Metrics for bug323 (missed optimization)

analyze0.0ms (0%)

Memory

0.8MiB live, 0.8MiB allocated

Algorithm

1×

Search

Probability	Valid	Unknown	Precondition	Infinite	Domain	Can't	Iter
0%	0%	25%	75%	0%	0%	0%	0
100%	25%	0%	75%	0%	0%	0%	1

Compiler

Compiled 12 to 10 computations (16.7% saved)

sample1.0s (22.2%)

Memory

10.5MiB live, 967.7MiB allocated

Samples

770.0ms	7 947×	1	valid
18.0ms	309×	0	valid

Precisions

Click to see histograms. Total time spent on operations: 574.0ms

ival-acos: 299.0ms (52.1% of total)

adjust: 110.0ms (19.2% of total)

ival-sub: 93.0ms (16.2% of total)

ival-<=: 44.0ms (7.7% of total)

exact: 13.0ms (2.3% of total)

ival-and: 11.0ms (1.9% of total)

ival-assert: 3.0ms (0.5% of total)

Bogosity

preprocess14.0ms (0.3%)

Memory

11.9MiB live, 11.9MiB allocated

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	11
1	15	9
2	27	9
3	49	9
4	67	9
5	89	9
6	102	9
0	4	4
0	6	4
1	10	4
2	14	4
3	19	4
4	26	4
5	34	4
6	44	4
7	55	4
8	58	4
0	58	4

Stop Event

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

Calls

Call 1

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

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

explain86.0ms (1.8%)

Memory

-2.0MiB live, 35.3MiB allocated

FPErrors

Click to see full error table

Ground Truth	Example	Example	Subexpression
254	-	-	`(acos.f64 (-.f64 #s(literal 1 binary64) x))`
0	-	-	`(-.f64 #s(literal 1 binary64) x)`
0	-	-	`#s(literal 1 binary64)`
0	-	-	`x`

Explanations

Click to see full explanations table

Operator	Subexpression	Explanation	Count
`acos.f64`	`(acos.f64 (-.f64 #s(literal 1 binary64) x))`	sensitivity	254	1

Confusion

	Predicted +	Predicted -
+	254	0
-	0	2

Precision

1.0

Recall

1.0

Confusion?

	Predicted +	Predicted Maybe	Predicted -
+	254	0	0
-	0	1	1

Precision?

0.996078431372549

Recall?

1.0

Freqs

test

number	freq
0	2
1	254

Total Confusion?

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

Precision?

1.0

Recall?

1.0

Samples

51.0ms	490×	1	valid
1.0ms	22×	0	valid

Compiler

Compiled 32 to 20 computations (37.5% saved)

Precisions

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

ival-acos: 24.0ms (65.6% of total)

ival-sub: 6.0ms (16.4% of total)

adjust: 6.0ms (16.4% of total)

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

exact: 0.0ms (0% of total)

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

eval0.0ms (0%)

Memory: 0.2MiB live, 0.2MiB allocated
Compiler: Compiled 1 to 1 computations (0% saved)

prune1.0ms (0%)

Memory

0.5MiB live, 0.5MiB allocated

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	7.7%	(acos.f64 (-.f64 #s(literal 1 binary64) x))

Compiler

Compiled 5 to 4 computations (20% saved)

simplify8.0ms (0.2%)

Memory

-42.5MiB live, 6.0MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 2 expressions of interest:

New	Metric	Score	Program
✓	cost-diff	0	(-.f64 #s(literal 1 binary64) x)
✓	cost-diff	0	(acos.f64 (-.f64 #s(literal 1 binary64) 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	9
0	6	9
1	10	9
2	14	9
3	19	9
4	26	9
5	34	9
6	44	9
7	55	9
8	58	9
0	58	9

Stop Event

1×	iter limit
1×	saturated
1×	iter limit

Calls

Call 1

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

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

localize29.0ms (0.6%)

Memory

28.2MiB live, 28.3MiB allocated

Localize:

Found 2 expressions of interest:

New	Metric	Score	Program
✓	accuracy	100.0%	(-.f64 #s(literal 1 binary64) x)
✓	accuracy	7.7%	(acos.f64 (-.f64 #s(literal 1 binary64) x))

Samples

22.0ms	245×	1	valid
1.0ms	11×	0	valid

Compiler

Compiled 11 to 6 computations (45.5% saved)

Precisions

Click to see histograms. Total time spent on operations: 15.0ms

ival-acos: 9.0ms (59.3% of total)

ival-sub: 3.0ms (19.8% of total)

adjust: 3.0ms (19.8% of total)

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

exact: 0.0ms (0% of total)

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

series1.0ms (0%)

Memory

0.9MiB live, 0.9MiB allocated

Counts

2 → 24

Calls

Call 1

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

Outputs
#<alt (acos (- 1 x))>
#<alt (acos (- 1 x))>
#<alt (acos (- 1 x))>
#<alt (acos (- 1 x))>
#<alt (acos (- 1 x))>
#<alt (acos (- 1 x))>
#<alt (acos (- 1 x))>
#<alt (acos (- 1 x))>
#<alt (acos (+ 1 (* -1 x)))>
#<alt (acos (+ 1 (* -1 x)))>
#<alt (acos (+ 1 (* -1 x)))>
#<alt (acos (+ 1 (* -1 x)))>
#<alt 1>
#<alt (+ 1 (* -1 x))>
#<alt (+ 1 (* -1 x))>
#<alt (+ 1 (* -1 x))>
#<alt (* -1 x)>
#<alt (* x (- (/ 1 x) 1))>
#<alt (* x (- (/ 1 x) 1))>
#<alt (* x (- (/ 1 x) 1))>
#<alt (* -1 x)>
#<alt (* -1 (* x (- 1 (/ 1 x))))>
#<alt (* -1 (* x (- 1 (/ 1 x))))>
#<alt (* -1 (* x (- 1 (/ 1 x))))>

Calls

6 calls:

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

simplify9.0ms (0.2%)

Memory

9.2MiB live, 9.2MiB allocated

Algorithm

1×	egg-herbie

Rules

112×	`lower-fma.f64`
112×	`lower-fma.f32`
80×	`lower-*.f64`
80×	`lower-*.f32`
48×	`lower-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	14	80
1	29	80
2	62	80
3	113	80
4	171	80
5	239	80
6	259	80
0	259	80

Stop Event

1×	iter limit
1×	saturated

Counts

24 → 24

Calls

Call 1

Inputs
(acos (- 1 x))
(acos (- 1 x))
(acos (- 1 x))
(acos (- 1 x))
(acos (- 1 x))
(acos (- 1 x))
(acos (- 1 x))
(acos (- 1 x))
(acos (+ 1 (* -1 x)))
(acos (+ 1 (* -1 x)))
(acos (+ 1 (* -1 x)))
(acos (+ 1 (* -1 x)))
1
(+ 1 (* -1 x))
(+ 1 (* -1 x))
(+ 1 (* -1 x))
(* -1 x)
(* x (- (/ 1 x) 1))
(* x (- (/ 1 x) 1))
(* x (- (/ 1 x) 1))
(* -1 x)
(* -1 (* x (- 1 (/ 1 x))))
(* -1 (* x (- 1 (/ 1 x))))
(* -1 (* x (- 1 (/ 1 x))))

Outputs
(acos (- 1 x))
(acos.f64 (-.f64 #s(literal 1 binary64) x))
(acos (- 1 x))
(acos.f64 (-.f64 #s(literal 1 binary64) x))
(acos (- 1 x))
(acos.f64 (-.f64 #s(literal 1 binary64) x))
(acos (- 1 x))
(acos.f64 (-.f64 #s(literal 1 binary64) x))
(acos (- 1 x))
(acos.f64 (-.f64 #s(literal 1 binary64) x))
(acos (- 1 x))
(acos.f64 (-.f64 #s(literal 1 binary64) x))
(acos (- 1 x))
(acos.f64 (-.f64 #s(literal 1 binary64) x))
(acos (- 1 x))
(acos.f64 (-.f64 #s(literal 1 binary64) x))
(acos (+ 1 (* -1 x)))
(acos.f64 (-.f64 #s(literal 1 binary64) x))
(acos (+ 1 (* -1 x)))
(acos.f64 (-.f64 #s(literal 1 binary64) x))
(acos (+ 1 (* -1 x)))
(acos.f64 (-.f64 #s(literal 1 binary64) x))
(acos (+ 1 (* -1 x)))
(acos.f64 (-.f64 #s(literal 1 binary64) x))
1
#s(literal 1 binary64)
(+ 1 (* -1 x))
(-.f64 #s(literal 1 binary64) x)
(+ 1 (* -1 x))
(-.f64 #s(literal 1 binary64) x)
(+ 1 (* -1 x))
(-.f64 #s(literal 1 binary64) x)
(* -1 x)
(neg.f64 x)
(* x (- (/ 1 x) 1))
(-.f64 #s(literal 1 binary64) x)
(* x (- (/ 1 x) 1))
(-.f64 #s(literal 1 binary64) x)
(* x (- (/ 1 x) 1))
(-.f64 #s(literal 1 binary64) x)
(* -1 x)
(neg.f64 x)
(* -1 (* x (- 1 (/ 1 x))))
(-.f64 #s(literal 1 binary64) x)
(* -1 (* x (- 1 (/ 1 x))))
(-.f64 #s(literal 1 binary64) x)
(* -1 (* x (- 1 (/ 1 x))))
(-.f64 #s(literal 1 binary64) x)

rewrite294.0ms (6.3%)

Memory

-5.9MiB live, 276.0MiB allocated

Algorithm

1×	batch-egg-rewrite

Rules

4 910×	`lower-fma.f64`
4 910×	`lower-fma.f32`
4 364×	`lower-*.f64`
4 364×	`lower-*.f32`
4 164×	`lower-/.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	4	7
0	6	7
1	28	7
2	171	7
3	1385	7
0	9386	7

Stop Event

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

Counts

2 → 339

Calls

Call 1

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

Outputs
(acos.f64 (+.f64 #s(literal 1 binary64) x))
(+.f64 (*.f64 (PI.f64) #s(literal 1/2 binary64)) (neg.f64 (asin.f64 (+.f64 #s(literal 1 binary64) x))))
(+.f64 (neg.f64 (asin.f64 (+.f64 #s(literal 1 binary64) x))) (*.f64 (PI.f64) #s(literal 1/2 binary64)))
(+.f64 (-.f64 (.f64 (PI.f64) #s(literal 1/2 binary64)) (.f64 (PI.f64) #s(literal 1/2 binary64))) (acos.f64 (+.f64 #s(literal 1 binary64) x)))
(-.f64 (PI.f64) (acos.f64 (+.f64 (neg.f64 x) #s(literal -1 binary64))))
(-.f64 (*.f64 (PI.f64) #s(literal 1/2 binary64)) (asin.f64 (+.f64 #s(literal 1 binary64) x)))
(-.f64 (/.f64 (.f64 (.f64 (PI.f64) (.f64 (PI.f64) (PI.f64))) #s(literal 1/8 binary64)) (fma.f64 (asin.f64 (+.f64 #s(literal 1 binary64) x)) (fma.f64 (PI.f64) #s(literal 1/2 binary64) (asin.f64 (+.f64 #s(literal 1 binary64) x))) (.f64 (.f64 (PI.f64) (PI.f64)) #s(literal 1/4 binary64)))) (/.f64 (pow.f64 (asin.f64 (+.f64 #s(literal 1 binary64) x)) #s(literal 3 binary64)) (fma.f64 (asin.f64 (+.f64 #s(literal 1 binary64) x)) (fma.f64 (PI.f64) #s(literal 1/2 binary64) (asin.f64 (+.f64 #s(literal 1 binary64) x))) (.f64 (*.f64 (PI.f64) (PI.f64)) #s(literal 1/4 binary64)))))
(-.f64 (/.f64 (.f64 (.f64 (PI.f64) (PI.f64)) #s(literal 1/4 binary64)) (fma.f64 (PI.f64) #s(literal 1/2 binary64) (asin.f64 (+.f64 #s(literal 1 binary64) x)))) (/.f64 (pow.f64 (asin.f64 (+.f64 #s(literal 1 binary64) x)) #s(literal 2 binary64)) (fma.f64 (PI.f64) #s(literal 1/2 binary64) (asin.f64 (+.f64 #s(literal 1 binary64) x)))))
(-.f64 (/.f64 (.f64 (.f64 (PI.f64) (PI.f64)) #s(literal 1/4 binary64)) (-.f64 (.f64 (PI.f64) #s(literal 1/2 binary64)) (neg.f64 (asin.f64 (+.f64 #s(literal 1 binary64) x))))) (/.f64 (pow.f64 (asin.f64 (+.f64 #s(literal 1 binary64) x)) #s(literal 2 binary64)) (-.f64 (.f64 (PI.f64) #s(literal 1/2 binary64)) (neg.f64 (asin.f64 (+.f64 #s(literal 1 binary64) x))))))
(fma.f64 #s(literal 1 binary64) (*.f64 (PI.f64) #s(literal 1/2 binary64)) (neg.f64 (asin.f64 (+.f64 #s(literal 1 binary64) x))))
(fma.f64 (PI.f64) #s(literal 1/2 binary64) (neg.f64 (asin.f64 (+.f64 #s(literal 1 binary64) x))))
(fma.f64 (pow.f64 (PI.f64) #s(literal 2/3 binary64)) (*.f64 (cbrt.f64 (PI.f64)) #s(literal 1/2 binary64)) (neg.f64 (asin.f64 (+.f64 #s(literal 1 binary64) x))))
(fma.f64 (pow.f64 (PI.f64) #s(literal 2/3 binary64)) (/.f64 (cbrt.f64 (PI.f64)) #s(literal 2 binary64)) (neg.f64 (asin.f64 (+.f64 #s(literal 1 binary64) x))))
(fma.f64 (sqrt.f64 (PI.f64)) (*.f64 (sqrt.f64 (PI.f64)) #s(literal 1/2 binary64)) (neg.f64 (asin.f64 (+.f64 #s(literal 1 binary64) x))))
(fma.f64 (sqrt.f64 (PI.f64)) (/.f64 (sqrt.f64 (PI.f64)) #s(literal 2 binary64)) (neg.f64 (asin.f64 (+.f64 #s(literal 1 binary64) x))))
(fma.f64 (neg.f64 (PI.f64)) #s(literal -1/2 binary64) (neg.f64 (asin.f64 (+.f64 #s(literal 1 binary64) x))))
(fma.f64 #s(literal 1/2 binary64) (PI.f64) (neg.f64 (asin.f64 (+.f64 #s(literal 1 binary64) x))))
(fma.f64 #s(literal 1/2 binary64) (pow.f64 (/.f64 #s(literal 1 binary64) (PI.f64)) #s(literal -1 binary64)) (neg.f64 (asin.f64 (+.f64 #s(literal 1 binary64) x))))
(fma.f64 #s(literal -1 binary64) (asin.f64 (+.f64 #s(literal 1 binary64) x)) (*.f64 (PI.f64) #s(literal 1/2 binary64)))
(/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 (asin.f64 (+.f64 #s(literal 1 binary64) x)) (fma.f64 (PI.f64) #s(literal 1/2 binary64) (asin.f64 (+.f64 #s(literal 1 binary64) x))) (.f64 (.f64 (PI.f64) (PI.f64)) #s(literal 1/4 binary64))) (-.f64 (.f64 (.f64 (PI.f64) (*.f64 (PI.f64) (PI.f64))) #s(literal 1/8 binary64)) (pow.f64 (asin.f64 (+.f64 #s(literal 1 binary64) x)) #s(literal 3 binary64)))))
(/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 (PI.f64) #s(literal 1/2 binary64) (asin.f64 (+.f64 #s(literal 1 binary64) x))) (*.f64 (fma.f64 (PI.f64) #s(literal 1/2 binary64) (asin.f64 (+.f64 #s(literal 1 binary64) x))) (acos.f64 (+.f64 #s(literal 1 binary64) x)))))
(/.f64 (-.f64 (.f64 (.f64 (PI.f64) (.f64 (PI.f64) (PI.f64))) #s(literal 1/8 binary64)) (pow.f64 (asin.f64 (+.f64 #s(literal 1 binary64) x)) #s(literal 3 binary64))) (fma.f64 (asin.f64 (+.f64 #s(literal 1 binary64) x)) (fma.f64 (PI.f64) #s(literal 1/2 binary64) (asin.f64 (+.f64 #s(literal 1 binary64) x))) (.f64 (*.f64 (PI.f64) (PI.f64)) #s(literal 1/4 binary64))))
(/.f64 (-.f64 (.f64 (.f64 (PI.f64) (.f64 (PI.f64) (PI.f64))) #s(literal 1/8 binary64)) (pow.f64 (asin.f64 (+.f64 #s(literal 1 binary64) x)) #s(literal 3 binary64))) (fma.f64 (.f64 (PI.f64) (PI.f64)) #s(literal 1/4 binary64) (-.f64 (pow.f64 (asin.f64 (+.f64 #s(literal 1 binary64) x)) #s(literal 2 binary64)) (.f64 (.f64 (PI.f64) #s(literal 1/2 binary64)) (neg.f64 (asin.f64 (+.f64 #s(literal 1 binary64) x)))))))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 (fma.f64 (asin.f64 (+.f64 #s(literal 1 binary64) x)) (fma.f64 (PI.f64) #s(literal 1/2 binary64) (asin.f64 (+.f64 #s(literal 1 binary64) x))) (.f64 (.f64 (PI.f64) (PI.f64)) #s(literal 1/4 binary64))) (-.f64 (.f64 (.f64 (PI.f64) (*.f64 (PI.f64) (PI.f64))) #s(literal 1/8 binary64)) (pow.f64 (asin.f64 (+.f64 #s(literal 1 binary64) x)) #s(literal 3 binary64))))))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 (fma.f64 (PI.f64) #s(literal 1/2 binary64) (asin.f64 (+.f64 #s(literal 1 binary64) x))) (*.f64 (fma.f64 (PI.f64) #s(literal 1/2 binary64) (asin.f64 (+.f64 #s(literal 1 binary64) x))) (acos.f64 (+.f64 #s(literal 1 binary64) x))))))
(/.f64 (*.f64 (fma.f64 (PI.f64) #s(literal 1/2 binary64) (asin.f64 (+.f64 #s(literal 1 binary64) x))) (acos.f64 (+.f64 #s(literal 1 binary64) x))) (fma.f64 (PI.f64) #s(literal 1/2 binary64) (asin.f64 (+.f64 #s(literal 1 binary64) x))))
(/.f64 (.f64 (fma.f64 (PI.f64) #s(literal 1/2 binary64) (asin.f64 (+.f64 #s(literal 1 binary64) x))) (acos.f64 (+.f64 #s(literal 1 binary64) x))) (-.f64 (.f64 (PI.f64) #s(literal 1/2 binary64)) (neg.f64 (asin.f64 (+.f64 #s(literal 1 binary64) x)))))
(/.f64 (neg.f64 (-.f64 (.f64 (.f64 (PI.f64) (.f64 (PI.f64) (PI.f64))) #s(literal 1/8 binary64)) (pow.f64 (asin.f64 (+.f64 #s(literal 1 binary64) x)) #s(literal 3 binary64)))) (neg.f64 (fma.f64 (asin.f64 (+.f64 #s(literal 1 binary64) x)) (fma.f64 (PI.f64) #s(literal 1/2 binary64) (asin.f64 (+.f64 #s(literal 1 binary64) x))) (.f64 (*.f64 (PI.f64) (PI.f64)) #s(literal 1/4 binary64)))))
(/.f64 (neg.f64 (-.f64 (.f64 (.f64 (PI.f64) (.f64 (PI.f64) (PI.f64))) #s(literal 1/8 binary64)) (pow.f64 (asin.f64 (+.f64 #s(literal 1 binary64) x)) #s(literal 3 binary64)))) (neg.f64 (fma.f64 (.f64 (PI.f64) (PI.f64)) #s(literal 1/4 binary64) (-.f64 (pow.f64 (asin.f64 (+.f64 #s(literal 1 binary64) x)) #s(literal 2 binary64)) (.f64 (.f64 (PI.f64) #s(literal 1/2 binary64)) (neg.f64 (asin.f64 (+.f64 #s(literal 1 binary64) x))))))))
(/.f64 (neg.f64 (*.f64 (fma.f64 (PI.f64) #s(literal 1/2 binary64) (asin.f64 (+.f64 #s(literal 1 binary64) x))) (acos.f64 (+.f64 #s(literal 1 binary64) x)))) (neg.f64 (fma.f64 (PI.f64) #s(literal 1/2 binary64) (asin.f64 (+.f64 #s(literal 1 binary64) x)))))
(/.f64 (neg.f64 (.f64 (fma.f64 (PI.f64) #s(literal 1/2 binary64) (asin.f64 (+.f64 #s(literal 1 binary64) x))) (acos.f64 (+.f64 #s(literal 1 binary64) x)))) (neg.f64 (-.f64 (.f64 (PI.f64) #s(literal 1/2 binary64)) (neg.f64 (asin.f64 (+.f64 #s(literal 1 binary64) x))))))
(/.f64 (-.f64 (.f64 #s(literal 1 binary64) (.f64 (/.f64 #s(literal 2 binary64) (PI.f64)) (fma.f64 (asin.f64 (+.f64 #s(literal 1 binary64) x)) (fma.f64 (PI.f64) #s(literal 1/2 binary64) (asin.f64 (+.f64 #s(literal 1 binary64) x))) (.f64 (.f64 (PI.f64) (PI.f64)) #s(literal 1/4 binary64))))) (.f64 (/.f64 #s(literal 2 binary64) (PI.f64)) (-.f64 (.f64 #s(literal 1 binary64) (fma.f64 (asin.f64 (+.f64 #s(literal 1 binary64) x)) (fma.f64 (PI.f64) #s(literal 1/2 binary64) (asin.f64 (+.f64 #s(literal 1 binary64) x))) (.f64 (.f64 (PI.f64) (PI.f64)) #s(literal 1/4 binary64)))) (.f64 (/.f64 #s(literal 2 binary64) (PI.f64)) (-.f64 (.f64 (.f64 (PI.f64) (.f64 (PI.f64) (PI.f64))) #s(literal 1/8 binary64)) (pow.f64 (asin.f64 (+.f64 #s(literal 1 binary64) x)) #s(literal 3 binary64))))))) (.f64 (/.f64 #s(literal 2 binary64) (PI.f64)) (.f64 (/.f64 #s(literal 2 binary64) (PI.f64)) (fma.f64 (asin.f64 (+.f64 #s(literal 1 binary64) x)) (fma.f64 (PI.f64) #s(literal 1/2 binary64) (asin.f64 (+.f64 #s(literal 1 binary64) x))) (.f64 (.f64 (PI.f64) (PI.f64)) #s(literal 1/4 binary64))))))
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(.f64 (+.f64 #s(literal -1 binary64) (.f64 x x)) (/.f64 #s(literal -1 binary64) (+.f64 #s(literal 1 binary64) x)))
(.f64 (+.f64 #s(literal -1 binary64) (.f64 x x)) (/.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x x #s(literal 1 binary64))) (/.f64 #s(literal -1 binary64) (+.f64 #s(literal 1 binary64) x))))
(.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (fma.f64 x x x))) (fma.f64 x (.f64 x x) #s(literal 1 binary64)))
(.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (fma.f64 x x x))) (pow.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x (.f64 x x) #s(literal 1 binary64))) #s(literal -1 binary64)))
(*.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) x)) (fma.f64 x x #s(literal 1 binary64)))
(*.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) x)) (pow.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x x #s(literal 1 binary64))) #s(literal -1 binary64)))
(.f64 (/.f64 (fma.f64 x x #s(literal 1 binary64)) (fma.f64 x (.f64 x x) #s(literal 1 binary64))) (+.f64 #s(literal 1 binary64) (fma.f64 x x x)))
(.f64 (/.f64 (fma.f64 x x #s(literal 1 binary64)) (fma.f64 x (.f64 x x) #s(literal 1 binary64))) (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (fma.f64 x x x)))))
(*.f64 (/.f64 (fma.f64 x x #s(literal 1 binary64)) (fma.f64 x x #s(literal 1 binary64))) (+.f64 #s(literal 1 binary64) x))
(*.f64 (/.f64 (fma.f64 x x #s(literal 1 binary64)) #s(literal 1 binary64)) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) x)))
(.f64 (/.f64 (fma.f64 x x #s(literal 1 binary64)) (+.f64 #s(literal -1 binary64) (.f64 x (*.f64 x x)))) (neg.f64 (+.f64 #s(literal 1 binary64) (fma.f64 x x x))))
(.f64 (/.f64 (fma.f64 x x #s(literal 1 binary64)) (+.f64 #s(literal -1 binary64) (.f64 x x))) (+.f64 (neg.f64 x) #s(literal -1 binary64)))
(.f64 (/.f64 (fma.f64 x (.f64 x x) #s(literal 1 binary64)) (fma.f64 (fma.f64 x x x) (.f64 (.f64 x x) (fma.f64 x x #s(literal 1 binary64))) #s(literal 1 binary64))) (fma.f64 (fma.f64 x x x) (-.f64 (fma.f64 x x x) #s(literal 1 binary64)) #s(literal 1 binary64)))
(.f64 (/.f64 (fma.f64 x (.f64 x x) #s(literal 1 binary64)) (fma.f64 (fma.f64 x x x) (.f64 (.f64 x x) (fma.f64 x x #s(literal 1 binary64))) #s(literal 1 binary64))) (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (fma.f64 (fma.f64 x x x) (-.f64 (fma.f64 x x x) #s(literal 1 binary64)) #s(literal 1 binary64)))))
(.f64 (/.f64 (fma.f64 x (.f64 x x) #s(literal 1 binary64)) (-.f64 #s(literal 1 binary64) (.f64 (.f64 x x) (fma.f64 x x #s(literal 1 binary64))))) (+.f64 #s(literal 1 binary64) (fma.f64 x x x)))
(.f64 (/.f64 (fma.f64 x (.f64 x x) #s(literal 1 binary64)) (-.f64 #s(literal 1 binary64) (.f64 (.f64 x x) (fma.f64 x x #s(literal 1 binary64))))) (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (fma.f64 x x x)))))
(.f64 (pow.f64 (/.f64 (+.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x))))) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (fma.f64 (*.f64 x x) (fma.f64 x x #s(literal 1 binary64)) #s(literal 1 binary64))))
(.f64 (pow.f64 (/.f64 (+.f64 #s(literal 1 binary64) x) (-.f64 #s(literal 1 binary64) (.f64 x (.f64 x (.f64 x x))))) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (fma.f64 x x #s(literal 1 binary64))))
(.f64 (pow.f64 (/.f64 (+.f64 #s(literal 1 binary64) (fma.f64 x x x)) (+.f64 #s(literal 1 binary64) (.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x)))))) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (fma.f64 (.f64 x (.f64 x x)) (fma.f64 x (.f64 x x) #s(literal 1 binary64)) #s(literal 1 binary64))))
(.f64 (pow.f64 (/.f64 (+.f64 #s(literal 1 binary64) (fma.f64 x x x)) (+.f64 #s(literal 1 binary64) (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x))))) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (fma.f64 x (*.f64 x x) #s(literal 1 binary64))))
(.f64 (/.f64 (+.f64 #s(literal 1 binary64) (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x)))) (fma.f64 x x #s(literal 1 binary64))) (/.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (*.f64 x x) (fma.f64 x x #s(literal 1 binary64)) #s(literal 1 binary64))) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) x))))
(.f64 (/.f64 (+.f64 #s(literal 1 binary64) (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x)))) #s(literal 1 binary64)) (/.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (*.f64 x x) (fma.f64 x x #s(literal 1 binary64)) #s(literal 1 binary64))) (+.f64 #s(literal 1 binary64) x)))
(.f64 (/.f64 (+.f64 #s(literal 1 binary64) (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x)))) (+.f64 #s(literal -1 binary64) (.f64 x x))) (/.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (.f64 x x) (fma.f64 x x #s(literal 1 binary64)) #s(literal 1 binary64))) (/.f64 #s(literal -1 binary64) (+.f64 #s(literal 1 binary64) x))))
(.f64 (/.f64 (+.f64 #s(literal 1 binary64) (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x)))) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (fma.f64 x x x)))) (/.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (.f64 x x) (fma.f64 x x #s(literal 1 binary64)) #s(literal 1 binary64))) (fma.f64 x (.f64 x x) #s(literal 1 binary64))))
(.f64 (/.f64 (+.f64 #s(literal 1 binary64) (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x)))) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) x))) (/.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (*.f64 x x) (fma.f64 x x #s(literal 1 binary64)) #s(literal 1 binary64))) (fma.f64 x x #s(literal 1 binary64))))
(.f64 (/.f64 (+.f64 #s(literal 1 binary64) (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x)))) (/.f64 (fma.f64 x x #s(literal 1 binary64)) (fma.f64 x x #s(literal 1 binary64)))) (/.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (*.f64 x x) (fma.f64 x x #s(literal 1 binary64)) #s(literal 1 binary64))) (+.f64 #s(literal 1 binary64) x)))
(.f64 (/.f64 (+.f64 #s(literal 1 binary64) (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x)))) (/.f64 (fma.f64 x (.f64 x x) #s(literal 1 binary64)) (fma.f64 (fma.f64 x x x) (.f64 (.f64 x x) (fma.f64 x x #s(literal 1 binary64))) #s(literal 1 binary64)))) (/.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (.f64 x x) (fma.f64 x x #s(literal 1 binary64)) #s(literal 1 binary64))) (fma.f64 (fma.f64 x x x) (-.f64 (fma.f64 x x x) #s(literal 1 binary64)) #s(literal 1 binary64))))
(.f64 (/.f64 (+.f64 #s(literal 1 binary64) (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x)))) (/.f64 (fma.f64 x (.f64 x x) #s(literal 1 binary64)) (-.f64 #s(literal 1 binary64) (.f64 (.f64 x x) (fma.f64 x x #s(literal 1 binary64)))))) (/.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (.f64 x x) (fma.f64 x x #s(literal 1 binary64)) #s(literal 1 binary64))) (+.f64 #s(literal 1 binary64) (fma.f64 x x x))))
(.f64 (/.f64 (-.f64 #s(literal 1 binary64) (.f64 x (.f64 x (.f64 x x)))) #s(literal 1 binary64)) (/.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x x #s(literal 1 binary64))) (+.f64 #s(literal 1 binary64) x)))
(.f64 (/.f64 (-.f64 #s(literal 1 binary64) (.f64 x (.f64 x (.f64 x x)))) (fma.f64 x (*.f64 x x) #s(literal 1 binary64))) (/.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x x #s(literal 1 binary64))) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (fma.f64 x x x)))))
(.f64 (/.f64 (-.f64 #s(literal 1 binary64) (.f64 x (.f64 x (.f64 x x)))) (+.f64 #s(literal -1 binary64) (.f64 x (.f64 x x)))) (/.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x x #s(literal 1 binary64))) (/.f64 #s(literal 1 binary64) (neg.f64 (+.f64 #s(literal 1 binary64) (fma.f64 x x x))))))
(.f64 (/.f64 (-.f64 #s(literal 1 binary64) (.f64 x (.f64 x (.f64 x x)))) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (fma.f64 x x x)))) (/.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x x #s(literal 1 binary64))) (fma.f64 x (*.f64 x x) #s(literal 1 binary64))))
(.f64 (/.f64 (-.f64 #s(literal 1 binary64) (.f64 x (.f64 x (.f64 x x)))) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) x))) (/.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x x #s(literal 1 binary64))) (fma.f64 x x #s(literal 1 binary64))))
(.f64 (/.f64 (-.f64 #s(literal 1 binary64) (.f64 x (.f64 x (.f64 x x)))) (/.f64 (fma.f64 x x #s(literal 1 binary64)) (fma.f64 x x #s(literal 1 binary64)))) (/.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x x #s(literal 1 binary64))) (+.f64 #s(literal 1 binary64) x)))
(.f64 (/.f64 (-.f64 #s(literal 1 binary64) (.f64 x (.f64 x (.f64 x x)))) (/.f64 (fma.f64 x (.f64 x x) #s(literal 1 binary64)) (fma.f64 (fma.f64 x x x) (.f64 (*.f64 x x) (fma.f64 x x #s(literal 1 binary64))) #s(literal 1 binary64)))) (/.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x x #s(literal 1 binary64))) (fma.f64 (fma.f64 x x x) (-.f64 (fma.f64 x x x) #s(literal 1 binary64)) #s(literal 1 binary64))))
(.f64 (/.f64 (-.f64 #s(literal 1 binary64) (.f64 x (.f64 x (.f64 x x)))) (/.f64 (fma.f64 x (.f64 x x) #s(literal 1 binary64)) (-.f64 #s(literal 1 binary64) (.f64 (*.f64 x x) (fma.f64 x x #s(literal 1 binary64)))))) (/.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x x #s(literal 1 binary64))) (+.f64 #s(literal 1 binary64) (fma.f64 x x x))))
(.f64 (/.f64 (+.f64 #s(literal 1 binary64) (.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x))))) (fma.f64 (fma.f64 x x x) (.f64 (.f64 x x) (fma.f64 x x #s(literal 1 binary64))) #s(literal 1 binary64))) (/.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (.f64 x (.f64 x x)) (fma.f64 x (.f64 x x) #s(literal 1 binary64)) #s(literal 1 binary64))) (/.f64 #s(literal 1 binary64) (fma.f64 (fma.f64 x x x) (-.f64 (fma.f64 x x x) #s(literal 1 binary64)) #s(literal 1 binary64)))))
(.f64 (/.f64 (+.f64 #s(literal 1 binary64) (.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x))))) (-.f64 #s(literal 1 binary64) (.f64 (.f64 x x) (fma.f64 x x #s(literal 1 binary64))))) (/.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (.f64 x (.f64 x x)) (fma.f64 x (.f64 x x) #s(literal 1 binary64)) #s(literal 1 binary64))) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (fma.f64 x x x)))))
(.f64 (/.f64 (+.f64 #s(literal 1 binary64) (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x)))) (fma.f64 (fma.f64 x x x) (.f64 (.f64 x x) (fma.f64 x x #s(literal 1 binary64))) #s(literal 1 binary64))) (/.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x (*.f64 x x) #s(literal 1 binary64))) (/.f64 #s(literal 1 binary64) (fma.f64 (fma.f64 x x x) (-.f64 (fma.f64 x x x) #s(literal 1 binary64)) #s(literal 1 binary64)))))
(.f64 (/.f64 (+.f64 #s(literal 1 binary64) (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x)))) (-.f64 #s(literal 1 binary64) (.f64 (.f64 x x) (fma.f64 x x #s(literal 1 binary64))))) (/.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x (*.f64 x x) #s(literal 1 binary64))) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (fma.f64 x x x)))))
(.f64 (/.f64 (+.f64 #s(literal 1 binary64) (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x)))) (+.f64 #s(literal 1 binary64) x)) (/.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (*.f64 x x) (fma.f64 x x #s(literal 1 binary64)) #s(literal 1 binary64))) #s(literal 1 binary64)))
(.f64 (/.f64 (+.f64 #s(literal 1 binary64) (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x)))) (/.f64 (fma.f64 x x #s(literal 1 binary64)) (fma.f64 x (.f64 x x) #s(literal 1 binary64)))) (/.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (.f64 x x) (fma.f64 x x #s(literal 1 binary64)) #s(literal 1 binary64))) (+.f64 #s(literal 1 binary64) (fma.f64 x x x))))
(.f64 (/.f64 (+.f64 #s(literal 1 binary64) (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x)))) (/.f64 (fma.f64 x x #s(literal 1 binary64)) #s(literal 1 binary64))) (/.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (*.f64 x x) (fma.f64 x x #s(literal 1 binary64)) #s(literal 1 binary64))) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) x))))
(.f64 (/.f64 (+.f64 #s(literal 1 binary64) (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x)))) (/.f64 (fma.f64 x x #s(literal 1 binary64)) (+.f64 #s(literal -1 binary64) (.f64 x (.f64 x x))))) (/.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (*.f64 x x) (fma.f64 x x #s(literal 1 binary64)) #s(literal 1 binary64))) (neg.f64 (+.f64 #s(literal 1 binary64) (fma.f64 x x x)))))
(.f64 (/.f64 (+.f64 #s(literal 1 binary64) (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x)))) (/.f64 (fma.f64 x x #s(literal 1 binary64)) (+.f64 #s(literal -1 binary64) (.f64 x x)))) (/.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (.f64 x x) (fma.f64 x x #s(literal 1 binary64)) #s(literal 1 binary64))) (+.f64 (neg.f64 x) #s(literal -1 binary64))))
(.f64 (/.f64 (-.f64 #s(literal 1 binary64) (.f64 x (.f64 x (.f64 x x)))) (+.f64 #s(literal 1 binary64) x)) (/.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x x #s(literal 1 binary64))) #s(literal 1 binary64)))
(.f64 (/.f64 (-.f64 #s(literal 1 binary64) (.f64 x (.f64 x (.f64 x x)))) (/.f64 (fma.f64 x x #s(literal 1 binary64)) (fma.f64 x (*.f64 x x) #s(literal 1 binary64)))) (/.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x x #s(literal 1 binary64))) (+.f64 #s(literal 1 binary64) (fma.f64 x x x))))
(.f64 (/.f64 (-.f64 #s(literal 1 binary64) (.f64 x (.f64 x (.f64 x x)))) (/.f64 (fma.f64 x x #s(literal 1 binary64)) #s(literal 1 binary64))) (/.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x x #s(literal 1 binary64))) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) x))))
(.f64 (/.f64 (-.f64 #s(literal 1 binary64) (.f64 x (.f64 x (.f64 x x)))) (/.f64 (fma.f64 x x #s(literal 1 binary64)) (+.f64 #s(literal -1 binary64) (.f64 x (.f64 x x))))) (/.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x x #s(literal 1 binary64))) (neg.f64 (+.f64 #s(literal 1 binary64) (fma.f64 x x x)))))
(.f64 (/.f64 (-.f64 #s(literal 1 binary64) (.f64 x (.f64 x (.f64 x x)))) (/.f64 (fma.f64 x x #s(literal 1 binary64)) (+.f64 #s(literal -1 binary64) (*.f64 x x)))) (/.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x x #s(literal 1 binary64))) (+.f64 (neg.f64 x) #s(literal -1 binary64))))
(.f64 (/.f64 (fma.f64 x x #s(literal 1 binary64)) (/.f64 (fma.f64 x x #s(literal 1 binary64)) (fma.f64 x (.f64 x x) #s(literal 1 binary64)))) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (fma.f64 x x x))))
(*.f64 (/.f64 (fma.f64 x x #s(literal 1 binary64)) (/.f64 (fma.f64 x x #s(literal 1 binary64)) (fma.f64 x x #s(literal 1 binary64)))) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) x)))
(*.f64 (/.f64 (fma.f64 x x #s(literal 1 binary64)) (/.f64 (fma.f64 x x #s(literal 1 binary64)) #s(literal 1 binary64))) (+.f64 #s(literal 1 binary64) x))
(.f64 (/.f64 (fma.f64 x x #s(literal 1 binary64)) (/.f64 (fma.f64 x x #s(literal 1 binary64)) (+.f64 #s(literal -1 binary64) (.f64 x (*.f64 x x))))) (/.f64 #s(literal 1 binary64) (neg.f64 (+.f64 #s(literal 1 binary64) (fma.f64 x x x)))))
(.f64 (/.f64 (fma.f64 x x #s(literal 1 binary64)) (/.f64 (fma.f64 x x #s(literal 1 binary64)) (+.f64 #s(literal -1 binary64) (.f64 x x)))) (/.f64 #s(literal -1 binary64) (+.f64 #s(literal 1 binary64) x)))

eval48.0ms (1%)

