Details

analyze2.0s (12.3%)

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)

sample154.0ms (0.9%)

Algorithm

1×

intervals

Results

36.0ms	256×	body	128	valid
34.0ms	281×	body	128	nan
23.0ms	158×	body	128	invalid

Compiler

Compiled 86 to 68 computations (20.9% saved)

simplify38.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

679×	`distribute-neg-frac_binary64`
437×	`*-commutative_binary64`
425×	`associate-/l*_binary64`
347×	`cancel-sign-sub-inv_binary64`
263×	`associate-/l/_binary64`

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	24	41
1	62	41
2	188	41
3	1060	41
4	3490	41
5	5207	41

prune6.0ms (0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

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

Error

26.5b

Counts

2 → 1

Alt Table

Status	Error	Program
▶	26.5b	(.f64 (.f64 (sqrt.f64 (/.f64 d h)) (sqrt.f64 (/.f64 d l))) (-.f64 1 (.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2)) (/.f64 h l))))

Compiler

Compiled 96 to 69 computations (28.1% saved)

localize25.0ms (0.2%)

Local error

Found 4 expressions with local error:

6.7b	(.f64 (.f64 (sqrt.f64 (/.f64 d h)) (sqrt.f64 (/.f64 d l))) (-.f64 1 (.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2)) (/.f64 h l))))
10.9b	(sqrt.f64 (/.f64 d h))
11.3b	(.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2)) (/.f64 h l))
11.9b	(sqrt.f64 (/.f64 d l))

rewrite353.0ms (2.2%)

Algorithm

1×	rewrite-expression-head

Error

12.7b

Rules

77×	`add-exp-log_binary64`
41×	`prod-exp_binary64`
32×	`add-sqr-sqrt_binary64`
29×	`times-frac_binary64`
26×	`*-un-lft-identity_binary64`

Counts

4 → 127

Calls

4 calls:

17.0ms	(.f64 (.f64 (sqrt.f64 (/.f64 d h)) (sqrt.f64 (/.f64 d l))) (-.f64 1 (.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2)) (/.f64 h l))))
11.0ms	(.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2)) (/.f64 h l))
3.0ms	(sqrt.f64 (/.f64 d l))
3.0ms	(sqrt.f64 (/.f64 d h))

Compiler

Compiled 4719 to 2207 computations (53.2% saved)

series359.0ms (2.2%)

Error

17.0b

Counts

4 → 50

Calls

4 calls:

197.0ms	(.f64 (.f64 (sqrt.f64 (/.f64 d h)) (sqrt.f64 (/.f64 d l))) (-.f64 1 (.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2)) (/.f64 h l))))
116.0ms	(.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2)) (/.f64 h l))
19.0ms	(sqrt.f64 (/.f64 d l))
18.0ms	(sqrt.f64 (/.f64 d h))

Compiler

Compiled 3123 to 2317 computations (25.8% saved)

simplify164.0ms (1%)

Algorithm

1×	egg-herbie

Rules

383×	`associate-l_binary64`
313×	`associate-r_binary64`
302×	`distribute-rgt-in_binary64`
278×	`distribute-lft-in_binary64`
200×	`*-commutative_binary64`

Counts

177 → 111

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	332	4611
1	760	4377
2	2817	4371
3	4778	4371
4	4982	4371

prune132.0ms (0.8%)

Pruning

17 alts after pruning (17 fresh and 0 done)

	Pruned	Kept	Total
New	94	17	111
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	95	17	112

Error

12.0b

Counts

112 → 17

Alt Table

Status	Error	Program
	22.7b	(.f64 (.f64 (sqrt.f64 (/.f64 d h)) (.f64 (fabs.f64 (cbrt.f64 d)) (sqrt.f64 (/.f64 (cbrt.f64 d) l)))) (-.f64 1 (.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (*.f64 d 2)) 2)) (/.f64 h l))))
	25.0b	(.f64 (.f64 (sqrt.f64 (/.f64 d h)) (sqrt.f64 (/.f64 d l))) (-.f64 1 (.f64 (.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2)) (.f64 (cbrt.f64 h) (cbrt.f64 h))) (/.f64 (cbrt.f64 h) l))))
	40.8b	(/.f64 (.f64 d (-.f64 1 (pow.f64 (.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2)) (/.f64 h l)) 3))) (.f64 (.f64 (sqrt.f64 l) (sqrt.f64 h)) (+.f64 1 (.f64 (/.f64 h l) (+.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2)) (.f64 (/.f64 h l) (.f64 1/4 (pow.f64 (/.f64 (.f64 M D) (*.f64 d 2)) 4))))))))
	44.6b	(cbrt.f64 (pow.f64 (.f64 (.f64 (sqrt.f64 (/.f64 d l)) (sqrt.f64 (/.f64 d h))) (-.f64 1 (.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2)) (/.f64 h l)))) 3))
	22.6b	(.f64 (.f64 (.f64 (fabs.f64 (/.f64 1 (cbrt.f64 h))) (sqrt.f64 (/.f64 d (cbrt.f64 h)))) (sqrt.f64 (/.f64 d l))) (-.f64 1 (.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (*.f64 d 2)) 2)) (/.f64 h l))))
	26.8b	(.f64 (.f64 (sqrt.f64 (/.f64 d h)) (.f64 (fabs.f64 (cbrt.f64 (/.f64 d l))) (sqrt.f64 (cbrt.f64 (/.f64 d l))))) (-.f64 1 (.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (*.f64 d 2)) 2)) (/.f64 h l))))
	22.1b	(.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))))) (-.f64 1 (.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (*.f64 d 2)) 2)) (/.f64 h l))))
	40.4b	(/.f64 (.f64 (-.f64 1 (.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2)) (/.f64 h l))) (.f64 (sqrt.f64 d) (sqrt.f64 (/.f64 d h)))) (sqrt.f64 l))
▶	21.7b	(.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))) (-.f64 1 (.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (*.f64 d 2)) 2)) (/.f64 h l))))
	48.7b	(+.f64 (.f64 -1/8 (.f64 (/.f64 (.f64 (.f64 M M) (.f64 D D)) d) (sqrt.f64 (/.f64 h (pow.f64 l 3))))) (.f64 d (sqrt.f64 (/.f64 1 (*.f64 l h)))))
	23.8b	(.f64 (.f64 (.f64 (fabs.f64 (cbrt.f64 d)) (sqrt.f64 (/.f64 (cbrt.f64 d) h))) (sqrt.f64 (/.f64 d l))) (-.f64 1 (.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (*.f64 d 2)) 2)) (/.f64 h l))))
	37.1b	(/.f64 (.f64 d (-.f64 1 (.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2)) (/.f64 h l)))) (.f64 (sqrt.f64 h) (sqrt.f64 l)))
	41.0b	(.f64 (.f64 (sqrt.f64 (/.f64 d h)) (sqrt.f64 (/.f64 d l))) (-.f64 1 (.f64 1/8 (/.f64 (.f64 (.f64 M M) (.f64 (.f64 D D) h)) (.f64 l (*.f64 d d))))))
	33.2b	(.f64 (.f64 (sqrt.f64 (/.f64 d h)) (cbrt.f64 (pow.f64 (sqrt.f64 (/.f64 d l)) 3))) (-.f64 1 (.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2)) (/.f64 h l))))
	37.4b	(.f64 (.f64 (cbrt.f64 (pow.f64 (sqrt.f64 (/.f64 d h)) 3)) (sqrt.f64 (/.f64 d l))) (-.f64 1 (.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2)) (/.f64 h l))))
	42.3b	(.f64 (.f64 (sqrt.f64 (/.f64 d h)) (sqrt.f64 (/.f64 d l))) (-.f64 1 (.f64 (/.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2)) (sqrt.f64 l)) (/.f64 h (sqrt.f64 l)))))
	34.5b	(.f64 (.f64 (sqrt.f64 (/.f64 d h)) (sqrt.f64 (/.f64 d l))) (-.f64 1 (log.f64 (sqrt.f64 (pow.f64 (exp.f64 (/.f64 h l)) (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2))))))

