Metrics for 2cos (problem 3.3.5)

start0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated

analyze39.0ms (0.2%)

Memory

17.4MiB live, 55.4MiB 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)

sample9.8s (56.5%)

Memory

55.1MiB live, 10 353.1MiB allocated

Samples

3.9s	26 194×	0	invalid
3.4s	5 662×	2	valid
746.0ms	2 459×	1	valid
17.0ms	135×	0	valid

Precisions

Click to see histograms. Total time spent on operations: 6.4s

ival-cos: 2.8s (42.8% of total)

const: 1.1s (17.8% of total)

adjust: 493.0ms (7.7% of total)

ival-mult: 398.0ms (6.2% of total)

ival-<=: 343.0ms (5.3% of total)

ival-sub: 332.0ms (5.2% of total)

ival-add: 294.0ms (4.6% of total)

ival-fabs: 285.0ms (4.4% of total)

ival-<: 236.0ms (3.7% of total)

ival-and: 97.0ms (1.5% of total)

exact: 42.0ms (0.7% of total)

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

Bogosity

explain214.0ms (1.2%)

Memory

-0.2MiB live, 317.3MiB allocated

FPErrors

Click to see full error table

Ground Truth	Example	Example	Subexpression
144	-	-	`(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))`
6	-	-	`(cos.f64 (+.f64 x eps))`
0	-	-	`eps`
0	-	-	`(+.f64 x eps)`
0	-	-	`(cos.f64 x)`
0	-	-	`x`

Explanations

Click to see full explanations table

Operator	Subexpression	Explanation	Count
`-.f64`	`(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))`	cancellation	144	1
`cos.f64`	`(cos.f64 (+.f64 x eps))`	sensitivity	6	0

Confusion

	Predicted +	Predicted -
+	146	1
-	0	109

Precision

1.0

Recall

0.9931972789115646

Confusion?

	Predicted +	Predicted Maybe	Predicted -
+	146	0	1
-	0	0	109

Precision?

1.0

Recall?

0.9931972789115646

Freqs

test

number	freq
0	110
1	142
2	4

Total Confusion?

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

Precision?

1.0

Recall?

1.0

Samples

134.0ms	324×	2	valid
25.0ms	178×	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: 135.0ms

ival-cos: 108.0ms (79.8% of total)

adjust: 17.0ms (12.6% of total)

ival-sub: 6.0ms (4.4% of total)

ival-add: 3.0ms (2.2% of total)

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

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

preprocess28.0ms (0.2%)

Memory

6.4MiB live, 44.1MiB 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

1.5MiB live, 1.5MiB allocated

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	48.7%	(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))

Compiler

Compiled 9 to 6 computations (33.3% saved)

simplify11.0ms (0.1%)

Memory

-21.6MiB live, 15.9MiB 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)

localize90.0ms (0.5%)

Memory

37.1MiB live, 151.7MiB allocated

Localize:

Found 4 expressions of interest:

New	Metric	Score
accuracy	0	(+.f64 x eps)
accuracy	0	(cos.f64 x)
accuracy	0.2219610884876477	(cos.f64 (+.f64 x eps))
accuracy	32.54229867221464	(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))

Samples

68.0ms	162×	2	valid
13.0ms	89×	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: 70.0ms

ival-cos: 55.0ms (78.1% of total)

adjust: 9.0ms (12.8% of total)

ival-add: 4.0ms (5.7% of total)

ival-sub: 3.0ms (4.3% of total)

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

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

series7.0ms (0%)

Memory

-25.5MiB live, 12.2MiB 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
2.0ms	x	@	0	(cos (+ x eps))
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))

simplify266.0ms (1.5%)

Memory

11.5MiB live, 422.9MiB 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)

rewrite232.0ms (1.3%)

Memory

20.5MiB live, 406.0MiB 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))

eval69.0ms (0.4%)

Memory: -51.6MiB live, 90.5MiB allocated
Compiler: Compiled 8 023 to 875 computations (89.1% saved)

prune64.0ms (0.4%)

Memory

7.9MiB live, 128.7MiB allocated

Pruning

16 alts after pruning (15 fresh and 1 done)

	Pruned	Kept	Total
New	291	15	306
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	291	16	307

Accuracy

99.8%

Counts

307 → 16

Alt Table

Click to see full alt table

Status	Accuracy	Program
	48.8%	(/.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)))))
	49.2%	(/.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))))))
▶	48.7%	(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))))
	49.2%	(-.f64 (fma.f64 (sin.f64 (neg.f64 x)) (sin.f64 eps) (*.f64 (cos.f64 x) (cos.f64 eps))) (cos.f64 x))
	49.2%	(-.f64 (*.f64 (cos.f64 x) (cos.f64 eps)) (fma.f64 (sin.f64 x) (sin.f64 eps) (cos.f64 x)))
✓	48.7%	(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))
▶	47.1%	(-.f64 (cos.f64 (+.f64 x eps)) #s(approx (cos x) (fma.f64 x (*.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64))))
	47.2%	(-.f64 (cos.f64 (+.f64 x eps)) #s(approx (cos x) #s(literal 1 binary64)))
	47.1%	(-.f64 #s(approx (cos (+ x eps)) (cos.f64 eps)) (cos.f64 x))
▶	48.8%	(.f64 (/.f64 #s(literal 1 binary64) (+.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))) (-.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))))
▶	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))
▶	47.1%	#s(approx (- (cos (+ x eps)) (cos x)) (+.f64 (cos.f64 eps) #s(literal -1 binary64)))
	76.1%	#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)))))
	99.1%	#s(approx (- (cos (+ x eps)) (cos 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))))))
	98.7%	#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 597 to 360 computations (39.7% saved)

simplify220.0ms (1.3%)

Memory

-4.1MiB live, 228.4MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 19 expressions of interest:

New	Metric	Score
cost-diff	0	(+.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))
cost-diff	0	(/.f64 #s(literal 1 binary64) (+.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x)))
cost-diff	320	(.f64 (/.f64 #s(literal 1 binary64) (+.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))) (-.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))))
cost-diff	448	(-.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)))
cost-diff	0	(cos.f64 (+.f64 x eps))
cost-diff	0	(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))
cost-diff	0	(/.f64 #s(literal 1 binary64) (-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x)))
cost-diff	1408	(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (-.f64 (cos.f64 (+.f64 x eps)) (cos.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

13 792×	`lower-fma.f32`
13 786×	`lower-fma.f64`
2 670×	`lower-*.f32`
2 656×	`lower-*.f64`
2 420×	`lower--.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	44	284
0	77	270
1	118	268
2	238	260
3	555	252
4	1285	252
5	3363	252
6	5744	252
0	8391	247

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

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

localize383.0ms (2.2%)

Memory

13.7MiB live, 419.6MiB allocated

Localize:

Found 19 expressions of interest:

New	Metric	Score
accuracy	0.05435890382357724	(fma.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 (+.f64 x eps) #s(literal 2 binary64))) #s(literal 1/2 binary64))
accuracy	0.21051355301585636	(cos.f64 (*.f64 (+.f64 x eps) #s(literal 2 binary64)))
accuracy	0.22196108848764773	(cos.f64 (+.f64 x eps))
accuracy	32.48427505454881	(-.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)))
accuracy	0.16015625	(/.f64 #s(literal 1 binary64) (-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x)))
accuracy	0.22196108848764773	(cos.f64 (+.f64 x eps))
accuracy	0.6591982251049965	(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))))
accuracy	32.54229867221464	(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))
accuracy	0	(*.f64 x #s(literal -1/2 binary64))
accuracy	0.22196108848764773	(cos.f64 (+.f64 x eps))
accuracy	1.8725369591439622	#s(approx (cos x) (fma.f64 x (*.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64)))
accuracy	32.54229867221464	(-.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	32.21940679149344	(+.f64 (cos.f64 eps) #s(literal -1 binary64))
accuracy	32.83146890767957	#s(approx (- (cos (+ x eps)) (cos x)) (+.f64 (cos.f64 eps) #s(literal -1 binary64)))
accuracy	0	(sin.f64 (*.f64 (+.f64 eps #s(literal 0 binary64)) #s(literal 1/2 binary64)))
accuracy	0.15234375	(.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	0.21158976492644632	(sin.f64 (*.f64 (+.f64 x (+.f64 x eps)) #s(literal 1/2 binary64)))
accuracy	0.26171875	(+.f64 x (+.f64 x eps))

Samples

209.0ms	136×	2	valid
51.0ms	28×	3	valid
45.0ms	87×	1	valid
17.0ms	5×	0	valid

Compiler

Compiled 274 to 42 computations (84.7% saved)

Precisions

Click to see histograms. Total time spent on operations: 255.0ms

ival-cos: 150.0ms (58.9% of total)

adjust: 38.0ms (14.9% of total)

ival-add: 24.0ms (9.4% of total)

ival-mult: 21.0ms (8.2% of total)

ival-div: 9.0ms (3.5% of total)

ival-sub: 6.0ms (2.4% of total)

ival-sin: 6.0ms (2.4% of total)

exact: 1.0ms (0.4% of total)

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

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

series53.0ms (0.3%)

Memory

-8.7MiB live, 103.1MiB allocated

Counts

24 → 504

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

Calls

126 calls:

Time	Variable		Point	Expression
3.0ms	eps	@	-inf	(+ (cos eps) -1)
3.0ms	eps	@	0	(- (+ (* 1/2 (cos (* (+ x eps) 2))) 1/2) (+ (* 1/2 (cos (+ x x))) 1/2))
2.0ms	eps	@	-inf	(/ 1 (+ (cos (+ x eps)) (cos x)))
1.0ms	x	@	0	(* (* (sin (* (+ eps 0) 1/2)) (sin (* (+ x (+ x eps)) 1/2))) -2)
1.0ms	x	@	0	(* (/ 1 (+ (cos (+ x eps)) (cos x))) (- (+ (* 1/2 (cos (* (+ x eps) 2))) 1/2) (+ (* 1/2 (cos (+ x x))) 1/2)))

simplify406.0ms (2.3%)

Memory

-10.2MiB live, 358.3MiB allocated

Algorithm

1×	egg-herbie

Rules

8 868×	`lower-fma.f64`
8 868×	`lower-fma.f32`
6 342×	`lower-*.f64`
6 342×	`lower-*.f32`
2 964×	`lower-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	673	6162
1	2040	5951
2	5823	5912
0	8076	5589

Stop Event

1×	iter limit
1×	node limit

Counts

504 → 480

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)
(- (cos eps) 1)
(- (+ (cos eps) (* -1 (* x (sin eps)))) 1)
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(+ 1/2 (* 1/2 (cos (* 2 (- eps (* -1 x))))))
(+ 1/2 (* 1/2 (cos (* 2 (- eps (* -1 x))))))
(+ 1/2 (* 1/2 (cos (* 2 x))))
(+ 1/2 (+ (* -1 (* eps (sin (* 2 x)))) (* 1/2 (cos (* 2 x)))))
(+ 1/2 (+ (* 1/2 (cos (* 2 x))) (* eps (+ (* -1 (sin (* 2 x))) (* -1 (* eps (cos (* 2 x))))))))
(+ 1/2 (+ (* 1/2 (cos (* 2 x))) (* eps (+ (* -1 (sin (* 2 x))) (* eps (+ (* -1 (cos (* 2 x))) (* 2/3 (* eps (sin (* 2 x))))))))))
(+ 1/2 (* 1/2 (cos (* 2 (+ eps x)))))
(+ 1/2 (* 1/2 (cos (* 2 (+ eps x)))))
(+ 1/2 (* 1/2 (cos (* 2 (+ eps x)))))
(+ 1/2 (* 1/2 (cos (* 2 (+ eps x)))))
(+ 1/2 (* 1/2 (cos (* 2 (- x (* -1 eps))))))
(+ 1/2 (* 1/2 (cos (* 2 (- x (* -1 eps))))))
(+ 1/2 (* 1/2 (cos (* 2 (- x (* -1 eps))))))
(+ 1/2 (* 1/2 (cos (* 2 (- x (* -1 eps))))))

Outputs
(* 1/2 eps)
(*.f64 #s(literal 1/2 binary64) eps)
(+ x (* 1/2 eps))
(fma.f64 #s(literal 1/2 binary64) eps x)
(+ x (* 1/2 eps))
(fma.f64 #s(literal 1/2 binary64) eps x)
(+ x (* 1/2 eps))
(fma.f64 #s(literal 1/2 binary64) eps x)
x
(* x (+ 1 (* 1/2 (/ eps x))))
(fma.f64 x (/.f64 (*.f64 #s(literal 1/2 binary64) eps) x) x)
(* x (+ 1 (* 1/2 (/ eps x))))
(fma.f64 x (/.f64 (*.f64 #s(literal 1/2 binary64) eps) x) x)
(* x (+ 1 (* 1/2 (/ eps x))))
(fma.f64 x (/.f64 (*.f64 #s(literal 1/2 binary64) eps) x) x)
x
(* -1 (* x (- (* -1/2 (/ eps x)) 1)))
(fma.f64 (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x) (neg.f64 x) x)
(* -1 (* x (- (* -1/2 (/ eps x)) 1)))
(fma.f64 (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x) (neg.f64 x) x)
(* -1 (* x (- (* -1/2 (/ eps x)) 1)))
(fma.f64 (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x) (neg.f64 x) x)
x
(+ x (* 1/2 eps))
(fma.f64 #s(literal 1/2 binary64) eps x)
(+ x (* 1/2 eps))
(fma.f64 #s(literal 1/2 binary64) eps x)
(+ x (* 1/2 eps))
(fma.f64 #s(literal 1/2 binary64) eps x)
(* 1/2 eps)
(*.f64 #s(literal 1/2 binary64) eps)
(* eps (+ 1/2 (/ x eps)))
(*.f64 eps (+.f64 #s(literal 1/2 binary64) (/.f64 x eps)))
(* eps (+ 1/2 (/ x eps)))
(*.f64 eps (+.f64 #s(literal 1/2 binary64) (/.f64 x eps)))
(* eps (+ 1/2 (/ x eps)))
(*.f64 eps (+.f64 #s(literal 1/2 binary64) (/.f64 x eps)))
(* 1/2 eps)
(*.f64 #s(literal 1/2 binary64) eps)
(* -1 (* eps (- (* -1 (/ x eps)) 1/2)))
(neg.f64 (*.f64 eps (-.f64 #s(literal -1/2 binary64) (/.f64 x eps))))
(* -1 (* eps (- (* -1 (/ x eps)) 1/2)))
(neg.f64 (*.f64 eps (-.f64 #s(literal -1/2 binary64) (/.f64 x eps))))
(* -1 (* eps (- (* -1 (/ x eps)) 1/2)))
(neg.f64 (*.f64 eps (-.f64 #s(literal -1/2 binary64) (/.f64 x eps))))
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 #s(literal -1/2 binary64) (*.f64 eps (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 (fma.f64 eps (fma.f64 eps (.f64 (sin.f64 x) #s(literal 1/6 binary64)) (*.f64 #s(literal -1/2 binary64) (cos.f64 x))) (neg.f64 (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 (fma.f64 eps (.f64 (cos.f64 x) #s(literal 1/24 binary64)) (.f64 (sin.f64 x) #s(literal 1/6 binary64))) (.f64 #s(literal -1/2 binary64) (cos.f64 x))) (neg.f64 (sin.f64 x))))
(* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (+ eps (* 2 x))))))
(.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (*.f64 (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) #s(literal -2 binary64)))
(* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (+ eps (* 2 x))))))
(.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (*.f64 (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) #s(literal -2 binary64)))
(* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (+ eps (* 2 x))))))
(.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (*.f64 (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) #s(literal -2 binary64)))
(* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (+ eps (* 2 x))))))
(.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (*.f64 (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) #s(literal -2 binary64)))
(* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (- (* 2 x) (* -1 eps))))))
(.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (*.f64 (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) #s(literal -2 binary64)))
(* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (- (* 2 x) (* -1 eps))))))
(.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (*.f64 (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) #s(literal -2 binary64)))
(* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (- (* 2 x) (* -1 eps))))))
(.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (*.f64 (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) #s(literal -2 binary64)))
(* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (- (* 2 x) (* -1 eps))))))
(.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (*.f64 (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) #s(literal -2 binary64)))
(* -2 (pow (sin (* 1/2 eps)) 2))
(.f64 #s(literal -2 binary64) (pow.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) #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 #s(literal 1/2 binary64) eps)) (fma.f64 x (cos.f64 (.f64 #s(literal 1/2 binary64) eps)) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)))))
(+ (* -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 #s(literal 1/2 binary64) eps)) (fma.f64 x (cos.f64 (.f64 #s(literal 1/2 binary64) eps)) (sin.f64 (.f64 #s(literal 1/2 binary64) eps)))) (.f64 (pow.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) #s(literal 2 binary64)) (*.f64 x x)))
(+ (* -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 #s(literal 1/2 binary64) eps)) (fma.f64 x (cos.f64 (.f64 #s(literal 1/2 binary64) eps)) (sin.f64 (.f64 #s(literal 1/2 binary64) eps)))) (.f64 (fma.f64 (.f64 (.f64 x #s(literal 1/3 binary64)) (sin.f64 (.f64 #s(literal 1/2 binary64) eps))) (cos.f64 (.f64 #s(literal 1/2 binary64) eps)) (pow.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) #s(literal 2 binary64))) (*.f64 x x)))
(* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (+ eps (* 2 x))))))
(.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (*.f64 (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) #s(literal -2 binary64)))
(* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (+ eps (* 2 x))))))
(.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (*.f64 (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) #s(literal -2 binary64)))
(* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (+ eps (* 2 x))))))
(.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (*.f64 (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) #s(literal -2 binary64)))
(* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (+ eps (* 2 x))))))
(.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (*.f64 (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) #s(literal -2 binary64)))
(* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (- eps (* -2 x))))))
(.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (*.f64 (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) #s(literal -2 binary64)))
(* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (- eps (* -2 x))))))
(.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (*.f64 (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) #s(literal -2 binary64)))
(* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (- eps (* -2 x))))))
(.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (*.f64 (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) #s(literal -2 binary64)))
(* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (- eps (* -2 x))))))
(.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (*.f64 (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) #s(literal -2 binary64)))
(* 1/2 (* eps (sin x)))
(.f64 #s(literal 1/2 binary64) (.f64 eps (sin.f64 x)))
(* eps (+ (* 1/4 (* eps (cos x))) (* 1/2 (sin x))))
(.f64 eps (fma.f64 (.f64 eps (cos.f64 x)) #s(literal 1/4 binary64) (*.f64 #s(literal 1/2 binary64) (sin.f64 x))))
(* 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 #s(literal 1/2 binary64) (sin.f64 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))))))))))
(.f64 eps (fma.f64 eps (fma.f64 eps (fma.f64 (.f64 eps (cos.f64 x)) #s(literal -1/48 binary64) (.f64 (sin.f64 x) #s(literal -1/12 binary64))) (.f64 (cos.f64 x) #s(literal 1/4 binary64))) (*.f64 #s(literal 1/2 binary64) (sin.f64 x))))
(* (sin (* 1/2 eps)) (sin (* 1/2 (+ eps (* 2 x)))))
(.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x)))
(* (sin (* 1/2 eps)) (sin (* 1/2 (+ eps (* 2 x)))))
(.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x)))
(* (sin (* 1/2 eps)) (sin (* 1/2 (+ eps (* 2 x)))))
(.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x)))
(* (sin (* 1/2 eps)) (sin (* 1/2 (+ eps (* 2 x)))))
(.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x)))
(* (sin (* 1/2 eps)) (sin (* 1/2 (- (* 2 x) (* -1 eps)))))
(.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x)))
(* (sin (* 1/2 eps)) (sin (* 1/2 (- (* 2 x) (* -1 eps)))))
(.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x)))
(* (sin (* 1/2 eps)) (sin (* 1/2 (- (* 2 x) (* -1 eps)))))
(.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x)))
(* (sin (* 1/2 eps)) (sin (* 1/2 (- (* 2 x) (* -1 eps)))))
(.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x)))
(pow (sin (* 1/2 eps)) 2)
(pow.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) #s(literal 2 binary64))
(+ (* x (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) (pow (sin (* 1/2 eps)) 2))
(.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (fma.f64 x (cos.f64 (.f64 #s(literal 1/2 binary64) eps)) (sin.f64 (.f64 #s(literal 1/2 binary64) eps))))
(+ (* x (+ (* -1/2 (* x (pow (sin (* 1/2 eps)) 2))) (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))) (pow (sin (* 1/2 eps)) 2))
(fma.f64 x (.f64 (pow.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) #s(literal 2 binary64)) (.f64 x #s(literal -1/2 binary64))) (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (fma.f64 x (cos.f64 (.f64 #s(literal 1/2 binary64) eps)) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)))))
(+ (* 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))
(fma.f64 (fma.f64 #s(literal -1/2 binary64) (pow.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) #s(literal 2 binary64)) (.f64 (.f64 (cos.f64 (.f64 #s(literal 1/2 binary64) eps)) (.f64 x #s(literal -1/6 binary64))) (sin.f64 (.f64 #s(literal 1/2 binary64) eps)))) (.f64 x x) (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (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)) (sin (* 1/2 (+ eps (* 2 x)))))
(.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x)))
(* (sin (* 1/2 eps)) (sin (* 1/2 (+ eps (* 2 x)))))
(.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x)))
(* (sin (* 1/2 eps)) (sin (* 1/2 (+ eps (* 2 x)))))
(.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x)))
(* (sin (* 1/2 eps)) (sin (* 1/2 (+ eps (* 2 x)))))
(.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x)))
(* (sin (* 1/2 eps)) (sin (* 1/2 (- eps (* -2 x)))))
(.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x)))
(* (sin (* 1/2 eps)) (sin (* 1/2 (- eps (* -2 x)))))
(.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x)))
(* (sin (* 1/2 eps)) (sin (* 1/2 (- eps (* -2 x)))))
(.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x)))
(* (sin (* 1/2 eps)) (sin (* 1/2 (- eps (* -2 x)))))
(.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x)))
(- (cos eps) 1)
(+.f64 #s(literal -1 binary64) (cos.f64 eps))
(- (+ (cos eps) (* -1 (* x (sin eps)))) 1)
(+.f64 (cos.f64 eps) (fma.f64 (sin.f64 eps) (neg.f64 x) #s(literal -1 binary64)))
(- (+ (cos eps) (* x (- (* x (+ 1/2 (* -1/2 (cos eps)))) (sin eps)))) 1)
(fma.f64 x (-.f64 (*.f64 x (fma.f64 #s(literal -1/2 binary64) (cos.f64 eps) #s(literal 1/2 binary64))) (sin.f64 eps)) (+.f64 #s(literal -1 binary64) (cos.f64 eps)))
(- (+ (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 (fma.f64 x (fma.f64 x (*.f64 (sin.f64 eps) #s(literal 1/6 binary64)) (fma.f64 #s(literal -1/2 binary64) (cos.f64 eps) #s(literal 1/2 binary64))) (neg.f64 (sin.f64 eps))) (cos.f64 eps)))
(- (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)))
(neg.f64 (*.f64 eps (sin.f64 x)))
(* eps (- (* -1/2 (* eps (cos x))) (sin x)))
(.f64 eps (-.f64 (.f64 #s(literal -1/2 binary64) (*.f64 eps (cos.f64 x))) (sin.f64 x)))
(* eps (- (* eps (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x))))) (sin x)))
(.f64 eps (fma.f64 eps (fma.f64 eps (.f64 (sin.f64 x) #s(literal 1/6 binary64)) (*.f64 #s(literal -1/2 binary64) (cos.f64 x))) (neg.f64 (sin.f64 x))))
(* 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 eps (fma.f64 eps (.f64 (cos.f64 x) #s(literal 1/24 binary64)) (.f64 (sin.f64 x) #s(literal 1/6 binary64))) (.f64 #s(literal -1/2 binary64) (cos.f64 x))) (neg.f64 (sin.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))
(* -1/2 (pow eps 2))
(.f64 eps (.f64 eps #s(literal -1/2 binary64)))
(* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2))
(.f64 eps (.f64 eps (fma.f64 eps (*.f64 eps #s(literal 1/24 binary64)) #s(literal -1/2 binary64))))
(* (pow eps 2) (- (* (pow eps 2) (+ 1/24 (* -1/720 (pow eps 2)))) 1/2))
(.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)))
(* (pow eps 2) (- (* (pow eps 2) (+ 1/24 (* (pow eps 2) (- (* 1/40320 (pow eps 2)) 1/720)))) 1/2))
(.f64 (.f64 eps eps) (fma.f64 (.f64 eps eps) (fma.f64 (.f64 eps eps) (fma.f64 (*.f64 eps eps) #s(literal 1/40320 binary64) #s(literal -1/720 binary64)) #s(literal 1/24 binary64)) #s(literal -1/2 binary64)))
(- (cos eps) 1)
(+.f64 #s(literal -1 binary64) (cos.f64 eps))
(- (cos eps) 1)
(+.f64 #s(literal -1 binary64) (cos.f64 eps))
(- (cos eps) 1)
(+.f64 #s(literal -1 binary64) (cos.f64 eps))
(- (cos eps) 1)
(+.f64 #s(literal -1 binary64) (cos.f64 eps))
(- (cos eps) 1)
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(+.f64 (cos.f64 x) (cos.f64 (+.f64 eps x)))
(+ (cos x) (cos (- x (* -1 eps))))
(+.f64 (cos.f64 x) (cos.f64 (+.f64 eps x)))
eps
(+ eps (* 2 x))
(fma.f64 x #s(literal 2 binary64) eps)
(+ eps (* 2 x))
(fma.f64 x #s(literal 2 binary64) eps)
(+ eps (* 2 x))
(fma.f64 x #s(literal 2 binary64) eps)
(* 2 x)
(*.f64 x #s(literal 2 binary64))
(* x (+ 2 (/ eps x)))
(*.f64 x (+.f64 (/.f64 eps x) #s(literal 2 binary64)))
(* x (+ 2 (/ eps x)))
(*.f64 x (+.f64 (/.f64 eps x) #s(literal 2 binary64)))
(* x (+ 2 (/ eps x)))
(*.f64 x (+.f64 (/.f64 eps x) #s(literal 2 binary64)))
(* 2 x)
(*.f64 x #s(literal 2 binary64))
(* -1 (* x (- (* -1 (/ eps x)) 2)))
(*.f64 (neg.f64 x) (-.f64 #s(literal -2 binary64) (/.f64 eps x)))
(* -1 (* x (- (* -1 (/ eps x)) 2)))
(*.f64 (neg.f64 x) (-.f64 #s(literal -2 binary64) (/.f64 eps x)))
(* -1 (* x (- (* -1 (/ eps x)) 2)))
(*.f64 (neg.f64 x) (-.f64 #s(literal -2 binary64) (/.f64 eps x)))
(* 2 x)
(*.f64 x #s(literal 2 binary64))
(+ eps (* 2 x))
(fma.f64 x #s(literal 2 binary64) eps)
(+ eps (* 2 x))
(fma.f64 x #s(literal 2 binary64) eps)
(+ eps (* 2 x))
(fma.f64 x #s(literal 2 binary64) eps)
eps
(* eps (+ 1 (* 2 (/ x eps))))
(fma.f64 eps (/.f64 (*.f64 x #s(literal 2 binary64)) eps) eps)
(* eps (+ 1 (* 2 (/ x eps))))
(fma.f64 eps (/.f64 (*.f64 x #s(literal 2 binary64)) eps) eps)
(* eps (+ 1 (* 2 (/ x eps))))
(fma.f64 eps (/.f64 (*.f64 x #s(literal 2 binary64)) eps) eps)
eps
(* -1 (* eps (- (* -2 (/ x eps)) 1)))
(fma.f64 (neg.f64 eps) (/.f64 (*.f64 x #s(literal -2 binary64)) eps) eps)
(* -1 (* eps (- (* -2 (/ x eps)) 1)))
(fma.f64 (neg.f64 eps) (/.f64 (*.f64 x #s(literal -2 binary64)) eps) eps)
(* -1 (* eps (- (* -2 (/ x eps)) 1)))
(fma.f64 (neg.f64 eps) (/.f64 (*.f64 x #s(literal -2 binary64)) eps) eps)
(sin (* 1/2 eps))
(sin.f64 (*.f64 #s(literal 1/2 binary64) eps))
(+ (sin (* 1/2 eps)) (* x (cos (* 1/2 eps))))
(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 #s(literal 1/2 binary64) (*.f64 eps (cos.f64 x)) (sin.f64 x))
(+ (sin x) (* eps (+ (* -1/8 (* eps (sin x))) (* 1/2 (cos x)))))
(fma.f64 eps (fma.f64 #s(literal 1/2 binary64) (cos.f64 x) (.f64 (.f64 eps (sin.f64 x)) #s(literal -1/8 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 (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 eps)
(*.f64 #s(literal 1/2 binary64) eps)
(* eps (+ 1/2 (* -1/48 (pow eps 2))))
(.f64 eps (fma.f64 eps (.f64 eps #s(literal -1/48 binary64)) #s(literal 1/2 binary64)))
(* eps (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48))))
(.f64 eps (fma.f64 eps (.f64 eps (fma.f64 (*.f64 eps eps) #s(literal 1/3840 binary64) #s(literal -1/48 binary64))) #s(literal 1/2 binary64)))
(* eps (+ 1/2 (* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48))))
(.f64 eps (fma.f64 (.f64 eps eps) (fma.f64 (.f64 eps eps) (fma.f64 (.f64 eps eps) #s(literal -1/645120 binary64) #s(literal 1/3840 binary64)) #s(literal -1/48 binary64)) #s(literal 1/2 binary64)))
(sin (* 1/2 eps))
(sin.f64 (*.f64 #s(literal 1/2 binary64) eps))
(sin (* 1/2 eps))
(sin.f64 (*.f64 #s(literal 1/2 binary64) eps))
(sin (* 1/2 eps))
(sin.f64 (*.f64 #s(literal 1/2 binary64) eps))
(sin (* 1/2 eps))
(sin.f64 (*.f64 #s(literal 1/2 binary64) eps))
(sin (* 1/2 eps))
(sin.f64 (*.f64 #s(literal 1/2 binary64) eps))
(sin (* 1/2 eps))
(sin.f64 (*.f64 #s(literal 1/2 binary64) eps))
(sin (* 1/2 eps))
(sin.f64 (*.f64 #s(literal 1/2 binary64) eps))
(sin (* 1/2 eps))
(sin.f64 (*.f64 #s(literal 1/2 binary64) eps))
(* -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))
(cos (* 2 eps))
(cos.f64 (*.f64 eps #s(literal 2 binary64)))
(+ (cos (* 2 eps)) (* -2 (* x (sin (* 2 eps)))))
(fma.f64 (.f64 x #s(literal -2 binary64)) (sin.f64 (.f64 eps #s(literal 2 binary64))) (cos.f64 (*.f64 eps #s(literal 2 binary64))))
(+ (cos (* 2 eps)) (* x (- (* -2 (* x (cos (* 2 eps)))) (* 2 (sin (* 2 eps))))))
(fma.f64 x (.f64 #s(literal -2 binary64) (fma.f64 x (cos.f64 (.f64 eps #s(literal 2 binary64))) (sin.f64 (.f64 eps #s(literal 2 binary64))))) (cos.f64 (.f64 eps #s(literal 2 binary64))))
(+ (cos (* 2 eps)) (* x (- (* x (+ (* -2 (cos (* 2 eps))) (* 4/3 (* x (sin (* 2 eps)))))) (* 2 (sin (* 2 eps))))))
(fma.f64 x (fma.f64 x (fma.f64 #s(literal -2 binary64) (cos.f64 (.f64 eps #s(literal 2 binary64))) (.f64 (sin.f64 (.f64 eps #s(literal 2 binary64))) (.f64 x #s(literal 4/3 binary64)))) (.f64 #s(literal -2 binary64) (sin.f64 (.f64 eps #s(literal 2 binary64))))) (cos.f64 (*.f64 eps #s(literal 2 binary64))))
(cos (* 2 (+ eps x)))
(cos.f64 (*.f64 #s(literal 2 binary64) (+.f64 eps x)))
(cos (* 2 (+ eps x)))
(cos.f64 (*.f64 #s(literal 2 binary64) (+.f64 eps x)))
(cos (* 2 (+ eps x)))
(cos.f64 (*.f64 #s(literal 2 binary64) (+.f64 eps x)))
(cos (* 2 (+ eps x)))
(cos.f64 (*.f64 #s(literal 2 binary64) (+.f64 eps x)))
(cos (* 2 (- eps (* -1 x))))
(cos.f64 (*.f64 #s(literal 2 binary64) (+.f64 eps x)))
(cos (* 2 (- eps (* -1 x))))
(cos.f64 (*.f64 #s(literal 2 binary64) (+.f64 eps x)))
(cos (* 2 (- eps (* -1 x))))
(cos.f64 (*.f64 #s(literal 2 binary64) (+.f64 eps x)))
(cos (* 2 (- eps (* -1 x))))
(cos.f64 (*.f64 #s(literal 2 binary64) (+.f64 eps x)))
(cos (* 2 x))
(cos.f64 (*.f64 x #s(literal 2 binary64)))
(+ (cos (* 2 x)) (* -2 (* eps (sin (* 2 x)))))
(fma.f64 (sin.f64 (.f64 x #s(literal 2 binary64))) (.f64 eps #s(literal -2 binary64)) (cos.f64 (*.f64 x #s(literal 2 binary64))))
(+ (cos (* 2 x)) (* eps (- (* -2 (* eps (cos (* 2 x)))) (* 2 (sin (* 2 x))))))
(fma.f64 eps (.f64 #s(literal -2 binary64) (fma.f64 eps (cos.f64 (.f64 x #s(literal 2 binary64))) (sin.f64 (.f64 x #s(literal 2 binary64))))) (cos.f64 (.f64 x #s(literal 2 binary64))))
(+ (cos (* 2 x)) (* eps (- (* eps (+ (* -2 (cos (* 2 x))) (* 4/3 (* eps (sin (* 2 x)))))) (* 2 (sin (* 2 x))))))
(fma.f64 eps (fma.f64 eps (fma.f64 #s(literal -2 binary64) (cos.f64 (.f64 x #s(literal 2 binary64))) (.f64 (sin.f64 (.f64 x #s(literal 2 binary64))) (.f64 eps #s(literal 4/3 binary64)))) (.f64 #s(literal -2 binary64) (sin.f64 (.f64 x #s(literal 2 binary64))))) (cos.f64 (*.f64 x #s(literal 2 binary64))))
(cos (* 2 (+ eps x)))
(cos.f64 (*.f64 #s(literal 2 binary64) (+.f64 eps x)))
(cos (* 2 (+ eps x)))
(cos.f64 (*.f64 #s(literal 2 binary64) (+.f64 eps x)))
(cos (* 2 (+ eps x)))
(cos.f64 (*.f64 #s(literal 2 binary64) (+.f64 eps x)))
(cos (* 2 (+ eps x)))
(cos.f64 (*.f64 #s(literal 2 binary64) (+.f64 eps x)))
(cos (* 2 (- x (* -1 eps))))
(cos.f64 (*.f64 #s(literal 2 binary64) (+.f64 eps x)))
(cos (* 2 (- x (* -1 eps))))
(cos.f64 (*.f64 #s(literal 2 binary64) (+.f64 eps x)))
(cos (* 2 (- x (* -1 eps))))
(cos.f64 (*.f64 #s(literal 2 binary64) (+.f64 eps x)))
(cos (* 2 (- x (* -1 eps))))
(cos.f64 (*.f64 #s(literal 2 binary64) (+.f64 eps x)))
(+ 1/2 (* 1/2 (cos (* 2 eps))))
(fma.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 eps #s(literal 2 binary64))) #s(literal 1/2 binary64))
(+ 1/2 (+ (* -1 (* x (sin (* 2 eps)))) (* 1/2 (cos (* 2 eps)))))
(fma.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 eps #s(literal 2 binary64))) (fma.f64 (neg.f64 x) (sin.f64 (.f64 eps #s(literal 2 binary64))) #s(literal 1/2 binary64)))
(+ 1/2 (+ (* 1/2 (cos (* 2 eps))) (* x (+ (* -1 (sin (* 2 eps))) (* -1 (* x (cos (* 2 eps))))))))
(fma.f64 x (neg.f64 (fma.f64 x (cos.f64 (.f64 eps #s(literal 2 binary64))) (sin.f64 (.f64 eps #s(literal 2 binary64))))) (fma.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 eps #s(literal 2 binary64))) #s(literal 1/2 binary64)))
(+ 1/2 (+ (* 1/2 (cos (* 2 eps))) (* x (+ (* -1 (sin (* 2 eps))) (* x (+ (* -1 (cos (* 2 eps))) (* 2/3 (* x (sin (* 2 eps))))))))))
(fma.f64 x (fma.f64 x (-.f64 (.f64 (sin.f64 (.f64 eps #s(literal 2 binary64))) (.f64 x #s(literal 2/3 binary64))) (cos.f64 (.f64 eps #s(literal 2 binary64)))) (neg.f64 (sin.f64 (.f64 eps #s(literal 2 binary64))))) (fma.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 eps #s(literal 2 binary64))) #s(literal 1/2 binary64)))
(+ 1/2 (* 1/2 (cos (* 2 (+ eps x)))))
(fma.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) (+.f64 eps x))) #s(literal 1/2 binary64))
(+ 1/2 (* 1/2 (cos (* 2 (+ eps x)))))
(fma.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) (+.f64 eps x))) #s(literal 1/2 binary64))
(+ 1/2 (* 1/2 (cos (* 2 (+ eps x)))))
(fma.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) (+.f64 eps x))) #s(literal 1/2 binary64))
(+ 1/2 (* 1/2 (cos (* 2 (+ eps x)))))
(fma.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) (+.f64 eps x))) #s(literal 1/2 binary64))
(+ 1/2 (* 1/2 (cos (* 2 (- eps (* -1 x))))))
(fma.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) (+.f64 eps x))) #s(literal 1/2 binary64))
(+ 1/2 (* 1/2 (cos (* 2 (- eps (* -1 x))))))
(fma.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) (+.f64 eps x))) #s(literal 1/2 binary64))
(+ 1/2 (* 1/2 (cos (* 2 (- eps (* -1 x))))))
(fma.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) (+.f64 eps x))) #s(literal 1/2 binary64))
(+ 1/2 (* 1/2 (cos (* 2 (- eps (* -1 x))))))
(fma.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) (+.f64 eps x))) #s(literal 1/2 binary64))
(+ 1/2 (* 1/2 (cos (* 2 x))))
(fma.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 x #s(literal 2 binary64))) #s(literal 1/2 binary64))
(+ 1/2 (+ (* -1 (* eps (sin (* 2 x)))) (* 1/2 (cos (* 2 x)))))
(fma.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 x #s(literal 2 binary64))) (fma.f64 eps (sin.f64 (.f64 x #s(literal -2 binary64))) #s(literal 1/2 binary64)))
(+ 1/2 (+ (* 1/2 (cos (* 2 x))) (* eps (+ (* -1 (sin (* 2 x))) (* -1 (* eps (cos (* 2 x))))))))
(fma.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 x #s(literal 2 binary64))) (fma.f64 eps (fma.f64 (neg.f64 eps) (cos.f64 (.f64 x #s(literal 2 binary64))) (sin.f64 (*.f64 x #s(literal -2 binary64)))) #s(literal 1/2 binary64)))
(+ 1/2 (+ (* 1/2 (cos (* 2 x))) (* eps (+ (* -1 (sin (* 2 x))) (* eps (+ (* -1 (cos (* 2 x))) (* 2/3 (* eps (sin (* 2 x))))))))))
(fma.f64 eps (fma.f64 eps (-.f64 (.f64 (sin.f64 (.f64 x #s(literal 2 binary64))) (.f64 eps #s(literal 2/3 binary64))) (cos.f64 (.f64 x #s(literal 2 binary64)))) (sin.f64 (.f64 x #s(literal -2 binary64)))) (fma.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 x #s(literal 2 binary64))) #s(literal 1/2 binary64)))
(+ 1/2 (* 1/2 (cos (* 2 (+ eps x)))))
(fma.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) (+.f64 eps x))) #s(literal 1/2 binary64))
(+ 1/2 (* 1/2 (cos (* 2 (+ eps x)))))
(fma.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) (+.f64 eps x))) #s(literal 1/2 binary64))
(+ 1/2 (* 1/2 (cos (* 2 (+ eps x)))))
(fma.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) (+.f64 eps x))) #s(literal 1/2 binary64))
(+ 1/2 (* 1/2 (cos (* 2 (+ eps x)))))
(fma.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) (+.f64 eps x))) #s(literal 1/2 binary64))
(+ 1/2 (* 1/2 (cos (* 2 (- x (* -1 eps))))))
(fma.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) (+.f64 eps x))) #s(literal 1/2 binary64))
(+ 1/2 (* 1/2 (cos (* 2 (- x (* -1 eps))))))
(fma.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) (+.f64 eps x))) #s(literal 1/2 binary64))
(+ 1/2 (* 1/2 (cos (* 2 (- x (* -1 eps))))))
(fma.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) (+.f64 eps x))) #s(literal 1/2 binary64))
(+ 1/2 (* 1/2 (cos (* 2 (- x (* -1 eps))))))
(fma.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) (+.f64 eps x))) #s(literal 1/2 binary64))

