Metrics for bug323 (missed optimization)

start0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated

analyze0.0ms (0%)

Memory

0.5MiB live, 0.5MiB 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)

sample1.4s (27.4%)

Memory

17.7MiB live, 2 166.7MiB allocated

Samples

1.1s	7 963×	1	valid
15.0ms	293×	0	valid

Precisions

Click to see histograms. Total time spent on operations: 868.0ms

ival-acos: 372.0ms (42.9% of total)

ival-sub: 277.0ms (31.9% of total)

adjust: 123.0ms (14.2% of total)

ival-<=: 65.0ms (7.5% of total)

ival-and: 14.0ms (1.6% of total)

exact: 13.0ms (1.5% of total)

ival-assert: 3.0ms (0.3% of total)

Bogosity

explain87.0ms (1.7%)

Memory

-16.5MiB live, 110.7MiB allocated

FPErrors

Click to see full error table

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

Explanations

Click to see full explanations table

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

Confusion

	Predicted +	Predicted -
+	254	0
-	0	2

Precision

1.0

Recall

1.0

Confusion?

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

Precision?

0.996078431372549

Recall?

1.0

Freqs

test

number	freq
0	2
1	254

Total Confusion?

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

Precision?

1.0

Recall?

1.0

Samples

48.0ms	494×	1	valid
1.0ms	18×	0	valid

Compiler

Compiled 27 to 16 computations (40.7% saved)

Precisions

Click to see histograms. Total time spent on operations: 32.0ms

ival-acos: 19.0ms (59.1% of total)

ival-sub: 6.0ms (18.7% of total)

adjust: 6.0ms (18.7% of total)

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

exact: 0.0ms (0% of total)

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

preprocess14.0ms (0.3%)

Memory

11.7MiB live, 11.7MiB 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))

Compiler

Compiled 5 to 4 computations (20% saved)

eval0.0ms (0%)

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

prune1.0ms (0%)

Memory

0.8MiB live, 0.8MiB allocated

Alt Table

Click to see full alt table

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

Compiler

Compiled 5 to 4 computations (20% saved)

simplify4.0ms (0.1%)

Memory

2.8MiB live, 2.8MiB 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

localize32.0ms (0.6%)

Memory

-18.0MiB live, 20.3MiB allocated

Localize:

Found 2 expressions of interest:

New	Metric	Score	Program
accuracy	0	(-.f64 #s(literal 1 binary64) x)
accuracy	59.465705675168344	(acos.f64 (-.f64 #s(literal 1 binary64) x))

Samples

23.0ms	247×	1	valid
0.0ms	9×	0	valid

Compiler

Compiled 11 to 6 computations (45.5% saved)

Precisions

Click to see histograms. Total time spent on operations: 16.0ms

ival-acos: 9.0ms (56.6% of total)

ival-sub: 3.0ms (18.9% of total)

adjust: 3.0ms (18.9% of total)

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

exact: 0.0ms (0% of total)

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

series1.0ms (0%)

Memory

0.9MiB live, 0.9MiB allocated

Counts

2 → 24

Calls

Call 1

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

Inputs

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

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

Outputs
#s(alt (acos (- 1 x)) (taylor 0 x) (#s(alt (acos.f64 (-.f64 #s(literal 1 binary64) x)) (patch (acos.f64 (-.f64 #s(literal 1 binary64) x)) #<representation binary64>) () ())) ())
#s(alt (acos (- 1 x)) (taylor 0 x) (#s(alt (acos.f64 (-.f64 #s(literal 1 binary64) x)) (patch (acos.f64 (-.f64 #s(literal 1 binary64) x)) #<representation binary64>) () ())) ())
#s(alt (acos (- 1 x)) (taylor 0 x) (#s(alt (acos.f64 (-.f64 #s(literal 1 binary64) x)) (patch (acos.f64 (-.f64 #s(literal 1 binary64) x)) #<representation binary64>) () ())) ())
#s(alt (acos (- 1 x)) (taylor 0 x) (#s(alt (acos.f64 (-.f64 #s(literal 1 binary64) x)) (patch (acos.f64 (-.f64 #s(literal 1 binary64) x)) #<representation binary64>) () ())) ())
#s(alt (acos (- 1 x)) (taylor inf x) (#s(alt (acos.f64 (-.f64 #s(literal 1 binary64) x)) (patch (acos.f64 (-.f64 #s(literal 1 binary64) x)) #<representation binary64>) () ())) ())
#s(alt (acos (- 1 x)) (taylor inf x) (#s(alt (acos.f64 (-.f64 #s(literal 1 binary64) x)) (patch (acos.f64 (-.f64 #s(literal 1 binary64) x)) #<representation binary64>) () ())) ())
#s(alt (acos (- 1 x)) (taylor inf x) (#s(alt (acos.f64 (-.f64 #s(literal 1 binary64) x)) (patch (acos.f64 (-.f64 #s(literal 1 binary64) x)) #<representation binary64>) () ())) ())
#s(alt (acos (- 1 x)) (taylor inf x) (#s(alt (acos.f64 (-.f64 #s(literal 1 binary64) x)) (patch (acos.f64 (-.f64 #s(literal 1 binary64) x)) #<representation binary64>) () ())) ())
#s(alt (acos (+ 1 (* -1 x))) (taylor -inf x) (#s(alt (acos.f64 (-.f64 #s(literal 1 binary64) x)) (patch (acos.f64 (-.f64 #s(literal 1 binary64) x)) #<representation binary64>) () ())) ())
#s(alt (acos (+ 1 (* -1 x))) (taylor -inf x) (#s(alt (acos.f64 (-.f64 #s(literal 1 binary64) x)) (patch (acos.f64 (-.f64 #s(literal 1 binary64) x)) #<representation binary64>) () ())) ())
#s(alt (acos (+ 1 (* -1 x))) (taylor -inf x) (#s(alt (acos.f64 (-.f64 #s(literal 1 binary64) x)) (patch (acos.f64 (-.f64 #s(literal 1 binary64) x)) #<representation binary64>) () ())) ())
#s(alt (acos (+ 1 (* -1 x))) (taylor -inf x) (#s(alt (acos.f64 (-.f64 #s(literal 1 binary64) x)) (patch (acos.f64 (-.f64 #s(literal 1 binary64) x)) #<representation binary64>) () ())) ())
#s(alt 1 (taylor 0 x) (#s(alt (-.f64 #s(literal 1 binary64) x) (patch (-.f64 #s(literal 1 binary64) x) #<representation binary64>) () ())) ())
#s(alt (+ 1 (* -1 x)) (taylor 0 x) (#s(alt (-.f64 #s(literal 1 binary64) x) (patch (-.f64 #s(literal 1 binary64) x) #<representation binary64>) () ())) ())
#s(alt (+ 1 (* -1 x)) (taylor 0 x) (#s(alt (-.f64 #s(literal 1 binary64) x) (patch (-.f64 #s(literal 1 binary64) x) #<representation binary64>) () ())) ())
#s(alt (+ 1 (* -1 x)) (taylor 0 x) (#s(alt (-.f64 #s(literal 1 binary64) x) (patch (-.f64 #s(literal 1 binary64) x) #<representation binary64>) () ())) ())
#s(alt (* -1 x) (taylor inf x) (#s(alt (-.f64 #s(literal 1 binary64) x) (patch (-.f64 #s(literal 1 binary64) x) #<representation binary64>) () ())) ())
#s(alt (* x (- (/ 1 x) 1)) (taylor inf x) (#s(alt (-.f64 #s(literal 1 binary64) x) (patch (-.f64 #s(literal 1 binary64) x) #<representation binary64>) () ())) ())
#s(alt (* x (- (/ 1 x) 1)) (taylor inf x) (#s(alt (-.f64 #s(literal 1 binary64) x) (patch (-.f64 #s(literal 1 binary64) x) #<representation binary64>) () ())) ())
#s(alt (* x (- (/ 1 x) 1)) (taylor inf x) (#s(alt (-.f64 #s(literal 1 binary64) x) (patch (-.f64 #s(literal 1 binary64) x) #<representation binary64>) () ())) ())
#s(alt (* -1 x) (taylor -inf x) (#s(alt (-.f64 #s(literal 1 binary64) x) (patch (-.f64 #s(literal 1 binary64) x) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (- 1 (/ 1 x)))) (taylor -inf x) (#s(alt (-.f64 #s(literal 1 binary64) x) (patch (-.f64 #s(literal 1 binary64) x) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (- 1 (/ 1 x)))) (taylor -inf x) (#s(alt (-.f64 #s(literal 1 binary64) x) (patch (-.f64 #s(literal 1 binary64) x) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (- 1 (/ 1 x)))) (taylor -inf x) (#s(alt (-.f64 #s(literal 1 binary64) x) (patch (-.f64 #s(literal 1 binary64) x) #<representation binary64>) () ())) ())

Calls

6 calls:

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

simplify8.0ms (0.2%)

Memory

5.1MiB live, 5.1MiB 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)

rewrite230.0ms (4.4%)

Memory

6.2MiB live, 167.8MiB allocated

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))))))
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(.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)))

eval51.0ms (1%)

Memory: -13.8MiB live, 69.3MiB allocated
Compiler: Compiled 12 893 to 1 318 computations (89.8% saved)

prune46.0ms (0.9%)

Memory

-1.6MiB live, 74.7MiB 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

9.6%

Counts

364 → 3

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	7.1%	(acos.f64 (-.f64 #s(literal 1 binary64) x))
▶	6.9%	(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

1.2MiB live, 1.2MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 5 expressions of interest:

New	Metric	Score	Program
cost-diff	0	(neg.f64 x)
cost-diff	0	#s(approx (- 1 x) (neg.f64 x))
cost-diff	0	(acos.f64 #s(approx (- 1 x) (neg.f64 x)))
cost-diff	0	#s(approx (- 1 x) #s(literal 1 binary64))
cost-diff	0	(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

localize35.0ms (0.7%)

Memory

11.3MiB live, 11.3MiB allocated

Localize:

Found 5 expressions of interest:

New	Metric	Score
accuracy	0	(neg.f64 x)
accuracy	59.465705675168344	(acos.f64 #s(approx (- 1 x) (neg.f64 x)))
accuracy	62.55953230886688	#s(approx (- 1 x) (neg.f64 x))
accuracy	1.413008777896765	#s(approx (- 1 x) #s(literal 1 binary64))
accuracy	59.465705675168344	(acos.f64 #s(approx (- 1 x) #s(literal 1 binary64)))

Samples

26.0ms	247×	1	valid
0.0ms	9×	0	valid

Compiler

Compiled 20 to 7 computations (65% saved)

Precisions

Click to see histograms. Total time spent on operations: 17.0ms

ival-acos: 9.0ms (53.5% of total)

adjust: 3.0ms (17.8% of total)

ival-sub: 3.0ms (17.8% of total)

ival-neg: 1.0ms (5.9% of total)

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

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

exact: 0.0ms (0% of total)

series2.0ms (0%)

