Metrics for 2sin (example 3.3)

start0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated

analyze39.0ms (0.3%)

Memory

27.0MiB live, 65.0MiB 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)

sample6.0s (45.3%)

Memory

-167.7MiB live, 6 866.5MiB allocated

Samples

3.0s	26 447×	0	invalid
824.0ms	2 833×	1	valid
625.0ms	5 423×	0	valid

Precisions

Click to see histograms. Total time spent on operations: 3.3s

ival-sin: 982.0ms (29.5% of total)

const: 668.0ms (20.1% of total)

ival-mult: 319.0ms (9.6% of total)

ival-fabs: 276.0ms (8.3% of total)

ival-add: 228.0ms (6.9% of total)

ival-<=: 224.0ms (6.7% of total)

ival-<: 190.0ms (5.7% of total)

ival-sub: 170.0ms (5.1% of total)

adjust: 114.0ms (3.4% of total)

ival-and: 101.0ms (3% of total)

exact: 43.0ms (1.3% of total)

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

Bogosity

explain87.0ms (0.7%)

Memory

-17.4MiB live, 180.2MiB allocated

FPErrors

Click to see full error table

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

Explanations

Click to see full explanations table

Operator	Subexpression	Explanation	Count
`-.f64`	`(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))`	cancellation	219	5

Confusion

	Predicted +	Predicted -
+	216	4
-	3	33

Precision

0.9863013698630136

Recall

0.9818181818181818

Confusion?

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

Precision?

0.9776785714285714

Recall?

0.9954545454545455

Freqs

test

number	freq
0	37
1	219

Total Confusion?

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

Precision?

1.0

Recall?

1.0

Samples

21.0ms	346×	0	valid
17.0ms	162×	1	valid
1.0ms	4×	3	valid

Compiler

Compiled 49 to 22 computations (55.1% saved)

Precisions

Click to see histograms. Total time spent on operations: 21.0ms

ival-sin: 9.0ms (43.8% of total)

ival-sub: 4.0ms (19.5% of total)

adjust: 3.0ms (14.6% of total)

ival-add: 3.0ms (14.6% of total)

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

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

preprocess29.0ms (0.2%)

Memory

5.2MiB live, 44.6MiB 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: 0.5MiB live, 0.5MiB allocated
Compiler: Compiled 2 to 2 computations (0% saved)

prune1.0ms (0%)

Memory

1.2MiB live, 1.2MiB allocated

Alt Table

Click to see full alt table

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

Compiler

Compiled 9 to 6 computations (33.3% saved)

simplify8.0ms (0.1%)

Memory

13.8MiB live, 13.8MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 4 expressions of interest:

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

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

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

Stop Event

1×	iter limit
1×	saturated
1×	iter limit

Calls

Call 1

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

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

localize28.0ms (0.2%)

Memory

-4.2MiB live, 31.9MiB allocated

Localize:

Found 4 expressions of interest:

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

Samples

9.0ms	173×	0	valid
8.0ms	81×	1	valid
1.0ms	2×	3	valid

Compiler

Compiled 20 to 8 computations (60% saved)

Precisions

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

ival-sin: 5.0ms (48.1% of total)

adjust: 2.0ms (19.2% of total)

ival-add: 2.0ms (19.2% of total)

ival-sub: 1.0ms (9.6% of total)

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

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

series4.0ms (0%)

Memory

6.5MiB live, 6.5MiB allocated

Counts

4 → 84

Calls

Call 1

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

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

Calls

21 calls:

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

simplify337.0ms (2.5%)

Memory

-16.1MiB live, 155.0MiB allocated

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	107	496
1	314	496
2	775	489
3	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)

rewrite321.0ms (2.4%)

Memory

-28.6MiB live, 252.5MiB 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))

eval114.0ms (0.9%)

Memory: 15.2MiB live, 51.9MiB allocated
Compiler: Compiled 7 823 to 844 computations (89.2% saved)

prune178.0ms (1.3%)

Memory

-3.6MiB live, 73.2MiB allocated

Pruning

7 alts after pruning (6 fresh and 1 done)

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

Accuracy

100.0%

Counts

292 → 7

Alt Table

Click to see full alt table

Status	Accuracy	Program
	62.6%	(fma.f64 (sin.f64 x) (cos.f64 eps) (-.f64 (*.f64 (cos.f64 x) (sin.f64 eps)) (sin.f64 x)))
✓	62.5%	(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
▶	61.8%	(-.f64 (sin.f64 (+.f64 x eps)) #s(approx (sin x) (fma.f64 (fma.f64 (.f64 x x) #s(literal 1/120 binary64) #s(literal -1/6 binary64)) (.f64 x (*.f64 x x)) x)))
▶	99.9%	(.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))
▶	99.7%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 eps (fma.f64 eps (.f64 #s(literal -1/2 binary64) (sin.f64 x)) (cos.f64 x))))
▶	99.3%	#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 eps (cos.f64 x)))
▶	98.1%	#s(approx (- (sin (+ x eps)) (sin x)) (sin.f64 eps))

Compiler

Compiled 167 to 102 computations (38.9% saved)

simplify312.0ms (2.3%)

Memory

6.9MiB live, 322.5MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 17 expressions of interest:

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

Rules

7 984×	`lower-fma.f32`
7 976×	`lower-fma.f64`
4 922×	`lower-*.f32`
4 904×	`lower-*.f64`
1 480×	`lower-+.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	38	221
0	65	203
1	104	203
2	202	203
3	384	199
4	634	199
5	1201	199
6	2127	199
7	2231	199
8	2293	199
9	2329	199
10	2437	199
11	2600	199
12	3013	199
13	3253	199
14	3459	199
15	3669	199
16	4084	199
17	5641	199
18	7067	199
19	7362	199
20	7445	199
21	7463	199
22	7463	199
0	8165	195

Stop Event

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

Calls

Call 1

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

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

localize170.0ms (1.3%)

Memory

14.7MiB live, 216.7MiB allocated

Localize:

Found 17 expressions of interest:

New	Metric	Score
accuracy	0	(sin.f64 x)
accuracy	0	(cos.f64 x)
accuracy	0.00390625	(.f64 eps (fma.f64 eps (.f64 #s(literal -1/2 binary64) (sin.f64 x)) (cos.f64 x)))
accuracy	0.1809942524239391	#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	0.04331040172363414	(sin.f64 (+.f64 x eps))
accuracy	0.09375	(.f64 x (.f64 x x))
accuracy	0.8047176853293299	#s(approx (sin x) (fma.f64 (fma.f64 (.f64 x x) #s(literal 1/120 binary64) #s(literal -1/6 binary64)) (.f64 x (*.f64 x x)) x))
accuracy	23.938343398647625	(-.f64 (sin.f64 (+.f64 x eps)) #s(approx (sin x) (fma.f64 (fma.f64 (.f64 x x) #s(literal 1/120 binary64) #s(literal -1/6 binary64)) (.f64 x (*.f64 x x)) x)))
accuracy	0	(cos.f64 x)
accuracy	0.00390625	(*.f64 eps (cos.f64 x))
accuracy	0.45925062897182506	#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 eps (cos.f64 x)))
accuracy	0	(sin.f64 eps)
accuracy	1.2471092528947976	#s(approx (- (sin (+ x eps)) (sin x)) (sin.f64 eps))
accuracy	0	(sin.f64 (*.f64 (+.f64 eps #s(literal 0 binary64)) #s(literal 1/2 binary64)))
accuracy	0.00390625	(.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	0.0078125	(.f64 (sin.f64 (.f64 (+.f64 eps #s(literal 0 binary64)) #s(literal 1/2 binary64))) (cos.f64 (*.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64))))
accuracy	0.0464165744115697	(cos.f64 (*.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)))

Samples

97.0ms	173×	0	valid
36.0ms	81×	1	valid
2.0ms	2×	3	valid

Compiler

Compiled 186 to 36 computations (80.6% saved)

Precisions

Click to see histograms. Total time spent on operations: 113.0ms

ival-mult: 49.0ms (43.5% of total)

ival-cos: 33.0ms (29.3% of total)

ival-add: 8.0ms (7.1% of total)

ival-sin: 7.0ms (6.2% of total)

const: 7.0ms (6.2% of total)

adjust: 6.0ms (5.3% of total)

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

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

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

exact: 0.0ms (0% of total)

series34.0ms (0.3%)

Memory

-2.3MiB live, 73.7MiB allocated

Counts

21 → 408

Calls

Call 1

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

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

102 calls:

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

simplify279.0ms (2.1%)

Memory

-4.9MiB live, 365.7MiB allocated

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	359	3403
1	1096	3265
2	2826	3225
3	6529	3225
0	8151	2971

Stop Event

1×	iter limit
1×	node limit

Counts

408 → 382

Calls

Call 1

Inputs
(* 1/2 eps)
(+ x (* 1/2 eps))
(+ x (* 1/2 eps))
(+ x (* 1/2 eps))
x
(* x (+ 1 (* 1/2 (/ eps x))))
(* x (+ 1 (* 1/2 (/ eps x))))
(* x (+ 1 (* 1/2 (/ eps x))))
x
(* -1 (* x (- (* -1/2 (/ eps x)) 1)))
(* -1 (* x (- (* -1/2 (/ eps x)) 1)))
(* -1 (* x (- (* -1/2 (/ eps x)) 1)))
x
(+ x (* 1/2 eps))
(+ x (* 1/2 eps))
(+ x (* 1/2 eps))
(* 1/2 eps)
(* eps (+ 1/2 (/ x eps)))
(* eps (+ 1/2 (/ x eps)))
(* eps (+ 1/2 (/ x eps)))
(* 1/2 eps)
(* -1 (* eps (- (* -1 (/ x eps)) 1/2)))
(* -1 (* eps (- (* -1 (/ x eps)) 1/2)))
(* -1 (* eps (- (* -1 (/ x eps)) 1/2)))
eps
eps
eps
eps
eps
eps
eps
eps
eps
eps
eps
eps
(* eps (cos x))
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* 2 (* eps (+ (* -1/16 (cos x)) (* -1/48 (cos x)))))))))
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* eps (+ (* 1/24 (* eps (sin x))) (* 2 (+ (* -1/16 (cos x)) (* -1/48 (cos x))))))))))
(* 2 (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))))
(* 2 (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))))
(* 2 (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))))
(* 2 (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))))
(* 2 (* (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps))))
(* 2 (* (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps))))
(* 2 (* (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps))))
(* 2 (* (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps))))
(* 2 (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))
(+ (* -2 (* x (pow (sin (* 1/2 eps)) 2))) (* 2 (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))))
(+ (* 2 (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) (* x (+ (* -2 (pow (sin (* 1/2 eps)) 2)) (* -1 (* x (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))))))
(+ (* 2 (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) (* x (+ (* -2 (pow (sin (* 1/2 eps)) 2)) (* x (+ (* -1 (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) (* 1/3 (* x (pow (sin (* 1/2 eps)) 2))))))))
(* 2 (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))))
(* 2 (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))))
(* 2 (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))))
(* 2 (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))))
(* 2 (* (cos (* 1/2 (- eps (* -2 x)))) (sin (* 1/2 eps))))
(* 2 (* (cos (* 1/2 (- eps (* -2 x)))) (sin (* 1/2 eps))))
(* 2 (* (cos (* 1/2 (- eps (* -2 x)))) (sin (* 1/2 eps))))
(* 2 (* (cos (* 1/2 (- eps (* -2 x)))) (sin (* 1/2 eps))))
(* 1/2 (* eps (cos x)))
(* eps (+ (* -1/4 (* eps (sin x))) (* 1/2 (cos x))))
(* eps (+ (* 1/2 (cos x)) (* eps (+ (* -1/4 (sin x)) (* eps (+ (* -1/16 (cos x)) (* -1/48 (cos x))))))))
(* eps (+ (* 1/2 (cos x)) (* eps (+ (* -1/4 (sin x)) (* eps (+ (* -1/16 (cos x)) (+ (* -1/48 (cos x)) (* 1/48 (* eps (sin x))))))))))
(* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps)))
(* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps)))
(* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps)))
(* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps)))
(* (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps)))
(* (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps)))
(* (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps)))
(* (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps)))
(* (cos (* 1/2 eps)) (sin (* 1/2 eps)))
(+ (* -1 (* x (pow (sin (* 1/2 eps)) 2))) (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))
(+ (* x (+ (* -1 (pow (sin (* 1/2 eps)) 2)) (* -1/2 (* x (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))))) (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))
(+ (* x (+ (* -1 (pow (sin (* 1/2 eps)) 2)) (* x (+ (* -1/2 (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) (* 1/6 (* x (pow (sin (* 1/2 eps)) 2))))))) (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))
(* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps)))
(* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps)))
(* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps)))
(* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps)))
(* (cos (* 1/2 (- eps (* -2 x)))) (sin (* 1/2 eps)))
(* (cos (* 1/2 (- eps (* -2 x)))) (sin (* 1/2 eps)))
(* (cos (* 1/2 (- eps (* -2 x)))) (sin (* 1/2 eps)))
(* (cos (* 1/2 (- eps (* -2 x)))) (sin (* 1/2 eps)))
(sin eps)
(+ (sin eps) (* x (- (cos eps) 1)))
(+ (sin eps) (* x (- (+ (cos eps) (* -1/2 (* x (sin eps)))) 1)))
(+ (sin eps) (* x (- (+ (cos eps) (* x (+ (* -1/2 (sin eps)) (* x (+ 1/6 (* -1/6 (cos eps))))))) 1)))
(- (sin (+ eps x)) (sin x))
(- (sin (+ eps x)) (sin x))
(- (sin (+ eps x)) (sin x))
(- (sin (+ eps x)) (sin x))
(- (sin (- eps (* -1 x))) (sin x))
(- (sin (- eps (* -1 x))) (sin x))
(- (sin (- eps (* -1 x))) (sin x))
(- (sin (- eps (* -1 x))) (sin x))
(* eps (cos x))
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x)))))))
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* eps (+ (* -1/6 (cos x)) (* 1/24 (* eps (sin x)))))))))
(- (sin (+ eps x)) (sin x))
(- (sin (+ eps x)) (sin x))
(- (sin (+ eps x)) (sin x))
(- (sin (+ eps x)) (sin x))
(- (sin (- x (* -1 eps))) (sin x))
(- (sin (- x (* -1 eps))) (sin x))
(- (sin (- x (* -1 eps))) (sin x))
(- (sin (- x (* -1 eps))) (sin x))
eps
(* eps (+ 1 (* -1/6 (pow eps 2))))
(* eps (+ 1 (* (pow eps 2) (- (* 1/120 (pow eps 2)) 1/6))))
(* eps (+ 1 (* (pow eps 2) (- (* (pow eps 2) (+ 1/120 (* -1/5040 (pow eps 2)))) 1/6))))
(sin eps)
(sin eps)
(sin eps)
(sin eps)
(sin eps)
(sin eps)
(sin eps)
(sin eps)
(sin eps)
(+ (sin eps) (* x (- (cos eps) 1)))
(+ (sin eps) (* x (- (+ (cos eps) (* -1/2 (* x (sin eps)))) 1)))
(+ (sin eps) (* x (- (+ (cos eps) (* x (+ (* -1/2 (sin eps)) (* x (+ 1/6 (* -1/6 (cos eps))))))) 1)))
(- (sin (+ eps x)) (sin x))
(- (sin (+ eps x)) (sin x))
(- (sin (+ eps x)) (sin x))
(- (sin (+ eps x)) (sin x))
(- (sin (- eps (* -1 x))) (sin x))
(- (sin (- eps (* -1 x))) (sin x))
(- (sin (- eps (* -1 x))) (sin x))
(- (sin (- eps (* -1 x))) (sin x))
(* eps (cos x))
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x)))))))
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* eps (+ (* -1/6 (cos x)) (* 1/24 (* eps (sin x)))))))))
(- (sin (+ eps x)) (sin x))
(- (sin (+ eps x)) (sin x))
(- (sin (+ eps x)) (sin x))
(- (sin (+ eps x)) (sin x))
(- (sin (- x (* -1 eps))) (sin x))
(- (sin (- x (* -1 eps))) (sin x))
(- (sin (- x (* -1 eps))) (sin x))
(- (sin (- x (* -1 eps))) (sin x))
(* eps (cos x))
(* eps (cos x))
(* eps (cos x))
(* eps (cos x))
(* eps (cos x))
(* eps (cos x))
(* eps (cos x))
(* eps (cos x))
(* eps (cos x))
(* eps (cos x))
(* eps (cos x))
(* eps (cos x))
eps
(+ eps (* -1/2 (* eps (pow x 2))))
(+ eps (* (pow x 2) (+ (* -1/2 eps) (* 1/24 (* eps (pow x 2))))))
(+ eps (* (pow x 2) (+ (* -1/2 eps) (* (pow x 2) (+ (* -1/720 (* eps (pow x 2))) (* 1/24 eps))))))
(* eps (cos x))
(* eps (cos x))
(* eps (cos x))
(* eps (cos x))
(* eps (cos x))
(* eps (cos x))
(* eps (cos x))
(* eps (cos x))
1
(+ 1 (* -1/2 (pow x 2)))
(+ 1 (* (pow x 2) (- (* 1/24 (pow x 2)) 1/2)))
(+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))) 1/2)))
(cos x)
(cos x)
(cos x)
(cos x)
(cos x)
(cos x)
(cos x)
(cos x)
(sin eps)
(+ (sin eps) (* x (- (cos eps) 1)))
(+ (sin eps) (* x (- (+ (cos eps) (* -1/2 (* x (sin eps)))) 1)))
(+ (sin eps) (* x (- (+ (cos eps) (* x (+ (* -1/2 (sin eps)) (* x (+ 1/6 (* -1/6 (cos eps))))))) 1)))
(- (sin (+ eps x)) (sin x))
(- (sin (+ eps x)) (sin x))
(- (sin (+ eps x)) (sin x))
(- (sin (+ eps x)) (sin x))
(- (sin (- eps (* -1 x))) (sin x))
(- (sin (- eps (* -1 x))) (sin x))
(- (sin (- eps (* -1 x))) (sin x))
(- (sin (- eps (* -1 x))) (sin x))
(* eps (cos x))
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x)))))))
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* eps (+ (* -1/6 (cos x)) (* 1/24 (* eps (sin x)))))))))
(- (sin (+ eps x)) (sin x))
(- (sin (+ eps x)) (sin x))
(- (sin (+ eps x)) (sin x))
(- (sin (+ eps x)) (sin x))
(- (sin (- x (* -1 eps))) (sin x))
(- (sin (- x (* -1 eps))) (sin x))
(- (sin (- x (* -1 eps))) (sin x))
(- (sin (- x (* -1 eps))) (sin x))
(sin eps)
(+ (sin eps) (* x (cos eps)))
(+ (sin eps) (* x (+ (cos eps) (* -1/2 (* x (sin eps))))))
(+ (sin eps) (* x (+ (cos eps) (* x (+ (* -1/2 (sin eps)) (* -1/6 (* x (cos eps))))))))
(sin (+ eps x))
(sin (+ eps x))
(sin (+ eps x))
(sin (+ eps x))
(sin (- eps (* -1 x)))
(sin (- eps (* -1 x)))
(sin (- eps (* -1 x)))
(sin (- eps (* -1 x)))
(sin x)
(+ (sin x) (* eps (cos x)))
(+ (sin x) (* eps (+ (cos x) (* -1/2 (* eps (sin x))))))
(+ (sin x) (* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x))))))))
(sin (+ eps x))
(sin (+ eps x))
(sin (+ eps x))
(sin (+ eps x))
(sin (- x (* -1 eps)))
(sin (- x (* -1 eps)))
(sin (- x (* -1 eps)))
(sin (- x (* -1 eps)))
eps
(+ eps x)
(+ eps x)
(+ eps x)
x
(* x (+ 1 (/ eps x)))
(* x (+ 1 (/ eps x)))
(* x (+ 1 (/ eps x)))
x
(* -1 (* x (- (* -1 (/ eps x)) 1)))
(* -1 (* x (- (* -1 (/ eps x)) 1)))
(* -1 (* x (- (* -1 (/ eps x)) 1)))
x
(+ eps x)
(+ eps x)
(+ eps x)
eps
(* eps (+ 1 (/ x eps)))
(* eps (+ 1 (/ x eps)))
(* eps (+ 1 (/ x eps)))
eps
(* -1 (* eps (- (* -1 (/ x eps)) 1)))
(* -1 (* eps (- (* -1 (/ x eps)) 1)))
(* -1 (* eps (- (* -1 (/ x eps)) 1)))
x
(* x (+ 1 (* -1/6 (pow x 2))))
(* x (+ 1 (* (pow x 2) (- (* 1/120 (pow x 2)) 1/6))))
(* x (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/120 (* -1/5040 (pow x 2)))) 1/6))))
(sin x)
(sin x)
(sin x)
(sin x)
(sin x)
(sin x)
(sin x)
(sin x)
(sin eps)
(+ (sin eps) (* x (- (cos eps) 1)))
(+ (sin eps) (* x (- (+ (cos eps) (* -1/2 (* x (sin eps)))) 1)))
(+ (sin eps) (* x (- (+ (cos eps) (* x (+ (* -1/2 (sin eps)) (* x (+ 1/6 (* -1/6 (cos eps))))))) 1)))
(- (sin (+ eps x)) (sin x))
(- (sin (+ eps x)) (sin x))
(- (sin (+ eps x)) (sin x))
(- (sin (+ eps x)) (sin x))
(- (sin (- eps (* -1 x))) (sin x))
(- (sin (- eps (* -1 x))) (sin x))
(- (sin (- eps (* -1 x))) (sin x))
(- (sin (- eps (* -1 x))) (sin x))
(* eps (cos x))
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x)))))))
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* eps (+ (* -1/6 (cos x)) (* 1/24 (* eps (sin x)))))))))
(- (sin (+ eps x)) (sin x))
(- (sin (+ eps x)) (sin x))
(- (sin (+ eps x)) (sin x))
(- (sin (+ eps x)) (sin x))
(- (sin (- x (* -1 eps))) (sin x))
(- (sin (- x (* -1 eps))) (sin x))
(- (sin (- x (* -1 eps))) (sin x))
(- (sin (- x (* -1 eps))) (sin x))
(* eps (cos x))
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(* -1/2 (* (pow eps 2) (sin x)))
(* (pow eps 2) (+ (* -1/2 (sin x)) (/ (cos x) eps)))
(* (pow eps 2) (+ (* -1/2 (sin x)) (/ (cos x) eps)))
(* (pow eps 2) (+ (* -1/2 (sin x)) (/ (cos x) eps)))
(* -1/2 (* (pow eps 2) (sin x)))
(* (pow eps 2) (+ (* -1/2 (sin x)) (/ (cos x) eps)))
(* (pow eps 2) (+ (* -1/2 (sin x)) (/ (cos x) eps)))
(* (pow eps 2) (+ (* -1/2 (sin x)) (/ (cos x) eps)))
eps
(+ eps (* -1/2 (* (pow eps 2) x)))
(+ eps (* x (+ (* -1/2 (* eps x)) (* -1/2 (pow eps 2)))))
(+ eps (* x (+ (* -1/2 (pow eps 2)) (* x (+ (* -1/2 eps) (* 1/12 (* (pow eps 2) x)))))))
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(cos x)
(+ (cos x) (* -1/2 (* eps (sin x))))
(+ (cos x) (* -1/2 (* eps (sin x))))
(+ (cos x) (* -1/2 (* eps (sin x))))
(* -1/2 (* eps (sin x)))
(* eps (+ (* -1/2 (sin x)) (/ (cos x) eps)))
(* eps (+ (* -1/2 (sin x)) (/ (cos x) eps)))
(* eps (+ (* -1/2 (sin x)) (/ (cos x) eps)))
(* -1/2 (* eps (sin x)))
(* -1 (* eps (+ (* -1 (/ (cos x) eps)) (* 1/2 (sin x)))))
(* -1 (* eps (+ (* -1 (/ (cos x) eps)) (* 1/2 (sin x)))))
(* -1 (* eps (+ (* -1 (/ (cos x) eps)) (* 1/2 (sin x)))))
1
(+ 1 (* -1/2 (* eps x)))
(+ 1 (* x (+ (* -1/2 eps) (* -1/2 x))))
(+ 1 (* x (+ (* -1/2 eps) (* x (- (* 1/12 (* eps x)) 1/2)))))
(+ (cos x) (* -1/2 (* eps (sin x))))
(+ (cos x) (* -1/2 (* eps (sin x))))
(+ (cos x) (* -1/2 (* eps (sin x))))
(+ (cos x) (* -1/2 (* eps (sin x))))
(+ (cos x) (* -1/2 (* eps (sin x))))
(+ (cos x) (* -1/2 (* eps (sin x))))
(+ (cos x) (* -1/2 (* eps (sin x))))
(+ (cos x) (* -1/2 (* eps (sin x))))
(* -1/2 x)
(* x (- (* 1/12 (pow x 2)) 1/2))
(* x (- (* (pow x 2) (+ 1/12 (* -1/240 (pow x 2)))) 1/2))
(* x (- (* (pow x 2) (+ 1/12 (* (pow x 2) (- (* 1/10080 (pow x 2)) 1/240)))) 1/2))
(* -1/2 (sin x))
(* -1/2 (sin x))
(* -1/2 (sin x))
(* -1/2 (sin x))
(* -1/2 (sin x))
(* -1/2 (sin x))
(* -1/2 (sin x))
(* -1/2 (sin x))
(cos (* 1/2 eps))
(+ (cos (* 1/2 eps)) (* -1 (* x (sin (* 1/2 eps)))))
(+ (cos (* 1/2 eps)) (* x (- (* -1/2 (* x (cos (* 1/2 eps)))) (sin (* 1/2 eps)))))
(+ (cos (* 1/2 eps)) (* x (- (* x (+ (* -1/2 (cos (* 1/2 eps))) (* 1/6 (* x (sin (* 1/2 eps)))))) (sin (* 1/2 eps)))))
(cos (* 1/2 (+ eps (* 2 x))))
(cos (* 1/2 (+ eps (* 2 x))))
(cos (* 1/2 (+ eps (* 2 x))))
(cos (* 1/2 (+ eps (* 2 x))))
(cos (* 1/2 (- eps (* -2 x))))
(cos (* 1/2 (- eps (* -2 x))))
(cos (* 1/2 (- eps (* -2 x))))
(cos (* 1/2 (- eps (* -2 x))))
(cos x)
(+ (cos x) (* -1/2 (* eps (sin x))))
(+ (cos x) (* eps (- (* -1/8 (* eps (cos x))) (* 1/2 (sin x)))))
(+ (cos x) (* eps (- (* eps (+ (* -1/8 (cos x)) (* 1/48 (* eps (sin x))))) (* 1/2 (sin x)))))
(cos (* 1/2 (+ eps (* 2 x))))
(cos (* 1/2 (+ eps (* 2 x))))
(cos (* 1/2 (+ eps (* 2 x))))
(cos (* 1/2 (+ eps (* 2 x))))
(cos (* 1/2 (- (* 2 x) (* -1 eps))))
(cos (* 1/2 (- (* 2 x) (* -1 eps))))
(cos (* 1/2 (- (* 2 x) (* -1 eps))))
(cos (* 1/2 (- (* 2 x) (* -1 eps))))
(* 1/2 eps)
(* eps (+ 1/2 (* -1/48 (pow eps 2))))
(* eps (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48))))
(* eps (+ 1/2 (* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48))))
(sin (* 1/2 eps))
(sin (* 1/2 eps))
(sin (* 1/2 eps))
(sin (* 1/2 eps))
(sin (* 1/2 eps))
(sin (* 1/2 eps))
(sin (* 1/2 eps))
(sin (* 1/2 eps))
(pow x 3)
(pow x 3)
(pow x 3)
(pow x 3)
(pow x 3)
(pow x 3)
(pow x 3)
(pow x 3)
(pow x 3)
(pow x 3)
(pow x 3)
(pow x 3)
x
(* x (+ 1 (* -1/6 (pow x 2))))
(* x (+ 1 (* (pow x 2) (- (* 1/120 (pow x 2)) 1/6))))
(* x (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/120 (* -1/5040 (pow x 2)))) 1/6))))
(sin x)
(sin x)
(sin x)
(sin x)
(sin x)
(sin x)
(sin x)
(sin x)

