Details

analyze2.9s (16.3%)

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)

sample251.0ms (1.4%)

Algorithm

1×

intervals

Results

74.0ms	158×	body	128	invalid
49.0ms	256×	body	128	valid
42.0ms	281×	body	128	nan

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

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

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)

localize20.0ms (0.1%)

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))

rewrite260.0ms (1.4%)

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))))
8.0ms	(.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2)) (/.f64 h l))
3.0ms	(sqrt.f64 (/.f64 d l))
2.0ms	(sqrt.f64 (/.f64 d h))

Compiler

Compiled 4719 to 2207 computations (53.2% saved)

series365.0ms (2%)

Error

17.5b

Counts

4 → 50

Calls

4 calls:

169.0ms	(.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2)) (/.f64 h l))
162.0ms	(.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))))
13.0ms	(sqrt.f64 (/.f64 d l))
12.0ms	(sqrt.f64 (/.f64 d h))

Compiler

Compiled 3210 to 2361 computations (26.4% saved)

simplify152.0ms (0.8%)

Algorithm

1×	egg-herbie

Rules

390×	`associate-l_binary64`
316×	`associate-r_binary64`
302×	`distribute-rgt-in_binary64`
278×	`distribute-lft-in_binary64`
205×	`*-commutative_binary64`

Counts

177 → 125

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	339	4611
1	768	4377
2	2871	4371
3	4833	4371
4	5030	4371

prune105.0ms (0.6%)

Pruning

18 alts after pruning (18 fresh and 0 done)

	Pruned	Kept	Total
New	107	18	125
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	108	18	126

Error

10.9b

Counts

126 → 18

Alt Table

Status	Error	Program
	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))))
	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 D M) (.f64 d 2)) 2))))))
	61.0b	(.f64 -1/8 (.f64 (/.f64 (.f64 (.f64 D D) (*.f64 M M)) d) (sqrt.f64 (/.f64 h (pow.f64 l 3)))))
	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 D M) (.f64 d 2)) 2)) (/.f64 h l)))) 3))
	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))))
	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))))
	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))))
	37.1b	(/.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)))
	40.8b	(/.f64 (.f64 d (-.f64 1 (pow.f64 (.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 D M) (.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 D M) (.f64 d 2)) 2)) (.f64 (/.f64 h l) (.f64 1/4 (pow.f64 (/.f64 (.f64 D M) (*.f64 d 2)) 4))))))))
	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))))
	40.4b	(/.f64 (.f64 (-.f64 1 (.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 D M) (.f64 d 2)) 2)) (/.f64 h l))) (.f64 (sqrt.f64 d) (sqrt.f64 (/.f64 d h)))) (sqrt.f64 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))))
	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))))
	26.5b	(.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 (/.f64 h l)) (cbrt.f64 (/.f64 h l)))) (cbrt.f64 (/.f64 h l)))))
	42.0b	(.f64 (.f64 (sqrt.f64 (/.f64 d h)) (sqrt.f64 (/.f64 d l))) (-.f64 1 (.f64 1/8 (/.f64 (.f64 (.f64 D D) (.f64 (.f64 M M) h)) (.f64 l (*.f64 d d))))))
▶	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))))
	40.6b	(.f64 d (sqrt.f64 (/.f64 1 (.f64 l h))))
	24.8b	(.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 (.f64 (cbrt.f64 h) (cbrt.f64 h)) (*.f64 (cbrt.f64 l) (cbrt.f64 l)))) (/.f64 (cbrt.f64 h) (cbrt.f64 l)))))

Compiler

Compiled 3580 to 1977 computations (44.8% saved)

localize26.0ms (0.1%)

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))

rewrite211.0ms (1.2%)

Algorithm

1×	rewrite-expression-head

Error

9.1b

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:

32.0ms	(.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))))
8.0ms	(.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))
3.0ms	(sqrt.f64 (/.f64 d l))

Compiler

Compiled 6784 to 2606 computations (61.6% saved)

series481.0ms (2.7%)

Error

10.9b

Counts

4 → 51

Calls

4 calls:

309.0ms	(.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))))
109.0ms	(.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2)) (/.f64 h l))
31.0ms	(/.f64 (.f64 M D) (.f64 d 2))
15.0ms	(sqrt.f64 (/.f64 d l))

Compiler

Compiled 5201 to 3773 computations (27.5% saved)

simplify200.0ms (1.1%)

