Details

analyze2.6s (9.1%)

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)

sample178.0ms (0.6%)

Algorithm

1×

intervals

Results

52.0ms	256×	body	128	valid
39.0ms	255×	body	128	nan
29.0ms	152×	body	128	invalid

Compiler

Compiled 86 to 68 computations (20.9% saved)

simplify47.0ms (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

prune4.0ms (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

27.0b

Counts

2 → 1

Alt Table

Status	Error	Program
▶	27.0b	(.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)

localize19.0ms (0.1%)

Local error

Found 4 expressions with local error:

6.0b	(.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))))
11.5b	(sqrt.f64 (/.f64 d l))
11.6b	(sqrt.f64 (/.f64 d h))
13.9b	(.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2)) (/.f64 h l))

rewrite255.0ms (0.9%)

Algorithm

1×	rewrite-expression-head

Error

11.8b

Rules

77×	`add-exp-log_binary64`
41×	`prod-exp_binary64`
32×	`add-sqr-sqrt_binary64`
29×	`times-frac_binary64`
26×	`sqrt-prod_binary64`

Counts

4 → 127

Calls

4 calls:

14.0ms	(.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))
2.0ms	(sqrt.f64 (/.f64 d l))
2.0ms	(sqrt.f64 (/.f64 d h))

Compiler

Compiled 4719 to 2207 computations (53.2% saved)

series333.0ms (1.2%)

Error

18.1b

Counts

4 → 50

Calls

4 calls:

173.0ms	(.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))
18.0ms	(sqrt.f64 (/.f64 d l))
15.0ms	(sqrt.f64 (/.f64 d h))

Compiler

Compiled 3210 to 2361 computations (26.4% saved)

simplify149.0ms (0.5%)

Algorithm

1×	egg-herbie

Rules

433×	`associate-l_binary64`
408×	`distribute-rgt-in_binary64`
356×	`associate-r_binary64`
242×	`*-commutative_binary64`
219×	`distribute-rgt-neg-in_binary64`

Counts

177 → 138

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	363	5316
1	833	5082
2	3174	5076
3	5072	5076

prune115.0ms (0.4%)

Pruning

20 alts after pruning (20 fresh and 0 done)

	Pruned	Kept	Total
New	118	20	138
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	119	20	139