Memory

0.9MiB live, 0.9MiB allocated

Counts

5 → 60

Calls

Call 1

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

Outputs
#s(alt (acos (- 1 x)) (taylor 0 x) (#s(alt (acos.f64 #s(approx (- 1 x) #s(literal 1 binary64))) (patch (acos.f64 #s(approx (- 1 x) #s(literal 1 binary64))) #<representation binary64>) () ())) ())
#s(alt (acos (- 1 x)) (taylor 0 x) (#s(alt (acos.f64 #s(approx (- 1 x) #s(literal 1 binary64))) (patch (acos.f64 #s(approx (- 1 x) #s(literal 1 binary64))) #<representation binary64>) () ())) ())
#s(alt (acos (- 1 x)) (taylor 0 x) (#s(alt (acos.f64 #s(approx (- 1 x) #s(literal 1 binary64))) (patch (acos.f64 #s(approx (- 1 x) #s(literal 1 binary64))) #<representation binary64>) () ())) ())
#s(alt (acos (- 1 x)) (taylor 0 x) (#s(alt (acos.f64 #s(approx (- 1 x) #s(literal 1 binary64))) (patch (acos.f64 #s(approx (- 1 x) #s(literal 1 binary64))) #<representation binary64>) () ())) ())
#s(alt (acos (- 1 x)) (taylor inf x) (#s(alt (acos.f64 #s(approx (- 1 x) #s(literal 1 binary64))) (patch (acos.f64 #s(approx (- 1 x) #s(literal 1 binary64))) #<representation binary64>) () ())) ())
#s(alt (acos (- 1 x)) (taylor inf x) (#s(alt (acos.f64 #s(approx (- 1 x) #s(literal 1 binary64))) (patch (acos.f64 #s(approx (- 1 x) #s(literal 1 binary64))) #<representation binary64>) () ())) ())
#s(alt (acos (- 1 x)) (taylor inf x) (#s(alt (acos.f64 #s(approx (- 1 x) #s(literal 1 binary64))) (patch (acos.f64 #s(approx (- 1 x) #s(literal 1 binary64))) #<representation binary64>) () ())) ())
#s(alt (acos (- 1 x)) (taylor inf x) (#s(alt (acos.f64 #s(approx (- 1 x) #s(literal 1 binary64))) (patch (acos.f64 #s(approx (- 1 x) #s(literal 1 binary64))) #<representation binary64>) () ())) ())
#s(alt (acos (+ 1 (* -1 x))) (taylor -inf x) (#s(alt (acos.f64 #s(approx (- 1 x) #s(literal 1 binary64))) (patch (acos.f64 #s(approx (- 1 x) #s(literal 1 binary64))) #<representation binary64>) () ())) ())
#s(alt (acos (+ 1 (* -1 x))) (taylor -inf x) (#s(alt (acos.f64 #s(approx (- 1 x) #s(literal 1 binary64))) (patch (acos.f64 #s(approx (- 1 x) #s(literal 1 binary64))) #<representation binary64>) () ())) ())
#s(alt (acos (+ 1 (* -1 x))) (taylor -inf x) (#s(alt (acos.f64 #s(approx (- 1 x) #s(literal 1 binary64))) (patch (acos.f64 #s(approx (- 1 x) #s(literal 1 binary64))) #<representation binary64>) () ())) ())
#s(alt (acos (+ 1 (* -1 x))) (taylor -inf x) (#s(alt (acos.f64 #s(approx (- 1 x) #s(literal 1 binary64))) (patch (acos.f64 #s(approx (- 1 x) #s(literal 1 binary64))) #<representation binary64>) () ())) ())
#s(alt 1 (taylor 0 x) (#s(alt #s(approx (- 1 x) #s(literal 1 binary64)) (patch #s(approx (- 1 x) #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (+ 1 (* -1 x)) (taylor 0 x) (#s(alt #s(approx (- 1 x) #s(literal 1 binary64)) (patch #s(approx (- 1 x) #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (+ 1 (* -1 x)) (taylor 0 x) (#s(alt #s(approx (- 1 x) #s(literal 1 binary64)) (patch #s(approx (- 1 x) #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (+ 1 (* -1 x)) (taylor 0 x) (#s(alt #s(approx (- 1 x) #s(literal 1 binary64)) (patch #s(approx (- 1 x) #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (* -1 x) (taylor inf x) (#s(alt #s(approx (- 1 x) #s(literal 1 binary64)) (patch #s(approx (- 1 x) #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (* x (- (/ 1 x) 1)) (taylor inf x) (#s(alt #s(approx (- 1 x) #s(literal 1 binary64)) (patch #s(approx (- 1 x) #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (* x (- (/ 1 x) 1)) (taylor inf x) (#s(alt #s(approx (- 1 x) #s(literal 1 binary64)) (patch #s(approx (- 1 x) #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (* x (- (/ 1 x) 1)) (taylor inf x) (#s(alt #s(approx (- 1 x) #s(literal 1 binary64)) (patch #s(approx (- 1 x) #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (* -1 x) (taylor -inf x) (#s(alt #s(approx (- 1 x) #s(literal 1 binary64)) (patch #s(approx (- 1 x) #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (- 1 (/ 1 x)))) (taylor -inf x) (#s(alt #s(approx (- 1 x) #s(literal 1 binary64)) (patch #s(approx (- 1 x) #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (- 1 (/ 1 x)))) (taylor -inf x) (#s(alt #s(approx (- 1 x) #s(literal 1 binary64)) (patch #s(approx (- 1 x) #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (- 1 (/ 1 x)))) (taylor -inf x) (#s(alt #s(approx (- 1 x) #s(literal 1 binary64)) (patch #s(approx (- 1 x) #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (acos (- 1 x)) (taylor 0 x) (#s(alt (acos.f64 #s(approx (- 1 x) (neg.f64 x))) (patch (acos.f64 #s(approx (- 1 x) (neg.f64 x))) #<representation binary64>) () ())) ())
#s(alt (acos (- 1 x)) (taylor 0 x) (#s(alt (acos.f64 #s(approx (- 1 x) (neg.f64 x))) (patch (acos.f64 #s(approx (- 1 x) (neg.f64 x))) #<representation binary64>) () ())) ())
#s(alt (acos (- 1 x)) (taylor 0 x) (#s(alt (acos.f64 #s(approx (- 1 x) (neg.f64 x))) (patch (acos.f64 #s(approx (- 1 x) (neg.f64 x))) #<representation binary64>) () ())) ())
#s(alt (acos (- 1 x)) (taylor 0 x) (#s(alt (acos.f64 #s(approx (- 1 x) (neg.f64 x))) (patch (acos.f64 #s(approx (- 1 x) (neg.f64 x))) #<representation binary64>) () ())) ())
#s(alt (acos (- 1 x)) (taylor inf x) (#s(alt (acos.f64 #s(approx (- 1 x) (neg.f64 x))) (patch (acos.f64 #s(approx (- 1 x) (neg.f64 x))) #<representation binary64>) () ())) ())
#s(alt (acos (- 1 x)) (taylor inf x) (#s(alt (acos.f64 #s(approx (- 1 x) (neg.f64 x))) (patch (acos.f64 #s(approx (- 1 x) (neg.f64 x))) #<representation binary64>) () ())) ())
#s(alt (acos (- 1 x)) (taylor inf x) (#s(alt (acos.f64 #s(approx (- 1 x) (neg.f64 x))) (patch (acos.f64 #s(approx (- 1 x) (neg.f64 x))) #<representation binary64>) () ())) ())
#s(alt (acos (- 1 x)) (taylor inf x) (#s(alt (acos.f64 #s(approx (- 1 x) (neg.f64 x))) (patch (acos.f64 #s(approx (- 1 x) (neg.f64 x))) #<representation binary64>) () ())) ())
#s(alt (acos (+ 1 (* -1 x))) (taylor -inf x) (#s(alt (acos.f64 #s(approx (- 1 x) (neg.f64 x))) (patch (acos.f64 #s(approx (- 1 x) (neg.f64 x))) #<representation binary64>) () ())) ())
#s(alt (acos (+ 1 (* -1 x))) (taylor -inf x) (#s(alt (acos.f64 #s(approx (- 1 x) (neg.f64 x))) (patch (acos.f64 #s(approx (- 1 x) (neg.f64 x))) #<representation binary64>) () ())) ())
#s(alt (acos (+ 1 (* -1 x))) (taylor -inf x) (#s(alt (acos.f64 #s(approx (- 1 x) (neg.f64 x))) (patch (acos.f64 #s(approx (- 1 x) (neg.f64 x))) #<representation binary64>) () ())) ())
#s(alt (acos (+ 1 (* -1 x))) (taylor -inf x) (#s(alt (acos.f64 #s(approx (- 1 x) (neg.f64 x))) (patch (acos.f64 #s(approx (- 1 x) (neg.f64 x))) #<representation binary64>) () ())) ())
#s(alt 1 (taylor 0 x) (#s(alt #s(approx (- 1 x) (neg.f64 x)) (patch #s(approx (- 1 x) (neg.f64 x)) #<representation binary64>) () ())) ())
#s(alt (+ 1 (* -1 x)) (taylor 0 x) (#s(alt #s(approx (- 1 x) (neg.f64 x)) (patch #s(approx (- 1 x) (neg.f64 x)) #<representation binary64>) () ())) ())
#s(alt (+ 1 (* -1 x)) (taylor 0 x) (#s(alt #s(approx (- 1 x) (neg.f64 x)) (patch #s(approx (- 1 x) (neg.f64 x)) #<representation binary64>) () ())) ())
#s(alt (+ 1 (* -1 x)) (taylor 0 x) (#s(alt #s(approx (- 1 x) (neg.f64 x)) (patch #s(approx (- 1 x) (neg.f64 x)) #<representation binary64>) () ())) ())
#s(alt (* -1 x) (taylor inf x) (#s(alt #s(approx (- 1 x) (neg.f64 x)) (patch #s(approx (- 1 x) (neg.f64 x)) #<representation binary64>) () ())) ())
#s(alt (* x (- (/ 1 x) 1)) (taylor inf x) (#s(alt #s(approx (- 1 x) (neg.f64 x)) (patch #s(approx (- 1 x) (neg.f64 x)) #<representation binary64>) () ())) ())
#s(alt (* x (- (/ 1 x) 1)) (taylor inf x) (#s(alt #s(approx (- 1 x) (neg.f64 x)) (patch #s(approx (- 1 x) (neg.f64 x)) #<representation binary64>) () ())) ())
#s(alt (* x (- (/ 1 x) 1)) (taylor inf x) (#s(alt #s(approx (- 1 x) (neg.f64 x)) (patch #s(approx (- 1 x) (neg.f64 x)) #<representation binary64>) () ())) ())
#s(alt (* -1 x) (taylor -inf x) (#s(alt #s(approx (- 1 x) (neg.f64 x)) (patch #s(approx (- 1 x) (neg.f64 x)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (- 1 (/ 1 x)))) (taylor -inf x) (#s(alt #s(approx (- 1 x) (neg.f64 x)) (patch #s(approx (- 1 x) (neg.f64 x)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (- 1 (/ 1 x)))) (taylor -inf x) (#s(alt #s(approx (- 1 x) (neg.f64 x)) (patch #s(approx (- 1 x) (neg.f64 x)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (- 1 (/ 1 x)))) (taylor -inf x) (#s(alt #s(approx (- 1 x) (neg.f64 x)) (patch #s(approx (- 1 x) (neg.f64 x)) #<representation binary64>) () ())) ())
#s(alt (* -1 x) (taylor 0 x) (#s(alt (neg.f64 x) (patch (neg.f64 x) #<representation binary64>) () ())) ())
#s(alt (* -1 x) (taylor 0 x) (#s(alt (neg.f64 x) (patch (neg.f64 x) #<representation binary64>) () ())) ())
#s(alt (* -1 x) (taylor 0 x) (#s(alt (neg.f64 x) (patch (neg.f64 x) #<representation binary64>) () ())) ())
#s(alt (* -1 x) (taylor 0 x) (#s(alt (neg.f64 x) (patch (neg.f64 x) #<representation binary64>) () ())) ())
#s(alt (* -1 x) (taylor inf x) (#s(alt (neg.f64 x) (patch (neg.f64 x) #<representation binary64>) () ())) ())
#s(alt (* -1 x) (taylor inf x) (#s(alt (neg.f64 x) (patch (neg.f64 x) #<representation binary64>) () ())) ())
#s(alt (* -1 x) (taylor inf x) (#s(alt (neg.f64 x) (patch (neg.f64 x) #<representation binary64>) () ())) ())
#s(alt (* -1 x) (taylor inf x) (#s(alt (neg.f64 x) (patch (neg.f64 x) #<representation binary64>) () ())) ())
#s(alt (* -1 x) (taylor -inf x) (#s(alt (neg.f64 x) (patch (neg.f64 x) #<representation binary64>) () ())) ())
#s(alt (* -1 x) (taylor -inf x) (#s(alt (neg.f64 x) (patch (neg.f64 x) #<representation binary64>) () ())) ())
#s(alt (* -1 x) (taylor -inf x) (#s(alt (neg.f64 x) (patch (neg.f64 x) #<representation binary64>) () ())) ())
#s(alt (* -1 x) (taylor -inf x) (#s(alt (neg.f64 x) (patch (neg.f64 x) #<representation binary64>) () ())) ())

