Metrics for 2sin (example 3.3)

start0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated

analyze57.0ms (0.5%)

Memory

-0.9MiB live, 38.0MiB allocated

Algorithm

1×

Search

Probability	Valid	Unknown	Precondition	Infinite	Domain	Can't	Iter
0%	0%	50.6%	49.4%	0%	0%	0%	0
0%	0%	50.6%	49.4%	0%	0%	0%	1
0%	0%	50.6%	49.4%	0%	0%	0%	2
0%	0%	25.3%	49.4%	0%	25.3%	0%	3
0%	0%	25.3%	49.4%	0%	25.3%	0%	4
0%	0%	19%	49.4%	0%	31.6%	0%	5
0%	0%	15.8%	49.4%	0%	34.8%	0%	6
0%	0%	11.1%	49.4%	0%	39.5%	0%	7
0%	0%	8.7%	49.4%	0%	41.9%	0%	8
0%	0%	5.9%	49.4%	0%	44.6%	0%	9
0%	0%	4.5%	49.4%	0%	46%	0%	10
0%	0%	3.1%	49.4%	0%	47.5%	0%	11
0%	0%	2.7%	49.4%	0%	47.9%	0%	12

Compiler

Compiled 27 to 19 computations (29.6% saved)

sample5.8s (49.6%)

Memory

-157.2MiB live, 6 415.1MiB allocated

Samples

3.2s	26 362×	0	invalid
672.0ms	5 575×	0	valid
471.0ms	2 681×	1	valid

Precisions

Click to see histograms. Total time spent on operations: 2.9s

ival-sin: 676.0ms (23.3% of total)

const: 650.0ms (22.4% of total)

ival-mult: 266.0ms (9.2% of total)

ival-<=: 254.0ms (8.7% of total)

ival-fabs: 215.0ms (7.4% of total)

ival-<: 209.0ms (7.2% of total)

ival-add: 204.0ms (7% of total)

ival-sub: 199.0ms (6.8% of total)

ival-and: 98.0ms (3.4% of total)

adjust: 82.0ms (2.8% of total)

exact: 41.0ms (1.4% of total)

ival-assert: 12.0ms (0.4% of total)

Bogosity

explain140.0ms (1.2%)

Memory

7.2MiB live, 82.5MiB allocated

FPErrors

Click to see full error table

Ground Truth	Overpredictions	Example	Underpredictions	Example	Subexpression
225	2	(-1.889798177677739e-146 1.227075656794296e-150)	6	(-1.2048120858646896e-35 1.3912270648591378e-37)	`(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))`
2	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	221	9
`sin.f64`	`(sin.f64 (+.f64 x eps))`	sensitivity	2	1

Confusion

	Predicted +	Predicted -
+	220	6
-	2	28

Precision

0.990990990990991

Recall

0.9734513274336283

Confusion?

	Predicted +	Predicted Maybe	Predicted -
+	220	6	0
-	2	3	25

Precision?

0.9783549783549783

Recall?

1.0

Freqs

test

number	freq
0	34
1	221
2	1

Total Confusion?

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

Precision?

1.0

Recall?

1.0

Samples

17.0ms	346×	0	valid
16.0ms	164×	1	valid
0.0ms	2×	2	valid

Compiler

Compiled 49 to 22 computations (55.1% saved)

Precisions

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

ival-sin: 9.0ms (48.5% of total)

adjust: 3.0ms (16.2% of total)

ival-add: 3.0ms (16.2% of total)

ival-sub: 3.0ms (16.2% of total)

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

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

preprocess29.0ms (0.2%)

Memory

-21.5MiB live, 20.3MiB allocated

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

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

Stop Event

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

Calls

Call 1

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

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

Compiler

Compiled 9 to 6 computations (33.3% saved)

eval0.0ms (0%)

Memory: 0.4MiB live, 0.4MiB allocated
Compiler: Compiled 2 to 2 computations (0% saved)

prune0.0ms (0%)

Memory

1.5MiB live, 1.5MiB allocated

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	62.1%	(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))

Compiler

Compiled 9 to 6 computations (33.3% saved)

simplify7.0ms (0.1%)

Memory

10.5MiB live, 10.5MiB 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))
(-.f64 (sin.f64 (+.f64 eps x)) (sin.f64 x))
(sin.f64 (+.f64 x eps))
(sin.f64 (+.f64 eps x))
(+.f64 x eps)
(+.f64 eps x)
x
eps
(sin.f64 x)

localize26.0ms (0.2%)

Memory

8.1MiB live, 42.7MiB allocated

Localize:

Found 4 expressions of interest:

New	Metric	Score
accuracy	0	(+.f64 x eps)
accuracy	0	(sin.f64 x)
accuracy	0.09759685670613527	(sin.f64 (+.f64 x eps))
accuracy	24.1195970857929	(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))

Samples

13.0ms	173×	0	valid
8.0ms	82×	1	valid
0.0ms	1×	2	valid

Compiler

Compiled 20 to 8 computations (60% saved)

Precisions

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

ival-sin: 8.0ms (62% of total)

adjust: 2.0ms (15.5% of total)

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

ival-sub: 1.0ms (7.7% of total)

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

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

series6.0ms (0.1%)

Memory

-26.3MiB live, 10.8MiB allocated

Counts

4 → 84

Calls

Call 1

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

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

Calls

6 calls:

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

simplify163.0ms (1.4%)

Memory

17.0MiB live, 132.0MiB allocated

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

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

Stop Event

1×	iter limit
1×	node limit

Counts

84 → 77

Calls

Call 1

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

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

rewrite159.0ms (1.4%)

Memory

9.7MiB live, 241.5MiB allocated

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

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

Stop Event

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

Counts

4 → 214

Calls

Call 1

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

Outputs
(.f64 (pow.f64 (/.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 #s(literal 2 binary64) (+.f64 eps x)))) #s(literal 1/2 binary64) (*.f64 (+.f64 (sin.f64 x) (sin.f64 (+.f64 eps x))) (sin.f64 x))) (-.f64 (pow.f64 (sin.f64 (+.f64 eps x)) #s(literal 6 binary64)) (pow.f64 (sin.f64 x) #s(literal 6 binary64)))) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (-.f64 (pow.f64 (sin.f64 (+.f64 eps x)) #s(literal 3 binary64)) (pow.f64 (sin.f64 x) #s(literal 3 binary64)))))
(.f64 (pow.f64 (/.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 #s(literal 2 binary64) (+.f64 eps x)))) #s(literal 1/2 binary64) (.f64 (+.f64 (sin.f64 x) (sin.f64 (+.f64 eps x))) (sin.f64 x))) (-.f64 (pow.f64 (sin.f64 (+.f64 eps x)) #s(literal 9 binary64)) (pow.f64 (sin.f64 x) #s(literal 9 binary64)))) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (sin.f64 (+.f64 eps x)) #s(literal 6 binary64)) (+.f64 (pow.f64 (.f64 (sin.f64 x) (sin.f64 (+.f64 eps x))) #s(literal 3 binary64)) (pow.f64 (sin.f64 x) #s(literal 6 binary64))))))
(.f64 (pow.f64 (/.f64 (+.f64 (sin.f64 x) (sin.f64 (+.f64 eps x))) (-.f64 (pow.f64 (sin.f64 (+.f64 eps x)) #s(literal 4 binary64)) (pow.f64 (sin.f64 x) #s(literal 4 binary64)))) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 x x))) #s(literal 1/2 binary64) (.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) (+.f64 eps x)))) #s(literal 1/2 binary64)))))
(.f64 (pow.f64 (/.f64 (+.f64 (sin.f64 x) (sin.f64 (+.f64 eps x))) (-.f64 (pow.f64 (sin.f64 (+.f64 eps x)) #s(literal 6 binary64)) (pow.f64 (sin.f64 x) #s(literal 6 binary64)))) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (fma.f64 (.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 x x))) #s(literal 1/2 binary64)) (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 x x))) #s(literal 1/2 binary64) (.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 #s(literal 2 binary64) (+.f64 eps x)))) #s(literal 1/2 binary64))) (pow.f64 (sin.f64 (+.f64 eps x)) #s(literal 4 binary64)))))
(.f64 (pow.f64 (/.f64 #s(literal 2 binary64) (+.f64 (sin.f64 x) (sin.f64 (+.f64 eps x)))) #s(literal -1 binary64)) (pow.f64 (/.f64 (.f64 (cos.f64 (.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 0 binary64) eps))) (sin.f64 (.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps)))) (-.f64 (sin.f64 (+.f64 eps x)) (sin.f64 x))) #s(literal -1 binary64)))
(.f64 (/.f64 (-.f64 (pow.f64 (sin.f64 (+.f64 eps x)) #s(literal 3 binary64)) (pow.f64 (sin.f64 x) #s(literal 3 binary64))) (-.f64 (pow.f64 (sin.f64 (+.f64 eps x)) #s(literal 4 binary64)) (pow.f64 (.f64 (+.f64 (sin.f64 x) (sin.f64 (+.f64 eps x))) (sin.f64 x)) #s(literal 2 binary64)))) (-.f64 #s(literal 1/2 binary64) (fma.f64 (cos.f64 (.f64 #s(literal 2 binary64) (+.f64 eps x))) #s(literal 1/2 binary64) (.f64 (+.f64 (sin.f64 x) (sin.f64 (+.f64 eps x))) (sin.f64 x)))))
(.f64 (/.f64 (-.f64 (pow.f64 (sin.f64 (+.f64 eps x)) #s(literal 3 binary64)) (pow.f64 (sin.f64 x) #s(literal 3 binary64))) (+.f64 (pow.f64 (.f64 (+.f64 (sin.f64 x) (sin.f64 (+.f64 eps x))) (sin.f64 x)) #s(literal 3 binary64)) (pow.f64 (sin.f64 (+.f64 eps x)) #s(literal 6 binary64)))) (fma.f64 (.f64 (+.f64 (sin.f64 x) (sin.f64 (+.f64 eps x))) (sin.f64 x)) (-.f64 (.f64 (+.f64 (sin.f64 x) (sin.f64 (+.f64 eps x))) (sin.f64 x)) (.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 #s(literal 2 binary64) (+.f64 eps x)))) #s(literal 1/2 binary64))) (pow.f64 (sin.f64 (+.f64 eps x)) #s(literal 4 binary64))))
(.f64 (/.f64 (-.f64 #s(literal 1/2 binary64) (fma.f64 (cos.f64 (.f64 #s(literal 2 binary64) (+.f64 eps x))) #s(literal 1/2 binary64) (.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 x x))) #s(literal 1/2 binary64)))) (-.f64 #s(literal 1/2 binary64) (fma.f64 (cos.f64 (.f64 #s(literal 2 binary64) (+.f64 eps x))) #s(literal 1/2 binary64) (*.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 x x))) #s(literal 1/2 binary64))))) (-.f64 (sin.f64 (+.f64 eps x)) (sin.f64 x)))
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(/.f64 (.f64 (.f64 (fma.f64 (.f64 eps eps) eps (.f64 (.f64 x x) x)) (.f64 (fma.f64 eps (+.f64 eps x) (.f64 x x)) (-.f64 x eps))) #s(literal 1 binary64)) (.f64 (fma.f64 (.f64 eps eps) (fma.f64 eps eps (.f64 x x)) (.f64 (.f64 x x) (*.f64 x x))) (-.f64 x eps)))
(/.f64 (.f64 (.f64 (fma.f64 (.f64 eps eps) eps (.f64 (.f64 x x) x)) (.f64 (fma.f64 eps (+.f64 eps x) (.f64 x x)) (-.f64 x eps))) #s(literal 1 binary64)) (.f64 (.f64 (fma.f64 eps (+.f64 eps x) (.f64 x x)) (-.f64 x eps)) (fma.f64 (-.f64 eps x) eps (*.f64 x x))))
(/.f64 (.f64 (fma.f64 (.f64 (.f64 (.f64 eps eps) eps) (.f64 (.f64 eps eps) eps)) (.f64 (.f64 eps eps) eps) (.f64 (.f64 (.f64 (.f64 x x) x) (.f64 (.f64 x x) x)) (.f64 (.f64 x x) x))) #s(literal 1 binary64)) (.f64 (fma.f64 (.f64 (.f64 eps eps) eps) (-.f64 (.f64 (.f64 eps eps) eps) (.f64 (.f64 x x) x)) (.f64 (.f64 (.f64 x x) x) (.f64 (.f64 x x) x))) (fma.f64 (-.f64 eps x) eps (*.f64 x x))))
(/.f64 (.f64 (fma.f64 (.f64 eps eps) eps (.f64 (.f64 x x) x)) #s(literal 1 binary64)) (fma.f64 (-.f64 eps x) eps (*.f64 x x)))
(/.f64 (-.f64 (.f64 (.f64 x x) (-.f64 x eps)) (.f64 (-.f64 x eps) (.f64 eps eps))) (*.f64 (-.f64 x eps) (-.f64 x eps)))
(/.f64 (.f64 (fma.f64 eps eps (.f64 x x)) (.f64 (-.f64 x eps) (+.f64 eps x))) (.f64 (-.f64 x eps) (fma.f64 eps eps (*.f64 x x))))
(/.f64 (*.f64 (+.f64 eps x) (-.f64 eps x)) (-.f64 eps x))
(/.f64 (.f64 (fma.f64 (.f64 eps eps) eps (.f64 (.f64 x x) x)) (.f64 (fma.f64 eps (+.f64 eps x) (.f64 x x)) (-.f64 x eps))) (.f64 (-.f64 x eps) (fma.f64 (.f64 eps eps) (fma.f64 eps eps (.f64 x x)) (.f64 (.f64 x x) (.f64 x x)))))
(/.f64 (.f64 (fma.f64 (.f64 eps eps) eps (.f64 (.f64 x x) x)) (.f64 (fma.f64 eps (+.f64 eps x) (.f64 x x)) (-.f64 x eps))) (.f64 (fma.f64 (-.f64 eps x) eps (.f64 x x)) (.f64 (fma.f64 eps (+.f64 eps x) (.f64 x x)) (-.f64 x eps))))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 #s(literal 1 binary64) (+.f64 eps x))))
(/.f64 #s(literal 1 binary64) (/.f64 (-.f64 eps x) (*.f64 (+.f64 eps x) (-.f64 eps x))))
(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 #s(literal 1 binary64) (+.f64 eps x)) #s(literal 1 binary64)))
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (+.f64 eps x)))
(/.f64 (fma.f64 (.f64 (.f64 (.f64 eps eps) eps) (.f64 (.f64 eps eps) eps)) (.f64 (.f64 eps eps) eps) (.f64 (.f64 (.f64 (.f64 x x) x) (.f64 (.f64 x x) x)) (.f64 (.f64 x x) x))) (.f64 (fma.f64 (-.f64 eps x) eps (.f64 x x)) (fma.f64 (.f64 (.f64 eps eps) eps) (-.f64 (.f64 (.f64 eps eps) eps) (.f64 (.f64 x x) x)) (.f64 (.f64 (.f64 x x) x) (.f64 (.f64 x x) x)))))
(/.f64 (neg.f64 (*.f64 (-.f64 x eps) (+.f64 eps x))) (neg.f64 (-.f64 x eps)))
(/.f64 (neg.f64 (fma.f64 (.f64 eps eps) eps (.f64 (.f64 x x) x))) (neg.f64 (fma.f64 (-.f64 eps x) eps (.f64 x x))))
(/.f64 (*.f64 (-.f64 x eps) (+.f64 eps x)) (-.f64 x eps))
(/.f64 (fma.f64 (.f64 eps eps) eps (.f64 (.f64 x x) x)) (fma.f64 (-.f64 eps x) eps (.f64 x x)))
(neg.f64 (/.f64 (neg.f64 (*.f64 (-.f64 x eps) (+.f64 eps x))) (-.f64 x eps)))
(neg.f64 (/.f64 (neg.f64 (fma.f64 (.f64 eps eps) eps (.f64 (.f64 x x) x))) (fma.f64 (-.f64 eps x) eps (.f64 x x))))
(neg.f64 (/.f64 (*.f64 (-.f64 x eps) (+.f64 eps x)) (neg.f64 (-.f64 x eps))))
(neg.f64 (/.f64 (fma.f64 (.f64 eps eps) eps (.f64 (.f64 x x) x)) (neg.f64 (fma.f64 (-.f64 eps x) eps (.f64 x x)))))
(fma.f64 (/.f64 (.f64 x x) (.f64 (fma.f64 eps (+.f64 eps x) (.f64 x x)) (-.f64 x eps))) (fma.f64 eps (+.f64 eps x) (.f64 x x)) (neg.f64 (*.f64 eps (/.f64 eps (-.f64 x eps)))))
(fma.f64 (/.f64 (.f64 x x) (.f64 (-.f64 x eps) (+.f64 eps x))) (+.f64 eps x) (neg.f64 (*.f64 eps (/.f64 eps (-.f64 x eps)))))
(fma.f64 (.f64 x x) (/.f64 #s(literal 1 binary64) (-.f64 x eps)) (neg.f64 (.f64 eps (/.f64 eps (-.f64 x eps)))))
(fma.f64 x (/.f64 x (-.f64 x eps)) (neg.f64 (*.f64 eps (/.f64 eps (-.f64 x eps)))))
(-.f64 (/.f64 (.f64 eps eps) (-.f64 eps x)) (/.f64 (.f64 x x) (-.f64 eps x)))
(-.f64 (.f64 x (/.f64 x (-.f64 x eps))) (.f64 eps (/.f64 eps (-.f64 x eps))))
(+.f64 (.f64 x (/.f64 x (-.f64 x eps))) (neg.f64 (.f64 eps (/.f64 eps (-.f64 x eps)))))
(+.f64 eps x)
(+.f64 x eps)
(exp.f64 (*.f64 (log.f64 (/.f64 #s(literal 1 binary64) (+.f64 eps x))) #s(literal -1 binary64)))
(pow.f64 (sin.f64 x) #s(literal 1 binary64))
(sin.f64 x)
(exp.f64 (*.f64 (log.f64 (sin.f64 x)) #s(literal 1 binary64)))

eval86.0ms (0.7%)

Memory: 5.3MiB live, 59.3MiB allocated
Compiler: Compiled 7 823 to 838 computations (89.3% saved)

prune26.0ms (0.2%)

Memory

-12.1MiB live, 25.8MiB allocated

Pruning

10 alts after pruning (9 fresh and 1 done)

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

Accuracy

100.0%

Counts

292 → 10

Alt Table

Click to see full alt table

Status	Accuracy	Program
	62.4%	(fma.f64 (sin.f64 x) (cos.f64 eps) (fma.f64 (sin.f64 eps) (cos.f64 x) (neg.f64 (sin.f64 x))))
✓	62.1%	(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
	61.2%	(-.f64 (sin.f64 (+.f64 x eps)) #s(approx (sin x) (.f64 (fma.f64 (fma.f64 #s(literal 1/120 binary64) (.f64 x x) #s(literal -1/6 binary64)) (*.f64 x x) #s(literal 1 binary64)) x)))
▶	61.1%	(-.f64 (sin.f64 (+.f64 x eps)) #s(approx (sin x) (.f64 (fma.f64 (.f64 x x) #s(literal -1/6 binary64) #s(literal 1 binary64)) x)))
▶	7.5%	(-.f64 #s(approx (sin (+ x eps)) (sin.f64 eps)) (sin.f64 x))
▶	99.9%	(.f64 (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 0 binary64) eps))) #s(literal 2 binary64)) (cos.f64 (.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps))))
▶	99.7%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 (fma.f64 (.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64)) (cos.f64 x) (.f64 (.f64 (sin.f64 x) #s(literal -1/2 binary64)) eps)) eps))
	99.5%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 (.f64 (sin.f64 x) #s(literal -1/2 binary64)) eps (cos.f64 x)) eps))
	99.0%	#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (cos.f64 x) eps))
▶	98.2%	#s(approx (- (sin (+ x eps)) (sin x)) (sin.f64 eps))

Compiler

Compiled 255 to 160 computations (37.3% saved)

simplify244.0ms (2.1%)

Memory

11.3MiB live, 199.7MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 18 expressions of interest:

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

Rules

10 588×	`lower-fma.f32`
10 580×	`lower-fma.f64`
6 696×	`lower-*.f32`
6 676×	`lower-*.f64`
1 858×	`distribute-lft-neg-in`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	40	236
0	70	226
1	115	226
2	221	223
3	402	220
4	934	220
5	1449	220
6	1617	220
7	1715	220
8	1845	220
9	1905	220
10	3166	220
11	3536	220
12	3920	220
13	4566	220
14	5134	220
15	5310	220
16	5809	220
17	6286	220
18	6795	220
19	7124	220
20	7235	220
0	8395	211

Stop Event

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

Calls

Call 1

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

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

localize122.0ms (1%)

Memory

6.9MiB live, 131.5MiB allocated

Localize:

Found 18 expressions of interest:

New	Metric	Score
accuracy	0.00390625	(fma.f64 (fma.f64 (.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64)) (cos.f64 x) (.f64 (*.f64 (sin.f64 x) #s(literal -1/2 binary64)) eps))
accuracy	0.00390625	(.f64 (fma.f64 (fma.f64 (.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64)) (cos.f64 x) (.f64 (.f64 (sin.f64 x) #s(literal -1/2 binary64)) eps)) eps)
accuracy	0.00390625	(.f64 (.f64 (sin.f64 x) #s(literal -1/2 binary64)) eps)
accuracy	0.21941333120599352	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 (fma.f64 (.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64)) (cos.f64 x) (.f64 (.f64 (sin.f64 x) #s(literal -1/2 binary64)) eps)) eps))
accuracy	0	(sin.f64 x)
accuracy	0	(sin.f64 eps)
accuracy	24.1195970857929	(-.f64 #s(approx (sin (+ x eps)) (sin.f64 eps)) (sin.f64 x))
accuracy	58.7829242189664	#s(approx (sin (+ x eps)) (sin.f64 eps))
accuracy	0.00390625	(.f64 (fma.f64 (.f64 x x) #s(literal -1/6 binary64) #s(literal 1 binary64)) x)
accuracy	0.09759685670613527	(sin.f64 (+.f64 x eps))
accuracy	1.0089719187545159	#s(approx (sin x) (.f64 (fma.f64 (.f64 x x) #s(literal -1/6 binary64) #s(literal 1 binary64)) x))
accuracy	24.1195970857929	(-.f64 (sin.f64 (+.f64 x eps)) #s(approx (sin x) (.f64 (fma.f64 (.f64 x x) #s(literal -1/6 binary64) #s(literal 1 binary64)) x)))
accuracy	0	(sin.f64 eps)
accuracy	1.1656792276757235	#s(approx (- (sin (+ x eps)) (sin x)) (sin.f64 eps))
accuracy	0	(*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 0 binary64) eps))
accuracy	0	(sin.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 0 binary64) eps)))
accuracy	0.0078125	(.f64 (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 0 binary64) eps))) #s(literal 2 binary64)) (cos.f64 (.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps))))
accuracy	0.09448630290560088	(cos.f64 (*.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps)))

Samples

61.0ms	173×	0	valid
36.0ms	82×	1	valid
1.0ms	1×	2	valid

Compiler

Compiled 204 to 37 computations (81.9% saved)

Precisions

Click to see histograms. Total time spent on operations: 75.0ms

ival-add: 29.0ms (38.5% of total)

ival-mult: 24.0ms (31.8% of total)

ival-sin: 7.0ms (9.3% of total)

adjust: 5.0ms (6.6% of total)

ival-cos: 4.0ms (5.3% of total)

const: 4.0ms (5.3% of total)

ival-sub: 1.0ms (1.3% of total)

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

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

exact: 0.0ms (0% of total)

series39.0ms (0.3%)

Memory

14.3MiB live, 50.1MiB allocated

Counts

22 → 420

Calls

Call 1

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

Outputs
#s(alt x (taylor 0 eps) (#s(alt (.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps)) (patch (.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps)) #<representation binary64>) () ())) ())
#s(alt (+ x (* 1/2 eps)) (taylor 0 eps) (#s(alt (.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps)) (patch (.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps)) #<representation binary64>) () ())) ())
#s(alt (+ x (* 1/2 eps)) (taylor 0 eps) (#s(alt (.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps)) (patch (.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps)) #<representation binary64>) () ())) ())
#s(alt (+ x (* 1/2 eps)) (taylor 0 eps) (#s(alt (.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps)) (patch (.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps)) #<representation binary64>) () ())) ())
#s(alt eps (taylor 0 eps) (#s(alt (+.f64 #s(literal 0 binary64) eps) (patch (+.f64 #s(literal 0 binary64) eps) #<representation binary64>) () ())) ())
#s(alt eps (taylor 0 eps) (#s(alt (+.f64 #s(literal 0 binary64) eps) (patch (+.f64 #s(literal 0 binary64) eps) #<representation binary64>) () ())) ())
#s(alt eps (taylor 0 eps) (#s(alt (+.f64 #s(literal 0 binary64) eps) (patch (+.f64 #s(literal 0 binary64) eps) #<representation binary64>) () ())) ())
#s(alt eps (taylor 0 eps) (#s(alt (+.f64 #s(literal 0 binary64) eps) (patch (+.f64 #s(literal 0 binary64) eps) #<representation binary64>) () ())) ())
#s(alt (* eps (cos x)) (taylor 0 eps) (#s(alt (.f64 (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 0 binary64) eps))) #s(literal 2 binary64)) (cos.f64 (.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps)))) (patch (.f64 (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 0 binary64) eps))) #s(literal 2 binary64)) (cos.f64 (.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps)))) #<representation binary64>) () ())) ())
#s(alt (* eps (+ (cos x) (* -1/2 (* eps (sin x))))) (taylor 0 eps) (#s(alt (.f64 (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 0 binary64) eps))) #s(literal 2 binary64)) (cos.f64 (.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps)))) (patch (.f64 (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 0 binary64) eps))) #s(literal 2 binary64)) (cos.f64 (.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps)))) #<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 #s(literal 1/2 binary64) (+.f64 #s(literal 0 binary64) eps))) #s(literal 2 binary64)) (cos.f64 (.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps)))) (patch (.f64 (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 0 binary64) eps))) #s(literal 2 binary64)) (cos.f64 (.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps)))) #<representation binary64>) () ())) ())
#s(alt (* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* eps (+ (* 1/24 (* eps (sin x))) (* 2 (+ (* -1/16 (cos x)) (* -1/48 (cos x)))))))))) (taylor 0 eps) (#s(alt (.f64 (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 0 binary64) eps))) #s(literal 2 binary64)) (cos.f64 (.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps)))) (patch (.f64 (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 0 binary64) eps))) #s(literal 2 binary64)) (cos.f64 (.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps)))) #<representation binary64>) () ())) ())
#s(alt eps (taylor 0 eps) (#s(alt (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 0 binary64) eps))) #s(literal 2 binary64)) (patch (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 0 binary64) eps))) #s(literal 2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* eps (+ 1 (* -1/24 (pow eps 2)))) (taylor 0 eps) (#s(alt (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 0 binary64) eps))) #s(literal 2 binary64)) (patch (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 0 binary64) eps))) #s(literal 2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* eps (+ 1 (* (pow eps 2) (- (* 1/1920 (pow eps 2)) 1/24)))) (taylor 0 eps) (#s(alt (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 0 binary64) eps))) #s(literal 2 binary64)) (patch (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 0 binary64) eps))) #s(literal 2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* eps (+ 1 (* (pow eps 2) (- (* (pow eps 2) (+ 1/1920 (* -1/322560 (pow eps 2)))) 1/24)))) (taylor 0 eps) (#s(alt (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 0 binary64) eps))) #s(literal 2 binary64)) (patch (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 0 binary64) eps))) #s(literal 2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* eps (cos x)) (taylor 0 eps) (#s(alt #s(approx (- (sin (+ x eps)) (sin x)) (sin.f64 eps)) (patch #s(approx (- (sin (+ x eps)) (sin x)) (sin.f64 eps)) #<representation binary64>) () ())) ())
#s(alt (* eps (+ (cos x) (* -1/2 (* eps (sin x))))) (taylor 0 eps) (#s(alt #s(approx (- (sin (+ x eps)) (sin x)) (sin.f64 eps)) (patch #s(approx (- (sin (+ x eps)) (sin x)) (sin.f64 eps)) #<representation binary64>) () ())) ())
#s(alt (* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x))))))) (taylor 0 eps) (#s(alt #s(approx (- (sin (+ x eps)) (sin x)) (sin.f64 eps)) (patch #s(approx (- (sin (+ x eps)) (sin x)) (sin.f64 eps)) #<representation binary64>) () ())) ())
#s(alt (* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* eps (+ (* -1/6 (cos x)) (* 1/24 (* eps (sin x))))))))) (taylor 0 eps) (#s(alt #s(approx (- (sin (+ x eps)) (sin x)) (sin.f64 eps)) (patch #s(approx (- (sin (+ x eps)) (sin x)) (sin.f64 eps)) #<representation binary64>) () ())) ())
#s(alt eps (taylor 0 eps) (#s(alt (sin.f64 eps) (patch (sin.f64 eps) #<representation binary64>) () ())) ())
#s(alt (* eps (+ 1 (* -1/6 (pow eps 2)))) (taylor 0 eps) (#s(alt (sin.f64 eps) (patch (sin.f64 eps) #<representation binary64>) () ())) ())
#s(alt (* eps (+ 1 (* (pow eps 2) (- (* 1/120 (pow eps 2)) 1/6)))) (taylor 0 eps) (#s(alt (sin.f64 eps) (patch (sin.f64 eps) #<representation binary64>) () ())) ())
#s(alt (* eps (+ 1 (* (pow eps 2) (- (* (pow eps 2) (+ 1/120 (* -1/5040 (pow eps 2)))) 1/6)))) (taylor 0 eps) (#s(alt (sin.f64 eps) (patch (sin.f64 eps) #<representation binary64>) () ())) ())
#s(alt (* eps (cos x)) (taylor 0 eps) (#s(alt (-.f64 (sin.f64 (+.f64 x eps)) #s(approx (sin x) (.f64 (fma.f64 (.f64 x x) #s(literal -1/6 binary64) #s(literal 1 binary64)) x))) (patch (-.f64 (sin.f64 (+.f64 x eps)) #s(approx (sin x) (.f64 (fma.f64 (.f64 x x) #s(literal -1/6 binary64) #s(literal 1 binary64)) x))) #<representation binary64>) () ())) ())
#s(alt (* eps (+ (cos x) (* -1/2 (* eps (sin x))))) (taylor 0 eps) (#s(alt (-.f64 (sin.f64 (+.f64 x eps)) #s(approx (sin x) (.f64 (fma.f64 (.f64 x x) #s(literal -1/6 binary64) #s(literal 1 binary64)) x))) (patch (-.f64 (sin.f64 (+.f64 x eps)) #s(approx (sin x) (.f64 (fma.f64 (.f64 x x) #s(literal -1/6 binary64) #s(literal 1 binary64)) 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)) #s(approx (sin x) (.f64 (fma.f64 (.f64 x x) #s(literal -1/6 binary64) #s(literal 1 binary64)) x))) (patch (-.f64 (sin.f64 (+.f64 x eps)) #s(approx (sin x) (.f64 (fma.f64 (.f64 x x) #s(literal -1/6 binary64) #s(literal 1 binary64)) 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)) #s(approx (sin x) (.f64 (fma.f64 (.f64 x x) #s(literal -1/6 binary64) #s(literal 1 binary64)) x))) (patch (-.f64 (sin.f64 (+.f64 x eps)) #s(approx (sin x) (.f64 (fma.f64 (.f64 x x) #s(literal -1/6 binary64) #s(literal 1 binary64)) x))) #<representation binary64>) () ())) ())
#s(alt (sin x) (taylor 0 eps) (#s(alt (sin.f64 (+.f64 x eps)) (patch (sin.f64 (+.f64 x eps)) #<representation binary64>) () ())) ())
#s(alt (+ (sin x) (* eps (cos x))) (taylor 0 eps) (#s(alt (sin.f64 (+.f64 x eps)) (patch (sin.f64 (+.f64 x eps)) #<representation binary64>) () ())) ())
#s(alt (+ (sin x) (* eps (+ (cos x) (* -1/2 (* eps (sin x)))))) (taylor 0 eps) (#s(alt (sin.f64 (+.f64 x eps)) (patch (sin.f64 (+.f64 x eps)) #<representation binary64>) () ())) ())
#s(alt (+ (sin x) (* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x)))))))) (taylor 0 eps) (#s(alt (sin.f64 (+.f64 x eps)) (patch (sin.f64 (+.f64 x eps)) #<representation binary64>) () ())) ())
#s(alt x (taylor 0 eps) (#s(alt (+.f64 x eps) (patch (+.f64 x eps) #<representation binary64>) () ())) ())
#s(alt (+ eps x) (taylor 0 eps) (#s(alt (+.f64 x eps) (patch (+.f64 x eps) #<representation binary64>) () ())) ())
#s(alt (+ eps x) (taylor 0 eps) (#s(alt (+.f64 x eps) (patch (+.f64 x eps) #<representation binary64>) () ())) ())
#s(alt (+ eps x) (taylor 0 eps) (#s(alt (+.f64 x eps) (patch (+.f64 x eps) #<representation binary64>) () ())) ())
#s(alt (* eps (cos x)) (taylor 0 eps) (#s(alt (-.f64 #s(approx (sin (+ x eps)) (sin.f64 eps)) (sin.f64 x)) (patch (-.f64 #s(approx (sin (+ x eps)) (sin.f64 eps)) (sin.f64 x)) #<representation binary64>) () ())) ())
#s(alt (* eps (+ (cos x) (* -1/2 (* eps (sin x))))) (taylor 0 eps) (#s(alt (-.f64 #s(approx (sin (+ x eps)) (sin.f64 eps)) (sin.f64 x)) (patch (-.f64 #s(approx (sin (+ x eps)) (sin.f64 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 #s(approx (sin (+ x eps)) (sin.f64 eps)) (sin.f64 x)) (patch (-.f64 #s(approx (sin (+ x eps)) (sin.f64 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 #s(approx (sin (+ x eps)) (sin.f64 eps)) (sin.f64 x)) (patch (-.f64 #s(approx (sin (+ x eps)) (sin.f64 eps)) (sin.f64 x)) #<representation binary64>) () ())) ())
#s(alt (sin x) (taylor 0 eps) (#s(alt #s(approx (sin (+ x eps)) (sin.f64 eps)) (patch #s(approx (sin (+ x eps)) (sin.f64 eps)) #<representation binary64>) () ())) ())
#s(alt (+ (sin x) (* eps (cos x))) (taylor 0 eps) (#s(alt #s(approx (sin (+ x eps)) (sin.f64 eps)) (patch #s(approx (sin (+ x eps)) (sin.f64 eps)) #<representation binary64>) () ())) ())
#s(alt (+ (sin x) (* eps (+ (cos x) (* -1/2 (* eps (sin x)))))) (taylor 0 eps) (#s(alt #s(approx (sin (+ x eps)) (sin.f64 eps)) (patch #s(approx (sin (+ x eps)) (sin.f64 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 #s(approx (sin (+ x eps)) (sin.f64 eps)) (patch #s(approx (sin (+ x eps)) (sin.f64 eps)) #<representation binary64>) () ())) ())
#s(alt (* eps (cos x)) (taylor 0 eps) (#s(alt #s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 (fma.f64 (.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64)) (cos.f64 x) (.f64 (.f64 (sin.f64 x) #s(literal -1/2 binary64)) eps)) eps)) (patch #s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 (fma.f64 (.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64)) (cos.f64 x) (.f64 (.f64 (sin.f64 x) #s(literal -1/2 binary64)) eps)) eps)) #<representation binary64>) () ())) ())
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#s(alt (cos (* 1/2 (- eps (* -2 x)))) (taylor -inf x) (#s(alt (cos.f64 (.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps))) (patch (cos.f64 (.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps))) #<representation binary64>) () ())) ())
#s(alt (* -1/6 (pow x 3)) (taylor -inf x) (#s(alt (.f64 (fma.f64 (.f64 x x) #s(literal -1/6 binary64) #s(literal 1 binary64)) x) (patch (.f64 (fma.f64 (.f64 x x) #s(literal -1/6 binary64) #s(literal 1 binary64)) x) #<representation binary64>) () ())) ())
#s(alt (* -1 (* (pow x 3) (- 1/6 (/ 1 (pow x 2))))) (taylor -inf x) (#s(alt (.f64 (fma.f64 (.f64 x x) #s(literal -1/6 binary64) #s(literal 1 binary64)) x) (patch (.f64 (fma.f64 (.f64 x x) #s(literal -1/6 binary64) #s(literal 1 binary64)) x) #<representation binary64>) () ())) ())
#s(alt (* -1 (* (pow x 3) (- 1/6 (/ 1 (pow x 2))))) (taylor -inf x) (#s(alt (.f64 (fma.f64 (.f64 x x) #s(literal -1/6 binary64) #s(literal 1 binary64)) x) (patch (.f64 (fma.f64 (.f64 x x) #s(literal -1/6 binary64) #s(literal 1 binary64)) x) #<representation binary64>) () ())) ())
#s(alt (* -1 (* (pow x 3) (- 1/6 (/ 1 (pow x 2))))) (taylor -inf x) (#s(alt (.f64 (fma.f64 (.f64 x x) #s(literal -1/6 binary64) #s(literal 1 binary64)) x) (patch (.f64 (fma.f64 (.f64 x x) #s(literal -1/6 binary64) #s(literal 1 binary64)) x) #<representation binary64>) () ())) ())
#s(alt (* -1/2 (* eps (sin x))) (taylor -inf x) (#s(alt (.f64 (.f64 (sin.f64 x) #s(literal -1/2 binary64)) eps) (patch (.f64 (.f64 (sin.f64 x) #s(literal -1/2 binary64)) eps) #<representation binary64>) () ())) ())
#s(alt (* -1/2 (* eps (sin x))) (taylor -inf x) (#s(alt (.f64 (.f64 (sin.f64 x) #s(literal -1/2 binary64)) eps) (patch (.f64 (.f64 (sin.f64 x) #s(literal -1/2 binary64)) eps) #<representation binary64>) () ())) ())
#s(alt (* -1/2 (* eps (sin x))) (taylor -inf x) (#s(alt (.f64 (.f64 (sin.f64 x) #s(literal -1/2 binary64)) eps) (patch (.f64 (.f64 (sin.f64 x) #s(literal -1/2 binary64)) eps) #<representation binary64>) () ())) ())
#s(alt (* -1/2 (* eps (sin x))) (taylor -inf x) (#s(alt (.f64 (.f64 (sin.f64 x) #s(literal -1/2 binary64)) eps) (patch (.f64 (.f64 (sin.f64 x) #s(literal -1/2 binary64)) eps) #<representation binary64>) () ())) ())

Calls

6 calls:

Time	Variable		Point	Expression
8.0ms	eps	@	inf	((* 1/2 (+ (* 2 x) eps)) (+ 0 eps) (* (* (sin (* 1/2 (+ 0 eps))) 2) (cos (* 1/2 (+ (* 2 x) eps)))) (* (sin (* 1/2 (+ 0 eps))) 2) (- (sin (+ x eps)) (sin x)) (sin eps) (- (sin (+ x eps)) (sin x)) (sin (+ x eps)) (+ x eps) (sin x) (- (sin (+ x eps)) (sin x)) (sin (+ x eps)) (sin x) (- (sin (+ x eps)) (sin x)) (* (+ (* (+ (* (* eps eps) -1/6) 1) (cos x)) (* (* (sin x) -1/2) eps)) eps) (+ (* (+ (* (* eps eps) -1/6) 1) (cos x)) (* (* (sin x) -1/2) eps)) (+ (* (* eps eps) -1/6) 1) (cos (* 1/2 (+ (* 2 x) eps))) (sin (* 1/2 (+ 0 eps))) (* 1/2 (+ 0 eps)) (* (+ (* (* x x) -1/6) 1) x) (* (* (sin x) -1/2) eps))
6.0ms	x	@	inf	((* 1/2 (+ (* 2 x) eps)) (+ 0 eps) (* (* (sin (* 1/2 (+ 0 eps))) 2) (cos (* 1/2 (+ (* 2 x) eps)))) (* (sin (* 1/2 (+ 0 eps))) 2) (- (sin (+ x eps)) (sin x)) (sin eps) (- (sin (+ x eps)) (sin x)) (sin (+ x eps)) (+ x eps) (sin x) (- (sin (+ x eps)) (sin x)) (sin (+ x eps)) (sin x) (- (sin (+ x eps)) (sin x)) (* (+ (* (+ (* (* eps eps) -1/6) 1) (cos x)) (* (* (sin x) -1/2) eps)) eps) (+ (* (+ (* (* eps eps) -1/6) 1) (cos x)) (* (* (sin x) -1/2) eps)) (+ (* (* eps eps) -1/6) 1) (cos (* 1/2 (+ (* 2 x) eps))) (sin (* 1/2 (+ 0 eps))) (* 1/2 (+ 0 eps)) (* (+ (* (* x x) -1/6) 1) x) (* (* (sin x) -1/2) eps))
4.0ms	eps	@	0	((* 1/2 (+ (* 2 x) eps)) (+ 0 eps) (* (* (sin (* 1/2 (+ 0 eps))) 2) (cos (* 1/2 (+ (* 2 x) eps)))) (* (sin (* 1/2 (+ 0 eps))) 2) (- (sin (+ x eps)) (sin x)) (sin eps) (- (sin (+ x eps)) (sin x)) (sin (+ x eps)) (+ x eps) (sin x) (- (sin (+ x eps)) (sin x)) (sin (+ x eps)) (sin x) (- (sin (+ x eps)) (sin x)) (* (+ (* (+ (* (* eps eps) -1/6) 1) (cos x)) (* (* (sin x) -1/2) eps)) eps) (+ (* (+ (* (* eps eps) -1/6) 1) (cos x)) (* (* (sin x) -1/2) eps)) (+ (* (* eps eps) -1/6) 1) (cos (* 1/2 (+ (* 2 x) eps))) (sin (* 1/2 (+ 0 eps))) (* 1/2 (+ 0 eps)) (* (+ (* (* x x) -1/6) 1) x) (* (* (sin x) -1/2) eps))
3.0ms	x	@	-inf	((* 1/2 (+ (* 2 x) eps)) (+ 0 eps) (* (* (sin (* 1/2 (+ 0 eps))) 2) (cos (* 1/2 (+ (* 2 x) eps)))) (* (sin (* 1/2 (+ 0 eps))) 2) (- (sin (+ x eps)) (sin x)) (sin eps) (- (sin (+ x eps)) (sin x)) (sin (+ x eps)) (+ x eps) (sin x) (- (sin (+ x eps)) (sin x)) (sin (+ x eps)) (sin x) (- (sin (+ x eps)) (sin x)) (* (+ (* (+ (* (* eps eps) -1/6) 1) (cos x)) (* (* (sin x) -1/2) eps)) eps) (+ (* (+ (* (* eps eps) -1/6) 1) (cos x)) (* (* (sin x) -1/2) eps)) (+ (* (* eps eps) -1/6) 1) (cos (* 1/2 (+ (* 2 x) eps))) (sin (* 1/2 (+ 0 eps))) (* 1/2 (+ 0 eps)) (* (+ (* (* x x) -1/6) 1) x) (* (* (sin x) -1/2) eps))
3.0ms	eps	@	-inf	((* 1/2 (+ (* 2 x) eps)) (+ 0 eps) (* (* (sin (* 1/2 (+ 0 eps))) 2) (cos (* 1/2 (+ (* 2 x) eps)))) (* (sin (* 1/2 (+ 0 eps))) 2) (- (sin (+ x eps)) (sin x)) (sin eps) (- (sin (+ x eps)) (sin x)) (sin (+ x eps)) (+ x eps) (sin x) (- (sin (+ x eps)) (sin x)) (sin (+ x eps)) (sin x) (- (sin (+ x eps)) (sin x)) (* (+ (* (+ (* (* eps eps) -1/6) 1) (cos x)) (* (* (sin x) -1/2) eps)) eps) (+ (* (+ (* (* eps eps) -1/6) 1) (cos x)) (* (* (sin x) -1/2) eps)) (+ (* (* eps eps) -1/6) 1) (cos (* 1/2 (+ (* 2 x) eps))) (sin (* 1/2 (+ 0 eps))) (* 1/2 (+ 0 eps)) (* (+ (* (* x x) -1/6) 1) x) (* (* (sin x) -1/2) eps))

simplify160.0ms (1.4%)