Memory: -17.2MiB live, 64.0MiB allocated
Compiler: Compiled 12 869 to 1 318 computations (89.8% saved)

prune39.0ms (0.8%)

Memory

-1.8MiB live, 74.6MiB allocated

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	361	2	363
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	361	3	364

Accuracy

10.2%

Counts

364 → 3

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	7.7%	(acos.f64 (-.f64 #s(literal 1 binary64) x))
▶	7.0%	(acos.f64 #s(approx (- 1 x) (neg.f64 x)))
▶	3.8%	(acos.f64 #s(approx (- 1 x) #s(literal 1 binary64)))

Compiler

Compiled 12 to 10 computations (16.7% saved)

simplify6.0ms (0.1%)

Memory

7.1MiB live, 7.1MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 5 expressions of interest:

New	Metric	Program
✓	cost-diff	(neg.f64 x)
✓	cost-diff	#s(approx (- 1 x) (neg.f64 x))
✓	cost-diff	(acos.f64 #s(approx (- 1 x) (neg.f64 x)))
✓	cost-diff	#s(approx (- 1 x) #s(literal 1 binary64))
✓	cost-diff	(acos.f64 #s(approx (- 1 x) #s(literal 1 binary64)))

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	28
0	11	28
1	17	28
2	21	28
3	26	28
4	34	28
5	44	28
6	59	28
7	62	28
0	62	28

Stop Event

1×	iter limit
1×	saturated
1×	iter limit

Calls

Call 1

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

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

localize38.0ms (0.8%)

Memory

-8.4MiB live, 36.3MiB allocated

Localize:

Found 5 expressions of interest:

New	Metric	Score	Program
✓	accuracy	100.0%	(neg.f64 x)
✓	accuracy	7.7%	(acos.f64 #s(approx (- 1 x) (neg.f64 x)))
✓	accuracy	2.3%	#s(approx (- 1 x) (neg.f64 x))
✓	accuracy	97.5%	#s(approx (- 1 x) #s(literal 1 binary64))
✓	accuracy	7.7%	(acos.f64 #s(approx (- 1 x) #s(literal 1 binary64)))

Samples

28.0ms	245×	1	valid
1.0ms	11×	0	valid

Compiler

Compiled 20 to 7 computations (65% saved)

Precisions

Click to see histograms. Total time spent on operations: 20.0ms

ival-acos: 9.0ms (46.1% of total)

ival-sub: 6.0ms (30.8% of total)

adjust: 3.0ms (15.4% of total)

ival-neg: 1.0ms (5.1% 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

1.1MiB live, 1.1MiB allocated

Counts

5 → 60

Calls

Call 1

Inputs
#<alt (acos.f64 #s(approx (- 1 x) #s(literal 1 binary64)))>
#<alt #s(approx (- 1 x) #s(literal 1 binary64))>
#<alt (acos.f64 #s(approx (- 1 x) (neg.f64 x)))>
#<alt #s(approx (- 1 x) (neg.f64 x))>
#<alt (neg.f64 x)>

Outputs
#<alt (acos (- 1 x))>
#<alt (acos (- 1 x))>
#<alt (acos (- 1 x))>
#<alt (acos (- 1 x))>
#<alt (acos (- 1 x))>
#<alt (acos (- 1 x))>
#<alt (acos (- 1 x))>
#<alt (acos (- 1 x))>
#<alt (acos (+ 1 (* -1 x)))>
#<alt (acos (+ 1 (* -1 x)))>
#<alt (acos (+ 1 (* -1 x)))>
#<alt (acos (+ 1 (* -1 x)))>
#<alt 1>
#<alt (+ 1 (* -1 x))>
#<alt (+ 1 (* -1 x))>
#<alt (+ 1 (* -1 x))>
#<alt (* -1 x)>
#<alt (* x (- (/ 1 x) 1))>
#<alt (* x (- (/ 1 x) 1))>
#<alt (* x (- (/ 1 x) 1))>
#<alt (* -1 x)>
#<alt (* -1 (* x (- 1 (/ 1 x))))>
#<alt (* -1 (* x (- 1 (/ 1 x))))>
#<alt (* -1 (* x (- 1 (/ 1 x))))>
#<alt (acos (- 1 x))>
#<alt (acos (- 1 x))>
#<alt (acos (- 1 x))>
#<alt (acos (- 1 x))>
#<alt (acos (- 1 x))>
#<alt (acos (- 1 x))>
#<alt (acos (- 1 x))>
#<alt (acos (- 1 x))>
#<alt (acos (+ 1 (* -1 x)))>
#<alt (acos (+ 1 (* -1 x)))>
#<alt (acos (+ 1 (* -1 x)))>
#<alt (acos (+ 1 (* -1 x)))>
#<alt 1>
#<alt (+ 1 (* -1 x))>
#<alt (+ 1 (* -1 x))>
#<alt (+ 1 (* -1 x))>
#<alt (* -1 x)>
#<alt (* x (- (/ 1 x) 1))>
#<alt (* x (- (/ 1 x) 1))>
#<alt (* x (- (/ 1 x) 1))>
#<alt (* -1 x)>
#<alt (* -1 (* x (- 1 (/ 1 x))))>
#<alt (* -1 (* x (- 1 (/ 1 x))))>
#<alt (* -1 (* x (- 1 (/ 1 x))))>
#<alt (* -1 x)>
#<alt (* -1 x)>
#<alt (* -1 x)>
#<alt (* -1 x)>
#<alt (* -1 x)>
#<alt (* -1 x)>
#<alt (* -1 x)>
#<alt (* -1 x)>
#<alt (* -1 x)>
#<alt (* -1 x)>
#<alt (* -1 x)>
#<alt (* -1 x)>

Calls

15 calls:

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

simplify11.0ms (0.2%)

Memory

10.2MiB live, 10.2MiB allocated

Algorithm

1×	egg-herbie

Rules

112×	`lower-fma.f64`
112×	`lower-fma.f32`
80×	`lower-*.f64`
80×	`lower-*.f32`
48×	`lower-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	14	184
1	29	184
2	62	184
3	113	184
4	171	184
5	239	184
6	259	184
0	259	184

Stop Event

1×	iter limit
1×	saturated

Counts

60 → 60

Calls

Call 1

Inputs
(acos (- 1 x))
(acos (- 1 x))
(acos (- 1 x))
(acos (- 1 x))
(acos (- 1 x))
(acos (- 1 x))
(acos (- 1 x))
(acos (- 1 x))
(acos (+ 1 (* -1 x)))
(acos (+ 1 (* -1 x)))
(acos (+ 1 (* -1 x)))
(acos (+ 1 (* -1 x)))
1
(+ 1 (* -1 x))
(+ 1 (* -1 x))
(+ 1 (* -1 x))
(* -1 x)
(* x (- (/ 1 x) 1))
(* x (- (/ 1 x) 1))
(* x (- (/ 1 x) 1))
(* -1 x)
(* -1 (* x (- 1 (/ 1 x))))
(* -1 (* x (- 1 (/ 1 x))))
(* -1 (* x (- 1 (/ 1 x))))
(acos (- 1 x))
(acos (- 1 x))
(acos (- 1 x))
(acos (- 1 x))
(acos (- 1 x))
(acos (- 1 x))
(acos (- 1 x))
(acos (- 1 x))
(acos (+ 1 (* -1 x)))
(acos (+ 1 (* -1 x)))
(acos (+ 1 (* -1 x)))
(acos (+ 1 (* -1 x)))
1
(+ 1 (* -1 x))
(+ 1 (* -1 x))
(+ 1 (* -1 x))
(* -1 x)
(* x (- (/ 1 x) 1))
(* x (- (/ 1 x) 1))
(* x (- (/ 1 x) 1))
(* -1 x)
(* -1 (* x (- 1 (/ 1 x))))
(* -1 (* x (- 1 (/ 1 x))))
(* -1 (* x (- 1 (/ 1 x))))
(* -1 x)
(* -1 x)
(* -1 x)
(* -1 x)
(* -1 x)
(* -1 x)
(* -1 x)
(* -1 x)
(* -1 x)
(* -1 x)
(* -1 x)
(* -1 x)

Outputs
(acos (- 1 x))
(acos.f64 (-.f64 #s(literal 1 binary64) x))
(acos (- 1 x))
(acos.f64 (-.f64 #s(literal 1 binary64) x))
(acos (- 1 x))
(acos.f64 (-.f64 #s(literal 1 binary64) x))
(acos (- 1 x))
(acos.f64 (-.f64 #s(literal 1 binary64) x))
(acos (- 1 x))
(acos.f64 (-.f64 #s(literal 1 binary64) x))
(acos (- 1 x))
(acos.f64 (-.f64 #s(literal 1 binary64) x))
(acos (- 1 x))
(acos.f64 (-.f64 #s(literal 1 binary64) x))
(acos (- 1 x))
(acos.f64 (-.f64 #s(literal 1 binary64) x))
(acos (+ 1 (* -1 x)))
(acos.f64 (-.f64 #s(literal 1 binary64) x))
(acos (+ 1 (* -1 x)))
(acos.f64 (-.f64 #s(literal 1 binary64) x))
(acos (+ 1 (* -1 x)))
(acos.f64 (-.f64 #s(literal 1 binary64) x))
(acos (+ 1 (* -1 x)))
(acos.f64 (-.f64 #s(literal 1 binary64) x))
1
#s(literal 1 binary64)
(+ 1 (* -1 x))
(-.f64 #s(literal 1 binary64) x)
(+ 1 (* -1 x))
(-.f64 #s(literal 1 binary64) x)
(+ 1 (* -1 x))
(-.f64 #s(literal 1 binary64) x)
(* -1 x)
(neg.f64 x)
(* x (- (/ 1 x) 1))
(-.f64 #s(literal 1 binary64) x)
(* x (- (/ 1 x) 1))
(-.f64 #s(literal 1 binary64) x)
(* x (- (/ 1 x) 1))
(-.f64 #s(literal 1 binary64) x)
(* -1 x)
(neg.f64 x)
(* -1 (* x (- 1 (/ 1 x))))
(-.f64 #s(literal 1 binary64) x)
(* -1 (* x (- 1 (/ 1 x))))
(-.f64 #s(literal 1 binary64) x)
(* -1 (* x (- 1 (/ 1 x))))
(-.f64 #s(literal 1 binary64) x)
(acos (- 1 x))
(acos.f64 (-.f64 #s(literal 1 binary64) x))
(acos (- 1 x))
(acos.f64 (-.f64 #s(literal 1 binary64) x))
(acos (- 1 x))
(acos.f64 (-.f64 #s(literal 1 binary64) x))
(acos (- 1 x))
(acos.f64 (-.f64 #s(literal 1 binary64) x))
(acos (- 1 x))
(acos.f64 (-.f64 #s(literal 1 binary64) x))
(acos (- 1 x))
(acos.f64 (-.f64 #s(literal 1 binary64) x))
(acos (- 1 x))
(acos.f64 (-.f64 #s(literal 1 binary64) x))
(acos (- 1 x))
(acos.f64 (-.f64 #s(literal 1 binary64) x))
(acos (+ 1 (* -1 x)))
(acos.f64 (-.f64 #s(literal 1 binary64) x))
(acos (+ 1 (* -1 x)))
(acos.f64 (-.f64 #s(literal 1 binary64) x))
(acos (+ 1 (* -1 x)))
(acos.f64 (-.f64 #s(literal 1 binary64) x))
(acos (+ 1 (* -1 x)))
(acos.f64 (-.f64 #s(literal 1 binary64) x))
1
#s(literal 1 binary64)
(+ 1 (* -1 x))
(-.f64 #s(literal 1 binary64) x)
(+ 1 (* -1 x))
(-.f64 #s(literal 1 binary64) x)
(+ 1 (* -1 x))
(-.f64 #s(literal 1 binary64) x)
(* -1 x)
(neg.f64 x)
(* x (- (/ 1 x) 1))
(-.f64 #s(literal 1 binary64) x)
(* x (- (/ 1 x) 1))
(-.f64 #s(literal 1 binary64) x)
(* x (- (/ 1 x) 1))
(-.f64 #s(literal 1 binary64) x)
(* -1 x)
(neg.f64 x)
(* -1 (* x (- 1 (/ 1 x))))
(-.f64 #s(literal 1 binary64) x)
(* -1 (* x (- 1 (/ 1 x))))
(-.f64 #s(literal 1 binary64) x)
(* -1 (* x (- 1 (/ 1 x))))
(-.f64 #s(literal 1 binary64) x)
(* -1 x)
(neg.f64 x)
(* -1 x)
(neg.f64 x)
(* -1 x)
(neg.f64 x)
(* -1 x)
(neg.f64 x)
(* -1 x)
(neg.f64 x)
(* -1 x)
(neg.f64 x)
(* -1 x)
(neg.f64 x)
(* -1 x)
(neg.f64 x)
(* -1 x)
(neg.f64 x)
(* -1 x)
(neg.f64 x)
(* -1 x)
(neg.f64 x)
(* -1 x)
(neg.f64 x)

rewrite217.0ms (4.6%)

Memory

-18.7MiB live, 140.2MiB allocated

Algorithm

1×	batch-egg-rewrite

Rules

4 396×	`lower-*.f64`
4 396×	`lower-*.f32`
2 938×	`lower-/.f64`
2 938×	`lower-/.f32`
1 988×	`frac-sub`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	8	26
0	11	26
1	37	26
2	203	26
3	1732	23
0	9154	23

Stop Event

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

Counts

5 → 205

Calls

Call 1

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

Outputs
(acos.f64 #s(approx (- 1 x) #s(literal 1 binary64)))
(+.f64 (*.f64 (PI.f64) #s(literal 1/2 binary64)) (neg.f64 (asin.f64 #s(approx (- 1 x) #s(literal 1 binary64)))))
(+.f64 (neg.f64 (asin.f64 #s(approx (- 1 x) #s(literal 1 binary64)))) (*.f64 (PI.f64) #s(literal 1/2 binary64)))
(+.f64 (-.f64 (.f64 (PI.f64) #s(literal 1/2 binary64)) (.f64 (PI.f64) #s(literal 1/2 binary64))) (acos.f64 #s(approx (- 1 x) #s(literal 1 binary64))))
(-.f64 (*.f64 (PI.f64) #s(literal 1/2 binary64)) (asin.f64 #s(approx (- 1 x) #s(literal 1 binary64))))
(-.f64 (/.f64 (.f64 (.f64 (PI.f64) (.f64 (PI.f64) (PI.f64))) #s(literal 1/8 binary64)) (fma.f64 (asin.f64 #s(approx (- 1 x) #s(literal 1 binary64))) (fma.f64 (PI.f64) #s(literal 1/2 binary64) (asin.f64 #s(approx (- 1 x) #s(literal 1 binary64)))) (.f64 (.f64 (PI.f64) (PI.f64)) #s(literal 1/4 binary64)))) (/.f64 (pow.f64 (asin.f64 #s(approx (- 1 x) #s(literal 1 binary64))) #s(literal 3 binary64)) (fma.f64 (asin.f64 #s(approx (- 1 x) #s(literal 1 binary64))) (fma.f64 (PI.f64) #s(literal 1/2 binary64) (asin.f64 #s(approx (- 1 x) #s(literal 1 binary64)))) (.f64 (*.f64 (PI.f64) (PI.f64)) #s(literal 1/4 binary64)))))
(-.f64 (/.f64 (.f64 (.f64 (PI.f64) (PI.f64)) #s(literal 1/4 binary64)) (fma.f64 (PI.f64) #s(literal 1/2 binary64) (asin.f64 #s(approx (- 1 x) #s(literal 1 binary64))))) (/.f64 (pow.f64 (asin.f64 #s(approx (- 1 x) #s(literal 1 binary64))) #s(literal 2 binary64)) (fma.f64 (PI.f64) #s(literal 1/2 binary64) (asin.f64 #s(approx (- 1 x) #s(literal 1 binary64))))))
(fma.f64 #s(literal 1 binary64) (*.f64 (PI.f64) #s(literal 1/2 binary64)) (neg.f64 (asin.f64 #s(approx (- 1 x) #s(literal 1 binary64)))))
(fma.f64 (PI.f64) #s(literal 1/2 binary64) (neg.f64 (asin.f64 #s(approx (- 1 x) #s(literal 1 binary64)))))
(fma.f64 #s(literal -1 binary64) (asin.f64 #s(approx (- 1 x) #s(literal 1 binary64))) (*.f64 (PI.f64) #s(literal 1/2 binary64)))
(fma.f64 (pow.f64 (PI.f64) #s(literal 2/3 binary64)) (*.f64 (cbrt.f64 (PI.f64)) #s(literal 1/2 binary64)) (neg.f64 (asin.f64 #s(approx (- 1 x) #s(literal 1 binary64)))))
(fma.f64 (pow.f64 (PI.f64) #s(literal 2/3 binary64)) (/.f64 (cbrt.f64 (PI.f64)) #s(literal 2 binary64)) (neg.f64 (asin.f64 #s(approx (- 1 x) #s(literal 1 binary64)))))
(fma.f64 (sqrt.f64 (PI.f64)) (*.f64 (sqrt.f64 (PI.f64)) #s(literal 1/2 binary64)) (neg.f64 (asin.f64 #s(approx (- 1 x) #s(literal 1 binary64)))))
(fma.f64 (sqrt.f64 (PI.f64)) (/.f64 (sqrt.f64 (PI.f64)) #s(literal 2 binary64)) (neg.f64 (asin.f64 #s(approx (- 1 x) #s(literal 1 binary64)))))
(fma.f64 (neg.f64 (PI.f64)) #s(literal -1/2 binary64) (neg.f64 (asin.f64 #s(approx (- 1 x) #s(literal 1 binary64)))))
(fma.f64 #s(literal 1/2 binary64) (PI.f64) (neg.f64 (asin.f64 #s(approx (- 1 x) #s(literal 1 binary64)))))
(fma.f64 #s(literal 1/2 binary64) (pow.f64 (/.f64 #s(literal 1 binary64) (PI.f64)) #s(literal -1 binary64)) (neg.f64 (asin.f64 #s(approx (- 1 x) #s(literal 1 binary64)))))
(/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 (asin.f64 #s(approx (- 1 x) #s(literal 1 binary64))) (fma.f64 (PI.f64) #s(literal 1/2 binary64) (asin.f64 #s(approx (- 1 x) #s(literal 1 binary64)))) (.f64 (.f64 (PI.f64) (PI.f64)) #s(literal 1/4 binary64))) (-.f64 (.f64 (.f64 (PI.f64) (*.f64 (PI.f64) (PI.f64))) #s(literal 1/8 binary64)) (pow.f64 (asin.f64 #s(approx (- 1 x) #s(literal 1 binary64))) #s(literal 3 binary64)))))
(/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 (PI.f64) #s(literal 1/2 binary64) (asin.f64 #s(approx (- 1 x) #s(literal 1 binary64)))) (*.f64 (fma.f64 (PI.f64) #s(literal 1/2 binary64) (asin.f64 #s(approx (- 1 x) #s(literal 1 binary64)))) (acos.f64 #s(approx (- 1 x) #s(literal 1 binary64))))))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 (fma.f64 (asin.f64 #s(approx (- 1 x) #s(literal 1 binary64))) (fma.f64 (PI.f64) #s(literal 1/2 binary64) (asin.f64 #s(approx (- 1 x) #s(literal 1 binary64)))) (.f64 (.f64 (PI.f64) (PI.f64)) #s(literal 1/4 binary64))) (-.f64 (.f64 (.f64 (PI.f64) (*.f64 (PI.f64) (PI.f64))) #s(literal 1/8 binary64)) (pow.f64 (asin.f64 #s(approx (- 1 x) #s(literal 1 binary64))) #s(literal 3 binary64))))))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 (fma.f64 (PI.f64) #s(literal 1/2 binary64) (asin.f64 #s(approx (- 1 x) #s(literal 1 binary64)))) (*.f64 (fma.f64 (PI.f64) #s(literal 1/2 binary64) (asin.f64 #s(approx (- 1 x) #s(literal 1 binary64)))) (acos.f64 #s(approx (- 1 x) #s(literal 1 binary64)))))))
(/.f64 (-.f64 (.f64 (.f64 (PI.f64) (.f64 (PI.f64) (PI.f64))) #s(literal 1/8 binary64)) (pow.f64 (asin.f64 #s(approx (- 1 x) #s(literal 1 binary64))) #s(literal 3 binary64))) (fma.f64 (asin.f64 #s(approx (- 1 x) #s(literal 1 binary64))) (fma.f64 (PI.f64) #s(literal 1/2 binary64) (asin.f64 #s(approx (- 1 x) #s(literal 1 binary64)))) (.f64 (*.f64 (PI.f64) (PI.f64)) #s(literal 1/4 binary64))))
(/.f64 (-.f64 (.f64 (.f64 (PI.f64) (.f64 (PI.f64) (PI.f64))) #s(literal 1/8 binary64)) (pow.f64 (asin.f64 #s(approx (- 1 x) #s(literal 1 binary64))) #s(literal 3 binary64))) (fma.f64 (.f64 (PI.f64) (PI.f64)) #s(literal 1/4 binary64) (-.f64 (pow.f64 (asin.f64 #s(approx (- 1 x) #s(literal 1 binary64))) #s(literal 2 binary64)) (.f64 (.f64 (PI.f64) #s(literal 1/2 binary64)) (neg.f64 (asin.f64 #s(approx (- 1 x) #s(literal 1 binary64))))))))
(/.f64 (*.f64 (fma.f64 (PI.f64) #s(literal 1/2 binary64) (asin.f64 #s(approx (- 1 x) #s(literal 1 binary64)))) (acos.f64 #s(approx (- 1 x) #s(literal 1 binary64)))) (fma.f64 (PI.f64) #s(literal 1/2 binary64) (asin.f64 #s(approx (- 1 x) #s(literal 1 binary64)))))
(/.f64 (.f64 (fma.f64 (PI.f64) #s(literal 1/2 binary64) (asin.f64 #s(approx (- 1 x) #s(literal 1 binary64)))) (acos.f64 #s(approx (- 1 x) #s(literal 1 binary64)))) (-.f64 (.f64 (PI.f64) #s(literal 1/2 binary64)) (neg.f64 (asin.f64 #s(approx (- 1 x) #s(literal 1 binary64))))))
(/.f64 (neg.f64 (-.f64 (.f64 (.f64 (PI.f64) (.f64 (PI.f64) (PI.f64))) #s(literal 1/8 binary64)) (pow.f64 (asin.f64 #s(approx (- 1 x) #s(literal 1 binary64))) #s(literal 3 binary64)))) (neg.f64 (fma.f64 (asin.f64 #s(approx (- 1 x) #s(literal 1 binary64))) (fma.f64 (PI.f64) #s(literal 1/2 binary64) (asin.f64 #s(approx (- 1 x) #s(literal 1 binary64)))) (.f64 (*.f64 (PI.f64) (PI.f64)) #s(literal 1/4 binary64)))))
(/.f64 (neg.f64 (-.f64 (.f64 (.f64 (PI.f64) (.f64 (PI.f64) (PI.f64))) #s(literal 1/8 binary64)) (pow.f64 (asin.f64 #s(approx (- 1 x) #s(literal 1 binary64))) #s(literal 3 binary64)))) (neg.f64 (fma.f64 (.f64 (PI.f64) (PI.f64)) #s(literal 1/4 binary64) (-.f64 (pow.f64 (asin.f64 #s(approx (- 1 x) #s(literal 1 binary64))) #s(literal 2 binary64)) (.f64 (.f64 (PI.f64) #s(literal 1/2 binary64)) (neg.f64 (asin.f64 #s(approx (- 1 x) #s(literal 1 binary64)))))))))
(/.f64 (neg.f64 (*.f64 (fma.f64 (PI.f64) #s(literal 1/2 binary64) (asin.f64 #s(approx (- 1 x) #s(literal 1 binary64)))) (acos.f64 #s(approx (- 1 x) #s(literal 1 binary64))))) (neg.f64 (fma.f64 (PI.f64) #s(literal 1/2 binary64) (asin.f64 #s(approx (- 1 x) #s(literal 1 binary64))))))
(/.f64 (neg.f64 (.f64 (fma.f64 (PI.f64) #s(literal 1/2 binary64) (asin.f64 #s(approx (- 1 x) #s(literal 1 binary64)))) (acos.f64 #s(approx (- 1 x) #s(literal 1 binary64))))) (neg.f64 (-.f64 (.f64 (PI.f64) #s(literal 1/2 binary64)) (neg.f64 (asin.f64 #s(approx (- 1 x) #s(literal 1 binary64)))))))
(/.f64 (-.f64 (.f64 #s(literal 1 binary64) (.f64 (/.f64 #s(literal 2 binary64) (PI.f64)) (fma.f64 (asin.f64 #s(approx (- 1 x) #s(literal 1 binary64))) (fma.f64 (PI.f64) #s(literal 1/2 binary64) (asin.f64 #s(approx (- 1 x) #s(literal 1 binary64)))) (.f64 (.f64 (PI.f64) (PI.f64)) #s(literal 1/4 binary64))))) (.f64 (/.f64 #s(literal 2 binary64) (PI.f64)) (-.f64 (.f64 #s(literal 1 binary64) (fma.f64 (asin.f64 #s(approx (- 1 x) #s(literal 1 binary64))) (fma.f64 (PI.f64) #s(literal 1/2 binary64) (asin.f64 #s(approx (- 1 x) #s(literal 1 binary64)))) (.f64 (.f64 (PI.f64) (PI.f64)) #s(literal 1/4 binary64)))) (.f64 (/.f64 #s(literal 2 binary64) (PI.f64)) (-.f64 (.f64 (.f64 (PI.f64) (.f64 (PI.f64) (PI.f64))) #s(literal 1/8 binary64)) (pow.f64 (asin.f64 #s(approx (- 1 x) #s(literal 1 binary64))) #s(literal 3 binary64))))))) (.f64 (/.f64 #s(literal 2 binary64) (PI.f64)) (.f64 (/.f64 #s(literal 2 binary64) (PI.f64)) (fma.f64 (asin.f64 #s(approx (- 1 x) #s(literal 1 binary64))) (fma.f64 (PI.f64) #s(literal 1/2 binary64) (asin.f64 #s(approx (- 1 x) #s(literal 1 binary64)))) (.f64 (.f64 (PI.f64) (PI.f64)) #s(literal 1/4 binary64))))))
(/.f64 (-.f64 (.f64 #s(literal 1 binary64) (.f64 (/.f64 #s(literal 2 binary64) (PI.f64)) (fma.f64 (PI.f64) #s(literal 1/2 binary64) (asin.f64 #s(approx (- 1 x) #s(literal 1 binary64)))))) (.f64 (/.f64 #s(literal 2 binary64) (PI.f64)) (-.f64 (.f64 #s(literal 1 binary64) (fma.f64 (PI.f64) #s(literal 1/2 binary64) (asin.f64 #s(approx (- 1 x) #s(literal 1 binary64))))) (.f64 (/.f64 #s(literal 2 binary64) (PI.f64)) (.f64 (fma.f64 (PI.f64) #s(literal 1/2 binary64) (asin.f64 #s(approx (- 1 x) #s(literal 1 binary64)))) (acos.f64 #s(approx (- 1 x) #s(literal 1 binary64)))))))) (.f64 (/.f64 #s(literal 2 binary64) (PI.f64)) (.f64 (/.f64 #s(literal 2 binary64) (PI.f64)) (fma.f64 (PI.f64) #s(literal 1/2 binary64) (asin.f64 #s(approx (- 1 x) #s(literal 1 binary64)))))))
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(/.f64 (-.f64 (.f64 (neg.f64 (neg.f64 (PI.f64))) (.f64 (/.f64 #s(literal 2 binary64) (PI.f64)) (fma.f64 (PI.f64) #s(literal 1/2 binary64) (asin.f64 #s(approx (- 1 x) x))))) (.f64 #s(literal 2 binary64) (-.f64 (.f64 #s(literal 1 binary64) (fma.f64 (PI.f64) #s(literal 1/2 binary64) (asin.f64 #s(approx (- 1 x) x)))) (.f64 (/.f64 #s(literal 2 binary64) (PI.f64)) (.f64 (fma.f64 (PI.f64) #s(literal 1/2 binary64) (asin.f64 #s(approx (- 1 x) x))) (acos.f64 #s(approx (- 1 x) x))))))) (.f64 #s(literal 2 binary64) (.f64 (/.f64 #s(literal 2 binary64) (PI.f64)) (fma.f64 (PI.f64) #s(literal 1/2 binary64) (asin.f64 #s(approx (- 1 x) x))))))
(/.f64 (-.f64 (.f64 (neg.f64 (neg.f64 (PI.f64))) (.f64 #s(literal 2 binary64) (fma.f64 (asin.f64 #s(approx (- 1 x) x)) (fma.f64 (PI.f64) #s(literal 1/2 binary64) (asin.f64 #s(approx (- 1 x) x))) (.f64 (.f64 (PI.f64) (PI.f64)) #s(literal 1/4 binary64))))) (.f64 #s(literal 2 binary64) (-.f64 (.f64 (PI.f64) (fma.f64 (asin.f64 #s(approx (- 1 x) x)) (fma.f64 (PI.f64) #s(literal 1/2 binary64) (asin.f64 #s(approx (- 1 x) x))) (.f64 (.f64 (PI.f64) (PI.f64)) #s(literal 1/4 binary64)))) (.f64 #s(literal 2 binary64) (-.f64 (.f64 (.f64 (PI.f64) (.f64 (PI.f64) (PI.f64))) #s(literal 1/8 binary64)) (pow.f64 (asin.f64 #s(approx (- 1 x) x)) #s(literal 3 binary64))))))) (.f64 #s(literal 2 binary64) (.f64 #s(literal 2 binary64) (fma.f64 (asin.f64 #s(approx (- 1 x) x)) (fma.f64 (PI.f64) #s(literal 1/2 binary64) (asin.f64 #s(approx (- 1 x) x))) (.f64 (.f64 (PI.f64) (PI.f64)) #s(literal 1/4 binary64))))))
(/.f64 (-.f64 (.f64 (neg.f64 (neg.f64 (PI.f64))) (.f64 #s(literal 2 binary64) (fma.f64 (PI.f64) #s(literal 1/2 binary64) (asin.f64 #s(approx (- 1 x) x))))) (.f64 #s(literal 2 binary64) (-.f64 (.f64 (PI.f64) (fma.f64 (PI.f64) #s(literal 1/2 binary64) (asin.f64 #s(approx (- 1 x) x)))) (.f64 #s(literal 2 binary64) (.f64 (fma.f64 (PI.f64) #s(literal 1/2 binary64) (asin.f64 #s(approx (- 1 x) x))) (acos.f64 #s(approx (- 1 x) x))))))) (.f64 #s(literal 2 binary64) (.f64 #s(literal 2 binary64) (fma.f64 (PI.f64) #s(literal 1/2 binary64) (asin.f64 #s(approx (- 1 x) x))))))
(/.f64 (-.f64 (.f64 (neg.f64 (neg.f64 (PI.f64))) (.f64 #s(literal -2 binary64) (fma.f64 (asin.f64 #s(approx (- 1 x) x)) (fma.f64 (PI.f64) #s(literal 1/2 binary64) (asin.f64 #s(approx (- 1 x) x))) (.f64 (.f64 (PI.f64) (PI.f64)) #s(literal 1/4 binary64))))) (.f64 #s(literal 2 binary64) (-.f64 (.f64 (neg.f64 (PI.f64)) (fma.f64 (asin.f64 #s(approx (- 1 x) x)) (fma.f64 (PI.f64) #s(literal 1/2 binary64) (asin.f64 #s(approx (- 1 x) x))) (.f64 (.f64 (PI.f64) (PI.f64)) #s(literal 1/4 binary64)))) (.f64 #s(literal -2 binary64) (-.f64 (.f64 (.f64 (PI.f64) (.f64 (PI.f64) (PI.f64))) #s(literal 1/8 binary64)) (pow.f64 (asin.f64 #s(approx (- 1 x) x)) #s(literal 3 binary64))))))) (.f64 #s(literal 2 binary64) (.f64 #s(literal -2 binary64) (fma.f64 (asin.f64 #s(approx (- 1 x) x)) (fma.f64 (PI.f64) #s(literal 1/2 binary64) (asin.f64 #s(approx (- 1 x) x))) (.f64 (.f64 (PI.f64) (PI.f64)) #s(literal 1/4 binary64))))))
(/.f64 (-.f64 (.f64 (neg.f64 (neg.f64 (PI.f64))) (.f64 #s(literal -2 binary64) (fma.f64 (PI.f64) #s(literal 1/2 binary64) (asin.f64 #s(approx (- 1 x) x))))) (.f64 #s(literal 2 binary64) (-.f64 (.f64 (neg.f64 (PI.f64)) (fma.f64 (PI.f64) #s(literal 1/2 binary64) (asin.f64 #s(approx (- 1 x) x)))) (.f64 #s(literal -2 binary64) (.f64 (fma.f64 (PI.f64) #s(literal 1/2 binary64) (asin.f64 #s(approx (- 1 x) x))) (acos.f64 #s(approx (- 1 x) x))))))) (.f64 #s(literal 2 binary64) (.f64 #s(literal -2 binary64) (fma.f64 (PI.f64) #s(literal 1/2 binary64) (asin.f64 #s(approx (- 1 x) x))))))
(/.f64 (-.f64 (.f64 (neg.f64 (neg.f64 (PI.f64))) (fma.f64 (.f64 (PI.f64) (PI.f64)) #s(literal 1/4 binary64) (+.f64 (pow.f64 (acos.f64 #s(approx (- 1 x) x)) #s(literal 2 binary64)) (.f64 (.f64 (PI.f64) #s(literal 1/2 binary64)) (acos.f64 #s(approx (- 1 x) x)))))) (.f64 #s(literal 2 binary64) (-.f64 (.f64 (.f64 (PI.f64) (.f64 (PI.f64) (PI.f64))) #s(literal 1/8 binary64)) (pow.f64 (acos.f64 #s(approx (- 1 x) x)) #s(literal 3 binary64))))) (.f64 #s(literal 2 binary64) (fma.f64 (.f64 (PI.f64) (PI.f64)) #s(literal 1/4 binary64) (+.f64 (pow.f64 (acos.f64 #s(approx (- 1 x) x)) #s(literal 2 binary64)) (.f64 (.f64 (PI.f64) #s(literal 1/2 binary64)) (acos.f64 #s(approx (- 1 x) x)))))))
(/.f64 (-.f64 (.f64 (neg.f64 (neg.f64 (PI.f64))) (fma.f64 (PI.f64) #s(literal 1/2 binary64) (acos.f64 #s(approx (- 1 x) x)))) (.f64 #s(literal 2 binary64) (-.f64 (.f64 (.f64 (PI.f64) (PI.f64)) #s(literal 1/4 binary64)) (pow.f64 (acos.f64 #s(approx (- 1 x) x)) #s(literal 2 binary64))))) (*.f64 #s(literal 2 binary64) (fma.f64 (PI.f64) #s(literal 1/2 binary64) (acos.f64 #s(approx (- 1 x) x)))))
(/.f64 (-.f64 (.f64 (.f64 (.f64 (PI.f64) (.f64 (PI.f64) (PI.f64))) #s(literal 1/8 binary64)) (fma.f64 (asin.f64 #s(approx (- 1 x) x)) (fma.f64 (PI.f64) #s(literal 1/2 binary64) (asin.f64 #s(approx (- 1 x) x))) (.f64 (.f64 (PI.f64) (PI.f64)) #s(literal 1/4 binary64)))) (.f64 (fma.f64 (asin.f64 #s(approx (- 1 x) x)) (fma.f64 (PI.f64) #s(literal 1/2 binary64) (asin.f64 #s(approx (- 1 x) x))) (.f64 (.f64 (PI.f64) (PI.f64)) #s(literal 1/4 binary64))) (pow.f64 (asin.f64 #s(approx (- 1 x) x)) #s(literal 3 binary64)))) (.f64 (fma.f64 (asin.f64 #s(approx (- 1 x) x)) (fma.f64 (PI.f64) #s(literal 1/2 binary64) (asin.f64 #s(approx (- 1 x) x))) (.f64 (.f64 (PI.f64) (PI.f64)) #s(literal 1/4 binary64))) (fma.f64 (asin.f64 #s(approx (- 1 x) x)) (fma.f64 (PI.f64) #s(literal 1/2 binary64) (asin.f64 #s(approx (- 1 x) x))) (.f64 (.f64 (PI.f64) (PI.f64)) #s(literal 1/4 binary64)))))
(/.f64 (-.f64 (.f64 (.f64 (.f64 (PI.f64) (PI.f64)) #s(literal 1/4 binary64)) (fma.f64 (PI.f64) #s(literal 1/2 binary64) (asin.f64 #s(approx (- 1 x) x)))) (.f64 (fma.f64 (PI.f64) #s(literal 1/2 binary64) (asin.f64 #s(approx (- 1 x) x))) (pow.f64 (asin.f64 #s(approx (- 1 x) x)) #s(literal 2 binary64)))) (*.f64 (fma.f64 (PI.f64) #s(literal 1/2 binary64) (asin.f64 #s(approx (- 1 x) x))) (fma.f64 (PI.f64) #s(literal 1/2 binary64) (asin.f64 #s(approx (- 1 x) x)))))
(/.f64 (neg.f64 (neg.f64 (-.f64 (.f64 (.f64 (PI.f64) (.f64 (PI.f64) (PI.f64))) #s(literal 1/8 binary64)) (pow.f64 (asin.f64 #s(approx (- 1 x) x)) #s(literal 3 binary64))))) (neg.f64 (neg.f64 (fma.f64 (asin.f64 #s(approx (- 1 x) x)) (fma.f64 (PI.f64) #s(literal 1/2 binary64) (asin.f64 #s(approx (- 1 x) x))) (.f64 (*.f64 (PI.f64) (PI.f64)) #s(literal 1/4 binary64))))))
(/.f64 (neg.f64 (neg.f64 (*.f64 (fma.f64 (PI.f64) #s(literal 1/2 binary64) (asin.f64 #s(approx (- 1 x) x))) (acos.f64 #s(approx (- 1 x) x))))) (neg.f64 (neg.f64 (fma.f64 (PI.f64) #s(literal 1/2 binary64) (asin.f64 #s(approx (- 1 x) x))))))
(pow.f64 (/.f64 (fma.f64 (asin.f64 #s(approx (- 1 x) x)) (fma.f64 (PI.f64) #s(literal 1/2 binary64) (asin.f64 #s(approx (- 1 x) x))) (.f64 (.f64 (PI.f64) (PI.f64)) #s(literal 1/4 binary64))) (-.f64 (.f64 (.f64 (PI.f64) (*.f64 (PI.f64) (PI.f64))) #s(literal 1/8 binary64)) (pow.f64 (asin.f64 #s(approx (- 1 x) x)) #s(literal 3 binary64)))) #s(literal -1 binary64))
(pow.f64 (/.f64 (fma.f64 (PI.f64) #s(literal 1/2 binary64) (asin.f64 #s(approx (- 1 x) x))) (*.f64 (fma.f64 (PI.f64) #s(literal 1/2 binary64) (asin.f64 #s(approx (- 1 x) x))) (acos.f64 #s(approx (- 1 x) x)))) #s(literal -1 binary64))
(.f64 (-.f64 (.f64 (.f64 (PI.f64) (.f64 (PI.f64) (PI.f64))) #s(literal 1/8 binary64)) (pow.f64 (asin.f64 #s(approx (- 1 x) x)) #s(literal 3 binary64))) (/.f64 #s(literal 1 binary64) (fma.f64 (asin.f64 #s(approx (- 1 x) x)) (fma.f64 (PI.f64) #s(literal 1/2 binary64) (asin.f64 #s(approx (- 1 x) x))) (.f64 (.f64 (PI.f64) (PI.f64)) #s(literal 1/4 binary64)))))
(.f64 (.f64 (fma.f64 (PI.f64) #s(literal 1/2 binary64) (asin.f64 #s(approx (- 1 x) x))) (acos.f64 #s(approx (- 1 x) x))) (/.f64 #s(literal 1 binary64) (fma.f64 (PI.f64) #s(literal 1/2 binary64) (asin.f64 #s(approx (- 1 x) x)))))
#s(approx (- 1 x) x)
x
(+.f64 x #s(literal 0 binary64))
(+.f64 #s(literal 0 binary64) x)
(exp.f64 (log.f64 x))
(exp.f64 (*.f64 (log.f64 x) #s(literal 1 binary64)))
(-.f64 #s(literal 0 binary64) x)
(-.f64 (/.f64 #s(literal 0 binary64) (*.f64 x x)) x)
(-.f64 (/.f64 #s(literal 0 binary64) x) x)
(fma.f64 #s(literal 1 binary64) x #s(literal 0 binary64))
(fma.f64 x #s(literal 1 binary64) #s(literal 0 binary64))
(fma.f64 x #s(literal -1 binary64) #s(literal 0 binary64))
(fma.f64 (.f64 x (.f64 x x)) (/.f64 #s(literal 1 binary64) (*.f64 x x)) #s(literal 0 binary64))
(fma.f64 (*.f64 x x) (/.f64 #s(literal 1 binary64) x) #s(literal 0 binary64))
(fma.f64 #s(literal -1 binary64) x #s(literal 0 binary64))
(neg.f64 x)
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) x))
(/.f64 #s(literal 1 binary64) (/.f64 x (*.f64 x x)))
(/.f64 (.f64 x (.f64 x x)) (*.f64 x x))
(/.f64 (.f64 x (.f64 x x)) (+.f64 #s(literal 0 binary64) (-.f64 (*.f64 x x) #s(literal 0 binary64))))
(/.f64 (.f64 x (.f64 x x)) (neg.f64 (+.f64 #s(literal 0 binary64) (-.f64 (*.f64 x x) #s(literal 0 binary64)))))
(/.f64 (*.f64 x x) x)
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 #s(literal 1 binary64) x)))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 x (*.f64 x x))))
(/.f64 (-.f64 (.f64 #s(literal 0 binary64) (.f64 x x)) (.f64 (.f64 x (.f64 x x)) (.f64 x x))) (.f64 x (.f64 x (*.f64 x x))))
(pow.f64 x #s(literal 1 binary64))
(pow.f64 (/.f64 #s(literal 1 binary64) x) #s(literal -1 binary64))
(pow.f64 (/.f64 x (*.f64 x x)) #s(literal -1 binary64))
(*.f64 #s(literal 1 binary64) x)
(*.f64 x #s(literal 1 binary64))
(*.f64 x #s(literal -1 binary64))
(.f64 (.f64 x (.f64 x x)) (/.f64 #s(literal 1 binary64) (.f64 x x)))
(.f64 (.f64 x x) (/.f64 #s(literal 1 binary64) x))
(*.f64 #s(literal -1 binary64) x)