Outputs
(* 1/2 eps)
(*.f64 #s(literal 1/2 binary64) eps)
(+ x (* 1/2 eps))
(fma.f64 #s(literal 1/2 binary64) eps x)
(+ x (* 1/2 eps))
(fma.f64 #s(literal 1/2 binary64) eps x)
(+ x (* 1/2 eps))
(fma.f64 #s(literal 1/2 binary64) eps x)
x
(* x (+ 1 (* 1/2 (/ eps x))))
(fma.f64 #s(literal 1/2 binary64) (/.f64 (*.f64 eps x) x) x)
(* x (+ 1 (* 1/2 (/ eps x))))
(fma.f64 #s(literal 1/2 binary64) (/.f64 (*.f64 eps x) x) x)
(* x (+ 1 (* 1/2 (/ eps x))))
(fma.f64 #s(literal 1/2 binary64) (/.f64 (*.f64 eps x) x) x)
x
(* -1 (* x (- (* -1/2 (/ eps x)) 1)))
(fma.f64 (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x) (neg.f64 x) x)
(* -1 (* x (- (* -1/2 (/ eps x)) 1)))
(fma.f64 (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x) (neg.f64 x) x)
(* -1 (* x (- (* -1/2 (/ eps x)) 1)))
(fma.f64 (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x) (neg.f64 x) x)
x
(+ x (* 1/2 eps))
(fma.f64 #s(literal 1/2 binary64) eps x)
(+ x (* 1/2 eps))
(fma.f64 #s(literal 1/2 binary64) eps x)
(+ x (* 1/2 eps))
(fma.f64 #s(literal 1/2 binary64) eps x)
(* 1/2 eps)
(*.f64 #s(literal 1/2 binary64) eps)
(* eps (+ 1/2 (/ x eps)))
(*.f64 eps (+.f64 #s(literal 1/2 binary64) (/.f64 x eps)))
(* eps (+ 1/2 (/ x eps)))
(*.f64 eps (+.f64 #s(literal 1/2 binary64) (/.f64 x eps)))
(* eps (+ 1/2 (/ x eps)))
(*.f64 eps (+.f64 #s(literal 1/2 binary64) (/.f64 x eps)))
(* 1/2 eps)
(*.f64 #s(literal 1/2 binary64) eps)
(* -1 (* eps (- (* -1 (/ x eps)) 1/2)))
(*.f64 eps (+.f64 #s(literal 1/2 binary64) (/.f64 x eps)))
(* -1 (* eps (- (* -1 (/ x eps)) 1/2)))
(*.f64 eps (+.f64 #s(literal 1/2 binary64) (/.f64 x eps)))
(* -1 (* eps (- (* -1 (/ x eps)) 1/2)))
(*.f64 eps (+.f64 #s(literal 1/2 binary64) (/.f64 x eps)))
eps
eps
eps
eps
eps
eps
eps
eps
eps
eps
eps
eps
(* eps (cos x))
(*.f64 eps (cos.f64 x))
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(.f64 eps (fma.f64 eps (.f64 #s(literal -1/2 binary64) (sin.f64 x)) (cos.f64 x)))
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* 2 (* eps (+ (* -1/16 (cos x)) (* -1/48 (cos x)))))))))
(.f64 eps (fma.f64 eps (.f64 #s(literal -1/2 binary64) (sin.f64 x)) (.f64 (fma.f64 #s(literal -1/6 binary64) (.f64 eps eps) #s(literal 1 binary64)) (cos.f64 x))))
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* eps (+ (* 1/24 (* eps (sin x))) (* 2 (+ (* -1/16 (cos x)) (* -1/48 (cos x))))))))))
(.f64 eps (fma.f64 eps (fma.f64 eps (.f64 (cos.f64 x) #s(literal -1/6 binary64)) (.f64 (sin.f64 x) (fma.f64 eps (.f64 eps #s(literal 1/24 binary64)) #s(literal -1/2 binary64)))) (cos.f64 x)))
(* 2 (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))))
(.f64 (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) (.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) #s(literal 2 binary64)))
(* 2 (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))))
(.f64 (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) (.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) #s(literal 2 binary64)))
(* 2 (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))))
(.f64 (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) (.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) #s(literal 2 binary64)))
(* 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)))))
(.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (fma.f64 #s(literal 2 binary64) (cos.f64 (.f64 #s(literal 1/2 binary64) eps)) (.f64 (.f64 x #s(literal -2 binary64)) (sin.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 #s(literal -2 binary64) (pow.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) #s(literal 2 binary64))) (.f64 (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (cos.f64 (.f64 #s(literal 1/2 binary64) eps))) (fma.f64 x (neg.f64 x) #s(literal 2 binary64))))
(+ (* 2 (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) (* x (+ (* -2 (pow (sin (* 1/2 eps)) 2)) (* x (+ (* -1 (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) (* 1/3 (* x (pow (sin (* 1/2 eps)) 2))))))))
(fma.f64 x (fma.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (.f64 (cos.f64 (.f64 #s(literal 1/2 binary64) eps)) (neg.f64 x)) (.f64 (pow.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) #s(literal 2 binary64)) (fma.f64 x (.f64 x #s(literal 1/3 binary64)) #s(literal -2 binary64)))) (.f64 #s(literal 2 binary64) (.f64 (sin.f64 (.f64 #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 #s(literal 1/2 binary64) (.f64 eps (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 (cos.f64 x) #s(literal -1/12 binary64) (.f64 (.f64 eps (sin.f64 x)) #s(literal 1/48 binary64))) (.f64 (sin.f64 x) #s(literal -1/4 binary64))) (*.f64 #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 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (fma.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (neg.f64 x) (cos.f64 (.f64 #s(literal 1/2 binary64) 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))))
(fma.f64 (pow.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) #s(literal 2 binary64)) (neg.f64 x) (.f64 (fma.f64 x (.f64 x #s(literal -1/2 binary64)) #s(literal 1 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 (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (cos.f64 (.f64 #s(literal 1/2 binary64) eps))) (.f64 x #s(literal -1/2 binary64)) (.f64 (pow.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) #s(literal 2 binary64)) (fma.f64 x (.f64 x #s(literal 1/6 binary64)) #s(literal -1 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)))
(+.f64 (fma.f64 (fma.f64 x (.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64)) (sin.f64 eps) (.f64 x (cos.f64 eps))) (neg.f64 x))
(+ (sin eps) (* x (- (+ (cos eps) (* x (+ (* -1/2 (sin eps)) (* x (+ 1/6 (* -1/6 (cos eps))))))) 1)))
(fma.f64 x (+.f64 #s(literal -1 binary64) (fma.f64 x (.f64 #s(literal -1/2 binary64) (sin.f64 eps)) (fma.f64 x (.f64 x #s(literal 1/6 binary64)) (.f64 (fma.f64 x (.f64 x #s(literal -1/6 binary64)) #s(literal 1 binary64)) (cos.f64 eps))))) (sin.f64 eps))
(- (sin (+ eps x)) (sin x))
(-.f64 (sin.f64 (+.f64 eps x)) (sin.f64 x))
(- (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)))))
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(*.f64 eps (cos.f64 x))
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(.f64 eps (fma.f64 eps (.f64 #s(literal -1/2 binary64) (sin.f64 x)) (cos.f64 x)))
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(.f64 eps (fma.f64 eps (.f64 #s(literal -1/2 binary64) (sin.f64 x)) (cos.f64 x)))
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(.f64 eps (fma.f64 eps (.f64 #s(literal -1/2 binary64) (sin.f64 x)) (cos.f64 x)))
(* -1/2 (* (pow eps 2) (sin x)))
(.f64 #s(literal -1/2 binary64) (.f64 eps (*.f64 eps (sin.f64 x))))
(* (pow eps 2) (+ (* -1/2 (sin x)) (/ (cos x) eps)))
(.f64 eps (.f64 eps (fma.f64 #s(literal -1/2 binary64) (sin.f64 x) (/.f64 (cos.f64 x) eps))))
(* (pow eps 2) (+ (* -1/2 (sin x)) (/ (cos x) eps)))
(.f64 eps (.f64 eps (fma.f64 #s(literal -1/2 binary64) (sin.f64 x) (/.f64 (cos.f64 x) eps))))
(* (pow eps 2) (+ (* -1/2 (sin x)) (/ (cos x) eps)))
(.f64 eps (.f64 eps (fma.f64 #s(literal -1/2 binary64) (sin.f64 x) (/.f64 (cos.f64 x) eps))))
(* -1/2 (* (pow eps 2) (sin x)))
(.f64 #s(literal -1/2 binary64) (.f64 eps (*.f64 eps (sin.f64 x))))
(* (pow eps 2) (+ (* -1/2 (sin x)) (/ (cos x) eps)))
(.f64 eps (.f64 eps (fma.f64 #s(literal -1/2 binary64) (sin.f64 x) (/.f64 (cos.f64 x) eps))))
(* (pow eps 2) (+ (* -1/2 (sin x)) (/ (cos x) eps)))
(.f64 eps (.f64 eps (fma.f64 #s(literal -1/2 binary64) (sin.f64 x) (/.f64 (cos.f64 x) eps))))
(* (pow eps 2) (+ (* -1/2 (sin x)) (/ (cos x) eps)))
(.f64 eps (.f64 eps (fma.f64 #s(literal -1/2 binary64) (sin.f64 x) (/.f64 (cos.f64 x) eps))))
eps
(+ eps (* -1/2 (* (pow eps 2) x)))
(fma.f64 x (.f64 eps (.f64 eps #s(literal -1/2 binary64))) eps)
(+ eps (* x (+ (* -1/2 (* eps x)) (* -1/2 (pow eps 2)))))
(fma.f64 x (.f64 eps (.f64 #s(literal -1/2 binary64) (+.f64 eps x))) eps)
(+ eps (* x (+ (* -1/2 (pow eps 2)) (* x (+ (* -1/2 eps) (* 1/12 (* (pow eps 2) x)))))))
(fma.f64 x (fma.f64 x (.f64 x (.f64 (.f64 eps eps) #s(literal 1/12 binary64))) (.f64 eps (*.f64 #s(literal -1/2 binary64) (+.f64 eps x)))) eps)
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(.f64 eps (fma.f64 eps (.f64 #s(literal -1/2 binary64) (sin.f64 x)) (cos.f64 x)))
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(.f64 eps (fma.f64 eps (.f64 #s(literal -1/2 binary64) (sin.f64 x)) (cos.f64 x)))
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(.f64 eps (fma.f64 eps (.f64 #s(literal -1/2 binary64) (sin.f64 x)) (cos.f64 x)))
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(.f64 eps (fma.f64 eps (.f64 #s(literal -1/2 binary64) (sin.f64 x)) (cos.f64 x)))
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(.f64 eps (fma.f64 eps (.f64 #s(literal -1/2 binary64) (sin.f64 x)) (cos.f64 x)))
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(.f64 eps (fma.f64 eps (.f64 #s(literal -1/2 binary64) (sin.f64 x)) (cos.f64 x)))
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(.f64 eps (fma.f64 eps (.f64 #s(literal -1/2 binary64) (sin.f64 x)) (cos.f64 x)))
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(.f64 eps (fma.f64 eps (.f64 #s(literal -1/2 binary64) (sin.f64 x)) (cos.f64 x)))
(cos x)
(cos.f64 x)
(+ (cos x) (* -1/2 (* eps (sin x))))
(fma.f64 eps (*.f64 #s(literal -1/2 binary64) (sin.f64 x)) (cos.f64 x))
(+ (cos x) (* -1/2 (* eps (sin x))))
(fma.f64 eps (*.f64 #s(literal -1/2 binary64) (sin.f64 x)) (cos.f64 x))
(+ (cos x) (* -1/2 (* eps (sin x))))
(fma.f64 eps (*.f64 #s(literal -1/2 binary64) (sin.f64 x)) (cos.f64 x))
(* -1/2 (* eps (sin x)))
(.f64 eps (.f64 #s(literal -1/2 binary64) (sin.f64 x)))
(* eps (+ (* -1/2 (sin x)) (/ (cos x) eps)))
(*.f64 eps (fma.f64 #s(literal -1/2 binary64) (sin.f64 x) (/.f64 (cos.f64 x) eps)))
(* eps (+ (* -1/2 (sin x)) (/ (cos x) eps)))
(*.f64 eps (fma.f64 #s(literal -1/2 binary64) (sin.f64 x) (/.f64 (cos.f64 x) eps)))
(* eps (+ (* -1/2 (sin x)) (/ (cos x) eps)))
(*.f64 eps (fma.f64 #s(literal -1/2 binary64) (sin.f64 x) (/.f64 (cos.f64 x) eps)))
(* -1/2 (* eps (sin x)))
(.f64 eps (.f64 #s(literal -1/2 binary64) (sin.f64 x)))
(* -1 (* eps (+ (* -1 (/ (cos x) eps)) (* 1/2 (sin x)))))
(*.f64 eps (fma.f64 #s(literal -1/2 binary64) (sin.f64 x) (/.f64 (cos.f64 x) eps)))
(* -1 (* eps (+ (* -1 (/ (cos x) eps)) (* 1/2 (sin x)))))
(*.f64 eps (fma.f64 #s(literal -1/2 binary64) (sin.f64 x) (/.f64 (cos.f64 x) eps)))
(* -1 (* eps (+ (* -1 (/ (cos x) eps)) (* 1/2 (sin x)))))
(*.f64 eps (fma.f64 #s(literal -1/2 binary64) (sin.f64 x) (/.f64 (cos.f64 x) eps)))
1
#s(literal 1 binary64)
(+ 1 (* -1/2 (* eps x)))
(fma.f64 eps (*.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64))
(+ 1 (* x (+ (* -1/2 eps) (* -1/2 x))))
(fma.f64 (*.f64 x #s(literal -1/2 binary64)) (+.f64 eps x) #s(literal 1 binary64))
(+ 1 (* x (+ (* -1/2 eps) (* x (- (* 1/12 (* eps x)) 1/2)))))
(fma.f64 x (fma.f64 eps #s(literal -1/2 binary64) (.f64 x (fma.f64 (.f64 eps x) #s(literal 1/12 binary64) #s(literal -1/2 binary64)))) #s(literal 1 binary64))
(+ (cos x) (* -1/2 (* eps (sin x))))
(fma.f64 eps (*.f64 #s(literal -1/2 binary64) (sin.f64 x)) (cos.f64 x))
(+ (cos x) (* -1/2 (* eps (sin x))))
(fma.f64 eps (*.f64 #s(literal -1/2 binary64) (sin.f64 x)) (cos.f64 x))
(+ (cos x) (* -1/2 (* eps (sin x))))
(fma.f64 eps (*.f64 #s(literal -1/2 binary64) (sin.f64 x)) (cos.f64 x))
(+ (cos x) (* -1/2 (* eps (sin x))))
(fma.f64 eps (*.f64 #s(literal -1/2 binary64) (sin.f64 x)) (cos.f64 x))
(+ (cos x) (* -1/2 (* eps (sin x))))
(fma.f64 eps (*.f64 #s(literal -1/2 binary64) (sin.f64 x)) (cos.f64 x))
(+ (cos x) (* -1/2 (* eps (sin x))))
(fma.f64 eps (*.f64 #s(literal -1/2 binary64) (sin.f64 x)) (cos.f64 x))
(+ (cos x) (* -1/2 (* eps (sin x))))
(fma.f64 eps (*.f64 #s(literal -1/2 binary64) (sin.f64 x)) (cos.f64 x))
(+ (cos x) (* -1/2 (* eps (sin x))))
(fma.f64 eps (*.f64 #s(literal -1/2 binary64) (sin.f64 x)) (cos.f64 x))
(* -1/2 x)
(*.f64 x #s(literal -1/2 binary64))
(* x (- (* 1/12 (pow x 2)) 1/2))
(.f64 x (fma.f64 (.f64 x x) #s(literal 1/12 binary64) #s(literal -1/2 binary64)))
(* x (- (* (pow x 2) (+ 1/12 (* -1/240 (pow x 2)))) 1/2))
(.f64 x (fma.f64 (.f64 x x) (fma.f64 (*.f64 x x) #s(literal -1/240 binary64) #s(literal 1/12 binary64)) #s(literal -1/2 binary64)))
(* x (- (* (pow x 2) (+ 1/12 (* (pow x 2) (- (* 1/10080 (pow x 2)) 1/240)))) 1/2))
(.f64 x (fma.f64 (.f64 x x) (fma.f64 (.f64 x x) (fma.f64 (.f64 x x) #s(literal 1/10080 binary64) #s(literal -1/240 binary64)) #s(literal 1/12 binary64)) #s(literal -1/2 binary64)))
(* -1/2 (sin x))
(*.f64 #s(literal -1/2 binary64) (sin.f64 x))
(* -1/2 (sin x))
(*.f64 #s(literal -1/2 binary64) (sin.f64 x))
(* -1/2 (sin x))
(*.f64 #s(literal -1/2 binary64) (sin.f64 x))
(* -1/2 (sin x))
(*.f64 #s(literal -1/2 binary64) (sin.f64 x))
(* -1/2 (sin x))
(*.f64 #s(literal -1/2 binary64) (sin.f64 x))
(* -1/2 (sin x))
(*.f64 #s(literal -1/2 binary64) (sin.f64 x))
(* -1/2 (sin x))
(*.f64 #s(literal -1/2 binary64) (sin.f64 x))
(* -1/2 (sin x))
(*.f64 #s(literal -1/2 binary64) (sin.f64 x))
(cos (* 1/2 eps))
(cos.f64 (*.f64 #s(literal 1/2 binary64) eps))
(+ (cos (* 1/2 eps)) (* -1 (* x (sin (* 1/2 eps)))))
(fma.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (neg.f64 x) (cos.f64 (.f64 #s(literal 1/2 binary64) eps)))
(+ (cos (* 1/2 eps)) (* x (- (* -1/2 (* x (cos (* 1/2 eps)))) (sin (* 1/2 eps)))))
(fma.f64 x (-.f64 (.f64 (cos.f64 (.f64 #s(literal 1/2 binary64) eps)) (.f64 x #s(literal -1/2 binary64))) (sin.f64 (.f64 #s(literal 1/2 binary64) eps))) (cos.f64 (*.f64 #s(literal 1/2 binary64) eps)))
(+ (cos (* 1/2 eps)) (* x (- (* x (+ (* -1/2 (cos (* 1/2 eps))) (* 1/6 (* x (sin (* 1/2 eps)))))) (sin (* 1/2 eps)))))
(fma.f64 x (fma.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (fma.f64 x (.f64 x #s(literal 1/6 binary64)) #s(literal -1 binary64)) (.f64 (cos.f64 (.f64 #s(literal 1/2 binary64) eps)) (.f64 x #s(literal -1/2 binary64)))) (cos.f64 (.f64 #s(literal 1/2 binary64) eps)))
(cos (* 1/2 (+ eps (* 2 x))))
(cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x))
(cos (* 1/2 (+ eps (* 2 x))))
(cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x))
(cos (* 1/2 (+ eps (* 2 x))))
(cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x))
(cos (* 1/2 (+ eps (* 2 x))))
(cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x))
(cos (* 1/2 (- eps (* -2 x))))
(cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x))
(cos (* 1/2 (- eps (* -2 x))))
(cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x))
(cos (* 1/2 (- eps (* -2 x))))
(cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x))
(cos (* 1/2 (- eps (* -2 x))))
(cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x))
(cos x)
(cos.f64 x)
(+ (cos x) (* -1/2 (* eps (sin x))))
(fma.f64 eps (*.f64 #s(literal -1/2 binary64) (sin.f64 x)) (cos.f64 x))
(+ (cos x) (* eps (- (* -1/8 (* eps (cos x))) (* 1/2 (sin x)))))
(fma.f64 eps (fma.f64 eps (.f64 (cos.f64 x) #s(literal -1/8 binary64)) (.f64 #s(literal -1/2 binary64) (sin.f64 x))) (cos.f64 x))
(+ (cos x) (* eps (- (* eps (+ (* -1/8 (cos x)) (* 1/48 (* eps (sin x))))) (* 1/2 (sin x)))))
(fma.f64 eps (fma.f64 (sin.f64 x) (fma.f64 eps (.f64 eps #s(literal 1/48 binary64)) #s(literal -1/2 binary64)) (.f64 eps (*.f64 (cos.f64 x) #s(literal -1/8 binary64)))) (cos.f64 x))
(cos (* 1/2 (+ eps (* 2 x))))
(cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x))
(cos (* 1/2 (+ eps (* 2 x))))
(cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x))
(cos (* 1/2 (+ eps (* 2 x))))
(cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x))
(cos (* 1/2 (+ eps (* 2 x))))
(cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x))
(cos (* 1/2 (- (* 2 x) (* -1 eps))))
(cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x))
(cos (* 1/2 (- (* 2 x) (* -1 eps))))
(cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x))
(cos (* 1/2 (- (* 2 x) (* -1 eps))))
(cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x))
(cos (* 1/2 (- (* 2 x) (* -1 eps))))
(cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x))
(* 1/2 eps)
(*.f64 #s(literal 1/2 binary64) eps)
(* eps (+ 1/2 (* -1/48 (pow eps 2))))
(.f64 eps (fma.f64 eps (.f64 eps #s(literal -1/48 binary64)) #s(literal 1/2 binary64)))
(* eps (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48))))
(.f64 eps (fma.f64 eps (.f64 eps (fma.f64 (*.f64 eps eps) #s(literal 1/3840 binary64) #s(literal -1/48 binary64))) #s(literal 1/2 binary64)))
(* eps (+ 1/2 (* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48))))
(.f64 eps (fma.f64 (.f64 eps eps) (fma.f64 eps (.f64 eps (fma.f64 (.f64 eps eps) #s(literal -1/645120 binary64) #s(literal 1/3840 binary64))) #s(literal -1/48 binary64)) #s(literal 1/2 binary64)))
(sin (* 1/2 eps))
(sin.f64 (*.f64 #s(literal 1/2 binary64) eps))
(sin (* 1/2 eps))
(sin.f64 (*.f64 #s(literal 1/2 binary64) eps))
(sin (* 1/2 eps))
(sin.f64 (*.f64 #s(literal 1/2 binary64) eps))
(sin (* 1/2 eps))
(sin.f64 (*.f64 #s(literal 1/2 binary64) eps))
(sin (* 1/2 eps))
(sin.f64 (*.f64 #s(literal 1/2 binary64) eps))
(sin (* 1/2 eps))
(sin.f64 (*.f64 #s(literal 1/2 binary64) eps))
(sin (* 1/2 eps))
(sin.f64 (*.f64 #s(literal 1/2 binary64) eps))
(sin (* 1/2 eps))
(sin.f64 (*.f64 #s(literal 1/2 binary64) eps))
(pow x 3)
(.f64 x (.f64 x x))
(pow x 3)
(.f64 x (.f64 x x))
(pow x 3)
(.f64 x (.f64 x x))
(pow x 3)
(.f64 x (.f64 x x))
(pow x 3)
(.f64 x (.f64 x x))
(pow x 3)
(.f64 x (.f64 x x))
(pow x 3)
(.f64 x (.f64 x x))
(pow x 3)
(.f64 x (.f64 x x))
(pow x 3)
(.f64 x (.f64 x x))
(pow x 3)
(.f64 x (.f64 x x))
(pow x 3)
(.f64 x (.f64 x x))
(pow x 3)
(.f64 x (.f64 x x))
x
(* x (+ 1 (* -1/6 (pow x 2))))
(fma.f64 x (.f64 #s(literal -1/6 binary64) (.f64 x x)) x)
(* x (+ 1 (* (pow x 2) (- (* 1/120 (pow x 2)) 1/6))))
(fma.f64 (fma.f64 x (.f64 x #s(literal 1/120 binary64)) #s(literal -1/6 binary64)) (.f64 x (*.f64 x x)) x)
(* x (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/120 (* -1/5040 (pow x 2)))) 1/6))))
(fma.f64 x (.f64 (.f64 (fma.f64 (.f64 x x) (fma.f64 x (.f64 x #s(literal -1/5040 binary64)) #s(literal 1/120 binary64)) #s(literal -1/6 binary64)) x) x) x)
(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)

rewrite290.0ms (2.2%)

Memory

-20.7MiB live, 340.1MiB allocated

Rules

5 532×	`lower-fma.f32`
5 524×	`lower-fma.f64`
4 358×	`lower-/.f64`
4 358×	`lower-/.f32`
4 046×	`lower-*.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	38	173
0	65	159
1	211	159
2	1630	159
0	8592	159

Stop Event

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

Counts

21 → 486

Calls

Call 1

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

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

eval112.0ms (0.8%)

Memory: 36.7MiB live, 148.0MiB allocated
Compiler: Compiled 21 141 to 1 926 computations (90.9% saved)

prune185.0ms (1.4%)

Memory

-7.8MiB live, 199.8MiB allocated

Pruning

19 alts after pruning (16 fresh and 3 done)

	Pruned	Kept	Total
New	865	16	881
Fresh	1	0	1
Picked	3	2	5
Done	0	1	1
Total	869	19	888

Accuracy

100.0%

Counts

888 → 19

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	62.5%	(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
	55.7%	(.f64 (.f64 (sin.f64 (.f64 (.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))
	99.9%	(.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))
▶	99.8%	(.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))
	99.7%	(.f64 (.f64 #s(approx (sin (* (+ eps 0) 1/2)) (.f64 eps (fma.f64 eps (.f64 eps #s(literal -1/48 binary64)) #s(literal 1/2 binary64)))) (cos.f64 (*.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)))) #s(literal 2 binary64))
	99.6%	(.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))
▶	99.9%	(.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))
	55.1%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (/.f64 (cos.f64 x) eps) (.f64 eps eps)))
✓	99.7%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 eps (fma.f64 eps (.f64 #s(literal -1/2 binary64) (sin.f64 x)) (cos.f64 x))))
▶	99.3%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 eps (fma.f64 eps #s(approx ( -1/2 (sin x)) (*.f64 x #s(literal -1/2 binary64))) (cos.f64 x))))
✓	99.3%	#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 eps (cos.f64 x)))
	98.6%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 eps #s(approx (+ ( eps (* -1/2 (sin x))) (cos x)) (fma.f64 (*.f64 x #s(literal -1/2 binary64)) (+.f64 eps x) #s(literal 1 binary64)))))
	98.6%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 eps #s(approx (+ ( eps (* -1/2 (sin x))) (cos x)) (fma.f64 x (fma.f64 eps #s(literal -1/2 binary64) (.f64 x (fma.f64 (.f64 eps x) #s(literal 1/12 binary64) #s(literal -1/2 binary64)))) #s(literal 1 binary64)))))
	98.1%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 eps #s(approx (+ ( eps (* -1/2 (sin x))) (cos x)) (fma.f64 eps (*.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64)))))
▶	98.1%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 eps #s(approx (+ ( eps (* -1/2 (sin x))) (cos x)) #s(literal 1 binary64))))
	98.8%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 eps #s(approx (cos x) (fma.f64 (.f64 x x) (fma.f64 x (.f64 x (fma.f64 (.f64 x x) #s(literal -1/720 binary64) #s(literal 1/24 binary64))) #s(literal -1/2 binary64)) #s(literal 1 binary64)))))
▶	98.6%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 eps #s(approx (cos x) (fma.f64 (.f64 x x) (fma.f64 #s(literal 1/24 binary64) (*.f64 x x) #s(literal -1/2 binary64)) #s(literal 1 binary64)))))
	98.5%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 eps #s(approx (cos x) (fma.f64 x (.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64)))))
	98.8%	#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* eps (cos x)) (fma.f64 (.f64 x x) (fma.f64 x (.f64 x (.f64 eps (fma.f64 (.f64 x x) #s(literal -1/720 binary64) #s(literal 1/24 binary64)))) (*.f64 eps #s(literal -1/2 binary64))) eps)))

Compiler

Compiled 595 to 348 computations (41.5% saved)

simplify225.0ms (1.7%)

Memory

-3.3MiB live, 148.4MiB 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 (fma.f64 (*.f64 eps eps) #s(literal 1/3840 binary64) #s(literal -1/48 binary64))) #s(literal 1/2 binary64))))
cost-diff	0	(.f64 #s(approx (sin ( (+ 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))))
cost-diff	0	(.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))
cost-diff	320	(*.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64))
cost-diff	0	#s(approx (* -1/2 (sin x)) (*.f64 x #s(literal -1/2 binary64)))
cost-diff	0	(fma.f64 eps #s(approx (* -1/2 (sin x)) (*.f64 x #s(literal -1/2 binary64))) (cos.f64 x))
cost-diff	0	(.f64 eps (fma.f64 eps #s(approx ( -1/2 (sin x)) (*.f64 x #s(literal -1/2 binary64))) (cos.f64 x)))
cost-diff	0	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 eps (fma.f64 eps #s(approx ( -1/2 (sin x)) (*.f64 x #s(literal -1/2 binary64))) (cos.f64 x))))
cost-diff	0	(fma.f64 (.f64 x x) (fma.f64 #s(literal 1/24 binary64) (.f64 x x) #s(literal -1/2 binary64)) #s(literal 1 binary64))
cost-diff	0	#s(approx (cos x) (fma.f64 (.f64 x x) (fma.f64 #s(literal 1/24 binary64) (.f64 x x) #s(literal -1/2 binary64)) #s(literal 1 binary64)))
cost-diff	0	(.f64 eps #s(approx (cos x) (fma.f64 (.f64 x x) (fma.f64 #s(literal 1/24 binary64) (*.f64 x x) #s(literal -1/2 binary64)) #s(literal 1 binary64))))
cost-diff	0	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 eps #s(approx (cos x) (fma.f64 (.f64 x x) (fma.f64 #s(literal 1/24 binary64) (*.f64 x x) #s(literal -1/2 binary64)) #s(literal 1 binary64)))))
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	(sin.f64 (*.f64 #s(literal 1/2 binary64) eps))
cost-diff	0	(.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)))
cost-diff	0	#s(approx (* (sin (* (+ eps 0) 1/2)) (cos (* (+ (* x 2) eps) 1/2))) (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x))))
cost-diff	0	(.f64 #s(approx ( (sin (* (+ eps 0) 1/2)) (cos (* (+ (* x 2) eps) 1/2))) (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)))) #s(literal 2 binary64))

Rules

6 308×	`lower-fma.f32`
6 294×	`lower-fma.f64`
3 790×	`lower-*.f32`
3 762×	`lower-*.f64`
1 586×	`lower--.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	59	414
0	89	400
1	160	400
2	377	400
3	778	392
4	1021	392
5	1399	392
6	1905	392
7	2060	392
8	2308	392
9	2629	392
10	3446	392
11	4948	392
12	6189	392
13	6601	392
14	6896	392
15	6982	392
16	7067	392
17	7866	392
0	8196	389

Stop Event

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

Calls

Call 1

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

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

localize162.0ms (1.2%)

Memory

1.1MiB live, 233.6MiB allocated

Localize:

Found 19 expressions of interest:

New	Metric	Score
accuracy	0.0078125	(.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))))
accuracy	0.0464165744115697	(cos.f64 (*.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)))
accuracy	0.08117142671031594	#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))))
accuracy	0.3125	(.f64 eps (fma.f64 (.f64 eps eps) #s(literal 1/3840 binary64) #s(literal -1/48 binary64)))
accuracy	0	(cos.f64 x)
accuracy	0.00390625	(.f64 eps (fma.f64 eps #s(approx ( -1/2 (sin x)) (*.f64 x #s(literal -1/2 binary64))) (cos.f64 x)))
accuracy	0.1809942524239391	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 eps (fma.f64 eps #s(approx ( -1/2 (sin x)) (*.f64 x #s(literal -1/2 binary64))) (cos.f64 x))))
accuracy	1.2191317641267825	#s(approx (* -1/2 (sin x)) (*.f64 x #s(literal -1/2 binary64)))
accuracy	0.0078125	(fma.f64 (.f64 x x) (fma.f64 #s(literal 1/24 binary64) (.f64 x x) #s(literal -1/2 binary64)) #s(literal 1 binary64))
accuracy	0.015625	(fma.f64 #s(literal 1/24 binary64) (*.f64 x x) #s(literal -1/2 binary64))
accuracy	0.45925062897182506	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 eps #s(approx (cos x) (fma.f64 (.f64 x x) (fma.f64 #s(literal 1/24 binary64) (*.f64 x x) #s(literal -1/2 binary64)) #s(literal 1 binary64)))))
accuracy	0.8214398162726576	#s(approx (cos x) (fma.f64 (.f64 x x) (fma.f64 #s(literal 1/24 binary64) (.f64 x x) #s(literal -1/2 binary64)) #s(literal 1 binary64)))
accuracy	0.00390625	(.f64 eps #s(approx (+ ( eps (* -1/2 (sin x))) (cos x)) #s(literal 1 binary64)))
accuracy	0.1809942524239391	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 eps #s(approx (+ ( eps (* -1/2 (sin x))) (cos x)) #s(literal 1 binary64))))
accuracy	1.257665500246664	#s(approx (+ (* eps (* -1/2 (sin x))) (cos x)) #s(literal 1 binary64))
accuracy	0	#s(approx (* (sin (* (+ eps 0) 1/2)) (cos (* (+ (* x 2) eps) 1/2))) (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x))))
accuracy	0.00390625	(.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))
accuracy	0.0078125	(.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)))
accuracy	0.0464165744115697	(cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x))

Samples

58.0ms	175×	0	valid
51.0ms	81×	1	valid

Compiler

Compiled 287 to 49 computations (82.9% saved)

Precisions

Click to see histograms. Total time spent on operations: 84.0ms

ival-mult: 38.0ms (45.5% of total)

ival-add: 11.0ms (13.2% of total)

const: 10.0ms (12% of total)

ival-cos: 8.0ms (9.6% of total)

adjust: 7.0ms (8.4% of total)

ival-sin: 7.0ms (8.4% of total)

ival-sub: 2.0ms (2.4% of total)

exact: 1.0ms (1.2% of total)

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

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

series27.0ms (0.2%)

Memory

5.8MiB live, 43.8MiB allocated

Counts

24 → 480

Calls

Call 1

Inputs
#s(alt (.f64 #s(approx ( (sin (* (+ eps 0) 1/2)) (cos (* (+ (* x 2) eps) 1/2))) (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)))) #s(literal 2 binary64)) (patch (.f64 #s(approx ( (sin (* (+ eps 0) 1/2)) (cos (* (+ (* x 2) eps) 1/2))) (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)))) #s(literal 2 binary64)) #<representation binary64>) () ())
#s(alt #s(approx (* (sin (* (+ eps 0) 1/2)) (cos (* (+ (* x 2) eps) 1/2))) (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)))) (patch #s(approx (* (sin (* (+ eps 0) 1/2)) (cos (* (+ (* x 2) eps) 1/2))) (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)))) #<representation binary64>) () ())
#s(alt (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x))) (patch (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x))) #<representation binary64>) () ())
#s(alt (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (patch (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) #<representation binary64>) () ())
#s(alt #s(approx (- (sin (+ x eps)) (sin x)) (.f64 eps #s(approx (+ ( eps (* -1/2 (sin x))) (cos x)) #s(literal 1 binary64)))) (patch #s(approx (- (sin (+ x eps)) (sin x)) (.f64 eps #s(approx (+ ( eps (* -1/2 (sin x))) (cos x)) #s(literal 1 binary64)))) #<representation binary64>) () ())
#s(alt (.f64 eps #s(approx (+ ( eps (* -1/2 (sin x))) (cos x)) #s(literal 1 binary64))) (patch (.f64 eps #s(approx (+ ( eps (* -1/2 (sin x))) (cos x)) #s(literal 1 binary64))) #<representation binary64>) () ())
#s(alt #s(approx (+ (* eps (* -1/2 (sin x))) (cos x)) #s(literal 1 binary64)) (patch #s(approx (+ (* eps (* -1/2 (sin x))) (cos x)) #s(literal 1 binary64)) #<representation binary64>) () ())
#s(alt #s(approx (- (sin (+ x eps)) (sin x)) (.f64 eps #s(approx (cos x) (fma.f64 (.f64 x x) (fma.f64 #s(literal 1/24 binary64) (.f64 x x) #s(literal -1/2 binary64)) #s(literal 1 binary64))))) (patch #s(approx (- (sin (+ x eps)) (sin x)) (.f64 eps #s(approx (cos x) (fma.f64 (.f64 x x) (fma.f64 #s(literal 1/24 binary64) (.f64 x x) #s(literal -1/2 binary64)) #s(literal 1 binary64))))) #<representation binary64>) () ())
#s(alt (.f64 eps #s(approx (cos x) (fma.f64 (.f64 x x) (fma.f64 #s(literal 1/24 binary64) (.f64 x x) #s(literal -1/2 binary64)) #s(literal 1 binary64)))) (patch (.f64 eps #s(approx (cos x) (fma.f64 (.f64 x x) (fma.f64 #s(literal 1/24 binary64) (.f64 x x) #s(literal -1/2 binary64)) #s(literal 1 binary64)))) #<representation binary64>) () ())
#s(alt #s(approx (cos x) (fma.f64 (.f64 x x) (fma.f64 #s(literal 1/24 binary64) (.f64 x x) #s(literal -1/2 binary64)) #s(literal 1 binary64))) (patch #s(approx (cos x) (fma.f64 (.f64 x x) (fma.f64 #s(literal 1/24 binary64) (.f64 x x) #s(literal -1/2 binary64)) #s(literal 1 binary64))) #<representation binary64>) () ())
#s(alt (fma.f64 (.f64 x x) (fma.f64 #s(literal 1/24 binary64) (.f64 x x) #s(literal -1/2 binary64)) #s(literal 1 binary64)) (patch (fma.f64 (.f64 x x) (fma.f64 #s(literal 1/24 binary64) (.f64 x x) #s(literal -1/2 binary64)) #s(literal 1 binary64)) #<representation binary64>) () ())
#s(alt #s(approx (- (sin (+ x eps)) (sin x)) (.f64 eps (fma.f64 eps #s(approx ( -1/2 (sin x)) (.f64 x #s(literal -1/2 binary64))) (cos.f64 x)))) (patch #s(approx (- (sin (+ x eps)) (sin x)) (.f64 eps (fma.f64 eps #s(approx (* -1/2 (sin x)) (*.f64 x #s(literal -1/2 binary64))) (cos.f64 x)))) #<representation binary64>) () ())
#s(alt (.f64 eps (fma.f64 eps #s(approx ( -1/2 (sin x)) (.f64 x #s(literal -1/2 binary64))) (cos.f64 x))) (patch (.f64 eps (fma.f64 eps #s(approx (* -1/2 (sin x)) (*.f64 x #s(literal -1/2 binary64))) (cos.f64 x))) #<representation binary64>) () ())
#s(alt (fma.f64 eps #s(approx (* -1/2 (sin x)) (.f64 x #s(literal -1/2 binary64))) (cos.f64 x)) (patch (fma.f64 eps #s(approx ( -1/2 (sin x)) (*.f64 x #s(literal -1/2 binary64))) (cos.f64 x)) #<representation binary64>) () ())
#s(alt #s(approx (* -1/2 (sin x)) (.f64 x #s(literal -1/2 binary64))) (patch #s(approx ( -1/2 (sin x)) (*.f64 x #s(literal -1/2 binary64))) #<representation binary64>) () ())
#s(alt (.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)) (patch (.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)) #<representation binary64>) () ())
#s(alt (.f64 (.f64 #s(approx (sin (* (+ eps 0) 1/2)) (.f64 eps (fma.f64 eps (.f64 eps (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)) (patch (.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)) #<representation binary64>) () ())
#s(alt (.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)))) (patch (.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)))) #<representation binary64>) () ())
#s(alt #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)))) (patch #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)))) #<representation binary64>) () ())
#s(alt (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) (patch (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) #<representation binary64>) () ())
#s(alt (fma.f64 #s(literal 1/24 binary64) (.f64 x x) #s(literal -1/2 binary64)) (patch (fma.f64 #s(literal 1/24 binary64) (.f64 x x) #s(literal -1/2 binary64)) #<representation binary64>) () ())
#s(alt (cos.f64 x) (patch (cos.f64 x) #<representation binary64>) () ())
#s(alt (.f64 eps (fma.f64 (.f64 eps eps) #s(literal 1/3840 binary64) #s(literal -1/48 binary64))) (patch (.f64 eps (fma.f64 (.f64 eps eps) #s(literal 1/3840 binary64) #s(literal -1/48 binary64))) #<representation binary64>) () ())
#s(alt (cos.f64 (.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 (* eps (cos x)) (taylor 0 eps) (#s(alt (.f64 #s(approx ( (sin (* (+ eps 0) 1/2)) (cos (* (+ (* x 2) eps) 1/2))) (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)))) #s(literal 2 binary64)) (patch (.f64 #s(approx ( (sin (* (+ eps 0) 1/2)) (cos (* (+ (* x 2) eps) 1/2))) (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)))) #s(literal 2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* eps (+ (cos x) (* -1/2 (* eps (sin x))))) (taylor 0 eps) (#s(alt (.f64 #s(approx ( (sin (* (+ eps 0) 1/2)) (cos (* (+ (* x 2) eps) 1/2))) (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)))) #s(literal 2 binary64)) (patch (.f64 #s(approx ( (sin (* (+ eps 0) 1/2)) (cos (* (+ (* x 2) eps) 1/2))) (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)))) #s(literal 2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* 2 (* eps (+ (* -1/16 (cos x)) (* -1/48 (cos x))))))))) (taylor 0 eps) (#s(alt (.f64 #s(approx ( (sin (* (+ eps 0) 1/2)) (cos (* (+ (* x 2) eps) 1/2))) (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)))) #s(literal 2 binary64)) (patch (.f64 #s(approx ( (sin (* (+ eps 0) 1/2)) (cos (* (+ (* x 2) eps) 1/2))) (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)))) #s(literal 2 binary64)) #<representation binary64>) () ())) ())
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#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

