Metrics for 2sin (example 3.3)

start0.0ms (0%)

Memory: 0.1MiB live, 0.1MiB allocated

analyze58.0ms (0.5%)

Memory

-5.0MiB live, 34.1MiB 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 (50.4%)

Memory

-241.9MiB live, 6 649.5MiB allocated

Samples

3.4s	26 218×	0	invalid
645.0ms	5 574×	0	valid
572.0ms	2 682×	1	valid

Precisions

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

const: 675.0ms (21.9% of total)

ival-sin: 621.0ms (20.2% of total)

ival-add: 328.0ms (10.6% of total)

ival-fabs: 279.0ms (9.1% of total)

ival-mult: 269.0ms (8.7% of total)

ival-<=: 245.0ms (8% of total)

ival-sub: 207.0ms (6.7% of total)

ival-<: 197.0ms (6.4% of total)

ival-and: 106.0ms (3.4% of total)

adjust: 93.0ms (3% of total)

exact: 48.0ms (1.6% of total)

ival-assert: 14.0ms (0.5% of total)

Bogosity

explain84.0ms (0.7%)

Memory

28.1MiB live, 111.7MiB allocated

FPErrors

Click to see full error table

Ground Truth	Overpredictions	Example	Underpredictions	Example	Subexpression
220	5	(2.0589138454576519e-147 1.5552208180545202e-149)	2	(-2.3106090244628977e-130 3.992576240859251e-132)	`(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))`
1	0	-	0	-	`(sin.f64 (+.f64 x eps))`
0	0	-	0	-	`eps`
0	0	-	0	-	`(+.f64 x eps)`
0	0	-	0	-	`(sin.f64 x)`
0	0	-	0	-	`x`

Explanations

Click to see full explanations table

Operator	Subexpression	Explanation	Count
`-.f64`	`(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))`	cancellation	223	9
`sin.f64`	`(sin.f64 (+.f64 x eps))`	sensitivity	1	0

Confusion

	Predicted +	Predicted -
+	218	2
-	5	31

Precision

0.9775784753363229

Recall

0.990909090909091

Confusion?

	Predicted +	Predicted Maybe	Predicted -
+	218	2	0
-	5	7	24

Precision?

0.9482758620689655

Recall?

1.0

Freqs

test

number	freq
0	33
1	222
2	1

Total Confusion?

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

Precision?

1.0

Recall?

1.0

Samples

18.0ms	360×	0	valid
15.0ms	150×	1	valid
1.0ms	2×	2	valid

Compiler

Compiled 47 to 22 computations (53.2% saved)

Precisions

Click to see histograms. Total time spent on operations: 19.0ms

ival-sin: 10.0ms (52.4% of total)

adjust: 3.0ms (15.7% of total)

ival-add: 3.0ms (15.7% of total)

ival-sub: 3.0ms (15.7% of total)

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

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

preprocess25.0ms (0.2%)

Memory

-15.6MiB live, 22.8MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

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

Stop Event

1×	iter limit
1×	saturated
1×	iter limit
1×	saturated

Calls

Call 1

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

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

Compiler

Compiled 7 to 6 computations (14.3% saved)

eval0.0ms (0%)

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

prune0.0ms (0%)

Memory

0.9MiB live, 0.9MiB allocated

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	65.3%	(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))

Compiler

Compiled 7 to 6 computations (14.3% saved)

simplify6.0ms (0%)

Memory

5.0MiB live, 5.0MiB 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))

Iterations

Useful iterations: 0 (0.0ms)

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

Stop Event

1×	iter limit
1×	saturated
1×	iter limit

Calls

Call 1

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

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

localize25.0ms (0.2%)

Memory

-10.1MiB live, 27.8MiB allocated

Localize:

Found 4 expressions of interest:

New	Metric	Score
accuracy	0	(+.f64 x eps)
accuracy	0	(sin.f64 x)
accuracy	0.057878842278341336	(sin.f64 (+.f64 x eps))
accuracy	22.121376323973404	(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))

Samples

10.0ms	180×	0	valid
7.0ms	75×	1	valid
0.0ms	1×	2	valid

Compiler

Compiled 20 to 8 computations (60% saved)

Precisions

Click to see histograms. Total time spent on operations: 9.0ms

ival-sin: 5.0ms (53.9% of total)

ival-add: 2.0ms (21.6% of total)

adjust: 1.0ms (10.8% of total)

ival-sub: 1.0ms (10.8% of total)

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

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

series5.0ms (0%)

Memory

6.6MiB live, 6.6MiB allocated

Counts

4 → 84

Calls

Call 1

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

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

Calls

6 calls:

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

simplify156.0ms (1.3%)

Memory

4.9MiB live, 119.3MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	107	496
1	314	496
2	775	489
3	2829	489
4	6198	489
0	8141	458

Stop Event

1×	iter limit
1×	node limit

Counts

84 → 77

Calls

Call 1

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

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

rewrite178.0ms (1.5%)

Memory

9.6MiB live, 166.0MiB allocated

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
#<batchref>
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eval68.0ms (0.6%)

Memory: 11.9MiB live, 49.9MiB allocated
Compiler: Compiled 6 625 to 852 computations (87.1% saved)

prune24.0ms (0.2%)

Memory

-12.9MiB live, 31.4MiB allocated

Pruning

8 alts after pruning (7 fresh and 1 done)

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

Accuracy

100.0%

Counts

292 → 8

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	65.3%	(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
▶	64.6%	(-.f64 (sin.f64 (+.f64 x eps)) #s(approx (sin x) (fma.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 #s(literal 1/120 binary64) (*.f64 x x) #s(literal -1/6 binary64)) x)))
	99.9%	(.f64 (.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 0 binary64) eps))) #s(literal 2 binary64)) (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64))))
▶	100.0%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 (fma.f64 (sin.f64 x) (fma.f64 (.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) (.f64 (.f64 #s(literal -1/6 binary64) (cos.f64 x)) eps)) eps (cos.f64 x)) eps))
	100.0%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 (fma.f64 #s(literal -1/6 binary64) (.f64 (cos.f64 x) eps) (*.f64 (sin.f64 x) #s(literal -1/2 binary64))) eps (cos.f64 x)) eps))
▶	99.7%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 (.f64 (sin.f64 x) #s(literal -1/2 binary64)) eps (cos.f64 x)) eps))
▶	99.0%	#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (cos.f64 x) eps))
▶	97.6%	#s(approx (- (sin (+ x eps)) (sin x)) (sin.f64 eps))

Compiler

Compiled 189 to 150 computations (20.6% saved)

simplify332.0ms (2.8%)

Memory

3.5MiB live, 162.6MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 17 expressions of interest:

New	Metric	Score	Program
cost-diff	0	#s(approx (sin x) (fma.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 #s(literal 1/120 binary64) (*.f64 x x) #s(literal -1/6 binary64)) x))
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 (pow.f64 x #s(literal 3 binary64)) (fma.f64 #s(literal 1/120 binary64) (*.f64 x x) #s(literal -1/6 binary64)) x)))
cost-diff	0	(*.f64 (sin.f64 x) #s(literal -1/2 binary64))
cost-diff	0	(fma.f64 (*.f64 (sin.f64 x) #s(literal -1/2 binary64)) eps (cos.f64 x))
cost-diff	0	(.f64 (fma.f64 (.f64 (sin.f64 x) #s(literal -1/2 binary64)) eps (cos.f64 x)) eps)
cost-diff	0	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 (.f64 (sin.f64 x) #s(literal -1/2 binary64)) eps (cos.f64 x)) eps))
cost-diff	0	(cos.f64 x)
cost-diff	0	(*.f64 (cos.f64 x) eps)
cost-diff	0	#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (cos.f64 x) eps))
cost-diff	0	(sin.f64 eps)
cost-diff	0	#s(approx (- (sin (+ x eps)) (sin x)) (sin.f64 eps))
cost-diff	0	(fma.f64 (sin.f64 x) (fma.f64 (.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) (.f64 (*.f64 #s(literal -1/6 binary64) (cos.f64 x)) eps))
cost-diff	0	(fma.f64 (fma.f64 (sin.f64 x) (fma.f64 (.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) (.f64 (*.f64 #s(literal -1/6 binary64) (cos.f64 x)) eps)) eps (cos.f64 x))
cost-diff	0	(.f64 (fma.f64 (fma.f64 (sin.f64 x) (fma.f64 (.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) (.f64 (.f64 #s(literal -1/6 binary64) (cos.f64 x)) eps)) eps (cos.f64 x)) eps)
cost-diff	0	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 (fma.f64 (sin.f64 x) (fma.f64 (.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) (.f64 (.f64 #s(literal -1/6 binary64) (cos.f64 x)) eps)) eps (cos.f64 x)) eps))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	37	260
0	65	260
1	108	260
2	222	260
3	431	260
4	700	260
5	1033	260
6	1129	260
7	1296	260
8	1716	260
9	1879	260
10	2563	260
11	3992	260
12	4945	260
13	5571	260
14	6178	260
15	6226	260
16	6314	260
17	6439	260
18	6685	260
19	6857	260
20	6886	260
21	6903	260
22	7048	260
23	7724	260
0	8025	260

Stop Event

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

Calls

Call 1

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

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

localize124.0ms (1%)

Memory

-16.1MiB live, 217.4MiB allocated

Localize:

Found 17 expressions of interest:

New	Metric	Score
accuracy	0.00390625	(fma.f64 #s(literal 1/120 binary64) (*.f64 x x) #s(literal -1/6 binary64))
accuracy	0.057878842278341336	(sin.f64 (+.f64 x eps))
accuracy	0.771349580683601	#s(approx (sin x) (fma.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 #s(literal 1/120 binary64) (*.f64 x x) #s(literal -1/6 binary64)) x))
accuracy	22.121376323973404	(-.f64 (sin.f64 (+.f64 x eps)) #s(approx (sin x) (fma.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 #s(literal 1/120 binary64) (*.f64 x x) #s(literal -1/6 binary64)) x)))
accuracy	0	(cos.f64 x)
accuracy	0.01171875	(fma.f64 (*.f64 (sin.f64 x) #s(literal -1/2 binary64)) eps (cos.f64 x))
accuracy	0.015625	(.f64 (fma.f64 (.f64 (sin.f64 x) #s(literal -1/2 binary64)) eps (cos.f64 x)) eps)
accuracy	0.21273808917513187	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 (.f64 (sin.f64 x) #s(literal -1/2 binary64)) eps (cos.f64 x)) eps))
accuracy	0	(cos.f64 x)
accuracy	0.01171875	(*.f64 (cos.f64 x) eps)
accuracy	0.6301620228595607	#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (cos.f64 x) eps))
accuracy	0	(sin.f64 eps)
accuracy	1.542129927903612	#s(approx (- (sin (+ x eps)) (sin x)) (sin.f64 eps))
accuracy	0.01171875	(*.f64 #s(literal -1/6 binary64) (cos.f64 x))
accuracy	0.01953125	(fma.f64 (fma.f64 (sin.f64 x) (fma.f64 (.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) (.f64 (*.f64 #s(literal -1/6 binary64) (cos.f64 x)) eps)) eps (cos.f64 x))
accuracy	0.03515625	(fma.f64 (sin.f64 x) (fma.f64 (.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) (.f64 (*.f64 #s(literal -1/6 binary64) (cos.f64 x)) eps))
accuracy	0.3515625	(.f64 (.f64 #s(literal -1/6 binary64) (cos.f64 x)) eps)

Samples

53.0ms	179×	0	valid
42.0ms	75×	1	valid
2.0ms	2×	2	valid

Compiler

Compiled 211 to 36 computations (82.9% saved)

Precisions

Click to see histograms. Total time spent on operations: 74.0ms

ival-mult: 26.0ms (35.1% of total)

const: 11.0ms (14.8% of total)

ival-add: 11.0ms (14.8% of total)

ival-pow: 7.0ms (9.4% of total)

ival-sin: 7.0ms (9.4% of total)

adjust: 5.0ms (6.7% of total)

ival-sub: 3.0ms (4% of total)

ival-cos: 3.0ms (4% of total)

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

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

exact: 0.0ms (0% of total)

series38.0ms (0.3%)

Memory

33.1MiB live, 70.5MiB allocated

Counts

20 → 408

Calls

Call 1

Inputs
#s(alt #s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 (fma.f64 (sin.f64 x) (fma.f64 (.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) (.f64 (.f64 #s(literal -1/6 binary64) (cos.f64 x)) eps)) eps (cos.f64 x)) eps)) (patch #s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 (fma.f64 (sin.f64 x) (fma.f64 (.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) (.f64 (.f64 #s(literal -1/6 binary64) (cos.f64 x)) eps)) eps (cos.f64 x)) eps)) #<representation binary64>) () ())
#s(alt (.f64 (fma.f64 (fma.f64 (sin.f64 x) (fma.f64 (.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) (.f64 (.f64 #s(literal -1/6 binary64) (cos.f64 x)) eps)) eps (cos.f64 x)) eps) (patch (.f64 (fma.f64 (fma.f64 (sin.f64 x) (fma.f64 (.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) (.f64 (.f64 #s(literal -1/6 binary64) (cos.f64 x)) eps)) eps (cos.f64 x)) eps) #<representation binary64>) () ())
#s(alt (fma.f64 (fma.f64 (sin.f64 x) (fma.f64 (.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) (.f64 (.f64 #s(literal -1/6 binary64) (cos.f64 x)) eps)) eps (cos.f64 x)) (patch (fma.f64 (fma.f64 (sin.f64 x) (fma.f64 (.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) (.f64 (.f64 #s(literal -1/6 binary64) (cos.f64 x)) eps)) eps (cos.f64 x)) #<representation binary64>) () ())
#s(alt (fma.f64 (sin.f64 x) (fma.f64 (.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) (.f64 (.f64 #s(literal -1/6 binary64) (cos.f64 x)) eps)) (patch (fma.f64 (sin.f64 x) (fma.f64 (.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) (.f64 (.f64 #s(literal -1/6 binary64) (cos.f64 x)) eps)) #<representation binary64>) () ())
#s(alt #s(approx (- (sin (+ x eps)) (sin x)) (sin.f64 eps)) (patch #s(approx (- (sin (+ x eps)) (sin x)) (sin.f64 eps)) #<representation binary64>) () ())
#s(alt (sin.f64 eps) (patch (sin.f64 eps) #<representation binary64>) () ())
#s(alt #s(approx (- (sin (+ x eps)) (sin x)) (.f64 (cos.f64 x) eps)) (patch #s(approx (- (sin (+ x eps)) (sin x)) (.f64 (cos.f64 x) eps)) #<representation binary64>) () ())
#s(alt (.f64 (cos.f64 x) eps) (patch (.f64 (cos.f64 x) eps) #<representation binary64>) () ())
#s(alt (cos.f64 x) (patch (cos.f64 x) #<representation binary64>) () ())
#s(alt #s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 (.f64 (sin.f64 x) #s(literal -1/2 binary64)) eps (cos.f64 x)) eps)) (patch #s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 (.f64 (sin.f64 x) #s(literal -1/2 binary64)) eps (cos.f64 x)) eps)) #<representation binary64>) () ())
#s(alt (.f64 (fma.f64 (.f64 (sin.f64 x) #s(literal -1/2 binary64)) eps (cos.f64 x)) eps) (patch (.f64 (fma.f64 (.f64 (sin.f64 x) #s(literal -1/2 binary64)) eps (cos.f64 x)) eps) #<representation binary64>) () ())
#s(alt (fma.f64 (.f64 (sin.f64 x) #s(literal -1/2 binary64)) eps (cos.f64 x)) (patch (fma.f64 (.f64 (sin.f64 x) #s(literal -1/2 binary64)) eps (cos.f64 x)) #<representation binary64>) () ())
#s(alt (.f64 (sin.f64 x) #s(literal -1/2 binary64)) (patch (.f64 (sin.f64 x) #s(literal -1/2 binary64)) #<representation binary64>) () ())
#s(alt (-.f64 (sin.f64 (+.f64 x eps)) #s(approx (sin x) (fma.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 #s(literal 1/120 binary64) (.f64 x x) #s(literal -1/6 binary64)) x))) (patch (-.f64 (sin.f64 (+.f64 x eps)) #s(approx (sin x) (fma.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 #s(literal 1/120 binary64) (.f64 x x) #s(literal -1/6 binary64)) x))) #<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 (pow.f64 x #s(literal 3 binary64)) (fma.f64 #s(literal 1/120 binary64) (.f64 x x) #s(literal -1/6 binary64)) x)) (patch #s(approx (sin x) (fma.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 #s(literal 1/120 binary64) (.f64 x x) #s(literal -1/6 binary64)) x)) #<representation binary64>) () ())
#s(alt (.f64 (.f64 #s(literal -1/6 binary64) (cos.f64 x)) eps) (patch (.f64 (.f64 #s(literal -1/6 binary64) (cos.f64 x)) eps) #<representation binary64>) () ())
#s(alt (.f64 #s(literal -1/6 binary64) (cos.f64 x)) (patch (.f64 #s(literal -1/6 binary64) (cos.f64 x)) #<representation binary64>) () ())
#s(alt (fma.f64 #s(literal 1/120 binary64) (.f64 x x) #s(literal -1/6 binary64)) (patch (fma.f64 #s(literal 1/120 binary64) (.f64 x x) #s(literal -1/6 binary64)) #<representation binary64>) () ())

Outputs
#s(alt (* eps (cos x)) (taylor 0 eps) (#s(alt #s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 (fma.f64 (sin.f64 x) (fma.f64 (.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) (.f64 (.f64 #s(literal -1/6 binary64) (cos.f64 x)) eps)) eps (cos.f64 x)) eps)) (patch #s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 (fma.f64 (sin.f64 x) (fma.f64 (.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) (.f64 (.f64 #s(literal -1/6 binary64) (cos.f64 x)) eps)) eps (cos.f64 x)) eps)) #<representation binary64>) () ())) ())
#s(alt (* eps (+ (cos x) (* -1/2 (* eps (sin x))))) (taylor 0 eps) (#s(alt #s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 (fma.f64 (sin.f64 x) (fma.f64 (.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) (.f64 (.f64 #s(literal -1/6 binary64) (cos.f64 x)) eps)) eps (cos.f64 x)) eps)) (patch #s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 (fma.f64 (sin.f64 x) (fma.f64 (.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) (.f64 (.f64 #s(literal -1/6 binary64) (cos.f64 x)) eps)) eps (cos.f64 x)) eps)) #<representation binary64>) () ())) ())
#s(alt (* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x))))))) (taylor 0 eps) (#s(alt #s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 (fma.f64 (sin.f64 x) (fma.f64 (.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) (.f64 (.f64 #s(literal -1/6 binary64) (cos.f64 x)) eps)) eps (cos.f64 x)) eps)) (patch #s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 (fma.f64 (sin.f64 x) (fma.f64 (.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) (.f64 (.f64 #s(literal -1/6 binary64) (cos.f64 x)) eps)) eps (cos.f64 x)) eps)) #<representation binary64>) () ())) ())
#s(alt (* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* eps (+ (* -1/6 (cos x)) (* 1/24 (* eps (sin x))))))))) (taylor 0 eps) (#s(alt #s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 (fma.f64 (sin.f64 x) (fma.f64 (.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) (.f64 (.f64 #s(literal -1/6 binary64) (cos.f64 x)) eps)) eps (cos.f64 x)) eps)) (patch #s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 (fma.f64 (sin.f64 x) (fma.f64 (.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) (.f64 (.f64 #s(literal -1/6 binary64) (cos.f64 x)) eps)) eps (cos.f64 x)) eps)) #<representation binary64>) () ())) ())
#s(alt (* eps (cos x)) (taylor 0 eps) (#s(alt (.f64 (fma.f64 (fma.f64 (sin.f64 x) (fma.f64 (.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) (.f64 (.f64 #s(literal -1/6 binary64) (cos.f64 x)) eps)) eps (cos.f64 x)) eps) (patch (.f64 (fma.f64 (fma.f64 (sin.f64 x) (fma.f64 (.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) (.f64 (.f64 #s(literal -1/6 binary64) (cos.f64 x)) eps)) eps (cos.f64 x)) eps) #<representation binary64>) () ())) ())
#s(alt (* eps (+ (cos x) (* -1/2 (* eps (sin x))))) (taylor 0 eps) (#s(alt (.f64 (fma.f64 (fma.f64 (sin.f64 x) (fma.f64 (.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) (.f64 (.f64 #s(literal -1/6 binary64) (cos.f64 x)) eps)) eps (cos.f64 x)) eps) (patch (.f64 (fma.f64 (fma.f64 (sin.f64 x) (fma.f64 (.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) (.f64 (.f64 #s(literal -1/6 binary64) (cos.f64 x)) eps)) eps (cos.f64 x)) eps) #<representation binary64>) () ())) ())
#s(alt (* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x))))))) (taylor 0 eps) (#s(alt (.f64 (fma.f64 (fma.f64 (sin.f64 x) (fma.f64 (.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) (.f64 (.f64 #s(literal -1/6 binary64) (cos.f64 x)) eps)) eps (cos.f64 x)) eps) (patch (.f64 (fma.f64 (fma.f64 (sin.f64 x) (fma.f64 (.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) (.f64 (.f64 #s(literal -1/6 binary64) (cos.f64 x)) eps)) eps (cos.f64 x)) eps) #<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 (fma.f64 (fma.f64 (sin.f64 x) (fma.f64 (.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) (.f64 (.f64 #s(literal -1/6 binary64) (cos.f64 x)) eps)) eps (cos.f64 x)) eps) (patch (.f64 (fma.f64 (fma.f64 (sin.f64 x) (fma.f64 (.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) (.f64 (.f64 #s(literal -1/6 binary64) (cos.f64 x)) eps)) eps (cos.f64 x)) eps) #<representation binary64>) () ())) ())
#s(alt (cos x) (taylor 0 eps) (#s(alt (fma.f64 (fma.f64 (sin.f64 x) (fma.f64 (.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) (.f64 (.f64 #s(literal -1/6 binary64) (cos.f64 x)) eps)) eps (cos.f64 x)) (patch (fma.f64 (fma.f64 (sin.f64 x) (fma.f64 (.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) (.f64 (.f64 #s(literal -1/6 binary64) (cos.f64 x)) eps)) eps (cos.f64 x)) #<representation binary64>) () ())) ())
#s(alt (+ (cos x) (* -1/2 (* eps (sin x)))) (taylor 0 eps) (#s(alt (fma.f64 (fma.f64 (sin.f64 x) (fma.f64 (.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) (.f64 (.f64 #s(literal -1/6 binary64) (cos.f64 x)) eps)) eps (cos.f64 x)) (patch (fma.f64 (fma.f64 (sin.f64 x) (fma.f64 (.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) (.f64 (.f64 #s(literal -1/6 binary64) (cos.f64 x)) eps)) eps (cos.f64 x)) #<representation binary64>) () ())) ())
#s(alt (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x)))))) (taylor 0 eps) (#s(alt (fma.f64 (fma.f64 (sin.f64 x) (fma.f64 (.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) (.f64 (.f64 #s(literal -1/6 binary64) (cos.f64 x)) eps)) eps (cos.f64 x)) (patch (fma.f64 (fma.f64 (sin.f64 x) (fma.f64 (.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) (.f64 (.f64 #s(literal -1/6 binary64) (cos.f64 x)) eps)) eps (cos.f64 x)) #<representation binary64>) () ())) ())
#s(alt (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* eps (+ (* -1/6 (cos x)) (* 1/24 (* eps (sin x)))))))) (taylor 0 eps) (#s(alt (fma.f64 (fma.f64 (sin.f64 x) (fma.f64 (.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) (.f64 (.f64 #s(literal -1/6 binary64) (cos.f64 x)) eps)) eps (cos.f64 x)) (patch (fma.f64 (fma.f64 (sin.f64 x) (fma.f64 (.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) (.f64 (.f64 #s(literal -1/6 binary64) (cos.f64 x)) eps)) eps (cos.f64 x)) #<representation binary64>) () ())) ())
#s(alt (* -1/2 (sin x)) (taylor 0 eps) (#s(alt (fma.f64 (sin.f64 x) (fma.f64 (.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) (.f64 (.f64 #s(literal -1/6 binary64) (cos.f64 x)) eps)) (patch (fma.f64 (sin.f64 x) (fma.f64 (.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) (.f64 (.f64 #s(literal -1/6 binary64) (cos.f64 x)) eps)) #<representation binary64>) () ())) ())
#s(alt (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x)))) (taylor 0 eps) (#s(alt (fma.f64 (sin.f64 x) (fma.f64 (.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) (.f64 (.f64 #s(literal -1/6 binary64) (cos.f64 x)) eps)) (patch (fma.f64 (sin.f64 x) (fma.f64 (.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) (.f64 (.f64 #s(literal -1/6 binary64) (cos.f64 x)) eps)) #<representation binary64>) () ())) ())
#s(alt (+ (* -1/2 (sin x)) (* eps (+ (* -1/6 (cos x)) (* 1/24 (* eps (sin x)))))) (taylor 0 eps) (#s(alt (fma.f64 (sin.f64 x) (fma.f64 (.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) (.f64 (.f64 #s(literal -1/6 binary64) (cos.f64 x)) eps)) (patch (fma.f64 (sin.f64 x) (fma.f64 (.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) (.f64 (.f64 #s(literal -1/6 binary64) (cos.f64 x)) eps)) #<representation binary64>) () ())) ())
#s(alt (+ (* -1/2 (sin x)) (* eps (+ (* -1/6 (cos x)) (* 1/24 (* eps (sin x)))))) (taylor 0 eps) (#s(alt (fma.f64 (sin.f64 x) (fma.f64 (.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) (.f64 (.f64 #s(literal -1/6 binary64) (cos.f64 x)) eps)) (patch (fma.f64 (sin.f64 x) (fma.f64 (.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) (.f64 (.f64 #s(literal -1/6 binary64) (cos.f64 x)) eps)) #<representation binary64>) () ())) ())
#s(alt (* eps (cos x)) (taylor 0 eps) (#s(alt #s(approx (- (sin (+ x eps)) (sin x)) (sin.f64 eps)) (patch #s(approx (- (sin (+ x eps)) (sin x)) (sin.f64 eps)) #<representation binary64>) () ())) ())
#s(alt (* eps (+ (cos x) (* -1/2 (* eps (sin x))))) (taylor 0 eps) (#s(alt #s(approx (- (sin (+ x eps)) (sin x)) (sin.f64 eps)) (patch #s(approx (- (sin (+ x eps)) (sin x)) (sin.f64 eps)) #<representation binary64>) () ())) ())
#s(alt (* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x))))))) (taylor 0 eps) (#s(alt #s(approx (- (sin (+ x eps)) (sin x)) (sin.f64 eps)) (patch #s(approx (- (sin (+ x eps)) (sin x)) (sin.f64 eps)) #<representation binary64>) () ())) ())
#s(alt (* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* eps (+ (* -1/6 (cos x)) (* 1/24 (* eps (sin x))))))))) (taylor 0 eps) (#s(alt #s(approx (- (sin (+ x eps)) (sin x)) (sin.f64 eps)) (patch #s(approx (- (sin (+ x eps)) (sin x)) (sin.f64 eps)) #<representation binary64>) () ())) ())
#s(alt eps (taylor 0 eps) (#s(alt (sin.f64 eps) (patch (sin.f64 eps) #<representation binary64>) () ())) ())
#s(alt (* eps (+ 1 (* -1/6 (pow eps 2)))) (taylor 0 eps) (#s(alt (sin.f64 eps) (patch (sin.f64 eps) #<representation binary64>) () ())) ())
#s(alt (* eps (+ 1 (* (pow eps 2) (- (* 1/120 (pow eps 2)) 1/6)))) (taylor 0 eps) (#s(alt (sin.f64 eps) (patch (sin.f64 eps) #<representation binary64>) () ())) ())
#s(alt (* eps (+ 1 (* (pow eps 2) (- (* (pow eps 2) (+ 1/120 (* -1/5040 (pow eps 2)))) 1/6)))) (taylor 0 eps) (#s(alt (sin.f64 eps) (patch (sin.f64 eps) #<representation binary64>) () ())) ())
#s(alt (* eps (cos x)) (taylor 0 eps) (#s(alt #s(approx (- (sin (+ x eps)) (sin x)) (.f64 (cos.f64 x) eps)) (patch #s(approx (- (sin (+ x eps)) (sin x)) (.f64 (cos.f64 x) eps)) #<representation binary64>) () ())) ())
#s(alt (* eps (+ (cos x) (* -1/2 (* eps (sin x))))) (taylor 0 eps) (#s(alt #s(approx (- (sin (+ x eps)) (sin x)) (.f64 (cos.f64 x) eps)) (patch #s(approx (- (sin (+ x eps)) (sin x)) (.f64 (cos.f64 x) eps)) #<representation binary64>) () ())) ())
#s(alt (* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x))))))) (taylor 0 eps) (#s(alt #s(approx (- (sin (+ x eps)) (sin x)) (.f64 (cos.f64 x) eps)) (patch #s(approx (- (sin (+ x eps)) (sin x)) (.f64 (cos.f64 x) eps)) #<representation binary64>) () ())) ())
#s(alt (* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* eps (+ (* -1/6 (cos x)) (* 1/24 (* eps (sin x))))))))) (taylor 0 eps) (#s(alt #s(approx (- (sin (+ x eps)) (sin x)) (.f64 (cos.f64 x) eps)) (patch #s(approx (- (sin (+ x eps)) (sin x)) (.f64 (cos.f64 x) eps)) #<representation binary64>) () ())) ())
#s(alt (* eps (cos x)) (taylor 0 eps) (#s(alt (.f64 (cos.f64 x) eps) (patch (.f64 (cos.f64 x) eps) #<representation binary64>) () ())) ())
#s(alt (* eps (cos x)) (taylor 0 eps) (#s(alt (.f64 (cos.f64 x) eps) (patch (.f64 (cos.f64 x) eps) #<representation binary64>) () ())) ())
#s(alt (* eps (cos x)) (taylor 0 eps) (#s(alt (.f64 (cos.f64 x) eps) (patch (.f64 (cos.f64 x) eps) #<representation binary64>) () ())) ())
#s(alt (* eps (cos x)) (taylor 0 eps) (#s(alt (.f64 (cos.f64 x) eps) (patch (.f64 (cos.f64 x) eps) #<representation binary64>) () ())) ())
#s(alt (* eps (cos x)) (taylor 0 eps) (#s(alt #s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 (.f64 (sin.f64 x) #s(literal -1/2 binary64)) eps (cos.f64 x)) eps)) (patch #s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 (.f64 (sin.f64 x) #s(literal -1/2 binary64)) eps (cos.f64 x)) eps)) #<representation binary64>) () ())) ())
#s(alt (* eps (+ (cos x) (* -1/2 (* eps (sin x))))) (taylor 0 eps) (#s(alt #s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 (.f64 (sin.f64 x) #s(literal -1/2 binary64)) eps (cos.f64 x)) eps)) (patch #s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 (.f64 (sin.f64 x) #s(literal -1/2 binary64)) eps (cos.f64 x)) eps)) #<representation binary64>) () ())) ())
#s(alt (* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x))))))) (taylor 0 eps) (#s(alt #s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 (.f64 (sin.f64 x) #s(literal -1/2 binary64)) eps (cos.f64 x)) eps)) (patch #s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 (.f64 (sin.f64 x) #s(literal -1/2 binary64)) eps (cos.f64 x)) eps)) #<representation binary64>) () ())) ())
#s(alt (* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* eps (+ (* -1/6 (cos x)) (* 1/24 (* eps (sin x))))))))) (taylor 0 eps) (#s(alt #s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 (.f64 (sin.f64 x) #s(literal -1/2 binary64)) eps (cos.f64 x)) eps)) (patch #s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 (.f64 (sin.f64 x) #s(literal -1/2 binary64)) eps (cos.f64 x)) eps)) #<representation binary64>) () ())) ())
#s(alt (* eps (cos x)) (taylor 0 eps) (#s(alt (.f64 (fma.f64 (.f64 (sin.f64 x) #s(literal -1/2 binary64)) eps (cos.f64 x)) eps) (patch (.f64 (fma.f64 (.f64 (sin.f64 x) #s(literal -1/2 binary64)) eps (cos.f64 x)) eps) #<representation binary64>) () ())) ())
#s(alt (* eps (+ (cos x) (* -1/2 (* eps (sin x))))) (taylor 0 eps) (#s(alt (.f64 (fma.f64 (.f64 (sin.f64 x) #s(literal -1/2 binary64)) eps (cos.f64 x)) eps) (patch (.f64 (fma.f64 (.f64 (sin.f64 x) #s(literal -1/2 binary64)) eps (cos.f64 x)) eps) #<representation binary64>) () ())) ())
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#s(alt (* eps (+ (cos x) (* -1/2 (* eps (sin x))))) (taylor 0 eps) (#s(alt (.f64 (fma.f64 (.f64 (sin.f64 x) #s(literal -1/2 binary64)) eps (cos.f64 x)) eps) (patch (.f64 (fma.f64 (.f64 (sin.f64 x) #s(literal -1/2 binary64)) eps (cos.f64 x)) eps) #<representation binary64>) () ())) ())
#s(alt (cos x) (taylor 0 eps) (#s(alt (fma.f64 (.f64 (sin.f64 x) #s(literal -1/2 binary64)) eps (cos.f64 x)) (patch (fma.f64 (.f64 (sin.f64 x) #s(literal -1/2 binary64)) eps (cos.f64 x)) #<representation binary64>) () ())) ())
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#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)) #s(approx (sin x) (fma.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 #s(literal 1/120 binary64) (.f64 x x) #s(literal -1/6 binary64)) x))) (patch (-.f64 (sin.f64 (+.f64 x eps)) #s(approx (sin x) (fma.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 #s(literal 1/120 binary64) (.f64 x x) #s(literal -1/6 binary64)) x))) #<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>) () ())) ())
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#s(alt (sin (- eps (* -1 x))) (taylor -inf x) (#s(alt (sin.f64 (+.f64 x eps)) (patch (sin.f64 (+.f64 x eps)) #<representation binary64>) () ())) ())
#s(alt (sin (- eps (* -1 x))) (taylor -inf x) (#s(alt (sin.f64 (+.f64 x eps)) (patch (sin.f64 (+.f64 x eps)) #<representation binary64>) () ())) ())
#s(alt (sin (- eps (* -1 x))) (taylor -inf x) (#s(alt (sin.f64 (+.f64 x eps)) (patch (sin.f64 (+.f64 x eps)) #<representation binary64>) () ())) ())
#s(alt (sin (- eps (* -1 x))) (taylor -inf x) (#s(alt (sin.f64 (+.f64 x eps)) (patch (sin.f64 (+.f64 x eps)) #<representation binary64>) () ())) ())
#s(alt x (taylor -inf x) (#s(alt (+.f64 x eps) (patch (+.f64 x eps) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (- (* -1 (/ eps x)) 1))) (taylor -inf x) (#s(alt (+.f64 x eps) (patch (+.f64 x eps) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (- (* -1 (/ eps x)) 1))) (taylor -inf x) (#s(alt (+.f64 x eps) (patch (+.f64 x eps) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (- (* -1 (/ eps x)) 1))) (taylor -inf x) (#s(alt (+.f64 x eps) (patch (+.f64 x eps) #<representation binary64>) () ())) ())
#s(alt (sin x) (taylor -inf x) (#s(alt #s(approx (sin x) (fma.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 #s(literal 1/120 binary64) (.f64 x x) #s(literal -1/6 binary64)) x)) (patch #s(approx (sin x) (fma.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 #s(literal 1/120 binary64) (.f64 x x) #s(literal -1/6 binary64)) x)) #<representation binary64>) () ())) ())
#s(alt (sin x) (taylor -inf x) (#s(alt #s(approx (sin x) (fma.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 #s(literal 1/120 binary64) (.f64 x x) #s(literal -1/6 binary64)) x)) (patch #s(approx (sin x) (fma.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 #s(literal 1/120 binary64) (.f64 x x) #s(literal -1/6 binary64)) x)) #<representation binary64>) () ())) ())
#s(alt (sin x) (taylor -inf x) (#s(alt #s(approx (sin x) (fma.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 #s(literal 1/120 binary64) (.f64 x x) #s(literal -1/6 binary64)) x)) (patch #s(approx (sin x) (fma.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 #s(literal 1/120 binary64) (.f64 x x) #s(literal -1/6 binary64)) x)) #<representation binary64>) () ())) ())
#s(alt (sin x) (taylor -inf x) (#s(alt #s(approx (sin x) (fma.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 #s(literal 1/120 binary64) (.f64 x x) #s(literal -1/6 binary64)) x)) (patch #s(approx (sin x) (fma.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 #s(literal 1/120 binary64) (.f64 x x) #s(literal -1/6 binary64)) x)) #<representation binary64>) () ())) ())
#s(alt (* -1/6 (* eps (cos x))) (taylor -inf x) (#s(alt (.f64 (.f64 #s(literal -1/6 binary64) (cos.f64 x)) eps) (patch (.f64 (.f64 #s(literal -1/6 binary64) (cos.f64 x)) eps) #<representation binary64>) () ())) ())
#s(alt (* -1/6 (* eps (cos x))) (taylor -inf x) (#s(alt (.f64 (.f64 #s(literal -1/6 binary64) (cos.f64 x)) eps) (patch (.f64 (.f64 #s(literal -1/6 binary64) (cos.f64 x)) eps) #<representation binary64>) () ())) ())
#s(alt (* -1/6 (* eps (cos x))) (taylor -inf x) (#s(alt (.f64 (.f64 #s(literal -1/6 binary64) (cos.f64 x)) eps) (patch (.f64 (.f64 #s(literal -1/6 binary64) (cos.f64 x)) eps) #<representation binary64>) () ())) ())
#s(alt (* -1/6 (* eps (cos x))) (taylor -inf x) (#s(alt (.f64 (.f64 #s(literal -1/6 binary64) (cos.f64 x)) eps) (patch (.f64 (.f64 #s(literal -1/6 binary64) (cos.f64 x)) eps) #<representation binary64>) () ())) ())
#s(alt (* -1/6 (cos x)) (taylor -inf x) (#s(alt (.f64 #s(literal -1/6 binary64) (cos.f64 x)) (patch (.f64 #s(literal -1/6 binary64) (cos.f64 x)) #<representation binary64>) () ())) ())
#s(alt (* -1/6 (cos x)) (taylor -inf x) (#s(alt (.f64 #s(literal -1/6 binary64) (cos.f64 x)) (patch (.f64 #s(literal -1/6 binary64) (cos.f64 x)) #<representation binary64>) () ())) ())
#s(alt (* -1/6 (cos x)) (taylor -inf x) (#s(alt (.f64 #s(literal -1/6 binary64) (cos.f64 x)) (patch (.f64 #s(literal -1/6 binary64) (cos.f64 x)) #<representation binary64>) () ())) ())
#s(alt (* -1/6 (cos x)) (taylor -inf x) (#s(alt (.f64 #s(literal -1/6 binary64) (cos.f64 x)) (patch (.f64 #s(literal -1/6 binary64) (cos.f64 x)) #<representation binary64>) () ())) ())
#s(alt (* 1/120 (pow x 2)) (taylor -inf x) (#s(alt (fma.f64 #s(literal 1/120 binary64) (.f64 x x) #s(literal -1/6 binary64)) (patch (fma.f64 #s(literal 1/120 binary64) (.f64 x x) #s(literal -1/6 binary64)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (- 1/120 (* 1/6 (/ 1 (pow x 2))))) (taylor -inf x) (#s(alt (fma.f64 #s(literal 1/120 binary64) (.f64 x x) #s(literal -1/6 binary64)) (patch (fma.f64 #s(literal 1/120 binary64) (.f64 x x) #s(literal -1/6 binary64)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (- 1/120 (* 1/6 (/ 1 (pow x 2))))) (taylor -inf x) (#s(alt (fma.f64 #s(literal 1/120 binary64) (.f64 x x) #s(literal -1/6 binary64)) (patch (fma.f64 #s(literal 1/120 binary64) (.f64 x x) #s(literal -1/6 binary64)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (- 1/120 (* 1/6 (/ 1 (pow x 2))))) (taylor -inf x) (#s(alt (fma.f64 #s(literal 1/120 binary64) (.f64 x x) #s(literal -1/6 binary64)) (patch (fma.f64 #s(literal 1/120 binary64) (.f64 x x) #s(literal -1/6 binary64)) #<representation binary64>) () ())) ())

Calls

6 calls:

Time	Variable		Point	Expression
8.0ms	x	@	inf	((- (sin (+ x eps)) (sin x)) (* (+ (* (+ (* (sin x) (+ (* (* eps eps) 1/24) -1/2)) (* (* -1/6 (cos x)) eps)) eps) (cos x)) eps) (+ (* (+ (* (sin x) (+ (* (* eps eps) 1/24) -1/2)) (* (* -1/6 (cos x)) eps)) eps) (cos x)) (+ (* (sin x) (+ (* (* eps eps) 1/24) -1/2)) (* (* -1/6 (cos x)) eps)) (- (sin (+ x eps)) (sin x)) (sin eps) (- (sin (+ x eps)) (sin x)) (* (cos x) eps) (cos x) (- (sin (+ x eps)) (sin x)) (* (+ (* (* (sin x) -1/2) eps) (cos x)) eps) (+ (* (* (sin x) -1/2) eps) (cos x)) (* (sin x) -1/2) (- (sin (+ x eps)) (sin x)) (sin (+ x eps)) (+ x eps) (sin x) (* (* -1/6 (cos x)) eps) (* -1/6 (cos x)) (+ (* 1/120 (* x x)) -1/6))
5.0ms	x	@	-inf	((- (sin (+ x eps)) (sin x)) (* (+ (* (+ (* (sin x) (+ (* (* eps eps) 1/24) -1/2)) (* (* -1/6 (cos x)) eps)) eps) (cos x)) eps) (+ (* (+ (* (sin x) (+ (* (* eps eps) 1/24) -1/2)) (* (* -1/6 (cos x)) eps)) eps) (cos x)) (+ (* (sin x) (+ (* (* eps eps) 1/24) -1/2)) (* (* -1/6 (cos x)) eps)) (- (sin (+ x eps)) (sin x)) (sin eps) (- (sin (+ x eps)) (sin x)) (* (cos x) eps) (cos x) (- (sin (+ x eps)) (sin x)) (* (+ (* (* (sin x) -1/2) eps) (cos x)) eps) (+ (* (* (sin x) -1/2) eps) (cos x)) (* (sin x) -1/2) (- (sin (+ x eps)) (sin x)) (sin (+ x eps)) (+ x eps) (sin x) (* (* -1/6 (cos x)) eps) (* -1/6 (cos x)) (+ (* 1/120 (* x x)) -1/6))
3.0ms	eps	@	-inf	((- (sin (+ x eps)) (sin x)) (* (+ (* (+ (* (sin x) (+ (* (* eps eps) 1/24) -1/2)) (* (* -1/6 (cos x)) eps)) eps) (cos x)) eps) (+ (* (+ (* (sin x) (+ (* (* eps eps) 1/24) -1/2)) (* (* -1/6 (cos x)) eps)) eps) (cos x)) (+ (* (sin x) (+ (* (* eps eps) 1/24) -1/2)) (* (* -1/6 (cos x)) eps)) (- (sin (+ x eps)) (sin x)) (sin eps) (- (sin (+ x eps)) (sin x)) (* (cos x) eps) (cos x) (- (sin (+ x eps)) (sin x)) (* (+ (* (* (sin x) -1/2) eps) (cos x)) eps) (+ (* (* (sin x) -1/2) eps) (cos x)) (* (sin x) -1/2) (- (sin (+ x eps)) (sin x)) (sin (+ x eps)) (+ x eps) (sin x) (* (* -1/6 (cos x)) eps) (* -1/6 (cos x)) (+ (* 1/120 (* x x)) -1/6))
3.0ms	eps	@	0	((- (sin (+ x eps)) (sin x)) (* (+ (* (+ (* (sin x) (+ (* (* eps eps) 1/24) -1/2)) (* (* -1/6 (cos x)) eps)) eps) (cos x)) eps) (+ (* (+ (* (sin x) (+ (* (* eps eps) 1/24) -1/2)) (* (* -1/6 (cos x)) eps)) eps) (cos x)) (+ (* (sin x) (+ (* (* eps eps) 1/24) -1/2)) (* (* -1/6 (cos x)) eps)) (- (sin (+ x eps)) (sin x)) (sin eps) (- (sin (+ x eps)) (sin x)) (* (cos x) eps) (cos x) (- (sin (+ x eps)) (sin x)) (* (+ (* (* (sin x) -1/2) eps) (cos x)) eps) (+ (* (* (sin x) -1/2) eps) (cos x)) (* (sin x) -1/2) (- (sin (+ x eps)) (sin x)) (sin (+ x eps)) (+ x eps) (sin x) (* (* -1/6 (cos x)) eps) (* -1/6 (cos x)) (+ (* 1/120 (* x x)) -1/6))
3.0ms	eps	@	inf	((- (sin (+ x eps)) (sin x)) (* (+ (* (+ (* (sin x) (+ (* (* eps eps) 1/24) -1/2)) (* (* -1/6 (cos x)) eps)) eps) (cos x)) eps) (+ (* (+ (* (sin x) (+ (* (* eps eps) 1/24) -1/2)) (* (* -1/6 (cos x)) eps)) eps) (cos x)) (+ (* (sin x) (+ (* (* eps eps) 1/24) -1/2)) (* (* -1/6 (cos x)) eps)) (- (sin (+ x eps)) (sin x)) (sin eps) (- (sin (+ x eps)) (sin x)) (* (cos x) eps) (cos x) (- (sin (+ x eps)) (sin x)) (* (+ (* (* (sin x) -1/2) eps) (cos x)) eps) (+ (* (* (sin x) -1/2) eps) (cos x)) (* (sin x) -1/2) (- (sin (+ x eps)) (sin x)) (sin (+ x eps)) (+ x eps) (sin x) (* (* -1/6 (cos x)) eps) (* -1/6 (cos x)) (+ (* 1/120 (* x x)) -1/6))

simplify206.0ms (1.7%)

Memory

-16.4MiB live, 219.4MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	358	4008
1	1094	3948
2	3176	3902
0	8144	3583