eval28.0ms (0.6%)

Memory: 26.6MiB live, 26.6MiB allocated
Compiler: Compiled 7 189 to 767 computations (89.3% saved)

prune36.0ms (0.8%)

Memory

-12.2MiB live, 26.2MiB allocated

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	263	2	265
Fresh	0	0	0
Picked	1	1	2
Done	0	1	1
Total	264	4	268

Accuracy

10.2%

Counts

268 → 4

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	7.0%	(fma.f64 (sqrt.f64 (PI.f64)) (*.f64 (sqrt.f64 (PI.f64)) #s(literal 1/2 binary64)) (neg.f64 (asin.f64 #s(approx (- 1 x) x))))
✓	7.7%	(acos.f64 (-.f64 #s(literal 1 binary64) x))
▶	7.0%	(acos.f64 #s(approx (- 1 x) x))
✓	3.8%	(acos.f64 #s(approx (- 1 x) #s(literal 1 binary64)))

Compiler

Compiled 22 to 17 computations (22.7% saved)

simplify17.0ms (0.4%)

Memory

5.0MiB live, 5.0MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 6 expressions of interest:

New	Metric	Score	Program
✓	cost-diff	0	(*.f64 (sqrt.f64 (PI.f64)) #s(literal 1/2 binary64))
✓	cost-diff	0	(PI.f64)
✓	cost-diff	0	(sqrt.f64 (PI.f64))
✓	cost-diff	1600	(fma.f64 (sqrt.f64 (PI.f64)) (*.f64 (sqrt.f64 (PI.f64)) #s(literal 1/2 binary64)) (neg.f64 (asin.f64 #s(approx (- 1 x) x))))
✓	cost-diff	0	#s(approx (- 1 x) x)
✓	cost-diff	0	(acos.f64 #s(approx (- 1 x) x))

Rules

228×	`lower-fma.f32`
226×	`lower-fma.f64`
160×	`lower-*.f32`
158×	`lower-*.f64`
80×	`lower-+.f64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	12	53
0	20	53
1	33	49
2	44	49
3	71	49
4	108	49
5	179	49
6	267	49
7	350	49
8	373	49
9	381	49
0	381	49

Stop Event

1×	iter limit
1×	saturated
1×	iter limit

Calls

Call 1

Inputs
(acos.f64 #s(approx (- 1 x) x))
#s(approx (- 1 x) x)
x
(fma.f64 (sqrt.f64 (PI.f64)) (*.f64 (sqrt.f64 (PI.f64)) #s(literal 1/2 binary64)) (neg.f64 (asin.f64 #s(approx (- 1 x) x))))
(sqrt.f64 (PI.f64))
(PI.f64)
(*.f64 (sqrt.f64 (PI.f64)) #s(literal 1/2 binary64))
#s(literal 1/2 binary64)
(neg.f64 (asin.f64 #s(approx (- 1 x) x)))
(asin.f64 #s(approx (- 1 x) x))
#s(approx (- 1 x) x)
x

Outputs
(acos.f64 #s(approx (- 1 x) x))
#s(approx (- 1 x) x)
x
(fma.f64 (sqrt.f64 (PI.f64)) (*.f64 (sqrt.f64 (PI.f64)) #s(literal 1/2 binary64)) (neg.f64 (asin.f64 #s(approx (- 1 x) x))))
(-.f64 (*.f64 (PI.f64) #s(literal 1/2 binary64)) (asin.f64 #s(approx (- 1 x) x)))
(sqrt.f64 (PI.f64))
(PI.f64)
(*.f64 (sqrt.f64 (PI.f64)) #s(literal 1/2 binary64))
#s(literal 1/2 binary64)
(neg.f64 (asin.f64 #s(approx (- 1 x) x)))
(asin.f64 #s(approx (- 1 x) x))
#s(approx (- 1 x) x)
x

localize85.0ms (1.8%)

Memory

-13.5MiB live, 25.8MiB allocated

Localize:

Found 6 expressions of interest:

New	Metric	Score	Program
✓	accuracy	98.4%	(sqrt.f64 (PI.f64))
✓	accuracy	98.0%	(asin.f64 #s(approx (- 1 x) x))
✓	accuracy	13.4%	(fma.f64 (sqrt.f64 (PI.f64)) (*.f64 (sqrt.f64 (PI.f64)) #s(literal 1/2 binary64)) (neg.f64 (asin.f64 #s(approx (- 1 x) x))))
✓	accuracy	5.4%	#s(approx (- 1 x) x)
✓	accuracy	7.7%	(acos.f64 #s(approx (- 1 x) x))
✓	accuracy	5.4%	#s(approx (- 1 x) x)

Samples

65.0ms	239×	1	valid
2.0ms	17×	0	valid

Compiler

Compiled 44 to 14 computations (68.2% saved)

Precisions

Click to see histograms. Total time spent on operations: 52.0ms

ival-pi: 12.0ms (22.9% of total)

ival-acos: 10.0ms (19.1% of total)

ival-asin: 8.0ms (15.3% of total)

adjust: 6.0ms (11.5% of total)

ival-mult: 5.0ms (9.5% of total)

ival-sub: 3.0ms (5.7% of total)

ival-sqrt: 3.0ms (5.7% of total)

ival-neg: 2.0ms (3.8% of total)

ival-add: 2.0ms (3.8% 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

0.6MiB live, 0.6MiB allocated

Counts

7 → 48

Calls

Call 1

Inputs
#<alt (acos.f64 #s(approx (- 1 x) x))>
#<alt #s(approx (- 1 x) x)>
#<alt (fma.f64 (sqrt.f64 (PI.f64)) (*.f64 (sqrt.f64 (PI.f64)) #s(literal 1/2 binary64)) (neg.f64 (asin.f64 #s(approx (- 1 x) x))))>
#<alt (sqrt.f64 (PI.f64))>
#<alt (PI.f64)>
#<alt (*.f64 (sqrt.f64 (PI.f64)) #s(literal 1/2 binary64))>
#<alt (asin.f64 #s(approx (- 1 x) x))>

Outputs
#<alt (acos (- 1 x))>
#<alt (acos (- 1 x))>
#<alt (acos (- 1 x))>
#<alt (acos (- 1 x))>
#<alt (acos (- 1 x))>
#<alt (acos (- 1 x))>
#<alt (acos (- 1 x))>
#<alt (acos (- 1 x))>
#<alt (acos (+ 1 (* -1 x)))>
#<alt (acos (+ 1 (* -1 x)))>
#<alt (acos (+ 1 (* -1 x)))>
#<alt (acos (+ 1 (* -1 x)))>
#<alt 1>
#<alt (+ 1 (* -1 x))>
#<alt (+ 1 (* -1 x))>
#<alt (+ 1 (* -1 x))>
#<alt (* -1 x)>
#<alt (* x (- (/ 1 x) 1))>
#<alt (* x (- (/ 1 x) 1))>
#<alt (* x (- (/ 1 x) 1))>
#<alt (* -1 x)>
#<alt (* -1 (* x (- 1 (/ 1 x))))>
#<alt (* -1 (* x (- 1 (/ 1 x))))>
#<alt (* -1 (* x (- 1 (/ 1 x))))>
#<alt (- (* 1/2 (PI)) (asin (- 1 x)))>
#<alt (- (* 1/2 (PI)) (asin (- 1 x)))>
#<alt (- (* 1/2 (PI)) (asin (- 1 x)))>
#<alt (- (* 1/2 (PI)) (asin (- 1 x)))>
#<alt (- (* 1/2 (PI)) (asin (- 1 x)))>
#<alt (- (* 1/2 (PI)) (asin (- 1 x)))>
#<alt (- (* 1/2 (PI)) (asin (- 1 x)))>
#<alt (- (* 1/2 (PI)) (asin (- 1 x)))>
#<alt (- (* 1/2 (PI)) (asin (+ 1 (* -1 x))))>
#<alt (- (* 1/2 (PI)) (asin (+ 1 (* -1 x))))>
#<alt (- (* 1/2 (PI)) (asin (+ 1 (* -1 x))))>
#<alt (- (* 1/2 (PI)) (asin (+ 1 (* -1 x))))>
#<alt (asin (- 1 x))>
#<alt (asin (- 1 x))>
#<alt (asin (- 1 x))>
#<alt (asin (- 1 x))>
#<alt (asin (- 1 x))>
#<alt (asin (- 1 x))>
#<alt (asin (- 1 x))>
#<alt (asin (- 1 x))>
#<alt (asin (+ 1 (* -1 x)))>
#<alt (asin (+ 1 (* -1 x)))>
#<alt (asin (+ 1 (* -1 x)))>
#<alt (asin (+ 1 (* -1 x)))>

Calls

12 calls:

Time	Variable		Point	Expression
0.0ms	x	@	0	(+ (* (sqrt (PI)) (* (sqrt (PI)) 1/2)) (neg (asin (- 1 x))))
0.0ms	x	@	-inf	(+ (* (sqrt (PI)) (* (sqrt (PI)) 1/2)) (neg (asin (- 1 x))))
0.0ms	x	@	inf	(+ (* (sqrt (PI)) (* (sqrt (PI)) 1/2)) (neg (asin (- 1 x))))
0.0ms	x	@	0	(acos (- 1 x))
0.0ms	x	@	0	(asin (- 1 x))

simplify19.0ms (0.4%)

Memory

5.4MiB live, 5.4MiB allocated

Algorithm

1×	egg-herbie

Rules

240×	`lower-fma.f64`
240×	`lower-fma.f32`
160×	`lower-*.f64`
160×	`lower-*.f32`
88×	`lower-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	21	224
1	41	224
2	77	224
3	134	224
4	206	224
5	292	224
6	353	224
7	387	224
8	438	224
9	455	224
10	463	224
0	463	224

Stop Event

1×	iter limit
1×	saturated

Counts

48 → 48

Calls

Call 1

Inputs
(acos (- 1 x))
(acos (- 1 x))
(acos (- 1 x))
(acos (- 1 x))
(acos (- 1 x))
(acos (- 1 x))
(acos (- 1 x))
(acos (- 1 x))
(acos (+ 1 (* -1 x)))
(acos (+ 1 (* -1 x)))
(acos (+ 1 (* -1 x)))
(acos (+ 1 (* -1 x)))
1
(+ 1 (* -1 x))
(+ 1 (* -1 x))
(+ 1 (* -1 x))
(* -1 x)
(* x (- (/ 1 x) 1))
(* x (- (/ 1 x) 1))
(* x (- (/ 1 x) 1))
(* -1 x)
(* -1 (* x (- 1 (/ 1 x))))
(* -1 (* x (- 1 (/ 1 x))))
(* -1 (* x (- 1 (/ 1 x))))
(- (* 1/2 (PI)) (asin (- 1 x)))
(- (* 1/2 (PI)) (asin (- 1 x)))
(- (* 1/2 (PI)) (asin (- 1 x)))
(- (* 1/2 (PI)) (asin (- 1 x)))
(- (* 1/2 (PI)) (asin (- 1 x)))
(- (* 1/2 (PI)) (asin (- 1 x)))
(- (* 1/2 (PI)) (asin (- 1 x)))
(- (* 1/2 (PI)) (asin (- 1 x)))
(- (* 1/2 (PI)) (asin (+ 1 (* -1 x))))
(- (* 1/2 (PI)) (asin (+ 1 (* -1 x))))
(- (* 1/2 (PI)) (asin (+ 1 (* -1 x))))
(- (* 1/2 (PI)) (asin (+ 1 (* -1 x))))
(asin (- 1 x))
(asin (- 1 x))
(asin (- 1 x))
(asin (- 1 x))
(asin (- 1 x))
(asin (- 1 x))
(asin (- 1 x))
(asin (- 1 x))
(asin (+ 1 (* -1 x)))
(asin (+ 1 (* -1 x)))
(asin (+ 1 (* -1 x)))
(asin (+ 1 (* -1 x)))

Outputs
(acos (- 1 x))
(acos.f64 (-.f64 #s(literal 1 binary64) x))
(acos (- 1 x))
(acos.f64 (-.f64 #s(literal 1 binary64) x))
(acos (- 1 x))
(acos.f64 (-.f64 #s(literal 1 binary64) x))
(acos (- 1 x))
(acos.f64 (-.f64 #s(literal 1 binary64) x))
(acos (- 1 x))
(acos.f64 (-.f64 #s(literal 1 binary64) x))
(acos (- 1 x))
(acos.f64 (-.f64 #s(literal 1 binary64) x))
(acos (- 1 x))
(acos.f64 (-.f64 #s(literal 1 binary64) x))
(acos (- 1 x))
(acos.f64 (-.f64 #s(literal 1 binary64) x))
(acos (+ 1 (* -1 x)))
(acos.f64 (-.f64 #s(literal 1 binary64) x))
(acos (+ 1 (* -1 x)))
(acos.f64 (-.f64 #s(literal 1 binary64) x))
(acos (+ 1 (* -1 x)))
(acos.f64 (-.f64 #s(literal 1 binary64) x))
(acos (+ 1 (* -1 x)))
(acos.f64 (-.f64 #s(literal 1 binary64) x))
1
#s(literal 1 binary64)
(+ 1 (* -1 x))
(-.f64 #s(literal 1 binary64) x)
(+ 1 (* -1 x))
(-.f64 #s(literal 1 binary64) x)
(+ 1 (* -1 x))
(-.f64 #s(literal 1 binary64) x)
(* -1 x)
(neg.f64 x)
(* x (- (/ 1 x) 1))
(-.f64 #s(literal 1 binary64) x)
(* x (- (/ 1 x) 1))
(-.f64 #s(literal 1 binary64) x)
(* x (- (/ 1 x) 1))
(-.f64 #s(literal 1 binary64) x)
(* -1 x)
(neg.f64 x)
(* -1 (* x (- 1 (/ 1 x))))
(-.f64 #s(literal 1 binary64) x)
(* -1 (* x (- 1 (/ 1 x))))
(-.f64 #s(literal 1 binary64) x)
(* -1 (* x (- 1 (/ 1 x))))
(-.f64 #s(literal 1 binary64) x)
(- (* 1/2 (PI)) (asin (- 1 x)))
(-.f64 (*.f64 #s(literal 1/2 binary64) (PI.f64)) (asin.f64 (-.f64 #s(literal 1 binary64) x)))
(- (* 1/2 (PI)) (asin (- 1 x)))
(-.f64 (*.f64 #s(literal 1/2 binary64) (PI.f64)) (asin.f64 (-.f64 #s(literal 1 binary64) x)))
(- (* 1/2 (PI)) (asin (- 1 x)))
(-.f64 (*.f64 #s(literal 1/2 binary64) (PI.f64)) (asin.f64 (-.f64 #s(literal 1 binary64) x)))
(- (* 1/2 (PI)) (asin (- 1 x)))
(-.f64 (*.f64 #s(literal 1/2 binary64) (PI.f64)) (asin.f64 (-.f64 #s(literal 1 binary64) x)))
(- (* 1/2 (PI)) (asin (- 1 x)))
(-.f64 (*.f64 #s(literal 1/2 binary64) (PI.f64)) (asin.f64 (-.f64 #s(literal 1 binary64) x)))
(- (* 1/2 (PI)) (asin (- 1 x)))
(-.f64 (*.f64 #s(literal 1/2 binary64) (PI.f64)) (asin.f64 (-.f64 #s(literal 1 binary64) x)))
(- (* 1/2 (PI)) (asin (- 1 x)))
(-.f64 (*.f64 #s(literal 1/2 binary64) (PI.f64)) (asin.f64 (-.f64 #s(literal 1 binary64) x)))
(- (* 1/2 (PI)) (asin (- 1 x)))
(-.f64 (*.f64 #s(literal 1/2 binary64) (PI.f64)) (asin.f64 (-.f64 #s(literal 1 binary64) x)))
(- (* 1/2 (PI)) (asin (+ 1 (* -1 x))))
(-.f64 (*.f64 #s(literal 1/2 binary64) (PI.f64)) (asin.f64 (-.f64 #s(literal 1 binary64) x)))
(- (* 1/2 (PI)) (asin (+ 1 (* -1 x))))
(-.f64 (*.f64 #s(literal 1/2 binary64) (PI.f64)) (asin.f64 (-.f64 #s(literal 1 binary64) x)))
(- (* 1/2 (PI)) (asin (+ 1 (* -1 x))))
(-.f64 (*.f64 #s(literal 1/2 binary64) (PI.f64)) (asin.f64 (-.f64 #s(literal 1 binary64) x)))
(- (* 1/2 (PI)) (asin (+ 1 (* -1 x))))
(-.f64 (*.f64 #s(literal 1/2 binary64) (PI.f64)) (asin.f64 (-.f64 #s(literal 1 binary64) x)))
(asin (- 1 x))
(asin.f64 (-.f64 #s(literal 1 binary64) x))
(asin (- 1 x))
(asin.f64 (-.f64 #s(literal 1 binary64) x))
(asin (- 1 x))
(asin.f64 (-.f64 #s(literal 1 binary64) x))
(asin (- 1 x))
(asin.f64 (-.f64 #s(literal 1 binary64) x))
(asin (- 1 x))
(asin.f64 (-.f64 #s(literal 1 binary64) x))
(asin (- 1 x))
(asin.f64 (-.f64 #s(literal 1 binary64) x))
(asin (- 1 x))
(asin.f64 (-.f64 #s(literal 1 binary64) x))
(asin (- 1 x))
(asin.f64 (-.f64 #s(literal 1 binary64) x))
(asin (+ 1 (* -1 x)))
(asin.f64 (-.f64 #s(literal 1 binary64) x))
(asin (+ 1 (* -1 x)))
(asin.f64 (-.f64 #s(literal 1 binary64) x))
(asin (+ 1 (* -1 x)))
(asin.f64 (-.f64 #s(literal 1 binary64) x))
(asin (+ 1 (* -1 x)))
(asin.f64 (-.f64 #s(literal 1 binary64) x))

rewrite300.0ms (6.4%)

Memory

-0.3MiB live, 248.0MiB allocated

Algorithm

1×	batch-egg-rewrite

Rules

6 028×	`lower-fma.f32`
6 026×	`lower-fma.f64`
3 660×	`lower-*.f32`
3 658×	`lower-*.f64`
1 574×	`lower-/.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	38
0	20	30
1	75	30
2	509	30
3	5919	30
0	8759	30

Stop Event

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

Counts

7 → 659

Calls

Call 1

Inputs
(acos.f64 #s(approx (- 1 x) x))
#s(approx (- 1 x) x)
(fma.f64 (sqrt.f64 (PI.f64)) (*.f64 (sqrt.f64 (PI.f64)) #s(literal 1/2 binary64)) (neg.f64 (asin.f64 #s(approx (- 1 x) x))))
(sqrt.f64 (PI.f64))
(PI.f64)
(*.f64 (sqrt.f64 (PI.f64)) #s(literal 1/2 binary64))
(asin.f64 #s(approx (- 1 x) x))

