Details

analyze3.2s (14%)

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
12.5%	87.2%	0.3%	7
12.5%	87.2%	0.3%	8
12.5%	87.2%	0.3%	9
12.5%	87.2%	0.3%	10
12.5%	87.2%	0.3%	11
18.7%	81%	0.3%	12
29.6%	70.1%	0.3%	13
29.6%	70.1%	0.3%	14

Compiler

Compiled 25 to 19 computations (24% saved)

sample2.9s (12.7%)

Symmetry

(sort M D)

Results

2.1s	8256×	body	128	valid
706.0ms	2795×	body	128	invalid

Compiler

Compiled 74 to 56 computations (24.3% saved)

simplify46.0ms (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

prune4.0ms (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

16.6b

Counts

2 → 1

Alt Table

Status	Error	Program
▶	16.6b	(.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)

localize27.0ms (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)))))
✓	5.6b	(/.f64 (.f64 M D) (.f64 2 d))
✓	7.5b	(sqrt.f64 (-.f64 1 (.f64 (pow.f64 (/.f64 (.f64 M D) (*.f64 2 d)) 2) (/.f64 h l))))
✓	13.7b	(.f64 (pow.f64 (/.f64 (.f64 M D) (*.f64 2 d)) 2) (/.f64 h l))

series1.5s (6.6%)

Counts

4 → 204

Calls

4 calls:

666.0ms	(.f64 w0 (sqrt.f64 (-.f64 1 (.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2) (/.f64 h l)))))
433.0ms	(.f64 (pow.f64 (/.f64 (.f64 M D) (*.f64 2 d)) 2) (/.f64 h l))
386.0ms	(sqrt.f64 (-.f64 1 (.f64 (pow.f64 (/.f64 (.f64 M D) (*.f64 2 d)) 2) (/.f64 h l))))
30.0ms	(/.f64 (.f64 M D) (.f64 2 d))

rewrite68.0ms (0.3%)

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:

21.0ms	(.f64 (pow.f64 (/.f64 (.f64 M D) (*.f64 2 d)) 2) (/.f64 h l))
11.0ms	(.f64 w0 (sqrt.f64 (-.f64 1 (.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2) (/.f64 h l)))))
8.0ms	(/.f64 (.f64 M D) (.f64 2 d))
6.0ms	(sqrt.f64 (-.f64 1 (.f64 (pow.f64 (/.f64 (.f64 M D) (*.f64 2 d)) 2) (/.f64 h l))))

simplify443.0ms (1.9%)

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

prune891.0ms (3.9%)

Pruning

14 alts after pruning (14 fresh and 0 done)

	Pruned	Kept	Total
New	300	14	314
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	301	14	315