rewrite129.0ms (0.7%)

Memory

34.4MiB live, 148.8MiB allocated

Rules

1 110×	`lower-fma.f32`
1 104×	`lower-fma.f64`
1 068×	`lower-*.f32`
1 056×	`lower-*.f64`
904×	`lower-/.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	44	214
0	77	206
1	286	149
0	2355	148

Stop Event

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

Counts

24 → 624

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

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

eval168.0ms (1%)

Memory: 4.5MiB live, 199.5MiB allocated
Compiler: Compiled 34 028 to 2 693 computations (92.1% saved)

prune173.0ms (1%)

Memory

-8.9MiB live, 264.7MiB allocated

Pruning

39 alts after pruning (37 fresh and 2 done)

	Pruned	Kept	Total
New	1 322	30	1 352
Fresh	3	7	10
Picked	4	1	5
Done	0	1	1
Total	1 329	39	1 368

Accuracy

100.0%

Counts

1 368 → 39

Alt Table

Click to see full alt table

Status	Accuracy	Program
	48.8%	(/.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)))))
	49.2%	(/.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))))))
	49.2%	(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (-.f64 (fma.f64 (cos.f64 x) (cos.f64 eps) (*.f64 (neg.f64 (sin.f64 x)) (sin.f64 eps))) (cos.f64 x))))
	97.9%	(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) #s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps (-.f64 (.f64 #s(literal -1/2 binary64) (*.f64 eps (cos.f64 x))) (sin.f64 x))))))
	47.5%	(/.f64 #s(literal 1 binary64) (exp.f64 (*.f64 (log.f64 (-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))) #s(literal -1 binary64))))
	59.5%	(/.f64 #s(literal 1 binary64) #s(approx (/ 1 (- (cos (+ x eps)) (cos x))) (fma.f64 (fma.f64 eps (fma.f64 (/.f64 (pow.f64 (cos.f64 x) #s(literal 2 binary64)) (pow.f64 (sin.f64 x) #s(literal 3 binary64))) #s(literal -1/4 binary64) (neg.f64 (/.f64 #s(literal 1/6 binary64) (sin.f64 x)))) (/.f64 (.f64 #s(literal 1/2 binary64) (cos.f64 x)) (pow.f64 (sin.f64 x) #s(literal 2 binary64)))) #s(literal 1 binary64) (/.f64 #s(literal -1 binary64) (.f64 eps (sin.f64 x))))))
	52.8%	(/.f64 #s(literal 1 binary64) #s(approx (/ 1 (- (cos (+ x eps)) (cos x))) (fma.f64 (fma.f64 #s(literal 1/2 binary64) (/.f64 (cos.f64 x) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (.f64 eps (neg.f64 (fma.f64 eps (fma.f64 #s(literal -1/2 binary64) (.f64 (fma.f64 #s(literal 1/4 binary64) (/.f64 (pow.f64 (cos.f64 x) #s(literal 2 binary64)) (pow.f64 (sin.f64 x) #s(literal 3 binary64))) (/.f64 #s(literal 1/6 binary64) (sin.f64 x))) (/.f64 (cos.f64 x) (sin.f64 x))) (/.f64 (.f64 (cos.f64 x) #s(literal -1/24 binary64)) (pow.f64 (sin.f64 x) #s(literal 2 binary64)))) (fma.f64 #s(literal 1/4 binary64) (/.f64 (pow.f64 (cos.f64 x) #s(literal 2 binary64)) (pow.f64 (sin.f64 x) #s(literal 3 binary64))) (/.f64 #s(literal 1/6 binary64) (sin.f64 x))))))) #s(literal 1 binary64) (/.f64 #s(literal -1 binary64) (.f64 eps (sin.f64 x))))))
	49.2%	(-.f64 (fma.f64 (sin.f64 (neg.f64 x)) (sin.f64 eps) (*.f64 (cos.f64 x) (cos.f64 eps))) (cos.f64 x))
	49.2%	(-.f64 (*.f64 (cos.f64 x) (cos.f64 eps)) (fma.f64 (sin.f64 x) (sin.f64 eps) (cos.f64 x)))
✓	48.7%	(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))
✓	47.1%	(-.f64 (cos.f64 (+.f64 x eps)) #s(approx (cos x) (fma.f64 x (*.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64))))
	47.2%	(-.f64 (cos.f64 (+.f64 x eps)) #s(approx (cos x) #s(literal 1 binary64)))
	47.0%	(-.f64 #s(approx (cos (+ x eps)) (cos.f64 x)) #s(approx (cos x) (fma.f64 x (*.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64))))
▶	98.5%	(.f64 (/.f64 #s(literal 1 binary64) (+.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))) #s(approx (- (+ ( 1/2 (cos (* (+ x eps) 2))) 1/2) (+ (* 1/2 (cos (+ x x))) 1/2)) (.f64 eps (fma.f64 (neg.f64 eps) (cos.f64 (.f64 x #s(literal 2 binary64))) (sin.f64 (*.f64 x #s(literal -2 binary64)))))))
	48.8%	(.f64 (/.f64 #s(literal 1 binary64) (+.f64 (cos.f64 (.f64 (.f64 (+.f64 x eps) (-.f64 x eps)) (/.f64 #s(literal 1 binary64) (-.f64 x eps)))) (cos.f64 x))) (-.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))))
	32.6%	(.f64 (.f64 (sin.f64 (.f64 (/.f64 (fma.f64 (.f64 (fma.f64 x x #s(literal 0 binary64)) #s(literal 0 binary64)) eps (.f64 (fma.f64 x x #s(literal 0 binary64)) (.f64 eps eps))) (.f64 (fma.f64 x x #s(literal 0 binary64)) eps)) #s(literal 1/2 binary64))) (sin.f64 (.f64 (+.f64 x (+.f64 x eps)) #s(literal 1/2 binary64)))) #s(literal -2 binary64))
	43.7%	(.f64 (.f64 (sin.f64 (.f64 (/.f64 (.f64 (fma.f64 x x (.f64 (+.f64 x eps) eps)) eps) (fma.f64 (+.f64 x eps) (+.f64 x eps) (-.f64 (.f64 x x) (.f64 x (+.f64 x eps))))) #s(literal 1/2 binary64))) (sin.f64 (.f64 (+.f64 x (+.f64 x eps)) #s(literal 1/2 binary64)))) #s(literal -2 binary64))
	98.4%	(.f64 (.f64 (sin.f64 (.f64 (/.f64 (.f64 eps eps) eps) #s(literal 1/2 binary64))) (sin.f64 (*.f64 (+.f64 x (+.f64 x eps)) #s(literal 1/2 binary64)))) #s(literal -2 binary64))
	98.4%	(.f64 (.f64 (sin.f64 (.f64 (/.f64 #s(literal 1 binary64) (/.f64 eps (.f64 eps eps))) #s(literal 1/2 binary64))) (sin.f64 (*.f64 (+.f64 x (+.f64 x eps)) #s(literal 1/2 binary64)))) #s(literal -2 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 (/.f64 (.f64 x x) (-.f64 x eps)) (/.f64 (.f64 eps eps) (-.f64 x eps)))) #s(literal 1/2 binary64)))) #s(literal -2 binary64))
	44.3%	(.f64 (.f64 (sin.f64 (.f64 (+.f64 eps #s(literal 0 binary64)) #s(literal 1/2 binary64))) (sin.f64 (.f64 (+.f64 x (.f64 (fma.f64 x (.f64 x x) (.f64 eps (.f64 eps eps))) (/.f64 #s(literal 1 binary64) (fma.f64 eps (-.f64 eps x) (*.f64 x x))))) #s(literal 1/2 binary64)))) #s(literal -2 binary64))
	99.4%	(.f64 (.f64 (sin.f64 (.f64 (+.f64 eps #s(literal 0 binary64)) #s(literal 1/2 binary64))) (sin.f64 (.f64 (+.f64 x #s(approx (+ x eps) (fma.f64 eps (/.f64 x eps) eps))) #s(literal 1/2 binary64)))) #s(literal -2 binary64))
	99.5%	(.f64 (.f64 (sin.f64 (.f64 (+.f64 eps #s(literal 0 binary64)) #s(literal 1/2 binary64))) (sin.f64 (.f64 #s(approx (+ x (+ x eps)) (*.f64 x (+.f64 (/.f64 eps x) #s(literal 2 binary64)))) #s(literal 1/2 binary64)))) #s(literal -2 binary64))
	99.4%	(.f64 (.f64 (sin.f64 (.f64 (+.f64 eps #s(literal 0 binary64)) #s(literal 1/2 binary64))) (sin.f64 #s(approx ( (+ x (+ x eps)) 1/2) (*.f64 eps (+.f64 #s(literal 1/2 binary64) (/.f64 x eps)))))) #s(literal -2 binary64))
	39.1%	(.f64 (.f64 (sin.f64 (.f64 (.f64 (.f64 eps (.f64 eps eps)) (/.f64 #s(literal 1 binary64) (.f64 eps eps))) #s(literal 1/2 binary64))) (sin.f64 (.f64 (+.f64 x (+.f64 x eps)) #s(literal 1/2 binary64)))) #s(literal -2 binary64))
▶	98.3%	(.f64 (.f64 (sin.f64 (.f64 (.f64 (.f64 eps eps) (/.f64 #s(literal 1 binary64) eps)) #s(literal 1/2 binary64))) (sin.f64 (.f64 (+.f64 x (+.f64 x eps)) #s(literal 1/2 binary64)))) #s(literal -2 binary64))
	99.5%	(.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))
▶	99.3%	(.f64 (.f64 #s(approx (sin (* (+ eps 0) 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)))) (sin.f64 (*.f64 (+.f64 x (+.f64 x eps)) #s(literal 1/2 binary64)))) #s(literal -2 binary64))
	99.3%	(.f64 (.f64 #s(approx (sin (* (+ eps 0) 1/2)) (.f64 eps (fma.f64 eps (.f64 eps (fma.f64 (.f64 eps eps) #s(literal 1/3840 binary64) #s(literal -1/48 binary64))) #s(literal 1/2 binary64)))) (sin.f64 (.f64 (+.f64 x (+.f64 x eps)) #s(literal 1/2 binary64)))) #s(literal -2 binary64))
	99.2%	(.f64 (.f64 #s(approx (sin (* (+ eps 0) 1/2)) (.f64 eps (fma.f64 eps (.f64 eps #s(literal -1/48 binary64)) #s(literal 1/2 binary64)))) (sin.f64 (*.f64 (+.f64 x (+.f64 x eps)) #s(literal 1/2 binary64)))) #s(literal -2 binary64))
	98.7%	(.f64 (.f64 #s(approx (sin (* (+ eps 0) 1/2)) (.f64 #s(literal 1/2 binary64) eps)) (sin.f64 (.f64 (+.f64 x (+.f64 x eps)) #s(literal 1/2 binary64)))) #s(literal -2 binary64))
▶	99.5%	(.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))
	98.7%	#s(approx (/ 1 (/ 1 (- (cos (+ x eps)) (cos x)))) (.f64 eps (-.f64 (.f64 #s(literal -1/2 binary64) (*.f64 eps (cos.f64 x))) (sin.f64 x))))
	76.1%	#s(approx (/ 1 (/ 1 (- (cos (+ x eps)) (cos x)))) (neg.f64 (*.f64 eps (sin.f64 x))))
	47.1%	#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)))
▶	46.9%	#s(approx (- (cos (+ x eps)) (cos x)) (+.f64 #s(approx (cos eps) #s(literal 1 binary64)) #s(literal -1 binary64)))
	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)))))
	99.1%	#s(approx (- (cos (+ x eps)) (cos 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))))))
	48.7%	#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (+ (cos eps) -1) (.f64 eps (.f64 eps #s(literal -1/2 binary64)))))

Compiler

Compiled 1 855 to 1 113 computations (40% saved)

simplify221.0ms (1.3%)

Memory

-26.1MiB live, 311.3MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 19 expressions of interest:

New	Metric	Score
cost-diff	0	(+.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))
cost-diff	0	(/.f64 #s(literal 1 binary64) (+.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x)))
cost-diff	128	(*.f64 x #s(literal 2 binary64))
cost-diff	320	(.f64 (/.f64 #s(literal 1 binary64) (+.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))) #s(approx (- (+ ( 1/2 (cos (* (+ x eps) 2))) 1/2) (+ (* 1/2 (cos (+ x x))) 1/2)) (.f64 eps (fma.f64 (neg.f64 eps) (cos.f64 (.f64 x #s(literal 2 binary64))) (sin.f64 (*.f64 x #s(literal -2 binary64)))))))
cost-diff	0	(.f64 (sin.f64 (.f64 (.f64 (.f64 eps eps) (/.f64 #s(literal 1 binary64) eps)) #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 (.f64 eps eps) (/.f64 #s(literal 1 binary64) eps)) #s(literal 1/2 binary64))) (sin.f64 (.f64 (+.f64 x (+.f64 x eps)) #s(literal 1/2 binary64)))) #s(literal -2 binary64))
cost-diff	320	(*.f64 (+.f64 x (+.f64 x eps)) #s(literal 1/2 binary64))
cost-diff	1344	(.f64 (.f64 eps eps) (/.f64 #s(literal 1 binary64) eps))
cost-diff	0	#s(approx (sin (* (+ eps 0) 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))))
cost-diff	0	(.f64 #s(approx (sin ( (+ eps 0) 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)))) (sin.f64 (*.f64 (+.f64 x (+.f64 x eps)) #s(literal 1/2 binary64))))
cost-diff	0	(.f64 (.f64 #s(approx (sin (* (+ eps 0) 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)))) (sin.f64 (*.f64 (+.f64 x (+.f64 x eps)) #s(literal 1/2 binary64)))) #s(literal -2 binary64))
cost-diff	320	(*.f64 (+.f64 x (+.f64 x eps)) #s(literal 1/2 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	(sin.f64 (*.f64 #s(literal 1/2 binary64) eps))
cost-diff	0	(.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x)))
cost-diff	0	#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))))
cost-diff	0	(.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))

