Metrics for 2sin (example 3.3)

start0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated

analyze57.0ms (0.4%)

Memory

0.2MiB live, 38.2MiB 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)

sample5.8s (45.4%)

Memory

-139.0MiB live, 6 755.2MiB allocated

Samples

3.3s	26 458×	0	invalid
548.0ms	5 496×	0	valid
432.0ms	2 760×	1	valid

Precisions

Click to see histograms. Total time spent on operations: 3.0s

const: 924.0ms (30.6% of total)

ival-sin: 518.0ms (17.2% of total)

ival-fabs: 283.0ms (9.4% of total)

ival-mult: 254.0ms (8.4% of total)

ival-add: 238.0ms (7.9% of total)

ival-<=: 216.0ms (7.2% of total)

ival-sub: 188.0ms (6.2% of total)

ival-<: 152.0ms (5% of total)

ival-and: 106.0ms (3.5% of total)

adjust: 80.0ms (2.7% of total)

exact: 45.0ms (1.5% of total)

ival-assert: 13.0ms (0.4% of total)

Bogosity

explain189.0ms (1.5%)

Memory

-20.2MiB live, 137.3MiB allocated

FPErrors

Click to see full error table

Ground Truth	Overpredictions	Example	Underpredictions	Example	Subexpression
222	1	(7.098671901067289e-281 3.468337395837275e-283)	4	(-5.10765458162282e-234 6.48440787637326e-236)	`(-.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	219	10
`sin.f64`	`(sin.f64 (+.f64 x eps))`	sensitivity	1	0

Confusion

	Predicted +	Predicted -
+	218	5
-	1	32

Precision

0.9954337899543378

Recall

0.9775784753363229

Confusion?

	Predicted +	Predicted Maybe	Predicted -
+	218	4	1
-	1	6	26

Precision?

0.9694323144104804

Recall?

0.9955156950672646

Freqs

test

number	freq
0	37
1	218
2	1

Total Confusion?

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

Precision?

1.0

Recall?

1.0

Samples

38.0ms	348×	0	valid
16.0ms	162×	1	valid
4.0ms	2×	3	valid

Compiler

Compiled 49 to 22 computations (55.1% saved)

Precisions

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

ival-sin: 12.0ms (55.7% of total)

adjust: 3.0ms (13.9% of total)

ival-add: 3.0ms (13.9% of total)

ival-sub: 3.0ms (13.9% of total)

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

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

preprocess24.0ms (0.2%)

Memory

28.4MiB live, 28.4MiB allocated

Algorithm

1×	egg-herbie

Rules

102×	`sub-neg`
80×	`lower-fma.f64`
80×	`lower-fma.f32`
68×	`cancel-sign-sub-inv`
64×	`associate--r+`

Iterations

Useful iterations: 0 (0.0ms)

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

Stop Event

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

Calls

Call 1

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

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

Compiler

Compiled 9 to 6 computations (33.3% saved)

eval0.0ms (0%)

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

prune1.0ms (0%)

Memory

1.0MiB live, 1.0MiB allocated

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	64.2%	(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))

Compiler

Compiled 9 to 6 computations (33.3% saved)

simplify87.0ms (0.7%)

Memory

-33.6MiB live, 9.8MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 4 expressions of interest:

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

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

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

Stop Event

1×	iter limit
1×	saturated
1×	iter limit

Calls

Call 1

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

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

localize24.0ms (0.2%)

Memory

32.6MiB live, 32.6MiB allocated

Localize:

Found 4 expressions of interest:

New	Metric	Score
accuracy	0	(+.f64 x eps)
accuracy	0	(sin.f64 x)
accuracy	0.06617166582991675	(sin.f64 (+.f64 x eps))
accuracy	22.848165987362542	(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))

Samples

8.0ms	174×	0	valid
8.0ms	81×	1	valid
2.0ms	1×	3	valid

Compiler

Compiled 20 to 8 computations (60% saved)

Precisions

Click to see histograms. Total time spent on operations: 11.0ms

ival-sin: 6.0ms (56.5% of total)

adjust: 2.0ms (18.8% of total)

ival-add: 2.0ms (18.8% of total)

ival-sub: 1.0ms (9.4% of total)

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

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

series73.0ms (0.6%)

Memory

-33.8MiB live, 5.6MiB 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 (sin eps) (taylor 0 x) (#s(alt (-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) (patch (-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) #<representation binary64>) () ())) ())
#s(alt (+ (sin eps) (* x (- (cos eps) 1))) (taylor 0 x) (#s(alt (-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) (patch (-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) #<representation binary64>) () ())) ())
#s(alt (+ (sin eps) (* x (- (+ (cos eps) (* -1/2 (* x (sin eps)))) 1))) (taylor 0 x) (#s(alt (-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) (patch (-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) #<representation binary64>) () ())) ())
#s(alt (+ (sin eps) (* x (- (+ (cos eps) (* x (+ (* -1/2 (sin eps)) (* x (+ 1/6 (* -1/6 (cos eps))))))) 1))) (taylor 0 x) (#s(alt (-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) (patch (-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) #<representation binary64>) () ())) ())
#s(alt (- (sin (+ eps x)) (sin x)) (taylor inf x) (#s(alt (-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) (patch (-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) #<representation binary64>) () ())) ())
#s(alt (- (sin (+ eps x)) (sin x)) (taylor inf x) (#s(alt (-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) (patch (-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) #<representation binary64>) () ())) ())
#s(alt (- (sin (+ eps x)) (sin x)) (taylor inf x) (#s(alt (-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) (patch (-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) #<representation binary64>) () ())) ())
#s(alt (- (sin (+ eps x)) (sin x)) (taylor inf x) (#s(alt (-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) (patch (-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) #<representation binary64>) () ())) ())
#s(alt (- (sin (- eps (* -1 x))) (sin x)) (taylor -inf x) (#s(alt (-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) (patch (-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) #<representation binary64>) () ())) ())
#s(alt (- (sin (- eps (* -1 x))) (sin x)) (taylor -inf x) (#s(alt (-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) (patch (-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) #<representation binary64>) () ())) ())
#s(alt (- (sin (- eps (* -1 x))) (sin x)) (taylor -inf x) (#s(alt (-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) (patch (-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) #<representation binary64>) () ())) ())
#s(alt (- (sin (- eps (* -1 x))) (sin x)) (taylor -inf x) (#s(alt (-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) (patch (-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) #<representation binary64>) () ())) ())
#s(alt (* eps (cos x)) (taylor 0 eps) (#s(alt (-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) (patch (-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) #<representation binary64>) () ())) ())
#s(alt (* eps (+ (cos x) (* -1/2 (* eps (sin x))))) (taylor 0 eps) (#s(alt (-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) (patch (-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) #<representation binary64>) () ())) ())
#s(alt (* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x))))))) (taylor 0 eps) (#s(alt (-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) (patch (-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) #<representation binary64>) () ())) ())
#s(alt (* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* eps (+ (* -1/6 (cos x)) (* 1/24 (* eps (sin x))))))))) (taylor 0 eps) (#s(alt (-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) (patch (-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) #<representation binary64>) () ())) ())
#s(alt (- (sin (+ eps x)) (sin x)) (taylor inf eps) (#s(alt (-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) (patch (-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) #<representation binary64>) () ())) ())
#s(alt (- (sin (+ eps x)) (sin x)) (taylor inf eps) (#s(alt (-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) (patch (-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) #<representation binary64>) () ())) ())
#s(alt (- (sin (+ eps x)) (sin x)) (taylor inf eps) (#s(alt (-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) (patch (-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) #<representation binary64>) () ())) ())
#s(alt (- (sin (+ eps x)) (sin x)) (taylor inf eps) (#s(alt (-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) (patch (-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) #<representation binary64>) () ())) ())
#s(alt (- (sin (- x (* -1 eps))) (sin x)) (taylor -inf eps) (#s(alt (-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) (patch (-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) #<representation binary64>) () ())) ())
#s(alt (- (sin (- x (* -1 eps))) (sin x)) (taylor -inf eps) (#s(alt (-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) (patch (-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) #<representation binary64>) () ())) ())
#s(alt (- (sin (- x (* -1 eps))) (sin x)) (taylor -inf eps) (#s(alt (-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) (patch (-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) #<representation binary64>) () ())) ())
#s(alt (- (sin (- x (* -1 eps))) (sin x)) (taylor -inf eps) (#s(alt (-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) (patch (-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) #<representation binary64>) () ())) ())
#s(alt (sin eps) (taylor 0 x) (#s(alt (sin.f64 (+.f64 x eps)) (patch (sin.f64 (+.f64 x eps)) #<representation binary64>) () ())) ())
#s(alt (+ (sin eps) (* x (cos eps))) (taylor 0 x) (#s(alt (sin.f64 (+.f64 x eps)) (patch (sin.f64 (+.f64 x eps)) #<representation binary64>) () ())) ())
#s(alt (+ (sin eps) (* x (+ (cos eps) (* -1/2 (* x (sin eps)))))) (taylor 0 x) (#s(alt (sin.f64 (+.f64 x eps)) (patch (sin.f64 (+.f64 x eps)) #<representation binary64>) () ())) ())
#s(alt (+ (sin eps) (* x (+ (cos eps) (* x (+ (* -1/2 (sin eps)) (* -1/6 (* x (cos eps)))))))) (taylor 0 x) (#s(alt (sin.f64 (+.f64 x eps)) (patch (sin.f64 (+.f64 x eps)) #<representation binary64>) () ())) ())
#s(alt (sin (+ eps x)) (taylor inf x) (#s(alt (sin.f64 (+.f64 x eps)) (patch (sin.f64 (+.f64 x eps)) #<representation binary64>) () ())) ())
#s(alt (sin (+ eps x)) (taylor inf x) (#s(alt (sin.f64 (+.f64 x eps)) (patch (sin.f64 (+.f64 x eps)) #<representation binary64>) () ())) ())
#s(alt (sin (+ eps x)) (taylor inf x) (#s(alt (sin.f64 (+.f64 x eps)) (patch (sin.f64 (+.f64 x eps)) #<representation binary64>) () ())) ())
#s(alt (sin (+ eps x)) (taylor inf x) (#s(alt (sin.f64 (+.f64 x eps)) (patch (sin.f64 (+.f64 x eps)) #<representation binary64>) () ())) ())
#s(alt (sin (- eps (* -1 x))) (taylor -inf x) (#s(alt (sin.f64 (+.f64 x eps)) (patch (sin.f64 (+.f64 x eps)) #<representation binary64>) () ())) ())
#s(alt (sin (- eps (* -1 x))) (taylor -inf x) (#s(alt (sin.f64 (+.f64 x eps)) (patch (sin.f64 (+.f64 x eps)) #<representation binary64>) () ())) ())
#s(alt (sin (- eps (* -1 x))) (taylor -inf x) (#s(alt (sin.f64 (+.f64 x eps)) (patch (sin.f64 (+.f64 x eps)) #<representation binary64>) () ())) ())
#s(alt (sin (- eps (* -1 x))) (taylor -inf x) (#s(alt (sin.f64 (+.f64 x eps)) (patch (sin.f64 (+.f64 x eps)) #<representation binary64>) () ())) ())
#s(alt (sin x) (taylor 0 eps) (#s(alt (sin.f64 (+.f64 x eps)) (patch (sin.f64 (+.f64 x eps)) #<representation binary64>) () ())) ())
#s(alt (+ (sin x) (* eps (cos x))) (taylor 0 eps) (#s(alt (sin.f64 (+.f64 x eps)) (patch (sin.f64 (+.f64 x eps)) #<representation binary64>) () ())) ())
#s(alt (+ (sin x) (* eps (+ (cos x) (* -1/2 (* eps (sin x)))))) (taylor 0 eps) (#s(alt (sin.f64 (+.f64 x eps)) (patch (sin.f64 (+.f64 x eps)) #<representation binary64>) () ())) ())
#s(alt (+ (sin x) (* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x)))))))) (taylor 0 eps) (#s(alt (sin.f64 (+.f64 x eps)) (patch (sin.f64 (+.f64 x eps)) #<representation binary64>) () ())) ())
#s(alt (sin (+ eps x)) (taylor inf eps) (#s(alt (sin.f64 (+.f64 x eps)) (patch (sin.f64 (+.f64 x eps)) #<representation binary64>) () ())) ())
#s(alt (sin (+ eps x)) (taylor inf eps) (#s(alt (sin.f64 (+.f64 x eps)) (patch (sin.f64 (+.f64 x eps)) #<representation binary64>) () ())) ())
#s(alt (sin (+ eps x)) (taylor inf eps) (#s(alt (sin.f64 (+.f64 x eps)) (patch (sin.f64 (+.f64 x eps)) #<representation binary64>) () ())) ())
#s(alt (sin (+ eps x)) (taylor inf eps) (#s(alt (sin.f64 (+.f64 x eps)) (patch (sin.f64 (+.f64 x eps)) #<representation binary64>) () ())) ())
#s(alt (sin (- x (* -1 eps))) (taylor -inf eps) (#s(alt (sin.f64 (+.f64 x eps)) (patch (sin.f64 (+.f64 x eps)) #<representation binary64>) () ())) ())
#s(alt (sin (- x (* -1 eps))) (taylor -inf eps) (#s(alt (sin.f64 (+.f64 x eps)) (patch (sin.f64 (+.f64 x eps)) #<representation binary64>) () ())) ())
#s(alt (sin (- x (* -1 eps))) (taylor -inf eps) (#s(alt (sin.f64 (+.f64 x eps)) (patch (sin.f64 (+.f64 x eps)) #<representation binary64>) () ())) ())
#s(alt (sin (- x (* -1 eps))) (taylor -inf eps) (#s(alt (sin.f64 (+.f64 x eps)) (patch (sin.f64 (+.f64 x eps)) #<representation binary64>) () ())) ())
#s(alt eps (taylor 0 x) (#s(alt (+.f64 x eps) (patch (+.f64 x eps) #<representation binary64>) () ())) ())
#s(alt (+ eps x) (taylor 0 x) (#s(alt (+.f64 x eps) (patch (+.f64 x eps) #<representation binary64>) () ())) ())
#s(alt (+ eps x) (taylor 0 x) (#s(alt (+.f64 x eps) (patch (+.f64 x eps) #<representation binary64>) () ())) ())
#s(alt (+ eps x) (taylor 0 x) (#s(alt (+.f64 x eps) (patch (+.f64 x eps) #<representation binary64>) () ())) ())
#s(alt x (taylor inf x) (#s(alt (+.f64 x eps) (patch (+.f64 x eps) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1 (/ eps x))) (taylor inf x) (#s(alt (+.f64 x eps) (patch (+.f64 x eps) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1 (/ eps x))) (taylor inf x) (#s(alt (+.f64 x eps) (patch (+.f64 x eps) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1 (/ eps x))) (taylor inf x) (#s(alt (+.f64 x eps) (patch (+.f64 x eps) #<representation binary64>) () ())) ())
#s(alt x (taylor -inf x) (#s(alt (+.f64 x eps) (patch (+.f64 x eps) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (- (* -1 (/ eps x)) 1))) (taylor -inf x) (#s(alt (+.f64 x eps) (patch (+.f64 x eps) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (- (* -1 (/ eps x)) 1))) (taylor -inf x) (#s(alt (+.f64 x eps) (patch (+.f64 x eps) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (- (* -1 (/ eps x)) 1))) (taylor -inf x) (#s(alt (+.f64 x eps) (patch (+.f64 x eps) #<representation binary64>) () ())) ())
#s(alt x (taylor 0 eps) (#s(alt (+.f64 x eps) (patch (+.f64 x eps) #<representation binary64>) () ())) ())
#s(alt (+ eps x) (taylor 0 eps) (#s(alt (+.f64 x eps) (patch (+.f64 x eps) #<representation binary64>) () ())) ())
#s(alt (+ eps x) (taylor 0 eps) (#s(alt (+.f64 x eps) (patch (+.f64 x eps) #<representation binary64>) () ())) ())
#s(alt (+ eps x) (taylor 0 eps) (#s(alt (+.f64 x eps) (patch (+.f64 x eps) #<representation binary64>) () ())) ())
#s(alt eps (taylor inf eps) (#s(alt (+.f64 x eps) (patch (+.f64 x eps) #<representation binary64>) () ())) ())
#s(alt (* eps (+ 1 (/ x eps))) (taylor inf eps) (#s(alt (+.f64 x eps) (patch (+.f64 x eps) #<representation binary64>) () ())) ())
#s(alt (* eps (+ 1 (/ x eps))) (taylor inf eps) (#s(alt (+.f64 x eps) (patch (+.f64 x eps) #<representation binary64>) () ())) ())
#s(alt (* eps (+ 1 (/ x eps))) (taylor inf eps) (#s(alt (+.f64 x eps) (patch (+.f64 x eps) #<representation binary64>) () ())) ())
#s(alt eps (taylor -inf eps) (#s(alt (+.f64 x eps) (patch (+.f64 x eps) #<representation binary64>) () ())) ())
#s(alt (* -1 (* eps (- (* -1 (/ x eps)) 1))) (taylor -inf eps) (#s(alt (+.f64 x eps) (patch (+.f64 x eps) #<representation binary64>) () ())) ())
#s(alt (* -1 (* eps (- (* -1 (/ x eps)) 1))) (taylor -inf eps) (#s(alt (+.f64 x eps) (patch (+.f64 x eps) #<representation binary64>) () ())) ())
#s(alt (* -1 (* eps (- (* -1 (/ x eps)) 1))) (taylor -inf eps) (#s(alt (+.f64 x eps) (patch (+.f64 x eps) #<representation binary64>) () ())) ())
#s(alt x (taylor 0 x) (#s(alt (sin.f64 x) (patch (sin.f64 x) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1 (* -1/6 (pow x 2)))) (taylor 0 x) (#s(alt (sin.f64 x) (patch (sin.f64 x) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1 (* (pow x 2) (- (* 1/120 (pow x 2)) 1/6)))) (taylor 0 x) (#s(alt (sin.f64 x) (patch (sin.f64 x) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/120 (* -1/5040 (pow x 2)))) 1/6)))) (taylor 0 x) (#s(alt (sin.f64 x) (patch (sin.f64 x) #<representation binary64>) () ())) ())
#s(alt (sin x) (taylor inf x) (#s(alt (sin.f64 x) (patch (sin.f64 x) #<representation binary64>) () ())) ())
#s(alt (sin x) (taylor inf x) (#s(alt (sin.f64 x) (patch (sin.f64 x) #<representation binary64>) () ())) ())
#s(alt (sin x) (taylor inf x) (#s(alt (sin.f64 x) (patch (sin.f64 x) #<representation binary64>) () ())) ())
#s(alt (sin x) (taylor inf x) (#s(alt (sin.f64 x) (patch (sin.f64 x) #<representation binary64>) () ())) ())
#s(alt (sin x) (taylor -inf x) (#s(alt (sin.f64 x) (patch (sin.f64 x) #<representation binary64>) () ())) ())
#s(alt (sin x) (taylor -inf x) (#s(alt (sin.f64 x) (patch (sin.f64 x) #<representation binary64>) () ())) ())
#s(alt (sin x) (taylor -inf x) (#s(alt (sin.f64 x) (patch (sin.f64 x) #<representation binary64>) () ())) ())
#s(alt (sin x) (taylor -inf x) (#s(alt (sin.f64 x) (patch (sin.f64 x) #<representation binary64>) () ())) ())

Calls

21 calls:

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

simplify278.0ms (2.2%)

Memory

22.8MiB live, 254.8MiB allocated

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

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

Stop Event

1×	iter limit
1×	node limit

Counts

84 → 77

Calls

Call 1

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

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

rewrite313.0ms (2.4%)

Memory

-12.8MiB live, 309.0MiB allocated

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

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

Stop Event

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

Counts

4 → 214

Calls

Call 1

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

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

eval38.0ms (0.3%)

Memory: 19.1MiB live, 66.0MiB allocated
Compiler: Compiled 7 823 to 844 computations (89.2% saved)

prune44.0ms (0.3%)

Memory

-24.5MiB live, 90.3MiB allocated

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	283	8	291
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	283	9	292

Accuracy

100.0%

Counts

292 → 9

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	64.2%	(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
	63.9%	(-.f64 (sin.f64 (+.f64 x eps)) #s(approx (sin x) (fma.f64 (fma.f64 (.f64 x x) #s(literal 1/120 binary64) #s(literal -1/6 binary64)) (.f64 x (*.f64 x x)) x)))
▶	64.0%	(-.f64 (sin.f64 (+.f64 x eps)) #s(approx (sin x) (fma.f64 (fma.f64 x (.f64 x (fma.f64 (.f64 x x) #s(literal -1/5040 binary64) #s(literal 1/120 binary64))) #s(literal -1/6 binary64)) (.f64 x (.f64 x x)) x)))
▶	63.7%	(-.f64 (sin.f64 (+.f64 x eps)) #s(approx (sin x) (fma.f64 #s(literal -1/6 binary64) (.f64 x (.f64 x x)) x)))
▶	99.9%	(.f64 (.f64 (sin.f64 (.f64 (+.f64 eps #s(literal 0 binary64)) #s(literal 1/2 binary64))) (cos.f64 (.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)))) #s(literal 2 binary64))
▶	64.0%	#s(approx (- (sin (+ x eps)) (sin x)) (-.f64 (fma.f64 (fma.f64 x (.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64)) (sin.f64 eps) (.f64 x (cos.f64 eps))) x))
	99.7%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 eps (fma.f64 eps (.f64 #s(literal -1/2 binary64) (sin.f64 x)) (cos.f64 x))))
	99.4%	#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 eps (cos.f64 x)))
▶	98.0%	#s(approx (- (sin (+ x eps)) (sin x)) (sin.f64 eps))

Compiler

Compiled 257 to 152 computations (40.9% saved)

simplify232.0ms (1.8%)

Memory

18.8MiB live, 303.2MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 18 expressions of interest:

New	Metric	Score
cost-diff	0	(fma.f64 x (*.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64))
cost-diff	0	(fma.f64 (fma.f64 x (.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64)) (sin.f64 eps) (.f64 x (cos.f64 eps)))
cost-diff	0	(-.f64 (fma.f64 (fma.f64 x (.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64)) (sin.f64 eps) (.f64 x (cos.f64 eps))) x)
cost-diff	0	#s(approx (- (sin (+ x eps)) (sin x)) (-.f64 (fma.f64 (fma.f64 x (.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64)) (sin.f64 eps) (.f64 x (cos.f64 eps))) x))
cost-diff	0	#s(approx (sin x) (fma.f64 (fma.f64 x (.f64 x (fma.f64 (.f64 x x) #s(literal -1/5040 binary64) #s(literal 1/120 binary64))) #s(literal -1/6 binary64)) (.f64 x (.f64 x x)) x))
cost-diff	0	(+.f64 x eps)
cost-diff	0	(sin.f64 (+.f64 x eps))
cost-diff	0	(-.f64 (sin.f64 (+.f64 x eps)) #s(approx (sin x) (fma.f64 (fma.f64 x (.f64 x (fma.f64 (.f64 x x) #s(literal -1/5040 binary64) #s(literal 1/120 binary64))) #s(literal -1/6 binary64)) (.f64 x (.f64 x x)) x)))
cost-diff	0	#s(approx (sin x) (fma.f64 #s(literal -1/6 binary64) (.f64 x (.f64 x x)) x))
cost-diff	0	(+.f64 x eps)
cost-diff	0	(sin.f64 (+.f64 x eps))
cost-diff	0	(-.f64 (sin.f64 (+.f64 x eps)) #s(approx (sin x) (fma.f64 #s(literal -1/6 binary64) (.f64 x (.f64 x x)) x)))
cost-diff	0	(sin.f64 eps)
cost-diff	0	#s(approx (- (sin (+ x eps)) (sin x)) (sin.f64 eps))
cost-diff	0	(.f64 (sin.f64 (.f64 (+.f64 eps #s(literal 0 binary64)) #s(literal 1/2 binary64))) (cos.f64 (*.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64))))
cost-diff	0	(.f64 (.f64 (sin.f64 (.f64 (+.f64 eps #s(literal 0 binary64)) #s(literal 1/2 binary64))) (cos.f64 (.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)))) #s(literal 2 binary64))
cost-diff	192	(+.f64 eps #s(literal 0 binary64))
cost-diff	320	(*.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64))

Rules

13 786×	`lower-fma.f32`
13 772×	`lower-fma.f64`
4 990×	`lower-*.f32`
4 972×	`lower-*.f64`
2 050×	`lower-+.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	44	314
0	77	288
1	132	288
2	248	288
3	501	284
4	1194	284
5	3752	284
6	5836	284
0	8063	277

Stop Event

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

Calls

Call 1

Inputs
(.f64 (.f64 (sin.f64 (.f64 (+.f64 eps #s(literal 0 binary64)) #s(literal 1/2 binary64))) (cos.f64 (.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)))) #s(literal 2 binary64))
(.f64 (sin.f64 (.f64 (+.f64 eps #s(literal 0 binary64)) #s(literal 1/2 binary64))) (cos.f64 (*.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64))))
(sin.f64 (*.f64 (+.f64 eps #s(literal 0 binary64)) #s(literal 1/2 binary64)))
(*.f64 (+.f64 eps #s(literal 0 binary64)) #s(literal 1/2 binary64))
(+.f64 eps #s(literal 0 binary64))
eps
#s(literal 0 binary64)
#s(literal 1/2 binary64)
(cos.f64 (*.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)))
(*.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64))
(fma.f64 x #s(literal 2 binary64) eps)
x
#s(literal 2 binary64)
#s(approx (- (sin (+ x eps)) (sin x)) (sin.f64 eps))
(sin.f64 eps)
eps
(-.f64 (sin.f64 (+.f64 x eps)) #s(approx (sin x) (fma.f64 #s(literal -1/6 binary64) (.f64 x (.f64 x x)) x)))
(sin.f64 (+.f64 x eps))
(+.f64 x eps)
x
eps
#s(approx (sin x) (fma.f64 #s(literal -1/6 binary64) (.f64 x (.f64 x x)) x))
(fma.f64 #s(literal -1/6 binary64) (.f64 x (.f64 x x)) x)
#s(literal -1/6 binary64)
(.f64 x (.f64 x x))
(*.f64 x x)
(-.f64 (sin.f64 (+.f64 x eps)) #s(approx (sin x) (fma.f64 (fma.f64 x (.f64 x (fma.f64 (.f64 x x) #s(literal -1/5040 binary64) #s(literal 1/120 binary64))) #s(literal -1/6 binary64)) (.f64 x (.f64 x x)) x)))
(sin.f64 (+.f64 x eps))
(+.f64 x eps)
x
eps
#s(approx (sin x) (fma.f64 (fma.f64 x (.f64 x (fma.f64 (.f64 x x) #s(literal -1/5040 binary64) #s(literal 1/120 binary64))) #s(literal -1/6 binary64)) (.f64 x (.f64 x x)) x))
(fma.f64 (fma.f64 x (.f64 x (fma.f64 (.f64 x x) #s(literal -1/5040 binary64) #s(literal 1/120 binary64))) #s(literal -1/6 binary64)) (.f64 x (.f64 x x)) x)
(fma.f64 x (.f64 x (fma.f64 (.f64 x x) #s(literal -1/5040 binary64) #s(literal 1/120 binary64))) #s(literal -1/6 binary64))
(.f64 x (fma.f64 (.f64 x x) #s(literal -1/5040 binary64) #s(literal 1/120 binary64)))
(fma.f64 (*.f64 x x) #s(literal -1/5040 binary64) #s(literal 1/120 binary64))
(*.f64 x x)
#s(literal -1/5040 binary64)
#s(literal 1/120 binary64)
#s(literal -1/6 binary64)
(.f64 x (.f64 x x))
#s(approx (- (sin (+ x eps)) (sin x)) (-.f64 (fma.f64 (fma.f64 x (.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64)) (sin.f64 eps) (.f64 x (cos.f64 eps))) x))
(-.f64 (fma.f64 (fma.f64 x (.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64)) (sin.f64 eps) (.f64 x (cos.f64 eps))) x)
(fma.f64 (fma.f64 x (.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64)) (sin.f64 eps) (.f64 x (cos.f64 eps)))
(fma.f64 x (*.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64))
x
(*.f64 x #s(literal -1/2 binary64))
#s(literal -1/2 binary64)
#s(literal 1 binary64)
(sin.f64 eps)
eps
(*.f64 x (cos.f64 eps))
(cos.f64 eps)

