Metrics for bug323 (missed optimization)

analyze0.0ms (0%)

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 9 computations (25% saved)

Precisions

Click to see histograms. Total time spent on operations: 0.0ms

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

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

const: 0.0ms (0% of total)

backward-pass: 0.0ms (0% of total)

ival-<=: 0.0ms (0% of total)

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

sample1.4s (31.3%)

Results

1.1s	8059×	1	valid
11.0ms	197×	0	valid

Precisions

Click to see histograms. Total time spent on operations: 751.0ms

ival-acos: 364.0ms (48.5% of total)

ival-sub: 180.0ms (24% of total)

backward-pass: 100.0ms (13.3% of total)

ival-<=: 75.0ms (10% of total)

const: 22.0ms (2.9% of total)

ival-and: 10.0ms (1.3% of total)

Bogosity

preprocess26.0ms (0.6%)

Algorithm

2×	egg-herbie

Rules

84×	`fmsub-define`
80×	`fnmsub-define`
80×	`fnmadd-define`
66×	`sum3-define`
54×	`fmm-def`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	15
1	18	13
2	32	13
3	66	13
4	134	13
5	212	13
6	294	13
7	335	13
0	4	4
1	8	4
2	12	4
3	18	4
4	27	4
5	40	4
6	57	4
7	71	4
8	83	4
9	84	4
0	84	4

Stop Event

1×	iter limit
1×	saturated
1×	saturated

Calls

Call 1

Inputs
(acos (- 1 x))

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

Call 2

Inputs
(acos (- 1 x))
(acos (- 1 (neg x)))
(neg (acos (- 1 (neg x))))

Outputs
(acos (- 1 x))
(acos (- 1 (neg x)))
(acos (+ 1 x))
(neg (acos (- 1 (neg x))))
(neg (acos (+ 1 x)))

explain113.0ms (2.5%)

FPErrors

Click to see full error table

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

Results

84.0ms	500×	1	valid
2.0ms	12×	0	valid

Compiler

Compiled 27 to 14 computations (48.1% saved)

Precisions

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

ival-acos: 22.0ms (57.8% of total)

backward-pass: 8.0ms (21% of total)

ival-sub: 7.0ms (18.4% of total)

const: 1.0ms (2.6% of total)

eval0.0ms (0%)

Compiler: Compiled 5 to 4 computations (20% saved)

prune1.0ms (0%)

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	6.6%	(acos.f64 (-.f64 #s(literal 1 binary64) x))

Compiler

Compiled 5 to 4 computations (20% saved)

simplify6.0ms (0.1%)

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

32×	`sum3-define`
24×	`+-lowering-+.f64`
24×	`+-lowering-+.f32`
18×	`--lowering--.f32`
18×	`--lowering--.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	4	9
1	8	9
2	12	9
3	18	9
4	27	9
5	40	9
6	57	9
7	71	9
8	83	9
9	84	9
0	84	9

Stop Event

1×	iter limit
1×	saturated

Calls

Call 1

Inputs
(acos (- 1 x))
(- 1 x)
1
x

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

localize68.0ms (1.5%)

Localize:

Found 2 expressions of interest:

New	Metric	Score	Program
✓	accuracy	100.0%	(-.f64 #s(literal 1 binary64) x)
✓	accuracy	6.6%	(acos.f64 (-.f64 #s(literal 1 binary64) x))

Results

57.0ms	250×	1	valid
0.0ms	6×	0	valid

Compiler

Compiled 11 to 5 computations (54.5% saved)

Precisions

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

ival-acos: 10.0ms (58% of total)

ival-sub: 3.0ms (17.4% of total)

backward-pass: 3.0ms (17.4% of total)

const: 1.0ms (5.8% of total)

series1.0ms (0%)

Counts

2 → 24

Calls

Call 1

Inputs
#<alt (acos (- 1 x))>
#<alt (- 1 x)>

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

Calls

6 calls:

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

rewrite298.0ms (6.6%)

Algorithm

1×	batch-egg-rewrite

Rules

3092×	`-lowering-.f32`
3092×	`-lowering-.f64`
2490×	`/-lowering-/.f32`
2490×	`/-lowering-/.f64`
1698×	`+-lowering-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	4	7
1	26	7
2	175	7
3	1475	7
0	8903	7

Stop Event

1×	iter limit
1×	node limit

Counts

2 → 257

Calls

Call 1

Inputs
(acos (- 1 x))
(- 1 x)

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

simplify18.0ms (0.4%)

Algorithm

1×	egg-herbie

Rules

136×	`fma-lowering-fma.f32`
136×	`fma-lowering-fma.f64`
116×	`fnmadd-define`
112×	`fnmsub-define`
112×	`fmsub-define`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	14	80
1	30	80
2	65	80
3	128	80
4	203	80
5	353	80
6	493	80
7	545	80
0	545	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)
(-.f64 #s(literal 0 binary64) 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)
(-.f64 #s(literal 0 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 (- 1 (/ 1 x))))
(-.f64 #s(literal 1 binary64) x)

eval43.0ms (1%)

Compiler: Compiled 10600 to 1023 computations (90.3% saved)

prune32.0ms (0.7%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	279	2	281
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	279	3	282

Accuracy

9.2%

Counts

282 → 3

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	6.6%	(acos.f64 (-.f64 #s(literal 1 binary64) x))
▶	6.9%	(acos.f64 (-.f64 #s(literal 0 binary64) x))
▶	3.8%	(acos.f64 #s(literal 1 binary64))

Compiler

Compiled 13 to 11 computations (15.4% saved)

simplify4.0ms (0.1%)

Algorithm

1×	egg-herbie

Localize:

Found 3 expressions of interest:

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

Rules

8×	`sum3-define`
8×	`+-lowering-+.f64`
8×	`+-lowering-+.f32`
6×	`--lowering--.f32`
6×	`sub-neg`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	10
1	10	10
2	14	10
3	20	10
4	25	10
5	31	10
6	34	10
0	34	10

Stop Event

1×	iter limit
1×	saturated

Calls

Call 1

Inputs
(acos 1)
1
(acos (- 0 x))
(- 0 x)
0
x

Outputs
(acos 1)
(acos.f64 #s(literal 1 binary64))
1
#s(literal 1 binary64)
(acos (- 0 x))
(acos.f64 (-.f64 #s(literal 0 binary64) x))
(- 0 x)
(-.f64 #s(literal 0 binary64) x)
0
#s(literal 0 binary64)
x

localize22.0ms (0.5%)

Localize:

Found 3 expressions of interest:

New	Metric	Score	Program
✓	accuracy	100.0%	(-.f64 #s(literal 0 binary64) x)
✓	accuracy	100.0%	(acos.f64 (-.f64 #s(literal 0 binary64) x))
✓	accuracy	100.0%	(acos.f64 #s(literal 1 binary64))

Results

15.0ms

256×

valid

Compiler

Compiled 14 to 7 computations (50% saved)

Precisions

Click to see histograms. Total time spent on operations: 6.0ms

ival-acos: 4.0ms (63.9% of total)

ival-sub: 1.0ms (16% of total)

const: 0.0ms (0% of total)

backward-pass: 0.0ms (0% of total)

series0.0ms (0%)

Counts

3 → 24

Calls

Call 1

Inputs
#<alt (acos 1)>
#<alt (acos (- 0 x))>
#<alt (- 0 x)>

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

Calls

6 calls:

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

rewrite272.0ms (6.1%)

Algorithm

1×	batch-egg-rewrite

Rules

3268×	`-lowering-.f32`
3268×	`-lowering-.f64`
1508×	`+-lowering-+.f64`
1508×	`+-lowering-+.f32`
1498×	`/-lowering-/.f32`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	6	7
1	30	7
2	218	7
3	2300	5
0	8979	5

Stop Event

1×	iter limit
1×	node limit

Counts

3 → 227

Calls

Call 1

Inputs
(acos 1)
(acos (- 0 x))
(- 0 x)

Outputs
(acos.f64 #s(literal 1 binary64))
(+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) (-.f64 #s(literal 0 binary64) (asin.f64 #s(literal 1 binary64))))
(+.f64 (-.f64 #s(literal 0 binary64) (asin.f64 #s(literal 1 binary64))) (/.f64 (PI.f64) #s(literal 2 binary64)))
(+.f64 (/.f64 #s(literal 0 binary64) (/.f64 #s(literal 2 binary64) (PI.f64))) (acos.f64 #s(literal 1 binary64)))
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(/.f64 (/.f64 (*.f64 x x) #s(literal -1 binary64)) x)
(pow.f64 x #s(literal 1 binary64))
(pow.f64 (*.f64 x x) #s(literal 1/2 binary64))
(pow.f64 (/.f64 #s(literal 1 binary64) x) #s(literal -1 binary64))
(pow.f64 (pow.f64 x #s(literal 1/2 binary64)) #s(literal 2 binary64))
(pow.f64 (/.f64 (/.f64 #s(literal 1 binary64) x) #s(literal 1 binary64)) #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 x) (/.f64 #s(literal 1 binary64) x))
(.f64 (.f64 x (.f64 x x)) (/.f64 #s(literal 1 binary64) (.f64 x x)))
(.f64 (.f64 x (.f64 x x)) (pow.f64 (/.f64 #s(literal 1 binary64) (.f64 x x)) #s(literal 1 binary64)))
(.f64 (/.f64 #s(literal 1 binary64) (.f64 x x)) (.f64 x (.f64 x x)))
(.f64 (/.f64 #s(literal 1 binary64) x) (.f64 x x))
(.f64 (/.f64 #s(literal 1 binary64) x) (pow.f64 (/.f64 x (.f64 x (*.f64 x x))) #s(literal -1 binary64)))
(*.f64 #s(literal -1 binary64) x)
(*.f64 (pow.f64 x #s(literal 3/2 binary64)) (pow.f64 x #s(literal -1/2 binary64)))
(.f64 (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x x))) (.f64 x (.f64 x (.f64 x x))))
(*.f64 (pow.f64 x #s(literal 1/2 binary64)) (pow.f64 x #s(literal 1/2 binary64)))
(*.f64 (pow.f64 (pow.f64 x #s(literal 3/2 binary64)) #s(literal 1 binary64)) (pow.f64 (pow.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64)))
(*.f64 (pow.f64 (pow.f64 x #s(literal 1/2 binary64)) #s(literal 1 binary64)) (pow.f64 (pow.f64 x #s(literal 1/2 binary64)) #s(literal 1 binary64)))
(.f64 (pow.f64 (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x x))) #s(literal 1 binary64)) (pow.f64 (.f64 x (.f64 x (.f64 x x))) #s(literal 1 binary64)))
(.f64 (pow.f64 (/.f64 (.f64 x x) (.f64 (.f64 x (.f64 x (.f64 x (.f64 x (.f64 x x))))) (.f64 x (.f64 x x)))) #s(literal -1 binary64)) (/.f64 (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x x))) (.f64 x (.f64 x x))))
(.f64 (pow.f64 (/.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x (.f64 x (.f64 x x)))))) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (.f64 x (*.f64 x x))))
(.f64 (pow.f64 (/.f64 x (.f64 x (.f64 x (.f64 x (.f64 x (.f64 x x)))))) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x (*.f64 x x)))))
(.f64 (pow.f64 (/.f64 x (.f64 x (.f64 x (.f64 x x)))) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (*.f64 x x)))

