Details

analyze2.1s (13.4%)

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)

sample5.8s (36.1%)

Symmetry

(sort M D)

Results

3.3s	13306×	body	128	invalid
2.3s	8256×	body	128	valid

Compiler

Compiled 122 to 95 computations (22.1% saved)

simplify41.0ms (0.3%)

Algorithm

1×	egg-herbie

Rules

466×	`fma-def_binary64`
437×	`*-commutative_binary64`
425×	`associate-/l*_binary64`
347×	`cancel-sign-sub-inv_binary64`
263×	`associate-/l/_binary64`

Counts

1 → 2

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	24	41
1	62	41
2	188	39
3	1071	39
4	3610	39
5	5106	39

prune4.0ms (0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

	Pruned	Kept	Total
New	1	1	2
Fresh	1	0	1
Picked	0	0	0
Done	0	0	0
Total	2	1	3

Error

29.7b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	29.7b	(.f64 (.f64 (sqrt.f64 (/.f64 d h)) (sqrt.f64 (/.f64 d l))) (fma.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2) (*.f64 (/.f64 h l) -1/2) 1))

Compiler

Compiled 128 to 88 computations (31.3% saved)

localize19.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	6.1b	(.f64 (.f64 (sqrt.f64 (/.f64 d h)) (sqrt.f64 (/.f64 d l))) (fma.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2) (*.f64 (/.f64 h l) -1/2) 1))
✓	10.7b	(fma.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2) (*.f64 (/.f64 h l) -1/2) 1)
✓	12.2b	(sqrt.f64 (/.f64 d h))
✓	15.1b	(sqrt.f64 (/.f64 d l))

series305.0ms (1.9%)

Counts

4 → 92

Calls

4 calls:

191.0ms	(.f64 (.f64 (sqrt.f64 (/.f64 d h)) (sqrt.f64 (/.f64 d l))) (fma.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2) (*.f64 (/.f64 h l) -1/2) 1))
80.0ms	(fma.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2) (*.f64 (/.f64 h l) -1/2) 1)
18.0ms	(sqrt.f64 (/.f64 d l))
17.0ms	(sqrt.f64 (/.f64 d h))

rewrite235.0ms (1.5%)

Algorithm

4×	egg-rewrite

Rules

60×	`egg`
60×	`egg`
23×	`egg`
22×	`egg`

Counts

4 → 165

Calls

4 calls:

73.0ms	(.f64 (.f64 (sqrt.f64 (/.f64 d h)) (sqrt.f64 (/.f64 d l))) (fma.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2) (*.f64 (/.f64 h l) -1/2) 1))
70.0ms	(fma.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2) (*.f64 (/.f64 h l) -1/2) 1)
46.0ms	(sqrt.f64 (/.f64 d l))
43.0ms	(sqrt.f64 (/.f64 d h))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	5	6
1	104	6
2	1317	6
3	5154	6
0	5	6
1	104	6
2	1317	6
3	5154	6
0	16	23
1	334	23
2	4185	23
3	5145	23
0	22	37
1	465	36
2	4917	36
3	5040	36

simplify96.0ms (0.6%)

Algorithm

1×	egg-herbie

Rules

724×	`associate-/l/_binary64`
373×	`distribute-rgt-neg-in_binary64`
355×	`distribute-lft-neg-in_binary64`
335×	`distribute-neg-frac_binary64`
327×	`neg-mul-1_binary64`

Counts

257 → 179

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	46	2622
1	101	2574
2	367	2484
3	2141	2484
4	4562	2484
5	5180	2484

prune502.0ms (3.1%)

Pruning

19 alts after pruning (19 fresh and 0 done)

	Pruned	Kept	Total
New	160	19	179
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	161	19	180