Outputs
(acos.f64 #s(approx (- 1 x) x))
(+.f64 (asin.f64 #s(approx (- 1 x) x)) (*.f64 (PI.f64) #s(literal 1/2 binary64)))
(+.f64 (*.f64 (PI.f64) #s(literal 1/2 binary64)) (asin.f64 #s(approx (- 1 x) x)))
(+.f64 #s(literal 0 binary64) (acos.f64 #s(approx (- 1 x) x)))
(+.f64 (acos.f64 #s(approx (- 1 x) x)) #s(literal 0 binary64))
(+.f64 (/.f64 (.f64 (PI.f64) (.f64 (PI.f64) #s(literal 1/4 binary64))) (acos.f64 #s(approx (- 1 x) x))) (/.f64 (pow.f64 (asin.f64 #s(approx (- 1 x) x)) #s(literal 2 binary64)) (acos.f64 #s(approx (- 1 x) x))))
(+.f64 (*.f64 (PI.f64) #s(literal -1/2 binary64)) (fma.f64 (PI.f64) #s(literal 1/2 binary64) (acos.f64 #s(approx (- 1 x) x))))
(+.f64 (fma.f64 (PI.f64) #s(literal 1/2 binary64) (*.f64 (PI.f64) #s(literal 1/2 binary64))) (neg.f64 (acos.f64 #s(approx (- 1 x) x))))
(exp.f64 (*.f64 (log.f64 (/.f64 #s(literal 1 binary64) (acos.f64 #s(approx (- 1 x) x)))) #s(literal -1 binary64)))
(-.f64 (*.f64 (PI.f64) #s(literal 1/2 binary64)) (asin.f64 #s(approx (- 1 x) x)))
(-.f64 #s(literal 0 binary64) (neg.f64 (acos.f64 #s(approx (- 1 x) x))))
(-.f64 (/.f64 (.f64 (PI.f64) (.f64 (PI.f64) #s(literal 1/4 binary64))) (acos.f64 #s(approx (- 1 x) x))) (/.f64 (pow.f64 (asin.f64 #s(approx (- 1 x) x)) #s(literal 2 binary64)) (acos.f64 #s(approx (- 1 x) x))))
(-.f64 (/.f64 (pow.f64 (asin.f64 #s(approx (- 1 x) x)) #s(literal 2 binary64)) (acos.f64 #s(approx (- 1 x) x))) (/.f64 (.f64 (PI.f64) (.f64 (PI.f64) #s(literal 1/4 binary64))) (neg.f64 (acos.f64 #s(approx (- 1 x) x)))))
(-.f64 (/.f64 (.f64 (PI.f64) (.f64 (.f64 (PI.f64) (PI.f64)) #s(literal 1/8 binary64))) (fma.f64 (asin.f64 #s(approx (- 1 x) x)) (acos.f64 #s(approx (- 1 x) x)) (.f64 (PI.f64) (.f64 (PI.f64) #s(literal 1/4 binary64))))) (/.f64 (pow.f64 (asin.f64 #s(approx (- 1 x) x)) #s(literal 3 binary64)) (fma.f64 (asin.f64 #s(approx (- 1 x) x)) (acos.f64 #s(approx (- 1 x) x)) (.f64 (PI.f64) (*.f64 (PI.f64) #s(literal 1/4 binary64))))))
(-.f64 (fma.f64 (PI.f64) #s(literal 1/2 binary64) (*.f64 (PI.f64) #s(literal 1/2 binary64))) (acos.f64 #s(approx (- 1 x) x)))
(-.f64 (+.f64 #s(literal 0 binary64) (/.f64 (.f64 (PI.f64) (.f64 (PI.f64) #s(literal 1/4 binary64))) (acos.f64 #s(approx (- 1 x) x)))) (/.f64 (pow.f64 (asin.f64 #s(approx (- 1 x) x)) #s(literal 2 binary64)) (acos.f64 #s(approx (- 1 x) x))))
(-.f64 (-.f64 (.f64 (PI.f64) #s(literal 1/2 binary64)) (.f64 (PI.f64) #s(literal -1/2 binary64))) (acos.f64 #s(approx (- 1 x) x)))
(fma.f64 #s(literal 1 binary64) (asin.f64 #s(approx (- 1 x) x)) (*.f64 (PI.f64) #s(literal 1/2 binary64)))
(fma.f64 #s(literal 1 binary64) (*.f64 (PI.f64) #s(literal 1/2 binary64)) (asin.f64 #s(approx (- 1 x) x)))
(fma.f64 #s(literal 1 binary64) (acos.f64 #s(approx (- 1 x) x)) #s(literal 0 binary64))
(fma.f64 #s(literal 1 binary64) (*.f64 (PI.f64) #s(literal -1/2 binary64)) (fma.f64 (PI.f64) #s(literal 1/2 binary64) (acos.f64 #s(approx (- 1 x) x))))
(fma.f64 (PI.f64) #s(literal 1/2 binary64) (asin.f64 #s(approx (- 1 x) x)))
(fma.f64 (PI.f64) #s(literal -1/2 binary64) (fma.f64 (PI.f64) #s(literal 1/2 binary64) (acos.f64 #s(approx (- 1 x) x))))
(fma.f64 (PI.f64) (/.f64 (*.f64 (PI.f64) #s(literal 1/4 binary64)) (acos.f64 #s(approx (- 1 x) x))) (/.f64 (pow.f64 (asin.f64 #s(approx (- 1 x) x)) #s(literal 2 binary64)) (acos.f64 #s(approx (- 1 x) x))))
(fma.f64 (sqrt.f64 (PI.f64)) (*.f64 (sqrt.f64 (PI.f64)) #s(literal 1/2 binary64)) (asin.f64 #s(approx (- 1 x) x)))
(fma.f64 (sqrt.f64 (PI.f64)) (neg.f64 (*.f64 (sqrt.f64 (PI.f64)) #s(literal 1/2 binary64))) (fma.f64 (PI.f64) #s(literal 1/2 binary64) (acos.f64 #s(approx (- 1 x) x))))
(fma.f64 (sqrt.f64 (PI.f64)) (.f64 (.f64 (sqrt.f64 (PI.f64)) #s(literal 1/2 binary64)) #s(literal -1 binary64)) (fma.f64 (PI.f64) #s(literal 1/2 binary64) (acos.f64 #s(approx (- 1 x) x))))
(fma.f64 (sqrt.f64 (PI.f64)) (/.f64 (.f64 (sqrt.f64 (PI.f64)) (.f64 (PI.f64) #s(literal 1/4 binary64))) (acos.f64 #s(approx (- 1 x) x))) (/.f64 (pow.f64 (asin.f64 #s(approx (- 1 x) x)) #s(literal 2 binary64)) (acos.f64 #s(approx (- 1 x) x))))
(fma.f64 #s(literal 1/2 binary64) (PI.f64) (asin.f64 #s(approx (- 1 x) x)))
(fma.f64 #s(literal 1/2 binary64) (neg.f64 (PI.f64)) (fma.f64 (PI.f64) #s(literal 1/2 binary64) (acos.f64 #s(approx (- 1 x) x))))
(fma.f64 (*.f64 (sqrt.f64 (PI.f64)) #s(literal 1/2 binary64)) (sqrt.f64 (PI.f64)) (asin.f64 #s(approx (- 1 x) x)))
(fma.f64 (*.f64 (sqrt.f64 (PI.f64)) #s(literal 1/2 binary64)) (neg.f64 (sqrt.f64 (PI.f64))) (fma.f64 (PI.f64) #s(literal 1/2 binary64) (acos.f64 #s(approx (- 1 x) x))))
(fma.f64 (.f64 (sqrt.f64 (PI.f64)) #s(literal 1/2 binary64)) (.f64 (sqrt.f64 (PI.f64)) #s(literal -1 binary64)) (fma.f64 (PI.f64) #s(literal 1/2 binary64) (acos.f64 #s(approx (- 1 x) x))))
(fma.f64 (.f64 (sqrt.f64 (PI.f64)) #s(literal 1/2 binary64)) (/.f64 (.f64 #s(literal 1/2 binary64) (*.f64 (PI.f64) (sqrt.f64 (PI.f64)))) (acos.f64 #s(approx (- 1 x) x))) (/.f64 (pow.f64 (asin.f64 #s(approx (- 1 x) x)) #s(literal 2 binary64)) (acos.f64 #s(approx (- 1 x) x))))
(fma.f64 (asin.f64 #s(approx (- 1 x) x)) #s(literal 1 binary64) (*.f64 (PI.f64) #s(literal 1/2 binary64)))
(fma.f64 (asin.f64 #s(approx (- 1 x) x)) #s(literal -1 binary64) (*.f64 (PI.f64) #s(literal 1/2 binary64)))
(fma.f64 (*.f64 (PI.f64) #s(literal 1/2 binary64)) #s(literal 1 binary64) (asin.f64 #s(approx (- 1 x) x)))
(fma.f64 (*.f64 (PI.f64) #s(literal 1/2 binary64)) #s(literal -1 binary64) (fma.f64 (PI.f64) #s(literal 1/2 binary64) (acos.f64 #s(approx (- 1 x) x))))
(fma.f64 (.f64 (PI.f64) #s(literal 1/2 binary64)) (/.f64 (.f64 (PI.f64) #s(literal 1/2 binary64)) (acos.f64 #s(approx (- 1 x) x))) (/.f64 (pow.f64 (asin.f64 #s(approx (- 1 x) x)) #s(literal 2 binary64)) (acos.f64 #s(approx (- 1 x) x))))
(fma.f64 (cbrt.f64 (PI.f64)) (*.f64 (pow.f64 (PI.f64) #s(literal 2/3 binary64)) #s(literal 1/2 binary64)) (asin.f64 #s(approx (- 1 x) x)))
(fma.f64 (cbrt.f64 (PI.f64)) (.f64 (pow.f64 (PI.f64) #s(literal 1/6 binary64)) (.f64 (sqrt.f64 (PI.f64)) #s(literal 1/2 binary64))) (asin.f64 #s(approx (- 1 x) x)))
(fma.f64 (cbrt.f64 (PI.f64)) (.f64 (cbrt.f64 (PI.f64)) (.f64 #s(literal 1/2 binary64) (cbrt.f64 (PI.f64)))) (asin.f64 #s(approx (- 1 x) x)))
(fma.f64 (cbrt.f64 (PI.f64)) (/.f64 (pow.f64 (PI.f64) #s(literal 2/3 binary64)) #s(literal 2 binary64)) (asin.f64 #s(approx (- 1 x) x)))
(fma.f64 (pow.f64 (PI.f64) #s(literal 2/3 binary64)) (*.f64 #s(literal 1/2 binary64) (cbrt.f64 (PI.f64))) (asin.f64 #s(approx (- 1 x) x)))
(fma.f64 (pow.f64 (PI.f64) #s(literal 2/3 binary64)) (neg.f64 (*.f64 #s(literal 1/2 binary64) (cbrt.f64 (PI.f64)))) (fma.f64 (PI.f64) #s(literal 1/2 binary64) (acos.f64 #s(approx (- 1 x) x))))
(fma.f64 (pow.f64 (PI.f64) #s(literal 2/3 binary64)) (.f64 (.f64 #s(literal 1/2 binary64) (cbrt.f64 (PI.f64))) #s(literal -1 binary64)) (fma.f64 (PI.f64) #s(literal 1/2 binary64) (acos.f64 #s(approx (- 1 x) x))))
(fma.f64 (*.f64 (PI.f64) (PI.f64)) (/.f64 #s(literal 1/4 binary64) (acos.f64 #s(approx (- 1 x) x))) (/.f64 (pow.f64 (asin.f64 #s(approx (- 1 x) x)) #s(literal 2 binary64)) (acos.f64 #s(approx (- 1 x) x))))
(fma.f64 (fma.f64 (PI.f64) (.f64 (.f64 (PI.f64) (PI.f64)) #s(literal 1/8 binary64)) (pow.f64 (asin.f64 #s(approx (- 1 x) x)) #s(literal 3 binary64))) (/.f64 #s(literal 1 binary64) (fma.f64 (asin.f64 #s(approx (- 1 x) x)) (acos.f64 #s(approx (- 1 x) x)) (.f64 (PI.f64) (.f64 (PI.f64) #s(literal 1/4 binary64))))) #s(literal 0 binary64))
(fma.f64 (.f64 (PI.f64) (.f64 (PI.f64) #s(literal 1/4 binary64))) (/.f64 #s(literal 1 binary64) (acos.f64 #s(approx (- 1 x) x))) (/.f64 (pow.f64 (asin.f64 #s(approx (- 1 x) x)) #s(literal 2 binary64)) (acos.f64 #s(approx (- 1 x) x))))
(fma.f64 (pow.f64 (asin.f64 #s(approx (- 1 x) x)) #s(literal 2 binary64)) (/.f64 #s(literal 1 binary64) (asin.f64 #s(approx (- 1 x) x))) (*.f64 (PI.f64) #s(literal 1/2 binary64)))
(fma.f64 (fma.f64 (asin.f64 #s(approx (- 1 x) x)) (acos.f64 #s(approx (- 1 x) x)) (.f64 (PI.f64) (.f64 (PI.f64) #s(literal 1/4 binary64)))) (.f64 (acos.f64 #s(approx (- 1 x) x)) (/.f64 #s(literal 1 binary64) (fma.f64 (asin.f64 #s(approx (- 1 x) x)) (acos.f64 #s(approx (- 1 x) x)) (.f64 (PI.f64) (*.f64 (PI.f64) #s(literal 1/4 binary64)))))) #s(literal 0 binary64))
(fma.f64 (fma.f64 (asin.f64 #s(approx (- 1 x) x)) (acos.f64 #s(approx (- 1 x) x)) (.f64 (PI.f64) (.f64 (PI.f64) #s(literal 1/4 binary64)))) (/.f64 (acos.f64 #s(approx (- 1 x) x)) (fma.f64 (asin.f64 #s(approx (- 1 x) x)) (acos.f64 #s(approx (- 1 x) x)) (.f64 (PI.f64) (.f64 (PI.f64) #s(literal 1/4 binary64))))) #s(literal 0 binary64))
(fma.f64 #s(literal -1 binary64) (asin.f64 #s(approx (- 1 x) x)) (*.f64 (PI.f64) #s(literal 1/2 binary64)))
(fma.f64 #s(literal -1 binary64) (*.f64 (PI.f64) #s(literal 1/2 binary64)) (fma.f64 (PI.f64) #s(literal 1/2 binary64) (acos.f64 #s(approx (- 1 x) x))))
(fma.f64 (pow.f64 (acos.f64 #s(approx (- 1 x) x)) #s(literal 2 binary64)) (/.f64 #s(literal 1 binary64) (acos.f64 #s(approx (- 1 x) x))) #s(literal 0 binary64))
(fma.f64 (acos.f64 #s(approx (- 1 x) x)) (*.f64 (acos.f64 #s(approx (- 1 x) x)) (/.f64 #s(literal 1 binary64) (acos.f64 #s(approx (- 1 x) x)))) #s(literal 0 binary64))
(fma.f64 (acos.f64 #s(approx (- 1 x) x)) (/.f64 (acos.f64 #s(approx (- 1 x) x)) (acos.f64 #s(approx (- 1 x) x))) #s(literal 0 binary64))
(fma.f64 (sqrt.f64 (sqrt.f64 (PI.f64))) (.f64 (sqrt.f64 (sqrt.f64 (PI.f64))) (.f64 (sqrt.f64 (PI.f64)) #s(literal 1/2 binary64))) (asin.f64 #s(approx (- 1 x) x)))
(fma.f64 (neg.f64 (PI.f64)) #s(literal 1/2 binary64) (fma.f64 (PI.f64) #s(literal 1/2 binary64) (acos.f64 #s(approx (- 1 x) x))))
(fma.f64 (neg.f64 (PI.f64)) #s(literal -1/2 binary64) (asin.f64 #s(approx (- 1 x) x)))
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(asin.f64 #s(approx (- 1 x) x))
(pow.f64 (/.f64 (pow.f64 (asin.f64 #s(approx (- 1 x) x)) #s(literal 2 binary64)) (pow.f64 (asin.f64 #s(approx (- 1 x) x)) #s(literal 3 binary64))) #s(literal -1 binary64))
(pow.f64 (/.f64 (asin.f64 #s(approx (- 1 x) x)) (pow.f64 (asin.f64 #s(approx (- 1 x) x)) #s(literal 2 binary64))) #s(literal -1 binary64))
(pow.f64 (/.f64 (fma.f64 (acos.f64 #s(approx (- 1 x) x)) (fma.f64 (PI.f64) #s(literal 1/2 binary64) (acos.f64 #s(approx (- 1 x) x))) (.f64 (PI.f64) (.f64 (PI.f64) #s(literal 1/4 binary64)))) (-.f64 (.f64 (PI.f64) (.f64 (*.f64 (PI.f64) (PI.f64)) #s(literal 1/8 binary64))) (pow.f64 (acos.f64 #s(approx (- 1 x) x)) #s(literal 3 binary64)))) #s(literal -1 binary64))
(pow.f64 (/.f64 (fma.f64 (PI.f64) #s(literal 1/2 binary64) (acos.f64 #s(approx (- 1 x) x))) (*.f64 (fma.f64 (PI.f64) #s(literal 1/2 binary64) (acos.f64 #s(approx (- 1 x) x))) (asin.f64 #s(approx (- 1 x) x)))) #s(literal -1 binary64))
(*.f64 #s(literal 1 binary64) (asin.f64 #s(approx (- 1 x) x)))
(*.f64 (asin.f64 #s(approx (- 1 x) x)) #s(literal 1 binary64))
(*.f64 (asin.f64 #s(approx (- 1 x) x)) #s(literal -1 binary64))
(*.f64 (pow.f64 (asin.f64 #s(approx (- 1 x) x)) #s(literal 2 binary64)) (/.f64 #s(literal 1 binary64) (asin.f64 #s(approx (- 1 x) x))))
(*.f64 #s(literal -1 binary64) (asin.f64 #s(approx (- 1 x) x)))
(*.f64 (pow.f64 (asin.f64 #s(approx (- 1 x) x)) #s(literal 3 binary64)) (/.f64 #s(literal 1 binary64) (pow.f64 (asin.f64 #s(approx (- 1 x) x)) #s(literal 2 binary64))))
(.f64 (-.f64 (.f64 (PI.f64) (.f64 (.f64 (PI.f64) (PI.f64)) #s(literal 1/8 binary64))) (pow.f64 (acos.f64 #s(approx (- 1 x) x)) #s(literal 3 binary64))) (/.f64 #s(literal 1 binary64) (fma.f64 (acos.f64 #s(approx (- 1 x) x)) (fma.f64 (PI.f64) #s(literal 1/2 binary64) (acos.f64 #s(approx (- 1 x) x))) (.f64 (PI.f64) (.f64 (PI.f64) #s(literal 1/4 binary64))))))
(.f64 (.f64 (fma.f64 (PI.f64) #s(literal 1/2 binary64) (acos.f64 #s(approx (- 1 x) x))) (asin.f64 #s(approx (- 1 x) x))) (/.f64 #s(literal 1 binary64) (fma.f64 (PI.f64) #s(literal 1/2 binary64) (acos.f64 #s(approx (- 1 x) x)))))

eval103.0ms (2.2%)

Memory: 0.7MiB live, 192.7MiB allocated
Compiler: Compiled 14 858 to 1 672 computations (88.7% saved)

prune71.0ms (1.5%)

Memory

-3.4MiB live, 120.6MiB allocated

Pruning

9 alts after pruning (6 fresh and 3 done)

	Pruned	Kept	Total
New	801	6	807
Fresh	0	0	0
Picked	1	1	2
Done	0	2	2
Total	802	9	811

Accuracy

10.2%

Counts

811 → 9

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	7.0%	(fma.f64 (*.f64 (sqrt.f64 (PI.f64)) #s(literal 1/2 binary64)) (sqrt.f64 (PI.f64)) (asin.f64 #s(approx (- 1 x) x)))
▶	7.0%	(fma.f64 (sqrt.f64 (PI.f64)) (.f64 (sqrt.f64 (PI.f64)) #s(literal 1/2 binary64)) (neg.f64 (fma.f64 (.f64 (sqrt.f64 (PI.f64)) #s(literal 1/2 binary64)) (neg.f64 (sqrt.f64 (PI.f64))) (acos.f64 #s(approx (- 1 x) x)))))
▶	5.9%	(fma.f64 (sqrt.f64 (PI.f64)) (*.f64 (sqrt.f64 (PI.f64)) #s(literal 1/2 binary64)) (neg.f64 (asin.f64 #s(approx (- 1 x) (-.f64 #s(literal 1 binary64) x)))))
	4.6%	(/.f64 (fma.f64 (pow.f64 (asin.f64 #s(approx (- 1 x) x)) #s(literal 3 binary64)) (/.f64 #s(literal 2 binary64) (PI.f64)) (pow.f64 (asin.f64 #s(approx (- 1 x) x)) #s(literal 2 binary64))) (*.f64 (pow.f64 (asin.f64 #s(approx (- 1 x) x)) #s(literal 2 binary64)) (/.f64 #s(literal 2 binary64) (PI.f64))))
▶	4.6%	(/.f64 (fma.f64 (pow.f64 (asin.f64 #s(approx (- 1 x) x)) #s(literal 3 binary64)) #s(literal 2 binary64) (.f64 (pow.f64 (asin.f64 #s(approx (- 1 x) x)) #s(literal 2 binary64)) (PI.f64))) (.f64 (pow.f64 (asin.f64 #s(approx (- 1 x) x)) #s(literal 2 binary64)) #s(literal 2 binary64)))
✓	7.7%	(acos.f64 (-.f64 #s(literal 1 binary64) x))
✓	7.0%	(acos.f64 #s(approx (- 1 x) x))
✓	3.8%	(acos.f64 #s(approx (- 1 x) #s(literal 1 binary64)))
▶	7.7%	#s(approx (+ (* (sqrt (PI)) (* (sqrt (PI)) 1/2)) (neg (asin (- 1 x)))) (-.f64 (*.f64 #s(literal 1/2 binary64) (PI.f64)) (asin.f64 (-.f64 #s(literal 1 binary64) x))))

Compiler

Compiled 197 to 123 computations (37.6% saved)

simplify320.0ms (6.8%)

Memory

-9.8MiB live, 230.8MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 20 expressions of interest:

New	Metric	Score	Program
✓	cost-diff	0	(asin.f64 #s(approx (- 1 x) x))
✓	cost-diff	0	(pow.f64 (asin.f64 #s(approx (- 1 x) x)) #s(literal 3 binary64))
✓	cost-diff	6464	(fma.f64 (pow.f64 (asin.f64 #s(approx (- 1 x) x)) #s(literal 3 binary64)) #s(literal 2 binary64) (*.f64 (pow.f64 (asin.f64 #s(approx (- 1 x) x)) #s(literal 2 binary64)) (PI.f64)))
✓	cost-diff	26752	(/.f64 (fma.f64 (pow.f64 (asin.f64 #s(approx (- 1 x) x)) #s(literal 3 binary64)) #s(literal 2 binary64) (.f64 (pow.f64 (asin.f64 #s(approx (- 1 x) x)) #s(literal 2 binary64)) (PI.f64))) (.f64 (pow.f64 (asin.f64 #s(approx (- 1 x) x)) #s(literal 2 binary64)) #s(literal 2 binary64)))
✓	cost-diff	0	(PI.f64)
✓	cost-diff	0	(sqrt.f64 (PI.f64))
✓	cost-diff	1728	(fma.f64 (*.f64 (sqrt.f64 (PI.f64)) #s(literal 1/2 binary64)) (neg.f64 (sqrt.f64 (PI.f64))) (acos.f64 #s(approx (- 1 x) x)))
✓	cost-diff	2304	(fma.f64 (sqrt.f64 (PI.f64)) (.f64 (sqrt.f64 (PI.f64)) #s(literal 1/2 binary64)) (neg.f64 (fma.f64 (.f64 (sqrt.f64 (PI.f64)) #s(literal 1/2 binary64)) (neg.f64 (sqrt.f64 (PI.f64))) (acos.f64 #s(approx (- 1 x) x)))))
✓	cost-diff	0	(*.f64 (sqrt.f64 (PI.f64)) #s(literal 1/2 binary64))
✓	cost-diff	0	(PI.f64)
✓	cost-diff	0	(sqrt.f64 (PI.f64))
✓	cost-diff	1600	(fma.f64 (sqrt.f64 (PI.f64)) (*.f64 (sqrt.f64 (PI.f64)) #s(literal 1/2 binary64)) (neg.f64 (asin.f64 #s(approx (- 1 x) (-.f64 #s(literal 1 binary64) x)))))
✓	cost-diff	0	(PI.f64)
✓	cost-diff	0	(sqrt.f64 (PI.f64))
✓	cost-diff	0	(*.f64 (sqrt.f64 (PI.f64)) #s(literal 1/2 binary64))
✓	cost-diff	1600	(fma.f64 (*.f64 (sqrt.f64 (PI.f64)) #s(literal 1/2 binary64)) (sqrt.f64 (PI.f64)) (asin.f64 #s(approx (- 1 x) x)))
✓	cost-diff	0	(PI.f64)
✓	cost-diff	0	(*.f64 #s(literal 1/2 binary64) (PI.f64))
✓	cost-diff	0	(-.f64 (*.f64 #s(literal 1/2 binary64) (PI.f64)) (asin.f64 (-.f64 #s(literal 1 binary64) x)))
✓	cost-diff	0	#s(approx (+ (* (sqrt (PI)) (* (sqrt (PI)) 1/2)) (neg (asin (- 1 x)))) (-.f64 (*.f64 #s(literal 1/2 binary64) (PI.f64)) (asin.f64 (-.f64 #s(literal 1 binary64) x))))

Rules

13 972×	`lower-fma.f32`
13 962×	`lower-fma.f64`
2 986×	`lower-*.f32`
2 978×	`lower-*.f64`
1 990×	`lower--.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	39	306
0	68	309
1	114	277
2	205	271
3	489	269
4	998	253
5	2329	251
6	6764	251
0	8029	247

Stop Event

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

Calls

Call 1

Inputs
#s(approx (+ (* (sqrt (PI)) (* (sqrt (PI)) 1/2)) (neg (asin (- 1 x)))) (-.f64 (*.f64 #s(literal 1/2 binary64) (PI.f64)) (asin.f64 (-.f64 #s(literal 1 binary64) x))))
(-.f64 (*.f64 #s(literal 1/2 binary64) (PI.f64)) (asin.f64 (-.f64 #s(literal 1 binary64) x)))
(*.f64 #s(literal 1/2 binary64) (PI.f64))
#s(literal 1/2 binary64)
(PI.f64)
(asin.f64 (-.f64 #s(literal 1 binary64) x))
(-.f64 #s(literal 1 binary64) x)
#s(literal 1 binary64)
x
(fma.f64 (*.f64 (sqrt.f64 (PI.f64)) #s(literal 1/2 binary64)) (sqrt.f64 (PI.f64)) (asin.f64 #s(approx (- 1 x) x)))
(*.f64 (sqrt.f64 (PI.f64)) #s(literal 1/2 binary64))
(sqrt.f64 (PI.f64))
(PI.f64)
#s(literal 1/2 binary64)
(asin.f64 #s(approx (- 1 x) x))
#s(approx (- 1 x) x)
x
(fma.f64 (sqrt.f64 (PI.f64)) (*.f64 (sqrt.f64 (PI.f64)) #s(literal 1/2 binary64)) (neg.f64 (asin.f64 #s(approx (- 1 x) (-.f64 #s(literal 1 binary64) x)))))
(sqrt.f64 (PI.f64))
(PI.f64)
(*.f64 (sqrt.f64 (PI.f64)) #s(literal 1/2 binary64))
#s(literal 1/2 binary64)
(neg.f64 (asin.f64 #s(approx (- 1 x) (-.f64 #s(literal 1 binary64) x))))
(asin.f64 #s(approx (- 1 x) (-.f64 #s(literal 1 binary64) x)))
#s(approx (- 1 x) (-.f64 #s(literal 1 binary64) x))
(-.f64 #s(literal 1 binary64) x)
#s(literal 1 binary64)
x
(fma.f64 (sqrt.f64 (PI.f64)) (.f64 (sqrt.f64 (PI.f64)) #s(literal 1/2 binary64)) (neg.f64 (fma.f64 (.f64 (sqrt.f64 (PI.f64)) #s(literal 1/2 binary64)) (neg.f64 (sqrt.f64 (PI.f64))) (acos.f64 #s(approx (- 1 x) x)))))
(sqrt.f64 (PI.f64))
(PI.f64)
(*.f64 (sqrt.f64 (PI.f64)) #s(literal 1/2 binary64))
#s(literal 1/2 binary64)
(neg.f64 (fma.f64 (*.f64 (sqrt.f64 (PI.f64)) #s(literal 1/2 binary64)) (neg.f64 (sqrt.f64 (PI.f64))) (acos.f64 #s(approx (- 1 x) x))))
(fma.f64 (*.f64 (sqrt.f64 (PI.f64)) #s(literal 1/2 binary64)) (neg.f64 (sqrt.f64 (PI.f64))) (acos.f64 #s(approx (- 1 x) x)))
(neg.f64 (sqrt.f64 (PI.f64)))
(acos.f64 #s(approx (- 1 x) x))
#s(approx (- 1 x) x)
x
(/.f64 (fma.f64 (pow.f64 (asin.f64 #s(approx (- 1 x) x)) #s(literal 3 binary64)) #s(literal 2 binary64) (.f64 (pow.f64 (asin.f64 #s(approx (- 1 x) x)) #s(literal 2 binary64)) (PI.f64))) (.f64 (pow.f64 (asin.f64 #s(approx (- 1 x) x)) #s(literal 2 binary64)) #s(literal 2 binary64)))
(fma.f64 (pow.f64 (asin.f64 #s(approx (- 1 x) x)) #s(literal 3 binary64)) #s(literal 2 binary64) (*.f64 (pow.f64 (asin.f64 #s(approx (- 1 x) x)) #s(literal 2 binary64)) (PI.f64)))
(pow.f64 (asin.f64 #s(approx (- 1 x) x)) #s(literal 3 binary64))
(asin.f64 #s(approx (- 1 x) x))
#s(approx (- 1 x) x)
x
#s(literal 3 binary64)
#s(literal 2 binary64)
(*.f64 (pow.f64 (asin.f64 #s(approx (- 1 x) x)) #s(literal 2 binary64)) (PI.f64))
(pow.f64 (asin.f64 #s(approx (- 1 x) x)) #s(literal 2 binary64))
(PI.f64)
(*.f64 (pow.f64 (asin.f64 #s(approx (- 1 x) x)) #s(literal 2 binary64)) #s(literal 2 binary64))

Outputs
#s(approx (+ (* (sqrt (PI)) (* (sqrt (PI)) 1/2)) (neg (asin (- 1 x)))) (-.f64 (*.f64 #s(literal 1/2 binary64) (PI.f64)) (asin.f64 (-.f64 #s(literal 1 binary64) x))))
(-.f64 (*.f64 #s(literal 1/2 binary64) (PI.f64)) (asin.f64 (-.f64 #s(literal 1 binary64) x)))
(*.f64 #s(literal 1/2 binary64) (PI.f64))
#s(literal 1/2 binary64)
(PI.f64)
(asin.f64 (-.f64 #s(literal 1 binary64) x))
(-.f64 #s(literal 1 binary64) x)
#s(literal 1 binary64)
x
(fma.f64 (*.f64 (sqrt.f64 (PI.f64)) #s(literal 1/2 binary64)) (sqrt.f64 (PI.f64)) (asin.f64 #s(approx (- 1 x) x)))
(fma.f64 #s(literal 1/2 binary64) (PI.f64) (asin.f64 #s(approx (- 1 x) x)))
(*.f64 (sqrt.f64 (PI.f64)) #s(literal 1/2 binary64))
(*.f64 #s(literal 1/2 binary64) (sqrt.f64 (PI.f64)))
(sqrt.f64 (PI.f64))
(PI.f64)
#s(literal 1/2 binary64)
(asin.f64 #s(approx (- 1 x) x))
#s(approx (- 1 x) x)
x
(fma.f64 (sqrt.f64 (PI.f64)) (*.f64 (sqrt.f64 (PI.f64)) #s(literal 1/2 binary64)) (neg.f64 (asin.f64 #s(approx (- 1 x) (-.f64 #s(literal 1 binary64) x)))))
(-.f64 (*.f64 #s(literal 1/2 binary64) (PI.f64)) (asin.f64 #s(approx (- 1 x) (-.f64 #s(literal 1 binary64) x))))
(sqrt.f64 (PI.f64))
(PI.f64)
(*.f64 (sqrt.f64 (PI.f64)) #s(literal 1/2 binary64))
(*.f64 #s(literal 1/2 binary64) (sqrt.f64 (PI.f64)))
#s(literal 1/2 binary64)
(neg.f64 (asin.f64 #s(approx (- 1 x) (-.f64 #s(literal 1 binary64) x))))
(asin.f64 #s(approx (- 1 x) (-.f64 #s(literal 1 binary64) x)))
#s(approx (- 1 x) (-.f64 #s(literal 1 binary64) x))
(-.f64 #s(literal 1 binary64) x)
#s(literal 1 binary64)
x
(fma.f64 (sqrt.f64 (PI.f64)) (.f64 (sqrt.f64 (PI.f64)) #s(literal 1/2 binary64)) (neg.f64 (fma.f64 (.f64 (sqrt.f64 (PI.f64)) #s(literal 1/2 binary64)) (neg.f64 (sqrt.f64 (PI.f64))) (acos.f64 #s(approx (- 1 x) x)))))
(-.f64 (PI.f64) (acos.f64 #s(approx (- 1 x) x)))
(sqrt.f64 (PI.f64))
(PI.f64)
(*.f64 (sqrt.f64 (PI.f64)) #s(literal 1/2 binary64))
(*.f64 #s(literal 1/2 binary64) (sqrt.f64 (PI.f64)))
#s(literal 1/2 binary64)
(neg.f64 (fma.f64 (*.f64 (sqrt.f64 (PI.f64)) #s(literal 1/2 binary64)) (neg.f64 (sqrt.f64 (PI.f64))) (acos.f64 #s(approx (- 1 x) x))))
(-.f64 (*.f64 #s(literal 1/2 binary64) (PI.f64)) (acos.f64 #s(approx (- 1 x) x)))
(fma.f64 (*.f64 (sqrt.f64 (PI.f64)) #s(literal 1/2 binary64)) (neg.f64 (sqrt.f64 (PI.f64))) (acos.f64 #s(approx (- 1 x) x)))
(fma.f64 (PI.f64) #s(literal -1/2 binary64) (acos.f64 #s(approx (- 1 x) x)))
(neg.f64 (sqrt.f64 (PI.f64)))
(acos.f64 #s(approx (- 1 x) x))
#s(approx (- 1 x) x)
x
(/.f64 (fma.f64 (pow.f64 (asin.f64 #s(approx (- 1 x) x)) #s(literal 3 binary64)) #s(literal 2 binary64) (.f64 (pow.f64 (asin.f64 #s(approx (- 1 x) x)) #s(literal 2 binary64)) (PI.f64))) (.f64 (pow.f64 (asin.f64 #s(approx (- 1 x) x)) #s(literal 2 binary64)) #s(literal 2 binary64)))
(*.f64 #s(literal 1/2 binary64) (fma.f64 (asin.f64 #s(approx (- 1 x) x)) #s(literal 2 binary64) (PI.f64)))
(fma.f64 (pow.f64 (asin.f64 #s(approx (- 1 x) x)) #s(literal 3 binary64)) #s(literal 2 binary64) (*.f64 (pow.f64 (asin.f64 #s(approx (- 1 x) x)) #s(literal 2 binary64)) (PI.f64)))
(*.f64 (pow.f64 (asin.f64 #s(approx (- 1 x) x)) #s(literal 2 binary64)) (fma.f64 (asin.f64 #s(approx (- 1 x) x)) #s(literal 2 binary64) (PI.f64)))
(pow.f64 (asin.f64 #s(approx (- 1 x) x)) #s(literal 3 binary64))
(asin.f64 #s(approx (- 1 x) x))
#s(approx (- 1 x) x)
x
#s(literal 3 binary64)
#s(literal 2 binary64)
(*.f64 (pow.f64 (asin.f64 #s(approx (- 1 x) x)) #s(literal 2 binary64)) (PI.f64))
(*.f64 (PI.f64) (pow.f64 (asin.f64 #s(approx (- 1 x) x)) #s(literal 2 binary64)))
(pow.f64 (asin.f64 #s(approx (- 1 x) x)) #s(literal 2 binary64))
(PI.f64)
(*.f64 (pow.f64 (asin.f64 #s(approx (- 1 x) x)) #s(literal 2 binary64)) #s(literal 2 binary64))
(*.f64 #s(literal 2 binary64) (pow.f64 (asin.f64 #s(approx (- 1 x) x)) #s(literal 2 binary64)))

localize179.0ms (3.8%)

Memory

3.2MiB live, 84.0MiB allocated

Localize:

Found 20 expressions of interest:

New	Metric	Score	Program
✓	accuracy	98.5%	(/.f64 (fma.f64 (pow.f64 (asin.f64 #s(approx (- 1 x) x)) #s(literal 3 binary64)) #s(literal 2 binary64) (.f64 (pow.f64 (asin.f64 #s(approx (- 1 x) x)) #s(literal 2 binary64)) (PI.f64))) (.f64 (pow.f64 (asin.f64 #s(approx (- 1 x) x)) #s(literal 2 binary64)) #s(literal 2 binary64)))
✓	accuracy	98.5%	(pow.f64 (asin.f64 #s(approx (- 1 x) x)) #s(literal 3 binary64))
✓	accuracy	98.0%	(asin.f64 #s(approx (- 1 x) x))
✓	accuracy	5.4%	#s(approx (- 1 x) x)
✓	accuracy	98.5%	(fma.f64 (*.f64 (sqrt.f64 (PI.f64)) #s(literal 1/2 binary64)) (neg.f64 (sqrt.f64 (PI.f64))) (acos.f64 #s(approx (- 1 x) x)))
✓	accuracy	98.4%	(sqrt.f64 (PI.f64))
✓	accuracy	7.7%	(acos.f64 #s(approx (- 1 x) x))
✓	accuracy	5.4%	#s(approx (- 1 x) x)
✓	accuracy	100.0%	#s(approx (- 1 x) (-.f64 #s(literal 1 binary64) x))
✓	accuracy	98.4%	(sqrt.f64 (PI.f64))
✓	accuracy	98.0%	(asin.f64 #s(approx (- 1 x) (-.f64 #s(literal 1 binary64) x)))
✓	accuracy	13.4%	(fma.f64 (sqrt.f64 (PI.f64)) (*.f64 (sqrt.f64 (PI.f64)) #s(literal 1/2 binary64)) (neg.f64 (asin.f64 #s(approx (- 1 x) (-.f64 #s(literal 1 binary64) x)))))
✓	accuracy	100.0%	(fma.f64 (*.f64 (sqrt.f64 (PI.f64)) #s(literal 1/2 binary64)) (sqrt.f64 (PI.f64)) (asin.f64 #s(approx (- 1 x) x)))
✓	accuracy	98.4%	(sqrt.f64 (PI.f64))
✓	accuracy	98.0%	(asin.f64 #s(approx (- 1 x) x))
✓	accuracy	5.4%	#s(approx (- 1 x) x)
✓	accuracy	100.0%	(PI.f64)
✓	accuracy	100.0%	#s(approx (+ (* (sqrt (PI)) (* (sqrt (PI)) 1/2)) (neg (asin (- 1 x)))) (-.f64 (*.f64 #s(literal 1/2 binary64) (PI.f64)) (asin.f64 (-.f64 #s(literal 1 binary64) x))))
✓	accuracy	98.0%	(asin.f64 (-.f64 #s(literal 1 binary64) x))
✓	accuracy	10.9%	(-.f64 (*.f64 #s(literal 1/2 binary64) (PI.f64)) (asin.f64 (-.f64 #s(literal 1 binary64) x)))

