Metrics for 2cos (problem 3.3.5)

start0.0ms (0%)

Memory: 0.1MiB live, 0.1MiB allocated

analyze84.0ms (0.5%)

Memory

-5.9MiB live, 33.3MiB 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)

sample9.4s (50.7%)

Memory

-146.2MiB live, 11 292.9MiB allocated

Samples

3.8s	5 709×	2	valid
3.3s	26 399×	0	invalid
720.0ms	2 434×	1	valid
46.0ms	113×	0	valid

Precisions

Click to see histograms. Total time spent on operations: 6.2s

ival-cos: 2.9s (47% of total)

const: 919.0ms (14.9% of total)

adjust: 502.0ms (8.2% of total)

ival-<=: 317.0ms (5.1% of total)

ival-sub: 282.0ms (4.6% of total)

ival-mult: 278.0ms (4.5% of total)

ival-<: 273.0ms (4.4% of total)

ival-add: 267.0ms (4.3% of total)

ival-fabs: 267.0ms (4.3% of total)

ival-and: 102.0ms (1.7% of total)

exact: 42.0ms (0.7% of total)

ival-assert: 12.0ms (0.2% of total)

Bogosity

explain224.0ms (1.2%)

Memory

2.6MiB live, 351.0MiB allocated

FPErrors

Click to see full error table

Ground Truth	Example	Underpredictions	Example	Subexpression
126	-	0	-	`(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))`
5	-	2	(106.280917856612 1.009385977186459e-8)	`(cos.f64 (+.f64 x eps))`
0	-	0	-	`eps`
0	-	0	-	`(+.f64 x eps)`
0	-	0	-	`(cos.f64 x)`
0	-	0	-	`x`

Explanations

Click to see full explanations table

Operator	Subexpression	Explanation	Count
`-.f64`	`(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))`	cancellation	126	1
`cos.f64`	`(cos.f64 (+.f64 x eps))`	sensitivity	3	2

Confusion

	Predicted +	Predicted -
+	128	1
-	0	127

Precision

1.0

Recall

0.9922480620155039

Confusion?

	Predicted +	Predicted Maybe	Predicted -
+	128	1	0
-	0	0	127

Precision?

1.0

Recall?

1.0

Freqs

test

number	freq
0	128
1	127
2	1

Total Confusion?

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

Precision?

1.0

Recall?

1.0

Samples

148.0ms	362×	2	valid
18.0ms	140×	1	valid
1.0ms	10×	0	valid

Compiler

Compiled 49 to 22 computations (55.1% saved)

Precisions

Click to see histograms. Total time spent on operations: 141.0ms

ival-cos: 113.0ms (79.9% of total)

adjust: 18.0ms (12.7% of total)

ival-sub: 6.0ms (4.2% of total)

ival-add: 3.0ms (2.1% of total)

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

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

preprocess28.0ms (0.2%)

Memory

7.8MiB live, 46.6MiB allocated

Algorithm

1×	egg-herbie

Rules

108×	`sub-neg`
80×	`lower-fma.f64`
80×	`lower-fma.f32`
80×	`associate--r+`
66×	`cancel-sign-sub-inv`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	18	41
1	38	37
2	81	35
3	152	35
4	278	35
5	370	35
6	448	35
7	485	35
8	531	35
9	546	35
10	554	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 (cos.f64 (+.f64 x eps)) (cos.f64 x))

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

Compiler

Compiled 9 to 6 computations (33.3% saved)

eval0.0ms (0%)

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

prune1.0ms (0%)

Memory

1.3MiB live, 1.3MiB allocated

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	56.6%	(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))

Compiler

Compiled 9 to 6 computations (33.3% saved)

simplify8.0ms (0%)

Memory

14.7MiB live, 14.7MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 4 expressions of interest:

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

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

localize152.0ms (0.8%)

Memory

-44.1MiB live, 99.9MiB allocated

Localize:

Found 4 expressions of interest:

New	Metric	Score
accuracy	0	(+.f64 x eps)
accuracy	0	(cos.f64 x)
accuracy	0.12674859825865142	(cos.f64 (+.f64 x eps))
accuracy	27.61780088482764	(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))

Samples

133.0ms	181×	2	valid
9.0ms	70×	1	valid
1.0ms	5×	0	valid

Compiler

Compiled 20 to 8 computations (60% saved)

Precisions

Click to see histograms. Total time spent on operations: 105.0ms

ival-cos: 86.0ms (82.2% of total)

adjust: 13.0ms (12.4% of total)

ival-sub: 3.0ms (2.9% of total)

ival-add: 2.0ms (1.9% of total)

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

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

series4.0ms (0%)

Memory

6.4MiB live, 6.4MiB allocated

Counts

4 → 84

Calls

Call 1

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

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

Calls

21 calls:

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

simplify310.0ms (1.7%)

Memory

29.7MiB live, 253.7MiB allocated

Algorithm

1×	egg-herbie

Rules

14 158×	`lower-fma.f64`
14 158×	`lower-fma.f32`
4 148×	`lower-*.f64`
4 148×	`lower-*.f32`
3 720×	`lower-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	105	498
1	277	495
2	609	495
3	2398	494
4	7880	494
0	8026	474

Stop Event

1×	iter limit
1×	node limit

Counts

84 → 78

Calls

Call 1

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

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

rewrite319.0ms (1.7%)

Memory

-14.8MiB live, 263.5MiB allocated

Rules

4 936×	`lower-fma.f64`
4 936×	`lower-fma.f32`
4 656×	`lower-*.f64`
4 656×	`lower-*.f32`
2 192×	`lower-/.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	16
0	10	16
1	54	16
2	380	16
3	4694	16
0	8209	16

Stop Event

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

Counts

4 → 228

Calls

Call 1

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

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

eval66.0ms (0.4%)

Memory: -5.9MiB live, 85.1MiB allocated
Compiler: Compiled 8 023 to 875 computations (89.1% saved)

prune130.0ms (0.7%)

Memory

2.0MiB live, 108.7MiB allocated

Pruning

14 alts after pruning (13 fresh and 1 done)

	Pruned	Kept	Total
New	293	13	306
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	293	14	307

Accuracy

99.9%

Counts

307 → 14

Alt Table

Click to see full alt table

Status	Accuracy	Program
	56.6%	(fma.f64 (*.f64 (cos.f64 (-.f64 x eps)) (cos.f64 (+.f64 x eps))) (/.f64 #s(literal 1 binary64) (cos.f64 (-.f64 x eps))) (neg.f64 (cos.f64 x)))
	56.8%	(fma.f64 (cos.f64 x) (cos.f64 eps) (neg.f64 (fma.f64 (sin.f64 x) (sin.f64 eps) (cos.f64 x))))
	56.6%	(/.f64 (/.f64 (-.f64 (fma.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 (+.f64 x eps) #s(literal 2 binary64))) #s(literal 1/2 binary64)) (fma.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64))) #s(literal 2 binary64)) (.f64 (cos.f64 (.f64 (+.f64 x (+.f64 x eps)) #s(literal 1/2 binary64))) (cos.f64 (.f64 (+.f64 eps #s(literal 0 binary64)) #s(literal 1/2 binary64)))))
	56.8%	(/.f64 (-.f64 (pow.f64 (.f64 (cos.f64 x) (cos.f64 eps)) #s(literal 3 binary64)) (pow.f64 (fma.f64 (sin.f64 x) (sin.f64 eps) (cos.f64 x)) #s(literal 3 binary64))) (fma.f64 (fma.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64)) (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 #s(literal 2 binary64) eps)))) (+.f64 (pow.f64 (fma.f64 (sin.f64 x) (sin.f64 eps) (cos.f64 x)) #s(literal 2 binary64)) (.f64 (*.f64 (cos.f64 x) (cos.f64 eps)) (fma.f64 (sin.f64 x) (sin.f64 eps) (cos.f64 x))))))
	56.6%	(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))))
▶	56.8%	(-.f64 (*.f64 (cos.f64 x) (cos.f64 eps)) (fma.f64 (sin.f64 x) (sin.f64 eps) (cos.f64 x)))
✓	56.6%	(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))
▶	55.2%	(-.f64 (cos.f64 (+.f64 x eps)) #s(approx (cos x) (fma.f64 x (*.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64))))
	54.8%	(-.f64 (cos.f64 (+.f64 x eps)) #s(approx (cos x) #s(literal 1 binary64)))
▶	99.5%	(.f64 (.f64 (sin.f64 (.f64 (+.f64 eps #s(literal 0 binary64)) #s(literal 1/2 binary64))) (sin.f64 (.f64 (+.f64 x (+.f64 x eps)) #s(literal 1/2 binary64)))) #s(literal -2 binary64))
▶	54.8%	#s(approx (- (cos (+ x eps)) (cos x)) (+.f64 (cos.f64 eps) #s(literal -1 binary64)))
	81.7%	#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (sin.f64 x) (neg.f64 eps)))
▶	99.3%	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps (fma.f64 eps (fma.f64 (cos.f64 x) (+.f64 #s(literal -1/2 binary64) (.f64 eps (.f64 eps #s(literal 1/24 binary64)))) (.f64 eps (*.f64 #s(literal 1/6 binary64) (sin.f64 x)))) (sin.f64 (neg.f64 x)))))
	98.9%	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps (-.f64 (.f64 eps (*.f64 #s(literal -1/2 binary64) (cos.f64 x))) (sin.f64 x))))

Compiler

Compiled 523 to 310 computations (40.7% saved)

simplify444.0ms (2.4%)

Memory

21.6MiB live, 303.1MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 19 expressions of interest:

New	Metric	Score
cost-diff	0	(cos.f64 eps)
cost-diff	0	(cos.f64 x)
cost-diff	0	(*.f64 (cos.f64 x) (cos.f64 eps))
cost-diff	6272	(-.f64 (*.f64 (cos.f64 x) (cos.f64 eps)) (fma.f64 (sin.f64 x) (sin.f64 eps) (cos.f64 x)))
cost-diff	0	(.f64 eps (fma.f64 eps (fma.f64 (cos.f64 x) (+.f64 #s(literal -1/2 binary64) (.f64 eps (.f64 eps #s(literal 1/24 binary64)))) (.f64 eps (*.f64 #s(literal 1/6 binary64) (sin.f64 x)))) (sin.f64 (neg.f64 x))))
cost-diff	0	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps (fma.f64 eps (fma.f64 (cos.f64 x) (+.f64 #s(literal -1/2 binary64) (.f64 eps (.f64 eps #s(literal 1/24 binary64)))) (.f64 eps (*.f64 #s(literal 1/6 binary64) (sin.f64 x)))) (sin.f64 (neg.f64 x)))))
cost-diff	128	(+.f64 #s(literal -1/2 binary64) (.f64 eps (.f64 eps #s(literal 1/24 binary64))))
cost-diff	6208	(fma.f64 eps (fma.f64 (cos.f64 x) (+.f64 #s(literal -1/2 binary64) (.f64 eps (.f64 eps #s(literal 1/24 binary64)))) (.f64 eps (.f64 #s(literal 1/6 binary64) (sin.f64 x)))) (sin.f64 (neg.f64 x)))
cost-diff	0	#s(approx (cos x) (fma.f64 x (*.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64)))
cost-diff	0	(+.f64 x eps)
cost-diff	0	(cos.f64 (+.f64 x eps))
cost-diff	0	(-.f64 (cos.f64 (+.f64 x eps)) #s(approx (cos x) (fma.f64 x (*.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64))))
cost-diff	0	(cos.f64 eps)
cost-diff	0	(+.f64 (cos.f64 eps) #s(literal -1 binary64))
cost-diff	0	#s(approx (- (cos (+ x eps)) (cos x)) (+.f64 (cos.f64 eps) #s(literal -1 binary64)))
cost-diff	0	(.f64 (sin.f64 (.f64 (+.f64 eps #s(literal 0 binary64)) #s(literal 1/2 binary64))) (sin.f64 (*.f64 (+.f64 x (+.f64 x eps)) #s(literal 1/2 binary64))))
cost-diff	0	(.f64 (.f64 (sin.f64 (.f64 (+.f64 eps #s(literal 0 binary64)) #s(literal 1/2 binary64))) (sin.f64 (.f64 (+.f64 x (+.f64 x eps)) #s(literal 1/2 binary64)))) #s(literal -2 binary64))
cost-diff	192	(+.f64 eps #s(literal 0 binary64))
cost-diff	320	(*.f64 (+.f64 x (+.f64 x eps)) #s(literal 1/2 binary64))

Rules

14 106×	`lower-fma.f32`
14 098×	`lower-fma.f64`
4 078×	`lower-*.f32`
4 056×	`lower-*.f64`
2 300×	`lower--.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	48	302
0	84	292
1	150	292
2	371	292
3	888	284
4	1646	284
5	2705	284
6	4315	284
7	5565	284
8	6601	284
9	7211	284
10	7331	284
11	7445	284
0	8179	274

Stop Event

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

Calls

Call 1

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

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

localize463.0ms (2.5%)

Memory

-3.4MiB live, 632.7MiB allocated

Localize:

Found 19 expressions of interest:

New	Metric	Score
accuracy	0	(cos.f64 eps)
accuracy	0.015625	(*.f64 (cos.f64 x) (cos.f64 eps))
accuracy	0.02734375	(fma.f64 (sin.f64 x) (sin.f64 eps) (cos.f64 x))
accuracy	27.620606753432394	(-.f64 (*.f64 (cos.f64 x) (cos.f64 eps)) (fma.f64 (sin.f64 x) (sin.f64 eps) (cos.f64 x)))
accuracy	0.1171875	(.f64 eps (.f64 eps #s(literal 1/24 binary64)))
accuracy	0.296875	(*.f64 #s(literal 1/6 binary64) (sin.f64 x))
accuracy	0.33203125	(*.f64 eps #s(literal 1/24 binary64))
accuracy	0.34131181601776905	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps (fma.f64 eps (fma.f64 (cos.f64 x) (+.f64 #s(literal -1/2 binary64) (.f64 eps (.f64 eps #s(literal 1/24 binary64)))) (.f64 eps (*.f64 #s(literal 1/6 binary64) (sin.f64 x)))) (sin.f64 (neg.f64 x)))))
accuracy	0	(*.f64 x #s(literal -1/2 binary64))
accuracy	0.12674859825865142	(cos.f64 (+.f64 x eps))
accuracy	1.3981565778666545	#s(approx (cos x) (fma.f64 x (*.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64)))
accuracy	27.61780088482764	(-.f64 (cos.f64 (+.f64 x eps)) #s(approx (cos x) (fma.f64 x (*.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64))))
accuracy	0	(cos.f64 eps)
accuracy	26.953051245831887	(+.f64 (cos.f64 eps) #s(literal -1 binary64))
accuracy	28.23878058521645	#s(approx (- (cos (+ x eps)) (cos x)) (+.f64 (cos.f64 eps) #s(literal -1 binary64)))
accuracy	0.03125	(.f64 (.f64 (sin.f64 (.f64 (+.f64 eps #s(literal 0 binary64)) #s(literal 1/2 binary64))) (sin.f64 (.f64 (+.f64 x (+.f64 x eps)) #s(literal 1/2 binary64)))) #s(literal -2 binary64))
accuracy	0.11328125	(.f64 (sin.f64 (.f64 (+.f64 eps #s(literal 0 binary64)) #s(literal 1/2 binary64))) (sin.f64 (*.f64 (+.f64 x (+.f64 x eps)) #s(literal 1/2 binary64))))
accuracy	0.1330883704405067	(sin.f64 (*.f64 (+.f64 x (+.f64 x eps)) #s(literal 1/2 binary64)))
accuracy	0.2421875	(+.f64 x (+.f64 x eps))

Samples

302.0ms	184×	2	valid
67.0ms	68×	1	valid
2.0ms	4×	0	valid

Compiler

Compiled 269 to 47 computations (82.5% saved)

Precisions

Click to see histograms. Total time spent on operations: 286.0ms

ival-cos: 106.0ms (37% of total)

adjust: 69.0ms (24.1% of total)

ival-mult: 51.0ms (17.8% of total)

ival-add: 27.0ms (9.4% of total)

ival-sin: 17.0ms (5.9% of total)

ival-sub: 7.0ms (2.4% of total)

const: 7.0ms (2.4% of total)

exact: 1.0ms (0.3% of total)

ival-neg: 1.0ms (0.3% of total)

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

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

series45.0ms (0.2%)

Memory

12.6MiB live, 49.9MiB allocated

Counts

25 → 480

Calls

Call 1

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

Outputs
#s(alt (* 1/2 eps) (taylor 0 x) (#s(alt (.f64 (+.f64 x (+.f64 x eps)) #s(literal 1/2 binary64)) (patch (.f64 (+.f64 x (+.f64 x eps)) #s(literal 1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt (+ x (* 1/2 eps)) (taylor 0 x) (#s(alt (.f64 (+.f64 x (+.f64 x eps)) #s(literal 1/2 binary64)) (patch (.f64 (+.f64 x (+.f64 x eps)) #s(literal 1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt (+ x (* 1/2 eps)) (taylor 0 x) (#s(alt (.f64 (+.f64 x (+.f64 x eps)) #s(literal 1/2 binary64)) (patch (.f64 (+.f64 x (+.f64 x eps)) #s(literal 1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt (+ x (* 1/2 eps)) (taylor 0 x) (#s(alt (.f64 (+.f64 x (+.f64 x eps)) #s(literal 1/2 binary64)) (patch (.f64 (+.f64 x (+.f64 x eps)) #s(literal 1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt x (taylor inf x) (#s(alt (.f64 (+.f64 x (+.f64 x eps)) #s(literal 1/2 binary64)) (patch (.f64 (+.f64 x (+.f64 x eps)) #s(literal 1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1 (* 1/2 (/ eps x)))) (taylor inf x) (#s(alt (.f64 (+.f64 x (+.f64 x eps)) #s(literal 1/2 binary64)) (patch (.f64 (+.f64 x (+.f64 x eps)) #s(literal 1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1 (* 1/2 (/ eps x)))) (taylor inf x) (#s(alt (.f64 (+.f64 x (+.f64 x eps)) #s(literal 1/2 binary64)) (patch (.f64 (+.f64 x (+.f64 x eps)) #s(literal 1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1 (* 1/2 (/ eps x)))) (taylor inf x) (#s(alt (.f64 (+.f64 x (+.f64 x eps)) #s(literal 1/2 binary64)) (patch (.f64 (+.f64 x (+.f64 x eps)) #s(literal 1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt x (taylor -inf x) (#s(alt (.f64 (+.f64 x (+.f64 x eps)) #s(literal 1/2 binary64)) (patch (.f64 (+.f64 x (+.f64 x eps)) #s(literal 1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (- (* -1/2 (/ eps x)) 1))) (taylor -inf x) (#s(alt (.f64 (+.f64 x (+.f64 x eps)) #s(literal 1/2 binary64)) (patch (.f64 (+.f64 x (+.f64 x eps)) #s(literal 1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (- (* -1/2 (/ eps x)) 1))) (taylor -inf x) (#s(alt (.f64 (+.f64 x (+.f64 x eps)) #s(literal 1/2 binary64)) (patch (.f64 (+.f64 x (+.f64 x eps)) #s(literal 1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (- (* -1/2 (/ eps x)) 1))) (taylor -inf x) (#s(alt (.f64 (+.f64 x (+.f64 x eps)) #s(literal 1/2 binary64)) (patch (.f64 (+.f64 x (+.f64 x eps)) #s(literal 1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt x (taylor 0 eps) (#s(alt (.f64 (+.f64 x (+.f64 x eps)) #s(literal 1/2 binary64)) (patch (.f64 (+.f64 x (+.f64 x eps)) #s(literal 1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt (+ x (* 1/2 eps)) (taylor 0 eps) (#s(alt (.f64 (+.f64 x (+.f64 x eps)) #s(literal 1/2 binary64)) (patch (.f64 (+.f64 x (+.f64 x eps)) #s(literal 1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt (+ x (* 1/2 eps)) (taylor 0 eps) (#s(alt (.f64 (+.f64 x (+.f64 x eps)) #s(literal 1/2 binary64)) (patch (.f64 (+.f64 x (+.f64 x eps)) #s(literal 1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt (+ x (* 1/2 eps)) (taylor 0 eps) (#s(alt (.f64 (+.f64 x (+.f64 x eps)) #s(literal 1/2 binary64)) (patch (.f64 (+.f64 x (+.f64 x eps)) #s(literal 1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* 1/2 eps) (taylor inf eps) (#s(alt (.f64 (+.f64 x (+.f64 x eps)) #s(literal 1/2 binary64)) (patch (.f64 (+.f64 x (+.f64 x eps)) #s(literal 1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* eps (+ 1/2 (/ x eps))) (taylor inf eps) (#s(alt (.f64 (+.f64 x (+.f64 x eps)) #s(literal 1/2 binary64)) (patch (.f64 (+.f64 x (+.f64 x eps)) #s(literal 1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* eps (+ 1/2 (/ x eps))) (taylor inf eps) (#s(alt (.f64 (+.f64 x (+.f64 x eps)) #s(literal 1/2 binary64)) (patch (.f64 (+.f64 x (+.f64 x eps)) #s(literal 1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* eps (+ 1/2 (/ x eps))) (taylor inf eps) (#s(alt (.f64 (+.f64 x (+.f64 x eps)) #s(literal 1/2 binary64)) (patch (.f64 (+.f64 x (+.f64 x eps)) #s(literal 1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* 1/2 eps) (taylor -inf eps) (#s(alt (.f64 (+.f64 x (+.f64 x eps)) #s(literal 1/2 binary64)) (patch (.f64 (+.f64 x (+.f64 x eps)) #s(literal 1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* eps (- (* -1 (/ x eps)) 1/2))) (taylor -inf eps) (#s(alt (.f64 (+.f64 x (+.f64 x eps)) #s(literal 1/2 binary64)) (patch (.f64 (+.f64 x (+.f64 x eps)) #s(literal 1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* eps (- (* -1 (/ x eps)) 1/2))) (taylor -inf eps) (#s(alt (.f64 (+.f64 x (+.f64 x eps)) #s(literal 1/2 binary64)) (patch (.f64 (+.f64 x (+.f64 x eps)) #s(literal 1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* eps (- (* -1 (/ x eps)) 1/2))) (taylor -inf eps) (#s(alt (.f64 (+.f64 x (+.f64 x eps)) #s(literal 1/2 binary64)) (patch (.f64 (+.f64 x (+.f64 x eps)) #s(literal 1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt eps (taylor 0 eps) (#s(alt (+.f64 eps #s(literal 0 binary64)) (patch (+.f64 eps #s(literal 0 binary64)) #<representation binary64>) () ())) ())
#s(alt eps (taylor 0 eps) (#s(alt (+.f64 eps #s(literal 0 binary64)) (patch (+.f64 eps #s(literal 0 binary64)) #<representation binary64>) () ())) ())
#s(alt eps (taylor 0 eps) (#s(alt (+.f64 eps #s(literal 0 binary64)) (patch (+.f64 eps #s(literal 0 binary64)) #<representation binary64>) () ())) ())
#s(alt eps (taylor 0 eps) (#s(alt (+.f64 eps #s(literal 0 binary64)) (patch (+.f64 eps #s(literal 0 binary64)) #<representation binary64>) () ())) ())
#s(alt eps (taylor inf eps) (#s(alt (+.f64 eps #s(literal 0 binary64)) (patch (+.f64 eps #s(literal 0 binary64)) #<representation binary64>) () ())) ())
#s(alt eps (taylor inf eps) (#s(alt (+.f64 eps #s(literal 0 binary64)) (patch (+.f64 eps #s(literal 0 binary64)) #<representation binary64>) () ())) ())
#s(alt eps (taylor inf eps) (#s(alt (+.f64 eps #s(literal 0 binary64)) (patch (+.f64 eps #s(literal 0 binary64)) #<representation binary64>) () ())) ())
#s(alt eps (taylor inf eps) (#s(alt (+.f64 eps #s(literal 0 binary64)) (patch (+.f64 eps #s(literal 0 binary64)) #<representation binary64>) () ())) ())
#s(alt eps (taylor -inf eps) (#s(alt (+.f64 eps #s(literal 0 binary64)) (patch (+.f64 eps #s(literal 0 binary64)) #<representation binary64>) () ())) ())
#s(alt eps (taylor -inf eps) (#s(alt (+.f64 eps #s(literal 0 binary64)) (patch (+.f64 eps #s(literal 0 binary64)) #<representation binary64>) () ())) ())
#s(alt eps (taylor -inf eps) (#s(alt (+.f64 eps #s(literal 0 binary64)) (patch (+.f64 eps #s(literal 0 binary64)) #<representation binary64>) () ())) ())
#s(alt eps (taylor -inf eps) (#s(alt (+.f64 eps #s(literal 0 binary64)) (patch (+.f64 eps #s(literal 0 binary64)) #<representation binary64>) () ())) ())
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#s(alt (* -1/2 x) (taylor 0 x) (#s(alt (.f64 x #s(literal -1/2 binary64)) (patch (.f64 x #s(literal -1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* -1/2 x) (taylor 0 x) (#s(alt (.f64 x #s(literal -1/2 binary64)) (patch (.f64 x #s(literal -1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* -1/2 x) (taylor inf x) (#s(alt (.f64 x #s(literal -1/2 binary64)) (patch (.f64 x #s(literal -1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* -1/2 x) (taylor inf x) (#s(alt (.f64 x #s(literal -1/2 binary64)) (patch (.f64 x #s(literal -1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* -1/2 x) (taylor inf x) (#s(alt (.f64 x #s(literal -1/2 binary64)) (patch (.f64 x #s(literal -1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* -1/2 x) (taylor inf x) (#s(alt (.f64 x #s(literal -1/2 binary64)) (patch (.f64 x #s(literal -1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* -1/2 x) (taylor -inf x) (#s(alt (.f64 x #s(literal -1/2 binary64)) (patch (.f64 x #s(literal -1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* -1/2 x) (taylor -inf x) (#s(alt (.f64 x #s(literal -1/2 binary64)) (patch (.f64 x #s(literal -1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* -1/2 x) (taylor -inf x) (#s(alt (.f64 x #s(literal -1/2 binary64)) (patch (.f64 x #s(literal -1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* -1/2 x) (taylor -inf x) (#s(alt (.f64 x #s(literal -1/2 binary64)) (patch (.f64 x #s(literal -1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* 1/24 eps) (taylor 0 eps) (#s(alt (.f64 eps #s(literal 1/24 binary64)) (patch (.f64 eps #s(literal 1/24 binary64)) #<representation binary64>) () ())) ())
#s(alt (* 1/24 eps) (taylor 0 eps) (#s(alt (.f64 eps #s(literal 1/24 binary64)) (patch (.f64 eps #s(literal 1/24 binary64)) #<representation binary64>) () ())) ())
#s(alt (* 1/24 eps) (taylor 0 eps) (#s(alt (.f64 eps #s(literal 1/24 binary64)) (patch (.f64 eps #s(literal 1/24 binary64)) #<representation binary64>) () ())) ())
#s(alt (* 1/24 eps) (taylor 0 eps) (#s(alt (.f64 eps #s(literal 1/24 binary64)) (patch (.f64 eps #s(literal 1/24 binary64)) #<representation binary64>) () ())) ())
#s(alt (* 1/24 eps) (taylor inf eps) (#s(alt (.f64 eps #s(literal 1/24 binary64)) (patch (.f64 eps #s(literal 1/24 binary64)) #<representation binary64>) () ())) ())
#s(alt (* 1/24 eps) (taylor inf eps) (#s(alt (.f64 eps #s(literal 1/24 binary64)) (patch (.f64 eps #s(literal 1/24 binary64)) #<representation binary64>) () ())) ())
#s(alt (* 1/24 eps) (taylor inf eps) (#s(alt (.f64 eps #s(literal 1/24 binary64)) (patch (.f64 eps #s(literal 1/24 binary64)) #<representation binary64>) () ())) ())
#s(alt (* 1/24 eps) (taylor inf eps) (#s(alt (.f64 eps #s(literal 1/24 binary64)) (patch (.f64 eps #s(literal 1/24 binary64)) #<representation binary64>) () ())) ())
#s(alt (* 1/24 eps) (taylor -inf eps) (#s(alt (.f64 eps #s(literal 1/24 binary64)) (patch (.f64 eps #s(literal 1/24 binary64)) #<representation binary64>) () ())) ())
#s(alt (* 1/24 eps) (taylor -inf eps) (#s(alt (.f64 eps #s(literal 1/24 binary64)) (patch (.f64 eps #s(literal 1/24 binary64)) #<representation binary64>) () ())) ())
#s(alt (* 1/24 eps) (taylor -inf eps) (#s(alt (.f64 eps #s(literal 1/24 binary64)) (patch (.f64 eps #s(literal 1/24 binary64)) #<representation binary64>) () ())) ())
#s(alt (* 1/24 eps) (taylor -inf eps) (#s(alt (.f64 eps #s(literal 1/24 binary64)) (patch (.f64 eps #s(literal 1/24 binary64)) #<representation binary64>) () ())) ())
#s(alt (* 1/6 x) (taylor 0 x) (#s(alt (.f64 #s(literal 1/6 binary64) (sin.f64 x)) (patch (.f64 #s(literal 1/6 binary64) (sin.f64 x)) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1/6 (* -1/36 (pow x 2)))) (taylor 0 x) (#s(alt (.f64 #s(literal 1/6 binary64) (sin.f64 x)) (patch (.f64 #s(literal 1/6 binary64) (sin.f64 x)) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1/6 (* (pow x 2) (- (* 1/720 (pow x 2)) 1/36)))) (taylor 0 x) (#s(alt (.f64 #s(literal 1/6 binary64) (sin.f64 x)) (patch (.f64 #s(literal 1/6 binary64) (sin.f64 x)) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1/6 (* (pow x 2) (- (* (pow x 2) (+ 1/720 (* -1/30240 (pow x 2)))) 1/36)))) (taylor 0 x) (#s(alt (.f64 #s(literal 1/6 binary64) (sin.f64 x)) (patch (.f64 #s(literal 1/6 binary64) (sin.f64 x)) #<representation binary64>) () ())) ())
#s(alt (* 1/6 (sin x)) (taylor inf x) (#s(alt (.f64 #s(literal 1/6 binary64) (sin.f64 x)) (patch (.f64 #s(literal 1/6 binary64) (sin.f64 x)) #<representation binary64>) () ())) ())
#s(alt (* 1/6 (sin x)) (taylor inf x) (#s(alt (.f64 #s(literal 1/6 binary64) (sin.f64 x)) (patch (.f64 #s(literal 1/6 binary64) (sin.f64 x)) #<representation binary64>) () ())) ())
#s(alt (* 1/6 (sin x)) (taylor inf x) (#s(alt (.f64 #s(literal 1/6 binary64) (sin.f64 x)) (patch (.f64 #s(literal 1/6 binary64) (sin.f64 x)) #<representation binary64>) () ())) ())
#s(alt (* 1/6 (sin x)) (taylor inf x) (#s(alt (.f64 #s(literal 1/6 binary64) (sin.f64 x)) (patch (.f64 #s(literal 1/6 binary64) (sin.f64 x)) #<representation binary64>) () ())) ())
#s(alt (* 1/6 (sin x)) (taylor -inf x) (#s(alt (.f64 #s(literal 1/6 binary64) (sin.f64 x)) (patch (.f64 #s(literal 1/6 binary64) (sin.f64 x)) #<representation binary64>) () ())) ())
#s(alt (* 1/6 (sin x)) (taylor -inf x) (#s(alt (.f64 #s(literal 1/6 binary64) (sin.f64 x)) (patch (.f64 #s(literal 1/6 binary64) (sin.f64 x)) #<representation binary64>) () ())) ())
#s(alt (* 1/6 (sin x)) (taylor -inf x) (#s(alt (.f64 #s(literal 1/6 binary64) (sin.f64 x)) (patch (.f64 #s(literal 1/6 binary64) (sin.f64 x)) #<representation binary64>) () ())) ())
#s(alt (* 1/6 (sin x)) (taylor -inf x) (#s(alt (.f64 #s(literal 1/6 binary64) (sin.f64 x)) (patch (.f64 #s(literal 1/6 binary64) (sin.f64 x)) #<representation binary64>) () ())) ())
#s(alt (* 1/24 (pow eps 2)) (taylor 0 eps) (#s(alt (.f64 eps (.f64 eps #s(literal 1/24 binary64))) (patch (.f64 eps (.f64 eps #s(literal 1/24 binary64))) #<representation binary64>) () ())) ())
#s(alt (* 1/24 (pow eps 2)) (taylor 0 eps) (#s(alt (.f64 eps (.f64 eps #s(literal 1/24 binary64))) (patch (.f64 eps (.f64 eps #s(literal 1/24 binary64))) #<representation binary64>) () ())) ())
#s(alt (* 1/24 (pow eps 2)) (taylor 0 eps) (#s(alt (.f64 eps (.f64 eps #s(literal 1/24 binary64))) (patch (.f64 eps (.f64 eps #s(literal 1/24 binary64))) #<representation binary64>) () ())) ())
#s(alt (* 1/24 (pow eps 2)) (taylor 0 eps) (#s(alt (.f64 eps (.f64 eps #s(literal 1/24 binary64))) (patch (.f64 eps (.f64 eps #s(literal 1/24 binary64))) #<representation binary64>) () ())) ())
#s(alt (* 1/24 (pow eps 2)) (taylor inf eps) (#s(alt (.f64 eps (.f64 eps #s(literal 1/24 binary64))) (patch (.f64 eps (.f64 eps #s(literal 1/24 binary64))) #<representation binary64>) () ())) ())
#s(alt (* 1/24 (pow eps 2)) (taylor inf eps) (#s(alt (.f64 eps (.f64 eps #s(literal 1/24 binary64))) (patch (.f64 eps (.f64 eps #s(literal 1/24 binary64))) #<representation binary64>) () ())) ())
#s(alt (* 1/24 (pow eps 2)) (taylor inf eps) (#s(alt (.f64 eps (.f64 eps #s(literal 1/24 binary64))) (patch (.f64 eps (.f64 eps #s(literal 1/24 binary64))) #<representation binary64>) () ())) ())
#s(alt (* 1/24 (pow eps 2)) (taylor inf eps) (#s(alt (.f64 eps (.f64 eps #s(literal 1/24 binary64))) (patch (.f64 eps (.f64 eps #s(literal 1/24 binary64))) #<representation binary64>) () ())) ())
#s(alt (* 1/24 (pow eps 2)) (taylor -inf eps) (#s(alt (.f64 eps (.f64 eps #s(literal 1/24 binary64))) (patch (.f64 eps (.f64 eps #s(literal 1/24 binary64))) #<representation binary64>) () ())) ())
#s(alt (* 1/24 (pow eps 2)) (taylor -inf eps) (#s(alt (.f64 eps (.f64 eps #s(literal 1/24 binary64))) (patch (.f64 eps (.f64 eps #s(literal 1/24 binary64))) #<representation binary64>) () ())) ())
#s(alt (* 1/24 (pow eps 2)) (taylor -inf eps) (#s(alt (.f64 eps (.f64 eps #s(literal 1/24 binary64))) (patch (.f64 eps (.f64 eps #s(literal 1/24 binary64))) #<representation binary64>) () ())) ())
#s(alt (* 1/24 (pow eps 2)) (taylor -inf eps) (#s(alt (.f64 eps (.f64 eps #s(literal 1/24 binary64))) (patch (.f64 eps (.f64 eps #s(literal 1/24 binary64))) #<representation binary64>) () ())) ())
#s(alt 1 (taylor 0 x) (#s(alt (fma.f64 (sin.f64 x) (sin.f64 eps) (cos.f64 x)) (patch (fma.f64 (sin.f64 x) (sin.f64 eps) (cos.f64 x)) #<representation binary64>) () ())) ())
#s(alt (+ 1 (* x (sin eps))) (taylor 0 x) (#s(alt (fma.f64 (sin.f64 x) (sin.f64 eps) (cos.f64 x)) (patch (fma.f64 (sin.f64 x) (sin.f64 eps) (cos.f64 x)) #<representation binary64>) () ())) ())
#s(alt (+ 1 (* x (+ (sin eps) (* -1/2 x)))) (taylor 0 x) (#s(alt (fma.f64 (sin.f64 x) (sin.f64 eps) (cos.f64 x)) (patch (fma.f64 (sin.f64 x) (sin.f64 eps) (cos.f64 x)) #<representation binary64>) () ())) ())
#s(alt (+ 1 (* x (+ (sin eps) (* x (- (* -1/6 (* x (sin eps))) 1/2))))) (taylor 0 x) (#s(alt (fma.f64 (sin.f64 x) (sin.f64 eps) (cos.f64 x)) (patch (fma.f64 (sin.f64 x) (sin.f64 eps) (cos.f64 x)) #<representation binary64>) () ())) ())
#s(alt (+ (cos x) (* (sin eps) (sin x))) (taylor inf x) (#s(alt (fma.f64 (sin.f64 x) (sin.f64 eps) (cos.f64 x)) (patch (fma.f64 (sin.f64 x) (sin.f64 eps) (cos.f64 x)) #<representation binary64>) () ())) ())
#s(alt (+ (cos x) (* (sin eps) (sin x))) (taylor inf x) (#s(alt (fma.f64 (sin.f64 x) (sin.f64 eps) (cos.f64 x)) (patch (fma.f64 (sin.f64 x) (sin.f64 eps) (cos.f64 x)) #<representation binary64>) () ())) ())
#s(alt (+ (cos x) (* (sin eps) (sin x))) (taylor inf x) (#s(alt (fma.f64 (sin.f64 x) (sin.f64 eps) (cos.f64 x)) (patch (fma.f64 (sin.f64 x) (sin.f64 eps) (cos.f64 x)) #<representation binary64>) () ())) ())
#s(alt (+ (cos x) (* (sin eps) (sin x))) (taylor inf x) (#s(alt (fma.f64 (sin.f64 x) (sin.f64 eps) (cos.f64 x)) (patch (fma.f64 (sin.f64 x) (sin.f64 eps) (cos.f64 x)) #<representation binary64>) () ())) ())
#s(alt (+ (cos x) (* (sin eps) (sin x))) (taylor -inf x) (#s(alt (fma.f64 (sin.f64 x) (sin.f64 eps) (cos.f64 x)) (patch (fma.f64 (sin.f64 x) (sin.f64 eps) (cos.f64 x)) #<representation binary64>) () ())) ())
#s(alt (+ (cos x) (* (sin eps) (sin x))) (taylor -inf x) (#s(alt (fma.f64 (sin.f64 x) (sin.f64 eps) (cos.f64 x)) (patch (fma.f64 (sin.f64 x) (sin.f64 eps) (cos.f64 x)) #<representation binary64>) () ())) ())
#s(alt (+ (cos x) (* (sin eps) (sin x))) (taylor -inf x) (#s(alt (fma.f64 (sin.f64 x) (sin.f64 eps) (cos.f64 x)) (patch (fma.f64 (sin.f64 x) (sin.f64 eps) (cos.f64 x)) #<representation binary64>) () ())) ())
#s(alt (+ (cos x) (* (sin eps) (sin x))) (taylor -inf x) (#s(alt (fma.f64 (sin.f64 x) (sin.f64 eps) (cos.f64 x)) (patch (fma.f64 (sin.f64 x) (sin.f64 eps) (cos.f64 x)) #<representation binary64>) () ())) ())
#s(alt (cos x) (taylor 0 eps) (#s(alt (fma.f64 (sin.f64 x) (sin.f64 eps) (cos.f64 x)) (patch (fma.f64 (sin.f64 x) (sin.f64 eps) (cos.f64 x)) #<representation binary64>) () ())) ())
#s(alt (+ (cos x) (* eps (sin x))) (taylor 0 eps) (#s(alt (fma.f64 (sin.f64 x) (sin.f64 eps) (cos.f64 x)) (patch (fma.f64 (sin.f64 x) (sin.f64 eps) (cos.f64 x)) #<representation binary64>) () ())) ())
#s(alt (+ (cos x) (* eps (+ (sin x) (* -1/6 (* (pow eps 2) (sin x)))))) (taylor 0 eps) (#s(alt (fma.f64 (sin.f64 x) (sin.f64 eps) (cos.f64 x)) (patch (fma.f64 (sin.f64 x) (sin.f64 eps) (cos.f64 x)) #<representation binary64>) () ())) ())
#s(alt (+ (cos x) (* eps (+ (sin x) (* (pow eps 2) (+ (* -1/6 (sin x)) (* 1/120 (* (pow eps 2) (sin x)))))))) (taylor 0 eps) (#s(alt (fma.f64 (sin.f64 x) (sin.f64 eps) (cos.f64 x)) (patch (fma.f64 (sin.f64 x) (sin.f64 eps) (cos.f64 x)) #<representation binary64>) () ())) ())
#s(alt (+ (cos x) (* (sin eps) (sin x))) (taylor inf eps) (#s(alt (fma.f64 (sin.f64 x) (sin.f64 eps) (cos.f64 x)) (patch (fma.f64 (sin.f64 x) (sin.f64 eps) (cos.f64 x)) #<representation binary64>) () ())) ())
#s(alt (+ (cos x) (* (sin eps) (sin x))) (taylor inf eps) (#s(alt (fma.f64 (sin.f64 x) (sin.f64 eps) (cos.f64 x)) (patch (fma.f64 (sin.f64 x) (sin.f64 eps) (cos.f64 x)) #<representation binary64>) () ())) ())
#s(alt (+ (cos x) (* (sin eps) (sin x))) (taylor inf eps) (#s(alt (fma.f64 (sin.f64 x) (sin.f64 eps) (cos.f64 x)) (patch (fma.f64 (sin.f64 x) (sin.f64 eps) (cos.f64 x)) #<representation binary64>) () ())) ())
#s(alt (+ (cos x) (* (sin eps) (sin x))) (taylor inf eps) (#s(alt (fma.f64 (sin.f64 x) (sin.f64 eps) (cos.f64 x)) (patch (fma.f64 (sin.f64 x) (sin.f64 eps) (cos.f64 x)) #<representation binary64>) () ())) ())
#s(alt (+ (cos x) (* (sin eps) (sin x))) (taylor -inf eps) (#s(alt (fma.f64 (sin.f64 x) (sin.f64 eps) (cos.f64 x)) (patch (fma.f64 (sin.f64 x) (sin.f64 eps) (cos.f64 x)) #<representation binary64>) () ())) ())
#s(alt (+ (cos x) (* (sin eps) (sin x))) (taylor -inf eps) (#s(alt (fma.f64 (sin.f64 x) (sin.f64 eps) (cos.f64 x)) (patch (fma.f64 (sin.f64 x) (sin.f64 eps) (cos.f64 x)) #<representation binary64>) () ())) ())
#s(alt (+ (cos x) (* (sin eps) (sin x))) (taylor -inf eps) (#s(alt (fma.f64 (sin.f64 x) (sin.f64 eps) (cos.f64 x)) (patch (fma.f64 (sin.f64 x) (sin.f64 eps) (cos.f64 x)) #<representation binary64>) () ())) ())
#s(alt (+ (cos x) (* (sin eps) (sin x))) (taylor -inf eps) (#s(alt (fma.f64 (sin.f64 x) (sin.f64 eps) (cos.f64 x)) (patch (fma.f64 (sin.f64 x) (sin.f64 eps) (cos.f64 x)) #<representation binary64>) () ())) ())

Calls

120 calls:

Time	Variable		Point	Expression
6.0ms	eps	@	0	(+ (cos eps) -1)
2.0ms	eps	@	0	(* eps (+ (* eps (+ (* (cos x) (+ -1/2 (* eps (* eps 1/24)))) (* eps (* 1/6 (sin x))))) (sin (neg x))))
1.0ms	x	@	inf	(+ (* eps (+ (* (cos x) (+ -1/2 (* eps (* eps 1/24)))) (* eps (* 1/6 (sin x))))) (sin (neg x)))
1.0ms	x	@	0	(* (* (sin (* (+ eps 0) 1/2)) (sin (* (+ x (+ x eps)) 1/2))) -2)
1.0ms	x	@	inf	(- (* (cos x) (cos eps)) (+ (* (sin x) (sin eps)) (cos x)))

simplify326.0ms (1.8%)

Memory

-34.8MiB live, 448.6MiB allocated

Algorithm

1×	egg-herbie

Rules

12 910×	`lower-fma.f64`
12 910×	`lower-fma.f32`
7 126×	`lower-*.f64`
7 126×	`lower-*.f32`
3 654×	`lower-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	473	4669
1	1443	4451
2	4089	4445
0	8233	4114

Stop Event

1×	iter limit
1×	node limit

Counts

480 → 456

Calls

Call 1

Inputs
(* 1/2 eps)
(+ x (* 1/2 eps))
(+ x (* 1/2 eps))
(+ x (* 1/2 eps))
x
(* x (+ 1 (* 1/2 (/ eps x))))
(* x (+ 1 (* 1/2 (/ eps x))))
(* x (+ 1 (* 1/2 (/ eps x))))
x
(* -1 (* x (- (* -1/2 (/ eps x)) 1)))
(* -1 (* x (- (* -1/2 (/ eps x)) 1)))
(* -1 (* x (- (* -1/2 (/ eps x)) 1)))
x
(+ x (* 1/2 eps))
(+ x (* 1/2 eps))
(+ x (* 1/2 eps))
(* 1/2 eps)
(* eps (+ 1/2 (/ x eps)))
(* eps (+ 1/2 (/ x eps)))
(* eps (+ 1/2 (/ x eps)))
(* 1/2 eps)
(* -1 (* eps (- (* -1 (/ x eps)) 1/2)))
(* -1 (* eps (- (* -1 (/ x eps)) 1/2)))
(* -1 (* eps (- (* -1 (/ x eps)) 1/2)))
eps
eps
eps
eps
eps
eps
eps
eps
eps
eps
eps
eps
(* -1 (* eps (sin x)))
(* eps (+ (* -1 (sin x)) (* -1/2 (* eps (cos x)))))
(* eps (+ (* -1 (sin x)) (* eps (+ (* -2 (* eps (+ (* -1/16 (sin x)) (* -1/48 (sin x))))) (* -1/2 (cos x))))))
(* eps (+ (* -1 (sin x)) (* eps (+ (* -1/2 (cos x)) (* eps (+ (* -2 (+ (* -1/16 (sin x)) (* -1/48 (sin x)))) (* 1/24 (* eps (cos x)))))))))
(* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (+ eps (* 2 x))))))
(* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (+ eps (* 2 x))))))
(* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (+ eps (* 2 x))))))
(* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (+ eps (* 2 x))))))
(* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (- (* 2 x) (* -1 eps))))))
(* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (- (* 2 x) (* -1 eps))))))
(* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (- (* 2 x) (* -1 eps))))))
(* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (- (* 2 x) (* -1 eps))))))
(* -2 (pow (sin (* 1/2 eps)) 2))
(+ (* -2 (* x (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))) (* -2 (pow (sin (* 1/2 eps)) 2)))
(+ (* -2 (pow (sin (* 1/2 eps)) 2)) (* x (+ (* -2 (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) (* x (pow (sin (* 1/2 eps)) 2)))))
(+ (* -2 (pow (sin (* 1/2 eps)) 2)) (* x (+ (* -2 (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) (* x (+ (* 1/3 (* x (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))) (pow (sin (* 1/2 eps)) 2))))))
(* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (+ eps (* 2 x))))))
(* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (+ eps (* 2 x))))))
(* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (+ eps (* 2 x))))))
(* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (+ eps (* 2 x))))))
(* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (- eps (* -2 x))))))
(* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (- eps (* -2 x))))))
(* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (- eps (* -2 x))))))
(* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (- eps (* -2 x))))))
(* 1/2 (* eps (sin x)))
(* eps (+ (* 1/4 (* eps (cos x))) (* 1/2 (sin x))))
(* eps (+ (* 1/2 (sin x)) (* eps (+ (* 1/4 (cos x)) (* eps (+ (* -1/16 (sin x)) (* -1/48 (sin x))))))))
(* eps (+ (* 1/2 (sin x)) (* eps (+ (* 1/4 (cos x)) (* eps (+ (* -1/16 (sin x)) (+ (* -1/48 (sin x)) (* -1/48 (* eps (cos x))))))))))
(* (sin (* 1/2 eps)) (sin (* 1/2 (+ eps (* 2 x)))))
(* (sin (* 1/2 eps)) (sin (* 1/2 (+ eps (* 2 x)))))
(* (sin (* 1/2 eps)) (sin (* 1/2 (+ eps (* 2 x)))))
(* (sin (* 1/2 eps)) (sin (* 1/2 (+ eps (* 2 x)))))
(* (sin (* 1/2 eps)) (sin (* 1/2 (- (* 2 x) (* -1 eps)))))
(* (sin (* 1/2 eps)) (sin (* 1/2 (- (* 2 x) (* -1 eps)))))
(* (sin (* 1/2 eps)) (sin (* 1/2 (- (* 2 x) (* -1 eps)))))
(* (sin (* 1/2 eps)) (sin (* 1/2 (- (* 2 x) (* -1 eps)))))
(pow (sin (* 1/2 eps)) 2)
(+ (* x (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) (pow (sin (* 1/2 eps)) 2))
(+ (* x (+ (* -1/2 (* x (pow (sin (* 1/2 eps)) 2))) (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))) (pow (sin (* 1/2 eps)) 2))
(+ (* x (+ (* x (+ (* -1/2 (pow (sin (* 1/2 eps)) 2)) (* -1/6 (* x (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))))) (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))) (pow (sin (* 1/2 eps)) 2))
(* (sin (* 1/2 eps)) (sin (* 1/2 (+ eps (* 2 x)))))
(* (sin (* 1/2 eps)) (sin (* 1/2 (+ eps (* 2 x)))))
(* (sin (* 1/2 eps)) (sin (* 1/2 (+ eps (* 2 x)))))
(* (sin (* 1/2 eps)) (sin (* 1/2 (+ eps (* 2 x)))))
(* (sin (* 1/2 eps)) (sin (* 1/2 (- eps (* -2 x)))))
(* (sin (* 1/2 eps)) (sin (* 1/2 (- eps (* -2 x)))))
(* (sin (* 1/2 eps)) (sin (* 1/2 (- eps (* -2 x)))))
(* (sin (* 1/2 eps)) (sin (* 1/2 (- eps (* -2 x)))))
(- (cos eps) 1)
(- (+ (cos eps) (* -1 (* x (sin eps)))) 1)
(- (+ (cos eps) (* x (- (* x (+ 1/2 (* -1/2 (cos eps)))) (sin eps)))) 1)
(- (+ (cos eps) (* x (- (* x (+ 1/2 (+ (* -1/2 (cos eps)) (* 1/6 (* x (sin eps)))))) (sin eps)))) 1)
(- (cos (+ eps x)) (cos x))
(- (cos (+ eps x)) (cos x))
(- (cos (+ eps x)) (cos x))
(- (cos (+ eps x)) (cos x))
(- (cos (- eps (* -1 x))) (cos x))
(- (cos (- eps (* -1 x))) (cos x))
(- (cos (- eps (* -1 x))) (cos x))
(- (cos (- eps (* -1 x))) (cos x))
(* -1 (* eps (sin x)))
(* eps (- (* -1/2 (* eps (cos x))) (sin x)))
(* eps (- (* eps (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x))))) (sin x)))
(* eps (- (* eps (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x)))))) (sin x)))
(- (cos (+ eps x)) (cos x))
(- (cos (+ eps x)) (cos x))
(- (cos (+ eps x)) (cos x))
(- (cos (+ eps x)) (cos x))
(- (cos (- x (* -1 eps))) (cos x))
(- (cos (- x (* -1 eps))) (cos x))
(- (cos (- x (* -1 eps))) (cos x))
(- (cos (- x (* -1 eps))) (cos x))
(* -1/2 (pow eps 2))
(* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2))
(* (pow eps 2) (- (* (pow eps 2) (+ 1/24 (* -1/720 (pow eps 2)))) 1/2))
(* (pow eps 2) (- (* (pow eps 2) (+ 1/24 (* (pow eps 2) (- (* 1/40320 (pow eps 2)) 1/720)))) 1/2))
(- (cos eps) 1)
(- (cos eps) 1)
(- (cos eps) 1)
(- (cos eps) 1)
(- (cos eps) 1)
(- (cos eps) 1)
(- (cos eps) 1)
(- (cos eps) 1)
1
(+ 1 (* -1/2 (pow eps 2)))
(+ 1 (* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2)))
(+ 1 (* (pow eps 2) (- (* (pow eps 2) (+ 1/24 (* -1/720 (pow eps 2)))) 1/2)))
(cos eps)
(cos eps)
(cos eps)
(cos eps)
(cos eps)
(cos eps)
(cos eps)
(cos eps)
(- (cos eps) 1)
(- (+ (cos eps) (* -1 (* x (sin eps)))) 1)
(- (+ (cos eps) (* x (- (* x (+ 1/2 (* -1/2 (cos eps)))) (sin eps)))) 1)
(- (+ (cos eps) (* x (- (* x (+ 1/2 (+ (* -1/2 (cos eps)) (* 1/6 (* x (sin eps)))))) (sin eps)))) 1)
(- (cos (+ eps x)) (cos x))
(- (cos (+ eps x)) (cos x))
(- (cos (+ eps x)) (cos x))
(- (cos (+ eps x)) (cos x))
(- (cos (- eps (* -1 x))) (cos x))
(- (cos (- eps (* -1 x))) (cos x))
(- (cos (- eps (* -1 x))) (cos x))
(- (cos (- eps (* -1 x))) (cos x))
(* -1 (* eps (sin x)))
(* eps (- (* -1/2 (* eps (cos x))) (sin x)))
(* eps (- (* eps (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x))))) (sin x)))
(* eps (- (* eps (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x)))))) (sin x)))
(- (cos (+ eps x)) (cos x))
(- (cos (+ eps x)) (cos x))
(- (cos (+ eps x)) (cos x))
(- (cos (+ eps x)) (cos x))
(- (cos (- x (* -1 eps))) (cos x))
(- (cos (- x (* -1 eps))) (cos x))
(- (cos (- x (* -1 eps))) (cos x))
(- (cos (- x (* -1 eps))) (cos x))
(cos eps)
(+ (cos eps) (* -1 (* x (sin eps))))
(+ (cos eps) (* x (- (* -1/2 (* x (cos eps))) (sin eps))))
(+ (cos eps) (* x (- (* x (+ (* -1/2 (cos eps)) (* 1/6 (* x (sin eps))))) (sin eps))))
(cos (+ eps x))
(cos (+ eps x))
(cos (+ eps x))
(cos (+ eps x))
(cos (- eps (* -1 x)))
(cos (- eps (* -1 x)))
(cos (- eps (* -1 x)))
(cos (- eps (* -1 x)))
(cos x)
(+ (cos x) (* -1 (* eps (sin x))))
(+ (cos x) (* eps (- (* -1/2 (* eps (cos x))) (sin x))))
(+ (cos x) (* eps (- (* eps (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x))))) (sin x))))
(cos (+ eps x))
(cos (+ eps x))
(cos (+ eps x))
(cos (+ eps x))
(cos (- x (* -1 eps)))
(cos (- x (* -1 eps)))
(cos (- x (* -1 eps)))
(cos (- x (* -1 eps)))
eps
(+ eps x)
(+ eps x)
(+ eps x)
x
(* x (+ 1 (/ eps x)))
(* x (+ 1 (/ eps x)))
(* x (+ 1 (/ eps x)))
x
(* -1 (* x (- (* -1 (/ eps x)) 1)))
(* -1 (* x (- (* -1 (/ eps x)) 1)))
(* -1 (* x (- (* -1 (/ eps x)) 1)))
x
(+ eps x)
(+ eps x)
(+ eps x)
eps
(* eps (+ 1 (/ x eps)))
(* eps (+ 1 (/ x eps)))
(* eps (+ 1 (/ x eps)))
eps
(* -1 (* eps (- (* -1 (/ x eps)) 1)))
(* -1 (* eps (- (* -1 (/ x eps)) 1)))
(* -1 (* eps (- (* -1 (/ x eps)) 1)))
1
(+ 1 (* -1/2 (pow x 2)))
(+ 1 (* (pow x 2) (- (* 1/24 (pow x 2)) 1/2)))
(+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))) 1/2)))
(cos x)
(cos x)
(cos x)
(cos x)
(cos x)
(cos x)
(cos x)
(cos x)
(sin (neg x))
(+ (sin (neg x)) (* -1/2 (* eps (cos x))))
(+ (sin (neg x)) (* eps (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x))))))
(+ (sin (neg x)) (* eps (+ (* -1/2 (cos x)) (* eps (+ (* 1/24 (* eps (cos x))) (* 1/6 (sin x)))))))
(* 1/24 (* (pow eps 3) (cos x)))
(* (pow eps 3) (+ (* 1/24 (cos x)) (* 1/6 (/ (sin x) eps))))
(* (pow eps 3) (+ (* -1/2 (/ (cos x) (pow eps 2))) (+ (* 1/24 (cos x)) (* 1/6 (/ (sin x) eps)))))
(* (pow eps 3) (+ (* -1/2 (/ (cos x) (pow eps 2))) (+ (* 1/24 (cos x)) (+ (* 1/6 (/ (sin x) eps)) (/ (sin (neg x)) (pow eps 3))))))
(* 1/24 (* (pow eps 3) (cos x)))
(* -1 (* (pow eps 3) (+ (* -1/6 (/ (sin x) eps)) (* -1/24 (cos x)))))
(* -1 (* (pow eps 3) (+ (* -1 (/ (+ (* -1/2 (/ (cos x) eps)) (* 1/6 (sin x))) eps)) (* -1/24 (cos x)))))
(* -1 (* (pow eps 3) (+ (* -1 (/ (+ (* -1 (/ (+ (* -1 (/ (sin (neg x)) eps)) (* 1/2 (cos x))) eps)) (* 1/6 (sin x))) eps)) (* -1/24 (cos x)))))
(* eps (- (* 1/24 (pow eps 2)) 1/2))
(+ (* eps (- (* 1/24 (pow eps 2)) 1/2)) (* x (- (* 1/6 (pow eps 2)) 1)))
(+ (* eps (- (* 1/24 (pow eps 2)) 1/2)) (* x (- (+ (* -1/2 (* eps (* x (- (* 1/24 (pow eps 2)) 1/2)))) (* 1/6 (pow eps 2))) 1)))
(+ (* eps (- (* 1/24 (pow eps 2)) 1/2)) (* x (- (+ (* 1/6 (pow eps 2)) (* x (+ (* -1/2 (* eps (- (* 1/24 (pow eps 2)) 1/2))) (* x (+ 1/6 (* -1/36 (pow eps 2))))))) 1)))
(+ (sin (neg x)) (* eps (+ (* 1/6 (* eps (sin x))) (* (cos x) (- (* 1/24 (pow eps 2)) 1/2)))))
(+ (sin (neg x)) (* eps (+ (* 1/6 (* eps (sin x))) (* (cos x) (- (* 1/24 (pow eps 2)) 1/2)))))
(+ (sin (neg x)) (* eps (+ (* 1/6 (* eps (sin x))) (* (cos x) (- (* 1/24 (pow eps 2)) 1/2)))))
(+ (sin (neg x)) (* eps (+ (* 1/6 (* eps (sin x))) (* (cos x) (- (* 1/24 (pow eps 2)) 1/2)))))
(+ (sin (* -1 x)) (* eps (+ (* 1/6 (* eps (sin x))) (* (cos x) (- (* 1/24 (pow eps 2)) 1/2)))))
(+ (sin (* -1 x)) (* eps (+ (* 1/6 (* eps (sin x))) (* (cos x) (- (* 1/24 (pow eps 2)) 1/2)))))
(+ (sin (* -1 x)) (* eps (+ (* 1/6 (* eps (sin x))) (* (cos x) (- (* 1/24 (pow eps 2)) 1/2)))))
(+ (sin (* -1 x)) (* eps (+ (* 1/6 (* eps (sin x))) (* (cos x) (- (* 1/24 (pow eps 2)) 1/2)))))
-1/2
(- (* 1/24 (pow eps 2)) 1/2)
(- (* 1/24 (pow eps 2)) 1/2)
(- (* 1/24 (pow eps 2)) 1/2)
(* 1/24 (pow eps 2))
(* (pow eps 2) (- 1/24 (* 1/2 (/ 1 (pow eps 2)))))
(* (pow eps 2) (- 1/24 (* 1/2 (/ 1 (pow eps 2)))))
(* (pow eps 2) (- 1/24 (* 1/2 (/ 1 (pow eps 2)))))
(* 1/24 (pow eps 2))
(* (pow eps 2) (- 1/24 (* 1/2 (/ 1 (pow eps 2)))))
(* (pow eps 2) (- 1/24 (* 1/2 (/ 1 (pow eps 2)))))
(* (pow eps 2) (- 1/24 (* 1/2 (/ 1 (pow eps 2)))))
(- (cos eps) 1)
(- (+ (cos eps) (* -1 (* x (sin eps)))) 1)
(- (+ (cos eps) (* x (- (* x (+ 1/2 (* -1/2 (cos eps)))) (sin eps)))) 1)
(- (+ (cos eps) (* x (- (* x (+ 1/2 (+ (* -1/2 (cos eps)) (* 1/6 (* x (sin eps)))))) (sin eps)))) 1)
(- (cos (+ eps x)) (cos x))
(- (cos (+ eps x)) (cos x))
(- (cos (+ eps x)) (cos x))
(- (cos (+ eps x)) (cos x))
(- (cos (- eps (* -1 x))) (cos x))
(- (cos (- eps (* -1 x))) (cos x))
(- (cos (- eps (* -1 x))) (cos x))
(- (cos (- eps (* -1 x))) (cos x))
(* -1 (* eps (sin x)))
(* eps (- (* -1/2 (* eps (cos x))) (sin x)))
(* eps (- (* eps (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x))))) (sin x)))
(* eps (- (* eps (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x)))))) (sin x)))
(- (cos (+ eps x)) (cos x))
(- (cos (+ eps x)) (cos x))
(- (cos (+ eps x)) (cos x))
(- (cos (+ eps x)) (cos x))
(- (cos (- x (* -1 eps))) (cos x))
(- (cos (- x (* -1 eps))) (cos x))
(- (cos (- x (* -1 eps))) (cos x))
(- (cos (- x (* -1 eps))) (cos x))
(* eps (sin (neg x)))
(* eps (+ (sin (neg x)) (* -1/2 (* eps (cos x)))))
(* eps (+ (sin (neg x)) (* eps (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x)))))))
(* eps (+ (sin (neg x)) (* eps (+ (* -1/2 (cos x)) (* eps (+ (* 1/24 (* eps (cos x))) (* 1/6 (sin x))))))))
(* 1/24 (* (pow eps 4) (cos x)))
(* (pow eps 4) (+ (* 1/24 (cos x)) (* 1/6 (/ (sin x) eps))))
(* (pow eps 4) (+ (* -1/2 (/ (cos x) (pow eps 2))) (+ (* 1/24 (cos x)) (* 1/6 (/ (sin x) eps)))))
(* (pow eps 4) (+ (* -1/2 (/ (cos x) (pow eps 2))) (+ (* 1/24 (cos x)) (+ (* 1/6 (/ (sin x) eps)) (/ (sin (neg x)) (pow eps 3))))))
(* 1/24 (* (pow eps 4) (cos x)))
(* (pow eps 4) (+ (* 1/24 (cos x)) (* 1/6 (/ (sin x) eps))))
(* (pow eps 4) (+ (* -1 (/ (+ (* -1/6 (sin x)) (* 1/2 (/ (cos x) eps))) eps)) (* 1/24 (cos x))))
(* (pow eps 4) (+ (* -1 (/ (+ (* -1 (/ (+ (* -1/2 (cos x)) (/ (sin (neg x)) eps)) eps)) (* -1/6 (sin x))) eps)) (* 1/24 (cos x))))
(* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2))
(+ (* eps (* x (- (* 1/6 (pow eps 2)) 1))) (* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2)))
(+ (* x (+ (* -1/2 (* (pow eps 2) (* x (- (* 1/24 (pow eps 2)) 1/2)))) (* eps (- (* 1/6 (pow eps 2)) 1)))) (* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2)))
(+ (* x (+ (* eps (- (* 1/6 (pow eps 2)) 1)) (* x (+ (* -1/2 (* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2))) (* eps (* x (+ 1/6 (* -1/36 (pow eps 2))))))))) (* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2)))
(* eps (+ (sin (neg x)) (* eps (+ (* 1/6 (* eps (sin x))) (* (cos x) (- (* 1/24 (pow eps 2)) 1/2))))))
(* eps (+ (sin (neg x)) (* eps (+ (* 1/6 (* eps (sin x))) (* (cos x) (- (* 1/24 (pow eps 2)) 1/2))))))
(* eps (+ (sin (neg x)) (* eps (+ (* 1/6 (* eps (sin x))) (* (cos x) (- (* 1/24 (pow eps 2)) 1/2))))))
(* eps (+ (sin (neg x)) (* eps (+ (* 1/6 (* eps (sin x))) (* (cos x) (- (* 1/24 (pow eps 2)) 1/2))))))
(* eps (+ (sin (* -1 x)) (* eps (+ (* 1/6 (* eps (sin x))) (* (cos x) (- (* 1/24 (pow eps 2)) 1/2))))))
(* eps (+ (sin (* -1 x)) (* eps (+ (* 1/6 (* eps (sin x))) (* (cos x) (- (* 1/24 (pow eps 2)) 1/2))))))
(* eps (+ (sin (* -1 x)) (* eps (+ (* 1/6 (* eps (sin x))) (* (cos x) (- (* 1/24 (pow eps 2)) 1/2))))))
(* eps (+ (sin (* -1 x)) (* eps (+ (* 1/6 (* eps (sin x))) (* (cos x) (- (* 1/24 (pow eps 2)) 1/2))))))
(- (cos eps) 1)
(- (+ (cos eps) (* -1 (* x (sin eps)))) 1)
(- (+ (cos eps) (* x (- (* x (+ 1/2 (* -1/2 (cos eps)))) (sin eps)))) 1)
(- (+ (cos eps) (* x (- (* x (+ 1/2 (+ (* -1/2 (cos eps)) (* 1/6 (* x (sin eps)))))) (sin eps)))) 1)
(- (* (cos eps) (cos x)) (+ (cos x) (* (sin eps) (sin x))))
(- (* (cos eps) (cos x)) (+ (cos x) (* (sin eps) (sin x))))
(- (* (cos eps) (cos x)) (+ (cos x) (* (sin eps) (sin x))))
(- (* (cos eps) (cos x)) (+ (cos x) (* (sin eps) (sin x))))
(- (* (cos eps) (cos x)) (+ (cos x) (* (sin eps) (sin x))))
(- (* (cos eps) (cos x)) (+ (cos x) (* (sin eps) (sin x))))
(- (* (cos eps) (cos x)) (+ (cos x) (* (sin eps) (sin x))))
(- (* (cos eps) (cos x)) (+ (cos x) (* (sin eps) (sin x))))
(* -1 (* eps (sin x)))
(* eps (- (* -1/2 (* eps (cos x))) (sin x)))
(* eps (- (* eps (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x))))) (sin x)))
(* eps (- (* eps (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x)))))) (sin x)))
(- (* (cos eps) (cos x)) (+ (cos x) (* (sin eps) (sin x))))
(- (* (cos eps) (cos x)) (+ (cos x) (* (sin eps) (sin x))))
(- (* (cos eps) (cos x)) (+ (cos x) (* (sin eps) (sin x))))
(- (* (cos eps) (cos x)) (+ (cos x) (* (sin eps) (sin x))))
(- (* (cos eps) (cos x)) (+ (cos x) (* (sin eps) (sin x))))
(- (* (cos eps) (cos x)) (+ (cos x) (* (sin eps) (sin x))))
(- (* (cos eps) (cos x)) (+ (cos x) (* (sin eps) (sin x))))
(- (* (cos eps) (cos x)) (+ (cos x) (* (sin eps) (sin x))))
(cos eps)
(+ (cos eps) (* -1/2 (* (pow x 2) (cos eps))))
(+ (cos eps) (* (pow x 2) (+ (* -1/2 (cos eps)) (* 1/24 (* (pow x 2) (cos eps))))))
(+ (cos eps) (* (pow x 2) (+ (* -1/2 (cos eps)) (* (pow x 2) (+ (* -1/720 (* (pow x 2) (cos eps))) (* 1/24 (cos eps)))))))
(* (cos eps) (cos x))
(* (cos eps) (cos x))
(* (cos eps) (cos x))
(* (cos eps) (cos x))
(* (cos eps) (cos x))
(* (cos eps) (cos x))
(* (cos eps) (cos x))
(* (cos eps) (cos x))
(cos x)
(+ (cos x) (* -1/2 (* (pow eps 2) (cos x))))
(+ (cos x) (* (pow eps 2) (+ (* -1/2 (cos x)) (* 1/24 (* (pow eps 2) (cos x))))))
(+ (cos x) (* (pow eps 2) (+ (* -1/2 (cos x)) (* (pow eps 2) (+ (* -1/720 (* (pow eps 2) (cos x))) (* 1/24 (cos x)))))))
(* (cos eps) (cos x))
(* (cos eps) (cos x))
(* (cos eps) (cos x))
(* (cos eps) (cos x))
(* (cos eps) (cos x))
(* (cos eps) (cos x))
(* (cos eps) (cos x))
(* (cos eps) (cos x))
1
(+ 1 (* -1/2 (pow x 2)))
(+ 1 (* (pow x 2) (- (* 1/24 (pow x 2)) 1/2)))
(+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))) 1/2)))
(cos x)
(cos x)
(cos x)
(cos x)
(cos x)
(cos x)
(cos x)
(cos x)
eps
(+ eps (* 2 x))
(+ eps (* 2 x))
(+ eps (* 2 x))
(* 2 x)
(* x (+ 2 (/ eps x)))
(* x (+ 2 (/ eps x)))
(* x (+ 2 (/ eps x)))
(* 2 x)
(* -1 (* x (- (* -1 (/ eps x)) 2)))
(* -1 (* x (- (* -1 (/ eps x)) 2)))
(* -1 (* x (- (* -1 (/ eps x)) 2)))
(* 2 x)
(+ eps (* 2 x))
(+ eps (* 2 x))
(+ eps (* 2 x))
eps
(* eps (+ 1 (* 2 (/ x eps))))
(* eps (+ 1 (* 2 (/ x eps))))
(* eps (+ 1 (* 2 (/ x eps))))
eps
(* -1 (* eps (- (* -2 (/ x eps)) 1)))
(* -1 (* eps (- (* -2 (/ x eps)) 1)))
(* -1 (* eps (- (* -2 (/ x eps)) 1)))
(sin (* 1/2 eps))
(+ (sin (* 1/2 eps)) (* x (cos (* 1/2 eps))))
(+ (sin (* 1/2 eps)) (* x (+ (cos (* 1/2 eps)) (* -1/2 (* x (sin (* 1/2 eps)))))))
(+ (sin (* 1/2 eps)) (* x (+ (cos (* 1/2 eps)) (* x (+ (* -1/2 (sin (* 1/2 eps))) (* -1/6 (* x (cos (* 1/2 eps)))))))))
(sin (* 1/2 (+ eps (* 2 x))))
(sin (* 1/2 (+ eps (* 2 x))))
(sin (* 1/2 (+ eps (* 2 x))))
(sin (* 1/2 (+ eps (* 2 x))))
(sin (* 1/2 (- eps (* -2 x))))
(sin (* 1/2 (- eps (* -2 x))))
(sin (* 1/2 (- eps (* -2 x))))
(sin (* 1/2 (- eps (* -2 x))))
(sin x)
(+ (sin x) (* 1/2 (* eps (cos x))))
(+ (sin x) (* eps (+ (* -1/8 (* eps (sin x))) (* 1/2 (cos x)))))
(+ (sin x) (* eps (+ (* 1/2 (cos x)) (* eps (+ (* -1/8 (sin x)) (* -1/48 (* eps (cos x))))))))
(sin (* 1/2 (+ eps (* 2 x))))
(sin (* 1/2 (+ eps (* 2 x))))
(sin (* 1/2 (+ eps (* 2 x))))
(sin (* 1/2 (+ eps (* 2 x))))
(sin (* 1/2 (- (* 2 x) (* -1 eps))))
(sin (* 1/2 (- (* 2 x) (* -1 eps))))
(sin (* 1/2 (- (* 2 x) (* -1 eps))))
(sin (* 1/2 (- (* 2 x) (* -1 eps))))
(* -1/2 x)
(* -1/2 x)
(* -1/2 x)
(* -1/2 x)
(* -1/2 x)
(* -1/2 x)
(* -1/2 x)
(* -1/2 x)
(* -1/2 x)
(* -1/2 x)
(* -1/2 x)
(* -1/2 x)
(* 1/24 eps)
(* 1/24 eps)
(* 1/24 eps)
(* 1/24 eps)
(* 1/24 eps)
(* 1/24 eps)
(* 1/24 eps)
(* 1/24 eps)
(* 1/24 eps)
(* 1/24 eps)
(* 1/24 eps)
(* 1/24 eps)
(* 1/6 x)
(* x (+ 1/6 (* -1/36 (pow x 2))))
(* x (+ 1/6 (* (pow x 2) (- (* 1/720 (pow x 2)) 1/36))))
(* x (+ 1/6 (* (pow x 2) (- (* (pow x 2) (+ 1/720 (* -1/30240 (pow x 2)))) 1/36))))
(* 1/6 (sin x))
(* 1/6 (sin x))
(* 1/6 (sin x))
(* 1/6 (sin x))
(* 1/6 (sin x))
(* 1/6 (sin x))
(* 1/6 (sin x))
(* 1/6 (sin x))
(* 1/24 (pow eps 2))
(* 1/24 (pow eps 2))
(* 1/24 (pow eps 2))
(* 1/24 (pow eps 2))
(* 1/24 (pow eps 2))
(* 1/24 (pow eps 2))
(* 1/24 (pow eps 2))
(* 1/24 (pow eps 2))
(* 1/24 (pow eps 2))
(* 1/24 (pow eps 2))
(* 1/24 (pow eps 2))
(* 1/24 (pow eps 2))
1
(+ 1 (* x (sin eps)))
(+ 1 (* x (+ (sin eps) (* -1/2 x))))
(+ 1 (* x (+ (sin eps) (* x (- (* -1/6 (* x (sin eps))) 1/2)))))
(+ (cos x) (* (sin eps) (sin x)))
(+ (cos x) (* (sin eps) (sin x)))
(+ (cos x) (* (sin eps) (sin x)))
(+ (cos x) (* (sin eps) (sin x)))
(+ (cos x) (* (sin eps) (sin x)))
(+ (cos x) (* (sin eps) (sin x)))
(+ (cos x) (* (sin eps) (sin x)))
(+ (cos x) (* (sin eps) (sin x)))
(cos x)
(+ (cos x) (* eps (sin x)))
(+ (cos x) (* eps (+ (sin x) (* -1/6 (* (pow eps 2) (sin x))))))
(+ (cos x) (* eps (+ (sin x) (* (pow eps 2) (+ (* -1/6 (sin x)) (* 1/120 (* (pow eps 2) (sin x))))))))
(+ (cos x) (* (sin eps) (sin x)))
(+ (cos x) (* (sin eps) (sin x)))
(+ (cos x) (* (sin eps) (sin x)))
(+ (cos x) (* (sin eps) (sin x)))
(+ (cos x) (* (sin eps) (sin x)))
(+ (cos x) (* (sin eps) (sin x)))
(+ (cos x) (* (sin eps) (sin x)))
(+ (cos x) (* (sin eps) (sin x)))

Outputs
(* 1/2 eps)
(*.f64 #s(literal 1/2 binary64) eps)
(+ x (* 1/2 eps))
(fma.f64 #s(literal 1/2 binary64) eps x)
(+ x (* 1/2 eps))
(fma.f64 #s(literal 1/2 binary64) eps x)
(+ x (* 1/2 eps))
(fma.f64 #s(literal 1/2 binary64) eps x)
x
(* x (+ 1 (* 1/2 (/ eps x))))
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(fma.f64 x (cos.f64 (.f64 #s(literal 1/2 binary64) eps)) (sin.f64 (.f64 #s(literal 1/2 binary64) eps)))
(+ (sin (* 1/2 eps)) (* x (+ (cos (* 1/2 eps)) (* -1/2 (* x (sin (* 1/2 eps)))))))
(fma.f64 x (fma.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (.f64 x #s(literal -1/2 binary64)) (cos.f64 (.f64 #s(literal 1/2 binary64) eps))) (sin.f64 (.f64 #s(literal 1/2 binary64) eps)))
(+ (sin (* 1/2 eps)) (* x (+ (cos (* 1/2 eps)) (* x (+ (* -1/2 (sin (* 1/2 eps))) (* -1/6 (* x (cos (* 1/2 eps)))))))))
(fma.f64 x (fma.f64 x (fma.f64 #s(literal -1/2 binary64) (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (.f64 (cos.f64 (.f64 #s(literal 1/2 binary64) eps)) (.f64 x #s(literal -1/6 binary64)))) (cos.f64 (.f64 #s(literal 1/2 binary64) eps))) (sin.f64 (.f64 #s(literal 1/2 binary64) eps)))
(sin (* 1/2 (+ eps (* 2 x))))
(sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x))
(sin (* 1/2 (+ eps (* 2 x))))
(sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x))
(sin (* 1/2 (+ eps (* 2 x))))
(sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x))
(sin (* 1/2 (+ eps (* 2 x))))
(sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x))
(sin (* 1/2 (- eps (* -2 x))))
(sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x))
(sin (* 1/2 (- eps (* -2 x))))
(sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x))
(sin (* 1/2 (- eps (* -2 x))))
(sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x))
(sin (* 1/2 (- eps (* -2 x))))
(sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x))
(sin x)
(sin.f64 x)
(+ (sin x) (* 1/2 (* eps (cos x))))
(fma.f64 eps (*.f64 #s(literal 1/2 binary64) (cos.f64 x)) (sin.f64 x))
(+ (sin x) (* eps (+ (* -1/8 (* eps (sin x))) (* 1/2 (cos x)))))
(fma.f64 eps (fma.f64 eps (.f64 (sin.f64 x) #s(literal -1/8 binary64)) (.f64 #s(literal 1/2 binary64) (cos.f64 x))) (sin.f64 x))
(+ (sin x) (* eps (+ (* 1/2 (cos x)) (* eps (+ (* -1/8 (sin x)) (* -1/48 (* eps (cos x))))))))
(fma.f64 eps (fma.f64 eps (fma.f64 eps (.f64 (cos.f64 x) #s(literal -1/48 binary64)) (.f64 (sin.f64 x) #s(literal -1/8 binary64))) (*.f64 #s(literal 1/2 binary64) (cos.f64 x))) (sin.f64 x))
(sin (* 1/2 (+ eps (* 2 x))))
(sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x))
(sin (* 1/2 (+ eps (* 2 x))))
(sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x))
(sin (* 1/2 (+ eps (* 2 x))))
(sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x))
(sin (* 1/2 (+ eps (* 2 x))))
(sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x))
(sin (* 1/2 (- (* 2 x) (* -1 eps))))
(sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x))
(sin (* 1/2 (- (* 2 x) (* -1 eps))))
(sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x))
(sin (* 1/2 (- (* 2 x) (* -1 eps))))
(sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x))
(sin (* 1/2 (- (* 2 x) (* -1 eps))))
(sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x))
(* -1/2 x)
(*.f64 x #s(literal -1/2 binary64))
(* -1/2 x)
(*.f64 x #s(literal -1/2 binary64))
(* -1/2 x)
(*.f64 x #s(literal -1/2 binary64))
(* -1/2 x)
(*.f64 x #s(literal -1/2 binary64))
(* -1/2 x)
(*.f64 x #s(literal -1/2 binary64))
(* -1/2 x)
(*.f64 x #s(literal -1/2 binary64))
(* -1/2 x)
(*.f64 x #s(literal -1/2 binary64))
(* -1/2 x)
(*.f64 x #s(literal -1/2 binary64))
(* -1/2 x)
(*.f64 x #s(literal -1/2 binary64))
(* -1/2 x)
(*.f64 x #s(literal -1/2 binary64))
(* -1/2 x)
(*.f64 x #s(literal -1/2 binary64))
(* -1/2 x)
(*.f64 x #s(literal -1/2 binary64))
(* 1/24 eps)
(*.f64 eps #s(literal 1/24 binary64))
(* 1/24 eps)
(*.f64 eps #s(literal 1/24 binary64))
(* 1/24 eps)
(*.f64 eps #s(literal 1/24 binary64))
(* 1/24 eps)
(*.f64 eps #s(literal 1/24 binary64))
(* 1/24 eps)
(*.f64 eps #s(literal 1/24 binary64))
(* 1/24 eps)
(*.f64 eps #s(literal 1/24 binary64))
(* 1/24 eps)
(*.f64 eps #s(literal 1/24 binary64))
(* 1/24 eps)
(*.f64 eps #s(literal 1/24 binary64))
(* 1/24 eps)
(*.f64 eps #s(literal 1/24 binary64))
(* 1/24 eps)
(*.f64 eps #s(literal 1/24 binary64))
(* 1/24 eps)
(*.f64 eps #s(literal 1/24 binary64))
(* 1/24 eps)
(*.f64 eps #s(literal 1/24 binary64))
(* 1/6 x)
(*.f64 x #s(literal 1/6 binary64))
(* x (+ 1/6 (* -1/36 (pow x 2))))
(.f64 x (fma.f64 x (.f64 x #s(literal -1/36 binary64)) #s(literal 1/6 binary64)))
(* x (+ 1/6 (* (pow x 2) (- (* 1/720 (pow x 2)) 1/36))))
(.f64 x (fma.f64 (.f64 x x) (fma.f64 #s(literal 1/720 binary64) (*.f64 x x) #s(literal -1/36 binary64)) #s(literal 1/6 binary64)))
(* x (+ 1/6 (* (pow x 2) (- (* (pow x 2) (+ 1/720 (* -1/30240 (pow x 2)))) 1/36))))
(.f64 x (fma.f64 (.f64 x x) (fma.f64 x (.f64 x (fma.f64 (.f64 x x) #s(literal -1/30240 binary64) #s(literal 1/720 binary64))) #s(literal -1/36 binary64)) #s(literal 1/6 binary64)))
(* 1/6 (sin x))
(*.f64 (sin.f64 x) #s(literal 1/6 binary64))
(* 1/6 (sin x))
(*.f64 (sin.f64 x) #s(literal 1/6 binary64))
(* 1/6 (sin x))
(*.f64 (sin.f64 x) #s(literal 1/6 binary64))
(* 1/6 (sin x))
(*.f64 (sin.f64 x) #s(literal 1/6 binary64))
(* 1/6 (sin x))
(*.f64 (sin.f64 x) #s(literal 1/6 binary64))
(* 1/6 (sin x))
(*.f64 (sin.f64 x) #s(literal 1/6 binary64))
(* 1/6 (sin x))
(*.f64 (sin.f64 x) #s(literal 1/6 binary64))
(* 1/6 (sin x))
(*.f64 (sin.f64 x) #s(literal 1/6 binary64))
(* 1/24 (pow eps 2))
(.f64 eps (.f64 eps #s(literal 1/24 binary64)))
(* 1/24 (pow eps 2))
(.f64 eps (.f64 eps #s(literal 1/24 binary64)))
(* 1/24 (pow eps 2))
(.f64 eps (.f64 eps #s(literal 1/24 binary64)))
(* 1/24 (pow eps 2))
(.f64 eps (.f64 eps #s(literal 1/24 binary64)))
(* 1/24 (pow eps 2))
(.f64 eps (.f64 eps #s(literal 1/24 binary64)))
(* 1/24 (pow eps 2))
(.f64 eps (.f64 eps #s(literal 1/24 binary64)))
(* 1/24 (pow eps 2))
(.f64 eps (.f64 eps #s(literal 1/24 binary64)))
(* 1/24 (pow eps 2))
(.f64 eps (.f64 eps #s(literal 1/24 binary64)))
(* 1/24 (pow eps 2))
(.f64 eps (.f64 eps #s(literal 1/24 binary64)))
(* 1/24 (pow eps 2))
(.f64 eps (.f64 eps #s(literal 1/24 binary64)))
(* 1/24 (pow eps 2))
(.f64 eps (.f64 eps #s(literal 1/24 binary64)))
(* 1/24 (pow eps 2))
(.f64 eps (.f64 eps #s(literal 1/24 binary64)))
1
#s(literal 1 binary64)
(+ 1 (* x (sin eps)))
(fma.f64 x (sin.f64 eps) #s(literal 1 binary64))
(+ 1 (* x (+ (sin eps) (* -1/2 x))))
(fma.f64 x (fma.f64 x #s(literal -1/2 binary64) (sin.f64 eps)) #s(literal 1 binary64))
(+ 1 (* x (+ (sin eps) (* x (- (* -1/6 (* x (sin eps))) 1/2)))))
(fma.f64 x (fma.f64 x (fma.f64 #s(literal -1/6 binary64) (*.f64 x (sin.f64 eps)) #s(literal -1/2 binary64)) (sin.f64 eps)) #s(literal 1 binary64))
(+ (cos x) (* (sin eps) (sin x)))
(fma.f64 (sin.f64 x) (sin.f64 eps) (cos.f64 x))
(+ (cos x) (* (sin eps) (sin x)))
(fma.f64 (sin.f64 x) (sin.f64 eps) (cos.f64 x))
(+ (cos x) (* (sin eps) (sin x)))
(fma.f64 (sin.f64 x) (sin.f64 eps) (cos.f64 x))
(+ (cos x) (* (sin eps) (sin x)))
(fma.f64 (sin.f64 x) (sin.f64 eps) (cos.f64 x))
(+ (cos x) (* (sin eps) (sin x)))
(fma.f64 (sin.f64 x) (sin.f64 eps) (cos.f64 x))
(+ (cos x) (* (sin eps) (sin x)))
(fma.f64 (sin.f64 x) (sin.f64 eps) (cos.f64 x))
(+ (cos x) (* (sin eps) (sin x)))
(fma.f64 (sin.f64 x) (sin.f64 eps) (cos.f64 x))
(+ (cos x) (* (sin eps) (sin x)))
(fma.f64 (sin.f64 x) (sin.f64 eps) (cos.f64 x))
(cos x)
(cos.f64 x)
(+ (cos x) (* eps (sin x)))
(fma.f64 eps (sin.f64 x) (cos.f64 x))
(+ (cos x) (* eps (+ (sin x) (* -1/6 (* (pow eps 2) (sin x))))))
(fma.f64 eps (.f64 (fma.f64 #s(literal -1/6 binary64) (.f64 eps eps) #s(literal 1 binary64)) (sin.f64 x)) (cos.f64 x))
(+ (cos x) (* eps (+ (sin x) (* (pow eps 2) (+ (* -1/6 (sin x)) (* 1/120 (* (pow eps 2) (sin x))))))))
(fma.f64 eps (fma.f64 eps (.f64 eps (.f64 (sin.f64 x) (fma.f64 (*.f64 eps eps) #s(literal 1/120 binary64) #s(literal -1/6 binary64)))) (sin.f64 x)) (cos.f64 x))
(+ (cos x) (* (sin eps) (sin x)))
(fma.f64 (sin.f64 x) (sin.f64 eps) (cos.f64 x))
(+ (cos x) (* (sin eps) (sin x)))
(fma.f64 (sin.f64 x) (sin.f64 eps) (cos.f64 x))
(+ (cos x) (* (sin eps) (sin x)))
(fma.f64 (sin.f64 x) (sin.f64 eps) (cos.f64 x))
(+ (cos x) (* (sin eps) (sin x)))
(fma.f64 (sin.f64 x) (sin.f64 eps) (cos.f64 x))
(+ (cos x) (* (sin eps) (sin x)))
(fma.f64 (sin.f64 x) (sin.f64 eps) (cos.f64 x))
(+ (cos x) (* (sin eps) (sin x)))
(fma.f64 (sin.f64 x) (sin.f64 eps) (cos.f64 x))
(+ (cos x) (* (sin eps) (sin x)))
(fma.f64 (sin.f64 x) (sin.f64 eps) (cos.f64 x))
(+ (cos x) (* (sin eps) (sin x)))
(fma.f64 (sin.f64 x) (sin.f64 eps) (cos.f64 x))

rewrite316.0ms (1.7%)

