Metrics for ENA, Section 1.4, Mentioned, A

analyze3.0ms (0%)

Memory

4.1MiB live, 4.1MiB allocated

Algorithm

1×

Search

Probability	Valid	Unknown	Precondition	Infinite	Domain	Can't	Iter
0%	0%	49.6%	50.4%	0%	0%	0%	0
0%	0%	49.6%	50.4%	0%	0%	0%	1
0%	0%	49.6%	50.4%	0%	0%	0%	2
50%	24.8%	24.8%	50.4%	0%	0%	0%	3
75%	37.2%	12.4%	50.4%	0%	0%	0%	4
87.5%	43.4%	6.2%	50.4%	0%	0%	0%	5
93.8%	46.5%	3.1%	50.4%	0%	0%	0%	6
96.9%	48.1%	1.6%	50.4%	0%	0%	0%	7
98.4%	48.8%	0.8%	50.4%	0%	0%	0%	8
99.2%	49.2%	0.4%	50.4%	0%	0%	0%	9
99.6%	49.4%	0.2%	50.4%	0%	0%	0%	10
99.8%	49.5%	0.1%	50.4%	0%	0%	0%	11
99.9%	49.6%	0%	50.4%	0%	0%	0%	12

Compiler

Compiled 12 to 10 computations (16.7% saved)

sample2.5s (29.1%)

Memory

62.1MiB live, 3 173.0MiB allocated

Samples

1.9s	5 698×	2	valid
309.0ms	2 479×	1	valid
5.0ms	79×	0	valid

Precisions

Click to see histograms. Total time spent on operations: 1.9s

ival-cos: 1.1s (57.4% of total)

const: 281.0ms (14.7% of total)

adjust: 244.0ms (12.7% of total)

ival-<=: 139.0ms (7.2% of total)

ival-sub: 134.0ms (7% of total)

ival-and: 12.0ms (0.6% of total)

exact: 5.0ms (0.3% of total)

ival-assert: 3.0ms (0.2% of total)

Bogosity

preprocess27.0ms (0.3%)

Memory

-64.4MiB live, 37.9MiB allocated

Algorithm

1×	egg-herbie

Rules

24×	`lower-+.f64`
24×	`lower-+.f32`
20×	`sub-neg`
18×	`lower--.f32`
16×	`sub-neg`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	9
1	16	8
2	35	8
3	55	8
4	87	8
5	101	8
6	107	8
0	4	4
0	6	4
1	10	4
2	14	4
3	19	4
4	25	4
5	33	4
6	43	4
7	54	4
8	57	4
0	57	4

Stop Event

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

Calls

Call 1

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

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

Symmetry

(abs x)

explain204.0ms (2.3%)

Memory

6.2MiB live, 204.7MiB allocated

FPErrors

Click to see full error table

Ground Truth	Overpredictions	Example	Example	Subexpression
131	2	(3.593744960146214e-162)	-	`(-.f64 #s(literal 1 binary64) (cos.f64 x))`
0	0	-	-	`#s(literal 1 binary64)`
0	0	-	-	`(cos.f64 x)`
0	0	-	-	`x`

Explanations

Click to see full explanations table

Operator	Subexpression	Explanation	Count
`-.f64`	`(-.f64 #s(literal 1 binary64) (cos.f64 x))`	cancellation	133	0

Confusion

	Predicted +	Predicted -
+	131	0
-	2	123

Precision

0.9849624060150376

Recall

1.0

Confusion?

	Predicted +	Predicted Maybe	Predicted -
+	131	0	0
-	2	0	123

Precision?

0.9849624060150376

Recall?

1.0

Freqs

test

number	freq
0	123
1	133

Total Confusion?

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

Precision?

1.0

Recall?

1.0

Samples

96.0ms	152×	1	valid
77.0ms	360×	2	valid

Compiler

Compiled 30 to 20 computations (33.3% saved)

Precisions

Click to see histograms. Total time spent on operations: 71.0ms

ival-cos: 53.0ms (74.3% of total)

adjust: 10.0ms (14% of total)

ival-sub: 8.0ms (11.2% of total)

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

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

exact: 0.0ms (0% of total)

eval0.0ms (0%)

Memory: 0.3MiB live, 0.3MiB allocated
Compiler: Compiled 1 to 1 computations (0% saved)

prune1.0ms (0%)

Memory

0.9MiB live, 0.9MiB allocated

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	53.0%	(-.f64 #s(literal 1 binary64) (cos.f64 x))

Compiler

Compiled 5 to 4 computations (20% saved)

simplify5.0ms (0.1%)

Memory

5.6MiB live, 5.6MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 2 expressions of interest:

New	Metric	Score	Program
✓	cost-diff	0	(cos.f64 x)
✓	cost-diff	0	(-.f64 #s(literal 1 binary64) (cos.f64 x))

Rules

24×	`lower-+.f64`
24×	`lower-+.f32`
18×	`lower--.f32`
16×	`sub-neg`
16×	`lower--.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	4	8
0	6	8
1	10	8
2	14	8
3	19	8
4	25	8
5	33	8
6	43	8
7	54	8
8	57	8
0	57	8

Stop Event

1×	iter limit
1×	saturated
1×	iter limit

Calls

Call 1

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

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

localize75.0ms (0.9%)

Memory

-3.7MiB live, 71.4MiB allocated

Localize:

Found 2 expressions of interest:

New	Metric	Score	Program
✓	accuracy	100.0%	(cos.f64 x)
✓	accuracy	53.0%	(-.f64 #s(literal 1 binary64) (cos.f64 x))

Samples

62.0ms	180×	2	valid
6.0ms	76×	1	valid

Compiler

Compiled 10 to 6 computations (40% saved)

Precisions

Click to see histograms. Total time spent on operations: 58.0ms

adjust: 28.0ms (48% of total)

ival-cos: 26.0ms (44.5% of total)

ival-sub: 4.0ms (6.9% of total)

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

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

exact: 0.0ms (0% of total)

series1.0ms (0%)

Memory

2.2MiB live, 2.2MiB allocated

Counts

2 → 24

Calls

Call 1

Inputs
#s(alt (-.f64 #s(literal 1 binary64) (cos.f64 x)) (patch (-.f64 #s(literal 1 binary64) (cos.f64 x)) #<representation binary64>) () ())
#s(alt (cos.f64 x) (patch (cos.f64 x) #<representation binary64>) () ())

Inputs

#s(alt (-.f64 #s(literal 1 binary64) (cos.f64 x)) (patch (-.f64 #s(literal 1 binary64) (cos.f64 x)) #<representation binary64>) () ())

#s(alt (cos.f64 x) (patch (cos.f64 x) #<representation binary64>) () ())

Outputs
#s(alt (* 1/2 (pow x 2)) (taylor 0 x) (#s(alt (-.f64 #s(literal 1 binary64) (cos.f64 x)) (patch (-.f64 #s(literal 1 binary64) (cos.f64 x)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (+ 1/2 (* -1/24 (pow x 2)))) (taylor 0 x) (#s(alt (-.f64 #s(literal 1 binary64) (cos.f64 x)) (patch (-.f64 #s(literal 1 binary64) (cos.f64 x)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (+ 1/2 (* (pow x 2) (- (* 1/720 (pow x 2)) 1/24)))) (taylor 0 x) (#s(alt (-.f64 #s(literal 1 binary64) (cos.f64 x)) (patch (-.f64 #s(literal 1 binary64) (cos.f64 x)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (+ 1/2 (* (pow x 2) (- (* (pow x 2) (+ 1/720 (* -1/40320 (pow x 2)))) 1/24)))) (taylor 0 x) (#s(alt (-.f64 #s(literal 1 binary64) (cos.f64 x)) (patch (-.f64 #s(literal 1 binary64) (cos.f64 x)) #<representation binary64>) () ())) ())
#s(alt (- 1 (cos x)) (taylor inf x) (#s(alt (-.f64 #s(literal 1 binary64) (cos.f64 x)) (patch (-.f64 #s(literal 1 binary64) (cos.f64 x)) #<representation binary64>) () ())) ())
#s(alt (- 1 (cos x)) (taylor inf x) (#s(alt (-.f64 #s(literal 1 binary64) (cos.f64 x)) (patch (-.f64 #s(literal 1 binary64) (cos.f64 x)) #<representation binary64>) () ())) ())
#s(alt (- 1 (cos x)) (taylor inf x) (#s(alt (-.f64 #s(literal 1 binary64) (cos.f64 x)) (patch (-.f64 #s(literal 1 binary64) (cos.f64 x)) #<representation binary64>) () ())) ())
#s(alt (- 1 (cos x)) (taylor inf x) (#s(alt (-.f64 #s(literal 1 binary64) (cos.f64 x)) (patch (-.f64 #s(literal 1 binary64) (cos.f64 x)) #<representation binary64>) () ())) ())
#s(alt (- 1 (cos x)) (taylor -inf x) (#s(alt (-.f64 #s(literal 1 binary64) (cos.f64 x)) (patch (-.f64 #s(literal 1 binary64) (cos.f64 x)) #<representation binary64>) () ())) ())
#s(alt (- 1 (cos x)) (taylor -inf x) (#s(alt (-.f64 #s(literal 1 binary64) (cos.f64 x)) (patch (-.f64 #s(literal 1 binary64) (cos.f64 x)) #<representation binary64>) () ())) ())
#s(alt (- 1 (cos x)) (taylor -inf x) (#s(alt (-.f64 #s(literal 1 binary64) (cos.f64 x)) (patch (-.f64 #s(literal 1 binary64) (cos.f64 x)) #<representation binary64>) () ())) ())
#s(alt (- 1 (cos x)) (taylor -inf x) (#s(alt (-.f64 #s(literal 1 binary64) (cos.f64 x)) (patch (-.f64 #s(literal 1 binary64) (cos.f64 x)) #<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

6 calls:

Time	Variable		Point	Expression
0.0ms	x	@	0	(- 1 (cos x))
0.0ms	x	@	0	(cos x)
0.0ms	x	@	-inf	(- 1 (cos x))
0.0ms	x	@	inf	(- 1 (cos x))
0.0ms	x	@	inf	(cos x)

simplify1.0s (11.5%)

Memory

32.7MiB live, 935.2MiB allocated

Algorithm

1×	egg-herbie

Rules

32 720×	`lower-fma.f64`
32 720×	`lower-fma.f32`
3 926×	`lower-*.f64`
3 926×	`lower-*.f32`
3 120×	`lower-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	41	144
1	101	144
2	246	144
3	589	144
4	1230	144
5	1905	144
6	2165	144
7	2814	144
8	4054	144
9	5622	144
10	6523	144
11	6804	144
12	6843	144
13	6843	144
14	7276	144
15	7552	144
16	7593	144
17	7595	144
18	7595	144
19	7595	144
20	7595	144
21	7605	144
22	7605	144
23	7605	144
0	8510	132

Stop Event

1×	iter limit
1×	node limit

Counts

24 → 24

Calls

Call 1

Inputs
(* 1/2 (pow x 2))
(* (pow x 2) (+ 1/2 (* -1/24 (pow x 2))))
(* (pow x 2) (+ 1/2 (* (pow x 2) (- (* 1/720 (pow x 2)) 1/24))))
(* (pow x 2) (+ 1/2 (* (pow x 2) (- (* (pow x 2) (+ 1/720 (* -1/40320 (pow x 2)))) 1/24))))
(- 1 (cos x))
(- 1 (cos x))
(- 1 (cos x))
(- 1 (cos x))
(- 1 (cos x))
(- 1 (cos x))
(- 1 (cos x))
(- 1 (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)

Outputs
(* 1/2 (pow x 2))
(.f64 #s(literal 1/2 binary64) (.f64 x x))
(* (pow x 2) (+ 1/2 (* -1/24 (pow x 2))))
(.f64 (.f64 x x) (fma.f64 (*.f64 x x) #s(literal -1/24 binary64) #s(literal 1/2 binary64)))
(* (pow x 2) (+ 1/2 (* (pow x 2) (- (* 1/720 (pow x 2)) 1/24))))
(.f64 (.f64 x x) (fma.f64 (.f64 x x) (fma.f64 x (.f64 x #s(literal 1/720 binary64)) #s(literal -1/24 binary64)) #s(literal 1/2 binary64)))
(* (pow x 2) (+ 1/2 (* (pow x 2) (- (* (pow x 2) (+ 1/720 (* -1/40320 (pow x 2)))) 1/24))))
(.f64 x (.f64 x (fma.f64 x (.f64 x (fma.f64 (.f64 x x) (fma.f64 x (*.f64 x #s(literal -1/40320 binary64)) #s(literal 1/720 binary64)) #s(literal -1/24 binary64))) #s(literal 1/2 binary64))))
(- 1 (cos x))
(-.f64 #s(literal 1 binary64) (cos.f64 x))
(- 1 (cos x))
(-.f64 #s(literal 1 binary64) (cos.f64 x))
(- 1 (cos x))
(-.f64 #s(literal 1 binary64) (cos.f64 x))
(- 1 (cos x))
(-.f64 #s(literal 1 binary64) (cos.f64 x))
(- 1 (cos x))
(-.f64 #s(literal 1 binary64) (cos.f64 x))
(- 1 (cos x))
(-.f64 #s(literal 1 binary64) (cos.f64 x))
(- 1 (cos x))
(-.f64 #s(literal 1 binary64) (cos.f64 x))
(- 1 (cos x))
(-.f64 #s(literal 1 binary64) (cos.f64 x))
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 x (.f64 x (fma.f64 (.f64 x x) #s(literal 1/24 binary64) #s(literal -1/2 binary64))) #s(literal 1 binary64))
(+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))) 1/2)))
(fma.f64 x (.f64 x (fma.f64 x (.f64 x (fma.f64 x (*.f64 x #s(literal -1/720 binary64)) #s(literal 1/24 binary64))) #s(literal -1/2 binary64))) #s(literal 1 binary64))
(cos x)
(cos.f64 x)
(cos x)
(cos.f64 x)
(cos x)
(cos.f64 x)
(cos x)
(cos.f64 x)
(cos x)
(cos.f64 x)
(cos x)
(cos.f64 x)
(cos x)
(cos.f64 x)
(cos x)
(cos.f64 x)

rewrite350.0ms (4%)

Memory

2.2MiB live, 519.9MiB allocated

Algorithm

1×	batch-egg-rewrite

Rules

4 830×	`lower-*.f64`
4 830×	`lower-*.f32`
4 620×	`lower-/.f64`
4 620×	`lower-/.f32`
3 866×	`lower-fma.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	4	6
0	6	6
1	23	6
2	142	6
3	1153	6
0	9240	6

Stop Event

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

Counts

2 → 314

Calls

Call 1

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

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

eval45.0ms (0.5%)

Memory: -8.4MiB live, 105.9MiB allocated
Compiler: Compiled 10 777 to 912 computations (91.5% saved)

prune68.0ms (0.8%)

Memory

-0.8MiB live, 133.6MiB allocated

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	334	4	338
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	335	4	339

Accuracy

100.0%

Counts

339 → 4

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	52.1%	(-.f64 #s(literal 1 binary64) #s(approx (cos x) #s(literal 1 binary64)))
▶	100.0%	#s(approx (- 1 (cos x)) (.f64 (.f64 x x) (fma.f64 (*.f64 x x) #s(literal -1/24 binary64) #s(literal 1/2 binary64))))
▶	100.0%	#s(approx (- 1 (cos x)) (.f64 x (.f64 x (fma.f64 x (.f64 x (fma.f64 (.f64 x x) (fma.f64 x (*.f64 x #s(literal -1/40320 binary64)) #s(literal 1/720 binary64)) #s(literal -1/24 binary64))) #s(literal 1/2 binary64)))))
▶	99.7%	#s(approx (- 1 (cos x)) (.f64 #s(literal 1/2 binary64) (.f64 x x)))

Compiler

Compiled 46 to 26 computations (43.5% saved)

simplify63.0ms (0.7%)

Memory

9.0MiB live, 159.0MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 13 expressions of interest:

New	Metric	Program
✓	cost-diff	#s(approx (cos x) #s(literal 1 binary64))
✓	cost-diff	(-.f64 #s(literal 1 binary64) #s(approx (cos x) #s(literal 1 binary64)))
✓	cost-diff	(fma.f64 (*.f64 x x) #s(literal -1/24 binary64) #s(literal 1/2 binary64))
✓	cost-diff	(*.f64 x x)
✓	cost-diff	(.f64 (.f64 x x) (fma.f64 (*.f64 x x) #s(literal -1/24 binary64) #s(literal 1/2 binary64)))
✓	cost-diff	#s(approx (- 1 (cos x)) (.f64 (.f64 x x) (fma.f64 (*.f64 x x) #s(literal -1/24 binary64) #s(literal 1/2 binary64))))
✓	cost-diff	(fma.f64 x (.f64 x (fma.f64 (.f64 x x) (fma.f64 x (*.f64 x #s(literal -1/40320 binary64)) #s(literal 1/720 binary64)) #s(literal -1/24 binary64))) #s(literal 1/2 binary64))
✓	cost-diff	(.f64 x (fma.f64 x (.f64 x (fma.f64 (.f64 x x) (fma.f64 x (.f64 x #s(literal -1/40320 binary64)) #s(literal 1/720 binary64)) #s(literal -1/24 binary64))) #s(literal 1/2 binary64)))
✓	cost-diff	(.f64 x (.f64 x (fma.f64 x (.f64 x (fma.f64 (.f64 x x) (fma.f64 x (*.f64 x #s(literal -1/40320 binary64)) #s(literal 1/720 binary64)) #s(literal -1/24 binary64))) #s(literal 1/2 binary64))))
✓	cost-diff	#s(approx (- 1 (cos x)) (.f64 x (.f64 x (fma.f64 x (.f64 x (fma.f64 (.f64 x x) (fma.f64 x (*.f64 x #s(literal -1/40320 binary64)) #s(literal 1/720 binary64)) #s(literal -1/24 binary64))) #s(literal 1/2 binary64)))))
✓	cost-diff	(*.f64 x x)
✓	cost-diff	(.f64 #s(literal 1/2 binary64) (.f64 x x))
✓	cost-diff	#s(approx (- 1 (cos x)) (.f64 #s(literal 1/2 binary64) (.f64 x x)))

Rules

2 176×	`lower-fma.f32`
2 168×	`lower-fma.f64`
640×	`lower-*.f32`
626×	`lower-*.f64`
530×	`distribute-lft-in`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	24	188
0	40	188
1	92	188
2	229	188
3	487	188
4	1048	188
5	1539	188
6	1633	188
7	1651	188
8	1655	188
0	1655	188

Stop Event

1×	iter limit
1×	saturated
1×	iter limit

Calls

Call 1

Inputs
#s(approx (- 1 (cos x)) (.f64 #s(literal 1/2 binary64) (.f64 x x)))
(.f64 #s(literal 1/2 binary64) (.f64 x x))
#s(literal 1/2 binary64)
(*.f64 x x)
x
#s(approx (- 1 (cos x)) (.f64 x (.f64 x (fma.f64 x (.f64 x (fma.f64 (.f64 x x) (fma.f64 x (*.f64 x #s(literal -1/40320 binary64)) #s(literal 1/720 binary64)) #s(literal -1/24 binary64))) #s(literal 1/2 binary64)))))
(.f64 x (.f64 x (fma.f64 x (.f64 x (fma.f64 (.f64 x x) (fma.f64 x (*.f64 x #s(literal -1/40320 binary64)) #s(literal 1/720 binary64)) #s(literal -1/24 binary64))) #s(literal 1/2 binary64))))
x
(.f64 x (fma.f64 x (.f64 x (fma.f64 (.f64 x x) (fma.f64 x (.f64 x #s(literal -1/40320 binary64)) #s(literal 1/720 binary64)) #s(literal -1/24 binary64))) #s(literal 1/2 binary64)))
(fma.f64 x (.f64 x (fma.f64 (.f64 x x) (fma.f64 x (*.f64 x #s(literal -1/40320 binary64)) #s(literal 1/720 binary64)) #s(literal -1/24 binary64))) #s(literal 1/2 binary64))
(.f64 x (fma.f64 (.f64 x x) (fma.f64 x (*.f64 x #s(literal -1/40320 binary64)) #s(literal 1/720 binary64)) #s(literal -1/24 binary64)))
(fma.f64 (.f64 x x) (fma.f64 x (.f64 x #s(literal -1/40320 binary64)) #s(literal 1/720 binary64)) #s(literal -1/24 binary64))
(*.f64 x x)
(fma.f64 x (*.f64 x #s(literal -1/40320 binary64)) #s(literal 1/720 binary64))
(*.f64 x #s(literal -1/40320 binary64))
#s(literal -1/40320 binary64)
#s(literal 1/720 binary64)
#s(literal -1/24 binary64)
#s(literal 1/2 binary64)
#s(approx (- 1 (cos x)) (.f64 (.f64 x x) (fma.f64 (*.f64 x x) #s(literal -1/24 binary64) #s(literal 1/2 binary64))))
(.f64 (.f64 x x) (fma.f64 (*.f64 x x) #s(literal -1/24 binary64) #s(literal 1/2 binary64)))
(*.f64 x x)
x
(fma.f64 (*.f64 x x) #s(literal -1/24 binary64) #s(literal 1/2 binary64))
#s(literal -1/24 binary64)
#s(literal 1/2 binary64)
(-.f64 #s(literal 1 binary64) #s(approx (cos x) #s(literal 1 binary64)))
#s(literal 1 binary64)
#s(approx (cos x) #s(literal 1 binary64))

Outputs
#s(approx (- 1 (cos x)) (.f64 #s(literal 1/2 binary64) (.f64 x x)))
#s(approx (- 1 (cos x)) (.f64 x (.f64 x #s(literal 1/2 binary64))))
(.f64 #s(literal 1/2 binary64) (.f64 x x))
(.f64 x (.f64 x #s(literal 1/2 binary64)))
#s(literal 1/2 binary64)
(*.f64 x x)
x
#s(approx (- 1 (cos x)) (.f64 x (.f64 x (fma.f64 x (.f64 x (fma.f64 (.f64 x x) (fma.f64 x (*.f64 x #s(literal -1/40320 binary64)) #s(literal 1/720 binary64)) #s(literal -1/24 binary64))) #s(literal 1/2 binary64)))))
#s(approx (- 1 (cos x)) (.f64 x (.f64 x (fma.f64 (.f64 x x) (fma.f64 (.f64 x x) (fma.f64 (*.f64 x x) #s(literal -1/40320 binary64) #s(literal 1/720 binary64)) #s(literal -1/24 binary64)) #s(literal 1/2 binary64)))))
(.f64 x (.f64 x (fma.f64 x (.f64 x (fma.f64 (.f64 x x) (fma.f64 x (*.f64 x #s(literal -1/40320 binary64)) #s(literal 1/720 binary64)) #s(literal -1/24 binary64))) #s(literal 1/2 binary64))))
(.f64 x (.f64 x (fma.f64 (.f64 x x) (fma.f64 (.f64 x x) (fma.f64 (*.f64 x x) #s(literal -1/40320 binary64) #s(literal 1/720 binary64)) #s(literal -1/24 binary64)) #s(literal 1/2 binary64))))
x
(.f64 x (fma.f64 x (.f64 x (fma.f64 (.f64 x x) (fma.f64 x (.f64 x #s(literal -1/40320 binary64)) #s(literal 1/720 binary64)) #s(literal -1/24 binary64))) #s(literal 1/2 binary64)))
(.f64 x (fma.f64 (.f64 x x) (fma.f64 (.f64 x x) (fma.f64 (.f64 x x) #s(literal -1/40320 binary64) #s(literal 1/720 binary64)) #s(literal -1/24 binary64)) #s(literal 1/2 binary64)))
(fma.f64 x (.f64 x (fma.f64 (.f64 x x) (fma.f64 x (*.f64 x #s(literal -1/40320 binary64)) #s(literal 1/720 binary64)) #s(literal -1/24 binary64))) #s(literal 1/2 binary64))
(fma.f64 (.f64 x x) (fma.f64 (.f64 x x) (fma.f64 (*.f64 x x) #s(literal -1/40320 binary64) #s(literal 1/720 binary64)) #s(literal -1/24 binary64)) #s(literal 1/2 binary64))
(.f64 x (fma.f64 (.f64 x x) (fma.f64 x (*.f64 x #s(literal -1/40320 binary64)) #s(literal 1/720 binary64)) #s(literal -1/24 binary64)))
(.f64 x (fma.f64 (.f64 x x) (fma.f64 (*.f64 x x) #s(literal -1/40320 binary64) #s(literal 1/720 binary64)) #s(literal -1/24 binary64)))
(fma.f64 (.f64 x x) (fma.f64 x (.f64 x #s(literal -1/40320 binary64)) #s(literal 1/720 binary64)) #s(literal -1/24 binary64))
(fma.f64 (.f64 x x) (fma.f64 (.f64 x x) #s(literal -1/40320 binary64) #s(literal 1/720 binary64)) #s(literal -1/24 binary64))
(*.f64 x x)
(fma.f64 x (*.f64 x #s(literal -1/40320 binary64)) #s(literal 1/720 binary64))
(fma.f64 (*.f64 x x) #s(literal -1/40320 binary64) #s(literal 1/720 binary64))
(*.f64 x #s(literal -1/40320 binary64))
#s(literal -1/40320 binary64)
#s(literal 1/720 binary64)
#s(literal -1/24 binary64)
#s(literal 1/2 binary64)
#s(approx (- 1 (cos x)) (.f64 (.f64 x x) (fma.f64 (*.f64 x x) #s(literal -1/24 binary64) #s(literal 1/2 binary64))))
#s(approx (- 1 (cos x)) (.f64 (.f64 x x) (fma.f64 x (*.f64 x #s(literal -1/24 binary64)) #s(literal 1/2 binary64))))
(.f64 (.f64 x x) (fma.f64 (*.f64 x x) #s(literal -1/24 binary64) #s(literal 1/2 binary64)))
(.f64 (.f64 x x) (fma.f64 x (*.f64 x #s(literal -1/24 binary64)) #s(literal 1/2 binary64)))
(*.f64 x x)
x
(fma.f64 (*.f64 x x) #s(literal -1/24 binary64) #s(literal 1/2 binary64))
(fma.f64 x (*.f64 x #s(literal -1/24 binary64)) #s(literal 1/2 binary64))
#s(literal -1/24 binary64)
#s(literal 1/2 binary64)
(-.f64 #s(literal 1 binary64) #s(approx (cos x) #s(literal 1 binary64)))
#s(literal 1 binary64)
#s(approx (cos x) #s(literal 1 binary64))

localize209.0ms (2.4%)