Samples

114.0ms	237×	1	valid
4.0ms	19×	0	valid

Compiler

Compiled 253 to 32 computations (87.4% saved)

Precisions

Click to see histograms. Total time spent on operations: 88.0ms

ival-mult: 19.0ms (21.6% of total)

adjust: 13.0ms (14.8% of total)

ival-asin: 9.0ms (10.2% of total)

ival-add: 9.0ms (10.2% of total)

ival-acos: 8.0ms (9.1% of total)

ival-neg: 5.0ms (5.7% of total)

ival-sub: 4.0ms (4.5% of total)

ival-pi: 4.0ms (4.5% of total)

ival-pow2: 4.0ms (4.5% of total)

ival-sqrt: 4.0ms (4.5% of total)

ival-pow: 4.0ms (4.5% of total)

ival-div: 3.0ms (3.4% of total)

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

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

exact: 0.0ms (0% of total)

series10.0ms (0.2%)

Memory

4.7MiB live, 4.7MiB allocated

Counts

19 → 180

Calls

Call 1

Inputs
#<alt #s(approx (+ (* (sqrt (PI)) (* (sqrt (PI)) 1/2)) (neg (asin (- 1 x)))) (-.f64 (*.f64 #s(literal 1/2 binary64) (PI.f64)) (asin.f64 (-.f64 #s(literal 1 binary64) x))))>
#<alt (-.f64 (*.f64 #s(literal 1/2 binary64) (PI.f64)) (asin.f64 (-.f64 #s(literal 1 binary64) x)))>
#<alt (*.f64 #s(literal 1/2 binary64) (PI.f64))>
#<alt (PI.f64)>
#<alt (fma.f64 (*.f64 (sqrt.f64 (PI.f64)) #s(literal 1/2 binary64)) (sqrt.f64 (PI.f64)) (asin.f64 #s(approx (- 1 x) x)))>
#<alt (*.f64 (sqrt.f64 (PI.f64)) #s(literal 1/2 binary64))>
#<alt (sqrt.f64 (PI.f64))>
#<alt (fma.f64 (sqrt.f64 (PI.f64)) (*.f64 (sqrt.f64 (PI.f64)) #s(literal 1/2 binary64)) (neg.f64 (asin.f64 #s(approx (- 1 x) (-.f64 #s(literal 1 binary64) x)))))>
#<alt (fma.f64 (sqrt.f64 (PI.f64)) (.f64 (sqrt.f64 (PI.f64)) #s(literal 1/2 binary64)) (neg.f64 (fma.f64 (.f64 (sqrt.f64 (PI.f64)) #s(literal 1/2 binary64)) (neg.f64 (sqrt.f64 (PI.f64))) (acos.f64 #s(approx (- 1 x) x)))))>
#<alt (fma.f64 (*.f64 (sqrt.f64 (PI.f64)) #s(literal 1/2 binary64)) (neg.f64 (sqrt.f64 (PI.f64))) (acos.f64 #s(approx (- 1 x) x)))>
#<alt (/.f64 (fma.f64 (pow.f64 (asin.f64 #s(approx (- 1 x) x)) #s(literal 3 binary64)) #s(literal 2 binary64) (.f64 (pow.f64 (asin.f64 #s(approx (- 1 x) x)) #s(literal 2 binary64)) (PI.f64))) (.f64 (pow.f64 (asin.f64 #s(approx (- 1 x) x)) #s(literal 2 binary64)) #s(literal 2 binary64)))>
#<alt (fma.f64 (pow.f64 (asin.f64 #s(approx (- 1 x) x)) #s(literal 3 binary64)) #s(literal 2 binary64) (*.f64 (pow.f64 (asin.f64 #s(approx (- 1 x) x)) #s(literal 2 binary64)) (PI.f64)))>
#<alt (pow.f64 (asin.f64 #s(approx (- 1 x) x)) #s(literal 3 binary64))>
#<alt (asin.f64 #s(approx (- 1 x) x))>
#<alt (asin.f64 (-.f64 #s(literal 1 binary64) x))>
#<alt #s(approx (- 1 x) x)>
#<alt (asin.f64 #s(approx (- 1 x) (-.f64 #s(literal 1 binary64) x)))>
#<alt #s(approx (- 1 x) (-.f64 #s(literal 1 binary64) x))>
#<alt (acos.f64 #s(approx (- 1 x) x))>

Outputs
#<alt (- (* 1/2 (PI)) (asin (- 1 x)))>
#<alt (- (* 1/2 (PI)) (asin (- 1 x)))>
#<alt (- (* 1/2 (PI)) (asin (- 1 x)))>
#<alt (- (* 1/2 (PI)) (asin (- 1 x)))>
#<alt (- (* 1/2 (PI)) (asin (- 1 x)))>
#<alt (- (* 1/2 (PI)) (asin (- 1 x)))>
#<alt (- (* 1/2 (PI)) (asin (- 1 x)))>
#<alt (- (* 1/2 (PI)) (asin (- 1 x)))>
#<alt (- (* 1/2 (PI)) (asin (+ 1 (* -1 x))))>
#<alt (- (* 1/2 (PI)) (asin (+ 1 (* -1 x))))>
#<alt (- (* 1/2 (PI)) (asin (+ 1 (* -1 x))))>
#<alt (- (* 1/2 (PI)) (asin (+ 1 (* -1 x))))>
#<alt (- (* 1/2 (PI)) (asin (- 1 x)))>
#<alt (- (* 1/2 (PI)) (asin (- 1 x)))>
#<alt (- (* 1/2 (PI)) (asin (- 1 x)))>
#<alt (- (* 1/2 (PI)) (asin (- 1 x)))>
#<alt (- (* 1/2 (PI)) (asin (- 1 x)))>
#<alt (- (* 1/2 (PI)) (asin (- 1 x)))>
#<alt (- (* 1/2 (PI)) (asin (- 1 x)))>
#<alt (- (* 1/2 (PI)) (asin (- 1 x)))>
#<alt (- (* 1/2 (PI)) (asin (+ 1 (* -1 x))))>
#<alt (- (* 1/2 (PI)) (asin (+ 1 (* -1 x))))>
#<alt (- (* 1/2 (PI)) (asin (+ 1 (* -1 x))))>
#<alt (- (* 1/2 (PI)) (asin (+ 1 (* -1 x))))>
#<alt (+ (asin (- 1 x)) (* 1/2 (PI)))>
#<alt (+ (asin (- 1 x)) (* 1/2 (PI)))>
#<alt (+ (asin (- 1 x)) (* 1/2 (PI)))>
#<alt (+ (asin (- 1 x)) (* 1/2 (PI)))>
#<alt (+ (asin (- 1 x)) (* 1/2 (PI)))>
#<alt (+ (asin (- 1 x)) (* 1/2 (PI)))>
#<alt (+ (asin (- 1 x)) (* 1/2 (PI)))>
#<alt (+ (asin (- 1 x)) (* 1/2 (PI)))>
#<alt (+ (asin (+ 1 (* -1 x))) (* 1/2 (PI)))>
#<alt (+ (asin (+ 1 (* -1 x))) (* 1/2 (PI)))>
#<alt (+ (asin (+ 1 (* -1 x))) (* 1/2 (PI)))>
#<alt (+ (asin (+ 1 (* -1 x))) (* 1/2 (PI)))>
#<alt (- (* 1/2 (PI)) (asin (- 1 x)))>
#<alt (- (* 1/2 (PI)) (asin (- 1 x)))>
#<alt (- (* 1/2 (PI)) (asin (- 1 x)))>
#<alt (- (* 1/2 (PI)) (asin (- 1 x)))>
#<alt (- (* 1/2 (PI)) (asin (- 1 x)))>
#<alt (- (* 1/2 (PI)) (asin (- 1 x)))>
#<alt (- (* 1/2 (PI)) (asin (- 1 x)))>
#<alt (- (* 1/2 (PI)) (asin (- 1 x)))>
#<alt (- (* 1/2 (PI)) (asin (+ 1 (* -1 x))))>
#<alt (- (* 1/2 (PI)) (asin (+ 1 (* -1 x))))>
#<alt (- (* 1/2 (PI)) (asin (+ 1 (* -1 x))))>
#<alt (- (* 1/2 (PI)) (asin (+ 1 (* -1 x))))>
#<alt (- (* 1/2 (PI)) (+ (acos (- 1 x)) (* -1/2 (PI))))>
#<alt (- (* 1/2 (PI)) (+ (acos (- 1 x)) (* -1/2 (PI))))>
#<alt (- (* 1/2 (PI)) (+ (acos (- 1 x)) (* -1/2 (PI))))>
#<alt (- (* 1/2 (PI)) (+ (acos (- 1 x)) (* -1/2 (PI))))>
#<alt (- (* 1/2 (PI)) (+ (acos (- 1 x)) (* -1/2 (PI))))>
#<alt (- (* 1/2 (PI)) (+ (acos (- 1 x)) (* -1/2 (PI))))>
#<alt (- (* 1/2 (PI)) (+ (acos (- 1 x)) (* -1/2 (PI))))>
#<alt (- (* 1/2 (PI)) (+ (acos (- 1 x)) (* -1/2 (PI))))>
#<alt (- (* 1/2 (PI)) (+ (acos (+ 1 (* -1 x))) (* -1/2 (PI))))>
#<alt (- (* 1/2 (PI)) (+ (acos (+ 1 (* -1 x))) (* -1/2 (PI))))>
#<alt (- (* 1/2 (PI)) (+ (acos (+ 1 (* -1 x))) (* -1/2 (PI))))>
#<alt (- (* 1/2 (PI)) (+ (acos (+ 1 (* -1 x))) (* -1/2 (PI))))>
#<alt (+ (acos (- 1 x)) (* -1/2 (PI)))>
#<alt (+ (acos (- 1 x)) (* -1/2 (PI)))>
#<alt (+ (acos (- 1 x)) (* -1/2 (PI)))>
#<alt (+ (acos (- 1 x)) (* -1/2 (PI)))>
#<alt (+ (acos (- 1 x)) (* -1/2 (PI)))>
#<alt (+ (acos (- 1 x)) (* -1/2 (PI)))>
#<alt (+ (acos (- 1 x)) (* -1/2 (PI)))>
#<alt (+ (acos (- 1 x)) (* -1/2 (PI)))>
#<alt (+ (acos (+ 1 (* -1 x))) (* -1/2 (PI)))>
#<alt (+ (acos (+ 1 (* -1 x))) (* -1/2 (PI)))>
#<alt (+ (acos (+ 1 (* -1 x))) (* -1/2 (PI)))>
#<alt (+ (acos (+ 1 (* -1 x))) (* -1/2 (PI)))>
#<alt (* 1/2 (/ (+ (* 2 (pow (asin (- 1 x)) 3)) (* (PI) (pow (asin (- 1 x)) 2))) (pow (asin (- 1 x)) 2)))>
#<alt (* 1/2 (/ (+ (* 2 (pow (asin (- 1 x)) 3)) (* (PI) (pow (asin (- 1 x)) 2))) (pow (asin (- 1 x)) 2)))>
#<alt (* 1/2 (/ (+ (* 2 (pow (asin (- 1 x)) 3)) (* (PI) (pow (asin (- 1 x)) 2))) (pow (asin (- 1 x)) 2)))>
#<alt (* 1/2 (/ (+ (* 2 (pow (asin (- 1 x)) 3)) (* (PI) (pow (asin (- 1 x)) 2))) (pow (asin (- 1 x)) 2)))>
#<alt (* 1/2 (/ (+ (* 2 (pow (asin (- 1 x)) 3)) (* (PI) (pow (asin (- 1 x)) 2))) (pow (asin (- 1 x)) 2)))>
#<alt (* 1/2 (/ (+ (* 2 (pow (asin (- 1 x)) 3)) (* (PI) (pow (asin (- 1 x)) 2))) (pow (asin (- 1 x)) 2)))>
#<alt (* 1/2 (/ (+ (* 2 (pow (asin (- 1 x)) 3)) (* (PI) (pow (asin (- 1 x)) 2))) (pow (asin (- 1 x)) 2)))>
#<alt (* 1/2 (/ (+ (* 2 (pow (asin (- 1 x)) 3)) (* (PI) (pow (asin (- 1 x)) 2))) (pow (asin (- 1 x)) 2)))>
#<alt (* 1/2 (/ (+ (* 2 (pow (asin (+ 1 (* -1 x))) 3)) (* (PI) (pow (asin (+ 1 (* -1 x))) 2))) (pow (asin (+ 1 (* -1 x))) 2)))>
#<alt (* 1/2 (/ (+ (* 2 (pow (asin (+ 1 (* -1 x))) 3)) (* (PI) (pow (asin (+ 1 (* -1 x))) 2))) (pow (asin (+ 1 (* -1 x))) 2)))>
#<alt (* 1/2 (/ (+ (* 2 (pow (asin (+ 1 (* -1 x))) 3)) (* (PI) (pow (asin (+ 1 (* -1 x))) 2))) (pow (asin (+ 1 (* -1 x))) 2)))>
#<alt (* 1/2 (/ (+ (* 2 (pow (asin (+ 1 (* -1 x))) 3)) (* (PI) (pow (asin (+ 1 (* -1 x))) 2))) (pow (asin (+ 1 (* -1 x))) 2)))>
#<alt (+ (* 2 (pow (asin (- 1 x)) 3)) (* (PI) (pow (asin (- 1 x)) 2)))>
#<alt (+ (* 2 (pow (asin (- 1 x)) 3)) (* (PI) (pow (asin (- 1 x)) 2)))>
#<alt (+ (* 2 (pow (asin (- 1 x)) 3)) (* (PI) (pow (asin (- 1 x)) 2)))>
#<alt (+ (* 2 (pow (asin (- 1 x)) 3)) (* (PI) (pow (asin (- 1 x)) 2)))>
#<alt (+ (* 2 (pow (asin (- 1 x)) 3)) (* (PI) (pow (asin (- 1 x)) 2)))>
#<alt (+ (* 2 (pow (asin (- 1 x)) 3)) (* (PI) (pow (asin (- 1 x)) 2)))>
#<alt (+ (* 2 (pow (asin (- 1 x)) 3)) (* (PI) (pow (asin (- 1 x)) 2)))>
#<alt (+ (* 2 (pow (asin (- 1 x)) 3)) (* (PI) (pow (asin (- 1 x)) 2)))>
#<alt (+ (* 2 (pow (asin (+ 1 (* -1 x))) 3)) (* (PI) (pow (asin (+ 1 (* -1 x))) 2)))>
#<alt (+ (* 2 (pow (asin (+ 1 (* -1 x))) 3)) (* (PI) (pow (asin (+ 1 (* -1 x))) 2)))>
#<alt (+ (* 2 (pow (asin (+ 1 (* -1 x))) 3)) (* (PI) (pow (asin (+ 1 (* -1 x))) 2)))>
#<alt (+ (* 2 (pow (asin (+ 1 (* -1 x))) 3)) (* (PI) (pow (asin (+ 1 (* -1 x))) 2)))>
#<alt (pow (asin (- 1 x)) 3)>
#<alt (pow (asin (- 1 x)) 3)>
#<alt (pow (asin (- 1 x)) 3)>
#<alt (pow (asin (- 1 x)) 3)>
#<alt (pow (asin (- 1 x)) 3)>
#<alt (pow (asin (- 1 x)) 3)>
#<alt (pow (asin (- 1 x)) 3)>
#<alt (pow (asin (- 1 x)) 3)>
#<alt (pow (asin (+ 1 (* -1 x))) 3)>
#<alt (pow (asin (+ 1 (* -1 x))) 3)>
#<alt (pow (asin (+ 1 (* -1 x))) 3)>
#<alt (pow (asin (+ 1 (* -1 x))) 3)>
#<alt (asin (- 1 x))>
#<alt (asin (- 1 x))>
#<alt (asin (- 1 x))>
#<alt (asin (- 1 x))>
#<alt (asin (- 1 x))>
#<alt (asin (- 1 x))>
#<alt (asin (- 1 x))>
#<alt (asin (- 1 x))>
#<alt (asin (+ 1 (* -1 x)))>
#<alt (asin (+ 1 (* -1 x)))>
#<alt (asin (+ 1 (* -1 x)))>
#<alt (asin (+ 1 (* -1 x)))>
#<alt (asin (- 1 x))>
#<alt (asin (- 1 x))>
#<alt (asin (- 1 x))>
#<alt (asin (- 1 x))>
#<alt (asin (- 1 x))>
#<alt (asin (- 1 x))>
#<alt (asin (- 1 x))>
#<alt (asin (- 1 x))>
#<alt (asin (+ 1 (* -1 x)))>
#<alt (asin (+ 1 (* -1 x)))>
#<alt (asin (+ 1 (* -1 x)))>
#<alt (asin (+ 1 (* -1 x)))>
#<alt 1>
#<alt (+ 1 (* -1 x))>
#<alt (+ 1 (* -1 x))>
#<alt (+ 1 (* -1 x))>
#<alt (* -1 x)>
#<alt (* x (- (/ 1 x) 1))>
#<alt (* x (- (/ 1 x) 1))>
#<alt (* x (- (/ 1 x) 1))>
#<alt (* -1 x)>
#<alt (* -1 (* x (- 1 (/ 1 x))))>
#<alt (* -1 (* x (- 1 (/ 1 x))))>
#<alt (* -1 (* x (- 1 (/ 1 x))))>
#<alt (asin (- 1 x))>
#<alt (asin (- 1 x))>
#<alt (asin (- 1 x))>
#<alt (asin (- 1 x))>
#<alt (asin (- 1 x))>
#<alt (asin (- 1 x))>
#<alt (asin (- 1 x))>
#<alt (asin (- 1 x))>
#<alt (asin (+ 1 (* -1 x)))>
#<alt (asin (+ 1 (* -1 x)))>
#<alt (asin (+ 1 (* -1 x)))>
#<alt (asin (+ 1 (* -1 x)))>
#<alt 1>
#<alt (+ 1 (* -1 x))>
#<alt (+ 1 (* -1 x))>
#<alt (+ 1 (* -1 x))>
#<alt (* -1 x)>
#<alt (* x (- (/ 1 x) 1))>
#<alt (* x (- (/ 1 x) 1))>
#<alt (* x (- (/ 1 x) 1))>
#<alt (* -1 x)>
#<alt (* -1 (* x (- 1 (/ 1 x))))>
#<alt (* -1 (* x (- 1 (/ 1 x))))>
#<alt (* -1 (* x (- 1 (/ 1 x))))>
#<alt (acos (- 1 x))>
#<alt (acos (- 1 x))>
#<alt (acos (- 1 x))>
#<alt (acos (- 1 x))>
#<alt (acos (- 1 x))>
#<alt (acos (- 1 x))>
#<alt (acos (- 1 x))>
#<alt (acos (- 1 x))>
#<alt (acos (+ 1 (* -1 x)))>
#<alt (acos (+ 1 (* -1 x)))>
#<alt (acos (+ 1 (* -1 x)))>
#<alt (acos (+ 1 (* -1 x)))>

Calls

45 calls:

Time	Variable		Point	Expression
2.0ms	x	@	inf	(/ (+ (* (pow (asin (- 1 x)) 3) 2) (* (pow (asin (- 1 x)) 2) (PI))) (* (pow (asin (- 1 x)) 2) 2))
2.0ms	x	@	-inf	(/ (+ (* (pow (asin (- 1 x)) 3) 2) (* (pow (asin (- 1 x)) 2) (PI))) (* (pow (asin (- 1 x)) 2) 2))
2.0ms	x	@	0	(/ (+ (* (pow (asin (- 1 x)) 3) 2) (* (pow (asin (- 1 x)) 2) (PI))) (* (pow (asin (- 1 x)) 2) 2))
0.0ms	x	@	0	(+ (* (sqrt (PI)) (* (sqrt (PI)) 1/2)) (neg (+ (* (* (sqrt (PI)) 1/2) (neg (sqrt (PI)))) (acos (- 1 x)))))
0.0ms	x	@	-inf	(+ (* (sqrt (PI)) (* (sqrt (PI)) 1/2)) (neg (+ (* (* (sqrt (PI)) 1/2) (neg (sqrt (PI)))) (acos (- 1 x)))))

simplify264.0ms (5.6%)

Memory

24.6MiB live, 138.7MiB allocated

Algorithm

1×	egg-herbie

Rules

12 552×	`lower-fma.f64`
12 552×	`lower-fma.f32`
3 448×	`lower-*.f64`
3 448×	`lower-*.f32`
1 798×	`lower--.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	45	1252
1	101	1252
2	182	1180
3	345	1156
4	697	1156
5	1454	1156
6	4544	1156
0	8296	1108

Stop Event

1×	iter limit
1×	node limit

Counts

180 → 180

Calls

Call 1

Inputs
(- (* 1/2 (PI)) (asin (- 1 x)))
(- (* 1/2 (PI)) (asin (- 1 x)))
(- (* 1/2 (PI)) (asin (- 1 x)))
(- (* 1/2 (PI)) (asin (- 1 x)))
(- (* 1/2 (PI)) (asin (- 1 x)))
(- (* 1/2 (PI)) (asin (- 1 x)))
(- (* 1/2 (PI)) (asin (- 1 x)))
(- (* 1/2 (PI)) (asin (- 1 x)))
(- (* 1/2 (PI)) (asin (+ 1 (* -1 x))))
(- (* 1/2 (PI)) (asin (+ 1 (* -1 x))))
(- (* 1/2 (PI)) (asin (+ 1 (* -1 x))))
(- (* 1/2 (PI)) (asin (+ 1 (* -1 x))))
(- (* 1/2 (PI)) (asin (- 1 x)))
(- (* 1/2 (PI)) (asin (- 1 x)))
(- (* 1/2 (PI)) (asin (- 1 x)))
(- (* 1/2 (PI)) (asin (- 1 x)))
(- (* 1/2 (PI)) (asin (- 1 x)))
(- (* 1/2 (PI)) (asin (- 1 x)))
(- (* 1/2 (PI)) (asin (- 1 x)))
(- (* 1/2 (PI)) (asin (- 1 x)))
(- (* 1/2 (PI)) (asin (+ 1 (* -1 x))))
(- (* 1/2 (PI)) (asin (+ 1 (* -1 x))))
(- (* 1/2 (PI)) (asin (+ 1 (* -1 x))))
(- (* 1/2 (PI)) (asin (+ 1 (* -1 x))))
(+ (asin (- 1 x)) (* 1/2 (PI)))
(+ (asin (- 1 x)) (* 1/2 (PI)))
(+ (asin (- 1 x)) (* 1/2 (PI)))
(+ (asin (- 1 x)) (* 1/2 (PI)))
(+ (asin (- 1 x)) (* 1/2 (PI)))
(+ (asin (- 1 x)) (* 1/2 (PI)))
(+ (asin (- 1 x)) (* 1/2 (PI)))
(+ (asin (- 1 x)) (* 1/2 (PI)))
(+ (asin (+ 1 (* -1 x))) (* 1/2 (PI)))
(+ (asin (+ 1 (* -1 x))) (* 1/2 (PI)))
(+ (asin (+ 1 (* -1 x))) (* 1/2 (PI)))
(+ (asin (+ 1 (* -1 x))) (* 1/2 (PI)))
(- (* 1/2 (PI)) (asin (- 1 x)))
(- (* 1/2 (PI)) (asin (- 1 x)))
(- (* 1/2 (PI)) (asin (- 1 x)))
(- (* 1/2 (PI)) (asin (- 1 x)))
(- (* 1/2 (PI)) (asin (- 1 x)))
(- (* 1/2 (PI)) (asin (- 1 x)))
(- (* 1/2 (PI)) (asin (- 1 x)))
(- (* 1/2 (PI)) (asin (- 1 x)))
(- (* 1/2 (PI)) (asin (+ 1 (* -1 x))))
(- (* 1/2 (PI)) (asin (+ 1 (* -1 x))))
(- (* 1/2 (PI)) (asin (+ 1 (* -1 x))))
(- (* 1/2 (PI)) (asin (+ 1 (* -1 x))))
(- (* 1/2 (PI)) (+ (acos (- 1 x)) (* -1/2 (PI))))
(- (* 1/2 (PI)) (+ (acos (- 1 x)) (* -1/2 (PI))))
(- (* 1/2 (PI)) (+ (acos (- 1 x)) (* -1/2 (PI))))
(- (* 1/2 (PI)) (+ (acos (- 1 x)) (* -1/2 (PI))))
(- (* 1/2 (PI)) (+ (acos (- 1 x)) (* -1/2 (PI))))
(- (* 1/2 (PI)) (+ (acos (- 1 x)) (* -1/2 (PI))))
(- (* 1/2 (PI)) (+ (acos (- 1 x)) (* -1/2 (PI))))
(- (* 1/2 (PI)) (+ (acos (- 1 x)) (* -1/2 (PI))))
(- (* 1/2 (PI)) (+ (acos (+ 1 (* -1 x))) (* -1/2 (PI))))
(- (* 1/2 (PI)) (+ (acos (+ 1 (* -1 x))) (* -1/2 (PI))))
(- (* 1/2 (PI)) (+ (acos (+ 1 (* -1 x))) (* -1/2 (PI))))
(- (* 1/2 (PI)) (+ (acos (+ 1 (* -1 x))) (* -1/2 (PI))))
(+ (acos (- 1 x)) (* -1/2 (PI)))
(+ (acos (- 1 x)) (* -1/2 (PI)))
(+ (acos (- 1 x)) (* -1/2 (PI)))
(+ (acos (- 1 x)) (* -1/2 (PI)))
(+ (acos (- 1 x)) (* -1/2 (PI)))
(+ (acos (- 1 x)) (* -1/2 (PI)))
(+ (acos (- 1 x)) (* -1/2 (PI)))
(+ (acos (- 1 x)) (* -1/2 (PI)))
(+ (acos (+ 1 (* -1 x))) (* -1/2 (PI)))
(+ (acos (+ 1 (* -1 x))) (* -1/2 (PI)))
(+ (acos (+ 1 (* -1 x))) (* -1/2 (PI)))
(+ (acos (+ 1 (* -1 x))) (* -1/2 (PI)))
(* 1/2 (/ (+ (* 2 (pow (asin (- 1 x)) 3)) (* (PI) (pow (asin (- 1 x)) 2))) (pow (asin (- 1 x)) 2)))
(* 1/2 (/ (+ (* 2 (pow (asin (- 1 x)) 3)) (* (PI) (pow (asin (- 1 x)) 2))) (pow (asin (- 1 x)) 2)))
(* 1/2 (/ (+ (* 2 (pow (asin (- 1 x)) 3)) (* (PI) (pow (asin (- 1 x)) 2))) (pow (asin (- 1 x)) 2)))
(* 1/2 (/ (+ (* 2 (pow (asin (- 1 x)) 3)) (* (PI) (pow (asin (- 1 x)) 2))) (pow (asin (- 1 x)) 2)))
(* 1/2 (/ (+ (* 2 (pow (asin (- 1 x)) 3)) (* (PI) (pow (asin (- 1 x)) 2))) (pow (asin (- 1 x)) 2)))
(* 1/2 (/ (+ (* 2 (pow (asin (- 1 x)) 3)) (* (PI) (pow (asin (- 1 x)) 2))) (pow (asin (- 1 x)) 2)))
(* 1/2 (/ (+ (* 2 (pow (asin (- 1 x)) 3)) (* (PI) (pow (asin (- 1 x)) 2))) (pow (asin (- 1 x)) 2)))
(* 1/2 (/ (+ (* 2 (pow (asin (- 1 x)) 3)) (* (PI) (pow (asin (- 1 x)) 2))) (pow (asin (- 1 x)) 2)))
(* 1/2 (/ (+ (* 2 (pow (asin (+ 1 (* -1 x))) 3)) (* (PI) (pow (asin (+ 1 (* -1 x))) 2))) (pow (asin (+ 1 (* -1 x))) 2)))
(* 1/2 (/ (+ (* 2 (pow (asin (+ 1 (* -1 x))) 3)) (* (PI) (pow (asin (+ 1 (* -1 x))) 2))) (pow (asin (+ 1 (* -1 x))) 2)))
(* 1/2 (/ (+ (* 2 (pow (asin (+ 1 (* -1 x))) 3)) (* (PI) (pow (asin (+ 1 (* -1 x))) 2))) (pow (asin (+ 1 (* -1 x))) 2)))
(* 1/2 (/ (+ (* 2 (pow (asin (+ 1 (* -1 x))) 3)) (* (PI) (pow (asin (+ 1 (* -1 x))) 2))) (pow (asin (+ 1 (* -1 x))) 2)))
(+ (* 2 (pow (asin (- 1 x)) 3)) (* (PI) (pow (asin (- 1 x)) 2)))
(+ (* 2 (pow (asin (- 1 x)) 3)) (* (PI) (pow (asin (- 1 x)) 2)))
(+ (* 2 (pow (asin (- 1 x)) 3)) (* (PI) (pow (asin (- 1 x)) 2)))
(+ (* 2 (pow (asin (- 1 x)) 3)) (* (PI) (pow (asin (- 1 x)) 2)))
(+ (* 2 (pow (asin (- 1 x)) 3)) (* (PI) (pow (asin (- 1 x)) 2)))
(+ (* 2 (pow (asin (- 1 x)) 3)) (* (PI) (pow (asin (- 1 x)) 2)))
(+ (* 2 (pow (asin (- 1 x)) 3)) (* (PI) (pow (asin (- 1 x)) 2)))
(+ (* 2 (pow (asin (- 1 x)) 3)) (* (PI) (pow (asin (- 1 x)) 2)))
(+ (* 2 (pow (asin (+ 1 (* -1 x))) 3)) (* (PI) (pow (asin (+ 1 (* -1 x))) 2)))
(+ (* 2 (pow (asin (+ 1 (* -1 x))) 3)) (* (PI) (pow (asin (+ 1 (* -1 x))) 2)))
(+ (* 2 (pow (asin (+ 1 (* -1 x))) 3)) (* (PI) (pow (asin (+ 1 (* -1 x))) 2)))
(+ (* 2 (pow (asin (+ 1 (* -1 x))) 3)) (* (PI) (pow (asin (+ 1 (* -1 x))) 2)))
(pow (asin (- 1 x)) 3)
(pow (asin (- 1 x)) 3)
(pow (asin (- 1 x)) 3)
(pow (asin (- 1 x)) 3)
(pow (asin (- 1 x)) 3)
(pow (asin (- 1 x)) 3)
(pow (asin (- 1 x)) 3)
(pow (asin (- 1 x)) 3)
(pow (asin (+ 1 (* -1 x))) 3)
(pow (asin (+ 1 (* -1 x))) 3)
(pow (asin (+ 1 (* -1 x))) 3)
(pow (asin (+ 1 (* -1 x))) 3)
(asin (- 1 x))
(asin (- 1 x))
(asin (- 1 x))
(asin (- 1 x))
(asin (- 1 x))
(asin (- 1 x))
(asin (- 1 x))
(asin (- 1 x))
(asin (+ 1 (* -1 x)))
(asin (+ 1 (* -1 x)))
(asin (+ 1 (* -1 x)))
(asin (+ 1 (* -1 x)))
(asin (- 1 x))
(asin (- 1 x))
(asin (- 1 x))
(asin (- 1 x))
(asin (- 1 x))
(asin (- 1 x))
(asin (- 1 x))
(asin (- 1 x))
(asin (+ 1 (* -1 x)))
(asin (+ 1 (* -1 x)))
(asin (+ 1 (* -1 x)))
(asin (+ 1 (* -1 x)))
1
(+ 1 (* -1 x))
(+ 1 (* -1 x))
(+ 1 (* -1 x))
(* -1 x)
(* x (- (/ 1 x) 1))
(* x (- (/ 1 x) 1))
(* x (- (/ 1 x) 1))
(* -1 x)
(* -1 (* x (- 1 (/ 1 x))))
(* -1 (* x (- 1 (/ 1 x))))
(* -1 (* x (- 1 (/ 1 x))))
(asin (- 1 x))
(asin (- 1 x))
(asin (- 1 x))
(asin (- 1 x))
(asin (- 1 x))
(asin (- 1 x))
(asin (- 1 x))
(asin (- 1 x))
(asin (+ 1 (* -1 x)))
(asin (+ 1 (* -1 x)))
(asin (+ 1 (* -1 x)))
(asin (+ 1 (* -1 x)))
1
(+ 1 (* -1 x))
(+ 1 (* -1 x))
(+ 1 (* -1 x))
(* -1 x)
(* x (- (/ 1 x) 1))
(* x (- (/ 1 x) 1))
(* x (- (/ 1 x) 1))
(* -1 x)
(* -1 (* x (- 1 (/ 1 x))))
(* -1 (* x (- 1 (/ 1 x))))
(* -1 (* x (- 1 (/ 1 x))))
(acos (- 1 x))
(acos (- 1 x))
(acos (- 1 x))
(acos (- 1 x))
(acos (- 1 x))
(acos (- 1 x))
(acos (- 1 x))
(acos (- 1 x))
(acos (+ 1 (* -1 x)))
(acos (+ 1 (* -1 x)))
(acos (+ 1 (* -1 x)))
(acos (+ 1 (* -1 x)))