120 calls:

Time	Variable		Point	Expression
0.0ms	eps	@	inf	(* eps (+ (* (* eps eps) 1/3840) -1/48))
0.0ms	x	@	inf	(+ (* (* x x) (+ (* 1/24 (* x x)) -1/2)) 1)
0.0ms	eps	@	0	(* eps (+ (* (* eps eps) 1/3840) -1/48))
0.0ms	x	@	inf	(* (sin (* 1/2 eps)) (cos (+ (* 1/2 eps) x)))
0.0ms	eps	@	-inf	(* (sin (* 1/2 eps)) (cos (+ (* 1/2 eps) x)))

simplify300.0ms (2.3%)

Memory

5.2MiB live, 281.5MiB allocated

Algorithm

1×	egg-herbie

Rules

14 424×	`lower-fma.f64`
14 424×	`lower-fma.f32`
5 898×	`lower-*.f64`
5 898×	`lower-*.f32`
3 770×	`lower-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	333	4949
1	995	4746
2	2580	4677
3	6064	4635
0	8448	4273

Stop Event

1×	iter limit
1×	node limit

Counts

480 → 474

Calls

Call 1

Inputs
(* eps (cos x))
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* 2 (* eps (+ (* -1/16 (cos x)) (* -1/48 (cos x)))))))))
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* eps (+ (* 1/24 (* eps (sin x))) (* 2 (+ (* -1/16 (cos x)) (* -1/48 (cos x))))))))))
(* 2 (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))))
(* 2 (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))))
(* 2 (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))))
(* 2 (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))))
(* 2 (* (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps))))
(* 2 (* (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps))))
(* 2 (* (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps))))
(* 2 (* (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps))))
(* 2 (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))
(+ (* -2 (* x (pow (sin (* 1/2 eps)) 2))) (* 2 (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))))
(+ (* 2 (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) (* x (+ (* -2 (pow (sin (* 1/2 eps)) 2)) (* -1 (* x (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))))))
(+ (* 2 (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) (* x (+ (* -2 (pow (sin (* 1/2 eps)) 2)) (* x (+ (* -1 (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) (* 1/3 (* x (pow (sin (* 1/2 eps)) 2))))))))
(* 2 (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))))
(* 2 (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))))
(* 2 (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))))
(* 2 (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))))
(* 2 (* (cos (* 1/2 (- eps (* -2 x)))) (sin (* 1/2 eps))))
(* 2 (* (cos (* 1/2 (- eps (* -2 x)))) (sin (* 1/2 eps))))
(* 2 (* (cos (* 1/2 (- eps (* -2 x)))) (sin (* 1/2 eps))))
(* 2 (* (cos (* 1/2 (- eps (* -2 x)))) (sin (* 1/2 eps))))
(* 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 (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 (+ x (* 1/2 eps))) (sin (* 1/2 eps)))
(* (cos (+ x (* 1/2 eps))) (sin (* 1/2 eps)))
(* (cos (+ x (* 1/2 eps))) (sin (* 1/2 eps)))
(* (cos (+ x (* 1/2 eps))) (sin (* 1/2 eps)))
(* (cos (- x (* -1/2 eps))) (sin (* 1/2 eps)))
(* (cos (- x (* -1/2 eps))) (sin (* 1/2 eps)))
(* (cos (- x (* -1/2 eps))) (sin (* 1/2 eps)))
(* (cos (- x (* -1/2 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 (+ x (* 1/2 eps))) (sin (* 1/2 eps)))
(* (cos (+ x (* 1/2 eps))) (sin (* 1/2 eps)))
(* (cos (+ x (* 1/2 eps))) (sin (* 1/2 eps)))
(* (cos (+ x (* 1/2 eps))) (sin (* 1/2 eps)))
(* (cos (- (* 1/2 eps) (* -1 x))) (sin (* 1/2 eps)))
(* (cos (- (* 1/2 eps) (* -1 x))) (sin (* 1/2 eps)))
(* (cos (- (* 1/2 eps) (* -1 x))) (sin (* 1/2 eps)))
(* (cos (- (* 1/2 eps) (* -1 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))))
(sin eps)
(+ (sin eps) (* x (- (cos eps) 1)))
(+ (sin eps) (* x (- (+ (cos eps) (* -1/2 (* x (sin eps)))) 1)))
(+ (sin eps) (* x (- (+ (cos eps) (* x (+ (* -1/2 (sin eps)) (* x (+ 1/6 (* -1/6 (cos eps))))))) 1)))
(- (sin (+ eps x)) (sin x))
(- (sin (+ eps x)) (sin x))
(- (sin (+ eps x)) (sin x))
(- (sin (+ eps x)) (sin x))
(- (sin (- eps (* -1 x))) (sin x))
(- (sin (- eps (* -1 x))) (sin x))
(- (sin (- eps (* -1 x))) (sin x))
(- (sin (- eps (* -1 x))) (sin x))
(* eps (cos x))
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x)))))))
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* eps (+ (* -1/6 (cos x)) (* 1/24 (* eps (sin x)))))))))
(- (sin (+ eps x)) (sin x))
(- (sin (+ eps x)) (sin x))
(- (sin (+ eps x)) (sin x))
(- (sin (+ eps x)) (sin x))
(- (sin (- x (* -1 eps))) (sin x))
(- (sin (- x (* -1 eps))) (sin x))
(- (sin (- x (* -1 eps))) (sin x))
(- (sin (- x (* -1 eps))) (sin x))
(* eps (cos x))
(* eps (cos x))
(* eps (cos x))
(* eps (cos x))
(* eps (cos x))
(* eps (cos x))
(* eps (cos x))
(* eps (cos x))
(* eps (cos x))
(* eps (cos x))
(* eps (cos x))
(* eps (cos x))
eps
(+ eps (* -1/2 (* eps (pow x 2))))
(+ eps (* (pow x 2) (+ (* -1/2 eps) (* 1/24 (* eps (pow x 2))))))
(+ eps (* (pow x 2) (+ (* -1/2 eps) (* (pow x 2) (+ (* -1/720 (* eps (pow x 2))) (* 1/24 eps))))))
(* eps (cos x))
(* eps (cos x))
(* eps (cos x))
(* eps (cos x))
(* eps (cos x))
(* eps (cos x))
(* eps (cos x))
(* eps (cos x))
1
(+ 1 (* -1/2 (pow x 2)))
(+ 1 (* (pow x 2) (- (* 1/24 (pow x 2)) 1/2)))
(+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))) 1/2)))
(cos x)
(cos x)
(cos x)
(cos x)
(cos x)
(cos x)
(cos x)
(cos x)
1
(+ 1 (* -1/2 (pow x 2)))
(+ 1 (* (pow x 2) (- (* 1/24 (pow x 2)) 1/2)))
(+ 1 (* (pow x 2) (- (* 1/24 (pow x 2)) 1/2)))
(* 1/24 (pow x 4))
(* (pow x 4) (- 1/24 (* 1/2 (/ 1 (pow x 2)))))
(* (pow x 4) (- (+ 1/24 (/ 1 (pow x 4))) (* 1/2 (/ 1 (pow x 2)))))
(* (pow x 4) (- (+ 1/24 (/ 1 (pow x 4))) (* 1/2 (/ 1 (pow x 2)))))
(* 1/24 (pow x 4))
(* (pow x 4) (- 1/24 (* 1/2 (/ 1 (pow x 2)))))
(* (pow x 4) (- (+ 1/24 (/ 1 (pow x 4))) (* 1/2 (/ 1 (pow x 2)))))
(* (pow x 4) (- (+ 1/24 (/ 1 (pow x 4))) (* 1/2 (/ 1 (pow x 2)))))
(sin eps)
(+ (sin eps) (* x (- (cos eps) 1)))
(+ (sin eps) (* x (- (+ (cos eps) (* -1/2 (* x (sin eps)))) 1)))
(+ (sin eps) (* x (- (+ (cos eps) (* x (+ (* -1/2 (sin eps)) (* x (+ 1/6 (* -1/6 (cos eps))))))) 1)))
(- (sin (+ eps x)) (sin x))
(- (sin (+ eps x)) (sin x))
(- (sin (+ eps x)) (sin x))
(- (sin (+ eps x)) (sin x))
(- (sin (- eps (* -1 x))) (sin x))
(- (sin (- eps (* -1 x))) (sin x))
(- (sin (- eps (* -1 x))) (sin x))
(- (sin (- eps (* -1 x))) (sin x))
(* eps (cos x))
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x)))))))
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* eps (+ (* -1/6 (cos x)) (* 1/24 (* eps (sin x)))))))))
(- (sin (+ eps x)) (sin x))
(- (sin (+ eps x)) (sin x))
(- (sin (+ eps x)) (sin x))
(- (sin (+ eps x)) (sin x))
(- (sin (- x (* -1 eps))) (sin x))
(- (sin (- x (* -1 eps))) (sin x))
(- (sin (- x (* -1 eps))) (sin x))
(- (sin (- x (* -1 eps))) (sin x))
(* eps (cos x))
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(* -1/2 (* (pow eps 2) (sin x)))
(* (pow eps 2) (+ (* -1/2 (sin x)) (/ (cos x) eps)))
(* (pow eps 2) (+ (* -1/2 (sin x)) (/ (cos x) eps)))
(* (pow eps 2) (+ (* -1/2 (sin x)) (/ (cos x) eps)))
(* -1/2 (* (pow eps 2) (sin x)))
(* (pow eps 2) (+ (* -1/2 (sin x)) (/ (cos x) eps)))
(* (pow eps 2) (+ (* -1/2 (sin x)) (/ (cos x) eps)))
(* (pow eps 2) (+ (* -1/2 (sin x)) (/ (cos x) eps)))
eps
(+ eps (* -1/2 (* (pow eps 2) x)))
(+ eps (* x (+ (* -1/2 (* eps x)) (* -1/2 (pow eps 2)))))
(+ eps (* x (+ (* -1/2 (pow eps 2)) (* x (+ (* -1/2 eps) (* 1/12 (* (pow eps 2) x)))))))
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(cos x)
(+ (cos x) (* -1/2 (* eps (sin x))))
(+ (cos x) (* -1/2 (* eps (sin x))))
(+ (cos x) (* -1/2 (* eps (sin x))))
(* -1/2 (* eps (sin x)))
(* eps (+ (* -1/2 (sin x)) (/ (cos x) eps)))
(* eps (+ (* -1/2 (sin x)) (/ (cos x) eps)))
(* eps (+ (* -1/2 (sin x)) (/ (cos x) eps)))
(* -1/2 (* eps (sin x)))
(* -1 (* eps (+ (* -1 (/ (cos x) eps)) (* 1/2 (sin x)))))
(* -1 (* eps (+ (* -1 (/ (cos x) eps)) (* 1/2 (sin x)))))
(* -1 (* eps (+ (* -1 (/ (cos x) eps)) (* 1/2 (sin x)))))
1
(+ 1 (* -1/2 (* eps x)))
(+ 1 (* x (+ (* -1/2 eps) (* -1/2 x))))
(+ 1 (* x (+ (* -1/2 eps) (* x (- (* 1/12 (* eps x)) 1/2)))))
(+ (cos x) (* -1/2 (* eps (sin x))))
(+ (cos x) (* -1/2 (* eps (sin x))))
(+ (cos x) (* -1/2 (* eps (sin x))))
(+ (cos x) (* -1/2 (* eps (sin x))))
(+ (cos x) (* -1/2 (* eps (sin x))))
(+ (cos x) (* -1/2 (* eps (sin x))))
(+ (cos x) (* -1/2 (* eps (sin x))))
(+ (cos x) (* -1/2 (* eps (sin x))))
(* -1/2 x)
(* x (- (* 1/12 (pow x 2)) 1/2))
(* x (- (* (pow x 2) (+ 1/12 (* -1/240 (pow x 2)))) 1/2))
(* x (- (* (pow x 2) (+ 1/12 (* (pow x 2) (- (* 1/10080 (pow x 2)) 1/240)))) 1/2))
(* -1/2 (sin x))
(* -1/2 (sin x))
(* -1/2 (sin x))
(* -1/2 (sin x))
(* -1/2 (sin x))
(* -1/2 (sin x))
(* -1/2 (sin x))
(* -1/2 (sin x))
(* 1/2 eps)
(+ x (* 1/2 eps))
(+ x (* 1/2 eps))
(+ x (* 1/2 eps))
x
(* x (+ 1 (* 1/2 (/ eps x))))
(* x (+ 1 (* 1/2 (/ eps x))))
(* x (+ 1 (* 1/2 (/ eps x))))
x
(* -1 (* x (- (* -1/2 (/ eps x)) 1)))
(* -1 (* x (- (* -1/2 (/ eps x)) 1)))
(* -1 (* x (- (* -1/2 (/ eps x)) 1)))
x
(+ x (* 1/2 eps))
(+ x (* 1/2 eps))
(+ x (* 1/2 eps))
(* 1/2 eps)
(* eps (+ 1/2 (/ x eps)))
(* eps (+ 1/2 (/ x eps)))
(* eps (+ 1/2 (/ x eps)))
(* 1/2 eps)
(* -1 (* eps (- (* -1 (/ x eps)) 1/2)))
(* -1 (* eps (- (* -1 (/ x eps)) 1/2)))
(* -1 (* eps (- (* -1 (/ x eps)) 1/2)))
(* eps (cos x))
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* 2 (* eps (+ (* -1/16 (cos x)) (* -1/48 (cos x)))))))))
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* eps (+ (* 1/24 (* eps (sin x))) (* 2 (+ (* -1/16 (cos x)) (* -1/48 (cos x))))))))))
(* 2 (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))))
(* 2 (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))))
(* 2 (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))))
(* 2 (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))))
(* 2 (* (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps))))
(* 2 (* (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps))))
(* 2 (* (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps))))
(* 2 (* (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps))))
(* 2 (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))
(+ (* -2 (* x (pow (sin (* 1/2 eps)) 2))) (* 2 (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))))
(+ (* 2 (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) (* x (+ (* -2 (pow (sin (* 1/2 eps)) 2)) (* -1 (* x (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))))))
(+ (* 2 (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) (* x (+ (* -2 (pow (sin (* 1/2 eps)) 2)) (* x (+ (* -1 (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) (* 1/3 (* x (pow (sin (* 1/2 eps)) 2))))))))
(* 2 (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))))
(* 2 (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))))
(* 2 (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))))
(* 2 (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))))
(* 2 (* (cos (* 1/2 (- eps (* -2 x)))) (sin (* 1/2 eps))))
(* 2 (* (cos (* 1/2 (- eps (* -2 x)))) (sin (* 1/2 eps))))
(* 2 (* (cos (* 1/2 (- eps (* -2 x)))) (sin (* 1/2 eps))))
(* 2 (* (cos (* 1/2 (- eps (* -2 x)))) (sin (* 1/2 eps))))
(* 1/2 (* eps (cos x)))
(* eps (+ (* -1/4 (* eps (sin x))) (* 1/2 (cos x))))
(* eps (+ (* 1/2 (cos x)) (* eps (+ (* -1/4 (sin x)) (* eps (+ (* -1/16 (cos x)) (* -1/48 (cos x))))))))
(* eps (+ (* 1/2 (cos x)) (* eps (+ (* -1/4 (sin x)) (* eps (+ (* -1/16 (cos x)) (+ (* -1/48 (cos x)) (* 1/48 (* eps (sin x))))))))))
(* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps)))
(* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps)))
(* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps)))
(* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps)))
(* (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps)))
(* (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps)))
(* (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps)))
(* (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps)))
(* (cos (* 1/2 eps)) (sin (* 1/2 eps)))
(+ (* -1 (* x (pow (sin (* 1/2 eps)) 2))) (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))
(+ (* x (+ (* -1 (pow (sin (* 1/2 eps)) 2)) (* -1/2 (* x (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))))) (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))
(+ (* x (+ (* -1 (pow (sin (* 1/2 eps)) 2)) (* x (+ (* -1/2 (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) (* 1/6 (* x (pow (sin (* 1/2 eps)) 2))))))) (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))
(* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps)))
(* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps)))
(* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps)))
(* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps)))
(* (cos (* 1/2 (- eps (* -2 x)))) (sin (* 1/2 eps)))
(* (cos (* 1/2 (- eps (* -2 x)))) (sin (* 1/2 eps)))
(* (cos (* 1/2 (- eps (* -2 x)))) (sin (* 1/2 eps)))
(* (cos (* 1/2 (- eps (* -2 x)))) (sin (* 1/2 eps)))
(* 1/2 eps)
(* eps (+ 1/2 (* -1/48 (pow eps 2))))
(* eps (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48))))
(* eps (+ 1/2 (* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48))))
(sin (* 1/2 eps))
(sin (* 1/2 eps))
(sin (* 1/2 eps))
(sin (* 1/2 eps))
(sin (* 1/2 eps))
(sin (* 1/2 eps))
(sin (* 1/2 eps))
(sin (* 1/2 eps))
(cos x)
(+ (cos x) (* -1/2 (* eps (sin x))))
(+ (cos x) (* eps (- (* -1/8 (* eps (cos x))) (* 1/2 (sin x)))))
(+ (cos x) (* eps (- (* eps (+ (* -1/8 (cos x)) (* 1/48 (* eps (sin x))))) (* 1/2 (sin x)))))
(cos (+ x (* 1/2 eps)))
(cos (+ x (* 1/2 eps)))
(cos (+ x (* 1/2 eps)))
(cos (+ x (* 1/2 eps)))
(cos (- x (* -1/2 eps)))
(cos (- x (* -1/2 eps)))
(cos (- x (* -1/2 eps)))
(cos (- x (* -1/2 eps)))
(cos (* 1/2 eps))
(+ (cos (* 1/2 eps)) (* -1 (* x (sin (* 1/2 eps)))))
(+ (cos (* 1/2 eps)) (* x (- (* -1/2 (* x (cos (* 1/2 eps)))) (sin (* 1/2 eps)))))
(+ (cos (* 1/2 eps)) (* x (- (* x (+ (* -1/2 (cos (* 1/2 eps))) (* 1/6 (* x (sin (* 1/2 eps)))))) (sin (* 1/2 eps)))))
(cos (+ x (* 1/2 eps)))
(cos (+ x (* 1/2 eps)))
(cos (+ x (* 1/2 eps)))
(cos (+ x (* 1/2 eps)))
(cos (- (* 1/2 eps) (* -1 x)))
(cos (- (* 1/2 eps) (* -1 x)))
(cos (- (* 1/2 eps) (* -1 x)))
(cos (- (* 1/2 eps) (* -1 x)))
-1/2
(- (* 1/24 (pow x 2)) 1/2)
(- (* 1/24 (pow x 2)) 1/2)
(- (* 1/24 (pow x 2)) 1/2)
(* 1/24 (pow x 2))
(* (pow x 2) (- 1/24 (* 1/2 (/ 1 (pow x 2)))))
(* (pow x 2) (- 1/24 (* 1/2 (/ 1 (pow x 2)))))
(* (pow x 2) (- 1/24 (* 1/2 (/ 1 (pow x 2)))))
(* 1/24 (pow x 2))
(* (pow x 2) (- 1/24 (* 1/2 (/ 1 (pow x 2)))))
(* (pow x 2) (- 1/24 (* 1/2 (/ 1 (pow x 2)))))
(* (pow x 2) (- 1/24 (* 1/2 (/ 1 (pow x 2)))))
1
(+ 1 (* -1/2 (pow x 2)))
(+ 1 (* (pow x 2) (- (* 1/24 (pow x 2)) 1/2)))
(+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))) 1/2)))
(cos x)
(cos x)
(cos x)
(cos x)
(cos x)
(cos x)
(cos x)
(cos x)
(* -1/48 eps)
(* eps (- (* 1/3840 (pow eps 2)) 1/48))
(* eps (- (* 1/3840 (pow eps 2)) 1/48))
(* eps (- (* 1/3840 (pow eps 2)) 1/48))
(* 1/3840 (pow eps 3))
(* (pow eps 3) (- 1/3840 (* 1/48 (/ 1 (pow eps 2)))))
(* (pow eps 3) (- 1/3840 (* 1/48 (/ 1 (pow eps 2)))))
(* (pow eps 3) (- 1/3840 (* 1/48 (/ 1 (pow eps 2)))))
(* 1/3840 (pow eps 3))
(* -1 (* (pow eps 3) (- (* 1/48 (/ 1 (pow eps 2))) 1/3840)))
(* -1 (* (pow eps 3) (- (* 1/48 (/ 1 (pow eps 2))) 1/3840)))
(* -1 (* (pow eps 3) (- (* 1/48 (/ 1 (pow eps 2))) 1/3840)))
(cos (* 1/2 eps))
(+ (cos (* 1/2 eps)) (* -1 (* x (sin (* 1/2 eps)))))
(+ (cos (* 1/2 eps)) (* x (- (* -1/2 (* x (cos (* 1/2 eps)))) (sin (* 1/2 eps)))))
(+ (cos (* 1/2 eps)) (* x (- (* x (+ (* -1/2 (cos (* 1/2 eps))) (* 1/6 (* x (sin (* 1/2 eps)))))) (sin (* 1/2 eps)))))
(cos (* 1/2 (+ eps (* 2 x))))
(cos (* 1/2 (+ eps (* 2 x))))
(cos (* 1/2 (+ eps (* 2 x))))
(cos (* 1/2 (+ eps (* 2 x))))
(cos (* 1/2 (- eps (* -2 x))))
(cos (* 1/2 (- eps (* -2 x))))
(cos (* 1/2 (- eps (* -2 x))))
(cos (* 1/2 (- eps (* -2 x))))
(cos x)
(+ (cos x) (* -1/2 (* eps (sin x))))
(+ (cos x) (* eps (- (* -1/8 (* eps (cos x))) (* 1/2 (sin x)))))
(+ (cos x) (* eps (- (* eps (+ (* -1/8 (cos x)) (* 1/48 (* eps (sin x))))) (* 1/2 (sin x)))))
(cos (* 1/2 (+ eps (* 2 x))))
(cos (* 1/2 (+ eps (* 2 x))))
(cos (* 1/2 (+ eps (* 2 x))))
(cos (* 1/2 (+ eps (* 2 x))))
(cos (* 1/2 (- (* 2 x) (* -1 eps))))
(cos (* 1/2 (- (* 2 x) (* -1 eps))))
(cos (* 1/2 (- (* 2 x) (* -1 eps))))
(cos (* 1/2 (- (* 2 x) (* -1 eps))))

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

rewrite242.0ms (1.8%)

Memory

9.4MiB live, 288.4MiB allocated

Rules

4 170×	`lower-/.f64`
4 170×	`lower-/.f32`
4 160×	`lower-*.f32`
4 132×	`lower-*.f64`
3 518×	`lower-fma.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	59	344
0	89	334
1	321	334
2	2592	334
0	8308	331

