Metrics for 2cos (problem 3.3.5)

start0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated

analyze40.0ms (0.2%)

Memory

6.8MiB live, 45.9MiB 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)

sample10.0s (53.9%)

Memory

-134.1MiB live, 10 288.1MiB allocated

Samples

4.0s	26 447×	0	invalid
3.3s	5 592×	2	valid
768.0ms	2 540×	1	valid
18.0ms	124×	0	valid

Precisions

Click to see histograms. Total time spent on operations: 6.3s

ival-cos: 2.8s (44.8% of total)

const: 752.0ms (11.9% of total)

ival-<=: 702.0ms (11.1% of total)

adjust: 480.0ms (7.6% of total)

ival-add: 335.0ms (5.3% of total)

ival-sub: 321.0ms (5.1% of total)

ival-mult: 298.0ms (4.7% of total)

ival-fabs: 280.0ms (4.4% of total)

ival-<: 163.0ms (2.6% of total)

ival-and: 99.0ms (1.6% of total)

exact: 45.0ms (0.7% of total)

ival-assert: 15.0ms (0.2% of total)

Bogosity

explain285.0ms (1.5%)

Memory

-10.5MiB live, 336.6MiB allocated

FPErrors

Click to see full error table

Ground Truth	Example	Underpredictions	Example	Subexpression
140	-	0	-	`(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))`
2	-	1	(32.20894738896712 8.664518947479058e-9)	`(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	140	0
`cos.f64`	`(cos.f64 (+.f64 x eps))`	sensitivity	1	1

Confusion

	Predicted +	Predicted -
+	140	0
-	0	116

Precision

1.0

Recall

1.0

Confusion?

	Predicted +	Predicted Maybe	Predicted -
+	140	0	0
-	0	0	116

Precision?

1.0

Recall?

1.0

Freqs

test

number	freq
0	116
1	139
2	1

Total Confusion?

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

Precision?

1.0

Recall?

1.0

Samples

189.0ms	348×	2	valid
19.0ms	156×	1	valid
1.0ms	8×	0	valid

Compiler

Compiled 49 to 22 computations (55.1% saved)

Precisions

Click to see histograms. Total time spent on operations: 182.0ms

ival-cos: 154.0ms (84.6% of total)

adjust: 18.0ms (9.9% of total)

ival-sub: 6.0ms (3.3% of total)

ival-add: 3.0ms (1.6% of total)

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

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

preprocess29.0ms (0.2%)

Memory

16.5MiB live, 53.8MiB 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))
(-.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x))

Compiler

Compiled 9 to 6 computations (33.3% saved)

eval0.0ms (0%)

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

prune1.0ms (0%)

Memory

1.5MiB live, 1.5MiB allocated

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	49.9%	(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))

Compiler

Compiled 9 to 6 computations (33.3% saved)

simplify7.0ms (0%)

Memory

15.1MiB live, 15.1MiB 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))
(-.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x))
(cos.f64 (+.f64 x eps))
(cos.f64 (+.f64 eps x))
(+.f64 x eps)
(+.f64 eps x)
x
eps
(cos.f64 x)

localize112.0ms (0.6%)

Memory

-52.6MiB live, 134.3MiB allocated

Localize:

Found 4 expressions of interest:

New	Metric	Score
accuracy	0	(+.f64 x eps)
accuracy	0	(cos.f64 x)
accuracy	0.05097464160568397	(cos.f64 (+.f64 x eps))
accuracy	31.99210319784825	(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))

Samples

90.0ms	174×	2	valid
13.0ms	78×	1	valid
0.0ms	4×	0	valid

Compiler

Compiled 20 to 8 computations (60% saved)

Precisions

Click to see histograms. Total time spent on operations: 83.0ms

ival-cos: 69.0ms (82.7% of total)

adjust: 9.0ms (10.8% of total)

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

ival-add: 2.0ms (2.4% of total)

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

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

series5.0ms (0%)

Memory

12.3MiB live, 12.3MiB allocated

Counts

4 → 84

Calls

Call 1

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

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

Calls

21 calls:

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

simplify149.0ms (0.8%)

Memory

12.8MiB live, 199.7MiB allocated

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

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

Stop Event

1×	iter limit
1×	node limit

Counts

84 → 78

Calls

Call 1

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

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

rewrite217.0ms (1.2%)

Memory

4.3MiB live, 240.5MiB allocated

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

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

Stop Event

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

Counts

4 → 228

Calls

Call 1

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

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

eval37.0ms (0.2%)

Memory: 19.6MiB live, 94.5MiB allocated
Compiler: Compiled 8 008 to 873 computations (89.1% saved)

prune77.0ms (0.4%)

Memory

-43.5MiB live, 163.7MiB allocated

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	300	6	306
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	300	7	307

Accuracy

99.8%

Counts

307 → 7

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	49.9%	(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))
▶	49.2%	(-.f64 (cos.f64 (+.f64 x eps)) #s(approx (cos x) (fma.f64 (fma.f64 (.f64 x x) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) (.f64 x x) #s(literal 1 binary64))))
▶	49.1%	(-.f64 (cos.f64 (+.f64 x eps)) #s(approx (cos x) #s(literal 1 binary64)))
▶	99.8%	(.f64 (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps))) (sin.f64 (.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 0 binary64) eps)))) #s(literal -2 binary64))
▶	49.0%	#s(approx (- (cos (+ x eps)) (cos x)) (-.f64 (cos.f64 eps) #s(literal 1 binary64)))
	99.5%	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 (-.f64 (.f64 (*.f64 (cos.f64 x) #s(literal -1/2 binary64)) eps) (sin.f64 x)) eps))
▶	79.2%	#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (neg.f64 eps) (sin.f64 x)))

Compiler

Compiled 159 to 106 computations (33.3% saved)

simplify529.0ms (2.9%)

Memory

21.2MiB live, 257.8MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 19 expressions of interest:

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

Rules

16 320×	`lower-fma.f32`
16 314×	`lower-fma.f64`
11 872×	`lower-*.f32`
11 860×	`lower-*.f64`
8 862×	`associate-r`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	37	199
0	60	189
1	106	189
2	183	185
3	278	185
4	670	185
5	1368	185
6	1661	185
7	1918	185
8	2574	185
9	3910	185
10	5011	185
11	5299	185
12	5430	185
13	5453	185
14	5462	185
15	5621	185
16	5791	185
17	5848	185
18	5867	185
19	5871	185
20	5875	185
21	5875	185
22	6555	185
23	6843	185
24	6843	185
25	6843	185
26	6843	185
27	6843	185
28	6843	185
29	6843	185
0	12772	181

Stop Event

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

Calls

Call 1

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

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

localize264.0ms (1.4%)

Memory

-12.9MiB live, 350.1MiB allocated

Localize:

Found 19 expressions of interest:

New	Metric	Score
accuracy	0.015625	(fma.f64 (*.f64 x x) #s(literal 1/24 binary64) #s(literal -1/2 binary64))
accuracy	0.05097464160568397	(cos.f64 (+.f64 x eps))
accuracy	0.8214398162726576	#s(approx (cos x) (fma.f64 (fma.f64 (.f64 x x) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) (.f64 x x) #s(literal 1 binary64)))
accuracy	31.99210319784825	(-.f64 (cos.f64 (+.f64 x eps)) #s(approx (cos x) (fma.f64 (fma.f64 (.f64 x x) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) (.f64 x x) #s(literal 1 binary64))))
accuracy	0	(sin.f64 x)
accuracy	0	(neg.f64 eps)
accuracy	0.00390625	(*.f64 (neg.f64 eps) (sin.f64 x))
accuracy	13.326141805054661	#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (neg.f64 eps) (sin.f64 x)))
accuracy	0	(+.f64 x eps)
accuracy	0.05097464160568397	(cos.f64 (+.f64 x eps))
accuracy	1.2576653983674058	#s(approx (cos x) #s(literal 1 binary64))
accuracy	31.99210319784825	(-.f64 (cos.f64 (+.f64 x eps)) #s(approx (cos x) #s(literal 1 binary64)))
accuracy	0	(cos.f64 eps)
accuracy	30.951668946883355	(-.f64 (cos.f64 eps) #s(literal 1 binary64))
accuracy	31.542721496794677	#s(approx (- (cos (+ x eps)) (cos x)) (-.f64 (cos.f64 eps) #s(literal 1 binary64)))
accuracy	0	(sin.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 0 binary64) eps)))
accuracy	0.0078125	(.f64 (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps))) (sin.f64 (.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 0 binary64) eps)))) #s(literal -2 binary64))
accuracy	0.04260504138909578	(sin.f64 (*.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps)))
accuracy	0.11328125	(.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps))) (sin.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 0 binary64) eps))))

Samples

160.0ms	180×	2	valid
30.0ms	74×	1	valid
2.0ms	1×	3	valid
0.0ms	1×	0	valid

Compiler

Compiled 170 to 34 computations (80% saved)

Precisions

Click to see histograms. Total time spent on operations: 149.0ms

ival-cos: 77.0ms (51.6% of total)

adjust: 31.0ms (20.8% of total)

ival-mult: 14.0ms (9.4% of total)

ival-sub: 8.0ms (5.4% of total)

ival-sin: 7.0ms (4.7% of total)

ival-add: 6.0ms (4% of total)

const: 4.0ms (2.7% of total)

exact: 1.0ms (0.7% of total)

ival-neg: 1.0ms (0.7% of total)

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

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

series24.0ms (0.1%)

Memory

26.1MiB live, 26.1MiB allocated

Counts

20 → 372

Calls

Call 1

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

Outputs
#s(alt (* 1/2 eps) (taylor 0 x) (#s(alt (.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps)) (patch (.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps)) #<representation binary64>) () ())) ())
#s(alt (+ x (* 1/2 eps)) (taylor 0 x) (#s(alt (.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps)) (patch (.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps)) #<representation binary64>) () ())) ())
#s(alt (+ x (* 1/2 eps)) (taylor 0 x) (#s(alt (.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps)) (patch (.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps)) #<representation binary64>) () ())) ())
#s(alt (+ x (* 1/2 eps)) (taylor 0 x) (#s(alt (.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps)) (patch (.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps)) #<representation binary64>) () ())) ())
#s(alt x (taylor inf x) (#s(alt (.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps)) (patch (.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps)) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1 (* 1/2 (/ eps x)))) (taylor inf x) (#s(alt (.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps)) (patch (.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps)) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1 (* 1/2 (/ eps x)))) (taylor inf x) (#s(alt (.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps)) (patch (.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps)) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1 (* 1/2 (/ eps x)))) (taylor inf x) (#s(alt (.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps)) (patch (.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps)) #<representation binary64>) () ())) ())
#s(alt x (taylor -inf x) (#s(alt (.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps)) (patch (.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (- (* -1/2 (/ eps x)) 1))) (taylor -inf x) (#s(alt (.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps)) (patch (.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (- (* -1/2 (/ eps x)) 1))) (taylor -inf x) (#s(alt (.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps)) (patch (.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (- (* -1/2 (/ eps x)) 1))) (taylor -inf x) (#s(alt (.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps)) (patch (.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps)) #<representation binary64>) () ())) ())
#s(alt x (taylor 0 eps) (#s(alt (.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps)) (patch (.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps)) #<representation binary64>) () ())) ())
#s(alt (+ x (* 1/2 eps)) (taylor 0 eps) (#s(alt (.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps)) (patch (.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps)) #<representation binary64>) () ())) ())
#s(alt (+ x (* 1/2 eps)) (taylor 0 eps) (#s(alt (.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps)) (patch (.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps)) #<representation binary64>) () ())) ())
#s(alt (+ x (* 1/2 eps)) (taylor 0 eps) (#s(alt (.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps)) (patch (.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps)) #<representation binary64>) () ())) ())
#s(alt (* 1/2 eps) (taylor inf eps) (#s(alt (.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps)) (patch (.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps)) #<representation binary64>) () ())) ())
#s(alt (* eps (+ 1/2 (/ x eps))) (taylor inf eps) (#s(alt (.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps)) (patch (.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps)) #<representation binary64>) () ())) ())
#s(alt (* eps (+ 1/2 (/ x eps))) (taylor inf eps) (#s(alt (.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps)) (patch (.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps)) #<representation binary64>) () ())) ())
#s(alt (* eps (+ 1/2 (/ x eps))) (taylor inf eps) (#s(alt (.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps)) (patch (.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps)) #<representation binary64>) () ())) ())
#s(alt (* 1/2 eps) (taylor -inf eps) (#s(alt (.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps)) (patch (.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* eps (- (* -1 (/ x eps)) 1/2))) (taylor -inf eps) (#s(alt (.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps)) (patch (.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* eps (- (* -1 (/ x eps)) 1/2))) (taylor -inf eps) (#s(alt (.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps)) (patch (.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* eps (- (* -1 (/ x eps)) 1/2))) (taylor -inf eps) (#s(alt (.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps)) (patch (.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps)) #<representation binary64>) () ())) ())
#s(alt eps (taylor 0 eps) (#s(alt (+.f64 #s(literal 0 binary64) eps) (patch (+.f64 #s(literal 0 binary64) eps) #<representation binary64>) () ())) ())
#s(alt eps (taylor 0 eps) (#s(alt (+.f64 #s(literal 0 binary64) eps) (patch (+.f64 #s(literal 0 binary64) eps) #<representation binary64>) () ())) ())
#s(alt eps (taylor 0 eps) (#s(alt (+.f64 #s(literal 0 binary64) eps) (patch (+.f64 #s(literal 0 binary64) eps) #<representation binary64>) () ())) ())
#s(alt eps (taylor 0 eps) (#s(alt (+.f64 #s(literal 0 binary64) eps) (patch (+.f64 #s(literal 0 binary64) eps) #<representation binary64>) () ())) ())
#s(alt eps (taylor inf eps) (#s(alt (+.f64 #s(literal 0 binary64) eps) (patch (+.f64 #s(literal 0 binary64) eps) #<representation binary64>) () ())) ())
#s(alt eps (taylor inf eps) (#s(alt (+.f64 #s(literal 0 binary64) eps) (patch (+.f64 #s(literal 0 binary64) eps) #<representation binary64>) () ())) ())
#s(alt eps (taylor inf eps) (#s(alt (+.f64 #s(literal 0 binary64) eps) (patch (+.f64 #s(literal 0 binary64) eps) #<representation binary64>) () ())) ())
#s(alt eps (taylor inf eps) (#s(alt (+.f64 #s(literal 0 binary64) eps) (patch (+.f64 #s(literal 0 binary64) eps) #<representation binary64>) () ())) ())
#s(alt eps (taylor -inf eps) (#s(alt (+.f64 #s(literal 0 binary64) eps) (patch (+.f64 #s(literal 0 binary64) eps) #<representation binary64>) () ())) ())
#s(alt eps (taylor -inf eps) (#s(alt (+.f64 #s(literal 0 binary64) eps) (patch (+.f64 #s(literal 0 binary64) eps) #<representation binary64>) () ())) ())
#s(alt eps (taylor -inf eps) (#s(alt (+.f64 #s(literal 0 binary64) eps) (patch (+.f64 #s(literal 0 binary64) eps) #<representation binary64>) () ())) ())
#s(alt eps (taylor -inf eps) (#s(alt (+.f64 #s(literal 0 binary64) eps) (patch (+.f64 #s(literal 0 binary64) eps) #<representation binary64>) () ())) ())
#s(alt (* -2 (pow (sin (* 1/2 eps)) 2)) (taylor 0 x) (#s(alt (.f64 (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps))) (sin.f64 (.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 0 binary64) eps)))) #s(literal -2 binary64)) (patch (.f64 (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps))) (sin.f64 (.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 0 binary64) eps)))) #s(literal -2 binary64)) #<representation binary64>) () ())) ())
#s(alt (+ (* -2 (* x (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))) (* -2 (pow (sin (* 1/2 eps)) 2))) (taylor 0 x) (#s(alt (.f64 (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps))) (sin.f64 (.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 0 binary64) eps)))) #s(literal -2 binary64)) (patch (.f64 (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps))) (sin.f64 (.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 0 binary64) eps)))) #s(literal -2 binary64)) #<representation binary64>) () ())) ())
#s(alt (+ (* -2 (pow (sin (* 1/2 eps)) 2)) (* x (+ (* -2 (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) (* x (pow (sin (* 1/2 eps)) 2))))) (taylor 0 x) (#s(alt (.f64 (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps))) (sin.f64 (.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 0 binary64) eps)))) #s(literal -2 binary64)) (patch (.f64 (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps))) (sin.f64 (.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 0 binary64) eps)))) #s(literal -2 binary64)) #<representation binary64>) () ())) ())
#s(alt (+ (* -2 (pow (sin (* 1/2 eps)) 2)) (* x (+ (* -2 (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) (* x (+ (* 1/3 (* x (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))) (pow (sin (* 1/2 eps)) 2)))))) (taylor 0 x) (#s(alt (.f64 (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps))) (sin.f64 (.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 0 binary64) eps)))) #s(literal -2 binary64)) (patch (.f64 (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps))) (sin.f64 (.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 0 binary64) eps)))) #s(literal -2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (+ eps (* 2 x)))))) (taylor inf x) (#s(alt (.f64 (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps))) (sin.f64 (.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 0 binary64) eps)))) #s(literal -2 binary64)) (patch (.f64 (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps))) (sin.f64 (.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 0 binary64) eps)))) #s(literal -2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (+ eps (* 2 x)))))) (taylor inf x) (#s(alt (.f64 (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps))) (sin.f64 (.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 0 binary64) eps)))) #s(literal -2 binary64)) (patch (.f64 (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps))) (sin.f64 (.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 0 binary64) eps)))) #s(literal -2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (+ eps (* 2 x)))))) (taylor inf x) (#s(alt (.f64 (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps))) (sin.f64 (.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 0 binary64) eps)))) #s(literal -2 binary64)) (patch (.f64 (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps))) (sin.f64 (.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 0 binary64) eps)))) #s(literal -2 binary64)) #<representation binary64>) () ())) ())
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#s(alt (cos x) (taylor inf x) (#s(alt #s(approx (cos x) (fma.f64 (fma.f64 (.f64 x x) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) (.f64 x x) #s(literal 1 binary64))) (patch #s(approx (cos x) (fma.f64 (fma.f64 (.f64 x x) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) (.f64 x x) #s(literal 1 binary64))) #<representation binary64>) () ())) ())
#s(alt (cos x) (taylor inf x) (#s(alt #s(approx (cos x) (fma.f64 (fma.f64 (.f64 x x) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) (.f64 x x) #s(literal 1 binary64))) (patch #s(approx (cos x) (fma.f64 (fma.f64 (.f64 x x) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) (.f64 x x) #s(literal 1 binary64))) #<representation binary64>) () ())) ())
#s(alt (cos x) (taylor -inf x) (#s(alt #s(approx (cos x) (fma.f64 (fma.f64 (.f64 x x) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) (.f64 x x) #s(literal 1 binary64))) (patch #s(approx (cos x) (fma.f64 (fma.f64 (.f64 x x) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) (.f64 x x) #s(literal 1 binary64))) #<representation binary64>) () ())) ())
#s(alt (cos x) (taylor -inf x) (#s(alt #s(approx (cos x) (fma.f64 (fma.f64 (.f64 x x) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) (.f64 x x) #s(literal 1 binary64))) (patch #s(approx (cos x) (fma.f64 (fma.f64 (.f64 x x) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) (.f64 x x) #s(literal 1 binary64))) #<representation binary64>) () ())) ())
#s(alt (cos x) (taylor -inf x) (#s(alt #s(approx (cos x) (fma.f64 (fma.f64 (.f64 x x) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) (.f64 x x) #s(literal 1 binary64))) (patch #s(approx (cos x) (fma.f64 (fma.f64 (.f64 x x) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) (.f64 x x) #s(literal 1 binary64))) #<representation binary64>) () ())) ())
#s(alt (cos x) (taylor -inf x) (#s(alt #s(approx (cos x) (fma.f64 (fma.f64 (.f64 x x) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) (.f64 x x) #s(literal 1 binary64))) (patch #s(approx (cos x) (fma.f64 (fma.f64 (.f64 x x) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) (.f64 x x) #s(literal 1 binary64))) #<representation binary64>) () ())) ())
#s(alt (sin (* 1/2 eps)) (taylor 0 x) (#s(alt (sin.f64 (.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps))) (patch (sin.f64 (.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps))) #<representation binary64>) () ())) ())
#s(alt (+ (sin (* 1/2 eps)) (* x (cos (* 1/2 eps)))) (taylor 0 x) (#s(alt (sin.f64 (.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps))) (patch (sin.f64 (.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps))) #<representation binary64>) () ())) ())
#s(alt (+ (sin (* 1/2 eps)) (* x (+ (cos (* 1/2 eps)) (* -1/2 (* x (sin (* 1/2 eps))))))) (taylor 0 x) (#s(alt (sin.f64 (.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps))) (patch (sin.f64 (.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps))) #<representation binary64>) () ())) ())
#s(alt (+ (sin (* 1/2 eps)) (* x (+ (cos (* 1/2 eps)) (* x (+ (* -1/2 (sin (* 1/2 eps))) (* -1/6 (* x (cos (* 1/2 eps))))))))) (taylor 0 x) (#s(alt (sin.f64 (.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps))) (patch (sin.f64 (.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps))) #<representation binary64>) () ())) ())
#s(alt (sin (* 1/2 (+ eps (* 2 x)))) (taylor inf x) (#s(alt (sin.f64 (.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps))) (patch (sin.f64 (.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps))) #<representation binary64>) () ())) ())
#s(alt (sin (* 1/2 (+ eps (* 2 x)))) (taylor inf x) (#s(alt (sin.f64 (.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps))) (patch (sin.f64 (.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps))) #<representation binary64>) () ())) ())
#s(alt (sin (* 1/2 (+ eps (* 2 x)))) (taylor inf x) (#s(alt (sin.f64 (.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps))) (patch (sin.f64 (.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps))) #<representation binary64>) () ())) ())
#s(alt (sin (* 1/2 (+ eps (* 2 x)))) (taylor inf x) (#s(alt (sin.f64 (.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps))) (patch (sin.f64 (.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps))) #<representation binary64>) () ())) ())
#s(alt (sin (* 1/2 (- eps (* -2 x)))) (taylor -inf x) (#s(alt (sin.f64 (.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps))) (patch (sin.f64 (.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps))) #<representation binary64>) () ())) ())
#s(alt (sin (* 1/2 (- eps (* -2 x)))) (taylor -inf x) (#s(alt (sin.f64 (.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps))) (patch (sin.f64 (.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps))) #<representation binary64>) () ())) ())
#s(alt (sin (* 1/2 (- eps (* -2 x)))) (taylor -inf x) (#s(alt (sin.f64 (.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps))) (patch (sin.f64 (.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps))) #<representation binary64>) () ())) ())
#s(alt (sin (* 1/2 (- eps (* -2 x)))) (taylor -inf x) (#s(alt (sin.f64 (.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps))) (patch (sin.f64 (.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps))) #<representation binary64>) () ())) ())
#s(alt (sin x) (taylor 0 eps) (#s(alt (sin.f64 (.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps))) (patch (sin.f64 (.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps))) #<representation binary64>) () ())) ())
#s(alt (+ (sin x) (* 1/2 (* eps (cos x)))) (taylor 0 eps) (#s(alt (sin.f64 (.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps))) (patch (sin.f64 (.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps))) #<representation binary64>) () ())) ())
#s(alt (+ (sin x) (* eps (+ (* -1/8 (* eps (sin x))) (* 1/2 (cos x))))) (taylor 0 eps) (#s(alt (sin.f64 (.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps))) (patch (sin.f64 (.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps))) #<representation binary64>) () ())) ())
#s(alt (+ (sin x) (* eps (+ (* 1/2 (cos x)) (* eps (+ (* -1/8 (sin x)) (* -1/48 (* eps (cos x)))))))) (taylor 0 eps) (#s(alt (sin.f64 (.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps))) (patch (sin.f64 (.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps))) #<representation binary64>) () ())) ())
#s(alt (sin (* 1/2 (+ eps (* 2 x)))) (taylor inf eps) (#s(alt (sin.f64 (.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps))) (patch (sin.f64 (.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps))) #<representation binary64>) () ())) ())
#s(alt (sin (* 1/2 (+ eps (* 2 x)))) (taylor inf eps) (#s(alt (sin.f64 (.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps))) (patch (sin.f64 (.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps))) #<representation binary64>) () ())) ())
#s(alt (sin (* 1/2 (+ eps (* 2 x)))) (taylor inf eps) (#s(alt (sin.f64 (.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps))) (patch (sin.f64 (.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps))) #<representation binary64>) () ())) ())
#s(alt (sin (* 1/2 (+ eps (* 2 x)))) (taylor inf eps) (#s(alt (sin.f64 (.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps))) (patch (sin.f64 (.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps))) #<representation binary64>) () ())) ())
#s(alt (sin (* 1/2 (- (* 2 x) (* -1 eps)))) (taylor -inf eps) (#s(alt (sin.f64 (.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps))) (patch (sin.f64 (.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps))) #<representation binary64>) () ())) ())
#s(alt (sin (* 1/2 (- (* 2 x) (* -1 eps)))) (taylor -inf eps) (#s(alt (sin.f64 (.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps))) (patch (sin.f64 (.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps))) #<representation binary64>) () ())) ())
#s(alt (sin (* 1/2 (- (* 2 x) (* -1 eps)))) (taylor -inf eps) (#s(alt (sin.f64 (.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps))) (patch (sin.f64 (.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps))) #<representation binary64>) () ())) ())
#s(alt (sin (* 1/2 (- (* 2 x) (* -1 eps)))) (taylor -inf eps) (#s(alt (sin.f64 (.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps))) (patch (sin.f64 (.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps))) #<representation binary64>) () ())) ())
#s(alt (* 1/2 eps) (taylor 0 eps) (#s(alt (sin.f64 (.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 0 binary64) eps))) (patch (sin.f64 (.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 0 binary64) eps))) #<representation binary64>) () ())) ())
#s(alt (* eps (+ 1/2 (* -1/48 (pow eps 2)))) (taylor 0 eps) (#s(alt (sin.f64 (.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 0 binary64) eps))) (patch (sin.f64 (.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 0 binary64) eps))) #<representation binary64>) () ())) ())
#s(alt (* eps (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48)))) (taylor 0 eps) (#s(alt (sin.f64 (.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 0 binary64) eps))) (patch (sin.f64 (.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 0 binary64) eps))) #<representation binary64>) () ())) ())
#s(alt (* eps (+ 1/2 (* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48)))) (taylor 0 eps) (#s(alt (sin.f64 (.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 0 binary64) eps))) (patch (sin.f64 (.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 0 binary64) eps))) #<representation binary64>) () ())) ())
#s(alt (sin (* 1/2 eps)) (taylor inf eps) (#s(alt (sin.f64 (.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 0 binary64) eps))) (patch (sin.f64 (.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 0 binary64) eps))) #<representation binary64>) () ())) ())
#s(alt (sin (* 1/2 eps)) (taylor inf eps) (#s(alt (sin.f64 (.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 0 binary64) eps))) (patch (sin.f64 (.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 0 binary64) eps))) #<representation binary64>) () ())) ())
#s(alt (sin (* 1/2 eps)) (taylor inf eps) (#s(alt (sin.f64 (.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 0 binary64) eps))) (patch (sin.f64 (.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 0 binary64) eps))) #<representation binary64>) () ())) ())
#s(alt (sin (* 1/2 eps)) (taylor inf eps) (#s(alt (sin.f64 (.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 0 binary64) eps))) (patch (sin.f64 (.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 0 binary64) eps))) #<representation binary64>) () ())) ())
#s(alt (sin (* 1/2 eps)) (taylor -inf eps) (#s(alt (sin.f64 (.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 0 binary64) eps))) (patch (sin.f64 (.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 0 binary64) eps))) #<representation binary64>) () ())) ())
#s(alt (sin (* 1/2 eps)) (taylor -inf eps) (#s(alt (sin.f64 (.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 0 binary64) eps))) (patch (sin.f64 (.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 0 binary64) eps))) #<representation binary64>) () ())) ())
#s(alt (sin (* 1/2 eps)) (taylor -inf eps) (#s(alt (sin.f64 (.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 0 binary64) eps))) (patch (sin.f64 (.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 0 binary64) eps))) #<representation binary64>) () ())) ())
#s(alt (sin (* 1/2 eps)) (taylor -inf eps) (#s(alt (sin.f64 (.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 0 binary64) eps))) (patch (sin.f64 (.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 0 binary64) eps))) #<representation binary64>) () ())) ())
#s(alt -1/2 (taylor 0 x) (#s(alt (fma.f64 (.f64 x x) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) (patch (fma.f64 (.f64 x x) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt (- (* 1/24 (pow x 2)) 1/2) (taylor 0 x) (#s(alt (fma.f64 (.f64 x x) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) (patch (fma.f64 (.f64 x x) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt (- (* 1/24 (pow x 2)) 1/2) (taylor 0 x) (#s(alt (fma.f64 (.f64 x x) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) (patch (fma.f64 (.f64 x x) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt (- (* 1/24 (pow x 2)) 1/2) (taylor 0 x) (#s(alt (fma.f64 (.f64 x x) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) (patch (fma.f64 (.f64 x x) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* 1/24 (pow x 2)) (taylor inf x) (#s(alt (fma.f64 (.f64 x x) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) (patch (fma.f64 (.f64 x x) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (- 1/24 (* 1/2 (/ 1 (pow x 2))))) (taylor inf x) (#s(alt (fma.f64 (.f64 x x) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) (patch (fma.f64 (.f64 x x) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (- 1/24 (* 1/2 (/ 1 (pow x 2))))) (taylor inf x) (#s(alt (fma.f64 (.f64 x x) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) (patch (fma.f64 (.f64 x x) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (- 1/24 (* 1/2 (/ 1 (pow x 2))))) (taylor inf x) (#s(alt (fma.f64 (.f64 x x) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) (patch (fma.f64 (.f64 x x) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* 1/24 (pow x 2)) (taylor -inf x) (#s(alt (fma.f64 (.f64 x x) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) (patch (fma.f64 (.f64 x x) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (- 1/24 (* 1/2 (/ 1 (pow x 2))))) (taylor -inf x) (#s(alt (fma.f64 (.f64 x x) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) (patch (fma.f64 (.f64 x x) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (- 1/24 (* 1/2 (/ 1 (pow x 2))))) (taylor -inf x) (#s(alt (fma.f64 (.f64 x x) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) (patch (fma.f64 (.f64 x x) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (- 1/24 (* 1/2 (/ 1 (pow x 2))))) (taylor -inf x) (#s(alt (fma.f64 (.f64 x x) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) (patch (fma.f64 (.f64 x x) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) #<representation binary64>) () ())) ())

Calls

93 calls:

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

simplify253.0ms (1.4%)

Memory

-15.2MiB live, 252.2MiB allocated

Algorithm

1×	egg-herbie

Rules

17 138×	`lower-fma.f64`
17 138×	`lower-fma.f32`
6 242×	`lower-*.f64`
6 242×	`lower-*.f32`
3 454×	`lower-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	320	2969
1	961	2826
2	2515	2790
3	5858	2790
0	8448	2606

Stop Event

1×	iter limit
1×	node limit

Counts

372 → 350

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

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

rewrite256.0ms (1.4%)

Memory

10.8MiB live, 292.0MiB allocated

Rules

4 464×	`lower-fma.f32`
4 458×	`lower-fma.f64`
4 138×	`lower-*.f32`
4 126×	`lower-*.f64`
4 066×	`lower-/.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	37	151
0	60	143
1	226	143
2	1663	143
0	8348	143

Stop Event

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

Counts

20 → 368

Calls

Call 1

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

Outputs
(*.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64))
(*.f64 #s(literal 1/2 binary64) (fma.f64 x #s(literal 2 binary64) eps))
(/.f64 (+.f64 (pow.f64 (fma.f64 #s(literal 1 binary64) x #s(literal 0 binary64)) #s(literal 3 binary64)) (.f64 #s(literal 1/8 binary64) (.f64 (.f64 eps eps) eps))) (fma.f64 (fma.f64 #s(literal 1 binary64) x #s(literal 0 binary64)) (fma.f64 #s(literal 1 binary64) x #s(literal 0 binary64)) (-.f64 (.f64 (.f64 eps #s(literal 1/2 binary64)) (.f64 eps #s(literal 1/2 binary64))) (.f64 (fma.f64 #s(literal 1 binary64) x #s(literal 0 binary64)) (.f64 eps #s(literal 1/2 binary64))))))
(/.f64 (fma.f64 #s(literal 1/8 binary64) (.f64 (.f64 eps eps) eps) (.f64 (.f64 (.f64 x x) x) #s(literal 1 binary64))) (fma.f64 (.f64 eps #s(literal 1/2 binary64)) (.f64 eps #s(literal 1/2 binary64)) (-.f64 (.f64 (.f64 #s(literal 1 binary64) x) (.f64 #s(literal 1 binary64) x)) (.f64 (.f64 eps #s(literal 1/2 binary64)) (*.f64 #s(literal 1 binary64) x)))))
(/.f64 (neg.f64 (.f64 (fma.f64 #s(literal 4 binary64) (.f64 x x) (*.f64 (neg.f64 eps) eps)) #s(literal 1/2 binary64))) (neg.f64 (fma.f64 x #s(literal 2 binary64) (neg.f64 eps))))
(/.f64 (neg.f64 (.f64 (fma.f64 #s(literal 8 binary64) (.f64 (.f64 x x) x) (.f64 (.f64 eps eps) eps)) #s(literal 1/2 binary64))) (neg.f64 (fma.f64 #s(literal 4 binary64) (.f64 x x) (.f64 eps (-.f64 eps (.f64 x #s(literal 2 binary64)))))))
(/.f64 (neg.f64 (.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 4 binary64) (.f64 x x) (*.f64 (neg.f64 eps) eps)))) (neg.f64 (fma.f64 x #s(literal 2 binary64) (neg.f64 eps))))
(/.f64 (neg.f64 (.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 8 binary64) (.f64 (.f64 x x) x) (.f64 (.f64 eps eps) eps)))) (neg.f64 (fma.f64 #s(literal 4 binary64) (.f64 x x) (.f64 eps (-.f64 eps (.f64 x #s(literal 2 binary64)))))))
(/.f64 (neg.f64 (-.f64 (.f64 (.f64 #s(literal 1 binary64) x) (.f64 #s(literal 1 binary64) x)) (.f64 (.f64 eps #s(literal 1/2 binary64)) (.f64 eps #s(literal 1/2 binary64))))) (neg.f64 (-.f64 (.f64 #s(literal 1 binary64) x) (.f64 eps #s(literal 1/2 binary64)))))
(/.f64 (neg.f64 (fma.f64 (.f64 (.f64 x x) x) #s(literal 1 binary64) (.f64 #s(literal 1/8 binary64) (.f64 (.f64 eps eps) eps)))) (neg.f64 (fma.f64 (.f64 #s(literal 1 binary64) x) (.f64 #s(literal 1 binary64) x) (-.f64 (.f64 (.f64 eps #s(literal 1/2 binary64)) (.f64 eps #s(literal 1/2 binary64))) (.f64 (.f64 #s(literal 1 binary64) x) (*.f64 eps #s(literal 1/2 binary64)))))))
(/.f64 (.f64 (fma.f64 #s(literal 4 binary64) (.f64 x x) (*.f64 (neg.f64 eps) eps)) #s(literal 1/2 binary64)) (fma.f64 x #s(literal 2 binary64) (neg.f64 eps)))
(/.f64 (.f64 (fma.f64 #s(literal 8 binary64) (.f64 (.f64 x x) x) (.f64 (.f64 eps eps) eps)) #s(literal 1/2 binary64)) (fma.f64 #s(literal 4 binary64) (.f64 x x) (.f64 eps (-.f64 eps (.f64 x #s(literal 2 binary64))))))
(/.f64 (.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 4 binary64) (.f64 x x) (*.f64 (neg.f64 eps) eps))) (fma.f64 x #s(literal 2 binary64) (neg.f64 eps)))
(/.f64 (.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 8 binary64) (.f64 (.f64 x x) x) (.f64 (.f64 eps eps) eps))) (fma.f64 #s(literal 4 binary64) (.f64 x x) (.f64 eps (-.f64 eps (.f64 x #s(literal 2 binary64))))))
(/.f64 (-.f64 (.f64 (.f64 #s(literal 1 binary64) x) (.f64 #s(literal 1 binary64) x)) (.f64 (.f64 eps #s(literal 1/2 binary64)) (.f64 eps #s(literal 1/2 binary64)))) (-.f64 (.f64 #s(literal 1 binary64) x) (.f64 eps #s(literal 1/2 binary64))))
(/.f64 (fma.f64 (.f64 (.f64 x x) x) #s(literal 1 binary64) (.f64 #s(literal 1/8 binary64) (.f64 (.f64 eps eps) eps))) (fma.f64 (.f64 #s(literal 1 binary64) x) (.f64 #s(literal 1 binary64) x) (-.f64 (.f64 (.f64 eps #s(literal 1/2 binary64)) (.f64 eps #s(literal 1/2 binary64))) (.f64 (.f64 #s(literal 1 binary64) x) (*.f64 eps #s(literal 1/2 binary64))))))
(fma.f64 (/.f64 #s(literal 1/2 binary64) eps) (/.f64 (.f64 (.f64 eps eps) eps) (-.f64 eps #s(literal 0 binary64))) (*.f64 #s(literal 1 binary64) x))
(fma.f64 (/.f64 #s(literal 1/2 binary64) eps) (/.f64 (.f64 (.f64 eps eps) eps) eps) (*.f64 #s(literal 1 binary64) x))
(fma.f64 (/.f64 #s(literal 1/2 binary64) eps) (/.f64 (neg.f64 (.f64 eps eps)) #s(literal -1 binary64)) (.f64 #s(literal 1 binary64) x))
(fma.f64 (/.f64 (.f64 (.f64 eps eps) eps) eps) (/.f64 #s(literal 1/2 binary64) (-.f64 eps #s(literal 0 binary64))) (*.f64 #s(literal 1 binary64) x))
(fma.f64 (/.f64 (.f64 (.f64 eps eps) eps) eps) (/.f64 #s(literal 1/2 binary64) eps) (*.f64 #s(literal 1 binary64) x))
(fma.f64 (/.f64 (neg.f64 (.f64 eps eps)) #s(literal -1 binary64)) (/.f64 #s(literal 1/2 binary64) eps) (.f64 #s(literal 1 binary64) x))
(fma.f64 (.f64 #s(literal 1/2 binary64) x) #s(literal 2 binary64) (.f64 eps #s(literal 1/2 binary64)))
(fma.f64 (.f64 x #s(literal 2 binary64)) #s(literal 1/2 binary64) (.f64 eps #s(literal 1/2 binary64)))
(fma.f64 #s(literal -1/2 binary64) (neg.f64 eps) (*.f64 #s(literal 1 binary64) x))
(fma.f64 (neg.f64 eps) #s(literal -1/2 binary64) (*.f64 #s(literal 1 binary64) x))
(fma.f64 #s(literal 1 binary64) x (*.f64 eps #s(literal 1/2 binary64)))
(fma.f64 eps #s(literal 1/2 binary64) (*.f64 #s(literal 1 binary64) x))
(fma.f64 x #s(literal 1 binary64) (*.f64 eps #s(literal 1/2 binary64)))
(fma.f64 #s(literal 2 binary64) (.f64 x #s(literal 1/2 binary64)) (.f64 eps #s(literal 1/2 binary64)))
(fma.f64 #s(literal 1/2 binary64) (.f64 x #s(literal 2 binary64)) (.f64 eps #s(literal 1/2 binary64)))
(fma.f64 #s(literal 1/2 binary64) eps (*.f64 #s(literal 1 binary64) x))
(-.f64 (/.f64 (.f64 (.f64 #s(literal 1 binary64) x) (.f64 #s(literal 1 binary64) x)) (-.f64 (.f64 #s(literal 1 binary64) x) (.f64 eps #s(literal 1/2 binary64)))) (/.f64 (.f64 (.f64 eps #s(literal 1/2 binary64)) (.f64 eps #s(literal 1/2 binary64))) (-.f64 (.f64 #s(literal 1 binary64) x) (.f64 eps #s(literal 1/2 binary64)))))
(+.f64 (fma.f64 #s(literal 1 binary64) x #s(literal 0 binary64)) (*.f64 eps #s(literal 1/2 binary64)))
(+.f64 (.f64 #s(literal 1 binary64) x) (.f64 eps #s(literal 1/2 binary64)))
(+.f64 (.f64 eps #s(literal 1/2 binary64)) (.f64 #s(literal 1 binary64) x))
(*.f64 (/.f64 (pow.f64 eps #s(literal 3/2 binary64)) eps) (/.f64 (pow.f64 eps #s(literal 3/2 binary64)) (-.f64 eps #s(literal 0 binary64))))
(*.f64 (/.f64 (pow.f64 eps #s(literal 3/2 binary64)) eps) (/.f64 (pow.f64 eps #s(literal 3/2 binary64)) eps))
(.f64 (/.f64 eps eps) (/.f64 (.f64 eps eps) eps))
(*.f64 (/.f64 eps eps) eps)
(.f64 (/.f64 (.f64 eps eps) eps) (/.f64 eps (-.f64 eps #s(literal 0 binary64))))
(.f64 (/.f64 (.f64 eps eps) eps) (/.f64 eps eps))
(.f64 (neg.f64 (.f64 eps eps)) (/.f64 #s(literal -1 binary64) eps))
(.f64 (.f64 (.f64 eps eps) eps) (/.f64 #s(literal 1 binary64) (.f64 eps eps)))
(pow.f64 (/.f64 (neg.f64 eps) (neg.f64 (*.f64 eps eps))) #s(literal -1 binary64))
(pow.f64 (/.f64 (.f64 eps eps) (.f64 (*.f64 eps eps) eps)) #s(literal -1 binary64))
(pow.f64 eps #s(literal 1 binary64))
(/.f64 (neg.f64 (/.f64 (neg.f64 (*.f64 eps eps)) #s(literal -1 binary64))) (neg.f64 eps))
(/.f64 (neg.f64 (neg.f64 (neg.f64 (*.f64 eps eps)))) (neg.f64 eps))
(/.f64 (-.f64 (.f64 #s(literal 0 binary64) (neg.f64 eps)) (.f64 (.f64 eps eps) (neg.f64 eps))) (.f64 eps eps))
(/.f64 (/.f64 (neg.f64 (*.f64 eps eps)) #s(literal -1 binary64)) eps)
(/.f64 (neg.f64 (neg.f64 (*.f64 eps eps))) eps)
(/.f64 (.f64 (.f64 eps eps) (neg.f64 eps)) (neg.f64 (*.f64 eps eps)))
(/.f64 (neg.f64 (*.f64 eps eps)) (neg.f64 (-.f64 eps #s(literal 0 binary64))))
(/.f64 (neg.f64 (*.f64 eps eps)) (neg.f64 eps))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 (neg.f64 eps) (neg.f64 (*.f64 eps eps)))))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 (.f64 eps eps) (.f64 (*.f64 eps eps) eps))))
(/.f64 (*.f64 eps eps) (-.f64 eps #s(literal 0 binary64)))
(/.f64 (.f64 (.f64 eps eps) eps) (neg.f64 (neg.f64 (*.f64 eps eps))))
(/.f64 (.f64 (.f64 eps eps) eps) (*.f64 eps eps))
(/.f64 #s(literal 1 binary64) (/.f64 (neg.f64 eps) (neg.f64 (*.f64 eps eps))))
(/.f64 #s(literal 1 binary64) (/.f64 (.f64 eps eps) (.f64 (*.f64 eps eps) eps)))
(neg.f64 (neg.f64 eps))
(fma.f64 (/.f64 (pow.f64 eps #s(literal 3/2 binary64)) eps) (/.f64 (pow.f64 eps #s(literal 3/2 binary64)) (-.f64 eps #s(literal 0 binary64))) #s(literal 0 binary64))
(fma.f64 (/.f64 (pow.f64 eps #s(literal 3/2 binary64)) eps) (/.f64 (pow.f64 eps #s(literal 3/2 binary64)) eps) #s(literal 0 binary64))
(fma.f64 (/.f64 eps eps) (/.f64 (*.f64 eps eps) eps) #s(literal 0 binary64))
(fma.f64 (/.f64 eps eps) eps #s(literal 0 binary64))
(fma.f64 (/.f64 (*.f64 eps eps) eps) (/.f64 eps (-.f64 eps #s(literal 0 binary64))) #s(literal 0 binary64))
(fma.f64 (/.f64 (*.f64 eps eps) eps) (/.f64 eps eps) #s(literal 0 binary64))
(fma.f64 (neg.f64 (*.f64 eps eps)) (/.f64 #s(literal -1 binary64) eps) #s(literal 0 binary64))
(fma.f64 (.f64 (.f64 eps eps) eps) (/.f64 #s(literal 1 binary64) (*.f64 eps eps)) #s(literal 0 binary64))
(-.f64 (/.f64 #s(literal 0 binary64) eps) (neg.f64 eps))
(-.f64 eps (/.f64 #s(literal 0 binary64) (-.f64 eps #s(literal 0 binary64))))
(+.f64 #s(literal 0 binary64) eps)
(+.f64 eps #s(literal 0 binary64))
eps
(.f64 (.f64 #s(literal -2 binary64) (sin.f64 (.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 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 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64))))
(.f64 #s(literal -2 binary64) (.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (sin.f64 (.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)))))
(.f64 (.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (sin.f64 (.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)))) #s(literal -2 binary64))
(.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (.f64 (sin.f64 (.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64))) #s(literal -2 binary64)))
(.f64 (sin.f64 (.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64))) (.f64 #s(literal -2 binary64) (sin.f64 (.f64 eps #s(literal 1/2 binary64)))))
(/.f64 (neg.f64 (.f64 (-.f64 (cos.f64 (.f64 #s(literal 1/2 binary64) (-.f64 (fma.f64 x #s(literal 2 binary64) eps) eps))) (cos.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 (fma.f64 x #s(literal 2 binary64) eps) eps)))) #s(literal -2 binary64))) #s(literal -2 binary64))
(/.f64 (neg.f64 (.f64 #s(literal -2 binary64) (-.f64 (cos.f64 (.f64 #s(literal 1/2 binary64) (-.f64 (fma.f64 x #s(literal 2 binary64) eps) eps))) (cos.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 (fma.f64 x #s(literal 2 binary64) eps) eps)))))) #s(literal -2 binary64))
(/.f64 (.f64 (-.f64 (cos.f64 (.f64 #s(literal 1/2 binary64) (-.f64 (fma.f64 x #s(literal 2 binary64) eps) eps))) (cos.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 (fma.f64 x #s(literal 2 binary64) eps) eps)))) #s(literal -2 binary64)) #s(literal 2 binary64))
(/.f64 (.f64 #s(literal -2 binary64) (-.f64 (cos.f64 (.f64 #s(literal 1/2 binary64) (-.f64 (fma.f64 x #s(literal 2 binary64) eps) eps))) (cos.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 (fma.f64 x #s(literal 2 binary64) eps) eps))))) #s(literal 2 binary64))
(.f64 (-.f64 (cos.f64 (.f64 #s(literal 1/2 binary64) (-.f64 (fma.f64 x #s(literal 2 binary64) eps) eps))) (cos.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 (fma.f64 x #s(literal 2 binary64) eps) eps)))) #s(literal 1/2 binary64))
(.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (sin.f64 (*.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64))))
(.f64 (sin.f64 (.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64))) (sin.f64 (*.f64 eps #s(literal 1/2 binary64))))
(pow.f64 (/.f64 #s(literal 2 binary64) (-.f64 (cos.f64 (.f64 #s(literal 1/2 binary64) (-.f64 (fma.f64 x #s(literal 2 binary64) eps) eps))) (cos.f64 (.f64 #s(literal 1/2 binary64) (+.f64 (fma.f64 x #s(literal 2 binary64) eps) eps))))) #s(literal -1 binary64))
(/.f64 (neg.f64 (neg.f64 (-.f64 (cos.f64 (.f64 #s(literal 1/2 binary64) (-.f64 (fma.f64 x #s(literal 2 binary64) eps) eps))) (cos.f64 (.f64 #s(literal 1/2 binary64) (+.f64 (fma.f64 x #s(literal 2 binary64) eps) eps)))))) #s(literal 2 binary64))
(/.f64 (neg.f64 (-.f64 (cos.f64 (-.f64 (.f64 eps #s(literal 1/2 binary64)) (.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)))) (cos.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 (fma.f64 x #s(literal 2 binary64) eps) eps))))) #s(literal -2 binary64))
(/.f64 (-.f64 (.f64 (cos.f64 (.f64 #s(literal 1/2 binary64) (-.f64 (fma.f64 x #s(literal 2 binary64) eps) eps))) #s(literal 2 binary64)) (.f64 #s(literal 2 binary64) (cos.f64 (.f64 #s(literal 1/2 binary64) (+.f64 (fma.f64 x #s(literal 2 binary64) eps) eps))))) #s(literal 4 binary64))
(/.f64 (neg.f64 (-.f64 (cos.f64 (.f64 #s(literal 1/2 binary64) (-.f64 (fma.f64 x #s(literal 2 binary64) eps) eps))) (cos.f64 (.f64 #s(literal 1/2 binary64) (+.f64 (fma.f64 x #s(literal 2 binary64) eps) eps))))) #s(literal -2 binary64))
(/.f64 (-.f64 (cos.f64 (-.f64 (.f64 eps #s(literal 1/2 binary64)) (.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)))) (cos.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 (fma.f64 x #s(literal 2 binary64) eps) eps)))) #s(literal 2 binary64))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 #s(literal 2 binary64) (-.f64 (cos.f64 (.f64 #s(literal 1/2 binary64) (-.f64 (fma.f64 x #s(literal 2 binary64) eps) eps))) (cos.f64 (.f64 #s(literal 1/2 binary64) (+.f64 (fma.f64 x #s(literal 2 binary64) eps) eps)))))))
(/.f64 (-.f64 (cos.f64 (.f64 #s(literal 1/2 binary64) (-.f64 (fma.f64 x #s(literal 2 binary64) eps) eps))) (cos.f64 (.f64 #s(literal 1/2 binary64) (+.f64 (fma.f64 x #s(literal 2 binary64) eps) 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 (fma.f64 x #s(literal 2 binary64) eps) eps))) (cos.f64 (.f64 #s(literal 1/2 binary64) (+.f64 (fma.f64 x #s(literal 2 binary64) eps) eps))))))
(-.f64 (/.f64 (cos.f64 (-.f64 (.f64 eps #s(literal 1/2 binary64)) (.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)))) #s(literal 2 binary64)) (/.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 (fma.f64 x #s(literal 2 binary64) eps) eps))) #s(literal 2 binary64)))
(-.f64 (/.f64 (cos.f64 (.f64 #s(literal 1/2 binary64) (-.f64 (fma.f64 x #s(literal 2 binary64) eps) eps))) #s(literal 2 binary64)) (/.f64 (cos.f64 (.f64 #s(literal 1/2 binary64) (+.f64 (fma.f64 x #s(literal 2 binary64) eps) eps))) #s(literal 2 binary64)))
#s(approx (- (cos (+ x eps)) (cos x)) (-.f64 (cos.f64 eps) #s(literal 1 binary64)))
(*.f64 (/.f64 (+.f64 #s(literal 1 binary64) (cos.f64 eps)) (+.f64 #s(literal 1 binary64) (cos.f64 eps))) (/.f64 (-.f64 (cos.f64 eps) #s(literal 1 binary64)) #s(literal 1 binary64)))
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(-.f64 (.f64 (cos.f64 eps) (cos.f64 x)) (-.f64 (.f64 (sin.f64 eps) (sin.f64 x)) (neg.f64 #s(approx (cos x) (fma.f64 (fma.f64 #s(literal 1/24 binary64) (.f64 x x) #s(literal -1/2 binary64)) (.f64 x x) #s(literal 1 binary64))))))
(-.f64 (cos.f64 (+.f64 eps x)) #s(approx (cos x) (fma.f64 (fma.f64 #s(literal 1/24 binary64) (.f64 x x) #s(literal -1/2 binary64)) (.f64 x x) #s(literal 1 binary64))))
(+.f64 (neg.f64 #s(approx (cos x) (fma.f64 (fma.f64 #s(literal 1/24 binary64) (.f64 x x) #s(literal -1/2 binary64)) (.f64 x x) #s(literal 1 binary64)))) (cos.f64 (+.f64 eps x)))
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(fma.f64 (sin.f64 (fma.f64 #s(literal 1 binary64) x #s(literal 0 binary64))) (cos.f64 (.f64 eps #s(literal 1/2 binary64))) (.f64 (cos.f64 (fma.f64 #s(literal 1 binary64) x #s(literal 0 binary64))) (sin.f64 (*.f64 eps #s(literal 1/2 binary64)))))
(fma.f64 (sin.f64 (.f64 #s(literal 1 binary64) x)) (cos.f64 (.f64 eps #s(literal 1/2 binary64))) (.f64 (cos.f64 (.f64 #s(literal 1 binary64) x)) (sin.f64 (*.f64 eps #s(literal 1/2 binary64)))))
(fma.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (cos.f64 (.f64 #s(literal 1 binary64) x)) (.f64 (cos.f64 (.f64 eps #s(literal 1/2 binary64))) (sin.f64 (*.f64 #s(literal 1 binary64) x))))
(sin.f64 (*.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)))
(+.f64 (.f64 (sin.f64 (fma.f64 #s(literal 1 binary64) x #s(literal 0 binary64))) (cos.f64 (.f64 eps #s(literal 1/2 binary64)))) (.f64 (cos.f64 (fma.f64 #s(literal 1 binary64) x #s(literal 0 binary64))) (sin.f64 (.f64 eps #s(literal 1/2 binary64)))))
(+.f64 (.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (cos.f64 (.f64 #s(literal 1 binary64) x))) (.f64 (cos.f64 (.f64 eps #s(literal 1/2 binary64))) (sin.f64 (.f64 #s(literal 1 binary64) x))))
(+.f64 (.f64 (sin.f64 (.f64 #s(literal 1 binary64) x)) (cos.f64 (.f64 eps #s(literal 1/2 binary64)))) (.f64 (cos.f64 (.f64 #s(literal 1 binary64) x)) (sin.f64 (.f64 eps #s(literal 1/2 binary64)))))
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(fma.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) #s(literal 1 binary64) (.f64 (cos.f64 (*.f64 eps #s(literal 1/2 binary64))) #s(literal 0 binary64)))
(fma.f64 #s(literal 0 binary64) (cos.f64 (.f64 eps #s(literal 1/2 binary64))) (.f64 #s(literal 1 binary64) (sin.f64 (*.f64 eps #s(literal 1/2 binary64)))))
(sin.f64 (*.f64 eps #s(literal 1/2 binary64)))
(+.f64 (.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) #s(literal 1 binary64)) (.f64 (cos.f64 (.f64 eps #s(literal 1/2 binary64))) #s(literal 0 binary64)))
(+.f64 (.f64 #s(literal 0 binary64) (cos.f64 (.f64 eps #s(literal 1/2 binary64)))) (.f64 #s(literal 1 binary64) (sin.f64 (.f64 eps #s(literal 1/2 binary64)))))
(.f64 (fma.f64 #s(literal 1/576 binary64) (.f64 (.f64 x x) (.f64 x x)) #s(literal -1/4 binary64)) (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/24 binary64) (*.f64 x x) #s(literal 1/2 binary64))))
(.f64 (fma.f64 (.f64 #s(literal 1/13824 binary64) (.f64 (.f64 x x) x)) (.f64 (.f64 x x) x) #s(literal -1/8 binary64)) (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/576 binary64) (.f64 (.f64 x x) (.f64 x x)) (-.f64 #s(literal 1/4 binary64) (.f64 (*.f64 x x) #s(literal -1/48 binary64))))))
(pow.f64 (/.f64 (fma.f64 #s(literal 1/24 binary64) (.f64 x x) #s(literal 1/2 binary64)) (fma.f64 #s(literal 1/576 binary64) (.f64 (.f64 x x) (.f64 x x)) #s(literal -1/4 binary64))) #s(literal -1 binary64))
(pow.f64 (/.f64 (fma.f64 #s(literal 1/576 binary64) (.f64 (.f64 x x) (.f64 x x)) (-.f64 #s(literal 1/4 binary64) (.f64 (.f64 x x) #s(literal -1/48 binary64)))) (fma.f64 (.f64 #s(literal 1/13824 binary64) (.f64 (.f64 x x) x)) (.f64 (.f64 x x) x) #s(literal -1/8 binary64))) #s(literal -1 binary64))
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(/.f64 (fma.f64 (.f64 #s(literal 1/13824 binary64) (.f64 (.f64 x x) x)) (.f64 (.f64 x x) x) #s(literal -1/8 binary64)) (fma.f64 #s(literal 1/576 binary64) (.f64 (.f64 x x) (.f64 x x)) (-.f64 #s(literal 1/4 binary64) (.f64 (.f64 x x) #s(literal -1/48 binary64)))))
(/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 #s(literal 1/24 binary64) (.f64 x x) #s(literal 1/2 binary64)) (fma.f64 #s(literal 1/576 binary64) (.f64 (.f64 x x) (.f64 x x)) #s(literal -1/4 binary64))))
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(fma.f64 (*.f64 #s(literal 1/24 binary64) x) x #s(literal -1/2 binary64))
(fma.f64 #s(literal 1/24 binary64) (*.f64 x x) #s(literal -1/2 binary64))
(fma.f64 (*.f64 x x) #s(literal 1/24 binary64) #s(literal -1/2 binary64))
(fma.f64 x (*.f64 #s(literal 1/24 binary64) x) #s(literal -1/2 binary64))
(-.f64 (/.f64 #s(literal 1/4 binary64) (-.f64 #s(literal -1/2 binary64) (.f64 #s(literal 1/24 binary64) (.f64 x x)))) (/.f64 (.f64 #s(literal 1/576 binary64) (.f64 (.f64 x x) (.f64 x x))) (-.f64 #s(literal -1/2 binary64) (.f64 #s(literal 1/24 binary64) (.f64 x x)))))
(-.f64 (/.f64 (.f64 #s(literal 1/576 binary64) (.f64 (.f64 x x) (.f64 x x))) (fma.f64 #s(literal 1/24 binary64) (.f64 x x) #s(literal 1/2 binary64))) (/.f64 #s(literal 1/4 binary64) (fma.f64 #s(literal 1/24 binary64) (.f64 x x) #s(literal 1/2 binary64))))
(+.f64 (.f64 #s(literal 1/24 binary64) (.f64 x x)) #s(literal -1/2 binary64))
(+.f64 #s(literal -1/2 binary64) (.f64 #s(literal 1/24 binary64) (.f64 x x)))

eval179.0ms (1%)