Error

11.4b

Counts

180 → 19

Alt Table

Status	Error	Program
	33.9b	(.f64 (.f64 (sqrt.f64 (/.f64 d h)) (sqrt.f64 (/.f64 d l))) 1)
	40.6b	(pow.f64 (cbrt.f64 (.f64 (/.f64 d (.f64 (sqrt.f64 h) (sqrt.f64 l))) (fma.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2) (*.f64 (/.f64 h l) -1/2) 1))) 3)
	39.2b	(.f64 (.f64 (.f64 (pow.f64 (/.f64 1 (cbrt.f64 (.f64 h h))) 1/2) (pow.f64 (/.f64 d (cbrt.f64 h)) 1/2)) (sqrt.f64 (/.f64 d l))) (fma.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2) (*.f64 (/.f64 h l) -1/2) 1))
	29.8b	(.f64 (.f64 (sqrt.f64 (/.f64 d h)) (.f64 (sqrt.f64 (cbrt.f64 (/.f64 d l))) (pow.f64 (.f64 (sqrt.f64 (cbrt.f64 (/.f64 d l))) (sqrt.f64 (/.f64 d l))) 1/2))) (fma.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2) (*.f64 (/.f64 h l) -1/2) 1))
	40.3b	(.f64 (/.f64 d (.f64 (sqrt.f64 h) (sqrt.f64 l))) (fma.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2) (*.f64 (/.f64 h l) -1/2) 1))
	43.7b	(.f64 (.f64 (.f64 (sqrt.f64 (neg.f64 d)) (pow.f64 (/.f64 1 (neg.f64 h)) 1/2)) (sqrt.f64 (/.f64 d l))) (fma.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2) (.f64 (/.f64 h l) -1/2) 1))
	43.8b	(.f64 (.f64 (sqrt.f64 (/.f64 d h)) (/.f64 (sqrt.f64 (neg.f64 d)) (sqrt.f64 (neg.f64 l)))) (fma.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2) (*.f64 (/.f64 h l) -1/2) 1))
	50.2b	(.f64 (.f64 (sqrt.f64 (/.f64 d h)) (.f64 (cbrt.f64 d) (pow.f64 (.f64 (/.f64 1 l) (sqrt.f64 (/.f64 d l))) 1/3))) (fma.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2) (*.f64 (/.f64 h l) -1/2) 1))
	44.3b	(.f64 (.f64 (sqrt.f64 (/.f64 d h)) (.f64 (pow.f64 (/.f64 1 (sqrt.f64 l)) 1/2) (pow.f64 (/.f64 d (sqrt.f64 l)) 1/2))) (fma.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2) (.f64 (/.f64 h l) -1/2) 1))
	42.9b	(.f64 (sqrt.f64 (/.f64 1 (.f64 l h))) d)
	43.8b	(.f64 (.f64 (sqrt.f64 (/.f64 d h)) (.f64 (sqrt.f64 (neg.f64 d)) (pow.f64 (/.f64 1 (neg.f64 l)) 1/2))) (fma.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2) (.f64 (/.f64 h l) -1/2) 1))
	39.6b	(.f64 (.f64 (cbrt.f64 (pow.f64 (/.f64 d h) 3/2)) (sqrt.f64 (/.f64 d l))) (fma.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2) (*.f64 (/.f64 h l) -1/2) 1))
	29.8b	(.f64 (.f64 (.f64 (sqrt.f64 (cbrt.f64 (/.f64 d h))) (pow.f64 (.f64 (sqrt.f64 (cbrt.f64 (/.f64 d h))) (sqrt.f64 (/.f64 d h))) 1/2)) (sqrt.f64 (/.f64 d l))) (fma.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2) (*.f64 (/.f64 h l) -1/2) 1))
▶	29.7b	(.f64 (sqrt.f64 (/.f64 d h)) (.f64 (sqrt.f64 (/.f64 d l)) (fma.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2) (*.f64 (/.f64 h l) -1/2) 1)))
	29.8b	(.f64 (.f64 (sqrt.f64 (/.f64 d h)) (.f64 (pow.f64 (.f64 (sqrt.f64 (/.f64 d l)) (cbrt.f64 (/.f64 d l))) 1/2) (sqrt.f64 (sqrt.f64 (cbrt.f64 (/.f64 d l)))))) (fma.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2) (*.f64 (/.f64 h l) -1/2) 1))
	42.7b	(.f64 (.f64 (/.f64 (sqrt.f64 d) (sqrt.f64 h)) (sqrt.f64 (/.f64 d l))) (fma.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2) (*.f64 (/.f64 h l) -1/2) 1))
	59.8b	(.f64 -1/8 (.f64 (/.f64 (*.f64 (pow.f64 D 2) (pow.f64 M 2)) d) (sqrt.f64 (/.f64 h (pow.f64 l 3)))))
	61.5b	(log.f64 (pow.f64 (exp.f64 (/.f64 d (.f64 (sqrt.f64 h) (sqrt.f64 l)))) (fma.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2) (.f64 (/.f64 h l) -1/2) 1)))
	39.3b	(.f64 (.f64 (.f64 (pow.f64 (/.f64 (cbrt.f64 (.f64 d d)) 1) 1/2) (pow.f64 (/.f64 (cbrt.f64 d) h) 1/2)) (sqrt.f64 (/.f64 d l))) (fma.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2) (*.f64 (/.f64 h l) -1/2) 1))