simplify7.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

8×	`sum3-define`
8×	`+-lowering-+.f64`
8×	`+-lowering-+.f32`
6×	`--lowering--.f32`
6×	`sub-neg`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	60
1	9	60
2	10	60
3	12	60
4	18	60
5	22	60
6	28	60
7	31	60
0	31	60

Stop Event

1×	iter limit
1×	saturated

Counts

24 → 24

Calls

Call 1

Inputs
(acos (neg x))
(acos (neg x))
(acos (neg x))
(acos (neg x))
(acos (neg x))
(acos (neg x))
(acos (neg x))
(acos (neg x))
(acos (* -1 x))
(acos (* -1 x))
(acos (* -1 x))
(acos (* -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 (neg x))
(acos.f64 (-.f64 #s(literal 0 binary64) x))
(acos (neg x))
(acos.f64 (-.f64 #s(literal 0 binary64) x))
(acos (neg x))
(acos.f64 (-.f64 #s(literal 0 binary64) x))
(acos (neg x))
(acos.f64 (-.f64 #s(literal 0 binary64) x))
(acos (neg x))
(acos.f64 (-.f64 #s(literal 0 binary64) x))
(acos (neg x))
(acos.f64 (-.f64 #s(literal 0 binary64) x))
(acos (neg x))
(acos.f64 (-.f64 #s(literal 0 binary64) x))
(acos (neg x))
(acos.f64 (-.f64 #s(literal 0 binary64) x))
(acos (* -1 x))
(acos.f64 (-.f64 #s(literal 0 binary64) x))
(acos (* -1 x))
(acos.f64 (-.f64 #s(literal 0 binary64) x))
(acos (* -1 x))
(acos.f64 (-.f64 #s(literal 0 binary64) x))
(acos (* -1 x))
(acos.f64 (-.f64 #s(literal 0 binary64) x))
(* -1 x)
(-.f64 #s(literal 0 binary64) x)
(* -1 x)
(-.f64 #s(literal 0 binary64) x)
(* -1 x)
(-.f64 #s(literal 0 binary64) x)
(* -1 x)
(-.f64 #s(literal 0 binary64) x)
(* -1 x)
(-.f64 #s(literal 0 binary64) x)
(* -1 x)
(-.f64 #s(literal 0 binary64) x)
(* -1 x)
(-.f64 #s(literal 0 binary64) x)
(* -1 x)
(-.f64 #s(literal 0 binary64) x)
(* -1 x)
(-.f64 #s(literal 0 binary64) x)
(* -1 x)
(-.f64 #s(literal 0 binary64) x)
(* -1 x)
(-.f64 #s(literal 0 binary64) x)
(* -1 x)
(-.f64 #s(literal 0 binary64) x)

eval31.0ms (0.7%)

Compiler: Compiled 6568 to 785 computations (88% saved)

prune30.0ms (0.7%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	249	2	251
Fresh	0	0	0
Picked	2	0	2
Done	0	1	1
Total	251	3	254

Accuracy

9.2%

Counts

254 → 3

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	6.9%	(fma.f64 (sqrt.f64 (PI.f64)) (sqrt.f64 (PI.f64)) (neg.f64 (acos.f64 x)))
✓	6.6%	(acos.f64 (-.f64 #s(literal 1 binary64) x))
▶	6.9%	(acos.f64 x)

Compiler

Compiled 17 to 12 computations (29.4% saved)

simplify18.0ms (0.4%)

Algorithm

1×	egg-herbie

Localize:

Found 5 expressions of interest:

New	Metric	Score	Program
✓	cost-diff	0	(acos.f64 x)
✓	cost-diff	0	(PI.f64)
✓	cost-diff	0	(sqrt.f64 (PI.f64))
✓	cost-diff	19264	(fma.f64 (sqrt.f64 (PI.f64)) (sqrt.f64 (PI.f64)) (neg.f64 (acos.f64 x)))
✓	cost-diff	0	(acos.f64 x)

Rules

196×	`fnmadd-define`
146×	`sum3-define`
124×	`fma-define`
124×	`fmsub-define`
120×	`fma-lowering-fma.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	16
1	15	16
2	24	16
3	38	16
4	73	16
5	147	16
6	293	16
7	459	16
8	605	16
9	691	16
10	697	16
0	697	16

Stop Event

1×	iter limit
1×	saturated

Calls

Call 1

Inputs
(acos x)
x
(+ (* (sqrt (PI)) (sqrt (PI))) (neg (acos x)))
(sqrt (PI))
(PI)
(neg (acos x))
(acos x)
x

Outputs
(acos x)
(acos.f64 x)
x
(+ (* (sqrt (PI)) (sqrt (PI))) (neg (acos x)))
(-.f64 (PI.f64) (acos.f64 x))
(sqrt (PI))
(sqrt.f64 (PI.f64))
(PI)
(PI.f64)
(neg (acos x))
(-.f64 #s(literal 0 binary64) (acos.f64 x))
(acos x)
(acos.f64 x)
x

localize33.0ms (0.7%)

Localize:

Found 5 expressions of interest:

New	Metric	Score	Program
✓	accuracy	100.0%	(acos.f64 x)
✓	accuracy	100.0%	(PI.f64)
✓	accuracy	98.4%	(sqrt.f64 (PI.f64))
✓	accuracy	97.5%	(fma.f64 (sqrt.f64 (PI.f64)) (sqrt.f64 (PI.f64)) (neg.f64 (acos.f64 x)))
✓	accuracy	100.0%	(acos.f64 x)

Results

21.0ms

256×

valid

Compiler

Compiled 22 to 7 computations (68.2% saved)

Precisions

Click to see histograms. Total time spent on operations: 14.0ms

compiled-spec: 4.0ms (28% of total)

ival-acos: 3.0ms (21% of total)

ival-mult: 2.0ms (14% of total)

ival-sqrt: 2.0ms (14% of total)

ival-pi: 1.0ms (7% of total)

ival-add: 1.0ms (7% of total)

ival-neg: 1.0ms (7% of total)

const: 0.0ms (0% of total)

backward-pass: 0.0ms (0% of total)

series1.0ms (0%)

Counts

4 → 24

Calls

Call 1

Inputs
#<alt (acos x)>
#<alt (+ (* (sqrt (PI)) (sqrt (PI))) (neg (acos x)))>
#<alt (sqrt (PI))>
#<alt (PI)>

Outputs
#<alt (acos x)>
#<alt (acos x)>
#<alt (acos x)>
#<alt (acos x)>
#<alt (acos x)>
#<alt (acos x)>
#<alt (acos x)>
#<alt (acos x)>
#<alt (acos x)>
#<alt (acos x)>
#<alt (acos x)>
#<alt (acos x)>
#<alt (- (PI) (acos x))>
#<alt (- (PI) (acos x))>
#<alt (- (PI) (acos x))>
#<alt (- (PI) (acos x))>
#<alt (- (PI) (acos x))>
#<alt (- (PI) (acos x))>
#<alt (- (PI) (acos x))>
#<alt (- (PI) (acos x))>
#<alt (- (PI) (acos x))>
#<alt (- (PI) (acos x))>
#<alt (- (PI) (acos x))>
#<alt (- (PI) (acos x))>

Calls

6 calls:

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

rewrite245.0ms (5.5%)

Algorithm

1×	batch-egg-rewrite

Rules

2930×	`-lowering-.f32`
2930×	`-lowering-.f64`
1482×	`pow-lowering-pow.f64`
1482×	`pow-lowering-pow.f32`
1344×	`fnmadd-define`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	9
1	52	9
2	402	9
3	4855	9
0	9364	9

Stop Event

1×	iter limit
1×	node limit

Counts

4 → 321

Calls

Call 1

Inputs
(acos x)
(+ (* (sqrt (PI)) (sqrt (PI))) (neg (acos x)))
(sqrt (PI))
(PI)

