Details

analyze589.0ms (3.9%)

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)

sample3.0s (20.1%)

Results

2.6s	7821×	body	256	valid
212.0ms	1278×	body	128	invalid
78.0ms	435×	body	128	valid

Compiler

Compiled 122 to 71 computations (41.8% saved)

simplify199.0ms (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`

Counts

1 → 2

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

prune5.0ms (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

35.6b

Counts

3 → 2

Alt Table

Status	Error	Program
	35.6b	(+.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)))
▶	35.6b	(+.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

35.6b

(+.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)))

▶

35.6b

(+.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)

localize18.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	2.0b	(-.f64 (.f64 g g) (.f64 h h))
✓	8.2b	(cbrt.f64 (.f64 (/.f64 1 (.f64 2 a)) (+.f64 (neg.f64 g) (sqrt.f64 (-.f64 (.f64 g g) (.f64 h h))))))
✓	8.4b	(cbrt.f64 (.f64 (/.f64 1 (.f64 2 a)) (-.f64 (neg.f64 g) (sqrt.f64 (-.f64 (.f64 g g) (.f64 h h))))))
✓	27.5b	(sqrt.f64 (-.f64 (.f64 g g) (.f64 h h)))

series1.2s (8%)

Counts

4 → 120

Calls

4 calls:

606.0ms	(cbrt.f64 (.f64 (/.f64 1 (.f64 2 a)) (-.f64 (neg.f64 g) (sqrt.f64 (-.f64 (.f64 g g) (.f64 h h))))))
569.0ms	(cbrt.f64 (.f64 (/.f64 1 (.f64 2 a)) (+.f64 (neg.f64 g) (sqrt.f64 (-.f64 (.f64 g g) (.f64 h h))))))
12.0ms	(sqrt.f64 (-.f64 (.f64 g g) (.f64 h h)))
9.0ms	(-.f64 (.f64 g g) (.f64 h h))

rewrite80.0ms (0.5%)

Algorithm

1×	batch-egg-rewrite

Rules

622×	`prod-diff_binary64`
200×	`add-sqr-sqrt_binary64`
191×	`log1p-expm1-u_binary64`
191×	`expm1-log1p-u_binary64`
188×	`add-cbrt-cube_binary64`

Counts

4 → 119

Calls

4 calls:

77.0ms	(-.f64 (.f64 g g) (.f64 h h))
77.0ms	(cbrt.f64 (.f64 (/.f64 1 (.f64 2 a)) (+.f64 (neg.f64 g) (sqrt.f64 (-.f64 (.f64 g g) (.f64 h h))))))
77.0ms	(cbrt.f64 (.f64 (/.f64 1 (.f64 2 a)) (-.f64 (neg.f64 g) (sqrt.f64 (-.f64 (.f64 g g) (.f64 h h))))))
77.0ms	(sqrt.f64 (-.f64 (.f64 g g) (.f64 h h)))

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	19	72
1	416	68
2	4524	68
3	5762	68

simplify140.0ms (0.9%)

Algorithm

1×	egg-herbie

Rules

350×	`associate-r_binary64`
325×	`times-frac_binary64`
274×	`fma-neg_binary64`
249×	`*-commutative_binary64`
243×	`fma-def_binary64`

Counts

239 → 270

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	408	5670
1	1271	5468
2	4551	5280
3	4981	5280

prune907.0ms (6%)

Pruning

16 alts after pruning (16 fresh and 0 done)

	Pruned	Kept	Total
New	375	15	390
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	376	16	392

