Details

analyze2.8s (14.5%)

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
12.5%	87.3%	0.2%	4
12.5%	87.3%	0.2%	5
12.5%	87.3%	0.2%	6
12.5%	68.6%	18.9%	7
12.5%	56.1%	31.4%	8
14%	45.2%	40.8%	9
14%	45.2%	40.8%	10
14%	45.2%	40.8%	11
14.8%	35.1%	50.1%	12
16%	29.2%	54.8%	13
17.7%	23.6%	58.7%	14

Compiler

Compiled 41 to 32 computations (22% saved)

sample5.6s (29.5%)

Symmetry

(sort M D)

Results

3.4s	8256×	body	128	valid
2.0s	5345×	body	128	invalid

Compiler

Compiled 122 to 95 computations (22.1% saved)

simplify65.0ms (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 → 2

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

prune7.0ms (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

17.8b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	17.8b	(.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 128 to 88 computations (31.3% saved)

localize29.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	4.8b	(/.f64 (.f64 M D) (.f64 d 2))
✓	5.9b	(fma.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2) (*.f64 (/.f64 h l) -1/2) 1)
✓	13.6b	(sqrt.f64 (/.f64 d l))
✓	14.6b	(sqrt.f64 (/.f64 d h))

series280.0ms (1.5%)

Counts

4 → 96

Calls

4 calls:

162.0ms	(fma.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2) (*.f64 (/.f64 h l) -1/2) 1)
49.0ms	(sqrt.f64 (/.f64 d h))
39.0ms	(sqrt.f64 (/.f64 d l))
29.0ms	(/.f64 (.f64 M D) (.f64 d 2))

rewrite29.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

26×	`sqrt-prod_binary64`
24×	`add-sqr-sqrt_binary64`
21×	`times-frac_binary64`
18×	`*-un-lft-identity_binary64`
18×	`add-cube-cbrt_binary64`

Counts

4 → 87

Calls

4 calls:

8.0ms	(/.f64 (.f64 M D) (.f64 d 2))
8.0ms	(sqrt.f64 (/.f64 d l))
4.0ms	(sqrt.f64 (/.f64 d h))
1.0ms	(fma.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2) (*.f64 (/.f64 h l) -1/2) 1)

simplify121.0ms (0.6%)

Algorithm

1×	egg-herbie

Rules

696×	`associate-l_binary64`
672×	`associate-/r*_binary64`
617×	`associate-*l/_binary64`
520×	`associate-*r/_binary64`
253×	`associate-/l/_binary64`

Counts

183 → 125

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	204	3113
1	366	2966
2	1312	2875
3	5122	2875

prune335.0ms (1.8%)

Pruning

17 alts after pruning (17 fresh and 0 done)

	Pruned	Kept	Total
New	108	17	125
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	109	17	126

Error

8.2b

Counts

126 → 17

Alt Table

Status	Error	Program
	15.5b	(.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))
	14.7b	(.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))
	34.1b	(.f64 (.f64 (sqrt.f64 (/.f64 d h)) (sqrt.f64 (/.f64 d l))) (fma.f64 (/.f64 (.f64 (.f64 D D) (.f64 (.f64 M M) h)) (.f64 (.f64 d d) l)) -1/8 1))
	15.2b	(.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))
	37.9b	(.f64 (.f64 (.f64 (sqrt.f64 (/.f64 (.f64 (cbrt.f64 d) (cbrt.f64 d)) (sqrt.f64 h))) (sqrt.f64 (/.f64 (cbrt.f64 d) (sqrt.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))
	38.6b	(.f64 (.f64 (sqrt.f64 (/.f64 d h)) (sqrt.f64 (/.f64 d l))) 1)
	40.1b	(.f64 (.f64 (sqrt.f64 (/.f64 d h)) (.f64 (sqrt.f64 d) (sqrt.f64 (/.f64 1 l)))) (fma.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2) (.f64 (/.f64 h l) -1/2) 1))
	17.9b	(.f64 (.f64 (sqrt.f64 (/.f64 d h)) (.f64 (sqrt.f64 (sqrt.f64 (/.f64 d l))) (sqrt.f64 (sqrt.f64 (/.f64 d l))))) (fma.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2) (.f64 (/.f64 h l) -1/2) 1))
	15.2b	(.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))
	37.8b	(.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))
▶	13.3b	(.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))
	40.2b	(.f64 (.f64 (sqrt.f64 (/.f64 d h)) (.f64 (sqrt.f64 (/.f64 (sqrt.f64 d) (sqrt.f64 l))) (sqrt.f64 (/.f64 (sqrt.f64 d) (sqrt.f64 l))))) (fma.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2) (.f64 (/.f64 h l) -1/2) 1))
	18.0b	(.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))
	17.6b	(.f64 (.f64 (sqrt.f64 (/.f64 d h)) (sqrt.f64 (/.f64 d l))) (fma.f64 (pow.f64 (/.f64 M (/.f64 (.f64 d 2) D)) 2) (.f64 (/.f64 h l) -1/2) 1))
	37.8b	(.f64 (.f64 (/.f64 (sqrt.f64 d) (sqrt.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))
	25.7b	(.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))
	23.5b	(.f64 (.f64 (sqrt.f64 (/.f64 d h)) (cbrt.f64 (.f64 (.f64 (sqrt.f64 (/.f64 d l)) (sqrt.f64 (/.f64 d l))) (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 5204 to 2593 computations (50.2% saved)

