Metrics for 2cos (problem 3.3.5)

start0.0ms (0%)

Memory: 0.1MiB live, 0.1MiB allocated

analyze45.0ms (0.3%)

Memory

-20.6MiB live, 76.7MiB 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)

sample10.4s (62.8%)

Memory

101.2MiB live, 11 453.4MiB allocated

Samples

4.1s	26 007×	0	invalid
3.6s	5 672×	2	valid
568.0ms	2 477×	1	valid
18.0ms	107×	0	valid

Precisions

Click to see histograms. Total time spent on operations: 6.8s

ival-cos: 3.3s (49% of total)

const: 870.0ms (12.9% of total)

adjust: 543.0ms (8% of total)

ival-<=: 442.0ms (6.5% of total)

ival-fabs: 357.0ms (5.3% of total)

ival-mult: 304.0ms (4.5% of total)

ival-sub: 302.0ms (4.5% of total)

ival-add: 262.0ms (3.9% of total)

ival-<: 207.0ms (3.1% of total)

ival-and: 102.0ms (1.5% of total)

exact: 47.0ms (0.7% of total)

ival-assert: 13.0ms (0.2% of total)

Bogosity

explain255.0ms (1.5%)

Memory

-39.8MiB live, 130.9MiB allocated

FPErrors

Click to see full error table

Ground Truth	Overpredictions	Example	Example	Subexpression
142	2	(8.425926440942669e-156 7.234868657330871e-169)	-	`(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))`
1	0	-	-	`(cos.f64 (+.f64 x eps))`
0	0	-	-	`eps`
0	0	-	-	`(+.f64 x eps)`
0	0	-	-	`(cos.f64 x)`
0	0	-	-	`x`

Explanations

Click to see full explanations table

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

Confusion

	Predicted +	Predicted -
+	142	0
-	2	112

Precision

0.9861111111111112

Recall

1.0

Confusion?

	Predicted +	Predicted Maybe	Predicted -
+	142	0	0
-	2	0	112

Precision?

0.9861111111111112

Recall?

1.0

Freqs

test

number	freq
0	112
1	143
2	1

Total Confusion?

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

Precision?

1.0

Recall?

1.0

Samples

133.0ms	340×	2	valid
33.0ms	172×	1	valid

Compiler

Compiled 49 to 22 computations (55.1% saved)

Precisions

Click to see histograms. Total time spent on operations: 130.0ms

ival-cos: 102.0ms (78.3% of total)

adjust: 18.0ms (13.8% of total)

ival-sub: 6.0ms (4.6% of total)

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

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

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

preprocess26.0ms (0.2%)

Memory

24.4MiB live, 24.4MiB 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: 0.3MiB live, 0.3MiB allocated
Compiler: Compiled 2 to 2 computations (0% saved)

prune1.0ms (0%)

Memory

0.9MiB live, 0.9MiB allocated

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	49.7%	(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))

Compiler

Compiled 9 to 6 computations (33.3% saved)

simplify26.0ms (0.2%)

Memory

-29.5MiB live, 8.0MiB 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)

localize89.0ms (0.5%)

Memory

33.8MiB live, 115.1MiB allocated

Localize:

Found 4 expressions of interest:

New	Metric	Score
accuracy	0	(+.f64 x eps)
accuracy	0	(cos.f64 x)
accuracy	0.03991862703305532	(cos.f64 (+.f64 x eps))
accuracy	32.133152329504924	(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))

Samples

61.0ms	170×	2	valid
15.0ms	86×	1	valid

Compiler

Compiled 20 to 8 computations (60% saved)

Precisions

Click to see histograms. Total time spent on operations: 60.0ms

ival-cos: 46.0ms (76.8% of total)

adjust: 9.0ms (15% of total)

ival-sub: 3.0ms (5% of total)

ival-add: 2.0ms (3.3% of total)

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

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

series8.0ms (0%)

Memory

-27.5MiB live, 9.7MiB 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
3.0ms	eps	@	0	(- (cos (+ x eps)) (cos x))
1.0ms	eps	@	inf	(- (cos (+ x eps)) (cos x))
0.0ms	x	@	0	(- (cos (+ x eps)) (cos x))
0.0ms	x	@	-inf	(- (cos (+ x eps)) (cos x))
0.0ms	x	@	inf	(+ x eps)

simplify216.0ms (1.3%)

Memory

6.9MiB live, 353.2MiB 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)

rewrite243.0ms (1.5%)

Memory

33.3MiB live, 395.8MiB 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))

eval36.0ms (0.2%)

Memory: -10.3MiB live, 75.0MiB allocated
Compiler: Compiled 8 023 to 875 computations (89.1% saved)

prune64.0ms (0.4%)

Memory

-24.9MiB live, 97.8MiB allocated

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	300	6	306
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	301	6	307

Accuracy

99.8%

Counts

307 → 6

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	49.5%	(-.f64 (cos.f64 (+.f64 x eps)) #s(approx (cos x) (fma.f64 x (*.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64))))
▶	49.5%	(-.f64 (cos.f64 (+.f64 x eps)) #s(approx (cos x) #s(literal 1 binary64)))
	99.6%	(.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))
▶	49.3%	#s(approx (- (cos (+ x eps)) (cos x)) (+.f64 (cos.f64 eps) #s(literal -1 binary64)))
▶	78.4%	#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (sin.f64 x) (neg.f64 eps)))
▶	99.8%	#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 142 to 96 computations (32.4% saved)

simplify133.0ms (0.8%)

Memory

21.6MiB live, 61.1MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 19 expressions of interest:

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

Rules

1 136×	`lower-fma.f32`
1 134×	`lower-fma.f64`
752×	`lower-*.f32`
742×	`lower-*.f64`
268×	`lower-+.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	30	166
0	48	166
1	75	166
2	110	166
3	164	166
4	233	166
5	345	166
6	618	166
7	915	166
8	1211	166
9	1311	166
10	1391	166
11	1456	166
12	1489	166
13	1506	166
14	1512	166
15	1516	166
0	1516	166

Stop Event

1×	iter limit
1×	saturated
1×	iter limit

Calls

Call 1

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

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

localize435.0ms (2.6%)

Memory

-28.6MiB live, 293.2MiB allocated

Localize:

Found 19 expressions of interest:

New	Metric	Score
accuracy	0	(*.f64 x #s(literal -1/2 binary64))
accuracy	0.03991862703305532	(cos.f64 (+.f64 x eps))
accuracy	0.5725825466978302	#s(approx (cos x) (fma.f64 x (*.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64)))
accuracy	32.133152329504924	(-.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	(sin.f64 x)
accuracy	0	(neg.f64 eps)
accuracy	0.0078125	(*.f64 (sin.f64 x) (neg.f64 eps))
accuracy	13.84587951907224	#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (sin.f64 x) (neg.f64 eps)))
accuracy	0	(+.f64 x eps)
accuracy	0.03991862703305532	(cos.f64 (+.f64 x eps))
accuracy	0.9953917419371034	#s(approx (cos x) #s(literal 1 binary64))
accuracy	32.133152329504924	(-.f64 (cos.f64 (+.f64 x eps)) #s(approx (cos x) #s(literal 1 binary64)))
accuracy	0	(cos.f64 eps)
accuracy	31.54806368935089	(+.f64 (cos.f64 eps) #s(literal -1 binary64))
accuracy	31.631218050216862	#s(approx (- (cos (+ x eps)) (cos x)) (+.f64 (cos.f64 eps) #s(literal -1 binary64)))
accuracy	0.00390625	(-.f64 (.f64 eps (.f64 #s(literal -1/2 binary64) (cos.f64 x))) (sin.f64 x))
accuracy	0.00390625	(.f64 eps (.f64 #s(literal -1/2 binary64) (cos.f64 x)))
accuracy	0.012382519536884034	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps (-.f64 (.f64 eps (*.f64 #s(literal -1/2 binary64) (cos.f64 x))) (sin.f64 x))))
accuracy	0.1171875	(.f64 eps (-.f64 (.f64 eps (*.f64 #s(literal -1/2 binary64) (cos.f64 x))) (sin.f64 x)))

Samples

348.0ms	171×	2	valid
28.0ms	85×	1	valid

Compiler

Compiled 128 to 23 computations (82% saved)

Precisions

Click to see histograms. Total time spent on operations: 251.0ms

ival-cos: 132.0ms (52.6% of total)

adjust: 86.0ms (34.2% of total)

ival-mult: 17.0ms (6.8% of total)

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

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

ival-sin: 3.0ms (1.2% of total)

ival-neg: 1.0ms (0.4% of total)

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

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

exact: 0.0ms (0% of total)

series20.0ms (0.1%)

Memory

26.1MiB live, 26.1MiB allocated

Counts

18 → 348

Calls

Call 1

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

Outputs
#s(alt (- (cos eps) 1) (taylor 0 x) (#s(alt #s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps (-.f64 (.f64 eps (.f64 #s(literal -1/2 binary64) (cos.f64 x))) (sin.f64 x)))) (patch #s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps (-.f64 (.f64 eps (.f64 #s(literal -1/2 binary64) (cos.f64 x))) (sin.f64 x)))) #<representation binary64>) () ())) ())
#s(alt (- (+ (cos eps) (* -1 (* x (sin eps)))) 1) (taylor 0 x) (#s(alt #s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps (-.f64 (.f64 eps (.f64 #s(literal -1/2 binary64) (cos.f64 x))) (sin.f64 x)))) (patch #s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps (-.f64 (.f64 eps (.f64 #s(literal -1/2 binary64) (cos.f64 x))) (sin.f64 x)))) #<representation binary64>) () ())) ())
#s(alt (- (+ (cos eps) (* x (- (* x (+ 1/2 (* -1/2 (cos eps)))) (sin eps)))) 1) (taylor 0 x) (#s(alt #s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps (-.f64 (.f64 eps (.f64 #s(literal -1/2 binary64) (cos.f64 x))) (sin.f64 x)))) (patch #s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps (-.f64 (.f64 eps (.f64 #s(literal -1/2 binary64) (cos.f64 x))) (sin.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 #s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps (-.f64 (.f64 eps (.f64 #s(literal -1/2 binary64) (cos.f64 x))) (sin.f64 x)))) (patch #s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps (-.f64 (.f64 eps (.f64 #s(literal -1/2 binary64) (cos.f64 x))) (sin.f64 x)))) #<representation binary64>) () ())) ())
#s(alt (- (cos (+ eps x)) (cos x)) (taylor inf x) (#s(alt #s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps (-.f64 (.f64 eps (.f64 #s(literal -1/2 binary64) (cos.f64 x))) (sin.f64 x)))) (patch #s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps (-.f64 (.f64 eps (.f64 #s(literal -1/2 binary64) (cos.f64 x))) (sin.f64 x)))) #<representation binary64>) () ())) ())
#s(alt (- (cos (+ eps x)) (cos x)) (taylor inf x) (#s(alt #s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps (-.f64 (.f64 eps (.f64 #s(literal -1/2 binary64) (cos.f64 x))) (sin.f64 x)))) (patch #s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps (-.f64 (.f64 eps (.f64 #s(literal -1/2 binary64) (cos.f64 x))) (sin.f64 x)))) #<representation binary64>) () ())) ())
#s(alt (- (cos (+ eps x)) (cos x)) (taylor inf x) (#s(alt #s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps (-.f64 (.f64 eps (.f64 #s(literal -1/2 binary64) (cos.f64 x))) (sin.f64 x)))) (patch #s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps (-.f64 (.f64 eps (.f64 #s(literal -1/2 binary64) (cos.f64 x))) (sin.f64 x)))) #<representation binary64>) () ())) ())
#s(alt (- (cos (+ eps x)) (cos x)) (taylor inf x) (#s(alt #s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps (-.f64 (.f64 eps (.f64 #s(literal -1/2 binary64) (cos.f64 x))) (sin.f64 x)))) (patch #s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps (-.f64 (.f64 eps (.f64 #s(literal -1/2 binary64) (cos.f64 x))) (sin.f64 x)))) #<representation binary64>) () ())) ())
#s(alt (- (cos (- eps (* -1 x))) (cos x)) (taylor -inf x) (#s(alt #s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps (-.f64 (.f64 eps (.f64 #s(literal -1/2 binary64) (cos.f64 x))) (sin.f64 x)))) (patch #s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps (-.f64 (.f64 eps (.f64 #s(literal -1/2 binary64) (cos.f64 x))) (sin.f64 x)))) #<representation binary64>) () ())) ())
#s(alt (- (cos (- eps (* -1 x))) (cos x)) (taylor -inf x) (#s(alt #s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps (-.f64 (.f64 eps (.f64 #s(literal -1/2 binary64) (cos.f64 x))) (sin.f64 x)))) (patch #s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps (-.f64 (.f64 eps (.f64 #s(literal -1/2 binary64) (cos.f64 x))) (sin.f64 x)))) #<representation binary64>) () ())) ())
#s(alt (- (cos (- eps (* -1 x))) (cos x)) (taylor -inf x) (#s(alt #s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps (-.f64 (.f64 eps (.f64 #s(literal -1/2 binary64) (cos.f64 x))) (sin.f64 x)))) (patch #s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps (-.f64 (.f64 eps (.f64 #s(literal -1/2 binary64) (cos.f64 x))) (sin.f64 x)))) #<representation binary64>) () ())) ())
#s(alt (- (cos (- eps (* -1 x))) (cos x)) (taylor -inf x) (#s(alt #s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps (-.f64 (.f64 eps (.f64 #s(literal -1/2 binary64) (cos.f64 x))) (sin.f64 x)))) (patch #s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps (-.f64 (.f64 eps (.f64 #s(literal -1/2 binary64) (cos.f64 x))) (sin.f64 x)))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* eps (sin x))) (taylor 0 eps) (#s(alt #s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps (-.f64 (.f64 eps (.f64 #s(literal -1/2 binary64) (cos.f64 x))) (sin.f64 x)))) (patch #s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps (-.f64 (.f64 eps (.f64 #s(literal -1/2 binary64) (cos.f64 x))) (sin.f64 x)))) #<representation binary64>) () ())) ())
#s(alt (* eps (- (* -1/2 (* eps (cos x))) (sin x))) (taylor 0 eps) (#s(alt #s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps (-.f64 (.f64 eps (.f64 #s(literal -1/2 binary64) (cos.f64 x))) (sin.f64 x)))) (patch #s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps (-.f64 (.f64 eps (.f64 #s(literal -1/2 binary64) (cos.f64 x))) (sin.f64 x)))) #<representation binary64>) () ())) ())
#s(alt (* eps (- (* eps (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x))))) (sin x))) (taylor 0 eps) (#s(alt #s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps (-.f64 (.f64 eps (.f64 #s(literal -1/2 binary64) (cos.f64 x))) (sin.f64 x)))) (patch #s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps (-.f64 (.f64 eps (.f64 #s(literal -1/2 binary64) (cos.f64 x))) (sin.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 #s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps (-.f64 (.f64 eps (.f64 #s(literal -1/2 binary64) (cos.f64 x))) (sin.f64 x)))) (patch #s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps (-.f64 (.f64 eps (.f64 #s(literal -1/2 binary64) (cos.f64 x))) (sin.f64 x)))) #<representation binary64>) () ())) ())
#s(alt (- (cos (+ eps x)) (cos x)) (taylor inf eps) (#s(alt #s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps (-.f64 (.f64 eps (.f64 #s(literal -1/2 binary64) (cos.f64 x))) (sin.f64 x)))) (patch #s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps (-.f64 (.f64 eps (.f64 #s(literal -1/2 binary64) (cos.f64 x))) (sin.f64 x)))) #<representation binary64>) () ())) ())
#s(alt (- (cos (+ eps x)) (cos x)) (taylor inf eps) (#s(alt #s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps (-.f64 (.f64 eps (.f64 #s(literal -1/2 binary64) (cos.f64 x))) (sin.f64 x)))) (patch #s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps (-.f64 (.f64 eps (.f64 #s(literal -1/2 binary64) (cos.f64 x))) (sin.f64 x)))) #<representation binary64>) () ())) ())
#s(alt (- (cos (+ eps x)) (cos x)) (taylor inf eps) (#s(alt #s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps (-.f64 (.f64 eps (.f64 #s(literal -1/2 binary64) (cos.f64 x))) (sin.f64 x)))) (patch #s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps (-.f64 (.f64 eps (.f64 #s(literal -1/2 binary64) (cos.f64 x))) (sin.f64 x)))) #<representation binary64>) () ())) ())
#s(alt (- (cos (+ eps x)) (cos x)) (taylor inf eps) (#s(alt #s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps (-.f64 (.f64 eps (.f64 #s(literal -1/2 binary64) (cos.f64 x))) (sin.f64 x)))) (patch #s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps (-.f64 (.f64 eps (.f64 #s(literal -1/2 binary64) (cos.f64 x))) (sin.f64 x)))) #<representation binary64>) () ())) ())
#s(alt (- (cos (- x (* -1 eps))) (cos x)) (taylor -inf eps) (#s(alt #s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps (-.f64 (.f64 eps (.f64 #s(literal -1/2 binary64) (cos.f64 x))) (sin.f64 x)))) (patch #s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps (-.f64 (.f64 eps (.f64 #s(literal -1/2 binary64) (cos.f64 x))) (sin.f64 x)))) #<representation binary64>) () ())) ())
#s(alt (- (cos (- x (* -1 eps))) (cos x)) (taylor -inf eps) (#s(alt #s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps (-.f64 (.f64 eps (.f64 #s(literal -1/2 binary64) (cos.f64 x))) (sin.f64 x)))) (patch #s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps (-.f64 (.f64 eps (.f64 #s(literal -1/2 binary64) (cos.f64 x))) (sin.f64 x)))) #<representation binary64>) () ())) ())
#s(alt (- (cos (- x (* -1 eps))) (cos x)) (taylor -inf eps) (#s(alt #s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps (-.f64 (.f64 eps (.f64 #s(literal -1/2 binary64) (cos.f64 x))) (sin.f64 x)))) (patch #s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps (-.f64 (.f64 eps (.f64 #s(literal -1/2 binary64) (cos.f64 x))) (sin.f64 x)))) #<representation binary64>) () ())) ())
#s(alt (- (cos (- x (* -1 eps))) (cos x)) (taylor -inf eps) (#s(alt #s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps (-.f64 (.f64 eps (.f64 #s(literal -1/2 binary64) (cos.f64 x))) (sin.f64 x)))) (patch #s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps (-.f64 (.f64 eps (.f64 #s(literal -1/2 binary64) (cos.f64 x))) (sin.f64 x)))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* eps (sin x))) (taylor 0 eps) (#s(alt (.f64 eps (-.f64 (.f64 eps (.f64 #s(literal -1/2 binary64) (cos.f64 x))) (sin.f64 x))) (patch (.f64 eps (-.f64 (.f64 eps (.f64 #s(literal -1/2 binary64) (cos.f64 x))) (sin.f64 x))) #<representation binary64>) () ())) ())
#s(alt (* eps (+ (* -1 (sin x)) (* -1/2 (* eps (cos x))))) (taylor 0 eps) (#s(alt (.f64 eps (-.f64 (.f64 eps (.f64 #s(literal -1/2 binary64) (cos.f64 x))) (sin.f64 x))) (patch (.f64 eps (-.f64 (.f64 eps (.f64 #s(literal -1/2 binary64) (cos.f64 x))) (sin.f64 x))) #<representation binary64>) () ())) ())
#s(alt (* eps (+ (* -1 (sin x)) (* -1/2 (* eps (cos x))))) (taylor 0 eps) (#s(alt (.f64 eps (-.f64 (.f64 eps (.f64 #s(literal -1/2 binary64) (cos.f64 x))) (sin.f64 x))) (patch (.f64 eps (-.f64 (.f64 eps (.f64 #s(literal -1/2 binary64) (cos.f64 x))) (sin.f64 x))) #<representation binary64>) () ())) ())
#s(alt (* eps (+ (* -1 (sin x)) (* -1/2 (* eps (cos x))))) (taylor 0 eps) (#s(alt (.f64 eps (-.f64 (.f64 eps (.f64 #s(literal -1/2 binary64) (cos.f64 x))) (sin.f64 x))) (patch (.f64 eps (-.f64 (.f64 eps (.f64 #s(literal -1/2 binary64) (cos.f64 x))) (sin.f64 x))) #<representation binary64>) () ())) ())
#s(alt (* -1/2 (* (pow eps 2) (cos x))) (taylor inf eps) (#s(alt (.f64 eps (-.f64 (.f64 eps (.f64 #s(literal -1/2 binary64) (cos.f64 x))) (sin.f64 x))) (patch (.f64 eps (-.f64 (.f64 eps (.f64 #s(literal -1/2 binary64) (cos.f64 x))) (sin.f64 x))) #<representation binary64>) () ())) ())
#s(alt (* (pow eps 2) (+ (* -1 (/ (sin x) eps)) (* -1/2 (cos x)))) (taylor inf eps) (#s(alt (.f64 eps (-.f64 (.f64 eps (.f64 #s(literal -1/2 binary64) (cos.f64 x))) (sin.f64 x))) (patch (.f64 eps (-.f64 (.f64 eps (.f64 #s(literal -1/2 binary64) (cos.f64 x))) (sin.f64 x))) #<representation binary64>) () ())) ())
#s(alt (* (pow eps 2) (+ (* -1 (/ (sin x) eps)) (* -1/2 (cos x)))) (taylor inf eps) (#s(alt (.f64 eps (-.f64 (.f64 eps (.f64 #s(literal -1/2 binary64) (cos.f64 x))) (sin.f64 x))) (patch (.f64 eps (-.f64 (.f64 eps (.f64 #s(literal -1/2 binary64) (cos.f64 x))) (sin.f64 x))) #<representation binary64>) () ())) ())
#s(alt (* (pow eps 2) (+ (* -1 (/ (sin x) eps)) (* -1/2 (cos x)))) (taylor inf eps) (#s(alt (.f64 eps (-.f64 (.f64 eps (.f64 #s(literal -1/2 binary64) (cos.f64 x))) (sin.f64 x))) (patch (.f64 eps (-.f64 (.f64 eps (.f64 #s(literal -1/2 binary64) (cos.f64 x))) (sin.f64 x))) #<representation binary64>) () ())) ())
#s(alt (* -1/2 (* (pow eps 2) (cos x))) (taylor -inf eps) (#s(alt (.f64 eps (-.f64 (.f64 eps (.f64 #s(literal -1/2 binary64) (cos.f64 x))) (sin.f64 x))) (patch (.f64 eps (-.f64 (.f64 eps (.f64 #s(literal -1/2 binary64) (cos.f64 x))) (sin.f64 x))) #<representation binary64>) () ())) ())
#s(alt (* (pow eps 2) (+ (* -1 (/ (sin x) eps)) (* -1/2 (cos x)))) (taylor -inf eps) (#s(alt (.f64 eps (-.f64 (.f64 eps (.f64 #s(literal -1/2 binary64) (cos.f64 x))) (sin.f64 x))) (patch (.f64 eps (-.f64 (.f64 eps (.f64 #s(literal -1/2 binary64) (cos.f64 x))) (sin.f64 x))) #<representation binary64>) () ())) ())
#s(alt (* (pow eps 2) (+ (* -1 (/ (sin x) eps)) (* -1/2 (cos x)))) (taylor -inf eps) (#s(alt (.f64 eps (-.f64 (.f64 eps (.f64 #s(literal -1/2 binary64) (cos.f64 x))) (sin.f64 x))) (patch (.f64 eps (-.f64 (.f64 eps (.f64 #s(literal -1/2 binary64) (cos.f64 x))) (sin.f64 x))) #<representation binary64>) () ())) ())
#s(alt (* (pow eps 2) (+ (* -1 (/ (sin x) eps)) (* -1/2 (cos x)))) (taylor -inf eps) (#s(alt (.f64 eps (-.f64 (.f64 eps (.f64 #s(literal -1/2 binary64) (cos.f64 x))) (sin.f64 x))) (patch (.f64 eps (-.f64 (.f64 eps (.f64 #s(literal -1/2 binary64) (cos.f64 x))) (sin.f64 x))) #<representation binary64>) () ())) ())
#s(alt (* -1/2 (pow eps 2)) (taylor 0 x) (#s(alt (.f64 eps (-.f64 (.f64 eps (.f64 #s(literal -1/2 binary64) (cos.f64 x))) (sin.f64 x))) (patch (.f64 eps (-.f64 (.f64 eps (.f64 #s(literal -1/2 binary64) (cos.f64 x))) (sin.f64 x))) #<representation binary64>) () ())) ())
#s(alt (+ (* -1 (* eps x)) (* -1/2 (pow eps 2))) (taylor 0 x) (#s(alt (.f64 eps (-.f64 (.f64 eps (.f64 #s(literal -1/2 binary64) (cos.f64 x))) (sin.f64 x))) (patch (.f64 eps (-.f64 (.f64 eps (.f64 #s(literal -1/2 binary64) (cos.f64 x))) (sin.f64 x))) #<representation binary64>) () ())) ())
#s(alt (+ (* -1/2 (pow eps 2)) (* x (+ (* -1 eps) (* 1/4 (* (pow eps 2) x))))) (taylor 0 x) (#s(alt (.f64 eps (-.f64 (.f64 eps (.f64 #s(literal -1/2 binary64) (cos.f64 x))) (sin.f64 x))) (patch (.f64 eps (-.f64 (.f64 eps (.f64 #s(literal -1/2 binary64) (cos.f64 x))) (sin.f64 x))) #<representation binary64>) () ())) ())
#s(alt (+ (* -1/2 (pow eps 2)) (* x (+ (* -1 eps) (* x (+ (* 1/6 (* eps x)) (* 1/4 (pow eps 2))))))) (taylor 0 x) (#s(alt (.f64 eps (-.f64 (.f64 eps (.f64 #s(literal -1/2 binary64) (cos.f64 x))) (sin.f64 x))) (patch (.f64 eps (-.f64 (.f64 eps (.f64 #s(literal -1/2 binary64) (cos.f64 x))) (sin.f64 x))) #<representation binary64>) () ())) ())
#s(alt (* eps (- (* -1/2 (* eps (cos x))) (sin x))) (taylor inf x) (#s(alt (.f64 eps (-.f64 (.f64 eps (.f64 #s(literal -1/2 binary64) (cos.f64 x))) (sin.f64 x))) (patch (.f64 eps (-.f64 (.f64 eps (.f64 #s(literal -1/2 binary64) (cos.f64 x))) (sin.f64 x))) #<representation binary64>) () ())) ())
#s(alt (* eps (- (* -1/2 (* eps (cos x))) (sin x))) (taylor inf x) (#s(alt (.f64 eps (-.f64 (.f64 eps (.f64 #s(literal -1/2 binary64) (cos.f64 x))) (sin.f64 x))) (patch (.f64 eps (-.f64 (.f64 eps (.f64 #s(literal -1/2 binary64) (cos.f64 x))) (sin.f64 x))) #<representation binary64>) () ())) ())
#s(alt (* eps (- (* -1/2 (* eps (cos x))) (sin x))) (taylor inf x) (#s(alt (.f64 eps (-.f64 (.f64 eps (.f64 #s(literal -1/2 binary64) (cos.f64 x))) (sin.f64 x))) (patch (.f64 eps (-.f64 (.f64 eps (.f64 #s(literal -1/2 binary64) (cos.f64 x))) (sin.f64 x))) #<representation binary64>) () ())) ())
#s(alt (* eps (- (* -1/2 (* eps (cos x))) (sin x))) (taylor inf x) (#s(alt (.f64 eps (-.f64 (.f64 eps (.f64 #s(literal -1/2 binary64) (cos.f64 x))) (sin.f64 x))) (patch (.f64 eps (-.f64 (.f64 eps (.f64 #s(literal -1/2 binary64) (cos.f64 x))) (sin.f64 x))) #<representation binary64>) () ())) ())
#s(alt (* eps (- (* -1/2 (* eps (cos x))) (sin x))) (taylor -inf x) (#s(alt (.f64 eps (-.f64 (.f64 eps (.f64 #s(literal -1/2 binary64) (cos.f64 x))) (sin.f64 x))) (patch (.f64 eps (-.f64 (.f64 eps (.f64 #s(literal -1/2 binary64) (cos.f64 x))) (sin.f64 x))) #<representation binary64>) () ())) ())
#s(alt (* eps (- (* -1/2 (* eps (cos x))) (sin x))) (taylor -inf x) (#s(alt (.f64 eps (-.f64 (.f64 eps (.f64 #s(literal -1/2 binary64) (cos.f64 x))) (sin.f64 x))) (patch (.f64 eps (-.f64 (.f64 eps (.f64 #s(literal -1/2 binary64) (cos.f64 x))) (sin.f64 x))) #<representation binary64>) () ())) ())
#s(alt (* eps (- (* -1/2 (* eps (cos x))) (sin x))) (taylor -inf x) (#s(alt (.f64 eps (-.f64 (.f64 eps (.f64 #s(literal -1/2 binary64) (cos.f64 x))) (sin.f64 x))) (patch (.f64 eps (-.f64 (.f64 eps (.f64 #s(literal -1/2 binary64) (cos.f64 x))) (sin.f64 x))) #<representation binary64>) () ())) ())
#s(alt (* eps (- (* -1/2 (* eps (cos x))) (sin x))) (taylor -inf x) (#s(alt (.f64 eps (-.f64 (.f64 eps (.f64 #s(literal -1/2 binary64) (cos.f64 x))) (sin.f64 x))) (patch (.f64 eps (-.f64 (.f64 eps (.f64 #s(literal -1/2 binary64) (cos.f64 x))) (sin.f64 x))) #<representation binary64>) () ())) ())
#s(alt (* -1 (sin x)) (taylor 0 eps) (#s(alt (-.f64 (.f64 eps (.f64 #s(literal -1/2 binary64) (cos.f64 x))) (sin.f64 x)) (patch (-.f64 (.f64 eps (.f64 #s(literal -1/2 binary64) (cos.f64 x))) (sin.f64 x)) #<representation binary64>) () ())) ())
#s(alt (- (* -1/2 (* eps (cos x))) (sin x)) (taylor 0 eps) (#s(alt (-.f64 (.f64 eps (.f64 #s(literal -1/2 binary64) (cos.f64 x))) (sin.f64 x)) (patch (-.f64 (.f64 eps (.f64 #s(literal -1/2 binary64) (cos.f64 x))) (sin.f64 x)) #<representation binary64>) () ())) ())
#s(alt (- (* -1/2 (* eps (cos x))) (sin x)) (taylor 0 eps) (#s(alt (-.f64 (.f64 eps (.f64 #s(literal -1/2 binary64) (cos.f64 x))) (sin.f64 x)) (patch (-.f64 (.f64 eps (.f64 #s(literal -1/2 binary64) (cos.f64 x))) (sin.f64 x)) #<representation binary64>) () ())) ())
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#s(alt (* -1 (* eps (sin x))) (taylor 0 eps) (#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 (* eps (- (* -1/2 (* eps (cos x))) (sin x))) (taylor 0 eps) (#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 (* eps (- (* eps (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x))))) (sin x))) (taylor 0 eps) (#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 (* 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)) #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 (+ eps x)) (cos x)) (taylor inf eps) (#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 (+ eps x)) (cos x)) (taylor inf eps) (#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 (+ eps x)) (cos x)) (taylor inf eps) (#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 (+ eps x)) (cos x)) (taylor inf eps) (#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 (- x (* -1 eps))) (cos x)) (taylor -inf eps) (#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 (- x (* -1 eps))) (cos x)) (taylor -inf eps) (#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 (- x (* -1 eps))) (cos x)) (taylor -inf eps) (#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 (- x (* -1 eps))) (cos x)) (taylor -inf eps) (#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 1 (taylor 0 x) (#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 (+ 1 (* -1/2 (pow x 2))) (taylor 0 x) (#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 (+ 1 (* (pow x 2) (- (* 1/24 (pow x 2)) 1/2))) (taylor 0 x) (#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 (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))) 1/2))) (taylor 0 x) (#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 (cos x) (taylor inf x) (#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 (cos x) (taylor inf x) (#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 (cos x) (taylor inf x) (#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 (cos x) (taylor inf x) (#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 (cos x) (taylor -inf x) (#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 (cos x) (taylor -inf x) (#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 (cos x) (taylor -inf x) (#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 (cos x) (taylor -inf x) (#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 (* -1/2 x) (taylor 0 x) (#s(alt (.f64 x #s(literal -1/2 binary64)) (patch (.f64 x #s(literal -1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* -1/2 x) (taylor 0 x) (#s(alt (.f64 x #s(literal -1/2 binary64)) (patch (.f64 x #s(literal -1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* -1/2 x) (taylor 0 x) (#s(alt (.f64 x #s(literal -1/2 binary64)) (patch (.f64 x #s(literal -1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* -1/2 x) (taylor 0 x) (#s(alt (.f64 x #s(literal -1/2 binary64)) (patch (.f64 x #s(literal -1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* -1/2 x) (taylor inf x) (#s(alt (.f64 x #s(literal -1/2 binary64)) (patch (.f64 x #s(literal -1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* -1/2 x) (taylor inf x) (#s(alt (.f64 x #s(literal -1/2 binary64)) (patch (.f64 x #s(literal -1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* -1/2 x) (taylor inf x) (#s(alt (.f64 x #s(literal -1/2 binary64)) (patch (.f64 x #s(literal -1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* -1/2 x) (taylor inf x) (#s(alt (.f64 x #s(literal -1/2 binary64)) (patch (.f64 x #s(literal -1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* -1/2 x) (taylor -inf x) (#s(alt (.f64 x #s(literal -1/2 binary64)) (patch (.f64 x #s(literal -1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* -1/2 x) (taylor -inf x) (#s(alt (.f64 x #s(literal -1/2 binary64)) (patch (.f64 x #s(literal -1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* -1/2 x) (taylor -inf x) (#s(alt (.f64 x #s(literal -1/2 binary64)) (patch (.f64 x #s(literal -1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* -1/2 x) (taylor -inf x) (#s(alt (.f64 x #s(literal -1/2 binary64)) (patch (.f64 x #s(literal -1/2 binary64)) #<representation binary64>) () ())) ())

Calls

87 calls:

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

simplify273.0ms (1.6%)

Memory

10.0MiB live, 353.5MiB allocated

Algorithm

1×	egg-herbie

Rules

19 422×	`lower-fma.f64`
19 422×	`lower-fma.f32`
4 772×	`lower-*.f64`
4 772×	`lower-*.f32`
3 536×	`lower-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	223	2548
1	636	2534
2	1605	2511
3	4016	2510
0	9256	2411

Stop Event

1×	iter limit
1×	node limit

Counts

348 → 341

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))
(* -1 (* eps (sin x)))
(* eps (+ (* -1 (sin x)) (* -1/2 (* eps (cos x)))))
(* eps (+ (* -1 (sin x)) (* -1/2 (* eps (cos x)))))
(* eps (+ (* -1 (sin x)) (* -1/2 (* eps (cos x)))))
(* -1/2 (* (pow eps 2) (cos x)))
(* (pow eps 2) (+ (* -1 (/ (sin x) eps)) (* -1/2 (cos x))))
(* (pow eps 2) (+ (* -1 (/ (sin x) eps)) (* -1/2 (cos x))))
(* (pow eps 2) (+ (* -1 (/ (sin x) eps)) (* -1/2 (cos x))))
(* -1/2 (* (pow eps 2) (cos x)))
(* (pow eps 2) (+ (* -1 (/ (sin x) eps)) (* -1/2 (cos x))))
(* (pow eps 2) (+ (* -1 (/ (sin x) eps)) (* -1/2 (cos x))))
(* (pow eps 2) (+ (* -1 (/ (sin x) eps)) (* -1/2 (cos x))))
(* -1/2 (pow eps 2))
(+ (* -1 (* eps x)) (* -1/2 (pow eps 2)))
(+ (* -1/2 (pow eps 2)) (* x (+ (* -1 eps) (* 1/4 (* (pow eps 2) x)))))
(+ (* -1/2 (pow eps 2)) (* x (+ (* -1 eps) (* x (+ (* 1/6 (* eps x)) (* 1/4 (pow eps 2)))))))
(* eps (- (* -1/2 (* eps (cos x))) (sin x)))
(* eps (- (* -1/2 (* eps (cos x))) (sin x)))
(* eps (- (* -1/2 (* eps (cos x))) (sin x)))
(* eps (- (* -1/2 (* eps (cos x))) (sin x)))
(* eps (- (* -1/2 (* eps (cos x))) (sin x)))
(* eps (- (* -1/2 (* eps (cos x))) (sin x)))
(* eps (- (* -1/2 (* eps (cos x))) (sin x)))
(* eps (- (* -1/2 (* eps (cos x))) (sin x)))
(* -1 (sin x))
(- (* -1/2 (* eps (cos x))) (sin x))
(- (* -1/2 (* eps (cos x))) (sin x))
(- (* -1/2 (* eps (cos x))) (sin x))
(* -1/2 (* eps (cos x)))
(* eps (+ (* -1 (/ (sin x) eps)) (* -1/2 (cos x))))
(* eps (+ (* -1 (/ (sin x) eps)) (* -1/2 (cos x))))
(* eps (+ (* -1 (/ (sin x) eps)) (* -1/2 (cos x))))
(* -1/2 (* eps (cos x)))
(* -1 (* eps (+ (* 1/2 (cos x)) (/ (sin x) eps))))
(* -1 (* eps (+ (* 1/2 (cos x)) (/ (sin x) eps))))
(* -1 (* eps (+ (* 1/2 (cos x)) (/ (sin x) eps))))
(* -1/2 eps)
(+ (* -1 x) (* -1/2 eps))
(+ (* -1/2 eps) (* x (- (* 1/4 (* eps x)) 1)))
(+ (* -1/2 eps) (* x (- (* x (+ (* 1/6 x) (* 1/4 eps))) 1)))
(- (* -1/2 (* eps (cos x))) (sin x))
(- (* -1/2 (* eps (cos x))) (sin x))
(- (* -1/2 (* eps (cos x))) (sin x))
(- (* -1/2 (* eps (cos x))) (sin x))
(- (* -1/2 (* eps (cos x))) (sin x))
(- (* -1/2 (* eps (cos x))) (sin x))
(- (* -1/2 (* eps (cos x))) (sin x))
(- (* -1/2 (* eps (cos x))) (sin x))
(* -1/2 (* eps (cos x)))
(* -1/2 (* eps (cos x)))
(* -1/2 (* eps (cos x)))
(* -1/2 (* eps (cos x)))
(* -1/2 (* eps (cos x)))
(* -1/2 (* eps (cos x)))
(* -1/2 (* eps (cos x)))
(* -1/2 (* eps (cos x)))
(* -1/2 (* eps (cos x)))
(* -1/2 (* eps (cos x)))
(* -1/2 (* eps (cos x)))
(* -1/2 (* eps (cos x)))
(* -1/2 eps)
(+ (* -1/2 eps) (* 1/4 (* eps (pow x 2))))
(+ (* -1/2 eps) (* (pow x 2) (+ (* -1/48 (* eps (pow x 2))) (* 1/4 eps))))
(+ (* -1/2 eps) (* (pow x 2) (+ (* 1/4 eps) (* (pow x 2) (+ (* -1/48 eps) (* 1/1440 (* eps (pow x 2))))))))
(* -1/2 (* eps (cos x)))
(* -1/2 (* eps (cos x)))
(* -1/2 (* eps (cos x)))
(* -1/2 (* eps (cos x)))
(* -1/2 (* eps (cos x)))
(* -1/2 (* eps (cos x)))
(* -1/2 (* eps (cos x)))
(* -1/2 (* eps (cos x)))
(- (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)
(- (+ (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 (* eps x))
(* x (+ (* -1 eps) (* 1/6 (* eps (pow x 2)))))
(* x (+ (* -1 eps) (* (pow x 2) (+ (* -1/120 (* eps (pow x 2))) (* 1/6 eps)))))
(* x (+ (* -1 eps) (* (pow x 2) (+ (* 1/6 eps) (* (pow x 2) (+ (* -1/120 eps) (* 1/5040 (* eps (pow x 2)))))))))
(* -1 (* eps (sin x)))
(* -1 (* eps (sin x)))
(* -1 (* eps (sin x)))
(* -1 (* eps (sin x)))
(* -1 (* eps (sin x)))
(* -1 (* eps (sin x)))
(* -1 (* eps (sin x)))
(* -1 (* eps (sin x)))
(* -1 (* eps (sin x)))
(* -1 (* eps (sin x)))
(* -1 (* eps (sin x)))
(* -1 (* eps (sin x)))
(* -1 (* eps (sin x)))
(* -1 (* eps (sin x)))
(* -1 (* eps (sin x)))
(* -1 (* eps (sin x)))
(* -1 (* eps (sin x)))
(* -1 (* eps (sin x)))
(* -1 (* eps (sin x)))
(* -1 (* eps (sin x)))
x
(* x (+ 1 (* -1/6 (pow x 2))))
(* x (+ 1 (* (pow x 2) (- (* 1/120 (pow x 2)) 1/6))))
(* x (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/120 (* -1/5040 (pow x 2)))) 1/6))))
(sin x)
(sin x)
(sin x)
(sin x)
(sin x)
(sin x)
(sin x)
(sin x)
(* -1 eps)
(* -1 eps)
(* -1 eps)
(* -1 eps)
(* -1 eps)
(* -1 eps)
(* -1 eps)
(* -1 eps)
(* -1 eps)
(* -1 eps)
(* -1 eps)
(* -1 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))
1
(+ 1 (* -1/2 (pow x 2)))
(+ 1 (* (pow x 2) (- (* 1/24 (pow x 2)) 1/2)))
(+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))) 1/2)))
(cos x)
(cos x)
(cos x)
(cos x)
(cos x)
(cos x)
(cos x)
(cos x)
(* -1/2 x)
(* -1/2 x)
(* -1/2 x)
(* -1/2 x)
(* -1/2 x)
(* -1/2 x)
(* -1/2 x)
(* -1/2 x)
(* -1/2 x)
(* -1/2 x)
(* -1/2 x)
(* -1/2 x)