Outputs
(acos.f64 x)
(+.f64 (acos.f64 x) #s(literal 0 binary64))
(+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) (-.f64 #s(literal 0 binary64) (asin.f64 x)))
(+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) (*.f64 #s(literal 1 binary64) (-.f64 #s(literal 0 binary64) (asin.f64 x))))
(+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) (*.f64 (-.f64 #s(literal 0 binary64) (asin.f64 x)) #s(literal 1 binary64)))
(+.f64 (asin.f64 x) (-.f64 #s(literal 0 binary64) (/.f64 (PI.f64) #s(literal 2 binary64))))
(+.f64 #s(literal 0 binary64) (acos.f64 x))
(+.f64 (-.f64 #s(literal 0 binary64) (asin.f64 x)) (/.f64 (PI.f64) #s(literal 2 binary64)))
(+.f64 (-.f64 #s(literal 0 binary64) (/.f64 (PI.f64) #s(literal 2 binary64))) (asin.f64 x))
(+.f64 (-.f64 #s(literal 0 binary64) (/.f64 (PI.f64) #s(literal 2 binary64))) (neg.f64 (-.f64 #s(literal 0 binary64) (asin.f64 x))))
(+.f64 (+.f64 #s(literal 0 binary64) (/.f64 (PI.f64) #s(literal 2 binary64))) (-.f64 #s(literal 0 binary64) (asin.f64 x)))
(+.f64 (.f64 #s(literal -1 binary64) (/.f64 (PI.f64) #s(literal 2 binary64))) (.f64 #s(literal -1 binary64) (-.f64 #s(literal 0 binary64) (asin.f64 x))))
(+.f64 (neg.f64 (-.f64 #s(literal 0 binary64) (/.f64 (PI.f64) #s(literal 2 binary64)))) (-.f64 #s(literal 0 binary64) (asin.f64 x)))
(+.f64 (.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) #s(literal -1 binary64)) (.f64 (-.f64 #s(literal 0 binary64) (asin.f64 x)) #s(literal -1 binary64)))
(+.f64 (-.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) (/.f64 (PI.f64) #s(literal 2 binary64))) (acos.f64 x))
(-.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) (asin.f64 x))
(-.f64 #s(literal 0 binary64) (acos.f64 x))
(-.f64 (-.f64 #s(literal 0 binary64) (/.f64 (PI.f64) #s(literal 2 binary64))) (-.f64 #s(literal 0 binary64) (asin.f64 x)))
(-.f64 (/.f64 #s(literal 0 binary64) (pow.f64 (acos.f64 x) #s(literal 2 binary64))) (acos.f64 x))
(-.f64 (/.f64 #s(literal 0 binary64) (acos.f64 x)) (acos.f64 x))
(-.f64 (/.f64 (/.f64 (.f64 (PI.f64) (.f64 (PI.f64) (PI.f64))) #s(literal 8 binary64)) (+.f64 (/.f64 (.f64 (PI.f64) (PI.f64)) #s(literal 4 binary64)) (.f64 (asin.f64 x) (+.f64 (acos.f64 x) (PI.f64))))) (/.f64 (pow.f64 (asin.f64 x) #s(literal 3 binary64)) (+.f64 (/.f64 (.f64 (PI.f64) (PI.f64)) #s(literal 4 binary64)) (.f64 (asin.f64 x) (+.f64 (acos.f64 x) (PI.f64))))))
(-.f64 (/.f64 (/.f64 (*.f64 (PI.f64) (PI.f64)) #s(literal 4 binary64)) (+.f64 (acos.f64 x) (PI.f64))) (/.f64 (pow.f64 (asin.f64 x) #s(literal 2 binary64)) (+.f64 (acos.f64 x) (PI.f64))))
(-.f64 (+.f64 #s(literal 0 binary64) (/.f64 (PI.f64) #s(literal 2 binary64))) (asin.f64 x))
(-.f64 (+.f64 (-.f64 #s(literal 0 binary64) (/.f64 (PI.f64) #s(literal 2 binary64))) (/.f64 (PI.f64) #s(literal 2 binary64))) (acos.f64 x))
(fma.f64 (PI.f64) #s(literal 1/2 binary64) (-.f64 #s(literal 0 binary64) (asin.f64 x)))
(fma.f64 (sqrt.f64 (PI.f64)) (/.f64 (sqrt.f64 (PI.f64)) #s(literal 2 binary64)) (-.f64 #s(literal 0 binary64) (asin.f64 x)))
(fma.f64 #s(literal 1 binary64) (/.f64 (PI.f64) #s(literal 2 binary64)) (-.f64 #s(literal 0 binary64) (asin.f64 x)))
(fma.f64 (pow.f64 (PI.f64) #s(literal 2/3 binary64)) (/.f64 (cbrt.f64 (PI.f64)) #s(literal 2 binary64)) (-.f64 #s(literal 0 binary64) (asin.f64 x)))
(neg.f64 (acos.f64 x))
(/.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (acos.f64 x) #s(literal 2 binary64)) (pow.f64 (acos.f64 x) #s(literal 3 binary64))))
(/.f64 #s(literal 1 binary64) (/.f64 (acos.f64 x) (pow.f64 (acos.f64 x) #s(literal 2 binary64))))
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 (/.f64 (.f64 (PI.f64) (PI.f64)) #s(literal 4 binary64)) (.f64 (asin.f64 x) (+.f64 (acos.f64 x) (PI.f64)))) (-.f64 (/.f64 (.f64 (PI.f64) (.f64 (PI.f64) (PI.f64))) #s(literal 8 binary64)) (pow.f64 (asin.f64 x) #s(literal 3 binary64)))))
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 (acos.f64 x) (PI.f64)) (*.f64 (+.f64 (acos.f64 x) (PI.f64)) (acos.f64 x))))
(/.f64 (pow.f64 (acos.f64 x) #s(literal 3 binary64)) (pow.f64 (acos.f64 x) #s(literal 2 binary64)))
(/.f64 (pow.f64 (acos.f64 x) #s(literal 3 binary64)) (+.f64 #s(literal 0 binary64) (-.f64 (pow.f64 (acos.f64 x) #s(literal 2 binary64)) #s(literal 0 binary64))))
(/.f64 (pow.f64 (acos.f64 x) #s(literal 2 binary64)) (acos.f64 x))
(/.f64 (-.f64 (/.f64 (.f64 (PI.f64) (.f64 (PI.f64) (PI.f64))) #s(literal 8 binary64)) (pow.f64 (asin.f64 x) #s(literal 3 binary64))) (+.f64 (/.f64 (.f64 (PI.f64) (PI.f64)) #s(literal 4 binary64)) (.f64 (asin.f64 x) (+.f64 (acos.f64 x) (PI.f64)))))
(/.f64 (-.f64 (/.f64 (.f64 (PI.f64) (.f64 (PI.f64) (PI.f64))) #s(literal 8 binary64)) (pow.f64 (asin.f64 x) #s(literal 3 binary64))) (neg.f64 (+.f64 (/.f64 (.f64 (PI.f64) (PI.f64)) #s(literal 4 binary64)) (.f64 (asin.f64 x) (+.f64 (acos.f64 x) (PI.f64))))))
(/.f64 (*.f64 (+.f64 (acos.f64 x) (PI.f64)) (acos.f64 x)) (+.f64 (acos.f64 x) (PI.f64)))
(/.f64 (*.f64 (+.f64 (acos.f64 x) (PI.f64)) (acos.f64 x)) (-.f64 (acos.f64 x) (PI.f64)))
(/.f64 (neg.f64 (-.f64 (/.f64 (.f64 (PI.f64) (.f64 (PI.f64) (PI.f64))) #s(literal 8 binary64)) (pow.f64 (asin.f64 x) #s(literal 3 binary64)))) (+.f64 (/.f64 (.f64 (PI.f64) (PI.f64)) #s(literal 4 binary64)) (.f64 (asin.f64 x) (+.f64 (acos.f64 x) (PI.f64)))))
(/.f64 (neg.f64 (-.f64 (/.f64 (.f64 (PI.f64) (.f64 (PI.f64) (PI.f64))) #s(literal 8 binary64)) (pow.f64 (asin.f64 x) #s(literal 3 binary64)))) (neg.f64 (+.f64 (/.f64 (.f64 (PI.f64) (PI.f64)) #s(literal 4 binary64)) (.f64 (asin.f64 x) (+.f64 (acos.f64 x) (PI.f64))))))
(/.f64 (neg.f64 (*.f64 (+.f64 (acos.f64 x) (PI.f64)) (acos.f64 x))) (+.f64 (acos.f64 x) (PI.f64)))
(/.f64 (neg.f64 (*.f64 (+.f64 (acos.f64 x) (PI.f64)) (acos.f64 x))) (-.f64 (acos.f64 x) (PI.f64)))
(/.f64 (+.f64 (/.f64 (.f64 (PI.f64) (.f64 (PI.f64) (PI.f64))) #s(literal 8 binary64)) (pow.f64 (-.f64 #s(literal 0 binary64) (asin.f64 x)) #s(literal 3 binary64))) (+.f64 (/.f64 (.f64 (PI.f64) (PI.f64)) #s(literal 4 binary64)) (-.f64 (pow.f64 (-.f64 #s(literal 0 binary64) (asin.f64 x)) #s(literal 2 binary64)) (.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) (-.f64 #s(literal 0 binary64) (asin.f64 x))))))
(/.f64 (+.f64 (pow.f64 (-.f64 #s(literal 0 binary64) (/.f64 (PI.f64) #s(literal 2 binary64))) #s(literal 3 binary64)) (pow.f64 (asin.f64 x) #s(literal 3 binary64))) (+.f64 (.f64 (-.f64 #s(literal 0 binary64) (/.f64 (PI.f64) #s(literal 2 binary64))) (-.f64 #s(literal 0 binary64) (/.f64 (PI.f64) #s(literal 2 binary64)))) (-.f64 (pow.f64 (asin.f64 x) #s(literal 2 binary64)) (.f64 (-.f64 #s(literal 0 binary64) (/.f64 (PI.f64) #s(literal 2 binary64))) (asin.f64 x)))))
(/.f64 (-.f64 (/.f64 (*.f64 (PI.f64) (PI.f64)) #s(literal 4 binary64)) (pow.f64 (-.f64 #s(literal 0 binary64) (asin.f64 x)) #s(literal 2 binary64))) (+.f64 (acos.f64 x) (PI.f64)))
(/.f64 (-.f64 (*.f64 (-.f64 #s(literal 0 binary64) (/.f64 (PI.f64) #s(literal 2 binary64))) (-.f64 #s(literal 0 binary64) (/.f64 (PI.f64) #s(literal 2 binary64)))) (pow.f64 (asin.f64 x) #s(literal 2 binary64))) (-.f64 (-.f64 #s(literal 0 binary64) (/.f64 (PI.f64) #s(literal 2 binary64))) (asin.f64 x)))
(/.f64 (.f64 #s(literal 1 binary64) (-.f64 (/.f64 (.f64 (PI.f64) (.f64 (PI.f64) (PI.f64))) #s(literal 8 binary64)) (pow.f64 (asin.f64 x) #s(literal 3 binary64)))) (+.f64 (/.f64 (.f64 (PI.f64) (PI.f64)) #s(literal 4 binary64)) (*.f64 (asin.f64 x) (+.f64 (acos.f64 x) (PI.f64)))))
(/.f64 (.f64 #s(literal 1 binary64) (.f64 (+.f64 (acos.f64 x) (PI.f64)) (acos.f64 x))) (+.f64 (acos.f64 x) (PI.f64)))
(/.f64 (.f64 #s(literal -1 binary64) (-.f64 (/.f64 (.f64 (PI.f64) (.f64 (PI.f64) (PI.f64))) #s(literal 8 binary64)) (pow.f64 (asin.f64 x) #s(literal 3 binary64)))) (+.f64 (/.f64 (.f64 (PI.f64) (PI.f64)) #s(literal 4 binary64)) (*.f64 (asin.f64 x) (+.f64 (acos.f64 x) (PI.f64)))))
(/.f64 (.f64 #s(literal -1 binary64) (.f64 (+.f64 (acos.f64 x) (PI.f64)) (acos.f64 x))) (+.f64 (acos.f64 x) (PI.f64)))
(/.f64 (.f64 (-.f64 (/.f64 (.f64 (PI.f64) (.f64 (PI.f64) (PI.f64))) #s(literal 8 binary64)) (pow.f64 (asin.f64 x) #s(literal 3 binary64))) #s(literal -1 binary64)) (+.f64 (/.f64 (.f64 (PI.f64) (PI.f64)) #s(literal 4 binary64)) (*.f64 (asin.f64 x) (+.f64 (acos.f64 x) (PI.f64)))))
(/.f64 (.f64 (.f64 (+.f64 (acos.f64 x) (PI.f64)) (acos.f64 x)) #s(literal -1 binary64)) (+.f64 (acos.f64 x) (PI.f64)))
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(*.f64 (pow.f64 (PI.f64) #s(literal 2/3 binary64)) (log.f64 (exp.f64 (cbrt.f64 (PI.f64)))))
(*.f64 (pow.f64 (PI.f64) #s(literal 1/4 binary64)) (pow.f64 (PI.f64) #s(literal 3/4 binary64)))
(.f64 (pow.f64 (PI.f64) #s(literal 1/4 binary64)) (.f64 (pow.f64 (PI.f64) #s(literal 1/4 binary64)) (sqrt.f64 (PI.f64))))
(*.f64 (pow.f64 (PI.f64) #s(literal 1/4 binary64)) (log.f64 (exp.f64 (pow.f64 (PI.f64) #s(literal 3/4 binary64)))))
(.f64 (pow.f64 (PI.f64) #s(literal 1/6 binary64)) (.f64 (pow.f64 (PI.f64) #s(literal 1/6 binary64)) (pow.f64 (PI.f64) #s(literal 2/3 binary64))))
(.f64 (pow.f64 (PI.f64) #s(literal 1/6 binary64)) (log.f64 (exp.f64 (.f64 (sqrt.f64 (PI.f64)) (cbrt.f64 (PI.f64))))))
(.f64 (pow.f64 (PI.f64) #s(literal 2/9 binary64)) (.f64 (pow.f64 (PI.f64) #s(literal 1/9 binary64)) (pow.f64 (PI.f64) #s(literal 2/3 binary64))))
(.f64 (pow.f64 (PI.f64) #s(literal 1/9 binary64)) (log.f64 (exp.f64 (.f64 (pow.f64 (PI.f64) #s(literal 2/3 binary64)) (pow.f64 (PI.f64) #s(literal 2/9 binary64))))))
(*.f64 (pow.f64 (PI.f64) #s(literal 3/4 binary64)) (pow.f64 (PI.f64) #s(literal 1/4 binary64)))
(.f64 (.f64 (sqrt.f64 (PI.f64)) (cbrt.f64 (PI.f64))) (pow.f64 (PI.f64) #s(literal 1/6 binary64)))
(.f64 (exp.f64 (.f64 #s(literal 2/3 binary64) (log.f64 (PI.f64)))) (exp.f64 (*.f64 #s(literal 1/3 binary64) (log.f64 (PI.f64)))))
(*.f64 (pow.f64 (PI.f64) #s(literal 5/6 binary64)) (pow.f64 (PI.f64) #s(literal 1/6 binary64)))
(*.f64 (pow.f64 (pow.f64 (PI.f64) #s(literal 4/3 binary64)) #s(literal 2/3 binary64)) (pow.f64 (PI.f64) #s(literal 1/9 binary64)))
(*.f64 (pow.f64 (cbrt.f64 (PI.f64)) #s(literal 5/2 binary64)) (pow.f64 (PI.f64) #s(literal 1/6 binary64)))
(*.f64 (fabs.f64 (pow.f64 (PI.f64) #s(literal 2/3 binary64))) (cbrt.f64 (PI.f64)))
(.f64 (.f64 (pow.f64 (PI.f64) #s(literal 2/3 binary64)) (pow.f64 (PI.f64) #s(literal 1/6 binary64))) (pow.f64 (PI.f64) #s(literal 1/6 binary64)))
(.f64 (.f64 (pow.f64 (PI.f64) #s(literal 2/3 binary64)) (pow.f64 (PI.f64) #s(literal 2/9 binary64))) (pow.f64 (PI.f64) #s(literal 1/9 binary64)))
(.f64 (pow.f64 (E.f64) (.f64 #s(literal 2/3 binary64) (log.f64 (PI.f64)))) (pow.f64 (E.f64) (*.f64 #s(literal 1/3 binary64) (log.f64 (PI.f64)))))
(.f64 (pow.f64 (E.f64) (.f64 #s(literal 1/3 binary64) (log.f64 (PI.f64)))) (pow.f64 (E.f64) (*.f64 #s(literal 2/3 binary64) (log.f64 (PI.f64)))))
(.f64 (pow.f64 (E.f64) (.f64 (.f64 #s(literal 2/3 binary64) (log.f64 (PI.f64))) #s(literal 1 binary64))) (pow.f64 (E.f64) (.f64 (*.f64 #s(literal 1/3 binary64) (log.f64 (PI.f64))) #s(literal 1 binary64))))
(.f64 (pow.f64 (E.f64) (.f64 (.f64 #s(literal 1/2 binary64) (log.f64 (PI.f64))) #s(literal 1 binary64))) (pow.f64 (E.f64) (.f64 (*.f64 #s(literal 1/2 binary64) (log.f64 (PI.f64))) #s(literal 1 binary64))))
(.f64 (pow.f64 (exp.f64 #s(literal 2 binary64)) (.f64 #s(literal 1/3 binary64) (log.f64 (PI.f64)))) (pow.f64 (exp.f64 #s(literal 2 binary64)) (*.f64 #s(literal 1/6 binary64) (log.f64 (PI.f64)))))
(.f64 (pow.f64 (exp.f64 #s(literal 2 binary64)) (.f64 #s(literal 1/4 binary64) (log.f64 (PI.f64)))) (pow.f64 (exp.f64 #s(literal 2 binary64)) (*.f64 #s(literal 1/4 binary64) (log.f64 (PI.f64)))))