Stop Event

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

Counts

24 → 388

Calls

Call 1

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

Outputs
(.f64 #s(literal 2 binary64) #s(approx ( (sin (* (+ eps 0) 1/2)) (cos (* (+ (* x 2) eps) 1/2))) (.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (cos.f64 (fma.f64 eps #s(literal 1/2 binary64) x)))))
(.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))
#s(approx (* (sin (* (+ eps 0) 1/2)) (cos (* (+ (* x 2) eps) 1/2))) (.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (cos.f64 (fma.f64 eps #s(literal 1/2 binary64) x))))
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 2 binary64) (+.f64 (sin.f64 (-.f64 (*.f64 eps #s(literal 1/2 binary64)) (fma.f64 eps #s(literal 1/2 binary64) x))) (sin.f64 (fma.f64 eps #s(literal 1/2 binary64) (fma.f64 eps #s(literal 1/2 binary64) x))))))
(/.f64 (+.f64 (sin.f64 (-.f64 (*.f64 eps #s(literal 1/2 binary64)) (fma.f64 eps #s(literal 1/2 binary64) x))) (sin.f64 (fma.f64 eps #s(literal 1/2 binary64) (fma.f64 eps #s(literal 1/2 binary64) x)))) #s(literal 2 binary64))
(/.f64 (neg.f64 (+.f64 (sin.f64 (-.f64 (*.f64 eps #s(literal 1/2 binary64)) (fma.f64 eps #s(literal 1/2 binary64) x))) (sin.f64 (fma.f64 eps #s(literal 1/2 binary64) (fma.f64 eps #s(literal 1/2 binary64) x))))) #s(literal -2 binary64))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 #s(literal 2 binary64) (+.f64 (sin.f64 (-.f64 (*.f64 eps #s(literal 1/2 binary64)) (fma.f64 eps #s(literal 1/2 binary64) x))) (sin.f64 (fma.f64 eps #s(literal 1/2 binary64) (fma.f64 eps #s(literal 1/2 binary64) x)))))))
(/.f64 (neg.f64 (neg.f64 (+.f64 (sin.f64 (-.f64 (*.f64 eps #s(literal 1/2 binary64)) (fma.f64 eps #s(literal 1/2 binary64) x))) (sin.f64 (fma.f64 eps #s(literal 1/2 binary64) (fma.f64 eps #s(literal 1/2 binary64) x)))))) #s(literal 2 binary64))
(pow.f64 (/.f64 #s(literal 2 binary64) (+.f64 (sin.f64 (-.f64 (*.f64 eps #s(literal 1/2 binary64)) (fma.f64 eps #s(literal 1/2 binary64) x))) (sin.f64 (fma.f64 eps #s(literal 1/2 binary64) (fma.f64 eps #s(literal 1/2 binary64) x))))) #s(literal -1 binary64))
(.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (cos.f64 (fma.f64 eps #s(literal 1/2 binary64) x)))
(.f64 (cos.f64 (fma.f64 eps #s(literal 1/2 binary64) x)) (sin.f64 (.f64 eps #s(literal 1/2 binary64))))
(.f64 (+.f64 (sin.f64 (-.f64 (.f64 eps #s(literal 1/2 binary64)) (fma.f64 eps #s(literal 1/2 binary64) x))) (sin.f64 (fma.f64 eps #s(literal 1/2 binary64) (fma.f64 eps #s(literal 1/2 binary64) x)))) #s(literal 1/2 binary64))
(+.f64 (.f64 #s(literal 0 binary64) (cos.f64 (.f64 eps #s(literal 1/2 binary64)))) (.f64 #s(literal 1 binary64) (sin.f64 (.f64 eps #s(literal 1/2 binary64)))))
(+.f64 (.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) #s(literal 1 binary64)) (.f64 (cos.f64 (.f64 eps #s(literal 1/2 binary64))) #s(literal 0 binary64)))
(sin.f64 (*.f64 eps #s(literal 1/2 binary64)))
(fma.f64 #s(literal 0 binary64) (cos.f64 (.f64 eps #s(literal 1/2 binary64))) (.f64 #s(literal 1 binary64) (sin.f64 (*.f64 eps #s(literal 1/2 binary64)))))
(fma.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) #s(literal 1 binary64) (.f64 (cos.f64 (*.f64 eps #s(literal 1/2 binary64))) #s(literal 0 binary64)))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 eps #s(approx (+ ( eps (* -1/2 (sin x))) (cos x)) #s(literal 1 binary64))))
(+.f64 (.f64 eps #s(approx (+ ( eps (* -1/2 (sin x))) (cos x)) #s(literal 1 binary64))) (.f64 #s(approx (+ ( eps (* -1/2 (sin x))) (cos x)) #s(literal 1 binary64)) #s(literal 0 binary64)))
(+.f64 (.f64 eps #s(approx (+ ( eps (* -1/2 (sin x))) (cos x)) #s(literal 1 binary64))) (.f64 #s(literal 0 binary64) #s(approx (+ ( eps (* -1/2 (sin x))) (cos x)) #s(literal 1 binary64))))
(+.f64 (.f64 #s(approx (+ ( eps (* -1/2 (sin x))) (cos x)) #s(literal 1 binary64)) #s(literal 0 binary64)) (.f64 eps #s(approx (+ ( eps (* -1/2 (sin x))) (cos x)) #s(literal 1 binary64))))
(+.f64 (.f64 #s(literal 0 binary64) #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))))
(fma.f64 eps #s(approx (+ (* eps (* -1/2 (sin x))) (cos x)) #s(literal 1 binary64)) (.f64 #s(approx (+ ( eps (* -1/2 (sin x))) (cos x)) #s(literal 1 binary64)) #s(literal 0 binary64)))
(fma.f64 eps #s(approx (+ (* eps (* -1/2 (sin x))) (cos x)) #s(literal 1 binary64)) (.f64 #s(literal 0 binary64) #s(approx (+ ( eps (* -1/2 (sin x))) (cos x)) #s(literal 1 binary64))))
(fma.f64 #s(literal 0 binary64) #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))))
(fma.f64 #s(approx (+ (* eps (* -1/2 (sin x))) (cos x)) #s(literal 1 binary64)) eps (.f64 #s(approx (+ ( eps (* -1/2 (sin x))) (cos x)) #s(literal 1 binary64)) #s(literal 0 binary64)))
(fma.f64 #s(approx (+ (* eps (* -1/2 (sin x))) (cos x)) #s(literal 1 binary64)) eps (.f64 #s(literal 0 binary64) #s(approx (+ ( eps (* -1/2 (sin x))) (cos x)) #s(literal 1 binary64))))
(fma.f64 #s(approx (+ (* eps (* -1/2 (sin x))) (cos x)) #s(literal 1 binary64)) #s(literal 0 binary64) (.f64 eps #s(approx (+ ( eps (* -1/2 (sin x))) (cos x)) #s(literal 1 binary64))))
(/.f64 (.f64 #s(approx (+ ( eps (* -1/2 (sin x))) (cos x)) #s(literal 1 binary64)) (.f64 eps (.f64 eps eps))) (*.f64 eps eps))
(/.f64 (.f64 #s(approx (+ ( eps (* -1/2 (sin x))) (cos x)) #s(literal 1 binary64)) (*.f64 eps eps)) eps)
(/.f64 (.f64 (.f64 eps (.f64 eps eps)) #s(approx (+ ( eps (* -1/2 (sin x))) (cos x)) #s(literal 1 binary64))) (*.f64 eps eps))
(/.f64 (.f64 (.f64 eps eps) #s(approx (+ (* eps (* -1/2 (sin x))) (cos x)) #s(literal 1 binary64))) eps)
(/.f64 (neg.f64 (.f64 #s(approx (+ ( eps (* -1/2 (sin x))) (cos x)) #s(literal 1 binary64)) (.f64 eps (.f64 eps eps)))) (neg.f64 (*.f64 eps eps)))
(/.f64 (neg.f64 (.f64 #s(approx (+ ( eps (* -1/2 (sin x))) (cos x)) #s(literal 1 binary64)) (*.f64 eps eps))) (neg.f64 eps))
(/.f64 (neg.f64 (.f64 (.f64 eps (.f64 eps eps)) #s(approx (+ ( eps (* -1/2 (sin x))) (cos x)) #s(literal 1 binary64)))) (neg.f64 (*.f64 eps eps)))
(/.f64 (neg.f64 (.f64 (.f64 eps eps) #s(approx (+ (* eps (* -1/2 (sin x))) (cos x)) #s(literal 1 binary64)))) (neg.f64 eps))
(.f64 eps #s(approx (+ ( eps (* -1/2 (sin x))) (cos x)) #s(literal 1 binary64)))
(.f64 #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(approx (- (sin (+ x eps)) (sin x)) (.f64 eps #s(approx (cos x) (fma.f64 x (.f64 x (fma.f64 x (*.f64 x #s(literal 1/24 binary64)) #s(literal -1/2 binary64))) #s(literal 1 binary64)))))
(+.f64 (.f64 eps #s(approx (cos x) (fma.f64 x (.f64 x (fma.f64 x (.f64 x #s(literal 1/24 binary64)) #s(literal -1/2 binary64))) #s(literal 1 binary64)))) (.f64 #s(approx (cos x) (fma.f64 x (.f64 x (fma.f64 x (.f64 x #s(literal 1/24 binary64)) #s(literal -1/2 binary64))) #s(literal 1 binary64))) #s(literal 0 binary64)))
(+.f64 (.f64 eps #s(approx (cos x) (fma.f64 x (.f64 x (fma.f64 x (.f64 x #s(literal 1/24 binary64)) #s(literal -1/2 binary64))) #s(literal 1 binary64)))) (.f64 #s(literal 0 binary64) #s(approx (cos x) (fma.f64 x (.f64 x (fma.f64 x (.f64 x #s(literal 1/24 binary64)) #s(literal -1/2 binary64))) #s(literal 1 binary64)))))
(+.f64 (.f64 #s(approx (cos x) (fma.f64 x (.f64 x (fma.f64 x (.f64 x #s(literal 1/24 binary64)) #s(literal -1/2 binary64))) #s(literal 1 binary64))) #s(literal 0 binary64)) (.f64 eps #s(approx (cos x) (fma.f64 x (.f64 x (fma.f64 x (.f64 x #s(literal 1/24 binary64)) #s(literal -1/2 binary64))) #s(literal 1 binary64)))))
(+.f64 (.f64 #s(literal 0 binary64) #s(approx (cos x) (fma.f64 x (.f64 x (fma.f64 x (.f64 x #s(literal 1/24 binary64)) #s(literal -1/2 binary64))) #s(literal 1 binary64)))) (.f64 eps #s(approx (cos x) (fma.f64 x (.f64 x (fma.f64 x (.f64 x #s(literal 1/24 binary64)) #s(literal -1/2 binary64))) #s(literal 1 binary64)))))
(fma.f64 eps #s(approx (cos x) (fma.f64 x (.f64 x (fma.f64 x (.f64 x #s(literal 1/24 binary64)) #s(literal -1/2 binary64))) #s(literal 1 binary64))) (.f64 #s(approx (cos x) (fma.f64 x (.f64 x (fma.f64 x (*.f64 x #s(literal 1/24 binary64)) #s(literal -1/2 binary64))) #s(literal 1 binary64))) #s(literal 0 binary64)))
(fma.f64 eps #s(approx (cos x) (fma.f64 x (.f64 x (fma.f64 x (.f64 x #s(literal 1/24 binary64)) #s(literal -1/2 binary64))) #s(literal 1 binary64))) (.f64 #s(literal 0 binary64) #s(approx (cos x) (fma.f64 x (.f64 x (fma.f64 x (*.f64 x #s(literal 1/24 binary64)) #s(literal -1/2 binary64))) #s(literal 1 binary64)))))
(fma.f64 #s(literal 0 binary64) #s(approx (cos x) (fma.f64 x (.f64 x (fma.f64 x (.f64 x #s(literal 1/24 binary64)) #s(literal -1/2 binary64))) #s(literal 1 binary64))) (.f64 eps #s(approx (cos x) (fma.f64 x (.f64 x (fma.f64 x (*.f64 x #s(literal 1/24 binary64)) #s(literal -1/2 binary64))) #s(literal 1 binary64)))))
(fma.f64 #s(approx (cos x) (fma.f64 x (.f64 x (fma.f64 x (.f64 x #s(literal 1/24 binary64)) #s(literal -1/2 binary64))) #s(literal 1 binary64))) eps (.f64 #s(approx (cos x) (fma.f64 x (.f64 x (fma.f64 x (*.f64 x #s(literal 1/24 binary64)) #s(literal -1/2 binary64))) #s(literal 1 binary64))) #s(literal 0 binary64)))
(fma.f64 #s(approx (cos x) (fma.f64 x (.f64 x (fma.f64 x (.f64 x #s(literal 1/24 binary64)) #s(literal -1/2 binary64))) #s(literal 1 binary64))) eps (.f64 #s(literal 0 binary64) #s(approx (cos x) (fma.f64 x (.f64 x (fma.f64 x (*.f64 x #s(literal 1/24 binary64)) #s(literal -1/2 binary64))) #s(literal 1 binary64)))))
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(/.f64 (fma.f64 (.f64 (.f64 eps (.f64 eps eps)) #s(literal -1/48 binary64)) eps (.f64 (.f64 eps eps) (.f64 (.f64 (.f64 eps eps) #s(literal 1/3840 binary64)) (.f64 eps eps)))) (.f64 eps (*.f64 eps eps)))
(/.f64 (fma.f64 (.f64 (.f64 eps (.f64 eps eps)) #s(literal -1/48 binary64)) (.f64 eps eps) (.f64 (.f64 eps eps) (.f64 (.f64 (.f64 eps eps) #s(literal 1/3840 binary64)) (.f64 eps (.f64 eps eps))))) (.f64 (.f64 eps (.f64 eps eps)) eps))
(/.f64 (fma.f64 (.f64 (.f64 eps (.f64 eps eps)) #s(literal -1/48 binary64)) (.f64 eps eps) (.f64 (.f64 eps eps) (.f64 (.f64 eps (.f64 eps eps)) (.f64 (.f64 eps eps) #s(literal 1/3840 binary64))))) (.f64 (.f64 eps (.f64 eps eps)) eps))
(/.f64 (neg.f64 (.f64 (.f64 eps eps) (.f64 eps (fma.f64 eps (.f64 eps #s(literal 1/3840 binary64)) #s(literal -1/48 binary64))))) (neg.f64 (*.f64 eps eps)))
(/.f64 (neg.f64 (.f64 (.f64 eps (.f64 eps eps)) (fma.f64 (.f64 eps (.f64 eps eps)) (.f64 (.f64 eps (.f64 eps eps)) #s(literal 1/56623104000 binary64)) #s(literal -1/110592 binary64)))) (neg.f64 (.f64 (.f64 eps eps) (-.f64 (fma.f64 (.f64 (.f64 eps (.f64 eps eps)) eps) #s(literal 1/14745600 binary64) #s(literal 1/2304 binary64)) (.f64 (*.f64 eps eps) #s(literal -1/184320 binary64))))))
(/.f64 (neg.f64 (.f64 (.f64 eps (.f64 eps eps)) (fma.f64 (.f64 (.f64 eps (.f64 eps eps)) eps) #s(literal 1/14745600 binary64) #s(literal -1/2304 binary64)))) (neg.f64 (.f64 (.f64 eps eps) (fma.f64 eps (*.f64 eps #s(literal 1/3840 binary64)) #s(literal 1/48 binary64)))))
(/.f64 (neg.f64 (.f64 (fma.f64 (.f64 eps (.f64 eps eps)) (.f64 (.f64 eps (.f64 eps eps)) #s(literal 1/56623104000 binary64)) #s(literal -1/110592 binary64)) (.f64 eps (.f64 eps eps)))) (neg.f64 (.f64 (-.f64 (fma.f64 (.f64 (.f64 eps (.f64 eps eps)) eps) #s(literal 1/14745600 binary64) #s(literal 1/2304 binary64)) (.f64 (.f64 eps eps) #s(literal -1/184320 binary64))) (*.f64 eps eps))))
(/.f64 (neg.f64 (.f64 (fma.f64 (.f64 eps (.f64 eps eps)) (.f64 (.f64 eps (.f64 eps eps)) #s(literal 1/56623104000 binary64)) #s(literal -1/110592 binary64)) (.f64 eps eps))) (neg.f64 (.f64 (-.f64 (fma.f64 (.f64 (.f64 eps (.f64 eps eps)) eps) #s(literal 1/14745600 binary64) #s(literal 1/2304 binary64)) (.f64 (*.f64 eps eps) #s(literal -1/184320 binary64))) eps)))
(/.f64 (neg.f64 (.f64 (fma.f64 (.f64 (.f64 eps (.f64 eps eps)) eps) #s(literal 1/14745600 binary64) #s(literal -1/2304 binary64)) (.f64 eps (.f64 eps eps)))) (neg.f64 (.f64 (fma.f64 eps (.f64 eps #s(literal 1/3840 binary64)) #s(literal 1/48 binary64)) (*.f64 eps eps))))
(/.f64 (neg.f64 (.f64 (fma.f64 (.f64 (.f64 eps (.f64 eps eps)) eps) #s(literal 1/14745600 binary64) #s(literal -1/2304 binary64)) (.f64 eps eps))) (neg.f64 (.f64 (fma.f64 eps (*.f64 eps #s(literal 1/3840 binary64)) #s(literal 1/48 binary64)) eps)))
(/.f64 (neg.f64 (fma.f64 (.f64 (.f64 eps eps) (.f64 (.f64 eps (.f64 eps eps)) eps)) (.f64 (.f64 eps (.f64 eps eps)) #s(literal 1/56623104000 binary64)) (.f64 (.f64 eps (.f64 eps eps)) #s(literal -1/110592 binary64)))) (neg.f64 (fma.f64 (.f64 eps (.f64 (.f64 eps eps) #s(literal 1/3840 binary64))) (.f64 eps (.f64 (.f64 eps eps) #s(literal 1/3840 binary64))) (-.f64 (.f64 (.f64 eps #s(literal -1/48 binary64)) (.f64 eps #s(literal -1/48 binary64))) (.f64 (.f64 eps (.f64 (.f64 eps eps) #s(literal 1/3840 binary64))) (*.f64 eps #s(literal -1/48 binary64)))))))
(/.f64 (neg.f64 (-.f64 (.f64 (.f64 eps (.f64 (.f64 eps eps) #s(literal 1/3840 binary64))) (.f64 eps (.f64 (.f64 eps eps) #s(literal 1/3840 binary64)))) (.f64 (.f64 eps #s(literal -1/48 binary64)) (.f64 eps #s(literal -1/48 binary64))))) (neg.f64 (-.f64 (.f64 eps (.f64 (.f64 eps eps) #s(literal 1/3840 binary64))) (.f64 eps #s(literal -1/48 binary64)))))
(/.f64 (neg.f64 (.f64 eps (fma.f64 (.f64 eps (.f64 eps eps)) (.f64 (.f64 eps (.f64 eps eps)) #s(literal 1/56623104000 binary64)) #s(literal -1/110592 binary64)))) (neg.f64 (-.f64 (fma.f64 (.f64 (.f64 eps (.f64 eps eps)) eps) #s(literal 1/14745600 binary64) #s(literal 1/2304 binary64)) (.f64 (*.f64 eps eps) #s(literal -1/184320 binary64)))))
(/.f64 (neg.f64 (.f64 eps (fma.f64 (.f64 (.f64 eps (.f64 eps eps)) eps) #s(literal 1/14745600 binary64) #s(literal -1/2304 binary64)))) (neg.f64 (fma.f64 eps (*.f64 eps #s(literal 1/3840 binary64)) #s(literal 1/48 binary64))))
(/.f64 (neg.f64 (.f64 (fma.f64 eps (.f64 eps #s(literal 1/3840 binary64)) #s(literal -1/48 binary64)) (.f64 eps (.f64 eps eps)))) (neg.f64 (*.f64 eps eps)))
(/.f64 (neg.f64 (.f64 (.f64 eps eps) (fma.f64 (.f64 eps (.f64 eps eps)) (.f64 (.f64 eps (.f64 eps eps)) #s(literal 1/56623104000 binary64)) #s(literal -1/110592 binary64)))) (neg.f64 (.f64 eps (-.f64 (fma.f64 (.f64 (.f64 eps (.f64 eps eps)) eps) #s(literal 1/14745600 binary64) #s(literal 1/2304 binary64)) (.f64 (*.f64 eps eps) #s(literal -1/184320 binary64))))))
(/.f64 (neg.f64 (.f64 (.f64 eps eps) (fma.f64 (.f64 (.f64 eps (.f64 eps eps)) eps) #s(literal 1/14745600 binary64) #s(literal -1/2304 binary64)))) (neg.f64 (.f64 eps (fma.f64 eps (*.f64 eps #s(literal 1/3840 binary64)) #s(literal 1/48 binary64)))))
(/.f64 (neg.f64 (.f64 (fma.f64 (.f64 eps (.f64 eps eps)) (.f64 (.f64 eps (.f64 eps eps)) #s(literal 1/56623104000 binary64)) #s(literal -1/110592 binary64)) eps)) (neg.f64 (-.f64 (fma.f64 (.f64 (.f64 eps (.f64 eps eps)) eps) #s(literal 1/14745600 binary64) #s(literal 1/2304 binary64)) (.f64 (*.f64 eps eps) #s(literal -1/184320 binary64)))))
(/.f64 (neg.f64 (.f64 (fma.f64 (.f64 (.f64 eps (.f64 eps eps)) eps) #s(literal 1/14745600 binary64) #s(literal -1/2304 binary64)) eps)) (neg.f64 (fma.f64 eps (*.f64 eps #s(literal 1/3840 binary64)) #s(literal 1/48 binary64))))
(.f64 eps (fma.f64 eps (.f64 eps #s(literal 1/3840 binary64)) #s(literal -1/48 binary64)))
(.f64 (fma.f64 eps (.f64 eps #s(literal 1/3840 binary64)) #s(literal -1/48 binary64)) eps)
(cos.f64 (*.f64 #s(literal 1/2 binary64) (fma.f64 x #s(literal 2 binary64) eps)))
(-.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)))))

eval137.0ms (1%)

Memory: -15.5MiB live, 187.7MiB allocated
Compiler: Compiled 19 873 to 1 790 computations (91% saved)

prune163.0ms (1.2%)

Memory

14.1MiB live, 174.2MiB allocated

Pruning

19 alts after pruning (13 fresh and 6 done)

	Pruned	Kept	Total
New	854	8	862
Fresh	6	5	11
Picked	2	3	5
Done	0	3	3
Total	862	19	881

Accuracy

100.0%

Counts

881 → 19

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	62.5%	(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
	55.7%	(.f64 (.f64 (sin.f64 (.f64 (.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))
	99.8%	(.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 #s(approx ( (+ (* x 2) eps) 1/2) (fma.f64 eps #s(literal 1/2 binary64) x)))) #s(literal 2 binary64))
✓	99.9%	(.f64 #s(approx ( (sin (* (+ eps 0) 1/2)) (cos (* (+ (* x 2) eps) 1/2))) (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)))) #s(literal 2 binary64))
▶	99.9%	(.f64 #s(approx ( (sin (* (+ eps 0) 1/2)) (cos (* (+ (* x 2) eps) 1/2))) (.f64 #s(approx (sin ( 1/2 eps)) (.f64 eps (fma.f64 eps (.f64 eps (fma.f64 (.f64 eps eps) (fma.f64 eps (.f64 eps #s(literal -1/645120 binary64)) #s(literal 1/3840 binary64)) #s(literal -1/48 binary64))) #s(literal 1/2 binary64)))) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)))) #s(literal 2 binary64))
▶	99.7%	(.f64 #s(approx ( (sin (* (+ eps 0) 1/2)) (cos (* (+ (* x 2) eps) 1/2))) (.f64 #s(approx (sin ( 1/2 eps)) (.f64 eps (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal 1/2 binary64)))) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)))) #s(literal 2 binary64))
	99.6%	(.f64 #s(approx ( (sin (* (+ eps 0) 1/2)) (cos (* (+ (* x 2) eps) 1/2))) (.f64 #s(approx (sin ( 1/2 eps)) (*.f64 eps #s(literal 1/2 binary64))) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)))) #s(literal 2 binary64))
	99.3%	#s(approx (- (sin (+ x eps)) (sin x)) (fma.f64 (cos.f64 x) eps (.f64 #s(approx ( -1/2 (sin x)) (.f64 x #s(literal -1/2 binary64))) (.f64 eps eps))))
✓	99.7%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 eps (fma.f64 eps (.f64 #s(literal -1/2 binary64) (sin.f64 x)) (cos.f64 x))))
	98.7%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 eps (fma.f64 eps #s(approx ( -1/2 (sin x)) (.f64 x #s(literal -1/2 binary64))) #s(approx (cos x) (fma.f64 x (.f64 x (fma.f64 #s(literal 1/24 binary64) (*.f64 x x) #s(literal -1/2 binary64))) #s(literal 1 binary64))))))
	98.1%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 eps (fma.f64 eps #s(approx ( -1/2 (sin x)) (*.f64 x #s(literal -1/2 binary64))) #s(approx (cos x) #s(literal 1 binary64)))))
✓	99.3%	#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 eps (cos.f64 x)))
	98.6%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 eps #s(approx (+ ( eps (* -1/2 (sin x))) (cos x)) (fma.f64 (*.f64 x #s(literal -1/2 binary64)) (+.f64 eps x) #s(literal 1 binary64)))))
▶	98.6%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 eps #s(approx (+ ( eps (* -1/2 (sin x))) (cos x)) (fma.f64 x (fma.f64 eps #s(literal -1/2 binary64) (.f64 x (fma.f64 (.f64 eps x) #s(literal 1/12 binary64) #s(literal -1/2 binary64)))) #s(literal 1 binary64)))))
✓	98.1%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 eps #s(approx (+ ( eps (* -1/2 (sin x))) (cos x)) #s(literal 1 binary64))))
	98.8%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 eps #s(approx (cos x) (fma.f64 (.f64 x x) (fma.f64 x (.f64 x (fma.f64 (.f64 x x) #s(literal -1/720 binary64) #s(literal 1/24 binary64))) #s(literal -1/2 binary64)) #s(literal 1 binary64)))))
✓	98.6%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 eps #s(approx (cos x) (fma.f64 (.f64 x x) (fma.f64 #s(literal 1/24 binary64) (*.f64 x x) #s(literal -1/2 binary64)) #s(literal 1 binary64)))))
▶	98.5%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 eps #s(approx (cos x) (fma.f64 (.f64 x x) #s(approx (+ (* 1/24 (* x x)) -1/2) #s(literal -1/2 binary64)) #s(literal 1 binary64)))))
▶	98.8%	#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* eps (cos x)) (fma.f64 (.f64 x x) (fma.f64 x (.f64 x (.f64 eps (fma.f64 (.f64 x x) #s(literal -1/720 binary64) #s(literal 1/24 binary64)))) (*.f64 eps #s(literal -1/2 binary64))) eps)))

Compiler

Compiled 580 to 333 computations (42.6% saved)

simplify311.0ms (2.3%)

Memory

-6.2MiB live, 230.3MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 20 expressions of interest:

New	Metric	Score
cost-diff	0	#s(approx (sin (* 1/2 eps)) (.f64 eps (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal 1/2 binary64))))
cost-diff	0	(.f64 #s(approx (sin ( 1/2 eps)) (.f64 eps (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal 1/2 binary64)))) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)))
cost-diff	0	#s(approx (* (sin (* (+ eps 0) 1/2)) (cos (* (+ (* x 2) eps) 1/2))) (.f64 #s(approx (sin ( 1/2 eps)) (.f64 eps (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal 1/2 binary64)))) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x))))
cost-diff	0	(.f64 #s(approx ( (sin (* (+ eps 0) 1/2)) (cos (* (+ (* x 2) eps) 1/2))) (.f64 #s(approx (sin ( 1/2 eps)) (.f64 eps (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal 1/2 binary64)))) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)))) #s(literal 2 binary64))
cost-diff	0	(fma.f64 (.f64 x x) (fma.f64 x (.f64 x (.f64 eps (fma.f64 (.f64 x x) #s(literal -1/720 binary64) #s(literal 1/24 binary64)))) (*.f64 eps #s(literal -1/2 binary64))) eps)
cost-diff	0	#s(approx (* eps (cos x)) (fma.f64 (.f64 x x) (fma.f64 x (.f64 x (.f64 eps (fma.f64 (.f64 x x) #s(literal -1/720 binary64) #s(literal 1/24 binary64)))) (*.f64 eps #s(literal -1/2 binary64))) eps))
cost-diff	0	#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* eps (cos x)) (fma.f64 (.f64 x x) (fma.f64 x (.f64 x (.f64 eps (fma.f64 (.f64 x x) #s(literal -1/720 binary64) #s(literal 1/24 binary64)))) (*.f64 eps #s(literal -1/2 binary64))) eps)))
cost-diff	320	(fma.f64 x (.f64 x (.f64 eps (fma.f64 (.f64 x x) #s(literal -1/720 binary64) #s(literal 1/24 binary64)))) (.f64 eps #s(literal -1/2 binary64)))
cost-diff	0	(fma.f64 x (fma.f64 eps #s(literal -1/2 binary64) (.f64 x (fma.f64 (.f64 eps x) #s(literal 1/12 binary64) #s(literal -1/2 binary64)))) #s(literal 1 binary64))
cost-diff	0	#s(approx (+ (* eps (* -1/2 (sin x))) (cos x)) (fma.f64 x (fma.f64 eps #s(literal -1/2 binary64) (.f64 x (fma.f64 (.f64 eps x) #s(literal 1/12 binary64) #s(literal -1/2 binary64)))) #s(literal 1 binary64)))
cost-diff	0	(.f64 eps #s(approx (+ ( eps (* -1/2 (sin x))) (cos x)) (fma.f64 x (fma.f64 eps #s(literal -1/2 binary64) (.f64 x (fma.f64 (.f64 eps x) #s(literal 1/12 binary64) #s(literal -1/2 binary64)))) #s(literal 1 binary64))))
cost-diff	0	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 eps #s(approx (+ ( eps (* -1/2 (sin x))) (cos x)) (fma.f64 x (fma.f64 eps #s(literal -1/2 binary64) (.f64 x (fma.f64 (.f64 eps x) #s(literal 1/12 binary64) #s(literal -1/2 binary64)))) #s(literal 1 binary64)))))
cost-diff	0	(fma.f64 (.f64 x x) #s(approx (+ ( 1/24 (* x x)) -1/2) #s(literal -1/2 binary64)) #s(literal 1 binary64))
cost-diff	0	#s(approx (cos x) (fma.f64 (.f64 x x) #s(approx (+ ( 1/24 (* x x)) -1/2) #s(literal -1/2 binary64)) #s(literal 1 binary64)))
cost-diff	0	(.f64 eps #s(approx (cos x) (fma.f64 (.f64 x x) #s(approx (+ (* 1/24 (* x x)) -1/2) #s(literal -1/2 binary64)) #s(literal 1 binary64))))
cost-diff	0	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 eps #s(approx (cos x) (fma.f64 (.f64 x x) #s(approx (+ (* 1/24 (* x x)) -1/2) #s(literal -1/2 binary64)) #s(literal 1 binary64)))))
cost-diff	0	#s(approx (sin (* 1/2 eps)) (.f64 eps (fma.f64 eps (.f64 eps (fma.f64 (.f64 eps eps) (fma.f64 eps (.f64 eps #s(literal -1/645120 binary64)) #s(literal 1/3840 binary64)) #s(literal -1/48 binary64))) #s(literal 1/2 binary64))))
cost-diff	0	(.f64 #s(approx (sin ( 1/2 eps)) (.f64 eps (fma.f64 eps (.f64 eps (fma.f64 (.f64 eps eps) (fma.f64 eps (.f64 eps #s(literal -1/645120 binary64)) #s(literal 1/3840 binary64)) #s(literal -1/48 binary64))) #s(literal 1/2 binary64)))) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)))
cost-diff	0	#s(approx (* (sin (* (+ eps 0) 1/2)) (cos (* (+ (* x 2) eps) 1/2))) (.f64 #s(approx (sin ( 1/2 eps)) (.f64 eps (fma.f64 eps (.f64 eps (fma.f64 (.f64 eps eps) (fma.f64 eps (.f64 eps #s(literal -1/645120 binary64)) #s(literal 1/3840 binary64)) #s(literal -1/48 binary64))) #s(literal 1/2 binary64)))) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x))))
cost-diff	0	(.f64 #s(approx ( (sin (* (+ eps 0) 1/2)) (cos (* (+ (* x 2) eps) 1/2))) (.f64 #s(approx (sin ( 1/2 eps)) (.f64 eps (fma.f64 eps (.f64 eps (fma.f64 (.f64 eps eps) (fma.f64 eps (.f64 eps #s(literal -1/645120 binary64)) #s(literal 1/3840 binary64)) #s(literal -1/48 binary64))) #s(literal 1/2 binary64)))) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)))) #s(literal 2 binary64))

Rules

12 422×	`lower-fma.f32`
12 398×	`lower-fma.f64`
4 040×	`lower-*.f32`
4 006×	`lower-*.f64`
3 162×	`lower-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	76	717
0	116	709
1	236	709
2	681	705
3	1879	693
4	3533	693
5	3908	693
6	4472	693
7	4663	693
8	4723	693
9	5066	693
10	5155	693
11	5225	693
12	5351	693
13	6484	693
0	8141	681

Stop Event

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

Calls

Call 1

Inputs
(.f64 #s(approx ( (sin (* (+ eps 0) 1/2)) (cos (* (+ (* x 2) eps) 1/2))) (.f64 #s(approx (sin ( 1/2 eps)) (.f64 eps (fma.f64 eps (.f64 eps (fma.f64 (.f64 eps eps) (fma.f64 eps (.f64 eps #s(literal -1/645120 binary64)) #s(literal 1/3840 binary64)) #s(literal -1/48 binary64))) #s(literal 1/2 binary64)))) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)))) #s(literal 2 binary64))
#s(approx (* (sin (* (+ eps 0) 1/2)) (cos (* (+ (* x 2) eps) 1/2))) (.f64 #s(approx (sin ( 1/2 eps)) (.f64 eps (fma.f64 eps (.f64 eps (fma.f64 (.f64 eps eps) (fma.f64 eps (.f64 eps #s(literal -1/645120 binary64)) #s(literal 1/3840 binary64)) #s(literal -1/48 binary64))) #s(literal 1/2 binary64)))) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x))))
(.f64 #s(approx (sin ( 1/2 eps)) (.f64 eps (fma.f64 eps (.f64 eps (fma.f64 (.f64 eps eps) (fma.f64 eps (.f64 eps #s(literal -1/645120 binary64)) #s(literal 1/3840 binary64)) #s(literal -1/48 binary64))) #s(literal 1/2 binary64)))) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)))
#s(approx (sin (* 1/2 eps)) (.f64 eps (fma.f64 eps (.f64 eps (fma.f64 (.f64 eps eps) (fma.f64 eps (.f64 eps #s(literal -1/645120 binary64)) #s(literal 1/3840 binary64)) #s(literal -1/48 binary64))) #s(literal 1/2 binary64))))
(.f64 eps (fma.f64 eps (.f64 eps (fma.f64 (.f64 eps eps) (fma.f64 eps (.f64 eps #s(literal -1/645120 binary64)) #s(literal 1/3840 binary64)) #s(literal -1/48 binary64))) #s(literal 1/2 binary64)))
eps
(fma.f64 eps (.f64 eps (fma.f64 (.f64 eps eps) (fma.f64 eps (*.f64 eps #s(literal -1/645120 binary64)) #s(literal 1/3840 binary64)) #s(literal -1/48 binary64))) #s(literal 1/2 binary64))
(.f64 eps (fma.f64 (.f64 eps eps) (fma.f64 eps (*.f64 eps #s(literal -1/645120 binary64)) #s(literal 1/3840 binary64)) #s(literal -1/48 binary64)))
(fma.f64 (.f64 eps eps) (fma.f64 eps (.f64 eps #s(literal -1/645120 binary64)) #s(literal 1/3840 binary64)) #s(literal -1/48 binary64))
(*.f64 eps eps)
(fma.f64 eps (*.f64 eps #s(literal -1/645120 binary64)) #s(literal 1/3840 binary64))
(*.f64 eps #s(literal -1/645120 binary64))
#s(literal -1/645120 binary64)
#s(literal 1/3840 binary64)
#s(literal -1/48 binary64)
#s(literal 1/2 binary64)
(cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x))
(fma.f64 #s(literal 1/2 binary64) eps x)
x
#s(literal 2 binary64)
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 eps #s(approx (cos x) (fma.f64 (.f64 x x) #s(approx (+ (* 1/24 (* x x)) -1/2) #s(literal -1/2 binary64)) #s(literal 1 binary64)))))
(.f64 eps #s(approx (cos x) (fma.f64 (.f64 x x) #s(approx (+ (* 1/24 (* x x)) -1/2) #s(literal -1/2 binary64)) #s(literal 1 binary64))))
eps
#s(approx (cos x) (fma.f64 (.f64 x x) #s(approx (+ ( 1/24 (* x x)) -1/2) #s(literal -1/2 binary64)) #s(literal 1 binary64)))
(fma.f64 (.f64 x x) #s(approx (+ ( 1/24 (* x x)) -1/2) #s(literal -1/2 binary64)) #s(literal 1 binary64))
(*.f64 x x)
x
#s(approx (+ (* 1/24 (* x x)) -1/2) #s(literal -1/2 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))) (cos x)) (fma.f64 x (fma.f64 eps #s(literal -1/2 binary64) (.f64 x (fma.f64 (.f64 eps x) #s(literal 1/12 binary64) #s(literal -1/2 binary64)))) #s(literal 1 binary64)))))
(.f64 eps #s(approx (+ ( eps (* -1/2 (sin x))) (cos x)) (fma.f64 x (fma.f64 eps #s(literal -1/2 binary64) (.f64 x (fma.f64 (.f64 eps x) #s(literal 1/12 binary64) #s(literal -1/2 binary64)))) #s(literal 1 binary64))))
eps
#s(approx (+ (* eps (* -1/2 (sin x))) (cos x)) (fma.f64 x (fma.f64 eps #s(literal -1/2 binary64) (.f64 x (fma.f64 (.f64 eps x) #s(literal 1/12 binary64) #s(literal -1/2 binary64)))) #s(literal 1 binary64)))
(fma.f64 x (fma.f64 eps #s(literal -1/2 binary64) (.f64 x (fma.f64 (.f64 eps x) #s(literal 1/12 binary64) #s(literal -1/2 binary64)))) #s(literal 1 binary64))
x
(fma.f64 eps #s(literal -1/2 binary64) (.f64 x (fma.f64 (.f64 eps x) #s(literal 1/12 binary64) #s(literal -1/2 binary64))))
#s(literal -1/2 binary64)
(.f64 x (fma.f64 (.f64 eps x) #s(literal 1/12 binary64) #s(literal -1/2 binary64)))
(fma.f64 (*.f64 eps x) #s(literal 1/12 binary64) #s(literal -1/2 binary64))
(*.f64 eps x)
#s(literal 1/12 binary64)
#s(literal 1 binary64)
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* eps (cos x)) (fma.f64 (.f64 x x) (fma.f64 x (.f64 x (.f64 eps (fma.f64 (.f64 x x) #s(literal -1/720 binary64) #s(literal 1/24 binary64)))) (*.f64 eps #s(literal -1/2 binary64))) eps)))
#s(approx (* eps (cos x)) (fma.f64 (.f64 x x) (fma.f64 x (.f64 x (.f64 eps (fma.f64 (.f64 x x) #s(literal -1/720 binary64) #s(literal 1/24 binary64)))) (*.f64 eps #s(literal -1/2 binary64))) eps))
(fma.f64 (.f64 x x) (fma.f64 x (.f64 x (.f64 eps (fma.f64 (.f64 x x) #s(literal -1/720 binary64) #s(literal 1/24 binary64)))) (*.f64 eps #s(literal -1/2 binary64))) eps)
(*.f64 x x)
x
(fma.f64 x (.f64 x (.f64 eps (fma.f64 (.f64 x x) #s(literal -1/720 binary64) #s(literal 1/24 binary64)))) (.f64 eps #s(literal -1/2 binary64)))
(.f64 x (.f64 eps (fma.f64 (*.f64 x x) #s(literal -1/720 binary64) #s(literal 1/24 binary64))))
(.f64 eps (fma.f64 (.f64 x x) #s(literal -1/720 binary64) #s(literal 1/24 binary64)))
eps
(fma.f64 (*.f64 x x) #s(literal -1/720 binary64) #s(literal 1/24 binary64))
#s(literal -1/720 binary64)
#s(literal 1/24 binary64)
(*.f64 eps #s(literal -1/2 binary64))
#s(literal -1/2 binary64)
(.f64 #s(approx ( (sin (* (+ eps 0) 1/2)) (cos (* (+ (* x 2) eps) 1/2))) (.f64 #s(approx (sin ( 1/2 eps)) (.f64 eps (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal 1/2 binary64)))) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)))) #s(literal 2 binary64))
#s(approx (* (sin (* (+ eps 0) 1/2)) (cos (* (+ (* x 2) eps) 1/2))) (.f64 #s(approx (sin ( 1/2 eps)) (.f64 eps (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal 1/2 binary64)))) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x))))
(.f64 #s(approx (sin ( 1/2 eps)) (.f64 eps (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal 1/2 binary64)))) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)))
#s(approx (sin (* 1/2 eps)) (.f64 eps (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal 1/2 binary64))))
(.f64 eps (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal 1/2 binary64)))
eps
(fma.f64 #s(literal -1/48 binary64) (*.f64 eps eps) #s(literal 1/2 binary64))
#s(literal -1/48 binary64)
(*.f64 eps eps)
#s(literal 1/2 binary64)
(cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x))
(fma.f64 #s(literal 1/2 binary64) eps x)
x
#s(literal 2 binary64)