Memory: 31.7MiB live, 211.4MiB allocated
Compiler: Compiled 16 885 to 1 690 computations (90% saved)

prune232.0ms (1.3%)

Memory

-8.1MiB live, 269.5MiB allocated

Pruning

29 alts after pruning (27 fresh and 2 done)

	Pruned	Kept	Total
New	807	26	833
Fresh	0	1	1
Picked	4	1	5
Done	0	1	1
Total	811	29	840

Accuracy

100.0%

Counts

840 → 29

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	49.9%	(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))
	40.4%	(.f64 (.f64 (sin.f64 (/.f64 (fma.f64 (.f64 (.f64 x x) x) #s(literal 1 binary64) (.f64 #s(literal 1/8 binary64) (.f64 (.f64 eps eps) eps))) (fma.f64 (.f64 #s(literal 1 binary64) x) (.f64 #s(literal 1 binary64) x) (-.f64 (.f64 (.f64 eps #s(literal 1/2 binary64)) (.f64 eps #s(literal 1/2 binary64))) (.f64 (.f64 #s(literal 1 binary64) x) (.f64 eps #s(literal 1/2 binary64))))))) (sin.f64 (.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 0 binary64) eps)))) #s(literal -2 binary64))
	40.4%	(.f64 (.f64 (sin.f64 (/.f64 (.f64 (fma.f64 #s(literal 8 binary64) (.f64 (.f64 x x) x) (.f64 (.f64 eps eps) eps)) #s(literal 1/2 binary64)) (fma.f64 #s(literal 4 binary64) (.f64 x x) (.f64 eps (-.f64 eps (.f64 x #s(literal 2 binary64))))))) (sin.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 0 binary64) eps)))) #s(literal -2 binary64))
	99.7%	(.f64 (.f64 (sin.f64 (/.f64 (.f64 (fma.f64 #s(literal 4 binary64) (.f64 x x) (.f64 (neg.f64 eps) eps)) #s(literal 1/2 binary64)) (fma.f64 x #s(literal 2 binary64) (neg.f64 eps)))) (sin.f64 (.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 0 binary64) eps)))) #s(literal -2 binary64))
	99.7%	(.f64 (.f64 (sin.f64 (-.f64 (/.f64 (.f64 (.f64 #s(literal 1 binary64) x) (.f64 #s(literal 1 binary64) x)) (-.f64 (.f64 #s(literal 1 binary64) x) (.f64 eps #s(literal 1/2 binary64)))) (/.f64 (.f64 (.f64 eps #s(literal 1/2 binary64)) (.f64 eps #s(literal 1/2 binary64))) (-.f64 (.f64 #s(literal 1 binary64) x) (.f64 eps #s(literal 1/2 binary64)))))) (sin.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 0 binary64) eps)))) #s(literal -2 binary64))
	36.8%	(.f64 (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps))) (sin.f64 (.f64 #s(literal 1/2 binary64) (/.f64 (.f64 (.f64 eps eps) eps) (*.f64 eps eps))))) #s(literal -2 binary64))
	98.1%	(.f64 (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps))) (sin.f64 (.f64 #s(literal 1/2 binary64) (/.f64 (*.f64 eps eps) (-.f64 eps #s(literal 0 binary64)))))) #s(literal -2 binary64))
	98.1%	(.f64 (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps))) (sin.f64 (.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1 binary64) (/.f64 (neg.f64 eps) (neg.f64 (*.f64 eps eps))))))) #s(literal -2 binary64))
▶	35.6%	(.f64 (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps))) (sin.f64 (.f64 #s(literal 1/2 binary64) (.f64 (.f64 (.f64 eps eps) eps) (/.f64 #s(literal 1 binary64) (.f64 eps eps)))))) #s(literal -2 binary64))
	98.1%	(.f64 (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps))) (sin.f64 (.f64 #s(literal 1/2 binary64) (.f64 (neg.f64 (.f64 eps eps)) (/.f64 #s(literal -1 binary64) eps))))) #s(literal -2 binary64))
	99.7%	(.f64 (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps))) #s(approx (sin ( 1/2 (+ 0 eps))) (.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -1/645120 binary64) (.f64 eps eps) #s(literal 1/3840 binary64)) (.f64 eps eps) #s(literal -1/48 binary64)) (.f64 eps eps) #s(literal 1/2 binary64)) eps))) #s(literal -2 binary64))
▶	99.6%	(.f64 (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps))) #s(approx (sin ( 1/2 (+ 0 eps))) (.f64 (fma.f64 (fma.f64 #s(literal 1/3840 binary64) (.f64 eps eps) #s(literal -1/48 binary64)) (*.f64 eps eps) #s(literal 1/2 binary64)) eps))) #s(literal -2 binary64))
	99.6%	(.f64 (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps))) #s(approx (sin ( 1/2 (+ 0 eps))) (.f64 (fma.f64 (.f64 eps eps) #s(literal -1/48 binary64) #s(literal 1/2 binary64)) eps))) #s(literal -2 binary64))
	99.5%	(.f64 (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps))) #s(approx (sin ( 1/2 (+ 0 eps))) (*.f64 eps #s(literal 1/2 binary64)))) #s(literal -2 binary64))
	79.2%	(.f64 #s(approx ( (sin (* 1/2 (+ (* 2 x) eps))) (sin (* 1/2 (+ 0 eps)))) (.f64 (.f64 (sin.f64 x) #s(literal 1/2 binary64)) eps)) #s(literal -2 binary64))
▶	99.8%	(.f64 #s(approx ( (sin (* 1/2 (+ (* 2 x) eps))) (sin (* 1/2 (+ 0 eps)))) (.f64 (sin.f64 (fma.f64 eps #s(literal 1/2 binary64) x)) (sin.f64 (.f64 eps #s(literal 1/2 binary64))))) #s(literal -2 binary64))
▶	49.0%	#s(approx (- (cos (+ x eps)) (cos x)) (-.f64 #s(approx (cos eps) #s(literal 1 binary64)) #s(literal 1 binary64)))
	78.6%	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 (/.f64 (.f64 eps eps) (neg.f64 eps)) (sin.f64 x)))
	99.5%	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 (-.f64 (.f64 (*.f64 (cos.f64 x) #s(literal -1/2 binary64)) eps) (sin.f64 x)) eps))
	78.6%	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 (.f64 (/.f64 #s(literal -1 binary64) eps) (/.f64 (neg.f64 (*.f64 eps eps)) #s(literal -1 binary64))) (sin.f64 x)))
✓	79.2%	#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (neg.f64 eps) (sin.f64 x)))
	78.6%	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 (neg.f64 eps) #s(approx (sin x) (.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -1/5040 binary64) (.f64 x x) #s(literal 1/120 binary64)) (.f64 x x) #s(literal -1/6 binary64)) (*.f64 x x) #s(literal 1 binary64)) x))))
	78.5%	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 (neg.f64 eps) #s(approx (sin x) (.f64 (fma.f64 (fma.f64 #s(literal 1/120 binary64) (.f64 x x) #s(literal -1/6 binary64)) (.f64 x x) #s(literal 1 binary64)) x))))
▶	78.7%	#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (.f64 (fma.f64 (fma.f64 (.f64 eps (fma.f64 (.f64 x x) #s(literal 1/5040 binary64) #s(literal -1/120 binary64))) (.f64 x x) (.f64 #s(literal 1/6 binary64) eps)) (.f64 x x) (neg.f64 eps)) x)))
	78.5%	#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (.f64 (fma.f64 (.f64 eps (fma.f64 (.f64 x x) #s(literal -1/120 binary64) #s(literal 1/6 binary64))) (.f64 x x) (neg.f64 eps)) x)))
	78.4%	#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (.f64 (.f64 eps (fma.f64 (*.f64 x x) #s(literal 1/6 binary64) #s(literal -1 binary64))) x)))
	78.2%	#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (*.f64 (neg.f64 x) eps)))
	98.6%	#s(approx (* (* (sin (* 1/2 (+ (* 2 x) eps))) (sin (* 1/2 (+ 0 eps)))) -2) (fma.f64 (fma.f64 (.f64 (cos.f64 (.f64 #s(literal -1/2 binary64) eps)) (sin.f64 (.f64 eps #s(literal 1/2 binary64)))) (+.f64 #s(literal -2 binary64) (.f64 x (.f64 #s(literal 1/3 binary64) x))) (.f64 (pow.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) #s(literal 2 binary64)) x)) x (.f64 (pow.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) #s(literal 2 binary64)) #s(literal -2 binary64))))
	97.9%	#s(approx (* (* (sin (* 1/2 (+ (* 2 x) eps))) (sin (* 1/2 (+ 0 eps)))) -2) (fma.f64 (pow.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) #s(literal 2 binary64)) (fma.f64 x x #s(literal -2 binary64)) (.f64 (.f64 (.f64 #s(literal -2 binary64) x) (cos.f64 (.f64 #s(literal -1/2 binary64) eps))) (sin.f64 (.f64 eps #s(literal 1/2 binary64))))))

Compiler

Compiled 1 271 to 763 computations (40% saved)

simplify180.0ms (1%)

Memory

-12.4MiB live, 179.2MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 19 expressions of interest:

New	Metric	Score
cost-diff	0	(.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps))) (sin.f64 (.f64 #s(literal 1/2 binary64) (.f64 (.f64 (.f64 eps eps) eps) (/.f64 #s(literal 1 binary64) (*.f64 eps eps))))))
cost-diff	0	(.f64 (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps))) (sin.f64 (.f64 #s(literal 1/2 binary64) (.f64 (.f64 (.f64 eps eps) eps) (/.f64 #s(literal 1 binary64) (.f64 eps eps)))))) #s(literal -2 binary64))
cost-diff	320	(*.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps))
cost-diff	1984	(.f64 (.f64 (.f64 eps eps) eps) (/.f64 #s(literal 1 binary64) (.f64 eps eps)))
cost-diff	0	(sin.f64 (*.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps)))
cost-diff	0	(.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps))) #s(approx (sin (* 1/2 (+ 0 eps))) (.f64 (fma.f64 (fma.f64 #s(literal 1/3840 binary64) (.f64 eps eps) #s(literal -1/48 binary64)) (*.f64 eps eps) #s(literal 1/2 binary64)) eps)))
cost-diff	0	(.f64 (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps))) #s(approx (sin ( 1/2 (+ 0 eps))) (.f64 (fma.f64 (fma.f64 #s(literal 1/3840 binary64) (.f64 eps eps) #s(literal -1/48 binary64)) (*.f64 eps eps) #s(literal 1/2 binary64)) eps))) #s(literal -2 binary64))
cost-diff	320	(*.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps))
cost-diff	0	#s(approx (* (neg eps) (sin x)) (.f64 (fma.f64 (fma.f64 (.f64 eps (fma.f64 (.f64 x x) #s(literal 1/5040 binary64) #s(literal -1/120 binary64))) (.f64 x x) (.f64 #s(literal 1/6 binary64) eps)) (.f64 x x) (neg.f64 eps)) x))
cost-diff	0	#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (.f64 (fma.f64 (fma.f64 (.f64 eps (fma.f64 (.f64 x x) #s(literal 1/5040 binary64) #s(literal -1/120 binary64))) (.f64 x x) (.f64 #s(literal 1/6 binary64) eps)) (.f64 x x) (neg.f64 eps)) x)))
cost-diff	128	(fma.f64 (fma.f64 (.f64 eps (fma.f64 (.f64 x x) #s(literal 1/5040 binary64) #s(literal -1/120 binary64))) (.f64 x x) (.f64 #s(literal 1/6 binary64) eps)) (*.f64 x x) (neg.f64 eps))
cost-diff	320	(fma.f64 (.f64 eps (fma.f64 (.f64 x x) #s(literal 1/5040 binary64) #s(literal -1/120 binary64))) (.f64 x x) (.f64 #s(literal 1/6 binary64) eps))
cost-diff	0	#s(approx (cos eps) #s(literal 1 binary64))
cost-diff	0	(-.f64 #s(approx (cos eps) #s(literal 1 binary64)) #s(literal 1 binary64))
cost-diff	0	#s(approx (- (cos (+ x eps)) (cos x)) (-.f64 #s(approx (cos eps) #s(literal 1 binary64)) #s(literal 1 binary64)))
cost-diff	0	(sin.f64 (fma.f64 eps #s(literal 1/2 binary64) x))
cost-diff	0	(.f64 (sin.f64 (fma.f64 eps #s(literal 1/2 binary64) x)) (sin.f64 (.f64 eps #s(literal 1/2 binary64))))
cost-diff	0	#s(approx (* (sin (* 1/2 (+ (* 2 x) eps))) (sin (* 1/2 (+ 0 eps)))) (.f64 (sin.f64 (fma.f64 eps #s(literal 1/2 binary64) x)) (sin.f64 (.f64 eps #s(literal 1/2 binary64)))))
cost-diff	0	(.f64 #s(approx ( (sin (* 1/2 (+ (* 2 x) eps))) (sin (* 1/2 (+ 0 eps)))) (.f64 (sin.f64 (fma.f64 eps #s(literal 1/2 binary64) x)) (sin.f64 (.f64 eps #s(literal 1/2 binary64))))) #s(literal -2 binary64))

Rules

7 622×	`lower-fma.f32`
7 608×	`lower-fma.f64`
4 328×	`lower-*.f32`
4 296×	`lower-*.f64`
1 308×	`lower-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	65	514
0	101	454
1	186	443
2	464	427
3	1295	427
4	4021	427
5	6418	427
0	8306	418

Stop Event

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

Calls

Call 1

Inputs
(.f64 #s(approx ( (sin (* 1/2 (+ (* 2 x) eps))) (sin (* 1/2 (+ 0 eps)))) (.f64 (sin.f64 (fma.f64 eps #s(literal 1/2 binary64) x)) (sin.f64 (.f64 eps #s(literal 1/2 binary64))))) #s(literal -2 binary64))
#s(approx (* (sin (* 1/2 (+ (* 2 x) eps))) (sin (* 1/2 (+ 0 eps)))) (.f64 (sin.f64 (fma.f64 eps #s(literal 1/2 binary64) x)) (sin.f64 (.f64 eps #s(literal 1/2 binary64)))))
(.f64 (sin.f64 (fma.f64 eps #s(literal 1/2 binary64) x)) (sin.f64 (.f64 eps #s(literal 1/2 binary64))))
(sin.f64 (fma.f64 eps #s(literal 1/2 binary64) x))
(fma.f64 eps #s(literal 1/2 binary64) x)
eps
#s(literal 1/2 binary64)
x
(sin.f64 (*.f64 eps #s(literal 1/2 binary64)))
(*.f64 eps #s(literal 1/2 binary64))
#s(literal -2 binary64)
#s(approx (- (cos (+ x eps)) (cos x)) (-.f64 #s(approx (cos eps) #s(literal 1 binary64)) #s(literal 1 binary64)))
(-.f64 #s(approx (cos eps) #s(literal 1 binary64)) #s(literal 1 binary64))
#s(approx (cos eps) #s(literal 1 binary64))
#s(literal 1 binary64)
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (.f64 (fma.f64 (fma.f64 (.f64 eps (fma.f64 (.f64 x x) #s(literal 1/5040 binary64) #s(literal -1/120 binary64))) (.f64 x x) (.f64 #s(literal 1/6 binary64) eps)) (.f64 x x) (neg.f64 eps)) x)))
#s(approx (* (neg eps) (sin x)) (.f64 (fma.f64 (fma.f64 (.f64 eps (fma.f64 (.f64 x x) #s(literal 1/5040 binary64) #s(literal -1/120 binary64))) (.f64 x x) (.f64 #s(literal 1/6 binary64) eps)) (.f64 x x) (neg.f64 eps)) x))
(.f64 (fma.f64 (fma.f64 (.f64 eps (fma.f64 (.f64 x x) #s(literal 1/5040 binary64) #s(literal -1/120 binary64))) (.f64 x x) (.f64 #s(literal 1/6 binary64) eps)) (.f64 x x) (neg.f64 eps)) x)
(fma.f64 (fma.f64 (.f64 eps (fma.f64 (.f64 x x) #s(literal 1/5040 binary64) #s(literal -1/120 binary64))) (.f64 x x) (.f64 #s(literal 1/6 binary64) eps)) (*.f64 x x) (neg.f64 eps))
(fma.f64 (.f64 eps (fma.f64 (.f64 x x) #s(literal 1/5040 binary64) #s(literal -1/120 binary64))) (.f64 x x) (.f64 #s(literal 1/6 binary64) eps))
(.f64 eps (fma.f64 (.f64 x x) #s(literal 1/5040 binary64) #s(literal -1/120 binary64)))
eps
(fma.f64 (*.f64 x x) #s(literal 1/5040 binary64) #s(literal -1/120 binary64))
(*.f64 x x)
x
#s(literal 1/5040 binary64)
#s(literal -1/120 binary64)
(*.f64 #s(literal 1/6 binary64) eps)
#s(literal 1/6 binary64)
(neg.f64 eps)
(.f64 (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps))) #s(approx (sin ( 1/2 (+ 0 eps))) (.f64 (fma.f64 (fma.f64 #s(literal 1/3840 binary64) (.f64 eps eps) #s(literal -1/48 binary64)) (*.f64 eps eps) #s(literal 1/2 binary64)) eps))) #s(literal -2 binary64))
(.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps))) #s(approx (sin (* 1/2 (+ 0 eps))) (.f64 (fma.f64 (fma.f64 #s(literal 1/3840 binary64) (.f64 eps eps) #s(literal -1/48 binary64)) (*.f64 eps eps) #s(literal 1/2 binary64)) eps)))
(sin.f64 (*.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps)))
(*.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps))
#s(literal 1/2 binary64)
(fma.f64 #s(literal 2 binary64) x eps)
#s(literal 2 binary64)
x
eps
#s(approx (sin (* 1/2 (+ 0 eps))) (.f64 (fma.f64 (fma.f64 #s(literal 1/3840 binary64) (.f64 eps eps) #s(literal -1/48 binary64)) (*.f64 eps eps) #s(literal 1/2 binary64)) eps))
(.f64 (fma.f64 (fma.f64 #s(literal 1/3840 binary64) (.f64 eps eps) #s(literal -1/48 binary64)) (*.f64 eps eps) #s(literal 1/2 binary64)) eps)
(fma.f64 (fma.f64 #s(literal 1/3840 binary64) (.f64 eps eps) #s(literal -1/48 binary64)) (.f64 eps eps) #s(literal 1/2 binary64))
(fma.f64 #s(literal 1/3840 binary64) (*.f64 eps eps) #s(literal -1/48 binary64))
#s(literal 1/3840 binary64)
(*.f64 eps eps)
#s(literal -1/48 binary64)
#s(literal -2 binary64)
(.f64 (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps))) (sin.f64 (.f64 #s(literal 1/2 binary64) (.f64 (.f64 (.f64 eps eps) eps) (/.f64 #s(literal 1 binary64) (.f64 eps eps)))))) #s(literal -2 binary64))
(.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps))) (sin.f64 (.f64 #s(literal 1/2 binary64) (.f64 (.f64 (.f64 eps eps) eps) (/.f64 #s(literal 1 binary64) (*.f64 eps eps))))))
(sin.f64 (*.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps)))
(*.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps))
#s(literal 1/2 binary64)
(fma.f64 #s(literal 2 binary64) x eps)
#s(literal 2 binary64)
x
eps
(sin.f64 (.f64 #s(literal 1/2 binary64) (.f64 (.f64 (.f64 eps eps) eps) (/.f64 #s(literal 1 binary64) (*.f64 eps eps)))))
(.f64 #s(literal 1/2 binary64) (.f64 (.f64 (.f64 eps eps) eps) (/.f64 #s(literal 1 binary64) (*.f64 eps eps))))
(.f64 (.f64 (.f64 eps eps) eps) (/.f64 #s(literal 1 binary64) (.f64 eps eps)))
(.f64 (.f64 eps eps) eps)
(*.f64 eps eps)
(/.f64 #s(literal 1 binary64) (*.f64 eps eps))
#s(literal 1 binary64)
#s(literal -2 binary64)

Outputs
(.f64 #s(approx ( (sin (* 1/2 (+ (* 2 x) eps))) (sin (* 1/2 (+ 0 eps)))) (.f64 (sin.f64 (fma.f64 eps #s(literal 1/2 binary64) x)) (sin.f64 (.f64 eps #s(literal 1/2 binary64))))) #s(literal -2 binary64))
(.f64 #s(literal -2 binary64) #s(approx ( (sin (* 1/2 (+ (* 2 x) eps))) (sin (* 1/2 (+ 0 eps)))) (.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (sin.f64 (fma.f64 eps #s(literal 1/2 binary64) x)))))
#s(approx (* (sin (* 1/2 (+ (* 2 x) eps))) (sin (* 1/2 (+ 0 eps)))) (.f64 (sin.f64 (fma.f64 eps #s(literal 1/2 binary64) x)) (sin.f64 (.f64 eps #s(literal 1/2 binary64)))))
#s(approx (* (sin (* 1/2 (+ (* 2 x) eps))) (sin (* 1/2 (+ 0 eps)))) (.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (sin.f64 (fma.f64 eps #s(literal 1/2 binary64) x))))
(.f64 (sin.f64 (fma.f64 eps #s(literal 1/2 binary64) x)) (sin.f64 (.f64 eps #s(literal 1/2 binary64))))
(.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (sin.f64 (fma.f64 eps #s(literal 1/2 binary64) x)))
(sin.f64 (fma.f64 eps #s(literal 1/2 binary64) x))
(fma.f64 eps #s(literal 1/2 binary64) x)
eps
#s(literal 1/2 binary64)
x
(sin.f64 (*.f64 eps #s(literal 1/2 binary64)))
(*.f64 eps #s(literal 1/2 binary64))
#s(literal -2 binary64)
#s(approx (- (cos (+ x eps)) (cos x)) (-.f64 #s(approx (cos eps) #s(literal 1 binary64)) #s(literal 1 binary64)))
(-.f64 #s(approx (cos eps) #s(literal 1 binary64)) #s(literal 1 binary64))
#s(approx (cos eps) #s(literal 1 binary64))
#s(literal 1 binary64)
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (.f64 (fma.f64 (fma.f64 (.f64 eps (fma.f64 (.f64 x x) #s(literal 1/5040 binary64) #s(literal -1/120 binary64))) (.f64 x x) (.f64 #s(literal 1/6 binary64) eps)) (.f64 x x) (neg.f64 eps)) x)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (.f64 (.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 1/5040 binary64) (.f64 x x) #s(literal -1/120 binary64)) (.f64 x x) #s(literal 1/6 binary64)) (*.f64 x x) #s(literal -1 binary64)) eps) x)))
#s(approx (* (neg eps) (sin x)) (.f64 (fma.f64 (fma.f64 (.f64 eps (fma.f64 (.f64 x x) #s(literal 1/5040 binary64) #s(literal -1/120 binary64))) (.f64 x x) (.f64 #s(literal 1/6 binary64) eps)) (.f64 x x) (neg.f64 eps)) x))
#s(approx (* (neg eps) (sin x)) (.f64 (.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 1/5040 binary64) (.f64 x x) #s(literal -1/120 binary64)) (.f64 x x) #s(literal 1/6 binary64)) (*.f64 x x) #s(literal -1 binary64)) eps) x))
(.f64 (fma.f64 (fma.f64 (.f64 eps (fma.f64 (.f64 x x) #s(literal 1/5040 binary64) #s(literal -1/120 binary64))) (.f64 x x) (.f64 #s(literal 1/6 binary64) eps)) (.f64 x x) (neg.f64 eps)) x)
(.f64 (.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 1/5040 binary64) (.f64 x x) #s(literal -1/120 binary64)) (.f64 x x) #s(literal 1/6 binary64)) (*.f64 x x) #s(literal -1 binary64)) eps) x)
(fma.f64 (fma.f64 (.f64 eps (fma.f64 (.f64 x x) #s(literal 1/5040 binary64) #s(literal -1/120 binary64))) (.f64 x x) (.f64 #s(literal 1/6 binary64) eps)) (*.f64 x x) (neg.f64 eps))
(.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 1/5040 binary64) (.f64 x x) #s(literal -1/120 binary64)) (.f64 x x) #s(literal 1/6 binary64)) (.f64 x x) #s(literal -1 binary64)) eps)
(fma.f64 (.f64 eps (fma.f64 (.f64 x x) #s(literal 1/5040 binary64) #s(literal -1/120 binary64))) (.f64 x x) (.f64 #s(literal 1/6 binary64) eps))
(.f64 (fma.f64 (fma.f64 #s(literal 1/5040 binary64) (.f64 x x) #s(literal -1/120 binary64)) (*.f64 x x) #s(literal 1/6 binary64)) eps)
(.f64 eps (fma.f64 (.f64 x x) #s(literal 1/5040 binary64) #s(literal -1/120 binary64)))
(.f64 (fma.f64 #s(literal 1/5040 binary64) (.f64 x x) #s(literal -1/120 binary64)) eps)
eps
(fma.f64 (*.f64 x x) #s(literal 1/5040 binary64) #s(literal -1/120 binary64))
(fma.f64 #s(literal 1/5040 binary64) (*.f64 x x) #s(literal -1/120 binary64))
(*.f64 x x)
x
#s(literal 1/5040 binary64)
#s(literal -1/120 binary64)
(*.f64 #s(literal 1/6 binary64) eps)
#s(literal 1/6 binary64)
(neg.f64 eps)
(.f64 (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps))) #s(approx (sin ( 1/2 (+ 0 eps))) (.f64 (fma.f64 (fma.f64 #s(literal 1/3840 binary64) (.f64 eps eps) #s(literal -1/48 binary64)) (*.f64 eps eps) #s(literal 1/2 binary64)) eps))) #s(literal -2 binary64))
(.f64 (.f64 (sin.f64 (fma.f64 eps #s(literal 1/2 binary64) x)) #s(literal -2 binary64)) #s(approx (sin (* 1/2 (+ 0 eps))) (.f64 (fma.f64 (fma.f64 (.f64 eps eps) #s(literal 1/3840 binary64) #s(literal -1/48 binary64)) (*.f64 eps eps) #s(literal 1/2 binary64)) eps)))
(.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps))) #s(approx (sin (* 1/2 (+ 0 eps))) (.f64 (fma.f64 (fma.f64 #s(literal 1/3840 binary64) (.f64 eps eps) #s(literal -1/48 binary64)) (*.f64 eps eps) #s(literal 1/2 binary64)) eps)))
(.f64 #s(approx (sin ( 1/2 (+ 0 eps))) (.f64 (fma.f64 (fma.f64 (.f64 eps eps) #s(literal 1/3840 binary64) #s(literal -1/48 binary64)) (*.f64 eps eps) #s(literal 1/2 binary64)) eps)) (sin.f64 (fma.f64 eps #s(literal 1/2 binary64) x)))
(sin.f64 (*.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps)))
(sin.f64 (fma.f64 eps #s(literal 1/2 binary64) x))
(*.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps))
(fma.f64 eps #s(literal 1/2 binary64) x)
#s(literal 1/2 binary64)
(fma.f64 #s(literal 2 binary64) x eps)
(fma.f64 x #s(literal 2 binary64) eps)
#s(literal 2 binary64)
x
eps
#s(approx (sin (* 1/2 (+ 0 eps))) (.f64 (fma.f64 (fma.f64 #s(literal 1/3840 binary64) (.f64 eps eps) #s(literal -1/48 binary64)) (*.f64 eps eps) #s(literal 1/2 binary64)) eps))
#s(approx (sin (* 1/2 (+ 0 eps))) (.f64 (fma.f64 (fma.f64 (.f64 eps eps) #s(literal 1/3840 binary64) #s(literal -1/48 binary64)) (*.f64 eps eps) #s(literal 1/2 binary64)) eps))
(.f64 (fma.f64 (fma.f64 #s(literal 1/3840 binary64) (.f64 eps eps) #s(literal -1/48 binary64)) (*.f64 eps eps) #s(literal 1/2 binary64)) eps)
(.f64 (fma.f64 (fma.f64 (.f64 eps eps) #s(literal 1/3840 binary64) #s(literal -1/48 binary64)) (*.f64 eps eps) #s(literal 1/2 binary64)) eps)
(fma.f64 (fma.f64 #s(literal 1/3840 binary64) (.f64 eps eps) #s(literal -1/48 binary64)) (.f64 eps eps) #s(literal 1/2 binary64))
(fma.f64 (fma.f64 (.f64 eps eps) #s(literal 1/3840 binary64) #s(literal -1/48 binary64)) (.f64 eps eps) #s(literal 1/2 binary64))
(fma.f64 #s(literal 1/3840 binary64) (*.f64 eps eps) #s(literal -1/48 binary64))
(fma.f64 (*.f64 eps eps) #s(literal 1/3840 binary64) #s(literal -1/48 binary64))
#s(literal 1/3840 binary64)
(*.f64 eps eps)
#s(literal -1/48 binary64)
#s(literal -2 binary64)
(.f64 (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps))) (sin.f64 (.f64 #s(literal 1/2 binary64) (.f64 (.f64 (.f64 eps eps) eps) (/.f64 #s(literal 1 binary64) (.f64 eps eps)))))) #s(literal -2 binary64))
(.f64 (.f64 (sin.f64 (fma.f64 eps #s(literal 1/2 binary64) x)) #s(literal -2 binary64)) (sin.f64 (*.f64 eps #s(literal 1/2 binary64))))
(.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps))) (sin.f64 (.f64 #s(literal 1/2 binary64) (.f64 (.f64 (.f64 eps eps) eps) (/.f64 #s(literal 1 binary64) (*.f64 eps eps))))))
(.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (sin.f64 (fma.f64 eps #s(literal 1/2 binary64) x)))
(sin.f64 (*.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps)))
(sin.f64 (fma.f64 eps #s(literal 1/2 binary64) x))
(*.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps))
(fma.f64 eps #s(literal 1/2 binary64) x)
#s(literal 1/2 binary64)
(fma.f64 #s(literal 2 binary64) x eps)
(fma.f64 x #s(literal 2 binary64) eps)
#s(literal 2 binary64)
x
eps
(sin.f64 (.f64 #s(literal 1/2 binary64) (.f64 (.f64 (.f64 eps eps) eps) (/.f64 #s(literal 1 binary64) (*.f64 eps eps)))))
(sin.f64 (*.f64 eps #s(literal 1/2 binary64)))
(.f64 #s(literal 1/2 binary64) (.f64 (.f64 (.f64 eps eps) eps) (/.f64 #s(literal 1 binary64) (*.f64 eps eps))))
(*.f64 eps #s(literal 1/2 binary64))
(.f64 (.f64 (.f64 eps eps) eps) (/.f64 #s(literal 1 binary64) (.f64 eps eps)))
eps
(.f64 (.f64 eps eps) eps)
(*.f64 eps eps)
(/.f64 #s(literal 1 binary64) (*.f64 eps eps))
#s(literal 1 binary64)
#s(literal -2 binary64)

localize600.0ms (3.2%)

Memory

-18.7MiB live, 567.4MiB allocated

Localize:

Found 19 expressions of interest:

New	Metric	Score
accuracy	0.05859375	(.f64 (.f64 eps eps) eps)
accuracy	0.11328125	(.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps))) (sin.f64 (.f64 #s(literal 1/2 binary64) (.f64 (.f64 (.f64 eps eps) eps) (/.f64 #s(literal 1 binary64) (*.f64 eps eps))))))
accuracy	0.14453125	(/.f64 #s(literal 1 binary64) (*.f64 eps eps))
accuracy	40.60205752550044	(.f64 (.f64 (.f64 eps eps) eps) (/.f64 #s(literal 1 binary64) (.f64 eps eps)))
accuracy	0.0078125	(.f64 (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps))) #s(approx (sin ( 1/2 (+ 0 eps))) (.f64 (fma.f64 (fma.f64 #s(literal 1/3840 binary64) (.f64 eps eps) #s(literal -1/48 binary64)) (*.f64 eps eps) #s(literal 1/2 binary64)) eps))) #s(literal -2 binary64))
accuracy	0.04260504138909578	(sin.f64 (*.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps)))
accuracy	0.08117142671031594	#s(approx (sin (* 1/2 (+ 0 eps))) (.f64 (fma.f64 (fma.f64 #s(literal 1/3840 binary64) (.f64 eps eps) #s(literal -1/48 binary64)) (*.f64 eps eps) #s(literal 1/2 binary64)) eps))
accuracy	0.11328125	(.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps))) #s(approx (sin (* 1/2 (+ 0 eps))) (.f64 (fma.f64 (fma.f64 #s(literal 1/3840 binary64) (.f64 eps eps) #s(literal -1/48 binary64)) (*.f64 eps eps) #s(literal 1/2 binary64)) eps)))
accuracy	0.09375	(.f64 eps (fma.f64 (.f64 x x) #s(literal 1/5040 binary64) #s(literal -1/120 binary64)))
accuracy	0.3125	(*.f64 #s(literal 1/6 binary64) eps)
accuracy	0.7197726703854297	#s(approx (* (neg eps) (sin x)) (.f64 (fma.f64 (fma.f64 (.f64 eps (fma.f64 (.f64 x x) #s(literal 1/5040 binary64) #s(literal -1/120 binary64))) (.f64 x x) (.f64 #s(literal 1/6 binary64) eps)) (.f64 x x) (neg.f64 eps)) x))
accuracy	13.326141805054661	#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (.f64 (fma.f64 (fma.f64 (.f64 eps (fma.f64 (.f64 x x) #s(literal 1/5040 binary64) #s(literal -1/120 binary64))) (.f64 x x) (.f64 #s(literal 1/6 binary64) eps)) (.f64 x x) (neg.f64 eps)) x)))
accuracy	0.1963025269454012	#s(approx (cos eps) #s(literal 1 binary64))
accuracy	30.951668946883355	(-.f64 #s(approx (cos eps) #s(literal 1 binary64)) #s(literal 1 binary64))
accuracy	31.542721496794677	#s(approx (- (cos (+ x eps)) (cos x)) (-.f64 #s(approx (cos eps) #s(literal 1 binary64)) #s(literal 1 binary64)))
accuracy	0	#s(approx (* (sin (* 1/2 (+ (* 2 x) eps))) (sin (* 1/2 (+ 0 eps)))) (.f64 (sin.f64 (fma.f64 eps #s(literal 1/2 binary64) x)) (sin.f64 (.f64 eps #s(literal 1/2 binary64)))))
accuracy	0.0078125	(.f64 #s(approx ( (sin (* 1/2 (+ (* 2 x) eps))) (sin (* 1/2 (+ 0 eps)))) (.f64 (sin.f64 (fma.f64 eps #s(literal 1/2 binary64) x)) (sin.f64 (.f64 eps #s(literal 1/2 binary64))))) #s(literal -2 binary64))
accuracy	0.04260504138909578	(sin.f64 (fma.f64 eps #s(literal 1/2 binary64) x))
accuracy	0.11328125	(.f64 (sin.f64 (fma.f64 eps #s(literal 1/2 binary64) x)) (sin.f64 (.f64 eps #s(literal 1/2 binary64))))

Samples

361.0ms	179×	2	valid
86.0ms	74×	1	valid
4.0ms	1×	5	exit
2.0ms	1×	3	valid
1.0ms	1×	0	valid

Compiler

Compiled 417 to 60 computations (85.6% saved)

Precisions

Click to see histograms. Total time spent on operations: 393.0ms

ival-cos: 114.0ms (29% of total)

ival-sin: 72.0ms (18.3% of total)

ival-mult: 60.0ms (15.3% of total)

const: 56.0ms (14.3% of total)

adjust: 50.0ms (12.7% of total)

ival-sub: 19.0ms (4.8% of total)

ival-add: 16.0ms (4.1% of total)

ival-div: 4.0ms (1% of total)

exact: 1.0ms (0.3% of total)

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

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

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

series69.0ms (0.4%)

Memory

-0.9MiB live, 59.8MiB allocated

Counts

23 → 468

Calls

Call 1

Inputs
#s(alt (.f64 #s(approx ( (sin (* 1/2 (+ (* 2 x) eps))) (sin (* 1/2 (+ 0 eps)))) (.f64 (sin.f64 (fma.f64 eps #s(literal 1/2 binary64) x)) (sin.f64 (.f64 eps #s(literal 1/2 binary64))))) #s(literal -2 binary64)) (patch (.f64 #s(approx ( (sin (* 1/2 (+ (* 2 x) eps))) (sin (* 1/2 (+ 0 eps)))) (.f64 (sin.f64 (fma.f64 eps #s(literal 1/2 binary64) x)) (sin.f64 (.f64 eps #s(literal 1/2 binary64))))) #s(literal -2 binary64)) #<representation binary64>) () ())
#s(alt #s(approx (* (sin (* 1/2 (+ (* 2 x) eps))) (sin (* 1/2 (+ 0 eps)))) (.f64 (sin.f64 (fma.f64 eps #s(literal 1/2 binary64) x)) (sin.f64 (.f64 eps #s(literal 1/2 binary64))))) (patch #s(approx (* (sin (* 1/2 (+ (* 2 x) eps))) (sin (* 1/2 (+ 0 eps)))) (.f64 (sin.f64 (fma.f64 eps #s(literal 1/2 binary64) x)) (sin.f64 (.f64 eps #s(literal 1/2 binary64))))) #<representation binary64>) () ())
#s(alt (.f64 (sin.f64 (fma.f64 eps #s(literal 1/2 binary64) x)) (sin.f64 (.f64 eps #s(literal 1/2 binary64)))) (patch (.f64 (sin.f64 (fma.f64 eps #s(literal 1/2 binary64) x)) (sin.f64 (.f64 eps #s(literal 1/2 binary64)))) #<representation binary64>) () ())
#s(alt (sin.f64 (fma.f64 eps #s(literal 1/2 binary64) x)) (patch (sin.f64 (fma.f64 eps #s(literal 1/2 binary64) 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 (fma.f64 (.f64 eps (fma.f64 (.f64 x x) #s(literal 1/5040 binary64) #s(literal -1/120 binary64))) (.f64 x x) (.f64 #s(literal 1/6 binary64) eps)) (patch (fma.f64 (.f64 eps (fma.f64 (.f64 x x) #s(literal 1/5040 binary64) #s(literal -1/120 binary64))) (.f64 x x) (.f64 #s(literal 1/6 binary64) eps)) #<representation binary64>) () ())
#s(alt (fma.f64 (fma.f64 (.f64 eps (fma.f64 (.f64 x x) #s(literal 1/5040 binary64) #s(literal -1/120 binary64))) (.f64 x x) (.f64 #s(literal 1/6 binary64) eps)) (.f64 x x) (neg.f64 eps)) (patch (fma.f64 (fma.f64 (.f64 eps (fma.f64 (.f64 x x) #s(literal 1/5040 binary64) #s(literal -1/120 binary64))) (.f64 x x) (.f64 #s(literal 1/6 binary64) eps)) (.f64 x x) (neg.f64 eps)) #<representation binary64>) () ())
#s(alt #s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (.f64 (fma.f64 (fma.f64 (.f64 eps (fma.f64 (.f64 x x) #s(literal 1/5040 binary64) #s(literal -1/120 binary64))) (.f64 x x) (.f64 #s(literal 1/6 binary64) eps)) (.f64 x x) (neg.f64 eps)) x))) (patch #s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (.f64 (fma.f64 (fma.f64 (.f64 eps (fma.f64 (.f64 x x) #s(literal 1/5040 binary64) #s(literal -1/120 binary64))) (.f64 x x) (.f64 #s(literal 1/6 binary64) eps)) (.f64 x x) (neg.f64 eps)) x))) #<representation binary64>) () ())
#s(alt #s(approx (* (neg eps) (sin x)) (.f64 (fma.f64 (fma.f64 (.f64 eps (fma.f64 (.f64 x x) #s(literal 1/5040 binary64) #s(literal -1/120 binary64))) (.f64 x x) (.f64 #s(literal 1/6 binary64) eps)) (.f64 x x) (neg.f64 eps)) x)) (patch #s(approx (* (neg eps) (sin x)) (.f64 (fma.f64 (fma.f64 (.f64 eps (fma.f64 (.f64 x x) #s(literal 1/5040 binary64) #s(literal -1/120 binary64))) (.f64 x x) (.f64 #s(literal 1/6 binary64) eps)) (.f64 x x) (neg.f64 eps)) x)) #<representation binary64>) () ())
#s(alt (.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps)) (patch (.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps)) #<representation binary64>) () ())
#s(alt (.f64 (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps))) #s(approx (sin ( 1/2 (+ 0 eps))) (.f64 (fma.f64 (fma.f64 #s(literal 1/3840 binary64) (.f64 eps eps) #s(literal -1/48 binary64)) (.f64 eps eps) #s(literal 1/2 binary64)) eps))) #s(literal -2 binary64)) (patch (.f64 (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps))) #s(approx (sin (* 1/2 (+ 0 eps))) (.f64 (fma.f64 (fma.f64 #s(literal 1/3840 binary64) (.f64 eps eps) #s(literal -1/48 binary64)) (*.f64 eps eps) #s(literal 1/2 binary64)) eps))) #s(literal -2 binary64)) #<representation binary64>) () ())
#s(alt (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps))) #s(approx (sin (* 1/2 (+ 0 eps))) (.f64 (fma.f64 (fma.f64 #s(literal 1/3840 binary64) (.f64 eps eps) #s(literal -1/48 binary64)) (.f64 eps eps) #s(literal 1/2 binary64)) eps))) (patch (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps))) #s(approx (sin ( 1/2 (+ 0 eps))) (.f64 (fma.f64 (fma.f64 #s(literal 1/3840 binary64) (.f64 eps eps) #s(literal -1/48 binary64)) (*.f64 eps eps) #s(literal 1/2 binary64)) eps))) #<representation binary64>) () ())
#s(alt (sin.f64 (.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps))) (patch (sin.f64 (.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps))) #<representation binary64>) () ())
#s(alt (.f64 (.f64 (.f64 eps eps) eps) (/.f64 #s(literal 1 binary64) (.f64 eps eps))) (patch (.f64 (.f64 (.f64 eps eps) eps) (/.f64 #s(literal 1 binary64) (.f64 eps eps))) #<representation binary64>) () ())
#s(alt (.f64 (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps))) (sin.f64 (.f64 #s(literal 1/2 binary64) (.f64 (.f64 (.f64 eps eps) eps) (/.f64 #s(literal 1 binary64) (.f64 eps eps)))))) #s(literal -2 binary64)) (patch (.f64 (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps))) (sin.f64 (.f64 #s(literal 1/2 binary64) (.f64 (.f64 (.f64 eps eps) eps) (/.f64 #s(literal 1 binary64) (.f64 eps eps)))))) #s(literal -2 binary64)) #<representation binary64>) () ())
#s(alt (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps))) (sin.f64 (.f64 #s(literal 1/2 binary64) (.f64 (.f64 (.f64 eps eps) eps) (/.f64 #s(literal 1 binary64) (.f64 eps eps)))))) (patch (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps))) (sin.f64 (.f64 #s(literal 1/2 binary64) (.f64 (.f64 (.f64 eps eps) eps) (/.f64 #s(literal 1 binary64) (.f64 eps eps)))))) #<representation binary64>) () ())
#s(alt (.f64 #s(literal 1/6 binary64) eps) (patch (.f64 #s(literal 1/6 binary64) eps) #<representation binary64>) () ())
#s(alt (.f64 eps (fma.f64 (.f64 x x) #s(literal 1/5040 binary64) #s(literal -1/120 binary64))) (patch (.f64 eps (fma.f64 (.f64 x x) #s(literal 1/5040 binary64) #s(literal -1/120 binary64))) #<representation binary64>) () ())
#s(alt #s(approx (sin (* 1/2 (+ 0 eps))) (.f64 (fma.f64 (fma.f64 #s(literal 1/3840 binary64) (.f64 eps eps) #s(literal -1/48 binary64)) (.f64 eps eps) #s(literal 1/2 binary64)) eps)) (patch #s(approx (sin ( 1/2 (+ 0 eps))) (.f64 (fma.f64 (fma.f64 #s(literal 1/3840 binary64) (.f64 eps eps) #s(literal -1/48 binary64)) (*.f64 eps eps) #s(literal 1/2 binary64)) eps)) #<representation binary64>) () ())
#s(alt (/.f64 #s(literal 1 binary64) (.f64 eps eps)) (patch (/.f64 #s(literal 1 binary64) (.f64 eps eps)) #<representation binary64>) () ())
#s(alt (.f64 (.f64 eps eps) eps) (patch (.f64 (.f64 eps eps) eps) #<representation binary64>) () ())