localize53.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	4.8b	(.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))
	4.8b	(/.f64 (.f64 M D) (.f64 d 2))
	5.9b	(fma.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2) (*.f64 (/.f64 h l) -1/2) 1)
	13.6b	(sqrt.f64 (/.f64 d l))

series481.0ms (2.5%)

Counts

1 → 32

Calls

1 calls:

481.0ms

(*.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))

rewrite45.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

12×	`associate-*l/_binary64`
12×	`sqrt-div_binary64`
10×	`add-cbrt-cube_binary64`
10×	`add-exp-log_binary64`
10×	`pow1_binary64`

Counts

1 → 32

Calls

1 calls:

37.0ms

(*.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))

simplify154.0ms (0.8%)

Algorithm

1×	egg-herbie

Rules

663×	`fma-def_binary64`
501×	`*-commutative_binary64`
492×	`associate-/l/_binary64`
458×	`associate-*l/_binary64`
321×	`associate-*r/_binary64`

Counts

64 → 55

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	115	3230
1	292	2872
2	1107	2872
3	3375	2872
4	5257	2872

prune476.0ms (2.5%)

Pruning

18 alts after pruning (18 fresh and 0 done)

	Pruned	Kept	Total
New	139	10	149
Fresh	8	8	16
Picked	1	0	1
Done	0	0	0
Total	148	18	166

