Details

analyze724.0ms (6.9%)

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
6.2%	74.9%	18.9%	6
9.4%	71.8%	18.9%	7
14%	64%	22%	8
20.3%	46.8%	32.9%	9
22.6%	44.5%	32.9%	10
27.7%	37.1%	35.3%	11
32%	26.9%	41.1%	12
34%	24.9%	41.1%	13
37.5%	20%	42.5%	14

Compiler

Compiled 41 to 24 computations (41.5% saved)

sample2.8s (26.7%)

Results

2.5s	7797×	body	256	valid
207.0ms	1196×	body	128	invalid
84.0ms	459×	body	128	valid

Compiler

Compiled 82 to 48 computations (41.5% saved)

preprocess33.0ms (0.3%)

Algorithm

2×	egg-herbie

Rules

371×	`fma-def_binary64`
300×	`associate-/l*_binary64`
260×	`distribute-rgt-in_binary64`
256×	`times-frac_binary64`
255×	`div-sub_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	54	208
1	165	200
2	545	200
3	1762	192
0	3	3

Stop Event

1×	saturated
1×	node limit

Compiler

Compiled 40 to 23 computations (42.5% saved)

simplify30.0ms (0.3%)

Algorithm

1×	egg-herbie

Rules

725×	`fma-neg_binary64`
355×	`fma-def_binary64`
203×	`distribute-rgt-in_binary64`
194×	`associate-/l*_binary64`
192×	`div-sub_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	20	52
1	54	50
2	154	50
3	478	48
4	1279	48
5	2581	48
6	3823	48

Stop Event

1×	node limit

Counts

1 → 2

prune4.0ms (0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

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

Error

37.7b

Counts

3 → 1

Alt Table

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

Compiler

Compiled 139 to 70 computations (49.6% saved)

localize15.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	2.8b	(-.f64 (.f64 g g) (.f64 h h))
✓	8.1b	(cbrt.f64 (.f64 (/.f64 1/2 a) (-.f64 (sqrt.f64 (-.f64 (.f64 g g) (*.f64 h h))) g)))
✓	9.3b	(cbrt.f64 (.f64 (+.f64 g (sqrt.f64 (-.f64 (.f64 g g) (*.f64 h h)))) (/.f64 -1/2 a)))
✓	30.6b	(sqrt.f64 (-.f64 (.f64 g g) (.f64 h h)))

series282.0ms (2.7%)

Counts

4 → 60

Calls

30 calls:

45.0ms	(cbrt.f64 (.f64 (+.f64 g (sqrt.f64 (-.f64 (.f64 g g) (*.f64 h h)))) (/.f64 -1/2 a)))	h	0
26.0ms	(cbrt.f64 (.f64 (+.f64 g (sqrt.f64 (-.f64 (.f64 g g) (*.f64 h h)))) (/.f64 -1/2 a)))	g	inf
26.0ms	(cbrt.f64 (.f64 (+.f64 g (sqrt.f64 (-.f64 (.f64 g g) (*.f64 h h)))) (/.f64 -1/2 a)))	g	0
20.0ms	(cbrt.f64 (.f64 (+.f64 g (sqrt.f64 (-.f64 (.f64 g g) (*.f64 h h)))) (/.f64 -1/2 a)))	h	-inf
19.0ms	(cbrt.f64 (.f64 (+.f64 g (sqrt.f64 (-.f64 (.f64 g g) (*.f64 h h)))) (/.f64 -1/2 a)))	h	inf

rewrite46.0ms (0.4%)

Algorithm

1×	batch-egg-rewrite

Rules

196×	`add-sqr-sqrt_binary64`
189×	`add-cbrt-cube_binary64`
189×	`log1p-expm1-u_binary64`
189×	`expm1-log1p-u_binary64`
185×	`add-cube-cbrt_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	18	68
1	408	68

Stop Event

1×	node limit

Counts

4 → 115

simplify55.0ms (0.5%)

Algorithm

1×	egg-herbie

Rules

854×	`times-frac_binary64`
533×	`cancel-sign-sub-inv_binary64`
274×	`fma-neg_binary64`
184×	`associate-r_binary64`
138×	`associate-l_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	200	2269
1	639	2190
2	2329	2168

Stop Event

1×	node limit

Counts

175 → 183

prune589.0ms (5.6%)

Pruning

14 alts after pruning (14 fresh and 0 done)

	Pruned	Kept	Total
New	284	14	298
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	285	14	299