Compiler

Compiled 3123 to 1784 computations (42.9% saved)

localize29.0ms (0.2%)

Local error

Found 4 expressions with local error:

4.5b	(/.f64 (.f64 M D) (.f64 d 2))
6.7b	(.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))) (-.f64 1 (.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (*.f64 d 2)) 2)) (/.f64 h l))))
11.3b	(.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2)) (/.f64 h l))
11.9b	(sqrt.f64 (/.f64 d l))

rewrite331.0ms (2%)

Algorithm

1×	rewrite-expression-head

Error

9.7b

Rules

93×	`add-exp-log_binary64`
48×	`prod-exp_binary64`
37×	`add-cbrt-cube_binary64`
29×	`frac-times_binary64`
25×	`sqrt-div_binary64`

Counts

4 → 138

Calls

4 calls:

35.0ms	(.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))) (-.f64 1 (.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (*.f64 d 2)) 2)) (/.f64 h l))))
11.0ms	(.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2)) (/.f64 h l))
6.0ms	(/.f64 (.f64 M D) (.f64 d 2))
3.0ms	(sqrt.f64 (/.f64 d l))

Compiler

Compiled 6784 to 2606 computations (61.6% saved)

series553.0ms (3.4%)

Error

11.7b

Counts

4 → 51

Calls

4 calls:

354.0ms	(.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))) (-.f64 1 (.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (*.f64 d 2)) 2)) (/.f64 h l))))
121.0ms	(.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2)) (/.f64 h l))
40.0ms	(/.f64 (.f64 M D) (.f64 d 2))
21.0ms	(sqrt.f64 (/.f64 d l))

Compiler

Compiled 4989 to 3652 computations (26.8% saved)

simplify178.0ms (1.1%)

Algorithm

1×	egg-herbie

Rules

786×	`associate-l_binary64`
624×	`associate-r_binary64`
210×	`times-frac_binary64`
178×	`associate-/l*_binary64`
151×	`associate-*r/_binary64`

Counts

189 → 133

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	423	7221
1	1111	6407
2	4617	6406
3	4980	6406

prune164.0ms (1%)

Pruning

22 alts after pruning (22 fresh and 0 done)

	Pruned	Kept	Total
New	123	10	133
Fresh	4	12	16
Picked	1	0	1
Done	0	0	0
Total	128	22	150

