Details

analyze585.0ms (4.3%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.9%	0.1%	0
0%	99.9%	0.1%	1
0%	99.9%	0.1%	2
0%	99.9%	0.1%	3
0%	99.9%	0.1%	4
0%	99.9%	0.1%	5
12.5%	68.6%	18.9%	6
18.7%	62.4%	18.9%	7
18.7%	59.3%	22%	8
28.1%	39%	32.9%	9
32.8%	34.3%	32.9%	10
32.8%	32%	35.3%	11
38.2%	20.7%	41.1%	12
41%	17.9%	41.1%	13
41%	16.6%	42.5%	14

Compiler

Compiled 41 to 24 computations (41.5% saved)

sample2.8s (21%)

Results

2.5s	7800×	body	256	valid
198.0ms	1261×	body	128	invalid
79.0ms	456×	body	128	valid

Compiler

Compiled 122 to 71 computations (41.8% saved)

simplify171.0ms (1.3%)

Algorithm

1×	egg-herbie

Rules

729×	`fma-neg_binary64`
636×	`times-frac_binary64`
620×	`div-sub_binary64`
565×	`unsub-neg_binary64`
481×	`sub-neg_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	20	52
1	54	50
2	144	50
3	406	48
4	826	48
5	1523	48
6	1911	48
7	2632	48
8	2589	48
9	2971	48
10	3625	48
11	4193	48
12	4375	48
13	4485	48
14	4533	48
15	4557	48
16	4607	48
17	4882	48
18	4848	48

Stop Event

1×	node limit

Counts

1 → 2

prune4.0ms (0%)

Pruning

3 alts after pruning (3 fresh and 0 done)

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

Error

37.7b

Counts

3 → 2

Alt Table

Status	Error	Program
▶	37.7b	(+.f64 (cbrt.f64 (/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 g g) (.f64 h h))) g) (.f64 2 a))) (cbrt.f64 (.f64 (/.f64 (+.f64 g (sqrt.f64 (-.f64 (.f64 g g) (.f64 h h)))) a) -1/2)))
	37.9b	(+.f64 (cbrt.f64 (.f64 (/.f64 1 (.f64 2 a)) (+.f64 (neg.f64 g) (sqrt.f64 (-.f64 (.f64 g g) (.f64 h h)))))) (cbrt.f64 (.f64 (/.f64 1 (.f64 2 a)) (-.f64 (neg.f64 g) (sqrt.f64 (-.f64 (.f64 g g) (.f64 h h)))))))

Status

Error

Program

▶

37.7b

(+.f64 (cbrt.f64 (/.f64 (-.f64 (sqrt.f64 (-.f64 (*.f64 g g) (*.f64 h h))) g) (*.f64 2 a))) (cbrt.f64 (*.f64 (/.f64 (+.f64 g (sqrt.f64 (-.f64 (*.f64 g g) (*.f64 h h)))) a) -1/2)))

37.9b

(+.f64 (cbrt.f64 (*.f64 (/.f64 1 (*.f64 2 a)) (+.f64 (neg.f64 g) (sqrt.f64 (-.f64 (*.f64 g g) (*.f64 h h)))))) (cbrt.f64 (*.f64 (/.f64 1 (*.f64 2 a)) (-.f64 (neg.f64 g) (sqrt.f64 (-.f64 (*.f64 g g) (*.f64 h h)))))))

Compiler

Compiled 219 to 116 computations (47% saved)

localize19.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	3.0b	(-.f64 (.f64 g g) (.f64 h h))
✓	9.5b	(cbrt.f64 (/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 g g) (.f64 h h))) g) (*.f64 2 a)))
✓	10.3b	(cbrt.f64 (.f64 (/.f64 (+.f64 g (sqrt.f64 (-.f64 (.f64 g g) (*.f64 h h)))) a) -1/2))
✓	30.4b	(sqrt.f64 (-.f64 (.f64 g g) (.f64 h h)))

series1.1s (8.5%)

Counts

4 → 120

Calls

4 calls:

598.0ms	(cbrt.f64 (.f64 (/.f64 (+.f64 g (sqrt.f64 (-.f64 (.f64 g g) (*.f64 h h)))) a) -1/2))
534.0ms	(cbrt.f64 (/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 g g) (.f64 h h))) g) (*.f64 2 a)))
11.0ms	(sqrt.f64 (-.f64 (.f64 g g) (.f64 h h)))
6.0ms	(-.f64 (.f64 g g) (.f64 h h))

rewrite71.0ms (0.5%)

Algorithm

1×	batch-egg-rewrite

Rules

671×	`prod-diff_binary64`
204×	`add-sqr-sqrt_binary64`
196×	`log1p-expm1-u_binary64`
196×	`expm1-log1p-u_binary64`
193×	`add-cube-cbrt_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	18	68
1	409	68
2	4843	68
3	6030	68

Stop Event

1×	node limit

Counts

4 → 117

Calls

4 calls:

69.0ms	(-.f64 (.f64 g g) (.f64 h h))
69.0ms	(cbrt.f64 (/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 g g) (.f64 h h))) g) (*.f64 2 a)))
69.0ms	(cbrt.f64 (.f64 (/.f64 (+.f64 g (sqrt.f64 (-.f64 (.f64 g g) (*.f64 h h)))) a) -1/2))
69.0ms	(sqrt.f64 (-.f64 (.f64 g g) (.f64 h h)))

simplify120.0ms (0.9%)

