Details

analyze2.2s (13.7%)

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)

sample5.8s (35.8%)

Symmetry

(sort M D)

Results

3.5s	13568×	body	128	invalid
2.2s	8256×	body	128	valid

Compiler

Compiled 122 to 95 computations (22.1% saved)

simplify34.0ms (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

25.4b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	25.4b	(.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))

Compiler

Compiled 128 to 88 computations (31.3% saved)

localize21.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	6.0b	(.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))
✓	9.4b	(fma.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2) (*.f64 (/.f64 h l) -1/2) 1)
✓	10.4b	(sqrt.f64 (/.f64 d h))
✓	13.5b	(sqrt.f64 (/.f64 d l))

series623.0ms (3.8%)

Counts

4 → 92

Calls

4 calls:

400.0ms	(.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))
185.0ms	(fma.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2) (*.f64 (/.f64 h l) -1/2) 1)
19.0ms	(sqrt.f64 (/.f64 d l))
19.0ms	(sqrt.f64 (/.f64 d h))

rewrite22.0ms (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:

12.0ms	(.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)

simplify136.0ms (0.8%)

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

prune188.0ms (1.1%)

Pruning

17 alts after pruning (17 fresh and 0 done)

	Pruned	Kept	Total
New	117	17	134
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	118	17	135

Error

11.2b

Counts

135 → 17

Alt Table

Status	Error	Program
	25.7b	(.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))
	25.6b	(.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)))
	30.0b	(.f64 (.f64 (sqrt.f64 (/.f64 d h)) (sqrt.f64 (/.f64 d l))) 1)
	21.2b	(.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))
	38.7b	(/.f64 (.f64 (.f64 (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 (sqrt.f64 h) (sqrt.f64 l)))
	25.4b	(.f64 (.f64 (.f64 (sqrt.f64 (/.f64 d h)) (sqrt.f64 (/.f64 d l))) (.f64 (cbrt.f64 (fma.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2) (.f64 (/.f64 h l) -1/2) 1)) (cbrt.f64 (fma.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2) (.f64 (/.f64 h l) -1/2) 1)))) (cbrt.f64 (fma.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2) (*.f64 (/.f64 h l) -1/2) 1)))
	21.8b	(.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))
	25.9b	(.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))
	42.2b	(.f64 (sqrt.f64 (/.f64 1 (.f64 l h))) d)
	41.5b	(/.f64 (.f64 (.f64 (sqrt.f64 d) (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 h))
	38.7b	(/.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)))
	60.9b	(.f64 -1/8 (.f64 (/.f64 (*.f64 (pow.f64 D 2) (pow.f64 M 2)) d) (sqrt.f64 (/.f64 h (pow.f64 l 3)))))
	31.9b	(.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))))
	21.9b	(.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))
	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))
▶	20.1b	(.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))
	20.9b	(.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))

Compiler

Compiled 5735 to 2840 computations (50.5% saved)

localize25.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	3.9b	(/.f64 (.f64 M D) (.f64 d 2))
✓	6.0b	(.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))
	9.4b	(fma.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2) (*.f64 (/.f64 h l) -1/2) 1)
	13.5b	(sqrt.f64 (/.f64 d l))

series964.0ms (5.9%)

Counts

2 → 80

Calls

2 calls:

947.0ms

(*.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))

16.0ms

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

rewrite35.0ms (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:

23.0ms

(*.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))

simplify155.0ms (0.9%)

Algorithm

1×	egg-herbie

Rules

842×	`fma-def_binary64`
579×	`associate-/r*_binary64`
437×	`associate-l_binary64`
380×	`associate-r_binary64`
212×	`associate-/l/_binary64`

Counts

135 → 102

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	241	6370
1	614	5500
2	2440	5500
3	4972	5500
4	5684	5500

prune203.0ms (1.2%)

Pruning

22 alts after pruning (22 fresh and 0 done)

	Pruned	Kept	Total
New	153	7	160
Fresh	1	15	16
Picked	1	0	1
Done	0	0	0
Total	155	22	177

