Details

analyze2.5s (12.7%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.8%	0.2%	0
0%	99.8%	0.2%	1
0%	99.8%	0.2%	2
0%	99.8%	0.2%	3
0%	99.8%	0.2%	4
0%	99.8%	0.2%	5
0%	99.8%	0.2%	6
0%	81.1%	18.9%	7
0%	68.6%	31.4%	8
0%	59.2%	40.8%	9
0%	59.2%	40.8%	10
0%	59.2%	40.8%	11
0.4%	49.5%	50.1%	12
0.8%	44.4%	54.8%	13
1.4%	39.9%	58.7%	14

Compiler

Compiled 41 to 32 computations (22% saved)

sample207.0ms (1.1%)

Algorithm

1×

intervals

Results

54.0ms	293×	body	128	nan
43.0ms	256×	body	128	valid
37.0ms	178×	body	128	invalid

Compiler

Compiled 86 to 68 computations (20.9% saved)

simplify58.0ms (0.3%)

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

28.1b

Counts

2 → 1

Alt Table

Status	Error	Program
▶	28.1b	(.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)

localize21.0ms (0.1%)

Local error

Found 4 expressions with local error:

5.1b	(.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 h))
11.5b	(.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2)) (/.f64 h l))
15.1b	(sqrt.f64 (/.f64 d l))

rewrite251.0ms (1.3%)

Algorithm

1×	rewrite-expression-head

Error

13.4b

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:

15.0ms	(.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))
2.0ms	(sqrt.f64 (/.f64 d l))
2.0ms	(sqrt.f64 (/.f64 d h))

Compiler

Compiled 4719 to 2207 computations (53.2% saved)

series303.0ms (1.6%)

Error

18.2b

Counts

4 → 50

Calls

4 calls:

168.0ms	(.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))))
101.0ms	(.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2)) (/.f64 h l))
13.0ms	(sqrt.f64 (/.f64 d h))
13.0ms	(sqrt.f64 (/.f64 d l))

Compiler

Compiled 3210 to 2361 computations (26.4% saved)

simplify135.0ms (0.7%)

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 → 125

Iterations

Useful iterations: 2 (0.0ms)

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

prune92.0ms (0.5%)

Pruning

21 alts after pruning (21 fresh and 0 done)

	Pruned	Kept	Total
New	104	21	125
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	105	21	126

Error

10.7b

Counts

126 → 21

Alt Table

Status	Error	Program
	23.4b	(.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))))
	22.9b	(.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))))
	43.0b	(/.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 h)) (sqrt.f64 d))) (sqrt.f64 l))
	23.7b	(.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))))
	34.4b	(.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))))
	42.1b	(/.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)) (sqrt.f64 d))) (sqrt.f64 h))
▶	22.1b	(.f64 (.f64 (.f64 (fabs.f64 (/.f64 (cbrt.f64 d) (cbrt.f64 h))) (sqrt.f64 (/.f64 (cbrt.f64 d) (cbrt.f64 h)))) (sqrt.f64 (/.f64 d l))) (-.f64 1 (.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (*.f64 d 2)) 2)) (/.f64 h l))))
	43.0b	(.f64 d (sqrt.f64 (/.f64 1 (.f64 h l))))
	39.3b	(/.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)))
	28.4b	(.f64 (.f64 (.f64 (fabs.f64 (cbrt.f64 (/.f64 d h))) (sqrt.f64 (cbrt.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))))
	28.6b	(.f64 (.f64 (cbrt.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 h)) (sqrt.f64 (/.f64 d l))))) (cbrt.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 h)) (sqrt.f64 (/.f64 d l)))))) (cbrt.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 h)) (sqrt.f64 (/.f64 d l))))))
	36.5b	(.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 M D) (.f64 d 2)) 2))) (/.f64 h l)))))
	28.7b	(.f64 (.f64 (sqrt.f64 (/.f64 d h)) (sqrt.f64 (/.f64 d l))) (-.f64 1 (exp.f64 (log.f64 (.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2)) (/.f64 h l))))))
	24.0b	(.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))))
	28.3b	(.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))))
	56.9b	(.f64 -1/8 (.f64 (/.f64 (.f64 (.f64 M D) (*.f64 M D)) d) (sqrt.f64 (/.f64 h (pow.f64 l 3)))))
	43.8b	(.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))))))
	27.1b	(.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 l) (cbrt.f64 l))) (/.f64 h (cbrt.f64 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 M D) (.f64 d 2)) 2)) (.f64 (cbrt.f64 h) (cbrt.f64 h))) (/.f64 (cbrt.f64 h) l))))
	26.7b	(.f64 (.f64 (sqrt.f64 (/.f64 d h)) (sqrt.f64 (/.f64 d l))) (-.f64 1 (/.f64 (.f64 h (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2))) l)))
	36.1b	(.f64 (sqrt.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 h)) (sqrt.f64 (/.f64 d l))))) (sqrt.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 h)) (sqrt.f64 (/.f64 d l))))))