Error

5.0b

Counts

315 → 14

Alt Table

Status	Error	Program
	57.4b	(/.f64 (.f64 (sqrt.f64 (neg.f64 (.f64 1/4 (/.f64 (.f64 (pow.f64 D 2) (.f64 h (pow.f64 M 2))) l)))) w0) d)
	30.7b	(.f64 w0 (sqrt.f64 (-.f64 1 (.f64 1/4 (/.f64 (.f64 (pow.f64 D 2) (.f64 (pow.f64 M 2) h)) (*.f64 l (pow.f64 d 2)))))))
	56.2b	(.f64 w0 (.f64 D (sqrt.f64 (.f64 (/.f64 (.f64 (.f64 M M) h) (.f64 l (*.f64 d d))) -1/4))))
	12.8b	(.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)))))
	16.1b	(.f64 w0 (sqrt.f64 (-.f64 1 (.f64 (pow.f64 (/.f64 M (/.f64 2 (/.f64 D d))) 2) (/.f64 h l)))))
	14.8b	(.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))))))
	56.8b	(.f64 w0 (sqrt.f64 (-.f64 1 (exp.f64 (+.f64 (.f64 (log.f64 (/.f64 (.f64 M D) (.f64 2 d))) 2) (-.f64 (log.f64 h) (log.f64 l)))))))
	24.8b	(-.f64 w0 (.f64 1/8 (.f64 (pow.f64 (/.f64 D d) 2) (/.f64 (.f64 (.f64 (*.f64 M M) h) w0) l))))
	22.7b	w0
▶	11.5b	(.f64 w0 (sqrt.f64 (-.f64 1 (/.f64 (.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2) h) l))))
	54.4b	(.f64 w0 (.f64 (sqrt.f64 (.f64 (.f64 (/.f64 h l) (pow.f64 (/.f64 D d) 2)) -1/4)) (neg.f64 M)))
	26.5b	(/.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)))))))
	59.6b	(.f64 w0 (.f64 M (sqrt.f64 (.f64 (.f64 (/.f64 h l) (pow.f64 (/.f64 D d) 2)) -1/4))))
	17.4b	(.f64 (.f64 (cbrt.f64 (.f64 w0 (sqrt.f64 (-.f64 1 (.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2) (/.f64 h l)))))) (cbrt.f64 (.f64 w0 (sqrt.f64 (-.f64 1 (.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2) (/.f64 h l))))))) (cbrt.f64 (.f64 w0 (sqrt.f64 (-.f64 1 (.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2) (/.f64 h l)))))))

Compiler

Compiled 12508 to 7561 computations (39.6% saved)

localize29.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	3.8b	(/.f64 (.f64 (pow.f64 (/.f64 (.f64 M D) (*.f64 2 d)) 2) h) l)
	5.6b	(/.f64 (.f64 M D) (.f64 2 d))
✓	6.7b	(.f64 (pow.f64 (/.f64 (.f64 M D) (*.f64 2 d)) 2) h)
✓	7.5b	(sqrt.f64 (-.f64 1 (/.f64 (.f64 (pow.f64 (/.f64 (.f64 M D) (*.f64 2 d)) 2) h) l)))

series1.1s (4.7%)

Counts

3 → 156

Calls

3 calls:

431.0ms	(/.f64 (.f64 (pow.f64 (/.f64 (.f64 M D) (*.f64 2 d)) 2) h) l)
361.0ms	(sqrt.f64 (-.f64 1 (/.f64 (.f64 (pow.f64 (/.f64 (.f64 M D) (*.f64 2 d)) 2) h) l)))
279.0ms	(.f64 (pow.f64 (/.f64 (.f64 M D) (*.f64 2 d)) 2) h)

rewrite47.0ms (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:

13.0ms	(sqrt.f64 (-.f64 1 (/.f64 (.f64 (pow.f64 (/.f64 (.f64 M D) (*.f64 2 d)) 2) h) l)))
12.0ms	(/.f64 (.f64 (pow.f64 (/.f64 (.f64 M D) (*.f64 2 d)) 2) h) l)
10.0ms	(.f64 (pow.f64 (/.f64 (.f64 M D) (*.f64 2 d)) 2) h)

simplify332.0ms (1.4%)

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

prune751.0ms (3.3%)

Pruning

14 alts after pruning (14 fresh and 0 done)

	Pruned	Kept	Total
New	224	5	229
Fresh	4	9	13
Picked	1	0	1
Done	0	0	0
Total	229	14	243