Outputs
(.f64 #s(approx ( (sin (* (+ eps 0) 1/2)) (cos (* (+ (* x 2) eps) 1/2))) (.f64 #s(approx (sin ( 1/2 eps)) (.f64 eps (fma.f64 eps (.f64 eps (fma.f64 (.f64 eps eps) (fma.f64 eps (.f64 eps #s(literal -1/645120 binary64)) #s(literal 1/3840 binary64)) #s(literal -1/48 binary64))) #s(literal 1/2 binary64)))) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)))) #s(literal 2 binary64))
(.f64 #s(literal 2 binary64) #s(approx ( (sin (* (+ eps 0) 1/2)) (cos (* (+ (* x 2) eps) 1/2))) (.f64 #s(approx (sin ( 1/2 eps)) (.f64 eps (fma.f64 (.f64 eps eps) (fma.f64 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 (fma.f64 eps #s(literal 1/2 binary64) x)))))
#s(approx (* (sin (* (+ eps 0) 1/2)) (cos (* (+ (* x 2) eps) 1/2))) (.f64 #s(approx (sin ( 1/2 eps)) (.f64 eps (fma.f64 eps (.f64 eps (fma.f64 (.f64 eps eps) (fma.f64 eps (.f64 eps #s(literal -1/645120 binary64)) #s(literal 1/3840 binary64)) #s(literal -1/48 binary64))) #s(literal 1/2 binary64)))) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x))))
#s(approx (* (sin (* (+ eps 0) 1/2)) (cos (* (+ (* x 2) eps) 1/2))) (.f64 #s(approx (sin ( 1/2 eps)) (.f64 eps (fma.f64 (.f64 eps eps) (fma.f64 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 (fma.f64 eps #s(literal 1/2 binary64) x))))
(.f64 #s(approx (sin ( 1/2 eps)) (.f64 eps (fma.f64 eps (.f64 eps (fma.f64 (.f64 eps eps) (fma.f64 eps (.f64 eps #s(literal -1/645120 binary64)) #s(literal 1/3840 binary64)) #s(literal -1/48 binary64))) #s(literal 1/2 binary64)))) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)))
(.f64 #s(approx (sin ( 1/2 eps)) (.f64 eps (fma.f64 (.f64 eps eps) (fma.f64 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 (fma.f64 eps #s(literal 1/2 binary64) x)))
#s(approx (sin (* 1/2 eps)) (.f64 eps (fma.f64 eps (.f64 eps (fma.f64 (.f64 eps eps) (fma.f64 eps (.f64 eps #s(literal -1/645120 binary64)) #s(literal 1/3840 binary64)) #s(literal -1/48 binary64))) #s(literal 1/2 binary64))))
#s(approx (sin (* 1/2 eps)) (.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))))
(.f64 eps (fma.f64 eps (.f64 eps (fma.f64 (.f64 eps eps) (fma.f64 eps (.f64 eps #s(literal -1/645120 binary64)) #s(literal 1/3840 binary64)) #s(literal -1/48 binary64))) #s(literal 1/2 binary64)))
(.f64 eps (fma.f64 (.f64 eps eps) (fma.f64 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)))
eps
(fma.f64 eps (.f64 eps (fma.f64 (.f64 eps eps) (fma.f64 eps (*.f64 eps #s(literal -1/645120 binary64)) #s(literal 1/3840 binary64)) #s(literal -1/48 binary64))) #s(literal 1/2 binary64))
(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))
(.f64 eps (fma.f64 (.f64 eps eps) (fma.f64 eps (*.f64 eps #s(literal -1/645120 binary64)) #s(literal 1/3840 binary64)) #s(literal -1/48 binary64)))
(.f64 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)))
(fma.f64 (.f64 eps eps) (fma.f64 eps (.f64 eps #s(literal -1/645120 binary64)) #s(literal 1/3840 binary64)) #s(literal -1/48 binary64))
(fma.f64 eps (.f64 eps (fma.f64 (.f64 eps eps) #s(literal -1/645120 binary64) #s(literal 1/3840 binary64))) #s(literal -1/48 binary64))
(*.f64 eps eps)
(fma.f64 eps (*.f64 eps #s(literal -1/645120 binary64)) #s(literal 1/3840 binary64))
(fma.f64 (*.f64 eps eps) #s(literal -1/645120 binary64) #s(literal 1/3840 binary64))
(*.f64 eps #s(literal -1/645120 binary64))
#s(literal -1/645120 binary64)
#s(literal 1/3840 binary64)
#s(literal -1/48 binary64)
#s(literal 1/2 binary64)
(cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x))
(cos.f64 (fma.f64 eps #s(literal 1/2 binary64) x))
(fma.f64 #s(literal 1/2 binary64) eps x)
(fma.f64 eps #s(literal 1/2 binary64) x)
x
#s(literal 2 binary64)
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 eps #s(approx (cos x) (fma.f64 (.f64 x x) #s(approx (+ (* 1/24 (* x x)) -1/2) #s(literal -1/2 binary64)) #s(literal 1 binary64)))))
(.f64 eps #s(approx (cos x) (fma.f64 (.f64 x x) #s(approx (+ (* 1/24 (* x x)) -1/2) #s(literal -1/2 binary64)) #s(literal 1 binary64))))
eps
#s(approx (cos x) (fma.f64 (.f64 x x) #s(approx (+ ( 1/24 (* x x)) -1/2) #s(literal -1/2 binary64)) #s(literal 1 binary64)))
(fma.f64 (.f64 x x) #s(approx (+ ( 1/24 (* x x)) -1/2) #s(literal -1/2 binary64)) #s(literal 1 binary64))
(*.f64 x x)
x
#s(approx (+ (* 1/24 (* x x)) -1/2) #s(literal -1/2 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))) (cos x)) (fma.f64 x (fma.f64 eps #s(literal -1/2 binary64) (.f64 x (fma.f64 (.f64 eps x) #s(literal 1/12 binary64) #s(literal -1/2 binary64)))) #s(literal 1 binary64)))))
(.f64 eps #s(approx (+ ( eps (* -1/2 (sin x))) (cos x)) (fma.f64 x (fma.f64 eps #s(literal -1/2 binary64) (.f64 x (fma.f64 (.f64 eps x) #s(literal 1/12 binary64) #s(literal -1/2 binary64)))) #s(literal 1 binary64))))
eps
#s(approx (+ (* eps (* -1/2 (sin x))) (cos x)) (fma.f64 x (fma.f64 eps #s(literal -1/2 binary64) (.f64 x (fma.f64 (.f64 eps x) #s(literal 1/12 binary64) #s(literal -1/2 binary64)))) #s(literal 1 binary64)))
(fma.f64 x (fma.f64 eps #s(literal -1/2 binary64) (.f64 x (fma.f64 (.f64 eps x) #s(literal 1/12 binary64) #s(literal -1/2 binary64)))) #s(literal 1 binary64))
x
(fma.f64 eps #s(literal -1/2 binary64) (.f64 x (fma.f64 (.f64 eps x) #s(literal 1/12 binary64) #s(literal -1/2 binary64))))
#s(literal -1/2 binary64)
(.f64 x (fma.f64 (.f64 eps x) #s(literal 1/12 binary64) #s(literal -1/2 binary64)))
(fma.f64 (*.f64 eps x) #s(literal 1/12 binary64) #s(literal -1/2 binary64))
(*.f64 eps x)
#s(literal 1/12 binary64)
#s(literal 1 binary64)
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* eps (cos x)) (fma.f64 (.f64 x x) (fma.f64 x (.f64 x (.f64 eps (fma.f64 (.f64 x x) #s(literal -1/720 binary64) #s(literal 1/24 binary64)))) (*.f64 eps #s(literal -1/2 binary64))) eps)))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* eps (cos x)) (fma.f64 x (.f64 x (.f64 eps (fma.f64 (.f64 x x) (fma.f64 x (.f64 x #s(literal -1/720 binary64)) #s(literal 1/24 binary64)) #s(literal -1/2 binary64)))) eps)))
#s(approx (* eps (cos x)) (fma.f64 (.f64 x x) (fma.f64 x (.f64 x (.f64 eps (fma.f64 (.f64 x x) #s(literal -1/720 binary64) #s(literal 1/24 binary64)))) (*.f64 eps #s(literal -1/2 binary64))) eps))
#s(approx (* eps (cos x)) (fma.f64 x (.f64 x (.f64 eps (fma.f64 (.f64 x x) (fma.f64 x (.f64 x #s(literal -1/720 binary64)) #s(literal 1/24 binary64)) #s(literal -1/2 binary64)))) eps))
(fma.f64 (.f64 x x) (fma.f64 x (.f64 x (.f64 eps (fma.f64 (.f64 x x) #s(literal -1/720 binary64) #s(literal 1/24 binary64)))) (*.f64 eps #s(literal -1/2 binary64))) eps)
(fma.f64 x (.f64 x (.f64 eps (fma.f64 (.f64 x x) (fma.f64 x (.f64 x #s(literal -1/720 binary64)) #s(literal 1/24 binary64)) #s(literal -1/2 binary64)))) eps)
(*.f64 x x)
x
(fma.f64 x (.f64 x (.f64 eps (fma.f64 (.f64 x x) #s(literal -1/720 binary64) #s(literal 1/24 binary64)))) (.f64 eps #s(literal -1/2 binary64)))
(.f64 eps (fma.f64 (.f64 x x) (fma.f64 x (*.f64 x #s(literal -1/720 binary64)) #s(literal 1/24 binary64)) #s(literal -1/2 binary64)))
(.f64 x (.f64 eps (fma.f64 (*.f64 x x) #s(literal -1/720 binary64) #s(literal 1/24 binary64))))
(.f64 (.f64 eps x) (fma.f64 x (*.f64 x #s(literal -1/720 binary64)) #s(literal 1/24 binary64)))
(.f64 eps (fma.f64 (.f64 x x) #s(literal -1/720 binary64) #s(literal 1/24 binary64)))
(.f64 eps (fma.f64 x (.f64 x #s(literal -1/720 binary64)) #s(literal 1/24 binary64)))
eps
(fma.f64 (*.f64 x x) #s(literal -1/720 binary64) #s(literal 1/24 binary64))
(fma.f64 x (*.f64 x #s(literal -1/720 binary64)) #s(literal 1/24 binary64))
#s(literal -1/720 binary64)
#s(literal 1/24 binary64)
(*.f64 eps #s(literal -1/2 binary64))
#s(literal -1/2 binary64)
(.f64 #s(approx ( (sin (* (+ eps 0) 1/2)) (cos (* (+ (* x 2) eps) 1/2))) (.f64 #s(approx (sin ( 1/2 eps)) (.f64 eps (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal 1/2 binary64)))) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)))) #s(literal 2 binary64))
(.f64 #s(literal 2 binary64) #s(approx ( (sin (* (+ eps 0) 1/2)) (cos (* (+ (* x 2) eps) 1/2))) (.f64 (cos.f64 (fma.f64 eps #s(literal 1/2 binary64) x)) #s(approx (sin ( 1/2 eps)) (.f64 eps (fma.f64 eps (.f64 eps #s(literal -1/48 binary64)) #s(literal 1/2 binary64)))))))
#s(approx (* (sin (* (+ eps 0) 1/2)) (cos (* (+ (* x 2) eps) 1/2))) (.f64 #s(approx (sin ( 1/2 eps)) (.f64 eps (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal 1/2 binary64)))) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x))))
#s(approx (* (sin (* (+ eps 0) 1/2)) (cos (* (+ (* x 2) eps) 1/2))) (.f64 (cos.f64 (fma.f64 eps #s(literal 1/2 binary64) x)) #s(approx (sin ( 1/2 eps)) (.f64 eps (fma.f64 eps (.f64 eps #s(literal -1/48 binary64)) #s(literal 1/2 binary64))))))
(.f64 #s(approx (sin ( 1/2 eps)) (.f64 eps (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal 1/2 binary64)))) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)))
(.f64 (cos.f64 (fma.f64 eps #s(literal 1/2 binary64) x)) #s(approx (sin ( 1/2 eps)) (.f64 eps (fma.f64 eps (.f64 eps #s(literal -1/48 binary64)) #s(literal 1/2 binary64)))))
#s(approx (sin (* 1/2 eps)) (.f64 eps (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal 1/2 binary64))))
#s(approx (sin (* 1/2 eps)) (.f64 eps (fma.f64 eps (.f64 eps #s(literal -1/48 binary64)) #s(literal 1/2 binary64))))
(.f64 eps (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal 1/2 binary64)))
(.f64 eps (fma.f64 eps (.f64 eps #s(literal -1/48 binary64)) #s(literal 1/2 binary64)))
eps
(fma.f64 #s(literal -1/48 binary64) (*.f64 eps eps) #s(literal 1/2 binary64))
(fma.f64 eps (*.f64 eps #s(literal -1/48 binary64)) #s(literal 1/2 binary64))
#s(literal -1/48 binary64)
(*.f64 eps eps)
#s(literal 1/2 binary64)
(cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x))
(cos.f64 (fma.f64 eps #s(literal 1/2 binary64) x))
(fma.f64 #s(literal 1/2 binary64) eps x)
(fma.f64 eps #s(literal 1/2 binary64) x)
x
#s(literal 2 binary64)

localize279.0ms (2.1%)

Memory

-1.2MiB live, 399.6MiB allocated

Localize:

Found 20 expressions of interest:

New	Metric	Score
accuracy	0.00390625	(.f64 eps (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal 1/2 binary64)))
accuracy	0.0078125	(.f64 #s(approx (sin ( 1/2 eps)) (.f64 eps (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal 1/2 binary64)))) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)))
accuracy	0.0464165744115697	(cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x))
accuracy	0.1278156975370348	#s(approx (sin (* 1/2 eps)) (.f64 eps (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal 1/2 binary64))))
accuracy	0.12109375	(.f64 x (.f64 eps (fma.f64 (*.f64 x x) #s(literal -1/720 binary64) #s(literal 1/24 binary64))))
accuracy	0.3046875	(.f64 eps (fma.f64 (.f64 x x) #s(literal -1/720 binary64) #s(literal 1/24 binary64)))
accuracy	0.45925062897182506	#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* eps (cos x)) (fma.f64 (.f64 x x) (fma.f64 x (.f64 x (.f64 eps (fma.f64 (.f64 x x) #s(literal -1/720 binary64) #s(literal 1/24 binary64)))) (*.f64 eps #s(literal -1/2 binary64))) eps)))
accuracy	0.7323134152972174	#s(approx (* eps (cos x)) (fma.f64 (.f64 x x) (fma.f64 x (.f64 x (.f64 eps (fma.f64 (.f64 x x) #s(literal -1/720 binary64) #s(literal 1/24 binary64)))) (*.f64 eps #s(literal -1/2 binary64))) eps))
accuracy	0.00390625	(.f64 eps #s(approx (+ ( eps (* -1/2 (sin x))) (cos x)) (fma.f64 x (fma.f64 eps #s(literal -1/2 binary64) (.f64 x (fma.f64 (.f64 eps x) #s(literal 1/12 binary64) #s(literal -1/2 binary64)))) #s(literal 1 binary64))))
accuracy	0.01953125	(fma.f64 eps #s(literal -1/2 binary64) (.f64 x (fma.f64 (.f64 eps x) #s(literal 1/12 binary64) #s(literal -1/2 binary64))))
accuracy	0.1809942524239391	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 eps #s(approx (+ ( eps (* -1/2 (sin x))) (cos x)) (fma.f64 x (fma.f64 eps #s(literal -1/2 binary64) (.f64 x (fma.f64 (.f64 eps x) #s(literal 1/12 binary64) #s(literal -1/2 binary64)))) #s(literal 1 binary64)))))
accuracy	0.915514254007739	#s(approx (+ (* eps (* -1/2 (sin x))) (cos x)) (fma.f64 x (fma.f64 eps #s(literal -1/2 binary64) (.f64 x (fma.f64 (.f64 eps x) #s(literal 1/12 binary64) #s(literal -1/2 binary64)))) #s(literal 1 binary64)))
accuracy	0.0078125	(fma.f64 (.f64 x x) #s(approx (+ ( 1/24 (* x x)) -1/2) #s(literal -1/2 binary64)) #s(literal 1 binary64))
accuracy	0.45925062897182506	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 eps #s(approx (cos x) (fma.f64 (.f64 x x) #s(approx (+ (* 1/24 (* x x)) -1/2) #s(literal -1/2 binary64)) #s(literal 1 binary64)))))
accuracy	0.8214398162726576	#s(approx (cos x) (fma.f64 (.f64 x x) #s(approx (+ ( 1/24 (* x x)) -1/2) #s(literal -1/2 binary64)) #s(literal 1 binary64)))
accuracy	1.243402245736372	#s(approx (+ (* 1/24 (* x x)) -1/2) #s(literal -1/2 binary64))
accuracy	0.0078125	(.f64 #s(approx (sin ( 1/2 eps)) (.f64 eps (fma.f64 eps (.f64 eps (fma.f64 (.f64 eps eps) (fma.f64 eps (.f64 eps #s(literal -1/645120 binary64)) #s(literal 1/3840 binary64)) #s(literal -1/48 binary64))) #s(literal 1/2 binary64)))) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)))
accuracy	0.03150816090022567	#s(approx (sin (* 1/2 eps)) (.f64 eps (fma.f64 eps (.f64 eps (fma.f64 (.f64 eps eps) (fma.f64 eps (.f64 eps #s(literal -1/645120 binary64)) #s(literal 1/3840 binary64)) #s(literal -1/48 binary64))) #s(literal 1/2 binary64))))
accuracy	0.0464165744115697	(cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x))
accuracy	0.3125	(.f64 eps (fma.f64 (.f64 eps eps) (fma.f64 eps (*.f64 eps #s(literal -1/645120 binary64)) #s(literal 1/3840 binary64)) #s(literal -1/48 binary64)))

Samples

97.0ms	171×	0	valid
93.0ms	81×	1	valid
4.0ms	3×	3	valid
1.0ms	1×	2	valid

Compiler

Compiled 440 to 73 computations (83.4% saved)

Precisions

Click to see histograms. Total time spent on operations: 157.0ms

ival-mult: 76.0ms (48.3% of total)

const: 27.0ms (17.2% of total)

ival-add: 27.0ms (17.2% of total)

adjust: 12.0ms (7.6% of total)

ival-sin: 7.0ms (4.4% of total)

ival-cos: 5.0ms (3.2% of total)

ival-sub: 2.0ms (1.3% of total)

exact: 1.0ms (0.6% of total)

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

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

series58.0ms (0.4%)

Memory

-5.3MiB live, 114.9MiB allocated

Counts

27 → 564

Calls

Call 1

Inputs
#s(alt (.f64 #s(approx ( (sin (* (+ eps 0) 1/2)) (cos (* (+ (* x 2) eps) 1/2))) (.f64 #s(approx (sin ( 1/2 eps)) (.f64 eps (fma.f64 eps (.f64 eps (fma.f64 (.f64 eps eps) (fma.f64 eps (.f64 eps #s(literal -1/645120 binary64)) #s(literal 1/3840 binary64)) #s(literal -1/48 binary64))) #s(literal 1/2 binary64)))) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)))) #s(literal 2 binary64)) (patch (.f64 #s(approx ( (sin (* (+ eps 0) 1/2)) (cos (* (+ (* x 2) eps) 1/2))) (.f64 #s(approx (sin ( 1/2 eps)) (.f64 eps (fma.f64 eps (.f64 eps (fma.f64 (.f64 eps eps) (fma.f64 eps (.f64 eps #s(literal -1/645120 binary64)) #s(literal 1/3840 binary64)) #s(literal -1/48 binary64))) #s(literal 1/2 binary64)))) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)))) #s(literal 2 binary64)) #<representation binary64>) () ())
#s(alt #s(approx (* (sin (* (+ eps 0) 1/2)) (cos (* (+ (* x 2) eps) 1/2))) (.f64 #s(approx (sin ( 1/2 eps)) (.f64 eps (fma.f64 eps (.f64 eps (fma.f64 (.f64 eps eps) (fma.f64 eps (.f64 eps #s(literal -1/645120 binary64)) #s(literal 1/3840 binary64)) #s(literal -1/48 binary64))) #s(literal 1/2 binary64)))) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)))) (patch #s(approx (* (sin (* (+ eps 0) 1/2)) (cos (* (+ (* x 2) eps) 1/2))) (.f64 #s(approx (sin ( 1/2 eps)) (.f64 eps (fma.f64 eps (.f64 eps (fma.f64 (.f64 eps eps) (fma.f64 eps (.f64 eps #s(literal -1/645120 binary64)) #s(literal 1/3840 binary64)) #s(literal -1/48 binary64))) #s(literal 1/2 binary64)))) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)))) #<representation binary64>) () ())
#s(alt (.f64 #s(approx (sin ( 1/2 eps)) (.f64 eps (fma.f64 eps (.f64 eps (fma.f64 (.f64 eps eps) (fma.f64 eps (.f64 eps #s(literal -1/645120 binary64)) #s(literal 1/3840 binary64)) #s(literal -1/48 binary64))) #s(literal 1/2 binary64)))) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x))) (patch (.f64 #s(approx (sin ( 1/2 eps)) (.f64 eps (fma.f64 eps (.f64 eps (fma.f64 (.f64 eps eps) (fma.f64 eps (.f64 eps #s(literal -1/645120 binary64)) #s(literal 1/3840 binary64)) #s(literal -1/48 binary64))) #s(literal 1/2 binary64)))) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x))) #<representation binary64>) () ())
#s(alt #s(approx (sin (* 1/2 eps)) (.f64 eps (fma.f64 eps (.f64 eps (fma.f64 (.f64 eps eps) (fma.f64 eps (.f64 eps #s(literal -1/645120 binary64)) #s(literal 1/3840 binary64)) #s(literal -1/48 binary64))) #s(literal 1/2 binary64)))) (patch #s(approx (sin (* 1/2 eps)) (.f64 eps (fma.f64 eps (.f64 eps (fma.f64 (.f64 eps eps) (fma.f64 eps (.f64 eps #s(literal -1/645120 binary64)) #s(literal 1/3840 binary64)) #s(literal -1/48 binary64))) #s(literal 1/2 binary64)))) #<representation binary64>) () ())
#s(alt #s(approx (- (sin (+ x eps)) (sin x)) (.f64 eps #s(approx (cos x) (fma.f64 (.f64 x x) #s(approx (+ (* 1/24 (* x x)) -1/2) #s(literal -1/2 binary64)) #s(literal 1 binary64))))) (patch #s(approx (- (sin (+ x eps)) (sin x)) (.f64 eps #s(approx (cos x) (fma.f64 (.f64 x x) #s(approx (+ (* 1/24 (* x x)) -1/2) #s(literal -1/2 binary64)) #s(literal 1 binary64))))) #<representation binary64>) () ())
#s(alt (.f64 eps #s(approx (cos x) (fma.f64 (.f64 x x) #s(approx (+ (* 1/24 (* x x)) -1/2) #s(literal -1/2 binary64)) #s(literal 1 binary64)))) (patch (.f64 eps #s(approx (cos x) (fma.f64 (.f64 x x) #s(approx (+ (* 1/24 (* x x)) -1/2) #s(literal -1/2 binary64)) #s(literal 1 binary64)))) #<representation binary64>) () ())
#s(alt #s(approx (cos x) (fma.f64 (.f64 x x) #s(approx (+ ( 1/24 (* x x)) -1/2) #s(literal -1/2 binary64)) #s(literal 1 binary64))) (patch #s(approx (cos x) (fma.f64 (.f64 x x) #s(approx (+ ( 1/24 (* x x)) -1/2) #s(literal -1/2 binary64)) #s(literal 1 binary64))) #<representation binary64>) () ())
#s(alt (fma.f64 (.f64 x x) #s(approx (+ ( 1/24 (* x x)) -1/2) #s(literal -1/2 binary64)) #s(literal 1 binary64)) (patch (fma.f64 (.f64 x x) #s(approx (+ ( 1/24 (* x x)) -1/2) #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))) (cos x)) (fma.f64 x (fma.f64 eps #s(literal -1/2 binary64) (.f64 x (fma.f64 (.f64 eps x) #s(literal 1/12 binary64) #s(literal -1/2 binary64)))) #s(literal 1 binary64))))) (patch #s(approx (- (sin (+ x eps)) (sin x)) (.f64 eps #s(approx (+ ( eps (* -1/2 (sin x))) (cos x)) (fma.f64 x (fma.f64 eps #s(literal -1/2 binary64) (.f64 x (fma.f64 (.f64 eps x) #s(literal 1/12 binary64) #s(literal -1/2 binary64)))) #s(literal 1 binary64))))) #<representation binary64>) () ())
#s(alt (.f64 eps #s(approx (+ ( eps (* -1/2 (sin x))) (cos x)) (fma.f64 x (fma.f64 eps #s(literal -1/2 binary64) (.f64 x (fma.f64 (.f64 eps x) #s(literal 1/12 binary64) #s(literal -1/2 binary64)))) #s(literal 1 binary64)))) (patch (.f64 eps #s(approx (+ ( eps (* -1/2 (sin x))) (cos x)) (fma.f64 x (fma.f64 eps #s(literal -1/2 binary64) (.f64 x (fma.f64 (.f64 eps x) #s(literal 1/12 binary64) #s(literal -1/2 binary64)))) #s(literal 1 binary64)))) #<representation binary64>) () ())
#s(alt #s(approx (+ (* eps (* -1/2 (sin x))) (cos x)) (fma.f64 x (fma.f64 eps #s(literal -1/2 binary64) (.f64 x (fma.f64 (.f64 eps x) #s(literal 1/12 binary64) #s(literal -1/2 binary64)))) #s(literal 1 binary64))) (patch #s(approx (+ (* eps (* -1/2 (sin x))) (cos x)) (fma.f64 x (fma.f64 eps #s(literal -1/2 binary64) (.f64 x (fma.f64 (.f64 eps x) #s(literal 1/12 binary64) #s(literal -1/2 binary64)))) #s(literal 1 binary64))) #<representation binary64>) () ())
#s(alt (fma.f64 x (fma.f64 eps #s(literal -1/2 binary64) (.f64 x (fma.f64 (.f64 eps x) #s(literal 1/12 binary64) #s(literal -1/2 binary64)))) #s(literal 1 binary64)) (patch (fma.f64 x (fma.f64 eps #s(literal -1/2 binary64) (.f64 x (fma.f64 (.f64 eps x) #s(literal 1/12 binary64) #s(literal -1/2 binary64)))) #s(literal 1 binary64)) #<representation binary64>) () ())
#s(alt (fma.f64 x (.f64 x (.f64 eps (fma.f64 (.f64 x x) #s(literal -1/720 binary64) #s(literal 1/24 binary64)))) (.f64 eps #s(literal -1/2 binary64))) (patch (fma.f64 x (.f64 x (.f64 eps (fma.f64 (.f64 x x) #s(literal -1/720 binary64) #s(literal 1/24 binary64)))) (.f64 eps #s(literal -1/2 binary64))) #<representation binary64>) () ())
#s(alt #s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* eps (cos x)) (fma.f64 (.f64 x x) (fma.f64 x (.f64 x (.f64 eps (fma.f64 (.f64 x x) #s(literal -1/720 binary64) #s(literal 1/24 binary64)))) (.f64 eps #s(literal -1/2 binary64))) eps))) (patch #s(approx (- (sin (+ x eps)) (sin x)) #s(approx ( eps (cos x)) (fma.f64 (.f64 x x) (fma.f64 x (.f64 x (.f64 eps (fma.f64 (.f64 x x) #s(literal -1/720 binary64) #s(literal 1/24 binary64)))) (*.f64 eps #s(literal -1/2 binary64))) eps))) #<representation binary64>) () ())
#s(alt #s(approx (* eps (cos x)) (fma.f64 (.f64 x x) (fma.f64 x (.f64 x (.f64 eps (fma.f64 (.f64 x x) #s(literal -1/720 binary64) #s(literal 1/24 binary64)))) (.f64 eps #s(literal -1/2 binary64))) eps)) (patch #s(approx ( eps (cos x)) (fma.f64 (.f64 x x) (fma.f64 x (.f64 x (.f64 eps (fma.f64 (.f64 x x) #s(literal -1/720 binary64) #s(literal 1/24 binary64)))) (*.f64 eps #s(literal -1/2 binary64))) eps)) #<representation binary64>) () ())
#s(alt (fma.f64 (.f64 x x) (fma.f64 x (.f64 x (.f64 eps (fma.f64 (.f64 x x) #s(literal -1/720 binary64) #s(literal 1/24 binary64)))) (.f64 eps #s(literal -1/2 binary64))) eps) (patch (fma.f64 (.f64 x x) (fma.f64 x (.f64 x (.f64 eps (fma.f64 (.f64 x x) #s(literal -1/720 binary64) #s(literal 1/24 binary64)))) (.f64 eps #s(literal -1/2 binary64))) eps) #<representation binary64>) () ())
#s(alt (.f64 #s(approx ( (sin (* (+ eps 0) 1/2)) (cos (* (+ (* x 2) eps) 1/2))) (.f64 #s(approx (sin ( 1/2 eps)) (.f64 eps (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal 1/2 binary64)))) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)))) #s(literal 2 binary64)) (patch (.f64 #s(approx ( (sin (* (+ eps 0) 1/2)) (cos (* (+ (* x 2) eps) 1/2))) (.f64 #s(approx (sin ( 1/2 eps)) (.f64 eps (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal 1/2 binary64)))) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)))) #s(literal 2 binary64)) #<representation binary64>) () ())
#s(alt #s(approx (* (sin (* (+ eps 0) 1/2)) (cos (* (+ (* x 2) eps) 1/2))) (.f64 #s(approx (sin ( 1/2 eps)) (.f64 eps (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal 1/2 binary64)))) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)))) (patch #s(approx (* (sin (* (+ eps 0) 1/2)) (cos (* (+ (* x 2) eps) 1/2))) (.f64 #s(approx (sin ( 1/2 eps)) (.f64 eps (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal 1/2 binary64)))) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)))) #<representation binary64>) () ())
#s(alt (.f64 #s(approx (sin ( 1/2 eps)) (.f64 eps (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal 1/2 binary64)))) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x))) (patch (.f64 #s(approx (sin ( 1/2 eps)) (.f64 eps (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal 1/2 binary64)))) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x))) #<representation binary64>) () ())
#s(alt #s(approx (sin (* 1/2 eps)) (.f64 eps (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal 1/2 binary64)))) (patch #s(approx (sin (* 1/2 eps)) (.f64 eps (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal 1/2 binary64)))) #<representation binary64>) () ())
#s(alt (.f64 eps (fma.f64 (.f64 eps eps) (fma.f64 eps (.f64 eps #s(literal -1/645120 binary64)) #s(literal 1/3840 binary64)) #s(literal -1/48 binary64))) (patch (.f64 eps (fma.f64 (.f64 eps eps) (fma.f64 eps (.f64 eps #s(literal -1/645120 binary64)) #s(literal 1/3840 binary64)) #s(literal -1/48 binary64))) #<representation binary64>) () ())
#s(alt (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) (patch (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) #<representation binary64>) () ())
#s(alt #s(approx (+ (* 1/24 (* x x)) -1/2) #s(literal -1/2 binary64)) (patch #s(approx (+ (* 1/24 (* x x)) -1/2) #s(literal -1/2 binary64)) #<representation binary64>) () ())
#s(alt (fma.f64 eps #s(literal -1/2 binary64) (.f64 x (fma.f64 (.f64 eps x) #s(literal 1/12 binary64) #s(literal -1/2 binary64)))) (patch (fma.f64 eps #s(literal -1/2 binary64) (.f64 x (fma.f64 (.f64 eps x) #s(literal 1/12 binary64) #s(literal -1/2 binary64)))) #<representation binary64>) () ())
#s(alt (.f64 eps (fma.f64 (.f64 x x) #s(literal -1/720 binary64) #s(literal 1/24 binary64))) (patch (.f64 eps (fma.f64 (.f64 x x) #s(literal -1/720 binary64) #s(literal 1/24 binary64))) #<representation binary64>) () ())
#s(alt (.f64 x (.f64 eps (fma.f64 (.f64 x x) #s(literal -1/720 binary64) #s(literal 1/24 binary64)))) (patch (.f64 x (.f64 eps (fma.f64 (.f64 x x) #s(literal -1/720 binary64) #s(literal 1/24 binary64)))) #<representation binary64>) () ())
#s(alt (.f64 eps (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal 1/2 binary64))) (patch (.f64 eps (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal 1/2 binary64))) #<representation binary64>) () ())