Error

29.4b

Counts

392 → 16

Alt Table

Status	Error	Program
	46.6b	(+.f64 (cbrt.f64 (.f64 (/.f64 1 (.f64 2 a)) (+.f64 (neg.f64 g) (cbrt.f64 (pow.f64 (-.f64 (.f64 g g) (.f64 h h)) 3/2))))) (cbrt.f64 (.f64 (/.f64 1 (.f64 2 a)) (-.f64 (neg.f64 g) (sqrt.f64 (-.f64 (.f64 g g) (.f64 h h)))))))
▶	35.6b	(+.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)))
	56.6b	(+.f64 (cbrt.f64 (.f64 (/.f64 1 (.f64 2 a)) (+.f64 (neg.f64 g) (sqrt.f64 (-.f64 (.f64 g g) (.f64 h h)))))) (.f64 (cbrt.f64 -1/2) (exp.f64 (.f64 1/3 (-.f64 (log.f64 (/.f64 2 a)) (log.f64 (/.f64 1 g)))))))
	40.6b	(+.f64 (cbrt.f64 (.f64 (/.f64 1 (.f64 2 a)) (+.f64 (neg.f64 g) (pow.f64 (cbrt.f64 (sqrt.f64 (-.f64 (.f64 g g) (.f64 h h)))) 3)))) (cbrt.f64 (.f64 (/.f64 1 (.f64 2 a)) (-.f64 (neg.f64 g) (sqrt.f64 (-.f64 (.f64 g g) (.f64 h h)))))))
	53.9b	(+.f64 (.f64 (exp.f64 (.f64 1/3 (-.f64 (log.f64 (/.f64 2 a)) (log.f64 (/.f64 -1 g))))) (cbrt.f64 1/2)) (cbrt.f64 (.f64 (/.f64 1 (.f64 2 a)) (-.f64 (neg.f64 g) (sqrt.f64 (-.f64 (.f64 g g) (.f64 h h)))))))
	42.4b	(+.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) (pow.f64 (cbrt.f64 (sqrt.f64 (-.f64 (.f64 g g) (.f64 h h)))) 3)))))
	52.6b	(+.f64 (.f64 (cbrt.f64 1/2) (cbrt.f64 (exp.f64 (-.f64 (log.f64 (.f64 -1/2 (/.f64 (.f64 h h) a))) (log.f64 g))))) (cbrt.f64 (.f64 (/.f64 1 (.f64 2 a)) (-.f64 (neg.f64 g) (sqrt.f64 (-.f64 (.f64 g g) (*.f64 h h)))))))
	40.2b	(+.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 (pow.f64 (cbrt.f64 (-.f64 (.f64 g g) (.f64 h h))) 2) (cbrt.f64 (-.f64 (.f64 g g) (*.f64 h h)))))))))
	56.0b	(+.f64 (cbrt.f64 (.f64 (/.f64 1 (.f64 2 a)) (+.f64 (neg.f64 g) (/.f64 (sqrt.f64 (-.f64 (pow.f64 g 6) (pow.f64 h 6))) (sqrt.f64 (+.f64 (pow.f64 g 4) (+.f64 (pow.f64 h 4) (pow.f64 (.f64 g h) 2)))))))) (cbrt.f64 (.f64 (/.f64 1 (.f64 2 a)) (-.f64 (neg.f64 g) (sqrt.f64 (-.f64 (.f64 g g) (*.f64 h h)))))))
	52.9b	(+.f64 (cbrt.f64 (.f64 (/.f64 1 (.f64 2 a)) (+.f64 (neg.f64 g) (.f64 (sqrt.f64 (+.f64 g h)) (sqrt.f64 (-.f64 g h)))))) (cbrt.f64 (.f64 (/.f64 1 (.f64 2 a)) (-.f64 (neg.f64 g) (sqrt.f64 (-.f64 (.f64 g g) (*.f64 h h)))))))
	50.6b	(+.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 1 (.f64 2 a)) (-.f64 (neg.f64 g) (sqrt.f64 (-.f64 (.f64 g g) (.f64 h h)))))))
	50.7b	(+.f64 (cbrt.f64 (.f64 (/.f64 1 (.f64 2 a)) (+.f64 (neg.f64 g) (sqrt.f64 (-.f64 (.f64 g g) (.f64 h h)))))) (.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)))))))
	47.9b	(+.f64 (cbrt.f64 (.f64 (/.f64 1 (.f64 2 a)) (+.f64 (neg.f64 g) (sqrt.f64 (-.f64 (.f64 g g) (.f64 h h)))))) (.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 a))))))
	47.8b	(+.f64 (cbrt.f64 (.f64 (/.f64 1 (.f64 2 a)) (+.f64 (neg.f64 g) (sqrt.f64 (-.f64 (.f64 g g) (.f64 h h)))))) (.f64 (cbrt.f64 -1/2) (cbrt.f64 (.f64 (/.f64 2 a) g))))
	41.0b	(+.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) (.f64 (cbrt.f64 (-.f64 (.f64 g g) (.f64 h h))) (cbrt.f64 (sqrt.f64 (-.f64 (.f64 g g) (*.f64 h h)))))))))
	52.0b	(+.f64 (cbrt.f64 (.f64 (/.f64 1 (.f64 2 a)) (+.f64 (neg.f64 g) (sqrt.f64 (-.f64 (.f64 g g) (.f64 h h)))))) (.f64 (cbrt.f64 1/2) (cbrt.f64 (exp.f64 (+.f64 (log.f64 (/.f64 -1 g)) (log.f64 (.f64 1/2 (/.f64 (*.f64 h h) a))))))))

