(literal 3 binary64))) (/.f64 #s(literal 1 binary64) (fma.f64 (.f64 (sin.f64 x) #s(literal -1/2 binary64)) (-.f64 (.f64 (sin.f64 x) #s(literal -1/2 binary64)) (.f64 (.f64 eps eps) (.f64 (sin.f64 x) (fma.f64 eps (.f64 eps #s(literal -1/720 binary64)) #s(literal 1/24 binary64))))) (pow.f64 (.f64 (.f64 eps eps) (.f64 (sin.f64 x) (fma.f64 eps (*.f64 eps #s(literal -1/720 binary64)) #s(literal 1/24 binary64)))) #s(literal 2 binary64)))))
(.f64 (-.f64 (pow.f64 (.f64 (.f64 eps eps) (.f64 (sin.f64 x) (fma.f64 eps (.f64 eps #s(literal -1/720 binary64)) #s(literal 1/24 binary64)))) #s(literal 2 binary64)) (.f64 #s(literal 1/4 binary64) (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x)))))) (/.f64 #s(literal 1 binary64) (fma.f64 eps (.f64 (.f64 eps (sin.f64 x)) (fma.f64 eps (.f64 eps #s(literal -1/720 binary64)) #s(literal 1/24 binary64))) (*.f64 #s(literal 1/2 binary64) (sin.f64 x)))))
(+.f64 #s(literal 0 binary64) (.f64 (.f64 eps eps) (fma.f64 (.f64 eps eps) (.f64 (sin.f64 x) (fma.f64 eps (.f64 eps #s(literal -1/720 binary64)) #s(literal 1/24 binary64))) (.f64 (sin.f64 x) #s(literal -1/2 binary64)))))
(+.f64 (.f64 (.f64 eps eps) (fma.f64 (.f64 eps eps) (.f64 (sin.f64 x) (fma.f64 eps (.f64 eps #s(literal -1/720 binary64)) #s(literal 1/24 binary64))) (.f64 (sin.f64 x) #s(literal -1/2 binary64)))) #s(literal 0 binary64))
(+.f64 (.f64 (.f64 (sin.f64 x) (fma.f64 eps (.f64 eps #s(literal -1/720 binary64)) #s(literal 1/24 binary64))) (.f64 (.f64 eps eps) (.f64 eps eps))) (.f64 (.f64 eps eps) (*.f64 (sin.f64 x) #s(literal -1/2 binary64))))
(+.f64 (.f64 (.f64 (sin.f64 x) (fma.f64 eps (.f64 eps #s(literal -1/720 binary64)) #s(literal 1/24 binary64))) (.f64 (.f64 eps eps) (.f64 eps eps))) (fma.f64 (sin.f64 x) (.f64 #s(literal -1/2 binary64) (.f64 eps eps)) #s(literal 0 binary64)))
(+.f64 (.f64 (.f64 (sin.f64 x) (fma.f64 eps (.f64 eps #s(literal -1/720 binary64)) #s(literal 1/24 binary64))) (.f64 (.f64 eps eps) (.f64 eps eps))) (-.f64 (.f64 (.f64 eps eps) (*.f64 (sin.f64 x) #s(literal -1/2 binary64))) #s(literal 0 binary64)))
(+.f64 (.f64 (.f64 eps eps) (.f64 (sin.f64 x) #s(literal -1/2 binary64))) (.f64 (.f64 (sin.f64 x) (fma.f64 eps (.f64 eps #s(literal -1/720 binary64)) #s(literal 1/24 binary64))) (.f64 (.f64 eps eps) (*.f64 eps eps))))
(+.f64 (+.f64 #s(literal 0 binary64) (.f64 (.f64 (sin.f64 x) (fma.f64 eps (.f64 eps #s(literal -1/720 binary64)) #s(literal 1/24 binary64))) (.f64 (.f64 eps eps) (.f64 eps eps)))) (.f64 (.f64 eps eps) (*.f64 (sin.f64 x) #s(literal -1/2 binary64))))
(-.f64 (.f64 (.f64 eps eps) (fma.f64 (.f64 eps eps) (.f64 (sin.f64 x) (fma.f64 eps (.f64 eps #s(literal -1/720 binary64)) #s(literal 1/24 binary64))) (.f64 (sin.f64 x) #s(literal -1/2 binary64)))) #s(literal 0 binary64))
(-.f64 (.f64 (.f64 eps eps) (fma.f64 (.f64 eps eps) (.f64 (sin.f64 x) (fma.f64 eps (.f64 eps #s(literal -1/720 binary64)) #s(literal 1/24 binary64))) (.f64 (sin.f64 x) #s(literal -1/2 binary64)))) (/.f64 #s(literal 0 binary64) (.f64 (.f64 eps eps) (fma.f64 (.f64 eps eps) (.f64 (sin.f64 x) (fma.f64 eps (.f64 eps #s(literal -1/720 binary64)) #s(literal 1/24 binary64))) (.f64 (sin.f64 x) #s(literal -1/2 binary64))))))
(fma.f64 eps (.f64 (sin.f64 x) (.f64 eps #s(literal -1/2 binary64))) (.f64 (.f64 (sin.f64 x) (fma.f64 eps (.f64 eps #s(literal -1/720 binary64)) #s(literal 1/24 binary64))) (.f64 (.f64 eps eps) (.f64 eps eps))))
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(+.f64 (.f64 (.f64 eps (fma.f64 x (.f64 x #s(literal 1/12 binary64)) #s(literal -1/6 binary64))) #s(literal 0 binary64)) (.f64 (.f64 eps eps) (fma.f64 x (.f64 x #s(literal 1/12 binary64)) #s(literal -1/6 binary64))))
(+.f64 (.f64 (.f64 eps (.f64 x (.f64 x #s(literal 1/12 binary64)))) eps) (.f64 eps (.f64 eps #s(literal -1/6 binary64))))
(+.f64 (.f64 (.f64 x (.f64 x #s(literal 1/12 binary64))) (.f64 eps eps)) (.f64 eps (.f64 eps #s(literal -1/6 binary64))))
(+.f64 (.f64 #s(literal 0 binary64) (.f64 eps (fma.f64 x (.f64 x #s(literal 1/12 binary64)) #s(literal -1/6 binary64)))) (.f64 (.f64 eps eps) (fma.f64 x (.f64 x #s(literal 1/12 binary64)) #s(literal -1/6 binary64))))
(fma.f64 eps (.f64 eps #s(literal -1/6 binary64)) (.f64 (.f64 eps eps) (.f64 x (*.f64 x #s(literal 1/12 binary64)))))
(fma.f64 eps (.f64 eps #s(literal -1/6 binary64)) (.f64 (.f64 x (.f64 x #s(literal 1/12 binary64))) (*.f64 eps eps)))
(fma.f64 eps (.f64 eps (fma.f64 x (.f64 x #s(literal 1/12 binary64)) #s(literal -1/6 binary64))) (.f64 (.f64 eps (fma.f64 x (*.f64 x #s(literal 1/12 binary64)) #s(literal -1/6 binary64))) #s(literal 0 binary64)))
(fma.f64 eps (.f64 eps (fma.f64 x (.f64 x #s(literal 1/12 binary64)) #s(literal -1/6 binary64))) (.f64 #s(literal 0 binary64) (.f64 eps (fma.f64 x (*.f64 x #s(literal 1/12 binary64)) #s(literal -1/6 binary64)))))
(fma.f64 eps (.f64 eps (.f64 x (.f64 x #s(literal 1/12 binary64)))) (.f64 eps (*.f64 eps #s(literal -1/6 binary64))))
(fma.f64 eps (.f64 (.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64)) (.f64 (.f64 eps eps) (.f64 x (.f64 x #s(literal 1/12 binary64)))))
(fma.f64 eps (.f64 (.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64)) (.f64 (.f64 x (.f64 x #s(literal 1/12 binary64))) (.f64 eps eps)))
(fma.f64 (.f64 eps eps) #s(literal -1/6 binary64) (.f64 (.f64 eps eps) (.f64 x (*.f64 x #s(literal 1/12 binary64)))))
(fma.f64 (.f64 eps eps) #s(literal -1/6 binary64) (.f64 (.f64 x (.f64 x #s(literal 1/12 binary64))) (*.f64 eps eps)))
(fma.f64 (.f64 eps eps) (fma.f64 x (.f64 x #s(literal 1/12 binary64)) #s(literal -1/6 binary64)) (.f64 (.f64 eps (fma.f64 x (*.f64 x #s(literal 1/12 binary64)) #s(literal -1/6 binary64))) #s(literal 0 binary64)))
