Details

analyze2.7s (11.8%)

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)

sample343.0ms (1.5%)

Algorithm

1×

intervals

Results

87.0ms	256×	body	128	valid
80.0ms	255×	body	128	nan
62.0ms	189×	body	128	invalid

Compiler

Compiled 86 to 68 computations (20.9% saved)

simplify55.0ms (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

prune8.0ms (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

26.7b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	26.7b	(.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))

Compiler

Compiled 128 to 88 computations (31.3% saved)

localize38.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	7.5b	(fma.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2) (*.f64 (/.f64 h l) -1/2) 1)
✓	7.9b	(.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))
✓	11.9b	(sqrt.f64 (/.f64 d l))
✓	12.4b	(sqrt.f64 (/.f64 d h))

rewrite115.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

24×	`sqrt-div_binary64`
24×	`add-sqr-sqrt_binary64`
21×	`add-cube-cbrt_binary64`
17×	`pow1_binary64`
14×	`add-exp-log_binary64`

Counts

4 → 163

Calls

4 calls:

32.0ms	(.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))
23.0ms	(sqrt.f64 (/.f64 d h))
23.0ms	(sqrt.f64 (/.f64 d l))
20.0ms	(fma.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2) (*.f64 (/.f64 h l) -1/2) 1)

series913.0ms (4%)

Counts

4 → 92

Calls

4 calls:

544.0ms	(.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))
315.0ms	(fma.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2) (*.f64 (/.f64 h l) -1/2) 1)
27.0ms	(sqrt.f64 (/.f64 d h))
26.0ms	(sqrt.f64 (/.f64 d l))

simplify363.0ms (1.6%)

Algorithm

1×	egg-herbie

Rules

486×	`fma-def_binary64`
447×	`times-frac_binary64`
407×	`fma-neg_binary64`
236×	`cancel-sign-sub-inv_binary64`
227×	`associate-l_binary64`

Counts

255 → 405

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	194	5787
1	460	5371
2	1867	5255
3	4721	5255
4	4999	5255
5	4982	5255

prune424.0ms (1.8%)

Pruning

17 alts after pruning (17 fresh and 0 done)

	Pruned	Kept	Total
New	388	17	405
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	389	17	406