Error

4.5b

Counts

243 → 14

Alt Table

Status	Error	Program
	24.8b	(-.f64 w0 (.f64 1/8 (.f64 (pow.f64 (/.f64 D d) 2) (/.f64 (.f64 (.f64 (*.f64 M M) h) w0) l))))
▶	9.6b	(.f64 w0 (sqrt.f64 (-.f64 1 (/.f64 (.f64 (/.f64 (.f64 M D) (.f64 2 d)) (.f64 (/.f64 (.f64 M D) (*.f64 2 d)) h)) l))))
	22.7b	w0
	11.0b	(.f64 w0 (sqrt.f64 (-.f64 1 (/.f64 (.f64 (pow.f64 (*.f64 (/.f64 M 2) (/.f64 D d)) 2) h) l))))
	16.1b	(.f64 w0 (sqrt.f64 (-.f64 1 (.f64 (pow.f64 (/.f64 M (/.f64 2 (/.f64 D d))) 2) (/.f64 h l)))))
	9.6b	(.f64 w0 (sqrt.f64 (-.f64 1 (/.f64 (.f64 (pow.f64 (.f64 (cbrt.f64 (/.f64 (.f64 M D) (.f64 2 d))) (cbrt.f64 (/.f64 (.f64 M D) (.f64 2 d)))) 2) (.f64 (pow.f64 (cbrt.f64 (/.f64 (.f64 M D) (.f64 2 d))) 2) h)) l))))
	11.5b	(.f64 w0 (.f64 (fabs.f64 (cbrt.f64 (-.f64 1 (/.f64 (.f64 h (pow.f64 (/.f64 (.f64 D M) (.f64 2 d)) 2)) l)))) (sqrt.f64 (cbrt.f64 (-.f64 1 (/.f64 (.f64 h (pow.f64 (/.f64 (.f64 D M) (.f64 2 d)) 2)) l))))))
	17.4b	(.f64 (.f64 (cbrt.f64 (.f64 w0 (sqrt.f64 (-.f64 1 (.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2) (/.f64 h l)))))) (cbrt.f64 (.f64 w0 (sqrt.f64 (-.f64 1 (.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2) (/.f64 h l))))))) (cbrt.f64 (.f64 w0 (sqrt.f64 (-.f64 1 (.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2) (/.f64 h l)))))))
	21.5b	(.f64 w0 (sqrt.f64 (-.f64 1 (/.f64 (.f64 1/4 (.f64 (pow.f64 (/.f64 D d) 2) (.f64 (*.f64 M M) h))) l))))
	57.4b	(/.f64 (.f64 (sqrt.f64 (neg.f64 (.f64 1/4 (/.f64 (.f64 (pow.f64 D 2) (.f64 h (pow.f64 M 2))) l)))) w0) d)
	56.2b	(.f64 w0 (.f64 D (sqrt.f64 (.f64 (/.f64 (.f64 (.f64 M M) h) (.f64 l (*.f64 d d))) -1/4))))
	54.4b	(.f64 w0 (.f64 (sqrt.f64 (.f64 (.f64 (/.f64 h l) (pow.f64 (/.f64 D d) 2)) -1/4)) (neg.f64 M)))
	26.5b	(/.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)))))))
	59.6b	(.f64 w0 (.f64 M (sqrt.f64 (.f64 (.f64 (/.f64 h l) (pow.f64 (/.f64 D d) 2)) -1/4))))

Compiler

Compiled 8369 to 5317 computations (36.5% saved)

localize26.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	3.8b	(/.f64 (.f64 (/.f64 (.f64 M D) (.f64 2 d)) (.f64 (/.f64 (.f64 M D) (.f64 2 d)) h)) l)
	5.6b	(/.f64 (.f64 M D) (.f64 2 d))
✓	7.5b	(.f64 (/.f64 (.f64 M D) (*.f64 2 d)) h)
✓	7.5b	(sqrt.f64 (-.f64 1 (/.f64 (.f64 (/.f64 (.f64 M D) (.f64 2 d)) (.f64 (/.f64 (.f64 M D) (.f64 2 d)) h)) l)))

series813.0ms (3.5%)

Counts

3 → 156

Calls

3 calls:

397.0ms

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

344.0ms

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

71.0ms

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

rewrite96.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

226×	`add-cbrt-cube_binary64`
226×	`add-exp-log_binary64`
108×	`cbrt-unprod_binary64`
108×	`prod-exp_binary64`
79×	`cbrt-undiv_binary64`

Counts

3 → 135

Calls

3 calls:

17.0ms

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

16.0ms

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

13.0ms

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

simplify345.0ms (1.5%)