(fma.f64 (.f64 eps eps) (fma.f64 x (.f64 x #s(literal 1/12 binary64)) #s(literal -1/6 binary64)) (.f64 #s(literal 0 binary64) (.f64 eps (fma.f64 x (*.f64 x #s(literal 1/12 binary64)) #s(literal -1/6 binary64)))))
(fma.f64 (.f64 eps eps) (.f64 x (.f64 x #s(literal 1/12 binary64))) (.f64 eps (*.f64 eps #s(literal -1/6 binary64))))
(fma.f64 #s(literal 0 binary64) (.f64 eps (fma.f64 x (.f64 x #s(literal 1/12 binary64)) #s(literal -1/6 binary64))) (.f64 (.f64 eps eps) (fma.f64 x (*.f64 x #s(literal 1/12 binary64)) #s(literal -1/6 binary64))))
(fma.f64 #s(literal -1/6 binary64) (.f64 eps eps) (.f64 (.f64 eps eps) (.f64 x (*.f64 x #s(literal 1/12 binary64)))))
(fma.f64 #s(literal -1/6 binary64) (.f64 eps eps) (.f64 (.f64 x (.f64 x #s(literal 1/12 binary64))) (*.f64 eps eps)))
(fma.f64 #s(literal -1/6 binary64) (.f64 (.f64 eps eps) #s(literal 1 binary64)) (.f64 (.f64 eps eps) (.f64 x (.f64 x #s(literal 1/12 binary64)))))
(fma.f64 #s(literal -1/6 binary64) (.f64 (.f64 eps eps) #s(literal 1 binary64)) (.f64 (.f64 x (.f64 x #s(literal 1/12 binary64))) (.f64 eps eps)))
(fma.f64 #s(literal 1 binary64) (.f64 eps (.f64 eps #s(literal -1/6 binary64))) (.f64 (.f64 eps eps) (.f64 x (.f64 x #s(literal 1/12 binary64)))))
(fma.f64 #s(literal 1 binary64) (.f64 eps (.f64 eps #s(literal -1/6 binary64))) (.f64 (.f64 x (.f64 x #s(literal 1/12 binary64))) (.f64 eps eps)))
(fma.f64 (.f64 eps #s(literal -1/6 binary64)) eps (.f64 (.f64 eps eps) (.f64 x (*.f64 x #s(literal 1/12 binary64)))))
(fma.f64 (.f64 eps #s(literal -1/6 binary64)) eps (.f64 (.f64 x (.f64 x #s(literal 1/12 binary64))) (*.f64 eps eps)))
(fma.f64 (.f64 eps #s(literal -1/6 binary64)) (.f64 eps #s(literal 1 binary64)) (.f64 (.f64 eps eps) (.f64 x (.f64 x #s(literal 1/12 binary64)))))
(fma.f64 (.f64 eps #s(literal -1/6 binary64)) (.f64 eps #s(literal 1 binary64)) (.f64 (.f64 x (.f64 x #s(literal 1/12 binary64))) (.f64 eps eps)))
(fma.f64 (.f64 eps (.f64 eps #s(literal -1/6 binary64))) #s(literal 1 binary64) (.f64 (.f64 eps eps) (.f64 x (.f64 x #s(literal 1/12 binary64)))))
(fma.f64 (.f64 eps (.f64 eps #s(literal -1/6 binary64))) #s(literal 1 binary64) (.f64 (.f64 x (.f64 x #s(literal 1/12 binary64))) (.f64 eps eps)))
(fma.f64 (fma.f64 x (.f64 x #s(literal 1/12 binary64)) #s(literal -1/6 binary64)) (.f64 eps eps) (.f64 (.f64 eps (fma.f64 x (*.f64 x #s(literal 1/12 binary64)) #s(literal -1/6 binary64))) #s(literal 0 binary64)))
(fma.f64 (fma.f64 x (.f64 x #s(literal 1/12 binary64)) #s(literal -1/6 binary64)) (.f64 eps eps) (.f64 #s(literal 0 binary64) (.f64 eps (fma.f64 x (*.f64 x #s(literal 1/12 binary64)) #s(literal -1/6 binary64)))))
(fma.f64 (.f64 eps (fma.f64 x (.f64 x #s(literal 1/12 binary64)) #s(literal -1/6 binary64))) eps (.f64 (.f64 eps (fma.f64 x (*.f64 x #s(literal 1/12 binary64)) #s(literal -1/6 binary64))) #s(literal 0 binary64)))
(fma.f64 (.f64 eps (fma.f64 x (.f64 x #s(literal 1/12 binary64)) #s(literal -1/6 binary64))) eps (.f64 #s(literal 0 binary64) (.f64 eps (fma.f64 x (*.f64 x #s(literal 1/12 binary64)) #s(literal -1/6 binary64)))))
(fma.f64 (.f64 eps (fma.f64 x (.f64 x #s(literal 1/12 binary64)) #s(literal -1/6 binary64))) #s(literal 0 binary64) (.f64 (.f64 eps eps) (fma.f64 x (*.f64 x #s(literal 1/12 binary64)) #s(literal -1/6 binary64))))
(fma.f64 (.f64 x (.f64 x #s(literal 1/12 binary64))) (.f64 eps eps) (.f64 eps (*.f64 eps #s(literal -1/6 binary64))))
(fma.f64 (.f64 eps (.f64 x (.f64 x #s(literal 1/12 binary64)))) eps (.f64 eps (*.f64 eps #s(literal -1/6 binary64))))
(/.f64 (.f64 (.f64 eps eps) (fma.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) #s(literal 1/1728 binary64)) #s(literal -1/216 binary64))) (-.f64 (fma.f64 (.f64 (.f64 x x) (.f64 x x)) #s(literal 1/144 binary64) #s(literal 1/36 binary64)) (.f64 (.f64 x x) #s(literal -1/72 binary64))))
(/.f64 (.f64 (.f64 eps eps) (fma.f64 (.f64 (.f64 x x) (.f64 x x)) #s(literal 1/144 binary64) #s(literal -1/36 binary64))) (fma.f64 x (.f64 x #s(literal 1/12 binary64)) #s(literal 1/6 binary64)))
(/.f64 (.f64 (.f64 eps (fma.f64 x (.f64 x #s(literal 1/12 binary64)) #s(literal -1/6 binary64))) (.f64 eps (.f64 eps eps))) (.f64 eps eps))
(/.f64 (.f64 (.f64 eps (fma.f64 x (.f64 x #s(literal 1/12 binary64)) #s(literal -1/6 binary64))) (.f64 eps eps)) eps)
(/.f64 (.f64 (.f64 eps (.f64 eps eps)) (.f64 eps (fma.f64 x (.f64 x #s(literal 1/12 binary64)) #s(literal -1/6 binary64)))) (.f64 eps eps))
(/.f64 (.f64 (.f64 eps eps) (.f64 eps (fma.f64 x (.f64 x #s(literal 1/12 binary64)) #s(literal -1/6 binary64)))) eps)
(.f64 eps (.f64 eps (fma.f64 x (*.f64 x #s(literal 1/12 binary64)) #s(literal -1/6 binary64))))
(.f64 (.f64 eps eps) (fma.f64 x (*.f64 x #s(literal 1/12 binary64)) #s(literal -1/6 binary64)))
(.f64 (fma.f64 x (.f64 x #s(literal 1/12 binary64)) #s(literal -1/6 binary64)) (*.f64 eps eps))
(.f64 (.f64 eps (fma.f64 x (*.f64 x #s(literal 1/12 binary64)) #s(literal -1/6 binary64))) eps)
(+.f64 #s(literal 0 binary64) (*.f64 eps #s(literal -1/48 binary64)))
(+.f64 (*.f64 eps #s(literal -1/48 binary64)) #s(literal 0 binary64))
(fma.f64 eps #s(literal -1/48 binary64) #s(literal 0 binary64))
(fma.f64 #s(literal -1/48 binary64) eps #s(literal 0 binary64))
(/.f64 (.f64 (.f64 eps eps) #s(literal -1/48 binary64)) eps)
(/.f64 (.f64 eps (.f64 (.f64 eps eps) #s(literal -1/48 binary64))) (.f64 eps eps))
(/.f64 (.f64 #s(literal -1/48 binary64) (.f64 eps (.f64 eps eps))) (.f64 eps eps))
(*.f64 eps #s(literal -1/48 binary64))
(*.f64 #s(literal -1/48 binary64) eps)
(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)))))