Memory

-4.0MiB live, 149.1MiB allocated

Algorithm

1×	egg-herbie

Rules

14 312×	`lower-fma.f64`
14 312×	`lower-fma.f32`
5 922×	`lower-*.f64`
5 922×	`lower-*.f32`
4 108×	`lower-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	365	3712
1	1136	3555
2	3251	3519
0	8165	3234

Stop Event

1×	iter limit
1×	node limit

Counts

420 → 394

Calls

Call 1

Inputs
x
(+ x (* 1/2 eps))
(+ x (* 1/2 eps))
(+ x (* 1/2 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))))))))))
eps
(* eps (+ 1 (* -1/24 (pow eps 2))))
(* eps (+ 1 (* (pow eps 2) (- (* 1/1920 (pow eps 2)) 1/24))))
(* eps (+ 1 (* (pow eps 2) (- (* (pow eps 2) (+ 1/1920 (* -1/322560 (pow eps 2)))) 1/24))))
(* eps (cos x))
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x)))))))
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* eps (+ (* -1/6 (cos x)) (* 1/24 (* eps (sin x)))))))))
eps
(* eps (+ 1 (* -1/6 (pow eps 2))))
(* eps (+ 1 (* (pow eps 2) (- (* 1/120 (pow eps 2)) 1/6))))
(* eps (+ 1 (* (pow eps 2) (- (* (pow eps 2) (+ 1/120 (* -1/5040 (pow eps 2)))) 1/6))))
(* eps (cos x))
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x)))))))
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* eps (+ (* -1/6 (cos x)) (* 1/24 (* eps (sin x)))))))))
(sin x)
(+ (sin x) (* eps (cos x)))
(+ (sin x) (* eps (+ (cos x) (* -1/2 (* eps (sin x))))))
(+ (sin x) (* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x))))))))
x
(+ eps x)
(+ eps x)
(+ eps x)
(* eps (cos x))
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x)))))))
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* eps (+ (* -1/6 (cos x)) (* 1/24 (* eps (sin x)))))))))
(sin x)
(+ (sin x) (* eps (cos x)))
(+ (sin x) (* eps (+ (cos x) (* -1/2 (* eps (sin x))))))
(+ (sin x) (* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x))))))))
(* eps (cos x))
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x)))))))
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* eps (+ (* -1/6 (cos x)) (* 1/24 (* eps (sin x)))))))))
(* eps (cos x))
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x)))))))
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x)))))))
(cos x)
(+ (cos x) (* -1/2 (* eps (sin x))))
(+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x))))))
(+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x))))))
1
(+ 1 (* -1/6 (pow eps 2)))
(+ 1 (* -1/6 (pow eps 2)))
(+ 1 (* -1/6 (pow eps 2)))
(cos x)
(+ (cos x) (* -1/2 (* eps (sin x))))
(+ (cos x) (* eps (- (* -1/8 (* eps (cos x))) (* 1/2 (sin x)))))
(+ (cos x) (* eps (- (* eps (+ (* -1/8 (cos x)) (* 1/48 (* eps (sin x))))) (* 1/2 (sin x)))))
(* 1/2 eps)
(* eps (+ 1/2 (* -1/48 (pow eps 2))))
(* eps (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48))))
(* eps (+ 1/2 (* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48))))
(* 1/2 eps)
(* 1/2 eps)
(* 1/2 eps)
(* 1/2 eps)
(* -1/2 (* eps (sin x)))
(* -1/2 (* eps (sin x)))
(* -1/2 (* eps (sin x)))
(* -1/2 (* eps (sin x)))
(* 1/2 eps)
(* eps (+ 1/2 (/ x eps)))
(* eps (+ 1/2 (/ x eps)))
(* eps (+ 1/2 (/ x eps)))
eps
eps
eps
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 (sin (* 1/2 eps)))
(* 2 (sin (* 1/2 eps)))
(* 2 (sin (* 1/2 eps)))
(* 2 (sin (* 1/2 eps)))
(- (sin (+ eps x)) (sin x))
(- (sin (+ eps x)) (sin x))
(- (sin (+ eps x)) (sin x))
(- (sin (+ eps x)) (sin x))
(sin eps)
(sin eps)
(sin eps)
(sin eps)
(- (sin (+ eps x)) (sin x))
(- (sin (+ eps x)) (sin x))
(- (sin (+ eps x)) (sin x))
(- (sin (+ eps x)) (sin x))
(sin (+ eps x))
(sin (+ eps x))
(sin (+ eps x))
(sin (+ eps x))
eps
(* eps (+ 1 (/ x eps)))
(* eps (+ 1 (/ x eps)))
(* eps (+ 1 (/ x eps)))
(- (sin (+ eps x)) (sin x))
(- (sin (+ eps x)) (sin x))
(- (sin (+ eps x)) (sin x))
(- (sin (+ eps x)) (sin x))
(sin (+ eps x))
(sin (+ eps x))
(sin (+ eps x))
(sin (+ eps x))
(- (sin (+ eps x)) (sin x))
(- (sin (+ eps x)) (sin x))
(- (sin (+ eps x)) (sin x))
(- (sin (+ eps x)) (sin x))
(* -1/6 (* (pow eps 3) (cos x)))
(* (pow eps 3) (+ (* -1/2 (/ (sin x) eps)) (* -1/6 (cos x))))
(* (pow eps 3) (+ (* -1/2 (/ (sin x) eps)) (+ (* -1/6 (cos x)) (/ (cos x) (pow eps 2)))))
(* (pow eps 3) (+ (* -1/2 (/ (sin x) eps)) (+ (* -1/6 (cos x)) (/ (cos x) (pow eps 2)))))
(* -1/6 (* (pow eps 2) (cos x)))
(* (pow eps 2) (+ (* -1/2 (/ (sin x) eps)) (* -1/6 (cos x))))
(* (pow eps 2) (+ (* -1/2 (/ (sin x) eps)) (+ (* -1/6 (cos x)) (/ (cos x) (pow eps 2)))))
(* (pow eps 2) (+ (* -1/2 (/ (sin x) eps)) (+ (* -1/6 (cos x)) (/ (cos x) (pow eps 2)))))
(* -1/6 (pow eps 2))
(* (pow eps 2) (- (/ 1 (pow eps 2)) 1/6))
(* (pow eps 2) (- (/ 1 (pow eps 2)) 1/6))
(* (pow eps 2) (- (/ 1 (pow eps 2)) 1/6))
(cos (* 1/2 (+ eps (* 2 x))))
(cos (* 1/2 (+ eps (* 2 x))))
(cos (* 1/2 (+ eps (* 2 x))))
(cos (* 1/2 (+ eps (* 2 x))))
(sin (* 1/2 eps))
(sin (* 1/2 eps))
(sin (* 1/2 eps))
(sin (* 1/2 eps))
(* 1/2 eps)
(* 1/2 eps)
(* 1/2 eps)
(* 1/2 eps)
(* -1/2 (* eps (sin x)))
(* -1/2 (* eps (sin x)))
(* -1/2 (* eps (sin x)))
(* -1/2 (* eps (sin x)))
(* 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
(* 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 (sin (* 1/2 eps)))
(* 2 (sin (* 1/2 eps)))
(* 2 (sin (* 1/2 eps)))
(* 2 (sin (* 1/2 eps)))
(- (sin (- x (* -1 eps))) (sin x))
(- (sin (- x (* -1 eps))) (sin x))
(- (sin (- x (* -1 eps))) (sin x))
(- (sin (- x (* -1 eps))) (sin x))
(sin eps)
(sin eps)
(sin eps)
(sin eps)
(- (sin (- x (* -1 eps))) (sin x))
(- (sin (- x (* -1 eps))) (sin x))
(- (sin (- x (* -1 eps))) (sin x))
(- (sin (- x (* -1 eps))) (sin x))
(sin (- x (* -1 eps)))
(sin (- x (* -1 eps)))
(sin (- x (* -1 eps)))
(sin (- x (* -1 eps)))
eps
(* -1 (* eps (- (* -1 (/ x eps)) 1)))
(* -1 (* eps (- (* -1 (/ x eps)) 1)))
(* -1 (* eps (- (* -1 (/ x eps)) 1)))
(- (sin (- x (* -1 eps))) (sin x))
(- (sin (- x (* -1 eps))) (sin x))
(- (sin (- x (* -1 eps))) (sin x))
(- (sin (- x (* -1 eps))) (sin x))
(sin (- x (* -1 eps)))
(sin (- x (* -1 eps)))
(sin (- x (* -1 eps)))
(sin (- x (* -1 eps)))
(- (sin (- x (* -1 eps))) (sin x))
(- (sin (- x (* -1 eps))) (sin x))
(- (sin (- x (* -1 eps))) (sin x))
(- (sin (- x (* -1 eps))) (sin x))
(* -1/6 (* (pow eps 3) (cos x)))
(* -1 (* (pow eps 3) (+ (* 1/6 (cos x)) (* 1/2 (/ (sin x) eps)))))
(* -1 (* (pow eps 3) (+ (* -1 (/ (+ (* -1/2 (sin x)) (/ (cos x) eps)) eps)) (* 1/6 (cos x)))))
(* -1 (* (pow eps 3) (+ (* -1 (/ (+ (* -1/2 (sin x)) (/ (cos x) eps)) eps)) (* 1/6 (cos x)))))
(* -1/6 (* (pow eps 2) (cos x)))
(* (pow eps 2) (+ (* -1/2 (/ (sin x) eps)) (* -1/6 (cos x))))
(* (pow eps 2) (+ (* -1 (/ (+ (* -1 (/ (cos x) eps)) (* 1/2 (sin x))) eps)) (* -1/6 (cos x))))
(* (pow eps 2) (+ (* -1 (/ (+ (* -1 (/ (cos x) eps)) (* 1/2 (sin x))) eps)) (* -1/6 (cos x))))
(* -1/6 (pow eps 2))
(* (pow eps 2) (- (/ 1 (pow eps 2)) 1/6))
(* (pow eps 2) (- (/ 1 (pow eps 2)) 1/6))
(* (pow eps 2) (- (/ 1 (pow eps 2)) 1/6))
(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))))
(sin (* 1/2 eps))
(sin (* 1/2 eps))
(sin (* 1/2 eps))
(sin (* 1/2 eps))
(* 1/2 eps)
(* 1/2 eps)
(* 1/2 eps)
(* 1/2 eps)
(* -1/2 (* eps (sin x)))
(* -1/2 (* eps (sin x)))
(* -1/2 (* eps (sin x)))
(* -1/2 (* eps (sin x)))
(* 1/2 eps)
(+ x (* 1/2 eps))
(+ x (* 1/2 eps))
(+ x (* 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))))))))
(sin eps)
(+ (sin eps) (* x (- (cos eps) 1)))
(+ (sin eps) (* x (- (+ (cos eps) (* -1/2 (* x (sin eps)))) 1)))
(+ (sin eps) (* x (- (+ (cos eps) (* x (+ (* -1/2 (sin eps)) (* x (+ 1/6 (* -1/6 (cos eps))))))) 1)))
(sin eps)
(+ (sin eps) (* x (- (cos eps) 1)))
(+ (sin eps) (* x (- (+ (cos eps) (* -1/2 (* x (sin eps)))) 1)))
(+ (sin eps) (* x (- (+ (cos eps) (* x (+ (* -1/2 (sin eps)) (* x (+ 1/6 (* -1/6 (cos eps))))))) 1)))
(sin eps)
(+ (sin eps) (* x (cos eps)))
(+ (sin eps) (* x (+ (cos eps) (* -1/2 (* x (sin eps))))))
(+ (sin eps) (* x (+ (cos eps) (* x (+ (* -1/2 (sin eps)) (* -1/6 (* x (cos eps))))))))
eps
(+ eps x)
(+ eps x)
(+ eps x)
x
(* x (+ 1 (* -1/6 (pow x 2))))
(* x (+ 1 (* (pow x 2) (- (* 1/120 (pow x 2)) 1/6))))
(* x (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/120 (* -1/5040 (pow x 2)))) 1/6))))
(sin eps)
(+ (sin eps) (* x (- (cos eps) 1)))
(+ (sin eps) (* x (- (+ (cos eps) (* -1/2 (* x (sin eps)))) 1)))
(+ (sin eps) (* x (- (+ (cos eps) (* x (+ (* -1/2 (sin eps)) (* x (+ 1/6 (* -1/6 (cos eps))))))) 1)))
(sin eps)
(+ (sin eps) (* x (cos eps)))
(+ (sin eps) (* x (+ (cos eps) (* -1/2 (* x (sin eps))))))
(+ (sin eps) (* x (+ (cos eps) (* x (+ (* -1/2 (sin eps)) (* -1/6 (* x (cos eps))))))))
x
(* x (+ 1 (* -1/6 (pow x 2))))
(* x (+ 1 (* (pow x 2) (- (* 1/120 (pow x 2)) 1/6))))
(* x (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/120 (* -1/5040 (pow x 2)))) 1/6))))
(sin eps)
(+ (sin eps) (* x (- (cos eps) 1)))
(+ (sin eps) (* x (- (+ (cos eps) (* -1/2 (* x (sin eps)))) 1)))
(+ (sin eps) (* x (- (+ (cos eps) (* x (+ (* -1/2 (sin eps)) (* x (+ 1/6 (* -1/6 (cos eps))))))) 1)))
(* eps (+ 1 (* -1/6 (pow eps 2))))
(+ (* -1/2 (* (pow eps 2) x)) (* eps (+ 1 (* -1/6 (pow eps 2)))))
(+ (* eps (+ 1 (* -1/6 (pow eps 2)))) (* x (+ (* -1/2 (* eps (* x (+ 1 (* -1/6 (pow eps 2)))))) (* -1/2 (pow eps 2)))))
(+ (* eps (+ 1 (* -1/6 (pow eps 2)))) (* x (+ (* -1/2 (pow eps 2)) (* x (+ (* -1/2 (* eps (+ 1 (* -1/6 (pow eps 2))))) (* 1/12 (* (pow eps 2) x)))))))
(+ 1 (* -1/6 (pow eps 2)))
(+ 1 (+ (* -1/2 (* eps x)) (* -1/6 (pow eps 2))))
(+ 1 (+ (* -1/6 (pow eps 2)) (* x (+ (* -1/2 eps) (* -1/2 (* x (+ 1 (* -1/6 (pow eps 2)))))))))
(+ 1 (+ (* -1/6 (pow eps 2)) (* x (+ (* -1/2 eps) (* x (+ (* -1/2 (+ 1 (* -1/6 (pow eps 2)))) (* 1/12 (* eps x))))))))
(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)))))
x
(* x (+ 1 (* -1/6 (pow x 2))))
(* x (+ 1 (* -1/6 (pow x 2))))
(* x (+ 1 (* -1/6 (pow x 2))))
(* -1/2 (* eps x))
(* x (+ (* -1/2 eps) (* 1/12 (* eps (pow x 2)))))
(* x (+ (* -1/2 eps) (* (pow x 2) (+ (* -1/240 (* eps (pow x 2))) (* 1/12 eps)))))
(* x (+ (* -1/2 eps) (* (pow x 2) (+ (* 1/12 eps) (* (pow x 2) (+ (* -1/240 eps) (* 1/10080 (* eps (pow x 2)))))))))
x
(* x (+ 1 (* 1/2 (/ eps x))))
(* x (+ 1 (* 1/2 (/ eps x))))
(* x (+ 1 (* 1/2 (/ eps 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))))
(- (sin (+ eps x)) (sin x))
(- (sin (+ eps x)) (sin x))
(- (sin (+ eps x)) (sin x))
(- (sin (+ eps x)) (sin x))
(- (sin (+ eps x)) (sin x))
(- (sin (+ eps x)) (sin x))
(- (sin (+ eps x)) (sin x))
(- (sin (+ eps x)) (sin x))
(sin (+ eps x))
(sin (+ eps x))
(sin (+ eps x))
(sin (+ eps x))
x
(* x (+ 1 (/ eps x)))
(* x (+ 1 (/ eps x)))
(* x (+ 1 (/ eps x)))
(sin x)
(sin x)
(sin x)
(sin x)
(- (sin (+ eps x)) (sin x))
(- (sin (+ eps x)) (sin x))
(- (sin (+ eps x)) (sin x))
(- (sin (+ eps x)) (sin x))
(sin (+ eps x))
(sin (+ eps x))
(sin (+ eps x))
(sin (+ eps x))
(sin x)
(sin x)
(sin x)
(sin x)
(- (sin (+ eps x)) (sin x))
(- (sin (+ eps x)) (sin x))
(- (sin (+ eps x)) (sin x))
(- (sin (+ eps x)) (sin x))
(* eps (+ (* -1/2 (* eps (sin x))) (* (cos x) (+ 1 (* -1/6 (pow eps 2))))))
(* eps (+ (* -1/2 (* eps (sin x))) (* (cos x) (+ 1 (* -1/6 (pow eps 2))))))
(* eps (+ (* -1/2 (* eps (sin x))) (* (cos x) (+ 1 (* -1/6 (pow eps 2))))))
(* eps (+ (* -1/2 (* eps (sin x))) (* (cos x) (+ 1 (* -1/6 (pow eps 2))))))
(+ (* -1/2 (* eps (sin x))) (* (cos x) (+ 1 (* -1/6 (pow eps 2)))))
(+ (* -1/2 (* eps (sin x))) (* (cos x) (+ 1 (* -1/6 (pow eps 2)))))
(+ (* -1/2 (* eps (sin x))) (* (cos x) (+ 1 (* -1/6 (pow eps 2)))))
(+ (* -1/2 (* eps (sin x))) (* (cos x) (+ 1 (* -1/6 (pow eps 2)))))
(cos (* 1/2 (+ eps (* 2 x))))
(cos (* 1/2 (+ eps (* 2 x))))
(cos (* 1/2 (+ eps (* 2 x))))
(cos (* 1/2 (+ eps (* 2 x))))
(* -1/6 (pow x 3))
(* (pow x 3) (- (/ 1 (pow x 2)) 1/6))
(* (pow x 3) (- (/ 1 (pow x 2)) 1/6))
(* (pow x 3) (- (/ 1 (pow x 2)) 1/6))
(* -1/2 (* eps (sin x)))
(* -1/2 (* eps (sin x)))
(* -1/2 (* eps (sin x)))
(* -1/2 (* eps (sin x)))
x
(* -1 (* x (- (* -1/2 (/ eps x)) 1)))
(* -1 (* x (- (* -1/2 (/ eps x)) 1)))
(* -1 (* x (- (* -1/2 (/ eps x)) 1)))
(* 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))))
(- (sin (- eps (* -1 x))) (sin x))
(- (sin (- eps (* -1 x))) (sin x))
(- (sin (- eps (* -1 x))) (sin x))
(- (sin (- eps (* -1 x))) (sin x))
(- (sin (- eps (* -1 x))) (sin x))
(- (sin (- eps (* -1 x))) (sin x))
(- (sin (- eps (* -1 x))) (sin x))
(- (sin (- eps (* -1 x))) (sin x))
(sin (- eps (* -1 x)))
(sin (- eps (* -1 x)))
(sin (- eps (* -1 x)))
(sin (- eps (* -1 x)))
x
(* -1 (* x (- (* -1 (/ eps x)) 1)))
(* -1 (* x (- (* -1 (/ eps x)) 1)))
(* -1 (* x (- (* -1 (/ eps x)) 1)))
(sin x)
(sin x)
(sin x)
(sin x)
(- (sin (- eps (* -1 x))) (sin x))
(- (sin (- eps (* -1 x))) (sin x))
(- (sin (- eps (* -1 x))) (sin x))
(- (sin (- eps (* -1 x))) (sin x))
(sin (- eps (* -1 x)))
(sin (- eps (* -1 x)))
(sin (- eps (* -1 x)))
(sin (- eps (* -1 x)))
(sin x)
(sin x)
(sin x)
(sin x)
(- (sin (- eps (* -1 x))) (sin x))
(- (sin (- eps (* -1 x))) (sin x))
(- (sin (- eps (* -1 x))) (sin x))
(- (sin (- eps (* -1 x))) (sin x))
(* eps (+ (* -1/2 (* eps (sin x))) (* (cos x) (+ 1 (* -1/6 (pow eps 2))))))
(* eps (+ (* -1/2 (* eps (sin x))) (* (cos x) (+ 1 (* -1/6 (pow eps 2))))))
(* eps (+ (* -1/2 (* eps (sin x))) (* (cos x) (+ 1 (* -1/6 (pow eps 2))))))
(* eps (+ (* -1/2 (* eps (sin x))) (* (cos x) (+ 1 (* -1/6 (pow eps 2))))))
(+ (* -1/2 (* eps (sin x))) (* (cos x) (+ 1 (* -1/6 (pow eps 2)))))
(+ (* -1/2 (* eps (sin x))) (* (cos x) (+ 1 (* -1/6 (pow eps 2)))))
(+ (* -1/2 (* eps (sin x))) (* (cos x) (+ 1 (* -1/6 (pow eps 2)))))
(+ (* -1/2 (* eps (sin x))) (* (cos x) (+ 1 (* -1/6 (pow eps 2)))))
(cos (* 1/2 (- eps (* -2 x))))
(cos (* 1/2 (- eps (* -2 x))))
(cos (* 1/2 (- eps (* -2 x))))
(cos (* 1/2 (- eps (* -2 x))))
(* -1/6 (pow x 3))
(* -1 (* (pow x 3) (- 1/6 (/ 1 (pow x 2)))))
(* -1 (* (pow x 3) (- 1/6 (/ 1 (pow x 2)))))
(* -1 (* (pow x 3) (- 1/6 (/ 1 (pow x 2)))))
(* -1/2 (* eps (sin x)))
(* -1/2 (* eps (sin x)))
(* -1/2 (* eps (sin x)))
(* -1/2 (* eps (sin x)))

Outputs
x
(+ x (* 1/2 eps))
(fma.f64 eps #s(literal 1/2 binary64) x)
(+ x (* 1/2 eps))
(fma.f64 eps #s(literal 1/2 binary64) x)
(+ x (* 1/2 eps))
(fma.f64 eps #s(literal 1/2 binary64) x)
eps
eps
eps
eps
(* eps (cos x))
(*.f64 (cos.f64 x) eps)
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(.f64 (fma.f64 (.f64 (sin.f64 x) #s(literal -1/2 binary64)) eps (cos.f64 x)) eps)
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* 2 (* eps (+ (* -1/16 (cos x)) (* -1/48 (cos x)))))))))
(.f64 (fma.f64 (fma.f64 #s(literal -1/6 binary64) (.f64 eps eps) #s(literal 1 binary64)) (cos.f64 x) (.f64 (.f64 (sin.f64 x) #s(literal -1/2 binary64)) eps)) eps)
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* eps (+ (* 1/24 (* eps (sin x))) (* 2 (+ (* -1/16 (cos x)) (* -1/48 (cos x))))))))))
(.f64 (fma.f64 (fma.f64 (sin.f64 x) (fma.f64 eps (.f64 #s(literal 1/24 binary64) eps) #s(literal -1/2 binary64)) (.f64 (.f64 #s(literal -1/6 binary64) (cos.f64 x)) eps)) eps (cos.f64 x)) eps)
eps
(* eps (+ 1 (* -1/24 (pow eps 2))))
(.f64 (fma.f64 (.f64 eps eps) #s(literal -1/24 binary64) #s(literal 1 binary64)) eps)
(* eps (+ 1 (* (pow eps 2) (- (* 1/1920 (pow eps 2)) 1/24))))
(.f64 (fma.f64 (fma.f64 #s(literal 1/1920 binary64) (.f64 eps eps) #s(literal -1/24 binary64)) (*.f64 eps eps) #s(literal 1 binary64)) eps)
(* eps (+ 1 (* (pow eps 2) (- (* (pow eps 2) (+ 1/1920 (* -1/322560 (pow eps 2)))) 1/24))))
(.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -1/322560 binary64) (.f64 eps eps) #s(literal 1/1920 binary64)) (.f64 eps eps) #s(literal -1/24 binary64)) (.f64 eps eps) #s(literal 1 binary64)) eps)
(* eps (cos x))
(*.f64 (cos.f64 x) eps)
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(.f64 (fma.f64 (.f64 (sin.f64 x) #s(literal -1/2 binary64)) eps (cos.f64 x)) eps)
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x)))))))
(.f64 (fma.f64 (fma.f64 #s(literal -1/6 binary64) (.f64 eps eps) #s(literal 1 binary64)) (cos.f64 x) (.f64 (.f64 (sin.f64 x) #s(literal -1/2 binary64)) eps)) eps)
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* eps (+ (* -1/6 (cos x)) (* 1/24 (* eps (sin x)))))))))
(.f64 (fma.f64 (fma.f64 (sin.f64 x) (fma.f64 eps (.f64 #s(literal 1/24 binary64) eps) #s(literal -1/2 binary64)) (.f64 (.f64 #s(literal -1/6 binary64) (cos.f64 x)) eps)) eps (cos.f64 x)) eps)
eps
(* eps (+ 1 (* -1/6 (pow eps 2))))
(.f64 (fma.f64 #s(literal -1/6 binary64) (.f64 eps eps) #s(literal 1 binary64)) eps)
(* eps (+ 1 (* (pow eps 2) (- (* 1/120 (pow eps 2)) 1/6))))
(.f64 (fma.f64 (fma.f64 #s(literal 1/120 binary64) (.f64 eps eps) #s(literal -1/6 binary64)) (*.f64 eps eps) #s(literal 1 binary64)) eps)
(* eps (+ 1 (* (pow eps 2) (- (* (pow eps 2) (+ 1/120 (* -1/5040 (pow eps 2)))) 1/6))))
(.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -1/5040 binary64) (.f64 eps eps) #s(literal 1/120 binary64)) (.f64 eps eps) #s(literal -1/6 binary64)) (.f64 eps eps) #s(literal 1 binary64)) eps)
(* eps (cos x))
(*.f64 (cos.f64 x) eps)
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(.f64 (fma.f64 (.f64 (sin.f64 x) #s(literal -1/2 binary64)) eps (cos.f64 x)) eps)
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x)))))))
(.f64 (fma.f64 (fma.f64 #s(literal -1/6 binary64) (.f64 eps eps) #s(literal 1 binary64)) (cos.f64 x) (.f64 (.f64 (sin.f64 x) #s(literal -1/2 binary64)) eps)) eps)
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* eps (+ (* -1/6 (cos x)) (* 1/24 (* eps (sin x)))))))))
(.f64 (fma.f64 (fma.f64 (sin.f64 x) (fma.f64 eps (.f64 #s(literal 1/24 binary64) eps) #s(literal -1/2 binary64)) (.f64 (.f64 #s(literal -1/6 binary64) (cos.f64 x)) eps)) eps (cos.f64 x)) eps)
(sin x)
(sin.f64 x)
(+ (sin x) (* eps (cos x)))
(fma.f64 (cos.f64 x) eps (sin.f64 x))
(+ (sin x) (* eps (+ (cos x) (* -1/2 (* eps (sin x))))))
(fma.f64 (fma.f64 (.f64 #s(literal -1/2 binary64) eps) eps #s(literal 1 binary64)) (sin.f64 x) (.f64 (cos.f64 x) eps))
(+ (sin x) (* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x))))))))
(fma.f64 (fma.f64 (.f64 #s(literal -1/2 binary64) eps) eps #s(literal 1 binary64)) (sin.f64 x) (.f64 (.f64 (fma.f64 #s(literal -1/6 binary64) (.f64 eps eps) #s(literal 1 binary64)) (cos.f64 x)) eps))
x
(+ eps x)
(+.f64 eps x)
(+ eps x)
(+.f64 eps x)
(+ eps x)
(+.f64 eps x)
(* eps (cos x))
(*.f64 (cos.f64 x) eps)
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(.f64 (fma.f64 (.f64 (sin.f64 x) #s(literal -1/2 binary64)) eps (cos.f64 x)) eps)
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x)))))))
(.f64 (fma.f64 (fma.f64 #s(literal -1/6 binary64) (.f64 eps eps) #s(literal 1 binary64)) (cos.f64 x) (.f64 (.f64 (sin.f64 x) #s(literal -1/2 binary64)) eps)) eps)
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* eps (+ (* -1/6 (cos x)) (* 1/24 (* eps (sin x)))))))))
(.f64 (fma.f64 (fma.f64 (sin.f64 x) (fma.f64 eps (.f64 #s(literal 1/24 binary64) eps) #s(literal -1/2 binary64)) (.f64 (.f64 #s(literal -1/6 binary64) (cos.f64 x)) eps)) eps (cos.f64 x)) eps)
(sin x)
(sin.f64 x)
(+ (sin x) (* eps (cos x)))
(fma.f64 (cos.f64 x) eps (sin.f64 x))
(+ (sin x) (* eps (+ (cos x) (* -1/2 (* eps (sin x))))))
(fma.f64 (fma.f64 (.f64 #s(literal -1/2 binary64) eps) eps #s(literal 1 binary64)) (sin.f64 x) (.f64 (cos.f64 x) eps))
(+ (sin x) (* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x))))))))
(fma.f64 (fma.f64 (.f64 #s(literal -1/2 binary64) eps) eps #s(literal 1 binary64)) (sin.f64 x) (.f64 (.f64 (fma.f64 #s(literal -1/6 binary64) (.f64 eps eps) #s(literal 1 binary64)) (cos.f64 x)) eps))
(* eps (cos x))
(*.f64 (cos.f64 x) eps)
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(.f64 (fma.f64 (.f64 (sin.f64 x) #s(literal -1/2 binary64)) eps (cos.f64 x)) eps)
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x)))))))
(.f64 (fma.f64 (fma.f64 #s(literal -1/6 binary64) (.f64 eps eps) #s(literal 1 binary64)) (cos.f64 x) (.f64 (.f64 (sin.f64 x) #s(literal -1/2 binary64)) eps)) eps)
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* eps (+ (* -1/6 (cos x)) (* 1/24 (* eps (sin x)))))))))
(.f64 (fma.f64 (fma.f64 (sin.f64 x) (fma.f64 eps (.f64 #s(literal 1/24 binary64) eps) #s(literal -1/2 binary64)) (.f64 (.f64 #s(literal -1/6 binary64) (cos.f64 x)) eps)) eps (cos.f64 x)) eps)
(* eps (cos x))
(*.f64 (cos.f64 x) eps)
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(.f64 (fma.f64 (.f64 (sin.f64 x) #s(literal -1/2 binary64)) eps (cos.f64 x)) eps)
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x)))))))
(.f64 (fma.f64 (fma.f64 #s(literal -1/6 binary64) (.f64 eps eps) #s(literal 1 binary64)) (cos.f64 x) (.f64 (.f64 (sin.f64 x) #s(literal -1/2 binary64)) eps)) eps)
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x)))))))
(.f64 (fma.f64 (fma.f64 #s(literal -1/6 binary64) (.f64 eps eps) #s(literal 1 binary64)) (cos.f64 x) (.f64 (.f64 (sin.f64 x) #s(literal -1/2 binary64)) eps)) eps)
(cos x)
(cos.f64 x)
(+ (cos x) (* -1/2 (* eps (sin x))))
(fma.f64 (*.f64 (sin.f64 x) #s(literal -1/2 binary64)) eps (cos.f64 x))
(+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x))))))
(fma.f64 (fma.f64 #s(literal -1/6 binary64) (.f64 eps eps) #s(literal 1 binary64)) (cos.f64 x) (.f64 (*.f64 (sin.f64 x) #s(literal -1/2 binary64)) eps))
(+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x))))))
(fma.f64 (fma.f64 #s(literal -1/6 binary64) (.f64 eps eps) #s(literal 1 binary64)) (cos.f64 x) (.f64 (*.f64 (sin.f64 x) #s(literal -1/2 binary64)) eps))
1
#s(literal 1 binary64)
(+ 1 (* -1/6 (pow eps 2)))
(fma.f64 #s(literal -1/6 binary64) (*.f64 eps eps) #s(literal 1 binary64))
(+ 1 (* -1/6 (pow eps 2)))
(fma.f64 #s(literal -1/6 binary64) (*.f64 eps eps) #s(literal 1 binary64))
(+ 1 (* -1/6 (pow eps 2)))
(fma.f64 #s(literal -1/6 binary64) (*.f64 eps eps) #s(literal 1 binary64))
(cos x)
(cos.f64 x)
(+ (cos x) (* -1/2 (* eps (sin x))))
(fma.f64 (*.f64 (sin.f64 x) #s(literal -1/2 binary64)) eps (cos.f64 x))
(+ (cos x) (* eps (- (* -1/8 (* eps (cos x))) (* 1/2 (sin x)))))
(fma.f64 (fma.f64 #s(literal -1/8 binary64) (.f64 (cos.f64 x) eps) (.f64 (sin.f64 x) #s(literal -1/2 binary64))) eps (cos.f64 x))
(+ (cos x) (* eps (- (* eps (+ (* -1/8 (cos x)) (* 1/48 (* eps (sin x))))) (* 1/2 (sin x)))))
(fma.f64 (fma.f64 (sin.f64 x) (fma.f64 eps (.f64 #s(literal 1/48 binary64) eps) #s(literal -1/2 binary64)) (.f64 #s(literal -1/8 binary64) (*.f64 (cos.f64 x) eps))) eps (cos.f64 x))
(* 1/2 eps)
(*.f64 eps #s(literal 1/2 binary64))
(* eps (+ 1/2 (* -1/48 (pow eps 2))))
(.f64 (fma.f64 (.f64 eps eps) #s(literal -1/48 binary64) #s(literal 1/2 binary64)) eps)
(* eps (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48))))
(.f64 (fma.f64 (fma.f64 #s(literal 1/3840 binary64) (.f64 eps eps) #s(literal -1/48 binary64)) (*.f64 eps eps) #s(literal 1/2 binary64)) eps)
(* eps (+ 1/2 (* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48))))
(.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -1/645120 binary64) (.f64 eps eps) #s(literal 1/3840 binary64)) (.f64 eps eps) #s(literal -1/48 binary64)) (.f64 eps eps) #s(literal 1/2 binary64)) eps)
(* 1/2 eps)
(*.f64 eps #s(literal 1/2 binary64))
(* 1/2 eps)
(*.f64 eps #s(literal 1/2 binary64))
(* 1/2 eps)
(*.f64 eps #s(literal 1/2 binary64))
(* 1/2 eps)
(*.f64 eps #s(literal 1/2 binary64))
(* -1/2 (* eps (sin x)))
(.f64 (.f64 (sin.f64 x) #s(literal -1/2 binary64)) eps)
(* -1/2 (* eps (sin x)))
(.f64 (.f64 (sin.f64 x) #s(literal -1/2 binary64)) eps)
(* -1/2 (* eps (sin x)))
(.f64 (.f64 (sin.f64 x) #s(literal -1/2 binary64)) eps)
(* -1/2 (* eps (sin x)))
(.f64 (.f64 (sin.f64 x) #s(literal -1/2 binary64)) eps)
(* 1/2 eps)
(*.f64 eps #s(literal 1/2 binary64))
(* eps (+ 1/2 (/ x eps)))
(*.f64 (+.f64 (/.f64 x eps) #s(literal 1/2 binary64)) eps)
(* eps (+ 1/2 (/ x eps)))
(*.f64 (+.f64 (/.f64 x eps) #s(literal 1/2 binary64)) eps)
(* eps (+ 1/2 (/ x eps)))
(*.f64 (+.f64 (/.f64 x eps) #s(literal 1/2 binary64)) eps)
eps
eps
eps
eps
(* 2 (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))))
(.f64 (cos.f64 (fma.f64 eps #s(literal 1/2 binary64) x)) (.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) #s(literal 2 binary64)))
(* 2 (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))))
(.f64 (cos.f64 (fma.f64 eps #s(literal 1/2 binary64) x)) (.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) #s(literal 2 binary64)))
(* 2 (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))))
(.f64 (cos.f64 (fma.f64 eps #s(literal 1/2 binary64) x)) (.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) #s(literal 2 binary64)))
(* 2 (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))))
(.f64 (cos.f64 (fma.f64 eps #s(literal 1/2 binary64) x)) (.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) #s(literal 2 binary64)))
(* 2 (sin (* 1/2 eps)))
(.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) #s(literal 2 binary64))
(* 2 (sin (* 1/2 eps)))
(.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) #s(literal 2 binary64))
(* 2 (sin (* 1/2 eps)))
(.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) #s(literal 2 binary64))
(* 2 (sin (* 1/2 eps)))
(.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) #s(literal 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))
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(-.f64 (sin.f64 (+.f64 eps x)) (sin.f64 x))
(* eps (+ (* -1/2 (* eps (sin x))) (* (cos x) (+ 1 (* -1/6 (pow eps 2))))))
(.f64 (fma.f64 (fma.f64 #s(literal -1/6 binary64) (.f64 eps eps) #s(literal 1 binary64)) (cos.f64 x) (.f64 (.f64 (sin.f64 x) #s(literal -1/2 binary64)) eps)) eps)
(* eps (+ (* -1/2 (* eps (sin x))) (* (cos x) (+ 1 (* -1/6 (pow eps 2))))))
(.f64 (fma.f64 (fma.f64 #s(literal -1/6 binary64) (.f64 eps eps) #s(literal 1 binary64)) (cos.f64 x) (.f64 (.f64 (sin.f64 x) #s(literal -1/2 binary64)) eps)) eps)
(* eps (+ (* -1/2 (* eps (sin x))) (* (cos x) (+ 1 (* -1/6 (pow eps 2))))))
(.f64 (fma.f64 (fma.f64 #s(literal -1/6 binary64) (.f64 eps eps) #s(literal 1 binary64)) (cos.f64 x) (.f64 (.f64 (sin.f64 x) #s(literal -1/2 binary64)) eps)) eps)
(* eps (+ (* -1/2 (* eps (sin x))) (* (cos x) (+ 1 (* -1/6 (pow eps 2))))))
(.f64 (fma.f64 (fma.f64 #s(literal -1/6 binary64) (.f64 eps eps) #s(literal 1 binary64)) (cos.f64 x) (.f64 (.f64 (sin.f64 x) #s(literal -1/2 binary64)) eps)) eps)
(+ (* -1/2 (* eps (sin x))) (* (cos x) (+ 1 (* -1/6 (pow eps 2)))))
(fma.f64 (fma.f64 #s(literal -1/6 binary64) (.f64 eps eps) #s(literal 1 binary64)) (cos.f64 x) (.f64 (*.f64 (sin.f64 x) #s(literal -1/2 binary64)) eps))
(+ (* -1/2 (* eps (sin x))) (* (cos x) (+ 1 (* -1/6 (pow eps 2)))))
(fma.f64 (fma.f64 #s(literal -1/6 binary64) (.f64 eps eps) #s(literal 1 binary64)) (cos.f64 x) (.f64 (*.f64 (sin.f64 x) #s(literal -1/2 binary64)) eps))
(+ (* -1/2 (* eps (sin x))) (* (cos x) (+ 1 (* -1/6 (pow eps 2)))))
(fma.f64 (fma.f64 #s(literal -1/6 binary64) (.f64 eps eps) #s(literal 1 binary64)) (cos.f64 x) (.f64 (*.f64 (sin.f64 x) #s(literal -1/2 binary64)) eps))
(+ (* -1/2 (* eps (sin x))) (* (cos x) (+ 1 (* -1/6 (pow eps 2)))))
(fma.f64 (fma.f64 #s(literal -1/6 binary64) (.f64 eps eps) #s(literal 1 binary64)) (cos.f64 x) (.f64 (*.f64 (sin.f64 x) #s(literal -1/2 binary64)) eps))
(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))
(* -1/6 (pow x 3))
(.f64 (.f64 (*.f64 x x) x) #s(literal -1/6 binary64))
(* -1 (* (pow x 3) (- 1/6 (/ 1 (pow x 2)))))
(.f64 (.f64 (-.f64 (/.f64 #s(literal 1 binary64) (.f64 x x)) #s(literal 1/6 binary64)) x) (.f64 x x))
(* -1 (* (pow x 3) (- 1/6 (/ 1 (pow x 2)))))
(.f64 (.f64 (-.f64 (/.f64 #s(literal 1 binary64) (.f64 x x)) #s(literal 1/6 binary64)) x) (.f64 x x))
(* -1 (* (pow x 3) (- 1/6 (/ 1 (pow x 2)))))
(.f64 (.f64 (-.f64 (/.f64 #s(literal 1 binary64) (.f64 x x)) #s(literal 1/6 binary64)) x) (.f64 x x))
(* -1/2 (* eps (sin x)))
(.f64 (.f64 (sin.f64 x) #s(literal -1/2 binary64)) eps)
(* -1/2 (* eps (sin x)))
(.f64 (.f64 (sin.f64 x) #s(literal -1/2 binary64)) eps)
(* -1/2 (* eps (sin x)))
(.f64 (.f64 (sin.f64 x) #s(literal -1/2 binary64)) eps)
(* -1/2 (* eps (sin x)))
(.f64 (.f64 (sin.f64 x) #s(literal -1/2 binary64)) eps)

rewrite234.0ms (2%)

Memory

-10.6MiB live, 244.5MiB allocated

Rules

5 304×	`lower-fma.f32`
5 296×	`lower-fma.f64`
4 210×	`lower-/.f64`
4 210×	`lower-/.f32`
3 780×	`lower-*.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	40	193
0	70	183
1	226	183
2	1715	183
0	8349	183

Stop Event

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

Counts

22 → 571

Calls

Call 1

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

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

eval161.0ms (1.4%)

Memory: 2.8MiB live, 185.2MiB allocated
Compiler: Compiled 27 626 to 2 437 computations (91.2% saved)

prune29.0ms (0.2%)

Memory

11.4MiB live, 86.8MiB allocated

Pruning

16 alts after pruning (12 fresh and 4 done)

	Pruned	Kept	Total
New	987	9	996
Fresh	1	3	4
Picked	2	3	5
Done	0	1	1
Total	990	16	1 006