Algorithm

1×	egg-herbie

Rules

584×	`associate-/l*_binary64`
484×	`associate-l_binary64`
455×	`associate-/r*_binary64`
414×	`associate-*l/_binary64`
390×	`associate-*r/_binary64`

Counts

291 → 252

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	458	9762
1	1205	8761
2	4703	8697
3	4996	8697

prune1.3s (5.5%)

Pruning

15 alts after pruning (14 fresh and 1 done)

	Pruned	Kept	Total
New	328	2	330
Fresh	1	12	13
Picked	0	1	1
Done	0	0	0
Total	329	15	344

Error

4.3b

Counts

344 → 15

Alt Table

Status	Error	Program
	24.8b	(-.f64 w0 (.f64 1/8 (.f64 (pow.f64 (/.f64 D d) 2) (/.f64 (.f64 (.f64 (*.f64 M M) h) w0) l))))
✓	9.6b	(.f64 w0 (sqrt.f64 (-.f64 1 (/.f64 (.f64 (/.f64 (.f64 M D) (.f64 2 d)) (.f64 (/.f64 (.f64 M D) (*.f64 2 d)) h)) l))))
	22.7b	w0
	11.0b	(.f64 w0 (sqrt.f64 (-.f64 1 (/.f64 (.f64 (pow.f64 (*.f64 (/.f64 M 2) (/.f64 D d)) 2) h) l))))
	26.5b	(/.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)))))))
	9.6b	(.f64 w0 (sqrt.f64 (-.f64 1 (/.f64 (.f64 (.f64 (pow.f64 (cbrt.f64 (/.f64 (.f64 D M) (.f64 2 d))) 2) (cbrt.f64 (/.f64 (.f64 D M) (.f64 2 d)))) (.f64 (/.f64 (.f64 M D) (.f64 2 d)) h)) l))))
	16.1b	(.f64 w0 (sqrt.f64 (-.f64 1 (.f64 (pow.f64 (/.f64 M (/.f64 2 (/.f64 D d))) 2) (/.f64 h l)))))
	11.5b	(.f64 w0 (.f64 (fabs.f64 (cbrt.f64 (-.f64 1 (/.f64 (.f64 h (pow.f64 (/.f64 (.f64 D M) (.f64 2 d)) 2)) l)))) (sqrt.f64 (cbrt.f64 (-.f64 1 (/.f64 (.f64 h (pow.f64 (/.f64 (.f64 D M) (.f64 2 d)) 2)) l))))))
	17.4b	(.f64 (.f64 (cbrt.f64 (.f64 w0 (sqrt.f64 (-.f64 1 (.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2) (/.f64 h l)))))) (cbrt.f64 (.f64 w0 (sqrt.f64 (-.f64 1 (.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2) (/.f64 h l))))))) (cbrt.f64 (.f64 w0 (sqrt.f64 (-.f64 1 (.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2) (/.f64 h l)))))))
	21.5b	(.f64 w0 (sqrt.f64 (-.f64 1 (/.f64 (.f64 1/4 (.f64 (pow.f64 (/.f64 D d) 2) (.f64 (*.f64 M M) h))) l))))
	57.4b	(/.f64 (.f64 (sqrt.f64 (neg.f64 (.f64 1/4 (/.f64 (.f64 (pow.f64 D 2) (.f64 h (pow.f64 M 2))) l)))) w0) d)
▶	8.8b	(.f64 w0 (sqrt.f64 (-.f64 1 (.f64 (/.f64 (.f64 D M) (.f64 2 d)) (/.f64 (.f64 h (/.f64 (.f64 D M) (*.f64 2 d))) l)))))
	56.2b	(.f64 w0 (.f64 D (sqrt.f64 (.f64 (/.f64 (.f64 (.f64 M M) h) (.f64 l (*.f64 d d))) -1/4))))
	54.4b	(.f64 w0 (.f64 (sqrt.f64 (.f64 (.f64 (/.f64 h l) (pow.f64 (/.f64 D d) 2)) -1/4)) (neg.f64 M)))
	59.6b	(.f64 w0 (.f64 M (sqrt.f64 (.f64 (.f64 (/.f64 h l) (pow.f64 (/.f64 D d) 2)) -1/4))))