eval156.0ms (1%)

Memory: 12.3MiB live, 241.7MiB allocated
Compiler: Compiled 36 985 to 2 466 computations (93.3% saved)

prune210.0ms (1.4%)

Memory

23.5MiB live, 258.0MiB allocated

Pruning

33 alts after pruning (27 fresh and 6 done)

	Pruned	Kept	Total
New	1 146	13	1 159
Fresh	9	14	23
Picked	4	1	5
Done	0	5	5
Total	1 159	33	1 192

Accuracy

100.0%

Counts

1 192 → 33

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	99.5%	(fma.f64 (sin.f64 eps) (cos.f64 x) (fma.f64 (sin.f64 x) (cos.f64 eps) (sin.f64 (neg.f64 x))))
	99.7%	(fma.f64 (cos.f64 x) #s(approx (sin eps) (fma.f64 (.f64 eps eps) (.f64 eps (fma.f64 (.f64 eps eps) #s(literal 1/120 binary64) #s(literal -1/6 binary64))) eps)) #s(approx (+ ( (sin x) (cos eps)) (sin (neg x))) (.f64 (.f64 eps eps) (fma.f64 (.f64 eps eps) (.f64 (sin.f64 x) (fma.f64 eps (.f64 eps #s(literal -1/720 binary64)) #s(literal 1/24 binary64))) (.f64 (sin.f64 x) #s(literal -1/2 binary64))))))
	99.6%	(fma.f64 #s(approx (sin eps) (fma.f64 eps (.f64 eps (.f64 eps (fma.f64 (.f64 eps eps) #s(literal 1/120 binary64) #s(literal -1/6 binary64)))) eps)) (cos.f64 x) #s(approx (+ ( (sin x) (cos eps)) (sin (neg x))) #s(approx (+ (* (* eps eps) (+ (* (* eps eps) (* (sin x) (+ (* eps (* eps -1/720)) 1/24))) (* -1/2 (sin x)))) 0) (.f64 (.f64 eps eps) (.f64 (sin.f64 x) (fma.f64 #s(literal 1/24 binary64) (.f64 eps eps) #s(literal -1/2 binary64)))))))
✓	62.9%	(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
	38.7%	(.f64 (.f64 (sin.f64 (.f64 (.f64 (.f64 eps (.f64 eps eps)) (/.f64 #s(literal 1 binary64) (.f64 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))
	57.6%	(.f64 (.f64 (sin.f64 (.f64 (.f64 (.f64 eps eps) (/.f64 #s(literal 1 binary64) 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))
	99.5%	(.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))
	99.4%	(.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))
	99.3%	(.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) (fma.f64 eps #s(literal 1/2 binary64) x)))) #s(literal 2 binary64))
	98.9%	(.f64 (.f64 #s(approx (sin (* (+ eps 0) 1/2)) (.f64 #s(literal 1/2 binary64) eps)) (cos.f64 #s(approx ( (+ (* x 2) eps) 1/2) (fma.f64 eps #s(literal 1/2 binary64) x)))) #s(literal 2 binary64))
	99.6%	(.f64 #s(approx ( (sin (* (+ eps 0) 1/2)) (cos (* (+ (* x 2) eps) 1/2))) (.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (cos.f64 (fma.f64 eps #s(literal 1/2 binary64) x)))) #s(literal 2 binary64))
	38.3%	#s(approx (- (sin (+ x eps)) (sin x)) (/.f64 (fma.f64 (.f64 (.f64 eps eps) (.f64 #s(literal -1/2 binary64) (.f64 eps (sin.f64 x)))) eps (.f64 eps (.f64 (.f64 eps eps) (cos.f64 x)))) (.f64 eps eps)))
	36.4%	#s(approx (- (sin (+ x eps)) (sin x)) (/.f64 (.f64 (.f64 eps (.f64 eps eps)) #s(approx (+ ( eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x))) #s(approx (+ (* eps (* eps -1/6)) (+ (* x (+ (* x (+ (* (* eps eps) 1/12) -1/2)) (* eps -1/2))) 1)) (fma.f64 (.f64 eps eps) (fma.f64 x (.f64 x #s(literal 1/12 binary64)) #s(literal -1/6 binary64)) (fma.f64 (.f64 x #s(literal -1/2 binary64)) (+.f64 eps x) #s(literal 1 binary64)))))) (.f64 eps eps)))
	96.4%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x))) (fma.f64 eps (fma.f64 x #s(literal -1/2 binary64) (*.f64 eps #s(literal -1/6 binary64))) #s(literal 1 binary64))) eps))
	99.5%	#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))))))
✓	99.3%	#s(approx (- (sin (+ x eps)) (sin 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)))))
✓	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))))
	98.1%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 eps (fma.f64 eps #s(approx ( -1/2 (sin x)) (*.f64 #s(literal -1/2 binary64) x)) (cos.f64 x))))
	98.4%	#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 eps (cos.f64 x)))
	97.0%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 eps #s(approx (+ ( eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x))) (fma.f64 eps (.f64 eps #s(literal -1/6 binary64)) (fma.f64 x #s(approx (+ ( x (+ (* (* eps eps) 1/12) -1/2)) (* eps -1/2)) (.f64 x (fma.f64 eps (.f64 eps #s(literal 1/12 binary64)) #s(literal -1/2 binary64)))) #s(literal 1 binary64))))))
	97.1%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 eps #s(approx (+ ( eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x))) (fma.f64 eps (.f64 eps #s(literal -1/6 binary64)) (fma.f64 x #s(approx (+ ( x (+ (* (* eps eps) 1/12) -1/2)) (* eps -1/2)) (*.f64 #s(literal -1/2 binary64) (+.f64 x eps))) #s(literal 1 binary64))))))
	96.4%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 eps #s(approx (+ ( eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x))) (fma.f64 eps (*.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64)))))
	96.4%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 eps #s(approx (+ ( eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x))) (/.f64 #s(literal 1 binary64) (/.f64 (-.f64 (.f64 eps (.f64 x #s(literal -1/2 binary64))) (fma.f64 eps (.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64))) (.f64 (fma.f64 eps (fma.f64 x #s(literal -1/2 binary64) (.f64 eps #s(literal -1/6 binary64))) #s(literal 1 binary64)) (-.f64 (.f64 eps (.f64 x #s(literal -1/2 binary64))) (fma.f64 eps (.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64)))))))))
	96.4%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 eps #s(approx (+ ( eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x))) #s(approx (+ (* eps (* x -1/2)) (+ (* -1/6 (* eps eps)) 1)) (fma.f64 #s(literal -1/2 binary64) (*.f64 x eps) #s(literal 1 binary64))))))
	5.0%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 eps #s(approx (+ ( eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x))) #s(approx (+ (* eps (* x -1/2)) (+ (* -1/6 (* eps eps)) 1)) (.f64 (.f64 eps eps) #s(literal -1/6 binary64))))))
	5.7%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 eps #s(approx (+ ( eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x))) #s(approx (+ (* eps (* x -1/2)) (+ (* -1/6 (* eps eps)) 1)) (.f64 eps (.f64 eps (fma.f64 #s(literal -1/2 binary64) (/.f64 x eps) #s(literal -1/6 binary64))))))))
	5.7%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 eps #s(approx (+ ( eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x))) #s(approx (+ (* eps (* x -1/2)) (+ (* -1/6 (* eps eps)) 1)) (.f64 #s(literal -1/2 binary64) (.f64 x eps))))))
	97.1%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 eps #s(approx (+ ( eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x))) #s(approx (+ (* eps (* eps -1/6)) (+ (* x (+ (* x (+ (* (* eps eps) 1/12) -1/2)) (* eps -1/2))) 1)) (fma.f64 (fma.f64 #s(literal 1/4 binary64) (.f64 (.f64 x (+.f64 eps x)) (.f64 x (+.f64 eps x))) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (fma.f64 (.f64 x #s(literal -1/2 binary64)) (+.f64 eps x) #s(literal -1 binary64))) (.f64 (.f64 eps eps) (fma.f64 x (*.f64 x #s(literal 1/12 binary64)) #s(literal -1/6 binary64))))))))
	97.0%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 eps #s(approx (+ ( eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x))) #s(approx (+ (* eps (* eps -1/6)) (+ (* x (+ (* x (+ (* (* eps eps) 1/12) -1/2)) (* eps -1/2))) 1)) (fma.f64 #s(literal -1/2 binary64) (*.f64 x x) #s(literal 1 binary64))))))
✓	96.4%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 eps #s(approx (+ ( eps (* -1/2 (sin x))) (cos x)) #s(literal 1 binary64))))
	96.4%	#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* eps (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x)))) (fma.f64 eps (fma.f64 #s(literal -1/6 binary64) (.f64 eps eps) #s(literal 1 binary64)) (.f64 x (.f64 #s(literal -1/2 binary64) (.f64 eps eps))))))
	97.1%	#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* eps (+ (* eps (* -1/2 (sin x))) (cos x))) (fma.f64 x (.f64 #s(literal -1/2 binary64) (.f64 eps (+.f64 x eps))) eps)))
✓	5.3%	#s(approx (+ (* (sin eps) (cos x)) (+ (* (sin x) (cos eps)) (sin (neg x)))) #s(literal 0 binary64))

Compiler

Compiled 1 816 to 626 computations (65.5% saved)

regimes79.0ms (0.5%)

