Details

analyze2.9s (20.7%)

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
4.3%	95.4%	0.3%	13
6.6%	93.1%	0.3%	14

Compiler

Compiled 25 to 19 computations (24% saved)

sample2.4s (17.5%)

Symmetry

(sort M D)

Results

1.6s	8256×	body	128	valid
805.0ms	4549×	body	128	invalid

Compiler

Compiled 74 to 56 computations (24.3% saved)

simplify27.0ms (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

15.8b

Counts

2 → 1

Alt Table

Status	Error	Program
▶	15.8b	(.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
✓	2.6b	(.f64 w0 (sqrt.f64 (-.f64 1 (.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2) (/.f64 h l)))))
✓	4.7b	(sqrt.f64 (-.f64 1 (.f64 (pow.f64 (/.f64 (.f64 M D) (*.f64 2 d)) 2) (/.f64 h l))))
✓	6.3b	(/.f64 (.f64 M D) (.f64 2 d))
✓	12.2b	(.f64 (pow.f64 (/.f64 (.f64 M D) (*.f64 2 d)) 2) (/.f64 h l))

series922.0ms (6.6%)

Counts

4 → 204

Calls

4 calls:

353.0ms	(.f64 (pow.f64 (/.f64 (.f64 M D) (*.f64 2 d)) 2) (/.f64 h l))
342.0ms	(.f64 w0 (sqrt.f64 (-.f64 1 (.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2) (/.f64 h l)))))
209.0ms	(sqrt.f64 (-.f64 1 (.f64 (pow.f64 (/.f64 (.f64 M D) (*.f64 2 d)) 2) (/.f64 h l))))
18.0ms	(/.f64 (.f64 M D) (.f64 2 d))

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))))

simplify159.0ms (1.1%)

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 → 314

Iterations

Useful iterations: 1 (0.0ms)

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

prune357.0ms (2.6%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	303	11	314
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	304	11	315

Error

5.3b

Counts

315 → 11

Alt Table

Status	Error	Program
	61.1b	(/.f64 (.f64 (sqrt.f64 (neg.f64 (.f64 1/4 (/.f64 (.f64 (pow.f64 D 2) (.f64 h (pow.f64 M 2))) l)))) w0) d)
	25.2b	(.f64 w0 (sqrt.f64 (-.f64 1 (.f64 1/4 (.f64 (pow.f64 (/.f64 D d) 2) (/.f64 (.f64 (*.f64 M M) h) l))))))
	57.6b	(.f64 (sqrt.f64 (.f64 (.f64 (/.f64 h l) (pow.f64 (/.f64 D d) 2)) -1/4)) (neg.f64 (.f64 M w0)))
	60.0b	(.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)))
	15.9b	w0
	15.8b	(.f64 (.f64 w0 (.f64 (cbrt.f64 (sqrt.f64 (-.f64 1 (.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2) (/.f64 h l))))) (cbrt.f64 (sqrt.f64 (-.f64 1 (.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2) (/.f64 h l))))))) (cbrt.f64 (sqrt.f64 (-.f64 1 (.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2) (/.f64 h l))))))
	13.5b	(.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))))))
	16.0b	(.f64 w0 (sqrt.f64 (-.f64 1 (.f64 (pow.f64 (*.f64 (/.f64 M 2) (/.f64 D d)) 2) (/.f64 h l)))))
	57.6b	(.f64 w0 (.f64 (sqrt.f64 (.f64 (.f64 (/.f64 h l) (pow.f64 (/.f64 D d) 2)) -1/4)) (neg.f64 M)))
▶	13.0b	(.f64 w0 (sqrt.f64 (-.f64 1 (/.f64 (.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2) h) l))))
	59.7b	(.f64 D (.f64 (sqrt.f64 (.f64 (/.f64 (.f64 (.f64 M M) h) (.f64 l (*.f64 d d))) -1/4)) w0))

