Metrics for bug323 (missed optimization)

analyze0.0ms (0%)

Memory

0.3MiB live, 0.3MiB 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)

sample1.8s (32.1%)

Memory

-159.5MiB live, 1 877.0MiB allocated

Samples

1.2s	7 953×	1	valid
17.0ms	303×	0	valid

Precisions

Click to see histograms. Total time spent on operations: 969.0ms

ival-acos: 395.0ms (40.7% of total)

ival-<=: 260.0ms (26.8% of total)

adjust: 153.0ms (15.8% of total)

ival-sub: 132.0ms (13.6% of total)

exact: 14.0ms (1.4% of total)

ival-and: 11.0ms (1.1% of total)

ival-assert: 4.0ms (0.4% of total)

Bogosity

preprocess15.0ms (0.3%)

Memory

29.0MiB live, 29.0MiB 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))

explain95.0ms (1.6%)

Memory

-15.2MiB live, 181.9MiB allocated

FPErrors

Click to see full error table

Ground Truth	Example	Example	Subexpression
253	-	-	`(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	253	0

Confusion

	Predicted +	Predicted -
+	253	0
-	0	3

Precision

1.0

Recall

1.0

Confusion?

	Predicted +	Predicted Maybe	Predicted -
+	253	0	0
-	0	0	3

Precision?

1.0

Recall?

1.0

Freqs

test

number	freq
0	3
1	253

Total Confusion?

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

Precision?

1.0

Recall?

1.0

Samples

58.0ms	484×	1	valid
1.0ms	28×	0	valid

Compiler

Compiled 32 to 20 computations (37.5% saved)

Precisions

Click to see histograms. Total time spent on operations: 38.0ms

ival-acos: 23.0ms (60.9% of total)

adjust: 8.0ms (21.2% of total)

ival-sub: 6.0ms (15.9% 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: 0.3MiB live, 0.3MiB allocated
Compiler: Compiled 1 to 1 computations (0% saved)

prune1.0ms (0%)

Memory

1.5MiB live, 1.5MiB allocated

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	8.2%	(acos.f64 (-.f64 #s(literal 1 binary64) x))

Compiler

Compiled 5 to 4 computations (20% saved)

simplify5.0ms (0.1%)

Memory

13.7MiB live, 13.7MiB 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

localize34.0ms (0.6%)

Memory

-12.6MiB live, 65.0MiB allocated

Localize:

Found 2 expressions of interest:

New	Metric	Score	Program
✓	accuracy	100.0%	(-.f64 #s(literal 1 binary64) x)
✓	accuracy	8.2%	(acos.f64 (-.f64 #s(literal 1 binary64) x))

Samples

26.0ms	242×	1	valid
1.0ms	14×	0	valid

Compiler

Compiled 11 to 6 computations (45.5% saved)

Precisions

Click to see histograms. Total time spent on operations: 18.0ms

ival-acos: 11.0ms (62.2% of total)

ival-sub: 3.0ms (17% of total)

adjust: 3.0ms (17% 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

1.2MiB live, 1.2MiB 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	(acos (- 1 x))
0.0ms	x	@	0	(- 1 x)

simplify12.0ms (0.2%)

Memory

-20.8MiB live, 19.9MiB 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)

rewrite304.0ms (5.3%)

Memory

11.3MiB live, 408.4MiB 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)))

eval44.0ms (0.8%)

Memory: 31.1MiB live, 68.9MiB allocated
Compiler: Compiled 12 893 to 1 318 computations (89.8% saved)

prune41.0ms (0.7%)

Memory

-9.2MiB live, 69.6MiB 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

10.8%

Counts

364 → 3

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	8.2%	(acos.f64 (-.f64 #s(literal 1 binary64) x))
▶	7.1%	(acos.f64 #s(approx (- 1 x) (neg.f64 x)))
▶	3.8%	(acos.f64 #s(approx (- 1 x) #s(literal 1 binary64)))

Compiler

Compiled 14 to 10 computations (28.6% saved)

simplify5.0ms (0.1%)

Memory

5.0MiB live, 5.0MiB 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

localize37.0ms (0.6%)

Memory

3.7MiB live, 42.2MiB allocated

Localize:

Found 5 expressions of interest:

New	Metric	Score	Program
✓	accuracy	100.0%	(neg.f64 x)
✓	accuracy	8.2%	(acos.f64 #s(approx (- 1 x) (neg.f64 x)))
✓	accuracy	2.2%	#s(approx (- 1 x) (neg.f64 x))
✓	accuracy	96.8%	#s(approx (- 1 x) #s(literal 1 binary64))
✓	accuracy	8.2%	(acos.f64 #s(approx (- 1 x) #s(literal 1 binary64)))

Samples

27.0ms	242×	1	valid
1.0ms	14×	0	valid

Compiler

Compiled 20 to 7 computations (65% saved)

Precisions

Click to see histograms. Total time spent on operations: 18.0ms

ival-acos: 10.0ms (55.6% of total)

adjust: 3.0ms (16.7% of total)

ival-sub: 3.0ms (16.7% of total)

ival-neg: 1.0ms (5.6% 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	@	0	(neg x)
0.0ms	x	@	inf	(acos (- 1 x))

simplify14.0ms (0.2%)

Memory

-27.3MiB live, 9.4MiB 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)

rewrite203.0ms (3.5%)

Memory

10.4MiB live, 212.0MiB 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)

eval92.0ms (1.6%)

Memory: -10.7MiB live, 26.7MiB allocated
Compiler: Compiled 8 006 to 767 computations (90.4% saved)

prune22.0ms (0.4%)

Memory

26.2MiB 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

10.8%

Counts

268 → 4

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	7.1%	(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))))
✓	8.2%	(acos.f64 (-.f64 #s(literal 1 binary64) x))
▶	7.1%	(acos.f64 #s(approx (- 1 x) x))
✓	3.8%	(acos.f64 #s(approx (- 1 x) #s(literal 1 binary64)))

Compiler

Compiled 25 to 17 computations (32% saved)

simplify17.0ms (0.3%)

Memory

4.8MiB live, 4.8MiB 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

localize83.0ms (1.4%)

Memory

-14.1MiB live, 25.5MiB allocated

Localize:

Found 6 expressions of interest:

New	Metric	Score	Program
✓	accuracy	98.4%	(sqrt.f64 (PI.f64))
✓	accuracy	98.1%	(asin.f64 #s(approx (- 1 x) x))
✓	accuracy	14.0%	(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))))
✓	accuracy	5.5%	#s(approx (- 1 x) x)
✓	accuracy	8.2%	(acos.f64 #s(approx (- 1 x) x))
✓	accuracy	5.5%	#s(approx (- 1 x) x)

Samples

63.0ms	242×	1	valid
1.0ms	14×	0	valid

Compiler

Compiled 44 to 14 computations (68.2% saved)

Precisions

Click to see histograms. Total time spent on operations: 50.0ms

ival-acos: 17.0ms (33.7% of total)

ival-asin: 8.0ms (15.9% of total)

adjust: 7.0ms (13.9% of total)

ival-mult: 6.0ms (11.9% of total)

ival-sqrt: 4.0ms (7.9% of total)

ival-sub: 3.0ms (5.9% of total)

ival-pi: 2.0ms (4% of total)

ival-neg: 2.0ms (4% of total)

ival-add: 2.0ms (4% of total)

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

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

exact: 0.0ms (0% of total)

series1.0ms (0%)

Memory

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 (0.3%)

Memory

5.0MiB live, 5.0MiB 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))

rewrite346.0ms (6%)

Memory

0.5MiB live, 132.2MiB 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)))
(fma.f64 (neg.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)) (neg.f64 (.f64 (PI.f64) (.f64 (PI.f64) #s(literal 1/4 binary64)))))) #s(literal 0 binary64))
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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)))))

eval134.0ms (2.3%)

Memory: 2.0MiB live, 77.0MiB allocated
Compiler: Compiled 16 417 to 1 672 computations (89.8% saved)

prune79.0ms (1.4%)

Memory

-5.2MiB live, 77.1MiB 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

10.8%

Counts

811 → 9

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	7.1%	(fma.f64 (*.f64 (sqrt.f64 (PI.f64)) #s(literal 1/2 binary64)) (sqrt.f64 (PI.f64)) (asin.f64 #s(approx (- 1 x) x)))
▶	7.1%	(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)))))
▶	6.3%	(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)))
✓	8.2%	(acos.f64 (-.f64 #s(literal 1 binary64) x))
✓	7.1%	(acos.f64 #s(approx (- 1 x) x))
✓	3.8%	(acos.f64 #s(approx (- 1 x) #s(literal 1 binary64)))
▶	8.2%	#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 219 to 123 computations (43.8% saved)

simplify311.0ms (5.4%)