Memory

-37.5MiB live, 57.4MiB allocated

Counts

59 → 1

Calls

Call 1

Inputs
#s(approx (+ (* (sin eps) (cos x)) (+ (* (sin x) (cos eps)) (sin (neg x)))) #s(literal 0 binary64))
#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)) (.f64 eps #s(approx (+ ( eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x))) #s(approx (+ (* eps (* x -1/2)) (+ (* -1/6 (* eps eps)) 1)) (.f64 #s(literal -1/2 binary64) (.f64 x eps))))))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 eps #s(approx (+ ( eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x))) #s(approx (+ (* eps (* x -1/2)) (+ (* -1/6 (* eps eps)) 1)) (.f64 (.f64 eps eps) #s(literal -1/6 binary64))))))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 eps #s(approx (+ ( eps (* -1/2 (sin x))) (cos x)) (fma.f64 #s(literal -1/2 binary64) (*.f64 x eps) #s(literal 1 binary64)))))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 eps #s(approx (+ ( eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x))) #s(approx (+ (* eps (* eps -1/6)) (+ (* x (+ (* x (+ (* (* eps eps) 1/12) -1/2)) (* eps -1/2))) 1)) (fma.f64 #s(literal -1/2 binary64) (*.f64 x x) #s(literal 1 binary64))))))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 eps #s(approx (+ ( eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x))) #s(approx (+ (* eps (* x -1/2)) (+ (* -1/6 (* eps eps)) 1)) (fma.f64 #s(literal -1/2 binary64) (*.f64 x eps) #s(literal 1 binary64))))))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 eps #s(approx (+ ( eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x))) (fma.f64 #s(literal -1/6 binary64) (*.f64 eps eps) #s(literal 1 binary64)))))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 eps #s(approx (+ ( eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x))) (fma.f64 eps (*.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64)))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* eps (+ (* eps (* -1/2 (sin x))) (cos x))) (fma.f64 #s(literal -1/2 binary64) (.f64 (.f64 eps (+.f64 x eps)) x) eps)))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* eps (+ (* eps (* -1/2 (sin x))) (cos x))) (fma.f64 x (.f64 #s(literal -1/2 binary64) (.f64 eps (+.f64 x eps))) eps)))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x))) (fma.f64 eps (fma.f64 x #s(literal -1/2 binary64) (*.f64 eps #s(literal -1/6 binary64))) #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 eps #s(approx (+ ( eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x))) #s(approx (+ (* eps (* eps -1/6)) (+ (* x (+ (* x (+ (* (* eps eps) 1/12) -1/2)) (* eps -1/2))) 1)) (.f64 (.f64 x x) (fma.f64 eps (*.f64 eps #s(literal 1/12 binary64)) #s(literal -1/2 binary64)))))))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 eps #s(approx (+ ( eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x))) (fma.f64 eps (.f64 x #s(literal -1/2 binary64)) (fma.f64 #s(literal -1/6 binary64) (.f64 eps eps) #s(literal 1 binary64))))))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 eps #s(approx (+ ( eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x))) (fma.f64 eps (.f64 eps #s(literal -1/6 binary64)) (fma.f64 x #s(approx (+ ( x (+ (* (* eps eps) 1/12) -1/2)) (* eps -1/2)) (*.f64 #s(literal -1/2 binary64) (+.f64 x eps))) #s(literal 1 binary64))))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* eps (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x)))) (fma.f64 eps (fma.f64 #s(literal -1/6 binary64) (.f64 eps eps) #s(literal 1 binary64)) (.f64 x (.f64 #s(literal -1/2 binary64) (.f64 eps eps))))))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 eps #s(approx (+ ( eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x))) #s(approx (+ (* eps (* x -1/2)) (+ (* -1/6 (* eps eps)) 1)) (.f64 eps (.f64 eps (fma.f64 #s(literal -1/2 binary64) (/.f64 x eps) #s(literal -1/6 binary64))))))))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 eps #s(approx (+ ( eps (* -1/2 (sin x))) (cos x)) (fma.f64 x (fma.f64 x (fma.f64 x (.f64 eps #s(literal 1/12 binary64)) #s(literal -1/2 binary64)) (.f64 #s(literal -1/2 binary64) eps)) #s(literal 1 binary64)))))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 eps #s(approx (+ ( eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x))) (fma.f64 eps (.f64 eps #s(literal -1/6 binary64)) (fma.f64 x #s(approx (+ ( x (+ (* (* eps eps) 1/12) -1/2)) (* eps -1/2)) (.f64 x (fma.f64 eps (.f64 eps #s(literal 1/12 binary64)) #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))) (* (+ (* eps (* eps -1/6)) 1) (cos x))) #s(approx (+ (* eps (* eps -1/6)) (+ (* x (+ (* x (+ (* (* eps eps) 1/12) -1/2)) (* eps -1/2))) 1)) (.f64 (.f64 eps eps) (fma.f64 #s(literal -1/2 binary64) (/.f64 x eps) (fma.f64 (*.f64 x x) #s(literal 1/12 binary64) #s(literal -1/6 binary64))))))))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 eps #s(approx (+ ( eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x))) #s(approx (+ (* eps (* eps -1/6)) (+ (* x (+ (* x (+ (* (* eps eps) 1/12) -1/2)) (* eps -1/2))) 1)) (+.f64 (fma.f64 (.f64 #s(literal -1/2 binary64) x) (+.f64 x eps) #s(literal 1 binary64)) (.f64 eps (.f64 eps (fma.f64 (.f64 x x) #s(literal 1/12 binary64) #s(literal -1/6 binary64)))))))))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 eps #s(approx (+ ( eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x))) (fma.f64 eps (.f64 eps #s(literal -1/6 binary64)) (fma.f64 x (fma.f64 eps #s(literal -1/2 binary64) (.f64 x (fma.f64 eps (*.f64 eps #s(literal 1/12 binary64)) #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))) (* (+ (* eps (* eps -1/6)) 1) (cos x))) (fma.f64 eps (.f64 eps #s(literal -1/6 binary64)) (fma.f64 x (fma.f64 x (fma.f64 (.f64 eps eps) #s(literal 1/12 binary64) #s(literal -1/2 binary64)) (*.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))) (* (+ (* eps (* eps -1/6)) 1) (cos x)))) (fma.f64 eps (fma.f64 #s(literal -1/6 binary64) (.f64 eps eps) #s(literal 1 binary64)) (.f64 (.f64 x #s(literal -1/2 binary64)) (.f64 eps (fma.f64 x (fma.f64 #s(literal -1/6 binary64) (*.f64 eps eps) #s(literal 1 binary64)) eps))))))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 eps #s(approx (+ ( eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x))) (fma.f64 x (fma.f64 x (fma.f64 eps (.f64 x #s(literal 1/12 binary64)) (fma.f64 (.f64 eps eps) #s(literal 1/12 binary64) #s(literal -1/2 binary64))) (.f64 eps #s(literal -1/2 binary64))) (fma.f64 #s(literal -1/6 binary64) (.f64 eps eps) #s(literal 1 binary64))))))
#s(approx (- (sin (+ x eps)) (sin x)) (/.f64 (.f64 (.f64 eps (.f64 eps eps)) #s(approx (+ ( eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x))) #s(approx (+ (* eps (* eps -1/6)) (+ (* x (+ (* x (+ (* (* eps eps) 1/12) -1/2)) (* eps -1/2))) 1)) (fma.f64 (.f64 eps eps) (fma.f64 x (.f64 x #s(literal 1/12 binary64)) #s(literal -1/6 binary64)) (fma.f64 (.f64 x #s(literal -1/2 binary64)) (+.f64 eps x) #s(literal 1 binary64)))))) (.f64 eps eps)))
#s(approx (- (sin (+ x eps)) (sin x)) (/.f64 (.f64 (.f64 eps (.f64 eps eps)) #s(approx (+ ( eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x))) (fma.f64 x (fma.f64 x (fma.f64 eps (.f64 eps #s(literal 1/12 binary64)) #s(literal -1/2 binary64)) (.f64 eps #s(literal -1/2 binary64))) (fma.f64 (.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64))))) (.f64 eps eps)))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 eps #s(approx (+ ( eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x))) #s(approx (+ (* eps (* eps -1/6)) (+ (* x (+ (* x (+ (* (* eps eps) 1/12) -1/2)) (* eps -1/2))) 1)) (fma.f64 (fma.f64 #s(literal 1/4 binary64) (.f64 (.f64 x (+.f64 eps x)) (.f64 x (+.f64 eps x))) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (fma.f64 (.f64 x #s(literal -1/2 binary64)) (+.f64 eps x) #s(literal -1 binary64))) (.f64 (.f64 eps eps) (fma.f64 x (*.f64 x #s(literal 1/12 binary64)) #s(literal -1/6 binary64))))))))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 eps #s(approx (+ ( eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x))) (/.f64 #s(literal 1 binary64) (/.f64 (-.f64 (.f64 eps (.f64 x #s(literal -1/2 binary64))) (fma.f64 eps (.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64))) (.f64 (fma.f64 eps (fma.f64 x #s(literal -1/2 binary64) (.f64 eps #s(literal -1/6 binary64))) #s(literal 1 binary64)) (-.f64 (.f64 eps (.f64 x #s(literal -1/2 binary64))) (fma.f64 eps (.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64)))))))))
#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 #s(literal -1/2 binary64) x)) (cos.f64 x))))
(.f64 (.f64 #s(approx (sin (* (+ eps 0) 1/2)) (.f64 #s(literal 1/2 binary64) eps)) (cos.f64 #s(approx ( (+ (* x 2) eps) 1/2) (fma.f64 eps #s(literal 1/2 binary64) x)))) #s(literal 2 binary64))
(-.f64 (sin.f64 (+.f64 x eps)) #s(approx (sin x) (fma.f64 #s(literal -1/6 binary64) (.f64 x (.f64 x x)) x)))
(.f64 (.f64 #s(approx (sin (* (+ eps 0) 1/2)) (.f64 #s(literal 1/2 binary64) eps)) (cos.f64 (.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)))) #s(literal 2 binary64))
(.f64 (.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) (fma.f64 eps #s(literal 1/2 binary64) x)))) #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)) (.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 (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 (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 #s(approx ( (sin (* (+ eps 0) 1/2)) (cos (* (+ (* x 2) eps) 1/2))) (.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (cos.f64 (fma.f64 eps #s(literal 1/2 binary64) x)))) #s(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))
#s(approx (- (sin (+ x eps)) (sin 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)))))
#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 (.f64 (sin.f64 (.f64 (.f64 (.f64 eps eps) (/.f64 #s(literal 1 binary64) 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 (fma.f64 (.f64 (.f64 eps eps) (.f64 #s(literal -1/2 binary64) (.f64 eps (sin.f64 x)))) eps (.f64 eps (.f64 (.f64 eps eps) (cos.f64 x)))) (.f64 eps eps)))
(.f64 (.f64 (sin.f64 (.f64 (.f64 (.f64 eps (.f64 eps eps)) (/.f64 #s(literal 1 binary64) (.f64 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))
(fma.f64 #s(approx (sin eps) (fma.f64 eps (.f64 eps (.f64 eps (fma.f64 (.f64 eps eps) #s(literal 1/120 binary64) #s(literal -1/6 binary64)))) eps)) (cos.f64 x) #s(approx (+ ( (sin x) (cos eps)) (sin (neg x))) #s(approx (+ (* (* eps eps) (+ (* (* eps eps) (* (sin x) (+ (* eps (* eps -1/720)) 1/24))) (* -1/2 (sin x)))) 0) (.f64 (.f64 eps eps) (.f64 (sin.f64 x) (fma.f64 #s(literal 1/24 binary64) (.f64 eps eps) #s(literal -1/2 binary64)))))))
#s(approx (- (sin (+ x eps)) (sin x)) (/.f64 (fma.f64 (.f64 (.f64 (fma.f64 eps (.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64)) (cos.f64 x)) (.f64 eps eps)) eps (.f64 eps (.f64 (.f64 eps (.f64 #s(literal -1/2 binary64) (sin.f64 x))) (.f64 eps eps)))) (.f64 eps eps)))
(fma.f64 (sin.f64 eps) (cos.f64 x) #s(approx (+ (* (sin x) (cos eps)) (sin (neg x))) #s(approx (+ (* (* eps eps) (+ (* (* eps eps) (* (sin x) (+ (* eps (* eps -1/720)) 1/24))) (* -1/2 (sin x)))) 0) (.f64 (.f64 eps eps) (.f64 (sin.f64 x) (fma.f64 #s(literal 1/24 binary64) (.f64 eps eps) #s(literal -1/2 binary64)))))))
(fma.f64 (sin.f64 eps) (cos.f64 x) #s(approx (+ (* (sin x) (cos eps)) (sin (neg x))) (fma.f64 (.f64 eps eps) (.f64 (sin.f64 x) (fma.f64 eps (*.f64 eps #s(literal 1/24 binary64)) #s(literal -1/2 binary64))) #s(literal 0 binary64))))
(fma.f64 (cos.f64 x) #s(approx (sin eps) (fma.f64 (.f64 eps eps) (.f64 eps (fma.f64 (.f64 eps eps) #s(literal 1/120 binary64) #s(literal -1/6 binary64))) eps)) #s(approx (+ ( (sin x) (cos eps)) (sin (neg x))) (.f64 (.f64 eps eps) (fma.f64 (.f64 eps eps) (.f64 (sin.f64 x) (fma.f64 eps (.f64 eps #s(literal -1/720 binary64)) #s(literal 1/24 binary64))) (.f64 (sin.f64 x) #s(literal -1/2 binary64))))))
(fma.f64 #s(approx (sin eps) (fma.f64 eps (.f64 eps (.f64 eps (fma.f64 (.f64 eps eps) #s(literal 1/120 binary64) #s(literal -1/6 binary64)))) eps)) (cos.f64 x) #s(approx (+ ( (sin x) (cos eps)) (sin (neg x))) (fma.f64 (.f64 eps eps) (fma.f64 (.f64 eps eps) (.f64 (sin.f64 x) (fma.f64 eps (.f64 eps #s(literal -1/720 binary64)) #s(literal 1/24 binary64))) (*.f64 #s(literal -1/2 binary64) (sin.f64 x))) #s(literal 0 binary64))))
(fma.f64 (sin.f64 eps) (cos.f64 x) #s(approx (+ (* (sin x) (cos eps)) (sin (neg x))) (fma.f64 (.f64 eps eps) (fma.f64 (.f64 eps eps) (.f64 (sin.f64 x) (fma.f64 eps (.f64 eps #s(literal -1/720 binary64)) #s(literal 1/24 binary64))) (*.f64 #s(literal -1/2 binary64) (sin.f64 x))) #s(literal 0 binary64))))
(fma.f64 (sin.f64 eps) (cos.f64 x) (fma.f64 (sin.f64 x) (cos.f64 eps) (sin.f64 (neg.f64 x))))
(fma.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)) (-.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))))))))

Outputs

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

Calls

3 calls:

40.0ms	x
16.0ms	(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
15.0ms	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)

regimes49.0ms (0.3%)