Error

9.9b

Counts

139 → 20

Alt Table

Status	Error	Program
	38.8b	(/.f64 (.f64 d (-.f64 1 (.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 D M) (.f64 d 2)) 2)) (/.f64 h l)))) (.f64 (sqrt.f64 h) (sqrt.f64 l)))
	22.8b	(.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))))
	21.4b	(.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))))
	27.0b	(.f64 (.f64 (sqrt.f64 (/.f64 d h)) (sqrt.f64 (/.f64 d l))) (-.f64 1 (.f64 (.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 D M) (*.f64 d 2)) 2)) (sqrt.f64 (/.f64 h l))) (sqrt.f64 (/.f64 h l)))))
	20.6b	(.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))))
	27.0b	(.f64 (.f64 (sqrt.f64 (/.f64 d h)) (sqrt.f64 (/.f64 d l))) (-.f64 1 (.f64 (sqrt.f64 (.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 D M) (.f64 d 2)) 2)) (/.f64 h l))) (sqrt.f64 (.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 D M) (*.f64 d 2)) 2)) (/.f64 h l))))))
▶	20.5b	(.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))))
	37.1b	(.f64 (.f64 (sqrt.f64 (/.f64 d h)) (sqrt.f64 (/.f64 d l))) (-.f64 1 (log.f64 (pow.f64 (sqrt.f64 (exp.f64 (pow.f64 (/.f64 (.f64 D M) (.f64 d 2)) 2))) (/.f64 h l)))))
	35.9b	(.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))))
	60.6b	(.f64 -1/8 (.f64 (/.f64 (.f64 (.f64 D D) (*.f64 M M)) d) (sqrt.f64 (/.f64 h (pow.f64 l 3)))))
	27.0b	(.f64 (.f64 (.f64 (sqrt.f64 (/.f64 d h)) (sqrt.f64 (/.f64 d l))) (.f64 (cbrt.f64 (-.f64 1 (.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 D M) (.f64 d 2)) 2)) (/.f64 h l)))) (cbrt.f64 (-.f64 1 (.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 D M) (.f64 d 2)) 2)) (/.f64 h l)))))) (cbrt.f64 (-.f64 1 (.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2)) (/.f64 h l)))))
	43.9b	(.f64 (.f64 (sqrt.f64 (/.f64 d h)) (sqrt.f64 (/.f64 d l))) (-.f64 1 (.f64 1/8 (/.f64 (.f64 (.f64 D D) (.f64 h (.f64 M M))) (.f64 l (*.f64 d d))))))
	41.9b	(/.f64 (.f64 (-.f64 1 (.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 D M) (.f64 d 2)) 2)) (/.f64 h l))) (.f64 (sqrt.f64 (/.f64 d l)) (sqrt.f64 d))) (sqrt.f64 h))
	26.3b	(.f64 (.f64 (sqrt.f64 (/.f64 d h)) (sqrt.f64 (/.f64 d l))) (-.f64 1 (.f64 (.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 D M) (.f64 d 2)) 2)) (.f64 (cbrt.f64 h) (cbrt.f64 h))) (/.f64 (cbrt.f64 h) l))))
	27.2b	(.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))))
	21.0b	(.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))))
	42.8b	(.f64 d (sqrt.f64 (/.f64 1 (.f64 h l))))
	27.5b	(.f64 (.f64 (cbrt.f64 (.f64 (.f64 (sqrt.f64 (/.f64 d h)) (sqrt.f64 (/.f64 d l))) (-.f64 1 (.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 D M) (.f64 d 2)) 2)) (/.f64 h l))))) (cbrt.f64 (.f64 (.f64 (sqrt.f64 (/.f64 d h)) (sqrt.f64 (/.f64 d l))) (-.f64 1 (.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 D M) (.f64 d 2)) 2)) (/.f64 h l)))))) (cbrt.f64 (.f64 (.f64 (sqrt.f64 (/.f64 d h)) (sqrt.f64 (/.f64 d l))) (-.f64 1 (.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 D M) (.f64 d 2)) 2)) (/.f64 h l))))))
	26.9b	(.f64 (sqrt.f64 (/.f64 d h)) (.f64 (sqrt.f64 (/.f64 d l)) (-.f64 1 (.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 D M) (.f64 d 2)) 2)) (/.f64 h l)))))
	42.0b	(/.f64 (.f64 (-.f64 1 (.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 D M) (.f64 d 2)) 2)) (/.f64 h l))) (.f64 (sqrt.f64 (/.f64 d h)) (sqrt.f64 d))) (sqrt.f64 l))

Compiler

Compiled 3838 to 2136 computations (44.3% saved)

localize26.0ms (0.1%)

Local error

Found 4 expressions with local error:

4.7b	(/.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))) (-.f64 1 (.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (*.f64 d 2)) 2)) (/.f64 h l))))
11.5b	(sqrt.f64 (/.f64 d l))
13.9b	(.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2)) (/.f64 h l))

rewrite261.0ms (0.9%)

Algorithm

1×	rewrite-expression-head

Error

9.0b

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:

29.0ms	(.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))))
10.0ms	(.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2)) (/.f64 h l))
5.0ms	(/.f64 (.f64 M D) (.f64 d 2))
2.0ms	(sqrt.f64 (/.f64 d l))

Compiler

Compiled 6784 to 2606 computations (61.6% saved)

series557.0ms (2%)

Error

9.9b

Counts

4 → 51

Calls

4 calls:

383.0ms	(.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))))
110.0ms	(.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2)) (/.f64 h l))
30.0ms	(/.f64 (.f64 M D) (.f64 d 2))
15.0ms	(sqrt.f64 (/.f64 d l))

Compiler

Compiled 5201 to 3773 computations (27.5% saved)

simplify239.0ms (0.9%)

Algorithm

1×	egg-herbie

Rules

746×	`associate-r_binary64`
438×	`*-commutative_binary64`
211×	`times-frac_binary64`
192×	`associate-/l*_binary64`
187×	`log-prod_binary64`

