Details

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 6 to 4 computations (33.3% saved)

sample712.0ms (47.8%)

Results

700.0ms

8256×

body

256

valid

Bogosity

preprocess13.0ms (0.8%)

Algorithm

2×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	4	5
0	1	1

Stop Event

1×	saturated
1×	saturated

Calls

Call 1

Inputs
0

Outputs
0

Call 2

Inputs
(acosh.f64 x)

Outputs
(acosh.f64 x)

Compiler

Compiled 11 to 8 computations (27.3% saved)

simplify164.0ms (11%)

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 (0.1%)

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

52.7%

Counts

3 → 1

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	52.7%	(log.f64 (+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) 1))))
▶	52.7%	(log.f64 (+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) 1))))

Compiler

Compiled 20 to 14 computations (30% saved)

localize45.0ms (3%)

Local Accuracy

Found 1 expressions with local accuracy:

New	Accuracy	Program
✓	54.5%	(sqrt.f64 (-.f64 (*.f64 x x) 1))

Compiler

Compiled 35 to 18 computations (48.6% saved)

series1.0ms (0.1%)

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))

rewrite57.0ms (3.8%)

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))))

simplify68.0ms (4.5%)

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))

eval30.0ms (2%)

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

prune9.0ms (0.6%)

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
▶	100.0%	(log.f64 (+.f64 x (-.f64 x (/.f64 1/2 x))))
✓	52.7%	(log.f64 (+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) 1))))
▶	99.8%	(log.f64 (+.f64 x x))
▶	100.0%	(log.f64 (+.f64 x (-.f64 x (/.f64 1/2 x))))
✓	52.7%	(log.f64 (+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) 1))))
▶	99.8%	(log.f64 (+.f64 x x))

Compiler

Compiled 48 to 32 computations (33.3% saved)

localize49.0ms (3.3%)

Local Accuracy

Found 1 expressions with local accuracy:

New	Accuracy	Program
✓	100.0%	(log.f64 (+.f64 x (-.f64 x (/.f64 1/2 x))))

Compiler

Compiled 35 to 19 computations (45.7% saved)

series2.0ms (0.1%)

Counts

1 → 12

Calls

3 calls:

Time	Variable		Point	Expression
1.0ms	x	@	0	(log.f64 (+.f64 x (-.f64 x (/.f64 1/2 x))))
1.0ms	x	@	-inf	(log.f64 (+.f64 x (-.f64 x (/.f64 1/2 x))))
1.0ms	x	@	inf	(log.f64 (+.f64 x (-.f64 x (/.f64 1/2 x))))

rewrite67.0ms (4.5%)

Algorithm

1×	batch-egg-rewrite

Rules

948×	`log-prod`
934×	`fma-def`
656×	`prod-exp`
628×	`pow-prod-down`
470×	`pow-exp`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	9	23
1	204	23
2	2950	19

Stop Event

1×	node limit

Counts

1 → 43

Calls

Call 1

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

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

simplify73.0ms (4.9%)

Algorithm

1×	egg-herbie

Rules

1110×	`fma-def`
988×	`sub-neg`
770×	`fma-neg`
696×	`cancel-sign-sub-inv`
528×	`log-prod`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	193	2195
1	462	2035
2	1384	1979
3	5304	1929