simplify18.0ms (0.4%)

Algorithm

1×	egg-herbie

Rules

124×	`fnmadd-define`
122×	`sum3-define`
80×	`fma-lowering-fma.f32`
80×	`fnmsub-define`
80×	`fmsub-define`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	4	72
1	6	72
2	11	72
3	18	72
4	28	72
5	60	72
6	119	72
7	208	72
8	291	72
9	397	72
10	475	72
11	481	72
0	481	72

Stop Event

1×	iter limit
1×	saturated

Counts

24 → 24

Calls

Call 1

Inputs
(acos x)
(acos x)
(acos x)
(acos x)
(acos x)
(acos x)
(acos x)
(acos x)
(acos x)
(acos x)
(acos x)
(acos x)
(- (PI) (acos x))
(- (PI) (acos x))
(- (PI) (acos x))
(- (PI) (acos x))
(- (PI) (acos x))
(- (PI) (acos x))
(- (PI) (acos x))
(- (PI) (acos x))
(- (PI) (acos x))
(- (PI) (acos x))
(- (PI) (acos x))
(- (PI) (acos x))

Outputs
(acos x)
(acos.f64 x)
(acos x)
(acos.f64 x)
(acos x)
(acos.f64 x)
(acos x)
(acos.f64 x)
(acos x)
(acos.f64 x)
(acos x)
(acos.f64 x)
(acos x)
(acos.f64 x)
(acos x)
(acos.f64 x)
(acos x)
(acos.f64 x)
(acos x)
(acos.f64 x)
(acos x)
(acos.f64 x)
(acos x)
(acos.f64 x)
(- (PI) (acos x))
(-.f64 (PI.f64) (acos.f64 x))
(- (PI) (acos x))
(-.f64 (PI.f64) (acos.f64 x))
(- (PI) (acos x))
(-.f64 (PI.f64) (acos.f64 x))
(- (PI) (acos x))
(-.f64 (PI.f64) (acos.f64 x))
(- (PI) (acos x))
(-.f64 (PI.f64) (acos.f64 x))
(- (PI) (acos x))
(-.f64 (PI.f64) (acos.f64 x))
(- (PI) (acos x))
(-.f64 (PI.f64) (acos.f64 x))
(- (PI) (acos x))
(-.f64 (PI.f64) (acos.f64 x))
(- (PI) (acos x))
(-.f64 (PI.f64) (acos.f64 x))
(- (PI) (acos x))
(-.f64 (PI.f64) (acos.f64 x))
(- (PI) (acos x))
(-.f64 (PI.f64) (acos.f64 x))
(- (PI) (acos x))
(-.f64 (PI.f64) (acos.f64 x))

eval75.0ms (1.7%)