Counts

189 → 163

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	464	8468
1	1222	7406
2	4226	7405
3	4906	7405
4	4995	7405

prune143.0ms (0.5%)

Pruning

22 alts after pruning (22 fresh and 0 done)

	Pruned	Kept	Total
New	158	5	163
Fresh	2	17	19
Picked	1	0	1
Done	0	0	0
Total	161	22	183

Error

9.9b

Counts

183 → 22

Alt Table

Status	Error	Program
	20.5b	(.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 (sqrt.f64 (.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 D M) (.f64 d 2)) 2)) (/.f64 h l))) (sqrt.f64 (.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 D M) (.f64 d 2)) 2)) (/.f64 h l))))))
	41.9b	(/.f64 (.f64 (-.f64 1 (.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 D M) (.f64 d 2)) 2)) (/.f64 h l))) (.f64 (sqrt.f64 (/.f64 d l)) (sqrt.f64 d))) (sqrt.f64 h))
▶	16.3b	(.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 (.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2)) (/.f64 h l))))
	52.3b	(.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))))
	38.8b	(/.f64 (.f64 d (-.f64 1 (.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 D M) (.f64 d 2)) 2)) (/.f64 h l)))) (.f64 (sqrt.f64 h) (sqrt.f64 l)))
	22.8b	(.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))))
	21.4b	(.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))))
	27.0b	(.f64 (.f64 (sqrt.f64 (/.f64 d h)) (sqrt.f64 (/.f64 d l))) (-.f64 1 (.f64 (.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 D M) (*.f64 d 2)) 2)) (sqrt.f64 (/.f64 h l))) (sqrt.f64 (/.f64 h l)))))
	20.0b	(.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))) (-.f64 1 (.f64 (/.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 D M) (.f64 d 2)) 2)) (.f64 (cbrt.f64 l) (cbrt.f64 l))) (/.f64 h (cbrt.f64 l)))))
	27.2b	(.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))))
	20.9b	(/.f64 (.f64 (-.f64 1 (.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 D M) (.f64 d 2)) 2)) (/.f64 h l))) (.f64 (sqrt.f64 (/.f64 d l)) (*.f64 (sqrt.f64 (/.f64 (cbrt.f64 d) (cbrt.f64 h))) (fabs.f64 (cbrt.f64 d))))) (fabs.f64 (cbrt.f64 h)))
	42.8b	(.f64 d (sqrt.f64 (/.f64 1 (.f64 h l))))
	35.9b	(.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))))
	60.6b	(.f64 -1/8 (.f64 (/.f64 (.f64 (.f64 D D) (*.f64 M M)) d) (sqrt.f64 (/.f64 h (pow.f64 l 3)))))
	27.0b	(.f64 (.f64 (.f64 (sqrt.f64 (/.f64 d h)) (sqrt.f64 (/.f64 d l))) (.f64 (cbrt.f64 (-.f64 1 (.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 D M) (.f64 d 2)) 2)) (/.f64 h l)))) (cbrt.f64 (-.f64 1 (.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 D M) (.f64 d 2)) 2)) (/.f64 h l)))))) (cbrt.f64 (-.f64 1 (.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2)) (/.f64 h l)))))
	43.9b	(.f64 (.f64 (sqrt.f64 (/.f64 d h)) (sqrt.f64 (/.f64 d l))) (-.f64 1 (.f64 1/8 (/.f64 (.f64 (.f64 D D) (.f64 h (.f64 M M))) (.f64 l (*.f64 d d))))))
	26.3b	(.f64 (.f64 (sqrt.f64 (/.f64 d h)) (sqrt.f64 (/.f64 d l))) (-.f64 1 (.f64 (.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 D M) (.f64 d 2)) 2)) (.f64 (cbrt.f64 h) (cbrt.f64 h))) (/.f64 (cbrt.f64 h) l))))
	20.6b	(.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))))
	21.0b	(.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))))
	27.5b	(.f64 (.f64 (cbrt.f64 (.f64 (.f64 (sqrt.f64 (/.f64 d h)) (sqrt.f64 (/.f64 d l))) (-.f64 1 (.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 D M) (.f64 d 2)) 2)) (/.f64 h l))))) (cbrt.f64 (.f64 (.f64 (sqrt.f64 (/.f64 d h)) (sqrt.f64 (/.f64 d l))) (-.f64 1 (.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 D M) (.f64 d 2)) 2)) (/.f64 h l)))))) (cbrt.f64 (.f64 (.f64 (sqrt.f64 (/.f64 d h)) (sqrt.f64 (/.f64 d l))) (-.f64 1 (.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 D M) (.f64 d 2)) 2)) (/.f64 h l))))))
	26.9b	(.f64 (sqrt.f64 (/.f64 d h)) (.f64 (sqrt.f64 (/.f64 d l)) (-.f64 1 (.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 D M) (.f64 d 2)) 2)) (/.f64 h l)))))
	42.0b	(/.f64 (.f64 (-.f64 1 (.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 D M) (.f64 d 2)) 2)) (/.f64 h l))) (.f64 (sqrt.f64 (/.f64 d h)) (sqrt.f64 d))) (sqrt.f64 l))