Error

33.4b

Counts

299 → 14

Alt Table

Status	Error	Program
	44.5b	(+.f64 (cbrt.f64 (.f64 (/.f64 1/2 a) (-.f64 (sqrt.f64 (-.f64 (.f64 g g) (.f64 h h))) g))) (sqrt.f64 (cbrt.f64 (pow.f64 (.f64 (+.f64 g (sqrt.f64 (-.f64 (.f64 g g) (.f64 h h)))) (/.f64 -1/2 a)) 2))))
	52.6b	(+.f64 (cbrt.f64 (.f64 (/.f64 1/2 a) (-.f64 (-.f64 g (.f64 1/2 (/.f64 (pow.f64 h 2) g))) g))) (cbrt.f64 (.f64 (+.f64 g (sqrt.f64 (-.f64 (.f64 g g) (*.f64 h h)))) (/.f64 -1/2 a))))
	45.0b	(+.f64 (cbrt.f64 (.f64 (/.f64 1/2 a) (-.f64 (sqrt.f64 (-.f64 (.f64 g g) (.f64 h h))) g))) (cbrt.f64 (.f64 (+.f64 g (pow.f64 (cbrt.f64 (sqrt.f64 (-.f64 (.f64 g g) (.f64 h h)))) 3)) (/.f64 -1/2 a))))
	47.3b	(+.f64 (cbrt.f64 (.f64 (/.f64 1/2 a) (-.f64 (sqrt.f64 (-.f64 (.f64 g g) (.f64 h h))) g))) (cbrt.f64 (.f64 (+.f64 g (-.f64 (*.f64 1/2 (/.f64 (pow.f64 h 2) g)) g)) (/.f64 -1/2 a))))
▶	35.6b	(+.f64 (/.f64 (cbrt.f64 (.f64 1/2 (-.f64 (sqrt.f64 (-.f64 (.f64 g g) (.f64 h h))) g))) (cbrt.f64 a)) (cbrt.f64 (.f64 (+.f64 g (sqrt.f64 (-.f64 (.f64 g g) (.f64 h h)))) (/.f64 -1/2 a))))
	37.9b	(+.f64 (cbrt.f64 (.f64 (/.f64 1/2 a) (-.f64 (sqrt.f64 (-.f64 (.f64 g g) (.f64 h h))) g))) (pow.f64 (cbrt.f64 (cbrt.f64 (.f64 (+.f64 g (sqrt.f64 (-.f64 (.f64 g g) (.f64 h h)))) (/.f64 -1/2 a)))) 3))
	35.7b	(+.f64 (cbrt.f64 (.f64 (/.f64 1/2 a) (-.f64 (sqrt.f64 (-.f64 (.f64 g g) (.f64 h h))) g))) (/.f64 (cbrt.f64 (.f64 (+.f64 g (sqrt.f64 (-.f64 (.f64 g g) (.f64 h h)))) -1/2)) (cbrt.f64 a)))
	35.8b	(+.f64 (cbrt.f64 (.f64 (/.f64 1/2 a) (-.f64 (sqrt.f64 (-.f64 (.f64 g g) (.f64 h h))) g))) (.f64 (cbrt.f64 (/.f64 -1/2 a)) (cbrt.f64 (+.f64 g (sqrt.f64 (-.f64 (.f64 g g) (.f64 h h)))))))
	43.4b	(+.f64 (cbrt.f64 (.f64 (/.f64 1/2 a) (-.f64 (exp.f64 (log.f64 (sqrt.f64 (-.f64 (.f64 g g) (.f64 h h))))) g))) (cbrt.f64 (.f64 (+.f64 g (sqrt.f64 (-.f64 (.f64 g g) (.f64 h h)))) (/.f64 -1/2 a))))
	46.3b	(+.f64 (cbrt.f64 (.f64 (/.f64 1/2 a) (-.f64 (sqrt.f64 (-.f64 (.f64 g g) (.f64 h h))) g))) (cbrt.f64 (.f64 (+.f64 g (exp.f64 (log.f64 (sqrt.f64 (-.f64 (.f64 g g) (.f64 h h)))))) (/.f64 -1/2 a))))
	54.4b	(+.f64 (cbrt.f64 (.f64 (/.f64 1/2 a) (-.f64 (sqrt.f64 (/.f64 1 (/.f64 (+.f64 (pow.f64 g 4) (+.f64 (pow.f64 h 4) (pow.f64 (.f64 g h) 2))) (-.f64 (pow.f64 g 6) (pow.f64 h 6))))) g))) (cbrt.f64 (.f64 (+.f64 g (sqrt.f64 (-.f64 (.f64 g g) (*.f64 h h)))) (/.f64 -1/2 a))))
	41.4b	(+.f64 (cbrt.f64 (.f64 (/.f64 1/2 a) (-.f64 (sqrt.f64 (.f64 (pow.f64 (cbrt.f64 (-.f64 (.f64 g g) (.f64 h h))) 2) (cbrt.f64 (-.f64 (.f64 g g) (.f64 h h))))) g))) (cbrt.f64 (.f64 (+.f64 g (sqrt.f64 (-.f64 (.f64 g g) (*.f64 h h)))) (/.f64 -1/2 a))))
	42.9b	(+.f64 (cbrt.f64 (.f64 (/.f64 1/2 a) (-.f64 (sqrt.f64 (-.f64 (.f64 g g) (.f64 h h))) g))) (cbrt.f64 (.f64 (+.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)))))) (/.f64 -1/2 a))))
	42.0b	(+.f64 (cbrt.f64 (.f64 (/.f64 1/2 a) (-.f64 (pow.f64 (cbrt.f64 (sqrt.f64 (-.f64 (.f64 g g) (.f64 h h)))) 3) g))) (cbrt.f64 (.f64 (+.f64 g (sqrt.f64 (-.f64 (.f64 g g) (.f64 h h)))) (/.f64 -1/2 a))))

Compiler

Compiled 13955 to 6758 computations (51.6% saved)

localize16.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	1.6b	(+.f64 g (sqrt.f64 (-.f64 (.f64 g g) (.f64 h h))))
	2.8b	(-.f64 (.f64 g g) (.f64 h h))
	9.3b	(cbrt.f64 (.f64 (+.f64 g (sqrt.f64 (-.f64 (.f64 g g) (*.f64 h h)))) (/.f64 -1/2 a)))
	30.6b	(sqrt.f64 (-.f64 (.f64 g g) (.f64 h h)))

series12.0ms (0.1%)