Compiler

Compiled 21398 to 11661 computations (45.5% saved)

localize16.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
	2.0b	(-.f64 (.f64 g g) (.f64 h h))
✓	8.2b	(cbrt.f64 (/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 g g) (.f64 h h))) g) (*.f64 2 a)))
✓	8.4b	(cbrt.f64 (.f64 (/.f64 (+.f64 g (sqrt.f64 (-.f64 (.f64 g g) (*.f64 h h)))) a) -1/2))
	27.5b	(sqrt.f64 (-.f64 (.f64 g g) (.f64 h h)))

series1.2s (8.3%)

Counts

2 → 72

Calls

2 calls:

660.0ms	(cbrt.f64 (.f64 (/.f64 (+.f64 g (sqrt.f64 (-.f64 (.f64 g g) (*.f64 h h)))) a) -1/2))
583.0ms	(cbrt.f64 (/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 g g) (.f64 h h))) g) (*.f64 2 a)))

rewrite70.0ms (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`

Counts

2 → 48

Calls

2 calls:

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))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	18	46
1	409	46
2	4843	46
3	6030	46

simplify147.0ms (1%)

Algorithm

1×	egg-herbie

Rules

339×	`associate-r_binary64`
293×	`times-frac_binary64`
228×	`*-commutative_binary64`
223×	`fma-neg_binary64`
207×	`fma-def_binary64`

Counts

120 → 154

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	356	4792
1	1093	4604
2	3960	4410
3	4984	4410
4	4959	4410

prune1.1s (7.2%)

Pruning

17 alts after pruning (17 fresh and 0 done)

	Pruned	Kept	Total
New	380	14	394
Fresh	12	3	15
Picked	1	0	1
Done	0	0	0
Total	393	17	410

