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)

sample1.5s (26.2%)

Results

1.2s	8064×	1	valid
11.0ms	192×	0	valid

Precisions

Click to see histograms. Total time spent on operations: 849.0ms

ival-acos: 432.0ms (50.9% of total)

ival-sub: 189.0ms (22.3% of total)

backward-pass: 98.0ms (11.5% of total)

ival-<=: 79.0ms (9.3% of total)

const: 39.0ms (4.6% of total)

ival-and: 11.0ms (1.3% of total)

Bogosity

preprocess18.0ms (0.3%)

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)))

explain111.0ms (2%)

FPErrors

Click to see full error table

Ground Truth	Example	Underpredictions	Example	Subexpression
256	-	1	(0.007107236475464794)	`(acos.f64 (-.f64 #s(literal 1 binary64) x))`
0	-	0	-	`x`
0	-	0	-	`(-.f64 #s(literal 1 binary64) x)`
0	-	0	-	`#s(literal 1 binary64)`

Results

80.0ms	502×	1	valid
1.0ms	10×	0	valid

Compiler

Compiled 27 to 14 computations (48.1% saved)

Precisions

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

ival-acos: 37.0ms (71.1% of total)

ival-sub: 7.0ms (13.5% of total)

backward-pass: 6.0ms (11.5% of total)

const: 1.0ms (1.9% 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
▶	6.1%	(acos.f64 (-.f64 #s(literal 1 binary64) x))

Compiler

Compiled 5 to 4 computations (20% saved)

simplify7.0ms (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

localize41.0ms (0.7%)

Localize:

Found 2 expressions of interest:

New	Metric	Score	Program
✓	accuracy	100.0%	(-.f64 #s(literal 1 binary64) x)
✓	accuracy	6.1%	(acos.f64 (-.f64 #s(literal 1 binary64) x))

Results

34.0ms	251×	1	valid
0.0ms	5×	0	valid

Compiler

Compiled 11 to 5 computations (54.5% saved)

Precisions

Click to see histograms. Total time spent on operations: 21.0ms

ival-acos: 11.0ms (53% of total)

backward-pass: 5.0ms (24.1% of total)

ival-sub: 4.0ms (19.3% of total)

const: 1.0ms (4.8% 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)

rewrite328.0ms (5.9%)

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	176	7
3	1486	7
0	8956	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))))))))
(/.f64 (-.f64 (.f64 #s(literal 1 binary64) (.f64 #s(literal 2 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 (PI.f64) (+.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) (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 #s(literal 2 binary64) (+.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 (-.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 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 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))))

simplify19.0ms (0.3%)

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)

eval41.0ms (0.7%)

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

prune52.0ms (0.9%)

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

8.7%

Counts

282 → 3

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	6.1%	(acos.f64 (-.f64 #s(literal 1 binary64) x))
▶	6.7%	(acos.f64 (-.f64 #s(literal 0 binary64) x))
▶	3.9%	(acos.f64 #s(literal 1 binary64))

Compiler

Compiled 13 to 11 computations (15.4% saved)

simplify5.0ms (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

localize44.0ms (0.8%)

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

37.0ms

256×

valid

Compiler

Compiled 14 to 7 computations (50% saved)

Precisions

Click to see histograms. Total time spent on operations: 7.0ms

ival-acos: 5.0ms (76.5% of total)

ival-sub: 1.0ms (15.3% of total)

const: 1.0ms (15.3% of total)

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

series1.0ms (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)

rewrite282.0ms (5.1%)

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	219	7
3	2312	5
0	9026	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 (.f64 x x) (.f64 x x)) (/.f64 #s(literal 1 binary64) x)) (*.f64 x x))
(/.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 (.f64 x 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 (.f64 x x) (.f64 x x)) #s(literal 1 binary64)))
(.f64 (pow.f64 (/.f64 (.f64 x x) (.f64 (.f64 (.f64 x x) (.f64 (.f64 x x) (.f64 x x))) (.f64 x (.f64 x x)))) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (.f64 (.f64 x x) (.f64 (.f64 x x) (*.f64 x x)))))
(.f64 (pow.f64 (/.f64 (.f64 x x) (.f64 (.f64 x x) (.f64 (.f64 x x) (.f64 x x)))) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (.f64 x (*.f64 x x))))
(.f64 (pow.f64 (/.f64 x (.f64 (.f64 x x) (.f64 (.f64 x x) (.f64 x x)))) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (.f64 (.f64 x x) (*.f64 x x))))
(.f64 (pow.f64 (/.f64 x (.f64 (.f64 x x) (.f64 x x))) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (*.f64 x x)))

simplify7.0ms (0.1%)

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)

eval33.0ms (0.6%)

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

prune37.0ms (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

8.7%

Counts

254 → 3

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	6.7%	(fma.f64 (sqrt.f64 (PI.f64)) (sqrt.f64 (PI.f64)) (neg.f64 (acos.f64 x)))
✓	6.1%	(acos.f64 (-.f64 #s(literal 1 binary64) x))
▶	6.7%	(acos.f64 x)

Compiler

Compiled 17 to 12 computations (29.4% saved)

simplify20.0ms (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	16	16
2	25	16
3	39	16
4	74	16
5	148	16
6	294	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

localize37.0ms (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

26.0ms

256×

valid

Compiler

Compiled 22 to 7 computations (68.2% saved)

Precisions

Click to see histograms. Total time spent on operations: 19.0ms

ival-sqrt: 6.0ms (31.1% of total)

compiled-spec: 4.0ms (20.7% of total)

ival-acos: 3.0ms (15.5% of total)

ival-add: 2.0ms (10.4% of total)

ival-mult: 2.0ms (10.4% of total)

ival-pi: 1.0ms (5.2% of total)

ival-neg: 1.0ms (5.2% 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	(acos x)
0.0ms	x	@	-inf	(+ (* (sqrt (PI)) (sqrt (PI))) (neg (acos x)))
0.0ms	x	@	0	(acos x)
0.0ms	x	@	inf	(+ (* (sqrt (PI)) (sqrt (PI))) (neg (acos x)))

rewrite241.0ms (4.3%)

Algorithm

1×	batch-egg-rewrite

Rules

2516×	`-lowering-.f32`
2516×	`-lowering-.f64`
1404×	`pow-lowering-pow.f64`
1404×	`pow-lowering-pow.f32`
1344×	`fnmadd-define`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	9
1	53	9
2	406	9
3	4869	9
0	8910	9

Stop Event

1×	iter limit
1×	node limit

Counts

4 → 295

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 (.f64 (-.f64 #s(literal 0 binary64) (asin.f64 x)) (-.f64 #s(literal 0 binary64) (asin.f64 x))) (*.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)) (.f64 (-.f64 #s(literal 0 binary64) (asin.f64 x)) (-.f64 #s(literal 0 binary64) (asin.f64 x)))) (+.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)))
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(.f64 (.f64 (sqrt.f64 (PI.f64)) (pow.f64 (PI.f64) #s(literal 1/4 binary64))) (pow.f64 (PI.f64) #s(literal 1/4 binary64)))
(.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)))))

simplify29.0ms (0.5%)