Outputs
#s(alt (* -2 (pow (sin (* 1/2 eps)) 2)) (taylor 0 x) (#s(alt (.f64 #s(approx ( (sin (* 1/2 (+ (* 2 x) eps))) (sin (* 1/2 (+ 0 eps)))) (.f64 (sin.f64 (fma.f64 eps #s(literal 1/2 binary64) x)) (sin.f64 (.f64 eps #s(literal 1/2 binary64))))) #s(literal -2 binary64)) (patch (.f64 #s(approx ( (sin (* 1/2 (+ (* 2 x) eps))) (sin (* 1/2 (+ 0 eps)))) (.f64 (sin.f64 (fma.f64 eps #s(literal 1/2 binary64) x)) (sin.f64 (.f64 eps #s(literal 1/2 binary64))))) #s(literal -2 binary64)) #<representation binary64>) () ())) ())
#s(alt (+ (* -2 (* x (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))) (* -2 (pow (sin (* 1/2 eps)) 2))) (taylor 0 x) (#s(alt (.f64 #s(approx ( (sin (* 1/2 (+ (* 2 x) eps))) (sin (* 1/2 (+ 0 eps)))) (.f64 (sin.f64 (fma.f64 eps #s(literal 1/2 binary64) x)) (sin.f64 (.f64 eps #s(literal 1/2 binary64))))) #s(literal -2 binary64)) (patch (.f64 #s(approx ( (sin (* 1/2 (+ (* 2 x) eps))) (sin (* 1/2 (+ 0 eps)))) (.f64 (sin.f64 (fma.f64 eps #s(literal 1/2 binary64) x)) (sin.f64 (.f64 eps #s(literal 1/2 binary64))))) #s(literal -2 binary64)) #<representation binary64>) () ())) ())
#s(alt (+ (* -2 (pow (sin (* 1/2 eps)) 2)) (* x (+ (* -2 (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) (* x (pow (sin (* 1/2 eps)) 2))))) (taylor 0 x) (#s(alt (.f64 #s(approx ( (sin (* 1/2 (+ (* 2 x) eps))) (sin (* 1/2 (+ 0 eps)))) (.f64 (sin.f64 (fma.f64 eps #s(literal 1/2 binary64) x)) (sin.f64 (.f64 eps #s(literal 1/2 binary64))))) #s(literal -2 binary64)) (patch (.f64 #s(approx ( (sin (* 1/2 (+ (* 2 x) eps))) (sin (* 1/2 (+ 0 eps)))) (.f64 (sin.f64 (fma.f64 eps #s(literal 1/2 binary64) x)) (sin.f64 (.f64 eps #s(literal 1/2 binary64))))) #s(literal -2 binary64)) #<representation binary64>) () ())) ())
#s(alt (+ (* -2 (pow (sin (* 1/2 eps)) 2)) (* x (+ (* -2 (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) (* x (+ (* 1/3 (* x (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))) (pow (sin (* 1/2 eps)) 2)))))) (taylor 0 x) (#s(alt (.f64 #s(approx ( (sin (* 1/2 (+ (* 2 x) eps))) (sin (* 1/2 (+ 0 eps)))) (.f64 (sin.f64 (fma.f64 eps #s(literal 1/2 binary64) x)) (sin.f64 (.f64 eps #s(literal 1/2 binary64))))) #s(literal -2 binary64)) (patch (.f64 #s(approx ( (sin (* 1/2 (+ (* 2 x) eps))) (sin (* 1/2 (+ 0 eps)))) (.f64 (sin.f64 (fma.f64 eps #s(literal 1/2 binary64) x)) (sin.f64 (.f64 eps #s(literal 1/2 binary64))))) #s(literal -2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (+ eps (* 2 x)))))) (taylor inf x) (#s(alt (.f64 #s(approx ( (sin (* 1/2 (+ (* 2 x) eps))) (sin (* 1/2 (+ 0 eps)))) (.f64 (sin.f64 (fma.f64 eps #s(literal 1/2 binary64) x)) (sin.f64 (.f64 eps #s(literal 1/2 binary64))))) #s(literal -2 binary64)) (patch (.f64 #s(approx ( (sin (* 1/2 (+ (* 2 x) eps))) (sin (* 1/2 (+ 0 eps)))) (.f64 (sin.f64 (fma.f64 eps #s(literal 1/2 binary64) x)) (sin.f64 (.f64 eps #s(literal 1/2 binary64))))) #s(literal -2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (+ eps (* 2 x)))))) (taylor inf x) (#s(alt (.f64 #s(approx ( (sin (* 1/2 (+ (* 2 x) eps))) (sin (* 1/2 (+ 0 eps)))) (.f64 (sin.f64 (fma.f64 eps #s(literal 1/2 binary64) x)) (sin.f64 (.f64 eps #s(literal 1/2 binary64))))) #s(literal -2 binary64)) (patch (.f64 #s(approx ( (sin (* 1/2 (+ (* 2 x) eps))) (sin (* 1/2 (+ 0 eps)))) (.f64 (sin.f64 (fma.f64 eps #s(literal 1/2 binary64) x)) (sin.f64 (.f64 eps #s(literal 1/2 binary64))))) #s(literal -2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (+ eps (* 2 x)))))) (taylor inf x) (#s(alt (.f64 #s(approx ( (sin (* 1/2 (+ (* 2 x) eps))) (sin (* 1/2 (+ 0 eps)))) (.f64 (sin.f64 (fma.f64 eps #s(literal 1/2 binary64) x)) (sin.f64 (.f64 eps #s(literal 1/2 binary64))))) #s(literal -2 binary64)) (patch (.f64 #s(approx ( (sin (* 1/2 (+ (* 2 x) eps))) (sin (* 1/2 (+ 0 eps)))) (.f64 (sin.f64 (fma.f64 eps #s(literal 1/2 binary64) x)) (sin.f64 (.f64 eps #s(literal 1/2 binary64))))) #s(literal -2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (+ eps (* 2 x)))))) (taylor inf x) (#s(alt (.f64 #s(approx ( (sin (* 1/2 (+ (* 2 x) eps))) (sin (* 1/2 (+ 0 eps)))) (.f64 (sin.f64 (fma.f64 eps #s(literal 1/2 binary64) x)) (sin.f64 (.f64 eps #s(literal 1/2 binary64))))) #s(literal -2 binary64)) (patch (.f64 #s(approx ( (sin (* 1/2 (+ (* 2 x) eps))) (sin (* 1/2 (+ 0 eps)))) (.f64 (sin.f64 (fma.f64 eps #s(literal 1/2 binary64) x)) (sin.f64 (.f64 eps #s(literal 1/2 binary64))))) #s(literal -2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (- eps (* -2 x)))))) (taylor -inf x) (#s(alt (.f64 #s(approx ( (sin (* 1/2 (+ (* 2 x) eps))) (sin (* 1/2 (+ 0 eps)))) (.f64 (sin.f64 (fma.f64 eps #s(literal 1/2 binary64) x)) (sin.f64 (.f64 eps #s(literal 1/2 binary64))))) #s(literal -2 binary64)) (patch (.f64 #s(approx ( (sin (* 1/2 (+ (* 2 x) eps))) (sin (* 1/2 (+ 0 eps)))) (.f64 (sin.f64 (fma.f64 eps #s(literal 1/2 binary64) x)) (sin.f64 (.f64 eps #s(literal 1/2 binary64))))) #s(literal -2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (- eps (* -2 x)))))) (taylor -inf x) (#s(alt (.f64 #s(approx ( (sin (* 1/2 (+ (* 2 x) eps))) (sin (* 1/2 (+ 0 eps)))) (.f64 (sin.f64 (fma.f64 eps #s(literal 1/2 binary64) x)) (sin.f64 (.f64 eps #s(literal 1/2 binary64))))) #s(literal -2 binary64)) (patch (.f64 #s(approx ( (sin (* 1/2 (+ (* 2 x) eps))) (sin (* 1/2 (+ 0 eps)))) (.f64 (sin.f64 (fma.f64 eps #s(literal 1/2 binary64) x)) (sin.f64 (.f64 eps #s(literal 1/2 binary64))))) #s(literal -2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (- eps (* -2 x)))))) (taylor -inf x) (#s(alt (.f64 #s(approx ( (sin (* 1/2 (+ (* 2 x) eps))) (sin (* 1/2 (+ 0 eps)))) (.f64 (sin.f64 (fma.f64 eps #s(literal 1/2 binary64) x)) (sin.f64 (.f64 eps #s(literal 1/2 binary64))))) #s(literal -2 binary64)) (patch (.f64 #s(approx ( (sin (* 1/2 (+ (* 2 x) eps))) (sin (* 1/2 (+ 0 eps)))) (.f64 (sin.f64 (fma.f64 eps #s(literal 1/2 binary64) x)) (sin.f64 (.f64 eps #s(literal 1/2 binary64))))) #s(literal -2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (- eps (* -2 x)))))) (taylor -inf x) (#s(alt (.f64 #s(approx ( (sin (* 1/2 (+ (* 2 x) eps))) (sin (* 1/2 (+ 0 eps)))) (.f64 (sin.f64 (fma.f64 eps #s(literal 1/2 binary64) x)) (sin.f64 (.f64 eps #s(literal 1/2 binary64))))) #s(literal -2 binary64)) (patch (.f64 #s(approx ( (sin (* 1/2 (+ (* 2 x) eps))) (sin (* 1/2 (+ 0 eps)))) (.f64 (sin.f64 (fma.f64 eps #s(literal 1/2 binary64) x)) (sin.f64 (.f64 eps #s(literal 1/2 binary64))))) #s(literal -2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* eps (sin x))) (taylor 0 eps) (#s(alt (.f64 #s(approx ( (sin (* 1/2 (+ (* 2 x) eps))) (sin (* 1/2 (+ 0 eps)))) (.f64 (sin.f64 (fma.f64 eps #s(literal 1/2 binary64) x)) (sin.f64 (.f64 eps #s(literal 1/2 binary64))))) #s(literal -2 binary64)) (patch (.f64 #s(approx ( (sin (* 1/2 (+ (* 2 x) eps))) (sin (* 1/2 (+ 0 eps)))) (.f64 (sin.f64 (fma.f64 eps #s(literal 1/2 binary64) x)) (sin.f64 (.f64 eps #s(literal 1/2 binary64))))) #s(literal -2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* eps (+ (* -1 (sin x)) (* -1/2 (* eps (cos x))))) (taylor 0 eps) (#s(alt (.f64 #s(approx ( (sin (* 1/2 (+ (* 2 x) eps))) (sin (* 1/2 (+ 0 eps)))) (.f64 (sin.f64 (fma.f64 eps #s(literal 1/2 binary64) x)) (sin.f64 (.f64 eps #s(literal 1/2 binary64))))) #s(literal -2 binary64)) (patch (.f64 #s(approx ( (sin (* 1/2 (+ (* 2 x) eps))) (sin (* 1/2 (+ 0 eps)))) (.f64 (sin.f64 (fma.f64 eps #s(literal 1/2 binary64) x)) (sin.f64 (.f64 eps #s(literal 1/2 binary64))))) #s(literal -2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* eps (+ (* -1 (sin x)) (* eps (+ (* -2 (* eps (+ (* -1/16 (sin x)) (* -1/48 (sin x))))) (* -1/2 (cos x)))))) (taylor 0 eps) (#s(alt (.f64 #s(approx ( (sin (* 1/2 (+ (* 2 x) eps))) (sin (* 1/2 (+ 0 eps)))) (.f64 (sin.f64 (fma.f64 eps #s(literal 1/2 binary64) x)) (sin.f64 (.f64 eps #s(literal 1/2 binary64))))) #s(literal -2 binary64)) (patch (.f64 #s(approx ( (sin (* 1/2 (+ (* 2 x) eps))) (sin (* 1/2 (+ 0 eps)))) (.f64 (sin.f64 (fma.f64 eps #s(literal 1/2 binary64) x)) (sin.f64 (.f64 eps #s(literal 1/2 binary64))))) #s(literal -2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* eps (+ (* -1 (sin x)) (* eps (+ (* -1/2 (cos x)) (* eps (+ (* -2 (+ (* -1/16 (sin x)) (* -1/48 (sin x)))) (* 1/24 (* eps (cos x))))))))) (taylor 0 eps) (#s(alt (.f64 #s(approx ( (sin (* 1/2 (+ (* 2 x) eps))) (sin (* 1/2 (+ 0 eps)))) (.f64 (sin.f64 (fma.f64 eps #s(literal 1/2 binary64) x)) (sin.f64 (.f64 eps #s(literal 1/2 binary64))))) #s(literal -2 binary64)) (patch (.f64 #s(approx ( (sin (* 1/2 (+ (* 2 x) eps))) (sin (* 1/2 (+ 0 eps)))) (.f64 (sin.f64 (fma.f64 eps #s(literal 1/2 binary64) x)) (sin.f64 (.f64 eps #s(literal 1/2 binary64))))) #s(literal -2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (+ eps (* 2 x)))))) (taylor inf eps) (#s(alt (.f64 #s(approx ( (sin (* 1/2 (+ (* 2 x) eps))) (sin (* 1/2 (+ 0 eps)))) (.f64 (sin.f64 (fma.f64 eps #s(literal 1/2 binary64) x)) (sin.f64 (.f64 eps #s(literal 1/2 binary64))))) #s(literal -2 binary64)) (patch (.f64 #s(approx ( (sin (* 1/2 (+ (* 2 x) eps))) (sin (* 1/2 (+ 0 eps)))) (.f64 (sin.f64 (fma.f64 eps #s(literal 1/2 binary64) x)) (sin.f64 (.f64 eps #s(literal 1/2 binary64))))) #s(literal -2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (+ eps (* 2 x)))))) (taylor inf eps) (#s(alt (.f64 #s(approx ( (sin (* 1/2 (+ (* 2 x) eps))) (sin (* 1/2 (+ 0 eps)))) (.f64 (sin.f64 (fma.f64 eps #s(literal 1/2 binary64) x)) (sin.f64 (.f64 eps #s(literal 1/2 binary64))))) #s(literal -2 binary64)) (patch (.f64 #s(approx ( (sin (* 1/2 (+ (* 2 x) eps))) (sin (* 1/2 (+ 0 eps)))) (.f64 (sin.f64 (fma.f64 eps #s(literal 1/2 binary64) x)) (sin.f64 (.f64 eps #s(literal 1/2 binary64))))) #s(literal -2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (+ eps (* 2 x)))))) (taylor inf eps) (#s(alt (.f64 #s(approx ( (sin (* 1/2 (+ (* 2 x) eps))) (sin (* 1/2 (+ 0 eps)))) (.f64 (sin.f64 (fma.f64 eps #s(literal 1/2 binary64) x)) (sin.f64 (.f64 eps #s(literal 1/2 binary64))))) #s(literal -2 binary64)) (patch (.f64 #s(approx ( (sin (* 1/2 (+ (* 2 x) eps))) (sin (* 1/2 (+ 0 eps)))) (.f64 (sin.f64 (fma.f64 eps #s(literal 1/2 binary64) x)) (sin.f64 (.f64 eps #s(literal 1/2 binary64))))) #s(literal -2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (+ eps (* 2 x)))))) (taylor inf eps) (#s(alt (.f64 #s(approx ( (sin (* 1/2 (+ (* 2 x) eps))) (sin (* 1/2 (+ 0 eps)))) (.f64 (sin.f64 (fma.f64 eps #s(literal 1/2 binary64) x)) (sin.f64 (.f64 eps #s(literal 1/2 binary64))))) #s(literal -2 binary64)) (patch (.f64 #s(approx ( (sin (* 1/2 (+ (* 2 x) eps))) (sin (* 1/2 (+ 0 eps)))) (.f64 (sin.f64 (fma.f64 eps #s(literal 1/2 binary64) x)) (sin.f64 (.f64 eps #s(literal 1/2 binary64))))) #s(literal -2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (- (* 2 x) (* -1 eps)))))) (taylor -inf eps) (#s(alt (.f64 #s(approx ( (sin (* 1/2 (+ (* 2 x) eps))) (sin (* 1/2 (+ 0 eps)))) (.f64 (sin.f64 (fma.f64 eps #s(literal 1/2 binary64) x)) (sin.f64 (.f64 eps #s(literal 1/2 binary64))))) #s(literal -2 binary64)) (patch (.f64 #s(approx ( (sin (* 1/2 (+ (* 2 x) eps))) (sin (* 1/2 (+ 0 eps)))) (.f64 (sin.f64 (fma.f64 eps #s(literal 1/2 binary64) x)) (sin.f64 (.f64 eps #s(literal 1/2 binary64))))) #s(literal -2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (- (* 2 x) (* -1 eps)))))) (taylor -inf eps) (#s(alt (.f64 #s(approx ( (sin (* 1/2 (+ (* 2 x) eps))) (sin (* 1/2 (+ 0 eps)))) (.f64 (sin.f64 (fma.f64 eps #s(literal 1/2 binary64) x)) (sin.f64 (.f64 eps #s(literal 1/2 binary64))))) #s(literal -2 binary64)) (patch (.f64 #s(approx ( (sin (* 1/2 (+ (* 2 x) eps))) (sin (* 1/2 (+ 0 eps)))) (.f64 (sin.f64 (fma.f64 eps #s(literal 1/2 binary64) x)) (sin.f64 (.f64 eps #s(literal 1/2 binary64))))) #s(literal -2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (- (* 2 x) (* -1 eps)))))) (taylor -inf eps) (#s(alt (.f64 #s(approx ( (sin (* 1/2 (+ (* 2 x) eps))) (sin (* 1/2 (+ 0 eps)))) (.f64 (sin.f64 (fma.f64 eps #s(literal 1/2 binary64) x)) (sin.f64 (.f64 eps #s(literal 1/2 binary64))))) #s(literal -2 binary64)) (patch (.f64 #s(approx ( (sin (* 1/2 (+ (* 2 x) eps))) (sin (* 1/2 (+ 0 eps)))) (.f64 (sin.f64 (fma.f64 eps #s(literal 1/2 binary64) x)) (sin.f64 (.f64 eps #s(literal 1/2 binary64))))) #s(literal -2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (- (* 2 x) (* -1 eps)))))) (taylor -inf eps) (#s(alt (.f64 #s(approx ( (sin (* 1/2 (+ (* 2 x) eps))) (sin (* 1/2 (+ 0 eps)))) (.f64 (sin.f64 (fma.f64 eps #s(literal 1/2 binary64) x)) (sin.f64 (.f64 eps #s(literal 1/2 binary64))))) #s(literal -2 binary64)) (patch (.f64 #s(approx ( (sin (* 1/2 (+ (* 2 x) eps))) (sin (* 1/2 (+ 0 eps)))) (.f64 (sin.f64 (fma.f64 eps #s(literal 1/2 binary64) x)) (sin.f64 (.f64 eps #s(literal 1/2 binary64))))) #s(literal -2 binary64)) #<representation binary64>) () ())) ())
#s(alt (pow (sin (* 1/2 eps)) 2) (taylor 0 x) (#s(alt #s(approx (* (sin (* 1/2 (+ (* 2 x) eps))) (sin (* 1/2 (+ 0 eps)))) (.f64 (sin.f64 (fma.f64 eps #s(literal 1/2 binary64) x)) (sin.f64 (.f64 eps #s(literal 1/2 binary64))))) (patch #s(approx (* (sin (* 1/2 (+ (* 2 x) eps))) (sin (* 1/2 (+ 0 eps)))) (.f64 (sin.f64 (fma.f64 eps #s(literal 1/2 binary64) x)) (sin.f64 (.f64 eps #s(literal 1/2 binary64))))) #<representation binary64>) () ())) ())
#s(alt (+ (* x (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) (pow (sin (* 1/2 eps)) 2)) (taylor 0 x) (#s(alt #s(approx (* (sin (* 1/2 (+ (* 2 x) eps))) (sin (* 1/2 (+ 0 eps)))) (.f64 (sin.f64 (fma.f64 eps #s(literal 1/2 binary64) x)) (sin.f64 (.f64 eps #s(literal 1/2 binary64))))) (patch #s(approx (* (sin (* 1/2 (+ (* 2 x) eps))) (sin (* 1/2 (+ 0 eps)))) (.f64 (sin.f64 (fma.f64 eps #s(literal 1/2 binary64) x)) (sin.f64 (.f64 eps #s(literal 1/2 binary64))))) #<representation binary64>) () ())) ())
#s(alt (+ (* x (+ (* -1/2 (* x (pow (sin (* 1/2 eps)) 2))) (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))) (pow (sin (* 1/2 eps)) 2)) (taylor 0 x) (#s(alt #s(approx (* (sin (* 1/2 (+ (* 2 x) eps))) (sin (* 1/2 (+ 0 eps)))) (.f64 (sin.f64 (fma.f64 eps #s(literal 1/2 binary64) x)) (sin.f64 (.f64 eps #s(literal 1/2 binary64))))) (patch #s(approx (* (sin (* 1/2 (+ (* 2 x) eps))) (sin (* 1/2 (+ 0 eps)))) (.f64 (sin.f64 (fma.f64 eps #s(literal 1/2 binary64) x)) (sin.f64 (.f64 eps #s(literal 1/2 binary64))))) #<representation binary64>) () ())) ())
#s(alt (+ (* x (+ (* x (+ (* -1/2 (pow (sin (* 1/2 eps)) 2)) (* -1/6 (* x (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))))) (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))) (pow (sin (* 1/2 eps)) 2)) (taylor 0 x) (#s(alt #s(approx (* (sin (* 1/2 (+ (* 2 x) eps))) (sin (* 1/2 (+ 0 eps)))) (.f64 (sin.f64 (fma.f64 eps #s(literal 1/2 binary64) x)) (sin.f64 (.f64 eps #s(literal 1/2 binary64))))) (patch #s(approx (* (sin (* 1/2 (+ (* 2 x) eps))) (sin (* 1/2 (+ 0 eps)))) (.f64 (sin.f64 (fma.f64 eps #s(literal 1/2 binary64) x)) (sin.f64 (.f64 eps #s(literal 1/2 binary64))))) #<representation binary64>) () ())) ())
#s(alt (* (sin (* 1/2 eps)) (sin (* 1/2 (+ eps (* 2 x))))) (taylor inf x) (#s(alt #s(approx (* (sin (* 1/2 (+ (* 2 x) eps))) (sin (* 1/2 (+ 0 eps)))) (.f64 (sin.f64 (fma.f64 eps #s(literal 1/2 binary64) x)) (sin.f64 (.f64 eps #s(literal 1/2 binary64))))) (patch #s(approx (* (sin (* 1/2 (+ (* 2 x) eps))) (sin (* 1/2 (+ 0 eps)))) (.f64 (sin.f64 (fma.f64 eps #s(literal 1/2 binary64) x)) (sin.f64 (.f64 eps #s(literal 1/2 binary64))))) #<representation binary64>) () ())) ())
#s(alt (* (sin (* 1/2 eps)) (sin (* 1/2 (+ eps (* 2 x))))) (taylor inf x) (#s(alt #s(approx (* (sin (* 1/2 (+ (* 2 x) eps))) (sin (* 1/2 (+ 0 eps)))) (.f64 (sin.f64 (fma.f64 eps #s(literal 1/2 binary64) x)) (sin.f64 (.f64 eps #s(literal 1/2 binary64))))) (patch #s(approx (* (sin (* 1/2 (+ (* 2 x) eps))) (sin (* 1/2 (+ 0 eps)))) (.f64 (sin.f64 (fma.f64 eps #s(literal 1/2 binary64) x)) (sin.f64 (.f64 eps #s(literal 1/2 binary64))))) #<representation binary64>) () ())) ())
#s(alt (* (sin (* 1/2 eps)) (sin (* 1/2 (+ eps (* 2 x))))) (taylor inf x) (#s(alt #s(approx (* (sin (* 1/2 (+ (* 2 x) eps))) (sin (* 1/2 (+ 0 eps)))) (.f64 (sin.f64 (fma.f64 eps #s(literal 1/2 binary64) x)) (sin.f64 (.f64 eps #s(literal 1/2 binary64))))) (patch #s(approx (* (sin (* 1/2 (+ (* 2 x) eps))) (sin (* 1/2 (+ 0 eps)))) (.f64 (sin.f64 (fma.f64 eps #s(literal 1/2 binary64) x)) (sin.f64 (.f64 eps #s(literal 1/2 binary64))))) #<representation binary64>) () ())) ())
#s(alt (* (sin (* 1/2 eps)) (sin (* 1/2 (+ eps (* 2 x))))) (taylor inf x) (#s(alt #s(approx (* (sin (* 1/2 (+ (* 2 x) eps))) (sin (* 1/2 (+ 0 eps)))) (.f64 (sin.f64 (fma.f64 eps #s(literal 1/2 binary64) x)) (sin.f64 (.f64 eps #s(literal 1/2 binary64))))) (patch #s(approx (* (sin (* 1/2 (+ (* 2 x) eps))) (sin (* 1/2 (+ 0 eps)))) (.f64 (sin.f64 (fma.f64 eps #s(literal 1/2 binary64) x)) (sin.f64 (.f64 eps #s(literal 1/2 binary64))))) #<representation binary64>) () ())) ())
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#s(alt (* 1/2 eps) (taylor 0 eps) (#s(alt #s(approx (sin (* 1/2 (+ 0 eps))) (.f64 (fma.f64 (fma.f64 #s(literal 1/3840 binary64) (.f64 eps eps) #s(literal -1/48 binary64)) (.f64 eps eps) #s(literal 1/2 binary64)) eps)) (patch #s(approx (sin ( 1/2 (+ 0 eps))) (.f64 (fma.f64 (fma.f64 #s(literal 1/3840 binary64) (.f64 eps eps) #s(literal -1/48 binary64)) (*.f64 eps eps) #s(literal 1/2 binary64)) eps)) #<representation binary64>) () ())) ())
#s(alt (* eps (+ 1/2 (* -1/48 (pow eps 2)))) (taylor 0 eps) (#s(alt #s(approx (sin (* 1/2 (+ 0 eps))) (.f64 (fma.f64 (fma.f64 #s(literal 1/3840 binary64) (.f64 eps eps) #s(literal -1/48 binary64)) (.f64 eps eps) #s(literal 1/2 binary64)) eps)) (patch #s(approx (sin ( 1/2 (+ 0 eps))) (.f64 (fma.f64 (fma.f64 #s(literal 1/3840 binary64) (.f64 eps eps) #s(literal -1/48 binary64)) (*.f64 eps eps) #s(literal 1/2 binary64)) eps)) #<representation binary64>) () ())) ())
#s(alt (* eps (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48)))) (taylor 0 eps) (#s(alt #s(approx (sin (* 1/2 (+ 0 eps))) (.f64 (fma.f64 (fma.f64 #s(literal 1/3840 binary64) (.f64 eps eps) #s(literal -1/48 binary64)) (.f64 eps eps) #s(literal 1/2 binary64)) eps)) (patch #s(approx (sin ( 1/2 (+ 0 eps))) (.f64 (fma.f64 (fma.f64 #s(literal 1/3840 binary64) (.f64 eps eps) #s(literal -1/48 binary64)) (*.f64 eps eps) #s(literal 1/2 binary64)) eps)) #<representation binary64>) () ())) ())
#s(alt (* eps (+ 1/2 (* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48)))) (taylor 0 eps) (#s(alt #s(approx (sin (* 1/2 (+ 0 eps))) (.f64 (fma.f64 (fma.f64 #s(literal 1/3840 binary64) (.f64 eps eps) #s(literal -1/48 binary64)) (.f64 eps eps) #s(literal 1/2 binary64)) eps)) (patch #s(approx (sin ( 1/2 (+ 0 eps))) (.f64 (fma.f64 (fma.f64 #s(literal 1/3840 binary64) (.f64 eps eps) #s(literal -1/48 binary64)) (*.f64 eps eps) #s(literal 1/2 binary64)) eps)) #<representation binary64>) () ())) ())
#s(alt (sin (* 1/2 eps)) (taylor inf eps) (#s(alt #s(approx (sin (* 1/2 (+ 0 eps))) (.f64 (fma.f64 (fma.f64 #s(literal 1/3840 binary64) (.f64 eps eps) #s(literal -1/48 binary64)) (.f64 eps eps) #s(literal 1/2 binary64)) eps)) (patch #s(approx (sin ( 1/2 (+ 0 eps))) (.f64 (fma.f64 (fma.f64 #s(literal 1/3840 binary64) (.f64 eps eps) #s(literal -1/48 binary64)) (*.f64 eps eps) #s(literal 1/2 binary64)) eps)) #<representation binary64>) () ())) ())
#s(alt (sin (* 1/2 eps)) (taylor inf eps) (#s(alt #s(approx (sin (* 1/2 (+ 0 eps))) (.f64 (fma.f64 (fma.f64 #s(literal 1/3840 binary64) (.f64 eps eps) #s(literal -1/48 binary64)) (.f64 eps eps) #s(literal 1/2 binary64)) eps)) (patch #s(approx (sin ( 1/2 (+ 0 eps))) (.f64 (fma.f64 (fma.f64 #s(literal 1/3840 binary64) (.f64 eps eps) #s(literal -1/48 binary64)) (*.f64 eps eps) #s(literal 1/2 binary64)) eps)) #<representation binary64>) () ())) ())
#s(alt (sin (* 1/2 eps)) (taylor inf eps) (#s(alt #s(approx (sin (* 1/2 (+ 0 eps))) (.f64 (fma.f64 (fma.f64 #s(literal 1/3840 binary64) (.f64 eps eps) #s(literal -1/48 binary64)) (.f64 eps eps) #s(literal 1/2 binary64)) eps)) (patch #s(approx (sin ( 1/2 (+ 0 eps))) (.f64 (fma.f64 (fma.f64 #s(literal 1/3840 binary64) (.f64 eps eps) #s(literal -1/48 binary64)) (*.f64 eps eps) #s(literal 1/2 binary64)) eps)) #<representation binary64>) () ())) ())
#s(alt (sin (* 1/2 eps)) (taylor inf eps) (#s(alt #s(approx (sin (* 1/2 (+ 0 eps))) (.f64 (fma.f64 (fma.f64 #s(literal 1/3840 binary64) (.f64 eps eps) #s(literal -1/48 binary64)) (.f64 eps eps) #s(literal 1/2 binary64)) eps)) (patch #s(approx (sin ( 1/2 (+ 0 eps))) (.f64 (fma.f64 (fma.f64 #s(literal 1/3840 binary64) (.f64 eps eps) #s(literal -1/48 binary64)) (*.f64 eps eps) #s(literal 1/2 binary64)) eps)) #<representation binary64>) () ())) ())
#s(alt (sin (* 1/2 eps)) (taylor -inf eps) (#s(alt #s(approx (sin (* 1/2 (+ 0 eps))) (.f64 (fma.f64 (fma.f64 #s(literal 1/3840 binary64) (.f64 eps eps) #s(literal -1/48 binary64)) (.f64 eps eps) #s(literal 1/2 binary64)) eps)) (patch #s(approx (sin ( 1/2 (+ 0 eps))) (.f64 (fma.f64 (fma.f64 #s(literal 1/3840 binary64) (.f64 eps eps) #s(literal -1/48 binary64)) (*.f64 eps eps) #s(literal 1/2 binary64)) eps)) #<representation binary64>) () ())) ())
#s(alt (sin (* 1/2 eps)) (taylor -inf eps) (#s(alt #s(approx (sin (* 1/2 (+ 0 eps))) (.f64 (fma.f64 (fma.f64 #s(literal 1/3840 binary64) (.f64 eps eps) #s(literal -1/48 binary64)) (.f64 eps eps) #s(literal 1/2 binary64)) eps)) (patch #s(approx (sin ( 1/2 (+ 0 eps))) (.f64 (fma.f64 (fma.f64 #s(literal 1/3840 binary64) (.f64 eps eps) #s(literal -1/48 binary64)) (*.f64 eps eps) #s(literal 1/2 binary64)) eps)) #<representation binary64>) () ())) ())
#s(alt (sin (* 1/2 eps)) (taylor -inf eps) (#s(alt #s(approx (sin (* 1/2 (+ 0 eps))) (.f64 (fma.f64 (fma.f64 #s(literal 1/3840 binary64) (.f64 eps eps) #s(literal -1/48 binary64)) (.f64 eps eps) #s(literal 1/2 binary64)) eps)) (patch #s(approx (sin ( 1/2 (+ 0 eps))) (.f64 (fma.f64 (fma.f64 #s(literal 1/3840 binary64) (.f64 eps eps) #s(literal -1/48 binary64)) (*.f64 eps eps) #s(literal 1/2 binary64)) eps)) #<representation binary64>) () ())) ())
#s(alt (sin (* 1/2 eps)) (taylor -inf eps) (#s(alt #s(approx (sin (* 1/2 (+ 0 eps))) (.f64 (fma.f64 (fma.f64 #s(literal 1/3840 binary64) (.f64 eps eps) #s(literal -1/48 binary64)) (.f64 eps eps) #s(literal 1/2 binary64)) eps)) (patch #s(approx (sin ( 1/2 (+ 0 eps))) (.f64 (fma.f64 (fma.f64 #s(literal 1/3840 binary64) (.f64 eps eps) #s(literal -1/48 binary64)) (*.f64 eps eps) #s(literal 1/2 binary64)) eps)) #<representation binary64>) () ())) ())
#s(alt (/ 1 (pow eps 2)) (taylor 0 eps) (#s(alt (/.f64 #s(literal 1 binary64) (.f64 eps eps)) (patch (/.f64 #s(literal 1 binary64) (.f64 eps eps)) #<representation binary64>) () ())) ())
#s(alt (/ 1 (pow eps 2)) (taylor 0 eps) (#s(alt (/.f64 #s(literal 1 binary64) (.f64 eps eps)) (patch (/.f64 #s(literal 1 binary64) (.f64 eps eps)) #<representation binary64>) () ())) ())
#s(alt (/ 1 (pow eps 2)) (taylor 0 eps) (#s(alt (/.f64 #s(literal 1 binary64) (.f64 eps eps)) (patch (/.f64 #s(literal 1 binary64) (.f64 eps eps)) #<representation binary64>) () ())) ())
#s(alt (/ 1 (pow eps 2)) (taylor 0 eps) (#s(alt (/.f64 #s(literal 1 binary64) (.f64 eps eps)) (patch (/.f64 #s(literal 1 binary64) (.f64 eps eps)) #<representation binary64>) () ())) ())
#s(alt (/ 1 (pow eps 2)) (taylor inf eps) (#s(alt (/.f64 #s(literal 1 binary64) (.f64 eps eps)) (patch (/.f64 #s(literal 1 binary64) (.f64 eps eps)) #<representation binary64>) () ())) ())
#s(alt (/ 1 (pow eps 2)) (taylor inf eps) (#s(alt (/.f64 #s(literal 1 binary64) (.f64 eps eps)) (patch (/.f64 #s(literal 1 binary64) (.f64 eps eps)) #<representation binary64>) () ())) ())
#s(alt (/ 1 (pow eps 2)) (taylor inf eps) (#s(alt (/.f64 #s(literal 1 binary64) (.f64 eps eps)) (patch (/.f64 #s(literal 1 binary64) (.f64 eps eps)) #<representation binary64>) () ())) ())
#s(alt (/ 1 (pow eps 2)) (taylor inf eps) (#s(alt (/.f64 #s(literal 1 binary64) (.f64 eps eps)) (patch (/.f64 #s(literal 1 binary64) (.f64 eps eps)) #<representation binary64>) () ())) ())
#s(alt (/ 1 (pow eps 2)) (taylor -inf eps) (#s(alt (/.f64 #s(literal 1 binary64) (.f64 eps eps)) (patch (/.f64 #s(literal 1 binary64) (.f64 eps eps)) #<representation binary64>) () ())) ())
#s(alt (/ 1 (pow eps 2)) (taylor -inf eps) (#s(alt (/.f64 #s(literal 1 binary64) (.f64 eps eps)) (patch (/.f64 #s(literal 1 binary64) (.f64 eps eps)) #<representation binary64>) () ())) ())
#s(alt (/ 1 (pow eps 2)) (taylor -inf eps) (#s(alt (/.f64 #s(literal 1 binary64) (.f64 eps eps)) (patch (/.f64 #s(literal 1 binary64) (.f64 eps eps)) #<representation binary64>) () ())) ())
#s(alt (/ 1 (pow eps 2)) (taylor -inf eps) (#s(alt (/.f64 #s(literal 1 binary64) (.f64 eps eps)) (patch (/.f64 #s(literal 1 binary64) (.f64 eps eps)) #<representation binary64>) () ())) ())
#s(alt (pow eps 3) (taylor 0 eps) (#s(alt (.f64 (.f64 eps eps) eps) (patch (.f64 (.f64 eps eps) eps) #<representation binary64>) () ())) ())
#s(alt (pow eps 3) (taylor 0 eps) (#s(alt (.f64 (.f64 eps eps) eps) (patch (.f64 (.f64 eps eps) eps) #<representation binary64>) () ())) ())
#s(alt (pow eps 3) (taylor 0 eps) (#s(alt (.f64 (.f64 eps eps) eps) (patch (.f64 (.f64 eps eps) eps) #<representation binary64>) () ())) ())
#s(alt (pow eps 3) (taylor 0 eps) (#s(alt (.f64 (.f64 eps eps) eps) (patch (.f64 (.f64 eps eps) eps) #<representation binary64>) () ())) ())
#s(alt (pow eps 3) (taylor inf eps) (#s(alt (.f64 (.f64 eps eps) eps) (patch (.f64 (.f64 eps eps) eps) #<representation binary64>) () ())) ())
#s(alt (pow eps 3) (taylor inf eps) (#s(alt (.f64 (.f64 eps eps) eps) (patch (.f64 (.f64 eps eps) eps) #<representation binary64>) () ())) ())
#s(alt (pow eps 3) (taylor inf eps) (#s(alt (.f64 (.f64 eps eps) eps) (patch (.f64 (.f64 eps eps) eps) #<representation binary64>) () ())) ())
#s(alt (pow eps 3) (taylor inf eps) (#s(alt (.f64 (.f64 eps eps) eps) (patch (.f64 (.f64 eps eps) eps) #<representation binary64>) () ())) ())
#s(alt (pow eps 3) (taylor -inf eps) (#s(alt (.f64 (.f64 eps eps) eps) (patch (.f64 (.f64 eps eps) eps) #<representation binary64>) () ())) ())
#s(alt (pow eps 3) (taylor -inf eps) (#s(alt (.f64 (.f64 eps eps) eps) (patch (.f64 (.f64 eps eps) eps) #<representation binary64>) () ())) ())
#s(alt (pow eps 3) (taylor -inf eps) (#s(alt (.f64 (.f64 eps eps) eps) (patch (.f64 (.f64 eps eps) eps) #<representation binary64>) () ())) ())
#s(alt (pow eps 3) (taylor -inf eps) (#s(alt (.f64 (.f64 eps eps) eps) (patch (.f64 (.f64 eps eps) eps) #<representation binary64>) () ())) ())

Calls

117 calls:

Time	Variable		Point	Expression
2.0ms	x	@	inf	(* (sin (+ (* eps 1/2) x)) (sin (* eps 1/2)))
1.0ms	eps	@	0	(+ (* (* eps (+ (* (* x x) 1/5040) -1/120)) (* x x)) (* 1/6 eps))
1.0ms	eps	@	inf	(+ (* (* eps (+ (* (* x x) 1/5040) -1/120)) (* x x)) (* 1/6 eps))
0.0ms	x	@	inf	(+ (* (* eps (+ (* (* x x) 1/5040) -1/120)) (* x x)) (* 1/6 eps))
0.0ms	eps	@	-inf	(+ (* (+ (* (* eps (+ (* (* x x) 1/5040) -1/120)) (* x x)) (* 1/6 eps)) (* x x)) (neg eps))

simplify297.0ms (1.6%)

Memory

-5.0MiB live, 188.2MiB allocated

Algorithm

1×	egg-herbie

Rules

13 924×	`lower-fma.f64`
13 924×	`lower-fma.f32`
5 930×	`lower-*.f64`
5 930×	`lower-*.f32`
3 698×	`lower-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	322	5313
1	975	5025
2	2606	4899
3	6333	4881
0	8266	4487

Stop Event

1×	iter limit
1×	node limit

Counts

468 → 453

Calls

Call 1

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

Outputs
(* -2 (pow (sin (* 1/2 eps)) 2))
(.f64 (pow.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) #s(literal 2 binary64)) #s(literal -2 binary64))
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(.f64 (fma.f64 (.f64 eps eps) #s(literal -1/48 binary64) #s(literal 1/2 binary64)) eps)
(* eps (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48))))
(.f64 (fma.f64 (fma.f64 #s(literal 1/3840 binary64) (.f64 eps eps) #s(literal -1/48 binary64)) (*.f64 eps eps) #s(literal 1/2 binary64)) eps)
(* eps (+ 1/2 (* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48))))
(.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -1/645120 binary64) (.f64 eps eps) #s(literal 1/3840 binary64)) (.f64 eps eps) #s(literal -1/48 binary64)) (.f64 eps eps) #s(literal 1/2 binary64)) eps)
(sin (* 1/2 eps))
(sin.f64 (*.f64 eps #s(literal 1/2 binary64)))
(sin (* 1/2 eps))
(sin.f64 (*.f64 eps #s(literal 1/2 binary64)))
(sin (* 1/2 eps))
(sin.f64 (*.f64 eps #s(literal 1/2 binary64)))
(sin (* 1/2 eps))
(sin.f64 (*.f64 eps #s(literal 1/2 binary64)))
(sin (* 1/2 eps))
(sin.f64 (*.f64 eps #s(literal 1/2 binary64)))
(sin (* 1/2 eps))
(sin.f64 (*.f64 eps #s(literal 1/2 binary64)))
(sin (* 1/2 eps))
(sin.f64 (*.f64 eps #s(literal 1/2 binary64)))
(sin (* 1/2 eps))
(sin.f64 (*.f64 eps #s(literal 1/2 binary64)))
(/ 1 (pow eps 2))
(/.f64 #s(literal 1 binary64) (*.f64 eps eps))
(/ 1 (pow eps 2))
(/.f64 #s(literal 1 binary64) (*.f64 eps eps))
(/ 1 (pow eps 2))
(/.f64 #s(literal 1 binary64) (*.f64 eps eps))
(/ 1 (pow eps 2))
(/.f64 #s(literal 1 binary64) (*.f64 eps eps))
(/ 1 (pow eps 2))
(/.f64 #s(literal 1 binary64) (*.f64 eps eps))
(/ 1 (pow eps 2))
(/.f64 #s(literal 1 binary64) (*.f64 eps eps))
(/ 1 (pow eps 2))
(/.f64 #s(literal 1 binary64) (*.f64 eps eps))
(/ 1 (pow eps 2))
(/.f64 #s(literal 1 binary64) (*.f64 eps eps))
(/ 1 (pow eps 2))
(/.f64 #s(literal 1 binary64) (*.f64 eps eps))
(/ 1 (pow eps 2))
(/.f64 #s(literal 1 binary64) (*.f64 eps eps))
(/ 1 (pow eps 2))
(/.f64 #s(literal 1 binary64) (*.f64 eps eps))
(/ 1 (pow eps 2))
(/.f64 #s(literal 1 binary64) (*.f64 eps eps))
(pow eps 3)
(.f64 (.f64 eps eps) eps)
(pow eps 3)
(.f64 (.f64 eps eps) eps)
(pow eps 3)
(.f64 (.f64 eps eps) eps)
(pow eps 3)
(.f64 (.f64 eps eps) eps)
(pow eps 3)
(.f64 (.f64 eps eps) eps)
(pow eps 3)
(.f64 (.f64 eps eps) eps)
(pow eps 3)
(.f64 (.f64 eps eps) eps)
(pow eps 3)
(.f64 (.f64 eps eps) eps)
(pow eps 3)
(.f64 (.f64 eps eps) eps)
(pow eps 3)
(.f64 (.f64 eps eps) eps)
(pow eps 3)
(.f64 (.f64 eps eps) eps)
(pow eps 3)
(.f64 (.f64 eps eps) eps)

rewrite229.0ms (1.2%)

Memory

8.6MiB live, 314.4MiB allocated

Rules

4 844×	`lower-fma.f32`
4 830×	`lower-fma.f64`
4 730×	`lower-*.f32`
4 696×	`lower-*.f64`
3 426×	`lower-/.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	65	362
0	101	338
1	361	314
2	2904	309
0	10065	305

Stop Event

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

Counts

23 → 493

Calls

Call 1

Inputs
(.f64 #s(approx ( (sin (* 1/2 (+ (* 2 x) eps))) (sin (* 1/2 (+ 0 eps)))) (.f64 (sin.f64 (fma.f64 eps #s(literal 1/2 binary64) x)) (sin.f64 (.f64 eps #s(literal 1/2 binary64))))) #s(literal -2 binary64))
#s(approx (* (sin (* 1/2 (+ (* 2 x) eps))) (sin (* 1/2 (+ 0 eps)))) (.f64 (sin.f64 (fma.f64 eps #s(literal 1/2 binary64) x)) (sin.f64 (.f64 eps #s(literal 1/2 binary64)))))
(.f64 (sin.f64 (fma.f64 eps #s(literal 1/2 binary64) x)) (sin.f64 (.f64 eps #s(literal 1/2 binary64))))
(sin.f64 (fma.f64 eps #s(literal 1/2 binary64) 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))
(fma.f64 (.f64 eps (fma.f64 (.f64 x x) #s(literal 1/5040 binary64) #s(literal -1/120 binary64))) (.f64 x x) (.f64 #s(literal 1/6 binary64) eps))
(fma.f64 (fma.f64 (.f64 eps (fma.f64 (.f64 x x) #s(literal 1/5040 binary64) #s(literal -1/120 binary64))) (.f64 x x) (.f64 #s(literal 1/6 binary64) eps)) (*.f64 x x) (neg.f64 eps))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (.f64 (fma.f64 (fma.f64 (.f64 eps (fma.f64 (.f64 x x) #s(literal 1/5040 binary64) #s(literal -1/120 binary64))) (.f64 x x) (.f64 #s(literal 1/6 binary64) eps)) (.f64 x x) (neg.f64 eps)) x)))
#s(approx (* (neg eps) (sin x)) (.f64 (fma.f64 (fma.f64 (.f64 eps (fma.f64 (.f64 x x) #s(literal 1/5040 binary64) #s(literal -1/120 binary64))) (.f64 x x) (.f64 #s(literal 1/6 binary64) eps)) (.f64 x x) (neg.f64 eps)) x))
(*.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps))
(.f64 (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps))) #s(approx (sin ( 1/2 (+ 0 eps))) (.f64 (fma.f64 (fma.f64 #s(literal 1/3840 binary64) (.f64 eps eps) #s(literal -1/48 binary64)) (*.f64 eps eps) #s(literal 1/2 binary64)) eps))) #s(literal -2 binary64))
(.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps))) #s(approx (sin (* 1/2 (+ 0 eps))) (.f64 (fma.f64 (fma.f64 #s(literal 1/3840 binary64) (.f64 eps eps) #s(literal -1/48 binary64)) (*.f64 eps eps) #s(literal 1/2 binary64)) eps)))
(sin.f64 (*.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps)))
(.f64 (.f64 (.f64 eps eps) eps) (/.f64 #s(literal 1 binary64) (.f64 eps eps)))
(.f64 (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps))) (sin.f64 (.f64 #s(literal 1/2 binary64) (.f64 (.f64 (.f64 eps eps) eps) (/.f64 #s(literal 1 binary64) (.f64 eps eps)))))) #s(literal -2 binary64))
(.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps))) (sin.f64 (.f64 #s(literal 1/2 binary64) (.f64 (.f64 (.f64 eps eps) eps) (/.f64 #s(literal 1 binary64) (*.f64 eps eps))))))
(*.f64 #s(literal 1/6 binary64) eps)
(.f64 eps (fma.f64 (.f64 x x) #s(literal 1/5040 binary64) #s(literal -1/120 binary64)))
#s(approx (sin (* 1/2 (+ 0 eps))) (.f64 (fma.f64 (fma.f64 #s(literal 1/3840 binary64) (.f64 eps eps) #s(literal -1/48 binary64)) (*.f64 eps eps) #s(literal 1/2 binary64)) eps))
(/.f64 #s(literal 1 binary64) (*.f64 eps eps))
(.f64 (.f64 eps eps) eps)