Stop Event

1×	node limit

Counts

55 → 119

Calls

Call 1

Inputs
(+.f64 (log.f64 -1/2) (*.f64 -1 (log.f64 x)))
(+.f64 (log.f64 -1/2) (+.f64 (.f64 -4 (pow.f64 x 2)) (.f64 -1 (log.f64 x))))
(+.f64 (log.f64 -1/2) (+.f64 (.f64 -4 (pow.f64 x 2)) (+.f64 (.f64 -8 (pow.f64 x 4)) (*.f64 -1 (log.f64 x)))))
(+.f64 (log.f64 -1/2) (+.f64 (.f64 -4 (pow.f64 x 2)) (+.f64 (.f64 -8 (pow.f64 x 4)) (+.f64 (.f64 -64/3 (pow.f64 x 6)) (.f64 -1 (log.f64 x))))))
(+.f64 (log.f64 2) (*.f64 -1 (log.f64 (/.f64 1 x))))
(-.f64 (+.f64 (.f64 -1 (log.f64 (/.f64 1 x))) (log.f64 2)) (.f64 1/4 (/.f64 1 (pow.f64 x 2))))
(-.f64 (+.f64 (.f64 -1 (log.f64 (/.f64 1 x))) (log.f64 2)) (+.f64 (.f64 1/32 (/.f64 1 (pow.f64 x 4))) (*.f64 1/4 (/.f64 1 (pow.f64 x 2)))))
(-.f64 (+.f64 (.f64 -1 (log.f64 (/.f64 1 x))) (log.f64 2)) (+.f64 (.f64 1/32 (/.f64 1 (pow.f64 x 4))) (+.f64 (.f64 1/192 (/.f64 1 (pow.f64 x 6))) (.f64 1/4 (/.f64 1 (pow.f64 x 2))))))
(+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -2))
(-.f64 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -2)) (.f64 1/4 (/.f64 1 (pow.f64 x 2))))
(-.f64 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -2)) (+.f64 (.f64 1/32 (/.f64 1 (pow.f64 x 4))) (*.f64 1/4 (/.f64 1 (pow.f64 x 2)))))
(-.f64 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -2)) (+.f64 (.f64 1/32 (/.f64 1 (pow.f64 x 4))) (+.f64 (.f64 1/192 (/.f64 1 (pow.f64 x 6))) (.f64 1/4 (/.f64 1 (pow.f64 x 2))))))
(+.f64 (log.f64 (fma.f64 x 2 (/.f64 -1/2 x))) 0)
(+.f64 (*.f64 2 (log.f64 (cbrt.f64 (fma.f64 x 2 (/.f64 -1/2 x))))) (log.f64 (cbrt.f64 (fma.f64 x 2 (/.f64 -1/2 x)))))
(+.f64 (log.f64 (sqrt.f64 (fma.f64 x 2 (/.f64 -1/2 x)))) (log.f64 (sqrt.f64 (fma.f64 x 2 (/.f64 -1/2 x)))))
(+.f64 0 (log.f64 (fma.f64 x 2 (/.f64 -1/2 x))))
(+.f64 (log.f64 (cbrt.f64 (fma.f64 x 2 (/.f64 -1/2 x)))) (*.f64 2 (log.f64 (cbrt.f64 (fma.f64 x 2 (/.f64 -1/2 x))))))
(+.f64 (log.f64 (-.f64 (*.f64 x x) (pow.f64 (-.f64 x (/.f64 1/2 x)) 2))) (log.f64 (/.f64 1 (+.f64 (-.f64 x x) (/.f64 1/2 x)))))
(+.f64 (log.f64 (+.f64 (pow.f64 (-.f64 x (/.f64 1/2 x)) 3) (pow.f64 x 3))) (log.f64 (/.f64 1 (fma.f64 (-.f64 x (/.f64 1/2 x)) (-.f64 (-.f64 x (/.f64 1/2 x)) x) (*.f64 x x)))))
(-.f64 0 (log.f64 (/.f64 (fma.f64 (-.f64 x (/.f64 1/2 x)) (-.f64 (-.f64 x (/.f64 1/2 x)) x) (*.f64 x x)) (+.f64 (pow.f64 (-.f64 x (/.f64 1/2 x)) 3) (pow.f64 x 3)))))
(-.f64 0 (log.f64 (/.f64 (+.f64 (-.f64 x x) (/.f64 1/2 x)) (-.f64 (*.f64 x x) (pow.f64 (-.f64 x (/.f64 1/2 x)) 2)))))
(-.f64 (log.f64 (-.f64 (*.f64 x x) (pow.f64 (-.f64 x (/.f64 1/2 x)) 2))) (log.f64 (+.f64 (-.f64 x x) (/.f64 1/2 x))))
(-.f64 (log.f64 (+.f64 (pow.f64 (-.f64 x (/.f64 1/2 x)) 3) (pow.f64 x 3))) (log.f64 (fma.f64 (-.f64 x (/.f64 1/2 x)) (-.f64 (-.f64 x (/.f64 1/2 x)) x) (*.f64 x x))))
