Details

analyze104.0ms (2.9%)

Algorithm

1×

Search

Probability	Valid	Unknown	Precondition	Infinite	Domain	Can't	Iter
0%	0%	100%	0%	0%	0%	0%	0
0%	0%	100%	0%	0%	0%	0%	1
0%	0%	100%	0%	0%	0%	0%	2
25%	25%	75%	0%	0%	0%	0%	3
33.3%	25%	50%	0%	0%	25%	0%	4
40%	25%	37.5%	0%	0%	37.5%	0%	5
44.4%	25%	31.2%	0%	0%	43.7%	0%	6
47.1%	25%	28.1%	0%	0%	46.9%	0%	7
48.5%	25%	26.5%	0%	0%	48.4%	0%	8
49.2%	25%	25.8%	0%	0%	49.2%	0%	9
49.6%	25%	25.4%	0%	0%	49.6%	0%	10
49.8%	25%	25.2%	0%	0%	49.8%	0%	11
49.9%	25%	25.1%	0%	0%	49.9%	0%	12

Compiler

Compiled 11 to 8 computations (27.3% saved)

sample2.5s (69.3%)

Results

978.0ms	8256×	body	256	valid
962.0ms	4082×	body	2048	invalid
338.0ms	1983×	body	1024	invalid
129.0ms	989×	body	512	invalid
74.0ms	1030×	body	256	invalid
2.0ms	7×	body	4096	invalid

Bogosity

preprocess172.0ms (4.8%)

Algorithm

2×	egg-herbie

Rules

1668×	`fma-neg`
1246×	`unsub-neg`
1016×	`sub-neg`
834×	`distribute-neg-in`
720×	`fma-def`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	23
1	21	23
2	25	23
3	40	23
4	81	23
5	157	23
6	366	23
7	764	23
8	2587	23
9	4531	23
10	5856	23
11	6543	23
12	6850	23
13	7040	23
14	7145	23
15	7465	23
0	1	1

Stop Event

1×	saturated
1×	node limit

Calls

Call 1

Inputs
0

Outputs
0

Call 2

Inputs
(log.f64 (+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) 1))))

Outputs
(log.f64 (+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) 1))))
(log.f64 (+.f64 x (sqrt.f64 (fma.f64 x x -1))))

Compiler

Compiled 11 to 8 computations (27.3% saved)

simplify173.0ms (4.8%)

Algorithm

1×	egg-herbie

Rules

1668×	`fma-neg`
1246×	`unsub-neg`
1016×	`sub-neg`
834×	`distribute-neg-in`
720×	`fma-def`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	23
1	21	23
2	25	23
3	40	23
4	81	23
5	157	23
6	366	23
7	764	23
8	2587	23
9	4531	23
10	5856	23
11	6543	23
12	6850	23
13	7040	23
14	7145	23
15	7465	23

Stop Event

1×	node limit

Counts

1 → 2

Calls

Call 1

Inputs
(log.f64 (+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) 1))))

Outputs
(log.f64 (+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) 1))))
(log.f64 (+.f64 x (sqrt.f64 (fma.f64 x x -1))))

eval1.0ms (0%)

Compiler: Compiled 18 to 12 computations (33.3% saved)

prune1.0ms (0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	1	1	2
Fresh	0	1	1
Picked	0	0	0
Done	0	0	0
Total	1	2	3

Accurracy

51.6%

Counts

3 → 1

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	51.6%	(log.f64 (+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) 1))))
▶	51.6%	(log.f64 (+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) 1))))

Compiler

Compiled 20 to 14 computations (30% saved)

localize43.0ms (1.2%)

Local Accuracy

Found 1 expressions with local accuracy:

New	Accuracy	Program
✓	53.4%	(sqrt.f64 (-.f64 (*.f64 x x) 1))

Compiler

Compiled 35 to 18 computations (48.6% saved)

series1.0ms (0%)

Counts

1 → 12

Calls

3 calls:

Time	Variable		Point	Expression
0.0ms	x	@	0	(sqrt.f64 (-.f64 (*.f64 x x) 1))
0.0ms	x	@	inf	(sqrt.f64 (-.f64 (*.f64 x x) 1))
0.0ms	x	@	-inf	(sqrt.f64 (-.f64 (*.f64 x x) 1))

rewrite167.0ms (4.6%)

Algorithm

1×	batch-egg-rewrite

Rules

1508×	`pow1`
1402×	`add-exp-log`
1398×	`log1p-expm1-u`
1398×	`expm1-log1p-u`
1378×	`add-log-exp`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	13
1	168	13
2	2052	13

Stop Event

1×	node limit

Counts

1 → 24

Calls

Call 1

Inputs
(sqrt.f64 (-.f64 (*.f64 x x) 1))

Outputs
(-.f64 (+.f64 1 (sqrt.f64 (fma.f64 x x -1))) 1)
(*.f64 1 (sqrt.f64 (fma.f64 x x -1)))
(*.f64 (sqrt.f64 (fma.f64 x x -1)) 1)
(*.f64 (cbrt.f64 (sqrt.f64 (fma.f64 x x -1))) (cbrt.f64 (fma.f64 x x -1)))
(*.f64 (cbrt.f64 (fma.f64 x x -1)) (cbrt.f64 (sqrt.f64 (fma.f64 x x -1))))
(*.f64 (pow.f64 (fma.f64 x x -1) 1/4) (pow.f64 (fma.f64 x x -1) 1/4))
(*.f64 (sqrt.f64 (pow.f64 (cbrt.f64 (fma.f64 x x -1)) 2)) (sqrt.f64 (cbrt.f64 (fma.f64 x x -1))))
(*.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 (+.f64 x -1)))
(*.f64 (pow.f64 1 1/2) (sqrt.f64 (fma.f64 x x -1)))
(*.f64 (pow.f64 (pow.f64 (cbrt.f64 (fma.f64 x x -1)) 2) 1/2) (pow.f64 (cbrt.f64 (fma.f64 x x -1)) 1/2))
(*.f64 (pow.f64 (+.f64 x 1) 1/2) (pow.f64 (+.f64 x -1) 1/2))
(/.f64 (sqrt.f64 (+.f64 (pow.f64 x 4) -1)) (sqrt.f64 (fma.f64 x x 1)))
(/.f64 (sqrt.f64 (+.f64 (pow.f64 x 6) -1)) (sqrt.f64 (+.f64 (pow.f64 x 4) (fma.f64 x x 1))))
(pow.f64 (fma.f64 x x -1) 1/2)
(pow.f64 (sqrt.f64 (fma.f64 x x -1)) 1)
(pow.f64 (cbrt.f64 (sqrt.f64 (fma.f64 x x -1))) 3)
(pow.f64 (pow.f64 (fma.f64 x x -1) 3/2) 1/3)
(pow.f64 (pow.f64 (fma.f64 x x -1) 1/4) 2)
(fabs.f64 (sqrt.f64 (fma.f64 x x -1)))
(log.f64 (exp.f64 (sqrt.f64 (fma.f64 x x -1))))
(cbrt.f64 (pow.f64 (fma.f64 x x -1) 3/2))
(expm1.f64 (log1p.f64 (sqrt.f64 (fma.f64 x x -1))))
(exp.f64 (log.f64 (sqrt.f64 (fma.f64 x x -1))))
(log1p.f64 (expm1.f64 (sqrt.f64 (fma.f64 x x -1))))

simplify188.0ms (5.2%)

Algorithm

1×	egg-herbie

Rules

1482×	`fma-def`
1296×	`associate-/l*`
880×	`associate-/r*`
478×	`associate-*r/`
444×	`*-commutative`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	111	1080
1	255	962
2	667	852
3	2198	816
4	7264	816