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))

simplify9.0ms (0.2%)

Memory

2.4MiB live, 2.4MiB 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)

rewrite178.0ms (3.4%)

Memory

-1.9MiB live, 181.9MiB allocated

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

eval34.0ms (0.6%)

Memory: -10.3MiB live, 45.5MiB allocated
Compiler: Compiled 8 006 to 767 computations (90.4% saved)

prune27.0ms (0.5%)

Memory

15.9MiB live, 54.5MiB allocated

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	263	2	265
Fresh	0	0	0
Picked	2	0	2
Done	0	1	1
Total	265	3	268

Accuracy

9.6%

Counts

268 → 3

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	6.9%	(fma.f64 (sqrt.f64 (PI.f64)) (*.f64 (sqrt.f64 (PI.f64)) #s(literal 1/2 binary64)) (neg.f64 (asin.f64 #s(approx (- 1 x) x))))
✓	7.1%	(acos.f64 (-.f64 #s(literal 1 binary64) x))
▶	6.9%	(acos.f64 #s(approx (- 1 x) x))

Compiler

Compiled 21 to 14 computations (33.3% saved)

simplify14.0ms (0.3%)

Memory

15.1MiB live, 15.1MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 6 expressions of interest:

New	Metric	Score
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

localize113.0ms (2.1%)

Memory

-46.8MiB live, 85.2MiB allocated

Localize:

Found 6 expressions of interest:

New	Metric	Score
accuracy	1.0	(sqrt.f64 (PI.f64))
accuracy	1.1692509973742442	(asin.f64 #s(approx (- 1 x) x))
accuracy	55.931173811568684	(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	60.558201166710774	#s(approx (- 1 x) x)
accuracy	59.465705675168344	(acos.f64 #s(approx (- 1 x) x))
accuracy	60.558201166710774	#s(approx (- 1 x) x)

Samples

62.0ms	244×	1	valid
1.0ms	12×	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: 11.0ms (21.8% of total)

ival-asin: 9.0ms (17.8% of total)

ival-sub: 7.0ms (13.9% of total)

adjust: 6.0ms (11.9% of total)

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

ival-sqrt: 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)

exact: 1.0ms (2% of total)

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

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

series2.0ms (0%)

Memory

1.0MiB live, 1.0MiB allocated

Counts

7 → 48

Calls

Call 1

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

Outputs
#s(alt (acos (- 1 x)) (taylor 0 x) (#s(alt (acos.f64 #s(approx (- 1 x) x)) (patch (acos.f64 #s(approx (- 1 x) x)) #<representation binary64>) () ())) ())
#s(alt (acos (- 1 x)) (taylor 0 x) (#s(alt (acos.f64 #s(approx (- 1 x) x)) (patch (acos.f64 #s(approx (- 1 x) x)) #<representation binary64>) () ())) ())
#s(alt (acos (- 1 x)) (taylor 0 x) (#s(alt (acos.f64 #s(approx (- 1 x) x)) (patch (acos.f64 #s(approx (- 1 x) x)) #<representation binary64>) () ())) ())
#s(alt (acos (- 1 x)) (taylor 0 x) (#s(alt (acos.f64 #s(approx (- 1 x) x)) (patch (acos.f64 #s(approx (- 1 x) x)) #<representation binary64>) () ())) ())
#s(alt (acos (- 1 x)) (taylor inf x) (#s(alt (acos.f64 #s(approx (- 1 x) x)) (patch (acos.f64 #s(approx (- 1 x) x)) #<representation binary64>) () ())) ())
#s(alt (acos (- 1 x)) (taylor inf x) (#s(alt (acos.f64 #s(approx (- 1 x) x)) (patch (acos.f64 #s(approx (- 1 x) x)) #<representation binary64>) () ())) ())
#s(alt (acos (- 1 x)) (taylor inf x) (#s(alt (acos.f64 #s(approx (- 1 x) x)) (patch (acos.f64 #s(approx (- 1 x) x)) #<representation binary64>) () ())) ())
#s(alt (acos (- 1 x)) (taylor inf x) (#s(alt (acos.f64 #s(approx (- 1 x) x)) (patch (acos.f64 #s(approx (- 1 x) x)) #<representation binary64>) () ())) ())
#s(alt (acos (+ 1 (* -1 x))) (taylor -inf x) (#s(alt (acos.f64 #s(approx (- 1 x) x)) (patch (acos.f64 #s(approx (- 1 x) x)) #<representation binary64>) () ())) ())
#s(alt (acos (+ 1 (* -1 x))) (taylor -inf x) (#s(alt (acos.f64 #s(approx (- 1 x) x)) (patch (acos.f64 #s(approx (- 1 x) x)) #<representation binary64>) () ())) ())
#s(alt (acos (+ 1 (* -1 x))) (taylor -inf x) (#s(alt (acos.f64 #s(approx (- 1 x) x)) (patch (acos.f64 #s(approx (- 1 x) x)) #<representation binary64>) () ())) ())
#s(alt (acos (+ 1 (* -1 x))) (taylor -inf x) (#s(alt (acos.f64 #s(approx (- 1 x) x)) (patch (acos.f64 #s(approx (- 1 x) x)) #<representation binary64>) () ())) ())
#s(alt 1 (taylor 0 x) (#s(alt #s(approx (- 1 x) x) (patch #s(approx (- 1 x) x) #<representation binary64>) () ())) ())
#s(alt (+ 1 (* -1 x)) (taylor 0 x) (#s(alt #s(approx (- 1 x) x) (patch #s(approx (- 1 x) x) #<representation binary64>) () ())) ())
#s(alt (+ 1 (* -1 x)) (taylor 0 x) (#s(alt #s(approx (- 1 x) x) (patch #s(approx (- 1 x) x) #<representation binary64>) () ())) ())
#s(alt (+ 1 (* -1 x)) (taylor 0 x) (#s(alt #s(approx (- 1 x) x) (patch #s(approx (- 1 x) x) #<representation binary64>) () ())) ())
#s(alt (* -1 x) (taylor inf x) (#s(alt #s(approx (- 1 x) x) (patch #s(approx (- 1 x) x) #<representation binary64>) () ())) ())
#s(alt (* x (- (/ 1 x) 1)) (taylor inf x) (#s(alt #s(approx (- 1 x) x) (patch #s(approx (- 1 x) x) #<representation binary64>) () ())) ())
#s(alt (* x (- (/ 1 x) 1)) (taylor inf x) (#s(alt #s(approx (- 1 x) x) (patch #s(approx (- 1 x) x) #<representation binary64>) () ())) ())
#s(alt (* x (- (/ 1 x) 1)) (taylor inf x) (#s(alt #s(approx (- 1 x) x) (patch #s(approx (- 1 x) x) #<representation binary64>) () ())) ())
#s(alt (* -1 x) (taylor -inf x) (#s(alt #s(approx (- 1 x) x) (patch #s(approx (- 1 x) x) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (- 1 (/ 1 x)))) (taylor -inf x) (#s(alt #s(approx (- 1 x) x) (patch #s(approx (- 1 x) x) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (- 1 (/ 1 x)))) (taylor -inf x) (#s(alt #s(approx (- 1 x) x) (patch #s(approx (- 1 x) x) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (- 1 (/ 1 x)))) (taylor -inf x) (#s(alt #s(approx (- 1 x) x) (patch #s(approx (- 1 x) x) #<representation binary64>) () ())) ())
#s(alt (- (* 1/2 (PI)) (asin (- 1 x))) (taylor 0 x) (#s(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)))) (patch (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)))) #<representation binary64>) () ())) ())
#s(alt (- (* 1/2 (PI)) (asin (- 1 x))) (taylor 0 x) (#s(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)))) (patch (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)))) #<representation binary64>) () ())) ())
#s(alt (- (* 1/2 (PI)) (asin (- 1 x))) (taylor 0 x) (#s(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)))) (patch (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)))) #<representation binary64>) () ())) ())
#s(alt (- (* 1/2 (PI)) (asin (- 1 x))) (taylor 0 x) (#s(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)))) (patch (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)))) #<representation binary64>) () ())) ())
#s(alt (- (* 1/2 (PI)) (asin (- 1 x))) (taylor inf x) (#s(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)))) (patch (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)))) #<representation binary64>) () ())) ())
#s(alt (- (* 1/2 (PI)) (asin (- 1 x))) (taylor inf x) (#s(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)))) (patch (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)))) #<representation binary64>) () ())) ())
#s(alt (- (* 1/2 (PI)) (asin (- 1 x))) (taylor inf x) (#s(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)))) (patch (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)))) #<representation binary64>) () ())) ())
#s(alt (- (* 1/2 (PI)) (asin (- 1 x))) (taylor inf x) (#s(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)))) (patch (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)))) #<representation binary64>) () ())) ())
#s(alt (- (* 1/2 (PI)) (asin (+ 1 (* -1 x)))) (taylor -inf x) (#s(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)))) (patch (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)))) #<representation binary64>) () ())) ())
#s(alt (- (* 1/2 (PI)) (asin (+ 1 (* -1 x)))) (taylor -inf x) (#s(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)))) (patch (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)))) #<representation binary64>) () ())) ())
#s(alt (- (* 1/2 (PI)) (asin (+ 1 (* -1 x)))) (taylor -inf x) (#s(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)))) (patch (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)))) #<representation binary64>) () ())) ())
#s(alt (- (* 1/2 (PI)) (asin (+ 1 (* -1 x)))) (taylor -inf x) (#s(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)))) (patch (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)))) #<representation binary64>) () ())) ())
#s(alt (asin (- 1 x)) (taylor 0 x) (#s(alt (asin.f64 #s(approx (- 1 x) x)) (patch (asin.f64 #s(approx (- 1 x) x)) #<representation binary64>) () ())) ())
#s(alt (asin (- 1 x)) (taylor 0 x) (#s(alt (asin.f64 #s(approx (- 1 x) x)) (patch (asin.f64 #s(approx (- 1 x) x)) #<representation binary64>) () ())) ())
#s(alt (asin (- 1 x)) (taylor 0 x) (#s(alt (asin.f64 #s(approx (- 1 x) x)) (patch (asin.f64 #s(approx (- 1 x) x)) #<representation binary64>) () ())) ())
#s(alt (asin (- 1 x)) (taylor 0 x) (#s(alt (asin.f64 #s(approx (- 1 x) x)) (patch (asin.f64 #s(approx (- 1 x) x)) #<representation binary64>) () ())) ())
#s(alt (asin (- 1 x)) (taylor inf x) (#s(alt (asin.f64 #s(approx (- 1 x) x)) (patch (asin.f64 #s(approx (- 1 x) x)) #<representation binary64>) () ())) ())
#s(alt (asin (- 1 x)) (taylor inf x) (#s(alt (asin.f64 #s(approx (- 1 x) x)) (patch (asin.f64 #s(approx (- 1 x) x)) #<representation binary64>) () ())) ())
#s(alt (asin (- 1 x)) (taylor inf x) (#s(alt (asin.f64 #s(approx (- 1 x) x)) (patch (asin.f64 #s(approx (- 1 x) x)) #<representation binary64>) () ())) ())
#s(alt (asin (- 1 x)) (taylor inf x) (#s(alt (asin.f64 #s(approx (- 1 x) x)) (patch (asin.f64 #s(approx (- 1 x) x)) #<representation binary64>) () ())) ())
#s(alt (asin (+ 1 (* -1 x))) (taylor -inf x) (#s(alt (asin.f64 #s(approx (- 1 x) x)) (patch (asin.f64 #s(approx (- 1 x) x)) #<representation binary64>) () ())) ())
#s(alt (asin (+ 1 (* -1 x))) (taylor -inf x) (#s(alt (asin.f64 #s(approx (- 1 x) x)) (patch (asin.f64 #s(approx (- 1 x) x)) #<representation binary64>) () ())) ())
#s(alt (asin (+ 1 (* -1 x))) (taylor -inf x) (#s(alt (asin.f64 #s(approx (- 1 x) x)) (patch (asin.f64 #s(approx (- 1 x) x)) #<representation binary64>) () ())) ())
#s(alt (asin (+ 1 (* -1 x))) (taylor -inf x) (#s(alt (asin.f64 #s(approx (- 1 x) x)) (patch (asin.f64 #s(approx (- 1 x) x)) #<representation binary64>) () ())) ())