Accuracy

100.0%

Counts

1 006 → 16

Alt Table

Click to see full alt table

Status	Accuracy	Program
	62.4%	(fma.f64 (sin.f64 x) (cos.f64 eps) (fma.f64 (sin.f64 eps) (cos.f64 x) (neg.f64 (sin.f64 x))))
✓	62.1%	(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
✓	7.5%	(-.f64 #s(approx (sin (+ x eps)) (sin.f64 eps)) (sin.f64 x))
▶	99.4%	(.f64 (.f64 #s(approx (sin (* 1/2 (+ 0 eps))) (.f64 eps #s(literal 1/2 binary64))) #s(literal 2 binary64)) (cos.f64 (.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps))))
	99.6%	(.f64 #s(approx ( (sin (* 1/2 (+ 0 eps))) 2) (.f64 (fma.f64 (.f64 eps eps) #s(literal -1/24 binary64) #s(literal 1 binary64)) eps)) (cos.f64 (*.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps))))
▶	99.7%	#s(approx (- (sin (+ x eps)) (sin x)) (/.f64 (.f64 (-.f64 (.f64 (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x)))) (.f64 (fma.f64 (.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64)) (fma.f64 (.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64)))) (.f64 (.f64 (.f64 #s(literal -1/2 binary64) eps) (.f64 #s(literal -1/2 binary64) eps)) (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x)))))) eps) (-.f64 (.f64 (cos.f64 x) (fma.f64 (.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64))) (.f64 (*.f64 #s(literal -1/2 binary64) (sin.f64 x)) eps))))
✓	99.7%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 (fma.f64 (.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64)) (cos.f64 x) (.f64 (.f64 (sin.f64 x) #s(literal -1/2 binary64)) eps)) eps))
	98.9%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 (fma.f64 (.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64)) (cos.f64 x) #s(approx (* (* (sin x) -1/2) eps) (.f64 (.f64 eps (fma.f64 #s(literal 1/12 binary64) (*.f64 x x) #s(literal -1/2 binary64))) x))) eps))
	99.5%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 (.f64 (sin.f64 x) #s(literal -1/2 binary64)) eps (cos.f64 x)) eps))
	99.0%	#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (cos.f64 x) eps))
	98.3%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (+ (* (* eps eps) -1/6) 1) (cos x)) (* (* (sin x) -1/2) eps)) (fma.f64 (fma.f64 (fma.f64 (.f64 #s(literal 1/12 binary64) eps) (+.f64 eps x) #s(literal -1/2 binary64)) x (.f64 #s(literal -1/2 binary64) eps)) x (fma.f64 #s(literal -1/6 binary64) (*.f64 eps eps) #s(literal 1 binary64)))) eps))
▶	98.3%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (+ (* (* eps eps) -1/6) 1) (cos x)) (* (* (sin x) -1/2) eps)) (fma.f64 (.f64 (fma.f64 (fma.f64 #s(literal -1/6 binary64) (.f64 eps eps) #s(literal 1 binary64)) x eps) #s(literal -1/2 binary64)) x (fma.f64 #s(literal -1/6 binary64) (*.f64 eps eps) #s(literal 1 binary64)))) eps))
	98.1%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (+ (* (* eps eps) -1/6) 1) (cos x)) (* (* (sin x) -1/2) eps)) (fma.f64 eps (fma.f64 #s(literal -1/2 binary64) x (*.f64 #s(literal -1/6 binary64) eps)) #s(literal 1 binary64))) eps))
▶	98.2%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (+ (* (* eps eps) -1/6) 1) (cos x)) (* (* (sin x) -1/2) eps)) (fma.f64 #s(literal -1/6 binary64) (*.f64 eps eps) #s(literal 1 binary64))) eps))
✓	98.2%	#s(approx (- (sin (+ x eps)) (sin x)) (sin.f64 eps))
▶	98.3%	#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (+ (* (* eps eps) -1/6) 1) (cos x)) (* (* (sin x) -1/2) eps)) eps) (fma.f64 (.f64 (fma.f64 (.f64 #s(literal 1/12 binary64) x) (.f64 eps eps) (.f64 (fma.f64 #s(literal 1/12 binary64) (.f64 eps eps) #s(literal -1/2 binary64)) eps)) x) x (fma.f64 (.f64 eps eps) (fma.f64 #s(literal -1/6 binary64) eps (*.f64 #s(literal -1/2 binary64) x)) eps))))

Compiler

Compiled 580 to 313 computations (46% saved)

simplify175.0ms (1.5%)

Memory

-5.3MiB live, 115.5MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 20 expressions of interest:

New	Metric	Score
cost-diff	0	#s(approx (sin (* 1/2 (+ 0 eps))) (*.f64 eps #s(literal 1/2 binary64)))
cost-diff	0	(.f64 #s(approx (sin ( 1/2 (+ 0 eps))) (*.f64 eps #s(literal 1/2 binary64))) #s(literal 2 binary64))
cost-diff	0	(.f64 (.f64 #s(approx (sin (* 1/2 (+ 0 eps))) (.f64 eps #s(literal 1/2 binary64))) #s(literal 2 binary64)) (cos.f64 (.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps))))
cost-diff	320	(*.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps))
cost-diff	0	#s(approx (* (+ (* (+ (* (* eps eps) -1/6) 1) (cos x)) (* (* (sin x) -1/2) eps)) eps) (fma.f64 (.f64 (fma.f64 (.f64 #s(literal 1/12 binary64) x) (.f64 eps eps) (.f64 (fma.f64 #s(literal 1/12 binary64) (.f64 eps eps) #s(literal -1/2 binary64)) eps)) x) x (fma.f64 (.f64 eps eps) (fma.f64 #s(literal -1/6 binary64) eps (*.f64 #s(literal -1/2 binary64) x)) eps)))
cost-diff	0	#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (+ (* (* eps eps) -1/6) 1) (cos x)) (* (* (sin x) -1/2) eps)) eps) (fma.f64 (.f64 (fma.f64 (.f64 #s(literal 1/12 binary64) x) (.f64 eps eps) (.f64 (fma.f64 #s(literal 1/12 binary64) (.f64 eps eps) #s(literal -1/2 binary64)) eps)) x) x (fma.f64 (.f64 eps eps) (fma.f64 #s(literal -1/6 binary64) eps (*.f64 #s(literal -1/2 binary64) x)) eps))))
cost-diff	320	(fma.f64 (.f64 (fma.f64 (.f64 #s(literal 1/12 binary64) x) (.f64 eps eps) (.f64 (fma.f64 #s(literal 1/12 binary64) (.f64 eps eps) #s(literal -1/2 binary64)) eps)) x) x (fma.f64 (.f64 eps eps) (fma.f64 #s(literal -1/6 binary64) eps (*.f64 #s(literal -1/2 binary64) x)) eps))
cost-diff	832	(fma.f64 (.f64 #s(literal 1/12 binary64) x) (.f64 eps eps) (.f64 (fma.f64 #s(literal 1/12 binary64) (.f64 eps eps) #s(literal -1/2 binary64)) eps))
cost-diff	0	(fma.f64 (.f64 (fma.f64 (fma.f64 #s(literal -1/6 binary64) (.f64 eps eps) #s(literal 1 binary64)) x eps) #s(literal -1/2 binary64)) x (fma.f64 #s(literal -1/6 binary64) (*.f64 eps eps) #s(literal 1 binary64)))
cost-diff	0	#s(approx (+ (* (+ (* (* eps eps) -1/6) 1) (cos x)) (* (* (sin x) -1/2) eps)) (fma.f64 (.f64 (fma.f64 (fma.f64 #s(literal -1/6 binary64) (.f64 eps eps) #s(literal 1 binary64)) x eps) #s(literal -1/2 binary64)) x (fma.f64 #s(literal -1/6 binary64) (*.f64 eps eps) #s(literal 1 binary64))))
cost-diff	0	(.f64 #s(approx (+ ( (+ (* (* eps eps) -1/6) 1) (cos x)) (* (* (sin x) -1/2) eps)) (fma.f64 (.f64 (fma.f64 (fma.f64 #s(literal -1/6 binary64) (.f64 eps eps) #s(literal 1 binary64)) x eps) #s(literal -1/2 binary64)) x (fma.f64 #s(literal -1/6 binary64) (*.f64 eps eps) #s(literal 1 binary64)))) eps)
cost-diff	0	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (+ (* (* eps eps) -1/6) 1) (cos x)) (* (* (sin x) -1/2) eps)) (fma.f64 (.f64 (fma.f64 (fma.f64 #s(literal -1/6 binary64) (.f64 eps eps) #s(literal 1 binary64)) x eps) #s(literal -1/2 binary64)) x (fma.f64 #s(literal -1/6 binary64) (*.f64 eps eps) #s(literal 1 binary64)))) eps))
cost-diff	0	(fma.f64 #s(literal -1/6 binary64) (*.f64 eps eps) #s(literal 1 binary64))
cost-diff	0	#s(approx (+ (* (+ (* (* eps eps) -1/6) 1) (cos x)) (* (* (sin x) -1/2) eps)) (fma.f64 #s(literal -1/6 binary64) (*.f64 eps eps) #s(literal 1 binary64)))
cost-diff	0	(.f64 #s(approx (+ ( (+ (* (* eps eps) -1/6) 1) (cos x)) (* (* (sin x) -1/2) eps)) (fma.f64 #s(literal -1/6 binary64) (*.f64 eps eps) #s(literal 1 binary64))) eps)
cost-diff	0	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (+ (* (* eps eps) -1/6) 1) (cos x)) (* (* (sin x) -1/2) eps)) (fma.f64 #s(literal -1/6 binary64) (*.f64 eps eps) #s(literal 1 binary64))) eps))
cost-diff	128	(+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x))))
cost-diff	192	(.f64 (.f64 (.f64 #s(literal -1/2 binary64) eps) (.f64 #s(literal -1/2 binary64) eps)) (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x)))))
cost-diff	320	(.f64 (.f64 #s(literal -1/2 binary64) eps) (*.f64 #s(literal -1/2 binary64) eps))
cost-diff	4480	(-.f64 (.f64 (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x)))) (.f64 (fma.f64 (.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64)) (fma.f64 (.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64)))) (.f64 (.f64 (.f64 #s(literal -1/2 binary64) eps) (.f64 #s(literal -1/2 binary64) eps)) (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x))))))

Rules

15 556×	`lower-fma.f32`
15 536×	`lower-fma.f64`
4 202×	`lower-*.f32`
4 158×	`lower-*.f64`
2 656×	`lower-+.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	75	893
0	128	875
1	264	870
2	778	867
3	2954	843
4	4287	842
0	8127	795

Stop Event

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

Calls

Call 1

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

Outputs
#s(approx (- (sin (+ x eps)) (sin x)) (/.f64 (.f64 (-.f64 (.f64 (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x)))) (.f64 (fma.f64 (.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64)) (fma.f64 (.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64)))) (.f64 (.f64 (.f64 #s(literal -1/2 binary64) eps) (.f64 #s(literal -1/2 binary64) eps)) (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x)))))) eps) (-.f64 (.f64 (cos.f64 x) (fma.f64 (.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64))) (.f64 (*.f64 #s(literal -1/2 binary64) (sin.f64 x)) eps))))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (/.f64 eps (fma.f64 (.f64 (sin.f64 x) eps) #s(literal 1/2 binary64) (.f64 (cos.f64 x) (fma.f64 #s(literal -1/6 binary64) (.f64 eps eps) #s(literal 1 binary64))))) (fma.f64 (fma.f64 (.f64 eps eps) (+.f64 (fma.f64 #s(literal 1/36 binary64) (.f64 eps eps) #s(literal -1/6 binary64)) #s(literal -1/6 binary64)) #s(literal 1 binary64)) #s(literal 1/2 binary64) (fma.f64 (.f64 (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64)) (-.f64 (fma.f64 (.f64 eps eps) (+.f64 (fma.f64 #s(literal 1/36 binary64) (.f64 eps eps) #s(literal -1/6 binary64)) #s(literal -1/6 binary64)) #s(literal 1 binary64)) (.f64 #s(literal -1/4 binary64) (.f64 eps eps))) (.f64 #s(literal -1/8 binary64) (*.f64 eps eps))))))
(/.f64 (.f64 (-.f64 (.f64 (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x)))) (.f64 (fma.f64 (.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64)) (fma.f64 (.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64)))) (.f64 (.f64 (.f64 #s(literal -1/2 binary64) eps) (.f64 #s(literal -1/2 binary64) eps)) (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x)))))) eps) (-.f64 (.f64 (cos.f64 x) (fma.f64 (.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64))) (.f64 (*.f64 #s(literal -1/2 binary64) (sin.f64 x)) eps)))
(.f64 (/.f64 eps (fma.f64 (.f64 (sin.f64 x) eps) #s(literal 1/2 binary64) (.f64 (cos.f64 x) (fma.f64 #s(literal -1/6 binary64) (.f64 eps eps) #s(literal 1 binary64))))) (fma.f64 (fma.f64 (.f64 eps eps) (+.f64 (fma.f64 #s(literal 1/36 binary64) (.f64 eps eps) #s(literal -1/6 binary64)) #s(literal -1/6 binary64)) #s(literal 1 binary64)) #s(literal 1/2 binary64) (fma.f64 (.f64 (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64)) (-.f64 (fma.f64 (.f64 eps eps) (+.f64 (fma.f64 #s(literal 1/36 binary64) (.f64 eps eps) #s(literal -1/6 binary64)) #s(literal -1/6 binary64)) #s(literal 1 binary64)) (.f64 #s(literal -1/4 binary64) (.f64 eps eps))) (.f64 #s(literal -1/8 binary64) (*.f64 eps eps)))))
(.f64 (-.f64 (.f64 (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x)))) (.f64 (fma.f64 (.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64)) (fma.f64 (.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64)))) (.f64 (.f64 (.f64 #s(literal -1/2 binary64) eps) (.f64 #s(literal -1/2 binary64) eps)) (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x)))))) eps)
(.f64 (fma.f64 (fma.f64 (.f64 eps eps) (+.f64 (fma.f64 #s(literal 1/36 binary64) (.f64 eps eps) #s(literal -1/6 binary64)) #s(literal -1/6 binary64)) #s(literal 1 binary64)) #s(literal 1/2 binary64) (fma.f64 (.f64 (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64)) (-.f64 (fma.f64 (.f64 eps eps) (+.f64 (fma.f64 #s(literal 1/36 binary64) (.f64 eps eps) #s(literal -1/6 binary64)) #s(literal -1/6 binary64)) #s(literal 1 binary64)) (.f64 #s(literal -1/4 binary64) (.f64 eps eps))) (.f64 #s(literal -1/8 binary64) (.f64 eps eps)))) eps)
(-.f64 (.f64 (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x)))) (.f64 (fma.f64 (.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64)) (fma.f64 (.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64)))) (.f64 (.f64 (.f64 #s(literal -1/2 binary64) eps) (.f64 #s(literal -1/2 binary64) eps)) (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x))))))
(fma.f64 (fma.f64 (.f64 eps eps) (+.f64 (fma.f64 #s(literal 1/36 binary64) (.f64 eps eps) #s(literal -1/6 binary64)) #s(literal -1/6 binary64)) #s(literal 1 binary64)) #s(literal 1/2 binary64) (fma.f64 (.f64 (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64)) (-.f64 (fma.f64 (.f64 eps eps) (+.f64 (fma.f64 #s(literal 1/36 binary64) (.f64 eps eps) #s(literal -1/6 binary64)) #s(literal -1/6 binary64)) #s(literal 1 binary64)) (.f64 #s(literal -1/4 binary64) (.f64 eps eps))) (.f64 #s(literal -1/8 binary64) (*.f64 eps eps))))
(.f64 (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x)))) (.f64 (fma.f64 (.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64)) (fma.f64 (*.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64))))
(.f64 (fma.f64 (.f64 eps eps) (+.f64 (fma.f64 #s(literal 1/36 binary64) (*.f64 eps eps) #s(literal -1/6 binary64)) #s(literal -1/6 binary64)) #s(literal 1 binary64)) (fma.f64 (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64) #s(literal 1/2 binary64)))
(+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x))))
(fma.f64 (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64) #s(literal 1/2 binary64))
#s(literal 1/2 binary64)
(*.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x)))
(*.f64 (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64))
(cos.f64 (+.f64 x x))
(+.f64 x x)
x
(.f64 (fma.f64 (.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64)) (fma.f64 (*.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64)))
(fma.f64 (.f64 eps eps) (+.f64 (fma.f64 #s(literal 1/36 binary64) (.f64 eps eps) #s(literal -1/6 binary64)) #s(literal -1/6 binary64)) #s(literal 1 binary64))
(fma.f64 (*.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64))
(fma.f64 #s(literal -1/6 binary64) (*.f64 eps eps) #s(literal 1 binary64))
(*.f64 eps eps)
eps
#s(literal -1/6 binary64)
#s(literal 1 binary64)
(.f64 (.f64 (.f64 #s(literal -1/2 binary64) eps) (.f64 #s(literal -1/2 binary64) eps)) (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x)))))
(.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 x x))) (.f64 #s(literal 1/8 binary64) (*.f64 eps eps)))
(.f64 (.f64 #s(literal -1/2 binary64) eps) (*.f64 #s(literal -1/2 binary64) eps))
(.f64 #s(literal 1/4 binary64) (.f64 eps eps))
(*.f64 #s(literal -1/2 binary64) eps)
#s(literal -1/2 binary64)
(-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x))))
(fma.f64 #s(literal -1/2 binary64) (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64))
(-.f64 (.f64 (cos.f64 x) (fma.f64 (.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64))) (.f64 (.f64 #s(literal -1/2 binary64) (sin.f64 x)) eps))
(fma.f64 (.f64 (sin.f64 x) eps) #s(literal 1/2 binary64) (.f64 (cos.f64 x) (fma.f64 #s(literal -1/6 binary64) (*.f64 eps eps) #s(literal 1 binary64))))
(.f64 (cos.f64 x) (fma.f64 (.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64)))
(.f64 (cos.f64 x) (fma.f64 #s(literal -1/6 binary64) (.f64 eps eps) #s(literal 1 binary64)))
(cos.f64 x)
(.f64 (.f64 #s(literal -1/2 binary64) (sin.f64 x)) eps)
(.f64 (.f64 (sin.f64 x) #s(literal -1/2 binary64)) eps)
(*.f64 #s(literal -1/2 binary64) (sin.f64 x))
(*.f64 (sin.f64 x) #s(literal -1/2 binary64))
(sin.f64 x)
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (+ (* (* eps eps) -1/6) 1) (cos x)) (* (* (sin x) -1/2) eps)) (fma.f64 #s(literal -1/6 binary64) (*.f64 eps eps) #s(literal 1 binary64))) eps))
(.f64 #s(approx (+ ( (+ (* (* eps eps) -1/6) 1) (cos x)) (* (* (sin x) -1/2) eps)) (fma.f64 #s(literal -1/6 binary64) (*.f64 eps eps) #s(literal 1 binary64))) eps)
#s(approx (+ (* (+ (* (* eps eps) -1/6) 1) (cos x)) (* (* (sin x) -1/2) eps)) (fma.f64 #s(literal -1/6 binary64) (*.f64 eps eps) #s(literal 1 binary64)))
(fma.f64 #s(literal -1/6 binary64) (*.f64 eps eps) #s(literal 1 binary64))
#s(literal -1/6 binary64)
(*.f64 eps eps)
eps
#s(literal 1 binary64)
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (+ (* (* eps eps) -1/6) 1) (cos x)) (* (* (sin x) -1/2) eps)) (fma.f64 (.f64 (fma.f64 (fma.f64 #s(literal -1/6 binary64) (.f64 eps eps) #s(literal 1 binary64)) x eps) #s(literal -1/2 binary64)) x (fma.f64 #s(literal -1/6 binary64) (*.f64 eps eps) #s(literal 1 binary64)))) eps))
(.f64 #s(approx (+ ( (+ (* (* eps eps) -1/6) 1) (cos x)) (* (* (sin x) -1/2) eps)) (fma.f64 (.f64 (fma.f64 (fma.f64 #s(literal -1/6 binary64) (.f64 eps eps) #s(literal 1 binary64)) x eps) #s(literal -1/2 binary64)) x (fma.f64 #s(literal -1/6 binary64) (*.f64 eps eps) #s(literal 1 binary64)))) eps)
#s(approx (+ (* (+ (* (* eps eps) -1/6) 1) (cos x)) (* (* (sin x) -1/2) eps)) (fma.f64 (.f64 (fma.f64 (fma.f64 #s(literal -1/6 binary64) (.f64 eps eps) #s(literal 1 binary64)) x eps) #s(literal -1/2 binary64)) x (fma.f64 #s(literal -1/6 binary64) (*.f64 eps eps) #s(literal 1 binary64))))
(fma.f64 (.f64 (fma.f64 (fma.f64 #s(literal -1/6 binary64) (.f64 eps eps) #s(literal 1 binary64)) x eps) #s(literal -1/2 binary64)) x (fma.f64 #s(literal -1/6 binary64) (*.f64 eps eps) #s(literal 1 binary64)))
(.f64 (fma.f64 (fma.f64 #s(literal -1/6 binary64) (.f64 eps eps) #s(literal 1 binary64)) x eps) #s(literal -1/2 binary64))
(fma.f64 (fma.f64 #s(literal -1/6 binary64) (*.f64 eps eps) #s(literal 1 binary64)) x eps)
(fma.f64 #s(literal -1/6 binary64) (*.f64 eps eps) #s(literal 1 binary64))
#s(literal -1/6 binary64)
(*.f64 eps eps)
eps
#s(literal 1 binary64)
x
#s(literal -1/2 binary64)
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (+ (* (* eps eps) -1/6) 1) (cos x)) (* (* (sin x) -1/2) eps)) eps) (fma.f64 (.f64 (fma.f64 (.f64 #s(literal 1/12 binary64) x) (.f64 eps eps) (.f64 (fma.f64 #s(literal 1/12 binary64) (.f64 eps eps) #s(literal -1/2 binary64)) eps)) x) x (fma.f64 (.f64 eps eps) (fma.f64 #s(literal -1/6 binary64) eps (*.f64 #s(literal -1/2 binary64) x)) eps))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (+ (* (* eps eps) -1/6) 1) (cos x)) (* (* (sin x) -1/2) eps)) eps) (fma.f64 eps (fma.f64 (fma.f64 (.f64 #s(literal 1/12 binary64) eps) (+.f64 eps x) #s(literal -1/2 binary64)) (.f64 x x) (.f64 (fma.f64 #s(literal -1/6 binary64) eps (.f64 #s(literal -1/2 binary64) x)) eps)) eps)))
#s(approx (* (+ (* (+ (* (* eps eps) -1/6) 1) (cos x)) (* (* (sin x) -1/2) eps)) eps) (fma.f64 (.f64 (fma.f64 (.f64 #s(literal 1/12 binary64) x) (.f64 eps eps) (.f64 (fma.f64 #s(literal 1/12 binary64) (.f64 eps eps) #s(literal -1/2 binary64)) eps)) x) x (fma.f64 (.f64 eps eps) (fma.f64 #s(literal -1/6 binary64) eps (*.f64 #s(literal -1/2 binary64) x)) eps)))
#s(approx (* (+ (* (+ (* (* eps eps) -1/6) 1) (cos x)) (* (* (sin x) -1/2) eps)) eps) (fma.f64 eps (fma.f64 (fma.f64 (.f64 #s(literal 1/12 binary64) eps) (+.f64 eps x) #s(literal -1/2 binary64)) (.f64 x x) (.f64 (fma.f64 #s(literal -1/6 binary64) eps (.f64 #s(literal -1/2 binary64) x)) eps)) eps))
(fma.f64 (.f64 (fma.f64 (.f64 #s(literal 1/12 binary64) x) (.f64 eps eps) (.f64 (fma.f64 #s(literal 1/12 binary64) (.f64 eps eps) #s(literal -1/2 binary64)) eps)) x) x (fma.f64 (.f64 eps eps) (fma.f64 #s(literal -1/6 binary64) eps (*.f64 #s(literal -1/2 binary64) x)) eps))
(fma.f64 eps (fma.f64 (fma.f64 (.f64 #s(literal 1/12 binary64) eps) (+.f64 eps x) #s(literal -1/2 binary64)) (.f64 x x) (.f64 (fma.f64 #s(literal -1/6 binary64) eps (.f64 #s(literal -1/2 binary64) x)) eps)) eps)
(.f64 (fma.f64 (.f64 #s(literal 1/12 binary64) x) (.f64 eps eps) (.f64 (fma.f64 #s(literal 1/12 binary64) (*.f64 eps eps) #s(literal -1/2 binary64)) eps)) x)
(.f64 (.f64 eps x) (fma.f64 (*.f64 #s(literal 1/12 binary64) eps) (+.f64 eps x) #s(literal -1/2 binary64)))
(fma.f64 (.f64 #s(literal 1/12 binary64) x) (.f64 eps eps) (.f64 (fma.f64 #s(literal 1/12 binary64) (.f64 eps eps) #s(literal -1/2 binary64)) eps))
(.f64 (fma.f64 (.f64 #s(literal 1/12 binary64) eps) (+.f64 eps x) #s(literal -1/2 binary64)) eps)
(*.f64 #s(literal 1/12 binary64) x)
#s(literal 1/12 binary64)
x
(*.f64 eps eps)
eps
(.f64 (fma.f64 #s(literal 1/12 binary64) (.f64 eps eps) #s(literal -1/2 binary64)) eps)
(fma.f64 #s(literal 1/12 binary64) (*.f64 eps eps) #s(literal -1/2 binary64))
#s(literal -1/2 binary64)
(fma.f64 (.f64 eps eps) (fma.f64 #s(literal -1/6 binary64) eps (.f64 #s(literal -1/2 binary64) x)) eps)
(fma.f64 (fma.f64 #s(literal -1/6 binary64) eps (.f64 #s(literal -1/2 binary64) x)) (.f64 eps eps) eps)
(fma.f64 #s(literal -1/6 binary64) eps (*.f64 #s(literal -1/2 binary64) x))
#s(literal -1/6 binary64)
(*.f64 #s(literal -1/2 binary64) x)
(.f64 (.f64 #s(approx (sin (* 1/2 (+ 0 eps))) (.f64 eps #s(literal 1/2 binary64))) #s(literal 2 binary64)) (cos.f64 (.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps))))
(.f64 (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) (.f64 #s(literal 2 binary64) #s(approx (sin (* 1/2 (+ 0 eps))) (*.f64 #s(literal 1/2 binary64) eps))))
(.f64 #s(approx (sin ( 1/2 (+ 0 eps))) (*.f64 eps #s(literal 1/2 binary64))) #s(literal 2 binary64))
(.f64 #s(literal 2 binary64) #s(approx (sin ( 1/2 (+ 0 eps))) (*.f64 #s(literal 1/2 binary64) eps)))
#s(approx (sin (* 1/2 (+ 0 eps))) (*.f64 eps #s(literal 1/2 binary64)))
#s(approx (sin (* 1/2 (+ 0 eps))) (*.f64 #s(literal 1/2 binary64) eps))
(*.f64 eps #s(literal 1/2 binary64))
(*.f64 #s(literal 1/2 binary64) eps)
eps
#s(literal 1/2 binary64)
#s(literal 2 binary64)
(cos.f64 (*.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps)))
(cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x))
(*.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps))
(fma.f64 #s(literal 1/2 binary64) eps x)
(fma.f64 #s(literal 2 binary64) x eps)
x

localize443.0ms (3.8%)

Memory

-36.6MiB live, 748.7MiB allocated

Localize:

Found 20 expressions of interest:

New	Metric	Score
accuracy	0	(*.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps))
accuracy	0.0078125	(.f64 (.f64 #s(approx (sin (* 1/2 (+ 0 eps))) (.f64 eps #s(literal 1/2 binary64))) #s(literal 2 binary64)) (cos.f64 (.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps))))
accuracy	0.09448630290560088	(cos.f64 (*.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps)))
accuracy	0.324187546809663	#s(approx (sin (* 1/2 (+ 0 eps))) (*.f64 eps #s(literal 1/2 binary64)))
accuracy	0.00390625	(fma.f64 (.f64 (fma.f64 (.f64 #s(literal 1/12 binary64) x) (.f64 eps eps) (.f64 (fma.f64 #s(literal 1/12 binary64) (.f64 eps eps) #s(literal -1/2 binary64)) eps)) x) x (fma.f64 (.f64 eps eps) (fma.f64 #s(literal -1/6 binary64) eps (*.f64 #s(literal -1/2 binary64) x)) eps))
accuracy	0.21941333120599352	#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (+ (* (* eps eps) -1/6) 1) (cos x)) (* (* (sin x) -1/2) eps)) eps) (fma.f64 (.f64 (fma.f64 (.f64 #s(literal 1/12 binary64) x) (.f64 eps eps) (.f64 (fma.f64 #s(literal 1/12 binary64) (.f64 eps eps) #s(literal -1/2 binary64)) eps)) x) x (fma.f64 (.f64 eps eps) (fma.f64 #s(literal -1/6 binary64) eps (*.f64 #s(literal -1/2 binary64) x)) eps))))
accuracy	0.296875	(*.f64 #s(literal 1/12 binary64) x)
accuracy	1.0846088443767707	#s(approx (* (+ (* (+ (* (* eps eps) -1/6) 1) (cos x)) (* (* (sin x) -1/2) eps)) eps) (fma.f64 (.f64 (fma.f64 (.f64 #s(literal 1/12 binary64) x) (.f64 eps eps) (.f64 (fma.f64 #s(literal 1/12 binary64) (.f64 eps eps) #s(literal -1/2 binary64)) eps)) x) x (fma.f64 (.f64 eps eps) (fma.f64 #s(literal -1/6 binary64) eps (*.f64 #s(literal -1/2 binary64) x)) eps)))
accuracy	0.00390625	(fma.f64 (fma.f64 #s(literal -1/6 binary64) (*.f64 eps eps) #s(literal 1 binary64)) x eps)
accuracy	0.00390625	(.f64 #s(approx (+ ( (+ (* (* eps eps) -1/6) 1) (cos x)) (* (* (sin x) -1/2) eps)) (fma.f64 (.f64 (fma.f64 (fma.f64 #s(literal -1/6 binary64) (.f64 eps eps) #s(literal 1 binary64)) x eps) #s(literal -1/2 binary64)) x (fma.f64 #s(literal -1/6 binary64) (*.f64 eps eps) #s(literal 1 binary64)))) eps)
accuracy	0.21941333120599352	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (+ (* (* eps eps) -1/6) 1) (cos x)) (* (* (sin x) -1/2) eps)) (fma.f64 (.f64 (fma.f64 (fma.f64 #s(literal -1/6 binary64) (.f64 eps eps) #s(literal 1 binary64)) x eps) #s(literal -1/2 binary64)) x (fma.f64 #s(literal -1/6 binary64) (*.f64 eps eps) #s(literal 1 binary64)))) eps))
accuracy	1.1159550957377529	#s(approx (+ (* (+ (* (* eps eps) -1/6) 1) (cos x)) (* (* (sin x) -1/2) eps)) (fma.f64 (.f64 (fma.f64 (fma.f64 #s(literal -1/6 binary64) (.f64 eps eps) #s(literal 1 binary64)) x eps) #s(literal -1/2 binary64)) x (fma.f64 #s(literal -1/6 binary64) (*.f64 eps eps) #s(literal 1 binary64))))
accuracy	0	(*.f64 eps eps)
accuracy	0.00390625	(.f64 #s(approx (+ ( (+ (* (* eps eps) -1/6) 1) (cos x)) (* (* (sin x) -1/2) eps)) (fma.f64 #s(literal -1/6 binary64) (*.f64 eps eps) #s(literal 1 binary64))) eps)
accuracy	0.21941333120599352	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (+ (* (* eps eps) -1/6) 1) (cos x)) (* (* (sin x) -1/2) eps)) (fma.f64 #s(literal -1/6 binary64) (*.f64 eps eps) #s(literal 1 binary64))) eps))
accuracy	1.1425821551459863	#s(approx (+ (* (+ (* (* eps eps) -1/6) 1) (cos x)) (* (* (sin x) -1/2) eps)) (fma.f64 #s(literal -1/6 binary64) (*.f64 eps eps) #s(literal 1 binary64)))
accuracy	0.01171875	(-.f64 (.f64 (cos.f64 x) (fma.f64 (.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64))) (.f64 (.f64 #s(literal -1/2 binary64) (sin.f64 x)) eps))
accuracy	0.0703125	(.f64 (.f64 (.f64 #s(literal -1/2 binary64) eps) (.f64 #s(literal -1/2 binary64) eps)) (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x)))))
accuracy	0.21941333120599352	#s(approx (- (sin (+ x eps)) (sin x)) (/.f64 (.f64 (-.f64 (.f64 (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x)))) (.f64 (fma.f64 (.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64)) (fma.f64 (.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64)))) (.f64 (.f64 (.f64 #s(literal -1/2 binary64) eps) (.f64 #s(literal -1/2 binary64) eps)) (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x)))))) eps) (-.f64 (.f64 (cos.f64 x) (fma.f64 (.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64))) (.f64 (*.f64 #s(literal -1/2 binary64) (sin.f64 x)) eps))))
accuracy	29.19512421165113	(-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x))))

Samples

284.0ms	165×	2	valid
77.0ms	83×	1	valid
4.0ms	8×	0	valid

Compiler

Compiled 671 to 72 computations (89.3% saved)

Precisions

Click to see histograms. Total time spent on operations: 291.0ms

ival-mult: 132.0ms (45.3% of total)

adjust: 63.0ms (21.6% of total)

ival-cos: 33.0ms (11.3% of total)

ival-add: 26.0ms (8.9% of total)

ival-sub: 17.0ms (5.8% of total)

ival-sin: 8.0ms (2.7% of total)

const: 7.0ms (2.4% of total)

ival-div: 4.0ms (1.4% of total)

exact: 1.0ms (0.3% of total)

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

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

series96.0ms (0.8%)

Memory

-4.0MiB live, 114.4MiB allocated

Counts

27 → 552

Calls

Call 1

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

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

Calls

6 calls:

Time	Variable		Point	Expression
9.0ms	x	@	inf	((- (* (+ 1/2 (* 1/2 (cos (+ x x)))) (* (+ (* (* eps eps) -1/6) 1) (+ (* (* eps eps) -1/6) 1))) (* (* (* -1/2 eps) (* -1/2 eps)) (- 1/2 (* 1/2 (cos (+ x x)))))) (* (* -1/2 eps) (* -1/2 eps)) (* (* (* -1/2 eps) (* -1/2 eps)) (- 1/2 (* 1/2 (cos (+ x x))))) (+ 1/2 (* 1/2 (cos (+ x x)))) (- (sin (+ x eps)) (sin x)) (* (+ (* (+ (* (* eps eps) -1/6) 1) (cos x)) (* (* (sin x) -1/2) eps)) eps) (+ (* (+ (* (* eps eps) -1/6) 1) (cos x)) (* (* (sin x) -1/2) eps)) (+ (* -1/6 (* eps eps)) 1) (- (sin (+ x eps)) (sin x)) (* (+ (* (+ (* (* eps eps) -1/6) 1) (cos x)) (* (* (sin x) -1/2) eps)) eps) (+ (* (+ (* (* eps eps) -1/6) 1) (cos x)) (* (* (sin x) -1/2) eps)) (+ (* (* (+ (* (+ (* -1/6 (* eps eps)) 1) x) eps) -1/2) x) (+ (* -1/6 (* eps eps)) 1)) (+ (* (* 1/12 x) (* eps eps)) (* (+ (* 1/12 (* eps eps)) -1/2) eps)) (+ (* (* (+ (* (* 1/12 x) (* eps eps)) (* (+ (* 1/12 (* eps eps)) -1/2) eps)) x) x) (+ (* (* eps eps) (+ (* -1/6 eps) (* -1/2 x))) eps)) (- (sin (+ x eps)) (sin x)) (* (+ (* (+ (* (* eps eps) -1/6) 1) (cos x)) (* (* (sin x) -1/2) eps)) eps) (* 1/2 (+ (* 2 x) eps)) (* (* (sin (* 1/2 (+ 0 eps))) 2) (cos (* 1/2 (+ (* 2 x) eps)))) (* (sin (* 1/2 (+ 0 eps))) 2) (sin (* 1/2 (+ 0 eps))) (- 1/2 (* 1/2 (cos (+ x x)))) (- (sin (+ x eps)) (sin x)) (- (* (cos x) (+ (* (* eps eps) -1/6) 1)) (* (* -1/2 (sin x)) eps)) (* eps eps) (+ (* (+ (* -1/6 (* eps eps)) 1) x) eps) (* 1/12 x) (cos (* 1/2 (+ (* 2 x) eps))))
7.0ms	eps	@	-inf	((- (* (+ 1/2 (* 1/2 (cos (+ x x)))) (* (+ (* (* eps eps) -1/6) 1) (+ (* (* eps eps) -1/6) 1))) (* (* (* -1/2 eps) (* -1/2 eps)) (- 1/2 (* 1/2 (cos (+ x x)))))) (* (* -1/2 eps) (* -1/2 eps)) (* (* (* -1/2 eps) (* -1/2 eps)) (- 1/2 (* 1/2 (cos (+ x x))))) (+ 1/2 (* 1/2 (cos (+ x x)))) (- (sin (+ x eps)) (sin x)) (* (+ (* (+ (* (* eps eps) -1/6) 1) (cos x)) (* (* (sin x) -1/2) eps)) eps) (+ (* (+ (* (* eps eps) -1/6) 1) (cos x)) (* (* (sin x) -1/2) eps)) (+ (* -1/6 (* eps eps)) 1) (- (sin (+ x eps)) (sin x)) (* (+ (* (+ (* (* eps eps) -1/6) 1) (cos x)) (* (* (sin x) -1/2) eps)) eps) (+ (* (+ (* (* eps eps) -1/6) 1) (cos x)) (* (* (sin x) -1/2) eps)) (+ (* (* (+ (* (+ (* -1/6 (* eps eps)) 1) x) eps) -1/2) x) (+ (* -1/6 (* eps eps)) 1)) (+ (* (* 1/12 x) (* eps eps)) (* (+ (* 1/12 (* eps eps)) -1/2) eps)) (+ (* (* (+ (* (* 1/12 x) (* eps eps)) (* (+ (* 1/12 (* eps eps)) -1/2) eps)) x) x) (+ (* (* eps eps) (+ (* -1/6 eps) (* -1/2 x))) eps)) (- (sin (+ x eps)) (sin x)) (* (+ (* (+ (* (* eps eps) -1/6) 1) (cos x)) (* (* (sin x) -1/2) eps)) eps) (* 1/2 (+ (* 2 x) eps)) (* (* (sin (* 1/2 (+ 0 eps))) 2) (cos (* 1/2 (+ (* 2 x) eps)))) (* (sin (* 1/2 (+ 0 eps))) 2) (sin (* 1/2 (+ 0 eps))) (- 1/2 (* 1/2 (cos (+ x x)))) (- (sin (+ x eps)) (sin x)) (- (* (cos x) (+ (* (* eps eps) -1/6) 1)) (* (* -1/2 (sin x)) eps)) (* eps eps) (+ (* (+ (* -1/6 (* eps eps)) 1) x) eps) (* 1/12 x) (cos (* 1/2 (+ (* 2 x) eps))))
5.0ms	x	@	-inf	((- (* (+ 1/2 (* 1/2 (cos (+ x x)))) (* (+ (* (* eps eps) -1/6) 1) (+ (* (* eps eps) -1/6) 1))) (* (* (* -1/2 eps) (* -1/2 eps)) (- 1/2 (* 1/2 (cos (+ x x)))))) (* (* -1/2 eps) (* -1/2 eps)) (* (* (* -1/2 eps) (* -1/2 eps)) (- 1/2 (* 1/2 (cos (+ x x))))) (+ 1/2 (* 1/2 (cos (+ x x)))) (- (sin (+ x eps)) (sin x)) (* (+ (* (+ (* (* eps eps) -1/6) 1) (cos x)) (* (* (sin x) -1/2) eps)) eps) (+ (* (+ (* (* eps eps) -1/6) 1) (cos x)) (* (* (sin x) -1/2) eps)) (+ (* -1/6 (* eps eps)) 1) (- (sin (+ x eps)) (sin x)) (* (+ (* (+ (* (* eps eps) -1/6) 1) (cos x)) (* (* (sin x) -1/2) eps)) eps) (+ (* (+ (* (* eps eps) -1/6) 1) (cos x)) (* (* (sin x) -1/2) eps)) (+ (* (* (+ (* (+ (* -1/6 (* eps eps)) 1) x) eps) -1/2) x) (+ (* -1/6 (* eps eps)) 1)) (+ (* (* 1/12 x) (* eps eps)) (* (+ (* 1/12 (* eps eps)) -1/2) eps)) (+ (* (* (+ (* (* 1/12 x) (* eps eps)) (* (+ (* 1/12 (* eps eps)) -1/2) eps)) x) x) (+ (* (* eps eps) (+ (* -1/6 eps) (* -1/2 x))) eps)) (- (sin (+ x eps)) (sin x)) (* (+ (* (+ (* (* eps eps) -1/6) 1) (cos x)) (* (* (sin x) -1/2) eps)) eps) (* 1/2 (+ (* 2 x) eps)) (* (* (sin (* 1/2 (+ 0 eps))) 2) (cos (* 1/2 (+ (* 2 x) eps)))) (* (sin (* 1/2 (+ 0 eps))) 2) (sin (* 1/2 (+ 0 eps))) (- 1/2 (* 1/2 (cos (+ x x)))) (- (sin (+ x eps)) (sin x)) (- (* (cos x) (+ (* (* eps eps) -1/6) 1)) (* (* -1/2 (sin x)) eps)) (* eps eps) (+ (* (+ (* -1/6 (* eps eps)) 1) x) eps) (* 1/12 x) (cos (* 1/2 (+ (* 2 x) eps))))
5.0ms	eps	@	inf	((- (* (+ 1/2 (* 1/2 (cos (+ x x)))) (* (+ (* (* eps eps) -1/6) 1) (+ (* (* eps eps) -1/6) 1))) (* (* (* -1/2 eps) (* -1/2 eps)) (- 1/2 (* 1/2 (cos (+ x x)))))) (* (* -1/2 eps) (* -1/2 eps)) (* (* (* -1/2 eps) (* -1/2 eps)) (- 1/2 (* 1/2 (cos (+ x x))))) (+ 1/2 (* 1/2 (cos (+ x x)))) (- (sin (+ x eps)) (sin x)) (* (+ (* (+ (* (* eps eps) -1/6) 1) (cos x)) (* (* (sin x) -1/2) eps)) eps) (+ (* (+ (* (* eps eps) -1/6) 1) (cos x)) (* (* (sin x) -1/2) eps)) (+ (* -1/6 (* eps eps)) 1) (- (sin (+ x eps)) (sin x)) (* (+ (* (+ (* (* eps eps) -1/6) 1) (cos x)) (* (* (sin x) -1/2) eps)) eps) (+ (* (+ (* (* eps eps) -1/6) 1) (cos x)) (* (* (sin x) -1/2) eps)) (+ (* (* (+ (* (+ (* -1/6 (* eps eps)) 1) x) eps) -1/2) x) (+ (* -1/6 (* eps eps)) 1)) (+ (* (* 1/12 x) (* eps eps)) (* (+ (* 1/12 (* eps eps)) -1/2) eps)) (+ (* (* (+ (* (* 1/12 x) (* eps eps)) (* (+ (* 1/12 (* eps eps)) -1/2) eps)) x) x) (+ (* (* eps eps) (+ (* -1/6 eps) (* -1/2 x))) eps)) (- (sin (+ x eps)) (sin x)) (* (+ (* (+ (* (* eps eps) -1/6) 1) (cos x)) (* (* (sin x) -1/2) eps)) eps) (* 1/2 (+ (* 2 x) eps)) (* (* (sin (* 1/2 (+ 0 eps))) 2) (cos (* 1/2 (+ (* 2 x) eps)))) (* (sin (* 1/2 (+ 0 eps))) 2) (sin (* 1/2 (+ 0 eps))) (- 1/2 (* 1/2 (cos (+ x x)))) (- (sin (+ x eps)) (sin x)) (- (* (cos x) (+ (* (* eps eps) -1/6) 1)) (* (* -1/2 (sin x)) eps)) (* eps eps) (+ (* (+ (* -1/6 (* eps eps)) 1) x) eps) (* 1/12 x) (cos (* 1/2 (+ (* 2 x) eps))))
4.0ms	eps	@	0	((- (* (+ 1/2 (* 1/2 (cos (+ x x)))) (* (+ (* (* eps eps) -1/6) 1) (+ (* (* eps eps) -1/6) 1))) (* (* (* -1/2 eps) (* -1/2 eps)) (- 1/2 (* 1/2 (cos (+ x x)))))) (* (* -1/2 eps) (* -1/2 eps)) (* (* (* -1/2 eps) (* -1/2 eps)) (- 1/2 (* 1/2 (cos (+ x x))))) (+ 1/2 (* 1/2 (cos (+ x x)))) (- (sin (+ x eps)) (sin x)) (* (+ (* (+ (* (* eps eps) -1/6) 1) (cos x)) (* (* (sin x) -1/2) eps)) eps) (+ (* (+ (* (* eps eps) -1/6) 1) (cos x)) (* (* (sin x) -1/2) eps)) (+ (* -1/6 (* eps eps)) 1) (- (sin (+ x eps)) (sin x)) (* (+ (* (+ (* (* eps eps) -1/6) 1) (cos x)) (* (* (sin x) -1/2) eps)) eps) (+ (* (+ (* (* eps eps) -1/6) 1) (cos x)) (* (* (sin x) -1/2) eps)) (+ (* (* (+ (* (+ (* -1/6 (* eps eps)) 1) x) eps) -1/2) x) (+ (* -1/6 (* eps eps)) 1)) (+ (* (* 1/12 x) (* eps eps)) (* (+ (* 1/12 (* eps eps)) -1/2) eps)) (+ (* (* (+ (* (* 1/12 x) (* eps eps)) (* (+ (* 1/12 (* eps eps)) -1/2) eps)) x) x) (+ (* (* eps eps) (+ (* -1/6 eps) (* -1/2 x))) eps)) (- (sin (+ x eps)) (sin x)) (* (+ (* (+ (* (* eps eps) -1/6) 1) (cos x)) (* (* (sin x) -1/2) eps)) eps) (* 1/2 (+ (* 2 x) eps)) (* (* (sin (* 1/2 (+ 0 eps))) 2) (cos (* 1/2 (+ (* 2 x) eps)))) (* (sin (* 1/2 (+ 0 eps))) 2) (sin (* 1/2 (+ 0 eps))) (- 1/2 (* 1/2 (cos (+ x x)))) (- (sin (+ x eps)) (sin x)) (- (* (cos x) (+ (* (* eps eps) -1/6) 1)) (* (* -1/2 (sin x)) eps)) (* eps eps) (+ (* (+ (* -1/6 (* eps eps)) 1) x) eps) (* 1/12 x) (cos (* 1/2 (+ (* 2 x) eps))))

simplify186.0ms (1.6%)