Rules

11 654×	`lower-fma.f32`
11 644×	`lower-fma.f64`
3 816×	`lower-*.f32`
3 786×	`lower-*.f64`
2 686×	`lower-+.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	73	535
0	114	492
1	209	480
2	513	472
3	1383	451
4	2439	451
5	5254	451
0	8066	449

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

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

localize514.0ms (3%)

Memory

44.9MiB live, 857.5MiB allocated

Localize:

Found 19 expressions of interest:

New	Metric	Score
accuracy	0.03582001953688403	(fma.f64 (neg.f64 eps) (cos.f64 (.f64 x #s(literal 2 binary64))) (sin.f64 (.f64 x #s(literal -2 binary64))))
accuracy	0.140625	(.f64 eps (fma.f64 (neg.f64 eps) (cos.f64 (.f64 x #s(literal 2 binary64))) (sin.f64 (*.f64 x #s(literal -2 binary64)))))
accuracy	0.2219610884876477	(cos.f64 (+.f64 x eps))
accuracy	0.7234893308688336	#s(approx (- (+ (* 1/2 (cos (* (+ x eps) 2))) 1/2) (+ (* 1/2 (cos (+ x x))) 1/2)) (.f64 eps (fma.f64 (neg.f64 eps) (cos.f64 (.f64 x #s(literal 2 binary64))) (sin.f64 (*.f64 x #s(literal -2 binary64))))))
accuracy	0.15234375	(.f64 (sin.f64 (.f64 (.f64 (.f64 eps eps) (/.f64 #s(literal 1 binary64) eps)) #s(literal 1/2 binary64))) (sin.f64 (*.f64 (+.f64 x (+.f64 x eps)) #s(literal 1/2 binary64))))
accuracy	0.21158976492644635	(sin.f64 (*.f64 (+.f64 x (+.f64 x eps)) #s(literal 1/2 binary64)))
accuracy	0.26171875	(+.f64 x (+.f64 x eps))
accuracy	26.913293192209373	(.f64 (.f64 eps eps) (/.f64 #s(literal 1 binary64) eps))
accuracy	0.11564352653852594	#s(approx (sin (* (+ eps 0) 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))))
accuracy	0.15234375	(.f64 #s(approx (sin ( (+ eps 0) 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)))) (sin.f64 (*.f64 (+.f64 x (+.f64 x eps)) #s(literal 1/2 binary64))))
accuracy	0.21158976492644635	(sin.f64 (*.f64 (+.f64 x (+.f64 x eps)) #s(literal 1/2 binary64)))
accuracy	0.26171875	(+.f64 x (+.f64 x eps))
accuracy	0.6901122721602273	#s(approx (cos eps) #s(literal 1 binary64))
accuracy	32.21940679149344	(+.f64 #s(approx (cos eps) #s(literal 1 binary64)) #s(literal -1 binary64))
accuracy	32.83146890767957	#s(approx (- (cos (+ x eps)) (cos x)) (+.f64 #s(approx (cos eps) #s(literal 1 binary64)) #s(literal -1 binary64)))
accuracy	0	(sin.f64 (*.f64 #s(literal 1/2 binary64) eps))
accuracy	0	#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))))
accuracy	0.15234375	(.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x)))
accuracy	0.21158976492644632	(sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x))

Samples

295.0ms	162×	2	valid
80.0ms	86×	1	valid
22.0ms	3×	3	valid
3.0ms	5×	0	valid

Compiler

Compiled 433 to 66 computations (84.8% saved)

Precisions

Click to see histograms. Total time spent on operations: 341.0ms

ival-cos: 143.0ms (41.9% of total)

ival-mult: 57.0ms (16.7% of total)

adjust: 54.0ms (15.8% of total)

ival-sin: 28.0ms (8.2% of total)

ival-add: 24.0ms (7% of total)

const: 20.0ms (5.9% of total)

ival-div: 7.0ms (2.1% of total)

ival-sub: 7.0ms (2.1% 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)

series34.0ms (0.2%)

Memory

-10.7MiB live, 66.2MiB allocated

Counts

25 → 528

Calls

Call 1

Inputs
#s(alt (.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)) (patch (.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)) #<representation binary64>) () ())
#s(alt #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)))) (patch #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)))) #<representation binary64>) () ())
#s(alt (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x))) (patch (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x))) #<representation binary64>) () ())
#s(alt (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (patch (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) #<representation binary64>) () ())
#s(alt #s(approx (- (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 (.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 (.f64 #s(approx (sin (* (+ eps 0) 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)))) (sin.f64 (.f64 (+.f64 x (+.f64 x eps)) #s(literal 1/2 binary64)))) #s(literal -2 binary64)) (patch (.f64 (.f64 #s(approx (sin ( (+ eps 0) 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)))) (sin.f64 (*.f64 (+.f64 x (+.f64 x eps)) #s(literal 1/2 binary64)))) #s(literal -2 binary64)) #<representation binary64>) () ())
#s(alt (.f64 #s(approx (sin ( (+ eps 0) 1/2)) (.f64 eps (fma.f64 (.f64 eps eps) (fma.f64 (.f64 eps eps) (fma.f64 (.f64 eps eps) #s(literal -1/645120 binary64) #s(literal 1/3840 binary64)) #s(literal -1/48 binary64)) #s(literal 1/2 binary64)))) (sin.f64 (.f64 (+.f64 x (+.f64 x eps)) #s(literal 1/2 binary64)))) (patch (.f64 #s(approx (sin (* (+ eps 0) 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)))) (sin.f64 (*.f64 (+.f64 x (+.f64 x eps)) #s(literal 1/2 binary64)))) #<representation binary64>) () ())
#s(alt #s(approx (sin (* (+ eps 0) 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)))) (patch #s(approx (sin (* (+ eps 0) 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)))) #<representation binary64>) () ())
#s(alt (.f64 (.f64 eps eps) (/.f64 #s(literal 1 binary64) eps)) (patch (.f64 (.f64 eps eps) (/.f64 #s(literal 1 binary64) eps)) #<representation binary64>) () ())
#s(alt (.f64 (.f64 (sin.f64 (.f64 (.f64 (.f64 eps eps) (/.f64 #s(literal 1 binary64) eps)) #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 (.f64 eps eps) (/.f64 #s(literal 1 binary64) eps)) #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 (.f64 eps eps) (/.f64 #s(literal 1 binary64) eps)) #s(literal 1/2 binary64))) (sin.f64 (.f64 (+.f64 x (+.f64 x eps)) #s(literal 1/2 binary64)))) (patch (.f64 (sin.f64 (.f64 (.f64 (.f64 eps eps) (/.f64 #s(literal 1 binary64) eps)) #s(literal 1/2 binary64))) (sin.f64 (.f64 (+.f64 x (+.f64 x eps)) #s(literal 1/2 binary64)))) #<representation binary64>) () ())
#s(alt (.f64 (/.f64 #s(literal 1 binary64) (+.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))) #s(approx (- (+ ( 1/2 (cos (* (+ x eps) 2))) 1/2) (+ (* 1/2 (cos (+ x x))) 1/2)) (.f64 eps (fma.f64 (neg.f64 eps) (cos.f64 (.f64 x #s(literal 2 binary64))) (sin.f64 (.f64 x #s(literal -2 binary64))))))) (patch (.f64 (/.f64 #s(literal 1 binary64) (+.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))) #s(approx (- (+ (* 1/2 (cos (* (+ x eps) 2))) 1/2) (+ (* 1/2 (cos (+ x x))) 1/2)) (.f64 eps (fma.f64 (neg.f64 eps) (cos.f64 (.f64 x #s(literal 2 binary64))) (sin.f64 (*.f64 x #s(literal -2 binary64))))))) #<representation binary64>) () ())
#s(alt (.f64 x #s(literal 2 binary64)) (patch (.f64 x #s(literal 2 binary64)) #<representation binary64>) () ())
#s(alt (/.f64 #s(literal 1 binary64) (+.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))) (patch (/.f64 #s(literal 1 binary64) (+.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))) #<representation binary64>) () ())
#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 (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) (patch (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps 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 #s(approx (- (+ (* 1/2 (cos (* (+ x eps) 2))) 1/2) (+ (* 1/2 (cos (+ x x))) 1/2)) (.f64 eps (fma.f64 (neg.f64 eps) (cos.f64 (.f64 x #s(literal 2 binary64))) (sin.f64 (.f64 x #s(literal -2 binary64)))))) (patch #s(approx (- (+ ( 1/2 (cos (* (+ x eps) 2))) 1/2) (+ (* 1/2 (cos (+ x x))) 1/2)) (.f64 eps (fma.f64 (neg.f64 eps) (cos.f64 (.f64 x #s(literal 2 binary64))) (sin.f64 (*.f64 x #s(literal -2 binary64)))))) #<representation binary64>) () ())
#s(alt (cos.f64 (+.f64 x eps)) (patch (cos.f64 (+.f64 x eps)) #<representation binary64>) () ())
#s(alt (.f64 eps (fma.f64 (neg.f64 eps) (cos.f64 (.f64 x #s(literal 2 binary64))) (sin.f64 (.f64 x #s(literal -2 binary64))))) (patch (.f64 eps (fma.f64 (neg.f64 eps) (cos.f64 (.f64 x #s(literal 2 binary64))) (sin.f64 (.f64 x #s(literal -2 binary64))))) #<representation binary64>) () ())
#s(alt (fma.f64 (neg.f64 eps) (cos.f64 (.f64 x #s(literal 2 binary64))) (sin.f64 (.f64 x #s(literal -2 binary64)))) (patch (fma.f64 (neg.f64 eps) (cos.f64 (.f64 x #s(literal 2 binary64))) (sin.f64 (.f64 x #s(literal -2 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 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)) (patch (.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)) #<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 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)) (patch (.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)) #<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 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)) (patch (.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)) #<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 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)) (patch (.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)) #<representation binary64>) () ())) ())
#s(alt (* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (+ eps (* 2 x)))))) (taylor inf eps) (#s(alt (.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)) (patch (.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)) #<representation binary64>) () ())) ())
#s(alt (* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (+ eps (* 2 x)))))) (taylor inf eps) (#s(alt (.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)) (patch (.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)) #<representation binary64>) () ())) ())
#s(alt (* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (+ eps (* 2 x)))))) (taylor inf eps) (#s(alt (.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)) (patch (.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)) #<representation binary64>) () ())) ())
#s(alt (* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (+ eps (* 2 x)))))) (taylor inf eps) (#s(alt (.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)) (patch (.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)) #<representation binary64>) () ())) ())
#s(alt (* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (- (* 2 x) (* -1 eps)))))) (taylor -inf eps) (#s(alt (.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)) (patch (.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)) #<representation binary64>) () ())) ())
#s(alt (* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (- (* 2 x) (* -1 eps)))))) (taylor -inf eps) (#s(alt (.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)) (patch (.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)) #<representation binary64>) () ())) ())
#s(alt (* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (- (* 2 x) (* -1 eps)))))) (taylor -inf eps) (#s(alt (.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)) (patch (.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)) #<representation binary64>) () ())) ())
#s(alt (* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (- (* 2 x) (* -1 eps)))))) (taylor -inf eps) (#s(alt (.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)) (patch (.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)) #<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 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)) (patch (.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)) #<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 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)) (patch (.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)) #<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 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)) (patch (.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)) #<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 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)) (patch (.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)) #<representation binary64>) () ())) ())
#s(alt (* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (+ eps (* 2 x)))))) (taylor inf x) (#s(alt (.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)) (patch (.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)) #<representation binary64>) () ())) ())
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#s(alt (* (pow eps 2) (+ (* -1 (cos (* 2 x))) (/ (sin (* -2 x)) eps))) (taylor inf eps) (#s(alt (.f64 eps (fma.f64 (neg.f64 eps) (cos.f64 (.f64 x #s(literal 2 binary64))) (sin.f64 (.f64 x #s(literal -2 binary64))))) (patch (.f64 eps (fma.f64 (neg.f64 eps) (cos.f64 (.f64 x #s(literal 2 binary64))) (sin.f64 (.f64 x #s(literal -2 binary64))))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* (pow eps 2) (cos (* 2 x)))) (taylor -inf eps) (#s(alt (.f64 eps (fma.f64 (neg.f64 eps) (cos.f64 (.f64 x #s(literal 2 binary64))) (sin.f64 (.f64 x #s(literal -2 binary64))))) (patch (.f64 eps (fma.f64 (neg.f64 eps) (cos.f64 (.f64 x #s(literal 2 binary64))) (sin.f64 (.f64 x #s(literal -2 binary64))))) #<representation binary64>) () ())) ())
#s(alt (* (pow eps 2) (+ (* -1 (cos (* 2 x))) (/ (sin (* -2 x)) eps))) (taylor -inf eps) (#s(alt (.f64 eps (fma.f64 (neg.f64 eps) (cos.f64 (.f64 x #s(literal 2 binary64))) (sin.f64 (.f64 x #s(literal -2 binary64))))) (patch (.f64 eps (fma.f64 (neg.f64 eps) (cos.f64 (.f64 x #s(literal 2 binary64))) (sin.f64 (.f64 x #s(literal -2 binary64))))) #<representation binary64>) () ())) ())
#s(alt (* (pow eps 2) (+ (* -1 (cos (* 2 x))) (/ (sin (* -2 x)) eps))) (taylor -inf eps) (#s(alt (.f64 eps (fma.f64 (neg.f64 eps) (cos.f64 (.f64 x #s(literal 2 binary64))) (sin.f64 (.f64 x #s(literal -2 binary64))))) (patch (.f64 eps (fma.f64 (neg.f64 eps) (cos.f64 (.f64 x #s(literal 2 binary64))) (sin.f64 (.f64 x #s(literal -2 binary64))))) #<representation binary64>) () ())) ())
#s(alt (* (pow eps 2) (+ (* -1 (cos (* 2 x))) (/ (sin (* -2 x)) eps))) (taylor -inf eps) (#s(alt (.f64 eps (fma.f64 (neg.f64 eps) (cos.f64 (.f64 x #s(literal 2 binary64))) (sin.f64 (.f64 x #s(literal -2 binary64))))) (patch (.f64 eps (fma.f64 (neg.f64 eps) (cos.f64 (.f64 x #s(literal 2 binary64))) (sin.f64 (.f64 x #s(literal -2 binary64))))) #<representation binary64>) () ())) ())
#s(alt (* -1 (pow eps 2)) (taylor 0 x) (#s(alt (.f64 eps (fma.f64 (neg.f64 eps) (cos.f64 (.f64 x #s(literal 2 binary64))) (sin.f64 (.f64 x #s(literal -2 binary64))))) (patch (.f64 eps (fma.f64 (neg.f64 eps) (cos.f64 (.f64 x #s(literal 2 binary64))) (sin.f64 (.f64 x #s(literal -2 binary64))))) #<representation binary64>) () ())) ())
#s(alt (+ (* -2 (* eps x)) (* -1 (pow eps 2))) (taylor 0 x) (#s(alt (.f64 eps (fma.f64 (neg.f64 eps) (cos.f64 (.f64 x #s(literal 2 binary64))) (sin.f64 (.f64 x #s(literal -2 binary64))))) (patch (.f64 eps (fma.f64 (neg.f64 eps) (cos.f64 (.f64 x #s(literal 2 binary64))) (sin.f64 (.f64 x #s(literal -2 binary64))))) #<representation binary64>) () ())) ())
#s(alt (+ (* -1 (pow eps 2)) (* x (+ (* -2 eps) (* 2 (* (pow eps 2) x))))) (taylor 0 x) (#s(alt (.f64 eps (fma.f64 (neg.f64 eps) (cos.f64 (.f64 x #s(literal 2 binary64))) (sin.f64 (.f64 x #s(literal -2 binary64))))) (patch (.f64 eps (fma.f64 (neg.f64 eps) (cos.f64 (.f64 x #s(literal 2 binary64))) (sin.f64 (.f64 x #s(literal -2 binary64))))) #<representation binary64>) () ())) ())
#s(alt (+ (* -1 (pow eps 2)) (* x (+ (* -2 eps) (* x (+ (* 4/3 (* eps x)) (* 2 (pow eps 2))))))) (taylor 0 x) (#s(alt (.f64 eps (fma.f64 (neg.f64 eps) (cos.f64 (.f64 x #s(literal 2 binary64))) (sin.f64 (.f64 x #s(literal -2 binary64))))) (patch (.f64 eps (fma.f64 (neg.f64 eps) (cos.f64 (.f64 x #s(literal 2 binary64))) (sin.f64 (.f64 x #s(literal -2 binary64))))) #<representation binary64>) () ())) ())
#s(alt (* eps (+ (sin (* -2 x)) (* -1 (* eps (cos (* 2 x)))))) (taylor inf x) (#s(alt (.f64 eps (fma.f64 (neg.f64 eps) (cos.f64 (.f64 x #s(literal 2 binary64))) (sin.f64 (.f64 x #s(literal -2 binary64))))) (patch (.f64 eps (fma.f64 (neg.f64 eps) (cos.f64 (.f64 x #s(literal 2 binary64))) (sin.f64 (.f64 x #s(literal -2 binary64))))) #<representation binary64>) () ())) ())
#s(alt (* eps (+ (sin (* -2 x)) (* -1 (* eps (cos (* 2 x)))))) (taylor inf x) (#s(alt (.f64 eps (fma.f64 (neg.f64 eps) (cos.f64 (.f64 x #s(literal 2 binary64))) (sin.f64 (.f64 x #s(literal -2 binary64))))) (patch (.f64 eps (fma.f64 (neg.f64 eps) (cos.f64 (.f64 x #s(literal 2 binary64))) (sin.f64 (.f64 x #s(literal -2 binary64))))) #<representation binary64>) () ())) ())
#s(alt (* eps (+ (sin (* -2 x)) (* -1 (* eps (cos (* 2 x)))))) (taylor inf x) (#s(alt (.f64 eps (fma.f64 (neg.f64 eps) (cos.f64 (.f64 x #s(literal 2 binary64))) (sin.f64 (.f64 x #s(literal -2 binary64))))) (patch (.f64 eps (fma.f64 (neg.f64 eps) (cos.f64 (.f64 x #s(literal 2 binary64))) (sin.f64 (.f64 x #s(literal -2 binary64))))) #<representation binary64>) () ())) ())
#s(alt (* eps (+ (sin (* -2 x)) (* -1 (* eps (cos (* 2 x)))))) (taylor inf x) (#s(alt (.f64 eps (fma.f64 (neg.f64 eps) (cos.f64 (.f64 x #s(literal 2 binary64))) (sin.f64 (.f64 x #s(literal -2 binary64))))) (patch (.f64 eps (fma.f64 (neg.f64 eps) (cos.f64 (.f64 x #s(literal 2 binary64))) (sin.f64 (.f64 x #s(literal -2 binary64))))) #<representation binary64>) () ())) ())
#s(alt (* eps (+ (sin (* -2 x)) (* -1 (* eps (cos (* 2 x)))))) (taylor -inf x) (#s(alt (.f64 eps (fma.f64 (neg.f64 eps) (cos.f64 (.f64 x #s(literal 2 binary64))) (sin.f64 (.f64 x #s(literal -2 binary64))))) (patch (.f64 eps (fma.f64 (neg.f64 eps) (cos.f64 (.f64 x #s(literal 2 binary64))) (sin.f64 (.f64 x #s(literal -2 binary64))))) #<representation binary64>) () ())) ())
#s(alt (* eps (+ (sin (* -2 x)) (* -1 (* eps (cos (* 2 x)))))) (taylor -inf x) (#s(alt (.f64 eps (fma.f64 (neg.f64 eps) (cos.f64 (.f64 x #s(literal 2 binary64))) (sin.f64 (.f64 x #s(literal -2 binary64))))) (patch (.f64 eps (fma.f64 (neg.f64 eps) (cos.f64 (.f64 x #s(literal 2 binary64))) (sin.f64 (.f64 x #s(literal -2 binary64))))) #<representation binary64>) () ())) ())
#s(alt (* eps (+ (sin (* -2 x)) (* -1 (* eps (cos (* 2 x)))))) (taylor -inf x) (#s(alt (.f64 eps (fma.f64 (neg.f64 eps) (cos.f64 (.f64 x #s(literal 2 binary64))) (sin.f64 (.f64 x #s(literal -2 binary64))))) (patch (.f64 eps (fma.f64 (neg.f64 eps) (cos.f64 (.f64 x #s(literal 2 binary64))) (sin.f64 (.f64 x #s(literal -2 binary64))))) #<representation binary64>) () ())) ())
#s(alt (* eps (+ (sin (* -2 x)) (* -1 (* eps (cos (* 2 x)))))) (taylor -inf x) (#s(alt (.f64 eps (fma.f64 (neg.f64 eps) (cos.f64 (.f64 x #s(literal 2 binary64))) (sin.f64 (.f64 x #s(literal -2 binary64))))) (patch (.f64 eps (fma.f64 (neg.f64 eps) (cos.f64 (.f64 x #s(literal 2 binary64))) (sin.f64 (.f64 x #s(literal -2 binary64))))) #<representation binary64>) () ())) ())
#s(alt (sin (* -2 x)) (taylor 0 eps) (#s(alt (fma.f64 (neg.f64 eps) (cos.f64 (.f64 x #s(literal 2 binary64))) (sin.f64 (.f64 x #s(literal -2 binary64)))) (patch (fma.f64 (neg.f64 eps) (cos.f64 (.f64 x #s(literal 2 binary64))) (sin.f64 (.f64 x #s(literal -2 binary64)))) #<representation binary64>) () ())) ())
#s(alt (+ (sin (* -2 x)) (* -1 (* eps (cos (* 2 x))))) (taylor 0 eps) (#s(alt (fma.f64 (neg.f64 eps) (cos.f64 (.f64 x #s(literal 2 binary64))) (sin.f64 (.f64 x #s(literal -2 binary64)))) (patch (fma.f64 (neg.f64 eps) (cos.f64 (.f64 x #s(literal 2 binary64))) (sin.f64 (.f64 x #s(literal -2 binary64)))) #<representation binary64>) () ())) ())
#s(alt (+ (sin (* -2 x)) (* -1 (* eps (cos (* 2 x))))) (taylor 0 eps) (#s(alt (fma.f64 (neg.f64 eps) (cos.f64 (.f64 x #s(literal 2 binary64))) (sin.f64 (.f64 x #s(literal -2 binary64)))) (patch (fma.f64 (neg.f64 eps) (cos.f64 (.f64 x #s(literal 2 binary64))) (sin.f64 (.f64 x #s(literal -2 binary64)))) #<representation binary64>) () ())) ())
#s(alt (+ (sin (* -2 x)) (* -1 (* eps (cos (* 2 x))))) (taylor 0 eps) (#s(alt (fma.f64 (neg.f64 eps) (cos.f64 (.f64 x #s(literal 2 binary64))) (sin.f64 (.f64 x #s(literal -2 binary64)))) (patch (fma.f64 (neg.f64 eps) (cos.f64 (.f64 x #s(literal 2 binary64))) (sin.f64 (.f64 x #s(literal -2 binary64)))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* eps (cos (* 2 x)))) (taylor inf eps) (#s(alt (fma.f64 (neg.f64 eps) (cos.f64 (.f64 x #s(literal 2 binary64))) (sin.f64 (.f64 x #s(literal -2 binary64)))) (patch (fma.f64 (neg.f64 eps) (cos.f64 (.f64 x #s(literal 2 binary64))) (sin.f64 (.f64 x #s(literal -2 binary64)))) #<representation binary64>) () ())) ())
#s(alt (* eps (+ (* -1 (cos (* 2 x))) (/ (sin (* -2 x)) eps))) (taylor inf eps) (#s(alt (fma.f64 (neg.f64 eps) (cos.f64 (.f64 x #s(literal 2 binary64))) (sin.f64 (.f64 x #s(literal -2 binary64)))) (patch (fma.f64 (neg.f64 eps) (cos.f64 (.f64 x #s(literal 2 binary64))) (sin.f64 (.f64 x #s(literal -2 binary64)))) #<representation binary64>) () ())) ())
#s(alt (* eps (+ (* -1 (cos (* 2 x))) (/ (sin (* -2 x)) eps))) (taylor inf eps) (#s(alt (fma.f64 (neg.f64 eps) (cos.f64 (.f64 x #s(literal 2 binary64))) (sin.f64 (.f64 x #s(literal -2 binary64)))) (patch (fma.f64 (neg.f64 eps) (cos.f64 (.f64 x #s(literal 2 binary64))) (sin.f64 (.f64 x #s(literal -2 binary64)))) #<representation binary64>) () ())) ())
#s(alt (* eps (+ (* -1 (cos (* 2 x))) (/ (sin (* -2 x)) eps))) (taylor inf eps) (#s(alt (fma.f64 (neg.f64 eps) (cos.f64 (.f64 x #s(literal 2 binary64))) (sin.f64 (.f64 x #s(literal -2 binary64)))) (patch (fma.f64 (neg.f64 eps) (cos.f64 (.f64 x #s(literal 2 binary64))) (sin.f64 (.f64 x #s(literal -2 binary64)))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* eps (cos (* 2 x)))) (taylor -inf eps) (#s(alt (fma.f64 (neg.f64 eps) (cos.f64 (.f64 x #s(literal 2 binary64))) (sin.f64 (.f64 x #s(literal -2 binary64)))) (patch (fma.f64 (neg.f64 eps) (cos.f64 (.f64 x #s(literal 2 binary64))) (sin.f64 (.f64 x #s(literal -2 binary64)))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* eps (+ (cos (* 2 x)) (* -1 (/ (sin (* -2 x)) eps))))) (taylor -inf eps) (#s(alt (fma.f64 (neg.f64 eps) (cos.f64 (.f64 x #s(literal 2 binary64))) (sin.f64 (.f64 x #s(literal -2 binary64)))) (patch (fma.f64 (neg.f64 eps) (cos.f64 (.f64 x #s(literal 2 binary64))) (sin.f64 (.f64 x #s(literal -2 binary64)))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* eps (+ (cos (* 2 x)) (* -1 (/ (sin (* -2 x)) eps))))) (taylor -inf eps) (#s(alt (fma.f64 (neg.f64 eps) (cos.f64 (.f64 x #s(literal 2 binary64))) (sin.f64 (.f64 x #s(literal -2 binary64)))) (patch (fma.f64 (neg.f64 eps) (cos.f64 (.f64 x #s(literal 2 binary64))) (sin.f64 (.f64 x #s(literal -2 binary64)))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* eps (+ (cos (* 2 x)) (* -1 (/ (sin (* -2 x)) eps))))) (taylor -inf eps) (#s(alt (fma.f64 (neg.f64 eps) (cos.f64 (.f64 x #s(literal 2 binary64))) (sin.f64 (.f64 x #s(literal -2 binary64)))) (patch (fma.f64 (neg.f64 eps) (cos.f64 (.f64 x #s(literal 2 binary64))) (sin.f64 (.f64 x #s(literal -2 binary64)))) #<representation binary64>) () ())) ())
#s(alt (* -1 eps) (taylor 0 x) (#s(alt (fma.f64 (neg.f64 eps) (cos.f64 (.f64 x #s(literal 2 binary64))) (sin.f64 (.f64 x #s(literal -2 binary64)))) (patch (fma.f64 (neg.f64 eps) (cos.f64 (.f64 x #s(literal 2 binary64))) (sin.f64 (.f64 x #s(literal -2 binary64)))) #<representation binary64>) () ())) ())
#s(alt (+ (* -2 x) (* -1 eps)) (taylor 0 x) (#s(alt (fma.f64 (neg.f64 eps) (cos.f64 (.f64 x #s(literal 2 binary64))) (sin.f64 (.f64 x #s(literal -2 binary64)))) (patch (fma.f64 (neg.f64 eps) (cos.f64 (.f64 x #s(literal 2 binary64))) (sin.f64 (.f64 x #s(literal -2 binary64)))) #<representation binary64>) () ())) ())
#s(alt (+ (* -1 eps) (* x (- (* 2 (* eps x)) 2))) (taylor 0 x) (#s(alt (fma.f64 (neg.f64 eps) (cos.f64 (.f64 x #s(literal 2 binary64))) (sin.f64 (.f64 x #s(literal -2 binary64)))) (patch (fma.f64 (neg.f64 eps) (cos.f64 (.f64 x #s(literal 2 binary64))) (sin.f64 (.f64 x #s(literal -2 binary64)))) #<representation binary64>) () ())) ())
#s(alt (+ (* -1 eps) (* x (- (* x (+ (* 4/3 x) (* 2 eps))) 2))) (taylor 0 x) (#s(alt (fma.f64 (neg.f64 eps) (cos.f64 (.f64 x #s(literal 2 binary64))) (sin.f64 (.f64 x #s(literal -2 binary64)))) (patch (fma.f64 (neg.f64 eps) (cos.f64 (.f64 x #s(literal 2 binary64))) (sin.f64 (.f64 x #s(literal -2 binary64)))) #<representation binary64>) () ())) ())
#s(alt (+ (sin (* -2 x)) (* -1 (* eps (cos (* 2 x))))) (taylor inf x) (#s(alt (fma.f64 (neg.f64 eps) (cos.f64 (.f64 x #s(literal 2 binary64))) (sin.f64 (.f64 x #s(literal -2 binary64)))) (patch (fma.f64 (neg.f64 eps) (cos.f64 (.f64 x #s(literal 2 binary64))) (sin.f64 (.f64 x #s(literal -2 binary64)))) #<representation binary64>) () ())) ())
#s(alt (+ (sin (* -2 x)) (* -1 (* eps (cos (* 2 x))))) (taylor inf x) (#s(alt (fma.f64 (neg.f64 eps) (cos.f64 (.f64 x #s(literal 2 binary64))) (sin.f64 (.f64 x #s(literal -2 binary64)))) (patch (fma.f64 (neg.f64 eps) (cos.f64 (.f64 x #s(literal 2 binary64))) (sin.f64 (.f64 x #s(literal -2 binary64)))) #<representation binary64>) () ())) ())
#s(alt (+ (sin (* -2 x)) (* -1 (* eps (cos (* 2 x))))) (taylor inf x) (#s(alt (fma.f64 (neg.f64 eps) (cos.f64 (.f64 x #s(literal 2 binary64))) (sin.f64 (.f64 x #s(literal -2 binary64)))) (patch (fma.f64 (neg.f64 eps) (cos.f64 (.f64 x #s(literal 2 binary64))) (sin.f64 (.f64 x #s(literal -2 binary64)))) #<representation binary64>) () ())) ())
#s(alt (+ (sin (* -2 x)) (* -1 (* eps (cos (* 2 x))))) (taylor inf x) (#s(alt (fma.f64 (neg.f64 eps) (cos.f64 (.f64 x #s(literal 2 binary64))) (sin.f64 (.f64 x #s(literal -2 binary64)))) (patch (fma.f64 (neg.f64 eps) (cos.f64 (.f64 x #s(literal 2 binary64))) (sin.f64 (.f64 x #s(literal -2 binary64)))) #<representation binary64>) () ())) ())
#s(alt (+ (sin (* -2 x)) (* -1 (* eps (cos (* 2 x))))) (taylor -inf x) (#s(alt (fma.f64 (neg.f64 eps) (cos.f64 (.f64 x #s(literal 2 binary64))) (sin.f64 (.f64 x #s(literal -2 binary64)))) (patch (fma.f64 (neg.f64 eps) (cos.f64 (.f64 x #s(literal 2 binary64))) (sin.f64 (.f64 x #s(literal -2 binary64)))) #<representation binary64>) () ())) ())
#s(alt (+ (sin (* -2 x)) (* -1 (* eps (cos (* 2 x))))) (taylor -inf x) (#s(alt (fma.f64 (neg.f64 eps) (cos.f64 (.f64 x #s(literal 2 binary64))) (sin.f64 (.f64 x #s(literal -2 binary64)))) (patch (fma.f64 (neg.f64 eps) (cos.f64 (.f64 x #s(literal 2 binary64))) (sin.f64 (.f64 x #s(literal -2 binary64)))) #<representation binary64>) () ())) ())
#s(alt (+ (sin (* -2 x)) (* -1 (* eps (cos (* 2 x))))) (taylor -inf x) (#s(alt (fma.f64 (neg.f64 eps) (cos.f64 (.f64 x #s(literal 2 binary64))) (sin.f64 (.f64 x #s(literal -2 binary64)))) (patch (fma.f64 (neg.f64 eps) (cos.f64 (.f64 x #s(literal 2 binary64))) (sin.f64 (.f64 x #s(literal -2 binary64)))) #<representation binary64>) () ())) ())
#s(alt (+ (sin (* -2 x)) (* -1 (* eps (cos (* 2 x))))) (taylor -inf x) (#s(alt (fma.f64 (neg.f64 eps) (cos.f64 (.f64 x #s(literal 2 binary64))) (sin.f64 (.f64 x #s(literal -2 binary64)))) (patch (fma.f64 (neg.f64 eps) (cos.f64 (.f64 x #s(literal 2 binary64))) (sin.f64 (.f64 x #s(literal -2 binary64)))) #<representation binary64>) () ())) ())

