Metrics for ENA, Section 1.4, Mentioned, A

start0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated

analyze3.0ms (0%)

Memory

5.9MiB live, 5.9MiB 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)

sample3.1s (37.2%)

Memory

66.1MiB live, 3 152.6MiB allocated

Samples

2.2s	5 707×	2	valid
564.0ms	2 472×	1	valid
5.0ms	77×	0	valid

Precisions

Click to see histograms. Total time spent on operations: 2.4s

ival-cos: 1.4s (57.8% of total)

const: 382.0ms (15.9% of total)

adjust: 211.0ms (8.8% of total)

ival-<=: 208.0ms (8.7% of total)

ival-sub: 190.0ms (7.9% of total)

ival-and: 12.0ms (0.5% of total)

exact: 5.0ms (0.2% of total)

ival-assert: 4.0ms (0.2% of total)

Bogosity

explain191.0ms (2.3%)

Memory

-8.5MiB live, 229.4MiB allocated

FPErrors

Click to see full error table

Ground Truth	Example	Example	Subexpression
133	-	-	`(-.f64 #s(literal 1 binary64) (cos.f64 x))`
0	-	-	`#s(literal 1 binary64)`
0	-	-	`(cos.f64 x)`
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 -
+	133	0
-	0	123

Precision

1.0

Recall

1.0

Confusion?

	Predicted +	Predicted Maybe	Predicted -
+	133	0	0
-	0	0	123

Precision?

1.0

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

105.0ms	348×	2	valid
13.0ms	160×	1	valid
0.0ms	4×	0	valid

Compiler

Compiled 25 to 16 computations (36% saved)

Precisions

Click to see histograms. Total time spent on operations: 100.0ms

ival-cos: 83.0ms (82.8% of total)

adjust: 9.0ms (9% of total)

ival-sub: 7.0ms (7% of total)

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

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

exact: 0.0ms (0% of total)

preprocess20.0ms (0.2%)

Memory

-0.5MiB live, 36.6MiB 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)

Compiler

Compiled 5 to 4 computations (20% saved)

eval0.0ms (0%)

Memory: 0.4MiB live, 0.4MiB allocated
Compiler: Compiled 1 to 1 computations (0% saved)

prune1.0ms (0%)

Memory

1.7MiB live, 1.7MiB allocated

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	52.2%	(-.f64 #s(literal 1 binary64) (cos.f64 x))

Compiler

Compiled 5 to 4 computations (20% saved)

simplify5.0ms (0.1%)

Memory

11.1MiB live, 11.0MiB 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

localize61.0ms (0.7%)

Memory

-15.9MiB live, 82.6MiB allocated

Localize:

Found 2 expressions of interest:

New	Metric	Score	Program
accuracy	0	(cos.f64 x)
accuracy	30.608519809947296	(-.f64 #s(literal 1 binary64) (cos.f64 x))

Samples

48.0ms	174×	2	valid
6.0ms	80×	1	valid
0.0ms	2×	0	valid

Compiler

Compiled 10 to 6 computations (40% saved)

Precisions

Click to see histograms. Total time spent on operations: 37.0ms

ival-cos: 28.0ms (76.1% of total)

adjust: 5.0ms (13.6% of total)

ival-sub: 3.0ms (8.2% 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

1.6MiB live, 1.6MiB allocated

Counts

2 → 24

Calls

Call 1

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

Outputs
#<alt (* 1/2 (pow x 2))>
#<alt (* (pow x 2) (+ 1/2 (* -1/24 (pow x 2))))>
#<alt (* (pow x 2) (+ 1/2 (* (pow x 2) (- (* 1/720 (pow x 2)) 1/24))))>
#<alt (* (pow x 2) (+ 1/2 (* (pow x 2) (- (* (pow x 2) (+ 1/720 (* -1/40320 (pow x 2)))) 1/24))))>
#<alt (- 1 (cos x))>
#<alt (- 1 (cos x))>
#<alt (- 1 (cos x))>
#<alt (- 1 (cos x))>
#<alt (- 1 (cos x))>
#<alt (- 1 (cos x))>
#<alt (- 1 (cos x))>
#<alt (- 1 (cos x))>
#<alt 1>
#<alt (+ 1 (* -1/2 (pow x 2)))>
#<alt (+ 1 (* (pow x 2) (- (* 1/24 (pow x 2)) 1/2)))>
#<alt (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))) 1/2)))>
#<alt (cos x)>
#<alt (cos x)>
#<alt (cos x)>
#<alt (cos x)>
#<alt (cos x)>
#<alt (cos x)>
#<alt (cos x)>
#<alt (cos x)>

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)

simplify693.0ms (8.3%)

Memory

-1.2MiB live, 569.3MiB 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 (.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))))
(- 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)

rewrite365.0ms (4.4%)