Memory

19.4MiB live, 56.1MiB allocated

Counts

56 → 1

Calls

Call 1

Inputs
#s(approx (+ (* (sin eps) (cos x)) (+ (* (sin x) (cos eps)) (sin (neg x)))) #s(literal 0 binary64))
#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)) (.f64 eps #s(approx (+ ( eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x))) #s(approx (+ (* eps (* x -1/2)) (+ (* -1/6 (* eps eps)) 1)) (.f64 #s(literal -1/2 binary64) (.f64 x eps))))))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 eps #s(approx (+ ( eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x))) #s(approx (+ (* eps (* x -1/2)) (+ (* -1/6 (* eps eps)) 1)) (.f64 (.f64 eps eps) #s(literal -1/6 binary64))))))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 eps #s(approx (+ ( eps (* -1/2 (sin x))) (cos x)) (fma.f64 #s(literal -1/2 binary64) (*.f64 x eps) #s(literal 1 binary64)))))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 eps #s(approx (+ ( eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x))) #s(approx (+ (* eps (* eps -1/6)) (+ (* x (+ (* x (+ (* (* eps eps) 1/12) -1/2)) (* eps -1/2))) 1)) (fma.f64 #s(literal -1/2 binary64) (*.f64 x x) #s(literal 1 binary64))))))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 eps #s(approx (+ ( eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x))) #s(approx (+ (* eps (* x -1/2)) (+ (* -1/6 (* eps eps)) 1)) (fma.f64 #s(literal -1/2 binary64) (*.f64 x eps) #s(literal 1 binary64))))))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 eps #s(approx (+ ( eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x))) (fma.f64 #s(literal -1/6 binary64) (*.f64 eps eps) #s(literal 1 binary64)))))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 eps #s(approx (+ ( eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x))) (fma.f64 eps (*.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64)))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* eps (+ (* eps (* -1/2 (sin x))) (cos x))) (fma.f64 #s(literal -1/2 binary64) (.f64 (.f64 eps (+.f64 x eps)) x) eps)))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* eps (+ (* eps (* -1/2 (sin x))) (cos x))) (fma.f64 x (.f64 #s(literal -1/2 binary64) (.f64 eps (+.f64 x eps))) eps)))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x))) (fma.f64 eps (fma.f64 x #s(literal -1/2 binary64) (*.f64 eps #s(literal -1/6 binary64))) #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 eps #s(approx (+ ( eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x))) #s(approx (+ (* eps (* eps -1/6)) (+ (* x (+ (* x (+ (* (* eps eps) 1/12) -1/2)) (* eps -1/2))) 1)) (.f64 (.f64 x x) (fma.f64 eps (*.f64 eps #s(literal 1/12 binary64)) #s(literal -1/2 binary64)))))))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 eps #s(approx (+ ( eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x))) (fma.f64 eps (.f64 x #s(literal -1/2 binary64)) (fma.f64 #s(literal -1/6 binary64) (.f64 eps eps) #s(literal 1 binary64))))))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 eps #s(approx (+ ( eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x))) (fma.f64 eps (.f64 eps #s(literal -1/6 binary64)) (fma.f64 x #s(approx (+ ( x (+ (* (* eps eps) 1/12) -1/2)) (* eps -1/2)) (*.f64 #s(literal -1/2 binary64) (+.f64 x eps))) #s(literal 1 binary64))))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* eps (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x)))) (fma.f64 eps (fma.f64 #s(literal -1/6 binary64) (.f64 eps eps) #s(literal 1 binary64)) (.f64 x (.f64 #s(literal -1/2 binary64) (.f64 eps eps))))))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 eps #s(approx (+ ( eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x))) #s(approx (+ (* eps (* x -1/2)) (+ (* -1/6 (* eps eps)) 1)) (.f64 eps (.f64 eps (fma.f64 #s(literal -1/2 binary64) (/.f64 x eps) #s(literal -1/6 binary64))))))))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 eps #s(approx (+ ( eps (* -1/2 (sin x))) (cos x)) (fma.f64 x (fma.f64 x (fma.f64 x (.f64 eps #s(literal 1/12 binary64)) #s(literal -1/2 binary64)) (.f64 #s(literal -1/2 binary64) eps)) #s(literal 1 binary64)))))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 eps #s(approx (+ ( eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x))) (fma.f64 eps (.f64 eps #s(literal -1/6 binary64)) (fma.f64 x #s(approx (+ ( x (+ (* (* eps eps) 1/12) -1/2)) (* eps -1/2)) (.f64 x (fma.f64 eps (.f64 eps #s(literal 1/12 binary64)) #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))) (* (+ (* eps (* eps -1/6)) 1) (cos x))) #s(approx (+ (* eps (* eps -1/6)) (+ (* x (+ (* x (+ (* (* eps eps) 1/12) -1/2)) (* eps -1/2))) 1)) (.f64 (.f64 eps eps) (fma.f64 #s(literal -1/2 binary64) (/.f64 x eps) (fma.f64 (*.f64 x x) #s(literal 1/12 binary64) #s(literal -1/6 binary64))))))))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 eps #s(approx (+ ( eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x))) #s(approx (+ (* eps (* eps -1/6)) (+ (* x (+ (* x (+ (* (* eps eps) 1/12) -1/2)) (* eps -1/2))) 1)) (+.f64 (fma.f64 (.f64 #s(literal -1/2 binary64) x) (+.f64 x eps) #s(literal 1 binary64)) (.f64 eps (.f64 eps (fma.f64 (.f64 x x) #s(literal 1/12 binary64) #s(literal -1/6 binary64)))))))))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 eps #s(approx (+ ( eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x))) (fma.f64 eps (.f64 eps #s(literal -1/6 binary64)) (fma.f64 x (fma.f64 eps #s(literal -1/2 binary64) (.f64 x (fma.f64 eps (*.f64 eps #s(literal 1/12 binary64)) #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))) (* (+ (* eps (* eps -1/6)) 1) (cos x))) (fma.f64 eps (.f64 eps #s(literal -1/6 binary64)) (fma.f64 x (fma.f64 x (fma.f64 (.f64 eps eps) #s(literal 1/12 binary64) #s(literal -1/2 binary64)) (*.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))) (* (+ (* eps (* eps -1/6)) 1) (cos x)))) (fma.f64 eps (fma.f64 #s(literal -1/6 binary64) (.f64 eps eps) #s(literal 1 binary64)) (.f64 (.f64 x #s(literal -1/2 binary64)) (.f64 eps (fma.f64 x (fma.f64 #s(literal -1/6 binary64) (*.f64 eps eps) #s(literal 1 binary64)) eps))))))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 eps #s(approx (+ ( eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x))) (fma.f64 x (fma.f64 x (fma.f64 eps (.f64 x #s(literal 1/12 binary64)) (fma.f64 (.f64 eps eps) #s(literal 1/12 binary64) #s(literal -1/2 binary64))) (.f64 eps #s(literal -1/2 binary64))) (fma.f64 #s(literal -1/6 binary64) (.f64 eps eps) #s(literal 1 binary64))))))
#s(approx (- (sin (+ x eps)) (sin x)) (/.f64 (.f64 (.f64 eps (.f64 eps eps)) #s(approx (+ ( eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x))) #s(approx (+ (* eps (* eps -1/6)) (+ (* x (+ (* x (+ (* (* eps eps) 1/12) -1/2)) (* eps -1/2))) 1)) (fma.f64 (.f64 eps eps) (fma.f64 x (.f64 x #s(literal 1/12 binary64)) #s(literal -1/6 binary64)) (fma.f64 (.f64 x #s(literal -1/2 binary64)) (+.f64 eps x) #s(literal 1 binary64)))))) (.f64 eps eps)))
#s(approx (- (sin (+ x eps)) (sin x)) (/.f64 (.f64 (.f64 eps (.f64 eps eps)) #s(approx (+ ( eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x))) (fma.f64 x (fma.f64 x (fma.f64 eps (.f64 eps #s(literal 1/12 binary64)) #s(literal -1/2 binary64)) (.f64 eps #s(literal -1/2 binary64))) (fma.f64 (.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64))))) (.f64 eps eps)))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 eps #s(approx (+ ( eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x))) #s(approx (+ (* eps (* eps -1/6)) (+ (* x (+ (* x (+ (* (* eps eps) 1/12) -1/2)) (* eps -1/2))) 1)) (fma.f64 (fma.f64 #s(literal 1/4 binary64) (.f64 (.f64 x (+.f64 eps x)) (.f64 x (+.f64 eps x))) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (fma.f64 (.f64 x #s(literal -1/2 binary64)) (+.f64 eps x) #s(literal -1 binary64))) (.f64 (.f64 eps eps) (fma.f64 x (*.f64 x #s(literal 1/12 binary64)) #s(literal -1/6 binary64))))))))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 eps #s(approx (+ ( eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x))) (/.f64 #s(literal 1 binary64) (/.f64 (-.f64 (.f64 eps (.f64 x #s(literal -1/2 binary64))) (fma.f64 eps (.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64))) (.f64 (fma.f64 eps (fma.f64 x #s(literal -1/2 binary64) (.f64 eps #s(literal -1/6 binary64))) #s(literal 1 binary64)) (-.f64 (.f64 eps (.f64 x #s(literal -1/2 binary64))) (fma.f64 eps (.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64)))))))))
#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 #s(literal -1/2 binary64) x)) (cos.f64 x))))
(.f64 (.f64 #s(approx (sin (* (+ eps 0) 1/2)) (.f64 #s(literal 1/2 binary64) eps)) (cos.f64 #s(approx ( (+ (* x 2) eps) 1/2) (fma.f64 eps #s(literal 1/2 binary64) x)))) #s(literal 2 binary64))
(-.f64 (sin.f64 (+.f64 x eps)) #s(approx (sin x) (fma.f64 #s(literal -1/6 binary64) (.f64 x (.f64 x x)) x)))
(.f64 (.f64 #s(approx (sin (* (+ eps 0) 1/2)) (.f64 #s(literal 1/2 binary64) eps)) (cos.f64 (.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)))) #s(literal 2 binary64))
(.f64 (.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) (fma.f64 eps #s(literal 1/2 binary64) x)))) #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)) (.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 (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 (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 #s(approx ( (sin (* (+ eps 0) 1/2)) (cos (* (+ (* x 2) eps) 1/2))) (.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (cos.f64 (fma.f64 eps #s(literal 1/2 binary64) x)))) #s(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))
#s(approx (- (sin (+ x eps)) (sin 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)))))
#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 (.f64 (sin.f64 (.f64 (.f64 (.f64 eps eps) (/.f64 #s(literal 1 binary64) 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 (fma.f64 (.f64 (.f64 eps eps) (.f64 #s(literal -1/2 binary64) (.f64 eps (sin.f64 x)))) eps (.f64 eps (.f64 (.f64 eps eps) (cos.f64 x)))) (.f64 eps eps)))
(.f64 (.f64 (sin.f64 (.f64 (.f64 (.f64 eps (.f64 eps eps)) (/.f64 #s(literal 1 binary64) (.f64 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))
(fma.f64 #s(approx (sin eps) (fma.f64 eps (.f64 eps (.f64 eps (fma.f64 (.f64 eps eps) #s(literal 1/120 binary64) #s(literal -1/6 binary64)))) eps)) (cos.f64 x) #s(approx (+ ( (sin x) (cos eps)) (sin (neg x))) #s(approx (+ (* (* eps eps) (+ (* (* eps eps) (* (sin x) (+ (* eps (* eps -1/720)) 1/24))) (* -1/2 (sin x)))) 0) (.f64 (.f64 eps eps) (.f64 (sin.f64 x) (fma.f64 #s(literal 1/24 binary64) (.f64 eps eps) #s(literal -1/2 binary64)))))))
#s(approx (- (sin (+ x eps)) (sin x)) (/.f64 (fma.f64 (.f64 (.f64 (fma.f64 eps (.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64)) (cos.f64 x)) (.f64 eps eps)) eps (.f64 eps (.f64 (.f64 eps (.f64 #s(literal -1/2 binary64) (sin.f64 x))) (.f64 eps eps)))) (.f64 eps eps)))
(fma.f64 (sin.f64 eps) (cos.f64 x) #s(approx (+ (* (sin x) (cos eps)) (sin (neg x))) #s(approx (+ (* (* eps eps) (+ (* (* eps eps) (* (sin x) (+ (* eps (* eps -1/720)) 1/24))) (* -1/2 (sin x)))) 0) (.f64 (.f64 eps eps) (.f64 (sin.f64 x) (fma.f64 #s(literal 1/24 binary64) (.f64 eps eps) #s(literal -1/2 binary64)))))))
(fma.f64 (sin.f64 eps) (cos.f64 x) #s(approx (+ (* (sin x) (cos eps)) (sin (neg x))) (fma.f64 (.f64 eps eps) (.f64 (sin.f64 x) (fma.f64 eps (*.f64 eps #s(literal 1/24 binary64)) #s(literal -1/2 binary64))) #s(literal 0 binary64))))
(fma.f64 (cos.f64 x) #s(approx (sin eps) (fma.f64 (.f64 eps eps) (.f64 eps (fma.f64 (.f64 eps eps) #s(literal 1/120 binary64) #s(literal -1/6 binary64))) eps)) #s(approx (+ ( (sin x) (cos eps)) (sin (neg x))) (.f64 (.f64 eps eps) (fma.f64 (.f64 eps eps) (.f64 (sin.f64 x) (fma.f64 eps (.f64 eps #s(literal -1/720 binary64)) #s(literal 1/24 binary64))) (.f64 (sin.f64 x) #s(literal -1/2 binary64))))))
(fma.f64 #s(approx (sin eps) (fma.f64 eps (.f64 eps (.f64 eps (fma.f64 (.f64 eps eps) #s(literal 1/120 binary64) #s(literal -1/6 binary64)))) eps)) (cos.f64 x) #s(approx (+ ( (sin x) (cos eps)) (sin (neg x))) (fma.f64 (.f64 eps eps) (fma.f64 (.f64 eps eps) (.f64 (sin.f64 x) (fma.f64 eps (.f64 eps #s(literal -1/720 binary64)) #s(literal 1/24 binary64))) (*.f64 #s(literal -1/2 binary64) (sin.f64 x))) #s(literal 0 binary64))))