Memory

1.0MiB live, 350.7MiB allocated

Localize:

Found 13 expressions of interest:

New	Metric	Score	Program
✓	accuracy	99.6%	#s(approx (cos x) #s(literal 1 binary64))
✓	accuracy	53.0%	(-.f64 #s(literal 1 binary64) #s(approx (cos x) #s(literal 1 binary64)))
✓	accuracy	100.0%	(fma.f64 (*.f64 x x) #s(literal -1/24 binary64) #s(literal 1/2 binary64))
✓	accuracy	100.0%	(*.f64 x x)
✓	accuracy	100.0%	#s(approx (- 1 (cos x)) (.f64 (.f64 x x) (fma.f64 (*.f64 x x) #s(literal -1/24 binary64) #s(literal 1/2 binary64))))
✓	accuracy	100.0%	(.f64 (.f64 x x) (fma.f64 (*.f64 x x) #s(literal -1/24 binary64) #s(literal 1/2 binary64)))
✓	accuracy	100.0%	(fma.f64 x (*.f64 x #s(literal -1/40320 binary64)) #s(literal 1/720 binary64))
✓	accuracy	100.0%	(.f64 x (.f64 x (fma.f64 x (.f64 x (fma.f64 (.f64 x x) (fma.f64 x (*.f64 x #s(literal -1/40320 binary64)) #s(literal 1/720 binary64)) #s(literal -1/24 binary64))) #s(literal 1/2 binary64))))
✓	accuracy	100.0%	(.f64 x (fma.f64 x (.f64 x (fma.f64 (.f64 x x) (fma.f64 x (.f64 x #s(literal -1/40320 binary64)) #s(literal 1/720 binary64)) #s(literal -1/24 binary64))) #s(literal 1/2 binary64)))
✓	accuracy	99.4%	(.f64 x (fma.f64 (.f64 x x) (fma.f64 x (*.f64 x #s(literal -1/40320 binary64)) #s(literal 1/720 binary64)) #s(literal -1/24 binary64)))
✓	accuracy	100.0%	(*.f64 x x)
✓	accuracy	100.0%	(.f64 #s(literal 1/2 binary64) (.f64 x x))
✓	accuracy	99.7%	#s(approx (- 1 (cos x)) (.f64 #s(literal 1/2 binary64) (.f64 x x)))

Samples

138.0ms	180×	2	valid
28.0ms	76×	1	valid

Compiler

Compiled 164 to 25 computations (84.8% saved)

Precisions

Click to see histograms. Total time spent on operations: 120.0ms

ival-mult: 45.0ms (37.5% of total)

ival-cos: 28.0ms (23.3% of total)

const: 17.0ms (14.2% of total)

adjust: 16.0ms (13.3% of total)

ival-add: 9.0ms (7.5% of total)

ival-sub: 4.0ms (3.3% of total)

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

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

exact: 0.0ms (0% of total)

series14.0ms (0.2%)

Memory

-11.6MiB live, 25.6MiB allocated

Counts

14 → 168

Calls

Call 1

Inputs
#s(alt #s(approx (- 1 (cos x)) (.f64 #s(literal 1/2 binary64) (.f64 x x))) (patch #s(approx (- 1 (cos x)) (.f64 #s(literal 1/2 binary64) (.f64 x x))) #<representation binary64>) () ())
#s(alt (.f64 #s(literal 1/2 binary64) (.f64 x x)) (patch (.f64 #s(literal 1/2 binary64) (.f64 x x)) #<representation binary64>) () ())
#s(alt (.f64 x x) (patch (.f64 x x) #<representation binary64>) () ())
#s(alt #s(approx (- 1 (cos x)) (.f64 x (.f64 x (fma.f64 x (.f64 x (fma.f64 (.f64 x x) (fma.f64 x (.f64 x #s(literal -1/40320 binary64)) #s(literal 1/720 binary64)) #s(literal -1/24 binary64))) #s(literal 1/2 binary64))))) (patch #s(approx (- 1 (cos x)) (.f64 x (.f64 x (fma.f64 x (.f64 x (fma.f64 (.f64 x x) (fma.f64 x (.f64 x #s(literal -1/40320 binary64)) #s(literal 1/720 binary64)) #s(literal -1/24 binary64))) #s(literal 1/2 binary64))))) #<representation binary64>) () ())
#s(alt (.f64 x (.f64 x (fma.f64 x (.f64 x (fma.f64 (.f64 x x) (fma.f64 x (.f64 x #s(literal -1/40320 binary64)) #s(literal 1/720 binary64)) #s(literal -1/24 binary64))) #s(literal 1/2 binary64)))) (patch (.f64 x (.f64 x (fma.f64 x (.f64 x (fma.f64 (.f64 x x) (fma.f64 x (.f64 x #s(literal -1/40320 binary64)) #s(literal 1/720 binary64)) #s(literal -1/24 binary64))) #s(literal 1/2 binary64)))) #<representation binary64>) () ())
#s(alt (.f64 x (fma.f64 x (.f64 x (fma.f64 (.f64 x x) (fma.f64 x (.f64 x #s(literal -1/40320 binary64)) #s(literal 1/720 binary64)) #s(literal -1/24 binary64))) #s(literal 1/2 binary64))) (patch (.f64 x (fma.f64 x (.f64 x (fma.f64 (.f64 x x) (fma.f64 x (.f64 x #s(literal -1/40320 binary64)) #s(literal 1/720 binary64)) #s(literal -1/24 binary64))) #s(literal 1/2 binary64))) #<representation binary64>) () ())
#s(alt (fma.f64 x (.f64 x (fma.f64 (.f64 x x) (fma.f64 x (.f64 x #s(literal -1/40320 binary64)) #s(literal 1/720 binary64)) #s(literal -1/24 binary64))) #s(literal 1/2 binary64)) (patch (fma.f64 x (.f64 x (fma.f64 (.f64 x x) (fma.f64 x (.f64 x #s(literal -1/40320 binary64)) #s(literal 1/720 binary64)) #s(literal -1/24 binary64))) #s(literal 1/2 binary64)) #<representation binary64>) () ())
#s(alt #s(approx (- 1 (cos x)) (.f64 (.f64 x x) (fma.f64 (.f64 x x) #s(literal -1/24 binary64) #s(literal 1/2 binary64)))) (patch #s(approx (- 1 (cos x)) (.f64 (.f64 x x) (fma.f64 (.f64 x x) #s(literal -1/24 binary64) #s(literal 1/2 binary64)))) #<representation binary64>) () ())
#s(alt (.f64 (.f64 x x) (fma.f64 (.f64 x x) #s(literal -1/24 binary64) #s(literal 1/2 binary64))) (patch (.f64 (.f64 x x) (fma.f64 (.f64 x x) #s(literal -1/24 binary64) #s(literal 1/2 binary64))) #<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>) () ())
#s(alt (-.f64 #s(literal 1 binary64) #s(approx (cos x) #s(literal 1 binary64))) (patch (-.f64 #s(literal 1 binary64) #s(approx (cos x) #s(literal 1 binary64))) #<representation binary64>) () ())
#s(alt #s(approx (cos x) #s(literal 1 binary64)) (patch #s(approx (cos x) #s(literal 1 binary64)) #<representation binary64>) () ())
#s(alt (.f64 x (fma.f64 (.f64 x x) (fma.f64 x (.f64 x #s(literal -1/40320 binary64)) #s(literal 1/720 binary64)) #s(literal -1/24 binary64))) (patch (.f64 x (fma.f64 (.f64 x x) (fma.f64 x (.f64 x #s(literal -1/40320 binary64)) #s(literal 1/720 binary64)) #s(literal -1/24 binary64))) #<representation binary64>) () ())
#s(alt (fma.f64 x (.f64 x #s(literal -1/40320 binary64)) #s(literal 1/720 binary64)) (patch (fma.f64 x (.f64 x #s(literal -1/40320 binary64)) #s(literal 1/720 binary64)) #<representation binary64>) () ())

Outputs
#s(alt (* 1/2 (pow x 2)) (taylor 0 x) (#s(alt #s(approx (- 1 (cos x)) (.f64 #s(literal 1/2 binary64) (.f64 x x))) (patch #s(approx (- 1 (cos x)) (.f64 #s(literal 1/2 binary64) (.f64 x x))) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (+ 1/2 (* -1/24 (pow x 2)))) (taylor 0 x) (#s(alt #s(approx (- 1 (cos x)) (.f64 #s(literal 1/2 binary64) (.f64 x x))) (patch #s(approx (- 1 (cos x)) (.f64 #s(literal 1/2 binary64) (.f64 x x))) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (+ 1/2 (* (pow x 2) (- (* 1/720 (pow x 2)) 1/24)))) (taylor 0 x) (#s(alt #s(approx (- 1 (cos x)) (.f64 #s(literal 1/2 binary64) (.f64 x x))) (patch #s(approx (- 1 (cos x)) (.f64 #s(literal 1/2 binary64) (.f64 x x))) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (+ 1/2 (* (pow x 2) (- (* (pow x 2) (+ 1/720 (* -1/40320 (pow x 2)))) 1/24)))) (taylor 0 x) (#s(alt #s(approx (- 1 (cos x)) (.f64 #s(literal 1/2 binary64) (.f64 x x))) (patch #s(approx (- 1 (cos x)) (.f64 #s(literal 1/2 binary64) (.f64 x x))) #<representation binary64>) () ())) ())
#s(alt (- 1 (cos x)) (taylor inf x) (#s(alt #s(approx (- 1 (cos x)) (.f64 #s(literal 1/2 binary64) (.f64 x x))) (patch #s(approx (- 1 (cos x)) (.f64 #s(literal 1/2 binary64) (.f64 x x))) #<representation binary64>) () ())) ())
#s(alt (- 1 (cos x)) (taylor inf x) (#s(alt #s(approx (- 1 (cos x)) (.f64 #s(literal 1/2 binary64) (.f64 x x))) (patch #s(approx (- 1 (cos x)) (.f64 #s(literal 1/2 binary64) (.f64 x x))) #<representation binary64>) () ())) ())
#s(alt (- 1 (cos x)) (taylor inf x) (#s(alt #s(approx (- 1 (cos x)) (.f64 #s(literal 1/2 binary64) (.f64 x x))) (patch #s(approx (- 1 (cos x)) (.f64 #s(literal 1/2 binary64) (.f64 x x))) #<representation binary64>) () ())) ())
#s(alt (- 1 (cos x)) (taylor inf x) (#s(alt #s(approx (- 1 (cos x)) (.f64 #s(literal 1/2 binary64) (.f64 x x))) (patch #s(approx (- 1 (cos x)) (.f64 #s(literal 1/2 binary64) (.f64 x x))) #<representation binary64>) () ())) ())
#s(alt (- 1 (cos x)) (taylor -inf x) (#s(alt #s(approx (- 1 (cos x)) (.f64 #s(literal 1/2 binary64) (.f64 x x))) (patch #s(approx (- 1 (cos x)) (.f64 #s(literal 1/2 binary64) (.f64 x x))) #<representation binary64>) () ())) ())
#s(alt (- 1 (cos x)) (taylor -inf x) (#s(alt #s(approx (- 1 (cos x)) (.f64 #s(literal 1/2 binary64) (.f64 x x))) (patch #s(approx (- 1 (cos x)) (.f64 #s(literal 1/2 binary64) (.f64 x x))) #<representation binary64>) () ())) ())
#s(alt (- 1 (cos x)) (taylor -inf x) (#s(alt #s(approx (- 1 (cos x)) (.f64 #s(literal 1/2 binary64) (.f64 x x))) (patch #s(approx (- 1 (cos x)) (.f64 #s(literal 1/2 binary64) (.f64 x x))) #<representation binary64>) () ())) ())
#s(alt (- 1 (cos x)) (taylor -inf x) (#s(alt #s(approx (- 1 (cos x)) (.f64 #s(literal 1/2 binary64) (.f64 x x))) (patch #s(approx (- 1 (cos x)) (.f64 #s(literal 1/2 binary64) (.f64 x x))) #<representation binary64>) () ())) ())
#s(alt (* 1/2 (pow x 2)) (taylor 0 x) (#s(alt (.f64 #s(literal 1/2 binary64) (.f64 x x)) (patch (.f64 #s(literal 1/2 binary64) (.f64 x x)) #<representation binary64>) () ())) ())
#s(alt (* 1/2 (pow x 2)) (taylor 0 x) (#s(alt (.f64 #s(literal 1/2 binary64) (.f64 x x)) (patch (.f64 #s(literal 1/2 binary64) (.f64 x x)) #<representation binary64>) () ())) ())
#s(alt (* 1/2 (pow x 2)) (taylor 0 x) (#s(alt (.f64 #s(literal 1/2 binary64) (.f64 x x)) (patch (.f64 #s(literal 1/2 binary64) (.f64 x x)) #<representation binary64>) () ())) ())
#s(alt (* 1/2 (pow x 2)) (taylor 0 x) (#s(alt (.f64 #s(literal 1/2 binary64) (.f64 x x)) (patch (.f64 #s(literal 1/2 binary64) (.f64 x x)) #<representation binary64>) () ())) ())
#s(alt (* 1/2 (pow x 2)) (taylor inf x) (#s(alt (.f64 #s(literal 1/2 binary64) (.f64 x x)) (patch (.f64 #s(literal 1/2 binary64) (.f64 x x)) #<representation binary64>) () ())) ())
#s(alt (* 1/2 (pow x 2)) (taylor inf x) (#s(alt (.f64 #s(literal 1/2 binary64) (.f64 x x)) (patch (.f64 #s(literal 1/2 binary64) (.f64 x x)) #<representation binary64>) () ())) ())
#s(alt (* 1/2 (pow x 2)) (taylor inf x) (#s(alt (.f64 #s(literal 1/2 binary64) (.f64 x x)) (patch (.f64 #s(literal 1/2 binary64) (.f64 x x)) #<representation binary64>) () ())) ())
#s(alt (* 1/2 (pow x 2)) (taylor inf x) (#s(alt (.f64 #s(literal 1/2 binary64) (.f64 x x)) (patch (.f64 #s(literal 1/2 binary64) (.f64 x x)) #<representation binary64>) () ())) ())
#s(alt (* 1/2 (pow x 2)) (taylor -inf x) (#s(alt (.f64 #s(literal 1/2 binary64) (.f64 x x)) (patch (.f64 #s(literal 1/2 binary64) (.f64 x x)) #<representation binary64>) () ())) ())
#s(alt (* 1/2 (pow x 2)) (taylor -inf x) (#s(alt (.f64 #s(literal 1/2 binary64) (.f64 x x)) (patch (.f64 #s(literal 1/2 binary64) (.f64 x x)) #<representation binary64>) () ())) ())
#s(alt (* 1/2 (pow x 2)) (taylor -inf x) (#s(alt (.f64 #s(literal 1/2 binary64) (.f64 x x)) (patch (.f64 #s(literal 1/2 binary64) (.f64 x x)) #<representation binary64>) () ())) ())
#s(alt (* 1/2 (pow x 2)) (taylor -inf x) (#s(alt (.f64 #s(literal 1/2 binary64) (.f64 x x)) (patch (.f64 #s(literal 1/2 binary64) (.f64 x x)) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor 0 x) (#s(alt (.f64 x x) (patch (.f64 x x) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor 0 x) (#s(alt (.f64 x x) (patch (.f64 x x) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor 0 x) (#s(alt (.f64 x x) (patch (.f64 x x) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor 0 x) (#s(alt (.f64 x x) (patch (.f64 x x) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor inf x) (#s(alt (.f64 x x) (patch (.f64 x x) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor inf x) (#s(alt (.f64 x x) (patch (.f64 x x) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor inf x) (#s(alt (.f64 x x) (patch (.f64 x x) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor inf x) (#s(alt (.f64 x x) (patch (.f64 x x) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor -inf x) (#s(alt (.f64 x x) (patch (.f64 x x) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor -inf x) (#s(alt (.f64 x x) (patch (.f64 x x) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor -inf x) (#s(alt (.f64 x x) (patch (.f64 x x) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor -inf x) (#s(alt (.f64 x x) (patch (.f64 x x) #<representation binary64>) () ())) ())
#s(alt (* 1/2 (pow x 2)) (taylor 0 x) (#s(alt #s(approx (- 1 (cos x)) (.f64 x (.f64 x (fma.f64 x (.f64 x (fma.f64 (.f64 x x) (fma.f64 x (.f64 x #s(literal -1/40320 binary64)) #s(literal 1/720 binary64)) #s(literal -1/24 binary64))) #s(literal 1/2 binary64))))) (patch #s(approx (- 1 (cos x)) (.f64 x (.f64 x (fma.f64 x (.f64 x (fma.f64 (.f64 x x) (fma.f64 x (.f64 x #s(literal -1/40320 binary64)) #s(literal 1/720 binary64)) #s(literal -1/24 binary64))) #s(literal 1/2 binary64))))) #<representation binary64>) () ())) ())
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#s(alt (* (pow x 2) (+ 1/2 (* (pow x 2) (- (* (pow x 2) (+ 1/720 (* -1/40320 (pow x 2)))) 1/24)))) (taylor 0 x) (#s(alt (-.f64 #s(literal 1 binary64) #s(approx (cos x) #s(literal 1 binary64))) (patch (-.f64 #s(literal 1 binary64) #s(approx (cos x) #s(literal 1 binary64))) #<representation binary64>) () ())) ())
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#s(alt (- 1 (cos x)) (taylor inf x) (#s(alt (-.f64 #s(literal 1 binary64) #s(approx (cos x) #s(literal 1 binary64))) (patch (-.f64 #s(literal 1 binary64) #s(approx (cos x) #s(literal 1 binary64))) #<representation binary64>) () ())) ())
#s(alt (- 1 (cos x)) (taylor inf x) (#s(alt (-.f64 #s(literal 1 binary64) #s(approx (cos x) #s(literal 1 binary64))) (patch (-.f64 #s(literal 1 binary64) #s(approx (cos x) #s(literal 1 binary64))) #<representation binary64>) () ())) ())
#s(alt (- 1 (cos x)) (taylor inf x) (#s(alt (-.f64 #s(literal 1 binary64) #s(approx (cos x) #s(literal 1 binary64))) (patch (-.f64 #s(literal 1 binary64) #s(approx (cos x) #s(literal 1 binary64))) #<representation binary64>) () ())) ())
#s(alt (- 1 (cos x)) (taylor -inf x) (#s(alt (-.f64 #s(literal 1 binary64) #s(approx (cos x) #s(literal 1 binary64))) (patch (-.f64 #s(literal 1 binary64) #s(approx (cos x) #s(literal 1 binary64))) #<representation binary64>) () ())) ())
#s(alt (- 1 (cos x)) (taylor -inf x) (#s(alt (-.f64 #s(literal 1 binary64) #s(approx (cos x) #s(literal 1 binary64))) (patch (-.f64 #s(literal 1 binary64) #s(approx (cos x) #s(literal 1 binary64))) #<representation binary64>) () ())) ())
#s(alt (- 1 (cos x)) (taylor -inf x) (#s(alt (-.f64 #s(literal 1 binary64) #s(approx (cos x) #s(literal 1 binary64))) (patch (-.f64 #s(literal 1 binary64) #s(approx (cos x) #s(literal 1 binary64))) #<representation binary64>) () ())) ())
#s(alt (- 1 (cos x)) (taylor -inf x) (#s(alt (-.f64 #s(literal 1 binary64) #s(approx (cos x) #s(literal 1 binary64))) (patch (-.f64 #s(literal 1 binary64) #s(approx (cos x) #s(literal 1 binary64))) #<representation binary64>) () ())) ())
#s(alt 1 (taylor 0 x) (#s(alt #s(approx (cos x) #s(literal 1 binary64)) (patch #s(approx (cos x) #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (+ 1 (* -1/2 (pow x 2))) (taylor 0 x) (#s(alt #s(approx (cos x) #s(literal 1 binary64)) (patch #s(approx (cos x) #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (+ 1 (* (pow x 2) (- (* 1/24 (pow x 2)) 1/2))) (taylor 0 x) (#s(alt #s(approx (cos x) #s(literal 1 binary64)) (patch #s(approx (cos x) #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))) 1/2))) (taylor 0 x) (#s(alt #s(approx (cos x) #s(literal 1 binary64)) (patch #s(approx (cos x) #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (cos x) (taylor inf x) (#s(alt #s(approx (cos x) #s(literal 1 binary64)) (patch #s(approx (cos x) #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (cos x) (taylor inf x) (#s(alt #s(approx (cos x) #s(literal 1 binary64)) (patch #s(approx (cos x) #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (cos x) (taylor inf x) (#s(alt #s(approx (cos x) #s(literal 1 binary64)) (patch #s(approx (cos x) #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (cos x) (taylor inf x) (#s(alt #s(approx (cos x) #s(literal 1 binary64)) (patch #s(approx (cos x) #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (cos x) (taylor -inf x) (#s(alt #s(approx (cos x) #s(literal 1 binary64)) (patch #s(approx (cos x) #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (cos x) (taylor -inf x) (#s(alt #s(approx (cos x) #s(literal 1 binary64)) (patch #s(approx (cos x) #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (cos x) (taylor -inf x) (#s(alt #s(approx (cos x) #s(literal 1 binary64)) (patch #s(approx (cos x) #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (cos x) (taylor -inf x) (#s(alt #s(approx (cos x) #s(literal 1 binary64)) (patch #s(approx (cos x) #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (* -1/24 x) (taylor 0 x) (#s(alt (.f64 x (fma.f64 (.f64 x x) (fma.f64 x (.f64 x #s(literal -1/40320 binary64)) #s(literal 1/720 binary64)) #s(literal -1/24 binary64))) (patch (.f64 x (fma.f64 (.f64 x x) (fma.f64 x (.f64 x #s(literal -1/40320 binary64)) #s(literal 1/720 binary64)) #s(literal -1/24 binary64))) #<representation binary64>) () ())) ())
#s(alt (* x (- (* 1/720 (pow x 2)) 1/24)) (taylor 0 x) (#s(alt (.f64 x (fma.f64 (.f64 x x) (fma.f64 x (.f64 x #s(literal -1/40320 binary64)) #s(literal 1/720 binary64)) #s(literal -1/24 binary64))) (patch (.f64 x (fma.f64 (.f64 x x) (fma.f64 x (.f64 x #s(literal -1/40320 binary64)) #s(literal 1/720 binary64)) #s(literal -1/24 binary64))) #<representation binary64>) () ())) ())
#s(alt (* x (- (* (pow x 2) (+ 1/720 (* -1/40320 (pow x 2)))) 1/24)) (taylor 0 x) (#s(alt (.f64 x (fma.f64 (.f64 x x) (fma.f64 x (.f64 x #s(literal -1/40320 binary64)) #s(literal 1/720 binary64)) #s(literal -1/24 binary64))) (patch (.f64 x (fma.f64 (.f64 x x) (fma.f64 x (.f64 x #s(literal -1/40320 binary64)) #s(literal 1/720 binary64)) #s(literal -1/24 binary64))) #<representation binary64>) () ())) ())
#s(alt (* x (- (* (pow x 2) (+ 1/720 (* -1/40320 (pow x 2)))) 1/24)) (taylor 0 x) (#s(alt (.f64 x (fma.f64 (.f64 x x) (fma.f64 x (.f64 x #s(literal -1/40320 binary64)) #s(literal 1/720 binary64)) #s(literal -1/24 binary64))) (patch (.f64 x (fma.f64 (.f64 x x) (fma.f64 x (.f64 x #s(literal -1/40320 binary64)) #s(literal 1/720 binary64)) #s(literal -1/24 binary64))) #<representation binary64>) () ())) ())
#s(alt (* -1/40320 (pow x 5)) (taylor inf x) (#s(alt (.f64 x (fma.f64 (.f64 x x) (fma.f64 x (.f64 x #s(literal -1/40320 binary64)) #s(literal 1/720 binary64)) #s(literal -1/24 binary64))) (patch (.f64 x (fma.f64 (.f64 x x) (fma.f64 x (.f64 x #s(literal -1/40320 binary64)) #s(literal 1/720 binary64)) #s(literal -1/24 binary64))) #<representation binary64>) () ())) ())
#s(alt (* (pow x 5) (- (* 1/720 (/ 1 (pow x 2))) 1/40320)) (taylor inf x) (#s(alt (.f64 x (fma.f64 (.f64 x x) (fma.f64 x (.f64 x #s(literal -1/40320 binary64)) #s(literal 1/720 binary64)) #s(literal -1/24 binary64))) (patch (.f64 x (fma.f64 (.f64 x x) (fma.f64 x (.f64 x #s(literal -1/40320 binary64)) #s(literal 1/720 binary64)) #s(literal -1/24 binary64))) #<representation binary64>) () ())) ())
#s(alt (* (pow x 5) (- (* 1/720 (/ 1 (pow x 2))) (+ 1/40320 (/ 1/24 (pow x 4))))) (taylor inf x) (#s(alt (.f64 x (fma.f64 (.f64 x x) (fma.f64 x (.f64 x #s(literal -1/40320 binary64)) #s(literal 1/720 binary64)) #s(literal -1/24 binary64))) (patch (.f64 x (fma.f64 (.f64 x x) (fma.f64 x (.f64 x #s(literal -1/40320 binary64)) #s(literal 1/720 binary64)) #s(literal -1/24 binary64))) #<representation binary64>) () ())) ())
#s(alt (* (pow x 5) (- (* 1/720 (/ 1 (pow x 2))) (+ 1/40320 (/ 1/24 (pow x 4))))) (taylor inf x) (#s(alt (.f64 x (fma.f64 (.f64 x x) (fma.f64 x (.f64 x #s(literal -1/40320 binary64)) #s(literal 1/720 binary64)) #s(literal -1/24 binary64))) (patch (.f64 x (fma.f64 (.f64 x x) (fma.f64 x (.f64 x #s(literal -1/40320 binary64)) #s(literal 1/720 binary64)) #s(literal -1/24 binary64))) #<representation binary64>) () ())) ())
#s(alt (* -1/40320 (pow x 5)) (taylor -inf x) (#s(alt (.f64 x (fma.f64 (.f64 x x) (fma.f64 x (.f64 x #s(literal -1/40320 binary64)) #s(literal 1/720 binary64)) #s(literal -1/24 binary64))) (patch (.f64 x (fma.f64 (.f64 x x) (fma.f64 x (.f64 x #s(literal -1/40320 binary64)) #s(literal 1/720 binary64)) #s(literal -1/24 binary64))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* (pow x 5) (- 1/40320 (* 1/720 (/ 1 (pow x 2)))))) (taylor -inf x) (#s(alt (.f64 x (fma.f64 (.f64 x x) (fma.f64 x (.f64 x #s(literal -1/40320 binary64)) #s(literal 1/720 binary64)) #s(literal -1/24 binary64))) (patch (.f64 x (fma.f64 (.f64 x x) (fma.f64 x (.f64 x #s(literal -1/40320 binary64)) #s(literal 1/720 binary64)) #s(literal -1/24 binary64))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* (pow x 5) (- (+ 1/40320 (/ 1/24 (pow x 4))) (* 1/720 (/ 1 (pow x 2)))))) (taylor -inf x) (#s(alt (.f64 x (fma.f64 (.f64 x x) (fma.f64 x (.f64 x #s(literal -1/40320 binary64)) #s(literal 1/720 binary64)) #s(literal -1/24 binary64))) (patch (.f64 x (fma.f64 (.f64 x x) (fma.f64 x (.f64 x #s(literal -1/40320 binary64)) #s(literal 1/720 binary64)) #s(literal -1/24 binary64))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* (pow x 5) (- (+ 1/40320 (/ 1/24 (pow x 4))) (* 1/720 (/ 1 (pow x 2)))))) (taylor -inf x) (#s(alt (.f64 x (fma.f64 (.f64 x x) (fma.f64 x (.f64 x #s(literal -1/40320 binary64)) #s(literal 1/720 binary64)) #s(literal -1/24 binary64))) (patch (.f64 x (fma.f64 (.f64 x x) (fma.f64 x (.f64 x #s(literal -1/40320 binary64)) #s(literal 1/720 binary64)) #s(literal -1/24 binary64))) #<representation binary64>) () ())) ())
#s(alt 1/720 (taylor 0 x) (#s(alt (fma.f64 x (.f64 x #s(literal -1/40320 binary64)) #s(literal 1/720 binary64)) (patch (fma.f64 x (.f64 x #s(literal -1/40320 binary64)) #s(literal 1/720 binary64)) #<representation binary64>) () ())) ())
#s(alt (+ 1/720 (* -1/40320 (pow x 2))) (taylor 0 x) (#s(alt (fma.f64 x (.f64 x #s(literal -1/40320 binary64)) #s(literal 1/720 binary64)) (patch (fma.f64 x (.f64 x #s(literal -1/40320 binary64)) #s(literal 1/720 binary64)) #<representation binary64>) () ())) ())
#s(alt (+ 1/720 (* -1/40320 (pow x 2))) (taylor 0 x) (#s(alt (fma.f64 x (.f64 x #s(literal -1/40320 binary64)) #s(literal 1/720 binary64)) (patch (fma.f64 x (.f64 x #s(literal -1/40320 binary64)) #s(literal 1/720 binary64)) #<representation binary64>) () ())) ())
#s(alt (+ 1/720 (* -1/40320 (pow x 2))) (taylor 0 x) (#s(alt (fma.f64 x (.f64 x #s(literal -1/40320 binary64)) #s(literal 1/720 binary64)) (patch (fma.f64 x (.f64 x #s(literal -1/40320 binary64)) #s(literal 1/720 binary64)) #<representation binary64>) () ())) ())
#s(alt (* -1/40320 (pow x 2)) (taylor inf x) (#s(alt (fma.f64 x (.f64 x #s(literal -1/40320 binary64)) #s(literal 1/720 binary64)) (patch (fma.f64 x (.f64 x #s(literal -1/40320 binary64)) #s(literal 1/720 binary64)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (- (* 1/720 (/ 1 (pow x 2))) 1/40320)) (taylor inf x) (#s(alt (fma.f64 x (.f64 x #s(literal -1/40320 binary64)) #s(literal 1/720 binary64)) (patch (fma.f64 x (.f64 x #s(literal -1/40320 binary64)) #s(literal 1/720 binary64)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (- (* 1/720 (/ 1 (pow x 2))) 1/40320)) (taylor inf x) (#s(alt (fma.f64 x (.f64 x #s(literal -1/40320 binary64)) #s(literal 1/720 binary64)) (patch (fma.f64 x (.f64 x #s(literal -1/40320 binary64)) #s(literal 1/720 binary64)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (- (* 1/720 (/ 1 (pow x 2))) 1/40320)) (taylor inf x) (#s(alt (fma.f64 x (.f64 x #s(literal -1/40320 binary64)) #s(literal 1/720 binary64)) (patch (fma.f64 x (.f64 x #s(literal -1/40320 binary64)) #s(literal 1/720 binary64)) #<representation binary64>) () ())) ())
#s(alt (* -1/40320 (pow x 2)) (taylor -inf x) (#s(alt (fma.f64 x (.f64 x #s(literal -1/40320 binary64)) #s(literal 1/720 binary64)) (patch (fma.f64 x (.f64 x #s(literal -1/40320 binary64)) #s(literal 1/720 binary64)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (- (* 1/720 (/ 1 (pow x 2))) 1/40320)) (taylor -inf x) (#s(alt (fma.f64 x (.f64 x #s(literal -1/40320 binary64)) #s(literal 1/720 binary64)) (patch (fma.f64 x (.f64 x #s(literal -1/40320 binary64)) #s(literal 1/720 binary64)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (- (* 1/720 (/ 1 (pow x 2))) 1/40320)) (taylor -inf x) (#s(alt (fma.f64 x (.f64 x #s(literal -1/40320 binary64)) #s(literal 1/720 binary64)) (patch (fma.f64 x (.f64 x #s(literal -1/40320 binary64)) #s(literal 1/720 binary64)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (- (* 1/720 (/ 1 (pow x 2))) 1/40320)) (taylor -inf x) (#s(alt (fma.f64 x (.f64 x #s(literal -1/40320 binary64)) #s(literal 1/720 binary64)) (patch (fma.f64 x (.f64 x #s(literal -1/40320 binary64)) #s(literal 1/720 binary64)) #<representation binary64>) () ())) ())