Compiler

Compiled 3342 to 1914 computations (42.7% saved)

localize30.0ms (0.2%)

Local error

Found 4 expressions with local error:

4.9b	(/.f64 (.f64 M D) (.f64 d 2))
5.1b	(.f64 (.f64 (.f64 (fabs.f64 (/.f64 (cbrt.f64 d) (cbrt.f64 h))) (sqrt.f64 (/.f64 (cbrt.f64 d) (cbrt.f64 h)))) (sqrt.f64 (/.f64 d l))) (-.f64 1 (.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (*.f64 d 2)) 2)) (/.f64 h l))))
11.5b	(.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2)) (/.f64 h l))
15.1b	(sqrt.f64 (/.f64 d l))

rewrite212.0ms (1.1%)

Algorithm

1×	rewrite-expression-head

Error

9.2b

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:

27.0ms	(.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))
2.0ms	(sqrt.f64 (/.f64 d l))

Compiler

Compiled 6784 to 2606 computations (61.6% saved)

series566.0ms (2.9%)

Error

10.7b

Counts

4 → 55

Calls

4 calls:

394.0ms	(.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))))
96.0ms	(.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2)) (/.f64 h l))
29.0ms	(/.f64 (.f64 M D) (.f64 d 2))
15.0ms	(sqrt.f64 (/.f64 d l))

Compiler

Compiled 5587 to 4079 computations (27% saved)

simplify226.0ms (1.2%)

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

193 → 152

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	466	8824
1	1228	7746
2	4226	7745
3	4906	7745
4	4995	7745

prune123.0ms (0.6%)

Pruning

22 alts after pruning (22 fresh and 0 done)

	Pruned	Kept	Total
New	141	11	152
Fresh	9	11	20
Picked	1	0	1
Done	0	0	0
Total	151	22	173

Error

9.6b

Counts

173 → 22

Alt Table

Status	Error	Program
	23.4b	(.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))))
	22.9b	(.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))))
	23.7b	(.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))))
	34.4b	(.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))))
	43.0b	(.f64 d (sqrt.f64 (/.f64 1 (.f64 h l))))
	22.6b	(/.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 (sqrt.f64 (/.f64 (cbrt.f64 d) (cbrt.f64 h))) (fabs.f64 (cbrt.f64 d))))) (fabs.f64 (cbrt.f64 h)))
	20.6b	(.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 M D) (.f64 d 2)) 2)) (*.f64 (cbrt.f64 h) (cbrt.f64 h))) (/.f64 (cbrt.f64 h) l))))
	56.9b	(.f64 -1/8 (.f64 (/.f64 (.f64 (.f64 M D) (*.f64 M D)) d) (sqrt.f64 (/.f64 h (pow.f64 l 3)))))
▶	20.2b	(.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 h (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (*.f64 d 2)) 2))) l)))
	39.8b	(/.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 (sqrt.f64 (/.f64 (cbrt.f64 d) (cbrt.f64 h))) (fabs.f64 (cbrt.f64 d))))) (.f64 (fabs.f64 (cbrt.f64 h)) (sqrt.f64 l)))
	29.7b	(.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 (log.f64 (pow.f64 (sqrt.f64 (exp.f64 (pow.f64 (/.f64 (.f64 M D) (*.f64 d 2)) 2))) (/.f64 h l)))))
	39.6b	(/.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)))
	22.2b	(.f64 (.f64 (.f64 (fabs.f64 (/.f64 (cbrt.f64 d) (cbrt.f64 h))) (sqrt.f64 (/.f64 (cbrt.f64 d) (cbrt.f64 h)))) (.f64 (fabs.f64 (cbrt.f64 (/.f64 d l))) (sqrt.f64 (cbrt.f64 (/.f64 d l))))) (-.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 M D) (.f64 d 2)) 2)) (.f64 (cbrt.f64 h) (cbrt.f64 h))) (/.f64 (cbrt.f64 h) l))))
	51.7b	(.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))))
	28.6b	(.f64 (.f64 (cbrt.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 h)) (sqrt.f64 (/.f64 d l))))) (cbrt.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 h)) (sqrt.f64 (/.f64 d l)))))) (cbrt.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 h)) (sqrt.f64 (/.f64 d l))))))
	38.9b	(.f64 (pow.f64 (sqrt.f64 (/.f64 (cbrt.f64 d) (cbrt.f64 h))) 3) (.f64 (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)))))))
	21.1b	(.f64 (.f64 (.f64 (fabs.f64 (/.f64 (cbrt.f64 d) (cbrt.f64 h))) (sqrt.f64 (/.f64 (cbrt.f64 d) (cbrt.f64 h)))) (sqrt.f64 (/.f64 d l))) (-.f64 1 (.f64 (*.f64 1/2 (pow.f64 (/.f64 M (/.f64 d (/.f64 D 2))) 2)) (/.f64 h l))))
	24.0b	(.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))))
	29.9b	(.f64 (sqrt.f64 (.f64 (pow.f64 (sqrt.f64 (/.f64 (cbrt.f64 d) (cbrt.f64 h))) 3) (.f64 (-.f64 1 (.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2)) (/.f64 h l))) (sqrt.f64 (/.f64 d l))))) (sqrt.f64 (.f64 (pow.f64 (sqrt.f64 (/.f64 (cbrt.f64 d) (cbrt.f64 h))) 3) (.f64 (-.f64 1 (.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (*.f64 d 2)) 2)) (/.f64 h l))) (sqrt.f64 (/.f64 d l))))))
	39.3b	(/.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)))
	27.1b	(.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 l) (cbrt.f64 l))) (/.f64 h (cbrt.f64 l)))))