Outputs
#s(alt (* eps (cos x)) (taylor 0 eps) (#s(alt (.f64 #s(approx ( (sin (* (+ eps 0) 1/2)) (cos (* (+ (* x 2) eps) 1/2))) (.f64 #s(approx (sin ( 1/2 eps)) (.f64 eps (fma.f64 eps (.f64 eps (fma.f64 (.f64 eps eps) (fma.f64 eps (.f64 eps #s(literal -1/645120 binary64)) #s(literal 1/3840 binary64)) #s(literal -1/48 binary64))) #s(literal 1/2 binary64)))) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)))) #s(literal 2 binary64)) (patch (.f64 #s(approx ( (sin (* (+ eps 0) 1/2)) (cos (* (+ (* x 2) eps) 1/2))) (.f64 #s(approx (sin ( 1/2 eps)) (.f64 eps (fma.f64 eps (.f64 eps (fma.f64 (.f64 eps eps) (fma.f64 eps (.f64 eps #s(literal -1/645120 binary64)) #s(literal 1/3840 binary64)) #s(literal -1/48 binary64))) #s(literal 1/2 binary64)))) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)))) #s(literal 2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* eps (+ (cos x) (* -1/2 (* eps (sin x))))) (taylor 0 eps) (#s(alt (.f64 #s(approx ( (sin (* (+ eps 0) 1/2)) (cos (* (+ (* x 2) eps) 1/2))) (.f64 #s(approx (sin ( 1/2 eps)) (.f64 eps (fma.f64 eps (.f64 eps (fma.f64 (.f64 eps eps) (fma.f64 eps (.f64 eps #s(literal -1/645120 binary64)) #s(literal 1/3840 binary64)) #s(literal -1/48 binary64))) #s(literal 1/2 binary64)))) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)))) #s(literal 2 binary64)) (patch (.f64 #s(approx ( (sin (* (+ eps 0) 1/2)) (cos (* (+ (* x 2) eps) 1/2))) (.f64 #s(approx (sin ( 1/2 eps)) (.f64 eps (fma.f64 eps (.f64 eps (fma.f64 (.f64 eps eps) (fma.f64 eps (.f64 eps #s(literal -1/645120 binary64)) #s(literal 1/3840 binary64)) #s(literal -1/48 binary64))) #s(literal 1/2 binary64)))) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)))) #s(literal 2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* 2 (* eps (+ (* -1/16 (cos x)) (* -1/48 (cos x))))))))) (taylor 0 eps) (#s(alt (.f64 #s(approx ( (sin (* (+ eps 0) 1/2)) (cos (* (+ (* x 2) eps) 1/2))) (.f64 #s(approx (sin ( 1/2 eps)) (.f64 eps (fma.f64 eps (.f64 eps (fma.f64 (.f64 eps eps) (fma.f64 eps (.f64 eps #s(literal -1/645120 binary64)) #s(literal 1/3840 binary64)) #s(literal -1/48 binary64))) #s(literal 1/2 binary64)))) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)))) #s(literal 2 binary64)) (patch (.f64 #s(approx ( (sin (* (+ eps 0) 1/2)) (cos (* (+ (* x 2) eps) 1/2))) (.f64 #s(approx (sin ( 1/2 eps)) (.f64 eps (fma.f64 eps (.f64 eps (fma.f64 (.f64 eps eps) (fma.f64 eps (.f64 eps #s(literal -1/645120 binary64)) #s(literal 1/3840 binary64)) #s(literal -1/48 binary64))) #s(literal 1/2 binary64)))) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)))) #s(literal 2 binary64)) #<representation binary64>) () ())) ())
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#s(alt (* x (+ (* -1/720 (* eps (pow x 2))) (* 1/24 eps))) (taylor 0 x) (#s(alt (.f64 x (.f64 eps (fma.f64 (.f64 x x) #s(literal -1/720 binary64) #s(literal 1/24 binary64)))) (patch (.f64 x (.f64 eps (fma.f64 (.f64 x x) #s(literal -1/720 binary64) #s(literal 1/24 binary64)))) #<representation binary64>) () ())) ())
#s(alt (* -1/720 (* eps (pow x 3))) (taylor inf x) (#s(alt (.f64 x (.f64 eps (fma.f64 (.f64 x x) #s(literal -1/720 binary64) #s(literal 1/24 binary64)))) (patch (.f64 x (.f64 eps (fma.f64 (.f64 x x) #s(literal -1/720 binary64) #s(literal 1/24 binary64)))) #<representation binary64>) () ())) ())
#s(alt (* (pow x 3) (+ (* -1/720 eps) (* 1/24 (/ eps (pow x 2))))) (taylor inf x) (#s(alt (.f64 x (.f64 eps (fma.f64 (.f64 x x) #s(literal -1/720 binary64) #s(literal 1/24 binary64)))) (patch (.f64 x (.f64 eps (fma.f64 (.f64 x x) #s(literal -1/720 binary64) #s(literal 1/24 binary64)))) #<representation binary64>) () ())) ())
#s(alt (* (pow x 3) (+ (* -1/720 eps) (* 1/24 (/ eps (pow x 2))))) (taylor inf x) (#s(alt (.f64 x (.f64 eps (fma.f64 (.f64 x x) #s(literal -1/720 binary64) #s(literal 1/24 binary64)))) (patch (.f64 x (.f64 eps (fma.f64 (.f64 x x) #s(literal -1/720 binary64) #s(literal 1/24 binary64)))) #<representation binary64>) () ())) ())
#s(alt (* (pow x 3) (+ (* -1/720 eps) (* 1/24 (/ eps (pow x 2))))) (taylor inf x) (#s(alt (.f64 x (.f64 eps (fma.f64 (.f64 x x) #s(literal -1/720 binary64) #s(literal 1/24 binary64)))) (patch (.f64 x (.f64 eps (fma.f64 (.f64 x x) #s(literal -1/720 binary64) #s(literal 1/24 binary64)))) #<representation binary64>) () ())) ())
#s(alt (* -1/720 (* eps (pow x 3))) (taylor -inf x) (#s(alt (.f64 x (.f64 eps (fma.f64 (.f64 x x) #s(literal -1/720 binary64) #s(literal 1/24 binary64)))) (patch (.f64 x (.f64 eps (fma.f64 (.f64 x x) #s(literal -1/720 binary64) #s(literal 1/24 binary64)))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* (pow x 3) (+ (* -1/24 (/ eps (pow x 2))) (* 1/720 eps)))) (taylor -inf x) (#s(alt (.f64 x (.f64 eps (fma.f64 (.f64 x x) #s(literal -1/720 binary64) #s(literal 1/24 binary64)))) (patch (.f64 x (.f64 eps (fma.f64 (.f64 x x) #s(literal -1/720 binary64) #s(literal 1/24 binary64)))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* (pow x 3) (+ (* -1/24 (/ eps (pow x 2))) (* 1/720 eps)))) (taylor -inf x) (#s(alt (.f64 x (.f64 eps (fma.f64 (.f64 x x) #s(literal -1/720 binary64) #s(literal 1/24 binary64)))) (patch (.f64 x (.f64 eps (fma.f64 (.f64 x x) #s(literal -1/720 binary64) #s(literal 1/24 binary64)))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* (pow x 3) (+ (* -1/24 (/ eps (pow x 2))) (* 1/720 eps)))) (taylor -inf x) (#s(alt (.f64 x (.f64 eps (fma.f64 (.f64 x x) #s(literal -1/720 binary64) #s(literal 1/24 binary64)))) (patch (.f64 x (.f64 eps (fma.f64 (.f64 x x) #s(literal -1/720 binary64) #s(literal 1/24 binary64)))) #<representation binary64>) () ())) ())
#s(alt (* eps (* x (+ 1/24 (* -1/720 (pow x 2))))) (taylor 0 eps) (#s(alt (.f64 x (.f64 eps (fma.f64 (.f64 x x) #s(literal -1/720 binary64) #s(literal 1/24 binary64)))) (patch (.f64 x (.f64 eps (fma.f64 (.f64 x x) #s(literal -1/720 binary64) #s(literal 1/24 binary64)))) #<representation binary64>) () ())) ())
#s(alt (* eps (* x (+ 1/24 (* -1/720 (pow x 2))))) (taylor 0 eps) (#s(alt (.f64 x (.f64 eps (fma.f64 (.f64 x x) #s(literal -1/720 binary64) #s(literal 1/24 binary64)))) (patch (.f64 x (.f64 eps (fma.f64 (.f64 x x) #s(literal -1/720 binary64) #s(literal 1/24 binary64)))) #<representation binary64>) () ())) ())
#s(alt (* eps (* x (+ 1/24 (* -1/720 (pow x 2))))) (taylor 0 eps) (#s(alt (.f64 x (.f64 eps (fma.f64 (.f64 x x) #s(literal -1/720 binary64) #s(literal 1/24 binary64)))) (patch (.f64 x (.f64 eps (fma.f64 (.f64 x x) #s(literal -1/720 binary64) #s(literal 1/24 binary64)))) #<representation binary64>) () ())) ())
#s(alt (* eps (* x (+ 1/24 (* -1/720 (pow x 2))))) (taylor 0 eps) (#s(alt (.f64 x (.f64 eps (fma.f64 (.f64 x x) #s(literal -1/720 binary64) #s(literal 1/24 binary64)))) (patch (.f64 x (.f64 eps (fma.f64 (.f64 x x) #s(literal -1/720 binary64) #s(literal 1/24 binary64)))) #<representation binary64>) () ())) ())
#s(alt (* eps (* x (+ 1/24 (* -1/720 (pow x 2))))) (taylor inf eps) (#s(alt (.f64 x (.f64 eps (fma.f64 (.f64 x x) #s(literal -1/720 binary64) #s(literal 1/24 binary64)))) (patch (.f64 x (.f64 eps (fma.f64 (.f64 x x) #s(literal -1/720 binary64) #s(literal 1/24 binary64)))) #<representation binary64>) () ())) ())
#s(alt (* eps (* x (+ 1/24 (* -1/720 (pow x 2))))) (taylor inf eps) (#s(alt (.f64 x (.f64 eps (fma.f64 (.f64 x x) #s(literal -1/720 binary64) #s(literal 1/24 binary64)))) (patch (.f64 x (.f64 eps (fma.f64 (.f64 x x) #s(literal -1/720 binary64) #s(literal 1/24 binary64)))) #<representation binary64>) () ())) ())
#s(alt (* eps (* x (+ 1/24 (* -1/720 (pow x 2))))) (taylor inf eps) (#s(alt (.f64 x (.f64 eps (fma.f64 (.f64 x x) #s(literal -1/720 binary64) #s(literal 1/24 binary64)))) (patch (.f64 x (.f64 eps (fma.f64 (.f64 x x) #s(literal -1/720 binary64) #s(literal 1/24 binary64)))) #<representation binary64>) () ())) ())
#s(alt (* eps (* x (+ 1/24 (* -1/720 (pow x 2))))) (taylor inf eps) (#s(alt (.f64 x (.f64 eps (fma.f64 (.f64 x x) #s(literal -1/720 binary64) #s(literal 1/24 binary64)))) (patch (.f64 x (.f64 eps (fma.f64 (.f64 x x) #s(literal -1/720 binary64) #s(literal 1/24 binary64)))) #<representation binary64>) () ())) ())
#s(alt (* eps (* x (+ 1/24 (* -1/720 (pow x 2))))) (taylor -inf eps) (#s(alt (.f64 x (.f64 eps (fma.f64 (.f64 x x) #s(literal -1/720 binary64) #s(literal 1/24 binary64)))) (patch (.f64 x (.f64 eps (fma.f64 (.f64 x x) #s(literal -1/720 binary64) #s(literal 1/24 binary64)))) #<representation binary64>) () ())) ())
#s(alt (* eps (* x (+ 1/24 (* -1/720 (pow x 2))))) (taylor -inf eps) (#s(alt (.f64 x (.f64 eps (fma.f64 (.f64 x x) #s(literal -1/720 binary64) #s(literal 1/24 binary64)))) (patch (.f64 x (.f64 eps (fma.f64 (.f64 x x) #s(literal -1/720 binary64) #s(literal 1/24 binary64)))) #<representation binary64>) () ())) ())
#s(alt (* eps (* x (+ 1/24 (* -1/720 (pow x 2))))) (taylor -inf eps) (#s(alt (.f64 x (.f64 eps (fma.f64 (.f64 x x) #s(literal -1/720 binary64) #s(literal 1/24 binary64)))) (patch (.f64 x (.f64 eps (fma.f64 (.f64 x x) #s(literal -1/720 binary64) #s(literal 1/24 binary64)))) #<representation binary64>) () ())) ())
#s(alt (* eps (* x (+ 1/24 (* -1/720 (pow x 2))))) (taylor -inf eps) (#s(alt (.f64 x (.f64 eps (fma.f64 (.f64 x x) #s(literal -1/720 binary64) #s(literal 1/24 binary64)))) (patch (.f64 x (.f64 eps (fma.f64 (.f64 x x) #s(literal -1/720 binary64) #s(literal 1/24 binary64)))) #<representation binary64>) () ())) ())
#s(alt (* 1/2 eps) (taylor 0 eps) (#s(alt (.f64 eps (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal 1/2 binary64))) (patch (.f64 eps (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal 1/2 binary64))) #<representation binary64>) () ())) ())
#s(alt (* eps (+ 1/2 (* -1/48 (pow eps 2)))) (taylor 0 eps) (#s(alt (.f64 eps (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal 1/2 binary64))) (patch (.f64 eps (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal 1/2 binary64))) #<representation binary64>) () ())) ())
#s(alt (* eps (+ 1/2 (* -1/48 (pow eps 2)))) (taylor 0 eps) (#s(alt (.f64 eps (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal 1/2 binary64))) (patch (.f64 eps (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal 1/2 binary64))) #<representation binary64>) () ())) ())
#s(alt (* eps (+ 1/2 (* -1/48 (pow eps 2)))) (taylor 0 eps) (#s(alt (.f64 eps (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal 1/2 binary64))) (patch (.f64 eps (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal 1/2 binary64))) #<representation binary64>) () ())) ())
#s(alt (* -1/48 (pow eps 3)) (taylor inf eps) (#s(alt (.f64 eps (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal 1/2 binary64))) (patch (.f64 eps (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal 1/2 binary64))) #<representation binary64>) () ())) ())
#s(alt (* (pow eps 3) (- (* 1/2 (/ 1 (pow eps 2))) 1/48)) (taylor inf eps) (#s(alt (.f64 eps (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal 1/2 binary64))) (patch (.f64 eps (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal 1/2 binary64))) #<representation binary64>) () ())) ())
#s(alt (* (pow eps 3) (- (* 1/2 (/ 1 (pow eps 2))) 1/48)) (taylor inf eps) (#s(alt (.f64 eps (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal 1/2 binary64))) (patch (.f64 eps (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal 1/2 binary64))) #<representation binary64>) () ())) ())
#s(alt (* (pow eps 3) (- (* 1/2 (/ 1 (pow eps 2))) 1/48)) (taylor inf eps) (#s(alt (.f64 eps (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal 1/2 binary64))) (patch (.f64 eps (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal 1/2 binary64))) #<representation binary64>) () ())) ())
#s(alt (* -1/48 (pow eps 3)) (taylor -inf eps) (#s(alt (.f64 eps (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal 1/2 binary64))) (patch (.f64 eps (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal 1/2 binary64))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* (pow eps 3) (- 1/48 (* 1/2 (/ 1 (pow eps 2)))))) (taylor -inf eps) (#s(alt (.f64 eps (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal 1/2 binary64))) (patch (.f64 eps (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal 1/2 binary64))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* (pow eps 3) (- 1/48 (* 1/2 (/ 1 (pow eps 2)))))) (taylor -inf eps) (#s(alt (.f64 eps (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal 1/2 binary64))) (patch (.f64 eps (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal 1/2 binary64))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* (pow eps 3) (- 1/48 (* 1/2 (/ 1 (pow eps 2)))))) (taylor -inf eps) (#s(alt (.f64 eps (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal 1/2 binary64))) (patch (.f64 eps (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal 1/2 binary64))) #<representation binary64>) () ())) ())

Calls

141 calls:

Time	Variable		Point	Expression
5.0ms	eps	@	inf	(* eps (+ (* (* x x) -1/720) 1/24))
3.0ms	x	@	inf	(+ (* (* x x) (+ (* x (* x (* eps (+ (* (* x x) -1/720) 1/24)))) (* eps -1/2))) eps)
1.0ms	eps	@	0	(+ (* x (* x (* eps (+ (* (* x x) -1/720) 1/24)))) (* eps -1/2))
1.0ms	eps	@	inf	(+ (* x (+ (* eps -1/2) (* x (+ (* (* eps x) 1/12) -1/2)))) 1)
1.0ms	eps	@	0	(* eps (+ (* (* eps eps) (+ (* eps (* eps -1/645120)) 1/3840)) -1/48))

simplify307.0ms (2.3%)

Memory

22.2MiB live, 343.1MiB allocated

Algorithm

1×	egg-herbie

Rules

13 018×	`lower-fma.f64`
13 018×	`lower-fma.f32`
7 368×	`lower-*.f64`
7 368×	`lower-*.f32`
3 582×	`lower-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	450	6809
1	1400	6474
2	4087	6417
0	8621	5902

Stop Event

1×	iter limit
1×	node limit

Counts

564 → 560

Calls

Call 1

Inputs
(* eps (cos x))
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* 2 (* eps (+ (* -1/16 (cos x)) (* -1/48 (cos x)))))))))
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* eps (+ (* 1/24 (* eps (sin x))) (* 2 (+ (* -1/16 (cos x)) (* -1/48 (cos x))))))))))
(* 2 (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))))
(* 2 (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))))
(* 2 (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))))
(* 2 (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))))
(* 2 (* (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps))))
(* 2 (* (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps))))
(* 2 (* (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps))))
(* 2 (* (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps))))
(* 2 (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))
(+ (* -2 (* x (pow (sin (* 1/2 eps)) 2))) (* 2 (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))))
(+ (* 2 (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) (* x (+ (* -2 (pow (sin (* 1/2 eps)) 2)) (* -1 (* x (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))))))
(+ (* 2 (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) (* x (+ (* -2 (pow (sin (* 1/2 eps)) 2)) (* x (+ (* -1 (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) (* 1/3 (* x (pow (sin (* 1/2 eps)) 2))))))))
(* 2 (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))))
(* 2 (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))))
(* 2 (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))))
(* 2 (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))))
(* 2 (* (cos (* 1/2 (- eps (* -2 x)))) (sin (* 1/2 eps))))
(* 2 (* (cos (* 1/2 (- eps (* -2 x)))) (sin (* 1/2 eps))))
(* 2 (* (cos (* 1/2 (- eps (* -2 x)))) (sin (* 1/2 eps))))
(* 2 (* (cos (* 1/2 (- eps (* -2 x)))) (sin (* 1/2 eps))))
(* 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 (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 (+ x (* 1/2 eps))) (sin (* 1/2 eps)))
(* (cos (+ x (* 1/2 eps))) (sin (* 1/2 eps)))
(* (cos (+ x (* 1/2 eps))) (sin (* 1/2 eps)))
(* (cos (+ x (* 1/2 eps))) (sin (* 1/2 eps)))
(* (cos (- x (* -1/2 eps))) (sin (* 1/2 eps)))
(* (cos (- x (* -1/2 eps))) (sin (* 1/2 eps)))
(* (cos (- x (* -1/2 eps))) (sin (* 1/2 eps)))
(* (cos (- x (* -1/2 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 (+ x (* 1/2 eps))) (sin (* 1/2 eps)))
(* (cos (+ x (* 1/2 eps))) (sin (* 1/2 eps)))
(* (cos (+ x (* 1/2 eps))) (sin (* 1/2 eps)))
(* (cos (+ x (* 1/2 eps))) (sin (* 1/2 eps)))
(* (cos (- (* 1/2 eps) (* -1 x))) (sin (* 1/2 eps)))
(* (cos (- (* 1/2 eps) (* -1 x))) (sin (* 1/2 eps)))
(* (cos (- (* 1/2 eps) (* -1 x))) (sin (* 1/2 eps)))
(* (cos (- (* 1/2 eps) (* -1 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))
(* eps (cos x))
(* eps (cos x))
(* eps (cos x))
(* eps (cos x))
(* eps (cos x))
(* eps (cos x))
(* eps (cos x))
(* eps (cos x))
(* eps (cos x))
(* eps (cos x))
eps
(+ eps (* -1/2 (* eps (pow x 2))))
(+ eps (* (pow x 2) (+ (* -1/2 eps) (* 1/24 (* eps (pow x 2))))))
(+ eps (* (pow x 2) (+ (* -1/2 eps) (* (pow x 2) (+ (* -1/720 (* eps (pow x 2))) (* 1/24 eps))))))
(* eps (cos x))
(* eps (cos x))
(* eps (cos x))
(* eps (cos x))
(* eps (cos x))
(* eps (cos x))
(* eps (cos x))
(* eps (cos x))
1
(+ 1 (* -1/2 (pow x 2)))
(+ 1 (* (pow x 2) (- (* 1/24 (pow x 2)) 1/2)))
(+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))) 1/2)))
(cos x)
(cos x)
(cos x)
(cos x)
(cos x)
(cos x)
(cos x)
(cos x)
1
(+ 1 (* -1/2 (pow x 2)))
(+ 1 (* (pow x 2) (- (* 1/24 (pow x 2)) 1/2)))
(+ 1 (* (pow x 2) (- (* 1/24 (pow x 2)) 1/2)))
(* 1/24 (pow x 4))
(* (pow x 4) (- 1/24 (* 1/2 (/ 1 (pow x 2)))))
(* (pow x 4) (- (+ 1/24 (/ 1 (pow x 4))) (* 1/2 (/ 1 (pow x 2)))))
(* (pow x 4) (- (+ 1/24 (/ 1 (pow x 4))) (* 1/2 (/ 1 (pow x 2)))))
(* 1/24 (pow x 4))
(* (pow x 4) (- 1/24 (* 1/2 (/ 1 (pow x 2)))))
(* (pow x 4) (- (+ 1/24 (/ 1 (pow x 4))) (* 1/2 (/ 1 (pow x 2)))))
(* (pow x 4) (- (+ 1/24 (/ 1 (pow x 4))) (* 1/2 (/ 1 (pow x 2)))))
(sin eps)
(+ (sin eps) (* x (- (cos eps) 1)))
(+ (sin eps) (* x (- (+ (cos eps) (* -1/2 (* x (sin eps)))) 1)))
(+ (sin eps) (* x (- (+ (cos eps) (* x (+ (* -1/2 (sin eps)) (* x (+ 1/6 (* -1/6 (cos eps))))))) 1)))
(- (sin (+ eps x)) (sin x))
(- (sin (+ eps x)) (sin x))
(- (sin (+ eps x)) (sin x))
(- (sin (+ eps x)) (sin x))
(- (sin (- eps (* -1 x))) (sin x))
(- (sin (- eps (* -1 x))) (sin x))
(- (sin (- eps (* -1 x))) (sin x))
(- (sin (- eps (* -1 x))) (sin x))
(* eps (cos x))
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x)))))))
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* eps (+ (* -1/6 (cos x)) (* 1/24 (* eps (sin x)))))))))
(- (sin (+ eps x)) (sin x))
(- (sin (+ eps x)) (sin x))
(- (sin (+ eps x)) (sin x))
(- (sin (+ eps x)) (sin x))
(- (sin (- x (* -1 eps))) (sin x))
(- (sin (- x (* -1 eps))) (sin x))
(- (sin (- x (* -1 eps))) (sin x))
(- (sin (- x (* -1 eps))) (sin x))
(* eps (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 (* x (+ (* -1/2 eps) (* -1/2 x))))
(+ 1 (* x (+ (* -1/2 eps) (* x (- (* 1/12 (* eps x)) 1/2)))))
(* 1/12 (* eps (pow x 3)))
(* (pow x 3) (- (* 1/12 eps) (* 1/2 (/ 1 x))))
(* (pow x 3) (- (+ (* -1/2 (/ eps (pow x 2))) (* 1/12 eps)) (* 1/2 (/ 1 x))))
(* (pow x 3) (- (+ (* -1/2 (/ eps (pow x 2))) (+ (* 1/12 eps) (/ 1 (pow x 3)))) (* 1/2 (/ 1 x))))
(* 1/12 (* eps (pow x 3)))
(* -1 (* (pow x 3) (+ (* -1/12 eps) (* 1/2 (/ 1 x)))))
(* -1 (* (pow x 3) (+ (* -1 (/ (- (* -1/2 (/ eps x)) 1/2) x)) (* -1/12 eps))))
(* -1 (* (pow x 3) (+ (* -1 (/ (- (* -1 (/ (- (* 1/2 eps) (/ 1 x)) x)) 1/2) x)) (* -1/12 eps))))
(+ 1 (* -1/2 (pow x 2)))
(+ 1 (+ (* -1/2 (pow x 2)) (* eps (* x (- (* 1/12 (pow x 2)) 1/2)))))
(+ 1 (+ (* -1/2 (pow x 2)) (* eps (* x (- (* 1/12 (pow x 2)) 1/2)))))
(+ 1 (+ (* -1/2 (pow x 2)) (* eps (* x (- (* 1/12 (pow x 2)) 1/2)))))
(* eps (* x (- (* 1/12 (pow x 2)) 1/2)))
(* eps (+ (* -1/2 (/ (pow x 2) eps)) (+ (* x (- (* 1/12 (pow x 2)) 1/2)) (/ 1 eps))))
(* eps (+ (* -1/2 (/ (pow x 2) eps)) (+ (* x (- (* 1/12 (pow x 2)) 1/2)) (/ 1 eps))))
(* eps (+ (* -1/2 (/ (pow x 2) eps)) (+ (* x (- (* 1/12 (pow x 2)) 1/2)) (/ 1 eps))))
(* -1 (* eps (* x (+ 1/2 (* -1/12 (pow x 2))))))
(* -1 (* eps (+ (* -1 (/ (+ 1 (* -1/2 (pow x 2))) eps)) (* x (+ 1/2 (* -1/12 (pow x 2)))))))
(* -1 (* eps (+ (* -1 (/ (+ 1 (* -1/2 (pow x 2))) eps)) (* x (+ 1/2 (* -1/12 (pow x 2)))))))
(* -1 (* eps (+ (* -1 (/ (+ 1 (* -1/2 (pow x 2))) eps)) (* x (+ 1/2 (* -1/12 (pow x 2)))))))
(* -1/2 eps)
(+ (* -1/2 eps) (* 1/24 (* eps (pow x 2))))
(+ (* -1/2 eps) (* (pow x 2) (+ (* -1/720 (* eps (pow x 2))) (* 1/24 eps))))
(+ (* -1/2 eps) (* (pow x 2) (+ (* -1/720 (* eps (pow x 2))) (* 1/24 eps))))
(* -1/720 (* eps (pow x 4)))
(* (pow x 4) (+ (* -1/720 eps) (* 1/24 (/ eps (pow x 2)))))
(* (pow x 4) (+ (* -1/2 (/ eps (pow x 4))) (+ (* -1/720 eps) (* 1/24 (/ eps (pow x 2))))))
(* (pow x 4) (+ (* -1/2 (/ eps (pow x 4))) (+ (* -1/720 eps) (* 1/24 (/ eps (pow x 2))))))
(* -1/720 (* eps (pow x 4)))
(* (pow x 4) (+ (* -1/720 eps) (* 1/24 (/ eps (pow x 2)))))
(* (pow x 4) (+ (* -1/2 (/ eps (pow x 4))) (+ (* -1/720 eps) (* 1/24 (/ eps (pow x 2))))))
(* (pow x 4) (+ (* -1/2 (/ eps (pow x 4))) (+ (* -1/720 eps) (* 1/24 (/ eps (pow x 2))))))
(* eps (- (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))) 1/2))
(* eps (- (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))) 1/2))
(* eps (- (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))) 1/2))
(* eps (- (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))) 1/2))
(* eps (- (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))) 1/2))
(* eps (- (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))) 1/2))
(* eps (- (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))) 1/2))
(* eps (- (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))) 1/2))
(* -1 (* eps (+ 1/2 (* -1 (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2))))))))
(* -1 (* eps (+ 1/2 (* -1 (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2))))))))
(* -1 (* eps (+ 1/2 (* -1 (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2))))))))
(* -1 (* eps (+ 1/2 (* -1 (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2))))))))
(sin eps)
(+ (sin eps) (* x (- (cos eps) 1)))
(+ (sin eps) (* x (- (+ (cos eps) (* -1/2 (* x (sin eps)))) 1)))
(+ (sin eps) (* x (- (+ (cos eps) (* x (+ (* -1/2 (sin eps)) (* x (+ 1/6 (* -1/6 (cos eps))))))) 1)))
(- (sin (+ eps x)) (sin x))
(- (sin (+ eps x)) (sin x))
(- (sin (+ eps x)) (sin x))
(- (sin (+ eps x)) (sin x))
(- (sin (- eps (* -1 x))) (sin x))
(- (sin (- eps (* -1 x))) (sin x))
(- (sin (- eps (* -1 x))) (sin x))
(- (sin (- eps (* -1 x))) (sin x))
(* eps (cos x))
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x)))))))
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* eps (+ (* -1/6 (cos x)) (* 1/24 (* eps (sin x)))))))))
(- (sin (+ eps x)) (sin x))
(- (sin (+ eps x)) (sin x))
(- (sin (+ eps x)) (sin x))
(- (sin (+ eps x)) (sin x))
(- (sin (- x (* -1 eps))) (sin x))
(- (sin (- x (* -1 eps))) (sin x))
(- (sin (- x (* -1 eps))) (sin x))
(- (sin (- x (* -1 eps))) (sin x))
(* eps (cos x))
(* eps (cos x))
(* eps (cos x))
(* eps (cos x))
(* eps (cos x))
(* eps (cos x))
(* eps (cos x))
(* eps (cos x))
(* eps (cos x))
(* eps (cos x))
(* eps (cos x))
(* eps (cos x))
eps
(+ eps (* -1/2 (* eps (pow x 2))))
(+ eps (* (pow x 2) (+ (* -1/2 eps) (* 1/24 (* eps (pow x 2))))))
(+ eps (* (pow x 2) (+ (* -1/2 eps) (* (pow x 2) (+ (* -1/720 (* eps (pow x 2))) (* 1/24 eps))))))
(* eps (cos x))
(* eps (cos x))
(* eps (cos x))
(* eps (cos x))
(* eps (cos x))
(* eps (cos x))
(* eps (cos x))
(* eps (cos x))
eps
(+ eps (* -1/2 (* eps (pow x 2))))
(+ eps (* (pow x 2) (+ (* -1/2 eps) (* 1/24 (* eps (pow x 2))))))
(+ eps (* (pow x 2) (+ (* -1/2 eps) (* (pow x 2) (+ (* -1/720 (* eps (pow x 2))) (* 1/24 eps))))))
(* -1/720 (* eps (pow x 6)))
(* (pow x 6) (+ (* -1/720 eps) (* 1/24 (/ eps (pow x 2)))))
(* (pow x 6) (+ (* -1/2 (/ eps (pow x 4))) (+ (* -1/720 eps) (* 1/24 (/ eps (pow x 2))))))
(* (pow x 6) (+ (* -1/2 (/ eps (pow x 4))) (+ (* -1/720 eps) (+ (* 1/24 (/ eps (pow x 2))) (/ eps (pow x 6))))))
(* -1/720 (* eps (pow x 6)))
(* (pow x 6) (+ (* -1/720 eps) (* 1/24 (/ eps (pow x 2)))))
(* (pow x 6) (+ (* -1/2 (/ eps (pow x 4))) (+ (* -1/720 eps) (* 1/24 (/ eps (pow x 2))))))
(* (pow x 6) (+ (* -1/2 (/ eps (pow x 4))) (+ (* -1/720 eps) (+ (* 1/24 (/ eps (pow x 2))) (/ eps (pow x 6))))))
(* eps (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))) 1/2))))
(* eps (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))) 1/2))))
(* eps (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))) 1/2))))
(* eps (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))) 1/2))))
(* eps (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))) 1/2))))
(* eps (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))) 1/2))))
(* eps (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))) 1/2))))
(* eps (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))) 1/2))))
(* -1 (* eps (- (* (pow x 2) (+ 1/2 (* -1 (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2))))))) 1)))
(* -1 (* eps (- (* (pow x 2) (+ 1/2 (* -1 (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2))))))) 1)))
(* -1 (* eps (- (* (pow x 2) (+ 1/2 (* -1 (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2))))))) 1)))
(* -1 (* eps (- (* (pow x 2) (+ 1/2 (* -1 (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2))))))) 1)))
(* eps (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 (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 (+ x (* 1/2 eps))) (sin (* 1/2 eps)))
(* (cos (+ x (* 1/2 eps))) (sin (* 1/2 eps)))
(* (cos (+ x (* 1/2 eps))) (sin (* 1/2 eps)))
(* (cos (+ x (* 1/2 eps))) (sin (* 1/2 eps)))
(* (cos (- x (* -1/2 eps))) (sin (* 1/2 eps)))
(* (cos (- x (* -1/2 eps))) (sin (* 1/2 eps)))
(* (cos (- x (* -1/2 eps))) (sin (* 1/2 eps)))
(* (cos (- x (* -1/2 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 (+ x (* 1/2 eps))) (sin (* 1/2 eps)))
(* (cos (+ x (* 1/2 eps))) (sin (* 1/2 eps)))
(* (cos (+ x (* 1/2 eps))) (sin (* 1/2 eps)))
(* (cos (+ x (* 1/2 eps))) (sin (* 1/2 eps)))
(* (cos (- (* 1/2 eps) (* -1 x))) (sin (* 1/2 eps)))
(* (cos (- (* 1/2 eps) (* -1 x))) (sin (* 1/2 eps)))
(* (cos (- (* 1/2 eps) (* -1 x))) (sin (* 1/2 eps)))
(* (cos (- (* 1/2 eps) (* -1 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))
(* -1/48 eps)
(* eps (- (* 1/3840 (pow eps 2)) 1/48))
(* eps (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48))
(* eps (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48))
(* -1/645120 (pow eps 5))
(* (pow eps 5) (- (* 1/3840 (/ 1 (pow eps 2))) 1/645120))
(* (pow eps 5) (- (* 1/3840 (/ 1 (pow eps 2))) (+ 1/645120 (/ 1/48 (pow eps 4)))))
(* (pow eps 5) (- (* 1/3840 (/ 1 (pow eps 2))) (+ 1/645120 (/ 1/48 (pow eps 4)))))
(* -1/645120 (pow eps 5))
(* -1 (* (pow eps 5) (- 1/645120 (* 1/3840 (/ 1 (pow eps 2))))))
(* -1 (* (pow eps 5) (- (+ 1/645120 (/ 1/48 (pow eps 4))) (* 1/3840 (/ 1 (pow eps 2))))))
(* -1 (* (pow eps 5) (- (+ 1/645120 (/ 1/48 (pow eps 4))) (* 1/3840 (/ 1 (pow eps 2))))))
(cos x)
(+ (cos x) (* -1/2 (* eps (sin x))))
(+ (cos x) (* eps (- (* -1/8 (* eps (cos x))) (* 1/2 (sin x)))))
(+ (cos x) (* eps (- (* eps (+ (* -1/8 (cos x)) (* 1/48 (* eps (sin x))))) (* 1/2 (sin x)))))
(cos (+ x (* 1/2 eps)))
(cos (+ x (* 1/2 eps)))
(cos (+ x (* 1/2 eps)))
(cos (+ x (* 1/2 eps)))
(cos (- x (* -1/2 eps)))
(cos (- x (* -1/2 eps)))
(cos (- x (* -1/2 eps)))
(cos (- x (* -1/2 eps)))
(cos (* 1/2 eps))
(+ (cos (* 1/2 eps)) (* -1 (* x (sin (* 1/2 eps)))))
(+ (cos (* 1/2 eps)) (* x (- (* -1/2 (* x (cos (* 1/2 eps)))) (sin (* 1/2 eps)))))
(+ (cos (* 1/2 eps)) (* x (- (* x (+ (* -1/2 (cos (* 1/2 eps))) (* 1/6 (* x (sin (* 1/2 eps)))))) (sin (* 1/2 eps)))))
(cos (+ x (* 1/2 eps)))
(cos (+ x (* 1/2 eps)))
(cos (+ x (* 1/2 eps)))
(cos (+ x (* 1/2 eps)))
(cos (- (* 1/2 eps) (* -1 x)))
(cos (- (* 1/2 eps) (* -1 x)))
(cos (- (* 1/2 eps) (* -1 x)))
(cos (- (* 1/2 eps) (* -1 x)))
-1/2
(- (* 1/24 (pow x 2)) 1/2)
(- (* 1/24 (pow x 2)) 1/2)
(- (* 1/24 (pow x 2)) 1/2)
(* 1/24 (pow x 2))
(* (pow x 2) (- 1/24 (* 1/2 (/ 1 (pow x 2)))))
(* (pow x 2) (- 1/24 (* 1/2 (/ 1 (pow x 2)))))
(* (pow x 2) (- 1/24 (* 1/2 (/ 1 (pow x 2)))))
(* 1/24 (pow x 2))
(* (pow x 2) (- 1/24 (* 1/2 (/ 1 (pow x 2)))))
(* (pow x 2) (- 1/24 (* 1/2 (/ 1 (pow x 2)))))
(* (pow x 2) (- 1/24 (* 1/2 (/ 1 (pow x 2)))))
(* -1/2 x)
(+ (* -1/2 x) (* eps (- (* 1/12 (pow x 2)) 1/2)))
(+ (* -1/2 x) (* eps (- (* 1/12 (pow x 2)) 1/2)))
(+ (* -1/2 x) (* eps (- (* 1/12 (pow x 2)) 1/2)))
(* eps (- (* 1/12 (pow x 2)) 1/2))
(* eps (- (+ (* -1/2 (/ x eps)) (* 1/12 (pow x 2))) 1/2))
(* eps (- (+ (* -1/2 (/ x eps)) (* 1/12 (pow x 2))) 1/2))
(* eps (- (+ (* -1/2 (/ x eps)) (* 1/12 (pow x 2))) 1/2))
(* -1 (* eps (+ 1/2 (* -1/12 (pow x 2)))))
(* -1 (* eps (+ 1/2 (+ (* -1/12 (pow x 2)) (* 1/2 (/ x eps))))))
(* -1 (* eps (+ 1/2 (+ (* -1/12 (pow x 2)) (* 1/2 (/ x eps))))))
(* -1 (* eps (+ 1/2 (+ (* -1/12 (pow x 2)) (* 1/2 (/ x eps))))))
(* -1/2 eps)
(+ (* -1/2 eps) (* -1/2 x))
(+ (* -1/2 eps) (* x (- (* 1/12 (* eps x)) 1/2)))
(+ (* -1/2 eps) (* x (- (* 1/12 (* eps x)) 1/2)))
(* 1/12 (* eps (pow x 2)))
(* (pow x 2) (- (* 1/12 eps) (* 1/2 (/ 1 x))))
(* (pow x 2) (- (+ (* -1/2 (/ eps (pow x 2))) (* 1/12 eps)) (* 1/2 (/ 1 x))))
(* (pow x 2) (- (+ (* -1/2 (/ eps (pow x 2))) (* 1/12 eps)) (* 1/2 (/ 1 x))))
(* 1/12 (* eps (pow x 2)))
(* (pow x 2) (- (* 1/12 eps) (* 1/2 (/ 1 x))))
(* (pow x 2) (+ (* -1 (/ (+ 1/2 (* 1/2 (/ eps x))) x)) (* 1/12 eps)))
(* (pow x 2) (+ (* -1 (/ (+ 1/2 (* 1/2 (/ eps x))) x)) (* 1/12 eps)))
(* eps (+ 1/24 (* -1/720 (pow x 2))))
(* eps (+ 1/24 (* -1/720 (pow x 2))))
(* eps (+ 1/24 (* -1/720 (pow x 2))))
(* eps (+ 1/24 (* -1/720 (pow x 2))))
(* eps (+ 1/24 (* -1/720 (pow x 2))))
(* eps (+ 1/24 (* -1/720 (pow x 2))))
(* eps (+ 1/24 (* -1/720 (pow x 2))))
(* eps (+ 1/24 (* -1/720 (pow x 2))))
(* eps (+ 1/24 (* -1/720 (pow x 2))))
(* eps (+ 1/24 (* -1/720 (pow x 2))))
(* eps (+ 1/24 (* -1/720 (pow x 2))))
(* eps (+ 1/24 (* -1/720 (pow x 2))))
(* 1/24 eps)
(+ (* -1/720 (* eps (pow x 2))) (* 1/24 eps))
(+ (* -1/720 (* eps (pow x 2))) (* 1/24 eps))
(+ (* -1/720 (* eps (pow x 2))) (* 1/24 eps))
(* -1/720 (* eps (pow x 2)))
(* (pow x 2) (+ (* -1/720 eps) (* 1/24 (/ eps (pow x 2)))))
(* (pow x 2) (+ (* -1/720 eps) (* 1/24 (/ eps (pow x 2)))))
(* (pow x 2) (+ (* -1/720 eps) (* 1/24 (/ eps (pow x 2)))))
(* -1/720 (* eps (pow x 2)))
(* (pow x 2) (+ (* -1/720 eps) (* 1/24 (/ eps (pow x 2)))))
(* (pow x 2) (+ (* -1/720 eps) (* 1/24 (/ eps (pow x 2)))))
(* (pow x 2) (+ (* -1/720 eps) (* 1/24 (/ eps (pow x 2)))))
(* 1/24 (* eps x))
(* x (+ (* -1/720 (* eps (pow x 2))) (* 1/24 eps)))
(* x (+ (* -1/720 (* eps (pow x 2))) (* 1/24 eps)))
(* x (+ (* -1/720 (* eps (pow x 2))) (* 1/24 eps)))
(* -1/720 (* eps (pow x 3)))
(* (pow x 3) (+ (* -1/720 eps) (* 1/24 (/ eps (pow x 2)))))
(* (pow x 3) (+ (* -1/720 eps) (* 1/24 (/ eps (pow x 2)))))
(* (pow x 3) (+ (* -1/720 eps) (* 1/24 (/ eps (pow x 2)))))
(* -1/720 (* eps (pow x 3)))
(* -1 (* (pow x 3) (+ (* -1/24 (/ eps (pow x 2))) (* 1/720 eps))))
(* -1 (* (pow x 3) (+ (* -1/24 (/ eps (pow x 2))) (* 1/720 eps))))
(* -1 (* (pow x 3) (+ (* -1/24 (/ eps (pow x 2))) (* 1/720 eps))))
(* eps (* x (+ 1/24 (* -1/720 (pow x 2)))))
(* eps (* x (+ 1/24 (* -1/720 (pow x 2)))))
(* eps (* x (+ 1/24 (* -1/720 (pow x 2)))))
(* eps (* x (+ 1/24 (* -1/720 (pow x 2)))))
(* eps (* x (+ 1/24 (* -1/720 (pow x 2)))))
(* eps (* x (+ 1/24 (* -1/720 (pow x 2)))))
(* eps (* x (+ 1/24 (* -1/720 (pow x 2)))))
(* eps (* x (+ 1/24 (* -1/720 (pow x 2)))))
(* eps (* x (+ 1/24 (* -1/720 (pow x 2)))))
(* eps (* x (+ 1/24 (* -1/720 (pow x 2)))))
(* eps (* x (+ 1/24 (* -1/720 (pow x 2)))))
(* eps (* x (+ 1/24 (* -1/720 (pow x 2)))))
(* 1/2 eps)
(* eps (+ 1/2 (* -1/48 (pow eps 2))))
(* eps (+ 1/2 (* -1/48 (pow eps 2))))
(* eps (+ 1/2 (* -1/48 (pow eps 2))))
(* -1/48 (pow eps 3))
(* (pow eps 3) (- (* 1/2 (/ 1 (pow eps 2))) 1/48))
(* (pow eps 3) (- (* 1/2 (/ 1 (pow eps 2))) 1/48))
(* (pow eps 3) (- (* 1/2 (/ 1 (pow eps 2))) 1/48))
(* -1/48 (pow eps 3))
(* -1 (* (pow eps 3) (- 1/48 (* 1/2 (/ 1 (pow eps 2))))))
(* -1 (* (pow eps 3) (- 1/48 (* 1/2 (/ 1 (pow eps 2))))))
(* -1 (* (pow eps 3) (- 1/48 (* 1/2 (/ 1 (pow eps 2))))))