Outputs
(- (* 1/2 (PI)) (asin (- 1 x)))
(-.f64 (*.f64 #s(literal 1/2 binary64) (PI.f64)) (asin.f64 (-.f64 #s(literal 1 binary64) x)))
(- (* 1/2 (PI)) (asin (- 1 x)))
(-.f64 (*.f64 #s(literal 1/2 binary64) (PI.f64)) (asin.f64 (-.f64 #s(literal 1 binary64) x)))
(- (* 1/2 (PI)) (asin (- 1 x)))
(-.f64 (*.f64 #s(literal 1/2 binary64) (PI.f64)) (asin.f64 (-.f64 #s(literal 1 binary64) x)))
(- (* 1/2 (PI)) (asin (- 1 x)))
(-.f64 (*.f64 #s(literal 1/2 binary64) (PI.f64)) (asin.f64 (-.f64 #s(literal 1 binary64) x)))
(- (* 1/2 (PI)) (asin (- 1 x)))
(-.f64 (*.f64 #s(literal 1/2 binary64) (PI.f64)) (asin.f64 (-.f64 #s(literal 1 binary64) x)))
(- (* 1/2 (PI)) (asin (- 1 x)))
(-.f64 (*.f64 #s(literal 1/2 binary64) (PI.f64)) (asin.f64 (-.f64 #s(literal 1 binary64) x)))
(- (* 1/2 (PI)) (asin (- 1 x)))
(-.f64 (*.f64 #s(literal 1/2 binary64) (PI.f64)) (asin.f64 (-.f64 #s(literal 1 binary64) x)))
(- (* 1/2 (PI)) (asin (- 1 x)))
(-.f64 (*.f64 #s(literal 1/2 binary64) (PI.f64)) (asin.f64 (-.f64 #s(literal 1 binary64) x)))
(- (* 1/2 (PI)) (asin (+ 1 (* -1 x))))
(-.f64 (*.f64 #s(literal 1/2 binary64) (PI.f64)) (asin.f64 (-.f64 #s(literal 1 binary64) x)))
(- (* 1/2 (PI)) (asin (+ 1 (* -1 x))))
(-.f64 (*.f64 #s(literal 1/2 binary64) (PI.f64)) (asin.f64 (-.f64 #s(literal 1 binary64) x)))
(- (* 1/2 (PI)) (asin (+ 1 (* -1 x))))
(-.f64 (*.f64 #s(literal 1/2 binary64) (PI.f64)) (asin.f64 (-.f64 #s(literal 1 binary64) x)))
(- (* 1/2 (PI)) (asin (+ 1 (* -1 x))))
(-.f64 (*.f64 #s(literal 1/2 binary64) (PI.f64)) (asin.f64 (-.f64 #s(literal 1 binary64) x)))
(- (* 1/2 (PI)) (asin (- 1 x)))
(-.f64 (*.f64 #s(literal 1/2 binary64) (PI.f64)) (asin.f64 (-.f64 #s(literal 1 binary64) x)))
(- (* 1/2 (PI)) (asin (- 1 x)))
(-.f64 (*.f64 #s(literal 1/2 binary64) (PI.f64)) (asin.f64 (-.f64 #s(literal 1 binary64) x)))
(- (* 1/2 (PI)) (asin (- 1 x)))
(-.f64 (*.f64 #s(literal 1/2 binary64) (PI.f64)) (asin.f64 (-.f64 #s(literal 1 binary64) x)))
(- (* 1/2 (PI)) (asin (- 1 x)))
(-.f64 (*.f64 #s(literal 1/2 binary64) (PI.f64)) (asin.f64 (-.f64 #s(literal 1 binary64) x)))
(- (* 1/2 (PI)) (asin (- 1 x)))
(-.f64 (*.f64 #s(literal 1/2 binary64) (PI.f64)) (asin.f64 (-.f64 #s(literal 1 binary64) x)))
(- (* 1/2 (PI)) (asin (- 1 x)))
(-.f64 (*.f64 #s(literal 1/2 binary64) (PI.f64)) (asin.f64 (-.f64 #s(literal 1 binary64) x)))
(- (* 1/2 (PI)) (asin (- 1 x)))
(-.f64 (*.f64 #s(literal 1/2 binary64) (PI.f64)) (asin.f64 (-.f64 #s(literal 1 binary64) x)))
(- (* 1/2 (PI)) (asin (- 1 x)))
(-.f64 (*.f64 #s(literal 1/2 binary64) (PI.f64)) (asin.f64 (-.f64 #s(literal 1 binary64) x)))
(- (* 1/2 (PI)) (asin (+ 1 (* -1 x))))
(-.f64 (*.f64 #s(literal 1/2 binary64) (PI.f64)) (asin.f64 (-.f64 #s(literal 1 binary64) x)))
(- (* 1/2 (PI)) (asin (+ 1 (* -1 x))))
(-.f64 (*.f64 #s(literal 1/2 binary64) (PI.f64)) (asin.f64 (-.f64 #s(literal 1 binary64) x)))
(- (* 1/2 (PI)) (asin (+ 1 (* -1 x))))
(-.f64 (*.f64 #s(literal 1/2 binary64) (PI.f64)) (asin.f64 (-.f64 #s(literal 1 binary64) x)))
(- (* 1/2 (PI)) (asin (+ 1 (* -1 x))))
(-.f64 (*.f64 #s(literal 1/2 binary64) (PI.f64)) (asin.f64 (-.f64 #s(literal 1 binary64) x)))
(+ (asin (- 1 x)) (* 1/2 (PI)))
(fma.f64 #s(literal 1/2 binary64) (PI.f64) (asin.f64 (-.f64 #s(literal 1 binary64) x)))
(+ (asin (- 1 x)) (* 1/2 (PI)))
(fma.f64 #s(literal 1/2 binary64) (PI.f64) (asin.f64 (-.f64 #s(literal 1 binary64) x)))
(+ (asin (- 1 x)) (* 1/2 (PI)))
(fma.f64 #s(literal 1/2 binary64) (PI.f64) (asin.f64 (-.f64 #s(literal 1 binary64) x)))
(+ (asin (- 1 x)) (* 1/2 (PI)))
(fma.f64 #s(literal 1/2 binary64) (PI.f64) (asin.f64 (-.f64 #s(literal 1 binary64) x)))
(+ (asin (- 1 x)) (* 1/2 (PI)))
(fma.f64 #s(literal 1/2 binary64) (PI.f64) (asin.f64 (-.f64 #s(literal 1 binary64) x)))
(+ (asin (- 1 x)) (* 1/2 (PI)))
(fma.f64 #s(literal 1/2 binary64) (PI.f64) (asin.f64 (-.f64 #s(literal 1 binary64) x)))
(+ (asin (- 1 x)) (* 1/2 (PI)))
(fma.f64 #s(literal 1/2 binary64) (PI.f64) (asin.f64 (-.f64 #s(literal 1 binary64) x)))
(+ (asin (- 1 x)) (* 1/2 (PI)))
(fma.f64 #s(literal 1/2 binary64) (PI.f64) (asin.f64 (-.f64 #s(literal 1 binary64) x)))
(+ (asin (+ 1 (* -1 x))) (* 1/2 (PI)))
(fma.f64 #s(literal 1/2 binary64) (PI.f64) (asin.f64 (-.f64 #s(literal 1 binary64) x)))
(+ (asin (+ 1 (* -1 x))) (* 1/2 (PI)))
(fma.f64 #s(literal 1/2 binary64) (PI.f64) (asin.f64 (-.f64 #s(literal 1 binary64) x)))
(+ (asin (+ 1 (* -1 x))) (* 1/2 (PI)))
(fma.f64 #s(literal 1/2 binary64) (PI.f64) (asin.f64 (-.f64 #s(literal 1 binary64) x)))
(+ (asin (+ 1 (* -1 x))) (* 1/2 (PI)))
(fma.f64 #s(literal 1/2 binary64) (PI.f64) (asin.f64 (-.f64 #s(literal 1 binary64) x)))
(- (* 1/2 (PI)) (asin (- 1 x)))
(-.f64 (*.f64 #s(literal 1/2 binary64) (PI.f64)) (asin.f64 (-.f64 #s(literal 1 binary64) x)))
(- (* 1/2 (PI)) (asin (- 1 x)))
(-.f64 (*.f64 #s(literal 1/2 binary64) (PI.f64)) (asin.f64 (-.f64 #s(literal 1 binary64) x)))
(- (* 1/2 (PI)) (asin (- 1 x)))
(-.f64 (*.f64 #s(literal 1/2 binary64) (PI.f64)) (asin.f64 (-.f64 #s(literal 1 binary64) x)))
(- (* 1/2 (PI)) (asin (- 1 x)))
(-.f64 (*.f64 #s(literal 1/2 binary64) (PI.f64)) (asin.f64 (-.f64 #s(literal 1 binary64) x)))
(- (* 1/2 (PI)) (asin (- 1 x)))
(-.f64 (*.f64 #s(literal 1/2 binary64) (PI.f64)) (asin.f64 (-.f64 #s(literal 1 binary64) x)))
(- (* 1/2 (PI)) (asin (- 1 x)))
(-.f64 (*.f64 #s(literal 1/2 binary64) (PI.f64)) (asin.f64 (-.f64 #s(literal 1 binary64) x)))
(- (* 1/2 (PI)) (asin (- 1 x)))
(-.f64 (*.f64 #s(literal 1/2 binary64) (PI.f64)) (asin.f64 (-.f64 #s(literal 1 binary64) x)))
(- (* 1/2 (PI)) (asin (- 1 x)))
(-.f64 (*.f64 #s(literal 1/2 binary64) (PI.f64)) (asin.f64 (-.f64 #s(literal 1 binary64) x)))
(- (* 1/2 (PI)) (asin (+ 1 (* -1 x))))
(-.f64 (*.f64 #s(literal 1/2 binary64) (PI.f64)) (asin.f64 (-.f64 #s(literal 1 binary64) x)))
(- (* 1/2 (PI)) (asin (+ 1 (* -1 x))))
(-.f64 (*.f64 #s(literal 1/2 binary64) (PI.f64)) (asin.f64 (-.f64 #s(literal 1 binary64) x)))
(- (* 1/2 (PI)) (asin (+ 1 (* -1 x))))
(-.f64 (*.f64 #s(literal 1/2 binary64) (PI.f64)) (asin.f64 (-.f64 #s(literal 1 binary64) x)))
(- (* 1/2 (PI)) (asin (+ 1 (* -1 x))))
(-.f64 (*.f64 #s(literal 1/2 binary64) (PI.f64)) (asin.f64 (-.f64 #s(literal 1 binary64) x)))
(- (* 1/2 (PI)) (+ (acos (- 1 x)) (* -1/2 (PI))))
(-.f64 (PI.f64) (acos.f64 (-.f64 #s(literal 1 binary64) x)))
(- (* 1/2 (PI)) (+ (acos (- 1 x)) (* -1/2 (PI))))
(-.f64 (PI.f64) (acos.f64 (-.f64 #s(literal 1 binary64) x)))
(- (* 1/2 (PI)) (+ (acos (- 1 x)) (* -1/2 (PI))))
(-.f64 (PI.f64) (acos.f64 (-.f64 #s(literal 1 binary64) x)))
(- (* 1/2 (PI)) (+ (acos (- 1 x)) (* -1/2 (PI))))
(-.f64 (PI.f64) (acos.f64 (-.f64 #s(literal 1 binary64) x)))
(- (* 1/2 (PI)) (+ (acos (- 1 x)) (* -1/2 (PI))))
(-.f64 (PI.f64) (acos.f64 (-.f64 #s(literal 1 binary64) x)))
(- (* 1/2 (PI)) (+ (acos (- 1 x)) (* -1/2 (PI))))
(-.f64 (PI.f64) (acos.f64 (-.f64 #s(literal 1 binary64) x)))
(- (* 1/2 (PI)) (+ (acos (- 1 x)) (* -1/2 (PI))))
(-.f64 (PI.f64) (acos.f64 (-.f64 #s(literal 1 binary64) x)))
(- (* 1/2 (PI)) (+ (acos (- 1 x)) (* -1/2 (PI))))
(-.f64 (PI.f64) (acos.f64 (-.f64 #s(literal 1 binary64) x)))
(- (* 1/2 (PI)) (+ (acos (+ 1 (* -1 x))) (* -1/2 (PI))))
(-.f64 (PI.f64) (acos.f64 (-.f64 #s(literal 1 binary64) x)))
(- (* 1/2 (PI)) (+ (acos (+ 1 (* -1 x))) (* -1/2 (PI))))
(-.f64 (PI.f64) (acos.f64 (-.f64 #s(literal 1 binary64) x)))
(- (* 1/2 (PI)) (+ (acos (+ 1 (* -1 x))) (* -1/2 (PI))))
(-.f64 (PI.f64) (acos.f64 (-.f64 #s(literal 1 binary64) x)))
(- (* 1/2 (PI)) (+ (acos (+ 1 (* -1 x))) (* -1/2 (PI))))
(-.f64 (PI.f64) (acos.f64 (-.f64 #s(literal 1 binary64) x)))
(+ (acos (- 1 x)) (* -1/2 (PI)))
(fma.f64 (PI.f64) #s(literal -1/2 binary64) (acos.f64 (-.f64 #s(literal 1 binary64) x)))
(+ (acos (- 1 x)) (* -1/2 (PI)))
(fma.f64 (PI.f64) #s(literal -1/2 binary64) (acos.f64 (-.f64 #s(literal 1 binary64) x)))
(+ (acos (- 1 x)) (* -1/2 (PI)))
(fma.f64 (PI.f64) #s(literal -1/2 binary64) (acos.f64 (-.f64 #s(literal 1 binary64) x)))
(+ (acos (- 1 x)) (* -1/2 (PI)))
(fma.f64 (PI.f64) #s(literal -1/2 binary64) (acos.f64 (-.f64 #s(literal 1 binary64) x)))
(+ (acos (- 1 x)) (* -1/2 (PI)))
(fma.f64 (PI.f64) #s(literal -1/2 binary64) (acos.f64 (-.f64 #s(literal 1 binary64) x)))
(+ (acos (- 1 x)) (* -1/2 (PI)))
(fma.f64 (PI.f64) #s(literal -1/2 binary64) (acos.f64 (-.f64 #s(literal 1 binary64) x)))
(+ (acos (- 1 x)) (* -1/2 (PI)))
(fma.f64 (PI.f64) #s(literal -1/2 binary64) (acos.f64 (-.f64 #s(literal 1 binary64) x)))
(+ (acos (- 1 x)) (* -1/2 (PI)))
(fma.f64 (PI.f64) #s(literal -1/2 binary64) (acos.f64 (-.f64 #s(literal 1 binary64) x)))
(+ (acos (+ 1 (* -1 x))) (* -1/2 (PI)))
(fma.f64 (PI.f64) #s(literal -1/2 binary64) (acos.f64 (-.f64 #s(literal 1 binary64) x)))
(+ (acos (+ 1 (* -1 x))) (* -1/2 (PI)))
(fma.f64 (PI.f64) #s(literal -1/2 binary64) (acos.f64 (-.f64 #s(literal 1 binary64) x)))
(+ (acos (+ 1 (* -1 x))) (* -1/2 (PI)))
(fma.f64 (PI.f64) #s(literal -1/2 binary64) (acos.f64 (-.f64 #s(literal 1 binary64) x)))
(+ (acos (+ 1 (* -1 x))) (* -1/2 (PI)))
(fma.f64 (PI.f64) #s(literal -1/2 binary64) (acos.f64 (-.f64 #s(literal 1 binary64) x)))
(* 1/2 (/ (+ (* 2 (pow (asin (- 1 x)) 3)) (* (PI) (pow (asin (- 1 x)) 2))) (pow (asin (- 1 x)) 2)))
(fma.f64 #s(literal 1/2 binary64) (PI.f64) (asin.f64 (-.f64 #s(literal 1 binary64) x)))
(* 1/2 (/ (+ (* 2 (pow (asin (- 1 x)) 3)) (* (PI) (pow (asin (- 1 x)) 2))) (pow (asin (- 1 x)) 2)))
(fma.f64 #s(literal 1/2 binary64) (PI.f64) (asin.f64 (-.f64 #s(literal 1 binary64) x)))
(* 1/2 (/ (+ (* 2 (pow (asin (- 1 x)) 3)) (* (PI) (pow (asin (- 1 x)) 2))) (pow (asin (- 1 x)) 2)))
(fma.f64 #s(literal 1/2 binary64) (PI.f64) (asin.f64 (-.f64 #s(literal 1 binary64) x)))
(* 1/2 (/ (+ (* 2 (pow (asin (- 1 x)) 3)) (* (PI) (pow (asin (- 1 x)) 2))) (pow (asin (- 1 x)) 2)))
(fma.f64 #s(literal 1/2 binary64) (PI.f64) (asin.f64 (-.f64 #s(literal 1 binary64) x)))
(* 1/2 (/ (+ (* 2 (pow (asin (- 1 x)) 3)) (* (PI) (pow (asin (- 1 x)) 2))) (pow (asin (- 1 x)) 2)))
(fma.f64 #s(literal 1/2 binary64) (PI.f64) (asin.f64 (-.f64 #s(literal 1 binary64) x)))
(* 1/2 (/ (+ (* 2 (pow (asin (- 1 x)) 3)) (* (PI) (pow (asin (- 1 x)) 2))) (pow (asin (- 1 x)) 2)))
(fma.f64 #s(literal 1/2 binary64) (PI.f64) (asin.f64 (-.f64 #s(literal 1 binary64) x)))
(* 1/2 (/ (+ (* 2 (pow (asin (- 1 x)) 3)) (* (PI) (pow (asin (- 1 x)) 2))) (pow (asin (- 1 x)) 2)))
(fma.f64 #s(literal 1/2 binary64) (PI.f64) (asin.f64 (-.f64 #s(literal 1 binary64) x)))
(* 1/2 (/ (+ (* 2 (pow (asin (- 1 x)) 3)) (* (PI) (pow (asin (- 1 x)) 2))) (pow (asin (- 1 x)) 2)))
(fma.f64 #s(literal 1/2 binary64) (PI.f64) (asin.f64 (-.f64 #s(literal 1 binary64) x)))
(* 1/2 (/ (+ (* 2 (pow (asin (+ 1 (* -1 x))) 3)) (* (PI) (pow (asin (+ 1 (* -1 x))) 2))) (pow (asin (+ 1 (* -1 x))) 2)))
(fma.f64 #s(literal 1/2 binary64) (PI.f64) (asin.f64 (-.f64 #s(literal 1 binary64) x)))
(* 1/2 (/ (+ (* 2 (pow (asin (+ 1 (* -1 x))) 3)) (* (PI) (pow (asin (+ 1 (* -1 x))) 2))) (pow (asin (+ 1 (* -1 x))) 2)))
(fma.f64 #s(literal 1/2 binary64) (PI.f64) (asin.f64 (-.f64 #s(literal 1 binary64) x)))
(* 1/2 (/ (+ (* 2 (pow (asin (+ 1 (* -1 x))) 3)) (* (PI) (pow (asin (+ 1 (* -1 x))) 2))) (pow (asin (+ 1 (* -1 x))) 2)))
(fma.f64 #s(literal 1/2 binary64) (PI.f64) (asin.f64 (-.f64 #s(literal 1 binary64) x)))
(* 1/2 (/ (+ (* 2 (pow (asin (+ 1 (* -1 x))) 3)) (* (PI) (pow (asin (+ 1 (* -1 x))) 2))) (pow (asin (+ 1 (* -1 x))) 2)))
(fma.f64 #s(literal 1/2 binary64) (PI.f64) (asin.f64 (-.f64 #s(literal 1 binary64) x)))
(+ (* 2 (pow (asin (- 1 x)) 3)) (* (PI) (pow (asin (- 1 x)) 2)))
(*.f64 (pow.f64 (asin.f64 (-.f64 #s(literal 1 binary64) x)) #s(literal 2 binary64)) (fma.f64 (asin.f64 (-.f64 #s(literal 1 binary64) x)) #s(literal 2 binary64) (PI.f64)))
(+ (* 2 (pow (asin (- 1 x)) 3)) (* (PI) (pow (asin (- 1 x)) 2)))
(*.f64 (pow.f64 (asin.f64 (-.f64 #s(literal 1 binary64) x)) #s(literal 2 binary64)) (fma.f64 (asin.f64 (-.f64 #s(literal 1 binary64) x)) #s(literal 2 binary64) (PI.f64)))
(+ (* 2 (pow (asin (- 1 x)) 3)) (* (PI) (pow (asin (- 1 x)) 2)))
(*.f64 (pow.f64 (asin.f64 (-.f64 #s(literal 1 binary64) x)) #s(literal 2 binary64)) (fma.f64 (asin.f64 (-.f64 #s(literal 1 binary64) x)) #s(literal 2 binary64) (PI.f64)))
(+ (* 2 (pow (asin (- 1 x)) 3)) (* (PI) (pow (asin (- 1 x)) 2)))
(*.f64 (pow.f64 (asin.f64 (-.f64 #s(literal 1 binary64) x)) #s(literal 2 binary64)) (fma.f64 (asin.f64 (-.f64 #s(literal 1 binary64) x)) #s(literal 2 binary64) (PI.f64)))
(+ (* 2 (pow (asin (- 1 x)) 3)) (* (PI) (pow (asin (- 1 x)) 2)))
(*.f64 (pow.f64 (asin.f64 (-.f64 #s(literal 1 binary64) x)) #s(literal 2 binary64)) (fma.f64 (asin.f64 (-.f64 #s(literal 1 binary64) x)) #s(literal 2 binary64) (PI.f64)))
(+ (* 2 (pow (asin (- 1 x)) 3)) (* (PI) (pow (asin (- 1 x)) 2)))
(*.f64 (pow.f64 (asin.f64 (-.f64 #s(literal 1 binary64) x)) #s(literal 2 binary64)) (fma.f64 (asin.f64 (-.f64 #s(literal 1 binary64) x)) #s(literal 2 binary64) (PI.f64)))
(+ (* 2 (pow (asin (- 1 x)) 3)) (* (PI) (pow (asin (- 1 x)) 2)))
(*.f64 (pow.f64 (asin.f64 (-.f64 #s(literal 1 binary64) x)) #s(literal 2 binary64)) (fma.f64 (asin.f64 (-.f64 #s(literal 1 binary64) x)) #s(literal 2 binary64) (PI.f64)))
(+ (* 2 (pow (asin (- 1 x)) 3)) (* (PI) (pow (asin (- 1 x)) 2)))
(*.f64 (pow.f64 (asin.f64 (-.f64 #s(literal 1 binary64) x)) #s(literal 2 binary64)) (fma.f64 (asin.f64 (-.f64 #s(literal 1 binary64) x)) #s(literal 2 binary64) (PI.f64)))
(+ (* 2 (pow (asin (+ 1 (* -1 x))) 3)) (* (PI) (pow (asin (+ 1 (* -1 x))) 2)))
(*.f64 (pow.f64 (asin.f64 (-.f64 #s(literal 1 binary64) x)) #s(literal 2 binary64)) (fma.f64 (asin.f64 (-.f64 #s(literal 1 binary64) x)) #s(literal 2 binary64) (PI.f64)))
(+ (* 2 (pow (asin (+ 1 (* -1 x))) 3)) (* (PI) (pow (asin (+ 1 (* -1 x))) 2)))
(*.f64 (pow.f64 (asin.f64 (-.f64 #s(literal 1 binary64) x)) #s(literal 2 binary64)) (fma.f64 (asin.f64 (-.f64 #s(literal 1 binary64) x)) #s(literal 2 binary64) (PI.f64)))
(+ (* 2 (pow (asin (+ 1 (* -1 x))) 3)) (* (PI) (pow (asin (+ 1 (* -1 x))) 2)))
(*.f64 (pow.f64 (asin.f64 (-.f64 #s(literal 1 binary64) x)) #s(literal 2 binary64)) (fma.f64 (asin.f64 (-.f64 #s(literal 1 binary64) x)) #s(literal 2 binary64) (PI.f64)))
(+ (* 2 (pow (asin (+ 1 (* -1 x))) 3)) (* (PI) (pow (asin (+ 1 (* -1 x))) 2)))
(*.f64 (pow.f64 (asin.f64 (-.f64 #s(literal 1 binary64) x)) #s(literal 2 binary64)) (fma.f64 (asin.f64 (-.f64 #s(literal 1 binary64) x)) #s(literal 2 binary64) (PI.f64)))
(pow (asin (- 1 x)) 3)
(pow.f64 (asin.f64 (-.f64 #s(literal 1 binary64) x)) #s(literal 3 binary64))
(pow (asin (- 1 x)) 3)
(pow.f64 (asin.f64 (-.f64 #s(literal 1 binary64) x)) #s(literal 3 binary64))
(pow (asin (- 1 x)) 3)
(pow.f64 (asin.f64 (-.f64 #s(literal 1 binary64) x)) #s(literal 3 binary64))
(pow (asin (- 1 x)) 3)
(pow.f64 (asin.f64 (-.f64 #s(literal 1 binary64) x)) #s(literal 3 binary64))
(pow (asin (- 1 x)) 3)
(pow.f64 (asin.f64 (-.f64 #s(literal 1 binary64) x)) #s(literal 3 binary64))
(pow (asin (- 1 x)) 3)
(pow.f64 (asin.f64 (-.f64 #s(literal 1 binary64) x)) #s(literal 3 binary64))
(pow (asin (- 1 x)) 3)
(pow.f64 (asin.f64 (-.f64 #s(literal 1 binary64) x)) #s(literal 3 binary64))
(pow (asin (- 1 x)) 3)
(pow.f64 (asin.f64 (-.f64 #s(literal 1 binary64) x)) #s(literal 3 binary64))
(pow (asin (+ 1 (* -1 x))) 3)
(pow.f64 (asin.f64 (-.f64 #s(literal 1 binary64) x)) #s(literal 3 binary64))
(pow (asin (+ 1 (* -1 x))) 3)
(pow.f64 (asin.f64 (-.f64 #s(literal 1 binary64) x)) #s(literal 3 binary64))
(pow (asin (+ 1 (* -1 x))) 3)
(pow.f64 (asin.f64 (-.f64 #s(literal 1 binary64) x)) #s(literal 3 binary64))
(pow (asin (+ 1 (* -1 x))) 3)
(pow.f64 (asin.f64 (-.f64 #s(literal 1 binary64) x)) #s(literal 3 binary64))
(asin (- 1 x))
(asin.f64 (-.f64 #s(literal 1 binary64) x))
(asin (- 1 x))
(asin.f64 (-.f64 #s(literal 1 binary64) x))
(asin (- 1 x))
(asin.f64 (-.f64 #s(literal 1 binary64) x))
(asin (- 1 x))
(asin.f64 (-.f64 #s(literal 1 binary64) x))
(asin (- 1 x))
(asin.f64 (-.f64 #s(literal 1 binary64) x))
(asin (- 1 x))
(asin.f64 (-.f64 #s(literal 1 binary64) x))
(asin (- 1 x))
(asin.f64 (-.f64 #s(literal 1 binary64) x))
(asin (- 1 x))
(asin.f64 (-.f64 #s(literal 1 binary64) x))
(asin (+ 1 (* -1 x)))
(asin.f64 (-.f64 #s(literal 1 binary64) x))
(asin (+ 1 (* -1 x)))
(asin.f64 (-.f64 #s(literal 1 binary64) x))
(asin (+ 1 (* -1 x)))
(asin.f64 (-.f64 #s(literal 1 binary64) x))
(asin (+ 1 (* -1 x)))
(asin.f64 (-.f64 #s(literal 1 binary64) x))
(asin (- 1 x))
(asin.f64 (-.f64 #s(literal 1 binary64) x))
(asin (- 1 x))
(asin.f64 (-.f64 #s(literal 1 binary64) x))
(asin (- 1 x))
(asin.f64 (-.f64 #s(literal 1 binary64) x))
(asin (- 1 x))
(asin.f64 (-.f64 #s(literal 1 binary64) x))
(asin (- 1 x))
(asin.f64 (-.f64 #s(literal 1 binary64) x))
(asin (- 1 x))
(asin.f64 (-.f64 #s(literal 1 binary64) x))
(asin (- 1 x))
(asin.f64 (-.f64 #s(literal 1 binary64) x))
(asin (- 1 x))
(asin.f64 (-.f64 #s(literal 1 binary64) x))
(asin (+ 1 (* -1 x)))
(asin.f64 (-.f64 #s(literal 1 binary64) x))
(asin (+ 1 (* -1 x)))
(asin.f64 (-.f64 #s(literal 1 binary64) x))
(asin (+ 1 (* -1 x)))
(asin.f64 (-.f64 #s(literal 1 binary64) x))
(asin (+ 1 (* -1 x)))
(asin.f64 (-.f64 #s(literal 1 binary64) x))
1
#s(literal 1 binary64)
(+ 1 (* -1 x))
(-.f64 #s(literal 1 binary64) x)
(+ 1 (* -1 x))
(-.f64 #s(literal 1 binary64) x)
(+ 1 (* -1 x))
(-.f64 #s(literal 1 binary64) x)
(* -1 x)
(neg.f64 x)
(* x (- (/ 1 x) 1))
(-.f64 #s(literal 1 binary64) x)
(* x (- (/ 1 x) 1))
(-.f64 #s(literal 1 binary64) x)
(* x (- (/ 1 x) 1))
(-.f64 #s(literal 1 binary64) x)
(* -1 x)
(neg.f64 x)
(* -1 (* x (- 1 (/ 1 x))))
(-.f64 #s(literal 1 binary64) x)
(* -1 (* x (- 1 (/ 1 x))))
(-.f64 #s(literal 1 binary64) x)
(* -1 (* x (- 1 (/ 1 x))))
(-.f64 #s(literal 1 binary64) x)
(asin (- 1 x))
(asin.f64 (-.f64 #s(literal 1 binary64) x))
(asin (- 1 x))
(asin.f64 (-.f64 #s(literal 1 binary64) x))
(asin (- 1 x))
(asin.f64 (-.f64 #s(literal 1 binary64) x))
(asin (- 1 x))
(asin.f64 (-.f64 #s(literal 1 binary64) x))
(asin (- 1 x))
(asin.f64 (-.f64 #s(literal 1 binary64) x))
(asin (- 1 x))
(asin.f64 (-.f64 #s(literal 1 binary64) x))
(asin (- 1 x))
(asin.f64 (-.f64 #s(literal 1 binary64) x))
(asin (- 1 x))
(asin.f64 (-.f64 #s(literal 1 binary64) x))
(asin (+ 1 (* -1 x)))
(asin.f64 (-.f64 #s(literal 1 binary64) x))
(asin (+ 1 (* -1 x)))
(asin.f64 (-.f64 #s(literal 1 binary64) x))
(asin (+ 1 (* -1 x)))
(asin.f64 (-.f64 #s(literal 1 binary64) x))
(asin (+ 1 (* -1 x)))
(asin.f64 (-.f64 #s(literal 1 binary64) x))
1
#s(literal 1 binary64)
(+ 1 (* -1 x))
(-.f64 #s(literal 1 binary64) x)
(+ 1 (* -1 x))
(-.f64 #s(literal 1 binary64) x)
(+ 1 (* -1 x))
(-.f64 #s(literal 1 binary64) x)
(* -1 x)
(neg.f64 x)
(* x (- (/ 1 x) 1))
(-.f64 #s(literal 1 binary64) x)
(* x (- (/ 1 x) 1))
(-.f64 #s(literal 1 binary64) x)
(* x (- (/ 1 x) 1))
(-.f64 #s(literal 1 binary64) x)
(* -1 x)
(neg.f64 x)
(* -1 (* x (- 1 (/ 1 x))))
(-.f64 #s(literal 1 binary64) x)
(* -1 (* x (- 1 (/ 1 x))))
(-.f64 #s(literal 1 binary64) x)
(* -1 (* x (- 1 (/ 1 x))))
(-.f64 #s(literal 1 binary64) x)
(acos (- 1 x))
(acos.f64 (-.f64 #s(literal 1 binary64) x))
(acos (- 1 x))
(acos.f64 (-.f64 #s(literal 1 binary64) x))
(acos (- 1 x))
(acos.f64 (-.f64 #s(literal 1 binary64) x))
(acos (- 1 x))
(acos.f64 (-.f64 #s(literal 1 binary64) x))
(acos (- 1 x))
(acos.f64 (-.f64 #s(literal 1 binary64) x))
(acos (- 1 x))
(acos.f64 (-.f64 #s(literal 1 binary64) x))
(acos (- 1 x))
(acos.f64 (-.f64 #s(literal 1 binary64) x))
(acos (- 1 x))
(acos.f64 (-.f64 #s(literal 1 binary64) x))
(acos (+ 1 (* -1 x)))
(acos.f64 (-.f64 #s(literal 1 binary64) x))
(acos (+ 1 (* -1 x)))
(acos.f64 (-.f64 #s(literal 1 binary64) x))
(acos (+ 1 (* -1 x)))
(acos.f64 (-.f64 #s(literal 1 binary64) x))
(acos (+ 1 (* -1 x)))
(acos.f64 (-.f64 #s(literal 1 binary64) x))

rewrite427.0ms (9.1%)

Memory

1.8MiB live, 242.7MiB allocated

Algorithm

1×	batch-egg-rewrite

Rules

12 734×	`lower-fma.f32`
12 724×	`lower-fma.f64`
4 584×	`lower-*.f32`
4 576×	`lower-*.f64`
3 366×	`lower-/.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	39	200
0	68	173
1	254	156
2	1787	156
0	8602	153

Stop Event

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

Counts

19 → 1 070

Calls

Call 1

Inputs
#s(approx (+ (* (sqrt (PI)) (* (sqrt (PI)) 1/2)) (neg (asin (- 1 x)))) (-.f64 (*.f64 #s(literal 1/2 binary64) (PI.f64)) (asin.f64 (-.f64 #s(literal 1 binary64) x))))
(-.f64 (*.f64 #s(literal 1/2 binary64) (PI.f64)) (asin.f64 (-.f64 #s(literal 1 binary64) x)))
(*.f64 #s(literal 1/2 binary64) (PI.f64))
(PI.f64)
(fma.f64 (*.f64 (sqrt.f64 (PI.f64)) #s(literal 1/2 binary64)) (sqrt.f64 (PI.f64)) (asin.f64 #s(approx (- 1 x) x)))
(*.f64 (sqrt.f64 (PI.f64)) #s(literal 1/2 binary64))
(sqrt.f64 (PI.f64))
(fma.f64 (sqrt.f64 (PI.f64)) (*.f64 (sqrt.f64 (PI.f64)) #s(literal 1/2 binary64)) (neg.f64 (asin.f64 #s(approx (- 1 x) (-.f64 #s(literal 1 binary64) x)))))
(fma.f64 (sqrt.f64 (PI.f64)) (.f64 (sqrt.f64 (PI.f64)) #s(literal 1/2 binary64)) (neg.f64 (fma.f64 (.f64 (sqrt.f64 (PI.f64)) #s(literal 1/2 binary64)) (neg.f64 (sqrt.f64 (PI.f64))) (acos.f64 #s(approx (- 1 x) x)))))
(fma.f64 (*.f64 (sqrt.f64 (PI.f64)) #s(literal 1/2 binary64)) (neg.f64 (sqrt.f64 (PI.f64))) (acos.f64 #s(approx (- 1 x) x)))
(/.f64 (fma.f64 (pow.f64 (asin.f64 #s(approx (- 1 x) x)) #s(literal 3 binary64)) #s(literal 2 binary64) (.f64 (pow.f64 (asin.f64 #s(approx (- 1 x) x)) #s(literal 2 binary64)) (PI.f64))) (.f64 (pow.f64 (asin.f64 #s(approx (- 1 x) x)) #s(literal 2 binary64)) #s(literal 2 binary64)))
(fma.f64 (pow.f64 (asin.f64 #s(approx (- 1 x) x)) #s(literal 3 binary64)) #s(literal 2 binary64) (*.f64 (pow.f64 (asin.f64 #s(approx (- 1 x) x)) #s(literal 2 binary64)) (PI.f64)))
(pow.f64 (asin.f64 #s(approx (- 1 x) x)) #s(literal 3 binary64))
(asin.f64 #s(approx (- 1 x) x))
(asin.f64 (-.f64 #s(literal 1 binary64) x))
#s(approx (- 1 x) x)
(asin.f64 #s(approx (- 1 x) (-.f64 #s(literal 1 binary64) x)))
#s(approx (- 1 x) (-.f64 #s(literal 1 binary64) x))
(acos.f64 #s(approx (- 1 x) x))