Compiler

Compiled 4826 to 2522 computations (47.7% saved)

localize31.0ms (0.2%)

Local error

Found 4 expressions with local error:

4.9b	(/.f64 (.f64 M D) (.f64 d 2))
5.1b	(.f64 (.f64 (.f64 (fabs.f64 (/.f64 (cbrt.f64 d) (cbrt.f64 h))) (sqrt.f64 (/.f64 (cbrt.f64 d) (cbrt.f64 h)))) (sqrt.f64 (/.f64 d l))) (-.f64 1 (/.f64 (.f64 h (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (*.f64 d 2)) 2))) l)))
6.2b	(.f64 h (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2)))
15.1b	(sqrt.f64 (/.f64 d l))

rewrite228.0ms (1.2%)

Algorithm

1×	rewrite-expression-head

Error

8.6b

Rules

55×	`add-exp-log_binary64`
30×	`add-cbrt-cube_binary64`
29×	`frac-times_binary64`
29×	`prod-exp_binary64`
25×	`sqrt-div_binary64`

Counts

4 → 132

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

Compiler

Compiled 6740 to 2740 computations (59.3% saved)

series546.0ms (2.8%)

Error

9.6b

Counts

4 → 52

Calls

4 calls:

408.0ms	(.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 h (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (*.f64 d 2)) 2))) l)))
76.0ms	(.f64 h (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2)))
30.0ms	(/.f64 (.f64 M D) (.f64 d 2))
16.0ms	(sqrt.f64 (/.f64 d l))

Compiler

Compiled 5253 to 3875 computations (26.2% saved)

simplify243.0ms (1.3%)

Algorithm

1×	egg-herbie

Rules

492×	`*-commutative_binary64`
171×	`times-frac_binary64`
158×	`associate-*l/_binary64`
154×	`associate-*r/_binary64`
151×	`associate-/l*_binary64`

Counts

184 → 146

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	458	9480
1	1240	7947
2	3305	7947
3	4883	7947
4	4970	7947

prune134.0ms (0.7%)

Pruning

24 alts after pruning (24 fresh and 0 done)

	Pruned	Kept	Total
New	140	6	146
Fresh	3	18	21
Picked	1	0	1
Done	0	0	0
Total	144	24	168