Error

10.3b

Counts

150 → 22

Alt Table

Status	Error	Program
	21.4b	(.f64 (.f64 (.f64 (fabs.f64 (/.f64 (cbrt.f64 d) (cbrt.f64 h))) (sqrt.f64 (/.f64 (cbrt.f64 d) (cbrt.f64 h)))) (sqrt.f64 (/.f64 d l))) (-.f64 1 (.f64 (*.f64 1/2 (pow.f64 (/.f64 M (/.f64 d (/.f64 D 2))) 2)) (/.f64 h l))))
	22.7b	(.f64 (.f64 (sqrt.f64 (/.f64 d h)) (.f64 (fabs.f64 (cbrt.f64 d)) (sqrt.f64 (/.f64 (cbrt.f64 d) l)))) (-.f64 1 (.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (*.f64 d 2)) 2)) (/.f64 h l))))
	25.0b	(.f64 (.f64 (sqrt.f64 (/.f64 d h)) (sqrt.f64 (/.f64 d l))) (-.f64 1 (.f64 (.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2)) (.f64 (cbrt.f64 h) (cbrt.f64 h))) (/.f64 (cbrt.f64 h) l))))
	27.8b	(.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))) (-.f64 1 (log.f64 (pow.f64 (sqrt.f64 (exp.f64 (pow.f64 (/.f64 (.f64 M D) (*.f64 d 2)) 2))) (/.f64 h l)))))
	21.8b	(.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))))) (-.f64 1 (.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2)) (/.f64 h l))))
	44.6b	(cbrt.f64 (pow.f64 (.f64 (.f64 (sqrt.f64 (/.f64 d l)) (sqrt.f64 (/.f64 d h))) (-.f64 1 (.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2)) (/.f64 h l)))) 3))
	21.7b	(.f64 (.f64 (sqrt.f64 (/.f64 d l)) (pow.f64 (sqrt.f64 (/.f64 (cbrt.f64 d) (cbrt.f64 h))) 3)) (-.f64 1 (.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2)) (/.f64 h l))))
	22.6b	(.f64 (.f64 (.f64 (fabs.f64 (/.f64 1 (cbrt.f64 h))) (sqrt.f64 (/.f64 d (cbrt.f64 h)))) (sqrt.f64 (/.f64 d l))) (-.f64 1 (.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (*.f64 d 2)) 2)) (/.f64 h l))))
	26.8b	(.f64 (.f64 (sqrt.f64 (/.f64 d h)) (.f64 (fabs.f64 (cbrt.f64 (/.f64 d l))) (sqrt.f64 (cbrt.f64 (/.f64 d l))))) (-.f64 1 (.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (*.f64 d 2)) 2)) (/.f64 h l))))
▶	17.8b	(.f64 (.f64 (.f64 (fabs.f64 (/.f64 (cbrt.f64 d) (cbrt.f64 h))) (sqrt.f64 (/.f64 (cbrt.f64 d) (cbrt.f64 h)))) (.f64 (fabs.f64 (cbrt.f64 d)) (sqrt.f64 (/.f64 (cbrt.f64 d) l)))) (-.f64 1 (.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2)) (/.f64 h l))))
	22.1b	(.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))))) (-.f64 1 (.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (*.f64 d 2)) 2)) (/.f64 h l))))
	49.9b	(.f64 (cbrt.f64 (.f64 d d)) (.f64 (pow.f64 (/.f64 1 h) 1/6) (.f64 (cbrt.f64 (/.f64 d h)) (sqrt.f64 (/.f64 1 l)))))
	21.9b	(.f64 (.f64 (cbrt.f64 (.f64 (.f64 (sqrt.f64 (/.f64 d l)) (pow.f64 (sqrt.f64 (/.f64 (cbrt.f64 d) (cbrt.f64 h))) 3)) (-.f64 1 (.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2)) (/.f64 h l))))) (cbrt.f64 (.f64 (.f64 (sqrt.f64 (/.f64 d l)) (pow.f64 (sqrt.f64 (/.f64 (cbrt.f64 d) (cbrt.f64 h))) 3)) (-.f64 1 (.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2)) (/.f64 h l)))))) (cbrt.f64 (.f64 (.f64 (sqrt.f64 (/.f64 d l)) (pow.f64 (sqrt.f64 (/.f64 (cbrt.f64 d) (cbrt.f64 h))) 3)) (-.f64 1 (.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2)) (/.f64 h l))))))
	21.5b	(/.f64 (.f64 (-.f64 1 (.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2)) (/.f64 h l))) (.f64 (sqrt.f64 (/.f64 d l)) (*.f64 (fabs.f64 (cbrt.f64 d)) (sqrt.f64 (/.f64 (cbrt.f64 d) (cbrt.f64 h)))))) (fabs.f64 (cbrt.f64 h)))
	48.7b	(+.f64 (.f64 -1/8 (.f64 (/.f64 (.f64 (.f64 M M) (.f64 D D)) d) (sqrt.f64 (/.f64 h (pow.f64 l 3))))) (.f64 d (sqrt.f64 (/.f64 1 (*.f64 l h)))))
	23.8b	(.f64 (.f64 (.f64 (fabs.f64 (cbrt.f64 d)) (sqrt.f64 (/.f64 (cbrt.f64 d) h))) (sqrt.f64 (/.f64 d l))) (-.f64 1 (.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (*.f64 d 2)) 2)) (/.f64 h l))))
	37.1b	(/.f64 (.f64 d (-.f64 1 (.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2)) (/.f64 h l)))) (.f64 (sqrt.f64 h) (sqrt.f64 l)))
	41.0b	(.f64 (.f64 (sqrt.f64 (/.f64 d h)) (sqrt.f64 (/.f64 d l))) (-.f64 1 (.f64 1/8 (/.f64 (.f64 (.f64 M M) (.f64 (.f64 D D) h)) (.f64 l (*.f64 d d))))))
	37.4b	(/.f64 (.f64 (-.f64 1 (.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2)) (/.f64 h l))) (.f64 (sqrt.f64 d) (.f64 (fabs.f64 (cbrt.f64 d)) (sqrt.f64 (cbrt.f64 d))))) (.f64 (*.f64 (fabs.f64 (cbrt.f64 h)) (sqrt.f64 (cbrt.f64 h))) (sqrt.f64 l)))
	41.6b	(/.f64 (.f64 (-.f64 1 (pow.f64 (.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2)) (/.f64 h l)) 3)) (.f64 (sqrt.f64 d) (.f64 (/.f64 (cbrt.f64 d) (cbrt.f64 h)) (sqrt.f64 (cbrt.f64 d))))) (.f64 (+.f64 1 (.f64 (/.f64 h l) (+.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2)) (.f64 (/.f64 h l) (.f64 1/4 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 4)))))) (*.f64 (sqrt.f64 l) (sqrt.f64 (cbrt.f64 h)))))
	33.2b	(.f64 (.f64 (sqrt.f64 (/.f64 d h)) (cbrt.f64 (pow.f64 (sqrt.f64 (/.f64 d l)) 3))) (-.f64 1 (.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2)) (/.f64 h l))))
	34.5b	(.f64 (.f64 (sqrt.f64 (/.f64 d h)) (sqrt.f64 (/.f64 d l))) (-.f64 1 (log.f64 (sqrt.f64 (pow.f64 (exp.f64 (/.f64 h l)) (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2))))))