Compiler

Compiled 5397 to 2718 computations (49.6% saved)

localize33.0ms (0.1%)

Local error

Found 4 expressions with local error:

2.3b	(sqrt.f64 (/.f64 (cbrt.f64 d) l))
4.7b	(/.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 (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))))
13.9b	(.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2)) (/.f64 h l))

rewrite277.0ms (1%)

Algorithm

1×	rewrite-expression-head

Error

8.1b

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:

35.0ms	(.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))))
13.0ms	(.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2)) (/.f64 h l))
7.0ms	(/.f64 (.f64 M D) (.f64 d 2))
3.0ms	(sqrt.f64 (/.f64 (cbrt.f64 d) l))

Compiler

Compiled 8383 to 2912 computations (65.3% saved)

series561.0ms (2%)

Error

9.4b

Counts

4 → 51

Calls

4 calls:

352.0ms	(.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))))
109.0ms	(.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2)) (/.f64 h l))
39.0ms	(sqrt.f64 (/.f64 (cbrt.f64 d) l))
34.0ms	(/.f64 (.f64 M D) (.f64 d 2))

Compiler

Compiled 6096 to 4330 computations (29% saved)

simplify291.0ms (1%)

Algorithm

1×	egg-herbie

Rules

596×	`*-commutative_binary64`
211×	`times-frac_binary64`
190×	`associate-/l*_binary64`
176×	`log-prod_binary64`
168×	`associate-*r/_binary64`

Counts

205 → 180

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	515	10297
1	1359	8587
2	3581	8518
3	4872	8518
4	4996	8518

prune153.0ms (0.5%)

Pruning

26 alts after pruning (26 fresh and 0 done)

	Pruned	Kept	Total
New	175	5	180
Fresh	0	21	21
Picked	1	0	1
Done	0	0	0
Total	176	26	202