Error

18.0b

Counts

406 → 17

Alt Table

Status	Error	Program
▶	26.6b	(+.f64 (.f64 (.f64 (sqrt.f64 (/.f64 d h)) (sqrt.f64 (/.f64 d l))) (.f64 (pow.f64 (/.f64 (.f64 D M) (.f64 2 d)) 2) (.f64 (/.f64 h l) -1/2))) (*.f64 (sqrt.f64 (/.f64 d h)) (sqrt.f64 (/.f64 d l))))
	28.9b	(.f64 (.f64 (sqrt.f64 (/.f64 d h)) (exp.f64 (.f64 (log.f64 (/.f64 d l)) 1/2))) (fma.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2) (.f64 (/.f64 h l) -1/2) 1))
	26.9b	(.f64 (.f64 (.f64 (cbrt.f64 (.f64 (sqrt.f64 (/.f64 d h)) (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))
	41.8b	(sqrt.f64 (.f64 (/.f64 d h) (.f64 (/.f64 d l) (pow.f64 (fma.f64 (pow.f64 (/.f64 (.f64 D M) (.f64 2 d)) 2) (*.f64 (/.f64 h l) -1/2) 1) 2))))
	27.2b	(pow.f64 (cbrt.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))) 3)
	45.7b	(/.f64 (.f64 (.f64 (/.f64 d h) (/.f64 d l)) (fma.f64 1/4 (.f64 (pow.f64 (/.f64 (.f64 D M) (.f64 2 d)) 4) (.f64 (/.f64 h l) (/.f64 h l))) -1)) (.f64 (sqrt.f64 (/.f64 d 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))))
	41.3b	(/.f64 1 (/.f64 (.f64 (sqrt.f64 h) (sqrt.f64 l)) (.f64 d (fma.f64 (pow.f64 (/.f64 (.f64 D M) (.f64 2 d)) 2) (*.f64 (/.f64 h l) -1/2) 1))))
	26.8b	(.f64 (.f64 (sqrt.f64 (/.f64 d h)) (.f64 (pow.f64 (/.f64 d l) 1/4) (pow.f64 (/.f64 d l) 1/4))) (fma.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2) (.f64 (/.f64 h l) -1/2) 1))
	41.1b	(.f64 (.f64 (sqrt.f64 (/.f64 d h)) (sqrt.f64 (/.f64 d l))) (fma.f64 -1/8 (/.f64 (.f64 (.f64 D D) (.f64 (.f64 M M) h)) (.f64 l (.f64 d d))) 1))
	32.0b	(.f64 (.f64 (sqrt.f64 (/.f64 d h)) (sqrt.f64 (/.f64 d l))) 1)
	45.8b	(.f64 (sqrt.f64 (/.f64 1 (.f64 l h))) d)
	41.3b	(/.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)))
	26.7b	(.f64 (.f64 (.f64 (pow.f64 (/.f64 d h) 1/4) (pow.f64 (/.f64 d h) 1/4)) (sqrt.f64 (/.f64 d l))) (fma.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2) (.f64 (/.f64 h l) -1/2) 1))
	43.2b	(.f64 (/.f64 d (sqrt.f64 h)) (/.f64 (fma.f64 (pow.f64 (/.f64 (.f64 D M) (.f64 2 d)) 2) (.f64 (/.f64 h l) -1/2) 1) (sqrt.f64 l)))
	38.5b	(.f64 (.f64 (pow.f64 (.f64 (.f64 (sqrt.f64 (/.f64 d h)) (sqrt.f64 (/.f64 d h))) (sqrt.f64 (/.f64 d h))) 1/3) (sqrt.f64 (/.f64 d l))) (fma.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2) (*.f64 (/.f64 h l) -1/2) 1))
	60.3b	(.f64 -1/8 (.f64 (/.f64 (*.f64 (pow.f64 D 2) (pow.f64 M 2)) d) (sqrt.f64 (/.f64 h (pow.f64 l 3)))))
	27.2b	(.f64 (.f64 (sqrt.f64 (/.f64 d h)) (.f64 (.f64 (cbrt.f64 (sqrt.f64 (/.f64 d l))) (cbrt.f64 (sqrt.f64 (/.f64 d l)))) (cbrt.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 7853 to 3752 computations (52.2% saved)

localize36.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
	11.9b	(sqrt.f64 (/.f64 d l))
	11.9b	(sqrt.f64 (/.f64 d l))
	12.4b	(sqrt.f64 (/.f64 d h))
	12.4b	(sqrt.f64 (/.f64 d h))

rewrite0.0ms (0%)

Algorithm

1×	rewrite-expression-head

Counts

0 → 0

series0.0ms (0%)

Counts: 0 → 0

simplify23.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

0 → 0

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	0	0
1	0	0

prune283.0ms (1.2%)

Pruning

17 alts after pruning (16 fresh and 1 done)

	Pruned	Kept	Total
New	285	0	285
Fresh	0	16	16
Picked	0	1	1
Done	0	0	0
Total	285	17	302