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	@	-inf	(asin (- 1 x))
0.0ms	x	@	0	(acos (- 1 x))

simplify17.0ms (0.3%)

Memory

3.4MiB live, 3.4MiB allocated

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

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

Stop Event

1×	iter limit
1×	saturated

Counts

48 → 48

Calls

Call 1

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

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

rewrite218.0ms (4.2%)

Memory

25.2MiB live, 243.8MiB allocated

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

eval104.0ms (2%)

Memory: 16.7MiB live, 175.9MiB allocated
Compiler: Compiled 16 417 to 1 672 computations (89.8% saved)

prune83.0ms (1.6%)

Memory

4.9MiB live, 166.9MiB allocated

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	801	6	807
Fresh	0	0	0
Picked	1	1	2
Done	0	1	1
Total	802	8	810

Accuracy

9.7%

Counts

810 → 8

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	6.9%	(fma.f64 (*.f64 (sqrt.f64 (PI.f64)) #s(literal 1/2 binary64)) (sqrt.f64 (PI.f64)) (asin.f64 #s(approx (- 1 x) x)))
▶	6.9%	(fma.f64 (sqrt.f64 (PI.f64)) (.f64 (sqrt.f64 (PI.f64)) #s(literal 1/2 binary64)) (neg.f64 (fma.f64 (.f64 (sqrt.f64 (PI.f64)) #s(literal 1/2 binary64)) (neg.f64 (sqrt.f64 (PI.f64))) (acos.f64 #s(approx (- 1 x) x)))))
▶	5.3%	(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)))))
	4.4%	(/.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))))
▶	4.4%	(/.f64 (fma.f64 (pow.f64 (asin.f64 #s(approx (- 1 x) x)) #s(literal 3 binary64)) #s(literal 2 binary64) (.f64 (pow.f64 (asin.f64 #s(approx (- 1 x) x)) #s(literal 2 binary64)) (PI.f64))) (.f64 (pow.f64 (asin.f64 #s(approx (- 1 x) x)) #s(literal 2 binary64)) #s(literal 2 binary64)))
✓	7.1%	(acos.f64 (-.f64 #s(literal 1 binary64) x))
✓	6.9%	(acos.f64 #s(approx (- 1 x) x))
▶	7.1%	#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 215 to 120 computations (44.2% saved)

simplify350.0ms (6.7%)

Memory

-18.6MiB live, 161.6MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 20 expressions of interest:

New	Metric	Score
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)))

localize199.0ms (3.8%)

Memory

-6.7MiB live, 154.0MiB allocated

Localize:

Found 20 expressions of interest:

New	Metric	Score
accuracy	0.94921875	(*.f64 (pow.f64 (asin.f64 #s(approx (- 1 x) x)) #s(literal 2 binary64)) (PI.f64))
accuracy	0.9801750488422102	(pow.f64 (asin.f64 #s(approx (- 1 x) x)) #s(literal 3 binary64))
accuracy	1.1692509973742446	(asin.f64 #s(approx (- 1 x) x))
accuracy	60.55820116671084	#s(approx (- 1 x) x)
accuracy	0.98046875	(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	1.0	(sqrt.f64 (PI.f64))
accuracy	59.465705675168344	(acos.f64 #s(approx (- 1 x) x))
accuracy	60.55820116671084	#s(approx (- 1 x) x)
accuracy	0	#s(approx (- 1 x) (-.f64 #s(literal 1 binary64) x))
accuracy	1.0	(sqrt.f64 (PI.f64))
accuracy	1.1692509973742442	(asin.f64 #s(approx (- 1 x) (-.f64 #s(literal 1 binary64) x)))
accuracy	55.931173811568684	(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	0	(PI.f64)
accuracy	1.0	(sqrt.f64 (PI.f64))
accuracy	1.1692509973742446	(asin.f64 #s(approx (- 1 x) x))
accuracy	60.55820116671084	#s(approx (- 1 x) x)
accuracy	0	(PI.f64)
accuracy	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	1.1692509973742442	(asin.f64 (-.f64 #s(literal 1 binary64) x))
accuracy	57.532865124506934	(-.f64 (*.f64 #s(literal 1/2 binary64) (PI.f64)) (asin.f64 (-.f64 #s(literal 1 binary64) x)))

Samples

143.0ms	240×	1	valid
4.0ms	16×	0	valid

Compiler

Compiled 253 to 32 computations (87.4% saved)

Precisions

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

ival-mult: 24.0ms (24.1% of total)

adjust: 14.0ms (14.1% of total)

ival-asin: 10.0ms (10% of total)

ival-add: 10.0ms (10% of total)

ival-acos: 9.0ms (9% of total)

ival-sqrt: 8.0ms (8% of total)

ival-neg: 6.0ms (6% of total)

ival-pow: 5.0ms (5% of total)

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

ival-pow2: 4.0ms (4% of total)

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

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

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

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

exact: 0.0ms (0% of total)

series14.0ms (0.3%)