Error

5.6b

Counts

166 → 18

Alt Table

Status	Error	Program
	15.5b	(.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))
	14.7b	(.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))
	34.1b	(.f64 (.f64 (sqrt.f64 (/.f64 d h)) (sqrt.f64 (/.f64 d l))) (fma.f64 (/.f64 (.f64 (.f64 D D) (.f64 (.f64 M M) h)) (.f64 (.f64 d d) l)) -1/8 1))
	34.7b	(.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))) 1)
	35.5b	(/.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 (cbrt.f64 h))) (sqrt.f64 d))) (.f64 (sqrt.f64 (*.f64 (cbrt.f64 h) (cbrt.f64 h))) (sqrt.f64 l)))
	13.4b	(.f64 (.f64 (.f64 (sqrt.f64 (/.f64 1 (.f64 (cbrt.f64 h) (cbrt.f64 h)))) (sqrt.f64 (/.f64 d (cbrt.f64 h)))) (.f64 (sqrt.f64 (sqrt.f64 (/.f64 d l))) (sqrt.f64 (sqrt.f64 (/.f64 d l))))) (fma.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2) (.f64 (/.f64 h l) -1/2) 1))
	25.7b	(.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))
	11.0b	(.f64 (.f64 (.f64 (sqrt.f64 (/.f64 1 (.f64 (cbrt.f64 h) (cbrt.f64 h)))) (sqrt.f64 (/.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))
	23.5b	(.f64 (.f64 (sqrt.f64 (/.f64 d h)) (cbrt.f64 (.f64 (.f64 (sqrt.f64 (/.f64 d l)) (sqrt.f64 (/.f64 d l))) (sqrt.f64 (/.f64 d l))))) (fma.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2) (*.f64 (/.f64 h l) -1/2) 1))
	35.2b	(/.f64 (.f64 d (fma.f64 (pow.f64 (/.f64 (.f64 D M) (.f64 2 d)) 2) (.f64 (/.f64 h l) -1/2) 1)) (.f64 (.f64 (sqrt.f64 (*.f64 (cbrt.f64 h) (cbrt.f64 h))) (sqrt.f64 (cbrt.f64 h))) (sqrt.f64 l)))
	12.9b	(/.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 (cbrt.f64 h))) (sqrt.f64 (/.f64 d l)))) (sqrt.f64 (.f64 (cbrt.f64 h) (cbrt.f64 h))))
	37.9b	(.f64 (.f64 (.f64 (sqrt.f64 (/.f64 (.f64 (cbrt.f64 d) (cbrt.f64 d)) (sqrt.f64 h))) (sqrt.f64 (/.f64 (cbrt.f64 d) (sqrt.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))
	18.0b	(.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))
	17.6b	(.f64 (.f64 (sqrt.f64 (/.f64 d h)) (sqrt.f64 (/.f64 d l))) (fma.f64 (pow.f64 (/.f64 M (/.f64 (.f64 d 2) D)) 2) (.f64 (/.f64 h l) -1/2) 1))
	45.8b	(.f64 (sqrt.f64 (/.f64 1 (.f64 l h))) d)
	12.9b	(.f64 (.f64 (sqrt.f64 (/.f64 1 (.f64 (cbrt.f64 h) (cbrt.f64 h)))) (sqrt.f64 (/.f64 d (cbrt.f64 h)))) (.f64 (sqrt.f64 (/.f64 d l)) (fma.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2) (*.f64 (/.f64 h l) -1/2) 1)))
▶	10.6b	(.f64 (.f64 (.f64 (sqrt.f64 (/.f64 1 (.f64 (cbrt.f64 h) (cbrt.f64 h)))) (sqrt.f64 (/.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))
	35.2b	(/.f64 (.f64 (.f64 (.f64 (sqrt.f64 1) (sqrt.f64 d)) (sqrt.f64 d)) (fma.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2) (.f64 (/.f64 h l) -1/2) 1)) (.f64 (.f64 (sqrt.f64 (*.f64 (cbrt.f64 h) (cbrt.f64 h))) (sqrt.f64 (cbrt.f64 h))) (sqrt.f64 l)))

Compiler

Compiled 7908 to 3831 computations (51.6% saved)

localize64.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	3.6b	(sqrt.f64 (/.f64 d (cbrt.f64 h)))
✓	4.8b	(.f64 (.f64 (.f64 (sqrt.f64 (/.f64 1 (.f64 (cbrt.f64 h) (cbrt.f64 h)))) (sqrt.f64 (/.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))
	4.8b	(/.f64 (.f64 M D) (.f64 d 2))
	5.9b	(fma.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2) (*.f64 (/.f64 h l) -1/2) 1)

series518.0ms (2.7%)

Counts

2 → 44

Calls

2 calls:

377.0ms

(*.f64 (*.f64 (*.f64 (sqrt.f64 (/.f64 1 (*.f64 (cbrt.f64 h) (cbrt.f64 h)))) (sqrt.f64 (/.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))

140.0ms

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

rewrite69.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

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

Counts

2 → 83

Calls

2 calls:

48.0ms

(*.f64 (*.f64 (*.f64 (sqrt.f64 (/.f64 1 (*.f64 (cbrt.f64 h) (cbrt.f64 h)))) (sqrt.f64 (/.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))

7.0ms

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

simplify337.0ms (1.8%)

Algorithm

1×	egg-herbie

Rules

678×	`associate-*l/_binary64`
462×	`associate-l_binary64`
392×	`associate-r_binary64`
275×	`distribute-rgt-in_binary64`
260×	`distribute-lft-in_binary64`

Counts

127 → 118

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	235	5607
1	525	4970
2	1855	4970
3	4970	4970
4	4999	4970
5	4969	4970

prune917.0ms (4.8%)

Pruning

20 alts after pruning (20 fresh and 0 done)

	Pruned	Kept	Total
New	174	7	181
Fresh	4	13	17
Picked	1	0	1
Done	0	0	0
Total	179	20	199

