Details

analyze2.8s (15.7%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.7%	0.3%	0
0%	99.7%	0.3%	1
0%	99.7%	0.3%	2
0%	99.7%	0.3%	3
0%	99.7%	0.3%	4
0%	99.7%	0.3%	5
0%	99.7%	0.3%	6
0%	99.7%	0.3%	7
0%	99.7%	0.3%	8
0%	99.7%	0.3%	9
0%	99.7%	0.3%	10
0%	99.7%	0.3%	11
0%	99.7%	0.3%	12
5.1%	94.6%	0.3%	13
7%	92.7%	0.3%	14

Compiler

Compiled 25 to 19 computations (24% saved)

sample104.0ms (0.6%)

Algorithm

1×

intervals

Symmetry

(sort M D)

Results

26.0ms	256×	body	128	valid
8.0ms	93×	body	128	nan
3.0ms	30×	body	128	invalid

Compiler

Compiled 55 to 43 computations (21.8% saved)

simplify35.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

645×	`distribute-neg-frac_binary64`
581×	`distribute-rgt-neg-in_binary64`
418×	`associate-/l*_binary64`
372×	`cancel-sign-sub-inv_binary64`
263×	`associate-/l/_binary64`

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	18	27
1	42	27
2	111	27
3	723	27
4	2855	27
5	4994	27

prune2.0ms (0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

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

Error

15.4b

Counts

2 → 1

Alt Table

Status	Error	Program
▶	15.4b	(.f64 w0 (sqrt.f64 (-.f64 1 (.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2) (/.f64 h l)))))

Compiler

Compiled 72 to 54 computations (25% saved)

localize12.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	1.7b	(.f64 w0 (sqrt.f64 (-.f64 1 (.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2) (/.f64 h l)))))
✓	4.2b	(sqrt.f64 (-.f64 1 (.f64 (pow.f64 (/.f64 (.f64 M D) (*.f64 2 d)) 2) (/.f64 h l))))
✓	5.3b	(/.f64 (.f64 M D) (.f64 2 d))
✓	12.2b	(.f64 (pow.f64 (/.f64 (.f64 M D) (*.f64 2 d)) 2) (/.f64 h l))

series769.0ms (4.3%)

Counts

4 → 204

Calls

4 calls:

333.0ms	(.f64 w0 (sqrt.f64 (-.f64 1 (.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2) (/.f64 h l)))))
250.0ms	(.f64 (pow.f64 (/.f64 (.f64 M D) (*.f64 2 d)) 2) (/.f64 h l))
171.0ms	(sqrt.f64 (-.f64 1 (.f64 (pow.f64 (/.f64 (.f64 M D) (*.f64 2 d)) 2) (/.f64 h l))))
15.0ms	(/.f64 (.f64 M D) (.f64 2 d))

rewrite33.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

67×	`add-exp-log_binary64`
38×	`add-sqr-sqrt_binary64`
27×	`prod-exp_binary64`
23×	`add-cbrt-cube_binary64`
19×	`associate-r_binary64`

Counts

4 → 124

Calls

4 calls:

8.0ms	(.f64 (pow.f64 (/.f64 (.f64 M D) (*.f64 2 d)) 2) (/.f64 h l))
6.0ms	(.f64 w0 (sqrt.f64 (-.f64 1 (.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2) (/.f64 h l)))))
4.0ms	(sqrt.f64 (-.f64 1 (.f64 (pow.f64 (/.f64 (.f64 M D) (*.f64 2 d)) 2) (/.f64 h l))))
4.0ms	(/.f64 (.f64 M D) (.f64 2 d))

simplify162.0ms (0.9%)

Algorithm

1×	egg-herbie

Rules

517×	`times-frac_binary64`
399×	`associate-l_binary64`
365×	`associate-/l*_binary64`
342×	`associate-/r*_binary64`
258×	`associate-*r/_binary64`

Counts

328 → 314

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	516	11209
1	1262	10441
2	4988	10441

prune438.0ms (2.4%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	302	12	314
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	303	12	315