Memory

7.0MiB live, 7.0MiB allocated

Counts

20 → 192

Calls

Call 1

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

Outputs
#s(alt (- (* 1/2 (PI)) (asin (- 1 x))) (taylor 0 x) (#s(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)))) (patch #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)))) #<representation binary64>) () ())) ())
#s(alt (- (* 1/2 (PI)) (asin (- 1 x))) (taylor 0 x) (#s(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)))) (patch #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)))) #<representation binary64>) () ())) ())
#s(alt (- (* 1/2 (PI)) (asin (- 1 x))) (taylor 0 x) (#s(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)))) (patch #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)))) #<representation binary64>) () ())) ())
#s(alt (- (* 1/2 (PI)) (asin (- 1 x))) (taylor 0 x) (#s(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)))) (patch #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)))) #<representation binary64>) () ())) ())
#s(alt (- (* 1/2 (PI)) (asin (- 1 x))) (taylor inf x) (#s(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)))) (patch #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)))) #<representation binary64>) () ())) ())
#s(alt (- (* 1/2 (PI)) (asin (- 1 x))) (taylor inf x) (#s(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)))) (patch #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)))) #<representation binary64>) () ())) ())
#s(alt (- (* 1/2 (PI)) (asin (- 1 x))) (taylor inf x) (#s(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)))) (patch #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)))) #<representation binary64>) () ())) ())
#s(alt (- (* 1/2 (PI)) (asin (- 1 x))) (taylor inf x) (#s(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)))) (patch #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)))) #<representation binary64>) () ())) ())
#s(alt (- (* 1/2 (PI)) (asin (+ 1 (* -1 x)))) (taylor -inf x) (#s(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)))) (patch #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)))) #<representation binary64>) () ())) ())
#s(alt (- (* 1/2 (PI)) (asin (+ 1 (* -1 x)))) (taylor -inf x) (#s(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)))) (patch #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)))) #<representation binary64>) () ())) ())
#s(alt (- (* 1/2 (PI)) (asin (+ 1 (* -1 x)))) (taylor -inf x) (#s(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)))) (patch #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)))) #<representation binary64>) () ())) ())
#s(alt (- (* 1/2 (PI)) (asin (+ 1 (* -1 x)))) (taylor -inf x) (#s(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)))) (patch #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)))) #<representation binary64>) () ())) ())
#s(alt (- (* 1/2 (PI)) (asin (- 1 x))) (taylor 0 x) (#s(alt (-.f64 (.f64 #s(literal 1/2 binary64) (PI.f64)) (asin.f64 (-.f64 #s(literal 1 binary64) x))) (patch (-.f64 (.f64 #s(literal 1/2 binary64) (PI.f64)) (asin.f64 (-.f64 #s(literal 1 binary64) x))) #<representation binary64>) () ())) ())
#s(alt (- (* 1/2 (PI)) (asin (- 1 x))) (taylor 0 x) (#s(alt (-.f64 (.f64 #s(literal 1/2 binary64) (PI.f64)) (asin.f64 (-.f64 #s(literal 1 binary64) x))) (patch (-.f64 (.f64 #s(literal 1/2 binary64) (PI.f64)) (asin.f64 (-.f64 #s(literal 1 binary64) x))) #<representation binary64>) () ())) ())
#s(alt (- (* 1/2 (PI)) (asin (- 1 x))) (taylor 0 x) (#s(alt (-.f64 (.f64 #s(literal 1/2 binary64) (PI.f64)) (asin.f64 (-.f64 #s(literal 1 binary64) x))) (patch (-.f64 (.f64 #s(literal 1/2 binary64) (PI.f64)) (asin.f64 (-.f64 #s(literal 1 binary64) x))) #<representation binary64>) () ())) ())
#s(alt (- (* 1/2 (PI)) (asin (- 1 x))) (taylor 0 x) (#s(alt (-.f64 (.f64 #s(literal 1/2 binary64) (PI.f64)) (asin.f64 (-.f64 #s(literal 1 binary64) x))) (patch (-.f64 (.f64 #s(literal 1/2 binary64) (PI.f64)) (asin.f64 (-.f64 #s(literal 1 binary64) x))) #<representation binary64>) () ())) ())
#s(alt (- (* 1/2 (PI)) (asin (- 1 x))) (taylor inf x) (#s(alt (-.f64 (.f64 #s(literal 1/2 binary64) (PI.f64)) (asin.f64 (-.f64 #s(literal 1 binary64) x))) (patch (-.f64 (.f64 #s(literal 1/2 binary64) (PI.f64)) (asin.f64 (-.f64 #s(literal 1 binary64) x))) #<representation binary64>) () ())) ())
#s(alt (- (* 1/2 (PI)) (asin (- 1 x))) (taylor inf x) (#s(alt (-.f64 (.f64 #s(literal 1/2 binary64) (PI.f64)) (asin.f64 (-.f64 #s(literal 1 binary64) x))) (patch (-.f64 (.f64 #s(literal 1/2 binary64) (PI.f64)) (asin.f64 (-.f64 #s(literal 1 binary64) x))) #<representation binary64>) () ())) ())
#s(alt (- (* 1/2 (PI)) (asin (- 1 x))) (taylor inf x) (#s(alt (-.f64 (.f64 #s(literal 1/2 binary64) (PI.f64)) (asin.f64 (-.f64 #s(literal 1 binary64) x))) (patch (-.f64 (.f64 #s(literal 1/2 binary64) (PI.f64)) (asin.f64 (-.f64 #s(literal 1 binary64) x))) #<representation binary64>) () ())) ())
#s(alt (- (* 1/2 (PI)) (asin (- 1 x))) (taylor inf x) (#s(alt (-.f64 (.f64 #s(literal 1/2 binary64) (PI.f64)) (asin.f64 (-.f64 #s(literal 1 binary64) x))) (patch (-.f64 (.f64 #s(literal 1/2 binary64) (PI.f64)) (asin.f64 (-.f64 #s(literal 1 binary64) x))) #<representation binary64>) () ())) ())
#s(alt (- (* 1/2 (PI)) (asin (+ 1 (* -1 x)))) (taylor -inf x) (#s(alt (-.f64 (.f64 #s(literal 1/2 binary64) (PI.f64)) (asin.f64 (-.f64 #s(literal 1 binary64) x))) (patch (-.f64 (.f64 #s(literal 1/2 binary64) (PI.f64)) (asin.f64 (-.f64 #s(literal 1 binary64) x))) #<representation binary64>) () ())) ())
#s(alt (- (* 1/2 (PI)) (asin (+ 1 (* -1 x)))) (taylor -inf x) (#s(alt (-.f64 (.f64 #s(literal 1/2 binary64) (PI.f64)) (asin.f64 (-.f64 #s(literal 1 binary64) x))) (patch (-.f64 (.f64 #s(literal 1/2 binary64) (PI.f64)) (asin.f64 (-.f64 #s(literal 1 binary64) x))) #<representation binary64>) () ())) ())
#s(alt (- (* 1/2 (PI)) (asin (+ 1 (* -1 x)))) (taylor -inf x) (#s(alt (-.f64 (.f64 #s(literal 1/2 binary64) (PI.f64)) (asin.f64 (-.f64 #s(literal 1 binary64) x))) (patch (-.f64 (.f64 #s(literal 1/2 binary64) (PI.f64)) (asin.f64 (-.f64 #s(literal 1 binary64) x))) #<representation binary64>) () ())) ())
#s(alt (- (* 1/2 (PI)) (asin (+ 1 (* -1 x)))) (taylor -inf x) (#s(alt (-.f64 (.f64 #s(literal 1/2 binary64) (PI.f64)) (asin.f64 (-.f64 #s(literal 1 binary64) x))) (patch (-.f64 (.f64 #s(literal 1/2 binary64) (PI.f64)) (asin.f64 (-.f64 #s(literal 1 binary64) x))) #<representation binary64>) () ())) ())
#s(alt (+ (asin (- 1 x)) (* 1/2 (PI))) (taylor 0 x) (#s(alt (fma.f64 (.f64 (sqrt.f64 (PI.f64)) #s(literal 1/2 binary64)) (sqrt.f64 (PI.f64)) (asin.f64 #s(approx (- 1 x) x))) (patch (fma.f64 (.f64 (sqrt.f64 (PI.f64)) #s(literal 1/2 binary64)) (sqrt.f64 (PI.f64)) (asin.f64 #s(approx (- 1 x) x))) #<representation binary64>) () ())) ())
#s(alt (+ (asin (- 1 x)) (* 1/2 (PI))) (taylor 0 x) (#s(alt (fma.f64 (.f64 (sqrt.f64 (PI.f64)) #s(literal 1/2 binary64)) (sqrt.f64 (PI.f64)) (asin.f64 #s(approx (- 1 x) x))) (patch (fma.f64 (.f64 (sqrt.f64 (PI.f64)) #s(literal 1/2 binary64)) (sqrt.f64 (PI.f64)) (asin.f64 #s(approx (- 1 x) x))) #<representation binary64>) () ())) ())
#s(alt (+ (asin (- 1 x)) (* 1/2 (PI))) (taylor 0 x) (#s(alt (fma.f64 (.f64 (sqrt.f64 (PI.f64)) #s(literal 1/2 binary64)) (sqrt.f64 (PI.f64)) (asin.f64 #s(approx (- 1 x) x))) (patch (fma.f64 (.f64 (sqrt.f64 (PI.f64)) #s(literal 1/2 binary64)) (sqrt.f64 (PI.f64)) (asin.f64 #s(approx (- 1 x) x))) #<representation binary64>) () ())) ())
#s(alt (+ (asin (- 1 x)) (* 1/2 (PI))) (taylor 0 x) (#s(alt (fma.f64 (.f64 (sqrt.f64 (PI.f64)) #s(literal 1/2 binary64)) (sqrt.f64 (PI.f64)) (asin.f64 #s(approx (- 1 x) x))) (patch (fma.f64 (.f64 (sqrt.f64 (PI.f64)) #s(literal 1/2 binary64)) (sqrt.f64 (PI.f64)) (asin.f64 #s(approx (- 1 x) x))) #<representation binary64>) () ())) ())
#s(alt (+ (asin (- 1 x)) (* 1/2 (PI))) (taylor inf x) (#s(alt (fma.f64 (.f64 (sqrt.f64 (PI.f64)) #s(literal 1/2 binary64)) (sqrt.f64 (PI.f64)) (asin.f64 #s(approx (- 1 x) x))) (patch (fma.f64 (.f64 (sqrt.f64 (PI.f64)) #s(literal 1/2 binary64)) (sqrt.f64 (PI.f64)) (asin.f64 #s(approx (- 1 x) x))) #<representation binary64>) () ())) ())
#s(alt (+ (asin (- 1 x)) (* 1/2 (PI))) (taylor inf x) (#s(alt (fma.f64 (.f64 (sqrt.f64 (PI.f64)) #s(literal 1/2 binary64)) (sqrt.f64 (PI.f64)) (asin.f64 #s(approx (- 1 x) x))) (patch (fma.f64 (.f64 (sqrt.f64 (PI.f64)) #s(literal 1/2 binary64)) (sqrt.f64 (PI.f64)) (asin.f64 #s(approx (- 1 x) x))) #<representation binary64>) () ())) ())
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#s(alt (pow (asin (- 1 x)) 3) (taylor inf x) (#s(alt (pow.f64 (asin.f64 #s(approx (- 1 x) x)) #s(literal 3 binary64)) (patch (pow.f64 (asin.f64 #s(approx (- 1 x) x)) #s(literal 3 binary64)) #<representation binary64>) () ())) ())