Algorithm

1×	egg-herbie

Rules

350×	`associate-r_binary64`
325×	`times-frac_binary64`
273×	`fma-neg_binary64`
247×	`*-commutative_binary64`
243×	`fma-def_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	405	5670
1	1260	5468
2	4531	5278
3	5054	5278

Stop Event

1×	node limit

Counts

237 → 268

prune874.0ms (6.4%)

Pruning

19 alts after pruning (19 fresh and 0 done)

	Pruned	Kept	Total
New	363	19	382
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	365	19	384

Error

32.5b

Counts

384 → 19

Alt Table

Status	Error	Program
	37.5b	(+.f64 (/.f64 1 (cbrt.f64 (/.f64 (.f64 a 2) (-.f64 (sqrt.f64 (-.f64 (.f64 g g) (.f64 h h))) g)))) (cbrt.f64 (.f64 (/.f64 (+.f64 g (sqrt.f64 (-.f64 (.f64 g g) (.f64 h h)))) a) -1/2)))
	55.3b	(+.f64 (cbrt.f64 (/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 g g) (.f64 h h))) g) (.f64 2 a))) (.f64 (cbrt.f64 -1/2) (exp.f64 (*.f64 1/3 (-.f64 (log.f64 (/.f64 2 a)) (log.f64 (/.f64 1 g)))))))
	40.9b	(+.f64 (cbrt.f64 (/.f64 (-.f64 (pow.f64 (pow.f64 (-.f64 (.f64 g g) (.f64 h h)) 1/4) 2) g) (.f64 2 a))) (cbrt.f64 (.f64 (/.f64 (+.f64 g (sqrt.f64 (-.f64 (.f64 g g) (.f64 h h)))) a) -1/2)))
	49.9b	(+.f64 (cbrt.f64 (/.f64 (-.f64 g g) (.f64 2 a))) (cbrt.f64 (.f64 (/.f64 (+.f64 g (sqrt.f64 (-.f64 (.f64 g g) (.f64 h h)))) a) -1/2)))
	37.9b	(+.f64 (cbrt.f64 (/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 g g) (.f64 h h))) g) (.f64 2 a))) (.f64 (pow.f64 (cbrt.f64 (cbrt.f64 (.f64 (/.f64 (+.f64 g (sqrt.f64 (-.f64 (.f64 g g) (.f64 h h)))) a) -1/2))) 2) (cbrt.f64 (cbrt.f64 (.f64 (/.f64 (+.f64 g (sqrt.f64 (-.f64 (.f64 g g) (.f64 h h)))) a) -1/2)))))
	41.4b	(+.f64 (cbrt.f64 (/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 g g) (.f64 h h))) g) (.f64 2 a))) (cbrt.f64 (.f64 (/.f64 (+.f64 g (pow.f64 (pow.f64 (-.f64 (.f64 g g) (.f64 h h)) 1/4) 2)) a) -1/2)))
	42.0b	(+.f64 (cbrt.f64 (/.f64 (-.f64 (sqrt.f64 (pow.f64 (cbrt.f64 (-.f64 (.f64 g g) (.f64 h h))) 3)) g) (.f64 2 a))) (cbrt.f64 (.f64 (/.f64 (+.f64 g (sqrt.f64 (-.f64 (.f64 g g) (.f64 h h)))) a) -1/2)))
	43.8b	(+.f64 (cbrt.f64 (/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 g g) (.f64 h h))) g) (.f64 2 a))) (cbrt.f64 (.f64 (/.f64 (+.f64 g (pow.f64 (cbrt.f64 (sqrt.f64 (-.f64 (.f64 g g) (.f64 h h)))) 3)) a) -1/2)))
	42.2b	(+.f64 (cbrt.f64 (/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 g g) (.f64 h h))) g) (.f64 2 a))) (cbrt.f64 (.f64 (/.f64 (+.f64 g (sqrt.f64 (pow.f64 (cbrt.f64 (-.f64 (.f64 g g) (.f64 h h))) 3))) a) -1/2)))
	48.2b	(+.f64 (cbrt.f64 (/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 g g) (.f64 h h))) g) (.f64 2 a))) (.f64 (cbrt.f64 -1/2) (cbrt.f64 (*.f64 (/.f64 2 a) g))))
	43.8b	(+.f64 (log1p.f64 (expm1.f64 (cbrt.f64 (/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 g g) (.f64 h h))) g) (.f64 a 2))))) (cbrt.f64 (.f64 (/.f64 (+.f64 g (sqrt.f64 (-.f64 (.f64 g g) (.f64 h h)))) a) -1/2)))
	45.2b	(+.f64 (cbrt.f64 (/.f64 (-.f64 (exp.f64 (log.f64 (sqrt.f64 (-.f64 (.f64 g g) (.f64 h h))))) g) (.f64 2 a))) (cbrt.f64 (.f64 (/.f64 (+.f64 g (sqrt.f64 (-.f64 (.f64 g g) (.f64 h h)))) a) -1/2)))
	55.5b	(+.f64 (cbrt.f64 (/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 g g) (.f64 h h))) g) (.f64 2 a))) (.f64 (cbrt.f64 -1/2) (pow.f64 (/.f64 (*.f64 2 g) a) 1/3)))
	35.3b	(+.f64 (/.f64 (cbrt.f64 (/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 g g) (.f64 h h))) g) 2)) (cbrt.f64 a)) (cbrt.f64 (.f64 (/.f64 (+.f64 g (sqrt.f64 (-.f64 (.f64 g g) (*.f64 h h)))) a) -1/2)))
	56.7b	(+.f64 (cbrt.f64 (/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 g g) (.f64 h h))) g) (.f64 2 a))) (.f64 (cbrt.f64 -1/2) (cbrt.f64 (exp.f64 (+.f64 (log.f64 (/.f64 2 a)) (log.f64 g))))))
	35.3b	(+.f64 (.f64 (cbrt.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 g g) (.f64 h h))) g)) (cbrt.f64 (/.f64 1 (.f64 a 2)))) (cbrt.f64 (.f64 (/.f64 (+.f64 g (sqrt.f64 (-.f64 (.f64 g g) (*.f64 h h)))) a) -1/2)))
	52.8b	(+.f64 (.f64 (cbrt.f64 -1/2) (exp.f64 (.f64 1/3 (+.f64 (log.f64 (-.f64 (sqrt.f64 (-.f64 (pow.f64 g 2) (pow.f64 h 2))) g)) (log.f64 (/.f64 -1 a)))))) (cbrt.f64 (.f64 (/.f64 (+.f64 g (sqrt.f64 (-.f64 (.f64 g g) (*.f64 h h)))) a) -1/2)))
▶	35.0b	(+.f64 (cbrt.f64 (/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 g g) (.f64 h h))) g) (.f64 2 a))) (/.f64 (cbrt.f64 (.f64 (+.f64 g (sqrt.f64 (-.f64 (.f64 g g) (.f64 h h)))) -1/2)) (cbrt.f64 a)))
	52.9b	(+.f64 (cbrt.f64 (/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 g g) (.f64 h h))) g) (.f64 2 a))) (.f64 (cbrt.f64 1/2) (exp.f64 (*.f64 1/3 (+.f64 (log.f64 (+.f64 (sqrt.f64 (-.f64 (pow.f64 g 2) (pow.f64 h 2))) g)) (log.f64 (/.f64 -1 a)))))))