Error

3.3b

Counts

315 → 12

Alt Table

Status	Error	Program
▶	10.6b	(.f64 w0 (sqrt.f64 (-.f64 1 (.f64 (/.f64 (pow.f64 (/.f64 (.f64 D M) (.f64 2 d)) 2) (*.f64 (cbrt.f64 l) (cbrt.f64 l))) (/.f64 h (cbrt.f64 l))))))
	14.4b	(.f64 w0 (sqrt.f64 (-.f64 1 (.f64 (/.f64 (.f64 M D) (.f64 2 d)) (.f64 (/.f64 (.f64 M D) (*.f64 2 d)) (/.f64 h l))))))
	14.6b	(.f64 w0 (sqrt.f64 (-.f64 1 (.f64 (pow.f64 (*.f64 (/.f64 M 2) (/.f64 D d)) 2) (/.f64 h l)))))
	61.2b	(.f64 w0 (.f64 D (sqrt.f64 (.f64 (/.f64 (.f64 (.f64 M M) h) (.f64 l (*.f64 d d))) -1/4))))
	61.0b	(.f64 w0 (.f64 -1 (.f64 (sqrt.f64 (neg.f64 (.f64 1/4 (/.f64 (.f64 (pow.f64 D 2) h) (.f64 l (pow.f64 d 2)))))) M)))
	62.0b	(/.f64 (.f64 (sqrt.f64 (neg.f64 (.f64 1/4 (/.f64 (.f64 (pow.f64 D 2) (.f64 h (pow.f64 M 2))) l)))) w0) d)
	21.6b	(.f64 w0 (sqrt.f64 (-.f64 1 (.f64 1/4 (.f64 (pow.f64 (/.f64 D d) 2) (/.f64 (.f64 (*.f64 M M) h) l))))))
	14.2b	w0
	57.9b	(.f64 (sqrt.f64 (.f64 (.f64 (/.f64 h l) (pow.f64 (/.f64 D d) 2)) -1/4)) (neg.f64 (.f64 M w0)))
	11.9b	(.f64 w0 (sqrt.f64 (-.f64 1 (.f64 (.f64 (pow.f64 (/.f64 (.f64 D M) (.f64 2 d)) 2) (.f64 (cbrt.f64 h) (cbrt.f64 h))) (/.f64 (cbrt.f64 h) l)))))
	27.3b	(-.f64 w0 (.f64 1/8 (.f64 (pow.f64 (/.f64 D d) 2) (/.f64 (.f64 (.f64 (*.f64 M M) h) w0) l))))
	18.1b	(/.f64 (.f64 w0 (sqrt.f64 (-.f64 1 (pow.f64 (.f64 (pow.f64 (/.f64 (.f64 D M) (.f64 2 d)) 2) (/.f64 h l)) 3)))) (sqrt.f64 (+.f64 (.f64 1 1) (+.f64 (.f64 (.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2) (/.f64 h l)) (.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2) (/.f64 h l))) (.f64 1 (.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2) (/.f64 h l)))))))

Compiler

Compiled 12342 to 7441 computations (39.7% saved)

localize16.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	3.6b	(/.f64 (pow.f64 (/.f64 (.f64 D M) (.f64 2 d)) 2) (*.f64 (cbrt.f64 l) (cbrt.f64 l)))
✓	4.2b	(sqrt.f64 (-.f64 1 (.f64 (/.f64 (pow.f64 (/.f64 (.f64 D M) (.f64 2 d)) 2) (.f64 (cbrt.f64 l) (cbrt.f64 l))) (/.f64 h (cbrt.f64 l)))))
✓	5.3b	(/.f64 (.f64 D M) (.f64 2 d))
✓	5.6b	(.f64 (/.f64 (pow.f64 (/.f64 (.f64 D M) (.f64 2 d)) 2) (.f64 (cbrt.f64 l) (cbrt.f64 l))) (/.f64 h (cbrt.f64 l)))

series1.8s (10.1%)

Counts

4 → 192

Calls

4 calls:

1.4s	(/.f64 (pow.f64 (/.f64 (.f64 D M) (.f64 2 d)) 2) (*.f64 (cbrt.f64 l) (cbrt.f64 l)))
247.0ms	(.f64 (/.f64 (pow.f64 (/.f64 (.f64 D M) (.f64 2 d)) 2) (.f64 (cbrt.f64 l) (cbrt.f64 l))) (/.f64 h (cbrt.f64 l)))
178.0ms	(sqrt.f64 (-.f64 1 (.f64 (/.f64 (pow.f64 (/.f64 (.f64 D M) (.f64 2 d)) 2) (.f64 (cbrt.f64 l) (cbrt.f64 l))) (/.f64 h (cbrt.f64 l)))))
16.0ms	(/.f64 (.f64 D M) (.f64 2 d))

rewrite62.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

210×	`add-exp-log_binary64`
85×	`div-exp_binary64`
79×	`prod-exp_binary64`
64×	`times-frac_binary64`
60×	`add-sqr-sqrt_binary64`

Counts

4 → 190

Calls

4 calls:

18.0ms	(.f64 (/.f64 (pow.f64 (/.f64 (.f64 D M) (.f64 2 d)) 2) (.f64 (cbrt.f64 l) (cbrt.f64 l))) (/.f64 h (cbrt.f64 l)))
9.0ms	(/.f64 (pow.f64 (/.f64 (.f64 D M) (.f64 2 d)) 2) (*.f64 (cbrt.f64 l) (cbrt.f64 l)))
4.0ms	(sqrt.f64 (-.f64 1 (.f64 (/.f64 (pow.f64 (/.f64 (.f64 D M) (.f64 2 d)) 2) (.f64 (cbrt.f64 l) (cbrt.f64 l))) (/.f64 h (cbrt.f64 l)))))
4.0ms	(/.f64 (.f64 D M) (.f64 2 d))

simplify225.0ms (1.2%)

Algorithm

1×	egg-herbie

Rules

451×	`times-frac_binary64`
371×	`associate-/l*_binary64`
316×	`associate-*r/_binary64`
310×	`associate-/r*_binary64`
306×	`associate-l_binary64`

Counts

382 → 323

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	493	12002
1	1193	10604
2	4727	10604
3	4961	10604

prune473.0ms (2.6%)

Pruning

14 alts after pruning (13 fresh and 1 done)

	Pruned	Kept	Total
New	318	5	323
Fresh	3	8	11
Picked	0	1	1
Done	0	0	0
Total	321	14	335

Error

2.8b

Counts

335 → 14

Alt Table

Status	Error	Program
	61.3b	(.f64 w0 (/.f64 (sqrt.f64 (.f64 (/.f64 (.f64 h (pow.f64 (.f64 D M) 2)) l) -1/4)) d))
	62.0b	(/.f64 (.f64 (sqrt.f64 (neg.f64 (.f64 1/4 (/.f64 (.f64 (pow.f64 D 2) (.f64 h (pow.f64 M 2))) l)))) w0) d)
	62.0b	(.f64 w0 (.f64 (sqrt.f64 (.f64 (.f64 (pow.f64 (/.f64 M d) 2) (/.f64 h l)) -1/4)) (neg.f64 D)))
	21.6b	(.f64 w0 (sqrt.f64 (-.f64 1 (.f64 1/4 (.f64 (pow.f64 (/.f64 D d) 2) (/.f64 (.f64 (*.f64 M M) h) l))))))
	59.9b	(.f64 w0 (.f64 D (sqrt.f64 (.f64 (.f64 (pow.f64 (/.f64 M d) 2) (/.f64 h l)) -1/4))))
	14.2b	w0
	57.9b	(.f64 (sqrt.f64 (.f64 (.f64 (/.f64 h l) (pow.f64 (/.f64 D d) 2)) -1/4)) (neg.f64 (.f64 M w0)))
▶	9.1b	(.f64 w0 (sqrt.f64 (-.f64 1 (.f64 (/.f64 (/.f64 (.f64 D M) (.f64 2 d)) (cbrt.f64 l)) (.f64 (/.f64 (/.f64 (.f64 D M) (*.f64 2 d)) (cbrt.f64 l)) (/.f64 h (cbrt.f64 l)))))))
✓	10.6b	(.f64 w0 (sqrt.f64 (-.f64 1 (.f64 (/.f64 (pow.f64 (/.f64 (.f64 D M) (.f64 2 d)) 2) (*.f64 (cbrt.f64 l) (cbrt.f64 l))) (/.f64 h (cbrt.f64 l))))))
	14.6b	(.f64 w0 (sqrt.f64 (-.f64 1 (.f64 (pow.f64 (*.f64 (/.f64 M 2) (/.f64 D d)) 2) (/.f64 h l)))))
	61.0b	(.f64 w0 (.f64 (sqrt.f64 (.f64 (/.f64 (.f64 (.f64 D D) h) (.f64 l (*.f64 d d))) -1/4)) (neg.f64 M)))
	11.9b	(.f64 w0 (sqrt.f64 (-.f64 1 (.f64 (.f64 (pow.f64 (/.f64 (.f64 D M) (.f64 2 d)) 2) (.f64 (cbrt.f64 h) (cbrt.f64 h))) (/.f64 (cbrt.f64 h) l)))))
	27.3b	(-.f64 w0 (.f64 1/8 (.f64 (pow.f64 (/.f64 D d) 2) (/.f64 (.f64 (.f64 (*.f64 M M) h) w0) l))))
	18.1b	(/.f64 (.f64 w0 (sqrt.f64 (-.f64 1 (pow.f64 (.f64 (pow.f64 (/.f64 (.f64 D M) (.f64 2 d)) 2) (/.f64 h l)) 3)))) (sqrt.f64 (+.f64 (.f64 1 1) (+.f64 (.f64 (.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2) (/.f64 h l)) (.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2) (/.f64 h l))) (.f64 1 (.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2) (/.f64 h l)))))))