Calls

42 calls:

Time	Variable		Point	Expression
1.0ms	x	@	inf	(* (* x x) (+ (* (* x x) -1/24) 1/2))
1.0ms	x	@	inf	(* x (* x (+ (* x (* x (+ (* (* x x) (+ (* x (* x -1/40320)) 1/720)) -1/24))) 1/2)))
0.0ms	x	@	0	(* 1/2 (* x x))
0.0ms	x	@	0	(* x (* x (+ (* x (* x (+ (* (* x x) (+ (* x (* x -1/40320)) 1/720)) -1/24))) 1/2)))
0.0ms	x	@	inf	(* x (+ (* (* x x) (+ (* x (* x -1/40320)) 1/720)) -1/24))

simplify342.0ms (3.9%)

Memory

-9.5MiB live, 554.2MiB allocated

Algorithm

1×	egg-herbie

Rules

11 564×	`lower-fma.f64`
11 564×	`lower-fma.f32`
3 554×	`lower-*.f64`
3 554×	`lower-*.f32`
1 788×	`lower-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	104	1388
1	262	1388
2	692	1388
3	1944	1388
4	4983	1380
0	8084	1298

Stop Event

1×	iter limit
1×	node limit

Counts

168 → 168

Calls

Call 1

Inputs
(* 1/2 (pow x 2))
(* (pow x 2) (+ 1/2 (* -1/24 (pow x 2))))
(* (pow x 2) (+ 1/2 (* (pow x 2) (- (* 1/720 (pow x 2)) 1/24))))
(* (pow x 2) (+ 1/2 (* (pow x 2) (- (* (pow x 2) (+ 1/720 (* -1/40320 (pow x 2)))) 1/24))))
(- 1 (cos x))
(- 1 (cos x))
(- 1 (cos x))
(- 1 (cos x))
(- 1 (cos x))
(- 1 (cos x))
(- 1 (cos x))
(- 1 (cos x))
(* 1/2 (pow x 2))
(* 1/2 (pow x 2))
(* 1/2 (pow x 2))
(* 1/2 (pow x 2))
(* 1/2 (pow x 2))
(* 1/2 (pow x 2))
(* 1/2 (pow x 2))
(* 1/2 (pow x 2))
(* 1/2 (pow x 2))
(* 1/2 (pow x 2))
(* 1/2 (pow x 2))
(* 1/2 (pow x 2))
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(* 1/2 (pow x 2))
(* (pow x 2) (+ 1/2 (* -1/24 (pow x 2))))
(* (pow x 2) (+ 1/2 (* (pow x 2) (- (* 1/720 (pow x 2)) 1/24))))
(* (pow x 2) (+ 1/2 (* (pow x 2) (- (* (pow x 2) (+ 1/720 (* -1/40320 (pow x 2)))) 1/24))))
(- 1 (cos x))
(- 1 (cos x))
(- 1 (cos x))
(- 1 (cos x))
(- 1 (cos x))
(- 1 (cos x))
(- 1 (cos x))
(- 1 (cos x))
(* 1/2 (pow x 2))
(* (pow x 2) (+ 1/2 (* -1/24 (pow x 2))))
(* (pow x 2) (+ 1/2 (* (pow x 2) (- (* 1/720 (pow x 2)) 1/24))))
(* (pow x 2) (+ 1/2 (* (pow x 2) (- (* (pow x 2) (+ 1/720 (* -1/40320 (pow x 2)))) 1/24))))
(* -1/40320 (pow x 8))
(* (pow x 8) (- (* 1/720 (/ 1 (pow x 2))) 1/40320))
(* (pow x 8) (- (* 1/720 (/ 1 (pow x 2))) (+ 1/40320 (/ 1/24 (pow x 4)))))
(* (pow x 8) (- (+ (* 1/720 (/ 1 (pow x 2))) (* 1/2 (/ 1 (pow x 6)))) (+ 1/40320 (/ 1/24 (pow x 4)))))
(* -1/40320 (pow x 8))
(* (pow x 8) (- (* 1/720 (/ 1 (pow x 2))) 1/40320))
(* (pow x 8) (- (* 1/720 (/ 1 (pow x 2))) (+ 1/40320 (/ 1/24 (pow x 4)))))
(* (pow x 8) (- (+ (* 1/720 (/ 1 (pow x 2))) (* 1/2 (/ 1 (pow x 6)))) (+ 1/40320 (/ 1/24 (pow x 4)))))
(* 1/2 x)
(* x (+ 1/2 (* -1/24 (pow x 2))))
(* x (+ 1/2 (* (pow x 2) (- (* 1/720 (pow x 2)) 1/24))))
(* x (+ 1/2 (* (pow x 2) (- (* (pow x 2) (+ 1/720 (* -1/40320 (pow x 2)))) 1/24))))
(* -1/40320 (pow x 7))
(* (pow x 7) (- (* 1/720 (/ 1 (pow x 2))) 1/40320))
(* (pow x 7) (- (* 1/720 (/ 1 (pow x 2))) (+ 1/40320 (/ 1/24 (pow x 4)))))
(* (pow x 7) (- (+ (* 1/720 (/ 1 (pow x 2))) (* 1/2 (/ 1 (pow x 6)))) (+ 1/40320 (/ 1/24 (pow x 4)))))
(* -1/40320 (pow x 7))
(* -1 (* (pow x 7) (- 1/40320 (* 1/720 (/ 1 (pow x 2))))))
(* -1 (* (pow x 7) (- (+ 1/40320 (/ 1/24 (pow x 4))) (* 1/720 (/ 1 (pow x 2))))))
(* -1 (* (pow x 7) (- (+ 1/40320 (/ 1/24 (pow x 4))) (+ (* 1/720 (/ 1 (pow x 2))) (* 1/2 (/ 1 (pow x 6)))))))
1/2
(+ 1/2 (* -1/24 (pow x 2)))
(+ 1/2 (* (pow x 2) (- (* 1/720 (pow x 2)) 1/24)))
(+ 1/2 (* (pow x 2) (- (* (pow x 2) (+ 1/720 (* -1/40320 (pow x 2)))) 1/24)))
(* -1/40320 (pow x 6))
(* (pow x 6) (- (* 1/720 (/ 1 (pow x 2))) 1/40320))
(* (pow x 6) (- (* 1/720 (/ 1 (pow x 2))) (+ 1/40320 (/ 1/24 (pow x 4)))))
(* (pow x 6) (- (+ (* 1/720 (/ 1 (pow x 2))) (* 1/2 (/ 1 (pow x 6)))) (+ 1/40320 (/ 1/24 (pow x 4)))))
(* -1/40320 (pow x 6))
(* (pow x 6) (- (* 1/720 (/ 1 (pow x 2))) 1/40320))
(* (pow x 6) (- (* 1/720 (/ 1 (pow x 2))) (+ 1/40320 (/ 1/24 (pow x 4)))))
(* (pow x 6) (- (+ (* 1/720 (/ 1 (pow x 2))) (* 1/2 (/ 1 (pow x 6)))) (+ 1/40320 (/ 1/24 (pow x 4)))))
(* 1/2 (pow x 2))
(* (pow x 2) (+ 1/2 (* -1/24 (pow x 2))))
(* (pow x 2) (+ 1/2 (* (pow x 2) (- (* 1/720 (pow x 2)) 1/24))))
(* (pow x 2) (+ 1/2 (* (pow x 2) (- (* (pow x 2) (+ 1/720 (* -1/40320 (pow x 2)))) 1/24))))
(- 1 (cos x))
(- 1 (cos x))
(- 1 (cos x))
(- 1 (cos x))
(- 1 (cos x))
(- 1 (cos x))
(- 1 (cos x))
(- 1 (cos x))
(* 1/2 (pow x 2))
(* (pow x 2) (+ 1/2 (* -1/24 (pow x 2))))
(* (pow x 2) (+ 1/2 (* -1/24 (pow x 2))))
(* (pow x 2) (+ 1/2 (* -1/24 (pow x 2))))
(* -1/24 (pow x 4))
(* (pow x 4) (- (* 1/2 (/ 1 (pow x 2))) 1/24))
(* (pow x 4) (- (* 1/2 (/ 1 (pow x 2))) 1/24))
(* (pow x 4) (- (* 1/2 (/ 1 (pow x 2))) 1/24))
(* -1/24 (pow x 4))
(* (pow x 4) (- (* 1/2 (/ 1 (pow x 2))) 1/24))
(* (pow x 4) (- (* 1/2 (/ 1 (pow x 2))) 1/24))
(* (pow x 4) (- (* 1/2 (/ 1 (pow x 2))) 1/24))
1/2
(+ 1/2 (* -1/24 (pow x 2)))
(+ 1/2 (* -1/24 (pow x 2)))
(+ 1/2 (* -1/24 (pow x 2)))
(* -1/24 (pow x 2))
(* (pow x 2) (- (* 1/2 (/ 1 (pow x 2))) 1/24))
(* (pow x 2) (- (* 1/2 (/ 1 (pow x 2))) 1/24))
(* (pow x 2) (- (* 1/2 (/ 1 (pow x 2))) 1/24))
(* -1/24 (pow x 2))
(* (pow x 2) (- (* 1/2 (/ 1 (pow x 2))) 1/24))
(* (pow x 2) (- (* 1/2 (/ 1 (pow x 2))) 1/24))
(* (pow x 2) (- (* 1/2 (/ 1 (pow x 2))) 1/24))
(* 1/2 (pow x 2))
(* (pow x 2) (+ 1/2 (* -1/24 (pow x 2))))
(* (pow x 2) (+ 1/2 (* (pow x 2) (- (* 1/720 (pow x 2)) 1/24))))
(* (pow x 2) (+ 1/2 (* (pow x 2) (- (* (pow x 2) (+ 1/720 (* -1/40320 (pow x 2)))) 1/24))))
(- 1 (cos x))
(- 1 (cos x))
(- 1 (cos x))
(- 1 (cos x))
(- 1 (cos x))
(- 1 (cos x))
(- 1 (cos x))
(- 1 (cos x))
1
(+ 1 (* -1/2 (pow x 2)))
(+ 1 (* (pow x 2) (- (* 1/24 (pow x 2)) 1/2)))
(+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))) 1/2)))
(cos x)
(cos x)
(cos x)
(cos x)
(cos x)
(cos x)
(cos x)
(cos x)
(* -1/24 x)
(* x (- (* 1/720 (pow x 2)) 1/24))
(* x (- (* (pow x 2) (+ 1/720 (* -1/40320 (pow x 2)))) 1/24))
(* x (- (* (pow x 2) (+ 1/720 (* -1/40320 (pow x 2)))) 1/24))
(* -1/40320 (pow x 5))
(* (pow x 5) (- (* 1/720 (/ 1 (pow x 2))) 1/40320))
(* (pow x 5) (- (* 1/720 (/ 1 (pow x 2))) (+ 1/40320 (/ 1/24 (pow x 4)))))
(* (pow x 5) (- (* 1/720 (/ 1 (pow x 2))) (+ 1/40320 (/ 1/24 (pow x 4)))))
(* -1/40320 (pow x 5))
(* -1 (* (pow x 5) (- 1/40320 (* 1/720 (/ 1 (pow x 2))))))
(* -1 (* (pow x 5) (- (+ 1/40320 (/ 1/24 (pow x 4))) (* 1/720 (/ 1 (pow x 2))))))
(* -1 (* (pow x 5) (- (+ 1/40320 (/ 1/24 (pow x 4))) (* 1/720 (/ 1 (pow x 2))))))
1/720
(+ 1/720 (* -1/40320 (pow x 2)))
(+ 1/720 (* -1/40320 (pow x 2)))
(+ 1/720 (* -1/40320 (pow x 2)))
(* -1/40320 (pow x 2))
(* (pow x 2) (- (* 1/720 (/ 1 (pow x 2))) 1/40320))
(* (pow x 2) (- (* 1/720 (/ 1 (pow x 2))) 1/40320))
(* (pow x 2) (- (* 1/720 (/ 1 (pow x 2))) 1/40320))
(* -1/40320 (pow x 2))
(* (pow x 2) (- (* 1/720 (/ 1 (pow x 2))) 1/40320))
(* (pow x 2) (- (* 1/720 (/ 1 (pow x 2))) 1/40320))
(* (pow x 2) (- (* 1/720 (/ 1 (pow x 2))) 1/40320))