Outputs

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

Calls

3 calls:

16.0ms	eps
15.0ms	(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
15.0ms	x

Results

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

Compiler

Compiled 15 to 10 computations (33.3% saved)

regimes52.0ms (0.3%)

Memory

-16.5MiB live, 63.8MiB allocated

Counts

54 → 1

Calls

Call 1

Inputs
#s(approx (+ (* (sin eps) (cos x)) (+ (* (sin x) (cos eps)) (sin (neg x)))) #s(literal 0 binary64))
#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)) (.f64 eps #s(approx (+ ( eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x))) #s(approx (+ (* eps (* x -1/2)) (+ (* -1/6 (* eps eps)) 1)) (.f64 #s(literal -1/2 binary64) (.f64 x eps))))))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 eps #s(approx (+ ( eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x))) #s(approx (+ (* eps (* x -1/2)) (+ (* -1/6 (* eps eps)) 1)) (.f64 (.f64 eps eps) #s(literal -1/6 binary64))))))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 eps #s(approx (+ ( eps (* -1/2 (sin x))) (cos x)) (fma.f64 #s(literal -1/2 binary64) (*.f64 x eps) #s(literal 1 binary64)))))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 eps #s(approx (+ ( eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x))) #s(approx (+ (* eps (* eps -1/6)) (+ (* x (+ (* x (+ (* (* eps eps) 1/12) -1/2)) (* eps -1/2))) 1)) (fma.f64 #s(literal -1/2 binary64) (*.f64 x x) #s(literal 1 binary64))))))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 eps #s(approx (+ ( eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x))) #s(approx (+ (* eps (* x -1/2)) (+ (* -1/6 (* eps eps)) 1)) (fma.f64 #s(literal -1/2 binary64) (*.f64 x eps) #s(literal 1 binary64))))))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 eps #s(approx (+ ( eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x))) (fma.f64 #s(literal -1/6 binary64) (*.f64 eps eps) #s(literal 1 binary64)))))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 eps #s(approx (+ ( eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x))) (fma.f64 eps (*.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64)))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* eps (+ (* eps (* -1/2 (sin x))) (cos x))) (fma.f64 #s(literal -1/2 binary64) (.f64 (.f64 eps (+.f64 x eps)) x) eps)))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* eps (+ (* eps (* -1/2 (sin x))) (cos x))) (fma.f64 x (.f64 #s(literal -1/2 binary64) (.f64 eps (+.f64 x eps))) eps)))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x))) (fma.f64 eps (fma.f64 x #s(literal -1/2 binary64) (*.f64 eps #s(literal -1/6 binary64))) #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 eps #s(approx (+ ( eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x))) #s(approx (+ (* eps (* eps -1/6)) (+ (* x (+ (* x (+ (* (* eps eps) 1/12) -1/2)) (* eps -1/2))) 1)) (.f64 (.f64 x x) (fma.f64 eps (*.f64 eps #s(literal 1/12 binary64)) #s(literal -1/2 binary64)))))))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 eps #s(approx (+ ( eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x))) (fma.f64 eps (.f64 x #s(literal -1/2 binary64)) (fma.f64 #s(literal -1/6 binary64) (.f64 eps eps) #s(literal 1 binary64))))))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 eps #s(approx (+ ( eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x))) (fma.f64 eps (.f64 eps #s(literal -1/6 binary64)) (fma.f64 x #s(approx (+ ( x (+ (* (* eps eps) 1/12) -1/2)) (* eps -1/2)) (*.f64 #s(literal -1/2 binary64) (+.f64 x eps))) #s(literal 1 binary64))))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* eps (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x)))) (fma.f64 eps (fma.f64 #s(literal -1/6 binary64) (.f64 eps eps) #s(literal 1 binary64)) (.f64 x (.f64 #s(literal -1/2 binary64) (.f64 eps eps))))))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 eps #s(approx (+ ( eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x))) #s(approx (+ (* eps (* x -1/2)) (+ (* -1/6 (* eps eps)) 1)) (.f64 eps (.f64 eps (fma.f64 #s(literal -1/2 binary64) (/.f64 x eps) #s(literal -1/6 binary64))))))))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 eps #s(approx (+ ( eps (* -1/2 (sin x))) (cos x)) (fma.f64 x (fma.f64 x (fma.f64 x (.f64 eps #s(literal 1/12 binary64)) #s(literal -1/2 binary64)) (.f64 #s(literal -1/2 binary64) eps)) #s(literal 1 binary64)))))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 eps #s(approx (+ ( eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x))) (fma.f64 eps (.f64 eps #s(literal -1/6 binary64)) (fma.f64 x #s(approx (+ ( x (+ (* (* eps eps) 1/12) -1/2)) (* eps -1/2)) (.f64 x (fma.f64 eps (.f64 eps #s(literal 1/12 binary64)) #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))) (* (+ (* eps (* eps -1/6)) 1) (cos x))) #s(approx (+ (* eps (* eps -1/6)) (+ (* x (+ (* x (+ (* (* eps eps) 1/12) -1/2)) (* eps -1/2))) 1)) (.f64 (.f64 eps eps) (fma.f64 #s(literal -1/2 binary64) (/.f64 x eps) (fma.f64 (*.f64 x x) #s(literal 1/12 binary64) #s(literal -1/6 binary64))))))))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 eps #s(approx (+ ( eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x))) #s(approx (+ (* eps (* eps -1/6)) (+ (* x (+ (* x (+ (* (* eps eps) 1/12) -1/2)) (* eps -1/2))) 1)) (+.f64 (fma.f64 (.f64 #s(literal -1/2 binary64) x) (+.f64 x eps) #s(literal 1 binary64)) (.f64 eps (.f64 eps (fma.f64 (.f64 x x) #s(literal 1/12 binary64) #s(literal -1/6 binary64)))))))))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 eps #s(approx (+ ( eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x))) (fma.f64 eps (.f64 eps #s(literal -1/6 binary64)) (fma.f64 x (fma.f64 eps #s(literal -1/2 binary64) (.f64 x (fma.f64 eps (*.f64 eps #s(literal 1/12 binary64)) #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))) (* (+ (* eps (* eps -1/6)) 1) (cos x))) (fma.f64 eps (.f64 eps #s(literal -1/6 binary64)) (fma.f64 x (fma.f64 x (fma.f64 (.f64 eps eps) #s(literal 1/12 binary64) #s(literal -1/2 binary64)) (*.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))) (* (+ (* eps (* eps -1/6)) 1) (cos x)))) (fma.f64 eps (fma.f64 #s(literal -1/6 binary64) (.f64 eps eps) #s(literal 1 binary64)) (.f64 (.f64 x #s(literal -1/2 binary64)) (.f64 eps (fma.f64 x (fma.f64 #s(literal -1/6 binary64) (*.f64 eps eps) #s(literal 1 binary64)) eps))))))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 eps #s(approx (+ ( eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x))) (fma.f64 x (fma.f64 x (fma.f64 eps (.f64 x #s(literal 1/12 binary64)) (fma.f64 (.f64 eps eps) #s(literal 1/12 binary64) #s(literal -1/2 binary64))) (.f64 eps #s(literal -1/2 binary64))) (fma.f64 #s(literal -1/6 binary64) (.f64 eps eps) #s(literal 1 binary64))))))
#s(approx (- (sin (+ x eps)) (sin x)) (/.f64 (.f64 (.f64 eps (.f64 eps eps)) #s(approx (+ ( eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x))) #s(approx (+ (* eps (* eps -1/6)) (+ (* x (+ (* x (+ (* (* eps eps) 1/12) -1/2)) (* eps -1/2))) 1)) (fma.f64 (.f64 eps eps) (fma.f64 x (.f64 x #s(literal 1/12 binary64)) #s(literal -1/6 binary64)) (fma.f64 (.f64 x #s(literal -1/2 binary64)) (+.f64 eps x) #s(literal 1 binary64)))))) (.f64 eps eps)))
#s(approx (- (sin (+ x eps)) (sin x)) (/.f64 (.f64 (.f64 eps (.f64 eps eps)) #s(approx (+ ( eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x))) (fma.f64 x (fma.f64 x (fma.f64 eps (.f64 eps #s(literal 1/12 binary64)) #s(literal -1/2 binary64)) (.f64 eps #s(literal -1/2 binary64))) (fma.f64 (.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64))))) (.f64 eps eps)))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 eps #s(approx (+ ( eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x))) #s(approx (+ (* eps (* eps -1/6)) (+ (* x (+ (* x (+ (* (* eps eps) 1/12) -1/2)) (* eps -1/2))) 1)) (fma.f64 (fma.f64 #s(literal 1/4 binary64) (.f64 (.f64 x (+.f64 eps x)) (.f64 x (+.f64 eps x))) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (fma.f64 (.f64 x #s(literal -1/2 binary64)) (+.f64 eps x) #s(literal -1 binary64))) (.f64 (.f64 eps eps) (fma.f64 x (*.f64 x #s(literal 1/12 binary64)) #s(literal -1/6 binary64))))))))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 eps #s(approx (+ ( eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x))) (/.f64 #s(literal 1 binary64) (/.f64 (-.f64 (.f64 eps (.f64 x #s(literal -1/2 binary64))) (fma.f64 eps (.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64))) (.f64 (fma.f64 eps (fma.f64 x #s(literal -1/2 binary64) (.f64 eps #s(literal -1/6 binary64))) #s(literal 1 binary64)) (-.f64 (.f64 eps (.f64 x #s(literal -1/2 binary64))) (fma.f64 eps (.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64)))))))))
#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 #s(literal -1/2 binary64) x)) (cos.f64 x))))
(.f64 (.f64 #s(approx (sin (* (+ eps 0) 1/2)) (.f64 #s(literal 1/2 binary64) eps)) (cos.f64 #s(approx ( (+ (* x 2) eps) 1/2) (fma.f64 eps #s(literal 1/2 binary64) x)))) #s(literal 2 binary64))
(-.f64 (sin.f64 (+.f64 x eps)) #s(approx (sin x) (fma.f64 #s(literal -1/6 binary64) (.f64 x (.f64 x x)) x)))
(.f64 (.f64 #s(approx (sin (* (+ eps 0) 1/2)) (.f64 #s(literal 1/2 binary64) eps)) (cos.f64 (.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)))) #s(literal 2 binary64))
(.f64 (.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) (fma.f64 eps #s(literal 1/2 binary64) x)))) #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)) (.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 (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 (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 #s(approx ( (sin (* (+ eps 0) 1/2)) (cos (* (+ (* x 2) eps) 1/2))) (.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (cos.f64 (fma.f64 eps #s(literal 1/2 binary64) x)))) #s(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))
#s(approx (- (sin (+ x eps)) (sin 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)))))
#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 (.f64 (sin.f64 (.f64 (.f64 (.f64 eps eps) (/.f64 #s(literal 1 binary64) 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 (fma.f64 (.f64 (.f64 eps eps) (.f64 #s(literal -1/2 binary64) (.f64 eps (sin.f64 x)))) eps (.f64 eps (.f64 (.f64 eps eps) (cos.f64 x)))) (.f64 eps eps)))
(.f64 (.f64 (sin.f64 (.f64 (.f64 (.f64 eps (.f64 eps eps)) (/.f64 #s(literal 1 binary64) (.f64 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))
(fma.f64 #s(approx (sin eps) (fma.f64 eps (.f64 eps (.f64 eps (fma.f64 (.f64 eps eps) #s(literal 1/120 binary64) #s(literal -1/6 binary64)))) eps)) (cos.f64 x) #s(approx (+ ( (sin x) (cos eps)) (sin (neg x))) #s(approx (+ (* (* eps eps) (+ (* (* eps eps) (* (sin x) (+ (* eps (* eps -1/720)) 1/24))) (* -1/2 (sin x)))) 0) (.f64 (.f64 eps eps) (.f64 (sin.f64 x) (fma.f64 #s(literal 1/24 binary64) (.f64 eps eps) #s(literal -1/2 binary64)))))))
#s(approx (- (sin (+ x eps)) (sin x)) (/.f64 (fma.f64 (.f64 (.f64 (fma.f64 eps (.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64)) (cos.f64 x)) (.f64 eps eps)) eps (.f64 eps (.f64 (.f64 eps (.f64 #s(literal -1/2 binary64) (sin.f64 x))) (.f64 eps eps)))) (.f64 eps eps)))
(fma.f64 (sin.f64 eps) (cos.f64 x) #s(approx (+ (* (sin x) (cos eps)) (sin (neg x))) #s(approx (+ (* (* eps eps) (+ (* (* eps eps) (* (sin x) (+ (* eps (* eps -1/720)) 1/24))) (* -1/2 (sin x)))) 0) (.f64 (.f64 eps eps) (.f64 (sin.f64 x) (fma.f64 #s(literal 1/24 binary64) (.f64 eps eps) #s(literal -1/2 binary64)))))))
(fma.f64 (sin.f64 eps) (cos.f64 x) #s(approx (+ (* (sin x) (cos eps)) (sin (neg x))) (fma.f64 (.f64 eps eps) (.f64 (sin.f64 x) (fma.f64 eps (*.f64 eps #s(literal 1/24 binary64)) #s(literal -1/2 binary64))) #s(literal 0 binary64))))