Compiler

Compiled 12950 to 6927 computations (46.5% saved)

localize14.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	3.1b	(/.f64 (/.f64 (.f64 D M) (.f64 2 d)) (cbrt.f64 l))
✓	4.2b	(sqrt.f64 (-.f64 1 (.f64 (/.f64 (/.f64 (.f64 D M) (.f64 2 d)) (cbrt.f64 l)) (.f64 (/.f64 (/.f64 (.f64 D M) (.f64 2 d)) (cbrt.f64 l)) (/.f64 h (cbrt.f64 l))))))
	5.3b	(/.f64 (.f64 D M) (.f64 2 d))
✓	6.2b	(.f64 (/.f64 (/.f64 (.f64 D M) (*.f64 2 d)) (cbrt.f64 l)) (/.f64 h (cbrt.f64 l)))

series2.7s (14.7%)

Counts

3 → 156

Calls

3 calls:

1.7s

(*.f64 (/.f64 (/.f64 (*.f64 D M) (*.f64 2 d)) (cbrt.f64 l)) (/.f64 h (cbrt.f64 l)))

782.0ms

(/.f64 (/.f64 (*.f64 D M) (*.f64 2 d)) (cbrt.f64 l))

180.0ms

(sqrt.f64 (-.f64 1 (*.f64 (/.f64 (/.f64 (*.f64 D M) (*.f64 2 d)) (cbrt.f64 l)) (*.f64 (/.f64 (/.f64 (*.f64 D M) (*.f64 2 d)) (cbrt.f64 l)) (/.f64 h (cbrt.f64 l))))))

rewrite56.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

103×	`times-frac_binary64`
84×	`add-sqr-sqrt_binary64`
77×	`add-exp-log_binary64`
56×	`add-cbrt-cube_binary64`
53×	`*-un-lft-identity_binary64`

Counts

3 → 184

Calls

3 calls:

22.0ms

(*.f64 (/.f64 (/.f64 (*.f64 D M) (*.f64 2 d)) (cbrt.f64 l)) (/.f64 h (cbrt.f64 l)))

6.0ms

(/.f64 (/.f64 (*.f64 D M) (*.f64 2 d)) (cbrt.f64 l))

5.0ms

(sqrt.f64 (-.f64 1 (*.f64 (/.f64 (/.f64 (*.f64 D M) (*.f64 2 d)) (cbrt.f64 l)) (*.f64 (/.f64 (/.f64 (*.f64 D M) (*.f64 2 d)) (cbrt.f64 l)) (/.f64 h (cbrt.f64 l))))))

simplify169.0ms (0.9%)

Algorithm

1×	egg-herbie

Rules

464×	`associate-*l/_binary64`
426×	`associate-/l*_binary64`
395×	`associate-*r/_binary64`
363×	`times-frac_binary64`
316×	`associate-l_binary64`

Counts

340 → 379

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	485	10891
1	1326	10326
2	5180	10326

prune859.0ms (4.8%)

Pruning

15 alts after pruning (14 fresh and 1 done)