Outputs
(.f64 #s(literal -2 binary64) #s(approx ( (sin (* 1/2 (+ (* 2 x) eps))) (sin (* 1/2 (+ 0 eps)))) (.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (sin.f64 (fma.f64 eps #s(literal 1/2 binary64) x)))))
(.f64 #s(approx ( (sin (* 1/2 (+ (* 2 x) eps))) (sin (* 1/2 (+ 0 eps)))) (.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (sin.f64 (fma.f64 eps #s(literal 1/2 binary64) x)))) #s(literal -2 binary64))
#s(approx (* (sin (* 1/2 (+ (* 2 x) eps))) (sin (* 1/2 (+ 0 eps)))) (.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (sin.f64 (fma.f64 eps #s(literal 1/2 binary64) x))))
(*.f64 (-.f64 (cos.f64 (fma.f64 eps #s(literal 1/2 binary64) (fma.f64 eps #s(literal 1/2 binary64) x))) (cos.f64 (fma.f64 eps #s(literal 1/2 binary64) (fma.f64 eps #s(literal 1/2 binary64) x)))) #s(literal 1/2 binary64))
(.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (sin.f64 (fma.f64 eps #s(literal 1/2 binary64) x)))
(.f64 (sin.f64 (fma.f64 eps #s(literal 1/2 binary64) x)) (sin.f64 (.f64 eps #s(literal 1/2 binary64))))
(pow.f64 (/.f64 #s(literal 2 binary64) (-.f64 (cos.f64 (fma.f64 eps #s(literal 1/2 binary64) (fma.f64 eps #s(literal 1/2 binary64) x))) (cos.f64 (fma.f64 eps #s(literal 1/2 binary64) (fma.f64 eps #s(literal 1/2 binary64) x))))) #s(literal -1 binary64))
(/.f64 (-.f64 (.f64 (cos.f64 (fma.f64 eps #s(literal 1/2 binary64) (fma.f64 eps #s(literal 1/2 binary64) x))) #s(literal 2 binary64)) (.f64 #s(literal 2 binary64) (cos.f64 (fma.f64 eps #s(literal 1/2 binary64) (fma.f64 eps #s(literal 1/2 binary64) x))))) #s(literal 4 binary64))
(/.f64 (neg.f64 (-.f64 (cos.f64 (fma.f64 eps #s(literal 1/2 binary64) (fma.f64 eps #s(literal 1/2 binary64) x))) (cos.f64 (fma.f64 eps #s(literal 1/2 binary64) (fma.f64 eps #s(literal 1/2 binary64) x))))) #s(literal -2 binary64))
(/.f64 (-.f64 (cos.f64 (-.f64 (*.f64 eps #s(literal 1/2 binary64)) (fma.f64 eps #s(literal 1/2 binary64) x))) (cos.f64 (fma.f64 eps #s(literal 1/2 binary64) (fma.f64 eps #s(literal 1/2 binary64) x)))) #s(literal 2 binary64))
(/.f64 (-.f64 (cos.f64 (fma.f64 eps #s(literal 1/2 binary64) (fma.f64 eps #s(literal 1/2 binary64) x))) (cos.f64 (fma.f64 eps #s(literal 1/2 binary64) (fma.f64 eps #s(literal 1/2 binary64) x)))) #s(literal 2 binary64))
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 2 binary64) (-.f64 (cos.f64 (fma.f64 eps #s(literal 1/2 binary64) (fma.f64 eps #s(literal 1/2 binary64) x))) (cos.f64 (fma.f64 eps #s(literal 1/2 binary64) (fma.f64 eps #s(literal 1/2 binary64) x))))))
(fma.f64 (.f64 (cos.f64 x) (sin.f64 (.f64 eps #s(literal 1/2 binary64)))) (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (.f64 (.f64 (cos.f64 (.f64 eps #s(literal 1/2 binary64))) (sin.f64 x)) (sin.f64 (*.f64 eps #s(literal 1/2 binary64)))))
(fma.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (.f64 (cos.f64 x) (sin.f64 (.f64 eps #s(literal 1/2 binary64)))) (.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (.f64 (cos.f64 (*.f64 eps #s(literal 1/2 binary64))) (sin.f64 x))))
(-.f64 (/.f64 (cos.f64 (fma.f64 eps #s(literal 1/2 binary64) (fma.f64 eps #s(literal 1/2 binary64) x))) #s(literal 2 binary64)) (/.f64 (cos.f64 (fma.f64 eps #s(literal 1/2 binary64) (fma.f64 eps #s(literal 1/2 binary64) x))) #s(literal 2 binary64)))
(+.f64 (.f64 (.f64 (cos.f64 x) (sin.f64 (.f64 eps #s(literal 1/2 binary64)))) (sin.f64 (.f64 eps #s(literal 1/2 binary64)))) (.f64 (.f64 (cos.f64 (.f64 eps #s(literal 1/2 binary64))) (sin.f64 x)) (sin.f64 (.f64 eps #s(literal 1/2 binary64)))))
(+.f64 (.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (.f64 (cos.f64 x) (sin.f64 (.f64 eps #s(literal 1/2 binary64))))) (.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (.f64 (cos.f64 (.f64 eps #s(literal 1/2 binary64))) (sin.f64 x))))
(/.f64 (-.f64 (pow.f64 (.f64 (cos.f64 x) (sin.f64 (.f64 eps #s(literal 1/2 binary64)))) #s(literal 2 binary64)) (pow.f64 (.f64 (cos.f64 (.f64 eps #s(literal 1/2 binary64))) (sin.f64 x)) #s(literal 2 binary64))) (sin.f64 (-.f64 (*.f64 eps #s(literal 1/2 binary64)) x)))
(/.f64 (+.f64 (pow.f64 (.f64 (cos.f64 x) (sin.f64 (.f64 eps #s(literal 1/2 binary64)))) #s(literal 3 binary64)) (pow.f64 (.f64 (cos.f64 (.f64 eps #s(literal 1/2 binary64))) (sin.f64 x)) #s(literal 3 binary64))) (+.f64 (pow.f64 (.f64 (cos.f64 x) (sin.f64 (.f64 eps #s(literal 1/2 binary64)))) #s(literal 2 binary64)) (-.f64 (pow.f64 (.f64 (cos.f64 (.f64 eps #s(literal 1/2 binary64))) (sin.f64 x)) #s(literal 2 binary64)) (.f64 (.f64 (cos.f64 x) (sin.f64 (.f64 eps #s(literal 1/2 binary64)))) (.f64 (cos.f64 (*.f64 eps #s(literal 1/2 binary64))) (sin.f64 x))))))
(fma.f64 (sin.f64 (+.f64 x #s(literal 0 binary64))) (cos.f64 (.f64 eps #s(literal 1/2 binary64))) (.f64 (cos.f64 (+.f64 x #s(literal 0 binary64))) (sin.f64 (*.f64 eps #s(literal 1/2 binary64)))))
(fma.f64 (cos.f64 (.f64 eps #s(literal 1/2 binary64))) (sin.f64 x) (.f64 (cos.f64 x) (sin.f64 (*.f64 eps #s(literal 1/2 binary64)))))
(fma.f64 (sin.f64 x) (cos.f64 (.f64 eps #s(literal 1/2 binary64))) (.f64 (cos.f64 x) (sin.f64 (*.f64 eps #s(literal 1/2 binary64)))))
(fma.f64 (cos.f64 x) (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (.f64 (cos.f64 (*.f64 eps #s(literal 1/2 binary64))) (sin.f64 x)))
(fma.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (cos.f64 x) (.f64 (cos.f64 (*.f64 eps #s(literal 1/2 binary64))) (sin.f64 x)))
(fma.f64 #s(literal 0 binary64) (cos.f64 (fma.f64 eps #s(literal 1/2 binary64) x)) (*.f64 #s(literal 1 binary64) (sin.f64 (fma.f64 eps #s(literal 1/2 binary64) x))))
(sin.f64 (fma.f64 eps #s(literal 1/2 binary64) x))
(-.f64 (.f64 (sin.f64 (/.f64 (.f64 #s(literal 1/4 binary64) (.f64 eps eps)) (-.f64 (.f64 eps #s(literal 1/2 binary64)) x))) (cos.f64 (/.f64 (.f64 x x) (-.f64 (.f64 eps #s(literal 1/2 binary64)) x)))) (.f64 (cos.f64 (/.f64 (.f64 #s(literal 1/4 binary64) (.f64 eps eps)) (-.f64 (.f64 eps #s(literal 1/2 binary64)) x))) (sin.f64 (/.f64 (.f64 x x) (-.f64 (.f64 eps #s(literal 1/2 binary64)) x)))))
(+.f64 (.f64 (sin.f64 (+.f64 x #s(literal 0 binary64))) (cos.f64 (.f64 eps #s(literal 1/2 binary64)))) (.f64 (cos.f64 (+.f64 x #s(literal 0 binary64))) (sin.f64 (.f64 eps #s(literal 1/2 binary64)))))
(+.f64 (.f64 #s(literal 0 binary64) (cos.f64 (fma.f64 eps #s(literal 1/2 binary64) x))) (.f64 #s(literal 1 binary64) (sin.f64 (fma.f64 eps #s(literal 1/2 binary64) x))))
(+.f64 (.f64 (cos.f64 (.f64 eps #s(literal 1/2 binary64))) (sin.f64 x)) (.f64 (cos.f64 x) (sin.f64 (.f64 eps #s(literal 1/2 binary64)))))
(+.f64 (.f64 (cos.f64 x) (sin.f64 (.f64 eps #s(literal 1/2 binary64)))) (.f64 (cos.f64 (.f64 eps #s(literal 1/2 binary64))) (sin.f64 x)))
#s(approx (- (cos (+ x eps)) (cos x)) (-.f64 #s(approx (cos eps) #s(literal 1 binary64)) #s(literal 1 binary64)))
(*.f64 (fma.f64 #s(approx (cos eps) #s(literal 1 binary64)) #s(approx (cos eps) #s(literal 1 binary64)) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (+.f64 #s(approx (cos eps) #s(literal 1 binary64)) #s(literal 1 binary64))))
(.f64 (fma.f64 (.f64 #s(approx (cos eps) #s(literal 1 binary64)) #s(approx (cos eps) #s(literal 1 binary64))) #s(approx (cos eps) #s(literal 1 binary64)) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (fma.f64 #s(approx (cos eps) #s(literal 1 binary64)) #s(approx (cos eps) #s(literal 1 binary64)) (+.f64 #s(approx (cos eps) #s(literal 1 binary64)) #s(literal 1 binary64)))))
(pow.f64 (/.f64 (+.f64 #s(approx (cos eps) #s(literal 1 binary64)) #s(literal 1 binary64)) (fma.f64 #s(approx (cos eps) #s(literal 1 binary64)) #s(approx (cos eps) #s(literal 1 binary64)) #s(literal -1 binary64))) #s(literal -1 binary64))
(pow.f64 (/.f64 (fma.f64 #s(approx (cos eps) #s(literal 1 binary64)) #s(approx (cos eps) #s(literal 1 binary64)) (+.f64 #s(approx (cos eps) #s(literal 1 binary64)) #s(literal 1 binary64))) (fma.f64 (*.f64 #s(approx (cos eps) #s(literal 1 binary64)) #s(approx (cos eps) #s(literal 1 binary64))) #s(approx (cos eps) #s(literal 1 binary64)) #s(literal -1 binary64))) #s(literal -1 binary64))
(/.f64 (-.f64 (.f64 (.f64 #s(approx (cos eps) #s(literal 1 binary64)) #s(approx (cos eps) #s(literal 1 binary64))) (+.f64 #s(approx (cos eps) #s(literal 1 binary64)) #s(literal 1 binary64))) (+.f64 #s(approx (cos eps) #s(literal 1 binary64)) #s(literal 1 binary64))) (*.f64 (+.f64 #s(approx (cos eps) #s(literal 1 binary64)) #s(literal 1 binary64)) (+.f64 #s(approx (cos eps) #s(literal 1 binary64)) #s(literal 1 binary64))))
(/.f64 (-.f64 (.f64 (.f64 (.f64 #s(approx (cos eps) #s(literal 1 binary64)) #s(approx (cos eps) #s(literal 1 binary64))) #s(approx (cos eps) #s(literal 1 binary64))) (fma.f64 #s(approx (cos eps) #s(literal 1 binary64)) #s(approx (cos eps) #s(literal 1 binary64)) (+.f64 #s(approx (cos eps) #s(literal 1 binary64)) #s(literal 1 binary64)))) (.f64 (fma.f64 #s(approx (cos eps) #s(literal 1 binary64)) #s(approx (cos eps) #s(literal 1 binary64)) (+.f64 #s(approx (cos eps) #s(literal 1 binary64)) #s(literal 1 binary64))) #s(literal 1 binary64))) (*.f64 (fma.f64 #s(approx (cos eps) #s(literal 1 binary64)) #s(approx (cos eps) #s(literal 1 binary64)) (+.f64 #s(approx (cos eps) #s(literal 1 binary64)) #s(literal 1 binary64))) (fma.f64 #s(approx (cos eps) #s(literal 1 binary64)) #s(approx (cos eps) #s(literal 1 binary64)) (+.f64 #s(approx (cos eps) #s(literal 1 binary64)) #s(literal 1 binary64)))))
(/.f64 (neg.f64 (fma.f64 #s(approx (cos eps) #s(literal 1 binary64)) #s(approx (cos eps) #s(literal 1 binary64)) #s(literal -1 binary64))) (neg.f64 (+.f64 #s(approx (cos eps) #s(literal 1 binary64)) #s(literal 1 binary64))))
(/.f64 (neg.f64 (fma.f64 (*.f64 #s(approx (cos eps) #s(literal 1 binary64)) #s(approx (cos eps) #s(literal 1 binary64))) #s(approx (cos eps) #s(literal 1 binary64)) #s(literal -1 binary64))) (neg.f64 (fma.f64 #s(approx (cos eps) #s(literal 1 binary64)) #s(approx (cos eps) #s(literal 1 binary64)) (+.f64 #s(approx (cos eps) #s(literal 1 binary64)) #s(literal 1 binary64)))))
(/.f64 (fma.f64 #s(approx (cos eps) #s(literal 1 binary64)) #s(approx (cos eps) #s(literal 1 binary64)) #s(literal -1 binary64)) (-.f64 #s(approx (cos eps) #s(literal 1 binary64)) #s(literal -1 binary64)))
(/.f64 (fma.f64 #s(approx (cos eps) #s(literal 1 binary64)) #s(approx (cos eps) #s(literal 1 binary64)) #s(literal -1 binary64)) (+.f64 #s(approx (cos eps) #s(literal 1 binary64)) #s(literal 1 binary64)))
(/.f64 (fma.f64 (.f64 #s(approx (cos eps) #s(literal 1 binary64)) #s(approx (cos eps) #s(literal 1 binary64))) #s(approx (cos eps) #s(literal 1 binary64)) #s(literal -1 binary64)) (fma.f64 #s(approx (cos eps) #s(literal 1 binary64)) #s(approx (cos eps) #s(literal 1 binary64)) (-.f64 #s(literal 1 binary64) (.f64 #s(approx (cos eps) #s(literal 1 binary64)) #s(literal -1 binary64)))))
(/.f64 (fma.f64 (*.f64 #s(approx (cos eps) #s(literal 1 binary64)) #s(approx (cos eps) #s(literal 1 binary64))) #s(approx (cos eps) #s(literal 1 binary64)) #s(literal -1 binary64)) (fma.f64 #s(approx (cos eps) #s(literal 1 binary64)) #s(approx (cos eps) #s(literal 1 binary64)) (+.f64 #s(approx (cos eps) #s(literal 1 binary64)) #s(literal 1 binary64))))
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 #s(approx (cos eps) #s(literal 1 binary64)) #s(literal 1 binary64)) (fma.f64 #s(approx (cos eps) #s(literal 1 binary64)) #s(approx (cos eps) #s(literal 1 binary64)) #s(literal -1 binary64))))
(/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 #s(approx (cos eps) #s(literal 1 binary64)) #s(approx (cos eps) #s(literal 1 binary64)) (+.f64 #s(approx (cos eps) #s(literal 1 binary64)) #s(literal 1 binary64))) (fma.f64 (*.f64 #s(approx (cos eps) #s(literal 1 binary64)) #s(approx (cos eps) #s(literal 1 binary64))) #s(approx (cos eps) #s(literal 1 binary64)) #s(literal -1 binary64))))
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(+.f64 (.f64 (fma.f64 #s(literal 1/5040 binary64) (.f64 x x) #s(literal -1/120 binary64)) eps) (.f64 (fma.f64 #s(literal 1/5040 binary64) (.f64 x x) #s(literal -1/120 binary64)) #s(literal 0 binary64)))
#s(approx (sin (* 1/2 (+ 0 eps))) (.f64 (fma.f64 (fma.f64 (.f64 eps eps) #s(literal 1/3840 binary64) #s(literal -1/48 binary64)) (*.f64 eps eps) #s(literal 1/2 binary64)) eps))
(.f64 (pow.f64 (/.f64 #s(literal -1 binary64) (.f64 eps eps)) #s(literal -2 binary64)) (pow.f64 (.f64 (.f64 eps eps) eps) #s(literal -2 binary64)))
(.f64 (pow.f64 (.f64 (.f64 eps eps) eps) #s(literal -2 binary64)) (pow.f64 (/.f64 #s(literal -1 binary64) (.f64 eps eps)) #s(literal -2 binary64)))
(.f64 (pow.f64 (/.f64 #s(literal -1 binary64) eps) #s(literal -2 binary64)) (pow.f64 (.f64 eps eps) #s(literal -2 binary64)))
(.f64 (pow.f64 (.f64 eps eps) #s(literal -2 binary64)) (pow.f64 (/.f64 #s(literal -1 binary64) eps) #s(literal -2 binary64)))
(.f64 (/.f64 (/.f64 #s(literal -1 binary64) eps) (.f64 eps eps)) eps)
(.f64 (/.f64 (/.f64 #s(literal -1 binary64) eps) (.f64 (.f64 eps eps) eps)) (.f64 eps eps))
(*.f64 (/.f64 #s(literal -1 binary64) eps) (/.f64 #s(literal -1 binary64) eps))
(.f64 #s(literal -1 binary64) (/.f64 #s(literal -1 binary64) (.f64 eps eps)))
(.f64 (/.f64 #s(literal -1 binary64) (.f64 eps eps)) #s(literal 1 binary64))
(.f64 #s(literal 1 binary64) (/.f64 #s(literal -1 binary64) (.f64 eps eps)))
(pow.f64 (.f64 (.f64 (*.f64 eps eps) eps) eps) #s(literal -1/2 binary64))
(pow.f64 (/.f64 #s(literal -1 binary64) eps) #s(literal 2 binary64))
(pow.f64 (*.f64 eps eps) #s(literal -1 binary64))
(pow.f64 eps #s(literal -2 binary64))
(/.f64 (neg.f64 (/.f64 #s(literal -1 binary64) eps)) eps)
(/.f64 (/.f64 #s(literal -1 binary64) eps) eps)
(/.f64 #s(literal -1 binary64) (*.f64 eps eps))
(/.f64 #s(literal 1 binary64) (*.f64 eps eps))
(neg.f64 (/.f64 #s(literal -1 binary64) (*.f64 eps eps)))
(exp.f64 (neg.f64 (*.f64 (log.f64 eps) #s(literal 2 binary64))))
(exp.f64 (*.f64 (log.f64 eps) #s(literal -2 binary64)))
(exp.f64 (.f64 (.f64 (log.f64 eps) #s(literal 2 binary64)) #s(literal -1 binary64)))
(.f64 (pow.f64 (/.f64 #s(literal -1 binary64) eps) #s(literal 3 binary64)) (.f64 (.f64 (.f64 (.f64 eps eps) eps) eps) (.f64 eps eps)))
(.f64 (pow.f64 (/.f64 #s(literal -1 binary64) (.f64 eps eps)) #s(literal 3 binary64)) (.f64 (.f64 (.f64 (.f64 (.f64 eps eps) eps) eps) (.f64 eps eps)) (.f64 (.f64 eps eps) eps)))
(*.f64 (pow.f64 eps #s(literal 3/2 binary64)) (pow.f64 eps #s(literal 3/2 binary64)))
(.f64 (.f64 (.f64 (.f64 (.f64 (.f64 eps eps) eps) eps) (.f64 eps eps)) (.f64 (.f64 eps eps) eps)) (pow.f64 (/.f64 #s(literal -1 binary64) (.f64 eps eps)) #s(literal 3 binary64)))
(.f64 (.f64 (.f64 (.f64 (.f64 eps eps) eps) eps) (.f64 eps eps)) (pow.f64 (/.f64 #s(literal -1 binary64) eps) #s(literal 3 binary64)))
(.f64 #s(literal -1 binary64) (.f64 (*.f64 eps eps) eps))
(.f64 (.f64 (*.f64 eps eps) eps) #s(literal -1 binary64))
(.f64 (.f64 (*.f64 eps eps) eps) #s(literal 1 binary64))
(.f64 (.f64 eps eps) eps)
(.f64 #s(literal 1 binary64) (.f64 (*.f64 eps eps) eps))
(.f64 eps (.f64 eps eps))
(pow.f64 (exp.f64 (log.f64 eps)) #s(literal 3 binary64))
(pow.f64 (pow.f64 eps #s(literal 3/2 binary64)) #s(literal 2 binary64))
(pow.f64 (*.f64 eps eps) #s(literal 3/2 binary64))
(pow.f64 eps #s(literal 3 binary64))
(/.f64 (pow.f64 (-.f64 #s(literal 0 binary64) (.f64 (.f64 eps eps) eps)) #s(literal 3 binary64)) (.f64 (.f64 (.f64 (.f64 eps eps) eps) eps) (*.f64 eps eps)))
(/.f64 (.f64 (.f64 (.f64 eps eps) eps) (.f64 eps eps)) (*.f64 eps eps))
(/.f64 (-.f64 #s(literal 0 binary64) (.f64 (.f64 (.f64 (.f64 eps eps) eps) eps) (.f64 eps eps))) (-.f64 #s(literal 0 binary64) (.f64 (*.f64 eps eps) eps)))
(/.f64 (.f64 (.f64 (*.f64 eps eps) eps) eps) eps)
(/.f64 (+.f64 #s(literal 0 binary64) (.f64 (.f64 (.f64 (.f64 (.f64 eps eps) eps) eps) (.f64 eps eps)) (.f64 (.f64 eps eps) eps))) (+.f64 #s(literal 0 binary64) (-.f64 (.f64 (.f64 (.f64 (.f64 eps eps) eps) eps) (.f64 eps eps)) (.f64 #s(literal 0 binary64) (.f64 (.f64 eps eps) eps)))))
(/.f64 (.f64 (.f64 (.f64 (.f64 (.f64 eps eps) eps) eps) (.f64 eps eps)) (.f64 (.f64 eps eps) eps)) (.f64 (.f64 (.f64 (.f64 eps eps) eps) eps) (*.f64 eps eps)))
(/.f64 (.f64 (.f64 (.f64 (.f64 eps eps) eps) eps) (.f64 eps eps)) (.f64 (*.f64 eps eps) eps))
(/.f64 #s(literal 1 binary64) (pow.f64 (/.f64 #s(literal -1 binary64) eps) #s(literal 3 binary64)))
(neg.f64 (.f64 (.f64 eps eps) eps))
(fma.f64 (pow.f64 (/.f64 #s(literal -1 binary64) eps) #s(literal 3 binary64)) (.f64 (.f64 (.f64 (.f64 eps eps) eps) eps) (.f64 eps eps)) (.f64 (*.f64 eps eps) #s(literal 0 binary64)))
(fma.f64 (pow.f64 (/.f64 #s(literal -1 binary64) eps) #s(literal 3 binary64)) (.f64 (.f64 (.f64 (.f64 eps eps) eps) eps) (.f64 eps eps)) (.f64 #s(literal 0 binary64) (*.f64 eps eps)))
(fma.f64 (pow.f64 (/.f64 #s(literal -1 binary64) eps) #s(literal 3 binary64)) (.f64 (.f64 (.f64 (.f64 eps eps) eps) eps) (*.f64 eps eps)) #s(literal 0 binary64))
(fma.f64 (pow.f64 (/.f64 #s(literal -1 binary64) (.f64 eps eps)) #s(literal 3 binary64)) (.f64 (.f64 (.f64 (.f64 (.f64 eps eps) eps) eps) (.f64 eps eps)) (.f64 (.f64 eps eps) eps)) (.f64 (*.f64 eps eps) #s(literal 0 binary64)))
(fma.f64 (pow.f64 (/.f64 #s(literal -1 binary64) (.f64 eps eps)) #s(literal 3 binary64)) (.f64 (.f64 (.f64 (.f64 (.f64 eps eps) eps) eps) (.f64 eps eps)) (.f64 (.f64 eps eps) eps)) (.f64 #s(literal 0 binary64) (*.f64 eps eps)))
(fma.f64 (pow.f64 (/.f64 #s(literal -1 binary64) (.f64 eps eps)) #s(literal 3 binary64)) (.f64 (.f64 (.f64 (.f64 (.f64 eps eps) eps) eps) (.f64 eps eps)) (.f64 (*.f64 eps eps) eps)) #s(literal 0 binary64))
(fma.f64 (pow.f64 eps #s(literal 3/2 binary64)) (pow.f64 eps #s(literal 3/2 binary64)) (.f64 (.f64 eps eps) #s(literal 0 binary64)))
(fma.f64 (pow.f64 eps #s(literal 3/2 binary64)) (pow.f64 eps #s(literal 3/2 binary64)) (.f64 #s(literal 0 binary64) (.f64 eps eps)))
(fma.f64 (pow.f64 eps #s(literal 3/2 binary64)) (pow.f64 eps #s(literal 3/2 binary64)) #s(literal 0 binary64))
(fma.f64 (.f64 (.f64 (.f64 (.f64 (.f64 eps eps) eps) eps) (.f64 eps eps)) (.f64 (.f64 eps eps) eps)) (pow.f64 (/.f64 #s(literal -1 binary64) (.f64 eps eps)) #s(literal 3 binary64)) (.f64 (*.f64 eps eps) #s(literal 0 binary64)))
(fma.f64 (.f64 (.f64 (.f64 (.f64 (.f64 eps eps) eps) eps) (.f64 eps eps)) (.f64 (.f64 eps eps) eps)) (pow.f64 (/.f64 #s(literal -1 binary64) (.f64 eps eps)) #s(literal 3 binary64)) (.f64 #s(literal 0 binary64) (*.f64 eps eps)))
(fma.f64 (.f64 (.f64 (.f64 (.f64 (.f64 eps eps) eps) eps) (.f64 eps eps)) (.f64 (.f64 eps eps) eps)) (pow.f64 (/.f64 #s(literal -1 binary64) (*.f64 eps eps)) #s(literal 3 binary64)) #s(literal 0 binary64))
(fma.f64 (.f64 (.f64 (.f64 (.f64 eps eps) eps) eps) (.f64 eps eps)) (pow.f64 (/.f64 #s(literal -1 binary64) eps) #s(literal 3 binary64)) (.f64 (*.f64 eps eps) #s(literal 0 binary64)))
(fma.f64 (.f64 (.f64 (.f64 (.f64 eps eps) eps) eps) (.f64 eps eps)) (pow.f64 (/.f64 #s(literal -1 binary64) eps) #s(literal 3 binary64)) (.f64 #s(literal 0 binary64) (*.f64 eps eps)))
(fma.f64 (.f64 (.f64 (.f64 (.f64 eps eps) eps) eps) (*.f64 eps eps)) (pow.f64 (/.f64 #s(literal -1 binary64) eps) #s(literal 3 binary64)) #s(literal 0 binary64))
(fma.f64 #s(literal -1 binary64) (.f64 (.f64 eps eps) eps) (.f64 (.f64 eps eps) #s(literal 0 binary64)))
(fma.f64 #s(literal -1 binary64) (.f64 (.f64 eps eps) eps) (.f64 #s(literal 0 binary64) (.f64 eps eps)))
(fma.f64 #s(literal -1 binary64) (.f64 (.f64 eps eps) eps) #s(literal 0 binary64))
(fma.f64 (.f64 (.f64 eps eps) eps) #s(literal -1 binary64) (.f64 (.f64 eps eps) #s(literal 0 binary64)))
(fma.f64 (.f64 (.f64 eps eps) eps) #s(literal -1 binary64) (.f64 #s(literal 0 binary64) (.f64 eps eps)))
(fma.f64 (.f64 (.f64 eps eps) eps) #s(literal -1 binary64) #s(literal 0 binary64))
(fma.f64 (.f64 (.f64 eps eps) eps) #s(literal 1 binary64) (.f64 (.f64 eps eps) #s(literal 0 binary64)))
(fma.f64 (.f64 (.f64 eps eps) eps) #s(literal 1 binary64) (.f64 #s(literal 0 binary64) (.f64 eps eps)))
(fma.f64 (.f64 (.f64 eps eps) eps) #s(literal 1 binary64) #s(literal 0 binary64))
(fma.f64 (.f64 eps eps) #s(literal 0 binary64) (.f64 (*.f64 eps eps) eps))
(fma.f64 (.f64 eps eps) eps (.f64 (*.f64 eps eps) #s(literal 0 binary64)))
(fma.f64 (.f64 eps eps) eps (.f64 #s(literal 0 binary64) (*.f64 eps eps)))
(fma.f64 (*.f64 eps eps) eps #s(literal 0 binary64))
(fma.f64 #s(literal 1 binary64) (.f64 (.f64 eps eps) eps) (.f64 (.f64 eps eps) #s(literal 0 binary64)))
(fma.f64 #s(literal 1 binary64) (.f64 (.f64 eps eps) eps) (.f64 #s(literal 0 binary64) (.f64 eps eps)))
(fma.f64 #s(literal 1 binary64) (.f64 (.f64 eps eps) eps) #s(literal 0 binary64))
(fma.f64 #s(literal 0 binary64) (.f64 eps eps) (.f64 (*.f64 eps eps) eps))
(fma.f64 eps (.f64 eps eps) (.f64 (*.f64 eps eps) #s(literal 0 binary64)))
(fma.f64 eps (.f64 eps eps) (.f64 #s(literal 0 binary64) (*.f64 eps eps)))
(fma.f64 eps (*.f64 eps eps) #s(literal 0 binary64))
(+.f64 (.f64 (.f64 eps eps) #s(literal 0 binary64)) (.f64 (.f64 eps eps) eps))
(+.f64 (.f64 #s(literal 0 binary64) (.f64 eps eps)) (.f64 (.f64 eps eps) eps))
(+.f64 (.f64 (.f64 eps eps) eps) (.f64 (.f64 eps eps) #s(literal 0 binary64)))
(+.f64 (.f64 (.f64 eps eps) eps) (.f64 #s(literal 0 binary64) (.f64 eps eps)))
(+.f64 (.f64 (.f64 eps eps) eps) #s(literal 0 binary64))
(+.f64 #s(literal 0 binary64) (.f64 (.f64 eps eps) eps))
(exp.f64 (*.f64 (log.f64 eps) #s(literal 3 binary64)))

eval183.0ms (1%)

Memory: 33.2MiB live, 420.5MiB allocated
Compiler: Compiled 30 085 to 2 578 computations (91.4% saved)

prune170.0ms (0.9%)

Memory

1.8MiB live, 408.8MiB allocated

Pruning

35 alts after pruning (31 fresh and 4 done)

	Pruned	Kept	Total
New	1 006	18	1 024
Fresh	9	13	22
Picked	3	2	5
Done	0	2	2
Total	1 018	35	1 053

Accuracy

100.0%

Counts

1 053 → 35

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	49.9%	(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))
	40.3%	(.f64 (.f64 (sin.f64 (/.f64 (fma.f64 (.f64 (.f64 x x) x) #s(literal 1 binary64) (.f64 #s(literal 1/8 binary64) (.f64 (.f64 eps eps) eps))) (fma.f64 (.f64 #s(literal 1 binary64) x) (.f64 #s(literal 1 binary64) x) (-.f64 (.f64 #s(literal 1/4 binary64) (.f64 eps eps)) (.f64 (.f64 #s(literal 1 binary64) x) (.f64 eps #s(literal 1/2 binary64))))))) #s(approx (sin (* 1/2 (+ 0 eps))) (.f64 (fma.f64 (fma.f64 #s(literal 1/3840 binary64) (.f64 eps eps) #s(literal -1/48 binary64)) (*.f64 eps eps) #s(literal 1/2 binary64)) eps))) #s(literal -2 binary64))
	99.5%	(.f64 (.f64 (sin.f64 (/.f64 (-.f64 (.f64 (.f64 #s(literal 1 binary64) x) (.f64 #s(literal 1 binary64) x)) (.f64 #s(literal 1/4 binary64) (.f64 eps eps))) (-.f64 (.f64 #s(literal 1 binary64) x) (.f64 eps #s(literal 1/2 binary64))))) #s(approx (sin ( 1/2 (+ 0 eps))) (.f64 (fma.f64 (fma.f64 #s(literal 1/3840 binary64) (.f64 eps eps) #s(literal -1/48 binary64)) (*.f64 eps eps) #s(literal 1/2 binary64)) eps))) #s(literal -2 binary64))
	40.3%	(.f64 (.f64 (sin.f64 (/.f64 (.f64 (fma.f64 #s(literal 8 binary64) (.f64 (.f64 x x) x) (.f64 (.f64 eps eps) eps)) #s(literal 1/2 binary64)) (fma.f64 #s(literal 4 binary64) (.f64 x x) (.f64 eps (-.f64 eps (.f64 x #s(literal 2 binary64))))))) #s(approx (sin (* 1/2 (+ 0 eps))) (.f64 (fma.f64 (fma.f64 #s(literal 1/3840 binary64) (.f64 eps eps) #s(literal -1/48 binary64)) (*.f64 eps eps) #s(literal 1/2 binary64)) eps))) #s(literal -2 binary64))
	99.7%	(.f64 (.f64 (sin.f64 (-.f64 (/.f64 (.f64 (.f64 #s(literal 1 binary64) x) (.f64 #s(literal 1 binary64) x)) (-.f64 (.f64 #s(literal 1 binary64) x) (.f64 eps #s(literal 1/2 binary64)))) (/.f64 (.f64 (.f64 eps #s(literal 1/2 binary64)) (.f64 eps #s(literal 1/2 binary64))) (-.f64 (.f64 #s(literal 1 binary64) x) (.f64 eps #s(literal 1/2 binary64)))))) (sin.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 0 binary64) eps)))) #s(literal -2 binary64))
	36.8%	(.f64 (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps))) (sin.f64 (.f64 #s(literal 1/2 binary64) (/.f64 (.f64 (.f64 eps eps) eps) (*.f64 eps eps))))) #s(literal -2 binary64))
	98.1%	(.f64 (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps))) (sin.f64 (.f64 #s(literal 1/2 binary64) (/.f64 (*.f64 eps eps) eps)))) #s(literal -2 binary64))
	35.6%	(.f64 (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps))) (sin.f64 (.f64 #s(literal 1/2 binary64) (.f64 (pow.f64 eps #s(literal 3 binary64)) (/.f64 #s(literal 1 binary64) (.f64 eps eps)))))) #s(literal -2 binary64))
	35.6%	(.f64 (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps))) (sin.f64 (.f64 #s(literal 1/2 binary64) (.f64 (.f64 (*.f64 eps eps) eps) (pow.f64 eps #s(literal -2 binary64)))))) #s(literal -2 binary64))
	35.5%	(.f64 (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps))) (sin.f64 (.f64 #s(literal 1/2 binary64) (.f64 (.f64 (.f64 eps eps) eps) (.f64 (/.f64 #s(literal -1 binary64) eps) (/.f64 #s(literal -1 binary64) eps)))))) #s(literal -2 binary64))
▶	98.1%	(.f64 (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps))) (sin.f64 (.f64 #s(literal 1/2 binary64) (.f64 (neg.f64 (.f64 eps eps)) (/.f64 #s(literal -1 binary64) eps))))) #s(literal -2 binary64))
▶	99.7%	(.f64 (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps))) #s(approx (sin ( 1/2 (+ 0 eps))) (.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -1/645120 binary64) (.f64 eps eps) #s(literal 1/3840 binary64)) (.f64 eps eps) #s(literal -1/48 binary64)) (.f64 eps eps) #s(literal 1/2 binary64)) eps))) #s(literal -2 binary64))
	99.6%	(.f64 (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps))) #s(approx (sin ( 1/2 (+ 0 eps))) (.f64 (fma.f64 (.f64 eps eps) #s(literal -1/48 binary64) #s(literal 1/2 binary64)) eps))) #s(literal -2 binary64))
	99.5%	(.f64 (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps))) #s(approx (sin ( 1/2 (+ 0 eps))) (*.f64 eps #s(literal 1/2 binary64)))) #s(literal -2 binary64))
	35.6%	(.f64 (.f64 (sin.f64 #s(approx (* 1/2 (+ (* 2 x) eps)) (fma.f64 eps #s(literal 1/2 binary64) x))) (sin.f64 (.f64 #s(literal 1/2 binary64) (.f64 (.f64 (.f64 eps eps) eps) (/.f64 #s(literal 1 binary64) (*.f64 eps eps)))))) #s(literal -2 binary64))
▶	99.6%	(.f64 (.f64 (sin.f64 #s(approx (* 1/2 (+ (* 2 x) eps)) (fma.f64 eps #s(literal 1/2 binary64) x))) #s(approx (sin (* 1/2 (+ 0 eps))) (.f64 (fma.f64 (fma.f64 #s(literal 1/3840 binary64) (.f64 eps eps) #s(literal -1/48 binary64)) (*.f64 eps eps) #s(literal 1/2 binary64)) eps))) #s(literal -2 binary64))
	99.6%	(.f64 (.f64 #s(approx (sin (* 1/2 (+ 0 eps))) (.f64 (fma.f64 (fma.f64 (.f64 eps eps) #s(literal 1/3840 binary64) #s(literal -1/48 binary64)) (.f64 eps eps) #s(literal 1/2 binary64)) eps)) #s(literal -2 binary64)) (sin.f64 (fma.f64 #s(literal 1 binary64) x (.f64 eps #s(literal 1/2 binary64)))))
✓	99.8%	(.f64 #s(approx ( (sin (* 1/2 (+ (* 2 x) eps))) (sin (* 1/2 (+ 0 eps)))) (.f64 (sin.f64 (fma.f64 eps #s(literal 1/2 binary64) x)) (sin.f64 (.f64 eps #s(literal 1/2 binary64))))) #s(literal -2 binary64))
✓	49.0%	#s(approx (- (cos (+ x eps)) (cos x)) (-.f64 #s(approx (cos eps) #s(literal 1 binary64)) #s(literal 1 binary64)))
	78.6%	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 (/.f64 (.f64 eps eps) (neg.f64 eps)) (sin.f64 x)))
	99.5%	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 (-.f64 (.f64 (*.f64 (cos.f64 x) #s(literal -1/2 binary64)) eps) (sin.f64 x)) eps))
✓	79.2%	#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (neg.f64 eps) (sin.f64 x)))
	78.5%	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 (neg.f64 eps) #s(approx (sin x) (.f64 (fma.f64 (fma.f64 #s(literal 1/120 binary64) (.f64 x x) #s(literal -1/6 binary64)) (.f64 x x) #s(literal 1 binary64)) x))))
	78.7%	#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (.f64 (fma.f64 (fma.f64 (fma.f64 eps #s(literal -1/120 binary64) (.f64 (.f64 #s(literal 1/5040 binary64) (.f64 x x)) eps)) (.f64 x x) (.f64 #s(literal 1/6 binary64) eps)) (*.f64 x x) (neg.f64 eps)) x)))
	21.1%	#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (.f64 (fma.f64 (/.f64 #s(literal -1 binary64) (.f64 eps eps)) (.f64 (.f64 eps eps) eps) (.f64 (.f64 eps (fma.f64 (fma.f64 #s(literal 1/5040 binary64) (.f64 x x) #s(literal -1/120 binary64)) (.f64 x x) #s(literal 1/6 binary64))) (*.f64 x x))) x)))
	78.0%	#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (.f64 (fma.f64 (/.f64 #s(literal -1 binary64) eps) (.f64 eps eps) (.f64 (.f64 eps (fma.f64 (fma.f64 #s(literal 1/5040 binary64) (.f64 x x) #s(literal -1/120 binary64)) (.f64 x x) #s(literal 1/6 binary64))) (*.f64 x x))) x)))
	78.7%	#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (.f64 (fma.f64 (.f64 (.f64 (fma.f64 (fma.f64 #s(literal 1/5040 binary64) (.f64 x x) #s(literal -1/120 binary64)) (*.f64 x x) #s(literal 1/6 binary64)) eps) x) x (neg.f64 eps)) x)))
	78.5%	#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (.f64 (fma.f64 (.f64 eps (fma.f64 (.f64 x x) #s(literal -1/120 binary64) #s(literal 1/6 binary64))) (.f64 x x) (neg.f64 eps)) x)))
▶	78.1%	#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (.f64 (fma.f64 (.f64 eps (-.f64 (.f64 (.f64 (fma.f64 #s(literal 1/5040 binary64) (.f64 x x) #s(literal -1/120 binary64)) x) x) #s(literal 1/6 binary64))) (.f64 x x) (neg.f64 eps)) x)))
	78.4%	#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (.f64 (fma.f64 #s(approx (+ ( (* eps (+ (* (* x x) 1/5040) -1/120)) (* x x)) (* 1/6 eps)) (.f64 #s(literal 1/6 binary64) eps)) (.f64 x x) (neg.f64 eps)) x)))
	78.4%	#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (.f64 (.f64 eps (fma.f64 (*.f64 x x) #s(literal 1/6 binary64) #s(literal -1 binary64))) x)))
▶	78.2%	#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (*.f64 (neg.f64 x) eps)))
	78.7%	#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (.f64 #s(approx (+ ( (+ (* (* eps (+ (* (* x x) 1/5040) -1/120)) (* x x)) (* 1/6 eps)) (* x x)) (neg eps)) (.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 1/5040 binary64) (.f64 x x) #s(literal -1/120 binary64)) (.f64 x x) #s(literal 1/6 binary64)) (.f64 x x) #s(literal -1 binary64)) eps)) x)))
	98.6%	#s(approx (* (* (sin (* 1/2 (+ (* 2 x) eps))) (sin (* 1/2 (+ 0 eps)))) -2) (fma.f64 (fma.f64 (.f64 (cos.f64 (.f64 #s(literal -1/2 binary64) eps)) (sin.f64 (.f64 eps #s(literal 1/2 binary64)))) (+.f64 #s(literal -2 binary64) (.f64 x (.f64 #s(literal 1/3 binary64) x))) (.f64 (pow.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) #s(literal 2 binary64)) x)) x (.f64 (pow.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) #s(literal 2 binary64)) #s(literal -2 binary64))))
	97.9%	#s(approx (* (* (sin (* 1/2 (+ (* 2 x) eps))) (sin (* 1/2 (+ 0 eps)))) -2) (fma.f64 (pow.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) #s(literal 2 binary64)) (fma.f64 x x #s(literal -2 binary64)) (.f64 (.f64 (.f64 x #s(literal -2 binary64)) (cos.f64 (.f64 #s(literal -1/2 binary64) eps))) (sin.f64 (.f64 eps #s(literal 1/2 binary64))))))

Compiler

Compiled 1 661 to 943 computations (43.2% saved)

simplify120.0ms (0.6%)

Memory

-8.0MiB live, 223.5MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 20 expressions of interest:

New	Metric	Score
cost-diff	0	(.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps))) (sin.f64 (.f64 #s(literal 1/2 binary64) (.f64 (neg.f64 (*.f64 eps eps)) (/.f64 #s(literal -1 binary64) eps)))))
cost-diff	0	(.f64 (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps))) (sin.f64 (.f64 #s(literal 1/2 binary64) (.f64 (neg.f64 (.f64 eps eps)) (/.f64 #s(literal -1 binary64) eps))))) #s(literal -2 binary64))
cost-diff	320	(*.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps))
cost-diff	1472	(.f64 (neg.f64 (.f64 eps eps)) (/.f64 #s(literal -1 binary64) eps))
cost-diff	0	#s(approx (* 1/2 (+ (* 2 x) eps)) (fma.f64 eps #s(literal 1/2 binary64) x))
cost-diff	0	(sin.f64 #s(approx (* 1/2 (+ (* 2 x) eps)) (fma.f64 eps #s(literal 1/2 binary64) x)))
cost-diff	0	(.f64 (sin.f64 #s(approx ( 1/2 (+ (* 2 x) eps)) (fma.f64 eps #s(literal 1/2 binary64) x))) #s(approx (sin (* 1/2 (+ 0 eps))) (.f64 (fma.f64 (fma.f64 #s(literal 1/3840 binary64) (.f64 eps eps) #s(literal -1/48 binary64)) (*.f64 eps eps) #s(literal 1/2 binary64)) eps)))
cost-diff	0	(.f64 (.f64 (sin.f64 #s(approx (* 1/2 (+ (* 2 x) eps)) (fma.f64 eps #s(literal 1/2 binary64) x))) #s(approx (sin (* 1/2 (+ 0 eps))) (.f64 (fma.f64 (fma.f64 #s(literal 1/3840 binary64) (.f64 eps eps) #s(literal -1/48 binary64)) (*.f64 eps eps) #s(literal 1/2 binary64)) eps))) #s(literal -2 binary64))
cost-diff	0	#s(approx (* (neg eps) (sin x)) (.f64 (fma.f64 (.f64 eps (-.f64 (.f64 (.f64 (fma.f64 #s(literal 1/5040 binary64) (.f64 x x) #s(literal -1/120 binary64)) x) x) #s(literal 1/6 binary64))) (.f64 x x) (neg.f64 eps)) x))
cost-diff	0	#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (.f64 (fma.f64 (.f64 eps (-.f64 (.f64 (.f64 (fma.f64 #s(literal 1/5040 binary64) (.f64 x x) #s(literal -1/120 binary64)) x) x) #s(literal 1/6 binary64))) (.f64 x x) (neg.f64 eps)) x)))
cost-diff	128	(-.f64 (.f64 (.f64 (fma.f64 #s(literal 1/5040 binary64) (*.f64 x x) #s(literal -1/120 binary64)) x) x) #s(literal 1/6 binary64))
cost-diff	128	(fma.f64 (.f64 eps (-.f64 (.f64 (.f64 (fma.f64 #s(literal 1/5040 binary64) (.f64 x x) #s(literal -1/120 binary64)) x) x) #s(literal 1/6 binary64))) (*.f64 x x) (neg.f64 eps))
cost-diff	0	(neg.f64 x)
cost-diff	0	(*.f64 (neg.f64 x) eps)
cost-diff	0	#s(approx (* (neg eps) (sin x)) (*.f64 (neg.f64 x) eps))
cost-diff	0	#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (*.f64 (neg.f64 x) eps)))
cost-diff	0	(sin.f64 (*.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps)))
cost-diff	0	(.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps))) #s(approx (sin (* 1/2 (+ 0 eps))) (.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -1/645120 binary64) (.f64 eps eps) #s(literal 1/3840 binary64)) (.f64 eps eps) #s(literal -1/48 binary64)) (.f64 eps eps) #s(literal 1/2 binary64)) eps)))
cost-diff	0	(.f64 (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps))) #s(approx (sin ( 1/2 (+ 0 eps))) (.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -1/645120 binary64) (.f64 eps eps) #s(literal 1/3840 binary64)) (.f64 eps eps) #s(literal -1/48 binary64)) (.f64 eps eps) #s(literal 1/2 binary64)) eps))) #s(literal -2 binary64))
cost-diff	320	(*.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps))

Rules

8 564×	`lower-fma.f32`
8 546×	`lower-fma.f64`
5 130×	`lower-*.f32`
5 094×	`lower-*.f64`
1 396×	`lower-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	68	630
0	111	613
1	205	609
2	557	575
3	1493	553
4	4734	553
0	8094	546

Stop Event

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

Calls

Call 1

Inputs
(.f64 (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps))) #s(approx (sin ( 1/2 (+ 0 eps))) (.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -1/645120 binary64) (.f64 eps eps) #s(literal 1/3840 binary64)) (.f64 eps eps) #s(literal -1/48 binary64)) (.f64 eps eps) #s(literal 1/2 binary64)) eps))) #s(literal -2 binary64))
(.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps))) #s(approx (sin (* 1/2 (+ 0 eps))) (.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -1/645120 binary64) (.f64 eps eps) #s(literal 1/3840 binary64)) (.f64 eps eps) #s(literal -1/48 binary64)) (.f64 eps eps) #s(literal 1/2 binary64)) eps)))
(sin.f64 (*.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps)))
(*.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps))
#s(literal 1/2 binary64)
(fma.f64 #s(literal 2 binary64) x eps)
#s(literal 2 binary64)
x
eps
#s(approx (sin (* 1/2 (+ 0 eps))) (.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -1/645120 binary64) (.f64 eps eps) #s(literal 1/3840 binary64)) (.f64 eps eps) #s(literal -1/48 binary64)) (.f64 eps eps) #s(literal 1/2 binary64)) eps))
(.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -1/645120 binary64) (.f64 eps eps) #s(literal 1/3840 binary64)) (.f64 eps eps) #s(literal -1/48 binary64)) (.f64 eps eps) #s(literal 1/2 binary64)) eps)
(fma.f64 (fma.f64 (fma.f64 #s(literal -1/645120 binary64) (.f64 eps eps) #s(literal 1/3840 binary64)) (.f64 eps eps) #s(literal -1/48 binary64)) (*.f64 eps eps) #s(literal 1/2 binary64))
(fma.f64 (fma.f64 #s(literal -1/645120 binary64) (.f64 eps eps) #s(literal 1/3840 binary64)) (.f64 eps eps) #s(literal -1/48 binary64))
(fma.f64 #s(literal -1/645120 binary64) (*.f64 eps eps) #s(literal 1/3840 binary64))
#s(literal -1/645120 binary64)
(*.f64 eps eps)
#s(literal 1/3840 binary64)
#s(literal -1/48 binary64)
#s(literal -2 binary64)
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (*.f64 (neg.f64 x) eps)))
#s(approx (* (neg eps) (sin x)) (*.f64 (neg.f64 x) eps))
(*.f64 (neg.f64 x) eps)
(neg.f64 x)
x
eps
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (.f64 (fma.f64 (.f64 eps (-.f64 (.f64 (.f64 (fma.f64 #s(literal 1/5040 binary64) (.f64 x x) #s(literal -1/120 binary64)) x) x) #s(literal 1/6 binary64))) (.f64 x x) (neg.f64 eps)) x)))
#s(approx (* (neg eps) (sin x)) (.f64 (fma.f64 (.f64 eps (-.f64 (.f64 (.f64 (fma.f64 #s(literal 1/5040 binary64) (.f64 x x) #s(literal -1/120 binary64)) x) x) #s(literal 1/6 binary64))) (.f64 x x) (neg.f64 eps)) x))
(.f64 (fma.f64 (.f64 eps (-.f64 (.f64 (.f64 (fma.f64 #s(literal 1/5040 binary64) (.f64 x x) #s(literal -1/120 binary64)) x) x) #s(literal 1/6 binary64))) (.f64 x x) (neg.f64 eps)) x)
(fma.f64 (.f64 eps (-.f64 (.f64 (.f64 (fma.f64 #s(literal 1/5040 binary64) (.f64 x x) #s(literal -1/120 binary64)) x) x) #s(literal 1/6 binary64))) (*.f64 x x) (neg.f64 eps))
(.f64 eps (-.f64 (.f64 (.f64 (fma.f64 #s(literal 1/5040 binary64) (.f64 x x) #s(literal -1/120 binary64)) x) x) #s(literal 1/6 binary64)))
eps
(-.f64 (.f64 (.f64 (fma.f64 #s(literal 1/5040 binary64) (*.f64 x x) #s(literal -1/120 binary64)) x) x) #s(literal 1/6 binary64))
(.f64 (.f64 (fma.f64 #s(literal 1/5040 binary64) (*.f64 x x) #s(literal -1/120 binary64)) x) x)
(.f64 (fma.f64 #s(literal 1/5040 binary64) (.f64 x x) #s(literal -1/120 binary64)) x)
(fma.f64 #s(literal 1/5040 binary64) (*.f64 x x) #s(literal -1/120 binary64))
#s(literal 1/5040 binary64)
(*.f64 x x)
x
#s(literal -1/120 binary64)
#s(literal 1/6 binary64)
(neg.f64 eps)
(.f64 (.f64 (sin.f64 #s(approx (* 1/2 (+ (* 2 x) eps)) (fma.f64 eps #s(literal 1/2 binary64) x))) #s(approx (sin (* 1/2 (+ 0 eps))) (.f64 (fma.f64 (fma.f64 #s(literal 1/3840 binary64) (.f64 eps eps) #s(literal -1/48 binary64)) (*.f64 eps eps) #s(literal 1/2 binary64)) eps))) #s(literal -2 binary64))
(.f64 (sin.f64 #s(approx ( 1/2 (+ (* 2 x) eps)) (fma.f64 eps #s(literal 1/2 binary64) x))) #s(approx (sin (* 1/2 (+ 0 eps))) (.f64 (fma.f64 (fma.f64 #s(literal 1/3840 binary64) (.f64 eps eps) #s(literal -1/48 binary64)) (*.f64 eps eps) #s(literal 1/2 binary64)) eps)))
(sin.f64 #s(approx (* 1/2 (+ (* 2 x) eps)) (fma.f64 eps #s(literal 1/2 binary64) x)))
#s(approx (* 1/2 (+ (* 2 x) eps)) (fma.f64 eps #s(literal 1/2 binary64) x))
(fma.f64 eps #s(literal 1/2 binary64) x)
eps
#s(literal 1/2 binary64)
x
#s(approx (sin (* 1/2 (+ 0 eps))) (.f64 (fma.f64 (fma.f64 #s(literal 1/3840 binary64) (.f64 eps eps) #s(literal -1/48 binary64)) (*.f64 eps eps) #s(literal 1/2 binary64)) eps))
(.f64 (fma.f64 (fma.f64 #s(literal 1/3840 binary64) (.f64 eps eps) #s(literal -1/48 binary64)) (*.f64 eps eps) #s(literal 1/2 binary64)) eps)
(fma.f64 (fma.f64 #s(literal 1/3840 binary64) (.f64 eps eps) #s(literal -1/48 binary64)) (.f64 eps eps) #s(literal 1/2 binary64))
(fma.f64 #s(literal 1/3840 binary64) (*.f64 eps eps) #s(literal -1/48 binary64))
#s(literal 1/3840 binary64)
(*.f64 eps eps)
#s(literal -1/48 binary64)
#s(literal -2 binary64)
(.f64 (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps))) (sin.f64 (.f64 #s(literal 1/2 binary64) (.f64 (neg.f64 (.f64 eps eps)) (/.f64 #s(literal -1 binary64) eps))))) #s(literal -2 binary64))
(.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps))) (sin.f64 (.f64 #s(literal 1/2 binary64) (.f64 (neg.f64 (*.f64 eps eps)) (/.f64 #s(literal -1 binary64) eps)))))
(sin.f64 (*.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps)))
(*.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps))
#s(literal 1/2 binary64)
(fma.f64 #s(literal 2 binary64) x eps)
#s(literal 2 binary64)
x
eps
(sin.f64 (.f64 #s(literal 1/2 binary64) (.f64 (neg.f64 (*.f64 eps eps)) (/.f64 #s(literal -1 binary64) eps))))
(.f64 #s(literal 1/2 binary64) (.f64 (neg.f64 (*.f64 eps eps)) (/.f64 #s(literal -1 binary64) eps)))
(.f64 (neg.f64 (.f64 eps eps)) (/.f64 #s(literal -1 binary64) eps))
(neg.f64 (*.f64 eps eps))
(*.f64 eps eps)
(/.f64 #s(literal -1 binary64) eps)
#s(literal -1 binary64)
#s(literal -2 binary64)

