Details

analyze2.4s (17.2%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.8%	0.2%	0
0%	99.8%	0.2%	1
0%	99.8%	0.2%	2
0%	99.8%	0.2%	3
0%	99.8%	0.2%	4
0%	99.8%	0.2%	5
0%	99.8%	0.2%	6
0%	81.1%	18.9%	7
0%	68.6%	31.4%	8
0%	59.2%	40.8%	9
0%	59.2%	40.8%	10
0%	59.2%	40.8%	11
0.4%	49.5%	50.1%	12
0.8%	44.4%	54.8%	13
1.4%	39.9%	58.7%	14

Compiler

Compiled 41 to 32 computations (22% saved)

sample176.0ms (1.3%)

Algorithm

1×

intervals

Results

44.0ms	256×	body	128	valid
42.0ms	293×	body	128	nan
27.0ms	164×	body	128	invalid

Compiler

Compiled 86 to 68 computations (20.9% saved)

simplify40.0ms (0.3%)

Algorithm

1×	egg-herbie

Rules

466×	`fma-def_binary64`
437×	`*-commutative_binary64`
425×	`associate-/l*_binary64`
347×	`cancel-sign-sub-inv_binary64`
263×	`associate-/l/_binary64`

Counts

1 → 1

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	24	41
1	62	41
2	188	39
3	1071	39
4	3610	39
5	5106	39

prune3.0ms (0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

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

Error

27.3b

Counts

2 → 1

Alt Table

Status	Error	Program
▶	27.3b	(.f64 (.f64 (sqrt.f64 (/.f64 d h)) (sqrt.f64 (/.f64 d l))) (fma.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2) (*.f64 (/.f64 h l) -1/2) 1))

Compiler

Compiled 93 to 66 computations (29% saved)

localize19.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	6.4b	(.f64 (.f64 (sqrt.f64 (/.f64 d h)) (sqrt.f64 (/.f64 d l))) (fma.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2) (*.f64 (/.f64 h l) -1/2) 1))
✓	8.5b	(fma.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2) (*.f64 (/.f64 h l) -1/2) 1)
✓	12.4b	(sqrt.f64 (/.f64 d h))
✓	13.2b	(sqrt.f64 (/.f64 d l))

rewrite19.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

26×	`sqrt-prod_binary64`
25×	`add-sqr-sqrt_binary64`
20×	`times-frac_binary64`
19×	`*-un-lft-identity_binary64`
19×	`add-cube-cbrt_binary64`

Counts

4 → 89

Calls

4 calls:

9.0ms	(.f64 (.f64 (sqrt.f64 (/.f64 d h)) (sqrt.f64 (/.f64 d l))) (fma.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2) (*.f64 (/.f64 h l) -1/2) 1))
2.0ms	(sqrt.f64 (/.f64 d l))
2.0ms	(sqrt.f64 (/.f64 d h))
0.0ms	(fma.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2) (*.f64 (/.f64 h l) -1/2) 1)

series440.0ms (3.1%)

Counts

4 → 168

Calls

4 calls:

257.0ms	(.f64 (.f64 (sqrt.f64 (/.f64 d h)) (sqrt.f64 (/.f64 d l))) (fma.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2) (*.f64 (/.f64 h l) -1/2) 1))
155.0ms	(fma.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2) (*.f64 (/.f64 h l) -1/2) 1)
14.0ms	(sqrt.f64 (/.f64 d h))
13.0ms	(sqrt.f64 (/.f64 d l))

simplify167.0ms (1.2%)

Algorithm

1×	egg-herbie

Rules

647×	`times-frac_binary64`
442×	`associate-/l*_binary64`
441×	`associate-/r*_binary64`
217×	`fma-def_binary64`
171×	`*-commutative_binary64`

Counts

257 → 257

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	592	9234
1	1610	8843
2	5050	8843

prune124.0ms (0.9%)

Pruning

21 alts after pruning (21 fresh and 0 done)

	Pruned	Kept	Total
New	236	21	257
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	237	21	258