Memory

-7.8MiB live, 556.6MiB allocated

Rules

5 790×	`lower-*.f32`
5 768×	`lower-*.f64`
3 936×	`lower-fma.f32`
3 928×	`lower-fma.f64`
3 116×	`lower-/.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	48	227
0	84	215
1	306	215
2	2726	215
0	8438	206

Stop Event

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

Counts

25 → 476

Calls

Call 1

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

Outputs
(+.f64 (.f64 #s(literal 1/2 binary64) x) (.f64 #s(literal 1/2 binary64) (+.f64 x eps)))
(+.f64 (.f64 #s(literal 1/2 binary64) (+.f64 x eps)) (.f64 #s(literal 1/2 binary64) x))
(+.f64 (.f64 #s(literal 1/2 binary64) (+.f64 x x)) (.f64 eps #s(literal 1/2 binary64)))
(+.f64 (.f64 x #s(literal 1/2 binary64)) (.f64 (+.f64 x eps) #s(literal 1/2 binary64)))
(+.f64 (.f64 (+.f64 x eps) #s(literal 1/2 binary64)) (.f64 x #s(literal 1/2 binary64)))
(+.f64 (.f64 (+.f64 x x) #s(literal 1/2 binary64)) (.f64 eps #s(literal 1/2 binary64)))
(fma.f64 x #s(literal 1/2 binary64) (*.f64 (+.f64 x eps) #s(literal 1/2 binary64)))
(fma.f64 (+.f64 x eps) #s(literal 1/2 binary64) (*.f64 x #s(literal 1/2 binary64)))
(fma.f64 #s(literal 1/2 binary64) x (*.f64 #s(literal 1/2 binary64) (+.f64 x eps)))
(fma.f64 #s(literal 1/2 binary64) (+.f64 x eps) (*.f64 #s(literal 1/2 binary64) x))
(fma.f64 #s(literal 1/2 binary64) (+.f64 x x) (*.f64 eps #s(literal 1/2 binary64)))
(fma.f64 (+.f64 x x) #s(literal 1/2 binary64) (*.f64 eps #s(literal 1/2 binary64)))
(/.f64 (+.f64 x (+.f64 x eps)) #s(literal 2 binary64))
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 2 binary64) (+.f64 x (+.f64 x eps))))
(/.f64 (fma.f64 (+.f64 x eps) (.f64 (+.f64 x eps) (+.f64 x eps)) (.f64 x (.f64 x x))) (.f64 #s(literal 2 binary64) (fma.f64 (+.f64 x eps) (+.f64 eps (-.f64 x x)) (*.f64 x x))))
(/.f64 (.f64 (+.f64 x (+.f64 x eps)) (-.f64 x (+.f64 x eps))) (.f64 #s(literal 2 binary64) (-.f64 x (+.f64 x eps))))
(/.f64 (neg.f64 (+.f64 x (+.f64 x eps))) #s(literal -2 binary64))
(/.f64 (.f64 #s(literal 1/2 binary64) (fma.f64 (+.f64 x eps) (.f64 (+.f64 x eps) (+.f64 x eps)) (.f64 x (.f64 x x)))) (fma.f64 (+.f64 x eps) (+.f64 eps (-.f64 x x)) (*.f64 x x)))
(/.f64 (.f64 #s(literal 1/2 binary64) (.f64 (+.f64 x (+.f64 x eps)) (-.f64 x (+.f64 x eps)))) (-.f64 x (+.f64 x eps)))
(/.f64 (.f64 (fma.f64 (+.f64 x eps) (.f64 (+.f64 x eps) (+.f64 x eps)) (.f64 x (.f64 x x))) #s(literal 1/2 binary64)) (fma.f64 (+.f64 x eps) (+.f64 eps (-.f64 x x)) (*.f64 x x)))
(/.f64 (.f64 (.f64 (+.f64 x (+.f64 x eps)) (-.f64 x (+.f64 x eps))) #s(literal 1/2 binary64)) (-.f64 x (+.f64 x eps)))
(pow.f64 (/.f64 #s(literal 2 binary64) (+.f64 x (+.f64 x eps))) #s(literal -1 binary64))
(*.f64 (+.f64 x (+.f64 x eps)) #s(literal 1/2 binary64))
(*.f64 #s(literal 1/2 binary64) (+.f64 x (+.f64 x eps)))
eps
(+.f64 eps #s(literal 0 binary64))
(+.f64 #s(literal 0 binary64) eps)
(-.f64 eps #s(literal 0 binary64))
(-.f64 eps (/.f64 #s(literal 0 binary64) eps))
(fma.f64 (.f64 eps (.f64 eps eps)) (/.f64 #s(literal 1 binary64) (*.f64 eps eps)) #s(literal 0 binary64))
(fma.f64 (*.f64 eps eps) (/.f64 #s(literal 1 binary64) eps) #s(literal 0 binary64))
(/.f64 #s(literal 1 binary64) (/.f64 eps (*.f64 eps eps)))
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) eps))
(/.f64 (.f64 eps (.f64 eps eps)) (*.f64 eps eps))
(/.f64 (*.f64 eps eps) eps)
(/.f64 (neg.f64 (.f64 eps (.f64 eps eps))) (neg.f64 (*.f64 eps eps)))
(/.f64 (-.f64 (.f64 eps (.f64 eps eps)) #s(literal 0 binary64)) (*.f64 eps eps))
(/.f64 (neg.f64 (*.f64 eps eps)) (neg.f64 eps))
(/.f64 (-.f64 #s(literal 0 binary64) (*.f64 eps eps)) (-.f64 #s(literal 0 binary64) eps))
(pow.f64 eps #s(literal 1 binary64))
(pow.f64 (/.f64 eps (*.f64 eps eps)) #s(literal -1 binary64))
(pow.f64 (/.f64 #s(literal 1 binary64) eps) #s(literal -1 binary64))
(.f64 (.f64 eps (.f64 eps eps)) (/.f64 #s(literal 1 binary64) (.f64 eps eps)))
(.f64 (.f64 eps eps) (/.f64 #s(literal 1 binary64) eps))
(/.f64 (.f64 #s(literal -2 binary64) (-.f64 (cos.f64 (.f64 #s(literal 1/2 binary64) (-.f64 eps (+.f64 x (+.f64 x eps))))) (cos.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 eps (+.f64 x (+.f64 x eps))))))) #s(literal 2 binary64))
(/.f64 (.f64 (-.f64 (cos.f64 (.f64 #s(literal 1/2 binary64) (-.f64 eps (+.f64 x (+.f64 x eps))))) (cos.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 eps (+.f64 x (+.f64 x eps)))))) #s(literal -2 binary64)) #s(literal 2 binary64))
(.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (.f64 (sin.f64 (.f64 (+.f64 x (+.f64 x eps)) #s(literal 1/2 binary64))) #s(literal -2 binary64)))
(.f64 (sin.f64 (.f64 (+.f64 x (+.f64 x 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))) (sin.f64 (.f64 (+.f64 x (+.f64 x eps)) #s(literal 1/2 binary64)))) #s(literal -2 binary64))
(.f64 #s(literal -2 binary64) (.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (sin.f64 (.f64 (+.f64 x (+.f64 x eps)) #s(literal 1/2 binary64)))))
(.f64 (.f64 (sin.f64 (.f64 (+.f64 x (+.f64 x eps)) #s(literal 1/2 binary64))) #s(literal -2 binary64)) (sin.f64 (.f64 eps #s(literal 1/2 binary64))))
(.f64 (.f64 #s(literal -2 binary64) (sin.f64 (.f64 eps #s(literal 1/2 binary64)))) (sin.f64 (.f64 (+.f64 x (+.f64 x eps)) #s(literal 1/2 binary64))))
(-.f64 (/.f64 (cos.f64 (.f64 #s(literal 1/2 binary64) (-.f64 eps (+.f64 x (+.f64 x eps))))) #s(literal 2 binary64)) (/.f64 (cos.f64 (.f64 #s(literal 1/2 binary64) (+.f64 eps (+.f64 x (+.f64 x eps))))) #s(literal 2 binary64)))
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 2 binary64) (-.f64 (cos.f64 (.f64 #s(literal 1/2 binary64) (-.f64 eps (+.f64 x (+.f64 x eps))))) (cos.f64 (.f64 #s(literal 1/2 binary64) (+.f64 eps (+.f64 x (+.f64 x eps))))))))
(/.f64 (-.f64 (cos.f64 (.f64 #s(literal 1/2 binary64) (-.f64 eps (+.f64 x (+.f64 x eps))))) (cos.f64 (.f64 #s(literal 1/2 binary64) (+.f64 eps (+.f64 x (+.f64 x eps)))))) #s(literal 2 binary64))
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eval127.0ms (0.7%)

Memory: 46.2MiB live, 345.1MiB allocated
Compiler: Compiled 25 882 to 2 410 computations (90.7% saved)

prune161.0ms (0.9%)

Memory

-3.7MiB live, 471.0MiB allocated

Pruning

20 alts after pruning (18 fresh and 2 done)

	Pruned	Kept	Total
New	1 006	14	1 020
Fresh	4	4	8
Picked	4	1	5
Done	0	1	1
Total	1 014	20	1 034

Accuracy

100.0%

Counts

1 034 → 20

Alt Table

Click to see full alt table

Status	Accuracy	Program
	56.6%	(fma.f64 (*.f64 (cos.f64 (-.f64 x eps)) (cos.f64 (+.f64 x eps))) (/.f64 #s(literal 1 binary64) (cos.f64 (-.f64 x eps))) (neg.f64 (cos.f64 x)))
	56.8%	(fma.f64 (cos.f64 x) (cos.f64 eps) (neg.f64 (fma.f64 (sin.f64 x) (sin.f64 eps) (cos.f64 x))))
	56.6%	(/.f64 (/.f64 (-.f64 (fma.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 (+.f64 x eps) #s(literal 2 binary64))) #s(literal 1/2 binary64)) (fma.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64))) #s(literal 2 binary64)) (.f64 (cos.f64 (.f64 (+.f64 x (+.f64 x eps)) #s(literal 1/2 binary64))) (cos.f64 (.f64 (+.f64 eps #s(literal 0 binary64)) #s(literal 1/2 binary64)))))
✓	56.8%	(-.f64 (*.f64 (cos.f64 x) (cos.f64 eps)) (fma.f64 (sin.f64 x) (sin.f64 eps) (cos.f64 x)))
	56.6%	(-.f64 (.f64 (cos.f64 x) #s(approx (cos eps) (fma.f64 (.f64 eps eps) (fma.f64 (.f64 eps eps) (fma.f64 (.f64 eps eps) #s(literal -1/720 binary64) #s(literal 1/24 binary64)) #s(literal -1/2 binary64)) #s(literal 1 binary64)))) (fma.f64 (sin.f64 x) (sin.f64 eps) (cos.f64 x)))
✓	56.6%	(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))
▶	54.8%	(-.f64 (cos.f64 (+.f64 x eps)) #s(approx (cos x) #s(literal 1 binary64)))
▶	99.8%	(.f64 (.f64 (sin.f64 (.f64 (+.f64 eps #s(literal 0 binary64)) #s(literal 1/2 binary64))) (fma.f64 (sin.f64 (.f64 (+.f64 x x) #s(literal 1/2 binary64))) (cos.f64 (.f64 eps #s(literal 1/2 binary64))) (.f64 (cos.f64 (.f64 (+.f64 x x) #s(literal 1/2 binary64))) (sin.f64 (.f64 eps #s(literal 1/2 binary64)))))) #s(literal -2 binary64))
	99.6%	(.f64 #s(approx ( (sin (* (+ eps 0) 1/2)) (sin (* (+ x (+ x eps)) 1/2))) (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x)))) #s(literal -2 binary64))
▶	99.3%	#s(approx (- (* (cos x) (cos eps)) (+ (* (sin x) (sin eps)) (cos x))) (.f64 eps (-.f64 (.f64 eps (fma.f64 eps (.f64 (sin.f64 x) #s(literal 1/6 binary64)) (.f64 (cos.f64 x) (fma.f64 eps (*.f64 eps #s(literal 1/24 binary64)) #s(literal -1/2 binary64))))) (sin.f64 x))))
	98.9%	#s(approx (- (* (cos x) (cos eps)) (+ (* (sin x) (sin eps)) (cos x))) (.f64 eps (-.f64 (.f64 eps (*.f64 #s(literal -1/2 binary64) (cos.f64 x))) (sin.f64 x))))
	81.7%	#s(approx (- (* (cos x) (cos eps)) (+ (* (sin x) (sin eps)) (cos x))) (neg.f64 (*.f64 eps (sin.f64 x))))
	54.8%	#s(approx (- (cos (+ x eps)) (cos x)) (+.f64 #s(approx (cos eps) (fma.f64 eps (*.f64 eps #s(literal -1/2 binary64)) #s(literal 1 binary64))) #s(literal -1 binary64)))
▶	54.6%	#s(approx (- (cos (+ x eps)) (cos x)) (+.f64 #s(approx (cos eps) #s(literal 1 binary64)) #s(literal -1 binary64)))
	97.8%	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps #s(approx (+ ( eps (+ (* (cos x) (+ -1/2 (* eps (* eps 1/24)))) (* eps (* 1/6 (sin x))))) (sin (neg x))) (fma.f64 x (fma.f64 x (fma.f64 eps (.f64 (fma.f64 eps (.f64 eps #s(literal 1/24 binary64)) #s(literal -1/2 binary64)) #s(literal -1/2 binary64)) (.f64 x (fma.f64 (.f64 eps eps) #s(literal -1/36 binary64) #s(literal 1/6 binary64)))) (fma.f64 eps (.f64 eps #s(literal 1/6 binary64)) #s(literal -1 binary64))) (.f64 eps (fma.f64 eps (*.f64 eps #s(literal 1/24 binary64)) #s(literal -1/2 binary64)))))))
	97.2%	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps #s(approx (+ ( eps (+ (* (cos x) (+ -1/2 (* eps (* eps 1/24)))) (* eps (* 1/6 (sin x))))) (sin (neg x))) (fma.f64 eps (fma.f64 eps (.f64 eps #s(literal 1/24 binary64)) #s(literal -1/2 binary64)) (.f64 x (fma.f64 eps (.f64 eps #s(literal 1/6 binary64)) (fma.f64 (.f64 x (fma.f64 eps (.f64 eps #s(literal 1/24 binary64)) #s(literal -1/2 binary64))) (.f64 eps #s(literal -1/2 binary64)) #s(literal -1 binary64))))))))
	97.2%	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps #s(approx (+ ( eps (+ (* (cos x) (+ -1/2 (* eps (* eps 1/24)))) (* eps (* 1/6 (sin x))))) (sin (neg x))) (fma.f64 eps (fma.f64 eps (.f64 eps #s(literal 1/24 binary64)) #s(literal -1/2 binary64)) (.f64 x (fma.f64 eps (*.f64 eps #s(literal 1/6 binary64)) #s(literal -1 binary64)))))))
	55.9%	#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (+ (cos eps) -1) (.f64 eps (.f64 eps #s(literal -1/2 binary64)))))
	98.0%	#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* eps (+ (* eps (+ (* (cos x) (+ -1/2 (* eps (* eps 1/24)))) (* eps (* 1/6 (sin x))))) (sin (neg x)))) (fma.f64 x (fma.f64 x (fma.f64 eps (.f64 x (fma.f64 (.f64 eps eps) #s(literal -1/36 binary64) #s(literal 1/6 binary64))) (.f64 #s(literal -1/2 binary64) (.f64 eps (.f64 eps (fma.f64 eps (.f64 eps #s(literal 1/24 binary64)) #s(literal -1/2 binary64)))))) (.f64 eps (fma.f64 eps (.f64 eps #s(literal 1/6 binary64)) #s(literal -1 binary64)))) (.f64 eps (.f64 eps (fma.f64 eps (*.f64 eps #s(literal 1/24 binary64)) #s(literal -1/2 binary64)))))))
▶	97.2%	#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* eps (+ (* eps (+ (* (cos x) (+ -1/2 (* eps (* eps 1/24)))) (* eps (* 1/6 (sin x))))) (sin (neg x)))) (fma.f64 eps (.f64 eps (fma.f64 eps (.f64 eps #s(literal 1/24 binary64)) #s(literal -1/2 binary64))) (.f64 eps (.f64 x (fma.f64 eps (*.f64 eps #s(literal 1/6 binary64)) #s(literal -1 binary64)))))))

Compiler

Compiled 834 to 465 computations (44.2% saved)

simplify228.0ms (1.2%)

Memory

13.1MiB live, 502.7MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 19 expressions of interest:

New	Metric	Score
cost-diff	0	(.f64 eps (fma.f64 eps (.f64 (sin.f64 x) #s(literal 1/6 binary64)) (.f64 (cos.f64 x) (fma.f64 eps (.f64 eps #s(literal 1/24 binary64)) #s(literal -1/2 binary64)))))
cost-diff	0	(.f64 eps (-.f64 (.f64 eps (fma.f64 eps (.f64 (sin.f64 x) #s(literal 1/6 binary64)) (.f64 (cos.f64 x) (fma.f64 eps (*.f64 eps #s(literal 1/24 binary64)) #s(literal -1/2 binary64))))) (sin.f64 x)))
cost-diff	0	#s(approx (- (* (cos x) (cos eps)) (+ (* (sin x) (sin eps)) (cos x))) (.f64 eps (-.f64 (.f64 eps (fma.f64 eps (.f64 (sin.f64 x) #s(literal 1/6 binary64)) (.f64 (cos.f64 x) (fma.f64 eps (*.f64 eps #s(literal 1/24 binary64)) #s(literal -1/2 binary64))))) (sin.f64 x))))
cost-diff	6208	(-.f64 (.f64 eps (fma.f64 eps (.f64 (sin.f64 x) #s(literal 1/6 binary64)) (.f64 (cos.f64 x) (fma.f64 eps (.f64 eps #s(literal 1/24 binary64)) #s(literal -1/2 binary64))))) (sin.f64 x))
cost-diff	0	#s(approx (cos x) #s(literal 1 binary64))
cost-diff	0	(+.f64 x eps)
cost-diff	0	(cos.f64 (+.f64 x eps))
cost-diff	0	(-.f64 (cos.f64 (+.f64 x eps)) #s(approx (cos x) #s(literal 1 binary64)))
cost-diff	0	(.f64 eps (fma.f64 eps (.f64 eps #s(literal 1/24 binary64)) #s(literal -1/2 binary64)))
cost-diff	0	#s(approx (* eps (+ (* eps (+ (* (cos x) (+ -1/2 (* eps (* eps 1/24)))) (* eps (* 1/6 (sin x))))) (sin (neg x)))) (fma.f64 eps (.f64 eps (fma.f64 eps (.f64 eps #s(literal 1/24 binary64)) #s(literal -1/2 binary64))) (.f64 eps (.f64 x (fma.f64 eps (*.f64 eps #s(literal 1/6 binary64)) #s(literal -1 binary64))))))
cost-diff	0	#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* eps (+ (* eps (+ (* (cos x) (+ -1/2 (* eps (* eps 1/24)))) (* eps (* 1/6 (sin x))))) (sin (neg x)))) (fma.f64 eps (.f64 eps (fma.f64 eps (.f64 eps #s(literal 1/24 binary64)) #s(literal -1/2 binary64))) (.f64 eps (.f64 x (fma.f64 eps (*.f64 eps #s(literal 1/6 binary64)) #s(literal -1 binary64)))))))
cost-diff	832	(fma.f64 eps (.f64 eps (fma.f64 eps (.f64 eps #s(literal 1/24 binary64)) #s(literal -1/2 binary64))) (.f64 eps (.f64 x (fma.f64 eps (*.f64 eps #s(literal 1/6 binary64)) #s(literal -1 binary64)))))
cost-diff	0	#s(approx (cos eps) #s(literal 1 binary64))
cost-diff	0	(+.f64 #s(approx (cos eps) #s(literal 1 binary64)) #s(literal -1 binary64))
cost-diff	0	#s(approx (- (cos (+ x eps)) (cos x)) (+.f64 #s(approx (cos eps) #s(literal 1 binary64)) #s(literal -1 binary64)))
cost-diff	0	(.f64 (sin.f64 (.f64 (+.f64 eps #s(literal 0 binary64)) #s(literal 1/2 binary64))) (fma.f64 (sin.f64 (.f64 (+.f64 x x) #s(literal 1/2 binary64))) (cos.f64 (.f64 eps #s(literal 1/2 binary64))) (.f64 (cos.f64 (.f64 (+.f64 x x) #s(literal 1/2 binary64))) (sin.f64 (*.f64 eps #s(literal 1/2 binary64))))))
cost-diff	0	(.f64 (.f64 (sin.f64 (.f64 (+.f64 eps #s(literal 0 binary64)) #s(literal 1/2 binary64))) (fma.f64 (sin.f64 (.f64 (+.f64 x x) #s(literal 1/2 binary64))) (cos.f64 (.f64 eps #s(literal 1/2 binary64))) (.f64 (cos.f64 (.f64 (+.f64 x x) #s(literal 1/2 binary64))) (sin.f64 (.f64 eps #s(literal 1/2 binary64)))))) #s(literal -2 binary64))
cost-diff	192	(+.f64 eps #s(literal 0 binary64))
cost-diff	512	(*.f64 (+.f64 x x) #s(literal 1/2 binary64))

Rules

14 556×	`lower-fma.f32`
14 546×	`lower-fma.f64`
3 868×	`lower-*.f32`
3 840×	`lower-*.f64`
2 486×	`lower-+.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	73	504
0	114	509
1	229	477
2	632	442
3	1785	441
4	3104	437
5	4995	437
6	7007	437
0	8100	431

Stop Event

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

Calls

Call 1

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

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

localize862.0ms (4.6%)

Memory

-47.7MiB live, 853.5MiB allocated

Localize:

Found 19 expressions of interest:

New	Metric	Score
accuracy	0.1015625	(.f64 eps (-.f64 (.f64 eps (fma.f64 eps (.f64 (sin.f64 x) #s(literal 1/6 binary64)) (.f64 (cos.f64 x) (fma.f64 eps (*.f64 eps #s(literal 1/24 binary64)) #s(literal -1/2 binary64))))) (sin.f64 x)))
accuracy	0.296875	(*.f64 (sin.f64 x) #s(literal 1/6 binary64))
accuracy	0.33203125	(*.f64 eps #s(literal 1/24 binary64))
accuracy	0.34131181601776905	#s(approx (- (* (cos x) (cos eps)) (+ (* (sin x) (sin eps)) (cos x))) (.f64 eps (-.f64 (.f64 eps (fma.f64 eps (.f64 (sin.f64 x) #s(literal 1/6 binary64)) (.f64 (cos.f64 x) (fma.f64 eps (*.f64 eps #s(literal 1/24 binary64)) #s(literal -1/2 binary64))))) (sin.f64 x))))
accuracy	0	(+.f64 x eps)
accuracy	0.12674859825865142	(cos.f64 (+.f64 x eps))
accuracy	1.6130182858237163	#s(approx (cos x) #s(literal 1 binary64))
accuracy	27.61780088482764	(-.f64 (cos.f64 (+.f64 x eps)) #s(approx (cos x) #s(literal 1 binary64)))
accuracy	0.33203125	(*.f64 eps #s(literal 1/6 binary64))
accuracy	0.33203125	(*.f64 eps #s(literal 1/24 binary64))
accuracy	0.34131181601776905	#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* eps (+ (* eps (+ (* (cos x) (+ -1/2 (* eps (* eps 1/24)))) (* eps (* 1/6 (sin x))))) (sin (neg x)))) (fma.f64 eps (.f64 eps (fma.f64 eps (.f64 eps #s(literal 1/24 binary64)) #s(literal -1/2 binary64))) (.f64 eps (.f64 x (fma.f64 eps (*.f64 eps #s(literal 1/6 binary64)) #s(literal -1 binary64)))))))
accuracy	1.7215412375959054	#s(approx (* eps (+ (* eps (+ (* (cos x) (+ -1/2 (* eps (* eps 1/24)))) (* eps (* 1/6 (sin x))))) (sin (neg x)))) (fma.f64 eps (.f64 eps (fma.f64 eps (.f64 eps #s(literal 1/24 binary64)) #s(literal -1/2 binary64))) (.f64 eps (.f64 x (fma.f64 eps (*.f64 eps #s(literal 1/6 binary64)) #s(literal -1 binary64))))))
accuracy	0.6575319965009595	#s(approx (cos eps) #s(literal 1 binary64))
accuracy	26.953051245831887	(+.f64 #s(approx (cos eps) #s(literal 1 binary64)) #s(literal -1 binary64))
accuracy	28.23878058521645	#s(approx (- (cos (+ x eps)) (cos x)) (+.f64 #s(approx (cos eps) #s(literal 1 binary64)) #s(literal -1 binary64)))
accuracy	0.01171875	(fma.f64 (sin.f64 (.f64 (+.f64 x x) #s(literal 1/2 binary64))) (cos.f64 (.f64 eps #s(literal 1/2 binary64))) (.f64 (cos.f64 (.f64 (+.f64 x x) #s(literal 1/2 binary64))) (sin.f64 (*.f64 eps #s(literal 1/2 binary64)))))
accuracy	0.015625	(.f64 (cos.f64 (.f64 (+.f64 x x) #s(literal 1/2 binary64))) (sin.f64 (*.f64 eps #s(literal 1/2 binary64))))
accuracy	0.03125	(.f64 (.f64 (sin.f64 (.f64 (+.f64 eps #s(literal 0 binary64)) #s(literal 1/2 binary64))) (fma.f64 (sin.f64 (.f64 (+.f64 x x) #s(literal 1/2 binary64))) (cos.f64 (.f64 eps #s(literal 1/2 binary64))) (.f64 (cos.f64 (.f64 (+.f64 x x) #s(literal 1/2 binary64))) (sin.f64 (.f64 eps #s(literal 1/2 binary64)))))) #s(literal -2 binary64))
accuracy	0.11328125	(.f64 (sin.f64 (.f64 (+.f64 eps #s(literal 0 binary64)) #s(literal 1/2 binary64))) (fma.f64 (sin.f64 (.f64 (+.f64 x x) #s(literal 1/2 binary64))) (cos.f64 (.f64 eps #s(literal 1/2 binary64))) (.f64 (cos.f64 (.f64 (+.f64 x x) #s(literal 1/2 binary64))) (sin.f64 (*.f64 eps #s(literal 1/2 binary64))))))

Samples

483.0ms	184×	2	valid
90.0ms	68×	1	valid
2.0ms	4×	0	valid

Compiler

Compiled 421 to 67 computations (84.1% saved)

Precisions

Click to see histograms. Total time spent on operations: 485.0ms

ival-mult: 124.0ms (25.5% of total)

adjust: 105.0ms (21.6% of total)

ival-cos: 86.0ms (17.7% of total)

ival-sin: 63.0ms (13% of total)

ival-add: 61.0ms (12.6% of total)

ival-sub: 38.0ms (7.8% of total)

const: 6.0ms (1.2% of total)

exact: 1.0ms (0.2% of total)

ival-neg: 1.0ms (0.2% of total)

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

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

series69.0ms (0.4%)

Memory

14.3MiB live, 55.4MiB allocated

Counts

24 → 468

Calls

Call 1

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

Outputs
#s(alt x (taylor 0 x) (#s(alt (.f64 (+.f64 x x) #s(literal 1/2 binary64)) (patch (.f64 (+.f64 x x) #s(literal 1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt x (taylor 0 x) (#s(alt (.f64 (+.f64 x x) #s(literal 1/2 binary64)) (patch (.f64 (+.f64 x x) #s(literal 1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt x (taylor 0 x) (#s(alt (.f64 (+.f64 x x) #s(literal 1/2 binary64)) (patch (.f64 (+.f64 x x) #s(literal 1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt x (taylor 0 x) (#s(alt (.f64 (+.f64 x x) #s(literal 1/2 binary64)) (patch (.f64 (+.f64 x x) #s(literal 1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt x (taylor inf x) (#s(alt (.f64 (+.f64 x x) #s(literal 1/2 binary64)) (patch (.f64 (+.f64 x x) #s(literal 1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt x (taylor inf x) (#s(alt (.f64 (+.f64 x x) #s(literal 1/2 binary64)) (patch (.f64 (+.f64 x x) #s(literal 1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt x (taylor inf x) (#s(alt (.f64 (+.f64 x x) #s(literal 1/2 binary64)) (patch (.f64 (+.f64 x x) #s(literal 1/2 binary64)) #<representation binary64>) () ())) ())
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#s(alt (* 1/6 eps) (taylor -inf eps) (#s(alt (.f64 eps #s(literal 1/6 binary64)) (patch (.f64 eps #s(literal 1/6 binary64)) #<representation binary64>) () ())) ())
#s(alt (* 1/6 x) (taylor 0 x) (#s(alt (.f64 (sin.f64 x) #s(literal 1/6 binary64)) (patch (.f64 (sin.f64 x) #s(literal 1/6 binary64)) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1/6 (* -1/36 (pow x 2)))) (taylor 0 x) (#s(alt (.f64 (sin.f64 x) #s(literal 1/6 binary64)) (patch (.f64 (sin.f64 x) #s(literal 1/6 binary64)) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1/6 (* (pow x 2) (- (* 1/720 (pow x 2)) 1/36)))) (taylor 0 x) (#s(alt (.f64 (sin.f64 x) #s(literal 1/6 binary64)) (patch (.f64 (sin.f64 x) #s(literal 1/6 binary64)) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1/6 (* (pow x 2) (- (* (pow x 2) (+ 1/720 (* -1/30240 (pow x 2)))) 1/36)))) (taylor 0 x) (#s(alt (.f64 (sin.f64 x) #s(literal 1/6 binary64)) (patch (.f64 (sin.f64 x) #s(literal 1/6 binary64)) #<representation binary64>) () ())) ())
#s(alt (* 1/6 (sin x)) (taylor inf x) (#s(alt (.f64 (sin.f64 x) #s(literal 1/6 binary64)) (patch (.f64 (sin.f64 x) #s(literal 1/6 binary64)) #<representation binary64>) () ())) ())
#s(alt (* 1/6 (sin x)) (taylor inf x) (#s(alt (.f64 (sin.f64 x) #s(literal 1/6 binary64)) (patch (.f64 (sin.f64 x) #s(literal 1/6 binary64)) #<representation binary64>) () ())) ())
#s(alt (* 1/6 (sin x)) (taylor inf x) (#s(alt (.f64 (sin.f64 x) #s(literal 1/6 binary64)) (patch (.f64 (sin.f64 x) #s(literal 1/6 binary64)) #<representation binary64>) () ())) ())
#s(alt (* 1/6 (sin x)) (taylor inf x) (#s(alt (.f64 (sin.f64 x) #s(literal 1/6 binary64)) (patch (.f64 (sin.f64 x) #s(literal 1/6 binary64)) #<representation binary64>) () ())) ())
#s(alt (* 1/6 (sin x)) (taylor -inf x) (#s(alt (.f64 (sin.f64 x) #s(literal 1/6 binary64)) (patch (.f64 (sin.f64 x) #s(literal 1/6 binary64)) #<representation binary64>) () ())) ())
#s(alt (* 1/6 (sin x)) (taylor -inf x) (#s(alt (.f64 (sin.f64 x) #s(literal 1/6 binary64)) (patch (.f64 (sin.f64 x) #s(literal 1/6 binary64)) #<representation binary64>) () ())) ())
#s(alt (* 1/6 (sin x)) (taylor -inf x) (#s(alt (.f64 (sin.f64 x) #s(literal 1/6 binary64)) (patch (.f64 (sin.f64 x) #s(literal 1/6 binary64)) #<representation binary64>) () ())) ())
#s(alt (* 1/6 (sin x)) (taylor -inf x) (#s(alt (.f64 (sin.f64 x) #s(literal 1/6 binary64)) (patch (.f64 (sin.f64 x) #s(literal 1/6 binary64)) #<representation binary64>) () ())) ())

Calls

117 calls:

Time	Variable		Point	Expression
29.0ms	eps	@	0	(* eps (+ (* eps (* (sin x) 1/6)) (* (cos x) (+ (* eps (* eps 1/24)) -1/2))))
5.0ms	eps	@	0	(* eps (+ (* eps (* eps 1/24)) -1/2))
2.0ms	x	@	-inf	(* (* (sin (* (+ eps 0) 1/2)) (+ (* (sin (* (+ x x) 1/2)) (cos (* eps 1/2))) (* (cos (* (+ x x) 1/2)) (sin (* eps 1/2))))) -2)
2.0ms	x	@	inf	(* (* (sin (* (+ eps 0) 1/2)) (+ (* (sin (* (+ x x) 1/2)) (cos (* eps 1/2))) (* (cos (* (+ x x) 1/2)) (sin (* eps 1/2))))) -2)
1.0ms	eps	@	inf	(* (* (sin (* (+ eps 0) 1/2)) (+ (* (sin (* (+ x x) 1/2)) (cos (* eps 1/2))) (* (cos (* (+ x x) 1/2)) (sin (* eps 1/2))))) -2)

simplify393.0ms (2.1%)

Memory

-5.5MiB live, 344.5MiB allocated

Algorithm

1×	egg-herbie

Rules

11 132×	`lower-fma.f64`
11 132×	`lower-fma.f32`
7 196×	`lower-*.f64`
7 196×	`lower-*.f32`
3 052×	`lower-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	507	5916
1	1567	5723
2	4515	5716
0	8304	5319

Stop Event

1×	iter limit
1×	node limit

Counts

468 → 438

Calls

Call 1

Inputs
x
x
x
x
x
x
x
x
x
x
x
x
eps
eps
eps
eps
eps
eps
eps
eps
eps
eps
eps
eps
(* -1 (* eps (sin x)))
(* eps (+ (* -1 (sin x)) (* -1/2 (* eps (cos x)))))
(* eps (+ (* -1 (sin x)) (* eps (+ (* -2 (* eps (+ (* -1/16 (sin x)) (* -1/48 (sin x))))) (* -1/2 (cos x))))))
(* eps (+ (* -1 (sin x)) (* eps (+ (* -1/2 (cos x)) (* eps (+ (* -2 (+ (* -1/16 (sin x)) (* -1/48 (sin x)))) (* 1/24 (* eps (cos x)))))))))
(* -2 (* (sin (* 1/2 eps)) (+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x)))))
(* -2 (* (sin (* 1/2 eps)) (+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x)))))
(* -2 (* (sin (* 1/2 eps)) (+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x)))))
(* -2 (* (sin (* 1/2 eps)) (+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x)))))
(* -2 (* (sin (* 1/2 eps)) (+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x)))))
(* -2 (* (sin (* 1/2 eps)) (+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x)))))
(* -2 (* (sin (* 1/2 eps)) (+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x)))))
(* -2 (* (sin (* 1/2 eps)) (+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x)))))
(* -2 (pow (sin (* 1/2 eps)) 2))
(+ (* -2 (* x (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))) (* -2 (pow (sin (* 1/2 eps)) 2)))
(+ (* -2 (pow (sin (* 1/2 eps)) 2)) (* x (+ (* -2 (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) (* x (pow (sin (* 1/2 eps)) 2)))))
(+ (* -2 (pow (sin (* 1/2 eps)) 2)) (* x (+ (* -2 (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) (* x (+ (* 1/3 (* x (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))) (pow (sin (* 1/2 eps)) 2))))))
(* -2 (* (sin (* 1/2 eps)) (+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x)))))
(* -2 (* (sin (* 1/2 eps)) (+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x)))))
(* -2 (* (sin (* 1/2 eps)) (+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x)))))
(* -2 (* (sin (* 1/2 eps)) (+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x)))))
(* -2 (* (sin (* 1/2 eps)) (+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x)))))
(* -2 (* (sin (* 1/2 eps)) (+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x)))))
(* -2 (* (sin (* 1/2 eps)) (+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x)))))
(* -2 (* (sin (* 1/2 eps)) (+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x)))))
(* 1/2 (* eps (sin x)))
(* eps (+ (* 1/4 (* eps (cos x))) (* 1/2 (sin x))))
(* eps (+ (* 1/2 (sin x)) (* eps (+ (* 1/4 (cos x)) (* eps (+ (* -1/16 (sin x)) (* -1/48 (sin x))))))))
(* eps (+ (* 1/2 (sin x)) (* eps (+ (* 1/4 (cos x)) (* eps (+ (* -1/16 (sin x)) (+ (* -1/48 (sin x)) (* -1/48 (* eps (cos x))))))))))
(* (sin (* 1/2 eps)) (+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x))))
(* (sin (* 1/2 eps)) (+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x))))
(* (sin (* 1/2 eps)) (+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x))))
(* (sin (* 1/2 eps)) (+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x))))
(* (sin (* 1/2 eps)) (+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x))))
(* (sin (* 1/2 eps)) (+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x))))
(* (sin (* 1/2 eps)) (+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x))))
(* (sin (* 1/2 eps)) (+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x))))
(pow (sin (* 1/2 eps)) 2)
(+ (* x (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) (pow (sin (* 1/2 eps)) 2))
(+ (* x (+ (* -1/2 (* x (pow (sin (* 1/2 eps)) 2))) (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))) (pow (sin (* 1/2 eps)) 2))
(+ (* x (+ (* x (+ (* -1/2 (pow (sin (* 1/2 eps)) 2)) (* -1/6 (* x (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))))) (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))) (pow (sin (* 1/2 eps)) 2))
(* (sin (* 1/2 eps)) (+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x))))
(* (sin (* 1/2 eps)) (+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x))))
(* (sin (* 1/2 eps)) (+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x))))
(* (sin (* 1/2 eps)) (+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x))))
(* (sin (* 1/2 eps)) (+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x))))
(* (sin (* 1/2 eps)) (+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x))))
(* (sin (* 1/2 eps)) (+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x))))
(* (sin (* 1/2 eps)) (+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x))))
(- (cos eps) 1)
(- (+ (cos eps) (* -1 (* x (sin eps)))) 1)
(- (+ (cos eps) (* x (- (* x (+ 1/2 (* -1/2 (cos eps)))) (sin eps)))) 1)
(- (+ (cos eps) (* x (- (* x (+ 1/2 (+ (* -1/2 (cos eps)) (* 1/6 (* x (sin eps)))))) (sin eps)))) 1)
(- (cos (+ eps x)) (cos x))
(- (cos (+ eps x)) (cos x))
(- (cos (+ eps x)) (cos x))
(- (cos (+ eps x)) (cos x))
(- (cos (- eps (* -1 x))) (cos x))
(- (cos (- eps (* -1 x))) (cos x))
(- (cos (- eps (* -1 x))) (cos x))
(- (cos (- eps (* -1 x))) (cos x))
(* -1 (* eps (sin x)))
(* eps (- (* -1/2 (* eps (cos x))) (sin x)))
(* eps (- (* eps (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x))))) (sin x)))
(* eps (- (* eps (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x)))))) (sin x)))
(- (cos (+ eps x)) (cos x))
(- (cos (+ eps x)) (cos x))
(- (cos (+ eps x)) (cos x))
(- (cos (+ eps x)) (cos x))
(- (cos (- x (* -1 eps))) (cos x))
(- (cos (- x (* -1 eps))) (cos x))
(- (cos (- x (* -1 eps))) (cos x))
(- (cos (- x (* -1 eps))) (cos x))
(* -1/2 (pow eps 2))
(* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2))
(* (pow eps 2) (- (* (pow eps 2) (+ 1/24 (* -1/720 (pow eps 2)))) 1/2))
(* (pow eps 2) (- (* (pow eps 2) (+ 1/24 (* (pow eps 2) (- (* 1/40320 (pow eps 2)) 1/720)))) 1/2))
(- (cos eps) 1)
(- (cos eps) 1)
(- (cos eps) 1)
(- (cos eps) 1)
(- (cos eps) 1)
(- (cos eps) 1)
(- (cos eps) 1)
(- (cos eps) 1)
1
(+ 1 (* -1/2 (pow eps 2)))
(+ 1 (* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2)))
(+ 1 (* (pow eps 2) (- (* (pow eps 2) (+ 1/24 (* -1/720 (pow eps 2)))) 1/2)))
(cos eps)
(cos eps)
(cos eps)
(cos eps)
(cos eps)
(cos eps)
(cos eps)
(cos eps)
(* -1 (* eps x))
(* eps (+ (* -1 x) (* -1/2 eps)))
(* eps (+ (* -1 x) (* eps (- (* 1/6 (* eps x)) 1/2))))
(* eps (+ (* -1 x) (* eps (- (* eps (+ (* 1/24 eps) (* 1/6 x))) 1/2))))
(* 1/24 (pow eps 4))
(* (pow eps 4) (+ 1/24 (* 1/6 (/ x eps))))
(* (pow eps 4) (- (+ 1/24 (* 1/6 (/ x eps))) (/ 1/2 (pow eps 2))))
(* (pow eps 4) (- (+ 1/24 (+ (* -1 (/ x (pow eps 3))) (* 1/6 (/ x eps)))) (/ 1/2 (pow eps 2))))
(* 1/24 (pow eps 4))
(* (pow eps 4) (+ 1/24 (* 1/6 (/ x eps))))
(* (pow eps 4) (+ 1/24 (* -1 (/ (+ (* -1/6 x) (* 1/2 (/ 1 eps))) eps))))
(* (pow eps 4) (+ 1/24 (* -1 (/ (+ (* -1 (/ (- (* -1 (/ x eps)) 1/2) eps)) (* -1/6 x)) eps))))
(* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2))
(+ (* eps (* x (- (* 1/6 (pow eps 2)) 1))) (* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2)))
(+ (* eps (* x (- (* 1/6 (pow eps 2)) 1))) (* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2)))
(+ (* eps (* x (- (* 1/6 (pow eps 2)) 1))) (* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2)))
(* eps (* x (- (* 1/6 (pow eps 2)) 1)))
(* x (+ (* eps (- (* 1/6 (pow eps 2)) 1)) (/ (* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2)) x)))
(* x (+ (* eps (- (* 1/6 (pow eps 2)) 1)) (/ (* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2)) x)))
(* x (+ (* eps (- (* 1/6 (pow eps 2)) 1)) (/ (* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2)) x)))
(* eps (* x (- (* 1/6 (pow eps 2)) 1)))
(* -1 (* x (+ (* -1 (* eps (- (* 1/6 (pow eps 2)) 1))) (* -1 (/ (* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2)) x)))))
(* -1 (* x (+ (* -1 (* eps (- (* 1/6 (pow eps 2)) 1))) (* -1 (/ (* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2)) x)))))
(* -1 (* x (+ (* -1 (* eps (- (* 1/6 (pow eps 2)) 1))) (* -1 (/ (* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2)) x)))))
(- (cos eps) 1)
(- (+ (cos eps) (* -1 (* x (sin eps)))) 1)
(- (+ (cos eps) (* x (- (* x (+ 1/2 (* -1/2 (cos eps)))) (sin eps)))) 1)
(- (+ (cos eps) (* x (- (* x (+ 1/2 (+ (* -1/2 (cos eps)) (* 1/6 (* x (sin eps)))))) (sin eps)))) 1)
(- (cos (+ eps x)) (cos x))
(- (cos (+ eps x)) (cos x))
(- (cos (+ eps x)) (cos x))
(- (cos (+ eps x)) (cos x))
(- (cos (- eps (* -1 x))) (cos x))
(- (cos (- eps (* -1 x))) (cos x))
(- (cos (- eps (* -1 x))) (cos x))
(- (cos (- eps (* -1 x))) (cos x))
(* -1 (* eps (sin x)))
(* eps (- (* -1/2 (* eps (cos x))) (sin x)))
(* eps (- (* eps (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x))))) (sin x)))
(* eps (- (* eps (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x)))))) (sin x)))
(- (cos (+ eps x)) (cos x))
(- (cos (+ eps x)) (cos x))
(- (cos (+ eps x)) (cos x))
(- (cos (+ eps x)) (cos x))
(- (cos (- x (* -1 eps))) (cos x))
(- (cos (- x (* -1 eps))) (cos x))
(- (cos (- x (* -1 eps))) (cos x))
(- (cos (- x (* -1 eps))) (cos x))
(* eps (sin (neg x)))
(* eps (+ (sin (neg x)) (* -1/2 (* eps (cos x)))))
(* eps (+ (sin (neg x)) (* eps (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x)))))))
(* eps (+ (sin (neg x)) (* eps (+ (* -1/2 (cos x)) (* eps (+ (* 1/24 (* eps (cos x))) (* 1/6 (sin x))))))))
(* 1/24 (* (pow eps 4) (cos x)))
(* (pow eps 4) (+ (* 1/24 (cos x)) (* 1/6 (/ (sin x) eps))))
(* (pow eps 4) (+ (* -1/2 (/ (cos x) (pow eps 2))) (+ (* 1/24 (cos x)) (* 1/6 (/ (sin x) eps)))))
(* (pow eps 4) (+ (* -1/2 (/ (cos x) (pow eps 2))) (+ (* 1/24 (cos x)) (+ (* 1/6 (/ (sin x) eps)) (/ (sin (neg x)) (pow eps 3))))))
(* 1/24 (* (pow eps 4) (cos x)))
(* (pow eps 4) (+ (* 1/24 (cos x)) (* 1/6 (/ (sin x) eps))))
(* (pow eps 4) (+ (* -1 (/ (+ (* -1/6 (sin x)) (* 1/2 (/ (cos x) eps))) eps)) (* 1/24 (cos x))))
(* (pow eps 4) (+ (* -1 (/ (+ (* -1 (/ (+ (* -1/2 (cos x)) (/ (sin (neg x)) eps)) eps)) (* -1/6 (sin x))) eps)) (* 1/24 (cos x))))
(* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2))
(+ (* eps (* x (- (* 1/6 (pow eps 2)) 1))) (* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2)))
(+ (* x (+ (* -1/2 (* (pow eps 2) (* x (- (* 1/24 (pow eps 2)) 1/2)))) (* eps (- (* 1/6 (pow eps 2)) 1)))) (* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2)))
(+ (* x (+ (* eps (- (* 1/6 (pow eps 2)) 1)) (* x (+ (* -1/2 (* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2))) (* eps (* x (+ 1/6 (* -1/36 (pow eps 2))))))))) (* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2)))
(* eps (+ (sin (neg x)) (* eps (+ (* 1/6 (* eps (sin x))) (* (cos x) (- (* 1/24 (pow eps 2)) 1/2))))))
(* eps (+ (sin (neg x)) (* eps (+ (* 1/6 (* eps (sin x))) (* (cos x) (- (* 1/24 (pow eps 2)) 1/2))))))
(* eps (+ (sin (neg x)) (* eps (+ (* 1/6 (* eps (sin x))) (* (cos x) (- (* 1/24 (pow eps 2)) 1/2))))))
(* eps (+ (sin (neg x)) (* eps (+ (* 1/6 (* eps (sin x))) (* (cos x) (- (* 1/24 (pow eps 2)) 1/2))))))
(* eps (+ (sin (* -1 x)) (* eps (+ (* 1/6 (* eps (sin x))) (* (cos x) (- (* 1/24 (pow eps 2)) 1/2))))))
(* eps (+ (sin (* -1 x)) (* eps (+ (* 1/6 (* eps (sin x))) (* (cos x) (- (* 1/24 (pow eps 2)) 1/2))))))
(* eps (+ (sin (* -1 x)) (* eps (+ (* 1/6 (* eps (sin x))) (* (cos x) (- (* 1/24 (pow eps 2)) 1/2))))))
(* eps (+ (sin (* -1 x)) (* eps (+ (* 1/6 (* eps (sin x))) (* (cos x) (- (* 1/24 (pow eps 2)) 1/2))))))
(* -1/2 eps)
(* eps (- (* 1/24 (pow eps 2)) 1/2))
(* eps (- (* 1/24 (pow eps 2)) 1/2))
(* eps (- (* 1/24 (pow eps 2)) 1/2))
(* 1/24 (pow eps 3))
(* (pow eps 3) (- 1/24 (* 1/2 (/ 1 (pow eps 2)))))
(* (pow eps 3) (- 1/24 (* 1/2 (/ 1 (pow eps 2)))))
(* (pow eps 3) (- 1/24 (* 1/2 (/ 1 (pow eps 2)))))
(* 1/24 (pow eps 3))
(* -1 (* (pow eps 3) (- (* 1/2 (/ 1 (pow eps 2))) 1/24)))
(* -1 (* (pow eps 3) (- (* 1/2 (/ 1 (pow eps 2))) 1/24)))
(* -1 (* (pow eps 3) (- (* 1/2 (/ 1 (pow eps 2))) 1/24)))
(- (cos eps) 1)
(- (+ (cos eps) (* -1 (* x (sin eps)))) 1)
(- (+ (cos eps) (* x (- (* x (+ 1/2 (* -1/2 (cos eps)))) (sin eps)))) 1)
(- (+ (cos eps) (* x (- (* x (+ 1/2 (+ (* -1/2 (cos eps)) (* 1/6 (* x (sin eps)))))) (sin eps)))) 1)
(- (cos (+ eps x)) (cos x))
(- (cos (+ eps x)) (cos x))
(- (cos (+ eps x)) (cos x))
(- (cos (+ eps x)) (cos x))
(- (cos (- eps (* -1 x))) (cos x))
(- (cos (- eps (* -1 x))) (cos x))
(- (cos (- eps (* -1 x))) (cos x))
(- (cos (- eps (* -1 x))) (cos x))
(* -1 (* eps (sin x)))
(* eps (- (* -1/2 (* eps (cos x))) (sin x)))
(* eps (- (* eps (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x))))) (sin x)))
(* eps (- (* eps (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x)))))) (sin x)))
(- (cos (+ eps x)) (cos x))
(- (cos (+ eps x)) (cos x))
(- (cos (+ eps x)) (cos x))
(- (cos (+ eps x)) (cos x))
(- (cos (- x (* -1 eps))) (cos x))
(- (cos (- x (* -1 eps))) (cos x))
(- (cos (- x (* -1 eps))) (cos x))
(- (cos (- x (* -1 eps))) (cos x))
(cos eps)
(+ (cos eps) (* -1 (* x (sin eps))))
(+ (cos eps) (* x (- (* -1/2 (* x (cos eps))) (sin eps))))
(+ (cos eps) (* x (- (* x (+ (* -1/2 (cos eps)) (* 1/6 (* x (sin eps))))) (sin eps))))
(cos (+ eps x))
(cos (+ eps x))
(cos (+ eps x))
(cos (+ eps x))
(cos (- eps (* -1 x)))
(cos (- eps (* -1 x)))
(cos (- eps (* -1 x)))
(cos (- eps (* -1 x)))
(cos x)
(+ (cos x) (* -1 (* eps (sin x))))
(+ (cos x) (* eps (- (* -1/2 (* eps (cos x))) (sin x))))
(+ (cos x) (* eps (- (* eps (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x))))) (sin x))))
(cos (+ eps x))
(cos (+ eps x))
(cos (+ eps x))
(cos (+ eps x))
(cos (- x (* -1 eps)))
(cos (- x (* -1 eps)))
(cos (- x (* -1 eps)))
(cos (- x (* -1 eps)))
eps
(+ eps x)
(+ eps x)
(+ eps x)
x
(* x (+ 1 (/ eps x)))
(* x (+ 1 (/ eps x)))
(* x (+ 1 (/ eps x)))
x
(* -1 (* x (- (* -1 (/ eps x)) 1)))
(* -1 (* x (- (* -1 (/ eps x)) 1)))
(* -1 (* x (- (* -1 (/ eps x)) 1)))
x
(+ eps x)
(+ eps x)
(+ eps x)
eps
(* eps (+ 1 (/ x eps)))
(* eps (+ 1 (/ x eps)))
(* eps (+ 1 (/ x eps)))
eps
(* -1 (* eps (- (* -1 (/ x eps)) 1)))
(* -1 (* eps (- (* -1 (/ x eps)) 1)))
(* -1 (* eps (- (* -1 (/ x eps)) 1)))
1
(+ 1 (* -1/2 (pow x 2)))
(+ 1 (* (pow x 2) (- (* 1/24 (pow x 2)) 1/2)))
(+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))) 1/2)))
(cos x)
(cos x)
(cos x)
(cos x)
(cos x)
(cos x)
(cos x)
(cos x)
(* -1 (sin x))
(- (* -1/2 (* eps (cos x))) (sin x))
(- (* eps (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x))))) (sin x))
(- (* eps (+ (* -1/2 (cos x)) (* eps (+ (* 1/24 (* eps (cos x))) (* 1/6 (sin x)))))) (sin x))
(* 1/24 (* (pow eps 3) (cos x)))
(* (pow eps 3) (+ (* 1/24 (cos x)) (* 1/6 (/ (sin x) eps))))
(* (pow eps 3) (+ (* -1/2 (/ (cos x) (pow eps 2))) (+ (* 1/24 (cos x)) (* 1/6 (/ (sin x) eps)))))
(* (pow eps 3) (+ (* -1 (/ (sin x) (pow eps 3))) (+ (* -1/2 (/ (cos x) (pow eps 2))) (+ (* 1/24 (cos x)) (* 1/6 (/ (sin x) eps))))))
(* 1/24 (* (pow eps 3) (cos x)))
(* -1 (* (pow eps 3) (+ (* -1/6 (/ (sin x) eps)) (* -1/24 (cos x)))))
(* -1 (* (pow eps 3) (+ (* -1 (/ (+ (* -1/2 (/ (cos x) eps)) (* 1/6 (sin x))) eps)) (* -1/24 (cos x)))))
(* -1 (* (pow eps 3) (+ (* -1 (/ (+ (* -1 (/ (+ (* 1/2 (cos x)) (/ (sin x) eps)) eps)) (* 1/6 (sin x))) eps)) (* -1/24 (cos x)))))
(* eps (- (* 1/24 (pow eps 2)) 1/2))
(+ (* eps (- (* 1/24 (pow eps 2)) 1/2)) (* x (- (* 1/6 (pow eps 2)) 1)))
(+ (* eps (- (* 1/24 (pow eps 2)) 1/2)) (* x (- (+ (* -1/2 (* eps (* x (- (* 1/24 (pow eps 2)) 1/2)))) (* 1/6 (pow eps 2))) 1)))
(+ (* eps (- (* 1/24 (pow eps 2)) 1/2)) (* x (- (+ (* 1/6 (pow eps 2)) (* x (+ (* -1/2 (* eps (- (* 1/24 (pow eps 2)) 1/2))) (* x (+ 1/6 (* -1/36 (pow eps 2))))))) 1)))
(- (* eps (+ (* 1/6 (* eps (sin x))) (* (cos x) (- (* 1/24 (pow eps 2)) 1/2)))) (sin x))
(- (* eps (+ (* 1/6 (* eps (sin x))) (* (cos x) (- (* 1/24 (pow eps 2)) 1/2)))) (sin x))
(- (* eps (+ (* 1/6 (* eps (sin x))) (* (cos x) (- (* 1/24 (pow eps 2)) 1/2)))) (sin x))
(- (* eps (+ (* 1/6 (* eps (sin x))) (* (cos x) (- (* 1/24 (pow eps 2)) 1/2)))) (sin x))
(- (* eps (+ (* 1/6 (* eps (sin x))) (* (cos x) (- (* 1/24 (pow eps 2)) 1/2)))) (sin x))
(- (* eps (+ (* 1/6 (* eps (sin x))) (* (cos x) (- (* 1/24 (pow eps 2)) 1/2)))) (sin x))
(- (* eps (+ (* 1/6 (* eps (sin x))) (* (cos x) (- (* 1/24 (pow eps 2)) 1/2)))) (sin x))
(- (* eps (+ (* 1/6 (* eps (sin x))) (* (cos x) (- (* 1/24 (pow eps 2)) 1/2)))) (sin x))
(- (cos eps) 1)
(- (+ (cos eps) (* -1 (* x (sin eps)))) 1)
(- (+ (cos eps) (* x (- (* x (+ 1/2 (* -1/2 (cos eps)))) (sin eps)))) 1)
(- (+ (cos eps) (* x (- (* x (+ 1/2 (+ (* -1/2 (cos eps)) (* 1/6 (* x (sin eps)))))) (sin eps)))) 1)
(- (* (cos eps) (cos x)) (+ (cos x) (* (sin eps) (sin x))))
(- (* (cos eps) (cos x)) (+ (cos x) (* (sin eps) (sin x))))
(- (* (cos eps) (cos x)) (+ (cos x) (* (sin eps) (sin x))))
(- (* (cos eps) (cos x)) (+ (cos x) (* (sin eps) (sin x))))
(- (* (cos eps) (cos x)) (+ (cos x) (* (sin eps) (sin x))))
(- (* (cos eps) (cos x)) (+ (cos x) (* (sin eps) (sin x))))
(- (* (cos eps) (cos x)) (+ (cos x) (* (sin eps) (sin x))))
(- (* (cos eps) (cos x)) (+ (cos x) (* (sin eps) (sin x))))
(* -1 (* eps (sin x)))
(* eps (- (* -1/2 (* eps (cos x))) (sin x)))
(* eps (- (* eps (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x))))) (sin x)))
(* eps (- (* eps (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x)))))) (sin x)))
(- (* (cos eps) (cos x)) (+ (cos x) (* (sin eps) (sin x))))
(- (* (cos eps) (cos x)) (+ (cos x) (* (sin eps) (sin x))))
(- (* (cos eps) (cos x)) (+ (cos x) (* (sin eps) (sin x))))
(- (* (cos eps) (cos x)) (+ (cos x) (* (sin eps) (sin x))))
(- (* (cos eps) (cos x)) (+ (cos x) (* (sin eps) (sin x))))
(- (* (cos eps) (cos x)) (+ (cos x) (* (sin eps) (sin x))))
(- (* (cos eps) (cos x)) (+ (cos x) (* (sin eps) (sin x))))
(- (* (cos eps) (cos x)) (+ (cos x) (* (sin eps) (sin x))))
(* -1 (* eps (sin x)))
(* eps (+ (* -1 (sin x)) (* -1/2 (* eps (cos x)))))
(* eps (+ (* -1 (sin x)) (* eps (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x)))))))
(* eps (+ (* -1 (sin x)) (* eps (+ (* -1/2 (cos x)) (* eps (+ (* 1/24 (* eps (cos x))) (* 1/6 (sin x))))))))
(* 1/24 (* (pow eps 4) (cos x)))
(* (pow eps 4) (+ (* 1/24 (cos x)) (* 1/6 (/ (sin x) eps))))
(* (pow eps 4) (+ (* -1/2 (/ (cos x) (pow eps 2))) (+ (* 1/24 (cos x)) (* 1/6 (/ (sin x) eps)))))
(* (pow eps 4) (+ (* -1 (/ (sin x) (pow eps 3))) (+ (* -1/2 (/ (cos x) (pow eps 2))) (+ (* 1/24 (cos x)) (* 1/6 (/ (sin x) eps))))))
(* 1/24 (* (pow eps 4) (cos x)))
(* (pow eps 4) (+ (* 1/24 (cos x)) (* 1/6 (/ (sin x) eps))))
(* (pow eps 4) (+ (* -1 (/ (+ (* -1/6 (sin x)) (* 1/2 (/ (cos x) eps))) eps)) (* 1/24 (cos x))))
(* (pow eps 4) (+ (* -1 (/ (+ (* -1 (/ (+ (* -1 (/ (sin x) eps)) (* -1/2 (cos x))) eps)) (* -1/6 (sin x))) eps)) (* 1/24 (cos x))))
(* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2))
(+ (* eps (* x (- (* 1/6 (pow eps 2)) 1))) (* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2)))
(+ (* x (+ (* -1/2 (* (pow eps 2) (* x (- (* 1/24 (pow eps 2)) 1/2)))) (* eps (- (* 1/6 (pow eps 2)) 1)))) (* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2)))
(+ (* x (+ (* eps (- (* 1/6 (pow eps 2)) 1)) (* x (+ (* -1/2 (* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2))) (* eps (* x (+ 1/6 (* -1/36 (pow eps 2))))))))) (* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2)))
(* eps (- (* eps (+ (* 1/6 (* eps (sin x))) (* (cos x) (- (* 1/24 (pow eps 2)) 1/2)))) (sin x)))
(* eps (- (* eps (+ (* 1/6 (* eps (sin x))) (* (cos x) (- (* 1/24 (pow eps 2)) 1/2)))) (sin x)))
(* eps (- (* eps (+ (* 1/6 (* eps (sin x))) (* (cos x) (- (* 1/24 (pow eps 2)) 1/2)))) (sin x)))
(* eps (- (* eps (+ (* 1/6 (* eps (sin x))) (* (cos x) (- (* 1/24 (pow eps 2)) 1/2)))) (sin x)))
(* eps (- (* eps (+ (* 1/6 (* eps (sin x))) (* (cos x) (- (* 1/24 (pow eps 2)) 1/2)))) (sin x)))
(* eps (- (* eps (+ (* 1/6 (* eps (sin x))) (* (cos x) (- (* 1/24 (pow eps 2)) 1/2)))) (sin x)))
(* eps (- (* eps (+ (* 1/6 (* eps (sin x))) (* (cos x) (- (* 1/24 (pow eps 2)) 1/2)))) (sin x)))
(* eps (- (* eps (+ (* 1/6 (* eps (sin x))) (* (cos x) (- (* 1/24 (pow eps 2)) 1/2)))) (sin x)))
(* -1/2 (* eps (cos x)))
(* eps (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x)))))
(* eps (+ (* -1/2 (cos x)) (* eps (+ (* 1/24 (* eps (cos x))) (* 1/6 (sin x))))))
(* eps (+ (* -1/2 (cos x)) (* eps (+ (* 1/24 (* eps (cos x))) (* 1/6 (sin x))))))
(* 1/24 (* (pow eps 3) (cos x)))
(* (pow eps 3) (+ (* 1/24 (cos x)) (* 1/6 (/ (sin x) eps))))
(* (pow eps 3) (+ (* -1/2 (/ (cos x) (pow eps 2))) (+ (* 1/24 (cos x)) (* 1/6 (/ (sin x) eps)))))
(* (pow eps 3) (+ (* -1/2 (/ (cos x) (pow eps 2))) (+ (* 1/24 (cos x)) (* 1/6 (/ (sin x) eps)))))
(* 1/24 (* (pow eps 3) (cos x)))
(* -1 (* (pow eps 3) (+ (* -1/6 (/ (sin x) eps)) (* -1/24 (cos x)))))
(* -1 (* (pow eps 3) (+ (* -1 (/ (+ (* -1/2 (/ (cos x) eps)) (* 1/6 (sin x))) eps)) (* -1/24 (cos x)))))
(* -1 (* (pow eps 3) (+ (* -1 (/ (+ (* -1/2 (/ (cos x) eps)) (* 1/6 (sin x))) eps)) (* -1/24 (cos x)))))
(* eps (- (* 1/24 (pow eps 2)) 1/2))
(+ (* 1/6 (* (pow eps 2) x)) (* eps (- (* 1/24 (pow eps 2)) 1/2)))
(+ (* eps (- (* 1/24 (pow eps 2)) 1/2)) (* x (+ (* -1/2 (* eps (* x (- (* 1/24 (pow eps 2)) 1/2)))) (* 1/6 (pow eps 2)))))
(+ (* eps (- (* 1/24 (pow eps 2)) 1/2)) (* x (+ (* 1/6 (pow eps 2)) (* x (+ (* -1/2 (* eps (- (* 1/24 (pow eps 2)) 1/2))) (* -1/36 (* (pow eps 2) x)))))))
(* eps (+ (* 1/6 (* eps (sin x))) (* (cos x) (- (* 1/24 (pow eps 2)) 1/2))))
(* eps (+ (* 1/6 (* eps (sin x))) (* (cos x) (- (* 1/24 (pow eps 2)) 1/2))))
(* eps (+ (* 1/6 (* eps (sin x))) (* (cos x) (- (* 1/24 (pow eps 2)) 1/2))))
(* eps (+ (* 1/6 (* eps (sin x))) (* (cos x) (- (* 1/24 (pow eps 2)) 1/2))))
(* eps (+ (* 1/6 (* eps (sin x))) (* (cos x) (- (* 1/24 (pow eps 2)) 1/2))))
(* eps (+ (* 1/6 (* eps (sin x))) (* (cos x) (- (* 1/24 (pow eps 2)) 1/2))))
(* eps (+ (* 1/6 (* eps (sin x))) (* (cos x) (- (* 1/24 (pow eps 2)) 1/2))))
(* eps (+ (* 1/6 (* eps (sin x))) (* (cos x) (- (* 1/24 (pow eps 2)) 1/2))))
(sin (* 1/2 eps))
(+ (sin (* 1/2 eps)) (* -1/2 (* (pow x 2) (sin (* 1/2 eps)))))
(+ (sin (* 1/2 eps)) (* (pow x 2) (+ (* -1/2 (sin (* 1/2 eps))) (* 1/24 (* (pow x 2) (sin (* 1/2 eps)))))))
(+ (sin (* 1/2 eps)) (* (pow x 2) (+ (* -1/2 (sin (* 1/2 eps))) (* (pow x 2) (+ (* -1/720 (* (pow x 2) (sin (* 1/2 eps)))) (* 1/24 (sin (* 1/2 eps))))))))
(* (cos x) (sin (* 1/2 eps)))
(* (cos x) (sin (* 1/2 eps)))
(* (cos x) (sin (* 1/2 eps)))
(* (cos x) (sin (* 1/2 eps)))
(* (cos x) (sin (* 1/2 eps)))
(* (cos x) (sin (* 1/2 eps)))
(* (cos x) (sin (* 1/2 eps)))
(* (cos x) (sin (* 1/2 eps)))
(* 1/2 (* eps (cos x)))
(* eps (+ (* -1/48 (* (pow eps 2) (cos x))) (* 1/2 (cos x))))
(* eps (+ (* 1/2 (cos x)) (* (pow eps 2) (+ (* -1/48 (cos x)) (* 1/3840 (* (pow eps 2) (cos x)))))))
(* eps (+ (* 1/2 (cos x)) (* (pow eps 2) (+ (* -1/48 (cos x)) (* (pow eps 2) (+ (* -1/645120 (* (pow eps 2) (cos x))) (* 1/3840 (cos x))))))))
(* (cos x) (sin (* 1/2 eps)))
(* (cos x) (sin (* 1/2 eps)))
(* (cos x) (sin (* 1/2 eps)))
(* (cos x) (sin (* 1/2 eps)))
(* (cos x) (sin (* 1/2 eps)))
(* (cos x) (sin (* 1/2 eps)))
(* (cos x) (sin (* 1/2 eps)))
(* (cos x) (sin (* 1/2 eps)))
(sin (* 1/2 eps))
(+ (sin (* 1/2 eps)) (* x (cos (* 1/2 eps))))
(+ (sin (* 1/2 eps)) (* x (+ (cos (* 1/2 eps)) (* -1/2 (* x (sin (* 1/2 eps)))))))
(+ (sin (* 1/2 eps)) (* x (+ (cos (* 1/2 eps)) (* x (+ (* -1/2 (sin (* 1/2 eps))) (* -1/6 (* x (cos (* 1/2 eps)))))))))
(+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x)))
(+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x)))
(+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x)))
(+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x)))
(+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x)))
(+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x)))
(+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x)))
(+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x)))
(sin x)
(+ (sin x) (* 1/2 (* eps (cos x))))
(+ (sin x) (* eps (+ (* -1/8 (* eps (sin x))) (* 1/2 (cos x)))))
(+ (sin x) (* eps (+ (* 1/2 (cos x)) (* eps (+ (* -1/8 (sin x)) (* -1/48 (* eps (cos x))))))))
(+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x)))
(+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x)))
(+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x)))
(+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x)))
(+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x)))
(+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x)))
(+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x)))
(+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x)))
(* 1/24 eps)
(* 1/24 eps)
(* 1/24 eps)
(* 1/24 eps)
(* 1/24 eps)
(* 1/24 eps)
(* 1/24 eps)
(* 1/24 eps)
(* 1/24 eps)
(* 1/24 eps)
(* 1/24 eps)
(* 1/24 eps)
(* 1/6 eps)
(* 1/6 eps)
(* 1/6 eps)
(* 1/6 eps)
(* 1/6 eps)
(* 1/6 eps)
(* 1/6 eps)
(* 1/6 eps)
(* 1/6 eps)
(* 1/6 eps)
(* 1/6 eps)
(* 1/6 eps)
(* 1/6 x)
(* x (+ 1/6 (* -1/36 (pow x 2))))
(* x (+ 1/6 (* (pow x 2) (- (* 1/720 (pow x 2)) 1/36))))
(* x (+ 1/6 (* (pow x 2) (- (* (pow x 2) (+ 1/720 (* -1/30240 (pow x 2)))) 1/36))))
(* 1/6 (sin x))
(* 1/6 (sin x))
(* 1/6 (sin x))
(* 1/6 (sin x))
(* 1/6 (sin x))
(* 1/6 (sin x))
(* 1/6 (sin x))
(* 1/6 (sin x))

Outputs
x
x
x
x
x
x
x
x
x
x
x
x
eps
eps
eps
eps
eps
eps
eps
eps
eps
eps
eps
eps
(* -1 (* eps (sin x)))
(neg.f64 (*.f64 eps (sin.f64 x)))
(* eps (+ (* -1 (sin x)) (* -1/2 (* eps (cos x)))))
(.f64 eps (-.f64 (.f64 eps (*.f64 #s(literal -1/2 binary64) (cos.f64 x))) (sin.f64 x)))
(* eps (+ (* -1 (sin x)) (* eps (+ (* -2 (* eps (+ (* -1/16 (sin x)) (* -1/48 (sin x))))) (* -1/2 (cos x))))))
(.f64 eps (-.f64 (.f64 eps (fma.f64 (.f64 eps (sin.f64 x)) #s(literal 1/6 binary64) (.f64 #s(literal -1/2 binary64) (cos.f64 x)))) (sin.f64 x)))
(* eps (+ (* -1 (sin x)) (* eps (+ (* -1/2 (cos x)) (* eps (+ (* -2 (+ (* -1/16 (sin x)) (* -1/48 (sin x)))) (* 1/24 (* eps (cos x)))))))))
(.f64 eps (fma.f64 eps (fma.f64 eps (.f64 (sin.f64 x) #s(literal 1/6 binary64)) (.f64 (cos.f64 x) (fma.f64 eps (.f64 eps #s(literal 1/24 binary64)) #s(literal -1/2 binary64)))) (sin.f64 (neg.f64 x))))
(* -2 (* (sin (* 1/2 eps)) (+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x)))))
(.f64 (fma.f64 (cos.f64 x) (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (.f64 (sin.f64 x) (cos.f64 (.f64 eps #s(literal 1/2 binary64))))) (.f64 #s(literal -2 binary64) (sin.f64 (.f64 eps #s(literal 1/2 binary64)))))
(* -2 (* (sin (* 1/2 eps)) (+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x)))))
(.f64 (fma.f64 (cos.f64 x) (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (.f64 (sin.f64 x) (cos.f64 (.f64 eps #s(literal 1/2 binary64))))) (.f64 #s(literal -2 binary64) (sin.f64 (.f64 eps #s(literal 1/2 binary64)))))
(* -2 (* (sin (* 1/2 eps)) (+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x)))))
(.f64 (fma.f64 (cos.f64 x) (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (.f64 (sin.f64 x) (cos.f64 (.f64 eps #s(literal 1/2 binary64))))) (.f64 #s(literal -2 binary64) (sin.f64 (.f64 eps #s(literal 1/2 binary64)))))
(* -2 (* (sin (* 1/2 eps)) (+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x)))))
(.f64 (fma.f64 (cos.f64 x) (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (.f64 (sin.f64 x) (cos.f64 (.f64 eps #s(literal 1/2 binary64))))) (.f64 #s(literal -2 binary64) (sin.f64 (.f64 eps #s(literal 1/2 binary64)))))
(* -2 (* (sin (* 1/2 eps)) (+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x)))))
(.f64 (fma.f64 (cos.f64 x) (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (.f64 (sin.f64 x) (cos.f64 (.f64 eps #s(literal 1/2 binary64))))) (.f64 #s(literal -2 binary64) (sin.f64 (.f64 eps #s(literal 1/2 binary64)))))
(* -2 (* (sin (* 1/2 eps)) (+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x)))))
(.f64 (fma.f64 (cos.f64 x) (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (.f64 (sin.f64 x) (cos.f64 (.f64 eps #s(literal 1/2 binary64))))) (.f64 #s(literal -2 binary64) (sin.f64 (.f64 eps #s(literal 1/2 binary64)))))
(* -2 (* (sin (* 1/2 eps)) (+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x)))))
(.f64 (fma.f64 (cos.f64 x) (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (.f64 (sin.f64 x) (cos.f64 (.f64 eps #s(literal 1/2 binary64))))) (.f64 #s(literal -2 binary64) (sin.f64 (.f64 eps #s(literal 1/2 binary64)))))
(* -2 (* (sin (* 1/2 eps)) (+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x)))))
(.f64 (fma.f64 (cos.f64 x) (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (.f64 (sin.f64 x) (cos.f64 (.f64 eps #s(literal 1/2 binary64))))) (.f64 #s(literal -2 binary64) (sin.f64 (.f64 eps #s(literal 1/2 binary64)))))
(* -2 (pow (sin (* 1/2 eps)) 2))
(.f64 #s(literal -2 binary64) (pow.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) #s(literal 2 binary64)))
(+ (* -2 (* x (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))) (* -2 (pow (sin (* 1/2 eps)) 2)))
(.f64 #s(literal -2 binary64) (.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (fma.f64 x (cos.f64 (.f64 eps #s(literal 1/2 binary64))) (sin.f64 (*.f64 eps #s(literal 1/2 binary64))))))
(+ (* -2 (pow (sin (* 1/2 eps)) 2)) (* x (+ (* -2 (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) (* x (pow (sin (* 1/2 eps)) 2)))))
(fma.f64 #s(literal -2 binary64) (.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (fma.f64 x (cos.f64 (.f64 eps #s(literal 1/2 binary64))) (sin.f64 (.f64 eps #s(literal 1/2 binary64))))) (.f64 x (.f64 x (pow.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) #s(literal 2 binary64)))))
(+ (* -2 (pow (sin (* 1/2 eps)) 2)) (* x (+ (* -2 (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) (* x (+ (* 1/3 (* x (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))) (pow (sin (* 1/2 eps)) 2))))))
(fma.f64 #s(literal -2 binary64) (.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (fma.f64 x (cos.f64 (.f64 eps #s(literal 1/2 binary64))) (sin.f64 (.f64 eps #s(literal 1/2 binary64))))) (.f64 (fma.f64 (.f64 (.f64 x #s(literal 1/3 binary64)) (sin.f64 (.f64 eps #s(literal 1/2 binary64)))) (cos.f64 (.f64 eps #s(literal 1/2 binary64))) (pow.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) #s(literal 2 binary64))) (*.f64 x x)))
(* -2 (* (sin (* 1/2 eps)) (+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x)))))
(.f64 (fma.f64 (cos.f64 x) (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (.f64 (sin.f64 x) (cos.f64 (.f64 eps #s(literal 1/2 binary64))))) (.f64 #s(literal -2 binary64) (sin.f64 (.f64 eps #s(literal 1/2 binary64)))))
(* -2 (* (sin (* 1/2 eps)) (+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x)))))
(.f64 (fma.f64 (cos.f64 x) (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (.f64 (sin.f64 x) (cos.f64 (.f64 eps #s(literal 1/2 binary64))))) (.f64 #s(literal -2 binary64) (sin.f64 (.f64 eps #s(literal 1/2 binary64)))))
(* -2 (* (sin (* 1/2 eps)) (+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x)))))
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(fma.f64 eps (fma.f64 (.f64 eps (sin.f64 x)) #s(literal -1/8 binary64) (.f64 (cos.f64 x) #s(literal 1/2 binary64))) (sin.f64 x))
(+ (sin x) (* eps (+ (* 1/2 (cos x)) (* eps (+ (* -1/8 (sin x)) (* -1/48 (* eps (cos x))))))))
(fma.f64 eps (fma.f64 eps (.f64 (sin.f64 x) #s(literal -1/8 binary64)) (.f64 (cos.f64 x) (fma.f64 #s(literal -1/48 binary64) (*.f64 eps eps) #s(literal 1/2 binary64)))) (sin.f64 x))
(+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x)))
(fma.f64 (cos.f64 x) (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (.f64 (sin.f64 x) (cos.f64 (*.f64 eps #s(literal 1/2 binary64)))))
(+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x)))
(fma.f64 (cos.f64 x) (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (.f64 (sin.f64 x) (cos.f64 (*.f64 eps #s(literal 1/2 binary64)))))
(+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x)))
(fma.f64 (cos.f64 x) (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (.f64 (sin.f64 x) (cos.f64 (*.f64 eps #s(literal 1/2 binary64)))))
(+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x)))
(fma.f64 (cos.f64 x) (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (.f64 (sin.f64 x) (cos.f64 (*.f64 eps #s(literal 1/2 binary64)))))
(+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x)))
(fma.f64 (cos.f64 x) (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (.f64 (sin.f64 x) (cos.f64 (*.f64 eps #s(literal 1/2 binary64)))))
(+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x)))
(fma.f64 (cos.f64 x) (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (.f64 (sin.f64 x) (cos.f64 (*.f64 eps #s(literal 1/2 binary64)))))
(+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x)))
(fma.f64 (cos.f64 x) (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (.f64 (sin.f64 x) (cos.f64 (*.f64 eps #s(literal 1/2 binary64)))))
(+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x)))
(fma.f64 (cos.f64 x) (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (.f64 (sin.f64 x) (cos.f64 (*.f64 eps #s(literal 1/2 binary64)))))
(* 1/24 eps)
(*.f64 eps #s(literal 1/24 binary64))
(* 1/24 eps)
(*.f64 eps #s(literal 1/24 binary64))
(* 1/24 eps)
(*.f64 eps #s(literal 1/24 binary64))
(* 1/24 eps)
(*.f64 eps #s(literal 1/24 binary64))
(* 1/24 eps)
(*.f64 eps #s(literal 1/24 binary64))
(* 1/24 eps)
(*.f64 eps #s(literal 1/24 binary64))
(* 1/24 eps)
(*.f64 eps #s(literal 1/24 binary64))
(* 1/24 eps)
(*.f64 eps #s(literal 1/24 binary64))
(* 1/24 eps)
(*.f64 eps #s(literal 1/24 binary64))
(* 1/24 eps)
(*.f64 eps #s(literal 1/24 binary64))
(* 1/24 eps)
(*.f64 eps #s(literal 1/24 binary64))
(* 1/24 eps)
(*.f64 eps #s(literal 1/24 binary64))
(* 1/6 eps)
(*.f64 eps #s(literal 1/6 binary64))
(* 1/6 eps)
(*.f64 eps #s(literal 1/6 binary64))
(* 1/6 eps)
(*.f64 eps #s(literal 1/6 binary64))
(* 1/6 eps)
(*.f64 eps #s(literal 1/6 binary64))
(* 1/6 eps)
(*.f64 eps #s(literal 1/6 binary64))
(* 1/6 eps)
(*.f64 eps #s(literal 1/6 binary64))
(* 1/6 eps)
(*.f64 eps #s(literal 1/6 binary64))
(* 1/6 eps)
(*.f64 eps #s(literal 1/6 binary64))
(* 1/6 eps)
(*.f64 eps #s(literal 1/6 binary64))
(* 1/6 eps)
(*.f64 eps #s(literal 1/6 binary64))
(* 1/6 eps)
(*.f64 eps #s(literal 1/6 binary64))
(* 1/6 eps)
(*.f64 eps #s(literal 1/6 binary64))
(* 1/6 x)
(*.f64 x #s(literal 1/6 binary64))
(* x (+ 1/6 (* -1/36 (pow x 2))))
(.f64 x (fma.f64 x (.f64 x #s(literal -1/36 binary64)) #s(literal 1/6 binary64)))
(* x (+ 1/6 (* (pow x 2) (- (* 1/720 (pow x 2)) 1/36))))
(.f64 x (fma.f64 (.f64 x x) (fma.f64 x (*.f64 x #s(literal 1/720 binary64)) #s(literal -1/36 binary64)) #s(literal 1/6 binary64)))
(* x (+ 1/6 (* (pow x 2) (- (* (pow x 2) (+ 1/720 (* -1/30240 (pow x 2)))) 1/36))))
(.f64 x (fma.f64 x (.f64 x (fma.f64 (.f64 x x) (fma.f64 (.f64 x x) #s(literal -1/30240 binary64) #s(literal 1/720 binary64)) #s(literal -1/36 binary64))) #s(literal 1/6 binary64)))
(* 1/6 (sin x))
(*.f64 (sin.f64 x) #s(literal 1/6 binary64))
(* 1/6 (sin x))
(*.f64 (sin.f64 x) #s(literal 1/6 binary64))
(* 1/6 (sin x))
(*.f64 (sin.f64 x) #s(literal 1/6 binary64))
(* 1/6 (sin x))
(*.f64 (sin.f64 x) #s(literal 1/6 binary64))
(* 1/6 (sin x))
(*.f64 (sin.f64 x) #s(literal 1/6 binary64))
(* 1/6 (sin x))
(*.f64 (sin.f64 x) #s(literal 1/6 binary64))
(* 1/6 (sin x))
(*.f64 (sin.f64 x) #s(literal 1/6 binary64))
(* 1/6 (sin x))
(*.f64 (sin.f64 x) #s(literal 1/6 binary64))

rewrite353.0ms (1.9%)