	Pruned	Kept	Total
New	553	3	556
Fresh	1	11	12
Picked	1	0	1
Done	0	1	1
Total	555	15	570

Error

2.5b

Counts

570 → 15

Alt Table

Status	Error	Program
	61.3b	(.f64 w0 (/.f64 (sqrt.f64 (.f64 (/.f64 (.f64 h (pow.f64 (.f64 D M) 2)) l) -1/4)) d))
	62.0b	(/.f64 (.f64 (sqrt.f64 (neg.f64 (.f64 1/4 (/.f64 (.f64 (pow.f64 D 2) (.f64 h (pow.f64 M 2))) l)))) w0) d)
	62.0b	(.f64 w0 (.f64 (sqrt.f64 (.f64 (.f64 (pow.f64 (/.f64 M d) 2) (/.f64 h l)) -1/4)) (neg.f64 D)))
	21.6b	(.f64 w0 (sqrt.f64 (-.f64 1 (.f64 1/4 (.f64 (pow.f64 (/.f64 D d) 2) (/.f64 (.f64 (*.f64 M M) h) l))))))
	59.9b	(.f64 w0 (.f64 D (sqrt.f64 (.f64 (.f64 (pow.f64 (/.f64 M d) 2) (/.f64 h l)) -1/4))))
	14.2b	w0
✓	10.6b	(.f64 w0 (sqrt.f64 (-.f64 1 (.f64 (/.f64 (pow.f64 (/.f64 (.f64 D M) (.f64 2 d)) 2) (*.f64 (cbrt.f64 l) (cbrt.f64 l))) (/.f64 h (cbrt.f64 l))))))
	14.6b	(.f64 w0 (sqrt.f64 (-.f64 1 (.f64 (pow.f64 (*.f64 (/.f64 M 2) (/.f64 D d)) 2) (/.f64 h l)))))
	61.0b	(.f64 w0 (.f64 (sqrt.f64 (.f64 (/.f64 (.f64 (.f64 D D) h) (.f64 l (*.f64 d d))) -1/4)) (neg.f64 M)))
	57.9b	(.f64 (sqrt.f64 (.f64 (.f64 (/.f64 h l) (pow.f64 (/.f64 D d) 2)) -1/4)) (neg.f64 (.f64 M w0)))
▶	7.9b	(.f64 w0 (sqrt.f64 (-.f64 1 (.f64 (/.f64 (/.f64 (.f64 D M) (.f64 2 d)) (cbrt.f64 l)) (/.f64 (.f64 h (/.f64 (/.f64 (.f64 D M) (*.f64 d 2)) (cbrt.f64 l))) (cbrt.f64 l))))))
	9.1b	(.f64 w0 (sqrt.f64 (-.f64 1 (.f64 (/.f64 (/.f64 (.f64 D M) (.f64 2 d)) (cbrt.f64 l)) (.f64 (.f64 1/2 (.f64 (/.f64 (.f64 D M) d) (cbrt.f64 (/.f64 1 l)))) (/.f64 h (cbrt.f64 l)))))))
	60.9b	(.f64 w0 (.f64 D (sqrt.f64 (.f64 (/.f64 (.f64 M (.f64 M h)) (.f64 l (*.f64 d d))) -1/4))))
	27.3b	(-.f64 w0 (.f64 1/8 (.f64 (pow.f64 (/.f64 D d) 2) (/.f64 (.f64 (.f64 (*.f64 M M) h) w0) l))))
	18.1b	(/.f64 (.f64 w0 (sqrt.f64 (-.f64 1 (pow.f64 (.f64 (pow.f64 (/.f64 (.f64 D M) (.f64 2 d)) 2) (/.f64 h l)) 3)))) (sqrt.f64 (+.f64 (.f64 1 1) (+.f64 (.f64 (.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2) (/.f64 h l)) (.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2) (/.f64 h l))) (.f64 1 (.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2) (/.f64 h l)))))))