Error

18.0b

Counts

302 → 17

Alt Table

Status	Error	Program
✓	26.6b	(+.f64 (.f64 (.f64 (sqrt.f64 (/.f64 d h)) (sqrt.f64 (/.f64 d l))) (.f64 (pow.f64 (/.f64 (.f64 D M) (.f64 2 d)) 2) (.f64 (/.f64 h l) -1/2))) (*.f64 (sqrt.f64 (/.f64 d h)) (sqrt.f64 (/.f64 d l))))
	28.9b	(.f64 (.f64 (sqrt.f64 (/.f64 d h)) (exp.f64 (.f64 (log.f64 (/.f64 d l)) 1/2))) (fma.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2) (.f64 (/.f64 h l) -1/2) 1))
	26.9b	(.f64 (.f64 (.f64 (cbrt.f64 (.f64 (sqrt.f64 (/.f64 d h)) (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))
	41.8b	(sqrt.f64 (.f64 (/.f64 d h) (.f64 (/.f64 d l) (pow.f64 (fma.f64 (pow.f64 (/.f64 (.f64 D M) (.f64 2 d)) 2) (*.f64 (/.f64 h l) -1/2) 1) 2))))
	27.2b	(pow.f64 (cbrt.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))) 3)
	45.7b	(/.f64 (.f64 (.f64 (/.f64 d h) (/.f64 d l)) (fma.f64 1/4 (.f64 (pow.f64 (/.f64 (.f64 D M) (.f64 2 d)) 4) (.f64 (/.f64 h l) (/.f64 h l))) -1)) (.f64 (sqrt.f64 (/.f64 d 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))))
	41.3b	(/.f64 1 (/.f64 (.f64 (sqrt.f64 h) (sqrt.f64 l)) (.f64 d (fma.f64 (pow.f64 (/.f64 (.f64 D M) (.f64 2 d)) 2) (*.f64 (/.f64 h l) -1/2) 1))))
	26.8b	(.f64 (.f64 (sqrt.f64 (/.f64 d h)) (.f64 (pow.f64 (/.f64 d l) 1/4) (pow.f64 (/.f64 d l) 1/4))) (fma.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2) (.f64 (/.f64 h l) -1/2) 1))
	41.1b	(.f64 (.f64 (sqrt.f64 (/.f64 d h)) (sqrt.f64 (/.f64 d l))) (fma.f64 -1/8 (/.f64 (.f64 (.f64 D D) (.f64 (.f64 M M) h)) (.f64 l (.f64 d d))) 1))
	32.0b	(.f64 (.f64 (sqrt.f64 (/.f64 d h)) (sqrt.f64 (/.f64 d l))) 1)
	45.8b	(.f64 (sqrt.f64 (/.f64 1 (.f64 l h))) d)
	41.3b	(/.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)))
▶	26.7b	(.f64 (.f64 (.f64 (pow.f64 (/.f64 d h) 1/4) (pow.f64 (/.f64 d h) 1/4)) (sqrt.f64 (/.f64 d l))) (fma.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2) (.f64 (/.f64 h l) -1/2) 1))
	43.2b	(.f64 (/.f64 d (sqrt.f64 h)) (/.f64 (fma.f64 (pow.f64 (/.f64 (.f64 D M) (.f64 2 d)) 2) (.f64 (/.f64 h l) -1/2) 1) (sqrt.f64 l)))
	38.5b	(.f64 (.f64 (pow.f64 (.f64 (.f64 (sqrt.f64 (/.f64 d h)) (sqrt.f64 (/.f64 d h))) (sqrt.f64 (/.f64 d h))) 1/3) (sqrt.f64 (/.f64 d l))) (fma.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2) (*.f64 (/.f64 h l) -1/2) 1))
	60.3b	(.f64 -1/8 (.f64 (/.f64 (*.f64 (pow.f64 D 2) (pow.f64 M 2)) d) (sqrt.f64 (/.f64 h (pow.f64 l 3)))))
	27.2b	(.f64 (.f64 (sqrt.f64 (/.f64 d h)) (.f64 (.f64 (cbrt.f64 (sqrt.f64 (/.f64 d l))) (cbrt.f64 (sqrt.f64 (/.f64 d l)))) (cbrt.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 6388 to 2438 computations (61.8% saved)

localize40.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	7.9b	(.f64 (.f64 (.f64 (pow.f64 (/.f64 d h) 1/4) (pow.f64 (/.f64 d h) 1/4)) (sqrt.f64 (/.f64 d l))) (fma.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2) (.f64 (/.f64 h l) -1/2) 1))
	11.9b	(sqrt.f64 (/.f64 d l))
	12.6b	(pow.f64 (/.f64 d h) 1/4)
✓	12.6b	(pow.f64 (/.f64 d h) 1/4)

rewrite69.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

14×	`pow1_binary64`
12×	`add-sqr-sqrt_binary64`
12×	`add-cube-cbrt_binary64`
10×	`add-exp-log_binary64`
8×	`fma-udef_binary64`