Compiler

Compiled 19096 to 9930 computations (48% saved)

localize17.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	1.2b	(-.f64 (sqrt.f64 (-.f64 (.f64 g g) (.f64 h h))) g)
	3.0b	(-.f64 (.f64 g g) (.f64 h h))
	9.5b	(cbrt.f64 (/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 g g) (.f64 h h))) g) (*.f64 2 a)))
	30.4b	(sqrt.f64 (-.f64 (.f64 g g) (.f64 h h)))

series13.0ms (0.1%)

Counts

1 → 24

Calls

1 calls:

13.0ms

(-.f64 (sqrt.f64 (-.f64 (*.f64 g g) (*.f64 h h))) g)

rewrite53.0ms (0.4%)

Algorithm

1×	batch-egg-rewrite

Rules

747×	`fma-def_binary64`
443×	`log-prod_binary64`
325×	`fma-neg_binary64`
166×	`expm1-udef_binary64`
166×	`log1p-udef_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	8	15
1	188	15
2	2466	14
3	5332	14

Stop Event

1×	node limit

Counts

1 → 99

Calls

1 calls:

51.0ms

(-.f64 (sqrt.f64 (-.f64 (*.f64 g g) (*.f64 h h))) g)

simplify58.0ms (0.4%)

Algorithm

1×	egg-herbie

Rules

447×	`distribute-neg-frac_binary64`
443×	`times-frac_binary64`
253×	`div-sub_binary64`
232×	`associate-/l*_binary64`
229×	`fma-def_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	83	618
1	249	598
2	787	584
3	3540	584
4	4802	584
5	5086	584

Stop Event

1×	node limit

Counts

123 → 139

prune1.5s (11%)

Pruning

20 alts after pruning (20 fresh and 0 done)

	Pruned	Kept	Total
New	438	8	446
Fresh	6	12	18
Picked	1	0	1
Done	0	0	0
Total	445	20	465