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)
(fma.f64 x (fma.f64 x (fma.f64 (cos.f64 eps) #s(literal -1/2 binary64) #s(literal 1/2 binary64)) (sin.f64 (neg.f64 eps))) (+.f64 (cos.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 (cos.f64 eps) (fma.f64 x (fma.f64 x (fma.f64 (cos.f64 eps) #s(literal -1/2 binary64) #s(literal 1/2 binary64)) (.f64 (sin.f64 eps) (fma.f64 x (.f64 x #s(literal 1/6 binary64)) #s(literal -1 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 #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 (.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 eps (fma.f64 eps (.f64 (cos.f64 x) #s(literal 1/24 binary64)) (.f64 #s(literal 1/6 binary64) (sin.f64 x))) (.f64 #s(literal -1/2 binary64) (cos.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))
(* -1 (* eps (sin x)))
(*.f64 (sin.f64 x) (neg.f64 eps))
(* 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)) (* -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)) (* -1/2 (* eps (cos x)))))
(.f64 eps (-.f64 (.f64 #s(literal -1/2 binary64) (*.f64 eps (cos.f64 x))) (sin.f64 x)))
(* -1/2 (* (pow eps 2) (cos x)))
(.f64 eps (.f64 #s(literal -1/2 binary64) (*.f64 eps (cos.f64 x))))
(* (pow eps 2) (+ (* -1 (/ (sin x) eps)) (* -1/2 (cos x))))
(.f64 eps (-.f64 (.f64 #s(literal -1/2 binary64) (*.f64 eps (cos.f64 x))) (sin.f64 x)))
(* (pow eps 2) (+ (* -1 (/ (sin x) eps)) (* -1/2 (cos x))))
(.f64 eps (-.f64 (.f64 #s(literal -1/2 binary64) (*.f64 eps (cos.f64 x))) (sin.f64 x)))
(* (pow eps 2) (+ (* -1 (/ (sin x) eps)) (* -1/2 (cos x))))
(.f64 eps (-.f64 (.f64 #s(literal -1/2 binary64) (*.f64 eps (cos.f64 x))) (sin.f64 x)))
(* -1/2 (* (pow eps 2) (cos x)))
(.f64 eps (.f64 #s(literal -1/2 binary64) (*.f64 eps (cos.f64 x))))
(* (pow eps 2) (+ (* -1 (/ (sin x) eps)) (* -1/2 (cos x))))
(.f64 eps (-.f64 (.f64 #s(literal -1/2 binary64) (*.f64 eps (cos.f64 x))) (sin.f64 x)))
(* (pow eps 2) (+ (* -1 (/ (sin x) eps)) (* -1/2 (cos x))))
(.f64 eps (-.f64 (.f64 #s(literal -1/2 binary64) (*.f64 eps (cos.f64 x))) (sin.f64 x)))
(* (pow eps 2) (+ (* -1 (/ (sin x) eps)) (* -1/2 (cos x))))
(.f64 eps (-.f64 (.f64 #s(literal -1/2 binary64) (*.f64 eps (cos.f64 x))) (sin.f64 x)))
(* -1/2 (pow eps 2))
(.f64 eps (.f64 eps #s(literal -1/2 binary64)))
(+ (* -1 (* eps x)) (* -1/2 (pow eps 2)))
(.f64 eps (-.f64 (.f64 eps #s(literal -1/2 binary64)) x))
(+ (* -1/2 (pow eps 2)) (* x (+ (* -1 eps) (* 1/4 (* (pow eps 2) x)))))
(fma.f64 eps (-.f64 (.f64 eps #s(literal -1/2 binary64)) x) (.f64 (.f64 eps (.f64 eps x)) (*.f64 x #s(literal 1/4 binary64))))
(+ (* -1/2 (pow eps 2)) (* x (+ (* -1 eps) (* x (+ (* 1/6 (* eps x)) (* 1/4 (pow eps 2)))))))
(fma.f64 eps (-.f64 (.f64 eps #s(literal -1/2 binary64)) x) (.f64 x (.f64 x (.f64 eps (fma.f64 eps #s(literal 1/4 binary64) (*.f64 x #s(literal 1/6 binary64)))))))
(* 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 (- (* -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 (- (* -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 (- (* -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 (- (* -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 (- (* -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 (- (* -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 (- (* -1/2 (* eps (cos x))) (sin x)))
(.f64 eps (-.f64 (.f64 #s(literal -1/2 binary64) (*.f64 eps (cos.f64 x))) (sin.f64 x)))
(* -1 (sin x))
(sin.f64 (neg.f64 x))
(- (* -1/2 (* eps (cos x))) (sin x))
(-.f64 (.f64 #s(literal -1/2 binary64) (.f64 eps (cos.f64 x))) (sin.f64 x))
(- (* -1/2 (* eps (cos x))) (sin x))
(-.f64 (.f64 #s(literal -1/2 binary64) (.f64 eps (cos.f64 x))) (sin.f64 x))
(- (* -1/2 (* eps (cos x))) (sin x))
(-.f64 (.f64 #s(literal -1/2 binary64) (.f64 eps (cos.f64 x))) (sin.f64 x))
(* -1/2 (* eps (cos x)))
(.f64 #s(literal -1/2 binary64) (.f64 eps (cos.f64 x)))
(* eps (+ (* -1 (/ (sin x) eps)) (* -1/2 (cos x))))
(-.f64 (.f64 #s(literal -1/2 binary64) (.f64 eps (cos.f64 x))) (sin.f64 x))
(* eps (+ (* -1 (/ (sin x) eps)) (* -1/2 (cos x))))
(-.f64 (.f64 #s(literal -1/2 binary64) (.f64 eps (cos.f64 x))) (sin.f64 x))
(* eps (+ (* -1 (/ (sin x) eps)) (* -1/2 (cos x))))
(-.f64 (.f64 #s(literal -1/2 binary64) (.f64 eps (cos.f64 x))) (sin.f64 x))
(* -1/2 (* eps (cos x)))
(.f64 #s(literal -1/2 binary64) (.f64 eps (cos.f64 x)))
(* -1 (* eps (+ (* 1/2 (cos x)) (/ (sin x) eps))))
(-.f64 (.f64 #s(literal -1/2 binary64) (.f64 eps (cos.f64 x))) (sin.f64 x))
(* -1 (* eps (+ (* 1/2 (cos x)) (/ (sin x) eps))))
(-.f64 (.f64 #s(literal -1/2 binary64) (.f64 eps (cos.f64 x))) (sin.f64 x))
(* -1 (* eps (+ (* 1/2 (cos x)) (/ (sin x) eps))))
(-.f64 (.f64 #s(literal -1/2 binary64) (.f64 eps (cos.f64 x))) (sin.f64 x))
(* -1/2 eps)
(*.f64 eps #s(literal -1/2 binary64))
(+ (* -1 x) (* -1/2 eps))
(-.f64 (*.f64 eps #s(literal -1/2 binary64)) x)
(+ (* -1/2 eps) (* x (- (* 1/4 (* eps x)) 1)))
(fma.f64 eps (fma.f64 #s(literal 1/4 binary64) (*.f64 x x) #s(literal -1/2 binary64)) (neg.f64 x))
(+ (* -1/2 eps) (* x (- (* x (+ (* 1/6 x) (* 1/4 eps))) 1)))
(fma.f64 x (fma.f64 x (fma.f64 eps #s(literal 1/4 binary64) (.f64 x #s(literal 1/6 binary64))) #s(literal -1 binary64)) (.f64 eps #s(literal -1/2 binary64)))
(- (* -1/2 (* eps (cos x))) (sin x))
(-.f64 (.f64 #s(literal -1/2 binary64) (.f64 eps (cos.f64 x))) (sin.f64 x))
(- (* -1/2 (* eps (cos x))) (sin x))
(-.f64 (.f64 #s(literal -1/2 binary64) (.f64 eps (cos.f64 x))) (sin.f64 x))
(- (* -1/2 (* eps (cos x))) (sin x))
(-.f64 (.f64 #s(literal -1/2 binary64) (.f64 eps (cos.f64 x))) (sin.f64 x))
(- (* -1/2 (* eps (cos x))) (sin x))
(-.f64 (.f64 #s(literal -1/2 binary64) (.f64 eps (cos.f64 x))) (sin.f64 x))
(- (* -1/2 (* eps (cos x))) (sin x))
(-.f64 (.f64 #s(literal -1/2 binary64) (.f64 eps (cos.f64 x))) (sin.f64 x))
(- (* -1/2 (* eps (cos x))) (sin x))
(-.f64 (.f64 #s(literal -1/2 binary64) (.f64 eps (cos.f64 x))) (sin.f64 x))
(- (* -1/2 (* eps (cos x))) (sin x))
(-.f64 (.f64 #s(literal -1/2 binary64) (.f64 eps (cos.f64 x))) (sin.f64 x))
(- (* -1/2 (* eps (cos x))) (sin x))
(-.f64 (.f64 #s(literal -1/2 binary64) (.f64 eps (cos.f64 x))) (sin.f64 x))
(* -1/2 (* eps (cos x)))
(.f64 #s(literal -1/2 binary64) (.f64 eps (cos.f64 x)))
(* -1/2 (* eps (cos x)))
(.f64 #s(literal -1/2 binary64) (.f64 eps (cos.f64 x)))
(* -1/2 (* eps (cos x)))
(.f64 #s(literal -1/2 binary64) (.f64 eps (cos.f64 x)))
(* -1/2 (* eps (cos x)))
(.f64 #s(literal -1/2 binary64) (.f64 eps (cos.f64 x)))
(* -1/2 (* eps (cos x)))
(.f64 #s(literal -1/2 binary64) (.f64 eps (cos.f64 x)))
(* -1/2 (* eps (cos x)))
(.f64 #s(literal -1/2 binary64) (.f64 eps (cos.f64 x)))
(* -1/2 (* eps (cos x)))
(.f64 #s(literal -1/2 binary64) (.f64 eps (cos.f64 x)))
(* -1/2 (* eps (cos x)))
(.f64 #s(literal -1/2 binary64) (.f64 eps (cos.f64 x)))
(* -1/2 (* eps (cos x)))
(.f64 #s(literal -1/2 binary64) (.f64 eps (cos.f64 x)))
(* -1/2 (* eps (cos x)))
(.f64 #s(literal -1/2 binary64) (.f64 eps (cos.f64 x)))
(* -1/2 (* eps (cos x)))
(.f64 #s(literal -1/2 binary64) (.f64 eps (cos.f64 x)))
(* -1/2 (* eps (cos x)))
(.f64 #s(literal -1/2 binary64) (.f64 eps (cos.f64 x)))
(* -1/2 eps)
(*.f64 eps #s(literal -1/2 binary64))
(+ (* -1/2 eps) (* 1/4 (* eps (pow x 2))))
(.f64 eps (fma.f64 #s(literal 1/4 binary64) (.f64 x x) #s(literal -1/2 binary64)))
(+ (* -1/2 eps) (* (pow x 2) (+ (* -1/48 (* eps (pow x 2))) (* 1/4 eps))))
(fma.f64 x (.f64 x (.f64 eps (fma.f64 (.f64 x x) #s(literal -1/48 binary64) #s(literal 1/4 binary64)))) (.f64 eps #s(literal -1/2 binary64)))
(+ (* -1/2 eps) (* (pow x 2) (+ (* 1/4 eps) (* (pow x 2) (+ (* -1/48 eps) (* 1/1440 (* eps (pow x 2))))))))
(fma.f64 (.f64 x x) (fma.f64 (.f64 x (.f64 eps x)) (fma.f64 (.f64 x x) #s(literal 1/1440 binary64) #s(literal -1/48 binary64)) (.f64 eps #s(literal 1/4 binary64))) (.f64 eps #s(literal -1/2 binary64)))
(* -1/2 (* eps (cos x)))
(.f64 #s(literal -1/2 binary64) (.f64 eps (cos.f64 x)))
(* -1/2 (* eps (cos x)))
(.f64 #s(literal -1/2 binary64) (.f64 eps (cos.f64 x)))
(* -1/2 (* eps (cos x)))
(.f64 #s(literal -1/2 binary64) (.f64 eps (cos.f64 x)))
(* -1/2 (* eps (cos x)))
(.f64 #s(literal -1/2 binary64) (.f64 eps (cos.f64 x)))
(* -1/2 (* eps (cos x)))
(.f64 #s(literal -1/2 binary64) (.f64 eps (cos.f64 x)))
(* -1/2 (* eps (cos x)))
(.f64 #s(literal -1/2 binary64) (.f64 eps (cos.f64 x)))
(* -1/2 (* eps (cos x)))
(.f64 #s(literal -1/2 binary64) (.f64 eps (cos.f64 x)))
(* -1/2 (* eps (cos x)))
(.f64 #s(literal -1/2 binary64) (.f64 eps (cos.f64 x)))
(- (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)
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(fma.f64 (.f64 x x) (.f64 x (fma.f64 (.f64 x x) (fma.f64 x (.f64 x #s(literal -1/5040 binary64)) #s(literal 1/120 binary64)) #s(literal -1/6 binary64))) x)
(sin x)
(sin.f64 x)
(sin x)
(sin.f64 x)
(sin x)
(sin.f64 x)
(sin x)
(sin.f64 x)
(sin x)
(sin.f64 x)
(sin x)
(sin.f64 x)
(sin x)
(sin.f64 x)
(sin x)
(sin.f64 x)
(* -1 eps)
(neg.f64 eps)
(* -1 eps)
(neg.f64 eps)
(* -1 eps)
(neg.f64 eps)
(* -1 eps)
(neg.f64 eps)
(* -1 eps)
(neg.f64 eps)
(* -1 eps)
(neg.f64 eps)
(* -1 eps)
(neg.f64 eps)
(* -1 eps)
(neg.f64 eps)
(* -1 eps)
(neg.f64 eps)
(* -1 eps)
(neg.f64 eps)
(* -1 eps)
(neg.f64 eps)
(* -1 eps)
(neg.f64 eps)
(- (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)
(fma.f64 x (fma.f64 x (fma.f64 (cos.f64 eps) #s(literal -1/2 binary64) #s(literal 1/2 binary64)) (sin.f64 (neg.f64 eps))) (+.f64 (cos.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 (cos.f64 eps) (fma.f64 x (fma.f64 x (fma.f64 (cos.f64 eps) #s(literal -1/2 binary64) #s(literal 1/2 binary64)) (.f64 (sin.f64 eps) (fma.f64 x (.f64 x #s(literal 1/6 binary64)) #s(literal -1 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 #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 (.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 eps (fma.f64 eps (.f64 (cos.f64 x) #s(literal 1/24 binary64)) (.f64 #s(literal 1/6 binary64) (sin.f64 x))) (.f64 #s(literal -1/2 binary64) (cos.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))
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 (*.f64 x 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)
(* -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))

rewrite246.0ms (1.5%)

Memory

-23.4MiB live, 278.7MiB allocated

Rules

5 732×	`lower-fma.f32`
5 730×	`lower-fma.f64`
4 350×	`lower-*.f32`
4 340×	`lower-*.f64`
3 902×	`lower-/.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	30	131
0	48	131
1	169	131
2	1105	131
0	8460	131

Stop Event

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

Counts

18 → 325

Calls

Call 1

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

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

eval83.0ms (0.5%)

Memory: -9.9MiB live, 108.0MiB allocated
Compiler: Compiled 19 074 to 1 345 computations (92.9% saved)

prune90.0ms (0.5%)

Memory

-3.9MiB live, 159.2MiB allocated

Pruning

23 alts after pruning (21 fresh and 2 done)

	Pruned	Kept	Total
New	769	20	789
Fresh	0	1	1
Picked	3	2	5
Done	0	0	0
Total	772	23	795

Accuracy

100.0%

Counts

795 → 23

Alt Table

Click to see full alt table

Status	Accuracy	Program
	99.6%	(.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))
▶	99.8%	#s(approx (- (cos (+ x eps)) (cos x)) (fma.f64 (.f64 (cos.f64 x) (.f64 eps #s(literal -1/2 binary64))) eps (neg.f64 (*.f64 eps (sin.f64 x)))))
	33.0%	#s(approx (- (cos (+ x eps)) (cos x)) (/.f64 (-.f64 (.f64 (.f64 (.f64 (cos.f64 x) (.f64 eps #s(literal -1/2 binary64))) eps) (.f64 (.f64 (cos.f64 x) (.f64 eps #s(literal -1/2 binary64))) eps)) (.f64 (neg.f64 (.f64 eps (sin.f64 x))) (neg.f64 (.f64 eps (sin.f64 x))))) (-.f64 (.f64 (.f64 (cos.f64 x) (.f64 eps #s(literal -1/2 binary64))) eps) (neg.f64 (.f64 eps (sin.f64 x))))))
	35.8%	#s(approx (- (cos (+ x eps)) (cos x)) (/.f64 (.f64 (-.f64 (pow.f64 (.f64 (cos.f64 x) (.f64 eps #s(literal -1/2 binary64))) #s(literal 3 binary64)) (pow.f64 (sin.f64 x) #s(literal 3 binary64))) eps) (fma.f64 (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x)))) (.f64 (.f64 eps eps) #s(literal 1/4 binary64)) (.f64 (sin.f64 x) (fma.f64 eps (.f64 (cos.f64 x) #s(literal -1/2 binary64)) (sin.f64 x))))))
▶	99.7%	#s(approx (- (cos (+ x eps)) (cos x)) (/.f64 eps (/.f64 #s(literal 1 binary64) (-.f64 (.f64 (cos.f64 x) (.f64 eps #s(literal -1/2 binary64))) (sin.f64 x)))))
▶	49.2%	#s(approx (- (cos (+ x eps)) (cos x)) (+.f64 #s(approx (cos eps) #s(literal 1 binary64)) #s(literal -1 binary64)))
	31.6%	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 (.f64 (-.f64 (pow.f64 (.f64 (cos.f64 x) (.f64 eps #s(literal -1/2 binary64))) #s(literal 3 binary64)) (pow.f64 (sin.f64 x) #s(literal 3 binary64))) eps) (/.f64 #s(literal 1 binary64) (fma.f64 (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x)))) (.f64 (.f64 eps eps) #s(literal 1/4 binary64)) (.f64 (sin.f64 x) (fma.f64 eps (*.f64 (cos.f64 x) #s(literal -1/2 binary64)) (sin.f64 x)))))))
	21.2%	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 (sin.f64 x) (.f64 (neg.f64 (.f64 eps (.f64 eps eps))) (/.f64 #s(literal 1 binary64) (fma.f64 eps eps #s(literal 0 binary64))))))
✓	78.4%	#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (sin.f64 x) (neg.f64 eps)))
▶	78.0%	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (sin x) (fma.f64 (.f64 x x) (.f64 x (fma.f64 (.f64 x x) (fma.f64 x (*.f64 x #s(literal -1/5040 binary64)) #s(literal 1/120 binary64)) #s(literal -1/6 binary64))) x)) (neg.f64 eps)))
	77.9%	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (sin x) (fma.f64 x (.f64 x (.f64 x (fma.f64 (.f64 x x) #s(literal 1/120 binary64) #s(literal -1/6 binary64)))) x)) (neg.f64 eps)))
	77.7%	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (sin x) (fma.f64 x (.f64 #s(literal -1/6 binary64) (*.f64 x x)) x)) (neg.f64 eps)))
	42.0%	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps (-.f64 (/.f64 (pow.f64 (.f64 (cos.f64 x) (.f64 eps #s(literal -1/2 binary64))) #s(literal 3 binary64)) (fma.f64 (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x)))) (.f64 (.f64 eps eps) #s(literal 1/4 binary64)) (.f64 (sin.f64 x) (fma.f64 eps (.f64 (cos.f64 x) #s(literal -1/2 binary64)) (sin.f64 x))))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (fma.f64 (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x)))) (.f64 (.f64 eps eps) #s(literal 1/4 binary64)) (.f64 (sin.f64 x) (fma.f64 eps (*.f64 (cos.f64 x) #s(literal -1/2 binary64)) (sin.f64 x))))))))
✓	99.8%	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps (-.f64 (.f64 eps (*.f64 #s(literal -1/2 binary64) (cos.f64 x))) (sin.f64 x))))
	99.6%	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps (-.f64 #s(approx ( eps (* -1/2 (cos x))) (.f64 eps (fma.f64 #s(literal 1/4 binary64) (.f64 x x) #s(literal -1/2 binary64)))) (sin.f64 x))))
	99.6%	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps (-.f64 #s(approx ( eps (* -1/2 (cos x))) (*.f64 eps #s(literal -1/2 binary64))) (sin.f64 x))))
	98.9%	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps #s(approx (- ( eps (* -1/2 (cos x))) (sin x)) (fma.f64 x (fma.f64 x (fma.f64 eps #s(literal 1/4 binary64) (.f64 x #s(literal 1/6 binary64))) #s(literal -1 binary64)) (.f64 eps #s(literal -1/2 binary64))))))
▶	98.4%	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps #s(approx (- ( eps (* -1/2 (cos x))) (sin x)) (fma.f64 eps (fma.f64 #s(literal 1/4 binary64) (*.f64 x x) #s(literal -1/2 binary64)) (neg.f64 x)))))
	98.4%	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps #s(approx (- ( eps (* -1/2 (cos x))) (sin x)) (-.f64 (*.f64 eps #s(literal -1/2 binary64)) x))))
	77.9%	#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (sin x) (neg eps)) (.f64 x (fma.f64 x (.f64 x (.f64 eps (fma.f64 (.f64 x x) #s(literal -1/120 binary64) #s(literal 1/6 binary64)))) (neg.f64 eps)))))
	77.7%	#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (sin x) (neg eps)) (.f64 x (.f64 eps (fma.f64 x (*.f64 x #s(literal 1/6 binary64)) #s(literal -1 binary64))))))
	77.5%	#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (sin x) (neg eps)) (*.f64 eps (neg.f64 x))))
	98.9%	#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* eps (- (* eps (* -1/2 (cos x))) (sin x))) (fma.f64 eps (-.f64 (.f64 eps #s(literal -1/2 binary64)) x) (.f64 x (.f64 x (.f64 eps (fma.f64 eps #s(literal 1/4 binary64) (*.f64 x #s(literal 1/6 binary64)))))))))

Compiler

Compiled 992 to 528 computations (46.8% saved)

simplify251.0ms (1.5%)

Memory

-2.8MiB live, 235.4MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 19 expressions of interest:

New	Metric	Score
cost-diff	0	(-.f64 (.f64 (cos.f64 x) (.f64 eps #s(literal -1/2 binary64))) (sin.f64 x))
cost-diff	0	#s(approx (- (cos (+ x eps)) (cos x)) (/.f64 eps (/.f64 #s(literal 1 binary64) (-.f64 (.f64 (cos.f64 x) (.f64 eps #s(literal -1/2 binary64))) (sin.f64 x)))))
cost-diff	128	(/.f64 #s(literal 1 binary64) (-.f64 (.f64 (cos.f64 x) (.f64 eps #s(literal -1/2 binary64))) (sin.f64 x)))
cost-diff	960	(/.f64 eps (/.f64 #s(literal 1 binary64) (-.f64 (.f64 (cos.f64 x) (.f64 eps #s(literal -1/2 binary64))) (sin.f64 x))))
cost-diff	0	(fma.f64 (.f64 x x) (.f64 x (fma.f64 (.f64 x x) (fma.f64 x (.f64 x #s(literal -1/5040 binary64)) #s(literal 1/120 binary64)) #s(literal -1/6 binary64))) x)
cost-diff	0	#s(approx (sin x) (fma.f64 (.f64 x x) (.f64 x (fma.f64 (.f64 x x) (fma.f64 x (.f64 x #s(literal -1/5040 binary64)) #s(literal 1/120 binary64)) #s(literal -1/6 binary64))) x))
cost-diff	0	(.f64 #s(approx (sin x) (fma.f64 (.f64 x x) (.f64 x (fma.f64 (.f64 x x) (fma.f64 x (*.f64 x #s(literal -1/5040 binary64)) #s(literal 1/120 binary64)) #s(literal -1/6 binary64))) x)) (neg.f64 eps))
cost-diff	0	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (sin x) (fma.f64 (.f64 x x) (.f64 x (fma.f64 (.f64 x x) (fma.f64 x (*.f64 x #s(literal -1/5040 binary64)) #s(literal 1/120 binary64)) #s(literal -1/6 binary64))) x)) (neg.f64 eps)))
cost-diff	0	(fma.f64 eps (fma.f64 #s(literal 1/4 binary64) (*.f64 x x) #s(literal -1/2 binary64)) (neg.f64 x))
cost-diff	0	#s(approx (- (* eps (* -1/2 (cos x))) (sin x)) (fma.f64 eps (fma.f64 #s(literal 1/4 binary64) (*.f64 x x) #s(literal -1/2 binary64)) (neg.f64 x)))
cost-diff	0	(.f64 eps #s(approx (- ( eps (* -1/2 (cos x))) (sin x)) (fma.f64 eps (fma.f64 #s(literal 1/4 binary64) (*.f64 x x) #s(literal -1/2 binary64)) (neg.f64 x))))
cost-diff	0	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps #s(approx (- ( eps (* -1/2 (cos x))) (sin x)) (fma.f64 eps (fma.f64 #s(literal 1/4 binary64) (*.f64 x x) #s(literal -1/2 binary64)) (neg.f64 x)))))
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	(cos.f64 x)
cost-diff	0	(.f64 (cos.f64 x) (.f64 eps #s(literal -1/2 binary64)))
cost-diff	0	#s(approx (- (cos (+ x eps)) (cos x)) (fma.f64 (.f64 (cos.f64 x) (.f64 eps #s(literal -1/2 binary64))) eps (neg.f64 (*.f64 eps (sin.f64 x)))))
cost-diff	320	(fma.f64 (.f64 (cos.f64 x) (.f64 eps #s(literal -1/2 binary64))) eps (neg.f64 (*.f64 eps (sin.f64 x))))

Rules

10 922×	`lower-fma.f32`
10 910×	`lower-fma.f64`
3 410×	`lower-*.f32`
3 394×	`lower-*.f64`
1 740×	`unsub-neg`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	49	391
0	80	391
1	155	383
2	344	379
3	733	379
4	1344	379
5	1926	379
6	2960	379
7	3887	379
8	4873	379
9	6063	379
10	7232	379
11	7563	379
12	7754	379
13	7768	379
0	8042	374

Stop Event

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

Calls

Call 1

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

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

localize313.0ms (1.9%)

Memory

31.6MiB live, 272.3MiB allocated

Localize:

Found 19 expressions of interest:

New	Metric	Score
accuracy	0.00390625	(.f64 (cos.f64 x) (.f64 eps #s(literal -1/2 binary64)))
accuracy	0.012382519536884034	#s(approx (- (cos (+ x eps)) (cos x)) (/.f64 eps (/.f64 #s(literal 1 binary64) (-.f64 (.f64 (cos.f64 x) (.f64 eps #s(literal -1/2 binary64))) (sin.f64 x)))))
accuracy	0.12890625	(/.f64 eps (/.f64 #s(literal 1 binary64) (-.f64 (.f64 (cos.f64 x) (.f64 eps #s(literal -1/2 binary64))) (sin.f64 x))))
accuracy	0.26171875	(/.f64 #s(literal 1 binary64) (-.f64 (.f64 (cos.f64 x) (.f64 eps #s(literal -1/2 binary64))) (sin.f64 x)))
accuracy	0.015625	(*.f64 x #s(literal -1/5040 binary64))
accuracy	0.3203125	(.f64 x (fma.f64 (.f64 x x) (fma.f64 x (*.f64 x #s(literal -1/5040 binary64)) #s(literal 1/120 binary64)) #s(literal -1/6 binary64)))
accuracy	0.35731169473286295	#s(approx (sin x) (fma.f64 (.f64 x x) (.f64 x (fma.f64 (.f64 x x) (fma.f64 x (.f64 x #s(literal -1/5040 binary64)) #s(literal 1/120 binary64)) #s(literal -1/6 binary64))) x))
accuracy	13.84587951907224	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (sin x) (fma.f64 (.f64 x x) (.f64 x (fma.f64 (.f64 x x) (fma.f64 x (*.f64 x #s(literal -1/5040 binary64)) #s(literal 1/120 binary64)) #s(literal -1/6 binary64))) x)) (neg.f64 eps)))
accuracy	0	(neg.f64 x)
accuracy	0.012382519536884034	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps #s(approx (- ( eps (* -1/2 (cos x))) (sin x)) (fma.f64 eps (fma.f64 #s(literal 1/4 binary64) (*.f64 x x) #s(literal -1/2 binary64)) (neg.f64 x)))))
accuracy	0.1171875	(.f64 eps #s(approx (- ( eps (* -1/2 (cos x))) (sin x)) (fma.f64 eps (fma.f64 #s(literal 1/4 binary64) (*.f64 x x) #s(literal -1/2 binary64)) (neg.f64 x))))
accuracy	0.9078141115803069	#s(approx (- (* eps (* -1/2 (cos x))) (sin x)) (fma.f64 eps (fma.f64 #s(literal 1/4 binary64) (*.f64 x x) #s(literal -1/2 binary64)) (neg.f64 x)))
accuracy	0.01953125	#s(approx (cos eps) #s(literal 1 binary64))
accuracy	31.54806368935089	(+.f64 #s(approx (cos eps) #s(literal 1 binary64)) #s(literal -1 binary64))
accuracy	31.631218050216862	#s(approx (- (cos (+ x eps)) (cos x)) (+.f64 #s(approx (cos eps) #s(literal 1 binary64)) #s(literal -1 binary64)))
accuracy	0.00390625	(.f64 (cos.f64 x) (.f64 eps #s(literal -1/2 binary64)))
accuracy	0.0078125	(*.f64 eps (sin.f64 x))
accuracy	0.012382519536884034	#s(approx (- (cos (+ x eps)) (cos x)) (fma.f64 (.f64 (cos.f64 x) (.f64 eps #s(literal -1/2 binary64))) eps (neg.f64 (*.f64 eps (sin.f64 x)))))
accuracy	0.1328125	(fma.f64 (.f64 (cos.f64 x) (.f64 eps #s(literal -1/2 binary64))) eps (neg.f64 (*.f64 eps (sin.f64 x))))

Samples

202.0ms	171×	2	valid
54.0ms	85×	1	valid

Compiler

Compiled 258 to 47 computations (81.8% saved)

Precisions

Click to see histograms. Total time spent on operations: 211.0ms

ival-cos: 73.0ms (34.6% of total)

ival-mult: 43.0ms (20.4% of total)

adjust: 35.0ms (16.6% of total)

ival-add: 15.0ms (7.1% of total)

const: 14.0ms (6.6% of total)

ival-sin: 10.0ms (4.7% of total)

ival-div: 8.0ms (3.8% of total)

ival-sub: 8.0ms (3.8% of total)

ival-neg: 4.0ms (1.9% of total)

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

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

exact: 0.0ms (0% of total)

series31.0ms (0.2%)

Memory

-23.2MiB live, 14.7MiB allocated

Counts

23 → 456

Calls

Call 1

Inputs
#s(alt (fma.f64 (.f64 (cos.f64 x) (.f64 eps #s(literal -1/2 binary64))) eps (neg.f64 (.f64 eps (sin.f64 x)))) (patch (fma.f64 (.f64 (cos.f64 x) (.f64 eps #s(literal -1/2 binary64))) eps (neg.f64 (.f64 eps (sin.f64 x)))) #<representation binary64>) () ())
#s(alt #s(approx (- (cos (+ x eps)) (cos x)) (fma.f64 (.f64 (cos.f64 x) (.f64 eps #s(literal -1/2 binary64))) eps (neg.f64 (.f64 eps (sin.f64 x))))) (patch #s(approx (- (cos (+ x eps)) (cos x)) (fma.f64 (.f64 (cos.f64 x) (.f64 eps #s(literal -1/2 binary64))) eps (neg.f64 (.f64 eps (sin.f64 x))))) #<representation binary64>) () ())
#s(alt (.f64 (cos.f64 x) (.f64 eps #s(literal -1/2 binary64))) (patch (.f64 (cos.f64 x) (.f64 eps #s(literal -1/2 binary64))) #<representation binary64>) () ())
#s(alt (cos.f64 x) (patch (cos.f64 x) #<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 #s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps #s(approx (- ( eps (* -1/2 (cos x))) (sin x)) (fma.f64 eps (fma.f64 #s(literal 1/4 binary64) (.f64 x x) #s(literal -1/2 binary64)) (neg.f64 x))))) (patch #s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps #s(approx (- (* eps (* -1/2 (cos x))) (sin x)) (fma.f64 eps (fma.f64 #s(literal 1/4 binary64) (*.f64 x x) #s(literal -1/2 binary64)) (neg.f64 x))))) #<representation binary64>) () ())
#s(alt (.f64 eps #s(approx (- ( eps (* -1/2 (cos x))) (sin x)) (fma.f64 eps (fma.f64 #s(literal 1/4 binary64) (.f64 x x) #s(literal -1/2 binary64)) (neg.f64 x)))) (patch (.f64 eps #s(approx (- (* eps (* -1/2 (cos x))) (sin x)) (fma.f64 eps (fma.f64 #s(literal 1/4 binary64) (*.f64 x x) #s(literal -1/2 binary64)) (neg.f64 x)))) #<representation binary64>) () ())
#s(alt #s(approx (- (* eps (* -1/2 (cos x))) (sin x)) (fma.f64 eps (fma.f64 #s(literal 1/4 binary64) (.f64 x x) #s(literal -1/2 binary64)) (neg.f64 x))) (patch #s(approx (- ( eps (* -1/2 (cos x))) (sin x)) (fma.f64 eps (fma.f64 #s(literal 1/4 binary64) (*.f64 x x) #s(literal -1/2 binary64)) (neg.f64 x))) #<representation binary64>) () ())
#s(alt (fma.f64 eps (fma.f64 #s(literal 1/4 binary64) (.f64 x x) #s(literal -1/2 binary64)) (neg.f64 x)) (patch (fma.f64 eps (fma.f64 #s(literal 1/4 binary64) (.f64 x x) #s(literal -1/2 binary64)) (neg.f64 x)) #<representation binary64>) () ())
#s(alt #s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (sin x) (fma.f64 (.f64 x x) (.f64 x (fma.f64 (.f64 x x) (fma.f64 x (.f64 x #s(literal -1/5040 binary64)) #s(literal 1/120 binary64)) #s(literal -1/6 binary64))) x)) (neg.f64 eps))) (patch #s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (sin x) (fma.f64 (.f64 x x) (.f64 x (fma.f64 (.f64 x x) (fma.f64 x (.f64 x #s(literal -1/5040 binary64)) #s(literal 1/120 binary64)) #s(literal -1/6 binary64))) x)) (neg.f64 eps))) #<representation binary64>) () ())
#s(alt (.f64 #s(approx (sin x) (fma.f64 (.f64 x x) (.f64 x (fma.f64 (.f64 x x) (fma.f64 x (.f64 x #s(literal -1/5040 binary64)) #s(literal 1/120 binary64)) #s(literal -1/6 binary64))) x)) (neg.f64 eps)) (patch (.f64 #s(approx (sin x) (fma.f64 (.f64 x x) (.f64 x (fma.f64 (.f64 x x) (fma.f64 x (.f64 x #s(literal -1/5040 binary64)) #s(literal 1/120 binary64)) #s(literal -1/6 binary64))) x)) (neg.f64 eps)) #<representation binary64>) () ())
#s(alt #s(approx (sin x) (fma.f64 (.f64 x x) (.f64 x (fma.f64 (.f64 x x) (fma.f64 x (.f64 x #s(literal -1/5040 binary64)) #s(literal 1/120 binary64)) #s(literal -1/6 binary64))) x)) (patch #s(approx (sin x) (fma.f64 (.f64 x x) (.f64 x (fma.f64 (.f64 x x) (fma.f64 x (.f64 x #s(literal -1/5040 binary64)) #s(literal 1/120 binary64)) #s(literal -1/6 binary64))) x)) #<representation binary64>) () ())
#s(alt (fma.f64 (.f64 x x) (.f64 x (fma.f64 (.f64 x x) (fma.f64 x (.f64 x #s(literal -1/5040 binary64)) #s(literal 1/120 binary64)) #s(literal -1/6 binary64))) x) (patch (fma.f64 (.f64 x x) (.f64 x (fma.f64 (.f64 x x) (fma.f64 x (.f64 x #s(literal -1/5040 binary64)) #s(literal 1/120 binary64)) #s(literal -1/6 binary64))) x) #<representation binary64>) () ())
#s(alt (/.f64 eps (/.f64 #s(literal 1 binary64) (-.f64 (.f64 (cos.f64 x) (.f64 eps #s(literal -1/2 binary64))) (sin.f64 x)))) (patch (/.f64 eps (/.f64 #s(literal 1 binary64) (-.f64 (.f64 (cos.f64 x) (.f64 eps #s(literal -1/2 binary64))) (sin.f64 x)))) #<representation binary64>) () ())
#s(alt (/.f64 #s(literal 1 binary64) (-.f64 (.f64 (cos.f64 x) (.f64 eps #s(literal -1/2 binary64))) (sin.f64 x))) (patch (/.f64 #s(literal 1 binary64) (-.f64 (.f64 (cos.f64 x) (.f64 eps #s(literal -1/2 binary64))) (sin.f64 x))) #<representation binary64>) () ())
#s(alt #s(approx (- (cos (+ x eps)) (cos x)) (/.f64 eps (/.f64 #s(literal 1 binary64) (-.f64 (.f64 (cos.f64 x) (.f64 eps #s(literal -1/2 binary64))) (sin.f64 x))))) (patch #s(approx (- (cos (+ x eps)) (cos x)) (/.f64 eps (/.f64 #s(literal 1 binary64) (-.f64 (.f64 (cos.f64 x) (.f64 eps #s(literal -1/2 binary64))) (sin.f64 x))))) #<representation binary64>) () ())
#s(alt (-.f64 (.f64 (cos.f64 x) (.f64 eps #s(literal -1/2 binary64))) (sin.f64 x)) (patch (-.f64 (.f64 (cos.f64 x) (.f64 eps #s(literal -1/2 binary64))) (sin.f64 x)) #<representation binary64>) () ())
#s(alt (.f64 eps (sin.f64 x)) (patch (.f64 eps (sin.f64 x)) #<representation binary64>) () ())
#s(alt (neg.f64 x) (patch (neg.f64 x) #<representation binary64>) () ())
#s(alt (.f64 x (fma.f64 (.f64 x x) (fma.f64 x (.f64 x #s(literal -1/5040 binary64)) #s(literal 1/120 binary64)) #s(literal -1/6 binary64))) (patch (.f64 x (fma.f64 (.f64 x x) (fma.f64 x (.f64 x #s(literal -1/5040 binary64)) #s(literal 1/120 binary64)) #s(literal -1/6 binary64))) #<representation binary64>) () ())
#s(alt (.f64 x #s(literal -1/5040 binary64)) (patch (.f64 x #s(literal -1/5040 binary64)) #<representation binary64>) () ())