Calls

132 calls:

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

simplify391.0ms (2.3%)

Memory

-17.9MiB live, 314.7MiB allocated

Algorithm

1×	egg-herbie

Rules

7 068×	`lower-fma.f64`
7 068×	`lower-fma.f32`
6 624×	`lower-*.f64`
6 624×	`lower-*.f32`
2 330×	`lower-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	576	7019
1	1740	6651
2	4712	6617
0	8161	6218

Stop Event

1×	iter limit
1×	node limit

Counts

528 → 510

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)) (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))
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(* 2 x)
(* 2 x)
(* 2 x)
(* 2 x)
(* 2 x)
(* 2 x)
(* 2 x)
(* 2 x)
(* 2 x)
(/ 1 (+ 1 (cos eps)))
(+ (/ 1 (+ 1 (cos eps))) (/ (* x (sin eps)) (pow (+ 1 (cos eps)) 2)))
(+ (* x (- (* x (- (* 1/2 (/ 1 (pow (+ 1 (cos eps)) 2))) (+ (* -1 (/ (pow (sin eps) 2) (pow (+ 1 (cos eps)) 3))) (* -1/2 (/ (cos eps) (pow (+ 1 (cos eps)) 2)))))) (* -1 (/ (sin eps) (pow (+ 1 (cos eps)) 2))))) (/ 1 (+ 1 (cos eps))))
(+ (* x (- (* x (- (+ (* -1 (* x (+ (* -1 (/ (* (sin eps) (- (* 1/2 (/ 1 (pow (+ 1 (cos eps)) 2))) (+ (* -1 (/ (pow (sin eps) 2) (pow (+ 1 (cos eps)) 3))) (* -1/2 (/ (cos eps) (pow (+ 1 (cos eps)) 2)))))) (+ 1 (cos eps)))) (+ (* 1/6 (/ (sin eps) (pow (+ 1 (cos eps)) 2))) (/ (* (sin eps) (- (* -1/2 (cos eps)) 1/2)) (pow (+ 1 (cos eps)) 3)))))) (* 1/2 (/ 1 (pow (+ 1 (cos eps)) 2)))) (+ (* -1 (/ (pow (sin eps) 2) (pow (+ 1 (cos eps)) 3))) (* -1/2 (/ (cos eps) (pow (+ 1 (cos eps)) 2)))))) (* -1 (/ (sin eps) (pow (+ 1 (cos eps)) 2))))) (/ 1 (+ 1 (cos eps))))
(/ 1 (+ (cos x) (cos (+ eps x))))
(/ 1 (+ (cos x) (cos (+ eps x))))
(/ 1 (+ (cos x) (cos (+ eps x))))
(/ 1 (+ (cos x) (cos (+ eps x))))
(/ 1 (+ (cos x) (cos (- eps (* -1 x)))))
(/ 1 (+ (cos x) (cos (- eps (* -1 x)))))
(/ 1 (+ (cos x) (cos (- eps (* -1 x)))))
(/ 1 (+ (cos x) (cos (- eps (* -1 x)))))
(/ 1/2 (cos x))
(+ (* 1/4 (/ (* eps (sin x)) (pow (cos x) 2))) (* 1/2 (/ 1 (cos x))))
(+ (* eps (- (* eps (- (* 1/8 (/ 1 (cos x))) (* -1/8 (/ (pow (sin x) 2) (pow (cos x) 3))))) (* -1/4 (/ (sin x) (pow (cos x) 2))))) (* 1/2 (/ 1 (cos x))))
(+ (* eps (- (* eps (- (+ (* -1 (* eps (+ (* -1/2 (/ (* (sin x) (- (* 1/8 (/ 1 (cos x))) (* -1/8 (/ (pow (sin x) 2) (pow (cos x) 3))))) (cos x))) (+ (* -1/16 (/ (sin x) (pow (cos x) 2))) (* 1/24 (/ (sin x) (pow (cos x) 2))))))) (* 1/8 (/ 1 (cos x)))) (* -1/8 (/ (pow (sin x) 2) (pow (cos x) 3))))) (* -1/4 (/ (sin x) (pow (cos x) 2))))) (* 1/2 (/ 1 (cos x))))
(/ 1 (+ (cos x) (cos (+ eps x))))
(/ 1 (+ (cos x) (cos (+ eps x))))
(/ 1 (+ (cos x) (cos (+ eps x))))
(/ 1 (+ (cos x) (cos (+ eps x))))
(/ 1 (+ (cos x) (cos (- x (* -1 eps)))))
(/ 1 (+ (cos x) (cos (- x (* -1 eps)))))
(/ 1 (+ (cos x) (cos (- x (* -1 eps)))))
(/ 1 (+ (cos x) (cos (- x (* -1 eps)))))
(+ 1 (cos eps))
(+ 1 (+ (cos eps) (* -1 (* x (sin eps)))))
(+ 1 (+ (cos eps) (* x (- (* x (- (* -1/2 (cos eps)) 1/2)) (sin eps)))))
(+ 1 (+ (cos eps) (* x (- (* x (- (+ (* -1/2 (cos eps)) (* 1/6 (* x (sin eps)))) 1/2)) (sin eps)))))
(+ (cos x) (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))))
(* 2 (cos x))
(+ (* -1 (* eps (sin x))) (* 2 (cos x)))
(+ (* 2 (cos x)) (* eps (- (* -1/2 (* eps (cos x))) (sin x))))
(+ (* 2 (cos x)) (* eps (- (* eps (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x))))) (sin x))))
(+ (cos 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))))
(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 (+ x (* 1/2 eps)))
(sin (+ x (* 1/2 eps)))
(sin (+ x (* 1/2 eps)))
(sin (+ x (* 1/2 eps)))
(sin (- x (* -1/2 eps)))
(sin (- x (* -1/2 eps)))
(sin (- x (* -1/2 eps)))
(sin (- x (* -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)))))))))
(sin (+ x (* 1/2 eps)))
(sin (+ x (* 1/2 eps)))
(sin (+ x (* 1/2 eps)))
(sin (+ x (* 1/2 eps)))
(sin (- (* 1/2 eps) (* -1 x)))
(sin (- (* 1/2 eps) (* -1 x)))
(sin (- (* 1/2 eps) (* -1 x)))
(sin (- (* 1/2 eps) (* -1 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 (cos (* 2 eps))) 1/2)
(- (+ (* -1 (* x (sin (* 2 eps)))) (* 1/2 (cos (* 2 eps)))) 1/2)
(- (+ (* 1/2 (cos (* 2 eps))) (* x (+ (* -1 (sin (* 2 eps))) (* x (+ 1 (* -1 (cos (* 2 eps)))))))) 1/2)
(- (+ (* 1/2 (cos (* 2 eps))) (* x (+ (* -1 (sin (* 2 eps))) (* x (+ 1 (+ (* -1 (cos (* 2 eps))) (* 2/3 (* x (sin (* 2 eps)))))))))) 1/2)
(- (* 1/2 (cos (* 2 (+ eps x)))) (* 1/2 (cos (* 2 x))))
(- (* 1/2 (cos (* 2 (+ eps x)))) (* 1/2 (cos (* 2 x))))
(- (* 1/2 (cos (* 2 (+ eps x)))) (* 1/2 (cos (* 2 x))))
(- (* 1/2 (cos (* 2 (+ eps x)))) (* 1/2 (cos (* 2 x))))
(- (* 1/2 (cos (* 2 (- eps (* -1 x))))) (* 1/2 (cos (neg (* -2 x)))))
(- (* 1/2 (cos (* 2 (- eps (* -1 x))))) (* 1/2 (cos (neg (* -2 x)))))
(- (* 1/2 (cos (* 2 (- eps (* -1 x))))) (* 1/2 (cos (neg (* -2 x)))))
(- (* 1/2 (cos (* 2 (- eps (* -1 x))))) (* 1/2 (cos (neg (* -2 x)))))
(* -1 (* eps (sin (* 2 x))))
(* eps (+ (* -1 (sin (* 2 x))) (* -1 (* eps (cos (* 2 x))))))
(* eps (+ (* -1 (sin (* 2 x))) (* eps (+ (* -1 (cos (* 2 x))) (* 2/3 (* eps (sin (* 2 x))))))))
(* eps (+ (* -1 (sin (* 2 x))) (* eps (+ (* -1 (cos (* 2 x))) (* eps (+ (* 1/3 (* eps (cos (* 2 x)))) (* 2/3 (sin (* 2 x)))))))))
(- (* 1/2 (cos (* 2 (+ eps x)))) (* 1/2 (cos (* 2 x))))
(- (* 1/2 (cos (* 2 (+ eps x)))) (* 1/2 (cos (* 2 x))))
(- (* 1/2 (cos (* 2 (+ eps x)))) (* 1/2 (cos (* 2 x))))
(- (* 1/2 (cos (* 2 (+ eps x)))) (* 1/2 (cos (* 2 x))))
(- (* 1/2 (cos (* 2 (- x (* -1 eps))))) (* 1/2 (cos (* 2 x))))
(- (* 1/2 (cos (* 2 (- x (* -1 eps))))) (* 1/2 (cos (* 2 x))))
(- (* 1/2 (cos (* 2 (- x (* -1 eps))))) (* 1/2 (cos (* 2 x))))
(- (* 1/2 (cos (* 2 (- x (* -1 eps))))) (* 1/2 (cos (* 2 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 (sin (* -2 x)))
(* eps (+ (sin (* -2 x)) (* -1 (* eps (cos (* 2 x))))))
(* eps (+ (sin (* -2 x)) (* -1 (* eps (cos (* 2 x))))))
(* eps (+ (sin (* -2 x)) (* -1 (* eps (cos (* 2 x))))))
(* -1 (* (pow eps 2) (cos (* 2 x))))
(* (pow eps 2) (+ (* -1 (cos (* 2 x))) (/ (sin (* -2 x)) eps)))
(* (pow eps 2) (+ (* -1 (cos (* 2 x))) (/ (sin (* -2 x)) eps)))
(* (pow eps 2) (+ (* -1 (cos (* 2 x))) (/ (sin (* -2 x)) eps)))
(* -1 (* (pow eps 2) (cos (* 2 x))))
(* (pow eps 2) (+ (* -1 (cos (* 2 x))) (/ (sin (* -2 x)) eps)))
(* (pow eps 2) (+ (* -1 (cos (* 2 x))) (/ (sin (* -2 x)) eps)))
(* (pow eps 2) (+ (* -1 (cos (* 2 x))) (/ (sin (* -2 x)) eps)))
(* -1 (pow eps 2))
(+ (* -2 (* eps x)) (* -1 (pow eps 2)))
(+ (* -1 (pow eps 2)) (* x (+ (* -2 eps) (* 2 (* (pow eps 2) x)))))
(+ (* -1 (pow eps 2)) (* x (+ (* -2 eps) (* x (+ (* 4/3 (* eps x)) (* 2 (pow eps 2)))))))
(* eps (+ (sin (* -2 x)) (* -1 (* eps (cos (* 2 x))))))
(* eps (+ (sin (* -2 x)) (* -1 (* eps (cos (* 2 x))))))
(* eps (+ (sin (* -2 x)) (* -1 (* eps (cos (* 2 x))))))
(* eps (+ (sin (* -2 x)) (* -1 (* eps (cos (* 2 x))))))
(* eps (+ (sin (* -2 x)) (* -1 (* eps (cos (* 2 x))))))
(* eps (+ (sin (* -2 x)) (* -1 (* eps (cos (* 2 x))))))
(* eps (+ (sin (* -2 x)) (* -1 (* eps (cos (* 2 x))))))
(* eps (+ (sin (* -2 x)) (* -1 (* eps (cos (* 2 x))))))
(sin (* -2 x))
(+ (sin (* -2 x)) (* -1 (* eps (cos (* 2 x)))))
(+ (sin (* -2 x)) (* -1 (* eps (cos (* 2 x)))))
(+ (sin (* -2 x)) (* -1 (* eps (cos (* 2 x)))))
(* -1 (* eps (cos (* 2 x))))
(* eps (+ (* -1 (cos (* 2 x))) (/ (sin (* -2 x)) eps)))
(* eps (+ (* -1 (cos (* 2 x))) (/ (sin (* -2 x)) eps)))
(* eps (+ (* -1 (cos (* 2 x))) (/ (sin (* -2 x)) eps)))
(* -1 (* eps (cos (* 2 x))))
(* -1 (* eps (+ (cos (* 2 x)) (* -1 (/ (sin (* -2 x)) eps)))))
(* -1 (* eps (+ (cos (* 2 x)) (* -1 (/ (sin (* -2 x)) eps)))))
(* -1 (* eps (+ (cos (* 2 x)) (* -1 (/ (sin (* -2 x)) eps)))))
(* -1 eps)
(+ (* -2 x) (* -1 eps))
(+ (* -1 eps) (* x (- (* 2 (* eps x)) 2)))
(+ (* -1 eps) (* x (- (* x (+ (* 4/3 x) (* 2 eps))) 2)))
(+ (sin (* -2 x)) (* -1 (* eps (cos (* 2 x)))))
(+ (sin (* -2 x)) (* -1 (* eps (cos (* 2 x)))))
(+ (sin (* -2 x)) (* -1 (* eps (cos (* 2 x)))))
(+ (sin (* -2 x)) (* -1 (* eps (cos (* 2 x)))))
(+ (sin (* -2 x)) (* -1 (* eps (cos (* 2 x)))))
(+ (sin (* -2 x)) (* -1 (* eps (cos (* 2 x)))))
(+ (sin (* -2 x)) (* -1 (* eps (cos (* 2 x)))))
(+ (sin (* -2 x)) (* -1 (* eps (cos (* 2 x)))))

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

rewrite215.0ms (1.2%)

Memory

27.8MiB live, 188.1MiB allocated

Rules

2 038×	`lower-fma.f32`
2 028×	`lower-fma.f64`
1 766×	`lower-*.f32`
1 738×	`lower-*.f64`
1 232×	`lower-/.f32`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	73	382
0	114	346
1	428	286
0	3568	286

Stop Event

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

Counts

25 → 369

Calls

Call 1

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

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

eval176.0ms (1%)

Memory: 9.9MiB live, 168.3MiB allocated
Compiler: Compiled 26 235 to 2 037 computations (92.2% saved)

prune211.0ms (1.2%)

Memory

-39.3MiB live, 166.9MiB allocated

Pruning

35 alts after pruning (32 fresh and 3 done)

	Pruned	Kept	Total
New	1 030	15	1 045
Fresh	15	17	32
Picked	4	1	5
Done	0	2	2
Total	1 049	35	1 084

Accuracy

100.0%

Counts

1 084 → 35

Alt Table

Click to see full alt table

Status	Accuracy	Program
	48.8%	(/.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)))))
	49.2%	(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (-.f64 (fma.f64 (cos.f64 x) (cos.f64 eps) (*.f64 (neg.f64 (sin.f64 x)) (sin.f64 eps))) (cos.f64 x))))
▶	47.5%	(/.f64 #s(literal 1 binary64) (exp.f64 (*.f64 (log.f64 (-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))) #s(literal -1 binary64))))
	49.2%	(-.f64 (fma.f64 (sin.f64 (neg.f64 x)) (sin.f64 eps) (*.f64 (cos.f64 x) (cos.f64 eps))) (cos.f64 x))
	49.2%	(-.f64 (*.f64 (cos.f64 x) (cos.f64 eps)) (fma.f64 (sin.f64 x) (sin.f64 eps) (cos.f64 x)))
✓	48.7%	(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))
✓	47.1%	(-.f64 (cos.f64 (+.f64 x eps)) #s(approx (cos x) (fma.f64 x (*.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64))))
	47.2%	(-.f64 (cos.f64 (+.f64 x eps)) #s(approx (cos x) #s(literal 1 binary64)))
	47.0%	(-.f64 #s(approx (cos (+ x eps)) (cos.f64 x)) #s(approx (cos x) (fma.f64 x (*.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64))))
	96.2%	(.f64 (/.f64 #s(literal 1 binary64) (+.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))) #s(approx (- (+ ( 1/2 (cos (* (+ x eps) 2))) 1/2) (+ (* 1/2 (cos (+ x x))) 1/2)) #s(approx (* eps (+ (* (neg eps) (cos (* x 2))) (sin (* x -2)))) (fma.f64 x (fma.f64 x (.f64 eps (.f64 eps #s(literal 2 binary64))) (.f64 eps #s(literal -2 binary64))) (.f64 eps (neg.f64 eps))))))
	96.0%	(.f64 (/.f64 #s(literal 1 binary64) (+.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))) #s(approx (- (+ ( 1/2 (cos (* (+ x eps) 2))) 1/2) (+ (* 1/2 (cos (+ x x))) 1/2)) #s(approx (* eps (+ (* (neg eps) (cos (* x 2))) (sin (* x -2)))) (fma.f64 eps (neg.f64 eps) (.f64 eps (.f64 x #s(literal -2 binary64)))))))
	48.8%	(.f64 (/.f64 #s(literal 1 binary64) (+.f64 (cos.f64 (.f64 (.f64 (+.f64 x eps) (-.f64 x eps)) (/.f64 #s(literal 1 binary64) (-.f64 x eps)))) (cos.f64 x))) (-.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))))
	43.7%	(.f64 (.f64 (sin.f64 (.f64 (/.f64 (.f64 (fma.f64 x x (.f64 (+.f64 x eps) eps)) eps) (fma.f64 (+.f64 x eps) (+.f64 x eps) (-.f64 (.f64 x x) (.f64 x (+.f64 x eps))))) #s(literal 1/2 binary64))) (sin.f64 (.f64 (+.f64 x (+.f64 x eps)) #s(literal 1/2 binary64)))) #s(literal -2 binary64))
	99.4%	(.f64 (.f64 (sin.f64 (.f64 (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) eps)) #s(literal 1/2 binary64))) (sin.f64 (.f64 (+.f64 x (+.f64 x eps)) #s(literal 1/2 binary64)))) #s(literal -2 binary64))
	99.4%	(.f64 (.f64 (sin.f64 (.f64 (+.f64 eps #s(literal 0 binary64)) #s(literal 1/2 binary64))) (sin.f64 (.f64 (+.f64 x #s(approx (+ x eps) (fma.f64 eps (/.f64 x eps) eps))) #s(literal 1/2 binary64)))) #s(literal -2 binary64))
▶	98.3%	(.f64 (.f64 (sin.f64 (.f64 (.f64 (.f64 eps eps) (/.f64 #s(literal 1 binary64) eps)) #s(literal 1/2 binary64))) (sin.f64 #s(approx ( (+ x (+ x eps)) 1/2) (fma.f64 eps #s(literal 1/2 binary64) x)))) #s(literal -2 binary64))
	97.6%	(.f64 (.f64 (sin.f64 (.f64 (.f64 (.f64 eps eps) (/.f64 #s(literal 1 binary64) eps)) #s(literal 1/2 binary64))) #s(approx (sin ( (+ x (+ x eps)) 1/2)) (fma.f64 eps (*.f64 (cos.f64 x) #s(literal 1/2 binary64)) (sin.f64 x)))) #s(literal -2 binary64))
	99.3%	(.f64 (.f64 #s(approx (sin (* (+ eps 0) 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)))) (sin.f64 (.f64 #s(approx (+ x (+ x eps)) (.f64 x (+.f64 #s(literal 2 binary64) (/.f64 eps x)))) #s(literal 1/2 binary64)))) #s(literal -2 binary64))
	99.3%	(.f64 (.f64 #s(approx (sin (* (+ eps 0) 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)))) (sin.f64 #s(approx (* (+ x (+ x eps)) 1/2) (fma.f64 eps #s(literal 1/2 binary64) x)))) #s(literal -2 binary64))
	99.2%	(.f64 (.f64 #s(approx (sin (* (+ eps 0) 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)))) (sin.f64 #s(approx (* (+ x (+ x eps)) 1/2) (*.f64 eps (+.f64 #s(literal 1/2 binary64) (/.f64 x eps)))))) #s(literal -2 binary64))
▶	99.2%	(.f64 (.f64 #s(approx (sin (* (+ eps 0) 1/2)) (.f64 eps (fma.f64 eps (.f64 eps #s(literal -1/48 binary64)) #s(literal 1/2 binary64)))) (sin.f64 (*.f64 (+.f64 x (+.f64 x eps)) #s(literal 1/2 binary64)))) #s(literal -2 binary64))
	98.7%	(.f64 (.f64 #s(approx (sin (* (+ eps 0) 1/2)) (.f64 eps #s(literal 1/2 binary64))) (sin.f64 (.f64 (+.f64 x (+.f64 x eps)) #s(literal 1/2 binary64)))) #s(literal -2 binary64))
	98.1%	(.f64 #s(approx (/ 1 (+ (cos (+ x eps)) (cos x))) (/.f64 #s(literal 1/2 binary64) (cos.f64 x))) #s(approx (- (+ ( 1/2 (cos (* (+ x eps) 2))) 1/2) (+ (* 1/2 (cos (+ x x))) 1/2)) (.f64 eps (fma.f64 (neg.f64 eps) (cos.f64 (.f64 x #s(literal 2 binary64))) (sin.f64 (*.f64 x #s(literal -2 binary64)))))))
▶	99.8%	(.f64 #s(approx ( (sin (* (+ eps 0) 1/2)) (sin (* (+ x (+ x eps)) 1/2))) (+.f64 (.f64 (.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (cos.f64 x)) (sin.f64 (.f64 eps #s(literal 1/2 binary64)))) (.f64 (.f64 (cos.f64 (.f64 eps #s(literal 1/2 binary64))) (sin.f64 x)) (sin.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 eps)) 1/2))) (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (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))
	99.3%	(.f64 #s(approx ( (sin (* (+ eps 0) 1/2)) (sin (* (+ x (+ x eps)) 1/2))) (.f64 #s(approx (sin ( 1/2 eps)) (.f64 eps (fma.f64 (.f64 eps eps) (fma.f64 eps (*.f64 eps #s(literal 1/3840 binary64)) #s(literal -1/48 binary64)) #s(literal 1/2 binary64)))) (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x)))) #s(literal -2 binary64))
	99.2%	(.f64 #s(approx ( (sin (* (+ eps 0) 1/2)) (sin (* (+ x (+ x eps)) 1/2))) (.f64 #s(approx (sin ( 1/2 eps)) (.f64 eps (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal 1/2 binary64)))) (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x)))) #s(literal -2 binary64))
	98.7%	(.f64 #s(approx ( (sin (* (+ eps 0) 1/2)) (sin (* (+ x (+ x eps)) 1/2))) (.f64 #s(approx (sin ( 1/2 eps)) (*.f64 eps #s(literal 1/2 binary64))) (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x)))) #s(literal -2 binary64))
	98.7%	#s(approx (/ 1 (/ 1 (- (cos (+ x eps)) (cos x)))) (.f64 eps (-.f64 (.f64 #s(literal -1/2 binary64) (*.f64 eps (cos.f64 x))) (sin.f64 x))))
	76.1%	#s(approx (/ 1 (/ 1 (- (cos (+ x eps)) (cos x)))) (neg.f64 (*.f64 eps (sin.f64 x))))
	47.1%	#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)))
✓	46.9%	#s(approx (- (cos (+ x eps)) (cos x)) (+.f64 #s(approx (cos eps) #s(literal 1 binary64)) #s(literal -1 binary64)))
	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)))))
	99.1%	#s(approx (- (cos (+ x eps)) (cos 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))))))
▶	48.7%	#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (+ (cos eps) -1) (.f64 eps (.f64 eps #s(literal -1/2 binary64)))))