Error

28.8b

Counts

410 → 17

Alt Table

Status	Error	Program
	41.0b	(+.f64 (cbrt.f64 (/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 g g) (.f64 h h))) g) (.f64 2 a))) (cbrt.f64 (.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)))))) a) -1/2)))
	35.8b	(+.f64 (cbrt.f64 (/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 g g) (.f64 h h))) g) (.f64 2 a))) (pow.f64 (cbrt.f64 (cbrt.f64 (.f64 (/.f64 (+.f64 g (sqrt.f64 (-.f64 (.f64 g g) (.f64 h h)))) a) -1/2))) 3))
	56.6b	(+.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)))))))
	52.9b	(+.f64 (cbrt.f64 (/.f64 (-.f64 (.f64 (sqrt.f64 (+.f64 g h)) (sqrt.f64 (-.f64 g h))) g) (.f64 2 a))) (cbrt.f64 (.f64 (/.f64 (+.f64 g (sqrt.f64 (-.f64 (.f64 g g) (*.f64 h h)))) a) -1/2)))
	33.1b	(+.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)))
	52.6b	(+.f64 (.f64 (cbrt.f64 1/2) (cbrt.f64 (exp.f64 (-.f64 (log.f64 (.f64 -1/2 (/.f64 (.f64 h h) a))) (log.f64 g))))) (cbrt.f64 (.f64 (/.f64 (+.f64 g (sqrt.f64 (-.f64 (.f64 g g) (.f64 h h)))) a) -1/2)))
	47.9b	(+.f64 (cbrt.f64 (.f64 (/.f64 1 (.f64 2 a)) (+.f64 (neg.f64 g) (sqrt.f64 (-.f64 (.f64 g g) (.f64 h h)))))) (.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 a))))))
▶	32.1b	(+.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)))
	50.6b	(+.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)))
	35.2b	(+.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)))
	40.2b	(+.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 (pow.f64 (cbrt.f64 (-.f64 (.f64 g g) (.f64 h h))) 2) (cbrt.f64 (-.f64 (.f64 g g) (*.f64 h h)))))))))
	47.1b	(+.f64 (.f64 (cbrt.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 g g) (.f64 h h))) g)) (pow.f64 (/.f64 1 (.f64 a 2)) 1/3)) (cbrt.f64 (.f64 (/.f64 (+.f64 g (sqrt.f64 (-.f64 (.f64 g g) (*.f64 h h)))) a) -1/2)))
	53.9b	(+.f64 (.f64 (exp.f64 (.f64 1/3 (-.f64 (log.f64 (/.f64 2 a)) (log.f64 (/.f64 -1 g))))) (cbrt.f64 1/2)) (cbrt.f64 (.f64 (/.f64 (+.f64 g (sqrt.f64 (-.f64 (.f64 g g) (*.f64 h h)))) a) -1/2)))
	35.6b	(+.f64 (cbrt.f64 (/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 g g) (.f64 h h))) g) (.f64 2 a))) (.f64 (cbrt.f64 (/.f64 (+.f64 g (sqrt.f64 (-.f64 (.f64 g g) (.f64 h h)))) a)) (cbrt.f64 -1/2)))
	32.2b	(+.f64 (/.f64 (cbrt.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 g g) (.f64 h h))) g)) (cbrt.f64 (.f64 a 2))) (cbrt.f64 (.f64 (/.f64 (+.f64 g (sqrt.f64 (-.f64 (.f64 g g) (.f64 h h)))) a) -1/2)))
	32.1b	(+.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)))
	52.0b	(+.f64 (cbrt.f64 (.f64 (/.f64 1 (.f64 2 a)) (+.f64 (neg.f64 g) (sqrt.f64 (-.f64 (.f64 g g) (.f64 h h)))))) (.f64 (cbrt.f64 1/2) (cbrt.f64 (exp.f64 (+.f64 (log.f64 (/.f64 -1 g)) (log.f64 (.f64 1/2 (/.f64 (*.f64 h h) a))))))))

Compiler

Compiled 19590 to 10120 computations (48.3% saved)

localize16.0ms (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)
	2.0b	(-.f64 (.f64 g g) (.f64 h h))
	8.4b	(cbrt.f64 (.f64 (/.f64 (+.f64 g (sqrt.f64 (-.f64 (.f64 g g) (*.f64 h h)))) a) -1/2))
	27.5b	(sqrt.f64 (-.f64 (.f64 g g) (.f64 h h)))

series14.0ms (0.1%)

Counts

1 → 24

Calls

1 calls:

14.0ms

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

rewrite61.0ms (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`

Counts

1 → 99

Calls

1 calls:

59.0ms

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

Iterations

Useful iterations: 2 (0.0ms)

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

simplify64.0ms (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`

Counts

123 → 139

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

prune1.5s (9.9%)

Pruning

19 alts after pruning (19 fresh and 0 done)

	Pruned	Kept	Total
New	446	8	454
Fresh	5	11	16
Picked	1	0	1
Done	0	0	0
Total	452	19	471