Stop Event

1×	iter limit
1×	node limit

Counts

408 → 398

Calls

Call 1

Inputs
(* eps (cos x))
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x)))))))
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* eps (+ (* -1/6 (cos x)) (* 1/24 (* eps (sin x)))))))))
(* 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)))))))))
(cos x)
(+ (cos x) (* -1/2 (* eps (sin x))))
(+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x))))))
(+ (cos x) (* eps (+ (* -1/2 (sin x)) (* eps (+ (* -1/6 (cos x)) (* 1/24 (* eps (sin x))))))))
(* -1/2 (sin x))
(+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x))))
(+ (* -1/2 (sin x)) (* eps (+ (* -1/6 (cos x)) (* 1/24 (* eps (sin x))))))
(+ (* -1/2 (sin x)) (* eps (+ (* -1/6 (cos x)) (* 1/24 (* eps (sin x))))))
(* eps (cos x))
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x)))))))
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* eps (+ (* -1/6 (cos x)) (* 1/24 (* eps (sin x)))))))))
eps
(* eps (+ 1 (* -1/6 (pow eps 2))))
(* eps (+ 1 (* (pow eps 2) (- (* 1/120 (pow eps 2)) 1/6))))
(* eps (+ 1 (* (pow eps 2) (- (* (pow eps 2) (+ 1/120 (* -1/5040 (pow eps 2)))) 1/6))))
(* eps (cos x))
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x)))))))
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* eps (+ (* -1/6 (cos x)) (* 1/24 (* eps (sin x)))))))))
(* eps (cos x))
(* eps (cos x))
(* eps (cos x))
(* eps (cos x))
(* eps (cos x))
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x)))))))
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* eps (+ (* -1/6 (cos x)) (* 1/24 (* eps (sin x)))))))))
(* eps (cos x))
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(cos x)
(+ (cos x) (* -1/2 (* eps (sin x))))
(+ (cos x) (* -1/2 (* eps (sin x))))
(+ (cos x) (* -1/2 (* eps (sin x))))
(* eps (cos x))
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x)))))))
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* eps (+ (* -1/6 (cos x)) (* 1/24 (* eps (sin x)))))))))
(sin x)
(+ (sin x) (* eps (cos x)))
(+ (sin x) (* eps (+ (cos x) (* -1/2 (* eps (sin x))))))
(+ (sin x) (* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x))))))))
x
(+ eps x)
(+ eps x)
(+ eps x)
(* -1/6 (* eps (cos x)))
(* -1/6 (* eps (cos x)))
(* -1/6 (* eps (cos x)))
(* -1/6 (* eps (cos x)))
(- (sin (+ eps x)) (sin x))
(- (sin (+ eps x)) (sin x))
(- (sin (+ eps x)) (sin x))
(- (sin (+ eps x)) (sin x))
(* 1/24 (* (pow eps 4) (sin x)))
(* (pow eps 4) (+ (* -1/6 (/ (cos x) eps)) (* 1/24 (sin x))))
(* (pow eps 4) (+ (* -1/2 (/ (sin x) (pow eps 2))) (+ (* -1/6 (/ (cos x) eps)) (* 1/24 (sin x)))))
(* (pow eps 4) (+ (* -1/2 (/ (sin x) (pow eps 2))) (+ (* -1/6 (/ (cos x) eps)) (+ (* 1/24 (sin x)) (/ (cos x) (pow eps 3))))))
(* 1/24 (* (pow eps 3) (sin x)))
(* (pow eps 3) (+ (* -1/6 (/ (cos x) eps)) (* 1/24 (sin x))))
(* (pow eps 3) (+ (* -1/2 (/ (sin x) (pow eps 2))) (+ (* -1/6 (/ (cos x) eps)) (* 1/24 (sin x)))))
(* (pow eps 3) (+ (* -1/2 (/ (sin x) (pow eps 2))) (+ (* -1/6 (/ (cos x) eps)) (+ (* 1/24 (sin x)) (/ (cos x) (pow eps 3))))))
(* 1/24 (* (pow eps 2) (sin x)))
(* (pow eps 2) (+ (* -1/6 (/ (cos x) eps)) (* 1/24 (sin x))))
(* (pow eps 2) (+ (* -1/2 (/ (sin x) (pow eps 2))) (+ (* -1/6 (/ (cos x) eps)) (* 1/24 (sin x)))))
(* (pow eps 2) (+ (* -1/2 (/ (sin x) (pow eps 2))) (+ (* -1/6 (/ (cos x) eps)) (* 1/24 (sin x)))))
(- (sin (+ eps x)) (sin x))
(- (sin (+ eps x)) (sin x))
(- (sin (+ eps x)) (sin x))
(- (sin (+ eps x)) (sin x))
(sin eps)
(sin eps)
(sin eps)
(sin eps)
(- (sin (+ eps x)) (sin x))
(- (sin (+ eps x)) (sin x))
(- (sin (+ eps x)) (sin x))
(- (sin (+ eps x)) (sin x))
(* eps (cos x))
(* eps (cos x))
(* eps (cos x))
(* eps (cos x))
(- (sin (+ eps x)) (sin x))
(- (sin (+ eps x)) (sin x))
(- (sin (+ eps x)) (sin x))
(- (sin (+ eps x)) (sin x))
(* -1/2 (* (pow eps 2) (sin x)))
(* (pow eps 2) (+ (* -1/2 (sin x)) (/ (cos x) eps)))
(* (pow eps 2) (+ (* -1/2 (sin x)) (/ (cos x) eps)))
(* (pow eps 2) (+ (* -1/2 (sin x)) (/ (cos x) eps)))
(* -1/2 (* eps (sin x)))
(* eps (+ (* -1/2 (sin x)) (/ (cos x) eps)))
(* eps (+ (* -1/2 (sin x)) (/ (cos x) eps)))
(* eps (+ (* -1/2 (sin x)) (/ (cos x) eps)))
(- (sin (+ eps x)) (sin x))
(- (sin (+ eps x)) (sin x))
(- (sin (+ eps x)) (sin x))
(- (sin (+ eps x)) (sin x))
(sin (+ eps x))
(sin (+ eps x))
(sin (+ eps x))
(sin (+ eps x))
eps
(* eps (+ 1 (/ x eps)))
(* eps (+ 1 (/ x eps)))
(* eps (+ 1 (/ x eps)))
(* -1/6 (* eps (cos x)))
(* -1/6 (* eps (cos x)))
(* -1/6 (* eps (cos x)))
(* -1/6 (* eps (cos x)))
(- (sin (- x (* -1 eps))) (sin x))
(- (sin (- x (* -1 eps))) (sin x))
(- (sin (- x (* -1 eps))) (sin x))
(- (sin (- x (* -1 eps))) (sin x))
(* 1/24 (* (pow eps 4) (sin x)))
(* (pow eps 4) (+ (* -1/6 (/ (cos x) eps)) (* 1/24 (sin x))))
(* (pow eps 4) (+ (* -1 (/ (+ (* 1/6 (cos x)) (* 1/2 (/ (sin x) eps))) eps)) (* 1/24 (sin x))))
(* (pow eps 4) (+ (* -1 (/ (+ (* -1 (/ (+ (* -1/2 (sin x)) (/ (cos x) eps)) eps)) (* 1/6 (cos x))) eps)) (* 1/24 (sin x))))
(* 1/24 (* (pow eps 3) (sin x)))
(* -1 (* (pow eps 3) (+ (* -1/24 (sin x)) (* 1/6 (/ (cos x) eps)))))
(* -1 (* (pow eps 3) (+ (* -1 (/ (+ (* -1/2 (/ (sin x) eps)) (* -1/6 (cos x))) eps)) (* -1/24 (sin x)))))
(* -1 (* (pow eps 3) (+ (* -1 (/ (+ (* -1 (/ (+ (* -1 (/ (cos x) eps)) (* 1/2 (sin x))) eps)) (* -1/6 (cos x))) eps)) (* -1/24 (sin x)))))
(* 1/24 (* (pow eps 2) (sin x)))
(* (pow eps 2) (+ (* -1/6 (/ (cos x) eps)) (* 1/24 (sin x))))
(* (pow eps 2) (+ (* -1 (/ (+ (* 1/6 (cos x)) (* 1/2 (/ (sin x) eps))) eps)) (* 1/24 (sin x))))
(* (pow eps 2) (+ (* -1 (/ (+ (* 1/6 (cos x)) (* 1/2 (/ (sin x) eps))) eps)) (* 1/24 (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)
(sin eps)
(sin eps)
(- (sin (- x (* -1 eps))) (sin x))
(- (sin (- x (* -1 eps))) (sin x))
(- (sin (- x (* -1 eps))) (sin x))
(- (sin (- x (* -1 eps))) (sin x))
(* eps (cos x))
(* eps (cos x))
(* eps (cos x))
(* eps (cos x))
(- (sin (- x (* -1 eps))) (sin x))
(- (sin (- x (* -1 eps))) (sin x))
(- (sin (- x (* -1 eps))) (sin x))
(- (sin (- x (* -1 eps))) (sin x))
(* -1/2 (* (pow eps 2) (sin x)))
(* (pow eps 2) (+ (* -1/2 (sin x)) (/ (cos x) eps)))
(* (pow eps 2) (+ (* -1/2 (sin x)) (/ (cos x) eps)))
(* (pow eps 2) (+ (* -1/2 (sin x)) (/ (cos x) eps)))
(* -1/2 (* eps (sin x)))
(* -1 (* eps (+ (* -1 (/ (cos x) eps)) (* 1/2 (sin x)))))
(* -1 (* eps (+ (* -1 (/ (cos x) eps)) (* 1/2 (sin x)))))
(* -1 (* eps (+ (* -1 (/ (cos x) eps)) (* 1/2 (sin x)))))
(- (sin (- x (* -1 eps))) (sin x))
(- (sin (- x (* -1 eps))) (sin x))
(- (sin (- x (* -1 eps))) (sin x))
(- (sin (- x (* -1 eps))) (sin x))
(sin (- x (* -1 eps)))
(sin (- x (* -1 eps)))
(sin (- x (* -1 eps)))
(sin (- x (* -1 eps)))
eps
(* -1 (* eps (- (* -1 (/ x eps)) 1)))
(* -1 (* eps (- (* -1 (/ x eps)) 1)))
(* -1 (* eps (- (* -1 (/ x eps)) 1)))
(* -1/6 (* eps (cos x)))
(* -1/6 (* eps (cos x)))
(* -1/6 (* eps (cos x)))
(* -1/6 (* eps (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)))
(* eps (+ 1 (* -1/6 (pow eps 2))))
(+ (* eps (+ 1 (* -1/6 (pow eps 2)))) (* (pow eps 2) (* x (- (* 1/24 (pow eps 2)) 1/2))))
(+ (* eps (+ 1 (* -1/6 (pow eps 2)))) (* x (+ (* eps (* x (- (* 1/12 (pow eps 2)) 1/2))) (* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2)))))
(+ (* eps (+ 1 (* -1/6 (pow eps 2)))) (* x (+ (* x (+ (* -1/6 (* (pow eps 2) (* x (- (* 1/24 (pow eps 2)) 1/2)))) (* eps (- (* 1/12 (pow eps 2)) 1/2)))) (* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2)))))
(+ 1 (* -1/6 (pow eps 2)))
(+ 1 (+ (* -1/6 (pow eps 2)) (* eps (* x (- (* 1/24 (pow eps 2)) 1/2)))))
(+ 1 (+ (* -1/6 (pow eps 2)) (* x (+ (* eps (- (* 1/24 (pow eps 2)) 1/2)) (* x (- (* 1/12 (pow eps 2)) 1/2))))))
(+ 1 (+ (* -1/6 (pow eps 2)) (* x (+ (* eps (- (* 1/24 (pow eps 2)) 1/2)) (* x (- (+ (* -1/6 (* eps (* x (- (* 1/24 (pow eps 2)) 1/2)))) (* 1/12 (pow eps 2))) 1/2))))))
(* -1/6 eps)
(+ (* -1/6 eps) (* x (- (* 1/24 (pow eps 2)) 1/2)))
(+ (* -1/6 eps) (* x (- (+ (* 1/24 (pow eps 2)) (* 1/12 (* eps x))) 1/2)))
(+ (* -1/6 eps) (* x (- (+ (* 1/24 (pow eps 2)) (* x (+ (* -1/6 (* x (- (* 1/24 (pow eps 2)) 1/2))) (* 1/12 eps)))) 1/2)))
(sin eps)
(+ (sin eps) (* x (- (cos eps) 1)))
(+ (sin eps) (* x (- (+ (cos eps) (* -1/2 (* x (sin eps)))) 1)))
(+ (sin eps) (* x (- (+ (cos eps) (* x (+ (* -1/2 (sin eps)) (* x (+ 1/6 (* -1/6 (cos eps))))))) 1)))
(sin eps)
(+ (sin eps) (* x (- (cos eps) 1)))
(+ (sin eps) (* x (- (+ (cos eps) (* -1/2 (* x (sin eps)))) 1)))
(+ (sin eps) (* x (- (+ (cos eps) (* x (+ (* -1/2 (sin eps)) (* x (+ 1/6 (* -1/6 (cos eps))))))) 1)))
eps
(+ eps (* -1/2 (* eps (pow x 2))))
(+ eps (* (pow x 2) (+ (* -1/2 eps) (* 1/24 (* eps (pow x 2))))))
(+ eps (* (pow x 2) (+ (* -1/2 eps) (* (pow x 2) (+ (* -1/720 (* eps (pow x 2))) (* 1/24 eps))))))
1
(+ 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)))
(sin eps)
(+ (sin eps) (* x (- (cos eps) 1)))
(+ (sin eps) (* x (- (+ (cos eps) (* -1/2 (* x (sin eps)))) 1)))
(+ (sin eps) (* x (- (+ (cos eps) (* x (+ (* -1/2 (sin eps)) (* x (+ 1/6 (* -1/6 (cos eps))))))) 1)))
eps
(+ eps (* -1/2 (* (pow eps 2) x)))
(+ eps (* x (+ (* -1/2 (* eps x)) (* -1/2 (pow eps 2)))))
(+ eps (* x (+ (* -1/2 (pow eps 2)) (* x (+ (* -1/2 eps) (* 1/12 (* (pow eps 2) x)))))))
1
(+ 1 (* -1/2 (* eps x)))
(+ 1 (* x (+ (* -1/2 eps) (* -1/2 x))))
(+ 1 (* x (+ (* -1/2 eps) (* x (- (* 1/12 (* eps x)) 1/2)))))
(* -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))
(sin eps)
(+ (sin eps) (* x (- (cos eps) 1)))
(+ (sin eps) (* x (- (+ (cos eps) (* -1/2 (* x (sin eps)))) 1)))
(+ (sin eps) (* x (- (+ (cos eps) (* x (+ (* -1/2 (sin eps)) (* x (+ 1/6 (* -1/6 (cos eps))))))) 1)))
(sin eps)
(+ (sin eps) (* x (cos eps)))
(+ (sin eps) (* x (+ (cos eps) (* -1/2 (* x (sin eps))))))
(+ (sin eps) (* x (+ (cos eps) (* x (+ (* -1/2 (sin eps)) (* -1/6 (* x (cos eps))))))))
eps
(+ eps x)
(+ eps x)
(+ eps x)
x
(* x (+ 1 (* -1/6 (pow x 2))))
(* x (+ 1 (* (pow x 2) (- (* 1/120 (pow x 2)) 1/6))))
(* x (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/120 (* -1/5040 (pow x 2)))) 1/6))))
(* -1/6 eps)
(+ (* -1/6 eps) (* 1/12 (* eps (pow x 2))))
(+ (* -1/6 eps) (* (pow x 2) (+ (* -1/144 (* eps (pow x 2))) (* 1/12 eps))))
(+ (* -1/6 eps) (* (pow x 2) (+ (* 1/12 eps) (* (pow x 2) (+ (* -1/144 eps) (* 1/4320 (* eps (pow x 2))))))))
-1/6
(- (* 1/12 (pow x 2)) 1/6)
(- (* (pow x 2) (+ 1/12 (* -1/144 (pow x 2)))) 1/6)
(- (* (pow x 2) (+ 1/12 (* (pow x 2) (- (* 1/4320 (pow x 2)) 1/144)))) 1/6)
-1/6
(- (* 1/120 (pow x 2)) 1/6)
(- (* 1/120 (pow x 2)) 1/6)
(- (* 1/120 (pow x 2)) 1/6)
(- (sin (+ eps x)) (sin x))
(- (sin (+ eps x)) (sin x))
(- (sin (+ eps x)) (sin x))
(- (sin (+ eps x)) (sin x))
(* eps (+ (cos x) (* eps (+ (* -1/6 (* eps (cos x))) (* (sin x) (- (* 1/24 (pow eps 2)) 1/2))))))
(* eps (+ (cos x) (* eps (+ (* -1/6 (* eps (cos x))) (* (sin x) (- (* 1/24 (pow eps 2)) 1/2))))))
(* eps (+ (cos x) (* eps (+ (* -1/6 (* eps (cos x))) (* (sin x) (- (* 1/24 (pow eps 2)) 1/2))))))
(* eps (+ (cos x) (* eps (+ (* -1/6 (* eps (cos x))) (* (sin x) (- (* 1/24 (pow eps 2)) 1/2))))))
(+ (cos x) (* eps (+ (* -1/6 (* eps (cos x))) (* (sin x) (- (* 1/24 (pow eps 2)) 1/2)))))
(+ (cos x) (* eps (+ (* -1/6 (* eps (cos x))) (* (sin x) (- (* 1/24 (pow eps 2)) 1/2)))))
(+ (cos x) (* eps (+ (* -1/6 (* eps (cos x))) (* (sin x) (- (* 1/24 (pow eps 2)) 1/2)))))
(+ (cos x) (* eps (+ (* -1/6 (* eps (cos x))) (* (sin x) (- (* 1/24 (pow eps 2)) 1/2)))))
(+ (* -1/6 (* eps (cos x))) (* (sin x) (- (* 1/24 (pow eps 2)) 1/2)))
(+ (* -1/6 (* eps (cos x))) (* (sin x) (- (* 1/24 (pow eps 2)) 1/2)))
(+ (* -1/6 (* eps (cos x))) (* (sin x) (- (* 1/24 (pow eps 2)) 1/2)))
(+ (* -1/6 (* eps (cos x))) (* (sin x) (- (* 1/24 (pow eps 2)) 1/2)))
(- (sin (+ eps x)) (sin x))
(- (sin (+ eps x)) (sin x))
(- (sin (+ eps x)) (sin x))
(- (sin (+ eps x)) (sin x))
(- (sin (+ eps x)) (sin x))
(- (sin (+ eps x)) (sin x))
(- (sin (+ eps x)) (sin x))
(- (sin (+ eps x)) (sin x))
(* eps (cos x))
(* eps (cos x))
(* eps (cos x))
(* eps (cos x))
(cos x)
(cos x)
(cos x)
(cos x)
(- (sin (+ eps x)) (sin x))
(- (sin (+ eps x)) (sin x))
(- (sin (+ eps x)) (sin x))
(- (sin (+ eps x)) (sin x))
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(+ (cos x) (* -1/2 (* eps (sin x))))
(+ (cos x) (* -1/2 (* eps (sin x))))
(+ (cos x) (* -1/2 (* eps (sin x))))
(+ (cos x) (* -1/2 (* eps (sin x))))
(* -1/2 (sin x))
(* -1/2 (sin x))
(* -1/2 (sin x))
(* -1/2 (sin x))
(- (sin (+ eps x)) (sin x))
(- (sin (+ eps x)) (sin x))
(- (sin (+ eps x)) (sin x))
(- (sin (+ eps x)) (sin x))
(sin (+ eps x))
(sin (+ eps x))
(sin (+ eps x))
(sin (+ eps x))
x
(* x (+ 1 (/ eps x)))
(* x (+ 1 (/ eps x)))
(* x (+ 1 (/ eps x)))
(sin x)
(sin x)
(sin x)
(sin x)
(* -1/6 (* eps (cos x)))
(* -1/6 (* eps (cos x)))
(* -1/6 (* eps (cos x)))
(* -1/6 (* eps (cos x)))
(* -1/6 (cos x))
(* -1/6 (cos x))
(* -1/6 (cos x))
(* -1/6 (cos x))
(* 1/120 (pow x 2))
(* (pow x 2) (- 1/120 (* 1/6 (/ 1 (pow x 2)))))
(* (pow x 2) (- 1/120 (* 1/6 (/ 1 (pow x 2)))))
(* (pow x 2) (- 1/120 (* 1/6 (/ 1 (pow x 2)))))
(- (sin (- eps (* -1 x))) (sin x))
(- (sin (- eps (* -1 x))) (sin x))
(- (sin (- eps (* -1 x))) (sin x))
(- (sin (- eps (* -1 x))) (sin x))
(* eps (+ (cos x) (* eps (+ (* -1/6 (* eps (cos x))) (* (sin x) (- (* 1/24 (pow eps 2)) 1/2))))))
(* eps (+ (cos x) (* eps (+ (* -1/6 (* eps (cos x))) (* (sin x) (- (* 1/24 (pow eps 2)) 1/2))))))
(* eps (+ (cos x) (* eps (+ (* -1/6 (* eps (cos x))) (* (sin x) (- (* 1/24 (pow eps 2)) 1/2))))))
(* eps (+ (cos x) (* eps (+ (* -1/6 (* eps (cos x))) (* (sin x) (- (* 1/24 (pow eps 2)) 1/2))))))
(+ (cos x) (* eps (+ (* -1/6 (* eps (cos x))) (* (sin x) (- (* 1/24 (pow eps 2)) 1/2)))))
(+ (cos x) (* eps (+ (* -1/6 (* eps (cos x))) (* (sin x) (- (* 1/24 (pow eps 2)) 1/2)))))
(+ (cos x) (* eps (+ (* -1/6 (* eps (cos x))) (* (sin x) (- (* 1/24 (pow eps 2)) 1/2)))))
(+ (cos x) (* eps (+ (* -1/6 (* eps (cos x))) (* (sin x) (- (* 1/24 (pow eps 2)) 1/2)))))
(+ (* -1/6 (* eps (cos x))) (* (sin x) (- (* 1/24 (pow eps 2)) 1/2)))
(+ (* -1/6 (* eps (cos x))) (* (sin x) (- (* 1/24 (pow eps 2)) 1/2)))
(+ (* -1/6 (* eps (cos x))) (* (sin x) (- (* 1/24 (pow eps 2)) 1/2)))
(+ (* -1/6 (* eps (cos x))) (* (sin x) (- (* 1/24 (pow eps 2)) 1/2)))
(- (sin (- eps (* -1 x))) (sin x))
(- (sin (- eps (* -1 x))) (sin x))
(- (sin (- eps (* -1 x))) (sin x))
(- (sin (- eps (* -1 x))) (sin x))
(- (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))
(* eps (cos x))
(* eps (cos x))
(cos x)
(cos x)
(cos x)
(cos 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) (* -1/2 (* eps (sin x)))))
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(+ (cos x) (* -1/2 (* eps (sin x))))
(+ (cos x) (* -1/2 (* eps (sin x))))
(+ (cos x) (* -1/2 (* eps (sin x))))
(+ (cos x) (* -1/2 (* eps (sin x))))
(* -1/2 (sin x))
(* -1/2 (sin x))
(* -1/2 (sin x))
(* -1/2 (sin x))
(- (sin (- eps (* -1 x))) (sin x))
(- (sin (- eps (* -1 x))) (sin x))
(- (sin (- eps (* -1 x))) (sin x))
(- (sin (- eps (* -1 x))) (sin x))
(sin (- eps (* -1 x)))
(sin (- eps (* -1 x)))
(sin (- eps (* -1 x)))
(sin (- eps (* -1 x)))
x
(* -1 (* x (- (* -1 (/ eps x)) 1)))
(* -1 (* x (- (* -1 (/ eps x)) 1)))
(* -1 (* x (- (* -1 (/ eps x)) 1)))
(sin x)
(sin x)
(sin x)
(sin x)
(* -1/6 (* eps (cos x)))
(* -1/6 (* eps (cos x)))
(* -1/6 (* eps (cos x)))
(* -1/6 (* eps (cos x)))
(* -1/6 (cos x))
(* -1/6 (cos x))
(* -1/6 (cos x))
(* -1/6 (cos x))
(* 1/120 (pow x 2))
(* (pow x 2) (- 1/120 (* 1/6 (/ 1 (pow x 2)))))
(* (pow x 2) (- 1/120 (* 1/6 (/ 1 (pow x 2)))))
(* (pow x 2) (- 1/120 (* 1/6 (/ 1 (pow x 2)))))

Outputs
(* eps (cos x))
(*.f64 (cos.f64 x) eps)
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(.f64 (fma.f64 (.f64 (sin.f64 x) #s(literal -1/2 binary64)) eps (cos.f64 x)) eps)
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x)))))))
(.f64 (fma.f64 (fma.f64 #s(literal -1/6 binary64) (.f64 (cos.f64 x) eps) (*.f64 (sin.f64 x) #s(literal -1/2 binary64))) eps (cos.f64 x)) eps)
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* eps (+ (* -1/6 (cos x)) (* 1/24 (* eps (sin x)))))))))
(.f64 (fma.f64 (fma.f64 (fma.f64 (.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) (sin.f64 x) (.f64 (.f64 #s(literal -1/6 binary64) (cos.f64 x)) eps)) eps (cos.f64 x)) eps)
(* eps (cos x))
(*.f64 (cos.f64 x) eps)
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(.f64 (fma.f64 (.f64 (sin.f64 x) #s(literal -1/2 binary64)) eps (cos.f64 x)) eps)
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x)))))))
(.f64 (fma.f64 (fma.f64 #s(literal -1/6 binary64) (.f64 (cos.f64 x) eps) (*.f64 (sin.f64 x) #s(literal -1/2 binary64))) eps (cos.f64 x)) eps)
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* eps (+ (* -1/6 (cos x)) (* 1/24 (* eps (sin x)))))))))
(.f64 (fma.f64 (fma.f64 (fma.f64 (.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) (sin.f64 x) (.f64 (.f64 #s(literal -1/6 binary64) (cos.f64 x)) eps)) eps (cos.f64 x)) eps)
(cos x)
(cos.f64 x)
(+ (cos x) (* -1/2 (* eps (sin x))))
(fma.f64 (*.f64 (sin.f64 x) #s(literal -1/2 binary64)) eps (cos.f64 x))
(+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x))))))
(fma.f64 (fma.f64 #s(literal -1/6 binary64) (.f64 (cos.f64 x) eps) (.f64 (sin.f64 x) #s(literal -1/2 binary64))) eps (cos.f64 x))
(+ (cos x) (* eps (+ (* -1/2 (sin x)) (* eps (+ (* -1/6 (cos x)) (* 1/24 (* eps (sin x))))))))
(fma.f64 (fma.f64 (fma.f64 (.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) (sin.f64 x) (.f64 (*.f64 #s(literal -1/6 binary64) (cos.f64 x)) eps)) eps (cos.f64 x))
(* -1/2 (sin x))
(*.f64 (sin.f64 x) #s(literal -1/2 binary64))
(+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x))))
(fma.f64 #s(literal -1/6 binary64) (.f64 (cos.f64 x) eps) (.f64 (sin.f64 x) #s(literal -1/2 binary64)))
(+ (* -1/2 (sin x)) (* eps (+ (* -1/6 (cos x)) (* 1/24 (* eps (sin x))))))
(fma.f64 (fma.f64 (.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) (sin.f64 x) (.f64 (*.f64 #s(literal -1/6 binary64) (cos.f64 x)) eps))
(+ (* -1/2 (sin x)) (* eps (+ (* -1/6 (cos x)) (* 1/24 (* eps (sin x))))))
(fma.f64 (fma.f64 (.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) (sin.f64 x) (.f64 (*.f64 #s(literal -1/6 binary64) (cos.f64 x)) eps))
(* eps (cos x))
(*.f64 (cos.f64 x) eps)
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(.f64 (fma.f64 (.f64 (sin.f64 x) #s(literal -1/2 binary64)) eps (cos.f64 x)) eps)
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x)))))))
(.f64 (fma.f64 (fma.f64 #s(literal -1/6 binary64) (.f64 (cos.f64 x) eps) (*.f64 (sin.f64 x) #s(literal -1/2 binary64))) eps (cos.f64 x)) eps)
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* eps (+ (* -1/6 (cos x)) (* 1/24 (* eps (sin x)))))))))
(.f64 (fma.f64 (fma.f64 (fma.f64 (.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) (sin.f64 x) (.f64 (.f64 #s(literal -1/6 binary64) (cos.f64 x)) eps)) eps (cos.f64 x)) eps)
eps
(* eps (+ 1 (* -1/6 (pow eps 2))))
(fma.f64 (pow.f64 eps #s(literal 3 binary64)) #s(literal -1/6 binary64) eps)
(* eps (+ 1 (* (pow eps 2) (- (* 1/120 (pow eps 2)) 1/6))))
(fma.f64 (pow.f64 eps #s(literal 3 binary64)) (fma.f64 #s(literal 1/120 binary64) (*.f64 eps eps) #s(literal -1/6 binary64)) eps)
(* eps (+ 1 (* (pow eps 2) (- (* (pow eps 2) (+ 1/120 (* -1/5040 (pow eps 2)))) 1/6))))
(fma.f64 (pow.f64 eps #s(literal 3 binary64)) (fma.f64 (fma.f64 #s(literal -1/5040 binary64) (.f64 eps eps) #s(literal 1/120 binary64)) (.f64 eps eps) #s(literal -1/6 binary64)) eps)
(* eps (cos x))
(*.f64 (cos.f64 x) eps)
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(.f64 (fma.f64 (.f64 (sin.f64 x) #s(literal -1/2 binary64)) eps (cos.f64 x)) eps)
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x)))))))
(.f64 (fma.f64 (fma.f64 #s(literal -1/6 binary64) (.f64 (cos.f64 x) eps) (*.f64 (sin.f64 x) #s(literal -1/2 binary64))) eps (cos.f64 x)) eps)
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* eps (+ (* -1/6 (cos x)) (* 1/24 (* eps (sin x)))))))))
(.f64 (fma.f64 (fma.f64 (fma.f64 (.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) (sin.f64 x) (.f64 (.f64 #s(literal -1/6 binary64) (cos.f64 x)) eps)) eps (cos.f64 x)) eps)
(* eps (cos x))
(*.f64 (cos.f64 x) eps)
(* eps (cos x))
(*.f64 (cos.f64 x) eps)
(* eps (cos x))
(*.f64 (cos.f64 x) eps)
(* eps (cos x))
(*.f64 (cos.f64 x) eps)
(* eps (cos x))
(*.f64 (cos.f64 x) eps)
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(.f64 (fma.f64 (.f64 (sin.f64 x) #s(literal -1/2 binary64)) eps (cos.f64 x)) eps)
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x)))))))
(.f64 (fma.f64 (fma.f64 #s(literal -1/6 binary64) (.f64 (cos.f64 x) eps) (*.f64 (sin.f64 x) #s(literal -1/2 binary64))) eps (cos.f64 x)) eps)
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* eps (+ (* -1/6 (cos x)) (* 1/24 (* eps (sin x)))))))))
(.f64 (fma.f64 (fma.f64 (fma.f64 (.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) (sin.f64 x) (.f64 (.f64 #s(literal -1/6 binary64) (cos.f64 x)) eps)) eps (cos.f64 x)) eps)
(* eps (cos x))
(*.f64 (cos.f64 x) eps)
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(.f64 (fma.f64 (.f64 (sin.f64 x) #s(literal -1/2 binary64)) eps (cos.f64 x)) eps)
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(.f64 (fma.f64 (.f64 (sin.f64 x) #s(literal -1/2 binary64)) eps (cos.f64 x)) eps)
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(.f64 (fma.f64 (.f64 (sin.f64 x) #s(literal -1/2 binary64)) eps (cos.f64 x)) eps)
(cos x)
(cos.f64 x)
(+ (cos x) (* -1/2 (* eps (sin x))))
(fma.f64 (*.f64 (sin.f64 x) #s(literal -1/2 binary64)) eps (cos.f64 x))
(+ (cos x) (* -1/2 (* eps (sin x))))
(fma.f64 (*.f64 (sin.f64 x) #s(literal -1/2 binary64)) eps (cos.f64 x))
(+ (cos x) (* -1/2 (* eps (sin x))))
(fma.f64 (*.f64 (sin.f64 x) #s(literal -1/2 binary64)) eps (cos.f64 x))
(* eps (cos x))
(*.f64 (cos.f64 x) eps)
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
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(fma.f64 (.f64 eps (fma.f64 (fma.f64 #s(literal 1/12 binary64) (.f64 eps eps) #s(literal -1/2 binary64)) x (.f64 (fma.f64 (.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) eps))) x (fma.f64 (pow.f64 eps #s(literal 3 binary64)) #s(literal -1/6 binary64) eps))
(+ (* eps (+ 1 (* -1/6 (pow eps 2)))) (* x (+ (* x (+ (* -1/6 (* (pow eps 2) (* x (- (* 1/24 (pow eps 2)) 1/2)))) (* eps (- (* 1/12 (pow eps 2)) 1/2)))) (* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2)))))
(fma.f64 (.f64 x x) (fma.f64 (.f64 (.f64 (.f64 eps eps) #s(literal -1/6 binary64)) x) (fma.f64 (.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) (.f64 (fma.f64 #s(literal 1/12 binary64) (.f64 eps eps) #s(literal -1/2 binary64)) eps)) (.f64 eps (fma.f64 eps (fma.f64 (fma.f64 (.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) x (.f64 #s(literal -1/6 binary64) eps)) #s(literal 1 binary64))))
(+ 1 (* -1/6 (pow eps 2)))
(fma.f64 (*.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64))
(+ 1 (+ (* -1/6 (pow eps 2)) (* eps (* x (- (* 1/24 (pow eps 2)) 1/2)))))
(fma.f64 eps (fma.f64 (fma.f64 (.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) x (.f64 #s(literal -1/6 binary64) eps)) #s(literal 1 binary64))
(+ 1 (+ (* -1/6 (pow eps 2)) (* x (+ (* eps (- (* 1/24 (pow eps 2)) 1/2)) (* x (- (* 1/12 (pow eps 2)) 1/2))))))
(fma.f64 (fma.f64 (fma.f64 #s(literal 1/12 binary64) (.f64 eps eps) #s(literal -1/2 binary64)) x (.f64 (fma.f64 (.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) eps)) x (fma.f64 (.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64)))
(+ 1 (+ (* -1/6 (pow eps 2)) (* x (+ (* eps (- (* 1/24 (pow eps 2)) 1/2)) (* x (- (+ (* -1/6 (* eps (* x (- (* 1/24 (pow eps 2)) 1/2)))) (* 1/12 (pow eps 2))) 1/2))))))
(fma.f64 (.f64 x x) (fma.f64 eps (fma.f64 #s(literal 1/12 binary64) eps (.f64 (.f64 (fma.f64 (.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) x) #s(literal -1/6 binary64))) #s(literal -1/2 binary64)) (fma.f64 eps (fma.f64 (fma.f64 (.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) x (.f64 #s(literal -1/6 binary64) eps)) #s(literal 1 binary64)))
(* -1/6 eps)
(*.f64 #s(literal -1/6 binary64) eps)
(+ (* -1/6 eps) (* x (- (* 1/24 (pow eps 2)) 1/2)))
(fma.f64 (fma.f64 (.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) x (.f64 #s(literal -1/6 binary64) eps))
(+ (* -1/6 eps) (* x (- (+ (* 1/24 (pow eps 2)) (* 1/12 (* eps x))) 1/2)))
(fma.f64 (fma.f64 eps (fma.f64 #s(literal 1/12 binary64) x (.f64 #s(literal 1/24 binary64) eps)) #s(literal -1/2 binary64)) x (.f64 #s(literal -1/6 binary64) eps))
(+ (* -1/6 eps) (* x (- (+ (* 1/24 (pow eps 2)) (* x (+ (* -1/6 (* x (- (* 1/24 (pow eps 2)) 1/2))) (* 1/12 eps)))) 1/2)))
(fma.f64 (fma.f64 (fma.f64 #s(literal 1/12 binary64) eps (.f64 (.f64 (fma.f64 (.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) x) #s(literal -1/6 binary64))) x (fma.f64 (.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64))) x (*.f64 #s(literal -1/6 binary64) eps))
(sin eps)
(sin.f64 eps)
(+ (sin eps) (* x (- (cos eps) 1)))
(fma.f64 (-.f64 (cos.f64 eps) #s(literal 1 binary64)) x (sin.f64 eps))
(+ (sin eps) (* x (- (+ (cos eps) (* -1/2 (* x (sin eps)))) 1)))
(fma.f64 (fma.f64 (*.f64 (sin.f64 eps) x) #s(literal -1/2 binary64) (-.f64 (cos.f64 eps) #s(literal 1 binary64))) x (sin.f64 eps))
(+ (sin eps) (* x (- (+ (cos eps) (* x (+ (* -1/2 (sin eps)) (* x (+ 1/6 (* -1/6 (cos eps))))))) 1)))
(fma.f64 (fma.f64 (fma.f64 (fma.f64 (cos.f64 eps) #s(literal -1/6 binary64) #s(literal 1/6 binary64)) x (*.f64 (sin.f64 eps) #s(literal -1/2 binary64))) x (-.f64 (cos.f64 eps) #s(literal 1 binary64))) x (sin.f64 eps))
(sin eps)
(sin.f64 eps)
(+ (sin eps) (* x (- (cos eps) 1)))
(fma.f64 (-.f64 (cos.f64 eps) #s(literal 1 binary64)) x (sin.f64 eps))
(+ (sin eps) (* x (- (+ (cos eps) (* -1/2 (* x (sin eps)))) 1)))
(fma.f64 (fma.f64 (*.f64 (sin.f64 eps) x) #s(literal -1/2 binary64) (-.f64 (cos.f64 eps) #s(literal 1 binary64))) x (sin.f64 eps))
(+ (sin eps) (* x (- (+ (cos eps) (* x (+ (* -1/2 (sin eps)) (* x (+ 1/6 (* -1/6 (cos eps))))))) 1)))
(fma.f64 (fma.f64 (fma.f64 (fma.f64 (cos.f64 eps) #s(literal -1/6 binary64) #s(literal 1/6 binary64)) x (*.f64 (sin.f64 eps) #s(literal -1/2 binary64))) x (-.f64 (cos.f64 eps) #s(literal 1 binary64))) x (sin.f64 eps))
eps
(+ eps (* -1/2 (* eps (pow x 2))))
(fma.f64 (.f64 #s(literal -1/2 binary64) x) (.f64 x eps) eps)
(+ eps (* (pow x 2) (+ (* -1/2 eps) (* 1/24 (* eps (pow x 2))))))
(fma.f64 (.f64 eps (fma.f64 (.f64 x x) #s(literal 1/24 binary64) #s(literal -1/2 binary64))) (*.f64 x x) eps)
(+ eps (* (pow x 2) (+ (* -1/2 eps) (* (pow x 2) (+ (* -1/720 (* eps (pow x 2))) (* 1/24 eps))))))
(fma.f64 (pow.f64 x #s(literal 4 binary64)) (.f64 eps (fma.f64 #s(literal -1/720 binary64) (.f64 x x) #s(literal 1/24 binary64))) (fma.f64 (.f64 #s(literal -1/2 binary64) x) (.f64 x eps) eps))
1
#s(literal 1 binary64)
(+ 1 (* -1/2 (pow x 2)))
(fma.f64 (*.f64 #s(literal -1/2 binary64) x) x #s(literal 1 binary64))
(+ 1 (* (pow x 2) (- (* 1/24 (pow x 2)) 1/2)))
(fma.f64 (fma.f64 (.f64 x x) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) (.f64 x x) #s(literal 1 binary64))
(+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))) 1/2)))
(fma.f64 (fma.f64 (fma.f64 #s(literal -1/720 binary64) (.f64 x x) #s(literal 1/24 binary64)) (.f64 x x) #s(literal -1/2 binary64)) (*.f64 x x) #s(literal 1 binary64))
(sin eps)
(sin.f64 eps)
(+ (sin eps) (* x (- (cos eps) 1)))
(fma.f64 (-.f64 (cos.f64 eps) #s(literal 1 binary64)) x (sin.f64 eps))
(+ (sin eps) (* x (- (+ (cos eps) (* -1/2 (* x (sin eps)))) 1)))
(fma.f64 (fma.f64 (*.f64 (sin.f64 eps) x) #s(literal -1/2 binary64) (-.f64 (cos.f64 eps) #s(literal 1 binary64))) x (sin.f64 eps))
(+ (sin eps) (* x (- (+ (cos eps) (* x (+ (* -1/2 (sin eps)) (* x (+ 1/6 (* -1/6 (cos eps))))))) 1)))
(fma.f64 (fma.f64 (fma.f64 (fma.f64 (cos.f64 eps) #s(literal -1/6 binary64) #s(literal 1/6 binary64)) x (*.f64 (sin.f64 eps) #s(literal -1/2 binary64))) x (-.f64 (cos.f64 eps) #s(literal 1 binary64))) x (sin.f64 eps))
eps
(+ eps (* -1/2 (* (pow eps 2) x)))
(fma.f64 (.f64 #s(literal -1/2 binary64) x) (.f64 eps eps) eps)
(+ eps (* x (+ (* -1/2 (* eps x)) (* -1/2 (pow eps 2)))))
(fma.f64 (.f64 #s(literal -1/2 binary64) x) (.f64 eps (+.f64 x eps)) eps)
(+ eps (* x (+ (* -1/2 (pow eps 2)) (* x (+ (* -1/2 eps) (* 1/12 (* (pow eps 2) x)))))))
(fma.f64 (fma.f64 (.f64 x (.f64 (.f64 x eps) eps)) #s(literal 1/12 binary64) (.f64 (*.f64 eps (+.f64 x eps)) #s(literal -1/2 binary64))) x eps)
1
#s(literal 1 binary64)
(+ 1 (* -1/2 (* eps x)))
(fma.f64 (*.f64 #s(literal -1/2 binary64) eps) x #s(literal 1 binary64))
(+ 1 (* x (+ (* -1/2 eps) (* -1/2 x))))
(fma.f64 (*.f64 (+.f64 x eps) #s(literal -1/2 binary64)) x #s(literal 1 binary64))
(+ 1 (* x (+ (* -1/2 eps) (* x (- (* 1/12 (* eps x)) 1/2)))))
(fma.f64 (fma.f64 (fma.f64 (.f64 #s(literal 1/12 binary64) eps) x #s(literal -1/2 binary64)) x (.f64 #s(literal -1/2 binary64) eps)) x #s(literal 1 binary64))
(* -1/2 x)
(*.f64 #s(literal -1/2 binary64) x)
(* x (- (* 1/12 (pow x 2)) 1/2))
(.f64 (fma.f64 (.f64 x x) #s(literal 1/12 binary64) #s(literal -1/2 binary64)) x)
(* x (- (* (pow x 2) (+ 1/12 (* -1/240 (pow x 2)))) 1/2))
(.f64 (fma.f64 (fma.f64 #s(literal -1/240 binary64) (.f64 x x) #s(literal 1/12 binary64)) (*.f64 x x) #s(literal -1/2 binary64)) x)
(* x (- (* (pow x 2) (+ 1/12 (* (pow x 2) (- (* 1/10080 (pow x 2)) 1/240)))) 1/2))
(.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 1/10080 binary64) (.f64 x x) #s(literal -1/240 binary64)) (.f64 x x) #s(literal 1/12 binary64)) (.f64 x x) #s(literal -1/2 binary64)) x)
(sin eps)
(sin.f64 eps)
(+ (sin eps) (* x (- (cos eps) 1)))
(fma.f64 (-.f64 (cos.f64 eps) #s(literal 1 binary64)) x (sin.f64 eps))
(+ (sin eps) (* x (- (+ (cos eps) (* -1/2 (* x (sin eps)))) 1)))
(fma.f64 (fma.f64 (*.f64 (sin.f64 eps) x) #s(literal -1/2 binary64) (-.f64 (cos.f64 eps) #s(literal 1 binary64))) x (sin.f64 eps))
(+ (sin eps) (* x (- (+ (cos eps) (* x (+ (* -1/2 (sin eps)) (* x (+ 1/6 (* -1/6 (cos eps))))))) 1)))
(fma.f64 (fma.f64 (fma.f64 (fma.f64 (cos.f64 eps) #s(literal -1/6 binary64) #s(literal 1/6 binary64)) x (*.f64 (sin.f64 eps) #s(literal -1/2 binary64))) x (-.f64 (cos.f64 eps) #s(literal 1 binary64))) x (sin.f64 eps))
(sin eps)
(sin.f64 eps)
(+ (sin eps) (* x (cos eps)))
(fma.f64 (cos.f64 eps) x (sin.f64 eps))
(+ (sin eps) (* x (+ (cos eps) (* -1/2 (* x (sin eps))))))
(fma.f64 (fma.f64 (*.f64 (sin.f64 eps) x) #s(literal -1/2 binary64) (cos.f64 eps)) x (sin.f64 eps))
(+ (sin eps) (* x (+ (cos eps) (* x (+ (* -1/2 (sin eps)) (* -1/6 (* x (cos eps))))))))
(fma.f64 (fma.f64 (fma.f64 (.f64 (cos.f64 eps) x) #s(literal -1/6 binary64) (.f64 (sin.f64 eps) #s(literal -1/2 binary64))) x (cos.f64 eps)) x (sin.f64 eps))
eps
(+ eps x)
(+.f64 x eps)
(+ eps x)
(+.f64 x eps)
(+ eps x)
(+.f64 x eps)
x
(* x (+ 1 (* -1/6 (pow x 2))))
(fma.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal -1/6 binary64) x)
(* x (+ 1 (* (pow x 2) (- (* 1/120 (pow x 2)) 1/6))))
(fma.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 (*.f64 x x) #s(literal 1/120 binary64) #s(literal -1/6 binary64)) x)
(* x (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/120 (* -1/5040 (pow x 2)))) 1/6))))
(fma.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 (fma.f64 (.f64 x x) #s(literal -1/5040 binary64) #s(literal 1/120 binary64)) (.f64 x x) #s(literal -1/6 binary64)) x)
(* -1/6 eps)
(*.f64 #s(literal -1/6 binary64) eps)
(+ (* -1/6 eps) (* 1/12 (* eps (pow x 2))))
(.f64 eps (fma.f64 (.f64 x x) #s(literal 1/12 binary64) #s(literal -1/6 binary64)))
(+ (* -1/6 eps) (* (pow x 2) (+ (* -1/144 (* eps (pow x 2))) (* 1/12 eps))))
(fma.f64 (.f64 #s(literal -1/144 binary64) eps) (pow.f64 x #s(literal 4 binary64)) (.f64 eps (fma.f64 (*.f64 x x) #s(literal 1/12 binary64) #s(literal -1/6 binary64))))
(+ (* -1/6 eps) (* (pow x 2) (+ (* 1/12 eps) (* (pow x 2) (+ (* -1/144 eps) (* 1/4320 (* eps (pow x 2))))))))
(fma.f64 (pow.f64 x #s(literal 4 binary64)) (.f64 eps (fma.f64 #s(literal 1/4320 binary64) (.f64 x x) #s(literal -1/144 binary64))) (.f64 eps (fma.f64 (.f64 x x) #s(literal 1/12 binary64) #s(literal -1/6 binary64))))
-1/6
#s(literal -1/6 binary64)
(- (* 1/12 (pow x 2)) 1/6)
(fma.f64 (*.f64 x x) #s(literal 1/12 binary64) #s(literal -1/6 binary64))
(- (* (pow x 2) (+ 1/12 (* -1/144 (pow x 2)))) 1/6)
(fma.f64 (fma.f64 #s(literal -1/144 binary64) (.f64 x x) #s(literal 1/12 binary64)) (.f64 x x) #s(literal -1/6 binary64))
(- (* (pow x 2) (+ 1/12 (* (pow x 2) (- (* 1/4320 (pow x 2)) 1/144)))) 1/6)
(fma.f64 (fma.f64 (fma.f64 #s(literal 1/4320 binary64) (.f64 x x) #s(literal -1/144 binary64)) (.f64 x x) #s(literal 1/12 binary64)) (*.f64 x x) #s(literal -1/6 binary64))
-1/6
#s(literal -1/6 binary64)
(- (* 1/120 (pow x 2)) 1/6)
(fma.f64 (*.f64 x x) #s(literal 1/120 binary64) #s(literal -1/6 binary64))
(- (* 1/120 (pow x 2)) 1/6)
(fma.f64 (*.f64 x x) #s(literal 1/120 binary64) #s(literal -1/6 binary64))
(- (* 1/120 (pow x 2)) 1/6)
(fma.f64 (*.f64 x x) #s(literal 1/120 binary64) #s(literal -1/6 binary64))
(- (sin (+ eps x)) (sin x))
(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
(- (sin (+ eps x)) (sin x))
(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
(- (sin (+ eps x)) (sin x))
(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
(- (sin (+ eps x)) (sin x))
(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
(* eps (+ (cos x) (* eps (+ (* -1/6 (* eps (cos x))) (* (sin x) (- (* 1/24 (pow eps 2)) 1/2))))))
(.f64 (fma.f64 (fma.f64 (fma.f64 (.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) (sin.f64 x) (.f64 (.f64 #s(literal -1/6 binary64) (cos.f64 x)) eps)) eps (cos.f64 x)) eps)
(* eps (+ (cos x) (* eps (+ (* -1/6 (* eps (cos x))) (* (sin x) (- (* 1/24 (pow eps 2)) 1/2))))))
(.f64 (fma.f64 (fma.f64 (fma.f64 (.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) (sin.f64 x) (.f64 (.f64 #s(literal -1/6 binary64) (cos.f64 x)) eps)) eps (cos.f64 x)) eps)
(* eps (+ (cos x) (* eps (+ (* -1/6 (* eps (cos x))) (* (sin x) (- (* 1/24 (pow eps 2)) 1/2))))))
(.f64 (fma.f64 (fma.f64 (fma.f64 (.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) (sin.f64 x) (.f64 (.f64 #s(literal -1/6 binary64) (cos.f64 x)) eps)) eps (cos.f64 x)) eps)
(* eps (+ (cos x) (* eps (+ (* -1/6 (* eps (cos x))) (* (sin x) (- (* 1/24 (pow eps 2)) 1/2))))))
(.f64 (fma.f64 (fma.f64 (fma.f64 (.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) (sin.f64 x) (.f64 (.f64 #s(literal -1/6 binary64) (cos.f64 x)) eps)) eps (cos.f64 x)) eps)
(+ (cos x) (* eps (+ (* -1/6 (* eps (cos x))) (* (sin x) (- (* 1/24 (pow eps 2)) 1/2)))))
(fma.f64 (fma.f64 (fma.f64 (.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) (sin.f64 x) (.f64 (*.f64 #s(literal -1/6 binary64) (cos.f64 x)) eps)) eps (cos.f64 x))
(+ (cos x) (* eps (+ (* -1/6 (* eps (cos x))) (* (sin x) (- (* 1/24 (pow eps 2)) 1/2)))))
(fma.f64 (fma.f64 (fma.f64 (.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) (sin.f64 x) (.f64 (*.f64 #s(literal -1/6 binary64) (cos.f64 x)) eps)) eps (cos.f64 x))
(+ (cos x) (* eps (+ (* -1/6 (* eps (cos x))) (* (sin x) (- (* 1/24 (pow eps 2)) 1/2)))))
(fma.f64 (fma.f64 (fma.f64 (.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) (sin.f64 x) (.f64 (*.f64 #s(literal -1/6 binary64) (cos.f64 x)) eps)) eps (cos.f64 x))
(+ (cos x) (* eps (+ (* -1/6 (* eps (cos x))) (* (sin x) (- (* 1/24 (pow eps 2)) 1/2)))))
(fma.f64 (fma.f64 (fma.f64 (.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) (sin.f64 x) (.f64 (*.f64 #s(literal -1/6 binary64) (cos.f64 x)) eps)) eps (cos.f64 x))
(+ (* -1/6 (* eps (cos x))) (* (sin x) (- (* 1/24 (pow eps 2)) 1/2)))
(fma.f64 (fma.f64 (.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) (sin.f64 x) (.f64 (*.f64 #s(literal -1/6 binary64) (cos.f64 x)) eps))
(+ (* -1/6 (* eps (cos x))) (* (sin x) (- (* 1/24 (pow eps 2)) 1/2)))
(fma.f64 (fma.f64 (.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) (sin.f64 x) (.f64 (*.f64 #s(literal -1/6 binary64) (cos.f64 x)) eps))
(+ (* -1/6 (* eps (cos x))) (* (sin x) (- (* 1/24 (pow eps 2)) 1/2)))
(fma.f64 (fma.f64 (.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) (sin.f64 x) (.f64 (*.f64 #s(literal -1/6 binary64) (cos.f64 x)) eps))
(+ (* -1/6 (* eps (cos x))) (* (sin x) (- (* 1/24 (pow eps 2)) 1/2)))
(fma.f64 (fma.f64 (.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) (sin.f64 x) (.f64 (*.f64 #s(literal -1/6 binary64) (cos.f64 x)) eps))
(- (sin (+ eps x)) (sin x))
(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
(- (sin (+ eps x)) (sin x))
(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
(- (sin (+ eps x)) (sin x))
(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
(- (sin (+ eps x)) (sin x))
(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
(- (sin (+ eps x)) (sin x))
(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
(- (sin (+ eps x)) (sin x))
(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
(- (sin (+ eps x)) (sin x))
(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
(- (sin (+ eps x)) (sin x))
(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
(* eps (cos x))
(*.f64 (cos.f64 x) eps)
(* eps (cos x))
(*.f64 (cos.f64 x) eps)
(* eps (cos x))
(*.f64 (cos.f64 x) eps)
(* eps (cos x))
(*.f64 (cos.f64 x) eps)
(cos x)
(cos.f64 x)
(cos x)
(cos.f64 x)
(cos x)
(cos.f64 x)
(cos x)
(cos.f64 x)
(- (sin (+ eps x)) (sin x))
(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
(- (sin (+ eps x)) (sin x))
(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
(- (sin (+ eps x)) (sin x))
(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
(- (sin (+ eps x)) (sin x))
(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(.f64 (fma.f64 (.f64 (sin.f64 x) #s(literal -1/2 binary64)) eps (cos.f64 x)) eps)
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(.f64 (fma.f64 (.f64 (sin.f64 x) #s(literal -1/2 binary64)) eps (cos.f64 x)) eps)
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(.f64 (fma.f64 (.f64 (sin.f64 x) #s(literal -1/2 binary64)) eps (cos.f64 x)) eps)
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(.f64 (fma.f64 (.f64 (sin.f64 x) #s(literal -1/2 binary64)) eps (cos.f64 x)) eps)
(+ (cos x) (* -1/2 (* eps (sin x))))
(fma.f64 (*.f64 (sin.f64 x) #s(literal -1/2 binary64)) eps (cos.f64 x))
(+ (cos x) (* -1/2 (* eps (sin x))))
(fma.f64 (*.f64 (sin.f64 x) #s(literal -1/2 binary64)) eps (cos.f64 x))
(+ (cos x) (* -1/2 (* eps (sin x))))
(fma.f64 (*.f64 (sin.f64 x) #s(literal -1/2 binary64)) eps (cos.f64 x))
(+ (cos x) (* -1/2 (* eps (sin x))))
(fma.f64 (*.f64 (sin.f64 x) #s(literal -1/2 binary64)) eps (cos.f64 x))
(* -1/2 (sin x))
(*.f64 (sin.f64 x) #s(literal -1/2 binary64))
(* -1/2 (sin x))
(*.f64 (sin.f64 x) #s(literal -1/2 binary64))
(* -1/2 (sin x))
(*.f64 (sin.f64 x) #s(literal -1/2 binary64))
(* -1/2 (sin x))
(*.f64 (sin.f64 x) #s(literal -1/2 binary64))
(- (sin (+ eps x)) (sin x))
(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
(- (sin (+ eps x)) (sin x))
(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
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(sin (+ eps x))
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(sin (+ eps x))
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(sin (+ eps x))
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x
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(* x (+ 1 (/ eps x)))
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(sin x)
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(sin x)
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(* -1/6 (* eps (cos x)))
(.f64 (.f64 #s(literal -1/6 binary64) (cos.f64 x)) eps)
(* -1/6 (* eps (cos x)))
(.f64 (.f64 #s(literal -1/6 binary64) (cos.f64 x)) eps)
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(.f64 (.f64 #s(literal -1/6 binary64) (cos.f64 x)) eps)
(* -1/6 (cos x))
(*.f64 #s(literal -1/6 binary64) (cos.f64 x))
(* -1/6 (cos x))
(*.f64 #s(literal -1/6 binary64) (cos.f64 x))
(* -1/6 (cos x))
(*.f64 #s(literal -1/6 binary64) (cos.f64 x))
(* -1/6 (cos x))
(*.f64 #s(literal -1/6 binary64) (cos.f64 x))
(* 1/120 (pow x 2))
(.f64 (.f64 x x) #s(literal 1/120 binary64))
(* (pow x 2) (- 1/120 (* 1/6 (/ 1 (pow x 2)))))
(.f64 (.f64 (-.f64 #s(literal 1/120 binary64) (/.f64 #s(literal 1/6 binary64) (*.f64 x x))) x) x)
(* (pow x 2) (- 1/120 (* 1/6 (/ 1 (pow x 2)))))
(.f64 (.f64 (-.f64 #s(literal 1/120 binary64) (/.f64 #s(literal 1/6 binary64) (*.f64 x x))) x) x)
(* (pow x 2) (- 1/120 (* 1/6 (/ 1 (pow x 2)))))
(.f64 (.f64 (-.f64 #s(literal 1/120 binary64) (/.f64 #s(literal 1/6 binary64) (*.f64 x x))) x) x)
(- (sin (- eps (* -1 x))) (sin x))
(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
(- (sin (- eps (* -1 x))) (sin x))
(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
(- (sin (- eps (* -1 x))) (sin x))
(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
(- (sin (- eps (* -1 x))) (sin x))
(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
(* eps (+ (cos x) (* eps (+ (* -1/6 (* eps (cos x))) (* (sin x) (- (* 1/24 (pow eps 2)) 1/2))))))
(.f64 (fma.f64 (fma.f64 (fma.f64 (.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) (sin.f64 x) (.f64 (.f64 #s(literal -1/6 binary64) (cos.f64 x)) eps)) eps (cos.f64 x)) eps)
(* eps (+ (cos x) (* eps (+ (* -1/6 (* eps (cos x))) (* (sin x) (- (* 1/24 (pow eps 2)) 1/2))))))
(.f64 (fma.f64 (fma.f64 (fma.f64 (.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) (sin.f64 x) (.f64 (.f64 #s(literal -1/6 binary64) (cos.f64 x)) eps)) eps (cos.f64 x)) eps)
(* eps (+ (cos x) (* eps (+ (* -1/6 (* eps (cos x))) (* (sin x) (- (* 1/24 (pow eps 2)) 1/2))))))
(.f64 (fma.f64 (fma.f64 (fma.f64 (.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) (sin.f64 x) (.f64 (.f64 #s(literal -1/6 binary64) (cos.f64 x)) eps)) eps (cos.f64 x)) eps)
(* eps (+ (cos x) (* eps (+ (* -1/6 (* eps (cos x))) (* (sin x) (- (* 1/24 (pow eps 2)) 1/2))))))
(.f64 (fma.f64 (fma.f64 (fma.f64 (.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) (sin.f64 x) (.f64 (.f64 #s(literal -1/6 binary64) (cos.f64 x)) eps)) eps (cos.f64 x)) eps)
(+ (cos x) (* eps (+ (* -1/6 (* eps (cos x))) (* (sin x) (- (* 1/24 (pow eps 2)) 1/2)))))
(fma.f64 (fma.f64 (fma.f64 (.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) (sin.f64 x) (.f64 (*.f64 #s(literal -1/6 binary64) (cos.f64 x)) eps)) eps (cos.f64 x))
(+ (cos x) (* eps (+ (* -1/6 (* eps (cos x))) (* (sin x) (- (* 1/24 (pow eps 2)) 1/2)))))
(fma.f64 (fma.f64 (fma.f64 (.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) (sin.f64 x) (.f64 (*.f64 #s(literal -1/6 binary64) (cos.f64 x)) eps)) eps (cos.f64 x))
(+ (cos x) (* eps (+ (* -1/6 (* eps (cos x))) (* (sin x) (- (* 1/24 (pow eps 2)) 1/2)))))
(fma.f64 (fma.f64 (fma.f64 (.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) (sin.f64 x) (.f64 (*.f64 #s(literal -1/6 binary64) (cos.f64 x)) eps)) eps (cos.f64 x))
(+ (cos x) (* eps (+ (* -1/6 (* eps (cos x))) (* (sin x) (- (* 1/24 (pow eps 2)) 1/2)))))
(fma.f64 (fma.f64 (fma.f64 (.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) (sin.f64 x) (.f64 (*.f64 #s(literal -1/6 binary64) (cos.f64 x)) eps)) eps (cos.f64 x))
(+ (* -1/6 (* eps (cos x))) (* (sin x) (- (* 1/24 (pow eps 2)) 1/2)))
(fma.f64 (fma.f64 (.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) (sin.f64 x) (.f64 (*.f64 #s(literal -1/6 binary64) (cos.f64 x)) eps))
(+ (* -1/6 (* eps (cos x))) (* (sin x) (- (* 1/24 (pow eps 2)) 1/2)))
(fma.f64 (fma.f64 (.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) (sin.f64 x) (.f64 (*.f64 #s(literal -1/6 binary64) (cos.f64 x)) eps))
(+ (* -1/6 (* eps (cos x))) (* (sin x) (- (* 1/24 (pow eps 2)) 1/2)))
(fma.f64 (fma.f64 (.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) (sin.f64 x) (.f64 (*.f64 #s(literal -1/6 binary64) (cos.f64 x)) eps))
(+ (* -1/6 (* eps (cos x))) (* (sin x) (- (* 1/24 (pow eps 2)) 1/2)))
(fma.f64 (fma.f64 (.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) (sin.f64 x) (.f64 (*.f64 #s(literal -1/6 binary64) (cos.f64 x)) eps))
(- (sin (- eps (* -1 x))) (sin x))
(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
(- (sin (- eps (* -1 x))) (sin x))
(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
(- (sin (- eps (* -1 x))) (sin x))
(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
(- (sin (- eps (* -1 x))) (sin x))
(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
(- (sin (- eps (* -1 x))) (sin x))
(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
(- (sin (- eps (* -1 x))) (sin x))
(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
(- (sin (- eps (* -1 x))) (sin x))
(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
(- (sin (- eps (* -1 x))) (sin x))
(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
(* eps (cos x))
(*.f64 (cos.f64 x) eps)
(* eps (cos x))
(*.f64 (cos.f64 x) eps)
(* eps (cos x))
(*.f64 (cos.f64 x) eps)
(* eps (cos x))
(*.f64 (cos.f64 x) eps)
(cos x)
(cos.f64 x)
(cos x)
(cos.f64 x)
(cos x)
(cos.f64 x)
(cos x)
(cos.f64 x)
(- (sin (- eps (* -1 x))) (sin x))
(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
(- (sin (- eps (* -1 x))) (sin x))
(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
(- (sin (- eps (* -1 x))) (sin x))
(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
(- (sin (- eps (* -1 x))) (sin x))
(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(.f64 (fma.f64 (.f64 (sin.f64 x) #s(literal -1/2 binary64)) eps (cos.f64 x)) eps)
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(.f64 (fma.f64 (.f64 (sin.f64 x) #s(literal -1/2 binary64)) eps (cos.f64 x)) eps)
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(.f64 (fma.f64 (.f64 (sin.f64 x) #s(literal -1/2 binary64)) eps (cos.f64 x)) eps)
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(.f64 (fma.f64 (.f64 (sin.f64 x) #s(literal -1/2 binary64)) eps (cos.f64 x)) eps)
(+ (cos x) (* -1/2 (* eps (sin x))))
(fma.f64 (*.f64 (sin.f64 x) #s(literal -1/2 binary64)) eps (cos.f64 x))
(+ (cos x) (* -1/2 (* eps (sin x))))
(fma.f64 (*.f64 (sin.f64 x) #s(literal -1/2 binary64)) eps (cos.f64 x))
(+ (cos x) (* -1/2 (* eps (sin x))))
(fma.f64 (*.f64 (sin.f64 x) #s(literal -1/2 binary64)) eps (cos.f64 x))
(+ (cos x) (* -1/2 (* eps (sin x))))
(fma.f64 (*.f64 (sin.f64 x) #s(literal -1/2 binary64)) eps (cos.f64 x))
(* -1/2 (sin x))
(*.f64 (sin.f64 x) #s(literal -1/2 binary64))
(* -1/2 (sin x))
(*.f64 (sin.f64 x) #s(literal -1/2 binary64))
(* -1/2 (sin x))
(*.f64 (sin.f64 x) #s(literal -1/2 binary64))
(* -1/2 (sin x))
(*.f64 (sin.f64 x) #s(literal -1/2 binary64))
(- (sin (- eps (* -1 x))) (sin x))
(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
(- (sin (- eps (* -1 x))) (sin x))
(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
(- (sin (- eps (* -1 x))) (sin x))
(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
(- (sin (- eps (* -1 x))) (sin x))
(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
(sin (- eps (* -1 x)))
(sin.f64 (+.f64 x eps))
(sin (- eps (* -1 x)))
(sin.f64 (+.f64 x eps))
(sin (- eps (* -1 x)))
(sin.f64 (+.f64 x eps))
(sin (- eps (* -1 x)))
(sin.f64 (+.f64 x eps))
x
(* -1 (* x (- (* -1 (/ eps x)) 1)))
(fma.f64 (/.f64 eps x) x x)
(* -1 (* x (- (* -1 (/ eps x)) 1)))
(fma.f64 (/.f64 eps x) x x)
(* -1 (* x (- (* -1 (/ eps x)) 1)))
(fma.f64 (/.f64 eps x) x x)
(sin x)
(sin.f64 x)
(sin x)
(sin.f64 x)
(sin x)
(sin.f64 x)
(sin x)
(sin.f64 x)
(* -1/6 (* eps (cos x)))
(.f64 (.f64 #s(literal -1/6 binary64) (cos.f64 x)) eps)
(* -1/6 (* eps (cos x)))
(.f64 (.f64 #s(literal -1/6 binary64) (cos.f64 x)) eps)
(* -1/6 (* eps (cos x)))
(.f64 (.f64 #s(literal -1/6 binary64) (cos.f64 x)) eps)
(* -1/6 (* eps (cos x)))
(.f64 (.f64 #s(literal -1/6 binary64) (cos.f64 x)) eps)
(* -1/6 (cos x))
(*.f64 #s(literal -1/6 binary64) (cos.f64 x))
(* -1/6 (cos x))
(*.f64 #s(literal -1/6 binary64) (cos.f64 x))
(* -1/6 (cos x))
(*.f64 #s(literal -1/6 binary64) (cos.f64 x))
(* -1/6 (cos x))
(*.f64 #s(literal -1/6 binary64) (cos.f64 x))
(* 1/120 (pow x 2))
(.f64 (.f64 x x) #s(literal 1/120 binary64))
(* (pow x 2) (- 1/120 (* 1/6 (/ 1 (pow x 2)))))
(.f64 (.f64 (-.f64 #s(literal 1/120 binary64) (/.f64 #s(literal 1/6 binary64) (*.f64 x x))) x) x)
(* (pow x 2) (- 1/120 (* 1/6 (/ 1 (pow x 2)))))
(.f64 (.f64 (-.f64 #s(literal 1/120 binary64) (/.f64 #s(literal 1/6 binary64) (*.f64 x x))) x) x)
(* (pow x 2) (- 1/120 (* 1/6 (/ 1 (pow x 2)))))
(.f64 (.f64 (-.f64 #s(literal 1/120 binary64) (/.f64 #s(literal 1/6 binary64) (*.f64 x x))) x) x)