Error

9.1b

Counts

202 → 26

Alt Table

Status	Error	Program
	20.5b	(.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 (sqrt.f64 (.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 D M) (.f64 d 2)) 2)) (/.f64 h l))) (sqrt.f64 (.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 D M) (.f64 d 2)) 2)) (/.f64 h l))))))
	16.4b	(.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)) (.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))))
	41.9b	(/.f64 (.f64 (-.f64 1 (.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 D M) (.f64 d 2)) 2)) (/.f64 h l))) (.f64 (sqrt.f64 (/.f64 d l)) (sqrt.f64 d))) (sqrt.f64 h))
	52.3b	(.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))))
	38.8b	(/.f64 (.f64 d (-.f64 1 (.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 D M) (.f64 d 2)) 2)) (/.f64 h l)))) (.f64 (sqrt.f64 h) (sqrt.f64 l)))
	22.8b	(.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))))
	21.4b	(.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))))
	27.0b	(.f64 (.f64 (sqrt.f64 (/.f64 d h)) (sqrt.f64 (/.f64 d l))) (-.f64 1 (.f64 (.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 D M) (*.f64 d 2)) 2)) (sqrt.f64 (/.f64 h l))) (sqrt.f64 (/.f64 h l)))))
	20.0b	(.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))) (-.f64 1 (.f64 (/.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 D M) (.f64 d 2)) 2)) (.f64 (cbrt.f64 l) (cbrt.f64 l))) (/.f64 h (cbrt.f64 l)))))
	27.2b	(.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))))
	20.9b	(/.f64 (.f64 (-.f64 1 (.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 D M) (.f64 d 2)) 2)) (/.f64 h l))) (.f64 (sqrt.f64 (/.f64 d l)) (*.f64 (sqrt.f64 (/.f64 (cbrt.f64 d) (cbrt.f64 h))) (fabs.f64 (cbrt.f64 d))))) (fabs.f64 (cbrt.f64 h)))
	42.8b	(.f64 d (sqrt.f64 (/.f64 1 (.f64 h l))))
	15.1b	(.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 (cbrt.f64 d))) (sqrt.f64 (/.f64 (cbrt.f64 (cbrt.f64 d)) l))))) (-.f64 1 (.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (*.f64 d 2)) 2)) (/.f64 h l))))
	35.9b	(.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))))
	60.6b	(.f64 -1/8 (.f64 (/.f64 (.f64 (.f64 D D) (*.f64 M M)) d) (sqrt.f64 (/.f64 h (pow.f64 l 3)))))
	45.4b	(.f64 (cbrt.f64 (neg.f64 d)) (.f64 (.f64 (sqrt.f64 (/.f64 1 l)) (pow.f64 (/.f64 1 h) 1/6)) (.f64 (cbrt.f64 -1) (.f64 (fabs.f64 (.f64 (cbrt.f64 -1) (cbrt.f64 (/.f64 (neg.f64 d) h)))) (fabs.f64 (*.f64 (cbrt.f64 (neg.f64 d)) (cbrt.f64 -1)))))))
	27.0b	(.f64 (.f64 (.f64 (sqrt.f64 (/.f64 d h)) (sqrt.f64 (/.f64 d l))) (.f64 (cbrt.f64 (-.f64 1 (.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 D M) (.f64 d 2)) 2)) (/.f64 h l)))) (cbrt.f64 (-.f64 1 (.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 D M) (.f64 d 2)) 2)) (/.f64 h l)))))) (cbrt.f64 (-.f64 1 (.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2)) (/.f64 h l)))))
	43.9b	(.f64 (.f64 (sqrt.f64 (/.f64 d h)) (sqrt.f64 (/.f64 d l))) (-.f64 1 (.f64 1/8 (/.f64 (.f64 (.f64 D D) (.f64 h (.f64 M M))) (.f64 l (*.f64 d d))))))
	26.3b	(.f64 (.f64 (sqrt.f64 (/.f64 d h)) (sqrt.f64 (/.f64 d l))) (-.f64 1 (.f64 (.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 D M) (.f64 d 2)) 2)) (.f64 (cbrt.f64 h) (cbrt.f64 h))) (/.f64 (cbrt.f64 h) l))))
	20.6b	(.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))))
	37.8b	(.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 (.f64 1/2 (pow.f64 (/.f64 (.f64 D M) (.f64 d 2)) 2)) (/.f64 (.f64 (cbrt.f64 h) (cbrt.f64 h)) (sqrt.f64 l))) (/.f64 (cbrt.f64 h) (sqrt.f64 l)))))
	21.0b	(.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))))
▶	14.1b	(.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 h (.f64 1/2 (pow.f64 (/.f64 (.f64 D M) (.f64 d 2)) 2))) l)))
	27.5b	(.f64 (.f64 (cbrt.f64 (.f64 (.f64 (sqrt.f64 (/.f64 d h)) (sqrt.f64 (/.f64 d l))) (-.f64 1 (.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 D M) (.f64 d 2)) 2)) (/.f64 h l))))) (cbrt.f64 (.f64 (.f64 (sqrt.f64 (/.f64 d h)) (sqrt.f64 (/.f64 d l))) (-.f64 1 (.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 D M) (.f64 d 2)) 2)) (/.f64 h l)))))) (cbrt.f64 (.f64 (.f64 (sqrt.f64 (/.f64 d h)) (sqrt.f64 (/.f64 d l))) (-.f64 1 (.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 D M) (.f64 d 2)) 2)) (/.f64 h l))))))
	26.9b	(.f64 (sqrt.f64 (/.f64 d h)) (.f64 (sqrt.f64 (/.f64 d l)) (-.f64 1 (.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 D M) (.f64 d 2)) 2)) (/.f64 h l)))))
	42.0b	(/.f64 (.f64 (-.f64 1 (.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 D M) (.f64 d 2)) 2)) (/.f64 h l))) (.f64 (sqrt.f64 (/.f64 d h)) (sqrt.f64 d))) (sqrt.f64 l))