Counts

1 → 24

Calls

6 calls:

4.0ms	(+.f64 g (sqrt.f64 (-.f64 (.f64 g g) (.f64 h h))))	g	-inf
2.0ms	(+.f64 g (sqrt.f64 (-.f64 (.f64 g g) (.f64 h h))))	g	0
2.0ms	(+.f64 g (sqrt.f64 (-.f64 (.f64 g g) (.f64 h h))))	g	inf
2.0ms	(+.f64 g (sqrt.f64 (-.f64 (.f64 g g) (.f64 h h))))	h	0
1.0ms	(+.f64 g (sqrt.f64 (-.f64 (.f64 g g) (.f64 h h))))	h	-inf

rewrite43.0ms (0.4%)

Algorithm

1×	batch-egg-rewrite

Rules

693×	`fma-def_binary64`
336×	`fma-neg_binary64`
164×	`expm1-udef_binary64`
164×	`log1p-udef_binary64`
149×	`log-pow_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	8	15
1	189	15
2	2820	14

Stop Event

1×	node limit

Counts

1 → 51

simplify37.0ms (0.4%)

Algorithm

1×	egg-herbie

Rules

521×	`fma-neg_binary64`
463×	`times-frac_binary64`
439×	`distribute-neg-frac_binary64`
231×	`associate-/r*_binary64`
229×	`associate-/l*_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	73	575
1	228	557
2	705	547
3	3695	543

Stop Event

1×	node limit

Counts

75 → 90

prune962.0ms (9.1%)

Pruning

17 alts after pruning (17 fresh and 0 done)

	Pruned	Kept	Total
New	350	8	358
Fresh	4	9	13
Picked	1	0	1
Done	0	0	0
Total	355	17	372