rewrite167.0ms (1.4%)

Memory

15.4MiB live, 236.2MiB allocated

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	37	210
0	65	210
1	233	210
2	1683	210
0	8707	210

Stop Event

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

Counts

20 → 290

Calls

Call 1

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

Outputs
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eval194.0ms (1.6%)

Memory: -20.2MiB live, 233.4MiB allocated
Compiler: Compiled 18 232 to 1 901 computations (89.6% saved)

prune61.0ms (0.5%)

Memory

30.0MiB live, 69.4MiB allocated

Pruning

28 alts after pruning (24 fresh and 4 done)

	Pruned	Kept	Total
New	705	22	727
Fresh	0	2	2
Picked	2	3	5
Done	0	1	1
Total	707	28	735

Accuracy

100.0%

Counts

735 → 28

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	65.3%	(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
	99.9%	(.f64 (.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 0 binary64) eps))) #s(literal 2 binary64)) (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64))))
▶	100.0%	#s(approx (- (sin (+ x eps)) (sin x)) (fma.f64 (.f64 (fma.f64 (fma.f64 #s(literal 1/24 binary64) (.f64 eps eps) #s(literal -1/2 binary64)) (sin.f64 x) (.f64 (.f64 (cos.f64 x) #s(literal -1/6 binary64)) eps)) eps) eps (*.f64 (cos.f64 x) eps)))
	99.7%	#s(approx (- (sin (+ x eps)) (sin x)) (fma.f64 (.f64 (.f64 #s(literal -1/2 binary64) (sin.f64 x)) eps) eps (*.f64 (cos.f64 x) eps)))
✓	100.0%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 (fma.f64 (sin.f64 x) (fma.f64 (.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) (.f64 (.f64 #s(literal -1/6 binary64) (cos.f64 x)) eps)) eps (cos.f64 x)) eps))
	99.6%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 (fma.f64 (sin.f64 x) (fma.f64 (.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) (.f64 #s(approx ( -1/6 (cos x)) (fma.f64 (fma.f64 #s(literal -1/144 binary64) (.f64 x x) #s(literal 1/12 binary64)) (.f64 x x) #s(literal -1/6 binary64))) eps)) eps (cos.f64 x)) eps))
	99.8%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 (fma.f64 (sin.f64 x) (fma.f64 (.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) (.f64 #s(approx ( -1/6 (cos x)) #s(literal -1/6 binary64)) eps)) eps (cos.f64 x)) eps))
	100.0%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 (fma.f64 #s(literal -1/6 binary64) (.f64 (cos.f64 x) eps) (*.f64 (sin.f64 x) #s(literal -1/2 binary64))) eps (cos.f64 x)) eps))
✓	99.7%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 (.f64 (sin.f64 x) #s(literal -1/2 binary64)) eps (cos.f64 x)) eps))
	99.5%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 #s(approx (+ ( (sin x) (+ (* (* eps eps) 1/24) -1/2)) (* (* -1/6 (cos x)) eps)) (fma.f64 (fma.f64 (fma.f64 #s(literal 1/12 binary64) eps (.f64 (.f64 (fma.f64 (.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) x) #s(literal -1/6 binary64))) x (fma.f64 (.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64))) x (*.f64 #s(literal -1/6 binary64) eps))) eps (cos.f64 x)) eps))
	99.4%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 #s(approx (+ ( (sin x) (+ (* (* eps eps) 1/24) -1/2)) (* (* -1/6 (cos x)) eps)) (fma.f64 (fma.f64 (.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) x (.f64 #s(literal -1/6 binary64) eps))) eps (cos.f64 x)) eps))
	99.0%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 #s(approx (+ ( (sin x) (+ (* (* eps eps) 1/24) -1/2)) (* (* -1/6 (cos x)) eps)) (*.f64 #s(literal -1/6 binary64) eps)) eps (cos.f64 x)) eps))
	99.4%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 #s(approx ( (sin x) -1/2) (.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 1/10080 binary64) (.f64 x x) #s(literal -1/240 binary64)) (.f64 x x) #s(literal 1/12 binary64)) (.f64 x x) #s(literal -1/2 binary64)) x)) eps (cos.f64 x)) eps))
	99.4%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 #s(approx ( (sin x) -1/2) (.f64 (fma.f64 (fma.f64 #s(literal -1/240 binary64) (.f64 x x) #s(literal 1/12 binary64)) (*.f64 x x) #s(literal -1/2 binary64)) x)) eps (cos.f64 x)) eps))
▶	99.4%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 #s(approx ( (sin x) -1/2) (.f64 (fma.f64 (.f64 x x) #s(literal 1/12 binary64) #s(literal -1/2 binary64)) x)) eps (cos.f64 x)) eps))
	99.3%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 #s(approx ( (sin x) -1/2) (*.f64 #s(literal -1/2 binary64) x)) eps (cos.f64 x)) eps))
✓	99.0%	#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (cos.f64 x) eps))
	98.3%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (+ (* (sin x) (+ (* (* eps eps) 1/24) -1/2)) (* (* -1/6 (cos x)) eps)) eps) (cos x)) (fma.f64 (fma.f64 (fma.f64 #s(literal 1/12 binary64) (.f64 eps eps) #s(literal -1/2 binary64)) x (.f64 (fma.f64 (.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) eps)) x (fma.f64 (.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64)))) eps))
	97.6%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (+ (* (sin x) (+ (* (* eps eps) 1/24) -1/2)) (* (* -1/6 (cos x)) eps)) eps) (cos x)) (fma.f64 eps (fma.f64 (fma.f64 (.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) x (.f64 #s(literal -1/6 binary64) eps)) #s(literal 1 binary64))) eps))
▶	98.3%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (* (sin x) -1/2) eps) (cos x)) (fma.f64 (fma.f64 (fma.f64 (.f64 #s(literal 1/12 binary64) eps) x #s(literal -1/2 binary64)) x (.f64 #s(literal -1/2 binary64) eps)) x #s(literal 1 binary64))) eps))
	98.3%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (* (sin x) -1/2) eps) (cos x)) (fma.f64 (*.f64 (+.f64 x eps) #s(literal -1/2 binary64)) x #s(literal 1 binary64))) eps))
	97.6%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (* (sin x) -1/2) eps) (cos x)) (fma.f64 (*.f64 #s(literal -1/2 binary64) eps) x #s(literal 1 binary64))) eps))
▶	99.4%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (* (sin x) -1/2) eps) (cos x)) (*.f64 (fma.f64 (sin.f64 x) #s(literal -1/2 binary64) (/.f64 (cos.f64 x) eps)) eps)) eps))
▶	97.6%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (* (sin x) -1/2) eps) (cos x)) #s(literal 1 binary64)) eps))
	98.4%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (cos x) (fma.f64 (fma.f64 (fma.f64 #s(literal -1/720 binary64) (.f64 x x) #s(literal 1/24 binary64)) (.f64 x x) #s(literal -1/2 binary64)) (.f64 x x) #s(literal 1 binary64))) eps))
	98.3%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (cos x) (fma.f64 (fma.f64 (.f64 x x) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) (*.f64 x x) #s(literal 1 binary64))) eps))
	98.3%	#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (cos x) eps) (fma.f64 (.f64 eps (fma.f64 (.f64 x x) #s(literal 1/24 binary64) #s(literal -1/2 binary64))) (*.f64 x x) eps)))
	98.1%	#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (cos x) eps) (fma.f64 (.f64 #s(literal -1/2 binary64) x) (.f64 x eps) eps)))

Compiler

Compiled 891 to 639 computations (28.3% saved)

simplify153.0ms (1.3%)

Memory

-8.3MiB live, 142.3MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 19 expressions of interest:

New	Metric	Score
cost-diff	0	#s(approx (+ (* (* (sin x) -1/2) eps) (cos x)) (*.f64 (fma.f64 (sin.f64 x) #s(literal -1/2 binary64) (/.f64 (cos.f64 x) eps)) eps))
cost-diff	0	(.f64 #s(approx (+ ( (* (sin x) -1/2) eps) (cos x)) (*.f64 (fma.f64 (sin.f64 x) #s(literal -1/2 binary64) (/.f64 (cos.f64 x) eps)) eps)) eps)
cost-diff	0	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (* (sin x) -1/2) eps) (cos x)) (*.f64 (fma.f64 (sin.f64 x) #s(literal -1/2 binary64) (/.f64 (cos.f64 x) eps)) eps)) eps))
cost-diff	704	(*.f64 (fma.f64 (sin.f64 x) #s(literal -1/2 binary64) (/.f64 (cos.f64 x) eps)) eps)
cost-diff	0	#s(approx (* (sin x) -1/2) (.f64 (fma.f64 (.f64 x x) #s(literal 1/12 binary64) #s(literal -1/2 binary64)) x))
cost-diff	0	(fma.f64 #s(approx (* (sin x) -1/2) (.f64 (fma.f64 (.f64 x x) #s(literal 1/12 binary64) #s(literal -1/2 binary64)) x)) eps (cos.f64 x))
cost-diff	0	(.f64 (fma.f64 #s(approx ( (sin x) -1/2) (.f64 (fma.f64 (.f64 x x) #s(literal 1/12 binary64) #s(literal -1/2 binary64)) x)) eps (cos.f64 x)) eps)
cost-diff	0	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 #s(approx ( (sin x) -1/2) (.f64 (fma.f64 (.f64 x x) #s(literal 1/12 binary64) #s(literal -1/2 binary64)) x)) eps (cos.f64 x)) eps))
cost-diff	0	(fma.f64 (fma.f64 (fma.f64 (.f64 #s(literal 1/12 binary64) eps) x #s(literal -1/2 binary64)) x (.f64 #s(literal -1/2 binary64) eps)) x #s(literal 1 binary64))
cost-diff	0	#s(approx (+ (* (* (sin x) -1/2) eps) (cos x)) (fma.f64 (fma.f64 (fma.f64 (.f64 #s(literal 1/12 binary64) eps) x #s(literal -1/2 binary64)) x (.f64 #s(literal -1/2 binary64) eps)) x #s(literal 1 binary64)))
cost-diff	0	(.f64 #s(approx (+ ( (* (sin x) -1/2) eps) (cos x)) (fma.f64 (fma.f64 (fma.f64 (.f64 #s(literal 1/12 binary64) eps) x #s(literal -1/2 binary64)) x (.f64 #s(literal -1/2 binary64) eps)) x #s(literal 1 binary64))) eps)
cost-diff	0	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (* (sin x) -1/2) eps) (cos x)) (fma.f64 (fma.f64 (fma.f64 (.f64 #s(literal 1/12 binary64) eps) x #s(literal -1/2 binary64)) x (.f64 #s(literal -1/2 binary64) eps)) x #s(literal 1 binary64))) eps))
cost-diff	0	#s(approx (+ (* (* (sin x) -1/2) eps) (cos x)) #s(literal 1 binary64))
cost-diff	0	(.f64 #s(approx (+ ( (* (sin x) -1/2) eps) (cos x)) #s(literal 1 binary64)) eps)
cost-diff	0	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (* (sin x) -1/2) eps) (cos x)) #s(literal 1 binary64)) eps))
cost-diff	0	(fma.f64 (fma.f64 #s(literal 1/24 binary64) (.f64 eps eps) #s(literal -1/2 binary64)) (sin.f64 x) (.f64 (*.f64 (cos.f64 x) #s(literal -1/6 binary64)) eps))
cost-diff	0	(.f64 (fma.f64 (fma.f64 #s(literal 1/24 binary64) (.f64 eps eps) #s(literal -1/2 binary64)) (sin.f64 x) (.f64 (.f64 (cos.f64 x) #s(literal -1/6 binary64)) eps)) eps)
cost-diff	0	#s(approx (- (sin (+ x eps)) (sin x)) (fma.f64 (.f64 (fma.f64 (fma.f64 #s(literal 1/24 binary64) (.f64 eps eps) #s(literal -1/2 binary64)) (sin.f64 x) (.f64 (.f64 (cos.f64 x) #s(literal -1/6 binary64)) eps)) eps) eps (*.f64 (cos.f64 x) eps)))
cost-diff	320	(fma.f64 (.f64 (fma.f64 (fma.f64 #s(literal 1/24 binary64) (.f64 eps eps) #s(literal -1/2 binary64)) (sin.f64 x) (.f64 (.f64 (cos.f64 x) #s(literal -1/6 binary64)) eps)) eps) eps (*.f64 (cos.f64 x) eps))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	50	491
0	86	489
1	135	489
2	214	489
3	423	489
4	837	489
5	1341	485
6	1475	485
7	1713	485
8	2534	485
9	4128	485
10	5838	485
0	8184	470

Stop Event

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

Calls

Call 1

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

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

localize175.0ms (1.5%)

Memory

4.3MiB live, 208.3MiB allocated

Localize:

Found 19 expressions of interest:

New	Metric	Score
accuracy	0.015625	(.f64 #s(approx (+ ( (* (sin x) -1/2) eps) (cos x)) (*.f64 (fma.f64 (sin.f64 x) #s(literal -1/2 binary64) (/.f64 (cos.f64 x) eps)) eps)) eps)
accuracy	0.01953125	(/.f64 (cos.f64 x) eps)
accuracy	0.16015625	(*.f64 (fma.f64 (sin.f64 x) #s(literal -1/2 binary64) (/.f64 (cos.f64 x) eps)) eps)
accuracy	0.21273808917513187	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (* (sin x) -1/2) eps) (cos x)) (*.f64 (fma.f64 (sin.f64 x) #s(literal -1/2 binary64) (/.f64 (cos.f64 x) eps)) eps)) eps))
accuracy	0.01171875	(fma.f64 #s(approx (* (sin x) -1/2) (.f64 (fma.f64 (.f64 x x) #s(literal 1/12 binary64) #s(literal -1/2 binary64)) x)) eps (cos.f64 x))
accuracy	0.015625	(.f64 (fma.f64 #s(approx ( (sin x) -1/2) (.f64 (fma.f64 (.f64 x x) #s(literal 1/12 binary64) #s(literal -1/2 binary64)) x)) eps (cos.f64 x)) eps)
accuracy	0.21273808917513187	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 #s(approx ( (sin x) -1/2) (.f64 (fma.f64 (.f64 x x) #s(literal 1/12 binary64) #s(literal -1/2 binary64)) x)) eps (cos.f64 x)) eps))
accuracy	1.018992005109586	#s(approx (* (sin x) -1/2) (.f64 (fma.f64 (.f64 x x) #s(literal 1/12 binary64) #s(literal -1/2 binary64)) x))
accuracy	0.01953125	(fma.f64 (fma.f64 (.f64 #s(literal 1/12 binary64) eps) x #s(literal -1/2 binary64)) x (.f64 #s(literal -1/2 binary64) eps))
accuracy	0.21273808917513187	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (* (sin x) -1/2) eps) (cos x)) (fma.f64 (fma.f64 (fma.f64 (.f64 #s(literal 1/12 binary64) eps) x #s(literal -1/2 binary64)) x (.f64 #s(literal -1/2 binary64) eps)) x #s(literal 1 binary64))) eps))
accuracy	0.359375	(*.f64 #s(literal 1/12 binary64) eps)
accuracy	1.0795034032154527	#s(approx (+ (* (* (sin x) -1/2) eps) (cos x)) (fma.f64 (fma.f64 (fma.f64 (.f64 #s(literal 1/12 binary64) eps) x #s(literal -1/2 binary64)) x (.f64 #s(literal -1/2 binary64) eps)) x #s(literal 1 binary64)))
accuracy	0.015625	(.f64 #s(approx (+ ( (* (sin x) -1/2) eps) (cos x)) #s(literal 1 binary64)) eps)
accuracy	0.21273808917513187	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (* (sin x) -1/2) eps) (cos x)) #s(literal 1 binary64)) eps))
accuracy	1.5569995107684405	#s(approx (+ (* (* (sin x) -1/2) eps) (cos x)) #s(literal 1 binary64))
accuracy	0.01171875	(*.f64 (cos.f64 x) #s(literal -1/6 binary64))
accuracy	0.03515625	(fma.f64 (fma.f64 #s(literal 1/24 binary64) (.f64 eps eps) #s(literal -1/2 binary64)) (sin.f64 x) (.f64 (*.f64 (cos.f64 x) #s(literal -1/6 binary64)) eps))
accuracy	0.1796875	(.f64 (fma.f64 (fma.f64 #s(literal 1/24 binary64) (.f64 eps eps) #s(literal -1/2 binary64)) (sin.f64 x) (.f64 (.f64 (cos.f64 x) #s(literal -1/6 binary64)) eps)) eps)
accuracy	0.3515625	(.f64 (.f64 (cos.f64 x) #s(literal -1/6 binary64)) eps)

Samples

59.0ms	180×	0	valid
56.0ms	74×	1	valid
2.0ms	2×	2	valid

Compiler

Compiled 322 to 44 computations (86.3% saved)

Precisions

Click to see histograms. Total time spent on operations: 88.0ms

ival-mult: 33.0ms (37.7% of total)

ival-add: 21.0ms (24% of total)

adjust: 11.0ms (12.6% of total)

const: 10.0ms (11.4% of total)

ival-sin: 5.0ms (5.7% of total)

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

ival-div: 2.0ms (2.3% of total)

ival-sub: 2.0ms (2.3% of total)

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

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

exact: 0.0ms (0% of total)

series50.0ms (0.4%)

Memory

-13.9MiB live, 63.4MiB allocated

Counts

24 → 540

Calls

Call 1

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

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

Calls

6 calls:

Time	Variable		Point	Expression
4.0ms	eps	@	-inf	((+ (* (* (+ (* (+ (* 1/24 (* eps eps)) -1/2) (sin x)) (* (* (cos x) -1/6) eps)) eps) eps) (* (cos x) eps)) (- (sin (+ x eps)) (sin x)) (* (+ (* (+ (* 1/24 (* eps eps)) -1/2) (sin x)) (* (* (cos x) -1/6) eps)) eps) (+ (* (+ (* 1/24 (* eps eps)) -1/2) (sin x)) (* (* (cos x) -1/6) eps)) (- (sin (+ x eps)) (sin x)) (* (+ (* (* (sin x) -1/2) eps) (cos x)) eps) (+ (* (* (sin x) -1/2) eps) (cos x)) (- (sin (+ x eps)) (sin x)) (* (+ (* (* (sin x) -1/2) eps) (cos x)) eps) (+ (* (* (sin x) -1/2) eps) (cos x)) (+ (* (+ (* (+ (* (* 1/12 eps) x) -1/2) x) (* -1/2 eps)) x) 1) (- (sin (+ x eps)) (sin x)) (* (+ (* (* (sin x) -1/2) eps) (cos x)) eps) (+ (* (* (sin x) -1/2) eps) (cos x)) (* (sin x) -1/2) (* (+ (* (sin x) -1/2) (/ (cos x) eps)) eps) (- (sin (+ x eps)) (sin x)) (* (+ (* (* (sin x) -1/2) eps) (cos x)) eps) (+ (* (* (sin x) -1/2) eps) (cos x)) (* (* (cos x) -1/6) eps) (* (cos x) -1/6) (* 1/12 eps) (+ (* (+ (* (* 1/12 eps) x) -1/2) x) (* -1/2 eps)) (/ (cos x) eps))
3.0ms	x	@	inf	((+ (* (* (+ (* (+ (* 1/24 (* eps eps)) -1/2) (sin x)) (* (* (cos x) -1/6) eps)) eps) eps) (* (cos x) eps)) (- (sin (+ x eps)) (sin x)) (* (+ (* (+ (* 1/24 (* eps eps)) -1/2) (sin x)) (* (* (cos x) -1/6) eps)) eps) (+ (* (+ (* 1/24 (* eps eps)) -1/2) (sin x)) (* (* (cos x) -1/6) eps)) (- (sin (+ x eps)) (sin x)) (* (+ (* (* (sin x) -1/2) eps) (cos x)) eps) (+ (* (* (sin x) -1/2) eps) (cos x)) (- (sin (+ x eps)) (sin x)) (* (+ (* (* (sin x) -1/2) eps) (cos x)) eps) (+ (* (* (sin x) -1/2) eps) (cos x)) (+ (* (+ (* (+ (* (* 1/12 eps) x) -1/2) x) (* -1/2 eps)) x) 1) (- (sin (+ x eps)) (sin x)) (* (+ (* (* (sin x) -1/2) eps) (cos x)) eps) (+ (* (* (sin x) -1/2) eps) (cos x)) (* (sin x) -1/2) (* (+ (* (sin x) -1/2) (/ (cos x) eps)) eps) (- (sin (+ x eps)) (sin x)) (* (+ (* (* (sin x) -1/2) eps) (cos x)) eps) (+ (* (* (sin x) -1/2) eps) (cos x)) (* (* (cos x) -1/6) eps) (* (cos x) -1/6) (* 1/12 eps) (+ (* (+ (* (* 1/12 eps) x) -1/2) x) (* -1/2 eps)) (/ (cos x) eps))
3.0ms	x	@	-inf	((+ (* (* (+ (* (+ (* 1/24 (* eps eps)) -1/2) (sin x)) (* (* (cos x) -1/6) eps)) eps) eps) (* (cos x) eps)) (- (sin (+ x eps)) (sin x)) (* (+ (* (+ (* 1/24 (* eps eps)) -1/2) (sin x)) (* (* (cos x) -1/6) eps)) eps) (+ (* (+ (* 1/24 (* eps eps)) -1/2) (sin x)) (* (* (cos x) -1/6) eps)) (- (sin (+ x eps)) (sin x)) (* (+ (* (* (sin x) -1/2) eps) (cos x)) eps) (+ (* (* (sin x) -1/2) eps) (cos x)) (- (sin (+ x eps)) (sin x)) (* (+ (* (* (sin x) -1/2) eps) (cos x)) eps) (+ (* (* (sin x) -1/2) eps) (cos x)) (+ (* (+ (* (+ (* (* 1/12 eps) x) -1/2) x) (* -1/2 eps)) x) 1) (- (sin (+ x eps)) (sin x)) (* (+ (* (* (sin x) -1/2) eps) (cos x)) eps) (+ (* (* (sin x) -1/2) eps) (cos x)) (* (sin x) -1/2) (* (+ (* (sin x) -1/2) (/ (cos x) eps)) eps) (- (sin (+ x eps)) (sin x)) (* (+ (* (* (sin x) -1/2) eps) (cos x)) eps) (+ (* (* (sin x) -1/2) eps) (cos x)) (* (* (cos x) -1/6) eps) (* (cos x) -1/6) (* 1/12 eps) (+ (* (+ (* (* 1/12 eps) x) -1/2) x) (* -1/2 eps)) (/ (cos x) eps))
3.0ms	eps	@	inf	((+ (* (* (+ (* (+ (* 1/24 (* eps eps)) -1/2) (sin x)) (* (* (cos x) -1/6) eps)) eps) eps) (* (cos x) eps)) (- (sin (+ x eps)) (sin x)) (* (+ (* (+ (* 1/24 (* eps eps)) -1/2) (sin x)) (* (* (cos x) -1/6) eps)) eps) (+ (* (+ (* 1/24 (* eps eps)) -1/2) (sin x)) (* (* (cos x) -1/6) eps)) (- (sin (+ x eps)) (sin x)) (* (+ (* (* (sin x) -1/2) eps) (cos x)) eps) (+ (* (* (sin x) -1/2) eps) (cos x)) (- (sin (+ x eps)) (sin x)) (* (+ (* (* (sin x) -1/2) eps) (cos x)) eps) (+ (* (* (sin x) -1/2) eps) (cos x)) (+ (* (+ (* (+ (* (* 1/12 eps) x) -1/2) x) (* -1/2 eps)) x) 1) (- (sin (+ x eps)) (sin x)) (* (+ (* (* (sin x) -1/2) eps) (cos x)) eps) (+ (* (* (sin x) -1/2) eps) (cos x)) (* (sin x) -1/2) (* (+ (* (sin x) -1/2) (/ (cos x) eps)) eps) (- (sin (+ x eps)) (sin x)) (* (+ (* (* (sin x) -1/2) eps) (cos x)) eps) (+ (* (* (sin x) -1/2) eps) (cos x)) (* (* (cos x) -1/6) eps) (* (cos x) -1/6) (* 1/12 eps) (+ (* (+ (* (* 1/12 eps) x) -1/2) x) (* -1/2 eps)) (/ (cos x) eps))
3.0ms	eps	@	0	((+ (* (* (+ (* (+ (* 1/24 (* eps eps)) -1/2) (sin x)) (* (* (cos x) -1/6) eps)) eps) eps) (* (cos x) eps)) (- (sin (+ x eps)) (sin x)) (* (+ (* (+ (* 1/24 (* eps eps)) -1/2) (sin x)) (* (* (cos x) -1/6) eps)) eps) (+ (* (+ (* 1/24 (* eps eps)) -1/2) (sin x)) (* (* (cos x) -1/6) eps)) (- (sin (+ x eps)) (sin x)) (* (+ (* (* (sin x) -1/2) eps) (cos x)) eps) (+ (* (* (sin x) -1/2) eps) (cos x)) (- (sin (+ x eps)) (sin x)) (* (+ (* (* (sin x) -1/2) eps) (cos x)) eps) (+ (* (* (sin x) -1/2) eps) (cos x)) (+ (* (+ (* (+ (* (* 1/12 eps) x) -1/2) x) (* -1/2 eps)) x) 1) (- (sin (+ x eps)) (sin x)) (* (+ (* (* (sin x) -1/2) eps) (cos x)) eps) (+ (* (* (sin x) -1/2) eps) (cos x)) (* (sin x) -1/2) (* (+ (* (sin x) -1/2) (/ (cos x) eps)) eps) (- (sin (+ x eps)) (sin x)) (* (+ (* (* (sin x) -1/2) eps) (cos x)) eps) (+ (* (* (sin x) -1/2) eps) (cos x)) (* (* (cos x) -1/6) eps) (* (cos x) -1/6) (* 1/12 eps) (+ (* (+ (* (* 1/12 eps) x) -1/2) x) (* -1/2 eps)) (/ (cos x) eps))

simplify209.0ms (1.7%)

Memory

-9.4MiB live, 206.5MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	359	5820
1	1114	5745
2	3457	5676
0	8212	5187