Memory

9.8MiB live, 205.0MiB allocated

Algorithm

1×	egg-herbie

Rules

13 680×	`lower-fma.f64`
13 680×	`lower-fma.f32`
6 670×	`lower-*.f64`
6 670×	`lower-*.f32`
3 828×	`lower-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	654	7701
1	2080	7448
2	6578	7426
0	8093	6725

Stop Event

1×	iter limit
1×	node limit

Counts

552 → 546

Calls

Call 1

Inputs
(+ 1/2 (* 1/2 (cos (* 2 x))))
(+ 1/2 (+ (* 1/2 (cos (* 2 x))) (* (pow eps 2) (- (* -1/3 (+ 1/2 (* 1/2 (cos (* 2 x))))) (* 1/4 (- 1/2 (* 1/2 (cos (* 2 x)))))))))
(+ 1/2 (+ (* 1/2 (cos (* 2 x))) (* (pow eps 2) (- (+ (* -1/3 (+ 1/2 (* 1/2 (cos (* 2 x))))) (* 1/36 (* (pow eps 2) (+ 1/2 (* 1/2 (cos (* 2 x))))))) (* 1/4 (- 1/2 (* 1/2 (cos (* 2 x)))))))))
(+ 1/2 (+ (* 1/2 (cos (* 2 x))) (* (pow eps 2) (- (+ (* -1/3 (+ 1/2 (* 1/2 (cos (* 2 x))))) (* 1/36 (* (pow eps 2) (+ 1/2 (* 1/2 (cos (* 2 x))))))) (* 1/4 (- 1/2 (* 1/2 (cos (* 2 x)))))))))
(* 1/4 (pow eps 2))
(* 1/4 (pow eps 2))
(* 1/4 (pow eps 2))
(* 1/4 (pow eps 2))
(* 1/4 (* (pow eps 2) (- 1/2 (* 1/2 (cos (* 2 x))))))
(* 1/4 (* (pow eps 2) (- 1/2 (* 1/2 (cos (* 2 x))))))
(* 1/4 (* (pow eps 2) (- 1/2 (* 1/2 (cos (* 2 x))))))
(* 1/4 (* (pow eps 2) (- 1/2 (* 1/2 (cos (* 2 x))))))
(* eps (cos x))
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x)))))))
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* eps (+ (* -1/6 (cos x)) (* 1/24 (* eps (sin x)))))))))
(* eps (cos x))
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x)))))))
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x)))))))
(cos x)
(+ (cos x) (* -1/2 (* eps (sin x))))
(+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x))))))
(+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x))))))
1
(+ 1 (* -1/6 (pow eps 2)))
(+ 1 (* -1/6 (pow eps 2)))
(+ 1 (* -1/6 (pow eps 2)))
(* eps (cos x))
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x)))))))
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* eps (+ (* -1/6 (cos x)) (* 1/24 (* eps (sin x)))))))))
(* eps (cos x))
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x)))))))
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x)))))))
(cos x)
(+ (cos x) (* -1/2 (* eps (sin x))))
(+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x))))))
(+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x))))))
(+ 1 (* -1/2 (pow x 2)))
(+ 1 (+ (* -1/2 (* eps x)) (* -1/2 (pow x 2))))
(+ 1 (+ (* -1/2 (pow x 2)) (* eps (+ (* -1/2 x) (* eps (- (* 1/12 (pow x 2)) 1/6))))))
(+ 1 (+ (* -1/2 (pow x 2)) (* eps (+ (* -1/2 x) (* eps (- (* 1/12 (pow x 2)) 1/6))))))
(* -1/2 eps)
(* eps (- (* 1/12 (* eps x)) 1/2))
(* eps (- (* eps (+ (* 1/12 eps) (* 1/12 x))) 1/2))
(* eps (- (* eps (+ (* 1/12 eps) (* 1/12 x))) 1/2))
(* eps (+ 1 (* -1/2 (pow x 2))))
(* eps (+ 1 (+ (* -1/2 (pow x 2)) (* eps (+ (* -1/2 x) (* 1/12 (pow x 3)))))))
(* eps (+ 1 (+ (* -1/2 (pow x 2)) (* eps (+ (* -1/2 x) (+ (* 1/12 (pow x 3)) (* eps (- (* 1/12 (pow x 2)) 1/6))))))))
(* eps (+ 1 (+ (* -1/2 (pow x 2)) (* eps (+ (* -1/2 x) (+ (* 1/12 (pow x 3)) (* eps (- (* 1/12 (pow x 2)) 1/6))))))))
(* eps (cos x))
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x)))))))
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* eps (+ (* -1/6 (cos x)) (* 1/24 (* eps (sin x)))))))))
(* eps (cos x))
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x)))))))
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x)))))))
x
(+ x (* 1/2 eps))
(+ x (* 1/2 eps))
(+ x (* 1/2 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))))))))))
eps
(* eps (+ 1 (* -1/24 (pow eps 2))))
(* eps (+ 1 (* (pow eps 2) (- (* 1/1920 (pow eps 2)) 1/24))))
(* eps (+ 1 (* (pow eps 2) (- (* (pow eps 2) (+ 1/1920 (* -1/322560 (pow eps 2)))) 1/24))))
(* 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))))
(* eps (cos x))
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x)))))))
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* eps (+ (* -1/6 (cos x)) (* 1/24 (* eps (sin x)))))))))
(cos x)
(+ (cos x) (* 1/2 (* eps (sin x))))
(+ (cos x) (* eps (- (* -1/6 (* eps (cos x))) (* -1/2 (sin x)))))
(+ (cos x) (* eps (- (* -1/6 (* eps (cos x))) (* -1/2 (sin x)))))
(pow eps 2)
(pow eps 2)
(pow eps 2)
(pow eps 2)
x
(+ eps x)
(+ x (* eps (+ 1 (* -1/6 (* eps x)))))
(+ x (* eps (+ 1 (* -1/6 (* eps 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)))))
(* 1/36 (* (pow eps 4) (+ 1/2 (* 1/2 (cos (* 2 x))))))
(* (pow eps 4) (- (+ (* -1/3 (/ (+ 1/2 (* 1/2 (cos (* 2 x)))) (pow eps 2))) (* 1/36 (+ 1/2 (* 1/2 (cos (* 2 x)))))) (* 1/4 (/ (- 1/2 (* 1/2 (cos (* 2 x)))) (pow eps 2)))))
(* (pow eps 4) (- (+ (* -1/3 (/ (+ 1/2 (* 1/2 (cos (* 2 x)))) (pow eps 2))) (+ (* 1/36 (+ 1/2 (* 1/2 (cos (* 2 x))))) (+ (* 1/2 (/ (cos (* 2 x)) (pow eps 4))) (/ 1/2 (pow eps 4))))) (* 1/4 (/ (- 1/2 (* 1/2 (cos (* 2 x)))) (pow eps 2)))))
(* (pow eps 4) (- (+ (* -1/3 (/ (+ 1/2 (* 1/2 (cos (* 2 x)))) (pow eps 2))) (+ (* 1/36 (+ 1/2 (* 1/2 (cos (* 2 x))))) (+ (* 1/2 (/ (cos (* 2 x)) (pow eps 4))) (/ 1/2 (pow eps 4))))) (* 1/4 (/ (- 1/2 (* 1/2 (cos (* 2 x)))) (pow eps 2)))))
(* 1/4 (pow eps 2))
(* 1/4 (pow eps 2))
(* 1/4 (pow eps 2))
(* 1/4 (pow eps 2))
(* 1/4 (* (pow eps 2) (- 1/2 (* 1/2 (cos (* 2 x))))))
(* 1/4 (* (pow eps 2) (- 1/2 (* 1/2 (cos (* 2 x))))))
(* 1/4 (* (pow eps 2) (- 1/2 (* 1/2 (cos (* 2 x))))))
(* 1/4 (* (pow eps 2) (- 1/2 (* 1/2 (cos (* 2 x))))))
(- (sin (+ eps x)) (sin x))
(- (sin (+ eps x)) (sin x))
(- (sin (+ eps x)) (sin x))
(- (sin (+ eps x)) (sin x))
(* -1/6 (* (pow eps 3) (cos x)))
(* (pow eps 3) (+ (* -1/2 (/ (sin x) eps)) (* -1/6 (cos x))))
(* (pow eps 3) (+ (* -1/2 (/ (sin x) eps)) (+ (* -1/6 (cos x)) (/ (cos x) (pow eps 2)))))
(* (pow eps 3) (+ (* -1/2 (/ (sin x) eps)) (+ (* -1/6 (cos x)) (/ (cos x) (pow eps 2)))))
(* -1/6 (* (pow eps 2) (cos x)))
(* (pow eps 2) (+ (* -1/2 (/ (sin x) eps)) (* -1/6 (cos x))))
(* (pow eps 2) (+ (* -1/2 (/ (sin x) eps)) (+ (* -1/6 (cos x)) (/ (cos x) (pow eps 2)))))
(* (pow eps 2) (+ (* -1/2 (/ (sin x) eps)) (+ (* -1/6 (cos x)) (/ (cos x) (pow eps 2)))))
(* -1/6 (pow eps 2))
(* (pow eps 2) (- (/ 1 (pow eps 2)) 1/6))
(* (pow eps 2) (- (/ 1 (pow eps 2)) 1/6))
(* (pow eps 2) (- (/ 1 (pow eps 2)) 1/6))
(- (sin (+ eps x)) (sin x))
(- (sin (+ eps x)) (sin x))
(- (sin (+ eps x)) (sin x))
(- (sin (+ eps x)) (sin x))
(* -1/6 (* (pow eps 3) (cos x)))
(* (pow eps 3) (+ (* -1/2 (/ (sin x) eps)) (* -1/6 (cos x))))
(* (pow eps 3) (+ (* -1/2 (/ (sin x) eps)) (+ (* -1/6 (cos x)) (/ (cos x) (pow eps 2)))))
(* (pow eps 3) (+ (* -1/2 (/ (sin x) eps)) (+ (* -1/6 (cos x)) (/ (cos x) (pow eps 2)))))
(* -1/6 (* (pow eps 2) (cos x)))
(* (pow eps 2) (+ (* -1/2 (/ (sin x) eps)) (* -1/6 (cos x))))
(* (pow eps 2) (+ (* -1/2 (/ (sin x) eps)) (+ (* -1/6 (cos x)) (/ (cos x) (pow eps 2)))))
(* (pow eps 2) (+ (* -1/2 (/ (sin x) eps)) (+ (* -1/6 (cos x)) (/ (cos x) (pow eps 2)))))
(* (pow eps 2) (- (* 1/12 (pow x 2)) 1/6))
(* (pow eps 2) (- (+ (* -1/2 (/ x eps)) (* 1/12 (pow x 2))) 1/6))
(* (pow eps 2) (- (+ (* -1/2 (/ x eps)) (+ (* -1/2 (/ (pow x 2) (pow eps 2))) (+ (* 1/12 (pow x 2)) (/ 1 (pow eps 2))))) 1/6))
(* (pow eps 2) (- (+ (* -1/2 (/ x eps)) (+ (* -1/2 (/ (pow x 2) (pow eps 2))) (+ (* 1/12 (pow x 2)) (/ 1 (pow eps 2))))) 1/6))
(* 1/12 (pow eps 3))
(* (pow eps 3) (+ 1/12 (* 1/12 (/ x eps))))
(* (pow eps 3) (- (+ 1/12 (* 1/12 (/ x eps))) (/ 1/2 (pow eps 2))))
(* (pow eps 3) (- (+ 1/12 (* 1/12 (/ x eps))) (/ 1/2 (pow eps 2))))
(* (pow eps 3) (- (* 1/12 (pow x 2)) 1/6))
(* (pow eps 3) (- (+ (* -1/2 (/ x eps)) (+ (* 1/12 (/ (pow x 3) 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 3) eps)) (+ (* 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 3) eps)) (+ (* 1/12 (pow x 2)) (/ 1 (pow eps 2)))))) 1/6))
(- (sin (+ eps x)) (sin x))
(- (sin (+ eps x)) (sin x))
(- (sin (+ eps x)) (sin x))
(- (sin (+ eps x)) (sin x))
(* -1/6 (* (pow eps 3) (cos x)))
(* (pow eps 3) (+ (* -1/2 (/ (sin x) eps)) (* -1/6 (cos x))))
(* (pow eps 3) (+ (* -1/2 (/ (sin x) eps)) (+ (* -1/6 (cos x)) (/ (cos x) (pow eps 2)))))
(* (pow eps 3) (+ (* -1/2 (/ (sin x) eps)) (+ (* -1/6 (cos x)) (/ (cos x) (pow eps 2)))))
(* 1/2 eps)
(* eps (+ 1/2 (/ x eps)))
(* eps (+ 1/2 (/ x eps)))
(* eps (+ 1/2 (/ x 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 (sin (* 1/2 eps)))
(* 2 (sin (* 1/2 eps)))
(* 2 (sin (* 1/2 eps)))
(* 2 (sin (* 1/2 eps)))
(sin (* 1/2 eps))
(sin (* 1/2 eps))
(sin (* 1/2 eps))
(sin (* 1/2 eps))
(- (sin (+ eps x)) (sin x))
(- (sin (+ eps x)) (sin x))
(- (sin (+ eps x)) (sin x))
(- (sin (+ eps x)) (sin x))
(* -1/6 (* (pow eps 2) (cos x)))
(* (pow eps 2) (+ (* -1/6 (cos x)) (* 1/2 (/ (sin x) eps))))
(* (pow eps 2) (- (+ (* -1/6 (cos x)) (/ (cos x) (pow eps 2))) (* -1/2 (/ (sin x) eps))))
(* (pow eps 2) (- (+ (* -1/6 (cos x)) (/ (cos x) (pow eps 2))) (* -1/2 (/ (sin x) eps))))
(pow eps 2)
(pow eps 2)
(pow eps 2)
(pow eps 2)
(* -1/6 (* (pow eps 2) x))
(* (pow eps 2) (+ (* -1/6 x) (/ 1 eps)))
(* (pow eps 2) (+ (* -1/6 x) (+ (/ 1 eps) (/ x (pow eps 2)))))
(* (pow eps 2) (+ (* -1/6 x) (+ (/ 1 eps) (/ x (pow eps 2)))))
(cos (* 1/2 (+ eps (* 2 x))))
(cos (* 1/2 (+ eps (* 2 x))))
(cos (* 1/2 (+ eps (* 2 x))))
(cos (* 1/2 (+ eps (* 2 x))))
(* 1/36 (* (pow eps 4) (+ 1/2 (* 1/2 (cos (* 2 x))))))
(* (pow eps 4) (- (+ (* -1/3 (/ (+ 1/2 (* 1/2 (cos (* 2 x)))) (pow eps 2))) (* 1/36 (+ 1/2 (* 1/2 (cos (* 2 x)))))) (* 1/4 (/ (- 1/2 (* 1/2 (cos (* 2 x)))) (pow eps 2)))))
(* (pow eps 4) (- (+ (* -1/3 (/ (+ 1/2 (* 1/2 (cos (* 2 x)))) (pow eps 2))) (+ (* 1/36 (+ 1/2 (* 1/2 (cos (* 2 x))))) (+ (* 1/2 (/ (cos (* 2 x)) (pow eps 4))) (/ 1/2 (pow eps 4))))) (* 1/4 (/ (- 1/2 (* 1/2 (cos (* 2 x)))) (pow eps 2)))))
(* (pow eps 4) (- (+ (* -1/3 (/ (+ 1/2 (* 1/2 (cos (* 2 x)))) (pow eps 2))) (+ (* 1/36 (+ 1/2 (* 1/2 (cos (* 2 x))))) (+ (* 1/2 (/ (cos (* 2 x)) (pow eps 4))) (/ 1/2 (pow eps 4))))) (* 1/4 (/ (- 1/2 (* 1/2 (cos (* 2 x)))) (pow eps 2)))))
(* 1/4 (pow eps 2))
(* 1/4 (pow eps 2))
(* 1/4 (pow eps 2))
(* 1/4 (pow eps 2))
(* 1/4 (* (pow eps 2) (- 1/2 (* 1/2 (cos (* 2 x))))))
(* 1/4 (* (pow eps 2) (- 1/2 (* 1/2 (cos (* 2 x))))))
(* 1/4 (* (pow eps 2) (- 1/2 (* 1/2 (cos (* 2 x))))))
(* 1/4 (* (pow eps 2) (- 1/2 (* 1/2 (cos (* 2 x))))))
(- (sin (- x (* -1 eps))) (sin x))
(- (sin (- x (* -1 eps))) (sin x))
(- (sin (- x (* -1 eps))) (sin x))
(- (sin (- x (* -1 eps))) (sin x))
(* -1/6 (* (pow eps 3) (cos x)))
(* -1 (* (pow eps 3) (+ (* 1/6 (cos x)) (* 1/2 (/ (sin x) eps)))))
(* -1 (* (pow eps 3) (+ (* -1 (/ (+ (* -1/2 (sin x)) (/ (cos x) eps)) eps)) (* 1/6 (cos x)))))
(* -1 (* (pow eps 3) (+ (* -1 (/ (+ (* -1/2 (sin x)) (/ (cos x) eps)) eps)) (* 1/6 (cos x)))))
(* -1/6 (* (pow eps 2) (cos x)))
(* (pow eps 2) (+ (* -1/2 (/ (sin x) eps)) (* -1/6 (cos x))))
(* (pow eps 2) (+ (* -1 (/ (+ (* -1 (/ (cos x) eps)) (* 1/2 (sin x))) eps)) (* -1/6 (cos x))))
(* (pow eps 2) (+ (* -1 (/ (+ (* -1 (/ (cos x) eps)) (* 1/2 (sin x))) eps)) (* -1/6 (cos x))))
(* -1/6 (pow eps 2))
(* (pow eps 2) (- (/ 1 (pow eps 2)) 1/6))
(* (pow eps 2) (- (/ 1 (pow eps 2)) 1/6))
(* (pow eps 2) (- (/ 1 (pow eps 2)) 1/6))
(- (sin (- x (* -1 eps))) (sin x))
(- (sin (- x (* -1 eps))) (sin x))
(- (sin (- x (* -1 eps))) (sin x))
(- (sin (- x (* -1 eps))) (sin x))
(* -1/6 (* (pow eps 3) (cos x)))
(* -1 (* (pow eps 3) (+ (* 1/6 (cos x)) (* 1/2 (/ (sin x) eps)))))
(* -1 (* (pow eps 3) (+ (* -1 (/ (+ (* -1/2 (sin x)) (/ (cos x) eps)) eps)) (* 1/6 (cos x)))))
(* -1 (* (pow eps 3) (+ (* -1 (/ (+ (* -1/2 (sin x)) (/ (cos x) eps)) eps)) (* 1/6 (cos x)))))
(* -1/6 (* (pow eps 2) (cos x)))
(* (pow eps 2) (+ (* -1/2 (/ (sin x) eps)) (* -1/6 (cos x))))
(* (pow eps 2) (+ (* -1 (/ (+ (* -1 (/ (cos x) eps)) (* 1/2 (sin x))) eps)) (* -1/6 (cos x))))
(* (pow eps 2) (+ (* -1 (/ (+ (* -1 (/ (cos x) eps)) (* 1/2 (sin x))) eps)) (* -1/6 (cos x))))
(* (pow eps 2) (- (* 1/12 (pow x 2)) 1/6))
(* (pow eps 2) (- (+ (* -1/2 (/ x eps)) (* 1/12 (pow x 2))) 1/6))
(* (pow eps 2) (- (+ (* -1 (/ (+ (* -1 (/ (+ 1 (* -1/2 (pow x 2))) eps)) (* 1/2 x)) eps)) (* 1/12 (pow x 2))) 1/6))
(* (pow eps 2) (- (+ (* -1 (/ (+ (* -1 (/ (+ 1 (* -1/2 (pow x 2))) eps)) (* 1/2 x)) eps)) (* 1/12 (pow x 2))) 1/6))
(* 1/12 (pow eps 3))
(* -1 (* (pow eps 3) (- (* -1/12 (/ x eps)) 1/12)))
(* -1 (* (pow eps 3) (- (* -1 (/ (- (* 1/12 x) (* 1/2 (/ 1 eps))) eps)) 1/12)))
(* -1 (* (pow eps 3) (- (* -1 (/ (- (* 1/12 x) (* 1/2 (/ 1 eps))) eps)) 1/12)))
(* -1 (* (pow eps 3) (+ 1/6 (* -1/12 (pow x 2)))))
(* -1 (* (pow eps 3) (+ 1/6 (+ (* -1 (/ (+ (* -1/2 x) (* 1/12 (pow x 3))) eps)) (* -1/12 (pow x 2))))))
(* -1 (* (pow eps 3) (+ 1/6 (+ (* -1 (/ (+ (* -1 (/ (- (* 1/2 (pow x 2)) 1) eps)) (+ (* -1/2 x) (* 1/12 (pow x 3)))) eps)) (* -1/12 (pow x 2))))))
(* -1 (* (pow eps 3) (+ 1/6 (+ (* -1 (/ (+ (* -1 (/ (- (* 1/2 (pow x 2)) 1) eps)) (+ (* -1/2 x) (* 1/12 (pow x 3)))) eps)) (* -1/12 (pow x 2))))))
(- (sin (- x (* -1 eps))) (sin x))
(- (sin (- x (* -1 eps))) (sin x))
(- (sin (- x (* -1 eps))) (sin x))
(- (sin (- x (* -1 eps))) (sin x))
(* -1/6 (* (pow eps 3) (cos x)))
(* -1 (* (pow eps 3) (+ (* 1/6 (cos x)) (* 1/2 (/ (sin x) eps)))))
(* -1 (* (pow eps 3) (+ (* -1 (/ (+ (* -1/2 (sin x)) (/ (cos x) eps)) eps)) (* 1/6 (cos x)))))
(* -1 (* (pow eps 3) (+ (* -1 (/ (+ (* -1/2 (sin x)) (/ (cos x) eps)) eps)) (* 1/6 (cos x)))))
(* 1/2 eps)
(* -1 (* eps (- (* -1 (/ x eps)) 1/2)))
(* -1 (* eps (- (* -1 (/ x eps)) 1/2)))
(* -1 (* eps (- (* -1 (/ x eps)) 1/2)))
(* 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 (sin (* 1/2 eps)))
(* 2 (sin (* 1/2 eps)))
(* 2 (sin (* 1/2 eps)))
(* 2 (sin (* 1/2 eps)))
(sin (* 1/2 eps))
(sin (* 1/2 eps))
(sin (* 1/2 eps))
(sin (* 1/2 eps))
(- (sin (- x (* -1 eps))) (sin x))
(- (sin (- x (* -1 eps))) (sin x))
(- (sin (- x (* -1 eps))) (sin x))
(- (sin (- x (* -1 eps))) (sin x))
(* -1/6 (* (pow eps 2) (cos x)))
(* (pow eps 2) (+ (* -1/6 (cos x)) (* 1/2 (/ (sin x) eps))))
(* (pow eps 2) (+ (* -1 (/ (- (* -1 (/ (cos x) eps)) (* 1/2 (sin x))) eps)) (* -1/6 (cos x))))
(* (pow eps 2) (+ (* -1 (/ (- (* -1 (/ (cos x) eps)) (* 1/2 (sin x))) eps)) (* -1/6 (cos x))))
(pow eps 2)
(pow eps 2)
(pow eps 2)
(pow eps 2)
(* -1/6 (* (pow eps 2) x))
(* (pow eps 2) (+ (* -1/6 x) (/ 1 eps)))
(* (pow eps 2) (+ (* -1 (/ (- (* -1 (/ x eps)) 1) eps)) (* -1/6 x)))
(* (pow eps 2) (+ (* -1 (/ (- (* -1 (/ x eps)) 1) eps)) (* -1/6 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))))
(pow (+ 1 (* -1/6 (pow eps 2))) 2)
(+ (* (pow x 2) (- (* -1 (pow (+ 1 (* -1/6 (pow eps 2))) 2)) (* 1/4 (pow eps 2)))) (pow (+ 1 (* -1/6 (pow eps 2))) 2))
(+ (* (pow x 2) (- (+ (* -1 (pow (+ 1 (* -1/6 (pow eps 2))) 2)) (* (pow x 2) (- (* 1/3 (pow (+ 1 (* -1/6 (pow eps 2))) 2)) (* -1/12 (pow eps 2))))) (* 1/4 (pow eps 2)))) (pow (+ 1 (* -1/6 (pow eps 2))) 2))
(+ (* (pow x 2) (- (+ (* -1 (pow (+ 1 (* -1/6 (pow eps 2))) 2)) (* (pow x 2) (- (+ (* 1/3 (pow (+ 1 (* -1/6 (pow eps 2))) 2)) (* (pow x 2) (- (* -2/45 (pow (+ 1 (* -1/6 (pow eps 2))) 2)) (* 1/90 (pow eps 2))))) (* -1/12 (pow eps 2))))) (* 1/4 (pow eps 2)))) (pow (+ 1 (* -1/6 (pow eps 2))) 2))
(* 1/4 (* (pow eps 2) (pow x 2)))
(* (pow x 2) (+ (* -1/12 (* (pow eps 2) (pow x 2))) (* 1/4 (pow eps 2))))
(* (pow x 2) (+ (* 1/4 (pow eps 2)) (* (pow x 2) (+ (* -1/12 (pow eps 2)) (* 1/90 (* (pow eps 2) (pow x 2)))))))
(* (pow x 2) (+ (* 1/4 (pow eps 2)) (* (pow x 2) (+ (* -1/12 (pow eps 2)) (* (pow x 2) (+ (* -1/1260 (* (pow eps 2) (pow x 2))) (* 1/90 (pow eps 2))))))))
1
(+ 1 (* -1 (pow x 2)))
(+ 1 (* (pow x 2) (- (* 1/3 (pow x 2)) 1)))
(+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/3 (* -2/45 (pow x 2)))) 1)))
(sin eps)
(+ (sin eps) (* x (- (cos eps) 1)))
(+ (sin eps) (* x (- (+ (cos eps) (* -1/2 (* x (sin eps)))) 1)))
(+ (sin eps) (* x (- (+ (cos eps) (* x (+ (* -1/2 (sin eps)) (* x (+ 1/6 (* -1/6 (cos eps))))))) 1)))
(* eps (+ 1 (* -1/6 (pow eps 2))))
(+ (* -1/2 (* (pow eps 2) x)) (* eps (+ 1 (* -1/6 (pow eps 2)))))
(+ (* eps (+ 1 (* -1/6 (pow eps 2)))) (* x (+ (* -1/2 (* eps (* x (+ 1 (* -1/6 (pow eps 2)))))) (* -1/2 (pow eps 2)))))
(+ (* eps (+ 1 (* -1/6 (pow eps 2)))) (* x (+ (* -1/2 (pow eps 2)) (* x (+ (* -1/2 (* eps (+ 1 (* -1/6 (pow eps 2))))) (* 1/12 (* (pow eps 2) x)))))))
(+ 1 (* -1/6 (pow eps 2)))
(+ 1 (+ (* -1/2 (* eps x)) (* -1/6 (pow eps 2))))
(+ 1 (+ (* -1/6 (pow eps 2)) (* x (+ (* -1/2 eps) (* -1/2 (* x (+ 1 (* -1/6 (pow eps 2)))))))))
(+ 1 (+ (* -1/6 (pow eps 2)) (* x (+ (* -1/2 eps) (* x (+ (* -1/2 (+ 1 (* -1/6 (pow eps 2)))) (* 1/12 (* eps x))))))))
(sin eps)
(+ (sin eps) (* x (- (cos eps) 1)))
(+ (sin eps) (* x (- (+ (cos eps) (* -1/2 (* x (sin eps)))) 1)))
(+ (sin eps) (* x (- (+ (cos eps) (* x (+ (* -1/2 (sin eps)) (* x (+ 1/6 (* -1/6 (cos eps))))))) 1)))
(* eps (+ 1 (* -1/6 (pow eps 2))))
(+ (* -1/2 (* (pow eps 2) x)) (* eps (+ 1 (* -1/6 (pow eps 2)))))
(+ (* eps (+ 1 (* -1/6 (pow eps 2)))) (* x (+ (* -1/2 (* eps (* x (+ 1 (* -1/6 (pow eps 2)))))) (* -1/2 (pow eps 2)))))
(+ (* eps (+ 1 (* -1/6 (pow eps 2)))) (* x (+ (* -1/2 (pow eps 2)) (* x (+ (* -1/2 (* eps (+ 1 (* -1/6 (pow eps 2))))) (* 1/12 (* (pow eps 2) x)))))))
(+ 1 (* -1/6 (pow eps 2)))
(+ 1 (+ (* -1/2 (* eps x)) (* -1/6 (pow eps 2))))
(+ 1 (+ (* -1/6 (pow eps 2)) (* x (+ (* -1/2 eps) (* -1/2 (* x (+ 1 (* -1/6 (pow eps 2)))))))))
(+ 1 (+ (* -1/6 (pow eps 2)) (* x (+ (* -1/2 eps) (* x (+ (* -1/2 (+ 1 (* -1/6 (pow eps 2)))) (* 1/12 (* eps x))))))))
(+ 1 (* -1/6 (pow eps 2)))
(+ 1 (+ (* -1/2 (* eps x)) (* -1/6 (pow eps 2))))
(+ 1 (+ (* -1/6 (pow eps 2)) (* x (+ (* -1/2 eps) (* -1/2 (* x (+ 1 (* -1/6 (pow eps 2)))))))))
(+ 1 (+ (* -1/6 (pow eps 2)) (* x (+ (* -1/2 eps) (* -1/2 (* x (+ 1 (* -1/6 (pow eps 2)))))))))
(* eps (- (* 1/12 (pow eps 2)) 1/2))
(+ (* 1/12 (* (pow eps 2) x)) (* eps (- (* 1/12 (pow eps 2)) 1/2)))
(+ (* 1/12 (* (pow eps 2) x)) (* eps (- (* 1/12 (pow eps 2)) 1/2)))
(+ (* 1/12 (* (pow eps 2) x)) (* eps (- (* 1/12 (pow eps 2)) 1/2)))
(+ 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)) (* x (+ (* 1/12 (* (pow eps 2) x)) (* eps (- (* 1/12 (pow eps 2)) 1/2))))))))
(sin eps)
(+ (sin eps) (* x (- (cos eps) 1)))
(+ (sin eps) (* x (- (+ (cos eps) (* -1/2 (* x (sin eps)))) 1)))
(+ (sin eps) (* x (- (+ (cos eps) (* x (+ (* -1/2 (sin eps)) (* x (+ 1/6 (* -1/6 (cos eps))))))) 1)))
(* eps (+ 1 (* -1/6 (pow eps 2))))
(+ (* -1/2 (* (pow eps 2) x)) (* eps (+ 1 (* -1/6 (pow eps 2)))))
(+ (* eps (+ 1 (* -1/6 (pow eps 2)))) (* x (+ (* -1/2 (* eps (* x (+ 1 (* -1/6 (pow eps 2)))))) (* -1/2 (pow eps 2)))))
(+ (* eps (+ 1 (* -1/6 (pow eps 2)))) (* x (+ (* -1/2 (pow eps 2)) (* x (+ (* -1/2 (* eps (+ 1 (* -1/6 (pow eps 2))))) (* 1/12 (* (pow eps 2) x)))))))
(* 1/2 eps)
(+ x (* 1/2 eps))
(+ x (* 1/2 eps))
(+ x (* 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))))))))
(pow x 2)
(* (pow x 2) (+ 1 (* -1/3 (pow x 2))))
(* (pow x 2) (+ 1 (* (pow x 2) (- (* 2/45 (pow x 2)) 1/3))))
(* (pow x 2) (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 2/45 (* -1/315 (pow x 2)))) 1/3))))
(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)))
(+ 1 (* -1/6 (pow eps 2)))
(+ 1 (+ (* -1/6 (pow eps 2)) (* 1/2 (* eps x))))
(+ 1 (+ (* -1/6 (pow eps 2)) (* x (- (* -1/2 (* x (+ 1 (* -1/6 (pow eps 2))))) (* -1/2 eps)))))
(+ 1 (+ (* -1/6 (pow eps 2)) (* x (- (* x (+ (* -1/2 (+ 1 (* -1/6 (pow eps 2)))) (* -1/12 (* eps x)))) (* -1/2 eps)))))
eps
(+ eps (* x (+ 1 (* -1/6 (pow eps 2)))))
(+ eps (* x (+ 1 (* -1/6 (pow eps 2)))))
(+ eps (* x (+ 1 (* -1/6 (pow eps 2)))))
(* 1/12 x)
(* 1/12 x)
(* 1/12 x)
(* 1/12 x)
(cos (* 1/2 eps))
(+ (cos (* 1/2 eps)) (* -1 (* x (sin (* 1/2 eps)))))
(+ (cos (* 1/2 eps)) (* x (- (* -1/2 (* x (cos (* 1/2 eps)))) (sin (* 1/2 eps)))))
(+ (cos (* 1/2 eps)) (* x (- (* x (+ (* -1/2 (cos (* 1/2 eps))) (* 1/6 (* x (sin (* 1/2 eps)))))) (sin (* 1/2 eps)))))
(- (* (+ 1/2 (* 1/2 (cos (* 2 x)))) (pow (+ 1 (* -1/6 (pow eps 2))) 2)) (* 1/4 (* (pow eps 2) (- 1/2 (* 1/2 (cos (* 2 x)))))))
(- (* (+ 1/2 (* 1/2 (cos (* 2 x)))) (pow (+ 1 (* -1/6 (pow eps 2))) 2)) (* 1/4 (* (pow eps 2) (- 1/2 (* 1/2 (cos (* 2 x)))))))
(- (* (+ 1/2 (* 1/2 (cos (* 2 x)))) (pow (+ 1 (* -1/6 (pow eps 2))) 2)) (* 1/4 (* (pow eps 2) (- 1/2 (* 1/2 (cos (* 2 x)))))))
(- (* (+ 1/2 (* 1/2 (cos (* 2 x)))) (pow (+ 1 (* -1/6 (pow eps 2))) 2)) (* 1/4 (* (pow eps 2) (- 1/2 (* 1/2 (cos (* 2 x)))))))
(* 1/4 (* (pow eps 2) (- 1/2 (* 1/2 (cos (* 2 x))))))
(* 1/4 (* (pow eps 2) (- 1/2 (* 1/2 (cos (* 2 x))))))
(* 1/4 (* (pow eps 2) (- 1/2 (* 1/2 (cos (* 2 x))))))
(* 1/4 (* (pow eps 2) (- 1/2 (* 1/2 (cos (* 2 x))))))
(+ 1/2 (* 1/2 (cos (* 2 x))))
(+ 1/2 (* 1/2 (cos (* 2 x))))
(+ 1/2 (* 1/2 (cos (* 2 x))))
(+ 1/2 (* 1/2 (cos (* 2 x))))
(- (sin (+ eps x)) (sin x))
(- (sin (+ eps x)) (sin x))
(- (sin (+ eps x)) (sin x))
(- (sin (+ eps x)) (sin x))
(* eps (+ (* -1/2 (* eps (sin x))) (* (cos x) (+ 1 (* -1/6 (pow eps 2))))))
(* eps (+ (* -1/2 (* eps (sin x))) (* (cos x) (+ 1 (* -1/6 (pow eps 2))))))
(* eps (+ (* -1/2 (* eps (sin x))) (* (cos x) (+ 1 (* -1/6 (pow eps 2))))))
(* eps (+ (* -1/2 (* eps (sin x))) (* (cos x) (+ 1 (* -1/6 (pow eps 2))))))
(+ (* -1/2 (* eps (sin x))) (* (cos x) (+ 1 (* -1/6 (pow eps 2)))))
(+ (* -1/2 (* eps (sin x))) (* (cos x) (+ 1 (* -1/6 (pow eps 2)))))
(+ (* -1/2 (* eps (sin x))) (* (cos x) (+ 1 (* -1/6 (pow eps 2)))))
(+ (* -1/2 (* eps (sin x))) (* (cos x) (+ 1 (* -1/6 (pow eps 2)))))
(- (sin (+ eps x)) (sin x))
(- (sin (+ eps x)) (sin x))
(- (sin (+ eps x)) (sin x))
(- (sin (+ eps x)) (sin x))
(* eps (+ (* -1/2 (* eps (sin x))) (* (cos x) (+ 1 (* -1/6 (pow eps 2))))))
(* eps (+ (* -1/2 (* eps (sin x))) (* (cos x) (+ 1 (* -1/6 (pow eps 2))))))
(* eps (+ (* -1/2 (* eps (sin x))) (* (cos x) (+ 1 (* -1/6 (pow eps 2))))))
(* eps (+ (* -1/2 (* eps (sin x))) (* (cos x) (+ 1 (* -1/6 (pow eps 2))))))
(+ (* -1/2 (* eps (sin x))) (* (cos x) (+ 1 (* -1/6 (pow eps 2)))))
(+ (* -1/2 (* eps (sin x))) (* (cos x) (+ 1 (* -1/6 (pow eps 2)))))
(+ (* -1/2 (* eps (sin x))) (* (cos x) (+ 1 (* -1/6 (pow eps 2)))))
(+ (* -1/2 (* eps (sin x))) (* (cos x) (+ 1 (* -1/6 (pow eps 2)))))
(* -1/2 (* (pow x 2) (+ 1 (* -1/6 (pow eps 2)))))
(* (pow x 2) (+ (* -1/2 (+ 1 (* -1/6 (pow eps 2)))) (* -1/2 (/ eps x))))
(* (pow x 2) (+ (* -1/2 (+ 1 (* -1/6 (pow eps 2)))) (+ (* -1/2 (/ eps x)) (+ (* -1/6 (/ (pow eps 2) (pow x 2))) (/ 1 (pow x 2))))))
(* (pow x 2) (+ (* -1/2 (+ 1 (* -1/6 (pow eps 2)))) (+ (* -1/2 (/ eps x)) (+ (* -1/6 (/ (pow eps 2) (pow x 2))) (/ 1 (pow x 2))))))
(* 1/12 (* (pow eps 2) x))
(* x (+ (* 1/12 (pow eps 2)) (/ (* eps (- (* 1/12 (pow eps 2)) 1/2)) x)))
(* x (+ (* 1/12 (pow eps 2)) (/ (* eps (- (* 1/12 (pow eps 2)) 1/2)) x)))
(* x (+ (* 1/12 (pow eps 2)) (/ (* eps (- (* 1/12 (pow eps 2)) 1/2)) x)))
(* 1/12 (* (pow eps 2) (pow x 3)))
(* (pow x 3) (+ (* 1/12 (pow eps 2)) (/ (* eps (- (* 1/12 (pow eps 2)) 1/2)) x)))
(* (pow x 3) (+ (* -1/2 (/ (pow eps 2) (pow x 2))) (+ (* 1/12 (pow eps 2)) (/ (* eps (- (* 1/12 (pow eps 2)) 1/2)) x))))
(* (pow x 3) (+ (* -1/2 (/ (pow eps 2) (pow x 2))) (+ (* -1/6 (/ (pow eps 3) (pow x 3))) (+ (* 1/12 (pow eps 2)) (+ (/ eps (pow x 3)) (/ (* eps (- (* 1/12 (pow eps 2)) 1/2)) x))))))
(- (sin (+ eps x)) (sin x))
(- (sin (+ eps x)) (sin x))
(- (sin (+ eps x)) (sin x))
(- (sin (+ eps x)) (sin x))
(* eps (+ (* -1/2 (* eps (sin x))) (* (cos x) (+ 1 (* -1/6 (pow eps 2))))))
(* eps (+ (* -1/2 (* eps (sin x))) (* (cos x) (+ 1 (* -1/6 (pow eps 2))))))
(* eps (+ (* -1/2 (* eps (sin x))) (* (cos x) (+ 1 (* -1/6 (pow eps 2))))))
(* eps (+ (* -1/2 (* eps (sin x))) (* (cos x) (+ 1 (* -1/6 (pow eps 2))))))
x
(* x (+ 1 (* 1/2 (/ eps x))))
(* x (+ 1 (* 1/2 (/ eps x))))
(* x (+ 1 (* 1/2 (/ eps 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))))
(- 1/2 (* 1/2 (cos (* 2 x))))
(- 1/2 (* 1/2 (cos (* 2 x))))
(- 1/2 (* 1/2 (cos (* 2 x))))
(- 1/2 (* 1/2 (cos (* 2 x))))
(- (sin (+ eps x)) (sin x))
(- (sin (+ eps x)) (sin x))
(- (sin (+ eps x)) (sin x))
(- (sin (+ eps x)) (sin x))
(- (* (cos x) (+ 1 (* -1/6 (pow eps 2)))) (* -1/2 (* eps (sin x))))
(- (* (cos x) (+ 1 (* -1/6 (pow eps 2)))) (* -1/2 (* eps (sin x))))
(- (* (cos x) (+ 1 (* -1/6 (pow eps 2)))) (* -1/2 (* eps (sin x))))
(- (* (cos x) (+ 1 (* -1/6 (pow eps 2)))) (* -1/2 (* eps (sin x))))
(* x (+ 1 (* -1/6 (pow eps 2))))
(* x (+ 1 (+ (* -1/6 (pow eps 2)) (/ eps x))))
(* x (+ 1 (+ (* -1/6 (pow eps 2)) (/ eps x))))
(* x (+ 1 (+ (* -1/6 (pow eps 2)) (/ eps x))))
(* 1/12 x)
(* 1/12 x)
(* 1/12 x)
(* 1/12 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))))
(- (* (+ 1/2 (* 1/2 (cos (neg (* -2 x))))) (pow (+ 1 (* -1/6 (pow eps 2))) 2)) (* 1/4 (* (pow eps 2) (- 1/2 (* 1/2 (cos (neg (* -2 x))))))))
(- (* (+ 1/2 (* 1/2 (cos (neg (* -2 x))))) (pow (+ 1 (* -1/6 (pow eps 2))) 2)) (* 1/4 (* (pow eps 2) (- 1/2 (* 1/2 (cos (neg (* -2 x))))))))
(- (* (+ 1/2 (* 1/2 (cos (neg (* -2 x))))) (pow (+ 1 (* -1/6 (pow eps 2))) 2)) (* 1/4 (* (pow eps 2) (- 1/2 (* 1/2 (cos (neg (* -2 x))))))))
(- (* (+ 1/2 (* 1/2 (cos (neg (* -2 x))))) (pow (+ 1 (* -1/6 (pow eps 2))) 2)) (* 1/4 (* (pow eps 2) (- 1/2 (* 1/2 (cos (neg (* -2 x))))))))
(* 1/4 (* (pow eps 2) (- 1/2 (* 1/2 (cos (neg (* -2 x)))))))
(* 1/4 (* (pow eps 2) (- 1/2 (* 1/2 (cos (neg (* -2 x)))))))
(* 1/4 (* (pow eps 2) (- 1/2 (* 1/2 (cos (neg (* -2 x)))))))
(* 1/4 (* (pow eps 2) (- 1/2 (* 1/2 (cos (neg (* -2 x)))))))
(+ 1/2 (* 1/2 (cos (neg (* -2 x)))))
(+ 1/2 (* 1/2 (cos (neg (* -2 x)))))
(+ 1/2 (* 1/2 (cos (neg (* -2 x)))))
(+ 1/2 (* 1/2 (cos (neg (* -2 x)))))
(- (sin (- eps (* -1 x))) (sin x))
(- (sin (- eps (* -1 x))) (sin x))
(- (sin (- eps (* -1 x))) (sin x))
(- (sin (- eps (* -1 x))) (sin x))
(* eps (+ (* -1/2 (* eps (sin x))) (* (cos x) (+ 1 (* -1/6 (pow eps 2))))))
(* eps (+ (* -1/2 (* eps (sin x))) (* (cos x) (+ 1 (* -1/6 (pow eps 2))))))
(* eps (+ (* -1/2 (* eps (sin x))) (* (cos x) (+ 1 (* -1/6 (pow eps 2))))))
(* eps (+ (* -1/2 (* eps (sin x))) (* (cos x) (+ 1 (* -1/6 (pow eps 2))))))
(+ (* -1/2 (* eps (sin x))) (* (cos x) (+ 1 (* -1/6 (pow eps 2)))))
(+ (* -1/2 (* eps (sin x))) (* (cos x) (+ 1 (* -1/6 (pow eps 2)))))
(+ (* -1/2 (* eps (sin x))) (* (cos x) (+ 1 (* -1/6 (pow eps 2)))))
(+ (* -1/2 (* eps (sin x))) (* (cos x) (+ 1 (* -1/6 (pow eps 2)))))
(- (sin (- eps (* -1 x))) (sin x))
(- (sin (- eps (* -1 x))) (sin x))
(- (sin (- eps (* -1 x))) (sin x))
(- (sin (- eps (* -1 x))) (sin x))
(* eps (+ (* -1/2 (* eps (sin x))) (* (cos x) (+ 1 (* -1/6 (pow eps 2))))))
(* eps (+ (* -1/2 (* eps (sin x))) (* (cos x) (+ 1 (* -1/6 (pow eps 2))))))
(* eps (+ (* -1/2 (* eps (sin x))) (* (cos x) (+ 1 (* -1/6 (pow eps 2))))))
(* eps (+ (* -1/2 (* eps (sin x))) (* (cos x) (+ 1 (* -1/6 (pow eps 2))))))
(+ (* -1/2 (* eps (sin x))) (* (cos x) (+ 1 (* -1/6 (pow eps 2)))))
(+ (* -1/2 (* eps (sin x))) (* (cos x) (+ 1 (* -1/6 (pow eps 2)))))
(+ (* -1/2 (* eps (sin x))) (* (cos x) (+ 1 (* -1/6 (pow eps 2)))))
(+ (* -1/2 (* eps (sin x))) (* (cos x) (+ 1 (* -1/6 (pow eps 2)))))
(* -1/2 (* (pow x 2) (+ 1 (* -1/6 (pow eps 2)))))
(* (pow x 2) (+ (* -1/2 (+ 1 (* -1/6 (pow eps 2)))) (* -1/2 (/ eps x))))
(* (pow x 2) (+ (* -1 (/ (+ (* -1 (/ (+ 1 (* -1/6 (pow eps 2))) x)) (* 1/2 eps)) x)) (* -1/2 (+ 1 (* -1/6 (pow eps 2))))))
(* (pow x 2) (+ (* -1 (/ (+ (* -1 (/ (+ 1 (* -1/6 (pow eps 2))) x)) (* 1/2 eps)) x)) (* -1/2 (+ 1 (* -1/6 (pow eps 2))))))
(* 1/12 (* (pow eps 2) x))
(* -1 (* x (+ (* -1 (/ (* eps (- (* 1/12 (pow eps 2)) 1/2)) x)) (* -1/12 (pow eps 2)))))
(* -1 (* x (+ (* -1 (/ (* eps (- (* 1/12 (pow eps 2)) 1/2)) x)) (* -1/12 (pow eps 2)))))
(* -1 (* x (+ (* -1 (/ (* eps (- (* 1/12 (pow eps 2)) 1/2)) x)) (* -1/12 (pow eps 2)))))
(* 1/12 (* (pow eps 2) (pow x 3)))
(* -1 (* (pow x 3) (+ (* -1 (/ (* eps (- (* 1/12 (pow eps 2)) 1/2)) x)) (* -1/12 (pow eps 2)))))
(* -1 (* (pow x 3) (+ (* -1 (/ (+ (* -1/2 (/ (pow eps 2) x)) (* eps (- (* 1/12 (pow eps 2)) 1/2))) x)) (* -1/12 (pow eps 2)))))
(* -1 (* (pow x 3) (+ (* -1 (/ (+ (* -1 (/ (+ (* -1 (/ (+ eps (* -1/6 (pow eps 3))) x)) (* 1/2 (pow eps 2))) x)) (* eps (- (* 1/12 (pow eps 2)) 1/2))) x)) (* -1/12 (pow eps 2)))))
(- (sin (- eps (* -1 x))) (sin x))
(- (sin (- eps (* -1 x))) (sin x))
(- (sin (- eps (* -1 x))) (sin x))
(- (sin (- eps (* -1 x))) (sin x))
(* eps (+ (* -1/2 (* eps (sin x))) (* (cos x) (+ 1 (* -1/6 (pow eps 2))))))
(* eps (+ (* -1/2 (* eps (sin x))) (* (cos x) (+ 1 (* -1/6 (pow eps 2))))))
(* eps (+ (* -1/2 (* eps (sin x))) (* (cos x) (+ 1 (* -1/6 (pow eps 2))))))
(* eps (+ (* -1/2 (* eps (sin x))) (* (cos x) (+ 1 (* -1/6 (pow eps 2))))))
x
(* -1 (* x (- (* -1/2 (/ eps x)) 1)))
(* -1 (* x (- (* -1/2 (/ eps x)) 1)))
(* -1 (* x (- (* -1/2 (/ eps x)) 1)))
(* 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 (* 1/2 (cos (neg (* -2 x)))))
(- 1/2 (* 1/2 (cos (neg (* -2 x)))))
(- 1/2 (* 1/2 (cos (neg (* -2 x)))))
(- 1/2 (* 1/2 (cos (neg (* -2 x)))))
(- (sin (- eps (* -1 x))) (sin x))
(- (sin (- eps (* -1 x))) (sin x))
(- (sin (- eps (* -1 x))) (sin x))
(- (sin (- eps (* -1 x))) (sin x))
(- (* (cos x) (+ 1 (* -1/6 (pow eps 2)))) (* -1/2 (* eps (sin x))))
(- (* (cos x) (+ 1 (* -1/6 (pow eps 2)))) (* -1/2 (* eps (sin x))))
(- (* (cos x) (+ 1 (* -1/6 (pow eps 2)))) (* -1/2 (* eps (sin x))))
(- (* (cos x) (+ 1 (* -1/6 (pow eps 2)))) (* -1/2 (* eps (sin x))))
(* x (+ 1 (* -1/6 (pow eps 2))))
(* -1 (* x (+ (* -1 (+ 1 (* -1/6 (pow eps 2)))) (* -1 (/ eps x)))))
(* -1 (* x (+ (* -1 (+ 1 (* -1/6 (pow eps 2)))) (* -1 (/ eps x)))))
(* -1 (* x (+ (* -1 (+ 1 (* -1/6 (pow eps 2)))) (* -1 (/ eps x)))))
(* 1/12 x)
(* 1/12 x)
(* 1/12 x)
(* 1/12 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))))