Error

28.4b

Counts

471 → 19

Alt Table

Status	Error	Program
	34.5b	(+.f64 (/.f64 (cbrt.f64 (/.f64 (-.f64 (pow.f64 (pow.f64 (-.f64 (.f64 g g) (.f64 h h)) 1/4) 2) g) 2)) (cbrt.f64 a)) (cbrt.f64 (.f64 (/.f64 (+.f64 g (sqrt.f64 (-.f64 (.f64 g g) (*.f64 h h)))) a) -1/2)))
	41.0b	(+.f64 (cbrt.f64 (/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 g g) (.f64 h h))) g) (.f64 2 a))) (cbrt.f64 (.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)))))) a) -1/2)))
	35.8b	(+.f64 (cbrt.f64 (/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 g g) (.f64 h h))) g) (.f64 2 a))) (pow.f64 (cbrt.f64 (cbrt.f64 (.f64 (/.f64 (+.f64 g (sqrt.f64 (-.f64 (.f64 g g) (.f64 h h)))) a) -1/2))) 3))
	41.2b	(+.f64 (/.f64 (cbrt.f64 (/.f64 (.f64 -2 g) 2)) (cbrt.f64 a)) (cbrt.f64 (.f64 (/.f64 (+.f64 g (sqrt.f64 (-.f64 (.f64 g g) (.f64 h h)))) a) -1/2)))
	35.2b	(+.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)))
	40.2b	(+.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 (pow.f64 (cbrt.f64 (-.f64 (.f64 g g) (.f64 h h))) 2) (cbrt.f64 (-.f64 (.f64 g g) (*.f64 h h)))))))))
	59.9b	(+.f64 (/.f64 (cbrt.f64 (/.f64 (fma.f64 (sqrt.f64 g) (neg.f64 (sqrt.f64 g)) (hypot.f64 g (sqrt.f64 (neg.f64 (.f64 h h))))) 2)) (cbrt.f64 a)) (cbrt.f64 (.f64 (/.f64 (+.f64 g (sqrt.f64 (-.f64 (.f64 g g) (.f64 h h)))) a) -1/2)))
	53.5b	(+.f64 (/.f64 (cbrt.f64 (/.f64 (-.f64 (.f64 -1/2 (/.f64 (.f64 h h) g)) (fma.f64 1/8 (/.f64 (pow.f64 h 4) (pow.f64 g 3)) (fma.f64 1/16 (/.f64 (pow.f64 h 6) (pow.f64 g 5)) (.f64 5/128 (/.f64 (pow.f64 h 8) (pow.f64 g 7)))))) 2)) (cbrt.f64 a)) (cbrt.f64 (.f64 (/.f64 (+.f64 g (sqrt.f64 (-.f64 (.f64 g g) (.f64 h h)))) a) -1/2)))
	47.1b	(+.f64 (.f64 (cbrt.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 g g) (.f64 h h))) g)) (pow.f64 (/.f64 1 (.f64 a 2)) 1/3)) (cbrt.f64 (.f64 (/.f64 (+.f64 g (sqrt.f64 (-.f64 (.f64 g g) (*.f64 h h)))) a) -1/2)))
	53.9b	(+.f64 (.f64 (exp.f64 (.f64 1/3 (-.f64 (log.f64 (/.f64 2 a)) (log.f64 (/.f64 -1 g))))) (cbrt.f64 1/2)) (cbrt.f64 (.f64 (/.f64 (+.f64 g (sqrt.f64 (-.f64 (.f64 g g) (*.f64 h h)))) a) -1/2)))
	52.9b	(+.f64 (cbrt.f64 (/.f64 (-.f64 (.f64 (sqrt.f64 (+.f64 g h)) (sqrt.f64 (-.f64 g h))) g) (.f64 2 a))) (cbrt.f64 (.f64 (/.f64 (+.f64 g (sqrt.f64 (-.f64 (.f64 g g) (*.f64 h h)))) a) -1/2)))
	47.7b	(+.f64 (/.f64 (cbrt.f64 (/.f64 (exp.f64 (log.f64 (-.f64 (hypot.f64 g (sqrt.f64 (neg.f64 (.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)))
	35.6b	(+.f64 (cbrt.f64 (/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 g g) (.f64 h h))) g) (.f64 2 a))) (.f64 (cbrt.f64 (/.f64 (+.f64 g (sqrt.f64 (-.f64 (.f64 g g) (.f64 h h)))) a)) (cbrt.f64 -1/2)))
▶	29.6b	(+.f64 (/.f64 (cbrt.f64 (/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 g g) (.f64 h h))) g) 2)) (cbrt.f64 a)) (/.f64 (cbrt.f64 (.f64 (+.f64 g (sqrt.f64 (-.f64 (.f64 g g) (*.f64 h h)))) -1/2)) (cbrt.f64 a)))
	32.2b	(+.f64 (/.f64 (cbrt.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 g g) (.f64 h h))) g)) (cbrt.f64 (.f64 a 2))) (cbrt.f64 (.f64 (/.f64 (+.f64 g (sqrt.f64 (-.f64 (.f64 g g) (.f64 h h)))) a) -1/2)))
	32.1b	(+.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)))
	44.7b	(+.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 (neg.f64 g)) a) -1/2)))
	52.0b	(+.f64 (cbrt.f64 (.f64 (/.f64 1 (.f64 2 a)) (+.f64 (neg.f64 g) (sqrt.f64 (-.f64 (.f64 g g) (.f64 h h)))))) (.f64 (cbrt.f64 1/2) (cbrt.f64 (exp.f64 (+.f64 (log.f64 (/.f64 -1 g)) (log.f64 (.f64 1/2 (/.f64 (*.f64 h h) a))))))))
	37.1b	(+.f64 (/.f64 (cbrt.f64 (/.f64 (-.f64 (pow.f64 (cbrt.f64 (sqrt.f64 (-.f64 (.f64 g g) (.f64 h h)))) 3) g) 2)) (cbrt.f64 a)) (cbrt.f64 (.f64 (/.f64 (+.f64 g (sqrt.f64 (-.f64 (.f64 g g) (*.f64 h h)))) a) -1/2)))