Memory

18.3MiB live, 462.3MiB allocated

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))))
(-.f64 (/.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) (cos.f64 x))) (/.f64 (/.f64 (pow.f64 (cos.f64 x) #s(literal 6 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) (cos.f64 x))))
(-.f64 (/.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) (cos.f64 x))) (/.f64 (/.f64 (pow.f64 (cos.f64 x) #s(literal 4 binary64)) (+.f64 #s(literal 3/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x))))) (+.f64 #s(literal 1 binary64) (cos.f64 x))))
(-.f64 (/.f64 #s(literal 1 binary64) (.f64 (fma.f64 (cos.f64 x) (+.f64 #s(literal 1 binary64) (cos.f64 x)) #s(literal 1 binary64)) (+.f64 #s(literal 1 binary64) (pow.f64 (cos.f64 x) #s(literal 3 binary64))))) (/.f64 (pow.f64 (cos.f64 x) #s(literal 6 binary64)) (.f64 (fma.f64 (cos.f64 x) (+.f64 #s(literal 1 binary64) (cos.f64 x)) #s(literal 1 binary64)) (+.f64 #s(literal 1 binary64) (pow.f64 (cos.f64 x) #s(literal 3 binary64))))))
(-.f64 (/.f64 #s(literal 1 binary64) (.f64 (fma.f64 (cos.f64 x) (+.f64 #s(literal 1 binary64) (cos.f64 x)) #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 (pow.f64 (cos.f64 x) #s(literal 9 binary64)) (.f64 (fma.f64 (cos.f64 x) (+.f64 #s(literal 1 binary64) (cos.f64 x)) #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 (/.f64 (.f64 #s(literal 1 binary64) (fma.f64 (cos.f64 x) (+.f64 #s(literal 1 binary64) (cos.f64 x)) #s(literal 1 binary64))) (pow.f64 (fma.f64 (cos.f64 x) (+.f64 #s(literal 1 binary64) (cos.f64 x)) #s(literal 1 binary64)) #s(literal 2 binary64))) (/.f64 (.f64 (fma.f64 (cos.f64 x) (+.f64 #s(literal 1 binary64) (cos.f64 x)) #s(literal 1 binary64)) (pow.f64 (cos.f64 x) #s(literal 3 binary64))) (pow.f64 (fma.f64 (cos.f64 x) (+.f64 #s(literal 1 binary64) (cos.f64 x)) #s(literal 1 binary64)) #s(literal 2 binary64))))
(-.f64 (/.f64 (+.f64 #s(literal 1 binary64) (cos.f64 x)) (pow.f64 (+.f64 #s(literal 1 binary64) (cos.f64 x)) #s(literal 2 binary64))) (/.f64 (*.f64 (+.f64 #s(literal 1 binary64) (cos.f64 x)) (fma.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64))) (pow.f64 (+.f64 #s(literal 1 binary64) (cos.f64 x)) #s(literal 2 binary64))))
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(.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))

eval61.0ms (0.7%)

Memory: -21.0MiB live, 137.7MiB allocated
Compiler: Compiled 10 777 to 911 computations (91.5% saved)

prune73.0ms (0.9%)

Memory

-11.6MiB live, 142.6MiB 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
▶	51.6%	(-.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 (.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)))))
▶	99.7%	#s(approx (- 1 (cos x)) (.f64 #s(literal 1/2 binary64) (.f64 x x)))

Compiler

Compiled 46 to 25 computations (45.7% saved)

simplify67.0ms (0.8%)

Memory

1.0MiB live, 76.4MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 13 expressions of interest:

New	Metric	Score	Program
cost-diff	0	#s(approx (cos x) #s(literal 1 binary64))
cost-diff	0	(-.f64 #s(literal 1 binary64) #s(approx (cos x) #s(literal 1 binary64)))
cost-diff	0	(fma.f64 (*.f64 x x) #s(literal -1/24 binary64) #s(literal 1/2 binary64))
cost-diff	0	(*.f64 x x)
cost-diff	0	(.f64 (.f64 x x) (fma.f64 (*.f64 x x) #s(literal -1/24 binary64) #s(literal 1/2 binary64)))
cost-diff	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))))
cost-diff	0	(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))
cost-diff	0	(.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)))
cost-diff	0	(.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))))
cost-diff	0	#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)))))
cost-diff	0	(*.f64 x x)
cost-diff	0	(.f64 #s(literal 1/2 binary64) (.f64 x x))
cost-diff	0	#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`
628×	`lower-*.f64`
494×	`distribute-lft-in`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	23	175
0	38	175
1	90	175
2	238	175
3	532	175
4	1017	175
5	1462	175
6	1522	175
7	1540	175
8	1544	175
0	1544	175

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 (.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 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))))
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)))
(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 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 -1/40320 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 (.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)))))
#s(approx (- 1 (cos x)) (.f64 x (.f64 x (fma.f64 (.f64 x x) (fma.f64 x (.f64 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 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 x (.f64 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 (.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 x (fma.f64 (.f64 x x) (fma.f64 x (.f64 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 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 x (.f64 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 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 (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))
(*.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))

localize202.0ms (2.4%)

Memory

24.0MiB live, 315.4MiB allocated

Localize:

Found 13 expressions of interest:

New	Metric	Score
accuracy	0.20356397171661583	#s(approx (cos x) #s(literal 1 binary64))
accuracy	30.608519809947296	(-.f64 #s(literal 1 binary64) #s(approx (cos x) #s(literal 1 binary64)))
accuracy	0	(fma.f64 (*.f64 x x) #s(literal -1/24 binary64) #s(literal 1/2 binary64))
accuracy	0	(*.f64 x x)
accuracy	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	0.00390625	(.f64 (.f64 x x) (fma.f64 (*.f64 x x) #s(literal -1/24 binary64) #s(literal 1/2 binary64)))
accuracy	0.00390625	(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	0.00390625	(fma.f64 x (*.f64 x #s(literal -1/40320 binary64)) #s(literal 1/720 binary64))
accuracy	0.00390625	(.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)))
accuracy	0.00390625	(*.f64 x #s(literal -1/40320 binary64))
accuracy	0	(*.f64 x x)
accuracy	0.00390625	(.f64 #s(literal 1/2 binary64) (.f64 x x))
accuracy	0.16590879897376654	#s(approx (- 1 (cos x)) (.f64 #s(literal 1/2 binary64) (.f64 x x)))