Outputs
(.f64 (.f64 (sin.f64 (.f64 (+.f64 eps #s(literal 0 binary64)) #s(literal 1/2 binary64))) (cos.f64 (.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)))) #s(literal 2 binary64))
(.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (*.f64 #s(literal 2 binary64) (cos.f64 (fma.f64 eps #s(literal 1/2 binary64) x))))
(.f64 (sin.f64 (.f64 (+.f64 eps #s(literal 0 binary64)) #s(literal 1/2 binary64))) (cos.f64 (*.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64))))
(.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (cos.f64 (fma.f64 eps #s(literal 1/2 binary64) x)))
(sin.f64 (*.f64 (+.f64 eps #s(literal 0 binary64)) #s(literal 1/2 binary64)))
(sin.f64 (*.f64 eps #s(literal 1/2 binary64)))
(*.f64 (+.f64 eps #s(literal 0 binary64)) #s(literal 1/2 binary64))
(*.f64 eps #s(literal 1/2 binary64))
(+.f64 eps #s(literal 0 binary64))
eps
eps
#s(literal 0 binary64)
#s(literal 1/2 binary64)
(cos.f64 (*.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)))
(cos.f64 (fma.f64 eps #s(literal 1/2 binary64) x))
(*.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64))
(fma.f64 eps #s(literal 1/2 binary64) x)
(fma.f64 x #s(literal 2 binary64) eps)
x
#s(literal 2 binary64)
#s(approx (- (sin (+ x eps)) (sin x)) (sin.f64 eps))
(sin.f64 eps)
eps
(-.f64 (sin.f64 (+.f64 x eps)) #s(approx (sin x) (fma.f64 #s(literal -1/6 binary64) (.f64 x (.f64 x x)) x)))
(-.f64 (sin.f64 (+.f64 eps x)) #s(approx (sin x) (fma.f64 x (.f64 #s(literal -1/6 binary64) (.f64 x x)) x)))
(sin.f64 (+.f64 x eps))
(sin.f64 (+.f64 eps x))
(+.f64 x eps)
(+.f64 eps x)
x
eps
#s(approx (sin x) (fma.f64 #s(literal -1/6 binary64) (.f64 x (.f64 x x)) x))
#s(approx (sin x) (fma.f64 x (.f64 #s(literal -1/6 binary64) (.f64 x x)) x))
(fma.f64 #s(literal -1/6 binary64) (.f64 x (.f64 x x)) x)
(fma.f64 x (.f64 #s(literal -1/6 binary64) (.f64 x x)) x)
#s(literal -1/6 binary64)
(.f64 x (.f64 x x))
(*.f64 x x)
(-.f64 (sin.f64 (+.f64 x eps)) #s(approx (sin x) (fma.f64 (fma.f64 x (.f64 x (fma.f64 (.f64 x x) #s(literal -1/5040 binary64) #s(literal 1/120 binary64))) #s(literal -1/6 binary64)) (.f64 x (.f64 x x)) x)))
(-.f64 (sin.f64 (+.f64 eps x)) #s(approx (sin x) (fma.f64 x (.f64 x (.f64 x (fma.f64 (.f64 x x) (fma.f64 (.f64 x x) #s(literal -1/5040 binary64) #s(literal 1/120 binary64)) #s(literal -1/6 binary64)))) x)))
(sin.f64 (+.f64 x eps))
(sin.f64 (+.f64 eps x))
(+.f64 x eps)
(+.f64 eps x)
x
eps
#s(approx (sin x) (fma.f64 (fma.f64 x (.f64 x (fma.f64 (.f64 x x) #s(literal -1/5040 binary64) #s(literal 1/120 binary64))) #s(literal -1/6 binary64)) (.f64 x (.f64 x x)) x))
#s(approx (sin x) (fma.f64 x (.f64 x (.f64 x (fma.f64 (.f64 x x) (fma.f64 (.f64 x x) #s(literal -1/5040 binary64) #s(literal 1/120 binary64)) #s(literal -1/6 binary64)))) x))
(fma.f64 (fma.f64 x (.f64 x (fma.f64 (.f64 x x) #s(literal -1/5040 binary64) #s(literal 1/120 binary64))) #s(literal -1/6 binary64)) (.f64 x (.f64 x x)) x)
(fma.f64 x (.f64 x (.f64 x (fma.f64 (.f64 x x) (fma.f64 (.f64 x x) #s(literal -1/5040 binary64) #s(literal 1/120 binary64)) #s(literal -1/6 binary64)))) x)
(fma.f64 x (.f64 x (fma.f64 (.f64 x x) #s(literal -1/5040 binary64) #s(literal 1/120 binary64))) #s(literal -1/6 binary64))
(fma.f64 (.f64 x x) (fma.f64 (.f64 x x) #s(literal -1/5040 binary64) #s(literal 1/120 binary64)) #s(literal -1/6 binary64))
(.f64 x (fma.f64 (.f64 x x) #s(literal -1/5040 binary64) #s(literal 1/120 binary64)))
(fma.f64 (*.f64 x x) #s(literal -1/5040 binary64) #s(literal 1/120 binary64))
(*.f64 x x)
#s(literal -1/5040 binary64)
#s(literal 1/120 binary64)
#s(literal -1/6 binary64)
(.f64 x (.f64 x x))
#s(approx (- (sin (+ x eps)) (sin x)) (-.f64 (fma.f64 (fma.f64 x (.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64)) (sin.f64 eps) (.f64 x (cos.f64 eps))) x))
#s(approx (- (sin (+ x eps)) (sin x)) (-.f64 (.f64 x (cos.f64 eps)) (fma.f64 (sin.f64 eps) (fma.f64 #s(literal 1/2 binary64) (.f64 x x) #s(literal -1 binary64)) x)))
(-.f64 (fma.f64 (fma.f64 x (.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64)) (sin.f64 eps) (.f64 x (cos.f64 eps))) x)
(-.f64 (.f64 x (cos.f64 eps)) (fma.f64 (sin.f64 eps) (fma.f64 #s(literal 1/2 binary64) (.f64 x x) #s(literal -1 binary64)) x))
(fma.f64 (fma.f64 x (.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64)) (sin.f64 eps) (.f64 x (cos.f64 eps)))
(fma.f64 x (cos.f64 eps) (.f64 (sin.f64 eps) (fma.f64 x (.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64))))
(fma.f64 x (*.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64))
x
(*.f64 x #s(literal -1/2 binary64))
#s(literal -1/2 binary64)
#s(literal 1 binary64)
(sin.f64 eps)
eps
(*.f64 x (cos.f64 eps))
(cos.f64 eps)

localize164.0ms (1.3%)

Memory

-21.6MiB live, 217.6MiB allocated

Localize:

Found 18 expressions of interest:

New	Metric	Score
accuracy	0.00390625	(*.f64 x (cos.f64 eps))
accuracy	0.01171875	(fma.f64 (fma.f64 x (.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64)) (sin.f64 eps) (.f64 x (cos.f64 eps)))
accuracy	0.6089016869101457	#s(approx (- (sin (+ x eps)) (sin x)) (-.f64 (fma.f64 (fma.f64 x (.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64)) (sin.f64 eps) (.f64 x (cos.f64 eps))) x))
accuracy	22.797516971885308	(-.f64 (fma.f64 (fma.f64 x (.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64)) (sin.f64 eps) (.f64 x (cos.f64 eps))) x)
accuracy	0.1015625	(.f64 x (fma.f64 (.f64 x x) #s(literal -1/5040 binary64) #s(literal 1/120 binary64)))
accuracy	0.1171875	(.f64 x (.f64 x x))
accuracy	0.2993589039382716	#s(approx (sin x) (fma.f64 (fma.f64 x (.f64 x (fma.f64 (.f64 x x) #s(literal -1/5040 binary64) #s(literal 1/120 binary64))) #s(literal -1/6 binary64)) (.f64 x (.f64 x x)) x))
accuracy	22.848165987362542	(-.f64 (sin.f64 (+.f64 x eps)) #s(approx (sin x) (fma.f64 (fma.f64 x (.f64 x (fma.f64 (.f64 x x) #s(literal -1/5040 binary64) #s(literal 1/120 binary64))) #s(literal -1/6 binary64)) (.f64 x (.f64 x x)) x)))
accuracy	0.06617166582991675	(sin.f64 (+.f64 x eps))
accuracy	0.1171875	(.f64 x (.f64 x x))
accuracy	0.5601548415582687	#s(approx (sin x) (fma.f64 #s(literal -1/6 binary64) (.f64 x (.f64 x x)) x))
accuracy	22.848165987362542	(-.f64 (sin.f64 (+.f64 x eps)) #s(approx (sin x) (fma.f64 #s(literal -1/6 binary64) (.f64 x (.f64 x x)) x)))
accuracy	0	(sin.f64 eps)
accuracy	1.2665934291908156	#s(approx (- (sin (+ x eps)) (sin x)) (sin.f64 eps))
accuracy	0.00390625	(.f64 (.f64 (sin.f64 (.f64 (+.f64 eps #s(literal 0 binary64)) #s(literal 1/2 binary64))) (cos.f64 (.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)))) #s(literal 2 binary64))
accuracy	0.00390625	(sin.f64 (*.f64 (+.f64 eps #s(literal 0 binary64)) #s(literal 1/2 binary64)))
accuracy	0.0078125	(.f64 (sin.f64 (.f64 (+.f64 eps #s(literal 0 binary64)) #s(literal 1/2 binary64))) (cos.f64 (*.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64))))
accuracy	0.04371266413587042	(cos.f64 (*.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)))

Samples

57.0ms	172×	0	valid
48.0ms	81×	1	valid
6.0ms	3×	3	valid

Compiler

Compiled 259 to 45 computations (82.6% saved)

Precisions

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

ival-mult: 30.0ms (35.6% of total)

ival-add: 16.0ms (19% of total)

const: 12.0ms (14.2% of total)

ival-sin: 10.0ms (11.9% of total)

adjust: 8.0ms (9.5% of total)

ival-cos: 5.0ms (5.9% of total)

ival-sub: 3.0ms (3.6% of total)

exact: 1.0ms (1.2% of total)

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

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

series31.0ms (0.2%)

Memory

34.6MiB live, 34.6MiB allocated

Counts

21 → 408

Calls

Call 1

Inputs
#s(alt (.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)) (patch (.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)) #<representation binary64>) () ())
#s(alt (+.f64 eps #s(literal 0 binary64)) (patch (+.f64 eps #s(literal 0 binary64)) #<representation binary64>) () ())
#s(alt (.f64 (.f64 (sin.f64 (.f64 (+.f64 eps #s(literal 0 binary64)) #s(literal 1/2 binary64))) (cos.f64 (.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)))) #s(literal 2 binary64)) (patch (.f64 (.f64 (sin.f64 (.f64 (+.f64 eps #s(literal 0 binary64)) #s(literal 1/2 binary64))) (cos.f64 (.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)))) #s(literal 2 binary64)) #<representation binary64>) () ())
#s(alt (.f64 (sin.f64 (.f64 (+.f64 eps #s(literal 0 binary64)) #s(literal 1/2 binary64))) (cos.f64 (.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)))) (patch (.f64 (sin.f64 (.f64 (+.f64 eps #s(literal 0 binary64)) #s(literal 1/2 binary64))) (cos.f64 (.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)))) #<representation binary64>) () ())
#s(alt #s(approx (- (sin (+ x eps)) (sin x)) (sin.f64 eps)) (patch #s(approx (- (sin (+ x eps)) (sin x)) (sin.f64 eps)) #<representation binary64>) () ())
#s(alt (sin.f64 eps) (patch (sin.f64 eps) #<representation binary64>) () ())
#s(alt (-.f64 (sin.f64 (+.f64 x eps)) #s(approx (sin x) (fma.f64 #s(literal -1/6 binary64) (.f64 x (.f64 x x)) x))) (patch (-.f64 (sin.f64 (+.f64 x eps)) #s(approx (sin x) (fma.f64 #s(literal -1/6 binary64) (.f64 x (.f64 x x)) x))) #<representation binary64>) () ())
#s(alt (sin.f64 (+.f64 x eps)) (patch (sin.f64 (+.f64 x eps)) #<representation binary64>) () ())
#s(alt (+.f64 x eps) (patch (+.f64 x eps) #<representation binary64>) () ())
#s(alt #s(approx (sin x) (fma.f64 #s(literal -1/6 binary64) (.f64 x (.f64 x x)) x)) (patch #s(approx (sin x) (fma.f64 #s(literal -1/6 binary64) (.f64 x (.f64 x x)) x)) #<representation binary64>) () ())
#s(alt (-.f64 (sin.f64 (+.f64 x eps)) #s(approx (sin x) (fma.f64 (fma.f64 x (.f64 x (fma.f64 (.f64 x x) #s(literal -1/5040 binary64) #s(literal 1/120 binary64))) #s(literal -1/6 binary64)) (.f64 x (.f64 x x)) x))) (patch (-.f64 (sin.f64 (+.f64 x eps)) #s(approx (sin x) (fma.f64 (fma.f64 x (.f64 x (fma.f64 (.f64 x x) #s(literal -1/5040 binary64) #s(literal 1/120 binary64))) #s(literal -1/6 binary64)) (.f64 x (.f64 x x)) x))) #<representation binary64>) () ())
#s(alt #s(approx (sin x) (fma.f64 (fma.f64 x (.f64 x (fma.f64 (.f64 x x) #s(literal -1/5040 binary64) #s(literal 1/120 binary64))) #s(literal -1/6 binary64)) (.f64 x (.f64 x x)) x)) (patch #s(approx (sin x) (fma.f64 (fma.f64 x (.f64 x (fma.f64 (.f64 x x) #s(literal -1/5040 binary64) #s(literal 1/120 binary64))) #s(literal -1/6 binary64)) (.f64 x (.f64 x x)) x)) #<representation binary64>) () ())
#s(alt #s(approx (- (sin (+ x eps)) (sin x)) (-.f64 (fma.f64 (fma.f64 x (.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64)) (sin.f64 eps) (.f64 x (cos.f64 eps))) x)) (patch #s(approx (- (sin (+ x eps)) (sin x)) (-.f64 (fma.f64 (fma.f64 x (.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64)) (sin.f64 eps) (.f64 x (cos.f64 eps))) x)) #<representation binary64>) () ())
#s(alt (-.f64 (fma.f64 (fma.f64 x (.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64)) (sin.f64 eps) (.f64 x (cos.f64 eps))) x) (patch (-.f64 (fma.f64 (fma.f64 x (.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64)) (sin.f64 eps) (.f64 x (cos.f64 eps))) x) #<representation binary64>) () ())
#s(alt (fma.f64 (fma.f64 x (.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64)) (sin.f64 eps) (.f64 x (cos.f64 eps))) (patch (fma.f64 (fma.f64 x (.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64)) (sin.f64 eps) (.f64 x (cos.f64 eps))) #<representation binary64>) () ())
#s(alt (fma.f64 x (.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64)) (patch (fma.f64 x (.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64)) #<representation binary64>) () ())
#s(alt (cos.f64 (.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64))) (patch (cos.f64 (.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64))) #<representation binary64>) () ())
#s(alt (sin.f64 (.f64 (+.f64 eps #s(literal 0 binary64)) #s(literal 1/2 binary64))) (patch (sin.f64 (.f64 (+.f64 eps #s(literal 0 binary64)) #s(literal 1/2 binary64))) #<representation binary64>) () ())
#s(alt (.f64 x (.f64 x x)) (patch (.f64 x (.f64 x x)) #<representation binary64>) () ())
#s(alt (.f64 x (fma.f64 (.f64 x x) #s(literal -1/5040 binary64) #s(literal 1/120 binary64))) (patch (.f64 x (fma.f64 (.f64 x x) #s(literal -1/5040 binary64) #s(literal 1/120 binary64))) #<representation binary64>) () ())
#s(alt (.f64 x (cos.f64 eps)) (patch (.f64 x (cos.f64 eps)) #<representation binary64>) () ())

Outputs
#s(alt (* 1/2 eps) (taylor 0 x) (#s(alt (.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)) (patch (.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt (+ x (* 1/2 eps)) (taylor 0 x) (#s(alt (.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)) (patch (.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt (+ x (* 1/2 eps)) (taylor 0 x) (#s(alt (.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)) (patch (.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt (+ x (* 1/2 eps)) (taylor 0 x) (#s(alt (.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)) (patch (.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt x (taylor inf x) (#s(alt (.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)) (patch (.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1 (* 1/2 (/ eps x)))) (taylor inf x) (#s(alt (.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)) (patch (.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1 (* 1/2 (/ eps x)))) (taylor inf x) (#s(alt (.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)) (patch (.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1 (* 1/2 (/ eps x)))) (taylor inf x) (#s(alt (.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)) (patch (.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt x (taylor -inf x) (#s(alt (.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)) (patch (.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (- (* -1/2 (/ eps x)) 1))) (taylor -inf x) (#s(alt (.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)) (patch (.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (- (* -1/2 (/ eps x)) 1))) (taylor -inf x) (#s(alt (.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)) (patch (.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (- (* -1/2 (/ eps x)) 1))) (taylor -inf x) (#s(alt (.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)) (patch (.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt x (taylor 0 eps) (#s(alt (.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)) (patch (.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt (+ x (* 1/2 eps)) (taylor 0 eps) (#s(alt (.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)) (patch (.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt (+ x (* 1/2 eps)) (taylor 0 eps) (#s(alt (.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)) (patch (.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt (+ x (* 1/2 eps)) (taylor 0 eps) (#s(alt (.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)) (patch (.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* 1/2 eps) (taylor inf eps) (#s(alt (.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)) (patch (.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* eps (+ 1/2 (/ x eps))) (taylor inf eps) (#s(alt (.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)) (patch (.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* eps (+ 1/2 (/ x eps))) (taylor inf eps) (#s(alt (.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)) (patch (.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* eps (+ 1/2 (/ x eps))) (taylor inf eps) (#s(alt (.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)) (patch (.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* 1/2 eps) (taylor -inf eps) (#s(alt (.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)) (patch (.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* eps (- (* -1 (/ x eps)) 1/2))) (taylor -inf eps) (#s(alt (.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)) (patch (.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* eps (- (* -1 (/ x eps)) 1/2))) (taylor -inf eps) (#s(alt (.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)) (patch (.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* eps (- (* -1 (/ x eps)) 1/2))) (taylor -inf eps) (#s(alt (.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)) (patch (.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt eps (taylor 0 eps) (#s(alt (+.f64 eps #s(literal 0 binary64)) (patch (+.f64 eps #s(literal 0 binary64)) #<representation binary64>) () ())) ())
#s(alt eps (taylor 0 eps) (#s(alt (+.f64 eps #s(literal 0 binary64)) (patch (+.f64 eps #s(literal 0 binary64)) #<representation binary64>) () ())) ())
#s(alt eps (taylor 0 eps) (#s(alt (+.f64 eps #s(literal 0 binary64)) (patch (+.f64 eps #s(literal 0 binary64)) #<representation binary64>) () ())) ())
#s(alt eps (taylor 0 eps) (#s(alt (+.f64 eps #s(literal 0 binary64)) (patch (+.f64 eps #s(literal 0 binary64)) #<representation binary64>) () ())) ())
#s(alt eps (taylor inf eps) (#s(alt (+.f64 eps #s(literal 0 binary64)) (patch (+.f64 eps #s(literal 0 binary64)) #<representation binary64>) () ())) ())
#s(alt eps (taylor inf eps) (#s(alt (+.f64 eps #s(literal 0 binary64)) (patch (+.f64 eps #s(literal 0 binary64)) #<representation binary64>) () ())) ())
#s(alt eps (taylor inf eps) (#s(alt (+.f64 eps #s(literal 0 binary64)) (patch (+.f64 eps #s(literal 0 binary64)) #<representation binary64>) () ())) ())
#s(alt eps (taylor inf eps) (#s(alt (+.f64 eps #s(literal 0 binary64)) (patch (+.f64 eps #s(literal 0 binary64)) #<representation binary64>) () ())) ())
#s(alt eps (taylor -inf eps) (#s(alt (+.f64 eps #s(literal 0 binary64)) (patch (+.f64 eps #s(literal 0 binary64)) #<representation binary64>) () ())) ())
#s(alt eps (taylor -inf eps) (#s(alt (+.f64 eps #s(literal 0 binary64)) (patch (+.f64 eps #s(literal 0 binary64)) #<representation binary64>) () ())) ())
#s(alt eps (taylor -inf eps) (#s(alt (+.f64 eps #s(literal 0 binary64)) (patch (+.f64 eps #s(literal 0 binary64)) #<representation binary64>) () ())) ())
#s(alt eps (taylor -inf eps) (#s(alt (+.f64 eps #s(literal 0 binary64)) (patch (+.f64 eps #s(literal 0 binary64)) #<representation binary64>) () ())) ())
#s(alt (* eps (cos x)) (taylor 0 eps) (#s(alt (.f64 (.f64 (sin.f64 (.f64 (+.f64 eps #s(literal 0 binary64)) #s(literal 1/2 binary64))) (cos.f64 (.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)))) #s(literal 2 binary64)) (patch (.f64 (.f64 (sin.f64 (.f64 (+.f64 eps #s(literal 0 binary64)) #s(literal 1/2 binary64))) (cos.f64 (.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)))) #s(literal 2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* eps (+ (cos x) (* -1/2 (* eps (sin x))))) (taylor 0 eps) (#s(alt (.f64 (.f64 (sin.f64 (.f64 (+.f64 eps #s(literal 0 binary64)) #s(literal 1/2 binary64))) (cos.f64 (.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)))) #s(literal 2 binary64)) (patch (.f64 (.f64 (sin.f64 (.f64 (+.f64 eps #s(literal 0 binary64)) #s(literal 1/2 binary64))) (cos.f64 (.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)))) #s(literal 2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* 2 (* eps (+ (* -1/16 (cos x)) (* -1/48 (cos x))))))))) (taylor 0 eps) (#s(alt (.f64 (.f64 (sin.f64 (.f64 (+.f64 eps #s(literal 0 binary64)) #s(literal 1/2 binary64))) (cos.f64 (.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)))) #s(literal 2 binary64)) (patch (.f64 (.f64 (sin.f64 (.f64 (+.f64 eps #s(literal 0 binary64)) #s(literal 1/2 binary64))) (cos.f64 (.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)))) #s(literal 2 binary64)) #<representation binary64>) () ())) ())
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#s(alt (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (taylor -inf eps) (#s(alt (cos.f64 (.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64))) (patch (cos.f64 (.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64))) #<representation binary64>) () ())) ())
#s(alt (* 1/2 eps) (taylor 0 eps) (#s(alt (sin.f64 (.f64 (+.f64 eps #s(literal 0 binary64)) #s(literal 1/2 binary64))) (patch (sin.f64 (.f64 (+.f64 eps #s(literal 0 binary64)) #s(literal 1/2 binary64))) #<representation binary64>) () ())) ())
#s(alt (* eps (+ 1/2 (* -1/48 (pow eps 2)))) (taylor 0 eps) (#s(alt (sin.f64 (.f64 (+.f64 eps #s(literal 0 binary64)) #s(literal 1/2 binary64))) (patch (sin.f64 (.f64 (+.f64 eps #s(literal 0 binary64)) #s(literal 1/2 binary64))) #<representation binary64>) () ())) ())
#s(alt (* eps (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48)))) (taylor 0 eps) (#s(alt (sin.f64 (.f64 (+.f64 eps #s(literal 0 binary64)) #s(literal 1/2 binary64))) (patch (sin.f64 (.f64 (+.f64 eps #s(literal 0 binary64)) #s(literal 1/2 binary64))) #<representation binary64>) () ())) ())
#s(alt (* eps (+ 1/2 (* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48)))) (taylor 0 eps) (#s(alt (sin.f64 (.f64 (+.f64 eps #s(literal 0 binary64)) #s(literal 1/2 binary64))) (patch (sin.f64 (.f64 (+.f64 eps #s(literal 0 binary64)) #s(literal 1/2 binary64))) #<representation binary64>) () ())) ())
#s(alt (sin (* 1/2 eps)) (taylor inf eps) (#s(alt (sin.f64 (.f64 (+.f64 eps #s(literal 0 binary64)) #s(literal 1/2 binary64))) (patch (sin.f64 (.f64 (+.f64 eps #s(literal 0 binary64)) #s(literal 1/2 binary64))) #<representation binary64>) () ())) ())
#s(alt (sin (* 1/2 eps)) (taylor inf eps) (#s(alt (sin.f64 (.f64 (+.f64 eps #s(literal 0 binary64)) #s(literal 1/2 binary64))) (patch (sin.f64 (.f64 (+.f64 eps #s(literal 0 binary64)) #s(literal 1/2 binary64))) #<representation binary64>) () ())) ())
#s(alt (sin (* 1/2 eps)) (taylor inf eps) (#s(alt (sin.f64 (.f64 (+.f64 eps #s(literal 0 binary64)) #s(literal 1/2 binary64))) (patch (sin.f64 (.f64 (+.f64 eps #s(literal 0 binary64)) #s(literal 1/2 binary64))) #<representation binary64>) () ())) ())
#s(alt (sin (* 1/2 eps)) (taylor inf eps) (#s(alt (sin.f64 (.f64 (+.f64 eps #s(literal 0 binary64)) #s(literal 1/2 binary64))) (patch (sin.f64 (.f64 (+.f64 eps #s(literal 0 binary64)) #s(literal 1/2 binary64))) #<representation binary64>) () ())) ())
#s(alt (sin (* 1/2 eps)) (taylor -inf eps) (#s(alt (sin.f64 (.f64 (+.f64 eps #s(literal 0 binary64)) #s(literal 1/2 binary64))) (patch (sin.f64 (.f64 (+.f64 eps #s(literal 0 binary64)) #s(literal 1/2 binary64))) #<representation binary64>) () ())) ())
#s(alt (sin (* 1/2 eps)) (taylor -inf eps) (#s(alt (sin.f64 (.f64 (+.f64 eps #s(literal 0 binary64)) #s(literal 1/2 binary64))) (patch (sin.f64 (.f64 (+.f64 eps #s(literal 0 binary64)) #s(literal 1/2 binary64))) #<representation binary64>) () ())) ())
#s(alt (sin (* 1/2 eps)) (taylor -inf eps) (#s(alt (sin.f64 (.f64 (+.f64 eps #s(literal 0 binary64)) #s(literal 1/2 binary64))) (patch (sin.f64 (.f64 (+.f64 eps #s(literal 0 binary64)) #s(literal 1/2 binary64))) #<representation binary64>) () ())) ())
#s(alt (sin (* 1/2 eps)) (taylor -inf eps) (#s(alt (sin.f64 (.f64 (+.f64 eps #s(literal 0 binary64)) #s(literal 1/2 binary64))) (patch (sin.f64 (.f64 (+.f64 eps #s(literal 0 binary64)) #s(literal 1/2 binary64))) #<representation binary64>) () ())) ())
#s(alt (pow x 3) (taylor 0 x) (#s(alt (.f64 x (.f64 x x)) (patch (.f64 x (.f64 x x)) #<representation binary64>) () ())) ())
#s(alt (pow x 3) (taylor 0 x) (#s(alt (.f64 x (.f64 x x)) (patch (.f64 x (.f64 x x)) #<representation binary64>) () ())) ())
#s(alt (pow x 3) (taylor 0 x) (#s(alt (.f64 x (.f64 x x)) (patch (.f64 x (.f64 x x)) #<representation binary64>) () ())) ())
#s(alt (pow x 3) (taylor 0 x) (#s(alt (.f64 x (.f64 x x)) (patch (.f64 x (.f64 x x)) #<representation binary64>) () ())) ())
#s(alt (pow x 3) (taylor inf x) (#s(alt (.f64 x (.f64 x x)) (patch (.f64 x (.f64 x x)) #<representation binary64>) () ())) ())
#s(alt (pow x 3) (taylor inf x) (#s(alt (.f64 x (.f64 x x)) (patch (.f64 x (.f64 x x)) #<representation binary64>) () ())) ())
#s(alt (pow x 3) (taylor inf x) (#s(alt (.f64 x (.f64 x x)) (patch (.f64 x (.f64 x x)) #<representation binary64>) () ())) ())
#s(alt (pow x 3) (taylor inf x) (#s(alt (.f64 x (.f64 x x)) (patch (.f64 x (.f64 x x)) #<representation binary64>) () ())) ())
#s(alt (pow x 3) (taylor -inf x) (#s(alt (.f64 x (.f64 x x)) (patch (.f64 x (.f64 x x)) #<representation binary64>) () ())) ())
#s(alt (pow x 3) (taylor -inf x) (#s(alt (.f64 x (.f64 x x)) (patch (.f64 x (.f64 x x)) #<representation binary64>) () ())) ())
#s(alt (pow x 3) (taylor -inf x) (#s(alt (.f64 x (.f64 x x)) (patch (.f64 x (.f64 x x)) #<representation binary64>) () ())) ())
#s(alt (pow x 3) (taylor -inf x) (#s(alt (.f64 x (.f64 x x)) (patch (.f64 x (.f64 x x)) #<representation binary64>) () ())) ())
#s(alt (* 1/120 x) (taylor 0 x) (#s(alt (.f64 x (fma.f64 (.f64 x x) #s(literal -1/5040 binary64) #s(literal 1/120 binary64))) (patch (.f64 x (fma.f64 (.f64 x x) #s(literal -1/5040 binary64) #s(literal 1/120 binary64))) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1/120 (* -1/5040 (pow x 2)))) (taylor 0 x) (#s(alt (.f64 x (fma.f64 (.f64 x x) #s(literal -1/5040 binary64) #s(literal 1/120 binary64))) (patch (.f64 x (fma.f64 (.f64 x x) #s(literal -1/5040 binary64) #s(literal 1/120 binary64))) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1/120 (* -1/5040 (pow x 2)))) (taylor 0 x) (#s(alt (.f64 x (fma.f64 (.f64 x x) #s(literal -1/5040 binary64) #s(literal 1/120 binary64))) (patch (.f64 x (fma.f64 (.f64 x x) #s(literal -1/5040 binary64) #s(literal 1/120 binary64))) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1/120 (* -1/5040 (pow x 2)))) (taylor 0 x) (#s(alt (.f64 x (fma.f64 (.f64 x x) #s(literal -1/5040 binary64) #s(literal 1/120 binary64))) (patch (.f64 x (fma.f64 (.f64 x x) #s(literal -1/5040 binary64) #s(literal 1/120 binary64))) #<representation binary64>) () ())) ())
#s(alt (* -1/5040 (pow x 3)) (taylor inf x) (#s(alt (.f64 x (fma.f64 (.f64 x x) #s(literal -1/5040 binary64) #s(literal 1/120 binary64))) (patch (.f64 x (fma.f64 (.f64 x x) #s(literal -1/5040 binary64) #s(literal 1/120 binary64))) #<representation binary64>) () ())) ())
#s(alt (* (pow x 3) (- (* 1/120 (/ 1 (pow x 2))) 1/5040)) (taylor inf x) (#s(alt (.f64 x (fma.f64 (.f64 x x) #s(literal -1/5040 binary64) #s(literal 1/120 binary64))) (patch (.f64 x (fma.f64 (.f64 x x) #s(literal -1/5040 binary64) #s(literal 1/120 binary64))) #<representation binary64>) () ())) ())
#s(alt (* (pow x 3) (- (* 1/120 (/ 1 (pow x 2))) 1/5040)) (taylor inf x) (#s(alt (.f64 x (fma.f64 (.f64 x x) #s(literal -1/5040 binary64) #s(literal 1/120 binary64))) (patch (.f64 x (fma.f64 (.f64 x x) #s(literal -1/5040 binary64) #s(literal 1/120 binary64))) #<representation binary64>) () ())) ())
#s(alt (* (pow x 3) (- (* 1/120 (/ 1 (pow x 2))) 1/5040)) (taylor inf x) (#s(alt (.f64 x (fma.f64 (.f64 x x) #s(literal -1/5040 binary64) #s(literal 1/120 binary64))) (patch (.f64 x (fma.f64 (.f64 x x) #s(literal -1/5040 binary64) #s(literal 1/120 binary64))) #<representation binary64>) () ())) ())
#s(alt (* -1/5040 (pow x 3)) (taylor -inf x) (#s(alt (.f64 x (fma.f64 (.f64 x x) #s(literal -1/5040 binary64) #s(literal 1/120 binary64))) (patch (.f64 x (fma.f64 (.f64 x x) #s(literal -1/5040 binary64) #s(literal 1/120 binary64))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* (pow x 3) (- 1/5040 (* 1/120 (/ 1 (pow x 2)))))) (taylor -inf x) (#s(alt (.f64 x (fma.f64 (.f64 x x) #s(literal -1/5040 binary64) #s(literal 1/120 binary64))) (patch (.f64 x (fma.f64 (.f64 x x) #s(literal -1/5040 binary64) #s(literal 1/120 binary64))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* (pow x 3) (- 1/5040 (* 1/120 (/ 1 (pow x 2)))))) (taylor -inf x) (#s(alt (.f64 x (fma.f64 (.f64 x x) #s(literal -1/5040 binary64) #s(literal 1/120 binary64))) (patch (.f64 x (fma.f64 (.f64 x x) #s(literal -1/5040 binary64) #s(literal 1/120 binary64))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* (pow x 3) (- 1/5040 (* 1/120 (/ 1 (pow x 2)))))) (taylor -inf x) (#s(alt (.f64 x (fma.f64 (.f64 x x) #s(literal -1/5040 binary64) #s(literal 1/120 binary64))) (patch (.f64 x (fma.f64 (.f64 x x) #s(literal -1/5040 binary64) #s(literal 1/120 binary64))) #<representation binary64>) () ())) ())
#s(alt (* x (cos eps)) (taylor 0 x) (#s(alt (.f64 x (cos.f64 eps)) (patch (.f64 x (cos.f64 eps)) #<representation binary64>) () ())) ())
#s(alt (* x (cos eps)) (taylor 0 x) (#s(alt (.f64 x (cos.f64 eps)) (patch (.f64 x (cos.f64 eps)) #<representation binary64>) () ())) ())
#s(alt (* x (cos eps)) (taylor 0 x) (#s(alt (.f64 x (cos.f64 eps)) (patch (.f64 x (cos.f64 eps)) #<representation binary64>) () ())) ())
#s(alt (* x (cos eps)) (taylor 0 x) (#s(alt (.f64 x (cos.f64 eps)) (patch (.f64 x (cos.f64 eps)) #<representation binary64>) () ())) ())
#s(alt (* x (cos eps)) (taylor inf x) (#s(alt (.f64 x (cos.f64 eps)) (patch (.f64 x (cos.f64 eps)) #<representation binary64>) () ())) ())
#s(alt (* x (cos eps)) (taylor inf x) (#s(alt (.f64 x (cos.f64 eps)) (patch (.f64 x (cos.f64 eps)) #<representation binary64>) () ())) ())
#s(alt (* x (cos eps)) (taylor inf x) (#s(alt (.f64 x (cos.f64 eps)) (patch (.f64 x (cos.f64 eps)) #<representation binary64>) () ())) ())
#s(alt (* x (cos eps)) (taylor inf x) (#s(alt (.f64 x (cos.f64 eps)) (patch (.f64 x (cos.f64 eps)) #<representation binary64>) () ())) ())
#s(alt (* x (cos eps)) (taylor -inf x) (#s(alt (.f64 x (cos.f64 eps)) (patch (.f64 x (cos.f64 eps)) #<representation binary64>) () ())) ())
#s(alt (* x (cos eps)) (taylor -inf x) (#s(alt (.f64 x (cos.f64 eps)) (patch (.f64 x (cos.f64 eps)) #<representation binary64>) () ())) ())
#s(alt (* x (cos eps)) (taylor -inf x) (#s(alt (.f64 x (cos.f64 eps)) (patch (.f64 x (cos.f64 eps)) #<representation binary64>) () ())) ())
#s(alt (* x (cos eps)) (taylor -inf x) (#s(alt (.f64 x (cos.f64 eps)) (patch (.f64 x (cos.f64 eps)) #<representation binary64>) () ())) ())
#s(alt x (taylor 0 eps) (#s(alt (.f64 x (cos.f64 eps)) (patch (.f64 x (cos.f64 eps)) #<representation binary64>) () ())) ())
#s(alt (+ x (* -1/2 (* (pow eps 2) x))) (taylor 0 eps) (#s(alt (.f64 x (cos.f64 eps)) (patch (.f64 x (cos.f64 eps)) #<representation binary64>) () ())) ())
#s(alt (+ x (* (pow eps 2) (+ (* -1/2 x) (* 1/24 (* (pow eps 2) x))))) (taylor 0 eps) (#s(alt (.f64 x (cos.f64 eps)) (patch (.f64 x (cos.f64 eps)) #<representation binary64>) () ())) ())
#s(alt (+ x (* (pow eps 2) (+ (* -1/2 x) (* (pow eps 2) (+ (* -1/720 (* (pow eps 2) x)) (* 1/24 x)))))) (taylor 0 eps) (#s(alt (.f64 x (cos.f64 eps)) (patch (.f64 x (cos.f64 eps)) #<representation binary64>) () ())) ())
#s(alt (* x (cos eps)) (taylor inf eps) (#s(alt (.f64 x (cos.f64 eps)) (patch (.f64 x (cos.f64 eps)) #<representation binary64>) () ())) ())
#s(alt (* x (cos eps)) (taylor inf eps) (#s(alt (.f64 x (cos.f64 eps)) (patch (.f64 x (cos.f64 eps)) #<representation binary64>) () ())) ())
#s(alt (* x (cos eps)) (taylor inf eps) (#s(alt (.f64 x (cos.f64 eps)) (patch (.f64 x (cos.f64 eps)) #<representation binary64>) () ())) ())
#s(alt (* x (cos eps)) (taylor inf eps) (#s(alt (.f64 x (cos.f64 eps)) (patch (.f64 x (cos.f64 eps)) #<representation binary64>) () ())) ())
#s(alt (* x (cos eps)) (taylor -inf eps) (#s(alt (.f64 x (cos.f64 eps)) (patch (.f64 x (cos.f64 eps)) #<representation binary64>) () ())) ())
#s(alt (* x (cos eps)) (taylor -inf eps) (#s(alt (.f64 x (cos.f64 eps)) (patch (.f64 x (cos.f64 eps)) #<representation binary64>) () ())) ())
#s(alt (* x (cos eps)) (taylor -inf eps) (#s(alt (.f64 x (cos.f64 eps)) (patch (.f64 x (cos.f64 eps)) #<representation binary64>) () ())) ())
#s(alt (* x (cos eps)) (taylor -inf eps) (#s(alt (.f64 x (cos.f64 eps)) (patch (.f64 x (cos.f64 eps)) #<representation binary64>) () ())) ())