Compiler

Compiled 24438 to 11789 computations (51.8% saved)

localize17.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	4.2b	(sqrt.f64 (-.f64 1 (.f64 (/.f64 (/.f64 (.f64 D M) (.f64 2 d)) (cbrt.f64 l)) (/.f64 (.f64 h (/.f64 (/.f64 (.f64 D M) (.f64 d 2)) (cbrt.f64 l))) (cbrt.f64 l)))))
✓	5.3b	(/.f64 (.f64 D M) (.f64 d 2))
	5.3b	(/.f64 (.f64 D M) (.f64 2 d))
✓	5.6b	(.f64 h (/.f64 (/.f64 (.f64 D M) (*.f64 d 2)) (cbrt.f64 l)))

series1.2s (6.9%)

Counts

3 → 144

Calls

3 calls:

1.0s

(*.f64 h (/.f64 (/.f64 (*.f64 D M) (*.f64 d 2)) (cbrt.f64 l)))

187.0ms

(sqrt.f64 (-.f64 1 (*.f64 (/.f64 (/.f64 (*.f64 D M) (*.f64 2 d)) (cbrt.f64 l)) (/.f64 (*.f64 h (/.f64 (/.f64 (*.f64 D M) (*.f64 d 2)) (cbrt.f64 l))) (cbrt.f64 l)))))

14.0ms

(/.f64 (*.f64 D M) (*.f64 d 2))

rewrite33.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

40×	`add-exp-log_binary64`
39×	`times-frac_binary64`
35×	`add-cbrt-cube_binary64`
34×	`associate-r_binary64`
31×	`add-sqr-sqrt_binary64`

Counts

3 → 104

Calls

3 calls:

11.0ms

(*.f64 h (/.f64 (/.f64 (*.f64 D M) (*.f64 d 2)) (cbrt.f64 l)))

5.0ms

(sqrt.f64 (-.f64 1 (*.f64 (/.f64 (/.f64 (*.f64 D M) (*.f64 2 d)) (cbrt.f64 l)) (/.f64 (*.f64 h (/.f64 (/.f64 (*.f64 D M) (*.f64 d 2)) (cbrt.f64 l))) (cbrt.f64 l)))))

4.0ms

(/.f64 (*.f64 D M) (*.f64 d 2))

simplify155.0ms (0.9%)

Algorithm

1×	egg-herbie

Rules

381×	`times-frac_binary64`
356×	`associate-/l*_binary64`
334×	`associate-r_binary64`
324×	`associate-l_binary64`
294×	`fma-def_binary64`

Counts

248 → 197

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	406	7270
1	1040	6889
2	4685	6889
3	4995	6889

prune366.0ms (2%)

Pruning

15 alts after pruning (13 fresh and 2 done)

	Pruned	Kept	Total
New	230	1	231
Fresh	1	12	13
Picked	0	1	1
Done	0	1	1
Total	231	15	246