Samples

138.0ms	174×	2	valid
30.0ms	80×	1	valid
0.0ms	2×	0	valid

Compiler

Compiled 149 to 24 computations (83.9% saved)

Precisions

Click to see histograms. Total time spent on operations: 125.0ms

ival-cos: 45.0ms (35.9% of total)

ival-mult: 29.0ms (23.1% of total)

const: 19.0ms (15.1% of total)

adjust: 17.0ms (13.5% of total)

ival-add: 11.0ms (8.8% of total)

ival-sub: 4.0ms (3.2% of total)

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

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

exact: 0.0ms (0% of total)

series19.0ms (0.2%)

Memory

-16.9MiB live, 27.4MiB allocated

Counts

15 → 180

Calls

Call 1

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

Outputs
#<alt (* 1/2 (pow x 2))>
#<alt (* (pow x 2) (+ 1/2 (* -1/24 (pow x 2))))>
#<alt (* (pow x 2) (+ 1/2 (* (pow x 2) (- (* 1/720 (pow x 2)) 1/24))))>
#<alt (* (pow x 2) (+ 1/2 (* (pow x 2) (- (* (pow x 2) (+ 1/720 (* -1/40320 (pow x 2)))) 1/24))))>
#<alt (- 1 (cos x))>
#<alt (- 1 (cos x))>
#<alt (- 1 (cos x))>
#<alt (- 1 (cos x))>
#<alt (- 1 (cos x))>
#<alt (- 1 (cos x))>
#<alt (- 1 (cos x))>
#<alt (- 1 (cos x))>
#<alt (* 1/2 (pow x 2))>
#<alt (* 1/2 (pow x 2))>
#<alt (* 1/2 (pow x 2))>
#<alt (* 1/2 (pow x 2))>
#<alt (* 1/2 (pow x 2))>
#<alt (* 1/2 (pow x 2))>
#<alt (* 1/2 (pow x 2))>
#<alt (* 1/2 (pow x 2))>
#<alt (* 1/2 (pow x 2))>
#<alt (* 1/2 (pow x 2))>
#<alt (* 1/2 (pow x 2))>
#<alt (* 1/2 (pow x 2))>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (* 1/2 (pow x 2))>
#<alt (* (pow x 2) (+ 1/2 (* -1/24 (pow x 2))))>
#<alt (* (pow x 2) (+ 1/2 (* (pow x 2) (- (* 1/720 (pow x 2)) 1/24))))>
#<alt (* (pow x 2) (+ 1/2 (* (pow x 2) (- (* (pow x 2) (+ 1/720 (* -1/40320 (pow x 2)))) 1/24))))>
#<alt (- 1 (cos x))>
#<alt (- 1 (cos x))>
#<alt (- 1 (cos x))>
#<alt (- 1 (cos x))>
#<alt (- 1 (cos x))>
#<alt (- 1 (cos x))>
#<alt (- 1 (cos x))>
#<alt (- 1 (cos x))>
#<alt (* 1/2 (pow x 2))>
#<alt (* (pow x 2) (+ 1/2 (* -1/24 (pow x 2))))>
#<alt (* (pow x 2) (+ 1/2 (* (pow x 2) (- (* 1/720 (pow x 2)) 1/24))))>
#<alt (* (pow x 2) (+ 1/2 (* (pow x 2) (- (* (pow x 2) (+ 1/720 (* -1/40320 (pow x 2)))) 1/24))))>
#<alt (* -1/40320 (pow x 8))>
#<alt (* (pow x 8) (- (* 1/720 (/ 1 (pow x 2))) 1/40320))>
#<alt (* (pow x 8) (- (* 1/720 (/ 1 (pow x 2))) (+ 1/40320 (/ 1/24 (pow x 4)))))>
#<alt (* (pow x 8) (- (+ (* 1/720 (/ 1 (pow x 2))) (* 1/2 (/ 1 (pow x 6)))) (+ 1/40320 (/ 1/24 (pow x 4)))))>
#<alt (* -1/40320 (pow x 8))>
#<alt (* (pow x 8) (- (* 1/720 (/ 1 (pow x 2))) 1/40320))>
#<alt (* (pow x 8) (- (* 1/720 (/ 1 (pow x 2))) (+ 1/40320 (/ 1/24 (pow x 4)))))>
#<alt (* (pow x 8) (- (+ (* 1/720 (/ 1 (pow x 2))) (* 1/2 (/ 1 (pow x 6)))) (+ 1/40320 (/ 1/24 (pow x 4)))))>
#<alt (* 1/2 x)>
#<alt (* x (+ 1/2 (* -1/24 (pow x 2))))>
#<alt (* x (+ 1/2 (* (pow x 2) (- (* 1/720 (pow x 2)) 1/24))))>
#<alt (* x (+ 1/2 (* (pow x 2) (- (* (pow x 2) (+ 1/720 (* -1/40320 (pow x 2)))) 1/24))))>
#<alt (* -1/40320 (pow x 7))>
#<alt (* (pow x 7) (- (* 1/720 (/ 1 (pow x 2))) 1/40320))>
#<alt (* (pow x 7) (- (* 1/720 (/ 1 (pow x 2))) (+ 1/40320 (/ 1/24 (pow x 4)))))>
#<alt (* (pow x 7) (- (+ (* 1/720 (/ 1 (pow x 2))) (* 1/2 (/ 1 (pow x 6)))) (+ 1/40320 (/ 1/24 (pow x 4)))))>
#<alt (* -1/40320 (pow x 7))>
#<alt (* -1 (* (pow x 7) (- 1/40320 (* 1/720 (/ 1 (pow x 2))))))>
#<alt (* -1 (* (pow x 7) (- (+ 1/40320 (/ 1/24 (pow x 4))) (* 1/720 (/ 1 (pow x 2))))))>
#<alt (* -1 (* (pow x 7) (- (+ 1/40320 (/ 1/24 (pow x 4))) (+ (* 1/720 (/ 1 (pow x 2))) (* 1/2 (/ 1 (pow x 6)))))))>
#<alt 1/2>
#<alt (+ 1/2 (* -1/24 (pow x 2)))>
#<alt (+ 1/2 (* (pow x 2) (- (* 1/720 (pow x 2)) 1/24)))>
#<alt (+ 1/2 (* (pow x 2) (- (* (pow x 2) (+ 1/720 (* -1/40320 (pow x 2)))) 1/24)))>
#<alt (* -1/40320 (pow x 6))>
#<alt (* (pow x 6) (- (* 1/720 (/ 1 (pow x 2))) 1/40320))>
#<alt (* (pow x 6) (- (* 1/720 (/ 1 (pow x 2))) (+ 1/40320 (/ 1/24 (pow x 4)))))>
#<alt (* (pow x 6) (- (+ (* 1/720 (/ 1 (pow x 2))) (* 1/2 (/ 1 (pow x 6)))) (+ 1/40320 (/ 1/24 (pow x 4)))))>