Calls

102 calls:

Time	Variable		Point	Expression
2.0ms	x	@	inf	(* x (+ (* (* x x) -1/5040) 1/120))
1.0ms	x	@	0	(* (* (sin (* (+ eps 0) 1/2)) (cos (* (+ (* x 2) eps) 1/2))) 2)
1.0ms	x	@	inf	(* (* (sin (* (+ eps 0) 1/2)) (cos (* (+ (* x 2) eps) 1/2))) 2)
1.0ms	eps	@	inf	(- (+ (* (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) x)
1.0ms	eps	@	0	(* (* (sin (* (+ eps 0) 1/2)) (cos (* (+ (* x 2) eps) 1/2))) 2)

simplify258.0ms (2%)

Memory

19.1MiB live, 277.9MiB allocated

Algorithm

1×	egg-herbie

Rules

13 690×	`lower-fma.f64`
13 690×	`lower-fma.f32`
5 568×	`lower-*.f64`
5 568×	`lower-*.f32`
4 302×	`lower-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	366	3695
1	1153	3529
2	3178	3491
0	8074	3210

Stop Event

1×	iter limit
1×	node limit

Counts

408 → 382

Calls

Call 1

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

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

rewrite420.0ms (3.3%)

Memory

-33.5MiB live, 385.5MiB allocated

Rules

6 672×	`lower-fma.f32`
6 658×	`lower-fma.f64`
5 200×	`lower-*.f32`
5 182×	`lower-*.f64`
4 374×	`lower-/.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	44	219
0	77	201
1	295	201
2	2293	201
0	9965	201

Stop Event

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

Counts

21 → 422

Calls

Call 1

Inputs
(*.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64))
(+.f64 eps #s(literal 0 binary64))
(.f64 (.f64 (sin.f64 (.f64 (+.f64 eps #s(literal 0 binary64)) #s(literal 1/2 binary64))) (cos.f64 (.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)))) #s(literal 2 binary64))
(.f64 (sin.f64 (.f64 (+.f64 eps #s(literal 0 binary64)) #s(literal 1/2 binary64))) (cos.f64 (*.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64))))
#s(approx (- (sin (+ x eps)) (sin x)) (sin.f64 eps))
(sin.f64 eps)
(-.f64 (sin.f64 (+.f64 x eps)) #s(approx (sin x) (fma.f64 #s(literal -1/6 binary64) (.f64 x (.f64 x x)) x)))
(sin.f64 (+.f64 x eps))
(+.f64 x eps)
#s(approx (sin x) (fma.f64 #s(literal -1/6 binary64) (.f64 x (.f64 x x)) x))
(-.f64 (sin.f64 (+.f64 x eps)) #s(approx (sin x) (fma.f64 (fma.f64 x (.f64 x (fma.f64 (.f64 x x) #s(literal -1/5040 binary64) #s(literal 1/120 binary64))) #s(literal -1/6 binary64)) (.f64 x (.f64 x x)) x)))
#s(approx (sin x) (fma.f64 (fma.f64 x (.f64 x (fma.f64 (.f64 x x) #s(literal -1/5040 binary64) #s(literal 1/120 binary64))) #s(literal -1/6 binary64)) (.f64 x (.f64 x x)) x))
#s(approx (- (sin (+ x eps)) (sin x)) (-.f64 (fma.f64 (fma.f64 x (.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64)) (sin.f64 eps) (.f64 x (cos.f64 eps))) x))
(-.f64 (fma.f64 (fma.f64 x (.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64)) (sin.f64 eps) (.f64 x (cos.f64 eps))) x)
(fma.f64 (fma.f64 x (.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64)) (sin.f64 eps) (.f64 x (cos.f64 eps)))
(fma.f64 x (*.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64))
(cos.f64 (*.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)))
(sin.f64 (*.f64 (+.f64 eps #s(literal 0 binary64)) #s(literal 1/2 binary64)))
(.f64 x (.f64 x x))
(.f64 x (fma.f64 (.f64 x x) #s(literal -1/5040 binary64) #s(literal 1/120 binary64)))
(*.f64 x (cos.f64 eps))