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))

eval76.0ms (1.4%)

Compiler: Compiled 8193 to 1145 computations (86% saved)

prune64.0ms (1.2%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	530	3	533
Fresh	0	0	0
Picked	1	1	2
Done	0	1	1
Total	531	5	536

Accuracy

8.7%

Counts

536 → 5

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	6.7%	(/.f64 (-.f64 (/.f64 (.f64 (PI.f64) (PI.f64)) #s(literal 4 binary64)) (.f64 (-.f64 #s(literal 0 binary64) (asin.f64 x)) (-.f64 #s(literal 0 binary64) (asin.f64 x)))) (+.f64 (acos.f64 x) (PI.f64)))
▶	6.8%	(/.f64 (-.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 (pow.f64 (acos.f64 x) #s(literal 2 binary64)) (-.f64 (acos.f64 x) (PI.f64))))) (+.f64 (acos.f64 x) (PI.f64)))
▶	6.7%	(+.f64 (/.f64 (*.f64 (PI.f64) (PI.f64)) (+.f64 (acos.f64 x) (PI.f64))) (/.f64 (pow.f64 (acos.f64 x) #s(literal 2 binary64)) (-.f64 (acos.f64 x) (PI.f64))))
✓	6.1%	(acos.f64 (-.f64 #s(literal 1 binary64) x))
✓	6.7%	(acos.f64 x)

Compiler

Compiled 91 to 44 computations (51.6% saved)

simplify197.0ms (3.5%)

Algorithm

1×	egg-herbie

Localize:

Found 12 expressions of interest:

New	Metric	Score	Program
✓	cost-diff	0	(/.f64 (*.f64 (PI.f64) (PI.f64)) #s(literal 4 binary64))
✓	cost-diff	256	(*.f64 (-.f64 #s(literal 0 binary64) (asin.f64 x)) (-.f64 #s(literal 0 binary64) (asin.f64 x)))
✓	cost-diff	256	(-.f64 (/.f64 (.f64 (PI.f64) (PI.f64)) #s(literal 4 binary64)) (.f64 (-.f64 #s(literal 0 binary64) (asin.f64 x)) (-.f64 #s(literal 0 binary64) (asin.f64 x))))
✓	cost-diff	256	(/.f64 (-.f64 (/.f64 (.f64 (PI.f64) (PI.f64)) #s(literal 4 binary64)) (.f64 (-.f64 #s(literal 0 binary64) (asin.f64 x)) (-.f64 #s(literal 0 binary64) (asin.f64 x)))) (+.f64 (acos.f64 x) (PI.f64)))
✓	cost-diff	0	(.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))))
✓	cost-diff	12992	(*.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))))
✓	cost-diff	12992	(-.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 (pow.f64 (acos.f64 x) #s(literal 2 binary64)) (-.f64 (acos.f64 x) (PI.f64)))))
✓	cost-diff	13440	(/.f64 (-.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 (pow.f64 (acos.f64 x) #s(literal 2 binary64)) (-.f64 (acos.f64 x) (PI.f64))))) (+.f64 (acos.f64 x) (PI.f64)))
✓	cost-diff	0	(PI.f64)
✓	cost-diff	0	(*.f64 (PI.f64) (PI.f64))
✓	cost-diff	0	(/.f64 (*.f64 (PI.f64) (PI.f64)) (+.f64 (acos.f64 x) (PI.f64)))
✓	cost-diff	0	(+.f64 (/.f64 (*.f64 (PI.f64) (PI.f64)) (+.f64 (acos.f64 x) (PI.f64))) (/.f64 (pow.f64 (acos.f64 x) #s(literal 2 binary64)) (-.f64 (acos.f64 x) (PI.f64))))

Rules

3654×	`-lowering-.f32`
3654×	`-lowering-.f64`
1278×	`fma-lowering-fma.f32`
1278×	`fma-lowering-fma.f64`
1168×	`distribute-lft-neg-in`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	23	196
1	67	188
2	171	185
3	516	185
4	1580	185
5	5689	185
0	8261	185

Stop Event

1×	iter limit
1×	node limit

Calls

Call 1

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

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

localize114.0ms (2%)

Localize:

Found 12 expressions of interest:

New	Metric	Score	Program
✓	accuracy	100.0%	(+.f64 (acos.f64 x) (PI.f64))
✓	accuracy	100.0%	(*.f64 (-.f64 #s(literal 0 binary64) (asin.f64 x)) (-.f64 #s(literal 0 binary64) (asin.f64 x)))
✓	accuracy	100.0%	(-.f64 (/.f64 (.f64 (PI.f64) (PI.f64)) #s(literal 4 binary64)) (.f64 (-.f64 #s(literal 0 binary64) (asin.f64 x)) (-.f64 #s(literal 0 binary64) (asin.f64 x))))
✓	accuracy	98.5%	(/.f64 (-.f64 (/.f64 (.f64 (PI.f64) (PI.f64)) #s(literal 4 binary64)) (.f64 (-.f64 #s(literal 0 binary64) (asin.f64 x)) (-.f64 #s(literal 0 binary64) (asin.f64 x)))) (+.f64 (acos.f64 x) (PI.f64)))
✓	accuracy	99.9%	(-.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 (pow.f64 (acos.f64 x) #s(literal 2 binary64)) (-.f64 (acos.f64 x) (PI.f64)))))
✓	accuracy	98.5%	(.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))))
✓	accuracy	98.5%	(/.f64 (*.f64 (PI.f64) (PI.f64)) (+.f64 (acos.f64 x) (PI.f64)))
✓	accuracy	98.5%	(/.f64 (-.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 (pow.f64 (acos.f64 x) #s(literal 2 binary64)) (-.f64 (acos.f64 x) (PI.f64))))) (+.f64 (acos.f64 x) (PI.f64)))
✓	accuracy	100.0%	(-.f64 (acos.f64 x) (PI.f64))
✓	accuracy	100.0%	(/.f64 (pow.f64 (acos.f64 x) #s(literal 2 binary64)) (-.f64 (acos.f64 x) (PI.f64)))
✓	accuracy	98.5%	(/.f64 (*.f64 (PI.f64) (PI.f64)) (+.f64 (acos.f64 x) (PI.f64)))
✓	accuracy	97.6%	(+.f64 (/.f64 (*.f64 (PI.f64) (PI.f64)) (+.f64 (acos.f64 x) (PI.f64))) (/.f64 (pow.f64 (acos.f64 x) #s(literal 2 binary64)) (-.f64 (acos.f64 x) (PI.f64))))

Results

64.0ms

256×

valid

Compiler

Compiled 277 to 24 computations (91.3% saved)

Precisions

Click to see histograms. Total time spent on operations: 31.0ms

ival-div: 8.0ms (25.4% of total)

ival-mult: 7.0ms (22.2% of total)

ival-sub: 5.0ms (15.9% of total)

ival-acos: 3.0ms (9.5% of total)

ival-pow: 3.0ms (9.5% of total)

ival-add: 2.0ms (6.4% of total)

ival-asin: 2.0ms (6.4% of total)

ival-pi: 1.0ms (3.2% of total)

const: 1.0ms (3.2% of total)