Outputs
#s(alt (* -1/2 (pow eps 2)) (taylor 0 x) (#s(alt (fma.f64 (.f64 (cos.f64 x) (.f64 eps #s(literal -1/2 binary64))) eps (neg.f64 (.f64 eps (sin.f64 x)))) (patch (fma.f64 (.f64 (cos.f64 x) (.f64 eps #s(literal -1/2 binary64))) eps (neg.f64 (.f64 eps (sin.f64 x)))) #<representation binary64>) () ())) ())
#s(alt (+ (* -1 (* eps x)) (* -1/2 (pow eps 2))) (taylor 0 x) (#s(alt (fma.f64 (.f64 (cos.f64 x) (.f64 eps #s(literal -1/2 binary64))) eps (neg.f64 (.f64 eps (sin.f64 x)))) (patch (fma.f64 (.f64 (cos.f64 x) (.f64 eps #s(literal -1/2 binary64))) eps (neg.f64 (.f64 eps (sin.f64 x)))) #<representation binary64>) () ())) ())
#s(alt (+ (* -1/2 (pow eps 2)) (* x (- (* 1/4 (* (pow eps 2) x)) eps))) (taylor 0 x) (#s(alt (fma.f64 (.f64 (cos.f64 x) (.f64 eps #s(literal -1/2 binary64))) eps (neg.f64 (.f64 eps (sin.f64 x)))) (patch (fma.f64 (.f64 (cos.f64 x) (.f64 eps #s(literal -1/2 binary64))) eps (neg.f64 (.f64 eps (sin.f64 x)))) #<representation binary64>) () ())) ())
#s(alt (+ (* -1/2 (pow eps 2)) (* x (- (* x (+ (* 1/6 (* eps x)) (* 1/4 (pow eps 2)))) eps))) (taylor 0 x) (#s(alt (fma.f64 (.f64 (cos.f64 x) (.f64 eps #s(literal -1/2 binary64))) eps (neg.f64 (.f64 eps (sin.f64 x)))) (patch (fma.f64 (.f64 (cos.f64 x) (.f64 eps #s(literal -1/2 binary64))) eps (neg.f64 (.f64 eps (sin.f64 x)))) #<representation binary64>) () ())) ())
#s(alt (- (* -1/2 (* (pow eps 2) (cos x))) (* eps (sin x))) (taylor inf x) (#s(alt (fma.f64 (.f64 (cos.f64 x) (.f64 eps #s(literal -1/2 binary64))) eps (neg.f64 (.f64 eps (sin.f64 x)))) (patch (fma.f64 (.f64 (cos.f64 x) (.f64 eps #s(literal -1/2 binary64))) eps (neg.f64 (.f64 eps (sin.f64 x)))) #<representation binary64>) () ())) ())
#s(alt (- (* -1/2 (* (pow eps 2) (cos x))) (* eps (sin x))) (taylor inf x) (#s(alt (fma.f64 (.f64 (cos.f64 x) (.f64 eps #s(literal -1/2 binary64))) eps (neg.f64 (.f64 eps (sin.f64 x)))) (patch (fma.f64 (.f64 (cos.f64 x) (.f64 eps #s(literal -1/2 binary64))) eps (neg.f64 (.f64 eps (sin.f64 x)))) #<representation binary64>) () ())) ())
#s(alt (- (* -1/2 (* (pow eps 2) (cos x))) (* eps (sin x))) (taylor inf x) (#s(alt (fma.f64 (.f64 (cos.f64 x) (.f64 eps #s(literal -1/2 binary64))) eps (neg.f64 (.f64 eps (sin.f64 x)))) (patch (fma.f64 (.f64 (cos.f64 x) (.f64 eps #s(literal -1/2 binary64))) eps (neg.f64 (.f64 eps (sin.f64 x)))) #<representation binary64>) () ())) ())
#s(alt (- (* -1/2 (* (pow eps 2) (cos x))) (* eps (sin x))) (taylor inf x) (#s(alt (fma.f64 (.f64 (cos.f64 x) (.f64 eps #s(literal -1/2 binary64))) eps (neg.f64 (.f64 eps (sin.f64 x)))) (patch (fma.f64 (.f64 (cos.f64 x) (.f64 eps #s(literal -1/2 binary64))) eps (neg.f64 (.f64 eps (sin.f64 x)))) #<representation binary64>) () ())) ())
#s(alt (- (* -1/2 (* (pow eps 2) (cos x))) (* eps (sin x))) (taylor -inf x) (#s(alt (fma.f64 (.f64 (cos.f64 x) (.f64 eps #s(literal -1/2 binary64))) eps (neg.f64 (.f64 eps (sin.f64 x)))) (patch (fma.f64 (.f64 (cos.f64 x) (.f64 eps #s(literal -1/2 binary64))) eps (neg.f64 (.f64 eps (sin.f64 x)))) #<representation binary64>) () ())) ())
#s(alt (- (* -1/2 (* (pow eps 2) (cos x))) (* eps (sin x))) (taylor -inf x) (#s(alt (fma.f64 (.f64 (cos.f64 x) (.f64 eps #s(literal -1/2 binary64))) eps (neg.f64 (.f64 eps (sin.f64 x)))) (patch (fma.f64 (.f64 (cos.f64 x) (.f64 eps #s(literal -1/2 binary64))) eps (neg.f64 (.f64 eps (sin.f64 x)))) #<representation binary64>) () ())) ())
#s(alt (- (* -1/2 (* (pow eps 2) (cos x))) (* eps (sin x))) (taylor -inf x) (#s(alt (fma.f64 (.f64 (cos.f64 x) (.f64 eps #s(literal -1/2 binary64))) eps (neg.f64 (.f64 eps (sin.f64 x)))) (patch (fma.f64 (.f64 (cos.f64 x) (.f64 eps #s(literal -1/2 binary64))) eps (neg.f64 (.f64 eps (sin.f64 x)))) #<representation binary64>) () ())) ())
#s(alt (- (* -1/2 (* (pow eps 2) (cos x))) (* eps (sin x))) (taylor -inf x) (#s(alt (fma.f64 (.f64 (cos.f64 x) (.f64 eps #s(literal -1/2 binary64))) eps (neg.f64 (.f64 eps (sin.f64 x)))) (patch (fma.f64 (.f64 (cos.f64 x) (.f64 eps #s(literal -1/2 binary64))) eps (neg.f64 (.f64 eps (sin.f64 x)))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* eps (sin x))) (taylor 0 eps) (#s(alt (fma.f64 (.f64 (cos.f64 x) (.f64 eps #s(literal -1/2 binary64))) eps (neg.f64 (.f64 eps (sin.f64 x)))) (patch (fma.f64 (.f64 (cos.f64 x) (.f64 eps #s(literal -1/2 binary64))) eps (neg.f64 (.f64 eps (sin.f64 x)))) #<representation binary64>) () ())) ())
#s(alt (* eps (- (* -1/2 (* eps (cos x))) (sin x))) (taylor 0 eps) (#s(alt (fma.f64 (.f64 (cos.f64 x) (.f64 eps #s(literal -1/2 binary64))) eps (neg.f64 (.f64 eps (sin.f64 x)))) (patch (fma.f64 (.f64 (cos.f64 x) (.f64 eps #s(literal -1/2 binary64))) eps (neg.f64 (.f64 eps (sin.f64 x)))) #<representation binary64>) () ())) ())
#s(alt (* eps (- (* -1/2 (* eps (cos x))) (sin x))) (taylor 0 eps) (#s(alt (fma.f64 (.f64 (cos.f64 x) (.f64 eps #s(literal -1/2 binary64))) eps (neg.f64 (.f64 eps (sin.f64 x)))) (patch (fma.f64 (.f64 (cos.f64 x) (.f64 eps #s(literal -1/2 binary64))) eps (neg.f64 (.f64 eps (sin.f64 x)))) #<representation binary64>) () ())) ())
#s(alt (* eps (- (* -1/2 (* eps (cos x))) (sin x))) (taylor 0 eps) (#s(alt (fma.f64 (.f64 (cos.f64 x) (.f64 eps #s(literal -1/2 binary64))) eps (neg.f64 (.f64 eps (sin.f64 x)))) (patch (fma.f64 (.f64 (cos.f64 x) (.f64 eps #s(literal -1/2 binary64))) eps (neg.f64 (.f64 eps (sin.f64 x)))) #<representation binary64>) () ())) ())
#s(alt (* -1/2 (* (pow eps 2) (cos x))) (taylor inf eps) (#s(alt (fma.f64 (.f64 (cos.f64 x) (.f64 eps #s(literal -1/2 binary64))) eps (neg.f64 (.f64 eps (sin.f64 x)))) (patch (fma.f64 (.f64 (cos.f64 x) (.f64 eps #s(literal -1/2 binary64))) eps (neg.f64 (.f64 eps (sin.f64 x)))) #<representation binary64>) () ())) ())
#s(alt (* (pow eps 2) (+ (* -1 (/ (sin x) eps)) (* -1/2 (cos x)))) (taylor inf eps) (#s(alt (fma.f64 (.f64 (cos.f64 x) (.f64 eps #s(literal -1/2 binary64))) eps (neg.f64 (.f64 eps (sin.f64 x)))) (patch (fma.f64 (.f64 (cos.f64 x) (.f64 eps #s(literal -1/2 binary64))) eps (neg.f64 (.f64 eps (sin.f64 x)))) #<representation binary64>) () ())) ())
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#s(alt (- (* -1/2 (* eps (cos x))) (sin x)) (taylor inf x) (#s(alt (-.f64 (.f64 (cos.f64 x) (.f64 eps #s(literal -1/2 binary64))) (sin.f64 x)) (patch (-.f64 (.f64 (cos.f64 x) (.f64 eps #s(literal -1/2 binary64))) (sin.f64 x)) #<representation binary64>) () ())) ())
#s(alt (- (* -1/2 (* eps (cos x))) (sin x)) (taylor -inf x) (#s(alt (-.f64 (.f64 (cos.f64 x) (.f64 eps #s(literal -1/2 binary64))) (sin.f64 x)) (patch (-.f64 (.f64 (cos.f64 x) (.f64 eps #s(literal -1/2 binary64))) (sin.f64 x)) #<representation binary64>) () ())) ())
#s(alt (- (* -1/2 (* eps (cos x))) (sin x)) (taylor -inf x) (#s(alt (-.f64 (.f64 (cos.f64 x) (.f64 eps #s(literal -1/2 binary64))) (sin.f64 x)) (patch (-.f64 (.f64 (cos.f64 x) (.f64 eps #s(literal -1/2 binary64))) (sin.f64 x)) #<representation binary64>) () ())) ())
#s(alt (- (* -1/2 (* eps (cos x))) (sin x)) (taylor -inf x) (#s(alt (-.f64 (.f64 (cos.f64 x) (.f64 eps #s(literal -1/2 binary64))) (sin.f64 x)) (patch (-.f64 (.f64 (cos.f64 x) (.f64 eps #s(literal -1/2 binary64))) (sin.f64 x)) #<representation binary64>) () ())) ())
#s(alt (- (* -1/2 (* eps (cos x))) (sin x)) (taylor -inf x) (#s(alt (-.f64 (.f64 (cos.f64 x) (.f64 eps #s(literal -1/2 binary64))) (sin.f64 x)) (patch (-.f64 (.f64 (cos.f64 x) (.f64 eps #s(literal -1/2 binary64))) (sin.f64 x)) #<representation binary64>) () ())) ())
#s(alt (* -1 (sin x)) (taylor 0 eps) (#s(alt (-.f64 (.f64 (cos.f64 x) (.f64 eps #s(literal -1/2 binary64))) (sin.f64 x)) (patch (-.f64 (.f64 (cos.f64 x) (.f64 eps #s(literal -1/2 binary64))) (sin.f64 x)) #<representation binary64>) () ())) ())
#s(alt (- (* -1/2 (* eps (cos x))) (sin x)) (taylor 0 eps) (#s(alt (-.f64 (.f64 (cos.f64 x) (.f64 eps #s(literal -1/2 binary64))) (sin.f64 x)) (patch (-.f64 (.f64 (cos.f64 x) (.f64 eps #s(literal -1/2 binary64))) (sin.f64 x)) #<representation binary64>) () ())) ())
#s(alt (- (* -1/2 (* eps (cos x))) (sin x)) (taylor 0 eps) (#s(alt (-.f64 (.f64 (cos.f64 x) (.f64 eps #s(literal -1/2 binary64))) (sin.f64 x)) (patch (-.f64 (.f64 (cos.f64 x) (.f64 eps #s(literal -1/2 binary64))) (sin.f64 x)) #<representation binary64>) () ())) ())
#s(alt (- (* -1/2 (* eps (cos x))) (sin x)) (taylor 0 eps) (#s(alt (-.f64 (.f64 (cos.f64 x) (.f64 eps #s(literal -1/2 binary64))) (sin.f64 x)) (patch (-.f64 (.f64 (cos.f64 x) (.f64 eps #s(literal -1/2 binary64))) (sin.f64 x)) #<representation binary64>) () ())) ())
#s(alt (* -1/2 (* eps (cos x))) (taylor inf eps) (#s(alt (-.f64 (.f64 (cos.f64 x) (.f64 eps #s(literal -1/2 binary64))) (sin.f64 x)) (patch (-.f64 (.f64 (cos.f64 x) (.f64 eps #s(literal -1/2 binary64))) (sin.f64 x)) #<representation binary64>) () ())) ())
#s(alt (* eps (+ (* -1 (/ (sin x) eps)) (* -1/2 (cos x)))) (taylor inf eps) (#s(alt (-.f64 (.f64 (cos.f64 x) (.f64 eps #s(literal -1/2 binary64))) (sin.f64 x)) (patch (-.f64 (.f64 (cos.f64 x) (.f64 eps #s(literal -1/2 binary64))) (sin.f64 x)) #<representation binary64>) () ())) ())
#s(alt (* eps (+ (* -1 (/ (sin x) eps)) (* -1/2 (cos x)))) (taylor inf eps) (#s(alt (-.f64 (.f64 (cos.f64 x) (.f64 eps #s(literal -1/2 binary64))) (sin.f64 x)) (patch (-.f64 (.f64 (cos.f64 x) (.f64 eps #s(literal -1/2 binary64))) (sin.f64 x)) #<representation binary64>) () ())) ())
#s(alt (* eps (+ (* -1 (/ (sin x) eps)) (* -1/2 (cos x)))) (taylor inf eps) (#s(alt (-.f64 (.f64 (cos.f64 x) (.f64 eps #s(literal -1/2 binary64))) (sin.f64 x)) (patch (-.f64 (.f64 (cos.f64 x) (.f64 eps #s(literal -1/2 binary64))) (sin.f64 x)) #<representation binary64>) () ())) ())
#s(alt (* -1/2 (* eps (cos x))) (taylor -inf eps) (#s(alt (-.f64 (.f64 (cos.f64 x) (.f64 eps #s(literal -1/2 binary64))) (sin.f64 x)) (patch (-.f64 (.f64 (cos.f64 x) (.f64 eps #s(literal -1/2 binary64))) (sin.f64 x)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* eps (+ (* 1/2 (cos x)) (/ (sin x) eps)))) (taylor -inf eps) (#s(alt (-.f64 (.f64 (cos.f64 x) (.f64 eps #s(literal -1/2 binary64))) (sin.f64 x)) (patch (-.f64 (.f64 (cos.f64 x) (.f64 eps #s(literal -1/2 binary64))) (sin.f64 x)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* eps (+ (* 1/2 (cos x)) (/ (sin x) eps)))) (taylor -inf eps) (#s(alt (-.f64 (.f64 (cos.f64 x) (.f64 eps #s(literal -1/2 binary64))) (sin.f64 x)) (patch (-.f64 (.f64 (cos.f64 x) (.f64 eps #s(literal -1/2 binary64))) (sin.f64 x)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* eps (+ (* 1/2 (cos x)) (/ (sin x) eps)))) (taylor -inf eps) (#s(alt (-.f64 (.f64 (cos.f64 x) (.f64 eps #s(literal -1/2 binary64))) (sin.f64 x)) (patch (-.f64 (.f64 (cos.f64 x) (.f64 eps #s(literal -1/2 binary64))) (sin.f64 x)) #<representation binary64>) () ())) ())
#s(alt (* eps (sin x)) (taylor 0 eps) (#s(alt (.f64 eps (sin.f64 x)) (patch (.f64 eps (sin.f64 x)) #<representation binary64>) () ())) ())
#s(alt (* eps (sin x)) (taylor 0 eps) (#s(alt (.f64 eps (sin.f64 x)) (patch (.f64 eps (sin.f64 x)) #<representation binary64>) () ())) ())
#s(alt (* eps (sin x)) (taylor 0 eps) (#s(alt (.f64 eps (sin.f64 x)) (patch (.f64 eps (sin.f64 x)) #<representation binary64>) () ())) ())
#s(alt (* eps (sin x)) (taylor 0 eps) (#s(alt (.f64 eps (sin.f64 x)) (patch (.f64 eps (sin.f64 x)) #<representation binary64>) () ())) ())
#s(alt (* eps (sin x)) (taylor inf eps) (#s(alt (.f64 eps (sin.f64 x)) (patch (.f64 eps (sin.f64 x)) #<representation binary64>) () ())) ())
#s(alt (* eps (sin x)) (taylor inf eps) (#s(alt (.f64 eps (sin.f64 x)) (patch (.f64 eps (sin.f64 x)) #<representation binary64>) () ())) ())
#s(alt (* eps (sin x)) (taylor inf eps) (#s(alt (.f64 eps (sin.f64 x)) (patch (.f64 eps (sin.f64 x)) #<representation binary64>) () ())) ())
#s(alt (* eps (sin x)) (taylor inf eps) (#s(alt (.f64 eps (sin.f64 x)) (patch (.f64 eps (sin.f64 x)) #<representation binary64>) () ())) ())
#s(alt (* eps (sin x)) (taylor -inf eps) (#s(alt (.f64 eps (sin.f64 x)) (patch (.f64 eps (sin.f64 x)) #<representation binary64>) () ())) ())
#s(alt (* eps (sin x)) (taylor -inf eps) (#s(alt (.f64 eps (sin.f64 x)) (patch (.f64 eps (sin.f64 x)) #<representation binary64>) () ())) ())
#s(alt (* eps (sin x)) (taylor -inf eps) (#s(alt (.f64 eps (sin.f64 x)) (patch (.f64 eps (sin.f64 x)) #<representation binary64>) () ())) ())
#s(alt (* eps (sin x)) (taylor -inf eps) (#s(alt (.f64 eps (sin.f64 x)) (patch (.f64 eps (sin.f64 x)) #<representation binary64>) () ())) ())
#s(alt (* eps x) (taylor 0 x) (#s(alt (.f64 eps (sin.f64 x)) (patch (.f64 eps (sin.f64 x)) #<representation binary64>) () ())) ())
#s(alt (* x (+ eps (* -1/6 (* eps (pow x 2))))) (taylor 0 x) (#s(alt (.f64 eps (sin.f64 x)) (patch (.f64 eps (sin.f64 x)) #<representation binary64>) () ())) ())
#s(alt (* x (+ eps (* (pow x 2) (+ (* -1/6 eps) (* 1/120 (* eps (pow x 2))))))) (taylor 0 x) (#s(alt (.f64 eps (sin.f64 x)) (patch (.f64 eps (sin.f64 x)) #<representation binary64>) () ())) ())
#s(alt (* x (+ eps (* (pow x 2) (+ (* -1/6 eps) (* (pow x 2) (+ (* -1/5040 (* eps (pow x 2))) (* 1/120 eps))))))) (taylor 0 x) (#s(alt (.f64 eps (sin.f64 x)) (patch (.f64 eps (sin.f64 x)) #<representation binary64>) () ())) ())
#s(alt (* eps (sin x)) (taylor inf x) (#s(alt (.f64 eps (sin.f64 x)) (patch (.f64 eps (sin.f64 x)) #<representation binary64>) () ())) ())
#s(alt (* eps (sin x)) (taylor inf x) (#s(alt (.f64 eps (sin.f64 x)) (patch (.f64 eps (sin.f64 x)) #<representation binary64>) () ())) ())
#s(alt (* eps (sin x)) (taylor inf x) (#s(alt (.f64 eps (sin.f64 x)) (patch (.f64 eps (sin.f64 x)) #<representation binary64>) () ())) ())
#s(alt (* eps (sin x)) (taylor inf x) (#s(alt (.f64 eps (sin.f64 x)) (patch (.f64 eps (sin.f64 x)) #<representation binary64>) () ())) ())
#s(alt (* eps (sin x)) (taylor -inf x) (#s(alt (.f64 eps (sin.f64 x)) (patch (.f64 eps (sin.f64 x)) #<representation binary64>) () ())) ())
#s(alt (* eps (sin x)) (taylor -inf x) (#s(alt (.f64 eps (sin.f64 x)) (patch (.f64 eps (sin.f64 x)) #<representation binary64>) () ())) ())
#s(alt (* eps (sin x)) (taylor -inf x) (#s(alt (.f64 eps (sin.f64 x)) (patch (.f64 eps (sin.f64 x)) #<representation binary64>) () ())) ())
#s(alt (* eps (sin x)) (taylor -inf x) (#s(alt (.f64 eps (sin.f64 x)) (patch (.f64 eps (sin.f64 x)) #<representation binary64>) () ())) ())
#s(alt (* -1 x) (taylor 0 x) (#s(alt (neg.f64 x) (patch (neg.f64 x) #<representation binary64>) () ())) ())
#s(alt (* -1 x) (taylor 0 x) (#s(alt (neg.f64 x) (patch (neg.f64 x) #<representation binary64>) () ())) ())
#s(alt (* -1 x) (taylor 0 x) (#s(alt (neg.f64 x) (patch (neg.f64 x) #<representation binary64>) () ())) ())
#s(alt (* -1 x) (taylor 0 x) (#s(alt (neg.f64 x) (patch (neg.f64 x) #<representation binary64>) () ())) ())
#s(alt (* -1 x) (taylor inf x) (#s(alt (neg.f64 x) (patch (neg.f64 x) #<representation binary64>) () ())) ())
#s(alt (* -1 x) (taylor inf x) (#s(alt (neg.f64 x) (patch (neg.f64 x) #<representation binary64>) () ())) ())
#s(alt (* -1 x) (taylor inf x) (#s(alt (neg.f64 x) (patch (neg.f64 x) #<representation binary64>) () ())) ())
#s(alt (* -1 x) (taylor inf x) (#s(alt (neg.f64 x) (patch (neg.f64 x) #<representation binary64>) () ())) ())
#s(alt (* -1 x) (taylor -inf x) (#s(alt (neg.f64 x) (patch (neg.f64 x) #<representation binary64>) () ())) ())
#s(alt (* -1 x) (taylor -inf x) (#s(alt (neg.f64 x) (patch (neg.f64 x) #<representation binary64>) () ())) ())
#s(alt (* -1 x) (taylor -inf x) (#s(alt (neg.f64 x) (patch (neg.f64 x) #<representation binary64>) () ())) ())
#s(alt (* -1 x) (taylor -inf x) (#s(alt (neg.f64 x) (patch (neg.f64 x) #<representation binary64>) () ())) ())
#s(alt (* -1/6 x) (taylor 0 x) (#s(alt (.f64 x (fma.f64 (.f64 x x) (fma.f64 x (.f64 x #s(literal -1/5040 binary64)) #s(literal 1/120 binary64)) #s(literal -1/6 binary64))) (patch (.f64 x (fma.f64 (.f64 x x) (fma.f64 x (.f64 x #s(literal -1/5040 binary64)) #s(literal 1/120 binary64)) #s(literal -1/6 binary64))) #<representation binary64>) () ())) ())
#s(alt (* x (- (* 1/120 (pow x 2)) 1/6)) (taylor 0 x) (#s(alt (.f64 x (fma.f64 (.f64 x x) (fma.f64 x (.f64 x #s(literal -1/5040 binary64)) #s(literal 1/120 binary64)) #s(literal -1/6 binary64))) (patch (.f64 x (fma.f64 (.f64 x x) (fma.f64 x (.f64 x #s(literal -1/5040 binary64)) #s(literal 1/120 binary64)) #s(literal -1/6 binary64))) #<representation binary64>) () ())) ())
#s(alt (* x (- (* (pow x 2) (+ 1/120 (* -1/5040 (pow x 2)))) 1/6)) (taylor 0 x) (#s(alt (.f64 x (fma.f64 (.f64 x x) (fma.f64 x (.f64 x #s(literal -1/5040 binary64)) #s(literal 1/120 binary64)) #s(literal -1/6 binary64))) (patch (.f64 x (fma.f64 (.f64 x x) (fma.f64 x (.f64 x #s(literal -1/5040 binary64)) #s(literal 1/120 binary64)) #s(literal -1/6 binary64))) #<representation binary64>) () ())) ())
#s(alt (* x (- (* (pow x 2) (+ 1/120 (* -1/5040 (pow x 2)))) 1/6)) (taylor 0 x) (#s(alt (.f64 x (fma.f64 (.f64 x x) (fma.f64 x (.f64 x #s(literal -1/5040 binary64)) #s(literal 1/120 binary64)) #s(literal -1/6 binary64))) (patch (.f64 x (fma.f64 (.f64 x x) (fma.f64 x (.f64 x #s(literal -1/5040 binary64)) #s(literal 1/120 binary64)) #s(literal -1/6 binary64))) #<representation binary64>) () ())) ())
#s(alt (* -1/5040 (pow x 5)) (taylor inf x) (#s(alt (.f64 x (fma.f64 (.f64 x x) (fma.f64 x (.f64 x #s(literal -1/5040 binary64)) #s(literal 1/120 binary64)) #s(literal -1/6 binary64))) (patch (.f64 x (fma.f64 (.f64 x x) (fma.f64 x (.f64 x #s(literal -1/5040 binary64)) #s(literal 1/120 binary64)) #s(literal -1/6 binary64))) #<representation binary64>) () ())) ())
#s(alt (* (pow x 5) (- (* 1/120 (/ 1 (pow x 2))) 1/5040)) (taylor inf x) (#s(alt (.f64 x (fma.f64 (.f64 x x) (fma.f64 x (.f64 x #s(literal -1/5040 binary64)) #s(literal 1/120 binary64)) #s(literal -1/6 binary64))) (patch (.f64 x (fma.f64 (.f64 x x) (fma.f64 x (.f64 x #s(literal -1/5040 binary64)) #s(literal 1/120 binary64)) #s(literal -1/6 binary64))) #<representation binary64>) () ())) ())
#s(alt (* (pow x 5) (- (* 1/120 (/ 1 (pow x 2))) (+ 1/5040 (/ 1/6 (pow x 4))))) (taylor inf x) (#s(alt (.f64 x (fma.f64 (.f64 x x) (fma.f64 x (.f64 x #s(literal -1/5040 binary64)) #s(literal 1/120 binary64)) #s(literal -1/6 binary64))) (patch (.f64 x (fma.f64 (.f64 x x) (fma.f64 x (.f64 x #s(literal -1/5040 binary64)) #s(literal 1/120 binary64)) #s(literal -1/6 binary64))) #<representation binary64>) () ())) ())
#s(alt (* (pow x 5) (- (* 1/120 (/ 1 (pow x 2))) (+ 1/5040 (/ 1/6 (pow x 4))))) (taylor inf x) (#s(alt (.f64 x (fma.f64 (.f64 x x) (fma.f64 x (.f64 x #s(literal -1/5040 binary64)) #s(literal 1/120 binary64)) #s(literal -1/6 binary64))) (patch (.f64 x (fma.f64 (.f64 x x) (fma.f64 x (.f64 x #s(literal -1/5040 binary64)) #s(literal 1/120 binary64)) #s(literal -1/6 binary64))) #<representation binary64>) () ())) ())
#s(alt (* -1/5040 (pow x 5)) (taylor -inf x) (#s(alt (.f64 x (fma.f64 (.f64 x x) (fma.f64 x (.f64 x #s(literal -1/5040 binary64)) #s(literal 1/120 binary64)) #s(literal -1/6 binary64))) (patch (.f64 x (fma.f64 (.f64 x x) (fma.f64 x (.f64 x #s(literal -1/5040 binary64)) #s(literal 1/120 binary64)) #s(literal -1/6 binary64))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* (pow x 5) (- 1/5040 (* 1/120 (/ 1 (pow x 2)))))) (taylor -inf x) (#s(alt (.f64 x (fma.f64 (.f64 x x) (fma.f64 x (.f64 x #s(literal -1/5040 binary64)) #s(literal 1/120 binary64)) #s(literal -1/6 binary64))) (patch (.f64 x (fma.f64 (.f64 x x) (fma.f64 x (.f64 x #s(literal -1/5040 binary64)) #s(literal 1/120 binary64)) #s(literal -1/6 binary64))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* (pow x 5) (- (+ 1/5040 (/ 1/6 (pow x 4))) (* 1/120 (/ 1 (pow x 2)))))) (taylor -inf x) (#s(alt (.f64 x (fma.f64 (.f64 x x) (fma.f64 x (.f64 x #s(literal -1/5040 binary64)) #s(literal 1/120 binary64)) #s(literal -1/6 binary64))) (patch (.f64 x (fma.f64 (.f64 x x) (fma.f64 x (.f64 x #s(literal -1/5040 binary64)) #s(literal 1/120 binary64)) #s(literal -1/6 binary64))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* (pow x 5) (- (+ 1/5040 (/ 1/6 (pow x 4))) (* 1/120 (/ 1 (pow x 2)))))) (taylor -inf x) (#s(alt (.f64 x (fma.f64 (.f64 x x) (fma.f64 x (.f64 x #s(literal -1/5040 binary64)) #s(literal 1/120 binary64)) #s(literal -1/6 binary64))) (patch (.f64 x (fma.f64 (.f64 x x) (fma.f64 x (.f64 x #s(literal -1/5040 binary64)) #s(literal 1/120 binary64)) #s(literal -1/6 binary64))) #<representation binary64>) () ())) ())
#s(alt (* -1/5040 x) (taylor 0 x) (#s(alt (.f64 x #s(literal -1/5040 binary64)) (patch (.f64 x #s(literal -1/5040 binary64)) #<representation binary64>) () ())) ())
#s(alt (* -1/5040 x) (taylor 0 x) (#s(alt (.f64 x #s(literal -1/5040 binary64)) (patch (.f64 x #s(literal -1/5040 binary64)) #<representation binary64>) () ())) ())
#s(alt (* -1/5040 x) (taylor 0 x) (#s(alt (.f64 x #s(literal -1/5040 binary64)) (patch (.f64 x #s(literal -1/5040 binary64)) #<representation binary64>) () ())) ())
#s(alt (* -1/5040 x) (taylor 0 x) (#s(alt (.f64 x #s(literal -1/5040 binary64)) (patch (.f64 x #s(literal -1/5040 binary64)) #<representation binary64>) () ())) ())
#s(alt (* -1/5040 x) (taylor inf x) (#s(alt (.f64 x #s(literal -1/5040 binary64)) (patch (.f64 x #s(literal -1/5040 binary64)) #<representation binary64>) () ())) ())
#s(alt (* -1/5040 x) (taylor inf x) (#s(alt (.f64 x #s(literal -1/5040 binary64)) (patch (.f64 x #s(literal -1/5040 binary64)) #<representation binary64>) () ())) ())
#s(alt (* -1/5040 x) (taylor inf x) (#s(alt (.f64 x #s(literal -1/5040 binary64)) (patch (.f64 x #s(literal -1/5040 binary64)) #<representation binary64>) () ())) ())
#s(alt (* -1/5040 x) (taylor inf x) (#s(alt (.f64 x #s(literal -1/5040 binary64)) (patch (.f64 x #s(literal -1/5040 binary64)) #<representation binary64>) () ())) ())
#s(alt (* -1/5040 x) (taylor -inf x) (#s(alt (.f64 x #s(literal -1/5040 binary64)) (patch (.f64 x #s(literal -1/5040 binary64)) #<representation binary64>) () ())) ())
#s(alt (* -1/5040 x) (taylor -inf x) (#s(alt (.f64 x #s(literal -1/5040 binary64)) (patch (.f64 x #s(literal -1/5040 binary64)) #<representation binary64>) () ())) ())
#s(alt (* -1/5040 x) (taylor -inf x) (#s(alt (.f64 x #s(literal -1/5040 binary64)) (patch (.f64 x #s(literal -1/5040 binary64)) #<representation binary64>) () ())) ())
#s(alt (* -1/5040 x) (taylor -inf x) (#s(alt (.f64 x #s(literal -1/5040 binary64)) (patch (.f64 x #s(literal -1/5040 binary64)) #<representation binary64>) () ())) ())

Calls

114 calls:

Time	Variable		Point	Expression
4.0ms	eps	@	-inf	(/ 1 (- (* (cos x) (* eps -1/2)) (sin x)))
2.0ms	eps	@	inf	(+ (* eps (+ (* 1/4 (* x x)) -1/2)) (neg x))
1.0ms	x	@	inf	(+ (* (* (cos x) (* eps -1/2)) eps) (neg (* eps (sin x))))
1.0ms	x	@	inf	(/ 1 (- (* (cos x) (* eps -1/2)) (sin x)))
1.0ms	x	@	-inf	(+ (* (* (cos x) (* eps -1/2)) eps) (neg (* eps (sin x))))

simplify214.0ms (1.3%)

Memory

29.4MiB live, 102.2MiB allocated

Algorithm

1×	egg-herbie

Rules

12 048×	`lower-fma.f64`
12 048×	`lower-fma.f32`
6 620×	`lower-*.f64`
6 620×	`lower-*.f32`
3 744×	`lower-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	405	4388
1	1164	4248
2	3297	4186
0	8213	4032

Stop Event

1×	iter limit
1×	node limit

Counts

456 → 454

Calls

Call 1

Inputs
(* -1/2 (pow eps 2))
(+ (* -1 (* eps x)) (* -1/2 (pow eps 2)))
(+ (* -1/2 (pow eps 2)) (* x (- (* 1/4 (* (pow eps 2) x)) eps)))
(+ (* -1/2 (pow eps 2)) (* x (- (* x (+ (* 1/6 (* eps x)) (* 1/4 (pow eps 2)))) eps)))
(- (* -1/2 (* (pow eps 2) (cos x))) (* eps (sin x)))
(- (* -1/2 (* (pow eps 2) (cos x))) (* eps (sin x)))
(- (* -1/2 (* (pow eps 2) (cos x))) (* eps (sin x)))
(- (* -1/2 (* (pow eps 2) (cos x))) (* eps (sin x)))
(- (* -1/2 (* (pow eps 2) (cos x))) (* eps (sin x)))
(- (* -1/2 (* (pow eps 2) (cos x))) (* eps (sin x)))
(- (* -1/2 (* (pow eps 2) (cos x))) (* eps (sin x)))
(- (* -1/2 (* (pow eps 2) (cos x))) (* eps (sin x)))
(* -1 (* eps (sin x)))
(* eps (- (* -1/2 (* eps (cos x))) (sin x)))
(* eps (- (* -1/2 (* eps (cos x))) (sin x)))
(* eps (- (* -1/2 (* eps (cos x))) (sin x)))
(* -1/2 (* (pow eps 2) (cos x)))
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(* (pow eps 2) (+ (* -1 (/ (sin x) eps)) (* -1/2 (cos x))))
(* (pow eps 2) (+ (* -1 (/ (sin x) eps)) (* -1/2 (cos x))))
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(* (pow eps 2) (+ (* -1 (/ (sin x) eps)) (* -1/2 (cos x))))
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(- (+ (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)
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(* eps (- (* eps (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x)))))) (sin x)))
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(- (cos (+ eps x)) (cos x))
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(- (cos (- x (* -1 eps))) (cos x))
(- (cos (- x (* -1 eps))) (cos x))
(- (cos (- x (* -1 eps))) (cos x))
(* -1/2 eps)
(+ (* -1/2 eps) (* 1/4 (* eps (pow x 2))))
(+ (* -1/2 eps) (* (pow x 2) (+ (* -1/48 (* eps (pow x 2))) (* 1/4 eps))))
(+ (* -1/2 eps) (* (pow x 2) (+ (* 1/4 eps) (* (pow x 2) (+ (* -1/48 eps) (* 1/1440 (* eps (pow x 2))))))))
(* -1/2 (* eps (cos x)))
(* -1/2 (* eps (cos x)))
(* -1/2 (* eps (cos x)))
(* -1/2 (* eps (cos x)))
(* -1/2 (* eps (cos x)))
(* -1/2 (* eps (cos x)))
(* -1/2 (* eps (cos x)))
(* -1/2 (* eps (cos x)))
(* -1/2 (* eps (cos x)))
(* -1/2 (* eps (cos x)))
(* -1/2 (* eps (cos x)))
(* -1/2 (* eps (cos x)))
(* -1/2 (* eps (cos x)))
(* -1/2 (* eps (cos x)))
(* -1/2 (* eps (cos x)))
(* -1/2 (* eps (cos x)))
(* -1/2 (* eps (cos x)))
(* -1/2 (* eps (cos x)))
(* -1/2 (* eps (cos x)))
(* -1/2 (* eps (cos x)))
1
(+ 1 (* -1/2 (pow x 2)))
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(+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))) 1/2)))
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(cos x)
(cos x)
(cos x)
(cos x)
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(- (+ (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))
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(- (cos (- eps (* -1 x))) (cos x))
(- (cos (- eps (* -1 x))) (cos x))
(* -1 (* eps (sin x)))
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(* 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))
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(- (cos (- x (* -1 eps))) (cos x))
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(* (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
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(cos eps)
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(- (+ (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))
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(* -1 (* eps (sin x)))
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(- (cos (+ eps x)) (cos x))
(- (cos (+ eps x)) (cos x))
(- (cos (+ eps x)) (cos x))
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(- (cos (- x (* -1 eps))) (cos x))
(- (cos (- x (* -1 eps))) (cos x))
(- (cos (- x (* -1 eps))) (cos x))
(* -1 (* eps (sin x)))
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(* eps (+ (* -1 (sin x)) (* -1/2 (* eps (cos x)))))
(* eps (+ (* -1 (sin x)) (* -1/2 (* eps (cos x)))))
(* -1/2 (* (pow eps 2) (cos x)))
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(* (pow eps 2) (+ (* -1 (/ (sin x) eps)) (* -1/2 (cos x))))
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(* -1/2 (* (pow eps 2) (cos x)))
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(* -1/2 (pow eps 2))
(+ (* -1 (* eps x)) (* -1/2 (pow eps 2)))
(+ (* -1/2 (pow eps 2)) (* x (+ (* -1 eps) (* 1/4 (* (pow eps 2) x)))))
(+ (* -1/2 (pow eps 2)) (* x (+ (* -1 eps) (* x (+ (* 1/6 (* eps x)) (* 1/4 (pow eps 2)))))))
(* eps (- (* -1/2 (* eps (cos x))) (sin x)))
(* eps (- (* -1/2 (* eps (cos x))) (sin x)))
(* eps (- (* -1/2 (* eps (cos x))) (sin x)))
(* eps (- (* -1/2 (* eps (cos x))) (sin x)))
(* eps (- (* -1/2 (* eps (cos x))) (sin x)))
(* eps (- (* -1/2 (* eps (cos x))) (sin x)))
(* eps (- (* -1/2 (* eps (cos x))) (sin x)))
(* eps (- (* -1/2 (* eps (cos x))) (sin x)))
(* -1 (sin x))
(- (* -1/2 (* eps (cos x))) (sin x))
(- (* -1/2 (* eps (cos x))) (sin x))
(- (* -1/2 (* eps (cos x))) (sin x))
(* -1/2 (* eps (cos x)))
(* eps (+ (* -1 (/ (sin x) eps)) (* -1/2 (cos x))))
(* eps (+ (* -1 (/ (sin x) eps)) (* -1/2 (cos x))))
(* eps (+ (* -1 (/ (sin x) eps)) (* -1/2 (cos x))))
(* -1/2 (* eps (cos x)))
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(* -1 (* eps (+ (* 1/2 (cos x)) (/ (sin x) eps))))
(* -1/2 eps)
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(+ (* -1/2 eps) (* x (- (* x (+ (* 1/6 x) (* 1/4 eps))) 1)))
(- (* -1/2 (* eps (cos x))) (sin x))
(- (* -1/2 (* eps (cos x))) (sin x))
(- (* -1/2 (* eps (cos x))) (sin x))
(- (* -1/2 (* eps (cos x))) (sin x))
(- (* -1/2 (* eps (cos x))) (sin x))
(- (* -1/2 (* eps (cos x))) (sin x))
(- (* -1/2 (* eps (cos x))) (sin x))
(- (* -1/2 (* eps (cos x))) (sin x))
(* -1 x)
(- (* eps (- (* 1/4 (pow x 2)) 1/2)) x)
(- (* eps (- (* 1/4 (pow x 2)) 1/2)) x)
(- (* eps (- (* 1/4 (pow x 2)) 1/2)) x)
(* eps (- (* 1/4 (pow x 2)) 1/2))
(* eps (- (+ (* -1 (/ x eps)) (* 1/4 (pow x 2))) 1/2))
(* eps (- (+ (* -1 (/ x eps)) (* 1/4 (pow x 2))) 1/2))
(* eps (- (+ (* -1 (/ x eps)) (* 1/4 (pow x 2))) 1/2))
(* eps (- (* 1/4 (pow x 2)) 1/2))
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(* (pow x 2) (- (+ (* -1/2 (/ eps (pow x 2))) (* 1/4 eps)) (/ 1 x)))
(* 1/4 (* eps (pow x 2)))
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(* (pow x 2) (+ (* -1 (/ (+ 1 (* 1/2 (/ eps x))) x)) (* 1/4 eps)))
(* (pow x 2) (+ (* -1 (/ (+ 1 (* 1/2 (/ eps x))) x)) (* 1/4 eps)))
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(- (+ (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)))
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(* eps (- (* eps (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x))))) (sin x)))
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(- (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 (* eps x))
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(* x (+ (* -1 eps) (* (pow x 2) (+ (* -1/120 (* eps (pow x 2))) (* 1/6 eps)))))
(* x (+ (* -1 eps) (* (pow x 2) (+ (* 1/6 eps) (* (pow x 2) (+ (* -1/120 eps) (* 1/5040 (* eps (pow x 2)))))))))
(* -1 (* eps (sin x)))
(* -1 (* eps (sin x)))
(* -1 (* eps (sin x)))
(* -1 (* eps (sin x)))
(* -1 (* eps (sin x)))
(* -1 (* eps (sin x)))
(* -1 (* eps (sin x)))
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(* -1 (* eps (sin x)))
(* -1 (* eps (sin x)))
(* -1 (* eps (sin x)))
(* -1 (* eps (sin x)))
(* -1 (* eps (sin x)))
x
(* x (+ 1 (* -1/6 (pow x 2))))
(* x (+ 1 (* (pow x 2) (- (* 1/120 (pow x 2)) 1/6))))
(* x (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/120 (* -1/5040 (pow x 2)))) 1/6))))
(sin x)
(sin x)
(sin x)
(sin x)
(sin x)
(sin x)
(sin x)
(sin x)
x
(* x (+ 1 (* -1/6 (pow x 2))))
(* x (+ 1 (* (pow x 2) (- (* 1/120 (pow x 2)) 1/6))))
(* x (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/120 (* -1/5040 (pow x 2)))) 1/6))))
(* -1/5040 (pow x 7))
(* (pow x 7) (- (* 1/120 (/ 1 (pow x 2))) 1/5040))
(* (pow x 7) (- (* 1/120 (/ 1 (pow x 2))) (+ 1/5040 (/ 1/6 (pow x 4)))))
(* (pow x 7) (- (+ (* 1/120 (/ 1 (pow x 2))) (/ 1 (pow x 6))) (+ 1/5040 (/ 1/6 (pow x 4)))))
(* -1/5040 (pow x 7))
(* -1 (* (pow x 7) (- 1/5040 (* 1/120 (/ 1 (pow x 2))))))
(* -1 (* (pow x 7) (- (+ 1/5040 (/ 1/6 (pow x 4))) (* 1/120 (/ 1 (pow x 2))))))
(* -1 (* (pow x 7) (- (+ 1/5040 (/ 1/6 (pow x 4))) (+ (* 1/120 (/ 1 (pow x 2))) (/ 1 (pow x 6))))))
(* -1 (* eps (sin x)))
(* eps (+ (* -1 (sin x)) (* -1/2 (* eps (cos x)))))
(* eps (+ (* -1 (sin x)) (* -1/2 (* eps (cos x)))))
(* eps (+ (* -1 (sin x)) (* -1/2 (* eps (cos x)))))
(* -1/2 (* (pow eps 2) (cos x)))
(* (pow eps 2) (+ (* -1 (/ (sin x) eps)) (* -1/2 (cos x))))
(* (pow eps 2) (+ (* -1 (/ (sin x) eps)) (* -1/2 (cos x))))
(* (pow eps 2) (+ (* -1 (/ (sin x) eps)) (* -1/2 (cos x))))
(* -1/2 (* (pow eps 2) (cos x)))
(* (pow eps 2) (+ (* -1 (/ (sin x) eps)) (* -1/2 (cos x))))
(* (pow eps 2) (+ (* -1 (/ (sin x) eps)) (* -1/2 (cos x))))
(* (pow eps 2) (+ (* -1 (/ (sin x) eps)) (* -1/2 (cos x))))
(* -1/2 (pow eps 2))
(+ (* -1 (* eps x)) (* -1/2 (pow eps 2)))
(+ (* -1/2 (pow eps 2)) (* x (+ (* -1 eps) (* 1/4 (* (pow eps 2) x)))))
(+ (* -1/2 (pow eps 2)) (* x (+ (* -1 eps) (* x (+ (* 1/6 (* eps x)) (* 1/4 (pow eps 2)))))))
(* eps (- (* -1/2 (* eps (cos x))) (sin x)))
(* eps (- (* -1/2 (* eps (cos x))) (sin x)))
(* eps (- (* -1/2 (* eps (cos x))) (sin x)))
(* eps (- (* -1/2 (* eps (cos x))) (sin x)))
(* eps (- (* -1/2 (* eps (cos x))) (sin x)))
(* eps (- (* -1/2 (* eps (cos x))) (sin x)))
(* eps (- (* -1/2 (* eps (cos x))) (sin x)))
(* eps (- (* -1/2 (* eps (cos x))) (sin x)))
(/ -2 eps)
(- (* 4 (/ x (pow eps 2))) (* 2 (/ 1 eps)))
(- (* x (+ (* -1 (* x (+ (* 8 (/ 1 (pow eps 3))) (/ 1 eps)))) (* 4 (/ 1 (pow eps 2))))) (* 2 (/ 1 eps)))
(- (* x (+ (* x (- (* x (- (* 4/3 (/ 1 (pow eps 2))) (* -2 (/ (+ (/ 1 eps) (* 8 (/ 1 (pow eps 3)))) eps)))) (+ (* 8 (/ 1 (pow eps 3))) (/ 1 eps)))) (* 4 (/ 1 (pow eps 2))))) (* 2 (/ 1 eps)))
(/ 1 (- (* -1/2 (* eps (cos x))) (sin x)))
(/ 1 (- (* -1/2 (* eps (cos x))) (sin x)))
(/ 1 (- (* -1/2 (* eps (cos x))) (sin x)))
(/ 1 (- (* -1/2 (* eps (cos x))) (sin x)))
(/ 1 (- (* -1/2 (* eps (cos x))) (sin x)))
(/ 1 (- (* -1/2 (* eps (cos x))) (sin x)))
(/ 1 (- (* -1/2 (* eps (cos x))) (sin x)))
(/ 1 (- (* -1/2 (* eps (cos x))) (sin x)))
(/ -1 (sin x))
(- (* 1/2 (/ (* eps (cos x)) (pow (sin x) 2))) (/ 1 (sin x)))
(- (* eps (- (* -1/4 (/ (* eps (pow (cos x) 2)) (pow (sin x) 3))) (* -1/2 (/ (cos x) (pow (sin x) 2))))) (/ 1 (sin x)))
(- (* eps (- (* eps (- (* 1/8 (/ (* eps (pow (cos x) 3)) (pow (sin x) 4))) (* 1/4 (/ (pow (cos x) 2) (pow (sin x) 3))))) (* -1/2 (/ (cos x) (pow (sin x) 2))))) (/ 1 (sin x)))
(/ -2 (* eps (cos x)))
(/ (- (* 4 (/ (sin x) (* eps (pow (cos x) 2)))) (* 2 (/ 1 (cos x)))) eps)
(/ (- (* -8 (/ (pow (sin x) 2) (* (pow eps 2) (pow (cos x) 3)))) (+ (* -4 (/ (sin x) (* eps (pow (cos x) 2)))) (* 2 (/ 1 (cos x))))) eps)
(/ (- (* 16 (/ (pow (sin x) 3) (* (pow eps 3) (pow (cos x) 4)))) (+ (* -4 (/ (sin x) (* eps (pow (cos x) 2)))) (+ (* 8 (/ (pow (sin x) 2) (* (pow eps 2) (pow (cos x) 3)))) (* 2 (/ 1 (cos x)))))) eps)
(/ -2 (* eps (cos x)))
(* -1 (/ (+ (* -4 (/ (sin x) (* eps (pow (cos x) 2)))) (* 2 (/ 1 (cos x)))) eps))
(* -1 (/ (+ (* -1 (/ (- (* -8 (/ (pow (sin x) 2) (* eps (pow (cos x) 3)))) (* -4 (/ (sin x) (pow (cos x) 2)))) eps)) (* 2 (/ 1 (cos x)))) eps))
(* -1 (/ (+ (* -1 (/ (- (* -1 (/ (- (* -16 (/ (pow (sin x) 3) (* eps (pow (cos x) 4)))) (* -8 (/ (pow (sin x) 2) (pow (cos x) 3)))) eps)) (* -4 (/ (sin x) (pow (cos x) 2)))) eps)) (* 2 (/ 1 (cos x)))) 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))
(* -1/2 eps)
(+ (* -1 x) (* -1/2 eps))
(+ (* -1/2 eps) (* x (- (* 1/4 (* eps x)) 1)))
(+ (* -1/2 eps) (* x (- (* x (+ (* 1/6 x) (* 1/4 eps))) 1)))
(- (* -1/2 (* eps (cos x))) (sin x))
(- (* -1/2 (* eps (cos x))) (sin x))
(- (* -1/2 (* eps (cos x))) (sin x))
(- (* -1/2 (* eps (cos x))) (sin x))
(- (* -1/2 (* eps (cos x))) (sin x))
(- (* -1/2 (* eps (cos x))) (sin x))
(- (* -1/2 (* eps (cos x))) (sin x))
(- (* -1/2 (* eps (cos x))) (sin x))
(* -1 (sin x))
(- (* -1/2 (* eps (cos x))) (sin x))
(- (* -1/2 (* eps (cos x))) (sin x))
(- (* -1/2 (* eps (cos x))) (sin x))
(* -1/2 (* eps (cos x)))
(* eps (+ (* -1 (/ (sin x) eps)) (* -1/2 (cos x))))
(* eps (+ (* -1 (/ (sin x) eps)) (* -1/2 (cos x))))
(* eps (+ (* -1 (/ (sin x) eps)) (* -1/2 (cos x))))
(* -1/2 (* eps (cos x)))
(* -1 (* eps (+ (* 1/2 (cos x)) (/ (sin x) eps))))
(* -1 (* eps (+ (* 1/2 (cos x)) (/ (sin x) eps))))
(* -1 (* eps (+ (* 1/2 (cos x)) (/ (sin x) eps))))
(* eps (sin x))
(* eps (sin x))
(* eps (sin x))
(* eps (sin x))
(* eps (sin x))
(* eps (sin x))
(* eps (sin x))
(* eps (sin x))
(* eps (sin x))
(* eps (sin x))
(* eps (sin x))
(* eps (sin x))
(* eps x)
(* x (+ eps (* -1/6 (* eps (pow x 2)))))
(* x (+ eps (* (pow x 2) (+ (* -1/6 eps) (* 1/120 (* eps (pow x 2)))))))
(* x (+ eps (* (pow x 2) (+ (* -1/6 eps) (* (pow x 2) (+ (* -1/5040 (* eps (pow x 2))) (* 1/120 eps)))))))
(* eps (sin x))
(* eps (sin x))
(* eps (sin x))
(* eps (sin x))
(* eps (sin x))
(* eps (sin x))
(* eps (sin x))
(* eps (sin x))
(* -1 x)
(* -1 x)
(* -1 x)
(* -1 x)
(* -1 x)
(* -1 x)
(* -1 x)
(* -1 x)
(* -1 x)
(* -1 x)
(* -1 x)
(* -1 x)
(* -1/6 x)
(* x (- (* 1/120 (pow x 2)) 1/6))
(* x (- (* (pow x 2) (+ 1/120 (* -1/5040 (pow x 2)))) 1/6))
(* x (- (* (pow x 2) (+ 1/120 (* -1/5040 (pow x 2)))) 1/6))
(* -1/5040 (pow x 5))
(* (pow x 5) (- (* 1/120 (/ 1 (pow x 2))) 1/5040))
(* (pow x 5) (- (* 1/120 (/ 1 (pow x 2))) (+ 1/5040 (/ 1/6 (pow x 4)))))
(* (pow x 5) (- (* 1/120 (/ 1 (pow x 2))) (+ 1/5040 (/ 1/6 (pow x 4)))))
(* -1/5040 (pow x 5))
(* -1 (* (pow x 5) (- 1/5040 (* 1/120 (/ 1 (pow x 2))))))
(* -1 (* (pow x 5) (- (+ 1/5040 (/ 1/6 (pow x 4))) (* 1/120 (/ 1 (pow x 2))))))
(* -1 (* (pow x 5) (- (+ 1/5040 (/ 1/6 (pow x 4))) (* 1/120 (/ 1 (pow x 2))))))
(* -1/5040 x)
(* -1/5040 x)
(* -1/5040 x)
(* -1/5040 x)
(* -1/5040 x)
(* -1/5040 x)
(* -1/5040 x)
(* -1/5040 x)
(* -1/5040 x)
(* -1/5040 x)
(* -1/5040 x)
(* -1/5040 x)