Error

8.6b

Counts

168 → 24

Alt Table

Status	Error	Program
▶	13.4b	(.f64 (.f64 (.f64 (fabs.f64 (/.f64 (cbrt.f64 d) (cbrt.f64 h))) (sqrt.f64 (/.f64 (cbrt.f64 d) (cbrt.f64 h)))) (.f64 (fabs.f64 (/.f64 (cbrt.f64 d) (cbrt.f64 l))) (sqrt.f64 (/.f64 (cbrt.f64 d) (cbrt.f64 l))))) (-.f64 1 (/.f64 (.f64 h (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2))) l)))
	20.1b	(.f64 (.f64 (.f64 (fabs.f64 (/.f64 (cbrt.f64 d) (cbrt.f64 h))) (sqrt.f64 (/.f64 (cbrt.f64 d) (cbrt.f64 h)))) (sqrt.f64 (/.f64 d l))) (-.f64 1 (/.f64 (.f64 h (.f64 1/2 (pow.f64 (.f64 (*.f64 M D) (/.f64 1/2 d)) 2))) l)))
	23.4b	(.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))))
	22.9b	(.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))))
	22.3b	(.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 h (.f64 1/2 (pow.f64 (cbrt.f64 (pow.f64 (/.f64 (.f64 M D) (*.f64 d 2)) 3)) 2))) l)))
	23.7b	(.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))))
	34.4b	(.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))))
	43.0b	(.f64 d (sqrt.f64 (/.f64 1 (.f64 h l))))
	22.6b	(/.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 (sqrt.f64 (/.f64 (cbrt.f64 d) (cbrt.f64 h))) (fabs.f64 (cbrt.f64 d))))) (fabs.f64 (cbrt.f64 h)))
	37.8b	(.f64 (pow.f64 (sqrt.f64 (/.f64 (cbrt.f64 d) (cbrt.f64 h))) 3) (.f64 (sqrt.f64 (/.f64 d l)) (-.f64 1 (/.f64 (.f64 1/8 (/.f64 (.f64 (.f64 D D) (.f64 h (.f64 M M))) (.f64 d d))) l))))
	56.9b	(.f64 -1/8 (.f64 (/.f64 (.f64 (.f64 M D) (*.f64 M D)) d) (sqrt.f64 (/.f64 h (pow.f64 l 3)))))
	29.7b	(.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 (log.f64 (pow.f64 (sqrt.f64 (exp.f64 (pow.f64 (/.f64 (.f64 M D) (*.f64 d 2)) 2))) (/.f64 h l)))))
	39.6b	(/.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)))
	22.2b	(.f64 (.f64 (.f64 (fabs.f64 (/.f64 (cbrt.f64 d) (cbrt.f64 h))) (sqrt.f64 (/.f64 (cbrt.f64 d) (cbrt.f64 h)))) (.f64 (fabs.f64 (cbrt.f64 (/.f64 d l))) (sqrt.f64 (cbrt.f64 (/.f64 d l))))) (-.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 M D) (.f64 d 2)) 2)) (.f64 (cbrt.f64 h) (cbrt.f64 h))) (/.f64 (cbrt.f64 h) l))))
	51.7b	(.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))))
	28.6b	(.f64 (.f64 (cbrt.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 h)) (sqrt.f64 (/.f64 d l))))) (cbrt.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 h)) (sqrt.f64 (/.f64 d l)))))) (cbrt.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 h)) (sqrt.f64 (/.f64 d l))))))
	19.0b	(.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 h (*.f64 1/2 (pow.f64 (/.f64 M (/.f64 d (/.f64 D 2))) 2))) l)))
	38.3b	(/.f64 (.f64 (-.f64 1 (/.f64 (.f64 h (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2))) l)) (.f64 (sqrt.f64 d) (.f64 (sqrt.f64 (/.f64 (cbrt.f64 d) (cbrt.f64 h))) (fabs.f64 (cbrt.f64 d))))) (.f64 (fabs.f64 (cbrt.f64 h)) (sqrt.f64 l)))
	21.1b	(.f64 (.f64 (.f64 (fabs.f64 (/.f64 (cbrt.f64 d) (cbrt.f64 h))) (sqrt.f64 (/.f64 (cbrt.f64 d) (cbrt.f64 h)))) (sqrt.f64 (/.f64 d l))) (-.f64 1 (.f64 (*.f64 1/2 (pow.f64 (/.f64 M (/.f64 d (/.f64 D 2))) 2)) (/.f64 h l))))
	24.0b	(.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))))
	29.9b	(.f64 (sqrt.f64 (.f64 (pow.f64 (sqrt.f64 (/.f64 (cbrt.f64 d) (cbrt.f64 h))) 3) (.f64 (-.f64 1 (.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2)) (/.f64 h l))) (sqrt.f64 (/.f64 d l))))) (sqrt.f64 (.f64 (pow.f64 (sqrt.f64 (/.f64 (cbrt.f64 d) (cbrt.f64 h))) 3) (.f64 (-.f64 1 (.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (*.f64 d 2)) 2)) (/.f64 h l))) (sqrt.f64 (/.f64 d l))))))
	39.3b	(/.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)))
	27.1b	(.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 l) (cbrt.f64 l))) (/.f64 h (cbrt.f64 l)))))