Error

4.6b

Counts

199 → 20

Alt Table

Status	Error	Program
	35.7b	(/.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 (cbrt.f64 h))) (.f64 (sqrt.f64 d) (sqrt.f64 (/.f64 1 (.f64 (cbrt.f64 l) (cbrt.f64 l))))))) (.f64 (sqrt.f64 (*.f64 (cbrt.f64 h) (cbrt.f64 h))) (sqrt.f64 (cbrt.f64 l))))
	14.7b	(.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))
	34.1b	(.f64 (.f64 (sqrt.f64 (/.f64 d h)) (sqrt.f64 (/.f64 d l))) (fma.f64 (/.f64 (.f64 (.f64 D D) (.f64 (.f64 M M) h)) (.f64 (.f64 d d) l)) -1/8 1))
	10.7b	(.f64 (.f64 (.f64 (sqrt.f64 (/.f64 1 (.f64 (cbrt.f64 h) (cbrt.f64 h)))) (.f64 (fabs.f64 (cbrt.f64 (/.f64 d (cbrt.f64 h)))) (sqrt.f64 (cbrt.f64 (/.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))
	13.4b	(.f64 (.f64 (.f64 (sqrt.f64 (/.f64 1 (.f64 (cbrt.f64 h) (cbrt.f64 h)))) (sqrt.f64 (/.f64 d (cbrt.f64 h)))) (.f64 (sqrt.f64 (sqrt.f64 (/.f64 d l))) (sqrt.f64 (sqrt.f64 (/.f64 d l))))) (fma.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2) (.f64 (/.f64 h l) -1/2) 1))
	25.7b	(.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))
	11.0b	(.f64 (.f64 (.f64 (sqrt.f64 (/.f64 1 (.f64 (cbrt.f64 h) (cbrt.f64 h)))) (sqrt.f64 (/.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))
	23.5b	(.f64 (.f64 (sqrt.f64 (/.f64 d h)) (cbrt.f64 (.f64 (.f64 (sqrt.f64 (/.f64 d l)) (sqrt.f64 (/.f64 d l))) (sqrt.f64 (/.f64 d l))))) (fma.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2) (*.f64 (/.f64 h l) -1/2) 1))
	35.2b	(/.f64 (.f64 d (fma.f64 (pow.f64 (/.f64 (.f64 D M) (.f64 2 d)) 2) (.f64 (/.f64 h l) -1/2) 1)) (.f64 (.f64 (sqrt.f64 (*.f64 (cbrt.f64 h) (cbrt.f64 h))) (sqrt.f64 (cbrt.f64 h))) (sqrt.f64 l)))
	9.8b	(/.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 (cbrt.f64 h))) (.f64 (sqrt.f64 (/.f64 1 (.f64 (cbrt.f64 l) (cbrt.f64 l)))) (sqrt.f64 (/.f64 d (cbrt.f64 l)))))) (sqrt.f64 (.f64 (cbrt.f64 h) (cbrt.f64 h))))
	12.9b	(/.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 (cbrt.f64 h))) (sqrt.f64 (/.f64 d l)))) (sqrt.f64 (.f64 (cbrt.f64 h) (cbrt.f64 h))))
	31.7b	(.f64 (.f64 (.f64 (sqrt.f64 (/.f64 1 (.f64 (cbrt.f64 h) (cbrt.f64 h)))) (sqrt.f64 (/.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)
▶	8.9b	(/.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 (cbrt.f64 h))) (sqrt.f64 (/.f64 d (cbrt.f64 l))))) (.f64 (sqrt.f64 (.f64 (cbrt.f64 h) (cbrt.f64 h))) (sqrt.f64 (.f64 (cbrt.f64 l) (cbrt.f64 l)))))
	28.7b	(.f64 (.f64 (.f64 (sqrt.f64 (/.f64 1 (.f64 (cbrt.f64 h) (cbrt.f64 h)))) (sqrt.f64 (/.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 (/.f64 (.f64 (.f64 D D) (.f64 (.f64 M M) h)) (.f64 (.f64 d d) l)) -1/8 1))
	18.0b	(.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))
	17.6b	(.f64 (.f64 (sqrt.f64 (/.f64 d h)) (sqrt.f64 (/.f64 d l))) (fma.f64 (pow.f64 (/.f64 M (/.f64 (.f64 d 2) D)) 2) (.f64 (/.f64 h l) -1/2) 1))
	45.8b	(.f64 (sqrt.f64 (/.f64 1 (.f64 l h))) d)
	10.8b	(.f64 (.f64 (cbrt.f64 (.f64 (.f64 (.f64 (sqrt.f64 (/.f64 1 (.f64 (cbrt.f64 h) (cbrt.f64 h)))) (sqrt.f64 (/.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))) (cbrt.f64 (.f64 (.f64 (.f64 (sqrt.f64 (/.f64 1 (.f64 (cbrt.f64 h) (cbrt.f64 h)))) (sqrt.f64 (/.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)))) (cbrt.f64 (.f64 (.f64 (.f64 (sqrt.f64 (/.f64 1 (.f64 (cbrt.f64 h) (cbrt.f64 h)))) (sqrt.f64 (/.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))))
	12.9b	(.f64 (.f64 (sqrt.f64 (/.f64 1 (.f64 (cbrt.f64 h) (cbrt.f64 h)))) (sqrt.f64 (/.f64 d (cbrt.f64 h)))) (.f64 (sqrt.f64 (/.f64 d l)) (fma.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2) (*.f64 (/.f64 h l) -1/2) 1)))
	35.2b	(/.f64 (.f64 (.f64 (.f64 (sqrt.f64 1) (sqrt.f64 d)) (sqrt.f64 d)) (fma.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2) (.f64 (/.f64 h l) -1/2) 1)) (.f64 (.f64 (sqrt.f64 (*.f64 (cbrt.f64 h) (cbrt.f64 h))) (sqrt.f64 (cbrt.f64 h))) (sqrt.f64 l)))