Outputs
(* 1/2 (pow x 2))
(.f64 #s(literal 1/2 binary64) (.f64 x x))
(* (pow x 2) (+ 1/2 (* -1/24 (pow x 2))))
(.f64 x (.f64 x (fma.f64 x (*.f64 x #s(literal -1/24 binary64)) #s(literal 1/2 binary64))))
(* (pow x 2) (+ 1/2 (* (pow x 2) (- (* 1/720 (pow x 2)) 1/24))))
(.f64 x (.f64 x (fma.f64 (.f64 x x) (fma.f64 (.f64 x x) #s(literal 1/720 binary64) #s(literal -1/24 binary64)) #s(literal 1/2 binary64))))
(* (pow x 2) (+ 1/2 (* (pow x 2) (- (* (pow x 2) (+ 1/720 (* -1/40320 (pow x 2)))) 1/24))))
(.f64 (.f64 x x) (fma.f64 (.f64 x x) (fma.f64 (.f64 x x) (fma.f64 (*.f64 x x) #s(literal -1/40320 binary64) #s(literal 1/720 binary64)) #s(literal -1/24 binary64)) #s(literal 1/2 binary64)))
(- 1 (cos x))
(-.f64 #s(literal 1 binary64) (cos.f64 x))
(- 1 (cos x))
(-.f64 #s(literal 1 binary64) (cos.f64 x))
(- 1 (cos x))
(-.f64 #s(literal 1 binary64) (cos.f64 x))
(- 1 (cos x))
(-.f64 #s(literal 1 binary64) (cos.f64 x))
(- 1 (cos x))
(-.f64 #s(literal 1 binary64) (cos.f64 x))
(- 1 (cos x))
(-.f64 #s(literal 1 binary64) (cos.f64 x))
(- 1 (cos x))
(-.f64 #s(literal 1 binary64) (cos.f64 x))
(- 1 (cos x))
(-.f64 #s(literal 1 binary64) (cos.f64 x))
(* 1/2 (pow x 2))
(.f64 #s(literal 1/2 binary64) (.f64 x x))
(* 1/2 (pow x 2))
(.f64 #s(literal 1/2 binary64) (.f64 x x))
(* 1/2 (pow x 2))
(.f64 #s(literal 1/2 binary64) (.f64 x x))
(* 1/2 (pow x 2))
(.f64 #s(literal 1/2 binary64) (.f64 x x))
(* 1/2 (pow x 2))
(.f64 #s(literal 1/2 binary64) (.f64 x x))
(* 1/2 (pow x 2))
(.f64 #s(literal 1/2 binary64) (.f64 x x))
(* 1/2 (pow x 2))
(.f64 #s(literal 1/2 binary64) (.f64 x x))
(* 1/2 (pow x 2))
(.f64 #s(literal 1/2 binary64) (.f64 x x))
(* 1/2 (pow x 2))
(.f64 #s(literal 1/2 binary64) (.f64 x x))
(* 1/2 (pow x 2))
(.f64 #s(literal 1/2 binary64) (.f64 x x))
(* 1/2 (pow x 2))
(.f64 #s(literal 1/2 binary64) (.f64 x x))
(* 1/2 (pow x 2))
(.f64 #s(literal 1/2 binary64) (.f64 x x))
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(* 1/2 (pow x 2))
(.f64 #s(literal 1/2 binary64) (.f64 x x))
(* (pow x 2) (+ 1/2 (* -1/24 (pow x 2))))
(.f64 x (.f64 x (fma.f64 x (*.f64 x #s(literal -1/24 binary64)) #s(literal 1/2 binary64))))
(* (pow x 2) (+ 1/2 (* (pow x 2) (- (* 1/720 (pow x 2)) 1/24))))
(.f64 x (.f64 x (fma.f64 (.f64 x x) (fma.f64 (.f64 x x) #s(literal 1/720 binary64) #s(literal -1/24 binary64)) #s(literal 1/2 binary64))))
(* (pow x 2) (+ 1/2 (* (pow x 2) (- (* (pow x 2) (+ 1/720 (* -1/40320 (pow x 2)))) 1/24))))
(.f64 (.f64 x x) (fma.f64 (.f64 x x) (fma.f64 (.f64 x x) (fma.f64 (*.f64 x x) #s(literal -1/40320 binary64) #s(literal 1/720 binary64)) #s(literal -1/24 binary64)) #s(literal 1/2 binary64)))
(- 1 (cos x))
(-.f64 #s(literal 1 binary64) (cos.f64 x))
(- 1 (cos x))
(-.f64 #s(literal 1 binary64) (cos.f64 x))
(- 1 (cos x))
(-.f64 #s(literal 1 binary64) (cos.f64 x))
(- 1 (cos x))
(-.f64 #s(literal 1 binary64) (cos.f64 x))
(- 1 (cos x))
(-.f64 #s(literal 1 binary64) (cos.f64 x))
(- 1 (cos x))
(-.f64 #s(literal 1 binary64) (cos.f64 x))
(- 1 (cos x))
(-.f64 #s(literal 1 binary64) (cos.f64 x))
(- 1 (cos x))
(-.f64 #s(literal 1 binary64) (cos.f64 x))
(* 1/2 (pow x 2))
(.f64 #s(literal 1/2 binary64) (.f64 x x))
(* (pow x 2) (+ 1/2 (* -1/24 (pow x 2))))
(.f64 x (.f64 x (fma.f64 x (*.f64 x #s(literal -1/24 binary64)) #s(literal 1/2 binary64))))
(* (pow x 2) (+ 1/2 (* (pow x 2) (- (* 1/720 (pow x 2)) 1/24))))
(.f64 x (.f64 x (fma.f64 (.f64 x x) (fma.f64 (.f64 x x) #s(literal 1/720 binary64) #s(literal -1/24 binary64)) #s(literal 1/2 binary64))))
(* (pow x 2) (+ 1/2 (* (pow x 2) (- (* (pow x 2) (+ 1/720 (* -1/40320 (pow x 2)))) 1/24))))
(.f64 (.f64 x x) (fma.f64 (.f64 x x) (fma.f64 (.f64 x x) (fma.f64 (*.f64 x x) #s(literal -1/40320 binary64) #s(literal 1/720 binary64)) #s(literal -1/24 binary64)) #s(literal 1/2 binary64)))
(* -1/40320 (pow x 8))
(*.f64 #s(literal -1/40320 binary64) (pow.f64 x #s(literal 8 binary64)))
(* (pow x 8) (- (* 1/720 (/ 1 (pow x 2))) 1/40320))
(.f64 (pow.f64 x #s(literal 8 binary64)) (-.f64 #s(literal -1/40320 binary64) (/.f64 #s(literal -1/720 binary64) (.f64 x x))))
(* (pow x 8) (- (* 1/720 (/ 1 (pow x 2))) (+ 1/40320 (/ 1/24 (pow x 4)))))
(.f64 (pow.f64 x #s(literal 8 binary64)) (+.f64 (-.f64 #s(literal -1/40320 binary64) (/.f64 #s(literal -1/720 binary64) (.f64 x x))) (/.f64 #s(literal -1/24 binary64) (.f64 x (.f64 x (*.f64 x x))))))
(* (pow x 8) (- (+ (* 1/720 (/ 1 (pow x 2))) (* 1/2 (/ 1 (pow x 6)))) (+ 1/40320 (/ 1/24 (pow x 4)))))
(.f64 (pow.f64 x #s(literal 8 binary64)) (+.f64 (-.f64 #s(literal -1/40320 binary64) (/.f64 #s(literal -1/720 binary64) (.f64 x x))) (+.f64 (/.f64 #s(literal 1/2 binary64) (pow.f64 x #s(literal 6 binary64))) (/.f64 #s(literal -1/24 binary64) (.f64 x (.f64 x (*.f64 x x)))))))
(* -1/40320 (pow x 8))
(*.f64 #s(literal -1/40320 binary64) (pow.f64 x #s(literal 8 binary64)))
(* (pow x 8) (- (* 1/720 (/ 1 (pow x 2))) 1/40320))
(.f64 (pow.f64 x #s(literal 8 binary64)) (-.f64 #s(literal -1/40320 binary64) (/.f64 #s(literal -1/720 binary64) (.f64 x x))))
(* (pow x 8) (- (* 1/720 (/ 1 (pow x 2))) (+ 1/40320 (/ 1/24 (pow x 4)))))
(.f64 (pow.f64 x #s(literal 8 binary64)) (+.f64 (-.f64 #s(literal -1/40320 binary64) (/.f64 #s(literal -1/720 binary64) (.f64 x x))) (/.f64 #s(literal -1/24 binary64) (.f64 x (.f64 x (*.f64 x x))))))
(* (pow x 8) (- (+ (* 1/720 (/ 1 (pow x 2))) (* 1/2 (/ 1 (pow x 6)))) (+ 1/40320 (/ 1/24 (pow x 4)))))
(.f64 (pow.f64 x #s(literal 8 binary64)) (+.f64 (-.f64 #s(literal -1/40320 binary64) (/.f64 #s(literal -1/720 binary64) (.f64 x x))) (+.f64 (/.f64 #s(literal 1/2 binary64) (pow.f64 x #s(literal 6 binary64))) (/.f64 #s(literal -1/24 binary64) (.f64 x (.f64 x (*.f64 x x)))))))
(* 1/2 x)
(*.f64 #s(literal 1/2 binary64) x)
(* x (+ 1/2 (* -1/24 (pow x 2))))
(.f64 x (fma.f64 x (.f64 x #s(literal -1/24 binary64)) #s(literal 1/2 binary64)))
(* x (+ 1/2 (* (pow x 2) (- (* 1/720 (pow x 2)) 1/24))))
(.f64 x (fma.f64 (.f64 x x) (fma.f64 (*.f64 x x) #s(literal 1/720 binary64) #s(literal -1/24 binary64)) #s(literal 1/2 binary64)))
(* x (+ 1/2 (* (pow x 2) (- (* (pow x 2) (+ 1/720 (* -1/40320 (pow x 2)))) 1/24))))
(.f64 x (fma.f64 (.f64 x x) (fma.f64 (.f64 x x) (fma.f64 (.f64 x x) #s(literal -1/40320 binary64) #s(literal 1/720 binary64)) #s(literal -1/24 binary64)) #s(literal 1/2 binary64)))
(* -1/40320 (pow x 7))
(*.f64 #s(literal -1/40320 binary64) (pow.f64 x #s(literal 7 binary64)))
(* (pow x 7) (- (* 1/720 (/ 1 (pow x 2))) 1/40320))
(.f64 (-.f64 #s(literal -1/40320 binary64) (/.f64 #s(literal -1/720 binary64) (.f64 x x))) (pow.f64 x #s(literal 7 binary64)))
(* (pow x 7) (- (* 1/720 (/ 1 (pow x 2))) (+ 1/40320 (/ 1/24 (pow x 4)))))
(.f64 (+.f64 (-.f64 #s(literal -1/40320 binary64) (/.f64 #s(literal -1/720 binary64) (.f64 x x))) (/.f64 #s(literal -1/24 binary64) (.f64 x (.f64 x (*.f64 x x))))) (pow.f64 x #s(literal 7 binary64)))
(* (pow x 7) (- (+ (* 1/720 (/ 1 (pow x 2))) (* 1/2 (/ 1 (pow x 6)))) (+ 1/40320 (/ 1/24 (pow x 4)))))
(.f64 (+.f64 (-.f64 #s(literal -1/40320 binary64) (/.f64 #s(literal -1/720 binary64) (.f64 x x))) (+.f64 (/.f64 #s(literal 1/2 binary64) (pow.f64 x #s(literal 6 binary64))) (/.f64 #s(literal -1/24 binary64) (.f64 x (.f64 x (*.f64 x x)))))) (pow.f64 x #s(literal 7 binary64)))
(* -1/40320 (pow x 7))
(*.f64 #s(literal -1/40320 binary64) (pow.f64 x #s(literal 7 binary64)))
(* -1 (* (pow x 7) (- 1/40320 (* 1/720 (/ 1 (pow x 2))))))
(.f64 (-.f64 #s(literal -1/40320 binary64) (/.f64 #s(literal -1/720 binary64) (.f64 x x))) (pow.f64 x #s(literal 7 binary64)))
(* -1 (* (pow x 7) (- (+ 1/40320 (/ 1/24 (pow x 4))) (* 1/720 (/ 1 (pow x 2))))))
(.f64 (+.f64 (-.f64 #s(literal -1/40320 binary64) (/.f64 #s(literal -1/720 binary64) (.f64 x x))) (/.f64 #s(literal -1/24 binary64) (.f64 x (.f64 x (*.f64 x x))))) (pow.f64 x #s(literal 7 binary64)))
(* -1 (* (pow x 7) (- (+ 1/40320 (/ 1/24 (pow x 4))) (+ (* 1/720 (/ 1 (pow x 2))) (* 1/2 (/ 1 (pow x 6)))))))
(.f64 (+.f64 (-.f64 #s(literal -1/40320 binary64) (/.f64 #s(literal -1/720 binary64) (.f64 x x))) (+.f64 (/.f64 #s(literal 1/2 binary64) (pow.f64 x #s(literal 6 binary64))) (/.f64 #s(literal -1/24 binary64) (.f64 x (.f64 x (*.f64 x x)))))) (pow.f64 x #s(literal 7 binary64)))
1/2
#s(literal 1/2 binary64)
(+ 1/2 (* -1/24 (pow x 2)))
(fma.f64 x (*.f64 x #s(literal -1/24 binary64)) #s(literal 1/2 binary64))
(+ 1/2 (* (pow x 2) (- (* 1/720 (pow x 2)) 1/24)))
(fma.f64 (.f64 x x) (fma.f64 (.f64 x x) #s(literal 1/720 binary64) #s(literal -1/24 binary64)) #s(literal 1/2 binary64))
(+ 1/2 (* (pow x 2) (- (* (pow x 2) (+ 1/720 (* -1/40320 (pow x 2)))) 1/24)))
(fma.f64 (.f64 x x) (fma.f64 (.f64 x x) (fma.f64 (*.f64 x x) #s(literal -1/40320 binary64) #s(literal 1/720 binary64)) #s(literal -1/24 binary64)) #s(literal 1/2 binary64))
(* -1/40320 (pow x 6))
(*.f64 #s(literal -1/40320 binary64) (pow.f64 x #s(literal 6 binary64)))
(* (pow x 6) (- (* 1/720 (/ 1 (pow x 2))) 1/40320))
(.f64 (-.f64 #s(literal -1/40320 binary64) (/.f64 #s(literal -1/720 binary64) (.f64 x x))) (pow.f64 x #s(literal 6 binary64)))
(* (pow x 6) (- (* 1/720 (/ 1 (pow x 2))) (+ 1/40320 (/ 1/24 (pow x 4)))))
(.f64 (+.f64 (-.f64 #s(literal -1/40320 binary64) (/.f64 #s(literal -1/720 binary64) (.f64 x x))) (/.f64 #s(literal -1/24 binary64) (.f64 x (.f64 x (*.f64 x x))))) (pow.f64 x #s(literal 6 binary64)))
(* (pow x 6) (- (+ (* 1/720 (/ 1 (pow x 2))) (* 1/2 (/ 1 (pow x 6)))) (+ 1/40320 (/ 1/24 (pow x 4)))))
(fma.f64 (+.f64 (-.f64 #s(literal -1/40320 binary64) (/.f64 #s(literal -1/720 binary64) (.f64 x x))) (/.f64 #s(literal -1/24 binary64) (.f64 x (.f64 x (.f64 x x))))) (pow.f64 x #s(literal 6 binary64)) #s(literal 1/2 binary64))
(* -1/40320 (pow x 6))
(*.f64 #s(literal -1/40320 binary64) (pow.f64 x #s(literal 6 binary64)))
(* (pow x 6) (- (* 1/720 (/ 1 (pow x 2))) 1/40320))
(.f64 (-.f64 #s(literal -1/40320 binary64) (/.f64 #s(literal -1/720 binary64) (.f64 x x))) (pow.f64 x #s(literal 6 binary64)))
(* (pow x 6) (- (* 1/720 (/ 1 (pow x 2))) (+ 1/40320 (/ 1/24 (pow x 4)))))
(.f64 (+.f64 (-.f64 #s(literal -1/40320 binary64) (/.f64 #s(literal -1/720 binary64) (.f64 x x))) (/.f64 #s(literal -1/24 binary64) (.f64 x (.f64 x (*.f64 x x))))) (pow.f64 x #s(literal 6 binary64)))
(* (pow x 6) (- (+ (* 1/720 (/ 1 (pow x 2))) (* 1/2 (/ 1 (pow x 6)))) (+ 1/40320 (/ 1/24 (pow x 4)))))
(fma.f64 (+.f64 (-.f64 #s(literal -1/40320 binary64) (/.f64 #s(literal -1/720 binary64) (.f64 x x))) (/.f64 #s(literal -1/24 binary64) (.f64 x (.f64 x (.f64 x x))))) (pow.f64 x #s(literal 6 binary64)) #s(literal 1/2 binary64))
(* 1/2 (pow x 2))
(.f64 #s(literal 1/2 binary64) (.f64 x x))
(* (pow x 2) (+ 1/2 (* -1/24 (pow x 2))))
(.f64 x (.f64 x (fma.f64 x (*.f64 x #s(literal -1/24 binary64)) #s(literal 1/2 binary64))))
(* (pow x 2) (+ 1/2 (* (pow x 2) (- (* 1/720 (pow x 2)) 1/24))))
(.f64 x (.f64 x (fma.f64 (.f64 x x) (fma.f64 (.f64 x x) #s(literal 1/720 binary64) #s(literal -1/24 binary64)) #s(literal 1/2 binary64))))
(* (pow x 2) (+ 1/2 (* (pow x 2) (- (* (pow x 2) (+ 1/720 (* -1/40320 (pow x 2)))) 1/24))))
(.f64 (.f64 x x) (fma.f64 (.f64 x x) (fma.f64 (.f64 x x) (fma.f64 (*.f64 x x) #s(literal -1/40320 binary64) #s(literal 1/720 binary64)) #s(literal -1/24 binary64)) #s(literal 1/2 binary64)))
(- 1 (cos x))
(-.f64 #s(literal 1 binary64) (cos.f64 x))
(- 1 (cos x))
(-.f64 #s(literal 1 binary64) (cos.f64 x))
(- 1 (cos x))
(-.f64 #s(literal 1 binary64) (cos.f64 x))
(- 1 (cos x))
(-.f64 #s(literal 1 binary64) (cos.f64 x))
(- 1 (cos x))
(-.f64 #s(literal 1 binary64) (cos.f64 x))
(- 1 (cos x))
(-.f64 #s(literal 1 binary64) (cos.f64 x))
(- 1 (cos x))
(-.f64 #s(literal 1 binary64) (cos.f64 x))
(- 1 (cos x))
(-.f64 #s(literal 1 binary64) (cos.f64 x))
(* 1/2 (pow x 2))
(.f64 #s(literal 1/2 binary64) (.f64 x x))
(* (pow x 2) (+ 1/2 (* -1/24 (pow x 2))))
(.f64 x (.f64 x (fma.f64 x (*.f64 x #s(literal -1/24 binary64)) #s(literal 1/2 binary64))))
(* (pow x 2) (+ 1/2 (* -1/24 (pow x 2))))
(.f64 x (.f64 x (fma.f64 x (*.f64 x #s(literal -1/24 binary64)) #s(literal 1/2 binary64))))
(* (pow x 2) (+ 1/2 (* -1/24 (pow x 2))))
(.f64 x (.f64 x (fma.f64 x (*.f64 x #s(literal -1/24 binary64)) #s(literal 1/2 binary64))))
(* -1/24 (pow x 4))
(.f64 #s(literal -1/24 binary64) (.f64 x (.f64 x (.f64 x x))))
(* (pow x 4) (- (* 1/2 (/ 1 (pow x 2))) 1/24))
(.f64 x (.f64 x (fma.f64 x (*.f64 x #s(literal -1/24 binary64)) #s(literal 1/2 binary64))))
(* (pow x 4) (- (* 1/2 (/ 1 (pow x 2))) 1/24))
(.f64 x (.f64 x (fma.f64 x (*.f64 x #s(literal -1/24 binary64)) #s(literal 1/2 binary64))))
(* (pow x 4) (- (* 1/2 (/ 1 (pow x 2))) 1/24))
(.f64 x (.f64 x (fma.f64 x (*.f64 x #s(literal -1/24 binary64)) #s(literal 1/2 binary64))))
(* -1/24 (pow x 4))
(.f64 #s(literal -1/24 binary64) (.f64 x (.f64 x (.f64 x x))))
(* (pow x 4) (- (* 1/2 (/ 1 (pow x 2))) 1/24))
(.f64 x (.f64 x (fma.f64 x (*.f64 x #s(literal -1/24 binary64)) #s(literal 1/2 binary64))))
(* (pow x 4) (- (* 1/2 (/ 1 (pow x 2))) 1/24))
(.f64 x (.f64 x (fma.f64 x (*.f64 x #s(literal -1/24 binary64)) #s(literal 1/2 binary64))))
(* (pow x 4) (- (* 1/2 (/ 1 (pow x 2))) 1/24))
(.f64 x (.f64 x (fma.f64 x (*.f64 x #s(literal -1/24 binary64)) #s(literal 1/2 binary64))))
1/2
#s(literal 1/2 binary64)
(+ 1/2 (* -1/24 (pow x 2)))
(fma.f64 x (*.f64 x #s(literal -1/24 binary64)) #s(literal 1/2 binary64))
(+ 1/2 (* -1/24 (pow x 2)))
(fma.f64 x (*.f64 x #s(literal -1/24 binary64)) #s(literal 1/2 binary64))
(+ 1/2 (* -1/24 (pow x 2)))
(fma.f64 x (*.f64 x #s(literal -1/24 binary64)) #s(literal 1/2 binary64))
(* -1/24 (pow x 2))
(.f64 x (.f64 x #s(literal -1/24 binary64)))
(* (pow x 2) (- (* 1/2 (/ 1 (pow x 2))) 1/24))
(fma.f64 x (*.f64 x #s(literal -1/24 binary64)) #s(literal 1/2 binary64))
(* (pow x 2) (- (* 1/2 (/ 1 (pow x 2))) 1/24))
(fma.f64 x (*.f64 x #s(literal -1/24 binary64)) #s(literal 1/2 binary64))
(* (pow x 2) (- (* 1/2 (/ 1 (pow x 2))) 1/24))
(fma.f64 x (*.f64 x #s(literal -1/24 binary64)) #s(literal 1/2 binary64))
(* -1/24 (pow x 2))
(.f64 x (.f64 x #s(literal -1/24 binary64)))
(* (pow x 2) (- (* 1/2 (/ 1 (pow x 2))) 1/24))
(fma.f64 x (*.f64 x #s(literal -1/24 binary64)) #s(literal 1/2 binary64))
(* (pow x 2) (- (* 1/2 (/ 1 (pow x 2))) 1/24))
(fma.f64 x (*.f64 x #s(literal -1/24 binary64)) #s(literal 1/2 binary64))
(* (pow x 2) (- (* 1/2 (/ 1 (pow x 2))) 1/24))
(fma.f64 x (*.f64 x #s(literal -1/24 binary64)) #s(literal 1/2 binary64))
(* 1/2 (pow x 2))
(.f64 #s(literal 1/2 binary64) (.f64 x x))
(* (pow x 2) (+ 1/2 (* -1/24 (pow x 2))))
(.f64 x (.f64 x (fma.f64 x (*.f64 x #s(literal -1/24 binary64)) #s(literal 1/2 binary64))))
(* (pow x 2) (+ 1/2 (* (pow x 2) (- (* 1/720 (pow x 2)) 1/24))))
(.f64 x (.f64 x (fma.f64 (.f64 x x) (fma.f64 (.f64 x x) #s(literal 1/720 binary64) #s(literal -1/24 binary64)) #s(literal 1/2 binary64))))
(* (pow x 2) (+ 1/2 (* (pow x 2) (- (* (pow x 2) (+ 1/720 (* -1/40320 (pow x 2)))) 1/24))))
(.f64 (.f64 x x) (fma.f64 (.f64 x x) (fma.f64 (.f64 x x) (fma.f64 (*.f64 x x) #s(literal -1/40320 binary64) #s(literal 1/720 binary64)) #s(literal -1/24 binary64)) #s(literal 1/2 binary64)))
(- 1 (cos x))
(-.f64 #s(literal 1 binary64) (cos.f64 x))
(- 1 (cos x))
(-.f64 #s(literal 1 binary64) (cos.f64 x))
(- 1 (cos x))
(-.f64 #s(literal 1 binary64) (cos.f64 x))
(- 1 (cos x))
(-.f64 #s(literal 1 binary64) (cos.f64 x))
(- 1 (cos x))
(-.f64 #s(literal 1 binary64) (cos.f64 x))
(- 1 (cos x))
(-.f64 #s(literal 1 binary64) (cos.f64 x))
(- 1 (cos x))
(-.f64 #s(literal 1 binary64) (cos.f64 x))
(- 1 (cos x))
(-.f64 #s(literal 1 binary64) (cos.f64 x))
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 x (.f64 x (fma.f64 x (.f64 x #s(literal 1/24 binary64)) #s(literal -1/2 binary64))) #s(literal 1 binary64))
(+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))) 1/2)))
(fma.f64 (.f64 x x) (fma.f64 x (.f64 x (fma.f64 (*.f64 x x) #s(literal -1/720 binary64) #s(literal 1/24 binary64))) #s(literal -1/2 binary64)) #s(literal 1 binary64))
(cos x)
(cos.f64 x)
(cos x)
(cos.f64 x)
(cos x)
(cos.f64 x)
(cos x)
(cos.f64 x)
(cos x)
(cos.f64 x)
(cos x)
(cos.f64 x)
(cos x)
(cos.f64 x)
(cos x)
(cos.f64 x)
(* -1/24 x)
(*.f64 x #s(literal -1/24 binary64))
(* x (- (* 1/720 (pow x 2)) 1/24))
(.f64 x (fma.f64 (.f64 x x) #s(literal 1/720 binary64) #s(literal -1/24 binary64)))
(* x (- (* (pow x 2) (+ 1/720 (* -1/40320 (pow x 2)))) 1/24))
(.f64 x (fma.f64 (.f64 x x) (fma.f64 (*.f64 x x) #s(literal -1/40320 binary64) #s(literal 1/720 binary64)) #s(literal -1/24 binary64)))
(* x (- (* (pow x 2) (+ 1/720 (* -1/40320 (pow x 2)))) 1/24))
(.f64 x (fma.f64 (.f64 x x) (fma.f64 (*.f64 x x) #s(literal -1/40320 binary64) #s(literal 1/720 binary64)) #s(literal -1/24 binary64)))
(* -1/40320 (pow x 5))
(.f64 (.f64 x x) (.f64 #s(literal -1/40320 binary64) (.f64 x (*.f64 x x))))
(* (pow x 5) (- (* 1/720 (/ 1 (pow x 2))) 1/40320))
(.f64 (-.f64 #s(literal -1/40320 binary64) (/.f64 #s(literal -1/720 binary64) (.f64 x x))) (.f64 (.f64 x (.f64 x (.f64 x x))) x))
(* (pow x 5) (- (* 1/720 (/ 1 (pow x 2))) (+ 1/40320 (/ 1/24 (pow x 4)))))
(.f64 (+.f64 (-.f64 #s(literal -1/40320 binary64) (/.f64 #s(literal -1/720 binary64) (.f64 x x))) (/.f64 #s(literal -1/24 binary64) (.f64 x (.f64 x (.f64 x x))))) (.f64 (.f64 x (.f64 x (*.f64 x x))) x))
(* (pow x 5) (- (* 1/720 (/ 1 (pow x 2))) (+ 1/40320 (/ 1/24 (pow x 4)))))
(.f64 (+.f64 (-.f64 #s(literal -1/40320 binary64) (/.f64 #s(literal -1/720 binary64) (.f64 x x))) (/.f64 #s(literal -1/24 binary64) (.f64 x (.f64 x (.f64 x x))))) (.f64 (.f64 x (.f64 x (*.f64 x x))) x))
(* -1/40320 (pow x 5))
(.f64 (.f64 x x) (.f64 #s(literal -1/40320 binary64) (.f64 x (*.f64 x x))))
(* -1 (* (pow x 5) (- 1/40320 (* 1/720 (/ 1 (pow x 2))))))
(.f64 (-.f64 #s(literal -1/40320 binary64) (/.f64 #s(literal -1/720 binary64) (.f64 x x))) (.f64 (.f64 x (.f64 x (.f64 x x))) x))
(* -1 (* (pow x 5) (- (+ 1/40320 (/ 1/24 (pow x 4))) (* 1/720 (/ 1 (pow x 2))))))
(.f64 (+.f64 (-.f64 #s(literal -1/40320 binary64) (/.f64 #s(literal -1/720 binary64) (.f64 x x))) (/.f64 #s(literal -1/24 binary64) (.f64 x (.f64 x (.f64 x x))))) (.f64 (.f64 x (.f64 x (*.f64 x x))) x))
(* -1 (* (pow x 5) (- (+ 1/40320 (/ 1/24 (pow x 4))) (* 1/720 (/ 1 (pow x 2))))))
(.f64 (+.f64 (-.f64 #s(literal -1/40320 binary64) (/.f64 #s(literal -1/720 binary64) (.f64 x x))) (/.f64 #s(literal -1/24 binary64) (.f64 x (.f64 x (.f64 x x))))) (.f64 (.f64 x (.f64 x (*.f64 x x))) x))
1/720
#s(literal 1/720 binary64)
(+ 1/720 (* -1/40320 (pow x 2)))
(fma.f64 (*.f64 x x) #s(literal -1/40320 binary64) #s(literal 1/720 binary64))
(+ 1/720 (* -1/40320 (pow x 2)))
(fma.f64 (*.f64 x x) #s(literal -1/40320 binary64) #s(literal 1/720 binary64))
(+ 1/720 (* -1/40320 (pow x 2)))
(fma.f64 (*.f64 x x) #s(literal -1/40320 binary64) #s(literal 1/720 binary64))
(* -1/40320 (pow x 2))
(.f64 (.f64 x x) #s(literal -1/40320 binary64))
(* (pow x 2) (- (* 1/720 (/ 1 (pow x 2))) 1/40320))
(fma.f64 (*.f64 x x) #s(literal -1/40320 binary64) #s(literal 1/720 binary64))
(* (pow x 2) (- (* 1/720 (/ 1 (pow x 2))) 1/40320))
(fma.f64 (*.f64 x x) #s(literal -1/40320 binary64) #s(literal 1/720 binary64))
(* (pow x 2) (- (* 1/720 (/ 1 (pow x 2))) 1/40320))
(fma.f64 (*.f64 x x) #s(literal -1/40320 binary64) #s(literal 1/720 binary64))
(* -1/40320 (pow x 2))
(.f64 (.f64 x x) #s(literal -1/40320 binary64))
(* (pow x 2) (- (* 1/720 (/ 1 (pow x 2))) 1/40320))
(fma.f64 (*.f64 x x) #s(literal -1/40320 binary64) #s(literal 1/720 binary64))
(* (pow x 2) (- (* 1/720 (/ 1 (pow x 2))) 1/40320))
(fma.f64 (*.f64 x x) #s(literal -1/40320 binary64) #s(literal 1/720 binary64))
(* (pow x 2) (- (* 1/720 (/ 1 (pow x 2))) 1/40320))
(fma.f64 (*.f64 x x) #s(literal -1/40320 binary64) #s(literal 1/720 binary64))