Error

2.2b

Counts

246 → 15

Alt Table

Status	Error	Program
	62.0b	(.f64 w0 (.f64 (sqrt.f64 (.f64 (.f64 (pow.f64 (/.f64 M d) 2) (/.f64 h l)) -1/4)) (neg.f64 D)))
	21.6b	(.f64 w0 (sqrt.f64 (-.f64 1 (.f64 1/4 (.f64 (pow.f64 (/.f64 D d) 2) (/.f64 (.f64 (*.f64 M M) h) l))))))
	59.9b	(.f64 w0 (.f64 D (sqrt.f64 (.f64 (.f64 (pow.f64 (/.f64 M d) 2) (/.f64 h l)) -1/4))))
	14.2b	w0
	60.9b	(.f64 w0 (.f64 D (sqrt.f64 (.f64 (/.f64 (.f64 M (.f64 M h)) (.f64 l (*.f64 d d))) -1/4))))
	60.6b	(.f64 w0 (/.f64 (sqrt.f64 (.f64 (/.f64 (.f64 (.f64 D M) (.f64 D (.f64 M h))) l) -1/4)) d))
✓	10.6b	(.f64 w0 (sqrt.f64 (-.f64 1 (.f64 (/.f64 (pow.f64 (/.f64 (.f64 D M) (.f64 2 d)) 2) (*.f64 (cbrt.f64 l) (cbrt.f64 l))) (/.f64 h (cbrt.f64 l))))))
	14.6b	(.f64 w0 (sqrt.f64 (-.f64 1 (.f64 (pow.f64 (*.f64 (/.f64 M 2) (/.f64 D d)) 2) (/.f64 h l)))))
	62.0b	(/.f64 (.f64 (sqrt.f64 (neg.f64 (.f64 1/4 (/.f64 (.f64 (pow.f64 D 2) (.f64 h (pow.f64 M 2))) l)))) w0) d)
	61.0b	(.f64 w0 (.f64 (sqrt.f64 (.f64 (/.f64 (.f64 (.f64 D D) h) (.f64 l (*.f64 d d))) -1/4)) (neg.f64 M)))
	57.9b	(.f64 (sqrt.f64 (.f64 (.f64 (/.f64 h l) (pow.f64 (/.f64 D d) 2)) -1/4)) (neg.f64 (.f64 M w0)))
✓	7.9b	(.f64 w0 (sqrt.f64 (-.f64 1 (.f64 (/.f64 (/.f64 (.f64 D M) (.f64 2 d)) (cbrt.f64 l)) (/.f64 (.f64 h (/.f64 (/.f64 (.f64 D M) (*.f64 d 2)) (cbrt.f64 l))) (cbrt.f64 l))))))
	9.1b	(.f64 w0 (sqrt.f64 (-.f64 1 (.f64 (/.f64 (/.f64 (.f64 D M) (.f64 2 d)) (cbrt.f64 l)) (.f64 (.f64 1/2 (.f64 (/.f64 (.f64 D M) d) (cbrt.f64 (/.f64 1 l)))) (/.f64 h (cbrt.f64 l)))))))
	27.3b	(-.f64 w0 (.f64 1/8 (.f64 (pow.f64 (/.f64 D d) 2) (/.f64 (.f64 (.f64 (*.f64 M M) h) w0) l))))
	18.1b	(/.f64 (.f64 w0 (sqrt.f64 (-.f64 1 (pow.f64 (.f64 (pow.f64 (/.f64 (.f64 D M) (.f64 2 d)) 2) (/.f64 h l)) 3)))) (sqrt.f64 (+.f64 (.f64 1 1) (+.f64 (.f64 (.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2) (/.f64 h l)) (.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2) (/.f64 h l))) (.f64 1 (.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2) (/.f64 h l)))))))

Compiler

Compiled 10641 to 5677 computations (46.6% saved)

regimes3.0s (16.7%)

Accuracy

Total 5.1b remaining (60.5%)

Threshold costs 0b (0%)

Counts

121 → 2

Compiler

Compiled 67899 to 47877 computations (29.5% saved)

bsearch6.0ms (0%)

Compiler: Compiled 13 to 10 computations (23.1% saved)

simplify8.0ms (0%)

Algorithm

1×	egg-herbie

Rules

23×	`*-commutative_binary64`
14×	`+-commutative_binary64`
14×	`sub-neg_binary64`
13×	`neg-sub0_binary64`
13×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	39	89
1	59	89
2	82	89
3	104	89
4	129	89
5	140	89
6	146	89
7	148	89
8	147	89

end8.0ms (0%)

Compiler: Compiled 192 to 120 computations (37.5% saved)

sample2.5s (13.6%)

Algorithm

1×

intervals

Results

809.0ms	8000×	body	128	valid
297.0ms	3132×	body	128	nan
124.0ms	1330×	body	128	invalid

Compiler

Compiled 525 to 362 computations (31% saved)

Details

analyze2.8s (15.7%)

sample104.0ms (0.6%)

simplify35.0ms (0.2%)

prune2.0ms (0%)

localize12.0ms (0.1%)

series769.0ms (4.3%)

rewrite33.0ms (0.2%)

simplify162.0ms (0.9%)

prune438.0ms (2.4%)

localize16.0ms (0.1%)

series1.8s (10.1%)

rewrite62.0ms (0.3%)

simplify225.0ms (1.2%)

prune473.0ms (2.6%)

localize14.0ms (0.1%)

series2.7s (14.7%)

rewrite56.0ms (0.3%)

simplify169.0ms (0.9%)

prune859.0ms (4.8%)

localize17.0ms (0.1%)

series1.2s (6.9%)

rewrite33.0ms (0.2%)

simplify155.0ms (0.9%)

prune366.0ms (2%)

regimes3.0s (16.7%)

bsearch6.0ms (0%)

simplify8.0ms (0%)

end8.0ms (0%)

sample2.5s (13.6%)

Profiling