Error

10.9b

Counts

258 → 21

Alt Table

Status	Error	Program
	21.3b	(.f64 (.f64 (.f64 (sqrt.f64 (/.f64 1 (.f64 (cbrt.f64 h) (cbrt.f64 h)))) (sqrt.f64 (/.f64 d (cbrt.f64 h)))) (sqrt.f64 (/.f64 d l))) (fma.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2) (*.f64 (/.f64 h l) -1/2) 1))
	42.2b	(.f64 (.f64 (sqrt.f64 (/.f64 d h)) (sqrt.f64 (/.f64 d l))) (-.f64 1 (.f64 1/8 (/.f64 (.f64 (.f64 D D) (.f64 h (.f64 M M))) (.f64 l (*.f64 d d))))))
	27.3b	(.f64 (.f64 (sqrt.f64 (/.f64 d l)) (sqrt.f64 (/.f64 d h))) (fma.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2) (*.f64 (/.f64 h l) -1/2) 1))
	23.8b	(.f64 (.f64 (sqrt.f64 (/.f64 d h)) (.f64 (sqrt.f64 (/.f64 1 (.f64 (cbrt.f64 l) (cbrt.f64 l)))) (sqrt.f64 (/.f64 d (cbrt.f64 l))))) (fma.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2) (*.f64 (/.f64 h l) -1/2) 1))
	32.0b	(.f64 (.f64 (sqrt.f64 (/.f64 d h)) (sqrt.f64 (/.f64 d l))) 1)
	38.8b	(/.f64 (.f64 d (fma.f64 (pow.f64 (/.f64 (.f64 D M) (.f64 d 2)) 2) (.f64 (/.f64 h l) -1/2) 1)) (*.f64 (sqrt.f64 h) (sqrt.f64 l)))
▶	20.5b	(.f64 (.f64 (.f64 (fabs.f64 (/.f64 (cbrt.f64 d) (cbrt.f64 h))) (sqrt.f64 (/.f64 (cbrt.f64 d) (cbrt.f64 h)))) (sqrt.f64 (/.f64 d l))) (fma.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2) (.f64 (/.f64 h l) -1/2) 1))
	23.3b	(.f64 (.f64 (sqrt.f64 (/.f64 d h)) (.f64 (fabs.f64 (/.f64 (cbrt.f64 d) (cbrt.f64 l))) (sqrt.f64 (/.f64 (cbrt.f64 d) (cbrt.f64 l))))) (fma.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2) (.f64 (/.f64 h l) -1/2) 1))
	27.7b	(.f64 (.f64 (cbrt.f64 (.f64 (fma.f64 (pow.f64 (/.f64 (.f64 D M) (.f64 d 2)) 2) (.f64 (/.f64 h l) -1/2) 1) (.f64 (sqrt.f64 (/.f64 d l)) (sqrt.f64 (/.f64 d h))))) (cbrt.f64 (.f64 (fma.f64 (pow.f64 (/.f64 (.f64 D M) (.f64 d 2)) 2) (.f64 (/.f64 h l) -1/2) 1) (.f64 (sqrt.f64 (/.f64 d l)) (sqrt.f64 (/.f64 d h)))))) (cbrt.f64 (.f64 (fma.f64 (pow.f64 (/.f64 (.f64 D M) (.f64 d 2)) 2) (.f64 (/.f64 h l) -1/2) 1) (*.f64 (sqrt.f64 (/.f64 d l)) (sqrt.f64 (/.f64 d h))))))
	27.4b	(.f64 (.f64 (.f64 (sqrt.f64 (sqrt.f64 (/.f64 d h))) (sqrt.f64 (sqrt.f64 (/.f64 d h)))) (sqrt.f64 (/.f64 d l))) (fma.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2) (.f64 (/.f64 h l) -1/2) 1))
	27.3b	(.f64 (.f64 (sqrt.f64 (/.f64 d h)) (sqrt.f64 (/.f64 d l))) (.f64 (.f64 (cbrt.f64 (fma.f64 (pow.f64 (/.f64 (.f64 D M) (.f64 d 2)) 2) (.f64 (/.f64 h l) -1/2) 1)) (cbrt.f64 (fma.f64 (pow.f64 (/.f64 (.f64 D M) (.f64 d 2)) 2) (.f64 (/.f64 h l) -1/2) 1))) (cbrt.f64 (fma.f64 (pow.f64 (/.f64 (.f64 D M) (.f64 d 2)) 2) (*.f64 (/.f64 h l) -1/2) 1))))
	35.9b	(.f64 (.f64 (cbrt.f64 (pow.f64 (sqrt.f64 (/.f64 d h)) 3)) (sqrt.f64 (/.f64 d l))) (fma.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2) (*.f64 (/.f64 h l) -1/2) 1))
	27.5b	(.f64 (sqrt.f64 (/.f64 d h)) (.f64 (sqrt.f64 (/.f64 d l)) (fma.f64 (pow.f64 (/.f64 (.f64 D M) (.f64 d 2)) 2) (*.f64 (/.f64 h l) -1/2) 1)))
	21.5b	(.f64 (.f64 (.f64 (fabs.f64 (cbrt.f64 d)) (sqrt.f64 (/.f64 (cbrt.f64 d) h))) (sqrt.f64 (/.f64 d l))) (fma.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2) (.f64 (/.f64 h l) -1/2) 1))
	24.2b	(.f64 (.f64 (sqrt.f64 (/.f64 d h)) (.f64 (fabs.f64 (cbrt.f64 d)) (sqrt.f64 (/.f64 (cbrt.f64 d) l)))) (fma.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2) (.f64 (/.f64 h l) -1/2) 1))
	27.5b	(.f64 (.f64 (sqrt.f64 (/.f64 d h)) (.f64 (fabs.f64 (cbrt.f64 (/.f64 d l))) (sqrt.f64 (cbrt.f64 (/.f64 d l))))) (fma.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2) (.f64 (/.f64 h l) -1/2) 1))
	33.5b	(.f64 (sqrt.f64 (.f64 (fma.f64 (pow.f64 (/.f64 (.f64 D M) (.f64 d 2)) 2) (.f64 (/.f64 h l) -1/2) 1) (.f64 (sqrt.f64 (/.f64 d l)) (sqrt.f64 (/.f64 d h))))) (sqrt.f64 (.f64 (fma.f64 (pow.f64 (/.f64 (.f64 D M) (.f64 d 2)) 2) (.f64 (/.f64 h l) -1/2) 1) (*.f64 (sqrt.f64 (/.f64 d l)) (sqrt.f64 (/.f64 d h))))))
	27.7b	(.f64 (.f64 (.f64 (.f64 (cbrt.f64 (sqrt.f64 (/.f64 d h))) (cbrt.f64 (sqrt.f64 (/.f64 d h)))) (cbrt.f64 (sqrt.f64 (/.f64 d h)))) (sqrt.f64 (/.f64 d l))) (fma.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2) (*.f64 (/.f64 h l) -1/2) 1))
	45.1b	(.f64 d (sqrt.f64 (/.f64 1 (.f64 l h))))
	40.9b	(.f64 (.f64 (.f64 (sqrt.f64 d) (sqrt.f64 (/.f64 1 h))) (sqrt.f64 (/.f64 d l))) (fma.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2) (.f64 (/.f64 h l) -1/2) 1))
	59.4b	(.f64 -1/8 (.f64 (/.f64 (.f64 (.f64 D D) (*.f64 M M)) d) (sqrt.f64 (/.f64 h (pow.f64 l 3)))))

Compiler

Compiled 4246 to 2246 computations (47.1% saved)

localize22.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	4.5b	(/.f64 (.f64 M D) (.f64 d 2))
✓	6.4b	(.f64 (.f64 (.f64 (fabs.f64 (/.f64 (cbrt.f64 d) (cbrt.f64 h))) (sqrt.f64 (/.f64 (cbrt.f64 d) (cbrt.f64 h)))) (sqrt.f64 (/.f64 d l))) (fma.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2) (.f64 (/.f64 h l) -1/2) 1))
	8.5b	(fma.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2) (*.f64 (/.f64 h l) -1/2) 1)
	13.2b	(sqrt.f64 (/.f64 d l))

rewrite29.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

23×	`add-cbrt-cube_binary64`
23×	`add-exp-log_binary64`
12×	`associate-*l/_binary64`
11×	`pow1_binary64`
10×	`cbrt-unprod_binary64`

Counts

2 → 55

Calls

2 calls:

21.0ms

(*.f64 (*.f64 (*.f64 (fabs.f64 (/.f64 (cbrt.f64 d) (cbrt.f64 h))) (sqrt.f64 (/.f64 (cbrt.f64 d) (cbrt.f64 h)))) (sqrt.f64 (/.f64 d l))) (fma.f64 (pow.f64 (/.f64 (*.f64 M D) (*.f64 d 2)) 2) (*.f64 (/.f64 h l) -1/2) 1))