Stop Event

1×	node limit

Counts

36 → 72

Calls

Call 1

Inputs
(sqrt.f64 -1)
(+.f64 (sqrt.f64 -1) (*.f64 1/2 (/.f64 (pow.f64 x 2) (sqrt.f64 -1))))
(+.f64 (.f64 -1/8 (/.f64 (pow.f64 x 4) (pow.f64 (sqrt.f64 -1) 3))) (+.f64 (sqrt.f64 -1) (.f64 1/2 (/.f64 (pow.f64 x 2) (sqrt.f64 -1)))))
(+.f64 (.f64 -1/8 (/.f64 (pow.f64 x 4) (pow.f64 (sqrt.f64 -1) 3))) (+.f64 (sqrt.f64 -1) (+.f64 (.f64 1/2 (/.f64 (pow.f64 x 2) (sqrt.f64 -1))) (*.f64 1/16 (/.f64 (pow.f64 x 6) (pow.f64 (sqrt.f64 -1) 5))))))
x
(-.f64 x (*.f64 1/2 (/.f64 1 x)))
(-.f64 x (+.f64 (.f64 1/2 (/.f64 1 x)) (.f64 1/8 (/.f64 1 (pow.f64 x 3)))))
(-.f64 x (+.f64 (.f64 1/2 (/.f64 1 x)) (+.f64 (.f64 1/16 (/.f64 1 (pow.f64 x 5))) (*.f64 1/8 (/.f64 1 (pow.f64 x 3))))))
(*.f64 -1 x)
(+.f64 (.f64 -1 x) (.f64 1/2 (/.f64 1 x)))
(+.f64 (.f64 1/2 (/.f64 1 x)) (+.f64 (.f64 1/8 (/.f64 1 (pow.f64 x 3))) (*.f64 -1 x)))
(+.f64 (.f64 1/2 (/.f64 1 x)) (+.f64 (.f64 1/16 (/.f64 1 (pow.f64 x 5))) (+.f64 (.f64 1/8 (/.f64 1 (pow.f64 x 3))) (.f64 -1 x))))
(-.f64 (+.f64 1 (sqrt.f64 (fma.f64 x x -1))) 1)
(*.f64 1 (sqrt.f64 (fma.f64 x x -1)))
(*.f64 (sqrt.f64 (fma.f64 x x -1)) 1)
(*.f64 (cbrt.f64 (sqrt.f64 (fma.f64 x x -1))) (cbrt.f64 (fma.f64 x x -1)))
(*.f64 (cbrt.f64 (fma.f64 x x -1)) (cbrt.f64 (sqrt.f64 (fma.f64 x x -1))))
(*.f64 (pow.f64 (fma.f64 x x -1) 1/4) (pow.f64 (fma.f64 x x -1) 1/4))
(*.f64 (sqrt.f64 (pow.f64 (cbrt.f64 (fma.f64 x x -1)) 2)) (sqrt.f64 (cbrt.f64 (fma.f64 x x -1))))
(*.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 (+.f64 x -1)))
(*.f64 (pow.f64 1 1/2) (sqrt.f64 (fma.f64 x x -1)))
(*.f64 (pow.f64 (pow.f64 (cbrt.f64 (fma.f64 x x -1)) 2) 1/2) (pow.f64 (cbrt.f64 (fma.f64 x x -1)) 1/2))
(*.f64 (pow.f64 (+.f64 x 1) 1/2) (pow.f64 (+.f64 x -1) 1/2))
(/.f64 (sqrt.f64 (+.f64 (pow.f64 x 4) -1)) (sqrt.f64 (fma.f64 x x 1)))
(/.f64 (sqrt.f64 (+.f64 (pow.f64 x 6) -1)) (sqrt.f64 (+.f64 (pow.f64 x 4) (fma.f64 x x 1))))
(pow.f64 (fma.f64 x x -1) 1/2)
(pow.f64 (sqrt.f64 (fma.f64 x x -1)) 1)
(pow.f64 (cbrt.f64 (sqrt.f64 (fma.f64 x x -1))) 3)
(pow.f64 (pow.f64 (fma.f64 x x -1) 3/2) 1/3)
(pow.f64 (pow.f64 (fma.f64 x x -1) 1/4) 2)
(fabs.f64 (sqrt.f64 (fma.f64 x x -1)))
(log.f64 (exp.f64 (sqrt.f64 (fma.f64 x x -1))))
(cbrt.f64 (pow.f64 (fma.f64 x x -1) 3/2))
(expm1.f64 (log1p.f64 (sqrt.f64 (fma.f64 x x -1))))
(exp.f64 (log.f64 (sqrt.f64 (fma.f64 x x -1))))
(log1p.f64 (expm1.f64 (sqrt.f64 (fma.f64 x x -1))))

