Details

analyze3.1s (16.5%)

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)

sample66.0ms (0.4%)

Algorithm

1×

intervals

Results

22.0ms	256×	body	128	valid
7.0ms	81×	body	128	nan
4.0ms	45×	body	128	invalid

Compiler

Compiled 55 to 43 computations (21.8% saved)

simplify32.0ms (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

14.6b

Counts

2 → 1

Alt Table

Status	Error	Program
▶	14.6b	(.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
✓	2.2b	(.f64 w0 (sqrt.f64 (-.f64 1 (.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2) (/.f64 h l)))))
✓	3.5b	(sqrt.f64 (-.f64 1 (.f64 (pow.f64 (/.f64 (.f64 M D) (*.f64 2 d)) 2) (/.f64 h l))))
✓	6.5b	(/.f64 (.f64 M D) (.f64 2 d))
✓	11.6b	(.f64 (pow.f64 (/.f64 (.f64 M D) (*.f64 2 d)) 2) (/.f64 h l))

rewrite34.0ms (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:

10.0ms	(.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	(/.f64 (.f64 M D) (.f64 2 d))
3.0ms	(sqrt.f64 (-.f64 1 (.f64 (pow.f64 (/.f64 (.f64 M D) (*.f64 2 d)) 2) (/.f64 h l))))

series894.0ms (4.8%)

Counts

4 → 204

Calls

4 calls:

351.0ms	(.f64 w0 (sqrt.f64 (-.f64 1 (.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2) (/.f64 h l)))))
322.0ms	(.f64 (pow.f64 (/.f64 (.f64 M D) (*.f64 2 d)) 2) (/.f64 h l))
162.0ms	(sqrt.f64 (-.f64 1 (.f64 (pow.f64 (/.f64 (.f64 M D) (*.f64 2 d)) 2) (/.f64 h l))))
58.0ms	(/.f64 (.f64 M D) (.f64 2 d))

simplify190.0ms (1%)

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 → 593

Iterations

Useful iterations: 1 (0.0ms)

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

prune425.0ms (2.3%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	582	11	593
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	583	11	594

Error

5.0b

Counts

594 → 11

Alt Table

Status	Error	Program
	14.1b	(.f64 w0 (sqrt.f64 (-.f64 1 (.f64 (pow.f64 (/.f64 M (/.f64 (*.f64 2 d) D)) 2) (/.f64 h l)))))
	61.1b	(.f64 w0 (/.f64 (sqrt.f64 (.f64 (/.f64 (.f64 (.f64 D D) (.f64 (.f64 M M) h)) l) -1/4)) d))
	14.6b	(.f64 (.f64 w0 (sqrt.f64 (sqrt.f64 (-.f64 1 (.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2) (/.f64 h l)))))) (sqrt.f64 (sqrt.f64 (-.f64 1 (.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2) (/.f64 h l))))))
	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)))
	17.1b	(/.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)))))))
	60.8b	(.f64 -1 (.f64 (sqrt.f64 (neg.f64 (.f64 1/4 (/.f64 (.f64 (pow.f64 D 2) h) (.f64 (pow.f64 d 2) l))))) (.f64 w0 M)))
	62.1b	(.f64 (sqrt.f64 (.f64 (.f64 (/.f64 h l) (pow.f64 (/.f64 D d) 2)) -1/4)) (.f64 M w0))
	14.0b	w0
▶	12.3b	(.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))))))
	60.7b	(.f64 w0 (.f64 D (sqrt.f64 (.f64 (/.f64 (.f64 (.f64 M M) h) (.f64 l (*.f64 d d))) -1/4))))
	25.9b	(.f64 w0 (sqrt.f64 (-.f64 1 (.f64 (pow.f64 (/.f64 M 2) 2) (*.f64 (pow.f64 (/.f64 D d) 2) (/.f64 h l))))))

Compiler

Compiled 12304 to 7419 computations (39.7% saved)

localize14.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	3.5b	(sqrt.f64 (-.f64 1 (.f64 (/.f64 (.f64 M D) (.f64 2 d)) (.f64 (/.f64 (.f64 M D) (.f64 2 d)) (/.f64 h l)))))
	6.5b	(/.f64 (.f64 M D) (.f64 2 d))
	6.5b	(/.f64 (.f64 M D) (.f64 2 d))
✓	9.5b	(.f64 (/.f64 (.f64 M D) (*.f64 2 d)) (/.f64 h l))

rewrite19.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

43×	`add-cbrt-cube_binary64`
43×	`add-exp-log_binary64`
18×	`cbrt-unprod_binary64`
18×	`prod-exp_binary64`
17×	`add-sqr-sqrt_binary64`

Counts

2 → 71

Calls

2 calls:

9.0ms	(.f64 (/.f64 (.f64 M D) (*.f64 2 d)) (/.f64 h l))
5.0ms	(sqrt.f64 (-.f64 1 (.f64 (/.f64 (.f64 M D) (.f64 2 d)) (.f64 (/.f64 (.f64 M D) (.f64 2 d)) (/.f64 h l)))))

series356.0ms (1.9%)

Counts

2 → 108

Calls

2 calls:

199.0ms	(.f64 (/.f64 (.f64 M D) (*.f64 2 d)) (/.f64 h l))
156.0ms	(sqrt.f64 (-.f64 1 (.f64 (/.f64 (.f64 M D) (.f64 2 d)) (.f64 (/.f64 (.f64 M D) (.f64 2 d)) (/.f64 h l)))))

simplify148.0ms (0.8%)

Algorithm

1×	egg-herbie

Rules

454×	`fma-def_binary64`
406×	`times-frac_binary64`
307×	`associate-r_binary64`
302×	`associate-l_binary64`
295×	`associate-/l*_binary64`

Counts

179 → 336

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	344	5832
1	913	5360
2	4389	5341
3	4976	5341

prune338.0ms (1.8%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	570	3	573
Fresh	3	7	10
Picked	0	1	1
Done	0	0	0
Total	573	11	584

Error

4.6b

Counts

584 → 11

Alt Table

Status	Error	Program
	17.1b	(/.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)))))))
	61.0b	(.f64 w0 (.f64 (sqrt.f64 (.f64 (/.f64 (.f64 h (.f64 D D)) (.f64 l (*.f64 d d))) -1/4)) (neg.f64 M)))
	14.1b	(.f64 w0 (sqrt.f64 (-.f64 1 (.f64 (pow.f64 (/.f64 M (/.f64 (*.f64 2 d) D)) 2) (/.f64 h l)))))
	61.1b	(.f64 w0 (/.f64 (sqrt.f64 (.f64 (/.f64 (.f64 (.f64 D D) (.f64 (.f64 M M) h)) l) -1/4)) d))
	60.4b	(.f64 w0 (.f64 D (sqrt.f64 (.f64 (/.f64 (.f64 M (.f64 M h)) (.f64 l (*.f64 d d))) -1/4))))
	60.8b	(.f64 -1 (.f64 (sqrt.f64 (neg.f64 (.f64 1/4 (/.f64 (.f64 (pow.f64 D 2) h) (.f64 (pow.f64 d 2) l))))) (.f64 w0 M)))
	62.1b	(.f64 (sqrt.f64 (.f64 (.f64 (/.f64 h l) (pow.f64 (/.f64 D d) 2)) -1/4)) (.f64 M w0))
	14.0b	w0
✓	12.3b	(.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))))))
	25.9b	(.f64 w0 (sqrt.f64 (-.f64 1 (.f64 (pow.f64 (/.f64 M 2) 2) (*.f64 (pow.f64 (/.f64 D d) 2) (/.f64 h l))))))
▶	9.4b	(.f64 w0 (sqrt.f64 (-.f64 1 (.f64 (/.f64 (.f64 M D) (.f64 2 d)) (.f64 (/.f64 (/.f64 (.f64 D M) (.f64 d 2)) (.f64 (cbrt.f64 l) (cbrt.f64 l))) (/.f64 h (cbrt.f64 l)))))))

Compiler

Compiled 9788 to 5300 computations (45.9% saved)

localize21.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	3.8b	(/.f64 (/.f64 (.f64 D M) (.f64 d 2)) (*.f64 (cbrt.f64 l) (cbrt.f64 l)))
✓	6.5b	(/.f64 (.f64 D M) (.f64 d 2))
	6.5b	(/.f64 (.f64 M D) (.f64 2 d))
✓	6.7b	(.f64 (/.f64 (/.f64 (.f64 D M) (.f64 d 2)) (.f64 (cbrt.f64 l) (cbrt.f64 l))) (/.f64 h (cbrt.f64 l)))

rewrite46.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

173×	`add-exp-log_binary64`
132×	`add-cbrt-cube_binary64`
69×	`cbrt-undiv_binary64`
69×	`div-exp_binary64`
65×	`cbrt-unprod_binary64`

Counts

3 → 162

Calls

3 calls:

18.0ms

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

9.0ms

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

4.0ms

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

series1.9s (10%)

Counts

3 → 144

Calls

3 calls:

1.6s

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

241.0ms

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

59.0ms

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

simplify211.0ms (1.1%)

Algorithm

1×	egg-herbie

Rules

414×	`times-frac_binary64`
377×	`associate-*l/_binary64`
299×	`associate-*r/_binary64`
299×	`associate-/l*_binary64`
285×	`sub-neg_binary64`

