Details

analyze2.2s (15.8%)

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)

sample6.0s (43.4%)

Symmetry

(sort M D)

Results

3.4s	13438×	body	128	invalid
2.5s	8256×	body	128	valid

Compiler

Compiled 122 to 95 computations (22.1% saved)

simplify33.0ms (0.2%)

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

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

25.5b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	25.5b	(.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)

localize19.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	6.8b	(fma.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2) (*.f64 (/.f64 h l) -1/2) 1)
✓	7.7b	(.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))
✓	11.5b	(sqrt.f64 (/.f64 d h))
✓	11.8b	(sqrt.f64 (/.f64 d l))

series338.0ms (2.4%)

Counts

4 → 92

Calls

4 calls:

216.0ms	(.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))
88.0ms	(fma.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2) (*.f64 (/.f64 h l) -1/2) 1)
17.0ms	(sqrt.f64 (/.f64 d h))
16.0ms	(sqrt.f64 (/.f64 d l))

rewrite20.0ms (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))
4.0ms	(sqrt.f64 (/.f64 d h))
2.0ms	(sqrt.f64 (/.f64 d l))
0.0ms	(fma.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2) (*.f64 (/.f64 h l) -1/2) 1)

simplify123.0ms (0.9%)

Algorithm

1×	egg-herbie

Rules

569×	`fma-def_binary64`
472×	`associate-*l/_binary64`
417×	`times-frac_binary64`
392×	`associate-*r/_binary64`
354×	`associate-/l*_binary64`

Counts

181 → 134

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	200	4766
1	369	4458
2	1174	4367
3	4643	4367
4	5175	4367

prune192.0ms (1.4%)

Pruning

20 alts after pruning (20 fresh and 0 done)

	Pruned	Kept	Total
New	114	20	134
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	115	20	135

Error

11.1b

Counts

135 → 20

Alt Table

Status	Error	Program
	21.3b	(.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))
	31.2b	(.f64 (.f64 (sqrt.f64 (/.f64 d h)) (sqrt.f64 (/.f64 d l))) 1)
	21.3b	(.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))
	42.9b	(.f64 (sqrt.f64 (/.f64 1 (.f64 l h))) d)
	25.5b	(.f64 (sqrt.f64 (/.f64 d 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)))
	40.2b	(.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))
	58.9b	(.f64 -1/8 (.f64 (/.f64 (*.f64 (pow.f64 D 2) (pow.f64 M 2)) d) (sqrt.f64 (/.f64 h (pow.f64 l 3)))))
	37.2b	(/.f64 (.f64 d (fma.f64 (pow.f64 (/.f64 (.f64 D M) (.f64 2 d)) 2) (.f64 (/.f64 h l) -1/2) 1)) (*.f64 (sqrt.f64 h) (sqrt.f64 l)))
	25.6b	(.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))
	21.4b	(.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))
	36.0b	(.f64 (.f64 (sqrt.f64 (/.f64 d h)) (cbrt.f64 (pow.f64 (sqrt.f64 (/.f64 d l)) 3))) (fma.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2) (*.f64 (/.f64 h l) -1/2) 1))
	32.1b	(.f64 (sqrt.f64 (.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))) (sqrt.f64 (.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))))
	35.7b	(.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))
▶	19.7b	(.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))) (fma.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2) (*.f64 (/.f64 h l) -1/2) 1))
	21.2b	(.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))
	39.5b	(.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))
	19.8b	(.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))) (fma.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2) (.f64 (/.f64 h l) -1/2) 1))
	40.5b	(/.f64 (.f64 (.f64 (sqrt.f64 (/.f64 d h)) (sqrt.f64 d)) (fma.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2) (*.f64 (/.f64 h l) -1/2) 1)) (sqrt.f64 l))
	42.1b	(cbrt.f64 (pow.f64 (.f64 (.f64 (sqrt.f64 (/.f64 d l)) (sqrt.f64 (/.f64 d h))) (fma.f64 (pow.f64 (/.f64 (.f64 D M) (.f64 2 d)) 2) (*.f64 (/.f64 h l) -1/2) 1)) 3))
	61.0b	(.f64 (.f64 (sqrt.f64 (/.f64 d h)) (sqrt.f64 (/.f64 d l))) (.f64 -1/8 (/.f64 (.f64 (pow.f64 D 2) (.f64 (pow.f64 M 2) h)) (.f64 (pow.f64 d 2) l))))