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

series19.0ms (0.3%)

Counts

15 → 144

Calls

Call 1

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

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

36 calls:

Time	Variable		Point	Expression
4.0ms	x	@	inf	(/ (- (* (/ (* (PI) (PI)) (+ (acos x) (PI))) (/ (* (PI) (PI)) (+ (acos x) (PI)))) (* (/ (pow (acos x) 2) (- (acos x) (PI))) (/ (pow (acos x) 2) (- (acos x) (PI))))) (+ (acos x) (PI)))
3.0ms	x	@	0	(/ (- (* (/ (* (PI) (PI)) (+ (acos x) (PI))) (/ (* (PI) (PI)) (+ (acos x) (PI)))) (* (/ (pow (acos x) 2) (- (acos x) (PI))) (/ (pow (acos x) 2) (- (acos x) (PI))))) (+ (acos x) (PI)))
2.0ms	x	@	-inf	(/ (- (* (/ (* (PI) (PI)) (+ (acos x) (PI))) (/ (* (PI) (PI)) (+ (acos x) (PI)))) (* (/ (pow (acos x) 2) (- (acos x) (PI))) (/ (pow (acos x) 2) (- (acos x) (PI))))) (+ (acos x) (PI)))
2.0ms	x	@	-inf	(+ (/ (* (PI) (PI)) (+ (acos x) (PI))) (/ (pow (acos x) 2) (- (acos x) (PI))))
2.0ms	x	@	0	(+ (/ (* (PI) (PI)) (+ (acos x) (PI))) (/ (pow (acos x) 2) (- (acos x) (PI))))

rewrite323.0ms (5.8%)

Algorithm

1×	batch-egg-rewrite

Rules

3438×	`/-lowering-/.f32`
3438×	`/-lowering-/.f64`
2688×	`-lowering-.f32`
2688×	`-lowering-.f64`
1936×	`pow-lowering-pow.f64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	23	136
1	203	126
2	2309	126
0	8828	126