Algorithm

1×	egg-herbie

Rules

695×	`associate-r_binary64`
398×	`*-commutative_binary64`
211×	`times-frac_binary64`
196×	`log-prod_binary64`
186×	`associate-/l*_binary64`

Counts

189 → 149

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	443	7214
1	1153	6422
2	3925	6421
3	4853	6421
4	4959	6421

prune126.0ms (0.7%)

Pruning

23 alts after pruning (23 fresh and 0 done)

	Pruned	Kept	Total
New	139	10	149
Fresh	4	13	17
Picked	1	0	1
Done	0	0	0
Total	144	23	167

Error

9.9b

Counts

167 → 23

Alt Table

Status	Error	Program
	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 D M) (*.f64 d 2)) 2))) (/.f64 h l)))))
	19.5b	(.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 (.f64 1/2 (pow.f64 (/.f64 (.f64 D M) (.f64 d 2)) 2)) (/.f64 (.f64 (cbrt.f64 h) (cbrt.f64 h)) (.f64 (cbrt.f64 l) (cbrt.f64 l)))) (/.f64 (cbrt.f64 h) (cbrt.f64 l)))))
	37.4b	(/.f64 (.f64 (-.f64 1 (.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 D M) (.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)))
	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))))
	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 D M) (.f64 d 2)) 2))))))
	61.0b	(.f64 -1/8 (.f64 (/.f64 (.f64 (.f64 D D) (*.f64 M M)) d) (sqrt.f64 (/.f64 h (pow.f64 l 3)))))
	21.5b	(/.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 (fabs.f64 (cbrt.f64 d)) (sqrt.f64 (/.f64 (cbrt.f64 d) (cbrt.f64 h)))))) (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 D M) (.f64 d 2)) 2)) (/.f64 h l)))) 3))
	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))))
	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 D M) (.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 D M) (.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 D M) (.f64 d 2)) 2)) (/.f64 h l))))))
	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))))
	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))))
	37.1b	(/.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)))
	40.8b	(/.f64 (.f64 d (-.f64 1 (pow.f64 (.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 D M) (.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 D M) (.f64 d 2)) 2)) (.f64 (/.f64 h l) (.f64 1/4 (pow.f64 (/.f64 (.f64 D M) (*.f64 d 2)) 4))))))))
	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))))
	49.9b	(.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))))
	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))))
	26.5b	(.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 (/.f64 h l)) (cbrt.f64 (/.f64 h l)))) (cbrt.f64 (/.f64 h l)))))
	42.0b	(.f64 (.f64 (sqrt.f64 (/.f64 d h)) (sqrt.f64 (/.f64 d l))) (-.f64 1 (.f64 1/8 (/.f64 (.f64 (.f64 D D) (.f64 (.f64 M M) h)) (.f64 l (*.f64 d d))))))
▶	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))))
	40.6b	(.f64 d (sqrt.f64 (/.f64 1 (.f64 l h))))
	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))))

Compiler

Compiled 5501 to 2782 computations (49.4% saved)

localize30.0ms (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))

rewrite232.0ms (1.3%)

Algorithm

1×	rewrite-expression-head

Error

7.7b

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:

32.0ms	(.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))))
8.0ms	(.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))
5.0ms	(sqrt.f64 (/.f64 (cbrt.f64 d) l))

Compiler

Compiled 8383 to 2912 computations (65.3% saved)

series531.0ms (2.9%)

Error

9.2b

Counts

4 → 51

Calls

4 calls:

323.0ms	(.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))))
110.0ms	(.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2)) (/.f64 h l))
37.0ms	(sqrt.f64 (/.f64 (cbrt.f64 d) l))
31.0ms	(/.f64 (.f64 M D) (.f64 d 2))

Compiler

Compiled 6096 to 4330 computations (29% saved)

simplify253.0ms (1.4%)

Algorithm

1×	egg-herbie

Rules

525×	`*-commutative_binary64`
211×	`times-frac_binary64`
189×	`associate-/l*_binary64`
176×	`log-prod_binary64`
170×	`distribute-rgt-neg-in_binary64`

Counts

205 → 168

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	487	8785
1	1264	7405
2	3309	7336
3	4748	7336
4	4983	7336

prune143.0ms (0.8%)

Pruning

26 alts after pruning (26 fresh and 0 done)

	Pruned	Kept	Total
New	161	7	168
Fresh	3	19	22
Picked	1	0	1
Done	0	0	0
Total	165	26	191