Outputs
(sqrt.f64 -1)
(+.f64 (sqrt.f64 -1) (*.f64 1/2 (/.f64 (pow.f64 x 2) (sqrt.f64 -1))))
(+.f64 (sqrt.f64 -1) (.f64 1/2 (/.f64 (.f64 x x) (sqrt.f64 -1))))
(fma.f64 1/2 (/.f64 x (/.f64 (sqrt.f64 -1) x)) (sqrt.f64 -1))
(+.f64 (.f64 -1/8 (/.f64 (pow.f64 x 4) (pow.f64 (sqrt.f64 -1) 3))) (+.f64 (sqrt.f64 -1) (.f64 1/2 (/.f64 (pow.f64 x 2) (sqrt.f64 -1)))))
(fma.f64 -1/8 (/.f64 (pow.f64 x 4) (pow.f64 (sqrt.f64 -1) 3)) (+.f64 (sqrt.f64 -1) (.f64 1/2 (/.f64 (.f64 x x) (sqrt.f64 -1)))))
(+.f64 (fma.f64 1/2 (/.f64 x (/.f64 (sqrt.f64 -1) x)) (sqrt.f64 -1)) (*.f64 1/8 (/.f64 (pow.f64 x 4) (sqrt.f64 -1))))
(fma.f64 1/2 (/.f64 x (/.f64 (sqrt.f64 -1) x)) (fma.f64 1/8 (/.f64 (pow.f64 x 4) (sqrt.f64 -1)) (sqrt.f64 -1)))
(+.f64 (sqrt.f64 -1) (.f64 (/.f64 x (/.f64 (sqrt.f64 -1) x)) (+.f64 1/2 (/.f64 (.f64 x x) 8))))
(+.f64 (.f64 -1/8 (/.f64 (pow.f64 x 4) (pow.f64 (sqrt.f64 -1) 3))) (+.f64 (sqrt.f64 -1) (+.f64 (.f64 1/2 (/.f64 (pow.f64 x 2) (sqrt.f64 -1))) (*.f64 1/16 (/.f64 (pow.f64 x 6) (pow.f64 (sqrt.f64 -1) 5))))))
(fma.f64 -1/8 (/.f64 (pow.f64 x 4) (pow.f64 (sqrt.f64 -1) 3)) (+.f64 (sqrt.f64 -1) (fma.f64 1/2 (/.f64 (.f64 x x) (sqrt.f64 -1)) (/.f64 (.f64 1/16 (pow.f64 x 6)) (pow.f64 (sqrt.f64 -1) 5)))))
(+.f64 (sqrt.f64 -1) (+.f64 (fma.f64 1/2 (/.f64 x (/.f64 (sqrt.f64 -1) x)) (.f64 1/16 (/.f64 (pow.f64 x 6) (pow.f64 (sqrt.f64 -1) 5)))) (.f64 1/8 (/.f64 (pow.f64 x 4) (sqrt.f64 -1)))))
(fma.f64 1/8 (/.f64 (pow.f64 x 4) (sqrt.f64 -1)) (fma.f64 1/2 (/.f64 x (/.f64 (sqrt.f64 -1) x)) (fma.f64 1/16 (/.f64 (pow.f64 x 6) (pow.f64 (sqrt.f64 -1) 5)) (sqrt.f64 -1))))
(+.f64 (fma.f64 (/.f64 1/16 (pow.f64 (sqrt.f64 -1) 5)) (pow.f64 x 6) (sqrt.f64 -1)) (.f64 (/.f64 x (/.f64 (sqrt.f64 -1) x)) (+.f64 1/2 (/.f64 (.f64 x x) 8))))
x
(-.f64 x (*.f64 1/2 (/.f64 1 x)))
(-.f64 x (/.f64 1/2 x))