Compiler

Compiled 6940 to 3622 computations (47.8% saved)

localize20.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	4.3b	(/.f64 (.f64 M D) (.f64 d 2))
	10.7b	(fma.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2) (*.f64 (/.f64 h l) -1/2) 1)
	12.2b	(sqrt.f64 (/.f64 d h))
	15.1b	(sqrt.f64 (/.f64 d l))

series15.0ms (0.1%)

Counts

1 → 36

Calls

1 calls:

15.0ms

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

rewrite53.0ms (0.3%)

Algorithm

1×	egg-rewrite

Rules

82× egg

Counts

1 → 82

Calls

1 calls:

52.0ms

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	10
1	171	10
2	2362	10
3	5133	10

simplify17.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

16×	`*-commutative_binary64`
15×	`associate-/l*_binary64`
11×	`associate-/r/_binary64`
10×	`associate-r_binary64`
8×	`associate-l_binary64`

Counts

118 → 82

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	360
1	14	360
2	28	360
3	47	360
4	73	360
5	72	360
6	72	360

prune280.0ms (1.7%)

Pruning

17 alts after pruning (17 fresh and 0 done)

	Pruned	Kept	Total
New	230	4	234
Fresh	5	13	18
Picked	1	0	1
Done	0	0	0
Total	236	17	253