Compiler

Compiled 5871 to 2958 computations (49.6% 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))
	6.8b	(fma.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2) (*.f64 (/.f64 h l) -1/2) 1)
✓	7.7b	(.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))) (fma.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2) (*.f64 (/.f64 h l) -1/2) 1))
	11.8b	(sqrt.f64 (/.f64 d l))

series238.0ms (1.7%)

Counts

2 → 68

Calls

2 calls:

223.0ms

(*.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))

15.0ms

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

rewrite33.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

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

Counts

2 → 55

Calls

2 calls:

21.0ms

(*.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))

4.0ms

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

simplify85.0ms (0.6%)

Algorithm

1×	egg-herbie

Rules

846×	`associate-*r/_binary64`
648×	`associate-/r*_binary64`
319×	`associate-l_binary64`
239×	`associate-/l/_binary64`
233×	`associate-r_binary64`

Counts

123 → 91

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	168	3922
1	431	3500
2	1873	3500
3	5331	3500

prune182.0ms (1.3%)

Pruning

21 alts after pruning (21 fresh and 0 done)

	Pruned	Kept	Total
New	141	8	149
Fresh	6	13	19
Picked	1	0	1
Done	0	0	0
Total	148	21	169

Error

11.0b

Counts

169 → 21

Alt Table

Status	Error	Program
	21.3b	(.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))
	31.2b	(.f64 (.f64 (sqrt.f64 (/.f64 d h)) (sqrt.f64 (/.f64 d l))) 1)
	21.3b	(.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))
	42.9b	(.f64 (sqrt.f64 (/.f64 1 (.f64 l h))) d)
	25.5b	(.f64 (sqrt.f64 (/.f64 d 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)))
	58.9b	(.f64 -1/8 (.f64 (/.f64 (*.f64 (pow.f64 D 2) (pow.f64 M 2)) d) (sqrt.f64 (/.f64 h (pow.f64 l 3)))))
	37.2b	(/.f64 (.f64 d (fma.f64 (pow.f64 (/.f64 (.f64 D M) (.f64 2 d)) 2) (.f64 (/.f64 h l) -1/2) 1)) (*.f64 (sqrt.f64 h) (sqrt.f64 l)))
	25.6b	(.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))
	26.0b	(.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)
	31.7b	(.f64 (.f64 (.f64 (sqrt.f64 (/.f64 1 (.f64 (cbrt.f64 h) (cbrt.f64 h)))) (sqrt.f64 (/.f64 d (cbrt.f64 h)))) (cbrt.f64 (pow.f64 (sqrt.f64 (/.f64 d l)) 3))) (fma.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2) (*.f64 (/.f64 h l) -1/2) 1))
	21.4b	(.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))
	42.1b	(cbrt.f64 (pow.f64 (.f64 (.f64 (sqrt.f64 (/.f64 d l)) (sqrt.f64 (/.f64 d h))) (fma.f64 (pow.f64 (/.f64 (.f64 D M) (.f64 2 d)) 2) (*.f64 (/.f64 h l) -1/2) 1)) 3))
	37.4b	(/.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)))
▶	15.4b	(.f64 (.f64 (.f64 (sqrt.f64 (/.f64 1 (.f64 (cbrt.f64 h) (cbrt.f64 h)))) (sqrt.f64 (/.f64 d (cbrt.f64 h)))) (.f64 (sqrt.f64 (/.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))
	61.0b	(.f64 (.f64 (sqrt.f64 (/.f64 d h)) (sqrt.f64 (/.f64 d l))) (.f64 -1/8 (/.f64 (.f64 (pow.f64 D 2) (.f64 (pow.f64 M 2) h)) (.f64 (pow.f64 d 2) l))))
	19.9b	(.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 M (/.f64 (.f64 d 2) D)) 2) (.f64 (/.f64 h l) -1/2) 1))
	21.2b	(.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))
	27.0b	(.f64 (sqrt.f64 (.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))) (sqrt.f64 (.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))))
	19.8b	(.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))) (fma.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2) (.f64 (/.f64 h l) -1/2) 1))
	19.6b	(/.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))))
	19.8b	(.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 (/.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))