Outputs
(.f64 (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps))) #s(approx (sin ( 1/2 (+ 0 eps))) (.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -1/645120 binary64) (.f64 eps eps) #s(literal 1/3840 binary64)) (.f64 eps eps) #s(literal -1/48 binary64)) (.f64 eps eps) #s(literal 1/2 binary64)) eps))) #s(literal -2 binary64))
(.f64 (.f64 #s(literal -2 binary64) (sin.f64 (fma.f64 eps #s(literal 1/2 binary64) x))) #s(approx (sin (* 1/2 (+ 0 eps))) (.f64 (fma.f64 (fma.f64 (fma.f64 (.f64 eps eps) #s(literal -1/645120 binary64) #s(literal 1/3840 binary64)) (.f64 eps eps) #s(literal -1/48 binary64)) (.f64 eps eps) #s(literal 1/2 binary64)) eps)))
(.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps))) #s(approx (sin (* 1/2 (+ 0 eps))) (.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -1/645120 binary64) (.f64 eps eps) #s(literal 1/3840 binary64)) (.f64 eps eps) #s(literal -1/48 binary64)) (.f64 eps eps) #s(literal 1/2 binary64)) eps)))
(.f64 #s(approx (sin ( 1/2 (+ 0 eps))) (.f64 (fma.f64 (fma.f64 (fma.f64 (.f64 eps eps) #s(literal -1/645120 binary64) #s(literal 1/3840 binary64)) (.f64 eps eps) #s(literal -1/48 binary64)) (.f64 eps eps) #s(literal 1/2 binary64)) eps)) (sin.f64 (fma.f64 eps #s(literal 1/2 binary64) x)))
(sin.f64 (*.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps)))
(sin.f64 (fma.f64 eps #s(literal 1/2 binary64) x))
(*.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps))
(fma.f64 eps #s(literal 1/2 binary64) x)
#s(literal 1/2 binary64)
(fma.f64 #s(literal 2 binary64) x eps)
(fma.f64 x #s(literal 2 binary64) eps)
#s(literal 2 binary64)
x
eps
#s(approx (sin (* 1/2 (+ 0 eps))) (.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -1/645120 binary64) (.f64 eps eps) #s(literal 1/3840 binary64)) (.f64 eps eps) #s(literal -1/48 binary64)) (.f64 eps eps) #s(literal 1/2 binary64)) eps))
#s(approx (sin (* 1/2 (+ 0 eps))) (.f64 (fma.f64 (fma.f64 (fma.f64 (.f64 eps eps) #s(literal -1/645120 binary64) #s(literal 1/3840 binary64)) (.f64 eps eps) #s(literal -1/48 binary64)) (.f64 eps eps) #s(literal 1/2 binary64)) eps))
(.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -1/645120 binary64) (.f64 eps eps) #s(literal 1/3840 binary64)) (.f64 eps eps) #s(literal -1/48 binary64)) (.f64 eps eps) #s(literal 1/2 binary64)) eps)
(.f64 (fma.f64 (fma.f64 (fma.f64 (.f64 eps eps) #s(literal -1/645120 binary64) #s(literal 1/3840 binary64)) (.f64 eps eps) #s(literal -1/48 binary64)) (.f64 eps eps) #s(literal 1/2 binary64)) eps)
(fma.f64 (fma.f64 (fma.f64 #s(literal -1/645120 binary64) (.f64 eps eps) #s(literal 1/3840 binary64)) (.f64 eps eps) #s(literal -1/48 binary64)) (*.f64 eps eps) #s(literal 1/2 binary64))
(fma.f64 (fma.f64 (fma.f64 (.f64 eps eps) #s(literal -1/645120 binary64) #s(literal 1/3840 binary64)) (.f64 eps eps) #s(literal -1/48 binary64)) (*.f64 eps eps) #s(literal 1/2 binary64))
(fma.f64 (fma.f64 #s(literal -1/645120 binary64) (.f64 eps eps) #s(literal 1/3840 binary64)) (.f64 eps eps) #s(literal -1/48 binary64))
(fma.f64 (fma.f64 (.f64 eps eps) #s(literal -1/645120 binary64) #s(literal 1/3840 binary64)) (.f64 eps eps) #s(literal -1/48 binary64))
(fma.f64 #s(literal -1/645120 binary64) (*.f64 eps eps) #s(literal 1/3840 binary64))
(fma.f64 (*.f64 eps eps) #s(literal -1/645120 binary64) #s(literal 1/3840 binary64))
#s(literal -1/645120 binary64)
(*.f64 eps eps)
#s(literal 1/3840 binary64)
#s(literal -1/48 binary64)
#s(literal -2 binary64)
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (*.f64 (neg.f64 x) eps)))
#s(approx (* (neg eps) (sin x)) (*.f64 (neg.f64 x) eps))
(*.f64 (neg.f64 x) eps)
(neg.f64 x)
x
eps
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (.f64 (fma.f64 (.f64 eps (-.f64 (.f64 (.f64 (fma.f64 #s(literal 1/5040 binary64) (.f64 x x) #s(literal -1/120 binary64)) x) x) #s(literal 1/6 binary64))) (.f64 x x) (neg.f64 eps)) x)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (.f64 (.f64 eps x) (fma.f64 (.f64 (fma.f64 (.f64 (fma.f64 (*.f64 x x) #s(literal 1/5040 binary64) #s(literal -1/120 binary64)) x) x #s(literal -1/6 binary64)) x) x #s(literal -1 binary64)))))
#s(approx (* (neg eps) (sin x)) (.f64 (fma.f64 (.f64 eps (-.f64 (.f64 (.f64 (fma.f64 #s(literal 1/5040 binary64) (.f64 x x) #s(literal -1/120 binary64)) x) x) #s(literal 1/6 binary64))) (.f64 x x) (neg.f64 eps)) x))
#s(approx (* (neg eps) (sin x)) (.f64 (.f64 eps x) (fma.f64 (.f64 (fma.f64 (.f64 (fma.f64 (*.f64 x x) #s(literal 1/5040 binary64) #s(literal -1/120 binary64)) x) x #s(literal -1/6 binary64)) x) x #s(literal -1 binary64))))
(.f64 (fma.f64 (.f64 eps (-.f64 (.f64 (.f64 (fma.f64 #s(literal 1/5040 binary64) (.f64 x x) #s(literal -1/120 binary64)) x) x) #s(literal 1/6 binary64))) (.f64 x x) (neg.f64 eps)) x)
(.f64 (.f64 eps x) (fma.f64 (.f64 (fma.f64 (.f64 (fma.f64 (*.f64 x x) #s(literal 1/5040 binary64) #s(literal -1/120 binary64)) x) x #s(literal -1/6 binary64)) x) x #s(literal -1 binary64)))
(fma.f64 (.f64 eps (-.f64 (.f64 (.f64 (fma.f64 #s(literal 1/5040 binary64) (.f64 x x) #s(literal -1/120 binary64)) x) x) #s(literal 1/6 binary64))) (*.f64 x x) (neg.f64 eps))
(.f64 (fma.f64 (.f64 (fma.f64 (.f64 (fma.f64 (.f64 x x) #s(literal 1/5040 binary64) #s(literal -1/120 binary64)) x) x #s(literal -1/6 binary64)) x) x #s(literal -1 binary64)) eps)
(.f64 eps (-.f64 (.f64 (.f64 (fma.f64 #s(literal 1/5040 binary64) (.f64 x x) #s(literal -1/120 binary64)) x) x) #s(literal 1/6 binary64)))
(.f64 (fma.f64 (.f64 (fma.f64 (*.f64 x x) #s(literal 1/5040 binary64) #s(literal -1/120 binary64)) x) x #s(literal -1/6 binary64)) eps)
eps
(-.f64 (.f64 (.f64 (fma.f64 #s(literal 1/5040 binary64) (*.f64 x x) #s(literal -1/120 binary64)) x) x) #s(literal 1/6 binary64))
(fma.f64 (.f64 (fma.f64 (.f64 x x) #s(literal 1/5040 binary64) #s(literal -1/120 binary64)) x) x #s(literal -1/6 binary64))
(.f64 (.f64 (fma.f64 #s(literal 1/5040 binary64) (*.f64 x x) #s(literal -1/120 binary64)) x) x)
(.f64 (.f64 (fma.f64 (*.f64 x x) #s(literal 1/5040 binary64) #s(literal -1/120 binary64)) x) x)
(.f64 (fma.f64 #s(literal 1/5040 binary64) (.f64 x x) #s(literal -1/120 binary64)) x)
(.f64 (fma.f64 (.f64 x x) #s(literal 1/5040 binary64) #s(literal -1/120 binary64)) x)
(fma.f64 #s(literal 1/5040 binary64) (*.f64 x x) #s(literal -1/120 binary64))
(fma.f64 (*.f64 x x) #s(literal 1/5040 binary64) #s(literal -1/120 binary64))
#s(literal 1/5040 binary64)
(*.f64 x x)
x
#s(literal -1/120 binary64)
#s(literal 1/6 binary64)
(neg.f64 eps)
(.f64 (.f64 (sin.f64 #s(approx (* 1/2 (+ (* 2 x) eps)) (fma.f64 eps #s(literal 1/2 binary64) x))) #s(approx (sin (* 1/2 (+ 0 eps))) (.f64 (fma.f64 (fma.f64 #s(literal 1/3840 binary64) (.f64 eps eps) #s(literal -1/48 binary64)) (*.f64 eps eps) #s(literal 1/2 binary64)) eps))) #s(literal -2 binary64))
(.f64 (.f64 #s(approx (sin (* 1/2 (+ 0 eps))) (.f64 (fma.f64 (fma.f64 #s(literal 1/3840 binary64) (.f64 eps eps) #s(literal -1/48 binary64)) (.f64 eps eps) #s(literal 1/2 binary64)) eps)) #s(literal -2 binary64)) (sin.f64 #s(approx ( 1/2 (+ (* 2 x) eps)) (fma.f64 eps #s(literal 1/2 binary64) x))))
(.f64 (sin.f64 #s(approx ( 1/2 (+ (* 2 x) eps)) (fma.f64 eps #s(literal 1/2 binary64) x))) #s(approx (sin (* 1/2 (+ 0 eps))) (.f64 (fma.f64 (fma.f64 #s(literal 1/3840 binary64) (.f64 eps eps) #s(literal -1/48 binary64)) (*.f64 eps eps) #s(literal 1/2 binary64)) eps)))
(.f64 #s(approx (sin ( 1/2 (+ 0 eps))) (.f64 (fma.f64 (fma.f64 #s(literal 1/3840 binary64) (.f64 eps eps) #s(literal -1/48 binary64)) (.f64 eps eps) #s(literal 1/2 binary64)) eps)) (sin.f64 #s(approx ( 1/2 (+ (* 2 x) eps)) (fma.f64 eps #s(literal 1/2 binary64) x))))
(sin.f64 #s(approx (* 1/2 (+ (* 2 x) eps)) (fma.f64 eps #s(literal 1/2 binary64) x)))
#s(approx (* 1/2 (+ (* 2 x) eps)) (fma.f64 eps #s(literal 1/2 binary64) x))
(fma.f64 eps #s(literal 1/2 binary64) x)
eps
#s(literal 1/2 binary64)
x
#s(approx (sin (* 1/2 (+ 0 eps))) (.f64 (fma.f64 (fma.f64 #s(literal 1/3840 binary64) (.f64 eps eps) #s(literal -1/48 binary64)) (*.f64 eps eps) #s(literal 1/2 binary64)) eps))
(.f64 (fma.f64 (fma.f64 #s(literal 1/3840 binary64) (.f64 eps eps) #s(literal -1/48 binary64)) (*.f64 eps eps) #s(literal 1/2 binary64)) eps)
(fma.f64 (fma.f64 #s(literal 1/3840 binary64) (.f64 eps eps) #s(literal -1/48 binary64)) (.f64 eps eps) #s(literal 1/2 binary64))
(fma.f64 #s(literal 1/3840 binary64) (*.f64 eps eps) #s(literal -1/48 binary64))
#s(literal 1/3840 binary64)
(*.f64 eps eps)
#s(literal -1/48 binary64)
#s(literal -2 binary64)
(.f64 (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps))) (sin.f64 (.f64 #s(literal 1/2 binary64) (.f64 (neg.f64 (.f64 eps eps)) (/.f64 #s(literal -1 binary64) eps))))) #s(literal -2 binary64))
(.f64 (.f64 #s(literal -2 binary64) (sin.f64 (fma.f64 eps #s(literal 1/2 binary64) x))) (sin.f64 (*.f64 eps #s(literal 1/2 binary64))))
(.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps))) (sin.f64 (.f64 #s(literal 1/2 binary64) (.f64 (neg.f64 (*.f64 eps eps)) (/.f64 #s(literal -1 binary64) eps)))))
(.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (sin.f64 (fma.f64 eps #s(literal 1/2 binary64) x)))
(sin.f64 (*.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps)))
(sin.f64 (fma.f64 eps #s(literal 1/2 binary64) x))
(*.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps))
(fma.f64 eps #s(literal 1/2 binary64) x)
#s(literal 1/2 binary64)
(fma.f64 #s(literal 2 binary64) x eps)
(fma.f64 x #s(literal 2 binary64) eps)
#s(literal 2 binary64)
x
eps
(sin.f64 (.f64 #s(literal 1/2 binary64) (.f64 (neg.f64 (*.f64 eps eps)) (/.f64 #s(literal -1 binary64) eps))))
(sin.f64 (*.f64 eps #s(literal 1/2 binary64)))
(.f64 #s(literal 1/2 binary64) (.f64 (neg.f64 (*.f64 eps eps)) (/.f64 #s(literal -1 binary64) eps)))
(*.f64 eps #s(literal 1/2 binary64))
(.f64 (neg.f64 (.f64 eps eps)) (/.f64 #s(literal -1 binary64) eps))
eps
(neg.f64 (*.f64 eps eps))
(*.f64 (neg.f64 eps) eps)
(*.f64 eps eps)
(/.f64 #s(literal -1 binary64) eps)
#s(literal -1 binary64)
#s(literal -2 binary64)

localize703.0ms (3.8%)

Memory

-34.7MiB live, 743.0MiB allocated

Localize:

Found 20 expressions of interest:

New	Metric	Score
accuracy	0.0078125	(.f64 (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps))) (sin.f64 (.f64 #s(literal 1/2 binary64) (.f64 (neg.f64 (.f64 eps eps)) (/.f64 #s(literal -1 binary64) eps))))) #s(literal -2 binary64))
accuracy	0.04260504138909578	(sin.f64 (*.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps)))
accuracy	0.11328125	(.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps))) (sin.f64 (.f64 #s(literal 1/2 binary64) (.f64 (neg.f64 (*.f64 eps eps)) (/.f64 #s(literal -1 binary64) eps)))))
accuracy	28.071482413660767	(.f64 (neg.f64 (.f64 eps eps)) (/.f64 #s(literal -1 binary64) eps))
accuracy	0.0078125	(.f64 (.f64 (sin.f64 #s(approx (* 1/2 (+ (* 2 x) eps)) (fma.f64 eps #s(literal 1/2 binary64) x))) #s(approx (sin (* 1/2 (+ 0 eps))) (.f64 (fma.f64 (fma.f64 #s(literal 1/3840 binary64) (.f64 eps eps) #s(literal -1/48 binary64)) (*.f64 eps eps) #s(literal 1/2 binary64)) eps))) #s(literal -2 binary64))
accuracy	0.04260504138909578	(sin.f64 #s(approx (* 1/2 (+ (* 2 x) eps)) (fma.f64 eps #s(literal 1/2 binary64) x)))
accuracy	0.08117142671031594	#s(approx (sin (* 1/2 (+ 0 eps))) (.f64 (fma.f64 (fma.f64 #s(literal 1/3840 binary64) (.f64 eps eps) #s(literal -1/48 binary64)) (*.f64 eps eps) #s(literal 1/2 binary64)) eps))
accuracy	0.11328125	(.f64 (sin.f64 #s(approx ( 1/2 (+ (* 2 x) eps)) (fma.f64 eps #s(literal 1/2 binary64) x))) #s(approx (sin (* 1/2 (+ 0 eps))) (.f64 (fma.f64 (fma.f64 #s(literal 1/3840 binary64) (.f64 eps eps) #s(literal -1/48 binary64)) (*.f64 eps eps) #s(literal 1/2 binary64)) eps)))
accuracy	0.16015625	(.f64 (.f64 (fma.f64 #s(literal 1/5040 binary64) (*.f64 x x) #s(literal -1/120 binary64)) x) x)
accuracy	0.30859375	(.f64 eps (-.f64 (.f64 (.f64 (fma.f64 #s(literal 1/5040 binary64) (.f64 x x) #s(literal -1/120 binary64)) x) x) #s(literal 1/6 binary64)))
accuracy	1.259623597896962	#s(approx (* (neg eps) (sin x)) (.f64 (fma.f64 (.f64 eps (-.f64 (.f64 (.f64 (fma.f64 #s(literal 1/5040 binary64) (.f64 x x) #s(literal -1/120 binary64)) x) x) #s(literal 1/6 binary64))) (.f64 x x) (neg.f64 eps)) x))
accuracy	13.326141805054661	#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (.f64 (fma.f64 (.f64 eps (-.f64 (.f64 (.f64 (fma.f64 #s(literal 1/5040 binary64) (.f64 x x) #s(literal -1/120 binary64)) x) x) #s(literal 1/6 binary64))) (.f64 x x) (neg.f64 eps)) x)))
accuracy	0	(*.f64 (neg.f64 x) eps)
accuracy	0	(neg.f64 x)
accuracy	1.2245372205972664	#s(approx (* (neg eps) (sin x)) (*.f64 (neg.f64 x) eps))
accuracy	13.326141805054661	#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (*.f64 (neg.f64 x) eps)))
accuracy	0.0078125	(.f64 (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps))) #s(approx (sin ( 1/2 (+ 0 eps))) (.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -1/645120 binary64) (.f64 eps eps) #s(literal 1/3840 binary64)) (.f64 eps eps) #s(literal -1/48 binary64)) (.f64 eps eps) #s(literal 1/2 binary64)) eps))) #s(literal -2 binary64))
accuracy	0.03150816090022567	#s(approx (sin (* 1/2 (+ 0 eps))) (.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -1/645120 binary64) (.f64 eps eps) #s(literal 1/3840 binary64)) (.f64 eps eps) #s(literal -1/48 binary64)) (.f64 eps eps) #s(literal 1/2 binary64)) eps))
accuracy	0.04260504138909578	(sin.f64 (*.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps)))
accuracy	0.11328125	(.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps))) #s(approx (sin (* 1/2 (+ 0 eps))) (.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -1/645120 binary64) (.f64 eps eps) #s(literal 1/3840 binary64)) (.f64 eps eps) #s(literal -1/48 binary64)) (.f64 eps eps) #s(literal 1/2 binary64)) eps)))

Samples

367.0ms	172×	2	valid
152.0ms	78×	1	valid
4.0ms	1×	5	exit
2.0ms	4×	0	valid
2.0ms	1×	3	valid

Compiler

Compiled 483 to 65 computations (86.5% saved)

Precisions

Click to see histograms. Total time spent on operations: 424.0ms

const: 162.0ms (38.2% of total)

ival-mult: 96.0ms (22.7% of total)

ival-cos: 77.0ms (18.2% of total)

adjust: 45.0ms (10.6% of total)

ival-add: 20.0ms (4.7% of total)

ival-sin: 10.0ms (2.4% of total)

ival-sub: 5.0ms (1.2% of total)

ival-div: 4.0ms (0.9% of total)

ival-neg: 3.0ms (0.7% of total)

exact: 1.0ms (0.2% of total)

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

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

series67.0ms (0.4%)

Memory

10.7MiB live, 49.2MiB allocated

Counts

23 → 480

Calls

Call 1

Inputs
#s(alt (.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps)) (patch (.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps)) #<representation binary64>) () ())
#s(alt (.f64 (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps))) #s(approx (sin ( 1/2 (+ 0 eps))) (.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -1/645120 binary64) (.f64 eps eps) #s(literal 1/3840 binary64)) (.f64 eps eps) #s(literal -1/48 binary64)) (.f64 eps eps) #s(literal 1/2 binary64)) eps))) #s(literal -2 binary64)) (patch (.f64 (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps))) #s(approx (sin ( 1/2 (+ 0 eps))) (.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -1/645120 binary64) (.f64 eps eps) #s(literal 1/3840 binary64)) (.f64 eps eps) #s(literal -1/48 binary64)) (.f64 eps eps) #s(literal 1/2 binary64)) eps))) #s(literal -2 binary64)) #<representation binary64>) () ())
#s(alt (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps))) #s(approx (sin (* 1/2 (+ 0 eps))) (.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -1/645120 binary64) (.f64 eps eps) #s(literal 1/3840 binary64)) (.f64 eps eps) #s(literal -1/48 binary64)) (.f64 eps eps) #s(literal 1/2 binary64)) eps))) (patch (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps))) #s(approx (sin (* 1/2 (+ 0 eps))) (.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -1/645120 binary64) (.f64 eps eps) #s(literal 1/3840 binary64)) (.f64 eps eps) #s(literal -1/48 binary64)) (.f64 eps eps) #s(literal 1/2 binary64)) eps))) #<representation binary64>) () ())
#s(alt (sin.f64 (.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps))) (patch (sin.f64 (.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps))) #<representation binary64>) () ())
#s(alt #s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (.f64 (neg.f64 x) eps))) (patch #s(approx (- (cos (+ x eps)) (cos x)) #s(approx ( (neg eps) (sin x)) (*.f64 (neg.f64 x) eps))) #<representation binary64>) () ())
#s(alt #s(approx (* (neg eps) (sin x)) (.f64 (neg.f64 x) eps)) (patch #s(approx ( (neg eps) (sin x)) (*.f64 (neg.f64 x) eps)) #<representation binary64>) () ())
#s(alt (.f64 (neg.f64 x) eps) (patch (.f64 (neg.f64 x) eps) #<representation binary64>) () ())
#s(alt (neg.f64 x) (patch (neg.f64 x) #<representation binary64>) () ())
#s(alt (fma.f64 (.f64 eps (-.f64 (.f64 (.f64 (fma.f64 #s(literal 1/5040 binary64) (.f64 x x) #s(literal -1/120 binary64)) x) x) #s(literal 1/6 binary64))) (.f64 x x) (neg.f64 eps)) (patch (fma.f64 (.f64 eps (-.f64 (.f64 (.f64 (fma.f64 #s(literal 1/5040 binary64) (.f64 x x) #s(literal -1/120 binary64)) x) x) #s(literal 1/6 binary64))) (.f64 x x) (neg.f64 eps)) #<representation binary64>) () ())
#s(alt (-.f64 (.f64 (.f64 (fma.f64 #s(literal 1/5040 binary64) (.f64 x x) #s(literal -1/120 binary64)) x) x) #s(literal 1/6 binary64)) (patch (-.f64 (.f64 (.f64 (fma.f64 #s(literal 1/5040 binary64) (.f64 x x) #s(literal -1/120 binary64)) x) x) #s(literal 1/6 binary64)) #<representation binary64>) () ())
#s(alt #s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (.f64 (fma.f64 (.f64 eps (-.f64 (.f64 (.f64 (fma.f64 #s(literal 1/5040 binary64) (.f64 x x) #s(literal -1/120 binary64)) x) x) #s(literal 1/6 binary64))) (.f64 x x) (neg.f64 eps)) x))) (patch #s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (.f64 (fma.f64 (.f64 eps (-.f64 (.f64 (.f64 (fma.f64 #s(literal 1/5040 binary64) (.f64 x x) #s(literal -1/120 binary64)) x) x) #s(literal 1/6 binary64))) (.f64 x x) (neg.f64 eps)) x))) #<representation binary64>) () ())
#s(alt #s(approx (* (neg eps) (sin x)) (.f64 (fma.f64 (.f64 eps (-.f64 (.f64 (.f64 (fma.f64 #s(literal 1/5040 binary64) (.f64 x x) #s(literal -1/120 binary64)) x) x) #s(literal 1/6 binary64))) (.f64 x x) (neg.f64 eps)) x)) (patch #s(approx (* (neg eps) (sin x)) (.f64 (fma.f64 (.f64 eps (-.f64 (.f64 (.f64 (fma.f64 #s(literal 1/5040 binary64) (.f64 x x) #s(literal -1/120 binary64)) x) x) #s(literal 1/6 binary64))) (.f64 x x) (neg.f64 eps)) x)) #<representation binary64>) () ())
#s(alt (.f64 (.f64 (sin.f64 #s(approx (* 1/2 (+ (* 2 x) eps)) (fma.f64 eps #s(literal 1/2 binary64) x))) #s(approx (sin (* 1/2 (+ 0 eps))) (.f64 (fma.f64 (fma.f64 #s(literal 1/3840 binary64) (.f64 eps eps) #s(literal -1/48 binary64)) (.f64 eps eps) #s(literal 1/2 binary64)) eps))) #s(literal -2 binary64)) (patch (.f64 (.f64 (sin.f64 #s(approx ( 1/2 (+ (* 2 x) eps)) (fma.f64 eps #s(literal 1/2 binary64) x))) #s(approx (sin (* 1/2 (+ 0 eps))) (.f64 (fma.f64 (fma.f64 #s(literal 1/3840 binary64) (.f64 eps eps) #s(literal -1/48 binary64)) (*.f64 eps eps) #s(literal 1/2 binary64)) eps))) #s(literal -2 binary64)) #<representation binary64>) () ())
#s(alt (.f64 (sin.f64 #s(approx ( 1/2 (+ (* 2 x) eps)) (fma.f64 eps #s(literal 1/2 binary64) x))) #s(approx (sin (* 1/2 (+ 0 eps))) (.f64 (fma.f64 (fma.f64 #s(literal 1/3840 binary64) (.f64 eps eps) #s(literal -1/48 binary64)) (.f64 eps eps) #s(literal 1/2 binary64)) eps))) (patch (.f64 (sin.f64 #s(approx (* 1/2 (+ (* 2 x) eps)) (fma.f64 eps #s(literal 1/2 binary64) x))) #s(approx (sin (* 1/2 (+ 0 eps))) (.f64 (fma.f64 (fma.f64 #s(literal 1/3840 binary64) (.f64 eps eps) #s(literal -1/48 binary64)) (*.f64 eps eps) #s(literal 1/2 binary64)) eps))) #<representation binary64>) () ())
#s(alt (sin.f64 #s(approx (* 1/2 (+ (* 2 x) eps)) (fma.f64 eps #s(literal 1/2 binary64) x))) (patch (sin.f64 #s(approx (* 1/2 (+ (* 2 x) eps)) (fma.f64 eps #s(literal 1/2 binary64) x))) #<representation binary64>) () ())
#s(alt #s(approx (* 1/2 (+ (* 2 x) eps)) (fma.f64 eps #s(literal 1/2 binary64) x)) (patch #s(approx (* 1/2 (+ (* 2 x) eps)) (fma.f64 eps #s(literal 1/2 binary64) x)) #<representation binary64>) () ())
#s(alt (.f64 (neg.f64 (.f64 eps eps)) (/.f64 #s(literal -1 binary64) eps)) (patch (.f64 (neg.f64 (.f64 eps eps)) (/.f64 #s(literal -1 binary64) eps)) #<representation binary64>) () ())
#s(alt (.f64 (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps))) (sin.f64 (.f64 #s(literal 1/2 binary64) (.f64 (neg.f64 (.f64 eps eps)) (/.f64 #s(literal -1 binary64) eps))))) #s(literal -2 binary64)) (patch (.f64 (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps))) (sin.f64 (.f64 #s(literal 1/2 binary64) (.f64 (neg.f64 (.f64 eps eps)) (/.f64 #s(literal -1 binary64) eps))))) #s(literal -2 binary64)) #<representation binary64>) () ())
#s(alt (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps))) (sin.f64 (.f64 #s(literal 1/2 binary64) (.f64 (neg.f64 (.f64 eps eps)) (/.f64 #s(literal -1 binary64) eps))))) (patch (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps))) (sin.f64 (.f64 #s(literal 1/2 binary64) (.f64 (neg.f64 (.f64 eps eps)) (/.f64 #s(literal -1 binary64) eps))))) #<representation binary64>) () ())
#s(alt #s(approx (sin (* 1/2 (+ 0 eps))) (.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -1/645120 binary64) (.f64 eps eps) #s(literal 1/3840 binary64)) (.f64 eps eps) #s(literal -1/48 binary64)) (.f64 eps eps) #s(literal 1/2 binary64)) eps)) (patch #s(approx (sin (* 1/2 (+ 0 eps))) (.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -1/645120 binary64) (.f64 eps eps) #s(literal 1/3840 binary64)) (.f64 eps eps) #s(literal -1/48 binary64)) (.f64 eps eps) #s(literal 1/2 binary64)) eps)) #<representation binary64>) () ())
#s(alt (.f64 eps (-.f64 (.f64 (.f64 (fma.f64 #s(literal 1/5040 binary64) (.f64 x x) #s(literal -1/120 binary64)) x) x) #s(literal 1/6 binary64))) (patch (.f64 eps (-.f64 (.f64 (.f64 (fma.f64 #s(literal 1/5040 binary64) (.f64 x x) #s(literal -1/120 binary64)) x) x) #s(literal 1/6 binary64))) #<representation binary64>) () ())
#s(alt (.f64 (.f64 (fma.f64 #s(literal 1/5040 binary64) (.f64 x x) #s(literal -1/120 binary64)) x) x) (patch (.f64 (.f64 (fma.f64 #s(literal 1/5040 binary64) (.f64 x x) #s(literal -1/120 binary64)) x) x) #<representation binary64>) () ())
#s(alt #s(approx (sin (* 1/2 (+ 0 eps))) (.f64 (fma.f64 (fma.f64 #s(literal 1/3840 binary64) (.f64 eps eps) #s(literal -1/48 binary64)) (.f64 eps eps) #s(literal 1/2 binary64)) eps)) (patch #s(approx (sin ( 1/2 (+ 0 eps))) (.f64 (fma.f64 (fma.f64 #s(literal 1/3840 binary64) (.f64 eps eps) #s(literal -1/48 binary64)) (*.f64 eps eps) #s(literal 1/2 binary64)) eps)) #<representation binary64>) () ())

Outputs
#s(alt (* 1/2 eps) (taylor 0 x) (#s(alt (.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps)) (patch (.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps)) #<representation binary64>) () ())) ())
#s(alt (+ x (* 1/2 eps)) (taylor 0 x) (#s(alt (.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps)) (patch (.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps)) #<representation binary64>) () ())) ())
#s(alt (+ x (* 1/2 eps)) (taylor 0 x) (#s(alt (.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps)) (patch (.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps)) #<representation binary64>) () ())) ())
#s(alt (+ x (* 1/2 eps)) (taylor 0 x) (#s(alt (.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps)) (patch (.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps)) #<representation binary64>) () ())) ())
#s(alt x (taylor inf x) (#s(alt (.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps)) (patch (.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps)) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1 (* 1/2 (/ eps x)))) (taylor inf x) (#s(alt (.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps)) (patch (.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps)) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1 (* 1/2 (/ eps x)))) (taylor inf x) (#s(alt (.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps)) (patch (.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps)) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1 (* 1/2 (/ eps x)))) (taylor inf x) (#s(alt (.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps)) (patch (.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps)) #<representation binary64>) () ())) ())
#s(alt x (taylor -inf x) (#s(alt (.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps)) (patch (.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (- (* -1/2 (/ eps x)) 1))) (taylor -inf x) (#s(alt (.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps)) (patch (.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (- (* -1/2 (/ eps x)) 1))) (taylor -inf x) (#s(alt (.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps)) (patch (.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (- (* -1/2 (/ eps x)) 1))) (taylor -inf x) (#s(alt (.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps)) (patch (.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps)) #<representation binary64>) () ())) ())
#s(alt x (taylor 0 eps) (#s(alt (.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps)) (patch (.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps)) #<representation binary64>) () ())) ())
#s(alt (+ x (* 1/2 eps)) (taylor 0 eps) (#s(alt (.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps)) (patch (.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps)) #<representation binary64>) () ())) ())
#s(alt (+ x (* 1/2 eps)) (taylor 0 eps) (#s(alt (.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps)) (patch (.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps)) #<representation binary64>) () ())) ())
#s(alt (+ x (* 1/2 eps)) (taylor 0 eps) (#s(alt (.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps)) (patch (.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps)) #<representation binary64>) () ())) ())
#s(alt (* 1/2 eps) (taylor inf eps) (#s(alt (.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps)) (patch (.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps)) #<representation binary64>) () ())) ())
#s(alt (* eps (+ 1/2 (/ x eps))) (taylor inf eps) (#s(alt (.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps)) (patch (.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps)) #<representation binary64>) () ())) ())
#s(alt (* eps (+ 1/2 (/ x eps))) (taylor inf eps) (#s(alt (.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps)) (patch (.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps)) #<representation binary64>) () ())) ())
#s(alt (* eps (+ 1/2 (/ x eps))) (taylor inf eps) (#s(alt (.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps)) (patch (.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps)) #<representation binary64>) () ())) ())
#s(alt (* 1/2 eps) (taylor -inf eps) (#s(alt (.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps)) (patch (.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* eps (- (* -1 (/ x eps)) 1/2))) (taylor -inf eps) (#s(alt (.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps)) (patch (.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* eps (- (* -1 (/ x eps)) 1/2))) (taylor -inf eps) (#s(alt (.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps)) (patch (.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* eps (- (* -1 (/ x eps)) 1/2))) (taylor -inf eps) (#s(alt (.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps)) (patch (.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps)) #<representation binary64>) () ())) ())
#s(alt (* -2 (pow (sin (* 1/2 eps)) 2)) (taylor 0 x) (#s(alt (.f64 (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps))) #s(approx (sin ( 1/2 (+ 0 eps))) (.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -1/645120 binary64) (.f64 eps eps) #s(literal 1/3840 binary64)) (.f64 eps eps) #s(literal -1/48 binary64)) (.f64 eps eps) #s(literal 1/2 binary64)) eps))) #s(literal -2 binary64)) (patch (.f64 (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps))) #s(approx (sin ( 1/2 (+ 0 eps))) (.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -1/645120 binary64) (.f64 eps eps) #s(literal 1/3840 binary64)) (.f64 eps eps) #s(literal -1/48 binary64)) (.f64 eps eps) #s(literal 1/2 binary64)) eps))) #s(literal -2 binary64)) #<representation binary64>) () ())) ())
#s(alt (+ (* -2 (* x (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))) (* -2 (pow (sin (* 1/2 eps)) 2))) (taylor 0 x) (#s(alt (.f64 (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps))) #s(approx (sin ( 1/2 (+ 0 eps))) (.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -1/645120 binary64) (.f64 eps eps) #s(literal 1/3840 binary64)) (.f64 eps eps) #s(literal -1/48 binary64)) (.f64 eps eps) #s(literal 1/2 binary64)) eps))) #s(literal -2 binary64)) (patch (.f64 (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps))) #s(approx (sin ( 1/2 (+ 0 eps))) (.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -1/645120 binary64) (.f64 eps eps) #s(literal 1/3840 binary64)) (.f64 eps eps) #s(literal -1/48 binary64)) (.f64 eps eps) #s(literal 1/2 binary64)) eps))) #s(literal -2 binary64)) #<representation binary64>) () ())) ())
#s(alt (+ (* -2 (pow (sin (* 1/2 eps)) 2)) (* x (+ (* -2 (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) (* x (pow (sin (* 1/2 eps)) 2))))) (taylor 0 x) (#s(alt (.f64 (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps))) #s(approx (sin ( 1/2 (+ 0 eps))) (.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -1/645120 binary64) (.f64 eps eps) #s(literal 1/3840 binary64)) (.f64 eps eps) #s(literal -1/48 binary64)) (.f64 eps eps) #s(literal 1/2 binary64)) eps))) #s(literal -2 binary64)) (patch (.f64 (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps))) #s(approx (sin ( 1/2 (+ 0 eps))) (.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -1/645120 binary64) (.f64 eps eps) #s(literal 1/3840 binary64)) (.f64 eps eps) #s(literal -1/48 binary64)) (.f64 eps eps) #s(literal 1/2 binary64)) eps))) #s(literal -2 binary64)) #<representation binary64>) () ())) ())
#s(alt (+ (* -2 (pow (sin (* 1/2 eps)) 2)) (* x (+ (* -2 (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) (* x (+ (* 1/3 (* x (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))) (pow (sin (* 1/2 eps)) 2)))))) (taylor 0 x) (#s(alt (.f64 (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps))) #s(approx (sin ( 1/2 (+ 0 eps))) (.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -1/645120 binary64) (.f64 eps eps) #s(literal 1/3840 binary64)) (.f64 eps eps) #s(literal -1/48 binary64)) (.f64 eps eps) #s(literal 1/2 binary64)) eps))) #s(literal -2 binary64)) (patch (.f64 (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps))) #s(approx (sin ( 1/2 (+ 0 eps))) (.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -1/645120 binary64) (.f64 eps eps) #s(literal 1/3840 binary64)) (.f64 eps eps) #s(literal -1/48 binary64)) (.f64 eps eps) #s(literal 1/2 binary64)) eps))) #s(literal -2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (+ eps (* 2 x)))))) (taylor inf x) (#s(alt (.f64 (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps))) #s(approx (sin ( 1/2 (+ 0 eps))) (.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -1/645120 binary64) (.f64 eps eps) #s(literal 1/3840 binary64)) (.f64 eps eps) #s(literal -1/48 binary64)) (.f64 eps eps) #s(literal 1/2 binary64)) eps))) #s(literal -2 binary64)) (patch (.f64 (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps))) #s(approx (sin ( 1/2 (+ 0 eps))) (.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -1/645120 binary64) (.f64 eps eps) #s(literal 1/3840 binary64)) (.f64 eps eps) #s(literal -1/48 binary64)) (.f64 eps eps) #s(literal 1/2 binary64)) eps))) #s(literal -2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (+ eps (* 2 x)))))) (taylor inf x) (#s(alt (.f64 (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps))) #s(approx (sin ( 1/2 (+ 0 eps))) (.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -1/645120 binary64) (.f64 eps eps) #s(literal 1/3840 binary64)) (.f64 eps eps) #s(literal -1/48 binary64)) (.f64 eps eps) #s(literal 1/2 binary64)) eps))) #s(literal -2 binary64)) (patch (.f64 (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps))) #s(approx (sin ( 1/2 (+ 0 eps))) (.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -1/645120 binary64) (.f64 eps eps) #s(literal 1/3840 binary64)) (.f64 eps eps) #s(literal -1/48 binary64)) (.f64 eps eps) #s(literal 1/2 binary64)) eps))) #s(literal -2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (+ eps (* 2 x)))))) (taylor inf x) (#s(alt (.f64 (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps))) #s(approx (sin ( 1/2 (+ 0 eps))) (.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -1/645120 binary64) (.f64 eps eps) #s(literal 1/3840 binary64)) (.f64 eps eps) #s(literal -1/48 binary64)) (.f64 eps eps) #s(literal 1/2 binary64)) eps))) #s(literal -2 binary64)) (patch (.f64 (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps))) #s(approx (sin ( 1/2 (+ 0 eps))) (.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -1/645120 binary64) (.f64 eps eps) #s(literal 1/3840 binary64)) (.f64 eps eps) #s(literal -1/48 binary64)) (.f64 eps eps) #s(literal 1/2 binary64)) eps))) #s(literal -2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (+ eps (* 2 x)))))) (taylor inf x) (#s(alt (.f64 (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps))) #s(approx (sin ( 1/2 (+ 0 eps))) (.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -1/645120 binary64) (.f64 eps eps) #s(literal 1/3840 binary64)) (.f64 eps eps) #s(literal -1/48 binary64)) (.f64 eps eps) #s(literal 1/2 binary64)) eps))) #s(literal -2 binary64)) (patch (.f64 (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps))) #s(approx (sin ( 1/2 (+ 0 eps))) (.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -1/645120 binary64) (.f64 eps eps) #s(literal 1/3840 binary64)) (.f64 eps eps) #s(literal -1/48 binary64)) (.f64 eps eps) #s(literal 1/2 binary64)) eps))) #s(literal -2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (- eps (* -2 x)))))) (taylor -inf x) (#s(alt (.f64 (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps))) #s(approx (sin ( 1/2 (+ 0 eps))) (.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -1/645120 binary64) (.f64 eps eps) #s(literal 1/3840 binary64)) (.f64 eps eps) #s(literal -1/48 binary64)) (.f64 eps eps) #s(literal 1/2 binary64)) eps))) #s(literal -2 binary64)) (patch (.f64 (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps))) #s(approx (sin ( 1/2 (+ 0 eps))) (.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -1/645120 binary64) (.f64 eps eps) #s(literal 1/3840 binary64)) (.f64 eps eps) #s(literal -1/48 binary64)) (.f64 eps eps) #s(literal 1/2 binary64)) eps))) #s(literal -2 binary64)) #<representation binary64>) () ())) ())
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#s(alt (* eps (- (* (pow x 2) (- (* 1/5040 (pow x 2)) 1/120)) 1/6)) (taylor inf eps) (#s(alt (.f64 eps (-.f64 (.f64 (.f64 (fma.f64 #s(literal 1/5040 binary64) (.f64 x x) #s(literal -1/120 binary64)) x) x) #s(literal 1/6 binary64))) (patch (.f64 eps (-.f64 (.f64 (.f64 (fma.f64 #s(literal 1/5040 binary64) (.f64 x x) #s(literal -1/120 binary64)) x) x) #s(literal 1/6 binary64))) #<representation binary64>) () ())) ())
#s(alt (* eps (- (* (pow x 2) (- (* 1/5040 (pow x 2)) 1/120)) 1/6)) (taylor inf eps) (#s(alt (.f64 eps (-.f64 (.f64 (.f64 (fma.f64 #s(literal 1/5040 binary64) (.f64 x x) #s(literal -1/120 binary64)) x) x) #s(literal 1/6 binary64))) (patch (.f64 eps (-.f64 (.f64 (.f64 (fma.f64 #s(literal 1/5040 binary64) (.f64 x x) #s(literal -1/120 binary64)) x) x) #s(literal 1/6 binary64))) #<representation binary64>) () ())) ())
#s(alt (* eps (- (* (pow x 2) (- (* 1/5040 (pow x 2)) 1/120)) 1/6)) (taylor -inf eps) (#s(alt (.f64 eps (-.f64 (.f64 (.f64 (fma.f64 #s(literal 1/5040 binary64) (.f64 x x) #s(literal -1/120 binary64)) x) x) #s(literal 1/6 binary64))) (patch (.f64 eps (-.f64 (.f64 (.f64 (fma.f64 #s(literal 1/5040 binary64) (.f64 x x) #s(literal -1/120 binary64)) x) x) #s(literal 1/6 binary64))) #<representation binary64>) () ())) ())
#s(alt (* eps (- (* (pow x 2) (- (* 1/5040 (pow x 2)) 1/120)) 1/6)) (taylor -inf eps) (#s(alt (.f64 eps (-.f64 (.f64 (.f64 (fma.f64 #s(literal 1/5040 binary64) (.f64 x x) #s(literal -1/120 binary64)) x) x) #s(literal 1/6 binary64))) (patch (.f64 eps (-.f64 (.f64 (.f64 (fma.f64 #s(literal 1/5040 binary64) (.f64 x x) #s(literal -1/120 binary64)) x) x) #s(literal 1/6 binary64))) #<representation binary64>) () ())) ())
#s(alt (* eps (- (* (pow x 2) (- (* 1/5040 (pow x 2)) 1/120)) 1/6)) (taylor -inf eps) (#s(alt (.f64 eps (-.f64 (.f64 (.f64 (fma.f64 #s(literal 1/5040 binary64) (.f64 x x) #s(literal -1/120 binary64)) x) x) #s(literal 1/6 binary64))) (patch (.f64 eps (-.f64 (.f64 (.f64 (fma.f64 #s(literal 1/5040 binary64) (.f64 x x) #s(literal -1/120 binary64)) x) x) #s(literal 1/6 binary64))) #<representation binary64>) () ())) ())
#s(alt (* eps (- (* (pow x 2) (- (* 1/5040 (pow x 2)) 1/120)) 1/6)) (taylor -inf eps) (#s(alt (.f64 eps (-.f64 (.f64 (.f64 (fma.f64 #s(literal 1/5040 binary64) (.f64 x x) #s(literal -1/120 binary64)) x) x) #s(literal 1/6 binary64))) (patch (.f64 eps (-.f64 (.f64 (.f64 (fma.f64 #s(literal 1/5040 binary64) (.f64 x x) #s(literal -1/120 binary64)) x) x) #s(literal 1/6 binary64))) #<representation binary64>) () ())) ())
#s(alt (* -1/6 eps) (taylor 0 x) (#s(alt (.f64 eps (-.f64 (.f64 (.f64 (fma.f64 #s(literal 1/5040 binary64) (.f64 x x) #s(literal -1/120 binary64)) x) x) #s(literal 1/6 binary64))) (patch (.f64 eps (-.f64 (.f64 (.f64 (fma.f64 #s(literal 1/5040 binary64) (.f64 x x) #s(literal -1/120 binary64)) x) x) #s(literal 1/6 binary64))) #<representation binary64>) () ())) ())
#s(alt (+ (* -1/6 eps) (* -1/120 (* eps (pow x 2)))) (taylor 0 x) (#s(alt (.f64 eps (-.f64 (.f64 (.f64 (fma.f64 #s(literal 1/5040 binary64) (.f64 x x) #s(literal -1/120 binary64)) x) x) #s(literal 1/6 binary64))) (patch (.f64 eps (-.f64 (.f64 (.f64 (fma.f64 #s(literal 1/5040 binary64) (.f64 x x) #s(literal -1/120 binary64)) x) x) #s(literal 1/6 binary64))) #<representation binary64>) () ())) ())
#s(alt (+ (* -1/6 eps) (* (pow x 2) (+ (* -1/120 eps) (* 1/5040 (* eps (pow x 2)))))) (taylor 0 x) (#s(alt (.f64 eps (-.f64 (.f64 (.f64 (fma.f64 #s(literal 1/5040 binary64) (.f64 x x) #s(literal -1/120 binary64)) x) x) #s(literal 1/6 binary64))) (patch (.f64 eps (-.f64 (.f64 (.f64 (fma.f64 #s(literal 1/5040 binary64) (.f64 x x) #s(literal -1/120 binary64)) x) x) #s(literal 1/6 binary64))) #<representation binary64>) () ())) ())
#s(alt (+ (* -1/6 eps) (* (pow x 2) (+ (* -1/120 eps) (* 1/5040 (* eps (pow x 2)))))) (taylor 0 x) (#s(alt (.f64 eps (-.f64 (.f64 (.f64 (fma.f64 #s(literal 1/5040 binary64) (.f64 x x) #s(literal -1/120 binary64)) x) x) #s(literal 1/6 binary64))) (patch (.f64 eps (-.f64 (.f64 (.f64 (fma.f64 #s(literal 1/5040 binary64) (.f64 x x) #s(literal -1/120 binary64)) x) x) #s(literal 1/6 binary64))) #<representation binary64>) () ())) ())
#s(alt (* 1/5040 (* eps (pow x 4))) (taylor inf x) (#s(alt (.f64 eps (-.f64 (.f64 (.f64 (fma.f64 #s(literal 1/5040 binary64) (.f64 x x) #s(literal -1/120 binary64)) x) x) #s(literal 1/6 binary64))) (patch (.f64 eps (-.f64 (.f64 (.f64 (fma.f64 #s(literal 1/5040 binary64) (.f64 x x) #s(literal -1/120 binary64)) x) x) #s(literal 1/6 binary64))) #<representation binary64>) () ())) ())
#s(alt (* (pow x 4) (+ (* -1/120 (/ eps (pow x 2))) (* 1/5040 eps))) (taylor inf x) (#s(alt (.f64 eps (-.f64 (.f64 (.f64 (fma.f64 #s(literal 1/5040 binary64) (.f64 x x) #s(literal -1/120 binary64)) x) x) #s(literal 1/6 binary64))) (patch (.f64 eps (-.f64 (.f64 (.f64 (fma.f64 #s(literal 1/5040 binary64) (.f64 x x) #s(literal -1/120 binary64)) x) x) #s(literal 1/6 binary64))) #<representation binary64>) () ())) ())
#s(alt (* (pow x 4) (+ (* -1/6 (/ eps (pow x 4))) (+ (* -1/120 (/ eps (pow x 2))) (* 1/5040 eps)))) (taylor inf x) (#s(alt (.f64 eps (-.f64 (.f64 (.f64 (fma.f64 #s(literal 1/5040 binary64) (.f64 x x) #s(literal -1/120 binary64)) x) x) #s(literal 1/6 binary64))) (patch (.f64 eps (-.f64 (.f64 (.f64 (fma.f64 #s(literal 1/5040 binary64) (.f64 x x) #s(literal -1/120 binary64)) x) x) #s(literal 1/6 binary64))) #<representation binary64>) () ())) ())
#s(alt (* (pow x 4) (+ (* -1/6 (/ eps (pow x 4))) (+ (* -1/120 (/ eps (pow x 2))) (* 1/5040 eps)))) (taylor inf x) (#s(alt (.f64 eps (-.f64 (.f64 (.f64 (fma.f64 #s(literal 1/5040 binary64) (.f64 x x) #s(literal -1/120 binary64)) x) x) #s(literal 1/6 binary64))) (patch (.f64 eps (-.f64 (.f64 (.f64 (fma.f64 #s(literal 1/5040 binary64) (.f64 x x) #s(literal -1/120 binary64)) x) x) #s(literal 1/6 binary64))) #<representation binary64>) () ())) ())
#s(alt (* 1/5040 (* eps (pow x 4))) (taylor -inf x) (#s(alt (.f64 eps (-.f64 (.f64 (.f64 (fma.f64 #s(literal 1/5040 binary64) (.f64 x x) #s(literal -1/120 binary64)) x) x) #s(literal 1/6 binary64))) (patch (.f64 eps (-.f64 (.f64 (.f64 (fma.f64 #s(literal 1/5040 binary64) (.f64 x x) #s(literal -1/120 binary64)) x) x) #s(literal 1/6 binary64))) #<representation binary64>) () ())) ())
#s(alt (* (pow x 4) (+ (* -1/120 (/ eps (pow x 2))) (* 1/5040 eps))) (taylor -inf x) (#s(alt (.f64 eps (-.f64 (.f64 (.f64 (fma.f64 #s(literal 1/5040 binary64) (.f64 x x) #s(literal -1/120 binary64)) x) x) #s(literal 1/6 binary64))) (patch (.f64 eps (-.f64 (.f64 (.f64 (fma.f64 #s(literal 1/5040 binary64) (.f64 x x) #s(literal -1/120 binary64)) x) x) #s(literal 1/6 binary64))) #<representation binary64>) () ())) ())
#s(alt (* (pow x 4) (+ (* -1/6 (/ eps (pow x 4))) (+ (* -1/120 (/ eps (pow x 2))) (* 1/5040 eps)))) (taylor -inf x) (#s(alt (.f64 eps (-.f64 (.f64 (.f64 (fma.f64 #s(literal 1/5040 binary64) (.f64 x x) #s(literal -1/120 binary64)) x) x) #s(literal 1/6 binary64))) (patch (.f64 eps (-.f64 (.f64 (.f64 (fma.f64 #s(literal 1/5040 binary64) (.f64 x x) #s(literal -1/120 binary64)) x) x) #s(literal 1/6 binary64))) #<representation binary64>) () ())) ())
#s(alt (* (pow x 4) (+ (* -1/6 (/ eps (pow x 4))) (+ (* -1/120 (/ eps (pow x 2))) (* 1/5040 eps)))) (taylor -inf x) (#s(alt (.f64 eps (-.f64 (.f64 (.f64 (fma.f64 #s(literal 1/5040 binary64) (.f64 x x) #s(literal -1/120 binary64)) x) x) #s(literal 1/6 binary64))) (patch (.f64 eps (-.f64 (.f64 (.f64 (fma.f64 #s(literal 1/5040 binary64) (.f64 x x) #s(literal -1/120 binary64)) x) x) #s(literal 1/6 binary64))) #<representation binary64>) () ())) ())
#s(alt (* -1/120 (pow x 2)) (taylor 0 x) (#s(alt (.f64 (.f64 (fma.f64 #s(literal 1/5040 binary64) (.f64 x x) #s(literal -1/120 binary64)) x) x) (patch (.f64 (.f64 (fma.f64 #s(literal 1/5040 binary64) (.f64 x x) #s(literal -1/120 binary64)) x) x) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (- (* 1/5040 (pow x 2)) 1/120)) (taylor 0 x) (#s(alt (.f64 (.f64 (fma.f64 #s(literal 1/5040 binary64) (.f64 x x) #s(literal -1/120 binary64)) x) x) (patch (.f64 (.f64 (fma.f64 #s(literal 1/5040 binary64) (.f64 x x) #s(literal -1/120 binary64)) x) x) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (- (* 1/5040 (pow x 2)) 1/120)) (taylor 0 x) (#s(alt (.f64 (.f64 (fma.f64 #s(literal 1/5040 binary64) (.f64 x x) #s(literal -1/120 binary64)) x) x) (patch (.f64 (.f64 (fma.f64 #s(literal 1/5040 binary64) (.f64 x x) #s(literal -1/120 binary64)) x) x) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (- (* 1/5040 (pow x 2)) 1/120)) (taylor 0 x) (#s(alt (.f64 (.f64 (fma.f64 #s(literal 1/5040 binary64) (.f64 x x) #s(literal -1/120 binary64)) x) x) (patch (.f64 (.f64 (fma.f64 #s(literal 1/5040 binary64) (.f64 x x) #s(literal -1/120 binary64)) x) x) #<representation binary64>) () ())) ())
#s(alt (* 1/5040 (pow x 4)) (taylor inf x) (#s(alt (.f64 (.f64 (fma.f64 #s(literal 1/5040 binary64) (.f64 x x) #s(literal -1/120 binary64)) x) x) (patch (.f64 (.f64 (fma.f64 #s(literal 1/5040 binary64) (.f64 x x) #s(literal -1/120 binary64)) x) x) #<representation binary64>) () ())) ())
#s(alt (* (pow x 4) (- 1/5040 (* 1/120 (/ 1 (pow x 2))))) (taylor inf x) (#s(alt (.f64 (.f64 (fma.f64 #s(literal 1/5040 binary64) (.f64 x x) #s(literal -1/120 binary64)) x) x) (patch (.f64 (.f64 (fma.f64 #s(literal 1/5040 binary64) (.f64 x x) #s(literal -1/120 binary64)) x) x) #<representation binary64>) () ())) ())
#s(alt (* (pow x 4) (- 1/5040 (* 1/120 (/ 1 (pow x 2))))) (taylor inf x) (#s(alt (.f64 (.f64 (fma.f64 #s(literal 1/5040 binary64) (.f64 x x) #s(literal -1/120 binary64)) x) x) (patch (.f64 (.f64 (fma.f64 #s(literal 1/5040 binary64) (.f64 x x) #s(literal -1/120 binary64)) x) x) #<representation binary64>) () ())) ())
#s(alt (* (pow x 4) (- 1/5040 (* 1/120 (/ 1 (pow x 2))))) (taylor inf x) (#s(alt (.f64 (.f64 (fma.f64 #s(literal 1/5040 binary64) (.f64 x x) #s(literal -1/120 binary64)) x) x) (patch (.f64 (.f64 (fma.f64 #s(literal 1/5040 binary64) (.f64 x x) #s(literal -1/120 binary64)) x) x) #<representation binary64>) () ())) ())
#s(alt (* 1/5040 (pow x 4)) (taylor -inf x) (#s(alt (.f64 (.f64 (fma.f64 #s(literal 1/5040 binary64) (.f64 x x) #s(literal -1/120 binary64)) x) x) (patch (.f64 (.f64 (fma.f64 #s(literal 1/5040 binary64) (.f64 x x) #s(literal -1/120 binary64)) x) x) #<representation binary64>) () ())) ())
#s(alt (* (pow x 4) (- 1/5040 (* 1/120 (/ 1 (pow x 2))))) (taylor -inf x) (#s(alt (.f64 (.f64 (fma.f64 #s(literal 1/5040 binary64) (.f64 x x) #s(literal -1/120 binary64)) x) x) (patch (.f64 (.f64 (fma.f64 #s(literal 1/5040 binary64) (.f64 x x) #s(literal -1/120 binary64)) x) x) #<representation binary64>) () ())) ())
#s(alt (* (pow x 4) (- 1/5040 (* 1/120 (/ 1 (pow x 2))))) (taylor -inf x) (#s(alt (.f64 (.f64 (fma.f64 #s(literal 1/5040 binary64) (.f64 x x) #s(literal -1/120 binary64)) x) x) (patch (.f64 (.f64 (fma.f64 #s(literal 1/5040 binary64) (.f64 x x) #s(literal -1/120 binary64)) x) x) #<representation binary64>) () ())) ())
#s(alt (* (pow x 4) (- 1/5040 (* 1/120 (/ 1 (pow x 2))))) (taylor -inf x) (#s(alt (.f64 (.f64 (fma.f64 #s(literal 1/5040 binary64) (.f64 x x) #s(literal -1/120 binary64)) x) x) (patch (.f64 (.f64 (fma.f64 #s(literal 1/5040 binary64) (.f64 x x) #s(literal -1/120 binary64)) x) x) #<representation binary64>) () ())) ())
#s(alt (* 1/2 eps) (taylor 0 eps) (#s(alt #s(approx (sin (* 1/2 (+ 0 eps))) (.f64 (fma.f64 (fma.f64 #s(literal 1/3840 binary64) (.f64 eps eps) #s(literal -1/48 binary64)) (.f64 eps eps) #s(literal 1/2 binary64)) eps)) (patch #s(approx (sin ( 1/2 (+ 0 eps))) (.f64 (fma.f64 (fma.f64 #s(literal 1/3840 binary64) (.f64 eps eps) #s(literal -1/48 binary64)) (*.f64 eps eps) #s(literal 1/2 binary64)) eps)) #<representation binary64>) () ())) ())
#s(alt (* eps (+ 1/2 (* -1/48 (pow eps 2)))) (taylor 0 eps) (#s(alt #s(approx (sin (* 1/2 (+ 0 eps))) (.f64 (fma.f64 (fma.f64 #s(literal 1/3840 binary64) (.f64 eps eps) #s(literal -1/48 binary64)) (.f64 eps eps) #s(literal 1/2 binary64)) eps)) (patch #s(approx (sin ( 1/2 (+ 0 eps))) (.f64 (fma.f64 (fma.f64 #s(literal 1/3840 binary64) (.f64 eps eps) #s(literal -1/48 binary64)) (*.f64 eps eps) #s(literal 1/2 binary64)) eps)) #<representation binary64>) () ())) ())
#s(alt (* eps (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48)))) (taylor 0 eps) (#s(alt #s(approx (sin (* 1/2 (+ 0 eps))) (.f64 (fma.f64 (fma.f64 #s(literal 1/3840 binary64) (.f64 eps eps) #s(literal -1/48 binary64)) (.f64 eps eps) #s(literal 1/2 binary64)) eps)) (patch #s(approx (sin ( 1/2 (+ 0 eps))) (.f64 (fma.f64 (fma.f64 #s(literal 1/3840 binary64) (.f64 eps eps) #s(literal -1/48 binary64)) (*.f64 eps eps) #s(literal 1/2 binary64)) eps)) #<representation binary64>) () ())) ())
#s(alt (* eps (+ 1/2 (* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48)))) (taylor 0 eps) (#s(alt #s(approx (sin (* 1/2 (+ 0 eps))) (.f64 (fma.f64 (fma.f64 #s(literal 1/3840 binary64) (.f64 eps eps) #s(literal -1/48 binary64)) (.f64 eps eps) #s(literal 1/2 binary64)) eps)) (patch #s(approx (sin ( 1/2 (+ 0 eps))) (.f64 (fma.f64 (fma.f64 #s(literal 1/3840 binary64) (.f64 eps eps) #s(literal -1/48 binary64)) (*.f64 eps eps) #s(literal 1/2 binary64)) eps)) #<representation binary64>) () ())) ())
#s(alt (sin (* 1/2 eps)) (taylor inf eps) (#s(alt #s(approx (sin (* 1/2 (+ 0 eps))) (.f64 (fma.f64 (fma.f64 #s(literal 1/3840 binary64) (.f64 eps eps) #s(literal -1/48 binary64)) (.f64 eps eps) #s(literal 1/2 binary64)) eps)) (patch #s(approx (sin ( 1/2 (+ 0 eps))) (.f64 (fma.f64 (fma.f64 #s(literal 1/3840 binary64) (.f64 eps eps) #s(literal -1/48 binary64)) (*.f64 eps eps) #s(literal 1/2 binary64)) eps)) #<representation binary64>) () ())) ())
#s(alt (sin (* 1/2 eps)) (taylor inf eps) (#s(alt #s(approx (sin (* 1/2 (+ 0 eps))) (.f64 (fma.f64 (fma.f64 #s(literal 1/3840 binary64) (.f64 eps eps) #s(literal -1/48 binary64)) (.f64 eps eps) #s(literal 1/2 binary64)) eps)) (patch #s(approx (sin ( 1/2 (+ 0 eps))) (.f64 (fma.f64 (fma.f64 #s(literal 1/3840 binary64) (.f64 eps eps) #s(literal -1/48 binary64)) (*.f64 eps eps) #s(literal 1/2 binary64)) eps)) #<representation binary64>) () ())) ())
#s(alt (sin (* 1/2 eps)) (taylor inf eps) (#s(alt #s(approx (sin (* 1/2 (+ 0 eps))) (.f64 (fma.f64 (fma.f64 #s(literal 1/3840 binary64) (.f64 eps eps) #s(literal -1/48 binary64)) (.f64 eps eps) #s(literal 1/2 binary64)) eps)) (patch #s(approx (sin ( 1/2 (+ 0 eps))) (.f64 (fma.f64 (fma.f64 #s(literal 1/3840 binary64) (.f64 eps eps) #s(literal -1/48 binary64)) (*.f64 eps eps) #s(literal 1/2 binary64)) eps)) #<representation binary64>) () ())) ())
#s(alt (sin (* 1/2 eps)) (taylor inf eps) (#s(alt #s(approx (sin (* 1/2 (+ 0 eps))) (.f64 (fma.f64 (fma.f64 #s(literal 1/3840 binary64) (.f64 eps eps) #s(literal -1/48 binary64)) (.f64 eps eps) #s(literal 1/2 binary64)) eps)) (patch #s(approx (sin ( 1/2 (+ 0 eps))) (.f64 (fma.f64 (fma.f64 #s(literal 1/3840 binary64) (.f64 eps eps) #s(literal -1/48 binary64)) (*.f64 eps eps) #s(literal 1/2 binary64)) eps)) #<representation binary64>) () ())) ())
#s(alt (sin (* 1/2 eps)) (taylor -inf eps) (#s(alt #s(approx (sin (* 1/2 (+ 0 eps))) (.f64 (fma.f64 (fma.f64 #s(literal 1/3840 binary64) (.f64 eps eps) #s(literal -1/48 binary64)) (.f64 eps eps) #s(literal 1/2 binary64)) eps)) (patch #s(approx (sin ( 1/2 (+ 0 eps))) (.f64 (fma.f64 (fma.f64 #s(literal 1/3840 binary64) (.f64 eps eps) #s(literal -1/48 binary64)) (*.f64 eps eps) #s(literal 1/2 binary64)) eps)) #<representation binary64>) () ())) ())
#s(alt (sin (* 1/2 eps)) (taylor -inf eps) (#s(alt #s(approx (sin (* 1/2 (+ 0 eps))) (.f64 (fma.f64 (fma.f64 #s(literal 1/3840 binary64) (.f64 eps eps) #s(literal -1/48 binary64)) (.f64 eps eps) #s(literal 1/2 binary64)) eps)) (patch #s(approx (sin ( 1/2 (+ 0 eps))) (.f64 (fma.f64 (fma.f64 #s(literal 1/3840 binary64) (.f64 eps eps) #s(literal -1/48 binary64)) (*.f64 eps eps) #s(literal 1/2 binary64)) eps)) #<representation binary64>) () ())) ())
#s(alt (sin (* 1/2 eps)) (taylor -inf eps) (#s(alt #s(approx (sin (* 1/2 (+ 0 eps))) (.f64 (fma.f64 (fma.f64 #s(literal 1/3840 binary64) (.f64 eps eps) #s(literal -1/48 binary64)) (.f64 eps eps) #s(literal 1/2 binary64)) eps)) (patch #s(approx (sin ( 1/2 (+ 0 eps))) (.f64 (fma.f64 (fma.f64 #s(literal 1/3840 binary64) (.f64 eps eps) #s(literal -1/48 binary64)) (*.f64 eps eps) #s(literal 1/2 binary64)) eps)) #<representation binary64>) () ())) ())
#s(alt (sin (* 1/2 eps)) (taylor -inf eps) (#s(alt #s(approx (sin (* 1/2 (+ 0 eps))) (.f64 (fma.f64 (fma.f64 #s(literal 1/3840 binary64) (.f64 eps eps) #s(literal -1/48 binary64)) (.f64 eps eps) #s(literal 1/2 binary64)) eps)) (patch #s(approx (sin ( 1/2 (+ 0 eps))) (.f64 (fma.f64 (fma.f64 #s(literal 1/3840 binary64) (.f64 eps eps) #s(literal -1/48 binary64)) (*.f64 eps eps) #s(literal 1/2 binary64)) eps)) #<representation binary64>) () ())) ())