Compiler: Compiled 8869 to 1264 computations (85.7% saved)

prune63.0ms (1.4%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	584	1	585
Fresh	0	0	0
Picked	1	1	2
Done	0	1	1
Total	585	3	588

Accuracy

9.3%

Counts

588 → 3

Alt Table

Click to see full alt table

Status

Accuracy

Program

▶

7.0%

(/.f64 (-.f64 (/.f64 (*.f64 (PI.f64) (PI.f64)) #s(literal 4 binary64)) (pow.f64 (-.f64 #s(literal 0 binary64) (asin.f64 x)) #s(literal 2 binary64))) (+.f64 (acos.f64 x) (PI.f64)))

✓

6.6%

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

✓

6.9%

(acos.f64 x)

Compiler

Compiled 26 to 20 computations (23.1% saved)

simplify135.0ms (3%)

Algorithm

1×	egg-herbie

Localize:

Found 4 expressions of interest:

New	Metric	Program
✓	cost-diff	(*.f64 (PI.f64) (PI.f64))
✓	cost-diff	(/.f64 (*.f64 (PI.f64) (PI.f64)) #s(literal 4 binary64))
✓	cost-diff	(-.f64 (/.f64 (*.f64 (PI.f64) (PI.f64)) #s(literal 4 binary64)) (pow.f64 (-.f64 #s(literal 0 binary64) (asin.f64 x)) #s(literal 2 binary64)))
✓	cost-diff	(/.f64 (-.f64 (/.f64 (*.f64 (PI.f64) (PI.f64)) #s(literal 4 binary64)) (pow.f64 (-.f64 #s(literal 0 binary64) (asin.f64 x)) #s(literal 2 binary64))) (+.f64 (acos.f64 x) (PI.f64)))

Rules

2356×	`fnmadd-define`
1526×	`fma-define`
1444×	`fnmsub-define`
1436×	`fmsub-define`
1146×	`fma-lowering-fma.f32`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	14	56
1	26	54
2	58	54
3	160	54
4	375	54
5	801	54
6	2022	54
7	3308	54
8	5258	54
9	6592	54
10	7530	54
11	7608	54
12	7628	54
0	7628	54

Stop Event

1×	iter limit
1×	saturated

Calls

Call 1

Inputs
(/ (- (/ (* (PI) (PI)) 4) (pow (- 0 (asin x)) 2)) (+ (acos x) (PI)))
(- (/ (* (PI) (PI)) 4) (pow (- 0 (asin x)) 2))
(/ (* (PI) (PI)) 4)
(* (PI) (PI))
(PI)
4
(pow (- 0 (asin x)) 2)
(- 0 (asin x))
0
(asin x)
x
2
(+ (acos x) (PI))
(acos x)

Outputs
(/ (- (/ (* (PI) (PI)) 4) (pow (- 0 (asin x)) 2)) (+ (acos x) (PI)))
(/.f64 (-.f64 (/.f64 (*.f64 (PI.f64) (PI.f64)) #s(literal 4 binary64)) (pow.f64 (-.f64 #s(literal 0 binary64) (asin.f64 x)) #s(literal 2 binary64))) (+.f64 (PI.f64) (acos.f64 x)))
(- (/ (* (PI) (PI)) 4) (pow (- 0 (asin x)) 2))
(-.f64 (/.f64 (*.f64 (PI.f64) (PI.f64)) #s(literal 4 binary64)) (pow.f64 (-.f64 #s(literal 0 binary64) (asin.f64 x)) #s(literal 2 binary64)))
(/ (* (PI) (PI)) 4)
(/.f64 (*.f64 (PI.f64) (PI.f64)) #s(literal 4 binary64))
(* (PI) (PI))
(*.f64 (PI.f64) (PI.f64))
(PI)
(PI.f64)
4
#s(literal 4 binary64)
(pow (- 0 (asin x)) 2)
(pow.f64 (-.f64 #s(literal 0 binary64) (asin.f64 x)) #s(literal 2 binary64))
(- 0 (asin x))
(-.f64 #s(literal 0 binary64) (asin.f64 x))
0
#s(literal 0 binary64)
(asin x)
(asin.f64 x)
x
2
#s(literal 2 binary64)
(+ (acos x) (PI))
(+.f64 (PI.f64) (acos.f64 x))
(acos x)
(acos.f64 x)

localize58.0ms (1.3%)

Localize:

Found 4 expressions of interest:

New	Metric	Score	Program
✓	accuracy	100.0%	(-.f64 (/.f64 (*.f64 (PI.f64) (PI.f64)) #s(literal 4 binary64)) (pow.f64 (-.f64 #s(literal 0 binary64) (asin.f64 x)) #s(literal 2 binary64)))
✓	accuracy	100.0%	(pow.f64 (-.f64 #s(literal 0 binary64) (asin.f64 x)) #s(literal 2 binary64))
✓	accuracy	100.0%	(+.f64 (acos.f64 x) (PI.f64))
✓	accuracy	98.5%	(/.f64 (-.f64 (/.f64 (*.f64 (PI.f64) (PI.f64)) #s(literal 4 binary64)) (pow.f64 (-.f64 #s(literal 0 binary64) (asin.f64 x)) #s(literal 2 binary64))) (+.f64 (acos.f64 x) (PI.f64)))

Results

36.0ms

256×

valid

Compiler

Compiled 62 to 15 computations (75.8% saved)

Precisions

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

ival-div: 3.0ms (16.6% of total)

ival-pow: 3.0ms (16.6% of total)

ival-mult: 2.0ms (11% of total)

ival-acos: 2.0ms (11% of total)

ival-asin: 2.0ms (11% of total)

ival-sub: 2.0ms (11% of total)

ival-pi: 1.0ms (5.5% of total)

ival-add: 1.0ms (5.5% of total)

const: 1.0ms (5.5% of total)

backward-pass: 0.0ms (0% of total)

series4.0ms (0.1%)

Counts

6 → 48

Calls

Call 1

Inputs
#<alt (/ (- (/ (* (PI) (PI)) 4) (pow (- 0 (asin x)) 2)) (+ (acos x) (PI)))>
#<alt (- (/ (* (PI) (PI)) 4) (pow (- 0 (asin x)) 2))>
#<alt (/ (* (PI) (PI)) 4)>
#<alt (* (PI) (PI))>
#<alt (+ (acos x) (PI))>
#<alt (pow (- 0 (asin x)) 2)>

Outputs
#<alt (/ (- (* 1/4 (pow (PI) 2)) (pow (asin x) 2)) (+ (PI) (acos x)))>
#<alt (/ (- (* 1/4 (pow (PI) 2)) (pow (asin x) 2)) (+ (PI) (acos x)))>
#<alt (/ (- (* 1/4 (pow (PI) 2)) (pow (asin x) 2)) (+ (PI) (acos x)))>
#<alt (/ (- (* 1/4 (pow (PI) 2)) (pow (asin x) 2)) (+ (PI) (acos x)))>
#<alt (/ (- (* 1/4 (pow (PI) 2)) (pow (asin x) 2)) (+ (PI) (acos x)))>
#<alt (/ (- (* 1/4 (pow (PI) 2)) (pow (asin x) 2)) (+ (PI) (acos x)))>
#<alt (/ (- (* 1/4 (pow (PI) 2)) (pow (asin x) 2)) (+ (PI) (acos x)))>
#<alt (/ (- (* 1/4 (pow (PI) 2)) (pow (asin x) 2)) (+ (PI) (acos x)))>
#<alt (/ (- (* 1/4 (pow (PI) 2)) (pow (asin x) 2)) (+ (PI) (acos x)))>
#<alt (/ (- (* 1/4 (pow (PI) 2)) (pow (asin x) 2)) (+ (PI) (acos x)))>
#<alt (/ (- (* 1/4 (pow (PI) 2)) (pow (asin x) 2)) (+ (PI) (acos x)))>
#<alt (/ (- (* 1/4 (pow (PI) 2)) (pow (asin x) 2)) (+ (PI) (acos x)))>
#<alt (- (* 1/4 (pow (PI) 2)) (pow (asin x) 2))>
#<alt (- (* 1/4 (pow (PI) 2)) (pow (asin x) 2))>
#<alt (- (* 1/4 (pow (PI) 2)) (pow (asin x) 2))>
#<alt (- (* 1/4 (pow (PI) 2)) (pow (asin x) 2))>
#<alt (- (* 1/4 (pow (PI) 2)) (pow (asin x) 2))>
#<alt (- (* 1/4 (pow (PI) 2)) (pow (asin x) 2))>
#<alt (- (* 1/4 (pow (PI) 2)) (pow (asin x) 2))>
#<alt (- (* 1/4 (pow (PI) 2)) (pow (asin x) 2))>
#<alt (- (* 1/4 (pow (PI) 2)) (pow (asin x) 2))>
#<alt (- (* 1/4 (pow (PI) 2)) (pow (asin x) 2))>
#<alt (- (* 1/4 (pow (PI) 2)) (pow (asin x) 2))>
#<alt (- (* 1/4 (pow (PI) 2)) (pow (asin x) 2))>
#<alt (+ (PI) (acos x))>
#<alt (+ (PI) (acos x))>
#<alt (+ (PI) (acos x))>
#<alt (+ (PI) (acos x))>
#<alt (+ (PI) (acos x))>
#<alt (+ (PI) (acos x))>
#<alt (+ (PI) (acos x))>
#<alt (+ (PI) (acos x))>
#<alt (+ (PI) (acos x))>
#<alt (+ (PI) (acos x))>
#<alt (+ (PI) (acos x))>
#<alt (+ (PI) (acos x))>
#<alt (pow (asin x) 2)>
#<alt (pow (asin x) 2)>
#<alt (pow (asin x) 2)>
#<alt (pow (asin x) 2)>
#<alt (pow (asin x) 2)>
#<alt (pow (asin x) 2)>
#<alt (pow (asin x) 2)>
#<alt (pow (asin x) 2)>
#<alt (pow (asin x) 2)>
#<alt (pow (asin x) 2)>
#<alt (pow (asin x) 2)>
#<alt (pow (asin x) 2)>