Error

10.9b

Counts

253 → 17

Alt Table

Status	Error	Program
	33.9b	(.f64 (.f64 (sqrt.f64 (/.f64 d h)) (sqrt.f64 (/.f64 d l))) 1)
	40.6b	(pow.f64 (cbrt.f64 (.f64 (/.f64 d (.f64 (sqrt.f64 h) (sqrt.f64 l))) (fma.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2) (*.f64 (/.f64 h l) -1/2) 1))) 3)
	39.2b	(.f64 (.f64 (.f64 (pow.f64 (/.f64 1 (cbrt.f64 (.f64 h h))) 1/2) (pow.f64 (/.f64 d (cbrt.f64 h)) 1/2)) (sqrt.f64 (/.f64 d l))) (fma.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2) (*.f64 (/.f64 h l) -1/2) 1))
	43.6b	(.f64 (sqrt.f64 (/.f64 d h)) (.f64 (/.f64 (sqrt.f64 (neg.f64 d)) (sqrt.f64 (neg.f64 l))) (fma.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2) (*.f64 (/.f64 h l) -1/2) 1)))
	40.3b	(.f64 (/.f64 d (.f64 (sqrt.f64 h) (sqrt.f64 l))) (fma.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2) (*.f64 (/.f64 h l) -1/2) 1))
	43.7b	(.f64 (.f64 (.f64 (sqrt.f64 (neg.f64 d)) (pow.f64 (/.f64 1 (neg.f64 h)) 1/2)) (sqrt.f64 (/.f64 d l))) (fma.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2) (.f64 (/.f64 h l) -1/2) 1))
▶	29.8b	(.f64 (.f64 (sqrt.f64 (/.f64 d h)) (.f64 (pow.f64 (.f64 (sqrt.f64 (/.f64 d l)) (cbrt.f64 (/.f64 d l))) 1/2) (sqrt.f64 (sqrt.f64 (cbrt.f64 (/.f64 d l)))))) (fma.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2) (*.f64 (/.f64 h l) -1/2) 1))
	30.9b	(.f64 (sqrt.f64 (/.f64 d h)) (.f64 (sqrt.f64 (/.f64 d l)) (fma.f64 (pow.f64 (.f64 M (/.f64 1 (/.f64 d (/.f64 D 2)))) 2) (.f64 (/.f64 h l) -1/2) 1)))
	44.3b	(.f64 (.f64 (sqrt.f64 (/.f64 d h)) (.f64 (pow.f64 (/.f64 1 (sqrt.f64 l)) 1/2) (pow.f64 (/.f64 d (sqrt.f64 l)) 1/2))) (fma.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2) (.f64 (/.f64 h l) -1/2) 1))
	42.9b	(.f64 (sqrt.f64 (/.f64 1 (.f64 l h))) d)
	43.8b	(.f64 (.f64 (sqrt.f64 (/.f64 d h)) (.f64 (sqrt.f64 (neg.f64 d)) (pow.f64 (/.f64 1 (neg.f64 l)) 1/2))) (fma.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2) (.f64 (/.f64 h l) -1/2) 1))
	39.6b	(.f64 (.f64 (cbrt.f64 (pow.f64 (/.f64 d h) 3/2)) (sqrt.f64 (/.f64 d l))) (fma.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2) (*.f64 (/.f64 h l) -1/2) 1))
	29.8b	(.f64 (.f64 (.f64 (sqrt.f64 (cbrt.f64 (/.f64 d h))) (pow.f64 (.f64 (sqrt.f64 (cbrt.f64 (/.f64 d h))) (sqrt.f64 (/.f64 d h))) 1/2)) (sqrt.f64 (/.f64 d l))) (fma.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2) (*.f64 (/.f64 h l) -1/2) 1))
	61.5b	(log.f64 (pow.f64 (exp.f64 (/.f64 d (.f64 (sqrt.f64 h) (sqrt.f64 l)))) (fma.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2) (.f64 (/.f64 h l) -1/2) 1)))
	42.7b	(.f64 (/.f64 (sqrt.f64 d) (sqrt.f64 h)) (.f64 (sqrt.f64 (/.f64 d l)) (fma.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2) (*.f64 (/.f64 h l) -1/2) 1)))
	59.8b	(.f64 -1/8 (.f64 (/.f64 (*.f64 (pow.f64 D 2) (pow.f64 M 2)) d) (sqrt.f64 (/.f64 h (pow.f64 l 3)))))
	43.5b	(.f64 (/.f64 (sqrt.f64 (neg.f64 d)) (sqrt.f64 (neg.f64 h))) (.f64 (sqrt.f64 (/.f64 d l)) (fma.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2) (*.f64 (/.f64 h l) -1/2) 1)))

Compiler

Compiled 8514 to 4141 computations (51.4% saved)

localize47.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
	10.7b	(fma.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2) (*.f64 (/.f64 h l) -1/2) 1)
	12.2b	(sqrt.f64 (/.f64 d h))
	15.1b	(sqrt.f64 (/.f64 d l))
✓	15.7b	(cbrt.f64 (/.f64 d l))

series799.0ms (5%)

Counts

1 → 24

Calls

1 calls:

799.0ms

(cbrt.f64 (/.f64 d l))

rewrite45.0ms (0.3%)

Algorithm

1×	egg-rewrite

Rules

50× egg

Counts

1 → 50

Calls

1 calls:

44.0ms

(cbrt.f64 (/.f64 d l))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	5	6
1	102	6
2	1298	6
3	5028	6

simplify70.0ms (0.4%)