Calls

120 calls:

Time	Variable		Point	Expression
1.0ms	eps	@	0	(+ (* (* eps (- (* (* (+ (* 1/5040 (* x x)) -1/120) x) x) 1/6)) (* x x)) (neg eps))
0.0ms	x	@	0	(* (neg x) eps)
0.0ms	x	@	inf	(+ (* (* eps (- (* (* (+ (* 1/5040 (* x x)) -1/120) x) x) 1/6)) (* x x)) (neg eps))
0.0ms	eps	@	0	(* (neg x) eps)
0.0ms	x	@	inf	(* (neg x) eps)

simplify395.0ms (2.1%)

Memory

-8.7MiB live, 234.9MiB allocated

Algorithm

1×	egg-herbie

Rules

14 784×	`lower-fma.f64`
14 784×	`lower-fma.f32`
5 806×	`lower-*.f64`
5 806×	`lower-*.f32`
3 812×	`lower-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	300	5236
1	933	4912
2	2534	4805
3	6145	4767
0	8386	4391

Stop Event

1×	iter limit
1×	node limit

Counts

480 → 462

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

Outputs
(* 1/2 eps)
(*.f64 eps #s(literal 1/2 binary64))
(+ x (* 1/2 eps))
(fma.f64 eps #s(literal 1/2 binary64) x)
(+ x (* 1/2 eps))
(fma.f64 eps #s(literal 1/2 binary64) x)
(+ x (* 1/2 eps))
(fma.f64 eps #s(literal 1/2 binary64) x)
x
(* x (+ 1 (* 1/2 (/ eps x))))
(fma.f64 #s(literal 1 binary64) (*.f64 eps #s(literal 1/2 binary64)) x)
(* x (+ 1 (* 1/2 (/ eps x))))
(fma.f64 #s(literal 1 binary64) (*.f64 eps #s(literal 1/2 binary64)) x)
(* x (+ 1 (* 1/2 (/ eps x))))
(fma.f64 #s(literal 1 binary64) (*.f64 eps #s(literal 1/2 binary64)) x)
x
(* -1 (* x (- (* -1/2 (/ eps x)) 1)))
(fma.f64 #s(literal 1 binary64) (*.f64 eps #s(literal 1/2 binary64)) x)
(* -1 (* x (- (* -1/2 (/ eps x)) 1)))
(fma.f64 #s(literal 1 binary64) (*.f64 eps #s(literal 1/2 binary64)) x)
(* -1 (* x (- (* -1/2 (/ eps x)) 1)))
(fma.f64 #s(literal 1 binary64) (*.f64 eps #s(literal 1/2 binary64)) x)
x
(+ x (* 1/2 eps))
(fma.f64 eps #s(literal 1/2 binary64) x)
(+ x (* 1/2 eps))
(fma.f64 eps #s(literal 1/2 binary64) x)
(+ x (* 1/2 eps))
(fma.f64 eps #s(literal 1/2 binary64) x)
(* 1/2 eps)
(*.f64 eps #s(literal 1/2 binary64))
(* eps (+ 1/2 (/ x eps)))
(fma.f64 eps #s(literal 1/2 binary64) x)
(* eps (+ 1/2 (/ x eps)))
(fma.f64 eps #s(literal 1/2 binary64) x)
(* eps (+ 1/2 (/ x eps)))
(fma.f64 eps #s(literal 1/2 binary64) x)
(* 1/2 eps)
(*.f64 eps #s(literal 1/2 binary64))
(* -1 (* eps (- (* -1 (/ x eps)) 1/2)))
(fma.f64 eps #s(literal 1/2 binary64) x)
(* -1 (* eps (- (* -1 (/ x eps)) 1/2)))
(fma.f64 eps #s(literal 1/2 binary64) x)
(* -1 (* eps (- (* -1 (/ x eps)) 1/2)))
(fma.f64 eps #s(literal 1/2 binary64) x)
(* -2 (pow (sin (* 1/2 eps)) 2))
(.f64 (pow.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) #s(literal 2 binary64)) #s(literal -2 binary64))
(+ (* -2 (* x (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))) (* -2 (pow (sin (* 1/2 eps)) 2)))
(.f64 (.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) #s(literal -2 binary64)) (fma.f64 (cos.f64 (.f64 eps #s(literal 1/2 binary64))) x (sin.f64 (*.f64 eps #s(literal 1/2 binary64)))))
(+ (* -2 (pow (sin (* 1/2 eps)) 2)) (* x (+ (* -2 (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) (* x (pow (sin (* 1/2 eps)) 2)))))
(fma.f64 (pow.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) #s(literal 2 binary64)) (fma.f64 x x #s(literal -2 binary64)) (.f64 (.f64 (.f64 #s(literal -2 binary64) x) (cos.f64 (.f64 eps #s(literal 1/2 binary64)))) (sin.f64 (.f64 eps #s(literal 1/2 binary64)))))
(+ (* -2 (pow (sin (* 1/2 eps)) 2)) (* x (+ (* -2 (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) (* x (+ (* 1/3 (* x (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))) (pow (sin (* 1/2 eps)) 2))))))
(fma.f64 (fma.f64 (.f64 (cos.f64 (.f64 eps #s(literal 1/2 binary64))) (sin.f64 (.f64 eps #s(literal 1/2 binary64)))) (+.f64 #s(literal -2 binary64) (.f64 x (.f64 #s(literal 1/3 binary64) x))) (.f64 (pow.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) #s(literal 2 binary64)) x)) x (.f64 (pow.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) #s(literal 2 binary64)) #s(literal -2 binary64)))
(* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (+ eps (* 2 x))))))
(.f64 (.f64 #s(literal -2 binary64) (sin.f64 (fma.f64 eps #s(literal 1/2 binary64) x))) (sin.f64 (*.f64 eps #s(literal 1/2 binary64))))
(* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (+ eps (* 2 x))))))
(.f64 (.f64 #s(literal -2 binary64) (sin.f64 (fma.f64 eps #s(literal 1/2 binary64) x))) (sin.f64 (*.f64 eps #s(literal 1/2 binary64))))
(* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (+ eps (* 2 x))))))
(.f64 (.f64 #s(literal -2 binary64) (sin.f64 (fma.f64 eps #s(literal 1/2 binary64) x))) (sin.f64 (*.f64 eps #s(literal 1/2 binary64))))
(* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (+ eps (* 2 x))))))
(.f64 (.f64 #s(literal -2 binary64) (sin.f64 (fma.f64 eps #s(literal 1/2 binary64) x))) (sin.f64 (*.f64 eps #s(literal 1/2 binary64))))
(* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (- eps (* -2 x))))))
(.f64 (.f64 #s(literal -2 binary64) (sin.f64 (fma.f64 eps #s(literal 1/2 binary64) x))) (sin.f64 (*.f64 eps #s(literal 1/2 binary64))))
(* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (- eps (* -2 x))))))
(.f64 (.f64 #s(literal -2 binary64) (sin.f64 (fma.f64 eps #s(literal 1/2 binary64) x))) (sin.f64 (*.f64 eps #s(literal 1/2 binary64))))
(* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (- eps (* -2 x))))))
(.f64 (.f64 #s(literal -2 binary64) (sin.f64 (fma.f64 eps #s(literal 1/2 binary64) x))) (sin.f64 (*.f64 eps #s(literal 1/2 binary64))))
(* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (- eps (* -2 x))))))
(.f64 (.f64 #s(literal -2 binary64) (sin.f64 (fma.f64 eps #s(literal 1/2 binary64) x))) (sin.f64 (*.f64 eps #s(literal 1/2 binary64))))
(* -1 (* eps (sin x)))
(*.f64 (neg.f64 eps) (sin.f64 x))
(* eps (+ (* -1 (sin x)) (* -1/2 (* eps (cos x)))))
(.f64 (neg.f64 (fma.f64 (.f64 (cos.f64 x) #s(literal 1/2 binary64)) eps (sin.f64 x))) eps)
(* eps (+ (* -1 (sin x)) (* eps (+ (* -2 (* eps (+ (* -1/16 (sin x)) (* -1/48 (sin x))))) (* -1/2 (cos x))))))
(.f64 (fma.f64 (sin.f64 x) (fma.f64 eps (.f64 #s(literal 1/6 binary64) eps) #s(literal -1 binary64)) (.f64 (.f64 (cos.f64 x) #s(literal -1/2 binary64)) eps)) eps)
(* 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 (fma.f64 (fma.f64 (cos.f64 x) (fma.f64 eps (.f64 #s(literal 1/24 binary64) eps) #s(literal -1/2 binary64)) (.f64 (.f64 #s(literal 1/6 binary64) (sin.f64 x)) eps)) eps (neg.f64 (sin.f64 x))) eps)
(* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (+ eps (* 2 x))))))
(.f64 (.f64 #s(literal -2 binary64) (sin.f64 (fma.f64 eps #s(literal 1/2 binary64) x))) (sin.f64 (*.f64 eps #s(literal 1/2 binary64))))
(* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (+ eps (* 2 x))))))
(.f64 (.f64 #s(literal -2 binary64) (sin.f64 (fma.f64 eps #s(literal 1/2 binary64) x))) (sin.f64 (*.f64 eps #s(literal 1/2 binary64))))
(* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (+ eps (* 2 x))))))
(.f64 (.f64 #s(literal -2 binary64) (sin.f64 (fma.f64 eps #s(literal 1/2 binary64) x))) (sin.f64 (*.f64 eps #s(literal 1/2 binary64))))
(* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (+ eps (* 2 x))))))
(.f64 (.f64 #s(literal -2 binary64) (sin.f64 (fma.f64 eps #s(literal 1/2 binary64) x))) (sin.f64 (*.f64 eps #s(literal 1/2 binary64))))
(* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (- (* 2 x) (* -1 eps))))))
(.f64 (.f64 #s(literal -2 binary64) (sin.f64 (fma.f64 eps #s(literal 1/2 binary64) x))) (sin.f64 (*.f64 eps #s(literal 1/2 binary64))))
(* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (- (* 2 x) (* -1 eps))))))
(.f64 (.f64 #s(literal -2 binary64) (sin.f64 (fma.f64 eps #s(literal 1/2 binary64) x))) (sin.f64 (*.f64 eps #s(literal 1/2 binary64))))
(* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (- (* 2 x) (* -1 eps))))))
(.f64 (.f64 #s(literal -2 binary64) (sin.f64 (fma.f64 eps #s(literal 1/2 binary64) x))) (sin.f64 (*.f64 eps #s(literal 1/2 binary64))))
(* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (- (* 2 x) (* -1 eps))))))
(.f64 (.f64 #s(literal -2 binary64) (sin.f64 (fma.f64 eps #s(literal 1/2 binary64) x))) (sin.f64 (*.f64 eps #s(literal 1/2 binary64))))
(pow (sin (* 1/2 eps)) 2)
(pow.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) #s(literal 2 binary64))
(+ (* x (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) (pow (sin (* 1/2 eps)) 2))
(.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (fma.f64 (cos.f64 (.f64 eps #s(literal 1/2 binary64))) x (sin.f64 (.f64 eps #s(literal 1/2 binary64)))))
(+ (* x (+ (* -1/2 (* x (pow (sin (* 1/2 eps)) 2))) (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))) (pow (sin (* 1/2 eps)) 2))
(fma.f64 (fma.f64 x (.f64 #s(literal -1/2 binary64) x) #s(literal 1 binary64)) (pow.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))) x) (cos.f64 (.f64 eps #s(literal 1/2 binary64)))))
(+ (* 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 (fma.f64 x (.f64 #s(literal -1/6 binary64) x) #s(literal 1 binary64)) (.f64 (cos.f64 (.f64 eps #s(literal 1/2 binary64))) (sin.f64 (.f64 eps #s(literal 1/2 binary64)))) (.f64 (.f64 #s(literal -1/2 binary64) x) (pow.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) #s(literal 2 binary64)))) x (pow.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) #s(literal 2 binary64)))
(* (sin (* 1/2 eps)) (sin (* 1/2 (+ eps (* 2 x)))))
(.f64 (sin.f64 (fma.f64 eps #s(literal 1/2 binary64) x)) (sin.f64 (.f64 eps #s(literal 1/2 binary64))))
(* (sin (* 1/2 eps)) (sin (* 1/2 (+ eps (* 2 x)))))
(.f64 (sin.f64 (fma.f64 eps #s(literal 1/2 binary64) x)) (sin.f64 (.f64 eps #s(literal 1/2 binary64))))
(* (sin (* 1/2 eps)) (sin (* 1/2 (+ eps (* 2 x)))))
(.f64 (sin.f64 (fma.f64 eps #s(literal 1/2 binary64) x)) (sin.f64 (.f64 eps #s(literal 1/2 binary64))))
(* (sin (* 1/2 eps)) (sin (* 1/2 (+ eps (* 2 x)))))
(.f64 (sin.f64 (fma.f64 eps #s(literal 1/2 binary64) x)) (sin.f64 (.f64 eps #s(literal 1/2 binary64))))
(* (sin (* 1/2 eps)) (sin (* 1/2 (- eps (* -2 x)))))
(.f64 (sin.f64 (fma.f64 eps #s(literal 1/2 binary64) x)) (sin.f64 (.f64 eps #s(literal 1/2 binary64))))
(* (sin (* 1/2 eps)) (sin (* 1/2 (- eps (* -2 x)))))
(.f64 (sin.f64 (fma.f64 eps #s(literal 1/2 binary64) x)) (sin.f64 (.f64 eps #s(literal 1/2 binary64))))
(* (sin (* 1/2 eps)) (sin (* 1/2 (- eps (* -2 x)))))
(.f64 (sin.f64 (fma.f64 eps #s(literal 1/2 binary64) x)) (sin.f64 (.f64 eps #s(literal 1/2 binary64))))
(* (sin (* 1/2 eps)) (sin (* 1/2 (- eps (* -2 x)))))
(.f64 (sin.f64 (fma.f64 eps #s(literal 1/2 binary64) x)) (sin.f64 (.f64 eps #s(literal 1/2 binary64))))
(* 1/2 (* eps (sin x)))
(.f64 (.f64 (sin.f64 x) #s(literal 1/2 binary64)) eps)
(* eps (+ (* 1/4 (* eps (cos x))) (* 1/2 (sin x))))
(.f64 (fma.f64 (.f64 #s(literal 1/4 binary64) (cos.f64 x)) eps (*.f64 (sin.f64 x) #s(literal 1/2 binary64))) eps)
(* eps (+ (* 1/2 (sin x)) (* eps (+ (* 1/4 (cos x)) (* eps (+ (* -1/16 (sin x)) (* -1/48 (sin x))))))))
(.f64 (fma.f64 (fma.f64 #s(literal 1/4 binary64) (cos.f64 x) (.f64 (.f64 #s(literal -1/12 binary64) (sin.f64 x)) eps)) eps (.f64 (sin.f64 x) #s(literal 1/2 binary64))) eps)
(* eps (+ (* 1/2 (sin x)) (* eps (+ (* 1/4 (cos x)) (* eps (+ (* -1/16 (sin x)) (+ (* -1/48 (sin x)) (* -1/48 (* eps (cos x))))))))))
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(.f64 (fma.f64 (fma.f64 #s(literal 1/5040 binary64) (.f64 x x) #s(literal -1/120 binary64)) (*.f64 x x) #s(literal -1/6 binary64)) eps)
(* eps (- (* (pow x 2) (- (* 1/5040 (pow x 2)) 1/120)) 1/6))
(.f64 (fma.f64 (fma.f64 #s(literal 1/5040 binary64) (.f64 x x) #s(literal -1/120 binary64)) (*.f64 x x) #s(literal -1/6 binary64)) eps)
(* eps (- (* (pow x 2) (- (* 1/5040 (pow x 2)) 1/120)) 1/6))
(.f64 (fma.f64 (fma.f64 #s(literal 1/5040 binary64) (.f64 x x) #s(literal -1/120 binary64)) (*.f64 x x) #s(literal -1/6 binary64)) eps)
(* eps (- (* (pow x 2) (- (* 1/5040 (pow x 2)) 1/120)) 1/6))
(.f64 (fma.f64 (fma.f64 #s(literal 1/5040 binary64) (.f64 x x) #s(literal -1/120 binary64)) (*.f64 x x) #s(literal -1/6 binary64)) eps)
(* eps (- (* (pow x 2) (- (* 1/5040 (pow x 2)) 1/120)) 1/6))
(.f64 (fma.f64 (fma.f64 #s(literal 1/5040 binary64) (.f64 x x) #s(literal -1/120 binary64)) (*.f64 x x) #s(literal -1/6 binary64)) eps)
(* eps (- (* (pow x 2) (- (* 1/5040 (pow x 2)) 1/120)) 1/6))
(.f64 (fma.f64 (fma.f64 #s(literal 1/5040 binary64) (.f64 x x) #s(literal -1/120 binary64)) (*.f64 x x) #s(literal -1/6 binary64)) eps)
(* eps (- (* (pow x 2) (- (* 1/5040 (pow x 2)) 1/120)) 1/6))
(.f64 (fma.f64 (fma.f64 #s(literal 1/5040 binary64) (.f64 x x) #s(literal -1/120 binary64)) (*.f64 x x) #s(literal -1/6 binary64)) eps)
(* eps (- (* (pow x 2) (- (* 1/5040 (pow x 2)) 1/120)) 1/6))
(.f64 (fma.f64 (fma.f64 #s(literal 1/5040 binary64) (.f64 x x) #s(literal -1/120 binary64)) (*.f64 x x) #s(literal -1/6 binary64)) eps)
(* eps (- (* (pow x 2) (- (* 1/5040 (pow x 2)) 1/120)) 1/6))
(.f64 (fma.f64 (fma.f64 #s(literal 1/5040 binary64) (.f64 x x) #s(literal -1/120 binary64)) (*.f64 x x) #s(literal -1/6 binary64)) eps)
(* -1/6 eps)
(*.f64 #s(literal -1/6 binary64) eps)
(+ (* -1/6 eps) (* -1/120 (* eps (pow x 2))))
(.f64 eps (fma.f64 #s(literal -1/120 binary64) (.f64 x x) #s(literal -1/6 binary64)))
(+ (* -1/6 eps) (* (pow x 2) (+ (* -1/120 eps) (* 1/5040 (* eps (pow x 2))))))
(fma.f64 (.f64 eps (fma.f64 #s(literal 1/5040 binary64) (.f64 x x) #s(literal -1/120 binary64))) (.f64 x x) (.f64 #s(literal -1/6 binary64) eps))
(+ (* -1/6 eps) (* (pow x 2) (+ (* -1/120 eps) (* 1/5040 (* eps (pow x 2))))))
(fma.f64 (.f64 eps (fma.f64 #s(literal 1/5040 binary64) (.f64 x x) #s(literal -1/120 binary64))) (.f64 x x) (.f64 #s(literal -1/6 binary64) eps))
(* 1/5040 (* eps (pow x 4)))
(.f64 (.f64 (.f64 #s(literal 1/5040 binary64) (.f64 (*.f64 x x) eps)) x) x)
(* (pow x 4) (+ (* -1/120 (/ eps (pow x 2))) (* 1/5040 eps)))
(.f64 (.f64 (.f64 x x) (.f64 x x)) (.f64 eps (-.f64 #s(literal 1/5040 binary64) (/.f64 #s(literal 1/120 binary64) (.f64 x x)))))
(* (pow x 4) (+ (* -1/6 (/ eps (pow x 4))) (+ (* -1/120 (/ eps (pow x 2))) (* 1/5040 eps))))
(fma.f64 (.f64 (.f64 x x) (.f64 x x)) (.f64 eps (-.f64 #s(literal 1/5040 binary64) (/.f64 #s(literal 1/120 binary64) (.f64 x x)))) (.f64 (*.f64 #s(literal -1/6 binary64) eps) #s(literal 1 binary64)))
(* (pow x 4) (+ (* -1/6 (/ eps (pow x 4))) (+ (* -1/120 (/ eps (pow x 2))) (* 1/5040 eps))))
(fma.f64 (.f64 (.f64 x x) (.f64 x x)) (.f64 eps (-.f64 #s(literal 1/5040 binary64) (/.f64 #s(literal 1/120 binary64) (.f64 x x)))) (.f64 (*.f64 #s(literal -1/6 binary64) eps) #s(literal 1 binary64)))
(* 1/5040 (* eps (pow x 4)))
(.f64 (.f64 (.f64 #s(literal 1/5040 binary64) (.f64 (*.f64 x x) eps)) x) x)
(* (pow x 4) (+ (* -1/120 (/ eps (pow x 2))) (* 1/5040 eps)))
(.f64 (.f64 (.f64 x x) (.f64 x x)) (.f64 eps (-.f64 #s(literal 1/5040 binary64) (/.f64 #s(literal 1/120 binary64) (.f64 x x)))))
(* (pow x 4) (+ (* -1/6 (/ eps (pow x 4))) (+ (* -1/120 (/ eps (pow x 2))) (* 1/5040 eps))))
(fma.f64 (.f64 (.f64 x x) (.f64 x x)) (.f64 eps (-.f64 #s(literal 1/5040 binary64) (/.f64 #s(literal 1/120 binary64) (.f64 x x)))) (.f64 (*.f64 #s(literal -1/6 binary64) eps) #s(literal 1 binary64)))
(* (pow x 4) (+ (* -1/6 (/ eps (pow x 4))) (+ (* -1/120 (/ eps (pow x 2))) (* 1/5040 eps))))
(fma.f64 (.f64 (.f64 x x) (.f64 x x)) (.f64 eps (-.f64 #s(literal 1/5040 binary64) (/.f64 #s(literal 1/120 binary64) (.f64 x x)))) (.f64 (*.f64 #s(literal -1/6 binary64) eps) #s(literal 1 binary64)))
(* -1/120 (pow x 2))
(.f64 #s(literal -1/120 binary64) (.f64 x x))
(* (pow x 2) (- (* 1/5040 (pow x 2)) 1/120))
(.f64 (.f64 (fma.f64 #s(literal 1/5040 binary64) (*.f64 x x) #s(literal -1/120 binary64)) x) x)
(* (pow x 2) (- (* 1/5040 (pow x 2)) 1/120))
(.f64 (.f64 (fma.f64 #s(literal 1/5040 binary64) (*.f64 x x) #s(literal -1/120 binary64)) x) x)
(* (pow x 2) (- (* 1/5040 (pow x 2)) 1/120))
(.f64 (.f64 (fma.f64 #s(literal 1/5040 binary64) (*.f64 x x) #s(literal -1/120 binary64)) x) x)
(* 1/5040 (pow x 4))
(.f64 (.f64 (.f64 x x) (.f64 x x)) #s(literal 1/5040 binary64))
(* (pow x 4) (- 1/5040 (* 1/120 (/ 1 (pow x 2)))))
(.f64 (-.f64 #s(literal 1/5040 binary64) (/.f64 #s(literal 1/120 binary64) (.f64 x x))) (.f64 (.f64 x x) (*.f64 x x)))
(* (pow x 4) (- 1/5040 (* 1/120 (/ 1 (pow x 2)))))
(.f64 (-.f64 #s(literal 1/5040 binary64) (/.f64 #s(literal 1/120 binary64) (.f64 x x))) (.f64 (.f64 x x) (*.f64 x x)))
(* (pow x 4) (- 1/5040 (* 1/120 (/ 1 (pow x 2)))))
(.f64 (-.f64 #s(literal 1/5040 binary64) (/.f64 #s(literal 1/120 binary64) (.f64 x x))) (.f64 (.f64 x x) (*.f64 x x)))
(* 1/5040 (pow x 4))
(.f64 (.f64 (.f64 x x) (.f64 x x)) #s(literal 1/5040 binary64))
(* (pow x 4) (- 1/5040 (* 1/120 (/ 1 (pow x 2)))))
(.f64 (-.f64 #s(literal 1/5040 binary64) (/.f64 #s(literal 1/120 binary64) (.f64 x x))) (.f64 (.f64 x x) (*.f64 x x)))
(* (pow x 4) (- 1/5040 (* 1/120 (/ 1 (pow x 2)))))
(.f64 (-.f64 #s(literal 1/5040 binary64) (/.f64 #s(literal 1/120 binary64) (.f64 x x))) (.f64 (.f64 x x) (*.f64 x x)))
(* (pow x 4) (- 1/5040 (* 1/120 (/ 1 (pow x 2)))))
(.f64 (-.f64 #s(literal 1/5040 binary64) (/.f64 #s(literal 1/120 binary64) (.f64 x x))) (.f64 (.f64 x x) (*.f64 x x)))
(* 1/2 eps)
(*.f64 eps #s(literal 1/2 binary64))
(* eps (+ 1/2 (* -1/48 (pow eps 2))))
(.f64 (fma.f64 (.f64 eps eps) #s(literal -1/48 binary64) #s(literal 1/2 binary64)) eps)
(* eps (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48))))
(.f64 (fma.f64 (fma.f64 #s(literal 1/3840 binary64) (.f64 eps eps) #s(literal -1/48 binary64)) (*.f64 eps eps) #s(literal 1/2 binary64)) eps)
(* eps (+ 1/2 (* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48))))
(.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -1/645120 binary64) (.f64 eps eps) #s(literal 1/3840 binary64)) (.f64 eps eps) #s(literal -1/48 binary64)) (.f64 eps eps) #s(literal 1/2 binary64)) eps)
(sin (* 1/2 eps))
(sin.f64 (*.f64 eps #s(literal 1/2 binary64)))
(sin (* 1/2 eps))
(sin.f64 (*.f64 eps #s(literal 1/2 binary64)))
(sin (* 1/2 eps))
(sin.f64 (*.f64 eps #s(literal 1/2 binary64)))
(sin (* 1/2 eps))
(sin.f64 (*.f64 eps #s(literal 1/2 binary64)))
(sin (* 1/2 eps))
(sin.f64 (*.f64 eps #s(literal 1/2 binary64)))
(sin (* 1/2 eps))
(sin.f64 (*.f64 eps #s(literal 1/2 binary64)))
(sin (* 1/2 eps))
(sin.f64 (*.f64 eps #s(literal 1/2 binary64)))
(sin (* 1/2 eps))
(sin.f64 (*.f64 eps #s(literal 1/2 binary64)))

rewrite283.0ms (1.5%)

Memory

18.3MiB live, 296.2MiB allocated

Rules

4 550×	`lower-*.f32`
4 514×	`lower-*.f64`
4 504×	`lower-fma.f32`
4 486×	`lower-fma.f64`
2 984×	`lower-/.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	68	419
0	111	407
1	385	386
2	3051	376
0	9348	371

Stop Event

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

Counts

23 → 333

Calls

Call 1

Inputs
(*.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps))
(.f64 (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps))) #s(approx (sin ( 1/2 (+ 0 eps))) (.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -1/645120 binary64) (.f64 eps eps) #s(literal 1/3840 binary64)) (.f64 eps eps) #s(literal -1/48 binary64)) (.f64 eps eps) #s(literal 1/2 binary64)) eps))) #s(literal -2 binary64))
(.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps))) #s(approx (sin (* 1/2 (+ 0 eps))) (.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -1/645120 binary64) (.f64 eps eps) #s(literal 1/3840 binary64)) (.f64 eps eps) #s(literal -1/48 binary64)) (.f64 eps eps) #s(literal 1/2 binary64)) eps)))
(sin.f64 (*.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (*.f64 (neg.f64 x) eps)))
#s(approx (* (neg eps) (sin x)) (*.f64 (neg.f64 x) eps))
(*.f64 (neg.f64 x) eps)
(neg.f64 x)
(fma.f64 (.f64 eps (-.f64 (.f64 (.f64 (fma.f64 #s(literal 1/5040 binary64) (.f64 x x) #s(literal -1/120 binary64)) x) x) #s(literal 1/6 binary64))) (*.f64 x x) (neg.f64 eps))
(-.f64 (.f64 (.f64 (fma.f64 #s(literal 1/5040 binary64) (*.f64 x x) #s(literal -1/120 binary64)) x) x) #s(literal 1/6 binary64))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (.f64 (fma.f64 (.f64 eps (-.f64 (.f64 (.f64 (fma.f64 #s(literal 1/5040 binary64) (.f64 x x) #s(literal -1/120 binary64)) x) x) #s(literal 1/6 binary64))) (.f64 x x) (neg.f64 eps)) x)))
#s(approx (* (neg eps) (sin x)) (.f64 (fma.f64 (.f64 eps (-.f64 (.f64 (.f64 (fma.f64 #s(literal 1/5040 binary64) (.f64 x x) #s(literal -1/120 binary64)) x) x) #s(literal 1/6 binary64))) (.f64 x x) (neg.f64 eps)) x))
(.f64 (.f64 (sin.f64 #s(approx (* 1/2 (+ (* 2 x) eps)) (fma.f64 eps #s(literal 1/2 binary64) x))) #s(approx (sin (* 1/2 (+ 0 eps))) (.f64 (fma.f64 (fma.f64 #s(literal 1/3840 binary64) (.f64 eps eps) #s(literal -1/48 binary64)) (*.f64 eps eps) #s(literal 1/2 binary64)) eps))) #s(literal -2 binary64))
(.f64 (sin.f64 #s(approx ( 1/2 (+ (* 2 x) eps)) (fma.f64 eps #s(literal 1/2 binary64) x))) #s(approx (sin (* 1/2 (+ 0 eps))) (.f64 (fma.f64 (fma.f64 #s(literal 1/3840 binary64) (.f64 eps eps) #s(literal -1/48 binary64)) (*.f64 eps eps) #s(literal 1/2 binary64)) eps)))
(sin.f64 #s(approx (* 1/2 (+ (* 2 x) eps)) (fma.f64 eps #s(literal 1/2 binary64) x)))
#s(approx (* 1/2 (+ (* 2 x) eps)) (fma.f64 eps #s(literal 1/2 binary64) x))
(.f64 (neg.f64 (.f64 eps eps)) (/.f64 #s(literal -1 binary64) eps))
(.f64 (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps))) (sin.f64 (.f64 #s(literal 1/2 binary64) (.f64 (neg.f64 (.f64 eps eps)) (/.f64 #s(literal -1 binary64) eps))))) #s(literal -2 binary64))
(.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps))) (sin.f64 (.f64 #s(literal 1/2 binary64) (.f64 (neg.f64 (*.f64 eps eps)) (/.f64 #s(literal -1 binary64) eps)))))
#s(approx (sin (* 1/2 (+ 0 eps))) (.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -1/645120 binary64) (.f64 eps eps) #s(literal 1/3840 binary64)) (.f64 eps eps) #s(literal -1/48 binary64)) (.f64 eps eps) #s(literal 1/2 binary64)) eps))
(.f64 eps (-.f64 (.f64 (.f64 (fma.f64 #s(literal 1/5040 binary64) (.f64 x x) #s(literal -1/120 binary64)) x) x) #s(literal 1/6 binary64)))
(.f64 (.f64 (fma.f64 #s(literal 1/5040 binary64) (*.f64 x x) #s(literal -1/120 binary64)) x) x)
#s(approx (sin (* 1/2 (+ 0 eps))) (.f64 (fma.f64 (fma.f64 #s(literal 1/3840 binary64) (.f64 eps eps) #s(literal -1/48 binary64)) (*.f64 eps eps) #s(literal 1/2 binary64)) eps))

Outputs
(*.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64))
(*.f64 #s(literal 1/2 binary64) (fma.f64 x #s(literal 2 binary64) eps))
(/.f64 (.f64 (fma.f64 #s(literal 4 binary64) (.f64 x x) (*.f64 eps eps)) #s(literal 1/2 binary64)) (fma.f64 x #s(literal 2 binary64) eps))
(/.f64 (.f64 (fma.f64 #s(literal 8 binary64) (.f64 (.f64 x x) x) (.f64 (.f64 eps eps) eps)) #s(literal 1/2 binary64)) (fma.f64 #s(literal 4 binary64) (.f64 x x) (.f64 eps (-.f64 eps (.f64 x #s(literal 2 binary64))))))
(/.f64 (.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 4 binary64) (.f64 x x) (*.f64 eps eps))) (fma.f64 x #s(literal 2 binary64) eps))
(/.f64 (.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 8 binary64) (.f64 (.f64 x x) x) (.f64 (.f64 eps eps) eps))) (fma.f64 #s(literal 4 binary64) (.f64 x x) (.f64 eps (-.f64 eps (.f64 x #s(literal 2 binary64))))))
(/.f64 (-.f64 (.f64 (.f64 #s(literal 1 binary64) x) (.f64 #s(literal 1 binary64) x)) (.f64 #s(literal 1/4 binary64) (.f64 eps eps))) (-.f64 (.f64 #s(literal 1 binary64) x) (*.f64 eps #s(literal 1/2 binary64))))
(/.f64 (fma.f64 (.f64 (.f64 x x) x) #s(literal 1 binary64) (.f64 (.f64 (.f64 eps eps) eps) #s(literal 1/8 binary64))) (fma.f64 (.f64 #s(literal 1 binary64) x) (.f64 #s(literal 1 binary64) x) (-.f64 (.f64 #s(literal 1/4 binary64) (.f64 eps eps)) (.f64 (.f64 #s(literal 1 binary64) x) (.f64 eps #s(literal 1/2 binary64))))))
(fma.f64 (.f64 #s(literal 1/2 binary64) x) #s(literal 2 binary64) (.f64 eps #s(literal 1/2 binary64)))
(fma.f64 (.f64 (.f64 #s(literal -1/2 binary64) (.f64 eps eps)) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) eps) (.f64 #s(literal 1 binary64) x))
(fma.f64 (.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1 binary64) eps)) (.f64 eps eps) (*.f64 #s(literal 1 binary64) x))
(fma.f64 (.f64 #s(literal -1/2 binary64) (.f64 eps eps)) (/.f64 #s(literal 1 binary64) eps) (*.f64 #s(literal 1 binary64) x))
(fma.f64 (/.f64 #s(literal 1 binary64) eps) (.f64 #s(literal -1/2 binary64) (.f64 eps eps)) (*.f64 #s(literal 1 binary64) x))
(fma.f64 #s(literal 1 binary64) x (*.f64 eps #s(literal 1/2 binary64)))
(fma.f64 (.f64 x #s(literal 2 binary64)) #s(literal 1/2 binary64) (.f64 eps #s(literal 1/2 binary64)))
(fma.f64 (.f64 eps eps) (.f64 (/.f64 #s(literal 1 binary64) eps) #s(literal 1/2 binary64)) (*.f64 #s(literal 1 binary64) x))
(fma.f64 eps #s(literal 1/2 binary64) (*.f64 #s(literal 1 binary64) x))
(fma.f64 x #s(literal 1 binary64) (*.f64 eps #s(literal 1/2 binary64)))
(fma.f64 #s(literal 2 binary64) (.f64 x #s(literal 1/2 binary64)) (.f64 eps #s(literal 1/2 binary64)))
(fma.f64 #s(literal 1/2 binary64) (.f64 x #s(literal 2 binary64)) (.f64 eps #s(literal 1/2 binary64)))
(fma.f64 #s(literal 1/2 binary64) eps (*.f64 #s(literal 1 binary64) x))
(+.f64 (fma.f64 #s(literal 1 binary64) x #s(literal 0 binary64)) (*.f64 eps #s(literal 1/2 binary64)))
(+.f64 (.f64 #s(literal 1 binary64) x) (.f64 eps #s(literal 1/2 binary64)))
(+.f64 (.f64 eps #s(literal 1/2 binary64)) (.f64 #s(literal 1 binary64) x))
(.f64 (.f64 #s(literal -2 binary64) (sin.f64 (.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)))) #s(approx (sin ( 1/2 (+ 0 eps))) (.f64 (fma.f64 (fma.f64 (fma.f64 (.f64 eps eps) #s(literal -1/645120 binary64) #s(literal 1/3840 binary64)) (.f64 eps eps) #s(literal -1/48 binary64)) (.f64 eps eps) #s(literal 1/2 binary64)) eps)))
(.f64 (.f64 #s(literal -2 binary64) #s(approx (sin (* 1/2 (+ 0 eps))) (.f64 (fma.f64 (fma.f64 (fma.f64 (.f64 eps eps) #s(literal -1/645120 binary64) #s(literal 1/3840 binary64)) (.f64 eps eps) #s(literal -1/48 binary64)) (.f64 eps eps) #s(literal 1/2 binary64)) eps))) (sin.f64 (*.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64))))
(.f64 #s(literal -2 binary64) (.f64 #s(approx (sin (* 1/2 (+ 0 eps))) (.f64 (fma.f64 (fma.f64 (fma.f64 (.f64 eps eps) #s(literal -1/645120 binary64) #s(literal 1/3840 binary64)) (.f64 eps eps) #s(literal -1/48 binary64)) (.f64 eps eps) #s(literal 1/2 binary64)) eps)) (sin.f64 (*.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)))))
(.f64 (.f64 #s(approx (sin (* 1/2 (+ 0 eps))) (.f64 (fma.f64 (fma.f64 (fma.f64 (.f64 eps eps) #s(literal -1/645120 binary64) #s(literal 1/3840 binary64)) (.f64 eps eps) #s(literal -1/48 binary64)) (.f64 eps eps) #s(literal 1/2 binary64)) eps)) (sin.f64 (*.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)))) #s(literal -2 binary64))
(.f64 #s(approx (sin ( 1/2 (+ 0 eps))) (.f64 (fma.f64 (fma.f64 (fma.f64 (.f64 eps eps) #s(literal -1/645120 binary64) #s(literal 1/3840 binary64)) (.f64 eps eps) #s(literal -1/48 binary64)) (.f64 eps eps) #s(literal 1/2 binary64)) eps)) (.f64 (sin.f64 (.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64))) #s(literal -2 binary64)))
(.f64 (sin.f64 (.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64))) (.f64 #s(literal -2 binary64) #s(approx (sin ( 1/2 (+ 0 eps))) (.f64 (fma.f64 (fma.f64 (fma.f64 (.f64 eps eps) #s(literal -1/645120 binary64) #s(literal 1/3840 binary64)) (.f64 eps eps) #s(literal -1/48 binary64)) (.f64 eps eps) #s(literal 1/2 binary64)) eps))))
(.f64 #s(approx (sin ( 1/2 (+ 0 eps))) (.f64 (fma.f64 (fma.f64 (fma.f64 (.f64 eps eps) #s(literal -1/645120 binary64) #s(literal 1/3840 binary64)) (.f64 eps eps) #s(literal -1/48 binary64)) (.f64 eps eps) #s(literal 1/2 binary64)) eps)) (sin.f64 (*.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64))))
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(fma.f64 eps (fma.f64 (.f64 (fma.f64 (.f64 x x) #s(literal 1/5040 binary64) #s(literal -1/120 binary64)) x) x #s(literal -1/6 binary64)) (.f64 (fma.f64 (.f64 (fma.f64 (*.f64 x x) #s(literal 1/5040 binary64) #s(literal -1/120 binary64)) x) x #s(literal -1/6 binary64)) #s(literal 0 binary64)))
(fma.f64 eps (.f64 (.f64 (fma.f64 (.f64 x x) #s(literal 1/5040 binary64) #s(literal -1/120 binary64)) x) x) (.f64 eps #s(literal -1/6 binary64)))
(+.f64 (.f64 #s(literal 0 binary64) (fma.f64 (.f64 (fma.f64 (.f64 x x) #s(literal 1/5040 binary64) #s(literal -1/120 binary64)) x) x #s(literal -1/6 binary64))) (.f64 (fma.f64 (.f64 (fma.f64 (.f64 x x) #s(literal 1/5040 binary64) #s(literal -1/120 binary64)) x) x #s(literal -1/6 binary64)) eps))
(+.f64 (.f64 (.f64 (.f64 (fma.f64 (.f64 x x) #s(literal 1/5040 binary64) #s(literal -1/120 binary64)) x) x) eps) (*.f64 #s(literal -1/6 binary64) eps))
(+.f64 (.f64 (fma.f64 (.f64 (fma.f64 (.f64 x x) #s(literal 1/5040 binary64) #s(literal -1/120 binary64)) x) x #s(literal -1/6 binary64)) #s(literal 0 binary64)) (.f64 (fma.f64 (.f64 (fma.f64 (.f64 x x) #s(literal 1/5040 binary64) #s(literal -1/120 binary64)) x) x #s(literal -1/6 binary64)) eps))
(+.f64 (.f64 eps (.f64 (.f64 (fma.f64 (.f64 x x) #s(literal 1/5040 binary64) #s(literal -1/120 binary64)) x) x)) (*.f64 eps #s(literal -1/6 binary64)))
(+.f64 (.f64 (fma.f64 (.f64 (fma.f64 (.f64 x x) #s(literal 1/5040 binary64) #s(literal -1/120 binary64)) x) x #s(literal -1/6 binary64)) eps) (.f64 #s(literal 0 binary64) (fma.f64 (.f64 (fma.f64 (.f64 x x) #s(literal 1/5040 binary64) #s(literal -1/120 binary64)) x) x #s(literal -1/6 binary64))))
(+.f64 (.f64 (fma.f64 (.f64 (fma.f64 (.f64 x x) #s(literal 1/5040 binary64) #s(literal -1/120 binary64)) x) x #s(literal -1/6 binary64)) eps) (.f64 (fma.f64 (.f64 (fma.f64 (.f64 x x) #s(literal 1/5040 binary64) #s(literal -1/120 binary64)) x) x #s(literal -1/6 binary64)) #s(literal 0 binary64)))
(.f64 (.f64 (fma.f64 (*.f64 x x) #s(literal 1/5040 binary64) #s(literal -1/120 binary64)) x) x)
(.f64 (fma.f64 (.f64 x x) #s(literal 1/5040 binary64) #s(literal -1/120 binary64)) (*.f64 x x))
(.f64 (.f64 x x) (fma.f64 (*.f64 x x) #s(literal 1/5040 binary64) #s(literal -1/120 binary64)))
(.f64 x (.f64 (fma.f64 (*.f64 x x) #s(literal 1/5040 binary64) #s(literal -1/120 binary64)) x))
(/.f64 (.f64 (fma.f64 #s(literal 1/25401600 binary64) (.f64 (.f64 x x) (.f64 x x)) #s(literal -1/14400 binary64)) (.f64 x x)) (fma.f64 (.f64 x x) #s(literal 1/5040 binary64) #s(literal 1/120 binary64)))
(/.f64 (.f64 (fma.f64 (.f64 #s(literal 1/128024064000 binary64) (.f64 (.f64 x x) x)) (.f64 (.f64 x x) x) #s(literal -1/1728000 binary64)) (.f64 x x)) (fma.f64 #s(literal 1/25401600 binary64) (.f64 (.f64 x x) (.f64 x x)) (-.f64 #s(literal 1/14400 binary64) (.f64 (.f64 x x) #s(literal -1/604800 binary64)))))
#s(approx (sin (* 1/2 (+ 0 eps))) (.f64 (fma.f64 (fma.f64 #s(literal 1/3840 binary64) (.f64 eps eps) #s(literal -1/48 binary64)) (*.f64 eps eps) #s(literal 1/2 binary64)) eps))

eval140.0ms (0.8%)