Compiler

Compiled 12234 to 7377 computations (39.7% saved)

localize14.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	4.6b	(.f64 (pow.f64 (/.f64 (.f64 M D) (*.f64 2 d)) 2) h)
✓	4.7b	(sqrt.f64 (-.f64 1 (/.f64 (.f64 (pow.f64 (/.f64 (.f64 M D) (*.f64 2 d)) 2) h) l)))
	6.3b	(/.f64 (.f64 M D) (.f64 2 d))
✓	6.4b	(/.f64 (.f64 (pow.f64 (/.f64 (.f64 M D) (*.f64 2 d)) 2) h) l)

series563.0ms (4%)

Counts

3 → 156

Calls

3 calls:

237.0ms	(/.f64 (.f64 (pow.f64 (/.f64 (.f64 M D) (*.f64 2 d)) 2) h) l)
183.0ms	(sqrt.f64 (-.f64 1 (/.f64 (.f64 (pow.f64 (/.f64 (.f64 M D) (*.f64 2 d)) 2) h) l)))
143.0ms	(.f64 (pow.f64 (/.f64 (.f64 M D) (*.f64 2 d)) 2) h)

rewrite24.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

54×	`add-exp-log_binary64`
22×	`prod-exp_binary64`
19×	`add-sqr-sqrt_binary64`
16×	`div-exp_binary64`
12×	`*-un-lft-identity_binary64`

Counts

3 → 84

Calls

3 calls:

6.0ms	(sqrt.f64 (-.f64 1 (/.f64 (.f64 (pow.f64 (/.f64 (.f64 M D) (*.f64 2 d)) 2) h) l)))
5.0ms	(.f64 (pow.f64 (/.f64 (.f64 M D) (*.f64 2 d)) 2) h)
5.0ms	(/.f64 (.f64 (pow.f64 (/.f64 (.f64 M D) (*.f64 2 d)) 2) h) l)

simplify136.0ms (1%)

Algorithm

1×	egg-herbie

Rules

315×	`fma-def_binary64`
298×	`unswap-sqr_binary64`
288×	`distribute-neg-frac_binary64`
241×	`cancel-sign-sub-inv_binary64`
191×	`times-frac_binary64`

Counts

240 → 190

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	334	7367
1	764	6748
2	2985	6661
3	4995	6661

prune301.0ms (2.2%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	226	3	229
Fresh	1	9	10
Picked	1	0	1
Done	0	0	0
Total	228	12	240

Error

5.1b

Counts

240 → 12

Alt Table

Status	Error	Program
	22.2b	(.f64 w0 (sqrt.f64 (-.f64 1 (/.f64 (.f64 (pow.f64 (/.f64 M 2) 2) (*.f64 (pow.f64 (/.f64 D d) 2) h)) l))))
	57.6b	(.f64 (sqrt.f64 (.f64 (.f64 (/.f64 h l) (pow.f64 (/.f64 D d) 2)) -1/4)) (neg.f64 (.f64 M w0)))
	61.1b	(/.f64 (.f64 (sqrt.f64 (neg.f64 (.f64 1/4 (/.f64 (.f64 (pow.f64 D 2) (.f64 h (pow.f64 M 2))) l)))) w0) d)
	25.2b	(.f64 w0 (sqrt.f64 (-.f64 1 (.f64 1/4 (.f64 (pow.f64 (/.f64 D d) 2) (/.f64 (.f64 (*.f64 M M) h) l))))))
	60.0b	(.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)))
▶	13.2b	(.f64 w0 (sqrt.f64 (-.f64 1 (/.f64 (.f64 (pow.f64 (*.f64 (/.f64 M 2) (/.f64 D d)) 2) h) l))))
	15.9b	w0
	40.3b	(.f64 w0 (sqrt.f64 (-.f64 1 (/.f64 (.f64 (.f64 (/.f64 (.f64 D M) (.f64 2 d)) (sqrt.f64 h)) (.f64 (/.f64 (.f64 D M) (.f64 2 d)) (sqrt.f64 h))) l))))
	15.8b	(.f64 (.f64 w0 (.f64 (cbrt.f64 (sqrt.f64 (-.f64 1 (.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2) (/.f64 h l))))) (cbrt.f64 (sqrt.f64 (-.f64 1 (.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2) (/.f64 h l))))))) (cbrt.f64 (sqrt.f64 (-.f64 1 (.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2) (/.f64 h l))))))
	13.5b	(.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))))))
	57.6b	(.f64 w0 (.f64 (sqrt.f64 (.f64 (.f64 (/.f64 h l) (pow.f64 (/.f64 D d) 2)) -1/4)) (neg.f64 M)))
	59.7b	(.f64 D (.f64 (sqrt.f64 (.f64 (/.f64 (.f64 (.f64 M M) h) (.f64 l (*.f64 d d))) -1/4)) w0))