Outputs
(* -1/2 (pow eps 2))
(.f64 #s(literal -1/2 binary64) (.f64 eps eps))
(+ (* -1 (* eps x)) (* -1/2 (pow eps 2)))
(.f64 eps (-.f64 (.f64 #s(literal -1/2 binary64) eps) x))
(+ (* -1/2 (pow eps 2)) (* x (- (* 1/4 (* (pow eps 2) x)) eps)))
(fma.f64 (.f64 x (.f64 eps (.f64 eps x))) #s(literal 1/4 binary64) (.f64 eps (-.f64 (*.f64 #s(literal -1/2 binary64) eps) x)))
(+ (* -1/2 (pow eps 2)) (* x (- (* x (+ (* 1/6 (* eps x)) (* 1/4 (pow eps 2)))) eps)))
(fma.f64 x (fma.f64 x (.f64 eps (fma.f64 eps #s(literal 1/4 binary64) (.f64 x #s(literal 1/6 binary64)))) (neg.f64 eps)) (.f64 #s(literal -1/2 binary64) (.f64 eps eps)))
(- (* -1/2 (* (pow eps 2) (cos x))) (* eps (sin x)))
(.f64 eps (-.f64 (.f64 #s(literal -1/2 binary64) (*.f64 eps (cos.f64 x))) (sin.f64 x)))
(- (* -1/2 (* (pow eps 2) (cos x))) (* eps (sin x)))
(.f64 eps (-.f64 (.f64 #s(literal -1/2 binary64) (*.f64 eps (cos.f64 x))) (sin.f64 x)))
(- (* -1/2 (* (pow eps 2) (cos x))) (* eps (sin x)))
(.f64 eps (-.f64 (.f64 #s(literal -1/2 binary64) (*.f64 eps (cos.f64 x))) (sin.f64 x)))
(- (* -1/2 (* (pow eps 2) (cos x))) (* eps (sin x)))
(.f64 eps (-.f64 (.f64 #s(literal -1/2 binary64) (*.f64 eps (cos.f64 x))) (sin.f64 x)))
(- (* -1/2 (* (pow eps 2) (cos x))) (* eps (sin x)))
(.f64 eps (-.f64 (.f64 #s(literal -1/2 binary64) (*.f64 eps (cos.f64 x))) (sin.f64 x)))
(- (* -1/2 (* (pow eps 2) (cos x))) (* eps (sin x)))
(.f64 eps (-.f64 (.f64 #s(literal -1/2 binary64) (*.f64 eps (cos.f64 x))) (sin.f64 x)))
(- (* -1/2 (* (pow eps 2) (cos x))) (* eps (sin x)))
(.f64 eps (-.f64 (.f64 #s(literal -1/2 binary64) (*.f64 eps (cos.f64 x))) (sin.f64 x)))
(- (* -1/2 (* (pow eps 2) (cos x))) (* eps (sin x)))
(.f64 eps (-.f64 (.f64 #s(literal -1/2 binary64) (*.f64 eps (cos.f64 x))) (sin.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 (- (* -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 (- (* -1/2 (* eps (cos x))) (sin x)))
(.f64 eps (-.f64 (.f64 #s(literal -1/2 binary64) (*.f64 eps (cos.f64 x))) (sin.f64 x)))
(* -1/2 (* (pow eps 2) (cos x)))
(.f64 #s(literal -1/2 binary64) (.f64 eps (*.f64 eps (cos.f64 x))))
(* (pow eps 2) (+ (* -1 (/ (sin x) eps)) (* -1/2 (cos x))))
(.f64 (.f64 eps eps) (-.f64 (*.f64 #s(literal -1/2 binary64) (cos.f64 x)) (/.f64 (sin.f64 x) eps)))
(* (pow eps 2) (+ (* -1 (/ (sin x) eps)) (* -1/2 (cos x))))
(.f64 (.f64 eps eps) (-.f64 (*.f64 #s(literal -1/2 binary64) (cos.f64 x)) (/.f64 (sin.f64 x) eps)))
(* (pow eps 2) (+ (* -1 (/ (sin x) eps)) (* -1/2 (cos x))))
(.f64 (.f64 eps eps) (-.f64 (*.f64 #s(literal -1/2 binary64) (cos.f64 x)) (/.f64 (sin.f64 x) eps)))
(* -1/2 (* (pow eps 2) (cos x)))
(.f64 #s(literal -1/2 binary64) (.f64 eps (*.f64 eps (cos.f64 x))))
(* (pow eps 2) (+ (* -1 (/ (sin x) eps)) (* -1/2 (cos x))))
(.f64 (.f64 eps eps) (-.f64 (*.f64 #s(literal -1/2 binary64) (cos.f64 x)) (/.f64 (sin.f64 x) eps)))
(* (pow eps 2) (+ (* -1 (/ (sin x) eps)) (* -1/2 (cos x))))
(.f64 (.f64 eps eps) (-.f64 (*.f64 #s(literal -1/2 binary64) (cos.f64 x)) (/.f64 (sin.f64 x) eps)))
(* (pow eps 2) (+ (* -1 (/ (sin x) eps)) (* -1/2 (cos x))))
(.f64 (.f64 eps eps) (-.f64 (*.f64 #s(literal -1/2 binary64) (cos.f64 x)) (/.f64 (sin.f64 x) eps)))
(- (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)
(+.f64 (cos.f64 eps) (fma.f64 x (-.f64 (*.f64 x (fma.f64 #s(literal -1/2 binary64) (cos.f64 eps) #s(literal 1/2 binary64))) (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)
(fma.f64 x (fma.f64 x (fma.f64 #s(literal -1/2 binary64) (cos.f64 eps) (fma.f64 (sin.f64 eps) (*.f64 x #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 #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 #s(literal -1/2 binary64) (.f64 eps (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 eps (fma.f64 #s(literal 1/6 binary64) (sin.f64 x) (.f64 (.f64 eps (cos.f64 x)) #s(literal 1/24 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 eps)
(*.f64 #s(literal -1/2 binary64) eps)
(+ (* -1/2 eps) (* 1/4 (* eps (pow x 2))))
(.f64 eps (fma.f64 #s(literal 1/4 binary64) (.f64 x x) #s(literal -1/2 binary64)))
(+ (* -1/2 eps) (* (pow x 2) (+ (* -1/48 (* eps (pow x 2))) (* 1/4 eps))))
(fma.f64 (.f64 x x) (.f64 eps (fma.f64 (.f64 x x) #s(literal -1/48 binary64) #s(literal 1/4 binary64))) (.f64 #s(literal -1/2 binary64) eps))
(+ (* -1/2 eps) (* (pow x 2) (+ (* 1/4 eps) (* (pow x 2) (+ (* -1/48 eps) (* 1/1440 (* eps (pow x 2))))))))
(fma.f64 x (.f64 x (fma.f64 x (.f64 x (.f64 eps (fma.f64 (.f64 x x) #s(literal 1/1440 binary64) #s(literal -1/48 binary64)))) (.f64 eps #s(literal 1/4 binary64)))) (.f64 #s(literal -1/2 binary64) eps))
(* -1/2 (* eps (cos x)))
(.f64 #s(literal -1/2 binary64) (.f64 eps (cos.f64 x)))
(* -1/2 (* eps (cos x)))
(.f64 #s(literal -1/2 binary64) (.f64 eps (cos.f64 x)))
(* -1/2 (* eps (cos x)))
(.f64 #s(literal -1/2 binary64) (.f64 eps (cos.f64 x)))
(* -1/2 (* eps (cos x)))
(.f64 #s(literal -1/2 binary64) (.f64 eps (cos.f64 x)))
(* -1/2 (* eps (cos x)))
(.f64 #s(literal -1/2 binary64) (.f64 eps (cos.f64 x)))
(* -1/2 (* eps (cos x)))
(.f64 #s(literal -1/2 binary64) (.f64 eps (cos.f64 x)))
(* -1/2 (* eps (cos x)))
(.f64 #s(literal -1/2 binary64) (.f64 eps (cos.f64 x)))
(* -1/2 (* eps (cos x)))
(.f64 #s(literal -1/2 binary64) (.f64 eps (cos.f64 x)))
(* -1/2 (* eps (cos x)))
(.f64 #s(literal -1/2 binary64) (.f64 eps (cos.f64 x)))
(* -1/2 (* eps (cos x)))
(.f64 #s(literal -1/2 binary64) (.f64 eps (cos.f64 x)))
(* -1/2 (* eps (cos x)))
(.f64 #s(literal -1/2 binary64) (.f64 eps (cos.f64 x)))
(* -1/2 (* eps (cos x)))
(.f64 #s(literal -1/2 binary64) (.f64 eps (cos.f64 x)))
(* -1/2 (* eps (cos x)))
(.f64 #s(literal -1/2 binary64) (.f64 eps (cos.f64 x)))
(* -1/2 (* eps (cos x)))
(.f64 #s(literal -1/2 binary64) (.f64 eps (cos.f64 x)))
(* -1/2 (* eps (cos x)))
(.f64 #s(literal -1/2 binary64) (.f64 eps (cos.f64 x)))
(* -1/2 (* eps (cos x)))
(.f64 #s(literal -1/2 binary64) (.f64 eps (cos.f64 x)))
(* -1/2 (* eps (cos x)))
(.f64 #s(literal -1/2 binary64) (.f64 eps (cos.f64 x)))
(* -1/2 (* eps (cos x)))
(.f64 #s(literal -1/2 binary64) (.f64 eps (cos.f64 x)))
(* -1/2 (* eps (cos x)))
(.f64 #s(literal -1/2 binary64) (.f64 eps (cos.f64 x)))
(* -1/2 (* eps (cos x)))
(.f64 #s(literal -1/2 binary64) (.f64 eps (cos.f64 x)))
1
#s(literal 1 binary64)
(+ 1 (* -1/2 (pow x 2)))
(fma.f64 #s(literal -1/2 binary64) (*.f64 x x) #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 x (.f64 x (fma.f64 (*.f64 x 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)
(- (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)
(+.f64 (cos.f64 eps) (fma.f64 x (-.f64 (*.f64 x (fma.f64 #s(literal -1/2 binary64) (cos.f64 eps) #s(literal 1/2 binary64))) (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)
(fma.f64 x (fma.f64 x (fma.f64 #s(literal -1/2 binary64) (cos.f64 eps) (fma.f64 (sin.f64 eps) (*.f64 x #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 #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 #s(literal -1/2 binary64) (.f64 eps (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 eps (fma.f64 #s(literal 1/6 binary64) (sin.f64 x) (.f64 (.f64 eps (cos.f64 x)) #s(literal 1/24 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 #s(literal -1/2 binary64) (.f64 eps eps))
(* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2))
(.f64 (.f64 eps eps) (fma.f64 (*.f64 eps 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 eps (.f64 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)
(+.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))
1
#s(literal 1 binary64)
(+ 1 (* -1/2 (pow eps 2)))
(fma.f64 #s(literal -1/2 binary64) (*.f64 eps eps) #s(literal 1 binary64))
(+ 1 (* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2)))
(fma.f64 (.f64 eps eps) (fma.f64 (.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) #s(literal 1 binary64))
(+ 1 (* (pow eps 2) (- (* (pow eps 2) (+ 1/24 (* -1/720 (pow eps 2)))) 1/2)))
(fma.f64 (.f64 eps eps) (fma.f64 (.f64 eps eps) (fma.f64 (*.f64 eps eps) #s(literal -1/720 binary64) #s(literal 1/24 binary64)) #s(literal -1/2 binary64)) #s(literal 1 binary64))
(cos eps)
(cos.f64 eps)
(cos eps)
(cos.f64 eps)
(cos eps)
(cos.f64 eps)
(cos eps)
(cos.f64 eps)
(cos eps)
(cos.f64 eps)
(cos eps)
(cos.f64 eps)
(cos eps)
(cos.f64 eps)
(cos eps)
(cos.f64 eps)
(- (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)
(+.f64 (cos.f64 eps) (fma.f64 x (-.f64 (*.f64 x (fma.f64 #s(literal -1/2 binary64) (cos.f64 eps) #s(literal 1/2 binary64))) (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)
(fma.f64 x (fma.f64 x (fma.f64 #s(literal -1/2 binary64) (cos.f64 eps) (fma.f64 (sin.f64 eps) (*.f64 x #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))
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(-.f64 (.f64 #s(literal -1/2 binary64) (.f64 eps (cos.f64 x))) (sin.f64 x))
(- (* -1/2 (* eps (cos x))) (sin x))
(-.f64 (.f64 #s(literal -1/2 binary64) (.f64 eps (cos.f64 x))) (sin.f64 x))
(- (* -1/2 (* eps (cos x))) (sin x))
(-.f64 (.f64 #s(literal -1/2 binary64) (.f64 eps (cos.f64 x))) (sin.f64 x))
(- (* -1/2 (* eps (cos x))) (sin x))
(-.f64 (.f64 #s(literal -1/2 binary64) (.f64 eps (cos.f64 x))) (sin.f64 x))
(- (* -1/2 (* eps (cos x))) (sin x))
(-.f64 (.f64 #s(literal -1/2 binary64) (.f64 eps (cos.f64 x))) (sin.f64 x))
(- (* -1/2 (* eps (cos x))) (sin x))
(-.f64 (.f64 #s(literal -1/2 binary64) (.f64 eps (cos.f64 x))) (sin.f64 x))
(* -1 (sin x))
(neg.f64 (sin.f64 x))
(- (* -1/2 (* eps (cos x))) (sin x))
(-.f64 (.f64 #s(literal -1/2 binary64) (.f64 eps (cos.f64 x))) (sin.f64 x))
(- (* -1/2 (* eps (cos x))) (sin x))
(-.f64 (.f64 #s(literal -1/2 binary64) (.f64 eps (cos.f64 x))) (sin.f64 x))
(- (* -1/2 (* eps (cos x))) (sin x))
(-.f64 (.f64 #s(literal -1/2 binary64) (.f64 eps (cos.f64 x))) (sin.f64 x))
(* -1/2 (* eps (cos x)))
(.f64 #s(literal -1/2 binary64) (.f64 eps (cos.f64 x)))
(* eps (+ (* -1 (/ (sin x) eps)) (* -1/2 (cos x))))
(neg.f64 (*.f64 eps (fma.f64 (cos.f64 x) #s(literal 1/2 binary64) (/.f64 (sin.f64 x) eps))))
(* eps (+ (* -1 (/ (sin x) eps)) (* -1/2 (cos x))))
(neg.f64 (*.f64 eps (fma.f64 (cos.f64 x) #s(literal 1/2 binary64) (/.f64 (sin.f64 x) eps))))
(* eps (+ (* -1 (/ (sin x) eps)) (* -1/2 (cos x))))
(neg.f64 (*.f64 eps (fma.f64 (cos.f64 x) #s(literal 1/2 binary64) (/.f64 (sin.f64 x) eps))))
(* -1/2 (* eps (cos x)))
(.f64 #s(literal -1/2 binary64) (.f64 eps (cos.f64 x)))
(* -1 (* eps (+ (* 1/2 (cos x)) (/ (sin x) eps))))
(neg.f64 (*.f64 eps (fma.f64 (cos.f64 x) #s(literal 1/2 binary64) (/.f64 (sin.f64 x) eps))))
(* -1 (* eps (+ (* 1/2 (cos x)) (/ (sin x) eps))))
(neg.f64 (*.f64 eps (fma.f64 (cos.f64 x) #s(literal 1/2 binary64) (/.f64 (sin.f64 x) eps))))
(* -1 (* eps (+ (* 1/2 (cos x)) (/ (sin x) eps))))
(neg.f64 (*.f64 eps (fma.f64 (cos.f64 x) #s(literal 1/2 binary64) (/.f64 (sin.f64 x) eps))))
(* eps (sin x))
(*.f64 eps (sin.f64 x))
(* eps (sin x))
(*.f64 eps (sin.f64 x))
(* eps (sin x))
(*.f64 eps (sin.f64 x))
(* eps (sin x))
(*.f64 eps (sin.f64 x))
(* eps (sin x))
(*.f64 eps (sin.f64 x))
(* eps (sin x))
(*.f64 eps (sin.f64 x))
(* eps (sin x))
(*.f64 eps (sin.f64 x))
(* eps (sin x))
(*.f64 eps (sin.f64 x))
(* eps (sin x))
(*.f64 eps (sin.f64 x))
(* eps (sin x))
(*.f64 eps (sin.f64 x))
(* eps (sin x))
(*.f64 eps (sin.f64 x))
(* eps (sin x))
(*.f64 eps (sin.f64 x))
(* eps x)
(*.f64 eps x)
(* x (+ eps (* -1/6 (* eps (pow x 2)))))
(.f64 x (fma.f64 eps (.f64 #s(literal -1/6 binary64) (*.f64 x x)) eps))
(* x (+ eps (* (pow x 2) (+ (* -1/6 eps) (* 1/120 (* eps (pow x 2)))))))
(.f64 x (fma.f64 (.f64 eps (.f64 x x)) (fma.f64 (.f64 x x) #s(literal 1/120 binary64) #s(literal -1/6 binary64)) eps))
(* x (+ eps (* (pow x 2) (+ (* -1/6 eps) (* (pow x 2) (+ (* -1/5040 (* eps (pow x 2))) (* 1/120 eps)))))))
(.f64 x (fma.f64 (.f64 x x) (fma.f64 (.f64 x x) (.f64 eps (fma.f64 (.f64 x x) #s(literal -1/5040 binary64) #s(literal 1/120 binary64))) (.f64 eps #s(literal -1/6 binary64))) eps))
(* eps (sin x))
(*.f64 eps (sin.f64 x))
(* eps (sin x))
(*.f64 eps (sin.f64 x))
(* eps (sin x))
(*.f64 eps (sin.f64 x))
(* eps (sin x))
(*.f64 eps (sin.f64 x))
(* eps (sin x))
(*.f64 eps (sin.f64 x))
(* eps (sin x))
(*.f64 eps (sin.f64 x))
(* eps (sin x))
(*.f64 eps (sin.f64 x))
(* eps (sin x))
(*.f64 eps (sin.f64 x))
(* -1 x)
(neg.f64 x)
(* -1 x)
(neg.f64 x)
(* -1 x)
(neg.f64 x)
(* -1 x)
(neg.f64 x)
(* -1 x)
(neg.f64 x)
(* -1 x)
(neg.f64 x)
(* -1 x)
(neg.f64 x)
(* -1 x)
(neg.f64 x)
(* -1 x)
(neg.f64 x)
(* -1 x)
(neg.f64 x)
(* -1 x)
(neg.f64 x)
(* -1 x)
(neg.f64 x)
(* -1/6 x)
(*.f64 x #s(literal -1/6 binary64))
(* x (- (* 1/120 (pow x 2)) 1/6))
(.f64 x (fma.f64 (.f64 x x) #s(literal 1/120 binary64) #s(literal -1/6 binary64)))
(* x (- (* (pow x 2) (+ 1/120 (* -1/5040 (pow x 2)))) 1/6))
(.f64 x (fma.f64 (.f64 x x) (fma.f64 (*.f64 x x) #s(literal -1/5040 binary64) #s(literal 1/120 binary64)) #s(literal -1/6 binary64)))
(* x (- (* (pow x 2) (+ 1/120 (* -1/5040 (pow x 2)))) 1/6))
(.f64 x (fma.f64 (.f64 x x) (fma.f64 (*.f64 x x) #s(literal -1/5040 binary64) #s(literal 1/120 binary64)) #s(literal -1/6 binary64)))
(* -1/5040 (pow x 5))
(*.f64 #s(literal -1/5040 binary64) (pow.f64 x #s(literal 5 binary64)))
(* (pow x 5) (- (* 1/120 (/ 1 (pow x 2))) 1/5040))
(.f64 (+.f64 #s(literal -1/5040 binary64) (/.f64 #s(literal 1/120 binary64) (.f64 x x))) (pow.f64 x #s(literal 5 binary64)))
(* (pow x 5) (- (* 1/120 (/ 1 (pow x 2))) (+ 1/5040 (/ 1/6 (pow x 4)))))
(.f64 (pow.f64 x #s(literal 5 binary64)) (+.f64 (+.f64 #s(literal -1/5040 binary64) (/.f64 #s(literal 1/120 binary64) (.f64 x x))) (/.f64 #s(literal -1/6 binary64) (.f64 (.f64 x x) (*.f64 x x)))))
(* (pow x 5) (- (* 1/120 (/ 1 (pow x 2))) (+ 1/5040 (/ 1/6 (pow x 4)))))
(.f64 (pow.f64 x #s(literal 5 binary64)) (+.f64 (+.f64 #s(literal -1/5040 binary64) (/.f64 #s(literal 1/120 binary64) (.f64 x x))) (/.f64 #s(literal -1/6 binary64) (.f64 (.f64 x x) (*.f64 x x)))))
(* -1/5040 (pow x 5))
(*.f64 #s(literal -1/5040 binary64) (pow.f64 x #s(literal 5 binary64)))
(* -1 (* (pow x 5) (- 1/5040 (* 1/120 (/ 1 (pow x 2))))))
(.f64 (+.f64 #s(literal -1/5040 binary64) (/.f64 #s(literal 1/120 binary64) (.f64 x x))) (pow.f64 x #s(literal 5 binary64)))
(* -1 (* (pow x 5) (- (+ 1/5040 (/ 1/6 (pow x 4))) (* 1/120 (/ 1 (pow x 2))))))
(.f64 (pow.f64 x #s(literal 5 binary64)) (+.f64 (+.f64 #s(literal -1/5040 binary64) (/.f64 #s(literal 1/120 binary64) (.f64 x x))) (/.f64 #s(literal -1/6 binary64) (.f64 (.f64 x x) (*.f64 x x)))))
(* -1 (* (pow x 5) (- (+ 1/5040 (/ 1/6 (pow x 4))) (* 1/120 (/ 1 (pow x 2))))))
(.f64 (pow.f64 x #s(literal 5 binary64)) (+.f64 (+.f64 #s(literal -1/5040 binary64) (/.f64 #s(literal 1/120 binary64) (.f64 x x))) (/.f64 #s(literal -1/6 binary64) (.f64 (.f64 x x) (*.f64 x x)))))
(* -1/5040 x)
(*.f64 x #s(literal -1/5040 binary64))
(* -1/5040 x)
(*.f64 x #s(literal -1/5040 binary64))
(* -1/5040 x)
(*.f64 x #s(literal -1/5040 binary64))
(* -1/5040 x)
(*.f64 x #s(literal -1/5040 binary64))
(* -1/5040 x)
(*.f64 x #s(literal -1/5040 binary64))
(* -1/5040 x)
(*.f64 x #s(literal -1/5040 binary64))
(* -1/5040 x)
(*.f64 x #s(literal -1/5040 binary64))
(* -1/5040 x)
(*.f64 x #s(literal -1/5040 binary64))
(* -1/5040 x)
(*.f64 x #s(literal -1/5040 binary64))
(* -1/5040 x)
(*.f64 x #s(literal -1/5040 binary64))
(* -1/5040 x)
(*.f64 x #s(literal -1/5040 binary64))
(* -1/5040 x)
(*.f64 x #s(literal -1/5040 binary64))

rewrite242.0ms (1.5%)

Memory

-0.7MiB live, 115.6MiB allocated

Rules

6 114×	`lower-fma.f32`
6 102×	`lower-fma.f64`
4 580×	`lower-*.f32`
4 564×	`lower-*.f64`
3 374×	`lower-/.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	49	319
0	80	319
1	319	307
2	2183	307
0	8293	303

Stop Event

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

Counts

23 → 465

Calls

Call 1

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

Outputs
(exp.f64 (.f64 (log.f64 (/.f64 #s(literal 1 binary64) (.f64 eps (-.f64 (.f64 (cos.f64 x) (.f64 eps #s(literal -1/2 binary64))) (sin.f64 x))))) #s(literal -1 binary64)))
(+.f64 (.f64 (sin.f64 x) (neg.f64 eps)) (.f64 (cos.f64 x) (.f64 #s(literal -1/2 binary64) (.f64 eps eps))))
(+.f64 (.f64 (cos.f64 x) (.f64 #s(literal -1/2 binary64) (.f64 eps eps))) (.f64 (sin.f64 x) (neg.f64 eps)))
(-.f64 (.f64 (cos.f64 x) (.f64 #s(literal -1/2 binary64) (.f64 eps eps))) (.f64 eps (sin.f64 x)))
(-.f64 #s(literal 0 binary64) (-.f64 (.f64 eps (sin.f64 x)) (.f64 (cos.f64 x) (.f64 #s(literal -1/2 binary64) (.f64 eps eps)))))
(-.f64 #s(literal 0 binary64) (/.f64 (-.f64 (.f64 eps (sin.f64 x)) (.f64 (cos.f64 x) (.f64 #s(literal -1/2 binary64) (.f64 eps eps)))) #s(literal 1 binary64)))
(-.f64 (/.f64 #s(literal 0 binary64) (/.f64 #s(literal 1 binary64) (-.f64 (.f64 (cos.f64 x) (.f64 eps #s(literal -1/2 binary64))) (sin.f64 x)))) (.f64 (.f64 eps (-.f64 (.f64 (cos.f64 x) (.f64 eps #s(literal -1/2 binary64))) (sin.f64 x))) #s(literal -1 binary64)))
(-.f64 (/.f64 (.f64 (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x)))) (.f64 (.f64 #s(literal -1/2 binary64) (.f64 eps eps)) (.f64 #s(literal -1/2 binary64) (.f64 eps eps)))) (.f64 eps (-.f64 (.f64 (cos.f64 x) (.f64 eps #s(literal -1/2 binary64))) (neg.f64 (sin.f64 x))))) (/.f64 (.f64 (.f64 eps eps) (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x))))) (.f64 eps (-.f64 (.f64 (cos.f64 x) (.f64 eps #s(literal -1/2 binary64))) (neg.f64 (sin.f64 x))))))
(-.f64 (fma.f64 (cos.f64 x) (.f64 #s(literal -1/2 binary64) (.f64 eps eps)) #s(literal 0 binary64)) (*.f64 eps (sin.f64 x)))
(-.f64 (/.f64 (.f64 (cos.f64 x) (.f64 #s(literal -1/2 binary64) (.f64 eps eps))) #s(literal 1 binary64)) (/.f64 (.f64 eps (sin.f64 x)) #s(literal 1 binary64)))
(-.f64 (/.f64 (/.f64 #s(literal 0 binary64) (/.f64 #s(literal 1 binary64) (-.f64 (.f64 (cos.f64 x) (.f64 eps #s(literal -1/2 binary64))) (sin.f64 x)))) #s(literal 1 binary64)) (/.f64 (.f64 (.f64 eps (-.f64 (.f64 (cos.f64 x) (.f64 eps #s(literal -1/2 binary64))) (sin.f64 x))) #s(literal -1 binary64)) #s(literal 1 binary64)))
(-.f64 (/.f64 (/.f64 (.f64 (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x)))) (.f64 (.f64 #s(literal -1/2 binary64) (.f64 eps eps)) (.f64 #s(literal -1/2 binary64) (.f64 eps eps)))) (.f64 eps (-.f64 (.f64 (cos.f64 x) (.f64 eps #s(literal -1/2 binary64))) (neg.f64 (sin.f64 x))))) #s(literal 1 binary64)) (/.f64 (/.f64 (.f64 (.f64 eps eps) (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x))))) (.f64 eps (-.f64 (.f64 (cos.f64 x) (.f64 eps #s(literal -1/2 binary64))) (neg.f64 (sin.f64 x))))) #s(literal 1 binary64)))
(-.f64 (/.f64 (fma.f64 (cos.f64 x) (.f64 #s(literal -1/2 binary64) (.f64 eps eps)) #s(literal 0 binary64)) #s(literal 1 binary64)) (/.f64 (*.f64 eps (sin.f64 x)) #s(literal 1 binary64)))
(-.f64 (/.f64 (pow.f64 (.f64 (cos.f64 x) (.f64 #s(literal -1/2 binary64) (.f64 eps eps))) #s(literal 3 binary64)) (fma.f64 (.f64 eps eps) (.f64 (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x)))) (.f64 (.f64 eps #s(literal -1/2 binary64)) (.f64 eps #s(literal -1/2 binary64)))) (fma.f64 (.f64 eps eps) (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x)))) (.f64 (.f64 (cos.f64 x) (.f64 #s(literal -1/2 binary64) (.f64 eps eps))) (.f64 eps (sin.f64 x)))))) (/.f64 (pow.f64 (.f64 eps (sin.f64 x)) #s(literal 3 binary64)) (fma.f64 (.f64 eps eps) (.f64 (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x)))) (.f64 (.f64 eps #s(literal -1/2 binary64)) (.f64 eps #s(literal -1/2 binary64)))) (fma.f64 (.f64 eps eps) (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x)))) (.f64 (.f64 (cos.f64 x) (.f64 #s(literal -1/2 binary64) (.f64 eps eps))) (.f64 eps (sin.f64 x)))))))
(-.f64 (/.f64 (.f64 (.f64 eps eps) (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x))))) (-.f64 (.f64 (sin.f64 x) (neg.f64 eps)) (.f64 (cos.f64 x) (.f64 #s(literal -1/2 binary64) (.f64 eps eps))))) (/.f64 (.f64 (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x)))) (.f64 (.f64 #s(literal -1/2 binary64) (.f64 eps eps)) (.f64 #s(literal -1/2 binary64) (.f64 eps eps)))) (-.f64 (.f64 (sin.f64 x) (neg.f64 eps)) (.f64 (cos.f64 x) (.f64 #s(literal -1/2 binary64) (.f64 eps eps))))))
(fma.f64 (cos.f64 x) (.f64 #s(literal -1/2 binary64) (.f64 eps eps)) (*.f64 (sin.f64 x) (neg.f64 eps)))
(fma.f64 eps (.f64 (cos.f64 x) (.f64 eps #s(literal -1/2 binary64))) (*.f64 (sin.f64 x) (neg.f64 eps)))
(fma.f64 eps (neg.f64 (sin.f64 x)) (.f64 (cos.f64 x) (.f64 #s(literal -1/2 binary64) (*.f64 eps eps))))
(fma.f64 (.f64 eps #s(literal -1/2 binary64)) (.f64 (cos.f64 x) eps) (*.f64 (sin.f64 x) (neg.f64 eps)))
(fma.f64 (.f64 (cos.f64 x) (.f64 eps #s(literal -1/2 binary64))) eps (*.f64 (sin.f64 x) (neg.f64 eps)))
(fma.f64 (sin.f64 x) (neg.f64 eps) (.f64 (cos.f64 x) (.f64 #s(literal -1/2 binary64) (*.f64 eps eps))))
(fma.f64 (.f64 eps (sin.f64 x)) #s(literal -1 binary64) (.f64 (cos.f64 x) (.f64 #s(literal -1/2 binary64) (.f64 eps eps))))
(fma.f64 #s(literal -1 binary64) (.f64 eps (sin.f64 x)) (.f64 (cos.f64 x) (.f64 #s(literal -1/2 binary64) (.f64 eps eps))))
(fma.f64 (.f64 (cos.f64 x) #s(literal -1/2 binary64)) (.f64 eps eps) (*.f64 (sin.f64 x) (neg.f64 eps)))
(fma.f64 (neg.f64 eps) (sin.f64 x) (.f64 (cos.f64 x) (.f64 #s(literal -1/2 binary64) (*.f64 eps eps))))
(fma.f64 (.f64 eps eps) (.f64 (cos.f64 x) #s(literal -1/2 binary64)) (*.f64 (sin.f64 x) (neg.f64 eps)))
(fma.f64 (neg.f64 (sin.f64 x)) eps (.f64 (cos.f64 x) (.f64 #s(literal -1/2 binary64) (*.f64 eps eps))))
(fma.f64 (.f64 (cos.f64 x) eps) (.f64 eps #s(literal -1/2 binary64)) (*.f64 (sin.f64 x) (neg.f64 eps)))
(fma.f64 (.f64 #s(literal -1/2 binary64) (.f64 eps eps)) (cos.f64 x) (*.f64 (sin.f64 x) (neg.f64 eps)))
(fma.f64 (.f64 eps (.f64 (cos.f64 x) eps)) #s(literal -1/2 binary64) (*.f64 (sin.f64 x) (neg.f64 eps)))
(neg.f64 (.f64 (.f64 eps (-.f64 (.f64 (cos.f64 x) (.f64 eps #s(literal -1/2 binary64))) (sin.f64 x))) #s(literal -1 binary64)))
(/.f64 eps (/.f64 #s(literal 1 binary64) (-.f64 (.f64 (cos.f64 x) (.f64 eps #s(literal -1/2 binary64))) (sin.f64 x))))
(/.f64 (.f64 eps (-.f64 (.f64 (cos.f64 x) (*.f64 eps #s(literal -1/2 binary64))) (sin.f64 x))) #s(literal 1 binary64))
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(-.f64 #s(literal 0 binary64) x)
(-.f64 (/.f64 #s(literal 0 binary64) (+.f64 #s(literal 0 binary64) (fma.f64 x x (.f64 #s(literal 0 binary64) x)))) (/.f64 (.f64 x (.f64 x x)) (+.f64 #s(literal 0 binary64) (fma.f64 x x (.f64 #s(literal 0 binary64) x)))))
(-.f64 (/.f64 #s(literal 0 binary64) (+.f64 #s(literal 0 binary64) x)) (/.f64 (*.f64 x x) (+.f64 #s(literal 0 binary64) x)))
(neg.f64 x)
(/.f64 (-.f64 #s(literal 0 binary64) (.f64 x (.f64 x x))) (+.f64 #s(literal 0 binary64) (fma.f64 x x (*.f64 #s(literal 0 binary64) x))))
(/.f64 (-.f64 #s(literal 0 binary64) (*.f64 x x)) (+.f64 #s(literal 0 binary64) x))
(/.f64 (neg.f64 (-.f64 #s(literal 0 binary64) (.f64 x (.f64 x x)))) (neg.f64 (+.f64 #s(literal 0 binary64) (fma.f64 x x (*.f64 #s(literal 0 binary64) x)))))
(/.f64 (neg.f64 (-.f64 #s(literal 0 binary64) (*.f64 x x))) (neg.f64 (+.f64 #s(literal 0 binary64) x)))
(/.f64 (+.f64 #s(literal 0 binary64) (.f64 x (.f64 x x))) (+.f64 #s(literal 0 binary64) (-.f64 (.f64 x x) (.f64 #s(literal 0 binary64) (neg.f64 x)))))
(*.f64 x #s(literal -1 binary64))
(*.f64 #s(literal -1 binary64) x)
(+.f64 (.f64 x #s(literal -1/6 binary64)) (.f64 x (.f64 x (.f64 x (fma.f64 x (*.f64 x #s(literal -1/5040 binary64)) #s(literal 1/120 binary64))))))
(+.f64 (.f64 x (.f64 x (.f64 x (fma.f64 x (.f64 x #s(literal -1/5040 binary64)) #s(literal 1/120 binary64))))) (*.f64 x #s(literal -1/6 binary64)))
(-.f64 (/.f64 (.f64 (.f64 x (.f64 x (.f64 x (fma.f64 x (.f64 x #s(literal -1/5040 binary64)) #s(literal 1/120 binary64))))) (.f64 x (.f64 x (.f64 x (fma.f64 x (.f64 x #s(literal -1/5040 binary64)) #s(literal 1/120 binary64)))))) (-.f64 (.f64 x (.f64 x (.f64 x (fma.f64 x (.f64 x #s(literal -1/5040 binary64)) #s(literal 1/120 binary64))))) (.f64 x #s(literal -1/6 binary64)))) (/.f64 (.f64 (.f64 x #s(literal -1/6 binary64)) (.f64 x #s(literal -1/6 binary64))) (-.f64 (.f64 x (.f64 x (.f64 x (fma.f64 x (.f64 x #s(literal -1/5040 binary64)) #s(literal 1/120 binary64))))) (.f64 x #s(literal -1/6 binary64)))))
(fma.f64 x #s(literal -1/6 binary64) (.f64 x (.f64 x (.f64 x (fma.f64 x (.f64 x #s(literal -1/5040 binary64)) #s(literal 1/120 binary64))))))
(fma.f64 x (.f64 x (.f64 x (fma.f64 x (.f64 x #s(literal -1/5040 binary64)) #s(literal 1/120 binary64)))) (.f64 x #s(literal -1/6 binary64)))
(fma.f64 (.f64 x x) (.f64 x (fma.f64 x (.f64 x #s(literal -1/5040 binary64)) #s(literal 1/120 binary64))) (.f64 x #s(literal -1/6 binary64)))
(fma.f64 (fma.f64 x (.f64 x #s(literal -1/5040 binary64)) #s(literal 1/120 binary64)) (.f64 x (.f64 x x)) (.f64 x #s(literal -1/6 binary64)))
(fma.f64 #s(literal -1/6 binary64) x (.f64 x (.f64 x (.f64 x (fma.f64 x (.f64 x #s(literal -1/5040 binary64)) #s(literal 1/120 binary64))))))
(fma.f64 (.f64 x (.f64 x (fma.f64 x (.f64 x #s(literal -1/5040 binary64)) #s(literal 1/120 binary64)))) x (.f64 x #s(literal -1/6 binary64)))
(fma.f64 (.f64 x (.f64 x x)) (fma.f64 x (.f64 x #s(literal -1/5040 binary64)) #s(literal 1/120 binary64)) (.f64 x #s(literal -1/6 binary64)))
(fma.f64 (.f64 x (fma.f64 x (.f64 x #s(literal -1/5040 binary64)) #s(literal 1/120 binary64))) (.f64 x x) (.f64 x #s(literal -1/6 binary64)))
(/.f64 (fma.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x (fma.f64 x (.f64 x #s(literal -1/5040 binary64)) #s(literal 1/120 binary64)))) (.f64 x (.f64 (.f64 x (fma.f64 x (.f64 x #s(literal -1/5040 binary64)) #s(literal 1/120 binary64))) (.f64 x (.f64 x (fma.f64 x (.f64 x #s(literal -1/5040 binary64)) #s(literal 1/120 binary64))))))) (.f64 (.f64 x (.f64 x x)) #s(literal -1/216 binary64))) (fma.f64 (.f64 x (.f64 x (.f64 x (fma.f64 x (.f64 x #s(literal -1/5040 binary64)) #s(literal 1/120 binary64))))) (.f64 x (.f64 x (.f64 x (fma.f64 x (.f64 x #s(literal -1/5040 binary64)) #s(literal 1/120 binary64))))) (-.f64 (.f64 (.f64 x #s(literal -1/6 binary64)) (.f64 x #s(literal -1/6 binary64))) (.f64 (.f64 x (.f64 x (.f64 x (fma.f64 x (.f64 x #s(literal -1/5040 binary64)) #s(literal 1/120 binary64))))) (*.f64 x #s(literal -1/6 binary64))))))
(/.f64 (-.f64 (.f64 (.f64 x (.f64 x (.f64 x (fma.f64 x (.f64 x #s(literal -1/5040 binary64)) #s(literal 1/120 binary64))))) (.f64 x (.f64 x (.f64 x (fma.f64 x (.f64 x #s(literal -1/5040 binary64)) #s(literal 1/120 binary64)))))) (.f64 (.f64 x #s(literal -1/6 binary64)) (.f64 x #s(literal -1/6 binary64)))) (-.f64 (.f64 x (.f64 x (.f64 x (fma.f64 x (.f64 x #s(literal -1/5040 binary64)) #s(literal 1/120 binary64))))) (*.f64 x #s(literal -1/6 binary64))))
(/.f64 (.f64 x (fma.f64 (.f64 x (.f64 x (fma.f64 x (.f64 x #s(literal -1/5040 binary64)) #s(literal 1/120 binary64)))) (.f64 x (.f64 (.f64 x (fma.f64 x (.f64 x #s(literal -1/5040 binary64)) #s(literal 1/120 binary64))) (.f64 x (.f64 x (fma.f64 x (.f64 x #s(literal -1/5040 binary64)) #s(literal 1/120 binary64)))))) #s(literal -1/216 binary64))) (-.f64 (fma.f64 x (.f64 (.f64 x (fma.f64 x (.f64 x #s(literal -1/5040 binary64)) #s(literal 1/120 binary64))) (.f64 x (.f64 x (fma.f64 x (.f64 x #s(literal -1/5040 binary64)) #s(literal 1/120 binary64))))) #s(literal 1/36 binary64)) (.f64 (.f64 x x) (.f64 (fma.f64 x (*.f64 x #s(literal -1/5040 binary64)) #s(literal 1/120 binary64)) #s(literal -1/6 binary64)))))
(/.f64 (.f64 x (fma.f64 (.f64 x (.f64 x (fma.f64 x (.f64 x #s(literal -1/5040 binary64)) #s(literal 1/120 binary64)))) (.f64 x (.f64 x (fma.f64 x (.f64 x #s(literal -1/5040 binary64)) #s(literal 1/120 binary64)))) #s(literal -1/36 binary64))) (fma.f64 x (.f64 x (fma.f64 x (*.f64 x #s(literal -1/5040 binary64)) #s(literal 1/120 binary64))) #s(literal 1/6 binary64)))
(/.f64 (.f64 (fma.f64 (.f64 x (.f64 x (fma.f64 x (.f64 x #s(literal -1/5040 binary64)) #s(literal 1/120 binary64)))) (.f64 x (.f64 (.f64 x (fma.f64 x (.f64 x #s(literal -1/5040 binary64)) #s(literal 1/120 binary64))) (.f64 x (.f64 x (fma.f64 x (.f64 x #s(literal -1/5040 binary64)) #s(literal 1/120 binary64)))))) #s(literal -1/216 binary64)) x) (-.f64 (fma.f64 x (.f64 (.f64 x (fma.f64 x (.f64 x #s(literal -1/5040 binary64)) #s(literal 1/120 binary64))) (.f64 x (.f64 x (fma.f64 x (.f64 x #s(literal -1/5040 binary64)) #s(literal 1/120 binary64))))) #s(literal 1/36 binary64)) (.f64 (.f64 x x) (.f64 (fma.f64 x (*.f64 x #s(literal -1/5040 binary64)) #s(literal 1/120 binary64)) #s(literal -1/6 binary64)))))
(/.f64 (.f64 (fma.f64 (.f64 x (.f64 x (fma.f64 x (.f64 x #s(literal -1/5040 binary64)) #s(literal 1/120 binary64)))) (.f64 x (.f64 x (fma.f64 x (.f64 x #s(literal -1/5040 binary64)) #s(literal 1/120 binary64)))) #s(literal -1/36 binary64)) x) (fma.f64 x (.f64 x (fma.f64 x (*.f64 x #s(literal -1/5040 binary64)) #s(literal 1/120 binary64))) #s(literal 1/6 binary64)))
(/.f64 (neg.f64 (fma.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x (fma.f64 x (.f64 x #s(literal -1/5040 binary64)) #s(literal 1/120 binary64)))) (.f64 x (.f64 (.f64 x (fma.f64 x (.f64 x #s(literal -1/5040 binary64)) #s(literal 1/120 binary64))) (.f64 x (.f64 x (fma.f64 x (.f64 x #s(literal -1/5040 binary64)) #s(literal 1/120 binary64))))))) (.f64 (.f64 x (.f64 x x)) #s(literal -1/216 binary64)))) (neg.f64 (fma.f64 (.f64 x (.f64 x (.f64 x (fma.f64 x (.f64 x #s(literal -1/5040 binary64)) #s(literal 1/120 binary64))))) (.f64 x (.f64 x (.f64 x (fma.f64 x (.f64 x #s(literal -1/5040 binary64)) #s(literal 1/120 binary64))))) (-.f64 (.f64 (.f64 x #s(literal -1/6 binary64)) (.f64 x #s(literal -1/6 binary64))) (.f64 (.f64 x (.f64 x (.f64 x (fma.f64 x (.f64 x #s(literal -1/5040 binary64)) #s(literal 1/120 binary64))))) (*.f64 x #s(literal -1/6 binary64)))))))
(/.f64 (neg.f64 (-.f64 (.f64 (.f64 x (.f64 x (.f64 x (fma.f64 x (.f64 x #s(literal -1/5040 binary64)) #s(literal 1/120 binary64))))) (.f64 x (.f64 x (.f64 x (fma.f64 x (.f64 x #s(literal -1/5040 binary64)) #s(literal 1/120 binary64)))))) (.f64 (.f64 x #s(literal -1/6 binary64)) (.f64 x #s(literal -1/6 binary64))))) (neg.f64 (-.f64 (.f64 x (.f64 x (.f64 x (fma.f64 x (.f64 x #s(literal -1/5040 binary64)) #s(literal 1/120 binary64))))) (*.f64 x #s(literal -1/6 binary64)))))
(/.f64 (neg.f64 (.f64 x (fma.f64 (.f64 x (.f64 x (fma.f64 x (.f64 x #s(literal -1/5040 binary64)) #s(literal 1/120 binary64)))) (.f64 x (.f64 (.f64 x (fma.f64 x (.f64 x #s(literal -1/5040 binary64)) #s(literal 1/120 binary64))) (.f64 x (.f64 x (fma.f64 x (.f64 x #s(literal -1/5040 binary64)) #s(literal 1/120 binary64)))))) #s(literal -1/216 binary64)))) (neg.f64 (-.f64 (fma.f64 x (.f64 (.f64 x (fma.f64 x (.f64 x #s(literal -1/5040 binary64)) #s(literal 1/120 binary64))) (.f64 x (.f64 x (fma.f64 x (.f64 x #s(literal -1/5040 binary64)) #s(literal 1/120 binary64))))) #s(literal 1/36 binary64)) (.f64 (.f64 x x) (.f64 (fma.f64 x (*.f64 x #s(literal -1/5040 binary64)) #s(literal 1/120 binary64)) #s(literal -1/6 binary64))))))
(/.f64 (neg.f64 (.f64 x (fma.f64 (.f64 x (.f64 x (fma.f64 x (.f64 x #s(literal -1/5040 binary64)) #s(literal 1/120 binary64)))) (.f64 x (.f64 x (fma.f64 x (.f64 x #s(literal -1/5040 binary64)) #s(literal 1/120 binary64)))) #s(literal -1/36 binary64)))) (neg.f64 (fma.f64 x (.f64 x (fma.f64 x (*.f64 x #s(literal -1/5040 binary64)) #s(literal 1/120 binary64))) #s(literal 1/6 binary64))))
(/.f64 (neg.f64 (.f64 (fma.f64 (.f64 x (.f64 x (fma.f64 x (.f64 x #s(literal -1/5040 binary64)) #s(literal 1/120 binary64)))) (.f64 x (.f64 (.f64 x (fma.f64 x (.f64 x #s(literal -1/5040 binary64)) #s(literal 1/120 binary64))) (.f64 x (.f64 x (fma.f64 x (.f64 x #s(literal -1/5040 binary64)) #s(literal 1/120 binary64)))))) #s(literal -1/216 binary64)) x)) (neg.f64 (-.f64 (fma.f64 x (.f64 (.f64 x (fma.f64 x (.f64 x #s(literal -1/5040 binary64)) #s(literal 1/120 binary64))) (.f64 x (.f64 x (fma.f64 x (.f64 x #s(literal -1/5040 binary64)) #s(literal 1/120 binary64))))) #s(literal 1/36 binary64)) (.f64 (.f64 x x) (.f64 (fma.f64 x (*.f64 x #s(literal -1/5040 binary64)) #s(literal 1/120 binary64)) #s(literal -1/6 binary64))))))
(/.f64 (neg.f64 (.f64 (fma.f64 (.f64 x (.f64 x (fma.f64 x (.f64 x #s(literal -1/5040 binary64)) #s(literal 1/120 binary64)))) (.f64 x (.f64 x (fma.f64 x (.f64 x #s(literal -1/5040 binary64)) #s(literal 1/120 binary64)))) #s(literal -1/36 binary64)) x)) (neg.f64 (fma.f64 x (.f64 x (fma.f64 x (*.f64 x #s(literal -1/5040 binary64)) #s(literal 1/120 binary64))) #s(literal 1/6 binary64))))
(/.f64 (fma.f64 (.f64 x (.f64 x x)) #s(literal -1/216 binary64) (.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x (fma.f64 x (.f64 x #s(literal -1/5040 binary64)) #s(literal 1/120 binary64)))) (.f64 x (.f64 (.f64 x (fma.f64 x (.f64 x #s(literal -1/5040 binary64)) #s(literal 1/120 binary64))) (.f64 x (.f64 x (fma.f64 x (.f64 x #s(literal -1/5040 binary64)) #s(literal 1/120 binary64))))))))) (fma.f64 (.f64 x #s(literal -1/6 binary64)) (.f64 x #s(literal -1/6 binary64)) (-.f64 (.f64 (.f64 x (.f64 x (.f64 x (fma.f64 x (.f64 x #s(literal -1/5040 binary64)) #s(literal 1/120 binary64))))) (.f64 x (.f64 x (.f64 x (fma.f64 x (.f64 x #s(literal -1/5040 binary64)) #s(literal 1/120 binary64)))))) (.f64 (.f64 x #s(literal -1/6 binary64)) (.f64 x (.f64 x (.f64 x (fma.f64 x (*.f64 x #s(literal -1/5040 binary64)) #s(literal 1/120 binary64)))))))))
(.f64 x (fma.f64 (.f64 x x) (fma.f64 x (*.f64 x #s(literal -1/5040 binary64)) #s(literal 1/120 binary64)) #s(literal -1/6 binary64)))
(.f64 (fma.f64 (.f64 x x) (fma.f64 x (*.f64 x #s(literal -1/5040 binary64)) #s(literal 1/120 binary64)) #s(literal -1/6 binary64)) x)
(*.f64 x #s(literal -1/5040 binary64))
(*.f64 #s(literal -1/5040 binary64) x)