Algorithm

1×	egg-herbie

Rules

782×	`div-sub_binary64`
558×	`fma-neg_binary64`
403×	`fma-def_binary64`
268×	`unswap-sqr_binary64`
265×	`associate-/l*_binary64`

Counts

74 → 56

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	34	312
1	69	312
2	127	288
3	362	144
4	873	144
5	2025	144
6	4170	144
7	5089	144

prune458.0ms (2.9%)

Pruning

18 alts after pruning (18 fresh and 0 done)

	Pruned	Kept	Total
New	262	2	264
Fresh	0	16	16
Picked	1	0	1
Done	0	0	0
Total	263	18	281

Error

10.9b

Counts

281 → 18

Alt Table

Status	Error	Program
	29.8b	(.f64 (.f64 (pow.f64 (sqrt.f64 (/.f64 h d)) -1) (.f64 (pow.f64 (.f64 (sqrt.f64 (/.f64 d l)) (cbrt.f64 (/.f64 d l))) 1/2) (sqrt.f64 (sqrt.f64 (cbrt.f64 (/.f64 d l)))))) (fma.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2) (*.f64 (/.f64 h l) -1/2) 1))
	33.9b	(.f64 (.f64 (sqrt.f64 (/.f64 d h)) (sqrt.f64 (/.f64 d l))) 1)
	40.6b	(pow.f64 (cbrt.f64 (.f64 (/.f64 d (.f64 (sqrt.f64 h) (sqrt.f64 l))) (fma.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2) (*.f64 (/.f64 h l) -1/2) 1))) 3)
	39.2b	(.f64 (.f64 (.f64 (pow.f64 (/.f64 1 (cbrt.f64 (.f64 h h))) 1/2) (pow.f64 (/.f64 d (cbrt.f64 h)) 1/2)) (sqrt.f64 (/.f64 d l))) (fma.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2) (*.f64 (/.f64 h l) -1/2) 1))
	43.6b	(.f64 (sqrt.f64 (/.f64 d h)) (.f64 (/.f64 (sqrt.f64 (neg.f64 d)) (sqrt.f64 (neg.f64 l))) (fma.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2) (*.f64 (/.f64 h l) -1/2) 1)))
	40.3b	(.f64 (/.f64 d (.f64 (sqrt.f64 h) (sqrt.f64 l))) (fma.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2) (*.f64 (/.f64 h l) -1/2) 1))
	43.7b	(.f64 (.f64 (.f64 (sqrt.f64 (neg.f64 d)) (pow.f64 (/.f64 1 (neg.f64 h)) 1/2)) (sqrt.f64 (/.f64 d l))) (fma.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2) (.f64 (/.f64 h l) -1/2) 1))
	44.3b	(.f64 (.f64 (sqrt.f64 (/.f64 d h)) (.f64 (pow.f64 (/.f64 1 (sqrt.f64 l)) 1/2) (pow.f64 (/.f64 d (sqrt.f64 l)) 1/2))) (fma.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2) (.f64 (/.f64 h l) -1/2) 1))
	42.9b	(.f64 (sqrt.f64 (/.f64 1 (.f64 l h))) d)
	43.8b	(.f64 (.f64 (sqrt.f64 (/.f64 d h)) (.f64 (sqrt.f64 (neg.f64 d)) (pow.f64 (/.f64 1 (neg.f64 l)) 1/2))) (fma.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2) (.f64 (/.f64 h l) -1/2) 1))
	39.6b	(.f64 (.f64 (cbrt.f64 (pow.f64 (/.f64 d h) 3/2)) (sqrt.f64 (/.f64 d l))) (fma.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2) (*.f64 (/.f64 h l) -1/2) 1))
▶	29.8b	(.f64 (.f64 (.f64 (sqrt.f64 (cbrt.f64 (/.f64 d h))) (pow.f64 (.f64 (sqrt.f64 (cbrt.f64 (/.f64 d h))) (sqrt.f64 (/.f64 d h))) 1/2)) (sqrt.f64 (/.f64 d l))) (fma.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2) (*.f64 (/.f64 h l) -1/2) 1))
	61.5b	(log.f64 (pow.f64 (exp.f64 (/.f64 d (.f64 (sqrt.f64 h) (sqrt.f64 l)))) (fma.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2) (.f64 (/.f64 h l) -1/2) 1)))
	42.7b	(.f64 (/.f64 (sqrt.f64 d) (sqrt.f64 h)) (.f64 (sqrt.f64 (/.f64 d l)) (fma.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2) (*.f64 (/.f64 h l) -1/2) 1)))
	30.0b	(.f64 (.f64 (pow.f64 (sqrt.f64 (cbrt.f64 (/.f64 d h))) 3) (.f64 (pow.f64 (.f64 (sqrt.f64 (/.f64 d l)) (cbrt.f64 (/.f64 d l))) 1/2) (sqrt.f64 (sqrt.f64 (cbrt.f64 (/.f64 d l)))))) (fma.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2) (*.f64 (/.f64 h l) -1/2) 1))
	43.5b	(.f64 (/.f64 (sqrt.f64 (neg.f64 d)) (sqrt.f64 (neg.f64 h))) (.f64 (sqrt.f64 (/.f64 d l)) (fma.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2) (*.f64 (/.f64 h l) -1/2) 1)))
	30.9b	(.f64 (sqrt.f64 (/.f64 d h)) (.f64 (sqrt.f64 (/.f64 d l)) (fma.f64 (pow.f64 (.f64 M (/.f64 1 (/.f64 d (/.f64 D 2)))) 2) (.f64 (/.f64 h l) -1/2) 1)))
	59.8b	(.f64 -1/8 (.f64 (/.f64 (*.f64 (pow.f64 D 2) (pow.f64 M 2)) d) (sqrt.f64 (/.f64 h (pow.f64 l 3)))))