Memory: -3.6MiB live, 346.1MiB allocated
Compiler: Compiled 20 387 to 1 584 computations (92.2% saved)

prune151.0ms (0.8%)

Memory

6.5MiB live, 483.1MiB allocated

Pruning

49 alts after pruning (44 fresh and 5 done)

	Pruned	Kept	Total
New	846	25	871
Fresh	7	19	26
Picked	4	1	5
Done	0	4	4
Total	857	49	906

Accuracy

100.0%

Counts

906 → 49

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	49.9%	(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))
	99.7%	(.f64 (.f64 (sin.f64 (fma.f64 (.f64 eps eps) (.f64 (/.f64 #s(literal 1 binary64) eps) #s(literal 1/2 binary64)) (.f64 #s(literal 1 binary64) x))) #s(approx (sin ( 1/2 (+ 0 eps))) (.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -1/645120 binary64) (.f64 eps eps) #s(literal 1/3840 binary64)) (.f64 eps eps) #s(literal -1/48 binary64)) (.f64 eps eps) #s(literal 1/2 binary64)) eps))) #s(literal -2 binary64))
	40.3%	(.f64 (.f64 (sin.f64 (/.f64 (fma.f64 (.f64 (.f64 x x) x) #s(literal 1 binary64) (.f64 #s(literal 1/8 binary64) (.f64 (.f64 eps eps) eps))) (fma.f64 (.f64 #s(literal 1 binary64) x) (.f64 #s(literal 1 binary64) x) (-.f64 (.f64 #s(literal 1/4 binary64) (.f64 eps eps)) (.f64 (.f64 #s(literal 1 binary64) x) (.f64 eps #s(literal 1/2 binary64))))))) #s(approx (sin (* 1/2 (+ 0 eps))) (.f64 (fma.f64 (fma.f64 #s(literal 1/3840 binary64) (.f64 eps eps) #s(literal -1/48 binary64)) (*.f64 eps eps) #s(literal 1/2 binary64)) eps))) #s(literal -2 binary64))
	99.5%	(.f64 (.f64 (sin.f64 (/.f64 (-.f64 (.f64 (.f64 #s(literal 1 binary64) x) (.f64 #s(literal 1 binary64) x)) (.f64 #s(literal 1/4 binary64) (.f64 eps eps))) (-.f64 (.f64 #s(literal 1 binary64) x) (.f64 eps #s(literal 1/2 binary64))))) #s(approx (sin ( 1/2 (+ 0 eps))) (.f64 (fma.f64 (fma.f64 #s(literal 1/3840 binary64) (.f64 eps eps) #s(literal -1/48 binary64)) (*.f64 eps eps) #s(literal 1/2 binary64)) eps))) #s(literal -2 binary64))
	40.3%	(.f64 (.f64 (sin.f64 (/.f64 (.f64 (fma.f64 #s(literal 8 binary64) (.f64 (.f64 x x) x) (.f64 (.f64 eps eps) eps)) #s(literal 1/2 binary64)) (fma.f64 #s(literal 4 binary64) (.f64 x x) (.f64 eps (-.f64 eps (.f64 x #s(literal 2 binary64))))))) #s(approx (sin (* 1/2 (+ 0 eps))) (.f64 (fma.f64 (fma.f64 #s(literal 1/3840 binary64) (.f64 eps eps) #s(literal -1/48 binary64)) (*.f64 eps eps) #s(literal 1/2 binary64)) eps))) #s(literal -2 binary64))
	99.7%	(.f64 (.f64 (sin.f64 (-.f64 (/.f64 (.f64 (.f64 #s(literal 1 binary64) x) (.f64 #s(literal 1 binary64) x)) (-.f64 (.f64 #s(literal 1 binary64) x) (.f64 eps #s(literal 1/2 binary64)))) (/.f64 (.f64 (.f64 eps #s(literal 1/2 binary64)) (.f64 eps #s(literal 1/2 binary64))) (-.f64 (.f64 #s(literal 1 binary64) x) (.f64 eps #s(literal 1/2 binary64)))))) (sin.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 0 binary64) eps)))) #s(literal -2 binary64))
	98.1%	(.f64 (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps))) (sin.f64 (.f64 #s(literal 1/2 binary64) (/.f64 (*.f64 eps eps) eps)))) #s(literal -2 binary64))
	99.7%	(.f64 (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps))) (sin.f64 (.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) eps))))) #s(literal -2 binary64))
	35.6%	(.f64 (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps))) (sin.f64 (.f64 #s(literal 1/2 binary64) (.f64 (pow.f64 eps #s(literal 3 binary64)) (/.f64 #s(literal 1 binary64) (.f64 eps eps)))))) #s(literal -2 binary64))
	35.6%	(.f64 (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps))) (sin.f64 (.f64 #s(literal 1/2 binary64) (.f64 (.f64 (*.f64 eps eps) eps) (pow.f64 eps #s(literal -2 binary64)))))) #s(literal -2 binary64))
	35.5%	(.f64 (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps))) (sin.f64 (.f64 #s(literal 1/2 binary64) (.f64 (.f64 (.f64 eps eps) eps) (.f64 (/.f64 #s(literal -1 binary64) eps) (/.f64 #s(literal -1 binary64) eps)))))) #s(literal -2 binary64))
	99.7%	(.f64 (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps))) (sin.f64 (.f64 #s(literal 1/2 binary64) (.f64 eps (.f64 eps (/.f64 #s(literal 1 binary64) eps)))))) #s(literal -2 binary64))
	35.6%	(.f64 (.f64 (sin.f64 #s(approx (* 1/2 (+ (* 2 x) eps)) (fma.f64 eps #s(literal 1/2 binary64) x))) (sin.f64 (.f64 #s(literal 1/2 binary64) (.f64 (.f64 (.f64 eps eps) eps) (/.f64 #s(literal 1 binary64) (*.f64 eps eps)))))) #s(literal -2 binary64))
	98.1%	(.f64 (.f64 (sin.f64 #s(approx (* 1/2 (+ (* 2 x) eps)) (fma.f64 eps #s(literal 1/2 binary64) x))) (sin.f64 (.f64 #s(literal 1/2 binary64) (.f64 (neg.f64 (*.f64 eps eps)) (/.f64 #s(literal -1 binary64) eps))))) #s(literal -2 binary64))
	99.7%	(.f64 (.f64 (sin.f64 #s(approx (* 1/2 (+ (* 2 x) eps)) (fma.f64 eps #s(literal 1/2 binary64) x))) #s(approx (sin (* 1/2 (+ 0 eps))) (.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -1/645120 binary64) (.f64 eps eps) #s(literal 1/3840 binary64)) (.f64 eps eps) #s(literal -1/48 binary64)) (.f64 eps eps) #s(literal 1/2 binary64)) eps))) #s(literal -2 binary64))
	99.6%	(.f64 (.f64 (sin.f64 #s(approx (* 1/2 (+ (* 2 x) eps)) (fma.f64 eps #s(literal 1/2 binary64) x))) #s(approx (sin (* 1/2 (+ 0 eps))) (.f64 (fma.f64 (.f64 eps eps) #s(literal -1/48 binary64) #s(literal 1/2 binary64)) eps))) #s(literal -2 binary64))
	99.5%	(.f64 (.f64 (sin.f64 #s(approx (* 1/2 (+ (* 2 x) eps)) (fma.f64 eps #s(literal 1/2 binary64) x))) #s(approx (sin (* 1/2 (+ 0 eps))) (*.f64 eps #s(literal 1/2 binary64)))) #s(literal -2 binary64))
	99.6%	(.f64 (.f64 #s(approx (sin (* 1/2 (+ 0 eps))) (.f64 (fma.f64 (fma.f64 #s(literal 1/3840 binary64) (.f64 eps eps) #s(literal -1/48 binary64)) (.f64 eps eps) #s(literal 1/2 binary64)) eps)) #s(literal -2 binary64)) (sin.f64 #s(approx ( 1/2 (+ (* 2 x) eps)) (fma.f64 eps #s(literal 1/2 binary64) x))))
✓	99.8%	(.f64 #s(approx ( (sin (* 1/2 (+ (* 2 x) eps))) (sin (* 1/2 (+ 0 eps)))) (.f64 (sin.f64 (fma.f64 eps #s(literal 1/2 binary64) x)) (sin.f64 (.f64 eps #s(literal 1/2 binary64))))) #s(literal -2 binary64))
✓	49.0%	#s(approx (- (cos (+ x eps)) (cos x)) (-.f64 #s(approx (cos eps) #s(literal 1 binary64)) #s(literal 1 binary64)))
	99.5%	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 (-.f64 (.f64 (*.f64 (cos.f64 x) #s(literal -1/2 binary64)) eps) (sin.f64 x)) eps))
✓	79.2%	#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (neg.f64 eps) (sin.f64 x)))
	78.5%	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 (neg.f64 eps) #s(approx (sin x) (.f64 (fma.f64 (fma.f64 #s(literal 1/120 binary64) (.f64 x x) #s(literal -1/6 binary64)) (.f64 x x) #s(literal 1 binary64)) x))))
	16.5%	#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (/.f64 (.f64 (.f64 (.f64 eps eps) eps) (neg.f64 x)) (.f64 eps eps))))
	67.5%	#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (/.f64 (.f64 (.f64 eps eps) (neg.f64 x)) eps)))
	78.7%	#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (.f64 (fma.f64 (fma.f64 (fma.f64 eps #s(literal -1/120 binary64) (.f64 (.f64 #s(literal 1/5040 binary64) (.f64 x x)) eps)) (.f64 x x) (.f64 #s(literal 1/6 binary64) eps)) (*.f64 x x) (neg.f64 eps)) x)))
	21.1%	#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (.f64 (fma.f64 (/.f64 #s(literal -1 binary64) (.f64 eps eps)) (.f64 (.f64 eps eps) eps) (.f64 (.f64 eps (fma.f64 (fma.f64 #s(literal 1/5040 binary64) (.f64 x x) #s(literal -1/120 binary64)) (.f64 x x) #s(literal 1/6 binary64))) (*.f64 x x))) x)))
	78.0%	#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (.f64 (fma.f64 (/.f64 #s(literal -1 binary64) eps) (.f64 eps eps) (.f64 (.f64 eps (fma.f64 (fma.f64 #s(literal 1/5040 binary64) (.f64 x x) #s(literal -1/120 binary64)) (.f64 x x) #s(literal 1/6 binary64))) (*.f64 x x))) x)))
	78.7%	#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (.f64 (fma.f64 (.f64 (.f64 (fma.f64 (fma.f64 #s(literal 1/5040 binary64) (.f64 x x) #s(literal -1/120 binary64)) (*.f64 x x) #s(literal 1/6 binary64)) eps) x) x (neg.f64 eps)) x)))
	78.5%	#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (.f64 (fma.f64 (.f64 eps (fma.f64 (.f64 x x) #s(literal -1/120 binary64) #s(literal 1/6 binary64))) (.f64 x x) (neg.f64 eps)) x)))
	78.1%	#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (.f64 (fma.f64 (.f64 eps #s(approx (- (* (* (+ (* 1/5040 (* x x)) -1/120) x) x) 1/6) (fma.f64 #s(literal -1/120 binary64) (.f64 x x) #s(literal -1/6 binary64)))) (.f64 x x) (neg.f64 eps)) x)))
	14.0%	#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (.f64 (/.f64 (fma.f64 (.f64 (.f64 (.f64 eps eps) eps) (.f64 (.f64 (fma.f64 (.f64 (fma.f64 (.f64 x x) #s(literal 1/5040 binary64) #s(literal -1/120 binary64)) x) x #s(literal -1/6 binary64)) x) x)) eps (.f64 (.f64 eps eps) (/.f64 (.f64 eps eps) #s(literal -1 binary64)))) (.f64 (*.f64 eps eps) eps)) x)))
	32.2%	#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (.f64 (/.f64 (-.f64 (.f64 (.f64 (.f64 (.f64 eps eps) eps) (.f64 (.f64 (fma.f64 (.f64 (fma.f64 (.f64 x x) #s(literal 1/5040 binary64) #s(literal -1/120 binary64)) x) x #s(literal -1/6 binary64)) x) x)) (/.f64 eps (.f64 eps eps))) (.f64 eps eps)) (.f64 (.f64 eps eps) (/.f64 eps (.f64 eps eps)))) x)))
	10.5%	#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (.f64 (/.f64 (-.f64 (.f64 (.f64 (.f64 (.f64 eps eps) eps) (.f64 (.f64 (fma.f64 (.f64 (fma.f64 (.f64 x x) #s(literal 1/5040 binary64) #s(literal -1/120 binary64)) x) x #s(literal -1/6 binary64)) x) x)) (.f64 eps eps)) (.f64 (.f64 eps eps) (.f64 (.f64 eps eps) eps))) (.f64 (.f64 (*.f64 eps eps) eps) eps)) x)))
	14.0%	#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (.f64 (/.f64 (-.f64 (.f64 (.f64 (.f64 (.f64 eps eps) eps) (.f64 (.f64 (fma.f64 (.f64 (fma.f64 (.f64 x x) #s(literal 1/5040 binary64) #s(literal -1/120 binary64)) x) x #s(literal -1/6 binary64)) x) x)) eps) (.f64 (.f64 (.f64 eps eps) eps) eps)) (.f64 (.f64 eps eps) eps)) x)))
	32.2%	#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (.f64 (/.f64 (-.f64 (.f64 (.f64 (.f64 eps eps) (.f64 (.f64 (fma.f64 (.f64 (fma.f64 (.f64 x x) #s(literal 1/5040 binary64) #s(literal -1/120 binary64)) x) x #s(literal -1/6 binary64)) x) x)) (/.f64 eps (.f64 eps eps))) (.f64 eps #s(literal 1 binary64))) (.f64 eps (/.f64 eps (.f64 eps eps)))) x)))
	78.1%	#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (.f64 (/.f64 (-.f64 (.f64 (.f64 (.f64 eps eps) (.f64 (.f64 (fma.f64 (.f64 (fma.f64 (.f64 x x) #s(literal 1/5040 binary64) #s(literal -1/120 binary64)) x) x #s(literal -1/6 binary64)) x) x)) (/.f64 #s(literal 1 binary64) eps)) (.f64 eps #s(literal 1 binary64))) (.f64 eps (/.f64 #s(literal 1 binary64) eps))) x)))
	21.7%	#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (.f64 (/.f64 (-.f64 (.f64 (.f64 (.f64 eps eps) (.f64 (.f64 (fma.f64 (.f64 (fma.f64 (.f64 x x) #s(literal 1/5040 binary64) #s(literal -1/120 binary64)) x) x #s(literal -1/6 binary64)) x) x)) eps) (.f64 (.f64 eps eps) eps)) (*.f64 eps eps)) x)))
	77.5%	#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (.f64 (/.f64 (-.f64 (.f64 (.f64 eps eps) (.f64 (.f64 (fma.f64 (.f64 (fma.f64 (.f64 x x) #s(literal 1/5040 binary64) #s(literal -1/120 binary64)) x) x #s(literal -1/6 binary64)) x) x)) (.f64 eps eps)) eps) x)))
	24.9%	#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (.f64 (/.f64 (-.f64 #s(literal 0 binary64) (.f64 (.f64 x x) x)) (+.f64 #s(literal 0 binary64) (fma.f64 x x (.f64 #s(literal 0 binary64) x)))) eps)))
	78.2%	#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (.f64 (/.f64 (-.f64 #s(literal 0 binary64) (.f64 x x)) (+.f64 #s(literal 0 binary64) x)) eps)))
	78.4%	#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (.f64 (.f64 eps (fma.f64 (*.f64 x x) #s(literal 1/6 binary64) #s(literal -1 binary64))) x)))
✓	78.2%	#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (*.f64 (neg.f64 x) eps)))
	78.7%	#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (.f64 #s(approx (+ ( (+ (* (* eps (+ (* (* x x) 1/5040) -1/120)) (* x x)) (* 1/6 eps)) (* x x)) (neg eps)) (.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 1/5040 binary64) (.f64 x x) #s(literal -1/120 binary64)) (.f64 x x) #s(literal 1/6 binary64)) (.f64 x x) #s(literal -1 binary64)) eps)) x)))
	78.1%	#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (.f64 #s(approx (+ ( (* eps (- (* (* (+ (* 1/5040 (* x x)) -1/120) x) x) 1/6)) (* x x)) (neg eps)) (.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 1/5040 binary64) (.f64 x x) #s(literal -1/120 binary64)) (.f64 x x) #s(literal -1/6 binary64)) (.f64 x x) #s(literal -1 binary64)) eps)) x)))
	78.1%	#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (.f64 #s(approx (+ ( (* eps (- (* (* (+ (* 1/5040 (* x x)) -1/120) x) x) 1/6)) (* x x)) (neg eps)) (.f64 eps (fma.f64 #s(literal -1/6 binary64) (.f64 x x) #s(literal -1 binary64)))) x)))
	48.2%	#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (*.f64 x eps)))
	98.6%	#s(approx (* (* (sin (* 1/2 (+ (* 2 x) eps))) (sin (* 1/2 (+ 0 eps)))) -2) (fma.f64 (fma.f64 (.f64 (cos.f64 (.f64 eps #s(literal 1/2 binary64))) (sin.f64 (.f64 eps #s(literal 1/2 binary64)))) (+.f64 #s(literal -2 binary64) (.f64 x (.f64 #s(literal 1/3 binary64) x))) (.f64 (pow.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) #s(literal 2 binary64)) x)) x (.f64 (pow.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) #s(literal 2 binary64)) #s(literal -2 binary64))))
	97.9%	#s(approx (* (* (sin (* 1/2 (+ (* 2 x) eps))) (sin (* 1/2 (+ 0 eps)))) -2) (fma.f64 (pow.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) #s(literal 2 binary64)) (fma.f64 x x #s(literal -2 binary64)) (.f64 (.f64 (.f64 x #s(literal -2 binary64)) (cos.f64 (.f64 #s(literal -1/2 binary64) eps))) (sin.f64 (.f64 eps #s(literal 1/2 binary64))))))

Compiler

Compiled 3 056 to 1 061 computations (65.3% saved)

regimes63.0ms (0.3%)

Memory

18.5MiB live, 187.5MiB allocated

Counts

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

Outputs

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

Calls

3 calls:

22.0ms	eps
20.0ms	x
17.0ms	(-.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)

regimes44.0ms (0.2%)

Memory

-1.2MiB live, 118.1MiB allocated

Counts

52 → 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 (* (neg eps) (sin x)) (*.f64 x eps)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (*.f64 (neg.f64 x) eps)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (.f64 #s(approx (+ ( (* eps (- (* (* (+ (* 1/5040 (* x x)) -1/120) x) x) 1/6)) (* x x)) (neg eps)) (.f64 eps (fma.f64 #s(literal -1/6 binary64) (.f64 x x) #s(literal -1 binary64)))) x)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (.f64 (.f64 eps (fma.f64 (*.f64 x x) #s(literal 1/6 binary64) #s(literal -1 binary64))) x)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (.f64 (fma.f64 #s(approx (+ ( (* eps (+ (* (* x x) 1/5040) -1/120)) (* x x)) (* 1/6 eps)) (.f64 #s(literal 1/6 binary64) eps)) (.f64 x x) (neg.f64 eps)) x)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (/.f64 (.f64 (.f64 eps eps) (neg.f64 x)) eps)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (.f64 (/.f64 (-.f64 #s(literal 0 binary64) (.f64 x x)) (+.f64 #s(literal 0 binary64) x)) eps)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (/.f64 (.f64 (.f64 (.f64 eps eps) eps) (neg.f64 x)) (.f64 eps eps))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (.f64 (fma.f64 (.f64 eps #s(approx (- (* (* (+ (* 1/5040 (* x x)) -1/120) x) x) 1/6) (fma.f64 #s(literal -1/120 binary64) (.f64 x x) #s(literal -1/6 binary64)))) (.f64 x x) (neg.f64 eps)) x)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (.f64 (fma.f64 (.f64 eps (fma.f64 (.f64 x x) #s(literal -1/120 binary64) #s(literal 1/6 binary64))) (.f64 x x) (neg.f64 eps)) x)))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 (neg.f64 eps) #s(approx (sin x) (.f64 (fma.f64 (fma.f64 #s(literal 1/120 binary64) (.f64 x x) #s(literal -1/6 binary64)) (.f64 x x) #s(literal 1 binary64)) x))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (.f64 #s(approx (+ ( (* eps (- (* (* (+ (* 1/5040 (* x x)) -1/120) x) x) 1/6)) (* x x)) (neg eps)) (.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 1/5040 binary64) (.f64 x x) #s(literal -1/120 binary64)) (.f64 x x) #s(literal -1/6 binary64)) (.f64 x x) #s(literal -1 binary64)) eps)) x)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (.f64 #s(approx (+ ( (+ (* (* eps (+ (* (* x x) 1/5040) -1/120)) (* x x)) (* 1/6 eps)) (* x x)) (neg eps)) (.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 1/5040 binary64) (.f64 x x) #s(literal -1/120 binary64)) (.f64 x x) #s(literal 1/6 binary64)) (.f64 x x) #s(literal -1 binary64)) eps)) x)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (.f64 (/.f64 (-.f64 #s(literal 0 binary64) (.f64 (.f64 x x) x)) (+.f64 #s(literal 0 binary64) (fma.f64 x x (.f64 #s(literal 0 binary64) x)))) eps)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (.f64 (fma.f64 (.f64 (.f64 (fma.f64 (fma.f64 #s(literal 1/5040 binary64) (.f64 x x) #s(literal -1/120 binary64)) (*.f64 x x) #s(literal 1/6 binary64)) eps) x) x (neg.f64 eps)) x)))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 (neg.f64 eps) #s(approx (sin x) (.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -1/5040 binary64) (.f64 x x) #s(literal 1/120 binary64)) (.f64 x x) #s(literal -1/6 binary64)) (*.f64 x x) #s(literal 1 binary64)) x))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (.f64 (fma.f64 (.f64 eps (-.f64 (.f64 (.f64 (fma.f64 #s(literal 1/5040 binary64) (.f64 x x) #s(literal -1/120 binary64)) x) x) #s(literal 1/6 binary64))) (.f64 x x) (neg.f64 eps)) x)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (.f64 (fma.f64 (fma.f64 (.f64 eps (fma.f64 (.f64 x x) #s(literal 1/5040 binary64) #s(literal -1/120 binary64))) (.f64 x x) (.f64 #s(literal 1/6 binary64) eps)) (.f64 x x) (neg.f64 eps)) x)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (.f64 (fma.f64 (fma.f64 (fma.f64 eps #s(literal -1/120 binary64) (.f64 (.f64 #s(literal 1/5040 binary64) (.f64 x x)) eps)) (.f64 x x) (.f64 #s(literal 1/6 binary64) eps)) (*.f64 x x) (neg.f64 eps)) x)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (.f64 (fma.f64 (/.f64 #s(literal -1 binary64) eps) (.f64 eps eps) (.f64 (.f64 eps (fma.f64 (fma.f64 #s(literal 1/5040 binary64) (.f64 x x) #s(literal -1/120 binary64)) (.f64 x x) #s(literal 1/6 binary64))) (*.f64 x x))) x)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (.f64 (/.f64 (-.f64 (.f64 (.f64 eps eps) (.f64 (.f64 (fma.f64 (.f64 (fma.f64 (.f64 x x) #s(literal 1/5040 binary64) #s(literal -1/120 binary64)) x) x #s(literal -1/6 binary64)) x) x)) (.f64 eps eps)) eps) x)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (.f64 (fma.f64 (/.f64 #s(literal -1 binary64) (.f64 eps eps)) (.f64 (.f64 eps eps) eps) (.f64 (.f64 eps (fma.f64 (fma.f64 #s(literal 1/5040 binary64) (.f64 x x) #s(literal -1/120 binary64)) (.f64 x x) #s(literal 1/6 binary64))) (*.f64 x x))) x)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (.f64 (/.f64 (-.f64 (.f64 (.f64 (.f64 eps eps) (.f64 (.f64 (fma.f64 (.f64 (fma.f64 (.f64 x x) #s(literal 1/5040 binary64) #s(literal -1/120 binary64)) x) x #s(literal -1/6 binary64)) x) x)) eps) (.f64 (.f64 eps eps) eps)) (*.f64 eps eps)) x)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (.f64 (/.f64 (-.f64 (.f64 (.f64 (.f64 (.f64 eps eps) eps) (.f64 (.f64 (fma.f64 (.f64 (fma.f64 (.f64 x x) #s(literal 1/5040 binary64) #s(literal -1/120 binary64)) x) x #s(literal -1/6 binary64)) x) x)) eps) (.f64 (.f64 (.f64 eps eps) eps) eps)) (.f64 (.f64 eps eps) eps)) x)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (.f64 (/.f64 (-.f64 (.f64 (.f64 (.f64 eps eps) (.f64 (.f64 (fma.f64 (.f64 (fma.f64 (.f64 x x) #s(literal 1/5040 binary64) #s(literal -1/120 binary64)) x) x #s(literal -1/6 binary64)) x) x)) (/.f64 #s(literal 1 binary64) eps)) (.f64 eps #s(literal 1 binary64))) (.f64 eps (/.f64 #s(literal 1 binary64) eps))) x)))
#s(approx (- (cos (+ x eps)) (cos x)) (-.f64 (cos.f64 eps) #s(literal 1 binary64)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (.f64 (/.f64 (fma.f64 (.f64 (.f64 (.f64 eps eps) eps) (.f64 (.f64 (fma.f64 (.f64 (fma.f64 (.f64 x x) #s(literal 1/5040 binary64) #s(literal -1/120 binary64)) x) x #s(literal -1/6 binary64)) x) x)) eps (.f64 (.f64 eps eps) (/.f64 (.f64 eps eps) #s(literal -1 binary64)))) (.f64 (*.f64 eps eps) eps)) x)))
(-.f64 (cos.f64 (+.f64 x eps)) #s(approx (cos x) #s(literal 1 binary64)))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (neg.f64 eps) (sin.f64 x)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (.f64 (/.f64 (-.f64 (.f64 (.f64 (.f64 eps eps) (.f64 (.f64 (fma.f64 (.f64 (fma.f64 (.f64 x x) #s(literal 1/5040 binary64) #s(literal -1/120 binary64)) x) x #s(literal -1/6 binary64)) x) x)) (/.f64 eps (.f64 eps eps))) (.f64 eps #s(literal 1 binary64))) (.f64 eps (/.f64 eps (.f64 eps eps)))) x)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (.f64 (/.f64 (-.f64 (.f64 (.f64 (.f64 (.f64 eps eps) eps) (.f64 (.f64 (fma.f64 (.f64 (fma.f64 (.f64 x x) #s(literal 1/5040 binary64) #s(literal -1/120 binary64)) x) x #s(literal -1/6 binary64)) x) x)) (.f64 eps eps)) (.f64 (.f64 eps eps) (.f64 (.f64 eps eps) eps))) (.f64 (.f64 (*.f64 eps eps) eps) eps)) x)))
(.f64 #s(approx ( (sin (* 1/2 (+ (* 2 x) eps))) (sin (* 1/2 (+ 0 eps)))) (.f64 (.f64 (sin.f64 x) #s(literal 1/2 binary64)) eps)) #s(literal -2 binary64))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (.f64 (/.f64 (-.f64 (.f64 (.f64 (.f64 (.f64 eps eps) eps) (.f64 (.f64 (fma.f64 (.f64 (fma.f64 (.f64 x x) #s(literal 1/5040 binary64) #s(literal -1/120 binary64)) x) x #s(literal -1/6 binary64)) x) x)) (/.f64 eps (.f64 eps eps))) (.f64 eps eps)) (.f64 (.f64 eps eps) (/.f64 eps (.f64 eps eps)))) x)))
(.f64 (.f64 (sin.f64 #s(approx (* 1/2 (+ (* 2 x) eps)) (fma.f64 eps #s(literal 1/2 binary64) x))) #s(approx (sin (* 1/2 (+ 0 eps))) (*.f64 eps #s(literal 1/2 binary64)))) #s(literal -2 binary64))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 (/.f64 (.f64 eps eps) (neg.f64 eps)) (sin.f64 x)))
(.f64 (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps))) #s(approx (sin ( 1/2 (+ 0 eps))) (*.f64 eps #s(literal 1/2 binary64)))) #s(literal -2 binary64))
(-.f64 (cos.f64 (+.f64 x eps)) #s(approx (cos x) (fma.f64 (fma.f64 (.f64 x x) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) (.f64 x x) #s(literal 1 binary64))))
(.f64 (.f64 (sin.f64 #s(approx (* 1/2 (+ (* 2 x) eps)) (fma.f64 eps #s(literal 1/2 binary64) x))) #s(approx (sin (* 1/2 (+ 0 eps))) (.f64 (fma.f64 (.f64 eps eps) #s(literal -1/48 binary64) #s(literal 1/2 binary64)) eps))) #s(literal -2 binary64))
(.f64 (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps))) #s(approx (sin ( 1/2 (+ 0 eps))) (.f64 (fma.f64 (.f64 eps eps) #s(literal -1/48 binary64) #s(literal 1/2 binary64)) eps))) #s(literal -2 binary64))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 (.f64 (/.f64 #s(literal -1 binary64) eps) (/.f64 (neg.f64 (*.f64 eps eps)) #s(literal -1 binary64))) (sin.f64 x)))
(.f64 (.f64 #s(approx (sin (* 1/2 (+ 0 eps))) (.f64 (fma.f64 (fma.f64 #s(literal 1/3840 binary64) (.f64 eps eps) #s(literal -1/48 binary64)) (.f64 eps eps) #s(literal 1/2 binary64)) eps)) #s(literal -2 binary64)) (sin.f64 #s(approx ( 1/2 (+ (* 2 x) eps)) (fma.f64 eps #s(literal 1/2 binary64) x))))
(.f64 (.f64 (sin.f64 #s(approx (* 1/2 (+ (* 2 x) eps)) (fma.f64 eps #s(literal 1/2 binary64) x))) #s(approx (sin (* 1/2 (+ 0 eps))) (.f64 (fma.f64 (fma.f64 #s(literal 1/3840 binary64) (.f64 eps eps) #s(literal -1/48 binary64)) (*.f64 eps eps) #s(literal 1/2 binary64)) eps))) #s(literal -2 binary64))
(.f64 (.f64 #s(approx (sin (* 1/2 (+ 0 eps))) (.f64 (fma.f64 (fma.f64 (.f64 eps eps) #s(literal 1/3840 binary64) #s(literal -1/48 binary64)) (.f64 eps eps) #s(literal 1/2 binary64)) eps)) #s(literal -2 binary64)) (sin.f64 (fma.f64 #s(literal 1 binary64) x (.f64 eps #s(literal 1/2 binary64)))))
(.f64 (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps))) #s(approx (sin ( 1/2 (+ 0 eps))) (.f64 (fma.f64 (fma.f64 #s(literal 1/3840 binary64) (.f64 eps eps) #s(literal -1/48 binary64)) (*.f64 eps eps) #s(literal 1/2 binary64)) eps))) #s(literal -2 binary64))
(.f64 (.f64 (sin.f64 #s(approx (* 1/2 (+ (* 2 x) eps)) (fma.f64 eps #s(literal 1/2 binary64) x))) #s(approx (sin (* 1/2 (+ 0 eps))) (.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -1/645120 binary64) (.f64 eps eps) #s(literal 1/3840 binary64)) (.f64 eps eps) #s(literal -1/48 binary64)) (.f64 eps eps) #s(literal 1/2 binary64)) eps))) #s(literal -2 binary64))
(.f64 (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps))) #s(approx (sin ( 1/2 (+ 0 eps))) (.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -1/645120 binary64) (.f64 eps eps) #s(literal 1/3840 binary64)) (.f64 eps eps) #s(literal -1/48 binary64)) (.f64 eps eps) #s(literal 1/2 binary64)) eps))) #s(literal -2 binary64))
(.f64 (.f64 (sin.f64 (fma.f64 (.f64 eps eps) (.f64 (/.f64 #s(literal 1 binary64) eps) #s(literal 1/2 binary64)) (.f64 #s(literal 1 binary64) x))) #s(approx (sin ( 1/2 (+ 0 eps))) (.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -1/645120 binary64) (.f64 eps eps) #s(literal 1/3840 binary64)) (.f64 eps eps) #s(literal -1/48 binary64)) (.f64 eps eps) #s(literal 1/2 binary64)) eps))) #s(literal -2 binary64))
(.f64 (.f64 (sin.f64 (/.f64 (-.f64 (.f64 (.f64 #s(literal 1 binary64) x) (.f64 #s(literal 1 binary64) x)) (.f64 #s(literal 1/4 binary64) (.f64 eps eps))) (-.f64 (.f64 #s(literal 1 binary64) x) (.f64 eps #s(literal 1/2 binary64))))) #s(approx (sin ( 1/2 (+ 0 eps))) (.f64 (fma.f64 (fma.f64 #s(literal 1/3840 binary64) (.f64 eps eps) #s(literal -1/48 binary64)) (*.f64 eps eps) #s(literal 1/2 binary64)) eps))) #s(literal -2 binary64))
(.f64 (.f64 (sin.f64 (/.f64 (.f64 (fma.f64 #s(literal 8 binary64) (.f64 (.f64 x x) x) (.f64 (.f64 eps eps) eps)) #s(literal 1/2 binary64)) (fma.f64 #s(literal 4 binary64) (.f64 x x) (.f64 eps (-.f64 eps (.f64 x #s(literal 2 binary64))))))) #s(approx (sin (* 1/2 (+ 0 eps))) (.f64 (fma.f64 (fma.f64 #s(literal 1/3840 binary64) (.f64 eps eps) #s(literal -1/48 binary64)) (*.f64 eps eps) #s(literal 1/2 binary64)) eps))) #s(literal -2 binary64))
(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 (-.f64 (.f64 (*.f64 (cos.f64 x) #s(literal -1/2 binary64)) eps) (sin.f64 x)) eps))

Outputs

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

Calls

3 calls:

15.0ms	x
15.0ms	eps
11.0ms	(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))

Results

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

Compiler

Compiled 15 to 10 computations (33.3% saved)

regimes40.0ms (0.2%)

Memory

-6.2MiB live, 111.9MiB allocated

Counts

47 → 1

Calls

Call 1

Inputs
#s(approx (- (cos (+ x eps)) (cos x)) (-.f64 #s(approx (cos eps) #s(literal 1 binary64)) #s(literal 1 binary64)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (*.f64 x eps)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (*.f64 (neg.f64 x) eps)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (.f64 #s(approx (+ ( (* eps (- (* (* (+ (* 1/5040 (* x x)) -1/120) x) x) 1/6)) (* x x)) (neg eps)) (.f64 eps (fma.f64 #s(literal -1/6 binary64) (.f64 x x) #s(literal -1 binary64)))) x)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (.f64 (.f64 eps (fma.f64 (*.f64 x x) #s(literal 1/6 binary64) #s(literal -1 binary64))) x)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (.f64 (fma.f64 #s(approx (+ ( (* eps (+ (* (* x x) 1/5040) -1/120)) (* x x)) (* 1/6 eps)) (.f64 #s(literal 1/6 binary64) eps)) (.f64 x x) (neg.f64 eps)) x)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (/.f64 (.f64 (.f64 eps eps) (neg.f64 x)) eps)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (.f64 (/.f64 (-.f64 #s(literal 0 binary64) (.f64 x x)) (+.f64 #s(literal 0 binary64) x)) eps)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (/.f64 (.f64 (.f64 (.f64 eps eps) eps) (neg.f64 x)) (.f64 eps eps))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (.f64 (fma.f64 (.f64 eps #s(approx (- (* (* (+ (* 1/5040 (* x x)) -1/120) x) x) 1/6) (fma.f64 #s(literal -1/120 binary64) (.f64 x x) #s(literal -1/6 binary64)))) (.f64 x x) (neg.f64 eps)) x)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (.f64 (fma.f64 (.f64 eps (fma.f64 (.f64 x x) #s(literal -1/120 binary64) #s(literal 1/6 binary64))) (.f64 x x) (neg.f64 eps)) x)))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 (neg.f64 eps) #s(approx (sin x) (.f64 (fma.f64 (fma.f64 #s(literal 1/120 binary64) (.f64 x x) #s(literal -1/6 binary64)) (.f64 x x) #s(literal 1 binary64)) x))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (.f64 #s(approx (+ ( (* eps (- (* (* (+ (* 1/5040 (* x x)) -1/120) x) x) 1/6)) (* x x)) (neg eps)) (.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 1/5040 binary64) (.f64 x x) #s(literal -1/120 binary64)) (.f64 x x) #s(literal -1/6 binary64)) (.f64 x x) #s(literal -1 binary64)) eps)) x)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (.f64 #s(approx (+ ( (+ (* (* eps (+ (* (* x x) 1/5040) -1/120)) (* x x)) (* 1/6 eps)) (* x x)) (neg eps)) (.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 1/5040 binary64) (.f64 x x) #s(literal -1/120 binary64)) (.f64 x x) #s(literal 1/6 binary64)) (.f64 x x) #s(literal -1 binary64)) eps)) x)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (.f64 (/.f64 (-.f64 #s(literal 0 binary64) (.f64 (.f64 x x) x)) (+.f64 #s(literal 0 binary64) (fma.f64 x x (.f64 #s(literal 0 binary64) x)))) eps)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (.f64 (fma.f64 (.f64 (.f64 (fma.f64 (fma.f64 #s(literal 1/5040 binary64) (.f64 x x) #s(literal -1/120 binary64)) (*.f64 x x) #s(literal 1/6 binary64)) eps) x) x (neg.f64 eps)) x)))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 (neg.f64 eps) #s(approx (sin x) (.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -1/5040 binary64) (.f64 x x) #s(literal 1/120 binary64)) (.f64 x x) #s(literal -1/6 binary64)) (*.f64 x x) #s(literal 1 binary64)) x))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (.f64 (fma.f64 (.f64 eps (-.f64 (.f64 (.f64 (fma.f64 #s(literal 1/5040 binary64) (.f64 x x) #s(literal -1/120 binary64)) x) x) #s(literal 1/6 binary64))) (.f64 x x) (neg.f64 eps)) x)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (.f64 (fma.f64 (fma.f64 (.f64 eps (fma.f64 (.f64 x x) #s(literal 1/5040 binary64) #s(literal -1/120 binary64))) (.f64 x x) (.f64 #s(literal 1/6 binary64) eps)) (.f64 x x) (neg.f64 eps)) x)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (.f64 (fma.f64 (fma.f64 (fma.f64 eps #s(literal -1/120 binary64) (.f64 (.f64 #s(literal 1/5040 binary64) (.f64 x x)) eps)) (.f64 x x) (.f64 #s(literal 1/6 binary64) eps)) (*.f64 x x) (neg.f64 eps)) x)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (.f64 (fma.f64 (/.f64 #s(literal -1 binary64) eps) (.f64 eps eps) (.f64 (.f64 eps (fma.f64 (fma.f64 #s(literal 1/5040 binary64) (.f64 x x) #s(literal -1/120 binary64)) (.f64 x x) #s(literal 1/6 binary64))) (*.f64 x x))) x)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (.f64 (/.f64 (-.f64 (.f64 (.f64 eps eps) (.f64 (.f64 (fma.f64 (.f64 (fma.f64 (.f64 x x) #s(literal 1/5040 binary64) #s(literal -1/120 binary64)) x) x #s(literal -1/6 binary64)) x) x)) (.f64 eps eps)) eps) x)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (.f64 (fma.f64 (/.f64 #s(literal -1 binary64) (.f64 eps eps)) (.f64 (.f64 eps eps) eps) (.f64 (.f64 eps (fma.f64 (fma.f64 #s(literal 1/5040 binary64) (.f64 x x) #s(literal -1/120 binary64)) (.f64 x x) #s(literal 1/6 binary64))) (*.f64 x x))) x)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (.f64 (/.f64 (-.f64 (.f64 (.f64 (.f64 eps eps) (.f64 (.f64 (fma.f64 (.f64 (fma.f64 (.f64 x x) #s(literal 1/5040 binary64) #s(literal -1/120 binary64)) x) x #s(literal -1/6 binary64)) x) x)) eps) (.f64 (.f64 eps eps) eps)) (*.f64 eps eps)) x)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (.f64 (/.f64 (-.f64 (.f64 (.f64 (.f64 (.f64 eps eps) eps) (.f64 (.f64 (fma.f64 (.f64 (fma.f64 (.f64 x x) #s(literal 1/5040 binary64) #s(literal -1/120 binary64)) x) x #s(literal -1/6 binary64)) x) x)) eps) (.f64 (.f64 (.f64 eps eps) eps) eps)) (.f64 (.f64 eps eps) eps)) x)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (.f64 (/.f64 (-.f64 (.f64 (.f64 (.f64 eps eps) (.f64 (.f64 (fma.f64 (.f64 (fma.f64 (.f64 x x) #s(literal 1/5040 binary64) #s(literal -1/120 binary64)) x) x #s(literal -1/6 binary64)) x) x)) (/.f64 #s(literal 1 binary64) eps)) (.f64 eps #s(literal 1 binary64))) (.f64 eps (/.f64 #s(literal 1 binary64) eps))) x)))
#s(approx (- (cos (+ x eps)) (cos x)) (-.f64 (cos.f64 eps) #s(literal 1 binary64)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (.f64 (/.f64 (fma.f64 (.f64 (.f64 (.f64 eps eps) eps) (.f64 (.f64 (fma.f64 (.f64 (fma.f64 (.f64 x x) #s(literal 1/5040 binary64) #s(literal -1/120 binary64)) x) x #s(literal -1/6 binary64)) x) x)) eps (.f64 (.f64 eps eps) (/.f64 (.f64 eps eps) #s(literal -1 binary64)))) (.f64 (*.f64 eps eps) eps)) x)))
(-.f64 (cos.f64 (+.f64 x eps)) #s(approx (cos x) #s(literal 1 binary64)))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (neg.f64 eps) (sin.f64 x)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (.f64 (/.f64 (-.f64 (.f64 (.f64 (.f64 eps eps) (.f64 (.f64 (fma.f64 (.f64 (fma.f64 (.f64 x x) #s(literal 1/5040 binary64) #s(literal -1/120 binary64)) x) x #s(literal -1/6 binary64)) x) x)) (/.f64 eps (.f64 eps eps))) (.f64 eps #s(literal 1 binary64))) (.f64 eps (/.f64 eps (.f64 eps eps)))) x)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (.f64 (/.f64 (-.f64 (.f64 (.f64 (.f64 (.f64 eps eps) eps) (.f64 (.f64 (fma.f64 (.f64 (fma.f64 (.f64 x x) #s(literal 1/5040 binary64) #s(literal -1/120 binary64)) x) x #s(literal -1/6 binary64)) x) x)) (.f64 eps eps)) (.f64 (.f64 eps eps) (.f64 (.f64 eps eps) eps))) (.f64 (.f64 (*.f64 eps eps) eps) eps)) x)))
(.f64 #s(approx ( (sin (* 1/2 (+ (* 2 x) eps))) (sin (* 1/2 (+ 0 eps)))) (.f64 (.f64 (sin.f64 x) #s(literal 1/2 binary64)) eps)) #s(literal -2 binary64))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (.f64 (/.f64 (-.f64 (.f64 (.f64 (.f64 (.f64 eps eps) eps) (.f64 (.f64 (fma.f64 (.f64 (fma.f64 (.f64 x x) #s(literal 1/5040 binary64) #s(literal -1/120 binary64)) x) x #s(literal -1/6 binary64)) x) x)) (/.f64 eps (.f64 eps eps))) (.f64 eps eps)) (.f64 (.f64 eps eps) (/.f64 eps (.f64 eps eps)))) x)))
(.f64 (.f64 (sin.f64 #s(approx (* 1/2 (+ (* 2 x) eps)) (fma.f64 eps #s(literal 1/2 binary64) x))) #s(approx (sin (* 1/2 (+ 0 eps))) (*.f64 eps #s(literal 1/2 binary64)))) #s(literal -2 binary64))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 (/.f64 (.f64 eps eps) (neg.f64 eps)) (sin.f64 x)))
(.f64 (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps))) #s(approx (sin ( 1/2 (+ 0 eps))) (*.f64 eps #s(literal 1/2 binary64)))) #s(literal -2 binary64))
(-.f64 (cos.f64 (+.f64 x eps)) #s(approx (cos x) (fma.f64 (fma.f64 (.f64 x x) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) (.f64 x x) #s(literal 1 binary64))))
(.f64 (.f64 (sin.f64 #s(approx (* 1/2 (+ (* 2 x) eps)) (fma.f64 eps #s(literal 1/2 binary64) x))) #s(approx (sin (* 1/2 (+ 0 eps))) (.f64 (fma.f64 (.f64 eps eps) #s(literal -1/48 binary64) #s(literal 1/2 binary64)) eps))) #s(literal -2 binary64))
(.f64 (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps))) #s(approx (sin ( 1/2 (+ 0 eps))) (.f64 (fma.f64 (.f64 eps eps) #s(literal -1/48 binary64) #s(literal 1/2 binary64)) eps))) #s(literal -2 binary64))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 (.f64 (/.f64 #s(literal -1 binary64) eps) (/.f64 (neg.f64 (*.f64 eps eps)) #s(literal -1 binary64))) (sin.f64 x)))
(.f64 (.f64 #s(approx (sin (* 1/2 (+ 0 eps))) (.f64 (fma.f64 (fma.f64 #s(literal 1/3840 binary64) (.f64 eps eps) #s(literal -1/48 binary64)) (.f64 eps eps) #s(literal 1/2 binary64)) eps)) #s(literal -2 binary64)) (sin.f64 #s(approx ( 1/2 (+ (* 2 x) eps)) (fma.f64 eps #s(literal 1/2 binary64) x))))
(.f64 (.f64 (sin.f64 #s(approx (* 1/2 (+ (* 2 x) eps)) (fma.f64 eps #s(literal 1/2 binary64) x))) #s(approx (sin (* 1/2 (+ 0 eps))) (.f64 (fma.f64 (fma.f64 #s(literal 1/3840 binary64) (.f64 eps eps) #s(literal -1/48 binary64)) (*.f64 eps eps) #s(literal 1/2 binary64)) eps))) #s(literal -2 binary64))
(.f64 (.f64 #s(approx (sin (* 1/2 (+ 0 eps))) (.f64 (fma.f64 (fma.f64 (.f64 eps eps) #s(literal 1/3840 binary64) #s(literal -1/48 binary64)) (.f64 eps eps) #s(literal 1/2 binary64)) eps)) #s(literal -2 binary64)) (sin.f64 (fma.f64 #s(literal 1 binary64) x (.f64 eps #s(literal 1/2 binary64)))))
(.f64 (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps))) #s(approx (sin ( 1/2 (+ 0 eps))) (.f64 (fma.f64 (fma.f64 #s(literal 1/3840 binary64) (.f64 eps eps) #s(literal -1/48 binary64)) (*.f64 eps eps) #s(literal 1/2 binary64)) eps))) #s(literal -2 binary64))
(.f64 (.f64 (sin.f64 #s(approx (* 1/2 (+ (* 2 x) eps)) (fma.f64 eps #s(literal 1/2 binary64) x))) #s(approx (sin (* 1/2 (+ 0 eps))) (.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -1/645120 binary64) (.f64 eps eps) #s(literal 1/3840 binary64)) (.f64 eps eps) #s(literal -1/48 binary64)) (.f64 eps eps) #s(literal 1/2 binary64)) eps))) #s(literal -2 binary64))
(.f64 (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps))) #s(approx (sin ( 1/2 (+ 0 eps))) (.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -1/645120 binary64) (.f64 eps eps) #s(literal 1/3840 binary64)) (.f64 eps eps) #s(literal -1/48 binary64)) (.f64 eps eps) #s(literal 1/2 binary64)) eps))) #s(literal -2 binary64))

Outputs

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

Calls

3 calls:

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

Results

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

Compiler

Compiled 15 to 10 computations (33.3% saved)

regimes61.0ms (0.3%)