Compiler

Compiled 4851 to 2556 computations (47.3% saved)

localize34.0ms (0.2%)

Local error

Found 4 expressions with local error:

3.2b	(sqrt.f64 (/.f64 (cbrt.f64 d) l))
4.5b	(/.f64 (.f64 M D) (.f64 d 2))
6.7b	(.f64 (.f64 (.f64 (fabs.f64 (/.f64 (cbrt.f64 d) (cbrt.f64 h))) (sqrt.f64 (/.f64 (cbrt.f64 d) (cbrt.f64 h)))) (.f64 (fabs.f64 (cbrt.f64 d)) (sqrt.f64 (/.f64 (cbrt.f64 d) l)))) (-.f64 1 (.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2)) (/.f64 h l))))
11.3b	(.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2)) (/.f64 h l))

rewrite346.0ms (2.1%)

Algorithm

1×	rewrite-expression-head

Error

7.6b

Rules

102×	`add-exp-log_binary64`
55×	`prod-exp_binary64`
46×	`add-cbrt-cube_binary64`
30×	`times-frac_binary64`
30×	`add-sqr-sqrt_binary64`

Counts

4 → 154

Calls

4 calls:

40.0ms	(.f64 (.f64 (.f64 (fabs.f64 (/.f64 (cbrt.f64 d) (cbrt.f64 h))) (sqrt.f64 (/.f64 (cbrt.f64 d) (cbrt.f64 h)))) (.f64 (fabs.f64 (cbrt.f64 d)) (sqrt.f64 (/.f64 (cbrt.f64 d) l)))) (-.f64 1 (.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2)) (/.f64 h l))))
11.0ms	(.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2)) (/.f64 h l))
6.0ms	(/.f64 (.f64 M D) (.f64 d 2))
4.0ms	(sqrt.f64 (/.f64 (cbrt.f64 d) l))

Compiler

Compiled 8383 to 2912 computations (65.3% saved)

series619.0ms (3.8%)

Error

9.1b

Counts

4 → 51

Calls

4 calls:

391.0ms	(.f64 (.f64 (.f64 (fabs.f64 (/.f64 (cbrt.f64 d) (cbrt.f64 h))) (sqrt.f64 (/.f64 (cbrt.f64 d) (cbrt.f64 h)))) (.f64 (fabs.f64 (cbrt.f64 d)) (sqrt.f64 (/.f64 (cbrt.f64 d) l)))) (-.f64 1 (.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2)) (/.f64 h l))))
126.0ms	(.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2)) (/.f64 h l))
38.0ms	(/.f64 (.f64 M D) (.f64 d 2))
37.0ms	(sqrt.f64 (/.f64 (cbrt.f64 d) l))

Compiler

Compiled 5814 to 4165 computations (28.4% saved)

simplify198.0ms (1.2%)

Algorithm

1×	egg-herbie

Rules

503×	`*-commutative_binary64`
378×	`distribute-rgt-in_binary64`
204×	`times-frac_binary64`
174×	`associate-/l*_binary64`
172×	`distribute-rgt-neg-in_binary64`

Counts

205 → 169

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	470	8786
1	1242	7405
2	3273	7336
3	5012	7336

prune205.0ms (1.3%)

Pruning

26 alts after pruning (26 fresh and 0 done)

	Pruned	Kept	Total
New	162	7	169
Fresh	2	19	21
Picked	1	0	1
Done	0	0	0
Total	165	26	191