Error

9.2b

Counts

191 → 26

Alt Table

Status	Error	Program
	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 D M) (.f64 2 d)) 2))) (/.f64 h l)))))
	49.9b	(.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))))
	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))))
	41.4b	(.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)))))))
	19.5b	(.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 (.f64 1/2 (pow.f64 (/.f64 (.f64 D M) (.f64 d 2)) 2)) (/.f64 (.f64 (cbrt.f64 h) (cbrt.f64 h)) (.f64 (cbrt.f64 l) (cbrt.f64 l)))) (/.f64 (cbrt.f64 h) (cbrt.f64 l)))))
	37.4b	(/.f64 (.f64 (-.f64 1 (.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 D M) (.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)))
▶	17.4b	(/.f64 (.f64 (-.f64 1 (.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 D M) (.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)))
	35.4b	(.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 D D) (.f64 (.f64 M M) h)) (.f64 l (*.f64 d d))))))
	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))))
	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 D M) (.f64 d 2)) 2))))))
	61.0b	(.f64 -1/8 (.f64 (/.f64 (.f64 (.f64 D D) (*.f64 M M)) d) (sqrt.f64 (/.f64 h (pow.f64 l 3)))))
	21.5b	(/.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 (fabs.f64 (cbrt.f64 d)) (sqrt.f64 (/.f64 (cbrt.f64 d) (cbrt.f64 h)))))) (fabs.f64 (cbrt.f64 h)))
	37.3b	(/.f64 (.f64 d (-.f64 1 (.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 D M) (.f64 2 d)) 2)) (/.f64 h l)))) (.f64 (*.f64 (fabs.f64 (cbrt.f64 h)) (sqrt.f64 (cbrt.f64 h))) (sqrt.f64 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 D M) (.f64 d 2)) 2)) (/.f64 h l)))) 3))
	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))))
	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 D M) (.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 D M) (.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 D M) (.f64 d 2)) 2)) (/.f64 h l))))))
	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))))
	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))))
	37.1b	(/.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)))
	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))))
	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))))
	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))))
	26.5b	(.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 (/.f64 h l)) (cbrt.f64 (/.f64 h l)))) (cbrt.f64 (/.f64 h l)))))
	42.0b	(.f64 (.f64 (sqrt.f64 (/.f64 d h)) (sqrt.f64 (/.f64 d l))) (-.f64 1 (.f64 1/8 (/.f64 (.f64 (.f64 D D) (.f64 (.f64 M M) h)) (.f64 l (*.f64 d d))))))
	40.6b	(.f64 d (sqrt.f64 (/.f64 1 (.f64 l h))))

Compiler

Compiled 6567 to 3228 computations (50.8% saved)

localize30.0ms (0.2%)

Local error

Found 4 expressions with local error:

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

rewrite251.0ms (1.4%)

Algorithm

1×	rewrite-expression-head

Error

7.6b

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:

22.0ms	(.f64 (-.f64 1 (.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 D M) (.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))))))
8.0ms	(.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 D M) (.f64 2 d)) 2)) (/.f64 h l))
5.0ms	(/.f64 (.f64 D M) (.f64 2 d))
3.0ms	(sqrt.f64 (/.f64 (cbrt.f64 d) l))

Compiler

Compiled 6953 to 2579 computations (62.9% saved)

series526.0ms (2.9%)

Error

9.2b

Counts

4 → 57

Calls

4 calls:

347.0ms	(.f64 (-.f64 1 (.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 D M) (.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))))))
102.0ms	(.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 D M) (.f64 2 d)) 2)) (/.f64 h l))
32.0ms	(sqrt.f64 (/.f64 (cbrt.f64 d) l))
30.0ms	(/.f64 (.f64 D M) (.f64 2 d))

Compiler

Compiled 5161 to 3634 computations (29.6% saved)

simplify213.0ms (1.2%)

Algorithm

1×	egg-herbie

Rules

597×	`associate-r_binary64`
589×	`associate-l_binary64`
305×	`*-commutative_binary64`
250×	`log-prod_binary64`
209×	`times-frac_binary64`

Counts

195 → 138

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	420	6582
1	998	5765
2	4274	5725
3	4771	5725
4	5110	5725

prune100.0ms (0.6%)

Pruning

26 alts after pruning (26 fresh and 0 done)

	Pruned	Kept	Total
New	135	3	138
Fresh	2	23	25
Picked	1	0	1
Done	0	0	0
Total	138	26	164