Outputs
#s(approx (+ (* (sqrt (PI)) (* (sqrt (PI)) 1/2)) (neg (asin (- 1 x)))) (acos.f64 (-.f64 #s(literal 1 binary64) x)))
(acos.f64 (-.f64 #s(literal 1 binary64) x))
(+.f64 (neg.f64 (asin.f64 (-.f64 #s(literal 1 binary64) x))) (*.f64 #s(literal 1/2 binary64) (PI.f64)))
(+.f64 (*.f64 #s(literal 1/2 binary64) (PI.f64)) (neg.f64 (asin.f64 (-.f64 #s(literal 1 binary64) x))))
(+.f64 (-.f64 (.f64 #s(literal 1/2 binary64) (PI.f64)) (.f64 #s(literal 1/2 binary64) (PI.f64))) (acos.f64 (-.f64 #s(literal 1 binary64) x)))
(-.f64 (*.f64 #s(literal 1/2 binary64) (PI.f64)) (asin.f64 (-.f64 #s(literal 1 binary64) x)))
(-.f64 #s(literal 0 binary64) (-.f64 (asin.f64 (-.f64 #s(literal 1 binary64) x)) (*.f64 #s(literal 1/2 binary64) (PI.f64))))
(-.f64 (/.f64 (.f64 #s(literal 1/8 binary64) (.f64 (PI.f64) (.f64 (PI.f64) (PI.f64)))) (fma.f64 (asin.f64 (-.f64 #s(literal 1 binary64) x)) (fma.f64 #s(literal 1/2 binary64) (PI.f64) (asin.f64 (-.f64 #s(literal 1 binary64) x))) (.f64 (.f64 (PI.f64) (PI.f64)) #s(literal 1/4 binary64)))) (/.f64 (pow.f64 (asin.f64 (-.f64 #s(literal 1 binary64) x)) #s(literal 3 binary64)) (fma.f64 (asin.f64 (-.f64 #s(literal 1 binary64) x)) (fma.f64 #s(literal 1/2 binary64) (PI.f64) (asin.f64 (-.f64 #s(literal 1 binary64) x))) (.f64 (*.f64 (PI.f64) (PI.f64)) #s(literal 1/4 binary64)))))
(-.f64 (/.f64 (.f64 (.f64 (PI.f64) (PI.f64)) #s(literal 1/4 binary64)) (fma.f64 #s(literal 1/2 binary64) (PI.f64) (asin.f64 (-.f64 #s(literal 1 binary64) x)))) (/.f64 (pow.f64 (asin.f64 (-.f64 #s(literal 1 binary64) x)) #s(literal 2 binary64)) (fma.f64 #s(literal 1/2 binary64) (PI.f64) (asin.f64 (-.f64 #s(literal 1 binary64) x)))))
(-.f64 (fma.f64 #s(literal 1/2 binary64) (PI.f64) #s(literal 0 binary64)) (asin.f64 (-.f64 #s(literal 1 binary64) x)))
(-.f64 (/.f64 (.f64 #s(literal 1/8 binary64) (.f64 (PI.f64) (.f64 (PI.f64) (PI.f64)))) (fma.f64 (neg.f64 (asin.f64 (-.f64 #s(literal 1 binary64) x))) (-.f64 (neg.f64 (asin.f64 (-.f64 #s(literal 1 binary64) x))) (.f64 #s(literal 1/2 binary64) (PI.f64))) (.f64 (.f64 (PI.f64) (PI.f64)) #s(literal 1/4 binary64)))) (/.f64 (pow.f64 (asin.f64 (-.f64 #s(literal 1 binary64) x)) #s(literal 3 binary64)) (fma.f64 (neg.f64 (asin.f64 (-.f64 #s(literal 1 binary64) x))) (-.f64 (neg.f64 (asin.f64 (-.f64 #s(literal 1 binary64) x))) (.f64 #s(literal 1/2 binary64) (PI.f64))) (.f64 (*.f64 (PI.f64) (PI.f64)) #s(literal 1/4 binary64)))))
(-.f64 (/.f64 (.f64 #s(literal 1/8 binary64) (.f64 (PI.f64) (.f64 (PI.f64) (PI.f64)))) (+.f64 (pow.f64 (asin.f64 (-.f64 #s(literal 1 binary64) x)) #s(literal 2 binary64)) (-.f64 (.f64 (.f64 (PI.f64) (PI.f64)) #s(literal 1/4 binary64)) (neg.f64 (.f64 (asin.f64 (-.f64 #s(literal 1 binary64) x)) (.f64 #s(literal 1/2 binary64) (PI.f64))))))) (/.f64 (pow.f64 (asin.f64 (-.f64 #s(literal 1 binary64) x)) #s(literal 3 binary64)) (+.f64 (pow.f64 (asin.f64 (-.f64 #s(literal 1 binary64) x)) #s(literal 2 binary64)) (-.f64 (.f64 (.f64 (PI.f64) (PI.f64)) #s(literal 1/4 binary64)) (neg.f64 (.f64 (asin.f64 (-.f64 #s(literal 1 binary64) x)) (*.f64 #s(literal 1/2 binary64) (PI.f64))))))))
(-.f64 (/.f64 (pow.f64 (asin.f64 (-.f64 #s(literal 1 binary64) x)) #s(literal 2 binary64)) (-.f64 (neg.f64 (asin.f64 (-.f64 #s(literal 1 binary64) x))) (.f64 #s(literal 1/2 binary64) (PI.f64)))) (/.f64 (.f64 (.f64 (PI.f64) (PI.f64)) #s(literal 1/4 binary64)) (-.f64 (neg.f64 (asin.f64 (-.f64 #s(literal 1 binary64) x))) (.f64 #s(literal 1/2 binary64) (PI.f64)))))
(fma.f64 #s(literal 1/2 binary64) (PI.f64) (neg.f64 (asin.f64 (-.f64 #s(literal 1 binary64) x))))
(fma.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/2 binary64) (PI.f64)) (neg.f64 (asin.f64 (-.f64 #s(literal 1 binary64) x))))
(fma.f64 (PI.f64) #s(literal 1/2 binary64) (neg.f64 (asin.f64 (-.f64 #s(literal 1 binary64) x))))
(fma.f64 (asin.f64 (-.f64 #s(literal 1 binary64) x)) #s(literal -1 binary64) (*.f64 #s(literal 1/2 binary64) (PI.f64)))
(fma.f64 (sqrt.f64 (PI.f64)) (*.f64 #s(literal 1/2 binary64) (sqrt.f64 (PI.f64))) (neg.f64 (asin.f64 (-.f64 #s(literal 1 binary64) x))))
(fma.f64 (sqrt.f64 (PI.f64)) (neg.f64 (*.f64 #s(literal -1/2 binary64) (sqrt.f64 (PI.f64)))) (neg.f64 (asin.f64 (-.f64 #s(literal 1 binary64) x))))
(fma.f64 (sqrt.f64 (PI.f64)) (/.f64 (sqrt.f64 (PI.f64)) #s(literal 2 binary64)) (neg.f64 (asin.f64 (-.f64 #s(literal 1 binary64) x))))
(fma.f64 (*.f64 #s(literal 1/2 binary64) (sqrt.f64 (PI.f64))) (sqrt.f64 (PI.f64)) (neg.f64 (asin.f64 (-.f64 #s(literal 1 binary64) x))))
(fma.f64 (*.f64 #s(literal 1/2 binary64) (sqrt.f64 (PI.f64))) (neg.f64 (neg.f64 (sqrt.f64 (PI.f64)))) (neg.f64 (asin.f64 (-.f64 #s(literal 1 binary64) x))))
(fma.f64 (neg.f64 (sqrt.f64 (PI.f64))) (*.f64 #s(literal -1/2 binary64) (sqrt.f64 (PI.f64))) (neg.f64 (asin.f64 (-.f64 #s(literal 1 binary64) x))))
(fma.f64 (pow.f64 (PI.f64) #s(literal 2/3 binary64)) (*.f64 (cbrt.f64 (PI.f64)) #s(literal 1/2 binary64)) (neg.f64 (asin.f64 (-.f64 #s(literal 1 binary64) x))))
(fma.f64 (pow.f64 (PI.f64) #s(literal 2/3 binary64)) (/.f64 (cbrt.f64 (PI.f64)) #s(literal 2 binary64)) (neg.f64 (asin.f64 (-.f64 #s(literal 1 binary64) x))))
(fma.f64 #s(literal -1 binary64) (asin.f64 (-.f64 #s(literal 1 binary64) x)) (*.f64 #s(literal 1/2 binary64) (PI.f64)))
(fma.f64 #s(literal -1 binary64) (*.f64 (PI.f64) #s(literal -1/2 binary64)) (neg.f64 (asin.f64 (-.f64 #s(literal 1 binary64) x))))
(fma.f64 (*.f64 #s(literal -1/2 binary64) (sqrt.f64 (PI.f64))) (neg.f64 (sqrt.f64 (PI.f64))) (neg.f64 (asin.f64 (-.f64 #s(literal 1 binary64) x))))
(fma.f64 (neg.f64 (neg.f64 (sqrt.f64 (PI.f64)))) (*.f64 #s(literal 1/2 binary64) (sqrt.f64 (PI.f64))) (neg.f64 (asin.f64 (-.f64 #s(literal 1 binary64) x))))
(fma.f64 (*.f64 #s(literal 1/2 binary64) (pow.f64 (PI.f64) #s(literal 2/3 binary64))) (cbrt.f64 (PI.f64)) (neg.f64 (asin.f64 (-.f64 #s(literal 1 binary64) x))))
(/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 (neg.f64 (asin.f64 (-.f64 #s(literal 1 binary64) x))) (-.f64 (neg.f64 (asin.f64 (-.f64 #s(literal 1 binary64) x))) (.f64 #s(literal 1/2 binary64) (PI.f64))) (.f64 (.f64 (PI.f64) (PI.f64)) #s(literal 1/4 binary64))) (fma.f64 #s(literal 1/8 binary64) (.f64 (PI.f64) (*.f64 (PI.f64) (PI.f64))) (pow.f64 (asin.f64 (-.f64 #s(literal 1 binary64) x)) #s(literal 3 binary64)))))
(/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 (asin.f64 (-.f64 #s(literal 1 binary64) x)) (fma.f64 #s(literal 1/2 binary64) (PI.f64) (asin.f64 (-.f64 #s(literal 1 binary64) x))) (.f64 (.f64 (PI.f64) (PI.f64)) #s(literal 1/4 binary64))) (fma.f64 #s(literal 1/8 binary64) (.f64 (PI.f64) (.f64 (PI.f64) (PI.f64))) (pow.f64 (asin.f64 (-.f64 #s(literal 1 binary64) x)) #s(literal 3 binary64)))))
(/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 #s(literal 1/2 binary64) (PI.f64) (asin.f64 (-.f64 #s(literal 1 binary64) x))) (-.f64 (.f64 (.f64 (PI.f64) (PI.f64)) #s(literal 1/4 binary64)) (pow.f64 (asin.f64 (-.f64 #s(literal 1 binary64) x)) #s(literal 2 binary64)))))
(/.f64 (fma.f64 #s(literal 1/8 binary64) (.f64 (PI.f64) (.f64 (PI.f64) (PI.f64))) (pow.f64 (asin.f64 (-.f64 #s(literal 1 binary64) x)) #s(literal 3 binary64))) (fma.f64 (neg.f64 (asin.f64 (-.f64 #s(literal 1 binary64) x))) (-.f64 (neg.f64 (asin.f64 (-.f64 #s(literal 1 binary64) x))) (.f64 #s(literal 1/2 binary64) (PI.f64))) (.f64 (*.f64 (PI.f64) (PI.f64)) #s(literal 1/4 binary64))))
(/.f64 (fma.f64 #s(literal 1/8 binary64) (.f64 (PI.f64) (.f64 (PI.f64) (PI.f64))) (pow.f64 (asin.f64 (-.f64 #s(literal 1 binary64) x)) #s(literal 3 binary64))) (fma.f64 (asin.f64 (-.f64 #s(literal 1 binary64) x)) (fma.f64 #s(literal 1/2 binary64) (PI.f64) (asin.f64 (-.f64 #s(literal 1 binary64) x))) (.f64 (.f64 (PI.f64) (PI.f64)) #s(literal 1/4 binary64))))
(/.f64 (fma.f64 #s(literal 1/8 binary64) (.f64 (PI.f64) (.f64 (PI.f64) (PI.f64))) (pow.f64 (asin.f64 (-.f64 #s(literal 1 binary64) x)) #s(literal 3 binary64))) (+.f64 (pow.f64 (asin.f64 (-.f64 #s(literal 1 binary64) x)) #s(literal 2 binary64)) (-.f64 (.f64 (.f64 (PI.f64) (PI.f64)) #s(literal 1/4 binary64)) (neg.f64 (.f64 (asin.f64 (-.f64 #s(literal 1 binary64) x)) (.f64 #s(literal 1/2 binary64) (PI.f64)))))))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 (fma.f64 (neg.f64 (asin.f64 (-.f64 #s(literal 1 binary64) x))) (-.f64 (neg.f64 (asin.f64 (-.f64 #s(literal 1 binary64) x))) (.f64 #s(literal 1/2 binary64) (PI.f64))) (.f64 (.f64 (PI.f64) (PI.f64)) #s(literal 1/4 binary64))) (fma.f64 #s(literal 1/8 binary64) (.f64 (PI.f64) (*.f64 (PI.f64) (PI.f64))) (pow.f64 (asin.f64 (-.f64 #s(literal 1 binary64) x)) #s(literal 3 binary64))))))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 (fma.f64 (asin.f64 (-.f64 #s(literal 1 binary64) x)) (fma.f64 #s(literal 1/2 binary64) (PI.f64) (asin.f64 (-.f64 #s(literal 1 binary64) x))) (.f64 (.f64 (PI.f64) (PI.f64)) #s(literal 1/4 binary64))) (fma.f64 #s(literal 1/8 binary64) (.f64 (PI.f64) (.f64 (PI.f64) (PI.f64))) (pow.f64 (asin.f64 (-.f64 #s(literal 1 binary64) x)) #s(literal 3 binary64))))))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 (fma.f64 #s(literal 1/2 binary64) (PI.f64) (asin.f64 (-.f64 #s(literal 1 binary64) x))) (-.f64 (.f64 (.f64 (PI.f64) (PI.f64)) #s(literal 1/4 binary64)) (pow.f64 (asin.f64 (-.f64 #s(literal 1 binary64) x)) #s(literal 2 binary64))))))
(/.f64 (-.f64 (.f64 (.f64 (PI.f64) (PI.f64)) #s(literal 1/4 binary64)) (pow.f64 (asin.f64 (-.f64 #s(literal 1 binary64) x)) #s(literal 2 binary64))) (fma.f64 #s(literal 1/2 binary64) (PI.f64) (asin.f64 (-.f64 #s(literal 1 binary64) x))))
(/.f64 (neg.f64 (fma.f64 #s(literal 1/8 binary64) (.f64 (PI.f64) (.f64 (PI.f64) (PI.f64))) (pow.f64 (asin.f64 (-.f64 #s(literal 1 binary64) x)) #s(literal 3 binary64)))) (neg.f64 (fma.f64 (neg.f64 (asin.f64 (-.f64 #s(literal 1 binary64) x))) (-.f64 (neg.f64 (asin.f64 (-.f64 #s(literal 1 binary64) x))) (.f64 #s(literal 1/2 binary64) (PI.f64))) (.f64 (*.f64 (PI.f64) (PI.f64)) #s(literal 1/4 binary64)))))
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(/.f64 (-.f64 (.f64 (neg.f64 (PI.f64)) (-.f64 (.f64 #s(literal 1/2 binary64) (PI.f64)) (neg.f64 (acos.f64 #s(approx (- 1 x) x))))) (.f64 #s(literal -2 binary64) (-.f64 (.f64 (.f64 (PI.f64) (PI.f64)) #s(literal 1/4 binary64)) (pow.f64 (acos.f64 #s(approx (- 1 x) x)) #s(literal 2 binary64))))) (.f64 #s(literal -2 binary64) (-.f64 (*.f64 #s(literal 1/2 binary64) (PI.f64)) (neg.f64 (acos.f64 #s(approx (- 1 x) x))))))
(/.f64 (-.f64 (.f64 (neg.f64 (PI.f64)) (+.f64 #s(literal 0 binary64) (fma.f64 (PI.f64) #s(literal -1/2 binary64) (acos.f64 #s(approx (- 1 x) x))))) (.f64 #s(literal -2 binary64) (-.f64 #s(literal 0 binary64) (pow.f64 (asin.f64 #s(approx (- 1 x) x)) #s(literal 2 binary64))))) (*.f64 #s(literal -2 binary64) (+.f64 #s(literal 0 binary64) (fma.f64 (PI.f64) #s(literal -1/2 binary64) (acos.f64 #s(approx (- 1 x) x))))))
(/.f64 (-.f64 (.f64 (neg.f64 (PI.f64)) (fma.f64 (acos.f64 #s(approx (- 1 x) x)) (-.f64 (acos.f64 #s(approx (- 1 x) x)) (.f64 (PI.f64) #s(literal -1/2 binary64))) (.f64 (.f64 (PI.f64) (PI.f64)) #s(literal 1/4 binary64)))) (.f64 #s(literal -2 binary64) (.f64 #s(literal -1 binary64) (fma.f64 #s(literal 1/8 binary64) (.f64 (PI.f64) (.f64 (PI.f64) (PI.f64))) (pow.f64 (acos.f64 #s(approx (- 1 x) x)) #s(literal 3 binary64)))))) (.f64 #s(literal -2 binary64) (fma.f64 (acos.f64 #s(approx (- 1 x) x)) (-.f64 (acos.f64 #s(approx (- 1 x) x)) (.f64 (PI.f64) #s(literal -1/2 binary64))) (.f64 (.f64 (PI.f64) (PI.f64)) #s(literal 1/4 binary64)))))
(/.f64 (-.f64 (.f64 (neg.f64 (PI.f64)) (-.f64 (.f64 (PI.f64) #s(literal -1/2 binary64)) (acos.f64 #s(approx (- 1 x) x)))) (.f64 #s(literal -2 binary64) (.f64 #s(literal -1 binary64) (-.f64 (.f64 (.f64 (PI.f64) (PI.f64)) #s(literal 1/4 binary64)) (pow.f64 (acos.f64 #s(approx (- 1 x) x)) #s(literal 2 binary64)))))) (.f64 #s(literal -2 binary64) (-.f64 (.f64 (PI.f64) #s(literal -1/2 binary64)) (acos.f64 #s(approx (- 1 x) x)))))
(/.f64 (neg.f64 (-.f64 (.f64 #s(literal 1/8 binary64) (.f64 (PI.f64) (.f64 (PI.f64) (PI.f64)))) (pow.f64 (asin.f64 #s(approx (- 1 x) x)) #s(literal 3 binary64)))) (neg.f64 (fma.f64 (.f64 (PI.f64) (PI.f64)) #s(literal 1/4 binary64) (+.f64 (pow.f64 (asin.f64 #s(approx (- 1 x) x)) #s(literal 2 binary64)) (.f64 (asin.f64 #s(approx (- 1 x) x)) (.f64 #s(literal 1/2 binary64) (PI.f64)))))))
(/.f64 (fma.f64 #s(literal 1/8 binary64) (.f64 (PI.f64) (.f64 (PI.f64) (PI.f64))) (pow.f64 (neg.f64 (asin.f64 #s(approx (- 1 x) x))) #s(literal 3 binary64))) (fma.f64 (.f64 (PI.f64) (PI.f64)) #s(literal 1/4 binary64) (-.f64 (.f64 (neg.f64 (asin.f64 #s(approx (- 1 x) x))) (neg.f64 (asin.f64 #s(approx (- 1 x) x)))) (.f64 (.f64 #s(literal 1/2 binary64) (PI.f64)) (neg.f64 (asin.f64 #s(approx (- 1 x) x)))))))
(/.f64 (fma.f64 #s(literal 1/8 binary64) (.f64 (PI.f64) (.f64 (PI.f64) (PI.f64))) (pow.f64 (.f64 #s(literal 1 binary64) (fma.f64 (PI.f64) #s(literal -1/2 binary64) (acos.f64 #s(approx (- 1 x) x)))) #s(literal 3 binary64))) (fma.f64 (.f64 (PI.f64) (PI.f64)) #s(literal 1/4 binary64) (-.f64 (.f64 (.f64 #s(literal 1 binary64) (fma.f64 (PI.f64) #s(literal -1/2 binary64) (acos.f64 #s(approx (- 1 x) x)))) (.f64 #s(literal 1 binary64) (fma.f64 (PI.f64) #s(literal -1/2 binary64) (acos.f64 #s(approx (- 1 x) x))))) (.f64 (.f64 #s(literal 1/2 binary64) (PI.f64)) (.f64 #s(literal 1 binary64) (fma.f64 (PI.f64) #s(literal -1/2 binary64) (acos.f64 #s(approx (- 1 x) x))))))))
(/.f64 (+.f64 (pow.f64 (-.f64 (.f64 #s(literal 1/2 binary64) (PI.f64)) (.f64 #s(literal 1/2 binary64) (PI.f64))) #s(literal 3 binary64)) (pow.f64 (acos.f64 #s(approx (- 1 x) x)) #s(literal 3 binary64))) (fma.f64 (-.f64 (.f64 #s(literal 1/2 binary64) (PI.f64)) (.f64 #s(literal 1/2 binary64) (PI.f64))) (-.f64 (.f64 #s(literal 1/2 binary64) (PI.f64)) (.f64 #s(literal 1/2 binary64) (PI.f64))) (-.f64 (pow.f64 (acos.f64 #s(approx (- 1 x) x)) #s(literal 2 binary64)) (.f64 (-.f64 (.f64 #s(literal 1/2 binary64) (PI.f64)) (*.f64 #s(literal 1/2 binary64) (PI.f64))) (acos.f64 #s(approx (- 1 x) x))))))
(/.f64 (+.f64 (pow.f64 (-.f64 (.f64 #s(literal 1/2 binary64) (PI.f64)) #s(literal 0 binary64)) #s(literal 3 binary64)) (pow.f64 (fma.f64 (PI.f64) #s(literal -1/2 binary64) (acos.f64 #s(approx (- 1 x) x))) #s(literal 3 binary64))) (fma.f64 (-.f64 (.f64 #s(literal 1/2 binary64) (PI.f64)) #s(literal 0 binary64)) (-.f64 (.f64 #s(literal 1/2 binary64) (PI.f64)) #s(literal 0 binary64)) (-.f64 (pow.f64 (asin.f64 #s(approx (- 1 x) x)) #s(literal 2 binary64)) (.f64 (-.f64 (*.f64 #s(literal 1/2 binary64) (PI.f64)) #s(literal 0 binary64)) (fma.f64 (PI.f64) #s(literal -1/2 binary64) (acos.f64 #s(approx (- 1 x) x)))))))
(/.f64 (-.f64 (pow.f64 (-.f64 (.f64 #s(literal 1/2 binary64) (PI.f64)) (.f64 #s(literal 1/2 binary64) (PI.f64))) #s(literal 3 binary64)) (neg.f64 (pow.f64 (acos.f64 #s(approx (- 1 x) x)) #s(literal 3 binary64)))) (fma.f64 (-.f64 (.f64 #s(literal 1/2 binary64) (PI.f64)) (.f64 #s(literal 1/2 binary64) (PI.f64))) (-.f64 (.f64 #s(literal 1/2 binary64) (PI.f64)) (.f64 #s(literal 1/2 binary64) (PI.f64))) (+.f64 (pow.f64 (acos.f64 #s(approx (- 1 x) x)) #s(literal 2 binary64)) (.f64 (-.f64 (.f64 #s(literal 1/2 binary64) (PI.f64)) (*.f64 #s(literal 1/2 binary64) (PI.f64))) (neg.f64 (acos.f64 #s(approx (- 1 x) x)))))))
(.f64 (/.f64 (fma.f64 #s(literal 1/2 binary64) (PI.f64) (asin.f64 #s(approx (- 1 x) x))) (fma.f64 #s(literal 1/8 binary64) (.f64 (PI.f64) (.f64 (PI.f64) (PI.f64))) (pow.f64 (asin.f64 #s(approx (- 1 x) x)) #s(literal 3 binary64)))) (/.f64 (acos.f64 #s(approx (- 1 x) x)) (/.f64 #s(literal 1 binary64) (fma.f64 (asin.f64 #s(approx (- 1 x) x)) (-.f64 (asin.f64 #s(approx (- 1 x) x)) (.f64 #s(literal 1/2 binary64) (PI.f64))) (.f64 (.f64 (PI.f64) (PI.f64)) #s(literal 1/4 binary64))))))
(.f64 (/.f64 (fma.f64 #s(literal 1/2 binary64) (PI.f64) (asin.f64 #s(approx (- 1 x) x))) (.f64 (fma.f64 #s(literal 1/2 binary64) (PI.f64) (asin.f64 #s(approx (- 1 x) x))) (acos.f64 #s(approx (- 1 x) x)))) (/.f64 (acos.f64 #s(approx (- 1 x) x)) (/.f64 #s(literal 1 binary64) (acos.f64 #s(approx (- 1 x) x)))))

eval275.0ms (5.9%)

Memory: -6.7MiB live, 217.1MiB allocated
Compiler: Compiled 58 964 to 4 938 computations (91.6% saved)

prune208.0ms (4.4%)

Memory

14.3MiB live, 223.8MiB allocated

Pruning

20 alts after pruning (15 fresh and 5 done)

	Pruned	Kept	Total
New	2 119	15	2 134
Fresh	1	0	1
Picked	3	2	5
Done	0	3	3
Total	2 123	20	2 143

Accuracy

11.3%

Counts

2 143 → 20

Alt Table

Click to see full alt table

Status	Accuracy	Program
	11.1%	(fma.f64 (.f64 (sqrt.f64 (sqrt.f64 (PI.f64))) (sqrt.f64 (sqrt.f64 (PI.f64)))) (.f64 (sqrt.f64 (PI.f64)) #s(literal 1/2 binary64)) (neg.f64 (asin.f64 #s(approx (- 1 x) (-.f64 #s(literal 1 binary64) x)))))
✓	7.0%	(fma.f64 (*.f64 (sqrt.f64 (PI.f64)) #s(literal 1/2 binary64)) (sqrt.f64 (PI.f64)) (asin.f64 #s(approx (- 1 x) x)))
	11.1%	(fma.f64 (sqrt.f64 (PI.f64)) (.f64 (sqrt.f64 (PI.f64)) #s(literal 1/2 binary64)) (neg.f64 (fma.f64 (.f64 #s(literal 1/2 binary64) (sqrt.f64 (PI.f64))) (sqrt.f64 (PI.f64)) (neg.f64 (acos.f64 #s(approx (- 1 x) (-.f64 #s(literal 1 binary64) x)))))))
	5.8%	(/.f64 (fma.f64 (pow.f64 (asin.f64 #s(approx (- 1 x) x)) #s(literal 3 binary64)) #s(literal 2 binary64) (.f64 (pow.f64 (asin.f64 #s(approx (- 1 x) x)) #s(literal 2 binary64)) (PI.f64))) (.f64 (pow.f64 (fma.f64 (pow.f64 (PI.f64) #s(literal 2/3 binary64)) (*.f64 (cbrt.f64 (PI.f64)) #s(literal 1/2 binary64)) (neg.f64 (acos.f64 #s(approx (- 1 x) x)))) #s(literal 2 binary64)) #s(literal 2 binary64)))
	5.8%	(/.f64 (fma.f64 (pow.f64 (asin.f64 #s(approx (- 1 x) x)) #s(literal 3 binary64)) #s(literal 2 binary64) (.f64 (pow.f64 (asin.f64 #s(approx (- 1 x) x)) #s(literal 2 binary64)) (PI.f64))) (.f64 (pow.f64 (fma.f64 (*.f64 #s(literal 1/2 binary64) (sqrt.f64 (PI.f64))) (sqrt.f64 (PI.f64)) (neg.f64 (acos.f64 #s(approx (- 1 x) x)))) #s(literal 2 binary64)) #s(literal 2 binary64)))
	11.1%	(/.f64 (fma.f64 (-.f64 #s(literal 0 binary64) (pow.f64 (asin.f64 #s(approx (- 1 x) (-.f64 #s(literal 1 binary64) x))) #s(literal 3 binary64))) (/.f64 #s(literal 2 binary64) (PI.f64)) (.f64 (+.f64 #s(literal 0 binary64) (+.f64 (pow.f64 (asin.f64 #s(approx (- 1 x) (-.f64 #s(literal 1 binary64) x))) #s(literal 2 binary64)) (.f64 #s(literal 0 binary64) (asin.f64 #s(approx (- 1 x) (-.f64 #s(literal 1 binary64) x)))))) #s(literal 1 binary64))) (.f64 (+.f64 #s(literal 0 binary64) (+.f64 (pow.f64 (asin.f64 #s(approx (- 1 x) (-.f64 #s(literal 1 binary64) x))) #s(literal 2 binary64)) (.f64 #s(literal 0 binary64) (asin.f64 #s(approx (- 1 x) (-.f64 #s(literal 1 binary64) x)))))) (/.f64 #s(literal 2 binary64) (PI.f64))))
	7.7%	(/.f64 (fma.f64 #s(literal 1 binary64) (+.f64 #s(literal 0 binary64) (+.f64 (pow.f64 (asin.f64 #s(approx (- 1 x) (-.f64 #s(literal 1 binary64) x))) #s(literal 2 binary64)) (.f64 #s(literal 0 binary64) (asin.f64 #s(approx (- 1 x) (-.f64 #s(literal 1 binary64) x)))))) (.f64 (/.f64 #s(literal 2 binary64) (PI.f64)) (-.f64 #s(literal 0 binary64) (pow.f64 (asin.f64 #s(approx (- 1 x) (-.f64 #s(literal 1 binary64) x))) #s(literal 3 binary64))))) (.f64 (/.f64 #s(literal 2 binary64) (PI.f64)) (+.f64 #s(literal 0 binary64) (+.f64 (pow.f64 (asin.f64 #s(approx (- 1 x) (-.f64 #s(literal 1 binary64) x))) #s(literal 2 binary64)) (.f64 #s(literal 0 binary64) (asin.f64 #s(approx (- 1 x) (-.f64 #s(literal 1 binary64) x))))))))
	7.7%	(/.f64 (-.f64 (.f64 (PI.f64) (fma.f64 (.f64 (PI.f64) (PI.f64)) #s(literal 1/4 binary64) (+.f64 (pow.f64 (acos.f64 #s(approx (- 1 x) (-.f64 #s(literal 1 binary64) x))) #s(literal 2 binary64)) (.f64 (.f64 #s(literal 1/2 binary64) (PI.f64)) (acos.f64 #s(approx (- 1 x) (-.f64 #s(literal 1 binary64) x))))))) (.f64 #s(literal 2 binary64) (-.f64 (.f64 #s(literal 1/8 binary64) (.f64 (PI.f64) (.f64 (PI.f64) (PI.f64)))) (pow.f64 (acos.f64 #s(approx (- 1 x) (-.f64 #s(literal 1 binary64) x))) #s(literal 3 binary64))))) (.f64 #s(literal 2 binary64) (fma.f64 (.f64 (PI.f64) (PI.f64)) #s(literal 1/4 binary64) (+.f64 (pow.f64 (acos.f64 #s(approx (- 1 x) (-.f64 #s(literal 1 binary64) x))) #s(literal 2 binary64)) (.f64 (.f64 #s(literal 1/2 binary64) (PI.f64)) (acos.f64 #s(approx (- 1 x) (-.f64 #s(literal 1 binary64) x))))))))
	7.7%	(/.f64 (-.f64 (.f64 (PI.f64) (fma.f64 #s(literal 1/2 binary64) (PI.f64) (acos.f64 #s(approx (- 1 x) (-.f64 #s(literal 1 binary64) x))))) (.f64 #s(literal 2 binary64) (-.f64 (.f64 (.f64 (PI.f64) (PI.f64)) #s(literal 1/4 binary64)) (pow.f64 (acos.f64 #s(approx (- 1 x) (-.f64 #s(literal 1 binary64) x))) #s(literal 2 binary64))))) (*.f64 #s(literal 2 binary64) (fma.f64 #s(literal 1/2 binary64) (PI.f64) (acos.f64 #s(approx (- 1 x) (-.f64 #s(literal 1 binary64) x))))))
✓	7.7%	(acos.f64 (-.f64 #s(literal 1 binary64) x))
✓	7.0%	(acos.f64 #s(approx (- 1 x) x))
✓	3.8%	(acos.f64 #s(approx (- 1 x) #s(literal 1 binary64)))
	7.7%	#s(approx (+ (* (sqrt (PI)) (* (sqrt (PI)) 1/2)) (neg (asin (- 1 x)))) (/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 #s(literal 1/2 binary64) (PI.f64) (asin.f64 (-.f64 #s(literal 1 binary64) x))) (-.f64 (.f64 (.f64 (PI.f64) (PI.f64)) #s(literal 1/4 binary64)) (pow.f64 (asin.f64 (-.f64 #s(literal 1 binary64) x)) #s(literal 2 binary64))))))
	5.9%	#s(approx (+ (* (sqrt (PI)) (* (sqrt (PI)) 1/2)) (neg (asin (- 1 x)))) (-.f64 (.f64 (.f64 #s(literal 1/2 binary64) (sqrt.f64 (PI.f64))) (sqrt.f64 (PI.f64))) (asin.f64 (-.f64 #s(literal 1 binary64) x))))
	5.9%	#s(approx (+ (* (sqrt (PI)) (* (sqrt (PI)) 1/2)) (neg (asin (- 1 x)))) (-.f64 (.f64 #s(literal 1/2 binary64) (.f64 (pow.f64 (.f64 (.f64 (PI.f64) (PI.f64)) (sqrt.f64 (PI.f64))) #s(literal 1/3 binary64)) (cbrt.f64 (sqrt.f64 (PI.f64))))) (asin.f64 (-.f64 #s(literal 1 binary64) x))))
	5.9%	#s(approx (+ (* (sqrt (PI)) (* (sqrt (PI)) 1/2)) (neg (asin (- 1 x)))) (-.f64 (.f64 #s(literal 1/2 binary64) (.f64 (pow.f64 (cbrt.f64 (sqrt.f64 (PI.f64))) #s(literal 3 binary64)) (pow.f64 (cbrt.f64 (sqrt.f64 (PI.f64))) #s(literal 3 binary64)))) (asin.f64 (-.f64 #s(literal 1 binary64) x))))
	11.1%	#s(approx (+ (* (sqrt (PI)) (* (sqrt (PI)) 1/2)) (neg (asin (- 1 x)))) (-.f64 (.f64 #s(literal 1/2 binary64) (PI.f64)) (fma.f64 (.f64 #s(literal 1/2 binary64) (sqrt.f64 (PI.f64))) (sqrt.f64 (PI.f64)) (neg.f64 (acos.f64 (-.f64 #s(literal 1 binary64) x))))))
	7.7%	#s(approx (+ (* (sqrt (PI)) (* (sqrt (PI)) 1/2)) (neg (asin (- 1 x)))) (-.f64 (*.f64 #s(literal 1/2 binary64) (PI.f64)) (fma.f64 (PI.f64) #s(literal 1/2 binary64) (neg.f64 (acos.f64 (-.f64 #s(literal 1 binary64) x))))))
	7.7%	#s(approx (+ (* (sqrt (PI)) (* (sqrt (PI)) 1/2)) (neg (asin (- 1 x)))) (-.f64 (.f64 #s(literal 1/2 binary64) (PI.f64)) (/.f64 (-.f64 (.f64 (*.f64 (PI.f64) (PI.f64)) #s(literal 1/4 binary64)) (pow.f64 (acos.f64 (-.f64 #s(literal 1 binary64) x)) #s(literal 2 binary64))) (fma.f64 #s(literal 1/2 binary64) (PI.f64) (acos.f64 (-.f64 #s(literal 1 binary64) x))))))
✓	7.7%	#s(approx (+ (* (sqrt (PI)) (* (sqrt (PI)) 1/2)) (neg (asin (- 1 x)))) (-.f64 (*.f64 #s(literal 1/2 binary64) (PI.f64)) (asin.f64 (-.f64 #s(literal 1 binary64) x))))