Counts

2 → 86

Calls

2 calls:

33.0ms

(*.f64 (*.f64 (*.f64 (pow.f64 (/.f64 d h) 1/4) (pow.f64 (/.f64 d h) 1/4)) (sqrt.f64 (/.f64 d l))) (fma.f64 (pow.f64 (/.f64 (*.f64 M D) (*.f64 d 2)) 2) (*.f64 (/.f64 h l) -1/2) 1))

23.0ms

(pow.f64 (/.f64 d h) 1/4)

series1.9s (8.2%)

Counts

2 → 56

Calls

2 calls:

1.2s

(pow.f64 (/.f64 d h) 1/4)

663.0ms

(*.f64 (*.f64 (*.f64 (pow.f64 (/.f64 d h) 1/4) (pow.f64 (/.f64 d h) 1/4)) (sqrt.f64 (/.f64 d l))) (fma.f64 (pow.f64 (/.f64 (*.f64 M D) (*.f64 d 2)) 2) (*.f64 (/.f64 h l) -1/2) 1))

simplify302.0ms (1.3%)

Algorithm

1×	egg-herbie

Rules

540×	`fma-neg_binary64`
487×	`fma-def_binary64`
284×	`distribute-rgt-in_binary64`
220×	`cancel-sign-sub-inv_binary64`
218×	`associate-l_binary64`

Counts

142 → 239

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	163	3836
1	408	3328
2	1669	3247
3	4605	3247
4	5070	3247

prune445.0ms (1.9%)

Pruning

17 alts after pruning (15 fresh and 2 done)

	Pruned	Kept	Total
New	523	2	525
Fresh	2	13	15
Picked	0	1	1
Done	0	1	1
Total	525	17	542