Memory

11.5MiB live, 534.9MiB allocated

Rules

6 898×	`lower-*.f32`
6 872×	`lower-*.f64`
4 030×	`lower-/.f64`
4 030×	`lower-/.f32`
3 904×	`lower-fma.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	73	379
0	114	357
1	452	291
2	4156	287
0	11313	284

Stop Event

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

Counts

24 → 542

Calls

Call 1

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

Outputs
#s(literal 0 binary64)
eps
(+.f64 x (+.f64 x eps))
(+.f64 x (-.f64 eps x))
(+.f64 eps #s(literal 0 binary64))
(+.f64 #s(literal 0 binary64) eps)
(+.f64 (+.f64 x eps) x)
(+.f64 (+.f64 x eps) (neg.f64 x))
(-.f64 eps #s(literal 0 binary64))
(-.f64 eps (/.f64 #s(literal 0 binary64) eps))
(-.f64 (+.f64 x eps) x)
(fma.f64 (fma.f64 x (.f64 x x) (.f64 eps (.f64 eps eps))) (/.f64 #s(literal 1 binary64) (fma.f64 x x (.f64 eps (-.f64 eps x)))) x)
(fma.f64 (fma.f64 x (.f64 x x) (.f64 eps (.f64 eps eps))) (/.f64 #s(literal 1 binary64) (fma.f64 x x (.f64 eps (-.f64 eps x)))) (neg.f64 x))
(fma.f64 (.f64 eps (.f64 eps eps)) (/.f64 #s(literal 1 binary64) (*.f64 eps eps)) #s(literal 0 binary64))
(fma.f64 (*.f64 (+.f64 x eps) (-.f64 x eps)) (/.f64 #s(literal 1 binary64) (-.f64 x eps)) x)
(fma.f64 (*.f64 (+.f64 x eps) (-.f64 x eps)) (/.f64 #s(literal 1 binary64) (-.f64 x eps)) (neg.f64 x))
(fma.f64 (*.f64 eps eps) (/.f64 #s(literal 1 binary64) eps) #s(literal 0 binary64))
(/.f64 #s(literal 1 binary64) (/.f64 eps (*.f64 eps eps)))
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) eps))
(/.f64 (.f64 eps (.f64 eps eps)) (*.f64 eps eps))
(/.f64 (*.f64 eps eps) eps)
(/.f64 (neg.f64 (.f64 eps (.f64 eps eps))) (neg.f64 (*.f64 eps eps)))
(/.f64 (neg.f64 (*.f64 eps eps)) (neg.f64 eps))
(/.f64 (fma.f64 (+.f64 x eps) (.f64 (+.f64 x eps) (+.f64 x eps)) (.f64 x (.f64 x x))) (fma.f64 (+.f64 x eps) (+.f64 x eps) (-.f64 (.f64 x x) (*.f64 (+.f64 x eps) x))))
(/.f64 (-.f64 (.f64 (+.f64 x eps) (.f64 (+.f64 x eps) (+.f64 x eps))) (.f64 x (.f64 x x))) (fma.f64 (+.f64 x eps) (+.f64 x eps) (fma.f64 x x (*.f64 (+.f64 x eps) x))))
(/.f64 (-.f64 (.f64 eps (.f64 eps eps)) #s(literal 0 binary64)) (*.f64 eps eps))
(/.f64 (-.f64 (.f64 (+.f64 x eps) (+.f64 x eps)) (.f64 x x)) eps)
(/.f64 (-.f64 #s(literal 0 binary64) (*.f64 eps eps)) (-.f64 #s(literal 0 binary64) eps))
(/.f64 (-.f64 (-.f64 (.f64 (+.f64 x eps) (+.f64 x eps)) (.f64 x x)) #s(literal 0 binary64)) eps)
(/.f64 (-.f64 (.f64 #s(literal 1 binary64) eps) (.f64 (/.f64 #s(literal 1 binary64) eps) #s(literal 0 binary64))) (*.f64 (/.f64 #s(literal 1 binary64) eps) eps))
(/.f64 (-.f64 (.f64 #s(literal 1 binary64) eps) (.f64 (/.f64 eps (.f64 eps eps)) #s(literal 0 binary64))) (.f64 (/.f64 eps (*.f64 eps eps)) eps))
(/.f64 (-.f64 (.f64 (.f64 eps (.f64 eps eps)) eps) (.f64 (.f64 eps eps) #s(literal 0 binary64))) (.f64 eps (*.f64 eps eps)))
(/.f64 (-.f64 (.f64 (neg.f64 (.f64 eps (.f64 eps eps))) eps) (.f64 (neg.f64 (.f64 eps eps)) #s(literal 0 binary64))) (.f64 (neg.f64 (*.f64 eps eps)) eps))
(/.f64 (-.f64 (.f64 (neg.f64 (.f64 eps eps)) eps) (.f64 (neg.f64 eps) #s(literal 0 binary64))) (.f64 (neg.f64 eps) eps))
(/.f64 (-.f64 (.f64 (fma.f64 (+.f64 x eps) (.f64 (+.f64 x eps) (+.f64 x eps)) (.f64 x (.f64 x x))) eps) (.f64 (fma.f64 (+.f64 x eps) (+.f64 x eps) (-.f64 (.f64 x x) (.f64 (+.f64 x eps) x))) #s(literal 0 binary64))) (.f64 (fma.f64 (+.f64 x eps) (+.f64 x eps) (-.f64 (.f64 x x) (.f64 (+.f64 x eps) x))) eps))
(/.f64 (-.f64 (.f64 (-.f64 (.f64 (+.f64 x eps) (.f64 (+.f64 x eps) (+.f64 x eps))) (.f64 x (.f64 x x))) eps) (.f64 (fma.f64 (+.f64 x eps) (+.f64 x eps) (fma.f64 x x (.f64 (+.f64 x eps) x))) #s(literal 0 binary64))) (.f64 (fma.f64 (+.f64 x eps) (+.f64 x eps) (fma.f64 x x (*.f64 (+.f64 x eps) x))) eps))
(/.f64 (-.f64 (.f64 (-.f64 (.f64 eps (.f64 eps eps)) #s(literal 0 binary64)) eps) (.f64 (.f64 eps eps) #s(literal 0 binary64))) (.f64 eps (*.f64 eps eps)))
(/.f64 (-.f64 (.f64 (-.f64 (.f64 (+.f64 x eps) (+.f64 x eps)) (.f64 x x)) eps) #s(literal 0 binary64)) (.f64 eps eps))
(/.f64 (-.f64 (.f64 (-.f64 #s(literal 0 binary64) (.f64 eps eps)) eps) (.f64 (-.f64 #s(literal 0 binary64) eps) #s(literal 0 binary64))) (.f64 (-.f64 #s(literal 0 binary64) eps) eps))
(pow.f64 eps #s(literal 1 binary64))
(pow.f64 (/.f64 eps (*.f64 eps eps)) #s(literal -1 binary64))
(pow.f64 (/.f64 #s(literal 1 binary64) eps) #s(literal -1 binary64))
(.f64 (.f64 eps (.f64 eps eps)) (/.f64 #s(literal 1 binary64) (.f64 eps eps)))
(.f64 (.f64 eps eps) (/.f64 #s(literal 1 binary64) eps))
(+.f64 (cos.f64 (+.f64 x eps)) (neg.f64 (cos.f64 x)))
(+.f64 (*.f64 (cos.f64 x) (cos.f64 eps)) (neg.f64 (fma.f64 (sin.f64 x) (sin.f64 eps) (cos.f64 x))))
(+.f64 (neg.f64 (fma.f64 (sin.f64 x) (sin.f64 eps) (cos.f64 x))) (*.f64 (cos.f64 x) (cos.f64 eps)))
(+.f64 (neg.f64 (cos.f64 x)) (cos.f64 (+.f64 x eps)))
(+.f64 (.f64 #s(literal -2 binary64) (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (.f64 #s(literal 0 binary64) (cos.f64 (.f64 #s(literal 1/2 binary64) eps))))) (.f64 #s(literal -2 binary64) (.f64 #s(literal 1 binary64) (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 #s(literal 2 binary64) (.f64 #s(literal 1/2 binary64) eps))))))))
(+.f64 (.f64 (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (.f64 #s(literal 0 binary64) (cos.f64 (.f64 #s(literal 1/2 binary64) eps)))) #s(literal -2 binary64)) (.f64 (.f64 #s(literal 1 binary64) (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 #s(literal 2 binary64) (.f64 #s(literal 1/2 binary64) eps)))))) #s(literal -2 binary64)))
(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))
(-.f64 (*.f64 (cos.f64 x) (cos.f64 eps)) (fma.f64 (sin.f64 x) (sin.f64 eps) (cos.f64 x)))
(-.f64 (.f64 (cos.f64 x) (cos.f64 eps)) (-.f64 (.f64 (sin.f64 x) (sin.f64 eps)) (neg.f64 (cos.f64 x))))
(-.f64 (/.f64 (pow.f64 (.f64 #s(literal 1 binary64) (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 #s(literal 2 binary64) eps))))) #s(literal 3/2 binary64)) (fma.f64 #s(literal 1 binary64) (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 #s(literal 2 binary64) eps)))) (.f64 (fma.f64 (sin.f64 x) (sin.f64 eps) (cos.f64 x)) (+.f64 (cos.f64 (-.f64 x eps)) (cos.f64 x))))) (/.f64 (pow.f64 (fma.f64 (sin.f64 x) (sin.f64 eps) (cos.f64 x)) #s(literal 3 binary64)) (fma.f64 #s(literal 1 binary64) (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 #s(literal 2 binary64) eps)))) (*.f64 (fma.f64 (sin.f64 x) (sin.f64 eps) (cos.f64 x)) (+.f64 (cos.f64 (-.f64 x eps)) (cos.f64 x))))))
(-.f64 (/.f64 (pow.f64 (cos.f64 (+.f64 x eps)) #s(literal 3 binary64)) (+.f64 (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 #s(literal 2 binary64) (+.f64 x eps))))) (fma.f64 (cos.f64 eps) #s(literal 1 binary64) #s(literal 1 binary64)))) (/.f64 (pow.f64 #s(literal 1 binary64) #s(literal 3/2 binary64)) (+.f64 (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 #s(literal 2 binary64) (+.f64 x eps))))) (fma.f64 (cos.f64 eps) #s(literal 1 binary64) #s(literal 1 binary64)))))
(-.f64 (/.f64 (.f64 #s(literal 1 binary64) (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) eps))))) (+.f64 (cos.f64 (-.f64 x eps)) (cos.f64 x))) (/.f64 (pow.f64 (fma.f64 (sin.f64 x) (sin.f64 eps) (cos.f64 x)) #s(literal 2 binary64)) (+.f64 (cos.f64 (-.f64 x eps)) (cos.f64 x))))
(-.f64 (/.f64 (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 #s(literal 2 binary64) (+.f64 x eps))))) (.f64 #s(literal 2 binary64) (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 #s(literal 2 binary64) (.f64 #s(literal 1/2 binary64) eps))))))) (/.f64 #s(literal 1 binary64) (.f64 #s(literal 2 binary64) (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 #s(literal 2 binary64) (.f64 #s(literal 1/2 binary64) eps))))))))
(-.f64 (-.f64 (.f64 (cos.f64 x) (cos.f64 eps)) (cos.f64 x)) (.f64 (sin.f64 x) (sin.f64 eps)))
(fma.f64 #s(literal -2 binary64) (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (.f64 #s(literal 0 binary64) (cos.f64 (.f64 #s(literal 1/2 binary64) eps)))) (.f64 #s(literal -2 binary64) (.f64 #s(literal 1 binary64) (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 #s(literal 2 binary64) (*.f64 #s(literal 1/2 binary64) eps))))))))
(fma.f64 (cos.f64 x) (cos.f64 eps) (neg.f64 (fma.f64 (sin.f64 x) (sin.f64 eps) (cos.f64 x))))
(fma.f64 (cos.f64 eps) (cos.f64 x) (neg.f64 (fma.f64 (sin.f64 x) (sin.f64 eps) (cos.f64 x))))
(fma.f64 #s(literal -1 binary64) (cos.f64 x) (cos.f64 (+.f64 x eps)))
(fma.f64 #s(literal -1 binary64) (fma.f64 (sin.f64 x) (sin.f64 eps) (cos.f64 x)) (*.f64 (cos.f64 x) (cos.f64 eps)))
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(/.f64 (.f64 eps (fma.f64 #s(literal 0 binary64) (.f64 eps (.f64 eps eps)) (pow.f64 (.f64 #s(literal 1 binary64) (.f64 (fma.f64 #s(literal 1/24 binary64) (.f64 eps eps) #s(literal -1/2 binary64)) (fma.f64 #s(literal 1/24 binary64) (.f64 eps eps) #s(literal -1/2 binary64)))) #s(literal 3/2 binary64)))) (-.f64 (fma.f64 #s(literal 1 binary64) (.f64 (fma.f64 #s(literal 1/24 binary64) (.f64 eps eps) #s(literal -1/2 binary64)) (fma.f64 #s(literal 1/24 binary64) (.f64 eps eps) #s(literal -1/2 binary64))) (.f64 #s(literal 0 binary64) (.f64 (.f64 eps #s(literal 1/6 binary64)) (.f64 eps #s(literal 1/6 binary64))))) (.f64 (fma.f64 #s(literal 1/24 binary64) (.f64 eps eps) #s(literal -1/2 binary64)) (.f64 (cos.f64 x) (.f64 (*.f64 eps #s(literal 1/6 binary64)) (sin.f64 x))))))
(/.f64 (.f64 eps (-.f64 (.f64 #s(literal 0 binary64) (.f64 (.f64 eps #s(literal 1/6 binary64)) (.f64 eps #s(literal 1/6 binary64)))) (.f64 #s(literal 1 binary64) (.f64 (fma.f64 #s(literal 1/24 binary64) (.f64 eps eps) #s(literal -1/2 binary64)) (fma.f64 #s(literal 1/24 binary64) (.f64 eps eps) #s(literal -1/2 binary64)))))) (-.f64 (.f64 (.f64 eps #s(literal 1/6 binary64)) (sin.f64 x)) (.f64 (cos.f64 x) (fma.f64 #s(literal 1/24 binary64) (*.f64 eps eps) #s(literal -1/2 binary64)))))
(/.f64 (.f64 eps (fma.f64 #s(literal 1 binary64) (.f64 (fma.f64 #s(literal 1/24 binary64) (.f64 eps eps) #s(literal -1/2 binary64)) (fma.f64 #s(literal 1/24 binary64) (.f64 eps eps) #s(literal -1/2 binary64))) (neg.f64 (.f64 #s(literal 0 binary64) (.f64 (.f64 eps #s(literal 1/6 binary64)) (.f64 eps #s(literal 1/6 binary64))))))) (-.f64 (.f64 (cos.f64 x) (fma.f64 #s(literal 1/24 binary64) (.f64 eps eps) #s(literal -1/2 binary64))) (.f64 (.f64 eps #s(literal 1/6 binary64)) (sin.f64 x))))
(/.f64 (.f64 (fma.f64 (cos.f64 x) (fma.f64 #s(literal 1/24 binary64) (.f64 eps eps) #s(literal -1/2 binary64)) (.f64 (.f64 eps #s(literal 1/6 binary64)) (sin.f64 x))) (.f64 eps (.f64 eps eps))) (*.f64 eps eps))
(/.f64 (.f64 (.f64 eps (.f64 eps eps)) (fma.f64 (cos.f64 x) (fma.f64 #s(literal 1/24 binary64) (.f64 eps eps) #s(literal -1/2 binary64)) (.f64 (.f64 eps #s(literal 1/6 binary64)) (sin.f64 x)))) (*.f64 eps eps))
(/.f64 (.f64 (fma.f64 #s(literal 0 binary64) (.f64 eps (.f64 eps eps)) (pow.f64 (.f64 #s(literal 1 binary64) (.f64 (fma.f64 #s(literal 1/24 binary64) (.f64 eps eps) #s(literal -1/2 binary64)) (fma.f64 #s(literal 1/24 binary64) (.f64 eps eps) #s(literal -1/2 binary64)))) #s(literal 3/2 binary64))) eps) (-.f64 (fma.f64 #s(literal 0 binary64) (.f64 (.f64 eps #s(literal 1/6 binary64)) (.f64 eps #s(literal 1/6 binary64))) (.f64 #s(literal 1 binary64) (.f64 (fma.f64 #s(literal 1/24 binary64) (.f64 eps eps) #s(literal -1/2 binary64)) (fma.f64 #s(literal 1/24 binary64) (.f64 eps eps) #s(literal -1/2 binary64))))) (.f64 (fma.f64 #s(literal 1/24 binary64) (.f64 eps eps) #s(literal -1/2 binary64)) (.f64 (cos.f64 x) (.f64 (*.f64 eps #s(literal 1/6 binary64)) (sin.f64 x))))))
(/.f64 (.f64 (fma.f64 #s(literal 0 binary64) (.f64 eps (.f64 eps eps)) (pow.f64 (.f64 #s(literal 1 binary64) (.f64 (fma.f64 #s(literal 1/24 binary64) (.f64 eps eps) #s(literal -1/2 binary64)) (fma.f64 #s(literal 1/24 binary64) (.f64 eps eps) #s(literal -1/2 binary64)))) #s(literal 3/2 binary64))) eps) (-.f64 (fma.f64 #s(literal 1 binary64) (.f64 (fma.f64 #s(literal 1/24 binary64) (.f64 eps eps) #s(literal -1/2 binary64)) (fma.f64 #s(literal 1/24 binary64) (.f64 eps eps) #s(literal -1/2 binary64))) (.f64 #s(literal 0 binary64) (.f64 (.f64 eps #s(literal 1/6 binary64)) (.f64 eps #s(literal 1/6 binary64))))) (.f64 (fma.f64 #s(literal 1/24 binary64) (.f64 eps eps) #s(literal -1/2 binary64)) (.f64 (cos.f64 x) (.f64 (*.f64 eps #s(literal 1/6 binary64)) (sin.f64 x))))))
(/.f64 (.f64 (-.f64 (.f64 #s(literal 0 binary64) (.f64 (.f64 eps #s(literal 1/6 binary64)) (.f64 eps #s(literal 1/6 binary64)))) (.f64 #s(literal 1 binary64) (.f64 (fma.f64 #s(literal 1/24 binary64) (.f64 eps eps) #s(literal -1/2 binary64)) (fma.f64 #s(literal 1/24 binary64) (.f64 eps eps) #s(literal -1/2 binary64))))) eps) (-.f64 (.f64 (.f64 eps #s(literal 1/6 binary64)) (sin.f64 x)) (.f64 (cos.f64 x) (fma.f64 #s(literal 1/24 binary64) (*.f64 eps eps) #s(literal -1/2 binary64)))))
(/.f64 (.f64 (fma.f64 #s(literal 1 binary64) (.f64 (fma.f64 #s(literal 1/24 binary64) (.f64 eps eps) #s(literal -1/2 binary64)) (fma.f64 #s(literal 1/24 binary64) (.f64 eps eps) #s(literal -1/2 binary64))) (neg.f64 (.f64 #s(literal 0 binary64) (.f64 (.f64 eps #s(literal 1/6 binary64)) (.f64 eps #s(literal 1/6 binary64)))))) eps) (-.f64 (.f64 (cos.f64 x) (fma.f64 #s(literal 1/24 binary64) (.f64 eps eps) #s(literal -1/2 binary64))) (.f64 (.f64 eps #s(literal 1/6 binary64)) (sin.f64 x))))
(.f64 eps (fma.f64 (cos.f64 x) (fma.f64 #s(literal 1/24 binary64) (.f64 eps eps) #s(literal -1/2 binary64)) (.f64 (.f64 eps #s(literal 1/6 binary64)) (sin.f64 x))))
(.f64 (fma.f64 (cos.f64 x) (fma.f64 #s(literal 1/24 binary64) (.f64 eps eps) #s(literal -1/2 binary64)) (.f64 (.f64 eps #s(literal 1/6 binary64)) (sin.f64 x))) eps)
(/.f64 (+.f64 (sin.f64 (-.f64 (.f64 #s(literal 1/2 binary64) eps) #s(literal 0 binary64))) (sin.f64 (.f64 #s(literal 1/2 binary64) eps))) #s(literal 2 binary64))
(.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) #s(literal 1 binary64))
(.f64 #s(literal 1 binary64) (sin.f64 (.f64 #s(literal 1/2 binary64) eps)))
(+.f64 (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) #s(literal 1 binary64)) (.f64 #s(literal 0 binary64) (cos.f64 (.f64 #s(literal 1/2 binary64) eps))))
(+.f64 (.f64 #s(literal 0 binary64) (cos.f64 (.f64 #s(literal 1/2 binary64) eps))) (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) #s(literal 1 binary64)))
(-.f64 (/.f64 (.f64 #s(literal 0 binary64) (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 #s(literal 2 binary64) (.f64 #s(literal 1/2 binary64) eps)))))) (sin.f64 (.f64 eps #s(literal -1/2 binary64)))) (/.f64 (.f64 #s(literal 1 binary64) (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 #s(literal 2 binary64) (.f64 #s(literal 1/2 binary64) eps)))))) (sin.f64 (.f64 eps #s(literal -1/2 binary64)))))
(-.f64 (.f64 (sin.f64 (/.f64 (+.f64 x eps) #s(literal 2 binary64))) (cos.f64 (/.f64 x #s(literal 2 binary64)))) (.f64 (cos.f64 (/.f64 (+.f64 x eps) #s(literal 2 binary64))) (sin.f64 (/.f64 x #s(literal 2 binary64)))))
(sin.f64 (*.f64 #s(literal 1/2 binary64) eps))
(fma.f64 #s(literal 0 binary64) (cos.f64 (.f64 #s(literal 1/2 binary64) eps)) (.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) #s(literal 1 binary64)))
(fma.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) #s(literal 1 binary64) (.f64 #s(literal 0 binary64) (cos.f64 (*.f64 #s(literal 1/2 binary64) eps))))
(fma.f64 (cos.f64 (.f64 #s(literal 1/2 binary64) eps)) #s(literal 0 binary64) (.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) #s(literal 1 binary64)))
(fma.f64 #s(literal 1 binary64) (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (.f64 #s(literal 0 binary64) (cos.f64 (*.f64 #s(literal 1/2 binary64) eps))))
(fma.f64 (+.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (sin.f64 (.f64 eps #s(literal -1/2 binary64)))) #s(literal 1/2 binary64) (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) #s(literal 1 binary64)))
(/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 #s(literal 0 binary64) (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 #s(literal 2 binary64) (.f64 #s(literal 1/2 binary64) eps))))) (.f64 (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) #s(literal 1 binary64)) (sin.f64 (-.f64 (.f64 #s(literal 1/2 binary64) eps) #s(literal 0 binary64))))) (fma.f64 #s(literal 0 binary64) (pow.f64 (cos.f64 (.f64 #s(literal 1/2 binary64) eps)) #s(literal 3 binary64)) (pow.f64 (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) #s(literal 1 binary64)) #s(literal 3 binary64)))))
(/.f64 #s(literal 1 binary64) (/.f64 (sin.f64 (.f64 eps #s(literal -1/2 binary64))) (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (sin.f64 (.f64 eps #s(literal -1/2 binary64))))))
(/.f64 (fma.f64 #s(literal 0 binary64) (pow.f64 (cos.f64 (.f64 #s(literal 1/2 binary64) eps)) #s(literal 3 binary64)) (pow.f64 (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) #s(literal 1 binary64)) #s(literal 3 binary64))) (fma.f64 #s(literal 0 binary64) (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 #s(literal 2 binary64) (.f64 #s(literal 1/2 binary64) eps))))) (.f64 (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) #s(literal 1 binary64)) (sin.f64 (-.f64 (.f64 #s(literal 1/2 binary64) eps) #s(literal 0 binary64))))))
(/.f64 (fma.f64 #s(literal 0 binary64) (pow.f64 (cos.f64 (.f64 #s(literal 1/2 binary64) eps)) #s(literal 3 binary64)) (pow.f64 (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) #s(literal 1 binary64)) #s(literal 3 binary64))) (fma.f64 #s(literal 1 binary64) (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 #s(literal 2 binary64) (.f64 #s(literal 1/2 binary64) eps))))) (-.f64 (.f64 #s(literal 0 binary64) (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 #s(literal 2 binary64) (.f64 #s(literal 1/2 binary64) eps)))))) (.f64 #s(literal 0 binary64) (.f64 (cos.f64 (.f64 #s(literal 1/2 binary64) eps)) (.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) #s(literal 1 binary64)))))))
(/.f64 (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (sin.f64 (.f64 eps #s(literal -1/2 binary64)))) (sin.f64 (.f64 eps #s(literal -1/2 binary64))))
(/.f64 (neg.f64 (fma.f64 #s(literal 0 binary64) (pow.f64 (cos.f64 (.f64 #s(literal 1/2 binary64) eps)) #s(literal 3 binary64)) (pow.f64 (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) #s(literal 1 binary64)) #s(literal 3 binary64)))) (neg.f64 (fma.f64 #s(literal 0 binary64) (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 #s(literal 2 binary64) (.f64 #s(literal 1/2 binary64) eps))))) (.f64 (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) #s(literal 1 binary64)) (sin.f64 (-.f64 (.f64 #s(literal 1/2 binary64) eps) #s(literal 0 binary64)))))))
(/.f64 (neg.f64 (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (sin.f64 (.f64 eps #s(literal -1/2 binary64))))) (neg.f64 (sin.f64 (.f64 eps #s(literal -1/2 binary64)))))
(/.f64 (-.f64 (.f64 #s(literal 1 binary64) (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 #s(literal 2 binary64) (.f64 #s(literal 1/2 binary64) eps)))))) (.f64 #s(literal 0 binary64) (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 #s(literal 2 binary64) (.f64 #s(literal 1/2 binary64) eps))))))) (sin.f64 (-.f64 (*.f64 #s(literal 1/2 binary64) eps) #s(literal 0 binary64))))
(/.f64 (-.f64 (.f64 (.f64 #s(literal 0 binary64) (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 #s(literal 2 binary64) (.f64 #s(literal 1/2 binary64) eps)))))) (sin.f64 (.f64 eps #s(literal -1/2 binary64)))) (.f64 (sin.f64 (.f64 eps #s(literal -1/2 binary64))) (.f64 #s(literal 1 binary64) (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 #s(literal 2 binary64) (.f64 #s(literal 1/2 binary64) eps)))))))) (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 #s(literal 2 binary64) (*.f64 eps #s(literal -1/2 binary64)))))))
(pow.f64 (/.f64 (fma.f64 #s(literal 0 binary64) (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 #s(literal 2 binary64) (.f64 #s(literal 1/2 binary64) eps))))) (.f64 (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) #s(literal 1 binary64)) (sin.f64 (-.f64 (.f64 #s(literal 1/2 binary64) eps) #s(literal 0 binary64))))) (fma.f64 #s(literal 0 binary64) (pow.f64 (cos.f64 (.f64 #s(literal 1/2 binary64) eps)) #s(literal 3 binary64)) (pow.f64 (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) #s(literal 1 binary64)) #s(literal 3 binary64)))) #s(literal -1 binary64))
(pow.f64 (/.f64 (sin.f64 (.f64 eps #s(literal -1/2 binary64))) (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (sin.f64 (.f64 eps #s(literal -1/2 binary64))))) #s(literal -1 binary64))
(.f64 (fma.f64 #s(literal 0 binary64) (pow.f64 (cos.f64 (.f64 #s(literal 1/2 binary64) eps)) #s(literal 3 binary64)) (pow.f64 (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) #s(literal 1 binary64)) #s(literal 3 binary64))) (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal 0 binary64) (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 #s(literal 2 binary64) (.f64 #s(literal 1/2 binary64) eps))))) (.f64 (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) #s(literal 1 binary64)) (sin.f64 (-.f64 (*.f64 #s(literal 1/2 binary64) eps) #s(literal 0 binary64)))))))
(.f64 (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (sin.f64 (.f64 eps #s(literal -1/2 binary64)))) (/.f64 #s(literal 1 binary64) (sin.f64 (*.f64 eps #s(literal -1/2 binary64)))))
(+.f64 #s(literal 0 binary64) (*.f64 eps #s(literal 1/24 binary64)))
(+.f64 (*.f64 eps #s(literal 1/24 binary64)) #s(literal 0 binary64))
(fma.f64 eps #s(literal 1/24 binary64) #s(literal 0 binary64))
(fma.f64 #s(literal 1/24 binary64) eps #s(literal 0 binary64))
(/.f64 (.f64 eps (.f64 eps #s(literal 1/24 binary64))) eps)
(/.f64 (.f64 (.f64 eps (.f64 eps eps)) #s(literal 1/24 binary64)) (.f64 eps eps))
(/.f64 (.f64 #s(literal 1/24 binary64) (.f64 eps (.f64 eps eps))) (.f64 eps eps))
(*.f64 eps #s(literal 1/24 binary64))
(*.f64 #s(literal 1/24 binary64) eps)
(+.f64 #s(literal 0 binary64) (*.f64 eps #s(literal 1/6 binary64)))
(+.f64 (*.f64 eps #s(literal 1/6 binary64)) #s(literal 0 binary64))
(fma.f64 eps #s(literal 1/6 binary64) #s(literal 0 binary64))
(fma.f64 #s(literal 1/6 binary64) eps #s(literal 0 binary64))
(/.f64 (.f64 eps (.f64 eps #s(literal 1/6 binary64))) eps)
(/.f64 (.f64 #s(literal 1/6 binary64) (.f64 eps (.f64 eps eps))) (.f64 eps eps))
(/.f64 (.f64 (.f64 eps (.f64 eps eps)) #s(literal 1/6 binary64)) (.f64 eps eps))
(*.f64 eps #s(literal 1/6 binary64))
(*.f64 #s(literal 1/6 binary64) eps)
(*.f64 #s(literal 1/6 binary64) (sin.f64 x))
(*.f64 (sin.f64 x) #s(literal 1/6 binary64))

eval121.0ms (0.7%)

Memory: -4.0MiB live, 298.9MiB allocated
Compiler: Compiled 28 801 to 2 379 computations (91.7% saved)

prune180.0ms (1%)

Memory

-7.8MiB live, 404.3MiB allocated

Pruning

34 alts after pruning (29 fresh and 5 done)

	Pruned	Kept	Total
New	982	20	1 002
Fresh	4	9	13
Picked	2	3	5
Done	0	2	2
Total	988	34	1 022

Accuracy

100.0%

Counts

1 022 → 34

Alt Table

Click to see full alt table

Status	Accuracy	Program
	56.6%	(fma.f64 (*.f64 (cos.f64 (-.f64 x eps)) (cos.f64 (+.f64 x eps))) (/.f64 #s(literal 1 binary64) (cos.f64 (-.f64 x eps))) (neg.f64 (cos.f64 x)))
	56.8%	(fma.f64 (cos.f64 x) (cos.f64 eps) (neg.f64 (fma.f64 (sin.f64 x) (sin.f64 eps) (cos.f64 x))))
	56.6%	(/.f64 (/.f64 (-.f64 (fma.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 (+.f64 x eps) #s(literal 2 binary64))) #s(literal 1/2 binary64)) (fma.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64))) #s(literal 2 binary64)) (.f64 (cos.f64 (.f64 (+.f64 x (+.f64 x eps)) #s(literal 1/2 binary64))) (cos.f64 (.f64 (+.f64 eps #s(literal 0 binary64)) #s(literal 1/2 binary64)))))
✓	56.8%	(-.f64 (*.f64 (cos.f64 x) (cos.f64 eps)) (fma.f64 (sin.f64 x) (sin.f64 eps) (cos.f64 x)))
	56.6%	(-.f64 (.f64 (cos.f64 x) #s(approx (cos eps) (fma.f64 (.f64 eps eps) (fma.f64 (.f64 eps eps) (fma.f64 (.f64 eps eps) #s(literal -1/720 binary64) #s(literal 1/24 binary64)) #s(literal -1/2 binary64)) #s(literal 1 binary64)))) (fma.f64 (sin.f64 x) (sin.f64 eps) (cos.f64 x)))
✓	56.6%	(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))
✓	54.8%	(-.f64 (cos.f64 (+.f64 x eps)) #s(approx (cos x) #s(literal 1 binary64)))
	54.8%	(-.f64 #s(approx (cos (+ x eps)) (cos.f64 x)) #s(approx (cos x) #s(literal 1 binary64)))
	98.3%	(.f64 (.f64 (sin.f64 (.f64 (.f64 (.f64 eps eps) (/.f64 #s(literal 1 binary64) eps)) #s(literal 1/2 binary64))) (fma.f64 (sin.f64 (.f64 (+.f64 x x) #s(literal 1/2 binary64))) (cos.f64 (.f64 eps #s(literal 1/2 binary64))) (.f64 (cos.f64 (.f64 (+.f64 x x) #s(literal 1/2 binary64))) (sin.f64 (.f64 eps #s(literal 1/2 binary64)))))) #s(literal -2 binary64))
▶	99.8%	(.f64 #s(approx ( (sin (* (+ eps 0) 1/2)) (+ (* (sin (* (+ x x) 1/2)) (cos (* eps 1/2))) (* (cos (* (+ x x) 1/2)) (sin (* eps 1/2))))) (.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (fma.f64 (cos.f64 x) (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (.f64 (sin.f64 x) (cos.f64 (*.f64 eps #s(literal 1/2 binary64))))))) #s(literal -2 binary64))
	99.6%	(.f64 #s(approx ( (sin (* (+ eps 0) 1/2)) (sin (* (+ x (+ x eps)) 1/2))) (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x)))) #s(literal -2 binary64))
✓	99.3%	#s(approx (- (* (cos x) (cos eps)) (+ (* (sin x) (sin eps)) (cos x))) (.f64 eps (-.f64 (.f64 eps (fma.f64 eps (.f64 (sin.f64 x) #s(literal 1/6 binary64)) (.f64 (cos.f64 x) (fma.f64 eps (*.f64 eps #s(literal 1/24 binary64)) #s(literal -1/2 binary64))))) (sin.f64 x))))
▶	98.9%	#s(approx (- (* (cos x) (cos eps)) (+ (* (sin x) (sin eps)) (cos x))) (.f64 eps (-.f64 (.f64 eps (*.f64 #s(literal -1/2 binary64) (cos.f64 x))) (sin.f64 x))))
	98.2%	#s(approx (- (* (cos x) (cos eps)) (+ (* (sin x) (sin eps)) (cos x))) (.f64 eps (-.f64 #s(approx ( eps (+ (* eps (* (sin x) 1/6)) (* (cos x) (+ (* eps (* eps 1/24)) -1/2)))) (fma.f64 x (fma.f64 eps (.f64 eps #s(literal 1/6 binary64)) (.f64 eps (.f64 (.f64 x (fma.f64 eps (.f64 eps #s(literal 1/24 binary64)) #s(literal -1/2 binary64))) #s(literal -1/2 binary64)))) (.f64 eps (fma.f64 eps (*.f64 eps #s(literal 1/24 binary64)) #s(literal -1/2 binary64))))) (sin.f64 x))))
	98.4%	#s(approx (- (* (cos x) (cos eps)) (+ (* (sin x) (sin eps)) (cos x))) (.f64 eps (-.f64 #s(approx ( eps (+ (* eps (* (sin x) 1/6)) (* (cos x) (+ (* eps (* eps 1/24)) -1/2)))) (fma.f64 x (.f64 eps (.f64 eps #s(literal 1/6 binary64))) (.f64 eps (fma.f64 eps (.f64 eps #s(literal 1/24 binary64)) #s(literal -1/2 binary64))))) (sin.f64 x))))
	98.5%	#s(approx (- (* (cos x) (cos eps)) (+ (* (sin x) (sin eps)) (cos x))) (.f64 eps (-.f64 #s(approx ( eps (+ (* eps (* (sin x) 1/6)) (* (cos x) (+ (* eps (* eps 1/24)) -1/2)))) (.f64 eps (fma.f64 eps (.f64 eps #s(literal 1/24 binary64)) #s(literal -1/2 binary64)))) (sin.f64 x))))
	97.2%	#s(approx (- (* (cos x) (cos eps)) (+ (* (sin x) (sin eps)) (cos x))) (.f64 eps #s(approx (- ( eps (+ (* eps (* (sin x) 1/6)) (* (cos x) (+ (* eps (* eps 1/24)) -1/2)))) (sin x)) (fma.f64 x (fma.f64 eps (.f64 (.f64 x (fma.f64 eps (.f64 eps #s(literal 1/24 binary64)) #s(literal -1/2 binary64))) #s(literal -1/2 binary64)) (fma.f64 eps (.f64 eps #s(literal 1/6 binary64)) #s(literal -1 binary64))) (.f64 eps (fma.f64 eps (.f64 eps #s(literal 1/24 binary64)) #s(literal -1/2 binary64)))))))
	81.7%	#s(approx (- (* (cos x) (cos eps)) (+ (* (sin x) (sin eps)) (cos x))) (.f64 eps #s(approx (- ( eps (+ (* eps (* (sin x) 1/6)) (* (cos x) (+ (* eps (* eps 1/24)) -1/2)))) (sin x)) (sin.f64 (neg.f64 x)))))
	98.0%	#s(approx (- (* (cos x) (cos eps)) (+ (* (sin x) (sin eps)) (cos x))) #s(approx (* eps (- (* eps (+ (* eps (* (sin x) 1/6)) (* (cos x) (+ (* eps (* eps 1/24)) -1/2)))) (sin x))) (fma.f64 x (fma.f64 x (fma.f64 x (.f64 eps (fma.f64 (.f64 eps eps) #s(literal -1/36 binary64) #s(literal 1/6 binary64))) (.f64 #s(literal -1/2 binary64) (.f64 (.f64 eps eps) (fma.f64 eps (.f64 eps #s(literal 1/24 binary64)) #s(literal -1/2 binary64))))) (.f64 eps (fma.f64 eps (.f64 eps #s(literal 1/6 binary64)) #s(literal -1 binary64)))) (.f64 (.f64 eps eps) (fma.f64 eps (*.f64 eps #s(literal 1/24 binary64)) #s(literal -1/2 binary64))))))
	54.8%	#s(approx (- (cos (+ x eps)) (cos x)) (+.f64 #s(approx (cos eps) (fma.f64 eps (*.f64 eps #s(literal -1/2 binary64)) #s(literal 1 binary64))) #s(literal -1 binary64)))
✓	54.6%	#s(approx (- (cos (+ x eps)) (cos x)) (+.f64 #s(approx (cos eps) #s(literal 1 binary64)) #s(literal -1 binary64)))
▶	97.8%	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps #s(approx (+ ( eps (+ (* (cos x) (+ -1/2 (* eps (* eps 1/24)))) (* eps (* 1/6 (sin x))))) (sin (neg x))) (fma.f64 x (fma.f64 x (fma.f64 eps (.f64 (fma.f64 eps (.f64 eps #s(literal 1/24 binary64)) #s(literal -1/2 binary64)) #s(literal -1/2 binary64)) (.f64 x (fma.f64 (.f64 eps eps) #s(literal -1/36 binary64) #s(literal 1/6 binary64)))) (fma.f64 eps (.f64 eps #s(literal 1/6 binary64)) #s(literal -1 binary64))) (.f64 eps (fma.f64 eps (*.f64 eps #s(literal 1/24 binary64)) #s(literal -1/2 binary64)))))))
	55.9%	#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (+ (cos eps) -1) (.f64 eps (.f64 eps #s(literal -1/2 binary64)))))
	97.3%	#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* eps (+ (* eps (+ (* (cos x) (+ -1/2 (* eps (* eps 1/24)))) (* eps (* 1/6 (sin x))))) (sin (neg x)))) (fma.f64 (.f64 x (fma.f64 eps (.f64 eps #s(literal 1/6 binary64)) #s(literal -1 binary64))) eps (.f64 eps (.f64 eps (fma.f64 #s(literal 1/24 binary64) (*.f64 eps eps) #s(literal -1/2 binary64)))))))
	97.2%	#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* eps (+ (* eps (+ (* (cos x) (+ -1/2 (* eps (* eps 1/24)))) (* eps (* 1/6 (sin x))))) (sin (neg x)))) (fma.f64 eps #s(approx (* eps (+ (* eps (* eps 1/24)) -1/2)) (.f64 eps #s(literal -1/2 binary64))) (.f64 eps (.f64 x (fma.f64 eps (.f64 eps #s(literal 1/6 binary64)) #s(literal -1 binary64)))))))
▶	54.6%	#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* eps (+ (* eps (+ (* (cos x) (+ -1/2 (* eps (* eps 1/24)))) (* eps (* 1/6 (sin x))))) (sin (neg x)))) #s(approx (+ (* eps (* eps (+ (* eps (* eps 1/24)) -1/2))) (* eps (* x (+ (* eps (* eps 1/6)) -1)))) (.f64 (.f64 (.f64 eps eps) (.f64 eps eps)) (fma.f64 x (/.f64 #s(literal 1/6 binary64) eps) #s(literal 1/24 binary64))))))
	22.2%	#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* eps (+ (* eps (+ (* (cos x) (+ -1/2 (* eps (* eps 1/24)))) (* eps (* 1/6 (sin x))))) (sin (neg x)))) #s(approx (+ (* eps (* eps (+ (* eps (* eps 1/24)) -1/2))) (* eps (* x (+ (* eps (* eps 1/6)) -1)))) (.f64 (.f64 (.f64 eps eps) (.f64 eps eps)) (-.f64 #s(literal 1/24 binary64) (/.f64 (fma.f64 x #s(literal -1/6 binary64) (/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 x eps)) eps)) eps))))))
	3.4%	#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* eps (+ (* eps (+ (* (cos x) (+ -1/2 (* eps (* eps 1/24)))) (* eps (* 1/6 (sin x))))) (sin (neg x)))) #s(approx (+ (* eps (* eps (+ (* eps (* eps 1/24)) -1/2))) (* eps (* x (+ (* eps (* eps 1/6)) -1)))) (.f64 (.f64 (.f64 eps eps) (.f64 eps eps)) (-.f64 #s(literal 1/24 binary64) (/.f64 (fma.f64 x #s(literal -1/6 binary64) (/.f64 #s(literal 1/2 binary64) eps)) eps))))))
	21.3%	#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* eps (+ (* eps (+ (* (cos x) (+ -1/2 (* eps (* eps 1/24)))) (* eps (* 1/6 (sin x))))) (sin (neg x)))) #s(approx (+ (* eps (* eps (+ (* eps (* eps 1/24)) -1/2))) (* eps (* x (+ (* eps (* eps 1/6)) -1)))) (.f64 (.f64 (.f64 eps eps) (.f64 eps eps)) (+.f64 (fma.f64 x (/.f64 #s(literal 1/6 binary64) eps) (-.f64 #s(literal 1/24 binary64) (/.f64 x (.f64 eps (.f64 eps eps))))) (/.f64 #s(literal -1/2 binary64) (*.f64 eps eps)))))))
	3.4%	#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* eps (+ (* eps (+ (* (cos x) (+ -1/2 (* eps (* eps 1/24)))) (* eps (* 1/6 (sin x))))) (sin (neg x)))) #s(approx (+ (* eps (* eps (+ (* eps (* eps 1/24)) -1/2))) (* eps (* x (+ (* eps (* eps 1/6)) -1)))) (.f64 (.f64 (.f64 eps eps) (.f64 eps eps)) (+.f64 #s(literal 1/24 binary64) (fma.f64 x (/.f64 #s(literal 1/6 binary64) eps) (/.f64 #s(literal -1/2 binary64) (*.f64 eps eps))))))))
▶	80.8%	#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* eps (+ (* eps (+ (* (cos x) (+ -1/2 (* eps (* eps 1/24)))) (* eps (* 1/6 (sin x))))) (sin (neg x)))) #s(approx (+ (* eps (* eps (+ (* eps (* eps 1/24)) -1/2))) (* eps (* x (+ (* eps (* eps 1/6)) -1)))) (*.f64 x (neg.f64 eps)))))
	97.2%	#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* eps (+ (* eps (+ (* (cos x) (+ -1/2 (* eps (* eps 1/24)))) (* eps (* 1/6 (sin x))))) (sin (neg x)))) #s(approx (+ (* eps (* eps (+ (* eps (* eps 1/24)) -1/2))) (* eps (* x (+ (* eps (* eps 1/6)) -1)))) (.f64 eps (fma.f64 eps (fma.f64 x (.f64 eps #s(literal 1/6 binary64)) #s(literal -1/2 binary64)) (neg.f64 x))))))
	97.2%	#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* eps (+ (* eps (+ (* (cos x) (+ -1/2 (* eps (* eps 1/24)))) (* eps (* 1/6 (sin x))))) (sin (neg x)))) #s(approx (+ (* eps (* eps (+ (* eps (* eps 1/24)) -1/2))) (* eps (* x (+ (* eps (* eps 1/6)) -1)))) (.f64 eps (-.f64 (.f64 eps #s(literal -1/2 binary64)) x)))))
	54.8%	#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* eps (+ (* eps (+ (* (cos x) (+ -1/2 (* eps (* eps 1/24)))) (* eps (* 1/6 (sin x))))) (sin (neg x)))) #s(approx (+ (* eps (* eps (+ (* eps (* eps 1/24)) -1/2))) (* eps (* x (+ (* eps (* eps 1/6)) -1)))) (.f64 #s(literal 1/24 binary64) (.f64 (.f64 eps eps) (.f64 eps eps))))))

Compiler

Compiled 1 375 to 729 computations (47% saved)

simplify256.0ms (1.4%)

Memory

28.9MiB live, 296.4MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 20 expressions of interest:

New	Metric	Score
cost-diff	0	(.f64 eps (.f64 #s(literal -1/2 binary64) (cos.f64 x)))
cost-diff	0	(-.f64 (.f64 eps (.f64 #s(literal -1/2 binary64) (cos.f64 x))) (sin.f64 x))
cost-diff	0	(.f64 eps (-.f64 (.f64 eps (*.f64 #s(literal -1/2 binary64) (cos.f64 x))) (sin.f64 x)))
cost-diff	0	#s(approx (- (* (cos x) (cos eps)) (+ (* (sin x) (sin eps)) (cos x))) (.f64 eps (-.f64 (.f64 eps (*.f64 #s(literal -1/2 binary64) (cos.f64 x))) (sin.f64 x))))
cost-diff	0	(.f64 eps #s(approx (+ ( eps (+ (* (cos x) (+ -1/2 (* eps (* eps 1/24)))) (* eps (* 1/6 (sin x))))) (sin (neg x))) (fma.f64 x (fma.f64 x (fma.f64 eps (.f64 (fma.f64 eps (.f64 eps #s(literal 1/24 binary64)) #s(literal -1/2 binary64)) #s(literal -1/2 binary64)) (.f64 x (fma.f64 (.f64 eps eps) #s(literal -1/36 binary64) #s(literal 1/6 binary64)))) (fma.f64 eps (.f64 eps #s(literal 1/6 binary64)) #s(literal -1 binary64))) (.f64 eps (fma.f64 eps (*.f64 eps #s(literal 1/24 binary64)) #s(literal -1/2 binary64))))))
cost-diff	0	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps #s(approx (+ ( eps (+ (* (cos x) (+ -1/2 (* eps (* eps 1/24)))) (* eps (* 1/6 (sin x))))) (sin (neg x))) (fma.f64 x (fma.f64 x (fma.f64 eps (.f64 (fma.f64 eps (.f64 eps #s(literal 1/24 binary64)) #s(literal -1/2 binary64)) #s(literal -1/2 binary64)) (.f64 x (fma.f64 (.f64 eps eps) #s(literal -1/36 binary64) #s(literal 1/6 binary64)))) (fma.f64 eps (.f64 eps #s(literal 1/6 binary64)) #s(literal -1 binary64))) (.f64 eps (fma.f64 eps (*.f64 eps #s(literal 1/24 binary64)) #s(literal -1/2 binary64)))))))
cost-diff	320	(.f64 (fma.f64 eps (.f64 eps #s(literal 1/24 binary64)) #s(literal -1/2 binary64)) #s(literal -1/2 binary64))
cost-diff	320	(fma.f64 x (fma.f64 x (fma.f64 eps (.f64 (fma.f64 eps (.f64 eps #s(literal 1/24 binary64)) #s(literal -1/2 binary64)) #s(literal -1/2 binary64)) (.f64 x (fma.f64 (.f64 eps eps) #s(literal -1/36 binary64) #s(literal 1/6 binary64)))) (fma.f64 eps (.f64 eps #s(literal 1/6 binary64)) #s(literal -1 binary64))) (.f64 eps (fma.f64 eps (*.f64 eps #s(literal 1/24 binary64)) #s(literal -1/2 binary64))))
cost-diff	0	#s(approx (+ (* eps (* eps (+ (* eps (* eps 1/24)) -1/2))) (* eps (* x (+ (* eps (* eps 1/6)) -1)))) (.f64 (.f64 (.f64 eps eps) (.f64 eps eps)) (fma.f64 x (/.f64 #s(literal 1/6 binary64) eps) #s(literal 1/24 binary64))))
cost-diff	0	#s(approx (* eps (+ (* eps (+ (* (cos x) (+ -1/2 (* eps (* eps 1/24)))) (* eps (* 1/6 (sin x))))) (sin (neg x)))) #s(approx (+ (* eps (* eps (+ (* eps (* eps 1/24)) -1/2))) (* eps (* x (+ (* eps (* eps 1/6)) -1)))) (.f64 (.f64 (.f64 eps eps) (.f64 eps eps)) (fma.f64 x (/.f64 #s(literal 1/6 binary64) eps) #s(literal 1/24 binary64)))))
cost-diff	0	#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* eps (+ (* eps (+ (* (cos x) (+ -1/2 (* eps (* eps 1/24)))) (* eps (* 1/6 (sin x))))) (sin (neg x)))) #s(approx (+ (* eps (* eps (+ (* eps (* eps 1/24)) -1/2))) (* eps (* x (+ (* eps (* eps 1/6)) -1)))) (.f64 (.f64 (.f64 eps eps) (.f64 eps eps)) (fma.f64 x (/.f64 #s(literal 1/6 binary64) eps) #s(literal 1/24 binary64))))))
cost-diff	704	(.f64 (.f64 (.f64 eps eps) (.f64 eps eps)) (fma.f64 x (/.f64 #s(literal 1/6 binary64) eps) #s(literal 1/24 binary64)))
cost-diff	0	(*.f64 x (neg.f64 eps))
cost-diff	0	#s(approx (+ (* eps (* eps (+ (* eps (* eps 1/24)) -1/2))) (* eps (* x (+ (* eps (* eps 1/6)) -1)))) (*.f64 x (neg.f64 eps)))
cost-diff	0	#s(approx (* eps (+ (* eps (+ (* (cos x) (+ -1/2 (* eps (* eps 1/24)))) (* eps (* 1/6 (sin x))))) (sin (neg x)))) #s(approx (+ (* eps (* eps (+ (* eps (* eps 1/24)) -1/2))) (* eps (* x (+ (* eps (* eps 1/6)) -1)))) (*.f64 x (neg.f64 eps))))
cost-diff	0	#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* eps (+ (* eps (+ (* (cos x) (+ -1/2 (* eps (* eps 1/24)))) (* eps (* 1/6 (sin x))))) (sin (neg x)))) #s(approx (+ (* eps (* eps (+ (* eps (* eps 1/24)) -1/2))) (* eps (* x (+ (* eps (* eps 1/6)) -1)))) (*.f64 x (neg.f64 eps)))))
cost-diff	0	(sin.f64 (*.f64 eps #s(literal 1/2 binary64)))
cost-diff	0	(.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (fma.f64 (cos.f64 x) (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (.f64 (sin.f64 x) (cos.f64 (*.f64 eps #s(literal 1/2 binary64))))))
cost-diff	0	#s(approx (* (sin (* (+ eps 0) 1/2)) (+ (* (sin (* (+ x x) 1/2)) (cos (* eps 1/2))) (* (cos (* (+ x x) 1/2)) (sin (* eps 1/2))))) (.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (fma.f64 (cos.f64 x) (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (.f64 (sin.f64 x) (cos.f64 (*.f64 eps #s(literal 1/2 binary64)))))))
cost-diff	0	(.f64 #s(approx ( (sin (* (+ eps 0) 1/2)) (+ (* (sin (* (+ x x) 1/2)) (cos (* eps 1/2))) (* (cos (* (+ x x) 1/2)) (sin (* eps 1/2))))) (.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (fma.f64 (cos.f64 x) (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (.f64 (sin.f64 x) (cos.f64 (*.f64 eps #s(literal 1/2 binary64))))))) #s(literal -2 binary64))

Rules

17 580×	`lower-fma.f32`
17 564×	`lower-fma.f64`
4 008×	`lower-*.f32`
3 974×	`lower-*.f64`
3 116×	`lower-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	98	905
0	142	891
1	300	862
2	924	824
3	2666	823
4	3602	817
5	6229	817
0	8076	783

Stop Event

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

Calls

Call 1

Inputs
(.f64 #s(approx ( (sin (* (+ eps 0) 1/2)) (+ (* (sin (* (+ x x) 1/2)) (cos (* eps 1/2))) (* (cos (* (+ x x) 1/2)) (sin (* eps 1/2))))) (.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (fma.f64 (cos.f64 x) (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (.f64 (sin.f64 x) (cos.f64 (*.f64 eps #s(literal 1/2 binary64))))))) #s(literal -2 binary64))
#s(approx (* (sin (* (+ eps 0) 1/2)) (+ (* (sin (* (+ x x) 1/2)) (cos (* eps 1/2))) (* (cos (* (+ x x) 1/2)) (sin (* eps 1/2))))) (.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (fma.f64 (cos.f64 x) (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (.f64 (sin.f64 x) (cos.f64 (*.f64 eps #s(literal 1/2 binary64)))))))
(.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (fma.f64 (cos.f64 x) (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (.f64 (sin.f64 x) (cos.f64 (*.f64 eps #s(literal 1/2 binary64))))))
(sin.f64 (*.f64 eps #s(literal 1/2 binary64)))
(*.f64 eps #s(literal 1/2 binary64))
eps
#s(literal 1/2 binary64)
(fma.f64 (cos.f64 x) (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (.f64 (sin.f64 x) (cos.f64 (*.f64 eps #s(literal 1/2 binary64)))))
(cos.f64 x)
x
(.f64 (sin.f64 x) (cos.f64 (.f64 eps #s(literal 1/2 binary64))))
(sin.f64 x)
(cos.f64 (*.f64 eps #s(literal 1/2 binary64)))
#s(literal -2 binary64)
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* eps (+ (* eps (+ (* (cos x) (+ -1/2 (* eps (* eps 1/24)))) (* eps (* 1/6 (sin x))))) (sin (neg x)))) #s(approx (+ (* eps (* eps (+ (* eps (* eps 1/24)) -1/2))) (* eps (* x (+ (* eps (* eps 1/6)) -1)))) (*.f64 x (neg.f64 eps)))))
#s(approx (* eps (+ (* eps (+ (* (cos x) (+ -1/2 (* eps (* eps 1/24)))) (* eps (* 1/6 (sin x))))) (sin (neg x)))) #s(approx (+ (* eps (* eps (+ (* eps (* eps 1/24)) -1/2))) (* eps (* x (+ (* eps (* eps 1/6)) -1)))) (*.f64 x (neg.f64 eps))))
#s(approx (+ (* eps (* eps (+ (* eps (* eps 1/24)) -1/2))) (* eps (* x (+ (* eps (* eps 1/6)) -1)))) (*.f64 x (neg.f64 eps)))
(*.f64 x (neg.f64 eps))
x
(neg.f64 eps)
eps
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* eps (+ (* eps (+ (* (cos x) (+ -1/2 (* eps (* eps 1/24)))) (* eps (* 1/6 (sin x))))) (sin (neg x)))) #s(approx (+ (* eps (* eps (+ (* eps (* eps 1/24)) -1/2))) (* eps (* x (+ (* eps (* eps 1/6)) -1)))) (.f64 (.f64 (.f64 eps eps) (.f64 eps eps)) (fma.f64 x (/.f64 #s(literal 1/6 binary64) eps) #s(literal 1/24 binary64))))))
#s(approx (* eps (+ (* eps (+ (* (cos x) (+ -1/2 (* eps (* eps 1/24)))) (* eps (* 1/6 (sin x))))) (sin (neg x)))) #s(approx (+ (* eps (* eps (+ (* eps (* eps 1/24)) -1/2))) (* eps (* x (+ (* eps (* eps 1/6)) -1)))) (.f64 (.f64 (.f64 eps eps) (.f64 eps eps)) (fma.f64 x (/.f64 #s(literal 1/6 binary64) eps) #s(literal 1/24 binary64)))))
#s(approx (+ (* eps (* eps (+ (* eps (* eps 1/24)) -1/2))) (* eps (* x (+ (* eps (* eps 1/6)) -1)))) (.f64 (.f64 (.f64 eps eps) (.f64 eps eps)) (fma.f64 x (/.f64 #s(literal 1/6 binary64) eps) #s(literal 1/24 binary64))))
(.f64 (.f64 (.f64 eps eps) (.f64 eps eps)) (fma.f64 x (/.f64 #s(literal 1/6 binary64) eps) #s(literal 1/24 binary64)))
(.f64 (.f64 eps eps) (*.f64 eps eps))
(*.f64 eps eps)
eps
(fma.f64 x (/.f64 #s(literal 1/6 binary64) eps) #s(literal 1/24 binary64))
x
(/.f64 #s(literal 1/6 binary64) eps)
#s(literal 1/6 binary64)
#s(literal 1/24 binary64)
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps #s(approx (+ ( eps (+ (* (cos x) (+ -1/2 (* eps (* eps 1/24)))) (* eps (* 1/6 (sin x))))) (sin (neg x))) (fma.f64 x (fma.f64 x (fma.f64 eps (.f64 (fma.f64 eps (.f64 eps #s(literal 1/24 binary64)) #s(literal -1/2 binary64)) #s(literal -1/2 binary64)) (.f64 x (fma.f64 (.f64 eps eps) #s(literal -1/36 binary64) #s(literal 1/6 binary64)))) (fma.f64 eps (.f64 eps #s(literal 1/6 binary64)) #s(literal -1 binary64))) (.f64 eps (fma.f64 eps (*.f64 eps #s(literal 1/24 binary64)) #s(literal -1/2 binary64)))))))
(.f64 eps #s(approx (+ ( eps (+ (* (cos x) (+ -1/2 (* eps (* eps 1/24)))) (* eps (* 1/6 (sin x))))) (sin (neg x))) (fma.f64 x (fma.f64 x (fma.f64 eps (.f64 (fma.f64 eps (.f64 eps #s(literal 1/24 binary64)) #s(literal -1/2 binary64)) #s(literal -1/2 binary64)) (.f64 x (fma.f64 (.f64 eps eps) #s(literal -1/36 binary64) #s(literal 1/6 binary64)))) (fma.f64 eps (.f64 eps #s(literal 1/6 binary64)) #s(literal -1 binary64))) (.f64 eps (fma.f64 eps (*.f64 eps #s(literal 1/24 binary64)) #s(literal -1/2 binary64))))))
eps
#s(approx (+ (* eps (+ (* (cos x) (+ -1/2 (* eps (* eps 1/24)))) (* eps (* 1/6 (sin x))))) (sin (neg x))) (fma.f64 x (fma.f64 x (fma.f64 eps (.f64 (fma.f64 eps (.f64 eps #s(literal 1/24 binary64)) #s(literal -1/2 binary64)) #s(literal -1/2 binary64)) (.f64 x (fma.f64 (.f64 eps eps) #s(literal -1/36 binary64) #s(literal 1/6 binary64)))) (fma.f64 eps (.f64 eps #s(literal 1/6 binary64)) #s(literal -1 binary64))) (.f64 eps (fma.f64 eps (*.f64 eps #s(literal 1/24 binary64)) #s(literal -1/2 binary64)))))
(fma.f64 x (fma.f64 x (fma.f64 eps (.f64 (fma.f64 eps (.f64 eps #s(literal 1/24 binary64)) #s(literal -1/2 binary64)) #s(literal -1/2 binary64)) (.f64 x (fma.f64 (.f64 eps eps) #s(literal -1/36 binary64) #s(literal 1/6 binary64)))) (fma.f64 eps (.f64 eps #s(literal 1/6 binary64)) #s(literal -1 binary64))) (.f64 eps (fma.f64 eps (*.f64 eps #s(literal 1/24 binary64)) #s(literal -1/2 binary64))))
x
(fma.f64 x (fma.f64 eps (.f64 (fma.f64 eps (.f64 eps #s(literal 1/24 binary64)) #s(literal -1/2 binary64)) #s(literal -1/2 binary64)) (.f64 x (fma.f64 (.f64 eps eps) #s(literal -1/36 binary64) #s(literal 1/6 binary64)))) (fma.f64 eps (*.f64 eps #s(literal 1/6 binary64)) #s(literal -1 binary64)))
(fma.f64 eps (.f64 (fma.f64 eps (.f64 eps #s(literal 1/24 binary64)) #s(literal -1/2 binary64)) #s(literal -1/2 binary64)) (.f64 x (fma.f64 (.f64 eps eps) #s(literal -1/36 binary64) #s(literal 1/6 binary64))))
(.f64 (fma.f64 eps (.f64 eps #s(literal 1/24 binary64)) #s(literal -1/2 binary64)) #s(literal -1/2 binary64))
(fma.f64 eps (*.f64 eps #s(literal 1/24 binary64)) #s(literal -1/2 binary64))
(*.f64 eps #s(literal 1/24 binary64))
#s(literal 1/24 binary64)
#s(literal -1/2 binary64)
(.f64 x (fma.f64 (.f64 eps eps) #s(literal -1/36 binary64) #s(literal 1/6 binary64)))
(fma.f64 (*.f64 eps eps) #s(literal -1/36 binary64) #s(literal 1/6 binary64))
(*.f64 eps eps)
#s(literal -1/36 binary64)
#s(literal 1/6 binary64)
(fma.f64 eps (*.f64 eps #s(literal 1/6 binary64)) #s(literal -1 binary64))
(*.f64 eps #s(literal 1/6 binary64))
#s(literal -1 binary64)
(.f64 eps (fma.f64 eps (.f64 eps #s(literal 1/24 binary64)) #s(literal -1/2 binary64)))
#s(approx (- (* (cos x) (cos eps)) (+ (* (sin x) (sin eps)) (cos x))) (.f64 eps (-.f64 (.f64 eps (*.f64 #s(literal -1/2 binary64) (cos.f64 x))) (sin.f64 x))))
(.f64 eps (-.f64 (.f64 eps (*.f64 #s(literal -1/2 binary64) (cos.f64 x))) (sin.f64 x)))
eps
(-.f64 (.f64 eps (.f64 #s(literal -1/2 binary64) (cos.f64 x))) (sin.f64 x))
(.f64 eps (.f64 #s(literal -1/2 binary64) (cos.f64 x)))
(*.f64 #s(literal -1/2 binary64) (cos.f64 x))
#s(literal -1/2 binary64)
(cos.f64 x)
x
(sin.f64 x)

Outputs
(.f64 #s(approx ( (sin (* (+ eps 0) 1/2)) (+ (* (sin (* (+ x x) 1/2)) (cos (* eps 1/2))) (* (cos (* (+ x x) 1/2)) (sin (* eps 1/2))))) (.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (fma.f64 (cos.f64 x) (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (.f64 (sin.f64 x) (cos.f64 (*.f64 eps #s(literal 1/2 binary64))))))) #s(literal -2 binary64))
(.f64 #s(approx ( (sin (* (+ eps 0) 1/2)) (+ (* (sin (* (+ x x) 1/2)) (cos (* eps 1/2))) (* (cos (* (+ x x) 1/2)) (sin (* eps 1/2))))) (.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (fma.f64 (sin.f64 x) (cos.f64 (.f64 eps #s(literal 1/2 binary64))) (.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) (cos.f64 x))))) #s(literal -2 binary64))
#s(approx (* (sin (* (+ eps 0) 1/2)) (+ (* (sin (* (+ x x) 1/2)) (cos (* eps 1/2))) (* (cos (* (+ x x) 1/2)) (sin (* eps 1/2))))) (.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (fma.f64 (cos.f64 x) (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (.f64 (sin.f64 x) (cos.f64 (*.f64 eps #s(literal 1/2 binary64)))))))
#s(approx (* (sin (* (+ eps 0) 1/2)) (+ (* (sin (* (+ x x) 1/2)) (cos (* eps 1/2))) (* (cos (* (+ x x) 1/2)) (sin (* eps 1/2))))) (.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (fma.f64 (sin.f64 x) (cos.f64 (.f64 eps #s(literal 1/2 binary64))) (.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) (cos.f64 x)))))
(.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (fma.f64 (cos.f64 x) (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (.f64 (sin.f64 x) (cos.f64 (*.f64 eps #s(literal 1/2 binary64))))))
(.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (fma.f64 (sin.f64 x) (cos.f64 (.f64 eps #s(literal 1/2 binary64))) (.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) (cos.f64 x))))
(sin.f64 (*.f64 eps #s(literal 1/2 binary64)))
(*.f64 eps #s(literal 1/2 binary64))
eps
#s(literal 1/2 binary64)
(fma.f64 (cos.f64 x) (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (.f64 (sin.f64 x) (cos.f64 (*.f64 eps #s(literal 1/2 binary64)))))
(fma.f64 (sin.f64 x) (cos.f64 (.f64 eps #s(literal 1/2 binary64))) (.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) (cos.f64 x)))
(cos.f64 x)
x
(.f64 (sin.f64 x) (cos.f64 (.f64 eps #s(literal 1/2 binary64))))
(sin.f64 x)
(cos.f64 (*.f64 eps #s(literal 1/2 binary64)))
#s(literal -2 binary64)
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* eps (+ (* eps (+ (* (cos x) (+ -1/2 (* eps (* eps 1/24)))) (* eps (* 1/6 (sin x))))) (sin (neg x)))) #s(approx (+ (* eps (* eps (+ (* eps (* eps 1/24)) -1/2))) (* eps (* x (+ (* eps (* eps 1/6)) -1)))) (*.f64 x (neg.f64 eps)))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* eps (+ (* eps (+ (* (cos x) (+ -1/2 (* eps (* eps 1/24)))) (* eps (* 1/6 (sin x))))) (sin (neg x)))) #s(approx (+ (* eps (* eps (+ (* eps (* eps 1/24)) -1/2))) (* eps (* x (+ (* eps (* eps 1/6)) -1)))) (*.f64 eps (neg.f64 x)))))
#s(approx (* eps (+ (* eps (+ (* (cos x) (+ -1/2 (* eps (* eps 1/24)))) (* eps (* 1/6 (sin x))))) (sin (neg x)))) #s(approx (+ (* eps (* eps (+ (* eps (* eps 1/24)) -1/2))) (* eps (* x (+ (* eps (* eps 1/6)) -1)))) (*.f64 x (neg.f64 eps))))
#s(approx (* eps (+ (* eps (+ (* (cos x) (+ -1/2 (* eps (* eps 1/24)))) (* eps (* 1/6 (sin x))))) (sin (neg x)))) #s(approx (+ (* eps (* eps (+ (* eps (* eps 1/24)) -1/2))) (* eps (* x (+ (* eps (* eps 1/6)) -1)))) (*.f64 eps (neg.f64 x))))
#s(approx (+ (* eps (* eps (+ (* eps (* eps 1/24)) -1/2))) (* eps (* x (+ (* eps (* eps 1/6)) -1)))) (*.f64 x (neg.f64 eps)))
#s(approx (+ (* eps (* eps (+ (* eps (* eps 1/24)) -1/2))) (* eps (* x (+ (* eps (* eps 1/6)) -1)))) (*.f64 eps (neg.f64 x)))
(*.f64 x (neg.f64 eps))
(*.f64 eps (neg.f64 x))
x
(neg.f64 eps)
eps
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* eps (+ (* eps (+ (* (cos x) (+ -1/2 (* eps (* eps 1/24)))) (* eps (* 1/6 (sin x))))) (sin (neg x)))) #s(approx (+ (* eps (* eps (+ (* eps (* eps 1/24)) -1/2))) (* eps (* x (+ (* eps (* eps 1/6)) -1)))) (.f64 (.f64 (.f64 eps eps) (.f64 eps eps)) (fma.f64 x (/.f64 #s(literal 1/6 binary64) eps) #s(literal 1/24 binary64))))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* eps (+ (* eps (+ (* (cos x) (+ -1/2 (* eps (* eps 1/24)))) (* eps (* 1/6 (sin x))))) (sin (neg x)))) #s(approx (+ (* eps (* eps (+ (* eps (* eps 1/24)) -1/2))) (* eps (* x (+ (* eps (* eps 1/6)) -1)))) (.f64 (.f64 eps eps) (.f64 eps (fma.f64 eps #s(literal 1/24 binary64) (.f64 x #s(literal 1/6 binary64))))))))
#s(approx (* eps (+ (* eps (+ (* (cos x) (+ -1/2 (* eps (* eps 1/24)))) (* eps (* 1/6 (sin x))))) (sin (neg x)))) #s(approx (+ (* eps (* eps (+ (* eps (* eps 1/24)) -1/2))) (* eps (* x (+ (* eps (* eps 1/6)) -1)))) (.f64 (.f64 (.f64 eps eps) (.f64 eps eps)) (fma.f64 x (/.f64 #s(literal 1/6 binary64) eps) #s(literal 1/24 binary64)))))
#s(approx (* eps (+ (* eps (+ (* (cos x) (+ -1/2 (* eps (* eps 1/24)))) (* eps (* 1/6 (sin x))))) (sin (neg x)))) #s(approx (+ (* eps (* eps (+ (* eps (* eps 1/24)) -1/2))) (* eps (* x (+ (* eps (* eps 1/6)) -1)))) (.f64 (.f64 eps eps) (.f64 eps (fma.f64 eps #s(literal 1/24 binary64) (.f64 x #s(literal 1/6 binary64)))))))
#s(approx (+ (* eps (* eps (+ (* eps (* eps 1/24)) -1/2))) (* eps (* x (+ (* eps (* eps 1/6)) -1)))) (.f64 (.f64 (.f64 eps eps) (.f64 eps eps)) (fma.f64 x (/.f64 #s(literal 1/6 binary64) eps) #s(literal 1/24 binary64))))
#s(approx (+ (* eps (* eps (+ (* eps (* eps 1/24)) -1/2))) (* eps (* x (+ (* eps (* eps 1/6)) -1)))) (.f64 (.f64 eps eps) (.f64 eps (fma.f64 eps #s(literal 1/24 binary64) (.f64 x #s(literal 1/6 binary64))))))
(.f64 (.f64 (.f64 eps eps) (.f64 eps eps)) (fma.f64 x (/.f64 #s(literal 1/6 binary64) eps) #s(literal 1/24 binary64)))
(.f64 (.f64 eps eps) (.f64 eps (fma.f64 eps #s(literal 1/24 binary64) (.f64 x #s(literal 1/6 binary64)))))
(.f64 (.f64 eps eps) (*.f64 eps eps))
(.f64 eps (.f64 eps (*.f64 eps eps)))
(*.f64 eps eps)
eps
(fma.f64 x (/.f64 #s(literal 1/6 binary64) eps) #s(literal 1/24 binary64))
x
(/.f64 #s(literal 1/6 binary64) eps)
#s(literal 1/6 binary64)
#s(literal 1/24 binary64)
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps #s(approx (+ ( eps (+ (* (cos x) (+ -1/2 (* eps (* eps 1/24)))) (* eps (* 1/6 (sin x))))) (sin (neg x))) (fma.f64 x (fma.f64 x (fma.f64 eps (.f64 (fma.f64 eps (.f64 eps #s(literal 1/24 binary64)) #s(literal -1/2 binary64)) #s(literal -1/2 binary64)) (.f64 x (fma.f64 (.f64 eps eps) #s(literal -1/36 binary64) #s(literal 1/6 binary64)))) (fma.f64 eps (.f64 eps #s(literal 1/6 binary64)) #s(literal -1 binary64))) (.f64 eps (fma.f64 eps (*.f64 eps #s(literal 1/24 binary64)) #s(literal -1/2 binary64)))))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps #s(approx (+ ( eps (+ (* (cos x) (+ -1/2 (* eps (* eps 1/24)))) (* eps (* 1/6 (sin x))))) (sin (neg x))) (fma.f64 eps (fma.f64 eps (fma.f64 eps #s(literal 1/24 binary64) (.f64 x #s(literal 1/6 binary64))) #s(literal -1/2 binary64)) (.f64 x (fma.f64 x (fma.f64 eps (fma.f64 (.f64 eps eps) #s(literal -1/48 binary64) #s(literal 1/4 binary64)) (.f64 x (fma.f64 (*.f64 eps eps) #s(literal -1/36 binary64) #s(literal 1/6 binary64)))) #s(literal -1 binary64)))))))
(.f64 eps #s(approx (+ ( eps (+ (* (cos x) (+ -1/2 (* eps (* eps 1/24)))) (* eps (* 1/6 (sin x))))) (sin (neg x))) (fma.f64 x (fma.f64 x (fma.f64 eps (.f64 (fma.f64 eps (.f64 eps #s(literal 1/24 binary64)) #s(literal -1/2 binary64)) #s(literal -1/2 binary64)) (.f64 x (fma.f64 (.f64 eps eps) #s(literal -1/36 binary64) #s(literal 1/6 binary64)))) (fma.f64 eps (.f64 eps #s(literal 1/6 binary64)) #s(literal -1 binary64))) (.f64 eps (fma.f64 eps (*.f64 eps #s(literal 1/24 binary64)) #s(literal -1/2 binary64))))))
(.f64 eps #s(approx (+ ( eps (+ (* (cos x) (+ -1/2 (* eps (* eps 1/24)))) (* eps (* 1/6 (sin x))))) (sin (neg x))) (fma.f64 eps (fma.f64 eps (fma.f64 eps #s(literal 1/24 binary64) (.f64 x #s(literal 1/6 binary64))) #s(literal -1/2 binary64)) (.f64 x (fma.f64 x (fma.f64 eps (fma.f64 (.f64 eps eps) #s(literal -1/48 binary64) #s(literal 1/4 binary64)) (.f64 x (fma.f64 (*.f64 eps eps) #s(literal -1/36 binary64) #s(literal 1/6 binary64)))) #s(literal -1 binary64))))))
eps
#s(approx (+ (* eps (+ (* (cos x) (+ -1/2 (* eps (* eps 1/24)))) (* eps (* 1/6 (sin x))))) (sin (neg x))) (fma.f64 x (fma.f64 x (fma.f64 eps (.f64 (fma.f64 eps (.f64 eps #s(literal 1/24 binary64)) #s(literal -1/2 binary64)) #s(literal -1/2 binary64)) (.f64 x (fma.f64 (.f64 eps eps) #s(literal -1/36 binary64) #s(literal 1/6 binary64)))) (fma.f64 eps (.f64 eps #s(literal 1/6 binary64)) #s(literal -1 binary64))) (.f64 eps (fma.f64 eps (*.f64 eps #s(literal 1/24 binary64)) #s(literal -1/2 binary64)))))
#s(approx (+ (* eps (+ (* (cos x) (+ -1/2 (* eps (* eps 1/24)))) (* eps (* 1/6 (sin x))))) (sin (neg x))) (fma.f64 eps (fma.f64 eps (fma.f64 eps #s(literal 1/24 binary64) (.f64 x #s(literal 1/6 binary64))) #s(literal -1/2 binary64)) (.f64 x (fma.f64 x (fma.f64 eps (fma.f64 (.f64 eps eps) #s(literal -1/48 binary64) #s(literal 1/4 binary64)) (.f64 x (fma.f64 (*.f64 eps eps) #s(literal -1/36 binary64) #s(literal 1/6 binary64)))) #s(literal -1 binary64)))))
(fma.f64 x (fma.f64 x (fma.f64 eps (.f64 (fma.f64 eps (.f64 eps #s(literal 1/24 binary64)) #s(literal -1/2 binary64)) #s(literal -1/2 binary64)) (.f64 x (fma.f64 (.f64 eps eps) #s(literal -1/36 binary64) #s(literal 1/6 binary64)))) (fma.f64 eps (.f64 eps #s(literal 1/6 binary64)) #s(literal -1 binary64))) (.f64 eps (fma.f64 eps (*.f64 eps #s(literal 1/24 binary64)) #s(literal -1/2 binary64))))
(fma.f64 eps (fma.f64 eps (fma.f64 eps #s(literal 1/24 binary64) (.f64 x #s(literal 1/6 binary64))) #s(literal -1/2 binary64)) (.f64 x (fma.f64 x (fma.f64 eps (fma.f64 (.f64 eps eps) #s(literal -1/48 binary64) #s(literal 1/4 binary64)) (.f64 x (fma.f64 (*.f64 eps eps) #s(literal -1/36 binary64) #s(literal 1/6 binary64)))) #s(literal -1 binary64))))
x
(fma.f64 x (fma.f64 eps (.f64 (fma.f64 eps (.f64 eps #s(literal 1/24 binary64)) #s(literal -1/2 binary64)) #s(literal -1/2 binary64)) (.f64 x (fma.f64 (.f64 eps eps) #s(literal -1/36 binary64) #s(literal 1/6 binary64)))) (fma.f64 eps (*.f64 eps #s(literal 1/6 binary64)) #s(literal -1 binary64)))
(fma.f64 eps (.f64 eps #s(literal 1/6 binary64)) (fma.f64 x (fma.f64 eps (fma.f64 (.f64 eps eps) #s(literal -1/48 binary64) #s(literal 1/4 binary64)) (.f64 x (fma.f64 (.f64 eps eps) #s(literal -1/36 binary64) #s(literal 1/6 binary64)))) #s(literal -1 binary64)))
(fma.f64 eps (.f64 (fma.f64 eps (.f64 eps #s(literal 1/24 binary64)) #s(literal -1/2 binary64)) #s(literal -1/2 binary64)) (.f64 x (fma.f64 (.f64 eps eps) #s(literal -1/36 binary64) #s(literal 1/6 binary64))))
(fma.f64 eps (fma.f64 (.f64 eps eps) #s(literal -1/48 binary64) #s(literal 1/4 binary64)) (.f64 x (fma.f64 (*.f64 eps eps) #s(literal -1/36 binary64) #s(literal 1/6 binary64))))
(.f64 (fma.f64 eps (.f64 eps #s(literal 1/24 binary64)) #s(literal -1/2 binary64)) #s(literal -1/2 binary64))
(fma.f64 (*.f64 eps eps) #s(literal -1/48 binary64) #s(literal 1/4 binary64))
(fma.f64 eps (*.f64 eps #s(literal 1/24 binary64)) #s(literal -1/2 binary64))
(*.f64 eps #s(literal 1/24 binary64))
#s(literal 1/24 binary64)
#s(literal -1/2 binary64)
(.f64 x (fma.f64 (.f64 eps eps) #s(literal -1/36 binary64) #s(literal 1/6 binary64)))
(fma.f64 (*.f64 eps eps) #s(literal -1/36 binary64) #s(literal 1/6 binary64))
(*.f64 eps eps)
#s(literal -1/36 binary64)
#s(literal 1/6 binary64)
(fma.f64 eps (*.f64 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 #s(literal 1/6 binary64))
#s(literal -1 binary64)
(.f64 eps (fma.f64 eps (.f64 eps #s(literal 1/24 binary64)) #s(literal -1/2 binary64)))
#s(approx (- (* (cos x) (cos eps)) (+ (* (sin x) (sin eps)) (cos x))) (.f64 eps (-.f64 (.f64 eps (*.f64 #s(literal -1/2 binary64) (cos.f64 x))) (sin.f64 x))))
#s(approx (- (* (cos x) (cos eps)) (+ (* (sin x) (sin eps)) (cos x))) (.f64 (neg.f64 eps) (fma.f64 eps (.f64 #s(literal 1/2 binary64) (cos.f64 x)) (sin.f64 x))))
(.f64 eps (-.f64 (.f64 eps (*.f64 #s(literal -1/2 binary64) (cos.f64 x))) (sin.f64 x)))
(.f64 (neg.f64 eps) (fma.f64 eps (.f64 #s(literal 1/2 binary64) (cos.f64 x)) (sin.f64 x)))
eps
(-.f64 (.f64 eps (.f64 #s(literal -1/2 binary64) (cos.f64 x))) (sin.f64 x))
(-.f64 (.f64 eps (.f64 (cos.f64 x) #s(literal -1/2 binary64))) (sin.f64 x))
(.f64 eps (.f64 #s(literal -1/2 binary64) (cos.f64 x)))
(.f64 eps (.f64 (cos.f64 x) #s(literal -1/2 binary64)))
(*.f64 #s(literal -1/2 binary64) (cos.f64 x))
(*.f64 (cos.f64 x) #s(literal -1/2 binary64))
#s(literal -1/2 binary64)
(cos.f64 x)
x
(sin.f64 x)

localize562.0ms (3%)

Memory

-34.4MiB live, 380.6MiB allocated

Localize:

Found 20 expressions of interest:

New	Metric	Score
accuracy	0.0078125	(-.f64 (.f64 eps (.f64 #s(literal -1/2 binary64) (cos.f64 x))) (sin.f64 x))
accuracy	0.01171875	(.f64 eps (.f64 #s(literal -1/2 binary64) (cos.f64 x)))
accuracy	0.109375	(.f64 eps (-.f64 (.f64 eps (*.f64 #s(literal -1/2 binary64) (cos.f64 x))) (sin.f64 x)))
accuracy	0.6103053857529747	#s(approx (- (* (cos x) (cos eps)) (+ (* (sin x) (sin eps)) (cos x))) (.f64 eps (-.f64 (.f64 eps (*.f64 #s(literal -1/2 binary64) (cos.f64 x))) (sin.f64 x))))
accuracy	0.33203125	(*.f64 eps #s(literal 1/6 binary64))
accuracy	0.33203125	(*.f64 eps #s(literal 1/24 binary64))
accuracy	0.34131181601776905	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps #s(approx (+ ( eps (+ (* (cos x) (+ -1/2 (* eps (* eps 1/24)))) (* eps (* 1/6 (sin x))))) (sin (neg x))) (fma.f64 x (fma.f64 x (fma.f64 eps (.f64 (fma.f64 eps (.f64 eps #s(literal 1/24 binary64)) #s(literal -1/2 binary64)) #s(literal -1/2 binary64)) (.f64 x (fma.f64 (.f64 eps eps) #s(literal -1/36 binary64) #s(literal 1/6 binary64)))) (fma.f64 eps (.f64 eps #s(literal 1/6 binary64)) #s(literal -1 binary64))) (.f64 eps (fma.f64 eps (*.f64 eps #s(literal 1/24 binary64)) #s(literal -1/2 binary64)))))))
accuracy	1.3028462465427286	#s(approx (+ (* eps (+ (* (cos x) (+ -1/2 (* eps (* eps 1/24)))) (* eps (* 1/6 (sin x))))) (sin (neg x))) (fma.f64 x (fma.f64 x (fma.f64 eps (.f64 (fma.f64 eps (.f64 eps #s(literal 1/24 binary64)) #s(literal -1/2 binary64)) #s(literal -1/2 binary64)) (.f64 x (fma.f64 (.f64 eps eps) #s(literal -1/36 binary64) #s(literal 1/6 binary64)))) (fma.f64 eps (.f64 eps #s(literal 1/6 binary64)) #s(literal -1 binary64))) (.f64 eps (fma.f64 eps (*.f64 eps #s(literal 1/24 binary64)) #s(literal -1/2 binary64)))))
accuracy	0.34131181601776905	#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* eps (+ (* eps (+ (* (cos x) (+ -1/2 (* eps (* eps 1/24)))) (* eps (* 1/6 (sin x))))) (sin (neg x)))) #s(approx (+ (* eps (* eps (+ (* eps (* eps 1/24)) -1/2))) (* eps (* x (+ (* eps (* eps 1/6)) -1)))) (.f64 (.f64 (.f64 eps eps) (.f64 eps eps)) (fma.f64 x (/.f64 #s(literal 1/6 binary64) eps) #s(literal 1/24 binary64))))))
accuracy	0.3671875	(/.f64 #s(literal 1/6 binary64) eps)
accuracy	1.7215412375959054	#s(approx (* eps (+ (* eps (+ (* (cos x) (+ -1/2 (* eps (* eps 1/24)))) (* eps (* 1/6 (sin x))))) (sin (neg x)))) #s(approx (+ (* eps (* eps (+ (* eps (* eps 1/24)) -1/2))) (* eps (* x (+ (* eps (* eps 1/6)) -1)))) (.f64 (.f64 (.f64 eps eps) (.f64 eps eps)) (fma.f64 x (/.f64 #s(literal 1/6 binary64) eps) #s(literal 1/24 binary64)))))
accuracy	29.192405278634702	#s(approx (+ (* eps (* eps (+ (* eps (* eps 1/24)) -1/2))) (* eps (* x (+ (* eps (* eps 1/6)) -1)))) (.f64 (.f64 (.f64 eps eps) (.f64 eps eps)) (fma.f64 x (/.f64 #s(literal 1/6 binary64) eps) #s(literal 1/24 binary64))))
accuracy	0	(neg.f64 eps)
accuracy	0.34131181601776905	#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* eps (+ (* eps (+ (* (cos x) (+ -1/2 (* eps (* eps 1/24)))) (* eps (* 1/6 (sin x))))) (sin (neg x)))) #s(approx (+ (* eps (* eps (+ (* eps (* eps 1/24)) -1/2))) (* eps (* x (+ (* eps (* eps 1/6)) -1)))) (*.f64 x (neg.f64 eps)))))
accuracy	1.7215412375959054	#s(approx (* eps (+ (* eps (+ (* (cos x) (+ -1/2 (* eps (* eps 1/24)))) (* eps (* 1/6 (sin x))))) (sin (neg x)))) #s(approx (+ (* eps (* eps (+ (* eps (* eps 1/24)) -1/2))) (* eps (* x (+ (* eps (* eps 1/6)) -1)))) (*.f64 x (neg.f64 eps))))
accuracy	11.56335282386882	#s(approx (+ (* eps (* eps (+ (* eps (* eps 1/24)) -1/2))) (* eps (* x (+ (* eps (* eps 1/6)) -1)))) (*.f64 x (neg.f64 eps)))
accuracy	0.00390625	(.f64 (sin.f64 x) (cos.f64 (.f64 eps #s(literal 1/2 binary64))))
accuracy	0.0078125	(fma.f64 (cos.f64 x) (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (.f64 (sin.f64 x) (cos.f64 (*.f64 eps #s(literal 1/2 binary64)))))
accuracy	0.03125	(.f64 #s(approx ( (sin (* (+ eps 0) 1/2)) (+ (* (sin (* (+ x x) 1/2)) (cos (* eps 1/2))) (* (cos (* (+ x x) 1/2)) (sin (* eps 1/2))))) (.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (fma.f64 (cos.f64 x) (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (.f64 (sin.f64 x) (cos.f64 (*.f64 eps #s(literal 1/2 binary64))))))) #s(literal -2 binary64))
accuracy	0.11328125	(.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (fma.f64 (cos.f64 x) (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (.f64 (sin.f64 x) (cos.f64 (*.f64 eps #s(literal 1/2 binary64))))))

Samples

341.0ms	178×	2	valid
81.0ms	70×	1	valid
7.0ms	3×	3	valid
3.0ms	5×	0	valid

Compiler

Compiled 547 to 85 computations (84.5% saved)

Precisions

Click to see histograms. Total time spent on operations: 374.0ms

ival-mult: 106.0ms (28.3% of total)

ival-cos: 85.0ms (22.7% of total)

adjust: 65.0ms (17.4% of total)

ival-sub: 47.0ms (12.6% of total)

ival-add: 32.0ms (8.5% of total)

ival-sin: 19.0ms (5.1% of total)

const: 13.0ms (3.5% of total)

ival-div: 3.0ms (0.8% of total)

ival-neg: 2.0ms (0.5% of total)

exact: 1.0ms (0.3% of total)

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

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

series50.0ms (0.3%)

Memory

21.2MiB live, 58.0MiB allocated

Counts

27 → 576

Calls

Call 1

Inputs
#s(alt (.f64 #s(approx ( (sin (* (+ eps 0) 1/2)) (+ (* (sin (* (+ x x) 1/2)) (cos (* eps 1/2))) (* (cos (* (+ x x) 1/2)) (sin (* eps 1/2))))) (.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (fma.f64 (cos.f64 x) (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (.f64 (sin.f64 x) (cos.f64 (.f64 eps #s(literal 1/2 binary64))))))) #s(literal -2 binary64)) (patch (.f64 #s(approx (* (sin (* (+ eps 0) 1/2)) (+ (* (sin (* (+ x x) 1/2)) (cos (* eps 1/2))) (* (cos (* (+ x x) 1/2)) (sin (* eps 1/2))))) (.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (fma.f64 (cos.f64 x) (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (.f64 (sin.f64 x) (cos.f64 (*.f64 eps #s(literal 1/2 binary64))))))) #s(literal -2 binary64)) #<representation binary64>) () ())
#s(alt #s(approx (* (sin (* (+ eps 0) 1/2)) (+ (* (sin (* (+ x x) 1/2)) (cos (* eps 1/2))) (* (cos (* (+ x x) 1/2)) (sin (* eps 1/2))))) (.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (fma.f64 (cos.f64 x) (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (.f64 (sin.f64 x) (cos.f64 (.f64 eps #s(literal 1/2 binary64))))))) (patch #s(approx ( (sin (* (+ eps 0) 1/2)) (+ (* (sin (* (+ x x) 1/2)) (cos (* eps 1/2))) (* (cos (* (+ x x) 1/2)) (sin (* eps 1/2))))) (.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (fma.f64 (cos.f64 x) (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (.f64 (sin.f64 x) (cos.f64 (*.f64 eps #s(literal 1/2 binary64))))))) #<representation binary64>) () ())
#s(alt (.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (fma.f64 (cos.f64 x) (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (.f64 (sin.f64 x) (cos.f64 (.f64 eps #s(literal 1/2 binary64)))))) (patch (.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (fma.f64 (cos.f64 x) (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (.f64 (sin.f64 x) (cos.f64 (.f64 eps #s(literal 1/2 binary64)))))) #<representation binary64>) () ())
#s(alt (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (patch (sin.f64 (.f64 eps #s(literal 1/2 binary64))) #<representation binary64>) () ())
#s(alt #s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* eps (+ (* eps (+ (* (cos x) (+ -1/2 (* eps (* eps 1/24)))) (* eps (* 1/6 (sin x))))) (sin (neg x)))) #s(approx (+ (* eps (* eps (+ (* eps (* eps 1/24)) -1/2))) (* eps (* x (+ (* eps (* eps 1/6)) -1)))) (.f64 x (neg.f64 eps))))) (patch #s(approx (- (cos (+ x eps)) (cos x)) #s(approx ( eps (+ (* eps (+ (* (cos x) (+ -1/2 (* eps (* eps 1/24)))) (* eps (* 1/6 (sin x))))) (sin (neg x)))) #s(approx (+ (* eps (* eps (+ (* eps (* eps 1/24)) -1/2))) (* eps (* x (+ (* eps (* eps 1/6)) -1)))) (*.f64 x (neg.f64 eps))))) #<representation binary64>) () ())
#s(alt #s(approx (* eps (+ (* eps (+ (* (cos x) (+ -1/2 (* eps (* eps 1/24)))) (* eps (* 1/6 (sin x))))) (sin (neg x)))) #s(approx (+ (* eps (* eps (+ (* eps (* eps 1/24)) -1/2))) (* eps (* x (+ (* eps (* eps 1/6)) -1)))) (.f64 x (neg.f64 eps)))) (patch #s(approx ( eps (+ (* eps (+ (* (cos x) (+ -1/2 (* eps (* eps 1/24)))) (* eps (* 1/6 (sin x))))) (sin (neg x)))) #s(approx (+ (* eps (* eps (+ (* eps (* eps 1/24)) -1/2))) (* eps (* x (+ (* eps (* eps 1/6)) -1)))) (*.f64 x (neg.f64 eps)))) #<representation binary64>) () ())
#s(alt #s(approx (+ (* eps (* eps (+ (* eps (* eps 1/24)) -1/2))) (* eps (* x (+ (* eps (* eps 1/6)) -1)))) (.f64 x (neg.f64 eps))) (patch #s(approx (+ ( eps (* eps (+ (* eps (* eps 1/24)) -1/2))) (* eps (* x (+ (* eps (* eps 1/6)) -1)))) (*.f64 x (neg.f64 eps))) #<representation binary64>) () ())
#s(alt (.f64 x (neg.f64 eps)) (patch (.f64 x (neg.f64 eps)) #<representation binary64>) () ())
#s(alt (.f64 (.f64 (.f64 eps eps) (.f64 eps eps)) (fma.f64 x (/.f64 #s(literal 1/6 binary64) eps) #s(literal 1/24 binary64))) (patch (.f64 (.f64 (.f64 eps eps) (.f64 eps eps)) (fma.f64 x (/.f64 #s(literal 1/6 binary64) eps) #s(literal 1/24 binary64))) #<representation binary64>) () ())
#s(alt #s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* eps (+ (* eps (+ (* (cos x) (+ -1/2 (* eps (* eps 1/24)))) (* eps (* 1/6 (sin x))))) (sin (neg x)))) #s(approx (+ (* eps (* eps (+ (* eps (* eps 1/24)) -1/2))) (* eps (* x (+ (* eps (* eps 1/6)) -1)))) (.f64 (.f64 (.f64 eps eps) (.f64 eps eps)) (fma.f64 x (/.f64 #s(literal 1/6 binary64) eps) #s(literal 1/24 binary64)))))) (patch #s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* eps (+ (* eps (+ (* (cos x) (+ -1/2 (* eps (* eps 1/24)))) (* eps (* 1/6 (sin x))))) (sin (neg x)))) #s(approx (+ (* eps (* eps (+ (* eps (* eps 1/24)) -1/2))) (* eps (* x (+ (* eps (* eps 1/6)) -1)))) (.f64 (.f64 (.f64 eps eps) (.f64 eps eps)) (fma.f64 x (/.f64 #s(literal 1/6 binary64) eps) #s(literal 1/24 binary64)))))) #<representation binary64>) () ())
#s(alt #s(approx (* eps (+ (* eps (+ (* (cos x) (+ -1/2 (* eps (* eps 1/24)))) (* eps (* 1/6 (sin x))))) (sin (neg x)))) #s(approx (+ (* eps (* eps (+ (* eps (* eps 1/24)) -1/2))) (* eps (* x (+ (* eps (* eps 1/6)) -1)))) (.f64 (.f64 (.f64 eps eps) (.f64 eps eps)) (fma.f64 x (/.f64 #s(literal 1/6 binary64) eps) #s(literal 1/24 binary64))))) (patch #s(approx (* eps (+ (* eps (+ (* (cos x) (+ -1/2 (* eps (* eps 1/24)))) (* eps (* 1/6 (sin x))))) (sin (neg x)))) #s(approx (+ (* eps (* eps (+ (* eps (* eps 1/24)) -1/2))) (* eps (* x (+ (* eps (* eps 1/6)) -1)))) (.f64 (.f64 (.f64 eps eps) (.f64 eps eps)) (fma.f64 x (/.f64 #s(literal 1/6 binary64) eps) #s(literal 1/24 binary64))))) #<representation binary64>) () ())
#s(alt #s(approx (+ (* eps (* eps (+ (* eps (* eps 1/24)) -1/2))) (* eps (* x (+ (* eps (* eps 1/6)) -1)))) (.f64 (.f64 (.f64 eps eps) (.f64 eps eps)) (fma.f64 x (/.f64 #s(literal 1/6 binary64) eps) #s(literal 1/24 binary64)))) (patch #s(approx (+ (* eps (* eps (+ (* eps (* eps 1/24)) -1/2))) (* eps (* x (+ (* eps (* eps 1/6)) -1)))) (.f64 (.f64 (.f64 eps eps) (.f64 eps eps)) (fma.f64 x (/.f64 #s(literal 1/6 binary64) eps) #s(literal 1/24 binary64)))) #<representation binary64>) () ())
#s(alt (fma.f64 x (fma.f64 x (fma.f64 eps (.f64 (fma.f64 eps (.f64 eps #s(literal 1/24 binary64)) #s(literal -1/2 binary64)) #s(literal -1/2 binary64)) (.f64 x (fma.f64 (.f64 eps eps) #s(literal -1/36 binary64) #s(literal 1/6 binary64)))) (fma.f64 eps (.f64 eps #s(literal 1/6 binary64)) #s(literal -1 binary64))) (.f64 eps (fma.f64 eps (.f64 eps #s(literal 1/24 binary64)) #s(literal -1/2 binary64)))) (patch (fma.f64 x (fma.f64 x (fma.f64 eps (.f64 (fma.f64 eps (.f64 eps #s(literal 1/24 binary64)) #s(literal -1/2 binary64)) #s(literal -1/2 binary64)) (.f64 x (fma.f64 (.f64 eps eps) #s(literal -1/36 binary64) #s(literal 1/6 binary64)))) (fma.f64 eps (.f64 eps #s(literal 1/6 binary64)) #s(literal -1 binary64))) (.f64 eps (fma.f64 eps (.f64 eps #s(literal 1/24 binary64)) #s(literal -1/2 binary64)))) #<representation binary64>) () ())
#s(alt (.f64 (fma.f64 eps (.f64 eps #s(literal 1/24 binary64)) #s(literal -1/2 binary64)) #s(literal -1/2 binary64)) (patch (.f64 (fma.f64 eps (.f64 eps #s(literal 1/24 binary64)) #s(literal -1/2 binary64)) #s(literal -1/2 binary64)) #<representation binary64>) () ())
#s(alt #s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps #s(approx (+ ( eps (+ (* (cos x) (+ -1/2 (* eps (* eps 1/24)))) (* eps (* 1/6 (sin x))))) (sin (neg x))) (fma.f64 x (fma.f64 x (fma.f64 eps (.f64 (fma.f64 eps (.f64 eps #s(literal 1/24 binary64)) #s(literal -1/2 binary64)) #s(literal -1/2 binary64)) (.f64 x (fma.f64 (.f64 eps eps) #s(literal -1/36 binary64) #s(literal 1/6 binary64)))) (fma.f64 eps (.f64 eps #s(literal 1/6 binary64)) #s(literal -1 binary64))) (.f64 eps (fma.f64 eps (.f64 eps #s(literal 1/24 binary64)) #s(literal -1/2 binary64))))))) (patch #s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps #s(approx (+ (* eps (+ (* (cos x) (+ -1/2 (* eps (* eps 1/24)))) (* eps (* 1/6 (sin x))))) (sin (neg x))) (fma.f64 x (fma.f64 x (fma.f64 eps (.f64 (fma.f64 eps (.f64 eps #s(literal 1/24 binary64)) #s(literal -1/2 binary64)) #s(literal -1/2 binary64)) (.f64 x (fma.f64 (.f64 eps eps) #s(literal -1/36 binary64) #s(literal 1/6 binary64)))) (fma.f64 eps (.f64 eps #s(literal 1/6 binary64)) #s(literal -1 binary64))) (.f64 eps (fma.f64 eps (*.f64 eps #s(literal 1/24 binary64)) #s(literal -1/2 binary64))))))) #<representation binary64>) () ())
#s(alt (.f64 eps #s(approx (+ ( eps (+ (* (cos x) (+ -1/2 (* eps (* eps 1/24)))) (* eps (* 1/6 (sin x))))) (sin (neg x))) (fma.f64 x (fma.f64 x (fma.f64 eps (.f64 (fma.f64 eps (.f64 eps #s(literal 1/24 binary64)) #s(literal -1/2 binary64)) #s(literal -1/2 binary64)) (.f64 x (fma.f64 (.f64 eps eps) #s(literal -1/36 binary64) #s(literal 1/6 binary64)))) (fma.f64 eps (.f64 eps #s(literal 1/6 binary64)) #s(literal -1 binary64))) (.f64 eps (fma.f64 eps (.f64 eps #s(literal 1/24 binary64)) #s(literal -1/2 binary64)))))) (patch (.f64 eps #s(approx (+ (* eps (+ (* (cos x) (+ -1/2 (* eps (* eps 1/24)))) (* eps (* 1/6 (sin x))))) (sin (neg x))) (fma.f64 x (fma.f64 x (fma.f64 eps (.f64 (fma.f64 eps (.f64 eps #s(literal 1/24 binary64)) #s(literal -1/2 binary64)) #s(literal -1/2 binary64)) (.f64 x (fma.f64 (.f64 eps eps) #s(literal -1/36 binary64) #s(literal 1/6 binary64)))) (fma.f64 eps (.f64 eps #s(literal 1/6 binary64)) #s(literal -1 binary64))) (.f64 eps (fma.f64 eps (*.f64 eps #s(literal 1/24 binary64)) #s(literal -1/2 binary64)))))) #<representation binary64>) () ())
#s(alt #s(approx (- (* (cos x) (cos eps)) (+ (* (sin x) (sin eps)) (cos x))) (.f64 eps (-.f64 (.f64 eps (.f64 #s(literal -1/2 binary64) (cos.f64 x))) (sin.f64 x)))) (patch #s(approx (- ( (cos x) (cos eps)) (+ (* (sin x) (sin eps)) (cos x))) (.f64 eps (-.f64 (.f64 eps (*.f64 #s(literal -1/2 binary64) (cos.f64 x))) (sin.f64 x)))) #<representation binary64>) () ())
#s(alt (.f64 eps (-.f64 (.f64 eps (.f64 #s(literal -1/2 binary64) (cos.f64 x))) (sin.f64 x))) (patch (.f64 eps (-.f64 (.f64 eps (.f64 #s(literal -1/2 binary64) (cos.f64 x))) (sin.f64 x))) #<representation binary64>) () ())
#s(alt (-.f64 (.f64 eps (.f64 #s(literal -1/2 binary64) (cos.f64 x))) (sin.f64 x)) (patch (-.f64 (.f64 eps (.f64 #s(literal -1/2 binary64) (cos.f64 x))) (sin.f64 x)) #<representation binary64>) () ())
#s(alt (.f64 eps (.f64 #s(literal -1/2 binary64) (cos.f64 x))) (patch (.f64 eps (.f64 #s(literal -1/2 binary64) (cos.f64 x))) #<representation binary64>) () ())
#s(alt (fma.f64 (cos.f64 x) (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (.f64 (sin.f64 x) (cos.f64 (.f64 eps #s(literal 1/2 binary64))))) (patch (fma.f64 (cos.f64 x) (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (.f64 (sin.f64 x) (cos.f64 (.f64 eps #s(literal 1/2 binary64))))) #<representation binary64>) () ())
#s(alt (.f64 (sin.f64 x) (cos.f64 (.f64 eps #s(literal 1/2 binary64)))) (patch (.f64 (sin.f64 x) (cos.f64 (.f64 eps #s(literal 1/2 binary64)))) #<representation binary64>) () ())
#s(alt (neg.f64 eps) (patch (neg.f64 eps) #<representation binary64>) () ())
#s(alt (/.f64 #s(literal 1/6 binary64) eps) (patch (/.f64 #s(literal 1/6 binary64) eps) #<representation binary64>) () ())
#s(alt #s(approx (+ (* eps (+ (* (cos x) (+ -1/2 (* eps (* eps 1/24)))) (* eps (* 1/6 (sin x))))) (sin (neg x))) (fma.f64 x (fma.f64 x (fma.f64 eps (.f64 (fma.f64 eps (.f64 eps #s(literal 1/24 binary64)) #s(literal -1/2 binary64)) #s(literal -1/2 binary64)) (.f64 x (fma.f64 (.f64 eps eps) #s(literal -1/36 binary64) #s(literal 1/6 binary64)))) (fma.f64 eps (.f64 eps #s(literal 1/6 binary64)) #s(literal -1 binary64))) (.f64 eps (fma.f64 eps (.f64 eps #s(literal 1/24 binary64)) #s(literal -1/2 binary64))))) (patch #s(approx (+ ( eps (+ (* (cos x) (+ -1/2 (* eps (* eps 1/24)))) (* eps (* 1/6 (sin x))))) (sin (neg x))) (fma.f64 x (fma.f64 x (fma.f64 eps (.f64 (fma.f64 eps (.f64 eps #s(literal 1/24 binary64)) #s(literal -1/2 binary64)) #s(literal -1/2 binary64)) (.f64 x (fma.f64 (.f64 eps eps) #s(literal -1/36 binary64) #s(literal 1/6 binary64)))) (fma.f64 eps (.f64 eps #s(literal 1/6 binary64)) #s(literal -1 binary64))) (.f64 eps (fma.f64 eps (*.f64 eps #s(literal 1/24 binary64)) #s(literal -1/2 binary64))))) #<representation binary64>) () ())
#s(alt (.f64 eps #s(literal 1/24 binary64)) (patch (.f64 eps #s(literal 1/24 binary64)) #<representation binary64>) () ())
#s(alt (.f64 eps #s(literal 1/6 binary64)) (patch (.f64 eps #s(literal 1/6 binary64)) #<representation binary64>) () ())

Outputs
#s(alt (* -1 (* eps (sin x))) (taylor 0 eps) (#s(alt (.f64 #s(approx ( (sin (* (+ eps 0) 1/2)) (+ (* (sin (* (+ x x) 1/2)) (cos (* eps 1/2))) (* (cos (* (+ x x) 1/2)) (sin (* eps 1/2))))) (.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (fma.f64 (cos.f64 x) (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (.f64 (sin.f64 x) (cos.f64 (.f64 eps #s(literal 1/2 binary64))))))) #s(literal -2 binary64)) (patch (.f64 #s(approx (* (sin (* (+ eps 0) 1/2)) (+ (* (sin (* (+ x x) 1/2)) (cos (* eps 1/2))) (* (cos (* (+ x x) 1/2)) (sin (* eps 1/2))))) (.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (fma.f64 (cos.f64 x) (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (.f64 (sin.f64 x) (cos.f64 (*.f64 eps #s(literal 1/2 binary64))))))) #s(literal -2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* eps (+ (* -1 (sin x)) (* -1/2 (* eps (cos x))))) (taylor 0 eps) (#s(alt (.f64 #s(approx ( (sin (* (+ eps 0) 1/2)) (+ (* (sin (* (+ x x) 1/2)) (cos (* eps 1/2))) (* (cos (* (+ x x) 1/2)) (sin (* eps 1/2))))) (.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (fma.f64 (cos.f64 x) (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (.f64 (sin.f64 x) (cos.f64 (.f64 eps #s(literal 1/2 binary64))))))) #s(literal -2 binary64)) (patch (.f64 #s(approx (* (sin (* (+ eps 0) 1/2)) (+ (* (sin (* (+ x x) 1/2)) (cos (* eps 1/2))) (* (cos (* (+ x x) 1/2)) (sin (* eps 1/2))))) (.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (fma.f64 (cos.f64 x) (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (.f64 (sin.f64 x) (cos.f64 (*.f64 eps #s(literal 1/2 binary64))))))) #s(literal -2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* eps (+ (* -1 (sin x)) (* eps (+ (* -2 (* eps (+ (* -1/16 (sin x)) (* -1/48 (sin x))))) (* -1/2 (cos x)))))) (taylor 0 eps) (#s(alt (.f64 #s(approx ( (sin (* (+ eps 0) 1/2)) (+ (* (sin (* (+ x x) 1/2)) (cos (* eps 1/2))) (* (cos (* (+ x x) 1/2)) (sin (* eps 1/2))))) (.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (fma.f64 (cos.f64 x) (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (.f64 (sin.f64 x) (cos.f64 (.f64 eps #s(literal 1/2 binary64))))))) #s(literal -2 binary64)) (patch (.f64 #s(approx (* (sin (* (+ eps 0) 1/2)) (+ (* (sin (* (+ x x) 1/2)) (cos (* eps 1/2))) (* (cos (* (+ x x) 1/2)) (sin (* eps 1/2))))) (.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (fma.f64 (cos.f64 x) (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (.f64 (sin.f64 x) (cos.f64 (*.f64 eps #s(literal 1/2 binary64))))))) #s(literal -2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* eps (+ (* -1 (sin x)) (* eps (+ (* -1/2 (cos x)) (* eps (+ (* -2 (+ (* -1/16 (sin x)) (* -1/48 (sin x)))) (* 1/24 (* eps (cos x))))))))) (taylor 0 eps) (#s(alt (.f64 #s(approx ( (sin (* (+ eps 0) 1/2)) (+ (* (sin (* (+ x x) 1/2)) (cos (* eps 1/2))) (* (cos (* (+ x x) 1/2)) (sin (* eps 1/2))))) (.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (fma.f64 (cos.f64 x) (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (.f64 (sin.f64 x) (cos.f64 (.f64 eps #s(literal 1/2 binary64))))))) #s(literal -2 binary64)) (patch (.f64 #s(approx (* (sin (* (+ eps 0) 1/2)) (+ (* (sin (* (+ x x) 1/2)) (cos (* eps 1/2))) (* (cos (* (+ x x) 1/2)) (sin (* eps 1/2))))) (.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (fma.f64 (cos.f64 x) (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (.f64 (sin.f64 x) (cos.f64 (*.f64 eps #s(literal 1/2 binary64))))))) #s(literal -2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* -2 (* (sin (* 1/2 eps)) (+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x))))) (taylor inf eps) (#s(alt (.f64 #s(approx ( (sin (* (+ eps 0) 1/2)) (+ (* (sin (* (+ x x) 1/2)) (cos (* eps 1/2))) (* (cos (* (+ x x) 1/2)) (sin (* eps 1/2))))) (.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (fma.f64 (cos.f64 x) (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (.f64 (sin.f64 x) (cos.f64 (.f64 eps #s(literal 1/2 binary64))))))) #s(literal -2 binary64)) (patch (.f64 #s(approx (* (sin (* (+ eps 0) 1/2)) (+ (* (sin (* (+ x x) 1/2)) (cos (* eps 1/2))) (* (cos (* (+ x x) 1/2)) (sin (* eps 1/2))))) (.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (fma.f64 (cos.f64 x) (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (.f64 (sin.f64 x) (cos.f64 (*.f64 eps #s(literal 1/2 binary64))))))) #s(literal -2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* -2 (* (sin (* 1/2 eps)) (+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x))))) (taylor inf eps) (#s(alt (.f64 #s(approx ( (sin (* (+ eps 0) 1/2)) (+ (* (sin (* (+ x x) 1/2)) (cos (* eps 1/2))) (* (cos (* (+ x x) 1/2)) (sin (* eps 1/2))))) (.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (fma.f64 (cos.f64 x) (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (.f64 (sin.f64 x) (cos.f64 (.f64 eps #s(literal 1/2 binary64))))))) #s(literal -2 binary64)) (patch (.f64 #s(approx (* (sin (* (+ eps 0) 1/2)) (+ (* (sin (* (+ x x) 1/2)) (cos (* eps 1/2))) (* (cos (* (+ x x) 1/2)) (sin (* eps 1/2))))) (.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (fma.f64 (cos.f64 x) (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (.f64 (sin.f64 x) (cos.f64 (*.f64 eps #s(literal 1/2 binary64))))))) #s(literal -2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* -2 (* (sin (* 1/2 eps)) (+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x))))) (taylor inf eps) (#s(alt (.f64 #s(approx ( (sin (* (+ eps 0) 1/2)) (+ (* (sin (* (+ x x) 1/2)) (cos (* eps 1/2))) (* (cos (* (+ x x) 1/2)) (sin (* eps 1/2))))) (.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (fma.f64 (cos.f64 x) (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (.f64 (sin.f64 x) (cos.f64 (.f64 eps #s(literal 1/2 binary64))))))) #s(literal -2 binary64)) (patch (.f64 #s(approx (* (sin (* (+ eps 0) 1/2)) (+ (* (sin (* (+ x x) 1/2)) (cos (* eps 1/2))) (* (cos (* (+ x x) 1/2)) (sin (* eps 1/2))))) (.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (fma.f64 (cos.f64 x) (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (.f64 (sin.f64 x) (cos.f64 (*.f64 eps #s(literal 1/2 binary64))))))) #s(literal -2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* -2 (* (sin (* 1/2 eps)) (+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x))))) (taylor inf eps) (#s(alt (.f64 #s(approx ( (sin (* (+ eps 0) 1/2)) (+ (* (sin (* (+ x x) 1/2)) (cos (* eps 1/2))) (* (cos (* (+ x x) 1/2)) (sin (* eps 1/2))))) (.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (fma.f64 (cos.f64 x) (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (.f64 (sin.f64 x) (cos.f64 (.f64 eps #s(literal 1/2 binary64))))))) #s(literal -2 binary64)) (patch (.f64 #s(approx (* (sin (* (+ eps 0) 1/2)) (+ (* (sin (* (+ x x) 1/2)) (cos (* eps 1/2))) (* (cos (* (+ x x) 1/2)) (sin (* eps 1/2))))) (.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (fma.f64 (cos.f64 x) (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (.f64 (sin.f64 x) (cos.f64 (*.f64 eps #s(literal 1/2 binary64))))))) #s(literal -2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* -2 (* (sin (* 1/2 eps)) (+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x))))) (taylor -inf eps) (#s(alt (.f64 #s(approx ( (sin (* (+ eps 0) 1/2)) (+ (* (sin (* (+ x x) 1/2)) (cos (* eps 1/2))) (* (cos (* (+ x x) 1/2)) (sin (* eps 1/2))))) (.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (fma.f64 (cos.f64 x) (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (.f64 (sin.f64 x) (cos.f64 (.f64 eps #s(literal 1/2 binary64))))))) #s(literal -2 binary64)) (patch (.f64 #s(approx (* (sin (* (+ eps 0) 1/2)) (+ (* (sin (* (+ x x) 1/2)) (cos (* eps 1/2))) (* (cos (* (+ x x) 1/2)) (sin (* eps 1/2))))) (.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (fma.f64 (cos.f64 x) (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (.f64 (sin.f64 x) (cos.f64 (*.f64 eps #s(literal 1/2 binary64))))))) #s(literal -2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* -2 (* (sin (* 1/2 eps)) (+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x))))) (taylor -inf eps) (#s(alt (.f64 #s(approx ( (sin (* (+ eps 0) 1/2)) (+ (* (sin (* (+ x x) 1/2)) (cos (* eps 1/2))) (* (cos (* (+ x x) 1/2)) (sin (* eps 1/2))))) (.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (fma.f64 (cos.f64 x) (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (.f64 (sin.f64 x) (cos.f64 (.f64 eps #s(literal 1/2 binary64))))))) #s(literal -2 binary64)) (patch (.f64 #s(approx (* (sin (* (+ eps 0) 1/2)) (+ (* (sin (* (+ x x) 1/2)) (cos (* eps 1/2))) (* (cos (* (+ x x) 1/2)) (sin (* eps 1/2))))) (.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (fma.f64 (cos.f64 x) (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (.f64 (sin.f64 x) (cos.f64 (*.f64 eps #s(literal 1/2 binary64))))))) #s(literal -2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* -2 (* (sin (* 1/2 eps)) (+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x))))) (taylor -inf eps) (#s(alt (.f64 #s(approx ( (sin (* (+ eps 0) 1/2)) (+ (* (sin (* (+ x x) 1/2)) (cos (* eps 1/2))) (* (cos (* (+ x x) 1/2)) (sin (* eps 1/2))))) (.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (fma.f64 (cos.f64 x) (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (.f64 (sin.f64 x) (cos.f64 (.f64 eps #s(literal 1/2 binary64))))))) #s(literal -2 binary64)) (patch (.f64 #s(approx (* (sin (* (+ eps 0) 1/2)) (+ (* (sin (* (+ x x) 1/2)) (cos (* eps 1/2))) (* (cos (* (+ x x) 1/2)) (sin (* eps 1/2))))) (.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (fma.f64 (cos.f64 x) (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (.f64 (sin.f64 x) (cos.f64 (*.f64 eps #s(literal 1/2 binary64))))))) #s(literal -2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* -2 (* (sin (* 1/2 eps)) (+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x))))) (taylor -inf eps) (#s(alt (.f64 #s(approx ( (sin (* (+ eps 0) 1/2)) (+ (* (sin (* (+ x x) 1/2)) (cos (* eps 1/2))) (* (cos (* (+ x x) 1/2)) (sin (* eps 1/2))))) (.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (fma.f64 (cos.f64 x) (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (.f64 (sin.f64 x) (cos.f64 (.f64 eps #s(literal 1/2 binary64))))))) #s(literal -2 binary64)) (patch (.f64 #s(approx (* (sin (* (+ eps 0) 1/2)) (+ (* (sin (* (+ x x) 1/2)) (cos (* eps 1/2))) (* (cos (* (+ x x) 1/2)) (sin (* eps 1/2))))) (.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (fma.f64 (cos.f64 x) (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (.f64 (sin.f64 x) (cos.f64 (*.f64 eps #s(literal 1/2 binary64))))))) #s(literal -2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* -2 (pow (sin (* 1/2 eps)) 2)) (taylor 0 x) (#s(alt (.f64 #s(approx ( (sin (* (+ eps 0) 1/2)) (+ (* (sin (* (+ x x) 1/2)) (cos (* eps 1/2))) (* (cos (* (+ x x) 1/2)) (sin (* eps 1/2))))) (.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (fma.f64 (cos.f64 x) (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (.f64 (sin.f64 x) (cos.f64 (.f64 eps #s(literal 1/2 binary64))))))) #s(literal -2 binary64)) (patch (.f64 #s(approx (* (sin (* (+ eps 0) 1/2)) (+ (* (sin (* (+ x x) 1/2)) (cos (* eps 1/2))) (* (cos (* (+ x x) 1/2)) (sin (* eps 1/2))))) (.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (fma.f64 (cos.f64 x) (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (.f64 (sin.f64 x) (cos.f64 (*.f64 eps #s(literal 1/2 binary64))))))) #s(literal -2 binary64)) #<representation binary64>) () ())) ())
#s(alt (+ (* -2 (* x (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))) (* -2 (pow (sin (* 1/2 eps)) 2))) (taylor 0 x) (#s(alt (.f64 #s(approx ( (sin (* (+ eps 0) 1/2)) (+ (* (sin (* (+ x x) 1/2)) (cos (* eps 1/2))) (* (cos (* (+ x x) 1/2)) (sin (* eps 1/2))))) (.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (fma.f64 (cos.f64 x) (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (.f64 (sin.f64 x) (cos.f64 (.f64 eps #s(literal 1/2 binary64))))))) #s(literal -2 binary64)) (patch (.f64 #s(approx (* (sin (* (+ eps 0) 1/2)) (+ (* (sin (* (+ x x) 1/2)) (cos (* eps 1/2))) (* (cos (* (+ x x) 1/2)) (sin (* eps 1/2))))) (.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (fma.f64 (cos.f64 x) (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (.f64 (sin.f64 x) (cos.f64 (*.f64 eps #s(literal 1/2 binary64))))))) #s(literal -2 binary64)) #<representation binary64>) () ())) ())
#s(alt (+ (* -2 (pow (sin (* 1/2 eps)) 2)) (* x (+ (* -2 (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) (* x (pow (sin (* 1/2 eps)) 2))))) (taylor 0 x) (#s(alt (.f64 #s(approx ( (sin (* (+ eps 0) 1/2)) (+ (* (sin (* (+ x x) 1/2)) (cos (* eps 1/2))) (* (cos (* (+ x x) 1/2)) (sin (* eps 1/2))))) (.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (fma.f64 (cos.f64 x) (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (.f64 (sin.f64 x) (cos.f64 (.f64 eps #s(literal 1/2 binary64))))))) #s(literal -2 binary64)) (patch (.f64 #s(approx (* (sin (* (+ eps 0) 1/2)) (+ (* (sin (* (+ x x) 1/2)) (cos (* eps 1/2))) (* (cos (* (+ x x) 1/2)) (sin (* eps 1/2))))) (.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (fma.f64 (cos.f64 x) (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (.f64 (sin.f64 x) (cos.f64 (*.f64 eps #s(literal 1/2 binary64))))))) #s(literal -2 binary64)) #<representation binary64>) () ())) ())
#s(alt (+ (* -2 (pow (sin (* 1/2 eps)) 2)) (* x (+ (* -2 (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) (* x (+ (* 1/3 (* x (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))) (pow (sin (* 1/2 eps)) 2)))))) (taylor 0 x) (#s(alt (.f64 #s(approx ( (sin (* (+ eps 0) 1/2)) (+ (* (sin (* (+ x x) 1/2)) (cos (* eps 1/2))) (* (cos (* (+ x x) 1/2)) (sin (* eps 1/2))))) (.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (fma.f64 (cos.f64 x) (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (.f64 (sin.f64 x) (cos.f64 (.f64 eps #s(literal 1/2 binary64))))))) #s(literal -2 binary64)) (patch (.f64 #s(approx (* (sin (* (+ eps 0) 1/2)) (+ (* (sin (* (+ x x) 1/2)) (cos (* eps 1/2))) (* (cos (* (+ x x) 1/2)) (sin (* eps 1/2))))) (.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (fma.f64 (cos.f64 x) (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (.f64 (sin.f64 x) (cos.f64 (*.f64 eps #s(literal 1/2 binary64))))))) #s(literal -2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* -2 (* (sin (* 1/2 eps)) (+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x))))) (taylor inf x) (#s(alt (.f64 #s(approx ( (sin (* (+ eps 0) 1/2)) (+ (* (sin (* (+ x x) 1/2)) (cos (* eps 1/2))) (* (cos (* (+ x x) 1/2)) (sin (* eps 1/2))))) (.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (fma.f64 (cos.f64 x) (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (.f64 (sin.f64 x) (cos.f64 (.f64 eps #s(literal 1/2 binary64))))))) #s(literal -2 binary64)) (patch (.f64 #s(approx (* (sin (* (+ eps 0) 1/2)) (+ (* (sin (* (+ x x) 1/2)) (cos (* eps 1/2))) (* (cos (* (+ x x) 1/2)) (sin (* eps 1/2))))) (.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (fma.f64 (cos.f64 x) (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (.f64 (sin.f64 x) (cos.f64 (*.f64 eps #s(literal 1/2 binary64))))))) #s(literal -2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* -2 (* (sin (* 1/2 eps)) (+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x))))) (taylor inf x) (#s(alt (.f64 #s(approx ( (sin (* (+ eps 0) 1/2)) (+ (* (sin (* (+ x x) 1/2)) (cos (* eps 1/2))) (* (cos (* (+ x x) 1/2)) (sin (* eps 1/2))))) (.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (fma.f64 (cos.f64 x) (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (.f64 (sin.f64 x) (cos.f64 (.f64 eps #s(literal 1/2 binary64))))))) #s(literal -2 binary64)) (patch (.f64 #s(approx (* (sin (* (+ eps 0) 1/2)) (+ (* (sin (* (+ x x) 1/2)) (cos (* eps 1/2))) (* (cos (* (+ x x) 1/2)) (sin (* eps 1/2))))) (.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (fma.f64 (cos.f64 x) (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (.f64 (sin.f64 x) (cos.f64 (*.f64 eps #s(literal 1/2 binary64))))))) #s(literal -2 binary64)) #<representation binary64>) () ())) ())
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#s(alt (+ (sin (* -1 x)) (* eps (+ (* 1/6 (* eps (sin x))) (* (cos x) (- (* 1/24 (pow eps 2)) 1/2))))) (taylor -inf x) (#s(alt #s(approx (+ (* eps (+ (* (cos x) (+ -1/2 (* eps (* eps 1/24)))) (* eps (* 1/6 (sin x))))) (sin (neg x))) (fma.f64 x (fma.f64 x (fma.f64 eps (.f64 (fma.f64 eps (.f64 eps #s(literal 1/24 binary64)) #s(literal -1/2 binary64)) #s(literal -1/2 binary64)) (.f64 x (fma.f64 (.f64 eps eps) #s(literal -1/36 binary64) #s(literal 1/6 binary64)))) (fma.f64 eps (.f64 eps #s(literal 1/6 binary64)) #s(literal -1 binary64))) (.f64 eps (fma.f64 eps (.f64 eps #s(literal 1/24 binary64)) #s(literal -1/2 binary64))))) (patch #s(approx (+ ( eps (+ (* (cos x) (+ -1/2 (* eps (* eps 1/24)))) (* eps (* 1/6 (sin x))))) (sin (neg x))) (fma.f64 x (fma.f64 x (fma.f64 eps (.f64 (fma.f64 eps (.f64 eps #s(literal 1/24 binary64)) #s(literal -1/2 binary64)) #s(literal -1/2 binary64)) (.f64 x (fma.f64 (.f64 eps eps) #s(literal -1/36 binary64) #s(literal 1/6 binary64)))) (fma.f64 eps (.f64 eps #s(literal 1/6 binary64)) #s(literal -1 binary64))) (.f64 eps (fma.f64 eps (*.f64 eps #s(literal 1/24 binary64)) #s(literal -1/2 binary64))))) #<representation binary64>) () ())) ())
#s(alt (* 1/24 eps) (taylor 0 eps) (#s(alt (.f64 eps #s(literal 1/24 binary64)) (patch (.f64 eps #s(literal 1/24 binary64)) #<representation binary64>) () ())) ())
#s(alt (* 1/24 eps) (taylor 0 eps) (#s(alt (.f64 eps #s(literal 1/24 binary64)) (patch (.f64 eps #s(literal 1/24 binary64)) #<representation binary64>) () ())) ())
#s(alt (* 1/24 eps) (taylor 0 eps) (#s(alt (.f64 eps #s(literal 1/24 binary64)) (patch (.f64 eps #s(literal 1/24 binary64)) #<representation binary64>) () ())) ())
#s(alt (* 1/24 eps) (taylor 0 eps) (#s(alt (.f64 eps #s(literal 1/24 binary64)) (patch (.f64 eps #s(literal 1/24 binary64)) #<representation binary64>) () ())) ())
#s(alt (* 1/24 eps) (taylor inf eps) (#s(alt (.f64 eps #s(literal 1/24 binary64)) (patch (.f64 eps #s(literal 1/24 binary64)) #<representation binary64>) () ())) ())
#s(alt (* 1/24 eps) (taylor inf eps) (#s(alt (.f64 eps #s(literal 1/24 binary64)) (patch (.f64 eps #s(literal 1/24 binary64)) #<representation binary64>) () ())) ())
#s(alt (* 1/24 eps) (taylor inf eps) (#s(alt (.f64 eps #s(literal 1/24 binary64)) (patch (.f64 eps #s(literal 1/24 binary64)) #<representation binary64>) () ())) ())
#s(alt (* 1/24 eps) (taylor inf eps) (#s(alt (.f64 eps #s(literal 1/24 binary64)) (patch (.f64 eps #s(literal 1/24 binary64)) #<representation binary64>) () ())) ())
#s(alt (* 1/24 eps) (taylor -inf eps) (#s(alt (.f64 eps #s(literal 1/24 binary64)) (patch (.f64 eps #s(literal 1/24 binary64)) #<representation binary64>) () ())) ())
#s(alt (* 1/24 eps) (taylor -inf eps) (#s(alt (.f64 eps #s(literal 1/24 binary64)) (patch (.f64 eps #s(literal 1/24 binary64)) #<representation binary64>) () ())) ())
#s(alt (* 1/24 eps) (taylor -inf eps) (#s(alt (.f64 eps #s(literal 1/24 binary64)) (patch (.f64 eps #s(literal 1/24 binary64)) #<representation binary64>) () ())) ())
#s(alt (* 1/24 eps) (taylor -inf eps) (#s(alt (.f64 eps #s(literal 1/24 binary64)) (patch (.f64 eps #s(literal 1/24 binary64)) #<representation binary64>) () ())) ())
#s(alt (* 1/6 eps) (taylor 0 eps) (#s(alt (.f64 eps #s(literal 1/6 binary64)) (patch (.f64 eps #s(literal 1/6 binary64)) #<representation binary64>) () ())) ())
#s(alt (* 1/6 eps) (taylor 0 eps) (#s(alt (.f64 eps #s(literal 1/6 binary64)) (patch (.f64 eps #s(literal 1/6 binary64)) #<representation binary64>) () ())) ())
#s(alt (* 1/6 eps) (taylor 0 eps) (#s(alt (.f64 eps #s(literal 1/6 binary64)) (patch (.f64 eps #s(literal 1/6 binary64)) #<representation binary64>) () ())) ())
#s(alt (* 1/6 eps) (taylor 0 eps) (#s(alt (.f64 eps #s(literal 1/6 binary64)) (patch (.f64 eps #s(literal 1/6 binary64)) #<representation binary64>) () ())) ())
#s(alt (* 1/6 eps) (taylor inf eps) (#s(alt (.f64 eps #s(literal 1/6 binary64)) (patch (.f64 eps #s(literal 1/6 binary64)) #<representation binary64>) () ())) ())
#s(alt (* 1/6 eps) (taylor inf eps) (#s(alt (.f64 eps #s(literal 1/6 binary64)) (patch (.f64 eps #s(literal 1/6 binary64)) #<representation binary64>) () ())) ())
#s(alt (* 1/6 eps) (taylor inf eps) (#s(alt (.f64 eps #s(literal 1/6 binary64)) (patch (.f64 eps #s(literal 1/6 binary64)) #<representation binary64>) () ())) ())
#s(alt (* 1/6 eps) (taylor inf eps) (#s(alt (.f64 eps #s(literal 1/6 binary64)) (patch (.f64 eps #s(literal 1/6 binary64)) #<representation binary64>) () ())) ())
#s(alt (* 1/6 eps) (taylor -inf eps) (#s(alt (.f64 eps #s(literal 1/6 binary64)) (patch (.f64 eps #s(literal 1/6 binary64)) #<representation binary64>) () ())) ())
#s(alt (* 1/6 eps) (taylor -inf eps) (#s(alt (.f64 eps #s(literal 1/6 binary64)) (patch (.f64 eps #s(literal 1/6 binary64)) #<representation binary64>) () ())) ())
#s(alt (* 1/6 eps) (taylor -inf eps) (#s(alt (.f64 eps #s(literal 1/6 binary64)) (patch (.f64 eps #s(literal 1/6 binary64)) #<representation binary64>) () ())) ())
#s(alt (* 1/6 eps) (taylor -inf eps) (#s(alt (.f64 eps #s(literal 1/6 binary64)) (patch (.f64 eps #s(literal 1/6 binary64)) #<representation binary64>) () ())) ())

Calls

144 calls:

Time	Variable		Point	Expression
1.0ms	x	@	inf	(* eps (- (* eps (* -1/2 (cos x))) (sin x)))
1.0ms	x	@	-inf	(* eps (- (* eps (* -1/2 (cos x))) (sin x)))
1.0ms	x	@	0	(* (* (* eps eps) (* eps eps)) (+ (* x (/ 1/6 eps)) 1/24))
1.0ms	x	@	-inf	(+ (* x (+ (* x (+ (* eps (* (+ (* eps (* eps 1/24)) -1/2) -1/2)) (* x (+ (* (* eps eps) -1/36) 1/6)))) (+ (* eps (* eps 1/6)) -1))) (* eps (+ (* eps (* eps 1/24)) -1/2)))
1.0ms	x	@	inf	(+ (* x (+ (* x (+ (* eps (* (+ (* eps (* eps 1/24)) -1/2) -1/2)) (* x (+ (* (* eps eps) -1/36) 1/6)))) (+ (* eps (* eps 1/6)) -1))) (* eps (+ (* eps (* eps 1/24)) -1/2)))

simplify275.0ms (1.5%)

Memory

18.2MiB live, 288.9MiB allocated

Algorithm

1×	egg-herbie

Rules

13 074×	`lower-fma.f64`
13 074×	`lower-fma.f32`
7 278×	`lower-*.f64`
7 278×	`lower-*.f32`
2 888×	`lower-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	609	8231
1	1939	7935
2	6108	7882
0	8080	7382

Stop Event

1×	iter limit
1×	node limit

Counts

576 → 576

Calls

Call 1

Inputs
(* -1 (* eps (sin x)))
(* eps (+ (* -1 (sin x)) (* -1/2 (* eps (cos x)))))
(* eps (+ (* -1 (sin x)) (* eps (+ (* -2 (* eps (+ (* -1/16 (sin x)) (* -1/48 (sin x))))) (* -1/2 (cos x))))))
(* eps (+ (* -1 (sin x)) (* eps (+ (* -1/2 (cos x)) (* eps (+ (* -2 (+ (* -1/16 (sin x)) (* -1/48 (sin x)))) (* 1/24 (* eps (cos x)))))))))
(* -2 (* (sin (* 1/2 eps)) (+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x)))))
(* -2 (* (sin (* 1/2 eps)) (+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x)))))
(* -2 (* (sin (* 1/2 eps)) (+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x)))))
(* -2 (* (sin (* 1/2 eps)) (+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x)))))
(* -2 (* (sin (* 1/2 eps)) (+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x)))))
(* -2 (* (sin (* 1/2 eps)) (+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x)))))
(* -2 (* (sin (* 1/2 eps)) (+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x)))))
(* -2 (* (sin (* 1/2 eps)) (+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x)))))
(* -2 (pow (sin (* 1/2 eps)) 2))
(+ (* -2 (* x (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))) (* -2 (pow (sin (* 1/2 eps)) 2)))
(+ (* -2 (pow (sin (* 1/2 eps)) 2)) (* x (+ (* -2 (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) (* x (pow (sin (* 1/2 eps)) 2)))))
(+ (* -2 (pow (sin (* 1/2 eps)) 2)) (* x (+ (* -2 (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) (* x (+ (* 1/3 (* x (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))) (pow (sin (* 1/2 eps)) 2))))))
(* -2 (* (sin (* 1/2 eps)) (+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x)))))
(* -2 (* (sin (* 1/2 eps)) (+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x)))))
(* -2 (* (sin (* 1/2 eps)) (+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x)))))
(* -2 (* (sin (* 1/2 eps)) (+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x)))))
(* -2 (* (sin (* 1/2 eps)) (+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x)))))
(* -2 (* (sin (* 1/2 eps)) (+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x)))))
(* -2 (* (sin (* 1/2 eps)) (+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x)))))
(* -2 (* (sin (* 1/2 eps)) (+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x)))))
(* 1/2 (* eps (sin x)))
(* eps (+ (* 1/4 (* eps (cos x))) (* 1/2 (sin x))))
(* eps (+ (* 1/2 (sin x)) (* eps (+ (* 1/4 (cos x)) (* eps (+ (* -1/16 (sin x)) (* -1/48 (sin x))))))))
(* eps (+ (* 1/2 (sin x)) (* eps (+ (* 1/4 (cos x)) (* eps (+ (* -1/16 (sin x)) (+ (* -1/48 (sin x)) (* -1/48 (* eps (cos x))))))))))
(* (sin (* 1/2 eps)) (+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x))))
(* (sin (* 1/2 eps)) (+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x))))
(* (sin (* 1/2 eps)) (+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x))))
(* (sin (* 1/2 eps)) (+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x))))
(* (sin (* 1/2 eps)) (+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x))))
(* (sin (* 1/2 eps)) (+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x))))
(* (sin (* 1/2 eps)) (+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x))))
(* (sin (* 1/2 eps)) (+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x))))
(pow (sin (* 1/2 eps)) 2)
(+ (* x (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) (pow (sin (* 1/2 eps)) 2))
(+ (* x (+ (* -1/2 (* x (pow (sin (* 1/2 eps)) 2))) (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))) (pow (sin (* 1/2 eps)) 2))
(+ (* x (+ (* x (+ (* -1/2 (pow (sin (* 1/2 eps)) 2)) (* -1/6 (* x (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))))) (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))) (pow (sin (* 1/2 eps)) 2))
(* (sin (* 1/2 eps)) (+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x))))
(* (sin (* 1/2 eps)) (+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x))))
(* (sin (* 1/2 eps)) (+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x))))
(* (sin (* 1/2 eps)) (+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x))))
(* (sin (* 1/2 eps)) (+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x))))
(* (sin (* 1/2 eps)) (+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x))))
(* (sin (* 1/2 eps)) (+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x))))
(* (sin (* 1/2 eps)) (+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x))))
(* 1/2 (* eps (sin x)))
(* eps (+ (* 1/4 (* eps (cos x))) (* 1/2 (sin x))))
(* eps (+ (* 1/2 (sin x)) (* eps (+ (* 1/4 (cos x)) (* eps (+ (* -1/16 (sin x)) (* -1/48 (sin x))))))))
(* eps (+ (* 1/2 (sin x)) (* eps (+ (* 1/4 (cos x)) (* eps (+ (* -1/16 (sin x)) (+ (* -1/48 (sin x)) (* -1/48 (* eps (cos x))))))))))
(* (sin (* 1/2 eps)) (+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x))))
(* (sin (* 1/2 eps)) (+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x))))
(* (sin (* 1/2 eps)) (+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x))))
(* (sin (* 1/2 eps)) (+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x))))
(* (sin (* 1/2 eps)) (+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x))))
(* (sin (* 1/2 eps)) (+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x))))
(* (sin (* 1/2 eps)) (+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x))))
(* (sin (* 1/2 eps)) (+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x))))
(pow (sin (* 1/2 eps)) 2)
(+ (* x (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) (pow (sin (* 1/2 eps)) 2))
(+ (* x (+ (* -1/2 (* x (pow (sin (* 1/2 eps)) 2))) (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))) (pow (sin (* 1/2 eps)) 2))
(+ (* x (+ (* x (+ (* -1/2 (pow (sin (* 1/2 eps)) 2)) (* -1/6 (* x (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))))) (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))) (pow (sin (* 1/2 eps)) 2))
(* (sin (* 1/2 eps)) (+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x))))
(* (sin (* 1/2 eps)) (+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x))))
(* (sin (* 1/2 eps)) (+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x))))
(* (sin (* 1/2 eps)) (+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x))))
(* (sin (* 1/2 eps)) (+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x))))
(* (sin (* 1/2 eps)) (+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x))))
(* (sin (* 1/2 eps)) (+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x))))
(* (sin (* 1/2 eps)) (+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (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))))
(sin (* 1/2 eps))
(sin (* 1/2 eps))
(sin (* 1/2 eps))
(sin (* 1/2 eps))
(sin (* 1/2 eps))
(sin (* 1/2 eps))
(sin (* 1/2 eps))
(sin (* 1/2 eps))
(- (cos eps) 1)
(- (+ (cos eps) (* -1 (* x (sin eps)))) 1)
(- (+ (cos eps) (* x (- (* x (+ 1/2 (* -1/2 (cos eps)))) (sin eps)))) 1)
(- (+ (cos eps) (* x (- (* x (+ 1/2 (+ (* -1/2 (cos eps)) (* 1/6 (* x (sin eps)))))) (sin eps)))) 1)
(- (cos (+ eps x)) (cos x))
(- (cos (+ eps x)) (cos x))
(- (cos (+ eps x)) (cos x))
(- (cos (+ eps x)) (cos x))
(- (cos (- eps (* -1 x))) (cos x))
(- (cos (- eps (* -1 x))) (cos x))
(- (cos (- eps (* -1 x))) (cos x))
(- (cos (- eps (* -1 x))) (cos x))
(* -1 (* eps (sin x)))
(* eps (- (* -1/2 (* eps (cos x))) (sin x)))
(* eps (- (* eps (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x))))) (sin x)))
(* eps (- (* eps (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x)))))) (sin x)))
(- (cos (+ eps x)) (cos x))
(- (cos (+ eps x)) (cos x))
(- (cos (+ eps x)) (cos x))
(- (cos (+ eps x)) (cos x))
(- (cos (- x (* -1 eps))) (cos x))
(- (cos (- x (* -1 eps))) (cos x))
(- (cos (- x (* -1 eps))) (cos x))
(- (cos (- x (* -1 eps))) (cos x))
(* eps (sin (neg x)))
(* eps (+ (sin (neg x)) (* -1/2 (* eps (cos x)))))
(* eps (+ (sin (neg x)) (* eps (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x)))))))
(* eps (+ (sin (neg x)) (* eps (+ (* -1/2 (cos x)) (* eps (+ (* 1/24 (* eps (cos x))) (* 1/6 (sin x))))))))
(* 1/24 (* (pow eps 4) (cos x)))
(* (pow eps 4) (+ (* 1/24 (cos x)) (* 1/6 (/ (sin x) eps))))
(* (pow eps 4) (+ (* -1/2 (/ (cos x) (pow eps 2))) (+ (* 1/24 (cos x)) (* 1/6 (/ (sin x) eps)))))
(* (pow eps 4) (+ (* -1/2 (/ (cos x) (pow eps 2))) (+ (* 1/24 (cos x)) (+ (* 1/6 (/ (sin x) eps)) (/ (sin (neg x)) (pow eps 3))))))
(* 1/24 (* (pow eps 4) (cos x)))
(* (pow eps 4) (+ (* 1/24 (cos x)) (* 1/6 (/ (sin x) eps))))
(* (pow eps 4) (+ (* -1 (/ (+ (* -1/6 (sin x)) (* 1/2 (/ (cos x) eps))) eps)) (* 1/24 (cos x))))
(* (pow eps 4) (+ (* -1 (/ (+ (* -1 (/ (+ (* -1/2 (cos x)) (/ (sin (neg x)) eps)) eps)) (* -1/6 (sin x))) eps)) (* 1/24 (cos x))))
(* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2))
(+ (* eps (* x (- (* 1/6 (pow eps 2)) 1))) (* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2)))
(+ (* x (+ (* -1/2 (* (pow eps 2) (* x (- (* 1/24 (pow eps 2)) 1/2)))) (* eps (- (* 1/6 (pow eps 2)) 1)))) (* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2)))
(+ (* x (+ (* eps (- (* 1/6 (pow eps 2)) 1)) (* x (+ (* -1/2 (* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2))) (* eps (* x (+ 1/6 (* -1/36 (pow eps 2))))))))) (* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2)))
(* eps (+ (sin (neg x)) (* eps (+ (* 1/6 (* eps (sin x))) (* (cos x) (- (* 1/24 (pow eps 2)) 1/2))))))
(* eps (+ (sin (neg x)) (* eps (+ (* 1/6 (* eps (sin x))) (* (cos x) (- (* 1/24 (pow eps 2)) 1/2))))))
(* eps (+ (sin (neg x)) (* eps (+ (* 1/6 (* eps (sin x))) (* (cos x) (- (* 1/24 (pow eps 2)) 1/2))))))
(* eps (+ (sin (neg x)) (* eps (+ (* 1/6 (* eps (sin x))) (* (cos x) (- (* 1/24 (pow eps 2)) 1/2))))))
(* eps (+ (sin (* -1 x)) (* eps (+ (* 1/6 (* eps (sin x))) (* (cos x) (- (* 1/24 (pow eps 2)) 1/2))))))
(* eps (+ (sin (* -1 x)) (* eps (+ (* 1/6 (* eps (sin x))) (* (cos x) (- (* 1/24 (pow eps 2)) 1/2))))))
(* eps (+ (sin (* -1 x)) (* eps (+ (* 1/6 (* eps (sin x))) (* (cos x) (- (* 1/24 (pow eps 2)) 1/2))))))
(* eps (+ (sin (* -1 x)) (* eps (+ (* 1/6 (* eps (sin x))) (* (cos x) (- (* 1/24 (pow eps 2)) 1/2))))))
(* -1 (* eps x))
(* eps (+ (* -1 x) (* -1/2 eps)))
(* eps (+ (* -1 x) (* eps (- (* 1/6 (* eps x)) 1/2))))
(* eps (+ (* -1 x) (* eps (- (* eps (+ (* 1/24 eps) (* 1/6 x))) 1/2))))
(* 1/24 (pow eps 4))
(* (pow eps 4) (+ 1/24 (* 1/6 (/ x eps))))
(* (pow eps 4) (- (+ 1/24 (* 1/6 (/ x eps))) (/ 1/2 (pow eps 2))))
(* (pow eps 4) (- (+ 1/24 (+ (* -1 (/ x (pow eps 3))) (* 1/6 (/ x eps)))) (/ 1/2 (pow eps 2))))
(* 1/24 (pow eps 4))
(* (pow eps 4) (+ 1/24 (* 1/6 (/ x eps))))
(* (pow eps 4) (+ 1/24 (* -1 (/ (+ (* -1/6 x) (* 1/2 (/ 1 eps))) eps))))
(* (pow eps 4) (+ 1/24 (* -1 (/ (+ (* -1 (/ (- (* -1 (/ x eps)) 1/2) eps)) (* -1/6 x)) eps))))
(* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2))
(+ (* eps (* x (- (* 1/6 (pow eps 2)) 1))) (* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2)))
(+ (* eps (* x (- (* 1/6 (pow eps 2)) 1))) (* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2)))
(+ (* eps (* x (- (* 1/6 (pow eps 2)) 1))) (* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2)))
(* eps (* x (- (* 1/6 (pow eps 2)) 1)))
(* x (+ (* eps (- (* 1/6 (pow eps 2)) 1)) (/ (* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2)) x)))
(* x (+ (* eps (- (* 1/6 (pow eps 2)) 1)) (/ (* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2)) x)))
(* x (+ (* eps (- (* 1/6 (pow eps 2)) 1)) (/ (* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2)) x)))
(* eps (* x (- (* 1/6 (pow eps 2)) 1)))
(* -1 (* x (+ (* -1 (* eps (- (* 1/6 (pow eps 2)) 1))) (* -1 (/ (* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2)) x)))))
(* -1 (* x (+ (* -1 (* eps (- (* 1/6 (pow eps 2)) 1))) (* -1 (/ (* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2)) x)))))
(* -1 (* x (+ (* -1 (* eps (- (* 1/6 (pow eps 2)) 1))) (* -1 (/ (* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2)) x)))))
(* -1 (* eps x))
(* -1 (* eps x))
(* -1 (* eps x))
(* -1 (* eps x))
(* -1 (* eps x))
(* -1 (* eps x))
(* -1 (* eps x))
(* -1 (* eps x))
(* -1 (* eps x))
(* -1 (* eps x))
(* -1 (* eps x))
(* -1 (* eps x))
(* -1 (* eps x))
(* -1 (* eps x))
(* -1 (* eps x))
(* -1 (* eps x))
(* -1 (* eps x))
(* -1 (* eps x))
(* -1 (* eps x))
(* -1 (* eps x))
(* -1 (* eps x))
(* -1 (* eps x))
(* -1 (* eps x))
(* -1 (* eps x))
(* 1/6 (* (pow eps 3) x))
(* (pow eps 3) (+ (* 1/24 eps) (* 1/6 x)))
(* (pow eps 3) (+ (* 1/24 eps) (* 1/6 x)))
(* (pow eps 3) (+ (* 1/24 eps) (* 1/6 x)))
(* 1/24 (pow eps 4))
(* (pow eps 4) (+ 1/24 (* 1/6 (/ x eps))))
(* (pow eps 4) (+ 1/24 (* 1/6 (/ x eps))))
(* (pow eps 4) (+ 1/24 (* 1/6 (/ x eps))))
(* 1/24 (pow eps 4))
(* (pow eps 4) (+ 1/24 (* 1/6 (/ x eps))))
(* (pow eps 4) (+ 1/24 (* 1/6 (/ x eps))))
(* (pow eps 4) (+ 1/24 (* 1/6 (/ x eps))))
(* 1/24 (pow eps 4))
(+ (* 1/24 (pow eps 4)) (* 1/6 (* (pow eps 3) x)))
(+ (* 1/24 (pow eps 4)) (* 1/6 (* (pow eps 3) x)))
(+ (* 1/24 (pow eps 4)) (* 1/6 (* (pow eps 3) x)))
(* 1/6 (* (pow eps 3) x))
(* x (+ (* 1/24 (/ (pow eps 4) x)) (* 1/6 (pow eps 3))))
(* x (+ (* 1/24 (/ (pow eps 4) x)) (* 1/6 (pow eps 3))))
(* x (+ (* 1/24 (/ (pow eps 4) x)) (* 1/6 (pow eps 3))))
(* 1/6 (* (pow eps 3) x))
(* -1 (* x (+ (* -1/6 (pow eps 3)) (* -1/24 (/ (pow eps 4) x)))))
(* -1 (* x (+ (* -1/6 (pow eps 3)) (* -1/24 (/ (pow eps 4) x)))))
(* -1 (* x (+ (* -1/6 (pow eps 3)) (* -1/24 (/ (pow eps 4) x)))))
(- (cos eps) 1)
(- (+ (cos eps) (* -1 (* x (sin eps)))) 1)
(- (+ (cos eps) (* x (- (* x (+ 1/2 (* -1/2 (cos eps)))) (sin eps)))) 1)
(- (+ (cos eps) (* x (- (* x (+ 1/2 (+ (* -1/2 (cos eps)) (* 1/6 (* x (sin eps)))))) (sin eps)))) 1)
(- (cos (+ eps x)) (cos x))
(- (cos (+ eps x)) (cos x))
(- (cos (+ eps x)) (cos x))
(- (cos (+ eps x)) (cos x))
(- (cos (- eps (* -1 x))) (cos x))
(- (cos (- eps (* -1 x))) (cos x))
(- (cos (- eps (* -1 x))) (cos x))
(- (cos (- eps (* -1 x))) (cos x))
(* -1 (* eps (sin x)))
(* eps (- (* -1/2 (* eps (cos x))) (sin x)))
(* eps (- (* eps (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x))))) (sin x)))
(* eps (- (* eps (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x)))))) (sin x)))
(- (cos (+ eps x)) (cos x))
(- (cos (+ eps x)) (cos x))
(- (cos (+ eps x)) (cos x))
(- (cos (+ eps x)) (cos x))
(- (cos (- x (* -1 eps))) (cos x))
(- (cos (- x (* -1 eps))) (cos x))
(- (cos (- x (* -1 eps))) (cos x))
(- (cos (- x (* -1 eps))) (cos x))
(* eps (sin (neg x)))
(* eps (+ (sin (neg x)) (* -1/2 (* eps (cos x)))))
(* eps (+ (sin (neg x)) (* eps (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x)))))))
(* eps (+ (sin (neg x)) (* eps (+ (* -1/2 (cos x)) (* eps (+ (* 1/24 (* eps (cos x))) (* 1/6 (sin x))))))))
(* 1/24 (* (pow eps 4) (cos x)))
(* (pow eps 4) (+ (* 1/24 (cos x)) (* 1/6 (/ (sin x) eps))))
(* (pow eps 4) (+ (* -1/2 (/ (cos x) (pow eps 2))) (+ (* 1/24 (cos x)) (* 1/6 (/ (sin x) eps)))))
(* (pow eps 4) (+ (* -1/2 (/ (cos x) (pow eps 2))) (+ (* 1/24 (cos x)) (+ (* 1/6 (/ (sin x) eps)) (/ (sin (neg x)) (pow eps 3))))))
(* 1/24 (* (pow eps 4) (cos x)))
(* (pow eps 4) (+ (* 1/24 (cos x)) (* 1/6 (/ (sin x) eps))))
(* (pow eps 4) (+ (* -1 (/ (+ (* -1/6 (sin x)) (* 1/2 (/ (cos x) eps))) eps)) (* 1/24 (cos x))))
(* (pow eps 4) (+ (* -1 (/ (+ (* -1 (/ (+ (* -1/2 (cos x)) (/ (sin (neg x)) eps)) eps)) (* -1/6 (sin x))) eps)) (* 1/24 (cos x))))
(* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2))
(+ (* eps (* x (- (* 1/6 (pow eps 2)) 1))) (* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2)))
(+ (* x (+ (* -1/2 (* (pow eps 2) (* x (- (* 1/24 (pow eps 2)) 1/2)))) (* eps (- (* 1/6 (pow eps 2)) 1)))) (* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2)))
(+ (* x (+ (* eps (- (* 1/6 (pow eps 2)) 1)) (* x (+ (* -1/2 (* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2))) (* eps (* x (+ 1/6 (* -1/36 (pow eps 2))))))))) (* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2)))
(* eps (+ (sin (neg x)) (* eps (+ (* 1/6 (* eps (sin x))) (* (cos x) (- (* 1/24 (pow eps 2)) 1/2))))))
(* eps (+ (sin (neg x)) (* eps (+ (* 1/6 (* eps (sin x))) (* (cos x) (- (* 1/24 (pow eps 2)) 1/2))))))
(* eps (+ (sin (neg x)) (* eps (+ (* 1/6 (* eps (sin x))) (* (cos x) (- (* 1/24 (pow eps 2)) 1/2))))))
(* eps (+ (sin (neg x)) (* eps (+ (* 1/6 (* eps (sin x))) (* (cos x) (- (* 1/24 (pow eps 2)) 1/2))))))
(* eps (+ (sin (* -1 x)) (* eps (+ (* 1/6 (* eps (sin x))) (* (cos x) (- (* 1/24 (pow eps 2)) 1/2))))))
(* eps (+ (sin (* -1 x)) (* eps (+ (* 1/6 (* eps (sin x))) (* (cos x) (- (* 1/24 (pow eps 2)) 1/2))))))
(* eps (+ (sin (* -1 x)) (* eps (+ (* 1/6 (* eps (sin x))) (* (cos x) (- (* 1/24 (pow eps 2)) 1/2))))))
(* eps (+ (sin (* -1 x)) (* eps (+ (* 1/6 (* eps (sin x))) (* (cos x) (- (* 1/24 (pow eps 2)) 1/2))))))
(* -1 (* eps x))
(* eps (+ (* -1 x) (* -1/2 eps)))
(* eps (+ (* -1 x) (* eps (- (* 1/6 (* eps x)) 1/2))))
(* eps (+ (* -1 x) (* eps (- (* eps (+ (* 1/24 eps) (* 1/6 x))) 1/2))))
(* 1/24 (pow eps 4))
(* (pow eps 4) (+ 1/24 (* 1/6 (/ x eps))))
(* (pow eps 4) (- (+ 1/24 (* 1/6 (/ x eps))) (/ 1/2 (pow eps 2))))
(* (pow eps 4) (- (+ 1/24 (+ (* -1 (/ x (pow eps 3))) (* 1/6 (/ x eps)))) (/ 1/2 (pow eps 2))))
(* 1/24 (pow eps 4))
(* (pow eps 4) (+ 1/24 (* 1/6 (/ x eps))))
(* (pow eps 4) (+ 1/24 (* -1 (/ (+ (* -1/6 x) (* 1/2 (/ 1 eps))) eps))))
(* (pow eps 4) (+ 1/24 (* -1 (/ (+ (* -1 (/ (- (* -1 (/ x eps)) 1/2) eps)) (* -1/6 x)) eps))))
(* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2))
(+ (* eps (* x (- (* 1/6 (pow eps 2)) 1))) (* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2)))
(+ (* eps (* x (- (* 1/6 (pow eps 2)) 1))) (* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2)))
(+ (* eps (* x (- (* 1/6 (pow eps 2)) 1))) (* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2)))
(* eps (* x (- (* 1/6 (pow eps 2)) 1)))
(* x (+ (* eps (- (* 1/6 (pow eps 2)) 1)) (/ (* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2)) x)))
(* x (+ (* eps (- (* 1/6 (pow eps 2)) 1)) (/ (* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2)) x)))
(* x (+ (* eps (- (* 1/6 (pow eps 2)) 1)) (/ (* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2)) x)))
(* eps (* x (- (* 1/6 (pow eps 2)) 1)))
(* -1 (* x (+ (* -1 (* eps (- (* 1/6 (pow eps 2)) 1))) (* -1 (/ (* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2)) x)))))
(* -1 (* x (+ (* -1 (* eps (- (* 1/6 (pow eps 2)) 1))) (* -1 (/ (* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2)) x)))))
(* -1 (* x (+ (* -1 (* eps (- (* 1/6 (pow eps 2)) 1))) (* -1 (/ (* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2)) x)))))
(* eps (- (* 1/24 (pow eps 2)) 1/2))
(+ (* eps (- (* 1/24 (pow eps 2)) 1/2)) (* x (- (* 1/6 (pow eps 2)) 1)))
(+ (* eps (- (* 1/24 (pow eps 2)) 1/2)) (* x (- (+ (* -1/2 (* eps (* x (- (* 1/24 (pow eps 2)) 1/2)))) (* 1/6 (pow eps 2))) 1)))
(+ (* eps (- (* 1/24 (pow eps 2)) 1/2)) (* x (- (+ (* 1/6 (pow eps 2)) (* x (+ (* -1/2 (* eps (- (* 1/24 (pow eps 2)) 1/2))) (* x (+ 1/6 (* -1/36 (pow eps 2))))))) 1)))
(* (pow x 3) (+ 1/6 (* -1/36 (pow eps 2))))
(* (pow x 3) (+ 1/6 (+ (* -1/2 (/ (* eps (- (* 1/24 (pow eps 2)) 1/2)) x)) (* -1/36 (pow eps 2)))))
(* (pow x 3) (- (+ 1/6 (+ (* -1/2 (/ (* eps (- (* 1/24 (pow eps 2)) 1/2)) x)) (+ (* -1/36 (pow eps 2)) (* 1/6 (/ (pow eps 2) (pow x 2)))))) (/ 1 (pow x 2))))
(* (pow x 3) (- (+ 1/6 (+ (* -1/2 (/ (* eps (- (* 1/24 (pow eps 2)) 1/2)) x)) (+ (* -1/36 (pow eps 2)) (+ (* 1/6 (/ (pow eps 2) (pow x 2))) (/ (* eps (- (* 1/24 (pow eps 2)) 1/2)) (pow x 3)))))) (/ 1 (pow x 2))))
(* (pow x 3) (+ 1/6 (* -1/36 (pow eps 2))))
(* -1 (* (pow x 3) (+ (* -1 (+ 1/6 (* -1/36 (pow eps 2)))) (* 1/2 (/ (* eps (- (* 1/24 (pow eps 2)) 1/2)) x)))))
(* -1 (* (pow x 3) (+ (* -1 (+ 1/6 (* -1/36 (pow eps 2)))) (* -1 (/ (- (+ (* -1/2 (* eps (- (* 1/24 (pow eps 2)) 1/2))) (* 1/6 (/ (pow eps 2) x))) (/ 1 x)) x)))))
(* -1 (* (pow x 3) (+ (* -1 (+ 1/6 (* -1/36 (pow eps 2)))) (* -1 (/ (+ (* -1 (/ (+ (* -1 (- (* 1/6 (pow eps 2)) 1)) (* -1 (/ (* eps (- (* 1/24 (pow eps 2)) 1/2)) x))) x)) (* -1/2 (* eps (- (* 1/24 (pow eps 2)) 1/2)))) x)))))
(* x (- (* 1/6 (pow x 2)) 1))
(+ (* eps (- (* 1/4 (pow x 2)) 1/2)) (* x (- (* 1/6 (pow x 2)) 1)))
(+ (* eps (- (+ (* 1/4 (pow x 2)) (* eps (* x (+ 1/6 (* -1/36 (pow x 2)))))) 1/2)) (* x (- (* 1/6 (pow x 2)) 1)))
(+ (* eps (- (+ (* 1/4 (pow x 2)) (* eps (+ (* eps (+ 1/24 (* -1/48 (pow x 2)))) (* x (+ 1/6 (* -1/36 (pow x 2))))))) 1/2)) (* x (- (* 1/6 (pow x 2)) 1)))
(* (pow eps 3) (+ 1/24 (* -1/48 (pow x 2))))
(* (pow eps 3) (+ 1/24 (+ (* -1/48 (pow x 2)) (/ (* x (+ 1/6 (* -1/36 (pow x 2)))) eps))))
(* (pow eps 3) (- (+ 1/24 (+ (* -1/48 (pow x 2)) (+ (* 1/4 (/ (pow x 2) (pow eps 2))) (/ (* x (+ 1/6 (* -1/36 (pow x 2)))) eps)))) (/ 1/2 (pow eps 2))))
(* (pow eps 3) (- (+ 1/24 (+ (* -1/48 (pow x 2)) (+ (* 1/4 (/ (pow x 2) (pow eps 2))) (+ (/ (* x (+ 1/6 (* -1/36 (pow x 2)))) eps) (/ (* x (- (* 1/6 (pow x 2)) 1)) (pow eps 3)))))) (/ 1/2 (pow eps 2))))
(* -1 (* (pow eps 3) (- (* 1/48 (pow x 2)) 1/24)))
(* -1 (* (pow eps 3) (- (+ (* -1 (/ (* x (+ 1/6 (* -1/36 (pow x 2)))) eps)) (* 1/48 (pow x 2))) 1/24)))
(* -1 (* (pow eps 3) (- (+ (* -1 (/ (+ (* -1 (/ (+ 1/2 (* -1/4 (pow x 2))) eps)) (* x (+ 1/6 (* -1/36 (pow x 2))))) eps)) (* 1/48 (pow x 2))) 1/24)))
(* -1 (* (pow eps 3) (- (+ (* -1 (/ (+ (* -1 (/ (+ 1/2 (+ (* -1 (/ (* x (- (* 1/6 (pow x 2)) 1)) eps)) (* -1/4 (pow x 2)))) eps)) (* x (+ 1/6 (* -1/36 (pow x 2))))) eps)) (* 1/48 (pow x 2))) 1/24)))
1/4
(+ 1/4 (* -1/48 (pow eps 2)))
(+ 1/4 (* -1/48 (pow eps 2)))
(+ 1/4 (* -1/48 (pow eps 2)))
(* -1/48 (pow eps 2))
(* (pow eps 2) (- (* 1/4 (/ 1 (pow eps 2))) 1/48))
(* (pow eps 2) (- (* 1/4 (/ 1 (pow eps 2))) 1/48))
(* (pow eps 2) (- (* 1/4 (/ 1 (pow eps 2))) 1/48))
(* -1/48 (pow eps 2))
(* (pow eps 2) (- (* 1/4 (/ 1 (pow eps 2))) 1/48))
(* (pow eps 2) (- (* 1/4 (/ 1 (pow eps 2))) 1/48))
(* (pow eps 2) (- (* 1/4 (/ 1 (pow eps 2))) 1/48))
(- (cos eps) 1)
(- (+ (cos eps) (* -1 (* x (sin eps)))) 1)
(- (+ (cos eps) (* x (- (* x (+ 1/2 (* -1/2 (cos eps)))) (sin eps)))) 1)
(- (+ (cos eps) (* x (- (* x (+ 1/2 (+ (* -1/2 (cos eps)) (* 1/6 (* x (sin eps)))))) (sin eps)))) 1)
(- (cos (+ eps x)) (cos x))
(- (cos (+ eps x)) (cos x))
(- (cos (+ eps x)) (cos x))
(- (cos (+ eps x)) (cos x))
(- (cos (- eps (* -1 x))) (cos x))
(- (cos (- eps (* -1 x))) (cos x))
(- (cos (- eps (* -1 x))) (cos x))
(- (cos (- eps (* -1 x))) (cos x))
(* -1 (* eps (sin x)))
(* eps (- (* -1/2 (* eps (cos x))) (sin x)))
(* eps (- (* eps (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x))))) (sin x)))
(* eps (- (* eps (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x)))))) (sin x)))
(- (cos (+ eps x)) (cos x))
(- (cos (+ eps x)) (cos x))
(- (cos (+ eps x)) (cos x))
(- (cos (+ eps x)) (cos x))
(- (cos (- x (* -1 eps))) (cos x))
(- (cos (- x (* -1 eps))) (cos x))
(- (cos (- x (* -1 eps))) (cos x))
(- (cos (- x (* -1 eps))) (cos x))
(* eps (sin (neg x)))
(* eps (+ (sin (neg x)) (* -1/2 (* eps (cos x)))))
(* eps (+ (sin (neg x)) (* eps (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x)))))))
(* eps (+ (sin (neg x)) (* eps (+ (* -1/2 (cos x)) (* eps (+ (* 1/24 (* eps (cos x))) (* 1/6 (sin x))))))))
(* 1/24 (* (pow eps 4) (cos x)))
(* (pow eps 4) (+ (* 1/24 (cos x)) (* 1/6 (/ (sin x) eps))))
(* (pow eps 4) (+ (* -1/2 (/ (cos x) (pow eps 2))) (+ (* 1/24 (cos x)) (* 1/6 (/ (sin x) eps)))))
(* (pow eps 4) (+ (* -1/2 (/ (cos x) (pow eps 2))) (+ (* 1/24 (cos x)) (+ (* 1/6 (/ (sin x) eps)) (/ (sin (neg x)) (pow eps 3))))))
(* 1/24 (* (pow eps 4) (cos x)))
(* (pow eps 4) (+ (* 1/24 (cos x)) (* 1/6 (/ (sin x) eps))))
(* (pow eps 4) (+ (* -1 (/ (+ (* -1/6 (sin x)) (* 1/2 (/ (cos x) eps))) eps)) (* 1/24 (cos x))))
(* (pow eps 4) (+ (* -1 (/ (+ (* -1 (/ (+ (* -1/2 (cos x)) (/ (sin (neg x)) eps)) eps)) (* -1/6 (sin x))) eps)) (* 1/24 (cos x))))
(* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2))
(+ (* eps (* x (- (* 1/6 (pow eps 2)) 1))) (* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2)))
(+ (* x (+ (* -1/2 (* (pow eps 2) (* x (- (* 1/24 (pow eps 2)) 1/2)))) (* eps (- (* 1/6 (pow eps 2)) 1)))) (* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2)))
(+ (* x (+ (* eps (- (* 1/6 (pow eps 2)) 1)) (* x (+ (* -1/2 (* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2))) (* eps (* x (+ 1/6 (* -1/36 (pow eps 2))))))))) (* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2)))
(* eps (+ (sin (neg x)) (* eps (+ (* 1/6 (* eps (sin x))) (* (cos x) (- (* 1/24 (pow eps 2)) 1/2))))))
(* eps (+ (sin (neg x)) (* eps (+ (* 1/6 (* eps (sin x))) (* (cos x) (- (* 1/24 (pow eps 2)) 1/2))))))
(* eps (+ (sin (neg x)) (* eps (+ (* 1/6 (* eps (sin x))) (* (cos x) (- (* 1/24 (pow eps 2)) 1/2))))))
(* eps (+ (sin (neg x)) (* eps (+ (* 1/6 (* eps (sin x))) (* (cos x) (- (* 1/24 (pow eps 2)) 1/2))))))
(* eps (+ (sin (* -1 x)) (* eps (+ (* 1/6 (* eps (sin x))) (* (cos x) (- (* 1/24 (pow eps 2)) 1/2))))))
(* eps (+ (sin (* -1 x)) (* eps (+ (* 1/6 (* eps (sin x))) (* (cos x) (- (* 1/24 (pow eps 2)) 1/2))))))
(* eps (+ (sin (* -1 x)) (* eps (+ (* 1/6 (* eps (sin x))) (* (cos x) (- (* 1/24 (pow eps 2)) 1/2))))))
(* eps (+ (sin (* -1 x)) (* eps (+ (* 1/6 (* eps (sin x))) (* (cos x) (- (* 1/24 (pow eps 2)) 1/2))))))
(- (cos eps) 1)
(- (+ (cos eps) (* -1 (* x (sin eps)))) 1)
(- (+ (cos eps) (* x (- (* x (+ 1/2 (* -1/2 (cos eps)))) (sin eps)))) 1)
(- (+ (cos eps) (* x (- (* x (+ 1/2 (+ (* -1/2 (cos eps)) (* 1/6 (* x (sin eps)))))) (sin eps)))) 1)
(- (* (cos eps) (cos x)) (+ (cos x) (* (sin eps) (sin x))))
(- (* (cos eps) (cos x)) (+ (cos x) (* (sin eps) (sin x))))
(- (* (cos eps) (cos x)) (+ (cos x) (* (sin eps) (sin x))))
(- (* (cos eps) (cos x)) (+ (cos x) (* (sin eps) (sin x))))
(- (* (cos eps) (cos x)) (+ (cos x) (* (sin eps) (sin x))))
(- (* (cos eps) (cos x)) (+ (cos x) (* (sin eps) (sin x))))
(- (* (cos eps) (cos x)) (+ (cos x) (* (sin eps) (sin x))))
(- (* (cos eps) (cos x)) (+ (cos x) (* (sin eps) (sin x))))
(* -1 (* eps (sin x)))
(* eps (- (* -1/2 (* eps (cos x))) (sin x)))
(* eps (- (* eps (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x))))) (sin x)))
(* eps (- (* eps (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x)))))) (sin x)))
(- (* (cos eps) (cos x)) (+ (cos x) (* (sin eps) (sin x))))
(- (* (cos eps) (cos x)) (+ (cos x) (* (sin eps) (sin x))))
(- (* (cos eps) (cos x)) (+ (cos x) (* (sin eps) (sin x))))
(- (* (cos eps) (cos x)) (+ (cos x) (* (sin eps) (sin x))))
(- (* (cos eps) (cos x)) (+ (cos x) (* (sin eps) (sin x))))
(- (* (cos eps) (cos x)) (+ (cos x) (* (sin eps) (sin x))))
(- (* (cos eps) (cos x)) (+ (cos x) (* (sin eps) (sin x))))
(- (* (cos eps) (cos x)) (+ (cos x) (* (sin eps) (sin x))))
(* -1 (* eps (sin x)))
(* eps (+ (* -1 (sin x)) (* -1/2 (* eps (cos x)))))
(* eps (+ (* -1 (sin x)) (* -1/2 (* eps (cos x)))))
(* eps (+ (* -1 (sin x)) (* -1/2 (* eps (cos x)))))
(* -1/2 (* (pow eps 2) (cos x)))
(* (pow eps 2) (+ (* -1 (/ (sin x) eps)) (* -1/2 (cos x))))
(* (pow eps 2) (+ (* -1 (/ (sin x) eps)) (* -1/2 (cos x))))
(* (pow eps 2) (+ (* -1 (/ (sin x) eps)) (* -1/2 (cos x))))
(* -1/2 (* (pow eps 2) (cos x)))
(* (pow eps 2) (+ (* -1 (/ (sin x) eps)) (* -1/2 (cos x))))
(* (pow eps 2) (+ (* -1 (/ (sin x) eps)) (* -1/2 (cos x))))
(* (pow eps 2) (+ (* -1 (/ (sin x) eps)) (* -1/2 (cos x))))
(* -1/2 (pow eps 2))
(+ (* -1 (* eps x)) (* -1/2 (pow eps 2)))
(+ (* -1/2 (pow eps 2)) (* x (+ (* -1 eps) (* 1/4 (* (pow eps 2) x)))))
(+ (* -1/2 (pow eps 2)) (* x (+ (* -1 eps) (* x (+ (* 1/6 (* eps x)) (* 1/4 (pow eps 2)))))))
(* eps (- (* -1/2 (* eps (cos x))) (sin x)))
(* eps (- (* -1/2 (* eps (cos x))) (sin x)))
(* eps (- (* -1/2 (* eps (cos x))) (sin x)))
(* eps (- (* -1/2 (* eps (cos x))) (sin x)))
(* eps (- (* -1/2 (* eps (cos x))) (sin x)))
(* eps (- (* -1/2 (* eps (cos x))) (sin x)))
(* eps (- (* -1/2 (* eps (cos x))) (sin x)))
(* eps (- (* -1/2 (* eps (cos x))) (sin x)))
(* -1 (sin x))
(- (* -1/2 (* eps (cos x))) (sin x))
(- (* -1/2 (* eps (cos x))) (sin x))
(- (* -1/2 (* eps (cos x))) (sin x))
(* -1/2 (* eps (cos x)))
(* eps (+ (* -1 (/ (sin x) eps)) (* -1/2 (cos x))))
(* eps (+ (* -1 (/ (sin x) eps)) (* -1/2 (cos x))))
(* eps (+ (* -1 (/ (sin x) eps)) (* -1/2 (cos x))))
(* -1/2 (* eps (cos x)))
(* -1 (* eps (+ (* 1/2 (cos x)) (/ (sin x) eps))))
(* -1 (* eps (+ (* 1/2 (cos x)) (/ (sin x) eps))))
(* -1 (* eps (+ (* 1/2 (cos x)) (/ (sin x) eps))))
(* -1/2 eps)
(+ (* -1 x) (* -1/2 eps))
(+ (* -1/2 eps) (* x (- (* 1/4 (* eps x)) 1)))
(+ (* -1/2 eps) (* x (- (* x (+ (* 1/6 x) (* 1/4 eps))) 1)))
(- (* -1/2 (* eps (cos x))) (sin x))
(- (* -1/2 (* eps (cos x))) (sin x))
(- (* -1/2 (* eps (cos x))) (sin x))
(- (* -1/2 (* eps (cos x))) (sin x))
(- (* -1/2 (* eps (cos x))) (sin x))
(- (* -1/2 (* eps (cos x))) (sin x))
(- (* -1/2 (* eps (cos x))) (sin x))
(- (* -1/2 (* eps (cos x))) (sin x))
(* -1/2 (* eps (cos x)))
(* -1/2 (* eps (cos x)))
(* -1/2 (* eps (cos x)))
(* -1/2 (* eps (cos x)))
(* -1/2 (* eps (cos x)))
(* -1/2 (* eps (cos x)))
(* -1/2 (* eps (cos x)))
(* -1/2 (* eps (cos x)))
(* -1/2 (* eps (cos x)))
(* -1/2 (* eps (cos x)))
(* -1/2 (* eps (cos x)))
(* -1/2 (* eps (cos x)))
(* -1/2 eps)
(+ (* -1/2 eps) (* 1/4 (* eps (pow x 2))))
(+ (* -1/2 eps) (* (pow x 2) (+ (* -1/48 (* eps (pow x 2))) (* 1/4 eps))))
(+ (* -1/2 eps) (* (pow x 2) (+ (* 1/4 eps) (* (pow x 2) (+ (* -1/48 eps) (* 1/1440 (* eps (pow x 2))))))))
(* -1/2 (* eps (cos x)))
(* -1/2 (* eps (cos x)))
(* -1/2 (* eps (cos x)))
(* -1/2 (* eps (cos x)))
(* -1/2 (* eps (cos x)))
(* -1/2 (* eps (cos x)))
(* -1/2 (* eps (cos x)))
(* -1/2 (* eps (cos x)))
(sin (* 1/2 eps))
(+ (sin (* 1/2 eps)) (* x (cos (* 1/2 eps))))
(+ (sin (* 1/2 eps)) (* x (+ (cos (* 1/2 eps)) (* -1/2 (* x (sin (* 1/2 eps)))))))
(+ (sin (* 1/2 eps)) (* x (+ (cos (* 1/2 eps)) (* x (+ (* -1/2 (sin (* 1/2 eps))) (* -1/6 (* x (cos (* 1/2 eps)))))))))
(+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x)))
(+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x)))
(+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x)))
(+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x)))
(+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x)))
(+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x)))
(+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x)))
(+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x)))
(sin x)
(+ (sin x) (* 1/2 (* eps (cos x))))
(+ (sin x) (* eps (+ (* -1/8 (* eps (sin x))) (* 1/2 (cos x)))))
(+ (sin x) (* eps (+ (* 1/2 (cos x)) (* eps (+ (* -1/8 (sin x)) (* -1/48 (* eps (cos x))))))))
(+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x)))
(+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x)))
(+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x)))
(+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x)))
(+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x)))
(+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x)))
(+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x)))
(+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x)))
(* x (cos (* 1/2 eps)))
(* x (+ (cos (* 1/2 eps)) (* -1/6 (* (pow x 2) (cos (* 1/2 eps))))))
(* x (+ (cos (* 1/2 eps)) (* (pow x 2) (+ (* -1/6 (cos (* 1/2 eps))) (* 1/120 (* (pow x 2) (cos (* 1/2 eps))))))))
(* x (+ (cos (* 1/2 eps)) (* (pow x 2) (+ (* -1/6 (cos (* 1/2 eps))) (* (pow x 2) (+ (* -1/5040 (* (pow x 2) (cos (* 1/2 eps)))) (* 1/120 (cos (* 1/2 eps)))))))))
(* (cos (* 1/2 eps)) (sin x))
(* (cos (* 1/2 eps)) (sin x))
(* (cos (* 1/2 eps)) (sin x))
(* (cos (* 1/2 eps)) (sin x))
(* (cos (* 1/2 eps)) (sin x))
(* (cos (* 1/2 eps)) (sin x))
(* (cos (* 1/2 eps)) (sin x))
(* (cos (* 1/2 eps)) (sin x))
(sin x)
(+ (sin x) (* -1/8 (* (pow eps 2) (sin x))))
(+ (sin x) (* (pow eps 2) (+ (* -1/8 (sin x)) (* 1/384 (* (pow eps 2) (sin x))))))
(+ (sin x) (* (pow eps 2) (+ (* -1/8 (sin x)) (* (pow eps 2) (+ (* -1/46080 (* (pow eps 2) (sin x))) (* 1/384 (sin x)))))))
(* (cos (* 1/2 eps)) (sin x))
(* (cos (* 1/2 eps)) (sin x))
(* (cos (* 1/2 eps)) (sin x))
(* (cos (* 1/2 eps)) (sin x))
(* (cos (* 1/2 eps)) (sin x))
(* (cos (* 1/2 eps)) (sin x))
(* (cos (* 1/2 eps)) (sin x))
(* (cos (* 1/2 eps)) (sin x))
(* -1 eps)
(* -1 eps)
(* -1 eps)
(* -1 eps)
(* -1 eps)
(* -1 eps)
(* -1 eps)
(* -1 eps)
(* -1 eps)
(* -1 eps)
(* -1 eps)
(* -1 eps)
(/ 1/6 eps)
(/ 1/6 eps)
(/ 1/6 eps)
(/ 1/6 eps)
(/ 1/6 eps)
(/ 1/6 eps)
(/ 1/6 eps)
(/ 1/6 eps)
(/ 1/6 eps)
(/ 1/6 eps)
(/ 1/6 eps)
(/ 1/6 eps)
(sin (neg x))
(+ (sin (neg x)) (* -1/2 (* eps (cos x))))
(+ (sin (neg x)) (* eps (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x))))))
(+ (sin (neg x)) (* eps (+ (* -1/2 (cos x)) (* eps (+ (* 1/24 (* eps (cos x))) (* 1/6 (sin x)))))))
(* 1/24 (* (pow eps 3) (cos x)))
(* (pow eps 3) (+ (* 1/24 (cos x)) (* 1/6 (/ (sin x) eps))))
(* (pow eps 3) (+ (* -1/2 (/ (cos x) (pow eps 2))) (+ (* 1/24 (cos x)) (* 1/6 (/ (sin x) eps)))))
(* (pow eps 3) (+ (* -1/2 (/ (cos x) (pow eps 2))) (+ (* 1/24 (cos x)) (+ (* 1/6 (/ (sin x) eps)) (/ (sin (neg x)) (pow eps 3))))))
(* 1/24 (* (pow eps 3) (cos x)))
(* -1 (* (pow eps 3) (+ (* -1/6 (/ (sin x) eps)) (* -1/24 (cos x)))))
(* -1 (* (pow eps 3) (+ (* -1 (/ (+ (* -1/2 (/ (cos x) eps)) (* 1/6 (sin x))) eps)) (* -1/24 (cos x)))))
(* -1 (* (pow eps 3) (+ (* -1 (/ (+ (* -1 (/ (+ (* -1 (/ (sin (neg x)) eps)) (* 1/2 (cos x))) eps)) (* 1/6 (sin x))) eps)) (* -1/24 (cos x)))))
(* eps (- (* 1/24 (pow eps 2)) 1/2))
(+ (* eps (- (* 1/24 (pow eps 2)) 1/2)) (* x (- (* 1/6 (pow eps 2)) 1)))
(+ (* eps (- (* 1/24 (pow eps 2)) 1/2)) (* x (- (+ (* -1/2 (* eps (* x (- (* 1/24 (pow eps 2)) 1/2)))) (* 1/6 (pow eps 2))) 1)))
(+ (* eps (- (* 1/24 (pow eps 2)) 1/2)) (* x (- (+ (* 1/6 (pow eps 2)) (* x (+ (* -1/2 (* eps (- (* 1/24 (pow eps 2)) 1/2))) (* x (+ 1/6 (* -1/36 (pow eps 2))))))) 1)))
(+ (sin (neg x)) (* eps (+ (* 1/6 (* eps (sin x))) (* (cos x) (- (* 1/24 (pow eps 2)) 1/2)))))
(+ (sin (neg x)) (* eps (+ (* 1/6 (* eps (sin x))) (* (cos x) (- (* 1/24 (pow eps 2)) 1/2)))))
(+ (sin (neg x)) (* eps (+ (* 1/6 (* eps (sin x))) (* (cos x) (- (* 1/24 (pow eps 2)) 1/2)))))
(+ (sin (neg x)) (* eps (+ (* 1/6 (* eps (sin x))) (* (cos x) (- (* 1/24 (pow eps 2)) 1/2)))))
(+ (sin (* -1 x)) (* eps (+ (* 1/6 (* eps (sin x))) (* (cos x) (- (* 1/24 (pow eps 2)) 1/2)))))
(+ (sin (* -1 x)) (* eps (+ (* 1/6 (* eps (sin x))) (* (cos x) (- (* 1/24 (pow eps 2)) 1/2)))))
(+ (sin (* -1 x)) (* eps (+ (* 1/6 (* eps (sin x))) (* (cos x) (- (* 1/24 (pow eps 2)) 1/2)))))
(+ (sin (* -1 x)) (* eps (+ (* 1/6 (* eps (sin x))) (* (cos x) (- (* 1/24 (pow eps 2)) 1/2)))))
(* 1/24 eps)
(* 1/24 eps)
(* 1/24 eps)
(* 1/24 eps)
(* 1/24 eps)
(* 1/24 eps)
(* 1/24 eps)
(* 1/24 eps)
(* 1/24 eps)
(* 1/24 eps)
(* 1/24 eps)
(* 1/24 eps)
(* 1/6 eps)
(* 1/6 eps)
(* 1/6 eps)
(* 1/6 eps)
(* 1/6 eps)
(* 1/6 eps)
(* 1/6 eps)
(* 1/6 eps)
(* 1/6 eps)
(* 1/6 eps)
(* 1/6 eps)
(* 1/6 eps)