Error

31.9b

Counts

372 → 17

Alt Table

Status	Error	Program
	44.5b	(+.f64 (cbrt.f64 (.f64 (/.f64 1/2 a) (-.f64 (sqrt.f64 (-.f64 (.f64 g g) (.f64 h h))) g))) (sqrt.f64 (cbrt.f64 (pow.f64 (.f64 (+.f64 g (sqrt.f64 (-.f64 (.f64 g g) (.f64 h h)))) (/.f64 -1/2 a)) 2))))
▶	33.5b	(+.f64 (/.f64 (cbrt.f64 (.f64 1/2 (-.f64 (sqrt.f64 (-.f64 (.f64 g g) (.f64 h h))) g))) (cbrt.f64 a)) (/.f64 (cbrt.f64 (.f64 (+.f64 g (sqrt.f64 (-.f64 (.f64 g g) (.f64 h h)))) -1/2)) (cbrt.f64 a)))
	52.6b	(+.f64 (cbrt.f64 (.f64 (/.f64 1/2 a) (-.f64 (-.f64 g (.f64 1/2 (/.f64 (pow.f64 h 2) g))) g))) (cbrt.f64 (.f64 (+.f64 g (sqrt.f64 (-.f64 (.f64 g g) (*.f64 h h)))) (/.f64 -1/2 a))))
	38.0b	(+.f64 (/.f64 (cbrt.f64 (.f64 1/2 (-.f64 (pow.f64 (pow.f64 (-.f64 (.f64 g g) (.f64 h h)) 1/4) 2) g))) (cbrt.f64 a)) (cbrt.f64 (.f64 (+.f64 g (sqrt.f64 (-.f64 (.f64 g g) (.f64 h h)))) (/.f64 -1/2 a))))
	44.6b	(+.f64 (/.f64 (cbrt.f64 (.f64 1/2 (-.f64 (sqrt.f64 (-.f64 (.f64 g g) (.f64 h h))) g))) (cbrt.f64 a)) (cbrt.f64 (.f64 (.f64 1/2 (.f64 (/.f64 h g) h)) (/.f64 -1/2 a))))
	54.4b	(+.f64 (cbrt.f64 (.f64 (/.f64 1/2 a) (-.f64 (sqrt.f64 (/.f64 1 (/.f64 (+.f64 (pow.f64 g 4) (+.f64 (pow.f64 h 4) (pow.f64 (.f64 g h) 2))) (-.f64 (pow.f64 g 6) (pow.f64 h 6))))) g))) (cbrt.f64 (.f64 (+.f64 g (sqrt.f64 (-.f64 (.f64 g g) (*.f64 h h)))) (/.f64 -1/2 a))))
	44.9b	(+.f64 (/.f64 (cbrt.f64 (.f64 1/2 (-.f64 (cbrt.f64 (pow.f64 (-.f64 (.f64 g g) (.f64 h h)) 3/2)) g))) (cbrt.f64 a)) (cbrt.f64 (.f64 (+.f64 g (sqrt.f64 (-.f64 (.f64 g g) (.f64 h h)))) (/.f64 -1/2 a))))
	41.4b	(+.f64 (cbrt.f64 (.f64 (/.f64 1/2 a) (-.f64 (sqrt.f64 (.f64 (pow.f64 (cbrt.f64 (-.f64 (.f64 g g) (.f64 h h))) 2) (cbrt.f64 (-.f64 (.f64 g g) (.f64 h h))))) g))) (cbrt.f64 (.f64 (+.f64 g (sqrt.f64 (-.f64 (.f64 g g) (*.f64 h h)))) (/.f64 -1/2 a))))
	41.2b	(+.f64 (/.f64 (cbrt.f64 (.f64 1/2 (-.f64 (exp.f64 (log.f64 (sqrt.f64 (-.f64 (.f64 g g) (.f64 h h))))) g))) (cbrt.f64 a)) (cbrt.f64 (.f64 (+.f64 g (sqrt.f64 (-.f64 (.f64 g g) (.f64 h h)))) (/.f64 -1/2 a))))
	37.9b	(+.f64 (cbrt.f64 (.f64 (/.f64 1/2 a) (-.f64 (sqrt.f64 (-.f64 (.f64 g g) (.f64 h h))) g))) (pow.f64 (cbrt.f64 (cbrt.f64 (.f64 (+.f64 g (sqrt.f64 (-.f64 (.f64 g g) (.f64 h h)))) (/.f64 -1/2 a)))) 3))
	42.8b	(+.f64 (/.f64 (cbrt.f64 (.f64 1/2 (-.f64 (neg.f64 g) g))) (cbrt.f64 a)) (cbrt.f64 (.f64 (+.f64 g (sqrt.f64 (-.f64 (.f64 g g) (.f64 h h)))) (/.f64 -1/2 a))))
	39.8b	(+.f64 (/.f64 (cbrt.f64 (.f64 1/2 (-.f64 (pow.f64 (cbrt.f64 (sqrt.f64 (-.f64 (.f64 g g) (.f64 h h)))) 3) g))) (cbrt.f64 a)) (cbrt.f64 (.f64 (+.f64 g (sqrt.f64 (-.f64 (.f64 g g) (.f64 h h)))) (/.f64 -1/2 a))))
	46.3b	(+.f64 (cbrt.f64 (.f64 (/.f64 1/2 a) (-.f64 (sqrt.f64 (-.f64 (.f64 g g) (.f64 h h))) g))) (cbrt.f64 (.f64 (+.f64 g (exp.f64 (log.f64 (sqrt.f64 (-.f64 (.f64 g g) (.f64 h h)))))) (/.f64 -1/2 a))))
	42.9b	(+.f64 (cbrt.f64 (.f64 (/.f64 1/2 a) (-.f64 (sqrt.f64 (-.f64 (.f64 g g) (.f64 h h))) g))) (cbrt.f64 (.f64 (+.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)))))) (/.f64 -1/2 a))))
	42.0b	(+.f64 (cbrt.f64 (.f64 (/.f64 1/2 a) (-.f64 (pow.f64 (cbrt.f64 (sqrt.f64 (-.f64 (.f64 g g) (.f64 h h)))) 3) g))) (cbrt.f64 (.f64 (+.f64 g (sqrt.f64 (-.f64 (.f64 g g) (.f64 h h)))) (/.f64 -1/2 a))))
	45.0b	(+.f64 (cbrt.f64 (.f64 (/.f64 1/2 a) (-.f64 (sqrt.f64 (-.f64 (.f64 g g) (.f64 h h))) g))) (cbrt.f64 (.f64 (+.f64 g (pow.f64 (cbrt.f64 (sqrt.f64 (-.f64 (.f64 g g) (.f64 h h)))) 3)) (/.f64 -1/2 a))))
	33.6b	(+.f64 (/.f64 (cbrt.f64 (.f64 1/2 (-.f64 (sqrt.f64 (-.f64 (.f64 g g) (.f64 h h))) g))) (cbrt.f64 a)) (.f64 (cbrt.f64 (+.f64 g (sqrt.f64 (-.f64 (.f64 g g) (.f64 h h))))) (cbrt.f64 (/.f64 -1/2 a))))

Compiler

Compiled 16423 to 7599 computations (53.7% saved)

localize17.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	1.4b	(-.f64 (sqrt.f64 (-.f64 (.f64 g g) (.f64 h h))) g)
	1.6b	(+.f64 g (sqrt.f64 (-.f64 (.f64 g g) (.f64 h h))))
	2.8b	(-.f64 (.f64 g g) (.f64 h h))
	30.6b	(sqrt.f64 (-.f64 (.f64 g g) (.f64 h h)))

series11.0ms (0.1%)

Counts

1 → 24

Calls

6 calls:

2.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 g g) (.f64 h h))) g)	g	inf
2.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 g g) (.f64 h h))) g)	h	0
2.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 g g) (.f64 h h))) g)	g	0
2.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 g g) (.f64 h h))) g)	g	-inf
1.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 g g) (.f64 h h))) g)	h	-inf

rewrite50.0ms (0.5%)

Algorithm

1×	batch-egg-rewrite

Rules

747×	`fma-def_binary64`
325×	`fma-neg_binary64`
166×	`expm1-udef_binary64`
166×	`log1p-udef_binary64`
150×	`log-pow_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	8	15
1	190	15
2	2816	14

Stop Event

1×	node limit

Counts

1 → 96

simplify40.0ms (0.4%)

Algorithm

1×	egg-herbie

Rules

447×	`distribute-neg-frac_binary64`
443×	`times-frac_binary64`
231×	`associate-/l*_binary64`
229×	`fma-def_binary64`
215×	`associate-/r*_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	83	618
1	257	598
2	841	584
3	4127	584