Error

18.0b

Counts

542 → 17

Alt Table

Status	Error	Program
	26.9b	(.f64 (.f64 (.f64 (cbrt.f64 (.f64 (sqrt.f64 (/.f64 d h)) (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))
	41.8b	(sqrt.f64 (.f64 (/.f64 d h) (.f64 (/.f64 d l) (pow.f64 (fma.f64 (pow.f64 (/.f64 (.f64 D M) (.f64 2 d)) 2) (*.f64 (/.f64 h l) -1/2) 1) 2))))
	27.2b	(pow.f64 (cbrt.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))) 3)
✓	26.7b	(.f64 (.f64 (.f64 (pow.f64 (/.f64 d h) 1/4) (pow.f64 (/.f64 d h) 1/4)) (sqrt.f64 (/.f64 d l))) (fma.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2) (.f64 (/.f64 h l) -1/2) 1))
	26.9b	(.f64 (.f64 (.f64 (pow.f64 (/.f64 d h) 1/4) (pow.f64 (/.f64 d h) 1/4)) (.f64 (cbrt.f64 (/.f64 d l)) (cbrt.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))
	28.9b	(.f64 (.f64 (.f64 (pow.f64 (/.f64 d h) 1/4) (pow.f64 (/.f64 d h) 1/4)) (exp.f64 (.f64 (log.f64 (/.f64 d l)) 1/2))) (fma.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2) (*.f64 (/.f64 h l) -1/2) 1))
	60.3b	(.f64 -1/8 (.f64 (/.f64 (*.f64 (pow.f64 D 2) (pow.f64 M 2)) d) (sqrt.f64 (/.f64 h (pow.f64 l 3)))))
▶	26.8b	(.f64 (.f64 (sqrt.f64 (/.f64 d h)) (.f64 (pow.f64 (/.f64 d l) 1/4) (pow.f64 (/.f64 d l) 1/4))) (fma.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2) (.f64 (/.f64 h l) -1/2) 1))
	41.1b	(.f64 (.f64 (sqrt.f64 (/.f64 d h)) (sqrt.f64 (/.f64 d l))) (fma.f64 -1/8 (/.f64 (.f64 (.f64 D D) (.f64 (.f64 M M) h)) (.f64 l (.f64 d d))) 1))
✓	26.6b	(+.f64 (.f64 (.f64 (sqrt.f64 (/.f64 d h)) (sqrt.f64 (/.f64 d l))) (.f64 (pow.f64 (/.f64 (.f64 D M) (.f64 2 d)) 2) (.f64 (/.f64 h l) -1/2))) (*.f64 (sqrt.f64 (/.f64 d h)) (sqrt.f64 (/.f64 d l))))
	32.0b	(.f64 (.f64 (sqrt.f64 (/.f64 d h)) (sqrt.f64 (/.f64 d l))) 1)
	45.8b	(.f64 (sqrt.f64 (/.f64 1 (.f64 l h))) d)
	41.3b	(/.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)))
	43.2b	(.f64 (/.f64 d (sqrt.f64 h)) (/.f64 (fma.f64 (pow.f64 (/.f64 (.f64 D M) (.f64 2 d)) 2) (.f64 (/.f64 h l) -1/2) 1) (sqrt.f64 l)))
	38.5b	(.f64 (.f64 (pow.f64 (.f64 (.f64 (sqrt.f64 (/.f64 d h)) (sqrt.f64 (/.f64 d h))) (sqrt.f64 (/.f64 d h))) 1/3) (sqrt.f64 (/.f64 d l))) (fma.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2) (*.f64 (/.f64 h l) -1/2) 1))
	41.3b	(/.f64 1 (/.f64 (.f64 (sqrt.f64 h) (sqrt.f64 l)) (.f64 d (fma.f64 (pow.f64 (/.f64 (.f64 D M) (.f64 2 d)) 2) (*.f64 (/.f64 h l) -1/2) 1))))
	27.2b	(.f64 (.f64 (sqrt.f64 (/.f64 d h)) (.f64 (.f64 (cbrt.f64 (sqrt.f64 (/.f64 d l))) (cbrt.f64 (sqrt.f64 (/.f64 d l)))) (cbrt.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 8754 to 4565 computations (47.9% saved)

localize42.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	7.9b	(.f64 (.f64 (sqrt.f64 (/.f64 d h)) (.f64 (pow.f64 (/.f64 d l) 1/4) (pow.f64 (/.f64 d l) 1/4))) (fma.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2) (.f64 (/.f64 h l) -1/2) 1))
	12.1b	(pow.f64 (/.f64 d l) 1/4)
✓	12.1b	(pow.f64 (/.f64 d l) 1/4)
	12.4b	(sqrt.f64 (/.f64 d h))

rewrite87.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

14×	`pow1_binary64`
12×	`add-sqr-sqrt_binary64`
12×	`add-cube-cbrt_binary64`
10×	`associate-*l/_binary64`
10×	`add-exp-log_binary64`

Counts

2 → 86

Calls

2 calls:

48.0ms

(*.f64 (*.f64 (sqrt.f64 (/.f64 d h)) (*.f64 (pow.f64 (/.f64 d l) 1/4) (pow.f64 (/.f64 d l) 1/4))) (fma.f64 (pow.f64 (/.f64 (*.f64 M D) (*.f64 d 2)) 2) (*.f64 (/.f64 h l) -1/2) 1))

24.0ms

(pow.f64 (/.f64 d l) 1/4)

series1.8s (7.6%)

Counts

2 → 56

Calls

2 calls:

1.2s

(pow.f64 (/.f64 d l) 1/4)