Compiler

Compiled 13401 to 5973 computations (55.4% saved)

localize32.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
	10.7b	(fma.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2) (*.f64 (/.f64 h l) -1/2) 1)
	12.2b	(sqrt.f64 (/.f64 d h))
✓	12.7b	(cbrt.f64 (/.f64 d h))
	15.1b	(sqrt.f64 (/.f64 d l))

series483.0ms (3%)

Counts

1 → 24

Calls

1 calls:

483.0ms

(cbrt.f64 (/.f64 d h))

rewrite44.0ms (0.3%)

Algorithm

1×	egg-rewrite

Rules

50× egg

Counts

1 → 50

Calls

1 calls:

43.0ms

(cbrt.f64 (/.f64 d h))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	5	6
1	102	6
2	1298	6
3	5028	6

simplify67.0ms (0.4%)

Algorithm

1×	egg-herbie

Rules

782×	`div-sub_binary64`
558×	`fma-neg_binary64`
403×	`fma-def_binary64`
268×	`unswap-sqr_binary64`
265×	`associate-/l*_binary64`

Counts

74 → 56

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	34	312
1	69	312
2	127	288
3	362	144
4	873	144
5	2025	144
6	4170	144
7	5089	144

prune303.0ms (1.9%)

Pruning

21 alts after pruning (20 fresh and 1 done)

	Pruned	Kept	Total
New	261	3	264
Fresh	0	17	17
Picked	0	1	1
Done	0	0	0
Total	261	21	282