Error

31.5b

Counts

465 → 20

Alt Table

Status	Error	Program
	35.3b	(+.f64 (/.f64 (cbrt.f64 (/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 g g) (.f64 h h))) g) 2)) (cbrt.f64 a)) (cbrt.f64 (.f64 (/.f64 (+.f64 g (sqrt.f64 (-.f64 (.f64 g g) (*.f64 h h)))) a) -1/2)))
	46.8b	(+.f64 (cbrt.f64 (/.f64 (.f64 -1/2 (/.f64 (pow.f64 h 2) g)) (.f64 2 a))) (/.f64 (cbrt.f64 (.f64 (+.f64 g (sqrt.f64 (-.f64 (.f64 g g) (*.f64 h h)))) -1/2)) (cbrt.f64 a)))
	43.9b	(+.f64 (cbrt.f64 (/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 g g) (.f64 h h))) g) (.f64 2 a))) (/.f64 (cbrt.f64 (.f64 (+.f64 g g) -1/2)) (cbrt.f64 a)))
	56.7b	(+.f64 (cbrt.f64 (/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 g g) (.f64 h h))) g) (.f64 2 a))) (.f64 (cbrt.f64 -1/2) (cbrt.f64 (exp.f64 (+.f64 (log.f64 (/.f64 2 a)) (log.f64 g))))))
	37.5b	(+.f64 (/.f64 1 (cbrt.f64 (/.f64 (.f64 a 2) (-.f64 (sqrt.f64 (-.f64 (.f64 g g) (.f64 h h))) g)))) (cbrt.f64 (.f64 (/.f64 (+.f64 g (sqrt.f64 (-.f64 (.f64 g g) (.f64 h h)))) a) -1/2)))
	46.6b	(+.f64 (cbrt.f64 (/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 g g) (.f64 h h))) g) (.f64 2 a))) (/.f64 (cbrt.f64 (.f64 (+.f64 g (cbrt.f64 (pow.f64 (-.f64 (.f64 g g) (.f64 h h)) 3/2))) -1/2)) (cbrt.f64 a)))
	37.9b	(+.f64 (cbrt.f64 (/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 g g) (.f64 h h))) g) (.f64 2 a))) (.f64 (pow.f64 (cbrt.f64 (cbrt.f64 (.f64 (/.f64 (+.f64 g (sqrt.f64 (-.f64 (.f64 g g) (.f64 h h)))) a) -1/2))) 2) (cbrt.f64 (cbrt.f64 (.f64 (/.f64 (+.f64 g (sqrt.f64 (-.f64 (.f64 g g) (.f64 h h)))) a) -1/2)))))
	41.4b	(+.f64 (cbrt.f64 (/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 g g) (.f64 h h))) g) (.f64 2 a))) (cbrt.f64 (.f64 (/.f64 (+.f64 g (pow.f64 (pow.f64 (-.f64 (.f64 g g) (.f64 h h)) 1/4) 2)) a) -1/2)))
	42.2b	(+.f64 (cbrt.f64 (/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 g g) (.f64 h h))) g) (.f64 2 a))) (cbrt.f64 (.f64 (/.f64 (+.f64 g (sqrt.f64 (pow.f64 (cbrt.f64 (-.f64 (.f64 g g) (.f64 h h))) 3))) a) -1/2)))
	48.2b	(+.f64 (cbrt.f64 (/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 g g) (.f64 h h))) g) (.f64 2 a))) (.f64 (cbrt.f64 -1/2) (cbrt.f64 (*.f64 (/.f64 2 a) g))))
▶	32.6b	(+.f64 (/.f64 (cbrt.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 g g) (.f64 h h))) g)) (cbrt.f64 (.f64 a 2))) (/.f64 (cbrt.f64 (.f64 (+.f64 g (sqrt.f64 (-.f64 (.f64 g g) (.f64 h h)))) -1/2)) (cbrt.f64 a)))
	43.8b	(+.f64 (log1p.f64 (expm1.f64 (cbrt.f64 (/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 g g) (.f64 h h))) g) (.f64 a 2))))) (cbrt.f64 (.f64 (/.f64 (+.f64 g (sqrt.f64 (-.f64 (.f64 g g) (.f64 h h)))) a) -1/2)))
	45.2b	(+.f64 (cbrt.f64 (/.f64 (-.f64 (exp.f64 (log.f64 (sqrt.f64 (-.f64 (.f64 g g) (.f64 h h))))) g) (.f64 2 a))) (cbrt.f64 (.f64 (/.f64 (+.f64 g (sqrt.f64 (-.f64 (.f64 g g) (.f64 h h)))) a) -1/2)))
	49.6b	(+.f64 (cbrt.f64 (/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 g g) (.f64 h h))) g) (.f64 2 a))) (/.f64 (cbrt.f64 (.f64 (+.f64 g (pow.f64 (pow.f64 (-.f64 (.f64 g g) (.f64 h h)) 3/2) 1/3)) -1/2)) (cbrt.f64 a)))
	35.3b	(+.f64 (.f64 (cbrt.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 g g) (.f64 h h))) g)) (cbrt.f64 (/.f64 1 (.f64 a 2)))) (cbrt.f64 (.f64 (/.f64 (+.f64 g (sqrt.f64 (-.f64 (.f64 g g) (*.f64 h h)))) a) -1/2)))
	59.0b	(+.f64 (cbrt.f64 (/.f64 (fma.f64 (sqrt.f64 g) (neg.f64 (sqrt.f64 g)) (hypot.f64 g (sqrt.f64 (neg.f64 (.f64 h h))))) (.f64 2 a))) (/.f64 (cbrt.f64 (.f64 (+.f64 g (sqrt.f64 (-.f64 (.f64 g g) (*.f64 h h)))) -1/2)) (cbrt.f64 a)))
	51.8b	(+.f64 (cbrt.f64 (/.f64 (fma.f64 (pow.f64 (cbrt.f64 g) 2) (neg.f64 (cbrt.f64 g)) (hypot.f64 g (sqrt.f64 (neg.f64 (.f64 h h))))) (.f64 2 a))) (/.f64 (cbrt.f64 (.f64 (+.f64 g (sqrt.f64 (-.f64 (.f64 g g) (*.f64 h h)))) -1/2)) (cbrt.f64 a)))
	40.9b	(+.f64 (cbrt.f64 (/.f64 (-.f64 (pow.f64 (pow.f64 (-.f64 (.f64 g g) (.f64 h h)) 1/4) 2) g) (.f64 2 a))) (cbrt.f64 (.f64 (/.f64 (+.f64 g (sqrt.f64 (-.f64 (.f64 g g) (.f64 h h)))) a) -1/2)))
	39.5b	(+.f64 (cbrt.f64 (/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 g g) (.f64 h h))) g) (.f64 2 a))) (/.f64 (cbrt.f64 (.f64 (+.f64 g (.f64 (cbrt.f64 (-.f64 (.f64 g g) (.f64 h h))) (cbrt.f64 (sqrt.f64 (-.f64 (.f64 g g) (*.f64 h h)))))) -1/2)) (cbrt.f64 a)))
	42.0b	(+.f64 (cbrt.f64 (/.f64 (-.f64 (sqrt.f64 (pow.f64 (cbrt.f64 (-.f64 (.f64 g g) (.f64 h h))) 3)) g) (.f64 2 a))) (cbrt.f64 (.f64 (/.f64 (+.f64 g (sqrt.f64 (-.f64 (.f64 g g) (.f64 h h)))) a) -1/2)))