4.0ms

(/.f64 (*.f64 M D) (*.f64 d 2))

series1.1s (7.7%)

Counts

2 → 96

Calls

2 calls:

1.0s

(*.f64 (*.f64 (*.f64 (fabs.f64 (/.f64 (cbrt.f64 d) (cbrt.f64 h))) (sqrt.f64 (/.f64 (cbrt.f64 d) (cbrt.f64 h)))) (sqrt.f64 (/.f64 d l))) (fma.f64 (pow.f64 (/.f64 (*.f64 M D) (*.f64 d 2)) 2) (*.f64 (/.f64 h l) -1/2) 1))

51.0ms

(/.f64 (*.f64 M D) (*.f64 d 2))

simplify192.0ms (1.4%)

Algorithm

1×	egg-herbie

Rules

819×	`fma-def_binary64`
787×	`associate-l_binary64`
363×	`times-frac_binary64`
227×	`associate-/l*_binary64`
189×	`associate-/r*_binary64`

Counts

151 → 151

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	425	9076
1	1291	7941
2	4847	7899
3	5492	7899

prune133.0ms (1%)

Pruning

26 alts after pruning (26 fresh and 0 done)

	Pruned	Kept	Total
New	265	7	272
Fresh	1	19	20
Picked	1	0	1
Done	0	0	0
Total	267	26	293

Error

10.3b

Counts

293 → 26

Alt Table

Status	Error	Program
	17.3b	(.f64 (.f64 (.f64 (fabs.f64 (/.f64 (cbrt.f64 d) (cbrt.f64 h))) (sqrt.f64 (/.f64 (cbrt.f64 d) (cbrt.f64 h)))) (.f64 (fabs.f64 (cbrt.f64 d)) (sqrt.f64 (/.f64 (cbrt.f64 d) l)))) (fma.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2) (*.f64 (/.f64 h l) -1/2) 1))
	21.3b	(.f64 (.f64 (.f64 (sqrt.f64 (/.f64 1 (.f64 (cbrt.f64 h) (cbrt.f64 h)))) (sqrt.f64 (/.f64 d (cbrt.f64 h)))) (sqrt.f64 (/.f64 d l))) (fma.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2) (*.f64 (/.f64 h l) -1/2) 1))
	42.2b	(.f64 (.f64 (sqrt.f64 (/.f64 d h)) (sqrt.f64 (/.f64 d l))) (-.f64 1 (.f64 1/8 (/.f64 (.f64 (.f64 D D) (.f64 h (.f64 M M))) (.f64 l (*.f64 d d))))))
▶	16.9b	(.f64 (.f64 (.f64 (fabs.f64 (/.f64 (cbrt.f64 d) (cbrt.f64 h))) (sqrt.f64 (/.f64 (cbrt.f64 d) (cbrt.f64 h)))) (.f64 (sqrt.f64 (/.f64 1 (.f64 (cbrt.f64 l) (cbrt.f64 l)))) (sqrt.f64 (/.f64 d (cbrt.f64 l))))) (fma.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2) (.f64 (/.f64 h l) -1/2) 1))
	27.3b	(.f64 (.f64 (sqrt.f64 (/.f64 d l)) (sqrt.f64 (/.f64 d h))) (fma.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2) (*.f64 (/.f64 h l) -1/2) 1))
	23.8b	(.f64 (.f64 (sqrt.f64 (/.f64 d h)) (.f64 (sqrt.f64 (/.f64 1 (.f64 (cbrt.f64 l) (cbrt.f64 l)))) (sqrt.f64 (/.f64 d (cbrt.f64 l))))) (fma.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2) (*.f64 (/.f64 h l) -1/2) 1))
	32.0b	(.f64 (.f64 (sqrt.f64 (/.f64 d h)) (sqrt.f64 (/.f64 d l))) 1)
	25.8b	(.f64 (.f64 (*.f64 (fabs.f64 (/.f64 (cbrt.f64 d) (cbrt.f64 h))) (sqrt.f64 (/.f64 (cbrt.f64 d) (cbrt.f64 h)))) (sqrt.f64 (/.f64 d l))) 1)
	27.5b	(.f64 (sqrt.f64 (/.f64 d h)) (.f64 (sqrt.f64 (/.f64 d l)) (fma.f64 (pow.f64 (/.f64 (.f64 D M) (.f64 d 2)) 2) (*.f64 (/.f64 h l) -1/2) 1)))
	20.5b	(.f64 (.f64 (pow.f64 (sqrt.f64 (/.f64 (cbrt.f64 d) (cbrt.f64 h))) 3) (sqrt.f64 (/.f64 d l))) (fma.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2) (*.f64 (/.f64 h l) -1/2) 1))
	24.2b	(.f64 (.f64 (sqrt.f64 (/.f64 d h)) (.f64 (fabs.f64 (cbrt.f64 d)) (sqrt.f64 (/.f64 (cbrt.f64 d) l)))) (fma.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2) (.f64 (/.f64 h l) -1/2) 1))
	20.5b	(.f64 (.f64 (fabs.f64 (/.f64 (cbrt.f64 d) (cbrt.f64 h))) (sqrt.f64 (/.f64 (cbrt.f64 d) (cbrt.f64 h)))) (.f64 (sqrt.f64 (/.f64 d l)) (fma.f64 (pow.f64 (/.f64 (.f64 D M) (.f64 2 d)) 2) (.f64 (/.f64 h l) -1/2) 1)))
	38.8b	(/.f64 (.f64 d (fma.f64 (pow.f64 (/.f64 (.f64 D M) (.f64 d 2)) 2) (.f64 (/.f64 h l) -1/2) 1)) (*.f64 (sqrt.f64 h) (sqrt.f64 l)))
	20.7b	(/.f64 (.f64 (fma.f64 (pow.f64 (/.f64 (.f64 D M) (.f64 2 d)) 2) (.f64 (/.f64 h l) -1/2) 1) (.f64 (sqrt.f64 (/.f64 d l)) (.f64 (sqrt.f64 (/.f64 (cbrt.f64 d) (cbrt.f64 h))) (fabs.f64 (cbrt.f64 d))))) (fabs.f64 (cbrt.f64 h)))
	33.5b	(.f64 (sqrt.f64 (.f64 (fma.f64 (pow.f64 (/.f64 (.f64 D M) (.f64 d 2)) 2) (.f64 (/.f64 h l) -1/2) 1) (.f64 (sqrt.f64 (/.f64 d l)) (sqrt.f64 (/.f64 d h))))) (sqrt.f64 (.f64 (fma.f64 (pow.f64 (/.f64 (.f64 D M) (.f64 d 2)) 2) (.f64 (/.f64 h l) -1/2) 1) (*.f64 (sqrt.f64 (/.f64 d l)) (sqrt.f64 (/.f64 d h))))))
	27.7b	(.f64 (.f64 (cbrt.f64 (.f64 (fma.f64 (pow.f64 (/.f64 (.f64 D M) (.f64 d 2)) 2) (.f64 (/.f64 h l) -1/2) 1) (.f64 (sqrt.f64 (/.f64 d l)) (sqrt.f64 (/.f64 d h))))) (cbrt.f64 (.f64 (fma.f64 (pow.f64 (/.f64 (.f64 D M) (.f64 d 2)) 2) (.f64 (/.f64 h l) -1/2) 1) (.f64 (sqrt.f64 (/.f64 d l)) (sqrt.f64 (/.f64 d h)))))) (cbrt.f64 (.f64 (fma.f64 (pow.f64 (/.f64 (.f64 D M) (.f64 d 2)) 2) (.f64 (/.f64 h l) -1/2) 1) (*.f64 (sqrt.f64 (/.f64 d l)) (sqrt.f64 (/.f64 d h))))))
	27.4b	(.f64 (.f64 (.f64 (sqrt.f64 (sqrt.f64 (/.f64 d h))) (sqrt.f64 (sqrt.f64 (/.f64 d h)))) (sqrt.f64 (/.f64 d l))) (fma.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2) (.f64 (/.f64 h l) -1/2) 1))
	27.3b	(.f64 (.f64 (sqrt.f64 (/.f64 d h)) (sqrt.f64 (/.f64 d l))) (.f64 (.f64 (cbrt.f64 (fma.f64 (pow.f64 (/.f64 (.f64 D M) (.f64 d 2)) 2) (.f64 (/.f64 h l) -1/2) 1)) (cbrt.f64 (fma.f64 (pow.f64 (/.f64 (.f64 D M) (.f64 d 2)) 2) (.f64 (/.f64 h l) -1/2) 1))) (cbrt.f64 (fma.f64 (pow.f64 (/.f64 (.f64 D M) (.f64 d 2)) 2) (*.f64 (/.f64 h l) -1/2) 1))))
	35.9b	(.f64 (.f64 (cbrt.f64 (pow.f64 (sqrt.f64 (/.f64 d h)) 3)) (sqrt.f64 (/.f64 d l))) (fma.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2) (*.f64 (/.f64 h l) -1/2) 1))
	50.4b	(.f64 (cbrt.f64 (.f64 d d)) (.f64 (sqrt.f64 (/.f64 1 l)) (.f64 (cbrt.f64 (/.f64 d h)) (pow.f64 (/.f64 1 h) 1/6))))
	59.4b	(.f64 -1/8 (.f64 (/.f64 (.f64 (.f64 D D) (*.f64 M M)) d) (sqrt.f64 (/.f64 h (pow.f64 l 3)))))
	21.5b	(.f64 (.f64 (.f64 (fabs.f64 (cbrt.f64 d)) (sqrt.f64 (/.f64 (cbrt.f64 d) h))) (sqrt.f64 (/.f64 d l))) (fma.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2) (.f64 (/.f64 h l) -1/2) 1))
	27.5b	(.f64 (.f64 (sqrt.f64 (/.f64 d h)) (.f64 (fabs.f64 (cbrt.f64 (/.f64 d l))) (sqrt.f64 (cbrt.f64 (/.f64 d l))))) (fma.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2) (.f64 (/.f64 h l) -1/2) 1))
	27.7b	(.f64 (.f64 (.f64 (.f64 (cbrt.f64 (sqrt.f64 (/.f64 d h))) (cbrt.f64 (sqrt.f64 (/.f64 d h)))) (cbrt.f64 (sqrt.f64 (/.f64 d h)))) (sqrt.f64 (/.f64 d l))) (fma.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2) (*.f64 (/.f64 h l) -1/2) 1))
	45.1b	(.f64 d (sqrt.f64 (/.f64 1 (.f64 l h))))
	40.9b	(.f64 (.f64 (.f64 (sqrt.f64 d) (sqrt.f64 (/.f64 1 h))) (sqrt.f64 (/.f64 d l))) (fma.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2) (.f64 (/.f64 h l) -1/2) 1))