Outputs

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

Calls

3 calls:

19.0ms	x
16.0ms	(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
14.0ms	eps

Results

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

Compiler

Compiled 15 to 10 computations (33.3% saved)

regimes42.0ms (0.3%)

Memory

20.9MiB live, 56.3MiB allocated

Counts

42 → 1

Calls

Call 1

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

Calls

3 calls:

16.0ms	eps
12.0ms	(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
12.0ms	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)

regimes38.0ms (0.2%)

Memory

-18.2MiB live, 56.2MiB allocated

Counts

38 → 1

Calls

Call 1

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

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:

13.0ms	(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
12.0ms	x
10.0ms	eps

Results

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

Compiler

Compiled 15 to 10 computations (33.3% saved)

regimes35.0ms (0.2%)

Memory

8.8MiB live, 57.1MiB allocated

Counts

37 → 1

Calls

Call 1

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

Calls

3 calls:

13.0ms	(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
10.0ms	x
10.0ms	eps

Results

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

Compiler

Compiled 15 to 10 computations (33.3% saved)

regimes33.0ms (0.2%)

Memory

12.0MiB live, 49.6MiB allocated

Counts

35 → 1

Calls

Call 1

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

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

Calls

3 calls:

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

Results

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

Compiler

Compiled 15 to 10 computations (33.3% saved)

regimes34.0ms (0.2%)

Memory

-27.0MiB live, 46.9MiB allocated

Counts

32 → 1

Calls

Call 1

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

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

Calls

3 calls:

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

Results

Accuracy	Segments	Branch
98.4%	1	`x`
98.4%	1	`eps`
98.4%	1	`(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))`

Compiler

Compiled 15 to 10 computations (33.3% saved)

regimes35.0ms (0.2%)

Memory

5.0MiB live, 43.8MiB allocated

Counts

30 → 1

Calls

Call 1

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

Outputs

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

Calls

3 calls:

16.0ms	x
8.0ms	(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
8.0ms	eps

Results

Accuracy	Segments	Branch
97.1%	1	`x`
97.1%	1	`eps`
97.1%	1	`(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))`

Compiler

Compiled 15 to 10 computations (33.3% saved)

regimes24.0ms (0.2%)

Memory

-1.2MiB live, 35.8MiB allocated

Counts

23 → 1

Calls

Call 1

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

Outputs

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

Calls

3 calls:

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

Results

Accuracy	Segments	Branch
97.1%	1	`x`
97.1%	1	`eps`
97.1%	1	`(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))`

Compiler

Compiled 15 to 10 computations (33.3% saved)

regimes19.0ms (0.1%)

Memory

32.0MiB live, 32.0MiB allocated

Counts

20 → 1

Calls

Call 1

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

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

Calls

3 calls:

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

Results

Accuracy	Segments	Branch
97.1%	1	`x`
97.1%	1	`eps`
97.1%	1	`(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))`

Compiler

Compiled 15 to 10 computations (33.3% saved)

regimes13.0ms (0.1%)

Memory

-17.9MiB live, 19.2MiB allocated

Counts

9 → 1

Calls

Call 1

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

Outputs

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

Calls

3 calls:

6.0ms	eps
3.0ms	(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
3.0ms	x

Results

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

Compiler

Compiled 15 to 10 computations (33.3% saved)

regimes7.0ms (0%)

Memory

17.4MiB live, 17.4MiB allocated

Counts

5 → 1

Calls

Call 1

Inputs
#s(approx (+ (* (sin eps) (cos x)) (+ (* (sin x) (cos eps)) (sin (neg x)))) #s(literal 0 binary64))
#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)) (.f64 eps #s(approx (+ ( eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x))) #s(approx (+ (* eps (* x -1/2)) (+ (* -1/6 (* eps eps)) 1)) (.f64 #s(literal -1/2 binary64) (.f64 x eps))))))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 eps #s(approx (+ ( eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x))) #s(approx (+ (* eps (* x -1/2)) (+ (* -1/6 (* eps eps)) 1)) (.f64 (.f64 eps eps) #s(literal -1/6 binary64))))))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 eps #s(approx (+ ( eps (* -1/2 (sin x))) (cos x)) (fma.f64 #s(literal -1/2 binary64) (*.f64 x eps) #s(literal 1 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	x
2.0ms	eps

Results

Accuracy	Segments	Branch
96.4%	1	`x`
96.4%	1	`eps`
96.4%	1	`(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))`

Compiler

Compiled 15 to 10 computations (33.3% saved)

regimes8.0ms (0.1%)

Memory

-17.9MiB live, 16.7MiB allocated

Accuracy

Total 0.0b remaining (0%)

Threshold costs 0b (0%)

Counts

1 → 1

Calls

Call 1

Inputs
#s(approx (+ (* (sin eps) (cos x)) (+ (* (sin x) (cos eps)) (sin (neg x)))) #s(literal 0 binary64))

Outputs
#s(approx (+ (* (sin eps) (cos x)) (+ (* (sin x) (cos eps)) (sin (neg x)))) #s(literal 0 binary64))

Calls

3 calls:

5.0ms	x
1.0ms	(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
1.0ms	eps

Results

Accuracy	Segments	Branch
5.3%	1	`x`
5.3%	1	`eps`
5.3%	1	`(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))`

Compiler

Compiled 15 to 10 computations (33.3% saved)

simplify10.0ms (0.1%)

Memory

21.9MiB live, 21.9MiB allocated

Algorithm

1×	egg-herbie

Rules

68×	`*-commutative_binary64`
4×	`+-commutative_binary64`
2×	`1-exp_binary64`
2×	`1-exp_binary32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	149	497
1	187	497