#<alt (* -1/40320 (pow x 6))>
#<alt (* (pow x 6) (- (* 1/720 (/ 1 (pow x 2))) 1/40320))>
#<alt (* (pow x 6) (- (* 1/720 (/ 1 (pow x 2))) (+ 1/40320 (/ 1/24 (pow x 4)))))>
#<alt (* (pow x 6) (- (+ (* 1/720 (/ 1 (pow x 2))) (* 1/2 (/ 1 (pow x 6)))) (+ 1/40320 (/ 1/24 (pow x 4)))))>
#<alt (* 1/2 (pow x 2))>
#<alt (* (pow x 2) (+ 1/2 (* -1/24 (pow x 2))))>
#<alt (* (pow x 2) (+ 1/2 (* (pow x 2) (- (* 1/720 (pow x 2)) 1/24))))>
#<alt (* (pow x 2) (+ 1/2 (* (pow x 2) (- (* (pow x 2) (+ 1/720 (* -1/40320 (pow x 2)))) 1/24))))>
#<alt (- 1 (cos x))>
#<alt (- 1 (cos x))>
#<alt (- 1 (cos x))>
#<alt (- 1 (cos x))>
#<alt (- 1 (cos x))>
#<alt (- 1 (cos x))>
#<alt (- 1 (cos x))>
#<alt (- 1 (cos x))>
#<alt (* 1/2 (pow x 2))>
#<alt (* (pow x 2) (+ 1/2 (* -1/24 (pow x 2))))>
#<alt (* (pow x 2) (+ 1/2 (* -1/24 (pow x 2))))>
#<alt (* (pow x 2) (+ 1/2 (* -1/24 (pow x 2))))>
#<alt (* -1/24 (pow x 4))>
#<alt (* (pow x 4) (- (* 1/2 (/ 1 (pow x 2))) 1/24))>
#<alt (* (pow x 4) (- (* 1/2 (/ 1 (pow x 2))) 1/24))>
#<alt (* (pow x 4) (- (* 1/2 (/ 1 (pow x 2))) 1/24))>
#<alt (* -1/24 (pow x 4))>
#<alt (* (pow x 4) (- (* 1/2 (/ 1 (pow x 2))) 1/24))>
#<alt (* (pow x 4) (- (* 1/2 (/ 1 (pow x 2))) 1/24))>
#<alt (* (pow x 4) (- (* 1/2 (/ 1 (pow x 2))) 1/24))>
#<alt 1/2>
#<alt (+ 1/2 (* -1/24 (pow x 2)))>
#<alt (+ 1/2 (* -1/24 (pow x 2)))>
#<alt (+ 1/2 (* -1/24 (pow x 2)))>
#<alt (* -1/24 (pow x 2))>
#<alt (* (pow x 2) (- (* 1/2 (/ 1 (pow x 2))) 1/24))>
#<alt (* (pow x 2) (- (* 1/2 (/ 1 (pow x 2))) 1/24))>
#<alt (* (pow x 2) (- (* 1/2 (/ 1 (pow x 2))) 1/24))>
#<alt (* -1/24 (pow x 2))>
#<alt (* (pow x 2) (- (* 1/2 (/ 1 (pow x 2))) 1/24))>
#<alt (* (pow x 2) (- (* 1/2 (/ 1 (pow x 2))) 1/24))>
#<alt (* (pow x 2) (- (* 1/2 (/ 1 (pow x 2))) 1/24))>
#<alt (* 1/2 (pow x 2))>
#<alt (* (pow x 2) (+ 1/2 (* -1/24 (pow x 2))))>
#<alt (* (pow x 2) (+ 1/2 (* (pow x 2) (- (* 1/720 (pow x 2)) 1/24))))>
#<alt (* (pow x 2) (+ 1/2 (* (pow x 2) (- (* (pow x 2) (+ 1/720 (* -1/40320 (pow x 2)))) 1/24))))>
#<alt (- 1 (cos x))>
#<alt (- 1 (cos x))>
#<alt (- 1 (cos x))>
#<alt (- 1 (cos x))>
#<alt (- 1 (cos x))>
#<alt (- 1 (cos x))>
#<alt (- 1 (cos x))>
#<alt (- 1 (cos x))>
#<alt 1>
#<alt (+ 1 (* -1/2 (pow x 2)))>
#<alt (+ 1 (* (pow x 2) (- (* 1/24 (pow x 2)) 1/2)))>
#<alt (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))) 1/2)))>
#<alt (cos x)>
#<alt (cos x)>
#<alt (cos x)>
#<alt (cos x)>
#<alt (cos x)>
#<alt (cos x)>
#<alt (cos x)>
#<alt (cos x)>
#<alt (* -1/40320 x)>
#<alt (* -1/40320 x)>
#<alt (* -1/40320 x)>
#<alt (* -1/40320 x)>
#<alt (* -1/40320 x)>
#<alt (* -1/40320 x)>
#<alt (* -1/40320 x)>
#<alt (* -1/40320 x)>
#<alt (* -1/40320 x)>
#<alt (* -1/40320 x)>
#<alt (* -1/40320 x)>
#<alt (* -1/40320 x)>
#<alt 1/720>
#<alt (+ 1/720 (* -1/40320 (pow x 2)))>
#<alt (+ 1/720 (* -1/40320 (pow x 2)))>
#<alt (+ 1/720 (* -1/40320 (pow x 2)))>
#<alt (* -1/40320 (pow x 2))>
#<alt (* (pow x 2) (- (* 1/720 (/ 1 (pow x 2))) 1/40320))>
#<alt (* (pow x 2) (- (* 1/720 (/ 1 (pow x 2))) 1/40320))>
#<alt (* (pow x 2) (- (* 1/720 (/ 1 (pow x 2))) 1/40320))>
#<alt (* -1/40320 (pow x 2))>
#<alt (* (pow x 2) (- (* 1/720 (/ 1 (pow x 2))) 1/40320))>
#<alt (* (pow x 2) (- (* 1/720 (/ 1 (pow x 2))) 1/40320))>
#<alt (* (pow x 2) (- (* 1/720 (/ 1 (pow x 2))) 1/40320))>
#<alt -1/24>
#<alt (- (* 1/720 (pow x 2)) 1/24)>
#<alt (- (* (pow x 2) (+ 1/720 (* -1/40320 (pow x 2)))) 1/24)>
#<alt (- (* (pow x 2) (+ 1/720 (* -1/40320 (pow x 2)))) 1/24)>
#<alt (* -1/40320 (pow x 4))>
#<alt (* (pow x 4) (- (* 1/720 (/ 1 (pow x 2))) 1/40320))>
#<alt (* (pow x 4) (- (* 1/720 (/ 1 (pow x 2))) (+ 1/40320 (/ 1/24 (pow x 4)))))>
#<alt (* (pow x 4) (- (* 1/720 (/ 1 (pow x 2))) (+ 1/40320 (/ 1/24 (pow x 4)))))>
#<alt (* -1/40320 (pow x 4))>
#<alt (* (pow x 4) (- (* 1/720 (/ 1 (pow x 2))) 1/40320))>
#<alt (* (pow x 4) (- (* 1/720 (/ 1 (pow x 2))) (+ 1/40320 (/ 1/24 (pow x 4)))))>
#<alt (* (pow x 4) (- (* 1/720 (/ 1 (pow x 2))) (+ 1/40320 (/ 1/24 (pow x 4)))))>