Compiler

Compiled 5395 to 2644 computations (51% saved)

localize30.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	3.2b	(sqrt.f64 (/.f64 d (cbrt.f64 l)))
	4.5b	(/.f64 (.f64 M D) (.f64 d 2))
✓	6.4b	(.f64 (.f64 (.f64 (fabs.f64 (/.f64 (cbrt.f64 d) (cbrt.f64 h))) (sqrt.f64 (/.f64 (cbrt.f64 d) (cbrt.f64 h)))) (.f64 (sqrt.f64 (/.f64 1 (.f64 (cbrt.f64 l) (cbrt.f64 l)))) (sqrt.f64 (/.f64 d (cbrt.f64 l))))) (fma.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2) (.f64 (/.f64 h l) -1/2) 1))
	8.5b	(fma.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2) (*.f64 (/.f64 h l) -1/2) 1)

rewrite46.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

26×	`associate-*l/_binary64`
25×	`sqrt-div_binary64`
22×	`sqrt-prod_binary64`
21×	`add-sqr-sqrt_binary64`
21×	`pow1_binary64`

Counts

2 → 83

Calls

2 calls:

33.0ms

(*.f64 (*.f64 (*.f64 (fabs.f64 (/.f64 (cbrt.f64 d) (cbrt.f64 h))) (sqrt.f64 (/.f64 (cbrt.f64 d) (cbrt.f64 h)))) (*.f64 (sqrt.f64 (/.f64 1 (*.f64 (cbrt.f64 l) (cbrt.f64 l)))) (sqrt.f64 (/.f64 d (cbrt.f64 l))))) (fma.f64 (pow.f64 (/.f64 (*.f64 M D) (*.f64 d 2)) 2) (*.f64 (/.f64 h l) -1/2) 1))