Outputs
(+.f64 (.f64 eps #s(literal 1/2 binary64)) (.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 2 binary64))))
(+.f64 (.f64 eps #s(literal 1/2 binary64)) (.f64 (*.f64 x #s(literal 2 binary64)) #s(literal 1/2 binary64)))
(+.f64 (.f64 #s(literal 1/2 binary64) (.f64 x #s(literal 2 binary64))) (*.f64 eps #s(literal 1/2 binary64)))
(+.f64 (.f64 (.f64 x #s(literal 2 binary64)) #s(literal 1/2 binary64)) (*.f64 eps #s(literal 1/2 binary64)))
(fma.f64 eps #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (.f64 x #s(literal 2 binary64))))
(fma.f64 eps #s(literal 1/2 binary64) (.f64 (.f64 x #s(literal 2 binary64)) #s(literal 1/2 binary64)))
(fma.f64 #s(literal 1/2 binary64) eps (.f64 #s(literal 1/2 binary64) (.f64 x #s(literal 2 binary64))))
(fma.f64 #s(literal 1/2 binary64) eps (.f64 (.f64 x #s(literal 2 binary64)) #s(literal 1/2 binary64)))
(fma.f64 #s(literal 1/2 binary64) (.f64 x #s(literal 2 binary64)) (.f64 eps #s(literal 1/2 binary64)))
(fma.f64 (.f64 x #s(literal 2 binary64)) #s(literal 1/2 binary64) (.f64 eps #s(literal 1/2 binary64)))
(fma.f64 (.f64 eps eps) (/.f64 #s(literal 1/2 binary64) eps) (.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 2 binary64))))
(fma.f64 (.f64 eps eps) (/.f64 #s(literal 1/2 binary64) eps) (.f64 (*.f64 x #s(literal 2 binary64)) #s(literal 1/2 binary64)))
(fma.f64 (/.f64 #s(literal 1 binary64) eps) (/.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1 binary64) (.f64 eps eps))) (.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 2 binary64))))
(fma.f64 (/.f64 #s(literal 1 binary64) eps) (/.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1 binary64) (.f64 eps eps))) (.f64 (*.f64 x #s(literal 2 binary64)) #s(literal 1/2 binary64)))
(fma.f64 (/.f64 (.f64 eps eps) (.f64 eps eps)) (/.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1 binary64) eps)) (.f64 #s(literal 1/2 binary64) (.f64 x #s(literal 2 binary64))))
(fma.f64 (/.f64 (.f64 eps eps) (.f64 eps eps)) (/.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1 binary64) eps)) (.f64 (.f64 x #s(literal 2 binary64)) #s(literal 1/2 binary64)))
(fma.f64 (/.f64 #s(literal 1/2 binary64) eps) (.f64 eps eps) (.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 2 binary64))))
(fma.f64 (/.f64 #s(literal 1/2 binary64) eps) (.f64 eps eps) (.f64 (*.f64 x #s(literal 2 binary64)) #s(literal 1/2 binary64)))
(fma.f64 (/.f64 #s(literal 1/2 binary64) (.f64 eps (.f64 eps eps))) (/.f64 (.f64 eps eps) (/.f64 #s(literal 1 binary64) (.f64 eps eps))) (.f64 #s(literal 1/2 binary64) (.f64 x #s(literal 2 binary64))))
(fma.f64 (/.f64 #s(literal 1/2 binary64) (.f64 eps (.f64 eps eps))) (/.f64 (.f64 eps eps) (/.f64 #s(literal 1 binary64) (.f64 eps eps))) (.f64 (.f64 x #s(literal 2 binary64)) #s(literal 1/2 binary64)))
(fma.f64 (/.f64 #s(literal 1/2 binary64) (.f64 eps eps)) (/.f64 (.f64 eps eps) (/.f64 #s(literal 1 binary64) eps)) (.f64 #s(literal 1/2 binary64) (.f64 x #s(literal 2 binary64))))
(fma.f64 (/.f64 #s(literal 1/2 binary64) (.f64 eps eps)) (/.f64 (.f64 eps eps) (/.f64 #s(literal 1 binary64) eps)) (.f64 (.f64 x #s(literal 2 binary64)) #s(literal 1/2 binary64)))
(/.f64 (.f64 #s(literal 1/2 binary64) (fma.f64 eps (.f64 eps eps) (.f64 (.f64 x (.f64 x x)) #s(literal 8 binary64)))) (fma.f64 eps (-.f64 eps (.f64 x #s(literal 2 binary64))) (.f64 (.f64 x x) #s(literal 4 binary64))))
(/.f64 (.f64 #s(literal 1/2 binary64) (-.f64 (.f64 (.f64 x x) #s(literal 4 binary64)) (.f64 eps eps))) (-.f64 (*.f64 x #s(literal 2 binary64)) eps))
(/.f64 (.f64 (fma.f64 eps (.f64 eps eps) (.f64 (.f64 x (.f64 x x)) #s(literal 8 binary64))) #s(literal 1/2 binary64)) (fma.f64 eps (-.f64 eps (.f64 x #s(literal 2 binary64))) (.f64 (.f64 x x) #s(literal 4 binary64))))
(/.f64 (.f64 (-.f64 (.f64 (.f64 x x) #s(literal 4 binary64)) (.f64 eps eps)) #s(literal 1/2 binary64)) (-.f64 (*.f64 x #s(literal 2 binary64)) eps))
(/.f64 (neg.f64 (.f64 #s(literal 1/2 binary64) (fma.f64 eps (.f64 eps eps) (.f64 (.f64 x (.f64 x x)) #s(literal 8 binary64))))) (neg.f64 (fma.f64 eps (-.f64 eps (.f64 x #s(literal 2 binary64))) (.f64 (.f64 x x) #s(literal 4 binary64)))))
(/.f64 (neg.f64 (.f64 #s(literal 1/2 binary64) (-.f64 (.f64 (.f64 x x) #s(literal 4 binary64)) (.f64 eps eps)))) (neg.f64 (-.f64 (*.f64 x #s(literal 2 binary64)) eps)))
(/.f64 (neg.f64 (.f64 (fma.f64 eps (.f64 eps eps) (.f64 (.f64 x (.f64 x x)) #s(literal 8 binary64))) #s(literal 1/2 binary64))) (neg.f64 (fma.f64 eps (-.f64 eps (.f64 x #s(literal 2 binary64))) (.f64 (.f64 x x) #s(literal 4 binary64)))))
(/.f64 (neg.f64 (.f64 (-.f64 (.f64 (.f64 x x) #s(literal 4 binary64)) (.f64 eps eps)) #s(literal 1/2 binary64))) (neg.f64 (-.f64 (*.f64 x #s(literal 2 binary64)) eps)))
(/.f64 (fma.f64 (.f64 eps (.f64 eps eps)) #s(literal 1/8 binary64) (pow.f64 (.f64 #s(literal 1/2 binary64) (.f64 x #s(literal 2 binary64))) #s(literal 3 binary64))) (fma.f64 (.f64 eps #s(literal 1/2 binary64)) (.f64 eps #s(literal 1/2 binary64)) (-.f64 (.f64 (.f64 #s(literal 1/2 binary64) (.f64 x #s(literal 2 binary64))) (.f64 #s(literal 1/2 binary64) (.f64 x #s(literal 2 binary64)))) (.f64 (.f64 eps #s(literal 1/2 binary64)) (.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 2 binary64)))))))
(/.f64 (fma.f64 (.f64 eps (.f64 eps eps)) #s(literal 1/8 binary64) (pow.f64 (.f64 (.f64 x #s(literal 2 binary64)) #s(literal 1/2 binary64)) #s(literal 3 binary64))) (fma.f64 (.f64 eps #s(literal 1/2 binary64)) (.f64 eps #s(literal 1/2 binary64)) (-.f64 (.f64 (.f64 (.f64 x #s(literal 2 binary64)) #s(literal 1/2 binary64)) (.f64 (.f64 x #s(literal 2 binary64)) #s(literal 1/2 binary64))) (.f64 (.f64 eps #s(literal 1/2 binary64)) (.f64 (*.f64 x #s(literal 2 binary64)) #s(literal 1/2 binary64))))))
(/.f64 (+.f64 (pow.f64 (.f64 #s(literal 1/2 binary64) (.f64 x #s(literal 2 binary64))) #s(literal 3 binary64)) (.f64 (.f64 eps (.f64 eps eps)) #s(literal 1/8 binary64))) (fma.f64 (.f64 #s(literal 1/2 binary64) (.f64 x #s(literal 2 binary64))) (.f64 #s(literal 1/2 binary64) (.f64 x #s(literal 2 binary64))) (-.f64 (.f64 (.f64 eps #s(literal 1/2 binary64)) (.f64 eps #s(literal 1/2 binary64))) (.f64 (.f64 #s(literal 1/2 binary64) (.f64 x #s(literal 2 binary64))) (.f64 eps #s(literal 1/2 binary64))))))
(/.f64 (+.f64 (pow.f64 (.f64 (.f64 x #s(literal 2 binary64)) #s(literal 1/2 binary64)) #s(literal 3 binary64)) (.f64 (.f64 eps (.f64 eps eps)) #s(literal 1/8 binary64))) (fma.f64 (.f64 (.f64 x #s(literal 2 binary64)) #s(literal 1/2 binary64)) (.f64 (.f64 x #s(literal 2 binary64)) #s(literal 1/2 binary64)) (-.f64 (.f64 (.f64 eps #s(literal 1/2 binary64)) (.f64 eps #s(literal 1/2 binary64))) (.f64 (.f64 (.f64 x #s(literal 2 binary64)) #s(literal 1/2 binary64)) (.f64 eps #s(literal 1/2 binary64))))))
(*.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64))
(*.f64 #s(literal 1/2 binary64) (fma.f64 x #s(literal 2 binary64) eps))
eps
(+.f64 eps #s(literal 0 binary64))
(+.f64 #s(literal 0 binary64) eps)
(-.f64 eps #s(literal 0 binary64))
(-.f64 eps (/.f64 #s(literal 0 binary64) eps))
(-.f64 eps (/.f64 #s(literal 0 binary64) (*.f64 eps eps)))
(-.f64 (/.f64 #s(literal 0 binary64) (-.f64 #s(literal 0 binary64) eps)) (/.f64 (*.f64 eps eps) (-.f64 #s(literal 0 binary64) eps)))
(fma.f64 eps (/.f64 eps eps) #s(literal 0 binary64))
(fma.f64 (.f64 eps (.f64 eps eps)) (/.f64 #s(literal 1 binary64) (*.f64 eps eps)) #s(literal 0 binary64))
(fma.f64 (*.f64 eps eps) (/.f64 #s(literal 1 binary64) eps) #s(literal 0 binary64))
(fma.f64 (/.f64 eps (*.f64 eps eps)) (/.f64 eps (/.f64 #s(literal 1 binary64) eps)) #s(literal 0 binary64))
(fma.f64 (/.f64 eps eps) eps #s(literal 0 binary64))
(fma.f64 (/.f64 (pow.f64 eps #s(literal 3/2 binary64)) eps) (/.f64 (pow.f64 eps #s(literal 3/2 binary64)) eps) #s(literal 0 binary64))
(fma.f64 (/.f64 eps (.f64 eps (.f64 eps eps))) (/.f64 eps (/.f64 #s(literal 1 binary64) (*.f64 eps eps))) #s(literal 0 binary64))
(/.f64 #s(literal 1 binary64) (/.f64 eps (*.f64 eps eps)))
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(+.f64 #s(literal 1 binary64) (.f64 x (.f64 x #s(literal -1/2 binary64))))
(+.f64 (.f64 x (.f64 x #s(literal -1/2 binary64))) #s(literal 1 binary64))
(-.f64 (/.f64 (.f64 (.f64 (.f64 x x) (.f64 x x)) #s(literal 1/4 binary64)) (fma.f64 (.f64 x x) #s(literal -1/2 binary64) #s(literal -1 binary64))) (/.f64 #s(literal 1 binary64) (fma.f64 (.f64 x x) #s(literal -1/2 binary64) #s(literal -1 binary64))))
(-.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (.f64 x (.f64 x #s(literal -1/2 binary64))))) (/.f64 (.f64 (.f64 (.f64 x x) (.f64 x x)) #s(literal 1/4 binary64)) (-.f64 #s(literal 1 binary64) (.f64 x (.f64 x #s(literal -1/2 binary64))))))
(fma.f64 x (*.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64))
(fma.f64 x (.f64 (.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64)) #s(literal 1 binary64))
(fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64))
(fma.f64 #s(literal -1/2 binary64) (*.f64 x x) #s(literal 1 binary64))
(fma.f64 (*.f64 x #s(literal -1/2 binary64)) x #s(literal 1 binary64))
(fma.f64 (.f64 x #s(literal -1/2 binary64)) (.f64 x #s(literal 1 binary64)) #s(literal 1 binary64))
(fma.f64 #s(literal 1 binary64) (.f64 x (.f64 x #s(literal -1/2 binary64))) #s(literal 1 binary64))
(fma.f64 (.f64 x (.f64 x #s(literal -1/2 binary64))) #s(literal 1 binary64) #s(literal 1 binary64))
(/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 (.f64 (.f64 x x) (.f64 x x)) #s(literal 1/4 binary64) (-.f64 #s(literal 1 binary64) (.f64 x (.f64 x #s(literal -1/2 binary64))))) (fma.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) #s(literal -1/8 binary64)) #s(literal 1 binary64))))
(/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 (.f64 x x) #s(literal -1/2 binary64) #s(literal -1 binary64)) (fma.f64 (.f64 (.f64 x x) (.f64 x x)) #s(literal 1/4 binary64) #s(literal -1 binary64))))
(/.f64 (fma.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) #s(literal -1/8 binary64)) #s(literal 1 binary64)) (fma.f64 (.f64 (.f64 x x) (.f64 x x)) #s(literal 1/4 binary64) (-.f64 #s(literal 1 binary64) (.f64 x (.f64 x #s(literal -1/2 binary64))))))
(/.f64 (fma.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) #s(literal -1/8 binary64)) #s(literal 1 binary64)) (+.f64 #s(literal 1 binary64) (-.f64 (.f64 (.f64 (.f64 x x) (.f64 x x)) #s(literal 1/4 binary64)) (.f64 x (*.f64 x #s(literal -1/2 binary64))))))
(/.f64 (fma.f64 (.f64 (.f64 x x) (.f64 x x)) #s(literal 1/4 binary64) #s(literal -1 binary64)) (fma.f64 (.f64 x x) #s(literal -1/2 binary64) #s(literal -1 binary64)))
(/.f64 (neg.f64 (fma.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) #s(literal -1/8 binary64)) #s(literal 1 binary64))) (neg.f64 (fma.f64 (.f64 (.f64 x x) (.f64 x x)) #s(literal 1/4 binary64) (-.f64 #s(literal 1 binary64) (.f64 x (.f64 x #s(literal -1/2 binary64)))))))
(/.f64 (neg.f64 (fma.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) #s(literal -1/8 binary64)) #s(literal 1 binary64))) (neg.f64 (+.f64 #s(literal 1 binary64) (-.f64 (.f64 (.f64 (.f64 x x) (.f64 x x)) #s(literal 1/4 binary64)) (.f64 x (*.f64 x #s(literal -1/2 binary64)))))))
(/.f64 (neg.f64 (fma.f64 (.f64 (.f64 x x) (.f64 x x)) #s(literal 1/4 binary64) #s(literal -1 binary64))) (neg.f64 (fma.f64 (.f64 x x) #s(literal -1/2 binary64) #s(literal -1 binary64))))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 (fma.f64 (.f64 (.f64 x x) (.f64 x x)) #s(literal 1/4 binary64) (-.f64 #s(literal 1 binary64) (.f64 x (.f64 x #s(literal -1/2 binary64))))) (fma.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) #s(literal -1/8 binary64)) #s(literal 1 binary64)))))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 (fma.f64 (.f64 x x) #s(literal -1/2 binary64) #s(literal -1 binary64)) (fma.f64 (.f64 (.f64 x x) (.f64 x x)) #s(literal 1/4 binary64) #s(literal -1 binary64)))))
(/.f64 (-.f64 #s(literal 1 binary64) (.f64 (.f64 (.f64 x x) (.f64 x x)) #s(literal 1/4 binary64))) (-.f64 #s(literal 1 binary64) (.f64 x (.f64 x #s(literal -1/2 binary64)))))
(/.f64 (-.f64 (.f64 (.f64 (.f64 (.f64 x x) (.f64 x x)) #s(literal 1/4 binary64)) (fma.f64 (.f64 x x) #s(literal -1/2 binary64) #s(literal -1 binary64))) (.f64 (fma.f64 (.f64 x x) #s(literal -1/2 binary64) #s(literal -1 binary64)) #s(literal 1 binary64))) (.f64 (fma.f64 (.f64 x x) #s(literal -1/2 binary64) #s(literal -1 binary64)) (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal -1 binary64))))
(/.f64 (neg.f64 (neg.f64 (fma.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) #s(literal -1/8 binary64)) #s(literal 1 binary64)))) (neg.f64 (neg.f64 (fma.f64 (.f64 (.f64 x x) (.f64 x x)) #s(literal 1/4 binary64) (-.f64 #s(literal 1 binary64) (.f64 x (.f64 x #s(literal -1/2 binary64))))))))
(/.f64 (neg.f64 (neg.f64 (fma.f64 (.f64 (.f64 x x) (.f64 x x)) #s(literal 1/4 binary64) #s(literal -1 binary64)))) (neg.f64 (neg.f64 (fma.f64 (.f64 x x) #s(literal -1/2 binary64) #s(literal -1 binary64)))))
(/.f64 (neg.f64 (-.f64 #s(literal 1 binary64) (.f64 (.f64 (.f64 x x) (.f64 x x)) #s(literal 1/4 binary64)))) (neg.f64 (-.f64 #s(literal 1 binary64) (.f64 x (.f64 x #s(literal -1/2 binary64))))))
(pow.f64 (/.f64 (fma.f64 (.f64 (.f64 x x) (.f64 x x)) #s(literal 1/4 binary64) (-.f64 #s(literal 1 binary64) (.f64 x (.f64 x #s(literal -1/2 binary64))))) (fma.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) #s(literal -1/8 binary64)) #s(literal 1 binary64))) #s(literal -1 binary64))
(pow.f64 (/.f64 (fma.f64 (.f64 x x) #s(literal -1/2 binary64) #s(literal -1 binary64)) (fma.f64 (.f64 (.f64 x x) (.f64 x x)) #s(literal 1/4 binary64) #s(literal -1 binary64))) #s(literal -1 binary64))
(.f64 (fma.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) #s(literal -1/8 binary64)) #s(literal 1 binary64)) (/.f64 #s(literal 1 binary64) (fma.f64 (.f64 (.f64 x x) (.f64 x x)) #s(literal 1/4 binary64) (-.f64 #s(literal 1 binary64) (.f64 x (*.f64 x #s(literal -1/2 binary64)))))))
(.f64 (fma.f64 (.f64 (.f64 x x) (.f64 x x)) #s(literal 1/4 binary64) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal -1 binary64))))
(cos.f64 (*.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)))
(-.f64 (.f64 (cos.f64 (.f64 eps #s(literal 1/2 binary64))) (cos.f64 (.f64 #s(literal 1/2 binary64) (.f64 x #s(literal 2 binary64))))) (.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (sin.f64 (.f64 #s(literal 1/2 binary64) (.f64 x #s(literal 2 binary64))))))
(-.f64 (.f64 (cos.f64 (.f64 eps #s(literal 1/2 binary64))) (cos.f64 (.f64 (.f64 x #s(literal 2 binary64)) #s(literal 1/2 binary64)))) (.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (sin.f64 (.f64 (.f64 x #s(literal 2 binary64)) #s(literal 1/2 binary64)))))
(-.f64 (.f64 (cos.f64 (.f64 #s(literal 1/2 binary64) (.f64 x #s(literal 2 binary64)))) (cos.f64 (.f64 eps #s(literal 1/2 binary64)))) (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) (.f64 x #s(literal 2 binary64)))) (sin.f64 (.f64 eps #s(literal 1/2 binary64)))))
(-.f64 (.f64 (cos.f64 (.f64 (.f64 x #s(literal 2 binary64)) #s(literal 1/2 binary64))) (cos.f64 (.f64 eps #s(literal 1/2 binary64)))) (.f64 (sin.f64 (.f64 (.f64 x #s(literal 2 binary64)) #s(literal 1/2 binary64))) (sin.f64 (.f64 eps #s(literal 1/2 binary64)))))
(+.f64 (.f64 #s(literal 0 binary64) (cos.f64 (.f64 eps #s(literal 1/2 binary64)))) (.f64 #s(literal 1 binary64) (sin.f64 (.f64 eps #s(literal 1/2 binary64)))))
(+.f64 (.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) #s(literal 1 binary64)) (.f64 (cos.f64 (.f64 eps #s(literal 1/2 binary64))) #s(literal 0 binary64)))
(sin.f64 (*.f64 eps #s(literal 1/2 binary64)))
(fma.f64 #s(literal 0 binary64) (cos.f64 (.f64 eps #s(literal 1/2 binary64))) (.f64 #s(literal 1 binary64) (sin.f64 (*.f64 eps #s(literal 1/2 binary64)))))
(fma.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) #s(literal 1 binary64) (.f64 (cos.f64 (*.f64 eps #s(literal 1/2 binary64))) #s(literal 0 binary64)))
(exp.f64 (*.f64 (log.f64 x) #s(literal 3 binary64)))
(pow.f64 x #s(literal 3 binary64))
(pow.f64 (*.f64 x x) #s(literal 3/2 binary64))
(pow.f64 (pow.f64 x #s(literal 3/2 binary64)) #s(literal 2 binary64))
(pow.f64 (exp.f64 (log.f64 x)) #s(literal 3 binary64))
(.f64 x (.f64 x x))
(.f64 (.f64 x x) x)
(*.f64 (pow.f64 x #s(literal 3/2 binary64)) (pow.f64 x #s(literal 3/2 binary64)))
(+.f64 (.f64 x #s(literal 1/120 binary64)) (.f64 x (.f64 (.f64 x x) #s(literal -1/5040 binary64))))
(+.f64 (.f64 x (.f64 (.f64 x x) #s(literal -1/5040 binary64))) (.f64 x #s(literal 1/120 binary64)))
(-.f64 (/.f64 (.f64 (.f64 x (.f64 (.f64 x x) #s(literal -1/5040 binary64))) (.f64 x (.f64 (.f64 x x) #s(literal -1/5040 binary64)))) (-.f64 (.f64 x (.f64 (.f64 x x) #s(literal -1/5040 binary64))) (.f64 x #s(literal 1/120 binary64)))) (/.f64 (.f64 (.f64 x #s(literal 1/120 binary64)) (.f64 x #s(literal 1/120 binary64))) (-.f64 (.f64 x (.f64 (.f64 x x) #s(literal -1/5040 binary64))) (.f64 x #s(literal 1/120 binary64)))))
(fma.f64 x #s(literal 1/120 binary64) (.f64 x (.f64 (*.f64 x x) #s(literal -1/5040 binary64))))
(fma.f64 x (.f64 (.f64 x x) #s(literal -1/5040 binary64)) (*.f64 x #s(literal 1/120 binary64)))
(fma.f64 (.f64 x x) (.f64 x #s(literal -1/5040 binary64)) (*.f64 x #s(literal 1/120 binary64)))
(fma.f64 (.f64 x (.f64 x x)) #s(literal -1/5040 binary64) (*.f64 x #s(literal 1/120 binary64)))
(fma.f64 #s(literal -1/5040 binary64) (.f64 x (.f64 x x)) (*.f64 x #s(literal 1/120 binary64)))
(fma.f64 #s(literal 1/120 binary64) x (.f64 x (.f64 (*.f64 x x) #s(literal -1/5040 binary64))))
(fma.f64 (.f64 (.f64 x x) #s(literal -1/5040 binary64)) x (*.f64 x #s(literal 1/120 binary64)))
(fma.f64 (.f64 x #s(literal -1/5040 binary64)) (.f64 x x) (*.f64 x #s(literal 1/120 binary64)))
(/.f64 (fma.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) #s(literal -1/128024064000 binary64))) (.f64 (.f64 x (.f64 x x)) #s(literal 1/1728000 binary64))) (fma.f64 (.f64 x (.f64 (.f64 x x) #s(literal -1/5040 binary64))) (.f64 x (.f64 (.f64 x x) #s(literal -1/5040 binary64))) (-.f64 (.f64 (.f64 x #s(literal 1/120 binary64)) (.f64 x #s(literal 1/120 binary64))) (.f64 (.f64 x (.f64 (.f64 x x) #s(literal -1/5040 binary64))) (*.f64 x #s(literal 1/120 binary64))))))
(/.f64 (-.f64 (.f64 (.f64 x (.f64 (.f64 x x) #s(literal -1/5040 binary64))) (.f64 x (.f64 (.f64 x x) #s(literal -1/5040 binary64)))) (.f64 (.f64 x #s(literal 1/120 binary64)) (.f64 x #s(literal 1/120 binary64)))) (-.f64 (.f64 x (.f64 (.f64 x x) #s(literal -1/5040 binary64))) (.f64 x #s(literal 1/120 binary64))))
(/.f64 (.f64 x (fma.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) #s(literal -1/128024064000 binary64)) #s(literal 1/1728000 binary64))) (-.f64 (fma.f64 (.f64 (.f64 x x) (.f64 x x)) #s(literal 1/25401600 binary64) #s(literal 1/14400 binary64)) (.f64 (*.f64 x x) #s(literal -1/604800 binary64))))
(/.f64 (.f64 x (fma.f64 (.f64 (.f64 x x) (.f64 x x)) #s(literal 1/25401600 binary64) #s(literal -1/14400 binary64))) (fma.f64 x (*.f64 x #s(literal -1/5040 binary64)) #s(literal -1/120 binary64)))
(/.f64 (.f64 (fma.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) #s(literal -1/128024064000 binary64)) #s(literal 1/1728000 binary64)) x) (-.f64 (fma.f64 (.f64 (.f64 x x) (.f64 x x)) #s(literal 1/25401600 binary64) #s(literal 1/14400 binary64)) (.f64 (*.f64 x x) #s(literal -1/604800 binary64))))
(/.f64 (.f64 (fma.f64 (.f64 (.f64 x x) (.f64 x x)) #s(literal 1/25401600 binary64) #s(literal -1/14400 binary64)) x) (fma.f64 x (*.f64 x #s(literal -1/5040 binary64)) #s(literal -1/120 binary64)))
(/.f64 (neg.f64 (fma.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) #s(literal -1/128024064000 binary64))) (.f64 (.f64 x (.f64 x x)) #s(literal 1/1728000 binary64)))) (neg.f64 (fma.f64 (.f64 x (.f64 (.f64 x x) #s(literal -1/5040 binary64))) (.f64 x (.f64 (.f64 x x) #s(literal -1/5040 binary64))) (-.f64 (.f64 (.f64 x #s(literal 1/120 binary64)) (.f64 x #s(literal 1/120 binary64))) (.f64 (.f64 x (.f64 (.f64 x x) #s(literal -1/5040 binary64))) (*.f64 x #s(literal 1/120 binary64)))))))
(/.f64 (neg.f64 (-.f64 (.f64 (.f64 x (.f64 (.f64 x x) #s(literal -1/5040 binary64))) (.f64 x (.f64 (.f64 x x) #s(literal -1/5040 binary64)))) (.f64 (.f64 x #s(literal 1/120 binary64)) (.f64 x #s(literal 1/120 binary64))))) (neg.f64 (-.f64 (.f64 x (.f64 (.f64 x x) #s(literal -1/5040 binary64))) (.f64 x #s(literal 1/120 binary64)))))
(/.f64 (neg.f64 (.f64 x (fma.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) #s(literal -1/128024064000 binary64)) #s(literal 1/1728000 binary64)))) (neg.f64 (-.f64 (fma.f64 (.f64 (.f64 x x) (.f64 x x)) #s(literal 1/25401600 binary64) #s(literal 1/14400 binary64)) (.f64 (*.f64 x x) #s(literal -1/604800 binary64)))))
(/.f64 (neg.f64 (.f64 x (fma.f64 (.f64 (.f64 x x) (.f64 x x)) #s(literal 1/25401600 binary64) #s(literal -1/14400 binary64)))) (neg.f64 (fma.f64 x (*.f64 x #s(literal -1/5040 binary64)) #s(literal -1/120 binary64))))
(/.f64 (neg.f64 (.f64 (fma.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) #s(literal -1/128024064000 binary64)) #s(literal 1/1728000 binary64)) x)) (neg.f64 (-.f64 (fma.f64 (.f64 (.f64 x x) (.f64 x x)) #s(literal 1/25401600 binary64) #s(literal 1/14400 binary64)) (.f64 (*.f64 x x) #s(literal -1/604800 binary64)))))
(/.f64 (neg.f64 (.f64 (fma.f64 (.f64 (.f64 x x) (.f64 x x)) #s(literal 1/25401600 binary64) #s(literal -1/14400 binary64)) x)) (neg.f64 (fma.f64 x (*.f64 x #s(literal -1/5040 binary64)) #s(literal -1/120 binary64))))
(/.f64 (fma.f64 (.f64 x (.f64 x x)) #s(literal 1/1728000 binary64) (.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) #s(literal -1/128024064000 binary64))))) (fma.f64 (.f64 x #s(literal 1/120 binary64)) (.f64 x #s(literal 1/120 binary64)) (-.f64 (.f64 (.f64 x (.f64 (.f64 x x) #s(literal -1/5040 binary64))) (.f64 x (.f64 (.f64 x x) #s(literal -1/5040 binary64)))) (.f64 (.f64 x #s(literal 1/120 binary64)) (.f64 x (.f64 (*.f64 x x) #s(literal -1/5040 binary64)))))))
(.f64 x (fma.f64 (.f64 x x) #s(literal -1/5040 binary64) #s(literal 1/120 binary64)))
(.f64 (fma.f64 (.f64 x x) #s(literal -1/5040 binary64) #s(literal 1/120 binary64)) x)
(*.f64 x (cos.f64 eps))
(*.f64 (cos.f64 eps) x)

eval133.0ms (1%)

Memory: 12.5MiB live, 169.1MiB allocated
Compiler: Compiled 27 409 to 2 109 computations (92.3% saved)

prune101.0ms (0.8%)

Memory

-10.7MiB live, 153.9MiB allocated

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	948	7	955
Fresh	1	2	3
Picked	5	0	5
Done	1	0	1
Total	955	9	964

Accuracy

100.0%

Counts

964 → 9

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	99.9%	(.f64 (.f64 #s(approx (sin (* (+ eps 0) 1/2)) (.f64 eps (fma.f64 eps (.f64 eps #s(literal -1/48 binary64)) #s(literal 1/2 binary64)))) (cos.f64 (*.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)))) #s(literal 2 binary64))
▶	99.7%	(.f64 (.f64 #s(approx (sin (* (+ eps 0) 1/2)) (.f64 #s(literal 1/2 binary64) eps)) (cos.f64 (.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)))) #s(literal 2 binary64))
	63.9%	#s(approx (- (sin (+ x eps)) (sin x)) (-.f64 #s(approx (+ (* (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) (fma.f64 eps (fma.f64 (*.f64 x #s(literal -1/2 binary64)) (+.f64 eps x) #s(literal 1 binary64)) x)) x))
	99.7%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 eps (fma.f64 eps (.f64 #s(literal -1/2 binary64) (sin.f64 x)) (cos.f64 x))))
	99.4%	#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 eps (cos.f64 x)))
	98.8%	#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (- (+ (* (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) x) (fma.f64 (.f64 eps (.f64 x x)) #s(literal -1/2 binary64) eps)))
▶	99.0%	#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (- (+ (* (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) x) (fma.f64 eps (fma.f64 eps (.f64 eps (fma.f64 (.f64 x x) #s(literal 1/12 binary64) #s(literal -1/6 binary64))) (.f64 (.f64 x #s(literal -1/2 binary64)) (+.f64 eps x))) eps)))
▶	98.9%	#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (- (+ (* (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) x) (fma.f64 eps (.f64 (.f64 x #s(literal -1/2 binary64)) (+.f64 eps x)) eps)))
▶	98.0%	#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (sin eps) (fma.f64 eps (.f64 eps (.f64 eps #s(literal -1/6 binary64))) eps)))

Compiler

Compiled 272 to 152 computations (44.1% saved)

simplify266.0ms (2.1%)

Memory

5.5MiB live, 313.1MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 20 expressions of interest:

New	Metric	Score
cost-diff	0	#s(approx (sin (* (+ eps 0) 1/2)) (*.f64 #s(literal 1/2 binary64) eps))
cost-diff	0	(.f64 #s(approx (sin ( (+ eps 0) 1/2)) (.f64 #s(literal 1/2 binary64) eps)) (cos.f64 (.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64))))
cost-diff	0	(.f64 (.f64 #s(approx (sin (* (+ eps 0) 1/2)) (.f64 #s(literal 1/2 binary64) eps)) (cos.f64 (.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)))) #s(literal 2 binary64))
cost-diff	320	(*.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64))
cost-diff	0	(fma.f64 eps (.f64 eps (fma.f64 (.f64 x x) #s(literal 1/12 binary64) #s(literal -1/6 binary64))) (.f64 (.f64 x #s(literal -1/2 binary64)) (+.f64 eps x)))
cost-diff	0	(fma.f64 eps (fma.f64 eps (.f64 eps (fma.f64 (.f64 x x) #s(literal 1/12 binary64) #s(literal -1/6 binary64))) (.f64 (.f64 x #s(literal -1/2 binary64)) (+.f64 eps x))) eps)
cost-diff	0	#s(approx (- (+ (* (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) x) (fma.f64 eps (fma.f64 eps (.f64 eps (fma.f64 (.f64 x x) #s(literal 1/12 binary64) #s(literal -1/6 binary64))) (.f64 (.f64 x #s(literal -1/2 binary64)) (+.f64 eps x))) eps))
cost-diff	0	#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (- (+ (* (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) x) (fma.f64 eps (fma.f64 eps (.f64 eps (fma.f64 (.f64 x x) #s(literal 1/12 binary64) #s(literal -1/6 binary64))) (.f64 (.f64 x #s(literal -1/2 binary64)) (+.f64 eps x))) eps)))
cost-diff	0	(.f64 (.f64 x #s(literal -1/2 binary64)) (+.f64 eps x))
cost-diff	0	(fma.f64 eps (.f64 (.f64 x #s(literal -1/2 binary64)) (+.f64 eps x)) eps)
cost-diff	0	#s(approx (- (+ (* (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) x) (fma.f64 eps (.f64 (.f64 x #s(literal -1/2 binary64)) (+.f64 eps x)) eps))
cost-diff	0	#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (- (+ (* (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) x) (fma.f64 eps (.f64 (.f64 x #s(literal -1/2 binary64)) (+.f64 eps x)) eps)))
cost-diff	0	(.f64 eps (.f64 eps #s(literal -1/6 binary64)))
cost-diff	0	(fma.f64 eps (.f64 eps (.f64 eps #s(literal -1/6 binary64))) eps)
cost-diff	0	#s(approx (sin eps) (fma.f64 eps (.f64 eps (.f64 eps #s(literal -1/6 binary64))) eps))
cost-diff	0	#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (sin eps) (fma.f64 eps (.f64 eps (.f64 eps #s(literal -1/6 binary64))) eps)))
cost-diff	0	#s(approx (sin (* (+ eps 0) 1/2)) (.f64 eps (fma.f64 eps (.f64 eps #s(literal -1/48 binary64)) #s(literal 1/2 binary64))))
cost-diff	0	(.f64 #s(approx (sin ( (+ eps 0) 1/2)) (.f64 eps (fma.f64 eps (.f64 eps #s(literal -1/48 binary64)) #s(literal 1/2 binary64)))) (cos.f64 (*.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64))))
cost-diff	0	(.f64 (.f64 #s(approx (sin (* (+ eps 0) 1/2)) (.f64 eps (fma.f64 eps (.f64 eps #s(literal -1/48 binary64)) #s(literal 1/2 binary64)))) (cos.f64 (*.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)))) #s(literal 2 binary64))
cost-diff	320	(*.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64))

Rules

18 718×	`lower-fma.f32`
18 704×	`lower-fma.f64`
4 364×	`lower-*.f32`
4 336×	`lower-*.f64`
2 746×	`lower-+.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	57	468
0	87	456
1	163	456
2	448	453
3	1268	441
4	2359	441
5	4059	441
6	5795	441
7	7780	441
0	8117	422

Stop Event

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

Calls

Call 1

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

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

localize224.0ms (1.7%)

Memory

3.1MiB live, 320.3MiB allocated

Localize:

Found 20 expressions of interest:

New	Metric	Score
accuracy	0	(*.f64 #s(literal 1/2 binary64) eps)
accuracy	0.0078125	(.f64 #s(approx (sin ( (+ eps 0) 1/2)) (.f64 #s(literal 1/2 binary64) eps)) (cos.f64 (.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64))))
accuracy	0.04371266413587042	(cos.f64 (*.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)))
accuracy	0.14077803463153277	#s(approx (sin (* (+ eps 0) 1/2)) (*.f64 #s(literal 1/2 binary64) eps))
accuracy	0.0625	(fma.f64 eps (.f64 eps (fma.f64 (.f64 x x) #s(literal 1/12 binary64) #s(literal -1/6 binary64))) (.f64 (.f64 x #s(literal -1/2 binary64)) (+.f64 eps x)))
accuracy	0.13671875	(.f64 (.f64 x #s(literal -1/2 binary64)) (+.f64 eps x))
accuracy	0.3671875	(.f64 eps (fma.f64 (.f64 x x) #s(literal 1/12 binary64) #s(literal -1/6 binary64)))
accuracy	0.6089016869101457	#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (- (+ (* (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) x) (fma.f64 eps (fma.f64 eps (.f64 eps (fma.f64 (.f64 x x) #s(literal 1/12 binary64) #s(literal -1/6 binary64))) (.f64 (.f64 x #s(literal -1/2 binary64)) (+.f64 eps x))) eps)))
accuracy	0.00390625	(fma.f64 eps (.f64 (.f64 x #s(literal -1/2 binary64)) (+.f64 eps x)) eps)
accuracy	0.13671875	(.f64 (.f64 x #s(literal -1/2 binary64)) (+.f64 eps x))
accuracy	0.1662252980290556	#s(approx (- (+ (* (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) x) (fma.f64 eps (.f64 (.f64 x #s(literal -1/2 binary64)) (+.f64 eps x)) eps))
accuracy	0.6089016869101457	#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (- (+ (* (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) x) (fma.f64 eps (.f64 (.f64 x #s(literal -1/2 binary64)) (+.f64 eps x)) eps)))
accuracy	0	#s(approx (sin eps) (fma.f64 eps (.f64 eps (.f64 eps #s(literal -1/6 binary64))) eps))
accuracy	0.08984375	(.f64 eps (.f64 eps #s(literal -1/6 binary64)))
accuracy	0.37109375	(*.f64 eps #s(literal -1/6 binary64))
accuracy	1.2665934291908156	#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (sin eps) (fma.f64 eps (.f64 eps (.f64 eps #s(literal -1/6 binary64))) eps)))
accuracy	0	#s(approx (sin (* (+ eps 0) 1/2)) (.f64 eps (fma.f64 eps (.f64 eps #s(literal -1/48 binary64)) #s(literal 1/2 binary64))))
accuracy	0.0078125	(.f64 #s(approx (sin ( (+ eps 0) 1/2)) (.f64 eps (fma.f64 eps (.f64 eps #s(literal -1/48 binary64)) #s(literal 1/2 binary64)))) (cos.f64 (*.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64))))
accuracy	0.04371266413587042	(cos.f64 (*.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)))
accuracy	0.37109375	(*.f64 eps #s(literal -1/48 binary64))

Samples

67.0ms	174×	0	valid
64.0ms	81×	1	valid
2.0ms	1×	5	exit

Compiler

Compiled 331 to 55 computations (83.4% saved)

Precisions

Click to see histograms. Total time spent on operations: 99.0ms

ival-mult: 49.0ms (49.4% of total)

ival-add: 16.0ms (16.1% of total)

const: 10.0ms (10.1% of total)

adjust: 9.0ms (9.1% of total)

ival-sin: 8.0ms (8.1% of total)

ival-cos: 4.0ms (4% of total)

ival-sub: 3.0ms (3% of total)

exact: 1.0ms (1% of total)

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

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

series37.0ms (0.3%)