Error

11.1b

Counts

177 → 22

Alt Table

Status	Error	Program
	25.7b	(.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))
	25.6b	(.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)))
	49.8b	(.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))))
	30.0b	(.f64 (.f64 (sqrt.f64 (/.f64 d h)) (sqrt.f64 (/.f64 d l))) 1)
	42.2b	(.f64 (sqrt.f64 (/.f64 1 (.f64 l h))) d)
	24.7b	(.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)
	21.2b	(.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))
	38.7b	(/.f64 (.f64 (.f64 (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 (sqrt.f64 h) (sqrt.f64 l)))
	20.2b	(.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 (/.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))
	60.9b	(.f64 -1/8 (.f64 (/.f64 (*.f64 (pow.f64 D 2) (pow.f64 M 2)) d) (sqrt.f64 (/.f64 h (pow.f64 l 3)))))
	24.0b	(.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))) (cbrt.f64 (pow.f64 (fma.f64 (pow.f64 (/.f64 (.f64 D M) (.f64 2 d)) 2) (.f64 (/.f64 h l) -1/2) 1) 3)))
▶	16.4b	(.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))
	20.9b	(.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))
	20.1b	(.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))
	25.4b	(.f64 (.f64 (.f64 (sqrt.f64 (/.f64 d h)) (sqrt.f64 (/.f64 d l))) (.f64 (cbrt.f64 (fma.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2) (.f64 (/.f64 h l) -1/2) 1)) (cbrt.f64 (fma.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2) (.f64 (/.f64 h l) -1/2) 1)))) (cbrt.f64 (fma.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2) (*.f64 (/.f64 h l) -1/2) 1)))
	21.8b	(.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))
	25.9b	(.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))
	41.5b	(/.f64 (.f64 (.f64 (sqrt.f64 d) (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 h))
	38.7b	(/.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)))
	50.0b	(.f64 (pow.f64 (pow.f64 d 2) 1/3) (.f64 (sqrt.f64 (/.f64 1 l)) (*.f64 (pow.f64 (/.f64 1 h) 1/6) (fabs.f64 (pow.f64 (/.f64 d h) 1/3)))))
	21.9b	(.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))
	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))

Compiler

Compiled 8580 to 3867 computations (54.9% saved)

localize35.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	3.9b	(sqrt.f64 (/.f64 d (cbrt.f64 l)))
	3.9b	(/.f64 (.f64 M D) (.f64 d 2))
✓	6.0b	(.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))
	9.4b	(fma.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2) (*.f64 (/.f64 h l) -1/2) 1)

series1.0s (6.2%)

Counts

2 → 56

Calls

2 calls:

933.0ms

(*.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))

82.0ms

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

rewrite54.0ms (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:

36.0ms

(*.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)))

simplify154.0ms (0.9%)

Algorithm

1×	egg-herbie

Rules

714×	`associate-*r/_binary64`
618×	`associate-l_binary64`
552×	`associate-r_binary64`
275×	`distribute-rgt-in_binary64`
270×	`*-commutative_binary64`

Counts

139 → 129

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	306	8099
1	718	6934
2	2521	6934
3	5931	6934

prune249.0ms (1.5%)

Pruning

24 alts after pruning (24 fresh and 0 done)

	Pruned	Kept	Total
New	188	4	192
Fresh	1	20	21
Picked	1	0	1
Done	0	0	0
Total	190	24	214

Error

10.1b

Counts

214 → 24

Alt Table

Status	Error	Program
	25.7b	(.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))
	25.6b	(.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)))
	49.8b	(.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))))
	30.0b	(.f64 (.f64 (sqrt.f64 (/.f64 d h)) (sqrt.f64 (/.f64 d l))) 1)
▶	16.4b	(/.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 l))) (.f64 (sqrt.f64 (/.f64 (cbrt.f64 d) (cbrt.f64 h))) (fabs.f64 (cbrt.f64 d))))) (.f64 (fabs.f64 (cbrt.f64 h)) (sqrt.f64 (.f64 (cbrt.f64 l) (cbrt.f64 l)))))
	25.9b	(.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))
	42.2b	(.f64 (sqrt.f64 (/.f64 1 (.f64 l h))) d)
	24.7b	(.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)
	21.2b	(.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))
	38.7b	(/.f64 (.f64 (.f64 (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 (sqrt.f64 h) (sqrt.f64 l)))
	20.2b	(.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 (/.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))
	60.9b	(.f64 -1/8 (.f64 (/.f64 (*.f64 (pow.f64 D 2) (pow.f64 M 2)) d) (sqrt.f64 (/.f64 h (pow.f64 l 3)))))
	24.0b	(.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))) (cbrt.f64 (pow.f64 (fma.f64 (pow.f64 (/.f64 (.f64 D M) (.f64 2 d)) 2) (.f64 (/.f64 h l) -1/2) 1) 3)))
	50.0b	(.f64 (pow.f64 (pow.f64 d 2) 1/3) (.f64 (sqrt.f64 (/.f64 1 l)) (*.f64 (pow.f64 (/.f64 1 h) 1/6) (fabs.f64 (pow.f64 (/.f64 d h) 1/3)))))
	19.5b	(.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)
	35.1b	(.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 (/.f64 (.f64 (.f64 D D) (.f64 (.f64 M M) h)) (.f64 (*.f64 d d) l)) -1/8 1))
	21.9b	(.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))
	25.4b	(.f64 (.f64 (.f64 (sqrt.f64 (/.f64 d h)) (sqrt.f64 (/.f64 d l))) (.f64 (cbrt.f64 (fma.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2) (.f64 (/.f64 h l) -1/2) 1)) (cbrt.f64 (fma.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2) (.f64 (/.f64 h l) -1/2) 1)))) (cbrt.f64 (fma.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2) (*.f64 (/.f64 h l) -1/2) 1)))
	21.8b	(.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))
	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))))
	41.5b	(/.f64 (.f64 (.f64 (sqrt.f64 d) (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 h))
	38.7b	(/.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))
	20.9b	(.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))