3.0ms

(sqrt.f64 (/.f64 d (cbrt.f64 l)))

series1.3s (9.4%)

Counts

2 → 84

Calls

2 calls:

1.1s

(*.f64 (*.f64 (*.f64 (fabs.f64 (/.f64 (cbrt.f64 d) (cbrt.f64 h))) (sqrt.f64 (/.f64 (cbrt.f64 d) (cbrt.f64 h)))) (*.f64 (sqrt.f64 (/.f64 1 (*.f64 (cbrt.f64 l) (cbrt.f64 l)))) (sqrt.f64 (/.f64 d (cbrt.f64 l))))) (fma.f64 (pow.f64 (/.f64 (*.f64 M D) (*.f64 d 2)) 2) (*.f64 (/.f64 h l) -1/2) 1))

251.0ms

(sqrt.f64 (/.f64 d (cbrt.f64 l)))

simplify231.0ms (1.7%)

Algorithm

1×	egg-herbie

Rules

616×	`*-commutative_binary64`
370×	`fma-neg_binary64`
289×	`fma-def_binary64`
277×	`times-frac_binary64`
231×	`associate-/l*_binary64`

Counts

167 → 167

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	545	11459
1	1593	9904
2	4675	9902
3	4968	9902

prune158.0ms (1.1%)

Pruning

24 alts after pruning (24 fresh and 0 done)

	Pruned	Kept	Total
New	363	3	366
Fresh	4	21	25
Picked	1	0	1
Done	0	0	0
Total	368	24	392

Error

9.6b

Counts

392 → 24

Alt Table

Status	Error	Program
	17.3b	(.f64 (.f64 (.f64 (fabs.f64 (/.f64 (cbrt.f64 d) (cbrt.f64 h))) (sqrt.f64 (/.f64 (cbrt.f64 d) (cbrt.f64 h)))) (.f64 (fabs.f64 (cbrt.f64 d)) (sqrt.f64 (/.f64 (cbrt.f64 d) l)))) (fma.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2) (*.f64 (/.f64 h l) -1/2) 1))
	21.3b	(.f64 (.f64 (.f64 (sqrt.f64 (/.f64 1 (.f64 (cbrt.f64 h) (cbrt.f64 h)))) (sqrt.f64 (/.f64 d (cbrt.f64 h)))) (sqrt.f64 (/.f64 d l))) (fma.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2) (*.f64 (/.f64 h l) -1/2) 1))
	42.2b	(.f64 (.f64 (sqrt.f64 (/.f64 d h)) (sqrt.f64 (/.f64 d l))) (-.f64 1 (.f64 1/8 (/.f64 (.f64 (.f64 D D) (.f64 h (.f64 M M))) (.f64 l (*.f64 d d))))))
	27.3b	(.f64 (.f64 (sqrt.f64 (/.f64 d l)) (sqrt.f64 (/.f64 d h))) (fma.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2) (*.f64 (/.f64 h l) -1/2) 1))
	23.8b	(.f64 (.f64 (sqrt.f64 (/.f64 d h)) (.f64 (sqrt.f64 (/.f64 1 (.f64 (cbrt.f64 l) (cbrt.f64 l)))) (sqrt.f64 (/.f64 d (cbrt.f64 l))))) (fma.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2) (*.f64 (/.f64 h l) -1/2) 1))
	32.0b	(.f64 (.f64 (sqrt.f64 (/.f64 d h)) (sqrt.f64 (/.f64 d l))) 1)
	25.8b	(.f64 (.f64 (*.f64 (fabs.f64 (/.f64 (cbrt.f64 d) (cbrt.f64 h))) (sqrt.f64 (/.f64 (cbrt.f64 d) (cbrt.f64 h)))) (sqrt.f64 (/.f64 d l))) 1)
	27.5b	(.f64 (sqrt.f64 (/.f64 d h)) (.f64 (sqrt.f64 (/.f64 d l)) (fma.f64 (pow.f64 (/.f64 (.f64 D M) (.f64 d 2)) 2) (*.f64 (/.f64 h l) -1/2) 1)))
	20.5b	(.f64 (.f64 (fabs.f64 (/.f64 (cbrt.f64 d) (cbrt.f64 h))) (sqrt.f64 (/.f64 (cbrt.f64 d) (cbrt.f64 h)))) (.f64 (sqrt.f64 (/.f64 d l)) (fma.f64 (pow.f64 (/.f64 (.f64 D M) (.f64 2 d)) 2) (.f64 (/.f64 h l) -1/2) 1)))
	38.8b	(/.f64 (.f64 d (fma.f64 (pow.f64 (/.f64 (.f64 D M) (.f64 d 2)) 2) (.f64 (/.f64 h l) -1/2) 1)) (*.f64 (sqrt.f64 h) (sqrt.f64 l)))
	27.5b	(.f64 (.f64 (sqrt.f64 (/.f64 d h)) (.f64 (fabs.f64 (cbrt.f64 (/.f64 d l))) (sqrt.f64 (cbrt.f64 (/.f64 d l))))) (fma.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2) (.f64 (/.f64 h l) -1/2) 1))
	20.7b	(.f64 (.f64 (.f64 (fabs.f64 (/.f64 (cbrt.f64 d) (cbrt.f64 h))) (sqrt.f64 (/.f64 (cbrt.f64 d) (cbrt.f64 h)))) (.f64 (sqrt.f64 (/.f64 1 (*.f64 (cbrt.f64 l) (cbrt.f64 l)))) (sqrt.f64 (/.f64 d (cbrt.f64 l))))) 1)
	27.7b	(.f64 (.f64 (cbrt.f64 (.f64 (fma.f64 (pow.f64 (/.f64 (.f64 D M) (.f64 d 2)) 2) (.f64 (/.f64 h l) -1/2) 1) (.f64 (sqrt.f64 (/.f64 d l)) (sqrt.f64 (/.f64 d h))))) (cbrt.f64 (.f64 (fma.f64 (pow.f64 (/.f64 (.f64 D M) (.f64 d 2)) 2) (.f64 (/.f64 h l) -1/2) 1) (.f64 (sqrt.f64 (/.f64 d l)) (sqrt.f64 (/.f64 d h)))))) (cbrt.f64 (.f64 (fma.f64 (pow.f64 (/.f64 (.f64 D M) (.f64 d 2)) 2) (.f64 (/.f64 h l) -1/2) 1) (*.f64 (sqrt.f64 (/.f64 d l)) (sqrt.f64 (/.f64 d h))))))
	27.4b	(.f64 (.f64 (.f64 (sqrt.f64 (sqrt.f64 (/.f64 d h))) (sqrt.f64 (sqrt.f64 (/.f64 d h)))) (sqrt.f64 (/.f64 d l))) (fma.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2) (.f64 (/.f64 h l) -1/2) 1))
	50.4b	(.f64 (cbrt.f64 (.f64 d d)) (.f64 (sqrt.f64 (/.f64 1 l)) (.f64 (cbrt.f64 (/.f64 d h)) (pow.f64 (/.f64 1 h) 1/6))))
	59.4b	(.f64 -1/8 (.f64 (/.f64 (.f64 (.f64 D D) (*.f64 M M)) d) (sqrt.f64 (/.f64 h (pow.f64 l 3)))))
	21.5b	(.f64 (.f64 (.f64 (fabs.f64 (cbrt.f64 d)) (sqrt.f64 (/.f64 (cbrt.f64 d) h))) (sqrt.f64 (/.f64 d l))) (fma.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2) (.f64 (/.f64 h l) -1/2) 1))
	24.2b	(.f64 (.f64 (sqrt.f64 (/.f64 d h)) (.f64 (fabs.f64 (cbrt.f64 d)) (sqrt.f64 (/.f64 (cbrt.f64 d) l)))) (fma.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2) (.f64 (/.f64 h l) -1/2) 1))
	20.7b	(/.f64 (.f64 (fma.f64 (pow.f64 (/.f64 (.f64 D M) (.f64 2 d)) 2) (.f64 (/.f64 h l) -1/2) 1) (.f64 (sqrt.f64 (/.f64 d l)) (.f64 (sqrt.f64 (/.f64 (cbrt.f64 d) (cbrt.f64 h))) (fabs.f64 (cbrt.f64 d))))) (fabs.f64 (cbrt.f64 h)))
	27.7b	(.f64 (.f64 (.f64 (.f64 (cbrt.f64 (sqrt.f64 (/.f64 d h))) (cbrt.f64 (sqrt.f64 (/.f64 d h)))) (cbrt.f64 (sqrt.f64 (/.f64 d h)))) (sqrt.f64 (/.f64 d l))) (fma.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2) (*.f64 (/.f64 h l) -1/2) 1))
	27.3b	(.f64 (.f64 (sqrt.f64 (/.f64 d h)) (sqrt.f64 (/.f64 d l))) (.f64 (.f64 (cbrt.f64 (fma.f64 (pow.f64 (/.f64 (.f64 D M) (.f64 d 2)) 2) (.f64 (/.f64 h l) -1/2) 1)) (cbrt.f64 (fma.f64 (pow.f64 (/.f64 (.f64 D M) (.f64 d 2)) 2) (.f64 (/.f64 h l) -1/2) 1))) (cbrt.f64 (fma.f64 (pow.f64 (/.f64 (.f64 D M) (.f64 d 2)) 2) (*.f64 (/.f64 h l) -1/2) 1))))
▶	16.9b	(.f64 (.f64 (pow.f64 (sqrt.f64 (/.f64 (cbrt.f64 d) (cbrt.f64 h))) 3) (.f64 (sqrt.f64 (/.f64 1 (.f64 (cbrt.f64 l) (cbrt.f64 l)))) (sqrt.f64 (/.f64 d (cbrt.f64 l))))) (fma.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2) (*.f64 (/.f64 h l) -1/2) 1))
	45.1b	(.f64 d (sqrt.f64 (/.f64 1 (.f64 l h))))
	17.2b	(/.f64 (.f64 (fma.f64 (pow.f64 (/.f64 (.f64 D M) (.f64 2 d)) 2) (.f64 (/.f64 h l) -1/2) 1) (.f64 (pow.f64 (sqrt.f64 (/.f64 (cbrt.f64 d) (cbrt.f64 h))) 3) (sqrt.f64 (/.f64 d (cbrt.f64 l))))) (sqrt.f64 (.f64 (cbrt.f64 l) (cbrt.f64 l))))