Error

9.1b

Counts

191 → 26

Alt Table

Status	Error	Program
	21.4b	(.f64 (.f64 (.f64 (fabs.f64 (/.f64 (cbrt.f64 d) (cbrt.f64 h))) (sqrt.f64 (/.f64 (cbrt.f64 d) (cbrt.f64 h)))) (sqrt.f64 (/.f64 d l))) (-.f64 1 (.f64 (*.f64 1/2 (pow.f64 (/.f64 M (/.f64 d (/.f64 D 2))) 2)) (/.f64 h l))))
	22.7b	(.f64 (.f64 (sqrt.f64 (/.f64 d h)) (.f64 (fabs.f64 (cbrt.f64 d)) (sqrt.f64 (/.f64 (cbrt.f64 d) l)))) (-.f64 1 (.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (*.f64 d 2)) 2)) (/.f64 h l))))
	25.0b	(.f64 (.f64 (sqrt.f64 (/.f64 d h)) (sqrt.f64 (/.f64 d l))) (-.f64 1 (.f64 (.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2)) (.f64 (cbrt.f64 h) (cbrt.f64 h))) (/.f64 (cbrt.f64 h) l))))
	27.8b	(.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))) (-.f64 1 (log.f64 (pow.f64 (sqrt.f64 (exp.f64 (pow.f64 (/.f64 (.f64 M D) (*.f64 d 2)) 2))) (/.f64 h l)))))
	44.6b	(cbrt.f64 (pow.f64 (.f64 (.f64 (sqrt.f64 (/.f64 d l)) (sqrt.f64 (/.f64 d h))) (-.f64 1 (.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2)) (/.f64 h l)))) 3))
	21.7b	(.f64 (.f64 (sqrt.f64 (/.f64 d l)) (pow.f64 (sqrt.f64 (/.f64 (cbrt.f64 d) (cbrt.f64 h))) 3)) (-.f64 1 (.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2)) (/.f64 h l))))
	22.6b	(.f64 (.f64 (.f64 (fabs.f64 (/.f64 1 (cbrt.f64 h))) (sqrt.f64 (/.f64 d (cbrt.f64 h)))) (sqrt.f64 (/.f64 d l))) (-.f64 1 (.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (*.f64 d 2)) 2)) (/.f64 h l))))
	26.8b	(.f64 (.f64 (sqrt.f64 (/.f64 d h)) (.f64 (fabs.f64 (cbrt.f64 (/.f64 d l))) (sqrt.f64 (cbrt.f64 (/.f64 d l))))) (-.f64 1 (.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (*.f64 d 2)) 2)) (/.f64 h l))))
	17.9b	(.f64 (.f64 (.f64 (fabs.f64 (/.f64 (cbrt.f64 d) (cbrt.f64 h))) (sqrt.f64 (/.f64 (cbrt.f64 d) (cbrt.f64 h)))) (.f64 (fabs.f64 (cbrt.f64 d)) (.f64 (fabs.f64 (cbrt.f64 (/.f64 (cbrt.f64 d) l))) (sqrt.f64 (cbrt.f64 (/.f64 (cbrt.f64 d) l)))))) (-.f64 1 (.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (*.f64 d 2)) 2)) (/.f64 h l))))
	22.1b	(.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))))) (-.f64 1 (.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (*.f64 d 2)) 2)) (/.f64 h l))))
	34.4b	(.f64 (.f64 (.f64 (fabs.f64 (/.f64 (cbrt.f64 d) (cbrt.f64 h))) (sqrt.f64 (/.f64 (cbrt.f64 d) (cbrt.f64 h)))) (.f64 (fabs.f64 (cbrt.f64 d)) (sqrt.f64 (/.f64 (cbrt.f64 d) l)))) (-.f64 1 (.f64 1/8 (/.f64 (.f64 (.f64 M M) (.f64 (.f64 D D) h)) (.f64 (*.f64 d d) l)))))
	49.9b	(.f64 (cbrt.f64 (.f64 d d)) (.f64 (pow.f64 (/.f64 1 h) 1/6) (.f64 (cbrt.f64 (/.f64 d h)) (sqrt.f64 (/.f64 1 l)))))
	21.9b	(.f64 (.f64 (cbrt.f64 (.f64 (.f64 (sqrt.f64 (/.f64 d l)) (pow.f64 (sqrt.f64 (/.f64 (cbrt.f64 d) (cbrt.f64 h))) 3)) (-.f64 1 (.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2)) (/.f64 h l))))) (cbrt.f64 (.f64 (.f64 (sqrt.f64 (/.f64 d l)) (pow.f64 (sqrt.f64 (/.f64 (cbrt.f64 d) (cbrt.f64 h))) 3)) (-.f64 1 (.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2)) (/.f64 h l)))))) (cbrt.f64 (.f64 (.f64 (sqrt.f64 (/.f64 d l)) (pow.f64 (sqrt.f64 (/.f64 (cbrt.f64 d) (cbrt.f64 h))) 3)) (-.f64 1 (.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2)) (/.f64 h l))))))
	17.8b	(.f64 (.f64 (.f64 (fabs.f64 (/.f64 (cbrt.f64 d) (cbrt.f64 h))) (sqrt.f64 (/.f64 (cbrt.f64 d) (cbrt.f64 h)))) (.f64 (fabs.f64 (cbrt.f64 d)) (sqrt.f64 (/.f64 (cbrt.f64 d) l)))) (-.f64 1 (.f64 (.f64 1/2 (pow.f64 (.f64 (.f64 M D) (/.f64 1/2 d)) 2)) (/.f64 h l))))
	37.3b	(/.f64 (.f64 d (-.f64 1 (.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2)) (/.f64 h l)))) (.f64 (*.f64 (fabs.f64 (cbrt.f64 h)) (sqrt.f64 (cbrt.f64 h))) (sqrt.f64 l)))
	21.5b	(/.f64 (.f64 (-.f64 1 (.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2)) (/.f64 h l))) (.f64 (sqrt.f64 (/.f64 d l)) (*.f64 (fabs.f64 (cbrt.f64 d)) (sqrt.f64 (/.f64 (cbrt.f64 d) (cbrt.f64 h)))))) (fabs.f64 (cbrt.f64 h)))
	48.7b	(+.f64 (.f64 -1/8 (.f64 (/.f64 (.f64 (.f64 M M) (.f64 D D)) d) (sqrt.f64 (/.f64 h (pow.f64 l 3))))) (.f64 d (sqrt.f64 (/.f64 1 (*.f64 l h)))))
	24.3b	(.f64 (.f64 (.f64 (fabs.f64 (/.f64 (cbrt.f64 d) (cbrt.f64 h))) (sqrt.f64 (/.f64 (cbrt.f64 d) (cbrt.f64 h)))) (.f64 (fabs.f64 (cbrt.f64 d)) (sqrt.f64 (/.f64 (cbrt.f64 d) l)))) (-.f64 1 (log.f64 (pow.f64 (sqrt.f64 (exp.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2))) (/.f64 h l)))))
	23.8b	(.f64 (.f64 (.f64 (fabs.f64 (cbrt.f64 d)) (sqrt.f64 (/.f64 (cbrt.f64 d) h))) (sqrt.f64 (/.f64 d l))) (-.f64 1 (.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (*.f64 d 2)) 2)) (/.f64 h l))))
	37.1b	(/.f64 (.f64 d (-.f64 1 (.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2)) (/.f64 h l)))) (.f64 (sqrt.f64 h) (sqrt.f64 l)))
	41.0b	(.f64 (.f64 (sqrt.f64 (/.f64 d h)) (sqrt.f64 (/.f64 d l))) (-.f64 1 (.f64 1/8 (/.f64 (.f64 (.f64 M M) (.f64 (.f64 D D) h)) (.f64 l (*.f64 d d))))))
▶	17.4b	(/.f64 (.f64 (-.f64 1 (.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2)) (/.f64 h l))) (.f64 (.f64 (cbrt.f64 d) (sqrt.f64 (/.f64 (cbrt.f64 d) l))) (.f64 (cbrt.f64 d) (sqrt.f64 (/.f64 (cbrt.f64 d) (cbrt.f64 h)))))) (fabs.f64 (cbrt.f64 h)))
	41.4b	(.f64 (cbrt.f64 d) (.f64 (pow.f64 (/.f64 1 h) 1/6) (.f64 (.f64 (cbrt.f64 d) (cbrt.f64 (/.f64 d h))) (sqrt.f64 (/.f64 1 l)))))
	37.4b	(/.f64 (.f64 (-.f64 1 (.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2)) (/.f64 h l))) (.f64 (sqrt.f64 d) (.f64 (fabs.f64 (cbrt.f64 d)) (sqrt.f64 (cbrt.f64 d))))) (.f64 (*.f64 (fabs.f64 (cbrt.f64 h)) (sqrt.f64 (cbrt.f64 h))) (sqrt.f64 l)))
	33.2b	(.f64 (.f64 (sqrt.f64 (/.f64 d h)) (cbrt.f64 (pow.f64 (sqrt.f64 (/.f64 d l)) 3))) (-.f64 1 (.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2)) (/.f64 h l))))
	34.5b	(.f64 (.f64 (sqrt.f64 (/.f64 d h)) (sqrt.f64 (/.f64 d l))) (-.f64 1 (log.f64 (sqrt.f64 (pow.f64 (exp.f64 (/.f64 h l)) (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2))))))