Memory

-1.9MiB live, 79.3MiB allocated

Counts

45 → 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 (* (neg eps) (sin x)) (*.f64 x eps)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (*.f64 (neg.f64 x) eps)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (.f64 #s(approx (+ ( (* eps (- (* (* (+ (* 1/5040 (* x x)) -1/120) x) x) 1/6)) (* x x)) (neg eps)) (.f64 eps (fma.f64 #s(literal -1/6 binary64) (.f64 x x) #s(literal -1 binary64)))) x)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (.f64 (.f64 eps (fma.f64 (*.f64 x x) #s(literal 1/6 binary64) #s(literal -1 binary64))) x)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (.f64 (fma.f64 #s(approx (+ ( (* eps (+ (* (* x x) 1/5040) -1/120)) (* x x)) (* 1/6 eps)) (.f64 #s(literal 1/6 binary64) eps)) (.f64 x x) (neg.f64 eps)) x)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (/.f64 (.f64 (.f64 eps eps) (neg.f64 x)) eps)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (.f64 (/.f64 (-.f64 #s(literal 0 binary64) (.f64 x x)) (+.f64 #s(literal 0 binary64) x)) eps)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (/.f64 (.f64 (.f64 (.f64 eps eps) eps) (neg.f64 x)) (.f64 eps eps))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (.f64 (fma.f64 (.f64 eps #s(approx (- (* (* (+ (* 1/5040 (* x x)) -1/120) x) x) 1/6) (fma.f64 #s(literal -1/120 binary64) (.f64 x x) #s(literal -1/6 binary64)))) (.f64 x x) (neg.f64 eps)) x)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (.f64 (fma.f64 (.f64 eps (fma.f64 (.f64 x x) #s(literal -1/120 binary64) #s(literal 1/6 binary64))) (.f64 x x) (neg.f64 eps)) x)))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 (neg.f64 eps) #s(approx (sin x) (.f64 (fma.f64 (fma.f64 #s(literal 1/120 binary64) (.f64 x x) #s(literal -1/6 binary64)) (.f64 x x) #s(literal 1 binary64)) x))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (.f64 #s(approx (+ ( (* eps (- (* (* (+ (* 1/5040 (* x x)) -1/120) x) x) 1/6)) (* x x)) (neg eps)) (.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 1/5040 binary64) (.f64 x x) #s(literal -1/120 binary64)) (.f64 x x) #s(literal -1/6 binary64)) (.f64 x x) #s(literal -1 binary64)) eps)) x)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (.f64 #s(approx (+ ( (+ (* (* eps (+ (* (* x x) 1/5040) -1/120)) (* x x)) (* 1/6 eps)) (* x x)) (neg eps)) (.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 1/5040 binary64) (.f64 x x) #s(literal -1/120 binary64)) (.f64 x x) #s(literal 1/6 binary64)) (.f64 x x) #s(literal -1 binary64)) eps)) x)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (.f64 (/.f64 (-.f64 #s(literal 0 binary64) (.f64 (.f64 x x) x)) (+.f64 #s(literal 0 binary64) (fma.f64 x x (.f64 #s(literal 0 binary64) x)))) eps)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (.f64 (fma.f64 (.f64 (.f64 (fma.f64 (fma.f64 #s(literal 1/5040 binary64) (.f64 x x) #s(literal -1/120 binary64)) (*.f64 x x) #s(literal 1/6 binary64)) eps) x) x (neg.f64 eps)) x)))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 (neg.f64 eps) #s(approx (sin x) (.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -1/5040 binary64) (.f64 x x) #s(literal 1/120 binary64)) (.f64 x x) #s(literal -1/6 binary64)) (*.f64 x x) #s(literal 1 binary64)) x))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (.f64 (fma.f64 (.f64 eps (-.f64 (.f64 (.f64 (fma.f64 #s(literal 1/5040 binary64) (.f64 x x) #s(literal -1/120 binary64)) x) x) #s(literal 1/6 binary64))) (.f64 x x) (neg.f64 eps)) x)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (.f64 (fma.f64 (fma.f64 (.f64 eps (fma.f64 (.f64 x x) #s(literal 1/5040 binary64) #s(literal -1/120 binary64))) (.f64 x x) (.f64 #s(literal 1/6 binary64) eps)) (.f64 x x) (neg.f64 eps)) x)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (.f64 (fma.f64 (fma.f64 (fma.f64 eps #s(literal -1/120 binary64) (.f64 (.f64 #s(literal 1/5040 binary64) (.f64 x x)) eps)) (.f64 x x) (.f64 #s(literal 1/6 binary64) eps)) (*.f64 x x) (neg.f64 eps)) x)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (.f64 (fma.f64 (/.f64 #s(literal -1 binary64) eps) (.f64 eps eps) (.f64 (.f64 eps (fma.f64 (fma.f64 #s(literal 1/5040 binary64) (.f64 x x) #s(literal -1/120 binary64)) (.f64 x x) #s(literal 1/6 binary64))) (*.f64 x x))) x)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (.f64 (/.f64 (-.f64 (.f64 (.f64 eps eps) (.f64 (.f64 (fma.f64 (.f64 (fma.f64 (.f64 x x) #s(literal 1/5040 binary64) #s(literal -1/120 binary64)) x) x #s(literal -1/6 binary64)) x) x)) (.f64 eps eps)) eps) x)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (.f64 (fma.f64 (/.f64 #s(literal -1 binary64) (.f64 eps eps)) (.f64 (.f64 eps eps) eps) (.f64 (.f64 eps (fma.f64 (fma.f64 #s(literal 1/5040 binary64) (.f64 x x) #s(literal -1/120 binary64)) (.f64 x x) #s(literal 1/6 binary64))) (*.f64 x x))) x)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (.f64 (/.f64 (-.f64 (.f64 (.f64 (.f64 eps eps) (.f64 (.f64 (fma.f64 (.f64 (fma.f64 (.f64 x x) #s(literal 1/5040 binary64) #s(literal -1/120 binary64)) x) x #s(literal -1/6 binary64)) x) x)) eps) (.f64 (.f64 eps eps) eps)) (*.f64 eps eps)) x)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (.f64 (/.f64 (-.f64 (.f64 (.f64 (.f64 (.f64 eps eps) eps) (.f64 (.f64 (fma.f64 (.f64 (fma.f64 (.f64 x x) #s(literal 1/5040 binary64) #s(literal -1/120 binary64)) x) x #s(literal -1/6 binary64)) x) x)) eps) (.f64 (.f64 (.f64 eps eps) eps) eps)) (.f64 (.f64 eps eps) eps)) x)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (.f64 (/.f64 (-.f64 (.f64 (.f64 (.f64 eps eps) (.f64 (.f64 (fma.f64 (.f64 (fma.f64 (.f64 x x) #s(literal 1/5040 binary64) #s(literal -1/120 binary64)) x) x #s(literal -1/6 binary64)) x) x)) (/.f64 #s(literal 1 binary64) eps)) (.f64 eps #s(literal 1 binary64))) (.f64 eps (/.f64 #s(literal 1 binary64) eps))) x)))
#s(approx (- (cos (+ x eps)) (cos x)) (-.f64 (cos.f64 eps) #s(literal 1 binary64)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (.f64 (/.f64 (fma.f64 (.f64 (.f64 (.f64 eps eps) eps) (.f64 (.f64 (fma.f64 (.f64 (fma.f64 (.f64 x x) #s(literal 1/5040 binary64) #s(literal -1/120 binary64)) x) x #s(literal -1/6 binary64)) x) x)) eps (.f64 (.f64 eps eps) (/.f64 (.f64 eps eps) #s(literal -1 binary64)))) (.f64 (*.f64 eps eps) eps)) x)))
(-.f64 (cos.f64 (+.f64 x eps)) #s(approx (cos x) #s(literal 1 binary64)))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (neg.f64 eps) (sin.f64 x)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (.f64 (/.f64 (-.f64 (.f64 (.f64 (.f64 eps eps) (.f64 (.f64 (fma.f64 (.f64 (fma.f64 (.f64 x x) #s(literal 1/5040 binary64) #s(literal -1/120 binary64)) x) x #s(literal -1/6 binary64)) x) x)) (/.f64 eps (.f64 eps eps))) (.f64 eps #s(literal 1 binary64))) (.f64 eps (/.f64 eps (.f64 eps eps)))) x)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (.f64 (/.f64 (-.f64 (.f64 (.f64 (.f64 (.f64 eps eps) eps) (.f64 (.f64 (fma.f64 (.f64 (fma.f64 (.f64 x x) #s(literal 1/5040 binary64) #s(literal -1/120 binary64)) x) x #s(literal -1/6 binary64)) x) x)) (.f64 eps eps)) (.f64 (.f64 eps eps) (.f64 (.f64 eps eps) eps))) (.f64 (.f64 (*.f64 eps eps) eps) eps)) x)))
(.f64 #s(approx ( (sin (* 1/2 (+ (* 2 x) eps))) (sin (* 1/2 (+ 0 eps)))) (.f64 (.f64 (sin.f64 x) #s(literal 1/2 binary64)) eps)) #s(literal -2 binary64))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (.f64 (/.f64 (-.f64 (.f64 (.f64 (.f64 (.f64 eps eps) eps) (.f64 (.f64 (fma.f64 (.f64 (fma.f64 (.f64 x x) #s(literal 1/5040 binary64) #s(literal -1/120 binary64)) x) x #s(literal -1/6 binary64)) x) x)) (/.f64 eps (.f64 eps eps))) (.f64 eps eps)) (.f64 (.f64 eps eps) (/.f64 eps (.f64 eps eps)))) x)))
(.f64 (.f64 (sin.f64 #s(approx (* 1/2 (+ (* 2 x) eps)) (fma.f64 eps #s(literal 1/2 binary64) x))) #s(approx (sin (* 1/2 (+ 0 eps))) (*.f64 eps #s(literal 1/2 binary64)))) #s(literal -2 binary64))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 (/.f64 (.f64 eps eps) (neg.f64 eps)) (sin.f64 x)))
(.f64 (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps))) #s(approx (sin ( 1/2 (+ 0 eps))) (*.f64 eps #s(literal 1/2 binary64)))) #s(literal -2 binary64))
(-.f64 (cos.f64 (+.f64 x eps)) #s(approx (cos x) (fma.f64 (fma.f64 (.f64 x x) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) (.f64 x x) #s(literal 1 binary64))))
(.f64 (.f64 (sin.f64 #s(approx (* 1/2 (+ (* 2 x) eps)) (fma.f64 eps #s(literal 1/2 binary64) x))) #s(approx (sin (* 1/2 (+ 0 eps))) (.f64 (fma.f64 (.f64 eps eps) #s(literal -1/48 binary64) #s(literal 1/2 binary64)) eps))) #s(literal -2 binary64))
(.f64 (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps))) #s(approx (sin ( 1/2 (+ 0 eps))) (.f64 (fma.f64 (.f64 eps eps) #s(literal -1/48 binary64) #s(literal 1/2 binary64)) eps))) #s(literal -2 binary64))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 (.f64 (/.f64 #s(literal -1 binary64) eps) (/.f64 (neg.f64 (*.f64 eps eps)) #s(literal -1 binary64))) (sin.f64 x)))
(.f64 (.f64 #s(approx (sin (* 1/2 (+ 0 eps))) (.f64 (fma.f64 (fma.f64 #s(literal 1/3840 binary64) (.f64 eps eps) #s(literal -1/48 binary64)) (.f64 eps eps) #s(literal 1/2 binary64)) eps)) #s(literal -2 binary64)) (sin.f64 #s(approx ( 1/2 (+ (* 2 x) eps)) (fma.f64 eps #s(literal 1/2 binary64) x))))
(.f64 (.f64 (sin.f64 #s(approx (* 1/2 (+ (* 2 x) eps)) (fma.f64 eps #s(literal 1/2 binary64) x))) #s(approx (sin (* 1/2 (+ 0 eps))) (.f64 (fma.f64 (fma.f64 #s(literal 1/3840 binary64) (.f64 eps eps) #s(literal -1/48 binary64)) (*.f64 eps eps) #s(literal 1/2 binary64)) eps))) #s(literal -2 binary64))
(.f64 (.f64 #s(approx (sin (* 1/2 (+ 0 eps))) (.f64 (fma.f64 (fma.f64 (.f64 eps eps) #s(literal 1/3840 binary64) #s(literal -1/48 binary64)) (.f64 eps eps) #s(literal 1/2 binary64)) eps)) #s(literal -2 binary64)) (sin.f64 (fma.f64 #s(literal 1 binary64) x (.f64 eps #s(literal 1/2 binary64)))))
(.f64 (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps))) #s(approx (sin ( 1/2 (+ 0 eps))) (.f64 (fma.f64 (fma.f64 #s(literal 1/3840 binary64) (.f64 eps eps) #s(literal -1/48 binary64)) (*.f64 eps eps) #s(literal 1/2 binary64)) eps))) #s(literal -2 binary64))

Outputs

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

Calls

3 calls:

28.0ms	x
19.0ms	(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))
12.0ms	eps

Results

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

Compiler

Compiled 15 to 10 computations (33.3% saved)

regimes64.0ms (0.3%)

Memory

-5.8MiB live, 73.0MiB allocated

Counts

41 → 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 (* (neg eps) (sin x)) (*.f64 x eps)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (*.f64 (neg.f64 x) eps)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (.f64 #s(approx (+ ( (* eps (- (* (* (+ (* 1/5040 (* x x)) -1/120) x) x) 1/6)) (* x x)) (neg eps)) (.f64 eps (fma.f64 #s(literal -1/6 binary64) (.f64 x x) #s(literal -1 binary64)))) x)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (.f64 (.f64 eps (fma.f64 (*.f64 x x) #s(literal 1/6 binary64) #s(literal -1 binary64))) x)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (.f64 (fma.f64 #s(approx (+ ( (* eps (+ (* (* x x) 1/5040) -1/120)) (* x x)) (* 1/6 eps)) (.f64 #s(literal 1/6 binary64) eps)) (.f64 x x) (neg.f64 eps)) x)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (/.f64 (.f64 (.f64 eps eps) (neg.f64 x)) eps)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (.f64 (/.f64 (-.f64 #s(literal 0 binary64) (.f64 x x)) (+.f64 #s(literal 0 binary64) x)) eps)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (/.f64 (.f64 (.f64 (.f64 eps eps) eps) (neg.f64 x)) (.f64 eps eps))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (.f64 (fma.f64 (.f64 eps #s(approx (- (* (* (+ (* 1/5040 (* x x)) -1/120) x) x) 1/6) (fma.f64 #s(literal -1/120 binary64) (.f64 x x) #s(literal -1/6 binary64)))) (.f64 x x) (neg.f64 eps)) x)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (.f64 (fma.f64 (.f64 eps (fma.f64 (.f64 x x) #s(literal -1/120 binary64) #s(literal 1/6 binary64))) (.f64 x x) (neg.f64 eps)) x)))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 (neg.f64 eps) #s(approx (sin x) (.f64 (fma.f64 (fma.f64 #s(literal 1/120 binary64) (.f64 x x) #s(literal -1/6 binary64)) (.f64 x x) #s(literal 1 binary64)) x))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (.f64 #s(approx (+ ( (* eps (- (* (* (+ (* 1/5040 (* x x)) -1/120) x) x) 1/6)) (* x x)) (neg eps)) (.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 1/5040 binary64) (.f64 x x) #s(literal -1/120 binary64)) (.f64 x x) #s(literal -1/6 binary64)) (.f64 x x) #s(literal -1 binary64)) eps)) x)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (.f64 #s(approx (+ ( (+ (* (* eps (+ (* (* x x) 1/5040) -1/120)) (* x x)) (* 1/6 eps)) (* x x)) (neg eps)) (.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 1/5040 binary64) (.f64 x x) #s(literal -1/120 binary64)) (.f64 x x) #s(literal 1/6 binary64)) (.f64 x x) #s(literal -1 binary64)) eps)) x)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (.f64 (/.f64 (-.f64 #s(literal 0 binary64) (.f64 (.f64 x x) x)) (+.f64 #s(literal 0 binary64) (fma.f64 x x (.f64 #s(literal 0 binary64) x)))) eps)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (.f64 (fma.f64 (.f64 (.f64 (fma.f64 (fma.f64 #s(literal 1/5040 binary64) (.f64 x x) #s(literal -1/120 binary64)) (*.f64 x x) #s(literal 1/6 binary64)) eps) x) x (neg.f64 eps)) x)))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 (neg.f64 eps) #s(approx (sin x) (.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -1/5040 binary64) (.f64 x x) #s(literal 1/120 binary64)) (.f64 x x) #s(literal -1/6 binary64)) (*.f64 x x) #s(literal 1 binary64)) x))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (.f64 (fma.f64 (.f64 eps (-.f64 (.f64 (.f64 (fma.f64 #s(literal 1/5040 binary64) (.f64 x x) #s(literal -1/120 binary64)) x) x) #s(literal 1/6 binary64))) (.f64 x x) (neg.f64 eps)) x)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (.f64 (fma.f64 (fma.f64 (.f64 eps (fma.f64 (.f64 x x) #s(literal 1/5040 binary64) #s(literal -1/120 binary64))) (.f64 x x) (.f64 #s(literal 1/6 binary64) eps)) (.f64 x x) (neg.f64 eps)) x)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (.f64 (fma.f64 (fma.f64 (fma.f64 eps #s(literal -1/120 binary64) (.f64 (.f64 #s(literal 1/5040 binary64) (.f64 x x)) eps)) (.f64 x x) (.f64 #s(literal 1/6 binary64) eps)) (*.f64 x x) (neg.f64 eps)) x)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (.f64 (fma.f64 (/.f64 #s(literal -1 binary64) eps) (.f64 eps eps) (.f64 (.f64 eps (fma.f64 (fma.f64 #s(literal 1/5040 binary64) (.f64 x x) #s(literal -1/120 binary64)) (.f64 x x) #s(literal 1/6 binary64))) (*.f64 x x))) x)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (.f64 (/.f64 (-.f64 (.f64 (.f64 eps eps) (.f64 (.f64 (fma.f64 (.f64 (fma.f64 (.f64 x x) #s(literal 1/5040 binary64) #s(literal -1/120 binary64)) x) x #s(literal -1/6 binary64)) x) x)) (.f64 eps eps)) eps) x)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (.f64 (fma.f64 (/.f64 #s(literal -1 binary64) (.f64 eps eps)) (.f64 (.f64 eps eps) eps) (.f64 (.f64 eps (fma.f64 (fma.f64 #s(literal 1/5040 binary64) (.f64 x x) #s(literal -1/120 binary64)) (.f64 x x) #s(literal 1/6 binary64))) (*.f64 x x))) x)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (.f64 (/.f64 (-.f64 (.f64 (.f64 (.f64 eps eps) (.f64 (.f64 (fma.f64 (.f64 (fma.f64 (.f64 x x) #s(literal 1/5040 binary64) #s(literal -1/120 binary64)) x) x #s(literal -1/6 binary64)) x) x)) eps) (.f64 (.f64 eps eps) eps)) (*.f64 eps eps)) x)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (.f64 (/.f64 (-.f64 (.f64 (.f64 (.f64 (.f64 eps eps) eps) (.f64 (.f64 (fma.f64 (.f64 (fma.f64 (.f64 x x) #s(literal 1/5040 binary64) #s(literal -1/120 binary64)) x) x #s(literal -1/6 binary64)) x) x)) eps) (.f64 (.f64 (.f64 eps eps) eps) eps)) (.f64 (.f64 eps eps) eps)) x)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (.f64 (/.f64 (-.f64 (.f64 (.f64 (.f64 eps eps) (.f64 (.f64 (fma.f64 (.f64 (fma.f64 (.f64 x x) #s(literal 1/5040 binary64) #s(literal -1/120 binary64)) x) x #s(literal -1/6 binary64)) x) x)) (/.f64 #s(literal 1 binary64) eps)) (.f64 eps #s(literal 1 binary64))) (.f64 eps (/.f64 #s(literal 1 binary64) eps))) x)))
#s(approx (- (cos (+ x eps)) (cos x)) (-.f64 (cos.f64 eps) #s(literal 1 binary64)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (.f64 (/.f64 (fma.f64 (.f64 (.f64 (.f64 eps eps) eps) (.f64 (.f64 (fma.f64 (.f64 (fma.f64 (.f64 x x) #s(literal 1/5040 binary64) #s(literal -1/120 binary64)) x) x #s(literal -1/6 binary64)) x) x)) eps (.f64 (.f64 eps eps) (/.f64 (.f64 eps eps) #s(literal -1 binary64)))) (.f64 (*.f64 eps eps) eps)) x)))
(-.f64 (cos.f64 (+.f64 x eps)) #s(approx (cos x) #s(literal 1 binary64)))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (neg.f64 eps) (sin.f64 x)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (.f64 (/.f64 (-.f64 (.f64 (.f64 (.f64 eps eps) (.f64 (.f64 (fma.f64 (.f64 (fma.f64 (.f64 x x) #s(literal 1/5040 binary64) #s(literal -1/120 binary64)) x) x #s(literal -1/6 binary64)) x) x)) (/.f64 eps (.f64 eps eps))) (.f64 eps #s(literal 1 binary64))) (.f64 eps (/.f64 eps (.f64 eps eps)))) x)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (.f64 (/.f64 (-.f64 (.f64 (.f64 (.f64 (.f64 eps eps) eps) (.f64 (.f64 (fma.f64 (.f64 (fma.f64 (.f64 x x) #s(literal 1/5040 binary64) #s(literal -1/120 binary64)) x) x #s(literal -1/6 binary64)) x) x)) (.f64 eps eps)) (.f64 (.f64 eps eps) (.f64 (.f64 eps eps) eps))) (.f64 (.f64 (*.f64 eps eps) eps) eps)) x)))
(.f64 #s(approx ( (sin (* 1/2 (+ (* 2 x) eps))) (sin (* 1/2 (+ 0 eps)))) (.f64 (.f64 (sin.f64 x) #s(literal 1/2 binary64)) eps)) #s(literal -2 binary64))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (.f64 (/.f64 (-.f64 (.f64 (.f64 (.f64 (.f64 eps eps) eps) (.f64 (.f64 (fma.f64 (.f64 (fma.f64 (.f64 x x) #s(literal 1/5040 binary64) #s(literal -1/120 binary64)) x) x #s(literal -1/6 binary64)) x) x)) (/.f64 eps (.f64 eps eps))) (.f64 eps eps)) (.f64 (.f64 eps eps) (/.f64 eps (.f64 eps eps)))) x)))
(.f64 (.f64 (sin.f64 #s(approx (* 1/2 (+ (* 2 x) eps)) (fma.f64 eps #s(literal 1/2 binary64) x))) #s(approx (sin (* 1/2 (+ 0 eps))) (*.f64 eps #s(literal 1/2 binary64)))) #s(literal -2 binary64))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 (/.f64 (.f64 eps eps) (neg.f64 eps)) (sin.f64 x)))
(.f64 (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps))) #s(approx (sin ( 1/2 (+ 0 eps))) (*.f64 eps #s(literal 1/2 binary64)))) #s(literal -2 binary64))
(-.f64 (cos.f64 (+.f64 x eps)) #s(approx (cos x) (fma.f64 (fma.f64 (.f64 x x) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) (.f64 x x) #s(literal 1 binary64))))
(.f64 (.f64 (sin.f64 #s(approx (* 1/2 (+ (* 2 x) eps)) (fma.f64 eps #s(literal 1/2 binary64) x))) #s(approx (sin (* 1/2 (+ 0 eps))) (.f64 (fma.f64 (.f64 eps eps) #s(literal -1/48 binary64) #s(literal 1/2 binary64)) eps))) #s(literal -2 binary64))
(.f64 (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps))) #s(approx (sin ( 1/2 (+ 0 eps))) (.f64 (fma.f64 (.f64 eps eps) #s(literal -1/48 binary64) #s(literal 1/2 binary64)) eps))) #s(literal -2 binary64))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 (.f64 (/.f64 #s(literal -1 binary64) eps) (/.f64 (neg.f64 (*.f64 eps eps)) #s(literal -1 binary64))) (sin.f64 x)))

Outputs

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

Calls

3 calls:

28.0ms	x
23.0ms	(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))
11.0ms	eps

Results

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

Compiler

Compiled 15 to 10 computations (33.3% saved)

regimes119.0ms (0.6%)

Memory

-9.7MiB live, 70.8MiB allocated

Counts

38 → 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 (* (neg eps) (sin x)) (*.f64 x eps)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (*.f64 (neg.f64 x) eps)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (.f64 #s(approx (+ ( (* eps (- (* (* (+ (* 1/5040 (* x x)) -1/120) x) x) 1/6)) (* x x)) (neg eps)) (.f64 eps (fma.f64 #s(literal -1/6 binary64) (.f64 x x) #s(literal -1 binary64)))) x)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (.f64 (.f64 eps (fma.f64 (*.f64 x x) #s(literal 1/6 binary64) #s(literal -1 binary64))) x)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (.f64 (fma.f64 #s(approx (+ ( (* eps (+ (* (* x x) 1/5040) -1/120)) (* x x)) (* 1/6 eps)) (.f64 #s(literal 1/6 binary64) eps)) (.f64 x x) (neg.f64 eps)) x)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (/.f64 (.f64 (.f64 eps eps) (neg.f64 x)) eps)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (.f64 (/.f64 (-.f64 #s(literal 0 binary64) (.f64 x x)) (+.f64 #s(literal 0 binary64) x)) eps)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (/.f64 (.f64 (.f64 (.f64 eps eps) eps) (neg.f64 x)) (.f64 eps eps))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (.f64 (fma.f64 (.f64 eps #s(approx (- (* (* (+ (* 1/5040 (* x x)) -1/120) x) x) 1/6) (fma.f64 #s(literal -1/120 binary64) (.f64 x x) #s(literal -1/6 binary64)))) (.f64 x x) (neg.f64 eps)) x)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (.f64 (fma.f64 (.f64 eps (fma.f64 (.f64 x x) #s(literal -1/120 binary64) #s(literal 1/6 binary64))) (.f64 x x) (neg.f64 eps)) x)))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 (neg.f64 eps) #s(approx (sin x) (.f64 (fma.f64 (fma.f64 #s(literal 1/120 binary64) (.f64 x x) #s(literal -1/6 binary64)) (.f64 x x) #s(literal 1 binary64)) x))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (.f64 #s(approx (+ ( (* eps (- (* (* (+ (* 1/5040 (* x x)) -1/120) x) x) 1/6)) (* x x)) (neg eps)) (.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 1/5040 binary64) (.f64 x x) #s(literal -1/120 binary64)) (.f64 x x) #s(literal -1/6 binary64)) (.f64 x x) #s(literal -1 binary64)) eps)) x)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (.f64 #s(approx (+ ( (+ (* (* eps (+ (* (* x x) 1/5040) -1/120)) (* x x)) (* 1/6 eps)) (* x x)) (neg eps)) (.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 1/5040 binary64) (.f64 x x) #s(literal -1/120 binary64)) (.f64 x x) #s(literal 1/6 binary64)) (.f64 x x) #s(literal -1 binary64)) eps)) x)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (.f64 (/.f64 (-.f64 #s(literal 0 binary64) (.f64 (.f64 x x) x)) (+.f64 #s(literal 0 binary64) (fma.f64 x x (.f64 #s(literal 0 binary64) x)))) eps)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (.f64 (fma.f64 (.f64 (.f64 (fma.f64 (fma.f64 #s(literal 1/5040 binary64) (.f64 x x) #s(literal -1/120 binary64)) (*.f64 x x) #s(literal 1/6 binary64)) eps) x) x (neg.f64 eps)) x)))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 (neg.f64 eps) #s(approx (sin x) (.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -1/5040 binary64) (.f64 x x) #s(literal 1/120 binary64)) (.f64 x x) #s(literal -1/6 binary64)) (*.f64 x x) #s(literal 1 binary64)) x))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (.f64 (fma.f64 (.f64 eps (-.f64 (.f64 (.f64 (fma.f64 #s(literal 1/5040 binary64) (.f64 x x) #s(literal -1/120 binary64)) x) x) #s(literal 1/6 binary64))) (.f64 x x) (neg.f64 eps)) x)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (.f64 (fma.f64 (fma.f64 (.f64 eps (fma.f64 (.f64 x x) #s(literal 1/5040 binary64) #s(literal -1/120 binary64))) (.f64 x x) (.f64 #s(literal 1/6 binary64) eps)) (.f64 x x) (neg.f64 eps)) x)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (.f64 (fma.f64 (fma.f64 (fma.f64 eps #s(literal -1/120 binary64) (.f64 (.f64 #s(literal 1/5040 binary64) (.f64 x x)) eps)) (.f64 x x) (.f64 #s(literal 1/6 binary64) eps)) (*.f64 x x) (neg.f64 eps)) x)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (.f64 (fma.f64 (/.f64 #s(literal -1 binary64) eps) (.f64 eps eps) (.f64 (.f64 eps (fma.f64 (fma.f64 #s(literal 1/5040 binary64) (.f64 x x) #s(literal -1/120 binary64)) (.f64 x x) #s(literal 1/6 binary64))) (*.f64 x x))) x)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (.f64 (/.f64 (-.f64 (.f64 (.f64 eps eps) (.f64 (.f64 (fma.f64 (.f64 (fma.f64 (.f64 x x) #s(literal 1/5040 binary64) #s(literal -1/120 binary64)) x) x #s(literal -1/6 binary64)) x) x)) (.f64 eps eps)) eps) x)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (.f64 (fma.f64 (/.f64 #s(literal -1 binary64) (.f64 eps eps)) (.f64 (.f64 eps eps) eps) (.f64 (.f64 eps (fma.f64 (fma.f64 #s(literal 1/5040 binary64) (.f64 x x) #s(literal -1/120 binary64)) (.f64 x x) #s(literal 1/6 binary64))) (*.f64 x x))) x)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (.f64 (/.f64 (-.f64 (.f64 (.f64 (.f64 eps eps) (.f64 (.f64 (fma.f64 (.f64 (fma.f64 (.f64 x x) #s(literal 1/5040 binary64) #s(literal -1/120 binary64)) x) x #s(literal -1/6 binary64)) x) x)) eps) (.f64 (.f64 eps eps) eps)) (*.f64 eps eps)) x)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (.f64 (/.f64 (-.f64 (.f64 (.f64 (.f64 (.f64 eps eps) eps) (.f64 (.f64 (fma.f64 (.f64 (fma.f64 (.f64 x x) #s(literal 1/5040 binary64) #s(literal -1/120 binary64)) x) x #s(literal -1/6 binary64)) x) x)) eps) (.f64 (.f64 (.f64 eps eps) eps) eps)) (.f64 (.f64 eps eps) eps)) x)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (.f64 (/.f64 (-.f64 (.f64 (.f64 (.f64 eps eps) (.f64 (.f64 (fma.f64 (.f64 (fma.f64 (.f64 x x) #s(literal 1/5040 binary64) #s(literal -1/120 binary64)) x) x #s(literal -1/6 binary64)) x) x)) (/.f64 #s(literal 1 binary64) eps)) (.f64 eps #s(literal 1 binary64))) (.f64 eps (/.f64 #s(literal 1 binary64) eps))) x)))
#s(approx (- (cos (+ x eps)) (cos x)) (-.f64 (cos.f64 eps) #s(literal 1 binary64)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (.f64 (/.f64 (fma.f64 (.f64 (.f64 (.f64 eps eps) eps) (.f64 (.f64 (fma.f64 (.f64 (fma.f64 (.f64 x x) #s(literal 1/5040 binary64) #s(literal -1/120 binary64)) x) x #s(literal -1/6 binary64)) x) x)) eps (.f64 (.f64 eps eps) (/.f64 (.f64 eps eps) #s(literal -1 binary64)))) (.f64 (*.f64 eps eps) eps)) x)))
(-.f64 (cos.f64 (+.f64 x eps)) #s(approx (cos x) #s(literal 1 binary64)))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (neg.f64 eps) (sin.f64 x)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (.f64 (/.f64 (-.f64 (.f64 (.f64 (.f64 eps eps) (.f64 (.f64 (fma.f64 (.f64 (fma.f64 (.f64 x x) #s(literal 1/5040 binary64) #s(literal -1/120 binary64)) x) x #s(literal -1/6 binary64)) x) x)) (/.f64 eps (.f64 eps eps))) (.f64 eps #s(literal 1 binary64))) (.f64 eps (/.f64 eps (.f64 eps eps)))) x)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (.f64 (/.f64 (-.f64 (.f64 (.f64 (.f64 (.f64 eps eps) eps) (.f64 (.f64 (fma.f64 (.f64 (fma.f64 (.f64 x x) #s(literal 1/5040 binary64) #s(literal -1/120 binary64)) x) x #s(literal -1/6 binary64)) x) x)) (.f64 eps eps)) (.f64 (.f64 eps eps) (.f64 (.f64 eps eps) eps))) (.f64 (.f64 (*.f64 eps eps) eps) eps)) x)))
(.f64 #s(approx ( (sin (* 1/2 (+ (* 2 x) eps))) (sin (* 1/2 (+ 0 eps)))) (.f64 (.f64 (sin.f64 x) #s(literal 1/2 binary64)) eps)) #s(literal -2 binary64))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (.f64 (/.f64 (-.f64 (.f64 (.f64 (.f64 (.f64 eps eps) eps) (.f64 (.f64 (fma.f64 (.f64 (fma.f64 (.f64 x x) #s(literal 1/5040 binary64) #s(literal -1/120 binary64)) x) x #s(literal -1/6 binary64)) x) x)) (/.f64 eps (.f64 eps eps))) (.f64 eps eps)) (.f64 (.f64 eps eps) (/.f64 eps (.f64 eps eps)))) x)))
(.f64 (.f64 (sin.f64 #s(approx (* 1/2 (+ (* 2 x) eps)) (fma.f64 eps #s(literal 1/2 binary64) x))) #s(approx (sin (* 1/2 (+ 0 eps))) (*.f64 eps #s(literal 1/2 binary64)))) #s(literal -2 binary64))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 (/.f64 (.f64 eps eps) (neg.f64 eps)) (sin.f64 x)))
(.f64 (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps))) #s(approx (sin ( 1/2 (+ 0 eps))) (*.f64 eps #s(literal 1/2 binary64)))) #s(literal -2 binary64))
(-.f64 (cos.f64 (+.f64 x eps)) #s(approx (cos x) (fma.f64 (fma.f64 (.f64 x x) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) (.f64 x x) #s(literal 1 binary64))))

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

Calls

3 calls:

89.0ms	x
18.0ms	(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))
10.0ms	eps

Results

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

Compiler

Compiled 15 to 10 computations (33.3% saved)

regimes95.0ms (0.5%)

Memory

23.1MiB live, 61.6MiB allocated

Counts

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

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

Calls

3 calls:

76.0ms	eps
9.0ms	x
7.0ms	(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))

Results

Accuracy	Segments	Branch
79.2%	1	`x`
79.2%	1	`eps`
79.2%	1	`(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))`

Compiler

Compiled 15 to 10 computations (33.3% saved)

regimes170.0ms (0.9%)

Memory

-33.4MiB live, 53.5MiB 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 (* (neg eps) (sin x)) (*.f64 x eps)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (*.f64 (neg.f64 x) eps)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (.f64 #s(approx (+ ( (* eps (- (* (* (+ (* 1/5040 (* x x)) -1/120) x) x) 1/6)) (* x x)) (neg eps)) (.f64 eps (fma.f64 #s(literal -1/6 binary64) (.f64 x x) #s(literal -1 binary64)))) x)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (.f64 (.f64 eps (fma.f64 (*.f64 x x) #s(literal 1/6 binary64) #s(literal -1 binary64))) x)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (.f64 (fma.f64 #s(approx (+ ( (* eps (+ (* (* x x) 1/5040) -1/120)) (* x x)) (* 1/6 eps)) (.f64 #s(literal 1/6 binary64) eps)) (.f64 x x) (neg.f64 eps)) x)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (/.f64 (.f64 (.f64 eps eps) (neg.f64 x)) eps)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (.f64 (/.f64 (-.f64 #s(literal 0 binary64) (.f64 x x)) (+.f64 #s(literal 0 binary64) x)) eps)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (/.f64 (.f64 (.f64 (.f64 eps eps) eps) (neg.f64 x)) (.f64 eps eps))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (.f64 (fma.f64 (.f64 eps #s(approx (- (* (* (+ (* 1/5040 (* x x)) -1/120) x) x) 1/6) (fma.f64 #s(literal -1/120 binary64) (.f64 x x) #s(literal -1/6 binary64)))) (.f64 x x) (neg.f64 eps)) x)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (.f64 (fma.f64 (.f64 eps (fma.f64 (.f64 x x) #s(literal -1/120 binary64) #s(literal 1/6 binary64))) (.f64 x x) (neg.f64 eps)) x)))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 (neg.f64 eps) #s(approx (sin x) (.f64 (fma.f64 (fma.f64 #s(literal 1/120 binary64) (.f64 x x) #s(literal -1/6 binary64)) (.f64 x x) #s(literal 1 binary64)) x))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (.f64 #s(approx (+ ( (* eps (- (* (* (+ (* 1/5040 (* x x)) -1/120) x) x) 1/6)) (* x x)) (neg eps)) (.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 1/5040 binary64) (.f64 x x) #s(literal -1/120 binary64)) (.f64 x x) #s(literal -1/6 binary64)) (.f64 x x) #s(literal -1 binary64)) eps)) x)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (.f64 #s(approx (+ ( (+ (* (* eps (+ (* (* x x) 1/5040) -1/120)) (* x x)) (* 1/6 eps)) (* x x)) (neg eps)) (.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 1/5040 binary64) (.f64 x x) #s(literal -1/120 binary64)) (.f64 x x) #s(literal 1/6 binary64)) (.f64 x x) #s(literal -1 binary64)) eps)) x)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (.f64 (/.f64 (-.f64 #s(literal 0 binary64) (.f64 (.f64 x x) x)) (+.f64 #s(literal 0 binary64) (fma.f64 x x (.f64 #s(literal 0 binary64) x)))) eps)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (.f64 (fma.f64 (.f64 (.f64 (fma.f64 (fma.f64 #s(literal 1/5040 binary64) (.f64 x x) #s(literal -1/120 binary64)) (*.f64 x x) #s(literal 1/6 binary64)) eps) x) x (neg.f64 eps)) x)))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 (neg.f64 eps) #s(approx (sin x) (.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -1/5040 binary64) (.f64 x x) #s(literal 1/120 binary64)) (.f64 x x) #s(literal -1/6 binary64)) (*.f64 x x) #s(literal 1 binary64)) x))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (.f64 (fma.f64 (.f64 eps (-.f64 (.f64 (.f64 (fma.f64 #s(literal 1/5040 binary64) (.f64 x x) #s(literal -1/120 binary64)) x) x) #s(literal 1/6 binary64))) (.f64 x x) (neg.f64 eps)) x)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (.f64 (fma.f64 (fma.f64 (.f64 eps (fma.f64 (.f64 x x) #s(literal 1/5040 binary64) #s(literal -1/120 binary64))) (.f64 x x) (.f64 #s(literal 1/6 binary64) eps)) (.f64 x x) (neg.f64 eps)) x)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (.f64 (fma.f64 (fma.f64 (fma.f64 eps #s(literal -1/120 binary64) (.f64 (.f64 #s(literal 1/5040 binary64) (.f64 x x)) eps)) (.f64 x x) (.f64 #s(literal 1/6 binary64) eps)) (*.f64 x x) (neg.f64 eps)) x)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (.f64 (fma.f64 (/.f64 #s(literal -1 binary64) eps) (.f64 eps eps) (.f64 (.f64 eps (fma.f64 (fma.f64 #s(literal 1/5040 binary64) (.f64 x x) #s(literal -1/120 binary64)) (.f64 x x) #s(literal 1/6 binary64))) (*.f64 x x))) x)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (.f64 (/.f64 (-.f64 (.f64 (.f64 eps eps) (.f64 (.f64 (fma.f64 (.f64 (fma.f64 (.f64 x x) #s(literal 1/5040 binary64) #s(literal -1/120 binary64)) x) x #s(literal -1/6 binary64)) x) x)) (.f64 eps eps)) eps) x)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (.f64 (fma.f64 (/.f64 #s(literal -1 binary64) (.f64 eps eps)) (.f64 (.f64 eps eps) eps) (.f64 (.f64 eps (fma.f64 (fma.f64 #s(literal 1/5040 binary64) (.f64 x x) #s(literal -1/120 binary64)) (.f64 x x) #s(literal 1/6 binary64))) (*.f64 x x))) x)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (.f64 (/.f64 (-.f64 (.f64 (.f64 (.f64 eps eps) (.f64 (.f64 (fma.f64 (.f64 (fma.f64 (.f64 x x) #s(literal 1/5040 binary64) #s(literal -1/120 binary64)) x) x #s(literal -1/6 binary64)) x) x)) eps) (.f64 (.f64 eps eps) eps)) (*.f64 eps eps)) x)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (.f64 (/.f64 (-.f64 (.f64 (.f64 (.f64 (.f64 eps eps) eps) (.f64 (.f64 (fma.f64 (.f64 (fma.f64 (.f64 x x) #s(literal 1/5040 binary64) #s(literal -1/120 binary64)) x) x #s(literal -1/6 binary64)) x) x)) eps) (.f64 (.f64 (.f64 eps eps) eps) eps)) (.f64 (.f64 eps eps) eps)) x)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (.f64 (/.f64 (-.f64 (.f64 (.f64 (.f64 eps eps) (.f64 (.f64 (fma.f64 (.f64 (fma.f64 (.f64 x x) #s(literal 1/5040 binary64) #s(literal -1/120 binary64)) x) x #s(literal -1/6 binary64)) x) x)) (/.f64 #s(literal 1 binary64) eps)) (.f64 eps #s(literal 1 binary64))) (.f64 eps (/.f64 #s(literal 1 binary64) eps))) x)))
#s(approx (- (cos (+ x eps)) (cos x)) (-.f64 (cos.f64 eps) #s(literal 1 binary64)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (.f64 (/.f64 (fma.f64 (.f64 (.f64 (.f64 eps eps) eps) (.f64 (.f64 (fma.f64 (.f64 (fma.f64 (.f64 x x) #s(literal 1/5040 binary64) #s(literal -1/120 binary64)) x) x #s(literal -1/6 binary64)) x) x)) eps (.f64 (.f64 eps eps) (/.f64 (.f64 eps eps) #s(literal -1 binary64)))) (.f64 (*.f64 eps eps) eps)) x)))
(-.f64 (cos.f64 (+.f64 x eps)) #s(approx (cos x) #s(literal 1 binary64)))

Outputs

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

Calls

3 calls:

84.0ms	(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))
76.0ms	eps
8.0ms	x

Results

Accuracy	Segments	Branch
78.7%	1	`(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))`
78.7%	1	`x`
78.7%	1	`eps`

Compiler

Compiled 15 to 10 computations (33.3% saved)

regimes13.0ms (0.1%)

Memory

18.4MiB live, 18.4MiB allocated

Counts

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

Outputs

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

Calls

3 calls:

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

Results

Accuracy	Segments	Branch
78.5%	1	`(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))`
78.5%	1	`eps`
78.5%	1	`x`

Compiler

Compiled 15 to 10 computations (33.3% saved)

regimes17.0ms (0.1%)

Memory

-11.7MiB live, 27.9MiB allocated

Counts

10 → 1

Calls

Call 1

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

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

Calls

3 calls:

9.0ms	(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))
4.0ms	x
4.0ms	eps

Results

Accuracy	Segments	Branch
78.4%	1	`eps`
78.4%	1	`(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))`
78.4%	1	`x`

Compiler

Compiled 15 to 10 computations (33.3% saved)

regimes6.0ms (0%)

Memory

16.7MiB live, 16.7MiB 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 (* (neg eps) (sin x)) (*.f64 x eps)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (*.f64 (neg.f64 x) eps)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (.f64 #s(approx (+ ( (* eps (- (* (* (+ (* 1/5040 (* x x)) -1/120) x) x) 1/6)) (* x x)) (neg eps)) (.f64 eps (fma.f64 #s(literal -1/6 binary64) (.f64 x x) #s(literal -1 binary64)))) x)))

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

Calls

3 calls:

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

Results

Accuracy	Segments	Branch
78.2%	1	`(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))`
78.2%	1	`x`
78.2%	1	`eps`

Compiler

Compiled 15 to 10 computations (33.3% saved)

regimes22.0ms (0.1%)

Memory

-26.6MiB live, 13.0MiB allocated

Accuracy

Total -0.5b remaining (-1.7%)

Threshold costs -0.5b (-1.7%)

Counts

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

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

Calls

3 calls:

18.0ms	(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))
2.0ms	eps
1.0ms	x

Results

Accuracy	Segments	Branch
49.0%	1	`(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))`
49.0%	1	`x`
49.0%	1	`eps`

Compiler

Compiled 15 to 10 computations (33.3% saved)

simplify10.0ms (0.1%)

Memory

21.5MiB live, 21.5MiB allocated

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	108	359
1	147	359
2	171	359
3	188	359
4	192	359
5	193	359

Stop Event

1×

saturated

Calls

Call 1

Inputs
(.f64 #s(approx ( (sin (* 1/2 (+ (* 2 x) eps))) (sin (* 1/2 (+ 0 eps)))) (.f64 (sin.f64 (fma.f64 eps #s(literal 1/2 binary64) x)) (sin.f64 (.f64 eps #s(literal 1/2 binary64))))) #s(literal -2 binary64))
(.f64 (.f64 (sin.f64 (fma.f64 (.f64 eps eps) (.f64 (/.f64 #s(literal 1 binary64) eps) #s(literal 1/2 binary64)) (.f64 #s(literal 1 binary64) x))) #s(approx (sin ( 1/2 (+ 0 eps))) (.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -1/645120 binary64) (.f64 eps eps) #s(literal 1/3840 binary64)) (.f64 eps eps) #s(literal -1/48 binary64)) (.f64 eps eps) #s(literal 1/2 binary64)) eps))) #s(literal -2 binary64))
(.f64 (.f64 (sin.f64 #s(approx (* 1/2 (+ (* 2 x) eps)) (fma.f64 eps #s(literal 1/2 binary64) x))) #s(approx (sin (* 1/2 (+ 0 eps))) (.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -1/645120 binary64) (.f64 eps eps) #s(literal 1/3840 binary64)) (.f64 eps eps) #s(literal -1/48 binary64)) (.f64 eps eps) #s(literal 1/2 binary64)) eps))) #s(literal -2 binary64))
(.f64 (.f64 #s(approx (sin (* 1/2 (+ 0 eps))) (.f64 (fma.f64 (fma.f64 #s(literal 1/3840 binary64) (.f64 eps eps) #s(literal -1/48 binary64)) (.f64 eps eps) #s(literal 1/2 binary64)) eps)) #s(literal -2 binary64)) (sin.f64 #s(approx ( 1/2 (+ (* 2 x) eps)) (fma.f64 eps #s(literal 1/2 binary64) x))))
(.f64 (.f64 (sin.f64 #s(approx (* 1/2 (+ (* 2 x) eps)) (fma.f64 eps #s(literal 1/2 binary64) x))) #s(approx (sin (* 1/2 (+ 0 eps))) (.f64 (fma.f64 (.f64 eps eps) #s(literal -1/48 binary64) #s(literal 1/2 binary64)) eps))) #s(literal -2 binary64))
(.f64 (.f64 (sin.f64 #s(approx (* 1/2 (+ (* 2 x) eps)) (fma.f64 eps #s(literal 1/2 binary64) x))) #s(approx (sin (* 1/2 (+ 0 eps))) (*.f64 eps #s(literal 1/2 binary64)))) #s(literal -2 binary64))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (neg.f64 eps) (sin.f64 x)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (.f64 #s(approx (+ ( (+ (* (* eps (+ (* (* x x) 1/5040) -1/120)) (* x x)) (* 1/6 eps)) (* x x)) (neg eps)) (.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 1/5040 binary64) (.f64 x x) #s(literal -1/120 binary64)) (.f64 x x) #s(literal 1/6 binary64)) (.f64 x x) #s(literal -1 binary64)) eps)) x)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (.f64 (fma.f64 (.f64 eps (fma.f64 (.f64 x x) #s(literal -1/120 binary64) #s(literal 1/6 binary64))) (.f64 x x) (neg.f64 eps)) x)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (.f64 (.f64 eps (fma.f64 (*.f64 x x) #s(literal 1/6 binary64) #s(literal -1 binary64))) x)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (*.f64 (neg.f64 x) eps)))
#s(approx (- (cos (+ x eps)) (cos x)) (-.f64 #s(approx (cos eps) #s(literal 1 binary64)) #s(literal 1 binary64)))

Outputs
(.f64 #s(approx ( (sin (* 1/2 (+ (* 2 x) eps))) (sin (* 1/2 (+ 0 eps)))) (.f64 (sin.f64 (fma.f64 eps #s(literal 1/2 binary64) x)) (sin.f64 (.f64 eps #s(literal 1/2 binary64))))) #s(literal -2 binary64))
(.f64 #s(literal -2 binary64) #s(approx ( (sin (* 1/2 (+ (* 2 x) eps))) (sin (* 1/2 (+ 0 eps)))) (.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (sin.f64 (fma.f64 eps #s(literal 1/2 binary64) x)))))
(.f64 (.f64 (sin.f64 (fma.f64 (.f64 eps eps) (.f64 (/.f64 #s(literal 1 binary64) eps) #s(literal 1/2 binary64)) (.f64 #s(literal 1 binary64) x))) #s(approx (sin ( 1/2 (+ 0 eps))) (.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -1/645120 binary64) (.f64 eps eps) #s(literal 1/3840 binary64)) (.f64 eps eps) #s(literal -1/48 binary64)) (.f64 eps eps) #s(literal 1/2 binary64)) eps))) #s(literal -2 binary64))
(.f64 (.f64 #s(approx (sin (* 1/2 (+ 0 eps))) (.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -1/645120 binary64) (.f64 eps eps) #s(literal 1/3840 binary64)) (.f64 eps eps) #s(literal -1/48 binary64)) (.f64 eps eps) #s(literal 1/2 binary64)) eps)) (sin.f64 (fma.f64 (.f64 eps eps) (.f64 (/.f64 #s(literal 1 binary64) eps) #s(literal 1/2 binary64)) x))) #s(literal -2 binary64))
(.f64 (.f64 (sin.f64 #s(approx (* 1/2 (+ (* 2 x) eps)) (fma.f64 eps #s(literal 1/2 binary64) x))) #s(approx (sin (* 1/2 (+ 0 eps))) (.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -1/645120 binary64) (.f64 eps eps) #s(literal 1/3840 binary64)) (.f64 eps eps) #s(literal -1/48 binary64)) (.f64 eps eps) #s(literal 1/2 binary64)) eps))) #s(literal -2 binary64))
(.f64 (.f64 #s(approx (sin (* 1/2 (+ 0 eps))) (.f64 (fma.f64 (fma.f64 #s(literal 1/3840 binary64) (.f64 eps eps) #s(literal -1/48 binary64)) (.f64 eps eps) #s(literal 1/2 binary64)) eps)) #s(literal -2 binary64)) (sin.f64 #s(approx ( 1/2 (+ (* 2 x) eps)) (fma.f64 eps #s(literal 1/2 binary64) x))))
(.f64 (.f64 (sin.f64 #s(approx (* 1/2 (+ (* 2 x) eps)) (fma.f64 eps #s(literal 1/2 binary64) x))) #s(approx (sin (* 1/2 (+ 0 eps))) (.f64 (fma.f64 (.f64 eps eps) #s(literal -1/48 binary64) #s(literal 1/2 binary64)) eps))) #s(literal -2 binary64))
(.f64 (.f64 #s(approx (sin (* 1/2 (+ 0 eps))) (.f64 (fma.f64 (.f64 eps eps) #s(literal -1/48 binary64) #s(literal 1/2 binary64)) eps)) (sin.f64 #s(approx (* 1/2 (+ (* 2 x) eps)) (fma.f64 eps #s(literal 1/2 binary64) x)))) #s(literal -2 binary64))
(.f64 (.f64 (sin.f64 #s(approx (* 1/2 (+ (* 2 x) eps)) (fma.f64 eps #s(literal 1/2 binary64) x))) #s(approx (sin (* 1/2 (+ 0 eps))) (*.f64 eps #s(literal 1/2 binary64)))) #s(literal -2 binary64))
(.f64 (.f64 #s(approx (sin (* 1/2 (+ 0 eps))) (.f64 eps #s(literal 1/2 binary64))) (sin.f64 #s(approx ( 1/2 (+ (* 2 x) eps)) (fma.f64 eps #s(literal 1/2 binary64) x)))) #s(literal -2 binary64))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (neg.f64 eps) (sin.f64 x)))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (sin.f64 x) (neg.f64 eps)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (.f64 #s(approx (+ ( (+ (* (* eps (+ (* (* x x) 1/5040) -1/120)) (* x x)) (* 1/6 eps)) (* x x)) (neg eps)) (.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 1/5040 binary64) (.f64 x x) #s(literal -1/120 binary64)) (.f64 x x) #s(literal 1/6 binary64)) (.f64 x x) #s(literal -1 binary64)) eps)) x)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (.f64 (fma.f64 (.f64 eps (fma.f64 (.f64 x x) #s(literal -1/120 binary64) #s(literal 1/6 binary64))) (.f64 x x) (neg.f64 eps)) x)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (.f64 (fma.f64 (.f64 (fma.f64 (.f64 x x) #s(literal -1/120 binary64) #s(literal 1/6 binary64)) eps) (.f64 x x) (neg.f64 eps)) x)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (.f64 (.f64 eps (fma.f64 (*.f64 x x) #s(literal 1/6 binary64) #s(literal -1 binary64))) x)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (.f64 (.f64 (fma.f64 (*.f64 x x) #s(literal 1/6 binary64) #s(literal -1 binary64)) eps) x)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (*.f64 (neg.f64 x) eps)))
#s(approx (- (cos (+ x eps)) (cos x)) (-.f64 #s(approx (cos eps) #s(literal 1 binary64)) #s(literal 1 binary64)))

soundness1.5s (7.8%)

Memory

7.4MiB live, 1 120.4MiB allocated

Rules

17 138×	`lower-fma.f64`
17 138×	`lower-fma.f32`
14 784×	`lower-fma.f64`
14 784×	`lower-fma.f32`
14 158×	`lower-fma.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	300	5236
1	933	4912
2	2534	4805
3	6145	4767
0	8386	4391
0	6	16
0	10	16
1	54	16
2	380	16
3	4694	16
0	8209	16
0	68	419
0	111	407
1	385	386
2	3051	376
0	9348	371
0	322	5313
1	975	5025
2	2606	4899
3	6333	4881
0	8266	4487
0	105	498
1	277	495
2	609	495
3	2398	494
4	7880	494
0	8026	474
0	320	2969
1	961	2826
2	2515	2790
3	5858	2790
0	8448	2606

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

Compiler

Compiled 628 to 320 computations (49% saved)

preprocess92.0ms (0.5%)

Memory: -14.8MiB live, 110.5MiB allocated
Compiler: Compiled 486 to 184 computations (62.1% 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%)

analyze40.0ms (0.2%)

sample10.0s (53.9%)

explain285.0ms (1.5%)

preprocess29.0ms (0.2%)

eval0.0ms (0%)

prune1.0ms (0%)

simplify7.0ms (0%)

localize112.0ms (0.6%)

series5.0ms (0%)

simplify149.0ms (0.8%)

rewrite217.0ms (1.2%)

eval37.0ms (0.2%)

prune77.0ms (0.4%)

simplify529.0ms (2.9%)

localize264.0ms (1.4%)

series24.0ms (0.1%)

simplify253.0ms (1.4%)

rewrite256.0ms (1.4%)

eval179.0ms (1%)

prune232.0ms (1.3%)

simplify180.0ms (1%)

localize600.0ms (3.2%)

series69.0ms (0.4%)

simplify297.0ms (1.6%)

rewrite229.0ms (1.2%)

eval183.0ms (1%)

prune170.0ms (0.9%)

simplify120.0ms (0.6%)

localize703.0ms (3.8%)

series67.0ms (0.4%)

simplify395.0ms (2.1%)

rewrite283.0ms (1.5%)

eval140.0ms (0.8%)

prune151.0ms (0.8%)

regimes63.0ms (0.3%)

regimes44.0ms (0.2%)

regimes40.0ms (0.2%)

regimes61.0ms (0.3%)

regimes64.0ms (0.3%)

regimes119.0ms (0.6%)

regimes95.0ms (0.5%)

regimes170.0ms (0.9%)

regimes13.0ms (0.1%)

regimes17.0ms (0.1%)

regimes6.0ms (0%)

regimes22.0ms (0.1%)

simplify10.0ms (0.1%)

soundness1.5s (7.8%)

preprocess92.0ms (0.5%)

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