Compiler

Compiled 6947 to 3209 computations (53.8% saved)

localize30.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
	3.2b	(sqrt.f64 (/.f64 d (cbrt.f64 l)))
	4.5b	(/.f64 (.f64 M D) (.f64 d 2))
✓	6.4b	(.f64 (.f64 (pow.f64 (sqrt.f64 (/.f64 (cbrt.f64 d) (cbrt.f64 h))) 3) (.f64 (sqrt.f64 (/.f64 1 (.f64 (cbrt.f64 l) (cbrt.f64 l)))) (sqrt.f64 (/.f64 d (cbrt.f64 l))))) (fma.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2) (*.f64 (/.f64 h l) -1/2) 1))
	8.5b	(fma.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2) (*.f64 (/.f64 h l) -1/2) 1)

rewrite28.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

22×	`add-exp-log_binary64`
16×	`prod-exp_binary64`
12×	`sqrt-div_binary64`
10×	`associate-*l/_binary64`
10×	`add-cbrt-cube_binary64`

Counts

1 → 34

Calls

1 calls:

25.0ms

(*.f64 (*.f64 (pow.f64 (sqrt.f64 (/.f64 (cbrt.f64 d) (cbrt.f64 h))) 3) (*.f64 (sqrt.f64 (/.f64 1 (*.f64 (cbrt.f64 l) (cbrt.f64 l)))) (sqrt.f64 (/.f64 d (cbrt.f64 l))))) (fma.f64 (pow.f64 (/.f64 (*.f64 M D) (*.f64 d 2)) 2) (*.f64 (/.f64 h l) -1/2) 1))

series425.0ms (3%)

Counts

1 → 60

Calls

1 calls:

425.0ms

(*.f64 (*.f64 (pow.f64 (sqrt.f64 (/.f64 (cbrt.f64 d) (cbrt.f64 h))) 3) (*.f64 (sqrt.f64 (/.f64 1 (*.f64 (cbrt.f64 l) (cbrt.f64 l)))) (sqrt.f64 (/.f64 d (cbrt.f64 l))))) (fma.f64 (pow.f64 (/.f64 (*.f64 M D) (*.f64 d 2)) 2) (*.f64 (/.f64 h l) -1/2) 1))

simplify164.0ms (1.2%)