Compiler

Compiled 972 to 378 computations (61.1% saved)

regimes21.0ms (0.4%)

Memory

-27.1MiB live, 12.0MiB allocated

Counts

26 → 1

Calls

Call 1

Inputs
(acos.f64 #s(approx (- 1 x) #s(literal 1 binary64)))
(acos.f64 #s(approx (- 1 x) x))
(acos.f64 #s(approx (- 1 x) (neg.f64 x)))
(acos.f64 (-.f64 #s(literal 1 binary64) x))
#s(approx (+ (* (sqrt (PI)) (* (sqrt (PI)) 1/2)) (neg (asin (- 1 x)))) (-.f64 (*.f64 #s(literal 1/2 binary64) (PI.f64)) (asin.f64 (-.f64 #s(literal 1 binary64) x))))
#s(approx (+ (* (sqrt (PI)) (* (sqrt (PI)) 1/2)) (neg (asin (- 1 x)))) (-.f64 (*.f64 #s(literal 1/2 binary64) (PI.f64)) (fma.f64 (PI.f64) #s(literal 1/2 binary64) (neg.f64 (acos.f64 (-.f64 #s(literal 1 binary64) x))))))
(fma.f64 (*.f64 (sqrt.f64 (PI.f64)) #s(literal 1/2 binary64)) (sqrt.f64 (PI.f64)) (asin.f64 #s(approx (- 1 x) x)))
(fma.f64 (sqrt.f64 (PI.f64)) (*.f64 (sqrt.f64 (PI.f64)) #s(literal 1/2 binary64)) (neg.f64 (asin.f64 #s(approx (- 1 x) x))))
#s(approx (+ (* (sqrt (PI)) (* (sqrt (PI)) 1/2)) (neg (asin (- 1 x)))) (-.f64 (.f64 (.f64 #s(literal 1/2 binary64) (sqrt.f64 (PI.f64))) (sqrt.f64 (PI.f64))) (asin.f64 (-.f64 #s(literal 1 binary64) x))))
(fma.f64 (sqrt.f64 (PI.f64)) (*.f64 (sqrt.f64 (PI.f64)) #s(literal 1/2 binary64)) (neg.f64 (asin.f64 #s(approx (- 1 x) (-.f64 #s(literal 1 binary64) x)))))
#s(approx (+ (* (sqrt (PI)) (* (sqrt (PI)) 1/2)) (neg (asin (- 1 x)))) (-.f64 (.f64 #s(literal 1/2 binary64) (PI.f64)) (fma.f64 (.f64 #s(literal 1/2 binary64) (sqrt.f64 (PI.f64))) (sqrt.f64 (PI.f64)) (neg.f64 (acos.f64 (-.f64 #s(literal 1 binary64) x))))))
(fma.f64 (sqrt.f64 (PI.f64)) (.f64 (sqrt.f64 (PI.f64)) #s(literal 1/2 binary64)) (neg.f64 (fma.f64 (.f64 (sqrt.f64 (PI.f64)) #s(literal 1/2 binary64)) (neg.f64 (sqrt.f64 (PI.f64))) (acos.f64 #s(approx (- 1 x) x)))))
(fma.f64 (sqrt.f64 (PI.f64)) (.f64 (sqrt.f64 (PI.f64)) #s(literal 1/2 binary64)) (neg.f64 (fma.f64 (.f64 #s(literal 1/2 binary64) (sqrt.f64 (PI.f64))) (sqrt.f64 (PI.f64)) (neg.f64 (acos.f64 #s(approx (- 1 x) (-.f64 #s(literal 1 binary64) x)))))))
(fma.f64 (.f64 (sqrt.f64 (sqrt.f64 (PI.f64))) (sqrt.f64 (sqrt.f64 (PI.f64)))) (.f64 (sqrt.f64 (PI.f64)) #s(literal 1/2 binary64)) (neg.f64 (asin.f64 #s(approx (- 1 x) (-.f64 #s(literal 1 binary64) x)))))
#s(approx (+ (* (sqrt (PI)) (* (sqrt (PI)) 1/2)) (neg (asin (- 1 x)))) (-.f64 (.f64 #s(literal 1/2 binary64) (PI.f64)) (/.f64 (-.f64 (.f64 (*.f64 (PI.f64) (PI.f64)) #s(literal 1/4 binary64)) (pow.f64 (acos.f64 (-.f64 #s(literal 1 binary64) x)) #s(literal 2 binary64))) (fma.f64 #s(literal 1/2 binary64) (PI.f64) (acos.f64 (-.f64 #s(literal 1 binary64) x))))))
#s(approx (+ (* (sqrt (PI)) (* (sqrt (PI)) 1/2)) (neg (asin (- 1 x)))) (-.f64 (.f64 #s(literal 1/2 binary64) (.f64 (pow.f64 (.f64 (.f64 (PI.f64) (PI.f64)) (sqrt.f64 (PI.f64))) #s(literal 1/3 binary64)) (cbrt.f64 (sqrt.f64 (PI.f64))))) (asin.f64 (-.f64 #s(literal 1 binary64) x))))
#s(approx (+ (* (sqrt (PI)) (* (sqrt (PI)) 1/2)) (neg (asin (- 1 x)))) (/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 #s(literal 1/2 binary64) (PI.f64) (asin.f64 (-.f64 #s(literal 1 binary64) x))) (-.f64 (.f64 (.f64 (PI.f64) (PI.f64)) #s(literal 1/4 binary64)) (pow.f64 (asin.f64 (-.f64 #s(literal 1 binary64) x)) #s(literal 2 binary64))))))
(/.f64 (-.f64 (.f64 (PI.f64) (fma.f64 #s(literal 1/2 binary64) (PI.f64) (acos.f64 #s(approx (- 1 x) (-.f64 #s(literal 1 binary64) x))))) (.f64 #s(literal 2 binary64) (-.f64 (.f64 (.f64 (PI.f64) (PI.f64)) #s(literal 1/4 binary64)) (pow.f64 (acos.f64 #s(approx (- 1 x) (-.f64 #s(literal 1 binary64) x))) #s(literal 2 binary64))))) (*.f64 #s(literal 2 binary64) (fma.f64 #s(literal 1/2 binary64) (PI.f64) (acos.f64 #s(approx (- 1 x) (-.f64 #s(literal 1 binary64) x))))))
#s(approx (+ (* (sqrt (PI)) (* (sqrt (PI)) 1/2)) (neg (asin (- 1 x)))) (-.f64 (.f64 #s(literal 1/2 binary64) (.f64 (pow.f64 (cbrt.f64 (sqrt.f64 (PI.f64))) #s(literal 3 binary64)) (pow.f64 (cbrt.f64 (sqrt.f64 (PI.f64))) #s(literal 3 binary64)))) (asin.f64 (-.f64 #s(literal 1 binary64) x))))
(/.f64 (fma.f64 (pow.f64 (asin.f64 #s(approx (- 1 x) x)) #s(literal 3 binary64)) #s(literal 2 binary64) (.f64 (pow.f64 (asin.f64 #s(approx (- 1 x) x)) #s(literal 2 binary64)) (PI.f64))) (.f64 (pow.f64 (asin.f64 #s(approx (- 1 x) x)) #s(literal 2 binary64)) #s(literal 2 binary64)))
(/.f64 (fma.f64 (pow.f64 (asin.f64 #s(approx (- 1 x) x)) #s(literal 3 binary64)) (/.f64 #s(literal 2 binary64) (PI.f64)) (pow.f64 (asin.f64 #s(approx (- 1 x) x)) #s(literal 2 binary64))) (*.f64 (pow.f64 (asin.f64 #s(approx (- 1 x) x)) #s(literal 2 binary64)) (/.f64 #s(literal 2 binary64) (PI.f64))))
(/.f64 (fma.f64 (pow.f64 (asin.f64 #s(approx (- 1 x) x)) #s(literal 3 binary64)) #s(literal 2 binary64) (.f64 (pow.f64 (asin.f64 #s(approx (- 1 x) x)) #s(literal 2 binary64)) (PI.f64))) (.f64 (pow.f64 (fma.f64 (*.f64 #s(literal 1/2 binary64) (sqrt.f64 (PI.f64))) (sqrt.f64 (PI.f64)) (neg.f64 (acos.f64 #s(approx (- 1 x) x)))) #s(literal 2 binary64)) #s(literal 2 binary64)))
(/.f64 (fma.f64 (pow.f64 (asin.f64 #s(approx (- 1 x) x)) #s(literal 3 binary64)) #s(literal 2 binary64) (.f64 (pow.f64 (asin.f64 #s(approx (- 1 x) x)) #s(literal 2 binary64)) (PI.f64))) (.f64 (pow.f64 (fma.f64 (pow.f64 (PI.f64) #s(literal 2/3 binary64)) (*.f64 (cbrt.f64 (PI.f64)) #s(literal 1/2 binary64)) (neg.f64 (acos.f64 #s(approx (- 1 x) x)))) #s(literal 2 binary64)) #s(literal 2 binary64)))
(/.f64 (fma.f64 #s(literal 1 binary64) (+.f64 #s(literal 0 binary64) (+.f64 (pow.f64 (asin.f64 #s(approx (- 1 x) (-.f64 #s(literal 1 binary64) x))) #s(literal 2 binary64)) (.f64 #s(literal 0 binary64) (asin.f64 #s(approx (- 1 x) (-.f64 #s(literal 1 binary64) x)))))) (.f64 (/.f64 #s(literal 2 binary64) (PI.f64)) (-.f64 #s(literal 0 binary64) (pow.f64 (asin.f64 #s(approx (- 1 x) (-.f64 #s(literal 1 binary64) x))) #s(literal 3 binary64))))) (.f64 (/.f64 #s(literal 2 binary64) (PI.f64)) (+.f64 #s(literal 0 binary64) (+.f64 (pow.f64 (asin.f64 #s(approx (- 1 x) (-.f64 #s(literal 1 binary64) x))) #s(literal 2 binary64)) (.f64 #s(literal 0 binary64) (asin.f64 #s(approx (- 1 x) (-.f64 #s(literal 1 binary64) x))))))))
(/.f64 (fma.f64 (-.f64 #s(literal 0 binary64) (pow.f64 (asin.f64 #s(approx (- 1 x) (-.f64 #s(literal 1 binary64) x))) #s(literal 3 binary64))) (/.f64 #s(literal 2 binary64) (PI.f64)) (.f64 (+.f64 #s(literal 0 binary64) (+.f64 (pow.f64 (asin.f64 #s(approx (- 1 x) (-.f64 #s(literal 1 binary64) x))) #s(literal 2 binary64)) (.f64 #s(literal 0 binary64) (asin.f64 #s(approx (- 1 x) (-.f64 #s(literal 1 binary64) x)))))) #s(literal 1 binary64))) (.f64 (+.f64 #s(literal 0 binary64) (+.f64 (pow.f64 (asin.f64 #s(approx (- 1 x) (-.f64 #s(literal 1 binary64) x))) #s(literal 2 binary64)) (.f64 #s(literal 0 binary64) (asin.f64 #s(approx (- 1 x) (-.f64 #s(literal 1 binary64) x)))))) (/.f64 #s(literal 2 binary64) (PI.f64))))
(/.f64 (-.f64 (.f64 (PI.f64) (fma.f64 (.f64 (PI.f64) (PI.f64)) #s(literal 1/4 binary64) (+.f64 (pow.f64 (acos.f64 #s(approx (- 1 x) (-.f64 #s(literal 1 binary64) x))) #s(literal 2 binary64)) (.f64 (.f64 #s(literal 1/2 binary64) (PI.f64)) (acos.f64 #s(approx (- 1 x) (-.f64 #s(literal 1 binary64) x))))))) (.f64 #s(literal 2 binary64) (-.f64 (.f64 #s(literal 1/8 binary64) (.f64 (PI.f64) (.f64 (PI.f64) (PI.f64)))) (pow.f64 (acos.f64 #s(approx (- 1 x) (-.f64 #s(literal 1 binary64) x))) #s(literal 3 binary64))))) (.f64 #s(literal 2 binary64) (fma.f64 (.f64 (PI.f64) (PI.f64)) #s(literal 1/4 binary64) (+.f64 (pow.f64 (acos.f64 #s(approx (- 1 x) (-.f64 #s(literal 1 binary64) x))) #s(literal 2 binary64)) (.f64 (.f64 #s(literal 1/2 binary64) (PI.f64)) (acos.f64 #s(approx (- 1 x) (-.f64 #s(literal 1 binary64) x))))))))

Outputs

(fma.f64 (*.f64 (sqrt.f64 (sqrt.f64 (PI.f64))) (sqrt.f64 (sqrt.f64 (PI.f64)))) (*.f64 (sqrt.f64 (PI.f64)) #s(literal 1/2 binary64)) (neg.f64 (asin.f64 #s(approx (- 1 x) (-.f64 #s(literal 1 binary64) x)))))

Calls

3 calls:

7.0ms	x
7.0ms	(-.f64 #s(literal 1 binary64) x)
5.0ms	(acos.f64 (-.f64 #s(literal 1 binary64) x))

Results

Accuracy	Segments	Branch
11.1%	1	`x`
11.1%	1	`(acos.f64 (-.f64 #s(literal 1 binary64) x))`
11.1%	1	`(-.f64 #s(literal 1 binary64) x)`

Compiler

Compiled 11 to 8 computations (27.3% saved)

regimes11.0ms (0.2%)

Memory

7.6MiB live, 7.6MiB allocated

Counts

13 → 1

Calls

Call 1

Inputs
(acos.f64 #s(approx (- 1 x) #s(literal 1 binary64)))
(acos.f64 #s(approx (- 1 x) x))
(acos.f64 #s(approx (- 1 x) (neg.f64 x)))
(acos.f64 (-.f64 #s(literal 1 binary64) x))
#s(approx (+ (* (sqrt (PI)) (* (sqrt (PI)) 1/2)) (neg (asin (- 1 x)))) (-.f64 (*.f64 #s(literal 1/2 binary64) (PI.f64)) (asin.f64 (-.f64 #s(literal 1 binary64) x))))
#s(approx (+ (* (sqrt (PI)) (* (sqrt (PI)) 1/2)) (neg (asin (- 1 x)))) (-.f64 (*.f64 #s(literal 1/2 binary64) (PI.f64)) (fma.f64 (PI.f64) #s(literal 1/2 binary64) (neg.f64 (acos.f64 (-.f64 #s(literal 1 binary64) x))))))
(fma.f64 (*.f64 (sqrt.f64 (PI.f64)) #s(literal 1/2 binary64)) (sqrt.f64 (PI.f64)) (asin.f64 #s(approx (- 1 x) x)))
(fma.f64 (sqrt.f64 (PI.f64)) (*.f64 (sqrt.f64 (PI.f64)) #s(literal 1/2 binary64)) (neg.f64 (asin.f64 #s(approx (- 1 x) x))))
#s(approx (+ (* (sqrt (PI)) (* (sqrt (PI)) 1/2)) (neg (asin (- 1 x)))) (-.f64 (.f64 (.f64 #s(literal 1/2 binary64) (sqrt.f64 (PI.f64))) (sqrt.f64 (PI.f64))) (asin.f64 (-.f64 #s(literal 1 binary64) x))))
(fma.f64 (sqrt.f64 (PI.f64)) (*.f64 (sqrt.f64 (PI.f64)) #s(literal 1/2 binary64)) (neg.f64 (asin.f64 #s(approx (- 1 x) (-.f64 #s(literal 1 binary64) x)))))
#s(approx (+ (* (sqrt (PI)) (* (sqrt (PI)) 1/2)) (neg (asin (- 1 x)))) (-.f64 (.f64 #s(literal 1/2 binary64) (PI.f64)) (fma.f64 (.f64 #s(literal 1/2 binary64) (sqrt.f64 (PI.f64))) (sqrt.f64 (PI.f64)) (neg.f64 (acos.f64 (-.f64 #s(literal 1 binary64) x))))))
(fma.f64 (sqrt.f64 (PI.f64)) (.f64 (sqrt.f64 (PI.f64)) #s(literal 1/2 binary64)) (neg.f64 (fma.f64 (.f64 (sqrt.f64 (PI.f64)) #s(literal 1/2 binary64)) (neg.f64 (sqrt.f64 (PI.f64))) (acos.f64 #s(approx (- 1 x) x)))))
(fma.f64 (sqrt.f64 (PI.f64)) (.f64 (sqrt.f64 (PI.f64)) #s(literal 1/2 binary64)) (neg.f64 (fma.f64 (.f64 #s(literal 1/2 binary64) (sqrt.f64 (PI.f64))) (sqrt.f64 (PI.f64)) (neg.f64 (acos.f64 #s(approx (- 1 x) (-.f64 #s(literal 1 binary64) x)))))))

Outputs

(fma.f64 (sqrt.f64 (PI.f64)) (*.f64 (sqrt.f64 (PI.f64)) #s(literal 1/2 binary64)) (neg.f64 (fma.f64 (*.f64 #s(literal 1/2 binary64) (sqrt.f64 (PI.f64))) (sqrt.f64 (PI.f64)) (neg.f64 (acos.f64 #s(approx (- 1 x) (-.f64 #s(literal 1 binary64) x)))))))

Calls

3 calls:

4.0ms	x
3.0ms	(-.f64 #s(literal 1 binary64) x)
3.0ms	(acos.f64 (-.f64 #s(literal 1 binary64) x))

Results

Accuracy	Segments	Branch
11.1%	1	`(acos.f64 (-.f64 #s(literal 1 binary64) x))`
11.1%	1	`(-.f64 #s(literal 1 binary64) x)`
11.1%	1	`x`

Compiler

Compiled 11 to 8 computations (27.3% saved)

regimes10.0ms (0.2%)

Memory

7.1MiB live, 7.1MiB allocated

Counts

12 → 1

Calls

Call 1

Inputs
(acos.f64 #s(approx (- 1 x) #s(literal 1 binary64)))
(acos.f64 #s(approx (- 1 x) x))
(acos.f64 #s(approx (- 1 x) (neg.f64 x)))
(acos.f64 (-.f64 #s(literal 1 binary64) x))
#s(approx (+ (* (sqrt (PI)) (* (sqrt (PI)) 1/2)) (neg (asin (- 1 x)))) (-.f64 (*.f64 #s(literal 1/2 binary64) (PI.f64)) (asin.f64 (-.f64 #s(literal 1 binary64) x))))
#s(approx (+ (* (sqrt (PI)) (* (sqrt (PI)) 1/2)) (neg (asin (- 1 x)))) (-.f64 (*.f64 #s(literal 1/2 binary64) (PI.f64)) (fma.f64 (PI.f64) #s(literal 1/2 binary64) (neg.f64 (acos.f64 (-.f64 #s(literal 1 binary64) x))))))
(fma.f64 (*.f64 (sqrt.f64 (PI.f64)) #s(literal 1/2 binary64)) (sqrt.f64 (PI.f64)) (asin.f64 #s(approx (- 1 x) x)))
(fma.f64 (sqrt.f64 (PI.f64)) (*.f64 (sqrt.f64 (PI.f64)) #s(literal 1/2 binary64)) (neg.f64 (asin.f64 #s(approx (- 1 x) x))))
#s(approx (+ (* (sqrt (PI)) (* (sqrt (PI)) 1/2)) (neg (asin (- 1 x)))) (-.f64 (.f64 (.f64 #s(literal 1/2 binary64) (sqrt.f64 (PI.f64))) (sqrt.f64 (PI.f64))) (asin.f64 (-.f64 #s(literal 1 binary64) x))))
(fma.f64 (sqrt.f64 (PI.f64)) (*.f64 (sqrt.f64 (PI.f64)) #s(literal 1/2 binary64)) (neg.f64 (asin.f64 #s(approx (- 1 x) (-.f64 #s(literal 1 binary64) x)))))
#s(approx (+ (* (sqrt (PI)) (* (sqrt (PI)) 1/2)) (neg (asin (- 1 x)))) (-.f64 (.f64 #s(literal 1/2 binary64) (PI.f64)) (fma.f64 (.f64 #s(literal 1/2 binary64) (sqrt.f64 (PI.f64))) (sqrt.f64 (PI.f64)) (neg.f64 (acos.f64 (-.f64 #s(literal 1 binary64) x))))))
(fma.f64 (sqrt.f64 (PI.f64)) (.f64 (sqrt.f64 (PI.f64)) #s(literal 1/2 binary64)) (neg.f64 (fma.f64 (.f64 (sqrt.f64 (PI.f64)) #s(literal 1/2 binary64)) (neg.f64 (sqrt.f64 (PI.f64))) (acos.f64 #s(approx (- 1 x) x)))))

Outputs

#s(approx (+ (* (sqrt (PI)) (* (sqrt (PI)) 1/2)) (neg (asin (- 1 x)))) (-.f64 (*.f64 #s(literal 1/2 binary64) (PI.f64)) (fma.f64 (*.f64 #s(literal 1/2 binary64) (sqrt.f64 (PI.f64))) (sqrt.f64 (PI.f64)) (neg.f64 (acos.f64 (-.f64 #s(literal 1 binary64) x))))))

Calls

3 calls:

4.0ms	x
3.0ms	(-.f64 #s(literal 1 binary64) x)
3.0ms	(acos.f64 (-.f64 #s(literal 1 binary64) x))

Results

Accuracy	Segments	Branch
11.1%	1	`(acos.f64 (-.f64 #s(literal 1 binary64) x))`
11.1%	1	`x`
11.1%	1	`(-.f64 #s(literal 1 binary64) x)`

Compiler

Compiled 11 to 8 computations (27.3% saved)

regimes9.0ms (0.2%)

Memory

6.5MiB live, 6.5MiB allocated

Counts

10 → 2

Calls

Call 1

Inputs
(acos.f64 #s(approx (- 1 x) #s(literal 1 binary64)))
(acos.f64 #s(approx (- 1 x) x))
(acos.f64 #s(approx (- 1 x) (neg.f64 x)))
(acos.f64 (-.f64 #s(literal 1 binary64) x))
#s(approx (+ (* (sqrt (PI)) (* (sqrt (PI)) 1/2)) (neg (asin (- 1 x)))) (-.f64 (*.f64 #s(literal 1/2 binary64) (PI.f64)) (asin.f64 (-.f64 #s(literal 1 binary64) x))))
#s(approx (+ (* (sqrt (PI)) (* (sqrt (PI)) 1/2)) (neg (asin (- 1 x)))) (-.f64 (*.f64 #s(literal 1/2 binary64) (PI.f64)) (fma.f64 (PI.f64) #s(literal 1/2 binary64) (neg.f64 (acos.f64 (-.f64 #s(literal 1 binary64) x))))))
(fma.f64 (*.f64 (sqrt.f64 (PI.f64)) #s(literal 1/2 binary64)) (sqrt.f64 (PI.f64)) (asin.f64 #s(approx (- 1 x) x)))
(fma.f64 (sqrt.f64 (PI.f64)) (*.f64 (sqrt.f64 (PI.f64)) #s(literal 1/2 binary64)) (neg.f64 (asin.f64 #s(approx (- 1 x) x))))
#s(approx (+ (* (sqrt (PI)) (* (sqrt (PI)) 1/2)) (neg (asin (- 1 x)))) (-.f64 (.f64 (.f64 #s(literal 1/2 binary64) (sqrt.f64 (PI.f64))) (sqrt.f64 (PI.f64))) (asin.f64 (-.f64 #s(literal 1 binary64) x))))
(fma.f64 (sqrt.f64 (PI.f64)) (*.f64 (sqrt.f64 (PI.f64)) #s(literal 1/2 binary64)) (neg.f64 (asin.f64 #s(approx (- 1 x) (-.f64 #s(literal 1 binary64) x)))))

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

Calls

3 calls:

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

Results

Accuracy	Segments	Branch
10.2%	2	`(acos.f64 (-.f64 #s(literal 1 binary64) x))`
10.2%	2	`(-.f64 #s(literal 1 binary64) x)`
10.2%	2	`x`

Compiler

Compiled 11 to 8 computations (27.3% saved)

regimes5.0ms (0.1%)

Memory

4.3MiB live, 4.3MiB allocated

Counts

3 → 1

Calls

Call 1

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

Outputs
(acos.f64 #s(approx (- 1 x) x))

Calls

3 calls:

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

Results

Accuracy	Segments	Branch
7.0%	1	`x`
7.0%	1	`(acos.f64 (-.f64 #s(literal 1 binary64) x))`
7.0%	1	`(-.f64 #s(literal 1 binary64) x)`

Compiler

Compiled 11 to 8 computations (27.3% saved)

regimes3.0ms (0.1%)

Memory

3.6MiB live, 3.6MiB allocated

Accuracy

Total 0.0b remaining (0%)

Threshold costs 0b (0%)

Counts

1 → 1

Calls

Call 1

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

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

Calls

3 calls:

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

Results

Accuracy	Segments	Branch
3.8%	1	`x`
3.8%	1	`(-.f64 #s(literal 1 binary64) x)`
3.8%	1	`(acos.f64 (-.f64 #s(literal 1 binary64) x))`

Compiler

Compiled 11 to 8 computations (27.3% saved)

bsearch0.0ms (0%)

Memory

0.1MiB live, 0.1MiB allocated

Algorithm

1×	left-value

Steps

Time	Left	Right
0.0ms	0.9999999999999997	1.0

Compiler

Compiled 8 to 8 computations (0% saved)

simplify7.0ms (0.2%)

Memory

-35.2MiB live, 4.6MiB allocated

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	40	103
1	59	103
2	73	103
3	81	103
4	83	103

Stop Event

1×

saturated

Calls

Call 1

Inputs
(fma.f64 (.f64 (sqrt.f64 (sqrt.f64 (PI.f64))) (sqrt.f64 (sqrt.f64 (PI.f64)))) (.f64 (sqrt.f64 (PI.f64)) #s(literal 1/2 binary64)) (neg.f64 (asin.f64 #s(approx (- 1 x) (-.f64 #s(literal 1 binary64) x)))))
(fma.f64 (sqrt.f64 (PI.f64)) (.f64 (sqrt.f64 (PI.f64)) #s(literal 1/2 binary64)) (neg.f64 (fma.f64 (.f64 #s(literal 1/2 binary64) (sqrt.f64 (PI.f64))) (sqrt.f64 (PI.f64)) (neg.f64 (acos.f64 #s(approx (- 1 x) (-.f64 #s(literal 1 binary64) x)))))))
#s(approx (+ (* (sqrt (PI)) (* (sqrt (PI)) 1/2)) (neg (asin (- 1 x)))) (-.f64 (.f64 #s(literal 1/2 binary64) (PI.f64)) (fma.f64 (.f64 #s(literal 1/2 binary64) (sqrt.f64 (PI.f64))) (sqrt.f64 (PI.f64)) (neg.f64 (acos.f64 (-.f64 #s(literal 1 binary64) x))))))
(if (<=.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 9007199254740989/9007199254740992 binary64)) (acos.f64 (-.f64 #s(literal 1 binary64) x)) (acos.f64 #s(approx (- 1 x) x)))
(acos.f64 #s(approx (- 1 x) x))
(acos.f64 #s(approx (- 1 x) #s(literal 1 binary64)))

Outputs
(fma.f64 (.f64 (sqrt.f64 (sqrt.f64 (PI.f64))) (sqrt.f64 (sqrt.f64 (PI.f64)))) (.f64 (sqrt.f64 (PI.f64)) #s(literal 1/2 binary64)) (neg.f64 (asin.f64 #s(approx (- 1 x) (-.f64 #s(literal 1 binary64) x)))))
(fma.f64 (sqrt.f64 (PI.f64)) (.f64 (sqrt.f64 (PI.f64)) #s(literal 1/2 binary64)) (neg.f64 (fma.f64 (.f64 #s(literal 1/2 binary64) (sqrt.f64 (PI.f64))) (sqrt.f64 (PI.f64)) (neg.f64 (acos.f64 #s(approx (- 1 x) (-.f64 #s(literal 1 binary64) x)))))))
(fma.f64 (sqrt.f64 (PI.f64)) (.f64 (sqrt.f64 (PI.f64)) #s(literal 1/2 binary64)) (neg.f64 (fma.f64 (.f64 (sqrt.f64 (PI.f64)) #s(literal 1/2 binary64)) (sqrt.f64 (PI.f64)) (neg.f64 (acos.f64 #s(approx (- 1 x) (-.f64 #s(literal 1 binary64) x)))))))
#s(approx (+ (* (sqrt (PI)) (* (sqrt (PI)) 1/2)) (neg (asin (- 1 x)))) (-.f64 (.f64 #s(literal 1/2 binary64) (PI.f64)) (fma.f64 (.f64 #s(literal 1/2 binary64) (sqrt.f64 (PI.f64))) (sqrt.f64 (PI.f64)) (neg.f64 (acos.f64 (-.f64 #s(literal 1 binary64) x))))))
#s(approx (+ (* (sqrt (PI)) (* (sqrt (PI)) 1/2)) (neg (asin (- 1 x)))) (-.f64 (.f64 (PI.f64) #s(literal 1/2 binary64)) (fma.f64 (.f64 (sqrt.f64 (PI.f64)) #s(literal 1/2 binary64)) (sqrt.f64 (PI.f64)) (neg.f64 (acos.f64 (-.f64 #s(literal 1 binary64) x))))))
(if (<=.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 9007199254740989/9007199254740992 binary64)) (acos.f64 (-.f64 #s(literal 1 binary64) x)) (acos.f64 #s(approx (- 1 x) x)))
(acos.f64 #s(approx (- 1 x) x))
(acos.f64 #s(approx (- 1 x) #s(literal 1 binary64)))

soundness364.0ms (7.8%)

Memory

13.7MiB live, 13.7MiB allocated

Rules

12 734×	`lower-fma.f32`
12 724×	`lower-fma.f64`
4 584×	`lower-*.f32`
4 576×	`lower-*.f64`
4 396×	`lower-*.f64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	39	200
0	68	173
1	254	156
2	1787	156
0	8602	153
0	14	80
1	29	80
2	62	80
3	113	80
4	171	80
5	239	80
6	259	80
0	259	80
0	21	224
1	41	224
2	77	224
3	134	224
4	206	224
5	292	224
6	353	224
7	387	224
8	438	224
9	455	224
10	463	224
0	463	224
0	8	26
0	11	26
1	37	26
2	203	26
3	1732	23
0	9154	23

Stop Event

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

Compiler

Compiled 253 to 143 computations (43.5% saved)

preprocess64.0ms (1.4%)

Memory: 5.5MiB live, 44.7MiB allocated
Compiler: Compiled 166 to 68 computations (59% saved)

end0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated

Iter	Nodes	Cost
0	6	11
1	15	9
2	27	9
3	49	9
4	67	9
5	89	9
6	102	9
0	4	4
0	6	4
1	10	4
2	14	4
3	19	4
4	26	4
5	34	4
6	44	4
7	55	4
8	58	4
0	58	4

Iter	Nodes	Cost
0	12	53
0	20	53
1	33	49
2	44	49
3	71	49
4	108	49
5	179	49
6	267	49
7	350	49
8	373	49
9	381	49
0	381	49

Iter	Nodes	Cost
0	21	224
1	41	224
2	77	224
3	134	224
4	206	224
5	292	224
6	353	224
7	387	224
8	438	224
9	455	224
10	463	224
0	463	224

Iter	Nodes	Cost
0	6	11
1	15	9
2	27	9
3	49	9
4	67	9
5	89	9
6	102	9
0	4	4
0	6	4
1	10	4
2	14	4
3	19	4
4	26	4
5	34	4
6	44	4
7	55	4
8	58	4
0	58	4

Iter	Nodes	Cost
0	12	53
0	20	53
1	33	49
2	44	49
3	71	49
4	108	49
5	179	49
6	267	49
7	350	49
8	373	49
9	381	49
0	381	49

Iter	Nodes	Cost
0	21	224
1	41	224
2	77	224
3	134	224
4	206	224
5	292	224
6	353	224
7	387	224
8	438	224
9	455	224
10	463	224
0	463	224

analyze0.0ms (0%)

sample1.0s (22.2%)

preprocess14.0ms (0.3%)

explain86.0ms (1.8%)

eval0.0ms (0%)

prune1.0ms (0%)

simplify8.0ms (0.2%)

localize29.0ms (0.6%)

series1.0ms (0%)

simplify9.0ms (0.2%)

rewrite294.0ms (6.3%)

eval48.0ms (1%)

prune39.0ms (0.8%)

simplify6.0ms (0.1%)

localize38.0ms (0.8%)

series1.0ms (0%)

simplify11.0ms (0.2%)

rewrite217.0ms (4.6%)

eval28.0ms (0.6%)

prune36.0ms (0.8%)

simplify17.0ms (0.4%)

localize85.0ms (1.8%)

series1.0ms (0%)

simplify19.0ms (0.4%)

rewrite300.0ms (6.4%)

eval103.0ms (2.2%)

prune71.0ms (1.5%)

simplify320.0ms (6.8%)

localize179.0ms (3.8%)

series10.0ms (0.2%)

simplify264.0ms (5.6%)

rewrite427.0ms (9.1%)

eval275.0ms (5.9%)

prune208.0ms (4.4%)

regimes21.0ms (0.4%)

regimes11.0ms (0.2%)

regimes10.0ms (0.2%)

regimes9.0ms (0.2%)

regimes5.0ms (0.1%)

regimes3.0ms (0.1%)

bsearch0.0ms (0%)

simplify7.0ms (0.2%)

soundness364.0ms (7.8%)

preprocess64.0ms (1.4%)

end0.0ms (0%)

Profiling

Iter	Nodes	Cost
0	6	11
1	15	9
2	27	9
3	49	9
4	67	9
5	89	9
6	102	9
0	4	4
0	6	4
1	10	4
2	14	4
3	19	4
4	26	4
5	34	4
6	44	4
7	55	4
8	58	4
0	58	4

Iter	Nodes	Cost
0	12	53
0	20	53
1	33	49
2	44	49
3	71	49
4	108	49
5	179	49
6	267	49
7	350	49
8	373	49
9	381	49
0	381	49

Iter	Nodes	Cost
0	21	224
1	41	224
2	77	224
3	134	224
4	206	224
5	292	224
6	353	224
7	387	224
8	438	224
9	455	224
10	463	224
0	463	224