Compiler

Compiled 8108 to 3974 computations (51% saved)

localize28.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	4.4b	(sqrt.f64 (/.f64 d (cbrt.f64 l)))
	4.5b	(/.f64 (.f64 M D) (.f64 d 2))
	6.8b	(fma.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2) (*.f64 (/.f64 h l) -1/2) 1)
✓	7.7b	(.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 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2) (*.f64 (/.f64 h l) -1/2) 1))

series305.0ms (2.2%)

Counts

2 → 44

Calls

2 calls:

226.0ms

(*.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))

79.0ms

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

rewrite50.0ms (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:

35.0ms

(*.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))

3.0ms

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

simplify173.0ms (1.2%)

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	524	4970
2	1855	4970
3	4969	4970
4	4998	4970
5	4968	4970

prune221.0ms (1.6%)

Pruning

22 alts after pruning (22 fresh and 0 done)

	Pruned	Kept	Total
New	177	4	181
Fresh	2	18	20
Picked	1	0	1
Done	0	0	0
Total	180	22	202

Error

11.0b

Counts

202 → 22

Alt Table

Status	Error	Program
▶	15.4b	(/.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)))))
	31.2b	(.f64 (.f64 (sqrt.f64 (/.f64 d h)) (sqrt.f64 (/.f64 d l))) 1)
	21.3b	(.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))
	42.9b	(.f64 (sqrt.f64 (/.f64 1 (.f64 l h))) d)
	37.2b	(/.f64 (.f64 d (fma.f64 (pow.f64 (/.f64 (.f64 D M) (.f64 2 d)) 2) (.f64 (/.f64 h l) -1/2) 1)) (*.f64 (sqrt.f64 h) (sqrt.f64 l)))
	25.6b	(.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))
	26.0b	(.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)
	31.7b	(.f64 (.f64 (.f64 (sqrt.f64 (/.f64 1 (.f64 (cbrt.f64 h) (cbrt.f64 h)))) (sqrt.f64 (/.f64 d (cbrt.f64 h)))) (cbrt.f64 (pow.f64 (sqrt.f64 (/.f64 d l)) 3))) (fma.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2) (*.f64 (/.f64 h l) -1/2) 1))
	21.4b	(.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))
	21.6b	(.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))))) 1)
	19.8b	(.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 (/.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))
	42.1b	(cbrt.f64 (pow.f64 (.f64 (.f64 (sqrt.f64 (/.f64 d l)) (sqrt.f64 (/.f64 d h))) (fma.f64 (pow.f64 (/.f64 (.f64 D M) (.f64 2 d)) 2) (*.f64 (/.f64 h l) -1/2) 1)) 3))
	37.4b	(/.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)))
	15.9b	(/.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 1) (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)) (sqrt.f64 (*.f64 (cbrt.f64 l) (cbrt.f64 l))))
	61.0b	(.f64 (.f64 (sqrt.f64 (/.f64 d h)) (sqrt.f64 (/.f64 d l))) (.f64 -1/8 (/.f64 (.f64 (pow.f64 D 2) (.f64 (pow.f64 M 2) h)) (.f64 (pow.f64 d 2) l))))
	15.6b	(/.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))))
	19.9b	(.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 M (/.f64 (.f64 d 2) D)) 2) (.f64 (/.f64 h l) -1/2) 1))
	21.2b	(.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))
	27.0b	(.f64 (sqrt.f64 (.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))) (sqrt.f64 (.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))))
	19.8b	(.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))) (fma.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2) (.f64 (/.f64 h l) -1/2) 1))
	58.9b	(.f64 -1/8 (.f64 (/.f64 (*.f64 (pow.f64 D 2) (pow.f64 M 2)) d) (sqrt.f64 (/.f64 h (pow.f64 l 3)))))
	19.6b	(/.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))))