Stop Event

1×	node limit

Counts

120 → 136

prune1.6s (15.2%)

Pruning

21 alts after pruning (21 fresh and 0 done)

	Pruned	Kept	Total
New	446	10	456
Fresh	5	11	16
Picked	1	0	1
Done	0	0	0
Total	452	21	473

Error

31.7b

Counts

473 → 21

Alt Table

Status	Error	Program
	44.5b	(+.f64 (cbrt.f64 (.f64 (/.f64 1/2 a) (-.f64 (sqrt.f64 (-.f64 (.f64 g g) (.f64 h h))) g))) (sqrt.f64 (cbrt.f64 (pow.f64 (.f64 (+.f64 g (sqrt.f64 (-.f64 (.f64 g g) (.f64 h h)))) (/.f64 -1/2 a)) 2))))
	52.6b	(+.f64 (cbrt.f64 (.f64 (/.f64 1/2 a) (-.f64 (-.f64 g (.f64 1/2 (/.f64 (pow.f64 h 2) g))) g))) (cbrt.f64 (.f64 (+.f64 g (sqrt.f64 (-.f64 (.f64 g g) (*.f64 h h)))) (/.f64 -1/2 a))))
	42.8b	(+.f64 (/.f64 (cbrt.f64 (.f64 1/2 (-.f64 (neg.f64 g) g))) (cbrt.f64 a)) (cbrt.f64 (.f64 (+.f64 g (sqrt.f64 (-.f64 (.f64 g g) (.f64 h h)))) (/.f64 -1/2 a))))
	57.6b	(+.f64 (/.f64 (cbrt.f64 (.f64 1/2 (fma.f64 (sqrt.f64 (+.f64 g h)) (sqrt.f64 (-.f64 g h)) (neg.f64 g)))) (cbrt.f64 a)) (/.f64 (cbrt.f64 (.f64 (+.f64 g (sqrt.f64 (-.f64 (.f64 g g) (.f64 h h)))) -1/2)) (cbrt.f64 a)))
	44.3b	(+.f64 (/.f64 (cbrt.f64 (.f64 1/2 (-.f64 (sqrt.f64 (-.f64 (.f64 g g) (.f64 h h))) g))) (cbrt.f64 a)) (/.f64 (cbrt.f64 (.f64 (.f64 1/2 (.f64 (/.f64 h g) h)) -1/2)) (cbrt.f64 a)))
	46.3b	(+.f64 (cbrt.f64 (.f64 (/.f64 1/2 a) (-.f64 (sqrt.f64 (-.f64 (.f64 g g) (.f64 h h))) g))) (cbrt.f64 (.f64 (+.f64 g (exp.f64 (log.f64 (sqrt.f64 (-.f64 (.f64 g g) (.f64 h h)))))) (/.f64 -1/2 a))))
	40.1b	(+.f64 (/.f64 (cbrt.f64 (.f64 1/2 (-.f64 (exp.f64 (log.f64 (sqrt.f64 (-.f64 (.f64 g g) (.f64 h h))))) g))) (cbrt.f64 a)) (/.f64 (cbrt.f64 (.f64 (+.f64 g (sqrt.f64 (-.f64 (.f64 g g) (.f64 h h)))) -1/2)) (cbrt.f64 a)))
	43.2b	(+.f64 (/.f64 (cbrt.f64 (.f64 1/2 (-.f64 (sqrt.f64 (-.f64 (.f64 g g) (.f64 h h))) g))) (cbrt.f64 a)) (/.f64 (cbrt.f64 (.f64 (+.f64 g (exp.f64 (log.f64 (sqrt.f64 (-.f64 (.f64 g g) (.f64 h h)))))) -1/2)) (cbrt.f64 a)))
	38.0b	(+.f64 (/.f64 (cbrt.f64 (.f64 1/2 (-.f64 (pow.f64 (pow.f64 (-.f64 (.f64 g g) (.f64 h h)) 1/4) 2) g))) (cbrt.f64 a)) (cbrt.f64 (.f64 (+.f64 g (sqrt.f64 (-.f64 (.f64 g g) (.f64 h h)))) (/.f64 -1/2 a))))
	54.4b	(+.f64 (cbrt.f64 (.f64 (/.f64 1/2 a) (-.f64 (sqrt.f64 (/.f64 1 (/.f64 (+.f64 (pow.f64 g 4) (+.f64 (pow.f64 h 4) (pow.f64 (.f64 g h) 2))) (-.f64 (pow.f64 g 6) (pow.f64 h 6))))) g))) (cbrt.f64 (.f64 (+.f64 g (sqrt.f64 (-.f64 (.f64 g g) (*.f64 h h)))) (/.f64 -1/2 a))))
	61.1b	(+.f64 (/.f64 (cbrt.f64 (.f64 1/2 (fma.f64 (sqrt.f64 g) (neg.f64 (sqrt.f64 g)) (hypot.f64 g (sqrt.f64 (.f64 h (neg.f64 h))))))) (cbrt.f64 a)) (/.f64 (cbrt.f64 (.f64 (+.f64 g (sqrt.f64 (-.f64 (.f64 g g) (*.f64 h h)))) -1/2)) (cbrt.f64 a)))
	40.4b	(+.f64 (/.f64 (cbrt.f64 (.f64 1/2 (-.f64 (sqrt.f64 (-.f64 (.f64 g g) (.f64 h h))) g))) (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)))
	41.4b	(+.f64 (cbrt.f64 (.f64 (/.f64 1/2 a) (-.f64 (sqrt.f64 (.f64 (pow.f64 (cbrt.f64 (-.f64 (.f64 g g) (.f64 h h))) 2) (cbrt.f64 (-.f64 (.f64 g g) (.f64 h h))))) g))) (cbrt.f64 (.f64 (+.f64 g (sqrt.f64 (-.f64 (.f64 g g) (*.f64 h h)))) (/.f64 -1/2 a))))
▶	33.5b	(+.f64 (/.f64 (cbrt.f64 (.f64 1/2 (-.f64 (sqrt.f64 (fma.f64 g g (.f64 h (neg.f64 h)))) g))) (cbrt.f64 a)) (/.f64 (cbrt.f64 (.f64 (+.f64 g (sqrt.f64 (-.f64 (.f64 g g) (*.f64 h h)))) -1/2)) (cbrt.f64 a)))
	42.9b	(+.f64 (cbrt.f64 (.f64 (/.f64 1/2 a) (-.f64 (sqrt.f64 (-.f64 (.f64 g g) (.f64 h h))) g))) (cbrt.f64 (.f64 (+.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)))))) (/.f64 -1/2 a))))
	52.2b	(+.f64 (/.f64 (cbrt.f64 (.f64 1/2 (fma.f64 (pow.f64 (cbrt.f64 g) 2) (neg.f64 (cbrt.f64 g)) (hypot.f64 g (sqrt.f64 (.f64 h (neg.f64 h))))))) (cbrt.f64 a)) (/.f64 (cbrt.f64 (.f64 (+.f64 g (sqrt.f64 (-.f64 (.f64 g g) (*.f64 h h)))) -1/2)) (cbrt.f64 a)))
	50.0b	(+.f64 (/.f64 (cbrt.f64 (.f64 1/2 (.f64 -1/2 (/.f64 (pow.f64 h 2) g)))) (cbrt.f64 a)) (/.f64 (cbrt.f64 (.f64 (+.f64 g (sqrt.f64 (-.f64 (.f64 g g) (*.f64 h h)))) -1/2)) (cbrt.f64 a)))
	45.0b	(+.f64 (cbrt.f64 (.f64 (/.f64 1/2 a) (-.f64 (sqrt.f64 (-.f64 (.f64 g g) (.f64 h h))) g))) (cbrt.f64 (.f64 (+.f64 g (pow.f64 (cbrt.f64 (sqrt.f64 (-.f64 (.f64 g g) (.f64 h h)))) 3)) (/.f64 -1/2 a))))
	51.6b	(+.f64 (/.f64 (cbrt.f64 (.f64 1/2 (cbrt.f64 (pow.f64 (-.f64 (hypot.f64 g (sqrt.f64 (.f64 h (neg.f64 h)))) g) 3)))) (cbrt.f64 a)) (/.f64 (cbrt.f64 (.f64 (+.f64 g (sqrt.f64 (-.f64 (.f64 g g) (*.f64 h h)))) -1/2)) (cbrt.f64 a)))
	42.0b	(+.f64 (cbrt.f64 (.f64 (/.f64 1/2 a) (-.f64 (pow.f64 (cbrt.f64 (sqrt.f64 (-.f64 (.f64 g g) (.f64 h h)))) 3) g))) (cbrt.f64 (.f64 (+.f64 g (sqrt.f64 (-.f64 (.f64 g g) (.f64 h h)))) (/.f64 -1/2 a))))
	33.6b	(+.f64 (/.f64 (cbrt.f64 (.f64 1/2 (-.f64 (sqrt.f64 (-.f64 (.f64 g g) (.f64 h h))) g))) (cbrt.f64 a)) (.f64 (cbrt.f64 (+.f64 g (sqrt.f64 (-.f64 (.f64 g g) (.f64 h h))))) (cbrt.f64 (/.f64 -1/2 a))))