Memory

28.5MiB live, 66.5MiB allocated

Counts

24 → 480

Calls

Call 1

Inputs
#s(alt (.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)) (patch (.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)) #<representation binary64>) () ())
#s(alt (.f64 (.f64 #s(approx (sin (* (+ eps 0) 1/2)) (.f64 eps (fma.f64 eps (.f64 eps #s(literal -1/48 binary64)) #s(literal 1/2 binary64)))) (cos.f64 (.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)))) #s(literal 2 binary64)) (patch (.f64 (.f64 #s(approx (sin ( (+ eps 0) 1/2)) (.f64 eps (fma.f64 eps (.f64 eps #s(literal -1/48 binary64)) #s(literal 1/2 binary64)))) (cos.f64 (*.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)))) #s(literal 2 binary64)) #<representation binary64>) () ())
#s(alt (.f64 #s(approx (sin ( (+ eps 0) 1/2)) (.f64 eps (fma.f64 eps (.f64 eps #s(literal -1/48 binary64)) #s(literal 1/2 binary64)))) (cos.f64 (.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)))) (patch (.f64 #s(approx (sin (* (+ eps 0) 1/2)) (.f64 eps (fma.f64 eps (.f64 eps #s(literal -1/48 binary64)) #s(literal 1/2 binary64)))) (cos.f64 (*.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)))) #<representation binary64>) () ())
#s(alt #s(approx (sin (* (+ eps 0) 1/2)) (.f64 eps (fma.f64 eps (.f64 eps #s(literal -1/48 binary64)) #s(literal 1/2 binary64)))) (patch #s(approx (sin (* (+ eps 0) 1/2)) (.f64 eps (fma.f64 eps (.f64 eps #s(literal -1/48 binary64)) #s(literal 1/2 binary64)))) #<representation binary64>) () ())
#s(alt #s(approx (- (sin (+ x eps)) (sin x)) #s(approx (sin eps) (fma.f64 eps (.f64 eps (.f64 eps #s(literal -1/6 binary64))) eps))) (patch #s(approx (- (sin (+ x eps)) (sin x)) #s(approx (sin eps) (fma.f64 eps (.f64 eps (.f64 eps #s(literal -1/6 binary64))) eps))) #<representation binary64>) () ())
#s(alt #s(approx (sin eps) (fma.f64 eps (.f64 eps (.f64 eps #s(literal -1/6 binary64))) eps)) (patch #s(approx (sin eps) (fma.f64 eps (.f64 eps (.f64 eps #s(literal -1/6 binary64))) eps)) #<representation binary64>) () ())
#s(alt (fma.f64 eps (.f64 eps (.f64 eps #s(literal -1/6 binary64))) eps) (patch (fma.f64 eps (.f64 eps (.f64 eps #s(literal -1/6 binary64))) eps) #<representation binary64>) () ())
#s(alt (.f64 eps (.f64 eps #s(literal -1/6 binary64))) (patch (.f64 eps (.f64 eps #s(literal -1/6 binary64))) #<representation binary64>) () ())
#s(alt #s(approx (- (sin (+ x eps)) (sin x)) #s(approx (- (+ (* (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) x) (fma.f64 eps (.f64 (.f64 x #s(literal -1/2 binary64)) (+.f64 eps x)) eps))) (patch #s(approx (- (sin (+ x eps)) (sin x)) #s(approx (- (+ (* (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) x) (fma.f64 eps (.f64 (.f64 x #s(literal -1/2 binary64)) (+.f64 eps x)) eps))) #<representation binary64>) () ())
#s(alt #s(approx (- (+ (* (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) x) (fma.f64 eps (.f64 (.f64 x #s(literal -1/2 binary64)) (+.f64 eps x)) eps)) (patch #s(approx (- (+ (* (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) x) (fma.f64 eps (.f64 (.f64 x #s(literal -1/2 binary64)) (+.f64 eps x)) eps)) #<representation binary64>) () ())
#s(alt (fma.f64 eps (.f64 (.f64 x #s(literal -1/2 binary64)) (+.f64 eps x)) eps) (patch (fma.f64 eps (.f64 (.f64 x #s(literal -1/2 binary64)) (+.f64 eps x)) eps) #<representation binary64>) () ())
#s(alt (.f64 (.f64 x #s(literal -1/2 binary64)) (+.f64 eps x)) (patch (.f64 (.f64 x #s(literal -1/2 binary64)) (+.f64 eps x)) #<representation binary64>) () ())
#s(alt #s(approx (- (sin (+ x eps)) (sin x)) #s(approx (- (+ (* (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) x) (fma.f64 eps (fma.f64 eps (.f64 eps (fma.f64 (.f64 x x) #s(literal 1/12 binary64) #s(literal -1/6 binary64))) (.f64 (.f64 x #s(literal -1/2 binary64)) (+.f64 eps x))) eps))) (patch #s(approx (- (sin (+ x eps)) (sin x)) #s(approx (- (+ (* (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) x) (fma.f64 eps (fma.f64 eps (.f64 eps (fma.f64 (.f64 x x) #s(literal 1/12 binary64) #s(literal -1/6 binary64))) (.f64 (.f64 x #s(literal -1/2 binary64)) (+.f64 eps x))) eps))) #<representation binary64>) () ())
#s(alt #s(approx (- (+ (* (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) x) (fma.f64 eps (fma.f64 eps (.f64 eps (fma.f64 (.f64 x x) #s(literal 1/12 binary64) #s(literal -1/6 binary64))) (.f64 (.f64 x #s(literal -1/2 binary64)) (+.f64 eps x))) eps)) (patch #s(approx (- (+ (* (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) x) (fma.f64 eps (fma.f64 eps (.f64 eps (fma.f64 (.f64 x x) #s(literal 1/12 binary64) #s(literal -1/6 binary64))) (.f64 (.f64 x #s(literal -1/2 binary64)) (+.f64 eps x))) eps)) #<representation binary64>) () ())
#s(alt (fma.f64 eps (fma.f64 eps (.f64 eps (fma.f64 (.f64 x x) #s(literal 1/12 binary64) #s(literal -1/6 binary64))) (.f64 (.f64 x #s(literal -1/2 binary64)) (+.f64 eps x))) eps) (patch (fma.f64 eps (fma.f64 eps (.f64 eps (fma.f64 (.f64 x x) #s(literal 1/12 binary64) #s(literal -1/6 binary64))) (.f64 (.f64 x #s(literal -1/2 binary64)) (+.f64 eps x))) eps) #<representation binary64>) () ())
#s(alt (fma.f64 eps (.f64 eps (fma.f64 (.f64 x x) #s(literal 1/12 binary64) #s(literal -1/6 binary64))) (.f64 (.f64 x #s(literal -1/2 binary64)) (+.f64 eps x))) (patch (fma.f64 eps (.f64 eps (fma.f64 (.f64 x x) #s(literal 1/12 binary64) #s(literal -1/6 binary64))) (.f64 (.f64 x #s(literal -1/2 binary64)) (+.f64 eps x))) #<representation binary64>) () ())
#s(alt (.f64 (.f64 #s(approx (sin (* (+ eps 0) 1/2)) (.f64 #s(literal 1/2 binary64) eps)) (cos.f64 (.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)))) #s(literal 2 binary64)) (patch (.f64 (.f64 #s(approx (sin (* (+ eps 0) 1/2)) (.f64 #s(literal 1/2 binary64) eps)) (cos.f64 (.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)))) #s(literal 2 binary64)) #<representation binary64>) () ())
#s(alt (.f64 #s(approx (sin ( (+ eps 0) 1/2)) (.f64 #s(literal 1/2 binary64) eps)) (cos.f64 (.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)))) (patch (.f64 #s(approx (sin ( (+ eps 0) 1/2)) (.f64 #s(literal 1/2 binary64) eps)) (cos.f64 (.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)))) #<representation binary64>) () ())
#s(alt #s(approx (sin (* (+ eps 0) 1/2)) (.f64 #s(literal 1/2 binary64) eps)) (patch #s(approx (sin ( (+ eps 0) 1/2)) (*.f64 #s(literal 1/2 binary64) eps)) #<representation binary64>) () ())
#s(alt (.f64 eps #s(literal -1/48 binary64)) (patch (.f64 eps #s(literal -1/48 binary64)) #<representation binary64>) () ())
#s(alt (cos.f64 (.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64))) (patch (cos.f64 (.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64))) #<representation binary64>) () ())
#s(alt (.f64 eps #s(literal -1/6 binary64)) (patch (.f64 eps #s(literal -1/6 binary64)) #<representation binary64>) () ())
#s(alt (.f64 eps (fma.f64 (.f64 x x) #s(literal 1/12 binary64) #s(literal -1/6 binary64))) (patch (.f64 eps (fma.f64 (.f64 x x) #s(literal 1/12 binary64) #s(literal -1/6 binary64))) #<representation binary64>) () ())
#s(alt (.f64 #s(literal 1/2 binary64) eps) (patch (.f64 #s(literal 1/2 binary64) eps) #<representation binary64>) () ())

Outputs
#s(alt (* 1/2 eps) (taylor 0 x) (#s(alt (.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)) (patch (.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt (+ x (* 1/2 eps)) (taylor 0 x) (#s(alt (.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)) (patch (.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt (+ x (* 1/2 eps)) (taylor 0 x) (#s(alt (.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)) (patch (.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt (+ x (* 1/2 eps)) (taylor 0 x) (#s(alt (.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)) (patch (.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt x (taylor inf x) (#s(alt (.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)) (patch (.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1 (* 1/2 (/ eps x)))) (taylor inf x) (#s(alt (.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)) (patch (.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1 (* 1/2 (/ eps x)))) (taylor inf x) (#s(alt (.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)) (patch (.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1 (* 1/2 (/ eps x)))) (taylor inf x) (#s(alt (.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)) (patch (.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt x (taylor -inf x) (#s(alt (.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)) (patch (.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (- (* -1/2 (/ eps x)) 1))) (taylor -inf x) (#s(alt (.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)) (patch (.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (- (* -1/2 (/ eps x)) 1))) (taylor -inf x) (#s(alt (.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)) (patch (.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (- (* -1/2 (/ eps x)) 1))) (taylor -inf x) (#s(alt (.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)) (patch (.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt x (taylor 0 eps) (#s(alt (.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)) (patch (.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt (+ x (* 1/2 eps)) (taylor 0 eps) (#s(alt (.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)) (patch (.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt (+ x (* 1/2 eps)) (taylor 0 eps) (#s(alt (.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)) (patch (.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt (+ x (* 1/2 eps)) (taylor 0 eps) (#s(alt (.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)) (patch (.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* 1/2 eps) (taylor inf eps) (#s(alt (.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)) (patch (.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* eps (+ 1/2 (/ x eps))) (taylor inf eps) (#s(alt (.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)) (patch (.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* eps (+ 1/2 (/ x eps))) (taylor inf eps) (#s(alt (.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)) (patch (.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* eps (+ 1/2 (/ x eps))) (taylor inf eps) (#s(alt (.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)) (patch (.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* 1/2 eps) (taylor -inf eps) (#s(alt (.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)) (patch (.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* eps (- (* -1 (/ x eps)) 1/2))) (taylor -inf eps) (#s(alt (.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)) (patch (.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* eps (- (* -1 (/ x eps)) 1/2))) (taylor -inf eps) (#s(alt (.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)) (patch (.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* eps (- (* -1 (/ x eps)) 1/2))) (taylor -inf eps) (#s(alt (.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)) (patch (.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* eps (cos x)) (taylor 0 eps) (#s(alt (.f64 (.f64 #s(approx (sin (* (+ eps 0) 1/2)) (.f64 eps (fma.f64 eps (.f64 eps #s(literal -1/48 binary64)) #s(literal 1/2 binary64)))) (cos.f64 (.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)))) #s(literal 2 binary64)) (patch (.f64 (.f64 #s(approx (sin ( (+ eps 0) 1/2)) (.f64 eps (fma.f64 eps (.f64 eps #s(literal -1/48 binary64)) #s(literal 1/2 binary64)))) (cos.f64 (*.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)))) #s(literal 2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* eps (+ (cos x) (* -1/2 (* eps (sin x))))) (taylor 0 eps) (#s(alt (.f64 (.f64 #s(approx (sin (* (+ eps 0) 1/2)) (.f64 eps (fma.f64 eps (.f64 eps #s(literal -1/48 binary64)) #s(literal 1/2 binary64)))) (cos.f64 (.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)))) #s(literal 2 binary64)) (patch (.f64 (.f64 #s(approx (sin ( (+ eps 0) 1/2)) (.f64 eps (fma.f64 eps (.f64 eps #s(literal -1/48 binary64)) #s(literal 1/2 binary64)))) (cos.f64 (*.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)))) #s(literal 2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* 2 (* eps (+ (* -1/16 (cos x)) (* -1/48 (cos x))))))))) (taylor 0 eps) (#s(alt (.f64 (.f64 #s(approx (sin (* (+ eps 0) 1/2)) (.f64 eps (fma.f64 eps (.f64 eps #s(literal -1/48 binary64)) #s(literal 1/2 binary64)))) (cos.f64 (.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)))) #s(literal 2 binary64)) (patch (.f64 (.f64 #s(approx (sin ( (+ eps 0) 1/2)) (.f64 eps (fma.f64 eps (.f64 eps #s(literal -1/48 binary64)) #s(literal 1/2 binary64)))) (cos.f64 (*.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)))) #s(literal 2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* eps (+ (* 1/24 (* eps (sin x))) (* 2 (+ (* -1/16 (cos x)) (* -1/48 (cos x)))))))))) (taylor 0 eps) (#s(alt (.f64 (.f64 #s(approx (sin (* (+ eps 0) 1/2)) (.f64 eps (fma.f64 eps (.f64 eps #s(literal -1/48 binary64)) #s(literal 1/2 binary64)))) (cos.f64 (.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)))) #s(literal 2 binary64)) (patch (.f64 (.f64 #s(approx (sin ( (+ eps 0) 1/2)) (.f64 eps (fma.f64 eps (.f64 eps #s(literal -1/48 binary64)) #s(literal 1/2 binary64)))) (cos.f64 (*.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)))) #s(literal 2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* 2 (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps)))) (taylor inf eps) (#s(alt (.f64 (.f64 #s(approx (sin (* (+ eps 0) 1/2)) (.f64 eps (fma.f64 eps (.f64 eps #s(literal -1/48 binary64)) #s(literal 1/2 binary64)))) (cos.f64 (.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)))) #s(literal 2 binary64)) (patch (.f64 (.f64 #s(approx (sin ( (+ eps 0) 1/2)) (.f64 eps (fma.f64 eps (.f64 eps #s(literal -1/48 binary64)) #s(literal 1/2 binary64)))) (cos.f64 (*.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)))) #s(literal 2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* 2 (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps)))) (taylor inf eps) (#s(alt (.f64 (.f64 #s(approx (sin (* (+ eps 0) 1/2)) (.f64 eps (fma.f64 eps (.f64 eps #s(literal -1/48 binary64)) #s(literal 1/2 binary64)))) (cos.f64 (.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)))) #s(literal 2 binary64)) (patch (.f64 (.f64 #s(approx (sin ( (+ eps 0) 1/2)) (.f64 eps (fma.f64 eps (.f64 eps #s(literal -1/48 binary64)) #s(literal 1/2 binary64)))) (cos.f64 (*.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)))) #s(literal 2 binary64)) #<representation binary64>) () ())) ())
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#s(alt (cos (* 1/2 (+ eps (* 2 x)))) (taylor inf eps) (#s(alt (cos.f64 (.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64))) (patch (cos.f64 (.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64))) #<representation binary64>) () ())) ())
#s(alt (cos (* 1/2 (+ eps (* 2 x)))) (taylor inf eps) (#s(alt (cos.f64 (.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64))) (patch (cos.f64 (.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64))) #<representation binary64>) () ())) ())
#s(alt (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (taylor -inf eps) (#s(alt (cos.f64 (.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64))) (patch (cos.f64 (.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64))) #<representation binary64>) () ())) ())
#s(alt (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (taylor -inf eps) (#s(alt (cos.f64 (.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64))) (patch (cos.f64 (.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64))) #<representation binary64>) () ())) ())
#s(alt (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (taylor -inf eps) (#s(alt (cos.f64 (.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64))) (patch (cos.f64 (.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64))) #<representation binary64>) () ())) ())
#s(alt (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (taylor -inf eps) (#s(alt (cos.f64 (.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64))) (patch (cos.f64 (.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64))) #<representation binary64>) () ())) ())
#s(alt (* -1/6 eps) (taylor 0 eps) (#s(alt (.f64 eps #s(literal -1/6 binary64)) (patch (.f64 eps #s(literal -1/6 binary64)) #<representation binary64>) () ())) ())
#s(alt (* -1/6 eps) (taylor 0 eps) (#s(alt (.f64 eps #s(literal -1/6 binary64)) (patch (.f64 eps #s(literal -1/6 binary64)) #<representation binary64>) () ())) ())
#s(alt (* -1/6 eps) (taylor 0 eps) (#s(alt (.f64 eps #s(literal -1/6 binary64)) (patch (.f64 eps #s(literal -1/6 binary64)) #<representation binary64>) () ())) ())
#s(alt (* -1/6 eps) (taylor 0 eps) (#s(alt (.f64 eps #s(literal -1/6 binary64)) (patch (.f64 eps #s(literal -1/6 binary64)) #<representation binary64>) () ())) ())
#s(alt (* -1/6 eps) (taylor inf eps) (#s(alt (.f64 eps #s(literal -1/6 binary64)) (patch (.f64 eps #s(literal -1/6 binary64)) #<representation binary64>) () ())) ())
#s(alt (* -1/6 eps) (taylor inf eps) (#s(alt (.f64 eps #s(literal -1/6 binary64)) (patch (.f64 eps #s(literal -1/6 binary64)) #<representation binary64>) () ())) ())
#s(alt (* -1/6 eps) (taylor inf eps) (#s(alt (.f64 eps #s(literal -1/6 binary64)) (patch (.f64 eps #s(literal -1/6 binary64)) #<representation binary64>) () ())) ())
#s(alt (* -1/6 eps) (taylor inf eps) (#s(alt (.f64 eps #s(literal -1/6 binary64)) (patch (.f64 eps #s(literal -1/6 binary64)) #<representation binary64>) () ())) ())
#s(alt (* -1/6 eps) (taylor -inf eps) (#s(alt (.f64 eps #s(literal -1/6 binary64)) (patch (.f64 eps #s(literal -1/6 binary64)) #<representation binary64>) () ())) ())
#s(alt (* -1/6 eps) (taylor -inf eps) (#s(alt (.f64 eps #s(literal -1/6 binary64)) (patch (.f64 eps #s(literal -1/6 binary64)) #<representation binary64>) () ())) ())
#s(alt (* -1/6 eps) (taylor -inf eps) (#s(alt (.f64 eps #s(literal -1/6 binary64)) (patch (.f64 eps #s(literal -1/6 binary64)) #<representation binary64>) () ())) ())
#s(alt (* -1/6 eps) (taylor -inf eps) (#s(alt (.f64 eps #s(literal -1/6 binary64)) (patch (.f64 eps #s(literal -1/6 binary64)) #<representation binary64>) () ())) ())
#s(alt (* eps (- (* 1/12 (pow x 2)) 1/6)) (taylor 0 eps) (#s(alt (.f64 eps (fma.f64 (.f64 x x) #s(literal 1/12 binary64) #s(literal -1/6 binary64))) (patch (.f64 eps (fma.f64 (.f64 x x) #s(literal 1/12 binary64) #s(literal -1/6 binary64))) #<representation binary64>) () ())) ())
#s(alt (* eps (- (* 1/12 (pow x 2)) 1/6)) (taylor 0 eps) (#s(alt (.f64 eps (fma.f64 (.f64 x x) #s(literal 1/12 binary64) #s(literal -1/6 binary64))) (patch (.f64 eps (fma.f64 (.f64 x x) #s(literal 1/12 binary64) #s(literal -1/6 binary64))) #<representation binary64>) () ())) ())
#s(alt (* eps (- (* 1/12 (pow x 2)) 1/6)) (taylor 0 eps) (#s(alt (.f64 eps (fma.f64 (.f64 x x) #s(literal 1/12 binary64) #s(literal -1/6 binary64))) (patch (.f64 eps (fma.f64 (.f64 x x) #s(literal 1/12 binary64) #s(literal -1/6 binary64))) #<representation binary64>) () ())) ())
#s(alt (* eps (- (* 1/12 (pow x 2)) 1/6)) (taylor 0 eps) (#s(alt (.f64 eps (fma.f64 (.f64 x x) #s(literal 1/12 binary64) #s(literal -1/6 binary64))) (patch (.f64 eps (fma.f64 (.f64 x x) #s(literal 1/12 binary64) #s(literal -1/6 binary64))) #<representation binary64>) () ())) ())
#s(alt (* eps (- (* 1/12 (pow x 2)) 1/6)) (taylor inf eps) (#s(alt (.f64 eps (fma.f64 (.f64 x x) #s(literal 1/12 binary64) #s(literal -1/6 binary64))) (patch (.f64 eps (fma.f64 (.f64 x x) #s(literal 1/12 binary64) #s(literal -1/6 binary64))) #<representation binary64>) () ())) ())
#s(alt (* eps (- (* 1/12 (pow x 2)) 1/6)) (taylor inf eps) (#s(alt (.f64 eps (fma.f64 (.f64 x x) #s(literal 1/12 binary64) #s(literal -1/6 binary64))) (patch (.f64 eps (fma.f64 (.f64 x x) #s(literal 1/12 binary64) #s(literal -1/6 binary64))) #<representation binary64>) () ())) ())
#s(alt (* eps (- (* 1/12 (pow x 2)) 1/6)) (taylor inf eps) (#s(alt (.f64 eps (fma.f64 (.f64 x x) #s(literal 1/12 binary64) #s(literal -1/6 binary64))) (patch (.f64 eps (fma.f64 (.f64 x x) #s(literal 1/12 binary64) #s(literal -1/6 binary64))) #<representation binary64>) () ())) ())
#s(alt (* eps (- (* 1/12 (pow x 2)) 1/6)) (taylor inf eps) (#s(alt (.f64 eps (fma.f64 (.f64 x x) #s(literal 1/12 binary64) #s(literal -1/6 binary64))) (patch (.f64 eps (fma.f64 (.f64 x x) #s(literal 1/12 binary64) #s(literal -1/6 binary64))) #<representation binary64>) () ())) ())
#s(alt (* eps (- (* 1/12 (pow x 2)) 1/6)) (taylor -inf eps) (#s(alt (.f64 eps (fma.f64 (.f64 x x) #s(literal 1/12 binary64) #s(literal -1/6 binary64))) (patch (.f64 eps (fma.f64 (.f64 x x) #s(literal 1/12 binary64) #s(literal -1/6 binary64))) #<representation binary64>) () ())) ())
#s(alt (* eps (- (* 1/12 (pow x 2)) 1/6)) (taylor -inf eps) (#s(alt (.f64 eps (fma.f64 (.f64 x x) #s(literal 1/12 binary64) #s(literal -1/6 binary64))) (patch (.f64 eps (fma.f64 (.f64 x x) #s(literal 1/12 binary64) #s(literal -1/6 binary64))) #<representation binary64>) () ())) ())
#s(alt (* eps (- (* 1/12 (pow x 2)) 1/6)) (taylor -inf eps) (#s(alt (.f64 eps (fma.f64 (.f64 x x) #s(literal 1/12 binary64) #s(literal -1/6 binary64))) (patch (.f64 eps (fma.f64 (.f64 x x) #s(literal 1/12 binary64) #s(literal -1/6 binary64))) #<representation binary64>) () ())) ())
#s(alt (* eps (- (* 1/12 (pow x 2)) 1/6)) (taylor -inf eps) (#s(alt (.f64 eps (fma.f64 (.f64 x x) #s(literal 1/12 binary64) #s(literal -1/6 binary64))) (patch (.f64 eps (fma.f64 (.f64 x x) #s(literal 1/12 binary64) #s(literal -1/6 binary64))) #<representation binary64>) () ())) ())
#s(alt (* -1/6 eps) (taylor 0 x) (#s(alt (.f64 eps (fma.f64 (.f64 x x) #s(literal 1/12 binary64) #s(literal -1/6 binary64))) (patch (.f64 eps (fma.f64 (.f64 x x) #s(literal 1/12 binary64) #s(literal -1/6 binary64))) #<representation binary64>) () ())) ())
#s(alt (+ (* -1/6 eps) (* 1/12 (* eps (pow x 2)))) (taylor 0 x) (#s(alt (.f64 eps (fma.f64 (.f64 x x) #s(literal 1/12 binary64) #s(literal -1/6 binary64))) (patch (.f64 eps (fma.f64 (.f64 x x) #s(literal 1/12 binary64) #s(literal -1/6 binary64))) #<representation binary64>) () ())) ())
#s(alt (+ (* -1/6 eps) (* 1/12 (* eps (pow x 2)))) (taylor 0 x) (#s(alt (.f64 eps (fma.f64 (.f64 x x) #s(literal 1/12 binary64) #s(literal -1/6 binary64))) (patch (.f64 eps (fma.f64 (.f64 x x) #s(literal 1/12 binary64) #s(literal -1/6 binary64))) #<representation binary64>) () ())) ())
#s(alt (+ (* -1/6 eps) (* 1/12 (* eps (pow x 2)))) (taylor 0 x) (#s(alt (.f64 eps (fma.f64 (.f64 x x) #s(literal 1/12 binary64) #s(literal -1/6 binary64))) (patch (.f64 eps (fma.f64 (.f64 x x) #s(literal 1/12 binary64) #s(literal -1/6 binary64))) #<representation binary64>) () ())) ())
#s(alt (* 1/12 (* eps (pow x 2))) (taylor inf x) (#s(alt (.f64 eps (fma.f64 (.f64 x x) #s(literal 1/12 binary64) #s(literal -1/6 binary64))) (patch (.f64 eps (fma.f64 (.f64 x x) #s(literal 1/12 binary64) #s(literal -1/6 binary64))) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (+ (* -1/6 (/ eps (pow x 2))) (* 1/12 eps))) (taylor inf x) (#s(alt (.f64 eps (fma.f64 (.f64 x x) #s(literal 1/12 binary64) #s(literal -1/6 binary64))) (patch (.f64 eps (fma.f64 (.f64 x x) #s(literal 1/12 binary64) #s(literal -1/6 binary64))) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (+ (* -1/6 (/ eps (pow x 2))) (* 1/12 eps))) (taylor inf x) (#s(alt (.f64 eps (fma.f64 (.f64 x x) #s(literal 1/12 binary64) #s(literal -1/6 binary64))) (patch (.f64 eps (fma.f64 (.f64 x x) #s(literal 1/12 binary64) #s(literal -1/6 binary64))) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (+ (* -1/6 (/ eps (pow x 2))) (* 1/12 eps))) (taylor inf x) (#s(alt (.f64 eps (fma.f64 (.f64 x x) #s(literal 1/12 binary64) #s(literal -1/6 binary64))) (patch (.f64 eps (fma.f64 (.f64 x x) #s(literal 1/12 binary64) #s(literal -1/6 binary64))) #<representation binary64>) () ())) ())
#s(alt (* 1/12 (* eps (pow x 2))) (taylor -inf x) (#s(alt (.f64 eps (fma.f64 (.f64 x x) #s(literal 1/12 binary64) #s(literal -1/6 binary64))) (patch (.f64 eps (fma.f64 (.f64 x x) #s(literal 1/12 binary64) #s(literal -1/6 binary64))) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (+ (* -1/6 (/ eps (pow x 2))) (* 1/12 eps))) (taylor -inf x) (#s(alt (.f64 eps (fma.f64 (.f64 x x) #s(literal 1/12 binary64) #s(literal -1/6 binary64))) (patch (.f64 eps (fma.f64 (.f64 x x) #s(literal 1/12 binary64) #s(literal -1/6 binary64))) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (+ (* -1/6 (/ eps (pow x 2))) (* 1/12 eps))) (taylor -inf x) (#s(alt (.f64 eps (fma.f64 (.f64 x x) #s(literal 1/12 binary64) #s(literal -1/6 binary64))) (patch (.f64 eps (fma.f64 (.f64 x x) #s(literal 1/12 binary64) #s(literal -1/6 binary64))) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (+ (* -1/6 (/ eps (pow x 2))) (* 1/12 eps))) (taylor -inf x) (#s(alt (.f64 eps (fma.f64 (.f64 x x) #s(literal 1/12 binary64) #s(literal -1/6 binary64))) (patch (.f64 eps (fma.f64 (.f64 x x) #s(literal 1/12 binary64) #s(literal -1/6 binary64))) #<representation binary64>) () ())) ())
#s(alt (* 1/2 eps) (taylor 0 eps) (#s(alt (.f64 #s(literal 1/2 binary64) eps) (patch (.f64 #s(literal 1/2 binary64) eps) #<representation binary64>) () ())) ())
#s(alt (* 1/2 eps) (taylor 0 eps) (#s(alt (.f64 #s(literal 1/2 binary64) eps) (patch (.f64 #s(literal 1/2 binary64) eps) #<representation binary64>) () ())) ())
#s(alt (* 1/2 eps) (taylor 0 eps) (#s(alt (.f64 #s(literal 1/2 binary64) eps) (patch (.f64 #s(literal 1/2 binary64) eps) #<representation binary64>) () ())) ())
#s(alt (* 1/2 eps) (taylor 0 eps) (#s(alt (.f64 #s(literal 1/2 binary64) eps) (patch (.f64 #s(literal 1/2 binary64) eps) #<representation binary64>) () ())) ())
#s(alt (* 1/2 eps) (taylor inf eps) (#s(alt (.f64 #s(literal 1/2 binary64) eps) (patch (.f64 #s(literal 1/2 binary64) eps) #<representation binary64>) () ())) ())
#s(alt (* 1/2 eps) (taylor inf eps) (#s(alt (.f64 #s(literal 1/2 binary64) eps) (patch (.f64 #s(literal 1/2 binary64) eps) #<representation binary64>) () ())) ())
#s(alt (* 1/2 eps) (taylor inf eps) (#s(alt (.f64 #s(literal 1/2 binary64) eps) (patch (.f64 #s(literal 1/2 binary64) eps) #<representation binary64>) () ())) ())
#s(alt (* 1/2 eps) (taylor inf eps) (#s(alt (.f64 #s(literal 1/2 binary64) eps) (patch (.f64 #s(literal 1/2 binary64) eps) #<representation binary64>) () ())) ())
#s(alt (* 1/2 eps) (taylor -inf eps) (#s(alt (.f64 #s(literal 1/2 binary64) eps) (patch (.f64 #s(literal 1/2 binary64) eps) #<representation binary64>) () ())) ())
#s(alt (* 1/2 eps) (taylor -inf eps) (#s(alt (.f64 #s(literal 1/2 binary64) eps) (patch (.f64 #s(literal 1/2 binary64) eps) #<representation binary64>) () ())) ())
#s(alt (* 1/2 eps) (taylor -inf eps) (#s(alt (.f64 #s(literal 1/2 binary64) eps) (patch (.f64 #s(literal 1/2 binary64) eps) #<representation binary64>) () ())) ())
#s(alt (* 1/2 eps) (taylor -inf eps) (#s(alt (.f64 #s(literal 1/2 binary64) eps) (patch (.f64 #s(literal 1/2 binary64) eps) #<representation binary64>) () ())) ())