(+.f64 x (/.f64 -1/2 x))
(-.f64 x (+.f64 (.f64 1/2 (/.f64 1 x)) (.f64 1/8 (/.f64 1 (pow.f64 x 3)))))
(-.f64 x (+.f64 (/.f64 1/2 x) (/.f64 1/8 (pow.f64 x 3))))
(+.f64 x (+.f64 (/.f64 -1/2 x) (/.f64 -1/8 (pow.f64 x 3))))
(+.f64 (/.f64 -1/2 x) (+.f64 x (/.f64 -1/8 (pow.f64 x 3))))
(-.f64 x (+.f64 (.f64 1/2 (/.f64 1 x)) (+.f64 (.f64 1/16 (/.f64 1 (pow.f64 x 5))) (*.f64 1/8 (/.f64 1 (pow.f64 x 3))))))
(-.f64 x (+.f64 (/.f64 1/2 x) (+.f64 (/.f64 1/8 (pow.f64 x 3)) (/.f64 1/16 (pow.f64 x 5)))))
(+.f64 x (-.f64 (/.f64 -1/2 x) (+.f64 (/.f64 1/8 (pow.f64 x 3)) (/.f64 1/16 (pow.f64 x 5)))))
(+.f64 x (-.f64 (+.f64 (/.f64 -1/2 x) (/.f64 -1/8 (pow.f64 x 3))) (/.f64 1/16 (pow.f64 x 5))))
(+.f64 (-.f64 (/.f64 -1/2 x) (/.f64 1/16 (pow.f64 x 5))) (+.f64 x (/.f64 -1/8 (pow.f64 x 3))))
(*.f64 -1 x)
(neg.f64 x)
(+.f64 (.f64 -1 x) (.f64 1/2 (/.f64 1 x)))
(fma.f64 -1 x (/.f64 1/2 x))
(-.f64 (/.f64 1/2 x) x)
(+.f64 (.f64 1/2 (/.f64 1 x)) (+.f64 (.f64 1/8 (/.f64 1 (pow.f64 x 3))) (*.f64 -1 x)))
(+.f64 (/.f64 1/2 x) (+.f64 (/.f64 1/8 (pow.f64 x 3)) (neg.f64 x)))
(+.f64 (/.f64 1/2 x) (-.f64 (/.f64 1/8 (pow.f64 x 3)) x))
(+.f64 (.f64 1/2 (/.f64 1 x)) (+.f64 (.f64 1/16 (/.f64 1 (pow.f64 x 5))) (+.f64 (.f64 1/8 (/.f64 1 (pow.f64 x 3))) (.f64 -1 x))))
(+.f64 (/.f64 1/2 x) (+.f64 (/.f64 1/16 (pow.f64 x 5)) (+.f64 (/.f64 1/8 (pow.f64 x 3)) (neg.f64 x))))
(+.f64 (/.f64 1/2 x) (+.f64 (/.f64 1/16 (pow.f64 x 5)) (-.f64 (/.f64 1/8 (pow.f64 x 3)) x)))
(-.f64 (+.f64 1 (sqrt.f64 (fma.f64 x x -1))) 1)
(+.f64 1 (-.f64 (sqrt.f64 (fma.f64 x x -1)) 1))
(+.f64 (sqrt.f64 (fma.f64 x x -1)) 0)
(sqrt.f64 (fma.f64 x x -1))
(*.f64 1 (sqrt.f64 (fma.f64 x x -1)))
(+.f64 1 (-.f64 (sqrt.f64 (fma.f64 x x -1)) 1))
(+.f64 (sqrt.f64 (fma.f64 x x -1)) 0)
(sqrt.f64 (fma.f64 x x -1))
(*.f64 (sqrt.f64 (fma.f64 x x -1)) 1)