Compiler

Compiled 4927 to 2718 computations (44.8% saved)

localize40.0ms (0.2%)

Local error

Found 4 expressions with local error:

4.4b	(/.f64 (.f64 h (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2))) l)
4.9b	(/.f64 (.f64 M D) (.f64 d 2))
5.1b	(.f64 (.f64 (.f64 (fabs.f64 (/.f64 (cbrt.f64 d) (cbrt.f64 h))) (sqrt.f64 (/.f64 (cbrt.f64 d) (cbrt.f64 h)))) (.f64 (fabs.f64 (/.f64 (cbrt.f64 d) (cbrt.f64 l))) (sqrt.f64 (/.f64 (cbrt.f64 d) (cbrt.f64 l))))) (-.f64 1 (/.f64 (.f64 h (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2))) l)))
6.2b	(.f64 h (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2)))

rewrite316.0ms (1.6%)

Algorithm

1×	rewrite-expression-head

Error

7.0b

Rules

104×	`add-exp-log_binary64`
81×	`frac-times_binary64`
55×	`prod-exp_binary64`
48×	`associate-*l/_binary64`
48×	`fabs-div_binary64`

Counts

4 → 166

Calls

4 calls:

44.0ms	(.f64 (.f64 (.f64 (fabs.f64 (/.f64 (cbrt.f64 d) (cbrt.f64 h))) (sqrt.f64 (/.f64 (cbrt.f64 d) (cbrt.f64 h)))) (.f64 (fabs.f64 (/.f64 (cbrt.f64 d) (cbrt.f64 l))) (sqrt.f64 (/.f64 (cbrt.f64 d) (cbrt.f64 l))))) (-.f64 1 (/.f64 (.f64 h (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2))) l)))
7.0ms	(/.f64 (.f64 h (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2))) l)
6.0ms	(.f64 h (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2)))
5.0ms	(/.f64 (.f64 M D) (.f64 d 2))

Compiler

Compiled 10666 to 3795 computations (64.4% saved)

series782.0ms (4%)

Error

8.2b

Counts

4 → 63

Calls

4 calls:

519.0ms	(.f64 (.f64 (.f64 (fabs.f64 (/.f64 (cbrt.f64 d) (cbrt.f64 h))) (sqrt.f64 (/.f64 (cbrt.f64 d) (cbrt.f64 h)))) (.f64 (fabs.f64 (/.f64 (cbrt.f64 d) (cbrt.f64 l))) (sqrt.f64 (/.f64 (cbrt.f64 d) (cbrt.f64 l))))) (-.f64 1 (/.f64 (.f64 h (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2))) l)))
124.0ms	(/.f64 (.f64 h (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2))) l)
68.0ms	(.f64 h (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2)))
30.0ms	(/.f64 (.f64 M D) (.f64 d 2))

Compiler

Compiled 7998 to 5373 computations (32.8% saved)

simplify353.0ms (1.8%)

Algorithm

1×	egg-herbie

Rules

276×	`*-commutative_binary64`
267×	`distribute-rgt-in_binary64`
266×	`distribute-lft-in_binary64`
252×	`times-frac_binary64`
231×	`associate-/l*_binary64`

Counts

229 → 216

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	591	16051
1	1644	12633
2	4353	12495
3	4891	12495
4	5008	12495

prune202.0ms (1%)

Pruning

26 alts after pruning (26 fresh and 0 done)

	Pruned	Kept	Total
New	208	8	216
Fresh	5	18	23
Picked	1	0	1
Done	0	0	0
Total	214	26	240