Counts

306 → 523

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	277	8486
1	715	5879
2	3527	5856
3	4213	5856
4	5019	5856

prune384.0ms (2.1%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	838	1	839
Fresh	0	9	9
Picked	1	0	1
Done	0	1	1
Total	839	11	850

Error

4.6b

Counts

850 → 11

Alt Table

Status	Error	Program
	17.1b	(/.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)))))))
	61.0b	(.f64 w0 (.f64 (sqrt.f64 (.f64 (/.f64 (.f64 h (.f64 D D)) (.f64 l (*.f64 d d))) -1/4)) (neg.f64 M)))
	14.1b	(.f64 w0 (sqrt.f64 (-.f64 1 (.f64 (pow.f64 (/.f64 M (/.f64 (*.f64 2 d) D)) 2) (/.f64 h l)))))
	61.1b	(.f64 w0 (/.f64 (sqrt.f64 (.f64 (/.f64 (.f64 (.f64 D D) (.f64 (.f64 M M) h)) l) -1/4)) d))
	60.4b	(.f64 w0 (.f64 D (sqrt.f64 (.f64 (/.f64 (.f64 M (.f64 M h)) (.f64 l (*.f64 d d))) -1/4))))
	60.8b	(.f64 -1 (.f64 (sqrt.f64 (neg.f64 (.f64 1/4 (/.f64 (.f64 (pow.f64 D 2) h) (.f64 (pow.f64 d 2) l))))) (.f64 w0 M)))
	62.1b	(.f64 (sqrt.f64 (.f64 (.f64 (/.f64 h l) (pow.f64 (/.f64 D d) 2)) -1/4)) (.f64 M w0))
	14.0b	w0
✓	12.3b	(.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))))))
▶	8.4b	(.f64 w0 (sqrt.f64 (-.f64 1 (.f64 (/.f64 (.f64 M D) (.f64 2 d)) (.f64 (.f64 (/.f64 (/.f64 (.f64 D M) (.f64 d 2)) (.f64 (cbrt.f64 l) (cbrt.f64 l))) (/.f64 (.f64 (cbrt.f64 h) (cbrt.f64 h)) (*.f64 (cbrt.f64 (cbrt.f64 l)) (cbrt.f64 (cbrt.f64 l))))) (/.f64 (cbrt.f64 h) (cbrt.f64 (cbrt.f64 l))))))))
	25.9b	(.f64 w0 (sqrt.f64 (-.f64 1 (.f64 (pow.f64 (/.f64 M 2) 2) (*.f64 (pow.f64 (/.f64 D d) 2) (/.f64 h l))))))

Compiler

Compiled 10837 to 4777 computations (55.9% saved)

localize29.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
	3.8b	(/.f64 (/.f64 (.f64 D M) (.f64 d 2)) (*.f64 (cbrt.f64 l) (cbrt.f64 l)))
✓	4.3b	(.f64 (/.f64 (/.f64 (.f64 D M) (.f64 d 2)) (.f64 (cbrt.f64 l) (cbrt.f64 l))) (/.f64 (.f64 (cbrt.f64 h) (cbrt.f64 h)) (.f64 (cbrt.f64 (cbrt.f64 l)) (cbrt.f64 (cbrt.f64 l)))))
	6.5b	(/.f64 (.f64 D M) (.f64 d 2))
	6.5b	(/.f64 (.f64 M D) (.f64 2 d))

rewrite51.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

354×	`add-exp-log_binary64`
216×	`add-cbrt-cube_binary64`
164×	`cbrt-unprod_binary64`
164×	`prod-exp_binary64`
134×	`cbrt-undiv_binary64`

Counts

1 → 142

Calls

1 calls:

26.0ms

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

series3.9s (21.1%)

Counts

1 → 60

Calls

1 calls:

3.9s	(.f64 (/.f64 (/.f64 (.f64 D M) (.f64 d 2)) (.f64 (cbrt.f64 l) (cbrt.f64 l))) (/.f64 (.f64 (cbrt.f64 h) (cbrt.f64 h)) (.f64 (cbrt.f64 (cbrt.f64 l)) (cbrt.f64 (cbrt.f64 l)))))

simplify301.0ms (1.6%)

Algorithm

1×	egg-herbie

Rules

676×	`associate-/r/_binary64`
456×	`times-frac_binary64`
426×	`associate-*l/_binary64`
349×	`associate-/r*_binary64`
309×	`associate-*r/_binary64`

Counts

202 → 399

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	287	13333
1	816	7443
2	2959	6980
3	4498	6980
4	4973	6980
5	4996	6980

prune417.0ms (2.2%)

Pruning

11 alts after pruning (9 fresh and 2 done)