rewrite438.0ms (5%)

Memory

40.8MiB live, 727.5MiB allocated

Algorithm

1×	batch-egg-rewrite

Rules

6 146×	`lower-fma.f32`
6 138×	`lower-fma.f64`
4 756×	`lower-*.f32`
4 742×	`lower-*.f64`
3 684×	`lower-/.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	24	157
0	40	157
1	169	157
2	1188	157
0	8220	157

Stop Event

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

Counts

14 → 394

Calls

Call 1

Inputs
#s(approx (- 1 (cos x)) (.f64 #s(literal 1/2 binary64) (.f64 x x)))
(.f64 #s(literal 1/2 binary64) (.f64 x x))
(*.f64 x x)
#s(approx (- 1 (cos x)) (.f64 x (.f64 x (fma.f64 x (.f64 x (fma.f64 (.f64 x x) (fma.f64 x (*.f64 x #s(literal -1/40320 binary64)) #s(literal 1/720 binary64)) #s(literal -1/24 binary64))) #s(literal 1/2 binary64)))))
(.f64 x (.f64 x (fma.f64 x (.f64 x (fma.f64 (.f64 x x) (fma.f64 x (*.f64 x #s(literal -1/40320 binary64)) #s(literal 1/720 binary64)) #s(literal -1/24 binary64))) #s(literal 1/2 binary64))))
(.f64 x (fma.f64 x (.f64 x (fma.f64 (.f64 x x) (fma.f64 x (.f64 x #s(literal -1/40320 binary64)) #s(literal 1/720 binary64)) #s(literal -1/24 binary64))) #s(literal 1/2 binary64)))
(fma.f64 x (.f64 x (fma.f64 (.f64 x x) (fma.f64 x (*.f64 x #s(literal -1/40320 binary64)) #s(literal 1/720 binary64)) #s(literal -1/24 binary64))) #s(literal 1/2 binary64))
#s(approx (- 1 (cos x)) (.f64 (.f64 x x) (fma.f64 (*.f64 x x) #s(literal -1/24 binary64) #s(literal 1/2 binary64))))
(.f64 (.f64 x x) (fma.f64 (*.f64 x x) #s(literal -1/24 binary64) #s(literal 1/2 binary64)))
(fma.f64 (*.f64 x x) #s(literal -1/24 binary64) #s(literal 1/2 binary64))
(-.f64 #s(literal 1 binary64) #s(approx (cos x) #s(literal 1 binary64)))
#s(approx (cos x) #s(literal 1 binary64))
(.f64 x (fma.f64 (.f64 x x) (fma.f64 x (*.f64 x #s(literal -1/40320 binary64)) #s(literal 1/720 binary64)) #s(literal -1/24 binary64)))
(fma.f64 x (*.f64 x #s(literal -1/40320 binary64)) #s(literal 1/720 binary64))

Outputs
#s(approx (- 1 (cos x)) (.f64 #s(literal 1/2 binary64) (.f64 x x)))
(.f64 x (.f64 x #s(literal 1/2 binary64)))
(.f64 #s(literal 1/2 binary64) (.f64 x x))
(.f64 (.f64 x x) #s(literal 1/2 binary64))
(.f64 (.f64 x #s(literal 1/2 binary64)) x)
(exp.f64 (*.f64 (log.f64 x) #s(literal 2 binary64)))
(pow.f64 x #s(literal 2 binary64))
(pow.f64 (*.f64 x x) #s(literal 1 binary64))
(pow.f64 (exp.f64 (log.f64 x)) #s(literal 2 binary64))
(*.f64 x x)
(*.f64 (exp.f64 (log.f64 x)) (exp.f64 (log.f64 x)))
#s(approx (- 1 (cos x)) (.f64 x (.f64 x (fma.f64 (.f64 x x) (fma.f64 (.f64 x x) (fma.f64 x (*.f64 x #s(literal -1/40320 binary64)) #s(literal 1/720 binary64)) #s(literal -1/24 binary64)) #s(literal 1/2 binary64)))))
(+.f64 (.f64 #s(literal 1/2 binary64) (.f64 x x)) (.f64 x (.f64 (.f64 x x) (.f64 x (fma.f64 (.f64 x x) (fma.f64 x (.f64 x #s(literal -1/40320 binary64)) #s(literal 1/720 binary64)) #s(literal -1/24 binary64))))))
(+.f64 (.f64 #s(literal 1/2 binary64) (.f64 x x)) (.f64 (.f64 x x) (.f64 (.f64 x x) (fma.f64 (.f64 x x) (fma.f64 x (.f64 x #s(literal -1/40320 binary64)) #s(literal 1/720 binary64)) #s(literal -1/24 binary64)))))
(+.f64 (.f64 #s(literal 1/2 binary64) (.f64 x x)) (.f64 (.f64 (.f64 x x) (.f64 x (fma.f64 (.f64 x x) (fma.f64 x (.f64 x #s(literal -1/40320 binary64)) #s(literal 1/720 binary64)) #s(literal -1/24 binary64)))) x))
(+.f64 (.f64 #s(literal 1/2 binary64) (.f64 x x)) (.f64 (.f64 (.f64 x x) (fma.f64 (.f64 x x) (fma.f64 x (.f64 x #s(literal -1/40320 binary64)) #s(literal 1/720 binary64)) #s(literal -1/24 binary64))) (.f64 x x)))
(+.f64 (.f64 x (.f64 (.f64 x x) (.f64 x (fma.f64 (.f64 x x) (fma.f64 x (.f64 x #s(literal -1/40320 binary64)) #s(literal 1/720 binary64)) #s(literal -1/24 binary64))))) (.f64 #s(literal 1/2 binary64) (.f64 x x)))
(+.f64 (.f64 (.f64 x x) (.f64 (.f64 x x) (fma.f64 (.f64 x x) (fma.f64 x (.f64 x #s(literal -1/40320 binary64)) #s(literal 1/720 binary64)) #s(literal -1/24 binary64)))) (.f64 #s(literal 1/2 binary64) (.f64 x x)))
(+.f64 (.f64 (.f64 (.f64 x x) (.f64 x (fma.f64 (.f64 x x) (fma.f64 x (.f64 x #s(literal -1/40320 binary64)) #s(literal 1/720 binary64)) #s(literal -1/24 binary64)))) x) (.f64 #s(literal 1/2 binary64) (.f64 x x)))
(+.f64 (.f64 (.f64 (.f64 x x) (fma.f64 (.f64 x x) (fma.f64 x (.f64 x #s(literal -1/40320 binary64)) #s(literal 1/720 binary64)) #s(literal -1/24 binary64))) (.f64 x x)) (.f64 #s(literal 1/2 binary64) (.f64 x x)))
(fma.f64 x (.f64 x #s(literal 1/2 binary64)) (.f64 x (.f64 (.f64 x x) (.f64 x (fma.f64 (.f64 x x) (fma.f64 x (*.f64 x #s(literal -1/40320 binary64)) #s(literal 1/720 binary64)) #s(literal -1/24 binary64))))))
(fma.f64 x (.f64 x #s(literal 1/2 binary64)) (.f64 (.f64 x x) (.f64 (.f64 x x) (fma.f64 (.f64 x x) (fma.f64 x (*.f64 x #s(literal -1/40320 binary64)) #s(literal 1/720 binary64)) #s(literal -1/24 binary64)))))
(fma.f64 x (.f64 x #s(literal 1/2 binary64)) (.f64 (.f64 (.f64 x x) (.f64 x (fma.f64 (.f64 x x) (fma.f64 x (*.f64 x #s(literal -1/40320 binary64)) #s(literal 1/720 binary64)) #s(literal -1/24 binary64)))) x))
(fma.f64 x (.f64 x #s(literal 1/2 binary64)) (.f64 (.f64 (.f64 x x) (fma.f64 (.f64 x x) (fma.f64 x (.f64 x #s(literal -1/40320 binary64)) #s(literal 1/720 binary64)) #s(literal -1/24 binary64))) (*.f64 x x)))
(fma.f64 x (.f64 (.f64 x x) (.f64 x (fma.f64 (.f64 x x) (fma.f64 x (.f64 x #s(literal -1/40320 binary64)) #s(literal 1/720 binary64)) #s(literal -1/24 binary64)))) (.f64 #s(literal 1/2 binary64) (*.f64 x x)))
(fma.f64 #s(literal 1/2 binary64) (.f64 x x) (.f64 x (.f64 (.f64 x x) (.f64 x (fma.f64 (.f64 x x) (fma.f64 x (*.f64 x #s(literal -1/40320 binary64)) #s(literal 1/720 binary64)) #s(literal -1/24 binary64))))))
(fma.f64 #s(literal 1/2 binary64) (.f64 x x) (.f64 (.f64 x x) (.f64 (.f64 x x) (fma.f64 (.f64 x x) (fma.f64 x (*.f64 x #s(literal -1/40320 binary64)) #s(literal 1/720 binary64)) #s(literal -1/24 binary64)))))
(fma.f64 #s(literal 1/2 binary64) (.f64 x x) (.f64 (.f64 (.f64 x x) (.f64 x (fma.f64 (.f64 x x) (fma.f64 x (*.f64 x #s(literal -1/40320 binary64)) #s(literal 1/720 binary64)) #s(literal -1/24 binary64)))) x))
(fma.f64 #s(literal 1/2 binary64) (.f64 x x) (.f64 (.f64 (.f64 x x) (fma.f64 (.f64 x x) (fma.f64 x (.f64 x #s(literal -1/40320 binary64)) #s(literal 1/720 binary64)) #s(literal -1/24 binary64))) (*.f64 x x)))
(fma.f64 (.f64 x x) #s(literal 1/2 binary64) (.f64 x (.f64 (.f64 x x) (.f64 x (fma.f64 (.f64 x x) (fma.f64 x (*.f64 x #s(literal -1/40320 binary64)) #s(literal 1/720 binary64)) #s(literal -1/24 binary64))))))
(fma.f64 (.f64 x x) #s(literal 1/2 binary64) (.f64 (.f64 x x) (.f64 (.f64 x x) (fma.f64 (.f64 x x) (fma.f64 x (*.f64 x #s(literal -1/40320 binary64)) #s(literal 1/720 binary64)) #s(literal -1/24 binary64)))))
(fma.f64 (.f64 x x) #s(literal 1/2 binary64) (.f64 (.f64 (.f64 x x) (.f64 x (fma.f64 (.f64 x x) (fma.f64 x (*.f64 x #s(literal -1/40320 binary64)) #s(literal 1/720 binary64)) #s(literal -1/24 binary64)))) x))
(fma.f64 (.f64 x x) #s(literal 1/2 binary64) (.f64 (.f64 (.f64 x x) (fma.f64 (.f64 x x) (fma.f64 x (.f64 x #s(literal -1/40320 binary64)) #s(literal 1/720 binary64)) #s(literal -1/24 binary64))) (*.f64 x x)))
(fma.f64 (.f64 x x) (.f64 (.f64 x x) (fma.f64 (.f64 x x) (fma.f64 x (.f64 x #s(literal -1/40320 binary64)) #s(literal 1/720 binary64)) #s(literal -1/24 binary64))) (.f64 #s(literal 1/2 binary64) (*.f64 x x)))
(fma.f64 (.f64 (.f64 x x) (fma.f64 (.f64 x x) (fma.f64 x (.f64 x #s(literal -1/40320 binary64)) #s(literal 1/720 binary64)) #s(literal -1/24 binary64))) (.f64 x x) (.f64 #s(literal 1/2 binary64) (*.f64 x x)))
(fma.f64 (.f64 x #s(literal 1/2 binary64)) x (.f64 x (.f64 (.f64 x x) (.f64 x (fma.f64 (.f64 x x) (fma.f64 x (*.f64 x #s(literal -1/40320 binary64)) #s(literal 1/720 binary64)) #s(literal -1/24 binary64))))))
(fma.f64 (.f64 x #s(literal 1/2 binary64)) x (.f64 (.f64 x x) (.f64 (.f64 x x) (fma.f64 (.f64 x x) (fma.f64 x (*.f64 x #s(literal -1/40320 binary64)) #s(literal 1/720 binary64)) #s(literal -1/24 binary64)))))
(fma.f64 (.f64 x #s(literal 1/2 binary64)) x (.f64 (.f64 (.f64 x x) (.f64 x (fma.f64 (.f64 x x) (fma.f64 x (*.f64 x #s(literal -1/40320 binary64)) #s(literal 1/720 binary64)) #s(literal -1/24 binary64)))) x))
(fma.f64 (.f64 x #s(literal 1/2 binary64)) x (.f64 (.f64 (.f64 x x) (fma.f64 (.f64 x x) (fma.f64 x (.f64 x #s(literal -1/40320 binary64)) #s(literal 1/720 binary64)) #s(literal -1/24 binary64))) (*.f64 x x)))
(fma.f64 (.f64 (.f64 x x) (.f64 x (fma.f64 (.f64 x x) (fma.f64 x (.f64 x #s(literal -1/40320 binary64)) #s(literal 1/720 binary64)) #s(literal -1/24 binary64)))) x (.f64 #s(literal 1/2 binary64) (*.f64 x x)))
(/.f64 #s(literal 1 binary64) (/.f64 (-.f64 (fma.f64 (.f64 x x) (.f64 (.f64 x x) (.f64 (fma.f64 (.f64 x x) (fma.f64 x (.f64 x #s(literal -1/40320 binary64)) #s(literal 1/720 binary64)) #s(literal -1/24 binary64)) (fma.f64 (.f64 x x) (fma.f64 x (.f64 x #s(literal -1/40320 binary64)) #s(literal 1/720 binary64)) #s(literal -1/24 binary64)))) #s(literal 1/4 binary64)) (.f64 (.f64 x x) (.f64 (fma.f64 (.f64 x x) (fma.f64 x (.f64 x #s(literal -1/40320 binary64)) #s(literal 1/720 binary64)) #s(literal -1/24 binary64)) #s(literal 1/2 binary64)))) (.f64 (.f64 x x) (fma.f64 (.f64 (.f64 x x) (fma.f64 (.f64 x x) (fma.f64 x (.f64 x #s(literal -1/40320 binary64)) #s(literal 1/720 binary64)) #s(literal -1/24 binary64))) (.f64 (.f64 x x) (.f64 (.f64 x x) (.f64 (fma.f64 (.f64 x x) (fma.f64 x (.f64 x #s(literal -1/40320 binary64)) #s(literal 1/720 binary64)) #s(literal -1/24 binary64)) (fma.f64 (.f64 x x) (fma.f64 x (.f64 x #s(literal -1/40320 binary64)) #s(literal 1/720 binary64)) #s(literal -1/24 binary64))))) #s(literal 1/8 binary64)))))
(/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 (.f64 x x) (fma.f64 (.f64 x x) (fma.f64 x (.f64 x #s(literal -1/40320 binary64)) #s(literal 1/720 binary64)) #s(literal -1/24 binary64)) #s(literal -1/2 binary64)) (.f64 (.f64 x x) (fma.f64 (.f64 x x) (.f64 (.f64 x x) (.f64 (fma.f64 (.f64 x x) (fma.f64 x (.f64 x #s(literal -1/40320 binary64)) #s(literal 1/720 binary64)) #s(literal -1/24 binary64)) (fma.f64 (.f64 x x) (fma.f64 x (*.f64 x #s(literal -1/40320 binary64)) #s(literal 1/720 binary64)) #s(literal -1/24 binary64)))) #s(literal -1/4 binary64)))))
(/.f64 (.f64 x x) (/.f64 #s(literal 1 binary64) (fma.f64 (.f64 x x) (fma.f64 (.f64 x x) (fma.f64 x (.f64 x #s(literal -1/40320 binary64)) #s(literal 1/720 binary64)) #s(literal -1/24 binary64)) #s(literal 1/2 binary64))))
(/.f64 (.f64 (.f64 x x) (fma.f64 (.f64 (.f64 x x) (fma.f64 (.f64 x x) (fma.f64 x (.f64 x #s(literal -1/40320 binary64)) #s(literal 1/720 binary64)) #s(literal -1/24 binary64))) (.f64 (.f64 x x) (.f64 (.f64 x x) (.f64 (fma.f64 (.f64 x x) (fma.f64 x (.f64 x #s(literal -1/40320 binary64)) #s(literal 1/720 binary64)) #s(literal -1/24 binary64)) (fma.f64 (.f64 x x) (fma.f64 x (.f64 x #s(literal -1/40320 binary64)) #s(literal 1/720 binary64)) #s(literal -1/24 binary64))))) #s(literal 1/8 binary64))) (-.f64 (fma.f64 (.f64 x x) (.f64 (.f64 x x) (.f64 (fma.f64 (.f64 x x) (fma.f64 x (.f64 x #s(literal -1/40320 binary64)) #s(literal 1/720 binary64)) #s(literal -1/24 binary64)) (fma.f64 (.f64 x x) (fma.f64 x (.f64 x #s(literal -1/40320 binary64)) #s(literal 1/720 binary64)) #s(literal -1/24 binary64)))) #s(literal 1/4 binary64)) (.f64 (.f64 x x) (.f64 (fma.f64 (.f64 x x) (fma.f64 x (.f64 x #s(literal -1/40320 binary64)) #s(literal 1/720 binary64)) #s(literal -1/24 binary64)) #s(literal 1/2 binary64)))))
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(/.f64 (neg.f64 (fma.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) #s(literal -1/65548320768000 binary64)) #s(literal 1/373248000 binary64))) (neg.f64 (+.f64 (fma.f64 (.f64 x x) (.f64 (.f64 x x) #s(literal 1/1625702400 binary64)) #s(literal 1/518400 binary64)) (.f64 (.f64 x x) #s(literal 1/29030400 binary64)))))
(/.f64 (neg.f64 (fma.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) #s(literal -1/65548320768000 binary64)) #s(literal 1/373248000 binary64))) (neg.f64 (+.f64 #s(literal 1/518400 binary64) (fma.f64 (.f64 x x) (.f64 (.f64 x x) #s(literal 1/1625702400 binary64)) (.f64 (.f64 x x) #s(literal 1/29030400 binary64))))))
(/.f64 (neg.f64 (fma.f64 (.f64 x x) (.f64 (.f64 x x) #s(literal 1/1625702400 binary64)) #s(literal -1/518400 binary64))) (fma.f64 (.f64 x x) #s(literal 1/40320 binary64) #s(literal 1/720 binary64)))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x (*.f64 x #s(literal -1/40320 binary64)) #s(literal 1/720 binary64)))))
(/.f64 (-.f64 #s(literal 1/518400 binary64) (.f64 (.f64 x x) (.f64 (.f64 x x) #s(literal 1/1625702400 binary64)))) (-.f64 #s(literal 1/720 binary64) (.f64 x (.f64 x #s(literal -1/40320 binary64)))))
(/.f64 (-.f64 (.f64 (.f64 (.f64 x x) (.f64 (.f64 x x) #s(literal 1/1625702400 binary64))) (fma.f64 (.f64 x x) #s(literal -1/40320 binary64) #s(literal -1/720 binary64))) (.f64 (fma.f64 (.f64 x x) #s(literal -1/40320 binary64) #s(literal -1/720 binary64)) #s(literal 1/518400 binary64))) (.f64 (fma.f64 (.f64 x x) #s(literal -1/40320 binary64) #s(literal -1/720 binary64)) (fma.f64 (*.f64 x x) #s(literal -1/40320 binary64) #s(literal -1/720 binary64))))
(/.f64 (.f64 (fma.f64 (.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) #s(literal -1/65548320768000 binary64))) (.f64 (.f64 (.f64 (.f64 x x) (.f64 (.f64 x x) (.f64 x x))) (.f64 (.f64 x x) (.f64 (.f64 x x) (.f64 x x)))) #s(literal 1/4296582355504620109824000000 binary64)) #s(literal 1/51998697814228992000000000 binary64)) #s(literal 1 binary64)) (.f64 (fma.f64 (.f64 (.f64 (.f64 x x) (.f64 (.f64 x x) (.f64 x x))) (.f64 (.f64 x x) (.f64 (.f64 x x) (.f64 x x)))) #s(literal 1/4296582355504620109824000000 binary64) (-.f64 #s(literal 1/139314069504000000 binary64) (.f64 (.f64 (.f64 x x) (.f64 (.f64 x x) (.f64 x x))) #s(literal -1/24465779630014464000000 binary64)))) (+.f64 (fma.f64 (.f64 x x) (.f64 (.f64 x x) #s(literal 1/1625702400 binary64)) #s(literal 1/518400 binary64)) (.f64 (.f64 x x) #s(literal 1/29030400 binary64)))))
(/.f64 (.f64 (fma.f64 (.f64 (.f64 (.f64 x x) (.f64 (.f64 x x) (.f64 x x))) (.f64 (.f64 x x) (.f64 (.f64 x x) (.f64 x x)))) #s(literal 1/4296582355504620109824000000 binary64) #s(literal -1/139314069504000000 binary64)) #s(literal 1 binary64)) (.f64 (fma.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) #s(literal -1/65548320768000 binary64)) #s(literal -1/373248000 binary64)) (+.f64 (fma.f64 (.f64 x x) (.f64 (.f64 x x) #s(literal 1/1625702400 binary64)) #s(literal 1/518400 binary64)) (.f64 (*.f64 x x) #s(literal 1/29030400 binary64)))))
(/.f64 (.f64 (fma.f64 (.f64 (.f64 (.f64 x x) (.f64 (.f64 x x) (.f64 x x))) (.f64 (.f64 x x) (.f64 (.f64 x x) (.f64 x x)))) #s(literal 1/4296582355504620109824000000 binary64) #s(literal -1/139314069504000000 binary64)) #s(literal 1 binary64)) (.f64 (fma.f64 (.f64 (.f64 (.f64 x x) (.f64 x x)) (.f64 (.f64 x x) (.f64 x x))) #s(literal 1/2642908293365760000 binary64) (+.f64 #s(literal 1/268738560000 binary64) (.f64 (.f64 (.f64 x x) (.f64 x x)) #s(literal 1/842764124160000 binary64)))) (fma.f64 (*.f64 x x) #s(literal -1/40320 binary64) #s(literal -1/720 binary64))))
(/.f64 (.f64 (fma.f64 (.f64 (.f64 (.f64 x x) (.f64 x x)) (.f64 (.f64 x x) (.f64 x x))) #s(literal 1/2642908293365760000 binary64) #s(literal -1/268738560000 binary64)) #s(literal 1 binary64)) (.f64 (fma.f64 (.f64 x x) (.f64 (.f64 x x) #s(literal 1/1625702400 binary64)) #s(literal 1/518400 binary64)) (fma.f64 (*.f64 x x) #s(literal -1/40320 binary64) #s(literal -1/720 binary64))))
(/.f64 (neg.f64 (neg.f64 (fma.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) #s(literal -1/65548320768000 binary64)) #s(literal 1/373248000 binary64)))) (neg.f64 (neg.f64 (+.f64 (fma.f64 (.f64 x x) (.f64 (.f64 x x) #s(literal 1/1625702400 binary64)) #s(literal 1/518400 binary64)) (.f64 (.f64 x x) #s(literal 1/29030400 binary64))))))
(/.f64 (neg.f64 (neg.f64 (fma.f64 (.f64 x x) (.f64 (.f64 x x) #s(literal 1/1625702400 binary64)) #s(literal -1/518400 binary64)))) (neg.f64 (fma.f64 (.f64 x x) #s(literal 1/40320 binary64) #s(literal 1/720 binary64))))
(/.f64 (neg.f64 (-.f64 #s(literal 1/518400 binary64) (.f64 (.f64 x x) (.f64 (.f64 x x) #s(literal 1/1625702400 binary64))))) (neg.f64 (-.f64 #s(literal 1/720 binary64) (.f64 x (.f64 x #s(literal -1/40320 binary64))))))
(/.f64 (-.f64 (pow.f64 (/.f64 (.f64 (.f64 x x) (.f64 (.f64 x x) #s(literal 1/1625702400 binary64))) (fma.f64 (.f64 x x) #s(literal -1/40320 binary64) #s(literal -1/720 binary64))) #s(literal 3 binary64)) (pow.f64 (/.f64 #s(literal 1/518400 binary64) (fma.f64 (.f64 x x) #s(literal -1/40320 binary64) #s(literal -1/720 binary64))) #s(literal 3 binary64))) (fma.f64 (/.f64 (.f64 (.f64 x x) (.f64 (.f64 x x) #s(literal 1/1625702400 binary64))) (fma.f64 (.f64 x x) #s(literal -1/40320 binary64) #s(literal -1/720 binary64))) (/.f64 (.f64 (.f64 x x) (.f64 (.f64 x x) #s(literal 1/1625702400 binary64))) (fma.f64 (.f64 x x) #s(literal -1/40320 binary64) #s(literal -1/720 binary64))) (fma.f64 (/.f64 #s(literal 1/518400 binary64) (fma.f64 (.f64 x x) #s(literal -1/40320 binary64) #s(literal -1/720 binary64))) (/.f64 #s(literal 1/518400 binary64) (fma.f64 (.f64 x x) #s(literal -1/40320 binary64) #s(literal -1/720 binary64))) (.f64 (/.f64 (.f64 (.f64 x x) (.f64 (.f64 x x) #s(literal 1/1625702400 binary64))) (fma.f64 (.f64 x x) #s(literal -1/40320 binary64) #s(literal -1/720 binary64))) (/.f64 #s(literal 1/518400 binary64) (fma.f64 (*.f64 x x) #s(literal -1/40320 binary64) #s(literal -1/720 binary64)))))))
(/.f64 (-.f64 (.f64 (/.f64 (.f64 (.f64 x x) (.f64 (.f64 x x) #s(literal 1/1625702400 binary64))) (fma.f64 (.f64 x x) #s(literal -1/40320 binary64) #s(literal -1/720 binary64))) (/.f64 (.f64 (.f64 x x) (.f64 (.f64 x x) #s(literal 1/1625702400 binary64))) (fma.f64 (.f64 x x) #s(literal -1/40320 binary64) #s(literal -1/720 binary64)))) (.f64 (/.f64 #s(literal 1/518400 binary64) (fma.f64 (.f64 x x) #s(literal -1/40320 binary64) #s(literal -1/720 binary64))) (/.f64 #s(literal 1/518400 binary64) (fma.f64 (.f64 x x) #s(literal -1/40320 binary64) #s(literal -1/720 binary64))))) (+.f64 (/.f64 (.f64 (.f64 x x) (.f64 (.f64 x x) #s(literal 1/1625702400 binary64))) (fma.f64 (.f64 x x) #s(literal -1/40320 binary64) #s(literal -1/720 binary64))) (/.f64 #s(literal 1/518400 binary64) (fma.f64 (.f64 x x) #s(literal -1/40320 binary64) #s(literal -1/720 binary64)))))
(pow.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x (*.f64 x #s(literal -1/40320 binary64)) #s(literal 1/720 binary64))) #s(literal -1 binary64))
(.f64 #s(literal 1 binary64) (fma.f64 x (.f64 x #s(literal -1/40320 binary64)) #s(literal 1/720 binary64)))
(.f64 (fma.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) #s(literal -1/65548320768000 binary64)) #s(literal 1/373248000 binary64)) (/.f64 #s(literal 1 binary64) (+.f64 (fma.f64 (.f64 x x) (.f64 (.f64 x x) #s(literal 1/1625702400 binary64)) #s(literal 1/518400 binary64)) (.f64 (*.f64 x x) #s(literal 1/29030400 binary64)))))
(.f64 (fma.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) #s(literal -1/65548320768000 binary64)) #s(literal 1/373248000 binary64)) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1/518400 binary64) (fma.f64 (.f64 x x) (.f64 (.f64 x x) #s(literal 1/1625702400 binary64)) (.f64 (*.f64 x x) #s(literal 1/29030400 binary64))))))
(.f64 (fma.f64 (.f64 x x) (.f64 (.f64 x x) #s(literal 1/1625702400 binary64)) #s(literal -1/518400 binary64)) (/.f64 #s(literal 1 binary64) (fma.f64 (*.f64 x x) #s(literal -1/40320 binary64) #s(literal -1/720 binary64))))
(.f64 (neg.f64 (fma.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) #s(literal -1/65548320768000 binary64)) #s(literal 1/373248000 binary64))) (/.f64 #s(literal 1 binary64) (neg.f64 (+.f64 (fma.f64 (.f64 x x) (.f64 (.f64 x x) #s(literal 1/1625702400 binary64)) #s(literal 1/518400 binary64)) (.f64 (*.f64 x x) #s(literal 1/29030400 binary64))))))
(.f64 (neg.f64 (fma.f64 (.f64 x x) (.f64 (.f64 x x) #s(literal 1/1625702400 binary64)) #s(literal -1/518400 binary64))) (/.f64 #s(literal 1 binary64) (fma.f64 (*.f64 x x) #s(literal 1/40320 binary64) #s(literal 1/720 binary64))))
(.f64 (-.f64 #s(literal 1/518400 binary64) (.f64 (.f64 x x) (.f64 (.f64 x x) #s(literal 1/1625702400 binary64)))) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1/720 binary64) (.f64 x (*.f64 x #s(literal -1/40320 binary64))))))