Error

8.5b

Counts

240 → 26

Alt Table

Status	Error	Program
	23.4b	(.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))))
	22.9b	(.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))))
	22.3b	(.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 h (.f64 1/2 (pow.f64 (cbrt.f64 (pow.f64 (/.f64 (.f64 M D) (*.f64 d 2)) 3)) 2))) l)))
	29.9b	(.f64 (sqrt.f64 (.f64 (pow.f64 (sqrt.f64 (/.f64 (cbrt.f64 d) (cbrt.f64 h))) 3) (.f64 (-.f64 1 (.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2)) (/.f64 h l))) (sqrt.f64 (/.f64 d l))))) (sqrt.f64 (.f64 (pow.f64 (sqrt.f64 (/.f64 (cbrt.f64 d) (cbrt.f64 h))) 3) (.f64 (-.f64 1 (.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (*.f64 d 2)) 2)) (/.f64 h l))) (sqrt.f64 (/.f64 d l))))))
	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 (/.f64 (cbrt.f64 d) (cbrt.f64 l))) (sqrt.f64 (/.f64 (cbrt.f64 d) (cbrt.f64 l))))) (-.f64 1 (/.f64 (log.f64 (exp.f64 (.f64 h (.f64 1/2 (pow.f64 (/.f64 (.f64 D M) (.f64 d 2)) 2))))) l)))
	23.7b	(.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))))
	34.4b	(.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))))
	43.0b	(.f64 d (sqrt.f64 (/.f64 1 (.f64 h l))))
	22.6b	(/.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 (sqrt.f64 (/.f64 (cbrt.f64 d) (cbrt.f64 h))) (fabs.f64 (cbrt.f64 d))))) (fabs.f64 (cbrt.f64 h)))
	39.3b	(/.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)))
	51.1b	(.f64 (cbrt.f64 d) (.f64 (pow.f64 (/.f64 1 (.f64 h l)) 1/6) (.f64 (cbrt.f64 (/.f64 d l)) (cbrt.f64 (/.f64 d h)))))
	56.9b	(.f64 -1/8 (.f64 (/.f64 (.f64 (.f64 M D) (*.f64 M D)) d) (sqrt.f64 (/.f64 h (pow.f64 l 3)))))
	33.8b	(.f64 (.f64 (pow.f64 (sqrt.f64 (/.f64 (cbrt.f64 d) (cbrt.f64 h))) 3) (pow.f64 (sqrt.f64 (/.f64 (cbrt.f64 d) (cbrt.f64 l))) 3)) (-.f64 1 (/.f64 (.f64 1/8 (/.f64 (.f64 (.f64 D D) (.f64 h (.f64 M M))) (.f64 d d))) l)))
	12.3b	(.f64 (.f64 (.f64 (fabs.f64 (/.f64 (cbrt.f64 d) (cbrt.f64 h))) (sqrt.f64 (/.f64 (cbrt.f64 d) (cbrt.f64 h)))) (.f64 (fabs.f64 (/.f64 (cbrt.f64 d) (cbrt.f64 l))) (sqrt.f64 (/.f64 (cbrt.f64 d) (cbrt.f64 l))))) (-.f64 1 (/.f64 (.f64 h (.f64 1/2 (pow.f64 (/.f64 M (/.f64 d (/.f64 D 2))) 2))) l)))
	39.6b	(/.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)))
	22.2b	(.f64 (.f64 (.f64 (fabs.f64 (/.f64 (cbrt.f64 d) (cbrt.f64 h))) (sqrt.f64 (/.f64 (cbrt.f64 d) (cbrt.f64 h)))) (.f64 (fabs.f64 (cbrt.f64 (/.f64 d l))) (sqrt.f64 (cbrt.f64 (/.f64 d l))))) (-.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 M D) (.f64 d 2)) 2)) (.f64 (cbrt.f64 h) (cbrt.f64 h))) (/.f64 (cbrt.f64 h) l))))
	51.7b	(.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))))
	14.1b	(/.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) (cbrt.f64 l)))) (.f64 (cbrt.f64 d) (sqrt.f64 (/.f64 (cbrt.f64 d) (cbrt.f64 h)))))) (*.f64 (fabs.f64 (cbrt.f64 h)) (fabs.f64 (cbrt.f64 l))))
	38.3b	(/.f64 (.f64 (-.f64 1 (/.f64 (.f64 h (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2))) l)) (.f64 (sqrt.f64 d) (.f64 (sqrt.f64 (/.f64 (cbrt.f64 d) (cbrt.f64 h))) (fabs.f64 (cbrt.f64 d))))) (.f64 (fabs.f64 (cbrt.f64 h)) (sqrt.f64 l)))
	21.1b	(.f64 (.f64 (.f64 (fabs.f64 (/.f64 (cbrt.f64 d) (cbrt.f64 h))) (sqrt.f64 (/.f64 (cbrt.f64 d) (cbrt.f64 h)))) (sqrt.f64 (/.f64 d l))) (-.f64 1 (.f64 (*.f64 1/2 (pow.f64 (/.f64 M (/.f64 d (/.f64 D 2))) 2)) (/.f64 h l))))
	24.0b	(.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))))
	13.4b	(.f64 (.f64 (.f64 (fabs.f64 (/.f64 (cbrt.f64 d) (cbrt.f64 h))) (sqrt.f64 (/.f64 (cbrt.f64 d) (cbrt.f64 h)))) (.f64 (fabs.f64 (/.f64 (cbrt.f64 d) (cbrt.f64 l))) (sqrt.f64 (/.f64 (cbrt.f64 d) (cbrt.f64 l))))) (-.f64 1 (/.f64 (.f64 (.f64 (cbrt.f64 h) (cbrt.f64 h)) (.f64 (cbrt.f64 h) (.f64 1/2 (pow.f64 (/.f64 (.f64 D M) (.f64 d 2)) 2)))) l)))
	27.1b	(.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 l) (cbrt.f64 l))) (/.f64 h (cbrt.f64 l)))))
	38.1b	(/.f64 (.f64 (-.f64 1 (/.f64 (.f64 h (.f64 1/2 (pow.f64 (/.f64 (.f64 D M) (.f64 d 2)) 2))) l)) (.f64 (pow.f64 (sqrt.f64 (/.f64 (cbrt.f64 d) (cbrt.f64 l))) 3) (*.f64 (cbrt.f64 d) (sqrt.f64 (/.f64 (cbrt.f64 d) (cbrt.f64 h)))))) (fabs.f64 (cbrt.f64 h)))
	38.2b	(/.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)) (*.f64 (fabs.f64 (cbrt.f64 l)) (sqrt.f64 (cbrt.f64 l)))))