Memory

-12.2MiB live, 265.9MiB 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)))

localize195.0ms (3.4%)

Memory

2.9MiB live, 284.1MiB allocated

Localize:

Found 20 expressions of interest:

New	Metric	Score	Program
✓	accuracy	98.6%	(*.f64 (pow.f64 (asin.f64 #s(approx (- 1 x) x)) #s(literal 2 binary64)) (PI.f64))
✓	accuracy	98.5%	(pow.f64 (asin.f64 #s(approx (- 1 x) x)) #s(literal 3 binary64))
✓	accuracy	98.1%	(asin.f64 #s(approx (- 1 x) x))
✓	accuracy	5.5%	#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	8.2%	(acos.f64 #s(approx (- 1 x) x))
✓	accuracy	5.5%	#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	98.1%	(asin.f64 #s(approx (- 1 x) (-.f64 #s(literal 1 binary64) x)))
✓	accuracy	14.0%	(fma.f64 (sqrt.f64 (PI.f64)) (*.f64 (sqrt.f64 (PI.f64)) #s(literal 1/2 binary64)) (neg.f64 (asin.f64 #s(approx (- 1 x) (-.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	98.1%	(asin.f64 #s(approx (- 1 x) x))
✓	accuracy	5.5%	#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	98.1%	(asin.f64 (-.f64 #s(literal 1 binary64) x))
✓	accuracy	11.3%	(-.f64 (*.f64 #s(literal 1/2 binary64) (PI.f64)) (asin.f64 (-.f64 #s(literal 1 binary64) x)))

Samples

131.0ms	241×	1	valid
3.0ms	15×	0	valid

Compiler

Compiled 253 to 32 computations (87.4% saved)

Precisions

Click to see histograms. Total time spent on operations: 99.0ms

ival-mult: 23.0ms (23.3% of total)

adjust: 15.0ms (15.2% of total)

ival-add: 11.0ms (11.1% of total)

ival-asin: 10.0ms (10.1% of total)

ival-acos: 9.0ms (9.1% of total)

ival-sub: 6.0ms (6.1% of total)

ival-pow2: 5.0ms (5.1% of total)

ival-pow: 5.0ms (5.1% of total)

ival-neg: 5.0ms (5.1% of total)

ival-sqrt: 4.0ms (4% of total)

ival-div: 3.0ms (3% of total)

ival-pi: 2.0ms (2% of total)

exact: 1.0ms (1% of total)

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

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

series10.0ms (0.2%)

Memory

16.6MiB live, 16.6MiB allocated

Counts

20 → 192

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))>
#<alt (*.f64 (pow.f64 (asin.f64 #s(approx (- 1 x) x)) #s(literal 2 binary64)) (PI.f64))>

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)))>
#<alt (* (PI) (pow (asin (- 1 x)) 2))>
#<alt (* (PI) (pow (asin (- 1 x)) 2))>
#<alt (* (PI) (pow (asin (- 1 x)) 2))>
#<alt (* (PI) (pow (asin (- 1 x)) 2))>
#<alt (* (PI) (pow (asin (- 1 x)) 2))>
#<alt (* (PI) (pow (asin (- 1 x)) 2))>
#<alt (* (PI) (pow (asin (- 1 x)) 2))>
#<alt (* (PI) (pow (asin (- 1 x)) 2))>
#<alt (* (PI) (pow (asin (+ 1 (* -1 x))) 2))>
#<alt (* (PI) (pow (asin (+ 1 (* -1 x))) 2))>
#<alt (* (PI) (pow (asin (+ 1 (* -1 x))) 2))>
#<alt (* (PI) (pow (asin (+ 1 (* -1 x))) 2))>

Calls

48 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)))))

simplify276.0ms (4.8%)

Memory

-4.2MiB live, 351.7MiB 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	1348
1	101	1348
2	182	1276
3	345	1252
4	697	1252
5	1454	1252
6	4544	1252
0	8296	1204