Compiler

Compiled 12134 to 5302 computations (56.3% saved)

localize31.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	3.9b	(.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 l))) (.f64 (sqrt.f64 (/.f64 (cbrt.f64 d) (cbrt.f64 h))) (fabs.f64 (cbrt.f64 d)))))
	3.9b	(sqrt.f64 (/.f64 d (cbrt.f64 l)))
✓	3.9b	(/.f64 (.f64 D M) (.f64 2 d))
✓	9.4b	(fma.f64 (pow.f64 (/.f64 (.f64 D M) (.f64 2 d)) 2) (*.f64 (/.f64 h l) -1/2) 1)

series1.3s (7.8%)

Counts

3 → 152

Calls

3 calls:

1.2s

(*.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 l))) (*.f64 (sqrt.f64 (/.f64 (cbrt.f64 d) (cbrt.f64 h))) (fabs.f64 (cbrt.f64 d)))))

88.0ms

(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))

rewrite26.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

24×	`add-cbrt-cube_binary64`
24×	`add-exp-log_binary64`
12×	`pow1_binary64`
10×	`cbrt-unprod_binary64`
10×	`prod-exp_binary64`

Counts

3 → 59

Calls

3 calls:

16.0ms

(*.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 l))) (*.f64 (sqrt.f64 (/.f64 (cbrt.f64 d) (cbrt.f64 h))) (fabs.f64 (cbrt.f64 d)))))

5.0ms

(/.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)

simplify255.0ms (1.6%)

Algorithm

1×	egg-herbie

Rules

590×	`fma-def_binary64`
429×	`associate-r_binary64`
344×	`associate-l_binary64`
274×	`*-commutative_binary64`
255×	`associate-/r/_binary64`

Counts

211 → 114

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	299	8172
1	663	7407
2	2676	7253
3	4847	7213
4	5285	7213

prune185.0ms (1.1%)

Pruning

27 alts after pruning (27 fresh and 0 done)

	Pruned	Kept	Total
New	151	6	157
Fresh	2	21	23
Picked	1	0	1
Done	0	0	0
Total	154	27	181