Compiler

Compiled 13658 to 7512 computations (45% saved)

localize24.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	5.6b	(/.f64 (.f64 D M) (.f64 2 d))
✓	6.5b	(/.f64 (.f64 h (/.f64 (.f64 D M) (*.f64 2 d))) l)
✓	7.5b	(.f64 h (/.f64 (.f64 D M) (*.f64 2 d)))
✓	7.5b	(sqrt.f64 (-.f64 1 (.f64 (/.f64 (.f64 D M) (.f64 2 d)) (/.f64 (.f64 h (/.f64 (.f64 D M) (.f64 2 d))) l))))

series506.0ms (2.2%)

Counts

4 → 192

Calls

4 calls:

303.0ms	(sqrt.f64 (-.f64 1 (.f64 (/.f64 (.f64 D M) (.f64 2 d)) (/.f64 (.f64 h (/.f64 (.f64 D M) (.f64 2 d))) l))))
114.0ms	(/.f64 (.f64 h (/.f64 (.f64 D M) (*.f64 2 d))) l)
59.0ms	(.f64 h (/.f64 (.f64 D M) (*.f64 2 d)))
30.0ms	(/.f64 (.f64 D M) (.f64 2 d))

rewrite62.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

59×	`add-cbrt-cube_binary64`
59×	`add-exp-log_binary64`
22×	`cbrt-unprod_binary64`
22×	`prod-exp_binary64`
18×	`cbrt-undiv_binary64`

Counts

4 → 103

Calls

4 calls:

14.0ms	(/.f64 (.f64 h (/.f64 (.f64 D M) (*.f64 2 d))) l)
12.0ms	(/.f64 (.f64 D M) (.f64 2 d))
11.0ms	(.f64 h (/.f64 (.f64 D M) (*.f64 2 d)))
9.0ms	(sqrt.f64 (-.f64 1 (.f64 (/.f64 (.f64 D M) (.f64 2 d)) (/.f64 (.f64 h (/.f64 (.f64 D M) (.f64 2 d))) l))))

simplify295.0ms (1.3%)

Algorithm

1×	egg-herbie

Rules

461×	`times-frac_binary64`
397×	`fma-def_binary64`
360×	`associate-/l*_binary64`
287×	`associate-r_binary64`
272×	`associate-/r*_binary64`

Counts

295 → 193

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	355	7289
1	926	6662
2	4367	6642
3	4979	6642
4	4985	6642

prune828.0ms (3.6%)

Pruning

14 alts after pruning (13 fresh and 1 done)

	Pruned	Kept	Total
New	223	1	224
Fresh	1	12	13
Picked	1	0	1
Done	0	1	1
Total	225	14	239