Compiler

Compiled 8113 to 5149 computations (36.5% saved)

localize13.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	4.6b	(.f64 (pow.f64 (.f64 (/.f64 M 2) (/.f64 D d)) 2) h)
✓	4.7b	(sqrt.f64 (-.f64 1 (/.f64 (.f64 (pow.f64 (.f64 (/.f64 M 2) (/.f64 D d)) 2) h) l)))
✓	4.9b	(*.f64 (/.f64 M 2) (/.f64 D d))
✓	6.4b	(/.f64 (.f64 (pow.f64 (.f64 (/.f64 M 2) (/.f64 D d)) 2) h) l)

series585.0ms (4.2%)

Counts

4 → 192

Calls

4 calls:

256.0ms	(/.f64 (.f64 (pow.f64 (.f64 (/.f64 M 2) (/.f64 D d)) 2) h) l)
171.0ms	(sqrt.f64 (-.f64 1 (/.f64 (.f64 (pow.f64 (.f64 (/.f64 M 2) (/.f64 D d)) 2) h) l)))
144.0ms	(.f64 (pow.f64 (.f64 (/.f64 M 2) (/.f64 D d)) 2) h)
15.0ms	(*.f64 (/.f64 M 2) (/.f64 D d))

rewrite35.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

67×	`add-exp-log_binary64`
43×	`add-sqr-sqrt_binary64`
26×	`*-un-lft-identity_binary64`
26×	`prod-exp_binary64`
25×	`times-frac_binary64`

Counts

4 → 131

Calls

4 calls:

10.0ms	(*.f64 (/.f64 M 2) (/.f64 D d))
6.0ms	(sqrt.f64 (-.f64 1 (/.f64 (.f64 (pow.f64 (.f64 (/.f64 M 2) (/.f64 D d)) 2) h) l)))
5.0ms	(/.f64 (.f64 (pow.f64 (.f64 (/.f64 M 2) (/.f64 D d)) 2) h) l)
4.0ms	(.f64 (pow.f64 (.f64 (/.f64 M 2) (/.f64 D d)) 2) h)

simplify252.0ms (1.8%)

Algorithm

1×	egg-herbie

Rules

344×	`fma-def_binary64`
291×	`associate-/l*_binary64`
277×	`associate-r_binary64`
270×	`associate-l_binary64`
226×	`associate-*r/_binary64`

Counts

323 → 251

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	415	8347
1	990	7727
2	3960	7619
3	4830	7619
4	5036	7619

prune324.0ms (2.3%)

Pruning

12 alts after pruning (11 fresh and 1 done)

	Pruned	Kept	Total
New	251	0	251
Fresh	0	11	11
Picked	0	1	1
Done	0	0	0
Total	251	12	263