(+.f64 1 (-.f64 (sqrt.f64 (fma.f64 x x -1)) 1))
(+.f64 (sqrt.f64 (fma.f64 x x -1)) 0)
(sqrt.f64 (fma.f64 x x -1))
(*.f64 (cbrt.f64 (sqrt.f64 (fma.f64 x x -1))) (cbrt.f64 (fma.f64 x x -1)))
(*.f64 (cbrt.f64 (fma.f64 x x -1)) (cbrt.f64 (sqrt.f64 (fma.f64 x x -1))))
(*.f64 (cbrt.f64 (sqrt.f64 (fma.f64 x x -1))) (cbrt.f64 (fma.f64 x x -1)))
(*.f64 (pow.f64 (fma.f64 x x -1) 1/4) (pow.f64 (fma.f64 x x -1) 1/4))
(+.f64 1 (-.f64 (sqrt.f64 (fma.f64 x x -1)) 1))
(+.f64 (sqrt.f64 (fma.f64 x x -1)) 0)
(sqrt.f64 (fma.f64 x x -1))
(*.f64 (sqrt.f64 (pow.f64 (cbrt.f64 (fma.f64 x x -1)) 2)) (sqrt.f64 (cbrt.f64 (fma.f64 x x -1))))
(*.f64 (fabs.f64 (cbrt.f64 (fma.f64 x x -1))) (sqrt.f64 (cbrt.f64 (fma.f64 x x -1))))
(*.f64 (cbrt.f64 (fma.f64 x x -1)) (sqrt.f64 (cbrt.f64 (fma.f64 x x -1))))
(pow.f64 (cbrt.f64 (fma.f64 x x -1)) 3/2)
(*.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 (+.f64 x -1)))
(*.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 (+.f64 -1 x)))
(*.f64 (pow.f64 1 1/2) (sqrt.f64 (fma.f64 x x -1)))
(+.f64 1 (-.f64 (sqrt.f64 (fma.f64 x x -1)) 1))
(+.f64 (sqrt.f64 (fma.f64 x x -1)) 0)
(sqrt.f64 (fma.f64 x x -1))
(*.f64 (pow.f64 (pow.f64 (cbrt.f64 (fma.f64 x x -1)) 2) 1/2) (pow.f64 (cbrt.f64 (fma.f64 x x -1)) 1/2))
(*.f64 (sqrt.f64 (pow.f64 (cbrt.f64 (fma.f64 x x -1)) 2)) (sqrt.f64 (cbrt.f64 (fma.f64 x x -1))))
(*.f64 (fabs.f64 (cbrt.f64 (fma.f64 x x -1))) (sqrt.f64 (cbrt.f64 (fma.f64 x x -1))))
(*.f64 (cbrt.f64 (fma.f64 x x -1)) (sqrt.f64 (cbrt.f64 (fma.f64 x x -1))))
(pow.f64 (cbrt.f64 (fma.f64 x x -1)) 3/2)
(*.f64 (pow.f64 (+.f64 x 1) 1/2) (pow.f64 (+.f64 x -1) 1/2))
(*.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 (+.f64 -1 x)))
(/.f64 (sqrt.f64 (+.f64 (pow.f64 x 4) -1)) (sqrt.f64 (fma.f64 x x 1)))
(/.f64 (sqrt.f64 (+.f64 -1 (pow.f64 x 4))) (sqrt.f64 (fma.f64 x x 1)))