eval119.0ms (1.4%)

Memory: 24.9MiB live, 230.8MiB allocated
Compiler: Compiled 20 279 to 1 645 computations (91.9% saved)

prune326.0ms (3.7%)

Memory

-143.0MiB live, 226.0MiB allocated

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	614	2	616
Fresh	0	0	0
Picked	3	1	4
Done	0	0	0
Total	617	3	620

Accuracy

100.0%

Counts

620 → 3

Alt Table

Click to see full alt table

Status

Accuracy

Program

✓

52.1%

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

▶

100.0%

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

▶

99.7%

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

Compiler

Compiled 24 to 14 computations (41.7% saved)

simplify10.0ms (0.1%)

Memory

-14.0MiB live, 24.9MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 7 expressions of interest:

New	Metric	Program
✓	cost-diff	(fma.f64 x (*.f64 x #s(literal -1/24 binary64)) #s(literal 1/2 binary64))
✓	cost-diff	(.f64 x (fma.f64 x (.f64 x #s(literal -1/24 binary64)) #s(literal 1/2 binary64)))
✓	cost-diff	(.f64 (.f64 x (fma.f64 x (*.f64 x #s(literal -1/24 binary64)) #s(literal 1/2 binary64))) x)
✓	cost-diff	#s(approx (- 1 (cos x)) (.f64 (.f64 x (fma.f64 x (*.f64 x #s(literal -1/24 binary64)) #s(literal 1/2 binary64))) x))
✓	cost-diff	(*.f64 x #s(literal 1/2 binary64))
✓	cost-diff	(.f64 (.f64 x #s(literal 1/2 binary64)) x)
✓	cost-diff	#s(approx (- 1 (cos x)) (.f64 (.f64 x #s(literal 1/2 binary64)) x))

Rules

84×	`lower-*.f32`
74×	`lower-*.f64`
60×	`lower-fma.f32`
58×	`lower-fma.f64`
36×	`lower-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	14	65
0	21	65
1	41	65
2	64	65
3	86	65
4	98	65
5	109	65
6	119	65
7	130	65
8	133	65
0	133	65

Stop Event

1×	iter limit
1×	saturated
1×	iter limit

Calls

Call 1

Inputs
#s(approx (- 1 (cos x)) (.f64 (.f64 x #s(literal 1/2 binary64)) x))
(.f64 (.f64 x #s(literal 1/2 binary64)) x)
(*.f64 x #s(literal 1/2 binary64))
x
#s(literal 1/2 binary64)
#s(approx (- 1 (cos x)) (.f64 (.f64 x (fma.f64 x (*.f64 x #s(literal -1/24 binary64)) #s(literal 1/2 binary64))) x))
(.f64 (.f64 x (fma.f64 x (*.f64 x #s(literal -1/24 binary64)) #s(literal 1/2 binary64))) x)
(.f64 x (fma.f64 x (.f64 x #s(literal -1/24 binary64)) #s(literal 1/2 binary64)))
x
(fma.f64 x (*.f64 x #s(literal -1/24 binary64)) #s(literal 1/2 binary64))
(*.f64 x #s(literal -1/24 binary64))
#s(literal -1/24 binary64)
#s(literal 1/2 binary64)

Outputs
#s(approx (- 1 (cos x)) (.f64 (.f64 x #s(literal 1/2 binary64)) x))
#s(approx (- 1 (cos x)) (.f64 #s(literal 1/2 binary64) (.f64 x x)))
(.f64 (.f64 x #s(literal 1/2 binary64)) x)
(.f64 #s(literal 1/2 binary64) (.f64 x x))
(*.f64 x #s(literal 1/2 binary64))
x
#s(literal 1/2 binary64)
#s(approx (- 1 (cos x)) (.f64 (.f64 x (fma.f64 x (*.f64 x #s(literal -1/24 binary64)) #s(literal 1/2 binary64))) x))
#s(approx (- 1 (cos x)) (.f64 x (.f64 x (fma.f64 x (*.f64 x #s(literal -1/24 binary64)) #s(literal 1/2 binary64)))))
(.f64 (.f64 x (fma.f64 x (*.f64 x #s(literal -1/24 binary64)) #s(literal 1/2 binary64))) x)
(.f64 x (.f64 x (fma.f64 x (*.f64 x #s(literal -1/24 binary64)) #s(literal 1/2 binary64))))
(.f64 x (fma.f64 x (.f64 x #s(literal -1/24 binary64)) #s(literal 1/2 binary64)))
x
(fma.f64 x (*.f64 x #s(literal -1/24 binary64)) #s(literal 1/2 binary64))
(*.f64 x #s(literal -1/24 binary64))
#s(literal -1/24 binary64)
#s(literal 1/2 binary64)

localize111.0ms (1.3%)

Memory

19.1MiB live, 216.7MiB allocated

Localize:

Found 7 expressions of interest:

New	Metric	Score	Program
✓	accuracy	100.0%	#s(approx (- 1 (cos x)) (.f64 (.f64 x (fma.f64 x (*.f64 x #s(literal -1/24 binary64)) #s(literal 1/2 binary64))) x))
✓	accuracy	100.0%	(.f64 (.f64 x (fma.f64 x (*.f64 x #s(literal -1/24 binary64)) #s(literal 1/2 binary64))) x)
✓	accuracy	100.0%	(.f64 x (fma.f64 x (.f64 x #s(literal -1/24 binary64)) #s(literal 1/2 binary64)))
✓	accuracy	99.4%	(*.f64 x #s(literal -1/24 binary64))
✓	accuracy	100.0%	(.f64 (.f64 x #s(literal 1/2 binary64)) x)
✓	accuracy	100.0%	(*.f64 x #s(literal 1/2 binary64))
✓	accuracy	99.7%	#s(approx (- 1 (cos x)) (.f64 (.f64 x #s(literal 1/2 binary64)) x))

Samples

82.0ms	180×	2	valid
12.0ms	76×	1	valid

Compiler

Compiled 53 to 15 computations (71.7% saved)

Precisions

Click to see histograms. Total time spent on operations: 55.0ms

ival-cos: 28.0ms (51.2% of total)

ival-mult: 9.0ms (16.4% of total)

adjust: 8.0ms (14.6% of total)

ival-sub: 5.0ms (9.1% of total)

const: 4.0ms (7.3% of total)

ival-add: 1.0ms (1.8% of total)

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

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

exact: 0.0ms (0% of total)

series5.0ms (0.1%)

Memory

12.0MiB live, 12.0MiB allocated

Counts

8 → 96

Calls

Call 1

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

Outputs
#s(alt (* 1/2 (pow x 2)) (taylor 0 x) (#s(alt #s(approx (- 1 (cos x)) (.f64 (.f64 x #s(literal 1/2 binary64)) x)) (patch #s(approx (- 1 (cos x)) (.f64 (.f64 x #s(literal 1/2 binary64)) x)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (+ 1/2 (* -1/24 (pow x 2)))) (taylor 0 x) (#s(alt #s(approx (- 1 (cos x)) (.f64 (.f64 x #s(literal 1/2 binary64)) x)) (patch #s(approx (- 1 (cos x)) (.f64 (.f64 x #s(literal 1/2 binary64)) x)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (+ 1/2 (* (pow x 2) (- (* 1/720 (pow x 2)) 1/24)))) (taylor 0 x) (#s(alt #s(approx (- 1 (cos x)) (.f64 (.f64 x #s(literal 1/2 binary64)) x)) (patch #s(approx (- 1 (cos x)) (.f64 (.f64 x #s(literal 1/2 binary64)) x)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (+ 1/2 (* (pow x 2) (- (* (pow x 2) (+ 1/720 (* -1/40320 (pow x 2)))) 1/24)))) (taylor 0 x) (#s(alt #s(approx (- 1 (cos x)) (.f64 (.f64 x #s(literal 1/2 binary64)) x)) (patch #s(approx (- 1 (cos x)) (.f64 (.f64 x #s(literal 1/2 binary64)) x)) #<representation binary64>) () ())) ())
#s(alt (- 1 (cos x)) (taylor inf x) (#s(alt #s(approx (- 1 (cos x)) (.f64 (.f64 x #s(literal 1/2 binary64)) x)) (patch #s(approx (- 1 (cos x)) (.f64 (.f64 x #s(literal 1/2 binary64)) x)) #<representation binary64>) () ())) ())
#s(alt (- 1 (cos x)) (taylor inf x) (#s(alt #s(approx (- 1 (cos x)) (.f64 (.f64 x #s(literal 1/2 binary64)) x)) (patch #s(approx (- 1 (cos x)) (.f64 (.f64 x #s(literal 1/2 binary64)) x)) #<representation binary64>) () ())) ())
#s(alt (- 1 (cos x)) (taylor inf x) (#s(alt #s(approx (- 1 (cos x)) (.f64 (.f64 x #s(literal 1/2 binary64)) x)) (patch #s(approx (- 1 (cos x)) (.f64 (.f64 x #s(literal 1/2 binary64)) x)) #<representation binary64>) () ())) ())
#s(alt (- 1 (cos x)) (taylor inf x) (#s(alt #s(approx (- 1 (cos x)) (.f64 (.f64 x #s(literal 1/2 binary64)) x)) (patch #s(approx (- 1 (cos x)) (.f64 (.f64 x #s(literal 1/2 binary64)) x)) #<representation binary64>) () ())) ())
#s(alt (- 1 (cos x)) (taylor -inf x) (#s(alt #s(approx (- 1 (cos x)) (.f64 (.f64 x #s(literal 1/2 binary64)) x)) (patch #s(approx (- 1 (cos x)) (.f64 (.f64 x #s(literal 1/2 binary64)) x)) #<representation binary64>) () ())) ())
#s(alt (- 1 (cos x)) (taylor -inf x) (#s(alt #s(approx (- 1 (cos x)) (.f64 (.f64 x #s(literal 1/2 binary64)) x)) (patch #s(approx (- 1 (cos x)) (.f64 (.f64 x #s(literal 1/2 binary64)) x)) #<representation binary64>) () ())) ())
#s(alt (- 1 (cos x)) (taylor -inf x) (#s(alt #s(approx (- 1 (cos x)) (.f64 (.f64 x #s(literal 1/2 binary64)) x)) (patch #s(approx (- 1 (cos x)) (.f64 (.f64 x #s(literal 1/2 binary64)) x)) #<representation binary64>) () ())) ())
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#s(alt (* -1/24 x) (taylor 0 x) (#s(alt (.f64 x #s(literal -1/24 binary64)) (patch (.f64 x #s(literal -1/24 binary64)) #<representation binary64>) () ())) ())
#s(alt (* -1/24 x) (taylor 0 x) (#s(alt (.f64 x #s(literal -1/24 binary64)) (patch (.f64 x #s(literal -1/24 binary64)) #<representation binary64>) () ())) ())
#s(alt (* -1/24 x) (taylor 0 x) (#s(alt (.f64 x #s(literal -1/24 binary64)) (patch (.f64 x #s(literal -1/24 binary64)) #<representation binary64>) () ())) ())
#s(alt (* -1/24 x) (taylor inf x) (#s(alt (.f64 x #s(literal -1/24 binary64)) (patch (.f64 x #s(literal -1/24 binary64)) #<representation binary64>) () ())) ())
#s(alt (* -1/24 x) (taylor inf x) (#s(alt (.f64 x #s(literal -1/24 binary64)) (patch (.f64 x #s(literal -1/24 binary64)) #<representation binary64>) () ())) ())
#s(alt (* -1/24 x) (taylor inf x) (#s(alt (.f64 x #s(literal -1/24 binary64)) (patch (.f64 x #s(literal -1/24 binary64)) #<representation binary64>) () ())) ())
#s(alt (* -1/24 x) (taylor inf x) (#s(alt (.f64 x #s(literal -1/24 binary64)) (patch (.f64 x #s(literal -1/24 binary64)) #<representation binary64>) () ())) ())
#s(alt (* -1/24 x) (taylor -inf x) (#s(alt (.f64 x #s(literal -1/24 binary64)) (patch (.f64 x #s(literal -1/24 binary64)) #<representation binary64>) () ())) ())
#s(alt (* -1/24 x) (taylor -inf x) (#s(alt (.f64 x #s(literal -1/24 binary64)) (patch (.f64 x #s(literal -1/24 binary64)) #<representation binary64>) () ())) ())
#s(alt (* -1/24 x) (taylor -inf x) (#s(alt (.f64 x #s(literal -1/24 binary64)) (patch (.f64 x #s(literal -1/24 binary64)) #<representation binary64>) () ())) ())
#s(alt (* -1/24 x) (taylor -inf x) (#s(alt (.f64 x #s(literal -1/24 binary64)) (patch (.f64 x #s(literal -1/24 binary64)) #<representation binary64>) () ())) ())

Calls

24 calls:

Time	Variable		Point	Expression
0.0ms	x	@	-inf	(* x 1/2)
0.0ms	x	@	-inf	(* x -1/24)
0.0ms	x	@	inf	(* x -1/24)
0.0ms	x	@	0	(* x 1/2)
0.0ms	x	@	0	(* x -1/24)

simplify234.0ms (2.7%)