(-.f64 (log.f64 (+.f64 (pow.f64 (-.f64 x (/.f64 1/2 x)) 3) (pow.f64 x 3))) (log.f64 (+.f64 (pow.f64 (-.f64 x (/.f64 1/2 x)) 2) (-.f64 (.f64 x x) (.f64 x (-.f64 x (/.f64 1/2 x)))))))
(-.f64 (exp.f64 (log1p.f64 (log.f64 (fma.f64 x 2 (/.f64 -1/2 x))))) 1)
(-.f64 (log.f64 (neg.f64 (+.f64 (pow.f64 (-.f64 x (/.f64 1/2 x)) 3) (pow.f64 x 3)))) (log.f64 (neg.f64 (fma.f64 (-.f64 x (/.f64 1/2 x)) (-.f64 (-.f64 x (/.f64 1/2 x)) x) (*.f64 x x)))))
(-.f64 (log.f64 (neg.f64 (-.f64 (*.f64 x x) (pow.f64 (-.f64 x (/.f64 1/2 x)) 2)))) (log.f64 (neg.f64 (+.f64 (-.f64 x x) (/.f64 1/2 x)))))
(-.f64 (log.f64 (-.f64 (pow.f64 (+.f64 x x) 3) (*.f64 1/8 (pow.f64 x -3)))) (log.f64 (+.f64 (pow.f64 (+.f64 x x) 2) (fma.f64 1/4 (pow.f64 x -2) 1))))
(-.f64 (log.f64 (-.f64 (pow.f64 (-.f64 x (/.f64 1/2 x)) 2) (*.f64 x x))) (log.f64 (-.f64 (-.f64 x (/.f64 1/2 x)) x)))
(-.f64 (log.f64 (-.f64 (pow.f64 (+.f64 x x) 2) (/.f64 1/4 (*.f64 x x)))) (log.f64 (fma.f64 x 2 (/.f64 1/2 x))))
(*.f64 (log.f64 (fma.f64 x 2 (/.f64 -1/2 x))) 1)
(*.f64 1 (log.f64 (fma.f64 x 2 (/.f64 -1/2 x))))
(*.f64 (cbrt.f64 (log.f64 (fma.f64 x 2 (/.f64 -1/2 x)))) (pow.f64 (cbrt.f64 (log.f64 (fma.f64 x 2 (/.f64 -1/2 x)))) 2))
(*.f64 (pow.f64 (cbrt.f64 (log.f64 (fma.f64 x 2 (/.f64 -1/2 x)))) 2) (cbrt.f64 (log.f64 (fma.f64 x 2 (/.f64 -1/2 x)))))
(*.f64 (sqrt.f64 (log.f64 (fma.f64 x 2 (/.f64 -1/2 x)))) (sqrt.f64 (log.f64 (fma.f64 x 2 (/.f64 -1/2 x)))))
(*.f64 3 (log.f64 (cbrt.f64 (fma.f64 x 2 (/.f64 -1/2 x)))))
(*.f64 2 (log.f64 (sqrt.f64 (fma.f64 x 2 (/.f64 -1/2 x)))))
(.f64 1/3 (.f64 3 (log.f64 (fma.f64 x 2 (/.f64 -1/2 x)))))
(pow.f64 (log.f64 (fma.f64 x 2 (/.f64 -1/2 x))) 1)
(pow.f64 (cbrt.f64 (log.f64 (fma.f64 x 2 (/.f64 -1/2 x)))) 3)
(pow.f64 (pow.f64 (log.f64 (fma.f64 x 2 (/.f64 -1/2 x))) 2) 1/2)
(pow.f64 (pow.f64 (log.f64 (fma.f64 x 2 (/.f64 -1/2 x))) 3) 1/3)
(pow.f64 (sqrt.f64 (log.f64 (fma.f64 x 2 (/.f64 -1/2 x)))) 2)
(neg.f64 (log.f64 (/.f64 (fma.f64 (-.f64 x (/.f64 1/2 x)) (-.f64 (-.f64 x (/.f64 1/2 x)) x) (*.f64 x x)) (+.f64 (pow.f64 (-.f64 x (/.f64 1/2 x)) 3) (pow.f64 x 3)))))
(neg.f64 (log.f64 (/.f64 (+.f64 (-.f64 x x) (/.f64 1/2 x)) (-.f64 (*.f64 x x) (pow.f64 (-.f64 x (/.f64 1/2 x)) 2)))))
(sqrt.f64 (pow.f64 (log.f64 (fma.f64 x 2 (/.f64 -1/2 x))) 2))
(cbrt.f64 (pow.f64 (log.f64 (fma.f64 x 2 (/.f64 -1/2 x))) 3))
(expm1.f64 (log1p.f64 (log.f64 (fma.f64 x 2 (/.f64 -1/2 x)))))
(exp.f64 (log.f64 (log.f64 (fma.f64 x 2 (/.f64 -1/2 x)))))
(exp.f64 (*.f64 (log.f64 (log.f64 (fma.f64 x 2 (/.f64 -1/2 x)))) 1))
(exp.f64 (.f64 (.f64 (log.f64 (log.f64 (fma.f64 x 2 (/.f64 -1/2 x)))) 1) 1))
(exp.f64 (*.f64 (log.f64 (cbrt.f64 (log.f64 (fma.f64 x 2 (/.f64 -1/2 x))))) 3))
(exp.f64 (*.f64 (log.f64 (pow.f64 (log.f64 (fma.f64 x 2 (/.f64 -1/2 x))) 3)) 1/3))
(exp.f64 (*.f64 (log.f64 (sqrt.f64 (log.f64 (fma.f64 x 2 (/.f64 -1/2 x))))) 2))
(log1p.f64 (-.f64 (fma.f64 x 2 (/.f64 -1/2 x)) 1))