eval114.0ms (0.7%)

Memory: -9.5MiB live, 80.0MiB allocated
Compiler: Compiled 24 167 to 1 634 computations (93.2% saved)

prune141.0ms (0.8%)

Memory

7.7MiB live, 84.9MiB allocated

Pruning

22 alts after pruning (17 fresh and 5 done)

	Pruned	Kept	Total
New	952	10	962
Fresh	9	7	16
Picked	2	3	5
Done	0	2	2
Total	963	22	985

Accuracy

100.0%

Counts

985 → 22

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	99.6%	(.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))
	98.3%	#s(approx (- (cos (+ x eps)) (cos x)) (/.f64 eps (/.f64 #s(literal 1 binary64) #s(approx (- (* (cos x) (* eps -1/2)) (sin x)) (-.f64 (*.f64 #s(literal -1/2 binary64) eps) x)))))
	78.4%	#s(approx (- (cos (+ x eps)) (cos x)) (/.f64 eps #s(approx (/ 1 (- (* (cos x) (* eps -1/2)) (sin x))) (/.f64 #s(literal -1 binary64) (sin.f64 x)))))
✓	49.2%	#s(approx (- (cos (+ x eps)) (cos x)) (+.f64 #s(approx (cos eps) #s(literal 1 binary64)) #s(literal -1 binary64)))
✓	78.4%	#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (sin.f64 x) (neg.f64 eps)))
✓	78.0%	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (sin x) (fma.f64 (.f64 x x) (.f64 x (fma.f64 (.f64 x x) (fma.f64 x (*.f64 x #s(literal -1/5040 binary64)) #s(literal 1/120 binary64)) #s(literal -1/6 binary64))) x)) (neg.f64 eps)))
	77.9%	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (sin x) (fma.f64 (.f64 x x) (.f64 x (fma.f64 (.f64 x x) #s(literal 1/120 binary64) #s(literal -1/6 binary64))) x)) (neg.f64 eps)))
▶	77.7%	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (sin x) (fma.f64 (.f64 x x) #s(approx (* x (+ (* (* x x) (+ (* x (* x -1/5040)) 1/120)) -1/6)) (*.f64 x #s(literal -1/6 binary64))) x)) (neg.f64 eps)))
✓	99.8%	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps (-.f64 (.f64 eps (*.f64 #s(literal -1/2 binary64) (cos.f64 x))) (sin.f64 x))))
	99.6%	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps (-.f64 #s(approx ( eps (* -1/2 (cos x))) (.f64 eps (fma.f64 #s(literal 1/4 binary64) (.f64 x x) #s(literal -1/2 binary64)))) (sin.f64 x))))
	99.6%	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps (-.f64 #s(approx ( eps (* -1/2 (cos x))) (*.f64 eps #s(literal -1/2 binary64))) (sin.f64 x))))
	98.4%	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps #s(approx (- ( eps (* -1/2 (cos x))) (sin x)) (fma.f64 (.f64 x x) (.f64 #s(literal 1/4 binary64) eps) (fma.f64 eps #s(literal -1/2 binary64) (neg.f64 x))))))
▶	98.9%	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps #s(approx (- ( eps (* -1/2 (cos x))) (sin x)) (fma.f64 x (fma.f64 x (fma.f64 eps #s(literal 1/4 binary64) (.f64 x #s(literal 1/6 binary64))) #s(literal -1 binary64)) (.f64 eps #s(literal -1/2 binary64))))))
✓	98.4%	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps #s(approx (- ( eps (* -1/2 (cos x))) (sin x)) (fma.f64 eps (fma.f64 #s(literal 1/4 binary64) (*.f64 x x) #s(literal -1/2 binary64)) (neg.f64 x)))))
	98.4%	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps #s(approx (- ( eps (* -1/2 (cos x))) (sin x)) (-.f64 (*.f64 eps #s(literal -1/2 binary64)) x))))
	98.3%	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps #s(approx (- ( eps (* -1/2 (cos x))) (sin x)) #s(approx (+ (* eps (+ (* 1/4 (* x x)) -1/2)) (neg x)) (*.f64 eps (fma.f64 x (fma.f64 x #s(literal 1/4 binary64) (/.f64 #s(literal -1 binary64) eps)) #s(literal -1/2 binary64)))))))
	49.5%	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps #s(approx (- ( eps (* -1/2 (cos x))) (sin x)) #s(approx (+ (* eps (+ (* 1/4 (* x x)) -1/2)) (neg x)) (.f64 #s(literal 1/4 binary64) (.f64 eps (*.f64 x x)))))))
▶	77.5%	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps #s(approx (- ( eps (* -1/2 (cos x))) (sin x)) #s(approx (+ (* eps (+ (* 1/4 (* x x)) -1/2)) (neg x)) (neg.f64 x)))))
▶	99.1%	#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (/ eps (/ 1 (- (* (cos x) (* eps -1/2)) (sin x)))) (fma.f64 x (fma.f64 x (.f64 eps (fma.f64 eps #s(literal 1/4 binary64) (.f64 x #s(literal 1/6 binary64)))) (neg.f64 eps)) (.f64 #s(literal -1/2 binary64) (.f64 eps eps)))))
	77.9%	#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (sin x) (neg eps)) (.f64 x (fma.f64 (.f64 x x) (.f64 eps (fma.f64 (.f64 x x) #s(literal -1/120 binary64) #s(literal 1/6 binary64))) (neg.f64 eps)))))
	77.7%	#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (sin x) (neg eps)) (.f64 x (.f64 eps (fma.f64 x (*.f64 x #s(literal 1/6 binary64)) #s(literal -1 binary64))))))
	98.9%	#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* eps (- (* eps (* -1/2 (cos x))) (sin x))) (fma.f64 eps (-.f64 (.f64 eps #s(literal -1/2 binary64)) x) (.f64 x (.f64 x (.f64 eps (fma.f64 eps #s(literal 1/4 binary64) (*.f64 x #s(literal 1/6 binary64)))))))))

Compiler

Compiled 624 to 353 computations (43.4% saved)

simplify178.0ms (1.1%)

Memory

-19.5MiB live, 64.4MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 20 expressions of interest:

New	Metric	Score
cost-diff	0	#s(approx (/ eps (/ 1 (- (* (cos x) (* eps -1/2)) (sin x)))) (fma.f64 x (fma.f64 x (.f64 eps (fma.f64 eps #s(literal 1/4 binary64) (.f64 x #s(literal 1/6 binary64)))) (neg.f64 eps)) (.f64 #s(literal -1/2 binary64) (.f64 eps eps))))
cost-diff	0	#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (/ eps (/ 1 (- (* (cos x) (* eps -1/2)) (sin x)))) (fma.f64 x (fma.f64 x (.f64 eps (fma.f64 eps #s(literal 1/4 binary64) (.f64 x #s(literal 1/6 binary64)))) (neg.f64 eps)) (.f64 #s(literal -1/2 binary64) (.f64 eps eps)))))
cost-diff	128	(fma.f64 x (.f64 eps (fma.f64 eps #s(literal 1/4 binary64) (.f64 x #s(literal 1/6 binary64)))) (neg.f64 eps))
cost-diff	320	(fma.f64 x (fma.f64 x (.f64 eps (fma.f64 eps #s(literal 1/4 binary64) (.f64 x #s(literal 1/6 binary64)))) (neg.f64 eps)) (.f64 #s(literal -1/2 binary64) (.f64 eps eps)))
cost-diff	0	(fma.f64 x (fma.f64 x (fma.f64 eps #s(literal 1/4 binary64) (.f64 x #s(literal 1/6 binary64))) #s(literal -1 binary64)) (.f64 eps #s(literal -1/2 binary64)))
cost-diff	0	#s(approx (- (* eps (* -1/2 (cos x))) (sin x)) (fma.f64 x (fma.f64 x (fma.f64 eps #s(literal 1/4 binary64) (.f64 x #s(literal 1/6 binary64))) #s(literal -1 binary64)) (.f64 eps #s(literal -1/2 binary64))))
cost-diff	0	(.f64 eps #s(approx (- ( eps (* -1/2 (cos x))) (sin x)) (fma.f64 x (fma.f64 x (fma.f64 eps #s(literal 1/4 binary64) (.f64 x #s(literal 1/6 binary64))) #s(literal -1 binary64)) (.f64 eps #s(literal -1/2 binary64)))))
cost-diff	0	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps #s(approx (- ( eps (* -1/2 (cos x))) (sin x)) (fma.f64 x (fma.f64 x (fma.f64 eps #s(literal 1/4 binary64) (.f64 x #s(literal 1/6 binary64))) #s(literal -1 binary64)) (.f64 eps #s(literal -1/2 binary64))))))
cost-diff	0	(fma.f64 (.f64 x x) #s(approx ( x (+ (* (* x x) (+ (* x (* x -1/5040)) 1/120)) -1/6)) (*.f64 x #s(literal -1/6 binary64))) x)
cost-diff	0	#s(approx (sin x) (fma.f64 (.f64 x x) #s(approx ( x (+ (* (* x x) (+ (* x (* x -1/5040)) 1/120)) -1/6)) (*.f64 x #s(literal -1/6 binary64))) x))
cost-diff	0	(.f64 #s(approx (sin x) (fma.f64 (.f64 x x) #s(approx (* x (+ (* (* x x) (+ (* x (* x -1/5040)) 1/120)) -1/6)) (*.f64 x #s(literal -1/6 binary64))) x)) (neg.f64 eps))
cost-diff	0	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (sin x) (fma.f64 (.f64 x x) #s(approx (* x (+ (* (* x x) (+ (* x (* x -1/5040)) 1/120)) -1/6)) (*.f64 x #s(literal -1/6 binary64))) x)) (neg.f64 eps)))
cost-diff	0	#s(approx (+ (* eps (+ (* 1/4 (* x x)) -1/2)) (neg x)) (neg.f64 x))
cost-diff	0	#s(approx (- (* eps (* -1/2 (cos x))) (sin x)) #s(approx (+ (* eps (+ (* 1/4 (* x x)) -1/2)) (neg x)) (neg.f64 x)))
cost-diff	0	(.f64 eps #s(approx (- ( eps (* -1/2 (cos x))) (sin x)) #s(approx (+ (* eps (+ (* 1/4 (* x x)) -1/2)) (neg x)) (neg.f64 x))))
cost-diff	0	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps #s(approx (- ( eps (* -1/2 (cos x))) (sin x)) #s(approx (+ (* eps (+ (* 1/4 (* x x)) -1/2)) (neg x)) (neg.f64 x)))))
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

11 894×	`lower-fma.f32`
11 882×	`lower-fma.f64`
3 556×	`lower-*.f32`
3 528×	`lower-*.f64`
1 716×	`lower-+.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	75	591
0	108	577
1	224	573
2	621	569
3	1386	555
4	2751	555
5	4010	555
6	5817	555
7	7935	555
0	8001	536

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

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

localize340.0ms (2%)

Memory

7.6MiB live, 122.5MiB allocated

Localize:

Found 20 expressions of interest:

New	Metric	Score
accuracy	0.15625	(.f64 eps (fma.f64 eps #s(literal 1/4 binary64) (.f64 x #s(literal 1/6 binary64))))
accuracy	0.224941259768442	(fma.f64 eps #s(literal 1/4 binary64) (*.f64 x #s(literal 1/6 binary64)))
accuracy	0.31640625	(*.f64 x #s(literal 1/6 binary64))
accuracy	0.5607008332885026	#s(approx (/ eps (/ 1 (- (* (cos x) (* eps -1/2)) (sin x)))) (fma.f64 x (fma.f64 x (.f64 eps (fma.f64 eps #s(literal 1/4 binary64) (.f64 x #s(literal 1/6 binary64)))) (neg.f64 eps)) (.f64 #s(literal -1/2 binary64) (.f64 eps eps))))
accuracy	0.1171875	(.f64 eps #s(approx (- ( eps (* -1/2 (cos x))) (sin x)) (fma.f64 x (fma.f64 x (fma.f64 eps #s(literal 1/4 binary64) (.f64 x #s(literal 1/6 binary64))) #s(literal -1 binary64)) (.f64 eps #s(literal -1/2 binary64)))))
accuracy	0.224941259768442	(fma.f64 eps #s(literal 1/4 binary64) (*.f64 x #s(literal 1/6 binary64)))
accuracy	0.31640625	(*.f64 x #s(literal 1/6 binary64))
accuracy	0.5636859616960326	#s(approx (- (* eps (* -1/2 (cos x))) (sin x)) (fma.f64 x (fma.f64 x (fma.f64 eps #s(literal 1/4 binary64) (.f64 x #s(literal 1/6 binary64))) #s(literal -1 binary64)) (.f64 eps #s(literal -1/2 binary64))))
accuracy	0.31640625	(*.f64 x #s(literal -1/6 binary64))
accuracy	0.35731169473286295	#s(approx (sin x) (fma.f64 (.f64 x x) #s(approx ( x (+ (* (* x x) (+ (* x (* x -1/5040)) 1/120)) -1/6)) (*.f64 x #s(literal -1/6 binary64))) x))
accuracy	0.872265176599925	#s(approx (* x (+ (* (* x x) (+ (* x (* x -1/5040)) 1/120)) -1/6)) (*.f64 x #s(literal -1/6 binary64)))
accuracy	13.653391578308023	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (sin x) (fma.f64 (.f64 x x) #s(approx (* x (+ (* (* x x) (+ (* x (* x -1/5040)) 1/120)) -1/6)) (*.f64 x #s(literal -1/6 binary64))) x)) (neg.f64 eps)))
accuracy	0.012382519536884034	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps #s(approx (- ( eps (* -1/2 (cos x))) (sin x)) #s(approx (+ (* eps (+ (* 1/4 (* x x)) -1/2)) (neg x)) (neg.f64 x)))))
accuracy	0.1171875	(.f64 eps #s(approx (- ( eps (* -1/2 (cos x))) (sin x)) #s(approx (+ (* eps (+ (* 1/4 (* x x)) -1/2)) (neg x)) (neg.f64 x))))
accuracy	0.9078141115803069	#s(approx (- (* eps (* -1/2 (cos x))) (sin x)) #s(approx (+ (* eps (+ (* 1/4 (* x x)) -1/2)) (neg x)) (neg.f64 x)))
accuracy	24.902133231443724	#s(approx (+ (* eps (+ (* 1/4 (* x x)) -1/2)) (neg x)) (neg.f64 x))
accuracy	0.03125	(.f64 (.f64 (sin.f64 (.f64 (+.f64 eps #s(literal 0 binary64)) #s(literal 1/2 binary64))) (sin.f64 (.f64 (+.f64 x (+.f64 x eps)) #s(literal 1/2 binary64)))) #s(literal -2 binary64))
accuracy	0.04125875946961357	(sin.f64 (*.f64 (+.f64 x (+.f64 x eps)) #s(literal 1/2 binary64)))
accuracy	0.1171875	(.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	0.25	(+.f64 x (+.f64 x eps))

Samples

201.0ms	168×	2	valid
66.0ms	86×	1	valid
2.0ms	1×	5	exit
0.0ms	1×	0	valid

Compiler

Compiled 344 to 68 computations (80.2% saved)

Precisions

Click to see histograms. Total time spent on operations: 220.0ms

ival-mult: 62.0ms (28.2% of total)

adjust: 47.0ms (21.4% of total)

ival-cos: 46.0ms (20.9% of total)

ival-add: 20.0ms (9.1% of total)

const: 19.0ms (8.6% of total)

ival-div: 8.0ms (3.6% of total)

ival-sub: 8.0ms (3.6% of total)

ival-sin: 8.0ms (3.6% of total)

ival-neg: 2.0ms (0.9% of total)

exact: 1.0ms (0.5% of total)

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

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

series48.0ms (0.3%)

Memory

-21.7MiB live, 21.4MiB allocated

Counts

27 → 576

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 eps #s(approx (- ( eps (* -1/2 (cos x))) (sin x)) #s(approx (+ (* eps (+ (* 1/4 (* x x)) -1/2)) (neg x)) (neg.f64 x))))) (patch #s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps #s(approx (- ( eps (* -1/2 (cos x))) (sin x)) #s(approx (+ (* eps (+ (* 1/4 (* x x)) -1/2)) (neg x)) (neg.f64 x))))) #<representation binary64>) () ())
#s(alt (.f64 eps #s(approx (- ( eps (* -1/2 (cos x))) (sin x)) #s(approx (+ (* eps (+ (* 1/4 (* x x)) -1/2)) (neg x)) (neg.f64 x)))) (patch (.f64 eps #s(approx (- ( eps (* -1/2 (cos x))) (sin x)) #s(approx (+ (* eps (+ (* 1/4 (* x x)) -1/2)) (neg x)) (neg.f64 x)))) #<representation binary64>) () ())
#s(alt #s(approx (- (* eps (* -1/2 (cos x))) (sin x)) #s(approx (+ (* eps (+ (* 1/4 (* x x)) -1/2)) (neg x)) (neg.f64 x))) (patch #s(approx (- (* eps (* -1/2 (cos x))) (sin x)) #s(approx (+ (* eps (+ (* 1/4 (* x x)) -1/2)) (neg x)) (neg.f64 x))) #<representation binary64>) () ())
#s(alt #s(approx (+ (* eps (+ (* 1/4 (* x x)) -1/2)) (neg x)) (neg.f64 x)) (patch #s(approx (+ (* eps (+ (* 1/4 (* x x)) -1/2)) (neg x)) (neg.f64 x)) #<representation binary64>) () ())
#s(alt #s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (sin x) (fma.f64 (.f64 x x) #s(approx (* x (+ (* (* x x) (+ (* x (* x -1/5040)) 1/120)) -1/6)) (.f64 x #s(literal -1/6 binary64))) x)) (neg.f64 eps))) (patch #s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (sin x) (fma.f64 (.f64 x x) #s(approx ( x (+ (* (* x x) (+ (* x (* x -1/5040)) 1/120)) -1/6)) (*.f64 x #s(literal -1/6 binary64))) x)) (neg.f64 eps))) #<representation binary64>) () ())
#s(alt (.f64 #s(approx (sin x) (fma.f64 (.f64 x x) #s(approx (* x (+ (* (* x x) (+ (* x (* x -1/5040)) 1/120)) -1/6)) (.f64 x #s(literal -1/6 binary64))) x)) (neg.f64 eps)) (patch (.f64 #s(approx (sin x) (fma.f64 (.f64 x x) #s(approx ( x (+ (* (* x x) (+ (* x (* x -1/5040)) 1/120)) -1/6)) (*.f64 x #s(literal -1/6 binary64))) x)) (neg.f64 eps)) #<representation binary64>) () ())
#s(alt #s(approx (sin x) (fma.f64 (.f64 x x) #s(approx ( x (+ (* (* x x) (+ (* x (* x -1/5040)) 1/120)) -1/6)) (.f64 x #s(literal -1/6 binary64))) x)) (patch #s(approx (sin x) (fma.f64 (.f64 x x) #s(approx (* x (+ (* (* x x) (+ (* x (* x -1/5040)) 1/120)) -1/6)) (*.f64 x #s(literal -1/6 binary64))) x)) #<representation binary64>) () ())
#s(alt (fma.f64 (.f64 x x) #s(approx ( x (+ (* (* x x) (+ (* x (* x -1/5040)) 1/120)) -1/6)) (.f64 x #s(literal -1/6 binary64))) x) (patch (fma.f64 (.f64 x x) #s(approx (* x (+ (* (* x x) (+ (* x (* x -1/5040)) 1/120)) -1/6)) (*.f64 x #s(literal -1/6 binary64))) x) #<representation binary64>) () ())
#s(alt #s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps #s(approx (- ( eps (* -1/2 (cos x))) (sin x)) (fma.f64 x (fma.f64 x (fma.f64 eps #s(literal 1/4 binary64) (.f64 x #s(literal 1/6 binary64))) #s(literal -1 binary64)) (.f64 eps #s(literal -1/2 binary64)))))) (patch #s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps #s(approx (- ( eps (* -1/2 (cos x))) (sin x)) (fma.f64 x (fma.f64 x (fma.f64 eps #s(literal 1/4 binary64) (.f64 x #s(literal 1/6 binary64))) #s(literal -1 binary64)) (.f64 eps #s(literal -1/2 binary64)))))) #<representation binary64>) () ())
#s(alt (.f64 eps #s(approx (- ( eps (* -1/2 (cos x))) (sin x)) (fma.f64 x (fma.f64 x (fma.f64 eps #s(literal 1/4 binary64) (.f64 x #s(literal 1/6 binary64))) #s(literal -1 binary64)) (.f64 eps #s(literal -1/2 binary64))))) (patch (.f64 eps #s(approx (- ( eps (* -1/2 (cos x))) (sin x)) (fma.f64 x (fma.f64 x (fma.f64 eps #s(literal 1/4 binary64) (.f64 x #s(literal 1/6 binary64))) #s(literal -1 binary64)) (.f64 eps #s(literal -1/2 binary64))))) #<representation binary64>) () ())
#s(alt #s(approx (- (* eps (* -1/2 (cos x))) (sin x)) (fma.f64 x (fma.f64 x (fma.f64 eps #s(literal 1/4 binary64) (.f64 x #s(literal 1/6 binary64))) #s(literal -1 binary64)) (.f64 eps #s(literal -1/2 binary64)))) (patch #s(approx (- (* eps (* -1/2 (cos x))) (sin x)) (fma.f64 x (fma.f64 x (fma.f64 eps #s(literal 1/4 binary64) (.f64 x #s(literal 1/6 binary64))) #s(literal -1 binary64)) (.f64 eps #s(literal -1/2 binary64)))) #<representation binary64>) () ())
#s(alt (fma.f64 x (fma.f64 x (fma.f64 eps #s(literal 1/4 binary64) (.f64 x #s(literal 1/6 binary64))) #s(literal -1 binary64)) (.f64 eps #s(literal -1/2 binary64))) (patch (fma.f64 x (fma.f64 x (fma.f64 eps #s(literal 1/4 binary64) (.f64 x #s(literal 1/6 binary64))) #s(literal -1 binary64)) (.f64 eps #s(literal -1/2 binary64))) #<representation binary64>) () ())
#s(alt (fma.f64 x (fma.f64 x (.f64 eps (fma.f64 eps #s(literal 1/4 binary64) (.f64 x #s(literal 1/6 binary64)))) (neg.f64 eps)) (.f64 #s(literal -1/2 binary64) (.f64 eps eps))) (patch (fma.f64 x (fma.f64 x (.f64 eps (fma.f64 eps #s(literal 1/4 binary64) (.f64 x #s(literal 1/6 binary64)))) (neg.f64 eps)) (.f64 #s(literal -1/2 binary64) (.f64 eps eps))) #<representation binary64>) () ())
#s(alt (fma.f64 x (.f64 eps (fma.f64 eps #s(literal 1/4 binary64) (.f64 x #s(literal 1/6 binary64)))) (neg.f64 eps)) (patch (fma.f64 x (.f64 eps (fma.f64 eps #s(literal 1/4 binary64) (.f64 x #s(literal 1/6 binary64)))) (neg.f64 eps)) #<representation binary64>) () ())
#s(alt #s(approx (- (cos (+ x eps)) (cos x)) #s(approx (/ eps (/ 1 (- (* (cos x) (* eps -1/2)) (sin x)))) (fma.f64 x (fma.f64 x (.f64 eps (fma.f64 eps #s(literal 1/4 binary64) (.f64 x #s(literal 1/6 binary64)))) (neg.f64 eps)) (.f64 #s(literal -1/2 binary64) (.f64 eps eps))))) (patch #s(approx (- (cos (+ x eps)) (cos x)) #s(approx (/ eps (/ 1 (- (* (cos x) (* eps -1/2)) (sin x)))) (fma.f64 x (fma.f64 x (.f64 eps (fma.f64 eps #s(literal 1/4 binary64) (.f64 x #s(literal 1/6 binary64)))) (neg.f64 eps)) (.f64 #s(literal -1/2 binary64) (.f64 eps eps))))) #<representation binary64>) () ())
#s(alt #s(approx (/ eps (/ 1 (- (* (cos x) (* eps -1/2)) (sin x)))) (fma.f64 x (fma.f64 x (.f64 eps (fma.f64 eps #s(literal 1/4 binary64) (.f64 x #s(literal 1/6 binary64)))) (neg.f64 eps)) (.f64 #s(literal -1/2 binary64) (.f64 eps eps)))) (patch #s(approx (/ eps (/ 1 (- (* (cos x) (* eps -1/2)) (sin x)))) (fma.f64 x (fma.f64 x (.f64 eps (fma.f64 eps #s(literal 1/4 binary64) (.f64 x #s(literal 1/6 binary64)))) (neg.f64 eps)) (.f64 #s(literal -1/2 binary64) (.f64 eps eps)))) #<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 (* x (+ (* (* x x) (+ (* x (* x -1/5040)) 1/120)) -1/6)) (.f64 x #s(literal -1/6 binary64))) (patch #s(approx ( x (+ (* (* x x) (+ (* x (* x -1/5040)) 1/120)) -1/6)) (*.f64 x #s(literal -1/6 binary64))) #<representation binary64>) () ())
#s(alt (.f64 x #s(literal -1/6 binary64)) (patch (.f64 x #s(literal -1/6 binary64)) #<representation binary64>) () ())
#s(alt (.f64 x #s(literal 1/6 binary64)) (patch (.f64 x #s(literal 1/6 binary64)) #<representation binary64>) () ())
#s(alt (fma.f64 eps #s(literal 1/4 binary64) (.f64 x #s(literal 1/6 binary64))) (patch (fma.f64 eps #s(literal 1/4 binary64) (.f64 x #s(literal 1/6 binary64))) #<representation binary64>) () ())
#s(alt (.f64 eps (fma.f64 eps #s(literal 1/4 binary64) (.f64 x #s(literal 1/6 binary64)))) (patch (.f64 eps (fma.f64 eps #s(literal 1/4 binary64) (.f64 x #s(literal 1/6 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>) () ())) ())
#s(alt (* -1 (* eps (sin x))) (taylor 0 eps) (#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 (* eps (+ (* -1 (sin x)) (* -1/2 (* eps (cos x))))) (taylor 0 eps) (#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 (* 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 (.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>) () ())) ())
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#s(alt (* 1/6 x) (taylor inf x) (#s(alt (.f64 x #s(literal 1/6 binary64)) (patch (.f64 x #s(literal 1/6 binary64)) #<representation binary64>) () ())) ())
#s(alt (* 1/6 x) (taylor inf x) (#s(alt (.f64 x #s(literal 1/6 binary64)) (patch (.f64 x #s(literal 1/6 binary64)) #<representation binary64>) () ())) ())
#s(alt (* 1/6 x) (taylor inf x) (#s(alt (.f64 x #s(literal 1/6 binary64)) (patch (.f64 x #s(literal 1/6 binary64)) #<representation binary64>) () ())) ())
#s(alt (* 1/6 x) (taylor -inf x) (#s(alt (.f64 x #s(literal 1/6 binary64)) (patch (.f64 x #s(literal 1/6 binary64)) #<representation binary64>) () ())) ())
#s(alt (* 1/6 x) (taylor -inf x) (#s(alt (.f64 x #s(literal 1/6 binary64)) (patch (.f64 x #s(literal 1/6 binary64)) #<representation binary64>) () ())) ())
#s(alt (* 1/6 x) (taylor -inf x) (#s(alt (.f64 x #s(literal 1/6 binary64)) (patch (.f64 x #s(literal 1/6 binary64)) #<representation binary64>) () ())) ())
#s(alt (* 1/6 x) (taylor -inf x) (#s(alt (.f64 x #s(literal 1/6 binary64)) (patch (.f64 x #s(literal 1/6 binary64)) #<representation binary64>) () ())) ())
#s(alt (* 1/6 x) (taylor 0 eps) (#s(alt (fma.f64 eps #s(literal 1/4 binary64) (.f64 x #s(literal 1/6 binary64))) (patch (fma.f64 eps #s(literal 1/4 binary64) (.f64 x #s(literal 1/6 binary64))) #<representation binary64>) () ())) ())
#s(alt (+ (* 1/6 x) (* 1/4 eps)) (taylor 0 eps) (#s(alt (fma.f64 eps #s(literal 1/4 binary64) (.f64 x #s(literal 1/6 binary64))) (patch (fma.f64 eps #s(literal 1/4 binary64) (.f64 x #s(literal 1/6 binary64))) #<representation binary64>) () ())) ())
#s(alt (+ (* 1/6 x) (* 1/4 eps)) (taylor 0 eps) (#s(alt (fma.f64 eps #s(literal 1/4 binary64) (.f64 x #s(literal 1/6 binary64))) (patch (fma.f64 eps #s(literal 1/4 binary64) (.f64 x #s(literal 1/6 binary64))) #<representation binary64>) () ())) ())
#s(alt (+ (* 1/6 x) (* 1/4 eps)) (taylor 0 eps) (#s(alt (fma.f64 eps #s(literal 1/4 binary64) (.f64 x #s(literal 1/6 binary64))) (patch (fma.f64 eps #s(literal 1/4 binary64) (.f64 x #s(literal 1/6 binary64))) #<representation binary64>) () ())) ())
#s(alt (* 1/4 eps) (taylor inf eps) (#s(alt (fma.f64 eps #s(literal 1/4 binary64) (.f64 x #s(literal 1/6 binary64))) (patch (fma.f64 eps #s(literal 1/4 binary64) (.f64 x #s(literal 1/6 binary64))) #<representation binary64>) () ())) ())
#s(alt (* eps (+ 1/4 (* 1/6 (/ x eps)))) (taylor inf eps) (#s(alt (fma.f64 eps #s(literal 1/4 binary64) (.f64 x #s(literal 1/6 binary64))) (patch (fma.f64 eps #s(literal 1/4 binary64) (.f64 x #s(literal 1/6 binary64))) #<representation binary64>) () ())) ())
#s(alt (* eps (+ 1/4 (* 1/6 (/ x eps)))) (taylor inf eps) (#s(alt (fma.f64 eps #s(literal 1/4 binary64) (.f64 x #s(literal 1/6 binary64))) (patch (fma.f64 eps #s(literal 1/4 binary64) (.f64 x #s(literal 1/6 binary64))) #<representation binary64>) () ())) ())
#s(alt (* eps (+ 1/4 (* 1/6 (/ x eps)))) (taylor inf eps) (#s(alt (fma.f64 eps #s(literal 1/4 binary64) (.f64 x #s(literal 1/6 binary64))) (patch (fma.f64 eps #s(literal 1/4 binary64) (.f64 x #s(literal 1/6 binary64))) #<representation binary64>) () ())) ())
#s(alt (* 1/4 eps) (taylor -inf eps) (#s(alt (fma.f64 eps #s(literal 1/4 binary64) (.f64 x #s(literal 1/6 binary64))) (patch (fma.f64 eps #s(literal 1/4 binary64) (.f64 x #s(literal 1/6 binary64))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* eps (- (* -1/6 (/ x eps)) 1/4))) (taylor -inf eps) (#s(alt (fma.f64 eps #s(literal 1/4 binary64) (.f64 x #s(literal 1/6 binary64))) (patch (fma.f64 eps #s(literal 1/4 binary64) (.f64 x #s(literal 1/6 binary64))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* eps (- (* -1/6 (/ x eps)) 1/4))) (taylor -inf eps) (#s(alt (fma.f64 eps #s(literal 1/4 binary64) (.f64 x #s(literal 1/6 binary64))) (patch (fma.f64 eps #s(literal 1/4 binary64) (.f64 x #s(literal 1/6 binary64))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* eps (- (* -1/6 (/ x eps)) 1/4))) (taylor -inf eps) (#s(alt (fma.f64 eps #s(literal 1/4 binary64) (.f64 x #s(literal 1/6 binary64))) (patch (fma.f64 eps #s(literal 1/4 binary64) (.f64 x #s(literal 1/6 binary64))) #<representation binary64>) () ())) ())
#s(alt (* 1/4 eps) (taylor 0 x) (#s(alt (fma.f64 eps #s(literal 1/4 binary64) (.f64 x #s(literal 1/6 binary64))) (patch (fma.f64 eps #s(literal 1/4 binary64) (.f64 x #s(literal 1/6 binary64))) #<representation binary64>) () ())) ())
#s(alt (+ (* 1/6 x) (* 1/4 eps)) (taylor 0 x) (#s(alt (fma.f64 eps #s(literal 1/4 binary64) (.f64 x #s(literal 1/6 binary64))) (patch (fma.f64 eps #s(literal 1/4 binary64) (.f64 x #s(literal 1/6 binary64))) #<representation binary64>) () ())) ())
#s(alt (+ (* 1/6 x) (* 1/4 eps)) (taylor 0 x) (#s(alt (fma.f64 eps #s(literal 1/4 binary64) (.f64 x #s(literal 1/6 binary64))) (patch (fma.f64 eps #s(literal 1/4 binary64) (.f64 x #s(literal 1/6 binary64))) #<representation binary64>) () ())) ())
#s(alt (+ (* 1/6 x) (* 1/4 eps)) (taylor 0 x) (#s(alt (fma.f64 eps #s(literal 1/4 binary64) (.f64 x #s(literal 1/6 binary64))) (patch (fma.f64 eps #s(literal 1/4 binary64) (.f64 x #s(literal 1/6 binary64))) #<representation binary64>) () ())) ())
#s(alt (* 1/6 x) (taylor inf x) (#s(alt (fma.f64 eps #s(literal 1/4 binary64) (.f64 x #s(literal 1/6 binary64))) (patch (fma.f64 eps #s(literal 1/4 binary64) (.f64 x #s(literal 1/6 binary64))) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1/6 (* 1/4 (/ eps x)))) (taylor inf x) (#s(alt (fma.f64 eps #s(literal 1/4 binary64) (.f64 x #s(literal 1/6 binary64))) (patch (fma.f64 eps #s(literal 1/4 binary64) (.f64 x #s(literal 1/6 binary64))) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1/6 (* 1/4 (/ eps x)))) (taylor inf x) (#s(alt (fma.f64 eps #s(literal 1/4 binary64) (.f64 x #s(literal 1/6 binary64))) (patch (fma.f64 eps #s(literal 1/4 binary64) (.f64 x #s(literal 1/6 binary64))) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1/6 (* 1/4 (/ eps x)))) (taylor inf x) (#s(alt (fma.f64 eps #s(literal 1/4 binary64) (.f64 x #s(literal 1/6 binary64))) (patch (fma.f64 eps #s(literal 1/4 binary64) (.f64 x #s(literal 1/6 binary64))) #<representation binary64>) () ())) ())
#s(alt (* 1/6 x) (taylor -inf x) (#s(alt (fma.f64 eps #s(literal 1/4 binary64) (.f64 x #s(literal 1/6 binary64))) (patch (fma.f64 eps #s(literal 1/4 binary64) (.f64 x #s(literal 1/6 binary64))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (- (* -1/4 (/ eps x)) 1/6))) (taylor -inf x) (#s(alt (fma.f64 eps #s(literal 1/4 binary64) (.f64 x #s(literal 1/6 binary64))) (patch (fma.f64 eps #s(literal 1/4 binary64) (.f64 x #s(literal 1/6 binary64))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (- (* -1/4 (/ eps x)) 1/6))) (taylor -inf x) (#s(alt (fma.f64 eps #s(literal 1/4 binary64) (.f64 x #s(literal 1/6 binary64))) (patch (fma.f64 eps #s(literal 1/4 binary64) (.f64 x #s(literal 1/6 binary64))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (- (* -1/4 (/ eps x)) 1/6))) (taylor -inf x) (#s(alt (fma.f64 eps #s(literal 1/4 binary64) (.f64 x #s(literal 1/6 binary64))) (patch (fma.f64 eps #s(literal 1/4 binary64) (.f64 x #s(literal 1/6 binary64))) #<representation binary64>) () ())) ())
#s(alt (* 1/6 (* eps x)) (taylor 0 eps) (#s(alt (.f64 eps (fma.f64 eps #s(literal 1/4 binary64) (.f64 x #s(literal 1/6 binary64)))) (patch (.f64 eps (fma.f64 eps #s(literal 1/4 binary64) (.f64 x #s(literal 1/6 binary64)))) #<representation binary64>) () ())) ())
#s(alt (* eps (+ (* 1/6 x) (* 1/4 eps))) (taylor 0 eps) (#s(alt (.f64 eps (fma.f64 eps #s(literal 1/4 binary64) (.f64 x #s(literal 1/6 binary64)))) (patch (.f64 eps (fma.f64 eps #s(literal 1/4 binary64) (.f64 x #s(literal 1/6 binary64)))) #<representation binary64>) () ())) ())
#s(alt (* eps (+ (* 1/6 x) (* 1/4 eps))) (taylor 0 eps) (#s(alt (.f64 eps (fma.f64 eps #s(literal 1/4 binary64) (.f64 x #s(literal 1/6 binary64)))) (patch (.f64 eps (fma.f64 eps #s(literal 1/4 binary64) (.f64 x #s(literal 1/6 binary64)))) #<representation binary64>) () ())) ())
#s(alt (* eps (+ (* 1/6 x) (* 1/4 eps))) (taylor 0 eps) (#s(alt (.f64 eps (fma.f64 eps #s(literal 1/4 binary64) (.f64 x #s(literal 1/6 binary64)))) (patch (.f64 eps (fma.f64 eps #s(literal 1/4 binary64) (.f64 x #s(literal 1/6 binary64)))) #<representation binary64>) () ())) ())
#s(alt (* 1/4 (pow eps 2)) (taylor inf eps) (#s(alt (.f64 eps (fma.f64 eps #s(literal 1/4 binary64) (.f64 x #s(literal 1/6 binary64)))) (patch (.f64 eps (fma.f64 eps #s(literal 1/4 binary64) (.f64 x #s(literal 1/6 binary64)))) #<representation binary64>) () ())) ())
#s(alt (* (pow eps 2) (+ 1/4 (* 1/6 (/ x eps)))) (taylor inf eps) (#s(alt (.f64 eps (fma.f64 eps #s(literal 1/4 binary64) (.f64 x #s(literal 1/6 binary64)))) (patch (.f64 eps (fma.f64 eps #s(literal 1/4 binary64) (.f64 x #s(literal 1/6 binary64)))) #<representation binary64>) () ())) ())
#s(alt (* (pow eps 2) (+ 1/4 (* 1/6 (/ x eps)))) (taylor inf eps) (#s(alt (.f64 eps (fma.f64 eps #s(literal 1/4 binary64) (.f64 x #s(literal 1/6 binary64)))) (patch (.f64 eps (fma.f64 eps #s(literal 1/4 binary64) (.f64 x #s(literal 1/6 binary64)))) #<representation binary64>) () ())) ())
#s(alt (* (pow eps 2) (+ 1/4 (* 1/6 (/ x eps)))) (taylor inf eps) (#s(alt (.f64 eps (fma.f64 eps #s(literal 1/4 binary64) (.f64 x #s(literal 1/6 binary64)))) (patch (.f64 eps (fma.f64 eps #s(literal 1/4 binary64) (.f64 x #s(literal 1/6 binary64)))) #<representation binary64>) () ())) ())
#s(alt (* 1/4 (pow eps 2)) (taylor -inf eps) (#s(alt (.f64 eps (fma.f64 eps #s(literal 1/4 binary64) (.f64 x #s(literal 1/6 binary64)))) (patch (.f64 eps (fma.f64 eps #s(literal 1/4 binary64) (.f64 x #s(literal 1/6 binary64)))) #<representation binary64>) () ())) ())
#s(alt (* (pow eps 2) (+ 1/4 (* 1/6 (/ x eps)))) (taylor -inf eps) (#s(alt (.f64 eps (fma.f64 eps #s(literal 1/4 binary64) (.f64 x #s(literal 1/6 binary64)))) (patch (.f64 eps (fma.f64 eps #s(literal 1/4 binary64) (.f64 x #s(literal 1/6 binary64)))) #<representation binary64>) () ())) ())
#s(alt (* (pow eps 2) (+ 1/4 (* 1/6 (/ x eps)))) (taylor -inf eps) (#s(alt (.f64 eps (fma.f64 eps #s(literal 1/4 binary64) (.f64 x #s(literal 1/6 binary64)))) (patch (.f64 eps (fma.f64 eps #s(literal 1/4 binary64) (.f64 x #s(literal 1/6 binary64)))) #<representation binary64>) () ())) ())
#s(alt (* (pow eps 2) (+ 1/4 (* 1/6 (/ x eps)))) (taylor -inf eps) (#s(alt (.f64 eps (fma.f64 eps #s(literal 1/4 binary64) (.f64 x #s(literal 1/6 binary64)))) (patch (.f64 eps (fma.f64 eps #s(literal 1/4 binary64) (.f64 x #s(literal 1/6 binary64)))) #<representation binary64>) () ())) ())
#s(alt (* 1/4 (pow eps 2)) (taylor 0 x) (#s(alt (.f64 eps (fma.f64 eps #s(literal 1/4 binary64) (.f64 x #s(literal 1/6 binary64)))) (patch (.f64 eps (fma.f64 eps #s(literal 1/4 binary64) (.f64 x #s(literal 1/6 binary64)))) #<representation binary64>) () ())) ())
#s(alt (+ (* 1/6 (* eps x)) (* 1/4 (pow eps 2))) (taylor 0 x) (#s(alt (.f64 eps (fma.f64 eps #s(literal 1/4 binary64) (.f64 x #s(literal 1/6 binary64)))) (patch (.f64 eps (fma.f64 eps #s(literal 1/4 binary64) (.f64 x #s(literal 1/6 binary64)))) #<representation binary64>) () ())) ())
#s(alt (+ (* 1/6 (* eps x)) (* 1/4 (pow eps 2))) (taylor 0 x) (#s(alt (.f64 eps (fma.f64 eps #s(literal 1/4 binary64) (.f64 x #s(literal 1/6 binary64)))) (patch (.f64 eps (fma.f64 eps #s(literal 1/4 binary64) (.f64 x #s(literal 1/6 binary64)))) #<representation binary64>) () ())) ())
#s(alt (+ (* 1/6 (* eps x)) (* 1/4 (pow eps 2))) (taylor 0 x) (#s(alt (.f64 eps (fma.f64 eps #s(literal 1/4 binary64) (.f64 x #s(literal 1/6 binary64)))) (patch (.f64 eps (fma.f64 eps #s(literal 1/4 binary64) (.f64 x #s(literal 1/6 binary64)))) #<representation binary64>) () ())) ())
#s(alt (* 1/6 (* eps x)) (taylor inf x) (#s(alt (.f64 eps (fma.f64 eps #s(literal 1/4 binary64) (.f64 x #s(literal 1/6 binary64)))) (patch (.f64 eps (fma.f64 eps #s(literal 1/4 binary64) (.f64 x #s(literal 1/6 binary64)))) #<representation binary64>) () ())) ())
#s(alt (* x (+ (* 1/6 eps) (* 1/4 (/ (pow eps 2) x)))) (taylor inf x) (#s(alt (.f64 eps (fma.f64 eps #s(literal 1/4 binary64) (.f64 x #s(literal 1/6 binary64)))) (patch (.f64 eps (fma.f64 eps #s(literal 1/4 binary64) (.f64 x #s(literal 1/6 binary64)))) #<representation binary64>) () ())) ())
#s(alt (* x (+ (* 1/6 eps) (* 1/4 (/ (pow eps 2) x)))) (taylor inf x) (#s(alt (.f64 eps (fma.f64 eps #s(literal 1/4 binary64) (.f64 x #s(literal 1/6 binary64)))) (patch (.f64 eps (fma.f64 eps #s(literal 1/4 binary64) (.f64 x #s(literal 1/6 binary64)))) #<representation binary64>) () ())) ())
#s(alt (* x (+ (* 1/6 eps) (* 1/4 (/ (pow eps 2) x)))) (taylor inf x) (#s(alt (.f64 eps (fma.f64 eps #s(literal 1/4 binary64) (.f64 x #s(literal 1/6 binary64)))) (patch (.f64 eps (fma.f64 eps #s(literal 1/4 binary64) (.f64 x #s(literal 1/6 binary64)))) #<representation binary64>) () ())) ())
#s(alt (* 1/6 (* eps x)) (taylor -inf x) (#s(alt (.f64 eps (fma.f64 eps #s(literal 1/4 binary64) (.f64 x #s(literal 1/6 binary64)))) (patch (.f64 eps (fma.f64 eps #s(literal 1/4 binary64) (.f64 x #s(literal 1/6 binary64)))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (+ (* -1/4 (/ (pow eps 2) x)) (* -1/6 eps)))) (taylor -inf x) (#s(alt (.f64 eps (fma.f64 eps #s(literal 1/4 binary64) (.f64 x #s(literal 1/6 binary64)))) (patch (.f64 eps (fma.f64 eps #s(literal 1/4 binary64) (.f64 x #s(literal 1/6 binary64)))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (+ (* -1/4 (/ (pow eps 2) x)) (* -1/6 eps)))) (taylor -inf x) (#s(alt (.f64 eps (fma.f64 eps #s(literal 1/4 binary64) (.f64 x #s(literal 1/6 binary64)))) (patch (.f64 eps (fma.f64 eps #s(literal 1/4 binary64) (.f64 x #s(literal 1/6 binary64)))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (+ (* -1/4 (/ (pow eps 2) x)) (* -1/6 eps)))) (taylor -inf x) (#s(alt (.f64 eps (fma.f64 eps #s(literal 1/4 binary64) (.f64 x #s(literal 1/6 binary64)))) (patch (.f64 eps (fma.f64 eps #s(literal 1/4 binary64) (.f64 x #s(literal 1/6 binary64)))) #<representation binary64>) () ())) ())