(/.f64 (sqrt.f64 (+.f64 -1 (pow.f64 x 4))) (hypot.f64 1 x))
(/.f64 (sqrt.f64 (+.f64 (pow.f64 x 6) -1)) (sqrt.f64 (+.f64 (pow.f64 x 4) (fma.f64 x x 1))))
(/.f64 (sqrt.f64 (+.f64 -1 (pow.f64 x 6))) (sqrt.f64 (+.f64 (pow.f64 x 4) (fma.f64 x x 1))))
(pow.f64 (fma.f64 x x -1) 1/2)
(+.f64 1 (-.f64 (sqrt.f64 (fma.f64 x x -1)) 1))
(+.f64 (sqrt.f64 (fma.f64 x x -1)) 0)
(sqrt.f64 (fma.f64 x x -1))
(pow.f64 (sqrt.f64 (fma.f64 x x -1)) 1)
(+.f64 1 (-.f64 (sqrt.f64 (fma.f64 x x -1)) 1))
(+.f64 (sqrt.f64 (fma.f64 x x -1)) 0)
(sqrt.f64 (fma.f64 x x -1))
(pow.f64 (cbrt.f64 (sqrt.f64 (fma.f64 x x -1))) 3)
(+.f64 1 (-.f64 (sqrt.f64 (fma.f64 x x -1)) 1))
(+.f64 (sqrt.f64 (fma.f64 x x -1)) 0)
(sqrt.f64 (fma.f64 x x -1))
(pow.f64 (pow.f64 (fma.f64 x x -1) 3/2) 1/3)
(cbrt.f64 (pow.f64 (fma.f64 x x -1) 3/2))
(pow.f64 (pow.f64 (fma.f64 x x -1) 1/4) 2)
(+.f64 1 (-.f64 (sqrt.f64 (fma.f64 x x -1)) 1))
(+.f64 (sqrt.f64 (fma.f64 x x -1)) 0)
(sqrt.f64 (fma.f64 x x -1))
(fabs.f64 (sqrt.f64 (fma.f64 x x -1)))
(+.f64 1 (-.f64 (sqrt.f64 (fma.f64 x x -1)) 1))
(+.f64 (sqrt.f64 (fma.f64 x x -1)) 0)
(sqrt.f64 (fma.f64 x x -1))
(log.f64 (exp.f64 (sqrt.f64 (fma.f64 x x -1))))
(+.f64 1 (-.f64 (sqrt.f64 (fma.f64 x x -1)) 1))
(+.f64 (sqrt.f64 (fma.f64 x x -1)) 0)
(sqrt.f64 (fma.f64 x x -1))
(cbrt.f64 (pow.f64 (fma.f64 x x -1) 3/2))
(expm1.f64 (log1p.f64 (sqrt.f64 (fma.f64 x x -1))))
(+.f64 1 (-.f64 (sqrt.f64 (fma.f64 x x -1)) 1))
(+.f64 (sqrt.f64 (fma.f64 x x -1)) 0)
(sqrt.f64 (fma.f64 x x -1))
(exp.f64 (log.f64 (sqrt.f64 (fma.f64 x x -1))))
(+.f64 1 (-.f64 (sqrt.f64 (fma.f64 x x -1)) 1))
(+.f64 (sqrt.f64 (fma.f64 x x -1)) 0)
(sqrt.f64 (fma.f64 x x -1))
(log1p.f64 (expm1.f64 (sqrt.f64 (fma.f64 x x -1))))
(+.f64 1 (-.f64 (sqrt.f64 (fma.f64 x x -1)) 1))
(+.f64 (sqrt.f64 (fma.f64 x x -1)) 0)
(sqrt.f64 (fma.f64 x x -1))