Compiler

Compiled 11794 to 5458 computations (53.7% saved)

localize53.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	3.2b	(sqrt.f64 (/.f64 d (cbrt.f64 l)))
	3.6b	(sqrt.f64 (/.f64 d (cbrt.f64 h)))
✓	4.8b	(/.f64 (.f64 D M) (.f64 2 d))
✓	5.9b	(fma.f64 (pow.f64 (/.f64 (.f64 D M) (.f64 2 d)) 2) (*.f64 (/.f64 h l) -1/2) 1)

series393.0ms (2.1%)

Counts

3 → 108

Calls

3 calls:

174.0ms	(fma.f64 (pow.f64 (/.f64 (.f64 D M) (.f64 2 d)) 2) (*.f64 (/.f64 h l) -1/2) 1)
168.0ms	(sqrt.f64 (/.f64 d (cbrt.f64 l)))
51.0ms	(/.f64 (.f64 D M) (.f64 2 d))

rewrite24.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

22×	`sqrt-prod_binary64`
21×	`times-frac_binary64`
21×	`add-sqr-sqrt_binary64`
16×	`*-un-lft-identity_binary64`
16×	`add-cube-cbrt_binary64`

Counts

3 → 70

Calls

3 calls:

8.0ms	(/.f64 (.f64 D M) (.f64 2 d))
6.0ms	(sqrt.f64 (/.f64 d (cbrt.f64 l)))
1.0ms	(fma.f64 (pow.f64 (/.f64 (.f64 D M) (.f64 2 d)) 2) (*.f64 (/.f64 h l) -1/2) 1)

simplify163.0ms (0.9%)

Algorithm

1×	egg-herbie

Rules

690×	`associate-l_binary64`
684×	`associate-/r*_binary64`
581×	`associate-*l/_binary64`
502×	`associate-*r/_binary64`
259×	`associate-/l/_binary64`

Counts

178 → 95

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	190	3235
1	350	3101
2	1271	3009
3	5028	3009

prune674.0ms (3.5%)

Pruning

20 alts after pruning (20 fresh and 0 done)

	Pruned	Kept	Total
New	133	5	138
Fresh	4	15	19
Picked	1	0	1
Done	0	0	0
Total	138	20	158