Outputs
(+ 1/2 (* 1/2 (cos (* 2 x))))
(fma.f64 (cos.f64 (*.f64 #s(literal -2 binary64) x)) #s(literal 1/2 binary64) #s(literal 1/2 binary64))
(+ 1/2 (+ (* 1/2 (cos (* 2 x))) (* (pow eps 2) (- (* -1/3 (+ 1/2 (* 1/2 (cos (* 2 x))))) (* 1/4 (- 1/2 (* 1/2 (cos (* 2 x)))))))))
(fma.f64 (fma.f64 #s(literal -1/4 binary64) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (.f64 #s(literal -2 binary64) x)) #s(literal 1/2 binary64)) (fma.f64 #s(literal -1/6 binary64) (cos.f64 (.f64 #s(literal -2 binary64) x)) #s(literal -1/6 binary64))) (.f64 eps eps) (fma.f64 (cos.f64 (.f64 #s(literal -2 binary64) x)) #s(literal 1/2 binary64) #s(literal 1/2 binary64)))
(+ 1/2 (+ (* 1/2 (cos (* 2 x))) (* (pow eps 2) (- (+ (* -1/3 (+ 1/2 (* 1/2 (cos (* 2 x))))) (* 1/36 (* (pow eps 2) (+ 1/2 (* 1/2 (cos (* 2 x))))))) (* 1/4 (- 1/2 (* 1/2 (cos (* 2 x)))))))))
(fma.f64 (fma.f64 #s(literal -1/4 binary64) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (.f64 #s(literal -2 binary64) x)) #s(literal 1/2 binary64)) (.f64 (fma.f64 (cos.f64 (.f64 #s(literal -2 binary64) x)) #s(literal 1/2 binary64) #s(literal 1/2 binary64)) (fma.f64 #s(literal 1/36 binary64) (.f64 eps eps) #s(literal -1/3 binary64)))) (.f64 eps eps) (fma.f64 (cos.f64 (.f64 #s(literal -2 binary64) x)) #s(literal 1/2 binary64) #s(literal 1/2 binary64)))
(+ 1/2 (+ (* 1/2 (cos (* 2 x))) (* (pow eps 2) (- (+ (* -1/3 (+ 1/2 (* 1/2 (cos (* 2 x))))) (* 1/36 (* (pow eps 2) (+ 1/2 (* 1/2 (cos (* 2 x))))))) (* 1/4 (- 1/2 (* 1/2 (cos (* 2 x)))))))))
(fma.f64 (fma.f64 #s(literal -1/4 binary64) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (.f64 #s(literal -2 binary64) x)) #s(literal 1/2 binary64)) (.f64 (fma.f64 (cos.f64 (.f64 #s(literal -2 binary64) x)) #s(literal 1/2 binary64) #s(literal 1/2 binary64)) (fma.f64 #s(literal 1/36 binary64) (.f64 eps eps) #s(literal -1/3 binary64)))) (.f64 eps eps) (fma.f64 (cos.f64 (.f64 #s(literal -2 binary64) x)) #s(literal 1/2 binary64) #s(literal 1/2 binary64)))
(* 1/4 (pow eps 2))
(.f64 #s(literal 1/4 binary64) (.f64 eps eps))
(* 1/4 (pow eps 2))
(.f64 #s(literal 1/4 binary64) (.f64 eps eps))
(* 1/4 (pow eps 2))
(.f64 #s(literal 1/4 binary64) (.f64 eps eps))
(* 1/4 (pow eps 2))
(.f64 #s(literal 1/4 binary64) (.f64 eps eps))
(* 1/4 (* (pow eps 2) (- 1/2 (* 1/2 (cos (* 2 x))))))
(.f64 (.f64 #s(literal 1/4 binary64) (.f64 eps eps)) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (.f64 #s(literal -2 binary64) x)) #s(literal 1/2 binary64)))
(* 1/4 (* (pow eps 2) (- 1/2 (* 1/2 (cos (* 2 x))))))
(.f64 (.f64 #s(literal 1/4 binary64) (.f64 eps eps)) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (.f64 #s(literal -2 binary64) x)) #s(literal 1/2 binary64)))
(* 1/4 (* (pow eps 2) (- 1/2 (* 1/2 (cos (* 2 x))))))
(.f64 (.f64 #s(literal 1/4 binary64) (.f64 eps eps)) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (.f64 #s(literal -2 binary64) x)) #s(literal 1/2 binary64)))
(* 1/4 (* (pow eps 2) (- 1/2 (* 1/2 (cos (* 2 x))))))
(.f64 (.f64 #s(literal 1/4 binary64) (.f64 eps eps)) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (.f64 #s(literal -2 binary64) x)) #s(literal 1/2 binary64)))
(* eps (cos x))
(*.f64 (cos.f64 x) eps)
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(.f64 (fma.f64 (.f64 (sin.f64 x) #s(literal -1/2 binary64)) eps (cos.f64 x)) eps)
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x)))))))
(.f64 (fma.f64 (fma.f64 #s(literal -1/6 binary64) (.f64 eps eps) #s(literal 1 binary64)) (cos.f64 x) (.f64 (.f64 (sin.f64 x) #s(literal -1/2 binary64)) eps)) eps)
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* eps (+ (* -1/6 (cos x)) (* 1/24 (* eps (sin x)))))))))
(.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 1/24 binary64) (.f64 (sin.f64 x) eps) (.f64 #s(literal -1/6 binary64) (cos.f64 x))) eps (.f64 (sin.f64 x) #s(literal -1/2 binary64))) eps (cos.f64 x)) eps)
(* eps (cos x))
(*.f64 (cos.f64 x) eps)
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(.f64 (fma.f64 (.f64 (sin.f64 x) #s(literal -1/2 binary64)) eps (cos.f64 x)) eps)
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x)))))))
(.f64 (fma.f64 (fma.f64 #s(literal -1/6 binary64) (.f64 eps eps) #s(literal 1 binary64)) (cos.f64 x) (.f64 (.f64 (sin.f64 x) #s(literal -1/2 binary64)) eps)) eps)
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x)))))))
(.f64 (fma.f64 (fma.f64 #s(literal -1/6 binary64) (.f64 eps eps) #s(literal 1 binary64)) (cos.f64 x) (.f64 (.f64 (sin.f64 x) #s(literal -1/2 binary64)) eps)) eps)
(cos x)
(cos.f64 x)
(+ (cos x) (* -1/2 (* eps (sin x))))
(fma.f64 (*.f64 (sin.f64 x) #s(literal -1/2 binary64)) eps (cos.f64 x))
(+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x))))))
(fma.f64 (fma.f64 #s(literal -1/6 binary64) (.f64 eps eps) #s(literal 1 binary64)) (cos.f64 x) (.f64 (*.f64 (sin.f64 x) #s(literal -1/2 binary64)) eps))
(+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x))))))
(fma.f64 (fma.f64 #s(literal -1/6 binary64) (.f64 eps eps) #s(literal 1 binary64)) (cos.f64 x) (.f64 (*.f64 (sin.f64 x) #s(literal -1/2 binary64)) eps))
1
#s(literal 1 binary64)
(+ 1 (* -1/6 (pow eps 2)))
(fma.f64 #s(literal -1/6 binary64) (*.f64 eps eps) #s(literal 1 binary64))
(+ 1 (* -1/6 (pow eps 2)))
(fma.f64 #s(literal -1/6 binary64) (*.f64 eps eps) #s(literal 1 binary64))
(+ 1 (* -1/6 (pow eps 2)))
(fma.f64 #s(literal -1/6 binary64) (*.f64 eps eps) #s(literal 1 binary64))
(* eps (cos x))
(*.f64 (cos.f64 x) eps)
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(.f64 (fma.f64 (.f64 (sin.f64 x) #s(literal -1/2 binary64)) eps (cos.f64 x)) eps)
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x)))))))
(.f64 (fma.f64 (fma.f64 #s(literal -1/6 binary64) (.f64 eps eps) #s(literal 1 binary64)) (cos.f64 x) (.f64 (.f64 (sin.f64 x) #s(literal -1/2 binary64)) eps)) eps)
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* eps (+ (* -1/6 (cos x)) (* 1/24 (* eps (sin x)))))))))
(.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 1/24 binary64) (.f64 (sin.f64 x) eps) (.f64 #s(literal -1/6 binary64) (cos.f64 x))) eps (.f64 (sin.f64 x) #s(literal -1/2 binary64))) eps (cos.f64 x)) eps)
(* eps (cos x))
(*.f64 (cos.f64 x) eps)
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(.f64 (fma.f64 (.f64 (sin.f64 x) #s(literal -1/2 binary64)) eps (cos.f64 x)) eps)
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x)))))))
(.f64 (fma.f64 (fma.f64 #s(literal -1/6 binary64) (.f64 eps eps) #s(literal 1 binary64)) (cos.f64 x) (.f64 (.f64 (sin.f64 x) #s(literal -1/2 binary64)) eps)) eps)
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x)))))))
(.f64 (fma.f64 (fma.f64 #s(literal -1/6 binary64) (.f64 eps eps) #s(literal 1 binary64)) (cos.f64 x) (.f64 (.f64 (sin.f64 x) #s(literal -1/2 binary64)) eps)) eps)
(cos x)
(cos.f64 x)
(+ (cos x) (* -1/2 (* eps (sin x))))
(fma.f64 (*.f64 (sin.f64 x) #s(literal -1/2 binary64)) eps (cos.f64 x))
(+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x))))))
(fma.f64 (fma.f64 #s(literal -1/6 binary64) (.f64 eps eps) #s(literal 1 binary64)) (cos.f64 x) (.f64 (*.f64 (sin.f64 x) #s(literal -1/2 binary64)) eps))
(+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x))))))
(fma.f64 (fma.f64 #s(literal -1/6 binary64) (.f64 eps eps) #s(literal 1 binary64)) (cos.f64 x) (.f64 (*.f64 (sin.f64 x) #s(literal -1/2 binary64)) eps))
(+ 1 (* -1/2 (pow x 2)))
(fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64))
(+ 1 (+ (* -1/2 (* eps x)) (* -1/2 (pow x 2))))
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eps
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(fma.f64 (fma.f64 #s(literal -1/6 binary64) (.f64 eps eps) #s(literal 1 binary64)) (cos.f64 x) (.f64 (*.f64 (sin.f64 x) #s(literal -1/2 binary64)) eps))
(+ (* -1/2 (* eps (sin x))) (* (cos x) (+ 1 (* -1/6 (pow eps 2)))))
(fma.f64 (fma.f64 #s(literal -1/6 binary64) (.f64 eps eps) #s(literal 1 binary64)) (cos.f64 x) (.f64 (*.f64 (sin.f64 x) #s(literal -1/2 binary64)) eps))
(+ (* -1/2 (* eps (sin x))) (* (cos x) (+ 1 (* -1/6 (pow eps 2)))))
(fma.f64 (fma.f64 #s(literal -1/6 binary64) (.f64 eps eps) #s(literal 1 binary64)) (cos.f64 x) (.f64 (*.f64 (sin.f64 x) #s(literal -1/2 binary64)) eps))
(+ (* -1/2 (* eps (sin x))) (* (cos x) (+ 1 (* -1/6 (pow eps 2)))))
(fma.f64 (fma.f64 #s(literal -1/6 binary64) (.f64 eps eps) #s(literal 1 binary64)) (cos.f64 x) (.f64 (*.f64 (sin.f64 x) #s(literal -1/2 binary64)) eps))
(- (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 (+ (* -1/2 (* eps (sin x))) (* (cos x) (+ 1 (* -1/6 (pow eps 2))))))
(.f64 (fma.f64 (fma.f64 #s(literal -1/6 binary64) (.f64 eps eps) #s(literal 1 binary64)) (cos.f64 x) (.f64 (.f64 (sin.f64 x) #s(literal -1/2 binary64)) eps)) eps)
(* eps (+ (* -1/2 (* eps (sin x))) (* (cos x) (+ 1 (* -1/6 (pow eps 2))))))
(.f64 (fma.f64 (fma.f64 #s(literal -1/6 binary64) (.f64 eps eps) #s(literal 1 binary64)) (cos.f64 x) (.f64 (.f64 (sin.f64 x) #s(literal -1/2 binary64)) eps)) eps)
(* eps (+ (* -1/2 (* eps (sin x))) (* (cos x) (+ 1 (* -1/6 (pow eps 2))))))
(.f64 (fma.f64 (fma.f64 #s(literal -1/6 binary64) (.f64 eps eps) #s(literal 1 binary64)) (cos.f64 x) (.f64 (.f64 (sin.f64 x) #s(literal -1/2 binary64)) eps)) eps)
(* eps (+ (* -1/2 (* eps (sin x))) (* (cos x) (+ 1 (* -1/6 (pow eps 2))))))
(.f64 (fma.f64 (fma.f64 #s(literal -1/6 binary64) (.f64 eps eps) #s(literal 1 binary64)) (cos.f64 x) (.f64 (.f64 (sin.f64 x) #s(literal -1/2 binary64)) eps)) eps)
(+ (* -1/2 (* eps (sin x))) (* (cos x) (+ 1 (* -1/6 (pow eps 2)))))
(fma.f64 (fma.f64 #s(literal -1/6 binary64) (.f64 eps eps) #s(literal 1 binary64)) (cos.f64 x) (.f64 (*.f64 (sin.f64 x) #s(literal -1/2 binary64)) eps))
(+ (* -1/2 (* eps (sin x))) (* (cos x) (+ 1 (* -1/6 (pow eps 2)))))
(fma.f64 (fma.f64 #s(literal -1/6 binary64) (.f64 eps eps) #s(literal 1 binary64)) (cos.f64 x) (.f64 (*.f64 (sin.f64 x) #s(literal -1/2 binary64)) eps))
(+ (* -1/2 (* eps (sin x))) (* (cos x) (+ 1 (* -1/6 (pow eps 2)))))
(fma.f64 (fma.f64 #s(literal -1/6 binary64) (.f64 eps eps) #s(literal 1 binary64)) (cos.f64 x) (.f64 (*.f64 (sin.f64 x) #s(literal -1/2 binary64)) eps))
(+ (* -1/2 (* eps (sin x))) (* (cos x) (+ 1 (* -1/6 (pow eps 2)))))
(fma.f64 (fma.f64 #s(literal -1/6 binary64) (.f64 eps eps) #s(literal 1 binary64)) (cos.f64 x) (.f64 (*.f64 (sin.f64 x) #s(literal -1/2 binary64)) eps))
(* -1/2 (* (pow x 2) (+ 1 (* -1/6 (pow eps 2)))))
(.f64 (.f64 (fma.f64 (*.f64 #s(literal 1/12 binary64) eps) eps #s(literal -1/2 binary64)) x) x)
(* (pow x 2) (+ (* -1/2 (+ 1 (* -1/6 (pow eps 2)))) (* -1/2 (/ eps x))))
(.f64 (.f64 (fma.f64 (/.f64 eps x) #s(literal -1/2 binary64) (fma.f64 (*.f64 #s(literal 1/12 binary64) eps) eps #s(literal -1/2 binary64))) x) x)
(* (pow x 2) (+ (* -1 (/ (+ (* -1 (/ (+ 1 (* -1/6 (pow eps 2))) x)) (* 1/2 eps)) x)) (* -1/2 (+ 1 (* -1/6 (pow eps 2))))))
(.f64 (.f64 (-.f64 (fma.f64 (.f64 #s(literal 1/12 binary64) eps) eps #s(literal -1/2 binary64)) (/.f64 (fma.f64 eps #s(literal 1/2 binary64) (/.f64 (fma.f64 #s(literal 1/6 binary64) (.f64 eps eps) #s(literal -1 binary64)) x)) x)) x) x)
(* (pow x 2) (+ (* -1 (/ (+ (* -1 (/ (+ 1 (* -1/6 (pow eps 2))) x)) (* 1/2 eps)) x)) (* -1/2 (+ 1 (* -1/6 (pow eps 2))))))
(.f64 (.f64 (-.f64 (fma.f64 (.f64 #s(literal 1/12 binary64) eps) eps #s(literal -1/2 binary64)) (/.f64 (fma.f64 eps #s(literal 1/2 binary64) (/.f64 (fma.f64 #s(literal 1/6 binary64) (.f64 eps eps) #s(literal -1 binary64)) x)) x)) x) x)
(* 1/12 (* (pow eps 2) x))
(.f64 (.f64 (*.f64 eps x) eps) #s(literal 1/12 binary64))
(* -1 (* x (+ (* -1 (/ (* eps (- (* 1/12 (pow eps 2)) 1/2)) x)) (* -1/12 (pow eps 2)))))
(.f64 (fma.f64 (.f64 #s(literal 1/12 binary64) eps) eps (/.f64 (.f64 (fma.f64 (.f64 #s(literal 1/12 binary64) eps) eps #s(literal -1/2 binary64)) eps) x)) x)
(* -1 (* x (+ (* -1 (/ (* eps (- (* 1/12 (pow eps 2)) 1/2)) x)) (* -1/12 (pow eps 2)))))
(.f64 (fma.f64 (.f64 #s(literal 1/12 binary64) eps) eps (/.f64 (.f64 (fma.f64 (.f64 #s(literal 1/12 binary64) eps) eps #s(literal -1/2 binary64)) eps) x)) x)
(* -1 (* x (+ (* -1 (/ (* eps (- (* 1/12 (pow eps 2)) 1/2)) x)) (* -1/12 (pow eps 2)))))
(.f64 (fma.f64 (.f64 #s(literal 1/12 binary64) eps) eps (/.f64 (.f64 (fma.f64 (.f64 #s(literal 1/12 binary64) eps) eps #s(literal -1/2 binary64)) eps) x)) x)
(* 1/12 (* (pow eps 2) (pow x 3)))
(.f64 (.f64 (.f64 (.f64 (*.f64 eps x) eps) x) x) #s(literal 1/12 binary64))
(* -1 (* (pow x 3) (+ (* -1 (/ (* eps (- (* 1/12 (pow eps 2)) 1/2)) x)) (* -1/12 (pow eps 2)))))
(.f64 (.f64 (fma.f64 (.f64 #s(literal 1/12 binary64) eps) eps (/.f64 (.f64 (fma.f64 (.f64 #s(literal 1/12 binary64) eps) eps #s(literal -1/2 binary64)) eps) x)) x) (.f64 x x))
(* -1 (* (pow x 3) (+ (* -1 (/ (+ (* -1/2 (/ (pow eps 2) x)) (* eps (- (* 1/12 (pow eps 2)) 1/2))) x)) (* -1/12 (pow eps 2)))))
(.f64 (neg.f64 (.f64 (fma.f64 (.f64 #s(literal -1/12 binary64) eps) eps (/.f64 (fma.f64 (.f64 eps (/.f64 eps x)) #s(literal -1/2 binary64) (.f64 (fma.f64 (.f64 #s(literal 1/12 binary64) eps) eps #s(literal -1/2 binary64)) eps)) (neg.f64 x))) x)) (*.f64 x x))
(* -1 (* (pow x 3) (+ (* -1 (/ (+ (* -1 (/ (+ (* -1 (/ (+ eps (* -1/6 (pow eps 3))) x)) (* 1/2 (pow eps 2))) x)) (* eps (- (* 1/12 (pow eps 2)) 1/2))) x)) (* -1/12 (pow eps 2)))))
(.f64 (neg.f64 (.f64 (fma.f64 (.f64 #s(literal -1/12 binary64) eps) eps (/.f64 (fma.f64 (fma.f64 (.f64 #s(literal 1/12 binary64) eps) eps #s(literal -1/2 binary64)) eps (/.f64 (fma.f64 (.f64 eps #s(literal 1/2 binary64)) eps (/.f64 (.f64 (fma.f64 #s(literal 1/6 binary64) (.f64 eps eps) #s(literal -1 binary64)) eps) x)) (neg.f64 x))) (neg.f64 x))) x)) (.f64 x 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 (+ (* -1/2 (* eps (sin x))) (* (cos x) (+ 1 (* -1/6 (pow eps 2))))))
(.f64 (fma.f64 (fma.f64 #s(literal -1/6 binary64) (.f64 eps eps) #s(literal 1 binary64)) (cos.f64 x) (.f64 (.f64 (sin.f64 x) #s(literal -1/2 binary64)) eps)) eps)
(* eps (+ (* -1/2 (* eps (sin x))) (* (cos x) (+ 1 (* -1/6 (pow eps 2))))))
(.f64 (fma.f64 (fma.f64 #s(literal -1/6 binary64) (.f64 eps eps) #s(literal 1 binary64)) (cos.f64 x) (.f64 (.f64 (sin.f64 x) #s(literal -1/2 binary64)) eps)) eps)
(* eps (+ (* -1/2 (* eps (sin x))) (* (cos x) (+ 1 (* -1/6 (pow eps 2))))))
(.f64 (fma.f64 (fma.f64 #s(literal -1/6 binary64) (.f64 eps eps) #s(literal 1 binary64)) (cos.f64 x) (.f64 (.f64 (sin.f64 x) #s(literal -1/2 binary64)) eps)) eps)
(* eps (+ (* -1/2 (* eps (sin x))) (* (cos x) (+ 1 (* -1/6 (pow eps 2))))))
(.f64 (fma.f64 (fma.f64 #s(literal -1/6 binary64) (.f64 eps eps) #s(literal 1 binary64)) (cos.f64 x) (.f64 (.f64 (sin.f64 x) #s(literal -1/2 binary64)) eps)) eps)
x
(* -1 (* x (- (* -1/2 (/ eps x)) 1)))
(fma.f64 (neg.f64 x) (*.f64 (/.f64 eps x) #s(literal -1/2 binary64)) x)
(* -1 (* x (- (* -1/2 (/ eps x)) 1)))
(fma.f64 (neg.f64 x) (*.f64 (/.f64 eps x) #s(literal -1/2 binary64)) x)
(* -1 (* x (- (* -1/2 (/ eps x)) 1)))
(fma.f64 (neg.f64 x) (*.f64 (/.f64 eps x) #s(literal -1/2 binary64)) x)
(* 2 (* (cos (* 1/2 (- eps (* -2 x)))) (sin (* 1/2 eps))))
(.f64 (cos.f64 (fma.f64 eps #s(literal 1/2 binary64) x)) (.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) #s(literal 2 binary64)))
(* 2 (* (cos (* 1/2 (- eps (* -2 x)))) (sin (* 1/2 eps))))
(.f64 (cos.f64 (fma.f64 eps #s(literal 1/2 binary64) x)) (.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) #s(literal 2 binary64)))
(* 2 (* (cos (* 1/2 (- eps (* -2 x)))) (sin (* 1/2 eps))))
(.f64 (cos.f64 (fma.f64 eps #s(literal 1/2 binary64) x)) (.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) #s(literal 2 binary64)))
(* 2 (* (cos (* 1/2 (- eps (* -2 x)))) (sin (* 1/2 eps))))
(.f64 (cos.f64 (fma.f64 eps #s(literal 1/2 binary64) x)) (.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) #s(literal 2 binary64)))
(- 1/2 (* 1/2 (cos (neg (* -2 x)))))
(fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal -2 binary64) x)) #s(literal 1/2 binary64))
(- 1/2 (* 1/2 (cos (neg (* -2 x)))))
(fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal -2 binary64) x)) #s(literal 1/2 binary64))
(- 1/2 (* 1/2 (cos (neg (* -2 x)))))
(fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal -2 binary64) x)) #s(literal 1/2 binary64))
(- 1/2 (* 1/2 (cos (neg (* -2 x)))))
(fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal -2 binary64) x)) #s(literal 1/2 binary64))
(- (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))
(- (* (cos x) (+ 1 (* -1/6 (pow eps 2)))) (* -1/2 (* eps (sin x))))
(fma.f64 (fma.f64 #s(literal -1/6 binary64) (.f64 eps eps) #s(literal 1 binary64)) (cos.f64 x) (.f64 (*.f64 (sin.f64 x) eps) #s(literal 1/2 binary64)))
(- (* (cos x) (+ 1 (* -1/6 (pow eps 2)))) (* -1/2 (* eps (sin x))))
(fma.f64 (fma.f64 #s(literal -1/6 binary64) (.f64 eps eps) #s(literal 1 binary64)) (cos.f64 x) (.f64 (*.f64 (sin.f64 x) eps) #s(literal 1/2 binary64)))
(- (* (cos x) (+ 1 (* -1/6 (pow eps 2)))) (* -1/2 (* eps (sin x))))
(fma.f64 (fma.f64 #s(literal -1/6 binary64) (.f64 eps eps) #s(literal 1 binary64)) (cos.f64 x) (.f64 (*.f64 (sin.f64 x) eps) #s(literal 1/2 binary64)))
(- (* (cos x) (+ 1 (* -1/6 (pow eps 2)))) (* -1/2 (* eps (sin x))))
(fma.f64 (fma.f64 #s(literal -1/6 binary64) (.f64 eps eps) #s(literal 1 binary64)) (cos.f64 x) (.f64 (*.f64 (sin.f64 x) eps) #s(literal 1/2 binary64)))
(* x (+ 1 (* -1/6 (pow eps 2))))
(.f64 (fma.f64 #s(literal -1/6 binary64) (.f64 eps eps) #s(literal 1 binary64)) x)
(* -1 (* x (+ (* -1 (+ 1 (* -1/6 (pow eps 2)))) (* -1 (/ eps x)))))
(fma.f64 (fma.f64 #s(literal -1/6 binary64) (*.f64 eps eps) (/.f64 eps x)) x x)
(* -1 (* x (+ (* -1 (+ 1 (* -1/6 (pow eps 2)))) (* -1 (/ eps x)))))
(fma.f64 (fma.f64 #s(literal -1/6 binary64) (*.f64 eps eps) (/.f64 eps x)) x x)
(* -1 (* x (+ (* -1 (+ 1 (* -1/6 (pow eps 2)))) (* -1 (/ eps x)))))
(fma.f64 (fma.f64 #s(literal -1/6 binary64) (*.f64 eps eps) (/.f64 eps x)) x x)
(* 1/12 x)
(*.f64 #s(literal 1/12 binary64) x)
(* 1/12 x)
(*.f64 #s(literal 1/12 binary64) x)
(* 1/12 x)
(*.f64 #s(literal 1/12 binary64) x)
(* 1/12 x)
(*.f64 #s(literal 1/12 binary64) x)
(cos (* 1/2 (- eps (* -2 x))))
(cos.f64 (fma.f64 eps #s(literal 1/2 binary64) x))
(cos (* 1/2 (- eps (* -2 x))))
(cos.f64 (fma.f64 eps #s(literal 1/2 binary64) x))
(cos (* 1/2 (- eps (* -2 x))))
(cos.f64 (fma.f64 eps #s(literal 1/2 binary64) x))
(cos (* 1/2 (- eps (* -2 x))))
(cos.f64 (fma.f64 eps #s(literal 1/2 binary64) x))

rewrite232.0ms (2%)

Memory

14.1MiB live, 243.0MiB allocated

Rules

8 798×	`lower-fma.f32`
8 778×	`lower-fma.f64`
4 920×	`lower-*.f32`
4 876×	`lower-*.f64`
2 754×	`lower-pow.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	75	607
0	128	583
1	511	520
2	4456	520
0	8365	506

Stop Event

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

Counts

27 → 578

Calls

Call 1

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

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

eval386.0ms (3.3%)

Memory: 11.1MiB live, 285.1MiB allocated
Compiler: Compiled 59 781 to 3 843 computations (93.6% saved)

prune84.0ms (0.7%)

Memory

-4.7MiB live, 85.5MiB allocated

Pruning

22 alts after pruning (18 fresh and 4 done)

	Pruned	Kept	Total
New	1 533	11	1 544
Fresh	0	7	7
Picked	5	0	5
Done	0	4	4
Total	1 538	22	1 560

Accuracy

100.0%

Counts

1 560 → 22

Alt Table

Click to see full alt table

Status	Accuracy	Program
	62.4%	(fma.f64 (sin.f64 x) (cos.f64 eps) (fma.f64 (sin.f64 eps) (cos.f64 x) (neg.f64 (sin.f64 x))))
✓	62.1%	(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
✓	7.5%	(-.f64 #s(approx (sin (+ x eps)) (sin.f64 eps)) (sin.f64 x))
▶	99.4%	(.f64 (.f64 #s(approx (sin (* 1/2 (+ 0 eps))) (.f64 eps #s(literal 1/2 binary64))) #s(literal 2 binary64)) (cos.f64 #s(approx ( 1/2 (+ (* 2 x) eps)) (fma.f64 eps #s(literal 1/2 binary64) x))))
▶	99.6%	(.f64 #s(approx ( (sin (* 1/2 (+ 0 eps))) 2) (.f64 (fma.f64 (.f64 eps eps) #s(literal -1/24 binary64) #s(literal 1 binary64)) eps)) (cos.f64 (*.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps))))
	99.5%	#s(approx (- (sin (+ x eps)) (sin x)) (/.f64 (.f64 #s(approx (- ( (+ 1/2 (* 1/2 (cos (+ x x)))) (* (+ (* (* eps eps) -1/6) 1) (+ (* (* eps eps) -1/6) 1))) (* (* (* -1/2 eps) (* -1/2 eps)) (- 1/2 (* 1/2 (cos (+ x x)))))) (fma.f64 (cos.f64 (.f64 #s(literal -2 binary64) x)) #s(literal 1/2 binary64) #s(literal 1/2 binary64))) eps) (-.f64 (.f64 (cos.f64 x) (fma.f64 (.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64))) (.f64 (*.f64 #s(literal -1/2 binary64) (sin.f64 x)) eps))))
✓	99.7%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 (fma.f64 (.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64)) (cos.f64 x) (.f64 (.f64 (sin.f64 x) #s(literal -1/2 binary64)) eps)) eps))
	98.9%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 (fma.f64 (.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64)) (cos.f64 x) #s(approx (* (* (sin x) -1/2) eps) (.f64 (.f64 eps (fma.f64 #s(literal 1/12 binary64) (*.f64 x x) #s(literal -1/2 binary64))) x))) eps))
	99.5%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 (.f64 (sin.f64 x) #s(literal -1/2 binary64)) eps (cos.f64 x)) eps))
	99.0%	#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (cos.f64 x) eps))
▶	98.3%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (+ (* (* eps eps) -1/6) 1) (cos x)) (* (* (sin x) -1/2) eps)) (fma.f64 (fma.f64 (fma.f64 (.f64 #s(literal 1/12 binary64) eps) (+.f64 eps x) #s(literal -1/2 binary64)) x (.f64 #s(literal -1/2 binary64) eps)) x (fma.f64 #s(literal -1/6 binary64) (*.f64 eps eps) #s(literal 1 binary64)))) eps))
	98.3%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (+ (* (* eps eps) -1/6) 1) (cos x)) (* (* (sin x) -1/2) eps)) (fma.f64 (.f64 #s(approx (+ ( (+ (* -1/6 (* eps eps)) 1) x) eps) (+.f64 eps x)) #s(literal -1/2 binary64)) x (fma.f64 #s(literal -1/6 binary64) (*.f64 eps eps) #s(literal 1 binary64)))) eps))
	98.2%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (+ (* (* eps eps) -1/6) 1) (cos x)) (* (* (sin x) -1/2) eps)) (fma.f64 (*.f64 #s(literal -1/6 binary64) eps) eps #s(literal 1 binary64))) eps))
	98.1%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (+ (* (* eps eps) -1/6) 1) (cos x)) (* (* (sin x) -1/2) eps)) (fma.f64 eps (fma.f64 #s(literal -1/2 binary64) x (*.f64 #s(literal -1/6 binary64) eps)) #s(literal 1 binary64))) eps))
	98.2%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (+ (* (* eps eps) -1/6) 1) (cos x)) (* (* (sin x) -1/2) eps)) #s(approx (+ (* (* (+ (* (+ (* -1/6 (* eps eps)) 1) x) eps) -1/2) x) (+ (* -1/6 (* eps eps)) 1)) (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64)))) eps))
▶	98.3%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (+ (* (* eps eps) -1/6) 1) (cos x)) (* (* (sin x) -1/2) eps)) #s(approx (+ (* (* (+ (* (+ (* -1/6 (* eps eps)) 1) x) eps) -1/2) x) (+ (* -1/6 (* eps eps)) 1)) (fma.f64 #s(literal -1/2 binary64) (*.f64 x (+.f64 eps x)) #s(literal 1 binary64)))) eps))
	5.1%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (+ (* (* eps eps) -1/6) 1) (cos x)) (* (* (sin x) -1/2) eps)) #s(approx (+ (* -1/6 (* eps eps)) 1) (.f64 #s(literal -1/6 binary64) (.f64 eps eps)))) eps))
▶	98.1%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (+ (* (* eps eps) -1/6) 1) (cos x)) (* (* (sin x) -1/2) eps)) #s(approx (+ (* -1/6 (* eps eps)) 1) #s(literal 1 binary64))) eps))
✓	98.2%	#s(approx (- (sin (+ x eps)) (sin x)) (sin.f64 eps))
	98.3%	#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (+ (* (* eps eps) -1/6) 1) (cos x)) (* (* (sin x) -1/2) eps)) eps) (fma.f64 (.f64 #s(approx (+ ( (* 1/12 x) (* eps eps)) (* (+ (* 1/12 (* eps eps)) -1/2) eps)) (.f64 (fma.f64 #s(literal 1/12 binary64) (.f64 eps x) #s(literal -1/2 binary64)) eps)) x) x (fma.f64 (.f64 eps eps) (fma.f64 #s(literal -1/6 binary64) eps (.f64 #s(literal -1/2 binary64) x)) eps))))
	98.1%	#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (+ (* (* eps eps) -1/6) 1) (cos x)) (* (* (sin x) -1/2) eps)) eps) (fma.f64 (.f64 #s(approx (+ ( (* 1/12 x) (* eps eps)) (* (+ (* 1/12 (* eps eps)) -1/2) eps)) (.f64 (.f64 (.f64 eps x) eps) #s(literal 1/12 binary64))) x) x (fma.f64 (.f64 eps eps) (fma.f64 #s(literal -1/6 binary64) eps (*.f64 #s(literal -1/2 binary64) x)) eps))))
	98.3%	#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (+ (* (* eps eps) -1/6) 1) (cos x)) (* (* (sin x) -1/2) eps)) eps) (fma.f64 (.f64 #s(approx (+ ( (* 1/12 x) (* eps eps)) (* (+ (* 1/12 (* eps eps)) -1/2) eps)) (.f64 #s(literal -1/2 binary64) eps)) x) x (fma.f64 (.f64 eps eps) (fma.f64 #s(literal -1/6 binary64) eps (*.f64 #s(literal -1/2 binary64) x)) eps))))