Compiler

Compiled 20642 to 8773 computations (57.5% saved)

localize21.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
	2.8b	(-.f64 (.f64 g g) (.f64 h h))
✓	3.5b	(fma.f64 g g (*.f64 h (neg.f64 h)))
✓	30.6b	(sqrt.f64 (fma.f64 g g (*.f64 h (neg.f64 h))))
	30.6b	(sqrt.f64 (-.f64 (.f64 g g) (.f64 h h)))

series20.0ms (0.2%)

Counts

2 → 48

Calls

12 calls:

3.0ms	(sqrt.f64 (fma.f64 g g (*.f64 h (neg.f64 h))))	g	-inf
3.0ms	(sqrt.f64 (fma.f64 g g (*.f64 h (neg.f64 h))))	g	0
2.0ms	(sqrt.f64 (fma.f64 g g (*.f64 h (neg.f64 h))))	h	-inf
2.0ms	(sqrt.f64 (fma.f64 g g (*.f64 h (neg.f64 h))))	h	inf
2.0ms	(sqrt.f64 (fma.f64 g g (*.f64 h (neg.f64 h))))	g	inf

rewrite47.0ms (0.4%)

Algorithm

1×	batch-egg-rewrite

Rules

486×	`log1p-expm1-u_binary64`
486×	`expm1-log1p-u_binary64`
379×	`unpow-prod-down_binary64`
263×	`log-prod_binary64`
145×	`pow2_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	7	22
1	142	11
2	1743	11

Stop Event

1×	node limit

Counts

2 → 131

simplify46.0ms (0.4%)

Algorithm

1×	egg-herbie

Rules

976×	`fma-neg_binary64`
685×	`times-frac_binary64`
307×	`associate-/l*_binary64`
290×	`associate-/r*_binary64`
193×	`associate-r_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	76	878
1	240	868
2	801	848
3	4812	848

Stop Event

1×	node limit

Counts

179 → 175

prune1.0s (9.6%)

Pruning

19 alts after pruning (19 fresh and 0 done)

	Pruned	Kept	Total
New	284	6	290
Fresh	7	13	20
Picked	1	0	1
Done	0	0	0
Total	292	19	311

Error

31.6b

Counts

311 → 19

Alt Table

Status	Error	Program
	44.5b	(+.f64 (cbrt.f64 (.f64 (/.f64 1/2 a) (-.f64 (sqrt.f64 (-.f64 (.f64 g g) (.f64 h h))) g))) (sqrt.f64 (cbrt.f64 (pow.f64 (.f64 (+.f64 g (sqrt.f64 (-.f64 (.f64 g g) (.f64 h h)))) (/.f64 -1/2 a)) 2))))
	52.6b	(+.f64 (cbrt.f64 (.f64 (/.f64 1/2 a) (-.f64 (-.f64 g (.f64 1/2 (/.f64 (pow.f64 h 2) g))) g))) (cbrt.f64 (.f64 (+.f64 g (sqrt.f64 (-.f64 (.f64 g g) (*.f64 h h)))) (/.f64 -1/2 a))))
	43.2b	(+.f64 (/.f64 (cbrt.f64 (.f64 1/2 (-.f64 (sqrt.f64 (fma.f64 g g (.f64 h (neg.f64 h)))) g))) (cbrt.f64 a)) (/.f64 (cbrt.f64 (.f64 (+.f64 g (exp.f64 (log.f64 (sqrt.f64 (-.f64 (.f64 g g) (*.f64 h h)))))) -1/2)) (cbrt.f64 a)))
	39.9b	(+.f64 (/.f64 (cbrt.f64 (.f64 1/2 (-.f64 (.f64 (pow.f64 (pow.f64 (cbrt.f64 (cbrt.f64 (hypot.f64 g h))) 2) 3) (cbrt.f64 (hypot.f64 g h))) g))) (cbrt.f64 a)) (/.f64 (cbrt.f64 (.f64 (+.f64 g (sqrt.f64 (-.f64 (.f64 g g) (*.f64 h h)))) -1/2)) (cbrt.f64 a)))
	44.3b	(+.f64 (/.f64 (cbrt.f64 (.f64 1/2 (-.f64 (sqrt.f64 (-.f64 (.f64 g g) (.f64 h h))) g))) (cbrt.f64 a)) (/.f64 (cbrt.f64 (.f64 (.f64 1/2 (.f64 (/.f64 h g) h)) -1/2)) (cbrt.f64 a)))
	46.3b	(+.f64 (cbrt.f64 (.f64 (/.f64 1/2 a) (-.f64 (sqrt.f64 (-.f64 (.f64 g g) (.f64 h h))) g))) (cbrt.f64 (.f64 (+.f64 g (exp.f64 (log.f64 (sqrt.f64 (-.f64 (.f64 g g) (.f64 h h)))))) (/.f64 -1/2 a))))