Calls

12 calls:

Time	Variable		Point	Expression
2.0ms	x	@	0	(/ (- (/ (* (PI) (PI)) 4) (pow (- 0 (asin x)) 2)) (+ (acos x) (PI)))
1.0ms	x	@	inf	(/ (- (/ (* (PI) (PI)) 4) (pow (- 0 (asin x)) 2)) (+ (acos x) (PI)))
1.0ms	x	@	-inf	(/ (- (/ (* (PI) (PI)) 4) (pow (- 0 (asin x)) 2)) (+ (acos x) (PI)))
0.0ms	x	@	0	(- (/ (* (PI) (PI)) 4) (pow (- 0 (asin x)) 2))
0.0ms	x	@	inf	(- (/ (* (PI) (PI)) 4) (pow (- 0 (asin x)) 2))

rewrite277.0ms (6.2%)

Algorithm

1×	batch-egg-rewrite

Rules

2934×	`-lowering-.f32`
2934×	`-lowering-.f64`
2852×	`/-lowering-/.f32`
2852×	`/-lowering-/.f64`
1334×	`+-lowering-+.f64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	14	44
1	106	39
2	970	39
0	8973	39

Stop Event

1×	iter limit
1×	node limit

Counts

6 → 423

Calls

Call 1

Inputs
(/ (- (/ (* (PI) (PI)) 4) (pow (- 0 (asin x)) 2)) (+ (acos x) (PI)))
(- (/ (* (PI) (PI)) 4) (pow (- 0 (asin x)) 2))
(/ (* (PI) (PI)) 4)
(* (PI) (PI))
(+ (acos x) (PI))
(pow (- 0 (asin x)) 2)

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

simplify138.0ms (3.1%)

Algorithm

1×	egg-herbie

Rules

2458×	`fnmadd-define`
2016×	`fma-define`
1286×	`fmsub-define`
1270×	`fnmsub-define`
1160×	`sum3-define`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	372
1	23	372
2	46	372
3	91	372
4	176	372
5	320	372
6	627	372
7	1262	372
8	2904	372
9	5453	372
10	7305	372
11	7432	372
12	7800	372
13	7816	372
0	7816	372

Stop Event

1×	iter limit
1×	saturated

Counts

48 → 48

Calls

Call 1

Inputs
(/ (- (* 1/4 (pow (PI) 2)) (pow (asin x) 2)) (+ (PI) (acos x)))
(/ (- (* 1/4 (pow (PI) 2)) (pow (asin x) 2)) (+ (PI) (acos x)))
(/ (- (* 1/4 (pow (PI) 2)) (pow (asin x) 2)) (+ (PI) (acos x)))
(/ (- (* 1/4 (pow (PI) 2)) (pow (asin x) 2)) (+ (PI) (acos x)))
(/ (- (* 1/4 (pow (PI) 2)) (pow (asin x) 2)) (+ (PI) (acos x)))
(/ (- (* 1/4 (pow (PI) 2)) (pow (asin x) 2)) (+ (PI) (acos x)))
(/ (- (* 1/4 (pow (PI) 2)) (pow (asin x) 2)) (+ (PI) (acos x)))
(/ (- (* 1/4 (pow (PI) 2)) (pow (asin x) 2)) (+ (PI) (acos x)))
(/ (- (* 1/4 (pow (PI) 2)) (pow (asin x) 2)) (+ (PI) (acos x)))
(/ (- (* 1/4 (pow (PI) 2)) (pow (asin x) 2)) (+ (PI) (acos x)))
(/ (- (* 1/4 (pow (PI) 2)) (pow (asin x) 2)) (+ (PI) (acos x)))
(/ (- (* 1/4 (pow (PI) 2)) (pow (asin x) 2)) (+ (PI) (acos x)))
(- (* 1/4 (pow (PI) 2)) (pow (asin x) 2))
(- (* 1/4 (pow (PI) 2)) (pow (asin x) 2))
(- (* 1/4 (pow (PI) 2)) (pow (asin x) 2))
(- (* 1/4 (pow (PI) 2)) (pow (asin x) 2))
(- (* 1/4 (pow (PI) 2)) (pow (asin x) 2))
(- (* 1/4 (pow (PI) 2)) (pow (asin x) 2))
(- (* 1/4 (pow (PI) 2)) (pow (asin x) 2))
(- (* 1/4 (pow (PI) 2)) (pow (asin x) 2))
(- (* 1/4 (pow (PI) 2)) (pow (asin x) 2))
(- (* 1/4 (pow (PI) 2)) (pow (asin x) 2))
(- (* 1/4 (pow (PI) 2)) (pow (asin x) 2))
(- (* 1/4 (pow (PI) 2)) (pow (asin x) 2))
(+ (PI) (acos x))
(+ (PI) (acos x))
(+ (PI) (acos x))
(+ (PI) (acos x))
(+ (PI) (acos x))
(+ (PI) (acos x))
(+ (PI) (acos x))
(+ (PI) (acos x))
(+ (PI) (acos x))
(+ (PI) (acos x))
(+ (PI) (acos x))
(+ (PI) (acos x))
(pow (asin x) 2)
(pow (asin x) 2)
(pow (asin x) 2)
(pow (asin x) 2)
(pow (asin x) 2)
(pow (asin x) 2)
(pow (asin x) 2)
(pow (asin x) 2)
(pow (asin x) 2)
(pow (asin x) 2)
(pow (asin x) 2)
(pow (asin x) 2)