Stop Event

1×	iter limit
1×	node limit

Counts

192 → 192

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)))
(* (PI) (pow (asin (- 1 x)) 2))
(* (PI) (pow (asin (- 1 x)) 2))
(* (PI) (pow (asin (- 1 x)) 2))
(* (PI) (pow (asin (- 1 x)) 2))
(* (PI) (pow (asin (- 1 x)) 2))
(* (PI) (pow (asin (- 1 x)) 2))
(* (PI) (pow (asin (- 1 x)) 2))
(* (PI) (pow (asin (- 1 x)) 2))
(* (PI) (pow (asin (+ 1 (* -1 x))) 2))
(* (PI) (pow (asin (+ 1 (* -1 x))) 2))
(* (PI) (pow (asin (+ 1 (* -1 x))) 2))
(* (PI) (pow (asin (+ 1 (* -1 x))) 2))

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))
(* (PI) (pow (asin (- 1 x)) 2))
(*.f64 (PI.f64) (pow.f64 (asin.f64 (-.f64 #s(literal 1 binary64) x)) #s(literal 2 binary64)))
(* (PI) (pow (asin (- 1 x)) 2))
(*.f64 (PI.f64) (pow.f64 (asin.f64 (-.f64 #s(literal 1 binary64) x)) #s(literal 2 binary64)))
(* (PI) (pow (asin (- 1 x)) 2))
(*.f64 (PI.f64) (pow.f64 (asin.f64 (-.f64 #s(literal 1 binary64) x)) #s(literal 2 binary64)))
(* (PI) (pow (asin (- 1 x)) 2))
(*.f64 (PI.f64) (pow.f64 (asin.f64 (-.f64 #s(literal 1 binary64) x)) #s(literal 2 binary64)))
(* (PI) (pow (asin (- 1 x)) 2))
(*.f64 (PI.f64) (pow.f64 (asin.f64 (-.f64 #s(literal 1 binary64) x)) #s(literal 2 binary64)))
(* (PI) (pow (asin (- 1 x)) 2))
(*.f64 (PI.f64) (pow.f64 (asin.f64 (-.f64 #s(literal 1 binary64) x)) #s(literal 2 binary64)))
(* (PI) (pow (asin (- 1 x)) 2))
(*.f64 (PI.f64) (pow.f64 (asin.f64 (-.f64 #s(literal 1 binary64) x)) #s(literal 2 binary64)))
(* (PI) (pow (asin (- 1 x)) 2))
(*.f64 (PI.f64) (pow.f64 (asin.f64 (-.f64 #s(literal 1 binary64) x)) #s(literal 2 binary64)))
(* (PI) (pow (asin (+ 1 (* -1 x))) 2))
(*.f64 (PI.f64) (pow.f64 (asin.f64 (-.f64 #s(literal 1 binary64) x)) #s(literal 2 binary64)))
(* (PI) (pow (asin (+ 1 (* -1 x))) 2))
(*.f64 (PI.f64) (pow.f64 (asin.f64 (-.f64 #s(literal 1 binary64) x)) #s(literal 2 binary64)))
(* (PI) (pow (asin (+ 1 (* -1 x))) 2))
(*.f64 (PI.f64) (pow.f64 (asin.f64 (-.f64 #s(literal 1 binary64) x)) #s(literal 2 binary64)))
(* (PI) (pow (asin (+ 1 (* -1 x))) 2))
(*.f64 (PI.f64) (pow.f64 (asin.f64 (-.f64 #s(literal 1 binary64) x)) #s(literal 2 binary64)))

rewrite427.0ms (7.4%)

Memory

-18.9MiB live, 305.3MiB 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	210
0	68	183
1	254	166
2	1787	166
0	8602	163

Stop Event

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

Counts

20 → 1 085

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))
(*.f64 (pow.f64 (asin.f64 #s(approx (- 1 x) x)) #s(literal 2 binary64)) (PI.f64))

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

eval285.0ms (4.9%)

Memory: 38.5MiB live, 217.1MiB allocated
Compiler: Compiled 64 729 to 4 981 computations (92.3% saved)

prune210.0ms (3.7%)

Memory

-15.9MiB live, 228.2MiB allocated

Pruning

21 alts after pruning (15 fresh and 6 done)