Memory

1.7MiB live, 470.8MiB allocated

Algorithm

1×	egg-herbie

Rules

9 576×	`lower-fma.f64`
9 576×	`lower-fma.f32`
2 846×	`lower-*.f64`
2 846×	`lower-*.f32`
1 448×	`times-frac`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	46	590
1	118	590
2	285	590
3	784	590
4	2245	590
5	5579	590
0	8100	551

Stop Event

1×	iter limit
1×	node limit

Counts

96 → 96

Calls

Call 1

Inputs
(* 1/2 (pow x 2))
(* (pow x 2) (+ 1/2 (* -1/24 (pow x 2))))
(* (pow x 2) (+ 1/2 (* (pow x 2) (- (* 1/720 (pow x 2)) 1/24))))
(* (pow x 2) (+ 1/2 (* (pow x 2) (- (* (pow x 2) (+ 1/720 (* -1/40320 (pow x 2)))) 1/24))))
(- 1 (cos x))
(- 1 (cos x))
(- 1 (cos x))
(- 1 (cos x))
(- 1 (cos x))
(- 1 (cos x))
(- 1 (cos x))
(- 1 (cos x))
(* 1/2 (pow x 2))
(* 1/2 (pow x 2))
(* 1/2 (pow x 2))
(* 1/2 (pow x 2))
(* 1/2 (pow x 2))
(* 1/2 (pow x 2))
(* 1/2 (pow x 2))
(* 1/2 (pow x 2))
(* 1/2 (pow x 2))
(* 1/2 (pow x 2))
(* 1/2 (pow x 2))
(* 1/2 (pow x 2))
(* 1/2 x)
(* 1/2 x)
(* 1/2 x)
(* 1/2 x)
(* 1/2 x)
(* 1/2 x)
(* 1/2 x)
(* 1/2 x)
(* 1/2 x)
(* 1/2 x)
(* 1/2 x)
(* 1/2 x)
(* 1/2 (pow x 2))
(* (pow x 2) (+ 1/2 (* -1/24 (pow x 2))))
(* (pow x 2) (+ 1/2 (* (pow x 2) (- (* 1/720 (pow x 2)) 1/24))))
(* (pow x 2) (+ 1/2 (* (pow x 2) (- (* (pow x 2) (+ 1/720 (* -1/40320 (pow x 2)))) 1/24))))
(- 1 (cos x))
(- 1 (cos x))
(- 1 (cos x))
(- 1 (cos x))
(- 1 (cos x))
(- 1 (cos x))
(- 1 (cos x))
(- 1 (cos x))
(* 1/2 (pow x 2))
(* (pow x 2) (+ 1/2 (* -1/24 (pow x 2))))
(* (pow x 2) (+ 1/2 (* -1/24 (pow x 2))))
(* (pow x 2) (+ 1/2 (* -1/24 (pow x 2))))
(* -1/24 (pow x 4))
(* (pow x 4) (- (* 1/2 (/ 1 (pow x 2))) 1/24))
(* (pow x 4) (- (* 1/2 (/ 1 (pow x 2))) 1/24))
(* (pow x 4) (- (* 1/2 (/ 1 (pow x 2))) 1/24))
(* -1/24 (pow x 4))
(* (pow x 4) (- (* 1/2 (/ 1 (pow x 2))) 1/24))
(* (pow x 4) (- (* 1/2 (/ 1 (pow x 2))) 1/24))
(* (pow x 4) (- (* 1/2 (/ 1 (pow x 2))) 1/24))
(* 1/2 x)
(* x (+ 1/2 (* -1/24 (pow x 2))))
(* x (+ 1/2 (* -1/24 (pow x 2))))
(* x (+ 1/2 (* -1/24 (pow x 2))))
(* -1/24 (pow x 3))
(* (pow x 3) (- (* 1/2 (/ 1 (pow x 2))) 1/24))
(* (pow x 3) (- (* 1/2 (/ 1 (pow x 2))) 1/24))
(* (pow x 3) (- (* 1/2 (/ 1 (pow x 2))) 1/24))
(* -1/24 (pow x 3))
(* -1 (* (pow x 3) (- 1/24 (* 1/2 (/ 1 (pow x 2))))))
(* -1 (* (pow x 3) (- 1/24 (* 1/2 (/ 1 (pow x 2))))))
(* -1 (* (pow x 3) (- 1/24 (* 1/2 (/ 1 (pow x 2))))))
1/2
(+ 1/2 (* -1/24 (pow x 2)))
(+ 1/2 (* -1/24 (pow x 2)))
(+ 1/2 (* -1/24 (pow x 2)))
(* -1/24 (pow x 2))
(* (pow x 2) (- (* 1/2 (/ 1 (pow x 2))) 1/24))
(* (pow x 2) (- (* 1/2 (/ 1 (pow x 2))) 1/24))
(* (pow x 2) (- (* 1/2 (/ 1 (pow x 2))) 1/24))
(* -1/24 (pow x 2))
(* (pow x 2) (- (* 1/2 (/ 1 (pow x 2))) 1/24))
(* (pow x 2) (- (* 1/2 (/ 1 (pow x 2))) 1/24))
(* (pow x 2) (- (* 1/2 (/ 1 (pow x 2))) 1/24))
(* -1/24 x)
(* -1/24 x)
(* -1/24 x)
(* -1/24 x)
(* -1/24 x)
(* -1/24 x)
(* -1/24 x)
(* -1/24 x)
(* -1/24 x)
(* -1/24 x)
(* -1/24 x)
(* -1/24 x)

Outputs
(* 1/2 (pow x 2))
(.f64 #s(literal 1/2 binary64) (.f64 x x))
(* (pow x 2) (+ 1/2 (* -1/24 (pow x 2))))
(.f64 (.f64 x x) (fma.f64 x (*.f64 x #s(literal -1/24 binary64)) #s(literal 1/2 binary64)))
(* (pow x 2) (+ 1/2 (* (pow x 2) (- (* 1/720 (pow x 2)) 1/24))))
(.f64 (.f64 x x) (fma.f64 x (.f64 x (fma.f64 x (.f64 x #s(literal 1/720 binary64)) #s(literal -1/24 binary64))) #s(literal 1/2 binary64)))
(* (pow x 2) (+ 1/2 (* (pow x 2) (- (* (pow x 2) (+ 1/720 (* -1/40320 (pow x 2)))) 1/24))))
(.f64 (.f64 x x) (fma.f64 (.f64 x x) (fma.f64 (.f64 x x) (fma.f64 (*.f64 x x) #s(literal -1/40320 binary64) #s(literal 1/720 binary64)) #s(literal -1/24 binary64)) #s(literal 1/2 binary64)))
(- 1 (cos x))
(-.f64 #s(literal 1 binary64) (cos.f64 x))
(- 1 (cos x))
(-.f64 #s(literal 1 binary64) (cos.f64 x))
(- 1 (cos x))
(-.f64 #s(literal 1 binary64) (cos.f64 x))
(- 1 (cos x))
(-.f64 #s(literal 1 binary64) (cos.f64 x))
(- 1 (cos x))
(-.f64 #s(literal 1 binary64) (cos.f64 x))
(- 1 (cos x))
(-.f64 #s(literal 1 binary64) (cos.f64 x))
(- 1 (cos x))
(-.f64 #s(literal 1 binary64) (cos.f64 x))
(- 1 (cos x))
(-.f64 #s(literal 1 binary64) (cos.f64 x))
(* 1/2 (pow x 2))
(.f64 #s(literal 1/2 binary64) (.f64 x x))
(* 1/2 (pow x 2))
(.f64 #s(literal 1/2 binary64) (.f64 x x))
(* 1/2 (pow x 2))
(.f64 #s(literal 1/2 binary64) (.f64 x x))
(* 1/2 (pow x 2))
(.f64 #s(literal 1/2 binary64) (.f64 x x))
(* 1/2 (pow x 2))
(.f64 #s(literal 1/2 binary64) (.f64 x x))
(* 1/2 (pow x 2))
(.f64 #s(literal 1/2 binary64) (.f64 x x))
(* 1/2 (pow x 2))
(.f64 #s(literal 1/2 binary64) (.f64 x x))
(* 1/2 (pow x 2))
(.f64 #s(literal 1/2 binary64) (.f64 x x))
(* 1/2 (pow x 2))
(.f64 #s(literal 1/2 binary64) (.f64 x x))
(* 1/2 (pow x 2))
(.f64 #s(literal 1/2 binary64) (.f64 x x))
(* 1/2 (pow x 2))
(.f64 #s(literal 1/2 binary64) (.f64 x x))
(* 1/2 (pow x 2))
(.f64 #s(literal 1/2 binary64) (.f64 x x))
(* 1/2 x)
(*.f64 #s(literal 1/2 binary64) x)
(* 1/2 x)
(*.f64 #s(literal 1/2 binary64) x)
(* 1/2 x)
(*.f64 #s(literal 1/2 binary64) x)
(* 1/2 x)
(*.f64 #s(literal 1/2 binary64) x)
(* 1/2 x)
(*.f64 #s(literal 1/2 binary64) x)
(* 1/2 x)
(*.f64 #s(literal 1/2 binary64) x)
(* 1/2 x)
(*.f64 #s(literal 1/2 binary64) x)
(* 1/2 x)
(*.f64 #s(literal 1/2 binary64) x)
(* 1/2 x)
(*.f64 #s(literal 1/2 binary64) x)
(* 1/2 x)
(*.f64 #s(literal 1/2 binary64) x)
(* 1/2 x)
(*.f64 #s(literal 1/2 binary64) x)
(* 1/2 x)
(*.f64 #s(literal 1/2 binary64) x)
(* 1/2 (pow x 2))
(.f64 #s(literal 1/2 binary64) (.f64 x x))
(* (pow x 2) (+ 1/2 (* -1/24 (pow x 2))))
(.f64 (.f64 x x) (fma.f64 x (*.f64 x #s(literal -1/24 binary64)) #s(literal 1/2 binary64)))
(* (pow x 2) (+ 1/2 (* (pow x 2) (- (* 1/720 (pow x 2)) 1/24))))
(.f64 (.f64 x x) (fma.f64 x (.f64 x (fma.f64 x (.f64 x #s(literal 1/720 binary64)) #s(literal -1/24 binary64))) #s(literal 1/2 binary64)))
(* (pow x 2) (+ 1/2 (* (pow x 2) (- (* (pow x 2) (+ 1/720 (* -1/40320 (pow x 2)))) 1/24))))
(.f64 (.f64 x x) (fma.f64 (.f64 x x) (fma.f64 (.f64 x x) (fma.f64 (*.f64 x x) #s(literal -1/40320 binary64) #s(literal 1/720 binary64)) #s(literal -1/24 binary64)) #s(literal 1/2 binary64)))
(- 1 (cos x))
(-.f64 #s(literal 1 binary64) (cos.f64 x))
(- 1 (cos x))
(-.f64 #s(literal 1 binary64) (cos.f64 x))
(- 1 (cos x))
(-.f64 #s(literal 1 binary64) (cos.f64 x))
(- 1 (cos x))
(-.f64 #s(literal 1 binary64) (cos.f64 x))
(- 1 (cos x))
(-.f64 #s(literal 1 binary64) (cos.f64 x))
(- 1 (cos x))
(-.f64 #s(literal 1 binary64) (cos.f64 x))
(- 1 (cos x))
(-.f64 #s(literal 1 binary64) (cos.f64 x))
(- 1 (cos x))
(-.f64 #s(literal 1 binary64) (cos.f64 x))
(* 1/2 (pow x 2))
(.f64 #s(literal 1/2 binary64) (.f64 x x))
(* (pow x 2) (+ 1/2 (* -1/24 (pow x 2))))
(.f64 (.f64 x x) (fma.f64 x (*.f64 x #s(literal -1/24 binary64)) #s(literal 1/2 binary64)))
(* (pow x 2) (+ 1/2 (* -1/24 (pow x 2))))
(.f64 (.f64 x x) (fma.f64 x (*.f64 x #s(literal -1/24 binary64)) #s(literal 1/2 binary64)))
(* (pow x 2) (+ 1/2 (* -1/24 (pow x 2))))
(.f64 (.f64 x x) (fma.f64 x (*.f64 x #s(literal -1/24 binary64)) #s(literal 1/2 binary64)))
(* -1/24 (pow x 4))
(.f64 x (.f64 #s(literal -1/24 binary64) (.f64 x (.f64 x x))))
(* (pow x 4) (- (* 1/2 (/ 1 (pow x 2))) 1/24))
(.f64 (.f64 x x) (fma.f64 x (*.f64 x #s(literal -1/24 binary64)) #s(literal 1/2 binary64)))
(* (pow x 4) (- (* 1/2 (/ 1 (pow x 2))) 1/24))
(.f64 (.f64 x x) (fma.f64 x (*.f64 x #s(literal -1/24 binary64)) #s(literal 1/2 binary64)))
(* (pow x 4) (- (* 1/2 (/ 1 (pow x 2))) 1/24))
(.f64 (.f64 x x) (fma.f64 x (*.f64 x #s(literal -1/24 binary64)) #s(literal 1/2 binary64)))
(* -1/24 (pow x 4))
(.f64 x (.f64 #s(literal -1/24 binary64) (.f64 x (.f64 x x))))
(* (pow x 4) (- (* 1/2 (/ 1 (pow x 2))) 1/24))
(.f64 (.f64 x x) (fma.f64 x (*.f64 x #s(literal -1/24 binary64)) #s(literal 1/2 binary64)))
(* (pow x 4) (- (* 1/2 (/ 1 (pow x 2))) 1/24))
(.f64 (.f64 x x) (fma.f64 x (*.f64 x #s(literal -1/24 binary64)) #s(literal 1/2 binary64)))
(* (pow x 4) (- (* 1/2 (/ 1 (pow x 2))) 1/24))
(.f64 (.f64 x x) (fma.f64 x (*.f64 x #s(literal -1/24 binary64)) #s(literal 1/2 binary64)))
(* 1/2 x)
(*.f64 #s(literal 1/2 binary64) x)
(* x (+ 1/2 (* -1/24 (pow x 2))))
(.f64 x (fma.f64 x (.f64 x #s(literal -1/24 binary64)) #s(literal 1/2 binary64)))
(* x (+ 1/2 (* -1/24 (pow x 2))))
(.f64 x (fma.f64 x (.f64 x #s(literal -1/24 binary64)) #s(literal 1/2 binary64)))
(* x (+ 1/2 (* -1/24 (pow x 2))))
(.f64 x (fma.f64 x (.f64 x #s(literal -1/24 binary64)) #s(literal 1/2 binary64)))
(* -1/24 (pow x 3))
(.f64 #s(literal -1/24 binary64) (.f64 x (*.f64 x x)))
(* (pow x 3) (- (* 1/2 (/ 1 (pow x 2))) 1/24))
(.f64 x (fma.f64 x (.f64 x #s(literal -1/24 binary64)) #s(literal 1/2 binary64)))
(* (pow x 3) (- (* 1/2 (/ 1 (pow x 2))) 1/24))
(.f64 x (fma.f64 x (.f64 x #s(literal -1/24 binary64)) #s(literal 1/2 binary64)))
(* (pow x 3) (- (* 1/2 (/ 1 (pow x 2))) 1/24))
(.f64 x (fma.f64 x (.f64 x #s(literal -1/24 binary64)) #s(literal 1/2 binary64)))
(* -1/24 (pow x 3))
(.f64 #s(literal -1/24 binary64) (.f64 x (*.f64 x x)))
(* -1 (* (pow x 3) (- 1/24 (* 1/2 (/ 1 (pow x 2))))))
(.f64 x (fma.f64 x (.f64 x #s(literal -1/24 binary64)) #s(literal 1/2 binary64)))
(* -1 (* (pow x 3) (- 1/24 (* 1/2 (/ 1 (pow x 2))))))
(.f64 x (fma.f64 x (.f64 x #s(literal -1/24 binary64)) #s(literal 1/2 binary64)))
(* -1 (* (pow x 3) (- 1/24 (* 1/2 (/ 1 (pow x 2))))))
(.f64 x (fma.f64 x (.f64 x #s(literal -1/24 binary64)) #s(literal 1/2 binary64)))
1/2
#s(literal 1/2 binary64)
(+ 1/2 (* -1/24 (pow x 2)))
(fma.f64 x (*.f64 x #s(literal -1/24 binary64)) #s(literal 1/2 binary64))
(+ 1/2 (* -1/24 (pow x 2)))
(fma.f64 x (*.f64 x #s(literal -1/24 binary64)) #s(literal 1/2 binary64))
(+ 1/2 (* -1/24 (pow x 2)))
(fma.f64 x (*.f64 x #s(literal -1/24 binary64)) #s(literal 1/2 binary64))
(* -1/24 (pow x 2))
(.f64 x (.f64 x #s(literal -1/24 binary64)))
(* (pow x 2) (- (* 1/2 (/ 1 (pow x 2))) 1/24))
(fma.f64 x (*.f64 x #s(literal -1/24 binary64)) #s(literal 1/2 binary64))
(* (pow x 2) (- (* 1/2 (/ 1 (pow x 2))) 1/24))
(fma.f64 x (*.f64 x #s(literal -1/24 binary64)) #s(literal 1/2 binary64))
(* (pow x 2) (- (* 1/2 (/ 1 (pow x 2))) 1/24))
(fma.f64 x (*.f64 x #s(literal -1/24 binary64)) #s(literal 1/2 binary64))
(* -1/24 (pow x 2))
(.f64 x (.f64 x #s(literal -1/24 binary64)))
(* (pow x 2) (- (* 1/2 (/ 1 (pow x 2))) 1/24))
(fma.f64 x (*.f64 x #s(literal -1/24 binary64)) #s(literal 1/2 binary64))
(* (pow x 2) (- (* 1/2 (/ 1 (pow x 2))) 1/24))
(fma.f64 x (*.f64 x #s(literal -1/24 binary64)) #s(literal 1/2 binary64))
(* (pow x 2) (- (* 1/2 (/ 1 (pow x 2))) 1/24))
(fma.f64 x (*.f64 x #s(literal -1/24 binary64)) #s(literal 1/2 binary64))
(* -1/24 x)
(*.f64 x #s(literal -1/24 binary64))
(* -1/24 x)
(*.f64 x #s(literal -1/24 binary64))
(* -1/24 x)
(*.f64 x #s(literal -1/24 binary64))
(* -1/24 x)
(*.f64 x #s(literal -1/24 binary64))
(* -1/24 x)
(*.f64 x #s(literal -1/24 binary64))
(* -1/24 x)
(*.f64 x #s(literal -1/24 binary64))
(* -1/24 x)
(*.f64 x #s(literal -1/24 binary64))
(* -1/24 x)
(*.f64 x #s(literal -1/24 binary64))
(* -1/24 x)
(*.f64 x #s(literal -1/24 binary64))
(* -1/24 x)
(*.f64 x #s(literal -1/24 binary64))
(* -1/24 x)
(*.f64 x #s(literal -1/24 binary64))
(* -1/24 x)
(*.f64 x #s(literal -1/24 binary64))

rewrite375.0ms (4.3%)

Memory

-33.3MiB live, 590.9MiB allocated

Algorithm

1×	batch-egg-rewrite

Rules

6 154×	`lower-*.f32`
6 144×	`lower-*.f64`
5 356×	`lower-fma.f32`
5 354×	`lower-fma.f64`
3 352×	`lower-/.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	14	60
0	21	60
1	68	60
2	368	60
3	2873	60
0	10124	60

Stop Event

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

Counts

8 → 200

Calls

Call 1

Inputs
#s(approx (- 1 (cos x)) (.f64 (.f64 x #s(literal 1/2 binary64)) x))
(.f64 (.f64 x #s(literal 1/2 binary64)) x)
(*.f64 x #s(literal 1/2 binary64))
#s(approx (- 1 (cos x)) (.f64 (.f64 x (fma.f64 x (*.f64 x #s(literal -1/24 binary64)) #s(literal 1/2 binary64))) x))
(.f64 (.f64 x (fma.f64 x (*.f64 x #s(literal -1/24 binary64)) #s(literal 1/2 binary64))) x)
(.f64 x (fma.f64 x (.f64 x #s(literal -1/24 binary64)) #s(literal 1/2 binary64)))
(fma.f64 x (*.f64 x #s(literal -1/24 binary64)) #s(literal 1/2 binary64))
(*.f64 x #s(literal -1/24 binary64))