Compiler

Compiled 21012 to 9780 computations (53.5% saved)

localize18.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.8b	(cbrt.f64 (*.f64 a 2))
	1.2b	(-.f64 (sqrt.f64 (-.f64 (.f64 g g) (.f64 h h))) g)
	3.0b	(-.f64 (.f64 g g) (.f64 h h))
	30.4b	(sqrt.f64 (-.f64 (.f64 g g) (.f64 h h)))

series34.0ms (0.3%)

Counts

1 → 12

Calls

1 calls:

34.0ms

(cbrt.f64 (*.f64 a 2))

rewrite64.0ms (0.5%)

Algorithm

1×	batch-egg-rewrite

Rules

707×	`log1p-udef_binary64`
388×	`log1p-expm1-u_binary64`
388×	`expm1-log1p-u_binary64`
337×	`pow1_binary64`
300×	`unpow-prod-down_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	5	6
1	98	6
2	1044	6
3	4636	6
4	5724	6

Stop Event

1×	node limit

Counts

1 → 44

Calls

1 calls:

64.0ms

(cbrt.f64 (*.f64 a 2))

simplify118.0ms (0.9%)

Algorithm

1×	egg-herbie

Rules

1252×	`sqr-pow_binary64`
710×	`cube-prod_binary64`
698×	`pow-sqr_binary64`
694×	`fabs-mul_binary64`
416×	`unswap-sqr_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	104
1	25	104
2	42	104
3	74	104
4	158	104
5	406	104
6	545	104
7	905	104
8	923	104
9	1082	104
10	1272	104
11	1537	104
12	1820	104
13	2238	104
14	2710	104
15	3373	104
16	3661	104
17	3957	104
18	4167	104
19	4255	104
20	4355	104
21	5365	104

Stop Event

1×	node limit

Counts

56 → 47

prune1.5s (10.8%)

Pruning

21 alts after pruning (21 fresh and 0 done)

	Pruned	Kept	Total
New	409	5	414
Fresh	3	16	19
Picked	1	0	1
Done	0	0	0
Total	413	21	434