Calls

120 calls:

Time	Variable		Point	Expression
3.0ms	eps	@	-inf	(* 1/2 eps)
1.0ms	eps	@	-inf	(+ (* eps (+ (* eps (* eps (+ (* (* x x) 1/12) -1/6))) (* (* x -1/2) (+ eps x)))) eps)
1.0ms	eps	@	-inf	(+ (* eps (* (* x -1/2) (+ eps x))) eps)
1.0ms	eps	@	0	(+ (* eps (* (* x -1/2) (+ eps x))) eps)
0.0ms	eps	@	0	(* eps (+ (* (* x x) 1/12) -1/6))

simplify339.0ms (2.6%)

Memory

-6.4MiB live, 424.4MiB allocated

Algorithm

1×	egg-herbie

Rules

15 332×	`lower-fma.f64`
15 332×	`lower-fma.f32`
7 726×	`lower-*.f64`
7 726×	`lower-*.f32`
4 126×	`lower-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	445	5705
1	1377	5412
2	3925	5392
0	8831	4994

Stop Event

1×	iter limit
1×	node limit

Counts

480 → 474

Calls

Call 1

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

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

rewrite325.0ms (2.5%)

Memory

-6.4MiB live, 441.2MiB allocated

Rules

6 356×	`lower-*.f32`
6 328×	`lower-*.f64`
3 674×	`lower-fma.f32`
3 660×	`lower-fma.f64`
3 636×	`lower-/.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	57	386
0	87	374
1	333	371
2	3005	371
0	9211	360

Stop Event

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

Counts

24 → 307

Calls

Call 1

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

Outputs
(+.f64 (.f64 eps #s(literal 1/2 binary64)) (.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 2 binary64))))
(+.f64 (.f64 eps #s(literal 1/2 binary64)) (.f64 (*.f64 x #s(literal 2 binary64)) #s(literal 1/2 binary64)))
(+.f64 (.f64 #s(literal 1/2 binary64) (.f64 x #s(literal 2 binary64))) (*.f64 eps #s(literal 1/2 binary64)))
(+.f64 (.f64 (.f64 x #s(literal 2 binary64)) #s(literal 1/2 binary64)) (*.f64 eps #s(literal 1/2 binary64)))
(fma.f64 eps #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (.f64 x #s(literal 2 binary64))))
(fma.f64 eps #s(literal 1/2 binary64) (.f64 (.f64 x #s(literal 2 binary64)) #s(literal 1/2 binary64)))
(fma.f64 #s(literal 1/2 binary64) eps (.f64 #s(literal 1/2 binary64) (.f64 x #s(literal 2 binary64))))
(fma.f64 #s(literal 1/2 binary64) eps (.f64 (.f64 x #s(literal 2 binary64)) #s(literal 1/2 binary64)))
(fma.f64 #s(literal 1/2 binary64) (.f64 x #s(literal 2 binary64)) (.f64 eps #s(literal 1/2 binary64)))
(fma.f64 (.f64 x #s(literal 2 binary64)) #s(literal 1/2 binary64) (.f64 eps #s(literal 1/2 binary64)))
(/.f64 (.f64 #s(literal 1/2 binary64) (fma.f64 eps (.f64 eps eps) (.f64 (.f64 x (.f64 x x)) #s(literal 8 binary64)))) (fma.f64 eps (-.f64 eps (.f64 x #s(literal 2 binary64))) (.f64 (.f64 x x) #s(literal 4 binary64))))
(/.f64 (.f64 #s(literal 1/2 binary64) (-.f64 (.f64 (.f64 x x) #s(literal 4 binary64)) (.f64 eps eps))) (-.f64 (*.f64 x #s(literal 2 binary64)) eps))
(/.f64 (.f64 (fma.f64 eps (.f64 eps eps) (.f64 (.f64 x (.f64 x x)) #s(literal 8 binary64))) #s(literal 1/2 binary64)) (fma.f64 eps (-.f64 eps (.f64 x #s(literal 2 binary64))) (.f64 (.f64 x x) #s(literal 4 binary64))))
(/.f64 (.f64 (-.f64 (.f64 (.f64 x x) #s(literal 4 binary64)) (.f64 eps eps)) #s(literal 1/2 binary64)) (-.f64 (*.f64 x #s(literal 2 binary64)) eps))
(*.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64))
(*.f64 #s(literal 1/2 binary64) (fma.f64 x #s(literal 2 binary64) eps))
(.f64 #s(literal 2 binary64) (.f64 #s(approx (sin (* (+ eps 0) 1/2)) (.f64 eps (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal 1/2 binary64)))) (cos.f64 (*.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)))))
(.f64 #s(approx (sin ( (+ eps 0) 1/2)) (.f64 eps (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal 1/2 binary64)))) (.f64 #s(literal 2 binary64) (cos.f64 (.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)))))
(.f64 (cos.f64 (.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64))) (.f64 #s(approx (sin ( (+ eps 0) 1/2)) (.f64 eps (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal 1/2 binary64)))) #s(literal 2 binary64)))
(.f64 (.f64 #s(approx (sin (* (+ eps 0) 1/2)) (.f64 eps (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal 1/2 binary64)))) (cos.f64 (*.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)))) #s(literal 2 binary64))
(.f64 (.f64 #s(literal 2 binary64) (cos.f64 (.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)))) #s(approx (sin ( (+ eps 0) 1/2)) (.f64 eps (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal 1/2 binary64)))))
(.f64 (.f64 #s(literal 2 binary64) #s(approx (sin (* (+ eps 0) 1/2)) (.f64 eps (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal 1/2 binary64))))) (cos.f64 (*.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64))))
(.f64 #s(approx (sin ( (+ eps 0) 1/2)) (.f64 eps (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal 1/2 binary64)))) (cos.f64 (*.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64))))
(.f64 (cos.f64 (.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64))) #s(approx (sin (* (+ eps 0) 1/2)) (.f64 eps (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal 1/2 binary64)))))
#s(approx (sin (* (+ eps 0) 1/2)) (.f64 eps (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal 1/2 binary64))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (sin eps) (fma.f64 eps (.f64 #s(literal -1/6 binary64) (.f64 eps eps)) eps)))
#s(approx (sin eps) (fma.f64 eps (.f64 #s(literal -1/6 binary64) (.f64 eps eps)) eps))
(+.f64 eps (.f64 eps (.f64 #s(literal -1/6 binary64) (*.f64 eps eps))))
(+.f64 eps (+.f64 #s(literal 0 binary64) (.f64 eps (.f64 #s(literal -1/6 binary64) (*.f64 eps eps)))))
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(fma.f64 eps #s(literal 1/2 binary64) #s(literal 0 binary64))
(fma.f64 #s(literal 1/2 binary64) eps #s(literal 0 binary64))
(/.f64 (.f64 #s(literal 1/2 binary64) (.f64 eps (.f64 eps eps))) (.f64 eps eps))
(/.f64 (.f64 #s(literal 1/2 binary64) (.f64 eps eps)) eps)
(/.f64 (.f64 (.f64 eps (.f64 eps eps)) #s(literal 1/2 binary64)) (.f64 eps eps))
(/.f64 (.f64 (.f64 eps eps) #s(literal 1/2 binary64)) eps)
(*.f64 eps #s(literal 1/2 binary64))
(*.f64 #s(literal 1/2 binary64) eps)

eval134.0ms (1%)

Memory: -1.7MiB live, 224.8MiB allocated
Compiler: Compiled 19 863 to 1 341 computations (93.2% saved)

prune192.0ms (1.5%)

Memory

-4.6MiB live, 214.3MiB allocated

Pruning

14 alts after pruning (12 fresh and 2 done)

	Pruned	Kept	Total
New	895	8	903
Fresh	0	4	4
Picked	3	2	5
Done	0	0	0
Total	898	14	912

Accuracy

100.0%

Counts

912 → 14

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	99.9%	(.f64 (.f64 #s(approx (sin (* (+ eps 0) 1/2)) (.f64 eps (fma.f64 eps (.f64 eps #s(literal -1/48 binary64)) #s(literal 1/2 binary64)))) (cos.f64 #s(approx (* (+ (* x 2) eps) 1/2) (fma.f64 #s(literal 1/2 binary64) eps x)))) #s(literal 2 binary64))
	99.7%	(.f64 (.f64 #s(approx (sin (* (+ eps 0) 1/2)) (.f64 #s(literal 1/2 binary64) eps)) (cos.f64 #s(approx ( (+ (* x 2) eps) 1/2) (fma.f64 #s(literal 1/2 binary64) eps x)))) #s(literal 2 binary64))
	63.9%	#s(approx (- (sin (+ x eps)) (sin x)) (-.f64 #s(approx (+ (* (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) (fma.f64 eps (fma.f64 (*.f64 x #s(literal -1/2 binary64)) (+.f64 eps x) #s(literal 1 binary64)) x)) x))
	99.7%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 eps (fma.f64 eps (.f64 #s(literal -1/2 binary64) (sin.f64 x)) (cos.f64 x))))
	99.4%	#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 eps (cos.f64 x)))
▶	98.8%	#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (- (+ (* (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) x) (fma.f64 (.f64 eps (.f64 x x)) #s(literal -1/2 binary64) eps)))
	36.7%	#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (- (+ (* (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) x) (fma.f64 (.f64 eps (.f64 eps eps)) (/.f64 #s(literal 1 binary64) (.f64 eps eps)) (.f64 (.f64 x #s(literal -1/2 binary64)) (.f64 (+.f64 x eps) eps)))))
	99.0%	#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (- (+ (* (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) x) (fma.f64 eps (fma.f64 eps #s(approx (* eps (+ (* (* x x) 1/12) -1/6)) (.f64 eps #s(literal -1/6 binary64))) (.f64 (*.f64 x #s(literal -1/2 binary64)) (+.f64 eps x))) eps)))
✓	98.9%	#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (- (+ (* (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) x) (fma.f64 eps (.f64 (.f64 x #s(literal -1/2 binary64)) (+.f64 eps x)) eps)))
▶	98.8%	#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (- (+ (* (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) x) (fma.f64 eps #s(approx (+ (* eps (* eps (+ (* (* x x) 1/12) -1/6))) (* (* x -1/2) (+ eps x))) (.f64 x (.f64 x (fma.f64 (*.f64 eps eps) #s(literal 1/12 binary64) #s(literal -1/2 binary64))))) eps)))
▶	55.1%	#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (- (+ (* (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) x) #s(approx (+ (* eps (* (* x -1/2) (+ eps x))) eps) (.f64 (.f64 x x) (fma.f64 #s(literal -1/2 binary64) (fma.f64 eps (/.f64 eps x) eps) (/.f64 eps (*.f64 x x)))))))
	5.6%	#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (- (+ (* (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) x) #s(approx (+ (* eps (* (* x -1/2) (+ eps x))) eps) (.f64 eps (.f64 eps (*.f64 x #s(literal -1/2 binary64)))))))
✓	98.0%	#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (sin eps) (fma.f64 eps (.f64 eps (.f64 eps #s(literal -1/6 binary64))) eps)))
▶	4.9%	#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (sin eps) #s(approx (+ (* eps (* eps (* eps -1/6))) eps) (.f64 eps (.f64 eps (*.f64 eps #s(literal -1/6 binary64)))))))

Compiler

Compiled 410 to 213 computations (48% saved)

simplify243.0ms (1.9%)

Memory

-6.9MiB live, 229.6MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 20 expressions of interest:

New	Metric	Score
cost-diff	0	#s(approx (+ (* eps (* (* x -1/2) (+ eps x))) eps) (.f64 (.f64 x x) (fma.f64 #s(literal -1/2 binary64) (fma.f64 eps (/.f64 eps x) eps) (/.f64 eps (*.f64 x x)))))
cost-diff	0	#s(approx (- (+ (* (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) x) #s(approx (+ (* eps (* (* x -1/2) (+ eps x))) eps) (.f64 (.f64 x x) (fma.f64 #s(literal -1/2 binary64) (fma.f64 eps (/.f64 eps x) eps) (/.f64 eps (*.f64 x x))))))
cost-diff	0	#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (- (+ (* (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) x) #s(approx (+ (* eps (* (* x -1/2) (+ eps x))) eps) (.f64 (.f64 x x) (fma.f64 #s(literal -1/2 binary64) (fma.f64 eps (/.f64 eps x) eps) (/.f64 eps (*.f64 x x)))))))
cost-diff	1920	(.f64 (.f64 x x) (fma.f64 #s(literal -1/2 binary64) (fma.f64 eps (/.f64 eps x) eps) (/.f64 eps (*.f64 x x))))
cost-diff	0	#s(approx (+ (* eps (* eps (+ (* (* x x) 1/12) -1/6))) (* (* x -1/2) (+ eps x))) (.f64 x (.f64 x (fma.f64 (*.f64 eps eps) #s(literal 1/12 binary64) #s(literal -1/2 binary64)))))
cost-diff	0	(fma.f64 eps #s(approx (+ (* eps (* eps (+ (* (* x x) 1/12) -1/6))) (* (* x -1/2) (+ eps x))) (.f64 x (.f64 x (fma.f64 (*.f64 eps eps) #s(literal 1/12 binary64) #s(literal -1/2 binary64))))) eps)
cost-diff	0	#s(approx (- (+ (* (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) x) (fma.f64 eps #s(approx (+ (* eps (* eps (+ (* (* x x) 1/12) -1/6))) (* (* x -1/2) (+ eps x))) (.f64 x (.f64 x (fma.f64 (*.f64 eps eps) #s(literal 1/12 binary64) #s(literal -1/2 binary64))))) eps))
cost-diff	0	#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (- (+ (* (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) x) (fma.f64 eps #s(approx (+ (* eps (* eps (+ (* (* x x) 1/12) -1/6))) (* (* x -1/2) (+ eps x))) (.f64 x (.f64 x (fma.f64 (*.f64 eps eps) #s(literal 1/12 binary64) #s(literal -1/2 binary64))))) eps)))
cost-diff	0	(.f64 eps (.f64 x x))
cost-diff	0	(fma.f64 (.f64 eps (.f64 x x)) #s(literal -1/2 binary64) eps)
cost-diff	0	#s(approx (- (+ (* (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) x) (fma.f64 (.f64 eps (.f64 x x)) #s(literal -1/2 binary64) eps))
cost-diff	0	#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (- (+ (* (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) x) (fma.f64 (.f64 eps (.f64 x x)) #s(literal -1/2 binary64) eps)))
cost-diff	0	(.f64 eps (.f64 eps (*.f64 eps #s(literal -1/6 binary64))))
cost-diff	0	#s(approx (+ (* eps (* eps (* eps -1/6))) eps) (.f64 eps (.f64 eps (*.f64 eps #s(literal -1/6 binary64)))))
cost-diff	0	#s(approx (sin eps) #s(approx (+ (* eps (* eps (* eps -1/6))) eps) (.f64 eps (.f64 eps (*.f64 eps #s(literal -1/6 binary64))))))
cost-diff	0	#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (sin eps) #s(approx (+ (* eps (* eps (* eps -1/6))) eps) (.f64 eps (.f64 eps (*.f64 eps #s(literal -1/6 binary64)))))))
cost-diff	0	(.f64 eps (fma.f64 eps (.f64 eps #s(literal -1/48 binary64)) #s(literal 1/2 binary64)))
cost-diff	0	#s(approx (sin (* (+ eps 0) 1/2)) (.f64 eps (fma.f64 eps (.f64 eps #s(literal -1/48 binary64)) #s(literal 1/2 binary64))))
cost-diff	0	(.f64 #s(approx (sin ( (+ eps 0) 1/2)) (.f64 eps (fma.f64 eps (.f64 eps #s(literal -1/48 binary64)) #s(literal 1/2 binary64)))) (cos.f64 #s(approx (* (+ (* x 2) eps) 1/2) (fma.f64 #s(literal 1/2 binary64) eps x))))
cost-diff	0	(.f64 (.f64 #s(approx (sin (* (+ eps 0) 1/2)) (.f64 eps (fma.f64 eps (.f64 eps #s(literal -1/48 binary64)) #s(literal 1/2 binary64)))) (cos.f64 #s(approx (* (+ (* x 2) eps) 1/2) (fma.f64 #s(literal 1/2 binary64) eps x)))) #s(literal 2 binary64))

Rules

12 696×	`lower-fma.f32`
12 682×	`lower-fma.f64`
4 490×	`lower-*.f32`
4 464×	`lower-*.f64`
1 892×	`lower-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	79	672
0	109	663
1	216	663
2	614	649
3	1426	610
4	2493	610
5	4294	610
6	5995	610
7	7644	610
0	8044	580

Stop Event

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

Calls

Call 1

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

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

localize227.0ms (1.8%)

Memory

21.0MiB live, 252.7MiB allocated

Localize:

Found 20 expressions of interest:

New	Metric	Score
accuracy	0.1662252980290556	#s(approx (- (+ (* (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) x) #s(approx (+ (* eps (* (* x -1/2) (+ eps x))) eps) (.f64 (.f64 x x) (fma.f64 #s(literal -1/2 binary64) (fma.f64 eps (/.f64 eps x) eps) (/.f64 eps (*.f64 x x))))))
accuracy	0.6089016869101457	#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (- (+ (* (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) x) #s(approx (+ (* eps (* (* x -1/2) (+ eps x))) eps) (.f64 (.f64 x x) (fma.f64 #s(literal -1/2 binary64) (fma.f64 eps (/.f64 eps x) eps) (/.f64 eps (*.f64 x x)))))))
accuracy	26.669011112680433	(.f64 (.f64 x x) (fma.f64 #s(literal -1/2 binary64) (fma.f64 eps (/.f64 eps x) eps) (/.f64 eps (*.f64 x x))))
accuracy	26.7955923568212	(/.f64 eps (*.f64 x x))
accuracy	0.00390625	(.f64 x (.f64 x (fma.f64 (*.f64 eps eps) #s(literal 1/12 binary64) #s(literal -1/2 binary64))))
accuracy	0.012382519536884034	#s(approx (- (+ (* (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) x) (fma.f64 eps #s(approx (+ (* eps (* eps (+ (* (* x x) 1/12) -1/6))) (* (* x -1/2) (+ eps x))) (.f64 x (.f64 x (fma.f64 (*.f64 eps eps) #s(literal 1/12 binary64) #s(literal -1/2 binary64))))) eps))
accuracy	0.6089016869101457	#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (- (+ (* (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) x) (fma.f64 eps #s(approx (+ (* eps (* eps (+ (* (* x x) 1/12) -1/6))) (* (* x -1/2) (+ eps x))) (.f64 x (.f64 x (fma.f64 (*.f64 eps eps) #s(literal 1/12 binary64) #s(literal -1/2 binary64))))) eps)))
accuracy	14.593578488847728	#s(approx (+ (* eps (* eps (+ (* (* x x) 1/12) -1/6))) (* (* x -1/2) (+ eps x))) (.f64 x (.f64 x (fma.f64 (*.f64 eps eps) #s(literal 1/12 binary64) #s(literal -1/2 binary64)))))
accuracy	0	(*.f64 x x)
accuracy	0.1171875	(.f64 eps (.f64 x x))
accuracy	0.35335046985691987	#s(approx (- (+ (* (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) x) (fma.f64 (.f64 eps (.f64 x x)) #s(literal -1/2 binary64) eps))
accuracy	0.6089016869101457	#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (- (+ (* (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) x) (fma.f64 (.f64 eps (.f64 x x)) #s(literal -1/2 binary64) eps)))
accuracy	0.08984375	(.f64 eps (.f64 eps #s(literal -1/6 binary64)))
accuracy	0.37109375	(*.f64 eps #s(literal -1/6 binary64))
accuracy	1.2665934291908156	#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (sin eps) #s(approx (+ (* eps (* eps (* eps -1/6))) eps) (.f64 eps (.f64 eps (*.f64 eps #s(literal -1/6 binary64)))))))
accuracy	60.6454721015446	#s(approx (+ (* eps (* eps (* eps -1/6))) eps) (.f64 eps (.f64 eps (*.f64 eps #s(literal -1/6 binary64)))))
accuracy	0	#s(approx (sin (* (+ eps 0) 1/2)) (.f64 eps (fma.f64 eps (.f64 eps #s(literal -1/48 binary64)) #s(literal 1/2 binary64))))
accuracy	0.0078125	(.f64 #s(approx (sin ( (+ eps 0) 1/2)) (.f64 eps (fma.f64 eps (.f64 eps #s(literal -1/48 binary64)) #s(literal 1/2 binary64)))) (cos.f64 #s(approx (* (+ (* x 2) eps) 1/2) (fma.f64 #s(literal 1/2 binary64) eps x))))
accuracy	0.04371266413587042	(cos.f64 #s(approx (* (+ (* x 2) eps) 1/2) (fma.f64 #s(literal 1/2 binary64) eps x)))
accuracy	0.37109375	(*.f64 eps #s(literal -1/48 binary64))

Samples

93.0ms	174×	0	valid
64.0ms	81×	1	valid
2.0ms	1×	5	exit

Compiler

Compiled 353 to 71 computations (79.9% saved)

Precisions

Click to see histograms. Total time spent on operations: 128.0ms

ival-mult: 61.0ms (47.5% of total)

ival-add: 21.0ms (16.4% of total)

const: 12.0ms (9.3% of total)

adjust: 11.0ms (8.6% of total)

ival-sin: 8.0ms (6.2% of total)

ival-div: 7.0ms (5.5% of total)

ival-cos: 4.0ms (3.1% of total)

ival-sub: 3.0ms (2.3% of total)

exact: 1.0ms (0.8% of total)

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

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

series55.0ms (0.4%)