Compiler

Compiled 6670 to 3298 computations (50.6% saved)

localize34.0ms (0.2%)

Local error

Found 4 expressions with local error:

3.2b	(sqrt.f64 (/.f64 (cbrt.f64 d) l))
4.5b	(/.f64 (.f64 M D) (.f64 2 d))
5.6b	(.f64 (-.f64 1 (.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2)) (/.f64 h l))) (.f64 (.f64 (cbrt.f64 d) (sqrt.f64 (/.f64 (cbrt.f64 d) l))) (.f64 (cbrt.f64 d) (sqrt.f64 (/.f64 (cbrt.f64 d) (cbrt.f64 h))))))
11.3b	(.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2)) (/.f64 h l))

rewrite314.0ms (1.9%)

Algorithm

1×	rewrite-expression-head

Error

7.5b

Rules

102×	`add-exp-log_binary64`
55×	`prod-exp_binary64`
42×	`add-cbrt-cube_binary64`
30×	`times-frac_binary64`
30×	`add-sqr-sqrt_binary64`

Counts

4 → 138

Calls

4 calls:

27.0ms	(.f64 (-.f64 1 (.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2)) (/.f64 h l))) (.f64 (.f64 (cbrt.f64 d) (sqrt.f64 (/.f64 (cbrt.f64 d) l))) (.f64 (cbrt.f64 d) (sqrt.f64 (/.f64 (cbrt.f64 d) (cbrt.f64 h))))))
11.0ms	(.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2)) (/.f64 h l))
6.0ms	(/.f64 (.f64 M D) (.f64 2 d))
4.0ms	(sqrt.f64 (/.f64 (cbrt.f64 d) l))

Compiler

Compiled 6953 to 2579 computations (62.9% saved)

series585.0ms (3.6%)

Error

9.1b

Counts

4 → 57

Calls

4 calls:

364.0ms	(.f64 (-.f64 1 (.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2)) (/.f64 h l))) (.f64 (.f64 (cbrt.f64 d) (sqrt.f64 (/.f64 (cbrt.f64 d) l))) (.f64 (cbrt.f64 d) (sqrt.f64 (/.f64 (cbrt.f64 d) (cbrt.f64 h))))))
120.0ms	(.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2)) (/.f64 h l))
39.0ms	(/.f64 (.f64 M D) (.f64 2 d))
36.0ms	(sqrt.f64 (/.f64 (cbrt.f64 d) l))

Compiler

Compiled 5104 to 3636 computations (28.8% saved)

simplify249.0ms (1.5%)

Algorithm

1×	egg-herbie

Rules

597×	`associate-r_binary64`
590×	`associate-l_binary64`
307×	`*-commutative_binary64`
274×	`log-prod_binary64`
208×	`times-frac_binary64`

Counts

195 → 142

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	411	6582
1	988	5765
2	4297	5725
3	4802	5725
4	4973	5725
5	4949	5725

prune143.0ms (0.9%)

Pruning

28 alts after pruning (27 fresh and 1 done)

	Pruned	Kept	Total
New	137	5	142
Fresh	3	22	25
Picked	0	1	1
Done	0	0	0
Total	140	28	168