Compiler

Compiled 6678 to 3297 computations (50.6% saved)

localize34.0ms (0.1%)

Local error

Found 4 expressions with local error:

4.7b	(/.f64 (.f64 D M) (.f64 d 2))
5.6b	(/.f64 (.f64 h (.f64 1/2 (pow.f64 (/.f64 (.f64 D M) (.f64 d 2)) 2))) l)
6.0b	(.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 h (.f64 1/2 (pow.f64 (/.f64 (.f64 D M) (.f64 d 2)) 2))) l)))
7.5b	(.f64 h (.f64 1/2 (pow.f64 (/.f64 (.f64 D M) (.f64 d 2)) 2)))

rewrite278.0ms (1%)

Algorithm

1×	rewrite-expression-head

Error

8.3b

Rules

104×	`add-exp-log_binary64`
55×	`prod-exp_binary64`
48×	`add-cbrt-cube_binary64`
29×	`frac-times_binary64`
24×	`sqrt-div_binary64`

Counts

4 → 142

Calls

4 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 (fabs.f64 (cbrt.f64 d)) (sqrt.f64 (/.f64 (cbrt.f64 d) l)))) (-.f64 1 (/.f64 (.f64 h (.f64 1/2 (pow.f64 (/.f64 (.f64 D M) (.f64 d 2)) 2))) l)))
9.0ms	(/.f64 (.f64 h (.f64 1/2 (pow.f64 (/.f64 (.f64 D M) (.f64 d 2)) 2))) l)
6.0ms	(.f64 h (.f64 1/2 (pow.f64 (/.f64 (.f64 D M) (.f64 d 2)) 2)))
5.0ms	(/.f64 (.f64 D M) (.f64 d 2))

Compiler

Compiled 8122 to 2951 computations (63.7% saved)

series591.0ms (2.1%)

Error

9.1b

Counts

4 → 57

Calls

4 calls:

331.0ms	(.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 h (.f64 1/2 (pow.f64 (/.f64 (.f64 D M) (.f64 d 2)) 2))) l)))
118.0ms	(/.f64 (.f64 h (.f64 1/2 (pow.f64 (/.f64 (.f64 D M) (.f64 d 2)) 2))) l)
80.0ms	(.f64 h (.f64 1/2 (pow.f64 (/.f64 (.f64 D M) (.f64 d 2)) 2)))
34.0ms	(/.f64 (.f64 D M) (.f64 d 2))

Compiler

Compiled 6621 to 4639 computations (29.9% saved)

simplify379.0ms (1.4%)

Algorithm

1×	egg-herbie

Rules

555×	`*-commutative_binary64`
271×	`times-frac_binary64`
225×	`associate-/l*_binary64`
185×	`log-prod_binary64`
156×	`associate-*r/_binary64`

Counts

199 → 167

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	458	11918
1	1281	9640
2	3634	9580
3	4799	9580
4	4947	9580

prune113.0ms (0.4%)

Pruning

26 alts after pruning (25 fresh and 1 done)

	Pruned	Kept	Total
New	163	4	167
Fresh	4	21	25
Picked	0	1	1
Done	0	0	0
Total	167	26	193