Outputs
(/ (- (* 1/4 (pow (PI) 2)) (pow (asin x) 2)) (+ (PI) (acos x)))
(/.f64 (-.f64 (.f64 (PI.f64) (.f64 #s(literal 1/4 binary64) (PI.f64))) (pow.f64 (asin.f64 x) #s(literal 2 binary64))) (+.f64 (PI.f64) (acos.f64 x)))
(/ (- (* 1/4 (pow (PI) 2)) (pow (asin x) 2)) (+ (PI) (acos x)))
(/.f64 (-.f64 (.f64 (PI.f64) (.f64 #s(literal 1/4 binary64) (PI.f64))) (pow.f64 (asin.f64 x) #s(literal 2 binary64))) (+.f64 (PI.f64) (acos.f64 x)))
(/ (- (* 1/4 (pow (PI) 2)) (pow (asin x) 2)) (+ (PI) (acos x)))
(/.f64 (-.f64 (.f64 (PI.f64) (.f64 #s(literal 1/4 binary64) (PI.f64))) (pow.f64 (asin.f64 x) #s(literal 2 binary64))) (+.f64 (PI.f64) (acos.f64 x)))
(/ (- (* 1/4 (pow (PI) 2)) (pow (asin x) 2)) (+ (PI) (acos x)))
(/.f64 (-.f64 (.f64 (PI.f64) (.f64 #s(literal 1/4 binary64) (PI.f64))) (pow.f64 (asin.f64 x) #s(literal 2 binary64))) (+.f64 (PI.f64) (acos.f64 x)))
(/ (- (* 1/4 (pow (PI) 2)) (pow (asin x) 2)) (+ (PI) (acos x)))
(/.f64 (-.f64 (.f64 (PI.f64) (.f64 #s(literal 1/4 binary64) (PI.f64))) (pow.f64 (asin.f64 x) #s(literal 2 binary64))) (+.f64 (PI.f64) (acos.f64 x)))
(/ (- (* 1/4 (pow (PI) 2)) (pow (asin x) 2)) (+ (PI) (acos x)))
(/.f64 (-.f64 (.f64 (PI.f64) (.f64 #s(literal 1/4 binary64) (PI.f64))) (pow.f64 (asin.f64 x) #s(literal 2 binary64))) (+.f64 (PI.f64) (acos.f64 x)))
(/ (- (* 1/4 (pow (PI) 2)) (pow (asin x) 2)) (+ (PI) (acos x)))
(/.f64 (-.f64 (.f64 (PI.f64) (.f64 #s(literal 1/4 binary64) (PI.f64))) (pow.f64 (asin.f64 x) #s(literal 2 binary64))) (+.f64 (PI.f64) (acos.f64 x)))
(/ (- (* 1/4 (pow (PI) 2)) (pow (asin x) 2)) (+ (PI) (acos x)))
(/.f64 (-.f64 (.f64 (PI.f64) (.f64 #s(literal 1/4 binary64) (PI.f64))) (pow.f64 (asin.f64 x) #s(literal 2 binary64))) (+.f64 (PI.f64) (acos.f64 x)))
(/ (- (* 1/4 (pow (PI) 2)) (pow (asin x) 2)) (+ (PI) (acos x)))
(/.f64 (-.f64 (.f64 (PI.f64) (.f64 #s(literal 1/4 binary64) (PI.f64))) (pow.f64 (asin.f64 x) #s(literal 2 binary64))) (+.f64 (PI.f64) (acos.f64 x)))
(/ (- (* 1/4 (pow (PI) 2)) (pow (asin x) 2)) (+ (PI) (acos x)))
(/.f64 (-.f64 (.f64 (PI.f64) (.f64 #s(literal 1/4 binary64) (PI.f64))) (pow.f64 (asin.f64 x) #s(literal 2 binary64))) (+.f64 (PI.f64) (acos.f64 x)))
(/ (- (* 1/4 (pow (PI) 2)) (pow (asin x) 2)) (+ (PI) (acos x)))
(/.f64 (-.f64 (.f64 (PI.f64) (.f64 #s(literal 1/4 binary64) (PI.f64))) (pow.f64 (asin.f64 x) #s(literal 2 binary64))) (+.f64 (PI.f64) (acos.f64 x)))
(/ (- (* 1/4 (pow (PI) 2)) (pow (asin x) 2)) (+ (PI) (acos x)))
(/.f64 (-.f64 (.f64 (PI.f64) (.f64 #s(literal 1/4 binary64) (PI.f64))) (pow.f64 (asin.f64 x) #s(literal 2 binary64))) (+.f64 (PI.f64) (acos.f64 x)))
(- (* 1/4 (pow (PI) 2)) (pow (asin x) 2))
(-.f64 (.f64 (PI.f64) (.f64 #s(literal 1/4 binary64) (PI.f64))) (pow.f64 (asin.f64 x) #s(literal 2 binary64)))
(- (* 1/4 (pow (PI) 2)) (pow (asin x) 2))
(-.f64 (.f64 (PI.f64) (.f64 #s(literal 1/4 binary64) (PI.f64))) (pow.f64 (asin.f64 x) #s(literal 2 binary64)))
(- (* 1/4 (pow (PI) 2)) (pow (asin x) 2))
(-.f64 (.f64 (PI.f64) (.f64 #s(literal 1/4 binary64) (PI.f64))) (pow.f64 (asin.f64 x) #s(literal 2 binary64)))
(- (* 1/4 (pow (PI) 2)) (pow (asin x) 2))
(-.f64 (.f64 (PI.f64) (.f64 #s(literal 1/4 binary64) (PI.f64))) (pow.f64 (asin.f64 x) #s(literal 2 binary64)))
(- (* 1/4 (pow (PI) 2)) (pow (asin x) 2))
(-.f64 (.f64 (PI.f64) (.f64 #s(literal 1/4 binary64) (PI.f64))) (pow.f64 (asin.f64 x) #s(literal 2 binary64)))
(- (* 1/4 (pow (PI) 2)) (pow (asin x) 2))
(-.f64 (.f64 (PI.f64) (.f64 #s(literal 1/4 binary64) (PI.f64))) (pow.f64 (asin.f64 x) #s(literal 2 binary64)))
(- (* 1/4 (pow (PI) 2)) (pow (asin x) 2))
(-.f64 (.f64 (PI.f64) (.f64 #s(literal 1/4 binary64) (PI.f64))) (pow.f64 (asin.f64 x) #s(literal 2 binary64)))
(- (* 1/4 (pow (PI) 2)) (pow (asin x) 2))
(-.f64 (.f64 (PI.f64) (.f64 #s(literal 1/4 binary64) (PI.f64))) (pow.f64 (asin.f64 x) #s(literal 2 binary64)))
(- (* 1/4 (pow (PI) 2)) (pow (asin x) 2))
(-.f64 (.f64 (PI.f64) (.f64 #s(literal 1/4 binary64) (PI.f64))) (pow.f64 (asin.f64 x) #s(literal 2 binary64)))
(- (* 1/4 (pow (PI) 2)) (pow (asin x) 2))
(-.f64 (.f64 (PI.f64) (.f64 #s(literal 1/4 binary64) (PI.f64))) (pow.f64 (asin.f64 x) #s(literal 2 binary64)))
(- (* 1/4 (pow (PI) 2)) (pow (asin x) 2))
(-.f64 (.f64 (PI.f64) (.f64 #s(literal 1/4 binary64) (PI.f64))) (pow.f64 (asin.f64 x) #s(literal 2 binary64)))
(- (* 1/4 (pow (PI) 2)) (pow (asin x) 2))
(-.f64 (.f64 (PI.f64) (.f64 #s(literal 1/4 binary64) (PI.f64))) (pow.f64 (asin.f64 x) #s(literal 2 binary64)))
(+ (PI) (acos x))
(+.f64 (PI.f64) (acos.f64 x))
(+ (PI) (acos x))
(+.f64 (PI.f64) (acos.f64 x))
(+ (PI) (acos x))
(+.f64 (PI.f64) (acos.f64 x))
(+ (PI) (acos x))
(+.f64 (PI.f64) (acos.f64 x))
(+ (PI) (acos x))
(+.f64 (PI.f64) (acos.f64 x))
(+ (PI) (acos x))
(+.f64 (PI.f64) (acos.f64 x))
(+ (PI) (acos x))
(+.f64 (PI.f64) (acos.f64 x))
(+ (PI) (acos x))
(+.f64 (PI.f64) (acos.f64 x))
(+ (PI) (acos x))
(+.f64 (PI.f64) (acos.f64 x))
(+ (PI) (acos x))
(+.f64 (PI.f64) (acos.f64 x))
(+ (PI) (acos x))
(+.f64 (PI.f64) (acos.f64 x))
(+ (PI) (acos x))
(+.f64 (PI.f64) (acos.f64 x))
(pow (asin x) 2)
(pow.f64 (asin.f64 x) #s(literal 2 binary64))
(pow (asin x) 2)
(pow.f64 (asin.f64 x) #s(literal 2 binary64))
(pow (asin x) 2)
(pow.f64 (asin.f64 x) #s(literal 2 binary64))
(pow (asin x) 2)
(pow.f64 (asin.f64 x) #s(literal 2 binary64))
(pow (asin x) 2)
(pow.f64 (asin.f64 x) #s(literal 2 binary64))
(pow (asin x) 2)
(pow.f64 (asin.f64 x) #s(literal 2 binary64))
(pow (asin x) 2)
(pow.f64 (asin.f64 x) #s(literal 2 binary64))
(pow (asin x) 2)
(pow.f64 (asin.f64 x) #s(literal 2 binary64))
(pow (asin x) 2)
(pow.f64 (asin.f64 x) #s(literal 2 binary64))
(pow (asin x) 2)
(pow.f64 (asin.f64 x) #s(literal 2 binary64))
(pow (asin x) 2)
(pow.f64 (asin.f64 x) #s(literal 2 binary64))
(pow (asin x) 2)
(pow.f64 (asin.f64 x) #s(literal 2 binary64))

eval59.0ms (1.3%)

Compiler: Compiled 15091 to 1498 computations (90.1% saved)

prune55.0ms (1.2%)

Pruning

11 alts after pruning (9 fresh and 2 done)

	Pruned	Kept	Total
New	462	9	471
Fresh	0	0	0
Picked	1	0	1
Done	0	2	2
Total	463	11	474

Accuracy

9.3%

Counts

474 → 11

Alt Table

Click to see full alt table

Status	Accuracy	Program
	4.6%	(/.f64 (/.f64 (-.f64 (pow.f64 (.f64 (PI.f64) (asin.f64 x)) #s(literal 2 binary64)) (.f64 #s(literal 4 binary64) (pow.f64 (asin.f64 x) #s(literal 4 binary64)))) (*.f64 #s(literal 4 binary64) (pow.f64 (asin.f64 x) #s(literal 2 binary64)))) (+.f64 (acos.f64 x) (PI.f64)))
	2.5%	(/.f64 (/.f64 (-.f64 (pow.f64 (asin.f64 x) #s(literal 4 binary64)) (.f64 (/.f64 #s(literal 4 binary64) (.f64 (PI.f64) (PI.f64))) (pow.f64 (asin.f64 x) #s(literal 6 binary64)))) (.f64 (/.f64 #s(literal 4 binary64) (.f64 (PI.f64) (PI.f64))) (pow.f64 (asin.f64 x) #s(literal 4 binary64)))) (+.f64 (acos.f64 x) (PI.f64)))
	4.6%	(/.f64 (/.f64 (-.f64 (pow.f64 (asin.f64 x) #s(literal 2 binary64)) (.f64 (/.f64 #s(literal 4 binary64) (.f64 (PI.f64) (PI.f64))) (pow.f64 (asin.f64 x) #s(literal 4 binary64)))) (.f64 (/.f64 #s(literal 4 binary64) (.f64 (PI.f64) (PI.f64))) (pow.f64 (asin.f64 x) #s(literal 2 binary64)))) (+.f64 (acos.f64 x) (PI.f64)))
	2.5%	(/.f64 (/.f64 (-.f64 (.f64 (.f64 (PI.f64) (PI.f64)) (pow.f64 (asin.f64 x) #s(literal 4 binary64))) (.f64 #s(literal 4 binary64) (pow.f64 (asin.f64 x) #s(literal 6 binary64)))) (.f64 #s(literal 4 binary64) (pow.f64 (asin.f64 x) #s(literal 4 binary64)))) (+.f64 (acos.f64 x) (PI.f64)))
	3.3%	(/.f64 (/.f64 (-.f64 (.f64 (.f64 (PI.f64) (PI.f64)) (pow.f64 (asin.f64 x) #s(literal 3 binary64))) (.f64 #s(literal 4 binary64) (.f64 (pow.f64 (asin.f64 x) #s(literal 3 binary64)) (pow.f64 (asin.f64 x) #s(literal 2 binary64))))) (*.f64 #s(literal 4 binary64) (pow.f64 (asin.f64 x) #s(literal 3 binary64)))) (+.f64 (acos.f64 x) (PI.f64)))
	3.3%	(/.f64 (/.f64 (-.f64 (.f64 #s(literal 1 binary64) (pow.f64 (asin.f64 x) #s(literal 3 binary64))) (.f64 (/.f64 #s(literal 4 binary64) (.f64 (PI.f64) (PI.f64))) (.f64 (pow.f64 (asin.f64 x) #s(literal 3 binary64)) (pow.f64 (asin.f64 x) #s(literal 2 binary64))))) (.f64 (/.f64 #s(literal 4 binary64) (.f64 (PI.f64) (PI.f64))) (pow.f64 (asin.f64 x) #s(literal 3 binary64)))) (+.f64 (acos.f64 x) (PI.f64)))
	4.6%	(/.f64 (/.f64 (+.f64 (.f64 (pow.f64 (asin.f64 x) #s(literal 4 binary64)) #s(literal 4 binary64)) (.f64 (pow.f64 (asin.f64 x) #s(literal 2 binary64)) (.f64 (PI.f64) (PI.f64)))) (.f64 (pow.f64 (asin.f64 x) #s(literal 2 binary64)) #s(literal 4 binary64))) (+.f64 (acos.f64 x) (PI.f64)))
	7.0%	(/.f64 (-.f64 (pow.f64 (asin.f64 x) #s(literal 2 binary64)) (/.f64 (*.f64 (PI.f64) (PI.f64)) #s(literal -4 binary64))) (+.f64 (acos.f64 x) (PI.f64)))
	7.0%	(/.f64 (-.f64 (/.f64 (pow.f64 (cbrt.f64 (PI.f64)) #s(literal 6 binary64)) #s(literal 4 binary64)) (pow.f64 (-.f64 #s(literal 0 binary64) (asin.f64 x)) #s(literal 2 binary64))) (+.f64 (acos.f64 x) (PI.f64)))
✓	6.6%	(acos.f64 (-.f64 #s(literal 1 binary64) x))
✓	6.9%	(acos.f64 x)