	Pruned	Kept	Total
New	1277	0	1277
Fresh	0	9	9
Picked	0	1	1
Done	0	1	1
Total	1277	11	1288

Error

4.6b

Counts

1288 → 11

Alt Table

Status	Error	Program
	17.1b	(/.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)))))))
	61.0b	(.f64 w0 (.f64 (sqrt.f64 (.f64 (/.f64 (.f64 h (.f64 D D)) (.f64 l (*.f64 d d))) -1/4)) (neg.f64 M)))
	14.1b	(.f64 w0 (sqrt.f64 (-.f64 1 (.f64 (pow.f64 (/.f64 M (/.f64 (*.f64 2 d) D)) 2) (/.f64 h l)))))
	61.1b	(.f64 w0 (/.f64 (sqrt.f64 (.f64 (/.f64 (.f64 (.f64 D D) (.f64 (.f64 M M) h)) l) -1/4)) d))
	60.4b	(.f64 w0 (.f64 D (sqrt.f64 (.f64 (/.f64 (.f64 M (.f64 M h)) (.f64 l (*.f64 d d))) -1/4))))
	60.8b	(.f64 -1 (.f64 (sqrt.f64 (neg.f64 (.f64 1/4 (/.f64 (.f64 (pow.f64 D 2) h) (.f64 (pow.f64 d 2) l))))) (.f64 w0 M)))
	62.1b	(.f64 (sqrt.f64 (.f64 (.f64 (/.f64 h l) (pow.f64 (/.f64 D d) 2)) -1/4)) (.f64 M w0))
	14.0b	w0
✓	12.3b	(.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))))))
✓	8.4b	(.f64 w0 (sqrt.f64 (-.f64 1 (.f64 (/.f64 (.f64 M D) (.f64 2 d)) (.f64 (.f64 (/.f64 (/.f64 (.f64 D M) (.f64 d 2)) (.f64 (cbrt.f64 l) (cbrt.f64 l))) (/.f64 (.f64 (cbrt.f64 h) (cbrt.f64 h)) (*.f64 (cbrt.f64 (cbrt.f64 l)) (cbrt.f64 (cbrt.f64 l))))) (/.f64 (cbrt.f64 h) (cbrt.f64 (cbrt.f64 l))))))))
	25.9b	(.f64 w0 (sqrt.f64 (-.f64 1 (.f64 (pow.f64 (/.f64 M 2) 2) (*.f64 (pow.f64 (/.f64 D d) 2) (/.f64 h l))))))

Compiler

Compiled 18328 to 5789 computations (68.4% saved)

regimes3.7s (19.8%)

Accuracy

Total 3.9b remaining (41.4%)

Threshold costs 0b (0%)

Compiler

Compiled 104966 to 71719 computations (31.7% saved)

bsearch121.0ms (0.6%)

Steps

Iters	Range		Point
4	-4.86159612553545e-277	-2.22724373775485e-280	-3.7513845546157e-280
11	#hash((type . real) (value . -inf))	-4.703287875294079e+279	-1.7768538554841292e+308

Compiler

Compiled 9 to 7 computations (22.2% saved)

simplify6.0ms (0%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	26	56
1	42	56
2	53	56
3	72	56
4	86	56
5	96	56
6	101	56
7	102	56
8	101	56

end8.0ms (0%)

Remove: (sort M D)
Compiler: Compiled 132 to 78 computations (40.9% saved)

sample2.0s (10.5%)

Algorithm

1×

intervals

Results

748.0ms	8000×	body	128	valid
279.0ms	3078×	body	128	nan
116.0ms	1249×	body	128	invalid

Compiler

Compiled 412 to 280 computations (32% saved)

Details

analyze3.1s (16.5%)

sample66.0ms (0.4%)

simplify32.0ms (0.2%)

prune2.0ms (0%)

localize12.0ms (0.1%)

rewrite34.0ms (0.2%)

series894.0ms (4.8%)

simplify190.0ms (1%)

prune425.0ms (2.3%)

localize14.0ms (0.1%)

rewrite19.0ms (0.1%)

series356.0ms (1.9%)

simplify148.0ms (0.8%)

prune338.0ms (1.8%)

localize21.0ms (0.1%)

rewrite46.0ms (0.2%)

series1.9s (10%)

simplify211.0ms (1.1%)

prune384.0ms (2.1%)

localize29.0ms (0.2%)

rewrite51.0ms (0.3%)

series3.9s (21.1%)

simplify301.0ms (1.6%)

prune417.0ms (2.2%)

regimes3.7s (19.8%)

bsearch121.0ms (0.6%)

simplify6.0ms (0%)

end8.0ms (0%)

sample2.0s (10.5%)

Profiling