Stop Event

1×	iter limit
1×	node limit

Counts

15 → 762

Calls

Call 1

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

Outputs
(+.f64 (/.f64 (*.f64 (PI.f64) (PI.f64)) (+.f64 (PI.f64) (acos.f64 x))) (/.f64 (pow.f64 (acos.f64 x) #s(literal 2 binary64)) (-.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 (PI.f64) (acos.f64 x))))
(-.f64 (/.f64 (*.f64 (PI.f64) (PI.f64)) (+.f64 (PI.f64) (acos.f64 x))) (/.f64 (pow.f64 (acos.f64 x) #s(literal 2 binary64)) (-.f64 #s(literal 0 binary64) (-.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 #s(literal 0 binary64) (+.f64 (PI.f64) (acos.f64 x)))))
(-.f64 (/.f64 (pow.f64 (acos.f64 x) #s(literal 2 binary64)) (-.f64 (acos.f64 x) (PI.f64))) (/.f64 (-.f64 #s(literal 0 binary64) (*.f64 (PI.f64) (PI.f64))) (+.f64 (PI.f64) (acos.f64 x))))
(-.f64 (/.f64 (pow.f64 (/.f64 (.f64 (PI.f64) (PI.f64)) (+.f64 (PI.f64) (acos.f64 x))) #s(literal 2 binary64)) (-.f64 (/.f64 (.f64 (PI.f64) (PI.f64)) (+.f64 (PI.f64) (acos.f64 x))) (/.f64 (pow.f64 (acos.f64 x) #s(literal 2 binary64)) (-.f64 (acos.f64 x) (PI.f64))))) (/.f64 (/.f64 (pow.f64 (acos.f64 x) #s(literal 4 binary64)) (pow.f64 (-.f64 (acos.f64 x) (PI.f64)) #s(literal 2 binary64))) (-.f64 (/.f64 (*.f64 (PI.f64) (PI.f64)) (+.f64 (PI.f64) (acos.f64 x))) (/.f64 (pow.f64 (acos.f64 x) #s(literal 2 binary64)) (-.f64 (acos.f64 x) (PI.f64))))))
(-.f64 (/.f64 (pow.f64 (/.f64 (.f64 (PI.f64) (PI.f64)) (+.f64 (PI.f64) (acos.f64 x))) #s(literal 2 binary64)) (-.f64 (/.f64 (.f64 (PI.f64) (PI.f64)) (+.f64 (PI.f64) (acos.f64 x))) (/.f64 (pow.f64 (acos.f64 x) #s(literal 2 binary64)) (-.f64 (acos.f64 x) (PI.f64))))) (/.f64 (-.f64 (/.f64 (pow.f64 (acos.f64 x) #s(literal 4 binary64)) (pow.f64 (-.f64 (acos.f64 x) (PI.f64)) #s(literal 2 binary64))) (+.f64 (-.f64 #s(literal 0 binary64) (/.f64 (pow.f64 (acos.f64 x) #s(literal 4 binary64)) (pow.f64 (-.f64 (acos.f64 x) (PI.f64)) #s(literal 2 binary64)))) (/.f64 (pow.f64 (acos.f64 x) #s(literal 4 binary64)) (pow.f64 (-.f64 (acos.f64 x) (PI.f64)) #s(literal 2 binary64))))) (-.f64 (/.f64 (*.f64 (PI.f64) (PI.f64)) (+.f64 (PI.f64) (acos.f64 x))) (/.f64 (pow.f64 (acos.f64 x) #s(literal 2 binary64)) (-.f64 (acos.f64 x) (PI.f64))))))
(-.f64 (/.f64 (/.f64 (pow.f64 (/.f64 (.f64 (PI.f64) (PI.f64)) (+.f64 (PI.f64) (acos.f64 x))) #s(literal 6 binary64)) (+.f64 (pow.f64 (/.f64 (.f64 (PI.f64) (PI.f64)) (+.f64 (PI.f64) (acos.f64 x))) #s(literal 4 binary64)) (+.f64 (/.f64 (pow.f64 (acos.f64 x) #s(literal 8 binary64)) (pow.f64 (-.f64 (acos.f64 x) (PI.f64)) #s(literal 4 binary64))) (pow.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (acos.f64 x)) #s(literal 2 binary64)) (-.f64 (pow.f64 (acos.f64 x) #s(literal 2 binary64)) (.f64 (PI.f64) (PI.f64)))) #s(literal 2 binary64))))) (-.f64 (/.f64 (.f64 (PI.f64) (PI.f64)) (+.f64 (PI.f64) (acos.f64 x))) (/.f64 (pow.f64 (acos.f64 x) #s(literal 2 binary64)) (-.f64 (acos.f64 x) (PI.f64))))) (/.f64 (/.f64 (/.f64 (pow.f64 (acos.f64 x) #s(literal 12 binary64)) (pow.f64 (-.f64 (acos.f64 x) (PI.f64)) #s(literal 6 binary64))) (+.f64 (pow.f64 (/.f64 (.f64 (PI.f64) (PI.f64)) (+.f64 (PI.f64) (acos.f64 x))) #s(literal 4 binary64)) (+.f64 (/.f64 (pow.f64 (acos.f64 x) #s(literal 8 binary64)) (pow.f64 (-.f64 (acos.f64 x) (PI.f64)) #s(literal 4 binary64))) (pow.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (acos.f64 x)) #s(literal 2 binary64)) (-.f64 (pow.f64 (acos.f64 x) #s(literal 2 binary64)) (.f64 (PI.f64) (PI.f64)))) #s(literal 2 binary64))))) (-.f64 (/.f64 (*.f64 (PI.f64) (PI.f64)) (+.f64 (PI.f64) (acos.f64 x))) (/.f64 (pow.f64 (acos.f64 x) #s(literal 2 binary64)) (-.f64 (acos.f64 x) (PI.f64))))))
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(-.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) (-.f64 (asin.f64 x) (-.f64 #s(literal 0 binary64) (PI.f64))))
(-.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) (+.f64 (asin.f64 x) (PI.f64)))
(-.f64 (/.f64 (pow.f64 (acos.f64 x) #s(literal 3 binary64)) (+.f64 (pow.f64 (acos.f64 x) #s(literal 2 binary64)) (.f64 (PI.f64) (+.f64 (PI.f64) (acos.f64 x))))) (/.f64 (.f64 (PI.f64) (.f64 (PI.f64) (PI.f64))) (+.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 2 binary64)) (+.f64 (PI.f64) (acos.f64 x))) (/.f64 (*.f64 (PI.f64) (PI.f64)) (+.f64 (PI.f64) (acos.f64 x))))
(-.f64 (/.f64 (pow.f64 (acos.f64 x) #s(literal 2 binary64)) (-.f64 (acos.f64 x) (-.f64 #s(literal 0 binary64) (PI.f64)))) (/.f64 (*.f64 (PI.f64) (PI.f64)) (-.f64 (acos.f64 x) (-.f64 #s(literal 0 binary64) (PI.f64)))))
(fma.f64 (PI.f64) #s(literal 1/2 binary64) (neg.f64 (-.f64 (asin.f64 x) (-.f64 #s(literal 0 binary64) (PI.f64)))))
(fma.f64 (PI.f64) #s(literal 1/2 binary64) (neg.f64 (+.f64 (asin.f64 x) (PI.f64))))
(fma.f64 #s(literal 1 binary64) (/.f64 (PI.f64) #s(literal 2 binary64)) (neg.f64 (-.f64 (asin.f64 x) (-.f64 #s(literal 0 binary64) (PI.f64)))))
(fma.f64 #s(literal 1 binary64) (/.f64 (PI.f64) #s(literal 2 binary64)) (neg.f64 (+.f64 (asin.f64 x) (PI.f64))))
(fma.f64 #s(literal 1 binary64) (-.f64 #s(literal 0 binary64) (PI.f64)) (acos.f64 x))
(fma.f64 (pow.f64 (PI.f64) #s(literal 2/3 binary64)) (neg.f64 (cbrt.f64 (PI.f64))) (acos.f64 x))
(fma.f64 (pow.f64 (PI.f64) #s(literal 2/3 binary64)) (/.f64 (cbrt.f64 (PI.f64)) #s(literal 2 binary64)) (neg.f64 (-.f64 (asin.f64 x) (-.f64 #s(literal 0 binary64) (PI.f64)))))