Compiler

Compiled 7100 to 3375 computations (52.5% saved)

regimes4.7s (24.5%)

Accuracy

Total 5.2b remaining (36.2%)

Threshold costs 0b (0%)

Compiler

Compiled 100846 to 67549 computations (33% saved)

bsearch550.0ms (2.8%)

Steps

Iters	Range		Point
6	3.285726403218473e+116	2.0385813999276118e+117	4.4903038537844864e+116
8	2.8740121833645547e-65	3.970048587788008e-61	3.886411138624743e-61

Compiler

Compiled 6 to 5 computations (16.7% saved)

simplify9.0ms (0%)

Algorithm

1×	egg-herbie

Rules

16×	`*-commutative_binary64`
7×	`+-commutative_binary64`
6×	`sub-neg_binary64`
5×	`neg-sub0_binary64`
5×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	52	128
1	76	128
2	82	128
3	92	128
4	106	128
5	113	128
6	117	128
7	118	128
8	116	128

end18.0ms (0.1%)

Compiler: Compiled 258 to 159 computations (38.4% saved)

sample6.5s (33.4%)

Algorithm

1×

intervals

Results

1.6s	8000×	body	128	valid
1.4s	8286×	body	128	nan
881.0ms	4643×	body	128	invalid

Compiler

Compiled 1183 to 794 computations (32.9% saved)

Details

analyze2.5s (12.7%)

sample207.0ms (1.1%)

simplify58.0ms (0.3%)

prune4.0ms (0%)

localize21.0ms (0.1%)

rewrite251.0ms (1.3%)

series303.0ms (1.6%)

simplify135.0ms (0.7%)

prune92.0ms (0.5%)

localize30.0ms (0.2%)

rewrite212.0ms (1.1%)

series566.0ms (2.9%)

simplify226.0ms (1.2%)

prune123.0ms (0.6%)

localize31.0ms (0.2%)

rewrite228.0ms (1.2%)

series546.0ms (2.8%)

simplify243.0ms (1.3%)

prune134.0ms (0.7%)

localize40.0ms (0.2%)

rewrite316.0ms (1.6%)

series782.0ms (4%)

simplify353.0ms (1.8%)

prune202.0ms (1%)

regimes4.7s (24.5%)

bsearch550.0ms (2.8%)

simplify9.0ms (0%)

end18.0ms (0.1%)

sample6.5s (33.4%)

Profiling