Memory

-30.9MiB live, 60.9MiB allocated

Counts

27 → 540

Calls

Call 1

Inputs
#s(alt (.f64 (.f64 #s(approx (sin (* (+ eps 0) 1/2)) (.f64 eps (fma.f64 eps (.f64 eps #s(literal -1/48 binary64)) #s(literal 1/2 binary64)))) (cos.f64 #s(approx (* (+ (* x 2) eps) 1/2) (fma.f64 #s(literal 1/2 binary64) eps x)))) #s(literal 2 binary64)) (patch (.f64 (.f64 #s(approx (sin (* (+ eps 0) 1/2)) (.f64 eps (fma.f64 eps (.f64 eps #s(literal -1/48 binary64)) #s(literal 1/2 binary64)))) (cos.f64 #s(approx (* (+ (* x 2) eps) 1/2) (fma.f64 #s(literal 1/2 binary64) eps x)))) #s(literal 2 binary64)) #<representation binary64>) () ())
#s(alt (.f64 #s(approx (sin ( (+ eps 0) 1/2)) (.f64 eps (fma.f64 eps (.f64 eps #s(literal -1/48 binary64)) #s(literal 1/2 binary64)))) (cos.f64 #s(approx (* (+ (* x 2) eps) 1/2) (fma.f64 #s(literal 1/2 binary64) eps x)))) (patch (.f64 #s(approx (sin ( (+ eps 0) 1/2)) (.f64 eps (fma.f64 eps (.f64 eps #s(literal -1/48 binary64)) #s(literal 1/2 binary64)))) (cos.f64 #s(approx (* (+ (* x 2) eps) 1/2) (fma.f64 #s(literal 1/2 binary64) eps x)))) #<representation binary64>) () ())
#s(alt #s(approx (sin (* (+ eps 0) 1/2)) (.f64 eps (fma.f64 eps (.f64 eps #s(literal -1/48 binary64)) #s(literal 1/2 binary64)))) (patch #s(approx (sin (* (+ eps 0) 1/2)) (.f64 eps (fma.f64 eps (.f64 eps #s(literal -1/48 binary64)) #s(literal 1/2 binary64)))) #<representation binary64>) () ())
#s(alt (.f64 eps (fma.f64 eps (.f64 eps #s(literal -1/48 binary64)) #s(literal 1/2 binary64))) (patch (.f64 eps (fma.f64 eps (.f64 eps #s(literal -1/48 binary64)) #s(literal 1/2 binary64))) #<representation binary64>) () ())
#s(alt #s(approx (- (sin (+ x eps)) (sin x)) #s(approx (sin eps) #s(approx (+ (* eps (* eps (* eps -1/6))) eps) (.f64 eps (.f64 eps (.f64 eps #s(literal -1/6 binary64))))))) (patch #s(approx (- (sin (+ x eps)) (sin x)) #s(approx (sin eps) #s(approx (+ ( eps (* eps (* eps -1/6))) eps) (.f64 eps (.f64 eps (*.f64 eps #s(literal -1/6 binary64))))))) #<representation binary64>) () ())
#s(alt #s(approx (sin eps) #s(approx (+ (* eps (* eps (* eps -1/6))) eps) (.f64 eps (.f64 eps (.f64 eps #s(literal -1/6 binary64)))))) (patch #s(approx (sin eps) #s(approx (+ ( eps (* eps (* eps -1/6))) eps) (.f64 eps (.f64 eps (*.f64 eps #s(literal -1/6 binary64)))))) #<representation binary64>) () ())
#s(alt #s(approx (+ (* eps (* eps (* eps -1/6))) eps) (.f64 eps (.f64 eps (.f64 eps #s(literal -1/6 binary64))))) (patch #s(approx (+ ( eps (* eps (* eps -1/6))) eps) (.f64 eps (.f64 eps (*.f64 eps #s(literal -1/6 binary64))))) #<representation binary64>) () ())
#s(alt (.f64 eps (.f64 eps (.f64 eps #s(literal -1/6 binary64)))) (patch (.f64 eps (.f64 eps (.f64 eps #s(literal -1/6 binary64)))) #<representation binary64>) () ())
#s(alt #s(approx (- (sin (+ x eps)) (sin x)) #s(approx (- (+ (* (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) x) (fma.f64 (.f64 eps (.f64 x x)) #s(literal -1/2 binary64) eps))) (patch #s(approx (- (sin (+ x eps)) (sin x)) #s(approx (- (+ (* (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) x) (fma.f64 (.f64 eps (.f64 x x)) #s(literal -1/2 binary64) eps))) #<representation binary64>) () ())
#s(alt #s(approx (- (+ (* (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) x) (fma.f64 (.f64 eps (.f64 x x)) #s(literal -1/2 binary64) eps)) (patch #s(approx (- (+ (* (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) x) (fma.f64 (.f64 eps (.f64 x x)) #s(literal -1/2 binary64) eps)) #<representation binary64>) () ())
#s(alt (fma.f64 (.f64 eps (.f64 x x)) #s(literal -1/2 binary64) eps) (patch (fma.f64 (.f64 eps (.f64 x x)) #s(literal -1/2 binary64) eps) #<representation binary64>) () ())
#s(alt (.f64 eps (.f64 x x)) (patch (.f64 eps (.f64 x x)) #<representation binary64>) () ())
#s(alt #s(approx (- (sin (+ x eps)) (sin x)) #s(approx (- (+ (* (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) x) (fma.f64 eps #s(approx (+ (* eps (* eps (+ (* (* x x) 1/12) -1/6))) (* (* x -1/2) (+ eps x))) (.f64 x (.f64 x (fma.f64 (.f64 eps eps) #s(literal 1/12 binary64) #s(literal -1/2 binary64))))) eps))) (patch #s(approx (- (sin (+ x eps)) (sin x)) #s(approx (- (+ ( (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) x) (fma.f64 eps #s(approx (+ (* eps (* eps (+ (* (* x x) 1/12) -1/6))) (* (* x -1/2) (+ eps x))) (.f64 x (.f64 x (fma.f64 (*.f64 eps eps) #s(literal 1/12 binary64) #s(literal -1/2 binary64))))) eps))) #<representation binary64>) () ())
#s(alt #s(approx (- (+ (* (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) x) (fma.f64 eps #s(approx (+ (* eps (* eps (+ (* (* x x) 1/12) -1/6))) (* (* x -1/2) (+ eps x))) (.f64 x (.f64 x (fma.f64 (.f64 eps eps) #s(literal 1/12 binary64) #s(literal -1/2 binary64))))) eps)) (patch #s(approx (- (+ ( (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) x) (fma.f64 eps #s(approx (+ (* eps (* eps (+ (* (* x x) 1/12) -1/6))) (* (* x -1/2) (+ eps x))) (.f64 x (.f64 x (fma.f64 (*.f64 eps eps) #s(literal 1/12 binary64) #s(literal -1/2 binary64))))) eps)) #<representation binary64>) () ())
#s(alt (fma.f64 eps #s(approx (+ (* eps (* eps (+ (* (* x x) 1/12) -1/6))) (* (* x -1/2) (+ eps x))) (.f64 x (.f64 x (fma.f64 (.f64 eps eps) #s(literal 1/12 binary64) #s(literal -1/2 binary64))))) eps) (patch (fma.f64 eps #s(approx (+ ( eps (* eps (+ (* (* x x) 1/12) -1/6))) (* (* x -1/2) (+ eps x))) (.f64 x (.f64 x (fma.f64 (*.f64 eps eps) #s(literal 1/12 binary64) #s(literal -1/2 binary64))))) eps) #<representation binary64>) () ())
#s(alt #s(approx (+ (* eps (* eps (+ (* (* x x) 1/12) -1/6))) (* (* x -1/2) (+ eps x))) (.f64 x (.f64 x (fma.f64 (.f64 eps eps) #s(literal 1/12 binary64) #s(literal -1/2 binary64))))) (patch #s(approx (+ ( eps (* eps (+ (* (* x x) 1/12) -1/6))) (* (* x -1/2) (+ eps x))) (.f64 x (.f64 x (fma.f64 (*.f64 eps eps) #s(literal 1/12 binary64) #s(literal -1/2 binary64))))) #<representation binary64>) () ())
#s(alt (.f64 (.f64 x x) (fma.f64 #s(literal -1/2 binary64) (fma.f64 eps (/.f64 eps x) eps) (/.f64 eps (.f64 x x)))) (patch (.f64 (.f64 x x) (fma.f64 #s(literal -1/2 binary64) (fma.f64 eps (/.f64 eps x) eps) (/.f64 eps (.f64 x x)))) #<representation binary64>) () ())
#s(alt #s(approx (- (sin (+ x eps)) (sin x)) #s(approx (- (+ (* (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) x) #s(approx (+ (* eps (* (* x -1/2) (+ eps x))) eps) (.f64 (.f64 x x) (fma.f64 #s(literal -1/2 binary64) (fma.f64 eps (/.f64 eps x) eps) (/.f64 eps (.f64 x x))))))) (patch #s(approx (- (sin (+ x eps)) (sin x)) #s(approx (- (+ ( (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) x) #s(approx (+ (* eps (* (* x -1/2) (+ eps x))) eps) (.f64 (.f64 x x) (fma.f64 #s(literal -1/2 binary64) (fma.f64 eps (/.f64 eps x) eps) (/.f64 eps (*.f64 x x))))))) #<representation binary64>) () ())
#s(alt #s(approx (- (+ (* (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) x) #s(approx (+ (* eps (* (* x -1/2) (+ eps x))) eps) (.f64 (.f64 x x) (fma.f64 #s(literal -1/2 binary64) (fma.f64 eps (/.f64 eps x) eps) (/.f64 eps (.f64 x x)))))) (patch #s(approx (- (+ ( (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) x) #s(approx (+ (* eps (* (* x -1/2) (+ eps x))) eps) (.f64 (.f64 x x) (fma.f64 #s(literal -1/2 binary64) (fma.f64 eps (/.f64 eps x) eps) (/.f64 eps (*.f64 x x)))))) #<representation binary64>) () ())
#s(alt #s(approx (+ (* eps (* (* x -1/2) (+ eps x))) eps) (.f64 (.f64 x x) (fma.f64 #s(literal -1/2 binary64) (fma.f64 eps (/.f64 eps x) eps) (/.f64 eps (.f64 x x))))) (patch #s(approx (+ ( eps (* (* x -1/2) (+ eps x))) eps) (.f64 (.f64 x x) (fma.f64 #s(literal -1/2 binary64) (fma.f64 eps (/.f64 eps x) eps) (/.f64 eps (*.f64 x x))))) #<representation binary64>) () ())
#s(alt (.f64 eps #s(literal -1/48 binary64)) (patch (.f64 eps #s(literal -1/48 binary64)) #<representation binary64>) () ())
#s(alt (cos.f64 #s(approx (* (+ (* x 2) eps) 1/2) (fma.f64 #s(literal 1/2 binary64) eps x))) (patch (cos.f64 #s(approx (* (+ (* x 2) eps) 1/2) (fma.f64 #s(literal 1/2 binary64) eps x))) #<representation binary64>) () ())
#s(alt (.f64 eps #s(literal -1/6 binary64)) (patch (.f64 eps #s(literal -1/6 binary64)) #<representation binary64>) () ())
#s(alt (.f64 eps (.f64 eps #s(literal -1/6 binary64))) (patch (.f64 eps (.f64 eps #s(literal -1/6 binary64))) #<representation binary64>) () ())
#s(alt (.f64 x x) (patch (.f64 x x) #<representation binary64>) () ())
#s(alt (.f64 x (.f64 x (fma.f64 (.f64 eps eps) #s(literal 1/12 binary64) #s(literal -1/2 binary64)))) (patch (.f64 x (.f64 x (fma.f64 (.f64 eps eps) #s(literal 1/12 binary64) #s(literal -1/2 binary64)))) #<representation binary64>) () ())
#s(alt (/.f64 eps (.f64 x x)) (patch (/.f64 eps (.f64 x x)) #<representation binary64>) () ())

Outputs
#s(alt (* eps (cos x)) (taylor 0 eps) (#s(alt (.f64 (.f64 #s(approx (sin (* (+ eps 0) 1/2)) (.f64 eps (fma.f64 eps (.f64 eps #s(literal -1/48 binary64)) #s(literal 1/2 binary64)))) (cos.f64 #s(approx (* (+ (* x 2) eps) 1/2) (fma.f64 #s(literal 1/2 binary64) eps x)))) #s(literal 2 binary64)) (patch (.f64 (.f64 #s(approx (sin (* (+ eps 0) 1/2)) (.f64 eps (fma.f64 eps (.f64 eps #s(literal -1/48 binary64)) #s(literal 1/2 binary64)))) (cos.f64 #s(approx (* (+ (* x 2) eps) 1/2) (fma.f64 #s(literal 1/2 binary64) eps x)))) #s(literal 2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* eps (+ (cos x) (* -1/2 (* eps (sin x))))) (taylor 0 eps) (#s(alt (.f64 (.f64 #s(approx (sin (* (+ eps 0) 1/2)) (.f64 eps (fma.f64 eps (.f64 eps #s(literal -1/48 binary64)) #s(literal 1/2 binary64)))) (cos.f64 #s(approx (* (+ (* x 2) eps) 1/2) (fma.f64 #s(literal 1/2 binary64) eps x)))) #s(literal 2 binary64)) (patch (.f64 (.f64 #s(approx (sin (* (+ eps 0) 1/2)) (.f64 eps (fma.f64 eps (.f64 eps #s(literal -1/48 binary64)) #s(literal 1/2 binary64)))) (cos.f64 #s(approx (* (+ (* x 2) eps) 1/2) (fma.f64 #s(literal 1/2 binary64) eps x)))) #s(literal 2 binary64)) #<representation binary64>) () ())) ())
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#s(alt (+ (* -1/2 (pow x 2)) (* 1/12 (* (pow eps 2) (pow x 2)))) (taylor 0 eps) (#s(alt (.f64 x (.f64 x (fma.f64 (.f64 eps eps) #s(literal 1/12 binary64) #s(literal -1/2 binary64)))) (patch (.f64 x (.f64 x (fma.f64 (.f64 eps eps) #s(literal 1/12 binary64) #s(literal -1/2 binary64)))) #<representation binary64>) () ())) ())
#s(alt (* 1/12 (* (pow eps 2) (pow x 2))) (taylor inf eps) (#s(alt (.f64 x (.f64 x (fma.f64 (.f64 eps eps) #s(literal 1/12 binary64) #s(literal -1/2 binary64)))) (patch (.f64 x (.f64 x (fma.f64 (.f64 eps eps) #s(literal 1/12 binary64) #s(literal -1/2 binary64)))) #<representation binary64>) () ())) ())
#s(alt (* (pow eps 2) (+ (* -1/2 (/ (pow x 2) (pow eps 2))) (* 1/12 (pow x 2)))) (taylor inf eps) (#s(alt (.f64 x (.f64 x (fma.f64 (.f64 eps eps) #s(literal 1/12 binary64) #s(literal -1/2 binary64)))) (patch (.f64 x (.f64 x (fma.f64 (.f64 eps eps) #s(literal 1/12 binary64) #s(literal -1/2 binary64)))) #<representation binary64>) () ())) ())
#s(alt (* (pow eps 2) (+ (* -1/2 (/ (pow x 2) (pow eps 2))) (* 1/12 (pow x 2)))) (taylor inf eps) (#s(alt (.f64 x (.f64 x (fma.f64 (.f64 eps eps) #s(literal 1/12 binary64) #s(literal -1/2 binary64)))) (patch (.f64 x (.f64 x (fma.f64 (.f64 eps eps) #s(literal 1/12 binary64) #s(literal -1/2 binary64)))) #<representation binary64>) () ())) ())
#s(alt (* (pow eps 2) (+ (* -1/2 (/ (pow x 2) (pow eps 2))) (* 1/12 (pow x 2)))) (taylor inf eps) (#s(alt (.f64 x (.f64 x (fma.f64 (.f64 eps eps) #s(literal 1/12 binary64) #s(literal -1/2 binary64)))) (patch (.f64 x (.f64 x (fma.f64 (.f64 eps eps) #s(literal 1/12 binary64) #s(literal -1/2 binary64)))) #<representation binary64>) () ())) ())
#s(alt (* 1/12 (* (pow eps 2) (pow x 2))) (taylor -inf eps) (#s(alt (.f64 x (.f64 x (fma.f64 (.f64 eps eps) #s(literal 1/12 binary64) #s(literal -1/2 binary64)))) (patch (.f64 x (.f64 x (fma.f64 (.f64 eps eps) #s(literal 1/12 binary64) #s(literal -1/2 binary64)))) #<representation binary64>) () ())) ())
#s(alt (* (pow eps 2) (+ (* -1/2 (/ (pow x 2) (pow eps 2))) (* 1/12 (pow x 2)))) (taylor -inf eps) (#s(alt (.f64 x (.f64 x (fma.f64 (.f64 eps eps) #s(literal 1/12 binary64) #s(literal -1/2 binary64)))) (patch (.f64 x (.f64 x (fma.f64 (.f64 eps eps) #s(literal 1/12 binary64) #s(literal -1/2 binary64)))) #<representation binary64>) () ())) ())
#s(alt (* (pow eps 2) (+ (* -1/2 (/ (pow x 2) (pow eps 2))) (* 1/12 (pow x 2)))) (taylor -inf eps) (#s(alt (.f64 x (.f64 x (fma.f64 (.f64 eps eps) #s(literal 1/12 binary64) #s(literal -1/2 binary64)))) (patch (.f64 x (.f64 x (fma.f64 (.f64 eps eps) #s(literal 1/12 binary64) #s(literal -1/2 binary64)))) #<representation binary64>) () ())) ())
#s(alt (* (pow eps 2) (+ (* -1/2 (/ (pow x 2) (pow eps 2))) (* 1/12 (pow x 2)))) (taylor -inf eps) (#s(alt (.f64 x (.f64 x (fma.f64 (.f64 eps eps) #s(literal 1/12 binary64) #s(literal -1/2 binary64)))) (patch (.f64 x (.f64 x (fma.f64 (.f64 eps eps) #s(literal 1/12 binary64) #s(literal -1/2 binary64)))) #<representation binary64>) () ())) ())
#s(alt (/ eps (pow x 2)) (taylor 0 eps) (#s(alt (/.f64 eps (.f64 x x)) (patch (/.f64 eps (.f64 x x)) #<representation binary64>) () ())) ())
#s(alt (/ eps (pow x 2)) (taylor 0 eps) (#s(alt (/.f64 eps (.f64 x x)) (patch (/.f64 eps (.f64 x x)) #<representation binary64>) () ())) ())
#s(alt (/ eps (pow x 2)) (taylor 0 eps) (#s(alt (/.f64 eps (.f64 x x)) (patch (/.f64 eps (.f64 x x)) #<representation binary64>) () ())) ())
#s(alt (/ eps (pow x 2)) (taylor 0 eps) (#s(alt (/.f64 eps (.f64 x x)) (patch (/.f64 eps (.f64 x x)) #<representation binary64>) () ())) ())
#s(alt (/ eps (pow x 2)) (taylor inf eps) (#s(alt (/.f64 eps (.f64 x x)) (patch (/.f64 eps (.f64 x x)) #<representation binary64>) () ())) ())
#s(alt (/ eps (pow x 2)) (taylor inf eps) (#s(alt (/.f64 eps (.f64 x x)) (patch (/.f64 eps (.f64 x x)) #<representation binary64>) () ())) ())
#s(alt (/ eps (pow x 2)) (taylor inf eps) (#s(alt (/.f64 eps (.f64 x x)) (patch (/.f64 eps (.f64 x x)) #<representation binary64>) () ())) ())
#s(alt (/ eps (pow x 2)) (taylor inf eps) (#s(alt (/.f64 eps (.f64 x x)) (patch (/.f64 eps (.f64 x x)) #<representation binary64>) () ())) ())
#s(alt (/ eps (pow x 2)) (taylor -inf eps) (#s(alt (/.f64 eps (.f64 x x)) (patch (/.f64 eps (.f64 x x)) #<representation binary64>) () ())) ())
#s(alt (/ eps (pow x 2)) (taylor -inf eps) (#s(alt (/.f64 eps (.f64 x x)) (patch (/.f64 eps (.f64 x x)) #<representation binary64>) () ())) ())
#s(alt (/ eps (pow x 2)) (taylor -inf eps) (#s(alt (/.f64 eps (.f64 x x)) (patch (/.f64 eps (.f64 x x)) #<representation binary64>) () ())) ())
#s(alt (/ eps (pow x 2)) (taylor -inf eps) (#s(alt (/.f64 eps (.f64 x x)) (patch (/.f64 eps (.f64 x x)) #<representation binary64>) () ())) ())
#s(alt (/ eps (pow x 2)) (taylor 0 x) (#s(alt (/.f64 eps (.f64 x x)) (patch (/.f64 eps (.f64 x x)) #<representation binary64>) () ())) ())
#s(alt (/ eps (pow x 2)) (taylor 0 x) (#s(alt (/.f64 eps (.f64 x x)) (patch (/.f64 eps (.f64 x x)) #<representation binary64>) () ())) ())
#s(alt (/ eps (pow x 2)) (taylor 0 x) (#s(alt (/.f64 eps (.f64 x x)) (patch (/.f64 eps (.f64 x x)) #<representation binary64>) () ())) ())
#s(alt (/ eps (pow x 2)) (taylor 0 x) (#s(alt (/.f64 eps (.f64 x x)) (patch (/.f64 eps (.f64 x x)) #<representation binary64>) () ())) ())
#s(alt (/ eps (pow x 2)) (taylor inf x) (#s(alt (/.f64 eps (.f64 x x)) (patch (/.f64 eps (.f64 x x)) #<representation binary64>) () ())) ())
#s(alt (/ eps (pow x 2)) (taylor inf x) (#s(alt (/.f64 eps (.f64 x x)) (patch (/.f64 eps (.f64 x x)) #<representation binary64>) () ())) ())
#s(alt (/ eps (pow x 2)) (taylor inf x) (#s(alt (/.f64 eps (.f64 x x)) (patch (/.f64 eps (.f64 x x)) #<representation binary64>) () ())) ())
#s(alt (/ eps (pow x 2)) (taylor inf x) (#s(alt (/.f64 eps (.f64 x x)) (patch (/.f64 eps (.f64 x x)) #<representation binary64>) () ())) ())
#s(alt (/ eps (pow x 2)) (taylor -inf x) (#s(alt (/.f64 eps (.f64 x x)) (patch (/.f64 eps (.f64 x x)) #<representation binary64>) () ())) ())
#s(alt (/ eps (pow x 2)) (taylor -inf x) (#s(alt (/.f64 eps (.f64 x x)) (patch (/.f64 eps (.f64 x x)) #<representation binary64>) () ())) ())
#s(alt (/ eps (pow x 2)) (taylor -inf x) (#s(alt (/.f64 eps (.f64 x x)) (patch (/.f64 eps (.f64 x x)) #<representation binary64>) () ())) ())
#s(alt (/ eps (pow x 2)) (taylor -inf x) (#s(alt (/.f64 eps (.f64 x x)) (patch (/.f64 eps (.f64 x x)) #<representation binary64>) () ())) ())

Calls

135 calls:

Time	Variable		Point	Expression
14.0ms	eps	@	-inf	(* eps (* x x))
1.0ms	eps	@	0	(* (* x x) (+ (* -1/2 (+ (* eps (/ eps x)) eps)) (/ eps (* x x))))
1.0ms	eps	@	inf	(* (* x x) (+ (* -1/2 (+ (* eps (/ eps x)) eps)) (/ eps (* x x))))
1.0ms	eps	@	-inf	(* eps (+ (* eps (* eps -1/48)) 1/2))
1.0ms	x	@	0	(* x (* x (+ (* (* eps eps) 1/12) -1/2)))

simplify329.0ms (2.6%)

Memory

27.1MiB live, 363.7MiB allocated

Algorithm

1×	egg-herbie

Rules

11 584×	`lower-fma.f64`
11 584×	`lower-fma.f32`
7 008×	`lower-*.f64`
7 008×	`lower-*.f32`
3 056×	`lower-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	449	6181
1	1382	5914
2	3972	5850
0	8049	5449

Stop Event

1×	iter limit
1×	node limit

Counts

540 → 535

Calls

Call 1

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

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

rewrite382.0ms (3%)

Memory

20.0MiB live, 457.7MiB allocated

Rules

5 340×	`lower-fma.f32`
5 326×	`lower-fma.f64`
4 508×	`lower-*.f32`
4 482×	`lower-*.f64`
4 072×	`lower-/.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	79	591
0	109	585
1	453	571
2	4245	567
0	9625	534