Compiler

Compiled 690 to 395 computations (42.8% saved)

simplify190.0ms (1.6%)

Memory

12.9MiB live, 118.9MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 20 expressions of interest:

New	Metric	Score
cost-diff	0	(*.f64 eps #s(literal 1/2 binary64))
cost-diff	0	#s(approx (sin (* 1/2 (+ 0 eps))) (*.f64 eps #s(literal 1/2 binary64)))
cost-diff	0	(.f64 #s(approx (sin ( 1/2 (+ 0 eps))) (*.f64 eps #s(literal 1/2 binary64))) #s(literal 2 binary64))
cost-diff	0	(.f64 (.f64 #s(approx (sin (* 1/2 (+ 0 eps))) (.f64 eps #s(literal 1/2 binary64))) #s(literal 2 binary64)) (cos.f64 #s(approx ( 1/2 (+ (* 2 x) eps)) (fma.f64 eps #s(literal 1/2 binary64) x))))
cost-diff	0	#s(approx (+ (* (+ (* (* eps eps) -1/6) 1) (cos x)) (* (* (sin x) -1/2) eps)) (fma.f64 (fma.f64 (fma.f64 (.f64 #s(literal 1/12 binary64) eps) (+.f64 eps x) #s(literal -1/2 binary64)) x (.f64 #s(literal -1/2 binary64) eps)) x (fma.f64 #s(literal -1/6 binary64) (*.f64 eps eps) #s(literal 1 binary64))))
cost-diff	0	(.f64 #s(approx (+ ( (+ (* (* eps eps) -1/6) 1) (cos x)) (* (* (sin x) -1/2) eps)) (fma.f64 (fma.f64 (fma.f64 (.f64 #s(literal 1/12 binary64) eps) (+.f64 eps x) #s(literal -1/2 binary64)) x (.f64 #s(literal -1/2 binary64) eps)) x (fma.f64 #s(literal -1/6 binary64) (*.f64 eps eps) #s(literal 1 binary64)))) eps)
cost-diff	0	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (+ (* (* eps eps) -1/6) 1) (cos x)) (* (* (sin x) -1/2) eps)) (fma.f64 (fma.f64 (fma.f64 (.f64 #s(literal 1/12 binary64) eps) (+.f64 eps x) #s(literal -1/2 binary64)) x (.f64 #s(literal -1/2 binary64) eps)) x (fma.f64 #s(literal -1/6 binary64) (*.f64 eps eps) #s(literal 1 binary64)))) eps))
cost-diff	384	(fma.f64 (fma.f64 (.f64 #s(literal 1/12 binary64) eps) (+.f64 eps x) #s(literal -1/2 binary64)) x (.f64 #s(literal -1/2 binary64) eps))
cost-diff	0	#s(approx (+ (* (* (+ (* (+ (* -1/6 (* eps eps)) 1) x) eps) -1/2) x) (+ (* -1/6 (* eps eps)) 1)) (fma.f64 #s(literal -1/2 binary64) (*.f64 x (+.f64 eps x)) #s(literal 1 binary64)))
cost-diff	0	#s(approx (+ (* (+ (* (* eps eps) -1/6) 1) (cos x)) (* (* (sin x) -1/2) eps)) #s(approx (+ (* (* (+ (* (+ (* -1/6 (* eps eps)) 1) x) eps) -1/2) x) (+ (* -1/6 (* eps eps)) 1)) (fma.f64 #s(literal -1/2 binary64) (*.f64 x (+.f64 eps x)) #s(literal 1 binary64))))
cost-diff	0	(.f64 #s(approx (+ ( (+ (* (* eps eps) -1/6) 1) (cos x)) (* (* (sin x) -1/2) eps)) #s(approx (+ (* (* (+ (* (+ (* -1/6 (* eps eps)) 1) x) eps) -1/2) x) (+ (* -1/6 (* eps eps)) 1)) (fma.f64 #s(literal -1/2 binary64) (*.f64 x (+.f64 eps x)) #s(literal 1 binary64)))) eps)
cost-diff	0	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (+ (* (* eps eps) -1/6) 1) (cos x)) (* (* (sin x) -1/2) eps)) #s(approx (+ (* (* (+ (* (+ (* -1/6 (* eps eps)) 1) x) eps) -1/2) x) (+ (* -1/6 (* eps eps)) 1)) (fma.f64 #s(literal -1/2 binary64) (*.f64 x (+.f64 eps x)) #s(literal 1 binary64)))) eps))
cost-diff	0	#s(approx (+ (* -1/6 (* eps eps)) 1) #s(literal 1 binary64))
cost-diff	0	#s(approx (+ (* (+ (* (* eps eps) -1/6) 1) (cos x)) (* (* (sin x) -1/2) eps)) #s(approx (+ (* -1/6 (* eps eps)) 1) #s(literal 1 binary64)))
cost-diff	0	(.f64 #s(approx (+ ( (+ (* (* eps eps) -1/6) 1) (cos x)) (* (* (sin x) -1/2) eps)) #s(approx (+ (* -1/6 (* eps eps)) 1) #s(literal 1 binary64))) eps)
cost-diff	0	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (+ (* (* eps eps) -1/6) 1) (cos x)) (* (* (sin x) -1/2) eps)) #s(approx (+ (* -1/6 (* eps eps)) 1) #s(literal 1 binary64))) eps))
cost-diff	0	(.f64 (fma.f64 (.f64 eps eps) #s(literal -1/24 binary64) #s(literal 1 binary64)) eps)
cost-diff	0	#s(approx (* (sin (* 1/2 (+ 0 eps))) 2) (.f64 (fma.f64 (.f64 eps eps) #s(literal -1/24 binary64) #s(literal 1 binary64)) eps))
cost-diff	0	(.f64 #s(approx ( (sin (* 1/2 (+ 0 eps))) 2) (.f64 (fma.f64 (.f64 eps eps) #s(literal -1/24 binary64) #s(literal 1 binary64)) eps)) (cos.f64 (*.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps))))
cost-diff	320	(*.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps))

Rules

17 018×	`lower-fma.f32`
17 002×	`lower-fma.f64`
3 956×	`lower--.f64`
3 956×	`lower--.f32`
3 732×	`lower-*.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	71	664
0	103	647
1	186	647
2	447	633
3	990	620
4	2829	616
5	3531	616
6	4096	616
7	4769	616
0	8491	582

Stop Event

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

Calls

Call 1

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

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

localize249.0ms (2.1%)

Memory

-22.5MiB live, 187.5MiB allocated

Localize:

Found 20 expressions of interest:

New	Metric	Score
accuracy	0	#s(approx (* 1/2 (+ (* 2 x) eps)) (fma.f64 eps #s(literal 1/2 binary64) x))
accuracy	0.0078125	(.f64 (.f64 #s(approx (sin (* 1/2 (+ 0 eps))) (.f64 eps #s(literal 1/2 binary64))) #s(literal 2 binary64)) (cos.f64 #s(approx ( 1/2 (+ (* 2 x) eps)) (fma.f64 eps #s(literal 1/2 binary64) x))))
accuracy	0.09448630290560088	(cos.f64 #s(approx (* 1/2 (+ (* 2 x) eps)) (fma.f64 eps #s(literal 1/2 binary64) x)))
accuracy	0.324187546809663	#s(approx (sin (* 1/2 (+ 0 eps))) (*.f64 eps #s(literal 1/2 binary64)))
accuracy	0.0078125	(fma.f64 (fma.f64 (.f64 #s(literal 1/12 binary64) eps) (+.f64 eps x) #s(literal -1/2 binary64)) x (.f64 #s(literal -1/2 binary64) eps))
accuracy	0.21941333120599352	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (+ (* (* eps eps) -1/6) 1) (cos x)) (* (* (sin x) -1/2) eps)) (fma.f64 (fma.f64 (fma.f64 (.f64 #s(literal 1/12 binary64) eps) (+.f64 eps x) #s(literal -1/2 binary64)) x (.f64 #s(literal -1/2 binary64) eps)) x (fma.f64 #s(literal -1/6 binary64) (*.f64 eps eps) #s(literal 1 binary64)))) eps))
accuracy	0.34375	(*.f64 #s(literal 1/12 binary64) eps)
accuracy	1.0899057460452377	#s(approx (+ (* (+ (* (* eps eps) -1/6) 1) (cos x)) (* (* (sin x) -1/2) eps)) (fma.f64 (fma.f64 (fma.f64 (.f64 #s(literal 1/12 binary64) eps) (+.f64 eps x) #s(literal -1/2 binary64)) x (.f64 #s(literal -1/2 binary64) eps)) x (fma.f64 #s(literal -1/6 binary64) (*.f64 eps eps) #s(literal 1 binary64))))
accuracy	0.11328125	(*.f64 x (+.f64 eps x))
accuracy	0.21941333120599352	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (+ (* (* eps eps) -1/6) 1) (cos x)) (* (* (sin x) -1/2) eps)) #s(approx (+ (* (* (+ (* (+ (* -1/6 (* eps eps)) 1) x) eps) -1/2) x) (+ (* -1/6 (* eps eps)) 1)) (fma.f64 #s(literal -1/2 binary64) (*.f64 x (+.f64 eps x)) #s(literal 1 binary64)))) eps))
accuracy	0.3457412397686604	#s(approx (+ (* (* (+ (* (+ (* -1/6 (* eps eps)) 1) x) eps) -1/2) x) (+ (* -1/6 (* eps eps)) 1)) (fma.f64 #s(literal -1/2 binary64) (*.f64 x (+.f64 eps x)) #s(literal 1 binary64)))
accuracy	1.1159550957377529	#s(approx (+ (* (+ (* (* eps eps) -1/6) 1) (cos x)) (* (* (sin x) -1/2) eps)) #s(approx (+ (* (* (+ (* (+ (* -1/6 (* eps eps)) 1) x) eps) -1/2) x) (+ (* -1/6 (* eps eps)) 1)) (fma.f64 #s(literal -1/2 binary64) (*.f64 x (+.f64 eps x)) #s(literal 1 binary64))))
accuracy	0.00390625	(.f64 #s(approx (+ ( (+ (* (* eps eps) -1/6) 1) (cos x)) (* (* (sin x) -1/2) eps)) #s(approx (+ (* -1/6 (* eps eps)) 1) #s(literal 1 binary64))) eps)
accuracy	0.21941333120599352	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (+ (* (* eps eps) -1/6) 1) (cos x)) (* (* (sin x) -1/2) eps)) #s(approx (+ (* -1/6 (* eps eps)) 1) #s(literal 1 binary64))) eps))
accuracy	0.3460843215374133	#s(approx (+ (* -1/6 (* eps eps)) 1) #s(literal 1 binary64))
accuracy	1.1425821551459863	#s(approx (+ (* (+ (* (* eps eps) -1/6) 1) (cos x)) (* (* (sin x) -1/2) eps)) #s(approx (+ (* -1/6 (* eps eps)) 1) #s(literal 1 binary64)))
accuracy	0.0078125	(.f64 #s(approx ( (sin (* 1/2 (+ 0 eps))) 2) (.f64 (fma.f64 (.f64 eps eps) #s(literal -1/24 binary64) #s(literal 1 binary64)) eps)) (cos.f64 (*.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps))))
accuracy	0.01171875	(.f64 (fma.f64 (.f64 eps eps) #s(literal -1/24 binary64) #s(literal 1 binary64)) eps)
accuracy	0.09448630290560088	(cos.f64 (*.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps)))
accuracy	0.21781470775979417	#s(approx (* (sin (* 1/2 (+ 0 eps))) 2) (.f64 (fma.f64 (.f64 eps eps) #s(literal -1/24 binary64) #s(literal 1 binary64)) eps))

Samples

113.0ms	172×	0	valid
73.0ms	82×	1	valid
1.0ms	1×	3	valid
1.0ms	1×	2	valid

Compiler

Compiled 386 to 58 computations (85% saved)

Precisions

Click to see histograms. Total time spent on operations: 94.0ms

ival-mult: 44.0ms (46.8% of total)

ival-add: 18.0ms (19.2% of total)

adjust: 9.0ms (9.6% of total)

const: 9.0ms (9.6% of total)

ival-sin: 6.0ms (6.4% of total)

ival-cos: 4.0ms (4.3% of total)

ival-sub: 1.0ms (1.1% of total)

exact: 1.0ms (1.1% of total)

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

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

series47.0ms (0.4%)

Memory

10.3MiB live, 47.6MiB allocated

Counts

25 → 516

Calls

Call 1

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

Outputs
#s(alt x (taylor 0 eps) (#s(alt (.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps)) (patch (.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps)) #<representation binary64>) () ())) ())
#s(alt (+ x (* 1/2 eps)) (taylor 0 eps) (#s(alt (.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps)) (patch (.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps)) #<representation binary64>) () ())) ())
#s(alt (+ x (* 1/2 eps)) (taylor 0 eps) (#s(alt (.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps)) (patch (.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps)) #<representation binary64>) () ())) ())
#s(alt (+ x (* 1/2 eps)) (taylor 0 eps) (#s(alt (.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps)) (patch (.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps)) #<representation binary64>) () ())) ())
#s(alt (* eps (cos x)) (taylor 0 eps) (#s(alt (.f64 #s(approx ( (sin (* 1/2 (+ 0 eps))) 2) (.f64 (fma.f64 (.f64 eps eps) #s(literal -1/24 binary64) #s(literal 1 binary64)) eps)) (cos.f64 (.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps)))) (patch (.f64 #s(approx (* (sin (* 1/2 (+ 0 eps))) 2) (.f64 (fma.f64 (.f64 eps eps) #s(literal -1/24 binary64) #s(literal 1 binary64)) eps)) (cos.f64 (*.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps)))) #<representation binary64>) () ())) ())
#s(alt (* eps (+ (cos x) (* -1/2 (* eps (sin x))))) (taylor 0 eps) (#s(alt (.f64 #s(approx ( (sin (* 1/2 (+ 0 eps))) 2) (.f64 (fma.f64 (.f64 eps eps) #s(literal -1/24 binary64) #s(literal 1 binary64)) eps)) (cos.f64 (.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps)))) (patch (.f64 #s(approx (* (sin (* 1/2 (+ 0 eps))) 2) (.f64 (fma.f64 (.f64 eps eps) #s(literal -1/24 binary64) #s(literal 1 binary64)) eps)) (cos.f64 (*.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps)))) #<representation binary64>) () ())) ())
#s(alt (* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* 2 (* eps (+ (* -1/16 (cos x)) (* -1/48 (cos x))))))))) (taylor 0 eps) (#s(alt (.f64 #s(approx ( (sin (* 1/2 (+ 0 eps))) 2) (.f64 (fma.f64 (.f64 eps eps) #s(literal -1/24 binary64) #s(literal 1 binary64)) eps)) (cos.f64 (.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps)))) (patch (.f64 #s(approx (* (sin (* 1/2 (+ 0 eps))) 2) (.f64 (fma.f64 (.f64 eps eps) #s(literal -1/24 binary64) #s(literal 1 binary64)) eps)) (cos.f64 (*.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps)))) #<representation binary64>) () ())) ())
#s(alt (* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* eps (+ (* 1/24 (* eps (sin x))) (* 2 (+ (* -1/16 (cos x)) (* -1/48 (cos x)))))))))) (taylor 0 eps) (#s(alt (.f64 #s(approx ( (sin (* 1/2 (+ 0 eps))) 2) (.f64 (fma.f64 (.f64 eps eps) #s(literal -1/24 binary64) #s(literal 1 binary64)) eps)) (cos.f64 (.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps)))) (patch (.f64 #s(approx (* (sin (* 1/2 (+ 0 eps))) 2) (.f64 (fma.f64 (.f64 eps eps) #s(literal -1/24 binary64) #s(literal 1 binary64)) eps)) (cos.f64 (*.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps)))) #<representation binary64>) () ())) ())
#s(alt eps (taylor 0 eps) (#s(alt #s(approx (* (sin (* 1/2 (+ 0 eps))) 2) (.f64 (fma.f64 (.f64 eps eps) #s(literal -1/24 binary64) #s(literal 1 binary64)) eps)) (patch #s(approx (* (sin (* 1/2 (+ 0 eps))) 2) (.f64 (fma.f64 (.f64 eps eps) #s(literal -1/24 binary64) #s(literal 1 binary64)) eps)) #<representation binary64>) () ())) ())
#s(alt (* eps (+ 1 (* -1/24 (pow eps 2)))) (taylor 0 eps) (#s(alt #s(approx (* (sin (* 1/2 (+ 0 eps))) 2) (.f64 (fma.f64 (.f64 eps eps) #s(literal -1/24 binary64) #s(literal 1 binary64)) eps)) (patch #s(approx (* (sin (* 1/2 (+ 0 eps))) 2) (.f64 (fma.f64 (.f64 eps eps) #s(literal -1/24 binary64) #s(literal 1 binary64)) eps)) #<representation binary64>) () ())) ())
#s(alt (* eps (+ 1 (* (pow eps 2) (- (* 1/1920 (pow eps 2)) 1/24)))) (taylor 0 eps) (#s(alt #s(approx (* (sin (* 1/2 (+ 0 eps))) 2) (.f64 (fma.f64 (.f64 eps eps) #s(literal -1/24 binary64) #s(literal 1 binary64)) eps)) (patch #s(approx (* (sin (* 1/2 (+ 0 eps))) 2) (.f64 (fma.f64 (.f64 eps eps) #s(literal -1/24 binary64) #s(literal 1 binary64)) eps)) #<representation binary64>) () ())) ())
#s(alt (* eps (+ 1 (* (pow eps 2) (- (* (pow eps 2) (+ 1/1920 (* -1/322560 (pow eps 2)))) 1/24)))) (taylor 0 eps) (#s(alt #s(approx (* (sin (* 1/2 (+ 0 eps))) 2) (.f64 (fma.f64 (.f64 eps eps) #s(literal -1/24 binary64) #s(literal 1 binary64)) eps)) (patch #s(approx (* (sin (* 1/2 (+ 0 eps))) 2) (.f64 (fma.f64 (.f64 eps eps) #s(literal -1/24 binary64) #s(literal 1 binary64)) eps)) #<representation binary64>) () ())) ())
#s(alt eps (taylor 0 eps) (#s(alt (.f64 (fma.f64 (.f64 eps eps) #s(literal -1/24 binary64) #s(literal 1 binary64)) eps) (patch (.f64 (fma.f64 (.f64 eps eps) #s(literal -1/24 binary64) #s(literal 1 binary64)) eps) #<representation binary64>) () ())) ())
#s(alt (* eps (+ 1 (* -1/24 (pow eps 2)))) (taylor 0 eps) (#s(alt (.f64 (fma.f64 (.f64 eps eps) #s(literal -1/24 binary64) #s(literal 1 binary64)) eps) (patch (.f64 (fma.f64 (.f64 eps eps) #s(literal -1/24 binary64) #s(literal 1 binary64)) eps) #<representation binary64>) () ())) ())
#s(alt (* eps (+ 1 (* -1/24 (pow eps 2)))) (taylor 0 eps) (#s(alt (.f64 (fma.f64 (.f64 eps eps) #s(literal -1/24 binary64) #s(literal 1 binary64)) eps) (patch (.f64 (fma.f64 (.f64 eps eps) #s(literal -1/24 binary64) #s(literal 1 binary64)) eps) #<representation binary64>) () ())) ())
#s(alt (* eps (+ 1 (* -1/24 (pow eps 2)))) (taylor 0 eps) (#s(alt (.f64 (fma.f64 (.f64 eps eps) #s(literal -1/24 binary64) #s(literal 1 binary64)) eps) (patch (.f64 (fma.f64 (.f64 eps eps) #s(literal -1/24 binary64) #s(literal 1 binary64)) eps) #<representation binary64>) () ())) ())
#s(alt (* eps (cos x)) (taylor 0 eps) (#s(alt #s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (+ (* (* eps eps) -1/6) 1) (cos x)) (* (* (sin x) -1/2) eps)) #s(approx (+ (* -1/6 (* eps eps)) 1) #s(literal 1 binary64))) eps)) (patch #s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (+ (* (* eps eps) -1/6) 1) (cos x)) (* (* (sin x) -1/2) eps)) #s(approx (+ (* -1/6 (* eps eps)) 1) #s(literal 1 binary64))) eps)) #<representation binary64>) () ())) ())
#s(alt (* eps (+ (cos x) (* -1/2 (* eps (sin x))))) (taylor 0 eps) (#s(alt #s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (+ (* (* eps eps) -1/6) 1) (cos x)) (* (* (sin x) -1/2) eps)) #s(approx (+ (* -1/6 (* eps eps)) 1) #s(literal 1 binary64))) eps)) (patch #s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (+ (* (* eps eps) -1/6) 1) (cos x)) (* (* (sin x) -1/2) eps)) #s(approx (+ (* -1/6 (* eps eps)) 1) #s(literal 1 binary64))) eps)) #<representation binary64>) () ())) ())
#s(alt (* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x))))))) (taylor 0 eps) (#s(alt #s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (+ (* (* eps eps) -1/6) 1) (cos x)) (* (* (sin x) -1/2) eps)) #s(approx (+ (* -1/6 (* eps eps)) 1) #s(literal 1 binary64))) eps)) (patch #s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (+ (* (* eps eps) -1/6) 1) (cos x)) (* (* (sin x) -1/2) eps)) #s(approx (+ (* -1/6 (* eps eps)) 1) #s(literal 1 binary64))) eps)) #<representation binary64>) () ())) ())
#s(alt (* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* eps (+ (* -1/6 (cos x)) (* 1/24 (* eps (sin x))))))))) (taylor 0 eps) (#s(alt #s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (+ (* (* eps eps) -1/6) 1) (cos x)) (* (* (sin x) -1/2) eps)) #s(approx (+ (* -1/6 (* eps eps)) 1) #s(literal 1 binary64))) eps)) (patch #s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (+ (* (* eps eps) -1/6) 1) (cos x)) (* (* (sin x) -1/2) eps)) #s(approx (+ (* -1/6 (* eps eps)) 1) #s(literal 1 binary64))) eps)) #<representation binary64>) () ())) ())
#s(alt (* eps (cos x)) (taylor 0 eps) (#s(alt (.f64 #s(approx (+ ( (+ (* (* eps eps) -1/6) 1) (cos x)) (* (* (sin x) -1/2) eps)) #s(approx (+ (* -1/6 (* eps eps)) 1) #s(literal 1 binary64))) eps) (patch (.f64 #s(approx (+ ( (+ (* (* eps eps) -1/6) 1) (cos x)) (* (* (sin x) -1/2) eps)) #s(approx (+ (* -1/6 (* eps eps)) 1) #s(literal 1 binary64))) eps) #<representation binary64>) () ())) ())
#s(alt (* eps (+ (cos x) (* -1/2 (* eps (sin x))))) (taylor 0 eps) (#s(alt (.f64 #s(approx (+ ( (+ (* (* eps eps) -1/6) 1) (cos x)) (* (* (sin x) -1/2) eps)) #s(approx (+ (* -1/6 (* eps eps)) 1) #s(literal 1 binary64))) eps) (patch (.f64 #s(approx (+ ( (+ (* (* eps eps) -1/6) 1) (cos x)) (* (* (sin x) -1/2) eps)) #s(approx (+ (* -1/6 (* eps eps)) 1) #s(literal 1 binary64))) eps) #<representation binary64>) () ())) ())
#s(alt (* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x))))))) (taylor 0 eps) (#s(alt (.f64 #s(approx (+ ( (+ (* (* eps eps) -1/6) 1) (cos x)) (* (* (sin x) -1/2) eps)) #s(approx (+ (* -1/6 (* eps eps)) 1) #s(literal 1 binary64))) eps) (patch (.f64 #s(approx (+ ( (+ (* (* eps eps) -1/6) 1) (cos x)) (* (* (sin x) -1/2) eps)) #s(approx (+ (* -1/6 (* eps eps)) 1) #s(literal 1 binary64))) eps) #<representation binary64>) () ())) ())
#s(alt (* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x))))))) (taylor 0 eps) (#s(alt (.f64 #s(approx (+ ( (+ (* (* eps eps) -1/6) 1) (cos x)) (* (* (sin x) -1/2) eps)) #s(approx (+ (* -1/6 (* eps eps)) 1) #s(literal 1 binary64))) eps) (patch (.f64 #s(approx (+ ( (+ (* (* eps eps) -1/6) 1) (cos x)) (* (* (sin x) -1/2) eps)) #s(approx (+ (* -1/6 (* eps eps)) 1) #s(literal 1 binary64))) eps) #<representation binary64>) () ())) ())
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#s(alt (- (sin (- eps (* -1 x))) (sin x)) (taylor -inf x) (#s(alt #s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (+ (* (* eps eps) -1/6) 1) (cos x)) (* (* (sin x) -1/2) eps)) (fma.f64 (fma.f64 (fma.f64 (.f64 #s(literal 1/12 binary64) eps) (+.f64 eps x) #s(literal -1/2 binary64)) x (.f64 #s(literal -1/2 binary64) eps)) x (fma.f64 #s(literal -1/6 binary64) (.f64 eps eps) #s(literal 1 binary64)))) eps)) (patch #s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ (* (+ (* (* eps eps) -1/6) 1) (cos x)) (* (* (sin x) -1/2) eps)) (fma.f64 (fma.f64 (fma.f64 (.f64 #s(literal 1/12 binary64) eps) (+.f64 eps x) #s(literal -1/2 binary64)) x (.f64 #s(literal -1/2 binary64) eps)) x (fma.f64 #s(literal -1/6 binary64) (*.f64 eps eps) #s(literal 1 binary64)))) eps)) #<representation binary64>) () ())) ())
#s(alt (- (sin (- eps (* -1 x))) (sin x)) (taylor -inf x) (#s(alt #s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (+ (* (* eps eps) -1/6) 1) (cos x)) (* (* (sin x) -1/2) eps)) (fma.f64 (fma.f64 (fma.f64 (.f64 #s(literal 1/12 binary64) eps) (+.f64 eps x) #s(literal -1/2 binary64)) x (.f64 #s(literal -1/2 binary64) eps)) x (fma.f64 #s(literal -1/6 binary64) (.f64 eps eps) #s(literal 1 binary64)))) eps)) (patch #s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ (* (+ (* (* eps eps) -1/6) 1) (cos x)) (* (* (sin x) -1/2) eps)) (fma.f64 (fma.f64 (fma.f64 (.f64 #s(literal 1/12 binary64) eps) (+.f64 eps x) #s(literal -1/2 binary64)) x (.f64 #s(literal -1/2 binary64) eps)) x (fma.f64 #s(literal -1/6 binary64) (*.f64 eps eps) #s(literal 1 binary64)))) eps)) #<representation binary64>) () ())) ())
#s(alt (* eps (+ (* -1/2 (* eps (sin x))) (* (cos x) (+ 1 (* -1/6 (pow eps 2)))))) (taylor -inf x) (#s(alt (.f64 #s(approx (+ ( (+ (* (* eps eps) -1/6) 1) (cos x)) (* (* (sin x) -1/2) eps)) (fma.f64 (fma.f64 (fma.f64 (.f64 #s(literal 1/12 binary64) eps) (+.f64 eps x) #s(literal -1/2 binary64)) x (.f64 #s(literal -1/2 binary64) eps)) x (fma.f64 #s(literal -1/6 binary64) (.f64 eps eps) #s(literal 1 binary64)))) eps) (patch (.f64 #s(approx (+ (* (+ (* (* eps eps) -1/6) 1) (cos x)) (* (* (sin x) -1/2) eps)) (fma.f64 (fma.f64 (fma.f64 (.f64 #s(literal 1/12 binary64) eps) (+.f64 eps x) #s(literal -1/2 binary64)) x (.f64 #s(literal -1/2 binary64) eps)) x (fma.f64 #s(literal -1/6 binary64) (*.f64 eps eps) #s(literal 1 binary64)))) eps) #<representation binary64>) () ())) ())
#s(alt (* eps (+ (* -1/2 (* eps (sin x))) (* (cos x) (+ 1 (* -1/6 (pow eps 2)))))) (taylor -inf x) (#s(alt (.f64 #s(approx (+ ( (+ (* (* eps eps) -1/6) 1) (cos x)) (* (* (sin x) -1/2) eps)) (fma.f64 (fma.f64 (fma.f64 (.f64 #s(literal 1/12 binary64) eps) (+.f64 eps x) #s(literal -1/2 binary64)) x (.f64 #s(literal -1/2 binary64) eps)) x (fma.f64 #s(literal -1/6 binary64) (.f64 eps eps) #s(literal 1 binary64)))) eps) (patch (.f64 #s(approx (+ (* (+ (* (* eps eps) -1/6) 1) (cos x)) (* (* (sin x) -1/2) eps)) (fma.f64 (fma.f64 (fma.f64 (.f64 #s(literal 1/12 binary64) eps) (+.f64 eps x) #s(literal -1/2 binary64)) x (.f64 #s(literal -1/2 binary64) eps)) x (fma.f64 #s(literal -1/6 binary64) (*.f64 eps eps) #s(literal 1 binary64)))) eps) #<representation binary64>) () ())) ())
#s(alt (* eps (+ (* -1/2 (* eps (sin x))) (* (cos x) (+ 1 (* -1/6 (pow eps 2)))))) (taylor -inf x) (#s(alt (.f64 #s(approx (+ ( (+ (* (* eps eps) -1/6) 1) (cos x)) (* (* (sin x) -1/2) eps)) (fma.f64 (fma.f64 (fma.f64 (.f64 #s(literal 1/12 binary64) eps) (+.f64 eps x) #s(literal -1/2 binary64)) x (.f64 #s(literal -1/2 binary64) eps)) x (fma.f64 #s(literal -1/6 binary64) (.f64 eps eps) #s(literal 1 binary64)))) eps) (patch (.f64 #s(approx (+ (* (+ (* (* eps eps) -1/6) 1) (cos x)) (* (* (sin x) -1/2) eps)) (fma.f64 (fma.f64 (fma.f64 (.f64 #s(literal 1/12 binary64) eps) (+.f64 eps x) #s(literal -1/2 binary64)) x (.f64 #s(literal -1/2 binary64) eps)) x (fma.f64 #s(literal -1/6 binary64) (*.f64 eps eps) #s(literal 1 binary64)))) eps) #<representation binary64>) () ())) ())
#s(alt (* eps (+ (* -1/2 (* eps (sin x))) (* (cos x) (+ 1 (* -1/6 (pow eps 2)))))) (taylor -inf x) (#s(alt (.f64 #s(approx (+ ( (+ (* (* eps eps) -1/6) 1) (cos x)) (* (* (sin x) -1/2) eps)) (fma.f64 (fma.f64 (fma.f64 (.f64 #s(literal 1/12 binary64) eps) (+.f64 eps x) #s(literal -1/2 binary64)) x (.f64 #s(literal -1/2 binary64) eps)) x (fma.f64 #s(literal -1/6 binary64) (.f64 eps eps) #s(literal 1 binary64)))) eps) (patch (.f64 #s(approx (+ (* (+ (* (* eps eps) -1/6) 1) (cos x)) (* (* (sin x) -1/2) eps)) (fma.f64 (fma.f64 (fma.f64 (.f64 #s(literal 1/12 binary64) eps) (+.f64 eps x) #s(literal -1/2 binary64)) x (.f64 #s(literal -1/2 binary64) eps)) x (fma.f64 #s(literal -1/6 binary64) (*.f64 eps eps) #s(literal 1 binary64)))) eps) #<representation binary64>) () ())) ())
#s(alt (+ (* -1/2 (* eps (sin x))) (* (cos x) (+ 1 (* -1/6 (pow eps 2))))) (taylor -inf x) (#s(alt #s(approx (+ (* (+ (* (* eps eps) -1/6) 1) (cos x)) (* (* (sin x) -1/2) eps)) (fma.f64 (fma.f64 (fma.f64 (.f64 #s(literal 1/12 binary64) eps) (+.f64 eps x) #s(literal -1/2 binary64)) x (.f64 #s(literal -1/2 binary64) eps)) x (fma.f64 #s(literal -1/6 binary64) (.f64 eps eps) #s(literal 1 binary64)))) (patch #s(approx (+ ( (+ (* (* eps eps) -1/6) 1) (cos x)) (* (* (sin x) -1/2) eps)) (fma.f64 (fma.f64 (fma.f64 (.f64 #s(literal 1/12 binary64) eps) (+.f64 eps x) #s(literal -1/2 binary64)) x (.f64 #s(literal -1/2 binary64) eps)) x (fma.f64 #s(literal -1/6 binary64) (*.f64 eps eps) #s(literal 1 binary64)))) #<representation binary64>) () ())) ())
#s(alt (+ (* -1/2 (* eps (sin x))) (* (cos x) (+ 1 (* -1/6 (pow eps 2))))) (taylor -inf x) (#s(alt #s(approx (+ (* (+ (* (* eps eps) -1/6) 1) (cos x)) (* (* (sin x) -1/2) eps)) (fma.f64 (fma.f64 (fma.f64 (.f64 #s(literal 1/12 binary64) eps) (+.f64 eps x) #s(literal -1/2 binary64)) x (.f64 #s(literal -1/2 binary64) eps)) x (fma.f64 #s(literal -1/6 binary64) (.f64 eps eps) #s(literal 1 binary64)))) (patch #s(approx (+ ( (+ (* (* eps eps) -1/6) 1) (cos x)) (* (* (sin x) -1/2) eps)) (fma.f64 (fma.f64 (fma.f64 (.f64 #s(literal 1/12 binary64) eps) (+.f64 eps x) #s(literal -1/2 binary64)) x (.f64 #s(literal -1/2 binary64) eps)) x (fma.f64 #s(literal -1/6 binary64) (*.f64 eps eps) #s(literal 1 binary64)))) #<representation binary64>) () ())) ())
#s(alt (+ (* -1/2 (* eps (sin x))) (* (cos x) (+ 1 (* -1/6 (pow eps 2))))) (taylor -inf x) (#s(alt #s(approx (+ (* (+ (* (* eps eps) -1/6) 1) (cos x)) (* (* (sin x) -1/2) eps)) (fma.f64 (fma.f64 (fma.f64 (.f64 #s(literal 1/12 binary64) eps) (+.f64 eps x) #s(literal -1/2 binary64)) x (.f64 #s(literal -1/2 binary64) eps)) x (fma.f64 #s(literal -1/6 binary64) (.f64 eps eps) #s(literal 1 binary64)))) (patch #s(approx (+ ( (+ (* (* eps eps) -1/6) 1) (cos x)) (* (* (sin x) -1/2) eps)) (fma.f64 (fma.f64 (fma.f64 (.f64 #s(literal 1/12 binary64) eps) (+.f64 eps x) #s(literal -1/2 binary64)) x (.f64 #s(literal -1/2 binary64) eps)) x (fma.f64 #s(literal -1/6 binary64) (*.f64 eps eps) #s(literal 1 binary64)))) #<representation binary64>) () ())) ())
#s(alt (+ (* -1/2 (* eps (sin x))) (* (cos x) (+ 1 (* -1/6 (pow eps 2))))) (taylor -inf x) (#s(alt #s(approx (+ (* (+ (* (* eps eps) -1/6) 1) (cos x)) (* (* (sin x) -1/2) eps)) (fma.f64 (fma.f64 (fma.f64 (.f64 #s(literal 1/12 binary64) eps) (+.f64 eps x) #s(literal -1/2 binary64)) x (.f64 #s(literal -1/2 binary64) eps)) x (fma.f64 #s(literal -1/6 binary64) (.f64 eps eps) #s(literal 1 binary64)))) (patch #s(approx (+ ( (+ (* (* eps eps) -1/6) 1) (cos x)) (* (* (sin x) -1/2) eps)) (fma.f64 (fma.f64 (fma.f64 (.f64 #s(literal 1/12 binary64) eps) (+.f64 eps x) #s(literal -1/2 binary64)) x (.f64 #s(literal -1/2 binary64) eps)) x (fma.f64 #s(literal -1/6 binary64) (*.f64 eps eps) #s(literal 1 binary64)))) #<representation binary64>) () ())) ())
#s(alt (* 2 (* (cos (* 1/2 (- eps (* -2 x)))) (sin (* 1/2 eps)))) (taylor -inf x) (#s(alt (.f64 (.f64 #s(approx (sin (* 1/2 (+ 0 eps))) (.f64 eps #s(literal 1/2 binary64))) #s(literal 2 binary64)) (cos.f64 #s(approx ( 1/2 (+ (* 2 x) eps)) (fma.f64 eps #s(literal 1/2 binary64) x)))) (patch (.f64 (.f64 #s(approx (sin (* 1/2 (+ 0 eps))) (.f64 eps #s(literal 1/2 binary64))) #s(literal 2 binary64)) (cos.f64 #s(approx ( 1/2 (+ (* 2 x) eps)) (fma.f64 eps #s(literal 1/2 binary64) x)))) #<representation binary64>) () ())) ())
#s(alt (* 2 (* (cos (* 1/2 (- eps (* -2 x)))) (sin (* 1/2 eps)))) (taylor -inf x) (#s(alt (.f64 (.f64 #s(approx (sin (* 1/2 (+ 0 eps))) (.f64 eps #s(literal 1/2 binary64))) #s(literal 2 binary64)) (cos.f64 #s(approx ( 1/2 (+ (* 2 x) eps)) (fma.f64 eps #s(literal 1/2 binary64) x)))) (patch (.f64 (.f64 #s(approx (sin (* 1/2 (+ 0 eps))) (.f64 eps #s(literal 1/2 binary64))) #s(literal 2 binary64)) (cos.f64 #s(approx ( 1/2 (+ (* 2 x) eps)) (fma.f64 eps #s(literal 1/2 binary64) x)))) #<representation binary64>) () ())) ())
#s(alt (* 2 (* (cos (* 1/2 (- eps (* -2 x)))) (sin (* 1/2 eps)))) (taylor -inf x) (#s(alt (.f64 (.f64 #s(approx (sin (* 1/2 (+ 0 eps))) (.f64 eps #s(literal 1/2 binary64))) #s(literal 2 binary64)) (cos.f64 #s(approx ( 1/2 (+ (* 2 x) eps)) (fma.f64 eps #s(literal 1/2 binary64) x)))) (patch (.f64 (.f64 #s(approx (sin (* 1/2 (+ 0 eps))) (.f64 eps #s(literal 1/2 binary64))) #s(literal 2 binary64)) (cos.f64 #s(approx ( 1/2 (+ (* 2 x) eps)) (fma.f64 eps #s(literal 1/2 binary64) x)))) #<representation binary64>) () ())) ())
#s(alt (* 2 (* (cos (* 1/2 (- eps (* -2 x)))) (sin (* 1/2 eps)))) (taylor -inf x) (#s(alt (.f64 (.f64 #s(approx (sin (* 1/2 (+ 0 eps))) (.f64 eps #s(literal 1/2 binary64))) #s(literal 2 binary64)) (cos.f64 #s(approx ( 1/2 (+ (* 2 x) eps)) (fma.f64 eps #s(literal 1/2 binary64) x)))) (patch (.f64 (.f64 #s(approx (sin (* 1/2 (+ 0 eps))) (.f64 eps #s(literal 1/2 binary64))) #s(literal 2 binary64)) (cos.f64 #s(approx ( 1/2 (+ (* 2 x) eps)) (fma.f64 eps #s(literal 1/2 binary64) x)))) #<representation binary64>) () ())) ())
#s(alt (cos (* 1/2 (- eps (* -2 x)))) (taylor -inf x) (#s(alt (cos.f64 (.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps))) (patch (cos.f64 (.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps))) #<representation binary64>) () ())) ())
#s(alt (cos (* 1/2 (- eps (* -2 x)))) (taylor -inf x) (#s(alt (cos.f64 (.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps))) (patch (cos.f64 (.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps))) #<representation binary64>) () ())) ())
#s(alt (cos (* 1/2 (- eps (* -2 x)))) (taylor -inf x) (#s(alt (cos.f64 (.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps))) (patch (cos.f64 (.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps))) #<representation binary64>) () ())) ())
#s(alt (cos (* 1/2 (- eps (* -2 x)))) (taylor -inf x) (#s(alt (cos.f64 (.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps))) (patch (cos.f64 (.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps))) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor -inf x) (#s(alt (.f64 x (+.f64 eps x)) (patch (.f64 x (+.f64 eps x)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (+ 1 (/ eps x))) (taylor -inf x) (#s(alt (.f64 x (+.f64 eps x)) (patch (.f64 x (+.f64 eps x)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (+ 1 (/ eps x))) (taylor -inf x) (#s(alt (.f64 x (+.f64 eps x)) (patch (.f64 x (+.f64 eps x)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (+ 1 (/ eps x))) (taylor -inf x) (#s(alt (.f64 x (+.f64 eps x)) (patch (.f64 x (+.f64 eps x)) #<representation binary64>) () ())) ())
#s(alt (cos (* 1/2 (- eps (* -2 x)))) (taylor -inf x) (#s(alt (cos.f64 #s(approx (* 1/2 (+ (* 2 x) eps)) (fma.f64 eps #s(literal 1/2 binary64) x))) (patch (cos.f64 #s(approx (* 1/2 (+ (* 2 x) eps)) (fma.f64 eps #s(literal 1/2 binary64) x))) #<representation binary64>) () ())) ())
#s(alt (cos (* 1/2 (- eps (* -2 x)))) (taylor -inf x) (#s(alt (cos.f64 #s(approx (* 1/2 (+ (* 2 x) eps)) (fma.f64 eps #s(literal 1/2 binary64) x))) (patch (cos.f64 #s(approx (* 1/2 (+ (* 2 x) eps)) (fma.f64 eps #s(literal 1/2 binary64) x))) #<representation binary64>) () ())) ())
#s(alt (cos (* 1/2 (- eps (* -2 x)))) (taylor -inf x) (#s(alt (cos.f64 #s(approx (* 1/2 (+ (* 2 x) eps)) (fma.f64 eps #s(literal 1/2 binary64) x))) (patch (cos.f64 #s(approx (* 1/2 (+ (* 2 x) eps)) (fma.f64 eps #s(literal 1/2 binary64) x))) #<representation binary64>) () ())) ())
#s(alt (cos (* 1/2 (- eps (* -2 x)))) (taylor -inf x) (#s(alt (cos.f64 #s(approx (* 1/2 (+ (* 2 x) eps)) (fma.f64 eps #s(literal 1/2 binary64) x))) (patch (cos.f64 #s(approx (* 1/2 (+ (* 2 x) eps)) (fma.f64 eps #s(literal 1/2 binary64) x))) #<representation binary64>) () ())) ())
#s(alt x (taylor -inf x) (#s(alt #s(approx (* 1/2 (+ (* 2 x) eps)) (fma.f64 eps #s(literal 1/2 binary64) x)) (patch #s(approx (* 1/2 (+ (* 2 x) eps)) (fma.f64 eps #s(literal 1/2 binary64) x)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (- (* -1/2 (/ eps x)) 1))) (taylor -inf x) (#s(alt #s(approx (* 1/2 (+ (* 2 x) eps)) (fma.f64 eps #s(literal 1/2 binary64) x)) (patch #s(approx (* 1/2 (+ (* 2 x) eps)) (fma.f64 eps #s(literal 1/2 binary64) x)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (- (* -1/2 (/ eps x)) 1))) (taylor -inf x) (#s(alt #s(approx (* 1/2 (+ (* 2 x) eps)) (fma.f64 eps #s(literal 1/2 binary64) x)) (patch #s(approx (* 1/2 (+ (* 2 x) eps)) (fma.f64 eps #s(literal 1/2 binary64) x)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (- (* -1/2 (/ eps x)) 1))) (taylor -inf x) (#s(alt #s(approx (* 1/2 (+ (* 2 x) eps)) (fma.f64 eps #s(literal 1/2 binary64) x)) (patch #s(approx (* 1/2 (+ (* 2 x) eps)) (fma.f64 eps #s(literal 1/2 binary64) x)) #<representation binary64>) () ())) ())