Error

4.3b

Counts

239 → 14

Alt Table

Status	Error	Program
	24.8b	(-.f64 w0 (.f64 1/8 (.f64 (pow.f64 (/.f64 D d) 2) (/.f64 (.f64 (.f64 (*.f64 M M) h) w0) l))))
✓	9.6b	(.f64 w0 (sqrt.f64 (-.f64 1 (/.f64 (.f64 (/.f64 (.f64 M D) (.f64 2 d)) (.f64 (/.f64 (.f64 M D) (*.f64 2 d)) h)) l))))
	22.7b	w0
	11.0b	(.f64 w0 (sqrt.f64 (-.f64 1 (/.f64 (.f64 (pow.f64 (*.f64 (/.f64 M 2) (/.f64 D d)) 2) h) l))))
	16.1b	(.f64 w0 (sqrt.f64 (-.f64 1 (.f64 (pow.f64 (/.f64 M (/.f64 2 (/.f64 D d))) 2) (/.f64 h l)))))
	11.5b	(.f64 w0 (.f64 (fabs.f64 (cbrt.f64 (-.f64 1 (/.f64 (.f64 h (pow.f64 (/.f64 (.f64 D M) (.f64 2 d)) 2)) l)))) (sqrt.f64 (cbrt.f64 (-.f64 1 (/.f64 (.f64 h (pow.f64 (/.f64 (.f64 D M) (.f64 2 d)) 2)) l))))))
	17.4b	(.f64 (.f64 (cbrt.f64 (.f64 w0 (sqrt.f64 (-.f64 1 (.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2) (/.f64 h l)))))) (cbrt.f64 (.f64 w0 (sqrt.f64 (-.f64 1 (.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2) (/.f64 h l))))))) (cbrt.f64 (.f64 w0 (sqrt.f64 (-.f64 1 (.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2) (/.f64 h l)))))))
	21.5b	(.f64 w0 (sqrt.f64 (-.f64 1 (/.f64 (.f64 1/4 (.f64 (pow.f64 (/.f64 D d) 2) (.f64 (*.f64 M M) h))) l))))
	57.4b	(/.f64 (.f64 (sqrt.f64 (neg.f64 (.f64 1/4 (/.f64 (.f64 (pow.f64 D 2) (.f64 h (pow.f64 M 2))) l)))) w0) d)
	8.9b	(.f64 w0 (sqrt.f64 (-.f64 1 (.f64 (/.f64 (.f64 D M) (.f64 2 d)) (/.f64 (.f64 (.f64 (cbrt.f64 h) (cbrt.f64 h)) (.f64 (cbrt.f64 h) (/.f64 (.f64 D M) (*.f64 2 d)))) l)))))
	56.2b	(.f64 w0 (.f64 D (sqrt.f64 (.f64 (/.f64 (.f64 (.f64 M M) h) (.f64 l (*.f64 d d))) -1/4))))
	54.4b	(.f64 w0 (.f64 (sqrt.f64 (.f64 (.f64 (/.f64 h l) (pow.f64 (/.f64 D d) 2)) -1/4)) (neg.f64 M)))
	26.5b	(/.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)))))))
	59.6b	(.f64 w0 (.f64 M (sqrt.f64 (.f64 (.f64 (/.f64 h l) (pow.f64 (/.f64 D d) 2)) -1/4))))

Compiler

Compiled 8815 to 4944 computations (43.9% saved)

regimes6.9s (30.2%)

Accuracy

Total 3.1b remaining (43.4%)

Threshold costs 0b (0%)

Counts

209 → 1

Compiler

Compiled 98402 to 70222 computations (28.6% saved)

simplify5.0ms (0%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	21	48
1	33	48
2	44	48
3	56	48
4	77	48
5	89	48
6	97	48
7	100	48
8	99	48

end423.0ms (1.8%)

Remove: (sort M D)
Compiler: Compiled 598 to 404 computations (32.4% saved)

Details

analyze3.2s (14%)

sample2.9s (12.7%)

simplify46.0ms (0.2%)

prune4.0ms (0%)

localize27.0ms (0.1%)

series1.5s (6.6%)

rewrite68.0ms (0.3%)

simplify443.0ms (1.9%)

prune891.0ms (3.9%)

localize29.0ms (0.1%)

series1.1s (4.7%)

rewrite47.0ms (0.2%)

simplify332.0ms (1.4%)

prune751.0ms (3.3%)

localize26.0ms (0.1%)

series813.0ms (3.5%)

rewrite96.0ms (0.4%)

simplify345.0ms (1.5%)

prune1.3s (5.5%)

localize24.0ms (0.1%)

series506.0ms (2.2%)

rewrite62.0ms (0.3%)

simplify295.0ms (1.3%)

prune828.0ms (3.6%)

regimes6.9s (30.2%)

simplify5.0ms (0%)

end423.0ms (1.8%)

Profiling