Outputs
#s(approx (- 1 (cos x)) (.f64 x (.f64 x #s(literal 1/2 binary64))))
(.f64 x (.f64 x #s(literal 1/2 binary64)))
(.f64 #s(literal 1/2 binary64) (.f64 x x))
(.f64 (.f64 x #s(literal 1/2 binary64)) x)
(.f64 (.f64 x x) #s(literal 1/2 binary64))
(*.f64 x #s(literal 1/2 binary64))
(*.f64 #s(literal 1/2 binary64) x)
#s(approx (- 1 (cos x)) (.f64 x (.f64 x (fma.f64 x (*.f64 x #s(literal -1/24 binary64)) #s(literal 1/2 binary64)))))
(+.f64 (.f64 x (.f64 x #s(literal 1/2 binary64))) (.f64 x (.f64 #s(literal -1/24 binary64) (.f64 x (.f64 x x)))))
(+.f64 (.f64 x (.f64 #s(literal -1/24 binary64) (.f64 x (.f64 x x)))) (.f64 x (.f64 x #s(literal 1/2 binary64))))
(fma.f64 x (.f64 x #s(literal 1/2 binary64)) (.f64 x (.f64 #s(literal -1/24 binary64) (.f64 x (*.f64 x x)))))
(fma.f64 x (.f64 #s(literal -1/24 binary64) (.f64 x (.f64 x x))) (.f64 x (*.f64 x #s(literal 1/2 binary64))))
(fma.f64 #s(literal 1/2 binary64) (.f64 x x) (.f64 x (.f64 #s(literal -1/24 binary64) (.f64 x (*.f64 x x)))))
(fma.f64 (.f64 x #s(literal 1/2 binary64)) x (.f64 x (.f64 #s(literal -1/24 binary64) (.f64 x (*.f64 x x)))))
(fma.f64 #s(literal -1/24 binary64) (.f64 x (.f64 x (.f64 x x))) (.f64 x (*.f64 x #s(literal 1/2 binary64))))
(fma.f64 (.f64 x #s(literal -1/24 binary64)) (.f64 x (.f64 x x)) (.f64 x (*.f64 x #s(literal 1/2 binary64))))
(fma.f64 (.f64 x (.f64 x #s(literal -1/24 binary64))) (.f64 x x) (.f64 x (*.f64 x #s(literal 1/2 binary64))))
(fma.f64 (.f64 #s(literal -1/24 binary64) (.f64 x (.f64 x x))) x (.f64 x (*.f64 x #s(literal 1/2 binary64))))
(fma.f64 (.f64 x x) #s(literal 1/2 binary64) (.f64 x (.f64 #s(literal -1/24 binary64) (.f64 x (*.f64 x x)))))
(fma.f64 (.f64 x x) (.f64 x (.f64 x #s(literal -1/24 binary64))) (.f64 x (*.f64 x #s(literal 1/2 binary64))))
(fma.f64 (.f64 x (.f64 x x)) (.f64 x #s(literal -1/24 binary64)) (.f64 x (*.f64 x #s(literal 1/2 binary64))))
(fma.f64 (.f64 x (.f64 x (.f64 x x))) #s(literal -1/24 binary64) (.f64 x (*.f64 x #s(literal 1/2 binary64))))
(/.f64 (.f64 x x) (/.f64 #s(literal 1 binary64) (fma.f64 x (.f64 x #s(literal -1/24 binary64)) #s(literal 1/2 binary64))))
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(/.f64 (-.f64 (.f64 (/.f64 (.f64 x (.f64 x (.f64 (.f64 x x) #s(literal 1/576 binary64)))) (fma.f64 x (.f64 x #s(literal -1/24 binary64)) #s(literal -1/2 binary64))) (.f64 (/.f64 (.f64 x (.f64 x (.f64 (.f64 x x) #s(literal 1/576 binary64)))) (fma.f64 x (.f64 x #s(literal -1/24 binary64)) #s(literal -1/2 binary64))) (/.f64 (.f64 x (.f64 x (.f64 (.f64 x x) #s(literal 1/576 binary64)))) (fma.f64 x (.f64 x #s(literal -1/24 binary64)) #s(literal -1/2 binary64))))) (.f64 (/.f64 #s(literal 1/4 binary64) (fma.f64 x (.f64 x #s(literal -1/24 binary64)) #s(literal -1/2 binary64))) (.f64 (/.f64 #s(literal 1/4 binary64) (fma.f64 x (.f64 x #s(literal -1/24 binary64)) #s(literal -1/2 binary64))) (/.f64 #s(literal 1/4 binary64) (fma.f64 x (.f64 x #s(literal -1/24 binary64)) #s(literal -1/2 binary64)))))) (fma.f64 (/.f64 (.f64 x (.f64 x (.f64 (.f64 x x) #s(literal 1/576 binary64)))) (fma.f64 x (.f64 x #s(literal -1/24 binary64)) #s(literal -1/2 binary64))) (/.f64 (.f64 x (.f64 x (.f64 (.f64 x x) #s(literal 1/576 binary64)))) (fma.f64 x (.f64 x #s(literal -1/24 binary64)) #s(literal -1/2 binary64))) (fma.f64 (/.f64 #s(literal 1/4 binary64) (fma.f64 x (.f64 x #s(literal -1/24 binary64)) #s(literal -1/2 binary64))) (/.f64 #s(literal 1/4 binary64) (fma.f64 x (.f64 x #s(literal -1/24 binary64)) #s(literal -1/2 binary64))) (.f64 (/.f64 (.f64 x (.f64 x (.f64 (.f64 x x) #s(literal 1/576 binary64)))) (fma.f64 x (.f64 x #s(literal -1/24 binary64)) #s(literal -1/2 binary64))) (/.f64 #s(literal 1/4 binary64) (fma.f64 x (*.f64 x #s(literal -1/24 binary64)) #s(literal -1/2 binary64)))))))
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(/.f64 (-.f64 (.f64 (neg.f64 (.f64 x (.f64 x (.f64 (.f64 x x) #s(literal 1/576 binary64))))) (/.f64 (fma.f64 x (.f64 x #s(literal -1/24 binary64)) #s(literal -1/2 binary64)) #s(literal 1/4 binary64))) (.f64 (fma.f64 (.f64 x x) #s(literal 1/24 binary64) #s(literal 1/2 binary64)) #s(literal 1 binary64))) (.f64 (fma.f64 (.f64 x x) #s(literal 1/24 binary64) #s(literal 1/2 binary64)) (/.f64 (fma.f64 x (*.f64 x #s(literal -1/24 binary64)) #s(literal -1/2 binary64)) #s(literal 1/4 binary64))))
(/.f64 (-.f64 (.f64 (neg.f64 (.f64 x (.f64 x (.f64 (.f64 x x) #s(literal 1/576 binary64))))) (fma.f64 x (.f64 x #s(literal -1/24 binary64)) #s(literal -1/2 binary64))) (.f64 (fma.f64 (.f64 x x) #s(literal 1/24 binary64) #s(literal 1/2 binary64)) #s(literal 1/4 binary64))) (.f64 (fma.f64 (.f64 x x) #s(literal 1/24 binary64) #s(literal 1/2 binary64)) (fma.f64 x (*.f64 x #s(literal -1/24 binary64)) #s(literal -1/2 binary64))))
(/.f64 (-.f64 (.f64 (neg.f64 (.f64 x (.f64 x (.f64 (.f64 x x) #s(literal 1/576 binary64))))) (fma.f64 (.f64 x x) #s(literal 1/24 binary64) #s(literal 1/2 binary64))) (.f64 (fma.f64 (.f64 x x) #s(literal 1/24 binary64) #s(literal 1/2 binary64)) #s(literal -1/4 binary64))) (.f64 (fma.f64 (.f64 x x) #s(literal 1/24 binary64) #s(literal 1/2 binary64)) (fma.f64 (*.f64 x x) #s(literal 1/24 binary64) #s(literal 1/2 binary64))))
(/.f64 (-.f64 (.f64 #s(literal 1/4 binary64) (+.f64 #s(literal 1/2 binary64) (.f64 (.f64 x x) #s(literal 1/24 binary64)))) (.f64 (+.f64 #s(literal 1/2 binary64) (.f64 (.f64 x x) #s(literal 1/24 binary64))) (.f64 x (.f64 x (.f64 (.f64 x x) #s(literal 1/576 binary64)))))) (.f64 (+.f64 #s(literal 1/2 binary64) (.f64 (.f64 x x) #s(literal 1/24 binary64))) (+.f64 #s(literal 1/2 binary64) (.f64 (*.f64 x x) #s(literal 1/24 binary64)))))
(pow.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x (*.f64 x #s(literal -1/24 binary64)) #s(literal 1/2 binary64))) #s(literal -1 binary64))
(pow.f64 (/.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x (*.f64 x #s(literal -1/24 binary64)) #s(literal 1/2 binary64))) #s(literal 1 binary64)) #s(literal -1 binary64))
(pow.f64 (/.f64 (+.f64 #s(literal 1/2 binary64) (.f64 (.f64 x x) #s(literal 1/24 binary64))) (-.f64 #s(literal 1/4 binary64) (.f64 x (.f64 x (.f64 (.f64 x x) #s(literal 1/576 binary64)))))) #s(literal -1 binary64))
(.f64 #s(literal 1 binary64) (fma.f64 x (.f64 x #s(literal -1/24 binary64)) #s(literal 1/2 binary64)))
(.f64 (fma.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) #s(literal -1/13824 binary64)) #s(literal 1/8 binary64)) (/.f64 #s(literal 1 binary64) (fma.f64 (.f64 x x) (-.f64 (.f64 (*.f64 x x) #s(literal 1/576 binary64)) #s(literal -1/48 binary64)) #s(literal 1/4 binary64))))
(.f64 (fma.f64 x (.f64 x (.f64 (.f64 x x) #s(literal 1/576 binary64))) #s(literal -1/4 binary64)) (/.f64 #s(literal 1 binary64) (fma.f64 x (*.f64 x #s(literal -1/24 binary64)) #s(literal -1/2 binary64))))
(.f64 (neg.f64 (fma.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) #s(literal -1/13824 binary64)) #s(literal 1/8 binary64))) (/.f64 #s(literal 1 binary64) (neg.f64 (fma.f64 (.f64 x x) (-.f64 (.f64 (*.f64 x x) #s(literal 1/576 binary64)) #s(literal -1/48 binary64)) #s(literal 1/4 binary64)))))
(.f64 (neg.f64 (fma.f64 x (.f64 x (.f64 (.f64 x x) #s(literal 1/576 binary64))) #s(literal -1/4 binary64))) (/.f64 #s(literal 1 binary64) (fma.f64 (*.f64 x x) #s(literal 1/24 binary64) #s(literal 1/2 binary64))))
(.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (.f64 x x) (-.f64 (.f64 (.f64 x x) #s(literal 1/576 binary64)) #s(literal -1/48 binary64)) #s(literal 1/4 binary64))) (fma.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (*.f64 x x)) #s(literal -1/13824 binary64)) #s(literal 1/8 binary64)))
(.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (.f64 x x) (-.f64 (.f64 (.f64 x x) #s(literal 1/576 binary64)) #s(literal -1/48 binary64)) #s(literal 1/4 binary64))) (pow.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (*.f64 x x)) #s(literal -1/13824 binary64)) #s(literal 1/8 binary64))) #s(literal -1 binary64)))
(.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x (.f64 x #s(literal -1/24 binary64)) #s(literal -1/2 binary64))) (fma.f64 x (.f64 x (.f64 (*.f64 x x) #s(literal 1/576 binary64))) #s(literal -1/4 binary64)))
(.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x (.f64 x #s(literal -1/24 binary64)) #s(literal -1/2 binary64))) (pow.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x (.f64 x (.f64 (*.f64 x x) #s(literal 1/576 binary64))) #s(literal -1/4 binary64))) #s(literal -1 binary64)))
(.f64 (-.f64 #s(literal 1/4 binary64) (.f64 x (.f64 x (.f64 (.f64 x x) #s(literal 1/576 binary64))))) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1/2 binary64) (.f64 (*.f64 x x) #s(literal 1/24 binary64)))))
(.f64 (/.f64 (fma.f64 x (.f64 x (.f64 (.f64 x x) #s(literal 1/576 binary64))) #s(literal -1/4 binary64)) (fma.f64 x (.f64 x (.f64 (.f64 x x) #s(literal 1/576 binary64))) #s(literal -1/4 binary64))) (fma.f64 x (.f64 x #s(literal -1/24 binary64)) #s(literal 1/2 binary64)))
(.f64 (/.f64 (fma.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) #s(literal -1/13824 binary64)) #s(literal 1/8 binary64)) (fma.f64 (fma.f64 (.f64 x x) #s(literal 1/48 binary64) #s(literal 1/4 binary64)) (.f64 (fma.f64 (.f64 x x) #s(literal 1/48 binary64) #s(literal 1/4 binary64)) (fma.f64 (.f64 x x) #s(literal 1/48 binary64) #s(literal 1/4 binary64))) (.f64 (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x)))) (.f64 (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x)))) #s(literal 1/191102976 binary64))))) (fma.f64 (fma.f64 (.f64 x x) #s(literal 1/48 binary64) #s(literal 1/4 binary64)) (-.f64 (fma.f64 (.f64 x x) #s(literal 1/48 binary64) #s(literal 1/4 binary64)) (.f64 x (.f64 x (.f64 (.f64 x x) #s(literal 1/576 binary64))))) (.f64 #s(literal 1/331776 binary64) (.f64 (.f64 x (.f64 x (.f64 x x))) (.f64 x (.f64 x (.f64 x x)))))))
(.f64 (/.f64 (fma.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) #s(literal -1/13824 binary64)) #s(literal 1/8 binary64)) (.f64 (fma.f64 (.f64 x x) (-.f64 (.f64 (.f64 x x) #s(literal 1/576 binary64)) #s(literal -1/48 binary64)) #s(literal 1/4 binary64)) (+.f64 (fma.f64 x (.f64 x (.f64 (.f64 x x) #s(literal 1/576 binary64))) #s(literal -1/4 binary64)) (.f64 (.f64 x x) #s(literal -1/48 binary64))))) (+.f64 (fma.f64 x (.f64 x (.f64 (.f64 x x) #s(literal 1/576 binary64))) #s(literal -1/4 binary64)) (.f64 (.f64 x x) #s(literal -1/48 binary64))))
(.f64 (/.f64 (fma.f64 x (.f64 x (.f64 (.f64 x x) #s(literal 1/576 binary64))) #s(literal -1/4 binary64)) (fma.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) #s(literal -1/13824 binary64)) #s(literal -1/8 binary64))) (fma.f64 x (.f64 x (.f64 (.f64 x x) #s(literal 1/576 binary64))) (fma.f64 x (*.f64 x #s(literal -1/48 binary64)) #s(literal 1/4 binary64))))
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(.f64 (pow.f64 (/.f64 (fma.f64 (.f64 x x) (-.f64 (.f64 (.f64 x x) #s(literal 1/576 binary64)) #s(literal -1/48 binary64)) #s(literal 1/4 binary64)) (fma.f64 (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x)))) (.f64 (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x)))) #s(literal 1/191102976 binary64)) #s(literal -1/64 binary64))) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (fma.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) #s(literal -1/13824 binary64)) #s(literal -1/8 binary64))))
(.f64 (pow.f64 (/.f64 (fma.f64 x (.f64 x #s(literal -1/24 binary64)) #s(literal -1/2 binary64)) (fma.f64 (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x)))) (.f64 (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x)))) #s(literal 1/191102976 binary64)) #s(literal -1/64 binary64))) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/331776 binary64) (.f64 (.f64 x (.f64 x (.f64 x x))) (.f64 x (.f64 x (.f64 x x)))) (fma.f64 (.f64 x (.f64 x (*.f64 x x))) #s(literal 1/2304 binary64) #s(literal 1/16 binary64)))))
(.f64 (pow.f64 (/.f64 (fma.f64 x (.f64 x #s(literal -1/24 binary64)) #s(literal -1/2 binary64)) (fma.f64 #s(literal 1/331776 binary64) (.f64 (.f64 x (.f64 x (.f64 x x))) (.f64 x (.f64 x (.f64 x x)))) #s(literal -1/16 binary64))) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (fma.f64 x (.f64 x (.f64 (.f64 x x) #s(literal 1/576 binary64))) #s(literal 1/4 binary64))))
(*.f64 x #s(literal -1/24 binary64))
(*.f64 #s(literal -1/24 binary64) x)

eval67.0ms (0.8%)

Memory: 11.4MiB live, 51.7MiB allocated
Compiler: Compiled 7 299 to 743 computations (89.8% saved)

prune71.0ms (0.8%)

Memory

-13.5MiB live, 63.3MiB allocated

Pruning

3 alts after pruning (0 fresh and 3 done)

	Pruned	Kept	Total
New	296	0	296
Fresh	0	0	0
Picked	0	2	2
Done	0	1	1
Total	296	3	299

Accuracy

100.0%

Counts

299 → 3

Alt Table

Click to see full alt table

Status

Accuracy

Program

✓

52.1%

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

✓

100.0%

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

✓

99.7%

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

Compiler

Compiled 88 to 40 computations (54.5% saved)

regimes7.0ms (0.1%)

Memory

14.8MiB live, 14.8MiB allocated

Counts

7 → 1

Calls

Call 1

Inputs
(-.f64 #s(literal 1 binary64) #s(approx (cos x) #s(literal 1 binary64)))
#s(approx (- 1 (cos x)) (.f64 #s(literal 1/2 binary64) (.f64 x x)))
#s(approx (- 1 (cos x)) (.f64 (.f64 x #s(literal 1/2 binary64)) x))
#s(approx (- 1 (cos x)) (.f64 (.f64 x x) (fma.f64 (*.f64 x x) #s(literal -1/24 binary64) #s(literal 1/2 binary64))))
#s(approx (- 1 (cos x)) (.f64 (.f64 x (fma.f64 x (*.f64 x #s(literal -1/24 binary64)) #s(literal 1/2 binary64))) x))
#s(approx (- 1 (cos x)) (.f64 x (.f64 x (fma.f64 x (.f64 x (fma.f64 (.f64 x x) (fma.f64 x (*.f64 x #s(literal -1/40320 binary64)) #s(literal 1/720 binary64)) #s(literal -1/24 binary64))) #s(literal 1/2 binary64)))))
(-.f64 #s(literal 1 binary64) (cos.f64 x))

Outputs
#s(approx (- 1 (cos x)) (.f64 (.f64 x (fma.f64 x (*.f64 x #s(literal -1/24 binary64)) #s(literal 1/2 binary64))) x))

Calls

3 calls:

3.0ms	x
2.0ms	(cos.f64 x)
2.0ms	(-.f64 #s(literal 1 binary64) (cos.f64 x))

Results

Accuracy	Segments	Branch
100.0%	1	`x`
100.0%	1	`(-.f64 #s(literal 1 binary64) (cos.f64 x))`
100.0%	1	`(cos.f64 x)`

Compiler

Compiled 10 to 7 computations (30% saved)

regimes5.0ms (0.1%)

Memory

11.1MiB live, 11.1MiB allocated

Counts

4 → 1

Calls

Call 1

Inputs
(-.f64 #s(literal 1 binary64) #s(approx (cos x) #s(literal 1 binary64)))
#s(approx (- 1 (cos x)) (.f64 #s(literal 1/2 binary64) (.f64 x x)))
#s(approx (- 1 (cos x)) (.f64 (.f64 x #s(literal 1/2 binary64)) x))
#s(approx (- 1 (cos x)) (.f64 (.f64 x x) (fma.f64 (*.f64 x x) #s(literal -1/24 binary64) #s(literal 1/2 binary64))))

Outputs
#s(approx (- 1 (cos x)) (.f64 (.f64 x x) (fma.f64 (*.f64 x x) #s(literal -1/24 binary64) #s(literal 1/2 binary64))))

Calls

3 calls:

2.0ms	x
1.0ms	(-.f64 #s(literal 1 binary64) (cos.f64 x))
1.0ms	(cos.f64 x)

Results

Accuracy	Segments	Branch
100.0%	1	`x`
100.0%	1	`(-.f64 #s(literal 1 binary64) (cos.f64 x))`
100.0%	1	`(cos.f64 x)`

Compiler

Compiled 10 to 7 computations (30% saved)

regimes26.0ms (0.3%)

Memory

-26.8MiB live, 11.1MiB allocated

Counts

3 → 1

Calls

Call 1

Inputs

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

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

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

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

Calls

3 calls:

2.0ms	x
1.0ms	(-.f64 #s(literal 1 binary64) (cos.f64 x))
1.0ms	(cos.f64 x)

Results

Accuracy	Segments	Branch
99.7%	1	`x`
99.7%	1	`(-.f64 #s(literal 1 binary64) (cos.f64 x))`
99.7%	1	`(cos.f64 x)`

Compiler

Compiled 10 to 7 computations (30% saved)

regimes4.0ms (0%)

Memory

9.9MiB live, 9.9MiB allocated

Counts

2 → 1

Calls

Call 1

Inputs
(-.f64 #s(literal 1 binary64) #s(approx (cos x) #s(literal 1 binary64)))
#s(approx (- 1 (cos x)) (.f64 #s(literal 1/2 binary64) (.f64 x x)))

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

Calls

3 calls:

1.0ms	x
1.0ms	(cos.f64 x)
1.0ms	(-.f64 #s(literal 1 binary64) (cos.f64 x))

Results

Accuracy	Segments	Branch
99.7%	1	`(cos.f64 x)`
99.7%	1	`x`
99.7%	1	`(-.f64 #s(literal 1 binary64) (cos.f64 x))`

Compiler

Compiled 10 to 7 computations (30% saved)

regimes3.0ms (0%)

Memory

9.3MiB live, 9.3MiB allocated

Accuracy

Total 0.0b remaining (0%)

Threshold costs 0b (0%)

Counts

1 → 1

Calls

Call 1

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

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

Calls

3 calls:

1.0ms	x
1.0ms	(-.f64 #s(literal 1 binary64) (cos.f64 x))
1.0ms	(cos.f64 x)

Results

Accuracy	Segments	Branch
52.1%	1	`(cos.f64 x)`
52.1%	1	`x`
52.1%	1	`(-.f64 #s(literal 1 binary64) (cos.f64 x))`

Compiler

Compiled 10 to 7 computations (30% saved)

simplify43.0ms (0.5%)

Memory

-30.9MiB live, 20.7MiB allocated

Algorithm

1×	egg-herbie

Rules

16×	`*-commutative_binary64`
4×	`+-commutative_binary64`
4×	`sub-neg_binary64`
2×	`1-exp_binary64`
2×	`neg-sub0_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	22	56
1	34	56
2	38	56
3	40	56
4	41	56

Stop Event

1×

saturated

Calls

Call 1

Inputs
#s(approx (- 1 (cos x)) (.f64 (.f64 x (fma.f64 x (*.f64 x #s(literal -1/24 binary64)) #s(literal 1/2 binary64))) x))
#s(approx (- 1 (cos x)) (.f64 (.f64 x x) (fma.f64 (*.f64 x x) #s(literal -1/24 binary64) #s(literal 1/2 binary64))))
#s(approx (- 1 (cos x)) (.f64 (.f64 x #s(literal 1/2 binary64)) x))
#s(approx (- 1 (cos x)) (.f64 #s(literal 1/2 binary64) (.f64 x x)))
(-.f64 #s(literal 1 binary64) #s(approx (cos x) #s(literal 1 binary64)))

Outputs
#s(approx (- 1 (cos x)) (.f64 (.f64 x (fma.f64 x (*.f64 x #s(literal -1/24 binary64)) #s(literal 1/2 binary64))) x))
#s(approx (- 1 (cos x)) (.f64 x (.f64 x (fma.f64 x (*.f64 x #s(literal -1/24 binary64)) #s(literal 1/2 binary64)))))
#s(approx (- 1 (cos x)) (.f64 (.f64 x x) (fma.f64 (*.f64 x x) #s(literal -1/24 binary64) #s(literal 1/2 binary64))))
#s(approx (- 1 (cos x)) (.f64 (.f64 x #s(literal 1/2 binary64)) x))
#s(approx (- 1 (cos x)) (.f64 x (.f64 x #s(literal 1/2 binary64))))
#s(approx (- 1 (cos x)) (.f64 #s(literal 1/2 binary64) (.f64 x x)))
(-.f64 #s(literal 1 binary64) #s(approx (cos x) #s(literal 1 binary64)))

soundness1.9s (21.3%)

Memory

12.1MiB live, 357.4MiB allocated

Rules

32 720×	`lower-fma.f64`
32 720×	`lower-fma.f32`
6 146×	`lower-fma.f32`
6 138×	`lower-fma.f64`
4 756×	`lower-*.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	41	144
1	101	144
2	246	144
3	589	144
4	1230	144
5	1905	144
6	2165	144
7	2814	144
8	4054	144
9	5622	144
10	6523	144
11	6804	144
12	6843	144
13	6843	144
14	7276	144
15	7552	144
16	7593	144
17	7595	144
18	7595	144
19	7595	144
20	7595	144
21	7605	144
22	7605	144
23	7605	144
0	8510	132
0	24	157
0	40	157
1	169	157
2	1188	157
0	8220	157

Stop Event

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

Compiler

Compiled 96 to 48 computations (50% saved)

preprocess74.0ms (0.8%)

Memory: 13.5MiB live, 125.0MiB allocated
Remove: (abs x)
Compiler: Compiled 182 to 94 computations (48.4% saved)

end0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated

Iter	Nodes	Cost
0	6	9
1	16	8
2	35	8
3	55	8
4	87	8
5	101	8
6	107	8
0	4	4
0	6	4
1	10	4
2	14	4
3	19	4
4	25	4
5	33	4
6	43	4
7	54	4
8	57	4
0	57	4

Iter	Nodes	Cost
0	14	65
0	21	65
1	41	65
2	64	65
3	86	65
4	98	65
5	109	65
6	119	65
7	130	65
8	133	65
0	133	65

Iter	Nodes	Cost
0	6	9
1	16	8
2	35	8
3	55	8
4	87	8
5	101	8
6	107	8
0	4	4
0	6	4
1	10	4
2	14	4
3	19	4
4	25	4
5	33	4
6	43	4
7	54	4
8	57	4
0	57	4

Iter	Nodes	Cost
0	14	65
0	21	65
1	41	65
2	64	65
3	86	65
4	98	65
5	109	65
6	119	65
7	130	65
8	133	65
0	133	65

analyze3.0ms (0%)

sample2.5s (29.1%)

preprocess27.0ms (0.3%)

explain204.0ms (2.3%)

eval0.0ms (0%)

prune1.0ms (0%)

simplify5.0ms (0.1%)

localize75.0ms (0.9%)

series1.0ms (0%)

simplify1.0s (11.5%)

rewrite350.0ms (4%)

eval45.0ms (0.5%)

prune68.0ms (0.8%)

simplify63.0ms (0.7%)

localize209.0ms (2.4%)

series14.0ms (0.2%)

simplify342.0ms (3.9%)

rewrite438.0ms (5%)

eval119.0ms (1.4%)

prune326.0ms (3.7%)

simplify10.0ms (0.1%)

localize111.0ms (1.3%)

series5.0ms (0.1%)

simplify234.0ms (2.7%)

rewrite375.0ms (4.3%)

eval67.0ms (0.8%)

prune71.0ms (0.8%)

regimes7.0ms (0.1%)

regimes5.0ms (0.1%)

regimes26.0ms (0.3%)

regimes4.0ms (0%)

regimes3.0ms (0%)

simplify43.0ms (0.5%)

soundness1.9s (21.3%)

preprocess74.0ms (0.8%)

end0.0ms (0%)

Profiling

Iter	Nodes	Cost
0	6	9
1	16	8
2	35	8
3	55	8
4	87	8
5	101	8
6	107	8
0	4	4
0	6	4
1	10	4
2	14	4
3	19	4
4	25	4
5	33	4
6	43	4
7	54	4
8	57	4
0	57	4

Iter	Nodes	Cost
0	14	65
0	21	65
1	41	65
2	64	65
3	86	65
4	98	65
5	109	65
6	119	65
7	130	65
8	133	65
0	133	65