Calls

45 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	(* 1/2 (* x x))

simplify284.0ms (3.4%)

Memory

-1.7MiB live, 441.4MiB allocated

Algorithm

1×	egg-herbie

Rules

15 110×	`lower-fma.f64`
15 110×	`lower-fma.f32`
3 676×	`lower-*.f64`
3 676×	`lower-*.f32`
2 172×	`lower-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	96	1416
1	243	1416
2	625	1416
3	1717	1416
4	4548	1408
0	8027	1320

Stop Event

1×	iter limit
1×	node limit

Counts

180 → 180

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

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

rewrite344.0ms (4.1%)

Memory

8.2MiB live, 647.9MiB allocated

Rules

6 504×	`lower-fma.f32`
6 496×	`lower-fma.f64`
4 974×	`lower-*.f32`
4 962×	`lower-*.f64`
3 842×	`lower-/.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	23	158
0	38	158
1	167	158
2	1205	158
0	8482	158

Stop Event

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

Counts

15 → 448

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 (.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 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 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)))
(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))
#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 #s(literal -1/40320 binary64))
(fma.f64 x (*.f64 x #s(literal -1/40320 binary64)) #s(literal 1/720 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))

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 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 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 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)))) 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 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 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 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)))) 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)))
(+.f64 (.f64 (.f64 x x) (.f64 (.f64 x x) (.f64 (.f64 x x) (fma.f64 x (.f64 x #s(literal -1/40320 binary64)) #s(literal 1/720 binary64))))) (.f64 x (.f64 x (fma.f64 x (.f64 x #s(literal -1/24 binary64)) #s(literal 1/2 binary64)))))
(+.f64 (.f64 (.f64 x x) (+.f64 #s(literal 1/2 binary64) (.f64 (.f64 x x) (.f64 (.f64 x x) (fma.f64 x (.f64 x #s(literal -1/40320 binary64)) #s(literal 1/720 binary64)))))) (.f64 x (.f64 x (.f64 (*.f64 x x) #s(literal -1/24 binary64)))))
(+.f64 (.f64 (.f64 (.f64 x x) (.f64 (.f64 x x) (fma.f64 x (.f64 x #s(literal -1/40320 binary64)) #s(literal 1/720 binary64)))) (.f64 x x)) (.f64 x (.f64 x (fma.f64 x (.f64 x #s(literal -1/24 binary64)) #s(literal 1/2 binary64)))))
(+.f64 (.f64 (+.f64 #s(literal 1/2 binary64) (.f64 (.f64 x x) (.f64 (.f64 x x) (fma.f64 x (.f64 x #s(literal -1/40320 binary64)) #s(literal 1/720 binary64))))) (.f64 x x)) (.f64 x (.f64 x (.f64 (*.f64 x x) #s(literal -1/24 binary64)))))
(fma.f64 x (.f64 x #s(literal 1/2 binary64)) (.f64 x (.f64 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 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 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)))) 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 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 #s(literal 1/2 binary64) (.f64 x x) (.f64 x (.f64 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 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 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)))) 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 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 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 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)))) 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 x x) (.f64 (.f64 x x) (.f64 (.f64 x x) (fma.f64 x (.f64 x #s(literal -1/40320 binary64)) #s(literal 1/720 binary64)))) (.f64 x (.f64 x (fma.f64 x (*.f64 x #s(literal -1/24 binary64)) #s(literal 1/2 binary64)))))