Stop Event

1×	iter limit
1×	node limit

Counts

540 → 536

Calls

Call 1

Inputs
(* eps (cos x))
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x)))))))
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* eps (+ (* -1/6 (cos x)) (* 1/24 (* eps (sin x)))))))))
(* eps (cos x))
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x)))))))
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* eps (+ (* -1/6 (cos x)) (* 1/24 (* eps (sin x)))))))))
(* -1/2 (* eps (sin x)))
(* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x)))))
(* eps (+ (* -1/2 (sin x)) (* eps (+ (* -1/6 (cos x)) (* 1/24 (* eps (sin x)))))))
(* eps (+ (* -1/2 (sin x)) (* eps (+ (* -1/6 (cos x)) (* 1/24 (* eps (sin x)))))))
(* -1/2 (sin x))
(+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x))))
(+ (* -1/2 (sin x)) (* eps (+ (* -1/6 (cos x)) (* 1/24 (* eps (sin x))))))
(+ (* -1/2 (sin x)) (* eps (+ (* -1/6 (cos x)) (* 1/24 (* eps (sin x))))))
(* eps (cos x))
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x)))))))
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* eps (+ (* -1/6 (cos x)) (* 1/24 (* eps (sin x)))))))))
(* eps (cos x))
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(cos x)
(+ (cos x) (* -1/2 (* eps (sin x))))
(+ (cos x) (* -1/2 (* eps (sin x))))
(+ (cos x) (* -1/2 (* eps (sin x))))
(* eps (cos x))
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x)))))))
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* eps (+ (* -1/6 (cos x)) (* 1/24 (* eps (sin x)))))))))
(* eps (cos x))
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(cos x)
(+ (cos x) (* -1/2 (* eps (sin x))))
(+ (cos x) (* -1/2 (* eps (sin x))))
(+ (cos x) (* -1/2 (* eps (sin x))))
(+ 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 (cos x))
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x)))))))
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* eps (+ (* -1/6 (cos x)) (* 1/24 (* eps (sin x)))))))))
(* eps (cos x))
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(cos x)
(+ (cos x) (* -1/2 (* eps (sin x))))
(+ (cos x) (* -1/2 (* eps (sin x))))
(+ (cos x) (* -1/2 (* eps (sin x))))
(cos x)
(+ (cos x) (* -1/2 (* eps (sin x))))
(+ (cos x) (* -1/2 (* eps (sin x))))
(+ (cos x) (* -1/2 (* eps (sin x))))
(* eps (cos x))
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x)))))))
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* eps (+ (* -1/6 (cos x)) (* 1/24 (* eps (sin x)))))))))
(* eps (cos x))
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(cos x)
(+ (cos x) (* -1/2 (* eps (sin x))))
(+ (cos x) (* -1/2 (* eps (sin x))))
(+ (cos x) (* -1/2 (* eps (sin x))))
(* -1/6 (* eps (cos x)))
(* -1/6 (* eps (cos x)))
(* -1/6 (* eps (cos x)))
(* -1/6 (* eps (cos x)))
(* 1/12 eps)
(* 1/12 eps)
(* 1/12 eps)
(* 1/12 eps)
(* -1/2 x)
(+ (* -1/2 x) (* eps (- (* 1/12 (pow x 2)) 1/2)))
(+ (* -1/2 x) (* eps (- (* 1/12 (pow x 2)) 1/2)))
(+ (* -1/2 x) (* eps (- (* 1/12 (pow x 2)) 1/2)))
(/ (cos x) eps)
(/ (cos x) eps)
(/ (cos x) eps)
(/ (cos x) eps)
(* 1/24 (* (pow eps 4) (sin x)))
(* (pow eps 4) (+ (* -1/6 (/ (cos x) eps)) (* 1/24 (sin x))))
(* (pow eps 4) (+ (* -1/2 (/ (sin x) (pow eps 2))) (+ (* -1/6 (/ (cos x) eps)) (* 1/24 (sin x)))))
(* (pow eps 4) (+ (* -1/2 (/ (sin x) (pow eps 2))) (+ (* -1/6 (/ (cos x) eps)) (+ (* 1/24 (sin x)) (/ (cos x) (pow eps 3))))))
(- (sin (+ eps x)) (sin x))
(- (sin (+ eps x)) (sin x))
(- (sin (+ eps x)) (sin x))
(- (sin (+ eps x)) (sin x))
(* 1/24 (* (pow eps 3) (sin x)))
(* (pow eps 3) (+ (* -1/6 (/ (cos x) eps)) (* 1/24 (sin x))))
(* (pow eps 3) (+ (* -1/2 (/ (sin x) (pow eps 2))) (+ (* -1/6 (/ (cos x) eps)) (* 1/24 (sin x)))))
(* (pow eps 3) (+ (* -1/2 (/ (sin x) (pow eps 2))) (+ (* -1/6 (/ (cos x) eps)) (* 1/24 (sin x)))))
(* 1/24 (* (pow eps 2) (sin x)))
(* (pow eps 2) (+ (* -1/6 (/ (cos x) eps)) (* 1/24 (sin x))))
(* (pow eps 2) (+ (* -1/2 (/ (sin x) (pow eps 2))) (+ (* -1/6 (/ (cos x) eps)) (* 1/24 (sin x)))))
(* (pow eps 2) (+ (* -1/2 (/ (sin x) (pow eps 2))) (+ (* -1/6 (/ (cos x) eps)) (* 1/24 (sin x)))))
(- (sin (+ eps x)) (sin x))
(- (sin (+ eps x)) (sin x))
(- (sin (+ eps x)) (sin x))
(- (sin (+ eps x)) (sin x))
(* -1/2 (* (pow eps 2) (sin x)))
(* (pow eps 2) (+ (* -1/2 (sin x)) (/ (cos x) eps)))
(* (pow eps 2) (+ (* -1/2 (sin x)) (/ (cos x) eps)))
(* (pow eps 2) (+ (* -1/2 (sin x)) (/ (cos x) eps)))
(* -1/2 (* eps (sin x)))
(* eps (+ (* -1/2 (sin x)) (/ (cos x) eps)))
(* eps (+ (* -1/2 (sin x)) (/ (cos x) eps)))
(* eps (+ (* -1/2 (sin x)) (/ (cos x) eps)))
(- (sin (+ eps x)) (sin x))
(- (sin (+ eps x)) (sin x))
(- (sin (+ eps x)) (sin x))
(- (sin (+ eps x)) (sin x))
(* -1/2 (* (pow eps 2) (sin x)))
(* (pow eps 2) (+ (* -1/2 (sin x)) (/ (cos x) eps)))
(* (pow eps 2) (+ (* -1/2 (sin x)) (/ (cos x) eps)))
(* (pow eps 2) (+ (* -1/2 (sin x)) (/ (cos x) eps)))
(* -1/2 (* eps (sin x)))
(* eps (+ (* -1/2 (sin x)) (/ (cos x) eps)))
(* eps (+ (* -1/2 (sin x)) (/ (cos x) eps)))
(* eps (+ (* -1/2 (sin x)) (/ (cos x) eps)))
(* eps (* 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))))
(- (sin (+ eps x)) (sin x))
(- (sin (+ eps x)) (sin x))
(- (sin (+ eps x)) (sin x))
(- (sin (+ eps x)) (sin x))
(* -1/2 (* (pow eps 2) (sin x)))
(* (pow eps 2) (+ (* -1/2 (sin x)) (/ (cos x) eps)))
(* (pow eps 2) (+ (* -1/2 (sin x)) (/ (cos x) eps)))
(* (pow eps 2) (+ (* -1/2 (sin x)) (/ (cos x) eps)))
(* -1/2 (* eps (sin x)))
(* eps (+ (* -1/2 (sin x)) (/ (cos x) eps)))
(* eps (+ (* -1/2 (sin x)) (/ (cos x) eps)))
(* eps (+ (* -1/2 (sin x)) (/ (cos x) eps)))
(* -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)))
(- (sin (+ eps x)) (sin x))
(- (sin (+ eps x)) (sin x))
(- (sin (+ eps x)) (sin x))
(- (sin (+ eps x)) (sin x))
(* -1/2 (* (pow eps 2) (sin x)))
(* (pow eps 2) (+ (* -1/2 (sin x)) (/ (cos x) eps)))
(* (pow eps 2) (+ (* -1/2 (sin x)) (/ (cos x) eps)))
(* (pow eps 2) (+ (* -1/2 (sin x)) (/ (cos x) eps)))
(* -1/2 (* eps (sin x)))
(* eps (+ (* -1/2 (sin x)) (/ (cos x) eps)))
(* eps (+ (* -1/2 (sin x)) (/ (cos x) eps)))
(* eps (+ (* -1/2 (sin x)) (/ (cos x) eps)))
(* -1/6 (* eps (cos x)))
(* -1/6 (* eps (cos x)))
(* -1/6 (* eps (cos x)))
(* -1/6 (* eps (cos x)))
(* 1/12 eps)
(* 1/12 eps)
(* 1/12 eps)
(* 1/12 eps)
(* 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))
(/ (cos x) eps)
(/ (cos x) eps)
(/ (cos x) eps)
(/ (cos x) eps)
(* 1/24 (* (pow eps 4) (sin x)))
(* (pow eps 4) (+ (* -1/6 (/ (cos x) eps)) (* 1/24 (sin x))))
(* (pow eps 4) (+ (* -1 (/ (+ (* 1/6 (cos x)) (* 1/2 (/ (sin x) eps))) eps)) (* 1/24 (sin x))))
(* (pow eps 4) (+ (* -1 (/ (+ (* -1 (/ (+ (* -1/2 (sin x)) (/ (cos x) eps)) eps)) (* 1/6 (cos x))) eps)) (* 1/24 (sin x))))
(- (sin (- x (* -1 eps))) (sin x))
(- (sin (- x (* -1 eps))) (sin x))
(- (sin (- x (* -1 eps))) (sin x))
(- (sin (- x (* -1 eps))) (sin x))
(* 1/24 (* (pow eps 3) (sin x)))
(* -1 (* (pow eps 3) (+ (* -1/24 (sin x)) (* 1/6 (/ (cos x) eps)))))
(* -1 (* (pow eps 3) (+ (* -1 (/ (+ (* -1/2 (/ (sin x) eps)) (* -1/6 (cos x))) eps)) (* -1/24 (sin x)))))
(* -1 (* (pow eps 3) (+ (* -1 (/ (+ (* -1/2 (/ (sin x) eps)) (* -1/6 (cos x))) eps)) (* -1/24 (sin x)))))
(* 1/24 (* (pow eps 2) (sin x)))
(* (pow eps 2) (+ (* -1/6 (/ (cos x) eps)) (* 1/24 (sin x))))
(* (pow eps 2) (+ (* -1 (/ (+ (* 1/6 (cos x)) (* 1/2 (/ (sin x) eps))) eps)) (* 1/24 (sin x))))
(* (pow eps 2) (+ (* -1 (/ (+ (* 1/6 (cos x)) (* 1/2 (/ (sin x) eps))) eps)) (* 1/24 (sin x))))
(- (sin (- x (* -1 eps))) (sin x))
(- (sin (- x (* -1 eps))) (sin x))
(- (sin (- x (* -1 eps))) (sin x))
(- (sin (- x (* -1 eps))) (sin x))
(* -1/2 (* (pow eps 2) (sin x)))
(* (pow eps 2) (+ (* -1/2 (sin x)) (/ (cos x) eps)))
(* (pow eps 2) (+ (* -1/2 (sin x)) (/ (cos x) eps)))
(* (pow eps 2) (+ (* -1/2 (sin x)) (/ (cos x) eps)))
(* -1/2 (* eps (sin x)))
(* -1 (* eps (+ (* -1 (/ (cos x) eps)) (* 1/2 (sin x)))))
(* -1 (* eps (+ (* -1 (/ (cos x) eps)) (* 1/2 (sin x)))))
(* -1 (* eps (+ (* -1 (/ (cos x) eps)) (* 1/2 (sin x)))))
(- (sin (- x (* -1 eps))) (sin x))
(- (sin (- x (* -1 eps))) (sin x))
(- (sin (- x (* -1 eps))) (sin x))
(- (sin (- x (* -1 eps))) (sin x))
(* -1/2 (* (pow eps 2) (sin x)))
(* (pow eps 2) (+ (* -1/2 (sin x)) (/ (cos x) eps)))
(* (pow eps 2) (+ (* -1/2 (sin x)) (/ (cos x) eps)))
(* (pow eps 2) (+ (* -1/2 (sin x)) (/ (cos x) eps)))
(* -1/2 (* eps (sin x)))
(* -1 (* eps (+ (* -1 (/ (cos x) eps)) (* 1/2 (sin x)))))
(* -1 (* eps (+ (* -1 (/ (cos x) eps)) (* 1/2 (sin x)))))
(* -1 (* eps (+ (* -1 (/ (cos x) eps)) (* 1/2 (sin x)))))
(* -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)))))))
(- (sin (- x (* -1 eps))) (sin x))
(- (sin (- x (* -1 eps))) (sin x))
(- (sin (- x (* -1 eps))) (sin x))
(- (sin (- x (* -1 eps))) (sin x))
(* -1/2 (* (pow eps 2) (sin x)))
(* (pow eps 2) (+ (* -1/2 (sin x)) (/ (cos x) eps)))
(* (pow eps 2) (+ (* -1/2 (sin x)) (/ (cos x) eps)))
(* (pow eps 2) (+ (* -1/2 (sin x)) (/ (cos x) eps)))
(* -1/2 (* eps (sin x)))
(* -1 (* eps (+ (* -1 (/ (cos x) eps)) (* 1/2 (sin x)))))
(* -1 (* eps (+ (* -1 (/ (cos x) eps)) (* 1/2 (sin x)))))
(* -1 (* eps (+ (* -1 (/ (cos x) eps)) (* 1/2 (sin x)))))
(* -1/2 (* eps (sin x)))
(* -1 (* eps (+ (* -1 (/ (cos x) eps)) (* 1/2 (sin x)))))
(* -1 (* eps (+ (* -1 (/ (cos x) eps)) (* 1/2 (sin x)))))
(* -1 (* eps (+ (* -1 (/ (cos x) eps)) (* 1/2 (sin x)))))
(- (sin (- x (* -1 eps))) (sin x))
(- (sin (- x (* -1 eps))) (sin x))
(- (sin (- x (* -1 eps))) (sin x))
(- (sin (- x (* -1 eps))) (sin x))
(* -1/2 (* (pow eps 2) (sin x)))
(* (pow eps 2) (+ (* -1/2 (sin x)) (/ (cos x) eps)))
(* (pow eps 2) (+ (* -1/2 (sin x)) (/ (cos x) eps)))
(* (pow eps 2) (+ (* -1/2 (sin x)) (/ (cos x) eps)))
(* -1/2 (* eps (sin x)))
(* -1 (* eps (+ (* -1 (/ (cos x) eps)) (* 1/2 (sin x)))))
(* -1 (* eps (+ (* -1 (/ (cos x) eps)) (* 1/2 (sin x)))))
(* -1 (* eps (+ (* -1 (/ (cos x) eps)) (* 1/2 (sin x)))))
(* -1/6 (* eps (cos x)))
(* -1/6 (* eps (cos x)))
(* -1/6 (* eps (cos x)))
(* -1/6 (* eps (cos x)))
(* 1/12 eps)
(* 1/12 eps)
(* 1/12 eps)
(* 1/12 eps)
(* -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))))))
(/ (cos x) eps)
(/ (cos x) eps)
(/ (cos x) eps)
(/ (cos x) eps)
(+ eps (* -1/6 (pow eps 3)))
(+ eps (+ (* -1/6 (pow eps 3)) (* (pow eps 2) (* x (- (* 1/24 (pow eps 2)) 1/2)))))
(+ eps (+ (* -1/6 (pow eps 3)) (* x (+ (* x (+ (* -1/2 eps) (* 1/12 (pow eps 3)))) (* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2))))))
(+ eps (+ (* -1/6 (pow eps 3)) (* x (+ (* x (+ (* -1/2 eps) (+ (* -1/6 (* (pow eps 2) (* x (- (* 1/24 (pow eps 2)) 1/2)))) (* 1/12 (pow eps 3))))) (* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2))))))
(sin eps)
(+ (sin eps) (* x (- (cos eps) 1)))
(+ (sin eps) (* x (- (+ (cos eps) (* -1/2 (* x (sin eps)))) 1)))
(+ (sin eps) (* x (- (+ (cos eps) (* x (+ (* -1/2 (sin eps)) (* x (+ 1/6 (* -1/6 (cos eps))))))) 1)))
(* -1/6 (pow eps 2))
(+ (* -1/6 (pow eps 2)) (* eps (* x (- (* 1/24 (pow eps 2)) 1/2))))
(+ (* -1/6 (pow eps 2)) (* x (+ (* 1/12 (* (pow eps 2) x)) (* eps (- (* 1/24 (pow eps 2)) 1/2)))))
(+ (* -1/6 (pow eps 2)) (* x (+ (* eps (- (* 1/24 (pow eps 2)) 1/2)) (* x (+ (* -1/6 (* eps (* x (- (* 1/24 (pow eps 2)) 1/2)))) (* 1/12 (pow eps 2)))))))
(* -1/6 eps)
(+ (* -1/6 eps) (* x (- (* 1/24 (pow eps 2)) 1/2)))
(+ (* -1/6 eps) (* x (- (+ (* 1/24 (pow eps 2)) (* 1/12 (* eps x))) 1/2)))
(+ (* -1/6 eps) (* x (- (+ (* 1/24 (pow eps 2)) (* x (+ (* -1/6 (* x (- (* 1/24 (pow eps 2)) 1/2))) (* 1/12 eps)))) 1/2)))
(sin eps)
(+ (sin eps) (* x (- (cos eps) 1)))
(+ (sin eps) (* x (- (+ (cos eps) (* -1/2 (* x (sin eps)))) 1)))
(+ (sin eps) (* x (- (+ (cos eps) (* x (+ (* -1/2 (sin eps)) (* x (+ 1/6 (* -1/6 (cos eps))))))) 1)))
eps
(+ eps (* -1/2 (* (pow eps 2) x)))
(+ eps (* x (+ (* -1/2 (* eps x)) (* -1/2 (pow eps 2)))))
(+ eps (* x (+ (* -1/2 (pow eps 2)) (* x (+ (* -1/2 eps) (* 1/12 (* (pow eps 2) x)))))))
1
(+ 1 (* -1/2 (* eps x)))
(+ 1 (* x (+ (* -1/2 eps) (* -1/2 x))))
(+ 1 (* x (+ (* -1/2 eps) (* x (- (* 1/12 (* eps x)) 1/2)))))
(sin eps)
(+ (sin eps) (* x (- (cos eps) 1)))
(+ (sin eps) (* x (- (+ (cos eps) (* -1/2 (* x (sin eps)))) 1)))
(+ (sin eps) (* x (- (+ (cos eps) (* x (+ (* -1/2 (sin eps)) (* x (+ 1/6 (* -1/6 (cos eps))))))) 1)))
eps
(+ eps (* -1/2 (* (pow eps 2) x)))
(+ eps (* x (+ (* -1/2 (* eps x)) (* -1/2 (pow eps 2)))))
(+ eps (* x (+ (* -1/2 (pow eps 2)) (* x (+ (* -1/2 eps) (* 1/12 (* (pow eps 2) x)))))))
1
(+ 1 (* -1/2 (* eps x)))
(+ 1 (* x (+ (* -1/2 eps) (* -1/2 x))))
(+ 1 (* x (+ (* -1/2 eps) (* x (- (* 1/12 (* eps x)) 1/2)))))
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)))))
(sin eps)
(+ (sin eps) (* x (- (cos eps) 1)))
(+ (sin eps) (* x (- (+ (cos eps) (* -1/2 (* x (sin eps)))) 1)))
(+ (sin eps) (* x (- (+ (cos eps) (* x (+ (* -1/2 (sin eps)) (* x (+ 1/6 (* -1/6 (cos eps))))))) 1)))
eps
(+ eps (* -1/2 (* (pow eps 2) x)))
(+ eps (* x (+ (* -1/2 (* eps x)) (* -1/2 (pow eps 2)))))
(+ eps (* x (+ (* -1/2 (pow eps 2)) (* x (+ (* -1/2 eps) (* 1/12 (* (pow eps 2) x)))))))
1
(+ 1 (* -1/2 (* eps x)))
(+ 1 (* x (+ (* -1/2 eps) (* -1/2 x))))
(+ 1 (* x (+ (* -1/2 eps) (* x (- (* 1/12 (* eps x)) 1/2)))))
(* -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
(+ 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)))))
(sin eps)
(+ (sin eps) (* x (- (cos eps) 1)))
(+ (sin eps) (* x (- (+ (cos eps) (* -1/2 (* x (sin eps)))) 1)))
(+ (sin eps) (* x (- (+ (cos eps) (* x (+ (* -1/2 (sin eps)) (* x (+ 1/6 (* -1/6 (cos eps))))))) 1)))
eps
(+ eps (* -1/2 (* (pow eps 2) x)))
(+ eps (* x (+ (* -1/2 (* eps x)) (* -1/2 (pow eps 2)))))
(+ eps (* x (+ (* -1/2 (pow eps 2)) (* x (+ (* -1/2 eps) (* 1/12 (* (pow eps 2) x)))))))
1
(+ 1 (* -1/2 (* eps x)))
(+ 1 (* x (+ (* -1/2 eps) (* -1/2 x))))
(+ 1 (* x (+ (* -1/2 eps) (* x (- (* 1/12 (* eps x)) 1/2)))))
(* -1/6 eps)
(+ (* -1/6 eps) (* 1/12 (* eps (pow x 2))))
(+ (* -1/6 eps) (* (pow x 2) (+ (* -1/144 (* eps (pow x 2))) (* 1/12 eps))))
(+ (* -1/6 eps) (* (pow x 2) (+ (* 1/12 eps) (* (pow x 2) (+ (* -1/144 eps) (* 1/4320 (* eps (pow x 2))))))))
-1/6
(- (* 1/12 (pow x 2)) 1/6)
(- (* (pow x 2) (+ 1/12 (* -1/144 (pow x 2)))) 1/6)
(- (* (pow x 2) (+ 1/12 (* (pow x 2) (- (* 1/4320 (pow x 2)) 1/144)))) 1/6)
(* -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 eps)
(+ (* -1/2 (/ (pow x 2) eps)) (/ 1 eps))
(+ (* (pow x 2) (- (* 1/24 (/ (pow x 2) eps)) (* 1/2 (/ 1 eps)))) (/ 1 eps))
(+ (* (pow x 2) (- (* (pow x 2) (+ (* -1/720 (/ (pow x 2) eps)) (* 1/24 (/ 1 eps)))) (* 1/2 (/ 1 eps)))) (/ 1 eps))
(+ (* eps (cos x)) (* (pow eps 2) (+ (* -1/6 (* eps (cos x))) (* (sin x) (- (* 1/24 (pow eps 2)) 1/2)))))
(+ (* eps (cos x)) (* (pow eps 2) (+ (* -1/6 (* eps (cos x))) (* (sin x) (- (* 1/24 (pow eps 2)) 1/2)))))
(+ (* eps (cos x)) (* (pow eps 2) (+ (* -1/6 (* eps (cos x))) (* (sin x) (- (* 1/24 (pow eps 2)) 1/2)))))
(+ (* eps (cos x)) (* (pow eps 2) (+ (* -1/6 (* eps (cos x))) (* (sin x) (- (* 1/24 (pow eps 2)) 1/2)))))
(- (sin (+ eps x)) (sin x))
(- (sin (+ eps x)) (sin x))
(- (sin (+ eps x)) (sin x))
(- (sin (+ eps x)) (sin x))
(* eps (+ (* -1/6 (* eps (cos x))) (* (sin x) (- (* 1/24 (pow eps 2)) 1/2))))
(* eps (+ (* -1/6 (* eps (cos x))) (* (sin x) (- (* 1/24 (pow eps 2)) 1/2))))
(* eps (+ (* -1/6 (* eps (cos x))) (* (sin x) (- (* 1/24 (pow eps 2)) 1/2))))
(* eps (+ (* -1/6 (* eps (cos x))) (* (sin x) (- (* 1/24 (pow eps 2)) 1/2))))
(+ (* -1/6 (* eps (cos x))) (* (sin x) (- (* 1/24 (pow eps 2)) 1/2)))
(+ (* -1/6 (* eps (cos x))) (* (sin x) (- (* 1/24 (pow eps 2)) 1/2)))
(+ (* -1/6 (* eps (cos x))) (* (sin x) (- (* 1/24 (pow eps 2)) 1/2)))
(+ (* -1/6 (* eps (cos x))) (* (sin x) (- (* 1/24 (pow eps 2)) 1/2)))
(- (sin (+ eps x)) (sin x))
(- (sin (+ eps x)) (sin x))
(- (sin (+ eps x)) (sin x))
(- (sin (+ eps x)) (sin x))
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(+ (cos x) (* -1/2 (* eps (sin x))))
(+ (cos x) (* -1/2 (* eps (sin x))))
(+ (cos x) (* -1/2 (* eps (sin x))))
(+ (cos x) (* -1/2 (* eps (sin x))))
(- (sin (+ eps x)) (sin x))
(- (sin (+ eps x)) (sin x))
(- (sin (+ eps x)) (sin x))
(- (sin (+ eps x)) (sin x))
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(+ (cos x) (* -1/2 (* eps (sin x))))
(+ (cos x) (* -1/2 (* eps (sin x))))
(+ (cos x) (* -1/2 (* eps (sin x))))
(+ (cos x) (* -1/2 (* eps (sin x))))
(* 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))))
(- (sin (+ eps x)) (sin x))
(- (sin (+ eps x)) (sin x))
(- (sin (+ eps x)) (sin x))
(- (sin (+ eps x)) (sin x))
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(+ (cos x) (* -1/2 (* eps (sin x))))
(+ (cos x) (* -1/2 (* eps (sin x))))
(+ (cos x) (* -1/2 (* eps (sin x))))
(+ (cos x) (* -1/2 (* eps (sin x))))
(* -1/2 (sin x))
(* -1/2 (sin x))
(* -1/2 (sin x))
(* -1/2 (sin x))
(* eps (+ (* -1/2 (sin x)) (/ (cos x) eps)))
(* eps (+ (* -1/2 (sin x)) (/ (cos x) eps)))
(* eps (+ (* -1/2 (sin x)) (/ (cos x) eps)))
(* eps (+ (* -1/2 (sin x)) (/ (cos x) eps)))
(- (sin (+ eps x)) (sin x))
(- (sin (+ eps x)) (sin x))
(- (sin (+ eps x)) (sin x))
(- (sin (+ eps x)) (sin x))
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(+ (cos x) (* -1/2 (* eps (sin x))))
(+ (cos x) (* -1/2 (* eps (sin x))))
(+ (cos x) (* -1/2 (* eps (sin x))))
(+ (cos x) (* -1/2 (* eps (sin x))))
(* -1/6 (* eps (cos x)))
(* -1/6 (* eps (cos x)))
(* -1/6 (* eps (cos x)))
(* -1/6 (* eps (cos x)))
(* -1/6 (cos x))
(* -1/6 (cos x))
(* -1/6 (cos x))
(* -1/6 (cos x))
(* 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))))
(/ (cos x) eps)
(/ (cos x) eps)
(/ (cos x) eps)
(/ (cos x) eps)
(+ (* eps (cos x)) (* (pow eps 2) (+ (* -1/6 (* eps (cos x))) (* (sin x) (- (* 1/24 (pow eps 2)) 1/2)))))
(+ (* eps (cos x)) (* (pow eps 2) (+ (* -1/6 (* eps (cos x))) (* (sin x) (- (* 1/24 (pow eps 2)) 1/2)))))
(+ (* eps (cos x)) (* (pow eps 2) (+ (* -1/6 (* eps (cos x))) (* (sin x) (- (* 1/24 (pow eps 2)) 1/2)))))
(+ (* eps (cos x)) (* (pow eps 2) (+ (* -1/6 (* eps (cos x))) (* (sin x) (- (* 1/24 (pow eps 2)) 1/2)))))
(- (sin (- eps (* -1 x))) (sin x))
(- (sin (- eps (* -1 x))) (sin x))
(- (sin (- eps (* -1 x))) (sin x))
(- (sin (- eps (* -1 x))) (sin x))
(* eps (+ (* -1/6 (* eps (cos x))) (* (sin x) (- (* 1/24 (pow eps 2)) 1/2))))
(* eps (+ (* -1/6 (* eps (cos x))) (* (sin x) (- (* 1/24 (pow eps 2)) 1/2))))
(* eps (+ (* -1/6 (* eps (cos x))) (* (sin x) (- (* 1/24 (pow eps 2)) 1/2))))
(* eps (+ (* -1/6 (* eps (cos x))) (* (sin x) (- (* 1/24 (pow eps 2)) 1/2))))
(+ (* -1/6 (* eps (cos x))) (* (sin x) (- (* 1/24 (pow eps 2)) 1/2)))
(+ (* -1/6 (* eps (cos x))) (* (sin x) (- (* 1/24 (pow eps 2)) 1/2)))
(+ (* -1/6 (* eps (cos x))) (* (sin x) (- (* 1/24 (pow eps 2)) 1/2)))
(+ (* -1/6 (* eps (cos x))) (* (sin x) (- (* 1/24 (pow eps 2)) 1/2)))
(- (sin (- eps (* -1 x))) (sin x))
(- (sin (- eps (* -1 x))) (sin x))
(- (sin (- eps (* -1 x))) (sin x))
(- (sin (- eps (* -1 x))) (sin x))
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(+ (cos x) (* -1/2 (* eps (sin x))))
(+ (cos x) (* -1/2 (* eps (sin x))))
(+ (cos x) (* -1/2 (* eps (sin x))))
(+ (cos x) (* -1/2 (* eps (sin x))))
(- (sin (- eps (* -1 x))) (sin x))
(- (sin (- eps (* -1 x))) (sin x))
(- (sin (- eps (* -1 x))) (sin x))
(- (sin (- eps (* -1 x))) (sin x))
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(+ (cos x) (* -1/2 (* eps (sin x))))
(+ (cos x) (* -1/2 (* eps (sin x))))
(+ (cos x) (* -1/2 (* eps (sin x))))
(+ (cos x) (* -1/2 (* eps (sin x))))
(* 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))))
(- (sin (- eps (* -1 x))) (sin x))
(- (sin (- eps (* -1 x))) (sin x))
(- (sin (- eps (* -1 x))) (sin x))
(- (sin (- eps (* -1 x))) (sin x))
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(+ (cos x) (* -1/2 (* eps (sin x))))
(+ (cos x) (* -1/2 (* eps (sin x))))
(+ (cos x) (* -1/2 (* eps (sin x))))
(+ (cos x) (* -1/2 (* eps (sin x))))
(* -1/2 (sin x))
(* -1/2 (sin x))
(* -1/2 (sin x))
(* -1/2 (sin x))
(* eps (+ (* -1/2 (sin x)) (/ (cos x) eps)))
(* eps (+ (* -1/2 (sin x)) (/ (cos x) eps)))
(* eps (+ (* -1/2 (sin x)) (/ (cos x) eps)))
(* eps (+ (* -1/2 (sin x)) (/ (cos x) eps)))
(- (sin (- eps (* -1 x))) (sin x))
(- (sin (- eps (* -1 x))) (sin x))
(- (sin (- eps (* -1 x))) (sin x))
(- (sin (- eps (* -1 x))) (sin x))
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(+ (cos x) (* -1/2 (* eps (sin x))))
(+ (cos x) (* -1/2 (* eps (sin x))))
(+ (cos x) (* -1/2 (* eps (sin x))))
(+ (cos x) (* -1/2 (* eps (sin x))))
(* -1/6 (* eps (cos x)))
(* -1/6 (* eps (cos x)))
(* -1/6 (* eps (cos x)))
(* -1/6 (* eps (cos x)))
(* -1/6 (cos x))
(* -1/6 (cos x))
(* -1/6 (cos x))
(* -1/6 (cos 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)))
(/ (cos x) eps)
(/ (cos x) eps)
(/ (cos x) eps)
(/ (cos x) eps)

Outputs
(* eps (cos x))
(*.f64 (cos.f64 x) eps)
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(.f64 (fma.f64 (.f64 (sin.f64 x) #s(literal -1/2 binary64)) eps (cos.f64 x)) eps)
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(.f64 (.f64 (fma.f64 (sin.f64 x) #s(literal -1/2 binary64) (/.f64 (cos.f64 x) eps)) eps) eps)
(* (pow eps 2) (+ (* -1/2 (sin x)) (/ (cos x) eps)))
(.f64 (.f64 (fma.f64 (sin.f64 x) #s(literal -1/2 binary64) (/.f64 (cos.f64 x) eps)) eps) eps)
(* (pow eps 2) (+ (* -1/2 (sin x)) (/ (cos x) eps)))
(.f64 (.f64 (fma.f64 (sin.f64 x) #s(literal -1/2 binary64) (/.f64 (cos.f64 x) eps)) eps) eps)
(* -1/2 (* eps (sin x)))
(.f64 (.f64 (sin.f64 x) #s(literal -1/2 binary64)) eps)
(* -1 (* eps (+ (* -1 (/ (cos x) eps)) (* 1/2 (sin x)))))
(*.f64 (fma.f64 (sin.f64 x) #s(literal -1/2 binary64) (/.f64 (cos.f64 x) eps)) eps)
(* -1 (* eps (+ (* -1 (/ (cos x) eps)) (* 1/2 (sin x)))))
(*.f64 (fma.f64 (sin.f64 x) #s(literal -1/2 binary64) (/.f64 (cos.f64 x) eps)) eps)
(* -1 (* eps (+ (* -1 (/ (cos x) eps)) (* 1/2 (sin x)))))
(*.f64 (fma.f64 (sin.f64 x) #s(literal -1/2 binary64) (/.f64 (cos.f64 x) eps)) eps)
(* -1/6 (* eps (cos x)))
(.f64 #s(literal -1/6 binary64) (.f64 (cos.f64 x) eps))
(* -1/6 (* eps (cos x)))
(.f64 #s(literal -1/6 binary64) (.f64 (cos.f64 x) eps))
(* -1/6 (* eps (cos x)))
(.f64 #s(literal -1/6 binary64) (.f64 (cos.f64 x) eps))
(* -1/6 (* eps (cos x)))
(.f64 #s(literal -1/6 binary64) (.f64 (cos.f64 x) eps))
(* 1/12 eps)
(*.f64 #s(literal 1/12 binary64) eps)
(* 1/12 eps)
(*.f64 #s(literal 1/12 binary64) eps)
(* 1/12 eps)
(*.f64 #s(literal 1/12 binary64) eps)
(* 1/12 eps)
(*.f64 #s(literal 1/12 binary64) eps)
(* -1 (* eps (+ 1/2 (* -1/12 (pow x 2)))))
(.f64 (fma.f64 #s(literal 1/12 binary64) (.f64 x x) #s(literal -1/2 binary64)) eps)
(* -1 (* eps (+ 1/2 (+ (* -1/12 (pow x 2)) (* 1/2 (/ x eps))))))
(.f64 (fma.f64 (/.f64 x eps) #s(literal 1/2 binary64) (fma.f64 #s(literal -1/12 binary64) (.f64 x x) #s(literal 1/2 binary64))) (neg.f64 eps))
(* -1 (* eps (+ 1/2 (+ (* -1/12 (pow x 2)) (* 1/2 (/ x eps))))))
(.f64 (fma.f64 (/.f64 x eps) #s(literal 1/2 binary64) (fma.f64 #s(literal -1/12 binary64) (.f64 x x) #s(literal 1/2 binary64))) (neg.f64 eps))
(* -1 (* eps (+ 1/2 (+ (* -1/12 (pow x 2)) (* 1/2 (/ x eps))))))
(.f64 (fma.f64 (/.f64 x eps) #s(literal 1/2 binary64) (fma.f64 #s(literal -1/12 binary64) (.f64 x x) #s(literal 1/2 binary64))) (neg.f64 eps))
(/ (cos x) eps)
(/.f64 (cos.f64 x) eps)
(/ (cos x) eps)
(/.f64 (cos.f64 x) eps)
(/ (cos x) eps)
(/.f64 (cos.f64 x) eps)
(/ (cos x) eps)
(/.f64 (cos.f64 x) eps)
(+ eps (* -1/6 (pow eps 3)))
(fma.f64 (pow.f64 eps #s(literal 3 binary64)) #s(literal -1/6 binary64) eps)
(+ eps (+ (* -1/6 (pow eps 3)) (* (pow eps 2) (* x (- (* 1/24 (pow eps 2)) 1/2)))))
(fma.f64 (.f64 eps eps) (fma.f64 (fma.f64 (.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) x (*.f64 #s(literal -1/6 binary64) eps)) eps)
(+ eps (+ (* -1/6 (pow eps 3)) (* x (+ (* x (+ (* -1/2 eps) (* 1/12 (pow eps 3)))) (* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2))))))
(fma.f64 (fma.f64 (.f64 (fma.f64 (.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) eps) eps (.f64 (fma.f64 (pow.f64 eps #s(literal 3 binary64)) #s(literal 1/12 binary64) (.f64 #s(literal -1/2 binary64) eps)) x)) x (fma.f64 (pow.f64 eps #s(literal 3 binary64)) #s(literal -1/6 binary64) eps))
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(sin eps)
(sin.f64 eps)
(+ (sin eps) (* x (- (cos eps) 1)))
(fma.f64 (-.f64 (cos.f64 eps) #s(literal 1 binary64)) x (sin.f64 eps))
(+ (sin eps) (* x (- (+ (cos eps) (* -1/2 (* x (sin eps)))) 1)))
(fma.f64 (fma.f64 (*.f64 (sin.f64 eps) x) #s(literal -1/2 binary64) (-.f64 (cos.f64 eps) #s(literal 1 binary64))) x (sin.f64 eps))
(+ (sin eps) (* x (- (+ (cos eps) (* x (+ (* -1/2 (sin eps)) (* x (+ 1/6 (* -1/6 (cos eps))))))) 1)))
(fma.f64 (fma.f64 (fma.f64 (fma.f64 (cos.f64 eps) #s(literal -1/6 binary64) #s(literal 1/6 binary64)) x (*.f64 (sin.f64 eps) #s(literal -1/2 binary64))) x (-.f64 (cos.f64 eps) #s(literal 1 binary64))) x (sin.f64 eps))
(* -1/6 (pow eps 2))
(.f64 (.f64 eps eps) #s(literal -1/6 binary64))
(+ (* -1/6 (pow eps 2)) (* eps (* x (- (* 1/24 (pow eps 2)) 1/2))))
(.f64 eps (fma.f64 (fma.f64 (.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) x (*.f64 #s(literal -1/6 binary64) eps)))
(+ (* -1/6 (pow eps 2)) (* x (+ (* 1/12 (* (pow eps 2) x)) (* eps (- (* 1/24 (pow eps 2)) 1/2)))))
(fma.f64 (fma.f64 (.f64 (.f64 eps eps) x) #s(literal 1/12 binary64) (.f64 (fma.f64 (.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) eps)) x (.f64 (.f64 eps eps) #s(literal -1/6 binary64)))
(+ (* -1/6 (pow eps 2)) (* x (+ (* eps (- (* 1/24 (pow eps 2)) 1/2)) (* x (+ (* -1/6 (* eps (* x (- (* 1/24 (pow eps 2)) 1/2)))) (* 1/12 (pow eps 2)))))))
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(* -1/6 eps)
(*.f64 #s(literal -1/6 binary64) eps)
(+ (* -1/6 eps) (* x (- (* 1/24 (pow eps 2)) 1/2)))
(fma.f64 (fma.f64 (.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) x (.f64 #s(literal -1/6 binary64) eps))
(+ (* -1/6 eps) (* x (- (+ (* 1/24 (pow eps 2)) (* 1/12 (* eps x))) 1/2)))
(fma.f64 (fma.f64 eps (fma.f64 x #s(literal 1/12 binary64) (.f64 #s(literal 1/24 binary64) eps)) #s(literal -1/2 binary64)) x (.f64 #s(literal -1/6 binary64) eps))
(+ (* -1/6 eps) (* x (- (+ (* 1/24 (pow eps 2)) (* x (+ (* -1/6 (* x (- (* 1/24 (pow eps 2)) 1/2))) (* 1/12 eps)))) 1/2)))
(fma.f64 (fma.f64 (fma.f64 (.f64 (fma.f64 (.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) x) #s(literal -1/6 binary64) (.f64 #s(literal 1/12 binary64) eps)) x (fma.f64 (.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64))) x (*.f64 #s(literal -1/6 binary64) eps))
(sin eps)
(sin.f64 eps)
(+ (sin eps) (* x (- (cos eps) 1)))
(fma.f64 (-.f64 (cos.f64 eps) #s(literal 1 binary64)) x (sin.f64 eps))
(+ (sin eps) (* x (- (+ (cos eps) (* -1/2 (* x (sin eps)))) 1)))
(fma.f64 (fma.f64 (*.f64 (sin.f64 eps) x) #s(literal -1/2 binary64) (-.f64 (cos.f64 eps) #s(literal 1 binary64))) x (sin.f64 eps))
(+ (sin eps) (* x (- (+ (cos eps) (* x (+ (* -1/2 (sin eps)) (* x (+ 1/6 (* -1/6 (cos eps))))))) 1)))
(fma.f64 (fma.f64 (fma.f64 (fma.f64 (cos.f64 eps) #s(literal -1/6 binary64) #s(literal 1/6 binary64)) x (*.f64 (sin.f64 eps) #s(literal -1/2 binary64))) x (-.f64 (cos.f64 eps) #s(literal 1 binary64))) x (sin.f64 eps))
eps
(+ eps (* -1/2 (* (pow eps 2) x)))
(fma.f64 (.f64 (.f64 #s(literal -1/2 binary64) eps) eps) x eps)
(+ eps (* x (+ (* -1/2 (* eps x)) (* -1/2 (pow eps 2)))))
(fma.f64 (.f64 (.f64 eps (+.f64 x eps)) #s(literal -1/2 binary64)) x eps)
(+ eps (* x (+ (* -1/2 (pow eps 2)) (* x (+ (* -1/2 eps) (* 1/12 (* (pow eps 2) x)))))))
(fma.f64 (fma.f64 (.f64 x (.f64 (.f64 eps eps) x)) #s(literal 1/12 binary64) (.f64 (*.f64 eps (+.f64 x eps)) #s(literal -1/2 binary64))) x eps)
1
#s(literal 1 binary64)
(+ 1 (* -1/2 (* eps x)))
(fma.f64 (*.f64 x eps) #s(literal -1/2 binary64) #s(literal 1 binary64))
(+ 1 (* x (+ (* -1/2 eps) (* -1/2 x))))
(fma.f64 (*.f64 (+.f64 x eps) #s(literal -1/2 binary64)) x #s(literal 1 binary64))
(+ 1 (* x (+ (* -1/2 eps) (* x (- (* 1/12 (* eps x)) 1/2)))))
(fma.f64 (fma.f64 (fma.f64 (.f64 x eps) #s(literal 1/12 binary64) #s(literal -1/2 binary64)) x (.f64 #s(literal -1/2 binary64) eps)) x #s(literal 1 binary64))
(sin eps)
(sin.f64 eps)
(+ (sin eps) (* x (- (cos eps) 1)))
(fma.f64 (-.f64 (cos.f64 eps) #s(literal 1 binary64)) x (sin.f64 eps))
(+ (sin eps) (* x (- (+ (cos eps) (* -1/2 (* x (sin eps)))) 1)))
(fma.f64 (fma.f64 (*.f64 (sin.f64 eps) x) #s(literal -1/2 binary64) (-.f64 (cos.f64 eps) #s(literal 1 binary64))) x (sin.f64 eps))
(+ (sin eps) (* x (- (+ (cos eps) (* x (+ (* -1/2 (sin eps)) (* x (+ 1/6 (* -1/6 (cos eps))))))) 1)))
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eps
(+ eps (* -1/2 (* (pow eps 2) x)))
(fma.f64 (.f64 (.f64 #s(literal -1/2 binary64) eps) eps) x eps)
(+ eps (* x (+ (* -1/2 (* eps x)) (* -1/2 (pow eps 2)))))
(fma.f64 (.f64 (.f64 eps (+.f64 x eps)) #s(literal -1/2 binary64)) x eps)
(+ eps (* x (+ (* -1/2 (pow eps 2)) (* x (+ (* -1/2 eps) (* 1/12 (* (pow eps 2) x)))))))
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1
#s(literal 1 binary64)
(+ 1 (* -1/2 (* eps x)))
(fma.f64 (*.f64 x eps) #s(literal -1/2 binary64) #s(literal 1 binary64))
(+ 1 (* x (+ (* -1/2 eps) (* -1/2 x))))
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(+ 1 (* x (+ (* -1/2 eps) (* x (- (* 1/12 (* eps x)) 1/2)))))
(fma.f64 (fma.f64 (fma.f64 (.f64 x eps) #s(literal 1/12 binary64) #s(literal -1/2 binary64)) x (.f64 #s(literal -1/2 binary64) eps)) x #s(literal 1 binary64))
1
#s(literal 1 binary64)
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(+ 1 (* x (+ (* -1/2 eps) (* -1/2 x))))
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(+ 1 (* x (+ (* -1/2 eps) (* x (- (* 1/12 (* eps x)) 1/2)))))
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(sin eps)
(sin.f64 eps)
(+ (sin eps) (* x (- (cos eps) 1)))
(fma.f64 (-.f64 (cos.f64 eps) #s(literal 1 binary64)) x (sin.f64 eps))
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eps
(+ eps (* -1/2 (* (pow eps 2) x)))
(fma.f64 (.f64 (.f64 #s(literal -1/2 binary64) eps) eps) x eps)
(+ eps (* x (+ (* -1/2 (* eps x)) (* -1/2 (pow eps 2)))))
(fma.f64 (.f64 (.f64 eps (+.f64 x eps)) #s(literal -1/2 binary64)) x eps)
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1
#s(literal 1 binary64)
(+ 1 (* -1/2 (* eps x)))
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(* -1/2 x)
(*.f64 #s(literal -1/2 binary64) x)
(* x (- (* 1/12 (pow x 2)) 1/2))
(.f64 (fma.f64 #s(literal 1/12 binary64) (.f64 x x) #s(literal -1/2 binary64)) x)
(* x (- (* (pow x 2) (+ 1/12 (* -1/240 (pow x 2)))) 1/2))
(.f64 (fma.f64 (fma.f64 #s(literal -1/240 binary64) (.f64 x x) #s(literal 1/12 binary64)) (*.f64 x x) #s(literal -1/2 binary64)) x)
(* x (- (* (pow x 2) (+ 1/12 (* (pow x 2) (- (* 1/10080 (pow x 2)) 1/240)))) 1/2))
(.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 1/10080 binary64) (.f64 x x) #s(literal -1/240 binary64)) (.f64 x x) #s(literal 1/12 binary64)) (.f64 x x) #s(literal -1/2 binary64)) x)
1
#s(literal 1 binary64)
(+ 1 (* -1/2 (* eps x)))
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(+ 1 (* x (+ (* -1/2 eps) (* -1/2 x))))
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(+ 1 (* x (+ (* -1/2 eps) (* x (- (* 1/12 (* eps x)) 1/2)))))
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(sin eps)
(sin.f64 eps)
(+ (sin eps) (* x (- (cos eps) 1)))
(fma.f64 (-.f64 (cos.f64 eps) #s(literal 1 binary64)) x (sin.f64 eps))
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(+ (sin eps) (* x (- (+ (cos eps) (* x (+ (* -1/2 (sin eps)) (* x (+ 1/6 (* -1/6 (cos eps))))))) 1)))
(fma.f64 (fma.f64 (fma.f64 (fma.f64 (cos.f64 eps) #s(literal -1/6 binary64) #s(literal 1/6 binary64)) x (*.f64 (sin.f64 eps) #s(literal -1/2 binary64))) x (-.f64 (cos.f64 eps) #s(literal 1 binary64))) x (sin.f64 eps))
eps
(+ eps (* -1/2 (* (pow eps 2) x)))
(fma.f64 (.f64 (.f64 #s(literal -1/2 binary64) eps) eps) x eps)
(+ eps (* x (+ (* -1/2 (* eps x)) (* -1/2 (pow eps 2)))))
(fma.f64 (.f64 (.f64 eps (+.f64 x eps)) #s(literal -1/2 binary64)) x eps)
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1
#s(literal 1 binary64)
(+ 1 (* -1/2 (* eps x)))
(fma.f64 (*.f64 x eps) #s(literal -1/2 binary64) #s(literal 1 binary64))
(+ 1 (* x (+ (* -1/2 eps) (* -1/2 x))))
(fma.f64 (*.f64 (+.f64 x eps) #s(literal -1/2 binary64)) x #s(literal 1 binary64))
(+ 1 (* x (+ (* -1/2 eps) (* x (- (* 1/12 (* eps x)) 1/2)))))
(fma.f64 (fma.f64 (fma.f64 (.f64 x eps) #s(literal 1/12 binary64) #s(literal -1/2 binary64)) x (.f64 #s(literal -1/2 binary64) eps)) x #s(literal 1 binary64))
(* -1/6 eps)
(*.f64 #s(literal -1/6 binary64) eps)
(+ (* -1/6 eps) (* 1/12 (* eps (pow x 2))))
(.f64 eps (fma.f64 #s(literal 1/12 binary64) (.f64 x x) #s(literal -1/6 binary64)))
(+ (* -1/6 eps) (* (pow x 2) (+ (* -1/144 (* eps (pow x 2))) (* 1/12 eps))))
(fma.f64 (.f64 (.f64 eps (fma.f64 #s(literal -1/144 binary64) (.f64 x x) #s(literal 1/12 binary64))) x) x (.f64 #s(literal -1/6 binary64) eps))
(+ (* -1/6 eps) (* (pow x 2) (+ (* 1/12 eps) (* (pow x 2) (+ (* -1/144 eps) (* 1/4320 (* eps (pow x 2))))))))
(fma.f64 (pow.f64 x #s(literal 4 binary64)) (.f64 eps (fma.f64 #s(literal 1/4320 binary64) (.f64 x x) #s(literal -1/144 binary64))) (.f64 eps (fma.f64 #s(literal 1/12 binary64) (.f64 x x) #s(literal -1/6 binary64))))
-1/6
#s(literal -1/6 binary64)
(- (* 1/12 (pow x 2)) 1/6)
(fma.f64 #s(literal 1/12 binary64) (*.f64 x x) #s(literal -1/6 binary64))
(- (* (pow x 2) (+ 1/12 (* -1/144 (pow x 2)))) 1/6)
(fma.f64 (fma.f64 #s(literal -1/144 binary64) (.f64 x x) #s(literal 1/12 binary64)) (.f64 x x) #s(literal -1/6 binary64))
(- (* (pow x 2) (+ 1/12 (* (pow x 2) (- (* 1/4320 (pow x 2)) 1/144)))) 1/6)
(fma.f64 (fma.f64 (fma.f64 #s(literal 1/4320 binary64) (.f64 x x) #s(literal -1/144 binary64)) (.f64 x x) #s(literal 1/12 binary64)) (*.f64 x x) #s(literal -1/6 binary64))
(* -1/2 eps)
(*.f64 #s(literal -1/2 binary64) eps)
(+ (* -1/2 eps) (* -1/2 x))
(*.f64 (+.f64 x eps) #s(literal -1/2 binary64))
(+ (* -1/2 eps) (* x (- (* 1/12 (* eps x)) 1/2)))
(fma.f64 (fma.f64 (.f64 x eps) #s(literal 1/12 binary64) #s(literal -1/2 binary64)) x (.f64 #s(literal -1/2 binary64) eps))
(+ (* -1/2 eps) (* x (- (* 1/12 (* eps x)) 1/2)))
(fma.f64 (fma.f64 (.f64 x eps) #s(literal 1/12 binary64) #s(literal -1/2 binary64)) x (.f64 #s(literal -1/2 binary64) eps))
(/ 1 eps)
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(.f64 (fma.f64 (.f64 (sin.f64 x) #s(literal -1/2 binary64)) eps (cos.f64 x)) eps)
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(.f64 (fma.f64 (.f64 (sin.f64 x) #s(literal -1/2 binary64)) eps (cos.f64 x)) eps)
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(.f64 (fma.f64 (.f64 (sin.f64 x) #s(literal -1/2 binary64)) eps (cos.f64 x)) eps)
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(.f64 (fma.f64 (.f64 (sin.f64 x) #s(literal -1/2 binary64)) eps (cos.f64 x)) eps)
(+ (cos x) (* -1/2 (* eps (sin x))))
(fma.f64 (*.f64 (sin.f64 x) #s(literal -1/2 binary64)) eps (cos.f64 x))
(+ (cos x) (* -1/2 (* eps (sin x))))
(fma.f64 (*.f64 (sin.f64 x) #s(literal -1/2 binary64)) eps (cos.f64 x))
(+ (cos x) (* -1/2 (* eps (sin x))))
(fma.f64 (*.f64 (sin.f64 x) #s(literal -1/2 binary64)) eps (cos.f64 x))
(+ (cos x) (* -1/2 (* eps (sin x))))
(fma.f64 (*.f64 (sin.f64 x) #s(literal -1/2 binary64)) eps (cos.f64 x))
(- (sin (- eps (* -1 x))) (sin x))
(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
(- (sin (- eps (* -1 x))) (sin x))
(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
(- (sin (- eps (* -1 x))) (sin x))
(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
(- (sin (- eps (* -1 x))) (sin x))
(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(.f64 (fma.f64 (.f64 (sin.f64 x) #s(literal -1/2 binary64)) eps (cos.f64 x)) eps)
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(.f64 (fma.f64 (.f64 (sin.f64 x) #s(literal -1/2 binary64)) eps (cos.f64 x)) eps)
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(.f64 (fma.f64 (.f64 (sin.f64 x) #s(literal -1/2 binary64)) eps (cos.f64 x)) eps)
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(.f64 (fma.f64 (.f64 (sin.f64 x) #s(literal -1/2 binary64)) eps (cos.f64 x)) eps)
(+ (cos x) (* -1/2 (* eps (sin x))))
(fma.f64 (*.f64 (sin.f64 x) #s(literal -1/2 binary64)) eps (cos.f64 x))
(+ (cos x) (* -1/2 (* eps (sin x))))
(fma.f64 (*.f64 (sin.f64 x) #s(literal -1/2 binary64)) eps (cos.f64 x))
(+ (cos x) (* -1/2 (* eps (sin x))))
(fma.f64 (*.f64 (sin.f64 x) #s(literal -1/2 binary64)) eps (cos.f64 x))
(+ (cos x) (* -1/2 (* eps (sin x))))
(fma.f64 (*.f64 (sin.f64 x) #s(literal -1/2 binary64)) eps (cos.f64 x))
(* 1/12 (* eps (pow x 3)))
(.f64 (.f64 (pow.f64 x #s(literal 3 binary64)) eps) #s(literal 1/12 binary64))
(* -1 (* (pow x 3) (+ (* -1/12 eps) (* 1/2 (/ 1 x)))))
(*.f64 (fma.f64 #s(literal 1/12 binary64) eps (/.f64 #s(literal -1/2 binary64) x)) (pow.f64 x #s(literal 3 binary64)))
(* -1 (* (pow x 3) (+ (* -1 (/ (- (* -1/2 (/ eps x)) 1/2) x)) (* -1/12 eps))))
(*.f64 (fma.f64 #s(literal 1/12 binary64) eps (/.f64 (fma.f64 (/.f64 eps x) #s(literal -1/2 binary64) #s(literal -1/2 binary64)) x)) (pow.f64 x #s(literal 3 binary64)))
(* -1 (* (pow x 3) (+ (* -1 (/ (- (* -1 (/ (- (* 1/2 eps) (/ 1 x)) x)) 1/2) x)) (* -1/12 eps))))
(*.f64 (neg.f64 (pow.f64 x #s(literal 3 binary64))) (fma.f64 #s(literal -1/12 binary64) eps (/.f64 (+.f64 (/.f64 (fma.f64 #s(literal 1/2 binary64) eps (/.f64 #s(literal -1 binary64) x)) x) #s(literal 1/2 binary64)) x)))
(- (sin (- eps (* -1 x))) (sin x))
(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
(- (sin (- eps (* -1 x))) (sin x))
(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
(- (sin (- eps (* -1 x))) (sin x))
(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
(- (sin (- eps (* -1 x))) (sin x))
(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(.f64 (fma.f64 (.f64 (sin.f64 x) #s(literal -1/2 binary64)) eps (cos.f64 x)) eps)
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(.f64 (fma.f64 (.f64 (sin.f64 x) #s(literal -1/2 binary64)) eps (cos.f64 x)) eps)
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(.f64 (fma.f64 (.f64 (sin.f64 x) #s(literal -1/2 binary64)) eps (cos.f64 x)) eps)
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(.f64 (fma.f64 (.f64 (sin.f64 x) #s(literal -1/2 binary64)) eps (cos.f64 x)) eps)
(+ (cos x) (* -1/2 (* eps (sin x))))
(fma.f64 (*.f64 (sin.f64 x) #s(literal -1/2 binary64)) eps (cos.f64 x))
(+ (cos x) (* -1/2 (* eps (sin x))))
(fma.f64 (*.f64 (sin.f64 x) #s(literal -1/2 binary64)) eps (cos.f64 x))
(+ (cos x) (* -1/2 (* eps (sin x))))
(fma.f64 (*.f64 (sin.f64 x) #s(literal -1/2 binary64)) eps (cos.f64 x))
(+ (cos x) (* -1/2 (* eps (sin x))))
(fma.f64 (*.f64 (sin.f64 x) #s(literal -1/2 binary64)) eps (cos.f64 x))
(* -1/2 (sin x))
(*.f64 (sin.f64 x) #s(literal -1/2 binary64))
(* -1/2 (sin x))
(*.f64 (sin.f64 x) #s(literal -1/2 binary64))
(* -1/2 (sin x))
(*.f64 (sin.f64 x) #s(literal -1/2 binary64))
(* -1/2 (sin x))
(*.f64 (sin.f64 x) #s(literal -1/2 binary64))
(* eps (+ (* -1/2 (sin x)) (/ (cos x) eps)))
(*.f64 (fma.f64 (sin.f64 x) #s(literal -1/2 binary64) (/.f64 (cos.f64 x) eps)) eps)
(* eps (+ (* -1/2 (sin x)) (/ (cos x) eps)))
(*.f64 (fma.f64 (sin.f64 x) #s(literal -1/2 binary64) (/.f64 (cos.f64 x) eps)) eps)
(* eps (+ (* -1/2 (sin x)) (/ (cos x) eps)))
(*.f64 (fma.f64 (sin.f64 x) #s(literal -1/2 binary64) (/.f64 (cos.f64 x) eps)) eps)
(* eps (+ (* -1/2 (sin x)) (/ (cos x) eps)))
(*.f64 (fma.f64 (sin.f64 x) #s(literal -1/2 binary64) (/.f64 (cos.f64 x) eps)) eps)
(- (sin (- eps (* -1 x))) (sin x))
(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
(- (sin (- eps (* -1 x))) (sin x))
(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
(- (sin (- eps (* -1 x))) (sin x))
(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
(- (sin (- eps (* -1 x))) (sin x))
(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(.f64 (fma.f64 (.f64 (sin.f64 x) #s(literal -1/2 binary64)) eps (cos.f64 x)) eps)
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(.f64 (fma.f64 (.f64 (sin.f64 x) #s(literal -1/2 binary64)) eps (cos.f64 x)) eps)
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(.f64 (fma.f64 (.f64 (sin.f64 x) #s(literal -1/2 binary64)) eps (cos.f64 x)) eps)
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(.f64 (fma.f64 (.f64 (sin.f64 x) #s(literal -1/2 binary64)) eps (cos.f64 x)) eps)
(+ (cos x) (* -1/2 (* eps (sin x))))
(fma.f64 (*.f64 (sin.f64 x) #s(literal -1/2 binary64)) eps (cos.f64 x))
(+ (cos x) (* -1/2 (* eps (sin x))))
(fma.f64 (*.f64 (sin.f64 x) #s(literal -1/2 binary64)) eps (cos.f64 x))
(+ (cos x) (* -1/2 (* eps (sin x))))
(fma.f64 (*.f64 (sin.f64 x) #s(literal -1/2 binary64)) eps (cos.f64 x))
(+ (cos x) (* -1/2 (* eps (sin x))))
(fma.f64 (*.f64 (sin.f64 x) #s(literal -1/2 binary64)) eps (cos.f64 x))
(* -1/6 (* eps (cos x)))
(.f64 #s(literal -1/6 binary64) (.f64 (cos.f64 x) eps))
(* -1/6 (* eps (cos x)))
(.f64 #s(literal -1/6 binary64) (.f64 (cos.f64 x) eps))
(* -1/6 (* eps (cos x)))
(.f64 #s(literal -1/6 binary64) (.f64 (cos.f64 x) eps))
(* -1/6 (* eps (cos x)))
(.f64 #s(literal -1/6 binary64) (.f64 (cos.f64 x) eps))
(* -1/6 (cos x))
(*.f64 #s(literal -1/6 binary64) (cos.f64 x))
(* -1/6 (cos x))
(*.f64 #s(literal -1/6 binary64) (cos.f64 x))
(* -1/6 (cos x))
(*.f64 #s(literal -1/6 binary64) (cos.f64 x))
(* -1/6 (cos x))
(*.f64 #s(literal -1/6 binary64) (cos.f64 x))
(* 1/12 (* eps (pow x 2)))
(.f64 (.f64 (*.f64 x eps) x) #s(literal 1/12 binary64))
(* (pow x 2) (- (* 1/12 eps) (* 1/2 (/ 1 x))))
(.f64 (fma.f64 #s(literal 1/12 binary64) eps (/.f64 #s(literal -1/2 binary64) x)) (.f64 x x))
(* (pow x 2) (+ (* -1 (/ (+ 1/2 (* 1/2 (/ eps x))) x)) (* 1/12 eps)))
(.f64 (fma.f64 #s(literal 1/12 binary64) eps (/.f64 (fma.f64 (/.f64 eps x) #s(literal -1/2 binary64) #s(literal -1/2 binary64)) x)) (.f64 x x))
(* (pow x 2) (+ (* -1 (/ (+ 1/2 (* 1/2 (/ eps x))) x)) (* 1/12 eps)))
(.f64 (fma.f64 #s(literal 1/12 binary64) eps (/.f64 (fma.f64 (/.f64 eps x) #s(literal -1/2 binary64) #s(literal -1/2 binary64)) x)) (.f64 x x))
(/ (cos x) eps)
(/.f64 (cos.f64 x) eps)
(/ (cos x) eps)
(/.f64 (cos.f64 x) eps)
(/ (cos x) eps)
(/.f64 (cos.f64 x) eps)
(/ (cos x) eps)
(/.f64 (cos.f64 x) eps)