Calls

144 calls:

Time	Variable		Point	Expression
4.0ms	x	@	inf	(+ (* x (+ (* x (* eps (+ (* eps 1/4) (* x 1/6)))) (neg eps))) (* -1/2 (* eps eps)))
1.0ms	x	@	inf	(* (* (sin (* (+ eps 0) 1/2)) (sin (* (+ x (+ x eps)) 1/2))) -2)
1.0ms	x	@	0	(* (* (sin (* (+ eps 0) 1/2)) (sin (* (+ x (+ x eps)) 1/2))) -2)
1.0ms	eps	@	-inf	(* (* (sin (* (+ eps 0) 1/2)) (sin (* (+ x (+ x eps)) 1/2))) -2)
1.0ms	eps	@	0	(+ (* x (+ (* x (+ (* eps 1/4) (* x 1/6))) -1)) (* eps -1/2))

simplify229.0ms (1.4%)

Memory

37.3MiB live, 110.5MiB allocated

Algorithm

1×	egg-herbie

Rules

13 232×	`lower-fma.f64`
13 232×	`lower-fma.f32`
6 848×	`lower-*.f64`
6 848×	`lower-*.f32`
4 148×	`lower-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	485	5979
1	1513	5710
2	4458	5680
0	8668	5355

Stop Event

1×	iter limit
1×	node limit

Counts

576 → 556

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))
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(+ (* 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)))))
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(* eps (+ (* -1 (sin x)) (* -1/2 (* eps (cos x)))))
(* eps (+ (* -1 (sin x)) (* -1/2 (* eps (cos x)))))
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(- (* -1/2 (* eps (cos x))) (sin x))
(- (* -1/2 (* eps (cos x))) (sin x))
(* -1/2 (* eps (cos x)))
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(* eps (+ (* -1 (/ (sin x) eps)) (* -1/2 (cos x))))
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(- (* -1/2 (* eps (cos x))) (sin x))
(- (* -1/2 (* eps (cos x))) (sin x))
(- (* -1/2 (* eps (cos x))) (sin x))
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(- (* eps (- (* 1/4 (pow x 2)) 1/2)) x)
(- (* eps (- (* 1/4 (pow x 2)) 1/2)) x)
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(* eps (- (+ (* -1 (/ x eps)) (* 1/4 (pow x 2))) 1/2))
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(- (cos (+ eps x)) (cos x))
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(- (cos (- eps (* -1 x))) (cos x))
(- (cos (- eps (* -1 x))) (cos x))
(* -1 (* eps (sin x)))
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(* 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 (* eps x))
(* x (+ (* -1 eps) (* 1/6 (* eps (pow x 2)))))
(* x (+ (* -1 eps) (* (pow x 2) (+ (* -1/120 (* eps (pow x 2))) (* 1/6 eps)))))
(* x (+ (* -1 eps) (* (pow x 2) (+ (* 1/6 eps) (* (pow x 2) (+ (* -1/120 eps) (* 1/5040 (* eps (pow x 2)))))))))
(* -1 (* eps (sin x)))
(* -1 (* eps (sin x)))
(* -1 (* eps (sin x)))
(* -1 (* eps (sin x)))
(* -1 (* eps (sin x)))
(* -1 (* eps (sin x)))
(* -1 (* eps (sin x)))
(* -1 (* eps (sin x)))
(* -1 (* eps (sin x)))
(* -1 (* eps (sin x)))
(* -1 (* eps (sin x)))
(* -1 (* eps (sin x)))
(* -1 (* eps (sin x)))
(* -1 (* eps (sin x)))
(* -1 (* eps (sin x)))
(* -1 (* eps (sin x)))
(* -1 (* eps (sin x)))
(* -1 (* eps (sin x)))
(* -1 (* eps (sin x)))
(* -1 (* eps (sin x)))
x
(* x (+ 1 (* -1/6 (pow x 2))))
(* x (+ 1 (* (pow x 2) (- (* 1/120 (pow x 2)) 1/6))))
(* x (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/120 (* -1/5040 (pow x 2)))) 1/6))))
(sin x)
(sin x)
(sin x)
(sin x)
(sin x)
(sin x)
(sin x)
(sin x)
x
(* x (+ 1 (* -1/6 (pow x 2))))
(* x (+ 1 (* (pow x 2) (- (* 1/120 (pow x 2)) 1/6))))
(* x (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/120 (* -1/5040 (pow x 2)))) 1/6))))
(* -1/5040 (pow x 7))
(* (pow x 7) (- (* 1/120 (/ 1 (pow x 2))) 1/5040))
(* (pow x 7) (- (* 1/120 (/ 1 (pow x 2))) (+ 1/5040 (/ 1/6 (pow x 4)))))
(* (pow x 7) (- (+ (* 1/120 (/ 1 (pow x 2))) (/ 1 (pow x 6))) (+ 1/5040 (/ 1/6 (pow x 4)))))
(* -1/5040 (pow x 7))
(* -1 (* (pow x 7) (- 1/5040 (* 1/120 (/ 1 (pow x 2))))))
(* -1 (* (pow x 7) (- (+ 1/5040 (/ 1/6 (pow x 4))) (* 1/120 (/ 1 (pow x 2))))))
(* -1 (* (pow x 7) (- (+ 1/5040 (/ 1/6 (pow x 4))) (+ (* 1/120 (/ 1 (pow x 2))) (/ 1 (pow x 6))))))
(- (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 (* eps (sin x)))
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(* eps (+ (* -1 (sin x)) (* -1/2 (* eps (cos x)))))
(* eps (+ (* -1 (sin x)) (* -1/2 (* eps (cos x)))))
(* -1/2 (* (pow eps 2) (cos x)))
(* (pow eps 2) (+ (* -1 (/ (sin x) eps)) (* -1/2 (cos x))))
(* (pow eps 2) (+ (* -1 (/ (sin x) eps)) (* -1/2 (cos x))))
(* (pow eps 2) (+ (* -1 (/ (sin x) eps)) (* -1/2 (cos x))))
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(* eps (- (* -1/2 (* eps (cos x))) (sin x)))
(* eps (- (* -1/2 (* eps (cos x))) (sin x)))
(* eps (- (* -1/2 (* eps (cos x))) (sin x)))
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(* -1 (sin x))
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(- (* -1/2 (* eps (cos x))) (sin x))
(- (* -1/2 (* eps (cos x))) (sin x))
(* -1/2 (* eps (cos x)))
(* eps (+ (* -1 (/ (sin x) eps)) (* -1/2 (cos x))))
(* eps (+ (* -1 (/ (sin x) eps)) (* -1/2 (cos x))))
(* eps (+ (* -1 (/ (sin x) eps)) (* -1/2 (cos x))))
(* -1/2 (* eps (cos x)))
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(* -1 (* eps (+ (* 1/2 (cos x)) (/ (sin x) eps))))
(* -1 (* eps (+ (* 1/2 (cos x)) (/ (sin x) eps))))
(* -1/2 eps)
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(+ (* -1/2 eps) (* x (- (* x (+ (* 1/6 x) (* 1/4 eps))) 1)))
(- (* -1/2 (* eps (cos x))) (sin x))
(- (* -1/2 (* eps (cos x))) (sin x))
(- (* -1/2 (* eps (cos x))) (sin x))
(- (* -1/2 (* eps (cos x))) (sin x))
(- (* -1/2 (* eps (cos x))) (sin x))
(- (* -1/2 (* eps (cos x))) (sin x))
(- (* -1/2 (* eps (cos x))) (sin x))
(- (* -1/2 (* eps (cos x))) (sin x))
(* -1/2 eps)
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(+ (* -1/2 eps) (* x (- (* 1/4 (* eps x)) 1)))
(+ (* -1/2 eps) (* x (- (* x (+ (* 1/6 x) (* 1/4 eps))) 1)))
(* 1/6 (pow x 3))
(* (pow x 3) (+ 1/6 (* 1/4 (/ eps x))))
(* (pow x 3) (- (+ 1/6 (* 1/4 (/ eps x))) (/ 1 (pow x 2))))
(* (pow x 3) (- (+ 1/6 (+ (* -1/2 (/ eps (pow x 3))) (* 1/4 (/ eps x)))) (/ 1 (pow x 2))))
(* 1/6 (pow x 3))
(* -1 (* (pow x 3) (- (* -1/4 (/ eps x)) 1/6)))
(* -1 (* (pow x 3) (- (* -1 (/ (- (* 1/4 eps) (/ 1 x)) x)) 1/6)))
(* -1 (* (pow x 3) (- (* -1 (/ (+ (* -1 (/ (+ 1 (* 1/2 (/ eps x))) x)) (* 1/4 eps)) x)) 1/6)))
(* x (- (* 1/6 (pow x 2)) 1))
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(+ (* eps (- (* 1/4 (pow x 2)) 1/2)) (* x (- (* 1/6 (pow x 2)) 1)))
(+ (* eps (- (* 1/4 (pow x 2)) 1/2)) (* x (- (* 1/6 (pow x 2)) 1)))
(* eps (- (* 1/4 (pow x 2)) 1/2))
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(* eps (- (+ (* 1/4 (pow x 2)) (/ (* x (- (* 1/6 (pow x 2)) 1)) eps)) 1/2))
(* eps (- (+ (* 1/4 (pow x 2)) (/ (* x (- (* 1/6 (pow x 2)) 1)) eps)) 1/2))
(* -1 (* eps (+ 1/2 (* -1/4 (pow x 2)))))
(* -1 (* eps (+ 1/2 (+ (* -1 (/ (* x (- (* 1/6 (pow x 2)) 1)) eps)) (* -1/4 (pow x 2))))))
(* -1 (* eps (+ 1/2 (+ (* -1 (/ (* x (- (* 1/6 (pow x 2)) 1)) eps)) (* -1/4 (pow x 2))))))
(* -1 (* eps (+ 1/2 (+ (* -1 (/ (* x (- (* 1/6 (pow x 2)) 1)) eps)) (* -1/4 (pow x 2))))))
(* -1/2 (pow eps 2))
(+ (* -1 (* eps x)) (* -1/2 (pow eps 2)))
(+ (* -1/2 (pow eps 2)) (* x (+ (* -1 eps) (* 1/4 (* (pow eps 2) x)))))
(+ (* -1/2 (pow eps 2)) (* x (+ (* -1 eps) (* x (+ (* 1/6 (* eps x)) (* 1/4 (pow eps 2)))))))
(* 1/6 (* eps (pow x 3)))
(* (pow x 3) (+ (* 1/6 eps) (* 1/4 (/ (pow eps 2) x))))
(* (pow x 3) (+ (* -1 (/ eps (pow x 2))) (+ (* 1/6 eps) (* 1/4 (/ (pow eps 2) x)))))
(* (pow x 3) (- (+ (* -1/2 (/ (pow eps 2) (pow x 3))) (+ (* 1/6 eps) (* 1/4 (/ (pow eps 2) x)))) (/ eps (pow x 2))))
(* 1/6 (* eps (pow x 3)))
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(* -1 (* (pow x 3) (+ (* -1 (/ (+ (* -1 (/ eps x)) (* 1/4 (pow eps 2))) x)) (* -1/6 eps))))
(* -1 (* (pow x 3) (+ (* -1 (/ (+ (* -1 (/ (+ eps (* 1/2 (/ (pow eps 2) x))) x)) (* 1/4 (pow eps 2))) x)) (* -1/6 eps))))
(* eps (* x (- (* 1/6 (pow x 2)) 1)))
(* eps (+ (* eps (- (* 1/4 (pow x 2)) 1/2)) (* x (- (* 1/6 (pow x 2)) 1))))
(* eps (+ (* eps (- (* 1/4 (pow x 2)) 1/2)) (* x (- (* 1/6 (pow x 2)) 1))))
(* eps (+ (* eps (- (* 1/4 (pow x 2)) 1/2)) (* x (- (* 1/6 (pow x 2)) 1))))
(* (pow eps 2) (- (* 1/4 (pow x 2)) 1/2))
(* (pow eps 2) (- (+ (* 1/4 (pow x 2)) (/ (* x (- (* 1/6 (pow x 2)) 1)) eps)) 1/2))
(* (pow eps 2) (- (+ (* 1/4 (pow x 2)) (/ (* x (- (* 1/6 (pow x 2)) 1)) eps)) 1/2))
(* (pow eps 2) (- (+ (* 1/4 (pow x 2)) (/ (* x (- (* 1/6 (pow x 2)) 1)) eps)) 1/2))
(* (pow eps 2) (- (* 1/4 (pow x 2)) 1/2))
(* (pow eps 2) (- (+ (* -1 (/ (* x (+ 1 (* -1/6 (pow x 2)))) eps)) (* 1/4 (pow x 2))) 1/2))
(* (pow eps 2) (- (+ (* -1 (/ (* x (+ 1 (* -1/6 (pow x 2)))) eps)) (* 1/4 (pow x 2))) 1/2))
(* (pow eps 2) (- (+ (* -1 (/ (* x (+ 1 (* -1/6 (pow x 2)))) eps)) (* 1/4 (pow x 2))) 1/2))
(* -1 eps)
(- (* 1/4 (* (pow eps 2) x)) eps)
(- (* x (+ (* 1/6 (* eps x)) (* 1/4 (pow eps 2)))) eps)
(- (* x (+ (* 1/6 (* eps x)) (* 1/4 (pow eps 2)))) eps)
(* 1/6 (* eps (pow x 2)))
(* (pow x 2) (+ (* 1/6 eps) (* 1/4 (/ (pow eps 2) x))))
(* (pow x 2) (+ (* -1 (/ eps (pow x 2))) (+ (* 1/6 eps) (* 1/4 (/ (pow eps 2) x)))))
(* (pow x 2) (+ (* -1 (/ eps (pow x 2))) (+ (* 1/6 eps) (* 1/4 (/ (pow eps 2) x)))))
(* 1/6 (* eps (pow x 2)))
(* (pow x 2) (+ (* 1/6 eps) (* 1/4 (/ (pow eps 2) x))))
(* (pow x 2) (+ (* -1 (/ (+ (* -1/4 (pow eps 2)) (/ eps x)) x)) (* 1/6 eps)))
(* (pow x 2) (+ (* -1 (/ (+ (* -1/4 (pow eps 2)) (/ eps x)) x)) (* 1/6 eps)))
(* eps (- (* 1/6 (pow x 2)) 1))
(* eps (- (+ (* 1/6 (pow x 2)) (* 1/4 (* eps x))) 1))
(* eps (- (+ (* 1/6 (pow x 2)) (* 1/4 (* eps x))) 1))
(* eps (- (+ (* 1/6 (pow x 2)) (* 1/4 (* eps x))) 1))
(* 1/4 (* (pow eps 2) x))
(* (pow eps 2) (- (+ (* 1/6 (/ (pow x 2) eps)) (* 1/4 x)) (/ 1 eps)))
(* (pow eps 2) (- (+ (* 1/6 (/ (pow x 2) eps)) (* 1/4 x)) (/ 1 eps)))
(* (pow eps 2) (- (+ (* 1/6 (/ (pow x 2) eps)) (* 1/4 x)) (/ 1 eps)))
(* 1/4 (* (pow eps 2) x))
(* (pow eps 2) (+ (* -1 (/ (+ 1 (* -1/6 (pow x 2))) eps)) (* 1/4 x)))
(* (pow eps 2) (+ (* -1 (/ (+ 1 (* -1/6 (pow x 2))) eps)) (* 1/4 x)))
(* (pow eps 2) (+ (* -1 (/ (+ 1 (* -1/6 (pow x 2))) eps)) (* 1/4 x)))
(- (cos eps) 1)
(- (+ (cos eps) (* -1 (* x (sin eps)))) 1)
(- (+ (cos eps) (* x (- (* x (+ 1/2 (* -1/2 (cos eps)))) (sin eps)))) 1)
(- (+ (cos eps) (* x (- (* x (+ 1/2 (+ (* -1/2 (cos eps)) (* 1/6 (* x (sin eps)))))) (sin eps)))) 1)
(- (cos (+ eps x)) (cos x))
(- (cos (+ eps x)) (cos x))
(- (cos (+ eps x)) (cos x))
(- (cos (+ eps x)) (cos x))
(- (cos (- eps (* -1 x))) (cos x))
(- (cos (- eps (* -1 x))) (cos x))
(- (cos (- eps (* -1 x))) (cos x))
(- (cos (- eps (* -1 x))) (cos x))
(* -1 (* eps (sin x)))
(* eps (- (* -1/2 (* eps (cos x))) (sin x)))
(* eps (- (* eps (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x))))) (sin x)))
(* eps (- (* eps (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x)))))) (sin x)))
(- (cos (+ eps x)) (cos x))
(- (cos (+ eps x)) (cos x))
(- (cos (+ eps x)) (cos x))
(- (cos (+ eps x)) (cos x))
(- (cos (- x (* -1 eps))) (cos x))
(- (cos (- x (* -1 eps))) (cos x))
(- (cos (- x (* -1 eps))) (cos x))
(- (cos (- x (* -1 eps))) (cos x))
(* -1 (* eps (sin x)))
(* eps (+ (* -1 (sin x)) (* -1/2 (* eps (cos x)))))
(* eps (+ (* -1 (sin x)) (* -1/2 (* eps (cos x)))))
(* eps (+ (* -1 (sin x)) (* -1/2 (* eps (cos x)))))
(* -1/2 (* (pow eps 2) (cos x)))
(* (pow eps 2) (+ (* -1 (/ (sin x) eps)) (* -1/2 (cos x))))
(* (pow eps 2) (+ (* -1 (/ (sin x) eps)) (* -1/2 (cos x))))
(* (pow eps 2) (+ (* -1 (/ (sin x) eps)) (* -1/2 (cos x))))
(* -1/2 (* (pow eps 2) (cos x)))
(* (pow eps 2) (+ (* -1 (/ (sin x) eps)) (* -1/2 (cos x))))
(* (pow eps 2) (+ (* -1 (/ (sin x) eps)) (* -1/2 (cos x))))
(* (pow eps 2) (+ (* -1 (/ (sin x) eps)) (* -1/2 (cos x))))
(* -1/2 (pow eps 2))
(+ (* -1 (* eps x)) (* -1/2 (pow eps 2)))
(+ (* -1/2 (pow eps 2)) (* x (+ (* -1 eps) (* 1/4 (* (pow eps 2) x)))))
(+ (* -1/2 (pow eps 2)) (* x (+ (* -1 eps) (* x (+ (* 1/6 (* eps x)) (* 1/4 (pow eps 2)))))))
(* eps (- (* -1/2 (* eps (cos x))) (sin x)))
(* eps (- (* -1/2 (* eps (cos x))) (sin x)))
(* eps (- (* -1/2 (* eps (cos x))) (sin x)))
(* eps (- (* -1/2 (* eps (cos x))) (sin x)))
(* eps (- (* -1/2 (* eps (cos x))) (sin x)))
(* eps (- (* -1/2 (* eps (cos x))) (sin x)))
(* eps (- (* -1/2 (* eps (cos x))) (sin x)))
(* eps (- (* -1/2 (* eps (cos x))) (sin x)))
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))))
(* -1/6 x)
(* x (- (* 1/120 (pow x 2)) 1/6))
(* x (- (* (pow x 2) (+ 1/120 (* -1/5040 (pow x 2)))) 1/6))
(* x (- (* (pow x 2) (+ 1/120 (* -1/5040 (pow x 2)))) 1/6))
(* -1/5040 (pow x 5))
(* (pow x 5) (- (* 1/120 (/ 1 (pow x 2))) 1/5040))
(* (pow x 5) (- (* 1/120 (/ 1 (pow x 2))) (+ 1/5040 (/ 1/6 (pow x 4)))))
(* (pow x 5) (- (* 1/120 (/ 1 (pow x 2))) (+ 1/5040 (/ 1/6 (pow x 4)))))
(* -1/5040 (pow x 5))
(* -1 (* (pow x 5) (- 1/5040 (* 1/120 (/ 1 (pow x 2))))))
(* -1 (* (pow x 5) (- (+ 1/5040 (/ 1/6 (pow x 4))) (* 1/120 (/ 1 (pow x 2))))))
(* -1 (* (pow x 5) (- (+ 1/5040 (/ 1/6 (pow x 4))) (* 1/120 (/ 1 (pow x 2))))))
(* -1/6 x)
(* -1/6 x)
(* -1/6 x)
(* -1/6 x)
(* -1/6 x)
(* -1/6 x)
(* -1/6 x)
(* -1/6 x)
(* -1/6 x)
(* -1/6 x)
(* -1/6 x)
(* -1/6 x)
(* 1/6 x)
(* 1/6 x)
(* 1/6 x)
(* 1/6 x)
(* 1/6 x)
(* 1/6 x)
(* 1/6 x)
(* 1/6 x)
(* 1/6 x)
(* 1/6 x)
(* 1/6 x)
(* 1/6 x)
(* 1/6 x)
(+ (* 1/6 x) (* 1/4 eps))
(+ (* 1/6 x) (* 1/4 eps))
(+ (* 1/6 x) (* 1/4 eps))
(* 1/4 eps)
(* eps (+ 1/4 (* 1/6 (/ x eps))))
(* eps (+ 1/4 (* 1/6 (/ x eps))))
(* eps (+ 1/4 (* 1/6 (/ x eps))))
(* 1/4 eps)
(* -1 (* eps (- (* -1/6 (/ x eps)) 1/4)))
(* -1 (* eps (- (* -1/6 (/ x eps)) 1/4)))
(* -1 (* eps (- (* -1/6 (/ x eps)) 1/4)))
(* 1/4 eps)
(+ (* 1/6 x) (* 1/4 eps))
(+ (* 1/6 x) (* 1/4 eps))
(+ (* 1/6 x) (* 1/4 eps))
(* 1/6 x)
(* x (+ 1/6 (* 1/4 (/ eps x))))
(* x (+ 1/6 (* 1/4 (/ eps x))))
(* x (+ 1/6 (* 1/4 (/ eps x))))
(* 1/6 x)
(* -1 (* x (- (* -1/4 (/ eps x)) 1/6)))
(* -1 (* x (- (* -1/4 (/ eps x)) 1/6)))
(* -1 (* x (- (* -1/4 (/ eps x)) 1/6)))
(* 1/6 (* eps x))
(* eps (+ (* 1/6 x) (* 1/4 eps)))
(* eps (+ (* 1/6 x) (* 1/4 eps)))
(* eps (+ (* 1/6 x) (* 1/4 eps)))
(* 1/4 (pow eps 2))
(* (pow eps 2) (+ 1/4 (* 1/6 (/ x eps))))
(* (pow eps 2) (+ 1/4 (* 1/6 (/ x eps))))
(* (pow eps 2) (+ 1/4 (* 1/6 (/ x eps))))
(* 1/4 (pow eps 2))
(* (pow eps 2) (+ 1/4 (* 1/6 (/ x eps))))
(* (pow eps 2) (+ 1/4 (* 1/6 (/ x eps))))
(* (pow eps 2) (+ 1/4 (* 1/6 (/ x eps))))
(* 1/4 (pow eps 2))
(+ (* 1/6 (* eps x)) (* 1/4 (pow eps 2)))
(+ (* 1/6 (* eps x)) (* 1/4 (pow eps 2)))
(+ (* 1/6 (* eps x)) (* 1/4 (pow eps 2)))
(* 1/6 (* eps x))
(* x (+ (* 1/6 eps) (* 1/4 (/ (pow eps 2) x))))
(* x (+ (* 1/6 eps) (* 1/4 (/ (pow eps 2) x))))
(* x (+ (* 1/6 eps) (* 1/4 (/ (pow eps 2) x))))
(* 1/6 (* eps x))
(* -1 (* x (+ (* -1/4 (/ (pow eps 2) x)) (* -1/6 eps))))
(* -1 (* x (+ (* -1/4 (/ (pow eps 2) x)) (* -1/6 eps))))
(* -1 (* x (+ (* -1/4 (/ (pow eps 2) x)) (* -1/6 eps))))