Error

9.0b

Counts

168 → 28

Alt Table

Status	Error	Program
	21.4b	(.f64 (.f64 (.f64 (fabs.f64 (/.f64 (cbrt.f64 d) (cbrt.f64 h))) (sqrt.f64 (/.f64 (cbrt.f64 d) (cbrt.f64 h)))) (sqrt.f64 (/.f64 d l))) (-.f64 1 (.f64 (*.f64 1/2 (pow.f64 (/.f64 M (/.f64 d (/.f64 D 2))) 2)) (/.f64 h l))))
	22.7b	(.f64 (.f64 (sqrt.f64 (/.f64 d h)) (.f64 (fabs.f64 (cbrt.f64 d)) (sqrt.f64 (/.f64 (cbrt.f64 d) l)))) (-.f64 1 (.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (*.f64 d 2)) 2)) (/.f64 h l))))
	25.0b	(.f64 (.f64 (sqrt.f64 (/.f64 d h)) (sqrt.f64 (/.f64 d l))) (-.f64 1 (.f64 (.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2)) (.f64 (cbrt.f64 h) (cbrt.f64 h))) (/.f64 (cbrt.f64 h) l))))
	27.8b	(.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))) (-.f64 1 (log.f64 (pow.f64 (sqrt.f64 (exp.f64 (pow.f64 (/.f64 (.f64 M D) (*.f64 d 2)) 2))) (/.f64 h l)))))
	63.8b	(/.f64 (+.f64 (.f64 -1/8 (.f64 (pow.f64 (neg.f64 (pow.f64 h 5)) 1/6) (.f64 (/.f64 (.f64 (.f64 M M) (.f64 D D)) d) (sqrt.f64 (/.f64 1 (.f64 (pow.f64 l 3) (cbrt.f64 -1))))))) (.f64 d (.f64 (sqrt.f64 (/.f64 1 (.f64 l (cbrt.f64 -1)))) (pow.f64 (/.f64 -1 h) 1/6)))) (fabs.f64 (cbrt.f64 h)))
	44.6b	(cbrt.f64 (pow.f64 (.f64 (.f64 (sqrt.f64 (/.f64 d l)) (sqrt.f64 (/.f64 d h))) (-.f64 1 (.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2)) (/.f64 h l)))) 3))
	21.7b	(.f64 (.f64 (sqrt.f64 (/.f64 d l)) (pow.f64 (sqrt.f64 (/.f64 (cbrt.f64 d) (cbrt.f64 h))) 3)) (-.f64 1 (.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2)) (/.f64 h l))))
	22.6b	(.f64 (.f64 (.f64 (fabs.f64 (/.f64 1 (cbrt.f64 h))) (sqrt.f64 (/.f64 d (cbrt.f64 h)))) (sqrt.f64 (/.f64 d l))) (-.f64 1 (.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (*.f64 d 2)) 2)) (/.f64 h l))))
	26.8b	(.f64 (.f64 (sqrt.f64 (/.f64 d h)) (.f64 (fabs.f64 (cbrt.f64 (/.f64 d l))) (sqrt.f64 (cbrt.f64 (/.f64 d l))))) (-.f64 1 (.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (*.f64 d 2)) 2)) (/.f64 h l))))
	17.4b	(/.f64 (.f64 (-.f64 1 (.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2)) (/.f64 h l))) (.f64 (.f64 (cbrt.f64 d) (.f64 (fabs.f64 (cbrt.f64 (/.f64 (cbrt.f64 d) l))) (sqrt.f64 (cbrt.f64 (/.f64 (cbrt.f64 d) l))))) (*.f64 (cbrt.f64 d) (sqrt.f64 (/.f64 (cbrt.f64 d) (cbrt.f64 h)))))) (fabs.f64 (cbrt.f64 h)))
	22.1b	(.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))))) (-.f64 1 (.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (*.f64 d 2)) 2)) (/.f64 h l))))
	49.9b	(.f64 (cbrt.f64 (.f64 d d)) (.f64 (pow.f64 (/.f64 1 h) 1/6) (.f64 (cbrt.f64 (/.f64 d h)) (sqrt.f64 (/.f64 1 l)))))
	21.9b	(.f64 (.f64 (cbrt.f64 (.f64 (.f64 (sqrt.f64 (/.f64 d l)) (pow.f64 (sqrt.f64 (/.f64 (cbrt.f64 d) (cbrt.f64 h))) 3)) (-.f64 1 (.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2)) (/.f64 h l))))) (cbrt.f64 (.f64 (.f64 (sqrt.f64 (/.f64 d l)) (pow.f64 (sqrt.f64 (/.f64 (cbrt.f64 d) (cbrt.f64 h))) 3)) (-.f64 1 (.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2)) (/.f64 h l)))))) (cbrt.f64 (.f64 (.f64 (sqrt.f64 (/.f64 d l)) (pow.f64 (sqrt.f64 (/.f64 (cbrt.f64 d) (cbrt.f64 h))) 3)) (-.f64 1 (.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2)) (/.f64 h l))))))
	17.8b	(.f64 (.f64 (.f64 (fabs.f64 (/.f64 (cbrt.f64 d) (cbrt.f64 h))) (sqrt.f64 (/.f64 (cbrt.f64 d) (cbrt.f64 h)))) (.f64 (fabs.f64 (cbrt.f64 d)) (sqrt.f64 (/.f64 (cbrt.f64 d) l)))) (-.f64 1 (.f64 (.f64 1/2 (pow.f64 (.f64 (.f64 M D) (/.f64 1/2 d)) 2)) (/.f64 h l))))
	37.3b	(/.f64 (.f64 d (-.f64 1 (.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2)) (/.f64 h l)))) (.f64 (*.f64 (fabs.f64 (cbrt.f64 h)) (sqrt.f64 (cbrt.f64 h))) (sqrt.f64 l)))
	21.5b	(/.f64 (.f64 (-.f64 1 (.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2)) (/.f64 h l))) (.f64 (sqrt.f64 (/.f64 d l)) (*.f64 (fabs.f64 (cbrt.f64 d)) (sqrt.f64 (/.f64 (cbrt.f64 d) (cbrt.f64 h)))))) (fabs.f64 (cbrt.f64 h)))
	48.7b	(+.f64 (.f64 -1/8 (.f64 (/.f64 (.f64 (.f64 M M) (.f64 D D)) d) (sqrt.f64 (/.f64 h (pow.f64 l 3))))) (.f64 d (sqrt.f64 (/.f64 1 (*.f64 l h)))))
	15.5b	(/.f64 (.f64 (-.f64 1 (.f64 (/.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2)) (.f64 (cbrt.f64 l) (cbrt.f64 l))) (/.f64 h (cbrt.f64 l)))) (.f64 (.f64 (cbrt.f64 d) (sqrt.f64 (/.f64 (cbrt.f64 d) l))) (*.f64 (cbrt.f64 d) (sqrt.f64 (/.f64 (cbrt.f64 d) (cbrt.f64 h)))))) (fabs.f64 (cbrt.f64 h)))
	24.3b	(.f64 (.f64 (.f64 (fabs.f64 (/.f64 (cbrt.f64 d) (cbrt.f64 h))) (sqrt.f64 (/.f64 (cbrt.f64 d) (cbrt.f64 h)))) (.f64 (fabs.f64 (cbrt.f64 d)) (sqrt.f64 (/.f64 (cbrt.f64 d) l)))) (-.f64 1 (log.f64 (pow.f64 (sqrt.f64 (exp.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2))) (/.f64 h l)))))
	37.1b	(/.f64 (.f64 d (-.f64 1 (.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2)) (/.f64 h l)))) (.f64 (sqrt.f64 h) (sqrt.f64 l)))
	17.3b	(/.f64 (.f64 (-.f64 1 (.f64 (.f64 1/2 (pow.f64 (/.f64 M (/.f64 2 (/.f64 D d))) 2)) (/.f64 h l))) (.f64 (.f64 (cbrt.f64 d) (sqrt.f64 (/.f64 (cbrt.f64 d) l))) (.f64 (cbrt.f64 d) (sqrt.f64 (/.f64 (cbrt.f64 d) (cbrt.f64 h)))))) (fabs.f64 (cbrt.f64 h)))
	41.0b	(.f64 (.f64 (sqrt.f64 (/.f64 d h)) (sqrt.f64 (/.f64 d l))) (-.f64 1 (.f64 1/8 (/.f64 (.f64 (.f64 M M) (.f64 (.f64 D D) h)) (.f64 l (*.f64 d d))))))
	17.4b	(/.f64 (.f64 (-.f64 1 (.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2)) (/.f64 h l))) (.f64 (.f64 (cbrt.f64 d) (sqrt.f64 (/.f64 (cbrt.f64 d) l))) (.f64 (cbrt.f64 d) (sqrt.f64 (/.f64 (cbrt.f64 d) (cbrt.f64 h)))))) (fabs.f64 (cbrt.f64 h)))
	41.4b	(.f64 (cbrt.f64 d) (.f64 (pow.f64 (/.f64 1 h) 1/6) (.f64 (.f64 (cbrt.f64 d) (cbrt.f64 (/.f64 d h))) (sqrt.f64 (/.f64 1 l)))))
	37.4b	(/.f64 (.f64 (-.f64 1 (.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2)) (/.f64 h l))) (.f64 (sqrt.f64 d) (.f64 (fabs.f64 (cbrt.f64 d)) (sqrt.f64 (cbrt.f64 d))))) (.f64 (*.f64 (fabs.f64 (cbrt.f64 h)) (sqrt.f64 (cbrt.f64 h))) (sqrt.f64 l)))
	33.2b	(.f64 (.f64 (sqrt.f64 (/.f64 d h)) (cbrt.f64 (pow.f64 (sqrt.f64 (/.f64 d l)) 3))) (-.f64 1 (.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2)) (/.f64 h l))))
	34.4b	(/.f64 (.f64 (-.f64 1 (.f64 1/8 (/.f64 (.f64 (.f64 M M) (.f64 (.f64 D D) h)) (.f64 (.f64 d d) l)))) (.f64 (.f64 (cbrt.f64 d) (sqrt.f64 (/.f64 (cbrt.f64 d) l))) (*.f64 (cbrt.f64 d) (sqrt.f64 (/.f64 (cbrt.f64 d) (cbrt.f64 h)))))) (fabs.f64 (cbrt.f64 h)))
	34.5b	(.f64 (.f64 (sqrt.f64 (/.f64 d h)) (sqrt.f64 (/.f64 d l))) (-.f64 1 (log.f64 (sqrt.f64 (pow.f64 (exp.f64 (/.f64 h l)) (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2))))))