Algorithm

1×	egg-herbie

Rules

681×	`times-frac_binary64`
482×	`associate-/l*_binary64`
424×	`associate-/r*_binary64`
219×	`fma-def_binary64`
182×	`*-commutative_binary64`

Counts

94 → 94

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	443	6681
1	1515	6100
2	4847	6095
3	4987	6095

prune121.0ms (0.9%)

Pruning

26 alts after pruning (26 fresh and 0 done)

	Pruned	Kept	Total
New	550	3	553
Fresh	0	23	23
Picked	1	0	1
Done	0	0	0
Total	551	26	577

Error

9.6b

Counts

577 → 26

Alt Table

Status	Error	Program
	17.3b	(.f64 (.f64 (.f64 (fabs.f64 (/.f64 (cbrt.f64 d) (cbrt.f64 h))) (sqrt.f64 (/.f64 (cbrt.f64 d) (cbrt.f64 h)))) (.f64 (fabs.f64 (cbrt.f64 d)) (sqrt.f64 (/.f64 (cbrt.f64 d) l)))) (fma.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2) (*.f64 (/.f64 h l) -1/2) 1))
	21.3b	(.f64 (.f64 (.f64 (sqrt.f64 (/.f64 1 (.f64 (cbrt.f64 h) (cbrt.f64 h)))) (sqrt.f64 (/.f64 d (cbrt.f64 h)))) (sqrt.f64 (/.f64 d l))) (fma.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2) (*.f64 (/.f64 h l) -1/2) 1))
	42.2b	(.f64 (.f64 (sqrt.f64 (/.f64 d h)) (sqrt.f64 (/.f64 d l))) (-.f64 1 (.f64 1/8 (/.f64 (.f64 (.f64 D D) (.f64 h (.f64 M M))) (.f64 l (*.f64 d d))))))
	27.3b	(.f64 (.f64 (sqrt.f64 (/.f64 d l)) (sqrt.f64 (/.f64 d h))) (fma.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2) (*.f64 (/.f64 h l) -1/2) 1))
	23.8b	(.f64 (.f64 (sqrt.f64 (/.f64 d h)) (.f64 (sqrt.f64 (/.f64 1 (.f64 (cbrt.f64 l) (cbrt.f64 l)))) (sqrt.f64 (/.f64 d (cbrt.f64 l))))) (fma.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2) (*.f64 (/.f64 h l) -1/2) 1))
	32.0b	(.f64 (.f64 (sqrt.f64 (/.f64 d h)) (sqrt.f64 (/.f64 d l))) 1)
	25.8b	(.f64 (.f64 (*.f64 (fabs.f64 (/.f64 (cbrt.f64 d) (cbrt.f64 h))) (sqrt.f64 (/.f64 (cbrt.f64 d) (cbrt.f64 h)))) (sqrt.f64 (/.f64 d l))) 1)
	27.5b	(.f64 (sqrt.f64 (/.f64 d h)) (.f64 (sqrt.f64 (/.f64 d l)) (fma.f64 (pow.f64 (/.f64 (.f64 D M) (.f64 d 2)) 2) (*.f64 (/.f64 h l) -1/2) 1)))
	20.5b	(.f64 (.f64 (fabs.f64 (/.f64 (cbrt.f64 d) (cbrt.f64 h))) (sqrt.f64 (/.f64 (cbrt.f64 d) (cbrt.f64 h)))) (.f64 (sqrt.f64 (/.f64 d l)) (fma.f64 (pow.f64 (/.f64 (.f64 D M) (.f64 2 d)) 2) (.f64 (/.f64 h l) -1/2) 1)))
	38.8b	(/.f64 (.f64 d (fma.f64 (pow.f64 (/.f64 (.f64 D M) (.f64 d 2)) 2) (.f64 (/.f64 h l) -1/2) 1)) (*.f64 (sqrt.f64 h) (sqrt.f64 l)))
	27.5b	(.f64 (.f64 (sqrt.f64 (/.f64 d h)) (.f64 (fabs.f64 (cbrt.f64 (/.f64 d l))) (sqrt.f64 (cbrt.f64 (/.f64 d l))))) (fma.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2) (.f64 (/.f64 h l) -1/2) 1))
	20.7b	(.f64 (.f64 (.f64 (fabs.f64 (/.f64 (cbrt.f64 d) (cbrt.f64 h))) (sqrt.f64 (/.f64 (cbrt.f64 d) (cbrt.f64 h)))) (.f64 (sqrt.f64 (/.f64 1 (*.f64 (cbrt.f64 l) (cbrt.f64 l)))) (sqrt.f64 (/.f64 d (cbrt.f64 l))))) 1)
	27.7b	(.f64 (.f64 (cbrt.f64 (.f64 (fma.f64 (pow.f64 (/.f64 (.f64 D M) (.f64 d 2)) 2) (.f64 (/.f64 h l) -1/2) 1) (.f64 (sqrt.f64 (/.f64 d l)) (sqrt.f64 (/.f64 d h))))) (cbrt.f64 (.f64 (fma.f64 (pow.f64 (/.f64 (.f64 D M) (.f64 d 2)) 2) (.f64 (/.f64 h l) -1/2) 1) (.f64 (sqrt.f64 (/.f64 d l)) (sqrt.f64 (/.f64 d h)))))) (cbrt.f64 (.f64 (fma.f64 (pow.f64 (/.f64 (.f64 D M) (.f64 d 2)) 2) (.f64 (/.f64 h l) -1/2) 1) (*.f64 (sqrt.f64 (/.f64 d l)) (sqrt.f64 (/.f64 d h))))))
	27.4b	(.f64 (.f64 (.f64 (sqrt.f64 (sqrt.f64 (/.f64 d h))) (sqrt.f64 (sqrt.f64 (/.f64 d h)))) (sqrt.f64 (/.f64 d l))) (fma.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2) (.f64 (/.f64 h l) -1/2) 1))
	20.7b	(.f64 (.f64 (pow.f64 (sqrt.f64 (/.f64 (cbrt.f64 d) (cbrt.f64 h))) 3) (.f64 (sqrt.f64 (/.f64 1 (.f64 (cbrt.f64 l) (cbrt.f64 l)))) (sqrt.f64 (/.f64 d (cbrt.f64 l))))) 1)
	27.3b	(.f64 (.f64 (sqrt.f64 (/.f64 d h)) (sqrt.f64 (/.f64 d l))) (.f64 (.f64 (cbrt.f64 (fma.f64 (pow.f64 (/.f64 (.f64 D M) (.f64 d 2)) 2) (.f64 (/.f64 h l) -1/2) 1)) (cbrt.f64 (fma.f64 (pow.f64 (/.f64 (.f64 D M) (.f64 d 2)) 2) (.f64 (/.f64 h l) -1/2) 1))) (cbrt.f64 (fma.f64 (pow.f64 (/.f64 (.f64 D M) (.f64 d 2)) 2) (*.f64 (/.f64 h l) -1/2) 1))))
	16.4b	(.f64 (.f64 (pow.f64 (sqrt.f64 (/.f64 (cbrt.f64 d) (cbrt.f64 h))) 3) (.f64 (sqrt.f64 (/.f64 1 (.f64 (cbrt.f64 l) (cbrt.f64 l)))) (.f64 (fabs.f64 (cbrt.f64 d)) (sqrt.f64 (/.f64 (cbrt.f64 d) (cbrt.f64 l)))))) (fma.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2) (.f64 (/.f64 h l) -1/2) 1))
	16.5b	(.f64 (pow.f64 (sqrt.f64 (/.f64 (cbrt.f64 d) (cbrt.f64 h))) 3) (.f64 (.f64 (sqrt.f64 (/.f64 1 (.f64 (cbrt.f64 l) (cbrt.f64 l)))) (sqrt.f64 (/.f64 d (cbrt.f64 l)))) (fma.f64 (pow.f64 (/.f64 (.f64 D M) (.f64 2 d)) 2) (*.f64 (/.f64 h l) -1/2) 1)))
	17.2b	(/.f64 (.f64 (fma.f64 (pow.f64 (/.f64 (.f64 D M) (.f64 2 d)) 2) (.f64 (/.f64 h l) -1/2) 1) (.f64 (pow.f64 (sqrt.f64 (/.f64 (cbrt.f64 d) (cbrt.f64 h))) 3) (sqrt.f64 (/.f64 d (cbrt.f64 l))))) (sqrt.f64 (.f64 (cbrt.f64 l) (cbrt.f64 l))))
	50.4b	(.f64 (cbrt.f64 (.f64 d d)) (.f64 (sqrt.f64 (/.f64 1 l)) (.f64 (cbrt.f64 (/.f64 d h)) (pow.f64 (/.f64 1 h) 1/6))))
	59.4b	(.f64 -1/8 (.f64 (/.f64 (.f64 (.f64 D D) (*.f64 M M)) d) (sqrt.f64 (/.f64 h (pow.f64 l 3)))))
	21.5b	(.f64 (.f64 (.f64 (fabs.f64 (cbrt.f64 d)) (sqrt.f64 (/.f64 (cbrt.f64 d) h))) (sqrt.f64 (/.f64 d l))) (fma.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2) (.f64 (/.f64 h l) -1/2) 1))
	24.2b	(.f64 (.f64 (sqrt.f64 (/.f64 d h)) (.f64 (fabs.f64 (cbrt.f64 d)) (sqrt.f64 (/.f64 (cbrt.f64 d) l)))) (fma.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2) (.f64 (/.f64 h l) -1/2) 1))
	20.7b	(/.f64 (.f64 (fma.f64 (pow.f64 (/.f64 (.f64 D M) (.f64 2 d)) 2) (.f64 (/.f64 h l) -1/2) 1) (.f64 (sqrt.f64 (/.f64 d l)) (.f64 (sqrt.f64 (/.f64 (cbrt.f64 d) (cbrt.f64 h))) (fabs.f64 (cbrt.f64 d))))) (fabs.f64 (cbrt.f64 h)))
	27.7b	(.f64 (.f64 (.f64 (.f64 (cbrt.f64 (sqrt.f64 (/.f64 d h))) (cbrt.f64 (sqrt.f64 (/.f64 d h)))) (cbrt.f64 (sqrt.f64 (/.f64 d h)))) (sqrt.f64 (/.f64 d l))) (fma.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2) (*.f64 (/.f64 h l) -1/2) 1))
	45.1b	(.f64 d (sqrt.f64 (/.f64 1 (.f64 l h))))