Error

9.1b

Counts

193 → 26

Alt Table

Status	Error	Program
	40.3b	(/.f64 (.f64 (pow.f64 (sqrt.f64 (/.f64 (cbrt.f64 d) (cbrt.f64 h))) 3) (.f64 (-.f64 1 (/.f64 (.f64 h (.f64 1/2 (pow.f64 (/.f64 (.f64 D M) (.f64 d 2)) 2))) l)) (pow.f64 (pow.f64 d 1/6) 3))) (sqrt.f64 l))
	20.5b	(.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 (sqrt.f64 (.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 D M) (.f64 d 2)) 2)) (/.f64 h l))) (sqrt.f64 (.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 D M) (.f64 d 2)) 2)) (/.f64 h l))))))
	16.4b	(.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)) (.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))))
	41.9b	(/.f64 (.f64 (-.f64 1 (.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 D M) (.f64 d 2)) 2)) (/.f64 h l))) (.f64 (sqrt.f64 (/.f64 d l)) (sqrt.f64 d))) (sqrt.f64 h))
	52.3b	(.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))))
	38.8b	(/.f64 (.f64 d (-.f64 1 (.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 D M) (.f64 d 2)) 2)) (/.f64 h l)))) (.f64 (sqrt.f64 h) (sqrt.f64 l)))
	22.8b	(.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))))
	36.4b	(/.f64 (.f64 (-.f64 1 (/.f64 (.f64 h (.f64 1/2 (pow.f64 (/.f64 (.f64 D M) (.f64 d 2)) 2))) l)) (/.f64 d (fabs.f64 (cbrt.f64 h)))) (.f64 (sqrt.f64 (cbrt.f64 h)) (sqrt.f64 l)))
	21.4b	(.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))))
	27.0b	(.f64 (.f64 (sqrt.f64 (/.f64 d h)) (sqrt.f64 (/.f64 d l))) (-.f64 1 (.f64 (.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 D M) (*.f64 d 2)) 2)) (sqrt.f64 (/.f64 h l))) (sqrt.f64 (/.f64 h l)))))
	20.0b	(.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))) (-.f64 1 (.f64 (/.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 D M) (.f64 d 2)) 2)) (.f64 (cbrt.f64 l) (cbrt.f64 l))) (/.f64 h (cbrt.f64 l)))))
	27.2b	(.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))))
	20.9b	(/.f64 (.f64 (-.f64 1 (.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 D M) (.f64 d 2)) 2)) (/.f64 h l))) (.f64 (sqrt.f64 (/.f64 d l)) (*.f64 (sqrt.f64 (/.f64 (cbrt.f64 d) (cbrt.f64 h))) (fabs.f64 (cbrt.f64 d))))) (fabs.f64 (cbrt.f64 h)))
	42.8b	(.f64 d (sqrt.f64 (/.f64 1 (.f64 h l))))
	15.1b	(.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 (cbrt.f64 d))) (sqrt.f64 (/.f64 (cbrt.f64 (cbrt.f64 d)) l))))) (-.f64 1 (.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (*.f64 d 2)) 2)) (/.f64 h l))))
	35.9b	(.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))))
	60.6b	(.f64 -1/8 (.f64 (/.f64 (.f64 (.f64 D D) (*.f64 M M)) d) (sqrt.f64 (/.f64 h (pow.f64 l 3)))))
	43.8b	(exp.f64 (log.f64 (.f64 (pow.f64 (sqrt.f64 (/.f64 (cbrt.f64 d) (cbrt.f64 h))) 3) (.f64 (.f64 (cbrt.f64 d) (sqrt.f64 (/.f64 (cbrt.f64 d) l))) (-.f64 1 (/.f64 (.f64 h (.f64 1/2 (pow.f64 (/.f64 (.f64 D M) (*.f64 d 2)) 2))) l))))))
	45.4b	(.f64 (cbrt.f64 (neg.f64 d)) (.f64 (.f64 (sqrt.f64 (/.f64 1 l)) (pow.f64 (/.f64 1 h) 1/6)) (.f64 (cbrt.f64 -1) (.f64 (fabs.f64 (.f64 (cbrt.f64 -1) (cbrt.f64 (/.f64 (neg.f64 d) h)))) (fabs.f64 (*.f64 (cbrt.f64 (neg.f64 d)) (cbrt.f64 -1)))))))
	43.9b	(.f64 (.f64 (sqrt.f64 (/.f64 d h)) (sqrt.f64 (/.f64 d l))) (-.f64 1 (.f64 1/8 (/.f64 (.f64 (.f64 D D) (.f64 h (.f64 M M))) (.f64 l (*.f64 d d))))))
	15.5b	(/.f64 (.f64 (-.f64 1 (/.f64 (.f64 h (.f64 1/2 (pow.f64 (/.f64 (.f64 D M) (.f64 d 2)) 2))) 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)))
	20.6b	(.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))))
	21.0b	(.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))))
✓	14.1b	(.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 h (.f64 1/2 (pow.f64 (/.f64 (.f64 D M) (.f64 d 2)) 2))) l)))
	27.5b	(.f64 (.f64 (cbrt.f64 (.f64 (.f64 (sqrt.f64 (/.f64 d h)) (sqrt.f64 (/.f64 d l))) (-.f64 1 (.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 D M) (.f64 d 2)) 2)) (/.f64 h l))))) (cbrt.f64 (.f64 (.f64 (sqrt.f64 (/.f64 d h)) (sqrt.f64 (/.f64 d l))) (-.f64 1 (.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 D M) (.f64 d 2)) 2)) (/.f64 h l)))))) (cbrt.f64 (.f64 (.f64 (sqrt.f64 (/.f64 d h)) (sqrt.f64 (/.f64 d l))) (-.f64 1 (.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 D M) (.f64 d 2)) 2)) (/.f64 h l))))))
	26.9b	(.f64 (sqrt.f64 (/.f64 d h)) (.f64 (sqrt.f64 (/.f64 d l)) (-.f64 1 (.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 D M) (.f64 d 2)) 2)) (/.f64 h l)))))