Error

10.9b

Counts

282 → 21

Alt Table

Status	Error	Program
	29.8b	(.f64 (.f64 (pow.f64 (sqrt.f64 (/.f64 h d)) -1) (.f64 (pow.f64 (.f64 (sqrt.f64 (/.f64 d l)) (cbrt.f64 (/.f64 d l))) 1/2) (sqrt.f64 (sqrt.f64 (cbrt.f64 (/.f64 d l)))))) (fma.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2) (*.f64 (/.f64 h l) -1/2) 1))
	33.9b	(.f64 (.f64 (sqrt.f64 (/.f64 d h)) (sqrt.f64 (/.f64 d l))) 1)
	40.6b	(pow.f64 (cbrt.f64 (.f64 (/.f64 d (.f64 (sqrt.f64 h) (sqrt.f64 l))) (fma.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2) (*.f64 (/.f64 h l) -1/2) 1))) 3)
	39.2b	(.f64 (.f64 (.f64 (pow.f64 (/.f64 1 (cbrt.f64 (.f64 h h))) 1/2) (pow.f64 (/.f64 d (cbrt.f64 h)) 1/2)) (sqrt.f64 (/.f64 d l))) (fma.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2) (*.f64 (/.f64 h l) -1/2) 1))
	43.6b	(.f64 (sqrt.f64 (/.f64 d h)) (.f64 (/.f64 (sqrt.f64 (neg.f64 d)) (sqrt.f64 (neg.f64 l))) (fma.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2) (*.f64 (/.f64 h l) -1/2) 1)))
	40.3b	(.f64 (/.f64 d (.f64 (sqrt.f64 h) (sqrt.f64 l))) (fma.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2) (*.f64 (/.f64 h l) -1/2) 1))
	43.7b	(.f64 (.f64 (.f64 (sqrt.f64 (neg.f64 d)) (pow.f64 (/.f64 1 (neg.f64 h)) 1/2)) (sqrt.f64 (/.f64 d l))) (fma.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2) (.f64 (/.f64 h l) -1/2) 1))
	44.3b	(.f64 (.f64 (sqrt.f64 (/.f64 d h)) (.f64 (pow.f64 (/.f64 1 (sqrt.f64 l)) 1/2) (pow.f64 (/.f64 d (sqrt.f64 l)) 1/2))) (fma.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2) (.f64 (/.f64 h l) -1/2) 1))
	42.9b	(.f64 (sqrt.f64 (/.f64 1 (.f64 l h))) d)
	43.8b	(.f64 (.f64 (sqrt.f64 (/.f64 d h)) (.f64 (sqrt.f64 (neg.f64 d)) (pow.f64 (/.f64 1 (neg.f64 l)) 1/2))) (fma.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2) (.f64 (/.f64 h l) -1/2) 1))
	39.6b	(.f64 (.f64 (cbrt.f64 (pow.f64 (/.f64 d h) 3/2)) (sqrt.f64 (/.f64 d l))) (fma.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2) (*.f64 (/.f64 h l) -1/2) 1))
✓	29.8b	(.f64 (.f64 (.f64 (sqrt.f64 (cbrt.f64 (/.f64 d h))) (pow.f64 (.f64 (sqrt.f64 (cbrt.f64 (/.f64 d h))) (sqrt.f64 (/.f64 d h))) 1/2)) (sqrt.f64 (/.f64 d l))) (fma.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2) (*.f64 (/.f64 h l) -1/2) 1))
	61.5b	(log.f64 (pow.f64 (exp.f64 (/.f64 d (.f64 (sqrt.f64 h) (sqrt.f64 l)))) (fma.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2) (.f64 (/.f64 h l) -1/2) 1)))
	42.7b	(.f64 (/.f64 (sqrt.f64 d) (sqrt.f64 h)) (.f64 (sqrt.f64 (/.f64 d l)) (fma.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2) (*.f64 (/.f64 h l) -1/2) 1)))
	30.0b	(.f64 (.f64 (pow.f64 (sqrt.f64 (cbrt.f64 (/.f64 d h))) 3) (.f64 (pow.f64 (.f64 (sqrt.f64 (/.f64 d l)) (cbrt.f64 (/.f64 d l))) 1/2) (sqrt.f64 (sqrt.f64 (cbrt.f64 (/.f64 d l)))))) (fma.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2) (*.f64 (/.f64 h l) -1/2) 1))
	43.5b	(.f64 (/.f64 (sqrt.f64 (neg.f64 d)) (sqrt.f64 (neg.f64 h))) (.f64 (sqrt.f64 (/.f64 d l)) (fma.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2) (*.f64 (/.f64 h l) -1/2) 1)))
	34.1b	(.f64 (.f64 (.f64 (sqrt.f64 (cbrt.f64 (/.f64 d h))) (pow.f64 (.f64 (sqrt.f64 (cbrt.f64 (/.f64 d h))) (sqrt.f64 (/.f64 d h))) 1/2)) (sqrt.f64 (/.f64 d l))) 1)
	30.9b	(.f64 (sqrt.f64 (/.f64 d h)) (.f64 (sqrt.f64 (/.f64 d l)) (fma.f64 (pow.f64 (.f64 M (/.f64 1 (/.f64 d (/.f64 D 2)))) 2) (.f64 (/.f64 h l) -1/2) 1)))
	30.2b	(.f64 (.f64 (.f64 (sqrt.f64 (cbrt.f64 (/.f64 d h))) (pow.f64 (.f64 (sqrt.f64 (cbrt.f64 (/.f64 d h))) (sqrt.f64 (/.f64 d h))) 1/2)) (.f64 (pow.f64 (sqrt.f64 (sqrt.f64 (cbrt.f64 (/.f64 d l)))) 3) (pow.f64 (sqrt.f64 (sqrt.f64 (cbrt.f64 (/.f64 d l)))) 3))) (fma.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2) (.f64 (/.f64 h l) -1/2) 1))
	59.8b	(.f64 -1/8 (.f64 (/.f64 (*.f64 (pow.f64 D 2) (pow.f64 M 2)) d) (sqrt.f64 (/.f64 h (pow.f64 l 3)))))
	41.7b	(.f64 (.f64 (.f64 (sqrt.f64 (cbrt.f64 (/.f64 d h))) (pow.f64 (.f64 (sqrt.f64 (.f64 (cbrt.f64 (cbrt.f64 (.f64 d d))) (pow.f64 (.f64 (cbrt.f64 d) (/.f64 1 h)) 1/3))) (sqrt.f64 (/.f64 d h))) 1/2)) (sqrt.f64 (/.f64 d l))) (fma.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2) (.f64 (/.f64 h l) -1/2) 1))