(fma.f64 (pow.f64 (PI.f64) #s(literal 2/3 binary64)) (/.f64 (cbrt.f64 (PI.f64)) #s(literal 2 binary64)) (neg.f64 (+.f64 (asin.f64 x) (PI.f64))))
(fma.f64 (sqrt.f64 (PI.f64)) (neg.f64 (sqrt.f64 (PI.f64))) (acos.f64 x))
(fma.f64 (sqrt.f64 (PI.f64)) (/.f64 (sqrt.f64 (PI.f64)) #s(literal 2 binary64)) (neg.f64 (-.f64 (asin.f64 x) (-.f64 #s(literal 0 binary64) (PI.f64)))))
(fma.f64 (sqrt.f64 (PI.f64)) (/.f64 (sqrt.f64 (PI.f64)) #s(literal 2 binary64)) (neg.f64 (+.f64 (asin.f64 x) (PI.f64))))
(fma.f64 #s(literal -1 binary64) (PI.f64) (acos.f64 x))
(fma.f64 (pow.f64 (acos.f64 x) #s(literal 1/2 binary64)) (pow.f64 (acos.f64 x) #s(literal 1/2 binary64)) (-.f64 #s(literal 0 binary64) (PI.f64)))
(fma.f64 (neg.f64 (pow.f64 (PI.f64) #s(literal 2/3 binary64))) (cbrt.f64 (PI.f64)) (acos.f64 x))
(fma.f64 (neg.f64 (sqrt.f64 (PI.f64))) (sqrt.f64 (PI.f64)) (acos.f64 x))
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 (pow.f64 (acos.f64 x) #s(literal 2 binary64)) (.f64 (PI.f64) (+.f64 (PI.f64) (acos.f64 x)))) (-.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) (acos.f64 x)) (-.f64 (pow.f64 (acos.f64 x) #s(literal 2 binary64)) (*.f64 (PI.f64) (PI.f64)))))
(/.f64 (-.f64 (pow.f64 (acos.f64 x) #s(literal 2 binary64)) (*.f64 (PI.f64) (PI.f64))) (+.f64 (PI.f64) (acos.f64 x)))
(/.f64 (-.f64 (pow.f64 (acos.f64 x) #s(literal 2 binary64)) (*.f64 (PI.f64) (PI.f64))) (-.f64 (acos.f64 x) (-.f64 #s(literal 0 binary64) (PI.f64))))
(/.f64 (-.f64 (pow.f64 (acos.f64 x) #s(literal 3 binary64)) (.f64 (PI.f64) (.f64 (PI.f64) (PI.f64)))) (+.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 (pow.f64 (acos.f64 x) #s(literal 2 binary64)) (-.f64 (.f64 (PI.f64) (PI.f64)) (.f64 (acos.f64 x) (-.f64 #s(literal 0 binary64) (PI.f64))))))
(/.f64 #s(literal -1 binary64) (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 (acos.f64 x) #s(literal 3 binary64)) (.f64 (PI.f64) (*.f64 (PI.f64) (PI.f64)))))))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 (+.f64 (PI.f64) (acos.f64 x)) (-.f64 (pow.f64 (acos.f64 x) #s(literal 2 binary64)) (*.f64 (PI.f64) (PI.f64))))))
(/.f64 (neg.f64 (-.f64 (pow.f64 (acos.f64 x) #s(literal 3 binary64)) (.f64 (PI.f64) (.f64 (PI.f64) (PI.f64))))) (neg.f64 (+.f64 (pow.f64 (acos.f64 x) #s(literal 2 binary64)) (*.f64 (PI.f64) (+.f64 (PI.f64) (acos.f64 x))))))
(/.f64 (neg.f64 (-.f64 (pow.f64 (acos.f64 x) #s(literal 3 binary64)) (.f64 (PI.f64) (.f64 (PI.f64) (PI.f64))))) (neg.f64 (+.f64 (pow.f64 (acos.f64 x) #s(literal 2 binary64)) (-.f64 (.f64 (PI.f64) (PI.f64)) (.f64 (acos.f64 x) (-.f64 #s(literal 0 binary64) (PI.f64)))))))
(/.f64 (neg.f64 (-.f64 (pow.f64 (acos.f64 x) #s(literal 2 binary64)) (*.f64 (PI.f64) (PI.f64)))) (-.f64 #s(literal 0 binary64) (+.f64 (PI.f64) (acos.f64 x))))
(/.f64 (neg.f64 (-.f64 (pow.f64 (acos.f64 x) #s(literal 2 binary64)) (*.f64 (PI.f64) (PI.f64)))) (neg.f64 (-.f64 (acos.f64 x) (-.f64 #s(literal 0 binary64) (PI.f64)))))
(/.f64 (neg.f64 (neg.f64 (-.f64 (pow.f64 (acos.f64 x) #s(literal 2 binary64)) (*.f64 (PI.f64) (PI.f64))))) (neg.f64 (-.f64 #s(literal 0 binary64) (+.f64 (PI.f64) (acos.f64 x)))))
(/.f64 (neg.f64 (neg.f64 (-.f64 (pow.f64 (acos.f64 x) #s(literal 3 binary64)) (.f64 (PI.f64) (.f64 (PI.f64) (PI.f64)))))) (neg.f64 (neg.f64 (+.f64 (pow.f64 (acos.f64 x) #s(literal 2 binary64)) (*.f64 (PI.f64) (+.f64 (PI.f64) (acos.f64 x)))))))
(pow.f64 (/.f64 (+.f64 (pow.f64 (acos.f64 x) #s(literal 2 binary64)) (.f64 (PI.f64) (+.f64 (PI.f64) (acos.f64 x)))) (-.f64 (pow.f64 (acos.f64 x) #s(literal 3 binary64)) (.f64 (PI.f64) (*.f64 (PI.f64) (PI.f64))))) #s(literal -1 binary64))
(pow.f64 (/.f64 (+.f64 (PI.f64) (acos.f64 x)) (-.f64 (pow.f64 (acos.f64 x) #s(literal 2 binary64)) (*.f64 (PI.f64) (PI.f64)))) #s(literal -1 binary64))
(.f64 (-.f64 (pow.f64 (acos.f64 x) #s(literal 2 binary64)) (.f64 (PI.f64) (PI.f64))) (/.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 (-.f64 (pow.f64 (acos.f64 x) #s(literal 2 binary64)) (.f64 (PI.f64) (PI.f64))) (+.f64 (pow.f64 (acos.f64 x) #s(literal 3 binary64)) (.f64 (PI.f64) (.f64 (PI.f64) (PI.f64))))) (+.f64 (pow.f64 (acos.f64 x) #s(literal 2 binary64)) (*.f64 (PI.f64) (-.f64 (PI.f64) (acos.f64 x)))))
(.f64 (/.f64 (-.f64 (pow.f64 (acos.f64 x) #s(literal 2 binary64)) (.f64 (PI.f64) (PI.f64))) (-.f64 (pow.f64 (acos.f64 x) #s(literal 2 binary64)) (*.f64 (PI.f64) (PI.f64)))) (-.f64 (acos.f64 x) (PI.f64)))
(+.f64 (PI.f64) (acos.f64 x))
(+.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 (PI.f64) #s(literal 2 binary64)) (-.f64 (asin.f64 x) (PI.f64)))
(-.f64 (+.f64 (PI.f64) (/.f64 (PI.f64) #s(literal 2 binary64))) (asin.f64 x))
(-.f64 (/.f64 (*.f64 (PI.f64) (PI.f64)) (-.f64 (PI.f64) (acos.f64 x))) (/.f64 (pow.f64 (acos.f64 x) #s(literal 2 binary64)) (-.f64 (PI.f64) (acos.f64 x))))
(fma.f64 (PI.f64) #s(literal 1 binary64) (acos.f64 x))
(fma.f64 (PI.f64) #s(literal 1/2 binary64) (neg.f64 (-.f64 (asin.f64 x) (PI.f64))))
(fma.f64 (acos.f64 x) (.f64 (acos.f64 x) (/.f64 #s(literal 1 binary64) (-.f64 (acos.f64 x) (PI.f64)))) (neg.f64 (/.f64 (.f64 (PI.f64) (PI.f64)) (-.f64 (acos.f64 x) (PI.f64)))))
(fma.f64 (acos.f64 x) (/.f64 (acos.f64 x) (-.f64 (acos.f64 x) (PI.f64))) (neg.f64 (/.f64 (*.f64 (PI.f64) (PI.f64)) (-.f64 (acos.f64 x) (PI.f64)))))
(fma.f64 (pow.f64 (acos.f64 x) #s(literal 2 binary64)) (/.f64 #s(literal 1 binary64) (-.f64 (acos.f64 x) (PI.f64))) (neg.f64 (/.f64 (*.f64 (PI.f64) (PI.f64)) (-.f64 (acos.f64 x) (PI.f64)))))