Outputs
(+.f64 (log.f64 -1/2) (*.f64 -1 (log.f64 x)))
(+.f64 (log.f64 -1/2) (neg.f64 (log.f64 x)))
(-.f64 (log.f64 -1/2) (log.f64 x))
(log.f64 (/.f64 -1/2 x))
(+.f64 (log.f64 -1/2) (+.f64 (.f64 -4 (pow.f64 x 2)) (.f64 -1 (log.f64 x))))
(+.f64 (log.f64 -1/2) (fma.f64 -4 (*.f64 x x) (neg.f64 (log.f64 x))))
(+.f64 (log.f64 -1/2) (-.f64 (.f64 (.f64 -4 x) x) (log.f64 x)))
(fma.f64 x (*.f64 x -4) (log.f64 (/.f64 -1/2 x)))
(+.f64 (log.f64 -1/2) (+.f64 (.f64 -4 (pow.f64 x 2)) (+.f64 (.f64 -8 (pow.f64 x 4)) (*.f64 -1 (log.f64 x)))))
(+.f64 (log.f64 -1/2) (fma.f64 -4 (*.f64 x x) (fma.f64 -8 (pow.f64 x 4) (neg.f64 (log.f64 x)))))
(+.f64 (log.f64 -1/2) (-.f64 (fma.f64 -4 (.f64 x x) (.f64 -8 (pow.f64 x 4))) (log.f64 x)))
(+.f64 (fma.f64 x (.f64 x -4) (log.f64 (/.f64 -1/2 x))) (.f64 -8 (pow.f64 x 4)))
(fma.f64 x (*.f64 x -4) (fma.f64 -8 (pow.f64 x 4) (log.f64 (/.f64 -1/2 x))))
(+.f64 (log.f64 -1/2) (+.f64 (.f64 -4 (pow.f64 x 2)) (+.f64 (.f64 -8 (pow.f64 x 4)) (+.f64 (.f64 -64/3 (pow.f64 x 6)) (.f64 -1 (log.f64 x))))))
(+.f64 (log.f64 -1/2) (fma.f64 -4 (*.f64 x x) (fma.f64 -8 (pow.f64 x 4) (fma.f64 -64/3 (pow.f64 x 6) (neg.f64 (log.f64 x))))))
(+.f64 (log.f64 -1/2) (fma.f64 -4 (.f64 x x) (-.f64 (fma.f64 -8 (pow.f64 x 4) (.f64 -64/3 (pow.f64 x 6))) (log.f64 x))))
(+.f64 (fma.f64 x (.f64 x -4) (fma.f64 -8 (pow.f64 x 4) (.f64 -64/3 (pow.f64 x 6)))) (log.f64 (/.f64 -1/2 x)))
(+.f64 (fma.f64 -8 (pow.f64 x 4) (.f64 -64/3 (pow.f64 x 6))) (fma.f64 x (.f64 x -4) (log.f64 (/.f64 -1/2 x))))
(+.f64 (log.f64 2) (*.f64 -1 (log.f64 (/.f64 1 x))))
(fma.f64 -1 (neg.f64 (log.f64 x)) (log.f64 2))
(+.f64 (log.f64 x) (log.f64 2))
(log.f64 (+.f64 x x))
(-.f64 (+.f64 (.f64 -1 (log.f64 (/.f64 1 x))) (log.f64 2)) (.f64 1/4 (/.f64 1 (pow.f64 x 2))))
(-.f64 (fma.f64 -1 (neg.f64 (log.f64 x)) (log.f64 2)) (/.f64 1/4 (*.f64 x x)))
(+.f64 (log.f64 x) (+.f64 (log.f64 2) (/.f64 -1/4 (*.f64 x x))))
(fma.f64 (pow.f64 x -2) -1/4 (log.f64 (+.f64 x x)))
(-.f64 (+.f64 (.f64 -1 (log.f64 (/.f64 1 x))) (log.f64 2)) (+.f64 (.f64 1/32 (/.f64 1 (pow.f64 x 4))) (*.f64 1/4 (/.f64 1 (pow.f64 x 2)))))
(-.f64 (fma.f64 -1 (neg.f64 (log.f64 x)) (log.f64 2)) (+.f64 (/.f64 1/4 (*.f64 x x)) (/.f64 1/32 (pow.f64 x 4))))
(-.f64 (+.f64 (log.f64 x) (+.f64 (log.f64 2) (/.f64 -1/4 (*.f64 x x)))) (/.f64 1/32 (pow.f64 x 4)))
(+.f64 (log.f64 2) (+.f64 (log.f64 x) (-.f64 (/.f64 -1/4 (*.f64 x x)) (/.f64 1/32 (pow.f64 x 4)))))
(+.f64 (fma.f64 (pow.f64 x -2) -1/4 (log.f64 (+.f64 x x))) (/.f64 -1/32 (pow.f64 x 4)))
(-.f64 (+.f64 (.f64 -1 (log.f64 (/.f64 1 x))) (log.f64 2)) (+.f64 (.f64 1/32 (/.f64 1 (pow.f64 x 4))) (+.f64 (.f64 1/192 (/.f64 1 (pow.f64 x 6))) (.f64 1/4 (/.f64 1 (pow.f64 x 2))))))
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(log.f64 (fma.f64 x 2 (/.f64 -1/2 x)))
(exp.f64 (.f64 (.f64 (log.f64 (log.f64 (fma.f64 x 2 (/.f64 -1/2 x)))) 1) 1))
(log.f64 (fma.f64 x 2 (/.f64 -1/2 x)))
(exp.f64 (*.f64 (log.f64 (cbrt.f64 (log.f64 (fma.f64 x 2 (/.f64 -1/2 x))))) 3))
(log.f64 (fma.f64 x 2 (/.f64 -1/2 x)))
(exp.f64 (*.f64 (log.f64 (pow.f64 (log.f64 (fma.f64 x 2 (/.f64 -1/2 x))) 3)) 1/3))
(log.f64 (fma.f64 x 2 (/.f64 -1/2 x)))
(exp.f64 (*.f64 (log.f64 (sqrt.f64 (log.f64 (fma.f64 x 2 (/.f64 -1/2 x))))) 2))
(log.f64 (fma.f64 x 2 (/.f64 -1/2 x)))
(log1p.f64 (-.f64 (fma.f64 x 2 (/.f64 -1/2 x)) 1))
(log1p.f64 (+.f64 (fma.f64 x 2 (/.f64 -1/2 x)) -1))
(log1p.f64 (+.f64 -1 (fma.f64 x 2 (/.f64 -1/2 x))))