	41.4b	(+.f64 (cbrt.f64 (.f64 (/.f64 1/2 a) (-.f64 (sqrt.f64 (.f64 (pow.f64 (cbrt.f64 (-.f64 (.f64 g g) (.f64 h h))) 2) (cbrt.f64 (-.f64 (.f64 g g) (.f64 h h))))) g))) (cbrt.f64 (.f64 (+.f64 g (sqrt.f64 (-.f64 (.f64 g g) (*.f64 h h)))) (/.f64 -1/2 a))))
	38.7b	(+.f64 (/.f64 (cbrt.f64 (.f64 1/2 (-.f64 (pow.f64 (cbrt.f64 (hypot.f64 g h)) 3) g))) (cbrt.f64 a)) (/.f64 (cbrt.f64 (.f64 (+.f64 g (sqrt.f64 (-.f64 (.f64 g g) (.f64 h h)))) -1/2)) (cbrt.f64 a)))
	40.4b	(+.f64 (/.f64 (cbrt.f64 (.f64 1/2 (-.f64 (sqrt.f64 (-.f64 (.f64 g g) (.f64 h h))) g))) (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)))
	50.0b	(+.f64 (/.f64 (cbrt.f64 (.f64 1/2 (.f64 -1/2 (/.f64 (pow.f64 h 2) g)))) (cbrt.f64 a)) (/.f64 (cbrt.f64 (.f64 (+.f64 g (sqrt.f64 (-.f64 (.f64 g g) (*.f64 h h)))) -1/2)) (cbrt.f64 a)))
	40.3b	(+.f64 (/.f64 (cbrt.f64 (.f64 1/2 (-.f64 (exp.f64 (log.f64 (hypot.f64 g h))) g))) (cbrt.f64 a)) (/.f64 (cbrt.f64 (.f64 (+.f64 g (sqrt.f64 (-.f64 (.f64 g g) (.f64 h h)))) -1/2)) (cbrt.f64 a)))
	45.0b	(+.f64 (cbrt.f64 (.f64 (/.f64 1/2 a) (-.f64 (sqrt.f64 (-.f64 (.f64 g g) (.f64 h h))) g))) (cbrt.f64 (.f64 (+.f64 g (pow.f64 (cbrt.f64 (sqrt.f64 (-.f64 (.f64 g g) (.f64 h h)))) 3)) (/.f64 -1/2 a))))
	35.9b	(+.f64 (/.f64 (cbrt.f64 (.f64 1/2 (-.f64 (.f64 (sqrt.f64 (sqrt.f64 (hypot.f64 g h))) (pow.f64 (.f64 (sqrt.f64 (hypot.f64 g h)) (hypot.f64 g h)) 1/2)) g))) (cbrt.f64 a)) (/.f64 (cbrt.f64 (.f64 (+.f64 g (sqrt.f64 (-.f64 (.f64 g g) (.f64 h h)))) -1/2)) (cbrt.f64 a)))
	33.6b	(+.f64 (/.f64 (cbrt.f64 (.f64 1/2 (-.f64 (sqrt.f64 (-.f64 (.f64 g g) (.f64 h h))) g))) (cbrt.f64 a)) (.f64 (cbrt.f64 (+.f64 g (sqrt.f64 (-.f64 (.f64 g g) (.f64 h h))))) (cbrt.f64 (/.f64 -1/2 a))))
	42.8b	(+.f64 (/.f64 (cbrt.f64 (.f64 1/2 (-.f64 (neg.f64 g) g))) (cbrt.f64 a)) (cbrt.f64 (.f64 (+.f64 g (sqrt.f64 (-.f64 (.f64 g g) (.f64 h h)))) (/.f64 -1/2 a))))
	36.7b	(+.f64 (/.f64 (cbrt.f64 (.f64 1/2 (-.f64 (pow.f64 (sqrt.f64 (hypot.f64 g h)) 2) g))) (cbrt.f64 a)) (/.f64 (cbrt.f64 (.f64 (+.f64 g (sqrt.f64 (-.f64 (.f64 g g) (.f64 h h)))) -1/2)) (cbrt.f64 a)))
	54.4b	(+.f64 (cbrt.f64 (.f64 (/.f64 1/2 a) (-.f64 (sqrt.f64 (/.f64 1 (/.f64 (+.f64 (pow.f64 g 4) (+.f64 (pow.f64 h 4) (pow.f64 (.f64 g h) 2))) (-.f64 (pow.f64 g 6) (pow.f64 h 6))))) g))) (cbrt.f64 (.f64 (+.f64 g (sqrt.f64 (-.f64 (.f64 g g) (*.f64 h h)))) (/.f64 -1/2 a))))
	42.9b	(+.f64 (cbrt.f64 (.f64 (/.f64 1/2 a) (-.f64 (sqrt.f64 (-.f64 (.f64 g g) (.f64 h h))) g))) (cbrt.f64 (.f64 (+.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)))))) (/.f64 -1/2 a))))
	42.0b	(+.f64 (cbrt.f64 (.f64 (/.f64 1/2 a) (-.f64 (pow.f64 (cbrt.f64 (sqrt.f64 (-.f64 (.f64 g g) (.f64 h h)))) 3) g))) (cbrt.f64 (.f64 (+.f64 g (sqrt.f64 (-.f64 (.f64 g g) (.f64 h h)))) (/.f64 -1/2 a))))