Error

31.5b

Counts

434 → 21

Alt Table

Status	Error	Program
	43.9b	(+.f64 (cbrt.f64 (/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 g g) (.f64 h h))) g) (.f64 2 a))) (/.f64 (cbrt.f64 (.f64 (+.f64 g g) -1/2)) (cbrt.f64 a)))
	56.7b	(+.f64 (cbrt.f64 (/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 g g) (.f64 h h))) g) (.f64 2 a))) (.f64 (cbrt.f64 -1/2) (cbrt.f64 (exp.f64 (+.f64 (log.f64 (/.f64 2 a)) (log.f64 g))))))
	38.8b	(+.f64 (/.f64 (cbrt.f64 (-.f64 (.f64 (sqrt.f64 (pow.f64 (cbrt.f64 (-.f64 (.f64 g g) (.f64 h h))) 2)) (sqrt.f64 (cbrt.f64 (-.f64 (.f64 g g) (.f64 h h))))) g)) (cbrt.f64 (.f64 a 2))) (/.f64 (cbrt.f64 (.f64 (+.f64 g (sqrt.f64 (-.f64 (.f64 g g) (*.f64 h h)))) -1/2)) (cbrt.f64 a)))
	37.5b	(+.f64 (/.f64 1 (cbrt.f64 (/.f64 (.f64 a 2) (-.f64 (sqrt.f64 (-.f64 (.f64 g g) (.f64 h h))) g)))) (cbrt.f64 (.f64 (/.f64 (+.f64 g (sqrt.f64 (-.f64 (.f64 g g) (.f64 h h)))) a) -1/2)))
	46.6b	(+.f64 (cbrt.f64 (/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 g g) (.f64 h h))) g) (.f64 2 a))) (/.f64 (cbrt.f64 (.f64 (+.f64 g (cbrt.f64 (pow.f64 (-.f64 (.f64 g g) (.f64 h h)) 3/2))) -1/2)) (cbrt.f64 a)))
	46.7b	(+.f64 (/.f64 (cbrt.f64 (.f64 -1/2 (/.f64 (.f64 h h) g))) (cbrt.f64 (.f64 a 2))) (/.f64 (cbrt.f64 (.f64 (+.f64 g (sqrt.f64 (-.f64 (.f64 g g) (.f64 h h)))) -1/2)) (cbrt.f64 a)))
	35.3b	(+.f64 (.f64 (cbrt.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 g g) (.f64 h h))) g)) (cbrt.f64 (/.f64 1 (.f64 a 2)))) (cbrt.f64 (.f64 (/.f64 (+.f64 g (sqrt.f64 (-.f64 (.f64 g g) (*.f64 h h)))) a) -1/2)))
	47.9b	(+.f64 (/.f64 (cbrt.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 g g) (.f64 h h))) g)) (cbrt.f64 (.f64 a 2))) (/.f64 (cbrt.f64 (.f64 (+.f64 g (neg.f64 g)) -1/2)) (cbrt.f64 a)))
	51.8b	(+.f64 (cbrt.f64 (/.f64 (fma.f64 (pow.f64 (cbrt.f64 g) 2) (neg.f64 (cbrt.f64 g)) (hypot.f64 g (sqrt.f64 (neg.f64 (.f64 h h))))) (.f64 2 a))) (/.f64 (cbrt.f64 (.f64 (+.f64 g (sqrt.f64 (-.f64 (.f64 g g) (*.f64 h h)))) -1/2)) (cbrt.f64 a)))
	37.9b	(+.f64 (cbrt.f64 (/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 g g) (.f64 h h))) g) (.f64 2 a))) (.f64 (pow.f64 (cbrt.f64 (cbrt.f64 (.f64 (/.f64 (+.f64 g (sqrt.f64 (-.f64 (.f64 g g) (.f64 h h)))) a) -1/2))) 2) (cbrt.f64 (cbrt.f64 (.f64 (/.f64 (+.f64 g (sqrt.f64 (-.f64 (.f64 g g) (.f64 h h)))) a) -1/2)))))
	41.4b	(+.f64 (cbrt.f64 (/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 g g) (.f64 h h))) g) (.f64 2 a))) (cbrt.f64 (.f64 (/.f64 (+.f64 g (pow.f64 (pow.f64 (-.f64 (.f64 g g) (.f64 h h)) 1/4) 2)) a) -1/2)))
	46.5b	(+.f64 (/.f64 (cbrt.f64 (pow.f64 (sqrt.f64 (-.f64 (hypot.f64 g (sqrt.f64 (neg.f64 (.f64 h h)))) g)) 2)) (cbrt.f64 (.f64 a 2))) (/.f64 (cbrt.f64 (.f64 (+.f64 g (sqrt.f64 (-.f64 (.f64 g g) (*.f64 h h)))) -1/2)) (cbrt.f64 a)))
	39.5b	(+.f64 (cbrt.f64 (/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 g g) (.f64 h h))) g) (.f64 2 a))) (/.f64 (cbrt.f64 (.f64 (+.f64 g (.f64 (cbrt.f64 (-.f64 (.f64 g g) (.f64 h h))) (cbrt.f64 (sqrt.f64 (-.f64 (.f64 g g) (*.f64 h h)))))) -1/2)) (cbrt.f64 a)))
	42.2b	(+.f64 (cbrt.f64 (/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 g g) (.f64 h h))) g) (.f64 2 a))) (cbrt.f64 (.f64 (/.f64 (+.f64 g (sqrt.f64 (pow.f64 (cbrt.f64 (-.f64 (.f64 g g) (.f64 h h))) 3))) a) -1/2)))
	48.2b	(+.f64 (cbrt.f64 (/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 g g) (.f64 h h))) g) (.f64 2 a))) (.f64 (cbrt.f64 -1/2) (cbrt.f64 (*.f64 (/.f64 2 a) g))))
	43.8b	(+.f64 (log1p.f64 (expm1.f64 (cbrt.f64 (/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 g g) (.f64 h h))) g) (.f64 a 2))))) (cbrt.f64 (.f64 (/.f64 (+.f64 g (sqrt.f64 (-.f64 (.f64 g g) (.f64 h h)))) a) -1/2)))
	45.2b	(+.f64 (cbrt.f64 (/.f64 (-.f64 (exp.f64 (log.f64 (sqrt.f64 (-.f64 (.f64 g g) (.f64 h h))))) g) (.f64 2 a))) (cbrt.f64 (.f64 (/.f64 (+.f64 g (sqrt.f64 (-.f64 (.f64 g g) (.f64 h h)))) a) -1/2)))
	35.3b	(+.f64 (/.f64 (cbrt.f64 (/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 g g) (.f64 h h))) g) 2)) (cbrt.f64 a)) (cbrt.f64 (.f64 (/.f64 (+.f64 g (sqrt.f64 (-.f64 (.f64 g g) (*.f64 h h)))) a) -1/2)))
▶	32.7b	(+.f64 (/.f64 (cbrt.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 g g) (.f64 h h))) g)) (.f64 (cbrt.f64 a) (cbrt.f64 2))) (/.f64 (cbrt.f64 (.f64 (+.f64 g (sqrt.f64 (-.f64 (.f64 g g) (.f64 h h)))) -1/2)) (cbrt.f64 a)))
	59.0b	(+.f64 (cbrt.f64 (/.f64 (fma.f64 (sqrt.f64 g) (neg.f64 (sqrt.f64 g)) (hypot.f64 g (sqrt.f64 (neg.f64 (.f64 h h))))) (.f64 2 a))) (/.f64 (cbrt.f64 (.f64 (+.f64 g (sqrt.f64 (-.f64 (.f64 g g) (*.f64 h h)))) -1/2)) (cbrt.f64 a)))
	40.9b	(+.f64 (cbrt.f64 (/.f64 (-.f64 (pow.f64 (pow.f64 (-.f64 (.f64 g g) (.f64 h h)) 1/4) 2) g) (.f64 2 a))) (cbrt.f64 (.f64 (/.f64 (+.f64 g (sqrt.f64 (-.f64 (.f64 g g) (.f64 h h)))) a) -1/2)))

Compiler

Compiled 18746 to 7939 computations (57.6% saved)

localize19.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	1.0b	(cbrt.f64 2)
	1.2b	(-.f64 (sqrt.f64 (-.f64 (.f64 g g) (.f64 h h))) g)
	3.0b	(-.f64 (.f64 g g) (.f64 h h))
	30.4b	(sqrt.f64 (-.f64 (.f64 g g) (.f64 h h)))

series0.0ms (0%)