Compiler

Compiled 4201 to 2151 computations (48.8% saved)

regimes9.6s (34.4%)

Accuracy

Total 5.3b remaining (34.2%)

Threshold costs 0b (0%)

Compiler

Compiled 118908 to 77937 computations (34.5% saved)

bsearch1.0s (3.6%)

Steps

Iters	Range		Point
8	2.177692576362018e-296	1.2291008228753532e-291	2.1521460601640103e-293

Compiler

Compiled 6 to 5 computations (16.7% saved)

simplify21.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

20×	`*-commutative_binary64`
9×	`+-commutative_binary64`
9×	`sub-neg_binary64`
7×	`neg-sub0_binary64`
7×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	53	135
1	71	135
2	92	135
3	110	135
4	121	135
5	126	135
6	127	135
7	125	135

end23.0ms (0.1%)

Remove: (sort M D)
Compiler: Compiled 267 to 165 computations (38.2% saved)

sample9.7s (34.7%)

Algorithm

1×

intervals

Results

2.8s	8343×	body	128	nan
2.8s	8000×	body	128	valid
1.7s	4853×	body	128	invalid

Compiler

Compiled 1185 to 798 computations (32.7% saved)

Details

analyze2.6s (9.1%)

sample178.0ms (0.6%)

simplify47.0ms (0.2%)

prune4.0ms (0%)

localize19.0ms (0.1%)

rewrite255.0ms (0.9%)

series333.0ms (1.2%)

simplify149.0ms (0.5%)

prune115.0ms (0.4%)

localize26.0ms (0.1%)

rewrite261.0ms (0.9%)

series557.0ms (2%)

simplify239.0ms (0.9%)

prune143.0ms (0.5%)

localize33.0ms (0.1%)

rewrite277.0ms (1%)

series561.0ms (2%)

simplify291.0ms (1%)

prune153.0ms (0.5%)

localize34.0ms (0.1%)

rewrite278.0ms (1%)

series591.0ms (2.1%)

simplify379.0ms (1.4%)

prune113.0ms (0.4%)

regimes9.6s (34.4%)

bsearch1.0s (3.6%)

simplify21.0ms (0.1%)

end23.0ms (0.1%)

sample9.7s (34.7%)

Profiling