(fma.f64 #s(literal 1 binary64) (PI.f64) (acos.f64 x))
(fma.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (acos.f64 x) #s(literal 2 binary64)) (-.f64 (acos.f64 x) (PI.f64))) (neg.f64 (/.f64 (*.f64 (PI.f64) (PI.f64)) (-.f64 (acos.f64 x) (PI.f64)))))
(fma.f64 #s(literal 1 binary64) (/.f64 (PI.f64) #s(literal 2 binary64)) (neg.f64 (-.f64 (asin.f64 x) (PI.f64))))
(fma.f64 (cbrt.f64 (PI.f64)) (pow.f64 (PI.f64) #s(literal 2/3 binary64)) (acos.f64 x))
(fma.f64 (pow.f64 (PI.f64) #s(literal 2/3 binary64)) (cbrt.f64 (PI.f64)) (acos.f64 x))
(fma.f64 (pow.f64 (PI.f64) #s(literal 2/3 binary64)) (/.f64 (cbrt.f64 (PI.f64)) #s(literal 2 binary64)) (neg.f64 (-.f64 (asin.f64 x) (PI.f64))))
(fma.f64 (sqrt.f64 (PI.f64)) (sqrt.f64 (PI.f64)) (acos.f64 x))
(fma.f64 (sqrt.f64 (PI.f64)) (/.f64 (sqrt.f64 (PI.f64)) #s(literal 2 binary64)) (neg.f64 (-.f64 (asin.f64 x) (PI.f64))))
(fma.f64 (-.f64 #s(literal 0 binary64) (pow.f64 (acos.f64 x) #s(literal 2 binary64))) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 0 binary64) (-.f64 (acos.f64 x) (PI.f64)))) (neg.f64 (/.f64 (*.f64 (PI.f64) (PI.f64)) (-.f64 (acos.f64 x) (PI.f64)))))
(fma.f64 (/.f64 #s(literal 1 binary64) (-.f64 (acos.f64 x) (PI.f64))) (pow.f64 (acos.f64 x) #s(literal 2 binary64)) (neg.f64 (/.f64 (*.f64 (PI.f64) (PI.f64)) (-.f64 (acos.f64 x) (PI.f64)))))
(fma.f64 (pow.f64 (acos.f64 x) #s(literal 1/2 binary64)) (pow.f64 (acos.f64 x) #s(literal 1/2 binary64)) (PI.f64))
(fma.f64 (/.f64 (pow.f64 (acos.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 (pow.f64 (acos.f64 x) #s(literal 2 binary64)) (.f64 (PI.f64) (+.f64 (PI.f64) (acos.f64 x)))) (neg.f64 (/.f64 (.f64 (PI.f64) (PI.f64)) (-.f64 (acos.f64 x) (PI.f64)))))
(fma.f64 (/.f64 (pow.f64 (acos.f64 x) #s(literal 2 binary64)) (-.f64 (pow.f64 (acos.f64 x) #s(literal 2 binary64)) (.f64 (PI.f64) (PI.f64)))) (+.f64 (PI.f64) (acos.f64 x)) (neg.f64 (/.f64 (.f64 (PI.f64) (PI.f64)) (-.f64 (acos.f64 x) (PI.f64)))))
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 (pow.f64 (acos.f64 x) #s(literal 2 binary64)) (.f64 (PI.f64) (-.f64 (PI.f64) (acos.f64 x)))) (+.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 (acos.f64 x) (PI.f64)) (-.f64 (pow.f64 (acos.f64 x) #s(literal 2 binary64)) (*.f64 (PI.f64) (PI.f64)))))
(/.f64 (-.f64 (pow.f64 (acos.f64 x) #s(literal 2 binary64)) (*.f64 (PI.f64) (PI.f64))) (-.f64 (acos.f64 x) (PI.f64)))
(/.f64 (+.f64 (pow.f64 (acos.f64 x) #s(literal 3 binary64)) (.f64 (PI.f64) (.f64 (PI.f64) (PI.f64)))) (+.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 (.f64 (PI.f64) (PI.f64)) (-.f64 (pow.f64 (acos.f64 x) #s(literal 2 binary64)) (.f64 (PI.f64) (acos.f64 x)))))
(/.f64 #s(literal -1 binary64) (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 (acos.f64 x) #s(literal 3 binary64)) (.f64 (PI.f64) (*.f64 (PI.f64) (PI.f64)))))))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 (-.f64 (acos.f64 x) (PI.f64)) (-.f64 (pow.f64 (acos.f64 x) #s(literal 2 binary64)) (*.f64 (PI.f64) (PI.f64))))))
(/.f64 (neg.f64 (+.f64 (pow.f64 (acos.f64 x) #s(literal 3 binary64)) (.f64 (PI.f64) (.f64 (PI.f64) (PI.f64))))) (neg.f64 (+.f64 (pow.f64 (acos.f64 x) #s(literal 2 binary64)) (*.f64 (PI.f64) (-.f64 (PI.f64) (acos.f64 x))))))
(/.f64 (neg.f64 (+.f64 (pow.f64 (acos.f64 x) #s(literal 3 binary64)) (.f64 (PI.f64) (.f64 (PI.f64) (PI.f64))))) (neg.f64 (+.f64 (.f64 (PI.f64) (PI.f64)) (-.f64 (pow.f64 (acos.f64 x) #s(literal 2 binary64)) (.f64 (PI.f64) (acos.f64 x))))))
(/.f64 (neg.f64 (-.f64 (pow.f64 (acos.f64 x) #s(literal 2 binary64)) (*.f64 (PI.f64) (PI.f64)))) (-.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 (PI.f64) (acos.f64 x)))
(/.f64 (-.f64 (.f64 (pow.f64 (acos.f64 x) #s(literal 2 binary64)) #s(literal 1 binary64)) (.f64 (PI.f64) (PI.f64))) (-.f64 (acos.f64 x) (PI.f64)))
(/.f64 (neg.f64 (neg.f64 (+.f64 (pow.f64 (acos.f64 x) #s(literal 3 binary64)) (.f64 (PI.f64) (.f64 (PI.f64) (PI.f64)))))) (neg.f64 (neg.f64 (+.f64 (pow.f64 (acos.f64 x) #s(literal 2 binary64)) (*.f64 (PI.f64) (-.f64 (PI.f64) (acos.f64 x)))))))
(/.f64 (neg.f64 (neg.f64 (-.f64 (pow.f64 (acos.f64 x) #s(literal 2 binary64)) (*.f64 (PI.f64) (PI.f64))))) (neg.f64 (-.f64 #s(literal 0 binary64) (-.f64 (acos.f64 x) (PI.f64)))))
(/.f64 (neg.f64 (-.f64 (*.f64 (PI.f64) (PI.f64)) (pow.f64 (acos.f64 x) #s(literal 2 binary64)))) (neg.f64 (-.f64 (PI.f64) (acos.f64 x))))
(pow.f64 (/.f64 (+.f64 (pow.f64 (acos.f64 x) #s(literal 2 binary64)) (.f64 (PI.f64) (-.f64 (PI.f64) (acos.f64 x)))) (+.f64 (pow.f64 (acos.f64 x) #s(literal 3 binary64)) (.f64 (PI.f64) (*.f64 (PI.f64) (PI.f64))))) #s(literal -1 binary64))
(pow.f64 (/.f64 (-.f64 (acos.f64 x) (PI.f64)) (-.f64 (pow.f64 (acos.f64 x) #s(literal 2 binary64)) (*.f64 (PI.f64) (PI.f64)))) #s(literal -1 binary64))
(.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 (+.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 (-.f64 (pow.f64 (acos.f64 x) #s(literal 2 binary64)) (.f64 (PI.f64) (PI.f64))) (-.f64 (pow.f64 (acos.f64 x) #s(literal 2 binary64)) (*.f64 (PI.f64) (PI.f64)))) (+.f64 (PI.f64) (acos.f64 x)))
(.f64 (/.f64 (-.f64 (pow.f64 (acos.f64 x) #s(literal 2 binary64)) (.f64 (PI.f64) (PI.f64))) (-.f64 (pow.f64 (acos.f64 x) #s(literal 3 binary64)) (.f64 (PI.f64) (.f64 (PI.f64) (PI.f64))))) (+.f64 (pow.f64 (acos.f64 x) #s(literal 2 binary64)) (*.f64 (PI.f64) (+.f64 (PI.f64) (acos.f64 x)))))