Error

9.1b

Counts

164 → 26

Alt Table

Status	Error	Program
	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 D M) (.f64 2 d)) 2))) (/.f64 h l)))))
	49.9b	(.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))))
	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))))
	41.4b	(.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)))))))
	19.5b	(.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 (.f64 1/2 (pow.f64 (/.f64 (.f64 D M) (.f64 d 2)) 2)) (/.f64 (.f64 (cbrt.f64 h) (cbrt.f64 h)) (.f64 (cbrt.f64 l) (cbrt.f64 l)))) (/.f64 (cbrt.f64 h) (cbrt.f64 l)))))
	37.4b	(/.f64 (.f64 (-.f64 1 (.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 D M) (.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)))
	17.4b	(/.f64 (.f64 (-.f64 1 (.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 D M) (.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)))
	22.6b	(.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))))
	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 D M) (.f64 d 2)) 2))))))
	61.0b	(.f64 -1/8 (.f64 (/.f64 (.f64 (.f64 D D) (*.f64 M M)) d) (sqrt.f64 (/.f64 h (pow.f64 l 3)))))
	21.5b	(/.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 (fabs.f64 (cbrt.f64 d)) (sqrt.f64 (/.f64 (cbrt.f64 d) (cbrt.f64 h)))))) (fabs.f64 (cbrt.f64 h)))
	17.6b	(/.f64 (.f64 (-.f64 1 (.f64 (.f64 1/2 (pow.f64 (/.f64 D (/.f64 2 (/.f64 M 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)))
	26.5b	(.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 (/.f64 h l)) (cbrt.f64 (/.f64 h l)))) (cbrt.f64 (/.f64 h l)))))
	37.3b	(/.f64 (.f64 d (-.f64 1 (.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 D M) (.f64 2 d)) 2)) (/.f64 h l)))) (.f64 (*.f64 (fabs.f64 (cbrt.f64 h)) (sqrt.f64 (cbrt.f64 h))) (sqrt.f64 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 D M) (.f64 d 2)) 2)) (/.f64 h l)))) 3))
	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))))
	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 D M) (.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 D M) (.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 D M) (.f64 d 2)) 2)) (/.f64 h l))))))
	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))))
	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))))
	37.1b	(/.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)))
	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))))
	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))))
	42.0b	(.f64 (.f64 (sqrt.f64 (/.f64 d h)) (sqrt.f64 (/.f64 d l))) (-.f64 1 (.f64 1/8 (/.f64 (.f64 (.f64 D D) (.f64 (.f64 M M) h)) (.f64 l (*.f64 d d))))))
	40.6b	(.f64 d (sqrt.f64 (/.f64 1 (.f64 l h))))
	35.4b	(/.f64 (.f64 (-.f64 1 (.f64 1/8 (/.f64 (.f64 (.f64 D D) (.f64 (.f64 M M) h)) (.f64 l (.f64 d d))))) (.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)))

Compiler

Compiled 4091 to 2044 computations (50% saved)

regimes4.9s (27.5%)

Accuracy

Total 4.3b remaining (29.4%)

Threshold costs 0b (0%)

Compiler

Compiled 101838 to 66928 computations (34.3% saved)

bsearch27.0ms (0.1%)

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

simplify10.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	64	198
1	83	198
2	102	198
3	114	198
4	123	198
5	127	198
6	128	198
7	125	198

end13.0ms (0.1%)

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

sample5.5s (30.7%)

Algorithm

1×

intervals

Results

1.5s	8000×	body	128	valid
1.5s	8576×	body	128	nan
851.0ms	4723×	body	128	invalid

Compiler

Compiled 1236 to 820 computations (33.7% saved)

Details

analyze2.9s (16.3%)

sample251.0ms (1.4%)

simplify38.0ms (0.2%)

prune4.0ms (0%)

localize20.0ms (0.1%)

rewrite260.0ms (1.4%)

series365.0ms (2%)

simplify152.0ms (0.8%)

prune105.0ms (0.6%)

localize26.0ms (0.1%)

rewrite211.0ms (1.2%)

series481.0ms (2.7%)

simplify200.0ms (1.1%)

prune126.0ms (0.7%)

localize30.0ms (0.2%)

rewrite232.0ms (1.3%)

series531.0ms (2.9%)

simplify253.0ms (1.4%)

prune143.0ms (0.8%)

localize30.0ms (0.2%)

rewrite251.0ms (1.4%)

series526.0ms (2.9%)

simplify213.0ms (1.2%)

prune100.0ms (0.6%)

regimes4.9s (27.5%)

bsearch27.0ms (0.1%)

simplify10.0ms (0.1%)

end13.0ms (0.1%)

sample5.5s (30.7%)

Profiling