(fma.f64 (.f64 x x) (+.f64 #s(literal 1/2 binary64) (.f64 (.f64 x x) (.f64 (.f64 x x) (fma.f64 x (.f64 x #s(literal -1/40320 binary64)) #s(literal 1/720 binary64))))) (.f64 x (.f64 x (.f64 (.f64 x x) #s(literal -1/24 binary64)))))
(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 (.f64 x x) (.f64 (.f64 x x) (fma.f64 x (.f64 x #s(literal -1/40320 binary64)) #s(literal 1/720 binary64)))) (.f64 x x) (.f64 x (.f64 x (fma.f64 x (*.f64 x #s(literal -1/24 binary64)) #s(literal 1/2 binary64)))))
(fma.f64 (.f64 x #s(literal 1/2 binary64)) x (.f64 x (.f64 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))))))
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(.f64 #s(literal 1 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 (fma.f64 (.f64 (.f64 x x) (fma.f64 x (.f64 x #s(literal -1/40320 binary64)) #s(literal 1/720 binary64))) (.f64 (.f64 x x) (.f64 (fma.f64 x (.f64 x #s(literal -1/40320 binary64)) #s(literal 1/720 binary64)) (.f64 (.f64 x x) (fma.f64 x (.f64 x #s(literal -1/40320 binary64)) #s(literal 1/720 binary64))))) #s(literal -1/13824 binary64)) (/.f64 #s(literal 1 binary64) (+.f64 (fma.f64 (.f64 x x) (.f64 (fma.f64 x (.f64 x #s(literal -1/40320 binary64)) #s(literal 1/720 binary64)) (.f64 (.f64 x x) (fma.f64 x (.f64 x #s(literal -1/40320 binary64)) #s(literal 1/720 binary64)))) #s(literal 1/576 binary64)) (.f64 (fma.f64 x (.f64 x #s(literal -1/40320 binary64)) #s(literal 1/720 binary64)) (.f64 (*.f64 x x) #s(literal 1/24 binary64))))))
(.f64 (fma.f64 (.f64 (.f64 x x) (fma.f64 x (.f64 x #s(literal -1/40320 binary64)) #s(literal 1/720 binary64))) (.f64 (.f64 x x) (.f64 (fma.f64 x (.f64 x #s(literal -1/40320 binary64)) #s(literal 1/720 binary64)) (.f64 (.f64 x x) (fma.f64 x (.f64 x #s(literal -1/40320 binary64)) #s(literal 1/720 binary64))))) #s(literal -1/13824 binary64)) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1/576 binary64) (fma.f64 x (.f64 (.f64 x (fma.f64 x (.f64 x #s(literal -1/40320 binary64)) #s(literal 1/720 binary64))) (.f64 (.f64 x x) (fma.f64 x (.f64 x #s(literal -1/40320 binary64)) #s(literal 1/720 binary64)))) (.f64 (fma.f64 x (.f64 x #s(literal -1/40320 binary64)) #s(literal 1/720 binary64)) (.f64 (*.f64 x x) #s(literal 1/24 binary64)))))))
(.f64 (fma.f64 (fma.f64 x (.f64 x #s(literal -1/40320 binary64)) #s(literal 1/720 binary64)) (.f64 (.f64 x x) (.f64 (.f64 x x) (fma.f64 x (.f64 x #s(literal -1/40320 binary64)) #s(literal 1/720 binary64)))) #s(literal -1/576 binary64)) (/.f64 #s(literal 1 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 (neg.f64 (fma.f64 (.f64 (.f64 x x) (fma.f64 x (.f64 x #s(literal -1/40320 binary64)) #s(literal 1/720 binary64))) (.f64 (.f64 x x) (.f64 (fma.f64 x (.f64 x #s(literal -1/40320 binary64)) #s(literal 1/720 binary64)) (.f64 (.f64 x x) (fma.f64 x (.f64 x #s(literal -1/40320 binary64)) #s(literal 1/720 binary64))))) #s(literal -1/13824 binary64))) (/.f64 #s(literal 1 binary64) (neg.f64 (+.f64 (fma.f64 (.f64 x x) (.f64 (fma.f64 x (.f64 x #s(literal -1/40320 binary64)) #s(literal 1/720 binary64)) (.f64 (.f64 x x) (fma.f64 x (.f64 x #s(literal -1/40320 binary64)) #s(literal 1/720 binary64)))) #s(literal 1/576 binary64)) (.f64 (fma.f64 x (.f64 x #s(literal -1/40320 binary64)) #s(literal 1/720 binary64)) (.f64 (*.f64 x x) #s(literal 1/24 binary64)))))))
(.f64 (neg.f64 (fma.f64 (fma.f64 x (.f64 x #s(literal -1/40320 binary64)) #s(literal 1/720 binary64)) (.f64 (.f64 x x) (.f64 (.f64 x x) (fma.f64 x (.f64 x #s(literal -1/40320 binary64)) #s(literal 1/720 binary64)))) #s(literal -1/576 binary64))) (/.f64 #s(literal 1 binary64) (fma.f64 (.f64 x (fma.f64 x (*.f64 x #s(literal -1/40320 binary64)) #s(literal 1/720 binary64))) (neg.f64 x) #s(literal -1/24 binary64))))
(.f64 (-.f64 #s(literal 1/576 binary64) (.f64 (.f64 x x) (.f64 (fma.f64 x (.f64 x #s(literal -1/40320 binary64)) #s(literal 1/720 binary64)) (.f64 (.f64 x x) (fma.f64 x (.f64 x #s(literal -1/40320 binary64)) #s(literal 1/720 binary64)))))) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal -1/24 binary64) (.f64 (.f64 x x) (fma.f64 x (*.f64 x #s(literal -1/40320 binary64)) #s(literal 1/720 binary64))))))