Compiler

Compiled 21287 to 9633 computations (54.7% saved)

localize17.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.9b	(+.f64 g (sqrt.f64 (-.f64 (.f64 g g) (.f64 h h))))
	1.2b	(-.f64 (sqrt.f64 (-.f64 (.f64 g g) (.f64 h h))) g)
	2.0b	(-.f64 (.f64 g g) (.f64 h h))
	27.5b	(sqrt.f64 (-.f64 (.f64 g g) (.f64 h h)))

series13.0ms (0.1%)

Counts

1 → 24

Calls

1 calls:

13.0ms

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

rewrite56.0ms (0.4%)

Algorithm

1×	batch-egg-rewrite

Rules

693×	`fma-def_binary64`
435×	`log-prod_binary64`
336×	`fma-neg_binary64`
164×	`expm1-udef_binary64`
164×	`log1p-udef_binary64`

Counts

1 → 51

Calls

1 calls:

54.0ms

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

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	8	15
1	187	15
2	2454	14
3	5280	14

simplify64.0ms (0.4%)

Algorithm

1×	egg-herbie

Rules

539×	`fma-neg_binary64`
463×	`times-frac_binary64`
439×	`distribute-neg-frac_binary64`
284×	`div-sub_binary64`
235×	`associate-/r*_binary64`

Counts

75 → 90

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	73	575
1	223	557
2	661	547
3	3225	543
4	4904	543
5	5238	543

prune1.6s (10.6%)

Pruning

21 alts after pruning (21 fresh and 0 done)

	Pruned	Kept	Total
New	462	7	469
Fresh	4	14	18
Picked	1	0	1
Done	0	0	0
Total	467	21	488