rewrite173.0ms (1.4%)

Memory

4.2MiB live, 200.5MiB allocated

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	50	415
0	86	413
1	297	413
2	2137	413
0	8552	402

Stop Event

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

Counts

24 → 271

Calls

Call 1

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

Outputs
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eval145.0ms (1.2%)

Memory: 7.9MiB live, 157.6MiB allocated
Compiler: Compiled 18 287 to 1 899 computations (89.6% saved)

prune44.0ms (0.4%)

Memory

1.5MiB live, 93.1MiB allocated

Pruning

29 alts after pruning (20 fresh and 9 done)

	Pruned	Kept	Total
New	805	2	807
Fresh	1	18	19
Picked	0	5	5
Done	0	4	4
Total	806	29	835

Accuracy

100.0%

Counts

835 → 29

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	65.3%	(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
	99.9%	(.f64 (.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 0 binary64) eps))) #s(literal 2 binary64)) (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64))))
✓	100.0%	#s(approx (- (sin (+ x eps)) (sin x)) (fma.f64 (.f64 (fma.f64 (fma.f64 #s(literal 1/24 binary64) (.f64 eps eps) #s(literal -1/2 binary64)) (sin.f64 x) (.f64 (.f64 (cos.f64 x) #s(literal -1/6 binary64)) eps)) eps) eps (*.f64 (cos.f64 x) eps)))
	99.7%	#s(approx (- (sin (+ x eps)) (sin x)) (fma.f64 (.f64 (.f64 #s(literal -1/2 binary64) (sin.f64 x)) eps) eps (*.f64 (cos.f64 x) eps)))
✓	100.0%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 (fma.f64 (sin.f64 x) (fma.f64 (.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) (.f64 (.f64 #s(literal -1/6 binary64) (cos.f64 x)) eps)) eps (cos.f64 x)) eps))
	99.6%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 (fma.f64 (sin.f64 x) (fma.f64 (.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) (.f64 #s(approx ( -1/6 (cos x)) (fma.f64 (fma.f64 #s(literal -1/144 binary64) (.f64 x x) #s(literal 1/12 binary64)) (.f64 x x) #s(literal -1/6 binary64))) eps)) eps (cos.f64 x)) eps))
	99.8%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 (fma.f64 (sin.f64 x) (fma.f64 (.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) (.f64 #s(approx ( -1/6 (cos x)) #s(literal -1/6 binary64)) eps)) eps (cos.f64 x)) eps))
▶	100.0%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 (fma.f64 #s(literal -1/6 binary64) (.f64 (cos.f64 x) eps) (*.f64 (sin.f64 x) #s(literal -1/2 binary64))) eps (cos.f64 x)) eps))
✓	99.7%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 (.f64 (sin.f64 x) #s(literal -1/2 binary64)) eps (cos.f64 x)) eps))
	99.5%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 #s(approx (+ ( (sin x) (+ (* (* eps eps) 1/24) -1/2)) (* (* -1/6 (cos x)) eps)) (fma.f64 (fma.f64 (fma.f64 #s(literal 1/12 binary64) eps (.f64 (.f64 (fma.f64 (.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) x) #s(literal -1/6 binary64))) x (fma.f64 (.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64))) x (*.f64 #s(literal -1/6 binary64) eps))) eps (cos.f64 x)) eps))
	99.4%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 #s(approx (+ ( (sin x) (+ (* (* eps eps) 1/24) -1/2)) (* (* -1/6 (cos x)) eps)) (fma.f64 (fma.f64 (.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) x (.f64 #s(literal -1/6 binary64) eps))) eps (cos.f64 x)) eps))
	99.0%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 #s(approx (+ ( (sin x) (+ (* (* eps eps) 1/24) -1/2)) (* (* -1/6 (cos x)) eps)) (*.f64 #s(literal -1/6 binary64) eps)) eps (cos.f64 x)) eps))
	99.4%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 #s(approx ( (sin x) -1/2) (.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 1/10080 binary64) (.f64 x x) #s(literal -1/240 binary64)) (.f64 x x) #s(literal 1/12 binary64)) (.f64 x x) #s(literal -1/2 binary64)) x)) eps (cos.f64 x)) eps))
▶	99.4%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 #s(approx ( (sin x) -1/2) (.f64 (fma.f64 (fma.f64 #s(literal -1/240 binary64) (.f64 x x) #s(literal 1/12 binary64)) (*.f64 x x) #s(literal -1/2 binary64)) x)) eps (cos.f64 x)) eps))
✓	99.4%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 #s(approx ( (sin x) -1/2) (.f64 (fma.f64 (.f64 x x) #s(literal 1/12 binary64) #s(literal -1/2 binary64)) x)) eps (cos.f64 x)) eps))
	99.3%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 #s(approx ( (sin x) -1/2) (*.f64 #s(literal -1/2 binary64) x)) eps (cos.f64 x)) eps))
✓	99.0%	#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (cos.f64 x) eps))
▶	98.3%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (+ (* (sin x) (+ (* (* eps eps) 1/24) -1/2)) (* (* -1/6 (cos x)) eps)) eps) (cos x)) (fma.f64 (fma.f64 (fma.f64 #s(literal 1/12 binary64) (.f64 eps eps) #s(literal -1/2 binary64)) x (.f64 (fma.f64 (.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) eps)) x (fma.f64 (.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64)))) eps))
	97.6%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (+ (* (sin x) (+ (* (* eps eps) 1/24) -1/2)) (* (* -1/6 (cos x)) eps)) eps) (cos x)) (fma.f64 eps (fma.f64 (fma.f64 (.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) x (.f64 #s(literal -1/6 binary64) eps)) #s(literal 1 binary64))) eps))
✓	98.3%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (* (sin x) -1/2) eps) (cos x)) (fma.f64 (fma.f64 (fma.f64 (.f64 #s(literal 1/12 binary64) eps) x #s(literal -1/2 binary64)) x (.f64 #s(literal -1/2 binary64) eps)) x #s(literal 1 binary64))) eps))
	98.3%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (* (sin x) -1/2) eps) (cos x)) (fma.f64 (*.f64 (+.f64 x eps) #s(literal -1/2 binary64)) x #s(literal 1 binary64))) eps))
	97.6%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (* (sin x) -1/2) eps) (cos x)) (fma.f64 (*.f64 x eps) #s(literal -1/2 binary64) #s(literal 1 binary64))) eps))
✓	99.4%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (* (sin x) -1/2) eps) (cos x)) (*.f64 (fma.f64 (sin.f64 x) #s(literal -1/2 binary64) (/.f64 (cos.f64 x) eps)) eps)) eps))
	98.1%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (* (sin x) -1/2) eps) (cos x)) #s(approx (+ (* (+ (* (+ (* (* 1/12 eps) x) -1/2) x) (* -1/2 eps)) x) 1) (.f64 (fma.f64 (neg.f64 (fma.f64 #s(literal -1/12 binary64) (.f64 x x) #s(literal 1/2 binary64))) x (/.f64 (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64)) eps)) eps))) eps))
✓	97.6%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (* (sin x) -1/2) eps) (cos x)) #s(literal 1 binary64)) eps))
	98.4%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (cos x) (fma.f64 (fma.f64 (fma.f64 #s(literal -1/720 binary64) (.f64 x x) #s(literal 1/24 binary64)) (.f64 x x) #s(literal -1/2 binary64)) (.f64 x x) #s(literal 1 binary64))) eps))
▶	98.3%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (cos x) (fma.f64 (fma.f64 (.f64 x x) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) (*.f64 x x) #s(literal 1 binary64))) eps))
	98.3%	#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (cos x) eps) (fma.f64 (.f64 eps (fma.f64 (.f64 x x) #s(literal 1/24 binary64) #s(literal -1/2 binary64))) (*.f64 x x) eps)))
▶	98.1%	#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (cos x) eps) (fma.f64 (.f64 #s(literal -1/2 binary64) x) (.f64 x eps) eps)))

Compiler

Compiled 862 to 615 computations (28.7% saved)

simplify315.0ms (2.6%)

Memory

-29.3MiB live, 252.4MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 20 expressions of interest:

New	Metric	Score
cost-diff	0	#s(approx (* (sin x) -1/2) (.f64 (fma.f64 (fma.f64 #s(literal -1/240 binary64) (.f64 x x) #s(literal 1/12 binary64)) (*.f64 x x) #s(literal -1/2 binary64)) x))
cost-diff	0	(fma.f64 #s(approx (* (sin x) -1/2) (.f64 (fma.f64 (fma.f64 #s(literal -1/240 binary64) (.f64 x x) #s(literal 1/12 binary64)) (*.f64 x x) #s(literal -1/2 binary64)) x)) eps (cos.f64 x))
cost-diff	0	(.f64 (fma.f64 #s(approx ( (sin x) -1/2) (.f64 (fma.f64 (fma.f64 #s(literal -1/240 binary64) (.f64 x x) #s(literal 1/12 binary64)) (*.f64 x x) #s(literal -1/2 binary64)) x)) eps (cos.f64 x)) eps)
cost-diff	0	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 #s(approx ( (sin x) -1/2) (.f64 (fma.f64 (fma.f64 #s(literal -1/240 binary64) (.f64 x x) #s(literal 1/12 binary64)) (*.f64 x x) #s(literal -1/2 binary64)) x)) eps (cos.f64 x)) eps))
cost-diff	0	(.f64 #s(approx (+ ( (+ (* (sin x) (+ (* (* eps eps) 1/24) -1/2)) (* (* -1/6 (cos x)) eps)) eps) (cos x)) (fma.f64 (fma.f64 (fma.f64 #s(literal 1/12 binary64) (.f64 eps eps) #s(literal -1/2 binary64)) x (.f64 (fma.f64 (.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) eps)) x (fma.f64 (.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64)))) eps)
cost-diff	0	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (+ (* (sin x) (+ (* (* eps eps) 1/24) -1/2)) (* (* -1/6 (cos x)) eps)) eps) (cos x)) (fma.f64 (fma.f64 (fma.f64 #s(literal 1/12 binary64) (.f64 eps eps) #s(literal -1/2 binary64)) x (.f64 (fma.f64 (.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) eps)) x (fma.f64 (.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64)))) eps))
cost-diff	192	(fma.f64 (fma.f64 (fma.f64 #s(literal 1/12 binary64) (.f64 eps eps) #s(literal -1/2 binary64)) x (.f64 (fma.f64 (.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) eps)) x (fma.f64 (.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64)))
cost-diff	320	(fma.f64 (fma.f64 #s(literal 1/12 binary64) (.f64 eps eps) #s(literal -1/2 binary64)) x (.f64 (fma.f64 (*.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) eps))
cost-diff	0	(fma.f64 (fma.f64 (.f64 x x) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) (.f64 x x) #s(literal 1 binary64))
cost-diff	0	#s(approx (cos x) (fma.f64 (fma.f64 (.f64 x x) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) (.f64 x x) #s(literal 1 binary64)))
cost-diff	0	(.f64 #s(approx (cos x) (fma.f64 (fma.f64 (.f64 x x) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) (*.f64 x x) #s(literal 1 binary64))) eps)
cost-diff	0	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (cos x) (fma.f64 (fma.f64 (.f64 x x) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) (*.f64 x x) #s(literal 1 binary64))) eps))
cost-diff	0	(*.f64 #s(literal -1/2 binary64) x)
cost-diff	0	(fma.f64 (.f64 #s(literal -1/2 binary64) x) (.f64 x eps) eps)
cost-diff	0	#s(approx (* (cos x) eps) (fma.f64 (.f64 #s(literal -1/2 binary64) x) (.f64 x eps) eps))
cost-diff	0	#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (cos x) eps) (fma.f64 (.f64 #s(literal -1/2 binary64) x) (.f64 x eps) eps)))
cost-diff	0	(fma.f64 #s(literal -1/6 binary64) (.f64 (cos.f64 x) eps) (.f64 (sin.f64 x) #s(literal -1/2 binary64)))
cost-diff	0	(fma.f64 (fma.f64 #s(literal -1/6 binary64) (.f64 (cos.f64 x) eps) (.f64 (sin.f64 x) #s(literal -1/2 binary64))) eps (cos.f64 x))
cost-diff	0	(.f64 (fma.f64 (fma.f64 #s(literal -1/6 binary64) (.f64 (cos.f64 x) eps) (*.f64 (sin.f64 x) #s(literal -1/2 binary64))) eps (cos.f64 x)) eps)
cost-diff	0	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 (fma.f64 #s(literal -1/6 binary64) (.f64 (cos.f64 x) eps) (*.f64 (sin.f64 x) #s(literal -1/2 binary64))) eps (cos.f64 x)) eps))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	60	572
0	104	572
1	177	572
2	322	572
3	732	572
4	1453	572
5	2323	572
6	2916	572
7	3164	572
8	3320	572
9	3440	572
10	3861	572
11	5102	572
12	5665	572
13	6612	572
14	7431	572
15	7689	572
16	7941	572
0	8532	552

Stop Event

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

Calls

Call 1

Inputs
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 (fma.f64 #s(literal -1/6 binary64) (.f64 (cos.f64 x) eps) (*.f64 (sin.f64 x) #s(literal -1/2 binary64))) eps (cos.f64 x)) eps))
(.f64 (fma.f64 (fma.f64 #s(literal -1/6 binary64) (.f64 (cos.f64 x) eps) (*.f64 (sin.f64 x) #s(literal -1/2 binary64))) eps (cos.f64 x)) eps)
(fma.f64 (fma.f64 #s(literal -1/6 binary64) (.f64 (cos.f64 x) eps) (.f64 (sin.f64 x) #s(literal -1/2 binary64))) eps (cos.f64 x))
(fma.f64 #s(literal -1/6 binary64) (.f64 (cos.f64 x) eps) (.f64 (sin.f64 x) #s(literal -1/2 binary64)))
#s(literal -1/6 binary64)
(*.f64 (cos.f64 x) eps)
(cos.f64 x)
x
eps
(*.f64 (sin.f64 x) #s(literal -1/2 binary64))
(sin.f64 x)
#s(literal -1/2 binary64)
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (cos x) eps) (fma.f64 (.f64 #s(literal -1/2 binary64) x) (.f64 x eps) eps)))
#s(approx (* (cos x) eps) (fma.f64 (.f64 #s(literal -1/2 binary64) x) (.f64 x eps) eps))
(fma.f64 (.f64 #s(literal -1/2 binary64) x) (.f64 x eps) eps)
(*.f64 #s(literal -1/2 binary64) x)
#s(literal -1/2 binary64)
x
(*.f64 x eps)
eps
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (cos x) (fma.f64 (fma.f64 (.f64 x x) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) (*.f64 x x) #s(literal 1 binary64))) eps))
(.f64 #s(approx (cos x) (fma.f64 (fma.f64 (.f64 x x) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) (*.f64 x x) #s(literal 1 binary64))) eps)
#s(approx (cos x) (fma.f64 (fma.f64 (.f64 x x) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) (.f64 x x) #s(literal 1 binary64)))
(fma.f64 (fma.f64 (.f64 x x) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) (.f64 x x) #s(literal 1 binary64))
(fma.f64 (*.f64 x x) #s(literal 1/24 binary64) #s(literal -1/2 binary64))
(*.f64 x x)
x
#s(literal 1/24 binary64)
#s(literal -1/2 binary64)
#s(literal 1 binary64)
eps
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (+ (* (sin x) (+ (* (* eps eps) 1/24) -1/2)) (* (* -1/6 (cos x)) eps)) eps) (cos x)) (fma.f64 (fma.f64 (fma.f64 #s(literal 1/12 binary64) (.f64 eps eps) #s(literal -1/2 binary64)) x (.f64 (fma.f64 (.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) eps)) x (fma.f64 (.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64)))) eps))
(.f64 #s(approx (+ ( (+ (* (sin x) (+ (* (* eps eps) 1/24) -1/2)) (* (* -1/6 (cos x)) eps)) eps) (cos x)) (fma.f64 (fma.f64 (fma.f64 #s(literal 1/12 binary64) (.f64 eps eps) #s(literal -1/2 binary64)) x (.f64 (fma.f64 (.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) eps)) x (fma.f64 (.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64)))) eps)
#s(approx (+ (* (+ (* (sin x) (+ (* (* eps eps) 1/24) -1/2)) (* (* -1/6 (cos x)) eps)) eps) (cos x)) (fma.f64 (fma.f64 (fma.f64 #s(literal 1/12 binary64) (.f64 eps eps) #s(literal -1/2 binary64)) x (.f64 (fma.f64 (.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) eps)) x (fma.f64 (.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64))))
(fma.f64 (fma.f64 (fma.f64 #s(literal 1/12 binary64) (.f64 eps eps) #s(literal -1/2 binary64)) x (.f64 (fma.f64 (.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) eps)) x (fma.f64 (.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64)))
(fma.f64 (fma.f64 #s(literal 1/12 binary64) (.f64 eps eps) #s(literal -1/2 binary64)) x (.f64 (fma.f64 (*.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) eps))
(fma.f64 #s(literal 1/12 binary64) (*.f64 eps eps) #s(literal -1/2 binary64))
#s(literal 1/12 binary64)
(*.f64 eps eps)
eps
#s(literal -1/2 binary64)
x
(.f64 (fma.f64 (.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) eps)
(fma.f64 (*.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64))
#s(literal 1/24 binary64)
(fma.f64 (*.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64))
#s(literal -1/6 binary64)
#s(literal 1 binary64)
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 #s(approx ( (sin x) -1/2) (.f64 (fma.f64 (fma.f64 #s(literal -1/240 binary64) (.f64 x x) #s(literal 1/12 binary64)) (*.f64 x x) #s(literal -1/2 binary64)) x)) eps (cos.f64 x)) eps))
(.f64 (fma.f64 #s(approx ( (sin x) -1/2) (.f64 (fma.f64 (fma.f64 #s(literal -1/240 binary64) (.f64 x x) #s(literal 1/12 binary64)) (*.f64 x x) #s(literal -1/2 binary64)) x)) eps (cos.f64 x)) eps)
(fma.f64 #s(approx (* (sin x) -1/2) (.f64 (fma.f64 (fma.f64 #s(literal -1/240 binary64) (.f64 x x) #s(literal 1/12 binary64)) (*.f64 x x) #s(literal -1/2 binary64)) x)) eps (cos.f64 x))
#s(approx (* (sin x) -1/2) (.f64 (fma.f64 (fma.f64 #s(literal -1/240 binary64) (.f64 x x) #s(literal 1/12 binary64)) (*.f64 x x) #s(literal -1/2 binary64)) x))
(.f64 (fma.f64 (fma.f64 #s(literal -1/240 binary64) (.f64 x x) #s(literal 1/12 binary64)) (*.f64 x x) #s(literal -1/2 binary64)) x)
(fma.f64 (fma.f64 #s(literal -1/240 binary64) (.f64 x x) #s(literal 1/12 binary64)) (.f64 x x) #s(literal -1/2 binary64))
(fma.f64 #s(literal -1/240 binary64) (*.f64 x x) #s(literal 1/12 binary64))
#s(literal -1/240 binary64)
(*.f64 x x)
x
#s(literal 1/12 binary64)
#s(literal -1/2 binary64)
eps
(cos.f64 x)

Outputs
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 (fma.f64 #s(literal -1/6 binary64) (.f64 (cos.f64 x) eps) (*.f64 (sin.f64 x) #s(literal -1/2 binary64))) eps (cos.f64 x)) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 (fma.f64 (.f64 (cos.f64 x) eps) #s(literal -1/6 binary64) (*.f64 #s(literal -1/2 binary64) (sin.f64 x))) eps (cos.f64 x)) eps))
(.f64 (fma.f64 (fma.f64 #s(literal -1/6 binary64) (.f64 (cos.f64 x) eps) (*.f64 (sin.f64 x) #s(literal -1/2 binary64))) eps (cos.f64 x)) eps)
(.f64 (fma.f64 (fma.f64 (.f64 (cos.f64 x) eps) #s(literal -1/6 binary64) (*.f64 #s(literal -1/2 binary64) (sin.f64 x))) eps (cos.f64 x)) eps)
(fma.f64 (fma.f64 #s(literal -1/6 binary64) (.f64 (cos.f64 x) eps) (.f64 (sin.f64 x) #s(literal -1/2 binary64))) eps (cos.f64 x))
(fma.f64 (fma.f64 (.f64 (cos.f64 x) eps) #s(literal -1/6 binary64) (.f64 #s(literal -1/2 binary64) (sin.f64 x))) eps (cos.f64 x))
(fma.f64 #s(literal -1/6 binary64) (.f64 (cos.f64 x) eps) (.f64 (sin.f64 x) #s(literal -1/2 binary64)))
(fma.f64 (.f64 (cos.f64 x) eps) #s(literal -1/6 binary64) (.f64 #s(literal -1/2 binary64) (sin.f64 x)))
#s(literal -1/6 binary64)
(*.f64 (cos.f64 x) eps)
(cos.f64 x)
x
eps
(*.f64 (sin.f64 x) #s(literal -1/2 binary64))
(*.f64 #s(literal -1/2 binary64) (sin.f64 x))
(sin.f64 x)
#s(literal -1/2 binary64)
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (cos x) eps) (fma.f64 (.f64 #s(literal -1/2 binary64) x) (.f64 x eps) eps)))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (cos x) eps) (fma.f64 (.f64 eps x) (.f64 #s(literal -1/2 binary64) x) eps)))
#s(approx (* (cos x) eps) (fma.f64 (.f64 #s(literal -1/2 binary64) x) (.f64 x eps) eps))
#s(approx (* (cos x) eps) (fma.f64 (.f64 eps x) (.f64 #s(literal -1/2 binary64) x) eps))
(fma.f64 (.f64 #s(literal -1/2 binary64) x) (.f64 x eps) eps)
(fma.f64 (.f64 eps x) (.f64 #s(literal -1/2 binary64) x) eps)
(*.f64 #s(literal -1/2 binary64) x)
#s(literal -1/2 binary64)
x
(*.f64 x eps)
(*.f64 eps x)
eps
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (cos x) (fma.f64 (fma.f64 (.f64 x x) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) (*.f64 x x) #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (cos x) (fma.f64 (fma.f64 #s(literal 1/24 binary64) (.f64 x x) #s(literal -1/2 binary64)) (*.f64 x x) #s(literal 1 binary64))) eps))
(.f64 #s(approx (cos x) (fma.f64 (fma.f64 (.f64 x x) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) (*.f64 x x) #s(literal 1 binary64))) eps)
(.f64 #s(approx (cos x) (fma.f64 (fma.f64 #s(literal 1/24 binary64) (.f64 x x) #s(literal -1/2 binary64)) (*.f64 x x) #s(literal 1 binary64))) eps)
#s(approx (cos x) (fma.f64 (fma.f64 (.f64 x x) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) (.f64 x x) #s(literal 1 binary64)))
#s(approx (cos x) (fma.f64 (fma.f64 #s(literal 1/24 binary64) (.f64 x x) #s(literal -1/2 binary64)) (.f64 x x) #s(literal 1 binary64)))
(fma.f64 (fma.f64 (.f64 x x) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) (.f64 x x) #s(literal 1 binary64))
(fma.f64 (fma.f64 #s(literal 1/24 binary64) (.f64 x x) #s(literal -1/2 binary64)) (.f64 x x) #s(literal 1 binary64))
(fma.f64 (*.f64 x x) #s(literal 1/24 binary64) #s(literal -1/2 binary64))
(fma.f64 #s(literal 1/24 binary64) (*.f64 x x) #s(literal -1/2 binary64))
(*.f64 x x)
x
#s(literal 1/24 binary64)
#s(literal -1/2 binary64)
#s(literal 1 binary64)
eps
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (+ (* (sin x) (+ (* (* eps eps) 1/24) -1/2)) (* (* -1/6 (cos x)) eps)) eps) (cos x)) (fma.f64 (fma.f64 (fma.f64 #s(literal 1/12 binary64) (.f64 eps eps) #s(literal -1/2 binary64)) x (.f64 (fma.f64 (.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) eps)) x (fma.f64 (.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64)))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (+ (* (sin x) (+ (* (* eps eps) 1/24) -1/2)) (* (* -1/6 (cos x)) eps)) eps) (cos x)) (fma.f64 (.f64 (fma.f64 (fma.f64 #s(literal 1/12 binary64) x (.f64 #s(literal 1/24 binary64) eps)) x #s(literal -1/6 binary64)) eps) eps (fma.f64 (*.f64 #s(literal -1/2 binary64) (+.f64 eps x)) x #s(literal 1 binary64)))) eps))
(.f64 #s(approx (+ ( (+ (* (sin x) (+ (* (* eps eps) 1/24) -1/2)) (* (* -1/6 (cos x)) eps)) eps) (cos x)) (fma.f64 (fma.f64 (fma.f64 #s(literal 1/12 binary64) (.f64 eps eps) #s(literal -1/2 binary64)) x (.f64 (fma.f64 (.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) eps)) x (fma.f64 (.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64)))) eps)
(.f64 #s(approx (+ ( (+ (* (sin x) (+ (* (* eps eps) 1/24) -1/2)) (* (* -1/6 (cos x)) eps)) eps) (cos x)) (fma.f64 (.f64 (fma.f64 (fma.f64 #s(literal 1/12 binary64) x (.f64 #s(literal 1/24 binary64) eps)) x #s(literal -1/6 binary64)) eps) eps (fma.f64 (*.f64 #s(literal -1/2 binary64) (+.f64 eps x)) x #s(literal 1 binary64)))) eps)
#s(approx (+ (* (+ (* (sin x) (+ (* (* eps eps) 1/24) -1/2)) (* (* -1/6 (cos x)) eps)) eps) (cos x)) (fma.f64 (fma.f64 (fma.f64 #s(literal 1/12 binary64) (.f64 eps eps) #s(literal -1/2 binary64)) x (.f64 (fma.f64 (.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) eps)) x (fma.f64 (.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64))))
#s(approx (+ (* (+ (* (sin x) (+ (* (* eps eps) 1/24) -1/2)) (* (* -1/6 (cos x)) eps)) eps) (cos x)) (fma.f64 (.f64 (fma.f64 (fma.f64 #s(literal 1/12 binary64) x (.f64 #s(literal 1/24 binary64) eps)) x #s(literal -1/6 binary64)) eps) eps (fma.f64 (*.f64 #s(literal -1/2 binary64) (+.f64 eps x)) x #s(literal 1 binary64))))
(fma.f64 (fma.f64 (fma.f64 #s(literal 1/12 binary64) (.f64 eps eps) #s(literal -1/2 binary64)) x (.f64 (fma.f64 (.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) eps)) x (fma.f64 (.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64)))
(fma.f64 (.f64 (fma.f64 (fma.f64 #s(literal 1/12 binary64) x (.f64 #s(literal 1/24 binary64) eps)) x #s(literal -1/6 binary64)) eps) eps (fma.f64 (*.f64 #s(literal -1/2 binary64) (+.f64 eps x)) x #s(literal 1 binary64)))
(fma.f64 (fma.f64 #s(literal 1/12 binary64) (.f64 eps eps) #s(literal -1/2 binary64)) x (.f64 (fma.f64 (*.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) eps))
(fma.f64 (fma.f64 (fma.f64 #s(literal 1/12 binary64) x (.f64 #s(literal 1/24 binary64) eps)) eps #s(literal -1/2 binary64)) eps (.f64 #s(literal -1/2 binary64) x))
(fma.f64 #s(literal 1/12 binary64) (*.f64 eps eps) #s(literal -1/2 binary64))
(fma.f64 (*.f64 eps eps) #s(literal 1/12 binary64) #s(literal -1/2 binary64))
#s(literal 1/12 binary64)
(*.f64 eps eps)
eps
#s(literal -1/2 binary64)
x
(.f64 (fma.f64 (.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) eps)
(fma.f64 (*.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64))
#s(literal 1/24 binary64)
(fma.f64 (*.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64))
#s(literal -1/6 binary64)
#s(literal 1 binary64)
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 #s(approx ( (sin x) -1/2) (.f64 (fma.f64 (fma.f64 #s(literal -1/240 binary64) (.f64 x x) #s(literal 1/12 binary64)) (*.f64 x x) #s(literal -1/2 binary64)) x)) eps (cos.f64 x)) eps))
(.f64 (fma.f64 #s(approx ( (sin x) -1/2) (.f64 (fma.f64 (fma.f64 #s(literal -1/240 binary64) (.f64 x x) #s(literal 1/12 binary64)) (*.f64 x x) #s(literal -1/2 binary64)) x)) eps (cos.f64 x)) eps)
(fma.f64 #s(approx (* (sin x) -1/2) (.f64 (fma.f64 (fma.f64 #s(literal -1/240 binary64) (.f64 x x) #s(literal 1/12 binary64)) (*.f64 x x) #s(literal -1/2 binary64)) x)) eps (cos.f64 x))
#s(approx (* (sin x) -1/2) (.f64 (fma.f64 (fma.f64 #s(literal -1/240 binary64) (.f64 x x) #s(literal 1/12 binary64)) (*.f64 x x) #s(literal -1/2 binary64)) x))
(.f64 (fma.f64 (fma.f64 #s(literal -1/240 binary64) (.f64 x x) #s(literal 1/12 binary64)) (*.f64 x x) #s(literal -1/2 binary64)) x)
(fma.f64 (fma.f64 #s(literal -1/240 binary64) (.f64 x x) #s(literal 1/12 binary64)) (.f64 x x) #s(literal -1/2 binary64))
(fma.f64 #s(literal -1/240 binary64) (*.f64 x x) #s(literal 1/12 binary64))
#s(literal -1/240 binary64)
(*.f64 x x)
x
#s(literal 1/12 binary64)
#s(literal -1/2 binary64)
eps
(cos.f64 x)

localize197.0ms (1.6%)

Memory

27.0MiB live, 326.0MiB allocated

Localize:

Found 20 expressions of interest:

New	Metric	Score
accuracy	0.015625	(.f64 (fma.f64 #s(approx ( (sin x) -1/2) (.f64 (fma.f64 (fma.f64 #s(literal -1/240 binary64) (.f64 x x) #s(literal 1/12 binary64)) (*.f64 x x) #s(literal -1/2 binary64)) x)) eps (cos.f64 x)) eps)
accuracy	0.0234375	(.f64 (fma.f64 (fma.f64 #s(literal -1/240 binary64) (.f64 x x) #s(literal 1/12 binary64)) (*.f64 x x) #s(literal -1/2 binary64)) x)
accuracy	0.21273808917513187	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 #s(approx ( (sin x) -1/2) (.f64 (fma.f64 (fma.f64 #s(literal -1/240 binary64) (.f64 x x) #s(literal 1/12 binary64)) (*.f64 x x) #s(literal -1/2 binary64)) x)) eps (cos.f64 x)) eps))
accuracy	0.771349580683601	#s(approx (* (sin x) -1/2) (.f64 (fma.f64 (fma.f64 #s(literal -1/240 binary64) (.f64 x x) #s(literal 1/12 binary64)) (*.f64 x x) #s(literal -1/2 binary64)) x))
accuracy	0.01171875	(fma.f64 (fma.f64 (fma.f64 #s(literal 1/12 binary64) (.f64 eps eps) #s(literal -1/2 binary64)) x (.f64 (fma.f64 (.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) eps)) x (fma.f64 (.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64)))
accuracy	0.01171875	(.f64 #s(approx (+ ( (+ (* (sin x) (+ (* (* eps eps) 1/24) -1/2)) (* (* -1/6 (cos x)) eps)) eps) (cos x)) (fma.f64 (fma.f64 (fma.f64 #s(literal 1/12 binary64) (.f64 eps eps) #s(literal -1/2 binary64)) x (.f64 (fma.f64 (.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) eps)) x (fma.f64 (.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64)))) eps)
accuracy	0.01953125	(fma.f64 (fma.f64 #s(literal 1/12 binary64) (.f64 eps eps) #s(literal -1/2 binary64)) x (.f64 (fma.f64 (*.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) eps))
accuracy	1.0834094206066003	#s(approx (+ (* (+ (* (sin x) (+ (* (* eps eps) 1/24) -1/2)) (* (* -1/6 (cos x)) eps)) eps) (cos x)) (fma.f64 (fma.f64 (fma.f64 #s(literal 1/12 binary64) (.f64 eps eps) #s(literal -1/2 binary64)) x (.f64 (fma.f64 (.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) eps)) x (fma.f64 (.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64))))
accuracy	0.010097509768442016	(fma.f64 (fma.f64 (.f64 x x) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) (.f64 x x) #s(literal 1 binary64))
accuracy	0.01171875	(.f64 #s(approx (cos x) (fma.f64 (fma.f64 (.f64 x x) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) (*.f64 x x) #s(literal 1 binary64))) eps)
accuracy	0.6301620228595607	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (cos x) (fma.f64 (fma.f64 (.f64 x x) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) (*.f64 x x) #s(literal 1 binary64))) eps))
accuracy	0.8245631236674169	#s(approx (cos x) (fma.f64 (fma.f64 (.f64 x x) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) (.f64 x x) #s(literal 1 binary64)))
accuracy	0	(*.f64 #s(literal -1/2 binary64) x)
accuracy	0.00390625	(fma.f64 (.f64 #s(literal -1/2 binary64) x) (.f64 x eps) eps)
accuracy	0.6301620228595607	#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (cos x) eps) (fma.f64 (.f64 #s(literal -1/2 binary64) x) (.f64 x eps) eps)))
accuracy	1.0742263342599288	#s(approx (* (cos x) eps) (fma.f64 (.f64 #s(literal -1/2 binary64) x) (.f64 x eps) eps))
accuracy	0.01171875	(*.f64 (cos.f64 x) eps)
accuracy	0.015625	(.f64 (fma.f64 (fma.f64 #s(literal -1/6 binary64) (.f64 (cos.f64 x) eps) (*.f64 (sin.f64 x) #s(literal -1/2 binary64))) eps (cos.f64 x)) eps)
accuracy	0.02483418751803939	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 (fma.f64 #s(literal -1/6 binary64) (.f64 (cos.f64 x) eps) (*.f64 (sin.f64 x) #s(literal -1/2 binary64))) eps (cos.f64 x)) eps))
accuracy	0.03515625	(fma.f64 #s(literal -1/6 binary64) (.f64 (cos.f64 x) eps) (.f64 (sin.f64 x) #s(literal -1/2 binary64)))

Samples

76.0ms	179×	0	valid
70.0ms	75×	1	valid
3.0ms	2×	2	valid

Compiler

Compiled 357 to 58 computations (83.8% saved)

Precisions

Click to see histograms. Total time spent on operations: 119.0ms

ival-mult: 47.0ms (39.5% of total)

ival-add: 33.0ms (27.7% of total)

const: 13.0ms (10.9% of total)

adjust: 11.0ms (9.2% of total)

ival-sin: 8.0ms (6.7% of total)

ival-cos: 5.0ms (4.2% of total)

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

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

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

exact: 0.0ms (0% of total)

series78.0ms (0.6%)

Memory

-4.9MiB live, 157.1MiB allocated

Counts

23 → 492

Calls

Call 1

Inputs
#s(alt #s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 (fma.f64 #s(literal -1/6 binary64) (.f64 (cos.f64 x) eps) (.f64 (sin.f64 x) #s(literal -1/2 binary64))) eps (cos.f64 x)) eps)) (patch #s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 (fma.f64 #s(literal -1/6 binary64) (.f64 (cos.f64 x) eps) (.f64 (sin.f64 x) #s(literal -1/2 binary64))) eps (cos.f64 x)) eps)) #<representation binary64>) () ())
#s(alt (.f64 (fma.f64 (fma.f64 #s(literal -1/6 binary64) (.f64 (cos.f64 x) eps) (.f64 (sin.f64 x) #s(literal -1/2 binary64))) eps (cos.f64 x)) eps) (patch (.f64 (fma.f64 (fma.f64 #s(literal -1/6 binary64) (.f64 (cos.f64 x) eps) (.f64 (sin.f64 x) #s(literal -1/2 binary64))) eps (cos.f64 x)) eps) #<representation binary64>) () ())
#s(alt (fma.f64 (fma.f64 #s(literal -1/6 binary64) (.f64 (cos.f64 x) eps) (.f64 (sin.f64 x) #s(literal -1/2 binary64))) eps (cos.f64 x)) (patch (fma.f64 (fma.f64 #s(literal -1/6 binary64) (.f64 (cos.f64 x) eps) (.f64 (sin.f64 x) #s(literal -1/2 binary64))) eps (cos.f64 x)) #<representation binary64>) () ())
#s(alt (fma.f64 #s(literal -1/6 binary64) (.f64 (cos.f64 x) eps) (.f64 (sin.f64 x) #s(literal -1/2 binary64))) (patch (fma.f64 #s(literal -1/6 binary64) (.f64 (cos.f64 x) eps) (.f64 (sin.f64 x) #s(literal -1/2 binary64))) #<representation binary64>) () ())
#s(alt #s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (cos x) eps) (fma.f64 (.f64 #s(literal -1/2 binary64) x) (.f64 x eps) eps))) (patch #s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (cos x) eps) (fma.f64 (.f64 #s(literal -1/2 binary64) x) (.f64 x eps) eps))) #<representation binary64>) () ())
#s(alt #s(approx (* (cos x) eps) (fma.f64 (.f64 #s(literal -1/2 binary64) x) (.f64 x eps) eps)) (patch #s(approx (* (cos x) eps) (fma.f64 (.f64 #s(literal -1/2 binary64) x) (.f64 x eps) eps)) #<representation binary64>) () ())
#s(alt (fma.f64 (.f64 #s(literal -1/2 binary64) x) (.f64 x eps) eps) (patch (fma.f64 (.f64 #s(literal -1/2 binary64) x) (.f64 x eps) eps) #<representation binary64>) () ())
#s(alt (.f64 #s(literal -1/2 binary64) x) (patch (.f64 #s(literal -1/2 binary64) x) #<representation binary64>) () ())
#s(alt #s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (cos x) (fma.f64 (fma.f64 (.f64 x x) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) (.f64 x x) #s(literal 1 binary64))) eps)) (patch #s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (cos x) (fma.f64 (fma.f64 (.f64 x x) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) (.f64 x x) #s(literal 1 binary64))) eps)) #<representation binary64>) () ())
#s(alt (.f64 #s(approx (cos x) (fma.f64 (fma.f64 (.f64 x x) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) (.f64 x x) #s(literal 1 binary64))) eps) (patch (.f64 #s(approx (cos x) (fma.f64 (fma.f64 (.f64 x x) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) (.f64 x x) #s(literal 1 binary64))) eps) #<representation binary64>) () ())
#s(alt #s(approx (cos x) (fma.f64 (fma.f64 (.f64 x x) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) (.f64 x x) #s(literal 1 binary64))) (patch #s(approx (cos x) (fma.f64 (fma.f64 (.f64 x x) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) (.f64 x x) #s(literal 1 binary64))) #<representation binary64>) () ())
#s(alt (fma.f64 (fma.f64 (.f64 x x) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) (.f64 x x) #s(literal 1 binary64)) (patch (fma.f64 (fma.f64 (.f64 x x) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) (.f64 x x) #s(literal 1 binary64)) #<representation binary64>) () ())
#s(alt (fma.f64 (fma.f64 #s(literal 1/12 binary64) (.f64 eps eps) #s(literal -1/2 binary64)) x (.f64 (fma.f64 (.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) eps)) (patch (fma.f64 (fma.f64 #s(literal 1/12 binary64) (.f64 eps eps) #s(literal -1/2 binary64)) x (.f64 (fma.f64 (.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) eps)) #<representation binary64>) () ())
#s(alt (fma.f64 (fma.f64 (fma.f64 #s(literal 1/12 binary64) (.f64 eps eps) #s(literal -1/2 binary64)) x (.f64 (fma.f64 (.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) eps)) x (fma.f64 (.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64))) (patch (fma.f64 (fma.f64 (fma.f64 #s(literal 1/12 binary64) (.f64 eps eps) #s(literal -1/2 binary64)) x (.f64 (fma.f64 (.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) eps)) x (fma.f64 (.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64))) #<representation binary64>) () ())
#s(alt #s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (+ (* (sin x) (+ (* (* eps eps) 1/24) -1/2)) (* (* -1/6 (cos x)) eps)) eps) (cos x)) (fma.f64 (fma.f64 (fma.f64 #s(literal 1/12 binary64) (.f64 eps eps) #s(literal -1/2 binary64)) x (.f64 (fma.f64 (.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) eps)) x (fma.f64 (.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64)))) eps)) (patch #s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (+ (* (sin x) (+ (* (* eps eps) 1/24) -1/2)) (* (* -1/6 (cos x)) eps)) eps) (cos x)) (fma.f64 (fma.f64 (fma.f64 #s(literal 1/12 binary64) (.f64 eps eps) #s(literal -1/2 binary64)) x (.f64 (fma.f64 (.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) eps)) x (fma.f64 (.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64)))) eps)) #<representation binary64>) () ())
#s(alt (.f64 #s(approx (+ ( (+ (* (sin x) (+ (* (* eps eps) 1/24) -1/2)) (* (* -1/6 (cos x)) eps)) eps) (cos x)) (fma.f64 (fma.f64 (fma.f64 #s(literal 1/12 binary64) (.f64 eps eps) #s(literal -1/2 binary64)) x (.f64 (fma.f64 (.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) eps)) x (fma.f64 (.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64)))) eps) (patch (.f64 #s(approx (+ ( (+ (* (sin x) (+ (* (* eps eps) 1/24) -1/2)) (* (* -1/6 (cos x)) eps)) eps) (cos x)) (fma.f64 (fma.f64 (fma.f64 #s(literal 1/12 binary64) (.f64 eps eps) #s(literal -1/2 binary64)) x (.f64 (fma.f64 (.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) eps)) x (fma.f64 (.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64)))) eps) #<representation binary64>) () ())
#s(alt #s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 #s(approx ( (sin x) -1/2) (.f64 (fma.f64 (fma.f64 #s(literal -1/240 binary64) (.f64 x x) #s(literal 1/12 binary64)) (.f64 x x) #s(literal -1/2 binary64)) x)) eps (cos.f64 x)) eps)) (patch #s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 #s(approx (* (sin x) -1/2) (.f64 (fma.f64 (fma.f64 #s(literal -1/240 binary64) (.f64 x x) #s(literal 1/12 binary64)) (*.f64 x x) #s(literal -1/2 binary64)) x)) eps (cos.f64 x)) eps)) #<representation binary64>) () ())
#s(alt (.f64 (fma.f64 #s(approx ( (sin x) -1/2) (.f64 (fma.f64 (fma.f64 #s(literal -1/240 binary64) (.f64 x x) #s(literal 1/12 binary64)) (.f64 x x) #s(literal -1/2 binary64)) x)) eps (cos.f64 x)) eps) (patch (.f64 (fma.f64 #s(approx (* (sin x) -1/2) (.f64 (fma.f64 (fma.f64 #s(literal -1/240 binary64) (.f64 x x) #s(literal 1/12 binary64)) (*.f64 x x) #s(literal -1/2 binary64)) x)) eps (cos.f64 x)) eps) #<representation binary64>) () ())
#s(alt (fma.f64 #s(approx (* (sin x) -1/2) (.f64 (fma.f64 (fma.f64 #s(literal -1/240 binary64) (.f64 x x) #s(literal 1/12 binary64)) (.f64 x x) #s(literal -1/2 binary64)) x)) eps (cos.f64 x)) (patch (fma.f64 #s(approx ( (sin x) -1/2) (.f64 (fma.f64 (fma.f64 #s(literal -1/240 binary64) (.f64 x x) #s(literal 1/12 binary64)) (*.f64 x x) #s(literal -1/2 binary64)) x)) eps (cos.f64 x)) #<representation binary64>) () ())
#s(alt #s(approx (* (sin x) -1/2) (.f64 (fma.f64 (fma.f64 #s(literal -1/240 binary64) (.f64 x x) #s(literal 1/12 binary64)) (.f64 x x) #s(literal -1/2 binary64)) x)) (patch #s(approx ( (sin x) -1/2) (.f64 (fma.f64 (fma.f64 #s(literal -1/240 binary64) (.f64 x x) #s(literal 1/12 binary64)) (*.f64 x x) #s(literal -1/2 binary64)) x)) #<representation binary64>) () ())
#s(alt (.f64 (cos.f64 x) eps) (patch (.f64 (cos.f64 x) eps) #<representation binary64>) () ())
#s(alt #s(approx (+ (* (+ (* (sin x) (+ (* (* eps eps) 1/24) -1/2)) (* (* -1/6 (cos x)) eps)) eps) (cos x)) (fma.f64 (fma.f64 (fma.f64 #s(literal 1/12 binary64) (.f64 eps eps) #s(literal -1/2 binary64)) x (.f64 (fma.f64 (.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) eps)) x (fma.f64 (.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64)))) (patch #s(approx (+ (* (+ (* (sin x) (+ (* (* eps eps) 1/24) -1/2)) (* (* -1/6 (cos x)) eps)) eps) (cos x)) (fma.f64 (fma.f64 (fma.f64 #s(literal 1/12 binary64) (.f64 eps eps) #s(literal -1/2 binary64)) x (.f64 (fma.f64 (.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) eps)) x (fma.f64 (.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64)))) #<representation binary64>) () ())
#s(alt (.f64 (fma.f64 (fma.f64 #s(literal -1/240 binary64) (.f64 x x) #s(literal 1/12 binary64)) (.f64 x x) #s(literal -1/2 binary64)) x) (patch (.f64 (fma.f64 (fma.f64 #s(literal -1/240 binary64) (.f64 x x) #s(literal 1/12 binary64)) (.f64 x x) #s(literal -1/2 binary64)) x) #<representation binary64>) () ())

Outputs
#s(alt (* eps (cos x)) (taylor 0 eps) (#s(alt #s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 (fma.f64 #s(literal -1/6 binary64) (.f64 (cos.f64 x) eps) (.f64 (sin.f64 x) #s(literal -1/2 binary64))) eps (cos.f64 x)) eps)) (patch #s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 (fma.f64 #s(literal -1/6 binary64) (.f64 (cos.f64 x) eps) (.f64 (sin.f64 x) #s(literal -1/2 binary64))) eps (cos.f64 x)) eps)) #<representation binary64>) () ())) ())
#s(alt (* eps (+ (cos x) (* -1/2 (* eps (sin x))))) (taylor 0 eps) (#s(alt #s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 (fma.f64 #s(literal -1/6 binary64) (.f64 (cos.f64 x) eps) (.f64 (sin.f64 x) #s(literal -1/2 binary64))) eps (cos.f64 x)) eps)) (patch #s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 (fma.f64 #s(literal -1/6 binary64) (.f64 (cos.f64 x) eps) (.f64 (sin.f64 x) #s(literal -1/2 binary64))) eps (cos.f64 x)) eps)) #<representation binary64>) () ())) ())
#s(alt (* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x))))))) (taylor 0 eps) (#s(alt #s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 (fma.f64 #s(literal -1/6 binary64) (.f64 (cos.f64 x) eps) (.f64 (sin.f64 x) #s(literal -1/2 binary64))) eps (cos.f64 x)) eps)) (patch #s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 (fma.f64 #s(literal -1/6 binary64) (.f64 (cos.f64 x) eps) (.f64 (sin.f64 x) #s(literal -1/2 binary64))) eps (cos.f64 x)) eps)) #<representation binary64>) () ())) ())
#s(alt (* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* eps (+ (* -1/6 (cos x)) (* 1/24 (* eps (sin x))))))))) (taylor 0 eps) (#s(alt #s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 (fma.f64 #s(literal -1/6 binary64) (.f64 (cos.f64 x) eps) (.f64 (sin.f64 x) #s(literal -1/2 binary64))) eps (cos.f64 x)) eps)) (patch #s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 (fma.f64 #s(literal -1/6 binary64) (.f64 (cos.f64 x) eps) (.f64 (sin.f64 x) #s(literal -1/2 binary64))) eps (cos.f64 x)) eps)) #<representation binary64>) () ())) ())
#s(alt (* eps (cos x)) (taylor 0 eps) (#s(alt (.f64 (fma.f64 (fma.f64 #s(literal -1/6 binary64) (.f64 (cos.f64 x) eps) (.f64 (sin.f64 x) #s(literal -1/2 binary64))) eps (cos.f64 x)) eps) (patch (.f64 (fma.f64 (fma.f64 #s(literal -1/6 binary64) (.f64 (cos.f64 x) eps) (.f64 (sin.f64 x) #s(literal -1/2 binary64))) eps (cos.f64 x)) eps) #<representation binary64>) () ())) ())
#s(alt (* eps (+ (cos x) (* -1/2 (* eps (sin x))))) (taylor 0 eps) (#s(alt (.f64 (fma.f64 (fma.f64 #s(literal -1/6 binary64) (.f64 (cos.f64 x) eps) (.f64 (sin.f64 x) #s(literal -1/2 binary64))) eps (cos.f64 x)) eps) (patch (.f64 (fma.f64 (fma.f64 #s(literal -1/6 binary64) (.f64 (cos.f64 x) eps) (.f64 (sin.f64 x) #s(literal -1/2 binary64))) eps (cos.f64 x)) eps) #<representation binary64>) () ())) ())
#s(alt (* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x))))))) (taylor 0 eps) (#s(alt (.f64 (fma.f64 (fma.f64 #s(literal -1/6 binary64) (.f64 (cos.f64 x) eps) (.f64 (sin.f64 x) #s(literal -1/2 binary64))) eps (cos.f64 x)) eps) (patch (.f64 (fma.f64 (fma.f64 #s(literal -1/6 binary64) (.f64 (cos.f64 x) eps) (.f64 (sin.f64 x) #s(literal -1/2 binary64))) eps (cos.f64 x)) eps) #<representation binary64>) () ())) ())
#s(alt (* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x))))))) (taylor 0 eps) (#s(alt (.f64 (fma.f64 (fma.f64 #s(literal -1/6 binary64) (.f64 (cos.f64 x) eps) (.f64 (sin.f64 x) #s(literal -1/2 binary64))) eps (cos.f64 x)) eps) (patch (.f64 (fma.f64 (fma.f64 #s(literal -1/6 binary64) (.f64 (cos.f64 x) eps) (.f64 (sin.f64 x) #s(literal -1/2 binary64))) eps (cos.f64 x)) eps) #<representation binary64>) () ())) ())
#s(alt (cos x) (taylor 0 eps) (#s(alt (fma.f64 (fma.f64 #s(literal -1/6 binary64) (.f64 (cos.f64 x) eps) (.f64 (sin.f64 x) #s(literal -1/2 binary64))) eps (cos.f64 x)) (patch (fma.f64 (fma.f64 #s(literal -1/6 binary64) (.f64 (cos.f64 x) eps) (.f64 (sin.f64 x) #s(literal -1/2 binary64))) eps (cos.f64 x)) #<representation binary64>) () ())) ())
#s(alt (+ (cos x) (* -1/2 (* eps (sin x)))) (taylor 0 eps) (#s(alt (fma.f64 (fma.f64 #s(literal -1/6 binary64) (.f64 (cos.f64 x) eps) (.f64 (sin.f64 x) #s(literal -1/2 binary64))) eps (cos.f64 x)) (patch (fma.f64 (fma.f64 #s(literal -1/6 binary64) (.f64 (cos.f64 x) eps) (.f64 (sin.f64 x) #s(literal -1/2 binary64))) eps (cos.f64 x)) #<representation binary64>) () ())) ())
#s(alt (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x)))))) (taylor 0 eps) (#s(alt (fma.f64 (fma.f64 #s(literal -1/6 binary64) (.f64 (cos.f64 x) eps) (.f64 (sin.f64 x) #s(literal -1/2 binary64))) eps (cos.f64 x)) (patch (fma.f64 (fma.f64 #s(literal -1/6 binary64) (.f64 (cos.f64 x) eps) (.f64 (sin.f64 x) #s(literal -1/2 binary64))) eps (cos.f64 x)) #<representation binary64>) () ())) ())
#s(alt (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x)))))) (taylor 0 eps) (#s(alt (fma.f64 (fma.f64 #s(literal -1/6 binary64) (.f64 (cos.f64 x) eps) (.f64 (sin.f64 x) #s(literal -1/2 binary64))) eps (cos.f64 x)) (patch (fma.f64 (fma.f64 #s(literal -1/6 binary64) (.f64 (cos.f64 x) eps) (.f64 (sin.f64 x) #s(literal -1/2 binary64))) eps (cos.f64 x)) #<representation binary64>) () ())) ())
#s(alt (* -1/2 (sin x)) (taylor 0 eps) (#s(alt (fma.f64 #s(literal -1/6 binary64) (.f64 (cos.f64 x) eps) (.f64 (sin.f64 x) #s(literal -1/2 binary64))) (patch (fma.f64 #s(literal -1/6 binary64) (.f64 (cos.f64 x) eps) (.f64 (sin.f64 x) #s(literal -1/2 binary64))) #<representation binary64>) () ())) ())
#s(alt (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x)))) (taylor 0 eps) (#s(alt (fma.f64 #s(literal -1/6 binary64) (.f64 (cos.f64 x) eps) (.f64 (sin.f64 x) #s(literal -1/2 binary64))) (patch (fma.f64 #s(literal -1/6 binary64) (.f64 (cos.f64 x) eps) (.f64 (sin.f64 x) #s(literal -1/2 binary64))) #<representation binary64>) () ())) ())
#s(alt (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x)))) (taylor 0 eps) (#s(alt (fma.f64 #s(literal -1/6 binary64) (.f64 (cos.f64 x) eps) (.f64 (sin.f64 x) #s(literal -1/2 binary64))) (patch (fma.f64 #s(literal -1/6 binary64) (.f64 (cos.f64 x) eps) (.f64 (sin.f64 x) #s(literal -1/2 binary64))) #<representation binary64>) () ())) ())
#s(alt (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x)))) (taylor 0 eps) (#s(alt (fma.f64 #s(literal -1/6 binary64) (.f64 (cos.f64 x) eps) (.f64 (sin.f64 x) #s(literal -1/2 binary64))) (patch (fma.f64 #s(literal -1/6 binary64) (.f64 (cos.f64 x) eps) (.f64 (sin.f64 x) #s(literal -1/2 binary64))) #<representation binary64>) () ())) ())
#s(alt (* eps (cos x)) (taylor 0 eps) (#s(alt #s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (cos x) eps) (fma.f64 (.f64 #s(literal -1/2 binary64) x) (.f64 x eps) eps))) (patch #s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (cos x) eps) (fma.f64 (.f64 #s(literal -1/2 binary64) x) (.f64 x eps) eps))) #<representation binary64>) () ())) ())
#s(alt (* eps (+ (cos x) (* -1/2 (* eps (sin x))))) (taylor 0 eps) (#s(alt #s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (cos x) eps) (fma.f64 (.f64 #s(literal -1/2 binary64) x) (.f64 x eps) eps))) (patch #s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (cos x) eps) (fma.f64 (.f64 #s(literal -1/2 binary64) x) (.f64 x eps) eps))) #<representation binary64>) () ())) ())
#s(alt (* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x))))))) (taylor 0 eps) (#s(alt #s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (cos x) eps) (fma.f64 (.f64 #s(literal -1/2 binary64) x) (.f64 x eps) eps))) (patch #s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (cos x) eps) (fma.f64 (.f64 #s(literal -1/2 binary64) x) (.f64 x eps) eps))) #<representation binary64>) () ())) ())
#s(alt (* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* eps (+ (* -1/6 (cos x)) (* 1/24 (* eps (sin x))))))))) (taylor 0 eps) (#s(alt #s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (cos x) eps) (fma.f64 (.f64 #s(literal -1/2 binary64) x) (.f64 x eps) eps))) (patch #s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (cos x) eps) (fma.f64 (.f64 #s(literal -1/2 binary64) x) (.f64 x eps) eps))) #<representation binary64>) () ())) ())
#s(alt (* eps (cos x)) (taylor 0 eps) (#s(alt #s(approx (* (cos x) eps) (fma.f64 (.f64 #s(literal -1/2 binary64) x) (.f64 x eps) eps)) (patch #s(approx (* (cos x) eps) (fma.f64 (.f64 #s(literal -1/2 binary64) x) (.f64 x eps) eps)) #<representation binary64>) () ())) ())
#s(alt (* eps (cos x)) (taylor 0 eps) (#s(alt #s(approx (* (cos x) eps) (fma.f64 (.f64 #s(literal -1/2 binary64) x) (.f64 x eps) eps)) (patch #s(approx (* (cos x) eps) (fma.f64 (.f64 #s(literal -1/2 binary64) x) (.f64 x eps) eps)) #<representation binary64>) () ())) ())
#s(alt (* eps (cos x)) (taylor 0 eps) (#s(alt #s(approx (* (cos x) eps) (fma.f64 (.f64 #s(literal -1/2 binary64) x) (.f64 x eps) eps)) (patch #s(approx (* (cos x) eps) (fma.f64 (.f64 #s(literal -1/2 binary64) x) (.f64 x eps) eps)) #<representation binary64>) () ())) ())
#s(alt (* eps (cos x)) (taylor 0 eps) (#s(alt #s(approx (* (cos x) eps) (fma.f64 (.f64 #s(literal -1/2 binary64) x) (.f64 x eps) eps)) (patch #s(approx (* (cos x) eps) (fma.f64 (.f64 #s(literal -1/2 binary64) x) (.f64 x eps) eps)) #<representation binary64>) () ())) ())
#s(alt (* eps (+ 1 (* -1/2 (pow x 2)))) (taylor 0 eps) (#s(alt (fma.f64 (.f64 #s(literal -1/2 binary64) x) (.f64 x eps) eps) (patch (fma.f64 (.f64 #s(literal -1/2 binary64) x) (.f64 x eps) eps) #<representation binary64>) () ())) ())
#s(alt (* eps (+ 1 (* -1/2 (pow x 2)))) (taylor 0 eps) (#s(alt (fma.f64 (.f64 #s(literal -1/2 binary64) x) (.f64 x eps) eps) (patch (fma.f64 (.f64 #s(literal -1/2 binary64) x) (.f64 x eps) eps) #<representation binary64>) () ())) ())
#s(alt (* eps (+ 1 (* -1/2 (pow x 2)))) (taylor 0 eps) (#s(alt (fma.f64 (.f64 #s(literal -1/2 binary64) x) (.f64 x eps) eps) (patch (fma.f64 (.f64 #s(literal -1/2 binary64) x) (.f64 x eps) eps) #<representation binary64>) () ())) ())
#s(alt (* eps (+ 1 (* -1/2 (pow x 2)))) (taylor 0 eps) (#s(alt (fma.f64 (.f64 #s(literal -1/2 binary64) x) (.f64 x eps) eps) (patch (fma.f64 (.f64 #s(literal -1/2 binary64) x) (.f64 x eps) eps) #<representation binary64>) () ())) ())
#s(alt (* eps (cos x)) (taylor 0 eps) (#s(alt #s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (cos x) (fma.f64 (fma.f64 (.f64 x x) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) (.f64 x x) #s(literal 1 binary64))) eps)) (patch #s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (cos x) (fma.f64 (fma.f64 (.f64 x x) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) (.f64 x x) #s(literal 1 binary64))) eps)) #<representation binary64>) () ())) ())
#s(alt (* eps (+ (cos x) (* -1/2 (* eps (sin x))))) (taylor 0 eps) (#s(alt #s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (cos x) (fma.f64 (fma.f64 (.f64 x x) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) (.f64 x x) #s(literal 1 binary64))) eps)) (patch #s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (cos x) (fma.f64 (fma.f64 (.f64 x x) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) (.f64 x x) #s(literal 1 binary64))) eps)) #<representation binary64>) () ())) ())
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#s(alt (* eps (+ (cos x) (* eps (+ (* -1/6 (* eps (cos x))) (* (sin x) (- (* 1/24 (pow eps 2)) 1/2)))))) (taylor -inf x) (#s(alt (.f64 #s(approx (+ ( (+ (* (sin x) (+ (* (* eps eps) 1/24) -1/2)) (* (* -1/6 (cos x)) eps)) eps) (cos x)) (fma.f64 (fma.f64 (fma.f64 #s(literal 1/12 binary64) (.f64 eps eps) #s(literal -1/2 binary64)) x (.f64 (fma.f64 (.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) eps)) x (fma.f64 (.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64)))) eps) (patch (.f64 #s(approx (+ ( (+ (* (sin x) (+ (* (* eps eps) 1/24) -1/2)) (* (* -1/6 (cos x)) eps)) eps) (cos x)) (fma.f64 (fma.f64 (fma.f64 #s(literal 1/12 binary64) (.f64 eps eps) #s(literal -1/2 binary64)) x (.f64 (fma.f64 (.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) eps)) x (fma.f64 (.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64)))) eps) #<representation binary64>) () ())) ())
#s(alt (- (sin (- eps (* -1 x))) (sin x)) (taylor -inf x) (#s(alt #s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 #s(approx ( (sin x) -1/2) (.f64 (fma.f64 (fma.f64 #s(literal -1/240 binary64) (.f64 x x) #s(literal 1/12 binary64)) (.f64 x x) #s(literal -1/2 binary64)) x)) eps (cos.f64 x)) eps)) (patch #s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 #s(approx (* (sin x) -1/2) (.f64 (fma.f64 (fma.f64 #s(literal -1/240 binary64) (.f64 x x) #s(literal 1/12 binary64)) (*.f64 x x) #s(literal -1/2 binary64)) x)) eps (cos.f64 x)) eps)) #<representation binary64>) () ())) ())
#s(alt (- (sin (- eps (* -1 x))) (sin x)) (taylor -inf x) (#s(alt #s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 #s(approx ( (sin x) -1/2) (.f64 (fma.f64 (fma.f64 #s(literal -1/240 binary64) (.f64 x x) #s(literal 1/12 binary64)) (.f64 x x) #s(literal -1/2 binary64)) x)) eps (cos.f64 x)) eps)) (patch #s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 #s(approx (* (sin x) -1/2) (.f64 (fma.f64 (fma.f64 #s(literal -1/240 binary64) (.f64 x x) #s(literal 1/12 binary64)) (*.f64 x x) #s(literal -1/2 binary64)) x)) eps (cos.f64 x)) eps)) #<representation binary64>) () ())) ())
#s(alt (- (sin (- eps (* -1 x))) (sin x)) (taylor -inf x) (#s(alt #s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 #s(approx ( (sin x) -1/2) (.f64 (fma.f64 (fma.f64 #s(literal -1/240 binary64) (.f64 x x) #s(literal 1/12 binary64)) (.f64 x x) #s(literal -1/2 binary64)) x)) eps (cos.f64 x)) eps)) (patch #s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 #s(approx (* (sin x) -1/2) (.f64 (fma.f64 (fma.f64 #s(literal -1/240 binary64) (.f64 x x) #s(literal 1/12 binary64)) (*.f64 x x) #s(literal -1/2 binary64)) x)) eps (cos.f64 x)) eps)) #<representation binary64>) () ())) ())
#s(alt (- (sin (- eps (* -1 x))) (sin x)) (taylor -inf x) (#s(alt #s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 #s(approx ( (sin x) -1/2) (.f64 (fma.f64 (fma.f64 #s(literal -1/240 binary64) (.f64 x x) #s(literal 1/12 binary64)) (.f64 x x) #s(literal -1/2 binary64)) x)) eps (cos.f64 x)) eps)) (patch #s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 #s(approx (* (sin x) -1/2) (.f64 (fma.f64 (fma.f64 #s(literal -1/240 binary64) (.f64 x x) #s(literal 1/12 binary64)) (*.f64 x x) #s(literal -1/2 binary64)) x)) eps (cos.f64 x)) eps)) #<representation binary64>) () ())) ())
#s(alt (* eps (+ (cos x) (* -1/2 (* eps (sin x))))) (taylor -inf x) (#s(alt (.f64 (fma.f64 #s(approx ( (sin x) -1/2) (.f64 (fma.f64 (fma.f64 #s(literal -1/240 binary64) (.f64 x x) #s(literal 1/12 binary64)) (.f64 x x) #s(literal -1/2 binary64)) x)) eps (cos.f64 x)) eps) (patch (.f64 (fma.f64 #s(approx (* (sin x) -1/2) (.f64 (fma.f64 (fma.f64 #s(literal -1/240 binary64) (.f64 x x) #s(literal 1/12 binary64)) (*.f64 x x) #s(literal -1/2 binary64)) x)) eps (cos.f64 x)) eps) #<representation binary64>) () ())) ())
#s(alt (* eps (+ (cos x) (* -1/2 (* eps (sin x))))) (taylor -inf x) (#s(alt (.f64 (fma.f64 #s(approx ( (sin x) -1/2) (.f64 (fma.f64 (fma.f64 #s(literal -1/240 binary64) (.f64 x x) #s(literal 1/12 binary64)) (.f64 x x) #s(literal -1/2 binary64)) x)) eps (cos.f64 x)) eps) (patch (.f64 (fma.f64 #s(approx (* (sin x) -1/2) (.f64 (fma.f64 (fma.f64 #s(literal -1/240 binary64) (.f64 x x) #s(literal 1/12 binary64)) (*.f64 x x) #s(literal -1/2 binary64)) x)) eps (cos.f64 x)) eps) #<representation binary64>) () ())) ())
#s(alt (* eps (+ (cos x) (* -1/2 (* eps (sin x))))) (taylor -inf x) (#s(alt (.f64 (fma.f64 #s(approx ( (sin x) -1/2) (.f64 (fma.f64 (fma.f64 #s(literal -1/240 binary64) (.f64 x x) #s(literal 1/12 binary64)) (.f64 x x) #s(literal -1/2 binary64)) x)) eps (cos.f64 x)) eps) (patch (.f64 (fma.f64 #s(approx (* (sin x) -1/2) (.f64 (fma.f64 (fma.f64 #s(literal -1/240 binary64) (.f64 x x) #s(literal 1/12 binary64)) (*.f64 x x) #s(literal -1/2 binary64)) x)) eps (cos.f64 x)) eps) #<representation binary64>) () ())) ())
#s(alt (* eps (+ (cos x) (* -1/2 (* eps (sin x))))) (taylor -inf x) (#s(alt (.f64 (fma.f64 #s(approx ( (sin x) -1/2) (.f64 (fma.f64 (fma.f64 #s(literal -1/240 binary64) (.f64 x x) #s(literal 1/12 binary64)) (.f64 x x) #s(literal -1/2 binary64)) x)) eps (cos.f64 x)) eps) (patch (.f64 (fma.f64 #s(approx (* (sin x) -1/2) (.f64 (fma.f64 (fma.f64 #s(literal -1/240 binary64) (.f64 x x) #s(literal 1/12 binary64)) (*.f64 x x) #s(literal -1/2 binary64)) x)) eps (cos.f64 x)) eps) #<representation binary64>) () ())) ())
#s(alt (+ (cos x) (* -1/2 (* eps (sin x)))) (taylor -inf x) (#s(alt (fma.f64 #s(approx (* (sin x) -1/2) (.f64 (fma.f64 (fma.f64 #s(literal -1/240 binary64) (.f64 x x) #s(literal 1/12 binary64)) (.f64 x x) #s(literal -1/2 binary64)) x)) eps (cos.f64 x)) (patch (fma.f64 #s(approx ( (sin x) -1/2) (.f64 (fma.f64 (fma.f64 #s(literal -1/240 binary64) (.f64 x x) #s(literal 1/12 binary64)) (*.f64 x x) #s(literal -1/2 binary64)) x)) eps (cos.f64 x)) #<representation binary64>) () ())) ())
#s(alt (+ (cos x) (* -1/2 (* eps (sin x)))) (taylor -inf x) (#s(alt (fma.f64 #s(approx (* (sin x) -1/2) (.f64 (fma.f64 (fma.f64 #s(literal -1/240 binary64) (.f64 x x) #s(literal 1/12 binary64)) (.f64 x x) #s(literal -1/2 binary64)) x)) eps (cos.f64 x)) (patch (fma.f64 #s(approx ( (sin x) -1/2) (.f64 (fma.f64 (fma.f64 #s(literal -1/240 binary64) (.f64 x x) #s(literal 1/12 binary64)) (*.f64 x x) #s(literal -1/2 binary64)) x)) eps (cos.f64 x)) #<representation binary64>) () ())) ())
#s(alt (+ (cos x) (* -1/2 (* eps (sin x)))) (taylor -inf x) (#s(alt (fma.f64 #s(approx (* (sin x) -1/2) (.f64 (fma.f64 (fma.f64 #s(literal -1/240 binary64) (.f64 x x) #s(literal 1/12 binary64)) (.f64 x x) #s(literal -1/2 binary64)) x)) eps (cos.f64 x)) (patch (fma.f64 #s(approx ( (sin x) -1/2) (.f64 (fma.f64 (fma.f64 #s(literal -1/240 binary64) (.f64 x x) #s(literal 1/12 binary64)) (*.f64 x x) #s(literal -1/2 binary64)) x)) eps (cos.f64 x)) #<representation binary64>) () ())) ())
#s(alt (+ (cos x) (* -1/2 (* eps (sin x)))) (taylor -inf x) (#s(alt (fma.f64 #s(approx (* (sin x) -1/2) (.f64 (fma.f64 (fma.f64 #s(literal -1/240 binary64) (.f64 x x) #s(literal 1/12 binary64)) (.f64 x x) #s(literal -1/2 binary64)) x)) eps (cos.f64 x)) (patch (fma.f64 #s(approx ( (sin x) -1/2) (.f64 (fma.f64 (fma.f64 #s(literal -1/240 binary64) (.f64 x x) #s(literal 1/12 binary64)) (*.f64 x x) #s(literal -1/2 binary64)) x)) eps (cos.f64 x)) #<representation binary64>) () ())) ())
#s(alt (* -1/2 (sin x)) (taylor -inf x) (#s(alt #s(approx (* (sin x) -1/2) (.f64 (fma.f64 (fma.f64 #s(literal -1/240 binary64) (.f64 x x) #s(literal 1/12 binary64)) (.f64 x x) #s(literal -1/2 binary64)) x)) (patch #s(approx ( (sin x) -1/2) (.f64 (fma.f64 (fma.f64 #s(literal -1/240 binary64) (.f64 x x) #s(literal 1/12 binary64)) (*.f64 x x) #s(literal -1/2 binary64)) x)) #<representation binary64>) () ())) ())
#s(alt (* -1/2 (sin x)) (taylor -inf x) (#s(alt #s(approx (* (sin x) -1/2) (.f64 (fma.f64 (fma.f64 #s(literal -1/240 binary64) (.f64 x x) #s(literal 1/12 binary64)) (.f64 x x) #s(literal -1/2 binary64)) x)) (patch #s(approx ( (sin x) -1/2) (.f64 (fma.f64 (fma.f64 #s(literal -1/240 binary64) (.f64 x x) #s(literal 1/12 binary64)) (*.f64 x x) #s(literal -1/2 binary64)) x)) #<representation binary64>) () ())) ())
#s(alt (* -1/2 (sin x)) (taylor -inf x) (#s(alt #s(approx (* (sin x) -1/2) (.f64 (fma.f64 (fma.f64 #s(literal -1/240 binary64) (.f64 x x) #s(literal 1/12 binary64)) (.f64 x x) #s(literal -1/2 binary64)) x)) (patch #s(approx ( (sin x) -1/2) (.f64 (fma.f64 (fma.f64 #s(literal -1/240 binary64) (.f64 x x) #s(literal 1/12 binary64)) (*.f64 x x) #s(literal -1/2 binary64)) x)) #<representation binary64>) () ())) ())
#s(alt (* -1/2 (sin x)) (taylor -inf x) (#s(alt #s(approx (* (sin x) -1/2) (.f64 (fma.f64 (fma.f64 #s(literal -1/240 binary64) (.f64 x x) #s(literal 1/12 binary64)) (.f64 x x) #s(literal -1/2 binary64)) x)) (patch #s(approx ( (sin x) -1/2) (.f64 (fma.f64 (fma.f64 #s(literal -1/240 binary64) (.f64 x x) #s(literal 1/12 binary64)) (*.f64 x x) #s(literal -1/2 binary64)) x)) #<representation binary64>) () ())) ())
#s(alt (* eps (cos x)) (taylor -inf x) (#s(alt (.f64 (cos.f64 x) eps) (patch (.f64 (cos.f64 x) eps) #<representation binary64>) () ())) ())
#s(alt (* eps (cos x)) (taylor -inf x) (#s(alt (.f64 (cos.f64 x) eps) (patch (.f64 (cos.f64 x) eps) #<representation binary64>) () ())) ())
#s(alt (* eps (cos x)) (taylor -inf x) (#s(alt (.f64 (cos.f64 x) eps) (patch (.f64 (cos.f64 x) eps) #<representation binary64>) () ())) ())
#s(alt (* eps (cos x)) (taylor -inf x) (#s(alt (.f64 (cos.f64 x) eps) (patch (.f64 (cos.f64 x) eps) #<representation binary64>) () ())) ())
#s(alt (+ (cos x) (* eps (+ (* -1/6 (* eps (cos x))) (* (sin x) (- (* 1/24 (pow eps 2)) 1/2))))) (taylor -inf x) (#s(alt #s(approx (+ (* (+ (* (sin x) (+ (* (* eps eps) 1/24) -1/2)) (* (* -1/6 (cos x)) eps)) eps) (cos x)) (fma.f64 (fma.f64 (fma.f64 #s(literal 1/12 binary64) (.f64 eps eps) #s(literal -1/2 binary64)) x (.f64 (fma.f64 (.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) eps)) x (fma.f64 (.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64)))) (patch #s(approx (+ (* (+ (* (sin x) (+ (* (* eps eps) 1/24) -1/2)) (* (* -1/6 (cos x)) eps)) eps) (cos x)) (fma.f64 (fma.f64 (fma.f64 #s(literal 1/12 binary64) (.f64 eps eps) #s(literal -1/2 binary64)) x (.f64 (fma.f64 (.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) eps)) x (fma.f64 (.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64)))) #<representation binary64>) () ())) ())
#s(alt (+ (cos x) (* eps (+ (* -1/6 (* eps (cos x))) (* (sin x) (- (* 1/24 (pow eps 2)) 1/2))))) (taylor -inf x) (#s(alt #s(approx (+ (* (+ (* (sin x) (+ (* (* eps eps) 1/24) -1/2)) (* (* -1/6 (cos x)) eps)) eps) (cos x)) (fma.f64 (fma.f64 (fma.f64 #s(literal 1/12 binary64) (.f64 eps eps) #s(literal -1/2 binary64)) x (.f64 (fma.f64 (.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) eps)) x (fma.f64 (.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64)))) (patch #s(approx (+ (* (+ (* (sin x) (+ (* (* eps eps) 1/24) -1/2)) (* (* -1/6 (cos x)) eps)) eps) (cos x)) (fma.f64 (fma.f64 (fma.f64 #s(literal 1/12 binary64) (.f64 eps eps) #s(literal -1/2 binary64)) x (.f64 (fma.f64 (.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) eps)) x (fma.f64 (.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64)))) #<representation binary64>) () ())) ())
#s(alt (+ (cos x) (* eps (+ (* -1/6 (* eps (cos x))) (* (sin x) (- (* 1/24 (pow eps 2)) 1/2))))) (taylor -inf x) (#s(alt #s(approx (+ (* (+ (* (sin x) (+ (* (* eps eps) 1/24) -1/2)) (* (* -1/6 (cos x)) eps)) eps) (cos x)) (fma.f64 (fma.f64 (fma.f64 #s(literal 1/12 binary64) (.f64 eps eps) #s(literal -1/2 binary64)) x (.f64 (fma.f64 (.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) eps)) x (fma.f64 (.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64)))) (patch #s(approx (+ (* (+ (* (sin x) (+ (* (* eps eps) 1/24) -1/2)) (* (* -1/6 (cos x)) eps)) eps) (cos x)) (fma.f64 (fma.f64 (fma.f64 #s(literal 1/12 binary64) (.f64 eps eps) #s(literal -1/2 binary64)) x (.f64 (fma.f64 (.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) eps)) x (fma.f64 (.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64)))) #<representation binary64>) () ())) ())
#s(alt (+ (cos x) (* eps (+ (* -1/6 (* eps (cos x))) (* (sin x) (- (* 1/24 (pow eps 2)) 1/2))))) (taylor -inf x) (#s(alt #s(approx (+ (* (+ (* (sin x) (+ (* (* eps eps) 1/24) -1/2)) (* (* -1/6 (cos x)) eps)) eps) (cos x)) (fma.f64 (fma.f64 (fma.f64 #s(literal 1/12 binary64) (.f64 eps eps) #s(literal -1/2 binary64)) x (.f64 (fma.f64 (.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) eps)) x (fma.f64 (.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64)))) (patch #s(approx (+ (* (+ (* (sin x) (+ (* (* eps eps) 1/24) -1/2)) (* (* -1/6 (cos x)) eps)) eps) (cos x)) (fma.f64 (fma.f64 (fma.f64 #s(literal 1/12 binary64) (.f64 eps eps) #s(literal -1/2 binary64)) x (.f64 (fma.f64 (.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) eps)) x (fma.f64 (.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64)))) #<representation binary64>) () ())) ())
#s(alt (* -1/240 (pow x 5)) (taylor -inf x) (#s(alt (.f64 (fma.f64 (fma.f64 #s(literal -1/240 binary64) (.f64 x x) #s(literal 1/12 binary64)) (.f64 x x) #s(literal -1/2 binary64)) x) (patch (.f64 (fma.f64 (fma.f64 #s(literal -1/240 binary64) (.f64 x x) #s(literal 1/12 binary64)) (.f64 x x) #s(literal -1/2 binary64)) x) #<representation binary64>) () ())) ())
#s(alt (* -1 (* (pow x 5) (- 1/240 (* 1/12 (/ 1 (pow x 2)))))) (taylor -inf x) (#s(alt (.f64 (fma.f64 (fma.f64 #s(literal -1/240 binary64) (.f64 x x) #s(literal 1/12 binary64)) (.f64 x x) #s(literal -1/2 binary64)) x) (patch (.f64 (fma.f64 (fma.f64 #s(literal -1/240 binary64) (.f64 x x) #s(literal 1/12 binary64)) (.f64 x x) #s(literal -1/2 binary64)) x) #<representation binary64>) () ())) ())
#s(alt (* -1 (* (pow x 5) (- (+ 1/240 (/ 1/2 (pow x 4))) (* 1/12 (/ 1 (pow x 2)))))) (taylor -inf x) (#s(alt (.f64 (fma.f64 (fma.f64 #s(literal -1/240 binary64) (.f64 x x) #s(literal 1/12 binary64)) (.f64 x x) #s(literal -1/2 binary64)) x) (patch (.f64 (fma.f64 (fma.f64 #s(literal -1/240 binary64) (.f64 x x) #s(literal 1/12 binary64)) (.f64 x x) #s(literal -1/2 binary64)) x) #<representation binary64>) () ())) ())
#s(alt (* -1 (* (pow x 5) (- (+ 1/240 (/ 1/2 (pow x 4))) (* 1/12 (/ 1 (pow x 2)))))) (taylor -inf x) (#s(alt (.f64 (fma.f64 (fma.f64 #s(literal -1/240 binary64) (.f64 x x) #s(literal 1/12 binary64)) (.f64 x x) #s(literal -1/2 binary64)) x) (patch (.f64 (fma.f64 (fma.f64 #s(literal -1/240 binary64) (.f64 x x) #s(literal 1/12 binary64)) (.f64 x x) #s(literal -1/2 binary64)) x) #<representation binary64>) () ())) ())