Compiler

Compiled 1 452 to 882 computations (39.3% saved)

simplify338.0ms (2%)

Memory

10.8MiB live, 321.4MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 20 expressions of interest:

New	Metric	Score
cost-diff	0	(log.f64 (-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x)))
cost-diff	192	(*.f64 (log.f64 (-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))) #s(literal -1 binary64))
cost-diff	1408	(/.f64 #s(literal 1 binary64) (exp.f64 (*.f64 (log.f64 (-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))) #s(literal -1 binary64))))
cost-diff	12224	(exp.f64 (*.f64 (log.f64 (-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))) #s(literal -1 binary64)))
cost-diff	0	(sin.f64 (.f64 (.f64 (*.f64 eps eps) (/.f64 #s(literal 1 binary64) eps)) #s(literal 1/2 binary64)))
cost-diff	0	(.f64 (sin.f64 (.f64 (.f64 (.f64 eps eps) (/.f64 #s(literal 1 binary64) eps)) #s(literal 1/2 binary64))) (sin.f64 #s(approx (* (+ x (+ x eps)) 1/2) (fma.f64 eps #s(literal 1/2 binary64) x))))
cost-diff	0	(.f64 (.f64 (sin.f64 (.f64 (.f64 (.f64 eps eps) (/.f64 #s(literal 1 binary64) eps)) #s(literal 1/2 binary64))) (sin.f64 #s(approx ( (+ x (+ x eps)) 1/2) (fma.f64 eps #s(literal 1/2 binary64) x)))) #s(literal -2 binary64))
cost-diff	1344	(.f64 (.f64 eps eps) (/.f64 #s(literal 1 binary64) eps))
cost-diff	0	#s(approx (sin (* (+ eps 0) 1/2)) (.f64 eps (fma.f64 eps (.f64 eps #s(literal -1/48 binary64)) #s(literal 1/2 binary64))))
cost-diff	0	(.f64 #s(approx (sin ( (+ eps 0) 1/2)) (.f64 eps (fma.f64 eps (.f64 eps #s(literal -1/48 binary64)) #s(literal 1/2 binary64)))) (sin.f64 (*.f64 (+.f64 x (+.f64 x eps)) #s(literal 1/2 binary64))))
cost-diff	0	(.f64 (.f64 #s(approx (sin (* (+ eps 0) 1/2)) (.f64 eps (fma.f64 eps (.f64 eps #s(literal -1/48 binary64)) #s(literal 1/2 binary64)))) (sin.f64 (*.f64 (+.f64 x (+.f64 x eps)) #s(literal 1/2 binary64)))) #s(literal -2 binary64))
cost-diff	320	(*.f64 (+.f64 x (+.f64 x eps)) #s(literal 1/2 binary64))
cost-diff	0	(*.f64 eps #s(literal -1/2 binary64))
cost-diff	0	(.f64 eps (.f64 eps #s(literal -1/2 binary64)))
cost-diff	0	#s(approx (+ (cos eps) -1) (.f64 eps (.f64 eps #s(literal -1/2 binary64))))
cost-diff	0	#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (+ (cos eps) -1) (.f64 eps (.f64 eps #s(literal -1/2 binary64)))))
cost-diff	0	(.f64 (.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (cos.f64 x)) (sin.f64 (.f64 eps #s(literal 1/2 binary64))))
cost-diff	0	#s(approx (* (sin (* (+ eps 0) 1/2)) (sin (* (+ x (+ x eps)) 1/2))) (+.f64 (.f64 (.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (cos.f64 x)) (sin.f64 (.f64 eps #s(literal 1/2 binary64)))) (.f64 (.f64 (cos.f64 (.f64 eps #s(literal 1/2 binary64))) (sin.f64 x)) (sin.f64 (.f64 eps #s(literal 1/2 binary64))))))
cost-diff	0	(.f64 #s(approx ( (sin (* (+ eps 0) 1/2)) (sin (* (+ x (+ x eps)) 1/2))) (+.f64 (.f64 (.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (cos.f64 x)) (sin.f64 (.f64 eps #s(literal 1/2 binary64)))) (.f64 (.f64 (cos.f64 (.f64 eps #s(literal 1/2 binary64))) (sin.f64 x)) (sin.f64 (.f64 eps #s(literal 1/2 binary64)))))) #s(literal -2 binary64))
cost-diff	7168	(+.f64 (.f64 (.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (cos.f64 x)) (sin.f64 (.f64 eps #s(literal 1/2 binary64)))) (.f64 (.f64 (cos.f64 (.f64 eps #s(literal 1/2 binary64))) (sin.f64 x)) (sin.f64 (.f64 eps #s(literal 1/2 binary64)))))

Rules

16 686×	`lower-fma.f32`
16 682×	`lower-fma.f64`
5 168×	`lower-*.f32`
5 132×	`lower-*.f64`
2 900×	`lower-+.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	64	492
0	104	444
1	166	431
2	314	431
3	496	398
4	834	398
5	2263	398
6	3569	398
7	4147	398
8	4930	398
9	6062	398
10	6548	398
11	6830	398
0	8435	394

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

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

localize406.0ms (2.3%)

Memory

-18.1MiB live, 559.7MiB allocated

Localize:

Found 20 expressions of interest:

New	Metric	Score
accuracy	0.2295982161796743	(/.f64 #s(literal 1 binary64) (exp.f64 (*.f64 (log.f64 (-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))) #s(literal -1 binary64))))
accuracy	1.4519214917146628	(exp.f64 (*.f64 (log.f64 (-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))) #s(literal -1 binary64)))
accuracy	14.435425226681616	(log.f64 (-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x)))
accuracy	15.256112936059601	(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))
accuracy	0	#s(approx (* (+ x (+ x eps)) 1/2) (fma.f64 eps #s(literal 1/2 binary64) x))
accuracy	0.078125	(.f64 (sin.f64 (.f64 (.f64 (.f64 eps eps) (/.f64 #s(literal 1 binary64) eps)) #s(literal 1/2 binary64))) (sin.f64 #s(approx (* (+ x (+ x eps)) 1/2) (fma.f64 eps #s(literal 1/2 binary64) x))))
accuracy	0.11969751705406045	(sin.f64 #s(approx (* (+ x (+ x eps)) 1/2) (fma.f64 eps #s(literal 1/2 binary64) x)))
accuracy	14.165826947017736	(.f64 (.f64 eps eps) (/.f64 #s(literal 1 binary64) eps))
accuracy	0.1171875	(+.f64 x (+.f64 x eps))
accuracy	0.11969751705406045	(sin.f64 (*.f64 (+.f64 x (+.f64 x eps)) #s(literal 1/2 binary64)))
accuracy	0.16796875	(*.f64 eps #s(literal -1/48 binary64))
accuracy	0.20365181473820088	#s(approx (sin (* (+ eps 0) 1/2)) (.f64 eps (fma.f64 eps (.f64 eps #s(literal -1/48 binary64)) #s(literal 1/2 binary64))))
accuracy	0	(.f64 eps (.f64 eps #s(literal -1/2 binary64)))
accuracy	0	(*.f64 eps #s(literal -1/2 binary64))
accuracy	0.3223031793629511	#s(approx (+ (cos eps) -1) (.f64 eps (.f64 eps #s(literal -1/2 binary64))))
accuracy	16.05015768892118	#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (+ (cos eps) -1) (.f64 eps (.f64 eps #s(literal -1/2 binary64)))))
accuracy	0.0078125	(.f64 (.f64 (cos.f64 (.f64 eps #s(literal 1/2 binary64))) (sin.f64 x)) (sin.f64 (.f64 eps #s(literal 1/2 binary64))))
accuracy	0.0078125	(.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (cos.f64 x))
accuracy	0.01171875	(.f64 (.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (cos.f64 x)) (sin.f64 (.f64 eps #s(literal 1/2 binary64))))
accuracy	0.0625	(+.f64 (.f64 (.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (cos.f64 x)) (sin.f64 (.f64 eps #s(literal 1/2 binary64)))) (.f64 (.f64 (cos.f64 (.f64 eps #s(literal 1/2 binary64))) (sin.f64 x)) (sin.f64 (.f64 eps #s(literal 1/2 binary64)))))

Samples

149.0ms	83×	2	valid
72.0ms	43×	2	invalid
59.0ms	75×	1	invalid
27.0ms	41×	1	valid
4.0ms	11×	0	invalid
3.0ms	1×	3	valid
1.0ms	2×	0	valid

Compiler

Compiled 381 to 52 computations (86.4% saved)

Precisions

Click to see histograms. Total time spent on operations: 265.0ms

ival-cos: 92.0ms (34.7% of total)

adjust: 47.0ms (17.7% of total)

ival-mult: 42.0ms (15.8% of total)

ival-sub: 30.0ms (11.3% of total)

ival-sin: 19.0ms (7.2% of total)

ival-add: 10.0ms (3.8% of total)

ival-log: 8.0ms (3% of total)

ival-div: 6.0ms (2.3% of total)

ival-exp: 6.0ms (2.3% of total)

const: 4.0ms (1.5% of total)

exact: 1.0ms (0.4% of total)

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

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

series160.0ms (0.9%)

Memory

9.0MiB live, 238.3MiB allocated

Counts

28 → 588

Calls

Call 1

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

Outputs
#s(alt (* 1/2 (* eps (sin x))) (taylor 0 eps) (#s(alt (+.f64 (.f64 (.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (cos.f64 x)) (sin.f64 (.f64 eps #s(literal 1/2 binary64)))) (.f64 (.f64 (cos.f64 (.f64 eps #s(literal 1/2 binary64))) (sin.f64 x)) (sin.f64 (.f64 eps #s(literal 1/2 binary64))))) (patch (+.f64 (.f64 (.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (cos.f64 x)) (sin.f64 (.f64 eps #s(literal 1/2 binary64)))) (.f64 (.f64 (cos.f64 (.f64 eps #s(literal 1/2 binary64))) (sin.f64 x)) (sin.f64 (.f64 eps #s(literal 1/2 binary64))))) #<representation binary64>) () ())) ())
#s(alt (* eps (+ (* 1/4 (* eps (cos x))) (* 1/2 (sin x)))) (taylor 0 eps) (#s(alt (+.f64 (.f64 (.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (cos.f64 x)) (sin.f64 (.f64 eps #s(literal 1/2 binary64)))) (.f64 (.f64 (cos.f64 (.f64 eps #s(literal 1/2 binary64))) (sin.f64 x)) (sin.f64 (.f64 eps #s(literal 1/2 binary64))))) (patch (+.f64 (.f64 (.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (cos.f64 x)) (sin.f64 (.f64 eps #s(literal 1/2 binary64)))) (.f64 (.f64 (cos.f64 (.f64 eps #s(literal 1/2 binary64))) (sin.f64 x)) (sin.f64 (.f64 eps #s(literal 1/2 binary64))))) #<representation binary64>) () ())) ())
#s(alt (* eps (+ (* 1/2 (sin x)) (* eps (+ (* 1/4 (cos x)) (* eps (+ (* -1/16 (sin x)) (* -1/48 (sin x)))))))) (taylor 0 eps) (#s(alt (+.f64 (.f64 (.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (cos.f64 x)) (sin.f64 (.f64 eps #s(literal 1/2 binary64)))) (.f64 (.f64 (cos.f64 (.f64 eps #s(literal 1/2 binary64))) (sin.f64 x)) (sin.f64 (.f64 eps #s(literal 1/2 binary64))))) (patch (+.f64 (.f64 (.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (cos.f64 x)) (sin.f64 (.f64 eps #s(literal 1/2 binary64)))) (.f64 (.f64 (cos.f64 (.f64 eps #s(literal 1/2 binary64))) (sin.f64 x)) (sin.f64 (.f64 eps #s(literal 1/2 binary64))))) #<representation binary64>) () ())) ())
#s(alt (* eps (+ (* 1/2 (sin x)) (* eps (+ (* 1/4 (cos x)) (* eps (+ (* -1/16 (sin x)) (+ (* -1/48 (sin x)) (* -1/48 (* eps (cos x)))))))))) (taylor 0 eps) (#s(alt (+.f64 (.f64 (.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (cos.f64 x)) (sin.f64 (.f64 eps #s(literal 1/2 binary64)))) (.f64 (.f64 (cos.f64 (.f64 eps #s(literal 1/2 binary64))) (sin.f64 x)) (sin.f64 (.f64 eps #s(literal 1/2 binary64))))) (patch (+.f64 (.f64 (.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (cos.f64 x)) (sin.f64 (.f64 eps #s(literal 1/2 binary64)))) (.f64 (.f64 (cos.f64 (.f64 eps #s(literal 1/2 binary64))) (sin.f64 x)) (sin.f64 (.f64 eps #s(literal 1/2 binary64))))) #<representation binary64>) () ())) ())
#s(alt (+ (* (cos x) (pow (sin (* 1/2 eps)) 2)) (* (cos (* 1/2 eps)) (* (sin x) (sin (* 1/2 eps))))) (taylor inf eps) (#s(alt (+.f64 (.f64 (.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (cos.f64 x)) (sin.f64 (.f64 eps #s(literal 1/2 binary64)))) (.f64 (.f64 (cos.f64 (.f64 eps #s(literal 1/2 binary64))) (sin.f64 x)) (sin.f64 (.f64 eps #s(literal 1/2 binary64))))) (patch (+.f64 (.f64 (.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (cos.f64 x)) (sin.f64 (.f64 eps #s(literal 1/2 binary64)))) (.f64 (.f64 (cos.f64 (.f64 eps #s(literal 1/2 binary64))) (sin.f64 x)) (sin.f64 (.f64 eps #s(literal 1/2 binary64))))) #<representation binary64>) () ())) ())
#s(alt (+ (* (cos x) (pow (sin (* 1/2 eps)) 2)) (* (cos (* 1/2 eps)) (* (sin x) (sin (* 1/2 eps))))) (taylor inf eps) (#s(alt (+.f64 (.f64 (.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (cos.f64 x)) (sin.f64 (.f64 eps #s(literal 1/2 binary64)))) (.f64 (.f64 (cos.f64 (.f64 eps #s(literal 1/2 binary64))) (sin.f64 x)) (sin.f64 (.f64 eps #s(literal 1/2 binary64))))) (patch (+.f64 (.f64 (.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (cos.f64 x)) (sin.f64 (.f64 eps #s(literal 1/2 binary64)))) (.f64 (.f64 (cos.f64 (.f64 eps #s(literal 1/2 binary64))) (sin.f64 x)) (sin.f64 (.f64 eps #s(literal 1/2 binary64))))) #<representation binary64>) () ())) ())
#s(alt (+ (* (cos x) (pow (sin (* 1/2 eps)) 2)) (* (cos (* 1/2 eps)) (* (sin x) (sin (* 1/2 eps))))) (taylor inf eps) (#s(alt (+.f64 (.f64 (.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (cos.f64 x)) (sin.f64 (.f64 eps #s(literal 1/2 binary64)))) (.f64 (.f64 (cos.f64 (.f64 eps #s(literal 1/2 binary64))) (sin.f64 x)) (sin.f64 (.f64 eps #s(literal 1/2 binary64))))) (patch (+.f64 (.f64 (.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (cos.f64 x)) (sin.f64 (.f64 eps #s(literal 1/2 binary64)))) (.f64 (.f64 (cos.f64 (.f64 eps #s(literal 1/2 binary64))) (sin.f64 x)) (sin.f64 (.f64 eps #s(literal 1/2 binary64))))) #<representation binary64>) () ())) ())
#s(alt (+ (* (cos x) (pow (sin (* 1/2 eps)) 2)) (* (cos (* 1/2 eps)) (* (sin x) (sin (* 1/2 eps))))) (taylor inf eps) (#s(alt (+.f64 (.f64 (.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (cos.f64 x)) (sin.f64 (.f64 eps #s(literal 1/2 binary64)))) (.f64 (.f64 (cos.f64 (.f64 eps #s(literal 1/2 binary64))) (sin.f64 x)) (sin.f64 (.f64 eps #s(literal 1/2 binary64))))) (patch (+.f64 (.f64 (.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (cos.f64 x)) (sin.f64 (.f64 eps #s(literal 1/2 binary64)))) (.f64 (.f64 (cos.f64 (.f64 eps #s(literal 1/2 binary64))) (sin.f64 x)) (sin.f64 (.f64 eps #s(literal 1/2 binary64))))) #<representation binary64>) () ())) ())
#s(alt (+ (* (cos x) (pow (sin (* 1/2 eps)) 2)) (* (cos (* 1/2 eps)) (* (sin x) (sin (* 1/2 eps))))) (taylor -inf eps) (#s(alt (+.f64 (.f64 (.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (cos.f64 x)) (sin.f64 (.f64 eps #s(literal 1/2 binary64)))) (.f64 (.f64 (cos.f64 (.f64 eps #s(literal 1/2 binary64))) (sin.f64 x)) (sin.f64 (.f64 eps #s(literal 1/2 binary64))))) (patch (+.f64 (.f64 (.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (cos.f64 x)) (sin.f64 (.f64 eps #s(literal 1/2 binary64)))) (.f64 (.f64 (cos.f64 (.f64 eps #s(literal 1/2 binary64))) (sin.f64 x)) (sin.f64 (.f64 eps #s(literal 1/2 binary64))))) #<representation binary64>) () ())) ())
#s(alt (+ (* (cos x) (pow (sin (* 1/2 eps)) 2)) (* (cos (* 1/2 eps)) (* (sin x) (sin (* 1/2 eps))))) (taylor -inf eps) (#s(alt (+.f64 (.f64 (.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (cos.f64 x)) (sin.f64 (.f64 eps #s(literal 1/2 binary64)))) (.f64 (.f64 (cos.f64 (.f64 eps #s(literal 1/2 binary64))) (sin.f64 x)) (sin.f64 (.f64 eps #s(literal 1/2 binary64))))) (patch (+.f64 (.f64 (.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (cos.f64 x)) (sin.f64 (.f64 eps #s(literal 1/2 binary64)))) (.f64 (.f64 (cos.f64 (.f64 eps #s(literal 1/2 binary64))) (sin.f64 x)) (sin.f64 (.f64 eps #s(literal 1/2 binary64))))) #<representation binary64>) () ())) ())
#s(alt (+ (* (cos x) (pow (sin (* 1/2 eps)) 2)) (* (cos (* 1/2 eps)) (* (sin x) (sin (* 1/2 eps))))) (taylor -inf eps) (#s(alt (+.f64 (.f64 (.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (cos.f64 x)) (sin.f64 (.f64 eps #s(literal 1/2 binary64)))) (.f64 (.f64 (cos.f64 (.f64 eps #s(literal 1/2 binary64))) (sin.f64 x)) (sin.f64 (.f64 eps #s(literal 1/2 binary64))))) (patch (+.f64 (.f64 (.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (cos.f64 x)) (sin.f64 (.f64 eps #s(literal 1/2 binary64)))) (.f64 (.f64 (cos.f64 (.f64 eps #s(literal 1/2 binary64))) (sin.f64 x)) (sin.f64 (.f64 eps #s(literal 1/2 binary64))))) #<representation binary64>) () ())) ())
#s(alt (+ (* (cos x) (pow (sin (* 1/2 eps)) 2)) (* (cos (* 1/2 eps)) (* (sin x) (sin (* 1/2 eps))))) (taylor -inf eps) (#s(alt (+.f64 (.f64 (.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (cos.f64 x)) (sin.f64 (.f64 eps #s(literal 1/2 binary64)))) (.f64 (.f64 (cos.f64 (.f64 eps #s(literal 1/2 binary64))) (sin.f64 x)) (sin.f64 (.f64 eps #s(literal 1/2 binary64))))) (patch (+.f64 (.f64 (.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (cos.f64 x)) (sin.f64 (.f64 eps #s(literal 1/2 binary64)))) (.f64 (.f64 (cos.f64 (.f64 eps #s(literal 1/2 binary64))) (sin.f64 x)) (sin.f64 (.f64 eps #s(literal 1/2 binary64))))) #<representation binary64>) () ())) ())
#s(alt (pow (sin (* 1/2 eps)) 2) (taylor 0 x) (#s(alt (+.f64 (.f64 (.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (cos.f64 x)) (sin.f64 (.f64 eps #s(literal 1/2 binary64)))) (.f64 (.f64 (cos.f64 (.f64 eps #s(literal 1/2 binary64))) (sin.f64 x)) (sin.f64 (.f64 eps #s(literal 1/2 binary64))))) (patch (+.f64 (.f64 (.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (cos.f64 x)) (sin.f64 (.f64 eps #s(literal 1/2 binary64)))) (.f64 (.f64 (cos.f64 (.f64 eps #s(literal 1/2 binary64))) (sin.f64 x)) (sin.f64 (.f64 eps #s(literal 1/2 binary64))))) #<representation binary64>) () ())) ())
#s(alt (+ (* x (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) (pow (sin (* 1/2 eps)) 2)) (taylor 0 x) (#s(alt (+.f64 (.f64 (.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (cos.f64 x)) (sin.f64 (.f64 eps #s(literal 1/2 binary64)))) (.f64 (.f64 (cos.f64 (.f64 eps #s(literal 1/2 binary64))) (sin.f64 x)) (sin.f64 (.f64 eps #s(literal 1/2 binary64))))) (patch (+.f64 (.f64 (.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (cos.f64 x)) (sin.f64 (.f64 eps #s(literal 1/2 binary64)))) (.f64 (.f64 (cos.f64 (.f64 eps #s(literal 1/2 binary64))) (sin.f64 x)) (sin.f64 (.f64 eps #s(literal 1/2 binary64))))) #<representation binary64>) () ())) ())
#s(alt (+ (* x (+ (* -1/2 (* x (pow (sin (* 1/2 eps)) 2))) (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))) (pow (sin (* 1/2 eps)) 2)) (taylor 0 x) (#s(alt (+.f64 (.f64 (.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (cos.f64 x)) (sin.f64 (.f64 eps #s(literal 1/2 binary64)))) (.f64 (.f64 (cos.f64 (.f64 eps #s(literal 1/2 binary64))) (sin.f64 x)) (sin.f64 (.f64 eps #s(literal 1/2 binary64))))) (patch (+.f64 (.f64 (.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (cos.f64 x)) (sin.f64 (.f64 eps #s(literal 1/2 binary64)))) (.f64 (.f64 (cos.f64 (.f64 eps #s(literal 1/2 binary64))) (sin.f64 x)) (sin.f64 (.f64 eps #s(literal 1/2 binary64))))) #<representation binary64>) () ())) ())
#s(alt (+ (* 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)) (taylor 0 x) (#s(alt (+.f64 (.f64 (.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (cos.f64 x)) (sin.f64 (.f64 eps #s(literal 1/2 binary64)))) (.f64 (.f64 (cos.f64 (.f64 eps #s(literal 1/2 binary64))) (sin.f64 x)) (sin.f64 (.f64 eps #s(literal 1/2 binary64))))) (patch (+.f64 (.f64 (.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (cos.f64 x)) (sin.f64 (.f64 eps #s(literal 1/2 binary64)))) (.f64 (.f64 (cos.f64 (.f64 eps #s(literal 1/2 binary64))) (sin.f64 x)) (sin.f64 (.f64 eps #s(literal 1/2 binary64))))) #<representation binary64>) () ())) ())
#s(alt (+ (* (cos x) (pow (sin (* 1/2 eps)) 2)) (* (cos (* 1/2 eps)) (* (sin x) (sin (* 1/2 eps))))) (taylor inf x) (#s(alt (+.f64 (.f64 (.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (cos.f64 x)) (sin.f64 (.f64 eps #s(literal 1/2 binary64)))) (.f64 (.f64 (cos.f64 (.f64 eps #s(literal 1/2 binary64))) (sin.f64 x)) (sin.f64 (.f64 eps #s(literal 1/2 binary64))))) (patch (+.f64 (.f64 (.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (cos.f64 x)) (sin.f64 (.f64 eps #s(literal 1/2 binary64)))) (.f64 (.f64 (cos.f64 (.f64 eps #s(literal 1/2 binary64))) (sin.f64 x)) (sin.f64 (.f64 eps #s(literal 1/2 binary64))))) #<representation binary64>) () ())) ())
#s(alt (+ (* (cos x) (pow (sin (* 1/2 eps)) 2)) (* (cos (* 1/2 eps)) (* (sin x) (sin (* 1/2 eps))))) (taylor inf x) (#s(alt (+.f64 (.f64 (.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (cos.f64 x)) (sin.f64 (.f64 eps #s(literal 1/2 binary64)))) (.f64 (.f64 (cos.f64 (.f64 eps #s(literal 1/2 binary64))) (sin.f64 x)) (sin.f64 (.f64 eps #s(literal 1/2 binary64))))) (patch (+.f64 (.f64 (.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (cos.f64 x)) (sin.f64 (.f64 eps #s(literal 1/2 binary64)))) (.f64 (.f64 (cos.f64 (.f64 eps #s(literal 1/2 binary64))) (sin.f64 x)) (sin.f64 (.f64 eps #s(literal 1/2 binary64))))) #<representation binary64>) () ())) ())
#s(alt (+ (* (cos x) (pow (sin (* 1/2 eps)) 2)) (* (cos (* 1/2 eps)) (* (sin x) (sin (* 1/2 eps))))) (taylor inf x) (#s(alt (+.f64 (.f64 (.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (cos.f64 x)) (sin.f64 (.f64 eps #s(literal 1/2 binary64)))) (.f64 (.f64 (cos.f64 (.f64 eps #s(literal 1/2 binary64))) (sin.f64 x)) (sin.f64 (.f64 eps #s(literal 1/2 binary64))))) (patch (+.f64 (.f64 (.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (cos.f64 x)) (sin.f64 (.f64 eps #s(literal 1/2 binary64)))) (.f64 (.f64 (cos.f64 (.f64 eps #s(literal 1/2 binary64))) (sin.f64 x)) (sin.f64 (.f64 eps #s(literal 1/2 binary64))))) #<representation binary64>) () ())) ())
#s(alt (+ (* (cos x) (pow (sin (* 1/2 eps)) 2)) (* (cos (* 1/2 eps)) (* (sin x) (sin (* 1/2 eps))))) (taylor inf x) (#s(alt (+.f64 (.f64 (.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (cos.f64 x)) (sin.f64 (.f64 eps #s(literal 1/2 binary64)))) (.f64 (.f64 (cos.f64 (.f64 eps #s(literal 1/2 binary64))) (sin.f64 x)) (sin.f64 (.f64 eps #s(literal 1/2 binary64))))) (patch (+.f64 (.f64 (.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (cos.f64 x)) (sin.f64 (.f64 eps #s(literal 1/2 binary64)))) (.f64 (.f64 (cos.f64 (.f64 eps #s(literal 1/2 binary64))) (sin.f64 x)) (sin.f64 (.f64 eps #s(literal 1/2 binary64))))) #<representation binary64>) () ())) ())
#s(alt (+ (* (cos x) (pow (sin (* 1/2 eps)) 2)) (* (cos (* 1/2 eps)) (* (sin x) (sin (* 1/2 eps))))) (taylor -inf x) (#s(alt (+.f64 (.f64 (.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (cos.f64 x)) (sin.f64 (.f64 eps #s(literal 1/2 binary64)))) (.f64 (.f64 (cos.f64 (.f64 eps #s(literal 1/2 binary64))) (sin.f64 x)) (sin.f64 (.f64 eps #s(literal 1/2 binary64))))) (patch (+.f64 (.f64 (.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (cos.f64 x)) (sin.f64 (.f64 eps #s(literal 1/2 binary64)))) (.f64 (.f64 (cos.f64 (.f64 eps #s(literal 1/2 binary64))) (sin.f64 x)) (sin.f64 (.f64 eps #s(literal 1/2 binary64))))) #<representation binary64>) () ())) ())
#s(alt (+ (* (cos x) (pow (sin (* 1/2 eps)) 2)) (* (cos (* 1/2 eps)) (* (sin x) (sin (* 1/2 eps))))) (taylor -inf x) (#s(alt (+.f64 (.f64 (.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (cos.f64 x)) (sin.f64 (.f64 eps #s(literal 1/2 binary64)))) (.f64 (.f64 (cos.f64 (.f64 eps #s(literal 1/2 binary64))) (sin.f64 x)) (sin.f64 (.f64 eps #s(literal 1/2 binary64))))) (patch (+.f64 (.f64 (.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (cos.f64 x)) (sin.f64 (.f64 eps #s(literal 1/2 binary64)))) (.f64 (.f64 (cos.f64 (.f64 eps #s(literal 1/2 binary64))) (sin.f64 x)) (sin.f64 (.f64 eps #s(literal 1/2 binary64))))) #<representation binary64>) () ())) ())
#s(alt (+ (* (cos x) (pow (sin (* 1/2 eps)) 2)) (* (cos (* 1/2 eps)) (* (sin x) (sin (* 1/2 eps))))) (taylor -inf x) (#s(alt (+.f64 (.f64 (.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (cos.f64 x)) (sin.f64 (.f64 eps #s(literal 1/2 binary64)))) (.f64 (.f64 (cos.f64 (.f64 eps #s(literal 1/2 binary64))) (sin.f64 x)) (sin.f64 (.f64 eps #s(literal 1/2 binary64))))) (patch (+.f64 (.f64 (.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (cos.f64 x)) (sin.f64 (.f64 eps #s(literal 1/2 binary64)))) (.f64 (.f64 (cos.f64 (.f64 eps #s(literal 1/2 binary64))) (sin.f64 x)) (sin.f64 (.f64 eps #s(literal 1/2 binary64))))) #<representation binary64>) () ())) ())
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#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>) () ())) ())