	Pruned	Kept	Total
New	2 146	15	2 161
Fresh	1	0	1
Picked	2	3	5
Done	0	3	3
Total	2 149	21	2 170

Accuracy

12.2%

Counts

2 170 → 21

Alt Table

Click to see full alt table

Status	Accuracy	Program
	6.4%	(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) (-.f64 #s(literal 1 binary64) x)))))
	11.8%	(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)))))
✓	7.1%	(fma.f64 (*.f64 (sqrt.f64 (PI.f64)) #s(literal 1/2 binary64)) (sqrt.f64 (PI.f64)) (asin.f64 #s(approx (- 1 x) x)))
	11.8%	(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)))))))
✓	6.3%	(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)))))
	6.0%	(/.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)))
	6.0%	(/.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)))
	11.9%	(/.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))))
	8.1%	(/.f64 (fma.f64 (-.f64 #s(literal 0 binary64) (pow.f64 (asin.f64 #s(approx (- 1 x) (-.f64 #s(literal 1 binary64) x))) #s(literal 2 binary64))) #s(literal 2 binary64) (.f64 (+.f64 #s(literal 0 binary64) (asin.f64 #s(approx (- 1 x) (-.f64 #s(literal 1 binary64) x)))) (PI.f64))) (.f64 (+.f64 #s(literal 0 binary64) (asin.f64 #s(approx (- 1 x) (-.f64 #s(literal 1 binary64) x)))) #s(literal 2 binary64)))
	11.8%	(/.f64 (fma.f64 (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 #s(literal 2 binary64) (-.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) (+.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))))))))
	8.1%	(/.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))))))))
	8.1%	(/.f64 (-.f64 (.f64 #s(literal 1 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))))))) (.f64 (/.f64 #s(literal 2 binary64) (PI.f64)) (-.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 (/.f64 #s(literal 2 binary64) (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))))))))
✓	8.2%	(acos.f64 (-.f64 #s(literal 1 binary64) x))
✓	7.1%	(acos.f64 #s(approx (- 1 x) x))
✓	3.8%	(acos.f64 #s(approx (- 1 x) #s(literal 1 binary64)))
	6.3%	#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))))
	6.3%	#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))))
	6.2%	#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))))
	11.7%	#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))))))
	8.2%	#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))))))
✓	8.2%	#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 1 122 to 388 computations (65.4% saved)

regimes20.0ms (0.4%)

Memory

12.2MiB live, 12.2MiB 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)))))
(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) (-.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))))
(/.f64 (fma.f64 (-.f64 #s(literal 0 binary64) (pow.f64 (asin.f64 #s(approx (- 1 x) (-.f64 #s(literal 1 binary64) x))) #s(literal 2 binary64))) #s(literal 2 binary64) (.f64 (+.f64 #s(literal 0 binary64) (asin.f64 #s(approx (- 1 x) (-.f64 #s(literal 1 binary64) x)))) (PI.f64))) (.f64 (+.f64 #s(literal 0 binary64) (asin.f64 #s(approx (- 1 x) (-.f64 #s(literal 1 binary64) x)))) #s(literal 2 binary64)))
#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 (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 #s(literal 2 binary64) (-.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) (+.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))))))))
(/.f64 (-.f64 (.f64 #s(literal 1 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))))))) (.f64 (/.f64 #s(literal 2 binary64) (PI.f64)) (-.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 (/.f64 #s(literal 2 binary64) (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))))))))

Outputs

(/.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))))

Calls

3 calls:

7.0ms	x
6.0ms	(-.f64 #s(literal 1 binary64) x)
5.0ms	(acos.f64 (-.f64 #s(literal 1 binary64) x))

Results

Accuracy	Segments	Branch
11.9%	1	`x`
11.9%	1	`(acos.f64 (-.f64 #s(literal 1 binary64) x))`
11.9%	1	`(-.f64 #s(literal 1 binary64) x)`

Compiler

Compiled 11 to 8 computations (27.3% saved)

regimes22.0ms (0.4%)