Stop Event

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

Counts

27 → 376

Calls

Call 1

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

Outputs
(.f64 #s(approx (sin ( (+ eps 0) 1/2)) (.f64 eps (fma.f64 eps (.f64 eps #s(literal -1/48 binary64)) #s(literal 1/2 binary64)))) (.f64 #s(literal 2 binary64) (cos.f64 #s(approx ( (+ (* x 2) eps) 1/2) (fma.f64 eps #s(literal 1/2 binary64) x)))))
(.f64 #s(literal 2 binary64) (.f64 #s(approx (sin (* (+ eps 0) 1/2)) (.f64 eps (fma.f64 eps (.f64 eps #s(literal -1/48 binary64)) #s(literal 1/2 binary64)))) (cos.f64 #s(approx (* (+ (* x 2) eps) 1/2) (fma.f64 eps #s(literal 1/2 binary64) x)))))
(.f64 (cos.f64 #s(approx ( (+ (* x 2) eps) 1/2) (fma.f64 eps #s(literal 1/2 binary64) x))) (.f64 #s(approx (sin ( (+ eps 0) 1/2)) (.f64 eps (fma.f64 eps (.f64 eps #s(literal -1/48 binary64)) #s(literal 1/2 binary64)))) #s(literal 2 binary64)))
(.f64 (.f64 #s(approx (sin (* (+ eps 0) 1/2)) (.f64 eps (fma.f64 eps (.f64 eps #s(literal -1/48 binary64)) #s(literal 1/2 binary64)))) (cos.f64 #s(approx (* (+ (* x 2) eps) 1/2) (fma.f64 eps #s(literal 1/2 binary64) x)))) #s(literal 2 binary64))
(.f64 (.f64 #s(literal 2 binary64) (cos.f64 #s(approx (* (+ (* x 2) eps) 1/2) (fma.f64 eps #s(literal 1/2 binary64) x)))) #s(approx (sin (* (+ eps 0) 1/2)) (.f64 eps (fma.f64 eps (.f64 eps #s(literal -1/48 binary64)) #s(literal 1/2 binary64)))))
(.f64 (.f64 #s(literal 2 binary64) #s(approx (sin (* (+ eps 0) 1/2)) (.f64 eps (fma.f64 eps (.f64 eps #s(literal -1/48 binary64)) #s(literal 1/2 binary64))))) (cos.f64 #s(approx (* (+ (* x 2) eps) 1/2) (fma.f64 eps #s(literal 1/2 binary64) x))))
(.f64 #s(approx (sin ( (+ eps 0) 1/2)) (.f64 eps (fma.f64 eps (.f64 eps #s(literal -1/48 binary64)) #s(literal 1/2 binary64)))) (cos.f64 #s(approx (* (+ (* x 2) eps) 1/2) (fma.f64 eps #s(literal 1/2 binary64) x))))
(.f64 (cos.f64 #s(approx ( (+ (* x 2) eps) 1/2) (fma.f64 eps #s(literal 1/2 binary64) x))) #s(approx (sin (* (+ eps 0) 1/2)) (.f64 eps (fma.f64 eps (.f64 eps #s(literal -1/48 binary64)) #s(literal 1/2 binary64)))))
#s(approx (sin (* (+ eps 0) 1/2)) (.f64 eps (fma.f64 eps (.f64 eps #s(literal -1/48 binary64)) #s(literal 1/2 binary64))))
(+.f64 (.f64 eps (fma.f64 eps (.f64 eps #s(literal -1/48 binary64)) #s(literal 1/2 binary64))) (.f64 (fma.f64 eps (.f64 eps #s(literal -1/48 binary64)) #s(literal 1/2 binary64)) #s(literal 0 binary64)))
(+.f64 (.f64 eps (fma.f64 eps (.f64 eps #s(literal -1/48 binary64)) #s(literal 1/2 binary64))) (.f64 #s(literal 0 binary64) (fma.f64 eps (.f64 eps #s(literal -1/48 binary64)) #s(literal 1/2 binary64))))
(+.f64 (.f64 eps #s(literal 1/2 binary64)) (.f64 (.f64 eps (.f64 eps eps)) #s(literal -1/48 binary64)))
(+.f64 (.f64 (.f64 eps (.f64 eps eps)) #s(literal -1/48 binary64)) (.f64 eps #s(literal 1/2 binary64)))
(+.f64 (.f64 (fma.f64 eps (.f64 eps #s(literal -1/48 binary64)) #s(literal 1/2 binary64)) #s(literal 0 binary64)) (.f64 eps (fma.f64 eps (.f64 eps #s(literal -1/48 binary64)) #s(literal 1/2 binary64))))
(+.f64 (.f64 #s(literal 0 binary64) (fma.f64 eps (.f64 eps #s(literal -1/48 binary64)) #s(literal 1/2 binary64))) (.f64 eps (fma.f64 eps (.f64 eps #s(literal -1/48 binary64)) #s(literal 1/2 binary64))))
(fma.f64 eps #s(literal 1/2 binary64) (.f64 (.f64 eps (*.f64 eps eps)) #s(literal -1/48 binary64)))
(fma.f64 eps (fma.f64 eps (.f64 eps #s(literal -1/48 binary64)) #s(literal 1/2 binary64)) (.f64 (fma.f64 eps (*.f64 eps #s(literal -1/48 binary64)) #s(literal 1/2 binary64)) #s(literal 0 binary64)))
(fma.f64 eps (fma.f64 eps (.f64 eps #s(literal -1/48 binary64)) #s(literal 1/2 binary64)) (.f64 #s(literal 0 binary64) (fma.f64 eps (*.f64 eps #s(literal -1/48 binary64)) #s(literal 1/2 binary64))))
(fma.f64 eps (.f64 eps (.f64 eps #s(literal -1/48 binary64))) (*.f64 eps #s(literal 1/2 binary64)))
(fma.f64 #s(literal 0 binary64) (fma.f64 eps (.f64 eps #s(literal -1/48 binary64)) #s(literal 1/2 binary64)) (.f64 eps (fma.f64 eps (*.f64 eps #s(literal -1/48 binary64)) #s(literal 1/2 binary64))))
(fma.f64 #s(literal 1/2 binary64) eps (.f64 (.f64 eps (*.f64 eps eps)) #s(literal -1/48 binary64)))
(fma.f64 (.f64 eps #s(literal -1/48 binary64)) (.f64 eps eps) (*.f64 eps #s(literal 1/2 binary64)))
(fma.f64 (fma.f64 eps (.f64 eps #s(literal -1/48 binary64)) #s(literal 1/2 binary64)) eps (.f64 (fma.f64 eps (*.f64 eps #s(literal -1/48 binary64)) #s(literal 1/2 binary64)) #s(literal 0 binary64)))
(fma.f64 (fma.f64 eps (.f64 eps #s(literal -1/48 binary64)) #s(literal 1/2 binary64)) eps (.f64 #s(literal 0 binary64) (fma.f64 eps (*.f64 eps #s(literal -1/48 binary64)) #s(literal 1/2 binary64))))
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(fma.f64 (.f64 x (.f64 x #s(literal -1/2 binary64))) #s(literal 1 binary64) (.f64 (.f64 eps (.f64 eps #s(literal 1/12 binary64))) (.f64 x x)))
(fma.f64 #s(literal 1 binary64) (.f64 x (.f64 x #s(literal -1/2 binary64))) (.f64 (.f64 x x) (.f64 eps (.f64 eps #s(literal 1/12 binary64)))))
(fma.f64 #s(literal 1 binary64) (.f64 x (.f64 x #s(literal -1/2 binary64))) (.f64 (.f64 eps (.f64 eps #s(literal 1/12 binary64))) (.f64 x x)))
(fma.f64 (.f64 x x) #s(literal -1/2 binary64) (.f64 (.f64 x x) (.f64 eps (*.f64 eps #s(literal 1/12 binary64)))))
(fma.f64 (.f64 x x) #s(literal -1/2 binary64) (.f64 (.f64 eps (.f64 eps #s(literal 1/12 binary64))) (*.f64 x x)))
(fma.f64 (.f64 x x) (.f64 eps (.f64 eps #s(literal 1/12 binary64))) (.f64 x (*.f64 x #s(literal -1/2 binary64))))
(fma.f64 (.f64 eps (.f64 eps #s(literal 1/12 binary64))) (.f64 x x) (.f64 x (*.f64 x #s(literal -1/2 binary64))))
(fma.f64 (.f64 x (.f64 eps (.f64 eps #s(literal 1/12 binary64)))) x (.f64 x (*.f64 x #s(literal -1/2 binary64))))
(/.f64 (.f64 (.f64 x x) (fma.f64 (.f64 eps (.f64 eps eps)) (.f64 (.f64 eps (.f64 eps eps)) #s(literal 1/1728 binary64)) #s(literal -1/8 binary64))) (-.f64 (fma.f64 (.f64 (.f64 eps (.f64 eps eps)) eps) #s(literal 1/144 binary64) #s(literal 1/4 binary64)) (.f64 (.f64 eps eps) #s(literal -1/24 binary64))))
(/.f64 (.f64 (.f64 x x) (fma.f64 (.f64 (.f64 eps (.f64 eps eps)) eps) #s(literal 1/144 binary64) #s(literal -1/4 binary64))) (fma.f64 eps (.f64 eps #s(literal 1/12 binary64)) #s(literal 1/2 binary64)))
(/.f64 (neg.f64 (.f64 (.f64 x x) (fma.f64 (.f64 eps (.f64 eps eps)) (.f64 (.f64 eps (.f64 eps eps)) #s(literal 1/1728 binary64)) #s(literal -1/8 binary64)))) (neg.f64 (-.f64 (fma.f64 (.f64 (.f64 eps (.f64 eps eps)) eps) #s(literal 1/144 binary64) #s(literal 1/4 binary64)) (.f64 (.f64 eps eps) #s(literal -1/24 binary64)))))
(/.f64 (neg.f64 (.f64 (.f64 x x) (fma.f64 (.f64 (.f64 eps (.f64 eps eps)) eps) #s(literal 1/144 binary64) #s(literal -1/4 binary64)))) (neg.f64 (fma.f64 eps (.f64 eps #s(literal 1/12 binary64)) #s(literal 1/2 binary64))))
(.f64 x (.f64 x (fma.f64 eps (*.f64 eps #s(literal 1/12 binary64)) #s(literal -1/2 binary64))))
(.f64 (.f64 x x) (fma.f64 eps (*.f64 eps #s(literal 1/12 binary64)) #s(literal -1/2 binary64)))
(.f64 (fma.f64 eps (.f64 eps #s(literal 1/12 binary64)) #s(literal -1/2 binary64)) (*.f64 x x))
(.f64 (.f64 x (fma.f64 eps (*.f64 eps #s(literal 1/12 binary64)) #s(literal -1/2 binary64))) x)
(exp.f64 (.f64 (log.f64 (/.f64 (.f64 x x) eps)) #s(literal -1 binary64)))
(neg.f64 (/.f64 eps (neg.f64 (*.f64 x x))))
(neg.f64 (/.f64 (neg.f64 eps) (*.f64 x x)))
(/.f64 eps (*.f64 x x))
(/.f64 #s(literal 1 binary64) (/.f64 (*.f64 x x) eps))
(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 (*.f64 x x) eps) #s(literal 1 binary64)))
(/.f64 #s(literal 1 binary64) (/.f64 x (/.f64 eps x)))
(/.f64 #s(literal 1 binary64) (neg.f64 (neg.f64 (/.f64 (*.f64 x x) eps))))
(/.f64 (.f64 eps eps) (.f64 eps (*.f64 x x)))
(/.f64 (/.f64 eps x) x)
(/.f64 (neg.f64 eps) (neg.f64 (*.f64 x x)))
(/.f64 (.f64 eps (.f64 eps eps)) (.f64 (.f64 x x) (*.f64 eps eps)))
(/.f64 (.f64 eps #s(literal 1 binary64)) (.f64 x x))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 (*.f64 x x) eps)))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 (/.f64 (*.f64 x x) eps) #s(literal 1 binary64))))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 x (/.f64 eps x))))
(/.f64 (neg.f64 (.f64 eps (.f64 eps eps))) (neg.f64 (.f64 (.f64 x x) (*.f64 eps eps))))
(/.f64 (.f64 (.f64 eps (.f64 eps eps)) #s(literal 1 binary64)) (.f64 (.f64 x x) (.f64 eps eps)))
(/.f64 (.f64 (.f64 eps eps) #s(literal 1 binary64)) (.f64 eps (.f64 x x)))
(/.f64 (neg.f64 (neg.f64 eps)) (neg.f64 (neg.f64 (*.f64 x x))))
(/.f64 (neg.f64 (/.f64 eps x)) (neg.f64 x))
(/.f64 (neg.f64 (.f64 eps eps)) (neg.f64 (.f64 eps (*.f64 x x))))
(/.f64 (.f64 (.f64 eps (.f64 eps eps)) (/.f64 #s(literal 1 binary64) (.f64 x x))) (*.f64 eps eps))
(/.f64 (.f64 (.f64 eps eps) (/.f64 #s(literal 1 binary64) (*.f64 x x))) eps)
(/.f64 (neg.f64 (.f64 (.f64 eps (.f64 eps eps)) #s(literal 1 binary64))) (neg.f64 (.f64 (.f64 x x) (.f64 eps eps))))
(/.f64 (neg.f64 (.f64 (.f64 eps eps) #s(literal 1 binary64))) (neg.f64 (.f64 eps (.f64 x x))))
(/.f64 (neg.f64 (.f64 eps #s(literal 1 binary64))) (neg.f64 (.f64 x x)))
(/.f64 (neg.f64 (neg.f64 (neg.f64 eps))) (neg.f64 (neg.f64 (neg.f64 (*.f64 x x)))))
(/.f64 (neg.f64 (neg.f64 (/.f64 eps x))) (neg.f64 (neg.f64 x)))
(/.f64 (neg.f64 (.f64 (.f64 eps (.f64 eps eps)) (/.f64 #s(literal 1 binary64) (.f64 x x)))) (neg.f64 (*.f64 eps eps)))
(/.f64 (neg.f64 (.f64 (.f64 eps eps) (/.f64 #s(literal 1 binary64) (*.f64 x x)))) (neg.f64 eps))
(pow.f64 (/.f64 (*.f64 x x) eps) #s(literal -1 binary64))
(pow.f64 (/.f64 (/.f64 (*.f64 x x) eps) #s(literal 1 binary64)) #s(literal -1 binary64))
(pow.f64 (/.f64 x (/.f64 eps x)) #s(literal -1 binary64))
(pow.f64 (*.f64 (/.f64 x eps) x) #s(literal -1 binary64))
(.f64 eps (/.f64 #s(literal 1 binary64) (.f64 x x)))
(.f64 #s(literal 1 binary64) (/.f64 eps (.f64 x x)))
(*.f64 (/.f64 eps x) (/.f64 #s(literal 1 binary64) x))
(.f64 (neg.f64 eps) (/.f64 #s(literal 1 binary64) (neg.f64 (.f64 x x))))
(*.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 eps x))
(.f64 (/.f64 #s(literal 1 binary64) (.f64 x x)) eps)
(.f64 (pow.f64 (/.f64 (.f64 x x) (.f64 eps (.f64 eps eps))) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (*.f64 eps eps)))
(.f64 (pow.f64 (/.f64 (.f64 x x) (*.f64 eps eps)) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) eps))

eval103.0ms (0.8%)

Memory: 10.2MiB live, 242.6MiB allocated
Compiler: Compiled 19 050 to 1 397 computations (92.7% saved)

prune212.0ms (1.7%)

Memory

-22.2MiB live, 313.1MiB allocated

Pruning

21 alts after pruning (14 fresh and 7 done)

	Pruned	Kept	Total
New	943	8	951
Fresh	1	6	7
Picked	0	5	5
Done	0	2	2
Total	944	21	965

Accuracy

100.0%

Counts

965 → 21

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	99.9%	(.f64 (.f64 #s(approx (sin (* (+ eps 0) 1/2)) (.f64 eps (fma.f64 eps (.f64 eps #s(literal -1/48 binary64)) #s(literal 1/2 binary64)))) (cos.f64 #s(approx (* (+ (* x 2) eps) 1/2) (fma.f64 #s(literal 1/2 binary64) eps x)))) #s(literal 2 binary64))
	99.7%	(.f64 (.f64 #s(approx (sin (* (+ eps 0) 1/2)) (.f64 eps #s(literal 1/2 binary64))) (cos.f64 #s(approx ( (+ (* x 2) eps) 1/2) (fma.f64 #s(literal 1/2 binary64) eps x)))) #s(literal 2 binary64))
	63.9%	#s(approx (- (sin (+ x eps)) (sin x)) (-.f64 #s(approx (+ (* (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) (fma.f64 eps (fma.f64 (*.f64 x #s(literal -1/2 binary64)) (+.f64 eps x) #s(literal 1 binary64)) x)) x))
	99.7%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 eps (fma.f64 eps (.f64 #s(literal -1/2 binary64) (sin.f64 x)) (cos.f64 x))))
	99.4%	#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 eps (cos.f64 x)))
✓	98.8%	#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (- (+ (* (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) x) (fma.f64 (.f64 eps (.f64 x x)) #s(literal -1/2 binary64) eps)))
	36.7%	#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (- (+ (* (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) x) (fma.f64 (.f64 eps (.f64 eps eps)) (/.f64 #s(literal 1 binary64) (.f64 eps eps)) (.f64 (.f64 x #s(literal -1/2 binary64)) (.f64 (+.f64 x eps) eps)))))
	99.0%	#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (- (+ (* (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) x) (fma.f64 eps (fma.f64 eps #s(approx (* eps (+ (* (* x x) 1/12) -1/6)) (.f64 eps #s(literal -1/6 binary64))) (.f64 (*.f64 x #s(literal -1/2 binary64)) (+.f64 eps x))) eps)))
✓	98.9%	#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (- (+ (* (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) x) (fma.f64 eps (.f64 (.f64 x #s(literal -1/2 binary64)) (+.f64 eps x)) eps)))
✓	98.8%	#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (- (+ (* (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) x) (fma.f64 eps #s(approx (+ (* eps (* eps (+ (* (* x x) 1/12) -1/6))) (* (* x -1/2) (+ eps x))) (.f64 x (.f64 x (fma.f64 (*.f64 eps eps) #s(literal 1/12 binary64) #s(literal -1/2 binary64))))) eps)))
	54.0%	#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (- (+ (* (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) x) (/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 #s(literal -1/2 binary64) (.f64 eps (.f64 x x)) (neg.f64 eps)) (-.f64 (.f64 (.f64 eps eps) (.f64 #s(literal 1/4 binary64) (.f64 (.f64 x x) (.f64 x x)))) (*.f64 eps eps))))))
	98.8%	#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (- (+ (* (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) x) (.f64 (+.f64 #s(approx (+ ( eps (* eps (+ (* (* x x) 1/12) -1/6))) (* (* x -1/2) (+ eps x))) (.f64 (.f64 x x) (fma.f64 eps (*.f64 eps #s(literal 1/12 binary64)) #s(literal -1/2 binary64)))) #s(literal 1 binary64)) eps)))
	56.9%	#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (- (+ (* (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) x) #s(approx (+ (* eps (* (* x -1/2) (+ eps x))) eps) (.f64 (.f64 x x) (fma.f64 #s(literal -1/2 binary64) (fma.f64 eps (/.f64 eps x) eps) (/.f64 (/.f64 eps x) x))))))
	28.0%	#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (- (+ (* (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) x) #s(approx (+ (* eps (* (* x -1/2) (+ eps x))) eps) (.f64 (.f64 x x) (fma.f64 #s(literal -1/2 binary64) (fma.f64 eps (/.f64 eps x) eps) (/.f64 (.f64 eps (.f64 eps eps)) (.f64 (.f64 x x) (*.f64 eps eps))))))))
✓	55.1%	#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (- (+ (* (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) x) #s(approx (+ (* eps (* (* x -1/2) (+ eps x))) eps) (.f64 (.f64 x x) (fma.f64 #s(literal -1/2 binary64) (fma.f64 eps (/.f64 eps x) eps) (/.f64 eps (*.f64 x x)))))))
	5.6%	#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (- (+ (* (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) x) #s(approx (+ (* eps (* (* x -1/2) (+ eps x))) eps) (.f64 x (.f64 eps (*.f64 eps #s(literal -1/2 binary64)))))))
	5.6%	#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (- (+ (* (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) x) #s(approx (+ (* eps (* (* x -1/2) (+ eps x))) eps) (.f64 eps (.f64 eps (*.f64 x #s(literal -1/2 binary64)))))))
✓	98.0%	#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (sin eps) (fma.f64 eps (.f64 eps (.f64 eps #s(literal -1/6 binary64))) eps)))
	4.9%	#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (sin eps) #s(approx (+ (* eps (* eps (* eps -1/6))) eps) (.f64 (.f64 eps (*.f64 eps eps)) #s(literal -1/6 binary64)))))
	4.9%	#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (sin eps) #s(approx (+ (* eps (* eps (* eps -1/6))) eps) (.f64 (.f64 #s(literal -1/6 binary64) (*.f64 eps eps)) eps))))
✓	4.9%	#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (sin eps) #s(approx (+ (* eps (* eps (* eps -1/6))) eps) (.f64 eps (.f64 eps (*.f64 eps #s(literal -1/6 binary64)))))))

Compiler

Compiled 843 to 306 computations (63.7% saved)

regimes34.0ms (0.3%)

Memory

-20.7MiB live, 60.0MiB allocated

Counts

32 → 1

Calls

Call 1

Inputs
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (sin eps) #s(approx (+ (* eps (* eps (* eps -1/6))) eps) (.f64 eps (.f64 eps (*.f64 eps #s(literal -1/6 binary64)))))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (sin eps) #s(approx (+ (* eps (* eps (* eps -1/6))) eps) (.f64 (.f64 #s(literal -1/6 binary64) (*.f64 eps eps)) eps))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (sin eps) #s(approx (+ (* eps (* eps (* eps -1/6))) eps) (.f64 (.f64 eps (*.f64 eps eps)) #s(literal -1/6 binary64)))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (- (+ (* (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) x) #s(approx (+ (* eps (* (* x -1/2) (+ eps x))) eps) (.f64 eps (.f64 eps (*.f64 x #s(literal -1/2 binary64)))))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (- (+ (* (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) x) #s(approx (+ (* eps (* (* x -1/2) (+ eps x))) eps) (.f64 x (.f64 eps (*.f64 eps #s(literal -1/2 binary64)))))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (sin eps) (fma.f64 eps (.f64 eps (.f64 eps #s(literal -1/6 binary64))) eps)))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (- (+ (* (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) x) (fma.f64 (.f64 eps (.f64 x x)) #s(literal -1/2 binary64) eps)))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (- (+ (* (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) x) (fma.f64 eps (.f64 (.f64 x #s(literal -1/2 binary64)) (+.f64 eps x)) eps)))
#s(approx (- (sin (+ x eps)) (sin x)) (-.f64 #s(approx (+ (* (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) (fma.f64 eps (fma.f64 (*.f64 x #s(literal -1/2 binary64)) (+.f64 eps x) #s(literal 1 binary64)) x)) x))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (- (+ (* (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) x) (fma.f64 eps #s(approx (+ (* eps (* eps (+ (* (* x x) 1/12) -1/6))) (* (* x -1/2) (+ eps x))) (.f64 x (.f64 x (fma.f64 (*.f64 eps eps) #s(literal 1/12 binary64) #s(literal -1/2 binary64))))) eps)))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (- (+ (* (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) x) (.f64 (+.f64 #s(approx (+ ( eps (* eps (+ (* (* x x) 1/12) -1/6))) (* (* x -1/2) (+ eps x))) (.f64 (.f64 x x) (fma.f64 eps (*.f64 eps #s(literal 1/12 binary64)) #s(literal -1/2 binary64)))) #s(literal 1 binary64)) eps)))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (- (+ (* (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) x) (fma.f64 eps (fma.f64 eps #s(approx (* eps (+ (* (* x x) 1/12) -1/6)) (.f64 eps #s(literal -1/6 binary64))) (.f64 (*.f64 x #s(literal -1/2 binary64)) (+.f64 eps x))) eps)))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (- (+ (* (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) x) (fma.f64 eps (fma.f64 eps (.f64 eps (fma.f64 (.f64 x x) #s(literal 1/12 binary64) #s(literal -1/6 binary64))) (.f64 (.f64 x #s(literal -1/2 binary64)) (+.f64 eps x))) eps)))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (- (+ (* (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) x) #s(approx (+ (* eps (* (* x -1/2) (+ eps x))) eps) (.f64 (.f64 x x) (fma.f64 #s(literal -1/2 binary64) (fma.f64 eps (/.f64 eps x) eps) (/.f64 eps (*.f64 x x)))))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (- (+ (* (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) x) (fma.f64 (.f64 eps (.f64 eps eps)) (/.f64 #s(literal 1 binary64) (.f64 eps eps)) (.f64 (.f64 x #s(literal -1/2 binary64)) (.f64 (+.f64 x eps) eps)))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (- (+ (* (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) x) #s(approx (+ (* eps (* (* x -1/2) (+ eps x))) eps) (.f64 (.f64 x x) (fma.f64 #s(literal -1/2 binary64) (fma.f64 eps (/.f64 eps x) eps) (/.f64 (/.f64 eps x) x))))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (- (+ (* (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) x) #s(approx (+ (* eps (* (* x -1/2) (+ eps x))) eps) (.f64 (.f64 x x) (fma.f64 #s(literal -1/2 binary64) (fma.f64 eps (/.f64 eps x) eps) (/.f64 (.f64 eps (.f64 eps eps)) (.f64 (.f64 x x) (*.f64 eps eps))))))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (- (+ (* (+ (* x (* x -1/2)) 1) (sin eps)) (* x (cos eps))) x) (/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 #s(literal -1/2 binary64) (.f64 eps (.f64 x x)) (neg.f64 eps)) (-.f64 (.f64 (.f64 eps eps) (.f64 #s(literal 1/4 binary64) (.f64 (.f64 x x) (.f64 x x)))) (*.f64 eps eps))))))
#s(approx (- (sin (+ x eps)) (sin x)) (sin.f64 eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 eps (cos.f64 x)))
(.f64 (.f64 #s(approx (sin (* (+ eps 0) 1/2)) (.f64 #s(literal 1/2 binary64) eps)) (cos.f64 #s(approx ( (+ (* x 2) eps) 1/2) (fma.f64 #s(literal 1/2 binary64) eps x)))) #s(literal 2 binary64))
(.f64 (.f64 #s(approx (sin (* (+ eps 0) 1/2)) (.f64 eps #s(literal 1/2 binary64))) (cos.f64 #s(approx ( (+ (* x 2) eps) 1/2) (fma.f64 #s(literal 1/2 binary64) eps x)))) #s(literal 2 binary64))
(-.f64 (sin.f64 (+.f64 x eps)) #s(approx (sin x) (fma.f64 #s(literal -1/6 binary64) (.f64 x (.f64 x x)) x)))
(.f64 (.f64 #s(approx (sin (* (+ eps 0) 1/2)) (.f64 #s(literal 1/2 binary64) eps)) (cos.f64 (.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)))) #s(literal 2 binary64))
(.f64 (.f64 #s(approx (sin (* (+ eps 0) 1/2)) (.f64 eps (fma.f64 eps (.f64 eps #s(literal -1/48 binary64)) #s(literal 1/2 binary64)))) (cos.f64 #s(approx (* (+ (* x 2) eps) 1/2) (fma.f64 #s(literal 1/2 binary64) eps x)))) #s(literal 2 binary64))
(-.f64 (sin.f64 (+.f64 x eps)) #s(approx (sin x) (fma.f64 (fma.f64 (.f64 x x) #s(literal 1/120 binary64) #s(literal -1/6 binary64)) (.f64 x (*.f64 x x)) x)))
(.f64 (.f64 #s(approx (sin (* (+ eps 0) 1/2)) (.f64 eps (fma.f64 eps (.f64 eps #s(literal -1/48 binary64)) #s(literal 1/2 binary64)))) (cos.f64 (*.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)))) #s(literal 2 binary64))
(-.f64 (sin.f64 (+.f64 x eps)) #s(approx (sin x) (fma.f64 (fma.f64 x (.f64 x (fma.f64 (.f64 x x) #s(literal -1/5040 binary64) #s(literal 1/120 binary64))) #s(literal -1/6 binary64)) (.f64 x (.f64 x x)) x)))
(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 eps (fma.f64 eps (.f64 #s(literal -1/2 binary64) (sin.f64 x)) (cos.f64 x))))
#s(approx (- (sin (+ x eps)) (sin x)) (-.f64 (fma.f64 (fma.f64 x (.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64)) (sin.f64 eps) (.f64 x (cos.f64 eps))) x))
(.f64 (.f64 (sin.f64 (.f64 (+.f64 eps #s(literal 0 binary64)) #s(literal 1/2 binary64))) (cos.f64 (.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)))) #s(literal 2 binary64))

Outputs

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

Calls

3 calls:

13.0ms	(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
9.0ms	eps
9.0ms	x

Results

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

Compiler

Compiled 15 to 10 computations (33.3% saved)

regimes22.0ms (0.2%)

Memory

4.5MiB live, 43.6MiB allocated

Counts

24 → 1

Calls

Call 1

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

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

Calls

3 calls:

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

Results

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

Compiler

Compiled 15 to 10 computations (33.3% saved)

regimes20.0ms (0.2%)

Memory

-2.7MiB live, 36.7MiB allocated

Counts

20 → 1

Calls

Call 1

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

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

Calls

3 calls:

6.0ms	eps
6.0ms	(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
6.0ms	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 15 to 10 computations (33.3% saved)

regimes18.0ms (0.1%)

Memory

34.8MiB live, 34.8MiB allocated

Counts

19 → 1

Calls

Call 1

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

Outputs

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

Calls

3 calls:

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

Results

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

Compiler

Compiled 15 to 10 computations (33.3% saved)

regimes14.0ms (0.1%)

Memory

-19.1MiB live, 25.8MiB allocated

Counts

12 → 1

Calls

Call 1

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

Outputs

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

Calls

3 calls:

6.0ms	(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
4.0ms	eps
4.0ms	x

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 15 to 10 computations (33.3% saved)

regimes13.0ms (0.1%)

Memory

-16.2MiB live, 23.1MiB allocated

Counts

11 → 1

Calls

Call 1

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

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

Calls

3 calls:

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

Results

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

Compiler

Compiled 15 to 10 computations (33.3% saved)

regimes9.0ms (0.1%)

Memory

18.9MiB live, 18.9MiB allocated

Counts

7 → 1

Calls

Call 1

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

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

Calls

3 calls:

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

Results

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

Compiler

Compiled 15 to 10 computations (33.3% saved)

regimes9.0ms (0.1%)

Memory

-21.6MiB live, 17.8MiB allocated

Counts

6 → 1

Calls

Call 1

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

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

Calls

3 calls:

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

Results

Accuracy	Segments	Branch
98.0%	1	`x`
98.0%	1	`eps`
98.0%	1	`(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))`

Compiler

Compiled 15 to 10 computations (33.3% saved)

regimes8.0ms (0.1%)

Memory

16.3MiB live, 16.3MiB allocated

Counts

5 → 1

Calls

Call 1

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

Outputs

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

Calls

3 calls:

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

Results

Accuracy	Segments	Branch
5.6%	1	`x`
5.6%	1	`eps`
5.6%	1	`(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))`

Compiler

Compiled 15 to 10 computations (33.3% saved)

regimes6.0ms (0%)

Memory

13.5MiB live, 13.5MiB allocated

Accuracy

Total -0.0b remaining (-0%)

Threshold costs -0b (-0%)

Counts

3 → 1

Calls

Call 1

Inputs

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

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

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

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

Calls

3 calls:

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

Results

Accuracy	Segments	Branch
4.9%	1	`x`
4.9%	1	`eps`
4.9%	1	`(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))`

Compiler

Compiled 15 to 10 computations (33.3% saved)

simplify9.0ms (0.1%)

Memory

-23.9MiB live, 15.7MiB allocated

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	93	328
1	113	328

Stop Event

1×

saturated

Calls

Call 1

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

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

soundness1.1s (8.7%)

Memory

8.6MiB live, 794.3MiB allocated

Rules

16 678×	`lower-fma.f64`
16 678×	`lower-fma.f32`
15 332×	`lower-fma.f64`
15 332×	`lower-fma.f32`
13 690×	`lower-fma.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	445	5705
1	1377	5412
2	3925	5392
0	8831	4994
0	366	3695
1	1153	3529
2	3178	3491
0	8074	3210
0	107	496
1	314	496
2	775	489
3	2836	489
4	6173	489
0	8126	458
0	6	16
0	10	16
1	53	16
2	380	16
3	4766	16
0	8210	16

Stop Event

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

Compiler

Compiled 260 to 135 computations (48.1% saved)

preprocess200.0ms (1.6%)

Memory: 22.0MiB live, 189.8MiB allocated
Compiler: Compiled 372 to 156 computations (58.1% saved)

end0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated

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

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

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

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

start0.0ms (0%)

analyze57.0ms (0.4%)

sample5.8s (45.4%)

explain189.0ms (1.5%)

preprocess24.0ms (0.2%)

eval0.0ms (0%)

prune1.0ms (0%)

simplify87.0ms (0.7%)

localize24.0ms (0.2%)

series73.0ms (0.6%)

simplify278.0ms (2.2%)

rewrite313.0ms (2.4%)

eval38.0ms (0.3%)

prune44.0ms (0.3%)

simplify232.0ms (1.8%)

localize164.0ms (1.3%)

series31.0ms (0.2%)

simplify258.0ms (2%)

rewrite420.0ms (3.3%)

eval133.0ms (1%)

prune101.0ms (0.8%)

simplify266.0ms (2.1%)

localize224.0ms (1.7%)

series37.0ms (0.3%)

simplify339.0ms (2.6%)

rewrite325.0ms (2.5%)

eval134.0ms (1%)

prune192.0ms (1.5%)

simplify243.0ms (1.9%)

localize227.0ms (1.8%)

series55.0ms (0.4%)

simplify329.0ms (2.6%)

rewrite382.0ms (3%)

eval103.0ms (0.8%)

prune212.0ms (1.7%)

regimes34.0ms (0.3%)

regimes22.0ms (0.2%)

regimes20.0ms (0.2%)

regimes18.0ms (0.1%)

regimes14.0ms (0.1%)

regimes13.0ms (0.1%)

regimes9.0ms (0.1%)

regimes9.0ms (0.1%)

regimes8.0ms (0.1%)

regimes6.0ms (0%)

simplify9.0ms (0.1%)

soundness1.1s (8.7%)

preprocess200.0ms (1.6%)

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