Compiler

Compiled 11634 to 5413 computations (53.5% saved)

localize30.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
	4.4b	(sqrt.f64 (/.f64 d (cbrt.f64 l)))
✓	4.5b	(/.f64 (.f64 D M) (.f64 2 d))
✓	6.6b	(.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)))))
✓	6.8b	(fma.f64 (pow.f64 (/.f64 (.f64 D M) (.f64 2 d)) 2) (*.f64 (/.f64 h l) -1/2) 1)

series704.0ms (5.1%)

Counts

3 → 152

Calls

3 calls:

605.0ms

(*.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)))))

83.0ms

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

15.0ms

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

rewrite19.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

20×	`add-cbrt-cube_binary64`
20×	`add-exp-log_binary64`
8×	`pow1_binary64`
7×	`cbrt-unprod_binary64`
7×	`prod-exp_binary64`

Counts

3 → 56

Calls

3 calls:

11.0ms

(*.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)))))

4.0ms

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

0.0ms

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

simplify150.0ms (1.1%)

Algorithm

1×	egg-herbie

Rules

517×	`fma-def_binary64`
367×	`associate-/r/_binary64`
310×	`associate-/l/_binary64`
262×	`times-frac_binary64`
225×	`associate-r_binary64`

Counts

208 → 100

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	244	6369
1	582	5913
2	2477	5809
3	4700	5781
4	5072	5781

prune165.0ms (1.2%)

Pruning

25 alts after pruning (25 fresh and 0 done)

	Pruned	Kept	Total
New	134	9	143
Fresh	5	16	21
Picked	1	0	1
Done	0	0	0
Total	140	25	165

Error

9.6b

Counts

165 → 25

Alt Table

Status	Error	Program
	58.7b	(/.f64 (.f64 -1/8 (.f64 (/.f64 (.f64 (.f64 D D) (.f64 (.f64 M M) h)) (.f64 d l)) (exp.f64 (fma.f64 (log.f64 h) -1/6 (.f64 (log.f64 l) -1/6))))) (.f64 (sqrt.f64 (.f64 (cbrt.f64 h) (cbrt.f64 h))) (sqrt.f64 (*.f64 (cbrt.f64 l) (cbrt.f64 l)))))
	31.2b	(.f64 (.f64 (sqrt.f64 (/.f64 d h)) (sqrt.f64 (/.f64 d l))) 1)
	21.3b	(.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))
	42.9b	(.f64 (sqrt.f64 (/.f64 1 (.f64 l h))) d)
	45.8b	(/.f64 (-.f64 (.f64 (exp.f64 (.f64 1/6 (-.f64 (log.f64 (/.f64 1 l)) (log.f64 h)))) d) (.f64 1/8 (/.f64 (.f64 (exp.f64 (.f64 1/6 (-.f64 (log.f64 (/.f64 1 l)) (log.f64 h)))) (.f64 (pow.f64 D 2) (.f64 h (pow.f64 M 2)))) (.f64 d l)))) (.f64 (sqrt.f64 (.f64 (cbrt.f64 h) (cbrt.f64 h))) (sqrt.f64 (*.f64 (cbrt.f64 l) (cbrt.f64 l)))))
	19.8b	(.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))) (fma.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2) (.f64 (/.f64 h l) -1/2) 1))
	15.4b	(/.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 (sqrt.f64 (/.f64 d (cbrt.f64 l)))) (sqrt.f64 (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)))))
	58.9b	(.f64 -1/8 (.f64 (/.f64 (*.f64 (pow.f64 D 2) (pow.f64 M 2)) d) (sqrt.f64 (/.f64 h (pow.f64 l 3)))))
	21.6b	(/.f64 (.f64 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)))))
	37.2b	(/.f64 (.f64 d (fma.f64 (pow.f64 (/.f64 (.f64 D M) (.f64 2 d)) 2) (.f64 (/.f64 h l) -1/2) 1)) (*.f64 (sqrt.f64 h) (sqrt.f64 l)))
	25.6b	(.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))
	15.3b	(/.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 (.f64 (cbrt.f64 d) (cbrt.f64 d)) (.f64 (cbrt.f64 (cbrt.f64 l)) (cbrt.f64 (cbrt.f64 l))))) (sqrt.f64 (/.f64 (cbrt.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)))))
	19.6b	(/.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)))) (cbrt.f64 (pow.f64 (sqrt.f64 (/.f64 d l)) 3))) (fma.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2) (*.f64 (/.f64 h l) -1/2) 1))
	21.4b	(.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))
	42.1b	(cbrt.f64 (pow.f64 (.f64 (.f64 (sqrt.f64 (/.f64 d l)) (sqrt.f64 (/.f64 d h))) (fma.f64 (pow.f64 (/.f64 (.f64 D M) (.f64 2 d)) 2) (*.f64 (/.f64 h l) -1/2) 1)) 3))
	37.4b	(/.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)))
	15.9b	(/.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 1) (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)) (sqrt.f64 (*.f64 (cbrt.f64 l) (cbrt.f64 l))))
	61.0b	(.f64 (.f64 (sqrt.f64 (/.f64 d h)) (sqrt.f64 (/.f64 d l))) (.f64 -1/8 (/.f64 (.f64 (pow.f64 D 2) (.f64 (pow.f64 M 2) h)) (.f64 (pow.f64 d 2) l))))
	15.7b	(/.f64 (.f64 (.f64 (cbrt.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)))))) (cbrt.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))))))) (cbrt.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)))))
	19.9b	(.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 M (/.f64 (.f64 d 2) D)) 2) (.f64 (/.f64 h l) -1/2) 1))
	21.2b	(.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))
	58.5b	(/.f64 (.f64 -1/8 (/.f64 (.f64 (pow.f64 D 2) (.f64 (exp.f64 (.f64 1/6 (-.f64 (log.f64 (/.f64 1 h)) (log.f64 l)))) (.f64 h (pow.f64 M 2)))) (.f64 d l))) (.f64 (sqrt.f64 (.f64 (cbrt.f64 h) (cbrt.f64 h))) (sqrt.f64 (*.f64 (cbrt.f64 l) (cbrt.f64 l)))))
	42.6b	(/.f64 (.f64 (exp.f64 (.f64 1/6 (-.f64 (log.f64 (/.f64 1 l)) (log.f64 h)))) d) (.f64 (sqrt.f64 (.f64 (cbrt.f64 h) (cbrt.f64 h))) (sqrt.f64 (*.f64 (cbrt.f64 l) (cbrt.f64 l)))))
	43.9b	(/.f64 (.f64 (pow.f64 (/.f64 1 (.f64 l h)) 1/6) d) (.f64 (sqrt.f64 (.f64 (cbrt.f64 h) (cbrt.f64 h))) (sqrt.f64 (*.f64 (cbrt.f64 l) (cbrt.f64 l)))))