Stop Event

1×

saturated

Calls

Call 1

Inputs
(fma.f64 (sin.f64 eps) (cos.f64 x) #s(approx (+ (* (sin x) (cos eps)) (sin (neg x))) (fma.f64 (.f64 eps eps) (fma.f64 (.f64 eps eps) (.f64 (sin.f64 x) (fma.f64 eps (.f64 eps #s(literal -1/720 binary64)) #s(literal 1/24 binary64))) (*.f64 #s(literal -1/2 binary64) (sin.f64 x))) #s(literal 0 binary64))))
(fma.f64 (cos.f64 x) #s(approx (sin eps) (fma.f64 (.f64 eps eps) (.f64 eps (fma.f64 (.f64 eps eps) #s(literal 1/120 binary64) #s(literal -1/6 binary64))) eps)) #s(approx (+ ( (sin x) (cos eps)) (sin (neg x))) (.f64 (.f64 eps eps) (fma.f64 (.f64 eps eps) (.f64 (sin.f64 x) (fma.f64 eps (.f64 eps #s(literal -1/720 binary64)) #s(literal 1/24 binary64))) (.f64 (sin.f64 x) #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 (.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 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 eps (.f64 eps #s(literal -1/48 binary64)) #s(literal 1/2 binary64)))) (cos.f64 #s(approx (* (+ (* x 2) eps) 1/2) (fma.f64 eps #s(literal 1/2 binary64) x)))) #s(literal 2 binary64))
(.f64 (.f64 #s(approx (sin (* (+ eps 0) 1/2)) (.f64 #s(literal 1/2 binary64) eps)) (cos.f64 #s(approx ( (+ (* x 2) eps) 1/2) (fma.f64 eps #s(literal 1/2 binary64) x)))) #s(literal 2 binary64))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 eps (cos.f64 x)))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* eps (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x)))) (fma.f64 eps (fma.f64 #s(literal -1/6 binary64) (.f64 eps eps) #s(literal 1 binary64)) (.f64 (.f64 x #s(literal -1/2 binary64)) (.f64 eps (fma.f64 x (fma.f64 #s(literal -1/6 binary64) (*.f64 eps eps) #s(literal 1 binary64)) eps))))))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 eps #s(approx (+ ( eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x))) #s(approx (+ (* eps (* eps -1/6)) (+ (* x (+ (* x (+ (* (* eps eps) 1/12) -1/2)) (* eps -1/2))) 1)) (+.f64 (fma.f64 (.f64 #s(literal -1/2 binary64) x) (+.f64 x eps) #s(literal 1 binary64)) (.f64 eps (.f64 eps (fma.f64 (.f64 x x) #s(literal 1/12 binary64) #s(literal -1/6 binary64)))))))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* eps (+ (* eps (* -1/2 (sin x))) (cos x))) (fma.f64 #s(literal -1/2 binary64) (.f64 (.f64 eps (+.f64 x eps)) x) eps)))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 eps #s(approx (+ ( eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x))) #s(approx (+ (* eps (* eps -1/6)) (+ (* x (+ (* x (+ (* (* eps eps) 1/12) -1/2)) (* eps -1/2))) 1)) (fma.f64 #s(literal -1/2 binary64) (*.f64 x x) #s(literal 1 binary64))))))
#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 eps) (cos x)) (+ (* (sin x) (cos eps)) (sin (neg x)))) #s(literal 0 binary64))

Outputs
(fma.f64 (sin.f64 eps) (cos.f64 x) #s(approx (+ (* (sin x) (cos eps)) (sin (neg x))) (fma.f64 (.f64 eps eps) (fma.f64 (.f64 eps eps) (.f64 (sin.f64 x) (fma.f64 eps (.f64 eps #s(literal -1/720 binary64)) #s(literal 1/24 binary64))) (*.f64 #s(literal -1/2 binary64) (sin.f64 x))) #s(literal 0 binary64))))
(fma.f64 (sin.f64 eps) (cos.f64 x) #s(approx (+ (* (sin x) (cos eps)) (sin (neg x))) (fma.f64 (.f64 eps eps) (fma.f64 (.f64 eps eps) (.f64 (sin.f64 x) (fma.f64 eps (.f64 eps #s(literal -1/720 binary64)) #s(literal 1/24 binary64))) (*.f64 (sin.f64 x) #s(literal -1/2 binary64))) #s(literal 0 binary64))))
(fma.f64 (cos.f64 x) #s(approx (sin eps) (fma.f64 (.f64 eps eps) (.f64 eps (fma.f64 (.f64 eps eps) #s(literal 1/120 binary64) #s(literal -1/6 binary64))) eps)) #s(approx (+ ( (sin x) (cos eps)) (sin (neg x))) (.f64 (.f64 eps eps) (fma.f64 (.f64 eps eps) (.f64 (sin.f64 x) (fma.f64 eps (.f64 eps #s(literal -1/720 binary64)) #s(literal 1/24 binary64))) (.f64 (sin.f64 x) #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 #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 #s(literal 2 binary64) (.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 #s(literal 1/2 binary64) (fma.f64 x #s(literal 2 binary64) eps)))))
(.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 (cos.f64 (.f64 #s(literal 1/2 binary64) (fma.f64 x #s(literal 2 binary64) eps))) #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))))))
(.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) (fma.f64 eps #s(literal 1/2 binary64) x)))) #s(literal 2 binary64))
(.f64 #s(literal 2 binary64) (.f64 #s(approx (sin (* (+ eps 0) 1/2)) (.f64 eps (fma.f64 eps (.f64 eps #s(literal -1/48 binary64)) #s(literal 1/2 binary64)))) (cos.f64 #s(approx (* (+ (* x 2) eps) 1/2) (fma.f64 eps #s(literal 1/2 binary64) x)))))
(.f64 (.f64 #s(approx (sin (* (+ eps 0) 1/2)) (.f64 #s(literal 1/2 binary64) eps)) (cos.f64 #s(approx ( (+ (* x 2) eps) 1/2) (fma.f64 eps #s(literal 1/2 binary64) x)))) #s(literal 2 binary64))
(.f64 #s(literal 2 binary64) (.f64 (cos.f64 #s(approx (* (+ (* x 2) eps) 1/2) (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)) #s(approx (* eps (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x)))) (fma.f64 eps (fma.f64 #s(literal -1/6 binary64) (.f64 eps eps) #s(literal 1 binary64)) (.f64 (.f64 x #s(literal -1/2 binary64)) (.f64 eps (fma.f64 x (fma.f64 #s(literal -1/6 binary64) (*.f64 eps eps) #s(literal 1 binary64)) eps))))))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 eps #s(approx (+ ( eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x))) #s(approx (+ (* eps (* eps -1/6)) (+ (* x (+ (* x (+ (* (* eps eps) 1/12) -1/2)) (* eps -1/2))) 1)) (+.f64 (fma.f64 (.f64 #s(literal -1/2 binary64) x) (+.f64 x eps) #s(literal 1 binary64)) (.f64 eps (.f64 eps (fma.f64 (.f64 x x) #s(literal 1/12 binary64) #s(literal -1/6 binary64)))))))))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 eps #s(approx (+ ( eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x))) #s(approx (+ (* eps (* eps -1/6)) (+ (* x (+ (* x (+ (* (* eps eps) 1/12) -1/2)) (* eps -1/2))) 1)) (+.f64 (fma.f64 (.f64 x #s(literal -1/2 binary64)) (+.f64 eps x) #s(literal 1 binary64)) (.f64 eps (.f64 eps (fma.f64 (.f64 x x) #s(literal 1/12 binary64) #s(literal -1/6 binary64)))))))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* eps (+ (* eps (* -1/2 (sin x))) (cos x))) (fma.f64 #s(literal -1/2 binary64) (.f64 (.f64 eps (+.f64 x eps)) x) eps)))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* eps (+ (* eps (* -1/2 (sin x))) (cos x))) (fma.f64 #s(literal -1/2 binary64) (.f64 x (.f64 eps (+.f64 eps x))) eps)))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 eps #s(approx (+ ( eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x))) #s(approx (+ (* eps (* eps -1/6)) (+ (* x (+ (* x (+ (* (* eps eps) 1/12) -1/2)) (* eps -1/2))) 1)) (fma.f64 #s(literal -1/2 binary64) (*.f64 x x) #s(literal 1 binary64))))))
#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 eps) (cos x)) (+ (* (sin x) (cos eps)) (sin (neg x)))) #s(literal 0 binary64))

soundness1.7s (10.9%)

Memory

-10.0MiB live, 905.3MiB allocated

Rules

16 678×	`lower-fma.f64`
16 678×	`lower-fma.f32`
14 218×	`lower-fma.f64`
14 218×	`lower-fma.f32`
11 964×	`lower-fma.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	563	7456
1	1823	7215
2	5700	7184
0	8813	6541
0	471	4424
1	1463	4173
2	4278	4141
0	8553	3792
0	601	6606
1	1920	6337
2	6056	6282
0	8283	5716
0	6	16
0	10	16
1	53	16
2	380	16
3	4766	16
0	8210	16
0	107	496
1	314	496
2	775	489
3	2836	489
4	6173	489
0	8126	458
0	90	595
0	140	581
1	582	575
2	5179	575
0	8180	543

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×	node limit
1×	iter limit
1×	node limit

Compiler

Compiled 693 to 366 computations (47.2% saved)

preprocess164.0ms (1.1%)

Memory: 19.0MiB live, 171.7MiB allocated
Compiler: Compiled 612 to 244 computations (60.1% 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%)

analyze39.0ms (0.3%)

sample6.4s (41.5%)

explain91.0ms (0.6%)

preprocess27.0ms (0.2%)

eval0.0ms (0%)

prune1.0ms (0%)

simplify7.0ms (0%)

localize37.0ms (0.2%)

series4.0ms (0%)

simplify261.0ms (1.7%)

rewrite261.0ms (1.7%)

eval38.0ms (0.2%)

prune50.0ms (0.3%)

simplify570.0ms (3.7%)

localize331.0ms (2.1%)

series41.0ms (0.3%)

simplify330.0ms (2.1%)

rewrite333.0ms (2.2%)

eval127.0ms (0.8%)

prune150.0ms (1%)

simplify267.0ms (1.7%)

localize342.0ms (2.2%)

series46.0ms (0.3%)

simplify424.0ms (2.8%)

rewrite483.0ms (3.1%)

eval244.0ms (1.6%)

prune261.0ms (1.7%)

simplify226.0ms (1.5%)

localize439.0ms (2.9%)

series44.0ms (0.3%)

simplify283.0ms (1.8%)

rewrite561.0ms (3.6%)

eval156.0ms (1%)

prune210.0ms (1.4%)

regimes79.0ms (0.5%)

regimes49.0ms (0.3%)

regimes52.0ms (0.3%)

regimes42.0ms (0.3%)

regimes38.0ms (0.2%)

regimes35.0ms (0.2%)

regimes33.0ms (0.2%)

regimes34.0ms (0.2%)

regimes35.0ms (0.2%)

regimes24.0ms (0.2%)

regimes19.0ms (0.1%)

regimes13.0ms (0.1%)

regimes7.0ms (0%)

regimes8.0ms (0.1%)

simplify10.0ms (0.1%)

soundness1.7s (10.9%)

preprocess164.0ms (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