Error

5.1b

Counts

263 → 12

Alt Table

Status	Error	Program
	22.2b	(.f64 w0 (sqrt.f64 (-.f64 1 (/.f64 (.f64 (pow.f64 (/.f64 M 2) 2) (*.f64 (pow.f64 (/.f64 D d) 2) h)) l))))
	57.6b	(.f64 (sqrt.f64 (.f64 (.f64 (/.f64 h l) (pow.f64 (/.f64 D d) 2)) -1/4)) (neg.f64 (.f64 M w0)))
	61.1b	(/.f64 (.f64 (sqrt.f64 (neg.f64 (.f64 1/4 (/.f64 (.f64 (pow.f64 D 2) (.f64 h (pow.f64 M 2))) l)))) w0) d)
	25.2b	(.f64 w0 (sqrt.f64 (-.f64 1 (.f64 1/4 (.f64 (pow.f64 (/.f64 D d) 2) (/.f64 (.f64 (*.f64 M M) h) l))))))
	60.0b	(.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)))
✓	13.2b	(.f64 w0 (sqrt.f64 (-.f64 1 (/.f64 (.f64 (pow.f64 (*.f64 (/.f64 M 2) (/.f64 D d)) 2) h) l))))
	15.9b	w0
	40.3b	(.f64 w0 (sqrt.f64 (-.f64 1 (/.f64 (.f64 (.f64 (/.f64 (.f64 D M) (.f64 2 d)) (sqrt.f64 h)) (.f64 (/.f64 (.f64 D M) (.f64 2 d)) (sqrt.f64 h))) l))))
	15.8b	(.f64 (.f64 w0 (.f64 (cbrt.f64 (sqrt.f64 (-.f64 1 (.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2) (/.f64 h l))))) (cbrt.f64 (sqrt.f64 (-.f64 1 (.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2) (/.f64 h l))))))) (cbrt.f64 (sqrt.f64 (-.f64 1 (.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2) (/.f64 h l))))))
▶	13.5b	(.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))))))
	57.6b	(.f64 w0 (.f64 (sqrt.f64 (.f64 (.f64 (/.f64 h l) (pow.f64 (/.f64 D d) 2)) -1/4)) (neg.f64 M)))
	59.7b	(.f64 D (.f64 (sqrt.f64 (.f64 (/.f64 (.f64 (.f64 M M) h) (.f64 l (*.f64 d d))) -1/4)) w0))

Compiler

Compiled 8698 to 5472 computations (37.1% saved)

localize13.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	2.6b	(.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))))))
✓	4.7b	(sqrt.f64 (-.f64 1 (.f64 (/.f64 (.f64 M D) (.f64 2 d)) (.f64 (/.f64 (.f64 M D) (.f64 2 d)) (/.f64 h l)))))
	6.3b	(/.f64 (.f64 M D) (.f64 2 d))
✓	11.1b	(.f64 (/.f64 (.f64 M D) (*.f64 2 d)) (/.f64 h l))

series555.0ms (4%)

Counts

3 → 168

Calls

3 calls:

335.0ms

(*.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))))))

171.0ms

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

49.0ms

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

rewrite38.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

46×	`add-cbrt-cube_binary64`
46×	`add-exp-log_binary64`
25×	`add-sqr-sqrt_binary64`
19×	`associate-r_binary64`
19×	`cbrt-unprod_binary64`

Counts

3 → 97

Calls

3 calls:

16.0ms

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

7.0ms

(*.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))))))

4.0ms

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

simplify151.0ms (1.1%)

Algorithm

1×	egg-herbie

Rules

604×	`times-frac_binary64`
414×	`associate-/l*_binary64`
405×	`associate-/r*_binary64`
333×	`associate-*r/_binary64`
281×	`associate-*l/_binary64`

Counts

265 → 270

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	498	10374
1	1286	9786
2	4989	9786

prune456.0ms (3.3%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	345	3	348
Fresh	2	8	10
Picked	1	0	1
Done	1	0	1
Total	349	11	360