Compiler

Compiled 12938 to 5621 computations (56.6% saved)

regimes3.3s (20.7%)

Accuracy

Total 6.3b remaining (34.6%)

Threshold costs 0b (0%)

Counts

170 → 3

Compiler

Compiled 43087 to 30399 computations (29.4% saved)

bsearch353.0ms (2.2%)

Steps

Iters	Range		Point
10	-5.567746969073129e-272	-1.349214698440699e-284	-1.3767179517938137e-284
4	-6.90104367990861e-90	-4.372262148684192e-90	-5.08348195434106e-90

Compiler

Compiled 6 to 5 computations (16.7% saved)

simplify12.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	46	142
1	65	142
2	71	142
3	74	142
4	73	142

end456.0ms (2.9%)

Remove: (sort M D)
Compiler: Compiled 1141 to 784 computations (31.3% saved)

Details

analyze2.1s (13.4%)

sample5.8s (36.1%)

simplify41.0ms (0.3%)

prune4.0ms (0%)

localize19.0ms (0.1%)

series305.0ms (1.9%)

rewrite235.0ms (1.5%)

simplify96.0ms (0.6%)

prune502.0ms (3.1%)

localize20.0ms (0.1%)

series15.0ms (0.1%)

rewrite53.0ms (0.3%)

simplify17.0ms (0.1%)

prune280.0ms (1.7%)

localize47.0ms (0.3%)

series799.0ms (5%)

rewrite45.0ms (0.3%)

simplify70.0ms (0.4%)

prune458.0ms (2.9%)

localize32.0ms (0.2%)

series483.0ms (3%)

rewrite44.0ms (0.3%)

simplify67.0ms (0.4%)

prune303.0ms (1.9%)

regimes3.3s (20.7%)

bsearch353.0ms (2.2%)

simplify12.0ms (0.1%)

end456.0ms (2.9%)

Profiling