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

rewrite356.0ms (2.7%)

Memory

-21.3MiB live, 367.5MiB allocated

Rules

6 200×	`lower-fma.f32`
6 176×	`lower-fma.f64`
6 162×	`lower-*.f32`
6 128×	`lower-*.f64`
2 976×	`lower-/.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	76	580
0	116	572
1	471	572
2	4150	572
0	9327	560

Stop Event

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

Counts

27 → 580

Calls

Call 1

Inputs
(.f64 #s(approx ( (sin (* (+ eps 0) 1/2)) (cos (* (+ (* x 2) eps) 1/2))) (.f64 #s(approx (sin ( 1/2 eps)) (.f64 eps (fma.f64 eps (.f64 eps (fma.f64 (.f64 eps eps) (fma.f64 eps (.f64 eps #s(literal -1/645120 binary64)) #s(literal 1/3840 binary64)) #s(literal -1/48 binary64))) #s(literal 1/2 binary64)))) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)))) #s(literal 2 binary64))
#s(approx (* (sin (* (+ eps 0) 1/2)) (cos (* (+ (* x 2) eps) 1/2))) (.f64 #s(approx (sin ( 1/2 eps)) (.f64 eps (fma.f64 eps (.f64 eps (fma.f64 (.f64 eps eps) (fma.f64 eps (.f64 eps #s(literal -1/645120 binary64)) #s(literal 1/3840 binary64)) #s(literal -1/48 binary64))) #s(literal 1/2 binary64)))) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x))))
(.f64 #s(approx (sin ( 1/2 eps)) (.f64 eps (fma.f64 eps (.f64 eps (fma.f64 (.f64 eps eps) (fma.f64 eps (.f64 eps #s(literal -1/645120 binary64)) #s(literal 1/3840 binary64)) #s(literal -1/48 binary64))) #s(literal 1/2 binary64)))) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)))
#s(approx (sin (* 1/2 eps)) (.f64 eps (fma.f64 eps (.f64 eps (fma.f64 (.f64 eps eps) (fma.f64 eps (.f64 eps #s(literal -1/645120 binary64)) #s(literal 1/3840 binary64)) #s(literal -1/48 binary64))) #s(literal 1/2 binary64))))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 eps #s(approx (cos x) (fma.f64 (.f64 x x) #s(approx (+ (* 1/24 (* x x)) -1/2) #s(literal -1/2 binary64)) #s(literal 1 binary64)))))
(.f64 eps #s(approx (cos x) (fma.f64 (.f64 x x) #s(approx (+ (* 1/24 (* x x)) -1/2) #s(literal -1/2 binary64)) #s(literal 1 binary64))))
#s(approx (cos x) (fma.f64 (.f64 x x) #s(approx (+ ( 1/24 (* x x)) -1/2) #s(literal -1/2 binary64)) #s(literal 1 binary64)))
(fma.f64 (.f64 x x) #s(approx (+ ( 1/24 (* x x)) -1/2) #s(literal -1/2 binary64)) #s(literal 1 binary64))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 eps #s(approx (+ ( eps (* -1/2 (sin x))) (cos x)) (fma.f64 x (fma.f64 eps #s(literal -1/2 binary64) (.f64 x (fma.f64 (.f64 eps x) #s(literal 1/12 binary64) #s(literal -1/2 binary64)))) #s(literal 1 binary64)))))
(.f64 eps #s(approx (+ ( eps (* -1/2 (sin x))) (cos x)) (fma.f64 x (fma.f64 eps #s(literal -1/2 binary64) (.f64 x (fma.f64 (.f64 eps x) #s(literal 1/12 binary64) #s(literal -1/2 binary64)))) #s(literal 1 binary64))))
#s(approx (+ (* eps (* -1/2 (sin x))) (cos x)) (fma.f64 x (fma.f64 eps #s(literal -1/2 binary64) (.f64 x (fma.f64 (.f64 eps x) #s(literal 1/12 binary64) #s(literal -1/2 binary64)))) #s(literal 1 binary64)))
(fma.f64 x (fma.f64 eps #s(literal -1/2 binary64) (.f64 x (fma.f64 (.f64 eps x) #s(literal 1/12 binary64) #s(literal -1/2 binary64)))) #s(literal 1 binary64))
(fma.f64 x (.f64 x (.f64 eps (fma.f64 (.f64 x x) #s(literal -1/720 binary64) #s(literal 1/24 binary64)))) (.f64 eps #s(literal -1/2 binary64)))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* eps (cos x)) (fma.f64 (.f64 x x) (fma.f64 x (.f64 x (.f64 eps (fma.f64 (.f64 x x) #s(literal -1/720 binary64) #s(literal 1/24 binary64)))) (*.f64 eps #s(literal -1/2 binary64))) eps)))
#s(approx (* eps (cos x)) (fma.f64 (.f64 x x) (fma.f64 x (.f64 x (.f64 eps (fma.f64 (.f64 x x) #s(literal -1/720 binary64) #s(literal 1/24 binary64)))) (*.f64 eps #s(literal -1/2 binary64))) eps))
(fma.f64 (.f64 x x) (fma.f64 x (.f64 x (.f64 eps (fma.f64 (.f64 x x) #s(literal -1/720 binary64) #s(literal 1/24 binary64)))) (*.f64 eps #s(literal -1/2 binary64))) eps)
(.f64 #s(approx ( (sin (* (+ eps 0) 1/2)) (cos (* (+ (* x 2) eps) 1/2))) (.f64 #s(approx (sin ( 1/2 eps)) (.f64 eps (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal 1/2 binary64)))) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)))) #s(literal 2 binary64))
#s(approx (* (sin (* (+ eps 0) 1/2)) (cos (* (+ (* x 2) eps) 1/2))) (.f64 #s(approx (sin ( 1/2 eps)) (.f64 eps (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal 1/2 binary64)))) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x))))
(.f64 #s(approx (sin ( 1/2 eps)) (.f64 eps (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal 1/2 binary64)))) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)))
#s(approx (sin (* 1/2 eps)) (.f64 eps (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal 1/2 binary64))))
(.f64 eps (fma.f64 (.f64 eps eps) (fma.f64 eps (*.f64 eps #s(literal -1/645120 binary64)) #s(literal 1/3840 binary64)) #s(literal -1/48 binary64)))
(cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x))
#s(approx (+ (* 1/24 (* x x)) -1/2) #s(literal -1/2 binary64))
(fma.f64 eps #s(literal -1/2 binary64) (.f64 x (fma.f64 (.f64 eps x) #s(literal 1/12 binary64) #s(literal -1/2 binary64))))
(.f64 eps (fma.f64 (.f64 x x) #s(literal -1/720 binary64) #s(literal 1/24 binary64)))
(.f64 x (.f64 eps (fma.f64 (*.f64 x x) #s(literal -1/720 binary64) #s(literal 1/24 binary64))))
(.f64 eps (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal 1/2 binary64)))

Outputs
(.f64 #s(literal 2 binary64) #s(approx ( (sin (* (+ eps 0) 1/2)) (cos (* (+ (* x 2) eps) 1/2))) (.f64 #s(approx (sin ( 1/2 eps)) (.f64 eps (fma.f64 eps (.f64 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 (fma.f64 eps #s(literal 1/2 binary64) x)))))
(.f64 #s(approx ( (sin (* (+ eps 0) 1/2)) (cos (* (+ (* x 2) eps) 1/2))) (.f64 #s(approx (sin ( 1/2 eps)) (.f64 eps (fma.f64 eps (.f64 eps (fma.f64 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 (fma.f64 eps #s(literal 1/2 binary64) x)))) #s(literal 2 binary64))
#s(approx (* (sin (* (+ eps 0) 1/2)) (cos (* (+ (* x 2) eps) 1/2))) (.f64 #s(approx (sin ( 1/2 eps)) (.f64 eps (fma.f64 eps (.f64 eps (fma.f64 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 (fma.f64 eps #s(literal 1/2 binary64) x))))
(.f64 #s(approx (sin ( 1/2 eps)) (.f64 eps (fma.f64 eps (.f64 eps (fma.f64 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 (fma.f64 eps #s(literal 1/2 binary64) x)))
(.f64 (cos.f64 (fma.f64 eps #s(literal 1/2 binary64) x)) #s(approx (sin ( 1/2 eps)) (.f64 eps (fma.f64 eps (.f64 eps (fma.f64 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)))))
#s(approx (sin (* 1/2 eps)) (.f64 eps (fma.f64 eps (.f64 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))))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 eps #s(approx (cos x) (fma.f64 x (.f64 x #s(approx (+ (* 1/24 (* x x)) -1/2) #s(literal -1/2 binary64))) #s(literal 1 binary64)))))
(+.f64 (.f64 eps #s(approx (cos x) (fma.f64 x (.f64 x #s(approx (+ (* 1/24 (* x x)) -1/2) #s(literal -1/2 binary64))) #s(literal 1 binary64)))) (.f64 #s(approx (cos x) (fma.f64 x (.f64 x #s(approx (+ (* 1/24 (* x x)) -1/2) #s(literal -1/2 binary64))) #s(literal 1 binary64))) #s(literal 0 binary64)))
(+.f64 (.f64 eps #s(approx (cos x) (fma.f64 x (.f64 x #s(approx (+ (* 1/24 (* x x)) -1/2) #s(literal -1/2 binary64))) #s(literal 1 binary64)))) (.f64 #s(literal 0 binary64) #s(approx (cos x) (fma.f64 x (.f64 x #s(approx (+ (* 1/24 (* x x)) -1/2) #s(literal -1/2 binary64))) #s(literal 1 binary64)))))
(+.f64 (.f64 #s(approx (cos x) (fma.f64 x (.f64 x #s(approx (+ (* 1/24 (* x x)) -1/2) #s(literal -1/2 binary64))) #s(literal 1 binary64))) #s(literal 0 binary64)) (.f64 eps #s(approx (cos x) (fma.f64 x (.f64 x #s(approx (+ (* 1/24 (* x x)) -1/2) #s(literal -1/2 binary64))) #s(literal 1 binary64)))))
(+.f64 (.f64 #s(literal 0 binary64) #s(approx (cos x) (fma.f64 x (.f64 x #s(approx (+ (* 1/24 (* x x)) -1/2) #s(literal -1/2 binary64))) #s(literal 1 binary64)))) (.f64 eps #s(approx (cos x) (fma.f64 x (.f64 x #s(approx (+ (* 1/24 (* x x)) -1/2) #s(literal -1/2 binary64))) #s(literal 1 binary64)))))
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(fma.f64 (.f64 eps (.f64 eps eps)) #s(literal -1/48 binary64) (*.f64 eps #s(literal 1/2 binary64)))
(fma.f64 (.f64 eps #s(literal -1/48 binary64)) (.f64 eps eps) (*.f64 eps #s(literal 1/2 binary64)))
(/.f64 (.f64 (.f64 eps (.f64 eps eps)) (fma.f64 (.f64 eps (.f64 eps eps)) (.f64 (.f64 eps (.f64 eps eps)) #s(literal -1/110592 binary64)) #s(literal 1/8 binary64))) (.f64 (.f64 eps eps) (-.f64 (fma.f64 #s(literal 1/2304 binary64) (.f64 (.f64 eps (.f64 eps eps)) eps) #s(literal 1/4 binary64)) (.f64 (*.f64 eps eps) #s(literal -1/96 binary64)))))
(/.f64 (.f64 (.f64 eps (.f64 eps eps)) (fma.f64 #s(literal 1/2304 binary64) (.f64 (.f64 eps (.f64 eps eps)) eps) #s(literal -1/4 binary64))) (.f64 (.f64 eps eps) (fma.f64 eps (*.f64 eps #s(literal -1/48 binary64)) #s(literal -1/2 binary64))))
(/.f64 (.f64 (.f64 eps eps) (fma.f64 (.f64 eps (.f64 eps eps)) (.f64 (.f64 eps (.f64 eps eps)) #s(literal -1/110592 binary64)) #s(literal 1/8 binary64))) (.f64 eps (-.f64 (fma.f64 #s(literal 1/2304 binary64) (.f64 (.f64 eps (.f64 eps eps)) eps) #s(literal 1/4 binary64)) (.f64 (*.f64 eps eps) #s(literal -1/96 binary64)))))
(/.f64 (.f64 (.f64 eps eps) (fma.f64 #s(literal 1/2304 binary64) (.f64 (.f64 eps (.f64 eps eps)) eps) #s(literal -1/4 binary64))) (.f64 eps (fma.f64 eps (*.f64 eps #s(literal -1/48 binary64)) #s(literal -1/2 binary64))))
(/.f64 (.f64 (fma.f64 (.f64 eps (.f64 eps eps)) (.f64 (.f64 eps (.f64 eps eps)) #s(literal -1/110592 binary64)) #s(literal 1/8 binary64)) (.f64 eps (.f64 eps eps))) (.f64 (-.f64 (fma.f64 #s(literal 1/2304 binary64) (.f64 (.f64 eps (.f64 eps eps)) eps) #s(literal 1/4 binary64)) (.f64 (.f64 eps eps) #s(literal -1/96 binary64))) (*.f64 eps eps)))
(/.f64 (.f64 (fma.f64 (.f64 eps (.f64 eps eps)) (.f64 (.f64 eps (.f64 eps eps)) #s(literal -1/110592 binary64)) #s(literal 1/8 binary64)) (.f64 eps eps)) (.f64 (-.f64 (fma.f64 #s(literal 1/2304 binary64) (.f64 (.f64 eps (.f64 eps eps)) eps) #s(literal 1/4 binary64)) (.f64 (*.f64 eps eps) #s(literal -1/96 binary64))) eps))
(/.f64 (.f64 (fma.f64 #s(literal 1/2304 binary64) (.f64 (.f64 eps (.f64 eps eps)) eps) #s(literal -1/4 binary64)) (.f64 eps (.f64 eps eps))) (.f64 (fma.f64 eps (.f64 eps #s(literal -1/48 binary64)) #s(literal -1/2 binary64)) (*.f64 eps eps)))
(/.f64 (.f64 (fma.f64 #s(literal 1/2304 binary64) (.f64 (.f64 eps (.f64 eps eps)) eps) #s(literal -1/4 binary64)) (.f64 eps eps)) (.f64 (fma.f64 eps (*.f64 eps #s(literal -1/48 binary64)) #s(literal -1/2 binary64)) eps))
(/.f64 (fma.f64 (.f64 eps (.f64 eps eps)) (.f64 (.f64 eps (.f64 eps eps)) (.f64 (.f64 eps (.f64 eps eps)) #s(literal -1/110592 binary64))) (.f64 (.f64 eps (.f64 eps eps)) #s(literal 1/8 binary64))) (fma.f64 (.f64 #s(literal -1/48 binary64) (.f64 eps (.f64 eps eps))) (.f64 #s(literal -1/48 binary64) (.f64 eps (.f64 eps eps))) (-.f64 (.f64 (.f64 eps eps) #s(literal 1/4 binary64)) (.f64 (.f64 #s(literal -1/48 binary64) (.f64 eps (.f64 eps eps))) (.f64 eps #s(literal 1/2 binary64))))))
(/.f64 (-.f64 (.f64 (.f64 #s(literal -1/48 binary64) (.f64 eps (.f64 eps eps))) (.f64 #s(literal -1/48 binary64) (.f64 eps (.f64 eps eps)))) (.f64 (.f64 eps eps) #s(literal 1/4 binary64))) (-.f64 (.f64 #s(literal -1/48 binary64) (.f64 eps (.f64 eps eps))) (*.f64 eps #s(literal 1/2 binary64))))
(/.f64 (.f64 eps (fma.f64 (.f64 eps (.f64 eps eps)) (.f64 (.f64 eps (.f64 eps eps)) #s(literal -1/110592 binary64)) #s(literal 1/8 binary64))) (-.f64 (fma.f64 #s(literal 1/2304 binary64) (.f64 (.f64 eps (.f64 eps eps)) eps) #s(literal 1/4 binary64)) (.f64 (*.f64 eps eps) #s(literal -1/96 binary64))))
(/.f64 (.f64 eps (fma.f64 #s(literal 1/2304 binary64) (.f64 (.f64 eps (.f64 eps eps)) eps) #s(literal -1/4 binary64))) (fma.f64 eps (*.f64 eps #s(literal -1/48 binary64)) #s(literal -1/2 binary64)))
(/.f64 (.f64 (fma.f64 eps (.f64 eps #s(literal -1/48 binary64)) #s(literal 1/2 binary64)) (.f64 eps (.f64 eps eps))) (*.f64 eps eps))
(/.f64 (.f64 (fma.f64 eps (.f64 eps #s(literal -1/48 binary64)) #s(literal 1/2 binary64)) (*.f64 eps eps)) eps)
(/.f64 (.f64 (.f64 eps (.f64 eps eps)) (fma.f64 eps (.f64 eps #s(literal -1/48 binary64)) #s(literal 1/2 binary64))) (*.f64 eps eps))
(/.f64 (.f64 (.f64 eps eps) (fma.f64 eps (*.f64 eps #s(literal -1/48 binary64)) #s(literal 1/2 binary64))) eps)
(/.f64 (.f64 (fma.f64 (.f64 eps (.f64 eps eps)) (.f64 (.f64 eps (.f64 eps eps)) #s(literal -1/110592 binary64)) #s(literal 1/8 binary64)) eps) (-.f64 (fma.f64 #s(literal 1/2304 binary64) (.f64 (.f64 eps (.f64 eps eps)) eps) #s(literal 1/4 binary64)) (.f64 (*.f64 eps eps) #s(literal -1/96 binary64))))
(/.f64 (.f64 (fma.f64 #s(literal 1/2304 binary64) (.f64 (.f64 eps (.f64 eps eps)) eps) #s(literal -1/4 binary64)) eps) (fma.f64 eps (*.f64 eps #s(literal -1/48 binary64)) #s(literal -1/2 binary64)))
(/.f64 (fma.f64 (.f64 (.f64 eps eps) #s(literal 1/2 binary64)) eps (.f64 eps (.f64 (.f64 (.f64 eps eps) #s(literal -1/48 binary64)) (.f64 eps eps)))) (.f64 eps eps))
(/.f64 (fma.f64 (.f64 (.f64 eps eps) #s(literal 1/2 binary64)) eps (.f64 eps (.f64 (.f64 eps eps) (.f64 (.f64 eps eps) #s(literal -1/48 binary64))))) (.f64 eps eps))
(/.f64 (fma.f64 (.f64 (.f64 eps eps) #s(literal 1/2 binary64)) (.f64 eps eps) (.f64 eps (.f64 (.f64 (.f64 eps eps) #s(literal -1/48 binary64)) (.f64 eps (.f64 eps eps))))) (.f64 eps (*.f64 eps eps)))
(/.f64 (fma.f64 (.f64 (.f64 eps eps) #s(literal 1/2 binary64)) (.f64 eps eps) (.f64 eps (.f64 (.f64 eps (.f64 eps eps)) (.f64 (.f64 eps eps) #s(literal -1/48 binary64))))) (.f64 eps (*.f64 eps eps)))
(/.f64 (fma.f64 (.f64 #s(literal 1/2 binary64) (.f64 eps (.f64 eps eps))) eps (.f64 (.f64 eps eps) (.f64 (.f64 (.f64 eps eps) #s(literal -1/48 binary64)) (.f64 eps eps)))) (.f64 eps (*.f64 eps eps)))
(/.f64 (fma.f64 (.f64 #s(literal 1/2 binary64) (.f64 eps (.f64 eps eps))) eps (.f64 (.f64 eps eps) (.f64 (.f64 eps eps) (.f64 (.f64 eps eps) #s(literal -1/48 binary64))))) (.f64 eps (*.f64 eps eps)))
(/.f64 (fma.f64 (.f64 #s(literal 1/2 binary64) (.f64 eps (.f64 eps eps))) (.f64 eps eps) (.f64 (.f64 eps eps) (.f64 (.f64 (.f64 eps eps) #s(literal -1/48 binary64)) (.f64 eps (.f64 eps eps))))) (.f64 (.f64 eps (.f64 eps eps)) eps))
(/.f64 (fma.f64 (.f64 #s(literal 1/2 binary64) (.f64 eps (.f64 eps eps))) (.f64 eps eps) (.f64 (.f64 eps eps) (.f64 (.f64 eps (.f64 eps eps)) (.f64 (.f64 eps eps) #s(literal -1/48 binary64))))) (.f64 (.f64 eps (.f64 eps eps)) eps))
(/.f64 (fma.f64 (.f64 #s(literal 1/2 binary64) (.f64 eps eps)) eps (.f64 eps (.f64 (.f64 (.f64 eps eps) #s(literal -1/48 binary64)) (.f64 eps eps)))) (.f64 eps eps))
(/.f64 (fma.f64 (.f64 #s(literal 1/2 binary64) (.f64 eps eps)) eps (.f64 eps (.f64 (.f64 eps eps) (.f64 (.f64 eps eps) #s(literal -1/48 binary64))))) (.f64 eps eps))
(/.f64 (fma.f64 (.f64 #s(literal 1/2 binary64) (.f64 eps eps)) (.f64 eps eps) (.f64 eps (.f64 (.f64 (.f64 eps eps) #s(literal -1/48 binary64)) (.f64 eps (.f64 eps eps))))) (.f64 eps (*.f64 eps eps)))
(/.f64 (fma.f64 (.f64 #s(literal 1/2 binary64) (.f64 eps eps)) (.f64 eps eps) (.f64 eps (.f64 (.f64 eps (.f64 eps eps)) (.f64 (.f64 eps eps) #s(literal -1/48 binary64))))) (.f64 eps (*.f64 eps eps)))
(/.f64 (fma.f64 (.f64 (.f64 eps (.f64 eps eps)) #s(literal 1/2 binary64)) eps (.f64 (.f64 eps eps) (.f64 (.f64 (.f64 eps eps) #s(literal -1/48 binary64)) (.f64 eps eps)))) (.f64 eps (*.f64 eps eps)))
(/.f64 (fma.f64 (.f64 (.f64 eps (.f64 eps eps)) #s(literal 1/2 binary64)) eps (.f64 (.f64 eps eps) (.f64 (.f64 eps eps) (.f64 (.f64 eps eps) #s(literal -1/48 binary64))))) (.f64 eps (*.f64 eps eps)))
(/.f64 (fma.f64 (.f64 (.f64 eps (.f64 eps eps)) #s(literal 1/2 binary64)) (.f64 eps eps) (.f64 (.f64 eps eps) (.f64 (.f64 (.f64 eps eps) #s(literal -1/48 binary64)) (.f64 eps (.f64 eps eps))))) (.f64 (.f64 eps (.f64 eps eps)) eps))
(/.f64 (fma.f64 (.f64 (.f64 eps (.f64 eps eps)) #s(literal 1/2 binary64)) (.f64 eps eps) (.f64 (.f64 eps eps) (.f64 (.f64 eps (.f64 eps eps)) (.f64 (.f64 eps eps) #s(literal -1/48 binary64))))) (.f64 (.f64 eps (.f64 eps eps)) eps))
(/.f64 (fma.f64 (.f64 (.f64 (.f64 eps eps) #s(literal -1/48 binary64)) (.f64 eps eps)) eps (.f64 eps (.f64 (.f64 eps eps) #s(literal 1/2 binary64)))) (.f64 eps eps))
(/.f64 (fma.f64 (.f64 (.f64 (.f64 eps eps) #s(literal -1/48 binary64)) (.f64 eps eps)) (.f64 eps eps) (.f64 eps (.f64 #s(literal 1/2 binary64) (.f64 eps (.f64 eps eps))))) (.f64 eps (*.f64 eps eps)))
(/.f64 (fma.f64 (.f64 (.f64 (.f64 eps eps) #s(literal -1/48 binary64)) (.f64 eps eps)) eps (.f64 eps (.f64 #s(literal 1/2 binary64) (.f64 eps eps)))) (.f64 eps eps))
(/.f64 (fma.f64 (.f64 (.f64 (.f64 eps eps) #s(literal -1/48 binary64)) (.f64 eps eps)) (.f64 eps eps) (.f64 eps (.f64 (.f64 eps (.f64 eps eps)) #s(literal 1/2 binary64)))) (.f64 eps (*.f64 eps eps)))
(/.f64 (fma.f64 (.f64 (.f64 eps eps) (.f64 (.f64 eps eps) #s(literal -1/48 binary64))) eps (.f64 eps (.f64 (.f64 eps eps) #s(literal 1/2 binary64)))) (.f64 eps eps))
(/.f64 (fma.f64 (.f64 (.f64 eps eps) (.f64 (.f64 eps eps) #s(literal -1/48 binary64))) (.f64 eps eps) (.f64 eps (.f64 #s(literal 1/2 binary64) (.f64 eps (.f64 eps eps))))) (.f64 eps (*.f64 eps eps)))
(/.f64 (fma.f64 (.f64 (.f64 eps eps) (.f64 (.f64 eps eps) #s(literal -1/48 binary64))) eps (.f64 eps (.f64 #s(literal 1/2 binary64) (.f64 eps eps)))) (.f64 eps eps))
(/.f64 (fma.f64 (.f64 (.f64 eps eps) (.f64 (.f64 eps eps) #s(literal -1/48 binary64))) (.f64 eps eps) (.f64 eps (.f64 (.f64 eps (.f64 eps eps)) #s(literal 1/2 binary64)))) (.f64 eps (*.f64 eps eps)))
(/.f64 (fma.f64 (.f64 (.f64 (.f64 eps eps) #s(literal -1/48 binary64)) (.f64 eps (.f64 eps eps))) eps (.f64 (.f64 eps eps) (.f64 (.f64 eps eps) #s(literal 1/2 binary64)))) (.f64 eps (*.f64 eps eps)))
(/.f64 (fma.f64 (.f64 (.f64 (.f64 eps eps) #s(literal -1/48 binary64)) (.f64 eps (.f64 eps eps))) (.f64 eps eps) (.f64 (.f64 eps eps) (.f64 #s(literal 1/2 binary64) (.f64 eps (.f64 eps eps))))) (.f64 (.f64 eps (.f64 eps eps)) eps))
(/.f64 (fma.f64 (.f64 (.f64 (.f64 eps eps) #s(literal -1/48 binary64)) (.f64 eps (.f64 eps eps))) eps (.f64 (.f64 eps eps) (.f64 #s(literal 1/2 binary64) (.f64 eps eps)))) (.f64 eps (*.f64 eps eps)))
(/.f64 (fma.f64 (.f64 (.f64 (.f64 eps eps) #s(literal -1/48 binary64)) (.f64 eps (.f64 eps eps))) (.f64 eps eps) (.f64 (.f64 eps eps) (.f64 (.f64 eps (.f64 eps eps)) #s(literal 1/2 binary64)))) (.f64 (.f64 eps (.f64 eps eps)) eps))
(/.f64 (fma.f64 (.f64 (.f64 eps (.f64 eps eps)) (.f64 (.f64 eps eps) #s(literal -1/48 binary64))) eps (.f64 (.f64 eps eps) (.f64 (.f64 eps eps) #s(literal 1/2 binary64)))) (.f64 eps (*.f64 eps eps)))
(/.f64 (fma.f64 (.f64 (.f64 eps (.f64 eps eps)) (.f64 (.f64 eps eps) #s(literal -1/48 binary64))) (.f64 eps eps) (.f64 (.f64 eps eps) (.f64 #s(literal 1/2 binary64) (.f64 eps (.f64 eps eps))))) (.f64 (.f64 eps (.f64 eps eps)) eps))
(/.f64 (fma.f64 (.f64 (.f64 eps (.f64 eps eps)) (.f64 (.f64 eps eps) #s(literal -1/48 binary64))) eps (.f64 (.f64 eps eps) (.f64 #s(literal 1/2 binary64) (.f64 eps eps)))) (.f64 eps (*.f64 eps eps)))
(/.f64 (fma.f64 (.f64 (.f64 eps (.f64 eps eps)) (.f64 (.f64 eps eps) #s(literal -1/48 binary64))) (.f64 eps eps) (.f64 (.f64 eps eps) (.f64 (.f64 eps (.f64 eps eps)) #s(literal 1/2 binary64)))) (.f64 (.f64 eps (.f64 eps eps)) eps))
(.f64 eps (fma.f64 eps (.f64 eps #s(literal -1/48 binary64)) #s(literal 1/2 binary64)))
(.f64 (fma.f64 eps (.f64 eps #s(literal -1/48 binary64)) #s(literal 1/2 binary64)) eps)