Compiler

Compiled 13108 to 5868 computations (55.2% saved)

regimes1.7s (15.6%)

Accuracy

Total 1.7b remaining (5.4%)

Threshold costs 0b (0%)

Counts

174 → 1

Compiler

Compiled 46003 to 29185 computations (36.6% saved)

simplify4.0ms (0%)

Algorithm

1×	egg-herbie

Rules

7×	`+-commutative_binary64`
6×	`*-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	39	52
2	47	52
3	52	52
4	54	52

Stop Event

1×

saturated

end361.0ms (3.4%)

Stop Event

1×

fuel

Compiler

Compiled 798 to 488 computations (38.8% saved)

Details

analyze724.0ms (6.9%)

sample2.8s (26.7%)

preprocess33.0ms (0.3%)

simplify30.0ms (0.3%)

prune4.0ms (0%)

localize15.0ms (0.1%)

series282.0ms (2.7%)

rewrite46.0ms (0.4%)

simplify55.0ms (0.5%)

prune589.0ms (5.6%)

localize16.0ms (0.2%)

series12.0ms (0.1%)

rewrite43.0ms (0.4%)

simplify37.0ms (0.4%)

prune962.0ms (9.1%)

localize17.0ms (0.2%)

series11.0ms (0.1%)

rewrite50.0ms (0.5%)

simplify40.0ms (0.4%)

prune1.6s (15.2%)

localize21.0ms (0.2%)

series20.0ms (0.2%)

rewrite47.0ms (0.4%)

simplify46.0ms (0.4%)

prune1.0s (9.6%)

regimes1.7s (15.6%)

simplify4.0ms (0%)

end361.0ms (3.4%)

Profiling