simplify239.0ms (4.3%)

Algorithm

1×	egg-herbie

Rules

2556×	`-lowering-.f32`
2556×	`-lowering-.f64`
1454×	`+-lowering-+.f64`
1454×	`+-lowering-+.f32`
1358×	`--lowering--.f32`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	26	1680
1	48	1500
2	113	1500
3	285	1500
4	893	1500
5	3691	1500
6	6651	1500
0	8103	1500

Stop Event

1×	iter limit
1×	node limit

Counts

144 → 144

Calls

Call 1

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

Outputs
(+ (/ (pow (PI) 2) (+ (PI) (acos x))) (/ (pow (acos x) 2) (- (acos x) (PI))))
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(/ (- (/ (pow (PI) 4) (pow (+ (PI) (acos x)) 2)) (/ (pow (acos x) 4) (pow (- (acos x) (PI)) 2))) (+ (PI) (acos x)))
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(/ (- (/ (pow (PI) 4) (pow (+ (PI) (acos x)) 2)) (/ (pow (acos x) 4) (pow (- (acos x) (PI)) 2))) (+ (PI) (acos x)))
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(/ (- (/ (pow (PI) 4) (pow (+ (PI) (acos x)) 2)) (/ (pow (acos x) 4) (pow (- (acos x) (PI)) 2))) (+ (PI) (acos x)))
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(/ (- (/ (pow (PI) 4) (pow (+ (PI) (acos x)) 2)) (/ (pow (acos x) 4) (pow (- (acos x) (PI)) 2))) (+ (PI) (acos x)))
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(/ (- (/ (pow (PI) 4) (pow (+ (PI) (acos x)) 2)) (/ (pow (acos x) 4) (pow (- (acos x) (PI)) 2))) (+ (PI) (acos x)))
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(/ (- (/ (pow (PI) 4) (pow (+ (PI) (acos x)) 2)) (/ (pow (acos x) 4) (pow (- (acos x) (PI)) 2))) (+ (PI) (acos x)))
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(/ (- (/ (pow (PI) 4) (pow (+ (PI) (acos x)) 2)) (/ (pow (acos x) 4) (pow (- (acos x) (PI)) 2))) (+ (PI) (acos x)))
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(/ (- (/ (pow (PI) 4) (pow (+ (PI) (acos x)) 2)) (/ (pow (acos x) 4) (pow (- (acos x) (PI)) 2))) (+ (PI) (acos x)))
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(/ (- (/ (pow (PI) 4) (pow (+ (PI) (acos x)) 2)) (/ (pow (acos x) 4) (pow (- (acos x) (PI)) 2))) (+ (PI) (acos x)))
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(-.f64 (acos.f64 x) (PI.f64))
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(-.f64 (acos.f64 x) (PI.f64))
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(+.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))
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(+ (PI) (acos x))
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eval332.0ms (6%)

Compiler: Compiled 85829 to 5569 computations (93.5% saved)

prune264.0ms (4.7%)

Pruning

9 alts after pruning (6 fresh and 3 done)

	Pruned	Kept	Total
New	2175	6	2181
Fresh	0	0	0
Picked	2	1	3
Done	0	2	2
Total	2177	9	2186

Accuracy

8.7%

Counts

2186 → 9

Alt Table

Click to see full alt table

Status	Accuracy	Program
	6.7%	(fma.f64 (pow.f64 (acos.f64 x) #s(literal 2 binary64)) (/.f64 #s(literal 1 binary64) (-.f64 (acos.f64 x) (PI.f64))) (/.f64 (*.f64 (PI.f64) (PI.f64)) (+.f64 (PI.f64) (acos.f64 x))))
	6.8%	(/.f64 (-.f64 (pow.f64 (/.f64 (*.f64 (PI.f64) (PI.f64)) (+.f64 (PI.f64) (acos.f64 x))) #s(literal 2 binary64)) (/.f64 (pow.f64 (acos.f64 x) #s(literal 4 binary64)) (pow.f64 (-.f64 (acos.f64 x) (PI.f64)) #s(literal 2 binary64)))) (+.f64 (acos.f64 x) (PI.f64)))
	6.7%	(/.f64 (-.f64 (/.f64 (*.f64 (PI.f64) (PI.f64)) #s(literal 4 binary64)) (pow.f64 (asin.f64 x) #s(literal 2 binary64))) (+.f64 (acos.f64 x) (PI.f64)))
	6.8%	(/.f64 (-.f64 (.f64 (/.f64 (pow.f64 (cbrt.f64 (PI.f64)) #s(literal 6 binary64)) (+.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 (pow.f64 (acos.f64 x) #s(literal 2 binary64)) (-.f64 (acos.f64 x) (PI.f64))))) (+.f64 (acos.f64 x) (PI.f64)))
	6.8%	(/.f64 (-.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)))) (pow.f64 (/.f64 (pow.f64 (acos.f64 x) #s(literal 2 binary64)) (-.f64 (acos.f64 x) (PI.f64))) #s(literal 2 binary64))) (+.f64 (acos.f64 x) (PI.f64)))
	6.7%	(+.f64 (/.f64 (pow.f64 (cbrt.f64 (PI.f64)) #s(literal 6 binary64)) (+.f64 (acos.f64 x) (PI.f64))) (/.f64 (pow.f64 (acos.f64 x) #s(literal 2 binary64)) (-.f64 (acos.f64 x) (PI.f64))))
✓	6.7%	(+.f64 (/.f64 (*.f64 (PI.f64) (PI.f64)) (+.f64 (acos.f64 x) (PI.f64))) (/.f64 (pow.f64 (acos.f64 x) #s(literal 2 binary64)) (-.f64 (acos.f64 x) (PI.f64))))
✓	6.1%	(acos.f64 (-.f64 #s(literal 1 binary64) x))
✓	6.7%	(acos.f64 x)

Compiler

Compiled 448 to 158 computations (64.7% saved)

regimes14.0ms (0.3%)

Counts

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

Outputs

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

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

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
8.7%	2	`x`
8.7%	2	`(acos.f64 (-.f64 #s(literal 1 binary64) x))`
8.7%	2	`(-.f64 #s(literal 1 binary64) x)`

Compiler

Compiled 11 to 8 computations (27.3% saved)

regimes10.0ms (0.2%)

Counts

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

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

Calls

3 calls:

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

Results

Accuracy	Segments	Branch
8.7%	2	`(acos.f64 (-.f64 #s(literal 1 binary64) x))`
8.7%	2	`(-.f64 #s(literal 1 binary64) x)`
8.7%	2	`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 x)
(acos.f64 (-.f64 #s(literal 1 binary64) x))

Calls

3 calls:

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

Results

Accuracy	Segments	Branch
8.7%	2	`(acos.f64 (-.f64 #s(literal 1 binary64) x))`
8.7%	2	`(-.f64 #s(literal 1 binary64) x)`
8.7%	2	`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
6.7%	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
3.9%	1	`x`

Compiler

Compiled 2 to 1 computations (50% saved)

bsearch23.0ms (0.4%)

Algorithm

1×	binary-search

Stop Event

1×	narrow-enough

Steps

Time	Left	Right
22.0ms	5.363972768999842e-20	1.2977842922181204e-11

Results

17.0ms

144×

valid

Compiler

Compiled 324 to 205 computations (36.7% saved)

Precisions

Click to see histograms. Total time spent on operations: 9.0ms

ival-acos: 5.0ms (55.5% of total)

ival-sub: 2.0ms (22.2% of total)

backward-pass: 1.0ms (11.1% of total)

const: 0.0ms (0% of total)

bsearch20.0ms (0.4%)

Algorithm

1×	binary-search

Stop Event

1×	narrow-enough

Steps

Time	Left	Right
19.0ms	5.363972768999842e-20	1.2977842922181204e-11

Results

14.0ms

144×

valid

Compiler

Compiled 216 to 169 computations (21.8% saved)