Calls

6 calls:

Time	Variable		Point	Expression
3.0ms	eps	@	-inf	((* 1/2 (+ (* 2 x) eps)) (* (* (sin (* 1/2 (+ 0 eps))) 2) (cos (* 1/2 (+ (* 2 x) eps)))) (* (sin (* 1/2 (+ 0 eps))) 2) (* (+ (* (* eps eps) -1/24) 1) eps) (- (sin (+ x eps)) (sin x)) (* (+ (* (+ (* (* eps eps) -1/6) 1) (cos x)) (* (* (sin x) -1/2) eps)) eps) (+ (* (+ (* (* eps eps) -1/6) 1) (cos x)) (* (* (sin x) -1/2) eps)) (+ (* -1/6 (* eps eps)) 1) (- (sin (+ x eps)) (sin x)) (* (+ (* (+ (* (* eps eps) -1/6) 1) (cos x)) (* (* (sin x) -1/2) eps)) eps) (+ (* (+ (* (* eps eps) -1/6) 1) (cos x)) (* (* (sin x) -1/2) eps)) (+ (* (* (+ (* (+ (* -1/6 (* eps eps)) 1) x) eps) -1/2) x) (+ (* -1/6 (* eps eps)) 1)) (+ (* (+ (* (* 1/12 eps) (+ eps x)) -1/2) x) (* -1/2 eps)) (- (sin (+ x eps)) (sin x)) (* (+ (* (+ (* (* eps eps) -1/6) 1) (cos x)) (* (* (sin x) -1/2) eps)) eps) (+ (* (+ (* (* eps eps) -1/6) 1) (cos x)) (* (* (sin x) -1/2) eps)) (* (* (sin (* 1/2 (+ 0 eps))) 2) (cos (* 1/2 (+ (* 2 x) eps)))) (* (sin (* 1/2 (+ 0 eps))) 2) (sin (* 1/2 (+ 0 eps))) (* eps 1/2) (cos (* 1/2 (+ (* 2 x) eps))) (* x (+ eps x)) (* 1/12 eps) (cos (* 1/2 (+ (* 2 x) eps))) (* 1/2 (+ (* 2 x) eps)))
3.0ms	eps	@	inf	((* 1/2 (+ (* 2 x) eps)) (* (* (sin (* 1/2 (+ 0 eps))) 2) (cos (* 1/2 (+ (* 2 x) eps)))) (* (sin (* 1/2 (+ 0 eps))) 2) (* (+ (* (* eps eps) -1/24) 1) eps) (- (sin (+ x eps)) (sin x)) (* (+ (* (+ (* (* eps eps) -1/6) 1) (cos x)) (* (* (sin x) -1/2) eps)) eps) (+ (* (+ (* (* eps eps) -1/6) 1) (cos x)) (* (* (sin x) -1/2) eps)) (+ (* -1/6 (* eps eps)) 1) (- (sin (+ x eps)) (sin x)) (* (+ (* (+ (* (* eps eps) -1/6) 1) (cos x)) (* (* (sin x) -1/2) eps)) eps) (+ (* (+ (* (* eps eps) -1/6) 1) (cos x)) (* (* (sin x) -1/2) eps)) (+ (* (* (+ (* (+ (* -1/6 (* eps eps)) 1) x) eps) -1/2) x) (+ (* -1/6 (* eps eps)) 1)) (+ (* (+ (* (* 1/12 eps) (+ eps x)) -1/2) x) (* -1/2 eps)) (- (sin (+ x eps)) (sin x)) (* (+ (* (+ (* (* eps eps) -1/6) 1) (cos x)) (* (* (sin x) -1/2) eps)) eps) (+ (* (+ (* (* eps eps) -1/6) 1) (cos x)) (* (* (sin x) -1/2) eps)) (* (* (sin (* 1/2 (+ 0 eps))) 2) (cos (* 1/2 (+ (* 2 x) eps)))) (* (sin (* 1/2 (+ 0 eps))) 2) (sin (* 1/2 (+ 0 eps))) (* eps 1/2) (cos (* 1/2 (+ (* 2 x) eps))) (* x (+ eps x)) (* 1/12 eps) (cos (* 1/2 (+ (* 2 x) eps))) (* 1/2 (+ (* 2 x) eps)))
3.0ms	x	@	-inf	((* 1/2 (+ (* 2 x) eps)) (* (* (sin (* 1/2 (+ 0 eps))) 2) (cos (* 1/2 (+ (* 2 x) eps)))) (* (sin (* 1/2 (+ 0 eps))) 2) (* (+ (* (* eps eps) -1/24) 1) eps) (- (sin (+ x eps)) (sin x)) (* (+ (* (+ (* (* eps eps) -1/6) 1) (cos x)) (* (* (sin x) -1/2) eps)) eps) (+ (* (+ (* (* eps eps) -1/6) 1) (cos x)) (* (* (sin x) -1/2) eps)) (+ (* -1/6 (* eps eps)) 1) (- (sin (+ x eps)) (sin x)) (* (+ (* (+ (* (* eps eps) -1/6) 1) (cos x)) (* (* (sin x) -1/2) eps)) eps) (+ (* (+ (* (* eps eps) -1/6) 1) (cos x)) (* (* (sin x) -1/2) eps)) (+ (* (* (+ (* (+ (* -1/6 (* eps eps)) 1) x) eps) -1/2) x) (+ (* -1/6 (* eps eps)) 1)) (+ (* (+ (* (* 1/12 eps) (+ eps x)) -1/2) x) (* -1/2 eps)) (- (sin (+ x eps)) (sin x)) (* (+ (* (+ (* (* eps eps) -1/6) 1) (cos x)) (* (* (sin x) -1/2) eps)) eps) (+ (* (+ (* (* eps eps) -1/6) 1) (cos x)) (* (* (sin x) -1/2) eps)) (* (* (sin (* 1/2 (+ 0 eps))) 2) (cos (* 1/2 (+ (* 2 x) eps)))) (* (sin (* 1/2 (+ 0 eps))) 2) (sin (* 1/2 (+ 0 eps))) (* eps 1/2) (cos (* 1/2 (+ (* 2 x) eps))) (* x (+ eps x)) (* 1/12 eps) (cos (* 1/2 (+ (* 2 x) eps))) (* 1/2 (+ (* 2 x) eps)))
3.0ms	x	@	inf	((* 1/2 (+ (* 2 x) eps)) (* (* (sin (* 1/2 (+ 0 eps))) 2) (cos (* 1/2 (+ (* 2 x) eps)))) (* (sin (* 1/2 (+ 0 eps))) 2) (* (+ (* (* eps eps) -1/24) 1) eps) (- (sin (+ x eps)) (sin x)) (* (+ (* (+ (* (* eps eps) -1/6) 1) (cos x)) (* (* (sin x) -1/2) eps)) eps) (+ (* (+ (* (* eps eps) -1/6) 1) (cos x)) (* (* (sin x) -1/2) eps)) (+ (* -1/6 (* eps eps)) 1) (- (sin (+ x eps)) (sin x)) (* (+ (* (+ (* (* eps eps) -1/6) 1) (cos x)) (* (* (sin x) -1/2) eps)) eps) (+ (* (+ (* (* eps eps) -1/6) 1) (cos x)) (* (* (sin x) -1/2) eps)) (+ (* (* (+ (* (+ (* -1/6 (* eps eps)) 1) x) eps) -1/2) x) (+ (* -1/6 (* eps eps)) 1)) (+ (* (+ (* (* 1/12 eps) (+ eps x)) -1/2) x) (* -1/2 eps)) (- (sin (+ x eps)) (sin x)) (* (+ (* (+ (* (* eps eps) -1/6) 1) (cos x)) (* (* (sin x) -1/2) eps)) eps) (+ (* (+ (* (* eps eps) -1/6) 1) (cos x)) (* (* (sin x) -1/2) eps)) (* (* (sin (* 1/2 (+ 0 eps))) 2) (cos (* 1/2 (+ (* 2 x) eps)))) (* (sin (* 1/2 (+ 0 eps))) 2) (sin (* 1/2 (+ 0 eps))) (* eps 1/2) (cos (* 1/2 (+ (* 2 x) eps))) (* x (+ eps x)) (* 1/12 eps) (cos (* 1/2 (+ (* 2 x) eps))) (* 1/2 (+ (* 2 x) eps)))
2.0ms	eps	@	0	((* 1/2 (+ (* 2 x) eps)) (* (* (sin (* 1/2 (+ 0 eps))) 2) (cos (* 1/2 (+ (* 2 x) eps)))) (* (sin (* 1/2 (+ 0 eps))) 2) (* (+ (* (* eps eps) -1/24) 1) eps) (- (sin (+ x eps)) (sin x)) (* (+ (* (+ (* (* eps eps) -1/6) 1) (cos x)) (* (* (sin x) -1/2) eps)) eps) (+ (* (+ (* (* eps eps) -1/6) 1) (cos x)) (* (* (sin x) -1/2) eps)) (+ (* -1/6 (* eps eps)) 1) (- (sin (+ x eps)) (sin x)) (* (+ (* (+ (* (* eps eps) -1/6) 1) (cos x)) (* (* (sin x) -1/2) eps)) eps) (+ (* (+ (* (* eps eps) -1/6) 1) (cos x)) (* (* (sin x) -1/2) eps)) (+ (* (* (+ (* (+ (* -1/6 (* eps eps)) 1) x) eps) -1/2) x) (+ (* -1/6 (* eps eps)) 1)) (+ (* (+ (* (* 1/12 eps) (+ eps x)) -1/2) x) (* -1/2 eps)) (- (sin (+ x eps)) (sin x)) (* (+ (* (+ (* (* eps eps) -1/6) 1) (cos x)) (* (* (sin x) -1/2) eps)) eps) (+ (* (+ (* (* eps eps) -1/6) 1) (cos x)) (* (* (sin x) -1/2) eps)) (* (* (sin (* 1/2 (+ 0 eps))) 2) (cos (* 1/2 (+ (* 2 x) eps)))) (* (sin (* 1/2 (+ 0 eps))) 2) (sin (* 1/2 (+ 0 eps))) (* eps 1/2) (cos (* 1/2 (+ (* 2 x) eps))) (* x (+ eps x)) (* 1/12 eps) (cos (* 1/2 (+ (* 2 x) eps))) (* 1/2 (+ (* 2 x) eps)))

simplify280.0ms (2.4%)

Memory

1.6MiB live, 232.9MiB allocated

Algorithm

1×	egg-herbie

Rules

14 890×	`lower-fma.f64`
14 890×	`lower-fma.f32`
6 998×	`lower-*.f64`
6 998×	`lower-*.f32`
3 666×	`lower-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	414	6293
1	1267	5942
2	3706	5934
0	8103	5384

Stop Event

1×	iter limit
1×	node limit

Counts

516 → 507

Calls

Call 1

Inputs
x
(+ x (* 1/2 eps))
(+ x (* 1/2 eps))
(+ x (* 1/2 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))))))))))
eps
(* eps (+ 1 (* -1/24 (pow eps 2))))
(* eps (+ 1 (* (pow eps 2) (- (* 1/1920 (pow eps 2)) 1/24))))
(* eps (+ 1 (* (pow eps 2) (- (* (pow eps 2) (+ 1/1920 (* -1/322560 (pow eps 2)))) 1/24))))
eps
(* eps (+ 1 (* -1/24 (pow eps 2))))
(* eps (+ 1 (* -1/24 (pow eps 2))))
(* eps (+ 1 (* -1/24 (pow eps 2))))
(* eps (cos x))
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x)))))))
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* eps (+ (* -1/6 (cos x)) (* 1/24 (* eps (sin x)))))))))
(* eps (cos x))
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x)))))))
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x)))))))
(cos x)
(+ (cos x) (* -1/2 (* eps (sin x))))
(+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x))))))
(+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x))))))
1
(+ 1 (* -1/6 (pow eps 2)))
(+ 1 (* -1/6 (pow eps 2)))
(+ 1 (* -1/6 (pow eps 2)))
(* eps (cos x))
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x)))))))
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* eps (+ (* -1/6 (cos x)) (* 1/24 (* eps (sin x)))))))))
(* eps (cos x))
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x)))))))
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x)))))))
(cos x)
(+ (cos x) (* -1/2 (* eps (sin x))))
(+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x))))))
(+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x))))))
(+ 1 (* -1/2 (pow x 2)))
(+ 1 (+ (* -1/2 (* eps x)) (* -1/2 (pow x 2))))
(+ 1 (+ (* -1/2 (pow x 2)) (* eps (+ (* -1/2 x) (* eps (- (* 1/12 (pow x 2)) 1/6))))))
(+ 1 (+ (* -1/2 (pow x 2)) (* eps (+ (* -1/2 x) (* eps (- (* 1/12 (pow x 2)) 1/6))))))
(* -1/2 x)
(+ (* -1/2 x) (* eps (- (* 1/12 (pow x 2)) 1/2)))
(+ (* -1/2 x) (* eps (- (+ (* 1/12 (* eps x)) (* 1/12 (pow x 2))) 1/2)))
(+ (* -1/2 x) (* eps (- (+ (* 1/12 (* eps x)) (* 1/12 (pow x 2))) 1/2)))
(* eps (cos x))
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x)))))))
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* eps (+ (* -1/6 (cos x)) (* 1/24 (* eps (sin x)))))))))
(* eps (cos x))
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x)))))))
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x)))))))
(cos x)
(+ (cos x) (* -1/2 (* eps (sin x))))
(+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x))))))
(+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x))))))
(* 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))))))))))
eps
(* eps (+ 1 (* -1/24 (pow eps 2))))
(* eps (+ 1 (* (pow eps 2) (- (* 1/1920 (pow eps 2)) 1/24))))
(* eps (+ 1 (* (pow eps 2) (- (* (pow eps 2) (+ 1/1920 (* -1/322560 (pow eps 2)))) 1/24))))
(* 1/2 eps)
(* eps (+ 1/2 (* -1/48 (pow eps 2))))
(* eps (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48))))
(* eps (+ 1/2 (* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48))))
(* 1/2 eps)
(* 1/2 eps)
(* 1/2 eps)
(* 1/2 eps)
(cos x)
(+ (cos x) (* -1/2 (* eps (sin x))))
(+ (cos x) (* eps (- (* -1/8 (* eps (cos x))) (* 1/2 (sin x)))))
(+ (cos x) (* eps (- (* eps (+ (* -1/8 (cos x)) (* 1/48 (* eps (sin x))))) (* 1/2 (sin x)))))
(pow x 2)
(+ (* eps x) (pow x 2))
(+ (* eps x) (pow x 2))
(+ (* eps x) (pow x 2))
(* 1/12 eps)
(* 1/12 eps)
(* 1/12 eps)
(* 1/12 eps)
(cos x)
(+ (cos x) (* -1/2 (* eps (sin x))))
(+ (cos x) (* eps (- (* -1/8 (* eps (cos x))) (* 1/2 (sin x)))))
(+ (cos x) (* eps (- (* eps (+ (* -1/8 (cos x)) (* 1/48 (* eps (sin x))))) (* 1/2 (sin x)))))
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)))
(* 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 (sin (* 1/2 eps)))
(* 2 (sin (* 1/2 eps)))
(* 2 (sin (* 1/2 eps)))
(* 2 (sin (* 1/2 eps)))
(* -1/24 (pow eps 3))
(* (pow eps 3) (- (/ 1 (pow eps 2)) 1/24))
(* (pow eps 3) (- (/ 1 (pow eps 2)) 1/24))
(* (pow eps 3) (- (/ 1 (pow eps 2)) 1/24))
(- (sin (+ eps x)) (sin x))
(- (sin (+ eps x)) (sin x))
(- (sin (+ eps x)) (sin x))
(- (sin (+ eps x)) (sin x))
(* -1/6 (* (pow eps 3) (cos x)))
(* (pow eps 3) (+ (* -1/2 (/ (sin x) eps)) (* -1/6 (cos x))))
(* (pow eps 3) (+ (* -1/2 (/ (sin x) eps)) (+ (* -1/6 (cos x)) (/ (cos x) (pow eps 2)))))
(* (pow eps 3) (+ (* -1/2 (/ (sin x) eps)) (+ (* -1/6 (cos x)) (/ (cos x) (pow eps 2)))))
(* -1/6 (* (pow eps 2) (cos x)))
(* (pow eps 2) (+ (* -1/2 (/ (sin x) eps)) (* -1/6 (cos x))))
(* (pow eps 2) (+ (* -1/2 (/ (sin x) eps)) (+ (* -1/6 (cos x)) (/ (cos x) (pow eps 2)))))
(* (pow eps 2) (+ (* -1/2 (/ (sin x) eps)) (+ (* -1/6 (cos x)) (/ (cos x) (pow eps 2)))))
(* -1/6 (pow eps 2))
(* (pow eps 2) (- (/ 1 (pow eps 2)) 1/6))
(* (pow eps 2) (- (/ 1 (pow eps 2)) 1/6))
(* (pow eps 2) (- (/ 1 (pow eps 2)) 1/6))
(- (sin (+ eps x)) (sin x))
(- (sin (+ eps x)) (sin x))
(- (sin (+ eps x)) (sin x))
(- (sin (+ eps x)) (sin x))
(* -1/6 (* (pow eps 3) (cos x)))
(* (pow eps 3) (+ (* -1/2 (/ (sin x) eps)) (* -1/6 (cos x))))
(* (pow eps 3) (+ (* -1/2 (/ (sin x) eps)) (+ (* -1/6 (cos x)) (/ (cos x) (pow eps 2)))))
(* (pow eps 3) (+ (* -1/2 (/ (sin x) eps)) (+ (* -1/6 (cos x)) (/ (cos x) (pow eps 2)))))
(* -1/6 (* (pow eps 2) (cos x)))
(* (pow eps 2) (+ (* -1/2 (/ (sin x) eps)) (* -1/6 (cos x))))
(* (pow eps 2) (+ (* -1/2 (/ (sin x) eps)) (+ (* -1/6 (cos x)) (/ (cos x) (pow eps 2)))))
(* (pow eps 2) (+ (* -1/2 (/ (sin x) eps)) (+ (* -1/6 (cos x)) (/ (cos x) (pow eps 2)))))
(* (pow eps 2) (- (* 1/12 (pow x 2)) 1/6))
(* (pow eps 2) (- (+ (* -1/2 (/ x eps)) (* 1/12 (pow x 2))) 1/6))
(* (pow eps 2) (- (+ (* -1/2 (/ x eps)) (+ (* -1/2 (/ (pow x 2) (pow eps 2))) (+ (* 1/12 (pow x 2)) (/ 1 (pow eps 2))))) 1/6))
(* (pow eps 2) (- (+ (* -1/2 (/ x eps)) (+ (* -1/2 (/ (pow x 2) (pow eps 2))) (+ (* 1/12 (pow x 2)) (/ 1 (pow eps 2))))) 1/6))
(* 1/12 (* (pow eps 2) x))
(* (pow eps 2) (- (+ (* 1/12 x) (* 1/12 (/ (pow x 2) eps))) (* 1/2 (/ 1 eps))))
(* (pow eps 2) (- (+ (* -1/2 (/ x (pow eps 2))) (+ (* 1/12 x) (* 1/12 (/ (pow x 2) eps)))) (* 1/2 (/ 1 eps))))
(* (pow eps 2) (- (+ (* -1/2 (/ x (pow eps 2))) (+ (* 1/12 x) (* 1/12 (/ (pow x 2) eps)))) (* 1/2 (/ 1 eps))))
(- (sin (+ eps x)) (sin x))
(- (sin (+ eps x)) (sin x))
(- (sin (+ eps x)) (sin x))
(- (sin (+ eps x)) (sin x))
(* -1/6 (* (pow eps 3) (cos x)))
(* (pow eps 3) (+ (* -1/2 (/ (sin x) eps)) (* -1/6 (cos x))))
(* (pow eps 3) (+ (* -1/2 (/ (sin x) eps)) (+ (* -1/6 (cos x)) (/ (cos x) (pow eps 2)))))
(* (pow eps 3) (+ (* -1/2 (/ (sin x) eps)) (+ (* -1/6 (cos x)) (/ (cos x) (pow eps 2)))))
(* -1/6 (* (pow eps 2) (cos x)))
(* (pow eps 2) (+ (* -1/2 (/ (sin x) eps)) (* -1/6 (cos x))))
(* (pow eps 2) (+ (* -1/2 (/ (sin x) eps)) (+ (* -1/6 (cos x)) (/ (cos x) (pow eps 2)))))
(* (pow eps 2) (+ (* -1/2 (/ (sin x) eps)) (+ (* -1/6 (cos x)) (/ (cos x) (pow eps 2)))))
(* 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 (sin (* 1/2 eps)))
(* 2 (sin (* 1/2 eps)))
(* 2 (sin (* 1/2 eps)))
(* 2 (sin (* 1/2 eps)))
(sin (* 1/2 eps))
(sin (* 1/2 eps))
(sin (* 1/2 eps))
(sin (* 1/2 eps))
(* 1/2 eps)
(* 1/2 eps)
(* 1/2 eps)
(* 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))))
(* eps x)
(* eps (+ x (/ (pow x 2) eps)))
(* eps (+ x (/ (pow x 2) eps)))
(* eps (+ x (/ (pow x 2) eps)))
(* 1/12 eps)
(* 1/12 eps)
(* 1/12 eps)
(* 1/12 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))))
(* 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)))
(* 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 (sin (* 1/2 eps)))
(* 2 (sin (* 1/2 eps)))
(* 2 (sin (* 1/2 eps)))
(* 2 (sin (* 1/2 eps)))
(* -1/24 (pow eps 3))
(* -1 (* (pow eps 3) (- 1/24 (/ 1 (pow eps 2)))))
(* -1 (* (pow eps 3) (- 1/24 (/ 1 (pow eps 2)))))
(* -1 (* (pow eps 3) (- 1/24 (/ 1 (pow eps 2)))))
(- (sin (- x (* -1 eps))) (sin x))
(- (sin (- x (* -1 eps))) (sin x))
(- (sin (- x (* -1 eps))) (sin x))
(- (sin (- x (* -1 eps))) (sin x))
(* -1/6 (* (pow eps 3) (cos x)))
(* -1 (* (pow eps 3) (+ (* 1/6 (cos x)) (* 1/2 (/ (sin x) eps)))))
(* -1 (* (pow eps 3) (+ (* -1 (/ (+ (* -1/2 (sin x)) (/ (cos x) eps)) eps)) (* 1/6 (cos x)))))
(* -1 (* (pow eps 3) (+ (* -1 (/ (+ (* -1/2 (sin x)) (/ (cos x) eps)) eps)) (* 1/6 (cos x)))))
(* -1/6 (* (pow eps 2) (cos x)))
(* (pow eps 2) (+ (* -1/2 (/ (sin x) eps)) (* -1/6 (cos x))))
(* (pow eps 2) (+ (* -1 (/ (+ (* -1 (/ (cos x) eps)) (* 1/2 (sin x))) eps)) (* -1/6 (cos x))))
(* (pow eps 2) (+ (* -1 (/ (+ (* -1 (/ (cos x) eps)) (* 1/2 (sin x))) eps)) (* -1/6 (cos x))))
(* -1/6 (pow eps 2))
(* (pow eps 2) (- (/ 1 (pow eps 2)) 1/6))
(* (pow eps 2) (- (/ 1 (pow eps 2)) 1/6))
(* (pow eps 2) (- (/ 1 (pow eps 2)) 1/6))
(- (sin (- x (* -1 eps))) (sin x))
(- (sin (- x (* -1 eps))) (sin x))
(- (sin (- x (* -1 eps))) (sin x))
(- (sin (- x (* -1 eps))) (sin x))
(* -1/6 (* (pow eps 3) (cos x)))
(* -1 (* (pow eps 3) (+ (* 1/6 (cos x)) (* 1/2 (/ (sin x) eps)))))
(* -1 (* (pow eps 3) (+ (* -1 (/ (+ (* -1/2 (sin x)) (/ (cos x) eps)) eps)) (* 1/6 (cos x)))))
(* -1 (* (pow eps 3) (+ (* -1 (/ (+ (* -1/2 (sin x)) (/ (cos x) eps)) eps)) (* 1/6 (cos x)))))
(* -1/6 (* (pow eps 2) (cos x)))
(* (pow eps 2) (+ (* -1/2 (/ (sin x) eps)) (* -1/6 (cos x))))
(* (pow eps 2) (+ (* -1 (/ (+ (* -1 (/ (cos x) eps)) (* 1/2 (sin x))) eps)) (* -1/6 (cos x))))
(* (pow eps 2) (+ (* -1 (/ (+ (* -1 (/ (cos x) eps)) (* 1/2 (sin x))) eps)) (* -1/6 (cos x))))
(* (pow eps 2) (- (* 1/12 (pow x 2)) 1/6))
(* (pow eps 2) (- (+ (* -1/2 (/ x eps)) (* 1/12 (pow x 2))) 1/6))
(* (pow eps 2) (- (+ (* -1 (/ (+ (* -1 (/ (+ 1 (* -1/2 (pow x 2))) eps)) (* 1/2 x)) eps)) (* 1/12 (pow x 2))) 1/6))
(* (pow eps 2) (- (+ (* -1 (/ (+ (* -1 (/ (+ 1 (* -1/2 (pow x 2))) eps)) (* 1/2 x)) eps)) (* 1/12 (pow x 2))) 1/6))
(* 1/12 (* (pow eps 2) x))
(* (pow eps 2) (+ (* -1 (/ (+ 1/2 (* -1/12 (pow x 2))) eps)) (* 1/12 x)))
(* (pow eps 2) (+ (* -1 (/ (+ 1/2 (+ (* -1/12 (pow x 2)) (* 1/2 (/ x eps)))) eps)) (* 1/12 x)))
(* (pow eps 2) (+ (* -1 (/ (+ 1/2 (+ (* -1/12 (pow x 2)) (* 1/2 (/ x eps)))) eps)) (* 1/12 x)))
(- (sin (- x (* -1 eps))) (sin x))
(- (sin (- x (* -1 eps))) (sin x))
(- (sin (- x (* -1 eps))) (sin x))
(- (sin (- x (* -1 eps))) (sin x))
(* -1/6 (* (pow eps 3) (cos x)))
(* -1 (* (pow eps 3) (+ (* 1/6 (cos x)) (* 1/2 (/ (sin x) eps)))))
(* -1 (* (pow eps 3) (+ (* -1 (/ (+ (* -1/2 (sin x)) (/ (cos x) eps)) eps)) (* 1/6 (cos x)))))
(* -1 (* (pow eps 3) (+ (* -1 (/ (+ (* -1/2 (sin x)) (/ (cos x) eps)) eps)) (* 1/6 (cos x)))))
(* -1/6 (* (pow eps 2) (cos x)))
(* (pow eps 2) (+ (* -1/2 (/ (sin x) eps)) (* -1/6 (cos x))))
(* (pow eps 2) (+ (* -1 (/ (+ (* -1 (/ (cos x) eps)) (* 1/2 (sin x))) eps)) (* -1/6 (cos x))))
(* (pow eps 2) (+ (* -1 (/ (+ (* -1 (/ (cos x) eps)) (* 1/2 (sin x))) eps)) (* -1/6 (cos x))))
(* 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 (sin (* 1/2 eps)))
(* 2 (sin (* 1/2 eps)))
(* 2 (sin (* 1/2 eps)))
(* 2 (sin (* 1/2 eps)))
(sin (* 1/2 eps))
(sin (* 1/2 eps))
(sin (* 1/2 eps))
(sin (* 1/2 eps))
(* 1/2 eps)
(* 1/2 eps)
(* 1/2 eps)
(* 1/2 eps)
(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))))
(* eps x)
(* -1 (* eps (+ (* -1 x) (* -1 (/ (pow x 2) eps)))))
(* -1 (* eps (+ (* -1 x) (* -1 (/ (pow x 2) eps)))))
(* -1 (* eps (+ (* -1 x) (* -1 (/ (pow x 2) eps)))))
(* 1/12 eps)
(* 1/12 eps)
(* 1/12 eps)
(* 1/12 eps)
(cos (* 1/2 (- (* 2 x) (* -1 eps))))
(cos (* 1/2 (- (* 2 x) (* -1 eps))))
(cos (* 1/2 (- (* 2 x) (* -1 eps))))
(cos (* 1/2 (- (* 2 x) (* -1 eps))))
(* 1/2 eps)
(* -1 (* eps (- (* -1 (/ x eps)) 1/2)))
(* -1 (* eps (- (* -1 (/ x eps)) 1/2)))
(* -1 (* eps (- (* -1 (/ x eps)) 1/2)))
(* 1/2 eps)
(+ x (* 1/2 eps))
(+ x (* 1/2 eps))
(+ x (* 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))))))))
(sin eps)
(+ (sin eps) (* x (- (cos eps) 1)))
(+ (sin eps) (* x (- (+ (cos eps) (* -1/2 (* x (sin eps)))) 1)))
(+ (sin eps) (* x (- (+ (cos eps) (* x (+ (* -1/2 (sin eps)) (* x (+ 1/6 (* -1/6 (cos eps))))))) 1)))
(* eps (+ 1 (* -1/6 (pow eps 2))))
(+ (* -1/2 (* (pow eps 2) x)) (* eps (+ 1 (* -1/6 (pow eps 2)))))
(+ (* eps (+ 1 (* -1/6 (pow eps 2)))) (* x (+ (* -1/2 (* eps (* x (+ 1 (* -1/6 (pow eps 2)))))) (* -1/2 (pow eps 2)))))
(+ (* eps (+ 1 (* -1/6 (pow eps 2)))) (* x (+ (* -1/2 (pow eps 2)) (* x (+ (* -1/2 (* eps (+ 1 (* -1/6 (pow eps 2))))) (* 1/12 (* (pow eps 2) x)))))))
(+ 1 (* -1/6 (pow eps 2)))
(+ 1 (+ (* -1/2 (* eps x)) (* -1/6 (pow eps 2))))
(+ 1 (+ (* -1/6 (pow eps 2)) (* x (+ (* -1/2 eps) (* -1/2 (* x (+ 1 (* -1/6 (pow eps 2)))))))))
(+ 1 (+ (* -1/6 (pow eps 2)) (* x (+ (* -1/2 eps) (* x (+ (* -1/2 (+ 1 (* -1/6 (pow eps 2)))) (* 1/12 (* eps x))))))))
(sin eps)
(+ (sin eps) (* x (- (cos eps) 1)))
(+ (sin eps) (* x (- (+ (cos eps) (* -1/2 (* x (sin eps)))) 1)))
(+ (sin eps) (* x (- (+ (cos eps) (* x (+ (* -1/2 (sin eps)) (* x (+ 1/6 (* -1/6 (cos eps))))))) 1)))
(* eps (+ 1 (* -1/6 (pow eps 2))))
(+ (* -1/2 (* (pow eps 2) x)) (* eps (+ 1 (* -1/6 (pow eps 2)))))
(+ (* eps (+ 1 (* -1/6 (pow eps 2)))) (* x (+ (* -1/2 (* eps (* x (+ 1 (* -1/6 (pow eps 2)))))) (* -1/2 (pow eps 2)))))
(+ (* eps (+ 1 (* -1/6 (pow eps 2)))) (* x (+ (* -1/2 (pow eps 2)) (* x (+ (* -1/2 (* eps (+ 1 (* -1/6 (pow eps 2))))) (* 1/12 (* (pow eps 2) x)))))))
(+ 1 (* -1/6 (pow eps 2)))
(+ 1 (+ (* -1/2 (* eps x)) (* -1/6 (pow eps 2))))
(+ 1 (+ (* -1/6 (pow eps 2)) (* x (+ (* -1/2 eps) (* -1/2 (* x (+ 1 (* -1/6 (pow eps 2)))))))))
(+ 1 (+ (* -1/6 (pow eps 2)) (* x (+ (* -1/2 eps) (* x (+ (* -1/2 (+ 1 (* -1/6 (pow eps 2)))) (* 1/12 (* eps x))))))))
(+ 1 (* -1/6 (pow eps 2)))
(+ 1 (+ (* -1/2 (* eps x)) (* -1/6 (pow eps 2))))
(+ 1 (+ (* -1/6 (pow eps 2)) (* x (+ (* -1/2 eps) (* -1/2 (* x (+ 1 (* -1/6 (pow eps 2)))))))))
(+ 1 (+ (* -1/6 (pow eps 2)) (* x (+ (* -1/2 eps) (* -1/2 (* x (+ 1 (* -1/6 (pow eps 2)))))))))
(* -1/2 eps)
(+ (* -1/2 eps) (* x (- (* 1/12 (pow eps 2)) 1/2)))
(+ (* -1/2 eps) (* x (- (+ (* 1/12 (* eps x)) (* 1/12 (pow eps 2))) 1/2)))
(+ (* -1/2 eps) (* x (- (+ (* 1/12 (* eps x)) (* 1/12 (pow eps 2))) 1/2)))
(sin eps)
(+ (sin eps) (* x (- (cos eps) 1)))
(+ (sin eps) (* x (- (+ (cos eps) (* -1/2 (* x (sin eps)))) 1)))
(+ (sin eps) (* x (- (+ (cos eps) (* x (+ (* -1/2 (sin eps)) (* x (+ 1/6 (* -1/6 (cos eps))))))) 1)))
(* eps (+ 1 (* -1/6 (pow eps 2))))
(+ (* -1/2 (* (pow eps 2) x)) (* eps (+ 1 (* -1/6 (pow eps 2)))))
(+ (* eps (+ 1 (* -1/6 (pow eps 2)))) (* x (+ (* -1/2 (* eps (* x (+ 1 (* -1/6 (pow eps 2)))))) (* -1/2 (pow eps 2)))))
(+ (* eps (+ 1 (* -1/6 (pow eps 2)))) (* x (+ (* -1/2 (pow eps 2)) (* x (+ (* -1/2 (* eps (+ 1 (* -1/6 (pow eps 2))))) (* 1/12 (* (pow eps 2) x)))))))
(+ 1 (* -1/6 (pow eps 2)))
(+ 1 (+ (* -1/2 (* eps x)) (* -1/6 (pow eps 2))))
(+ 1 (+ (* -1/6 (pow eps 2)) (* x (+ (* -1/2 eps) (* -1/2 (* x (+ 1 (* -1/6 (pow eps 2)))))))))
(+ 1 (+ (* -1/6 (pow eps 2)) (* x (+ (* -1/2 eps) (* x (+ (* -1/2 (+ 1 (* -1/6 (pow eps 2)))) (* 1/12 (* eps x))))))))
(* 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))))))))
(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)))))
(* eps x)
(* x (+ eps x))
(* x (+ eps x))
(* x (+ eps x))
(cos (* 1/2 eps))
(+ (cos (* 1/2 eps)) (* -1 (* x (sin (* 1/2 eps)))))
(+ (cos (* 1/2 eps)) (* x (- (* -1/2 (* x (cos (* 1/2 eps)))) (sin (* 1/2 eps)))))
(+ (cos (* 1/2 eps)) (* x (- (* x (+ (* -1/2 (cos (* 1/2 eps))) (* 1/6 (* x (sin (* 1/2 eps)))))) (sin (* 1/2 eps)))))
(* 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))))
(* 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))))
(- (sin (+ eps x)) (sin x))
(- (sin (+ eps x)) (sin x))
(- (sin (+ eps x)) (sin x))
(- (sin (+ eps x)) (sin x))
(* eps (+ (* -1/2 (* eps (sin x))) (* (cos x) (+ 1 (* -1/6 (pow eps 2))))))
(* eps (+ (* -1/2 (* eps (sin x))) (* (cos x) (+ 1 (* -1/6 (pow eps 2))))))
(* eps (+ (* -1/2 (* eps (sin x))) (* (cos x) (+ 1 (* -1/6 (pow eps 2))))))
(* eps (+ (* -1/2 (* eps (sin x))) (* (cos x) (+ 1 (* -1/6 (pow eps 2))))))
(+ (* -1/2 (* eps (sin x))) (* (cos x) (+ 1 (* -1/6 (pow eps 2)))))
(+ (* -1/2 (* eps (sin x))) (* (cos x) (+ 1 (* -1/6 (pow eps 2)))))
(+ (* -1/2 (* eps (sin x))) (* (cos x) (+ 1 (* -1/6 (pow eps 2)))))
(+ (* -1/2 (* eps (sin x))) (* (cos x) (+ 1 (* -1/6 (pow eps 2)))))
(- (sin (+ eps x)) (sin x))
(- (sin (+ eps x)) (sin x))
(- (sin (+ eps x)) (sin x))
(- (sin (+ eps x)) (sin x))
(* eps (+ (* -1/2 (* eps (sin x))) (* (cos x) (+ 1 (* -1/6 (pow eps 2))))))
(* eps (+ (* -1/2 (* eps (sin x))) (* (cos x) (+ 1 (* -1/6 (pow eps 2))))))
(* eps (+ (* -1/2 (* eps (sin x))) (* (cos x) (+ 1 (* -1/6 (pow eps 2))))))
(* eps (+ (* -1/2 (* eps (sin x))) (* (cos x) (+ 1 (* -1/6 (pow eps 2))))))
(+ (* -1/2 (* eps (sin x))) (* (cos x) (+ 1 (* -1/6 (pow eps 2)))))
(+ (* -1/2 (* eps (sin x))) (* (cos x) (+ 1 (* -1/6 (pow eps 2)))))
(+ (* -1/2 (* eps (sin x))) (* (cos x) (+ 1 (* -1/6 (pow eps 2)))))
(+ (* -1/2 (* eps (sin x))) (* (cos x) (+ 1 (* -1/6 (pow eps 2)))))
(* -1/2 (* (pow x 2) (+ 1 (* -1/6 (pow eps 2)))))
(* (pow x 2) (+ (* -1/2 (+ 1 (* -1/6 (pow eps 2)))) (* -1/2 (/ eps x))))
(* (pow x 2) (+ (* -1/2 (+ 1 (* -1/6 (pow eps 2)))) (+ (* -1/2 (/ eps x)) (+ (* -1/6 (/ (pow eps 2) (pow x 2))) (/ 1 (pow x 2))))))
(* (pow x 2) (+ (* -1/2 (+ 1 (* -1/6 (pow eps 2)))) (+ (* -1/2 (/ eps x)) (+ (* -1/6 (/ (pow eps 2) (pow x 2))) (/ 1 (pow x 2))))))
(* 1/12 (* eps (pow x 2)))
(* (pow x 2) (- (+ (* 1/12 eps) (* 1/12 (/ (pow eps 2) x))) (* 1/2 (/ 1 x))))
(* (pow x 2) (- (+ (* -1/2 (/ eps (pow x 2))) (+ (* 1/12 eps) (* 1/12 (/ (pow eps 2) x)))) (* 1/2 (/ 1 x))))
(* (pow x 2) (- (+ (* -1/2 (/ eps (pow x 2))) (+ (* 1/12 eps) (* 1/12 (/ (pow eps 2) x)))) (* 1/2 (/ 1 x))))
(- (sin (+ eps x)) (sin x))
(- (sin (+ eps x)) (sin x))
(- (sin (+ eps x)) (sin x))
(- (sin (+ eps x)) (sin x))
(* eps (+ (* -1/2 (* eps (sin x))) (* (cos x) (+ 1 (* -1/6 (pow eps 2))))))
(* eps (+ (* -1/2 (* eps (sin x))) (* (cos x) (+ 1 (* -1/6 (pow eps 2))))))
(* eps (+ (* -1/2 (* eps (sin x))) (* (cos x) (+ 1 (* -1/6 (pow eps 2))))))
(* eps (+ (* -1/2 (* eps (sin x))) (* (cos x) (+ 1 (* -1/6 (pow eps 2))))))
(+ (* -1/2 (* eps (sin x))) (* (cos x) (+ 1 (* -1/6 (pow eps 2)))))
(+ (* -1/2 (* eps (sin x))) (* (cos x) (+ 1 (* -1/6 (pow eps 2)))))
(+ (* -1/2 (* eps (sin x))) (* (cos x) (+ 1 (* -1/6 (pow eps 2)))))
(+ (* -1/2 (* eps (sin x))) (* (cos x) (+ 1 (* -1/6 (pow eps 2)))))
(* 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))))
(cos (* 1/2 (+ eps (* 2 x))))
(cos (* 1/2 (+ eps (* 2 x))))
(cos (* 1/2 (+ eps (* 2 x))))
(cos (* 1/2 (+ eps (* 2 x))))
(pow x 2)
(* (pow x 2) (+ 1 (/ eps x)))
(* (pow x 2) (+ 1 (/ eps x)))
(* (pow x 2) (+ 1 (/ eps 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))))
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)))
(* 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))))
(- (sin (- eps (* -1 x))) (sin x))
(- (sin (- eps (* -1 x))) (sin x))
(- (sin (- eps (* -1 x))) (sin x))
(- (sin (- eps (* -1 x))) (sin x))
(* eps (+ (* -1/2 (* eps (sin x))) (* (cos x) (+ 1 (* -1/6 (pow eps 2))))))
(* eps (+ (* -1/2 (* eps (sin x))) (* (cos x) (+ 1 (* -1/6 (pow eps 2))))))
(* eps (+ (* -1/2 (* eps (sin x))) (* (cos x) (+ 1 (* -1/6 (pow eps 2))))))
(* eps (+ (* -1/2 (* eps (sin x))) (* (cos x) (+ 1 (* -1/6 (pow eps 2))))))
(+ (* -1/2 (* eps (sin x))) (* (cos x) (+ 1 (* -1/6 (pow eps 2)))))
(+ (* -1/2 (* eps (sin x))) (* (cos x) (+ 1 (* -1/6 (pow eps 2)))))
(+ (* -1/2 (* eps (sin x))) (* (cos x) (+ 1 (* -1/6 (pow eps 2)))))
(+ (* -1/2 (* eps (sin x))) (* (cos x) (+ 1 (* -1/6 (pow eps 2)))))
(- (sin (- eps (* -1 x))) (sin x))
(- (sin (- eps (* -1 x))) (sin x))
(- (sin (- eps (* -1 x))) (sin x))
(- (sin (- eps (* -1 x))) (sin x))
(* eps (+ (* -1/2 (* eps (sin x))) (* (cos x) (+ 1 (* -1/6 (pow eps 2))))))
(* eps (+ (* -1/2 (* eps (sin x))) (* (cos x) (+ 1 (* -1/6 (pow eps 2))))))
(* eps (+ (* -1/2 (* eps (sin x))) (* (cos x) (+ 1 (* -1/6 (pow eps 2))))))
(* eps (+ (* -1/2 (* eps (sin x))) (* (cos x) (+ 1 (* -1/6 (pow eps 2))))))
(+ (* -1/2 (* eps (sin x))) (* (cos x) (+ 1 (* -1/6 (pow eps 2)))))
(+ (* -1/2 (* eps (sin x))) (* (cos x) (+ 1 (* -1/6 (pow eps 2)))))
(+ (* -1/2 (* eps (sin x))) (* (cos x) (+ 1 (* -1/6 (pow eps 2)))))
(+ (* -1/2 (* eps (sin x))) (* (cos x) (+ 1 (* -1/6 (pow eps 2)))))
(* -1/2 (* (pow x 2) (+ 1 (* -1/6 (pow eps 2)))))
(* (pow x 2) (+ (* -1/2 (+ 1 (* -1/6 (pow eps 2)))) (* -1/2 (/ eps x))))
(* (pow x 2) (+ (* -1 (/ (+ (* -1 (/ (+ 1 (* -1/6 (pow eps 2))) x)) (* 1/2 eps)) x)) (* -1/2 (+ 1 (* -1/6 (pow eps 2))))))
(* (pow x 2) (+ (* -1 (/ (+ (* -1 (/ (+ 1 (* -1/6 (pow eps 2))) x)) (* 1/2 eps)) x)) (* -1/2 (+ 1 (* -1/6 (pow eps 2))))))
(* 1/12 (* eps (pow x 2)))
(* (pow x 2) (- (+ (* 1/12 eps) (* 1/12 (/ (pow eps 2) x))) (* 1/2 (/ 1 x))))
(* (pow x 2) (+ (* -1 (/ (+ (* -1 (- (* 1/12 (pow eps 2)) 1/2)) (* 1/2 (/ eps x))) x)) (* 1/12 eps)))
(* (pow x 2) (+ (* -1 (/ (+ (* -1 (- (* 1/12 (pow eps 2)) 1/2)) (* 1/2 (/ eps x))) x)) (* 1/12 eps)))
(- (sin (- eps (* -1 x))) (sin x))
(- (sin (- eps (* -1 x))) (sin x))
(- (sin (- eps (* -1 x))) (sin x))
(- (sin (- eps (* -1 x))) (sin x))
(* eps (+ (* -1/2 (* eps (sin x))) (* (cos x) (+ 1 (* -1/6 (pow eps 2))))))
(* eps (+ (* -1/2 (* eps (sin x))) (* (cos x) (+ 1 (* -1/6 (pow eps 2))))))
(* eps (+ (* -1/2 (* eps (sin x))) (* (cos x) (+ 1 (* -1/6 (pow eps 2))))))
(* eps (+ (* -1/2 (* eps (sin x))) (* (cos x) (+ 1 (* -1/6 (pow eps 2))))))
(+ (* -1/2 (* eps (sin x))) (* (cos x) (+ 1 (* -1/6 (pow eps 2)))))
(+ (* -1/2 (* eps (sin x))) (* (cos x) (+ 1 (* -1/6 (pow eps 2)))))
(+ (* -1/2 (* eps (sin x))) (* (cos x) (+ 1 (* -1/6 (pow eps 2)))))
(+ (* -1/2 (* eps (sin x))) (* (cos x) (+ 1 (* -1/6 (pow eps 2)))))
(* 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))))
(cos (* 1/2 (- eps (* -2 x))))
(cos (* 1/2 (- eps (* -2 x))))
(cos (* 1/2 (- eps (* -2 x))))
(cos (* 1/2 (- eps (* -2 x))))
(pow x 2)
(* (pow x 2) (+ 1 (/ eps x)))
(* (pow x 2) (+ 1 (/ eps x)))
(* (pow x 2) (+ 1 (/ eps 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))))
x
(* -1 (* x (- (* -1/2 (/ eps x)) 1)))
(* -1 (* x (- (* -1/2 (/ eps x)) 1)))
(* -1 (* x (- (* -1/2 (/ eps x)) 1)))