eval257.0ms (1.9%)

Memory: 11.6MiB live, 161.8MiB allocated
Compiler: Compiled 43 295 to 2 733 computations (93.7% saved)

prune371.0ms (2.8%)

Memory

20.0MiB live, 272.0MiB allocated

Pruning

24 alts after pruning (14 fresh and 10 done)

	Pruned	Kept	Total
New	1 171	6	1 177
Fresh	0	8	8
Picked	1	4	5
Done	0	6	6
Total	1 172	24	1 196

Accuracy

100.0%

Counts

1 196 → 24

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	62.5%	(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
	55.7%	(.f64 (.f64 (sin.f64 (.f64 (.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))
	99.8%	(.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 #s(approx ( (+ (* x 2) eps) 1/2) (fma.f64 eps #s(literal 1/2 binary64) x)))) #s(literal 2 binary64))
✓	99.9%	(.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))
	24.9%	(.f64 #s(approx ( (sin (* (+ eps 0) 1/2)) (cos (* (+ (* x 2) eps) 1/2))) (.f64 #s(approx (sin ( 1/2 eps)) (/.f64 (fma.f64 (.f64 (.f64 (.f64 eps eps) #s(literal -1/48 binary64)) (.f64 eps (.f64 eps eps))) eps (.f64 (.f64 eps eps) (.f64 (.f64 eps eps) #s(literal 1/2 binary64)))) (.f64 eps (*.f64 eps eps)))) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)))) #s(literal 2 binary64))
✓	99.9%	(.f64 #s(approx ( (sin (* (+ eps 0) 1/2)) (cos (* (+ (* x 2) eps) 1/2))) (.f64 #s(approx (sin ( 1/2 eps)) (.f64 eps (fma.f64 eps (.f64 eps (fma.f64 (.f64 eps eps) (fma.f64 eps (.f64 eps #s(literal -1/645120 binary64)) #s(literal 1/3840 binary64)) #s(literal -1/48 binary64))) #s(literal 1/2 binary64)))) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)))) #s(literal 2 binary64))
✓	99.7%	(.f64 #s(approx ( (sin (* (+ eps 0) 1/2)) (cos (* (+ (* x 2) eps) 1/2))) (.f64 #s(approx (sin ( 1/2 eps)) (.f64 eps (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal 1/2 binary64)))) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)))) #s(literal 2 binary64))
	99.6%	(.f64 #s(approx ( (sin (* (+ eps 0) 1/2)) (cos (* (+ (* x 2) eps) 1/2))) (.f64 #s(approx (sin ( 1/2 eps)) (*.f64 eps #s(literal 1/2 binary64))) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)))) #s(literal 2 binary64))
	99.3%	#s(approx (- (sin (+ x eps)) (sin x)) (fma.f64 (cos.f64 x) eps (.f64 #s(approx ( -1/2 (sin x)) (.f64 x #s(literal -1/2 binary64))) (.f64 eps eps))))
✓	99.7%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 eps (fma.f64 eps (.f64 #s(literal -1/2 binary64) (sin.f64 x)) (cos.f64 x))))
	98.7%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 eps (fma.f64 eps #s(approx ( -1/2 (sin x)) (.f64 x #s(literal -1/2 binary64))) #s(approx (cos x) (fma.f64 x (.f64 x (fma.f64 #s(literal 1/24 binary64) (*.f64 x x) #s(literal -1/2 binary64))) #s(literal 1 binary64))))))
	98.1%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 eps (fma.f64 eps #s(approx ( -1/2 (sin x)) (*.f64 x #s(literal -1/2 binary64))) #s(approx (cos x) #s(literal 1 binary64)))))
✓	99.3%	#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 eps (cos.f64 x)))
	98.6%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 eps #s(approx (+ ( eps (* -1/2 (sin x))) (cos x)) (fma.f64 (*.f64 x #s(literal -1/2 binary64)) (+.f64 eps x) #s(literal 1 binary64)))))
✓	98.6%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 eps #s(approx (+ ( eps (* -1/2 (sin x))) (cos x)) (fma.f64 x (fma.f64 eps #s(literal -1/2 binary64) (.f64 x (fma.f64 (.f64 eps x) #s(literal 1/12 binary64) #s(literal -1/2 binary64)))) #s(literal 1 binary64)))))
	98.5%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 eps #s(approx (+ ( eps (* -1/2 (sin x))) (cos x)) (fma.f64 x #s(approx (+ (* eps -1/2) (* x (+ (* (* eps x) 1/12) -1/2))) (.f64 (.f64 x x) (fma.f64 eps #s(literal 1/12 binary64) (/.f64 #s(literal -1/2 binary64) x)))) #s(literal 1 binary64)))))
✓	98.1%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 eps #s(approx (+ ( eps (* -1/2 (sin x))) (cos x)) #s(literal 1 binary64))))
	98.8%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 eps #s(approx (cos x) (fma.f64 (.f64 x x) (fma.f64 x (.f64 x (fma.f64 (.f64 x x) #s(literal -1/720 binary64) #s(literal 1/24 binary64))) #s(literal -1/2 binary64)) #s(literal 1 binary64)))))
✓	98.6%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 eps #s(approx (cos x) (fma.f64 (.f64 x x) (fma.f64 #s(literal 1/24 binary64) (*.f64 x x) #s(literal -1/2 binary64)) #s(literal 1 binary64)))))
✓	98.5%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 eps #s(approx (cos x) (fma.f64 (.f64 x x) #s(approx (+ (* 1/24 (* x x)) -1/2) #s(literal -1/2 binary64)) #s(literal 1 binary64)))))
	98.8%	#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* eps (cos x)) (fma.f64 (.f64 x (fma.f64 (.f64 x x) (.f64 eps (fma.f64 x (.f64 x #s(literal -1/720 binary64)) #s(literal 1/24 binary64))) (*.f64 eps #s(literal -1/2 binary64)))) x eps)))
	34.3%	#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* eps (cos x)) (fma.f64 (.f64 x x) (fma.f64 x (.f64 x (/.f64 (fma.f64 (.f64 (.f64 x (.f64 x #s(literal -1/720 binary64))) (.f64 eps (.f64 eps eps))) eps (.f64 (.f64 eps eps) (.f64 (.f64 eps eps) #s(literal 1/24 binary64)))) (.f64 eps (.f64 eps eps)))) (.f64 eps #s(literal -1/2 binary64))) eps)))
	98.8%	#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* eps (cos x)) (fma.f64 (.f64 x x) (fma.f64 x (.f64 x (/.f64 (.f64 (fma.f64 x (.f64 x #s(literal -1/720 binary64)) #s(literal 1/24 binary64)) (.f64 eps eps)) eps)) (.f64 eps #s(literal -1/2 binary64))) eps)))
	98.1%	#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* eps (cos x)) (fma.f64 (.f64 x x) #s(approx (+ ( x (* x (* eps (+ (* (* x x) -1/720) 1/24)))) (* eps -1/2)) (.f64 x (.f64 x (.f64 eps (.f64 (*.f64 x x) #s(literal -1/720 binary64)))))) eps)))

Compiler

Compiled 1 107 to 432 computations (61% saved)

regimes50.0ms (0.4%)

Memory

0.2MiB live, 38.2MiB allocated

Counts

37 → 1

Calls

Call 1

Inputs
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 eps #s(approx (+ ( eps (* -1/2 (sin x))) (cos x)) #s(literal 1 binary64))))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 eps #s(approx (cos x) (fma.f64 x (.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64)))))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 eps #s(approx (cos x) (fma.f64 (.f64 x x) #s(approx (+ (* 1/24 (* x x)) -1/2) #s(literal -1/2 binary64)) #s(literal 1 binary64)))))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 eps #s(approx (+ ( eps (* -1/2 (sin x))) (cos x)) (fma.f64 eps (*.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64)))))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 eps (fma.f64 eps #s(approx ( -1/2 (sin x)) (*.f64 x #s(literal -1/2 binary64))) #s(approx (cos x) #s(literal 1 binary64)))))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 eps #s(approx (+ ( eps (* -1/2 (sin x))) (cos x)) (fma.f64 (*.f64 x #s(literal -1/2 binary64)) (+.f64 eps x) #s(literal 1 binary64)))))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 eps #s(approx (cos x) (fma.f64 (.f64 x x) (fma.f64 #s(literal 1/24 binary64) (*.f64 x x) #s(literal -1/2 binary64)) #s(literal 1 binary64)))))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 eps #s(approx (+ ( eps (* -1/2 (sin x))) (cos x)) (fma.f64 x (fma.f64 eps #s(literal -1/2 binary64) (.f64 x (fma.f64 (.f64 eps x) #s(literal 1/12 binary64) #s(literal -1/2 binary64)))) #s(literal 1 binary64)))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* eps (cos x)) (fma.f64 (.f64 x x) #s(approx (+ ( x (* x (* eps (+ (* (* x x) -1/720) 1/24)))) (* eps -1/2)) (.f64 x (.f64 x (.f64 eps (.f64 (*.f64 x x) #s(literal -1/720 binary64)))))) eps)))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 eps #s(approx (cos x) (fma.f64 (.f64 x x) (fma.f64 x (.f64 x (fma.f64 (.f64 x x) #s(literal -1/720 binary64) #s(literal 1/24 binary64))) #s(literal -1/2 binary64)) #s(literal 1 binary64)))))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 eps #s(approx (+ ( eps (* -1/2 (sin x))) (cos x)) (fma.f64 x #s(approx (+ (* eps -1/2) (* x (+ (* (* eps x) 1/12) -1/2))) (.f64 (.f64 x x) (fma.f64 eps #s(literal 1/12 binary64) (/.f64 #s(literal -1/2 binary64) x)))) #s(literal 1 binary64)))))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 eps (fma.f64 eps #s(approx ( -1/2 (sin x)) (.f64 x #s(literal -1/2 binary64))) #s(approx (cos x) (fma.f64 x (.f64 x (fma.f64 #s(literal 1/24 binary64) (*.f64 x x) #s(literal -1/2 binary64))) #s(literal 1 binary64))))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* eps (cos x)) (fma.f64 (.f64 x x) (fma.f64 x (.f64 x (.f64 eps (fma.f64 (.f64 x x) #s(literal -1/720 binary64) #s(literal 1/24 binary64)))) (*.f64 eps #s(literal -1/2 binary64))) eps)))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* eps (cos x)) (fma.f64 (.f64 x (fma.f64 (.f64 x x) (.f64 eps (fma.f64 x (.f64 x #s(literal -1/720 binary64)) #s(literal 1/24 binary64))) (*.f64 eps #s(literal -1/2 binary64)))) x eps)))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* eps (cos x)) (fma.f64 (.f64 x x) (fma.f64 x (.f64 x (/.f64 (.f64 (fma.f64 x (.f64 x #s(literal -1/720 binary64)) #s(literal 1/24 binary64)) (.f64 eps eps)) eps)) (.f64 eps #s(literal -1/2 binary64))) eps)))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* eps (cos x)) (fma.f64 (.f64 x x) (fma.f64 x (.f64 x (/.f64 (fma.f64 (.f64 (.f64 x (.f64 x #s(literal -1/720 binary64))) (.f64 eps (.f64 eps eps))) eps (.f64 (.f64 eps eps) (.f64 (.f64 eps eps) #s(literal 1/24 binary64)))) (.f64 eps (.f64 eps eps)))) (.f64 eps #s(literal -1/2 binary64))) eps)))
#s(approx (- (sin (+ x eps)) (sin x)) (sin.f64 eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 eps (cos.f64 x)))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 eps (fma.f64 eps #s(approx ( -1/2 (sin x)) (*.f64 x #s(literal -1/2 binary64))) (cos.f64 x))))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (/.f64 (cos.f64 x) eps) (.f64 eps eps)))
#s(approx (- (sin (+ x eps)) (sin x)) (fma.f64 (cos.f64 x) eps (.f64 #s(approx ( -1/2 (sin x)) (.f64 x #s(literal -1/2 binary64))) (.f64 eps eps))))
(.f64 #s(approx ( (sin (* (+ eps 0) 1/2)) (cos (* (+ (* x 2) eps) 1/2))) (.f64 #s(approx (sin ( 1/2 eps)) (*.f64 eps #s(literal 1/2 binary64))) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)))) #s(literal 2 binary64))
(.f64 (.f64 #s(approx (sin (* (+ eps 0) 1/2)) (.f64 #s(literal 1/2 binary64) eps)) (cos.f64 (.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)))) #s(literal 2 binary64))
(.f64 #s(approx ( (sin (* (+ eps 0) 1/2)) (cos (* (+ (* x 2) eps) 1/2))) (.f64 #s(approx (sin ( 1/2 eps)) (.f64 eps (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal 1/2 binary64)))) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)))) #s(literal 2 binary64))
(-.f64 (sin.f64 (+.f64 x eps)) #s(approx (sin x) (fma.f64 (fma.f64 (.f64 x x) #s(literal 1/120 binary64) #s(literal -1/6 binary64)) (.f64 x (*.f64 x x)) x)))
(.f64 (.f64 #s(approx (sin (* (+ eps 0) 1/2)) (.f64 eps (fma.f64 eps (.f64 eps #s(literal -1/48 binary64)) #s(literal 1/2 binary64)))) (cos.f64 (*.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)))) #s(literal 2 binary64))
(.f64 (.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 #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 (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(approx ( (sin (* (+ eps 0) 1/2)) (cos (* (+ (* x 2) eps) 1/2))) (.f64 #s(approx (sin ( 1/2 eps)) (.f64 eps (fma.f64 eps (.f64 eps (fma.f64 (.f64 eps eps) (fma.f64 eps (.f64 eps #s(literal -1/645120 binary64)) #s(literal 1/3840 binary64)) #s(literal -1/48 binary64))) #s(literal 1/2 binary64)))) (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 #s(approx ( (sin (* (+ eps 0) 1/2)) (cos (* (+ (* x 2) eps) 1/2))) (.f64 #s(approx (sin ( 1/2 eps)) (/.f64 (fma.f64 (.f64 (.f64 (.f64 eps eps) #s(literal -1/48 binary64)) (.f64 eps (.f64 eps eps))) eps (.f64 (.f64 eps eps) (.f64 (.f64 eps eps) #s(literal 1/2 binary64)))) (.f64 eps (*.f64 eps eps)))) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)))) #s(literal 2 binary64))
(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 eps (fma.f64 eps (.f64 #s(literal -1/2 binary64) (sin.f64 x)) (cos.f64 x))))
(.f64 #s(approx ( (sin (* (+ eps 0) 1/2)) (cos (* (+ (* x 2) eps) 1/2))) (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)))) #s(literal 2 binary64))
(.f64 (.f64 (sin.f64 (.f64 (+.f64 eps #s(literal 0 binary64)) #s(literal 1/2 binary64))) (cos.f64 (.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)))) #s(literal 2 binary64))
(.f64 (.f64 (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))
(fma.f64 (sin.f64 x) (cos.f64 eps) (-.f64 (*.f64 (cos.f64 x) (sin.f64 eps)) (sin.f64 x)))

Outputs

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

Calls

3 calls:

29.0ms	(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
9.0ms	eps
9.0ms	x

Results

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

Compiler

Compiled 15 to 10 computations (33.3% saved)

regimes39.0ms (0.3%)

Memory

-2.2MiB live, 35.9MiB allocated

Counts

33 → 1

Calls

Call 1

Inputs
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 eps #s(approx (+ ( eps (* -1/2 (sin x))) (cos x)) #s(literal 1 binary64))))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 eps #s(approx (cos x) (fma.f64 x (.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64)))))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 eps #s(approx (cos x) (fma.f64 (.f64 x x) #s(approx (+ (* 1/24 (* x x)) -1/2) #s(literal -1/2 binary64)) #s(literal 1 binary64)))))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 eps #s(approx (+ ( eps (* -1/2 (sin x))) (cos x)) (fma.f64 eps (*.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64)))))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 eps (fma.f64 eps #s(approx ( -1/2 (sin x)) (*.f64 x #s(literal -1/2 binary64))) #s(approx (cos x) #s(literal 1 binary64)))))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 eps #s(approx (+ ( eps (* -1/2 (sin x))) (cos x)) (fma.f64 (*.f64 x #s(literal -1/2 binary64)) (+.f64 eps x) #s(literal 1 binary64)))))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 eps #s(approx (cos x) (fma.f64 (.f64 x x) (fma.f64 #s(literal 1/24 binary64) (*.f64 x x) #s(literal -1/2 binary64)) #s(literal 1 binary64)))))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 eps #s(approx (+ ( eps (* -1/2 (sin x))) (cos x)) (fma.f64 x (fma.f64 eps #s(literal -1/2 binary64) (.f64 x (fma.f64 (.f64 eps x) #s(literal 1/12 binary64) #s(literal -1/2 binary64)))) #s(literal 1 binary64)))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* eps (cos x)) (fma.f64 (.f64 x x) #s(approx (+ ( x (* x (* eps (+ (* (* x x) -1/720) 1/24)))) (* eps -1/2)) (.f64 x (.f64 x (.f64 eps (.f64 (*.f64 x x) #s(literal -1/720 binary64)))))) eps)))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 eps #s(approx (cos x) (fma.f64 (.f64 x x) (fma.f64 x (.f64 x (fma.f64 (.f64 x x) #s(literal -1/720 binary64) #s(literal 1/24 binary64))) #s(literal -1/2 binary64)) #s(literal 1 binary64)))))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 eps #s(approx (+ ( eps (* -1/2 (sin x))) (cos x)) (fma.f64 x #s(approx (+ (* eps -1/2) (* x (+ (* (* eps x) 1/12) -1/2))) (.f64 (.f64 x x) (fma.f64 eps #s(literal 1/12 binary64) (/.f64 #s(literal -1/2 binary64) x)))) #s(literal 1 binary64)))))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 eps (fma.f64 eps #s(approx ( -1/2 (sin x)) (.f64 x #s(literal -1/2 binary64))) #s(approx (cos x) (fma.f64 x (.f64 x (fma.f64 #s(literal 1/24 binary64) (*.f64 x x) #s(literal -1/2 binary64))) #s(literal 1 binary64))))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* eps (cos x)) (fma.f64 (.f64 x x) (fma.f64 x (.f64 x (.f64 eps (fma.f64 (.f64 x x) #s(literal -1/720 binary64) #s(literal 1/24 binary64)))) (*.f64 eps #s(literal -1/2 binary64))) eps)))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* eps (cos x)) (fma.f64 (.f64 x (fma.f64 (.f64 x x) (.f64 eps (fma.f64 x (.f64 x #s(literal -1/720 binary64)) #s(literal 1/24 binary64))) (*.f64 eps #s(literal -1/2 binary64)))) x eps)))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* eps (cos x)) (fma.f64 (.f64 x x) (fma.f64 x (.f64 x (/.f64 (.f64 (fma.f64 x (.f64 x #s(literal -1/720 binary64)) #s(literal 1/24 binary64)) (.f64 eps eps)) eps)) (.f64 eps #s(literal -1/2 binary64))) eps)))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* eps (cos x)) (fma.f64 (.f64 x x) (fma.f64 x (.f64 x (/.f64 (fma.f64 (.f64 (.f64 x (.f64 x #s(literal -1/720 binary64))) (.f64 eps (.f64 eps eps))) eps (.f64 (.f64 eps eps) (.f64 (.f64 eps eps) #s(literal 1/24 binary64)))) (.f64 eps (.f64 eps eps)))) (.f64 eps #s(literal -1/2 binary64))) eps)))
#s(approx (- (sin (+ x eps)) (sin x)) (sin.f64 eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 eps (cos.f64 x)))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 eps (fma.f64 eps #s(approx ( -1/2 (sin x)) (*.f64 x #s(literal -1/2 binary64))) (cos.f64 x))))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (/.f64 (cos.f64 x) eps) (.f64 eps eps)))
#s(approx (- (sin (+ x eps)) (sin x)) (fma.f64 (cos.f64 x) eps (.f64 #s(approx ( -1/2 (sin x)) (.f64 x #s(literal -1/2 binary64))) (.f64 eps eps))))
(.f64 #s(approx ( (sin (* (+ eps 0) 1/2)) (cos (* (+ (* x 2) eps) 1/2))) (.f64 #s(approx (sin ( 1/2 eps)) (*.f64 eps #s(literal 1/2 binary64))) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)))) #s(literal 2 binary64))
(.f64 (.f64 #s(approx (sin (* (+ eps 0) 1/2)) (.f64 #s(literal 1/2 binary64) eps)) (cos.f64 (.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)))) #s(literal 2 binary64))
(.f64 #s(approx ( (sin (* (+ eps 0) 1/2)) (cos (* (+ (* x 2) eps) 1/2))) (.f64 #s(approx (sin ( 1/2 eps)) (.f64 eps (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal 1/2 binary64)))) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)))) #s(literal 2 binary64))
(-.f64 (sin.f64 (+.f64 x eps)) #s(approx (sin x) (fma.f64 (fma.f64 (.f64 x x) #s(literal 1/120 binary64) #s(literal -1/6 binary64)) (.f64 x (*.f64 x x)) x)))
(.f64 (.f64 #s(approx (sin (* (+ eps 0) 1/2)) (.f64 eps (fma.f64 eps (.f64 eps #s(literal -1/48 binary64)) #s(literal 1/2 binary64)))) (cos.f64 (*.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)))) #s(literal 2 binary64))
(.f64 (.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 #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 (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(approx ( (sin (* (+ eps 0) 1/2)) (cos (* (+ (* x 2) eps) 1/2))) (.f64 #s(approx (sin ( 1/2 eps)) (.f64 eps (fma.f64 eps (.f64 eps (fma.f64 (.f64 eps eps) (fma.f64 eps (.f64 eps #s(literal -1/645120 binary64)) #s(literal 1/3840 binary64)) #s(literal -1/48 binary64))) #s(literal 1/2 binary64)))) (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 #s(approx ( (sin (* (+ eps 0) 1/2)) (cos (* (+ (* x 2) eps) 1/2))) (.f64 #s(approx (sin ( 1/2 eps)) (/.f64 (fma.f64 (.f64 (.f64 (.f64 eps eps) #s(literal -1/48 binary64)) (.f64 eps (.f64 eps eps))) eps (.f64 (.f64 eps eps) (.f64 (.f64 eps eps) #s(literal 1/2 binary64)))) (.f64 eps (*.f64 eps eps)))) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)))) #s(literal 2 binary64))
(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 eps (fma.f64 eps (.f64 #s(literal -1/2 binary64) (sin.f64 x)) (cos.f64 x))))

Outputs

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

Calls

3 calls:

21.0ms	(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
8.0ms	eps
8.0ms	x

Results

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

Compiler

Compiled 15 to 10 computations (33.3% saved)

regimes46.0ms (0.3%)

Memory

-13.8MiB live, 27.2MiB allocated

Counts

28 → 1

Calls

Call 1

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

Calls

3 calls:

30.0ms	(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
7.0ms	eps
7.0ms	x

Results

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

Compiler

Compiled 15 to 10 computations (33.3% saved)

regimes38.0ms (0.3%)

Memory

-6.8MiB live, 30.2MiB allocated

Counts

26 → 1

Calls

Call 1

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

Outputs

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

Calls

3 calls:

23.0ms	x
7.0ms	(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
7.0ms	eps

Results

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

Compiler

Compiled 15 to 10 computations (33.3% saved)

regimes27.0ms (0.2%)

Memory

-2.2MiB live, 35.7MiB allocated

Counts

23 → 1

Calls

Call 1

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

Outputs

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

Calls

3 calls:

13.0ms	x
6.0ms	(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
6.0ms	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)

regimes18.0ms (0.1%)

Memory

21.1MiB live, 21.1MiB allocated

Counts

21 → 1

Calls

Call 1

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

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

Calls

3 calls:

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

Results

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

Compiler

Compiled 15 to 10 computations (33.3% saved)

regimes38.0ms (0.3%)

Memory

-15.1MiB live, 22.9MiB allocated

Counts

17 → 1

Calls

Call 1

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

Outputs

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

Calls

3 calls:

28.0ms	(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
5.0ms	eps
5.0ms	x

Results

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

Compiler

Compiled 15 to 10 computations (33.3% saved)

regimes10.0ms (0.1%)

Memory

14.4MiB live, 14.4MiB allocated

Counts

9 → 1

Calls

Call 1

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

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

Calls

3 calls:

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

Results

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

Compiler

Compiled 15 to 10 computations (33.3% saved)

regimes8.0ms (0.1%)

Memory

11.9MiB live, 11.9MiB allocated

Counts

6 → 1

Calls

Call 1

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

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

Calls

3 calls:

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

Results

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

Compiler

Compiled 15 to 10 computations (33.3% saved)

regimes21.0ms (0.2%)

Memory

-33.4MiB live, 13.7MiB allocated

Counts

5 → 1

Calls

Call 1

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

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

Calls

3 calls:

16.0ms	eps
2.0ms	(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
2.0ms	x

Results

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

Compiler

Compiled 15 to 10 computations (33.3% saved)

regimes4.0ms (0%)

Memory

9.3MiB live, 9.3MiB allocated

Accuracy

Total -0.0b remaining (-0%)

Threshold costs -0b (-0%)

Counts

1 → 1

Calls

Call 1

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

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:

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

Results

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

Compiler

Compiled 15 to 10 computations (33.3% saved)

simplify8.0ms (0.1%)

Memory

15.2MiB live, 15.2MiB allocated

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	98	313
1	126	313

Stop Event

1×

saturated

Calls

Call 1

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

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

soundness1.1s (7.9%)

Memory

14.1MiB live, 754.9MiB allocated

Rules

16 678×	`lower-fma.f64`
16 678×	`lower-fma.f32`
14 424×	`lower-fma.f64`
14 424×	`lower-fma.f32`
13 684×	`lower-fma.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	359	3403
1	1096	3265
2	2826	3225
3	6529	3225
0	8151	2971
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	333	4949
1	995	4746
2	2580	4677
3	6064	4635
0	8448	4273

Stop Event

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

Compiler

Compiled 382 to 209 computations (45.3% saved)

preprocess206.0ms (1.5%)

Memory: -5.4MiB live, 328.8MiB allocated
Compiler: Compiled 440 to 194 computations (55.9% saved)

end0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated

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

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

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

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

start0.0ms (0%)

analyze39.0ms (0.3%)

sample6.0s (45.3%)

explain87.0ms (0.7%)

preprocess29.0ms (0.2%)

eval0.0ms (0%)

prune1.0ms (0%)

simplify8.0ms (0.1%)

localize28.0ms (0.2%)

series4.0ms (0%)

simplify337.0ms (2.5%)

rewrite321.0ms (2.4%)

eval114.0ms (0.9%)

prune178.0ms (1.3%)

simplify312.0ms (2.3%)

localize170.0ms (1.3%)

series34.0ms (0.3%)

simplify279.0ms (2.1%)

rewrite290.0ms (2.2%)

eval112.0ms (0.8%)

prune185.0ms (1.4%)

simplify225.0ms (1.7%)

localize162.0ms (1.2%)

series27.0ms (0.2%)

simplify300.0ms (2.3%)

rewrite242.0ms (1.8%)

eval137.0ms (1%)

prune163.0ms (1.2%)

simplify311.0ms (2.3%)

localize279.0ms (2.1%)

series58.0ms (0.4%)

simplify307.0ms (2.3%)

rewrite356.0ms (2.7%)

eval257.0ms (1.9%)

prune371.0ms (2.8%)

regimes50.0ms (0.4%)

regimes39.0ms (0.3%)

regimes46.0ms (0.3%)

regimes38.0ms (0.3%)

regimes27.0ms (0.2%)

regimes18.0ms (0.1%)

regimes38.0ms (0.3%)

regimes10.0ms (0.1%)

regimes8.0ms (0.1%)

regimes21.0ms (0.2%)

regimes4.0ms (0%)

simplify8.0ms (0.1%)

soundness1.1s (7.9%)

preprocess206.0ms (1.5%)

end0.0ms (0%)

Profiling

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

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