Outputs
(* 1/2 eps)
(*.f64 #s(literal 1/2 binary64) eps)
(+ x (* 1/2 eps))
(fma.f64 #s(literal 1/2 binary64) eps x)
(+ x (* 1/2 eps))
(fma.f64 #s(literal 1/2 binary64) eps x)
(+ x (* 1/2 eps))
(fma.f64 #s(literal 1/2 binary64) eps x)
x
(* x (+ 1 (* 1/2 (/ eps x))))
(fma.f64 #s(literal 1/2 binary64) (/.f64 (*.f64 eps x) x) x)
(* x (+ 1 (* 1/2 (/ eps x))))
(fma.f64 #s(literal 1/2 binary64) (/.f64 (*.f64 eps x) x) x)
(* x (+ 1 (* 1/2 (/ eps x))))
(fma.f64 #s(literal 1/2 binary64) (/.f64 (*.f64 eps x) x) x)
x
(* -1 (* x (- (* -1/2 (/ eps x)) 1)))
(fma.f64 (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x) (neg.f64 x) x)
(* -1 (* x (- (* -1/2 (/ eps x)) 1)))
(fma.f64 (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x) (neg.f64 x) x)
(* -1 (* x (- (* -1/2 (/ eps x)) 1)))
(fma.f64 (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x) (neg.f64 x) x)
x
(+ x (* 1/2 eps))
(fma.f64 #s(literal 1/2 binary64) eps x)
(+ x (* 1/2 eps))
(fma.f64 #s(literal 1/2 binary64) eps x)
(+ x (* 1/2 eps))
(fma.f64 #s(literal 1/2 binary64) eps x)
(* 1/2 eps)
(*.f64 #s(literal 1/2 binary64) eps)
(* eps (+ 1/2 (/ x eps)))
(*.f64 eps (+.f64 #s(literal 1/2 binary64) (/.f64 x eps)))
(* eps (+ 1/2 (/ x eps)))
(*.f64 eps (+.f64 #s(literal 1/2 binary64) (/.f64 x eps)))
(* eps (+ 1/2 (/ x eps)))
(*.f64 eps (+.f64 #s(literal 1/2 binary64) (/.f64 x eps)))
(* 1/2 eps)
(*.f64 #s(literal 1/2 binary64) eps)
(* -1 (* eps (- (* -1 (/ x eps)) 1/2)))
(*.f64 eps (+.f64 #s(literal 1/2 binary64) (/.f64 x eps)))
(* -1 (* eps (- (* -1 (/ x eps)) 1/2)))
(*.f64 eps (+.f64 #s(literal 1/2 binary64) (/.f64 x eps)))
(* -1 (* eps (- (* -1 (/ x eps)) 1/2)))
(*.f64 eps (+.f64 #s(literal 1/2 binary64) (/.f64 x eps)))
eps
eps
eps
eps
eps
eps
eps
eps
eps
eps
eps
eps
(* -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 (-.f64 (.f64 eps (fma.f64 eps (.f64 (sin.f64 x) #s(literal 1/6 binary64)) (.f64 #s(literal -1/2 binary64) (cos.f64 x)))) (sin.f64 x)))
(* eps (+ (* -1 (sin x)) (* eps (+ (* -1/2 (cos x)) (* eps (+ (* -2 (+ (* -1/16 (sin x)) (* -1/48 (sin x)))) (* 1/24 (* eps (cos x)))))))))
(.f64 eps (fma.f64 eps (fma.f64 eps (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 (fma.f64 #s(literal 1/2 binary64) eps x)) (.f64 #s(literal -2 binary64) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps))))
(* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (+ eps (* 2 x))))))
(.f64 (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) (.f64 #s(literal -2 binary64) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps))))
(* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (+ eps (* 2 x))))))
(.f64 (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) (.f64 #s(literal -2 binary64) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps))))
(* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (+ eps (* 2 x))))))
(.f64 (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) (.f64 #s(literal -2 binary64) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps))))
(* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (- (* 2 x) (* -1 eps))))))
(.f64 (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) (.f64 #s(literal -2 binary64) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps))))
(* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (- (* 2 x) (* -1 eps))))))
(.f64 (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) (.f64 #s(literal -2 binary64) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps))))
(* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (- (* 2 x) (* -1 eps))))))
(.f64 (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) (.f64 #s(literal -2 binary64) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps))))
(* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (- (* 2 x) (* -1 eps))))))
(.f64 (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) (.f64 #s(literal -2 binary64) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps))))
(* -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 (fma.f64 #s(literal 1/2 binary64) eps x)) (.f64 #s(literal -2 binary64) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps))))
(* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (+ eps (* 2 x))))))
(.f64 (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) (.f64 #s(literal -2 binary64) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps))))
(* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (+ eps (* 2 x))))))
(.f64 (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) (.f64 #s(literal -2 binary64) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps))))
(* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (+ eps (* 2 x))))))
(.f64 (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) (.f64 #s(literal -2 binary64) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps))))
(* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (- eps (* -2 x))))))
(.f64 (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) (.f64 #s(literal -2 binary64) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps))))
(* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (- eps (* -2 x))))))
(.f64 (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) (.f64 #s(literal -2 binary64) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps))))
(* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (- eps (* -2 x))))))
(.f64 (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) (.f64 #s(literal -2 binary64) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps))))
(* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (- eps (* -2 x))))))
(.f64 (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) (.f64 #s(literal -2 binary64) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps))))
(* 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 (*.f64 eps (cos.f64 x)) #s(literal 1/4 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 #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 (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)))))
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(fma.f64 eps (.f64 eps #s(literal -1/2 binary64)) (.f64 x (.f64 eps (fma.f64 eps (.f64 x #s(literal 1/4 binary64)) #s(literal -1 binary64)))))
(+ (* -1/2 (pow eps 2)) (* x (+ (* -1 eps) (* x (+ (* 1/6 (* eps x)) (* 1/4 (pow eps 2)))))))
(fma.f64 x (.f64 eps (fma.f64 x (fma.f64 eps #s(literal 1/4 binary64) (.f64 x #s(literal 1/6 binary64))) #s(literal -1 binary64))) (.f64 eps (.f64 eps #s(literal -1/2 binary64))))
(* 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 (- (* -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 (- (* -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 (- (* -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 (- (* -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 (- (* -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 (- (* -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 (- (* -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 (* 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 x (+.f64 (/.f64 eps x) #s(literal 2 binary64)))
(* -1 (* x (- (* -1 (/ eps x)) 2)))
(*.f64 x (+.f64 (/.f64 eps x) #s(literal 2 binary64)))
(* -1 (* x (- (* -1 (/ eps x)) 2)))
(*.f64 x (+.f64 (/.f64 eps x) #s(literal 2 binary64)))
(* 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 (/.f64 x eps) (*.f64 #s(literal 2 binary64) eps) eps)
(* eps (+ 1 (* 2 (/ x eps))))
(fma.f64 (/.f64 x eps) (*.f64 #s(literal 2 binary64) eps) eps)
(* eps (+ 1 (* 2 (/ x eps))))
(fma.f64 (/.f64 x eps) (*.f64 #s(literal 2 binary64) eps) eps)
eps
(* -1 (* eps (- (* -2 (/ x eps)) 1)))
(fma.f64 (/.f64 x eps) (*.f64 #s(literal 2 binary64) eps) eps)
(* -1 (* eps (- (* -2 (/ x eps)) 1)))
(fma.f64 (/.f64 x eps) (*.f64 #s(literal 2 binary64) eps) eps)
(* -1 (* eps (- (* -2 (/ x eps)) 1)))
(fma.f64 (/.f64 x eps) (*.f64 #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))
(* -1/6 x)
(*.f64 x #s(literal -1/6 binary64))
(* x (- (* 1/120 (pow x 2)) 1/6))
(.f64 x (fma.f64 (.f64 x x) #s(literal 1/120 binary64) #s(literal -1/6 binary64)))
(* x (- (* (pow x 2) (+ 1/120 (* -1/5040 (pow x 2)))) 1/6))
(.f64 x (fma.f64 (.f64 x x) (fma.f64 (*.f64 x x) #s(literal -1/5040 binary64) #s(literal 1/120 binary64)) #s(literal -1/6 binary64)))
(* x (- (* (pow x 2) (+ 1/120 (* -1/5040 (pow x 2)))) 1/6))
(.f64 x (fma.f64 (.f64 x x) (fma.f64 (*.f64 x x) #s(literal -1/5040 binary64) #s(literal 1/120 binary64)) #s(literal -1/6 binary64)))
(* -1/5040 (pow x 5))
(*.f64 #s(literal -1/5040 binary64) (pow.f64 x #s(literal 5 binary64)))
(* (pow x 5) (- (* 1/120 (/ 1 (pow x 2))) 1/5040))
(.f64 (+.f64 #s(literal -1/5040 binary64) (/.f64 #s(literal 1/120 binary64) (.f64 x x))) (pow.f64 x #s(literal 5 binary64)))
(* (pow x 5) (- (* 1/120 (/ 1 (pow x 2))) (+ 1/5040 (/ 1/6 (pow x 4)))))
(.f64 (pow.f64 x #s(literal 5 binary64)) (+.f64 (/.f64 #s(literal 1/120 binary64) (.f64 x x)) (-.f64 #s(literal -1/5040 binary64) (/.f64 #s(literal 1/6 binary64) (.f64 (.f64 x x) (*.f64 x x))))))
(* (pow x 5) (- (* 1/120 (/ 1 (pow x 2))) (+ 1/5040 (/ 1/6 (pow x 4)))))
(.f64 (pow.f64 x #s(literal 5 binary64)) (+.f64 (/.f64 #s(literal 1/120 binary64) (.f64 x x)) (-.f64 #s(literal -1/5040 binary64) (/.f64 #s(literal 1/6 binary64) (.f64 (.f64 x x) (*.f64 x x))))))
(* -1/5040 (pow x 5))
(*.f64 #s(literal -1/5040 binary64) (pow.f64 x #s(literal 5 binary64)))
(* -1 (* (pow x 5) (- 1/5040 (* 1/120 (/ 1 (pow x 2))))))
(.f64 (+.f64 #s(literal -1/5040 binary64) (/.f64 #s(literal 1/120 binary64) (.f64 x x))) (pow.f64 x #s(literal 5 binary64)))
(* -1 (* (pow x 5) (- (+ 1/5040 (/ 1/6 (pow x 4))) (* 1/120 (/ 1 (pow x 2))))))
(.f64 (pow.f64 x #s(literal 5 binary64)) (+.f64 (/.f64 #s(literal 1/120 binary64) (.f64 x x)) (-.f64 #s(literal -1/5040 binary64) (/.f64 #s(literal 1/6 binary64) (.f64 (.f64 x x) (*.f64 x x))))))
(* -1 (* (pow x 5) (- (+ 1/5040 (/ 1/6 (pow x 4))) (* 1/120 (/ 1 (pow x 2))))))
(.f64 (pow.f64 x #s(literal 5 binary64)) (+.f64 (/.f64 #s(literal 1/120 binary64) (.f64 x x)) (-.f64 #s(literal -1/5040 binary64) (/.f64 #s(literal 1/6 binary64) (.f64 (.f64 x x) (*.f64 x x))))))
(* -1/6 x)
(*.f64 x #s(literal -1/6 binary64))
(* -1/6 x)
(*.f64 x #s(literal -1/6 binary64))
(* -1/6 x)
(*.f64 x #s(literal -1/6 binary64))
(* -1/6 x)
(*.f64 x #s(literal -1/6 binary64))
(* -1/6 x)
(*.f64 x #s(literal -1/6 binary64))
(* -1/6 x)
(*.f64 x #s(literal -1/6 binary64))
(* -1/6 x)
(*.f64 x #s(literal -1/6 binary64))
(* -1/6 x)
(*.f64 x #s(literal -1/6 binary64))
(* -1/6 x)
(*.f64 x #s(literal -1/6 binary64))
(* -1/6 x)
(*.f64 x #s(literal -1/6 binary64))
(* -1/6 x)
(*.f64 x #s(literal -1/6 binary64))
(* -1/6 x)
(*.f64 x #s(literal -1/6 binary64))
(* 1/6 x)
(*.f64 x #s(literal 1/6 binary64))
(* 1/6 x)
(*.f64 x #s(literal 1/6 binary64))
(* 1/6 x)
(*.f64 x #s(literal 1/6 binary64))
(* 1/6 x)
(*.f64 x #s(literal 1/6 binary64))
(* 1/6 x)
(*.f64 x #s(literal 1/6 binary64))
(* 1/6 x)
(*.f64 x #s(literal 1/6 binary64))
(* 1/6 x)
(*.f64 x #s(literal 1/6 binary64))
(* 1/6 x)
(*.f64 x #s(literal 1/6 binary64))
(* 1/6 x)
(*.f64 x #s(literal 1/6 binary64))
(* 1/6 x)
(*.f64 x #s(literal 1/6 binary64))
(* 1/6 x)
(*.f64 x #s(literal 1/6 binary64))
(* 1/6 x)
(*.f64 x #s(literal 1/6 binary64))
(* 1/6 x)
(*.f64 x #s(literal 1/6 binary64))
(+ (* 1/6 x) (* 1/4 eps))
(fma.f64 eps #s(literal 1/4 binary64) (*.f64 x #s(literal 1/6 binary64)))
(+ (* 1/6 x) (* 1/4 eps))
(fma.f64 eps #s(literal 1/4 binary64) (*.f64 x #s(literal 1/6 binary64)))
(+ (* 1/6 x) (* 1/4 eps))
(fma.f64 eps #s(literal 1/4 binary64) (*.f64 x #s(literal 1/6 binary64)))
(* 1/4 eps)
(*.f64 eps #s(literal 1/4 binary64))
(* eps (+ 1/4 (* 1/6 (/ x eps))))
(*.f64 eps (fma.f64 (/.f64 x eps) #s(literal 1/6 binary64) #s(literal 1/4 binary64)))
(* eps (+ 1/4 (* 1/6 (/ x eps))))
(*.f64 eps (fma.f64 (/.f64 x eps) #s(literal 1/6 binary64) #s(literal 1/4 binary64)))
(* eps (+ 1/4 (* 1/6 (/ x eps))))
(*.f64 eps (fma.f64 (/.f64 x eps) #s(literal 1/6 binary64) #s(literal 1/4 binary64)))
(* 1/4 eps)
(*.f64 eps #s(literal 1/4 binary64))
(* -1 (* eps (- (* -1/6 (/ x eps)) 1/4)))
(neg.f64 (*.f64 eps (fma.f64 (/.f64 x eps) #s(literal -1/6 binary64) #s(literal -1/4 binary64))))
(* -1 (* eps (- (* -1/6 (/ x eps)) 1/4)))
(neg.f64 (*.f64 eps (fma.f64 (/.f64 x eps) #s(literal -1/6 binary64) #s(literal -1/4 binary64))))
(* -1 (* eps (- (* -1/6 (/ x eps)) 1/4)))
(neg.f64 (*.f64 eps (fma.f64 (/.f64 x eps) #s(literal -1/6 binary64) #s(literal -1/4 binary64))))
(* 1/4 eps)
(*.f64 eps #s(literal 1/4 binary64))
(+ (* 1/6 x) (* 1/4 eps))
(fma.f64 eps #s(literal 1/4 binary64) (*.f64 x #s(literal 1/6 binary64)))
(+ (* 1/6 x) (* 1/4 eps))
(fma.f64 eps #s(literal 1/4 binary64) (*.f64 x #s(literal 1/6 binary64)))
(+ (* 1/6 x) (* 1/4 eps))
(fma.f64 eps #s(literal 1/4 binary64) (*.f64 x #s(literal 1/6 binary64)))
(* 1/6 x)
(*.f64 x #s(literal 1/6 binary64))
(* x (+ 1/6 (* 1/4 (/ eps x))))
(*.f64 x (fma.f64 (/.f64 eps x) #s(literal 1/4 binary64) #s(literal 1/6 binary64)))
(* x (+ 1/6 (* 1/4 (/ eps x))))
(*.f64 x (fma.f64 (/.f64 eps x) #s(literal 1/4 binary64) #s(literal 1/6 binary64)))
(* x (+ 1/6 (* 1/4 (/ eps x))))
(*.f64 x (fma.f64 (/.f64 eps x) #s(literal 1/4 binary64) #s(literal 1/6 binary64)))
(* 1/6 x)
(*.f64 x #s(literal 1/6 binary64))
(* -1 (* x (- (* -1/4 (/ eps x)) 1/6)))
(*.f64 (neg.f64 x) (fma.f64 (/.f64 eps x) #s(literal -1/4 binary64) #s(literal -1/6 binary64)))
(* -1 (* x (- (* -1/4 (/ eps x)) 1/6)))
(*.f64 (neg.f64 x) (fma.f64 (/.f64 eps x) #s(literal -1/4 binary64) #s(literal -1/6 binary64)))
(* -1 (* x (- (* -1/4 (/ eps x)) 1/6)))
(*.f64 (neg.f64 x) (fma.f64 (/.f64 eps x) #s(literal -1/4 binary64) #s(literal -1/6 binary64)))
(* 1/6 (* eps x))
(.f64 x (.f64 eps #s(literal 1/6 binary64)))
(* eps (+ (* 1/6 x) (* 1/4 eps)))
(.f64 eps (fma.f64 eps #s(literal 1/4 binary64) (.f64 x #s(literal 1/6 binary64))))
(* eps (+ (* 1/6 x) (* 1/4 eps)))
(.f64 eps (fma.f64 eps #s(literal 1/4 binary64) (.f64 x #s(literal 1/6 binary64))))
(* eps (+ (* 1/6 x) (* 1/4 eps)))
(.f64 eps (fma.f64 eps #s(literal 1/4 binary64) (.f64 x #s(literal 1/6 binary64))))
(* 1/4 (pow eps 2))
(.f64 #s(literal 1/4 binary64) (.f64 eps eps))
(* (pow eps 2) (+ 1/4 (* 1/6 (/ x eps))))
(.f64 (.f64 eps eps) (fma.f64 (/.f64 x eps) #s(literal 1/6 binary64) #s(literal 1/4 binary64)))
(* (pow eps 2) (+ 1/4 (* 1/6 (/ x eps))))
(.f64 (.f64 eps eps) (fma.f64 (/.f64 x eps) #s(literal 1/6 binary64) #s(literal 1/4 binary64)))
(* (pow eps 2) (+ 1/4 (* 1/6 (/ x eps))))
(.f64 (.f64 eps eps) (fma.f64 (/.f64 x eps) #s(literal 1/6 binary64) #s(literal 1/4 binary64)))
(* 1/4 (pow eps 2))
(.f64 #s(literal 1/4 binary64) (.f64 eps eps))
(* (pow eps 2) (+ 1/4 (* 1/6 (/ x eps))))
(.f64 (.f64 eps eps) (fma.f64 (/.f64 x eps) #s(literal 1/6 binary64) #s(literal 1/4 binary64)))
(* (pow eps 2) (+ 1/4 (* 1/6 (/ x eps))))
(.f64 (.f64 eps eps) (fma.f64 (/.f64 x eps) #s(literal 1/6 binary64) #s(literal 1/4 binary64)))
(* (pow eps 2) (+ 1/4 (* 1/6 (/ x eps))))
(.f64 (.f64 eps eps) (fma.f64 (/.f64 x eps) #s(literal 1/6 binary64) #s(literal 1/4 binary64)))
(* 1/4 (pow eps 2))
(.f64 #s(literal 1/4 binary64) (.f64 eps eps))
(+ (* 1/6 (* eps x)) (* 1/4 (pow eps 2)))
(.f64 eps (fma.f64 eps #s(literal 1/4 binary64) (.f64 x #s(literal 1/6 binary64))))
(+ (* 1/6 (* eps x)) (* 1/4 (pow eps 2)))
(.f64 eps (fma.f64 eps #s(literal 1/4 binary64) (.f64 x #s(literal 1/6 binary64))))
(+ (* 1/6 (* eps x)) (* 1/4 (pow eps 2)))
(.f64 eps (fma.f64 eps #s(literal 1/4 binary64) (.f64 x #s(literal 1/6 binary64))))
(* 1/6 (* eps x))
(.f64 x (.f64 eps #s(literal 1/6 binary64)))
(* x (+ (* 1/6 eps) (* 1/4 (/ (pow eps 2) x))))
(.f64 x (fma.f64 eps #s(literal 1/6 binary64) (.f64 #s(literal 1/4 binary64) (/.f64 (*.f64 eps eps) x))))
(* x (+ (* 1/6 eps) (* 1/4 (/ (pow eps 2) x))))
(.f64 x (fma.f64 eps #s(literal 1/6 binary64) (.f64 #s(literal 1/4 binary64) (/.f64 (*.f64 eps eps) x))))
(* x (+ (* 1/6 eps) (* 1/4 (/ (pow eps 2) x))))
(.f64 x (fma.f64 eps #s(literal 1/6 binary64) (.f64 #s(literal 1/4 binary64) (/.f64 (*.f64 eps eps) x))))
(* 1/6 (* eps x))
(.f64 x (.f64 eps #s(literal 1/6 binary64)))
(* -1 (* x (+ (* -1/4 (/ (pow eps 2) x)) (* -1/6 eps))))
(.f64 x (fma.f64 eps #s(literal 1/6 binary64) (.f64 #s(literal 1/4 binary64) (/.f64 (*.f64 eps eps) x))))
(* -1 (* x (+ (* -1/4 (/ (pow eps 2) x)) (* -1/6 eps))))
(.f64 x (fma.f64 eps #s(literal 1/6 binary64) (.f64 #s(literal 1/4 binary64) (/.f64 (*.f64 eps eps) x))))
(* -1 (* x (+ (* -1/4 (/ (pow eps 2) x)) (* -1/6 eps))))
(.f64 x (fma.f64 eps #s(literal 1/6 binary64) (.f64 #s(literal 1/4 binary64) (/.f64 (*.f64 eps eps) x))))

rewrite264.0ms (1.6%)

Memory

6.3MiB live, 123.7MiB allocated

Rules

6 238×	`lower-*.f32`
6 210×	`lower-*.f64`
5 582×	`lower-fma.f32`
5 570×	`lower-fma.f64`
2 962×	`lower-/.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	75	518
0	108	508
1	449	504
2	3774	498
0	9911	479

Stop Event

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

Counts

27 → 586

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

Outputs
(+.f64 (.f64 #s(literal 1/2 binary64) x) (.f64 #s(literal 1/2 binary64) (+.f64 x eps)))
(+.f64 (.f64 #s(literal 1/2 binary64) (+.f64 x eps)) (.f64 #s(literal 1/2 binary64) x))
(+.f64 (.f64 #s(literal 1/2 binary64) (+.f64 x x)) (.f64 eps #s(literal 1/2 binary64)))
(+.f64 (.f64 x #s(literal 1/2 binary64)) (.f64 (+.f64 x eps) #s(literal 1/2 binary64)))
(+.f64 (.f64 (+.f64 x eps) #s(literal 1/2 binary64)) (.f64 x #s(literal 1/2 binary64)))
(+.f64 (.f64 (+.f64 x x) #s(literal 1/2 binary64)) (.f64 eps #s(literal 1/2 binary64)))
(fma.f64 x #s(literal 1/2 binary64) (*.f64 (+.f64 x eps) #s(literal 1/2 binary64)))
(fma.f64 #s(literal 1/2 binary64) x (*.f64 #s(literal 1/2 binary64) (+.f64 x eps)))
(fma.f64 #s(literal 1/2 binary64) (+.f64 x eps) (*.f64 #s(literal 1/2 binary64) x))
(fma.f64 #s(literal 1/2 binary64) (+.f64 x x) (*.f64 eps #s(literal 1/2 binary64)))
(fma.f64 (+.f64 x eps) #s(literal 1/2 binary64) (*.f64 x #s(literal 1/2 binary64)))
(fma.f64 (+.f64 x x) #s(literal 1/2 binary64) (*.f64 eps #s(literal 1/2 binary64)))
(/.f64 (+.f64 x (+.f64 x eps)) #s(literal 2 binary64))
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 2 binary64) (+.f64 x (+.f64 x eps))))
(/.f64 (fma.f64 x (.f64 x x) (.f64 (fma.f64 x x (.f64 eps eps)) (+.f64 x eps))) (.f64 #s(literal 2 binary64) (fma.f64 (+.f64 x eps) (-.f64 x (+.f64 x eps)) (*.f64 x x))))
(/.f64 (.f64 (+.f64 x (+.f64 x eps)) (-.f64 x (+.f64 x eps))) (.f64 #s(literal 2 binary64) (-.f64 x (+.f64 x eps))))
(/.f64 (neg.f64 (+.f64 x (+.f64 x eps))) #s(literal -2 binary64))
(/.f64 (.f64 #s(literal 1/2 binary64) (fma.f64 x (.f64 x x) (.f64 (fma.f64 x x (.f64 eps eps)) (+.f64 x eps)))) (fma.f64 (+.f64 x eps) (-.f64 x (+.f64 x eps)) (*.f64 x x)))
(/.f64 (.f64 #s(literal 1/2 binary64) (.f64 (+.f64 x (+.f64 x eps)) (-.f64 x (+.f64 x eps)))) (-.f64 x (+.f64 x eps)))
(/.f64 (.f64 (fma.f64 x (.f64 x x) (.f64 (fma.f64 x x (.f64 eps eps)) (+.f64 x eps))) #s(literal 1/2 binary64)) (fma.f64 (+.f64 x eps) (-.f64 x (+.f64 x eps)) (*.f64 x x)))
(/.f64 (.f64 (.f64 (+.f64 x (+.f64 x eps)) (-.f64 x (+.f64 x eps))) #s(literal 1/2 binary64)) (-.f64 x (+.f64 x eps)))
(pow.f64 (/.f64 #s(literal 2 binary64) (+.f64 x (+.f64 x eps))) #s(literal -1 binary64))
(*.f64 (+.f64 x (+.f64 x eps)) #s(literal 1/2 binary64))
(*.f64 #s(literal 1/2 binary64) (+.f64 x (+.f64 x eps)))
eps
(exp.f64 (*.f64 (log.f64 eps) #s(literal 1 binary64)))
(exp.f64 (-.f64 (.f64 (log.f64 eps) #s(literal 3 binary64)) (.f64 (log.f64 eps) #s(literal 2 binary64))))
(+.f64 eps #s(literal 0 binary64))
(+.f64 #s(literal 0 binary64) eps)
(-.f64 eps #s(literal 0 binary64))
(-.f64 eps (/.f64 #s(literal 0 binary64) eps))
(-.f64 #s(literal 0 binary64) eps)
(fma.f64 eps #s(literal -1 binary64) #s(literal 0 binary64))
(fma.f64 eps #s(literal 1 binary64) #s(literal 0 binary64))
(fma.f64 #s(literal -1 binary64) eps #s(literal 0 binary64))
(fma.f64 (*.f64 eps eps) (/.f64 #s(literal 1 binary64) eps) #s(literal 0 binary64))
(fma.f64 (*.f64 eps eps) (pow.f64 (/.f64 #s(literal 1 binary64) eps) #s(literal 1 binary64)) #s(literal 0 binary64))
(fma.f64 (.f64 eps (.f64 eps eps)) (/.f64 #s(literal 1 binary64) (*.f64 eps eps)) #s(literal 0 binary64))
(fma.f64 (pow.f64 (.f64 eps (.f64 eps eps)) #s(literal 1 binary64)) (pow.f64 (/.f64 #s(literal 1 binary64) (*.f64 eps eps)) #s(literal 1 binary64)) #s(literal 0 binary64))
(neg.f64 eps)
(/.f64 eps #s(literal -1 binary64))
(/.f64 eps #s(literal 1 binary64))
(/.f64 (*.f64 eps eps) eps)
(/.f64 (.f64 eps eps) (.f64 #s(literal 1 binary64) eps))
(/.f64 #s(literal 1 binary64) (/.f64 eps (*.f64 eps eps)))
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) eps))
(/.f64 (.f64 eps (.f64 eps eps)) (*.f64 eps eps))
(/.f64 (-.f64 #s(literal 0 binary64) (.f64 eps (.f64 eps eps))) (*.f64 eps eps))
(/.f64 (-.f64 (.f64 eps (.f64 eps eps)) #s(literal 0 binary64)) (*.f64 eps eps))
(/.f64 (-.f64 #s(literal 0 binary64) (*.f64 eps eps)) eps)
(pow.f64 eps #s(literal 1 binary64))
(pow.f64 (/.f64 eps (*.f64 eps eps)) #s(literal -1 binary64))
(pow.f64 (/.f64 #s(literal 1 binary64) eps) #s(literal -1 binary64))
(*.f64 eps #s(literal -1 binary64))
(*.f64 eps #s(literal 1 binary64))
(*.f64 #s(literal -1 binary64) eps)
(.f64 (.f64 eps eps) (/.f64 #s(literal 1 binary64) eps))
(.f64 (.f64 eps eps) (pow.f64 (/.f64 #s(literal 1 binary64) eps) #s(literal 1 binary64)))
(.f64 (.f64 eps (.f64 eps eps)) (/.f64 #s(literal 1 binary64) (.f64 eps eps)))
(.f64 (pow.f64 (.f64 eps (.f64 eps eps)) #s(literal 1 binary64)) (pow.f64 (/.f64 #s(literal 1 binary64) (.f64 eps eps)) #s(literal 1 binary64)))
(/.f64 (.f64 #s(literal -2 binary64) (-.f64 (cos.f64 (.f64 #s(literal 1/2 binary64) (-.f64 eps (+.f64 x (+.f64 x eps))))) (cos.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 eps (+.f64 x (+.f64 x eps))))))) #s(literal 2 binary64))
(/.f64 (.f64 (-.f64 (cos.f64 (.f64 #s(literal 1/2 binary64) (-.f64 eps (+.f64 x (+.f64 x eps))))) (cos.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 eps (+.f64 x (+.f64 x eps)))))) #s(literal -2 binary64)) #s(literal 2 binary64))
(.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (.f64 (sin.f64 (.f64 (+.f64 x (+.f64 x eps)) #s(literal 1/2 binary64))) #s(literal -2 binary64)))
(.f64 (sin.f64 (.f64 (+.f64 x (+.f64 x eps)) #s(literal 1/2 binary64))) (.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) #s(literal -2 binary64)))
(.f64 (.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (sin.f64 (.f64 (+.f64 x (+.f64 x eps)) #s(literal 1/2 binary64)))) #s(literal -2 binary64))
(.f64 #s(literal -2 binary64) (.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (sin.f64 (.f64 (+.f64 x (+.f64 x eps)) #s(literal 1/2 binary64)))))
(.f64 (.f64 (sin.f64 (.f64 (+.f64 x (+.f64 x eps)) #s(literal 1/2 binary64))) #s(literal -2 binary64)) (sin.f64 (.f64 eps #s(literal 1/2 binary64))))
(.f64 (.f64 #s(literal -2 binary64) (sin.f64 (.f64 eps #s(literal 1/2 binary64)))) (sin.f64 (.f64 (+.f64 x (+.f64 x eps)) #s(literal 1/2 binary64))))
(-.f64 (/.f64 (cos.f64 (.f64 #s(literal 1/2 binary64) (-.f64 eps (+.f64 x (+.f64 x eps))))) #s(literal 2 binary64)) (/.f64 (cos.f64 (.f64 #s(literal 1/2 binary64) (+.f64 eps (+.f64 x (+.f64 x eps))))) #s(literal 2 binary64)))
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 2 binary64) (-.f64 (cos.f64 (.f64 #s(literal 1/2 binary64) (-.f64 eps (+.f64 x (+.f64 x eps))))) (cos.f64 (.f64 #s(literal 1/2 binary64) (+.f64 eps (+.f64 x (+.f64 x eps))))))))
(/.f64 (-.f64 (cos.f64 (.f64 #s(literal 1/2 binary64) (-.f64 eps (+.f64 x (+.f64 x eps))))) (cos.f64 (.f64 #s(literal 1/2 binary64) (+.f64 eps (+.f64 x (+.f64 x eps)))))) #s(literal 2 binary64))
(/.f64 (-.f64 (cos.f64 (-.f64 (.f64 (+.f64 x (+.f64 x eps)) #s(literal 1/2 binary64)) (.f64 eps #s(literal 1/2 binary64)))) (cos.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 eps (+.f64 x (+.f64 x eps)))))) #s(literal 2 binary64))
(/.f64 (neg.f64 (-.f64 (cos.f64 (.f64 #s(literal 1/2 binary64) (-.f64 eps (+.f64 x (+.f64 x eps))))) (cos.f64 (.f64 #s(literal 1/2 binary64) (+.f64 eps (+.f64 x (+.f64 x eps))))))) #s(literal -2 binary64))
(pow.f64 (/.f64 #s(literal 2 binary64) (-.f64 (cos.f64 (.f64 #s(literal 1/2 binary64) (-.f64 eps (+.f64 x (+.f64 x eps))))) (cos.f64 (.f64 #s(literal 1/2 binary64) (+.f64 eps (+.f64 x (+.f64 x eps))))))) #s(literal -1 binary64))
(.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (sin.f64 (*.f64 (+.f64 x (+.f64 x eps)) #s(literal 1/2 binary64))))
(.f64 (sin.f64 (.f64 (+.f64 x (+.f64 x eps)) #s(literal 1/2 binary64))) (sin.f64 (*.f64 eps #s(literal 1/2 binary64))))
(.f64 (-.f64 (cos.f64 (.f64 #s(literal 1/2 binary64) (-.f64 eps (+.f64 x (+.f64 x eps))))) (cos.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 eps (+.f64 x (+.f64 x eps)))))) #s(literal 1/2 binary64))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps #s(approx (- ( eps (* -1/2 (cos x))) (sin x)) #s(approx (+ (* eps (+ (* 1/4 (* x x)) -1/2)) (neg x)) (neg.f64 x)))))
(+.f64 (.f64 eps #s(approx (- ( eps (* -1/2 (cos x))) (sin x)) #s(approx (+ (* eps (+ (* 1/4 (* x x)) -1/2)) (neg x)) (neg.f64 x)))) (.f64 #s(approx (- ( eps (* -1/2 (cos x))) (sin x)) #s(approx (+ (* eps (+ (* 1/4 (* x x)) -1/2)) (neg x)) (neg.f64 x))) #s(literal 0 binary64)))
(+.f64 (.f64 eps #s(approx (- ( eps (* -1/2 (cos x))) (sin x)) #s(approx (+ (* eps (+ (* 1/4 (* x x)) -1/2)) (neg x)) (neg.f64 x)))) (.f64 #s(literal 0 binary64) #s(approx (- ( eps (* -1/2 (cos x))) (sin x)) #s(approx (+ (* eps (+ (* 1/4 (* x x)) -1/2)) (neg x)) (neg.f64 x)))))
(+.f64 (.f64 #s(approx (- ( eps (* -1/2 (cos x))) (sin x)) #s(approx (+ (* eps (+ (* 1/4 (* x x)) -1/2)) (neg x)) (neg.f64 x))) #s(literal 0 binary64)) (.f64 eps #s(approx (- ( eps (* -1/2 (cos x))) (sin x)) #s(approx (+ (* eps (+ (* 1/4 (* x x)) -1/2)) (neg x)) (neg.f64 x)))))
(+.f64 (.f64 #s(literal 0 binary64) #s(approx (- ( eps (* -1/2 (cos x))) (sin x)) #s(approx (+ (* eps (+ (* 1/4 (* x x)) -1/2)) (neg x)) (neg.f64 x)))) (.f64 eps #s(approx (- ( eps (* -1/2 (cos x))) (sin x)) #s(approx (+ (* eps (+ (* 1/4 (* x x)) -1/2)) (neg x)) (neg.f64 x)))))
(fma.f64 eps #s(approx (- (* eps (* -1/2 (cos x))) (sin x)) #s(approx (+ (* eps (+ (* 1/4 (* x x)) -1/2)) (neg x)) (neg.f64 x))) (.f64 #s(approx (- ( eps (* -1/2 (cos x))) (sin x)) #s(approx (+ (* eps (+ (* 1/4 (* x x)) -1/2)) (neg x)) (neg.f64 x))) #s(literal 0 binary64)))
(fma.f64 eps #s(approx (- (* eps (* -1/2 (cos x))) (sin x)) #s(approx (+ (* eps (+ (* 1/4 (* x x)) -1/2)) (neg x)) (neg.f64 x))) (.f64 #s(literal 0 binary64) #s(approx (- ( eps (* -1/2 (cos x))) (sin x)) #s(approx (+ (* eps (+ (* 1/4 (* x x)) -1/2)) (neg x)) (neg.f64 x)))))
(fma.f64 #s(literal 0 binary64) #s(approx (- (* eps (* -1/2 (cos x))) (sin x)) #s(approx (+ (* eps (+ (* 1/4 (* x x)) -1/2)) (neg x)) (neg.f64 x))) (.f64 eps #s(approx (- ( eps (* -1/2 (cos x))) (sin x)) #s(approx (+ (* eps (+ (* 1/4 (* x x)) -1/2)) (neg x)) (neg.f64 x)))))
(fma.f64 #s(approx (- (* eps (* -1/2 (cos x))) (sin x)) #s(approx (+ (* eps (+ (* 1/4 (* x x)) -1/2)) (neg x)) (neg.f64 x))) eps (.f64 #s(approx (- ( eps (* -1/2 (cos x))) (sin x)) #s(approx (+ (* eps (+ (* 1/4 (* x x)) -1/2)) (neg x)) (neg.f64 x))) #s(literal 0 binary64)))
(fma.f64 #s(approx (- (* eps (* -1/2 (cos x))) (sin x)) #s(approx (+ (* eps (+ (* 1/4 (* x x)) -1/2)) (neg x)) (neg.f64 x))) eps (.f64 #s(literal 0 binary64) #s(approx (- ( eps (* -1/2 (cos x))) (sin x)) #s(approx (+ (* eps (+ (* 1/4 (* x x)) -1/2)) (neg x)) (neg.f64 x)))))
(fma.f64 #s(approx (- (* eps (* -1/2 (cos x))) (sin x)) #s(approx (+ (* eps (+ (* 1/4 (* x x)) -1/2)) (neg x)) (neg.f64 x))) #s(literal 0 binary64) (.f64 eps #s(approx (- ( eps (* -1/2 (cos x))) (sin x)) #s(approx (+ (* eps (+ (* 1/4 (* x x)) -1/2)) (neg x)) (neg.f64 x)))))
(/.f64 (.f64 #s(approx (- ( eps (* -1/2 (cos x))) (sin x)) #s(approx (+ (* eps (+ (* 1/4 (* x x)) -1/2)) (neg x)) (neg.f64 x))) (.f64 eps (.f64 eps eps))) (*.f64 eps eps))
(/.f64 (.f64 #s(approx (- ( eps (* -1/2 (cos x))) (sin x)) #s(approx (+ (* eps (+ (* 1/4 (* x x)) -1/2)) (neg x)) (neg.f64 x))) (*.f64 eps eps)) eps)
(/.f64 (.f64 (.f64 eps (.f64 eps eps)) #s(approx (- ( eps (* -1/2 (cos x))) (sin x)) #s(approx (+ (* eps (+ (* 1/4 (* x x)) -1/2)) (neg x)) (neg.f64 x)))) (*.f64 eps eps))
(/.f64 (.f64 (.f64 eps eps) #s(approx (- (* eps (* -1/2 (cos x))) (sin x)) #s(approx (+ (* eps (+ (* 1/4 (* x x)) -1/2)) (neg x)) (neg.f64 x)))) eps)
(.f64 eps #s(approx (- ( eps (* -1/2 (cos x))) (sin x)) #s(approx (+ (* eps (+ (* 1/4 (* x x)) -1/2)) (neg x)) (neg.f64 x))))
(.f64 #s(approx (- ( eps (* -1/2 (cos x))) (sin x)) #s(approx (+ (* eps (+ (* 1/4 (* x x)) -1/2)) (neg x)) (neg.f64 x))) eps)
#s(approx (- (* eps (* -1/2 (cos x))) (sin x)) #s(approx (+ (* eps (+ (* 1/4 (* x x)) -1/2)) (neg x)) (neg.f64 x)))
#s(approx (+ (* eps (+ (* 1/4 (* x x)) -1/2)) (neg x)) (neg.f64 x))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps #s(approx (sin x) (fma.f64 (.f64 x x) #s(approx (* x (+ (* (* x x) (+ (* x (* x -1/5040)) 1/120)) -1/6)) (*.f64 x #s(literal -1/6 binary64))) x))))
(+.f64 (.f64 eps #s(approx (sin x) (fma.f64 (.f64 x x) #s(approx (* x (+ (* (* x x) (+ (* x (* x -1/5040)) 1/120)) -1/6)) (.f64 x #s(literal -1/6 binary64))) x))) (.f64 #s(approx (sin x) (fma.f64 (.f64 x x) #s(approx ( x (+ (* (* x x) (+ (* x (* x -1/5040)) 1/120)) -1/6)) (*.f64 x #s(literal -1/6 binary64))) x)) #s(literal 0 binary64)))
(+.f64 (.f64 eps #s(approx (sin x) (fma.f64 (.f64 x x) #s(approx (* x (+ (* (* x x) (+ (* x (* x -1/5040)) 1/120)) -1/6)) (.f64 x #s(literal -1/6 binary64))) x))) (.f64 #s(literal 0 binary64) #s(approx (sin x) (fma.f64 (.f64 x x) #s(approx ( x (+ (* (* x x) (+ (* x (* x -1/5040)) 1/120)) -1/6)) (*.f64 x #s(literal -1/6 binary64))) x))))
(+.f64 (.f64 #s(approx (sin x) (fma.f64 (.f64 x x) #s(approx (* x (+ (* (* x x) (+ (* x (* x -1/5040)) 1/120)) -1/6)) (.f64 x #s(literal -1/6 binary64))) x)) #s(literal 0 binary64)) (.f64 eps #s(approx (sin x) (fma.f64 (.f64 x x) #s(approx ( x (+ (* (* x x) (+ (* x (* x -1/5040)) 1/120)) -1/6)) (*.f64 x #s(literal -1/6 binary64))) x))))
(+.f64 (.f64 #s(literal 0 binary64) #s(approx (sin x) (fma.f64 (.f64 x x) #s(approx (* x (+ (* (* x x) (+ (* x (* x -1/5040)) 1/120)) -1/6)) (.f64 x #s(literal -1/6 binary64))) x))) (.f64 eps #s(approx (sin x) (fma.f64 (.f64 x x) #s(approx ( x (+ (* (* x x) (+ (* x (* x -1/5040)) 1/120)) -1/6)) (*.f64 x #s(literal -1/6 binary64))) x))))
(-.f64 #s(literal 0 binary64) (.f64 eps #s(approx (sin x) (fma.f64 (.f64 x x) #s(approx (* x (+ (* (* x x) (+ (* x (* x -1/5040)) 1/120)) -1/6)) (*.f64 x #s(literal -1/6 binary64))) x))))
(fma.f64 eps #s(approx (sin x) (fma.f64 (.f64 x x) #s(approx ( x (+ (* (* x x) (+ (* x (* x -1/5040)) 1/120)) -1/6)) (.f64 x #s(literal -1/6 binary64))) x)) (.f64 #s(approx (sin x) (fma.f64 (.f64 x x) #s(approx ( x (+ (* (* x x) (+ (* x (* x -1/5040)) 1/120)) -1/6)) (*.f64 x #s(literal -1/6 binary64))) x)) #s(literal 0 binary64)))
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(fma.f64 (fma.f64 x #s(literal 1/6 binary64) (.f64 eps #s(literal 1/4 binary64))) eps (.f64 (fma.f64 x #s(literal 1/6 binary64) (*.f64 eps #s(literal 1/4 binary64))) #s(literal 0 binary64)))
(fma.f64 (fma.f64 x #s(literal 1/6 binary64) (.f64 eps #s(literal 1/4 binary64))) eps (.f64 #s(literal 0 binary64) (fma.f64 x #s(literal 1/6 binary64) (*.f64 eps #s(literal 1/4 binary64)))))
(fma.f64 (fma.f64 x #s(literal 1/6 binary64) (.f64 eps #s(literal 1/4 binary64))) #s(literal 0 binary64) (.f64 eps (fma.f64 x #s(literal 1/6 binary64) (*.f64 eps #s(literal 1/4 binary64)))))
(fma.f64 (.f64 eps #s(literal -1/2 binary64)) (.f64 eps #s(literal -1/2 binary64)) (.f64 #s(literal 1/6 binary64) (.f64 x eps)))
(fma.f64 (.f64 eps eps) #s(literal 1/4 binary64) (.f64 #s(literal 1/6 binary64) (*.f64 x eps)))
(fma.f64 (.f64 eps (.f64 eps #s(literal -1/2 binary64))) #s(literal -1/2 binary64) (.f64 #s(literal 1/6 binary64) (.f64 x eps)))
(fma.f64 (.f64 eps #s(literal 1/4 binary64)) eps (.f64 #s(literal 1/6 binary64) (*.f64 x eps)))
(fma.f64 (.f64 x eps) #s(literal 1/6 binary64) (.f64 eps (*.f64 eps #s(literal 1/4 binary64))))
(fma.f64 (.f64 eps #s(literal 1/6 binary64)) x (.f64 eps (*.f64 eps #s(literal 1/4 binary64))))
(fma.f64 (.f64 (.f64 eps #s(literal -1/2 binary64)) #s(literal -1/2 binary64)) eps (.f64 #s(literal 1/6 binary64) (.f64 x eps)))
(/.f64 (.f64 (.f64 eps (.f64 eps eps)) (fma.f64 (.f64 eps (.f64 eps eps)) #s(literal 1/64 binary64) (.f64 (.f64 x (.f64 x x)) #s(literal 1/216 binary64)))) (.f64 (.f64 eps eps) (fma.f64 (.f64 x #s(literal 1/6 binary64)) (-.f64 (.f64 x #s(literal 1/6 binary64)) (.f64 eps #s(literal 1/4 binary64))) (.f64 (*.f64 eps eps) #s(literal 1/16 binary64)))))
(/.f64 (.f64 (.f64 eps (.f64 eps eps)) (-.f64 (.f64 (.f64 eps eps) #s(literal 1/16 binary64)) (.f64 (.f64 x x) #s(literal 1/36 binary64)))) (.f64 (.f64 eps eps) (fma.f64 eps #s(literal 1/4 binary64) (.f64 x #s(literal -1/6 binary64)))))
(/.f64 (.f64 (.f64 eps eps) (fma.f64 (.f64 eps (.f64 eps eps)) #s(literal 1/64 binary64) (.f64 (.f64 x (.f64 x x)) #s(literal 1/216 binary64)))) (.f64 eps (fma.f64 (.f64 x #s(literal 1/6 binary64)) (-.f64 (.f64 x #s(literal 1/6 binary64)) (.f64 eps #s(literal 1/4 binary64))) (.f64 (*.f64 eps eps) #s(literal 1/16 binary64)))))
(/.f64 (.f64 (.f64 eps eps) (-.f64 (.f64 (.f64 eps eps) #s(literal 1/16 binary64)) (.f64 (.f64 x x) #s(literal 1/36 binary64)))) (.f64 eps (fma.f64 eps #s(literal 1/4 binary64) (.f64 x #s(literal -1/6 binary64)))))
(/.f64 (.f64 (fma.f64 (.f64 eps (.f64 eps eps)) #s(literal 1/64 binary64) (.f64 (.f64 x (.f64 x x)) #s(literal 1/216 binary64))) (.f64 eps (.f64 eps eps))) (.f64 (fma.f64 (.f64 x #s(literal 1/6 binary64)) (-.f64 (.f64 x #s(literal 1/6 binary64)) (.f64 eps #s(literal 1/4 binary64))) (.f64 (.f64 eps eps) #s(literal 1/16 binary64))) (*.f64 eps eps)))
(/.f64 (.f64 (fma.f64 (.f64 eps (.f64 eps eps)) #s(literal 1/64 binary64) (.f64 (.f64 x (.f64 x x)) #s(literal 1/216 binary64))) (.f64 eps eps)) (.f64 (fma.f64 (.f64 x #s(literal 1/6 binary64)) (-.f64 (.f64 x #s(literal 1/6 binary64)) (.f64 eps #s(literal 1/4 binary64))) (.f64 (*.f64 eps eps) #s(literal 1/16 binary64))) eps))
(/.f64 (.f64 (-.f64 (.f64 (.f64 eps eps) #s(literal 1/16 binary64)) (.f64 (.f64 x x) #s(literal 1/36 binary64))) (.f64 eps (.f64 eps eps))) (.f64 (fma.f64 eps #s(literal 1/4 binary64) (.f64 x #s(literal -1/6 binary64))) (.f64 eps eps)))
(/.f64 (.f64 (-.f64 (.f64 (.f64 eps eps) #s(literal 1/16 binary64)) (.f64 (.f64 x x) #s(literal 1/36 binary64))) (.f64 eps eps)) (.f64 (fma.f64 eps #s(literal 1/4 binary64) (.f64 x #s(literal -1/6 binary64))) eps))
(/.f64 (fma.f64 (.f64 eps (.f64 eps eps)) (.f64 (.f64 eps (.f64 eps eps)) #s(literal 1/64 binary64)) (.f64 (.f64 eps (.f64 eps eps)) (.f64 (.f64 x (.f64 x x)) #s(literal 1/216 binary64)))) (fma.f64 (.f64 eps (.f64 eps #s(literal 1/4 binary64))) (.f64 eps (.f64 eps #s(literal 1/4 binary64))) (-.f64 (.f64 (.f64 #s(literal 1/6 binary64) (.f64 x eps)) (.f64 #s(literal 1/6 binary64) (.f64 x eps))) (.f64 (.f64 eps (.f64 eps #s(literal 1/4 binary64))) (.f64 #s(literal 1/6 binary64) (*.f64 x eps))))))
(/.f64 (-.f64 (.f64 (.f64 eps (.f64 eps #s(literal 1/4 binary64))) (.f64 eps (.f64 eps #s(literal 1/4 binary64)))) (.f64 (.f64 #s(literal 1/6 binary64) (.f64 x eps)) (.f64 #s(literal 1/6 binary64) (.f64 x eps)))) (-.f64 (.f64 eps (.f64 eps #s(literal 1/4 binary64))) (.f64 #s(literal 1/6 binary64) (.f64 x eps))))
(/.f64 (.f64 eps (fma.f64 (.f64 eps (.f64 eps eps)) #s(literal 1/64 binary64) (.f64 (.f64 x (.f64 x x)) #s(literal 1/216 binary64)))) (fma.f64 (.f64 x #s(literal 1/6 binary64)) (-.f64 (.f64 x #s(literal 1/6 binary64)) (.f64 eps #s(literal 1/4 binary64))) (.f64 (*.f64 eps eps) #s(literal 1/16 binary64))))
(/.f64 (.f64 eps (-.f64 (.f64 (.f64 eps eps) #s(literal 1/16 binary64)) (.f64 (.f64 x x) #s(literal 1/36 binary64)))) (fma.f64 eps #s(literal 1/4 binary64) (.f64 x #s(literal -1/6 binary64))))
(/.f64 (.f64 (fma.f64 x #s(literal 1/6 binary64) (.f64 eps #s(literal 1/4 binary64))) (.f64 eps (.f64 eps eps))) (*.f64 eps eps))
(/.f64 (.f64 (fma.f64 x #s(literal 1/6 binary64) (.f64 eps #s(literal 1/4 binary64))) (*.f64 eps eps)) eps)
(/.f64 (.f64 (.f64 eps (.f64 eps eps)) (fma.f64 x #s(literal 1/6 binary64) (.f64 eps #s(literal 1/4 binary64)))) (*.f64 eps eps))
(/.f64 (.f64 (.f64 eps eps) (fma.f64 x #s(literal 1/6 binary64) (*.f64 eps #s(literal 1/4 binary64)))) eps)
(/.f64 (.f64 (fma.f64 (.f64 eps (.f64 eps eps)) #s(literal 1/64 binary64) (.f64 (.f64 x (.f64 x x)) #s(literal 1/216 binary64))) eps) (fma.f64 (.f64 x #s(literal 1/6 binary64)) (-.f64 (.f64 x #s(literal 1/6 binary64)) (.f64 eps #s(literal 1/4 binary64))) (.f64 (*.f64 eps eps) #s(literal 1/16 binary64))))
(/.f64 (.f64 (-.f64 (.f64 (.f64 eps eps) #s(literal 1/16 binary64)) (.f64 (.f64 x x) #s(literal 1/36 binary64))) eps) (fma.f64 eps #s(literal 1/4 binary64) (.f64 x #s(literal -1/6 binary64))))
(/.f64 (fma.f64 (.f64 (.f64 eps #s(literal 1/4 binary64)) (.f64 eps (.f64 eps eps))) (.f64 eps eps) (.f64 (.f64 eps eps) (.f64 (.f64 x #s(literal 1/6 binary64)) (.f64 eps (.f64 eps eps))))) (.f64 (.f64 eps eps) (.f64 eps eps)))
(/.f64 (fma.f64 (.f64 (.f64 eps #s(literal 1/4 binary64)) (.f64 eps (.f64 eps eps))) eps (.f64 (.f64 eps eps) (.f64 (.f64 x #s(literal 1/6 binary64)) (.f64 eps eps)))) (.f64 eps (*.f64 eps eps)))
(/.f64 (fma.f64 (.f64 (.f64 eps #s(literal 1/4 binary64)) (.f64 eps (.f64 eps eps))) (.f64 eps eps) (.f64 (.f64 eps eps) (.f64 (.f64 eps (.f64 eps eps)) (.f64 x #s(literal 1/6 binary64))))) (.f64 (.f64 eps eps) (.f64 eps eps)))
(/.f64 (fma.f64 (.f64 (.f64 eps #s(literal 1/4 binary64)) (.f64 eps (.f64 eps eps))) eps (.f64 (.f64 eps eps) (.f64 (.f64 eps eps) (.f64 x #s(literal 1/6 binary64))))) (.f64 eps (*.f64 eps eps)))
(/.f64 (fma.f64 (.f64 (.f64 eps #s(literal 1/4 binary64)) (.f64 eps eps)) (.f64 eps eps) (.f64 eps (.f64 (.f64 x #s(literal 1/6 binary64)) (.f64 eps (.f64 eps eps))))) (.f64 eps (*.f64 eps eps)))
(/.f64 (fma.f64 (.f64 (.f64 eps #s(literal 1/4 binary64)) (.f64 eps eps)) eps (.f64 eps (.f64 (.f64 x #s(literal 1/6 binary64)) (.f64 eps eps)))) (.f64 eps eps))
(/.f64 (fma.f64 (.f64 (.f64 eps #s(literal 1/4 binary64)) (.f64 eps eps)) (.f64 eps eps) (.f64 eps (.f64 (.f64 eps (.f64 eps eps)) (.f64 x #s(literal 1/6 binary64))))) (.f64 eps (*.f64 eps eps)))
(/.f64 (fma.f64 (.f64 (.f64 eps #s(literal 1/4 binary64)) (.f64 eps eps)) eps (.f64 eps (.f64 (.f64 eps eps) (.f64 x #s(literal 1/6 binary64))))) (.f64 eps eps))
(/.f64 (fma.f64 (.f64 (.f64 eps (.f64 eps eps)) (.f64 eps #s(literal 1/4 binary64))) (.f64 eps eps) (.f64 (.f64 eps eps) (.f64 (.f64 x #s(literal 1/6 binary64)) (.f64 eps (.f64 eps eps))))) (.f64 (.f64 eps eps) (.f64 eps eps)))
(/.f64 (fma.f64 (.f64 (.f64 eps (.f64 eps eps)) (.f64 eps #s(literal 1/4 binary64))) eps (.f64 (.f64 eps eps) (.f64 (.f64 x #s(literal 1/6 binary64)) (.f64 eps eps)))) (.f64 eps (*.f64 eps eps)))
(/.f64 (fma.f64 (.f64 (.f64 eps (.f64 eps eps)) (.f64 eps #s(literal 1/4 binary64))) (.f64 eps eps) (.f64 (.f64 eps eps) (.f64 (.f64 eps (.f64 eps eps)) (.f64 x #s(literal 1/6 binary64))))) (.f64 (.f64 eps eps) (.f64 eps eps)))
(/.f64 (fma.f64 (.f64 (.f64 eps (.f64 eps eps)) (.f64 eps #s(literal 1/4 binary64))) eps (.f64 (.f64 eps eps) (.f64 (.f64 eps eps) (.f64 x #s(literal 1/6 binary64))))) (.f64 eps (*.f64 eps eps)))
(/.f64 (fma.f64 (.f64 (.f64 eps eps) (.f64 eps #s(literal 1/4 binary64))) (.f64 eps eps) (.f64 eps (.f64 (.f64 x #s(literal 1/6 binary64)) (.f64 eps (.f64 eps eps))))) (.f64 eps (*.f64 eps eps)))
(/.f64 (fma.f64 (.f64 (.f64 eps eps) (.f64 eps #s(literal 1/4 binary64))) eps (.f64 eps (.f64 (.f64 x #s(literal 1/6 binary64)) (.f64 eps eps)))) (.f64 eps eps))
(/.f64 (fma.f64 (.f64 (.f64 eps eps) (.f64 eps #s(literal 1/4 binary64))) (.f64 eps eps) (.f64 eps (.f64 (.f64 eps (.f64 eps eps)) (.f64 x #s(literal 1/6 binary64))))) (.f64 eps (*.f64 eps eps)))
(/.f64 (fma.f64 (.f64 (.f64 eps eps) (.f64 eps #s(literal 1/4 binary64))) eps (.f64 eps (.f64 (.f64 eps eps) (.f64 x #s(literal 1/6 binary64))))) (.f64 eps eps))
(/.f64 (fma.f64 (.f64 (.f64 x #s(literal 1/6 binary64)) (.f64 eps (.f64 eps eps))) (.f64 eps eps) (.f64 (.f64 eps eps) (.f64 (.f64 eps #s(literal 1/4 binary64)) (.f64 eps (.f64 eps eps))))) (.f64 (.f64 eps eps) (.f64 eps eps)))
(/.f64 (fma.f64 (.f64 (.f64 x #s(literal 1/6 binary64)) (.f64 eps (.f64 eps eps))) eps (.f64 (.f64 eps eps) (.f64 (.f64 eps #s(literal 1/4 binary64)) (.f64 eps eps)))) (.f64 eps (*.f64 eps eps)))
(/.f64 (fma.f64 (.f64 (.f64 x #s(literal 1/6 binary64)) (.f64 eps (.f64 eps eps))) (.f64 eps eps) (.f64 (.f64 eps eps) (.f64 (.f64 eps (.f64 eps eps)) (.f64 eps #s(literal 1/4 binary64))))) (.f64 (.f64 eps eps) (.f64 eps eps)))
(/.f64 (fma.f64 (.f64 (.f64 x #s(literal 1/6 binary64)) (.f64 eps (.f64 eps eps))) eps (.f64 (.f64 eps eps) (.f64 (.f64 eps eps) (.f64 eps #s(literal 1/4 binary64))))) (.f64 eps (*.f64 eps eps)))
(/.f64 (fma.f64 (.f64 (.f64 x #s(literal 1/6 binary64)) (.f64 eps eps)) (.f64 eps eps) (.f64 eps (.f64 (.f64 eps #s(literal 1/4 binary64)) (.f64 eps (.f64 eps eps))))) (.f64 eps (*.f64 eps eps)))
(/.f64 (fma.f64 (.f64 (.f64 x #s(literal 1/6 binary64)) (.f64 eps eps)) eps (.f64 eps (.f64 (.f64 eps #s(literal 1/4 binary64)) (.f64 eps eps)))) (.f64 eps eps))
(/.f64 (fma.f64 (.f64 (.f64 x #s(literal 1/6 binary64)) (.f64 eps eps)) (.f64 eps eps) (.f64 eps (.f64 (.f64 eps (.f64 eps eps)) (.f64 eps #s(literal 1/4 binary64))))) (.f64 eps (*.f64 eps eps)))
(/.f64 (fma.f64 (.f64 (.f64 x #s(literal 1/6 binary64)) (.f64 eps eps)) eps (.f64 eps (.f64 (.f64 eps eps) (.f64 eps #s(literal 1/4 binary64))))) (.f64 eps eps))
(/.f64 (fma.f64 (.f64 (.f64 eps (.f64 eps eps)) (.f64 x #s(literal 1/6 binary64))) (.f64 eps eps) (.f64 (.f64 eps eps) (.f64 (.f64 eps #s(literal 1/4 binary64)) (.f64 eps (.f64 eps eps))))) (.f64 (.f64 eps eps) (.f64 eps eps)))
(/.f64 (fma.f64 (.f64 (.f64 eps (.f64 eps eps)) (.f64 x #s(literal 1/6 binary64))) eps (.f64 (.f64 eps eps) (.f64 (.f64 eps #s(literal 1/4 binary64)) (.f64 eps eps)))) (.f64 eps (*.f64 eps eps)))
(/.f64 (fma.f64 (.f64 (.f64 eps (.f64 eps eps)) (.f64 x #s(literal 1/6 binary64))) (.f64 eps eps) (.f64 (.f64 eps eps) (.f64 (.f64 eps (.f64 eps eps)) (.f64 eps #s(literal 1/4 binary64))))) (.f64 (.f64 eps eps) (.f64 eps eps)))
(/.f64 (fma.f64 (.f64 (.f64 eps (.f64 eps eps)) (.f64 x #s(literal 1/6 binary64))) eps (.f64 (.f64 eps eps) (.f64 (.f64 eps eps) (.f64 eps #s(literal 1/4 binary64))))) (.f64 eps (*.f64 eps eps)))
(/.f64 (fma.f64 (.f64 (.f64 eps eps) (.f64 x #s(literal 1/6 binary64))) (.f64 eps eps) (.f64 eps (.f64 (.f64 eps #s(literal 1/4 binary64)) (.f64 eps (.f64 eps eps))))) (.f64 eps (*.f64 eps eps)))
(/.f64 (fma.f64 (.f64 (.f64 eps eps) (.f64 x #s(literal 1/6 binary64))) eps (.f64 eps (.f64 (.f64 eps #s(literal 1/4 binary64)) (.f64 eps eps)))) (.f64 eps eps))
(/.f64 (fma.f64 (.f64 (.f64 eps eps) (.f64 x #s(literal 1/6 binary64))) (.f64 eps eps) (.f64 eps (.f64 (.f64 eps (.f64 eps eps)) (.f64 eps #s(literal 1/4 binary64))))) (.f64 eps (*.f64 eps eps)))
(/.f64 (fma.f64 (.f64 (.f64 eps eps) (.f64 x #s(literal 1/6 binary64))) eps (.f64 eps (.f64 (.f64 eps eps) (.f64 eps #s(literal 1/4 binary64))))) (.f64 eps eps))
(.f64 eps (fma.f64 x #s(literal 1/6 binary64) (.f64 eps #s(literal 1/4 binary64))))
(.f64 (fma.f64 x #s(literal 1/6 binary64) (.f64 eps #s(literal 1/4 binary64))) eps)