Calls

147 calls:

Time	Variable		Point	Expression
40.0ms	x	@	inf	(* (log (- (cos (+ x eps)) (cos x))) -1)
37.0ms	eps	@	inf	(* (log (- (cos (+ x eps)) (cos x))) -1)
17.0ms	eps	@	-inf	(* (log (- (cos (+ x eps)) (cos x))) -1)
16.0ms	x	@	-inf	(* (log (- (cos (+ x eps)) (cos x))) -1)
7.0ms	eps	@	inf	(+ (* (* (sin (* eps 1/2)) (cos x)) (sin (* eps 1/2))) (* (* (cos (* eps 1/2)) (sin x)) (sin (* eps 1/2))))

simplify267.0ms (1.5%)

Memory

32.8MiB live, 312.5MiB allocated

Algorithm

1×	egg-herbie

Rules

9 294×	`lower-fma.f64`
9 294×	`lower-fma.f32`
7 948×	`lower-*.f64`
7 948×	`lower-*.f32`
2 534×	`lower-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	557	7233
1	1811	6753
2	5890	6710
0	8895	6297

Stop Event

1×	iter limit
1×	node limit

Counts

588 → 567

Calls

Call 1

Inputs
(* 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))))))))))
(+ (* (cos x) (pow (sin (* 1/2 eps)) 2)) (* (cos (* 1/2 eps)) (* (sin x) (sin (* 1/2 eps)))))
(+ (* (cos x) (pow (sin (* 1/2 eps)) 2)) (* (cos (* 1/2 eps)) (* (sin x) (sin (* 1/2 eps)))))
(+ (* (cos x) (pow (sin (* 1/2 eps)) 2)) (* (cos (* 1/2 eps)) (* (sin x) (sin (* 1/2 eps)))))
(+ (* (cos x) (pow (sin (* 1/2 eps)) 2)) (* (cos (* 1/2 eps)) (* (sin x) (sin (* 1/2 eps)))))
(+ (* (cos x) (pow (sin (* 1/2 eps)) 2)) (* (cos (* 1/2 eps)) (* (sin x) (sin (* 1/2 eps)))))
(+ (* (cos x) (pow (sin (* 1/2 eps)) 2)) (* (cos (* 1/2 eps)) (* (sin x) (sin (* 1/2 eps)))))
(+ (* (cos x) (pow (sin (* 1/2 eps)) 2)) (* (cos (* 1/2 eps)) (* (sin x) (sin (* 1/2 eps)))))
(+ (* (cos x) (pow (sin (* 1/2 eps)) 2)) (* (cos (* 1/2 eps)) (* (sin x) (sin (* 1/2 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))
(+ (* (cos x) (pow (sin (* 1/2 eps)) 2)) (* (cos (* 1/2 eps)) (* (sin x) (sin (* 1/2 eps)))))
(+ (* (cos x) (pow (sin (* 1/2 eps)) 2)) (* (cos (* 1/2 eps)) (* (sin x) (sin (* 1/2 eps)))))
(+ (* (cos x) (pow (sin (* 1/2 eps)) 2)) (* (cos (* 1/2 eps)) (* (sin x) (sin (* 1/2 eps)))))
(+ (* (cos x) (pow (sin (* 1/2 eps)) 2)) (* (cos (* 1/2 eps)) (* (sin x) (sin (* 1/2 eps)))))
(+ (* (cos x) (pow (sin (* 1/2 eps)) 2)) (* (cos (* 1/2 eps)) (* (sin x) (sin (* 1/2 eps)))))
(+ (* (cos x) (pow (sin (* 1/2 eps)) 2)) (* (cos (* 1/2 eps)) (* (sin x) (sin (* 1/2 eps)))))
(+ (* (cos x) (pow (sin (* 1/2 eps)) 2)) (* (cos (* 1/2 eps)) (* (sin x) (sin (* 1/2 eps)))))
(+ (* (cos x) (pow (sin (* 1/2 eps)) 2)) (* (cos (* 1/2 eps)) (* (sin x) (sin (* 1/2 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)))))
(* 1/4 (* (pow eps 2) (cos x)))
(* (pow eps 2) (+ (* -1/48 (* (pow eps 2) (cos x))) (* 1/4 (cos x))))
(* (pow eps 2) (+ (* 1/4 (cos x)) (* (pow eps 2) (+ (* -1/48 (cos x)) (* 1/1440 (* (pow eps 2) (cos x)))))))
(* (pow eps 2) (+ (* 1/4 (cos x)) (* (pow eps 2) (+ (* -1/48 (cos x)) (* (pow eps 2) (+ (* -1/80640 (* (pow eps 2) (cos x))) (* 1/1440 (cos x))))))))
(* (cos x) (pow (sin (* 1/2 eps)) 2))
(* (cos x) (pow (sin (* 1/2 eps)) 2))
(* (cos x) (pow (sin (* 1/2 eps)) 2))
(* (cos x) (pow (sin (* 1/2 eps)) 2))
(* (cos x) (pow (sin (* 1/2 eps)) 2))
(* (cos x) (pow (sin (* 1/2 eps)) 2))
(* (cos x) (pow (sin (* 1/2 eps)) 2))
(* (cos x) (pow (sin (* 1/2 eps)) 2))
(pow (sin (* 1/2 eps)) 2)
(+ (* -1/2 (* (pow x 2) (pow (sin (* 1/2 eps)) 2))) (pow (sin (* 1/2 eps)) 2))
(+ (* (pow x 2) (+ (* -1/2 (pow (sin (* 1/2 eps)) 2)) (* 1/24 (* (pow x 2) (pow (sin (* 1/2 eps)) 2))))) (pow (sin (* 1/2 eps)) 2))
(+ (* (pow x 2) (+ (* -1/2 (pow (sin (* 1/2 eps)) 2)) (* (pow x 2) (+ (* -1/720 (* (pow x 2) (pow (sin (* 1/2 eps)) 2))) (* 1/24 (pow (sin (* 1/2 eps)) 2)))))) (pow (sin (* 1/2 eps)) 2))
(* (cos x) (pow (sin (* 1/2 eps)) 2))
(* (cos x) (pow (sin (* 1/2 eps)) 2))
(* (cos x) (pow (sin (* 1/2 eps)) 2))
(* (cos x) (pow (sin (* 1/2 eps)) 2))
(* (cos x) (pow (sin (* 1/2 eps)) 2))
(* (cos x) (pow (sin (* 1/2 eps)) 2))
(* (cos x) (pow (sin (* 1/2 eps)) 2))
(* (cos x) (pow (sin (* 1/2 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))
(* -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)
(* -1/2 (pow eps 2))
(* -1/2 (pow eps 2))
(* -1/2 (pow eps 2))
(* -1/2 (pow eps 2))
(* -1/2 (pow eps 2))
(* -1/2 (pow eps 2))
(* -1/2 (pow eps 2))
(* -1/2 (pow eps 2))
(* -1/2 (pow eps 2))
(* -1/2 (pow eps 2))
(* -1/2 (pow eps 2))
(* -1/2 (pow eps 2))
(* -1/2 eps)
(* -1/2 eps)
(* -1/2 eps)
(* -1/2 eps)
(* -1/2 eps)
(* -1/2 eps)
(* -1/2 eps)
(* -1/2 eps)
(* -1/2 eps)
(* -1/2 eps)
(* -1/2 eps)
(* -1/2 eps)
(* 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)))
(* -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)))))
(* 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))
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))))))
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(- (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))

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

rewrite228.0ms (1.3%)

Memory

6.3MiB live, 195.1MiB allocated

Rules

4 284×	`lower-/.f32`
4 280×	`lower-/.f64`
3 974×	`lower-*.f32`
3 938×	`lower-*.f64`
3 244×	`lower-fma.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	64	405
0	104	360
1	304	317
2	2049	314
0	8205	303

Stop Event

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

Counts

28 → 525

Calls

Call 1

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

Outputs
(+.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 (cos.f64 (.f64 eps #s(literal 1/2 binary64))) (sin.f64 x))))
(+.f64 (.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (.f64 (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))))))))
(-.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 2 binary64)) (.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (sin.f64 (-.f64 (.f64 eps #s(literal 1/2 binary64)) x)))) (/.f64 (pow.f64 (.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (.f64 (cos.f64 (.f64 eps #s(literal 1/2 binary64))) (sin.f64 x))) #s(literal 2 binary64)) (.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (sin.f64 (-.f64 (.f64 eps #s(literal 1/2 binary64)) x)))))
(-.f64 (/.f64 (pow.f64 (.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (.f64 (cos.f64 (.f64 eps #s(literal 1/2 binary64))) (sin.f64 x))) #s(literal 2 binary64)) (-.f64 (.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (.f64 (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))))))))) (/.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 2 binary64)) (-.f64 (.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (.f64 (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 (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 (cos.f64 (*.f64 eps #s(literal 1/2 binary64))) (sin.f64 x))))
(fma.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (.f64 (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 (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 (cos.f64 (*.f64 eps #s(literal 1/2 binary64))) (sin.f64 x))))
(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 (cos.f64 (*.f64 eps #s(literal 1/2 binary64))) (sin.f64 x))))
(fma.f64 (cos.f64 (.f64 eps #s(literal 1/2 binary64))) (.f64 (sin.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 (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 (.f64 (cos.f64 (.f64 eps #s(literal 1/2 binary64))) (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 (.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))))))))
(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 (cos.f64 (*.f64 eps #s(literal 1/2 binary64))) (sin.f64 x))))
(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))))))))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 (fma.f64 (.f64 (sin.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 (.f64 eps #s(literal 1/2 binary64))) (.f64 (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)))))))) (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 2 binary64))) (+.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 (cos.f64 (.f64 eps #s(literal 1/2 binary64))) (sin.f64 x))) #s(literal 3 binary64))))))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 (.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (sin.f64 (-.f64 (.f64 eps #s(literal 1/2 binary64)) x))) (.f64 (.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (sin.f64 (fma.f64 eps #s(literal 1/2 binary64) x))) (.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (sin.f64 (-.f64 (*.f64 eps #s(literal 1/2 binary64)) x)))))))
(/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 (.f64 (sin.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 (.f64 eps #s(literal 1/2 binary64))) (.f64 (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)))))))) (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 2 binary64))) (+.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 (cos.f64 (.f64 eps #s(literal 1/2 binary64))) (sin.f64 x))) #s(literal 3 binary64)))))
(/.f64 #s(literal 1 binary64) (/.f64 (.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (sin.f64 (-.f64 (.f64 eps #s(literal 1/2 binary64)) x))) (.f64 (.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (sin.f64 (fma.f64 eps #s(literal 1/2 binary64) x))) (.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (sin.f64 (-.f64 (*.f64 eps #s(literal 1/2 binary64)) x))))))
(/.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 (cos.f64 (.f64 eps #s(literal 1/2 binary64))) (sin.f64 x))) #s(literal 3 binary64))) (fma.f64 (.f64 (sin.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 (.f64 eps #s(literal 1/2 binary64))) (.f64 (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)))))))) (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 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 (cos.f64 (.f64 eps #s(literal 1/2 binary64))) (sin.f64 x))) #s(literal 3 binary64))) (+.f64 (pow.f64 (.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (.f64 (cos.f64 (.f64 eps #s(literal 1/2 binary64))) (sin.f64 x))) #s(literal 2 binary64)) (-.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 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 (cos.f64 (*.f64 eps #s(literal 1/2 binary64))) (sin.f64 x)))))))
(/.f64 (.f64 (.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (sin.f64 (fma.f64 eps #s(literal 1/2 binary64) x))) (.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (sin.f64 (-.f64 (.f64 eps #s(literal 1/2 binary64)) x)))) (.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (sin.f64 (-.f64 (*.f64 eps #s(literal 1/2 binary64)) x))))
(/.f64 (neg.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 (cos.f64 (.f64 eps #s(literal 1/2 binary64))) (sin.f64 x))) #s(literal 3 binary64)))) (neg.f64 (fma.f64 (.f64 (sin.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 (.f64 eps #s(literal 1/2 binary64))) (.f64 (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)))))))) (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 2 binary64)))))
(/.f64 (neg.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 (cos.f64 (.f64 eps #s(literal 1/2 binary64))) (sin.f64 x))) #s(literal 3 binary64)))) (neg.f64 (+.f64 (pow.f64 (.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (.f64 (cos.f64 (.f64 eps #s(literal 1/2 binary64))) (sin.f64 x))) #s(literal 2 binary64)) (-.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 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 (cos.f64 (*.f64 eps #s(literal 1/2 binary64))) (sin.f64 x))))))))
(/.f64 (neg.f64 (.f64 (.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (sin.f64 (fma.f64 eps #s(literal 1/2 binary64) x))) (.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (sin.f64 (-.f64 (.f64 eps #s(literal 1/2 binary64)) x))))) (neg.f64 (.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (sin.f64 (-.f64 (*.f64 eps #s(literal 1/2 binary64)) x)))))
(/.f64 (-.f64 (pow.f64 (.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (.f64 (cos.f64 (.f64 eps #s(literal 1/2 binary64))) (sin.f64 x))) #s(literal 2 binary64)) (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 2 binary64))) (-.f64 (.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (.f64 (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)))))))))
(/.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 (-.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 2 binary64)) (.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (sin.f64 (-.f64 (.f64 eps #s(literal 1/2 binary64)) x)))) (.f64 (.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (sin.f64 (-.f64 (.f64 eps #s(literal 1/2 binary64)) x))) (pow.f64 (.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (.f64 (cos.f64 (.f64 eps #s(literal 1/2 binary64))) (sin.f64 x))) #s(literal 2 binary64)))) (.f64 (.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (sin.f64 (-.f64 (.f64 eps #s(literal 1/2 binary64)) x))) (.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (sin.f64 (-.f64 (*.f64 eps #s(literal 1/2 binary64)) x)))))
(/.f64 (neg.f64 (neg.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 (cos.f64 (.f64 eps #s(literal 1/2 binary64))) (sin.f64 x))) #s(literal 3 binary64))))) (neg.f64 (neg.f64 (fma.f64 (.f64 (sin.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 (.f64 eps #s(literal 1/2 binary64))) (.f64 (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)))))))) (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 2 binary64))))))
(/.f64 (neg.f64 (neg.f64 (.f64 (.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (sin.f64 (fma.f64 eps #s(literal 1/2 binary64) x))) (.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (sin.f64 (-.f64 (.f64 eps #s(literal 1/2 binary64)) x)))))) (neg.f64 (neg.f64 (.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (sin.f64 (-.f64 (*.f64 eps #s(literal 1/2 binary64)) x))))))
(/.f64 (neg.f64 (-.f64 (pow.f64 (.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (.f64 (cos.f64 (.f64 eps #s(literal 1/2 binary64))) (sin.f64 x))) #s(literal 2 binary64)) (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 2 binary64)))) (neg.f64 (-.f64 (.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (.f64 (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))))))))))
(pow.f64 (/.f64 (fma.f64 (.f64 (sin.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 (.f64 eps #s(literal 1/2 binary64))) (.f64 (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)))))))) (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 2 binary64))) (+.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 (cos.f64 (.f64 eps #s(literal 1/2 binary64))) (sin.f64 x))) #s(literal 3 binary64)))) #s(literal -1 binary64))
(pow.f64 (/.f64 (.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (sin.f64 (-.f64 (.f64 eps #s(literal 1/2 binary64)) x))) (.f64 (.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (sin.f64 (fma.f64 eps #s(literal 1/2 binary64) x))) (.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (sin.f64 (-.f64 (*.f64 eps #s(literal 1/2 binary64)) x))))) #s(literal -1 binary64))
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eval133.0ms (0.8%)

Memory: -15.4MiB live, 149.0MiB allocated
Compiler: Compiled 25 824 to 2 769 computations (89.3% saved)

prune206.0ms (1.2%)

Memory

-23.3MiB live, 185.4MiB allocated

Pruning

40 alts after pruning (34 fresh and 6 done)

	Pruned	Kept	Total
New	1 079	13	1 092
Fresh	6	21	27
Picked	2	3	5
Done	0	3	3
Total	1 087	40	1 127