Error

4.5b

Counts

158 → 20

Alt Table

Status	Error	Program
	9.8b	(/.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 (cbrt.f64 h))) (.f64 (sqrt.f64 (/.f64 1 (.f64 (cbrt.f64 l) (cbrt.f64 l)))) (sqrt.f64 (/.f64 d (cbrt.f64 l)))))) (sqrt.f64 (.f64 (cbrt.f64 h) (cbrt.f64 h))))
	34.3b	(/.f64 (.f64 (expm1.f64 (log1p.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 (cbrt.f64 h))) (sqrt.f64 (/.f64 d (cbrt.f64 l))))) (.f64 (sqrt.f64 (.f64 (cbrt.f64 h) (cbrt.f64 h))) (sqrt.f64 (.f64 (cbrt.f64 l) (cbrt.f64 l)))))
	35.7b	(/.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 (cbrt.f64 h))) (.f64 (sqrt.f64 d) (sqrt.f64 (/.f64 1 (.f64 (cbrt.f64 l) (cbrt.f64 l))))))) (.f64 (sqrt.f64 (*.f64 (cbrt.f64 h) (cbrt.f64 h))) (sqrt.f64 (cbrt.f64 l))))
	14.7b	(.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))
	34.1b	(.f64 (.f64 (sqrt.f64 (/.f64 d h)) (sqrt.f64 (/.f64 d l))) (fma.f64 (/.f64 (.f64 (.f64 D D) (.f64 (.f64 M M) h)) (.f64 (.f64 d d) l)) -1/8 1))
	10.7b	(.f64 (.f64 (.f64 (sqrt.f64 (/.f64 1 (.f64 (cbrt.f64 h) (cbrt.f64 h)))) (.f64 (fabs.f64 (cbrt.f64 (/.f64 d (cbrt.f64 h)))) (sqrt.f64 (cbrt.f64 (/.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))
	13.4b	(.f64 (.f64 (.f64 (sqrt.f64 (/.f64 1 (.f64 (cbrt.f64 h) (cbrt.f64 h)))) (sqrt.f64 (/.f64 d (cbrt.f64 h)))) (.f64 (sqrt.f64 (sqrt.f64 (/.f64 d l))) (sqrt.f64 (sqrt.f64 (/.f64 d l))))) (fma.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2) (.f64 (/.f64 h l) -1/2) 1))
	9.1b	(/.f64 (.f64 (fma.f64 (pow.f64 (/.f64 (.f64 D M) (.f64 2 d)) 2) (.f64 (/.f64 h l) -1/2) 1) (.f64 (.f64 (.f64 (cbrt.f64 (sqrt.f64 (/.f64 d (cbrt.f64 h)))) (cbrt.f64 (sqrt.f64 (/.f64 d (cbrt.f64 h))))) (cbrt.f64 (sqrt.f64 (/.f64 d (cbrt.f64 h))))) (sqrt.f64 (/.f64 d (cbrt.f64 l))))) (.f64 (sqrt.f64 (.f64 (cbrt.f64 h) (cbrt.f64 h))) (sqrt.f64 (.f64 (cbrt.f64 l) (cbrt.f64 l)))))
	8.9b	(/.f64 (.f64 (fma.f64 (pow.f64 (/.f64 (.f64 D M) (.f64 2 d)) 2) (.f64 (/.f64 h l) -1/2) 1) (.f64 (.f64 (fabs.f64 (cbrt.f64 (/.f64 d (cbrt.f64 h)))) (sqrt.f64 (cbrt.f64 (/.f64 d (cbrt.f64 h))))) (sqrt.f64 (/.f64 d (cbrt.f64 l))))) (.f64 (sqrt.f64 (.f64 (cbrt.f64 h) (cbrt.f64 h))) (sqrt.f64 (*.f64 (cbrt.f64 l) (cbrt.f64 l)))))
	8.9b	(/.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 (cbrt.f64 h))) (.f64 (sqrt.f64 (/.f64 1 (.f64 (cbrt.f64 (cbrt.f64 l)) (cbrt.f64 (cbrt.f64 l))))) (sqrt.f64 (/.f64 d (cbrt.f64 (cbrt.f64 l))))))) (.f64 (sqrt.f64 (.f64 (cbrt.f64 h) (cbrt.f64 h))) (sqrt.f64 (.f64 (cbrt.f64 l) (cbrt.f64 l)))))
	11.0b	(.f64 (.f64 (.f64 (sqrt.f64 (/.f64 1 (.f64 (cbrt.f64 h) (cbrt.f64 h)))) (sqrt.f64 (/.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))
	23.5b	(.f64 (.f64 (sqrt.f64 (/.f64 d h)) (cbrt.f64 (.f64 (.f64 (sqrt.f64 (/.f64 d l)) (sqrt.f64 (/.f64 d l))) (sqrt.f64 (/.f64 d l))))) (fma.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2) (*.f64 (/.f64 h l) -1/2) 1))
	12.9b	(/.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 (cbrt.f64 h))) (sqrt.f64 (/.f64 d l)))) (sqrt.f64 (.f64 (cbrt.f64 h) (cbrt.f64 h))))
	31.7b	(.f64 (.f64 (.f64 (sqrt.f64 (/.f64 1 (.f64 (cbrt.f64 h) (cbrt.f64 h)))) (sqrt.f64 (/.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)
	27.6b	(/.f64 (.f64 (fma.f64 (/.f64 (.f64 (.f64 D D) (.f64 (.f64 M M) h)) (.f64 (.f64 d d) l)) -1/8 1) (.f64 (sqrt.f64 (/.f64 d (cbrt.f64 h))) (sqrt.f64 (/.f64 d (cbrt.f64 l))))) (.f64 (sqrt.f64 (.f64 (cbrt.f64 h) (cbrt.f64 h))) (sqrt.f64 (*.f64 (cbrt.f64 l) (cbrt.f64 l)))))
	18.0b	(.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))
	17.6b	(.f64 (.f64 (sqrt.f64 (/.f64 d h)) (sqrt.f64 (/.f64 d l))) (fma.f64 (pow.f64 (/.f64 M (/.f64 (.f64 d 2) D)) 2) (.f64 (/.f64 h l) -1/2) 1))
	45.8b	(.f64 (sqrt.f64 (/.f64 1 (.f64 l h))) d)
	12.9b	(.f64 (.f64 (sqrt.f64 (/.f64 1 (.f64 (cbrt.f64 h) (cbrt.f64 h)))) (sqrt.f64 (/.f64 d (cbrt.f64 h)))) (.f64 (sqrt.f64 (/.f64 d l)) (fma.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2) (*.f64 (/.f64 h l) -1/2) 1)))
	35.2b	(/.f64 (.f64 (.f64 (.f64 (sqrt.f64 1) (sqrt.f64 d)) (sqrt.f64 d)) (fma.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2) (.f64 (/.f64 h l) -1/2) 1)) (.f64 (.f64 (sqrt.f64 (*.f64 (cbrt.f64 h) (cbrt.f64 h))) (sqrt.f64 (cbrt.f64 h))) (sqrt.f64 l)))