Counts

1 → 0

Calls

1 calls:

0.0ms

(cbrt.f64 2)

rewrite53.0ms (0.4%)

Algorithm

1×	batch-egg-rewrite

Rules

361×	`log1p-udef_binary64`
216×	`log1p-expm1-u_binary64`
216×	`expm1-log1p-u_binary64`
214×	`prod-diff_binary64`
213×	`add-sqr-sqrt_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	3	3
1	58	3
2	578	3
3	4445	3
4	5288	3

Stop Event

1×	node limit

Counts

1 → 31

Calls

1 calls:

53.0ms

(cbrt.f64 2)

simplify7.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	0	0
1	0	0

Stop Event

1×

saturated

Counts

31 → 31

prune1.5s (11.1%)

Pruning

21 alts after pruning (20 fresh and 1 done)

	Pruned	Kept	Total
New	395	3	398
Fresh	3	17	20
Picked	0	1	1
Done	0	0	0
Total	398	21	419

Error

31.5b

Counts

419 → 21

Alt Table

Status	Error	Program
	43.9b	(+.f64 (cbrt.f64 (/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 g g) (.f64 h h))) g) (.f64 2 a))) (/.f64 (cbrt.f64 (.f64 (+.f64 g g) -1/2)) (cbrt.f64 a)))
	56.7b	(+.f64 (cbrt.f64 (/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 g g) (.f64 h h))) g) (.f64 2 a))) (.f64 (cbrt.f64 -1/2) (cbrt.f64 (exp.f64 (+.f64 (log.f64 (/.f64 2 a)) (log.f64 g))))))
	37.5b	(+.f64 (/.f64 1 (cbrt.f64 (/.f64 (.f64 a 2) (-.f64 (sqrt.f64 (-.f64 (.f64 g g) (.f64 h h))) g)))) (cbrt.f64 (.f64 (/.f64 (+.f64 g (sqrt.f64 (-.f64 (.f64 g g) (.f64 h h)))) a) -1/2)))
	46.6b	(+.f64 (cbrt.f64 (/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 g g) (.f64 h h))) g) (.f64 2 a))) (/.f64 (cbrt.f64 (.f64 (+.f64 g (cbrt.f64 (pow.f64 (-.f64 (.f64 g g) (.f64 h h)) 3/2))) -1/2)) (cbrt.f64 a)))
	46.7b	(+.f64 (/.f64 (cbrt.f64 (.f64 -1/2 (/.f64 (.f64 h h) g))) (cbrt.f64 (.f64 a 2))) (/.f64 (cbrt.f64 (.f64 (+.f64 g (sqrt.f64 (-.f64 (.f64 g g) (.f64 h h)))) -1/2)) (cbrt.f64 a)))
	35.3b	(+.f64 (.f64 (cbrt.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 g g) (.f64 h h))) g)) (cbrt.f64 (/.f64 1 (.f64 a 2)))) (cbrt.f64 (.f64 (/.f64 (+.f64 g (sqrt.f64 (-.f64 (.f64 g g) (*.f64 h h)))) a) -1/2)))
	32.6b	(+.f64 (/.f64 (cbrt.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 g g) (.f64 h h))) g)) (.f64 (cbrt.f64 a) (pow.f64 2 1/3))) (/.f64 (cbrt.f64 (.f64 (+.f64 g (sqrt.f64 (-.f64 (.f64 g g) (.f64 h h)))) -1/2)) (cbrt.f64 a)))
	47.9b	(+.f64 (/.f64 (cbrt.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 g g) (.f64 h h))) g)) (cbrt.f64 (.f64 a 2))) (/.f64 (cbrt.f64 (.f64 (+.f64 g (neg.f64 g)) -1/2)) (cbrt.f64 a)))
	51.8b	(+.f64 (cbrt.f64 (/.f64 (fma.f64 (pow.f64 (cbrt.f64 g) 2) (neg.f64 (cbrt.f64 g)) (hypot.f64 g (sqrt.f64 (neg.f64 (.f64 h h))))) (.f64 2 a))) (/.f64 (cbrt.f64 (.f64 (+.f64 g (sqrt.f64 (-.f64 (.f64 g g) (*.f64 h h)))) -1/2)) (cbrt.f64 a)))
	32.7b	(+.f64 (/.f64 (cbrt.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 g g) (.f64 h h))) g)) (.f64 (cbrt.f64 a) (+.f64 (log.f64 (pow.f64 (cbrt.f64 (exp.f64 (cbrt.f64 2))) 2)) (log.f64 (cbrt.f64 (exp.f64 (cbrt.f64 2))))))) (/.f64 (cbrt.f64 (.f64 (+.f64 g (sqrt.f64 (-.f64 (.f64 g g) (.f64 h h)))) -1/2)) (cbrt.f64 a)))
	37.9b	(+.f64 (cbrt.f64 (/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 g g) (.f64 h h))) g) (.f64 2 a))) (.f64 (pow.f64 (cbrt.f64 (cbrt.f64 (.f64 (/.f64 (+.f64 g (sqrt.f64 (-.f64 (.f64 g g) (.f64 h h)))) a) -1/2))) 2) (cbrt.f64 (cbrt.f64 (.f64 (/.f64 (+.f64 g (sqrt.f64 (-.f64 (.f64 g g) (.f64 h h)))) a) -1/2)))))
	41.4b	(+.f64 (cbrt.f64 (/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 g g) (.f64 h h))) g) (.f64 2 a))) (cbrt.f64 (.f64 (/.f64 (+.f64 g (pow.f64 (pow.f64 (-.f64 (.f64 g g) (.f64 h h)) 1/4) 2)) a) -1/2)))
	46.5b	(+.f64 (/.f64 (cbrt.f64 (pow.f64 (sqrt.f64 (-.f64 (hypot.f64 g (sqrt.f64 (neg.f64 (.f64 h h)))) g)) 2)) (cbrt.f64 (.f64 a 2))) (/.f64 (cbrt.f64 (.f64 (+.f64 g (sqrt.f64 (-.f64 (.f64 g g) (*.f64 h h)))) -1/2)) (cbrt.f64 a)))
	39.5b	(+.f64 (cbrt.f64 (/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 g g) (.f64 h h))) g) (.f64 2 a))) (/.f64 (cbrt.f64 (.f64 (+.f64 g (.f64 (cbrt.f64 (-.f64 (.f64 g g) (.f64 h h))) (cbrt.f64 (sqrt.f64 (-.f64 (.f64 g g) (*.f64 h h)))))) -1/2)) (cbrt.f64 a)))
	42.2b	(+.f64 (cbrt.f64 (/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 g g) (.f64 h h))) g) (.f64 2 a))) (cbrt.f64 (.f64 (/.f64 (+.f64 g (sqrt.f64 (pow.f64 (cbrt.f64 (-.f64 (.f64 g g) (.f64 h h))) 3))) a) -1/2)))
	48.2b	(+.f64 (cbrt.f64 (/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 g g) (.f64 h h))) g) (.f64 2 a))) (.f64 (cbrt.f64 -1/2) (cbrt.f64 (*.f64 (/.f64 2 a) g))))
✓	32.7b	(+.f64 (/.f64 (cbrt.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 g g) (.f64 h h))) g)) (.f64 (cbrt.f64 a) (cbrt.f64 2))) (/.f64 (cbrt.f64 (.f64 (+.f64 g (sqrt.f64 (-.f64 (.f64 g g) (.f64 h h)))) -1/2)) (cbrt.f64 a)))
	32.8b	(+.f64 (/.f64 (cbrt.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 g g) (.f64 h h))) g)) (.f64 (cbrt.f64 a) (pow.f64 (cbrt.f64 (cbrt.f64 2)) 3))) (/.f64 (cbrt.f64 (.f64 (+.f64 g (sqrt.f64 (-.f64 (.f64 g g) (.f64 h h)))) -1/2)) (cbrt.f64 a)))
	59.0b	(+.f64 (cbrt.f64 (/.f64 (fma.f64 (sqrt.f64 g) (neg.f64 (sqrt.f64 g)) (hypot.f64 g (sqrt.f64 (neg.f64 (.f64 h h))))) (.f64 2 a))) (/.f64 (cbrt.f64 (.f64 (+.f64 g (sqrt.f64 (-.f64 (.f64 g g) (*.f64 h h)))) -1/2)) (cbrt.f64 a)))
	40.9b	(+.f64 (cbrt.f64 (/.f64 (-.f64 (pow.f64 (pow.f64 (-.f64 (.f64 g g) (.f64 h h)) 1/4) 2) g) (.f64 2 a))) (cbrt.f64 (.f64 (/.f64 (+.f64 g (sqrt.f64 (-.f64 (.f64 g g) (.f64 h h)))) a) -1/2)))
	43.8b	(+.f64 (log1p.f64 (expm1.f64 (cbrt.f64 (/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 g g) (.f64 h h))) g) (.f64 a 2))))) (cbrt.f64 (.f64 (/.f64 (+.f64 g (sqrt.f64 (-.f64 (.f64 g g) (.f64 h h)))) a) -1/2)))