Outputs
(* -1 (* eps (sin x)))
(*.f64 eps (sin.f64 (neg.f64 x)))
(* eps (+ (* -1 (sin x)) (* -1/2 (* eps (cos x)))))
(.f64 eps (-.f64 (.f64 eps (*.f64 #s(literal -1/2 binary64) (cos.f64 x))) (sin.f64 x)))
(* eps (+ (* -1 (sin x)) (* eps (+ (* -2 (* eps (+ (* -1/16 (sin x)) (* -1/48 (sin x))))) (* -1/2 (cos x))))))
(.f64 eps (-.f64 (.f64 eps (fma.f64 eps (.f64 (sin.f64 x) #s(literal 1/6 binary64)) (.f64 #s(literal -1/2 binary64) (cos.f64 x)))) (sin.f64 x)))
(* eps (+ (* -1 (sin x)) (* eps (+ (* -1/2 (cos x)) (* eps (+ (* -2 (+ (* -1/16 (sin x)) (* -1/48 (sin x)))) (* 1/24 (* eps (cos x)))))))))
(.f64 eps (fma.f64 eps (fma.f64 eps (.f64 (sin.f64 x) #s(literal 1/6 binary64)) (.f64 (cos.f64 x) (fma.f64 #s(literal 1/24 binary64) (.f64 eps eps) #s(literal -1/2 binary64)))) (sin.f64 (neg.f64 x))))
(* -2 (* (sin (* 1/2 eps)) (+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x)))))
(.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (.f64 (fma.f64 (cos.f64 x) (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (.f64 (sin.f64 x) (cos.f64 (.f64 eps #s(literal 1/2 binary64))))) #s(literal -2 binary64)))
(* -2 (* (sin (* 1/2 eps)) (+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x)))))
(.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (.f64 (fma.f64 (cos.f64 x) (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (.f64 (sin.f64 x) (cos.f64 (.f64 eps #s(literal 1/2 binary64))))) #s(literal -2 binary64)))
(* -2 (* (sin (* 1/2 eps)) (+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x)))))
(.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (.f64 (fma.f64 (cos.f64 x) (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (.f64 (sin.f64 x) (cos.f64 (.f64 eps #s(literal 1/2 binary64))))) #s(literal -2 binary64)))
(* -2 (* (sin (* 1/2 eps)) (+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x)))))
(.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (.f64 (fma.f64 (cos.f64 x) (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (.f64 (sin.f64 x) (cos.f64 (.f64 eps #s(literal 1/2 binary64))))) #s(literal -2 binary64)))
(* -2 (* (sin (* 1/2 eps)) (+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x)))))
(.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (.f64 (fma.f64 (cos.f64 x) (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (.f64 (sin.f64 x) (cos.f64 (.f64 eps #s(literal 1/2 binary64))))) #s(literal -2 binary64)))
(* -2 (* (sin (* 1/2 eps)) (+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x)))))
(.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (.f64 (fma.f64 (cos.f64 x) (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (.f64 (sin.f64 x) (cos.f64 (.f64 eps #s(literal 1/2 binary64))))) #s(literal -2 binary64)))
(* -2 (* (sin (* 1/2 eps)) (+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x)))))
(.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (.f64 (fma.f64 (cos.f64 x) (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (.f64 (sin.f64 x) (cos.f64 (.f64 eps #s(literal 1/2 binary64))))) #s(literal -2 binary64)))
(* -2 (* (sin (* 1/2 eps)) (+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x)))))
(.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (.f64 (fma.f64 (cos.f64 x) (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (.f64 (sin.f64 x) (cos.f64 (.f64 eps #s(literal 1/2 binary64))))) #s(literal -2 binary64)))
(* -2 (pow (sin (* 1/2 eps)) 2))
(.f64 #s(literal -2 binary64) (pow.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) #s(literal 2 binary64)))
(+ (* -2 (* x (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))) (* -2 (pow (sin (* 1/2 eps)) 2)))
(.f64 #s(literal -2 binary64) (.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (fma.f64 x (cos.f64 (.f64 eps #s(literal 1/2 binary64))) (sin.f64 (*.f64 eps #s(literal 1/2 binary64))))))
(+ (* -2 (pow (sin (* 1/2 eps)) 2)) (* x (+ (* -2 (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) (* x (pow (sin (* 1/2 eps)) 2)))))
(fma.f64 #s(literal -2 binary64) (.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (fma.f64 x (cos.f64 (.f64 eps #s(literal 1/2 binary64))) (sin.f64 (.f64 eps #s(literal 1/2 binary64))))) (.f64 x (.f64 x (pow.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) #s(literal 2 binary64)))))
(+ (* -2 (pow (sin (* 1/2 eps)) 2)) (* x (+ (* -2 (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) (* x (+ (* 1/3 (* x (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))) (pow (sin (* 1/2 eps)) 2))))))
(fma.f64 #s(literal -2 binary64) (.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (fma.f64 x (cos.f64 (.f64 eps #s(literal 1/2 binary64))) (sin.f64 (.f64 eps #s(literal 1/2 binary64))))) (.f64 (fma.f64 (.f64 (.f64 x #s(literal 1/3 binary64)) (sin.f64 (.f64 eps #s(literal 1/2 binary64)))) (cos.f64 (.f64 eps #s(literal 1/2 binary64))) (pow.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) #s(literal 2 binary64))) (*.f64 x x)))
(* -2 (* (sin (* 1/2 eps)) (+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x)))))
(.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (.f64 (fma.f64 (cos.f64 x) (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (.f64 (sin.f64 x) (cos.f64 (.f64 eps #s(literal 1/2 binary64))))) #s(literal -2 binary64)))
(* -2 (* (sin (* 1/2 eps)) (+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x)))))
(.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (.f64 (fma.f64 (cos.f64 x) (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (.f64 (sin.f64 x) (cos.f64 (.f64 eps #s(literal 1/2 binary64))))) #s(literal -2 binary64)))
(* -2 (* (sin (* 1/2 eps)) (+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x)))))
(.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (.f64 (fma.f64 (cos.f64 x) (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (.f64 (sin.f64 x) (cos.f64 (.f64 eps #s(literal 1/2 binary64))))) #s(literal -2 binary64)))
(* -2 (* (sin (* 1/2 eps)) (+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x)))))
(.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (.f64 (fma.f64 (cos.f64 x) (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (.f64 (sin.f64 x) (cos.f64 (.f64 eps #s(literal 1/2 binary64))))) #s(literal -2 binary64)))
(* -2 (* (sin (* 1/2 eps)) (+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x)))))
(.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (.f64 (fma.f64 (cos.f64 x) (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (.f64 (sin.f64 x) (cos.f64 (.f64 eps #s(literal 1/2 binary64))))) #s(literal -2 binary64)))
(* -2 (* (sin (* 1/2 eps)) (+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x)))))
(.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (.f64 (fma.f64 (cos.f64 x) (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (.f64 (sin.f64 x) (cos.f64 (.f64 eps #s(literal 1/2 binary64))))) #s(literal -2 binary64)))
(* -2 (* (sin (* 1/2 eps)) (+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x)))))
(.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (.f64 (fma.f64 (cos.f64 x) (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (.f64 (sin.f64 x) (cos.f64 (.f64 eps #s(literal 1/2 binary64))))) #s(literal -2 binary64)))
(* -2 (* (sin (* 1/2 eps)) (+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x)))))
(.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (.f64 (fma.f64 (cos.f64 x) (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (.f64 (sin.f64 x) (cos.f64 (.f64 eps #s(literal 1/2 binary64))))) #s(literal -2 binary64)))
(* 1/2 (* eps (sin x)))
(.f64 eps (.f64 (sin.f64 x) #s(literal 1/2 binary64)))
(* eps (+ (* 1/4 (* eps (cos x))) (* 1/2 (sin x))))
(.f64 eps (fma.f64 eps (.f64 (cos.f64 x) #s(literal 1/4 binary64)) (*.f64 (sin.f64 x) #s(literal 1/2 binary64))))
(* eps (+ (* 1/2 (sin x)) (* eps (+ (* 1/4 (cos x)) (* eps (+ (* -1/16 (sin x)) (* -1/48 (sin x))))))))
(.f64 eps (fma.f64 eps (fma.f64 eps (.f64 (sin.f64 x) #s(literal -1/12 binary64)) (.f64 (cos.f64 x) #s(literal 1/4 binary64))) (.f64 (sin.f64 x) #s(literal 1/2 binary64))))
(* eps (+ (* 1/2 (sin x)) (* eps (+ (* 1/4 (cos x)) (* eps (+ (* -1/16 (sin x)) (+ (* -1/48 (sin x)) (* -1/48 (* eps (cos x))))))))))
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(- (cos (+ eps x)) (cos x))
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(+ (sin (* 1/2 eps)) (* x (+ (cos (* 1/2 eps)) (* x (+ (* -1/2 (sin (* 1/2 eps))) (* -1/6 (* x (cos (* 1/2 eps)))))))))
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(+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x)))
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(+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x)))
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(+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x)))
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(+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x)))
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(* x (cos (* 1/2 eps)))
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(* x (+ (cos (* 1/2 eps)) (* (pow x 2) (+ (* -1/6 (cos (* 1/2 eps))) (* 1/120 (* (pow x 2) (cos (* 1/2 eps))))))))
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(* x (+ (cos (* 1/2 eps)) (* (pow x 2) (+ (* -1/6 (cos (* 1/2 eps))) (* (pow x 2) (+ (* -1/5040 (* (pow x 2) (cos (* 1/2 eps)))) (* 1/120 (cos (* 1/2 eps)))))))))
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(* (cos (* 1/2 eps)) (sin x))
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(.f64 (sin.f64 x) (cos.f64 (.f64 eps #s(literal 1/2 binary64))))
(* (cos (* 1/2 eps)) (sin x))
(.f64 (sin.f64 x) (cos.f64 (.f64 eps #s(literal 1/2 binary64))))
(* (cos (* 1/2 eps)) (sin x))
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(* (cos (* 1/2 eps)) (sin x))
(.f64 (sin.f64 x) (cos.f64 (.f64 eps #s(literal 1/2 binary64))))
(sin x)
(sin.f64 x)
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(.f64 (fma.f64 (.f64 eps eps) #s(literal -1/8 binary64) #s(literal 1 binary64)) (sin.f64 x))
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(+ (sin x) (* (pow eps 2) (+ (* -1/8 (sin x)) (* (pow eps 2) (+ (* -1/46080 (* (pow eps 2) (sin x))) (* 1/384 (sin x)))))))
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(* (cos (* 1/2 eps)) (sin x))
(.f64 (sin.f64 x) (cos.f64 (.f64 eps #s(literal 1/2 binary64))))
(* (cos (* 1/2 eps)) (sin x))
(.f64 (sin.f64 x) (cos.f64 (.f64 eps #s(literal 1/2 binary64))))
(* (cos (* 1/2 eps)) (sin x))
(.f64 (sin.f64 x) (cos.f64 (.f64 eps #s(literal 1/2 binary64))))
(* (cos (* 1/2 eps)) (sin x))
(.f64 (sin.f64 x) (cos.f64 (.f64 eps #s(literal 1/2 binary64))))
(* (cos (* 1/2 eps)) (sin x))
(.f64 (sin.f64 x) (cos.f64 (.f64 eps #s(literal 1/2 binary64))))
(* (cos (* 1/2 eps)) (sin x))
(.f64 (sin.f64 x) (cos.f64 (.f64 eps #s(literal 1/2 binary64))))
(* (cos (* 1/2 eps)) (sin x))
(.f64 (sin.f64 x) (cos.f64 (.f64 eps #s(literal 1/2 binary64))))
(* (cos (* 1/2 eps)) (sin x))
(.f64 (sin.f64 x) (cos.f64 (.f64 eps #s(literal 1/2 binary64))))
(* -1 eps)
(neg.f64 eps)
(* -1 eps)
(neg.f64 eps)
(* -1 eps)
(neg.f64 eps)
(* -1 eps)
(neg.f64 eps)
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(neg.f64 eps)
(* -1 eps)
(neg.f64 eps)
(* -1 eps)
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(* -1 eps)
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(/.f64 #s(literal 1/6 binary64) eps)
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(/ 1/6 eps)
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(/ 1/6 eps)
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(/ 1/6 eps)
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(sin.f64 (neg.f64 x))
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(-.f64 (.f64 eps (.f64 #s(literal -1/2 binary64) (cos.f64 x))) (sin.f64 x))
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(-.f64 (.f64 eps (fma.f64 eps (.f64 (sin.f64 x) #s(literal 1/6 binary64)) (*.f64 #s(literal -1/2 binary64) (cos.f64 x)))) (sin.f64 x))
(+ (sin (neg x)) (* eps (+ (* -1/2 (cos x)) (* eps (+ (* 1/24 (* eps (cos x))) (* 1/6 (sin x)))))))
(fma.f64 eps (fma.f64 eps (.f64 (sin.f64 x) #s(literal 1/6 binary64)) (.f64 (cos.f64 x) (fma.f64 #s(literal 1/24 binary64) (*.f64 eps eps) #s(literal -1/2 binary64)))) (sin.f64 (neg.f64 x)))
(* 1/24 (* (pow eps 3) (cos x)))
(.f64 (cos.f64 x) (.f64 eps (.f64 #s(literal 1/24 binary64) (.f64 eps eps))))
(* (pow eps 3) (+ (* 1/24 (cos x)) (* 1/6 (/ (sin x) eps))))
(.f64 (fma.f64 (sin.f64 x) (/.f64 #s(literal 1/6 binary64) eps) (.f64 (cos.f64 x) #s(literal 1/24 binary64))) (.f64 eps (.f64 eps eps)))
(* (pow eps 3) (+ (* -1/2 (/ (cos x) (pow eps 2))) (+ (* 1/24 (cos x)) (* 1/6 (/ (sin x) eps)))))
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(* (pow eps 3) (+ (* -1/2 (/ (cos x) (pow eps 2))) (+ (* 1/24 (cos x)) (+ (* 1/6 (/ (sin x) eps)) (/ (sin (neg x)) (pow eps 3))))))
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(* 1/24 (* (pow eps 3) (cos x)))
(.f64 (cos.f64 x) (.f64 eps (.f64 #s(literal 1/24 binary64) (.f64 eps eps))))
(* -1 (* (pow eps 3) (+ (* -1/6 (/ (sin x) eps)) (* -1/24 (cos x)))))
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(* -1 (* (pow eps 3) (+ (* -1 (/ (+ (* -1/2 (/ (cos x) eps)) (* 1/6 (sin x))) eps)) (* -1/24 (cos x)))))
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(* eps (- (* 1/24 (pow eps 2)) 1/2))
(.f64 eps (fma.f64 #s(literal 1/24 binary64) (.f64 eps eps) #s(literal -1/2 binary64)))
(+ (* eps (- (* 1/24 (pow eps 2)) 1/2)) (* x (- (* 1/6 (pow eps 2)) 1)))
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(+ (sin (neg x)) (* eps (+ (* 1/6 (* eps (sin x))) (* (cos x) (- (* 1/24 (pow eps 2)) 1/2)))))
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(*.f64 eps #s(literal 1/6 binary64))
(* 1/6 eps)
(*.f64 eps #s(literal 1/6 binary64))
(* 1/6 eps)
(*.f64 eps #s(literal 1/6 binary64))

rewrite247.0ms (1.3%)

Memory

-18.0MiB live, 306.1MiB allocated

Rules

5 962×	`lower-fma.f32`
5 946×	`lower-fma.f64`
5 268×	`lower-*.f32`
5 234×	`lower-*.f64`
1 838×	`lower-/.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	98	769
0	142	731
1	566	641
2	5410	641
0	8519	619

Stop Event

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

Counts

27 → 330

Calls

Call 1

Inputs
(.f64 #s(approx ( (sin (* (+ eps 0) 1/2)) (+ (* (sin (* (+ x x) 1/2)) (cos (* eps 1/2))) (* (cos (* (+ x x) 1/2)) (sin (* eps 1/2))))) (.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (fma.f64 (cos.f64 x) (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (.f64 (sin.f64 x) (cos.f64 (*.f64 eps #s(literal 1/2 binary64))))))) #s(literal -2 binary64))
#s(approx (* (sin (* (+ eps 0) 1/2)) (+ (* (sin (* (+ x x) 1/2)) (cos (* eps 1/2))) (* (cos (* (+ x x) 1/2)) (sin (* eps 1/2))))) (.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (fma.f64 (cos.f64 x) (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (.f64 (sin.f64 x) (cos.f64 (*.f64 eps #s(literal 1/2 binary64)))))))
(.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (fma.f64 (cos.f64 x) (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (.f64 (sin.f64 x) (cos.f64 (*.f64 eps #s(literal 1/2 binary64))))))
(sin.f64 (*.f64 eps #s(literal 1/2 binary64)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* eps (+ (* eps (+ (* (cos x) (+ -1/2 (* eps (* eps 1/24)))) (* eps (* 1/6 (sin x))))) (sin (neg x)))) #s(approx (+ (* eps (* eps (+ (* eps (* eps 1/24)) -1/2))) (* eps (* x (+ (* eps (* eps 1/6)) -1)))) (*.f64 x (neg.f64 eps)))))
#s(approx (* eps (+ (* eps (+ (* (cos x) (+ -1/2 (* eps (* eps 1/24)))) (* eps (* 1/6 (sin x))))) (sin (neg x)))) #s(approx (+ (* eps (* eps (+ (* eps (* eps 1/24)) -1/2))) (* eps (* x (+ (* eps (* eps 1/6)) -1)))) (*.f64 x (neg.f64 eps))))
#s(approx (+ (* eps (* eps (+ (* eps (* eps 1/24)) -1/2))) (* eps (* x (+ (* eps (* eps 1/6)) -1)))) (*.f64 x (neg.f64 eps)))
(*.f64 x (neg.f64 eps))
(.f64 (.f64 (.f64 eps eps) (.f64 eps eps)) (fma.f64 x (/.f64 #s(literal 1/6 binary64) eps) #s(literal 1/24 binary64)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* eps (+ (* eps (+ (* (cos x) (+ -1/2 (* eps (* eps 1/24)))) (* eps (* 1/6 (sin x))))) (sin (neg x)))) #s(approx (+ (* eps (* eps (+ (* eps (* eps 1/24)) -1/2))) (* eps (* x (+ (* eps (* eps 1/6)) -1)))) (.f64 (.f64 (.f64 eps eps) (.f64 eps eps)) (fma.f64 x (/.f64 #s(literal 1/6 binary64) eps) #s(literal 1/24 binary64))))))
#s(approx (* eps (+ (* eps (+ (* (cos x) (+ -1/2 (* eps (* eps 1/24)))) (* eps (* 1/6 (sin x))))) (sin (neg x)))) #s(approx (+ (* eps (* eps (+ (* eps (* eps 1/24)) -1/2))) (* eps (* x (+ (* eps (* eps 1/6)) -1)))) (.f64 (.f64 (.f64 eps eps) (.f64 eps eps)) (fma.f64 x (/.f64 #s(literal 1/6 binary64) eps) #s(literal 1/24 binary64)))))
#s(approx (+ (* eps (* eps (+ (* eps (* eps 1/24)) -1/2))) (* eps (* x (+ (* eps (* eps 1/6)) -1)))) (.f64 (.f64 (.f64 eps eps) (.f64 eps eps)) (fma.f64 x (/.f64 #s(literal 1/6 binary64) eps) #s(literal 1/24 binary64))))
(fma.f64 x (fma.f64 x (fma.f64 eps (.f64 (fma.f64 eps (.f64 eps #s(literal 1/24 binary64)) #s(literal -1/2 binary64)) #s(literal -1/2 binary64)) (.f64 x (fma.f64 (.f64 eps eps) #s(literal -1/36 binary64) #s(literal 1/6 binary64)))) (fma.f64 eps (.f64 eps #s(literal 1/6 binary64)) #s(literal -1 binary64))) (.f64 eps (fma.f64 eps (*.f64 eps #s(literal 1/24 binary64)) #s(literal -1/2 binary64))))
(.f64 (fma.f64 eps (.f64 eps #s(literal 1/24 binary64)) #s(literal -1/2 binary64)) #s(literal -1/2 binary64))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps #s(approx (+ ( eps (+ (* (cos x) (+ -1/2 (* eps (* eps 1/24)))) (* eps (* 1/6 (sin x))))) (sin (neg x))) (fma.f64 x (fma.f64 x (fma.f64 eps (.f64 (fma.f64 eps (.f64 eps #s(literal 1/24 binary64)) #s(literal -1/2 binary64)) #s(literal -1/2 binary64)) (.f64 x (fma.f64 (.f64 eps eps) #s(literal -1/36 binary64) #s(literal 1/6 binary64)))) (fma.f64 eps (.f64 eps #s(literal 1/6 binary64)) #s(literal -1 binary64))) (.f64 eps (fma.f64 eps (*.f64 eps #s(literal 1/24 binary64)) #s(literal -1/2 binary64)))))))
(.f64 eps #s(approx (+ ( eps (+ (* (cos x) (+ -1/2 (* eps (* eps 1/24)))) (* eps (* 1/6 (sin x))))) (sin (neg x))) (fma.f64 x (fma.f64 x (fma.f64 eps (.f64 (fma.f64 eps (.f64 eps #s(literal 1/24 binary64)) #s(literal -1/2 binary64)) #s(literal -1/2 binary64)) (.f64 x (fma.f64 (.f64 eps eps) #s(literal -1/36 binary64) #s(literal 1/6 binary64)))) (fma.f64 eps (.f64 eps #s(literal 1/6 binary64)) #s(literal -1 binary64))) (.f64 eps (fma.f64 eps (*.f64 eps #s(literal 1/24 binary64)) #s(literal -1/2 binary64))))))
#s(approx (- (* (cos x) (cos eps)) (+ (* (sin x) (sin eps)) (cos x))) (.f64 eps (-.f64 (.f64 eps (*.f64 #s(literal -1/2 binary64) (cos.f64 x))) (sin.f64 x))))
(.f64 eps (-.f64 (.f64 eps (*.f64 #s(literal -1/2 binary64) (cos.f64 x))) (sin.f64 x)))
(-.f64 (.f64 eps (.f64 #s(literal -1/2 binary64) (cos.f64 x))) (sin.f64 x))
(.f64 eps (.f64 #s(literal -1/2 binary64) (cos.f64 x)))
(fma.f64 (cos.f64 x) (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (.f64 (sin.f64 x) (cos.f64 (*.f64 eps #s(literal 1/2 binary64)))))
(.f64 (sin.f64 x) (cos.f64 (.f64 eps #s(literal 1/2 binary64))))
(neg.f64 eps)
(/.f64 #s(literal 1/6 binary64) eps)
#s(approx (+ (* eps (+ (* (cos x) (+ -1/2 (* eps (* eps 1/24)))) (* eps (* 1/6 (sin x))))) (sin (neg x))) (fma.f64 x (fma.f64 x (fma.f64 eps (.f64 (fma.f64 eps (.f64 eps #s(literal 1/24 binary64)) #s(literal -1/2 binary64)) #s(literal -1/2 binary64)) (.f64 x (fma.f64 (.f64 eps eps) #s(literal -1/36 binary64) #s(literal 1/6 binary64)))) (fma.f64 eps (.f64 eps #s(literal 1/6 binary64)) #s(literal -1 binary64))) (.f64 eps (fma.f64 eps (*.f64 eps #s(literal 1/24 binary64)) #s(literal -1/2 binary64)))))
(*.f64 eps #s(literal 1/24 binary64))
(*.f64 eps #s(literal 1/6 binary64))

Outputs
(.f64 #s(approx ( (sin (* (+ eps 0) 1/2)) (+ (* (sin (* (+ x x) 1/2)) (cos (* eps 1/2))) (* (cos (* (+ x x) 1/2)) (sin (* eps 1/2))))) (.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (sin.f64 (fma.f64 eps #s(literal 1/2 binary64) x)))) #s(literal -2 binary64))
(.f64 #s(literal -2 binary64) #s(approx ( (sin (* (+ eps 0) 1/2)) (+ (* (sin (* (+ x x) 1/2)) (cos (* eps 1/2))) (* (cos (* (+ x x) 1/2)) (sin (* eps 1/2))))) (.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (sin.f64 (fma.f64 eps #s(literal 1/2 binary64) x)))))
#s(approx (* (sin (* (+ eps 0) 1/2)) (+ (* (sin (* (+ x x) 1/2)) (cos (* eps 1/2))) (* (cos (* (+ x x) 1/2)) (sin (* eps 1/2))))) (.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (sin.f64 (fma.f64 eps #s(literal 1/2 binary64) x))))
(+.f64 (.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (.f64 (sin.f64 x) (cos.f64 (.f64 eps #s(literal 1/2 binary64))))) (.f64 (cos.f64 x) (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 #s(literal 2 binary64) (.f64 eps #s(literal 1/2 binary64))))))))
(+.f64 (.f64 (cos.f64 x) (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 #s(literal 2 binary64) (.f64 eps #s(literal 1/2 binary64))))))) (.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (.f64 (sin.f64 x) (cos.f64 (.f64 eps #s(literal 1/2 binary64))))))
(fma.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (.f64 (sin.f64 x) (cos.f64 (.f64 eps #s(literal 1/2 binary64)))) (.f64 (cos.f64 x) (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 #s(literal 2 binary64) (*.f64 eps #s(literal 1/2 binary64))))))))
(fma.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (cos.f64 x)) (.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (.f64 (sin.f64 x) (cos.f64 (*.f64 eps #s(literal 1/2 binary64))))))
(fma.f64 (sin.f64 x) (.f64 (cos.f64 (.f64 eps #s(literal 1/2 binary64))) (sin.f64 (.f64 eps #s(literal 1/2 binary64)))) (.f64 (cos.f64 x) (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 #s(literal 2 binary64) (*.f64 eps #s(literal 1/2 binary64))))))))
(fma.f64 (cos.f64 (.f64 eps #s(literal 1/2 binary64))) (.f64 (sin.f64 x) (sin.f64 (.f64 eps #s(literal 1/2 binary64)))) (.f64 (cos.f64 x) (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 #s(literal 2 binary64) (*.f64 eps #s(literal 1/2 binary64))))))))
(fma.f64 (.f64 (sin.f64 x) (cos.f64 (.f64 eps #s(literal 1/2 binary64)))) (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (.f64 (cos.f64 x) (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 #s(literal 2 binary64) (*.f64 eps #s(literal 1/2 binary64))))))))
(fma.f64 (cos.f64 x) (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 #s(literal 2 binary64) (.f64 eps #s(literal 1/2 binary64)))))) (.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (.f64 (sin.f64 x) (cos.f64 (*.f64 eps #s(literal 1/2 binary64))))))
(fma.f64 (.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (cos.f64 x)) (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (.f64 (sin.f64 x) (cos.f64 (*.f64 eps #s(literal 1/2 binary64))))))
(fma.f64 (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 #s(literal 2 binary64) (.f64 eps #s(literal 1/2 binary64)))))) (cos.f64 x) (.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (.f64 (sin.f64 x) (cos.f64 (*.f64 eps #s(literal 1/2 binary64))))))
(fma.f64 (.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (cos.f64 (.f64 eps #s(literal 1/2 binary64)))) (sin.f64 x) (.f64 (cos.f64 x) (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 #s(literal 2 binary64) (*.f64 eps #s(literal 1/2 binary64))))))))
(fma.f64 (.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (sin.f64 x)) (cos.f64 (.f64 eps #s(literal 1/2 binary64))) (.f64 (cos.f64 x) (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 #s(literal 2 binary64) (*.f64 eps #s(literal 1/2 binary64))))))))
(/.f64 (+.f64 (pow.f64 (.f64 (cos.f64 x) (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 #s(literal 2 binary64) (.f64 eps #s(literal 1/2 binary64))))))) #s(literal 3 binary64)) (pow.f64 (.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (.f64 (sin.f64 x) (cos.f64 (.f64 eps #s(literal 1/2 binary64))))) #s(literal 3 binary64))) (fma.f64 (.f64 (cos.f64 x) (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 #s(literal 2 binary64) (.f64 eps #s(literal 1/2 binary64))))))) (.f64 (cos.f64 x) (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 #s(literal 2 binary64) (.f64 eps #s(literal 1/2 binary64))))))) (-.f64 (.f64 (.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (.f64 (sin.f64 x) (cos.f64 (.f64 eps #s(literal 1/2 binary64))))) (.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (.f64 (sin.f64 x) (cos.f64 (.f64 eps #s(literal 1/2 binary64)))))) (.f64 (.f64 (cos.f64 x) (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 #s(literal 2 binary64) (.f64 eps #s(literal 1/2 binary64))))))) (.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (.f64 (sin.f64 x) (cos.f64 (.f64 eps #s(literal 1/2 binary64)))))))))
(/.f64 (-.f64 (.f64 (.f64 (cos.f64 x) (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 #s(literal 2 binary64) (.f64 eps #s(literal 1/2 binary64))))))) (.f64 (cos.f64 x) (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 #s(literal 2 binary64) (.f64 eps #s(literal 1/2 binary64)))))))) (.f64 (.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (.f64 (sin.f64 x) (cos.f64 (.f64 eps #s(literal 1/2 binary64))))) (.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (.f64 (sin.f64 x) (cos.f64 (.f64 eps #s(literal 1/2 binary64))))))) (-.f64 (.f64 (cos.f64 x) (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 #s(literal 2 binary64) (.f64 eps #s(literal 1/2 binary64))))))) (.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (.f64 (sin.f64 x) (cos.f64 (.f64 eps #s(literal 1/2 binary64)))))))
(/.f64 (.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (.f64 (fma.f64 #s(literal 1 binary64) (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 #s(literal 2 binary64) (.f64 eps #s(literal 1/2 binary64)))))) (.f64 (.f64 (sin.f64 x) (cos.f64 (.f64 eps #s(literal 1/2 binary64)))) (sin.f64 (-.f64 x (.f64 eps #s(literal 1/2 binary64)))))) (sin.f64 (fma.f64 eps #s(literal 1/2 binary64) x)))) (fma.f64 #s(literal 1 binary64) (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 #s(literal 2 binary64) (.f64 eps #s(literal 1/2 binary64)))))) (.f64 (.f64 (sin.f64 x) (cos.f64 (.f64 eps #s(literal 1/2 binary64)))) (sin.f64 (-.f64 x (*.f64 eps #s(literal 1/2 binary64)))))))
(/.f64 (.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (.f64 (sin.f64 (fma.f64 eps #s(literal 1/2 binary64) x)) (sin.f64 (-.f64 (.f64 eps #s(literal 1/2 binary64)) x)))) (sin.f64 (-.f64 (*.f64 eps #s(literal 1/2 binary64)) x)))
(/.f64 (.f64 (.f64 (fma.f64 #s(literal 1 binary64) (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 #s(literal 2 binary64) (.f64 eps #s(literal 1/2 binary64)))))) (.f64 (.f64 (sin.f64 x) (cos.f64 (.f64 eps #s(literal 1/2 binary64)))) (sin.f64 (-.f64 x (.f64 eps #s(literal 1/2 binary64)))))) (sin.f64 (fma.f64 eps #s(literal 1/2 binary64) x))) (sin.f64 (.f64 eps #s(literal 1/2 binary64)))) (fma.f64 #s(literal 1 binary64) (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 #s(literal 2 binary64) (.f64 eps #s(literal 1/2 binary64)))))) (.f64 (.f64 (sin.f64 x) (cos.f64 (.f64 eps #s(literal 1/2 binary64)))) (sin.f64 (-.f64 x (*.f64 eps #s(literal 1/2 binary64)))))))
(/.f64 (.f64 (.f64 (sin.f64 (fma.f64 eps #s(literal 1/2 binary64) x)) (sin.f64 (-.f64 (.f64 eps #s(literal 1/2 binary64)) x))) (sin.f64 (.f64 eps #s(literal 1/2 binary64)))) (sin.f64 (-.f64 (*.f64 eps #s(literal 1/2 binary64)) x)))
(/.f64 (-.f64 (cos.f64 (-.f64 (*.f64 eps #s(literal 1/2 binary64)) (fma.f64 eps #s(literal 1/2 binary64) x))) (cos.f64 (fma.f64 eps #s(literal 1/2 binary64) (fma.f64 eps #s(literal 1/2 binary64) x)))) #s(literal 2 binary64))
(/.f64 (-.f64 (cos.f64 (-.f64 (fma.f64 eps #s(literal 1/2 binary64) x) (.f64 eps #s(literal 1/2 binary64)))) (cos.f64 (+.f64 (fma.f64 eps #s(literal 1/2 binary64) x) (.f64 eps #s(literal 1/2 binary64))))) #s(literal 2 binary64))
(.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (sin.f64 (fma.f64 eps #s(literal 1/2 binary64) x)))
(.f64 (sin.f64 (fma.f64 eps #s(literal 1/2 binary64) x)) (sin.f64 (.f64 eps #s(literal 1/2 binary64))))
(+.f64 (.f64 #s(literal 0 binary64) (cos.f64 (.f64 eps #s(literal 1/2 binary64)))) (.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) #s(literal 1 binary64)))
(+.f64 (.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) #s(literal 1 binary64)) (.f64 #s(literal 0 binary64) (cos.f64 (.f64 eps #s(literal 1/2 binary64)))))
(-.f64 (/.f64 (.f64 #s(literal 0 binary64) (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 #s(literal 2 binary64) (.f64 eps #s(literal 1/2 binary64))))))) (sin.f64 (.f64 eps #s(literal -1/2 binary64)))) (/.f64 (.f64 #s(literal 1 binary64) (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 #s(literal 2 binary64) (.f64 eps #s(literal 1/2 binary64))))))) (sin.f64 (.f64 eps #s(literal -1/2 binary64)))))
(-.f64 (.f64 (sin.f64 (/.f64 (+.f64 eps x) #s(literal 2 binary64))) (cos.f64 (/.f64 x #s(literal 2 binary64)))) (.f64 (cos.f64 (/.f64 (+.f64 eps x) #s(literal 2 binary64))) (sin.f64 (/.f64 x #s(literal 2 binary64)))))
(sin.f64 (*.f64 eps #s(literal 1/2 binary64)))
(fma.f64 #s(literal 0 binary64) (cos.f64 (.f64 eps #s(literal 1/2 binary64))) (.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) #s(literal 1 binary64)))
(fma.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) #s(literal 1 binary64) (.f64 #s(literal 0 binary64) (cos.f64 (*.f64 eps #s(literal 1/2 binary64)))))
(fma.f64 (cos.f64 (.f64 eps #s(literal 1/2 binary64))) #s(literal 0 binary64) (.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) #s(literal 1 binary64)))
(fma.f64 (+.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (sin.f64 (.f64 eps #s(literal -1/2 binary64)))) #s(literal 1/2 binary64) (.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) #s(literal 1 binary64)))
(fma.f64 #s(literal 1 binary64) (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (.f64 #s(literal 0 binary64) (cos.f64 (*.f64 eps #s(literal 1/2 binary64)))))
(/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 #s(literal 0 binary64) (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 #s(literal 2 binary64) (.f64 eps #s(literal 1/2 binary64)))))) (.f64 (.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) #s(literal 1 binary64)) (sin.f64 (-.f64 (.f64 eps #s(literal 1/2 binary64)) #s(literal 0 binary64))))) (fma.f64 #s(literal 0 binary64) (pow.f64 (cos.f64 (.f64 eps #s(literal 1/2 binary64))) #s(literal 3 binary64)) (pow.f64 (.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) #s(literal 1 binary64)) #s(literal 3 binary64)))))
(/.f64 #s(literal 1 binary64) (/.f64 (sin.f64 (.f64 eps #s(literal -1/2 binary64))) (.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (sin.f64 (.f64 eps #s(literal -1/2 binary64))))))
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(pow.f64 (/.f64 #s(literal 2 binary64) (+.f64 (sin.f64 (fma.f64 eps #s(literal 1/2 binary64) x)) (sin.f64 (-.f64 x (*.f64 eps #s(literal 1/2 binary64)))))) #s(literal -1 binary64))
(.f64 (sin.f64 x) (cos.f64 (.f64 eps #s(literal 1/2 binary64))))
(.f64 (cos.f64 (.f64 eps #s(literal 1/2 binary64))) (sin.f64 x))
(.f64 (+.f64 (sin.f64 (fma.f64 eps #s(literal 1/2 binary64) x)) (sin.f64 (-.f64 x (.f64 eps #s(literal 1/2 binary64))))) #s(literal 1/2 binary64))
(+.f64 #s(literal 0 binary64) (neg.f64 eps))
(+.f64 (neg.f64 eps) #s(literal 0 binary64))
(-.f64 #s(literal 0 binary64) eps)
(-.f64 (neg.f64 eps) #s(literal 0 binary64))
(fma.f64 eps #s(literal -1 binary64) #s(literal 0 binary64))
(fma.f64 #s(literal -1 binary64) eps #s(literal 0 binary64))
(neg.f64 eps)
(/.f64 (*.f64 eps eps) (neg.f64 eps))
(/.f64 (.f64 eps (.f64 eps eps)) (neg.f64 (*.f64 eps eps)))
(/.f64 (-.f64 #s(literal 0 binary64) (.f64 eps (.f64 eps eps))) (*.f64 eps eps))
(/.f64 (neg.f64 (*.f64 eps eps)) eps)
(/.f64 (-.f64 #s(literal 0 binary64) (*.f64 eps eps)) eps)
(/.f64 (neg.f64 (.f64 eps (.f64 eps eps))) (*.f64 eps eps))
(/.f64 (.f64 #s(literal -1 binary64) (.f64 eps (.f64 eps eps))) (.f64 eps eps))
(/.f64 (.f64 #s(literal -1 binary64) (.f64 eps eps)) eps)
(*.f64 eps #s(literal -1 binary64))
(*.f64 #s(literal -1 binary64) eps)
(exp.f64 (.f64 (log.f64 (.f64 eps #s(literal 6 binary64))) #s(literal -1 binary64)))
(neg.f64 (/.f64 #s(literal -1/6 binary64) eps))
(/.f64 #s(literal 1/6 binary64) eps)
(/.f64 #s(literal 1/6 binary64) (neg.f64 (neg.f64 eps)))
(/.f64 #s(literal -1 binary64) (neg.f64 (*.f64 eps #s(literal 6 binary64))))
(/.f64 #s(literal -1/6 binary64) (neg.f64 eps))
(/.f64 #s(literal 1 binary64) (*.f64 eps #s(literal 6 binary64)))
(/.f64 #s(literal 1 binary64) (/.f64 (*.f64 eps #s(literal 6 binary64)) #s(literal 1 binary64)))
(pow.f64 (*.f64 eps #s(literal 6 binary64)) #s(literal -1 binary64))
(pow.f64 (/.f64 (*.f64 eps #s(literal 6 binary64)) #s(literal 1 binary64)) #s(literal -1 binary64))
(*.f64 #s(literal 1/6 binary64) (/.f64 #s(literal 1 binary64) eps))
(*.f64 #s(literal -1/6 binary64) (/.f64 #s(literal 1 binary64) (neg.f64 eps)))
(*.f64 #s(literal 1 binary64) (/.f64 #s(literal 1/6 binary64) eps))
(*.f64 (/.f64 #s(literal 1 binary64) eps) #s(literal 1/6 binary64))
(.f64 (/.f64 #s(literal 1/6 binary64) (.f64 eps (.f64 eps eps))) (.f64 eps eps))
(.f64 (/.f64 #s(literal 1/6 binary64) (.f64 eps eps)) eps)
#s(approx (+ (* eps (+ (* (cos x) (+ -1/2 (* eps (* eps 1/24)))) (* eps (* 1/6 (sin x))))) (sin (neg x))) (fma.f64 x (fma.f64 x (fma.f64 eps (fma.f64 (.f64 eps eps) #s(literal -1/48 binary64) #s(literal 1/4 binary64)) (.f64 x (fma.f64 (.f64 eps eps) #s(literal -1/36 binary64) #s(literal 1/6 binary64)))) (fma.f64 eps (.f64 eps #s(literal 1/6 binary64)) #s(literal -1 binary64))) (.f64 eps (fma.f64 #s(literal 1/24 binary64) (.f64 eps eps) #s(literal -1/2 binary64)))))
(+.f64 #s(literal 0 binary64) (*.f64 eps #s(literal 1/24 binary64)))
(+.f64 (*.f64 eps #s(literal 1/24 binary64)) #s(literal 0 binary64))
(fma.f64 eps #s(literal 1/24 binary64) #s(literal 0 binary64))
(fma.f64 #s(literal 1/24 binary64) eps #s(literal 0 binary64))
(/.f64 (.f64 #s(literal 1/24 binary64) (.f64 eps eps)) eps)
(/.f64 (.f64 (.f64 eps (.f64 eps eps)) #s(literal 1/24 binary64)) (.f64 eps eps))
(/.f64 (.f64 #s(literal 1/24 binary64) (.f64 eps (.f64 eps eps))) (.f64 eps eps))
(*.f64 eps #s(literal 1/24 binary64))
(*.f64 #s(literal 1/24 binary64) eps)
(+.f64 #s(literal 0 binary64) (*.f64 eps #s(literal 1/6 binary64)))
(+.f64 (*.f64 eps #s(literal 1/6 binary64)) #s(literal 0 binary64))
(fma.f64 eps #s(literal 1/6 binary64) #s(literal 0 binary64))
(fma.f64 #s(literal 1/6 binary64) eps #s(literal 0 binary64))
(/.f64 (.f64 #s(literal 1/6 binary64) (.f64 eps eps)) eps)
(/.f64 (.f64 #s(literal 1/6 binary64) (.f64 eps (.f64 eps eps))) (.f64 eps eps))
(/.f64 (.f64 (.f64 eps (.f64 eps eps)) #s(literal 1/6 binary64)) (.f64 eps eps))
(*.f64 eps #s(literal 1/6 binary64))
(*.f64 #s(literal 1/6 binary64) eps)

eval105.0ms (0.6%)

Memory: -7.6MiB live, 145.1MiB allocated
Compiler: Compiled 25 171 to 1 665 computations (93.4% saved)

prune210.0ms (1.1%)

Memory

-5.3MiB live, 121.0MiB allocated

Pruning

43 alts after pruning (35 fresh and 8 done)

	Pruned	Kept	Total
New	938	23	961
Fresh	12	12	24
Picked	2	3	5
Done	0	5	5
Total	952	43	995

Accuracy

100.0%

Counts

995 → 43

Alt Table

Click to see full alt table

Status	Accuracy	Program
	56.6%	(fma.f64 (*.f64 (cos.f64 (-.f64 x eps)) (cos.f64 (+.f64 x eps))) (/.f64 #s(literal 1 binary64) (cos.f64 (-.f64 x eps))) (neg.f64 (cos.f64 x)))
	56.6%	(/.f64 (/.f64 (-.f64 (fma.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 (+.f64 x eps) #s(literal 2 binary64))) #s(literal 1/2 binary64)) (fma.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64))) #s(literal 2 binary64)) (.f64 (cos.f64 (.f64 (+.f64 x (+.f64 x eps)) #s(literal 1/2 binary64))) (cos.f64 (.f64 (+.f64 eps #s(literal 0 binary64)) #s(literal 1/2 binary64)))))
✓	56.8%	(-.f64 (*.f64 (cos.f64 x) (cos.f64 eps)) (fma.f64 (sin.f64 x) (sin.f64 eps) (cos.f64 x)))
	56.6%	(-.f64 (.f64 (cos.f64 x) #s(approx (cos eps) (fma.f64 (.f64 eps eps) (fma.f64 (.f64 eps eps) (fma.f64 (.f64 eps eps) #s(literal -1/720 binary64) #s(literal 1/24 binary64)) #s(literal -1/2 binary64)) #s(literal 1 binary64)))) (fma.f64 (sin.f64 x) (sin.f64 eps) (cos.f64 x)))
✓	56.6%	(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))
✓	54.8%	(-.f64 (cos.f64 (+.f64 x eps)) #s(approx (cos x) #s(literal 1 binary64)))
	54.8%	(-.f64 #s(approx (cos (+ x eps)) (cos.f64 x)) #s(approx (cos x) #s(literal 1 binary64)))
	82.8%	(.f64 #s(approx ( (sin (* (+ eps 0) 1/2)) (+ (* (sin (* (+ x x) 1/2)) (cos (* eps 1/2))) (* (cos (* (+ x x) 1/2)) (sin (* eps 1/2))))) (fma.f64 (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 #s(literal 2 binary64) (.f64 eps #s(literal 1/2 binary64)))))) (cos.f64 x) (.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (.f64 (sin.f64 x) (cos.f64 (*.f64 eps #s(literal 1/2 binary64))))))) #s(literal -2 binary64))
	99.6%	(.f64 #s(approx ( (sin (* (+ eps 0) 1/2)) (+ (* (sin (* (+ x x) 1/2)) (cos (* eps 1/2))) (* (cos (* (+ x x) 1/2)) (sin (* eps 1/2))))) (.f64 (sin.f64 (fma.f64 eps #s(literal 1/2 binary64) x)) (sin.f64 (.f64 eps #s(literal 1/2 binary64))))) #s(literal -2 binary64))
✓	99.8%	(.f64 #s(approx ( (sin (* (+ eps 0) 1/2)) (+ (* (sin (* (+ x x) 1/2)) (cos (* eps 1/2))) (* (cos (* (+ x x) 1/2)) (sin (* eps 1/2))))) (.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (fma.f64 (cos.f64 x) (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (.f64 (sin.f64 x) (cos.f64 (*.f64 eps #s(literal 1/2 binary64))))))) #s(literal -2 binary64))
	99.6%	(.f64 #s(approx ( (sin (* (+ eps 0) 1/2)) (+ (* (sin (* (+ x x) 1/2)) (cos (* eps 1/2))) (* (cos (* (+ x x) 1/2)) (sin (* eps 1/2))))) (.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (fma.f64 (cos.f64 x) #s(approx (sin (* eps 1/2)) (.f64 eps (fma.f64 eps (.f64 eps (fma.f64 eps (.f64 eps #s(literal 1/3840 binary64)) #s(literal -1/48 binary64))) #s(literal 1/2 binary64)))) (.f64 (sin.f64 x) (cos.f64 (*.f64 eps #s(literal 1/2 binary64))))))) #s(literal -2 binary64))
	99.7%	(.f64 #s(approx ( (sin (* (+ eps 0) 1/2)) (+ (* (sin (* (+ x x) 1/2)) (cos (* eps 1/2))) (* (cos (* (+ x x) 1/2)) (sin (* eps 1/2))))) (.f64 #s(approx (sin ( eps 1/2)) (.f64 eps (fma.f64 (.f64 eps eps) (fma.f64 (.f64 eps eps) (fma.f64 (.f64 eps eps) #s(literal -1/645120 binary64) #s(literal 1/3840 binary64)) #s(literal -1/48 binary64)) #s(literal 1/2 binary64)))) (fma.f64 (cos.f64 x) (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (.f64 (sin.f64 x) (cos.f64 (*.f64 eps #s(literal 1/2 binary64))))))) #s(literal -2 binary64))
✓	99.3%	#s(approx (- (* (cos x) (cos eps)) (+ (* (sin x) (sin eps)) (cos x))) (.f64 eps (-.f64 (.f64 eps (fma.f64 eps (.f64 (sin.f64 x) #s(literal 1/6 binary64)) (.f64 (cos.f64 x) (fma.f64 eps (*.f64 eps #s(literal 1/24 binary64)) #s(literal -1/2 binary64))))) (sin.f64 x))))
✓	98.9%	#s(approx (- (* (cos x) (cos eps)) (+ (* (sin x) (sin eps)) (cos x))) (.f64 eps (-.f64 (.f64 eps (*.f64 #s(literal -1/2 binary64) (cos.f64 x))) (sin.f64 x))))
	98.4%	#s(approx (- (* (cos x) (cos eps)) (+ (* (sin x) (sin eps)) (cos x))) (.f64 eps (-.f64 #s(approx ( eps (+ (* eps (* (sin x) 1/6)) (* (cos x) (+ (* eps (* eps 1/24)) -1/2)))) (fma.f64 x (.f64 eps (.f64 eps #s(literal 1/6 binary64))) (.f64 eps (fma.f64 eps (.f64 eps #s(literal 1/24 binary64)) #s(literal -1/2 binary64))))) (sin.f64 x))))
	98.5%	#s(approx (- (* (cos x) (cos eps)) (+ (* (sin x) (sin eps)) (cos x))) (.f64 eps (-.f64 #s(approx ( eps (+ (* eps (* (sin x) 1/6)) (* (cos x) (+ (* eps (* eps 1/24)) -1/2)))) (.f64 eps (fma.f64 eps (.f64 eps #s(literal 1/24 binary64)) #s(literal -1/2 binary64)))) (sin.f64 x))))
	98.1%	#s(approx (- (* (cos x) (cos eps)) (+ (* (sin x) (sin eps)) (cos x))) (.f64 eps (-.f64 #s(approx ( eps (* -1/2 (cos x))) (.f64 eps (fma.f64 #s(literal 1/4 binary64) (.f64 x x) #s(literal -1/2 binary64)))) (sin.f64 x))))
	98.5%	#s(approx (- (* (cos x) (cos eps)) (+ (* (sin x) (sin eps)) (cos x))) (.f64 eps (-.f64 #s(approx ( eps (* -1/2 (cos x))) (*.f64 eps #s(literal -1/2 binary64))) (sin.f64 x))))
	81.7%	#s(approx (- (* (cos x) (cos eps)) (+ (* (sin x) (sin eps)) (cos x))) (*.f64 eps (sin.f64 (neg.f64 x))))
	97.8%	#s(approx (- (* (cos x) (cos eps)) (+ (* (sin x) (sin eps)) (cos x))) (.f64 eps #s(approx (- ( eps (* -1/2 (cos x))) (sin x)) (fma.f64 x (fma.f64 x (fma.f64 eps #s(literal 1/4 binary64) (.f64 x #s(literal 1/6 binary64))) #s(literal -1 binary64)) (.f64 eps #s(literal -1/2 binary64))))))
	97.2%	#s(approx (- (* (cos x) (cos eps)) (+ (* (sin x) (sin eps)) (cos x))) (.f64 eps #s(approx (- ( eps (* -1/2 (cos x))) (sin x)) (fma.f64 x (fma.f64 #s(literal 1/4 binary64) (.f64 eps x) #s(literal -1 binary64)) (.f64 eps #s(literal -1/2 binary64))))))
	97.2%	#s(approx (- (* (cos x) (cos eps)) (+ (* (sin x) (sin eps)) (cos x))) (.f64 eps #s(approx (- ( eps (* -1/2 (cos x))) (sin x)) (-.f64 (*.f64 eps #s(literal -1/2 binary64)) x))))
	55.9%	#s(approx (- (* (cos x) (cos eps)) (+ (* (sin x) (sin eps)) (cos x))) (.f64 eps #s(approx (- ( eps (* -1/2 (cos x))) (sin x)) (*.f64 eps #s(literal -1/2 binary64)))))
	97.9%	#s(approx (- (* (cos x) (cos eps)) (+ (* (sin x) (sin eps)) (cos x))) #s(approx (* eps (- (* eps (* -1/2 (cos x))) (sin x))) (fma.f64 x (fma.f64 x (fma.f64 eps (.f64 x #s(literal 1/6 binary64)) (.f64 eps (.f64 eps #s(literal 1/4 binary64)))) (neg.f64 eps)) (.f64 #s(literal -1/2 binary64) (*.f64 eps eps)))))
	54.8%	#s(approx (- (cos (+ x eps)) (cos x)) (+.f64 #s(approx (cos eps) (fma.f64 eps (*.f64 eps #s(literal -1/2 binary64)) #s(literal 1 binary64))) #s(literal -1 binary64)))
✓	54.6%	#s(approx (- (cos (+ x eps)) (cos x)) (+.f64 #s(approx (cos eps) #s(literal 1 binary64)) #s(literal -1 binary64)))
	97.7%	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps #s(approx (+ ( eps (+ (* (cos x) (+ -1/2 (* eps (* eps 1/24)))) (* eps (* 1/6 (sin x))))) (sin (neg x))) (fma.f64 x (fma.f64 x (fma.f64 eps #s(approx (* (+ (* eps (* eps 1/24)) -1/2) -1/2) (.f64 #s(literal -1/48 binary64) (.f64 eps eps))) (.f64 x (fma.f64 (.f64 eps eps) #s(literal -1/36 binary64) #s(literal 1/6 binary64)))) (fma.f64 eps (.f64 eps #s(literal 1/6 binary64)) #s(literal -1 binary64))) (.f64 eps (fma.f64 eps (*.f64 eps #s(literal 1/24 binary64)) #s(literal -1/2 binary64)))))))
	97.8%	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps #s(approx (+ ( eps (+ (* (cos x) (+ -1/2 (* eps (* eps 1/24)))) (* eps (* 1/6 (sin x))))) (sin (neg x))) (fma.f64 x (fma.f64 x (fma.f64 eps #s(approx (* (+ (* eps (* eps 1/24)) -1/2) -1/2) #s(literal 1/4 binary64)) (.f64 x (fma.f64 (.f64 eps eps) #s(literal -1/36 binary64) #s(literal 1/6 binary64)))) (fma.f64 eps (.f64 eps #s(literal 1/6 binary64)) #s(literal -1 binary64))) (.f64 eps (fma.f64 eps (*.f64 eps #s(literal 1/24 binary64)) #s(literal -1/2 binary64)))))))
	97.8%	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps #s(approx (+ ( eps (+ (* (cos x) (+ -1/2 (* eps (* eps 1/24)))) (* eps (* 1/6 (sin x))))) (sin (neg x))) #s(approx (+ (* x (+ (* x (+ (* eps (* (+ (* eps (* eps 1/24)) -1/2) -1/2)) (* x (+ (* (* eps eps) -1/36) 1/6)))) (+ (* eps (* eps 1/6)) -1))) (* eps (+ (* eps (* eps 1/24)) -1/2))) (fma.f64 eps (fma.f64 eps (.f64 x (fma.f64 #s(literal -1/36 binary64) (.f64 x x) #s(literal 1/6 binary64))) (fma.f64 #s(literal 1/4 binary64) (.f64 x x) #s(literal -1/2 binary64))) (.f64 x (fma.f64 x (*.f64 x #s(literal 1/6 binary64)) #s(literal -1 binary64))))))))
	54.4%	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps #s(approx (+ ( eps (+ (* (cos x) (+ -1/2 (* eps (* eps 1/24)))) (* eps (* 1/6 (sin x))))) (sin (neg x))) #s(approx (+ (* x (+ (* x (+ (* eps (* (+ (* eps (* eps 1/24)) -1/2) -1/2)) (* x (+ (* (* eps eps) -1/36) 1/6)))) (+ (* eps (* eps 1/6)) -1))) (* eps (+ (* eps (* eps 1/24)) -1/2))) (.f64 (.f64 eps eps) (.f64 eps (fma.f64 x (/.f64 (fma.f64 #s(literal -1/36 binary64) (.f64 x x) #s(literal 1/6 binary64)) eps) (fma.f64 x (*.f64 x #s(literal -1/48 binary64)) #s(literal 1/24 binary64)))))))))
	81.0%	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps #s(approx (+ ( eps (+ (* (cos x) (+ -1/2 (* eps (* eps 1/24)))) (* eps (* 1/6 (sin x))))) (sin (neg x))) #s(approx (+ (* x (+ (* x (+ (* eps (* (+ (* eps (* eps 1/24)) -1/2) -1/2)) (* x (+ (* (* eps eps) -1/36) 1/6)))) (+ (* eps (* eps 1/6)) -1))) (* eps (+ (* eps (* eps 1/24)) -1/2))) (.f64 x (fma.f64 x (.f64 x #s(literal 1/6 binary64)) #s(literal -1 binary64)))))))
	3.5%	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps #s(approx (+ ( eps (+ (* (cos x) (+ -1/2 (* eps (* eps 1/24)))) (* eps (* 1/6 (sin x))))) (sin (neg x))) #s(approx (+ (* x (+ (* x (+ (* eps (* (+ (* eps (* eps 1/24)) -1/2) -1/2)) (* x (+ (* (* eps eps) -1/36) 1/6)))) (+ (* eps (* eps 1/6)) -1))) (* eps (+ (* eps (* eps 1/24)) -1/2))) (neg.f64 (.f64 (.f64 eps (.f64 eps eps)) (-.f64 (fma.f64 x (.f64 x #s(literal 1/48 binary64)) #s(literal -1/24 binary64)) (/.f64 (-.f64 (.f64 x (fma.f64 #s(literal -1/36 binary64) (.f64 x x) #s(literal 1/6 binary64))) (/.f64 (fma.f64 (*.f64 x x) #s(literal -1/4 binary64) #s(literal 1/2 binary64)) eps)) eps))))))))
	54.4%	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps #s(approx (+ ( eps (+ (* (cos x) (+ -1/2 (* eps (* eps 1/24)))) (* eps (* 1/6 (sin x))))) (sin (neg x))) #s(approx (+ (* x (+ (* x (+ (* eps (* (+ (* eps (* eps 1/24)) -1/2) -1/2)) (* x (+ (* (* eps eps) -1/36) 1/6)))) (+ (* eps (* eps 1/6)) -1))) (* eps (+ (* eps (* eps 1/24)) -1/2))) (neg.f64 (.f64 (.f64 eps (.f64 eps eps)) (-.f64 (fma.f64 x (.f64 x #s(literal 1/48 binary64)) #s(literal -1/24 binary64)) (.f64 x (/.f64 (fma.f64 #s(literal -1/36 binary64) (.f64 x x) #s(literal 1/6 binary64)) eps)))))))))
	97.3%	#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* eps (+ (* eps (+ (* (cos x) (+ -1/2 (* eps (* eps 1/24)))) (* eps (* 1/6 (sin x))))) (sin (neg x)))) (fma.f64 (.f64 x (fma.f64 eps (.f64 eps #s(literal 1/6 binary64)) #s(literal -1 binary64))) eps (.f64 eps (.f64 eps (fma.f64 #s(literal 1/24 binary64) (*.f64 eps eps) #s(literal -1/2 binary64)))))))
	97.2%	#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* eps (+ (* eps (+ (* (cos x) (+ -1/2 (* eps (* eps 1/24)))) (* eps (* 1/6 (sin x))))) (sin (neg x)))) (fma.f64 eps #s(approx (* eps (+ (* eps (* eps 1/24)) -1/2)) (.f64 eps #s(literal -1/2 binary64))) (.f64 eps (.f64 x (fma.f64 eps (.f64 eps #s(literal 1/6 binary64)) #s(literal -1 binary64)))))))
	3.4%	#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* eps (+ (* eps (+ (* (cos x) (+ -1/2 (* eps (* eps 1/24)))) (* eps (* 1/6 (sin x))))) (sin (neg x)))) #s(approx (+ (* eps (* eps (+ (* eps (* eps 1/24)) -1/2))) (* eps (* x (+ (* eps (* eps 1/6)) -1)))) (.f64 (.f64 (.f64 eps eps) (.f64 eps eps)) (-.f64 #s(literal 1/24 binary64) (/.f64 (fma.f64 x #s(literal -1/6 binary64) (/.f64 #s(literal 1/2 binary64) eps)) eps))))))
	3.4%	#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* eps (+ (* eps (+ (* (cos x) (+ -1/2 (* eps (* eps 1/24)))) (* eps (* 1/6 (sin x))))) (sin (neg x)))) #s(approx (+ (* eps (* eps (+ (* eps (* eps 1/24)) -1/2))) (* eps (* x (+ (* eps (* eps 1/6)) -1)))) (.f64 (.f64 (.f64 eps eps) (.f64 eps eps)) (+.f64 #s(literal 1/24 binary64) (fma.f64 x (/.f64 #s(literal 1/6 binary64) eps) (/.f64 #s(literal -1/2 binary64) (*.f64 eps eps))))))))
	97.1%	#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* eps (+ (* eps (+ (* (cos x) (+ -1/2 (* eps (* eps 1/24)))) (* eps (* 1/6 (sin x))))) (sin (neg x)))) #s(approx (+ (* eps (* eps (+ (* eps (* eps 1/24)) -1/2))) (* eps (* x (+ (* eps (* eps 1/6)) -1)))) (.f64 x (fma.f64 eps (fma.f64 eps (.f64 eps #s(literal 1/6 binary64)) #s(literal -1 binary64)) (.f64 (.f64 eps eps) (/.f64 (fma.f64 #s(literal 1/24 binary64) (*.f64 eps eps) #s(literal -1/2 binary64)) x)))))))
✓	80.8%	#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* eps (+ (* eps (+ (* (cos x) (+ -1/2 (* eps (* eps 1/24)))) (* eps (* 1/6 (sin x))))) (sin (neg x)))) #s(approx (+ (* eps (* eps (+ (* eps (* eps 1/24)) -1/2))) (* eps (* x (+ (* eps (* eps 1/6)) -1)))) (*.f64 x (neg.f64 eps)))))
	97.2%	#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* eps (+ (* eps (+ (* (cos x) (+ -1/2 (* eps (* eps 1/24)))) (* eps (* 1/6 (sin x))))) (sin (neg x)))) #s(approx (+ (* eps (* eps (+ (* eps (* eps 1/24)) -1/2))) (* eps (* x (+ (* eps (* eps 1/6)) -1)))) (.f64 eps (fma.f64 eps (fma.f64 x (.f64 eps #s(literal 1/6 binary64)) #s(literal -1/2 binary64)) (neg.f64 x))))))
	54.6%	#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* eps (+ (* eps (+ (* (cos x) (+ -1/2 (* eps (* eps 1/24)))) (* eps (* 1/6 (sin x))))) (sin (neg x)))) #s(approx (+ (* eps (* eps (+ (* eps (* eps 1/24)) -1/2))) (* eps (* x (+ (* eps (* eps 1/6)) -1)))) #s(approx (* (* (* eps eps) (* eps eps)) (+ (* x (/ 1/6 eps)) 1/24)) (.f64 (.f64 eps eps) (.f64 eps (fma.f64 eps #s(literal 1/24 binary64) (.f64 x #s(literal 1/6 binary64)))))))))
	54.6%	#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* eps (+ (* eps (+ (* (cos x) (+ -1/2 (* eps (* eps 1/24)))) (* eps (* 1/6 (sin x))))) (sin (neg x)))) #s(approx (+ (* eps (* eps (+ (* eps (* eps 1/24)) -1/2))) (* eps (* x (+ (* eps (* eps 1/6)) -1)))) #s(approx (* (* (* eps eps) (* eps eps)) (+ (* x (/ 1/6 eps)) 1/24)) (.f64 x (fma.f64 eps (.f64 eps (.f64 eps #s(literal 1/6 binary64))) (/.f64 (.f64 eps (.f64 eps (.f64 #s(literal 1/24 binary64) (*.f64 eps eps)))) x)))))))
	54.6%	#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* eps (+ (* eps (+ (* (cos x) (+ -1/2 (* eps (* eps 1/24)))) (* eps (* 1/6 (sin x))))) (sin (neg x)))) #s(approx (+ (* eps (* eps (+ (* eps (* eps 1/24)) -1/2))) (* eps (* x (+ (* eps (* eps 1/6)) -1)))) #s(approx (* (* (* eps eps) (* eps eps)) (+ (* x (/ 1/6 eps)) 1/24)) (.f64 x (.f64 eps (.f64 eps (.f64 eps #s(literal 1/6 binary64)))))))))

Compiler

Compiled 2 373 to 846 computations (64.3% saved)

regimes54.0ms (0.3%)