Accuracy

100.0%

Counts

1 127 → 40

Alt Table

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Status	Accuracy	Program
	48.8%	(/.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)))))
	49.2%	(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (-.f64 (fma.f64 (cos.f64 x) (cos.f64 eps) (*.f64 (neg.f64 (sin.f64 x)) (sin.f64 eps))) (cos.f64 x))))
	49.2%	(-.f64 (fma.f64 (sin.f64 (neg.f64 x)) (sin.f64 eps) (*.f64 (cos.f64 x) (cos.f64 eps))) (cos.f64 x))
	49.2%	(-.f64 (*.f64 (cos.f64 x) (cos.f64 eps)) (fma.f64 (sin.f64 x) (sin.f64 eps) (cos.f64 x)))
✓	48.7%	(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))
✓	47.1%	(-.f64 (cos.f64 (+.f64 x eps)) #s(approx (cos x) (fma.f64 x (*.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64))))
	47.2%	(-.f64 (cos.f64 (+.f64 x eps)) #s(approx (cos x) #s(literal 1 binary64)))
	47.0%	(-.f64 #s(approx (cos (+ x eps)) (cos.f64 x)) #s(approx (cos x) (fma.f64 x (*.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64))))
	96.2%	(.f64 (/.f64 #s(literal 1 binary64) (+.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))) #s(approx (- (+ ( 1/2 (cos (* (+ x eps) 2))) 1/2) (+ (* 1/2 (cos (+ x x))) 1/2)) #s(approx (* eps (+ (* (neg eps) (cos (* x 2))) (sin (* x -2)))) (fma.f64 x (fma.f64 x (.f64 eps (.f64 eps #s(literal 2 binary64))) (.f64 eps #s(literal -2 binary64))) (.f64 eps (neg.f64 eps))))))
	96.0%	(.f64 (/.f64 #s(literal 1 binary64) (+.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))) #s(approx (- (+ ( 1/2 (cos (* (+ x eps) 2))) 1/2) (+ (* 1/2 (cos (+ x x))) 1/2)) #s(approx (* eps (+ (* (neg eps) (cos (* x 2))) (sin (* x -2)))) (fma.f64 eps (neg.f64 eps) (.f64 eps (.f64 x #s(literal -2 binary64)))))))
	48.8%	(.f64 (/.f64 #s(literal 1 binary64) (+.f64 (cos.f64 (.f64 (.f64 (+.f64 x eps) (-.f64 x eps)) (/.f64 #s(literal 1 binary64) (-.f64 x eps)))) (cos.f64 x))) (-.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))))
	43.7%	(.f64 (.f64 (sin.f64 (.f64 (/.f64 (.f64 (fma.f64 x x (.f64 (+.f64 x eps) eps)) eps) (fma.f64 (+.f64 x eps) (+.f64 x eps) (-.f64 (.f64 x x) (.f64 x (+.f64 x eps))))) #s(literal 1/2 binary64))) (sin.f64 (.f64 (+.f64 x (+.f64 x eps)) #s(literal 1/2 binary64)))) #s(literal -2 binary64))
	97.6%	(.f64 (.f64 (sin.f64 (.f64 (.f64 (.f64 eps eps) (/.f64 #s(literal 1 binary64) eps)) #s(literal 1/2 binary64))) #s(approx (sin ( (+ x (+ x eps)) 1/2)) (fma.f64 eps (*.f64 (cos.f64 x) #s(literal 1/2 binary64)) (sin.f64 x)))) #s(literal -2 binary64))
	99.3%	(.f64 (.f64 #s(approx (sin (* (+ eps 0) 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)))) (sin.f64 #s(approx (* (+ x (+ x eps)) 1/2) (fma.f64 eps #s(literal 1/2 binary64) x)))) #s(literal -2 binary64))
	99.2%	(.f64 (.f64 #s(approx (sin (* (+ eps 0) 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)))) (sin.f64 #s(approx (* (+ x (+ x eps)) 1/2) (*.f64 eps (+.f64 #s(literal 1/2 binary64) (/.f64 x eps)))))) #s(literal -2 binary64))
	43.8%	(.f64 (.f64 #s(approx (sin (* (+ eps 0) 1/2)) (.f64 eps (fma.f64 eps (.f64 eps #s(literal -1/48 binary64)) #s(literal 1/2 binary64)))) (sin.f64 (.f64 (/.f64 (fma.f64 (+.f64 eps x) (.f64 (+.f64 eps x) (+.f64 eps x)) (.f64 x (.f64 x x))) (fma.f64 (+.f64 eps x) (+.f64 eps x) (-.f64 (.f64 x x) (.f64 x (+.f64 eps x))))) #s(literal 1/2 binary64)))) #s(literal -2 binary64))
	99.1%	(.f64 (.f64 #s(approx (sin (* (+ eps 0) 1/2)) (.f64 eps (fma.f64 eps (.f64 eps #s(literal -1/48 binary64)) #s(literal 1/2 binary64)))) (sin.f64 (.f64 (/.f64 (-.f64 (.f64 (+.f64 x x) (+.f64 x x)) (*.f64 eps eps)) (-.f64 (+.f64 x x) eps)) #s(literal 1/2 binary64)))) #s(literal -2 binary64))
	98.6%	(.f64 (.f64 #s(approx (sin (* (+ eps 0) 1/2)) (.f64 eps (fma.f64 eps (.f64 eps #s(literal -1/48 binary64)) #s(literal 1/2 binary64)))) (sin.f64 (.f64 (/.f64 #s(literal 1 binary64) (/.f64 (-.f64 x (+.f64 eps x)) (.f64 (+.f64 eps (+.f64 x x)) (-.f64 x (+.f64 eps x))))) #s(literal 1/2 binary64)))) #s(literal -2 binary64))
✓	99.2%	(.f64 (.f64 #s(approx (sin (* (+ eps 0) 1/2)) (.f64 eps (fma.f64 eps (.f64 eps #s(literal -1/48 binary64)) #s(literal 1/2 binary64)))) (sin.f64 (*.f64 (+.f64 x (+.f64 x eps)) #s(literal 1/2 binary64)))) #s(literal -2 binary64))
	98.6%	(.f64 (.f64 #s(approx (sin (* (+ eps 0) 1/2)) (.f64 eps (fma.f64 eps (.f64 eps #s(literal -1/48 binary64)) #s(literal 1/2 binary64)))) (sin.f64 (.f64 (.f64 (*.f64 (+.f64 eps (+.f64 x x)) (-.f64 x (+.f64 eps x))) (/.f64 #s(literal 1 binary64) (-.f64 x (+.f64 eps x)))) #s(literal 1/2 binary64)))) #s(literal -2 binary64))
	99.2%	(.f64 (.f64 #s(approx (sin (* (+ eps 0) 1/2)) (.f64 eps (fma.f64 eps (.f64 eps #s(literal -1/48 binary64)) #s(literal 1/2 binary64)))) (sin.f64 (.f64 #s(approx (+ x (+ x eps)) (.f64 x (+.f64 #s(literal 2 binary64) (/.f64 eps x)))) #s(literal 1/2 binary64)))) #s(literal -2 binary64))
	99.2%	(.f64 (.f64 #s(approx (sin (* (+ eps 0) 1/2)) (.f64 eps (fma.f64 eps (.f64 eps #s(literal -1/48 binary64)) #s(literal 1/2 binary64)))) (sin.f64 #s(approx (* (+ x (+ x eps)) 1/2) (fma.f64 #s(literal 1/2 binary64) eps x)))) #s(literal -2 binary64))
	99.1%	(.f64 (.f64 #s(approx (sin (* (+ eps 0) 1/2)) (.f64 eps (fma.f64 eps (.f64 eps #s(literal -1/48 binary64)) #s(literal 1/2 binary64)))) (sin.f64 #s(approx (* (+ x (+ x eps)) 1/2) (*.f64 eps (+.f64 #s(literal 1/2 binary64) (/.f64 x eps)))))) #s(literal -2 binary64))
	98.7%	(.f64 (.f64 #s(approx (sin (* (+ eps 0) 1/2)) (.f64 eps #s(literal 1/2 binary64))) (sin.f64 (.f64 (+.f64 x (+.f64 x eps)) #s(literal 1/2 binary64)))) #s(literal -2 binary64))
	99.3%	(.f64 (.f64 #s(approx (sin (* (* (* eps eps) (/ 1 eps)) 1/2)) (.f64 eps (fma.f64 eps (.f64 eps (fma.f64 (.f64 eps eps) #s(literal 1/3840 binary64) #s(literal -1/48 binary64))) #s(literal 1/2 binary64)))) (sin.f64 #s(approx ( (+ x (+ x eps)) 1/2) (fma.f64 eps #s(literal 1/2 binary64) x)))) #s(literal -2 binary64))
	98.7%	(.f64 (.f64 #s(approx (sin (* (* (* eps eps) (/ 1 eps)) 1/2)) (.f64 #s(literal 1/2 binary64) eps)) (sin.f64 #s(approx ( (+ x (+ x eps)) 1/2) (fma.f64 eps #s(literal 1/2 binary64) x)))) #s(literal -2 binary64))
	98.1%	(.f64 #s(approx (/ 1 (+ (cos (+ x eps)) (cos x))) (/.f64 #s(literal 1/2 binary64) (cos.f64 x))) #s(approx (- (+ ( 1/2 (cos (* (+ x eps) 2))) 1/2) (+ (* 1/2 (cos (+ x x))) 1/2)) (.f64 eps (fma.f64 (neg.f64 eps) (cos.f64 (.f64 x #s(literal 2 binary64))) (sin.f64 (*.f64 x #s(literal -2 binary64)))))))
✓	99.8%	(.f64 #s(approx ( (sin (* (+ eps 0) 1/2)) (sin (* (+ x (+ x eps)) 1/2))) (+.f64 (.f64 (.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (cos.f64 x)) (sin.f64 (.f64 eps #s(literal 1/2 binary64)))) (.f64 (.f64 (cos.f64 (.f64 eps #s(literal 1/2 binary64))) (sin.f64 x)) (sin.f64 (.f64 eps #s(literal 1/2 binary64)))))) #s(literal -2 binary64))
	99.5%	(.f64 #s(approx ( (sin (* (+ eps 0) 1/2)) (sin (* (+ x (+ x eps)) 1/2))) (+.f64 #s(approx (* (* (sin (* eps 1/2)) (cos x)) (sin (* eps 1/2))) (.f64 eps (.f64 eps (.f64 (cos.f64 x) (fma.f64 eps (.f64 eps #s(literal -1/48 binary64)) #s(literal 1/4 binary64)))))) (.f64 (.f64 (cos.f64 (.f64 eps #s(literal 1/2 binary64))) (sin.f64 x)) (sin.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 eps)) 1/2))) (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (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))
	47.5%	(exp.f64 (log.f64 (-.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x))))
	98.7%	#s(approx (/ 1 (/ 1 (- (cos (+ x eps)) (cos x)))) (.f64 eps (-.f64 (.f64 #s(literal -1/2 binary64) (*.f64 eps (cos.f64 x))) (sin.f64 x))))
	76.1%	#s(approx (/ 1 (/ 1 (- (cos (+ x eps)) (cos x)))) (neg.f64 (*.f64 eps (sin.f64 x))))
	47.1%	#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)))
✓	46.9%	#s(approx (- (cos (+ x eps)) (cos x)) (+.f64 #s(approx (cos eps) #s(literal 1 binary64)) #s(literal -1 binary64)))
	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)))))
	99.1%	#s(approx (- (cos (+ x eps)) (cos 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))))))
	4.5%	#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (+ (cos eps) -1) (/.f64 (.f64 (.f64 eps (.f64 eps eps)) (.f64 eps #s(literal -1/2 binary64))) (*.f64 eps eps))))
	48.4%	#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (+ (cos eps) -1) (/.f64 (.f64 (.f64 eps eps) (*.f64 eps #s(literal -1/2 binary64))) eps)))
✓	48.7%	#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (+ (cos eps) -1) (.f64 eps (.f64 eps #s(literal -1/2 binary64)))))

Compiler

Compiled 2 501 to 917 computations (63.3% saved)

regimes55.0ms (0.3%)

Memory

31.7MiB live, 68.3MiB allocated

Counts

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

Outputs

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

Calls

3 calls:

20.0ms	eps
18.0ms	x
14.0ms	(-.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)

regimes57.0ms (0.3%)

Memory

-17.6MiB live, 54.9MiB allocated

Counts

70 → 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 (+ (cos eps) -1) (.f64 eps (.f64 eps #s(literal -1/2 binary64)))))
#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 (+ (cos eps) -1) (/.f64 (.f64 (.f64 eps eps) (*.f64 eps #s(literal -1/2 binary64))) eps)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (+ (cos eps) -1) (/.f64 (.f64 (.f64 eps (.f64 eps eps)) (.f64 eps #s(literal -1/2 binary64))) (*.f64 eps eps))))
#s(approx (- (cos (+ x eps)) (cos x)) (+.f64 (cos.f64 eps) #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 (/ 1 (/ 1 (- (cos (+ x eps)) (cos x)))) (neg.f64 (*.f64 eps (sin.f64 x))))
(-.f64 #s(approx (cos (+ x eps)) (cos.f64 x)) #s(approx (cos x) (fma.f64 x (*.f64 x #s(literal -1/2 binary64)) #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 #s(approx ( (sin (* (+ eps 0) 1/2)) (sin (* (+ x (+ x eps)) 1/2))) (.f64 #s(approx (sin ( 1/2 eps)) (*.f64 eps #s(literal 1/2 binary64))) (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x)))) #s(literal -2 binary64))
(.f64 (.f64 #s(approx (sin (* (* (* eps eps) (/ 1 eps)) 1/2)) (.f64 #s(literal 1/2 binary64) eps)) (sin.f64 #s(approx ( (+ x (+ x eps)) 1/2) (fma.f64 eps #s(literal 1/2 binary64) x)))) #s(literal -2 binary64))
(.f64 (.f64 #s(approx (sin (* (+ eps 0) 1/2)) (.f64 #s(literal 1/2 binary64) eps)) (sin.f64 (.f64 (+.f64 x (+.f64 x eps)) #s(literal 1/2 binary64)))) #s(literal -2 binary64))
(.f64 (.f64 #s(approx (sin (* (+ eps 0) 1/2)) (.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(approx ( (sin (* (+ eps 0) 1/2)) (sin (* (+ x (+ x eps)) 1/2))) (.f64 #s(approx (sin ( 1/2 eps)) (.f64 eps (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal 1/2 binary64)))) (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x)))) #s(literal -2 binary64))
(.f64 (.f64 #s(approx (sin (* (+ eps 0) 1/2)) (.f64 eps (fma.f64 eps (.f64 eps #s(literal -1/48 binary64)) #s(literal 1/2 binary64)))) (sin.f64 #s(approx (* (+ x (+ x eps)) 1/2) (fma.f64 #s(literal 1/2 binary64) eps x)))) #s(literal -2 binary64))
(.f64 (.f64 #s(approx (sin (* (+ eps 0) 1/2)) (.f64 eps (fma.f64 eps (.f64 eps #s(literal -1/48 binary64)) #s(literal 1/2 binary64)))) (sin.f64 (*.f64 (+.f64 x (+.f64 x 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 #s(approx (sin ( 1/2 eps)) (.f64 eps (fma.f64 (.f64 eps eps) (fma.f64 eps (*.f64 eps #s(literal 1/3840 binary64)) #s(literal -1/48 binary64)) #s(literal 1/2 binary64)))) (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x)))) #s(literal -2 binary64))
(.f64 (.f64 #s(approx (sin (* (* (* eps eps) (/ 1 eps)) 1/2)) (.f64 eps (fma.f64 eps (.f64 eps (fma.f64 (.f64 eps eps) #s(literal 1/3840 binary64) #s(literal -1/48 binary64))) #s(literal 1/2 binary64)))) (sin.f64 #s(approx ( (+ x (+ x eps)) 1/2) (fma.f64 eps #s(literal 1/2 binary64) x)))) #s(literal -2 binary64))
(.f64 (.f64 #s(approx (sin (* (+ eps 0) 1/2)) (.f64 eps (fma.f64 eps (.f64 eps #s(literal -1/48 binary64)) #s(literal 1/2 binary64)))) (sin.f64 #s(approx (* (+ x (+ x eps)) 1/2) (*.f64 eps (+.f64 #s(literal 1/2 binary64) (/.f64 x eps)))))) #s(literal -2 binary64))
(.f64 (.f64 #s(approx (sin (* (+ eps 0) 1/2)) (.f64 eps (fma.f64 eps (.f64 eps (fma.f64 (.f64 eps eps) #s(literal 1/3840 binary64) #s(literal -1/48 binary64))) #s(literal 1/2 binary64)))) (sin.f64 (.f64 (+.f64 x (+.f64 x eps)) #s(literal 1/2 binary64)))) #s(literal -2 binary64))
(.f64 (.f64 #s(approx (sin (* (+ eps 0) 1/2)) (.f64 eps (fma.f64 eps (.f64 eps #s(literal -1/48 binary64)) #s(literal 1/2 binary64)))) (sin.f64 (.f64 #s(approx (+ x (+ x eps)) (.f64 x (+.f64 #s(literal 2 binary64) (/.f64 eps x)))) #s(literal 1/2 binary64)))) #s(literal -2 binary64))
(.f64 (.f64 #s(approx (sin (* (+ eps 0) 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)))) (sin.f64 #s(approx (* (+ x (+ x eps)) 1/2) (fma.f64 eps #s(literal 1/2 binary64) x)))) #s(literal -2 binary64))
(.f64 (.f64 #s(approx (sin (* (+ eps 0) 1/2)) (.f64 eps (fma.f64 (.f64 eps eps) (fma.f64 (.f64 eps eps) (fma.f64 (.f64 eps eps) #s(literal -1/645120 binary64) #s(literal 1/3840 binary64)) #s(literal -1/48 binary64)) #s(literal 1/2 binary64)))) (sin.f64 (*.f64 (+.f64 x (+.f64 x eps)) #s(literal 1/2 binary64)))) #s(literal -2 binary64))
(.f64 (.f64 #s(approx (sin (* (+ eps 0) 1/2)) (.f64 eps (fma.f64 eps (.f64 eps #s(literal -1/48 binary64)) #s(literal 1/2 binary64)))) (sin.f64 (.f64 (/.f64 (-.f64 (.f64 (+.f64 x x) (+.f64 x x)) (*.f64 eps eps)) (-.f64 (+.f64 x x) eps)) #s(literal 1/2 binary64)))) #s(literal -2 binary64))
(.f64 (.f64 #s(approx (sin (* (+ eps 0) 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)))) (sin.f64 #s(approx (* (+ x (+ x eps)) 1/2) (*.f64 eps (+.f64 #s(literal 1/2 binary64) (/.f64 x eps)))))) #s(literal -2 binary64))
(.f64 (.f64 #s(approx (sin (* (+ eps 0) 1/2)) (.f64 eps (fma.f64 eps (.f64 eps #s(literal -1/48 binary64)) #s(literal 1/2 binary64)))) (sin.f64 (.f64 (.f64 (*.f64 (+.f64 eps (+.f64 x x)) (-.f64 x (+.f64 eps x))) (/.f64 #s(literal 1 binary64) (-.f64 x (+.f64 eps x)))) #s(literal 1/2 binary64)))) #s(literal -2 binary64))
(.f64 (.f64 #s(approx (sin (* (+ eps 0) 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)))) (sin.f64 (.f64 #s(approx (+ x (+ x eps)) (.f64 x (+.f64 #s(literal 2 binary64) (/.f64 eps x)))) #s(literal 1/2 binary64)))) #s(literal -2 binary64))
(.f64 (.f64 #s(approx (sin (* (+ eps 0) 1/2)) (.f64 eps (fma.f64 eps (.f64 eps #s(literal -1/48 binary64)) #s(literal 1/2 binary64)))) (sin.f64 (.f64 (/.f64 #s(literal 1 binary64) (/.f64 (-.f64 x (+.f64 eps x)) (.f64 (+.f64 eps (+.f64 x x)) (-.f64 x (+.f64 eps x))))) #s(literal 1/2 binary64)))) #s(literal -2 binary64))
(.f64 (.f64 #s(approx (sin (* (+ eps 0) 1/2)) (.f64 eps (fma.f64 eps (.f64 eps #s(literal -1/48 binary64)) #s(literal 1/2 binary64)))) (sin.f64 (.f64 (/.f64 (fma.f64 (+.f64 eps x) (.f64 (+.f64 eps x) (+.f64 eps x)) (.f64 x (.f64 x x))) (fma.f64 (+.f64 eps x) (+.f64 eps x) (-.f64 (.f64 x x) (.f64 x (+.f64 eps x))))) #s(literal 1/2 binary64)))) #s(literal -2 binary64))
(-.f64 #s(approx (cos (+ x eps)) (cos.f64 eps)) (cos.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 (/ 1 (/ 1 (- (cos (+ x eps)) (cos x)))) (.f64 eps (-.f64 (.f64 #s(literal -1/2 binary64) (*.f64 eps (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 (.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 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 eps)) (cos 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))))))
(.f64 (.f64 (sin.f64 (.f64 (+.f64 eps #s(literal 0 binary64)) #s(literal 1/2 binary64))) (sin.f64 #s(approx ( (+ x (+ x eps)) 1/2) (*.f64 eps (+.f64 #s(literal 1/2 binary64) (/.f64 x eps)))))) #s(literal -2 binary64))
(.f64 (/.f64 #s(literal 1 binary64) (+.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))) #s(approx (- (+ ( 1/2 (cos (* (+ x eps) 2))) 1/2) (+ (* 1/2 (cos (+ x x))) 1/2)) #s(approx (* eps (+ (* (neg eps) (cos (* x 2))) (sin (* x -2)))) (fma.f64 eps (neg.f64 eps) (.f64 eps (.f64 x #s(literal -2 binary64)))))))
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) #s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps (-.f64 (.f64 #s(literal -1/2 binary64) (*.f64 eps (cos.f64 x))) (sin.f64 x))))))
(.f64 (.f64 (sin.f64 (.f64 (.f64 (.f64 eps eps) (/.f64 #s(literal 1 binary64) eps)) #s(literal 1/2 binary64))) (sin.f64 #s(approx ( (+ x (+ x eps)) 1/2) (fma.f64 eps #s(literal 1/2 binary64) x)))) #s(literal -2 binary64))
(.f64 (.f64 (sin.f64 (.f64 (+.f64 eps #s(literal 0 binary64)) #s(literal 1/2 binary64))) (sin.f64 (.f64 #s(approx (+ x (+ x eps)) (*.f64 x (+.f64 (/.f64 eps x) #s(literal 2 binary64)))) #s(literal 1/2 binary64)))) #s(literal -2 binary64))
(.f64 (.f64 (sin.f64 (.f64 (/.f64 (.f64 eps eps) eps) #s(literal 1/2 binary64))) (sin.f64 (*.f64 (+.f64 x (+.f64 x 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))) (sin.f64 (.f64 (+.f64 x #s(approx (+ x eps) (fma.f64 eps (/.f64 x eps) 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))) (sin.f64 (.f64 (+.f64 x (+.f64 x eps)) #s(literal 1/2 binary64)))) #s(literal -2 binary64))
(.f64 (.f64 (sin.f64 (.f64 (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) eps)) #s(literal 1/2 binary64))) (sin.f64 (.f64 (+.f64 x (+.f64 x eps)) #s(literal 1/2 binary64)))) #s(literal -2 binary64))
(.f64 (.f64 (sin.f64 (.f64 (/.f64 #s(literal 1 binary64) (/.f64 eps (.f64 eps eps))) #s(literal 1/2 binary64))) (sin.f64 (*.f64 (+.f64 x (+.f64 x eps)) #s(literal 1/2 binary64)))) #s(literal -2 binary64))
(.f64 (/.f64 #s(literal 1 binary64) (+.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))) #s(approx (- (+ ( 1/2 (cos (* (+ x eps) 2))) 1/2) (+ (* 1/2 (cos (+ x x))) 1/2)) #s(approx (* eps (+ (* (neg eps) (cos (* x 2))) (sin (* x -2)))) (fma.f64 x (fma.f64 x (.f64 eps (.f64 eps #s(literal 2 binary64))) (.f64 eps #s(literal -2 binary64))) (.f64 eps (neg.f64 eps))))))
(.f64 (.f64 (sin.f64 (.f64 (.f64 (.f64 eps (.f64 eps eps)) (/.f64 #s(literal 1 binary64) (.f64 eps eps))) #s(literal 1/2 binary64))) (sin.f64 (.f64 (+.f64 x (+.f64 x 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))) (sin.f64 (.f64 (+.f64 x (-.f64 (/.f64 (.f64 x x) (-.f64 x eps)) (/.f64 (.f64 eps eps) (-.f64 x 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))) (sin.f64 (.f64 (+.f64 x (.f64 (fma.f64 x (.f64 x x) (.f64 eps (.f64 eps eps))) (/.f64 #s(literal 1 binary64) (fma.f64 eps (-.f64 eps x) (*.f64 x x))))) #s(literal 1/2 binary64)))) #s(literal -2 binary64))
(.f64 (.f64 (sin.f64 (.f64 (/.f64 (fma.f64 (.f64 (fma.f64 x x #s(literal 0 binary64)) #s(literal 0 binary64)) eps (.f64 (fma.f64 x x #s(literal 0 binary64)) (.f64 eps eps))) (.f64 (fma.f64 x x #s(literal 0 binary64)) eps)) #s(literal 1/2 binary64))) (sin.f64 (.f64 (+.f64 x (+.f64 x eps)) #s(literal 1/2 binary64)))) #s(literal -2 binary64))
(.f64 (.f64 (sin.f64 (.f64 (/.f64 (.f64 (fma.f64 x x (.f64 (+.f64 x eps) eps)) eps) (fma.f64 (+.f64 x eps) (+.f64 x eps) (-.f64 (.f64 x x) (.f64 x (+.f64 x 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(approx (/ 1 (+ (cos (+ x eps)) (cos x))) (/.f64 #s(literal 1/2 binary64) (cos.f64 x))) #s(approx (- (+ ( 1/2 (cos (* (+ x eps) 2))) 1/2) (+ (* 1/2 (cos (+ x x))) 1/2)) (.f64 eps (fma.f64 (neg.f64 eps) (cos.f64 (.f64 x #s(literal 2 binary64))) (sin.f64 (*.f64 x #s(literal -2 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 (.f64 (sin.f64 (.f64 (.f64 (.f64 eps eps) (/.f64 #s(literal 1 binary64) eps)) #s(literal 1/2 binary64))) #s(approx (sin ( (+ x (+ x eps)) 1/2)) (fma.f64 eps (*.f64 (cos.f64 x) #s(literal 1/2 binary64)) (sin.f64 x)))) #s(literal -2 binary64))
(exp.f64 (log.f64 (-.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x))))
(/.f64 #s(literal 1 binary64) (exp.f64 (*.f64 (log.f64 (-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))) #s(literal -1 binary64))))
(.f64 (/.f64 #s(literal 1 binary64) (+.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))) #s(approx (- (+ ( 1/2 (cos (* (+ x eps) 2))) 1/2) (+ (* 1/2 (cos (+ x x))) 1/2)) (.f64 eps (fma.f64 (neg.f64 eps) (cos.f64 (.f64 x #s(literal 2 binary64))) (sin.f64 (*.f64 x #s(literal -2 binary64)))))))
(.f64 (/.f64 #s(literal 1 binary64) (+.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))) (-.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))))
(.f64 #s(approx ( (sin (* (+ eps 0) 1/2)) (sin (* (+ x (+ x eps)) 1/2))) (+.f64 #s(approx (* (* (sin (* eps 1/2)) (cos x)) (sin (* eps 1/2))) (.f64 eps (.f64 eps (.f64 (cos.f64 x) (fma.f64 eps (.f64 eps #s(literal -1/48 binary64)) #s(literal 1/4 binary64)))))) (.f64 (.f64 (cos.f64 (.f64 eps #s(literal 1/2 binary64))) (sin.f64 x)) (sin.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 #s(literal 1 binary64) (+.f64 (cos.f64 (.f64 (.f64 (+.f64 x eps) (-.f64 x eps)) (/.f64 #s(literal 1 binary64) (-.f64 x eps)))) (cos.f64 x))) (-.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))))
(-.f64 (*.f64 (cos.f64 x) (cos.f64 eps)) (fma.f64 (sin.f64 x) (sin.f64 eps) (cos.f64 x)))
(-.f64 (fma.f64 (sin.f64 (neg.f64 x)) (sin.f64 eps) (*.f64 (cos.f64 x) (cos.f64 eps))) (cos.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)) (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))
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (-.f64 (fma.f64 (cos.f64 x) (cos.f64 eps) (*.f64 (neg.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)) (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))

Calls

3 calls:

20.0ms	(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))
18.0ms	x
17.0ms	eps