Compiler

Compiled 7986 to 3062 computations (61.7% saved)

regimes2.0s (14.3%)

Accuracy

Total 5.5b remaining (34.8%)

Threshold costs 0b (0%)

Counts

155 → 2

Compiler

Compiled 49578 to 33106 computations (33.2% saved)

bsearch12.0ms (0.1%)

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

simplify6.0ms (0%)

Algorithm

1×	egg-herbie

Rules

18×	`*-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	55	136
1	72	136
2	87	136
3	97	136
4	105	136
5	109	136
6	110	136
7	107	136

end521.0ms (3.8%)

Remove: (sort M D)
Compiler: Compiled 1391 to 908 computations (34.7% saved)

Details

analyze2.2s (15.8%)

sample6.0s (43.4%)

simplify33.0ms (0.2%)

prune4.0ms (0%)

localize19.0ms (0.1%)

series338.0ms (2.4%)

rewrite20.0ms (0.1%)

simplify123.0ms (0.9%)

prune192.0ms (1.4%)

localize22.0ms (0.2%)

series238.0ms (1.7%)

rewrite33.0ms (0.2%)

simplify85.0ms (0.6%)

prune182.0ms (1.3%)

localize28.0ms (0.2%)

series305.0ms (2.2%)

rewrite50.0ms (0.4%)

simplify173.0ms (1.2%)

prune221.0ms (1.6%)

localize30.0ms (0.2%)

series704.0ms (5.1%)

rewrite19.0ms (0.1%)

simplify150.0ms (1.1%)

prune165.0ms (1.2%)

regimes2.0s (14.3%)

bsearch12.0ms (0.1%)

simplify6.0ms (0%)

end521.0ms (3.8%)

Profiling