Compiler

Compiled 543 to 231 computations (57.5% saved)

regimes13.0ms (0.3%)

Counts

15 → 2

Calls

Call 1

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

Outputs
(acos.f64 (-.f64 #s(literal 1 binary64) x))
(/.f64 (-.f64 (pow.f64 (asin.f64 x) #s(literal 2 binary64)) (/.f64 (*.f64 (PI.f64) (PI.f64)) #s(literal -4 binary64))) (+.f64 (acos.f64 x) (PI.f64)))

Calls

3 calls:

5.0ms	x
4.0ms	(-.f64 #s(literal 1 binary64) x)
4.0ms	(acos.f64 (-.f64 #s(literal 1 binary64) x))

Results

Accuracy	Segments	Branch
9.3%	2	`x`
9.3%	2	`(acos.f64 (-.f64 #s(literal 1 binary64) x))`
9.3%	2	`(-.f64 #s(literal 1 binary64) x)`

Compiler

Compiled 11 to 8 computations (27.3% saved)

regimes7.0ms (0.1%)

Counts

4 → 2

Calls

Call 1

Inputs
(acos.f64 #s(literal 1 binary64))
(acos.f64 x)
(acos.f64 (-.f64 #s(literal 0 binary64) x))
(acos.f64 (-.f64 #s(literal 1 binary64) x))

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

Calls

3 calls:

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

Results

Accuracy	Segments	Branch
9.2%	2	`x`
9.2%	2	`(acos.f64 (-.f64 #s(literal 1 binary64) x))`
9.2%	2	`(-.f64 #s(literal 1 binary64) x)`

Compiler

Compiled 11 to 8 computations (27.3% saved)

regimes2.0ms (0%)

Counts

3 → 1

Calls

Call 1

Inputs
(acos.f64 #s(literal 1 binary64))
(acos.f64 x)
(acos.f64 (-.f64 #s(literal 0 binary64) x))

Outputs
(acos.f64 x)

Calls

1 calls:

2.0ms

Results

Accuracy	Segments	Branch
6.9%	1	`x`

Compiler

Compiled 2 to 1 computations (50% saved)

regimes1.0ms (0%)

Accuracy

Total -0.0b remaining (-0%)

Threshold costs -0b (-0%)

Counts

1 → 1

Calls

Call 1

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

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

Calls

1 calls:

1.0ms

Results

Accuracy	Segments	Branch
3.8%	1	`x`

Compiler

Compiled 2 to 1 computations (50% saved)

bsearch0.0ms (0%)

Algorithm

1×	left-value

Steps

Time	Left	Right
0.0ms	0.9999999999999998	1.0

Compiler

Compiled 9 to 7 computations (22.2% saved)

bsearch0.0ms (0%)

Algorithm

1×	left-value

Steps

Time	Left	Right
0.0ms	0.9999999999999998	1.0

Compiler

Compiled 9 to 7 computations (22.2% saved)

simplify9.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	19	41
1	27	41
2	38	41
3	49	41
4	57	41
5	61	41
6	62	41

Stop Event

1×

saturated

Calls

Call 1

Inputs
(if (<=.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 1 binary64)) (acos.f64 (-.f64 #s(literal 1 binary64) x)) (/.f64 (-.f64 (pow.f64 (asin.f64 x) #s(literal 2 binary64)) (/.f64 (*.f64 (PI.f64) (PI.f64)) #s(literal -4 binary64))) (+.f64 (acos.f64 x) (PI.f64))))
(if (<=.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 1 binary64)) (acos.f64 (-.f64 #s(literal 1 binary64) x)) (acos.f64 x))
(acos.f64 x)
(acos.f64 #s(literal 1 binary64))

Outputs
(if (<=.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 1 binary64)) (acos.f64 (-.f64 #s(literal 1 binary64) x)) (/.f64 (-.f64 (pow.f64 (asin.f64 x) #s(literal 2 binary64)) (/.f64 (*.f64 (PI.f64) (PI.f64)) #s(literal -4 binary64))) (+.f64 (acos.f64 x) (PI.f64))))
(if (<=.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 1 binary64)) (acos.f64 (-.f64 #s(literal 1 binary64) x)) (/.f64 (-.f64 (pow.f64 (asin.f64 x) #s(literal 2 binary64)) (/.f64 (*.f64 (PI.f64) (PI.f64)) #s(literal -4 binary64))) (+.f64 (PI.f64) (acos.f64 x))))
(if (<=.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 1 binary64)) (acos.f64 (-.f64 #s(literal 1 binary64) x)) (acos.f64 x))
(acos.f64 x)
(acos.f64 #s(literal 1 binary64))

soundness859.0ms (19.1%)

Rules

3268×	`-lowering-.f32`
3268×	`-lowering-.f64`
2934×	`-lowering-.f32`
2934×	`-lowering-.f64`
2930×	`-lowering-.f32`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	7	9
1	52	9
2	402	9
3	4855	9
0	9364	9
0	6	7
1	30	7
2	218	7
3	2300	5
0	8979	5
0	14	44
1	106	39
2	970	39
0	8973	39
0	14	80
1	30	80
2	65	80
3	128	80
4	203	80
5	353	80
6	493	80
7	545	80
0	545	80

Stop Event

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

Compiler

Compiled 70 to 41 computations (41.4% saved)

preprocess40.0ms (0.9%)

Compiler: Compiled 110 to 58 computations (47.3% saved)

Iter	Nodes	Cost
0	8	15
1	18	13
2	32	13
3	66	13
4	134	13
5	212	13
6	294	13
7	335	13
0	4	4
1	8	4
2	12	4
3	18	4
4	27	4
5	40	4
6	57	4
7	71	4
8	83	4
9	84	4
0	84	4

Iter	Nodes	Cost
0	7	16
1	15	16
2	24	16
3	38	16
4	73	16
5	147	16
6	293	16
7	459	16
8	605	16
9	691	16
10	697	16
0	697	16

Iter	Nodes	Cost
0	4	72
1	6	72
2	11	72
3	18	72
4	28	72
5	60	72
6	119	72
7	208	72
8	291	72
9	397	72
10	475	72
11	481	72
0	481	72

Iter	Nodes	Cost
0	8	15
1	18	13
2	32	13
3	66	13
4	134	13
5	212	13
6	294	13
7	335	13
0	4	4
1	8	4
2	12	4
3	18	4
4	27	4
5	40	4
6	57	4
7	71	4
8	83	4
9	84	4
0	84	4

Iter	Nodes	Cost
0	7	16
1	15	16
2	24	16
3	38	16
4	73	16
5	147	16
6	293	16
7	459	16
8	605	16
9	691	16
10	697	16
0	697	16

Iter	Nodes	Cost
0	4	72
1	6	72
2	11	72
3	18	72
4	28	72
5	60	72
6	119	72
7	208	72
8	291	72
9	397	72
10	475	72
11	481	72
0	481	72

analyze0.0ms (0%)

sample1.4s (31.3%)

preprocess26.0ms (0.6%)

explain113.0ms (2.5%)

eval0.0ms (0%)

prune1.0ms (0%)

simplify6.0ms (0.1%)

localize68.0ms (1.5%)

series1.0ms (0%)

rewrite298.0ms (6.6%)

simplify18.0ms (0.4%)

eval43.0ms (1%)

prune32.0ms (0.7%)

simplify4.0ms (0.1%)

localize22.0ms (0.5%)

series0.0ms (0%)

rewrite272.0ms (6.1%)

simplify7.0ms (0.2%)

eval31.0ms (0.7%)

prune30.0ms (0.7%)

simplify18.0ms (0.4%)

localize33.0ms (0.7%)

series1.0ms (0%)

rewrite245.0ms (5.5%)

simplify18.0ms (0.4%)

eval75.0ms (1.7%)

prune63.0ms (1.4%)

simplify135.0ms (3%)

localize58.0ms (1.3%)

series4.0ms (0.1%)

rewrite277.0ms (6.2%)

simplify138.0ms (3.1%)

eval59.0ms (1.3%)

prune55.0ms (1.2%)

regimes13.0ms (0.3%)

regimes7.0ms (0.1%)

regimes2.0ms (0%)

regimes1.0ms (0%)

bsearch0.0ms (0%)

bsearch0.0ms (0%)

simplify9.0ms (0.2%)

soundness859.0ms (19.1%)

preprocess40.0ms (0.9%)

end0.0ms (0%)

Profiling

Iter	Nodes	Cost
0	8	15
1	18	13
2	32	13
3	66	13
4	134	13
5	212	13
6	294	13
7	335	13
0	4	4
1	8	4
2	12	4
3	18	4
4	27	4
5	40	4
6	57	4
7	71	4
8	83	4
9	84	4
0	84	4

Iter	Nodes	Cost
0	7	16
1	15	16
2	24	16
3	38	16
4	73	16
5	147	16
6	293	16
7	459	16
8	605	16
9	691	16
10	697	16
0	697	16

Iter	Nodes	Cost
0	4	72
1	6	72
2	11	72
3	18	72
4	28	72
5	60	72
6	119	72
7	208	72
8	291	72
9	397	72
10	475	72
11	481	72
0	481	72