Memory

24.9MiB live, 24.9MiB allocated

Counts

71 → 1

Calls

Call 1

Inputs
#s(approx (- (cos (+ x eps)) (cos x)) (+.f64 #s(approx (cos eps) #s(literal 1 binary64)) #s(literal -1 binary64)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* eps (+ (* eps (+ (* (cos x) (+ -1/2 (* eps (* eps 1/24)))) (* eps (* 1/6 (sin x))))) (sin (neg x)))) #s(approx (+ (* eps (* eps (+ (* eps (* eps 1/24)) -1/2))) (* eps (* x (+ (* eps (* eps 1/6)) -1)))) (*.f64 x (neg.f64 eps)))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (+ (cos eps) -1) (.f64 eps (.f64 eps #s(literal -1/2 binary64)))))
#s(approx (- (* (cos x) (cos eps)) (+ (* (sin x) (sin eps)) (cos x))) (.f64 eps #s(approx (- ( eps (* -1/2 (cos x))) (sin x)) (*.f64 eps #s(literal -1/2 binary64)))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* eps (+ (* eps (+ (* (cos x) (+ -1/2 (* eps (* eps 1/24)))) (* eps (* 1/6 (sin x))))) (sin (neg x)))) #s(approx (+ (* eps (* eps (+ (* eps (* eps 1/24)) -1/2))) (* eps (* x (+ (* eps (* eps 1/6)) -1)))) (.f64 eps (-.f64 (.f64 eps #s(literal -1/2 binary64)) x)))))
#s(approx (- (* (cos x) (cos eps)) (+ (* (sin x) (sin eps)) (cos x))) (.f64 eps #s(approx (- ( eps (* -1/2 (cos x))) (sin x)) (-.f64 (*.f64 eps #s(literal -1/2 binary64)) x))))
#s(approx (- (cos (+ x eps)) (cos x)) (+.f64 #s(approx (cos eps) (fma.f64 eps (*.f64 eps #s(literal -1/2 binary64)) #s(literal 1 binary64))) #s(literal -1 binary64)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* eps (+ (* eps (+ (* (cos x) (+ -1/2 (* eps (* eps 1/24)))) (* eps (* 1/6 (sin x))))) (sin (neg x)))) #s(approx (+ (* eps (* eps (+ (* eps (* eps 1/24)) -1/2))) (* eps (* x (+ (* eps (* eps 1/6)) -1)))) #s(approx (* (* (* eps eps) (* eps eps)) (+ (* x (/ 1/6 eps)) 1/24)) (.f64 x (.f64 eps (.f64 eps (.f64 eps #s(literal 1/6 binary64)))))))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* eps (+ (* eps (+ (* (cos x) (+ -1/2 (* eps (* eps 1/24)))) (* eps (* 1/6 (sin x))))) (sin (neg x)))) #s(approx (+ (* eps (* eps (+ (* eps (* eps 1/24)) -1/2))) (* eps (* x (+ (* eps (* eps 1/6)) -1)))) (.f64 #s(literal 1/24 binary64) (.f64 (.f64 eps eps) (.f64 eps eps))))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps #s(approx (+ ( eps (+ (* (cos x) (+ -1/2 (* eps (* eps 1/24)))) (* eps (* 1/6 (sin x))))) (sin (neg x))) #s(approx (+ (* x (+ (* x (+ (* eps (* (+ (* eps (* eps 1/24)) -1/2) -1/2)) (* x (+ (* (* eps eps) -1/36) 1/6)))) (+ (* eps (* eps 1/6)) -1))) (* eps (+ (* eps (* eps 1/24)) -1/2))) (.f64 x (fma.f64 x (.f64 x #s(literal 1/6 binary64)) #s(literal -1 binary64)))))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* eps (+ (* eps (+ (* (cos x) (+ -1/2 (* eps (* eps 1/24)))) (* eps (* 1/6 (sin x))))) (sin (neg x)))) #s(approx (+ (* eps (* eps (+ (* eps (* eps 1/24)) -1/2))) (* eps (* x (+ (* eps (* eps 1/6)) -1)))) (.f64 eps (fma.f64 eps (fma.f64 x (.f64 eps #s(literal 1/6 binary64)) #s(literal -1/2 binary64)) (neg.f64 x))))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* eps (+ (* eps (+ (* (cos x) (+ -1/2 (* eps (* eps 1/24)))) (* eps (* 1/6 (sin x))))) (sin (neg x)))) #s(approx (+ (* eps (* eps (+ (* eps (* eps 1/24)) -1/2))) (* eps (* x (+ (* eps (* eps 1/6)) -1)))) #s(approx (* (* (* eps eps) (* eps eps)) (+ (* x (/ 1/6 eps)) 1/24)) (.f64 (.f64 eps eps) (.f64 eps (fma.f64 eps #s(literal 1/24 binary64) (.f64 x #s(literal 1/6 binary64)))))))))
#s(approx (- (* (cos x) (cos eps)) (+ (* (sin x) (sin eps)) (cos x))) (.f64 eps #s(approx (- ( eps (* -1/2 (cos x))) (sin x)) (fma.f64 x (fma.f64 #s(literal 1/4 binary64) (.f64 eps x) #s(literal -1 binary64)) (.f64 eps #s(literal -1/2 binary64))))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* eps (+ (* eps (+ (* (cos x) (+ -1/2 (* eps (* eps 1/24)))) (* eps (* 1/6 (sin x))))) (sin (neg x)))) (fma.f64 eps #s(approx (* eps (+ (* eps (* eps 1/24)) -1/2)) (.f64 eps #s(literal -1/2 binary64))) (.f64 eps (.f64 x (fma.f64 eps (.f64 eps #s(literal 1/6 binary64)) #s(literal -1 binary64)))))))
#s(approx (- (* (cos x) (cos eps)) (+ (* (sin x) (sin eps)) (cos x))) (.f64 eps #s(approx (- ( eps (* -1/2 (cos x))) (sin x)) (fma.f64 x (fma.f64 x (fma.f64 eps #s(literal 1/4 binary64) (.f64 x #s(literal 1/6 binary64))) #s(literal -1 binary64)) (.f64 eps #s(literal -1/2 binary64))))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* eps (+ (* eps (+ (* (cos x) (+ -1/2 (* eps (* eps 1/24)))) (* eps (* 1/6 (sin x))))) (sin (neg x)))) #s(approx (+ (* eps (* eps (+ (* eps (* eps 1/24)) -1/2))) (* eps (* x (+ (* eps (* eps 1/6)) -1)))) (.f64 (.f64 (.f64 eps eps) (.f64 eps eps)) (fma.f64 x (/.f64 #s(literal 1/6 binary64) eps) #s(literal 1/24 binary64))))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps #s(approx (+ ( eps (+ (* (cos x) (+ -1/2 (* eps (* eps 1/24)))) (* eps (* 1/6 (sin x))))) (sin (neg x))) (fma.f64 eps (fma.f64 eps (.f64 eps #s(literal 1/24 binary64)) #s(literal -1/2 binary64)) (.f64 x (fma.f64 eps (*.f64 eps #s(literal 1/6 binary64)) #s(literal -1 binary64)))))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* eps (+ (* eps (+ (* (cos x) (+ -1/2 (* eps (* eps 1/24)))) (* eps (* 1/6 (sin x))))) (sin (neg x)))) (fma.f64 eps (.f64 eps (fma.f64 eps (.f64 eps #s(literal 1/24 binary64)) #s(literal -1/2 binary64))) (.f64 eps (.f64 x (fma.f64 eps (*.f64 eps #s(literal 1/6 binary64)) #s(literal -1 binary64)))))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* eps (+ (* eps (+ (* (cos x) (+ -1/2 (* eps (* eps 1/24)))) (* eps (* 1/6 (sin x))))) (sin (neg x)))) (fma.f64 (.f64 x (fma.f64 eps (.f64 eps #s(literal 1/6 binary64)) #s(literal -1 binary64))) eps (.f64 eps (.f64 eps (fma.f64 #s(literal 1/24 binary64) (*.f64 eps eps) #s(literal -1/2 binary64)))))))
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#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* eps (+ (* eps (+ (* (cos x) (+ -1/2 (* eps (* eps 1/24)))) (* eps (* 1/6 (sin x))))) (sin (neg x)))) #s(approx (+ (* eps (* eps (+ (* eps (* eps 1/24)) -1/2))) (* eps (* x (+ (* eps (* eps 1/6)) -1)))) #s(approx (* (* (* eps eps) (* eps eps)) (+ (* x (/ 1/6 eps)) 1/24)) (.f64 x (fma.f64 eps (.f64 eps (.f64 eps #s(literal 1/6 binary64))) (/.f64 (.f64 eps (.f64 eps (.f64 #s(literal 1/24 binary64) (*.f64 eps eps)))) x)))))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* eps (+ (* eps (+ (* (cos x) (+ -1/2 (* eps (* eps 1/24)))) (* eps (* 1/6 (sin x))))) (sin (neg x)))) #s(approx (+ (* eps (* eps (+ (* eps (* eps 1/24)) -1/2))) (* eps (* x (+ (* eps (* eps 1/6)) -1)))) (.f64 x (fma.f64 eps (fma.f64 eps (.f64 eps #s(literal 1/6 binary64)) #s(literal -1 binary64)) (.f64 (.f64 eps eps) (/.f64 (fma.f64 #s(literal 1/24 binary64) (*.f64 eps eps) #s(literal -1/2 binary64)) x)))))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* eps (+ (* eps (+ (* (cos x) (+ -1/2 (* eps (* eps 1/24)))) (* eps (* 1/6 (sin x))))) (sin (neg x)))) #s(approx (+ (* eps (* eps (+ (* eps (* eps 1/24)) -1/2))) (* eps (* x (+ (* eps (* eps 1/6)) -1)))) (.f64 (.f64 (.f64 eps eps) (.f64 eps eps)) (+.f64 #s(literal 1/24 binary64) (fma.f64 x (/.f64 #s(literal 1/6 binary64) eps) (/.f64 #s(literal -1/2 binary64) (*.f64 eps eps))))))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps #s(approx (+ ( eps (+ (* (cos x) (+ -1/2 (* eps (* eps 1/24)))) (* eps (* 1/6 (sin x))))) (sin (neg x))) #s(approx (+ (* x (+ (* x (+ (* eps (* (+ (* eps (* eps 1/24)) -1/2) -1/2)) (* x (+ (* (* eps eps) -1/36) 1/6)))) (+ (* eps (* eps 1/6)) -1))) (* eps (+ (* eps (* eps 1/24)) -1/2))) (.f64 (.f64 eps eps) (.f64 eps (fma.f64 x (/.f64 (fma.f64 #s(literal -1/36 binary64) (.f64 x x) #s(literal 1/6 binary64)) eps) (fma.f64 x (*.f64 x #s(literal -1/48 binary64)) #s(literal 1/24 binary64)))))))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps #s(approx (+ ( eps (+ (* (cos x) (+ -1/2 (* eps (* eps 1/24)))) (* eps (* 1/6 (sin x))))) (sin (neg x))) #s(approx (+ (* x (+ (* x (+ (* eps (* (+ (* eps (* eps 1/24)) -1/2) -1/2)) (* x (+ (* (* eps eps) -1/36) 1/6)))) (+ (* eps (* eps 1/6)) -1))) (* eps (+ (* eps (* eps 1/24)) -1/2))) (fma.f64 eps (fma.f64 eps (.f64 x (fma.f64 #s(literal -1/36 binary64) (.f64 x x) #s(literal 1/6 binary64))) (fma.f64 #s(literal 1/4 binary64) (.f64 x x) #s(literal -1/2 binary64))) (.f64 x (fma.f64 x (*.f64 x #s(literal 1/6 binary64)) #s(literal -1 binary64))))))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps #s(approx (+ ( eps (+ (* (cos x) (+ -1/2 (* eps (* eps 1/24)))) (* eps (* 1/6 (sin x))))) (sin (neg x))) #s(approx (+ (* x (+ (* x (+ (* eps (* (+ (* eps (* eps 1/24)) -1/2) -1/2)) (* x (+ (* (* eps eps) -1/36) 1/6)))) (+ (* eps (* eps 1/6)) -1))) (* eps (+ (* eps (* eps 1/24)) -1/2))) (neg.f64 (.f64 (.f64 eps (.f64 eps eps)) (-.f64 (fma.f64 x (.f64 x #s(literal 1/48 binary64)) #s(literal -1/24 binary64)) (.f64 x (/.f64 (fma.f64 #s(literal -1/36 binary64) (.f64 x x) #s(literal 1/6 binary64)) eps)))))))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* eps (+ (* eps (+ (* (cos x) (+ -1/2 (* eps (* eps 1/24)))) (* eps (* 1/6 (sin x))))) (sin (neg x)))) #s(approx (+ (* eps (* eps (+ (* eps (* eps 1/24)) -1/2))) (* eps (* x (+ (* eps (* eps 1/6)) -1)))) (.f64 (.f64 (.f64 eps eps) (.f64 eps eps)) (-.f64 #s(literal 1/24 binary64) (/.f64 (fma.f64 x #s(literal -1/6 binary64) (/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 x eps)) eps)) eps))))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps #s(approx (+ ( eps (+ (* (cos x) (+ -1/2 (* eps (* eps 1/24)))) (* eps (* 1/6 (sin x))))) (sin (neg x))) (fma.f64 eps (fma.f64 eps (.f64 eps #s(literal 1/24 binary64)) #s(literal -1/2 binary64)) (.f64 x (fma.f64 eps (.f64 eps #s(literal 1/6 binary64)) (fma.f64 (.f64 x (fma.f64 eps (.f64 eps #s(literal 1/24 binary64)) #s(literal -1/2 binary64))) (.f64 eps #s(literal -1/2 binary64)) #s(literal -1 binary64))))))))
#s(approx (- (* (cos x) (cos eps)) (+ (* (sin x) (sin eps)) (cos x))) (.f64 eps #s(approx (- ( eps (+ (* eps (* (sin x) 1/6)) (* (cos x) (+ (* eps (* eps 1/24)) -1/2)))) (sin x)) (fma.f64 x (fma.f64 eps (.f64 (.f64 x (fma.f64 eps (.f64 eps #s(literal 1/24 binary64)) #s(literal -1/2 binary64))) #s(literal -1/2 binary64)) (fma.f64 eps (.f64 eps #s(literal 1/6 binary64)) #s(literal -1 binary64))) (.f64 eps (fma.f64 eps (.f64 eps #s(literal 1/24 binary64)) #s(literal -1/2 binary64)))))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps #s(approx (+ ( eps (+ (* (cos x) (+ -1/2 (* eps (* eps 1/24)))) (* eps (* 1/6 (sin x))))) (sin (neg x))) (fma.f64 x (fma.f64 x (fma.f64 eps #s(approx (* (+ (* eps (* eps 1/24)) -1/2) -1/2) #s(literal 1/4 binary64)) (.f64 x (fma.f64 (.f64 eps eps) #s(literal -1/36 binary64) #s(literal 1/6 binary64)))) (fma.f64 eps (.f64 eps #s(literal 1/6 binary64)) #s(literal -1 binary64))) (.f64 eps (fma.f64 eps (*.f64 eps #s(literal 1/24 binary64)) #s(literal -1/2 binary64)))))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps #s(approx (+ ( eps (+ (* (cos x) (+ -1/2 (* eps (* eps 1/24)))) (* eps (* 1/6 (sin x))))) (sin (neg x))) (fma.f64 x (fma.f64 x (fma.f64 eps #s(approx (* (+ (* eps (* eps 1/24)) -1/2) -1/2) (.f64 #s(literal -1/48 binary64) (.f64 eps eps))) (.f64 x (fma.f64 (.f64 eps eps) #s(literal -1/36 binary64) #s(literal 1/6 binary64)))) (fma.f64 eps (.f64 eps #s(literal 1/6 binary64)) #s(literal -1 binary64))) (.f64 eps (fma.f64 eps (*.f64 eps #s(literal 1/24 binary64)) #s(literal -1/2 binary64)))))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* eps (+ (* eps (+ (* (cos x) (+ -1/2 (* eps (* eps 1/24)))) (* eps (* 1/6 (sin x))))) (sin (neg x)))) #s(approx (+ (* eps (* eps (+ (* eps (* eps 1/24)) -1/2))) (* eps (* x (+ (* eps (* eps 1/6)) -1)))) (.f64 (.f64 (.f64 eps eps) (.f64 eps eps)) (+.f64 (fma.f64 x (/.f64 #s(literal 1/6 binary64) eps) (-.f64 #s(literal 1/24 binary64) (/.f64 x (.f64 eps (.f64 eps eps))))) (/.f64 #s(literal -1/2 binary64) (*.f64 eps eps)))))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps #s(approx (+ ( eps (+ (* (cos x) (+ -1/2 (* eps (* eps 1/24)))) (* eps (* 1/6 (sin x))))) (sin (neg x))) (fma.f64 x (fma.f64 x (fma.f64 eps (.f64 (fma.f64 eps (.f64 eps #s(literal 1/24 binary64)) #s(literal -1/2 binary64)) #s(literal -1/2 binary64)) (.f64 x (fma.f64 (.f64 eps eps) #s(literal -1/36 binary64) #s(literal 1/6 binary64)))) (fma.f64 eps (.f64 eps #s(literal 1/6 binary64)) #s(literal -1 binary64))) (.f64 eps (fma.f64 eps (*.f64 eps #s(literal 1/24 binary64)) #s(literal -1/2 binary64)))))))
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#s(approx (- (* (cos x) (cos eps)) (+ (* (sin x) (sin eps)) (cos x))) #s(approx (* eps (- (* eps (+ (* eps (* (sin x) 1/6)) (* (cos x) (+ (* eps (* eps 1/24)) -1/2)))) (sin x))) (fma.f64 x (fma.f64 x (fma.f64 x (.f64 eps (fma.f64 (.f64 eps eps) #s(literal -1/36 binary64) #s(literal 1/6 binary64))) (.f64 #s(literal -1/2 binary64) (.f64 (.f64 eps eps) (fma.f64 eps (.f64 eps #s(literal 1/24 binary64)) #s(literal -1/2 binary64))))) (.f64 eps (fma.f64 eps (.f64 eps #s(literal 1/6 binary64)) #s(literal -1 binary64)))) (.f64 (.f64 eps eps) (fma.f64 eps (*.f64 eps #s(literal 1/24 binary64)) #s(literal -1/2 binary64))))))
#s(approx (- (cos (+ x eps)) (cos x)) (+.f64 (cos.f64 eps) #s(literal -1 binary64)))
(-.f64 #s(approx (cos (+ x eps)) (cos.f64 x)) #s(approx (cos x) #s(literal 1 binary64)))
(-.f64 (cos.f64 (+.f64 x eps)) #s(approx (cos x) #s(literal 1 binary64)))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (sin.f64 x) (neg.f64 eps)))
#s(approx (- (* (cos x) (cos eps)) (+ (* (sin x) (sin eps)) (cos x))) (neg.f64 (*.f64 eps (sin.f64 x))))
#s(approx (- (* (cos x) (cos eps)) (+ (* (sin x) (sin eps)) (cos x))) (.f64 eps #s(approx (- ( eps (+ (* eps (* (sin x) 1/6)) (* (cos x) (+ (* eps (* eps 1/24)) -1/2)))) (sin x)) (sin.f64 (neg.f64 x)))))
#s(approx (- (* (cos x) (cos eps)) (+ (* (sin x) (sin eps)) (cos x))) (*.f64 eps (sin.f64 (neg.f64 x))))
#s(approx (- (* (cos x) (cos eps)) (+ (* (sin x) (sin eps)) (cos x))) (.f64 eps (-.f64 #s(approx ( eps (* -1/2 (cos x))) (*.f64 eps #s(literal -1/2 binary64))) (sin.f64 x))))
(-.f64 (cos.f64 (+.f64 x eps)) #s(approx (cos x) (fma.f64 x (*.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64))))
#s(approx (- (* (cos x) (cos eps)) (+ (* (sin x) (sin eps)) (cos x))) (.f64 eps (-.f64 #s(approx ( eps (* -1/2 (cos x))) (.f64 eps (fma.f64 #s(literal 1/4 binary64) (.f64 x x) #s(literal -1/2 binary64)))) (sin.f64 x))))
#s(approx (- (* (cos x) (cos eps)) (+ (* (sin x) (sin eps)) (cos x))) (.f64 eps (-.f64 #s(approx ( eps (+ (* eps (* (sin x) 1/6)) (* (cos x) (+ (* eps (* eps 1/24)) -1/2)))) (.f64 eps (fma.f64 eps (.f64 eps #s(literal 1/24 binary64)) #s(literal -1/2 binary64)))) (sin.f64 x))))
#s(approx (- (* (cos x) (cos eps)) (+ (* (sin x) (sin eps)) (cos x))) (.f64 eps (-.f64 #s(approx ( eps (+ (* eps (* (sin x) 1/6)) (* (cos x) (+ (* eps (* eps 1/24)) -1/2)))) (fma.f64 x (.f64 eps (.f64 eps #s(literal 1/6 binary64))) (.f64 eps (fma.f64 eps (.f64 eps #s(literal 1/24 binary64)) #s(literal -1/2 binary64))))) (sin.f64 x))))
#s(approx (- (* (cos x) (cos eps)) (+ (* (sin x) (sin eps)) (cos x))) (.f64 eps (-.f64 #s(approx ( eps (+ (* eps (* (sin x) 1/6)) (* (cos x) (+ (* eps (* eps 1/24)) -1/2)))) (fma.f64 x (fma.f64 eps (.f64 eps #s(literal 1/6 binary64)) (.f64 eps (.f64 (.f64 x (fma.f64 eps (.f64 eps #s(literal 1/24 binary64)) #s(literal -1/2 binary64))) #s(literal -1/2 binary64)))) (.f64 eps (fma.f64 eps (*.f64 eps #s(literal 1/24 binary64)) #s(literal -1/2 binary64))))) (sin.f64 x))))
(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps (-.f64 (.f64 eps (*.f64 #s(literal -1/2 binary64) (cos.f64 x))) (sin.f64 x))))
#s(approx (- (* (cos x) (cos eps)) (+ (* (sin x) (sin eps)) (cos x))) (.f64 eps (-.f64 (.f64 eps (*.f64 #s(literal -1/2 binary64) (cos.f64 x))) (sin.f64 x))))
(.f64 #s(approx ( (sin (* (+ eps 0) 1/2)) (sin (* (+ x (+ x eps)) 1/2))) (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x)))) #s(literal -2 binary64))
(.f64 #s(approx ( (sin (* (+ eps 0) 1/2)) (+ (* (sin (* (+ x x) 1/2)) (cos (* eps 1/2))) (* (cos (* (+ x x) 1/2)) (sin (* eps 1/2))))) (.f64 (sin.f64 (fma.f64 eps #s(literal 1/2 binary64) x)) (sin.f64 (.f64 eps #s(literal 1/2 binary64))))) #s(literal -2 binary64))
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))))
(.f64 (.f64 (sin.f64 (.f64 (+.f64 eps #s(literal 0 binary64)) #s(literal 1/2 binary64))) (sin.f64 (.f64 (+.f64 x (+.f64 x eps)) #s(literal 1/2 binary64)))) #s(literal -2 binary64))
#s(approx (- (* (cos x) (cos eps)) (+ (* (sin x) (sin eps)) (cos x))) (.f64 eps (-.f64 (.f64 eps (fma.f64 eps (.f64 (sin.f64 x) #s(literal 1/6 binary64)) (.f64 (cos.f64 x) (fma.f64 eps (*.f64 eps #s(literal 1/24 binary64)) #s(literal -1/2 binary64))))) (sin.f64 x))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps (fma.f64 eps (fma.f64 (cos.f64 x) (+.f64 #s(literal -1/2 binary64) (.f64 eps (.f64 eps #s(literal 1/24 binary64)))) (.f64 eps (*.f64 #s(literal 1/6 binary64) (sin.f64 x)))) (sin.f64 (neg.f64 x)))))
(fma.f64 (*.f64 (cos.f64 (-.f64 x eps)) (cos.f64 (+.f64 x eps))) (/.f64 #s(literal 1 binary64) (cos.f64 (-.f64 x eps))) (neg.f64 (cos.f64 x)))
(-.f64 (.f64 (cos.f64 x) #s(approx (cos eps) (fma.f64 (.f64 eps eps) (fma.f64 (.f64 eps eps) (fma.f64 (.f64 eps eps) #s(literal -1/720 binary64) #s(literal 1/24 binary64)) #s(literal -1/2 binary64)) #s(literal 1 binary64)))) (fma.f64 (sin.f64 x) (sin.f64 eps) (cos.f64 x)))
(.f64 #s(approx ( (sin (* (+ eps 0) 1/2)) (+ (* (sin (* (+ x x) 1/2)) (cos (* eps 1/2))) (* (cos (* (+ x x) 1/2)) (sin (* eps 1/2))))) (.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (fma.f64 (cos.f64 x) #s(approx (sin (* eps 1/2)) (.f64 eps (fma.f64 eps (.f64 eps (fma.f64 eps (.f64 eps #s(literal 1/3840 binary64)) #s(literal -1/48 binary64))) #s(literal 1/2 binary64)))) (.f64 (sin.f64 x) (cos.f64 (*.f64 eps #s(literal 1/2 binary64))))))) #s(literal -2 binary64))
(.f64 #s(approx ( (sin (* (+ eps 0) 1/2)) (+ (* (sin (* (+ x x) 1/2)) (cos (* eps 1/2))) (* (cos (* (+ x x) 1/2)) (sin (* eps 1/2))))) (.f64 #s(approx (sin ( eps 1/2)) (.f64 eps (fma.f64 (.f64 eps eps) (fma.f64 (.f64 eps eps) (fma.f64 (.f64 eps eps) #s(literal -1/645120 binary64) #s(literal 1/3840 binary64)) #s(literal -1/48 binary64)) #s(literal 1/2 binary64)))) (fma.f64 (cos.f64 x) (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (.f64 (sin.f64 x) (cos.f64 (*.f64 eps #s(literal 1/2 binary64))))))) #s(literal -2 binary64))
(/.f64 (/.f64 (-.f64 (fma.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 (+.f64 x eps) #s(literal 2 binary64))) #s(literal 1/2 binary64)) (fma.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64))) #s(literal 2 binary64)) (.f64 (cos.f64 (.f64 (+.f64 x (+.f64 x eps)) #s(literal 1/2 binary64))) (cos.f64 (.f64 (+.f64 eps #s(literal 0 binary64)) #s(literal 1/2 binary64)))))
(-.f64 (*.f64 (cos.f64 x) (cos.f64 eps)) (fma.f64 (sin.f64 x) (sin.f64 eps) (cos.f64 x)))
(fma.f64 (cos.f64 x) (cos.f64 eps) (neg.f64 (fma.f64 (sin.f64 x) (sin.f64 eps) (cos.f64 x))))
(.f64 #s(approx ( (sin (* (+ eps 0) 1/2)) (+ (* (sin (* (+ x x) 1/2)) (cos (* eps 1/2))) (* (cos (* (+ x x) 1/2)) (sin (* eps 1/2))))) (.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (fma.f64 (cos.f64 x) (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (.f64 (sin.f64 x) (cos.f64 (*.f64 eps #s(literal 1/2 binary64))))))) #s(literal -2 binary64))
(.f64 #s(approx ( (sin (* (+ eps 0) 1/2)) (+ (* (sin (* (+ x x) 1/2)) (cos (* eps 1/2))) (* (cos (* (+ x x) 1/2)) (sin (* eps 1/2))))) (fma.f64 (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 #s(literal 2 binary64) (.f64 eps #s(literal 1/2 binary64)))))) (cos.f64 x) (.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (.f64 (sin.f64 x) (cos.f64 (*.f64 eps #s(literal 1/2 binary64))))))) #s(literal -2 binary64))
(.f64 (.f64 (sin.f64 (.f64 (+.f64 eps #s(literal 0 binary64)) #s(literal 1/2 binary64))) (fma.f64 (sin.f64 (.f64 (+.f64 x x) #s(literal 1/2 binary64))) (cos.f64 (.f64 eps #s(literal 1/2 binary64))) (.f64 (cos.f64 (.f64 (+.f64 x x) #s(literal 1/2 binary64))) (sin.f64 (.f64 eps #s(literal 1/2 binary64)))))) #s(literal -2 binary64))
(.f64 (.f64 (sin.f64 (.f64 (.f64 (.f64 eps eps) (/.f64 #s(literal 1 binary64) eps)) #s(literal 1/2 binary64))) (fma.f64 (sin.f64 (.f64 (+.f64 x x) #s(literal 1/2 binary64))) (cos.f64 (.f64 eps #s(literal 1/2 binary64))) (.f64 (cos.f64 (.f64 (+.f64 x x) #s(literal 1/2 binary64))) (sin.f64 (.f64 eps #s(literal 1/2 binary64)))))) #s(literal -2 binary64))
(/.f64 (-.f64 (pow.f64 (.f64 (cos.f64 x) (cos.f64 eps)) #s(literal 3 binary64)) (pow.f64 (fma.f64 (sin.f64 x) (sin.f64 eps) (cos.f64 x)) #s(literal 3 binary64))) (fma.f64 (fma.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64)) (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 #s(literal 2 binary64) eps)))) (+.f64 (pow.f64 (fma.f64 (sin.f64 x) (sin.f64 eps) (cos.f64 x)) #s(literal 2 binary64)) (.f64 (*.f64 (cos.f64 x) (cos.f64 eps)) (fma.f64 (sin.f64 x) (sin.f64 eps) (cos.f64 x))))))

Outputs

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

Calls

3 calls:

18.0ms	x
18.0ms	eps
15.0ms	(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))

Results

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

Compiler

Compiled 15 to 10 computations (33.3% saved)

regimes110.0ms (0.6%)

Memory

-13.9MiB live, 24.6MiB allocated

Counts

66 → 1

Calls

Call 1

Inputs
#s(approx (- (cos (+ x eps)) (cos x)) (+.f64 #s(approx (cos eps) #s(literal 1 binary64)) #s(literal -1 binary64)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* eps (+ (* eps (+ (* (cos x) (+ -1/2 (* eps (* eps 1/24)))) (* eps (* 1/6 (sin x))))) (sin (neg x)))) #s(approx (+ (* eps (* eps (+ (* eps (* eps 1/24)) -1/2))) (* eps (* x (+ (* eps (* eps 1/6)) -1)))) (*.f64 x (neg.f64 eps)))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (+ (cos eps) -1) (.f64 eps (.f64 eps #s(literal -1/2 binary64)))))
#s(approx (- (* (cos x) (cos eps)) (+ (* (sin x) (sin eps)) (cos x))) (.f64 eps #s(approx (- ( eps (* -1/2 (cos x))) (sin x)) (*.f64 eps #s(literal -1/2 binary64)))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* eps (+ (* eps (+ (* (cos x) (+ -1/2 (* eps (* eps 1/24)))) (* eps (* 1/6 (sin x))))) (sin (neg x)))) #s(approx (+ (* eps (* eps (+ (* eps (* eps 1/24)) -1/2))) (* eps (* x (+ (* eps (* eps 1/6)) -1)))) (.f64 eps (-.f64 (.f64 eps #s(literal -1/2 binary64)) x)))))
#s(approx (- (* (cos x) (cos eps)) (+ (* (sin x) (sin eps)) (cos x))) (.f64 eps #s(approx (- ( eps (* -1/2 (cos x))) (sin x)) (-.f64 (*.f64 eps #s(literal -1/2 binary64)) x))))
#s(approx (- (cos (+ x eps)) (cos x)) (+.f64 #s(approx (cos eps) (fma.f64 eps (*.f64 eps #s(literal -1/2 binary64)) #s(literal 1 binary64))) #s(literal -1 binary64)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* eps (+ (* eps (+ (* (cos x) (+ -1/2 (* eps (* eps 1/24)))) (* eps (* 1/6 (sin x))))) (sin (neg x)))) #s(approx (+ (* eps (* eps (+ (* eps (* eps 1/24)) -1/2))) (* eps (* x (+ (* eps (* eps 1/6)) -1)))) #s(approx (* (* (* eps eps) (* eps eps)) (+ (* x (/ 1/6 eps)) 1/24)) (.f64 x (.f64 eps (.f64 eps (.f64 eps #s(literal 1/6 binary64)))))))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* eps (+ (* eps (+ (* (cos x) (+ -1/2 (* eps (* eps 1/24)))) (* eps (* 1/6 (sin x))))) (sin (neg x)))) #s(approx (+ (* eps (* eps (+ (* eps (* eps 1/24)) -1/2))) (* eps (* x (+ (* eps (* eps 1/6)) -1)))) (.f64 #s(literal 1/24 binary64) (.f64 (.f64 eps eps) (.f64 eps eps))))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps #s(approx (+ ( eps (+ (* (cos x) (+ -1/2 (* eps (* eps 1/24)))) (* eps (* 1/6 (sin x))))) (sin (neg x))) #s(approx (+ (* x (+ (* x (+ (* eps (* (+ (* eps (* eps 1/24)) -1/2) -1/2)) (* x (+ (* (* eps eps) -1/36) 1/6)))) (+ (* eps (* eps 1/6)) -1))) (* eps (+ (* eps (* eps 1/24)) -1/2))) (.f64 x (fma.f64 x (.f64 x #s(literal 1/6 binary64)) #s(literal -1 binary64)))))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* eps (+ (* eps (+ (* (cos x) (+ -1/2 (* eps (* eps 1/24)))) (* eps (* 1/6 (sin x))))) (sin (neg x)))) #s(approx (+ (* eps (* eps (+ (* eps (* eps 1/24)) -1/2))) (* eps (* x (+ (* eps (* eps 1/6)) -1)))) (.f64 eps (fma.f64 eps (fma.f64 x (.f64 eps #s(literal 1/6 binary64)) #s(literal -1/2 binary64)) (neg.f64 x))))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* eps (+ (* eps (+ (* (cos x) (+ -1/2 (* eps (* eps 1/24)))) (* eps (* 1/6 (sin x))))) (sin (neg x)))) #s(approx (+ (* eps (* eps (+ (* eps (* eps 1/24)) -1/2))) (* eps (* x (+ (* eps (* eps 1/6)) -1)))) #s(approx (* (* (* eps eps) (* eps eps)) (+ (* x (/ 1/6 eps)) 1/24)) (.f64 (.f64 eps eps) (.f64 eps (fma.f64 eps #s(literal 1/24 binary64) (.f64 x #s(literal 1/6 binary64)))))))))
#s(approx (- (* (cos x) (cos eps)) (+ (* (sin x) (sin eps)) (cos x))) (.f64 eps #s(approx (- ( eps (* -1/2 (cos x))) (sin x)) (fma.f64 x (fma.f64 #s(literal 1/4 binary64) (.f64 eps x) #s(literal -1 binary64)) (.f64 eps #s(literal -1/2 binary64))))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* eps (+ (* eps (+ (* (cos x) (+ -1/2 (* eps (* eps 1/24)))) (* eps (* 1/6 (sin x))))) (sin (neg x)))) (fma.f64 eps #s(approx (* eps (+ (* eps (* eps 1/24)) -1/2)) (.f64 eps #s(literal -1/2 binary64))) (.f64 eps (.f64 x (fma.f64 eps (.f64 eps #s(literal 1/6 binary64)) #s(literal -1 binary64)))))))
#s(approx (- (* (cos x) (cos eps)) (+ (* (sin x) (sin eps)) (cos x))) (.f64 eps #s(approx (- ( eps (* -1/2 (cos x))) (sin x)) (fma.f64 x (fma.f64 x (fma.f64 eps #s(literal 1/4 binary64) (.f64 x #s(literal 1/6 binary64))) #s(literal -1 binary64)) (.f64 eps #s(literal -1/2 binary64))))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* eps (+ (* eps (+ (* (cos x) (+ -1/2 (* eps (* eps 1/24)))) (* eps (* 1/6 (sin x))))) (sin (neg x)))) #s(approx (+ (* eps (* eps (+ (* eps (* eps 1/24)) -1/2))) (* eps (* x (+ (* eps (* eps 1/6)) -1)))) (.f64 (.f64 (.f64 eps eps) (.f64 eps eps)) (fma.f64 x (/.f64 #s(literal 1/6 binary64) eps) #s(literal 1/24 binary64))))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps #s(approx (+ ( eps (+ (* (cos x) (+ -1/2 (* eps (* eps 1/24)))) (* eps (* 1/6 (sin x))))) (sin (neg x))) (fma.f64 eps (fma.f64 eps (.f64 eps #s(literal 1/24 binary64)) #s(literal -1/2 binary64)) (.f64 x (fma.f64 eps (*.f64 eps #s(literal 1/6 binary64)) #s(literal -1 binary64)))))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* eps (+ (* eps (+ (* (cos x) (+ -1/2 (* eps (* eps 1/24)))) (* eps (* 1/6 (sin x))))) (sin (neg x)))) (fma.f64 eps (.f64 eps (fma.f64 eps (.f64 eps #s(literal 1/24 binary64)) #s(literal -1/2 binary64))) (.f64 eps (.f64 x (fma.f64 eps (*.f64 eps #s(literal 1/6 binary64)) #s(literal -1 binary64)))))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* eps (+ (* eps (+ (* (cos x) (+ -1/2 (* eps (* eps 1/24)))) (* eps (* 1/6 (sin x))))) (sin (neg x)))) (fma.f64 (.f64 x (fma.f64 eps (.f64 eps #s(literal 1/6 binary64)) #s(literal -1 binary64))) eps (.f64 eps (.f64 eps (fma.f64 #s(literal 1/24 binary64) (*.f64 eps eps) #s(literal -1/2 binary64)))))))
#s(approx (- (* (cos x) (cos eps)) (+ (* (sin x) (sin eps)) (cos x))) #s(approx (* eps (- (* eps (* -1/2 (cos x))) (sin x))) (fma.f64 x (fma.f64 x (fma.f64 eps (.f64 x #s(literal 1/6 binary64)) (.f64 eps (.f64 eps #s(literal 1/4 binary64)))) (neg.f64 eps)) (.f64 #s(literal -1/2 binary64) (*.f64 eps eps)))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* eps (+ (* eps (+ (* (cos x) (+ -1/2 (* eps (* eps 1/24)))) (* eps (* 1/6 (sin x))))) (sin (neg x)))) #s(approx (+ (* eps (* eps (+ (* eps (* eps 1/24)) -1/2))) (* eps (* x (+ (* eps (* eps 1/6)) -1)))) (.f64 (.f64 (.f64 eps eps) (.f64 eps eps)) (-.f64 #s(literal 1/24 binary64) (/.f64 (fma.f64 x #s(literal -1/6 binary64) (/.f64 #s(literal 1/2 binary64) eps)) eps))))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* eps (+ (* eps (+ (* (cos x) (+ -1/2 (* eps (* eps 1/24)))) (* eps (* 1/6 (sin x))))) (sin (neg x)))) #s(approx (+ (* eps (* eps (+ (* eps (* eps 1/24)) -1/2))) (* eps (* x (+ (* eps (* eps 1/6)) -1)))) #s(approx (* (* (* eps eps) (* eps eps)) (+ (* x (/ 1/6 eps)) 1/24)) (.f64 x (fma.f64 eps (.f64 eps (.f64 eps #s(literal 1/6 binary64))) (/.f64 (.f64 eps (.f64 eps (.f64 #s(literal 1/24 binary64) (*.f64 eps eps)))) x)))))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* eps (+ (* eps (+ (* (cos x) (+ -1/2 (* eps (* eps 1/24)))) (* eps (* 1/6 (sin x))))) (sin (neg x)))) #s(approx (+ (* eps (* eps (+ (* eps (* eps 1/24)) -1/2))) (* eps (* x (+ (* eps (* eps 1/6)) -1)))) (.f64 x (fma.f64 eps (fma.f64 eps (.f64 eps #s(literal 1/6 binary64)) #s(literal -1 binary64)) (.f64 (.f64 eps eps) (/.f64 (fma.f64 #s(literal 1/24 binary64) (*.f64 eps eps) #s(literal -1/2 binary64)) x)))))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* eps (+ (* eps (+ (* (cos x) (+ -1/2 (* eps (* eps 1/24)))) (* eps (* 1/6 (sin x))))) (sin (neg x)))) #s(approx (+ (* eps (* eps (+ (* eps (* eps 1/24)) -1/2))) (* eps (* x (+ (* eps (* eps 1/6)) -1)))) (.f64 (.f64 (.f64 eps eps) (.f64 eps eps)) (+.f64 #s(literal 1/24 binary64) (fma.f64 x (/.f64 #s(literal 1/6 binary64) eps) (/.f64 #s(literal -1/2 binary64) (*.f64 eps eps))))))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps #s(approx (+ ( eps (+ (* (cos x) (+ -1/2 (* eps (* eps 1/24)))) (* eps (* 1/6 (sin x))))) (sin (neg x))) #s(approx (+ (* x (+ (* x (+ (* eps (* (+ (* eps (* eps 1/24)) -1/2) -1/2)) (* x (+ (* (* eps eps) -1/36) 1/6)))) (+ (* eps (* eps 1/6)) -1))) (* eps (+ (* eps (* eps 1/24)) -1/2))) (.f64 (.f64 eps eps) (.f64 eps (fma.f64 x (/.f64 (fma.f64 #s(literal -1/36 binary64) (.f64 x x) #s(literal 1/6 binary64)) eps) (fma.f64 x (*.f64 x #s(literal -1/48 binary64)) #s(literal 1/24 binary64)))))))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps #s(approx (+ ( eps (+ (* (cos x) (+ -1/2 (* eps (* eps 1/24)))) (* eps (* 1/6 (sin x))))) (sin (neg x))) #s(approx (+ (* x (+ (* x (+ (* eps (* (+ (* eps (* eps 1/24)) -1/2) -1/2)) (* x (+ (* (* eps eps) -1/36) 1/6)))) (+ (* eps (* eps 1/6)) -1))) (* eps (+ (* eps (* eps 1/24)) -1/2))) (fma.f64 eps (fma.f64 eps (.f64 x (fma.f64 #s(literal -1/36 binary64) (.f64 x x) #s(literal 1/6 binary64))) (fma.f64 #s(literal 1/4 binary64) (.f64 x x) #s(literal -1/2 binary64))) (.f64 x (fma.f64 x (*.f64 x #s(literal 1/6 binary64)) #s(literal -1 binary64))))))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps #s(approx (+ ( eps (+ (* (cos x) (+ -1/2 (* eps (* eps 1/24)))) (* eps (* 1/6 (sin x))))) (sin (neg x))) #s(approx (+ (* x (+ (* x (+ (* eps (* (+ (* eps (* eps 1/24)) -1/2) -1/2)) (* x (+ (* (* eps eps) -1/36) 1/6)))) (+ (* eps (* eps 1/6)) -1))) (* eps (+ (* eps (* eps 1/24)) -1/2))) (neg.f64 (.f64 (.f64 eps (.f64 eps eps)) (-.f64 (fma.f64 x (.f64 x #s(literal 1/48 binary64)) #s(literal -1/24 binary64)) (.f64 x (/.f64 (fma.f64 #s(literal -1/36 binary64) (.f64 x x) #s(literal 1/6 binary64)) eps)))))))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* eps (+ (* eps (+ (* (cos x) (+ -1/2 (* eps (* eps 1/24)))) (* eps (* 1/6 (sin x))))) (sin (neg x)))) #s(approx (+ (* eps (* eps (+ (* eps (* eps 1/24)) -1/2))) (* eps (* x (+ (* eps (* eps 1/6)) -1)))) (.f64 (.f64 (.f64 eps eps) (.f64 eps eps)) (-.f64 #s(literal 1/24 binary64) (/.f64 (fma.f64 x #s(literal -1/6 binary64) (/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 x eps)) eps)) eps))))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps #s(approx (+ ( eps (+ (* (cos x) (+ -1/2 (* eps (* eps 1/24)))) (* eps (* 1/6 (sin x))))) (sin (neg x))) (fma.f64 eps (fma.f64 eps (.f64 eps #s(literal 1/24 binary64)) #s(literal -1/2 binary64)) (.f64 x (fma.f64 eps (.f64 eps #s(literal 1/6 binary64)) (fma.f64 (.f64 x (fma.f64 eps (.f64 eps #s(literal 1/24 binary64)) #s(literal -1/2 binary64))) (.f64 eps #s(literal -1/2 binary64)) #s(literal -1 binary64))))))))
#s(approx (- (* (cos x) (cos eps)) (+ (* (sin x) (sin eps)) (cos x))) (.f64 eps #s(approx (- ( eps (+ (* eps (* (sin x) 1/6)) (* (cos x) (+ (* eps (* eps 1/24)) -1/2)))) (sin x)) (fma.f64 x (fma.f64 eps (.f64 (.f64 x (fma.f64 eps (.f64 eps #s(literal 1/24 binary64)) #s(literal -1/2 binary64))) #s(literal -1/2 binary64)) (fma.f64 eps (.f64 eps #s(literal 1/6 binary64)) #s(literal -1 binary64))) (.f64 eps (fma.f64 eps (.f64 eps #s(literal 1/24 binary64)) #s(literal -1/2 binary64)))))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps #s(approx (+ ( eps (+ (* (cos x) (+ -1/2 (* eps (* eps 1/24)))) (* eps (* 1/6 (sin x))))) (sin (neg x))) (fma.f64 x (fma.f64 x (fma.f64 eps #s(approx (* (+ (* eps (* eps 1/24)) -1/2) -1/2) #s(literal 1/4 binary64)) (.f64 x (fma.f64 (.f64 eps eps) #s(literal -1/36 binary64) #s(literal 1/6 binary64)))) (fma.f64 eps (.f64 eps #s(literal 1/6 binary64)) #s(literal -1 binary64))) (.f64 eps (fma.f64 eps (*.f64 eps #s(literal 1/24 binary64)) #s(literal -1/2 binary64)))))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps #s(approx (+ ( eps (+ (* (cos x) (+ -1/2 (* eps (* eps 1/24)))) (* eps (* 1/6 (sin x))))) (sin (neg x))) (fma.f64 x (fma.f64 x (fma.f64 eps #s(approx (* (+ (* eps (* eps 1/24)) -1/2) -1/2) (.f64 #s(literal -1/48 binary64) (.f64 eps eps))) (.f64 x (fma.f64 (.f64 eps eps) #s(literal -1/36 binary64) #s(literal 1/6 binary64)))) (fma.f64 eps (.f64 eps #s(literal 1/6 binary64)) #s(literal -1 binary64))) (.f64 eps (fma.f64 eps (*.f64 eps #s(literal 1/24 binary64)) #s(literal -1/2 binary64)))))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* eps (+ (* eps (+ (* (cos x) (+ -1/2 (* eps (* eps 1/24)))) (* eps (* 1/6 (sin x))))) (sin (neg x)))) #s(approx (+ (* eps (* eps (+ (* eps (* eps 1/24)) -1/2))) (* eps (* x (+ (* eps (* eps 1/6)) -1)))) (.f64 (.f64 (.f64 eps eps) (.f64 eps eps)) (+.f64 (fma.f64 x (/.f64 #s(literal 1/6 binary64) eps) (-.f64 #s(literal 1/24 binary64) (/.f64 x (.f64 eps (.f64 eps eps))))) (/.f64 #s(literal -1/2 binary64) (*.f64 eps eps)))))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps #s(approx (+ ( eps (+ (* (cos x) (+ -1/2 (* eps (* eps 1/24)))) (* eps (* 1/6 (sin x))))) (sin (neg x))) (fma.f64 x (fma.f64 x (fma.f64 eps (.f64 (fma.f64 eps (.f64 eps #s(literal 1/24 binary64)) #s(literal -1/2 binary64)) #s(literal -1/2 binary64)) (.f64 x (fma.f64 (.f64 eps eps) #s(literal -1/36 binary64) #s(literal 1/6 binary64)))) (fma.f64 eps (.f64 eps #s(literal 1/6 binary64)) #s(literal -1 binary64))) (.f64 eps (fma.f64 eps (*.f64 eps #s(literal 1/24 binary64)) #s(literal -1/2 binary64)))))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps #s(approx (+ ( eps (+ (* (cos x) (+ -1/2 (* eps (* eps 1/24)))) (* eps (* 1/6 (sin x))))) (sin (neg x))) #s(approx (+ (* x (+ (* x (+ (* eps (* (+ (* eps (* eps 1/24)) -1/2) -1/2)) (* x (+ (* (* eps eps) -1/36) 1/6)))) (+ (* eps (* eps 1/6)) -1))) (* eps (+ (* eps (* eps 1/24)) -1/2))) (neg.f64 (.f64 (.f64 eps (.f64 eps eps)) (-.f64 (fma.f64 x (.f64 x #s(literal 1/48 binary64)) #s(literal -1/24 binary64)) (/.f64 (-.f64 (.f64 x (fma.f64 #s(literal -1/36 binary64) (.f64 x x) #s(literal 1/6 binary64))) (/.f64 (fma.f64 (*.f64 x x) #s(literal -1/4 binary64) #s(literal 1/2 binary64)) eps)) eps))))))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* eps (+ (* eps (+ (* (cos x) (+ -1/2 (* eps (* eps 1/24)))) (* eps (* 1/6 (sin x))))) (sin (neg x)))) (fma.f64 x (fma.f64 x (fma.f64 eps (.f64 x (fma.f64 (.f64 eps eps) #s(literal -1/36 binary64) #s(literal 1/6 binary64))) (.f64 #s(literal -1/2 binary64) (.f64 eps (.f64 eps (fma.f64 eps (.f64 eps #s(literal 1/24 binary64)) #s(literal -1/2 binary64)))))) (.f64 eps (fma.f64 eps (.f64 eps #s(literal 1/6 binary64)) #s(literal -1 binary64)))) (.f64 eps (.f64 eps (fma.f64 eps (*.f64 eps #s(literal 1/24 binary64)) #s(literal -1/2 binary64)))))))
#s(approx (- (* (cos x) (cos eps)) (+ (* (sin x) (sin eps)) (cos x))) #s(approx (* eps (- (* eps (+ (* eps (* (sin x) 1/6)) (* (cos x) (+ (* eps (* eps 1/24)) -1/2)))) (sin x))) (fma.f64 x (fma.f64 x (fma.f64 x (.f64 eps (fma.f64 (.f64 eps eps) #s(literal -1/36 binary64) #s(literal 1/6 binary64))) (.f64 #s(literal -1/2 binary64) (.f64 (.f64 eps eps) (fma.f64 eps (.f64 eps #s(literal 1/24 binary64)) #s(literal -1/2 binary64))))) (.f64 eps (fma.f64 eps (.f64 eps #s(literal 1/6 binary64)) #s(literal -1 binary64)))) (.f64 (.f64 eps eps) (fma.f64 eps (*.f64 eps #s(literal 1/24 binary64)) #s(literal -1/2 binary64))))))
#s(approx (- (cos (+ x eps)) (cos x)) (+.f64 (cos.f64 eps) #s(literal -1 binary64)))
(-.f64 #s(approx (cos (+ x eps)) (cos.f64 x)) #s(approx (cos x) #s(literal 1 binary64)))
(-.f64 (cos.f64 (+.f64 x eps)) #s(approx (cos x) #s(literal 1 binary64)))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (sin.f64 x) (neg.f64 eps)))
#s(approx (- (* (cos x) (cos eps)) (+ (* (sin x) (sin eps)) (cos x))) (neg.f64 (*.f64 eps (sin.f64 x))))
#s(approx (- (* (cos x) (cos eps)) (+ (* (sin x) (sin eps)) (cos x))) (.f64 eps #s(approx (- ( eps (+ (* eps (* (sin x) 1/6)) (* (cos x) (+ (* eps (* eps 1/24)) -1/2)))) (sin x)) (sin.f64 (neg.f64 x)))))
#s(approx (- (* (cos x) (cos eps)) (+ (* (sin x) (sin eps)) (cos x))) (*.f64 eps (sin.f64 (neg.f64 x))))
#s(approx (- (* (cos x) (cos eps)) (+ (* (sin x) (sin eps)) (cos x))) (.f64 eps (-.f64 #s(approx ( eps (* -1/2 (cos x))) (*.f64 eps #s(literal -1/2 binary64))) (sin.f64 x))))
(-.f64 (cos.f64 (+.f64 x eps)) #s(approx (cos x) (fma.f64 x (*.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64))))
#s(approx (- (* (cos x) (cos eps)) (+ (* (sin x) (sin eps)) (cos x))) (.f64 eps (-.f64 #s(approx ( eps (* -1/2 (cos x))) (.f64 eps (fma.f64 #s(literal 1/4 binary64) (.f64 x x) #s(literal -1/2 binary64)))) (sin.f64 x))))
#s(approx (- (* (cos x) (cos eps)) (+ (* (sin x) (sin eps)) (cos x))) (.f64 eps (-.f64 #s(approx ( eps (+ (* eps (* (sin x) 1/6)) (* (cos x) (+ (* eps (* eps 1/24)) -1/2)))) (.f64 eps (fma.f64 eps (.f64 eps #s(literal 1/24 binary64)) #s(literal -1/2 binary64)))) (sin.f64 x))))
#s(approx (- (* (cos x) (cos eps)) (+ (* (sin x) (sin eps)) (cos x))) (.f64 eps (-.f64 #s(approx ( eps (+ (* eps (* (sin x) 1/6)) (* (cos x) (+ (* eps (* eps 1/24)) -1/2)))) (fma.f64 x (.f64 eps (.f64 eps #s(literal 1/6 binary64))) (.f64 eps (fma.f64 eps (.f64 eps #s(literal 1/24 binary64)) #s(literal -1/2 binary64))))) (sin.f64 x))))
#s(approx (- (* (cos x) (cos eps)) (+ (* (sin x) (sin eps)) (cos x))) (.f64 eps (-.f64 #s(approx ( eps (+ (* eps (* (sin x) 1/6)) (* (cos x) (+ (* eps (* eps 1/24)) -1/2)))) (fma.f64 x (fma.f64 eps (.f64 eps #s(literal 1/6 binary64)) (.f64 eps (.f64 (.f64 x (fma.f64 eps (.f64 eps #s(literal 1/24 binary64)) #s(literal -1/2 binary64))) #s(literal -1/2 binary64)))) (.f64 eps (fma.f64 eps (*.f64 eps #s(literal 1/24 binary64)) #s(literal -1/2 binary64))))) (sin.f64 x))))
(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps (-.f64 (.f64 eps (*.f64 #s(literal -1/2 binary64) (cos.f64 x))) (sin.f64 x))))
#s(approx (- (* (cos x) (cos eps)) (+ (* (sin x) (sin eps)) (cos x))) (.f64 eps (-.f64 (.f64 eps (*.f64 #s(literal -1/2 binary64) (cos.f64 x))) (sin.f64 x))))
(.f64 #s(approx ( (sin (* (+ eps 0) 1/2)) (sin (* (+ x (+ x eps)) 1/2))) (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x)))) #s(literal -2 binary64))
(.f64 #s(approx ( (sin (* (+ eps 0) 1/2)) (+ (* (sin (* (+ x x) 1/2)) (cos (* eps 1/2))) (* (cos (* (+ x x) 1/2)) (sin (* eps 1/2))))) (.f64 (sin.f64 (fma.f64 eps #s(literal 1/2 binary64) x)) (sin.f64 (.f64 eps #s(literal 1/2 binary64))))) #s(literal -2 binary64))
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))))
(.f64 (.f64 (sin.f64 (.f64 (+.f64 eps #s(literal 0 binary64)) #s(literal 1/2 binary64))) (sin.f64 (.f64 (+.f64 x (+.f64 x eps)) #s(literal 1/2 binary64)))) #s(literal -2 binary64))
#s(approx (- (* (cos x) (cos eps)) (+ (* (sin x) (sin eps)) (cos x))) (.f64 eps (-.f64 (.f64 eps (fma.f64 eps (.f64 (sin.f64 x) #s(literal 1/6 binary64)) (.f64 (cos.f64 x) (fma.f64 eps (*.f64 eps #s(literal 1/24 binary64)) #s(literal -1/2 binary64))))) (sin.f64 x))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps (fma.f64 eps (fma.f64 (cos.f64 x) (+.f64 #s(literal -1/2 binary64) (.f64 eps (.f64 eps #s(literal 1/24 binary64)))) (.f64 eps (*.f64 #s(literal 1/6 binary64) (sin.f64 x)))) (sin.f64 (neg.f64 x)))))
(fma.f64 (*.f64 (cos.f64 (-.f64 x eps)) (cos.f64 (+.f64 x eps))) (/.f64 #s(literal 1 binary64) (cos.f64 (-.f64 x eps))) (neg.f64 (cos.f64 x)))
(-.f64 (.f64 (cos.f64 x) #s(approx (cos eps) (fma.f64 (.f64 eps eps) (fma.f64 (.f64 eps eps) (fma.f64 (.f64 eps eps) #s(literal -1/720 binary64) #s(literal 1/24 binary64)) #s(literal -1/2 binary64)) #s(literal 1 binary64)))) (fma.f64 (sin.f64 x) (sin.f64 eps) (cos.f64 x)))
(.f64 #s(approx ( (sin (* (+ eps 0) 1/2)) (+ (* (sin (* (+ x x) 1/2)) (cos (* eps 1/2))) (* (cos (* (+ x x) 1/2)) (sin (* eps 1/2))))) (.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (fma.f64 (cos.f64 x) #s(approx (sin (* eps 1/2)) (.f64 eps (fma.f64 eps (.f64 eps (fma.f64 eps (.f64 eps #s(literal 1/3840 binary64)) #s(literal -1/48 binary64))) #s(literal 1/2 binary64)))) (.f64 (sin.f64 x) (cos.f64 (*.f64 eps #s(literal 1/2 binary64))))))) #s(literal -2 binary64))
(.f64 #s(approx ( (sin (* (+ eps 0) 1/2)) (+ (* (sin (* (+ x x) 1/2)) (cos (* eps 1/2))) (* (cos (* (+ x x) 1/2)) (sin (* eps 1/2))))) (.f64 #s(approx (sin ( eps 1/2)) (.f64 eps (fma.f64 (.f64 eps eps) (fma.f64 (.f64 eps eps) (fma.f64 (.f64 eps eps) #s(literal -1/645120 binary64) #s(literal 1/3840 binary64)) #s(literal -1/48 binary64)) #s(literal 1/2 binary64)))) (fma.f64 (cos.f64 x) (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (.f64 (sin.f64 x) (cos.f64 (*.f64 eps #s(literal 1/2 binary64))))))) #s(literal -2 binary64))
(/.f64 (/.f64 (-.f64 (fma.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 (+.f64 x eps) #s(literal 2 binary64))) #s(literal 1/2 binary64)) (fma.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64))) #s(literal 2 binary64)) (.f64 (cos.f64 (.f64 (+.f64 x (+.f64 x eps)) #s(literal 1/2 binary64))) (cos.f64 (.f64 (+.f64 eps #s(literal 0 binary64)) #s(literal 1/2 binary64)))))
(-.f64 (*.f64 (cos.f64 x) (cos.f64 eps)) (fma.f64 (sin.f64 x) (sin.f64 eps) (cos.f64 x)))
(fma.f64 (cos.f64 x) (cos.f64 eps) (neg.f64 (fma.f64 (sin.f64 x) (sin.f64 eps) (cos.f64 x))))

Outputs

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

Calls

3 calls:

75.0ms	eps
17.0ms	x
14.0ms	(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))

Results

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

Compiler

Compiled 15 to 10 computations (33.3% saved)

regimes48.0ms (0.3%)

Memory

22.6MiB live, 22.6MiB allocated

Counts

62 → 1

Calls

Call 1

Inputs
#s(approx (- (cos (+ x eps)) (cos x)) (+.f64 #s(approx (cos eps) #s(literal 1 binary64)) #s(literal -1 binary64)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* eps (+ (* eps (+ (* (cos x) (+ -1/2 (* eps (* eps 1/24)))) (* eps (* 1/6 (sin x))))) (sin (neg x)))) #s(approx (+ (* eps (* eps (+ (* eps (* eps 1/24)) -1/2))) (* eps (* x (+ (* eps (* eps 1/6)) -1)))) (*.f64 x (neg.f64 eps)))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (+ (cos eps) -1) (.f64 eps (.f64 eps #s(literal -1/2 binary64)))))
#s(approx (- (* (cos x) (cos eps)) (+ (* (sin x) (sin eps)) (cos x))) (.f64 eps #s(approx (- ( eps (* -1/2 (cos x))) (sin x)) (*.f64 eps #s(literal -1/2 binary64)))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* eps (+ (* eps (+ (* (cos x) (+ -1/2 (* eps (* eps 1/24)))) (* eps (* 1/6 (sin x))))) (sin (neg x)))) #s(approx (+ (* eps (* eps (+ (* eps (* eps 1/24)) -1/2))) (* eps (* x (+ (* eps (* eps 1/6)) -1)))) (.f64 eps (-.f64 (.f64 eps #s(literal -1/2 binary64)) x)))))
#s(approx (- (* (cos x) (cos eps)) (+ (* (sin x) (sin eps)) (cos x))) (.f64 eps #s(approx (- ( eps (* -1/2 (cos x))) (sin x)) (-.f64 (*.f64 eps #s(literal -1/2 binary64)) x))))
#s(approx (- (cos (+ x eps)) (cos x)) (+.f64 #s(approx (cos eps) (fma.f64 eps (*.f64 eps #s(literal -1/2 binary64)) #s(literal 1 binary64))) #s(literal -1 binary64)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* eps (+ (* eps (+ (* (cos x) (+ -1/2 (* eps (* eps 1/24)))) (* eps (* 1/6 (sin x))))) (sin (neg x)))) #s(approx (+ (* eps (* eps (+ (* eps (* eps 1/24)) -1/2))) (* eps (* x (+ (* eps (* eps 1/6)) -1)))) #s(approx (* (* (* eps eps) (* eps eps)) (+ (* x (/ 1/6 eps)) 1/24)) (.f64 x (.f64 eps (.f64 eps (.f64 eps #s(literal 1/6 binary64)))))))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* eps (+ (* eps (+ (* (cos x) (+ -1/2 (* eps (* eps 1/24)))) (* eps (* 1/6 (sin x))))) (sin (neg x)))) #s(approx (+ (* eps (* eps (+ (* eps (* eps 1/24)) -1/2))) (* eps (* x (+ (* eps (* eps 1/6)) -1)))) (.f64 #s(literal 1/24 binary64) (.f64 (.f64 eps eps) (.f64 eps eps))))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps #s(approx (+ ( eps (+ (* (cos x) (+ -1/2 (* eps (* eps 1/24)))) (* eps (* 1/6 (sin x))))) (sin (neg x))) #s(approx (+ (* x (+ (* x (+ (* eps (* (+ (* eps (* eps 1/24)) -1/2) -1/2)) (* x (+ (* (* eps eps) -1/36) 1/6)))) (+ (* eps (* eps 1/6)) -1))) (* eps (+ (* eps (* eps 1/24)) -1/2))) (.f64 x (fma.f64 x (.f64 x #s(literal 1/6 binary64)) #s(literal -1 binary64)))))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* eps (+ (* eps (+ (* (cos x) (+ -1/2 (* eps (* eps 1/24)))) (* eps (* 1/6 (sin x))))) (sin (neg x)))) #s(approx (+ (* eps (* eps (+ (* eps (* eps 1/24)) -1/2))) (* eps (* x (+ (* eps (* eps 1/6)) -1)))) (.f64 eps (fma.f64 eps (fma.f64 x (.f64 eps #s(literal 1/6 binary64)) #s(literal -1/2 binary64)) (neg.f64 x))))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* eps (+ (* eps (+ (* (cos x) (+ -1/2 (* eps (* eps 1/24)))) (* eps (* 1/6 (sin x))))) (sin (neg x)))) #s(approx (+ (* eps (* eps (+ (* eps (* eps 1/24)) -1/2))) (* eps (* x (+ (* eps (* eps 1/6)) -1)))) #s(approx (* (* (* eps eps) (* eps eps)) (+ (* x (/ 1/6 eps)) 1/24)) (.f64 (.f64 eps eps) (.f64 eps (fma.f64 eps #s(literal 1/24 binary64) (.f64 x #s(literal 1/6 binary64)))))))))
#s(approx (- (* (cos x) (cos eps)) (+ (* (sin x) (sin eps)) (cos x))) (.f64 eps #s(approx (- ( eps (* -1/2 (cos x))) (sin x)) (fma.f64 x (fma.f64 #s(literal 1/4 binary64) (.f64 eps x) #s(literal -1 binary64)) (.f64 eps #s(literal -1/2 binary64))))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* eps (+ (* eps (+ (* (cos x) (+ -1/2 (* eps (* eps 1/24)))) (* eps (* 1/6 (sin x))))) (sin (neg x)))) (fma.f64 eps #s(approx (* eps (+ (* eps (* eps 1/24)) -1/2)) (.f64 eps #s(literal -1/2 binary64))) (.f64 eps (.f64 x (fma.f64 eps (.f64 eps #s(literal 1/6 binary64)) #s(literal -1 binary64)))))))
#s(approx (- (* (cos x) (cos eps)) (+ (* (sin x) (sin eps)) (cos x))) (.f64 eps #s(approx (- ( eps (* -1/2 (cos x))) (sin x)) (fma.f64 x (fma.f64 x (fma.f64 eps #s(literal 1/4 binary64) (.f64 x #s(literal 1/6 binary64))) #s(literal -1 binary64)) (.f64 eps #s(literal -1/2 binary64))))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* eps (+ (* eps (+ (* (cos x) (+ -1/2 (* eps (* eps 1/24)))) (* eps (* 1/6 (sin x))))) (sin (neg x)))) #s(approx (+ (* eps (* eps (+ (* eps (* eps 1/24)) -1/2))) (* eps (* x (+ (* eps (* eps 1/6)) -1)))) (.f64 (.f64 (.f64 eps eps) (.f64 eps eps)) (fma.f64 x (/.f64 #s(literal 1/6 binary64) eps) #s(literal 1/24 binary64))))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps #s(approx (+ ( eps (+ (* (cos x) (+ -1/2 (* eps (* eps 1/24)))) (* eps (* 1/6 (sin x))))) (sin (neg x))) (fma.f64 eps (fma.f64 eps (.f64 eps #s(literal 1/24 binary64)) #s(literal -1/2 binary64)) (.f64 x (fma.f64 eps (*.f64 eps #s(literal 1/6 binary64)) #s(literal -1 binary64)))))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* eps (+ (* eps (+ (* (cos x) (+ -1/2 (* eps (* eps 1/24)))) (* eps (* 1/6 (sin x))))) (sin (neg x)))) (fma.f64 eps (.f64 eps (fma.f64 eps (.f64 eps #s(literal 1/24 binary64)) #s(literal -1/2 binary64))) (.f64 eps (.f64 x (fma.f64 eps (*.f64 eps #s(literal 1/6 binary64)) #s(literal -1 binary64)))))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* eps (+ (* eps (+ (* (cos x) (+ -1/2 (* eps (* eps 1/24)))) (* eps (* 1/6 (sin x))))) (sin (neg x)))) (fma.f64 (.f64 x (fma.f64 eps (.f64 eps #s(literal 1/6 binary64)) #s(literal -1 binary64))) eps (.f64 eps (.f64 eps (fma.f64 #s(literal 1/24 binary64) (*.f64 eps eps) #s(literal -1/2 binary64)))))))
#s(approx (- (* (cos x) (cos eps)) (+ (* (sin x) (sin eps)) (cos x))) #s(approx (* eps (- (* eps (* -1/2 (cos x))) (sin x))) (fma.f64 x (fma.f64 x (fma.f64 eps (.f64 x #s(literal 1/6 binary64)) (.f64 eps (.f64 eps #s(literal 1/4 binary64)))) (neg.f64 eps)) (.f64 #s(literal -1/2 binary64) (*.f64 eps eps)))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* eps (+ (* eps (+ (* (cos x) (+ -1/2 (* eps (* eps 1/24)))) (* eps (* 1/6 (sin x))))) (sin (neg x)))) #s(approx (+ (* eps (* eps (+ (* eps (* eps 1/24)) -1/2))) (* eps (* x (+ (* eps (* eps 1/6)) -1)))) (.f64 (.f64 (.f64 eps eps) (.f64 eps eps)) (-.f64 #s(literal 1/24 binary64) (/.f64 (fma.f64 x #s(literal -1/6 binary64) (/.f64 #s(literal 1/2 binary64) eps)) eps))))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* eps (+ (* eps (+ (* (cos x) (+ -1/2 (* eps (* eps 1/24)))) (* eps (* 1/6 (sin x))))) (sin (neg x)))) #s(approx (+ (* eps (* eps (+ (* eps (* eps 1/24)) -1/2))) (* eps (* x (+ (* eps (* eps 1/6)) -1)))) #s(approx (* (* (* eps eps) (* eps eps)) (+ (* x (/ 1/6 eps)) 1/24)) (.f64 x (fma.f64 eps (.f64 eps (.f64 eps #s(literal 1/6 binary64))) (/.f64 (.f64 eps (.f64 eps (.f64 #s(literal 1/24 binary64) (*.f64 eps eps)))) x)))))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* eps (+ (* eps (+ (* (cos x) (+ -1/2 (* eps (* eps 1/24)))) (* eps (* 1/6 (sin x))))) (sin (neg x)))) #s(approx (+ (* eps (* eps (+ (* eps (* eps 1/24)) -1/2))) (* eps (* x (+ (* eps (* eps 1/6)) -1)))) (.f64 x (fma.f64 eps (fma.f64 eps (.f64 eps #s(literal 1/6 binary64)) #s(literal -1 binary64)) (.f64 (.f64 eps eps) (/.f64 (fma.f64 #s(literal 1/24 binary64) (*.f64 eps eps) #s(literal -1/2 binary64)) x)))))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* eps (+ (* eps (+ (* (cos x) (+ -1/2 (* eps (* eps 1/24)))) (* eps (* 1/6 (sin x))))) (sin (neg x)))) #s(approx (+ (* eps (* eps (+ (* eps (* eps 1/24)) -1/2))) (* eps (* x (+ (* eps (* eps 1/6)) -1)))) (.f64 (.f64 (.f64 eps eps) (.f64 eps eps)) (+.f64 #s(literal 1/24 binary64) (fma.f64 x (/.f64 #s(literal 1/6 binary64) eps) (/.f64 #s(literal -1/2 binary64) (*.f64 eps eps))))))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps #s(approx (+ ( eps (+ (* (cos x) (+ -1/2 (* eps (* eps 1/24)))) (* eps (* 1/6 (sin x))))) (sin (neg x))) #s(approx (+ (* x (+ (* x (+ (* eps (* (+ (* eps (* eps 1/24)) -1/2) -1/2)) (* x (+ (* (* eps eps) -1/36) 1/6)))) (+ (* eps (* eps 1/6)) -1))) (* eps (+ (* eps (* eps 1/24)) -1/2))) (.f64 (.f64 eps eps) (.f64 eps (fma.f64 x (/.f64 (fma.f64 #s(literal -1/36 binary64) (.f64 x x) #s(literal 1/6 binary64)) eps) (fma.f64 x (*.f64 x #s(literal -1/48 binary64)) #s(literal 1/24 binary64)))))))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps #s(approx (+ ( eps (+ (* (cos x) (+ -1/2 (* eps (* eps 1/24)))) (* eps (* 1/6 (sin x))))) (sin (neg x))) #s(approx (+ (* x (+ (* x (+ (* eps (* (+ (* eps (* eps 1/24)) -1/2) -1/2)) (* x (+ (* (* eps eps) -1/36) 1/6)))) (+ (* eps (* eps 1/6)) -1))) (* eps (+ (* eps (* eps 1/24)) -1/2))) (fma.f64 eps (fma.f64 eps (.f64 x (fma.f64 #s(literal -1/36 binary64) (.f64 x x) #s(literal 1/6 binary64))) (fma.f64 #s(literal 1/4 binary64) (.f64 x x) #s(literal -1/2 binary64))) (.f64 x (fma.f64 x (*.f64 x #s(literal 1/6 binary64)) #s(literal -1 binary64))))))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps #s(approx (+ ( eps (+ (* (cos x) (+ -1/2 (* eps (* eps 1/24)))) (* eps (* 1/6 (sin x))))) (sin (neg x))) #s(approx (+ (* x (+ (* x (+ (* eps (* (+ (* eps (* eps 1/24)) -1/2) -1/2)) (* x (+ (* (* eps eps) -1/36) 1/6)))) (+ (* eps (* eps 1/6)) -1))) (* eps (+ (* eps (* eps 1/24)) -1/2))) (neg.f64 (.f64 (.f64 eps (.f64 eps eps)) (-.f64 (fma.f64 x (.f64 x #s(literal 1/48 binary64)) #s(literal -1/24 binary64)) (.f64 x (/.f64 (fma.f64 #s(literal -1/36 binary64) (.f64 x x) #s(literal 1/6 binary64)) eps)))))))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* eps (+ (* eps (+ (* (cos x) (+ -1/2 (* eps (* eps 1/24)))) (* eps (* 1/6 (sin x))))) (sin (neg x)))) #s(approx (+ (* eps (* eps (+ (* eps (* eps 1/24)) -1/2))) (* eps (* x (+ (* eps (* eps 1/6)) -1)))) (.f64 (.f64 (.f64 eps eps) (.f64 eps eps)) (-.f64 #s(literal 1/24 binary64) (/.f64 (fma.f64 x #s(literal -1/6 binary64) (/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 x eps)) eps)) eps))))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps #s(approx (+ ( eps (+ (* (cos x) (+ -1/2 (* eps (* eps 1/24)))) (* eps (* 1/6 (sin x))))) (sin (neg x))) (fma.f64 eps (fma.f64 eps (.f64 eps #s(literal 1/24 binary64)) #s(literal -1/2 binary64)) (.f64 x (fma.f64 eps (.f64 eps #s(literal 1/6 binary64)) (fma.f64 (.f64 x (fma.f64 eps (.f64 eps #s(literal 1/24 binary64)) #s(literal -1/2 binary64))) (.f64 eps #s(literal -1/2 binary64)) #s(literal -1 binary64))))))))
#s(approx (- (* (cos x) (cos eps)) (+ (* (sin x) (sin eps)) (cos x))) (.f64 eps #s(approx (- ( eps (+ (* eps (* (sin x) 1/6)) (* (cos x) (+ (* eps (* eps 1/24)) -1/2)))) (sin x)) (fma.f64 x (fma.f64 eps (.f64 (.f64 x (fma.f64 eps (.f64 eps #s(literal 1/24 binary64)) #s(literal -1/2 binary64))) #s(literal -1/2 binary64)) (fma.f64 eps (.f64 eps #s(literal 1/6 binary64)) #s(literal -1 binary64))) (.f64 eps (fma.f64 eps (.f64 eps #s(literal 1/24 binary64)) #s(literal -1/2 binary64)))))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps #s(approx (+ ( eps (+ (* (cos x) (+ -1/2 (* eps (* eps 1/24)))) (* eps (* 1/6 (sin x))))) (sin (neg x))) (fma.f64 x (fma.f64 x (fma.f64 eps #s(approx (* (+ (* eps (* eps 1/24)) -1/2) -1/2) #s(literal 1/4 binary64)) (.f64 x (fma.f64 (.f64 eps eps) #s(literal -1/36 binary64) #s(literal 1/6 binary64)))) (fma.f64 eps (.f64 eps #s(literal 1/6 binary64)) #s(literal -1 binary64))) (.f64 eps (fma.f64 eps (*.f64 eps #s(literal 1/24 binary64)) #s(literal -1/2 binary64)))))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps #s(approx (+ ( eps (+ (* (cos x) (+ -1/2 (* eps (* eps 1/24)))) (* eps (* 1/6 (sin x))))) (sin (neg x))) (fma.f64 x (fma.f64 x (fma.f64 eps #s(approx (* (+ (* eps (* eps 1/24)) -1/2) -1/2) (.f64 #s(literal -1/48 binary64) (.f64 eps eps))) (.f64 x (fma.f64 (.f64 eps eps) #s(literal -1/36 binary64) #s(literal 1/6 binary64)))) (fma.f64 eps (.f64 eps #s(literal 1/6 binary64)) #s(literal -1 binary64))) (.f64 eps (fma.f64 eps (*.f64 eps #s(literal 1/24 binary64)) #s(literal -1/2 binary64)))))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* eps (+ (* eps (+ (* (cos x) (+ -1/2 (* eps (* eps 1/24)))) (* eps (* 1/6 (sin x))))) (sin (neg x)))) #s(approx (+ (* eps (* eps (+ (* eps (* eps 1/24)) -1/2))) (* eps (* x (+ (* eps (* eps 1/6)) -1)))) (.f64 (.f64 (.f64 eps eps) (.f64 eps eps)) (+.f64 (fma.f64 x (/.f64 #s(literal 1/6 binary64) eps) (-.f64 #s(literal 1/24 binary64) (/.f64 x (.f64 eps (.f64 eps eps))))) (/.f64 #s(literal -1/2 binary64) (*.f64 eps eps)))))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps #s(approx (+ ( eps (+ (* (cos x) (+ -1/2 (* eps (* eps 1/24)))) (* eps (* 1/6 (sin x))))) (sin (neg x))) (fma.f64 x (fma.f64 x (fma.f64 eps (.f64 (fma.f64 eps (.f64 eps #s(literal 1/24 binary64)) #s(literal -1/2 binary64)) #s(literal -1/2 binary64)) (.f64 x (fma.f64 (.f64 eps eps) #s(literal -1/36 binary64) #s(literal 1/6 binary64)))) (fma.f64 eps (.f64 eps #s(literal 1/6 binary64)) #s(literal -1 binary64))) (.f64 eps (fma.f64 eps (*.f64 eps #s(literal 1/24 binary64)) #s(literal -1/2 binary64)))))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps #s(approx (+ ( eps (+ (* (cos x) (+ -1/2 (* eps (* eps 1/24)))) (* eps (* 1/6 (sin x))))) (sin (neg x))) #s(approx (+ (* x (+ (* x (+ (* eps (* (+ (* eps (* eps 1/24)) -1/2) -1/2)) (* x (+ (* (* eps eps) -1/36) 1/6)))) (+ (* eps (* eps 1/6)) -1))) (* eps (+ (* eps (* eps 1/24)) -1/2))) (neg.f64 (.f64 (.f64 eps (.f64 eps eps)) (-.f64 (fma.f64 x (.f64 x #s(literal 1/48 binary64)) #s(literal -1/24 binary64)) (/.f64 (-.f64 (.f64 x (fma.f64 #s(literal -1/36 binary64) (.f64 x x) #s(literal 1/6 binary64))) (/.f64 (fma.f64 (*.f64 x x) #s(literal -1/4 binary64) #s(literal 1/2 binary64)) eps)) eps))))))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* eps (+ (* eps (+ (* (cos x) (+ -1/2 (* eps (* eps 1/24)))) (* eps (* 1/6 (sin x))))) (sin (neg x)))) (fma.f64 x (fma.f64 x (fma.f64 eps (.f64 x (fma.f64 (.f64 eps eps) #s(literal -1/36 binary64) #s(literal 1/6 binary64))) (.f64 #s(literal -1/2 binary64) (.f64 eps (.f64 eps (fma.f64 eps (.f64 eps #s(literal 1/24 binary64)) #s(literal -1/2 binary64)))))) (.f64 eps (fma.f64 eps (.f64 eps #s(literal 1/6 binary64)) #s(literal -1 binary64)))) (.f64 eps (.f64 eps (fma.f64 eps (*.f64 eps #s(literal 1/24 binary64)) #s(literal -1/2 binary64)))))))
#s(approx (- (* (cos x) (cos eps)) (+ (* (sin x) (sin eps)) (cos x))) #s(approx (* eps (- (* eps (+ (* eps (* (sin x) 1/6)) (* (cos x) (+ (* eps (* eps 1/24)) -1/2)))) (sin x))) (fma.f64 x (fma.f64 x (fma.f64 x (.f64 eps (fma.f64 (.f64 eps eps) #s(literal -1/36 binary64) #s(literal 1/6 binary64))) (.f64 #s(literal -1/2 binary64) (.f64 (.f64 eps eps) (fma.f64 eps (.f64 eps #s(literal 1/24 binary64)) #s(literal -1/2 binary64))))) (.f64 eps (fma.f64 eps (.f64 eps #s(literal 1/6 binary64)) #s(literal -1 binary64)))) (.f64 (.f64 eps eps) (fma.f64 eps (*.f64 eps #s(literal 1/24 binary64)) #s(literal -1/2 binary64))))))
#s(approx (- (cos (+ x eps)) (cos x)) (+.f64 (cos.f64 eps) #s(literal -1 binary64)))
(-.f64 #s(approx (cos (+ x eps)) (cos.f64 x)) #s(approx (cos x) #s(literal 1 binary64)))
(-.f64 (cos.f64 (+.f64 x eps)) #s(approx (cos x) #s(literal 1 binary64)))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (sin.f64 x) (neg.f64 eps)))
#s(approx (- (* (cos x) (cos eps)) (+ (* (sin x) (sin eps)) (cos x))) (neg.f64 (*.f64 eps (sin.f64 x))))
#s(approx (- (* (cos x) (cos eps)) (+ (* (sin x) (sin eps)) (cos x))) (.f64 eps #s(approx (- ( eps (+ (* eps (* (sin x) 1/6)) (* (cos x) (+ (* eps (* eps 1/24)) -1/2)))) (sin x)) (sin.f64 (neg.f64 x)))))
#s(approx (- (* (cos x) (cos eps)) (+ (* (sin x) (sin eps)) (cos x))) (*.f64 eps (sin.f64 (neg.f64 x))))
#s(approx (- (* (cos x) (cos eps)) (+ (* (sin x) (sin eps)) (cos x))) (.f64 eps (-.f64 #s(approx ( eps (* -1/2 (cos x))) (*.f64 eps #s(literal -1/2 binary64))) (sin.f64 x))))
(-.f64 (cos.f64 (+.f64 x eps)) #s(approx (cos x) (fma.f64 x (*.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64))))
#s(approx (- (* (cos x) (cos eps)) (+ (* (sin x) (sin eps)) (cos x))) (.f64 eps (-.f64 #s(approx ( eps (* -1/2 (cos x))) (.f64 eps (fma.f64 #s(literal 1/4 binary64) (.f64 x x) #s(literal -1/2 binary64)))) (sin.f64 x))))
#s(approx (- (* (cos x) (cos eps)) (+ (* (sin x) (sin eps)) (cos x))) (.f64 eps (-.f64 #s(approx ( eps (+ (* eps (* (sin x) 1/6)) (* (cos x) (+ (* eps (* eps 1/24)) -1/2)))) (.f64 eps (fma.f64 eps (.f64 eps #s(literal 1/24 binary64)) #s(literal -1/2 binary64)))) (sin.f64 x))))
#s(approx (- (* (cos x) (cos eps)) (+ (* (sin x) (sin eps)) (cos x))) (.f64 eps (-.f64 #s(approx ( eps (+ (* eps (* (sin x) 1/6)) (* (cos x) (+ (* eps (* eps 1/24)) -1/2)))) (fma.f64 x (.f64 eps (.f64 eps #s(literal 1/6 binary64))) (.f64 eps (fma.f64 eps (.f64 eps #s(literal 1/24 binary64)) #s(literal -1/2 binary64))))) (sin.f64 x))))
#s(approx (- (* (cos x) (cos eps)) (+ (* (sin x) (sin eps)) (cos x))) (.f64 eps (-.f64 #s(approx ( eps (+ (* eps (* (sin x) 1/6)) (* (cos x) (+ (* eps (* eps 1/24)) -1/2)))) (fma.f64 x (fma.f64 eps (.f64 eps #s(literal 1/6 binary64)) (.f64 eps (.f64 (.f64 x (fma.f64 eps (.f64 eps #s(literal 1/24 binary64)) #s(literal -1/2 binary64))) #s(literal -1/2 binary64)))) (.f64 eps (fma.f64 eps (*.f64 eps #s(literal 1/24 binary64)) #s(literal -1/2 binary64))))) (sin.f64 x))))
(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps (-.f64 (.f64 eps (*.f64 #s(literal -1/2 binary64) (cos.f64 x))) (sin.f64 x))))
#s(approx (- (* (cos x) (cos eps)) (+ (* (sin x) (sin eps)) (cos x))) (.f64 eps (-.f64 (.f64 eps (*.f64 #s(literal -1/2 binary64) (cos.f64 x))) (sin.f64 x))))
(.f64 #s(approx ( (sin (* (+ eps 0) 1/2)) (sin (* (+ x (+ x eps)) 1/2))) (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x)))) #s(literal -2 binary64))
(.f64 #s(approx ( (sin (* (+ eps 0) 1/2)) (+ (* (sin (* (+ x x) 1/2)) (cos (* eps 1/2))) (* (cos (* (+ x x) 1/2)) (sin (* eps 1/2))))) (.f64 (sin.f64 (fma.f64 eps #s(literal 1/2 binary64) x)) (sin.f64 (.f64 eps #s(literal 1/2 binary64))))) #s(literal -2 binary64))
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))))
(.f64 (.f64 (sin.f64 (.f64 (+.f64 eps #s(literal 0 binary64)) #s(literal 1/2 binary64))) (sin.f64 (.f64 (+.f64 x (+.f64 x eps)) #s(literal 1/2 binary64)))) #s(literal -2 binary64))
#s(approx (- (* (cos x) (cos eps)) (+ (* (sin x) (sin eps)) (cos x))) (.f64 eps (-.f64 (.f64 eps (fma.f64 eps (.f64 (sin.f64 x) #s(literal 1/6 binary64)) (.f64 (cos.f64 x) (fma.f64 eps (*.f64 eps #s(literal 1/24 binary64)) #s(literal -1/2 binary64))))) (sin.f64 x))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps (fma.f64 eps (fma.f64 (cos.f64 x) (+.f64 #s(literal -1/2 binary64) (.f64 eps (.f64 eps #s(literal 1/24 binary64)))) (.f64 eps (*.f64 #s(literal 1/6 binary64) (sin.f64 x)))) (sin.f64 (neg.f64 x)))))
(fma.f64 (*.f64 (cos.f64 (-.f64 x eps)) (cos.f64 (+.f64 x eps))) (/.f64 #s(literal 1 binary64) (cos.f64 (-.f64 x eps))) (neg.f64 (cos.f64 x)))
(-.f64 (.f64 (cos.f64 x) #s(approx (cos eps) (fma.f64 (.f64 eps eps) (fma.f64 (.f64 eps eps) (fma.f64 (.f64 eps eps) #s(literal -1/720 binary64) #s(literal 1/24 binary64)) #s(literal -1/2 binary64)) #s(literal 1 binary64)))) (fma.f64 (sin.f64 x) (sin.f64 eps) (cos.f64 x)))
(.f64 #s(approx ( (sin (* (+ eps 0) 1/2)) (+ (* (sin (* (+ x x) 1/2)) (cos (* eps 1/2))) (* (cos (* (+ x x) 1/2)) (sin (* eps 1/2))))) (.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (fma.f64 (cos.f64 x) #s(approx (sin (* eps 1/2)) (.f64 eps (fma.f64 eps (.f64 eps (fma.f64 eps (.f64 eps #s(literal 1/3840 binary64)) #s(literal -1/48 binary64))) #s(literal 1/2 binary64)))) (.f64 (sin.f64 x) (cos.f64 (*.f64 eps #s(literal 1/2 binary64))))))) #s(literal -2 binary64))

Outputs

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

Calls

3 calls:

16.0ms	x
16.0ms	eps
13.0ms	(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))

Results

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

Compiler

Compiled 15 to 10 computations (33.3% saved)

regimes51.0ms (0.3%)