eval32.0ms (0.9%)

Compiler: Compiled 1106 to 832 computations (24.8% saved)

prune10.0ms (0.3%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	70	2	72
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	70	3	73

Accurracy

100.0%

Counts

73 → 3

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	99.8%	(log.f64 (+.f64 x (-.f64 x (/.f64 1/2 x))))
✓	51.6%	(log.f64 (+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) 1))))
▶	99.6%	(log.f64 (+.f64 x x))
▶	99.8%	(log.f64 (+.f64 x (-.f64 x (/.f64 1/2 x))))
✓	51.6%	(log.f64 (+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) 1))))
▶	99.6%	(log.f64 (+.f64 x x))

Compiler

Compiled 48 to 32 computations (33.3% saved)

localize47.0ms (1.3%)

Compiler: Compiled 35 to 19 computations (45.7% saved)

eval0.0ms (0%)

Compiler: Compiled 1 to 1 computations (0% saved)

prune2.0ms (0.1%)

Pruning

3 alts after pruning (0 fresh and 3 done)

	Kept	Total
New	0	0
Fresh	0	0
Picked	2	2
Done	1	1
Total	3	3

Accurracy

100.0%

Counts

3 → 3

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	99.8%	(log.f64 (+.f64 x (-.f64 x (/.f64 1/2 x))))
✓	51.6%	(log.f64 (+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) 1))))
✓	99.6%	(log.f64 (+.f64 x x))

Compiler

Compiled 46 to 30 computations (34.8% saved)

regimes43.0ms (1.2%)

Counts

3 → 1

Calls

Call 1

Inputs
(log.f64 (+.f64 x x))
(log.f64 (+.f64 x (-.f64 x (/.f64 1/2 x))))
(log.f64 (+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) 1))))

Outputs
(log.f64 (+.f64 x (-.f64 x (/.f64 1/2 x))))

Calls

3 calls:

35.0ms	(+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) 1)))
3.0ms	x
3.0ms	(log.f64 (+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) 1))))

Results

Accuracy	Segments	Branch
99.8%	1	`x`
99.8%	1	`(log.f64 (+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) 1))))`
99.8%	1	`(+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) 1)))`

Compiler

Compiled 43 to 28 computations (34.9% saved)

regimes3.0ms (0.1%)

Accuracy

Total 0.0b remaining (0%)

Threshold costs 0b (0%)

Counts

1 → 1

Calls

Call 1

Inputs
(log.f64 (+.f64 x x))

Outputs
(log.f64 (+.f64 x x))

Calls

1 calls:

2.0ms

Results

Accuracy	Segments	Branch
99.6%	1	`x`

Compiler

Compiled 7 to 4 computations (42.9% saved)

simplify5.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

8×	`+-commutative`
6×	`sub-neg`
4×	`neg-mul-1`
4×	`*-commutative`
4×	`neg-sub0`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	34
1	14	34
2	21	34
3	25	34
4	28	34
5	29	34

Stop Event

1×	done
1×	saturated

Calls

Call 1

Inputs
(log.f64 (+.f64 x (-.f64 x (/.f64 1/2 x))))
(log.f64 (+.f64 x x))

Outputs
(log.f64 (+.f64 x (-.f64 x (/.f64 1/2 x))))
(log.f64 (+.f64 x x))

Compiler

Compiled 14 to 9 computations (35.7% saved)

soundness89.0ms (2.5%)

Rules

1482×	`fma-def`
1296×	`associate-/l*`
880×	`associate-/r*`
478×	`associate-*r/`
444×	`*-commutative`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	111	1080
1	255	962
2	667	852
3	2198	816
4	7264	816

Stop Event

1×	node limit

Compiler

Compiled 29 to 20 computations (31% saved)

end31.0ms (0.9%)

Compiler: Compiled 46 to 30 computations (34.8% saved)

Hyperbolic arc-cosine

Details

analyze104.0ms (2.9%)

sample2.5s (69.3%)

preprocess172.0ms (4.8%)

simplify173.0ms (4.8%)

eval1.0ms (0%)

prune1.0ms (0%)

localize43.0ms (1.2%)

series1.0ms (0%)

rewrite167.0ms (4.6%)

simplify188.0ms (5.2%)

eval32.0ms (0.9%)

prune10.0ms (0.3%)

localize47.0ms (1.3%)

eval0.0ms (0%)

prune2.0ms (0.1%)

regimes43.0ms (1.2%)

regimes3.0ms (0.1%)

simplify5.0ms (0.1%)

soundness89.0ms (2.5%)

end31.0ms (0.9%)

Profiling