Error

4.9b

Counts

360 → 11

Alt Table

Status	Error	Program
	13.5b	(.f64 w0 (sqrt.f64 (-.f64 1 (.f64 (/.f64 (.f64 M D) (.f64 2 d)) (.f64 (.f64 (cbrt.f64 (/.f64 (.f64 M D) (.f64 2 d))) (cbrt.f64 (/.f64 (.f64 M D) (.f64 2 d)))) (.f64 (cbrt.f64 (/.f64 (.f64 M D) (*.f64 2 d))) (/.f64 h l)))))))
	15.9b	w0
	40.3b	(.f64 w0 (sqrt.f64 (-.f64 1 (/.f64 (.f64 (.f64 (/.f64 (.f64 D M) (.f64 2 d)) (sqrt.f64 h)) (.f64 (/.f64 (.f64 D M) (.f64 2 d)) (sqrt.f64 h))) l))))
	13.6b	(.f64 w0 (sqrt.f64 (-.f64 1 (.f64 (/.f64 (.f64 M D) (.f64 2 d)) (/.f64 (.f64 (.f64 M D) h) (.f64 (.f64 2 d) l))))))
	15.8b	(.f64 (.f64 w0 (.f64 (cbrt.f64 (sqrt.f64 (-.f64 1 (.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2) (/.f64 h l))))) (cbrt.f64 (sqrt.f64 (-.f64 1 (.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2) (/.f64 h l))))))) (cbrt.f64 (sqrt.f64 (-.f64 1 (.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2) (/.f64 h l))))))
	60.0b	(.f64 (sqrt.f64 (.f64 (/.f64 (.f64 h (.f64 D D)) (.f64 l (.f64 d d))) -1/4)) (neg.f64 (*.f64 M w0)))
	61.1b	(/.f64 (.f64 (sqrt.f64 (neg.f64 (.f64 1/4 (/.f64 (.f64 (pow.f64 D 2) (.f64 h (pow.f64 M 2))) l)))) w0) d)
	25.2b	(.f64 w0 (sqrt.f64 (-.f64 1 (.f64 1/4 (.f64 (pow.f64 (/.f64 D d) 2) (/.f64 (.f64 (*.f64 M M) h) l))))))
	57.6b	(.f64 (sqrt.f64 (.f64 (.f64 (/.f64 h l) (pow.f64 (/.f64 D d) 2)) -1/4)) (neg.f64 (.f64 M w0)))
	57.6b	(.f64 w0 (.f64 (sqrt.f64 (.f64 (.f64 (/.f64 h l) (pow.f64 (/.f64 D d) 2)) -1/4)) (neg.f64 M)))
	59.7b	(.f64 D (.f64 (sqrt.f64 (.f64 (/.f64 (.f64 (.f64 M M) h) (.f64 l (*.f64 d d))) -1/4)) w0))

Compiler

Compiled 14461 to 7797 computations (46.1% saved)

regimes3.4s (24.4%)

Accuracy

Total 3.1b remaining (36.1%)

Threshold costs 0b (0%)

Counts

144 → 3

Compiler

Compiled 76924 to 53827 computations (30% saved)

bsearch8.0ms (0.1%)

Compiler: Compiled 9 to 8 computations (11.1% saved)

simplify8.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

31×	`*-commutative_binary64`
22×	`+-commutative_binary64`
22×	`sub-neg_binary64`
19×	`neg-sub0_binary64`
19×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	49	144
1	71	144
2	93	144
3	133	144
4	174	144
5	200	144
6	216	144
7	220	144
8	221	144
9	219	144

end217.0ms (1.6%)

Remove: (sort M D)
Compiler: Compiled 727 to 477 computations (34.4% saved)

Iter	Nodes	Cost
0	49	144
1	71	144
2	93	144
3	133	144
4	174	144
5	200	144
6	216	144
7	220	144
8	221	144
9	219	144

Iter	Nodes	Cost
0	49	144
1	71	144
2	93	144
3	133	144
4	174	144
5	200	144
6	216	144
7	220	144
8	221	144
9	219	144

Details

analyze2.9s (20.7%)

sample2.4s (17.5%)

simplify27.0ms (0.2%)

prune2.0ms (0%)

localize12.0ms (0.1%)

series922.0ms (6.6%)

rewrite34.0ms (0.2%)

simplify159.0ms (1.1%)

prune357.0ms (2.6%)

localize14.0ms (0.1%)

series563.0ms (4%)

rewrite24.0ms (0.2%)

simplify136.0ms (1%)

prune301.0ms (2.2%)

localize13.0ms (0.1%)

series585.0ms (4.2%)

rewrite35.0ms (0.3%)

simplify252.0ms (1.8%)

prune324.0ms (2.3%)

localize13.0ms (0.1%)

series555.0ms (4%)

rewrite38.0ms (0.3%)

simplify151.0ms (1.1%)

prune456.0ms (3.3%)

regimes3.4s (24.4%)

bsearch8.0ms (0.1%)

simplify8.0ms (0.1%)

end217.0ms (1.6%)

Profiling

Iter	Nodes	Cost
0	49	144
1	71	144
2	93	144
3	133	144
4	174	144
5	200	144
6	216	144
7	220	144
8	221	144
9	219	144