Error

10.1b

Counts

181 → 27

Alt Table

Status	Error	Program
	25.7b	(.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))
	25.6b	(.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)))
	30.0b	(.f64 (.f64 (sqrt.f64 (/.f64 d h)) (sqrt.f64 (/.f64 d l))) 1)
	25.9b	(.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))
	19.5b	(/.f64 (.f64 1 (.f64 (sqrt.f64 (/.f64 d (cbrt.f64 l))) (.f64 (sqrt.f64 (/.f64 (cbrt.f64 d) (cbrt.f64 h))) (fabs.f64 (cbrt.f64 d))))) (.f64 (fabs.f64 (cbrt.f64 h)) (sqrt.f64 (*.f64 (cbrt.f64 l) (cbrt.f64 l)))))
	42.2b	(.f64 (sqrt.f64 (/.f64 1 (.f64 l h))) d)
	24.7b	(.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)
	16.6b	(/.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 l))) (.f64 (sqrt.f64 (/.f64 (cbrt.f64 d) (cbrt.f64 h))) (fabs.f64 (cbrt.f64 d)))))) (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 l))) (.f64 (sqrt.f64 (/.f64 (cbrt.f64 d) (cbrt.f64 h))) (fabs.f64 (cbrt.f64 d))))))) (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 l))) (.f64 (sqrt.f64 (/.f64 (cbrt.f64 d) (cbrt.f64 h))) (fabs.f64 (cbrt.f64 d))))))) (.f64 (fabs.f64 (cbrt.f64 h)) (sqrt.f64 (.f64 (cbrt.f64 l) (cbrt.f64 l)))))
	41.5b	(/.f64 (.f64 (.f64 (sqrt.f64 d) (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 h))
	21.2b	(.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))
	38.7b	(/.f64 (.f64 (.f64 (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 (sqrt.f64 h) (sqrt.f64 l)))
	20.2b	(.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 (/.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))
	60.9b	(.f64 -1/8 (.f64 (/.f64 (*.f64 (pow.f64 D 2) (pow.f64 M 2)) d) (sqrt.f64 (/.f64 h (pow.f64 l 3)))))
	24.0b	(.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))) (cbrt.f64 (pow.f64 (fma.f64 (pow.f64 (/.f64 (.f64 D M) (.f64 2 d)) 2) (.f64 (/.f64 h l) -1/2) 1) 3)))
	50.0b	(.f64 (pow.f64 (pow.f64 d 2) 1/3) (.f64 (sqrt.f64 (/.f64 1 l)) (*.f64 (pow.f64 (/.f64 1 h) 1/6) (fabs.f64 (pow.f64 (/.f64 d h) 1/3)))))
	19.5b	(.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)
	50.0b	(/.f64 (.f64 (cbrt.f64 d) (.f64 (cbrt.f64 (.f64 d d)) (pow.f64 (/.f64 1 (.f64 h l)) 1/6))) (.f64 (fabs.f64 (cbrt.f64 h)) (sqrt.f64 (.f64 (cbrt.f64 l) (cbrt.f64 l)))))
	35.1b	(.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 (/.f64 (.f64 (.f64 D D) (.f64 (.f64 M M) h)) (.f64 (*.f64 d d) l)) -1/8 1))
	21.9b	(.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))
	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))
	16.5b	(/.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 l)))) (sqrt.f64 (cbrt.f64 (/.f64 d (cbrt.f64 l))))) (.f64 (sqrt.f64 (/.f64 (cbrt.f64 d) (cbrt.f64 h))) (fabs.f64 (cbrt.f64 d))))) (.f64 (fabs.f64 (cbrt.f64 h)) (sqrt.f64 (*.f64 (cbrt.f64 l) (cbrt.f64 l)))))
	20.9b	(.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))
	48.5b	(/.f64 (.f64 (.f64 (exp.f64 (.f64 1/6 (-.f64 (log.f64 (/.f64 1 l)) (log.f64 h)))) (fabs.f64 (pow.f64 d 1/3))) (pow.f64 (pow.f64 d 2) 1/3)) (.f64 (fabs.f64 (cbrt.f64 h)) (sqrt.f64 (*.f64 (cbrt.f64 l) (cbrt.f64 l)))))
	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))))
	21.8b	(.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))
	38.7b	(/.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)))
	48.3b	(/.f64 (.f64 (cbrt.f64 (.f64 d d)) (.f64 (cbrt.f64 d) (exp.f64 (fma.f64 (log.f64 h) -1/6 (.f64 (log.f64 l) -1/6))))) (.f64 (fabs.f64 (cbrt.f64 h)) (sqrt.f64 (.f64 (cbrt.f64 l) (cbrt.f64 l)))))

Compiler

Compiled 9365 to 3641 computations (61.1% saved)

regimes1.9s (11.9%)

Accuracy

Total 3.0b remaining (23.1%)

Threshold costs 0b (0%)

Counts

130 → 2

Compiler

Compiled 37074 to 24743 computations (33.3% saved)

bsearch9.0ms (0.1%)

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

simplify8.0ms (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	163
1	77	163
2	92	163
3	102	163
4	110	163
5	114	163
6	115	163
7	111	163

end582.0ms (3.6%)

Remove: (sort M D)
Compiler: Compiled 1464 to 906 computations (38.1% saved)

Details

analyze2.2s (13.7%)

sample5.8s (35.8%)

simplify34.0ms (0.2%)

prune4.0ms (0%)

localize21.0ms (0.1%)

series623.0ms (3.8%)

rewrite22.0ms (0.1%)

simplify136.0ms (0.8%)

prune188.0ms (1.1%)

localize25.0ms (0.2%)

series964.0ms (5.9%)

rewrite35.0ms (0.2%)

simplify155.0ms (0.9%)

prune203.0ms (1.2%)

localize35.0ms (0.2%)

series1.0s (6.2%)

rewrite54.0ms (0.3%)

simplify154.0ms (0.9%)

prune249.0ms (1.5%)

localize31.0ms (0.2%)

series1.3s (7.8%)

rewrite26.0ms (0.2%)

simplify255.0ms (1.6%)

prune185.0ms (1.1%)

regimes1.9s (11.9%)

bsearch9.0ms (0.1%)

simplify8.0ms (0.1%)

end582.0ms (3.6%)

Profiling