Error

28.3b

Counts

488 → 21

Alt Table

Status	Error	Program
	34.5b	(+.f64 (/.f64 (cbrt.f64 (/.f64 (-.f64 (pow.f64 (pow.f64 (-.f64 (.f64 g g) (.f64 h h)) 1/4) 2) g) 2)) (cbrt.f64 a)) (cbrt.f64 (.f64 (/.f64 (+.f64 g (sqrt.f64 (-.f64 (.f64 g g) (*.f64 h h)))) a) -1/2)))
	50.4b	(+.f64 (/.f64 (cbrt.f64 (/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 g g) (.f64 h h))) g) 2)) (cbrt.f64 a)) (/.f64 (cbrt.f64 (.f64 (fma.f64 (cbrt.f64 g) (pow.f64 (cbrt.f64 g) 2) (hypot.f64 g (sqrt.f64 (neg.f64 (.f64 h h))))) -1/2)) (cbrt.f64 a)))
	35.8b	(+.f64 (cbrt.f64 (/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 g g) (.f64 h h))) g) (.f64 2 a))) (pow.f64 (cbrt.f64 (cbrt.f64 (.f64 (/.f64 (+.f64 g (sqrt.f64 (-.f64 (.f64 g g) (.f64 h h)))) a) -1/2))) 3))
	30.1b	(+.f64 (/.f64 (cbrt.f64 (/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 g g) (.f64 h h))) g) 2)) (cbrt.f64 a)) (/.f64 (cbrt.f64 (.f64 (+.f64 g (sqrt.f64 (.f64 g g))) -1/2)) (cbrt.f64 a)))
	37.9b	(+.f64 (/.f64 (cbrt.f64 (/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 g g) (.f64 h h))) g) 2)) (cbrt.f64 a)) (/.f64 (cbrt.f64 (.f64 (+.f64 g (pow.f64 (cbrt.f64 (sqrt.f64 (-.f64 (.f64 g g) (*.f64 h h)))) 3)) -1/2)) (cbrt.f64 a)))
	32.2b	(+.f64 (/.f64 (cbrt.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 g g) (.f64 h h))) g)) (cbrt.f64 (.f64 a 2))) (cbrt.f64 (.f64 (/.f64 (+.f64 g (sqrt.f64 (-.f64 (.f64 g g) (.f64 h h)))) a) -1/2)))
	41.2b	(+.f64 (/.f64 (cbrt.f64 (/.f64 (.f64 -2 g) 2)) (cbrt.f64 a)) (cbrt.f64 (.f64 (/.f64 (+.f64 g (sqrt.f64 (-.f64 (.f64 g g) (.f64 h h)))) a) -1/2)))
	35.2b	(+.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)))
	40.2b	(+.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 (pow.f64 (cbrt.f64 (-.f64 (.f64 g g) (.f64 h h))) 2) (cbrt.f64 (-.f64 (.f64 g g) (*.f64 h h)))))))))
	59.9b	(+.f64 (/.f64 (cbrt.f64 (/.f64 (fma.f64 (sqrt.f64 g) (neg.f64 (sqrt.f64 g)) (hypot.f64 g (sqrt.f64 (neg.f64 (.f64 h h))))) 2)) (cbrt.f64 a)) (cbrt.f64 (.f64 (/.f64 (+.f64 g (sqrt.f64 (-.f64 (.f64 g g) (.f64 h h)))) a) -1/2)))
	53.5b	(+.f64 (/.f64 (cbrt.f64 (/.f64 (-.f64 (.f64 -1/2 (/.f64 (.f64 h h) g)) (fma.f64 1/8 (/.f64 (pow.f64 h 4) (pow.f64 g 3)) (fma.f64 1/16 (/.f64 (pow.f64 h 6) (pow.f64 g 5)) (.f64 5/128 (/.f64 (pow.f64 h 8) (pow.f64 g 7)))))) 2)) (cbrt.f64 a)) (cbrt.f64 (.f64 (/.f64 (+.f64 g (sqrt.f64 (-.f64 (.f64 g g) (.f64 h h)))) a) -1/2)))
	47.1b	(+.f64 (.f64 (cbrt.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 g g) (.f64 h h))) g)) (pow.f64 (/.f64 1 (.f64 a 2)) 1/3)) (cbrt.f64 (.f64 (/.f64 (+.f64 g (sqrt.f64 (-.f64 (.f64 g g) (*.f64 h h)))) a) -1/2)))
	36.3b	(+.f64 (/.f64 (cbrt.f64 (/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 g g) (.f64 h h))) g) 2)) (cbrt.f64 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)))
	46.0b	(+.f64 (/.f64 (cbrt.f64 (/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 g g) (.f64 h h))) g) 2)) (cbrt.f64 a)) (/.f64 (cbrt.f64 (.f64 (pow.f64 (sqrt.f64 (+.f64 g (hypot.f64 g (sqrt.f64 (neg.f64 (.f64 h h)))))) 2) -1/2)) (cbrt.f64 a)))
	47.7b	(+.f64 (/.f64 (cbrt.f64 (/.f64 (exp.f64 (log.f64 (-.f64 (hypot.f64 g (sqrt.f64 (neg.f64 (.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)))
	35.6b	(+.f64 (cbrt.f64 (/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 g g) (.f64 h h))) g) (.f64 2 a))) (.f64 (cbrt.f64 (/.f64 (+.f64 g (sqrt.f64 (-.f64 (.f64 g g) (.f64 h h)))) a)) (cbrt.f64 -1/2)))
	44.3b	(+.f64 (/.f64 (cbrt.f64 (/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 g g) (.f64 h h))) g) 2)) (cbrt.f64 a)) (/.f64 (cbrt.f64 (.f64 (.f64 1/2 (/.f64 (pow.f64 h 2) g)) -1/2)) (cbrt.f64 a)))
	51.0b	(+.f64 (/.f64 (cbrt.f64 (/.f64 (-.f64 (.f64 (sqrt.f64 (+.f64 g h)) (sqrt.f64 (-.f64 g h))) g) 2)) (cbrt.f64 a)) (/.f64 (cbrt.f64 (.f64 (+.f64 g (sqrt.f64 (-.f64 (.f64 g g) (.f64 h h)))) -1/2)) (cbrt.f64 a)))
	32.1b	(+.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)))
	52.0b	(+.f64 (cbrt.f64 (.f64 (/.f64 1 (.f64 2 a)) (+.f64 (neg.f64 g) (sqrt.f64 (-.f64 (.f64 g g) (.f64 h h)))))) (.f64 (cbrt.f64 1/2) (cbrt.f64 (exp.f64 (+.f64 (log.f64 (/.f64 -1 g)) (log.f64 (.f64 1/2 (/.f64 (*.f64 h h) a))))))))
	37.1b	(+.f64 (/.f64 (cbrt.f64 (/.f64 (-.f64 (pow.f64 (cbrt.f64 (sqrt.f64 (-.f64 (.f64 g g) (.f64 h h)))) 3) g) 2)) (cbrt.f64 a)) (cbrt.f64 (.f64 (/.f64 (+.f64 g (sqrt.f64 (-.f64 (.f64 g g) (*.f64 h h)))) a) -1/2)))