Memory

-15.9MiB live, 22.9MiB allocated

Counts

61 → 1

Calls

Call 1

Inputs
#s(approx (- (cos (+ x eps)) (cos x)) (+.f64 #s(approx (cos eps) #s(literal 1 binary64)) #s(literal -1 binary64)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* eps (+ (* eps (+ (* (cos x) (+ -1/2 (* eps (* eps 1/24)))) (* eps (* 1/6 (sin x))))) (sin (neg x)))) #s(approx (+ (* eps (* eps (+ (* eps (* eps 1/24)) -1/2))) (* eps (* x (+ (* eps (* eps 1/6)) -1)))) (*.f64 x (neg.f64 eps)))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (+ (cos eps) -1) (.f64 eps (.f64 eps #s(literal -1/2 binary64)))))
#s(approx (- (* (cos x) (cos eps)) (+ (* (sin x) (sin eps)) (cos x))) (.f64 eps #s(approx (- ( eps (* -1/2 (cos x))) (sin x)) (*.f64 eps #s(literal -1/2 binary64)))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* eps (+ (* eps (+ (* (cos x) (+ -1/2 (* eps (* eps 1/24)))) (* eps (* 1/6 (sin x))))) (sin (neg x)))) #s(approx (+ (* eps (* eps (+ (* eps (* eps 1/24)) -1/2))) (* eps (* x (+ (* eps (* eps 1/6)) -1)))) (.f64 eps (-.f64 (.f64 eps #s(literal -1/2 binary64)) x)))))
#s(approx (- (* (cos x) (cos eps)) (+ (* (sin x) (sin eps)) (cos x))) (.f64 eps #s(approx (- ( eps (* -1/2 (cos x))) (sin x)) (-.f64 (*.f64 eps #s(literal -1/2 binary64)) x))))
#s(approx (- (cos (+ x eps)) (cos x)) (+.f64 #s(approx (cos eps) (fma.f64 eps (*.f64 eps #s(literal -1/2 binary64)) #s(literal 1 binary64))) #s(literal -1 binary64)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* eps (+ (* eps (+ (* (cos x) (+ -1/2 (* eps (* eps 1/24)))) (* eps (* 1/6 (sin x))))) (sin (neg x)))) #s(approx (+ (* eps (* eps (+ (* eps (* eps 1/24)) -1/2))) (* eps (* x (+ (* eps (* eps 1/6)) -1)))) #s(approx (* (* (* eps eps) (* eps eps)) (+ (* x (/ 1/6 eps)) 1/24)) (.f64 x (.f64 eps (.f64 eps (.f64 eps #s(literal 1/6 binary64)))))))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* eps (+ (* eps (+ (* (cos x) (+ -1/2 (* eps (* eps 1/24)))) (* eps (* 1/6 (sin x))))) (sin (neg x)))) #s(approx (+ (* eps (* eps (+ (* eps (* eps 1/24)) -1/2))) (* eps (* x (+ (* eps (* eps 1/6)) -1)))) (.f64 #s(literal 1/24 binary64) (.f64 (.f64 eps eps) (.f64 eps eps))))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps #s(approx (+ ( eps (+ (* (cos x) (+ -1/2 (* eps (* eps 1/24)))) (* eps (* 1/6 (sin x))))) (sin (neg x))) #s(approx (+ (* x (+ (* x (+ (* eps (* (+ (* eps (* eps 1/24)) -1/2) -1/2)) (* x (+ (* (* eps eps) -1/36) 1/6)))) (+ (* eps (* eps 1/6)) -1))) (* eps (+ (* eps (* eps 1/24)) -1/2))) (.f64 x (fma.f64 x (.f64 x #s(literal 1/6 binary64)) #s(literal -1 binary64)))))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* eps (+ (* eps (+ (* (cos x) (+ -1/2 (* eps (* eps 1/24)))) (* eps (* 1/6 (sin x))))) (sin (neg x)))) #s(approx (+ (* eps (* eps (+ (* eps (* eps 1/24)) -1/2))) (* eps (* x (+ (* eps (* eps 1/6)) -1)))) (.f64 eps (fma.f64 eps (fma.f64 x (.f64 eps #s(literal 1/6 binary64)) #s(literal -1/2 binary64)) (neg.f64 x))))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* eps (+ (* eps (+ (* (cos x) (+ -1/2 (* eps (* eps 1/24)))) (* eps (* 1/6 (sin x))))) (sin (neg x)))) #s(approx (+ (* eps (* eps (+ (* eps (* eps 1/24)) -1/2))) (* eps (* x (+ (* eps (* eps 1/6)) -1)))) #s(approx (* (* (* eps eps) (* eps eps)) (+ (* x (/ 1/6 eps)) 1/24)) (.f64 (.f64 eps eps) (.f64 eps (fma.f64 eps #s(literal 1/24 binary64) (.f64 x #s(literal 1/6 binary64)))))))))
#s(approx (- (* (cos x) (cos eps)) (+ (* (sin x) (sin eps)) (cos x))) (.f64 eps #s(approx (- ( eps (* -1/2 (cos x))) (sin x)) (fma.f64 x (fma.f64 #s(literal 1/4 binary64) (.f64 eps x) #s(literal -1 binary64)) (.f64 eps #s(literal -1/2 binary64))))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* eps (+ (* eps (+ (* (cos x) (+ -1/2 (* eps (* eps 1/24)))) (* eps (* 1/6 (sin x))))) (sin (neg x)))) (fma.f64 eps #s(approx (* eps (+ (* eps (* eps 1/24)) -1/2)) (.f64 eps #s(literal -1/2 binary64))) (.f64 eps (.f64 x (fma.f64 eps (.f64 eps #s(literal 1/6 binary64)) #s(literal -1 binary64)))))))
#s(approx (- (* (cos x) (cos eps)) (+ (* (sin x) (sin eps)) (cos x))) (.f64 eps #s(approx (- ( eps (* -1/2 (cos x))) (sin x)) (fma.f64 x (fma.f64 x (fma.f64 eps #s(literal 1/4 binary64) (.f64 x #s(literal 1/6 binary64))) #s(literal -1 binary64)) (.f64 eps #s(literal -1/2 binary64))))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* eps (+ (* eps (+ (* (cos x) (+ -1/2 (* eps (* eps 1/24)))) (* eps (* 1/6 (sin x))))) (sin (neg x)))) #s(approx (+ (* eps (* eps (+ (* eps (* eps 1/24)) -1/2))) (* eps (* x (+ (* eps (* eps 1/6)) -1)))) (.f64 (.f64 (.f64 eps eps) (.f64 eps eps)) (fma.f64 x (/.f64 #s(literal 1/6 binary64) eps) #s(literal 1/24 binary64))))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps #s(approx (+ ( eps (+ (* (cos x) (+ -1/2 (* eps (* eps 1/24)))) (* eps (* 1/6 (sin x))))) (sin (neg x))) (fma.f64 eps (fma.f64 eps (.f64 eps #s(literal 1/24 binary64)) #s(literal -1/2 binary64)) (.f64 x (fma.f64 eps (*.f64 eps #s(literal 1/6 binary64)) #s(literal -1 binary64)))))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* eps (+ (* eps (+ (* (cos x) (+ -1/2 (* eps (* eps 1/24)))) (* eps (* 1/6 (sin x))))) (sin (neg x)))) (fma.f64 eps (.f64 eps (fma.f64 eps (.f64 eps #s(literal 1/24 binary64)) #s(literal -1/2 binary64))) (.f64 eps (.f64 x (fma.f64 eps (*.f64 eps #s(literal 1/6 binary64)) #s(literal -1 binary64)))))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* eps (+ (* eps (+ (* (cos x) (+ -1/2 (* eps (* eps 1/24)))) (* eps (* 1/6 (sin x))))) (sin (neg x)))) (fma.f64 (.f64 x (fma.f64 eps (.f64 eps #s(literal 1/6 binary64)) #s(literal -1 binary64))) eps (.f64 eps (.f64 eps (fma.f64 #s(literal 1/24 binary64) (*.f64 eps eps) #s(literal -1/2 binary64)))))))
#s(approx (- (* (cos x) (cos eps)) (+ (* (sin x) (sin eps)) (cos x))) #s(approx (* eps (- (* eps (* -1/2 (cos x))) (sin x))) (fma.f64 x (fma.f64 x (fma.f64 eps (.f64 x #s(literal 1/6 binary64)) (.f64 eps (.f64 eps #s(literal 1/4 binary64)))) (neg.f64 eps)) (.f64 #s(literal -1/2 binary64) (*.f64 eps eps)))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* eps (+ (* eps (+ (* (cos x) (+ -1/2 (* eps (* eps 1/24)))) (* eps (* 1/6 (sin x))))) (sin (neg x)))) #s(approx (+ (* eps (* eps (+ (* eps (* eps 1/24)) -1/2))) (* eps (* x (+ (* eps (* eps 1/6)) -1)))) (.f64 (.f64 (.f64 eps eps) (.f64 eps eps)) (-.f64 #s(literal 1/24 binary64) (/.f64 (fma.f64 x #s(literal -1/6 binary64) (/.f64 #s(literal 1/2 binary64) eps)) eps))))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* eps (+ (* eps (+ (* (cos x) (+ -1/2 (* eps (* eps 1/24)))) (* eps (* 1/6 (sin x))))) (sin (neg x)))) #s(approx (+ (* eps (* eps (+ (* eps (* eps 1/24)) -1/2))) (* eps (* x (+ (* eps (* eps 1/6)) -1)))) #s(approx (* (* (* eps eps) (* eps eps)) (+ (* x (/ 1/6 eps)) 1/24)) (.f64 x (fma.f64 eps (.f64 eps (.f64 eps #s(literal 1/6 binary64))) (/.f64 (.f64 eps (.f64 eps (.f64 #s(literal 1/24 binary64) (*.f64 eps eps)))) x)))))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* eps (+ (* eps (+ (* (cos x) (+ -1/2 (* eps (* eps 1/24)))) (* eps (* 1/6 (sin x))))) (sin (neg x)))) #s(approx (+ (* eps (* eps (+ (* eps (* eps 1/24)) -1/2))) (* eps (* x (+ (* eps (* eps 1/6)) -1)))) (.f64 x (fma.f64 eps (fma.f64 eps (.f64 eps #s(literal 1/6 binary64)) #s(literal -1 binary64)) (.f64 (.f64 eps eps) (/.f64 (fma.f64 #s(literal 1/24 binary64) (*.f64 eps eps) #s(literal -1/2 binary64)) x)))))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* eps (+ (* eps (+ (* (cos x) (+ -1/2 (* eps (* eps 1/24)))) (* eps (* 1/6 (sin x))))) (sin (neg x)))) #s(approx (+ (* eps (* eps (+ (* eps (* eps 1/24)) -1/2))) (* eps (* x (+ (* eps (* eps 1/6)) -1)))) (.f64 (.f64 (.f64 eps eps) (.f64 eps eps)) (+.f64 #s(literal 1/24 binary64) (fma.f64 x (/.f64 #s(literal 1/6 binary64) eps) (/.f64 #s(literal -1/2 binary64) (*.f64 eps eps))))))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps #s(approx (+ ( eps (+ (* (cos x) (+ -1/2 (* eps (* eps 1/24)))) (* eps (* 1/6 (sin x))))) (sin (neg x))) #s(approx (+ (* x (+ (* x (+ (* eps (* (+ (* eps (* eps 1/24)) -1/2) -1/2)) (* x (+ (* (* eps eps) -1/36) 1/6)))) (+ (* eps (* eps 1/6)) -1))) (* eps (+ (* eps (* eps 1/24)) -1/2))) (.f64 (.f64 eps eps) (.f64 eps (fma.f64 x (/.f64 (fma.f64 #s(literal -1/36 binary64) (.f64 x x) #s(literal 1/6 binary64)) eps) (fma.f64 x (*.f64 x #s(literal -1/48 binary64)) #s(literal 1/24 binary64)))))))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps #s(approx (+ ( eps (+ (* (cos x) (+ -1/2 (* eps (* eps 1/24)))) (* eps (* 1/6 (sin x))))) (sin (neg x))) #s(approx (+ (* x (+ (* x (+ (* eps (* (+ (* eps (* eps 1/24)) -1/2) -1/2)) (* x (+ (* (* eps eps) -1/36) 1/6)))) (+ (* eps (* eps 1/6)) -1))) (* eps (+ (* eps (* eps 1/24)) -1/2))) (fma.f64 eps (fma.f64 eps (.f64 x (fma.f64 #s(literal -1/36 binary64) (.f64 x x) #s(literal 1/6 binary64))) (fma.f64 #s(literal 1/4 binary64) (.f64 x x) #s(literal -1/2 binary64))) (.f64 x (fma.f64 x (*.f64 x #s(literal 1/6 binary64)) #s(literal -1 binary64))))))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps #s(approx (+ ( eps (+ (* (cos x) (+ -1/2 (* eps (* eps 1/24)))) (* eps (* 1/6 (sin x))))) (sin (neg x))) #s(approx (+ (* x (+ (* x (+ (* eps (* (+ (* eps (* eps 1/24)) -1/2) -1/2)) (* x (+ (* (* eps eps) -1/36) 1/6)))) (+ (* eps (* eps 1/6)) -1))) (* eps (+ (* eps (* eps 1/24)) -1/2))) (neg.f64 (.f64 (.f64 eps (.f64 eps eps)) (-.f64 (fma.f64 x (.f64 x #s(literal 1/48 binary64)) #s(literal -1/24 binary64)) (.f64 x (/.f64 (fma.f64 #s(literal -1/36 binary64) (.f64 x x) #s(literal 1/6 binary64)) eps)))))))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* eps (+ (* eps (+ (* (cos x) (+ -1/2 (* eps (* eps 1/24)))) (* eps (* 1/6 (sin x))))) (sin (neg x)))) #s(approx (+ (* eps (* eps (+ (* eps (* eps 1/24)) -1/2))) (* eps (* x (+ (* eps (* eps 1/6)) -1)))) (.f64 (.f64 (.f64 eps eps) (.f64 eps eps)) (-.f64 #s(literal 1/24 binary64) (/.f64 (fma.f64 x #s(literal -1/6 binary64) (/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 x eps)) eps)) eps))))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps #s(approx (+ ( eps (+ (* (cos x) (+ -1/2 (* eps (* eps 1/24)))) (* eps (* 1/6 (sin x))))) (sin (neg x))) (fma.f64 eps (fma.f64 eps (.f64 eps #s(literal 1/24 binary64)) #s(literal -1/2 binary64)) (.f64 x (fma.f64 eps (.f64 eps #s(literal 1/6 binary64)) (fma.f64 (.f64 x (fma.f64 eps (.f64 eps #s(literal 1/24 binary64)) #s(literal -1/2 binary64))) (.f64 eps #s(literal -1/2 binary64)) #s(literal -1 binary64))))))))
#s(approx (- (* (cos x) (cos eps)) (+ (* (sin x) (sin eps)) (cos x))) (.f64 eps #s(approx (- ( eps (+ (* eps (* (sin x) 1/6)) (* (cos x) (+ (* eps (* eps 1/24)) -1/2)))) (sin x)) (fma.f64 x (fma.f64 eps (.f64 (.f64 x (fma.f64 eps (.f64 eps #s(literal 1/24 binary64)) #s(literal -1/2 binary64))) #s(literal -1/2 binary64)) (fma.f64 eps (.f64 eps #s(literal 1/6 binary64)) #s(literal -1 binary64))) (.f64 eps (fma.f64 eps (.f64 eps #s(literal 1/24 binary64)) #s(literal -1/2 binary64)))))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps #s(approx (+ ( eps (+ (* (cos x) (+ -1/2 (* eps (* eps 1/24)))) (* eps (* 1/6 (sin x))))) (sin (neg x))) (fma.f64 x (fma.f64 x (fma.f64 eps #s(approx (* (+ (* eps (* eps 1/24)) -1/2) -1/2) #s(literal 1/4 binary64)) (.f64 x (fma.f64 (.f64 eps eps) #s(literal -1/36 binary64) #s(literal 1/6 binary64)))) (fma.f64 eps (.f64 eps #s(literal 1/6 binary64)) #s(literal -1 binary64))) (.f64 eps (fma.f64 eps (*.f64 eps #s(literal 1/24 binary64)) #s(literal -1/2 binary64)))))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps #s(approx (+ ( eps (+ (* (cos x) (+ -1/2 (* eps (* eps 1/24)))) (* eps (* 1/6 (sin x))))) (sin (neg x))) (fma.f64 x (fma.f64 x (fma.f64 eps #s(approx (* (+ (* eps (* eps 1/24)) -1/2) -1/2) (.f64 #s(literal -1/48 binary64) (.f64 eps eps))) (.f64 x (fma.f64 (.f64 eps eps) #s(literal -1/36 binary64) #s(literal 1/6 binary64)))) (fma.f64 eps (.f64 eps #s(literal 1/6 binary64)) #s(literal -1 binary64))) (.f64 eps (fma.f64 eps (*.f64 eps #s(literal 1/24 binary64)) #s(literal -1/2 binary64)))))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* eps (+ (* eps (+ (* (cos x) (+ -1/2 (* eps (* eps 1/24)))) (* eps (* 1/6 (sin x))))) (sin (neg x)))) #s(approx (+ (* eps (* eps (+ (* eps (* eps 1/24)) -1/2))) (* eps (* x (+ (* eps (* eps 1/6)) -1)))) (.f64 (.f64 (.f64 eps eps) (.f64 eps eps)) (+.f64 (fma.f64 x (/.f64 #s(literal 1/6 binary64) eps) (-.f64 #s(literal 1/24 binary64) (/.f64 x (.f64 eps (.f64 eps eps))))) (/.f64 #s(literal -1/2 binary64) (*.f64 eps eps)))))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps #s(approx (+ ( eps (+ (* (cos x) (+ -1/2 (* eps (* eps 1/24)))) (* eps (* 1/6 (sin x))))) (sin (neg x))) (fma.f64 x (fma.f64 x (fma.f64 eps (.f64 (fma.f64 eps (.f64 eps #s(literal 1/24 binary64)) #s(literal -1/2 binary64)) #s(literal -1/2 binary64)) (.f64 x (fma.f64 (.f64 eps eps) #s(literal -1/36 binary64) #s(literal 1/6 binary64)))) (fma.f64 eps (.f64 eps #s(literal 1/6 binary64)) #s(literal -1 binary64))) (.f64 eps (fma.f64 eps (*.f64 eps #s(literal 1/24 binary64)) #s(literal -1/2 binary64)))))))
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#s(approx (- (cos (+ x eps)) (cos x)) (+.f64 (cos.f64 eps) #s(literal -1 binary64)))
(-.f64 #s(approx (cos (+ x eps)) (cos.f64 x)) #s(approx (cos x) #s(literal 1 binary64)))
(-.f64 (cos.f64 (+.f64 x eps)) #s(approx (cos x) #s(literal 1 binary64)))
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#s(approx (- (* (cos x) (cos eps)) (+ (* (sin x) (sin eps)) (cos x))) (*.f64 eps (sin.f64 (neg.f64 x))))
#s(approx (- (* (cos x) (cos eps)) (+ (* (sin x) (sin eps)) (cos x))) (.f64 eps (-.f64 #s(approx ( eps (* -1/2 (cos x))) (*.f64 eps #s(literal -1/2 binary64))) (sin.f64 x))))
(-.f64 (cos.f64 (+.f64 x eps)) #s(approx (cos x) (fma.f64 x (*.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64))))
#s(approx (- (* (cos x) (cos eps)) (+ (* (sin x) (sin eps)) (cos x))) (.f64 eps (-.f64 #s(approx ( eps (* -1/2 (cos x))) (.f64 eps (fma.f64 #s(literal 1/4 binary64) (.f64 x x) #s(literal -1/2 binary64)))) (sin.f64 x))))
#s(approx (- (* (cos x) (cos eps)) (+ (* (sin x) (sin eps)) (cos x))) (.f64 eps (-.f64 #s(approx ( eps (+ (* eps (* (sin x) 1/6)) (* (cos x) (+ (* eps (* eps 1/24)) -1/2)))) (.f64 eps (fma.f64 eps (.f64 eps #s(literal 1/24 binary64)) #s(literal -1/2 binary64)))) (sin.f64 x))))
#s(approx (- (* (cos x) (cos eps)) (+ (* (sin x) (sin eps)) (cos x))) (.f64 eps (-.f64 #s(approx ( eps (+ (* eps (* (sin x) 1/6)) (* (cos x) (+ (* eps (* eps 1/24)) -1/2)))) (fma.f64 x (.f64 eps (.f64 eps #s(literal 1/6 binary64))) (.f64 eps (fma.f64 eps (.f64 eps #s(literal 1/24 binary64)) #s(literal -1/2 binary64))))) (sin.f64 x))))
#s(approx (- (* (cos x) (cos eps)) (+ (* (sin x) (sin eps)) (cos x))) (.f64 eps (-.f64 #s(approx ( eps (+ (* eps (* (sin x) 1/6)) (* (cos x) (+ (* eps (* eps 1/24)) -1/2)))) (fma.f64 x (fma.f64 eps (.f64 eps #s(literal 1/6 binary64)) (.f64 eps (.f64 (.f64 x (fma.f64 eps (.f64 eps #s(literal 1/24 binary64)) #s(literal -1/2 binary64))) #s(literal -1/2 binary64)))) (.f64 eps (fma.f64 eps (*.f64 eps #s(literal 1/24 binary64)) #s(literal -1/2 binary64))))) (sin.f64 x))))
(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps (-.f64 (.f64 eps (*.f64 #s(literal -1/2 binary64) (cos.f64 x))) (sin.f64 x))))
#s(approx (- (* (cos x) (cos eps)) (+ (* (sin x) (sin eps)) (cos x))) (.f64 eps (-.f64 (.f64 eps (*.f64 #s(literal -1/2 binary64) (cos.f64 x))) (sin.f64 x))))
(.f64 #s(approx ( (sin (* (+ eps 0) 1/2)) (sin (* (+ x (+ x eps)) 1/2))) (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x)))) #s(literal -2 binary64))
(.f64 #s(approx ( (sin (* (+ eps 0) 1/2)) (+ (* (sin (* (+ x x) 1/2)) (cos (* eps 1/2))) (* (cos (* (+ x x) 1/2)) (sin (* eps 1/2))))) (.f64 (sin.f64 (fma.f64 eps #s(literal 1/2 binary64) x)) (sin.f64 (.f64 eps #s(literal 1/2 binary64))))) #s(literal -2 binary64))
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))))
(.f64 (.f64 (sin.f64 (.f64 (+.f64 eps #s(literal 0 binary64)) #s(literal 1/2 binary64))) (sin.f64 (.f64 (+.f64 x (+.f64 x eps)) #s(literal 1/2 binary64)))) #s(literal -2 binary64))
#s(approx (- (* (cos x) (cos eps)) (+ (* (sin x) (sin eps)) (cos x))) (.f64 eps (-.f64 (.f64 eps (fma.f64 eps (.f64 (sin.f64 x) #s(literal 1/6 binary64)) (.f64 (cos.f64 x) (fma.f64 eps (*.f64 eps #s(literal 1/24 binary64)) #s(literal -1/2 binary64))))) (sin.f64 x))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps (fma.f64 eps (fma.f64 (cos.f64 x) (+.f64 #s(literal -1/2 binary64) (.f64 eps (.f64 eps #s(literal 1/24 binary64)))) (.f64 eps (*.f64 #s(literal 1/6 binary64) (sin.f64 x)))) (sin.f64 (neg.f64 x)))))
(fma.f64 (*.f64 (cos.f64 (-.f64 x eps)) (cos.f64 (+.f64 x eps))) (/.f64 #s(literal 1 binary64) (cos.f64 (-.f64 x eps))) (neg.f64 (cos.f64 x)))
(-.f64 (.f64 (cos.f64 x) #s(approx (cos eps) (fma.f64 (.f64 eps eps) (fma.f64 (.f64 eps eps) (fma.f64 (.f64 eps eps) #s(literal -1/720 binary64) #s(literal 1/24 binary64)) #s(literal -1/2 binary64)) #s(literal 1 binary64)))) (fma.f64 (sin.f64 x) (sin.f64 eps) (cos.f64 x)))

Outputs

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

Calls

3 calls:

16.0ms	(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))
16.0ms	x
16.0ms	eps

Results

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

Compiler

Compiled 15 to 10 computations (33.3% saved)

regimes42.0ms (0.2%)

Memory

20.5MiB live, 20.5MiB allocated

Counts

53 → 1

Calls

Call 1

Inputs
#s(approx (- (cos (+ x eps)) (cos x)) (+.f64 #s(approx (cos eps) #s(literal 1 binary64)) #s(literal -1 binary64)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* eps (+ (* eps (+ (* (cos x) (+ -1/2 (* eps (* eps 1/24)))) (* eps (* 1/6 (sin x))))) (sin (neg x)))) #s(approx (+ (* eps (* eps (+ (* eps (* eps 1/24)) -1/2))) (* eps (* x (+ (* eps (* eps 1/6)) -1)))) (*.f64 x (neg.f64 eps)))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (+ (cos eps) -1) (.f64 eps (.f64 eps #s(literal -1/2 binary64)))))
#s(approx (- (* (cos x) (cos eps)) (+ (* (sin x) (sin eps)) (cos x))) (.f64 eps #s(approx (- ( eps (* -1/2 (cos x))) (sin x)) (*.f64 eps #s(literal -1/2 binary64)))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* eps (+ (* eps (+ (* (cos x) (+ -1/2 (* eps (* eps 1/24)))) (* eps (* 1/6 (sin x))))) (sin (neg x)))) #s(approx (+ (* eps (* eps (+ (* eps (* eps 1/24)) -1/2))) (* eps (* x (+ (* eps (* eps 1/6)) -1)))) (.f64 eps (-.f64 (.f64 eps #s(literal -1/2 binary64)) x)))))
#s(approx (- (* (cos x) (cos eps)) (+ (* (sin x) (sin eps)) (cos x))) (.f64 eps #s(approx (- ( eps (* -1/2 (cos x))) (sin x)) (-.f64 (*.f64 eps #s(literal -1/2 binary64)) x))))
#s(approx (- (cos (+ x eps)) (cos x)) (+.f64 #s(approx (cos eps) (fma.f64 eps (*.f64 eps #s(literal -1/2 binary64)) #s(literal 1 binary64))) #s(literal -1 binary64)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* eps (+ (* eps (+ (* (cos x) (+ -1/2 (* eps (* eps 1/24)))) (* eps (* 1/6 (sin x))))) (sin (neg x)))) #s(approx (+ (* eps (* eps (+ (* eps (* eps 1/24)) -1/2))) (* eps (* x (+ (* eps (* eps 1/6)) -1)))) #s(approx (* (* (* eps eps) (* eps eps)) (+ (* x (/ 1/6 eps)) 1/24)) (.f64 x (.f64 eps (.f64 eps (.f64 eps #s(literal 1/6 binary64)))))))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* eps (+ (* eps (+ (* (cos x) (+ -1/2 (* eps (* eps 1/24)))) (* eps (* 1/6 (sin x))))) (sin (neg x)))) #s(approx (+ (* eps (* eps (+ (* eps (* eps 1/24)) -1/2))) (* eps (* x (+ (* eps (* eps 1/6)) -1)))) (.f64 #s(literal 1/24 binary64) (.f64 (.f64 eps eps) (.f64 eps eps))))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps #s(approx (+ ( eps (+ (* (cos x) (+ -1/2 (* eps (* eps 1/24)))) (* eps (* 1/6 (sin x))))) (sin (neg x))) #s(approx (+ (* x (+ (* x (+ (* eps (* (+ (* eps (* eps 1/24)) -1/2) -1/2)) (* x (+ (* (* eps eps) -1/36) 1/6)))) (+ (* eps (* eps 1/6)) -1))) (* eps (+ (* eps (* eps 1/24)) -1/2))) (.f64 x (fma.f64 x (.f64 x #s(literal 1/6 binary64)) #s(literal -1 binary64)))))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* eps (+ (* eps (+ (* (cos x) (+ -1/2 (* eps (* eps 1/24)))) (* eps (* 1/6 (sin x))))) (sin (neg x)))) #s(approx (+ (* eps (* eps (+ (* eps (* eps 1/24)) -1/2))) (* eps (* x (+ (* eps (* eps 1/6)) -1)))) (.f64 eps (fma.f64 eps (fma.f64 x (.f64 eps #s(literal 1/6 binary64)) #s(literal -1/2 binary64)) (neg.f64 x))))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* eps (+ (* eps (+ (* (cos x) (+ -1/2 (* eps (* eps 1/24)))) (* eps (* 1/6 (sin x))))) (sin (neg x)))) #s(approx (+ (* eps (* eps (+ (* eps (* eps 1/24)) -1/2))) (* eps (* x (+ (* eps (* eps 1/6)) -1)))) #s(approx (* (* (* eps eps) (* eps eps)) (+ (* x (/ 1/6 eps)) 1/24)) (.f64 (.f64 eps eps) (.f64 eps (fma.f64 eps #s(literal 1/24 binary64) (.f64 x #s(literal 1/6 binary64)))))))))
#s(approx (- (* (cos x) (cos eps)) (+ (* (sin x) (sin eps)) (cos x))) (.f64 eps #s(approx (- ( eps (* -1/2 (cos x))) (sin x)) (fma.f64 x (fma.f64 #s(literal 1/4 binary64) (.f64 eps x) #s(literal -1 binary64)) (.f64 eps #s(literal -1/2 binary64))))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* eps (+ (* eps (+ (* (cos x) (+ -1/2 (* eps (* eps 1/24)))) (* eps (* 1/6 (sin x))))) (sin (neg x)))) (fma.f64 eps #s(approx (* eps (+ (* eps (* eps 1/24)) -1/2)) (.f64 eps #s(literal -1/2 binary64))) (.f64 eps (.f64 x (fma.f64 eps (.f64 eps #s(literal 1/6 binary64)) #s(literal -1 binary64)))))))
#s(approx (- (* (cos x) (cos eps)) (+ (* (sin x) (sin eps)) (cos x))) (.f64 eps #s(approx (- ( eps (* -1/2 (cos x))) (sin x)) (fma.f64 x (fma.f64 x (fma.f64 eps #s(literal 1/4 binary64) (.f64 x #s(literal 1/6 binary64))) #s(literal -1 binary64)) (.f64 eps #s(literal -1/2 binary64))))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* eps (+ (* eps (+ (* (cos x) (+ -1/2 (* eps (* eps 1/24)))) (* eps (* 1/6 (sin x))))) (sin (neg x)))) #s(approx (+ (* eps (* eps (+ (* eps (* eps 1/24)) -1/2))) (* eps (* x (+ (* eps (* eps 1/6)) -1)))) (.f64 (.f64 (.f64 eps eps) (.f64 eps eps)) (fma.f64 x (/.f64 #s(literal 1/6 binary64) eps) #s(literal 1/24 binary64))))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps #s(approx (+ ( eps (+ (* (cos x) (+ -1/2 (* eps (* eps 1/24)))) (* eps (* 1/6 (sin x))))) (sin (neg x))) (fma.f64 eps (fma.f64 eps (.f64 eps #s(literal 1/24 binary64)) #s(literal -1/2 binary64)) (.f64 x (fma.f64 eps (*.f64 eps #s(literal 1/6 binary64)) #s(literal -1 binary64)))))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* eps (+ (* eps (+ (* (cos x) (+ -1/2 (* eps (* eps 1/24)))) (* eps (* 1/6 (sin x))))) (sin (neg x)))) (fma.f64 eps (.f64 eps (fma.f64 eps (.f64 eps #s(literal 1/24 binary64)) #s(literal -1/2 binary64))) (.f64 eps (.f64 x (fma.f64 eps (*.f64 eps #s(literal 1/6 binary64)) #s(literal -1 binary64)))))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* eps (+ (* eps (+ (* (cos x) (+ -1/2 (* eps (* eps 1/24)))) (* eps (* 1/6 (sin x))))) (sin (neg x)))) (fma.f64 (.f64 x (fma.f64 eps (.f64 eps #s(literal 1/6 binary64)) #s(literal -1 binary64))) eps (.f64 eps (.f64 eps (fma.f64 #s(literal 1/24 binary64) (*.f64 eps eps) #s(literal -1/2 binary64)))))))
#s(approx (- (* (cos x) (cos eps)) (+ (* (sin x) (sin eps)) (cos x))) #s(approx (* eps (- (* eps (* -1/2 (cos x))) (sin x))) (fma.f64 x (fma.f64 x (fma.f64 eps (.f64 x #s(literal 1/6 binary64)) (.f64 eps (.f64 eps #s(literal 1/4 binary64)))) (neg.f64 eps)) (.f64 #s(literal -1/2 binary64) (*.f64 eps eps)))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* eps (+ (* eps (+ (* (cos x) (+ -1/2 (* eps (* eps 1/24)))) (* eps (* 1/6 (sin x))))) (sin (neg x)))) #s(approx (+ (* eps (* eps (+ (* eps (* eps 1/24)) -1/2))) (* eps (* x (+ (* eps (* eps 1/6)) -1)))) (.f64 (.f64 (.f64 eps eps) (.f64 eps eps)) (-.f64 #s(literal 1/24 binary64) (/.f64 (fma.f64 x #s(literal -1/6 binary64) (/.f64 #s(literal 1/2 binary64) eps)) eps))))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* eps (+ (* eps (+ (* (cos x) (+ -1/2 (* eps (* eps 1/24)))) (* eps (* 1/6 (sin x))))) (sin (neg x)))) #s(approx (+ (* eps (* eps (+ (* eps (* eps 1/24)) -1/2))) (* eps (* x (+ (* eps (* eps 1/6)) -1)))) #s(approx (* (* (* eps eps) (* eps eps)) (+ (* x (/ 1/6 eps)) 1/24)) (.f64 x (fma.f64 eps (.f64 eps (.f64 eps #s(literal 1/6 binary64))) (/.f64 (.f64 eps (.f64 eps (.f64 #s(literal 1/24 binary64) (*.f64 eps eps)))) x)))))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* eps (+ (* eps (+ (* (cos x) (+ -1/2 (* eps (* eps 1/24)))) (* eps (* 1/6 (sin x))))) (sin (neg x)))) #s(approx (+ (* eps (* eps (+ (* eps (* eps 1/24)) -1/2))) (* eps (* x (+ (* eps (* eps 1/6)) -1)))) (.f64 x (fma.f64 eps (fma.f64 eps (.f64 eps #s(literal 1/6 binary64)) #s(literal -1 binary64)) (.f64 (.f64 eps eps) (/.f64 (fma.f64 #s(literal 1/24 binary64) (*.f64 eps eps) #s(literal -1/2 binary64)) x)))))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* eps (+ (* eps (+ (* (cos x) (+ -1/2 (* eps (* eps 1/24)))) (* eps (* 1/6 (sin x))))) (sin (neg x)))) #s(approx (+ (* eps (* eps (+ (* eps (* eps 1/24)) -1/2))) (* eps (* x (+ (* eps (* eps 1/6)) -1)))) (.f64 (.f64 (.f64 eps eps) (.f64 eps eps)) (+.f64 #s(literal 1/24 binary64) (fma.f64 x (/.f64 #s(literal 1/6 binary64) eps) (/.f64 #s(literal -1/2 binary64) (*.f64 eps eps))))))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps #s(approx (+ ( eps (+ (* (cos x) (+ -1/2 (* eps (* eps 1/24)))) (* eps (* 1/6 (sin x))))) (sin (neg x))) #s(approx (+ (* x (+ (* x (+ (* eps (* (+ (* eps (* eps 1/24)) -1/2) -1/2)) (* x (+ (* (* eps eps) -1/36) 1/6)))) (+ (* eps (* eps 1/6)) -1))) (* eps (+ (* eps (* eps 1/24)) -1/2))) (.f64 (.f64 eps eps) (.f64 eps (fma.f64 x (/.f64 (fma.f64 #s(literal -1/36 binary64) (.f64 x x) #s(literal 1/6 binary64)) eps) (fma.f64 x (*.f64 x #s(literal -1/48 binary64)) #s(literal 1/24 binary64)))))))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps #s(approx (+ ( eps (+ (* (cos x) (+ -1/2 (* eps (* eps 1/24)))) (* eps (* 1/6 (sin x))))) (sin (neg x))) #s(approx (+ (* x (+ (* x (+ (* eps (* (+ (* eps (* eps 1/24)) -1/2) -1/2)) (* x (+ (* (* eps eps) -1/36) 1/6)))) (+ (* eps (* eps 1/6)) -1))) (* eps (+ (* eps (* eps 1/24)) -1/2))) (fma.f64 eps (fma.f64 eps (.f64 x (fma.f64 #s(literal -1/36 binary64) (.f64 x x) #s(literal 1/6 binary64))) (fma.f64 #s(literal 1/4 binary64) (.f64 x x) #s(literal -1/2 binary64))) (.f64 x (fma.f64 x (*.f64 x #s(literal 1/6 binary64)) #s(literal -1 binary64))))))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps #s(approx (+ ( eps (+ (* (cos x) (+ -1/2 (* eps (* eps 1/24)))) (* eps (* 1/6 (sin x))))) (sin (neg x))) #s(approx (+ (* x (+ (* x (+ (* eps (* (+ (* eps (* eps 1/24)) -1/2) -1/2)) (* x (+ (* (* eps eps) -1/36) 1/6)))) (+ (* eps (* eps 1/6)) -1))) (* eps (+ (* eps (* eps 1/24)) -1/2))) (neg.f64 (.f64 (.f64 eps (.f64 eps eps)) (-.f64 (fma.f64 x (.f64 x #s(literal 1/48 binary64)) #s(literal -1/24 binary64)) (.f64 x (/.f64 (fma.f64 #s(literal -1/36 binary64) (.f64 x x) #s(literal 1/6 binary64)) eps)))))))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* eps (+ (* eps (+ (* (cos x) (+ -1/2 (* eps (* eps 1/24)))) (* eps (* 1/6 (sin x))))) (sin (neg x)))) #s(approx (+ (* eps (* eps (+ (* eps (* eps 1/24)) -1/2))) (* eps (* x (+ (* eps (* eps 1/6)) -1)))) (.f64 (.f64 (.f64 eps eps) (.f64 eps eps)) (-.f64 #s(literal 1/24 binary64) (/.f64 (fma.f64 x #s(literal -1/6 binary64) (/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 x eps)) eps)) eps))))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps #s(approx (+ ( eps (+ (* (cos x) (+ -1/2 (* eps (* eps 1/24)))) (* eps (* 1/6 (sin x))))) (sin (neg x))) (fma.f64 eps (fma.f64 eps (.f64 eps #s(literal 1/24 binary64)) #s(literal -1/2 binary64)) (.f64 x (fma.f64 eps (.f64 eps #s(literal 1/6 binary64)) (fma.f64 (.f64 x (fma.f64 eps (.f64 eps #s(literal 1/24 binary64)) #s(literal -1/2 binary64))) (.f64 eps #s(literal -1/2 binary64)) #s(literal -1 binary64))))))))
#s(approx (- (* (cos x) (cos eps)) (+ (* (sin x) (sin eps)) (cos x))) (.f64 eps #s(approx (- ( eps (+ (* eps (* (sin x) 1/6)) (* (cos x) (+ (* eps (* eps 1/24)) -1/2)))) (sin x)) (fma.f64 x (fma.f64 eps (.f64 (.f64 x (fma.f64 eps (.f64 eps #s(literal 1/24 binary64)) #s(literal -1/2 binary64))) #s(literal -1/2 binary64)) (fma.f64 eps (.f64 eps #s(literal 1/6 binary64)) #s(literal -1 binary64))) (.f64 eps (fma.f64 eps (.f64 eps #s(literal 1/24 binary64)) #s(literal -1/2 binary64)))))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps #s(approx (+ ( eps (+ (* (cos x) (+ -1/2 (* eps (* eps 1/24)))) (* eps (* 1/6 (sin x))))) (sin (neg x))) (fma.f64 x (fma.f64 x (fma.f64 eps #s(approx (* (+ (* eps (* eps 1/24)) -1/2) -1/2) #s(literal 1/4 binary64)) (.f64 x (fma.f64 (.f64 eps eps) #s(literal -1/36 binary64) #s(literal 1/6 binary64)))) (fma.f64 eps (.f64 eps #s(literal 1/6 binary64)) #s(literal -1 binary64))) (.f64 eps (fma.f64 eps (*.f64 eps #s(literal 1/24 binary64)) #s(literal -1/2 binary64)))))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps #s(approx (+ ( eps (+ (* (cos x) (+ -1/2 (* eps (* eps 1/24)))) (* eps (* 1/6 (sin x))))) (sin (neg x))) (fma.f64 x (fma.f64 x (fma.f64 eps #s(approx (* (+ (* eps (* eps 1/24)) -1/2) -1/2) (.f64 #s(literal -1/48 binary64) (.f64 eps eps))) (.f64 x (fma.f64 (.f64 eps eps) #s(literal -1/36 binary64) #s(literal 1/6 binary64)))) (fma.f64 eps (.f64 eps #s(literal 1/6 binary64)) #s(literal -1 binary64))) (.f64 eps (fma.f64 eps (*.f64 eps #s(literal 1/24 binary64)) #s(literal -1/2 binary64)))))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* eps (+ (* eps (+ (* (cos x) (+ -1/2 (* eps (* eps 1/24)))) (* eps (* 1/6 (sin x))))) (sin (neg x)))) #s(approx (+ (* eps (* eps (+ (* eps (* eps 1/24)) -1/2))) (* eps (* x (+ (* eps (* eps 1/6)) -1)))) (.f64 (.f64 (.f64 eps eps) (.f64 eps eps)) (+.f64 (fma.f64 x (/.f64 #s(literal 1/6 binary64) eps) (-.f64 #s(literal 1/24 binary64) (/.f64 x (.f64 eps (.f64 eps eps))))) (/.f64 #s(literal -1/2 binary64) (*.f64 eps eps)))))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps #s(approx (+ ( eps (+ (* (cos x) (+ -1/2 (* eps (* eps 1/24)))) (* eps (* 1/6 (sin x))))) (sin (neg x))) (fma.f64 x (fma.f64 x (fma.f64 eps (.f64 (fma.f64 eps (.f64 eps #s(literal 1/24 binary64)) #s(literal -1/2 binary64)) #s(literal -1/2 binary64)) (.f64 x (fma.f64 (.f64 eps eps) #s(literal -1/36 binary64) #s(literal 1/6 binary64)))) (fma.f64 eps (.f64 eps #s(literal 1/6 binary64)) #s(literal -1 binary64))) (.f64 eps (fma.f64 eps (*.f64 eps #s(literal 1/24 binary64)) #s(literal -1/2 binary64)))))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps #s(approx (+ ( eps (+ (* (cos x) (+ -1/2 (* eps (* eps 1/24)))) (* eps (* 1/6 (sin x))))) (sin (neg x))) #s(approx (+ (* x (+ (* x (+ (* eps (* (+ (* eps (* eps 1/24)) -1/2) -1/2)) (* x (+ (* (* eps eps) -1/36) 1/6)))) (+ (* eps (* eps 1/6)) -1))) (* eps (+ (* eps (* eps 1/24)) -1/2))) (neg.f64 (.f64 (.f64 eps (.f64 eps eps)) (-.f64 (fma.f64 x (.f64 x #s(literal 1/48 binary64)) #s(literal -1/24 binary64)) (/.f64 (-.f64 (.f64 x (fma.f64 #s(literal -1/36 binary64) (.f64 x x) #s(literal 1/6 binary64))) (/.f64 (fma.f64 (*.f64 x x) #s(literal -1/4 binary64) #s(literal 1/2 binary64)) eps)) eps))))))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* eps (+ (* eps (+ (* (cos x) (+ -1/2 (* eps (* eps 1/24)))) (* eps (* 1/6 (sin x))))) (sin (neg x)))) (fma.f64 x (fma.f64 x (fma.f64 eps (.f64 x (fma.f64 (.f64 eps eps) #s(literal -1/36 binary64) #s(literal 1/6 binary64))) (.f64 #s(literal -1/2 binary64) (.f64 eps (.f64 eps (fma.f64 eps (.f64 eps #s(literal 1/24 binary64)) #s(literal -1/2 binary64)))))) (.f64 eps (fma.f64 eps (.f64 eps #s(literal 1/6 binary64)) #s(literal -1 binary64)))) (.f64 eps (.f64 eps (fma.f64 eps (*.f64 eps #s(literal 1/24 binary64)) #s(literal -1/2 binary64)))))))
#s(approx (- (* (cos x) (cos eps)) (+ (* (sin x) (sin eps)) (cos x))) #s(approx (* eps (- (* eps (+ (* eps (* (sin x) 1/6)) (* (cos x) (+ (* eps (* eps 1/24)) -1/2)))) (sin x))) (fma.f64 x (fma.f64 x (fma.f64 x (.f64 eps (fma.f64 (.f64 eps eps) #s(literal -1/36 binary64) #s(literal 1/6 binary64))) (.f64 #s(literal -1/2 binary64) (.f64 (.f64 eps eps) (fma.f64 eps (.f64 eps #s(literal 1/24 binary64)) #s(literal -1/2 binary64))))) (.f64 eps (fma.f64 eps (.f64 eps #s(literal 1/6 binary64)) #s(literal -1 binary64)))) (.f64 (.f64 eps eps) (fma.f64 eps (*.f64 eps #s(literal 1/24 binary64)) #s(literal -1/2 binary64))))))
#s(approx (- (cos (+ x eps)) (cos x)) (+.f64 (cos.f64 eps) #s(literal -1 binary64)))
(-.f64 #s(approx (cos (+ x eps)) (cos.f64 x)) #s(approx (cos x) #s(literal 1 binary64)))
(-.f64 (cos.f64 (+.f64 x eps)) #s(approx (cos x) #s(literal 1 binary64)))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (sin.f64 x) (neg.f64 eps)))
#s(approx (- (* (cos x) (cos eps)) (+ (* (sin x) (sin eps)) (cos x))) (neg.f64 (*.f64 eps (sin.f64 x))))
#s(approx (- (* (cos x) (cos eps)) (+ (* (sin x) (sin eps)) (cos x))) (.f64 eps #s(approx (- ( eps (+ (* eps (* (sin x) 1/6)) (* (cos x) (+ (* eps (* eps 1/24)) -1/2)))) (sin x)) (sin.f64 (neg.f64 x)))))
#s(approx (- (* (cos x) (cos eps)) (+ (* (sin x) (sin eps)) (cos x))) (*.f64 eps (sin.f64 (neg.f64 x))))
#s(approx (- (* (cos x) (cos eps)) (+ (* (sin x) (sin eps)) (cos x))) (.f64 eps (-.f64 #s(approx ( eps (* -1/2 (cos x))) (*.f64 eps #s(literal -1/2 binary64))) (sin.f64 x))))
(-.f64 (cos.f64 (+.f64 x eps)) #s(approx (cos x) (fma.f64 x (*.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64))))
#s(approx (- (* (cos x) (cos eps)) (+ (* (sin x) (sin eps)) (cos x))) (.f64 eps (-.f64 #s(approx ( eps (* -1/2 (cos x))) (.f64 eps (fma.f64 #s(literal 1/4 binary64) (.f64 x x) #s(literal -1/2 binary64)))) (sin.f64 x))))
#s(approx (- (* (cos x) (cos eps)) (+ (* (sin x) (sin eps)) (cos x))) (.f64 eps (-.f64 #s(approx ( eps (+ (* eps (* (sin x) 1/6)) (* (cos x) (+ (* eps (* eps 1/24)) -1/2)))) (.f64 eps (fma.f64 eps (.f64 eps #s(literal 1/24 binary64)) #s(literal -1/2 binary64)))) (sin.f64 x))))
#s(approx (- (* (cos x) (cos eps)) (+ (* (sin x) (sin eps)) (cos x))) (.f64 eps (-.f64 #s(approx ( eps (+ (* eps (* (sin x) 1/6)) (* (cos x) (+ (* eps (* eps 1/24)) -1/2)))) (fma.f64 x (.f64 eps (.f64 eps #s(literal 1/6 binary64))) (.f64 eps (fma.f64 eps (.f64 eps #s(literal 1/24 binary64)) #s(literal -1/2 binary64))))) (sin.f64 x))))
#s(approx (- (* (cos x) (cos eps)) (+ (* (sin x) (sin eps)) (cos x))) (.f64 eps (-.f64 #s(approx ( eps (+ (* eps (* (sin x) 1/6)) (* (cos x) (+ (* eps (* eps 1/24)) -1/2)))) (fma.f64 x (fma.f64 eps (.f64 eps #s(literal 1/6 binary64)) (.f64 eps (.f64 (.f64 x (fma.f64 eps (.f64 eps #s(literal 1/24 binary64)) #s(literal -1/2 binary64))) #s(literal -1/2 binary64)))) (.f64 eps (fma.f64 eps (*.f64 eps #s(literal 1/24 binary64)) #s(literal -1/2 binary64))))) (sin.f64 x))))
(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps (-.f64 (.f64 eps (*.f64 #s(literal -1/2 binary64) (cos.f64 x))) (sin.f64 x))))
#s(approx (- (* (cos x) (cos eps)) (+ (* (sin x) (sin eps)) (cos x))) (.f64 eps (-.f64 (.f64 eps (*.f64 #s(literal -1/2 binary64) (cos.f64 x))) (sin.f64 x))))

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

Calls

3 calls:

14.0ms	eps
14.0ms	x
11.0ms	(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))

Results

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

Compiler

Compiled 15 to 10 computations (33.3% saved)

regimes80.0ms (0.4%)

Memory

-41.1MiB live, 49.8MiB allocated

Counts

51 → 1

Calls

Call 1

Inputs
#s(approx (- (cos (+ x eps)) (cos x)) (+.f64 #s(approx (cos eps) #s(literal 1 binary64)) #s(literal -1 binary64)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* eps (+ (* eps (+ (* (cos x) (+ -1/2 (* eps (* eps 1/24)))) (* eps (* 1/6 (sin x))))) (sin (neg x)))) #s(approx (+ (* eps (* eps (+ (* eps (* eps 1/24)) -1/2))) (* eps (* x (+ (* eps (* eps 1/6)) -1)))) (*.f64 x (neg.f64 eps)))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (+ (cos eps) -1) (.f64 eps (.f64 eps #s(literal -1/2 binary64)))))
#s(approx (- (* (cos x) (cos eps)) (+ (* (sin x) (sin eps)) (cos x))) (.f64 eps #s(approx (- ( eps (* -1/2 (cos x))) (sin x)) (*.f64 eps #s(literal -1/2 binary64)))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* eps (+ (* eps (+ (* (cos x) (+ -1/2 (* eps (* eps 1/24)))) (* eps (* 1/6 (sin x))))) (sin (neg x)))) #s(approx (+ (* eps (* eps (+ (* eps (* eps 1/24)) -1/2))) (* eps (* x (+ (* eps (* eps 1/6)) -1)))) (.f64 eps (-.f64 (.f64 eps #s(literal -1/2 binary64)) x)))))
#s(approx (- (* (cos x) (cos eps)) (+ (* (sin x) (sin eps)) (cos x))) (.f64 eps #s(approx (- ( eps (* -1/2 (cos x))) (sin x)) (-.f64 (*.f64 eps #s(literal -1/2 binary64)) x))))
#s(approx (- (cos (+ x eps)) (cos x)) (+.f64 #s(approx (cos eps) (fma.f64 eps (*.f64 eps #s(literal -1/2 binary64)) #s(literal 1 binary64))) #s(literal -1 binary64)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* eps (+ (* eps (+ (* (cos x) (+ -1/2 (* eps (* eps 1/24)))) (* eps (* 1/6 (sin x))))) (sin (neg x)))) #s(approx (+ (* eps (* eps (+ (* eps (* eps 1/24)) -1/2))) (* eps (* x (+ (* eps (* eps 1/6)) -1)))) #s(approx (* (* (* eps eps) (* eps eps)) (+ (* x (/ 1/6 eps)) 1/24)) (.f64 x (.f64 eps (.f64 eps (.f64 eps #s(literal 1/6 binary64)))))))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* eps (+ (* eps (+ (* (cos x) (+ -1/2 (* eps (* eps 1/24)))) (* eps (* 1/6 (sin x))))) (sin (neg x)))) #s(approx (+ (* eps (* eps (+ (* eps (* eps 1/24)) -1/2))) (* eps (* x (+ (* eps (* eps 1/6)) -1)))) (.f64 #s(literal 1/24 binary64) (.f64 (.f64 eps eps) (.f64 eps eps))))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps #s(approx (+ ( eps (+ (* (cos x) (+ -1/2 (* eps (* eps 1/24)))) (* eps (* 1/6 (sin x))))) (sin (neg x))) #s(approx (+ (* x (+ (* x (+ (* eps (* (+ (* eps (* eps 1/24)) -1/2) -1/2)) (* x (+ (* (* eps eps) -1/36) 1/6)))) (+ (* eps (* eps 1/6)) -1))) (* eps (+ (* eps (* eps 1/24)) -1/2))) (.f64 x (fma.f64 x (.f64 x #s(literal 1/6 binary64)) #s(literal -1 binary64)))))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* eps (+ (* eps (+ (* (cos x) (+ -1/2 (* eps (* eps 1/24)))) (* eps (* 1/6 (sin x))))) (sin (neg x)))) #s(approx (+ (* eps (* eps (+ (* eps (* eps 1/24)) -1/2))) (* eps (* x (+ (* eps (* eps 1/6)) -1)))) (.f64 eps (fma.f64 eps (fma.f64 x (.f64 eps #s(literal 1/6 binary64)) #s(literal -1/2 binary64)) (neg.f64 x))))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* eps (+ (* eps (+ (* (cos x) (+ -1/2 (* eps (* eps 1/24)))) (* eps (* 1/6 (sin x))))) (sin (neg x)))) #s(approx (+ (* eps (* eps (+ (* eps (* eps 1/24)) -1/2))) (* eps (* x (+ (* eps (* eps 1/6)) -1)))) #s(approx (* (* (* eps eps) (* eps eps)) (+ (* x (/ 1/6 eps)) 1/24)) (.f64 (.f64 eps eps) (.f64 eps (fma.f64 eps #s(literal 1/24 binary64) (.f64 x #s(literal 1/6 binary64)))))))))
#s(approx (- (* (cos x) (cos eps)) (+ (* (sin x) (sin eps)) (cos x))) (.f64 eps #s(approx (- ( eps (* -1/2 (cos x))) (sin x)) (fma.f64 x (fma.f64 #s(literal 1/4 binary64) (.f64 eps x) #s(literal -1 binary64)) (.f64 eps #s(literal -1/2 binary64))))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* eps (+ (* eps (+ (* (cos x) (+ -1/2 (* eps (* eps 1/24)))) (* eps (* 1/6 (sin x))))) (sin (neg x)))) (fma.f64 eps #s(approx (* eps (+ (* eps (* eps 1/24)) -1/2)) (.f64 eps #s(literal -1/2 binary64))) (.f64 eps (.f64 x (fma.f64 eps (.f64 eps #s(literal 1/6 binary64)) #s(literal -1 binary64)))))))
#s(approx (- (* (cos x) (cos eps)) (+ (* (sin x) (sin eps)) (cos x))) (.f64 eps #s(approx (- ( eps (* -1/2 (cos x))) (sin x)) (fma.f64 x (fma.f64 x (fma.f64 eps #s(literal 1/4 binary64) (.f64 x #s(literal 1/6 binary64))) #s(literal -1 binary64)) (.f64 eps #s(literal -1/2 binary64))))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* eps (+ (* eps (+ (* (cos x) (+ -1/2 (* eps (* eps 1/24)))) (* eps (* 1/6 (sin x))))) (sin (neg x)))) #s(approx (+ (* eps (* eps (+ (* eps (* eps 1/24)) -1/2))) (* eps (* x (+ (* eps (* eps 1/6)) -1)))) (.f64 (.f64 (.f64 eps eps) (.f64 eps eps)) (fma.f64 x (/.f64 #s(literal 1/6 binary64) eps) #s(literal 1/24 binary64))))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps #s(approx (+ ( eps (+ (* (cos x) (+ -1/2 (* eps (* eps 1/24)))) (* eps (* 1/6 (sin x))))) (sin (neg x))) (fma.f64 eps (fma.f64 eps (.f64 eps #s(literal 1/24 binary64)) #s(literal -1/2 binary64)) (.f64 x (fma.f64 eps (*.f64 eps #s(literal 1/6 binary64)) #s(literal -1 binary64)))))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* eps (+ (* eps (+ (* (cos x) (+ -1/2 (* eps (* eps 1/24)))) (* eps (* 1/6 (sin x))))) (sin (neg x)))) (fma.f64 eps (.f64 eps (fma.f64 eps (.f64 eps #s(literal 1/24 binary64)) #s(literal -1/2 binary64))) (.f64 eps (.f64 x (fma.f64 eps (*.f64 eps #s(literal 1/6 binary64)) #s(literal -1 binary64)))))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* eps (+ (* eps (+ (* (cos x) (+ -1/2 (* eps (* eps 1/24)))) (* eps (* 1/6 (sin x))))) (sin (neg x)))) (fma.f64 (.f64 x (fma.f64 eps (.f64 eps #s(literal 1/6 binary64)) #s(literal -1 binary64))) eps (.f64 eps (.f64 eps (fma.f64 #s(literal 1/24 binary64) (*.f64 eps eps) #s(literal -1/2 binary64)))))))
#s(approx (- (* (cos x) (cos eps)) (+ (* (sin x) (sin eps)) (cos x))) #s(approx (* eps (- (* eps (* -1/2 (cos x))) (sin x))) (fma.f64 x (fma.f64 x (fma.f64 eps (.f64 x #s(literal 1/6 binary64)) (.f64 eps (.f64 eps #s(literal 1/4 binary64)))) (neg.f64 eps)) (.f64 #s(literal -1/2 binary64) (*.f64 eps eps)))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* eps (+ (* eps (+ (* (cos x) (+ -1/2 (* eps (* eps 1/24)))) (* eps (* 1/6 (sin x))))) (sin (neg x)))) #s(approx (+ (* eps (* eps (+ (* eps (* eps 1/24)) -1/2))) (* eps (* x (+ (* eps (* eps 1/6)) -1)))) (.f64 (.f64 (.f64 eps eps) (.f64 eps eps)) (-.f64 #s(literal 1/24 binary64) (/.f64 (fma.f64 x #s(literal -1/6 binary64) (/.f64 #s(literal 1/2 binary64) eps)) eps))))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* eps (+ (* eps (+ (* (cos x) (+ -1/2 (* eps (* eps 1/24)))) (* eps (* 1/6 (sin x))))) (sin (neg x)))) #s(approx (+ (* eps (* eps (+ (* eps (* eps 1/24)) -1/2))) (* eps (* x (+ (* eps (* eps 1/6)) -1)))) #s(approx (* (* (* eps eps) (* eps eps)) (+ (* x (/ 1/6 eps)) 1/24)) (.f64 x (fma.f64 eps (.f64 eps (.f64 eps #s(literal 1/6 binary64))) (/.f64 (.f64 eps (.f64 eps (.f64 #s(literal 1/24 binary64) (*.f64 eps eps)))) x)))))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* eps (+ (* eps (+ (* (cos x) (+ -1/2 (* eps (* eps 1/24)))) (* eps (* 1/6 (sin x))))) (sin (neg x)))) #s(approx (+ (* eps (* eps (+ (* eps (* eps 1/24)) -1/2))) (* eps (* x (+ (* eps (* eps 1/6)) -1)))) (.f64 x (fma.f64 eps (fma.f64 eps (.f64 eps #s(literal 1/6 binary64)) #s(literal -1 binary64)) (.f64 (.f64 eps eps) (/.f64 (fma.f64 #s(literal 1/24 binary64) (*.f64 eps eps) #s(literal -1/2 binary64)) x)))))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* eps (+ (* eps (+ (* (cos x) (+ -1/2 (* eps (* eps 1/24)))) (* eps (* 1/6 (sin x))))) (sin (neg x)))) #s(approx (+ (* eps (* eps (+ (* eps (* eps 1/24)) -1/2))) (* eps (* x (+ (* eps (* eps 1/6)) -1)))) (.f64 (.f64 (.f64 eps eps) (.f64 eps eps)) (+.f64 #s(literal 1/24 binary64) (fma.f64 x (/.f64 #s(literal 1/6 binary64) eps) (/.f64 #s(literal -1/2 binary64) (*.f64 eps eps))))))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps #s(approx (+ ( eps (+ (* (cos x) (+ -1/2 (* eps (* eps 1/24)))) (* eps (* 1/6 (sin x))))) (sin (neg x))) #s(approx (+ (* x (+ (* x (+ (* eps (* (+ (* eps (* eps 1/24)) -1/2) -1/2)) (* x (+ (* (* eps eps) -1/36) 1/6)))) (+ (* eps (* eps 1/6)) -1))) (* eps (+ (* eps (* eps 1/24)) -1/2))) (.f64 (.f64 eps eps) (.f64 eps (fma.f64 x (/.f64 (fma.f64 #s(literal -1/36 binary64) (.f64 x x) #s(literal 1/6 binary64)) eps) (fma.f64 x (*.f64 x #s(literal -1/48 binary64)) #s(literal 1/24 binary64)))))))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps #s(approx (+ ( eps (+ (* (cos x) (+ -1/2 (* eps (* eps 1/24)))) (* eps (* 1/6 (sin x))))) (sin (neg x))) #s(approx (+ (* x (+ (* x (+ (* eps (* (+ (* eps (* eps 1/24)) -1/2) -1/2)) (* x (+ (* (* eps eps) -1/36) 1/6)))) (+ (* eps (* eps 1/6)) -1))) (* eps (+ (* eps (* eps 1/24)) -1/2))) (fma.f64 eps (fma.f64 eps (.f64 x (fma.f64 #s(literal -1/36 binary64) (.f64 x x) #s(literal 1/6 binary64))) (fma.f64 #s(literal 1/4 binary64) (.f64 x x) #s(literal -1/2 binary64))) (.f64 x (fma.f64 x (*.f64 x #s(literal 1/6 binary64)) #s(literal -1 binary64))))))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps #s(approx (+ ( eps (+ (* (cos x) (+ -1/2 (* eps (* eps 1/24)))) (* eps (* 1/6 (sin x))))) (sin (neg x))) #s(approx (+ (* x (+ (* x (+ (* eps (* (+ (* eps (* eps 1/24)) -1/2) -1/2)) (* x (+ (* (* eps eps) -1/36) 1/6)))) (+ (* eps (* eps 1/6)) -1))) (* eps (+ (* eps (* eps 1/24)) -1/2))) (neg.f64 (.f64 (.f64 eps (.f64 eps eps)) (-.f64 (fma.f64 x (.f64 x #s(literal 1/48 binary64)) #s(literal -1/24 binary64)) (.f64 x (/.f64 (fma.f64 #s(literal -1/36 binary64) (.f64 x x) #s(literal 1/6 binary64)) eps)))))))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* eps (+ (* eps (+ (* (cos x) (+ -1/2 (* eps (* eps 1/24)))) (* eps (* 1/6 (sin x))))) (sin (neg x)))) #s(approx (+ (* eps (* eps (+ (* eps (* eps 1/24)) -1/2))) (* eps (* x (+ (* eps (* eps 1/6)) -1)))) (.f64 (.f64 (.f64 eps eps) (.f64 eps eps)) (-.f64 #s(literal 1/24 binary64) (/.f64 (fma.f64 x #s(literal -1/6 binary64) (/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 x eps)) eps)) eps))))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps #s(approx (+ ( eps (+ (* (cos x) (+ -1/2 (* eps (* eps 1/24)))) (* eps (* 1/6 (sin x))))) (sin (neg x))) (fma.f64 eps (fma.f64 eps (.f64 eps #s(literal 1/24 binary64)) #s(literal -1/2 binary64)) (.f64 x (fma.f64 eps (.f64 eps #s(literal 1/6 binary64)) (fma.f64 (.f64 x (fma.f64 eps (.f64 eps #s(literal 1/24 binary64)) #s(literal -1/2 binary64))) (.f64 eps #s(literal -1/2 binary64)) #s(literal -1 binary64))))))))
#s(approx (- (* (cos x) (cos eps)) (+ (* (sin x) (sin eps)) (cos x))) (.f64 eps #s(approx (- ( eps (+ (* eps (* (sin x) 1/6)) (* (cos x) (+ (* eps (* eps 1/24)) -1/2)))) (sin x)) (fma.f64 x (fma.f64 eps (.f64 (.f64 x (fma.f64 eps (.f64 eps #s(literal 1/24 binary64)) #s(literal -1/2 binary64))) #s(literal -1/2 binary64)) (fma.f64 eps (.f64 eps #s(literal 1/6 binary64)) #s(literal -1 binary64))) (.f64 eps (fma.f64 eps (.f64 eps #s(literal 1/24 binary64)) #s(literal -1/2 binary64)))))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps #s(approx (+ ( eps (+ (* (cos x) (+ -1/2 (* eps (* eps 1/24)))) (* eps (* 1/6 (sin x))))) (sin (neg x))) (fma.f64 x (fma.f64 x (fma.f64 eps #s(approx (* (+ (* eps (* eps 1/24)) -1/2) -1/2) #s(literal 1/4 binary64)) (.f64 x (fma.f64 (.f64 eps eps) #s(literal -1/36 binary64) #s(literal 1/6 binary64)))) (fma.f64 eps (.f64 eps #s(literal 1/6 binary64)) #s(literal -1 binary64))) (.f64 eps (fma.f64 eps (*.f64 eps #s(literal 1/24 binary64)) #s(literal -1/2 binary64)))))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps #s(approx (+ ( eps (+ (* (cos x) (+ -1/2 (* eps (* eps 1/24)))) (* eps (* 1/6 (sin x))))) (sin (neg x))) (fma.f64 x (fma.f64 x (fma.f64 eps #s(approx (* (+ (* eps (* eps 1/24)) -1/2) -1/2) (.f64 #s(literal -1/48 binary64) (.f64 eps eps))) (.f64 x (fma.f64 (.f64 eps eps) #s(literal -1/36 binary64) #s(literal 1/6 binary64)))) (fma.f64 eps (.f64 eps #s(literal 1/6 binary64)) #s(literal -1 binary64))) (.f64 eps (fma.f64 eps (*.f64 eps #s(literal 1/24 binary64)) #s(literal -1/2 binary64)))))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* eps (+ (* eps (+ (* (cos x) (+ -1/2 (* eps (* eps 1/24)))) (* eps (* 1/6 (sin x))))) (sin (neg x)))) #s(approx (+ (* eps (* eps (+ (* eps (* eps 1/24)) -1/2))) (* eps (* x (+ (* eps (* eps 1/6)) -1)))) (.f64 (.f64 (.f64 eps eps) (.f64 eps eps)) (+.f64 (fma.f64 x (/.f64 #s(literal 1/6 binary64) eps) (-.f64 #s(literal 1/24 binary64) (/.f64 x (.f64 eps (.f64 eps eps))))) (/.f64 #s(literal -1/2 binary64) (*.f64 eps eps)))))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps #s(approx (+ ( eps (+ (* (cos x) (+ -1/2 (* eps (* eps 1/24)))) (* eps (* 1/6 (sin x))))) (sin (neg x))) (fma.f64 x (fma.f64 x (fma.f64 eps (.f64 (fma.f64 eps (.f64 eps #s(literal 1/24 binary64)) #s(literal -1/2 binary64)) #s(literal -1/2 binary64)) (.f64 x (fma.f64 (.f64 eps eps) #s(literal -1/36 binary64) #s(literal 1/6 binary64)))) (fma.f64 eps (.f64 eps #s(literal 1/6 binary64)) #s(literal -1 binary64))) (.f64 eps (fma.f64 eps (*.f64 eps #s(literal 1/24 binary64)) #s(literal -1/2 binary64)))))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps #s(approx (+ ( eps (+ (* (cos x) (+ -1/2 (* eps (* eps 1/24)))) (* eps (* 1/6 (sin x))))) (sin (neg x))) #s(approx (+ (* x (+ (* x (+ (* eps (* (+ (* eps (* eps 1/24)) -1/2) -1/2)) (* x (+ (* (* eps eps) -1/36) 1/6)))) (+ (* eps (* eps 1/6)) -1))) (* eps (+ (* eps (* eps 1/24)) -1/2))) (neg.f64 (.f64 (.f64 eps (.f64 eps eps)) (-.f64 (fma.f64 x (.f64 x #s(literal 1/48 binary64)) #s(literal -1/24 binary64)) (/.f64 (-.f64 (.f64 x (fma.f64 #s(literal -1/36 binary64) (.f64 x x) #s(literal 1/6 binary64))) (/.f64 (fma.f64 (*.f64 x x) #s(literal -1/4 binary64) #s(literal 1/2 binary64)) eps)) eps))))))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* eps (+ (* eps (+ (* (cos x) (+ -1/2 (* eps (* eps 1/24)))) (* eps (* 1/6 (sin x))))) (sin (neg x)))) (fma.f64 x (fma.f64 x (fma.f64 eps (.f64 x (fma.f64 (.f64 eps eps) #s(literal -1/36 binary64) #s(literal 1/6 binary64))) (.f64 #s(literal -1/2 binary64) (.f64 eps (.f64 eps (fma.f64 eps (.f64 eps #s(literal 1/24 binary64)) #s(literal -1/2 binary64)))))) (.f64 eps (fma.f64 eps (.f64 eps #s(literal 1/6 binary64)) #s(literal -1 binary64)))) (.f64 eps (.f64 eps (fma.f64 eps (*.f64 eps #s(literal 1/24 binary64)) #s(literal -1/2 binary64)))))))
#s(approx (- (* (cos x) (cos eps)) (+ (* (sin x) (sin eps)) (cos x))) #s(approx (* eps (- (* eps (+ (* eps (* (sin x) 1/6)) (* (cos x) (+ (* eps (* eps 1/24)) -1/2)))) (sin x))) (fma.f64 x (fma.f64 x (fma.f64 x (.f64 eps (fma.f64 (.f64 eps eps) #s(literal -1/36 binary64) #s(literal 1/6 binary64))) (.f64 #s(literal -1/2 binary64) (.f64 (.f64 eps eps) (fma.f64 eps (.f64 eps #s(literal 1/24 binary64)) #s(literal -1/2 binary64))))) (.f64 eps (fma.f64 eps (.f64 eps #s(literal 1/6 binary64)) #s(literal -1 binary64)))) (.f64 (.f64 eps eps) (fma.f64 eps (*.f64 eps #s(literal 1/24 binary64)) #s(literal -1/2 binary64))))))
#s(approx (- (cos (+ x eps)) (cos x)) (+.f64 (cos.f64 eps) #s(literal -1 binary64)))
(-.f64 #s(approx (cos (+ x eps)) (cos.f64 x)) #s(approx (cos x) #s(literal 1 binary64)))
(-.f64 (cos.f64 (+.f64 x eps)) #s(approx (cos x) #s(literal 1 binary64)))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (sin.f64 x) (neg.f64 eps)))
#s(approx (- (* (cos x) (cos eps)) (+ (* (sin x) (sin eps)) (cos x))) (neg.f64 (*.f64 eps (sin.f64 x))))
#s(approx (- (* (cos x) (cos eps)) (+ (* (sin x) (sin eps)) (cos x))) (.f64 eps #s(approx (- ( eps (+ (* eps (* (sin x) 1/6)) (* (cos x) (+ (* eps (* eps 1/24)) -1/2)))) (sin x)) (sin.f64 (neg.f64 x)))))
#s(approx (- (* (cos x) (cos eps)) (+ (* (sin x) (sin eps)) (cos x))) (*.f64 eps (sin.f64 (neg.f64 x))))
#s(approx (- (* (cos x) (cos eps)) (+ (* (sin x) (sin eps)) (cos x))) (.f64 eps (-.f64 #s(approx ( eps (* -1/2 (cos x))) (*.f64 eps #s(literal -1/2 binary64))) (sin.f64 x))))
(-.f64 (cos.f64 (+.f64 x eps)) #s(approx (cos x) (fma.f64 x (*.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64))))
#s(approx (- (* (cos x) (cos eps)) (+ (* (sin x) (sin eps)) (cos x))) (.f64 eps (-.f64 #s(approx ( eps (* -1/2 (cos x))) (.f64 eps (fma.f64 #s(literal 1/4 binary64) (.f64 x x) #s(literal -1/2 binary64)))) (sin.f64 x))))
#s(approx (- (* (cos x) (cos eps)) (+ (* (sin x) (sin eps)) (cos x))) (.f64 eps (-.f64 #s(approx ( eps (+ (* eps (* (sin x) 1/6)) (* (cos x) (+ (* eps (* eps 1/24)) -1/2)))) (.f64 eps (fma.f64 eps (.f64 eps #s(literal 1/24 binary64)) #s(literal -1/2 binary64)))) (sin.f64 x))))
#s(approx (- (* (cos x) (cos eps)) (+ (* (sin x) (sin eps)) (cos x))) (.f64 eps (-.f64 #s(approx ( eps (+ (* eps (* (sin x) 1/6)) (* (cos x) (+ (* eps (* eps 1/24)) -1/2)))) (fma.f64 x (.f64 eps (.f64 eps #s(literal 1/6 binary64))) (.f64 eps (fma.f64 eps (.f64 eps #s(literal 1/24 binary64)) #s(literal -1/2 binary64))))) (sin.f64 x))))
#s(approx (- (* (cos x) (cos eps)) (+ (* (sin x) (sin eps)) (cos x))) (.f64 eps (-.f64 #s(approx ( eps (+ (* eps (* (sin x) 1/6)) (* (cos x) (+ (* eps (* eps 1/24)) -1/2)))) (fma.f64 x (fma.f64 eps (.f64 eps #s(literal 1/6 binary64)) (.f64 eps (.f64 (.f64 x (fma.f64 eps (.f64 eps #s(literal 1/24 binary64)) #s(literal -1/2 binary64))) #s(literal -1/2 binary64)))) (.f64 eps (fma.f64 eps (*.f64 eps #s(literal 1/24 binary64)) #s(literal -1/2 binary64))))) (sin.f64 x))))
(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))

Outputs

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

Calls

3 calls:

29.0ms	x
13.0ms	eps
11.0ms	(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))

Results

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

Compiler

Compiled 15 to 10 computations (33.3% saved)

regimes39.0ms (0.2%)

Memory

18.6MiB live, 57.2MiB allocated

Counts

47 → 1

Calls

Call 1

Inputs
#s(approx (- (cos (+ x eps)) (cos x)) (+.f64 #s(approx (cos eps) #s(literal 1 binary64)) #s(literal -1 binary64)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* eps (+ (* eps (+ (* (cos x) (+ -1/2 (* eps (* eps 1/24)))) (* eps (* 1/6 (sin x))))) (sin (neg x)))) #s(approx (+ (* eps (* eps (+ (* eps (* eps 1/24)) -1/2))) (* eps (* x (+ (* eps (* eps 1/6)) -1)))) (*.f64 x (neg.f64 eps)))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (+ (cos eps) -1) (.f64 eps (.f64 eps #s(literal -1/2 binary64)))))
#s(approx (- (* (cos x) (cos eps)) (+ (* (sin x) (sin eps)) (cos x))) (.f64 eps #s(approx (- ( eps (* -1/2 (cos x))) (sin x)) (*.f64 eps #s(literal -1/2 binary64)))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* eps (+ (* eps (+ (* (cos x) (+ -1/2 (* eps (* eps 1/24)))) (* eps (* 1/6 (sin x))))) (sin (neg x)))) #s(approx (+ (* eps (* eps (+ (* eps (* eps 1/24)) -1/2))) (* eps (* x (+ (* eps (* eps 1/6)) -1)))) (.f64 eps (-.f64 (.f64 eps #s(literal -1/2 binary64)) x)))))
#s(approx (- (* (cos x) (cos eps)) (+ (* (sin x) (sin eps)) (cos x))) (.f64 eps #s(approx (- ( eps (* -1/2 (cos x))) (sin x)) (-.f64 (*.f64 eps #s(literal -1/2 binary64)) x))))
#s(approx (- (cos (+ x eps)) (cos x)) (+.f64 #s(approx (cos eps) (fma.f64 eps (*.f64 eps #s(literal -1/2 binary64)) #s(literal 1 binary64))) #s(literal -1 binary64)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* eps (+ (* eps (+ (* (cos x) (+ -1/2 (* eps (* eps 1/24)))) (* eps (* 1/6 (sin x))))) (sin (neg x)))) #s(approx (+ (* eps (* eps (+ (* eps (* eps 1/24)) -1/2))) (* eps (* x (+ (* eps (* eps 1/6)) -1)))) #s(approx (* (* (* eps eps) (* eps eps)) (+ (* x (/ 1/6 eps)) 1/24)) (.f64 x (.f64 eps (.f64 eps (.f64 eps #s(literal 1/6 binary64)))))))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* eps (+ (* eps (+ (* (cos x) (+ -1/2 (* eps (* eps 1/24)))) (* eps (* 1/6 (sin x))))) (sin (neg x)))) #s(approx (+ (* eps (* eps (+ (* eps (* eps 1/24)) -1/2))) (* eps (* x (+ (* eps (* eps 1/6)) -1)))) (.f64 #s(literal 1/24 binary64) (.f64 (.f64 eps eps) (.f64 eps eps))))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps #s(approx (+ ( eps (+ (* (cos x) (+ -1/2 (* eps (* eps 1/24)))) (* eps (* 1/6 (sin x))))) (sin (neg x))) #s(approx (+ (* x (+ (* x (+ (* eps (* (+ (* eps (* eps 1/24)) -1/2) -1/2)) (* x (+ (* (* eps eps) -1/36) 1/6)))) (+ (* eps (* eps 1/6)) -1))) (* eps (+ (* eps (* eps 1/24)) -1/2))) (.f64 x (fma.f64 x (.f64 x #s(literal 1/6 binary64)) #s(literal -1 binary64)))))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* eps (+ (* eps (+ (* (cos x) (+ -1/2 (* eps (* eps 1/24)))) (* eps (* 1/6 (sin x))))) (sin (neg x)))) #s(approx (+ (* eps (* eps (+ (* eps (* eps 1/24)) -1/2))) (* eps (* x (+ (* eps (* eps 1/6)) -1)))) (.f64 eps (fma.f64 eps (fma.f64 x (.f64 eps #s(literal 1/6 binary64)) #s(literal -1/2 binary64)) (neg.f64 x))))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* eps (+ (* eps (+ (* (cos x) (+ -1/2 (* eps (* eps 1/24)))) (* eps (* 1/6 (sin x))))) (sin (neg x)))) #s(approx (+ (* eps (* eps (+ (* eps (* eps 1/24)) -1/2))) (* eps (* x (+ (* eps (* eps 1/6)) -1)))) #s(approx (* (* (* eps eps) (* eps eps)) (+ (* x (/ 1/6 eps)) 1/24)) (.f64 (.f64 eps eps) (.f64 eps (fma.f64 eps #s(literal 1/24 binary64) (.f64 x #s(literal 1/6 binary64)))))))))
#s(approx (- (* (cos x) (cos eps)) (+ (* (sin x) (sin eps)) (cos x))) (.f64 eps #s(approx (- ( eps (* -1/2 (cos x))) (sin x)) (fma.f64 x (fma.f64 #s(literal 1/4 binary64) (.f64 eps x) #s(literal -1 binary64)) (.f64 eps #s(literal -1/2 binary64))))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* eps (+ (* eps (+ (* (cos x) (+ -1/2 (* eps (* eps 1/24)))) (* eps (* 1/6 (sin x))))) (sin (neg x)))) (fma.f64 eps #s(approx (* eps (+ (* eps (* eps 1/24)) -1/2)) (.f64 eps #s(literal -1/2 binary64))) (.f64 eps (.f64 x (fma.f64 eps (.f64 eps #s(literal 1/6 binary64)) #s(literal -1 binary64)))))))
#s(approx (- (* (cos x) (cos eps)) (+ (* (sin x) (sin eps)) (cos x))) (.f64 eps #s(approx (- ( eps (* -1/2 (cos x))) (sin x)) (fma.f64 x (fma.f64 x (fma.f64 eps #s(literal 1/4 binary64) (.f64 x #s(literal 1/6 binary64))) #s(literal -1 binary64)) (.f64 eps #s(literal -1/2 binary64))))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* eps (+ (* eps (+ (* (cos x) (+ -1/2 (* eps (* eps 1/24)))) (* eps (* 1/6 (sin x))))) (sin (neg x)))) #s(approx (+ (* eps (* eps (+ (* eps (* eps 1/24)) -1/2))) (* eps (* x (+ (* eps (* eps 1/6)) -1)))) (.f64 (.f64 (.f64 eps eps) (.f64 eps eps)) (fma.f64 x (/.f64 #s(literal 1/6 binary64) eps) #s(literal 1/24 binary64))))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps #s(approx (+ ( eps (+ (* (cos x) (+ -1/2 (* eps (* eps 1/24)))) (* eps (* 1/6 (sin x))))) (sin (neg x))) (fma.f64 eps (fma.f64 eps (.f64 eps #s(literal 1/24 binary64)) #s(literal -1/2 binary64)) (.f64 x (fma.f64 eps (*.f64 eps #s(literal 1/6 binary64)) #s(literal -1 binary64)))))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* eps (+ (* eps (+ (* (cos x) (+ -1/2 (* eps (* eps 1/24)))) (* eps (* 1/6 (sin x))))) (sin (neg x)))) (fma.f64 eps (.f64 eps (fma.f64 eps (.f64 eps #s(literal 1/24 binary64)) #s(literal -1/2 binary64))) (.f64 eps (.f64 x (fma.f64 eps (*.f64 eps #s(literal 1/6 binary64)) #s(literal -1 binary64)))))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* eps (+ (* eps (+ (* (cos x) (+ -1/2 (* eps (* eps 1/24)))) (* eps (* 1/6 (sin x))))) (sin (neg x)))) (fma.f64 (.f64 x (fma.f64 eps (.f64 eps #s(literal 1/6 binary64)) #s(literal -1 binary64))) eps (.f64 eps (.f64 eps (fma.f64 #s(literal 1/24 binary64) (*.f64 eps eps) #s(literal -1/2 binary64)))))))
#s(approx (- (* (cos x) (cos eps)) (+ (* (sin x) (sin eps)) (cos x))) #s(approx (* eps (- (* eps (* -1/2 (cos x))) (sin x))) (fma.f64 x (fma.f64 x (fma.f64 eps (.f64 x #s(literal 1/6 binary64)) (.f64 eps (.f64 eps #s(literal 1/4 binary64)))) (neg.f64 eps)) (.f64 #s(literal -1/2 binary64) (*.f64 eps eps)))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* eps (+ (* eps (+ (* (cos x) (+ -1/2 (* eps (* eps 1/24)))) (* eps (* 1/6 (sin x))))) (sin (neg x)))) #s(approx (+ (* eps (* eps (+ (* eps (* eps 1/24)) -1/2))) (* eps (* x (+ (* eps (* eps 1/6)) -1)))) (.f64 (.f64 (.f64 eps eps) (.f64 eps eps)) (-.f64 #s(literal 1/24 binary64) (/.f64 (fma.f64 x #s(literal -1/6 binary64) (/.f64 #s(literal 1/2 binary64) eps)) eps))))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* eps (+ (* eps (+ (* (cos x) (+ -1/2 (* eps (* eps 1/24)))) (* eps (* 1/6 (sin x))))) (sin (neg x)))) #s(approx (+ (* eps (* eps (+ (* eps (* eps 1/24)) -1/2))) (* eps (* x (+ (* eps (* eps 1/6)) -1)))) #s(approx (* (* (* eps eps) (* eps eps)) (+ (* x (/ 1/6 eps)) 1/24)) (.f64 x (fma.f64 eps (.f64 eps (.f64 eps #s(literal 1/6 binary64))) (/.f64 (.f64 eps (.f64 eps (.f64 #s(literal 1/24 binary64) (*.f64 eps eps)))) x)))))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* eps (+ (* eps (+ (* (cos x) (+ -1/2 (* eps (* eps 1/24)))) (* eps (* 1/6 (sin x))))) (sin (neg x)))) #s(approx (+ (* eps (* eps (+ (* eps (* eps 1/24)) -1/2))) (* eps (* x (+ (* eps (* eps 1/6)) -1)))) (.f64 x (fma.f64 eps (fma.f64 eps (.f64 eps #s(literal 1/6 binary64)) #s(literal -1 binary64)) (.f64 (.f64 eps eps) (/.f64 (fma.f64 #s(literal 1/24 binary64) (*.f64 eps eps) #s(literal -1/2 binary64)) x)))))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* eps (+ (* eps (+ (* (cos x) (+ -1/2 (* eps (* eps 1/24)))) (* eps (* 1/6 (sin x))))) (sin (neg x)))) #s(approx (+ (* eps (* eps (+ (* eps (* eps 1/24)) -1/2))) (* eps (* x (+ (* eps (* eps 1/6)) -1)))) (.f64 (.f64 (.f64 eps eps) (.f64 eps eps)) (+.f64 #s(literal 1/24 binary64) (fma.f64 x (/.f64 #s(literal 1/6 binary64) eps) (/.f64 #s(literal -1/2 binary64) (*.f64 eps eps))))))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps #s(approx (+ ( eps (+ (* (cos x) (+ -1/2 (* eps (* eps 1/24)))) (* eps (* 1/6 (sin x))))) (sin (neg x))) #s(approx (+ (* x (+ (* x (+ (* eps (* (+ (* eps (* eps 1/24)) -1/2) -1/2)) (* x (+ (* (* eps eps) -1/36) 1/6)))) (+ (* eps (* eps 1/6)) -1))) (* eps (+ (* eps (* eps 1/24)) -1/2))) (.f64 (.f64 eps eps) (.f64 eps (fma.f64 x (/.f64 (fma.f64 #s(literal -1/36 binary64) (.f64 x x) #s(literal 1/6 binary64)) eps) (fma.f64 x (*.f64 x #s(literal -1/48 binary64)) #s(literal 1/24 binary64)))))))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps #s(approx (+ ( eps (+ (* (cos x) (+ -1/2 (* eps (* eps 1/24)))) (* eps (* 1/6 (sin x))))) (sin (neg x))) #s(approx (+ (* x (+ (* x (+ (* eps (* (+ (* eps (* eps 1/24)) -1/2) -1/2)) (* x (+ (* (* eps eps) -1/36) 1/6)))) (+ (* eps (* eps 1/6)) -1))) (* eps (+ (* eps (* eps 1/24)) -1/2))) (fma.f64 eps (fma.f64 eps (.f64 x (fma.f64 #s(literal -1/36 binary64) (.f64 x x) #s(literal 1/6 binary64))) (fma.f64 #s(literal 1/4 binary64) (.f64 x x) #s(literal -1/2 binary64))) (.f64 x (fma.f64 x (*.f64 x #s(literal 1/6 binary64)) #s(literal -1 binary64))))))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps #s(approx (+ ( eps (+ (* (cos x) (+ -1/2 (* eps (* eps 1/24)))) (* eps (* 1/6 (sin x))))) (sin (neg x))) #s(approx (+ (* x (+ (* x (+ (* eps (* (+ (* eps (* eps 1/24)) -1/2) -1/2)) (* x (+ (* (* eps eps) -1/36) 1/6)))) (+ (* eps (* eps 1/6)) -1))) (* eps (+ (* eps (* eps 1/24)) -1/2))) (neg.f64 (.f64 (.f64 eps (.f64 eps eps)) (-.f64 (fma.f64 x (.f64 x #s(literal 1/48 binary64)) #s(literal -1/24 binary64)) (.f64 x (/.f64 (fma.f64 #s(literal -1/36 binary64) (.f64 x x) #s(literal 1/6 binary64)) eps)))))))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* eps (+ (* eps (+ (* (cos x) (+ -1/2 (* eps (* eps 1/24)))) (* eps (* 1/6 (sin x))))) (sin (neg x)))) #s(approx (+ (* eps (* eps (+ (* eps (* eps 1/24)) -1/2))) (* eps (* x (+ (* eps (* eps 1/6)) -1)))) (.f64 (.f64 (.f64 eps eps) (.f64 eps eps)) (-.f64 #s(literal 1/24 binary64) (/.f64 (fma.f64 x #s(literal -1/6 binary64) (/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 x eps)) eps)) eps))))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps #s(approx (+ ( eps (+ (* (cos x) (+ -1/2 (* eps (* eps 1/24)))) (* eps (* 1/6 (sin x))))) (sin (neg x))) (fma.f64 eps (fma.f64 eps (.f64 eps #s(literal 1/24 binary64)) #s(literal -1/2 binary64)) (.f64 x (fma.f64 eps (.f64 eps #s(literal 1/6 binary64)) (fma.f64 (.f64 x (fma.f64 eps (.f64 eps #s(literal 1/24 binary64)) #s(literal -1/2 binary64))) (.f64 eps #s(literal -1/2 binary64)) #s(literal -1 binary64))))))))
#s(approx (- (* (cos x) (cos eps)) (+ (* (sin x) (sin eps)) (cos x))) (.f64 eps #s(approx (- ( eps (+ (* eps (* (sin x) 1/6)) (* (cos x) (+ (* eps (* eps 1/24)) -1/2)))) (sin x)) (fma.f64 x (fma.f64 eps (.f64 (.f64 x (fma.f64 eps (.f64 eps #s(literal 1/24 binary64)) #s(literal -1/2 binary64))) #s(literal -1/2 binary64)) (fma.f64 eps (.f64 eps #s(literal 1/6 binary64)) #s(literal -1 binary64))) (.f64 eps (fma.f64 eps (.f64 eps #s(literal 1/24 binary64)) #s(literal -1/2 binary64)))))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps #s(approx (+ ( eps (+ (* (cos x) (+ -1/2 (* eps (* eps 1/24)))) (* eps (* 1/6 (sin x))))) (sin (neg x))) (fma.f64 x (fma.f64 x (fma.f64 eps #s(approx (* (+ (* eps (* eps 1/24)) -1/2) -1/2) #s(literal 1/4 binary64)) (.f64 x (fma.f64 (.f64 eps eps) #s(literal -1/36 binary64) #s(literal 1/6 binary64)))) (fma.f64 eps (.f64 eps #s(literal 1/6 binary64)) #s(literal -1 binary64))) (.f64 eps (fma.f64 eps (*.f64 eps #s(literal 1/24 binary64)) #s(literal -1/2 binary64)))))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps #s(approx (+ ( eps (+ (* (cos x) (+ -1/2 (* eps (* eps 1/24)))) (* eps (* 1/6 (sin x))))) (sin (neg x))) (fma.f64 x (fma.f64 x (fma.f64 eps #s(approx (* (+ (* eps (* eps 1/24)) -1/2) -1/2) (.f64 #s(literal -1/48 binary64) (.f64 eps eps))) (.f64 x (fma.f64 (.f64 eps eps) #s(literal -1/36 binary64) #s(literal 1/6 binary64)))) (fma.f64 eps (.f64 eps #s(literal 1/6 binary64)) #s(literal -1 binary64))) (.f64 eps (fma.f64 eps (*.f64 eps #s(literal 1/24 binary64)) #s(literal -1/2 binary64)))))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* eps (+ (* eps (+ (* (cos x) (+ -1/2 (* eps (* eps 1/24)))) (* eps (* 1/6 (sin x))))) (sin (neg x)))) #s(approx (+ (* eps (* eps (+ (* eps (* eps 1/24)) -1/2))) (* eps (* x (+ (* eps (* eps 1/6)) -1)))) (.f64 (.f64 (.f64 eps eps) (.f64 eps eps)) (+.f64 (fma.f64 x (/.f64 #s(literal 1/6 binary64) eps) (-.f64 #s(literal 1/24 binary64) (/.f64 x (.f64 eps (.f64 eps eps))))) (/.f64 #s(literal -1/2 binary64) (*.f64 eps eps)))))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps #s(approx (+ ( eps (+ (* (cos x) (+ -1/2 (* eps (* eps 1/24)))) (* eps (* 1/6 (sin x))))) (sin (neg x))) (fma.f64 x (fma.f64 x (fma.f64 eps (.f64 (fma.f64 eps (.f64 eps #s(literal 1/24 binary64)) #s(literal -1/2 binary64)) #s(literal -1/2 binary64)) (.f64 x (fma.f64 (.f64 eps eps) #s(literal -1/36 binary64) #s(literal 1/6 binary64)))) (fma.f64 eps (.f64 eps #s(literal 1/6 binary64)) #s(literal -1 binary64))) (.f64 eps (fma.f64 eps (*.f64 eps #s(literal 1/24 binary64)) #s(literal -1/2 binary64)))))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps #s(approx (+ ( eps (+ (* (cos x) (+ -1/2 (* eps (* eps 1/24)))) (* eps (* 1/6 (sin x))))) (sin (neg x))) #s(approx (+ (* x (+ (* x (+ (* eps (* (+ (* eps (* eps 1/24)) -1/2) -1/2)) (* x (+ (* (* eps eps) -1/36) 1/6)))) (+ (* eps (* eps 1/6)) -1))) (* eps (+ (* eps (* eps 1/24)) -1/2))) (neg.f64 (.f64 (.f64 eps (.f64 eps eps)) (-.f64 (fma.f64 x (.f64 x #s(literal 1/48 binary64)) #s(literal -1/24 binary64)) (/.f64 (-.f64 (.f64 x (fma.f64 #s(literal -1/36 binary64) (.f64 x x) #s(literal 1/6 binary64))) (/.f64 (fma.f64 (*.f64 x x) #s(literal -1/4 binary64) #s(literal 1/2 binary64)) eps)) eps))))))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* eps (+ (* eps (+ (* (cos x) (+ -1/2 (* eps (* eps 1/24)))) (* eps (* 1/6 (sin x))))) (sin (neg x)))) (fma.f64 x (fma.f64 x (fma.f64 eps (.f64 x (fma.f64 (.f64 eps eps) #s(literal -1/36 binary64) #s(literal 1/6 binary64))) (.f64 #s(literal -1/2 binary64) (.f64 eps (.f64 eps (fma.f64 eps (.f64 eps #s(literal 1/24 binary64)) #s(literal -1/2 binary64)))))) (.f64 eps (fma.f64 eps (.f64 eps #s(literal 1/6 binary64)) #s(literal -1 binary64)))) (.f64 eps (.f64 eps (fma.f64 eps (*.f64 eps #s(literal 1/24 binary64)) #s(literal -1/2 binary64)))))))
#s(approx (- (* (cos x) (cos eps)) (+ (* (sin x) (sin eps)) (cos x))) #s(approx (* eps (- (* eps (+ (* eps (* (sin x) 1/6)) (* (cos x) (+ (* eps (* eps 1/24)) -1/2)))) (sin x))) (fma.f64 x (fma.f64 x (fma.f64 x (.f64 eps (fma.f64 (.f64 eps eps) #s(literal -1/36 binary64) #s(literal 1/6 binary64))) (.f64 #s(literal -1/2 binary64) (.f64 (.f64 eps eps) (fma.f64 eps (.f64 eps #s(literal 1/24 binary64)) #s(literal -1/2 binary64))))) (.f64 eps (fma.f64 eps (.f64 eps #s(literal 1/6 binary64)) #s(literal -1 binary64)))) (.f64 (.f64 eps eps) (fma.f64 eps (*.f64 eps #s(literal 1/24 binary64)) #s(literal -1/2 binary64))))))
#s(approx (- (cos (+ x eps)) (cos x)) (+.f64 (cos.f64 eps) #s(literal -1 binary64)))
(-.f64 #s(approx (cos (+ x eps)) (cos.f64 x)) #s(approx (cos x) #s(literal 1 binary64)))
(-.f64 (cos.f64 (+.f64 x eps)) #s(approx (cos x) #s(literal 1 binary64)))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (sin.f64 x) (neg.f64 eps)))
#s(approx (- (* (cos x) (cos eps)) (+ (* (sin x) (sin eps)) (cos x))) (neg.f64 (*.f64 eps (sin.f64 x))))
#s(approx (- (* (cos x) (cos eps)) (+ (* (sin x) (sin eps)) (cos x))) (.f64 eps #s(approx (- ( eps (+ (* eps (* (sin x) 1/6)) (* (cos x) (+ (* eps (* eps 1/24)) -1/2)))) (sin x)) (sin.f64 (neg.f64 x)))))
#s(approx (- (* (cos x) (cos eps)) (+ (* (sin x) (sin eps)) (cos x))) (*.f64 eps (sin.f64 (neg.f64 x))))
#s(approx (- (* (cos x) (cos eps)) (+ (* (sin x) (sin eps)) (cos x))) (.f64 eps (-.f64 #s(approx ( eps (* -1/2 (cos x))) (*.f64 eps #s(literal -1/2 binary64))) (sin.f64 x))))
(-.f64 (cos.f64 (+.f64 x eps)) #s(approx (cos x) (fma.f64 x (*.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64))))
#s(approx (- (* (cos x) (cos eps)) (+ (* (sin x) (sin eps)) (cos x))) (.f64 eps (-.f64 #s(approx ( eps (* -1/2 (cos x))) (.f64 eps (fma.f64 #s(literal 1/4 binary64) (.f64 x x) #s(literal -1/2 binary64)))) (sin.f64 x))))