Calls

6 calls:

Time	Variable		Point	Expression
11.0ms	x	@	0	((- (sin (+ x eps)) (sin x)) (* (+ (* (+ (* -1/6 (* (cos x) eps)) (* (sin x) -1/2)) eps) (cos x)) eps) (+ (* (+ (* -1/6 (* (cos x) eps)) (* (sin x) -1/2)) eps) (cos x)) (+ (* -1/6 (* (cos x) eps)) (* (sin x) -1/2)) (- (sin (+ x eps)) (sin x)) (* (cos x) eps) (+ (* (* -1/2 x) (* x eps)) eps) (* -1/2 x) (- (sin (+ x eps)) (sin x)) (* (cos x) eps) (cos x) (+ (* (+ (* (* x x) 1/24) -1/2) (* x x)) 1) (+ (* (+ (* 1/12 (* eps eps)) -1/2) x) (* (+ (* (* eps eps) 1/24) -1/2) eps)) (+ (* (+ (* (+ (* 1/12 (* eps eps)) -1/2) x) (* (+ (* (* eps eps) 1/24) -1/2) eps)) x) (+ (* (* eps eps) -1/6) 1)) (- (sin (+ x eps)) (sin x)) (* (+ (* (+ (* (sin x) (+ (* (* eps eps) 1/24) -1/2)) (* (* -1/6 (cos x)) eps)) eps) (cos x)) eps) (- (sin (+ x eps)) (sin x)) (* (+ (* (* (sin x) -1/2) eps) (cos x)) eps) (+ (* (* (sin x) -1/2) eps) (cos x)) (* (sin x) -1/2) (* (cos x) eps) (+ (* (+ (* (sin x) (+ (* (* eps eps) 1/24) -1/2)) (* (* -1/6 (cos x)) eps)) eps) (cos x)) (* (+ (* (+ (* -1/240 (* x x)) 1/12) (* x x)) -1/2) x))
5.0ms	x	@	inf	((- (sin (+ x eps)) (sin x)) (* (+ (* (+ (* -1/6 (* (cos x) eps)) (* (sin x) -1/2)) eps) (cos x)) eps) (+ (* (+ (* -1/6 (* (cos x) eps)) (* (sin x) -1/2)) eps) (cos x)) (+ (* -1/6 (* (cos x) eps)) (* (sin x) -1/2)) (- (sin (+ x eps)) (sin x)) (* (cos x) eps) (+ (* (* -1/2 x) (* x eps)) eps) (* -1/2 x) (- (sin (+ x eps)) (sin x)) (* (cos x) eps) (cos x) (+ (* (+ (* (* x x) 1/24) -1/2) (* x x)) 1) (+ (* (+ (* 1/12 (* eps eps)) -1/2) x) (* (+ (* (* eps eps) 1/24) -1/2) eps)) (+ (* (+ (* (+ (* 1/12 (* eps eps)) -1/2) x) (* (+ (* (* eps eps) 1/24) -1/2) eps)) x) (+ (* (* eps eps) -1/6) 1)) (- (sin (+ x eps)) (sin x)) (* (+ (* (+ (* (sin x) (+ (* (* eps eps) 1/24) -1/2)) (* (* -1/6 (cos x)) eps)) eps) (cos x)) eps) (- (sin (+ x eps)) (sin x)) (* (+ (* (* (sin x) -1/2) eps) (cos x)) eps) (+ (* (* (sin x) -1/2) eps) (cos x)) (* (sin x) -1/2) (* (cos x) eps) (+ (* (+ (* (sin x) (+ (* (* eps eps) 1/24) -1/2)) (* (* -1/6 (cos x)) eps)) eps) (cos x)) (* (+ (* (+ (* -1/240 (* x x)) 1/12) (* x x)) -1/2) x))
4.0ms	x	@	-inf	((- (sin (+ x eps)) (sin x)) (* (+ (* (+ (* -1/6 (* (cos x) eps)) (* (sin x) -1/2)) eps) (cos x)) eps) (+ (* (+ (* -1/6 (* (cos x) eps)) (* (sin x) -1/2)) eps) (cos x)) (+ (* -1/6 (* (cos x) eps)) (* (sin x) -1/2)) (- (sin (+ x eps)) (sin x)) (* (cos x) eps) (+ (* (* -1/2 x) (* x eps)) eps) (* -1/2 x) (- (sin (+ x eps)) (sin x)) (* (cos x) eps) (cos x) (+ (* (+ (* (* x x) 1/24) -1/2) (* x x)) 1) (+ (* (+ (* 1/12 (* eps eps)) -1/2) x) (* (+ (* (* eps eps) 1/24) -1/2) eps)) (+ (* (+ (* (+ (* 1/12 (* eps eps)) -1/2) x) (* (+ (* (* eps eps) 1/24) -1/2) eps)) x) (+ (* (* eps eps) -1/6) 1)) (- (sin (+ x eps)) (sin x)) (* (+ (* (+ (* (sin x) (+ (* (* eps eps) 1/24) -1/2)) (* (* -1/6 (cos x)) eps)) eps) (cos x)) eps) (- (sin (+ x eps)) (sin x)) (* (+ (* (* (sin x) -1/2) eps) (cos x)) eps) (+ (* (* (sin x) -1/2) eps) (cos x)) (* (sin x) -1/2) (* (cos x) eps) (+ (* (+ (* (sin x) (+ (* (* eps eps) 1/24) -1/2)) (* (* -1/6 (cos x)) eps)) eps) (cos x)) (* (+ (* (+ (* -1/240 (* x x)) 1/12) (* x x)) -1/2) x))
4.0ms	eps	@	0	((- (sin (+ x eps)) (sin x)) (* (+ (* (+ (* -1/6 (* (cos x) eps)) (* (sin x) -1/2)) eps) (cos x)) eps) (+ (* (+ (* -1/6 (* (cos x) eps)) (* (sin x) -1/2)) eps) (cos x)) (+ (* -1/6 (* (cos x) eps)) (* (sin x) -1/2)) (- (sin (+ x eps)) (sin x)) (* (cos x) eps) (+ (* (* -1/2 x) (* x eps)) eps) (* -1/2 x) (- (sin (+ x eps)) (sin x)) (* (cos x) eps) (cos x) (+ (* (+ (* (* x x) 1/24) -1/2) (* x x)) 1) (+ (* (+ (* 1/12 (* eps eps)) -1/2) x) (* (+ (* (* eps eps) 1/24) -1/2) eps)) (+ (* (+ (* (+ (* 1/12 (* eps eps)) -1/2) x) (* (+ (* (* eps eps) 1/24) -1/2) eps)) x) (+ (* (* eps eps) -1/6) 1)) (- (sin (+ x eps)) (sin x)) (* (+ (* (+ (* (sin x) (+ (* (* eps eps) 1/24) -1/2)) (* (* -1/6 (cos x)) eps)) eps) (cos x)) eps) (- (sin (+ x eps)) (sin x)) (* (+ (* (* (sin x) -1/2) eps) (cos x)) eps) (+ (* (* (sin x) -1/2) eps) (cos x)) (* (sin x) -1/2) (* (cos x) eps) (+ (* (+ (* (sin x) (+ (* (* eps eps) 1/24) -1/2)) (* (* -1/6 (cos x)) eps)) eps) (cos x)) (* (+ (* (+ (* -1/240 (* x x)) 1/12) (* x x)) -1/2) x))
3.0ms	eps	@	-inf	((- (sin (+ x eps)) (sin x)) (* (+ (* (+ (* -1/6 (* (cos x) eps)) (* (sin x) -1/2)) eps) (cos x)) eps) (+ (* (+ (* -1/6 (* (cos x) eps)) (* (sin x) -1/2)) eps) (cos x)) (+ (* -1/6 (* (cos x) eps)) (* (sin x) -1/2)) (- (sin (+ x eps)) (sin x)) (* (cos x) eps) (+ (* (* -1/2 x) (* x eps)) eps) (* -1/2 x) (- (sin (+ x eps)) (sin x)) (* (cos x) eps) (cos x) (+ (* (+ (* (* x x) 1/24) -1/2) (* x x)) 1) (+ (* (+ (* 1/12 (* eps eps)) -1/2) x) (* (+ (* (* eps eps) 1/24) -1/2) eps)) (+ (* (+ (* (+ (* 1/12 (* eps eps)) -1/2) x) (* (+ (* (* eps eps) 1/24) -1/2) eps)) x) (+ (* (* eps eps) -1/6) 1)) (- (sin (+ x eps)) (sin x)) (* (+ (* (+ (* (sin x) (+ (* (* eps eps) 1/24) -1/2)) (* (* -1/6 (cos x)) eps)) eps) (cos x)) eps) (- (sin (+ x eps)) (sin x)) (* (+ (* (* (sin x) -1/2) eps) (cos x)) eps) (+ (* (* (sin x) -1/2) eps) (cos x)) (* (sin x) -1/2) (* (cos x) eps) (+ (* (+ (* (sin x) (+ (* (* eps eps) 1/24) -1/2)) (* (* -1/6 (cos x)) eps)) eps) (cos x)) (* (+ (* (+ (* -1/240 (* x x)) 1/12) (* x x)) -1/2) x))

simplify192.0ms (1.6%)

Memory

40.4MiB live, 311.9MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	475	5649
1	1465	5566
2	4629	5562
0	8236	5080

Stop Event

1×	iter limit
1×	node limit

Counts

492 → 487

Calls

Call 1

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

Outputs
(* eps (cos x))
(*.f64 (cos.f64 x) eps)
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(.f64 (fma.f64 (.f64 (sin.f64 x) #s(literal -1/2 binary64)) eps (cos.f64 x)) eps)
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x)))))))
(.f64 (fma.f64 (fma.f64 #s(literal -1/6 binary64) (.f64 (cos.f64 x) eps) (*.f64 (sin.f64 x) #s(literal -1/2 binary64))) eps (cos.f64 x)) eps)
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* eps (+ (* -1/6 (cos x)) (* 1/24 (* eps (sin x)))))))))
(.f64 (fma.f64 (fma.f64 (fma.f64 (.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) (sin.f64 x) (.f64 (.f64 #s(literal -1/6 binary64) (cos.f64 x)) eps)) eps (cos.f64 x)) eps)
(* eps (cos x))
(*.f64 (cos.f64 x) eps)
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(.f64 (fma.f64 (.f64 (sin.f64 x) #s(literal -1/2 binary64)) eps (cos.f64 x)) eps)
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x)))))))
(.f64 (fma.f64 (fma.f64 #s(literal -1/6 binary64) (.f64 (cos.f64 x) eps) (*.f64 (sin.f64 x) #s(literal -1/2 binary64))) eps (cos.f64 x)) eps)
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x)))))))
(.f64 (fma.f64 (fma.f64 #s(literal -1/6 binary64) (.f64 (cos.f64 x) eps) (*.f64 (sin.f64 x) #s(literal -1/2 binary64))) eps (cos.f64 x)) eps)
(cos x)
(cos.f64 x)
(+ (cos x) (* -1/2 (* eps (sin x))))
(fma.f64 (*.f64 (sin.f64 x) #s(literal -1/2 binary64)) eps (cos.f64 x))
(+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x))))))
(fma.f64 (fma.f64 #s(literal -1/6 binary64) (.f64 (cos.f64 x) eps) (.f64 (sin.f64 x) #s(literal -1/2 binary64))) eps (cos.f64 x))
(+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x))))))
(fma.f64 (fma.f64 #s(literal -1/6 binary64) (.f64 (cos.f64 x) eps) (.f64 (sin.f64 x) #s(literal -1/2 binary64))) eps (cos.f64 x))
(* -1/2 (sin x))
(*.f64 (sin.f64 x) #s(literal -1/2 binary64))
(+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x))))
(fma.f64 #s(literal -1/6 binary64) (.f64 (cos.f64 x) eps) (.f64 (sin.f64 x) #s(literal -1/2 binary64)))
(+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x))))
(fma.f64 #s(literal -1/6 binary64) (.f64 (cos.f64 x) eps) (.f64 (sin.f64 x) #s(literal -1/2 binary64)))
(+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x))))
(fma.f64 #s(literal -1/6 binary64) (.f64 (cos.f64 x) eps) (.f64 (sin.f64 x) #s(literal -1/2 binary64)))
(* eps (cos x))
(*.f64 (cos.f64 x) eps)
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(.f64 (fma.f64 (.f64 (sin.f64 x) #s(literal -1/2 binary64)) eps (cos.f64 x)) eps)
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x)))))))
(.f64 (fma.f64 (fma.f64 #s(literal -1/6 binary64) (.f64 (cos.f64 x) eps) (*.f64 (sin.f64 x) #s(literal -1/2 binary64))) eps (cos.f64 x)) eps)
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* eps (+ (* -1/6 (cos x)) (* 1/24 (* eps (sin x)))))))))
(.f64 (fma.f64 (fma.f64 (fma.f64 (.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) (sin.f64 x) (.f64 (.f64 #s(literal -1/6 binary64) (cos.f64 x)) eps)) eps (cos.f64 x)) eps)
(* eps (cos x))
(*.f64 (cos.f64 x) eps)
(* eps (cos x))
(*.f64 (cos.f64 x) eps)
(* eps (cos x))
(*.f64 (cos.f64 x) eps)
(* eps (cos x))
(*.f64 (cos.f64 x) eps)
(* eps (+ 1 (* -1/2 (pow x 2))))
(.f64 (fma.f64 (.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64)) eps)
(* eps (+ 1 (* -1/2 (pow x 2))))
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(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
(- (sin (- eps (* -1 x))) (sin x))
(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(.f64 (fma.f64 (.f64 (sin.f64 x) #s(literal -1/2 binary64)) eps (cos.f64 x)) eps)
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(.f64 (fma.f64 (.f64 (sin.f64 x) #s(literal -1/2 binary64)) eps (cos.f64 x)) eps)
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(.f64 (fma.f64 (.f64 (sin.f64 x) #s(literal -1/2 binary64)) eps (cos.f64 x)) eps)
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(.f64 (fma.f64 (.f64 (sin.f64 x) #s(literal -1/2 binary64)) eps (cos.f64 x)) eps)
(+ (cos x) (* -1/2 (* eps (sin x))))
(fma.f64 (*.f64 (sin.f64 x) #s(literal -1/2 binary64)) eps (cos.f64 x))
(+ (cos x) (* -1/2 (* eps (sin x))))
(fma.f64 (*.f64 (sin.f64 x) #s(literal -1/2 binary64)) eps (cos.f64 x))
(+ (cos x) (* -1/2 (* eps (sin x))))
(fma.f64 (*.f64 (sin.f64 x) #s(literal -1/2 binary64)) eps (cos.f64 x))
(+ (cos x) (* -1/2 (* eps (sin x))))
(fma.f64 (*.f64 (sin.f64 x) #s(literal -1/2 binary64)) eps (cos.f64 x))
(* -1/2 (sin x))
(*.f64 (sin.f64 x) #s(literal -1/2 binary64))
(* -1/2 (sin x))
(*.f64 (sin.f64 x) #s(literal -1/2 binary64))
(* -1/2 (sin x))
(*.f64 (sin.f64 x) #s(literal -1/2 binary64))
(* -1/2 (sin x))
(*.f64 (sin.f64 x) #s(literal -1/2 binary64))
(* eps (cos x))
(*.f64 (cos.f64 x) eps)
(* eps (cos x))
(*.f64 (cos.f64 x) eps)
(* eps (cos x))
(*.f64 (cos.f64 x) eps)
(* eps (cos x))
(*.f64 (cos.f64 x) eps)
(+ (cos x) (* eps (+ (* -1/6 (* eps (cos x))) (* (sin x) (- (* 1/24 (pow eps 2)) 1/2)))))
(fma.f64 (fma.f64 (fma.f64 (.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) (sin.f64 x) (.f64 (*.f64 #s(literal -1/6 binary64) (cos.f64 x)) eps)) eps (cos.f64 x))
(+ (cos x) (* eps (+ (* -1/6 (* eps (cos x))) (* (sin x) (- (* 1/24 (pow eps 2)) 1/2)))))
(fma.f64 (fma.f64 (fma.f64 (.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) (sin.f64 x) (.f64 (*.f64 #s(literal -1/6 binary64) (cos.f64 x)) eps)) eps (cos.f64 x))
(+ (cos x) (* eps (+ (* -1/6 (* eps (cos x))) (* (sin x) (- (* 1/24 (pow eps 2)) 1/2)))))
(fma.f64 (fma.f64 (fma.f64 (.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) (sin.f64 x) (.f64 (*.f64 #s(literal -1/6 binary64) (cos.f64 x)) eps)) eps (cos.f64 x))
(+ (cos x) (* eps (+ (* -1/6 (* eps (cos x))) (* (sin x) (- (* 1/24 (pow eps 2)) 1/2)))))
(fma.f64 (fma.f64 (fma.f64 (.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) (sin.f64 x) (.f64 (*.f64 #s(literal -1/6 binary64) (cos.f64 x)) eps)) eps (cos.f64 x))
(* -1/240 (pow x 5))
(*.f64 (pow.f64 x #s(literal 5 binary64)) #s(literal -1/240 binary64))
(* -1 (* (pow x 5) (- 1/240 (* 1/12 (/ 1 (pow x 2))))))
(.f64 (neg.f64 (-.f64 #s(literal 1/240 binary64) (/.f64 #s(literal 1/12 binary64) (.f64 x x)))) (pow.f64 x #s(literal 5 binary64)))
(* -1 (* (pow x 5) (- (+ 1/240 (/ 1/2 (pow x 4))) (* 1/12 (/ 1 (pow x 2))))))
(.f64 (neg.f64 (-.f64 (+.f64 (/.f64 #s(literal 1/2 binary64) (pow.f64 x #s(literal 4 binary64))) #s(literal 1/240 binary64)) (/.f64 #s(literal 1/12 binary64) (.f64 x x)))) (pow.f64 x #s(literal 5 binary64)))
(* -1 (* (pow x 5) (- (+ 1/240 (/ 1/2 (pow x 4))) (* 1/12 (/ 1 (pow x 2))))))
(.f64 (neg.f64 (-.f64 (+.f64 (/.f64 #s(literal 1/2 binary64) (pow.f64 x #s(literal 4 binary64))) #s(literal 1/240 binary64)) (/.f64 #s(literal 1/12 binary64) (.f64 x x)))) (pow.f64 x #s(literal 5 binary64)))

rewrite189.0ms (1.6%)

Memory

-14.4MiB live, 189.5MiB allocated

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	60	477
0	104	477
1	390	477
2	2908	477
0	8582	471

Stop Event

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

Counts

23 → 391

Calls

Call 1

Inputs
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 (fma.f64 #s(literal -1/6 binary64) (.f64 (cos.f64 x) eps) (*.f64 (sin.f64 x) #s(literal -1/2 binary64))) eps (cos.f64 x)) eps))
(.f64 (fma.f64 (fma.f64 #s(literal -1/6 binary64) (.f64 (cos.f64 x) eps) (*.f64 (sin.f64 x) #s(literal -1/2 binary64))) eps (cos.f64 x)) eps)
(fma.f64 (fma.f64 #s(literal -1/6 binary64) (.f64 (cos.f64 x) eps) (.f64 (sin.f64 x) #s(literal -1/2 binary64))) eps (cos.f64 x))
(fma.f64 #s(literal -1/6 binary64) (.f64 (cos.f64 x) eps) (.f64 (sin.f64 x) #s(literal -1/2 binary64)))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (cos x) eps) (fma.f64 (.f64 #s(literal -1/2 binary64) x) (.f64 x eps) eps)))
#s(approx (* (cos x) eps) (fma.f64 (.f64 #s(literal -1/2 binary64) x) (.f64 x eps) eps))
(fma.f64 (.f64 #s(literal -1/2 binary64) x) (.f64 x eps) eps)
(*.f64 #s(literal -1/2 binary64) x)
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (cos x) (fma.f64 (fma.f64 (.f64 x x) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) (*.f64 x x) #s(literal 1 binary64))) eps))
(.f64 #s(approx (cos x) (fma.f64 (fma.f64 (.f64 x x) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) (*.f64 x x) #s(literal 1 binary64))) eps)
#s(approx (cos x) (fma.f64 (fma.f64 (.f64 x x) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) (.f64 x x) #s(literal 1 binary64)))
(fma.f64 (fma.f64 (.f64 x x) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) (.f64 x x) #s(literal 1 binary64))
(fma.f64 (fma.f64 #s(literal 1/12 binary64) (.f64 eps eps) #s(literal -1/2 binary64)) x (.f64 (fma.f64 (*.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) eps))
(fma.f64 (fma.f64 (fma.f64 #s(literal 1/12 binary64) (.f64 eps eps) #s(literal -1/2 binary64)) x (.f64 (fma.f64 (.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) eps)) x (fma.f64 (.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64)))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (+ (* (sin x) (+ (* (* eps eps) 1/24) -1/2)) (* (* -1/6 (cos x)) eps)) eps) (cos x)) (fma.f64 (fma.f64 (fma.f64 #s(literal 1/12 binary64) (.f64 eps eps) #s(literal -1/2 binary64)) x (.f64 (fma.f64 (.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) eps)) x (fma.f64 (.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64)))) eps))
(.f64 #s(approx (+ ( (+ (* (sin x) (+ (* (* eps eps) 1/24) -1/2)) (* (* -1/6 (cos x)) eps)) eps) (cos x)) (fma.f64 (fma.f64 (fma.f64 #s(literal 1/12 binary64) (.f64 eps eps) #s(literal -1/2 binary64)) x (.f64 (fma.f64 (.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) eps)) x (fma.f64 (.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64)))) eps)
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 #s(approx ( (sin x) -1/2) (.f64 (fma.f64 (fma.f64 #s(literal -1/240 binary64) (.f64 x x) #s(literal 1/12 binary64)) (*.f64 x x) #s(literal -1/2 binary64)) x)) eps (cos.f64 x)) eps))
(.f64 (fma.f64 #s(approx ( (sin x) -1/2) (.f64 (fma.f64 (fma.f64 #s(literal -1/240 binary64) (.f64 x x) #s(literal 1/12 binary64)) (*.f64 x x) #s(literal -1/2 binary64)) x)) eps (cos.f64 x)) eps)
(fma.f64 #s(approx (* (sin x) -1/2) (.f64 (fma.f64 (fma.f64 #s(literal -1/240 binary64) (.f64 x x) #s(literal 1/12 binary64)) (*.f64 x x) #s(literal -1/2 binary64)) x)) eps (cos.f64 x))
#s(approx (* (sin x) -1/2) (.f64 (fma.f64 (fma.f64 #s(literal -1/240 binary64) (.f64 x x) #s(literal 1/12 binary64)) (*.f64 x x) #s(literal -1/2 binary64)) x))
(*.f64 (cos.f64 x) eps)
#s(approx (+ (* (+ (* (sin x) (+ (* (* eps eps) 1/24) -1/2)) (* (* -1/6 (cos x)) eps)) eps) (cos x)) (fma.f64 (fma.f64 (fma.f64 #s(literal 1/12 binary64) (.f64 eps eps) #s(literal -1/2 binary64)) x (.f64 (fma.f64 (.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) eps)) x (fma.f64 (.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64))))
(.f64 (fma.f64 (fma.f64 #s(literal -1/240 binary64) (.f64 x x) #s(literal 1/12 binary64)) (*.f64 x x) #s(literal -1/2 binary64)) x)

Outputs
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eval134.0ms (1.1%)

Memory: 4.8MiB live, 210.0MiB allocated
Compiler: Compiled 28 293 to 2 807 computations (90.1% saved)

prune101.0ms (0.8%)

Memory

-34.7MiB live, 87.2MiB allocated

Pruning

32 alts after pruning (19 fresh and 13 done)

	Pruned	Kept	Total
New	868	10	878
Fresh	6	9	15
Picked	1	4	5
Done	0	9	9
Total	875	32	907

Accuracy

100.0%

Counts

907 → 32

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	65.3%	(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
	99.9%	(.f64 (.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 0 binary64) eps))) #s(literal 2 binary64)) (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64))))
✓	100.0%	#s(approx (- (sin (+ x eps)) (sin x)) (fma.f64 (.f64 (fma.f64 (fma.f64 #s(literal 1/24 binary64) (.f64 eps eps) #s(literal -1/2 binary64)) (sin.f64 x) (.f64 (.f64 (cos.f64 x) #s(literal -1/6 binary64)) eps)) eps) eps (*.f64 (cos.f64 x) eps)))
	99.7%	#s(approx (- (sin (+ x eps)) (sin x)) (fma.f64 (.f64 (.f64 #s(literal -1/2 binary64) (sin.f64 x)) eps) eps (*.f64 (cos.f64 x) eps)))
✓	100.0%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 (fma.f64 (sin.f64 x) (fma.f64 (.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) (.f64 (.f64 #s(literal -1/6 binary64) (cos.f64 x)) eps)) eps (cos.f64 x)) eps))
	99.8%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 (fma.f64 (sin.f64 x) (fma.f64 (.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) (.f64 #s(approx ( -1/6 (cos x)) #s(literal -1/6 binary64)) eps)) eps (cos.f64 x)) eps))
✓	100.0%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 (fma.f64 #s(literal -1/6 binary64) (.f64 (cos.f64 x) eps) (*.f64 (sin.f64 x) #s(literal -1/2 binary64))) eps (cos.f64 x)) eps))
	99.6%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 (fma.f64 #s(literal -1/6 binary64) #s(approx ( (cos x) eps) (fma.f64 (fma.f64 (.f64 (.f64 x eps) x) #s(literal 1/24 binary64) (.f64 #s(literal -1/2 binary64) eps)) (.f64 x x) eps)) (*.f64 (sin.f64 x) #s(literal -1/2 binary64))) eps (cos.f64 x)) eps))
✓	99.7%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 (.f64 (sin.f64 x) #s(literal -1/2 binary64)) eps (cos.f64 x)) eps))
	99.0%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 #s(approx (+ ( (sin x) (+ (* (* eps eps) 1/24) -1/2)) (* (* -1/6 (cos x)) eps)) (*.f64 #s(literal -1/6 binary64) eps)) eps (cos.f64 x)) eps))
	99.5%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 #s(approx (+ ( -1/6 (* (cos x) eps)) (* (sin x) -1/2)) (fma.f64 (fma.f64 (.f64 (+.f64 x eps) #s(literal 1/12 binary64)) x #s(literal -1/2 binary64)) x (.f64 #s(literal -1/6 binary64) eps))) eps (cos.f64 x)) eps))
	99.4%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 #s(approx (+ ( -1/6 (* (cos x) eps)) (* (sin x) -1/2)) (fma.f64 #s(literal -1/6 binary64) eps (*.f64 #s(literal -1/2 binary64) x))) eps (cos.f64 x)) eps))
	99.4%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 #s(approx ( (sin x) -1/2) (.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 1/10080 binary64) (.f64 x x) #s(literal -1/240 binary64)) (.f64 x x) #s(literal 1/12 binary64)) (.f64 x x) #s(literal -1/2 binary64)) x)) eps (cos.f64 x)) eps))
✓	99.4%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 #s(approx ( (sin x) -1/2) (.f64 (fma.f64 (fma.f64 #s(literal -1/240 binary64) (.f64 x x) #s(literal 1/12 binary64)) (*.f64 x x) #s(literal -1/2 binary64)) x)) eps (cos.f64 x)) eps))
✓	99.4%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 #s(approx ( (sin x) -1/2) (.f64 (fma.f64 (.f64 x x) #s(literal 1/12 binary64) #s(literal -1/2 binary64)) x)) eps (cos.f64 x)) eps))
	99.3%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 #s(approx ( (sin x) -1/2) (*.f64 #s(literal -1/2 binary64) x)) eps (cos.f64 x)) eps))
✓	99.0%	#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (cos.f64 x) eps))
	98.3%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (+ (* (sin x) (+ (* (* eps eps) 1/24) -1/2)) (* (* -1/6 (cos x)) eps)) eps) (cos x)) (fma.f64 #s(approx (+ (* (+ (* 1/12 (* eps eps)) -1/2) x) (* (+ (* (* eps eps) 1/24) -1/2) eps)) (.f64 (+.f64 x eps) #s(literal -1/2 binary64))) x (fma.f64 (.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64)))) eps))
	98.3%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (+ (* (sin x) (+ (* (* eps eps) 1/24) -1/2)) (* (* -1/6 (cos x)) eps)) eps) (cos x)) #s(approx (+ (* (+ (* (+ (* 1/12 (* eps eps)) -1/2) x) (* (+ (* (* eps eps) 1/24) -1/2) eps)) x) (+ (* (* eps eps) -1/6) 1)) (fma.f64 (*.f64 x (+.f64 x eps)) #s(literal -1/2 binary64) #s(literal 1 binary64)))) eps))
	97.6%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (+ (* -1/6 (* (cos x) eps)) (* (sin x) -1/2)) eps) (cos x)) (fma.f64 (.f64 x eps) #s(literal -1/2 binary64) (fma.f64 (.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64)))) eps))
✓	98.3%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (* (sin x) -1/2) eps) (cos x)) (fma.f64 (fma.f64 (fma.f64 (.f64 #s(literal 1/12 binary64) eps) x #s(literal -1/2 binary64)) x (.f64 #s(literal -1/2 binary64) eps)) x #s(literal 1 binary64))) eps))
	97.6%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (* (sin x) -1/2) eps) (cos x)) (fma.f64 (*.f64 x eps) #s(literal -1/2 binary64) #s(literal 1 binary64))) eps))
✓	99.4%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (* (sin x) -1/2) eps) (cos x)) (*.f64 (fma.f64 (sin.f64 x) #s(literal -1/2 binary64) (/.f64 (cos.f64 x) eps)) eps)) eps))
	98.1%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (* (sin x) -1/2) eps) (cos x)) #s(approx (+ (* (+ (* (+ (* (* 1/12 eps) x) -1/2) x) (* -1/2 eps)) x) 1) (.f64 (fma.f64 (neg.f64 (fma.f64 #s(literal -1/12 binary64) (.f64 x x) #s(literal 1/2 binary64))) x (/.f64 (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64)) eps)) eps))) eps))
✓	97.6%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (* (sin x) -1/2) eps) (cos x)) #s(literal 1 binary64)) eps))
	98.4%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (cos x) (fma.f64 (fma.f64 (fma.f64 #s(literal -1/720 binary64) (.f64 x x) #s(literal 1/24 binary64)) (.f64 x x) #s(literal -1/2 binary64)) (.f64 x x) #s(literal 1 binary64))) eps))
✓	98.3%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (cos x) (fma.f64 (fma.f64 (.f64 x x) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) (*.f64 x x) #s(literal 1 binary64))) eps))
	98.3%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (cos x) (fma.f64 (.f64 (fma.f64 #s(literal 1/24 binary64) (*.f64 x x) #s(literal -1/2 binary64)) x) x #s(literal 1 binary64))) eps))
	98.3%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (cos x) (+.f64 (.f64 (.f64 (fma.f64 #s(literal 1/24 binary64) (.f64 x x) #s(literal -1/2 binary64)) x) x) #s(literal 1 binary64))) eps))
✓	98.1%	#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (cos x) eps) (fma.f64 (.f64 #s(literal -1/2 binary64) x) (.f64 x eps) eps)))
	98.1%	#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (cos x) eps) (+.f64 (.f64 (.f64 (*.f64 eps x) #s(literal -1/2 binary64)) x) eps)))
	5.2%	#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (cos x) eps) #s(approx (+ (* (* -1/2 x) (* x eps)) eps) (.f64 (.f64 (*.f64 x eps) x) #s(literal -1/2 binary64)))))

Compiler

Compiled 1 182 to 629 computations (46.8% saved)

regimes33.0ms (0.3%)

Memory

30.6MiB live, 30.6MiB allocated

Counts

42 → 1

Calls

Call 1

Inputs
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (* (sin x) -1/2) eps) (cos x)) #s(literal 1 binary64)) eps))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (cos x) eps) #s(approx (+ (* (* -1/2 x) (* x eps)) eps) (.f64 (.f64 (*.f64 x eps) x) #s(literal -1/2 binary64)))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (cos x) eps) (fma.f64 (.f64 #s(literal -1/2 binary64) x) (.f64 x eps) eps)))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (* (sin x) -1/2) eps) (cos x)) (fma.f64 (*.f64 #s(literal -1/2 binary64) eps) x #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (* (sin x) -1/2) eps) (cos x)) (fma.f64 (*.f64 x eps) #s(literal -1/2 binary64) #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (cos x) eps) (+.f64 (.f64 (.f64 (*.f64 eps x) #s(literal -1/2 binary64)) x) eps)))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (* (sin x) -1/2) eps) (cos x)) (fma.f64 (*.f64 (+.f64 x eps) #s(literal -1/2 binary64)) x #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (+ (* (sin x) (+ (* (* eps eps) 1/24) -1/2)) (* (* -1/6 (cos x)) eps)) eps) (cos x)) #s(approx (+ (* (+ (* (+ (* 1/12 (* eps eps)) -1/2) x) (* (+ (* (* eps eps) 1/24) -1/2) eps)) x) (+ (* (* eps eps) -1/6) 1)) (fma.f64 (*.f64 x (+.f64 x eps)) #s(literal -1/2 binary64) #s(literal 1 binary64)))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (cos x) eps) (fma.f64 (.f64 eps (fma.f64 (.f64 x x) #s(literal 1/24 binary64) #s(literal -1/2 binary64))) (*.f64 x x) eps)))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (cos x) (fma.f64 (.f64 (fma.f64 #s(literal 1/24 binary64) (*.f64 x x) #s(literal -1/2 binary64)) x) x #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (cos x) (fma.f64 (fma.f64 (.f64 x x) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) (*.f64 x x) #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (+ (* -1/6 (* (cos x) eps)) (* (sin x) -1/2)) eps) (cos x)) (fma.f64 (.f64 x eps) #s(literal -1/2 binary64) (fma.f64 (.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64)))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (cos x) (+.f64 (.f64 (.f64 (fma.f64 #s(literal 1/24 binary64) (.f64 x x) #s(literal -1/2 binary64)) x) x) #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (+ (* (sin x) (+ (* (* eps eps) 1/24) -1/2)) (* (* -1/6 (cos x)) eps)) eps) (cos x)) (fma.f64 #s(approx (+ (* (+ (* 1/12 (* eps eps)) -1/2) x) (* (+ (* (* eps eps) 1/24) -1/2) eps)) (.f64 (+.f64 x eps) #s(literal -1/2 binary64))) x (fma.f64 (.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64)))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (* (sin x) -1/2) eps) (cos x)) (fma.f64 (fma.f64 (fma.f64 (.f64 #s(literal 1/12 binary64) eps) x #s(literal -1/2 binary64)) x (.f64 #s(literal -1/2 binary64) eps)) x #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (+ (* (sin x) (+ (* (* eps eps) 1/24) -1/2)) (* (* -1/6 (cos x)) eps)) eps) (cos x)) (fma.f64 eps (fma.f64 (fma.f64 (.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) x (.f64 #s(literal -1/6 binary64) eps)) #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (cos x) (fma.f64 (fma.f64 (fma.f64 #s(literal -1/720 binary64) (.f64 x x) #s(literal 1/24 binary64)) (.f64 x x) #s(literal -1/2 binary64)) (.f64 x x) #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (* (sin x) -1/2) eps) (cos x)) #s(approx (+ (* (+ (* (+ (* (* 1/12 eps) x) -1/2) x) (* -1/2 eps)) x) 1) (.f64 (fma.f64 (neg.f64 (fma.f64 #s(literal -1/12 binary64) (.f64 x x) #s(literal 1/2 binary64))) x (/.f64 (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64)) eps)) eps))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (+ (* (sin x) (+ (* (* eps eps) 1/24) -1/2)) (* (* -1/6 (cos x)) eps)) eps) (cos x)) (fma.f64 (fma.f64 (fma.f64 #s(literal 1/12 binary64) (.f64 eps eps) #s(literal -1/2 binary64)) x (.f64 (fma.f64 (.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) eps)) x (fma.f64 (.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64)))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (sin.f64 eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (cos.f64 x) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 #s(approx ( (sin x) -1/2) (*.f64 #s(literal -1/2 binary64) x)) eps (cos.f64 x)) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 #s(approx (+ ( (sin x) (+ (* (* eps eps) 1/24) -1/2)) (* (* -1/6 (cos x)) eps)) (*.f64 #s(literal -1/6 binary64) eps)) eps (cos.f64 x)) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 #s(approx (+ ( -1/6 (* (cos x) eps)) (* (sin x) -1/2)) (fma.f64 #s(literal -1/6 binary64) eps (*.f64 #s(literal -1/2 binary64) x))) eps (cos.f64 x)) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 #s(approx ( (sin x) -1/2) (.f64 (fma.f64 (.f64 x x) #s(literal 1/12 binary64) #s(literal -1/2 binary64)) x)) eps (cos.f64 x)) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 #s(approx (+ ( (sin x) (+ (* (* eps eps) 1/24) -1/2)) (* (* -1/6 (cos x)) eps)) (fma.f64 (fma.f64 (.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) x (.f64 #s(literal -1/6 binary64) eps))) eps (cos.f64 x)) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 #s(approx (+ ( -1/6 (* (cos x) eps)) (* (sin x) -1/2)) (fma.f64 (fma.f64 (.f64 (+.f64 x eps) #s(literal 1/12 binary64)) x #s(literal -1/2 binary64)) x (.f64 #s(literal -1/6 binary64) eps))) eps (cos.f64 x)) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 #s(approx ( (sin x) -1/2) (.f64 (fma.f64 (fma.f64 #s(literal -1/240 binary64) (.f64 x x) #s(literal 1/12 binary64)) (*.f64 x x) #s(literal -1/2 binary64)) x)) eps (cos.f64 x)) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 #s(approx ( (sin x) -1/2) (.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 1/10080 binary64) (.f64 x x) #s(literal -1/240 binary64)) (.f64 x x) #s(literal 1/12 binary64)) (.f64 x x) #s(literal -1/2 binary64)) x)) eps (cos.f64 x)) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 #s(approx (+ ( (sin x) (+ (* (* eps eps) 1/24) -1/2)) (* (* -1/6 (cos x)) eps)) (fma.f64 (fma.f64 (fma.f64 #s(literal 1/12 binary64) eps (.f64 (.f64 (fma.f64 (.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) x) #s(literal -1/6 binary64))) x (fma.f64 (.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64))) x (*.f64 #s(literal -1/6 binary64) eps))) eps (cos.f64 x)) eps))
(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 (.f64 (sin.f64 x) #s(literal -1/2 binary64)) eps (cos.f64 x)) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (fma.f64 (.f64 (.f64 #s(literal -1/2 binary64) (sin.f64 x)) eps) eps (*.f64 (cos.f64 x) eps)))
(-.f64 (sin.f64 (+.f64 x eps)) #s(approx (sin x) (fma.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 #s(literal 1/120 binary64) (*.f64 x x) #s(literal -1/6 binary64)) x)))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (* (sin x) -1/2) eps) (cos x)) (*.f64 (fma.f64 (sin.f64 x) #s(literal -1/2 binary64) (/.f64 (cos.f64 x) eps)) eps)) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 (fma.f64 (sin.f64 x) (fma.f64 (.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) (.f64 #s(approx ( -1/6 (cos x)) #s(literal -1/6 binary64)) eps)) eps (cos.f64 x)) eps))
(.f64 (.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 0 binary64) eps))) #s(literal 2 binary64)) (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64))))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 (fma.f64 #s(literal -1/6 binary64) #s(approx ( (cos x) eps) (fma.f64 (fma.f64 (.f64 (.f64 x eps) x) #s(literal 1/24 binary64) (.f64 #s(literal -1/2 binary64) eps)) (.f64 x x) eps)) (*.f64 (sin.f64 x) #s(literal -1/2 binary64))) eps (cos.f64 x)) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 (fma.f64 (sin.f64 x) (fma.f64 (.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) (.f64 #s(approx ( -1/6 (cos x)) (fma.f64 (fma.f64 #s(literal -1/144 binary64) (.f64 x x) #s(literal 1/12 binary64)) (.f64 x x) #s(literal -1/6 binary64))) eps)) eps (cos.f64 x)) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 (fma.f64 #s(literal -1/6 binary64) (.f64 (cos.f64 x) eps) (*.f64 (sin.f64 x) #s(literal -1/2 binary64))) eps (cos.f64 x)) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 (fma.f64 (sin.f64 x) (fma.f64 (.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) (.f64 (.f64 #s(literal -1/6 binary64) (cos.f64 x)) eps)) eps (cos.f64 x)) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (fma.f64 (.f64 (fma.f64 (fma.f64 #s(literal 1/24 binary64) (.f64 eps eps) #s(literal -1/2 binary64)) (sin.f64 x) (.f64 (.f64 (cos.f64 x) #s(literal -1/6 binary64)) eps)) eps) eps (*.f64 (cos.f64 x) eps)))

Outputs

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

Calls

3 calls:

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

Results

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

Compiler

Compiled 9 to 10 computations (-11.1% saved)

regimes60.0ms (0.5%)

Memory

-3.4MiB live, 35.1MiB allocated

Counts

40 → 1

Calls

Call 1

Inputs
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (* (sin x) -1/2) eps) (cos x)) #s(literal 1 binary64)) eps))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (cos x) eps) #s(approx (+ (* (* -1/2 x) (* x eps)) eps) (.f64 (.f64 (*.f64 x eps) x) #s(literal -1/2 binary64)))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (cos x) eps) (fma.f64 (.f64 #s(literal -1/2 binary64) x) (.f64 x eps) eps)))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (* (sin x) -1/2) eps) (cos x)) (fma.f64 (*.f64 #s(literal -1/2 binary64) eps) x #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (* (sin x) -1/2) eps) (cos x)) (fma.f64 (*.f64 x eps) #s(literal -1/2 binary64) #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (cos x) eps) (+.f64 (.f64 (.f64 (*.f64 eps x) #s(literal -1/2 binary64)) x) eps)))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (* (sin x) -1/2) eps) (cos x)) (fma.f64 (*.f64 (+.f64 x eps) #s(literal -1/2 binary64)) x #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (+ (* (sin x) (+ (* (* eps eps) 1/24) -1/2)) (* (* -1/6 (cos x)) eps)) eps) (cos x)) #s(approx (+ (* (+ (* (+ (* 1/12 (* eps eps)) -1/2) x) (* (+ (* (* eps eps) 1/24) -1/2) eps)) x) (+ (* (* eps eps) -1/6) 1)) (fma.f64 (*.f64 x (+.f64 x eps)) #s(literal -1/2 binary64) #s(literal 1 binary64)))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (cos x) eps) (fma.f64 (.f64 eps (fma.f64 (.f64 x x) #s(literal 1/24 binary64) #s(literal -1/2 binary64))) (*.f64 x x) eps)))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (cos x) (fma.f64 (.f64 (fma.f64 #s(literal 1/24 binary64) (*.f64 x x) #s(literal -1/2 binary64)) x) x #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (cos x) (fma.f64 (fma.f64 (.f64 x x) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) (*.f64 x x) #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (+ (* -1/6 (* (cos x) eps)) (* (sin x) -1/2)) eps) (cos x)) (fma.f64 (.f64 x eps) #s(literal -1/2 binary64) (fma.f64 (.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64)))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (cos x) (+.f64 (.f64 (.f64 (fma.f64 #s(literal 1/24 binary64) (.f64 x x) #s(literal -1/2 binary64)) x) x) #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (+ (* (sin x) (+ (* (* eps eps) 1/24) -1/2)) (* (* -1/6 (cos x)) eps)) eps) (cos x)) (fma.f64 #s(approx (+ (* (+ (* 1/12 (* eps eps)) -1/2) x) (* (+ (* (* eps eps) 1/24) -1/2) eps)) (.f64 (+.f64 x eps) #s(literal -1/2 binary64))) x (fma.f64 (.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64)))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (* (sin x) -1/2) eps) (cos x)) (fma.f64 (fma.f64 (fma.f64 (.f64 #s(literal 1/12 binary64) eps) x #s(literal -1/2 binary64)) x (.f64 #s(literal -1/2 binary64) eps)) x #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (+ (* (sin x) (+ (* (* eps eps) 1/24) -1/2)) (* (* -1/6 (cos x)) eps)) eps) (cos x)) (fma.f64 eps (fma.f64 (fma.f64 (.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) x (.f64 #s(literal -1/6 binary64) eps)) #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (cos x) (fma.f64 (fma.f64 (fma.f64 #s(literal -1/720 binary64) (.f64 x x) #s(literal 1/24 binary64)) (.f64 x x) #s(literal -1/2 binary64)) (.f64 x x) #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (* (sin x) -1/2) eps) (cos x)) #s(approx (+ (* (+ (* (+ (* (* 1/12 eps) x) -1/2) x) (* -1/2 eps)) x) 1) (.f64 (fma.f64 (neg.f64 (fma.f64 #s(literal -1/12 binary64) (.f64 x x) #s(literal 1/2 binary64))) x (/.f64 (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64)) eps)) eps))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (+ (* (sin x) (+ (* (* eps eps) 1/24) -1/2)) (* (* -1/6 (cos x)) eps)) eps) (cos x)) (fma.f64 (fma.f64 (fma.f64 #s(literal 1/12 binary64) (.f64 eps eps) #s(literal -1/2 binary64)) x (.f64 (fma.f64 (.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) eps)) x (fma.f64 (.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64)))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (sin.f64 eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (cos.f64 x) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 #s(approx ( (sin x) -1/2) (*.f64 #s(literal -1/2 binary64) x)) eps (cos.f64 x)) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 #s(approx (+ ( (sin x) (+ (* (* eps eps) 1/24) -1/2)) (* (* -1/6 (cos x)) eps)) (*.f64 #s(literal -1/6 binary64) eps)) eps (cos.f64 x)) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 #s(approx (+ ( -1/6 (* (cos x) eps)) (* (sin x) -1/2)) (fma.f64 #s(literal -1/6 binary64) eps (*.f64 #s(literal -1/2 binary64) x))) eps (cos.f64 x)) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 #s(approx ( (sin x) -1/2) (.f64 (fma.f64 (.f64 x x) #s(literal 1/12 binary64) #s(literal -1/2 binary64)) x)) eps (cos.f64 x)) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 #s(approx (+ ( (sin x) (+ (* (* eps eps) 1/24) -1/2)) (* (* -1/6 (cos x)) eps)) (fma.f64 (fma.f64 (.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) x (.f64 #s(literal -1/6 binary64) eps))) eps (cos.f64 x)) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 #s(approx (+ ( -1/6 (* (cos x) eps)) (* (sin x) -1/2)) (fma.f64 (fma.f64 (.f64 (+.f64 x eps) #s(literal 1/12 binary64)) x #s(literal -1/2 binary64)) x (.f64 #s(literal -1/6 binary64) eps))) eps (cos.f64 x)) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 #s(approx ( (sin x) -1/2) (.f64 (fma.f64 (fma.f64 #s(literal -1/240 binary64) (.f64 x x) #s(literal 1/12 binary64)) (*.f64 x x) #s(literal -1/2 binary64)) x)) eps (cos.f64 x)) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 #s(approx ( (sin x) -1/2) (.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 1/10080 binary64) (.f64 x x) #s(literal -1/240 binary64)) (.f64 x x) #s(literal 1/12 binary64)) (.f64 x x) #s(literal -1/2 binary64)) x)) eps (cos.f64 x)) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 #s(approx (+ ( (sin x) (+ (* (* eps eps) 1/24) -1/2)) (* (* -1/6 (cos x)) eps)) (fma.f64 (fma.f64 (fma.f64 #s(literal 1/12 binary64) eps (.f64 (.f64 (fma.f64 (.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) x) #s(literal -1/6 binary64))) x (fma.f64 (.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64))) x (*.f64 #s(literal -1/6 binary64) eps))) eps (cos.f64 x)) eps))
(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 (.f64 (sin.f64 x) #s(literal -1/2 binary64)) eps (cos.f64 x)) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (fma.f64 (.f64 (.f64 #s(literal -1/2 binary64) (sin.f64 x)) eps) eps (*.f64 (cos.f64 x) eps)))
(-.f64 (sin.f64 (+.f64 x eps)) #s(approx (sin x) (fma.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 #s(literal 1/120 binary64) (*.f64 x x) #s(literal -1/6 binary64)) x)))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (* (sin x) -1/2) eps) (cos x)) (*.f64 (fma.f64 (sin.f64 x) #s(literal -1/2 binary64) (/.f64 (cos.f64 x) eps)) eps)) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 (fma.f64 (sin.f64 x) (fma.f64 (.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) (.f64 #s(approx ( -1/6 (cos x)) #s(literal -1/6 binary64)) eps)) eps (cos.f64 x)) eps))
(.f64 (.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 0 binary64) eps))) #s(literal 2 binary64)) (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64))))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 (fma.f64 #s(literal -1/6 binary64) #s(approx ( (cos x) eps) (fma.f64 (fma.f64 (.f64 (.f64 x eps) x) #s(literal 1/24 binary64) (.f64 #s(literal -1/2 binary64) eps)) (.f64 x x) eps)) (*.f64 (sin.f64 x) #s(literal -1/2 binary64))) eps (cos.f64 x)) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 (fma.f64 (sin.f64 x) (fma.f64 (.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) (.f64 #s(approx ( -1/6 (cos x)) (fma.f64 (fma.f64 #s(literal -1/144 binary64) (.f64 x x) #s(literal 1/12 binary64)) (.f64 x x) #s(literal -1/6 binary64))) eps)) eps (cos.f64 x)) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 (fma.f64 #s(literal -1/6 binary64) (.f64 (cos.f64 x) eps) (*.f64 (sin.f64 x) #s(literal -1/2 binary64))) eps (cos.f64 x)) eps))