Memory

-45.5MiB live, 10.8MiB allocated

Counts

23 → 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)))))
(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) (-.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))))
(/.f64 (fma.f64 (-.f64 #s(literal 0 binary64) (pow.f64 (asin.f64 #s(approx (- 1 x) (-.f64 #s(literal 1 binary64) x))) #s(literal 2 binary64))) #s(literal 2 binary64) (.f64 (+.f64 #s(literal 0 binary64) (asin.f64 #s(approx (- 1 x) (-.f64 #s(literal 1 binary64) x)))) (PI.f64))) (.f64 (+.f64 #s(literal 0 binary64) (asin.f64 #s(approx (- 1 x) (-.f64 #s(literal 1 binary64) x)))) #s(literal 2 binary64)))
#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 (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 #s(literal 2 binary64) (-.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) (+.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))))))))

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:

10.0ms	x
5.0ms	(-.f64 #s(literal 1 binary64) x)
5.0ms	(acos.f64 (-.f64 #s(literal 1 binary64) x))

Results

Accuracy	Segments	Branch
11.8%	1	`x`
11.8%	1	`(acos.f64 (-.f64 #s(literal 1 binary64) x))`
11.8%	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
11.8%	1	`(acos.f64 (-.f64 #s(literal 1 binary64) x))`
11.8%	1	`(-.f64 #s(literal 1 binary64) x)`
11.8%	1	`x`

Compiler

Compiled 11 to 8 computations (27.3% saved)

regimes10.0ms (0.2%)

Memory

7.2MiB live, 7.2MiB 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
11.7%	1	`(acos.f64 (-.f64 #s(literal 1 binary64) x))`
11.7%	1	`(-.f64 #s(literal 1 binary64) x)`
11.7%	1	`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 #s(approx (- 1 x) 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))))

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
10.8%	2	`(-.f64 #s(literal 1 binary64) x)`
10.8%	2	`(acos.f64 (-.f64 #s(literal 1 binary64) x))`
10.8%	2	`x`

Compiler

Compiled 11 to 8 computations (27.3% saved)

regimes5.0ms (0.1%)

Memory

4.7MiB live, 4.7MiB allocated

Counts

4 → 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))

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

Calls

3 calls:

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

Results

Accuracy	Segments	Branch
10.8%	2	`(-.f64 #s(literal 1 binary64) x)`
10.8%	2	`(acos.f64 (-.f64 #s(literal 1 binary64) x))`
10.8%	2	`x`

Compiler

Compiled 11 to 8 computations (27.3% saved)

regimes5.0ms (0.1%)

Memory

4.2MiB live, 4.2MiB 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	(acos.f64 (-.f64 #s(literal 1 binary64) x))
1.0ms	(-.f64 #s(literal 1 binary64) x)

Results

Accuracy	Segments	Branch
7.1%	1	`(-.f64 #s(literal 1 binary64) x)`
7.1%	1	`(acos.f64 (-.f64 #s(literal 1 binary64) x))`
7.1%	1	`x`

Compiler

Compiled 11 to 8 computations (27.3% saved)

regimes3.0ms (0.1%)

Memory

3.5MiB live, 3.5MiB 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	`(acos.f64 (-.f64 #s(literal 1 binary64) x))`
3.8%	1	`(-.f64 #s(literal 1 binary64) x)`
3.8%	1	`x`

Compiler

Compiled 11 to 8 computations (27.3% saved)

bsearch17.0ms (0.3%)

Memory

-35.3MiB live, 4.4MiB allocated

Algorithm

1×	binary-search

Stop Event

1×	narrow-enough

Steps

Time	Left	Right
16.0ms	3.3437855568358613e-18	6.522356091566256e-15

Samples

11.0ms

128×

valid

Compiler

Compiled 136 to 104 computations (23.5% saved)

Precisions

Click to see histograms. Total time spent on operations: 8.0ms

ival-acos: 4.0ms (49.9% of total)

ival-sub: 2.0ms (25% of total)

adjust: 2.0ms (25% of total)

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

exact: 0.0ms (0% of total)

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

bsearch1.0ms (0%)

Memory

0.5MiB live, 0.5MiB allocated

Algorithm

1×	binary-search

Stop Event

1×	narrow-enough

Steps

Time	Left	Right
0.0ms	3.3437855568358613e-18	6.522356091566256e-15

Compiler

Compiled 96 to 72 computations (25% saved)

simplify8.0ms (0.1%)