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

Calls

3 calls:

12.0ms	eps
12.0ms	x
11.0ms	(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))

Results

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

Compiler

Compiled 15 to 10 computations (33.3% saved)

regimes36.0ms (0.2%)

Memory

0.9MiB live, 39.3MiB allocated

Counts

44 → 1

Calls

Call 1

Inputs
#s(approx (- (cos (+ x eps)) (cos x)) (+.f64 #s(approx (cos eps) #s(literal 1 binary64)) #s(literal -1 binary64)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* eps (+ (* eps (+ (* (cos x) (+ -1/2 (* eps (* eps 1/24)))) (* eps (* 1/6 (sin x))))) (sin (neg x)))) #s(approx (+ (* eps (* eps (+ (* eps (* eps 1/24)) -1/2))) (* eps (* x (+ (* eps (* eps 1/6)) -1)))) (*.f64 x (neg.f64 eps)))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (+ (cos eps) -1) (.f64 eps (.f64 eps #s(literal -1/2 binary64)))))
#s(approx (- (* (cos x) (cos eps)) (+ (* (sin x) (sin eps)) (cos x))) (.f64 eps #s(approx (- ( eps (* -1/2 (cos x))) (sin x)) (*.f64 eps #s(literal -1/2 binary64)))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* eps (+ (* eps (+ (* (cos x) (+ -1/2 (* eps (* eps 1/24)))) (* eps (* 1/6 (sin x))))) (sin (neg x)))) #s(approx (+ (* eps (* eps (+ (* eps (* eps 1/24)) -1/2))) (* eps (* x (+ (* eps (* eps 1/6)) -1)))) (.f64 eps (-.f64 (.f64 eps #s(literal -1/2 binary64)) x)))))
#s(approx (- (* (cos x) (cos eps)) (+ (* (sin x) (sin eps)) (cos x))) (.f64 eps #s(approx (- ( eps (* -1/2 (cos x))) (sin x)) (-.f64 (*.f64 eps #s(literal -1/2 binary64)) x))))
#s(approx (- (cos (+ x eps)) (cos x)) (+.f64 #s(approx (cos eps) (fma.f64 eps (*.f64 eps #s(literal -1/2 binary64)) #s(literal 1 binary64))) #s(literal -1 binary64)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* eps (+ (* eps (+ (* (cos x) (+ -1/2 (* eps (* eps 1/24)))) (* eps (* 1/6 (sin x))))) (sin (neg x)))) #s(approx (+ (* eps (* eps (+ (* eps (* eps 1/24)) -1/2))) (* eps (* x (+ (* eps (* eps 1/6)) -1)))) #s(approx (* (* (* eps eps) (* eps eps)) (+ (* x (/ 1/6 eps)) 1/24)) (.f64 x (.f64 eps (.f64 eps (.f64 eps #s(literal 1/6 binary64)))))))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* eps (+ (* eps (+ (* (cos x) (+ -1/2 (* eps (* eps 1/24)))) (* eps (* 1/6 (sin x))))) (sin (neg x)))) #s(approx (+ (* eps (* eps (+ (* eps (* eps 1/24)) -1/2))) (* eps (* x (+ (* eps (* eps 1/6)) -1)))) (.f64 #s(literal 1/24 binary64) (.f64 (.f64 eps eps) (.f64 eps eps))))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps #s(approx (+ ( eps (+ (* (cos x) (+ -1/2 (* eps (* eps 1/24)))) (* eps (* 1/6 (sin x))))) (sin (neg x))) #s(approx (+ (* x (+ (* x (+ (* eps (* (+ (* eps (* eps 1/24)) -1/2) -1/2)) (* x (+ (* (* eps eps) -1/36) 1/6)))) (+ (* eps (* eps 1/6)) -1))) (* eps (+ (* eps (* eps 1/24)) -1/2))) (.f64 x (fma.f64 x (.f64 x #s(literal 1/6 binary64)) #s(literal -1 binary64)))))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* eps (+ (* eps (+ (* (cos x) (+ -1/2 (* eps (* eps 1/24)))) (* eps (* 1/6 (sin x))))) (sin (neg x)))) #s(approx (+ (* eps (* eps (+ (* eps (* eps 1/24)) -1/2))) (* eps (* x (+ (* eps (* eps 1/6)) -1)))) (.f64 eps (fma.f64 eps (fma.f64 x (.f64 eps #s(literal 1/6 binary64)) #s(literal -1/2 binary64)) (neg.f64 x))))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* eps (+ (* eps (+ (* (cos x) (+ -1/2 (* eps (* eps 1/24)))) (* eps (* 1/6 (sin x))))) (sin (neg x)))) #s(approx (+ (* eps (* eps (+ (* eps (* eps 1/24)) -1/2))) (* eps (* x (+ (* eps (* eps 1/6)) -1)))) #s(approx (* (* (* eps eps) (* eps eps)) (+ (* x (/ 1/6 eps)) 1/24)) (.f64 (.f64 eps eps) (.f64 eps (fma.f64 eps #s(literal 1/24 binary64) (.f64 x #s(literal 1/6 binary64)))))))))
#s(approx (- (* (cos x) (cos eps)) (+ (* (sin x) (sin eps)) (cos x))) (.f64 eps #s(approx (- ( eps (* -1/2 (cos x))) (sin x)) (fma.f64 x (fma.f64 #s(literal 1/4 binary64) (.f64 eps x) #s(literal -1 binary64)) (.f64 eps #s(literal -1/2 binary64))))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* eps (+ (* eps (+ (* (cos x) (+ -1/2 (* eps (* eps 1/24)))) (* eps (* 1/6 (sin x))))) (sin (neg x)))) (fma.f64 eps #s(approx (* eps (+ (* eps (* eps 1/24)) -1/2)) (.f64 eps #s(literal -1/2 binary64))) (.f64 eps (.f64 x (fma.f64 eps (.f64 eps #s(literal 1/6 binary64)) #s(literal -1 binary64)))))))
#s(approx (- (* (cos x) (cos eps)) (+ (* (sin x) (sin eps)) (cos x))) (.f64 eps #s(approx (- ( eps (* -1/2 (cos x))) (sin x)) (fma.f64 x (fma.f64 x (fma.f64 eps #s(literal 1/4 binary64) (.f64 x #s(literal 1/6 binary64))) #s(literal -1 binary64)) (.f64 eps #s(literal -1/2 binary64))))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* eps (+ (* eps (+ (* (cos x) (+ -1/2 (* eps (* eps 1/24)))) (* eps (* 1/6 (sin x))))) (sin (neg x)))) #s(approx (+ (* eps (* eps (+ (* eps (* eps 1/24)) -1/2))) (* eps (* x (+ (* eps (* eps 1/6)) -1)))) (.f64 (.f64 (.f64 eps eps) (.f64 eps eps)) (fma.f64 x (/.f64 #s(literal 1/6 binary64) eps) #s(literal 1/24 binary64))))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps #s(approx (+ ( eps (+ (* (cos x) (+ -1/2 (* eps (* eps 1/24)))) (* eps (* 1/6 (sin x))))) (sin (neg x))) (fma.f64 eps (fma.f64 eps (.f64 eps #s(literal 1/24 binary64)) #s(literal -1/2 binary64)) (.f64 x (fma.f64 eps (*.f64 eps #s(literal 1/6 binary64)) #s(literal -1 binary64)))))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* eps (+ (* eps (+ (* (cos x) (+ -1/2 (* eps (* eps 1/24)))) (* eps (* 1/6 (sin x))))) (sin (neg x)))) (fma.f64 eps (.f64 eps (fma.f64 eps (.f64 eps #s(literal 1/24 binary64)) #s(literal -1/2 binary64))) (.f64 eps (.f64 x (fma.f64 eps (*.f64 eps #s(literal 1/6 binary64)) #s(literal -1 binary64)))))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* eps (+ (* eps (+ (* (cos x) (+ -1/2 (* eps (* eps 1/24)))) (* eps (* 1/6 (sin x))))) (sin (neg x)))) (fma.f64 (.f64 x (fma.f64 eps (.f64 eps #s(literal 1/6 binary64)) #s(literal -1 binary64))) eps (.f64 eps (.f64 eps (fma.f64 #s(literal 1/24 binary64) (*.f64 eps eps) #s(literal -1/2 binary64)))))))
#s(approx (- (* (cos x) (cos eps)) (+ (* (sin x) (sin eps)) (cos x))) #s(approx (* eps (- (* eps (* -1/2 (cos x))) (sin x))) (fma.f64 x (fma.f64 x (fma.f64 eps (.f64 x #s(literal 1/6 binary64)) (.f64 eps (.f64 eps #s(literal 1/4 binary64)))) (neg.f64 eps)) (.f64 #s(literal -1/2 binary64) (*.f64 eps eps)))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* eps (+ (* eps (+ (* (cos x) (+ -1/2 (* eps (* eps 1/24)))) (* eps (* 1/6 (sin x))))) (sin (neg x)))) #s(approx (+ (* eps (* eps (+ (* eps (* eps 1/24)) -1/2))) (* eps (* x (+ (* eps (* eps 1/6)) -1)))) (.f64 (.f64 (.f64 eps eps) (.f64 eps eps)) (-.f64 #s(literal 1/24 binary64) (/.f64 (fma.f64 x #s(literal -1/6 binary64) (/.f64 #s(literal 1/2 binary64) eps)) eps))))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* eps (+ (* eps (+ (* (cos x) (+ -1/2 (* eps (* eps 1/24)))) (* eps (* 1/6 (sin x))))) (sin (neg x)))) #s(approx (+ (* eps (* eps (+ (* eps (* eps 1/24)) -1/2))) (* eps (* x (+ (* eps (* eps 1/6)) -1)))) #s(approx (* (* (* eps eps) (* eps eps)) (+ (* x (/ 1/6 eps)) 1/24)) (.f64 x (fma.f64 eps (.f64 eps (.f64 eps #s(literal 1/6 binary64))) (/.f64 (.f64 eps (.f64 eps (.f64 #s(literal 1/24 binary64) (*.f64 eps eps)))) x)))))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* eps (+ (* eps (+ (* (cos x) (+ -1/2 (* eps (* eps 1/24)))) (* eps (* 1/6 (sin x))))) (sin (neg x)))) #s(approx (+ (* eps (* eps (+ (* eps (* eps 1/24)) -1/2))) (* eps (* x (+ (* eps (* eps 1/6)) -1)))) (.f64 x (fma.f64 eps (fma.f64 eps (.f64 eps #s(literal 1/6 binary64)) #s(literal -1 binary64)) (.f64 (.f64 eps eps) (/.f64 (fma.f64 #s(literal 1/24 binary64) (*.f64 eps eps) #s(literal -1/2 binary64)) x)))))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* eps (+ (* eps (+ (* (cos x) (+ -1/2 (* eps (* eps 1/24)))) (* eps (* 1/6 (sin x))))) (sin (neg x)))) #s(approx (+ (* eps (* eps (+ (* eps (* eps 1/24)) -1/2))) (* eps (* x (+ (* eps (* eps 1/6)) -1)))) (.f64 (.f64 (.f64 eps eps) (.f64 eps eps)) (+.f64 #s(literal 1/24 binary64) (fma.f64 x (/.f64 #s(literal 1/6 binary64) eps) (/.f64 #s(literal -1/2 binary64) (*.f64 eps eps))))))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps #s(approx (+ ( eps (+ (* (cos x) (+ -1/2 (* eps (* eps 1/24)))) (* eps (* 1/6 (sin x))))) (sin (neg x))) #s(approx (+ (* x (+ (* x (+ (* eps (* (+ (* eps (* eps 1/24)) -1/2) -1/2)) (* x (+ (* (* eps eps) -1/36) 1/6)))) (+ (* eps (* eps 1/6)) -1))) (* eps (+ (* eps (* eps 1/24)) -1/2))) (.f64 (.f64 eps eps) (.f64 eps (fma.f64 x (/.f64 (fma.f64 #s(literal -1/36 binary64) (.f64 x x) #s(literal 1/6 binary64)) eps) (fma.f64 x (*.f64 x #s(literal -1/48 binary64)) #s(literal 1/24 binary64)))))))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps #s(approx (+ ( eps (+ (* (cos x) (+ -1/2 (* eps (* eps 1/24)))) (* eps (* 1/6 (sin x))))) (sin (neg x))) #s(approx (+ (* x (+ (* x (+ (* eps (* (+ (* eps (* eps 1/24)) -1/2) -1/2)) (* x (+ (* (* eps eps) -1/36) 1/6)))) (+ (* eps (* eps 1/6)) -1))) (* eps (+ (* eps (* eps 1/24)) -1/2))) (fma.f64 eps (fma.f64 eps (.f64 x (fma.f64 #s(literal -1/36 binary64) (.f64 x x) #s(literal 1/6 binary64))) (fma.f64 #s(literal 1/4 binary64) (.f64 x x) #s(literal -1/2 binary64))) (.f64 x (fma.f64 x (*.f64 x #s(literal 1/6 binary64)) #s(literal -1 binary64))))))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps #s(approx (+ ( eps (+ (* (cos x) (+ -1/2 (* eps (* eps 1/24)))) (* eps (* 1/6 (sin x))))) (sin (neg x))) #s(approx (+ (* x (+ (* x (+ (* eps (* (+ (* eps (* eps 1/24)) -1/2) -1/2)) (* x (+ (* (* eps eps) -1/36) 1/6)))) (+ (* eps (* eps 1/6)) -1))) (* eps (+ (* eps (* eps 1/24)) -1/2))) (neg.f64 (.f64 (.f64 eps (.f64 eps eps)) (-.f64 (fma.f64 x (.f64 x #s(literal 1/48 binary64)) #s(literal -1/24 binary64)) (.f64 x (/.f64 (fma.f64 #s(literal -1/36 binary64) (.f64 x x) #s(literal 1/6 binary64)) eps)))))))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* eps (+ (* eps (+ (* (cos x) (+ -1/2 (* eps (* eps 1/24)))) (* eps (* 1/6 (sin x))))) (sin (neg x)))) #s(approx (+ (* eps (* eps (+ (* eps (* eps 1/24)) -1/2))) (* eps (* x (+ (* eps (* eps 1/6)) -1)))) (.f64 (.f64 (.f64 eps eps) (.f64 eps eps)) (-.f64 #s(literal 1/24 binary64) (/.f64 (fma.f64 x #s(literal -1/6 binary64) (/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 x eps)) eps)) eps))))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps #s(approx (+ ( eps (+ (* (cos x) (+ -1/2 (* eps (* eps 1/24)))) (* eps (* 1/6 (sin x))))) (sin (neg x))) (fma.f64 eps (fma.f64 eps (.f64 eps #s(literal 1/24 binary64)) #s(literal -1/2 binary64)) (.f64 x (fma.f64 eps (.f64 eps #s(literal 1/6 binary64)) (fma.f64 (.f64 x (fma.f64 eps (.f64 eps #s(literal 1/24 binary64)) #s(literal -1/2 binary64))) (.f64 eps #s(literal -1/2 binary64)) #s(literal -1 binary64))))))))
#s(approx (- (* (cos x) (cos eps)) (+ (* (sin x) (sin eps)) (cos x))) (.f64 eps #s(approx (- ( eps (+ (* eps (* (sin x) 1/6)) (* (cos x) (+ (* eps (* eps 1/24)) -1/2)))) (sin x)) (fma.f64 x (fma.f64 eps (.f64 (.f64 x (fma.f64 eps (.f64 eps #s(literal 1/24 binary64)) #s(literal -1/2 binary64))) #s(literal -1/2 binary64)) (fma.f64 eps (.f64 eps #s(literal 1/6 binary64)) #s(literal -1 binary64))) (.f64 eps (fma.f64 eps (.f64 eps #s(literal 1/24 binary64)) #s(literal -1/2 binary64)))))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps #s(approx (+ ( eps (+ (* (cos x) (+ -1/2 (* eps (* eps 1/24)))) (* eps (* 1/6 (sin x))))) (sin (neg x))) (fma.f64 x (fma.f64 x (fma.f64 eps #s(approx (* (+ (* eps (* eps 1/24)) -1/2) -1/2) #s(literal 1/4 binary64)) (.f64 x (fma.f64 (.f64 eps eps) #s(literal -1/36 binary64) #s(literal 1/6 binary64)))) (fma.f64 eps (.f64 eps #s(literal 1/6 binary64)) #s(literal -1 binary64))) (.f64 eps (fma.f64 eps (*.f64 eps #s(literal 1/24 binary64)) #s(literal -1/2 binary64)))))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps #s(approx (+ ( eps (+ (* (cos x) (+ -1/2 (* eps (* eps 1/24)))) (* eps (* 1/6 (sin x))))) (sin (neg x))) (fma.f64 x (fma.f64 x (fma.f64 eps #s(approx (* (+ (* eps (* eps 1/24)) -1/2) -1/2) (.f64 #s(literal -1/48 binary64) (.f64 eps eps))) (.f64 x (fma.f64 (.f64 eps eps) #s(literal -1/36 binary64) #s(literal 1/6 binary64)))) (fma.f64 eps (.f64 eps #s(literal 1/6 binary64)) #s(literal -1 binary64))) (.f64 eps (fma.f64 eps (*.f64 eps #s(literal 1/24 binary64)) #s(literal -1/2 binary64)))))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* eps (+ (* eps (+ (* (cos x) (+ -1/2 (* eps (* eps 1/24)))) (* eps (* 1/6 (sin x))))) (sin (neg x)))) #s(approx (+ (* eps (* eps (+ (* eps (* eps 1/24)) -1/2))) (* eps (* x (+ (* eps (* eps 1/6)) -1)))) (.f64 (.f64 (.f64 eps eps) (.f64 eps eps)) (+.f64 (fma.f64 x (/.f64 #s(literal 1/6 binary64) eps) (-.f64 #s(literal 1/24 binary64) (/.f64 x (.f64 eps (.f64 eps eps))))) (/.f64 #s(literal -1/2 binary64) (*.f64 eps eps)))))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps #s(approx (+ ( eps (+ (* (cos x) (+ -1/2 (* eps (* eps 1/24)))) (* eps (* 1/6 (sin x))))) (sin (neg x))) (fma.f64 x (fma.f64 x (fma.f64 eps (.f64 (fma.f64 eps (.f64 eps #s(literal 1/24 binary64)) #s(literal -1/2 binary64)) #s(literal -1/2 binary64)) (.f64 x (fma.f64 (.f64 eps eps) #s(literal -1/36 binary64) #s(literal 1/6 binary64)))) (fma.f64 eps (.f64 eps #s(literal 1/6 binary64)) #s(literal -1 binary64))) (.f64 eps (fma.f64 eps (*.f64 eps #s(literal 1/24 binary64)) #s(literal -1/2 binary64)))))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps #s(approx (+ ( eps (+ (* (cos x) (+ -1/2 (* eps (* eps 1/24)))) (* eps (* 1/6 (sin x))))) (sin (neg x))) #s(approx (+ (* x (+ (* x (+ (* eps (* (+ (* eps (* eps 1/24)) -1/2) -1/2)) (* x (+ (* (* eps eps) -1/36) 1/6)))) (+ (* eps (* eps 1/6)) -1))) (* eps (+ (* eps (* eps 1/24)) -1/2))) (neg.f64 (.f64 (.f64 eps (.f64 eps eps)) (-.f64 (fma.f64 x (.f64 x #s(literal 1/48 binary64)) #s(literal -1/24 binary64)) (/.f64 (-.f64 (.f64 x (fma.f64 #s(literal -1/36 binary64) (.f64 x x) #s(literal 1/6 binary64))) (/.f64 (fma.f64 (*.f64 x x) #s(literal -1/4 binary64) #s(literal 1/2 binary64)) eps)) eps))))))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* eps (+ (* eps (+ (* (cos x) (+ -1/2 (* eps (* eps 1/24)))) (* eps (* 1/6 (sin x))))) (sin (neg x)))) (fma.f64 x (fma.f64 x (fma.f64 eps (.f64 x (fma.f64 (.f64 eps eps) #s(literal -1/36 binary64) #s(literal 1/6 binary64))) (.f64 #s(literal -1/2 binary64) (.f64 eps (.f64 eps (fma.f64 eps (.f64 eps #s(literal 1/24 binary64)) #s(literal -1/2 binary64)))))) (.f64 eps (fma.f64 eps (.f64 eps #s(literal 1/6 binary64)) #s(literal -1 binary64)))) (.f64 eps (.f64 eps (fma.f64 eps (*.f64 eps #s(literal 1/24 binary64)) #s(literal -1/2 binary64)))))))
#s(approx (- (* (cos x) (cos eps)) (+ (* (sin x) (sin eps)) (cos x))) #s(approx (* eps (- (* eps (+ (* eps (* (sin x) 1/6)) (* (cos x) (+ (* eps (* eps 1/24)) -1/2)))) (sin x))) (fma.f64 x (fma.f64 x (fma.f64 x (.f64 eps (fma.f64 (.f64 eps eps) #s(literal -1/36 binary64) #s(literal 1/6 binary64))) (.f64 #s(literal -1/2 binary64) (.f64 (.f64 eps eps) (fma.f64 eps (.f64 eps #s(literal 1/24 binary64)) #s(literal -1/2 binary64))))) (.f64 eps (fma.f64 eps (.f64 eps #s(literal 1/6 binary64)) #s(literal -1 binary64)))) (.f64 (.f64 eps eps) (fma.f64 eps (*.f64 eps #s(literal 1/24 binary64)) #s(literal -1/2 binary64))))))
#s(approx (- (cos (+ x eps)) (cos x)) (+.f64 (cos.f64 eps) #s(literal -1 binary64)))
(-.f64 #s(approx (cos (+ x eps)) (cos.f64 x)) #s(approx (cos x) #s(literal 1 binary64)))
(-.f64 (cos.f64 (+.f64 x eps)) #s(approx (cos x) #s(literal 1 binary64)))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (sin.f64 x) (neg.f64 eps)))
#s(approx (- (* (cos x) (cos eps)) (+ (* (sin x) (sin eps)) (cos x))) (neg.f64 (*.f64 eps (sin.f64 x))))
#s(approx (- (* (cos x) (cos eps)) (+ (* (sin x) (sin eps)) (cos x))) (.f64 eps #s(approx (- ( eps (+ (* eps (* (sin x) 1/6)) (* (cos x) (+ (* eps (* eps 1/24)) -1/2)))) (sin x)) (sin.f64 (neg.f64 x)))))
#s(approx (- (* (cos x) (cos eps)) (+ (* (sin x) (sin eps)) (cos x))) (*.f64 eps (sin.f64 (neg.f64 x))))

Outputs

#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* eps (+ (* eps (+ (* (cos x) (+ -1/2 (* eps (* eps 1/24)))) (* eps (* 1/6 (sin x))))) (sin (neg x)))) (fma.f64 x (fma.f64 x (fma.f64 eps (*.f64 x (fma.f64 (*.f64 eps eps) #s(literal -1/36 binary64) #s(literal 1/6 binary64))) (*.f64 #s(literal -1/2 binary64) (*.f64 eps (*.f64 eps (fma.f64 eps (*.f64 eps #s(literal 1/24 binary64)) #s(literal -1/2 binary64)))))) (*.f64 eps (fma.f64 eps (*.f64 eps #s(literal 1/6 binary64)) #s(literal -1 binary64)))) (*.f64 eps (*.f64 eps (fma.f64 eps (*.f64 eps #s(literal 1/24 binary64)) #s(literal -1/2 binary64)))))))

Calls

3 calls:

13.0ms	eps
11.0ms	x
9.0ms	(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))

Results

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

Compiler

Compiled 15 to 10 computations (33.3% saved)

regimes29.0ms (0.2%)

Memory

-6.5MiB live, 32.7MiB allocated

Counts

35 → 1

Calls

Call 1

Inputs
#s(approx (- (cos (+ x eps)) (cos x)) (+.f64 #s(approx (cos eps) #s(literal 1 binary64)) #s(literal -1 binary64)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* eps (+ (* eps (+ (* (cos x) (+ -1/2 (* eps (* eps 1/24)))) (* eps (* 1/6 (sin x))))) (sin (neg x)))) #s(approx (+ (* eps (* eps (+ (* eps (* eps 1/24)) -1/2))) (* eps (* x (+ (* eps (* eps 1/6)) -1)))) (*.f64 x (neg.f64 eps)))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (+ (cos eps) -1) (.f64 eps (.f64 eps #s(literal -1/2 binary64)))))
#s(approx (- (* (cos x) (cos eps)) (+ (* (sin x) (sin eps)) (cos x))) (.f64 eps #s(approx (- ( eps (* -1/2 (cos x))) (sin x)) (*.f64 eps #s(literal -1/2 binary64)))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* eps (+ (* eps (+ (* (cos x) (+ -1/2 (* eps (* eps 1/24)))) (* eps (* 1/6 (sin x))))) (sin (neg x)))) #s(approx (+ (* eps (* eps (+ (* eps (* eps 1/24)) -1/2))) (* eps (* x (+ (* eps (* eps 1/6)) -1)))) (.f64 eps (-.f64 (.f64 eps #s(literal -1/2 binary64)) x)))))
#s(approx (- (* (cos x) (cos eps)) (+ (* (sin x) (sin eps)) (cos x))) (.f64 eps #s(approx (- ( eps (* -1/2 (cos x))) (sin x)) (-.f64 (*.f64 eps #s(literal -1/2 binary64)) x))))
#s(approx (- (cos (+ x eps)) (cos x)) (+.f64 #s(approx (cos eps) (fma.f64 eps (*.f64 eps #s(literal -1/2 binary64)) #s(literal 1 binary64))) #s(literal -1 binary64)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* eps (+ (* eps (+ (* (cos x) (+ -1/2 (* eps (* eps 1/24)))) (* eps (* 1/6 (sin x))))) (sin (neg x)))) #s(approx (+ (* eps (* eps (+ (* eps (* eps 1/24)) -1/2))) (* eps (* x (+ (* eps (* eps 1/6)) -1)))) #s(approx (* (* (* eps eps) (* eps eps)) (+ (* x (/ 1/6 eps)) 1/24)) (.f64 x (.f64 eps (.f64 eps (.f64 eps #s(literal 1/6 binary64)))))))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* eps (+ (* eps (+ (* (cos x) (+ -1/2 (* eps (* eps 1/24)))) (* eps (* 1/6 (sin x))))) (sin (neg x)))) #s(approx (+ (* eps (* eps (+ (* eps (* eps 1/24)) -1/2))) (* eps (* x (+ (* eps (* eps 1/6)) -1)))) (.f64 #s(literal 1/24 binary64) (.f64 (.f64 eps eps) (.f64 eps eps))))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps #s(approx (+ ( eps (+ (* (cos x) (+ -1/2 (* eps (* eps 1/24)))) (* eps (* 1/6 (sin x))))) (sin (neg x))) #s(approx (+ (* x (+ (* x (+ (* eps (* (+ (* eps (* eps 1/24)) -1/2) -1/2)) (* x (+ (* (* eps eps) -1/36) 1/6)))) (+ (* eps (* eps 1/6)) -1))) (* eps (+ (* eps (* eps 1/24)) -1/2))) (.f64 x (fma.f64 x (.f64 x #s(literal 1/6 binary64)) #s(literal -1 binary64)))))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* eps (+ (* eps (+ (* (cos x) (+ -1/2 (* eps (* eps 1/24)))) (* eps (* 1/6 (sin x))))) (sin (neg x)))) #s(approx (+ (* eps (* eps (+ (* eps (* eps 1/24)) -1/2))) (* eps (* x (+ (* eps (* eps 1/6)) -1)))) (.f64 eps (fma.f64 eps (fma.f64 x (.f64 eps #s(literal 1/6 binary64)) #s(literal -1/2 binary64)) (neg.f64 x))))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* eps (+ (* eps (+ (* (cos x) (+ -1/2 (* eps (* eps 1/24)))) (* eps (* 1/6 (sin x))))) (sin (neg x)))) #s(approx (+ (* eps (* eps (+ (* eps (* eps 1/24)) -1/2))) (* eps (* x (+ (* eps (* eps 1/6)) -1)))) #s(approx (* (* (* eps eps) (* eps eps)) (+ (* x (/ 1/6 eps)) 1/24)) (.f64 (.f64 eps eps) (.f64 eps (fma.f64 eps #s(literal 1/24 binary64) (.f64 x #s(literal 1/6 binary64)))))))))
#s(approx (- (* (cos x) (cos eps)) (+ (* (sin x) (sin eps)) (cos x))) (.f64 eps #s(approx (- ( eps (* -1/2 (cos x))) (sin x)) (fma.f64 x (fma.f64 #s(literal 1/4 binary64) (.f64 eps x) #s(literal -1 binary64)) (.f64 eps #s(literal -1/2 binary64))))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* eps (+ (* eps (+ (* (cos x) (+ -1/2 (* eps (* eps 1/24)))) (* eps (* 1/6 (sin x))))) (sin (neg x)))) (fma.f64 eps #s(approx (* eps (+ (* eps (* eps 1/24)) -1/2)) (.f64 eps #s(literal -1/2 binary64))) (.f64 eps (.f64 x (fma.f64 eps (.f64 eps #s(literal 1/6 binary64)) #s(literal -1 binary64)))))))
#s(approx (- (* (cos x) (cos eps)) (+ (* (sin x) (sin eps)) (cos x))) (.f64 eps #s(approx (- ( eps (* -1/2 (cos x))) (sin x)) (fma.f64 x (fma.f64 x (fma.f64 eps #s(literal 1/4 binary64) (.f64 x #s(literal 1/6 binary64))) #s(literal -1 binary64)) (.f64 eps #s(literal -1/2 binary64))))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* eps (+ (* eps (+ (* (cos x) (+ -1/2 (* eps (* eps 1/24)))) (* eps (* 1/6 (sin x))))) (sin (neg x)))) #s(approx (+ (* eps (* eps (+ (* eps (* eps 1/24)) -1/2))) (* eps (* x (+ (* eps (* eps 1/6)) -1)))) (.f64 (.f64 (.f64 eps eps) (.f64 eps eps)) (fma.f64 x (/.f64 #s(literal 1/6 binary64) eps) #s(literal 1/24 binary64))))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps #s(approx (+ ( eps (+ (* (cos x) (+ -1/2 (* eps (* eps 1/24)))) (* eps (* 1/6 (sin x))))) (sin (neg x))) (fma.f64 eps (fma.f64 eps (.f64 eps #s(literal 1/24 binary64)) #s(literal -1/2 binary64)) (.f64 x (fma.f64 eps (*.f64 eps #s(literal 1/6 binary64)) #s(literal -1 binary64)))))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* eps (+ (* eps (+ (* (cos x) (+ -1/2 (* eps (* eps 1/24)))) (* eps (* 1/6 (sin x))))) (sin (neg x)))) (fma.f64 eps (.f64 eps (fma.f64 eps (.f64 eps #s(literal 1/24 binary64)) #s(literal -1/2 binary64))) (.f64 eps (.f64 x (fma.f64 eps (*.f64 eps #s(literal 1/6 binary64)) #s(literal -1 binary64)))))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* eps (+ (* eps (+ (* (cos x) (+ -1/2 (* eps (* eps 1/24)))) (* eps (* 1/6 (sin x))))) (sin (neg x)))) (fma.f64 (.f64 x (fma.f64 eps (.f64 eps #s(literal 1/6 binary64)) #s(literal -1 binary64))) eps (.f64 eps (.f64 eps (fma.f64 #s(literal 1/24 binary64) (*.f64 eps eps) #s(literal -1/2 binary64)))))))
#s(approx (- (* (cos x) (cos eps)) (+ (* (sin x) (sin eps)) (cos x))) #s(approx (* eps (- (* eps (* -1/2 (cos x))) (sin x))) (fma.f64 x (fma.f64 x (fma.f64 eps (.f64 x #s(literal 1/6 binary64)) (.f64 eps (.f64 eps #s(literal 1/4 binary64)))) (neg.f64 eps)) (.f64 #s(literal -1/2 binary64) (*.f64 eps eps)))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* eps (+ (* eps (+ (* (cos x) (+ -1/2 (* eps (* eps 1/24)))) (* eps (* 1/6 (sin x))))) (sin (neg x)))) #s(approx (+ (* eps (* eps (+ (* eps (* eps 1/24)) -1/2))) (* eps (* x (+ (* eps (* eps 1/6)) -1)))) (.f64 (.f64 (.f64 eps eps) (.f64 eps eps)) (-.f64 #s(literal 1/24 binary64) (/.f64 (fma.f64 x #s(literal -1/6 binary64) (/.f64 #s(literal 1/2 binary64) eps)) eps))))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* eps (+ (* eps (+ (* (cos x) (+ -1/2 (* eps (* eps 1/24)))) (* eps (* 1/6 (sin x))))) (sin (neg x)))) #s(approx (+ (* eps (* eps (+ (* eps (* eps 1/24)) -1/2))) (* eps (* x (+ (* eps (* eps 1/6)) -1)))) #s(approx (* (* (* eps eps) (* eps eps)) (+ (* x (/ 1/6 eps)) 1/24)) (.f64 x (fma.f64 eps (.f64 eps (.f64 eps #s(literal 1/6 binary64))) (/.f64 (.f64 eps (.f64 eps (.f64 #s(literal 1/24 binary64) (*.f64 eps eps)))) x)))))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* eps (+ (* eps (+ (* (cos x) (+ -1/2 (* eps (* eps 1/24)))) (* eps (* 1/6 (sin x))))) (sin (neg x)))) #s(approx (+ (* eps (* eps (+ (* eps (* eps 1/24)) -1/2))) (* eps (* x (+ (* eps (* eps 1/6)) -1)))) (.f64 x (fma.f64 eps (fma.f64 eps (.f64 eps #s(literal 1/6 binary64)) #s(literal -1 binary64)) (.f64 (.f64 eps eps) (/.f64 (fma.f64 #s(literal 1/24 binary64) (*.f64 eps eps) #s(literal -1/2 binary64)) x)))))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* eps (+ (* eps (+ (* (cos x) (+ -1/2 (* eps (* eps 1/24)))) (* eps (* 1/6 (sin x))))) (sin (neg x)))) #s(approx (+ (* eps (* eps (+ (* eps (* eps 1/24)) -1/2))) (* eps (* x (+ (* eps (* eps 1/6)) -1)))) (.f64 (.f64 (.f64 eps eps) (.f64 eps eps)) (+.f64 #s(literal 1/24 binary64) (fma.f64 x (/.f64 #s(literal 1/6 binary64) eps) (/.f64 #s(literal -1/2 binary64) (*.f64 eps eps))))))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps #s(approx (+ ( eps (+ (* (cos x) (+ -1/2 (* eps (* eps 1/24)))) (* eps (* 1/6 (sin x))))) (sin (neg x))) #s(approx (+ (* x (+ (* x (+ (* eps (* (+ (* eps (* eps 1/24)) -1/2) -1/2)) (* x (+ (* (* eps eps) -1/36) 1/6)))) (+ (* eps (* eps 1/6)) -1))) (* eps (+ (* eps (* eps 1/24)) -1/2))) (.f64 (.f64 eps eps) (.f64 eps (fma.f64 x (/.f64 (fma.f64 #s(literal -1/36 binary64) (.f64 x x) #s(literal 1/6 binary64)) eps) (fma.f64 x (*.f64 x #s(literal -1/48 binary64)) #s(literal 1/24 binary64)))))))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps #s(approx (+ ( eps (+ (* (cos x) (+ -1/2 (* eps (* eps 1/24)))) (* eps (* 1/6 (sin x))))) (sin (neg x))) #s(approx (+ (* x (+ (* x (+ (* eps (* (+ (* eps (* eps 1/24)) -1/2) -1/2)) (* x (+ (* (* eps eps) -1/36) 1/6)))) (+ (* eps (* eps 1/6)) -1))) (* eps (+ (* eps (* eps 1/24)) -1/2))) (fma.f64 eps (fma.f64 eps (.f64 x (fma.f64 #s(literal -1/36 binary64) (.f64 x x) #s(literal 1/6 binary64))) (fma.f64 #s(literal 1/4 binary64) (.f64 x x) #s(literal -1/2 binary64))) (.f64 x (fma.f64 x (*.f64 x #s(literal 1/6 binary64)) #s(literal -1 binary64))))))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps #s(approx (+ ( eps (+ (* (cos x) (+ -1/2 (* eps (* eps 1/24)))) (* eps (* 1/6 (sin x))))) (sin (neg x))) #s(approx (+ (* x (+ (* x (+ (* eps (* (+ (* eps (* eps 1/24)) -1/2) -1/2)) (* x (+ (* (* eps eps) -1/36) 1/6)))) (+ (* eps (* eps 1/6)) -1))) (* eps (+ (* eps (* eps 1/24)) -1/2))) (neg.f64 (.f64 (.f64 eps (.f64 eps eps)) (-.f64 (fma.f64 x (.f64 x #s(literal 1/48 binary64)) #s(literal -1/24 binary64)) (.f64 x (/.f64 (fma.f64 #s(literal -1/36 binary64) (.f64 x x) #s(literal 1/6 binary64)) eps)))))))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* eps (+ (* eps (+ (* (cos x) (+ -1/2 (* eps (* eps 1/24)))) (* eps (* 1/6 (sin x))))) (sin (neg x)))) #s(approx (+ (* eps (* eps (+ (* eps (* eps 1/24)) -1/2))) (* eps (* x (+ (* eps (* eps 1/6)) -1)))) (.f64 (.f64 (.f64 eps eps) (.f64 eps eps)) (-.f64 #s(literal 1/24 binary64) (/.f64 (fma.f64 x #s(literal -1/6 binary64) (/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 x eps)) eps)) eps))))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps #s(approx (+ ( eps (+ (* (cos x) (+ -1/2 (* eps (* eps 1/24)))) (* eps (* 1/6 (sin x))))) (sin (neg x))) (fma.f64 eps (fma.f64 eps (.f64 eps #s(literal 1/24 binary64)) #s(literal -1/2 binary64)) (.f64 x (fma.f64 eps (.f64 eps #s(literal 1/6 binary64)) (fma.f64 (.f64 x (fma.f64 eps (.f64 eps #s(literal 1/24 binary64)) #s(literal -1/2 binary64))) (.f64 eps #s(literal -1/2 binary64)) #s(literal -1 binary64))))))))
#s(approx (- (* (cos x) (cos eps)) (+ (* (sin x) (sin eps)) (cos x))) (.f64 eps #s(approx (- ( eps (+ (* eps (* (sin x) 1/6)) (* (cos x) (+ (* eps (* eps 1/24)) -1/2)))) (sin x)) (fma.f64 x (fma.f64 eps (.f64 (.f64 x (fma.f64 eps (.f64 eps #s(literal 1/24 binary64)) #s(literal -1/2 binary64))) #s(literal -1/2 binary64)) (fma.f64 eps (.f64 eps #s(literal 1/6 binary64)) #s(literal -1 binary64))) (.f64 eps (fma.f64 eps (.f64 eps #s(literal 1/24 binary64)) #s(literal -1/2 binary64)))))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps #s(approx (+ ( eps (+ (* (cos x) (+ -1/2 (* eps (* eps 1/24)))) (* eps (* 1/6 (sin x))))) (sin (neg x))) (fma.f64 x (fma.f64 x (fma.f64 eps #s(approx (* (+ (* eps (* eps 1/24)) -1/2) -1/2) #s(literal 1/4 binary64)) (.f64 x (fma.f64 (.f64 eps eps) #s(literal -1/36 binary64) #s(literal 1/6 binary64)))) (fma.f64 eps (.f64 eps #s(literal 1/6 binary64)) #s(literal -1 binary64))) (.f64 eps (fma.f64 eps (*.f64 eps #s(literal 1/24 binary64)) #s(literal -1/2 binary64)))))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps #s(approx (+ ( eps (+ (* (cos x) (+ -1/2 (* eps (* eps 1/24)))) (* eps (* 1/6 (sin x))))) (sin (neg x))) (fma.f64 x (fma.f64 x (fma.f64 eps #s(approx (* (+ (* eps (* eps 1/24)) -1/2) -1/2) (.f64 #s(literal -1/48 binary64) (.f64 eps eps))) (.f64 x (fma.f64 (.f64 eps eps) #s(literal -1/36 binary64) #s(literal 1/6 binary64)))) (fma.f64 eps (.f64 eps #s(literal 1/6 binary64)) #s(literal -1 binary64))) (.f64 eps (fma.f64 eps (*.f64 eps #s(literal 1/24 binary64)) #s(literal -1/2 binary64)))))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* eps (+ (* eps (+ (* (cos x) (+ -1/2 (* eps (* eps 1/24)))) (* eps (* 1/6 (sin x))))) (sin (neg x)))) #s(approx (+ (* eps (* eps (+ (* eps (* eps 1/24)) -1/2))) (* eps (* x (+ (* eps (* eps 1/6)) -1)))) (.f64 (.f64 (.f64 eps eps) (.f64 eps eps)) (+.f64 (fma.f64 x (/.f64 #s(literal 1/6 binary64) eps) (-.f64 #s(literal 1/24 binary64) (/.f64 x (.f64 eps (.f64 eps eps))))) (/.f64 #s(literal -1/2 binary64) (*.f64 eps eps)))))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps #s(approx (+ ( eps (+ (* (cos x) (+ -1/2 (* eps (* eps 1/24)))) (* eps (* 1/6 (sin x))))) (sin (neg x))) (fma.f64 x (fma.f64 x (fma.f64 eps (.f64 (fma.f64 eps (.f64 eps #s(literal 1/24 binary64)) #s(literal -1/2 binary64)) #s(literal -1/2 binary64)) (.f64 x (fma.f64 (.f64 eps eps) #s(literal -1/36 binary64) #s(literal 1/6 binary64)))) (fma.f64 eps (.f64 eps #s(literal 1/6 binary64)) #s(literal -1 binary64))) (.f64 eps (fma.f64 eps (*.f64 eps #s(literal 1/24 binary64)) #s(literal -1/2 binary64)))))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps #s(approx (+ ( eps (+ (* (cos x) (+ -1/2 (* eps (* eps 1/24)))) (* eps (* 1/6 (sin x))))) (sin (neg x))) #s(approx (+ (* x (+ (* x (+ (* eps (* (+ (* eps (* eps 1/24)) -1/2) -1/2)) (* x (+ (* (* eps eps) -1/36) 1/6)))) (+ (* eps (* eps 1/6)) -1))) (* eps (+ (* eps (* eps 1/24)) -1/2))) (neg.f64 (.f64 (.f64 eps (.f64 eps eps)) (-.f64 (fma.f64 x (.f64 x #s(literal 1/48 binary64)) #s(literal -1/24 binary64)) (/.f64 (-.f64 (.f64 x (fma.f64 #s(literal -1/36 binary64) (.f64 x x) #s(literal 1/6 binary64))) (/.f64 (fma.f64 (*.f64 x x) #s(literal -1/4 binary64) #s(literal 1/2 binary64)) eps)) eps))))))))

Outputs

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

Calls

3 calls:

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

Results

Accuracy	Segments	Branch
97.9%	1	`x`
97.9%	1	`(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))`
97.9%	1	`eps`

Compiler

Compiled 15 to 10 computations (33.3% saved)

regimes17.0ms (0.1%)

Memory

18.8MiB live, 18.8MiB allocated

Counts

19 → 1

Calls

Call 1

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

Outputs

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

Calls

3 calls:

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

Results

Accuracy	Segments	Branch
97.8%	1	`x`
97.8%	1	`eps`
97.8%	1	`(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))`

Compiler

Compiled 15 to 10 computations (33.3% saved)

regimes15.0ms (0.1%)

Memory

-26.5MiB live, 15.6MiB allocated

Counts

14 → 1

Calls

Call 1

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

Outputs

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

Calls

3 calls:

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

Results

Accuracy	Segments	Branch
97.2%	1	`x`
97.2%	1	`eps`
97.2%	1	`(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))`

Compiler

Compiled 15 to 10 computations (33.3% saved)

regimes12.0ms (0.1%)

Memory

14.7MiB live, 14.7MiB allocated

Counts

12 → 1

Calls

Call 1

Inputs
#s(approx (- (cos (+ x eps)) (cos x)) (+.f64 #s(approx (cos eps) #s(literal 1 binary64)) #s(literal -1 binary64)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* eps (+ (* eps (+ (* (cos x) (+ -1/2 (* eps (* eps 1/24)))) (* eps (* 1/6 (sin x))))) (sin (neg x)))) #s(approx (+ (* eps (* eps (+ (* eps (* eps 1/24)) -1/2))) (* eps (* x (+ (* eps (* eps 1/6)) -1)))) (*.f64 x (neg.f64 eps)))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (+ (cos eps) -1) (.f64 eps (.f64 eps #s(literal -1/2 binary64)))))
#s(approx (- (* (cos x) (cos eps)) (+ (* (sin x) (sin eps)) (cos x))) (.f64 eps #s(approx (- ( eps (* -1/2 (cos x))) (sin x)) (*.f64 eps #s(literal -1/2 binary64)))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* eps (+ (* eps (+ (* (cos x) (+ -1/2 (* eps (* eps 1/24)))) (* eps (* 1/6 (sin x))))) (sin (neg x)))) #s(approx (+ (* eps (* eps (+ (* eps (* eps 1/24)) -1/2))) (* eps (* x (+ (* eps (* eps 1/6)) -1)))) (.f64 eps (-.f64 (.f64 eps #s(literal -1/2 binary64)) x)))))
#s(approx (- (* (cos x) (cos eps)) (+ (* (sin x) (sin eps)) (cos x))) (.f64 eps #s(approx (- ( eps (* -1/2 (cos x))) (sin x)) (-.f64 (*.f64 eps #s(literal -1/2 binary64)) x))))
#s(approx (- (cos (+ x eps)) (cos x)) (+.f64 #s(approx (cos eps) (fma.f64 eps (*.f64 eps #s(literal -1/2 binary64)) #s(literal 1 binary64))) #s(literal -1 binary64)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* eps (+ (* eps (+ (* (cos x) (+ -1/2 (* eps (* eps 1/24)))) (* eps (* 1/6 (sin x))))) (sin (neg x)))) #s(approx (+ (* eps (* eps (+ (* eps (* eps 1/24)) -1/2))) (* eps (* x (+ (* eps (* eps 1/6)) -1)))) #s(approx (* (* (* eps eps) (* eps eps)) (+ (* x (/ 1/6 eps)) 1/24)) (.f64 x (.f64 eps (.f64 eps (.f64 eps #s(literal 1/6 binary64)))))))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* eps (+ (* eps (+ (* (cos x) (+ -1/2 (* eps (* eps 1/24)))) (* eps (* 1/6 (sin x))))) (sin (neg x)))) #s(approx (+ (* eps (* eps (+ (* eps (* eps 1/24)) -1/2))) (* eps (* x (+ (* eps (* eps 1/6)) -1)))) (.f64 #s(literal 1/24 binary64) (.f64 (.f64 eps eps) (.f64 eps eps))))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps #s(approx (+ ( eps (+ (* (cos x) (+ -1/2 (* eps (* eps 1/24)))) (* eps (* 1/6 (sin x))))) (sin (neg x))) #s(approx (+ (* x (+ (* x (+ (* eps (* (+ (* eps (* eps 1/24)) -1/2) -1/2)) (* x (+ (* (* eps eps) -1/36) 1/6)))) (+ (* eps (* eps 1/6)) -1))) (* eps (+ (* eps (* eps 1/24)) -1/2))) (.f64 x (fma.f64 x (.f64 x #s(literal 1/6 binary64)) #s(literal -1 binary64)))))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* eps (+ (* eps (+ (* (cos x) (+ -1/2 (* eps (* eps 1/24)))) (* eps (* 1/6 (sin x))))) (sin (neg x)))) #s(approx (+ (* eps (* eps (+ (* eps (* eps 1/24)) -1/2))) (* eps (* x (+ (* eps (* eps 1/6)) -1)))) (.f64 eps (fma.f64 eps (fma.f64 x (.f64 eps #s(literal 1/6 binary64)) #s(literal -1/2 binary64)) (neg.f64 x))))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* eps (+ (* eps (+ (* (cos x) (+ -1/2 (* eps (* eps 1/24)))) (* eps (* 1/6 (sin x))))) (sin (neg x)))) #s(approx (+ (* eps (* eps (+ (* eps (* eps 1/24)) -1/2))) (* eps (* x (+ (* eps (* eps 1/6)) -1)))) #s(approx (* (* (* eps eps) (* eps eps)) (+ (* x (/ 1/6 eps)) 1/24)) (.f64 (.f64 eps eps) (.f64 eps (fma.f64 eps #s(literal 1/24 binary64) (.f64 x #s(literal 1/6 binary64)))))))))

Outputs

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

Calls

3 calls:

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

Results

Accuracy	Segments	Branch
97.2%	1	`x`
97.2%	1	`eps`
97.2%	1	`(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))`

Compiler

Compiled 15 to 10 computations (33.3% saved)

regimes10.0ms (0.1%)

Memory

13.0MiB live, 13.0MiB allocated

Counts

10 → 1

Calls

Call 1

Inputs
#s(approx (- (cos (+ x eps)) (cos x)) (+.f64 #s(approx (cos eps) #s(literal 1 binary64)) #s(literal -1 binary64)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* eps (+ (* eps (+ (* (cos x) (+ -1/2 (* eps (* eps 1/24)))) (* eps (* 1/6 (sin x))))) (sin (neg x)))) #s(approx (+ (* eps (* eps (+ (* eps (* eps 1/24)) -1/2))) (* eps (* x (+ (* eps (* eps 1/6)) -1)))) (*.f64 x (neg.f64 eps)))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (+ (cos eps) -1) (.f64 eps (.f64 eps #s(literal -1/2 binary64)))))
#s(approx (- (* (cos x) (cos eps)) (+ (* (sin x) (sin eps)) (cos x))) (.f64 eps #s(approx (- ( eps (* -1/2 (cos x))) (sin x)) (*.f64 eps #s(literal -1/2 binary64)))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* eps (+ (* eps (+ (* (cos x) (+ -1/2 (* eps (* eps 1/24)))) (* eps (* 1/6 (sin x))))) (sin (neg x)))) #s(approx (+ (* eps (* eps (+ (* eps (* eps 1/24)) -1/2))) (* eps (* x (+ (* eps (* eps 1/6)) -1)))) (.f64 eps (-.f64 (.f64 eps #s(literal -1/2 binary64)) x)))))
#s(approx (- (* (cos x) (cos eps)) (+ (* (sin x) (sin eps)) (cos x))) (.f64 eps #s(approx (- ( eps (* -1/2 (cos x))) (sin x)) (-.f64 (*.f64 eps #s(literal -1/2 binary64)) x))))
#s(approx (- (cos (+ x eps)) (cos x)) (+.f64 #s(approx (cos eps) (fma.f64 eps (*.f64 eps #s(literal -1/2 binary64)) #s(literal 1 binary64))) #s(literal -1 binary64)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* eps (+ (* eps (+ (* (cos x) (+ -1/2 (* eps (* eps 1/24)))) (* eps (* 1/6 (sin x))))) (sin (neg x)))) #s(approx (+ (* eps (* eps (+ (* eps (* eps 1/24)) -1/2))) (* eps (* x (+ (* eps (* eps 1/6)) -1)))) #s(approx (* (* (* eps eps) (* eps eps)) (+ (* x (/ 1/6 eps)) 1/24)) (.f64 x (.f64 eps (.f64 eps (.f64 eps #s(literal 1/6 binary64)))))))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* eps (+ (* eps (+ (* (cos x) (+ -1/2 (* eps (* eps 1/24)))) (* eps (* 1/6 (sin x))))) (sin (neg x)))) #s(approx (+ (* eps (* eps (+ (* eps (* eps 1/24)) -1/2))) (* eps (* x (+ (* eps (* eps 1/6)) -1)))) (.f64 #s(literal 1/24 binary64) (.f64 (.f64 eps eps) (.f64 eps eps))))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps #s(approx (+ ( eps (+ (* (cos x) (+ -1/2 (* eps (* eps 1/24)))) (* eps (* 1/6 (sin x))))) (sin (neg x))) #s(approx (+ (* x (+ (* x (+ (* eps (* (+ (* eps (* eps 1/24)) -1/2) -1/2)) (* x (+ (* (* eps eps) -1/36) 1/6)))) (+ (* eps (* eps 1/6)) -1))) (* eps (+ (* eps (* eps 1/24)) -1/2))) (.f64 x (fma.f64 x (.f64 x #s(literal 1/6 binary64)) #s(literal -1 binary64)))))))

Outputs

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

Calls

3 calls:

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

Results

Accuracy	Segments	Branch
97.2%	1	`x`
97.2%	1	`eps`
97.2%	1	`(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))`

Compiler

Compiled 15 to 10 computations (33.3% saved)

regimes6.0ms (0%)

Memory

-29.9MiB live, 9.9MiB allocated

Counts

4 → 1

Calls

Call 1

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

Outputs

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

Calls

3 calls:

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

Results

Accuracy	Segments	Branch
80.8%	1	`eps`
80.8%	1	`x`
80.8%	1	`(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))`

Compiler

Compiled 15 to 10 computations (33.3% saved)

regimes4.0ms (0%)

Memory

6.0MiB live, 6.0MiB allocated

Accuracy

Total -0.0b remaining (-0%)

Threshold costs -0b (-0%)

Counts

1 → 1

Calls

Call 1

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

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

Calls

3 calls:

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

Results

Accuracy	Segments	Branch
54.6%	1	`(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))`
54.6%	1	`x`
54.6%	1	`eps`

Compiler

Compiled 15 to 10 computations (33.3% saved)

simplify13.0ms (0.1%)

Memory

14.6MiB live, 14.6MiB allocated

Algorithm

1×	egg-herbie

Rules

82×	`*-commutative_binary64`
18×	`+-commutative_binary64`
16×	`sub-neg_binary64`
8×	`neg-sub0_binary64`
8×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	180	730
1	232	730
2	246	730
3	252	730
4	254	730

Stop Event

1×

saturated

Calls

Call 1

Inputs
(.f64 #s(approx ( (sin (* (+ eps 0) 1/2)) (+ (* (sin (* (+ x x) 1/2)) (cos (* eps 1/2))) (* (cos (* (+ x x) 1/2)) (sin (* eps 1/2))))) (.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (fma.f64 (cos.f64 x) (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (.f64 (sin.f64 x) (cos.f64 (*.f64 eps #s(literal 1/2 binary64))))))) #s(literal -2 binary64))
(.f64 #s(approx ( (sin (* (+ eps 0) 1/2)) (+ (* (sin (* (+ x x) 1/2)) (cos (* eps 1/2))) (* (cos (* (+ x x) 1/2)) (sin (* eps 1/2))))) (.f64 #s(approx (sin ( eps 1/2)) (.f64 eps (fma.f64 (.f64 eps eps) (fma.f64 (.f64 eps eps) (fma.f64 (.f64 eps eps) #s(literal -1/645120 binary64) #s(literal 1/3840 binary64)) #s(literal -1/48 binary64)) #s(literal 1/2 binary64)))) (fma.f64 (cos.f64 x) (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (.f64 (sin.f64 x) (cos.f64 (*.f64 eps #s(literal 1/2 binary64))))))) #s(literal -2 binary64))
(.f64 #s(approx ( (sin (* (+ eps 0) 1/2)) (+ (* (sin (* (+ x x) 1/2)) (cos (* eps 1/2))) (* (cos (* (+ x x) 1/2)) (sin (* eps 1/2))))) (.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (fma.f64 (cos.f64 x) #s(approx (sin (* eps 1/2)) (.f64 eps (fma.f64 eps (.f64 eps (fma.f64 eps (.f64 eps #s(literal 1/3840 binary64)) #s(literal -1/48 binary64))) #s(literal 1/2 binary64)))) (.f64 (sin.f64 x) (cos.f64 (*.f64 eps #s(literal 1/2 binary64))))))) #s(literal -2 binary64))
(.f64 #s(approx ( (sin (* (+ eps 0) 1/2)) (sin (* (+ x (+ x eps)) 1/2))) (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x)))) #s(literal -2 binary64))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps (-.f64 (.f64 eps (*.f64 #s(literal -1/2 binary64) (cos.f64 x))) (sin.f64 x))))
#s(approx (- (* (cos x) (cos eps)) (+ (* (sin x) (sin eps)) (cos x))) (.f64 eps (-.f64 #s(approx ( eps (+ (* eps (* (sin x) 1/6)) (* (cos x) (+ (* eps (* eps 1/24)) -1/2)))) (.f64 eps (fma.f64 eps (.f64 eps #s(literal 1/24 binary64)) #s(literal -1/2 binary64)))) (sin.f64 x))))
#s(approx (- (* (cos x) (cos eps)) (+ (* (sin x) (sin eps)) (cos x))) (.f64 eps (-.f64 #s(approx ( eps (* -1/2 (cos x))) (*.f64 eps #s(literal -1/2 binary64))) (sin.f64 x))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* eps (+ (* eps (+ (* (cos x) (+ -1/2 (* eps (* eps 1/24)))) (* eps (* 1/6 (sin x))))) (sin (neg x)))) (fma.f64 x (fma.f64 x (fma.f64 eps (.f64 x (fma.f64 (.f64 eps eps) #s(literal -1/36 binary64) #s(literal 1/6 binary64))) (.f64 #s(literal -1/2 binary64) (.f64 eps (.f64 eps (fma.f64 eps (.f64 eps #s(literal 1/24 binary64)) #s(literal -1/2 binary64)))))) (.f64 eps (fma.f64 eps (.f64 eps #s(literal 1/6 binary64)) #s(literal -1 binary64)))) (.f64 eps (.f64 eps (fma.f64 eps (*.f64 eps #s(literal 1/24 binary64)) #s(literal -1/2 binary64)))))))
#s(approx (- (* (cos x) (cos eps)) (+ (* (sin x) (sin eps)) (cos x))) #s(approx (* eps (- (* eps (* -1/2 (cos x))) (sin x))) (fma.f64 x (fma.f64 x (fma.f64 eps (.f64 x #s(literal 1/6 binary64)) (.f64 eps (.f64 eps #s(literal 1/4 binary64)))) (neg.f64 eps)) (.f64 #s(literal -1/2 binary64) (*.f64 eps eps)))))
#s(approx (- (* (cos x) (cos eps)) (+ (* (sin x) (sin eps)) (cos x))) (.f64 eps #s(approx (- ( eps (* -1/2 (cos x))) (sin x)) (fma.f64 x (fma.f64 x (fma.f64 eps #s(literal 1/4 binary64) (.f64 x #s(literal 1/6 binary64))) #s(literal -1 binary64)) (.f64 eps #s(literal -1/2 binary64))))))
#s(approx (- (* (cos x) (cos eps)) (+ (* (sin x) (sin eps)) (cos x))) (.f64 eps #s(approx (- ( eps (* -1/2 (cos x))) (sin x)) (fma.f64 x (fma.f64 #s(literal 1/4 binary64) (.f64 eps x) #s(literal -1 binary64)) (.f64 eps #s(literal -1/2 binary64))))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* eps (+ (* eps (+ (* (cos x) (+ -1/2 (* eps (* eps 1/24)))) (* eps (* 1/6 (sin x))))) (sin (neg x)))) #s(approx (+ (* eps (* eps (+ (* eps (* eps 1/24)) -1/2))) (* eps (* x (+ (* eps (* eps 1/6)) -1)))) (.f64 eps (fma.f64 eps (fma.f64 x (.f64 eps #s(literal 1/6 binary64)) #s(literal -1/2 binary64)) (neg.f64 x))))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* eps (+ (* eps (+ (* (cos x) (+ -1/2 (* eps (* eps 1/24)))) (* eps (* 1/6 (sin x))))) (sin (neg x)))) #s(approx (+ (* eps (* eps (+ (* eps (* eps 1/24)) -1/2))) (* eps (* x (+ (* eps (* eps 1/6)) -1)))) (.f64 eps (-.f64 (.f64 eps #s(literal -1/2 binary64)) x)))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* eps (+ (* eps (+ (* (cos x) (+ -1/2 (* eps (* eps 1/24)))) (* eps (* 1/6 (sin x))))) (sin (neg x)))) #s(approx (+ (* eps (* eps (+ (* eps (* eps 1/24)) -1/2))) (* eps (* x (+ (* eps (* eps 1/6)) -1)))) (*.f64 x (neg.f64 eps)))))
#s(approx (- (cos (+ x eps)) (cos x)) (+.f64 #s(approx (cos eps) #s(literal 1 binary64)) #s(literal -1 binary64)))

Outputs
(.f64 #s(approx ( (sin (* (+ eps 0) 1/2)) (+ (* (sin (* (+ x x) 1/2)) (cos (* eps 1/2))) (* (cos (* (+ x x) 1/2)) (sin (* eps 1/2))))) (.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (fma.f64 (cos.f64 x) (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (.f64 (sin.f64 x) (cos.f64 (*.f64 eps #s(literal 1/2 binary64))))))) #s(literal -2 binary64))
(.f64 #s(approx ( (sin (* (+ eps 0) 1/2)) (+ (* (sin (* (+ x x) 1/2)) (cos (* eps 1/2))) (* (cos (* (+ x x) 1/2)) (sin (* eps 1/2))))) (.f64 #s(approx (sin ( eps 1/2)) (.f64 eps (fma.f64 (.f64 eps eps) (fma.f64 (.f64 eps eps) (fma.f64 (.f64 eps eps) #s(literal -1/645120 binary64) #s(literal 1/3840 binary64)) #s(literal -1/48 binary64)) #s(literal 1/2 binary64)))) (fma.f64 (cos.f64 x) (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (.f64 (sin.f64 x) (cos.f64 (*.f64 eps #s(literal 1/2 binary64))))))) #s(literal -2 binary64))
(.f64 #s(literal -2 binary64) #s(approx ( (sin (* (+ eps 0) 1/2)) (+ (* (sin (* (+ x x) 1/2)) (cos (* eps 1/2))) (* (cos (* (+ x x) 1/2)) (sin (* eps 1/2))))) (.f64 (fma.f64 (cos.f64 x) (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (.f64 (sin.f64 x) (cos.f64 (.f64 eps #s(literal 1/2 binary64))))) #s(approx (sin (* eps 1/2)) (.f64 eps (fma.f64 (.f64 eps eps) (fma.f64 (.f64 eps eps) (fma.f64 (.f64 eps eps) #s(literal -1/645120 binary64) #s(literal 1/3840 binary64)) #s(literal -1/48 binary64)) #s(literal 1/2 binary64)))))))
(.f64 #s(approx ( (sin (* (+ eps 0) 1/2)) (+ (* (sin (* (+ x x) 1/2)) (cos (* eps 1/2))) (* (cos (* (+ x x) 1/2)) (sin (* eps 1/2))))) (.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (fma.f64 (cos.f64 x) #s(approx (sin (* eps 1/2)) (.f64 eps (fma.f64 eps (.f64 eps (fma.f64 eps (.f64 eps #s(literal 1/3840 binary64)) #s(literal -1/48 binary64))) #s(literal 1/2 binary64)))) (.f64 (sin.f64 x) (cos.f64 (*.f64 eps #s(literal 1/2 binary64))))))) #s(literal -2 binary64))
(.f64 #s(literal -2 binary64) #s(approx ( (sin (* (+ eps 0) 1/2)) (+ (* (sin (* (+ x x) 1/2)) (cos (* eps 1/2))) (* (cos (* (+ x x) 1/2)) (sin (* eps 1/2))))) (.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (fma.f64 (cos.f64 x) #s(approx (sin (* eps 1/2)) (.f64 eps (fma.f64 eps (.f64 eps (fma.f64 eps (.f64 eps #s(literal 1/3840 binary64)) #s(literal -1/48 binary64))) #s(literal 1/2 binary64)))) (.f64 (sin.f64 x) (cos.f64 (*.f64 eps #s(literal 1/2 binary64))))))))
(.f64 #s(approx ( (sin (* (+ eps 0) 1/2)) (sin (* (+ x (+ x eps)) 1/2))) (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x)))) #s(literal -2 binary64))
(.f64 #s(literal -2 binary64) #s(approx ( (sin (* (+ eps 0) 1/2)) (sin (* (+ x (+ x eps)) 1/2))) (.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x)))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps (-.f64 (.f64 eps (*.f64 #s(literal -1/2 binary64) (cos.f64 x))) (sin.f64 x))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps (-.f64 (.f64 eps (*.f64 (cos.f64 x) #s(literal -1/2 binary64))) (sin.f64 x))))
#s(approx (- (* (cos x) (cos eps)) (+ (* (sin x) (sin eps)) (cos x))) (.f64 eps (-.f64 #s(approx ( eps (+ (* eps (* (sin x) 1/6)) (* (cos x) (+ (* eps (* eps 1/24)) -1/2)))) (.f64 eps (fma.f64 eps (.f64 eps #s(literal 1/24 binary64)) #s(literal -1/2 binary64)))) (sin.f64 x))))
#s(approx (- (* (cos x) (cos eps)) (+ (* (sin x) (sin eps)) (cos x))) (.f64 eps (-.f64 #s(approx ( eps (* -1/2 (cos x))) (*.f64 eps #s(literal -1/2 binary64))) (sin.f64 x))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* eps (+ (* eps (+ (* (cos x) (+ -1/2 (* eps (* eps 1/24)))) (* eps (* 1/6 (sin x))))) (sin (neg x)))) (fma.f64 x (fma.f64 x (fma.f64 eps (.f64 x (fma.f64 (.f64 eps eps) #s(literal -1/36 binary64) #s(literal 1/6 binary64))) (.f64 #s(literal -1/2 binary64) (.f64 eps (.f64 eps (fma.f64 eps (.f64 eps #s(literal 1/24 binary64)) #s(literal -1/2 binary64)))))) (.f64 eps (fma.f64 eps (.f64 eps #s(literal 1/6 binary64)) #s(literal -1 binary64)))) (.f64 eps (.f64 eps (fma.f64 eps (*.f64 eps #s(literal 1/24 binary64)) #s(literal -1/2 binary64)))))))
#s(approx (- (* (cos x) (cos eps)) (+ (* (sin x) (sin eps)) (cos x))) #s(approx (* eps (- (* eps (* -1/2 (cos x))) (sin x))) (fma.f64 x (fma.f64 x (fma.f64 eps (.f64 x #s(literal 1/6 binary64)) (.f64 eps (.f64 eps #s(literal 1/4 binary64)))) (neg.f64 eps)) (.f64 #s(literal -1/2 binary64) (*.f64 eps eps)))))
#s(approx (- (* (cos x) (cos eps)) (+ (* (sin x) (sin eps)) (cos x))) #s(approx (* eps (- (* eps (* -1/2 (cos x))) (sin x))) (fma.f64 x (fma.f64 x (fma.f64 eps (.f64 x #s(literal 1/6 binary64)) (.f64 eps (.f64 eps #s(literal 1/4 binary64)))) (neg.f64 eps)) (.f64 (*.f64 eps eps) #s(literal -1/2 binary64)))))
#s(approx (- (* (cos x) (cos eps)) (+ (* (sin x) (sin eps)) (cos x))) (.f64 eps #s(approx (- ( eps (* -1/2 (cos x))) (sin x)) (fma.f64 x (fma.f64 x (fma.f64 eps #s(literal 1/4 binary64) (.f64 x #s(literal 1/6 binary64))) #s(literal -1 binary64)) (.f64 eps #s(literal -1/2 binary64))))))
#s(approx (- (* (cos x) (cos eps)) (+ (* (sin x) (sin eps)) (cos x))) (.f64 eps #s(approx (- ( eps (* -1/2 (cos x))) (sin x)) (fma.f64 x (fma.f64 #s(literal 1/4 binary64) (.f64 eps x) #s(literal -1 binary64)) (.f64 eps #s(literal -1/2 binary64))))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* eps (+ (* eps (+ (* (cos x) (+ -1/2 (* eps (* eps 1/24)))) (* eps (* 1/6 (sin x))))) (sin (neg x)))) #s(approx (+ (* eps (* eps (+ (* eps (* eps 1/24)) -1/2))) (* eps (* x (+ (* eps (* eps 1/6)) -1)))) (.f64 eps (fma.f64 eps (fma.f64 x (.f64 eps #s(literal 1/6 binary64)) #s(literal -1/2 binary64)) (neg.f64 x))))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* eps (+ (* eps (+ (* (cos x) (+ -1/2 (* eps (* eps 1/24)))) (* eps (* 1/6 (sin x))))) (sin (neg x)))) #s(approx (+ (* eps (* eps (+ (* eps (* eps 1/24)) -1/2))) (* eps (* x (+ (* eps (* eps 1/6)) -1)))) (.f64 eps (-.f64 (.f64 eps #s(literal -1/2 binary64)) x)))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* eps (+ (* eps (+ (* (cos x) (+ -1/2 (* eps (* eps 1/24)))) (* eps (* 1/6 (sin x))))) (sin (neg x)))) #s(approx (+ (* eps (* eps (+ (* eps (* eps 1/24)) -1/2))) (* eps (* x (+ (* eps (* eps 1/6)) -1)))) (*.f64 x (neg.f64 eps)))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* eps (+ (* eps (+ (* (cos x) (+ -1/2 (* eps (* eps 1/24)))) (* eps (* 1/6 (sin x))))) (sin (neg x)))) #s(approx (+ (* eps (* eps (+ (* eps (* eps 1/24)) -1/2))) (* eps (* x (+ (* eps (* eps 1/6)) -1)))) (neg.f64 (*.f64 eps x)))))
#s(approx (- (cos (+ x eps)) (cos x)) (+.f64 #s(approx (cos eps) #s(literal 1 binary64)) #s(literal -1 binary64)))
#s(approx (- (cos (+ x eps)) (cos x)) (+.f64 #s(literal -1 binary64) #s(approx (cos eps) #s(literal 1 binary64))))

soundness1.4s (7.4%)

Memory

10.1MiB live, 565.8MiB allocated

Rules

14 158×	`lower-fma.f64`
14 158×	`lower-fma.f32`
13 074×	`lower-fma.f64`
13 074×	`lower-fma.f32`
12 910×	`lower-fma.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	473	4669
1	1443	4451
2	4089	4445
0	8233	4114
0	48	227
0	84	215
1	306	215
2	2726	215
0	8438	206
0	609	8231
1	1939	7935
2	6108	7882
0	8080	7382
0	6	16
0	10	16
1	54	16
2	380	16
3	4694	16
0	8209	16
0	105	498
1	277	495
2	609	495
3	2398	494
4	7880	494
0	8026	474
0	507	5916
1	1567	5723
2	4515	5716
0	8304	5319

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

Compiler

Compiled 681 to 354 computations (48% saved)

preprocess125.0ms (0.7%)

Memory: -0.6MiB live, 83.1MiB allocated
Compiler: Compiled 650 to 238 computations (63.4% saved)

end0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated

Iter	Nodes	Cost
0	18	41
1	38	37
2	81	35
3	152	35
4	278	35
5	370	35
6	448	35
7	485	35
8	531	35
9	546	35
10	554	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	41
1	38	37
2	81	35
3	152	35
4	278	35
5	370	35
6	448	35
7	485	35
8	531	35
9	546	35
10	554	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%)

analyze84.0ms (0.5%)

sample9.4s (50.7%)

explain224.0ms (1.2%)

preprocess28.0ms (0.2%)

eval0.0ms (0%)

prune1.0ms (0%)

simplify8.0ms (0%)

localize152.0ms (0.8%)

series4.0ms (0%)

simplify310.0ms (1.7%)

rewrite319.0ms (1.7%)

eval66.0ms (0.4%)

prune130.0ms (0.7%)

simplify444.0ms (2.4%)

localize463.0ms (2.5%)

series45.0ms (0.2%)

simplify326.0ms (1.8%)

rewrite316.0ms (1.7%)

eval127.0ms (0.7%)

prune161.0ms (0.9%)

simplify228.0ms (1.2%)

localize862.0ms (4.6%)

series69.0ms (0.4%)

simplify393.0ms (2.1%)

rewrite353.0ms (1.9%)

eval121.0ms (0.7%)

prune180.0ms (1%)

simplify256.0ms (1.4%)

localize562.0ms (3%)

series50.0ms (0.3%)

simplify275.0ms (1.5%)

rewrite247.0ms (1.3%)

eval105.0ms (0.6%)

prune210.0ms (1.1%)

regimes54.0ms (0.3%)

regimes110.0ms (0.6%)

regimes48.0ms (0.3%)

regimes51.0ms (0.3%)

regimes42.0ms (0.2%)

regimes80.0ms (0.4%)

regimes39.0ms (0.2%)

regimes36.0ms (0.2%)

regimes29.0ms (0.2%)

regimes17.0ms (0.1%)

regimes15.0ms (0.1%)

regimes12.0ms (0.1%)

regimes10.0ms (0.1%)

regimes6.0ms (0%)

regimes4.0ms (0%)

simplify13.0ms (0.1%)

soundness1.4s (7.4%)

preprocess125.0ms (0.7%)

end0.0ms (0%)

Profiling

Iter	Nodes	Cost
0	18	41
1	38	37
2	81	35
3	152	35
4	278	35
5	370	35
6	448	35
7	485	35
8	531	35
9	546	35
10	554	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