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

Calls

3 calls:

38.0ms	(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
10.0ms	eps
10.0ms	x

Results

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

Compiler

Compiled 9 to 10 computations (-11.1% saved)

regimes48.0ms (0.4%)

Memory

-18.9MiB live, 19.5MiB allocated

Counts

39 → 1

Calls

Call 1

Inputs
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (* (sin x) -1/2) eps) (cos x)) #s(literal 1 binary64)) eps))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (cos x) eps) #s(approx (+ (* (* -1/2 x) (* x eps)) eps) (.f64 (.f64 (*.f64 x eps) x) #s(literal -1/2 binary64)))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (cos x) eps) (fma.f64 (.f64 #s(literal -1/2 binary64) x) (.f64 x eps) eps)))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (* (sin x) -1/2) eps) (cos x)) (fma.f64 (*.f64 #s(literal -1/2 binary64) eps) x #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (* (sin x) -1/2) eps) (cos x)) (fma.f64 (*.f64 x eps) #s(literal -1/2 binary64) #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (cos x) eps) (+.f64 (.f64 (.f64 (*.f64 eps x) #s(literal -1/2 binary64)) x) eps)))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (* (sin x) -1/2) eps) (cos x)) (fma.f64 (*.f64 (+.f64 x eps) #s(literal -1/2 binary64)) x #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (+ (* (sin x) (+ (* (* eps eps) 1/24) -1/2)) (* (* -1/6 (cos x)) eps)) eps) (cos x)) #s(approx (+ (* (+ (* (+ (* 1/12 (* eps eps)) -1/2) x) (* (+ (* (* eps eps) 1/24) -1/2) eps)) x) (+ (* (* eps eps) -1/6) 1)) (fma.f64 (*.f64 x (+.f64 x eps)) #s(literal -1/2 binary64) #s(literal 1 binary64)))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (cos x) eps) (fma.f64 (.f64 eps (fma.f64 (.f64 x x) #s(literal 1/24 binary64) #s(literal -1/2 binary64))) (*.f64 x x) eps)))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (cos x) (fma.f64 (.f64 (fma.f64 #s(literal 1/24 binary64) (*.f64 x x) #s(literal -1/2 binary64)) x) x #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (cos x) (fma.f64 (fma.f64 (.f64 x x) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) (*.f64 x x) #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (+ (* -1/6 (* (cos x) eps)) (* (sin x) -1/2)) eps) (cos x)) (fma.f64 (.f64 x eps) #s(literal -1/2 binary64) (fma.f64 (.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64)))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (cos x) (+.f64 (.f64 (.f64 (fma.f64 #s(literal 1/24 binary64) (.f64 x x) #s(literal -1/2 binary64)) x) x) #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (+ (* (sin x) (+ (* (* eps eps) 1/24) -1/2)) (* (* -1/6 (cos x)) eps)) eps) (cos x)) (fma.f64 #s(approx (+ (* (+ (* 1/12 (* eps eps)) -1/2) x) (* (+ (* (* eps eps) 1/24) -1/2) eps)) (.f64 (+.f64 x eps) #s(literal -1/2 binary64))) x (fma.f64 (.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64)))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (* (sin x) -1/2) eps) (cos x)) (fma.f64 (fma.f64 (fma.f64 (.f64 #s(literal 1/12 binary64) eps) x #s(literal -1/2 binary64)) x (.f64 #s(literal -1/2 binary64) eps)) x #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (+ (* (sin x) (+ (* (* eps eps) 1/24) -1/2)) (* (* -1/6 (cos x)) eps)) eps) (cos x)) (fma.f64 eps (fma.f64 (fma.f64 (.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) x (.f64 #s(literal -1/6 binary64) eps)) #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (cos x) (fma.f64 (fma.f64 (fma.f64 #s(literal -1/720 binary64) (.f64 x x) #s(literal 1/24 binary64)) (.f64 x x) #s(literal -1/2 binary64)) (.f64 x x) #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (* (sin x) -1/2) eps) (cos x)) #s(approx (+ (* (+ (* (+ (* (* 1/12 eps) x) -1/2) x) (* -1/2 eps)) x) 1) (.f64 (fma.f64 (neg.f64 (fma.f64 #s(literal -1/12 binary64) (.f64 x x) #s(literal 1/2 binary64))) x (/.f64 (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64)) eps)) eps))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (+ (* (sin x) (+ (* (* eps eps) 1/24) -1/2)) (* (* -1/6 (cos x)) eps)) eps) (cos x)) (fma.f64 (fma.f64 (fma.f64 #s(literal 1/12 binary64) (.f64 eps eps) #s(literal -1/2 binary64)) x (.f64 (fma.f64 (.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) eps)) x (fma.f64 (.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64)))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (sin.f64 eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (cos.f64 x) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 #s(approx ( (sin x) -1/2) (*.f64 #s(literal -1/2 binary64) x)) eps (cos.f64 x)) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 #s(approx (+ ( (sin x) (+ (* (* eps eps) 1/24) -1/2)) (* (* -1/6 (cos x)) eps)) (*.f64 #s(literal -1/6 binary64) eps)) eps (cos.f64 x)) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 #s(approx (+ ( -1/6 (* (cos x) eps)) (* (sin x) -1/2)) (fma.f64 #s(literal -1/6 binary64) eps (*.f64 #s(literal -1/2 binary64) x))) eps (cos.f64 x)) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 #s(approx ( (sin x) -1/2) (.f64 (fma.f64 (.f64 x x) #s(literal 1/12 binary64) #s(literal -1/2 binary64)) x)) eps (cos.f64 x)) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 #s(approx (+ ( (sin x) (+ (* (* eps eps) 1/24) -1/2)) (* (* -1/6 (cos x)) eps)) (fma.f64 (fma.f64 (.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) x (.f64 #s(literal -1/6 binary64) eps))) eps (cos.f64 x)) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 #s(approx (+ ( -1/6 (* (cos x) eps)) (* (sin x) -1/2)) (fma.f64 (fma.f64 (.f64 (+.f64 x eps) #s(literal 1/12 binary64)) x #s(literal -1/2 binary64)) x (.f64 #s(literal -1/6 binary64) eps))) eps (cos.f64 x)) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 #s(approx ( (sin x) -1/2) (.f64 (fma.f64 (fma.f64 #s(literal -1/240 binary64) (.f64 x x) #s(literal 1/12 binary64)) (*.f64 x x) #s(literal -1/2 binary64)) x)) eps (cos.f64 x)) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 #s(approx ( (sin x) -1/2) (.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 1/10080 binary64) (.f64 x x) #s(literal -1/240 binary64)) (.f64 x x) #s(literal 1/12 binary64)) (.f64 x x) #s(literal -1/2 binary64)) x)) eps (cos.f64 x)) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 #s(approx (+ ( (sin x) (+ (* (* eps eps) 1/24) -1/2)) (* (* -1/6 (cos x)) eps)) (fma.f64 (fma.f64 (fma.f64 #s(literal 1/12 binary64) eps (.f64 (.f64 (fma.f64 (.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) x) #s(literal -1/6 binary64))) x (fma.f64 (.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64))) x (*.f64 #s(literal -1/6 binary64) eps))) eps (cos.f64 x)) eps))
(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 (.f64 (sin.f64 x) #s(literal -1/2 binary64)) eps (cos.f64 x)) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (fma.f64 (.f64 (.f64 #s(literal -1/2 binary64) (sin.f64 x)) eps) eps (*.f64 (cos.f64 x) eps)))
(-.f64 (sin.f64 (+.f64 x eps)) #s(approx (sin x) (fma.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 #s(literal 1/120 binary64) (*.f64 x x) #s(literal -1/6 binary64)) x)))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (* (sin x) -1/2) eps) (cos x)) (*.f64 (fma.f64 (sin.f64 x) #s(literal -1/2 binary64) (/.f64 (cos.f64 x) eps)) eps)) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 (fma.f64 (sin.f64 x) (fma.f64 (.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) (.f64 #s(approx ( -1/6 (cos x)) #s(literal -1/6 binary64)) eps)) eps (cos.f64 x)) eps))
(.f64 (.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 0 binary64) eps))) #s(literal 2 binary64)) (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64))))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 (fma.f64 #s(literal -1/6 binary64) #s(approx ( (cos x) eps) (fma.f64 (fma.f64 (.f64 (.f64 x eps) x) #s(literal 1/24 binary64) (.f64 #s(literal -1/2 binary64) eps)) (.f64 x x) eps)) (*.f64 (sin.f64 x) #s(literal -1/2 binary64))) eps (cos.f64 x)) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 (fma.f64 (sin.f64 x) (fma.f64 (.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) (.f64 #s(approx ( -1/6 (cos x)) (fma.f64 (fma.f64 #s(literal -1/144 binary64) (.f64 x x) #s(literal 1/12 binary64)) (.f64 x x) #s(literal -1/6 binary64))) eps)) eps (cos.f64 x)) eps))

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

Calls

3 calls:

27.0ms	x
10.0ms	(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
10.0ms	eps

Results

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

Compiler

Compiled 9 to 10 computations (-11.1% saved)

regimes29.0ms (0.2%)

Memory

17.1MiB live, 17.1MiB allocated

Counts

36 → 1

Calls

Call 1

Inputs
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (* (sin x) -1/2) eps) (cos x)) #s(literal 1 binary64)) eps))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (cos x) eps) #s(approx (+ (* (* -1/2 x) (* x eps)) eps) (.f64 (.f64 (*.f64 x eps) x) #s(literal -1/2 binary64)))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (cos x) eps) (fma.f64 (.f64 #s(literal -1/2 binary64) x) (.f64 x eps) eps)))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (* (sin x) -1/2) eps) (cos x)) (fma.f64 (*.f64 #s(literal -1/2 binary64) eps) x #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (* (sin x) -1/2) eps) (cos x)) (fma.f64 (*.f64 x eps) #s(literal -1/2 binary64) #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (cos x) eps) (+.f64 (.f64 (.f64 (*.f64 eps x) #s(literal -1/2 binary64)) x) eps)))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (* (sin x) -1/2) eps) (cos x)) (fma.f64 (*.f64 (+.f64 x eps) #s(literal -1/2 binary64)) x #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (+ (* (sin x) (+ (* (* eps eps) 1/24) -1/2)) (* (* -1/6 (cos x)) eps)) eps) (cos x)) #s(approx (+ (* (+ (* (+ (* 1/12 (* eps eps)) -1/2) x) (* (+ (* (* eps eps) 1/24) -1/2) eps)) x) (+ (* (* eps eps) -1/6) 1)) (fma.f64 (*.f64 x (+.f64 x eps)) #s(literal -1/2 binary64) #s(literal 1 binary64)))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (cos x) eps) (fma.f64 (.f64 eps (fma.f64 (.f64 x x) #s(literal 1/24 binary64) #s(literal -1/2 binary64))) (*.f64 x x) eps)))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (cos x) (fma.f64 (.f64 (fma.f64 #s(literal 1/24 binary64) (*.f64 x x) #s(literal -1/2 binary64)) x) x #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (cos x) (fma.f64 (fma.f64 (.f64 x x) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) (*.f64 x x) #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (+ (* -1/6 (* (cos x) eps)) (* (sin x) -1/2)) eps) (cos x)) (fma.f64 (.f64 x eps) #s(literal -1/2 binary64) (fma.f64 (.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64)))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (cos x) (+.f64 (.f64 (.f64 (fma.f64 #s(literal 1/24 binary64) (.f64 x x) #s(literal -1/2 binary64)) x) x) #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (+ (* (sin x) (+ (* (* eps eps) 1/24) -1/2)) (* (* -1/6 (cos x)) eps)) eps) (cos x)) (fma.f64 #s(approx (+ (* (+ (* 1/12 (* eps eps)) -1/2) x) (* (+ (* (* eps eps) 1/24) -1/2) eps)) (.f64 (+.f64 x eps) #s(literal -1/2 binary64))) x (fma.f64 (.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64)))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (* (sin x) -1/2) eps) (cos x)) (fma.f64 (fma.f64 (fma.f64 (.f64 #s(literal 1/12 binary64) eps) x #s(literal -1/2 binary64)) x (.f64 #s(literal -1/2 binary64) eps)) x #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (+ (* (sin x) (+ (* (* eps eps) 1/24) -1/2)) (* (* -1/6 (cos x)) eps)) eps) (cos x)) (fma.f64 eps (fma.f64 (fma.f64 (.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) x (.f64 #s(literal -1/6 binary64) eps)) #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (cos x) (fma.f64 (fma.f64 (fma.f64 #s(literal -1/720 binary64) (.f64 x x) #s(literal 1/24 binary64)) (.f64 x x) #s(literal -1/2 binary64)) (.f64 x x) #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (* (sin x) -1/2) eps) (cos x)) #s(approx (+ (* (+ (* (+ (* (* 1/12 eps) x) -1/2) x) (* -1/2 eps)) x) 1) (.f64 (fma.f64 (neg.f64 (fma.f64 #s(literal -1/12 binary64) (.f64 x x) #s(literal 1/2 binary64))) x (/.f64 (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64)) eps)) eps))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (+ (* (sin x) (+ (* (* eps eps) 1/24) -1/2)) (* (* -1/6 (cos x)) eps)) eps) (cos x)) (fma.f64 (fma.f64 (fma.f64 #s(literal 1/12 binary64) (.f64 eps eps) #s(literal -1/2 binary64)) x (.f64 (fma.f64 (.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) eps)) x (fma.f64 (.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64)))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (sin.f64 eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (cos.f64 x) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 #s(approx ( (sin x) -1/2) (*.f64 #s(literal -1/2 binary64) x)) eps (cos.f64 x)) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 #s(approx (+ ( (sin x) (+ (* (* eps eps) 1/24) -1/2)) (* (* -1/6 (cos x)) eps)) (*.f64 #s(literal -1/6 binary64) eps)) eps (cos.f64 x)) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 #s(approx (+ ( -1/6 (* (cos x) eps)) (* (sin x) -1/2)) (fma.f64 #s(literal -1/6 binary64) eps (*.f64 #s(literal -1/2 binary64) x))) eps (cos.f64 x)) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 #s(approx ( (sin x) -1/2) (.f64 (fma.f64 (.f64 x x) #s(literal 1/12 binary64) #s(literal -1/2 binary64)) x)) eps (cos.f64 x)) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 #s(approx (+ ( (sin x) (+ (* (* eps eps) 1/24) -1/2)) (* (* -1/6 (cos x)) eps)) (fma.f64 (fma.f64 (.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) x (.f64 #s(literal -1/6 binary64) eps))) eps (cos.f64 x)) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 #s(approx (+ ( -1/6 (* (cos x) eps)) (* (sin x) -1/2)) (fma.f64 (fma.f64 (.f64 (+.f64 x eps) #s(literal 1/12 binary64)) x #s(literal -1/2 binary64)) x (.f64 #s(literal -1/6 binary64) eps))) eps (cos.f64 x)) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 #s(approx ( (sin x) -1/2) (.f64 (fma.f64 (fma.f64 #s(literal -1/240 binary64) (.f64 x x) #s(literal 1/12 binary64)) (*.f64 x x) #s(literal -1/2 binary64)) x)) eps (cos.f64 x)) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 #s(approx ( (sin x) -1/2) (.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 1/10080 binary64) (.f64 x x) #s(literal -1/240 binary64)) (.f64 x x) #s(literal 1/12 binary64)) (.f64 x x) #s(literal -1/2 binary64)) x)) eps (cos.f64 x)) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 #s(approx (+ ( (sin x) (+ (* (* eps eps) 1/24) -1/2)) (* (* -1/6 (cos x)) eps)) (fma.f64 (fma.f64 (fma.f64 #s(literal 1/12 binary64) eps (.f64 (.f64 (fma.f64 (.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) x) #s(literal -1/6 binary64))) x (fma.f64 (.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64))) x (*.f64 #s(literal -1/6 binary64) eps))) eps (cos.f64 x)) eps))
(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 (.f64 (sin.f64 x) #s(literal -1/2 binary64)) eps (cos.f64 x)) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (fma.f64 (.f64 (.f64 #s(literal -1/2 binary64) (sin.f64 x)) eps) eps (*.f64 (cos.f64 x) eps)))
(-.f64 (sin.f64 (+.f64 x eps)) #s(approx (sin x) (fma.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 #s(literal 1/120 binary64) (*.f64 x x) #s(literal -1/6 binary64)) x)))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (* (sin x) -1/2) eps) (cos x)) (*.f64 (fma.f64 (sin.f64 x) #s(literal -1/2 binary64) (/.f64 (cos.f64 x) eps)) eps)) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 (fma.f64 (sin.f64 x) (fma.f64 (.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) (.f64 #s(approx ( -1/6 (cos x)) #s(literal -1/6 binary64)) eps)) eps (cos.f64 x)) eps))

Outputs

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

Calls

3 calls:

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

regimes108.0ms (0.9%)

Memory

-14.0MiB live, 24.4MiB allocated

Counts

35 → 1

Calls

Call 1

Inputs
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (* (sin x) -1/2) eps) (cos x)) #s(literal 1 binary64)) eps))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (cos x) eps) #s(approx (+ (* (* -1/2 x) (* x eps)) eps) (.f64 (.f64 (*.f64 x eps) x) #s(literal -1/2 binary64)))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (cos x) eps) (fma.f64 (.f64 #s(literal -1/2 binary64) x) (.f64 x eps) eps)))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (* (sin x) -1/2) eps) (cos x)) (fma.f64 (*.f64 #s(literal -1/2 binary64) eps) x #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (* (sin x) -1/2) eps) (cos x)) (fma.f64 (*.f64 x eps) #s(literal -1/2 binary64) #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (cos x) eps) (+.f64 (.f64 (.f64 (*.f64 eps x) #s(literal -1/2 binary64)) x) eps)))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (* (sin x) -1/2) eps) (cos x)) (fma.f64 (*.f64 (+.f64 x eps) #s(literal -1/2 binary64)) x #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (+ (* (sin x) (+ (* (* eps eps) 1/24) -1/2)) (* (* -1/6 (cos x)) eps)) eps) (cos x)) #s(approx (+ (* (+ (* (+ (* 1/12 (* eps eps)) -1/2) x) (* (+ (* (* eps eps) 1/24) -1/2) eps)) x) (+ (* (* eps eps) -1/6) 1)) (fma.f64 (*.f64 x (+.f64 x eps)) #s(literal -1/2 binary64) #s(literal 1 binary64)))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (cos x) eps) (fma.f64 (.f64 eps (fma.f64 (.f64 x x) #s(literal 1/24 binary64) #s(literal -1/2 binary64))) (*.f64 x x) eps)))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (cos x) (fma.f64 (.f64 (fma.f64 #s(literal 1/24 binary64) (*.f64 x x) #s(literal -1/2 binary64)) x) x #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (cos x) (fma.f64 (fma.f64 (.f64 x x) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) (*.f64 x x) #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (+ (* -1/6 (* (cos x) eps)) (* (sin x) -1/2)) eps) (cos x)) (fma.f64 (.f64 x eps) #s(literal -1/2 binary64) (fma.f64 (.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64)))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (cos x) (+.f64 (.f64 (.f64 (fma.f64 #s(literal 1/24 binary64) (.f64 x x) #s(literal -1/2 binary64)) x) x) #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (+ (* (sin x) (+ (* (* eps eps) 1/24) -1/2)) (* (* -1/6 (cos x)) eps)) eps) (cos x)) (fma.f64 #s(approx (+ (* (+ (* 1/12 (* eps eps)) -1/2) x) (* (+ (* (* eps eps) 1/24) -1/2) eps)) (.f64 (+.f64 x eps) #s(literal -1/2 binary64))) x (fma.f64 (.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64)))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (* (sin x) -1/2) eps) (cos x)) (fma.f64 (fma.f64 (fma.f64 (.f64 #s(literal 1/12 binary64) eps) x #s(literal -1/2 binary64)) x (.f64 #s(literal -1/2 binary64) eps)) x #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (+ (* (sin x) (+ (* (* eps eps) 1/24) -1/2)) (* (* -1/6 (cos x)) eps)) eps) (cos x)) (fma.f64 eps (fma.f64 (fma.f64 (.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) x (.f64 #s(literal -1/6 binary64) eps)) #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (cos x) (fma.f64 (fma.f64 (fma.f64 #s(literal -1/720 binary64) (.f64 x x) #s(literal 1/24 binary64)) (.f64 x x) #s(literal -1/2 binary64)) (.f64 x x) #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (* (sin x) -1/2) eps) (cos x)) #s(approx (+ (* (+ (* (+ (* (* 1/12 eps) x) -1/2) x) (* -1/2 eps)) x) 1) (.f64 (fma.f64 (neg.f64 (fma.f64 #s(literal -1/12 binary64) (.f64 x x) #s(literal 1/2 binary64))) x (/.f64 (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64)) eps)) eps))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (+ (* (sin x) (+ (* (* eps eps) 1/24) -1/2)) (* (* -1/6 (cos x)) eps)) eps) (cos x)) (fma.f64 (fma.f64 (fma.f64 #s(literal 1/12 binary64) (.f64 eps eps) #s(literal -1/2 binary64)) x (.f64 (fma.f64 (.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) eps)) x (fma.f64 (.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64)))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (sin.f64 eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (cos.f64 x) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 #s(approx ( (sin x) -1/2) (*.f64 #s(literal -1/2 binary64) x)) eps (cos.f64 x)) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 #s(approx (+ ( (sin x) (+ (* (* eps eps) 1/24) -1/2)) (* (* -1/6 (cos x)) eps)) (*.f64 #s(literal -1/6 binary64) eps)) eps (cos.f64 x)) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 #s(approx (+ ( -1/6 (* (cos x) eps)) (* (sin x) -1/2)) (fma.f64 #s(literal -1/6 binary64) eps (*.f64 #s(literal -1/2 binary64) x))) eps (cos.f64 x)) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 #s(approx ( (sin x) -1/2) (.f64 (fma.f64 (.f64 x x) #s(literal 1/12 binary64) #s(literal -1/2 binary64)) x)) eps (cos.f64 x)) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 #s(approx (+ ( (sin x) (+ (* (* eps eps) 1/24) -1/2)) (* (* -1/6 (cos x)) eps)) (fma.f64 (fma.f64 (.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) x (.f64 #s(literal -1/6 binary64) eps))) eps (cos.f64 x)) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 #s(approx (+ ( -1/6 (* (cos x) eps)) (* (sin x) -1/2)) (fma.f64 (fma.f64 (.f64 (+.f64 x eps) #s(literal 1/12 binary64)) x #s(literal -1/2 binary64)) x (.f64 #s(literal -1/6 binary64) eps))) eps (cos.f64 x)) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 #s(approx ( (sin x) -1/2) (.f64 (fma.f64 (fma.f64 #s(literal -1/240 binary64) (.f64 x x) #s(literal 1/12 binary64)) (*.f64 x x) #s(literal -1/2 binary64)) x)) eps (cos.f64 x)) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 #s(approx ( (sin x) -1/2) (.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 1/10080 binary64) (.f64 x x) #s(literal -1/240 binary64)) (.f64 x x) #s(literal 1/12 binary64)) (.f64 x x) #s(literal -1/2 binary64)) x)) eps (cos.f64 x)) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 #s(approx (+ ( (sin x) (+ (* (* eps eps) 1/24) -1/2)) (* (* -1/6 (cos x)) eps)) (fma.f64 (fma.f64 (fma.f64 #s(literal 1/12 binary64) eps (.f64 (.f64 (fma.f64 (.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) x) #s(literal -1/6 binary64))) x (fma.f64 (.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64))) x (*.f64 #s(literal -1/6 binary64) eps))) eps (cos.f64 x)) eps))
(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 (.f64 (sin.f64 x) #s(literal -1/2 binary64)) eps (cos.f64 x)) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (fma.f64 (.f64 (.f64 #s(literal -1/2 binary64) (sin.f64 x)) eps) eps (*.f64 (cos.f64 x) eps)))
(-.f64 (sin.f64 (+.f64 x eps)) #s(approx (sin x) (fma.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 #s(literal 1/120 binary64) (*.f64 x x) #s(literal -1/6 binary64)) x)))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (* (sin x) -1/2) eps) (cos x)) (*.f64 (fma.f64 (sin.f64 x) #s(literal -1/2 binary64) (/.f64 (cos.f64 x) eps)) eps)) eps))

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

Calls

3 calls:

89.0ms	x
9.0ms	(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
9.0ms	eps

Results

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

Compiler

Compiled 9 to 10 computations (-11.1% saved)

regimes26.0ms (0.2%)

Memory

31.8MiB live, 31.8MiB allocated

Counts

31 → 1

Calls

Call 1

Inputs
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (* (sin x) -1/2) eps) (cos x)) #s(literal 1 binary64)) eps))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (cos x) eps) #s(approx (+ (* (* -1/2 x) (* x eps)) eps) (.f64 (.f64 (*.f64 x eps) x) #s(literal -1/2 binary64)))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (cos x) eps) (fma.f64 (.f64 #s(literal -1/2 binary64) x) (.f64 x eps) eps)))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (* (sin x) -1/2) eps) (cos x)) (fma.f64 (*.f64 #s(literal -1/2 binary64) eps) x #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (* (sin x) -1/2) eps) (cos x)) (fma.f64 (*.f64 x eps) #s(literal -1/2 binary64) #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (cos x) eps) (+.f64 (.f64 (.f64 (*.f64 eps x) #s(literal -1/2 binary64)) x) eps)))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (* (sin x) -1/2) eps) (cos x)) (fma.f64 (*.f64 (+.f64 x eps) #s(literal -1/2 binary64)) x #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (+ (* (sin x) (+ (* (* eps eps) 1/24) -1/2)) (* (* -1/6 (cos x)) eps)) eps) (cos x)) #s(approx (+ (* (+ (* (+ (* 1/12 (* eps eps)) -1/2) x) (* (+ (* (* eps eps) 1/24) -1/2) eps)) x) (+ (* (* eps eps) -1/6) 1)) (fma.f64 (*.f64 x (+.f64 x eps)) #s(literal -1/2 binary64) #s(literal 1 binary64)))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (cos x) eps) (fma.f64 (.f64 eps (fma.f64 (.f64 x x) #s(literal 1/24 binary64) #s(literal -1/2 binary64))) (*.f64 x x) eps)))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (cos x) (fma.f64 (.f64 (fma.f64 #s(literal 1/24 binary64) (*.f64 x x) #s(literal -1/2 binary64)) x) x #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (cos x) (fma.f64 (fma.f64 (.f64 x x) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) (*.f64 x x) #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (+ (* -1/6 (* (cos x) eps)) (* (sin x) -1/2)) eps) (cos x)) (fma.f64 (.f64 x eps) #s(literal -1/2 binary64) (fma.f64 (.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64)))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (cos x) (+.f64 (.f64 (.f64 (fma.f64 #s(literal 1/24 binary64) (.f64 x x) #s(literal -1/2 binary64)) x) x) #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (+ (* (sin x) (+ (* (* eps eps) 1/24) -1/2)) (* (* -1/6 (cos x)) eps)) eps) (cos x)) (fma.f64 #s(approx (+ (* (+ (* 1/12 (* eps eps)) -1/2) x) (* (+ (* (* eps eps) 1/24) -1/2) eps)) (.f64 (+.f64 x eps) #s(literal -1/2 binary64))) x (fma.f64 (.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64)))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (* (sin x) -1/2) eps) (cos x)) (fma.f64 (fma.f64 (fma.f64 (.f64 #s(literal 1/12 binary64) eps) x #s(literal -1/2 binary64)) x (.f64 #s(literal -1/2 binary64) eps)) x #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (+ (* (sin x) (+ (* (* eps eps) 1/24) -1/2)) (* (* -1/6 (cos x)) eps)) eps) (cos x)) (fma.f64 eps (fma.f64 (fma.f64 (.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) x (.f64 #s(literal -1/6 binary64) eps)) #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (cos x) (fma.f64 (fma.f64 (fma.f64 #s(literal -1/720 binary64) (.f64 x x) #s(literal 1/24 binary64)) (.f64 x x) #s(literal -1/2 binary64)) (.f64 x x) #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (* (sin x) -1/2) eps) (cos x)) #s(approx (+ (* (+ (* (+ (* (* 1/12 eps) x) -1/2) x) (* -1/2 eps)) x) 1) (.f64 (fma.f64 (neg.f64 (fma.f64 #s(literal -1/12 binary64) (.f64 x x) #s(literal 1/2 binary64))) x (/.f64 (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64)) eps)) eps))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (+ (* (sin x) (+ (* (* eps eps) 1/24) -1/2)) (* (* -1/6 (cos x)) eps)) eps) (cos x)) (fma.f64 (fma.f64 (fma.f64 #s(literal 1/12 binary64) (.f64 eps eps) #s(literal -1/2 binary64)) x (.f64 (fma.f64 (.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) eps)) x (fma.f64 (.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64)))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (sin.f64 eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (cos.f64 x) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 #s(approx ( (sin x) -1/2) (*.f64 #s(literal -1/2 binary64) x)) eps (cos.f64 x)) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 #s(approx (+ ( (sin x) (+ (* (* eps eps) 1/24) -1/2)) (* (* -1/6 (cos x)) eps)) (*.f64 #s(literal -1/6 binary64) eps)) eps (cos.f64 x)) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 #s(approx (+ ( -1/6 (* (cos x) eps)) (* (sin x) -1/2)) (fma.f64 #s(literal -1/6 binary64) eps (*.f64 #s(literal -1/2 binary64) x))) eps (cos.f64 x)) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 #s(approx ( (sin x) -1/2) (.f64 (fma.f64 (.f64 x x) #s(literal 1/12 binary64) #s(literal -1/2 binary64)) x)) eps (cos.f64 x)) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 #s(approx (+ ( (sin x) (+ (* (* eps eps) 1/24) -1/2)) (* (* -1/6 (cos x)) eps)) (fma.f64 (fma.f64 (.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) x (.f64 #s(literal -1/6 binary64) eps))) eps (cos.f64 x)) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 #s(approx (+ ( -1/6 (* (cos x) eps)) (* (sin x) -1/2)) (fma.f64 (fma.f64 (.f64 (+.f64 x eps) #s(literal 1/12 binary64)) x #s(literal -1/2 binary64)) x (.f64 #s(literal -1/6 binary64) eps))) eps (cos.f64 x)) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 #s(approx ( (sin x) -1/2) (.f64 (fma.f64 (fma.f64 #s(literal -1/240 binary64) (.f64 x x) #s(literal 1/12 binary64)) (*.f64 x x) #s(literal -1/2 binary64)) x)) eps (cos.f64 x)) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 #s(approx ( (sin x) -1/2) (.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 1/10080 binary64) (.f64 x x) #s(literal -1/240 binary64)) (.f64 x x) #s(literal 1/12 binary64)) (.f64 x x) #s(literal -1/2 binary64)) x)) eps (cos.f64 x)) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 #s(approx (+ ( (sin x) (+ (* (* eps eps) 1/24) -1/2)) (* (* -1/6 (cos x)) eps)) (fma.f64 (fma.f64 (fma.f64 #s(literal 1/12 binary64) eps (.f64 (.f64 (fma.f64 (.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) x) #s(literal -1/6 binary64))) x (fma.f64 (.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64))) x (*.f64 #s(literal -1/6 binary64) eps))) eps (cos.f64 x)) eps))
(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))

Outputs

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

Calls

3 calls:

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

Results

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

Compiler

Compiled 9 to 10 computations (-11.1% saved)

regimes32.0ms (0.3%)

Memory

-11.4MiB live, 27.4MiB allocated

Counts

29 → 1

Calls

Call 1

Inputs
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (* (sin x) -1/2) eps) (cos x)) #s(literal 1 binary64)) eps))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (cos x) eps) #s(approx (+ (* (* -1/2 x) (* x eps)) eps) (.f64 (.f64 (*.f64 x eps) x) #s(literal -1/2 binary64)))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (cos x) eps) (fma.f64 (.f64 #s(literal -1/2 binary64) x) (.f64 x eps) eps)))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (* (sin x) -1/2) eps) (cos x)) (fma.f64 (*.f64 #s(literal -1/2 binary64) eps) x #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (* (sin x) -1/2) eps) (cos x)) (fma.f64 (*.f64 x eps) #s(literal -1/2 binary64) #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (cos x) eps) (+.f64 (.f64 (.f64 (*.f64 eps x) #s(literal -1/2 binary64)) x) eps)))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (* (sin x) -1/2) eps) (cos x)) (fma.f64 (*.f64 (+.f64 x eps) #s(literal -1/2 binary64)) x #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (+ (* (sin x) (+ (* (* eps eps) 1/24) -1/2)) (* (* -1/6 (cos x)) eps)) eps) (cos x)) #s(approx (+ (* (+ (* (+ (* 1/12 (* eps eps)) -1/2) x) (* (+ (* (* eps eps) 1/24) -1/2) eps)) x) (+ (* (* eps eps) -1/6) 1)) (fma.f64 (*.f64 x (+.f64 x eps)) #s(literal -1/2 binary64) #s(literal 1 binary64)))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (cos x) eps) (fma.f64 (.f64 eps (fma.f64 (.f64 x x) #s(literal 1/24 binary64) #s(literal -1/2 binary64))) (*.f64 x x) eps)))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (cos x) (fma.f64 (.f64 (fma.f64 #s(literal 1/24 binary64) (*.f64 x x) #s(literal -1/2 binary64)) x) x #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (cos x) (fma.f64 (fma.f64 (.f64 x x) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) (*.f64 x x) #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (+ (* -1/6 (* (cos x) eps)) (* (sin x) -1/2)) eps) (cos x)) (fma.f64 (.f64 x eps) #s(literal -1/2 binary64) (fma.f64 (.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64)))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (cos x) (+.f64 (.f64 (.f64 (fma.f64 #s(literal 1/24 binary64) (.f64 x x) #s(literal -1/2 binary64)) x) x) #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (+ (* (sin x) (+ (* (* eps eps) 1/24) -1/2)) (* (* -1/6 (cos x)) eps)) eps) (cos x)) (fma.f64 #s(approx (+ (* (+ (* 1/12 (* eps eps)) -1/2) x) (* (+ (* (* eps eps) 1/24) -1/2) eps)) (.f64 (+.f64 x eps) #s(literal -1/2 binary64))) x (fma.f64 (.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64)))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (* (sin x) -1/2) eps) (cos x)) (fma.f64 (fma.f64 (fma.f64 (.f64 #s(literal 1/12 binary64) eps) x #s(literal -1/2 binary64)) x (.f64 #s(literal -1/2 binary64) eps)) x #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (+ (* (sin x) (+ (* (* eps eps) 1/24) -1/2)) (* (* -1/6 (cos x)) eps)) eps) (cos x)) (fma.f64 eps (fma.f64 (fma.f64 (.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) x (.f64 #s(literal -1/6 binary64) eps)) #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (cos x) (fma.f64 (fma.f64 (fma.f64 #s(literal -1/720 binary64) (.f64 x x) #s(literal 1/24 binary64)) (.f64 x x) #s(literal -1/2 binary64)) (.f64 x x) #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (* (sin x) -1/2) eps) (cos x)) #s(approx (+ (* (+ (* (+ (* (* 1/12 eps) x) -1/2) x) (* -1/2 eps)) x) 1) (.f64 (fma.f64 (neg.f64 (fma.f64 #s(literal -1/12 binary64) (.f64 x x) #s(literal 1/2 binary64))) x (/.f64 (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64)) eps)) eps))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (+ (* (sin x) (+ (* (* eps eps) 1/24) -1/2)) (* (* -1/6 (cos x)) eps)) eps) (cos x)) (fma.f64 (fma.f64 (fma.f64 #s(literal 1/12 binary64) (.f64 eps eps) #s(literal -1/2 binary64)) x (.f64 (fma.f64 (.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) eps)) x (fma.f64 (.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64)))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (sin.f64 eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (cos.f64 x) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 #s(approx ( (sin x) -1/2) (*.f64 #s(literal -1/2 binary64) x)) eps (cos.f64 x)) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 #s(approx (+ ( (sin x) (+ (* (* eps eps) 1/24) -1/2)) (* (* -1/6 (cos x)) eps)) (*.f64 #s(literal -1/6 binary64) eps)) eps (cos.f64 x)) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 #s(approx (+ ( -1/6 (* (cos x) eps)) (* (sin x) -1/2)) (fma.f64 #s(literal -1/6 binary64) eps (*.f64 #s(literal -1/2 binary64) x))) eps (cos.f64 x)) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 #s(approx ( (sin x) -1/2) (.f64 (fma.f64 (.f64 x x) #s(literal 1/12 binary64) #s(literal -1/2 binary64)) x)) eps (cos.f64 x)) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 #s(approx (+ ( (sin x) (+ (* (* eps eps) 1/24) -1/2)) (* (* -1/6 (cos x)) eps)) (fma.f64 (fma.f64 (.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) x (.f64 #s(literal -1/6 binary64) eps))) eps (cos.f64 x)) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 #s(approx (+ ( -1/6 (* (cos x) eps)) (* (sin x) -1/2)) (fma.f64 (fma.f64 (.f64 (+.f64 x eps) #s(literal 1/12 binary64)) x #s(literal -1/2 binary64)) x (.f64 #s(literal -1/6 binary64) eps))) eps (cos.f64 x)) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 #s(approx ( (sin x) -1/2) (.f64 (fma.f64 (fma.f64 #s(literal -1/240 binary64) (.f64 x x) #s(literal 1/12 binary64)) (*.f64 x x) #s(literal -1/2 binary64)) x)) eps (cos.f64 x)) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 #s(approx ( (sin x) -1/2) (.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 1/10080 binary64) (.f64 x x) #s(literal -1/240 binary64)) (.f64 x x) #s(literal 1/12 binary64)) (.f64 x x) #s(literal -1/2 binary64)) x)) eps (cos.f64 x)) eps))

Outputs

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

Calls

3 calls:

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

Results

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

Compiler

Compiled 9 to 10 computations (-11.1% saved)

regimes42.0ms (0.3%)

Memory

-2.8MiB live, 33.0MiB allocated

Counts

26 → 1

Calls

Call 1

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

Outputs

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

Calls

3 calls:

27.0ms	eps
7.0ms	(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
7.0ms	x

Results

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

Compiler

Compiled 9 to 10 computations (-11.1% saved)

regimes41.0ms (0.3%)

Memory

-8.8MiB live, 29.7MiB allocated

Counts

25 → 1

Calls

Call 1

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

Outputs

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

Calls

3 calls:

26.0ms	x
7.0ms	(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
7.0ms	eps

Results

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

Compiler

Compiled 9 to 10 computations (-11.1% saved)

regimes20.0ms (0.2%)

Memory

19.1MiB live, 19.1MiB allocated

Counts

23 → 1

Calls

Call 1

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

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

Calls

3 calls:

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

Results

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

Compiler

Compiled 9 to 10 computations (-11.1% saved)

regimes21.0ms (0.2%)

Memory

-26.3MiB live, 12.3MiB allocated

Counts

21 → 1

Calls

Call 1

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

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

Calls

3 calls:

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

Results

Accuracy	Segments	Branch
99.0%	1	`x`
99.0%	1	`eps`
99.0%	1	`(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))`

Compiler

Compiled 9 to 10 computations (-11.1% saved)

regimes18.0ms (0.2%)

Memory

11.3MiB live, 11.3MiB allocated

Counts

20 → 1

Calls

Call 1

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

Outputs

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

Calls

3 calls:

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

Results

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

Compiler

Compiled 9 to 10 computations (-11.1% saved)

regimes15.0ms (0.1%)

Memory

10.9MiB live, 10.9MiB allocated

Counts

16 → 1

Calls

Call 1

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

Outputs

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

Calls

3 calls:

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

Results

Accuracy	Segments	Branch
98.3%	1	`x`
98.3%	1	`eps`
98.3%	1	`(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))`

Compiler

Compiled 9 to 10 computations (-11.1% saved)

regimes13.0ms (0.1%)

Memory

14.3MiB live, 14.3MiB allocated

Counts

13 → 1

Calls

Call 1

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

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

Calls

3 calls:

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

Results

Accuracy	Segments	Branch
98.3%	1	`x`
98.3%	1	`eps`
98.3%	1	`(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))`

Compiler

Compiled 9 to 10 computations (-11.1% saved)

regimes28.0ms (0.2%)

Memory

-33.8MiB live, 10.6MiB allocated

Counts

6 → 1

Calls

Call 1

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

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

Calls

3 calls:

23.0ms	(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
2.0ms	x
2.0ms	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 9 to 10 computations (-11.1% saved)

regimes5.0ms (0%)

Memory

8.3MiB live, 8.3MiB allocated

Accuracy

Total -59.2b remaining (-3839.9%)

Threshold costs -59.2b (-3839.9%)

Counts

2 → 1

Calls

Call 1

Inputs

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

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

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

Calls

3 calls:

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

Results

Accuracy	Segments	Branch
97.6%	1	`x`
97.6%	1	`eps`
97.6%	1	`(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))`

Compiler

Compiled 9 to 10 computations (-11.1% saved)

simplify50.0ms (0.4%)

Memory

1.1MiB live, 39.1MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	129	487
1	162	487

Stop Event

1×

saturated

Calls

Call 1

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

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

soundness1.3s (11.1%)

Memory

2.9MiB live, 852.0MiB allocated

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	358	4008
1	1094	3948
2	3176	3902
0	8144	3583
0	6	16
0	10	16
1	53	16
2	380	16
3	4766	16
0	8210	16
0	475	5649
1	1465	5566
2	4629	5562
0	8236	5080
0	107	496
1	314	496
2	775	489
3	2829	489
4	6198	489
0	8141	458

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 383 to 234 computations (38.9% saved)

preprocess125.0ms (1%)

Memory: -5.1MiB live, 184.3MiB allocated
Compiler: Compiled 550 to 242 computations (56% 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%)

analyze58.0ms (0.5%)

sample6.0s (50.4%)

explain84.0ms (0.7%)

preprocess25.0ms (0.2%)

eval0.0ms (0%)

prune0.0ms (0%)

simplify6.0ms (0%)

localize25.0ms (0.2%)

series5.0ms (0%)

simplify156.0ms (1.3%)

rewrite178.0ms (1.5%)

eval68.0ms (0.6%)

prune24.0ms (0.2%)

simplify332.0ms (2.8%)

localize124.0ms (1%)

series38.0ms (0.3%)

simplify206.0ms (1.7%)

rewrite167.0ms (1.4%)

eval194.0ms (1.6%)

prune61.0ms (0.5%)

simplify153.0ms (1.3%)

localize175.0ms (1.5%)

series50.0ms (0.4%)

simplify209.0ms (1.7%)

rewrite173.0ms (1.4%)

eval145.0ms (1.2%)

prune44.0ms (0.4%)

simplify315.0ms (2.6%)

localize197.0ms (1.6%)

series78.0ms (0.6%)

simplify192.0ms (1.6%)

rewrite189.0ms (1.6%)

eval134.0ms (1.1%)

prune101.0ms (0.8%)

regimes33.0ms (0.3%)

regimes60.0ms (0.5%)

regimes48.0ms (0.4%)

regimes29.0ms (0.2%)

regimes108.0ms (0.9%)

regimes26.0ms (0.2%)

regimes32.0ms (0.3%)

regimes42.0ms (0.3%)

regimes41.0ms (0.3%)

regimes20.0ms (0.2%)

regimes21.0ms (0.2%)

regimes18.0ms (0.2%)

regimes15.0ms (0.1%)

regimes13.0ms (0.1%)

regimes28.0ms (0.2%)

regimes5.0ms (0%)

simplify50.0ms (0.4%)

soundness1.3s (11.1%)

preprocess125.0ms (1%)

end0.0ms (0%)

Profiling

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

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