Compiler

Compiled 4249 to 2147 computations (49.5% saved)

regimes4.2s (25.6%)

Accuracy

Total 4.1b remaining (28.3%)

Threshold costs 0b (0%)

Compiler

Compiled 85577 to 56887 computations (33.5% saved)

bsearch18.0ms (0.1%)

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

simplify10.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

21×	`*-commutative_binary64`
8×	`+-commutative_binary64`
8×	`sub-neg_binary64`
6×	`neg-sub0_binary64`
6×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	58	198
1	83	198
2	102	198
3	114	198
4	123	198
5	127	198
6	128	198
7	125	198

end16.0ms (0.1%)

Remove: (sort M D)
Compiler: Compiled 387 to 225 computations (41.9% saved)

sample4.8s (29.8%)

Algorithm

1×

intervals

Results

1.2s	8000×	body	128	valid
1.1s	8576×	body	128	nan
690.0ms	4723×	body	128	invalid

Compiler

Compiled 1351 to 903 computations (33.2% saved)

Details

analyze2.0s (12.3%)

sample154.0ms (0.9%)

simplify38.0ms (0.2%)

prune6.0ms (0%)

localize25.0ms (0.2%)

rewrite353.0ms (2.2%)

series359.0ms (2.2%)

simplify164.0ms (1%)

prune132.0ms (0.8%)

localize29.0ms (0.2%)

rewrite331.0ms (2%)

series553.0ms (3.4%)

simplify178.0ms (1.1%)

prune164.0ms (1%)

localize34.0ms (0.2%)

rewrite346.0ms (2.1%)

series619.0ms (3.8%)

simplify198.0ms (1.2%)

prune205.0ms (1.3%)

localize34.0ms (0.2%)

rewrite314.0ms (1.9%)

series585.0ms (3.6%)

simplify249.0ms (1.5%)

prune143.0ms (0.9%)

regimes4.2s (25.6%)

bsearch18.0ms (0.1%)

simplify10.0ms (0.1%)

end16.0ms (0.1%)

sample4.8s (29.8%)

Profiling