#s(alt (pow (asin (- 1 x)) 3) (taylor inf x) (#s(alt (pow.f64 (asin.f64 #s(approx (- 1 x) x)) #s(literal 3 binary64)) (patch (pow.f64 (asin.f64 #s(approx (- 1 x) x)) #s(literal 3 binary64)) #<representation binary64>) () ())) ())
#s(alt (pow (asin (- 1 x)) 3) (taylor inf x) (#s(alt (pow.f64 (asin.f64 #s(approx (- 1 x) x)) #s(literal 3 binary64)) (patch (pow.f64 (asin.f64 #s(approx (- 1 x) x)) #s(literal 3 binary64)) #<representation binary64>) () ())) ())
#s(alt (pow (asin (- 1 x)) 3) (taylor inf x) (#s(alt (pow.f64 (asin.f64 #s(approx (- 1 x) x)) #s(literal 3 binary64)) (patch (pow.f64 (asin.f64 #s(approx (- 1 x) x)) #s(literal 3 binary64)) #<representation binary64>) () ())) ())
#s(alt (pow (asin (+ 1 (* -1 x))) 3) (taylor -inf x) (#s(alt (pow.f64 (asin.f64 #s(approx (- 1 x) x)) #s(literal 3 binary64)) (patch (pow.f64 (asin.f64 #s(approx (- 1 x) x)) #s(literal 3 binary64)) #<representation binary64>) () ())) ())
#s(alt (pow (asin (+ 1 (* -1 x))) 3) (taylor -inf x) (#s(alt (pow.f64 (asin.f64 #s(approx (- 1 x) x)) #s(literal 3 binary64)) (patch (pow.f64 (asin.f64 #s(approx (- 1 x) x)) #s(literal 3 binary64)) #<representation binary64>) () ())) ())
#s(alt (pow (asin (+ 1 (* -1 x))) 3) (taylor -inf x) (#s(alt (pow.f64 (asin.f64 #s(approx (- 1 x) x)) #s(literal 3 binary64)) (patch (pow.f64 (asin.f64 #s(approx (- 1 x) x)) #s(literal 3 binary64)) #<representation binary64>) () ())) ())
#s(alt (pow (asin (+ 1 (* -1 x))) 3) (taylor -inf x) (#s(alt (pow.f64 (asin.f64 #s(approx (- 1 x) x)) #s(literal 3 binary64)) (patch (pow.f64 (asin.f64 #s(approx (- 1 x) x)) #s(literal 3 binary64)) #<representation binary64>) () ())) ())
#s(alt (asin (- 1 x)) (taylor 0 x) (#s(alt (asin.f64 #s(approx (- 1 x) x)) (patch (asin.f64 #s(approx (- 1 x) x)) #<representation binary64>) () ())) ())
#s(alt (asin (- 1 x)) (taylor 0 x) (#s(alt (asin.f64 #s(approx (- 1 x) x)) (patch (asin.f64 #s(approx (- 1 x) x)) #<representation binary64>) () ())) ())
#s(alt (asin (- 1 x)) (taylor 0 x) (#s(alt (asin.f64 #s(approx (- 1 x) x)) (patch (asin.f64 #s(approx (- 1 x) x)) #<representation binary64>) () ())) ())
#s(alt (asin (- 1 x)) (taylor 0 x) (#s(alt (asin.f64 #s(approx (- 1 x) x)) (patch (asin.f64 #s(approx (- 1 x) x)) #<representation binary64>) () ())) ())
#s(alt (asin (- 1 x)) (taylor inf x) (#s(alt (asin.f64 #s(approx (- 1 x) x)) (patch (asin.f64 #s(approx (- 1 x) x)) #<representation binary64>) () ())) ())
#s(alt (asin (- 1 x)) (taylor inf x) (#s(alt (asin.f64 #s(approx (- 1 x) x)) (patch (asin.f64 #s(approx (- 1 x) x)) #<representation binary64>) () ())) ())
#s(alt (asin (- 1 x)) (taylor inf x) (#s(alt (asin.f64 #s(approx (- 1 x) x)) (patch (asin.f64 #s(approx (- 1 x) x)) #<representation binary64>) () ())) ())
#s(alt (asin (- 1 x)) (taylor inf x) (#s(alt (asin.f64 #s(approx (- 1 x) x)) (patch (asin.f64 #s(approx (- 1 x) x)) #<representation binary64>) () ())) ())
#s(alt (asin (+ 1 (* -1 x))) (taylor -inf x) (#s(alt (asin.f64 #s(approx (- 1 x) x)) (patch (asin.f64 #s(approx (- 1 x) x)) #<representation binary64>) () ())) ())
#s(alt (asin (+ 1 (* -1 x))) (taylor -inf x) (#s(alt (asin.f64 #s(approx (- 1 x) x)) (patch (asin.f64 #s(approx (- 1 x) x)) #<representation binary64>) () ())) ())
#s(alt (asin (+ 1 (* -1 x))) (taylor -inf x) (#s(alt (asin.f64 #s(approx (- 1 x) x)) (patch (asin.f64 #s(approx (- 1 x) x)) #<representation binary64>) () ())) ())
#s(alt (asin (+ 1 (* -1 x))) (taylor -inf x) (#s(alt (asin.f64 #s(approx (- 1 x) x)) (patch (asin.f64 #s(approx (- 1 x) x)) #<representation binary64>) () ())) ())
#s(alt (asin (- 1 x)) (taylor 0 x) (#s(alt (asin.f64 (-.f64 #s(literal 1 binary64) x)) (patch (asin.f64 (-.f64 #s(literal 1 binary64) x)) #<representation binary64>) () ())) ())
#s(alt (asin (- 1 x)) (taylor 0 x) (#s(alt (asin.f64 (-.f64 #s(literal 1 binary64) x)) (patch (asin.f64 (-.f64 #s(literal 1 binary64) x)) #<representation binary64>) () ())) ())
#s(alt (asin (- 1 x)) (taylor 0 x) (#s(alt (asin.f64 (-.f64 #s(literal 1 binary64) x)) (patch (asin.f64 (-.f64 #s(literal 1 binary64) x)) #<representation binary64>) () ())) ())
#s(alt (asin (- 1 x)) (taylor 0 x) (#s(alt (asin.f64 (-.f64 #s(literal 1 binary64) x)) (patch (asin.f64 (-.f64 #s(literal 1 binary64) x)) #<representation binary64>) () ())) ())
#s(alt (asin (- 1 x)) (taylor inf x) (#s(alt (asin.f64 (-.f64 #s(literal 1 binary64) x)) (patch (asin.f64 (-.f64 #s(literal 1 binary64) x)) #<representation binary64>) () ())) ())
#s(alt (asin (- 1 x)) (taylor inf x) (#s(alt (asin.f64 (-.f64 #s(literal 1 binary64) x)) (patch (asin.f64 (-.f64 #s(literal 1 binary64) x)) #<representation binary64>) () ())) ())
#s(alt (asin (- 1 x)) (taylor inf x) (#s(alt (asin.f64 (-.f64 #s(literal 1 binary64) x)) (patch (asin.f64 (-.f64 #s(literal 1 binary64) x)) #<representation binary64>) () ())) ())
#s(alt (asin (- 1 x)) (taylor inf x) (#s(alt (asin.f64 (-.f64 #s(literal 1 binary64) x)) (patch (asin.f64 (-.f64 #s(literal 1 binary64) x)) #<representation binary64>) () ())) ())
#s(alt (asin (+ 1 (* -1 x))) (taylor -inf x) (#s(alt (asin.f64 (-.f64 #s(literal 1 binary64) x)) (patch (asin.f64 (-.f64 #s(literal 1 binary64) x)) #<representation binary64>) () ())) ())
#s(alt (asin (+ 1 (* -1 x))) (taylor -inf x) (#s(alt (asin.f64 (-.f64 #s(literal 1 binary64) x)) (patch (asin.f64 (-.f64 #s(literal 1 binary64) x)) #<representation binary64>) () ())) ())
#s(alt (asin (+ 1 (* -1 x))) (taylor -inf x) (#s(alt (asin.f64 (-.f64 #s(literal 1 binary64) x)) (patch (asin.f64 (-.f64 #s(literal 1 binary64) x)) #<representation binary64>) () ())) ())
#s(alt (asin (+ 1 (* -1 x))) (taylor -inf x) (#s(alt (asin.f64 (-.f64 #s(literal 1 binary64) x)) (patch (asin.f64 (-.f64 #s(literal 1 binary64) x)) #<representation binary64>) () ())) ())
#s(alt 1 (taylor 0 x) (#s(alt #s(approx (- 1 x) x) (patch #s(approx (- 1 x) x) #<representation binary64>) () ())) ())
#s(alt (+ 1 (* -1 x)) (taylor 0 x) (#s(alt #s(approx (- 1 x) x) (patch #s(approx (- 1 x) x) #<representation binary64>) () ())) ())
#s(alt (+ 1 (* -1 x)) (taylor 0 x) (#s(alt #s(approx (- 1 x) x) (patch #s(approx (- 1 x) x) #<representation binary64>) () ())) ())
#s(alt (+ 1 (* -1 x)) (taylor 0 x) (#s(alt #s(approx (- 1 x) x) (patch #s(approx (- 1 x) x) #<representation binary64>) () ())) ())
#s(alt (* -1 x) (taylor inf x) (#s(alt #s(approx (- 1 x) x) (patch #s(approx (- 1 x) x) #<representation binary64>) () ())) ())
#s(alt (* x (- (/ 1 x) 1)) (taylor inf x) (#s(alt #s(approx (- 1 x) x) (patch #s(approx (- 1 x) x) #<representation binary64>) () ())) ())
#s(alt (* x (- (/ 1 x) 1)) (taylor inf x) (#s(alt #s(approx (- 1 x) x) (patch #s(approx (- 1 x) x) #<representation binary64>) () ())) ())
#s(alt (* x (- (/ 1 x) 1)) (taylor inf x) (#s(alt #s(approx (- 1 x) x) (patch #s(approx (- 1 x) x) #<representation binary64>) () ())) ())
#s(alt (* -1 x) (taylor -inf x) (#s(alt #s(approx (- 1 x) x) (patch #s(approx (- 1 x) x) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (- 1 (/ 1 x)))) (taylor -inf x) (#s(alt #s(approx (- 1 x) x) (patch #s(approx (- 1 x) x) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (- 1 (/ 1 x)))) (taylor -inf x) (#s(alt #s(approx (- 1 x) x) (patch #s(approx (- 1 x) x) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (- 1 (/ 1 x)))) (taylor -inf x) (#s(alt #s(approx (- 1 x) x) (patch #s(approx (- 1 x) x) #<representation binary64>) () ())) ())
#s(alt (asin (- 1 x)) (taylor 0 x) (#s(alt (asin.f64 #s(approx (- 1 x) (-.f64 #s(literal 1 binary64) x))) (patch (asin.f64 #s(approx (- 1 x) (-.f64 #s(literal 1 binary64) x))) #<representation binary64>) () ())) ())
#s(alt (asin (- 1 x)) (taylor 0 x) (#s(alt (asin.f64 #s(approx (- 1 x) (-.f64 #s(literal 1 binary64) x))) (patch (asin.f64 #s(approx (- 1 x) (-.f64 #s(literal 1 binary64) x))) #<representation binary64>) () ())) ())
#s(alt (asin (- 1 x)) (taylor 0 x) (#s(alt (asin.f64 #s(approx (- 1 x) (-.f64 #s(literal 1 binary64) x))) (patch (asin.f64 #s(approx (- 1 x) (-.f64 #s(literal 1 binary64) x))) #<representation binary64>) () ())) ())
#s(alt (asin (- 1 x)) (taylor 0 x) (#s(alt (asin.f64 #s(approx (- 1 x) (-.f64 #s(literal 1 binary64) x))) (patch (asin.f64 #s(approx (- 1 x) (-.f64 #s(literal 1 binary64) x))) #<representation binary64>) () ())) ())
#s(alt (asin (- 1 x)) (taylor inf x) (#s(alt (asin.f64 #s(approx (- 1 x) (-.f64 #s(literal 1 binary64) x))) (patch (asin.f64 #s(approx (- 1 x) (-.f64 #s(literal 1 binary64) x))) #<representation binary64>) () ())) ())
#s(alt (asin (- 1 x)) (taylor inf x) (#s(alt (asin.f64 #s(approx (- 1 x) (-.f64 #s(literal 1 binary64) x))) (patch (asin.f64 #s(approx (- 1 x) (-.f64 #s(literal 1 binary64) x))) #<representation binary64>) () ())) ())
#s(alt (asin (- 1 x)) (taylor inf x) (#s(alt (asin.f64 #s(approx (- 1 x) (-.f64 #s(literal 1 binary64) x))) (patch (asin.f64 #s(approx (- 1 x) (-.f64 #s(literal 1 binary64) x))) #<representation binary64>) () ())) ())