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

24.0MiB live, 24.0MiB allocated

Counts

68 → 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 (+ (cos eps) -1) (.f64 eps (.f64 eps #s(literal -1/2 binary64)))))
#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 (+ (cos eps) -1) (/.f64 (.f64 (.f64 eps eps) (*.f64 eps #s(literal -1/2 binary64))) eps)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (+ (cos eps) -1) (/.f64 (.f64 (.f64 eps (.f64 eps eps)) (.f64 eps #s(literal -1/2 binary64))) (*.f64 eps eps))))
#s(approx (- (cos (+ x eps)) (cos x)) (+.f64 (cos.f64 eps) #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 (/ 1 (/ 1 (- (cos (+ x eps)) (cos x)))) (neg.f64 (*.f64 eps (sin.f64 x))))
(-.f64 #s(approx (cos (+ x eps)) (cos.f64 x)) #s(approx (cos x) (fma.f64 x (*.f64 x #s(literal -1/2 binary64)) #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 #s(approx ( (sin (* (+ eps 0) 1/2)) (sin (* (+ x (+ x eps)) 1/2))) (.f64 #s(approx (sin ( 1/2 eps)) (*.f64 eps #s(literal 1/2 binary64))) (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x)))) #s(literal -2 binary64))
(.f64 (.f64 #s(approx (sin (* (* (* eps eps) (/ 1 eps)) 1/2)) (.f64 #s(literal 1/2 binary64) eps)) (sin.f64 #s(approx ( (+ x (+ x eps)) 1/2) (fma.f64 eps #s(literal 1/2 binary64) x)))) #s(literal -2 binary64))
(.f64 (.f64 #s(approx (sin (* (+ eps 0) 1/2)) (.f64 #s(literal 1/2 binary64) eps)) (sin.f64 (.f64 (+.f64 x (+.f64 x eps)) #s(literal 1/2 binary64)))) #s(literal -2 binary64))
(.f64 (.f64 #s(approx (sin (* (+ eps 0) 1/2)) (.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(approx ( (sin (* (+ eps 0) 1/2)) (sin (* (+ x (+ x eps)) 1/2))) (.f64 #s(approx (sin ( 1/2 eps)) (.f64 eps (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal 1/2 binary64)))) (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x)))) #s(literal -2 binary64))
(.f64 (.f64 #s(approx (sin (* (+ eps 0) 1/2)) (.f64 eps (fma.f64 eps (.f64 eps #s(literal -1/48 binary64)) #s(literal 1/2 binary64)))) (sin.f64 #s(approx (* (+ x (+ x eps)) 1/2) (fma.f64 #s(literal 1/2 binary64) eps x)))) #s(literal -2 binary64))
(.f64 (.f64 #s(approx (sin (* (+ eps 0) 1/2)) (.f64 eps (fma.f64 eps (.f64 eps #s(literal -1/48 binary64)) #s(literal 1/2 binary64)))) (sin.f64 (*.f64 (+.f64 x (+.f64 x 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 #s(approx (sin ( 1/2 eps)) (.f64 eps (fma.f64 (.f64 eps eps) (fma.f64 eps (*.f64 eps #s(literal 1/3840 binary64)) #s(literal -1/48 binary64)) #s(literal 1/2 binary64)))) (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x)))) #s(literal -2 binary64))
(.f64 (.f64 #s(approx (sin (* (* (* eps eps) (/ 1 eps)) 1/2)) (.f64 eps (fma.f64 eps (.f64 eps (fma.f64 (.f64 eps eps) #s(literal 1/3840 binary64) #s(literal -1/48 binary64))) #s(literal 1/2 binary64)))) (sin.f64 #s(approx ( (+ x (+ x eps)) 1/2) (fma.f64 eps #s(literal 1/2 binary64) x)))) #s(literal -2 binary64))
(.f64 (.f64 #s(approx (sin (* (+ eps 0) 1/2)) (.f64 eps (fma.f64 eps (.f64 eps #s(literal -1/48 binary64)) #s(literal 1/2 binary64)))) (sin.f64 #s(approx (* (+ x (+ x eps)) 1/2) (*.f64 eps (+.f64 #s(literal 1/2 binary64) (/.f64 x eps)))))) #s(literal -2 binary64))
(.f64 (.f64 #s(approx (sin (* (+ eps 0) 1/2)) (.f64 eps (fma.f64 eps (.f64 eps (fma.f64 (.f64 eps eps) #s(literal 1/3840 binary64) #s(literal -1/48 binary64))) #s(literal 1/2 binary64)))) (sin.f64 (.f64 (+.f64 x (+.f64 x eps)) #s(literal 1/2 binary64)))) #s(literal -2 binary64))
(.f64 (.f64 #s(approx (sin (* (+ eps 0) 1/2)) (.f64 eps (fma.f64 eps (.f64 eps #s(literal -1/48 binary64)) #s(literal 1/2 binary64)))) (sin.f64 (.f64 #s(approx (+ x (+ x eps)) (.f64 x (+.f64 #s(literal 2 binary64) (/.f64 eps x)))) #s(literal 1/2 binary64)))) #s(literal -2 binary64))
(.f64 (.f64 #s(approx (sin (* (+ eps 0) 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)))) (sin.f64 #s(approx (* (+ x (+ x eps)) 1/2) (fma.f64 eps #s(literal 1/2 binary64) x)))) #s(literal -2 binary64))
(.f64 (.f64 #s(approx (sin (* (+ eps 0) 1/2)) (.f64 eps (fma.f64 (.f64 eps eps) (fma.f64 (.f64 eps eps) (fma.f64 (.f64 eps eps) #s(literal -1/645120 binary64) #s(literal 1/3840 binary64)) #s(literal -1/48 binary64)) #s(literal 1/2 binary64)))) (sin.f64 (*.f64 (+.f64 x (+.f64 x eps)) #s(literal 1/2 binary64)))) #s(literal -2 binary64))
(.f64 (.f64 #s(approx (sin (* (+ eps 0) 1/2)) (.f64 eps (fma.f64 eps (.f64 eps #s(literal -1/48 binary64)) #s(literal 1/2 binary64)))) (sin.f64 (.f64 (/.f64 (-.f64 (.f64 (+.f64 x x) (+.f64 x x)) (*.f64 eps eps)) (-.f64 (+.f64 x x) eps)) #s(literal 1/2 binary64)))) #s(literal -2 binary64))
(.f64 (.f64 #s(approx (sin (* (+ eps 0) 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)))) (sin.f64 #s(approx (* (+ x (+ x eps)) 1/2) (*.f64 eps (+.f64 #s(literal 1/2 binary64) (/.f64 x eps)))))) #s(literal -2 binary64))
(.f64 (.f64 #s(approx (sin (* (+ eps 0) 1/2)) (.f64 eps (fma.f64 eps (.f64 eps #s(literal -1/48 binary64)) #s(literal 1/2 binary64)))) (sin.f64 (.f64 (.f64 (*.f64 (+.f64 eps (+.f64 x x)) (-.f64 x (+.f64 eps x))) (/.f64 #s(literal 1 binary64) (-.f64 x (+.f64 eps x)))) #s(literal 1/2 binary64)))) #s(literal -2 binary64))
(.f64 (.f64 #s(approx (sin (* (+ eps 0) 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)))) (sin.f64 (.f64 #s(approx (+ x (+ x eps)) (.f64 x (+.f64 #s(literal 2 binary64) (/.f64 eps x)))) #s(literal 1/2 binary64)))) #s(literal -2 binary64))
(.f64 (.f64 #s(approx (sin (* (+ eps 0) 1/2)) (.f64 eps (fma.f64 eps (.f64 eps #s(literal -1/48 binary64)) #s(literal 1/2 binary64)))) (sin.f64 (.f64 (/.f64 #s(literal 1 binary64) (/.f64 (-.f64 x (+.f64 eps x)) (.f64 (+.f64 eps (+.f64 x x)) (-.f64 x (+.f64 eps x))))) #s(literal 1/2 binary64)))) #s(literal -2 binary64))
(.f64 (.f64 #s(approx (sin (* (+ eps 0) 1/2)) (.f64 eps (fma.f64 eps (.f64 eps #s(literal -1/48 binary64)) #s(literal 1/2 binary64)))) (sin.f64 (.f64 (/.f64 (fma.f64 (+.f64 eps x) (.f64 (+.f64 eps x) (+.f64 eps x)) (.f64 x (.f64 x x))) (fma.f64 (+.f64 eps x) (+.f64 eps x) (-.f64 (.f64 x x) (.f64 x (+.f64 eps x))))) #s(literal 1/2 binary64)))) #s(literal -2 binary64))
(-.f64 #s(approx (cos (+ x eps)) (cos.f64 eps)) (cos.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 (/ 1 (/ 1 (- (cos (+ x eps)) (cos x)))) (.f64 eps (-.f64 (.f64 #s(literal -1/2 binary64) (*.f64 eps (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 (.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 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 eps)) (cos 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))))))
(.f64 (.f64 (sin.f64 (.f64 (+.f64 eps #s(literal 0 binary64)) #s(literal 1/2 binary64))) (sin.f64 #s(approx ( (+ x (+ x eps)) 1/2) (*.f64 eps (+.f64 #s(literal 1/2 binary64) (/.f64 x eps)))))) #s(literal -2 binary64))
(.f64 (/.f64 #s(literal 1 binary64) (+.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))) #s(approx (- (+ ( 1/2 (cos (* (+ x eps) 2))) 1/2) (+ (* 1/2 (cos (+ x x))) 1/2)) #s(approx (* eps (+ (* (neg eps) (cos (* x 2))) (sin (* x -2)))) (fma.f64 eps (neg.f64 eps) (.f64 eps (.f64 x #s(literal -2 binary64)))))))
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) #s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps (-.f64 (.f64 #s(literal -1/2 binary64) (*.f64 eps (cos.f64 x))) (sin.f64 x))))))
(.f64 (.f64 (sin.f64 (.f64 (.f64 (.f64 eps eps) (/.f64 #s(literal 1 binary64) eps)) #s(literal 1/2 binary64))) (sin.f64 #s(approx ( (+ x (+ x eps)) 1/2) (fma.f64 eps #s(literal 1/2 binary64) x)))) #s(literal -2 binary64))
(.f64 (.f64 (sin.f64 (.f64 (+.f64 eps #s(literal 0 binary64)) #s(literal 1/2 binary64))) (sin.f64 (.f64 #s(approx (+ x (+ x eps)) (*.f64 x (+.f64 (/.f64 eps x) #s(literal 2 binary64)))) #s(literal 1/2 binary64)))) #s(literal -2 binary64))
(.f64 (.f64 (sin.f64 (.f64 (/.f64 (.f64 eps eps) eps) #s(literal 1/2 binary64))) (sin.f64 (*.f64 (+.f64 x (+.f64 x 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))) (sin.f64 (.f64 (+.f64 x #s(approx (+ x eps) (fma.f64 eps (/.f64 x eps) 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))) (sin.f64 (.f64 (+.f64 x (+.f64 x eps)) #s(literal 1/2 binary64)))) #s(literal -2 binary64))
(.f64 (.f64 (sin.f64 (.f64 (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) eps)) #s(literal 1/2 binary64))) (sin.f64 (.f64 (+.f64 x (+.f64 x eps)) #s(literal 1/2 binary64)))) #s(literal -2 binary64))
(.f64 (.f64 (sin.f64 (.f64 (/.f64 #s(literal 1 binary64) (/.f64 eps (.f64 eps eps))) #s(literal 1/2 binary64))) (sin.f64 (*.f64 (+.f64 x (+.f64 x eps)) #s(literal 1/2 binary64)))) #s(literal -2 binary64))
(.f64 (/.f64 #s(literal 1 binary64) (+.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))) #s(approx (- (+ ( 1/2 (cos (* (+ x eps) 2))) 1/2) (+ (* 1/2 (cos (+ x x))) 1/2)) #s(approx (* eps (+ (* (neg eps) (cos (* x 2))) (sin (* x -2)))) (fma.f64 x (fma.f64 x (.f64 eps (.f64 eps #s(literal 2 binary64))) (.f64 eps #s(literal -2 binary64))) (.f64 eps (neg.f64 eps))))))
(.f64 (.f64 (sin.f64 (.f64 (.f64 (.f64 eps (.f64 eps eps)) (/.f64 #s(literal 1 binary64) (.f64 eps eps))) #s(literal 1/2 binary64))) (sin.f64 (.f64 (+.f64 x (+.f64 x 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))) (sin.f64 (.f64 (+.f64 x (-.f64 (/.f64 (.f64 x x) (-.f64 x eps)) (/.f64 (.f64 eps eps) (-.f64 x 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))) (sin.f64 (.f64 (+.f64 x (.f64 (fma.f64 x (.f64 x x) (.f64 eps (.f64 eps eps))) (/.f64 #s(literal 1 binary64) (fma.f64 eps (-.f64 eps x) (*.f64 x x))))) #s(literal 1/2 binary64)))) #s(literal -2 binary64))
(.f64 (.f64 (sin.f64 (.f64 (/.f64 (fma.f64 (.f64 (fma.f64 x x #s(literal 0 binary64)) #s(literal 0 binary64)) eps (.f64 (fma.f64 x x #s(literal 0 binary64)) (.f64 eps eps))) (.f64 (fma.f64 x x #s(literal 0 binary64)) eps)) #s(literal 1/2 binary64))) (sin.f64 (.f64 (+.f64 x (+.f64 x eps)) #s(literal 1/2 binary64)))) #s(literal -2 binary64))
(.f64 (.f64 (sin.f64 (.f64 (/.f64 (.f64 (fma.f64 x x (.f64 (+.f64 x eps) eps)) eps) (fma.f64 (+.f64 x eps) (+.f64 x eps) (-.f64 (.f64 x x) (.f64 x (+.f64 x 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(approx (/ 1 (+ (cos (+ x eps)) (cos x))) (/.f64 #s(literal 1/2 binary64) (cos.f64 x))) #s(approx (- (+ ( 1/2 (cos (* (+ x eps) 2))) 1/2) (+ (* 1/2 (cos (+ x x))) 1/2)) (.f64 eps (fma.f64 (neg.f64 eps) (cos.f64 (.f64 x #s(literal 2 binary64))) (sin.f64 (*.f64 x #s(literal -2 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 (.f64 (sin.f64 (.f64 (.f64 (.f64 eps eps) (/.f64 #s(literal 1 binary64) eps)) #s(literal 1/2 binary64))) #s(approx (sin ( (+ x (+ x eps)) 1/2)) (fma.f64 eps (*.f64 (cos.f64 x) #s(literal 1/2 binary64)) (sin.f64 x)))) #s(literal -2 binary64))
(exp.f64 (log.f64 (-.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x))))
(/.f64 #s(literal 1 binary64) (exp.f64 (*.f64 (log.f64 (-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))) #s(literal -1 binary64))))
(.f64 (/.f64 #s(literal 1 binary64) (+.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))) #s(approx (- (+ ( 1/2 (cos (* (+ x eps) 2))) 1/2) (+ (* 1/2 (cos (+ x x))) 1/2)) (.f64 eps (fma.f64 (neg.f64 eps) (cos.f64 (.f64 x #s(literal 2 binary64))) (sin.f64 (*.f64 x #s(literal -2 binary64)))))))
(.f64 (/.f64 #s(literal 1 binary64) (+.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))) (-.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))))
(.f64 #s(approx ( (sin (* (+ eps 0) 1/2)) (sin (* (+ x (+ x eps)) 1/2))) (+.f64 #s(approx (* (* (sin (* eps 1/2)) (cos x)) (sin (* eps 1/2))) (.f64 eps (.f64 eps (.f64 (cos.f64 x) (fma.f64 eps (.f64 eps #s(literal -1/48 binary64)) #s(literal 1/4 binary64)))))) (.f64 (.f64 (cos.f64 (.f64 eps #s(literal 1/2 binary64))) (sin.f64 x)) (sin.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 #s(literal 1 binary64) (+.f64 (cos.f64 (.f64 (.f64 (+.f64 x eps) (-.f64 x eps)) (/.f64 #s(literal 1 binary64) (-.f64 x eps)))) (cos.f64 x))) (-.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))))
(-.f64 (*.f64 (cos.f64 x) (cos.f64 eps)) (fma.f64 (sin.f64 x) (sin.f64 eps) (cos.f64 x)))
(-.f64 (fma.f64 (sin.f64 (neg.f64 x)) (sin.f64 eps) (*.f64 (cos.f64 x) (cos.f64 eps))) (cos.f64 x))

Outputs

(*.f64 #s(approx (* (sin (* (+ eps 0) 1/2)) (sin (* (+ x (+ x eps)) 1/2))) (+.f64 #s(approx (* (* (sin (* eps 1/2)) (cos x)) (sin (* eps 1/2))) (*.f64 eps (*.f64 eps (*.f64 (cos.f64 x) (fma.f64 eps (*.f64 eps #s(literal -1/48 binary64)) #s(literal 1/4 binary64)))))) (*.f64 (*.f64 (cos.f64 (*.f64 eps #s(literal 1/2 binary64))) (sin.f64 x)) (sin.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
99.5%	1	`x`
99.5%	1	`eps`
99.5%	1	`(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))`

Compiler

Compiled 15 to 10 computations (33.3% saved)

regimes47.0ms (0.3%)

Memory

-3.1MiB live, 46.2MiB allocated

Counts

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

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:

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

Results

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

Compiler

Compiled 15 to 10 computations (33.3% saved)

regimes28.0ms (0.2%)

Memory

-4.4MiB live, 33.3MiB 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 (+ (cos eps) -1) (.f64 eps (.f64 eps #s(literal -1/2 binary64)))))
#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 (+ (cos eps) -1) (/.f64 (.f64 (.f64 eps eps) (*.f64 eps #s(literal -1/2 binary64))) eps)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (+ (cos eps) -1) (/.f64 (.f64 (.f64 eps (.f64 eps eps)) (.f64 eps #s(literal -1/2 binary64))) (*.f64 eps eps))))
#s(approx (- (cos (+ x eps)) (cos x)) (+.f64 (cos.f64 eps) #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 (/ 1 (/ 1 (- (cos (+ x eps)) (cos x)))) (neg.f64 (*.f64 eps (sin.f64 x))))
(-.f64 #s(approx (cos (+ x eps)) (cos.f64 x)) #s(approx (cos x) (fma.f64 x (*.f64 x #s(literal -1/2 binary64)) #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 #s(approx ( (sin (* (+ eps 0) 1/2)) (sin (* (+ x (+ x eps)) 1/2))) (.f64 #s(approx (sin ( 1/2 eps)) (*.f64 eps #s(literal 1/2 binary64))) (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x)))) #s(literal -2 binary64))
(.f64 (.f64 #s(approx (sin (* (* (* eps eps) (/ 1 eps)) 1/2)) (.f64 #s(literal 1/2 binary64) eps)) (sin.f64 #s(approx ( (+ x (+ x eps)) 1/2) (fma.f64 eps #s(literal 1/2 binary64) x)))) #s(literal -2 binary64))
(.f64 (.f64 #s(approx (sin (* (+ eps 0) 1/2)) (.f64 #s(literal 1/2 binary64) eps)) (sin.f64 (.f64 (+.f64 x (+.f64 x eps)) #s(literal 1/2 binary64)))) #s(literal -2 binary64))
(.f64 (.f64 #s(approx (sin (* (+ eps 0) 1/2)) (.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(approx ( (sin (* (+ eps 0) 1/2)) (sin (* (+ x (+ x eps)) 1/2))) (.f64 #s(approx (sin ( 1/2 eps)) (.f64 eps (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal 1/2 binary64)))) (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x)))) #s(literal -2 binary64))
(.f64 (.f64 #s(approx (sin (* (+ eps 0) 1/2)) (.f64 eps (fma.f64 eps (.f64 eps #s(literal -1/48 binary64)) #s(literal 1/2 binary64)))) (sin.f64 #s(approx (* (+ x (+ x eps)) 1/2) (fma.f64 #s(literal 1/2 binary64) eps x)))) #s(literal -2 binary64))
(.f64 (.f64 #s(approx (sin (* (+ eps 0) 1/2)) (.f64 eps (fma.f64 eps (.f64 eps #s(literal -1/48 binary64)) #s(literal 1/2 binary64)))) (sin.f64 (*.f64 (+.f64 x (+.f64 x 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 #s(approx (sin ( 1/2 eps)) (.f64 eps (fma.f64 (.f64 eps eps) (fma.f64 eps (*.f64 eps #s(literal 1/3840 binary64)) #s(literal -1/48 binary64)) #s(literal 1/2 binary64)))) (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x)))) #s(literal -2 binary64))
(.f64 (.f64 #s(approx (sin (* (* (* eps eps) (/ 1 eps)) 1/2)) (.f64 eps (fma.f64 eps (.f64 eps (fma.f64 (.f64 eps eps) #s(literal 1/3840 binary64) #s(literal -1/48 binary64))) #s(literal 1/2 binary64)))) (sin.f64 #s(approx ( (+ x (+ x eps)) 1/2) (fma.f64 eps #s(literal 1/2 binary64) x)))) #s(literal -2 binary64))
(.f64 (.f64 #s(approx (sin (* (+ eps 0) 1/2)) (.f64 eps (fma.f64 eps (.f64 eps #s(literal -1/48 binary64)) #s(literal 1/2 binary64)))) (sin.f64 #s(approx (* (+ x (+ x eps)) 1/2) (*.f64 eps (+.f64 #s(literal 1/2 binary64) (/.f64 x eps)))))) #s(literal -2 binary64))
(.f64 (.f64 #s(approx (sin (* (+ eps 0) 1/2)) (.f64 eps (fma.f64 eps (.f64 eps (fma.f64 (.f64 eps eps) #s(literal 1/3840 binary64) #s(literal -1/48 binary64))) #s(literal 1/2 binary64)))) (sin.f64 (.f64 (+.f64 x (+.f64 x eps)) #s(literal 1/2 binary64)))) #s(literal -2 binary64))
(.f64 (.f64 #s(approx (sin (* (+ eps 0) 1/2)) (.f64 eps (fma.f64 eps (.f64 eps #s(literal -1/48 binary64)) #s(literal 1/2 binary64)))) (sin.f64 (.f64 #s(approx (+ x (+ x eps)) (.f64 x (+.f64 #s(literal 2 binary64) (/.f64 eps x)))) #s(literal 1/2 binary64)))) #s(literal -2 binary64))
(.f64 (.f64 #s(approx (sin (* (+ eps 0) 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)))) (sin.f64 #s(approx (* (+ x (+ x eps)) 1/2) (fma.f64 eps #s(literal 1/2 binary64) x)))) #s(literal -2 binary64))
(.f64 (.f64 #s(approx (sin (* (+ eps 0) 1/2)) (.f64 eps (fma.f64 (.f64 eps eps) (fma.f64 (.f64 eps eps) (fma.f64 (.f64 eps eps) #s(literal -1/645120 binary64) #s(literal 1/3840 binary64)) #s(literal -1/48 binary64)) #s(literal 1/2 binary64)))) (sin.f64 (*.f64 (+.f64 x (+.f64 x eps)) #s(literal 1/2 binary64)))) #s(literal -2 binary64))
(.f64 (.f64 #s(approx (sin (* (+ eps 0) 1/2)) (.f64 eps (fma.f64 eps (.f64 eps #s(literal -1/48 binary64)) #s(literal 1/2 binary64)))) (sin.f64 (.f64 (/.f64 (-.f64 (.f64 (+.f64 x x) (+.f64 x x)) (*.f64 eps eps)) (-.f64 (+.f64 x x) eps)) #s(literal 1/2 binary64)))) #s(literal -2 binary64))
(.f64 (.f64 #s(approx (sin (* (+ eps 0) 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)))) (sin.f64 #s(approx (* (+ x (+ x eps)) 1/2) (*.f64 eps (+.f64 #s(literal 1/2 binary64) (/.f64 x eps)))))) #s(literal -2 binary64))
(.f64 (.f64 #s(approx (sin (* (+ eps 0) 1/2)) (.f64 eps (fma.f64 eps (.f64 eps #s(literal -1/48 binary64)) #s(literal 1/2 binary64)))) (sin.f64 (.f64 (.f64 (*.f64 (+.f64 eps (+.f64 x x)) (-.f64 x (+.f64 eps x))) (/.f64 #s(literal 1 binary64) (-.f64 x (+.f64 eps x)))) #s(literal 1/2 binary64)))) #s(literal -2 binary64))
(.f64 (.f64 #s(approx (sin (* (+ eps 0) 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)))) (sin.f64 (.f64 #s(approx (+ x (+ x eps)) (.f64 x (+.f64 #s(literal 2 binary64) (/.f64 eps x)))) #s(literal 1/2 binary64)))) #s(literal -2 binary64))
(.f64 (.f64 #s(approx (sin (* (+ eps 0) 1/2)) (.f64 eps (fma.f64 eps (.f64 eps #s(literal -1/48 binary64)) #s(literal 1/2 binary64)))) (sin.f64 (.f64 (/.f64 #s(literal 1 binary64) (/.f64 (-.f64 x (+.f64 eps x)) (.f64 (+.f64 eps (+.f64 x x)) (-.f64 x (+.f64 eps x))))) #s(literal 1/2 binary64)))) #s(literal -2 binary64))
(.f64 (.f64 #s(approx (sin (* (+ eps 0) 1/2)) (.f64 eps (fma.f64 eps (.f64 eps #s(literal -1/48 binary64)) #s(literal 1/2 binary64)))) (sin.f64 (.f64 (/.f64 (fma.f64 (+.f64 eps x) (.f64 (+.f64 eps x) (+.f64 eps x)) (.f64 x (.f64 x x))) (fma.f64 (+.f64 eps x) (+.f64 eps x) (-.f64 (.f64 x x) (.f64 x (+.f64 eps x))))) #s(literal 1/2 binary64)))) #s(literal -2 binary64))
(-.f64 #s(approx (cos (+ x eps)) (cos.f64 eps)) (cos.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 (/ 1 (/ 1 (- (cos (+ x eps)) (cos x)))) (.f64 eps (-.f64 (.f64 #s(literal -1/2 binary64) (*.f64 eps (cos.f64 x))) (sin.f64 x))))

Outputs

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

Calls

3 calls:

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

Results

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

Compiler

Compiled 15 to 10 computations (33.3% saved)

regimes23.0ms (0.1%)

Memory

-10.6MiB live, 25.2MiB allocated

Counts

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

Outputs

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

Calls

3 calls:

10.0ms	eps
6.0ms	x
5.0ms	(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))

Results

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

Compiler

Compiled 15 to 10 computations (33.3% saved)

regimes15.0ms (0.1%)

Memory

17.8MiB live, 17.8MiB allocated

Counts

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

Outputs

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

Calls

3 calls:

5.0ms	eps
5.0ms	x
4.0ms	(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))

Results

Accuracy	Segments	Branch
99.2%	1	`x`
99.2%	1	`eps`
99.2%	1	`(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))`

Compiler

Compiled 15 to 10 computations (33.3% saved)

regimes17.0ms (0.1%)

Memory

-19.9MiB live, 16.4MiB allocated

Counts

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

Outputs

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

Calls

3 calls:

8.0ms	eps
5.0ms	x
3.0ms	(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))

Results

Accuracy	Segments	Branch
98.7%	1	`x`
98.7%	1	`eps`
98.7%	1	`(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))`

Compiler

Compiled 15 to 10 computations (33.3% saved)

regimes10.0ms (0.1%)

Memory

17.9MiB live, 17.9MiB allocated

Counts

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

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

Calls

3 calls:

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

Results

Accuracy	Segments	Branch
76.1%	1	`x`
76.1%	1	`eps`
76.1%	1	`(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))`

Compiler

Compiled 15 to 10 computations (33.3% saved)

regimes11.0ms (0.1%)

Memory

-36.3MiB live, 13.6MiB allocated

Counts

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

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

Calls

3 calls:

6.0ms	x
3.0ms	eps
2.0ms	(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))

Results

Accuracy	Segments	Branch
48.7%	1	`x`
48.7%	1	`eps`
48.7%	1	`(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))`

Compiler

Compiled 15 to 10 computations (33.3% saved)

regimes4.0ms (0%)

Memory

4.1MiB live, 4.1MiB 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
46.9%	1	`eps`
46.9%	1	`x`
46.9%	1	`(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))`

Compiler

Compiled 15 to 10 computations (33.3% saved)

simplify11.0ms (0.1%)

Memory

10.7MiB live, 10.7MiB allocated

Algorithm

1×	egg-herbie

Rules

68×	`*-commutative_binary64`
12×	`+-commutative_binary64`
6×	`sub-neg_binary64`
6×	`neg-sub0_binary64`
6×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	102	362
1	144	362
2	152	362
3	158	362
4	161	362
5	162	362

Stop Event

1×

saturated

Calls

Call 1

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

soundness1.0s (5.9%)

Memory

26.2MiB live, 656.6MiB allocated

Rules

14 158×	`lower-fma.f64`
14 158×	`lower-fma.f32`
9 294×	`lower-fma.f64`
9 294×	`lower-fma.f32`
8 868×	`lower-fma.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
0	557	7233
1	1811	6753
2	5890	6710
0	8895	6297
0	673	6162
1	2040	5951
2	5823	5912
0	8076	5589
0	576	7019
1	1740	6651
2	4712	6617
0	8161	6218
0	105	498
1	277	495
2	609	495
3	2398	494
4	7880	494
0	8026	474
0	73	382
0	114	346
1	428	286
0	3568	286

Stop Event

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

Compiler

Compiled 505 to 274 computations (45.7% saved)

preprocess118.0ms (0.7%)

Memory: -5.3MiB live, 72.8MiB allocated
Compiler: Compiled 476 to 186 computations (60.9% 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%)

analyze39.0ms (0.2%)

sample9.8s (56.5%)

explain214.0ms (1.2%)

preprocess28.0ms (0.2%)

eval0.0ms (0%)

prune1.0ms (0%)

simplify11.0ms (0.1%)

localize90.0ms (0.5%)

series7.0ms (0%)

simplify266.0ms (1.5%)

rewrite232.0ms (1.3%)

eval69.0ms (0.4%)

prune64.0ms (0.4%)

simplify220.0ms (1.3%)

localize383.0ms (2.2%)

series53.0ms (0.3%)

simplify406.0ms (2.3%)

rewrite129.0ms (0.7%)

eval168.0ms (1%)

prune173.0ms (1%)

simplify221.0ms (1.3%)

localize514.0ms (3%)

series34.0ms (0.2%)

simplify391.0ms (2.3%)

rewrite215.0ms (1.2%)

eval176.0ms (1%)

prune211.0ms (1.2%)

simplify338.0ms (2%)

localize406.0ms (2.3%)

series160.0ms (0.9%)

simplify267.0ms (1.5%)

rewrite228.0ms (1.3%)

eval133.0ms (0.8%)

prune206.0ms (1.2%)

regimes55.0ms (0.3%)

regimes57.0ms (0.3%)

regimes48.0ms (0.3%)

regimes47.0ms (0.3%)

regimes28.0ms (0.2%)

regimes23.0ms (0.1%)

regimes15.0ms (0.1%)

regimes17.0ms (0.1%)

regimes10.0ms (0.1%)

regimes11.0ms (0.1%)

regimes4.0ms (0%)

simplify11.0ms (0.1%)

soundness1.0s (5.9%)

preprocess118.0ms (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