530.0ms

(*.f64 (*.f64 (sqrt.f64 (/.f64 d h)) (*.f64 (pow.f64 (/.f64 d l) 1/4) (pow.f64 (/.f64 d l) 1/4))) (fma.f64 (pow.f64 (/.f64 (*.f64 M D) (*.f64 d 2)) 2) (*.f64 (/.f64 h l) -1/2) 1))

simplify212.0ms (0.9%)

Algorithm

1×	egg-herbie

Rules

518×	`fma-neg_binary64`
480×	`fma-def_binary64`
288×	`distribute-rgt-in_binary64`
220×	`cancel-sign-sub-inv_binary64`
215×	`associate-l_binary64`

Counts

142 → 239

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	163	3837
1	408	3328
2	1673	3247
3	4662	3247
4	4967	3247

prune395.0ms (1.7%)

Pruning

19 alts after pruning (17 fresh and 2 done)

	Pruned	Kept	Total
New	515	6	521
Fresh	3	11	14
Picked	0	1	1
Done	1	1	2
Total	519	19	538

Error

17.9b

Counts

538 → 19

Alt Table

Status	Error	Program
	27.2b	(.f64 (.f64 (sqrt.f64 (/.f64 d h)) (.f64 (pow.f64 (cbrt.f64 (pow.f64 (/.f64 d l) 1/4)) 3) (pow.f64 (/.f64 d l) 1/4))) (fma.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2) (.f64 (/.f64 h l) -1/2) 1))
✓	26.8b	(.f64 (.f64 (sqrt.f64 (/.f64 d h)) (.f64 (pow.f64 (/.f64 d l) 1/4) (pow.f64 (/.f64 d l) 1/4))) (fma.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2) (.f64 (/.f64 h l) -1/2) 1))
	44.9b	(.f64 (.f64 (sqrt.f64 (/.f64 d h)) (.f64 (exp.f64 (.f64 1/4 (+.f64 (log.f64 (/.f64 -1 l)) (log.f64 (neg.f64 d))))) (pow.f64 (/.f64 d l) 1/4))) (fma.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2) (*.f64 (/.f64 h l) -1/2) 1))
	41.1b	(.f64 (.f64 (sqrt.f64 (/.f64 d h)) (sqrt.f64 (/.f64 d l))) (fma.f64 -1/8 (/.f64 (.f64 (.f64 D D) (.f64 (.f64 M M) h)) (.f64 l (.f64 d d))) 1))
	43.9b	(/.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 d))) (sqrt.f64 h))
✓	26.6b	(+.f64 (.f64 (.f64 (sqrt.f64 (/.f64 d h)) (sqrt.f64 (/.f64 d l))) (.f64 (pow.f64 (/.f64 (.f64 D M) (.f64 2 d)) 2) (.f64 (/.f64 h l) -1/2))) (*.f64 (sqrt.f64 (/.f64 d h)) (sqrt.f64 (/.f64 d l))))
	43.7b	(/.f64 (.f64 (sqrt.f64 d) (.f64 (pow.f64 (/.f64 d l) 1/4) (pow.f64 (/.f64 d l) 1/4))) (/.f64 (sqrt.f64 h) (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)
	41.8b	(sqrt.f64 (.f64 (/.f64 d h) (.f64 (/.f64 d l) (pow.f64 (fma.f64 (pow.f64 (/.f64 (.f64 D M) (.f64 2 d)) 2) (*.f64 (/.f64 h l) -1/2) 1) 2))))
	27.2b	(pow.f64 (cbrt.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))) 3)
	57.7b	(.f64 (.f64 (sqrt.f64 (/.f64 d h)) (.f64 (log.f64 (exp.f64 (pow.f64 (/.f64 d l) 1/4))) (pow.f64 (/.f64 d l) 1/4))) (fma.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2) (.f64 (/.f64 h l) -1/2) 1))
	27.2b	(.f64 (.f64 (sqrt.f64 (/.f64 d h)) (.f64 (.f64 (cbrt.f64 (sqrt.f64 (/.f64 d l))) (cbrt.f64 (sqrt.f64 (/.f64 d l)))) (cbrt.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))
	45.8b	(.f64 (sqrt.f64 (/.f64 1 (.f64 l h))) d)
	41.3b	(/.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)))
	27.0b	(.f64 (.f64 (.f64 (cbrt.f64 (/.f64 d h)) (cbrt.f64 (sqrt.f64 (/.f64 d h)))) (.f64 (pow.f64 (/.f64 d l) 1/4) (pow.f64 (/.f64 d l) 1/4))) (fma.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2) (*.f64 (/.f64 h l) -1/2) 1))
	26.9b	(.f64 (.f64 (.f64 (pow.f64 (/.f64 d h) 1/4) (pow.f64 (/.f64 d h) 1/4)) (.f64 (cbrt.f64 (/.f64 d l)) (cbrt.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))
	43.2b	(.f64 (/.f64 d (sqrt.f64 h)) (/.f64 (fma.f64 (pow.f64 (/.f64 (.f64 D M) (.f64 2 d)) 2) (.f64 (/.f64 h l) -1/2) 1) (sqrt.f64 l)))
	60.3b	(.f64 -1/8 (.f64 (/.f64 (*.f64 (pow.f64 D 2) (pow.f64 M 2)) d) (sqrt.f64 (/.f64 h (pow.f64 l 3)))))
	41.3b	(/.f64 1 (/.f64 (.f64 (sqrt.f64 h) (sqrt.f64 l)) (.f64 d (fma.f64 (pow.f64 (/.f64 (.f64 D M) (.f64 2 d)) 2) (*.f64 (/.f64 h l) -1/2) 1))))