Compiler

Compiled 5094 to 2506 computations (50.8% saved)

regimes1.2s (8.4%)

Accuracy

Total 3.4b remaining (25%)

Threshold costs 0b (0%)

Compiler

Compiled 27081 to 18447 computations (31.9% saved)

bsearch6.0ms (0%)

Compiler: Compiled 40 to 31 computations (22.5% saved)

simplify12.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

20×	`*-commutative_binary64`
6×	`+-commutative_binary64`
6×	`sub-neg_binary64`
5×	`neg-sub0_binary64`
5×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	57	166
1	77	166
2	92	166
3	102	166
4	110	166
5	114	166
6	115	166
7	112	166

end11.0ms (0.1%)

Remove: (sort M D)
Compiler: Compiled 327 to 180 computations (45% saved)

sample5.4s (38.6%)

Algorithm

1×

intervals

Results

1.5s	8676×	body	128	nan
1.4s	8000×	body	128	valid
932.0ms	4832×	body	128	invalid

Compiler

Compiled 1141 to 751 computations (34.2% saved)

Details

analyze2.4s (17.2%)

sample176.0ms (1.3%)

simplify40.0ms (0.3%)

prune3.0ms (0%)

localize19.0ms (0.1%)

rewrite19.0ms (0.1%)

series440.0ms (3.1%)

simplify167.0ms (1.2%)

prune124.0ms (0.9%)

localize22.0ms (0.2%)

rewrite29.0ms (0.2%)

series1.1s (7.7%)

simplify192.0ms (1.4%)

prune133.0ms (1%)

localize30.0ms (0.2%)

rewrite46.0ms (0.3%)

series1.3s (9.4%)

simplify231.0ms (1.7%)

prune158.0ms (1.1%)

localize30.0ms (0.2%)

rewrite28.0ms (0.2%)

series425.0ms (3%)

simplify164.0ms (1.2%)

prune121.0ms (0.9%)

regimes1.2s (8.4%)

bsearch6.0ms (0%)

simplify12.0ms (0.1%)

end11.0ms (0.1%)

sample5.4s (38.6%)

Profiling