Precisions

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

ival-acos: 5.0ms (60.1% of total)

ival-sub: 2.0ms (24% of total)

backward-pass: 1.0ms (12% of total)

const: 0.0ms (0% of total)

bsearch25.0ms (0.4%)

Algorithm

1×	binary-search

Stop Event

1×	narrow-enough

Steps

Time	Left	Right
23.0ms	5.363972768999842e-20	1.2977842922181204e-11

Results

19.0ms

144×

valid

Compiler

Compiled 99 to 79 computations (20.2% saved)

Precisions

Click to see histograms. Total time spent on operations: 13.0ms

ival-sub: 7.0ms (53.7% of total)

ival-acos: 5.0ms (38.4% of total)

backward-pass: 1.0ms (7.7% of total)

const: 0.0ms (0% of total)

simplify9.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	30	72
1	42	72
2	59	72
3	71	72
4	79	72
5	81	72

Stop Event

1×

saturated

Calls

Call 1

Inputs
(if (<=.f64 x #s(literal 8924260225606735/162259276829213363391578010288128 binary64)) (/.f64 (-.f64 (pow.f64 (/.f64 (*.f64 (PI.f64) (PI.f64)) (+.f64 (PI.f64) (acos.f64 x))) #s(literal 2 binary64)) (/.f64 (pow.f64 (acos.f64 x) #s(literal 4 binary64)) (pow.f64 (-.f64 (acos.f64 x) (PI.f64)) #s(literal 2 binary64)))) (+.f64 (acos.f64 x) (PI.f64))) (acos.f64 (-.f64 #s(literal 1 binary64) x)))
(if (<=.f64 x #s(literal 8924260225606735/162259276829213363391578010288128 binary64)) (/.f64 (-.f64 (/.f64 (*.f64 (PI.f64) (PI.f64)) #s(literal 4 binary64)) (pow.f64 (asin.f64 x) #s(literal 2 binary64))) (+.f64 (acos.f64 x) (PI.f64))) (acos.f64 (-.f64 #s(literal 1 binary64) x)))
(if (<=.f64 x #s(literal 8924260225606735/162259276829213363391578010288128 binary64)) (acos.f64 x) (acos.f64 (-.f64 #s(literal 1 binary64) x)))
(acos.f64 x)
(acos.f64 #s(literal 1 binary64))

Outputs
(if (<=.f64 x #s(literal 8924260225606735/162259276829213363391578010288128 binary64)) (/.f64 (-.f64 (pow.f64 (/.f64 (*.f64 (PI.f64) (PI.f64)) (+.f64 (PI.f64) (acos.f64 x))) #s(literal 2 binary64)) (/.f64 (pow.f64 (acos.f64 x) #s(literal 4 binary64)) (pow.f64 (-.f64 (acos.f64 x) (PI.f64)) #s(literal 2 binary64)))) (+.f64 (acos.f64 x) (PI.f64))) (acos.f64 (-.f64 #s(literal 1 binary64) x)))
(if (<=.f64 x #s(literal 8924260225606735/162259276829213363391578010288128 binary64)) (/.f64 (-.f64 (pow.f64 (/.f64 (*.f64 (PI.f64) (PI.f64)) (+.f64 (PI.f64) (acos.f64 x))) #s(literal 2 binary64)) (/.f64 (pow.f64 (acos.f64 x) #s(literal 4 binary64)) (pow.f64 (-.f64 (acos.f64 x) (PI.f64)) #s(literal 2 binary64)))) (+.f64 (PI.f64) (acos.f64 x))) (acos.f64 (-.f64 #s(literal 1 binary64) x)))
(if (<=.f64 x #s(literal 8924260225606735/162259276829213363391578010288128 binary64)) (/.f64 (-.f64 (/.f64 (*.f64 (PI.f64) (PI.f64)) #s(literal 4 binary64)) (pow.f64 (asin.f64 x) #s(literal 2 binary64))) (+.f64 (acos.f64 x) (PI.f64))) (acos.f64 (-.f64 #s(literal 1 binary64) x)))
(if (<=.f64 x #s(literal 8924260225606735/162259276829213363391578010288128 binary64)) (/.f64 (-.f64 (/.f64 (*.f64 (PI.f64) (PI.f64)) #s(literal 4 binary64)) (pow.f64 (asin.f64 x) #s(literal 2 binary64))) (+.f64 (PI.f64) (acos.f64 x))) (acos.f64 (-.f64 #s(literal 1 binary64) x)))
(if (<=.f64 x #s(literal 8924260225606735/162259276829213363391578010288128 binary64)) (acos.f64 x) (acos.f64 (-.f64 #s(literal 1 binary64) x)))
(acos.f64 x)
(acos.f64 #s(literal 1 binary64))

soundness973.0ms (17.5%)

Rules

3438×	`/-lowering-/.f32`
3438×	`/-lowering-/.f64`
3268×	`-lowering-.f32`
3268×	`-lowering-.f64`
2688×	`-lowering-.f32`

Iterations

Useful iterations: 3 (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
0	23	136
1	203	126
2	2309	126
0	8828	126
0	7	9
1	53	9
2	406	9
3	4869	9
0	8910	9
0	6	7
1	30	7
2	219	7
3	2312	5
0	9026	5

Stop Event

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

Compiler

Compiled 116 to 62 computations (46.6% saved)

preprocess42.0ms (0.8%)

Compiler: Compiled 172 to 78 computations (54.7% 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	16	16
2	25	16
3	39	16
4	74	16
5	148	16
6	294	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	16	16
2	25	16
3	39	16
4	74	16
5	148	16
6	294	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%)

sample1.5s (26.2%)

preprocess18.0ms (0.3%)

explain111.0ms (2%)

eval0.0ms (0%)

prune1.0ms (0%)

simplify7.0ms (0.1%)

localize41.0ms (0.7%)

series1.0ms (0%)

rewrite328.0ms (5.9%)

simplify19.0ms (0.3%)

eval41.0ms (0.7%)

prune52.0ms (0.9%)

simplify5.0ms (0.1%)

localize44.0ms (0.8%)

series1.0ms (0%)

rewrite282.0ms (5.1%)

simplify7.0ms (0.1%)

eval33.0ms (0.6%)

prune37.0ms (0.7%)

simplify20.0ms (0.4%)

localize37.0ms (0.7%)

series1.0ms (0%)

rewrite241.0ms (4.3%)

simplify29.0ms (0.5%)

eval76.0ms (1.4%)

prune64.0ms (1.2%)

simplify197.0ms (3.5%)

localize114.0ms (2%)

series19.0ms (0.3%)

rewrite323.0ms (5.8%)

simplify239.0ms (4.3%)

eval332.0ms (6%)

prune264.0ms (4.7%)

regimes14.0ms (0.3%)

regimes10.0ms (0.2%)

regimes7.0ms (0.1%)

regimes2.0ms (0%)

regimes1.0ms (0%)

bsearch23.0ms (0.4%)

bsearch20.0ms (0.4%)

bsearch25.0ms (0.4%)

simplify9.0ms (0.2%)

soundness973.0ms (17.5%)

preprocess42.0ms (0.8%)

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	16	16
2	25	16
3	39	16
4	74	16
5	148	16
6	294	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