eval152.0ms (0.9%)

Memory: -18.5MiB live, 105.1MiB allocated
Compiler: Compiled 34 611 to 2 731 computations (92.1% saved)

prune145.0ms (0.9%)

Memory

-8.3MiB live, 109.4MiB allocated

Pruning

20 alts after pruning (13 fresh and 7 done)

	Pruned	Kept	Total
New	1 192	7	1 199
Fresh	6	6	12
Picked	3	2	5
Done	0	5	5
Total	1 201	20	1 221

Accuracy

100.0%

Counts

1 221 → 20

Alt Table

Click to see full alt table

Status	Accuracy	Program
	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)) (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x)))) #s(literal -2 binary64))
	78.4%	#s(approx (- (cos (+ x eps)) (cos x)) (/.f64 eps #s(approx (/ 1 (- (* (cos x) (* eps -1/2)) (sin x))) (/.f64 #s(literal -1 binary64) (sin.f64 x)))))
✓	49.2%	#s(approx (- (cos (+ x eps)) (cos x)) (+.f64 #s(approx (cos eps) #s(literal 1 binary64)) #s(literal -1 binary64)))
✓	78.4%	#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (sin.f64 x) (neg.f64 eps)))
	77.9%	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (sin x) (fma.f64 (fma.f64 (.f64 x x) #s(literal 1/120 binary64) #s(literal -1/6 binary64)) (.f64 x (.f64 x x)) x)) (neg.f64 eps)))
✓	78.0%	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (sin x) (fma.f64 (.f64 x x) (.f64 x (fma.f64 (.f64 x x) (fma.f64 x (*.f64 x #s(literal -1/5040 binary64)) #s(literal 1/120 binary64)) #s(literal -1/6 binary64))) x)) (neg.f64 eps)))
✓	99.8%	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps (-.f64 (.f64 eps (*.f64 #s(literal -1/2 binary64) (cos.f64 x))) (sin.f64 x))))
	99.6%	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps (-.f64 #s(approx ( eps (* -1/2 (cos x))) (.f64 eps (fma.f64 #s(literal 1/4 binary64) (.f64 x x) #s(literal -1/2 binary64)))) (sin.f64 x))))
	99.6%	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps (-.f64 #s(approx ( eps (* -1/2 (cos x))) (*.f64 eps #s(literal -1/2 binary64))) (sin.f64 x))))
✓	98.9%	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps #s(approx (- ( eps (* -1/2 (cos x))) (sin x)) (fma.f64 x (fma.f64 x (fma.f64 eps #s(literal 1/4 binary64) (.f64 x #s(literal 1/6 binary64))) #s(literal -1 binary64)) (.f64 eps #s(literal -1/2 binary64))))))
	98.9%	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps #s(approx (- ( eps (* -1/2 (cos x))) (sin x)) (fma.f64 x (fma.f64 x #s(approx (+ (* eps 1/4) (* x 1/6)) (.f64 x #s(literal 1/6 binary64))) #s(literal -1 binary64)) (.f64 eps #s(literal -1/2 binary64))))))
✓	98.4%	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps #s(approx (- ( eps (* -1/2 (cos x))) (sin x)) (fma.f64 eps (fma.f64 #s(literal 1/4 binary64) (*.f64 x x) #s(literal -1/2 binary64)) (neg.f64 x)))))
	98.4%	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps #s(approx (- ( eps (* -1/2 (cos x))) (sin x)) (-.f64 (*.f64 eps #s(literal -1/2 binary64)) x))))
	77.7%	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps #s(approx (- ( eps (* -1/2 (cos x))) (sin x)) #s(approx (+ (* x (+ (* x (+ (* eps 1/4) (* x 1/6))) -1)) (* eps -1/2)) (.f64 x (fma.f64 x (.f64 x #s(literal 1/6 binary64)) #s(literal -1 binary64)))))))
	49.5%	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps #s(approx (- ( eps (* -1/2 (cos x))) (sin x)) #s(approx (+ (* eps (+ (* 1/4 (* x x)) -1/2)) (neg x)) (.f64 eps (.f64 #s(literal 1/4 binary64) (*.f64 x x)))))))
✓	77.5%	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps #s(approx (- ( eps (* -1/2 (cos x))) (sin x)) #s(approx (+ (* eps (+ (* 1/4 (* x x)) -1/2)) (neg x)) (neg.f64 x)))))
	99.0%	#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (/ eps (/ 1 (- (* (cos x) (* eps -1/2)) (sin x)))) (fma.f64 x #s(approx (+ (* x (* eps (+ (* eps 1/4) (* x 1/6)))) (neg eps)) (.f64 eps (fma.f64 x (.f64 x #s(literal 1/6 binary64)) #s(literal -1 binary64)))) (.f64 #s(literal -1/2 binary64) (.f64 eps eps)))))
	98.6%	#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (/ eps (/ 1 (- (* (cos x) (* eps -1/2)) (sin x)))) (fma.f64 x #s(approx (+ (* x (* eps (+ (* eps 1/4) (* x 1/6)))) (neg eps)) (neg.f64 eps)) (.f64 #s(literal -1/2 binary64) (.f64 eps eps)))))
	77.9%	#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (sin x) (neg eps)) (.f64 x (fma.f64 (.f64 x x) (.f64 eps (fma.f64 (.f64 x x) #s(literal -1/120 binary64) #s(literal 1/6 binary64))) (neg.f64 eps)))))
	98.9%	#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* eps (- (* eps (* -1/2 (cos x))) (sin x))) (fma.f64 eps (-.f64 (.f64 eps #s(literal -1/2 binary64)) x) (.f64 x (.f64 x (.f64 eps (fma.f64 eps #s(literal 1/4 binary64) (*.f64 x #s(literal 1/6 binary64)))))))))

Compiler

Compiled 1 045 to 344 computations (67.1% saved)

regimes31.0ms (0.2%)

Memory

16.5MiB live, 16.5MiB allocated

Counts

44 → 1

Calls

Call 1

Inputs
#s(approx (- (cos (+ x eps)) (cos x)) (+.f64 #s(approx (cos eps) #s(literal 1 binary64)) #s(literal -1 binary64)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (sin x) (neg eps)) (*.f64 eps (neg.f64 x))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps #s(approx (- ( eps (* -1/2 (cos x))) (sin x)) #s(approx (+ (* eps (+ (* 1/4 (* x x)) -1/2)) (neg x)) (neg.f64 x)))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps #s(approx (- ( eps (* -1/2 (cos x))) (sin x)) (-.f64 (*.f64 eps #s(literal -1/2 binary64)) x))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (/ eps (/ 1 (- (* (cos x) (* eps -1/2)) (sin x)))) (fma.f64 x #s(approx (+ (* x (* eps (+ (* eps 1/4) (* x 1/6)))) (neg eps)) (neg.f64 eps)) (.f64 #s(literal -1/2 binary64) (.f64 eps eps)))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps #s(approx (- ( eps (* -1/2 (cos x))) (sin x)) #s(approx (+ (* eps (+ (* 1/4 (* x x)) -1/2)) (neg x)) (.f64 #s(literal 1/4 binary64) (.f64 eps (*.f64 x x)))))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps #s(approx (- ( eps (* -1/2 (cos x))) (sin x)) #s(approx (+ (* eps (+ (* 1/4 (* x x)) -1/2)) (neg x)) (.f64 eps (.f64 #s(literal 1/4 binary64) (*.f64 x x)))))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (sin x) (neg eps)) (.f64 x (.f64 eps (fma.f64 x (*.f64 x #s(literal 1/6 binary64)) #s(literal -1 binary64))))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps #s(approx (- ( eps (* -1/2 (cos x))) (sin x)) #s(approx (+ (* x (+ (* x (+ (* eps 1/4) (* x 1/6))) -1)) (* eps -1/2)) (.f64 x (fma.f64 x (.f64 x #s(literal 1/6 binary64)) #s(literal -1 binary64)))))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (sin x) (fma.f64 x (.f64 #s(literal -1/6 binary64) (*.f64 x x)) x)) (neg.f64 eps)))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (sin x) (fma.f64 (.f64 x x) #s(approx (* x (+ (* (* x x) (+ (* x (* x -1/5040)) 1/120)) -1/6)) (*.f64 x #s(literal -1/6 binary64))) x)) (neg.f64 eps)))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps #s(approx (- ( eps (* -1/2 (cos x))) (sin x)) (fma.f64 eps (fma.f64 #s(literal 1/4 binary64) (*.f64 x x) #s(literal -1/2 binary64)) (neg.f64 x)))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps #s(approx (- ( eps (* -1/2 (cos x))) (sin x)) (fma.f64 x (fma.f64 x #s(approx (+ (* eps 1/4) (* x 1/6)) (.f64 x #s(literal 1/6 binary64))) #s(literal -1 binary64)) (.f64 eps #s(literal -1/2 binary64))))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps #s(approx (- ( eps (* -1/2 (cos x))) (sin x)) (fma.f64 (.f64 x x) (.f64 #s(literal 1/4 binary64) eps) (fma.f64 eps #s(literal -1/2 binary64) (neg.f64 x))))))
#s(approx (- (cos (+ x eps)) (cos x)) (/.f64 eps (/.f64 #s(literal 1 binary64) #s(approx (- (* (cos x) (* eps -1/2)) (sin x)) (-.f64 (*.f64 #s(literal -1/2 binary64) eps) x)))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (/ eps (/ 1 (- (* (cos x) (* eps -1/2)) (sin x)))) (fma.f64 x #s(approx (+ (* x (* eps (+ (* eps 1/4) (* x 1/6)))) (neg eps)) (.f64 eps (fma.f64 x (.f64 x #s(literal 1/6 binary64)) #s(literal -1 binary64)))) (.f64 #s(literal -1/2 binary64) (.f64 eps eps)))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps #s(approx (- ( eps (* -1/2 (cos x))) (sin x)) #s(approx (+ (* eps (+ (* 1/4 (* x x)) -1/2)) (neg x)) (*.f64 eps (fma.f64 x (fma.f64 x #s(literal 1/4 binary64) (/.f64 #s(literal -1 binary64) eps)) #s(literal -1/2 binary64)))))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps #s(approx (- ( eps (* -1/2 (cos x))) (sin x)) (fma.f64 x (fma.f64 x (fma.f64 eps #s(literal 1/4 binary64) (.f64 x #s(literal 1/6 binary64))) #s(literal -1 binary64)) (.f64 eps #s(literal -1/2 binary64))))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (sin x) (neg eps)) (.f64 x (fma.f64 x (.f64 x (.f64 eps (fma.f64 (.f64 x x) #s(literal -1/120 binary64) #s(literal 1/6 binary64)))) (neg.f64 eps)))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (sin x) (neg eps)) (.f64 x (fma.f64 (.f64 x x) (.f64 eps (fma.f64 (.f64 x x) #s(literal -1/120 binary64) #s(literal 1/6 binary64))) (neg.f64 eps)))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (sin x) (fma.f64 x (.f64 x (.f64 x (fma.f64 (.f64 x x) #s(literal 1/120 binary64) #s(literal -1/6 binary64)))) x)) (neg.f64 eps)))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (sin x) (fma.f64 (.f64 x x) (.f64 x (fma.f64 (.f64 x x) #s(literal 1/120 binary64) #s(literal -1/6 binary64))) x)) (neg.f64 eps)))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (sin x) (fma.f64 (fma.f64 (.f64 x x) #s(literal 1/120 binary64) #s(literal -1/6 binary64)) (.f64 x (.f64 x x)) x)) (neg.f64 eps)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* eps (- (* eps (* -1/2 (cos x))) (sin x))) (fma.f64 eps (-.f64 (.f64 eps #s(literal -1/2 binary64)) x) (.f64 x (.f64 x (.f64 eps (fma.f64 eps #s(literal 1/4 binary64) (*.f64 x #s(literal 1/6 binary64)))))))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (/ eps (/ 1 (- (* (cos x) (* eps -1/2)) (sin x)))) (fma.f64 x (fma.f64 x (.f64 eps (fma.f64 eps #s(literal 1/4 binary64) (.f64 x #s(literal 1/6 binary64)))) (neg.f64 eps)) (.f64 #s(literal -1/2 binary64) (.f64 eps eps)))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (sin x) (fma.f64 (.f64 x x) (.f64 x (fma.f64 (.f64 x x) (fma.f64 x (*.f64 x #s(literal -1/5040 binary64)) #s(literal 1/120 binary64)) #s(literal -1/6 binary64))) x)) (neg.f64 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 (- (cos (+ x eps)) (cos x)) (.f64 eps (-.f64 #s(approx ( eps (* -1/2 (cos x))) (*.f64 eps #s(literal -1/2 binary64))) (sin.f64 x))))
(-.f64 (cos.f64 (+.f64 x eps)) #s(approx (cos x) (fma.f64 x (*.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64))))
#s(approx (- (cos (+ x eps)) (cos x)) (/.f64 eps #s(approx (/ 1 (- (* (cos x) (* eps -1/2)) (sin x))) (/.f64 #s(literal -1 binary64) (sin.f64 x)))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps (-.f64 #s(approx ( eps (* -1/2 (cos x))) (.f64 eps (fma.f64 #s(literal 1/4 binary64) (.f64 x x) #s(literal -1/2 binary64)))) (sin.f64 x))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 (sin.f64 x) (.f64 (neg.f64 (.f64 eps (.f64 eps eps))) (/.f64 #s(literal 1 binary64) (fma.f64 eps eps #s(literal 0 binary64))))))
(-.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))))
(.f64 #s(approx ( (sin (* (+ eps 0) 1/2)) (sin (* (+ x (+ x eps)) 1/2))) (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x)))) #s(literal -2 binary64))
#s(approx (- (cos (+ x eps)) (cos x)) (fma.f64 (.f64 (cos.f64 x) (.f64 eps #s(literal -1/2 binary64))) eps (neg.f64 (*.f64 eps (sin.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 (/.f64 #s(literal 1 binary64) (-.f64 (.f64 (cos.f64 x) (.f64 eps #s(literal -1/2 binary64))) (sin.f64 x)))))
#s(approx (- (cos (+ x eps)) (cos x)) (/.f64 (-.f64 (.f64 (.f64 (.f64 (cos.f64 x) (.f64 eps #s(literal -1/2 binary64))) eps) (.f64 (.f64 (cos.f64 x) (.f64 eps #s(literal -1/2 binary64))) eps)) (.f64 (neg.f64 (.f64 eps (sin.f64 x))) (neg.f64 (.f64 eps (sin.f64 x))))) (-.f64 (.f64 (.f64 (cos.f64 x) (.f64 eps #s(literal -1/2 binary64))) eps) (neg.f64 (.f64 eps (sin.f64 x))))))
#s(approx (- (cos (+ x eps)) (cos x)) (/.f64 (.f64 (-.f64 (pow.f64 (.f64 (cos.f64 x) (.f64 eps #s(literal -1/2 binary64))) #s(literal 3 binary64)) (pow.f64 (sin.f64 x) #s(literal 3 binary64))) eps) (fma.f64 (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x)))) (.f64 (.f64 eps eps) #s(literal 1/4 binary64)) (.f64 (sin.f64 x) (fma.f64 eps (.f64 (cos.f64 x) #s(literal -1/2 binary64)) (sin.f64 x))))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 (.f64 (-.f64 (pow.f64 (.f64 (cos.f64 x) (.f64 eps #s(literal -1/2 binary64))) #s(literal 3 binary64)) (pow.f64 (sin.f64 x) #s(literal 3 binary64))) eps) (/.f64 #s(literal 1 binary64) (fma.f64 (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x)))) (.f64 (.f64 eps eps) #s(literal 1/4 binary64)) (.f64 (sin.f64 x) (fma.f64 eps (*.f64 (cos.f64 x) #s(literal -1/2 binary64)) (sin.f64 x)))))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps (-.f64 (/.f64 (pow.f64 (.f64 (cos.f64 x) (.f64 eps #s(literal -1/2 binary64))) #s(literal 3 binary64)) (fma.f64 (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x)))) (.f64 (.f64 eps eps) #s(literal 1/4 binary64)) (.f64 (sin.f64 x) (fma.f64 eps (.f64 (cos.f64 x) #s(literal -1/2 binary64)) (sin.f64 x))))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (fma.f64 (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x)))) (.f64 (.f64 eps eps) #s(literal 1/4 binary64)) (.f64 (sin.f64 x) (fma.f64 eps (*.f64 (cos.f64 x) #s(literal -1/2 binary64)) (sin.f64 x))))))))

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

Calls

3 calls:

10.0ms	x
10.0ms	eps
8.0ms	(-.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)

regimes25.0ms (0.1%)

Memory

13.9MiB live, 13.9MiB 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 (* (sin x) (neg eps)) (*.f64 eps (neg.f64 x))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps #s(approx (- ( eps (* -1/2 (cos x))) (sin x)) #s(approx (+ (* eps (+ (* 1/4 (* x x)) -1/2)) (neg x)) (neg.f64 x)))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps #s(approx (- ( eps (* -1/2 (cos x))) (sin x)) (-.f64 (*.f64 eps #s(literal -1/2 binary64)) x))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (/ eps (/ 1 (- (* (cos x) (* eps -1/2)) (sin x)))) (fma.f64 x #s(approx (+ (* x (* eps (+ (* eps 1/4) (* x 1/6)))) (neg eps)) (neg.f64 eps)) (.f64 #s(literal -1/2 binary64) (.f64 eps eps)))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps #s(approx (- ( eps (* -1/2 (cos x))) (sin x)) #s(approx (+ (* eps (+ (* 1/4 (* x x)) -1/2)) (neg x)) (.f64 #s(literal 1/4 binary64) (.f64 eps (*.f64 x x)))))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps #s(approx (- ( eps (* -1/2 (cos x))) (sin x)) #s(approx (+ (* eps (+ (* 1/4 (* x x)) -1/2)) (neg x)) (.f64 eps (.f64 #s(literal 1/4 binary64) (*.f64 x x)))))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (sin x) (neg eps)) (.f64 x (.f64 eps (fma.f64 x (*.f64 x #s(literal 1/6 binary64)) #s(literal -1 binary64))))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps #s(approx (- ( eps (* -1/2 (cos x))) (sin x)) #s(approx (+ (* x (+ (* x (+ (* eps 1/4) (* x 1/6))) -1)) (* eps -1/2)) (.f64 x (fma.f64 x (.f64 x #s(literal 1/6 binary64)) #s(literal -1 binary64)))))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (sin x) (fma.f64 x (.f64 #s(literal -1/6 binary64) (*.f64 x x)) x)) (neg.f64 eps)))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (sin x) (fma.f64 (.f64 x x) #s(approx (* x (+ (* (* x x) (+ (* x (* x -1/5040)) 1/120)) -1/6)) (*.f64 x #s(literal -1/6 binary64))) x)) (neg.f64 eps)))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps #s(approx (- ( eps (* -1/2 (cos x))) (sin x)) (fma.f64 eps (fma.f64 #s(literal 1/4 binary64) (*.f64 x x) #s(literal -1/2 binary64)) (neg.f64 x)))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps #s(approx (- ( eps (* -1/2 (cos x))) (sin x)) (fma.f64 x (fma.f64 x #s(approx (+ (* eps 1/4) (* x 1/6)) (.f64 x #s(literal 1/6 binary64))) #s(literal -1 binary64)) (.f64 eps #s(literal -1/2 binary64))))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps #s(approx (- ( eps (* -1/2 (cos x))) (sin x)) (fma.f64 (.f64 x x) (.f64 #s(literal 1/4 binary64) eps) (fma.f64 eps #s(literal -1/2 binary64) (neg.f64 x))))))
#s(approx (- (cos (+ x eps)) (cos x)) (/.f64 eps (/.f64 #s(literal 1 binary64) #s(approx (- (* (cos x) (* eps -1/2)) (sin x)) (-.f64 (*.f64 #s(literal -1/2 binary64) eps) x)))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (/ eps (/ 1 (- (* (cos x) (* eps -1/2)) (sin x)))) (fma.f64 x #s(approx (+ (* x (* eps (+ (* eps 1/4) (* x 1/6)))) (neg eps)) (.f64 eps (fma.f64 x (.f64 x #s(literal 1/6 binary64)) #s(literal -1 binary64)))) (.f64 #s(literal -1/2 binary64) (.f64 eps eps)))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps #s(approx (- ( eps (* -1/2 (cos x))) (sin x)) #s(approx (+ (* eps (+ (* 1/4 (* x x)) -1/2)) (neg x)) (*.f64 eps (fma.f64 x (fma.f64 x #s(literal 1/4 binary64) (/.f64 #s(literal -1 binary64) eps)) #s(literal -1/2 binary64)))))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps #s(approx (- ( eps (* -1/2 (cos x))) (sin x)) (fma.f64 x (fma.f64 x (fma.f64 eps #s(literal 1/4 binary64) (.f64 x #s(literal 1/6 binary64))) #s(literal -1 binary64)) (.f64 eps #s(literal -1/2 binary64))))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (sin x) (neg eps)) (.f64 x (fma.f64 x (.f64 x (.f64 eps (fma.f64 (.f64 x x) #s(literal -1/120 binary64) #s(literal 1/6 binary64)))) (neg.f64 eps)))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (sin x) (neg eps)) (.f64 x (fma.f64 (.f64 x x) (.f64 eps (fma.f64 (.f64 x x) #s(literal -1/120 binary64) #s(literal 1/6 binary64))) (neg.f64 eps)))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (sin x) (fma.f64 x (.f64 x (.f64 x (fma.f64 (.f64 x x) #s(literal 1/120 binary64) #s(literal -1/6 binary64)))) x)) (neg.f64 eps)))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (sin x) (fma.f64 (.f64 x x) (.f64 x (fma.f64 (.f64 x x) #s(literal 1/120 binary64) #s(literal -1/6 binary64))) x)) (neg.f64 eps)))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (sin x) (fma.f64 (fma.f64 (.f64 x x) #s(literal 1/120 binary64) #s(literal -1/6 binary64)) (.f64 x (.f64 x x)) x)) (neg.f64 eps)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* eps (- (* eps (* -1/2 (cos x))) (sin x))) (fma.f64 eps (-.f64 (.f64 eps #s(literal -1/2 binary64)) x) (.f64 x (.f64 x (.f64 eps (fma.f64 eps #s(literal 1/4 binary64) (*.f64 x #s(literal 1/6 binary64)))))))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (/ eps (/ 1 (- (* (cos x) (* eps -1/2)) (sin x)))) (fma.f64 x (fma.f64 x (.f64 eps (fma.f64 eps #s(literal 1/4 binary64) (.f64 x #s(literal 1/6 binary64)))) (neg.f64 eps)) (.f64 #s(literal -1/2 binary64) (.f64 eps eps)))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (sin x) (fma.f64 (.f64 x x) (.f64 x (fma.f64 (.f64 x x) (fma.f64 x (*.f64 x #s(literal -1/5040 binary64)) #s(literal 1/120 binary64)) #s(literal -1/6 binary64))) x)) (neg.f64 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 (- (cos (+ x eps)) (cos x)) (.f64 eps (-.f64 #s(approx ( eps (* -1/2 (cos x))) (*.f64 eps #s(literal -1/2 binary64))) (sin.f64 x))))
(-.f64 (cos.f64 (+.f64 x eps)) #s(approx (cos x) (fma.f64 x (*.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64))))
#s(approx (- (cos (+ x eps)) (cos x)) (/.f64 eps #s(approx (/ 1 (- (* (cos x) (* eps -1/2)) (sin x))) (/.f64 #s(literal -1 binary64) (sin.f64 x)))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps (-.f64 #s(approx ( eps (* -1/2 (cos x))) (.f64 eps (fma.f64 #s(literal 1/4 binary64) (.f64 x x) #s(literal -1/2 binary64)))) (sin.f64 x))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 (sin.f64 x) (.f64 (neg.f64 (.f64 eps (.f64 eps eps))) (/.f64 #s(literal 1 binary64) (fma.f64 eps eps #s(literal 0 binary64))))))
(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))

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

Calls

3 calls:

8.0ms	eps
8.0ms	x
7.0ms	(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))

Results

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

Compiler

Compiled 15 to 10 computations (33.3% saved)

regimes22.0ms (0.1%)

Memory

-33.9MiB live, 12.2MiB allocated

Counts

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

Outputs

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

Calls

3 calls:

7.0ms	eps
7.0ms	x
6.0ms	(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))

Results

Accuracy	Segments	Branch
99.1%	1	`x`
99.1%	1	`eps`
99.1%	1	`(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))`

Compiler

Compiled 15 to 10 computations (33.3% saved)

regimes18.0ms (0.1%)

Memory

10.8MiB live, 10.8MiB allocated

Counts

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

Outputs

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

Calls

3 calls:

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

Results

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

Compiler

Compiled 15 to 10 computations (33.3% saved)

regimes12.0ms (0.1%)

Memory

8.1MiB live, 8.1MiB 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 (* (sin x) (neg eps)) (*.f64 eps (neg.f64 x))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps #s(approx (- ( eps (* -1/2 (cos x))) (sin x)) #s(approx (+ (* eps (+ (* 1/4 (* x x)) -1/2)) (neg x)) (neg.f64 x)))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps #s(approx (- ( eps (* -1/2 (cos x))) (sin x)) (-.f64 (*.f64 eps #s(literal -1/2 binary64)) x))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (/ eps (/ 1 (- (* (cos x) (* eps -1/2)) (sin x)))) (fma.f64 x #s(approx (+ (* x (* eps (+ (* eps 1/4) (* x 1/6)))) (neg eps)) (neg.f64 eps)) (.f64 #s(literal -1/2 binary64) (.f64 eps eps)))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps #s(approx (- ( eps (* -1/2 (cos x))) (sin x)) #s(approx (+ (* eps (+ (* 1/4 (* x x)) -1/2)) (neg x)) (.f64 #s(literal 1/4 binary64) (.f64 eps (*.f64 x x)))))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps #s(approx (- ( eps (* -1/2 (cos x))) (sin x)) #s(approx (+ (* eps (+ (* 1/4 (* x x)) -1/2)) (neg x)) (.f64 eps (.f64 #s(literal 1/4 binary64) (*.f64 x x)))))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (sin x) (neg eps)) (.f64 x (.f64 eps (fma.f64 x (*.f64 x #s(literal 1/6 binary64)) #s(literal -1 binary64))))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps #s(approx (- ( eps (* -1/2 (cos x))) (sin x)) #s(approx (+ (* x (+ (* x (+ (* eps 1/4) (* x 1/6))) -1)) (* eps -1/2)) (.f64 x (fma.f64 x (.f64 x #s(literal 1/6 binary64)) #s(literal -1 binary64)))))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (sin x) (fma.f64 x (.f64 #s(literal -1/6 binary64) (*.f64 x x)) x)) (neg.f64 eps)))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (sin x) (fma.f64 (.f64 x x) #s(approx (* x (+ (* (* x x) (+ (* x (* x -1/5040)) 1/120)) -1/6)) (*.f64 x #s(literal -1/6 binary64))) x)) (neg.f64 eps)))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps #s(approx (- ( eps (* -1/2 (cos x))) (sin x)) (fma.f64 eps (fma.f64 #s(literal 1/4 binary64) (*.f64 x x) #s(literal -1/2 binary64)) (neg.f64 x)))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps #s(approx (- ( eps (* -1/2 (cos x))) (sin x)) (fma.f64 x (fma.f64 x #s(approx (+ (* eps 1/4) (* x 1/6)) (.f64 x #s(literal 1/6 binary64))) #s(literal -1 binary64)) (.f64 eps #s(literal -1/2 binary64))))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 eps #s(approx (- ( eps (* -1/2 (cos x))) (sin x)) (fma.f64 (.f64 x x) (.f64 #s(literal 1/4 binary64) eps) (fma.f64 eps #s(literal -1/2 binary64) (neg.f64 x))))))
#s(approx (- (cos (+ x eps)) (cos x)) (/.f64 eps (/.f64 #s(literal 1 binary64) #s(approx (- (* (cos x) (* eps -1/2)) (sin x)) (-.f64 (*.f64 #s(literal -1/2 binary64) eps) x)))))

Outputs

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

Calls

3 calls:

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

Results

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

Compiler

Compiled 15 to 10 computations (33.3% saved)

regimes11.0ms (0.1%)

Memory

7.2MiB live, 7.2MiB allocated

Counts

12 → 1

Calls

Call 1

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

Outputs

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

Calls

3 calls:

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

Results

Accuracy	Segments	Branch
98.6%	1	`x`
98.6%	1	`eps`
98.6%	1	`(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))`

Compiler

Compiled 15 to 10 computations (33.3% saved)

regimes6.0ms (0%)

Memory

-34.9MiB live, 4.9MiB allocated

Counts

4 → 1

Calls

Call 1

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

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

Calls

3 calls:

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

Results

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

Compiler

Compiled 15 to 10 computations (33.3% saved)

regimes5.0ms (0%)

Memory

4.9MiB live, 4.9MiB allocated

Counts

3 → 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 (* (sin x) (neg eps)) (*.f64 eps (neg.f64 x))))

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

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

Calls

3 calls:

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

Results

Accuracy	Segments	Branch
77.5%	1	`x`
77.5%	1	`eps`
77.5%	1	`(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))`

Compiler

Compiled 15 to 10 computations (33.3% saved)

regimes3.0ms (0%)

Memory

4.0MiB live, 4.0MiB allocated

Accuracy

Total -0.0b remaining (-0%)

Threshold costs -0b (-0%)

Counts

1 → 1

Calls

Call 1

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

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

Calls

3 calls:

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

Results

Accuracy	Segments	Branch
49.2%	1	`eps`
49.2%	1	`x`
49.2%	1	`(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))`

Compiler

Compiled 15 to 10 computations (33.3% saved)

simplify8.0ms (0%)

Memory

4.9MiB live, 4.9MiB allocated

Algorithm

1×	egg-herbie

Rules

34×	`*-commutative_binary64`
16×	`+-commutative_binary64`
14×	`sub-neg_binary64`
8×	`neg-sub0_binary64`
8×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	78	277
1	104	277
2	118	277
3	125	277
4	127	277

Stop Event

1×

saturated

Calls

Call 1

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

soundness986.0ms (5.9%)

Memory

16.5MiB live, 16.5MiB allocated

Rules

19 422×	`lower-fma.f64`
19 422×	`lower-fma.f32`
14 158×	`lower-fma.f64`
14 158×	`lower-fma.f32`
13 232×	`lower-fma.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	223	2548
1	636	2534
2	1605	2511
3	4016	2510
0	9256	2411
0	30	131
0	48	131
1	169	131
2	1105	131
0	8460	131
0	405	4388
1	1164	4248
2	3297	4186
0	8213	4032
0	105	498
1	277	495
2	609	495
3	2398	494
4	7880	494
0	8026	474
0	485	5979
1	1513	5710
2	4458	5680
0	8668	5355

Stop Event

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

Compiler

Compiled 283 to 159 computations (43.8% saved)

preprocess125.0ms (0.7%)

Memory: -17.5MiB live, 60.6MiB allocated
Compiler: Compiled 308 to 130 computations (57.8% 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%)

analyze45.0ms (0.3%)

sample10.4s (62.8%)

explain255.0ms (1.5%)

preprocess26.0ms (0.2%)

eval0.0ms (0%)

prune1.0ms (0%)

simplify26.0ms (0.2%)

localize89.0ms (0.5%)

series8.0ms (0%)

simplify216.0ms (1.3%)

rewrite243.0ms (1.5%)

eval36.0ms (0.2%)

prune64.0ms (0.4%)

simplify133.0ms (0.8%)

localize435.0ms (2.6%)

series20.0ms (0.1%)

simplify273.0ms (1.6%)

rewrite246.0ms (1.5%)

eval83.0ms (0.5%)

prune90.0ms (0.5%)

simplify251.0ms (1.5%)

localize313.0ms (1.9%)

series31.0ms (0.2%)

simplify214.0ms (1.3%)

rewrite242.0ms (1.5%)

eval114.0ms (0.7%)

prune141.0ms (0.8%)

simplify178.0ms (1.1%)

localize340.0ms (2%)

series48.0ms (0.3%)

simplify229.0ms (1.4%)

rewrite264.0ms (1.6%)

eval152.0ms (0.9%)

prune145.0ms (0.9%)

regimes31.0ms (0.2%)

regimes25.0ms (0.1%)

regimes22.0ms (0.1%)

regimes18.0ms (0.1%)

regimes12.0ms (0.1%)

regimes11.0ms (0.1%)

regimes6.0ms (0%)

regimes5.0ms (0%)

regimes3.0ms (0%)

simplify8.0ms (0%)

soundness986.0ms (5.9%)

preprocess125.0ms (0.7%)

end0.0ms (0%)

Profiling

Iter	Nodes	Cost
0	18	41
1	38	37
2	81	35
3	152	35
4	278	35
5	370	35
6	448	35
7	485	35
8	531	35
9	546	35
10	554	35
0	6	7
0	10	7
1	13	7
2	18	7
3	24	7
4	32	7
5	47	7
6	80	7
7	107	7
8	151	7
9	166	7
10	174	7
0	174	7

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