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

rewrite206.0ms (1.8%)

Memory

19.3MiB live, 137.6MiB allocated

Rules

5 942×	`lower-*.f32`
5 916×	`lower-*.f64`
5 640×	`lower-fma.f32`
5 624×	`lower-fma.f64`
3 222×	`lower-/.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	71	570
0	103	551
1	376	551
2	3178	551
0	8891	534

Stop Event

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

Counts

25 → 219

Calls

Call 1

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

Outputs
(*.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64))
(*.f64 #s(literal 1/2 binary64) (fma.f64 x #s(literal 2 binary64) eps))
(/.f64 (.f64 (fma.f64 #s(literal 4 binary64) (.f64 x x) (*.f64 (neg.f64 eps) eps)) #s(literal 1/2 binary64)) (fma.f64 x #s(literal 2 binary64) (neg.f64 eps)))
(/.f64 (.f64 (fma.f64 #s(literal 8 binary64) (.f64 (.f64 x x) x) (.f64 (.f64 eps eps) eps)) #s(literal 1/2 binary64)) (fma.f64 #s(literal 4 binary64) (.f64 x x) (.f64 eps (-.f64 eps (.f64 x #s(literal 2 binary64))))))
(/.f64 (.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 4 binary64) (.f64 x x) (*.f64 (neg.f64 eps) eps))) (fma.f64 x #s(literal 2 binary64) (neg.f64 eps)))
(/.f64 (.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 8 binary64) (.f64 (.f64 x x) x) (.f64 (.f64 eps eps) eps))) (fma.f64 #s(literal 4 binary64) (.f64 x x) (.f64 eps (-.f64 eps (.f64 x #s(literal 2 binary64))))))
(/.f64 (-.f64 (.f64 (.f64 #s(literal 1 binary64) x) (.f64 #s(literal 1 binary64) x)) (.f64 #s(literal 1/4 binary64) (.f64 eps eps))) (-.f64 (.f64 #s(literal 1 binary64) x) (*.f64 eps #s(literal 1/2 binary64))))
(/.f64 (fma.f64 (.f64 (.f64 x x) x) #s(literal 1 binary64) (.f64 #s(literal 1/8 binary64) (.f64 (.f64 eps eps) eps))) (fma.f64 (.f64 #s(literal 1 binary64) x) (.f64 #s(literal 1 binary64) x) (-.f64 (.f64 #s(literal 1/4 binary64) (.f64 eps eps)) (.f64 (.f64 #s(literal 1 binary64) x) (.f64 eps #s(literal 1/2 binary64))))))
(fma.f64 (.f64 #s(literal 1/2 binary64) 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 #s(literal 1 binary64) x (*.f64 eps #s(literal 1/2 binary64)))
(fma.f64 eps #s(literal 1/2 binary64) (*.f64 #s(literal 1 binary64) x))
(fma.f64 x #s(literal 1 binary64) (*.f64 eps #s(literal 1/2 binary64)))
(fma.f64 #s(literal 2 binary64) (.f64 x #s(literal 1/2 binary64)) (.f64 eps #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 #s(literal 1/2 binary64) eps (*.f64 #s(literal 1 binary64) x))
(+.f64 (fma.f64 #s(literal 1 binary64) x #s(literal 0 binary64)) (*.f64 eps #s(literal 1/2 binary64)))
(+.f64 (.f64 #s(literal 1 binary64) x) (.f64 eps #s(literal 1/2 binary64)))
(+.f64 (.f64 eps #s(literal 1/2 binary64)) (.f64 #s(literal 1 binary64) x))
(.f64 (cos.f64 (.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64))) #s(approx (* (sin (* 1/2 (+ 0 eps))) 2) (.f64 (fma.f64 #s(literal -1/24 binary64) (.f64 eps eps) #s(literal 1 binary64)) eps)))
(.f64 #s(approx ( (sin (* 1/2 (+ 0 eps))) 2) (.f64 (fma.f64 #s(literal -1/24 binary64) (.f64 eps eps) #s(literal 1 binary64)) eps)) (cos.f64 (*.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64))))
#s(approx (* (sin (* 1/2 (+ 0 eps))) 2) (.f64 (fma.f64 #s(literal -1/24 binary64) (.f64 eps eps) #s(literal 1 binary64)) eps))
(.f64 (fma.f64 #s(literal -1/24 binary64) (.f64 eps eps) #s(literal 1 binary64)) eps)
(.f64 eps (fma.f64 #s(literal -1/24 binary64) (.f64 eps eps) #s(literal 1 binary64)))
(/.f64 (.f64 (fma.f64 #s(literal 1/576 binary64) (.f64 (.f64 (.f64 eps eps) eps) eps) #s(literal -1 binary64)) eps) (fma.f64 #s(literal -1/24 binary64) (*.f64 eps eps) #s(literal -1 binary64)))
(/.f64 (.f64 (fma.f64 (.f64 #s(literal -1/13824 binary64) (.f64 (.f64 eps eps) eps)) (.f64 (.f64 eps eps) eps) #s(literal 1 binary64)) eps) (fma.f64 #s(literal 1/576 binary64) (.f64 (.f64 (.f64 eps eps) eps) eps) (-.f64 #s(literal 1 binary64) (.f64 #s(literal -1/24 binary64) (*.f64 eps eps)))))
(/.f64 (.f64 (neg.f64 (.f64 eps eps)) (fma.f64 #s(literal -1/24 binary64) (*.f64 eps eps) #s(literal 1 binary64))) (neg.f64 eps))
(/.f64 (.f64 (.f64 (.f64 eps eps) eps) (fma.f64 #s(literal -1/24 binary64) (.f64 eps eps) #s(literal 1 binary64))) (*.f64 eps eps))
(/.f64 (.f64 (fma.f64 #s(literal -1/24 binary64) (.f64 eps eps) #s(literal 1 binary64)) (neg.f64 (*.f64 eps eps))) (neg.f64 eps))
(/.f64 (.f64 (fma.f64 #s(literal -1/24 binary64) (.f64 eps eps) #s(literal 1 binary64)) (.f64 (.f64 eps eps) eps)) (*.f64 eps eps))
(/.f64 (.f64 eps (fma.f64 #s(literal 1/576 binary64) (.f64 (.f64 (.f64 eps eps) eps) eps) #s(literal -1 binary64))) (fma.f64 #s(literal -1/24 binary64) (*.f64 eps eps) #s(literal -1 binary64)))
(/.f64 (.f64 eps (fma.f64 (.f64 #s(literal -1/13824 binary64) (.f64 (.f64 eps eps) eps)) (.f64 (.f64 eps eps) eps) #s(literal 1 binary64))) (fma.f64 #s(literal 1/576 binary64) (.f64 (.f64 (.f64 eps eps) eps) eps) (-.f64 #s(literal 1 binary64) (.f64 #s(literal -1/24 binary64) (*.f64 eps eps)))))
(/.f64 (.f64 (fma.f64 #s(literal 1/576 binary64) (.f64 (.f64 (.f64 eps eps) eps) eps) #s(literal -1 binary64)) (neg.f64 (.f64 eps eps))) (.f64 (fma.f64 #s(literal -1/24 binary64) (*.f64 eps eps) #s(literal -1 binary64)) (neg.f64 eps)))
(/.f64 (.f64 (fma.f64 #s(literal 1/576 binary64) (.f64 (.f64 (.f64 eps eps) eps) eps) #s(literal -1 binary64)) (.f64 (.f64 eps eps) eps)) (.f64 (fma.f64 #s(literal -1/24 binary64) (.f64 eps eps) #s(literal -1 binary64)) (*.f64 eps eps)))
(/.f64 (.f64 (fma.f64 (.f64 #s(literal -1/13824 binary64) (.f64 (.f64 eps eps) eps)) (.f64 (.f64 eps eps) eps) #s(literal 1 binary64)) (neg.f64 (.f64 eps eps))) (.f64 (fma.f64 #s(literal 1/576 binary64) (.f64 (.f64 (.f64 eps eps) eps) eps) (-.f64 #s(literal 1 binary64) (.f64 #s(literal -1/24 binary64) (*.f64 eps eps)))) (neg.f64 eps)))
(/.f64 (.f64 (fma.f64 (.f64 #s(literal -1/13824 binary64) (.f64 (.f64 eps eps) eps)) (.f64 (.f64 eps eps) eps) #s(literal 1 binary64)) (.f64 (.f64 eps eps) eps)) (.f64 (fma.f64 #s(literal 1/576 binary64) (.f64 (.f64 (.f64 eps eps) eps) eps) (-.f64 #s(literal 1 binary64) (.f64 #s(literal -1/24 binary64) (.f64 eps eps)))) (*.f64 eps eps)))
(/.f64 (.f64 (neg.f64 (.f64 eps eps)) (fma.f64 #s(literal 1/576 binary64) (.f64 (.f64 (.f64 eps eps) eps) eps) #s(literal -1 binary64))) (.f64 (neg.f64 eps) (fma.f64 #s(literal -1/24 binary64) (*.f64 eps eps) #s(literal -1 binary64))))
(/.f64 (.f64 (neg.f64 (.f64 eps eps)) (fma.f64 (.f64 #s(literal -1/13824 binary64) (.f64 (.f64 eps eps) eps)) (.f64 (.f64 eps eps) eps) #s(literal 1 binary64))) (.f64 (neg.f64 eps) (fma.f64 #s(literal 1/576 binary64) (.f64 (.f64 (.f64 eps eps) eps) eps) (-.f64 #s(literal 1 binary64) (.f64 #s(literal -1/24 binary64) (*.f64 eps eps))))))
(/.f64 (.f64 (.f64 (.f64 eps eps) eps) (fma.f64 #s(literal 1/576 binary64) (.f64 (.f64 (.f64 eps eps) eps) eps) #s(literal -1 binary64))) (.f64 (.f64 eps eps) (fma.f64 #s(literal -1/24 binary64) (*.f64 eps eps) #s(literal -1 binary64))))
(/.f64 (.f64 (.f64 (.f64 eps eps) eps) (fma.f64 (.f64 #s(literal -1/13824 binary64) (.f64 (.f64 eps eps) eps)) (.f64 (.f64 eps eps) eps) #s(literal 1 binary64))) (.f64 (.f64 eps eps) (fma.f64 #s(literal 1/576 binary64) (.f64 (.f64 (.f64 eps eps) eps) eps) (-.f64 #s(literal 1 binary64) (.f64 #s(literal -1/24 binary64) (*.f64 eps eps))))))
(fma.f64 (.f64 #s(literal -1/24 binary64) (.f64 eps eps)) eps (*.f64 #s(literal 1 binary64) eps))
(fma.f64 (fma.f64 #s(literal -1/24 binary64) (.f64 eps eps) #s(literal 1 binary64)) #s(literal 0 binary64) (.f64 (fma.f64 #s(literal -1/24 binary64) (*.f64 eps eps) #s(literal 1 binary64)) eps))
(fma.f64 (fma.f64 #s(literal -1/24 binary64) (.f64 eps eps) #s(literal 1 binary64)) eps (.f64 #s(literal 0 binary64) (fma.f64 #s(literal -1/24 binary64) (*.f64 eps eps) #s(literal 1 binary64))))
(fma.f64 (fma.f64 #s(literal -1/24 binary64) (.f64 eps eps) #s(literal 1 binary64)) eps (.f64 (fma.f64 #s(literal -1/24 binary64) (*.f64 eps eps) #s(literal 1 binary64)) #s(literal 0 binary64)))
(fma.f64 #s(literal 1 binary64) eps (.f64 (.f64 #s(literal -1/24 binary64) (*.f64 eps eps)) eps))
(fma.f64 #s(literal 0 binary64) (fma.f64 #s(literal -1/24 binary64) (.f64 eps eps) #s(literal 1 binary64)) (.f64 (fma.f64 #s(literal -1/24 binary64) (*.f64 eps eps) #s(literal 1 binary64)) eps))
(fma.f64 eps (.f64 #s(literal -1/24 binary64) (.f64 eps eps)) (*.f64 eps #s(literal 1 binary64)))
(fma.f64 eps (fma.f64 #s(literal -1/24 binary64) (.f64 eps eps) #s(literal 1 binary64)) (.f64 #s(literal 0 binary64) (fma.f64 #s(literal -1/24 binary64) (*.f64 eps eps) #s(literal 1 binary64))))
(fma.f64 eps (fma.f64 #s(literal -1/24 binary64) (.f64 eps eps) #s(literal 1 binary64)) (.f64 (fma.f64 #s(literal -1/24 binary64) (*.f64 eps eps) #s(literal 1 binary64)) #s(literal 0 binary64)))
(fma.f64 eps #s(literal 1 binary64) (.f64 eps (.f64 #s(literal -1/24 binary64) (*.f64 eps eps))))
(+.f64 (.f64 #s(literal 0 binary64) (fma.f64 #s(literal -1/24 binary64) (.f64 eps eps) #s(literal 1 binary64))) (.f64 (fma.f64 #s(literal -1/24 binary64) (.f64 eps eps) #s(literal 1 binary64)) eps))
(+.f64 (.f64 (.f64 #s(literal -1/24 binary64) (.f64 eps eps)) eps) (.f64 #s(literal 1 binary64) eps))
(+.f64 (.f64 #s(literal 1 binary64) eps) (.f64 (.f64 #s(literal -1/24 binary64) (.f64 eps eps)) eps))
(+.f64 (.f64 (fma.f64 #s(literal -1/24 binary64) (.f64 eps eps) #s(literal 1 binary64)) #s(literal 0 binary64)) (.f64 (fma.f64 #s(literal -1/24 binary64) (.f64 eps eps) #s(literal 1 binary64)) eps))
(+.f64 (.f64 eps (.f64 #s(literal -1/24 binary64) (.f64 eps eps))) (.f64 eps #s(literal 1 binary64)))
(+.f64 (.f64 eps #s(literal 1 binary64)) (.f64 eps (.f64 #s(literal -1/24 binary64) (.f64 eps eps))))
(+.f64 (.f64 (fma.f64 #s(literal -1/24 binary64) (.f64 eps eps) #s(literal 1 binary64)) eps) (.f64 #s(literal 0 binary64) (fma.f64 #s(literal -1/24 binary64) (.f64 eps eps) #s(literal 1 binary64))))
(+.f64 (.f64 (fma.f64 #s(literal -1/24 binary64) (.f64 eps eps) #s(literal 1 binary64)) eps) (.f64 (fma.f64 #s(literal -1/24 binary64) (.f64 eps eps) #s(literal 1 binary64)) #s(literal 0 binary64)))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (+ (* (* eps eps) -1/6) 1) (cos x)) (* (* (sin x) -1/2) eps)) #s(approx (+ (* -1/6 (* eps eps)) 1) #s(literal 1 binary64))) eps))
(.f64 #s(approx (+ ( (+ (* (* eps eps) -1/6) 1) (cos x)) (* (* (sin x) -1/2) eps)) #s(approx (+ (* -1/6 (* eps eps)) 1) #s(literal 1 binary64))) eps)
(.f64 eps #s(approx (+ ( (+ (* (* eps eps) -1/6) 1) (cos x)) (* (* (sin x) -1/2) eps)) #s(approx (+ (* -1/6 (* eps eps)) 1) #s(literal 1 binary64))))
(/.f64 (.f64 (neg.f64 (.f64 eps eps)) #s(approx (+ (* (+ (* (* eps eps) -1/6) 1) (cos x)) (* (* (sin x) -1/2) eps)) #s(approx (+ (* -1/6 (* eps eps)) 1) #s(literal 1 binary64)))) (neg.f64 eps))
(/.f64 (.f64 (.f64 (.f64 eps eps) eps) #s(approx (+ ( (+ (* (* eps eps) -1/6) 1) (cos x)) (* (* (sin x) -1/2) eps)) #s(approx (+ (* -1/6 (* eps eps)) 1) #s(literal 1 binary64)))) (*.f64 eps eps))
(/.f64 (.f64 #s(approx (+ ( (+ (* (* eps eps) -1/6) 1) (cos x)) (* (* (sin x) -1/2) eps)) #s(approx (+ (* -1/6 (* eps eps)) 1) #s(literal 1 binary64))) (neg.f64 (*.f64 eps eps))) (neg.f64 eps))
(/.f64 (.f64 #s(approx (+ ( (+ (* (* eps eps) -1/6) 1) (cos x)) (* (* (sin x) -1/2) eps)) #s(approx (+ (* -1/6 (* eps eps)) 1) #s(literal 1 binary64))) (.f64 (.f64 eps eps) eps)) (*.f64 eps eps))
(fma.f64 #s(approx (+ (* (+ (* (* eps eps) -1/6) 1) (cos x)) (* (* (sin x) -1/2) eps)) #s(approx (+ (* -1/6 (* eps eps)) 1) #s(literal 1 binary64))) #s(literal 0 binary64) (.f64 #s(approx (+ ( (+ (* (* eps eps) -1/6) 1) (cos x)) (* (* (sin x) -1/2) eps)) #s(approx (+ (* -1/6 (* eps eps)) 1) #s(literal 1 binary64))) eps))
(fma.f64 #s(approx (+ (* (+ (* (* eps eps) -1/6) 1) (cos x)) (* (* (sin x) -1/2) eps)) #s(approx (+ (* -1/6 (* eps eps)) 1) #s(literal 1 binary64))) eps (.f64 #s(literal 0 binary64) #s(approx (+ ( (+ (* (* eps eps) -1/6) 1) (cos x)) (* (* (sin x) -1/2) eps)) #s(approx (+ (* -1/6 (* eps eps)) 1) #s(literal 1 binary64)))))
(fma.f64 #s(approx (+ (* (+ (* (* eps eps) -1/6) 1) (cos x)) (* (* (sin x) -1/2) eps)) #s(approx (+ (* -1/6 (* eps eps)) 1) #s(literal 1 binary64))) eps (.f64 #s(approx (+ ( (+ (* (* eps eps) -1/6) 1) (cos x)) (* (* (sin x) -1/2) eps)) #s(approx (+ (* -1/6 (* eps eps)) 1) #s(literal 1 binary64))) #s(literal 0 binary64)))
(fma.f64 #s(literal 0 binary64) #s(approx (+ (* (+ (* (* eps eps) -1/6) 1) (cos x)) (* (* (sin x) -1/2) eps)) #s(approx (+ (* -1/6 (* eps eps)) 1) #s(literal 1 binary64))) (.f64 #s(approx (+ ( (+ (* (* eps eps) -1/6) 1) (cos x)) (* (* (sin x) -1/2) eps)) #s(approx (+ (* -1/6 (* eps eps)) 1) #s(literal 1 binary64))) eps))
(fma.f64 eps #s(approx (+ (* (+ (* (* eps eps) -1/6) 1) (cos x)) (* (* (sin x) -1/2) eps)) #s(approx (+ (* -1/6 (* eps eps)) 1) #s(literal 1 binary64))) (.f64 #s(literal 0 binary64) #s(approx (+ ( (+ (* (* eps eps) -1/6) 1) (cos x)) (* (* (sin x) -1/2) eps)) #s(approx (+ (* -1/6 (* eps eps)) 1) #s(literal 1 binary64)))))
(fma.f64 eps #s(approx (+ (* (+ (* (* eps eps) -1/6) 1) (cos x)) (* (* (sin x) -1/2) eps)) #s(approx (+ (* -1/6 (* eps eps)) 1) #s(literal 1 binary64))) (.f64 #s(approx (+ ( (+ (* (* eps eps) -1/6) 1) (cos x)) (* (* (sin x) -1/2) eps)) #s(approx (+ (* -1/6 (* eps eps)) 1) #s(literal 1 binary64))) #s(literal 0 binary64)))
(+.f64 (.f64 #s(literal 0 binary64) #s(approx (+ ( (+ (* (* eps eps) -1/6) 1) (cos x)) (* (* (sin x) -1/2) eps)) #s(approx (+ (* -1/6 (* eps eps)) 1) #s(literal 1 binary64)))) (.f64 #s(approx (+ ( (+ (* (* eps eps) -1/6) 1) (cos x)) (* (* (sin x) -1/2) eps)) #s(approx (+ (* -1/6 (* eps eps)) 1) #s(literal 1 binary64))) eps))
(+.f64 (.f64 #s(approx (+ ( (+ (* (* eps eps) -1/6) 1) (cos x)) (* (* (sin x) -1/2) eps)) #s(approx (+ (* -1/6 (* eps eps)) 1) #s(literal 1 binary64))) #s(literal 0 binary64)) (.f64 #s(approx (+ ( (+ (* (* eps eps) -1/6) 1) (cos x)) (* (* (sin x) -1/2) eps)) #s(approx (+ (* -1/6 (* eps eps)) 1) #s(literal 1 binary64))) eps))
(+.f64 (.f64 #s(approx (+ ( (+ (* (* eps eps) -1/6) 1) (cos x)) (* (* (sin x) -1/2) eps)) #s(approx (+ (* -1/6 (* eps eps)) 1) #s(literal 1 binary64))) eps) (.f64 #s(literal 0 binary64) #s(approx (+ ( (+ (* (* eps eps) -1/6) 1) (cos x)) (* (* (sin x) -1/2) eps)) #s(approx (+ (* -1/6 (* eps eps)) 1) #s(literal 1 binary64)))))
(+.f64 (.f64 #s(approx (+ ( (+ (* (* eps eps) -1/6) 1) (cos x)) (* (* (sin x) -1/2) eps)) #s(approx (+ (* -1/6 (* eps eps)) 1) #s(literal 1 binary64))) eps) (.f64 #s(approx (+ ( (+ (* (* eps eps) -1/6) 1) (cos x)) (* (* (sin x) -1/2) eps)) #s(approx (+ (* -1/6 (* eps eps)) 1) #s(literal 1 binary64))) #s(literal 0 binary64)))
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(/.f64 (.f64 x (.f64 (+.f64 eps x) (-.f64 x eps))) (-.f64 x eps))
(/.f64 (.f64 x (fma.f64 (.f64 x x) x (.f64 (.f64 eps eps) eps))) (fma.f64 x (-.f64 x eps) (*.f64 eps eps)))
(/.f64 (.f64 x (fma.f64 (.f64 x x) x (.f64 (.f64 eps eps) eps))) (fma.f64 eps (-.f64 eps x) (*.f64 x x)))
(/.f64 (-.f64 (.f64 (.f64 eps x) (.f64 eps x)) (.f64 (.f64 x x) (.f64 x x))) (-.f64 (.f64 eps x) (.f64 x x)))
(/.f64 (fma.f64 (.f64 (.f64 x x) x) (.f64 (.f64 eps eps) eps) (.f64 (.f64 (.f64 x x) x) (.f64 (.f64 x x) x))) (fma.f64 (.f64 eps x) (.f64 eps x) (-.f64 (.f64 (.f64 x x) (.f64 x x)) (.f64 (.f64 eps x) (*.f64 x x)))))
(fma.f64 eps x (*.f64 x x))
(fma.f64 x eps (*.f64 x x))
(fma.f64 x x (*.f64 eps x))
(+.f64 (.f64 eps x) (.f64 x x))
(+.f64 (.f64 x x) (.f64 eps x))
(*.f64 #s(literal 1/12 binary64) eps)
(*.f64 eps #s(literal 1/12 binary64))
(/.f64 (.f64 (neg.f64 (.f64 eps eps)) #s(literal 1/12 binary64)) (neg.f64 eps))
(/.f64 (.f64 (.f64 (.f64 eps eps) eps) #s(literal 1/12 binary64)) (.f64 eps eps))
(/.f64 (.f64 #s(literal 1/12 binary64) (neg.f64 (.f64 eps eps))) (neg.f64 eps))
(/.f64 (.f64 #s(literal 1/12 binary64) (.f64 (.f64 eps eps) eps)) (.f64 eps eps))
(fma.f64 #s(literal 1/12 binary64) eps #s(literal 0 binary64))
(fma.f64 eps #s(literal 1/12 binary64) #s(literal 0 binary64))
(+.f64 (*.f64 #s(literal 1/12 binary64) eps) #s(literal 0 binary64))
(+.f64 #s(literal 0 binary64) (*.f64 #s(literal 1/12 binary64) eps))
(cos.f64 #s(approx (* 1/2 (+ (* 2 x) eps)) (fma.f64 eps #s(literal 1/2 binary64) x)))
#s(approx (* 1/2 (+ (* 2 x) eps)) (fma.f64 eps #s(literal 1/2 binary64) x))

eval96.0ms (0.8%)

Memory: 14.5MiB live, 174.0MiB allocated
Compiler: Compiled 16 106 to 1 070 computations (93.4% saved)

prune69.0ms (0.6%)

Memory

-40.2MiB live, 93.3MiB allocated

Pruning

22 alts after pruning (15 fresh and 7 done)

	Pruned	Kept	Total
New	721	5	726
Fresh	3	10	13
Picked	2	3	5
Done	0	4	4
Total	726	22	748

Accuracy

100.0%

Counts

748 → 22

Alt Table

Click to see full alt table

Status	Accuracy	Program
	62.4%	(fma.f64 (sin.f64 x) (cos.f64 eps) (fma.f64 (sin.f64 eps) (cos.f64 x) (neg.f64 (sin.f64 x))))
✓	62.1%	(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
✓	7.5%	(-.f64 #s(approx (sin (+ x eps)) (sin.f64 eps)) (sin.f64 x))
✓	99.4%	(.f64 (.f64 #s(approx (sin (* 1/2 (+ 0 eps))) (.f64 eps #s(literal 1/2 binary64))) #s(literal 2 binary64)) (cos.f64 #s(approx ( 1/2 (+ (* 2 x) eps)) (fma.f64 eps #s(literal 1/2 binary64) x))))
	99.6%	(.f64 #s(approx ( (sin (* 1/2 (+ 0 eps))) 2) (fma.f64 (.f64 #s(literal -1/24 binary64) (.f64 eps eps)) eps (.f64 #s(literal 1 binary64) eps))) (cos.f64 (.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps))))
	99.6%	(.f64 #s(approx ( (sin (* 1/2 (+ 0 eps))) 2) (.f64 (fma.f64 (.f64 eps eps) #s(literal -1/24 binary64) #s(literal 1 binary64)) eps)) (cos.f64 #s(approx (* 1/2 (+ (* 2 x) eps)) (fma.f64 eps #s(literal 1/2 binary64) x))))
	99.5%	#s(approx (- (sin (+ x eps)) (sin x)) (/.f64 (.f64 #s(approx (- ( (+ 1/2 (* 1/2 (cos (+ x x)))) (* (+ (* (* eps eps) -1/6) 1) (+ (* (* eps eps) -1/6) 1))) (* (* (* -1/2 eps) (* -1/2 eps)) (- 1/2 (* 1/2 (cos (+ x x)))))) (fma.f64 (cos.f64 (.f64 #s(literal -2 binary64) x)) #s(literal 1/2 binary64) #s(literal 1/2 binary64))) eps) (-.f64 (.f64 (cos.f64 x) (fma.f64 (.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64))) (.f64 (*.f64 #s(literal -1/2 binary64) (sin.f64 x)) eps))))
✓	99.7%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 (fma.f64 (.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64)) (cos.f64 x) (.f64 (.f64 (sin.f64 x) #s(literal -1/2 binary64)) eps)) eps))
	99.5%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 (.f64 (sin.f64 x) #s(literal -1/2 binary64)) eps (cos.f64 x)) eps))
	99.0%	#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (cos.f64 x) eps))
	98.3%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (+ (* (* eps eps) -1/6) 1) (cos x)) (* (* (sin x) -1/2) eps)) (fma.f64 (.f64 #s(approx (+ ( (+ (* -1/6 (* eps eps)) 1) x) eps) (+.f64 eps x)) #s(literal -1/2 binary64)) x (fma.f64 #s(literal -1/6 binary64) (*.f64 eps eps) #s(literal 1 binary64)))) eps))
	98.2%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (+ (* (* eps eps) -1/6) 1) (cos x)) (* (* (sin x) -1/2) eps)) (fma.f64 (*.f64 #s(literal -1/6 binary64) eps) eps #s(literal 1 binary64))) eps))
	98.3%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (+ (* (* eps eps) -1/6) 1) (cos x)) (* (* (sin x) -1/2) eps)) (fma.f64 #s(approx (+ (* (+ (* (* 1/12 eps) (+ eps x)) -1/2) x) (* -1/2 eps)) (fma.f64 (fma.f64 #s(literal 1/12 binary64) (.f64 x x) #s(literal -1/2 binary64)) eps (.f64 #s(literal -1/2 binary64) x))) x (fma.f64 #s(literal -1/6 binary64) (*.f64 eps eps) #s(literal 1 binary64)))) eps))
	98.1%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (+ (* (* eps eps) -1/6) 1) (cos x)) (* (* (sin x) -1/2) eps)) (fma.f64 #s(approx (+ (* (+ (* (* 1/12 eps) (+ eps x)) -1/2) x) (* -1/2 eps)) (.f64 (.f64 (.f64 eps x) x) #s(literal 1/12 binary64))) x (fma.f64 #s(literal -1/6 binary64) (.f64 eps eps) #s(literal 1 binary64)))) eps))
	98.2%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (+ (* (* eps eps) -1/6) 1) (cos x)) (* (* (sin x) -1/2) eps)) #s(approx (+ (* (* (+ (* (+ (* -1/6 (* eps eps)) 1) x) eps) -1/2) x) (+ (* -1/6 (* eps eps)) 1)) (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64)))) eps))
✓	98.3%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (+ (* (* eps eps) -1/6) 1) (cos x)) (* (* (sin x) -1/2) eps)) #s(approx (+ (* (* (+ (* (+ (* -1/6 (* eps eps)) 1) x) eps) -1/2) x) (+ (* -1/6 (* eps eps)) 1)) (fma.f64 #s(literal -1/2 binary64) (*.f64 x (+.f64 eps x)) #s(literal 1 binary64)))) eps))
	98.1%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (+ (* (* eps eps) -1/6) 1) (cos x)) (* (* (sin x) -1/2) eps)) #s(approx (+ (* (* (+ (* (+ (* -1/6 (* eps eps)) 1) x) eps) -1/2) x) (+ (* -1/6 (* eps eps)) 1)) (fma.f64 #s(literal -1/2 binary64) #s(approx (* x (+ eps x)) (*.f64 eps x)) #s(literal 1 binary64)))) eps))
	5.1%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (+ (* (* eps eps) -1/6) 1) (cos x)) (* (* (sin x) -1/2) eps)) #s(approx (+ (* -1/6 (* eps eps)) 1) (.f64 #s(literal -1/6 binary64) (.f64 eps eps)))) eps))
✓	98.1%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (+ (* (* eps eps) -1/6) 1) (cos x)) (* (* (sin x) -1/2) eps)) #s(approx (+ (* -1/6 (* eps eps)) 1) #s(literal 1 binary64))) eps))
✓	98.2%	#s(approx (- (sin (+ x eps)) (sin x)) (sin.f64 eps))
	98.3%	#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (+ (* (* eps eps) -1/6) 1) (cos x)) (* (* (sin x) -1/2) eps)) eps) (fma.f64 (.f64 #s(approx (+ ( (* 1/12 x) (* eps eps)) (* (+ (* 1/12 (* eps eps)) -1/2) eps)) (.f64 (fma.f64 #s(literal 1/12 binary64) (.f64 eps x) #s(literal -1/2 binary64)) eps)) x) x (fma.f64 (.f64 eps eps) (fma.f64 #s(literal -1/6 binary64) eps (.f64 #s(literal -1/2 binary64) x)) eps))))
	98.3%	#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (+ (* (* eps eps) -1/6) 1) (cos x)) (* (* (sin x) -1/2) eps)) eps) (fma.f64 (.f64 #s(approx (+ ( (* 1/12 x) (* eps eps)) (* (+ (* 1/12 (* eps eps)) -1/2) eps)) (.f64 #s(literal -1/2 binary64) eps)) x) x (fma.f64 (.f64 eps eps) (fma.f64 #s(literal -1/6 binary64) eps (*.f64 #s(literal -1/2 binary64) x)) eps))))

Compiler

Compiled 956 to 349 computations (63.5% saved)

regimes29.0ms (0.2%)

Memory

10.5MiB live, 49.3MiB allocated

Counts

35 → 1

Calls

Call 1

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

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

Calls

3 calls:

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

Results

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

Compiler

Compiled 15 to 10 computations (33.3% saved)

regimes26.0ms (0.2%)

Memory

7.9MiB live, 46.7MiB allocated

Counts

30 → 1

Calls

Call 1

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

Outputs

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

Calls

3 calls:

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

Results

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

Compiler

Compiled 15 to 10 computations (33.3% saved)

regimes23.0ms (0.2%)

Memory

-5.9MiB live, 35.2MiB allocated

Counts

22 → 1

Calls

Call 1

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

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

Calls

3 calls:

10.0ms	eps
6.0ms	x
6.0ms	(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 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 (0.2%)

Memory

-15.3MiB live, 24.0MiB allocated

Counts

19 → 1

Calls

Call 1

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

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

Calls

3 calls:

7.0ms	x
5.0ms	(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
5.0ms	eps

Results

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

Compiler

Compiled 15 to 10 computations (33.3% saved)

regimes16.0ms (0.1%)

Memory

29.2MiB live, 29.2MiB allocated

Counts

18 → 1

Calls

Call 1

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

Outputs

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

Calls

3 calls:

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

Results

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

Compiler

Compiled 15 to 10 computations (33.3% saved)

regimes12.0ms (0.1%)

Memory

-22.8MiB live, 16.4MiB allocated

Counts

10 → 1

Calls

Call 1

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

Outputs

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

Calls

3 calls:

4.0ms	(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
3.0ms	eps
3.0ms	x

Results

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

Compiler

Compiled 15 to 10 computations (33.3% saved)

regimes9.0ms (0.1%)

Memory

12.4MiB live, 12.4MiB allocated

Counts

8 → 1

Calls

Call 1

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

Outputs

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

Calls

3 calls:

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

Results

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

Compiler

Compiled 15 to 10 computations (33.3% saved)

regimes8.0ms (0.1%)

Memory

10.9MiB live, 10.9MiB allocated

Counts

6 → 1

Calls

Call 1

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

Outputs

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

Calls

3 calls:

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

Results

Accuracy	Segments	Branch
98.2%	1	`x`
98.2%	1	`eps`
98.2%	1	`(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))`

Compiler

Compiled 15 to 10 computations (33.3% saved)

regimes7.0ms (0.1%)

Memory

-26.9MiB live, 12.1MiB allocated

Counts

3 → 1

Calls

Call 1

Inputs

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

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

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

Outputs

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

Calls

3 calls:

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

Results

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

Compiler

Compiled 15 to 10 computations (33.3% saved)

regimes5.0ms (0%)

Memory

11.4MiB live, 11.3MiB allocated

Accuracy

Total -59.6b remaining (-4946.8%)

Threshold costs -59.6b (-4946.8%)

Counts

2 → 1

Calls

Call 1

Inputs

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

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

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

Calls

3 calls:

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

Results

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

Compiler

Compiled 15 to 10 computations (33.3% saved)

simplify7.0ms (0.1%)

Memory

13.1MiB live, 13.1MiB allocated

Algorithm

1×	egg-herbie

Rules

40×	`*-commutative_binary64`
4×	`+-commutative_binary64`
2×	`+-lft-identity_binary64`
2×	`1-exp_binary64`
2×	`1-exp_binary32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	108	419
1	133	419

Stop Event

1×

saturated

Calls

Call 1

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

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

soundness1.2s (10.5%)

Memory

-2.5MiB live, 1 111.0MiB allocated

Rules

16 678×	`lower-fma.f64`
16 678×	`lower-fma.f32`
14 890×	`lower-fma.f64`
14 890×	`lower-fma.f32`
14 312×	`lower-fma.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	654	7701
1	2080	7448
2	6578	7426
0	8093	6725
0	414	6293
1	1267	5942
2	3706	5934
0	8103	5384
0	6	16
0	10	16
1	53	16
2	380	16
3	4766	16
0	8210	16
0	107	496
1	314	496
2	775	489
3	2829	489
4	6198	489
0	8141	458
0	365	3712
1	1136	3555
2	3251	3519
0	8165	3234

Stop Event

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

Compiler

Compiled 269 to 149 computations (44.6% saved)

preprocess82.0ms (0.7%)

Memory: 6.1MiB live, 204.1MiB allocated
Compiler: Compiled 374 to 170 computations (54.5% 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 (0.5%)

sample5.8s (49.6%)

explain140.0ms (1.2%)

preprocess29.0ms (0.2%)

eval0.0ms (0%)

prune0.0ms (0%)

simplify7.0ms (0.1%)

localize26.0ms (0.2%)

series6.0ms (0.1%)

simplify163.0ms (1.4%)

rewrite159.0ms (1.4%)

eval86.0ms (0.7%)

prune26.0ms (0.2%)

simplify244.0ms (2.1%)

localize122.0ms (1%)

series39.0ms (0.3%)

simplify160.0ms (1.4%)

rewrite234.0ms (2%)

eval161.0ms (1.4%)

prune29.0ms (0.2%)

simplify175.0ms (1.5%)

localize443.0ms (3.8%)

series96.0ms (0.8%)

simplify186.0ms (1.6%)

rewrite232.0ms (2%)

eval386.0ms (3.3%)

prune84.0ms (0.7%)

simplify190.0ms (1.6%)

localize249.0ms (2.1%)

series47.0ms (0.4%)

simplify280.0ms (2.4%)

rewrite206.0ms (1.8%)

eval96.0ms (0.8%)

prune69.0ms (0.6%)

regimes29.0ms (0.2%)

regimes26.0ms (0.2%)

regimes23.0ms (0.2%)

regimes18.0ms (0.2%)

regimes16.0ms (0.1%)

regimes12.0ms (0.1%)

regimes9.0ms (0.1%)

regimes8.0ms (0.1%)

regimes7.0ms (0.1%)

regimes5.0ms (0%)

simplify7.0ms (0.1%)

soundness1.2s (10.5%)

preprocess82.0ms (0.7%)

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