Compiler

Compiled 8289 to 4265 computations (48.5% saved)

regimes3.5s (15.4%)

Accuracy

Total 4.7b remaining (21.6%)

Threshold costs 0b (0%)

Compiler

Compiled 43490 to 30261 computations (30.4% saved)

bsearch1.3s (5.8%)

Steps

Iters	Range		Point
11	2.1033922180519267e-281	1.944013045056867e-249	1.062904038339468e-264

Compiler

Compiled 6 to 5 computations (16.7% saved)

simplify9.0ms (0%)

Algorithm

1×	egg-herbie

Rules

6×	`*-commutative_binary64`
1×	`1-exp_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	33	88
1	41	88
2	40	88

end22.0ms (0.1%)

Remove: (sort M D)
Compiler: Compiled 189 to 123 computations (34.9% saved)

sample7.6s (32.8%)

Algorithm

1×

intervals

Results

2.2s	8000×	body	128	valid
2.1s	8394×	body	128	nan
1.3s	4784×	body	128	invalid

Compiler

Compiled 759 to 525 computations (30.8% saved)

Details

analyze2.7s (11.8%)

sample343.0ms (1.5%)

simplify55.0ms (0.2%)

prune8.0ms (0%)

localize38.0ms (0.2%)

rewrite115.0ms (0.5%)

series913.0ms (4%)

simplify363.0ms (1.6%)

prune424.0ms (1.8%)

localize36.0ms (0.2%)

rewrite0.0ms (0%)

series0.0ms (0%)

simplify23.0ms (0.1%)

prune283.0ms (1.2%)

localize40.0ms (0.2%)

rewrite69.0ms (0.3%)

series1.9s (8.2%)

simplify302.0ms (1.3%)

prune445.0ms (1.9%)

localize42.0ms (0.2%)

rewrite87.0ms (0.4%)

series1.8s (7.6%)

simplify212.0ms (0.9%)

prune395.0ms (1.7%)

regimes3.5s (15.4%)

bsearch1.3s (5.8%)

simplify9.0ms (0%)

end22.0ms (0.1%)

sample7.6s (32.8%)

Profiling