#s(alt (asin (- 1 x)) (taylor inf x) (#s(alt (asin.f64 #s(approx (- 1 x) (-.f64 #s(literal 1 binary64) x))) (patch (asin.f64 #s(approx (- 1 x) (-.f64 #s(literal 1 binary64) x))) #<representation binary64>) () ())) ())
#s(alt (asin (+ 1 (* -1 x))) (taylor -inf x) (#s(alt (asin.f64 #s(approx (- 1 x) (-.f64 #s(literal 1 binary64) x))) (patch (asin.f64 #s(approx (- 1 x) (-.f64 #s(literal 1 binary64) x))) #<representation binary64>) () ())) ())
#s(alt (asin (+ 1 (* -1 x))) (taylor -inf x) (#s(alt (asin.f64 #s(approx (- 1 x) (-.f64 #s(literal 1 binary64) x))) (patch (asin.f64 #s(approx (- 1 x) (-.f64 #s(literal 1 binary64) x))) #<representation binary64>) () ())) ())
#s(alt (asin (+ 1 (* -1 x))) (taylor -inf x) (#s(alt (asin.f64 #s(approx (- 1 x) (-.f64 #s(literal 1 binary64) x))) (patch (asin.f64 #s(approx (- 1 x) (-.f64 #s(literal 1 binary64) x))) #<representation binary64>) () ())) ())
#s(alt (asin (+ 1 (* -1 x))) (taylor -inf x) (#s(alt (asin.f64 #s(approx (- 1 x) (-.f64 #s(literal 1 binary64) x))) (patch (asin.f64 #s(approx (- 1 x) (-.f64 #s(literal 1 binary64) x))) #<representation binary64>) () ())) ())
#s(alt 1 (taylor 0 x) (#s(alt #s(approx (- 1 x) (-.f64 #s(literal 1 binary64) x)) (patch #s(approx (- 1 x) (-.f64 #s(literal 1 binary64) x)) #<representation binary64>) () ())) ())
#s(alt (+ 1 (* -1 x)) (taylor 0 x) (#s(alt #s(approx (- 1 x) (-.f64 #s(literal 1 binary64) x)) (patch #s(approx (- 1 x) (-.f64 #s(literal 1 binary64) x)) #<representation binary64>) () ())) ())
#s(alt (+ 1 (* -1 x)) (taylor 0 x) (#s(alt #s(approx (- 1 x) (-.f64 #s(literal 1 binary64) x)) (patch #s(approx (- 1 x) (-.f64 #s(literal 1 binary64) x)) #<representation binary64>) () ())) ())
#s(alt (+ 1 (* -1 x)) (taylor 0 x) (#s(alt #s(approx (- 1 x) (-.f64 #s(literal 1 binary64) x)) (patch #s(approx (- 1 x) (-.f64 #s(literal 1 binary64) x)) #<representation binary64>) () ())) ())
#s(alt (* -1 x) (taylor inf x) (#s(alt #s(approx (- 1 x) (-.f64 #s(literal 1 binary64) x)) (patch #s(approx (- 1 x) (-.f64 #s(literal 1 binary64) x)) #<representation binary64>) () ())) ())
#s(alt (* x (- (/ 1 x) 1)) (taylor inf x) (#s(alt #s(approx (- 1 x) (-.f64 #s(literal 1 binary64) x)) (patch #s(approx (- 1 x) (-.f64 #s(literal 1 binary64) x)) #<representation binary64>) () ())) ())
#s(alt (* x (- (/ 1 x) 1)) (taylor inf x) (#s(alt #s(approx (- 1 x) (-.f64 #s(literal 1 binary64) x)) (patch #s(approx (- 1 x) (-.f64 #s(literal 1 binary64) x)) #<representation binary64>) () ())) ())
#s(alt (* x (- (/ 1 x) 1)) (taylor inf x) (#s(alt #s(approx (- 1 x) (-.f64 #s(literal 1 binary64) x)) (patch #s(approx (- 1 x) (-.f64 #s(literal 1 binary64) x)) #<representation binary64>) () ())) ())
#s(alt (* -1 x) (taylor -inf x) (#s(alt #s(approx (- 1 x) (-.f64 #s(literal 1 binary64) x)) (patch #s(approx (- 1 x) (-.f64 #s(literal 1 binary64) x)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (- 1 (/ 1 x)))) (taylor -inf x) (#s(alt #s(approx (- 1 x) (-.f64 #s(literal 1 binary64) x)) (patch #s(approx (- 1 x) (-.f64 #s(literal 1 binary64) x)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (- 1 (/ 1 x)))) (taylor -inf x) (#s(alt #s(approx (- 1 x) (-.f64 #s(literal 1 binary64) x)) (patch #s(approx (- 1 x) (-.f64 #s(literal 1 binary64) x)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (- 1 (/ 1 x)))) (taylor -inf x) (#s(alt #s(approx (- 1 x) (-.f64 #s(literal 1 binary64) x)) (patch #s(approx (- 1 x) (-.f64 #s(literal 1 binary64) x)) #<representation binary64>) () ())) ())
#s(alt (acos (- 1 x)) (taylor 0 x) (#s(alt (acos.f64 #s(approx (- 1 x) x)) (patch (acos.f64 #s(approx (- 1 x) x)) #<representation binary64>) () ())) ())
#s(alt (acos (- 1 x)) (taylor 0 x) (#s(alt (acos.f64 #s(approx (- 1 x) x)) (patch (acos.f64 #s(approx (- 1 x) x)) #<representation binary64>) () ())) ())
#s(alt (acos (- 1 x)) (taylor 0 x) (#s(alt (acos.f64 #s(approx (- 1 x) x)) (patch (acos.f64 #s(approx (- 1 x) x)) #<representation binary64>) () ())) ())
#s(alt (acos (- 1 x)) (taylor 0 x) (#s(alt (acos.f64 #s(approx (- 1 x) x)) (patch (acos.f64 #s(approx (- 1 x) x)) #<representation binary64>) () ())) ())
#s(alt (acos (- 1 x)) (taylor inf x) (#s(alt (acos.f64 #s(approx (- 1 x) x)) (patch (acos.f64 #s(approx (- 1 x) x)) #<representation binary64>) () ())) ())
#s(alt (acos (- 1 x)) (taylor inf x) (#s(alt (acos.f64 #s(approx (- 1 x) x)) (patch (acos.f64 #s(approx (- 1 x) x)) #<representation binary64>) () ())) ())
#s(alt (acos (- 1 x)) (taylor inf x) (#s(alt (acos.f64 #s(approx (- 1 x) x)) (patch (acos.f64 #s(approx (- 1 x) x)) #<representation binary64>) () ())) ())
#s(alt (acos (- 1 x)) (taylor inf x) (#s(alt (acos.f64 #s(approx (- 1 x) x)) (patch (acos.f64 #s(approx (- 1 x) x)) #<representation binary64>) () ())) ())
#s(alt (acos (+ 1 (* -1 x))) (taylor -inf x) (#s(alt (acos.f64 #s(approx (- 1 x) x)) (patch (acos.f64 #s(approx (- 1 x) x)) #<representation binary64>) () ())) ())
#s(alt (acos (+ 1 (* -1 x))) (taylor -inf x) (#s(alt (acos.f64 #s(approx (- 1 x) x)) (patch (acos.f64 #s(approx (- 1 x) x)) #<representation binary64>) () ())) ())
#s(alt (acos (+ 1 (* -1 x))) (taylor -inf x) (#s(alt (acos.f64 #s(approx (- 1 x) x)) (patch (acos.f64 #s(approx (- 1 x) x)) #<representation binary64>) () ())) ())
#s(alt (acos (+ 1 (* -1 x))) (taylor -inf x) (#s(alt (acos.f64 #s(approx (- 1 x) x)) (patch (acos.f64 #s(approx (- 1 x) x)) #<representation binary64>) () ())) ())
#s(alt (* (PI) (pow (asin (- 1 x)) 2)) (taylor 0 x) (#s(alt (.f64 (pow.f64 (asin.f64 #s(approx (- 1 x) x)) #s(literal 2 binary64)) (PI.f64)) (patch (.f64 (pow.f64 (asin.f64 #s(approx (- 1 x) x)) #s(literal 2 binary64)) (PI.f64)) #<representation binary64>) () ())) ())
#s(alt (* (PI) (pow (asin (- 1 x)) 2)) (taylor 0 x) (#s(alt (.f64 (pow.f64 (asin.f64 #s(approx (- 1 x) x)) #s(literal 2 binary64)) (PI.f64)) (patch (.f64 (pow.f64 (asin.f64 #s(approx (- 1 x) x)) #s(literal 2 binary64)) (PI.f64)) #<representation binary64>) () ())) ())
#s(alt (* (PI) (pow (asin (- 1 x)) 2)) (taylor 0 x) (#s(alt (.f64 (pow.f64 (asin.f64 #s(approx (- 1 x) x)) #s(literal 2 binary64)) (PI.f64)) (patch (.f64 (pow.f64 (asin.f64 #s(approx (- 1 x) x)) #s(literal 2 binary64)) (PI.f64)) #<representation binary64>) () ())) ())
#s(alt (* (PI) (pow (asin (- 1 x)) 2)) (taylor 0 x) (#s(alt (.f64 (pow.f64 (asin.f64 #s(approx (- 1 x) x)) #s(literal 2 binary64)) (PI.f64)) (patch (.f64 (pow.f64 (asin.f64 #s(approx (- 1 x) x)) #s(literal 2 binary64)) (PI.f64)) #<representation binary64>) () ())) ())
#s(alt (* (PI) (pow (asin (- 1 x)) 2)) (taylor inf x) (#s(alt (.f64 (pow.f64 (asin.f64 #s(approx (- 1 x) x)) #s(literal 2 binary64)) (PI.f64)) (patch (.f64 (pow.f64 (asin.f64 #s(approx (- 1 x) x)) #s(literal 2 binary64)) (PI.f64)) #<representation binary64>) () ())) ())
#s(alt (* (PI) (pow (asin (- 1 x)) 2)) (taylor inf x) (#s(alt (.f64 (pow.f64 (asin.f64 #s(approx (- 1 x) x)) #s(literal 2 binary64)) (PI.f64)) (patch (.f64 (pow.f64 (asin.f64 #s(approx (- 1 x) x)) #s(literal 2 binary64)) (PI.f64)) #<representation binary64>) () ())) ())
#s(alt (* (PI) (pow (asin (- 1 x)) 2)) (taylor inf x) (#s(alt (.f64 (pow.f64 (asin.f64 #s(approx (- 1 x) x)) #s(literal 2 binary64)) (PI.f64)) (patch (.f64 (pow.f64 (asin.f64 #s(approx (- 1 x) x)) #s(literal 2 binary64)) (PI.f64)) #<representation binary64>) () ())) ())
#s(alt (* (PI) (pow (asin (- 1 x)) 2)) (taylor inf x) (#s(alt (.f64 (pow.f64 (asin.f64 #s(approx (- 1 x) x)) #s(literal 2 binary64)) (PI.f64)) (patch (.f64 (pow.f64 (asin.f64 #s(approx (- 1 x) x)) #s(literal 2 binary64)) (PI.f64)) #<representation binary64>) () ())) ())
#s(alt (* (PI) (pow (asin (+ 1 (* -1 x))) 2)) (taylor -inf x) (#s(alt (.f64 (pow.f64 (asin.f64 #s(approx (- 1 x) x)) #s(literal 2 binary64)) (PI.f64)) (patch (.f64 (pow.f64 (asin.f64 #s(approx (- 1 x) x)) #s(literal 2 binary64)) (PI.f64)) #<representation binary64>) () ())) ())
#s(alt (* (PI) (pow (asin (+ 1 (* -1 x))) 2)) (taylor -inf x) (#s(alt (.f64 (pow.f64 (asin.f64 #s(approx (- 1 x) x)) #s(literal 2 binary64)) (PI.f64)) (patch (.f64 (pow.f64 (asin.f64 #s(approx (- 1 x) x)) #s(literal 2 binary64)) (PI.f64)) #<representation binary64>) () ())) ())
#s(alt (* (PI) (pow (asin (+ 1 (* -1 x))) 2)) (taylor -inf x) (#s(alt (.f64 (pow.f64 (asin.f64 #s(approx (- 1 x) x)) #s(literal 2 binary64)) (PI.f64)) (patch (.f64 (pow.f64 (asin.f64 #s(approx (- 1 x) x)) #s(literal 2 binary64)) (PI.f64)) #<representation binary64>) () ())) ())
#s(alt (* (PI) (pow (asin (+ 1 (* -1 x))) 2)) (taylor -inf x) (#s(alt (.f64 (pow.f64 (asin.f64 #s(approx (- 1 x) x)) #s(literal 2 binary64)) (PI.f64)) (patch (.f64 (pow.f64 (asin.f64 #s(approx (- 1 x) x)) #s(literal 2 binary64)) (PI.f64)) #<representation binary64>) () ())) ())