eval115.0ms (1.4%)

Memory: 25.9MiB live, 176.4MiB allocated
Compiler: Compiled 23 605 to 1 869 computations (92.1% saved)

prune113.0ms (1.4%)

Memory

-2.6MiB live, 152.0MiB allocated

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	699	1	700
Fresh	0	0	0
Picked	2	2	4
Done	0	0	0
Total	701	3	704

Accuracy

100.0%

Counts

704 → 3

Alt Table

Click to see full alt table

Status

Accuracy

Program

✓

51.6%

(-.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))))

▶

99.7%

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

Compiler

Compiled 24 to 13 computations (45.8% saved)

simplify6.0ms (0.1%)

Memory

16.3MiB live, 16.3MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 3 expressions of interest:

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

Rules

24×	`lower-+.f64`
24×	`lower-+.f32`
22×	`lower-*.f32`
18×	`lower-*.f64`
18×	`lower--.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	20
0	10	20
1	17	20
2	24	20
3	29	20
4	36	20
5	44	20
6	54	20
7	65	20
8	68	20
0	68	20

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)

Outputs
#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))))
(.f64 (.f64 x #s(literal 1/2 binary64)) x)
(.f64 x (.f64 x #s(literal 1/2 binary64)))
(*.f64 x #s(literal 1/2 binary64))
x
#s(literal 1/2 binary64)

localize66.0ms (0.8%)

Memory

-34.0MiB live, 101.5MiB allocated

Localize:

Found 3 expressions of interest:

New	Metric	Score
accuracy	0	(.f64 (.f64 x #s(literal 1/2 binary64)) x)
accuracy	0	(*.f64 x #s(literal 1/2 binary64))
accuracy	0.16590879897376654	#s(approx (- 1 (cos x)) (.f64 (.f64 x #s(literal 1/2 binary64)) x))

Samples

42.0ms	174×	2	valid
15.0ms	80×	1	valid
0.0ms	2×	0	valid

Compiler

Compiled 16 to 9 computations (43.8% saved)

Precisions

Click to see histograms. Total time spent on operations: 40.0ms

ival-cos: 26.0ms (64.4% of total)

ival-sub: 6.0ms (14.9% of total)

adjust: 5.0ms (12.4% of total)

ival-mult: 3.0ms (7.4% 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

3.5MiB live, 3.5MiB allocated

Counts

3 → 36

Calls

Call 1

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

Outputs
#<alt (* 1/2 (pow x 2))>
#<alt (* (pow x 2) (+ 1/2 (* -1/24 (pow x 2))))>
#<alt (* (pow x 2) (+ 1/2 (* (pow x 2) (- (* 1/720 (pow x 2)) 1/24))))>
#<alt (* (pow x 2) (+ 1/2 (* (pow x 2) (- (* (pow x 2) (+ 1/720 (* -1/40320 (pow x 2)))) 1/24))))>
#<alt (- 1 (cos x))>
#<alt (- 1 (cos x))>
#<alt (- 1 (cos x))>
#<alt (- 1 (cos x))>
#<alt (- 1 (cos x))>
#<alt (- 1 (cos x))>
#<alt (- 1 (cos x))>
#<alt (- 1 (cos x))>
#<alt (* 1/2 (pow x 2))>
#<alt (* 1/2 (pow x 2))>
#<alt (* 1/2 (pow x 2))>
#<alt (* 1/2 (pow x 2))>
#<alt (* 1/2 (pow x 2))>
#<alt (* 1/2 (pow x 2))>
#<alt (* 1/2 (pow x 2))>
#<alt (* 1/2 (pow x 2))>
#<alt (* 1/2 (pow x 2))>
#<alt (* 1/2 (pow x 2))>
#<alt (* 1/2 (pow x 2))>
#<alt (* 1/2 (pow x 2))>
#<alt (* 1/2 x)>
#<alt (* 1/2 x)>
#<alt (* 1/2 x)>
#<alt (* 1/2 x)>
#<alt (* 1/2 x)>
#<alt (* 1/2 x)>
#<alt (* 1/2 x)>
#<alt (* 1/2 x)>
#<alt (* 1/2 x)>
#<alt (* 1/2 x)>
#<alt (* 1/2 x)>
#<alt (* 1/2 x)>