Compiler

Compiled 20389 to 8444 computations (58.6% saved)

regimes2.4s (15.8%)

Accuracy

Total 1.6b remaining (4.9%)

Threshold costs 0b (0%)

Counts

226 → 1

Compiler

Compiled 68352 to 44478 computations (34.9% 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	24	52
1	36	52
2	44	52
3	49	52
4	51	52
5	51	52

end560.0ms (3.7%)

Compiler: Compiled 885 to 542 computations (38.8% saved)

Details

analyze589.0ms (3.9%)

sample3.0s (20.1%)

simplify199.0ms (1.3%)

prune5.0ms (0%)

localize18.0ms (0.1%)

series1.2s (8%)

rewrite80.0ms (0.5%)

simplify140.0ms (0.9%)

prune907.0ms (6%)

localize16.0ms (0.1%)

series1.2s (8.3%)

rewrite70.0ms (0.5%)

simplify147.0ms (1%)

prune1.1s (7.2%)

localize16.0ms (0.1%)

series14.0ms (0.1%)

rewrite61.0ms (0.4%)

simplify64.0ms (0.4%)

prune1.5s (9.9%)

localize17.0ms (0.1%)

series13.0ms (0.1%)

rewrite56.0ms (0.4%)

simplify64.0ms (0.4%)

prune1.6s (10.6%)

regimes2.4s (15.8%)

simplify3.0ms (0%)

end560.0ms (3.7%)

Profiling