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	@	0	(/ (+ (* (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))
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)))))

simplify199.0ms (3.8%)

Memory

13.9MiB live, 163.4MiB 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)))

rewrite360.0ms (6.9%)

Memory

-14.1MiB live, 347.4MiB allocated

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)))))
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(/.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) (neg.f64 (-.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 (-.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)))

eval342.0ms (6.5%)

Memory: 25.1MiB live, 289.5MiB allocated
Compiler: Compiled 64 729 to 4 981 computations (92.3% saved)

prune396.0ms (7.5%)

Memory

-26.6MiB live, 235.1MiB allocated

Pruning

16 alts after pruning (12 fresh and 4 done)

	Pruned	Kept	Total
New	2 149	12	2 161
Fresh	1	0	1
Picked	3	2	5
Done	0	2	2
Total	2 153	16	2 169

Accuracy

10.8%

Counts

2 169 → 16

Alt Table

Click to see full alt table

Status	Accuracy	Program
	10.6%	(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)))))
✓	6.9%	(fma.f64 (*.f64 (sqrt.f64 (PI.f64)) #s(literal 1/2 binary64)) (sqrt.f64 (PI.f64)) (asin.f64 #s(approx (- 1 x) x)))
	5.3%	(fma.f64 (sqrt.f64 (.f64 (pow.f64 (.f64 (.f64 (PI.f64) (PI.f64)) (sqrt.f64 (PI.f64))) #s(literal 1/3 binary64)) (cbrt.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)))))
	10.5%	(fma.f64 (sqrt.f64 (PI.f64)) (.f64 (sqrt.f64 (PI.f64)) #s(literal 1/2 binary64)) (neg.f64 (fma.f64 (.f64 #s(literal 1/2 binary64) (sqrt.f64 (PI.f64))) (sqrt.f64 (PI.f64)) (neg.f64 (acos.f64 #s(approx (- 1 x) (-.f64 #s(literal 1 binary64) x)))))))
	5.7%	(/.f64 (fma.f64 (pow.f64 (asin.f64 #s(approx (- 1 x) x)) #s(literal 3 binary64)) #s(literal 2 binary64) (.f64 (pow.f64 (asin.f64 #s(approx (- 1 x) x)) #s(literal 2 binary64)) (PI.f64))) (.f64 (pow.f64 (fma.f64 (pow.f64 (PI.f64) #s(literal 2/3 binary64)) (*.f64 (cbrt.f64 (PI.f64)) #s(literal 1/2 binary64)) (neg.f64 (acos.f64 #s(approx (- 1 x) x)))) #s(literal 2 binary64)) #s(literal 2 binary64)))
	5.7%	(/.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)))
	10.5%	(/.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))))))))
✓	7.1%	(acos.f64 (-.f64 #s(literal 1 binary64) x))
✓	6.9%	(acos.f64 #s(approx (- 1 x) x))
	5.3%	#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))))
	5.3%	#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))))
	5.2%	#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))))
	10.5%	#s(approx (+ (* (sqrt (PI)) (* (sqrt (PI)) 1/2)) (neg (asin (- 1 x)))) (-.f64 (.f64 #s(literal 1/2 binary64) (.f64 (sqrt.f64 (*.f64 (PI.f64) (sqrt.f64 (PI.f64)))) (sqrt.f64 (sqrt.f64 (PI.f64))))) (asin.f64 (-.f64 #s(literal 1 binary64) x))))
	10.5%	#s(approx (+ (* (sqrt (PI)) (* (sqrt (PI)) 1/2)) (neg (asin (- 1 x)))) (-.f64 (.f64 #s(literal 1/2 binary64) (PI.f64)) (fma.f64 (.f64 #s(literal 1/2 binary64) (sqrt.f64 (PI.f64))) (sqrt.f64 (PI.f64)) (neg.f64 (acos.f64 (-.f64 #s(literal 1 binary64) x))))))
	7.1%	#s(approx (+ (* (sqrt (PI)) (* (sqrt (PI)) 1/2)) (neg (asin (- 1 x)))) (-.f64 (*.f64 #s(literal 1/2 binary64) (PI.f64)) (fma.f64 (PI.f64) #s(literal 1/2 binary64) (neg.f64 (acos.f64 (-.f64 #s(literal 1 binary64) x))))))
✓	7.1%	#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 711 to 285 computations (59.9% saved)

regimes19.0ms (0.4%)

Memory

11.1MiB live, 11.1MiB 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))))))
#s(approx (+ (* (sqrt (PI)) (* (sqrt (PI)) 1/2)) (neg (asin (- 1 x)))) (-.f64 (.f64 #s(literal 1/2 binary64) (.f64 (sqrt.f64 (*.f64 (PI.f64) (sqrt.f64 (PI.f64)))) (sqrt.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 (fma.f64 (.f64 (sqrt.f64 (PI.f64)) #s(literal 1/2 binary64)) (neg.f64 (sqrt.f64 (PI.f64))) (acos.f64 #s(approx (- 1 x) x)))))
(fma.f64 (sqrt.f64 (PI.f64)) (.f64 (sqrt.f64 (PI.f64)) #s(literal 1/2 binary64)) (neg.f64 (fma.f64 (.f64 #s(literal 1/2 binary64) (sqrt.f64 (PI.f64))) (sqrt.f64 (PI.f64)) (neg.f64 (acos.f64 #s(approx (- 1 x) (-.f64 #s(literal 1 binary64) x)))))))
(fma.f64 (.f64 (sqrt.f64 (sqrt.f64 (PI.f64))) (sqrt.f64 (sqrt.f64 (PI.f64)))) (.f64 (sqrt.f64 (PI.f64)) #s(literal 1/2 binary64)) (neg.f64 (asin.f64 #s(approx (- 1 x) (-.f64 #s(literal 1 binary64) x)))))
#s(approx (+ (* (sqrt (PI)) (* (sqrt (PI)) 1/2)) (neg (asin (- 1 x)))) (-.f64 (.f64 #s(literal 1/2 binary64) (.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))))
(fma.f64 (sqrt.f64 (.f64 (pow.f64 (.f64 (.f64 (PI.f64) (PI.f64)) (sqrt.f64 (PI.f64))) #s(literal 1/3 binary64)) (cbrt.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) (.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:

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
10.6%	1	`x`
10.6%	1	`(acos.f64 (-.f64 #s(literal 1 binary64) x))`
10.6%	1	`(-.f64 #s(literal 1 binary64) x)`

Compiler

Compiled 11 to 8 computations (27.3% saved)

regimes31.0ms (0.6%)

Memory

-31.1MiB live, 8.5MiB allocated

Counts

14 → 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))))))
#s(approx (+ (* (sqrt (PI)) (* (sqrt (PI)) 1/2)) (neg (asin (- 1 x)))) (-.f64 (.f64 #s(literal 1/2 binary64) (.f64 (sqrt.f64 (*.f64 (PI.f64) (sqrt.f64 (PI.f64)))) (sqrt.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 (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
4.0ms	(-.f64 #s(literal 1 binary64) x)
4.0ms	(acos.f64 (-.f64 #s(literal 1 binary64) x))

Results

Accuracy	Segments	Branch
10.5%	1	`x`
10.5%	1	`(-.f64 #s(literal 1 binary64) x)`
10.5%	1	`(acos.f64 (-.f64 #s(literal 1 binary64) x))`

Compiler

Compiled 11 to 8 computations (27.3% saved)

regimes12.0ms (0.2%)

Memory

7.8MiB live, 7.8MiB 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))))))
#s(approx (+ (* (sqrt (PI)) (* (sqrt (PI)) 1/2)) (neg (asin (- 1 x)))) (-.f64 (.f64 #s(literal 1/2 binary64) (.f64 (sqrt.f64 (*.f64 (PI.f64) (sqrt.f64 (PI.f64)))) (sqrt.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 (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) (*.f64 (sqrt.f64 (*.f64 (PI.f64) (sqrt.f64 (PI.f64)))) (sqrt.f64 (sqrt.f64 (PI.f64))))) (asin.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
10.5%	1	`(acos.f64 (-.f64 #s(literal 1 binary64) x))`
10.5%	1	`(-.f64 #s(literal 1 binary64) x)`
10.5%	1	`x`

Compiler

Compiled 11 to 8 computations (27.3% saved)

regimes10.0ms (0.2%)

Memory

6.8MiB live, 6.8MiB allocated

Counts

11 → 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))))))

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
10.5%	1	`(acos.f64 (-.f64 #s(literal 1 binary64) x))`
10.5%	1	`(-.f64 #s(literal 1 binary64) x)`
10.5%	1	`x`

Compiler

Compiled 11 to 8 computations (27.3% saved)

regimes10.0ms (0.2%)

Memory

6.6MiB live, 6.6MiB 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))
(acos.f64 (-.f64 #s(literal 1 binary64) x))

Calls

3 calls:

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

Results

Accuracy	Segments	Branch
9.6%	2	`(acos.f64 (-.f64 #s(literal 1 binary64) x))`
9.6%	2	`(-.f64 #s(literal 1 binary64) x)`
9.6%	2	`x`

Compiler

Compiled 11 to 8 computations (27.3% saved)

regimes5.0ms (0.1%)

Memory

4.3MiB live, 4.3MiB allocated

Counts

3 → 1

Calls

Call 1

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

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

Calls

3 calls:

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

Results

Accuracy	Segments	Branch
6.9%	1	`x`
6.9%	1	`(-.f64 #s(literal 1 binary64) x)`
6.9%	1	`(acos.f64 (-.f64 #s(literal 1 binary64) 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	`x`
3.8%	1	`(-.f64 #s(literal 1 binary64) x)`
3.8%	1	`(acos.f64 (-.f64 #s(literal 1 binary64) x))`

Compiler

Compiled 11 to 8 computations (27.3% saved)

bsearch0.0ms (0%)

Memory

0.1MiB live, 0.1MiB allocated

Algorithm

1×	left-value

Steps

Time	Left	Right
0.0ms	0.0	2.1073424255447017e-8

Compiler

Compiled 8 to 8 computations (0% saved)

simplify25.0ms (0.5%)

Memory

-29.9MiB live, 10.0MiB allocated

Algorithm

1×	egg-herbie

Rules

24×	`*-commutative_binary64`
20×	`+-commutative_binary64`
20×	`sub-neg_binary64`
14×	`neg-sub0_binary64`
14×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	47	134
1	70	134
2	87	134
3	97	134
4	100	134

Stop Event

1×

saturated

Calls

Call 1

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

soundness469.0ms (8.9%)

Memory

16.8MiB live, 295.7MiB allocated

Rules

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

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	14	80
1	29	80
2	62	80
3	113	80
4	171	80
5	239	80
6	259	80
0	259	80
0	21	224
1	41	224
2	77	224
3	134	224
4	206	224
5	292	224
6	353	224
7	387	224
8	438	224
9	455	224
10	463	224
0	463	224
0	39	210
0	68	183
1	254	166
2	1787	166
0	8602	163
0	8	26
0	11	26
1	37	26
2	203	26
3	1732	23
0	9154	23

Stop Event

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

Compiler

Compiled 330 to 177 computations (46.4% saved)

preprocess49.0ms (0.9%)

Memory: -14.2MiB live, 104.0MiB allocated
Compiler: Compiled 214 to 78 computations (63.6% 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

start0.0ms (0%)

analyze0.0ms (0%)

sample1.4s (27.4%)

explain87.0ms (1.7%)

preprocess14.0ms (0.3%)

eval0.0ms (0%)

prune1.0ms (0%)

simplify4.0ms (0.1%)

localize32.0ms (0.6%)

series1.0ms (0%)

simplify8.0ms (0.2%)

rewrite230.0ms (4.4%)

eval51.0ms (1%)

prune46.0ms (0.9%)

simplify5.0ms (0.1%)

localize35.0ms (0.7%)

series2.0ms (0%)

simplify9.0ms (0.2%)

rewrite178.0ms (3.4%)

eval34.0ms (0.6%)

prune27.0ms (0.5%)

simplify14.0ms (0.3%)

localize113.0ms (2.1%)

series2.0ms (0%)

simplify17.0ms (0.3%)

rewrite218.0ms (4.2%)

eval104.0ms (2%)

prune83.0ms (1.6%)

simplify350.0ms (6.7%)

localize199.0ms (3.8%)

series14.0ms (0.3%)

simplify199.0ms (3.8%)

rewrite360.0ms (6.9%)

eval342.0ms (6.5%)

prune396.0ms (7.5%)

regimes19.0ms (0.4%)

regimes31.0ms (0.6%)

regimes12.0ms (0.2%)

regimes10.0ms (0.2%)

regimes10.0ms (0.2%)

regimes5.0ms (0.1%)

regimes3.0ms (0.1%)

bsearch0.0ms (0%)

simplify25.0ms (0.5%)

soundness469.0ms (8.9%)

preprocess49.0ms (0.9%)

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