Calls

9 calls:

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

simplify294.0ms (3.5%)

Memory

10.3MiB live, 280.2MiB allocated

Algorithm

1×	egg-herbie

Rules

11 932×	`lower-fma.f64`
11 932×	`lower-fma.f32`
3 102×	`lower-*.f64`
3 102×	`lower-*.f32`
1 304×	`lower-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	28	184
1	71	184
2	164	184
3	391	184
4	869	184
5	1419	184
6	1614	184
7	1988	184
8	2623	184
9	4468	184
10	6314	184
11	7663	184
12	7784	184
13	7795	184
14	7808	184
0	8046	178

Stop Event

1×	iter limit
1×	node limit

Counts

36 → 36

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)

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 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 (.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))))
(- 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)

rewrite275.0ms (3.3%)

Memory

1.7MiB live, 458.9MiB allocated

Rules

4 844×	`lower-*.f32`
4 840×	`lower-*.f64`
4 620×	`lower-/.f64`
4 620×	`lower-/.f32`
3 866×	`lower-fma.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	18
0	10	18
1	30	18
2	151	18
3	1162	18
0	9249	18

Stop Event

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

Counts

3 → 7

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))

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 #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)

eval13.0ms (0.2%)

Memory: -28.6MiB live, 10.1MiB allocated
Compiler: Compiled 305 to 31 computations (89.8% saved)

prune3.0ms (0%)

Memory

9.0MiB live, 9.0MiB allocated

Pruning

3 alts after pruning (0 fresh and 3 done)

	Pruned	Kept	Total
New	43	0	43
Fresh	0	0	0
Picked	0	1	1
Done	0	2	2
Total	43	3	46

Accuracy

100.0%

Counts

46 → 3

Alt Table

Click to see full alt table

Status

Accuracy

Program

✓

51.6%

(-.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))))

✓

99.7%

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

Compiler

Compiled 77 to 34 computations (55.8% saved)

regimes7.0ms (0.1%)

Memory

16.8MiB live, 16.8MiB allocated

Counts

6 → 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 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 #s(literal 1 binary64) (cos.f64 x))

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:

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)

regimes21.0ms (0.3%)

Memory

-25.8MiB live, 13.1MiB 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:

17.0ms	(-.f64 #s(literal 1 binary64) (cos.f64 x))
2.0ms	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

10.9MiB live, 10.9MiB 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	(-.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

12.6MiB live, 12.6MiB 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
51.6%	1	`x`
51.6%	1	`(-.f64 #s(literal 1 binary64) (cos.f64 x))`
51.6%	1	`(cos.f64 x)`

Compiler

Compiled 10 to 7 computations (30% saved)

simplify7.0ms (0.1%)

Memory

-19.2MiB live, 19.4MiB allocated

Algorithm

1×	egg-herbie

Rules

10×	`*-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	17	41
1	26	41
2	30	41
3	32	41
4	33	41

Stop Event

1×

saturated

Calls

Call 1

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

soundness1.8s (21.5%)

Memory

4.6MiB live, 315.7MiB allocated

Rules

32 720×	`lower-fma.f64`
32 720×	`lower-fma.f32`
6 504×	`lower-fma.f32`
6 496×	`lower-fma.f64`
4 974×	`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	23	158
0	38	158
1	167	158
2	1205	158
0	8482	158

Stop Event

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

Compiler

Compiled 62 to 32 computations (48.4% saved)

preprocess115.0ms (1.4%)

Memory: 11.1MiB live, 153.4MiB allocated
Remove: (abs x)
Compiler: Compiled 160 to 80 computations (50% 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	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

start0.0ms (0%)

analyze3.0ms (0%)

sample3.1s (37.2%)

explain191.0ms (2.3%)

preprocess20.0ms (0.2%)

eval0.0ms (0%)

prune1.0ms (0%)

simplify5.0ms (0.1%)

localize61.0ms (0.7%)

series1.0ms (0%)

simplify693.0ms (8.3%)

rewrite365.0ms (4.4%)

eval61.0ms (0.7%)

prune73.0ms (0.9%)

simplify67.0ms (0.8%)

localize202.0ms (2.4%)

series19.0ms (0.2%)

simplify284.0ms (3.4%)

rewrite344.0ms (4.1%)

eval115.0ms (1.4%)

prune113.0ms (1.4%)

simplify6.0ms (0.1%)

localize66.0ms (0.8%)

series1.0ms (0%)

simplify294.0ms (3.5%)

rewrite275.0ms (3.3%)

eval13.0ms (0.2%)

prune3.0ms (0%)

regimes7.0ms (0.1%)

regimes21.0ms (0.3%)

regimes4.0ms (0%)

regimes4.0ms (0%)

simplify7.0ms (0.1%)

soundness1.8s (21.5%)

preprocess115.0ms (1.4%)

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