eval37.0ms (2.5%)

Compiler: Compiled 2022 to 1447 computations (28.4% saved)

prune15.0ms (1%)

Pruning

3 alts after pruning (0 fresh and 3 done)

	Pruned	Kept	Total
New	119	0	119
Fresh	0	0	0
Picked	0	2	2
Done	0	1	1
Total	119	3	122

Accurracy

100.0%

Counts

122 → 3

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	100.0%	(log.f64 (+.f64 x (-.f64 x (/.f64 1/2 x))))
✓	52.7%	(log.f64 (+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) 1))))
✓	99.8%	(log.f64 (+.f64 x x))

Compiler

Compiled 46 to 30 computations (34.8% saved)

regimes11.0ms (0.7%)

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:

4.0ms	x
3.0ms	(+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) 1)))
3.0ms	(log.f64 (+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) 1))))

Results

Accuracy	Segments	Branch
100.0%	1	`x`
100.0%	1	`(log.f64 (+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) 1))))`
100.0%	1	`(+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) 1)))`

Compiler

Compiled 43 to 28 computations (34.9% saved)

regimes3.0ms (0.2%)

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
99.8%	1	`x`

Compiler

Compiled 7 to 4 computations (42.9% saved)

simplify5.0ms (0.3%)

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)

soundness91.0ms (6.1%)

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)

end37.0ms (2.5%)

Compiler: Compiled 72 to 50 computations (30.6% saved)

Rust f64::acosh

Details

analyze0.0ms (0%)

sample712.0ms (47.8%)

preprocess13.0ms (0.8%)

simplify164.0ms (11%)

eval1.0ms (0%)

prune1.0ms (0.1%)

localize45.0ms (3%)

series1.0ms (0.1%)

rewrite57.0ms (3.8%)

simplify68.0ms (4.5%)

eval30.0ms (2%)

prune9.0ms (0.6%)

localize49.0ms (3.3%)

series2.0ms (0.1%)

rewrite67.0ms (4.5%)

simplify73.0ms (4.9%)

eval37.0ms (2.5%)

prune15.0ms (1%)

regimes11.0ms (0.7%)

regimes3.0ms (0.2%)

simplify5.0ms (0.3%)

soundness91.0ms (6.1%)

end37.0ms (2.5%)

Profiling