Compiler

Compiled 7563 to 2680 computations (64.6% saved)

regimes4.2s (22%)

Accuracy

Total 4.1b remaining (36.1%)

Threshold costs 0b (0%)

Counts

154 → 2

Compiler

Compiled 49221 to 32688 computations (33.6% saved)

bsearch22.0ms (0.1%)

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

simplify14.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

21×	`*-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	67	204
1	87	204
2	102	204
3	112	204
4	120	204
5	124	204
6	125	204
7	122	204

end1.2s (6.1%)

Compiler: Compiled 1415 to 850 computations (39.9% saved)

Details

analyze2.8s (14.5%)

sample5.6s (29.5%)

simplify65.0ms (0.3%)

prune7.0ms (0%)

localize29.0ms (0.2%)

series280.0ms (1.5%)

rewrite29.0ms (0.2%)

simplify121.0ms (0.6%)

prune335.0ms (1.8%)

localize53.0ms (0.3%)

series481.0ms (2.5%)

rewrite45.0ms (0.2%)

simplify154.0ms (0.8%)

prune476.0ms (2.5%)

localize64.0ms (0.3%)

series518.0ms (2.7%)

rewrite69.0ms (0.4%)

simplify337.0ms (1.8%)

prune917.0ms (4.8%)

localize53.0ms (0.3%)

series393.0ms (2.1%)

rewrite24.0ms (0.1%)

simplify163.0ms (0.9%)

prune674.0ms (3.5%)

regimes4.2s (22%)

bsearch22.0ms (0.1%)

simplify14.0ms (0.1%)

end1.2s (6.1%)

Profiling