Compiler

Compiled 17734 to 7426 computations (58.1% saved)

regimes2.3s (17.2%)

Accuracy

Total 1.6b remaining (4.9%)

Threshold costs 0b (0%)

Counts

227 → 1

Compiler

Compiled 58769 to 36552 computations (37.8% saved)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Rules

7×	`+-commutative_binary64`
5×	`*-commutative_binary64`
5×	`sub-neg_binary64`
3×	`neg-sub0_binary64`
3×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	22	4294967295
1	33	4294967295
2	43	4294967295
3	49	4294967295
4	52	4294967295
5	52	4294967295

Stop Event

1×

saturated

end479.0ms (3.5%)

Compiler: Compiled 861 to 515 computations (40.2% saved)

Details

analyze585.0ms (4.3%)

sample2.8s (21%)

simplify171.0ms (1.3%)

prune4.0ms (0%)

localize19.0ms (0.1%)

series1.1s (8.5%)

rewrite71.0ms (0.5%)

simplify120.0ms (0.9%)

prune874.0ms (6.4%)

localize17.0ms (0.1%)

series13.0ms (0.1%)

rewrite53.0ms (0.4%)

simplify58.0ms (0.4%)

prune1.5s (11%)

localize18.0ms (0.1%)

series34.0ms (0.3%)

rewrite64.0ms (0.5%)

simplify118.0ms (0.9%)

prune1.5s (10.8%)

localize19.0ms (0.1%)

series0.0ms (0%)

rewrite53.0ms (0.4%)

simplify7.0ms (0.1%)

prune1.5s (11.1%)

regimes2.3s (17.2%)

simplify3.0ms (0%)

end479.0ms (3.5%)

Profiling