Memory

5.0MiB live, 5.0MiB allocated

Algorithm

1×	egg-herbie

Rules

26×	`*-commutative_binary64`
26×	`+-commutative_binary64`
22×	`sub-neg_binary64`
16×	`neg-mul-1_binary64`
14×	`neg-sub0_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	58	195
1	88	195
2	107	195
3	118	195
4	121	195

Stop Event

1×

saturated

Calls

Call 1

Inputs
(/.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))))
(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 x #s(literal 8924260225606735/162259276829213363391578010288128 binary64)) (acos.f64 #s(approx (- 1 x) 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)))))
(if (<=.f64 x #s(literal 8924260225606735/162259276829213363391578010288128 binary64)) (acos.f64 #s(approx (- 1 x) x)) (acos.f64 (-.f64 #s(literal 1 binary64) x)))
(acos.f64 #s(approx (- 1 x) x))
(acos.f64 #s(approx (- 1 x) #s(literal 1 binary64)))

Outputs
(/.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 (fma.f64 (neg.f64 (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 (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 (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)))))))
(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 x #s(literal 8924260225606735/162259276829213363391578010288128 binary64)) (acos.f64 #s(approx (- 1 x) 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)))))
(if (<=.f64 x #s(literal 8924260225606735/162259276829213363391578010288128 binary64)) (acos.f64 #s(approx (- 1 x) x)) #s(approx (+ (* (sqrt (PI)) (* (sqrt (PI)) 1/2)) (neg (asin (- 1 x)))) (-.f64 (*.f64 (PI.f64) #s(literal 1/2 binary64)) (asin.f64 (-.f64 #s(literal 1 binary64) x)))))
(if (<=.f64 x #s(literal 8924260225606735/162259276829213363391578010288128 binary64)) (acos.f64 #s(approx (- 1 x) x)) (acos.f64 (-.f64 #s(literal 1 binary64) x)))
(acos.f64 #s(approx (- 1 x) x))
(acos.f64 #s(approx (- 1 x) #s(literal 1 binary64)))

soundness411.0ms (7.1%)

Memory

18.4MiB live, 18.4MiB 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	8	26
0	11	26
1	37	26
2	203	26
3	1732	23
0	9154	23
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	39	210
0	68	183
1	254	166
2	1787	166
0	8602	163
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×	fuel
1×	iter limit
1×	saturated
1×	iter limit
1×	node limit
1×	iter limit
1×	iter limit
1×	saturated
1×	iter limit
1×	node limit
1×	iter limit

Compiler

Compiled 420 to 217 computations (48.3% saved)

preprocess72.0ms (1.3%)

Memory: 11.4MiB live, 50.6MiB allocated
Compiler: Compiled 300 to 96 computations (68% 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%)

sample1.8s (32.1%)

preprocess15.0ms (0.3%)

explain95.0ms (1.6%)

eval0.0ms (0%)

prune1.0ms (0%)

simplify5.0ms (0.1%)

localize34.0ms (0.6%)

series1.0ms (0%)

simplify12.0ms (0.2%)

rewrite304.0ms (5.3%)

eval44.0ms (0.8%)

prune41.0ms (0.7%)

simplify5.0ms (0.1%)

localize37.0ms (0.6%)

series1.0ms (0%)

simplify14.0ms (0.2%)

rewrite203.0ms (3.5%)

eval92.0ms (1.6%)

prune22.0ms (0.4%)

simplify17.0ms (0.3%)

localize83.0ms (1.4%)

series1.0ms (0%)

simplify19.0ms (0.3%)

rewrite346.0ms (6%)

eval134.0ms (2.3%)

prune79.0ms (1.4%)

simplify311.0ms (5.4%)

localize195.0ms (3.4%)

series10.0ms (0.2%)

simplify276.0ms (4.8%)

rewrite427.0ms (7.4%)

eval285.0ms (4.9%)

prune210.0ms (3.7%)

regimes20.0ms (0.4%)

regimes22.0ms (0.4%)

regimes11.0ms (0.2%)

regimes10.0ms (0.2%)

regimes9.0ms (0.2%)

regimes5.0ms (0.1%)

regimes5.0ms (0.1%)

regimes3.0ms (0.1%)

bsearch17.0ms (0.3%)

bsearch1.0ms (0%)

simplify8.0ms (0.1%)

soundness411.0ms (7.1%)

preprocess72.0ms (1.3%)

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