Details

analyze2.2s (16.5%)

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)

sample6.3s (47.6%)

Symmetry

(sort M D)

Results

3.7s	13232×	body	128	invalid
2.5s	8256×	body	128	valid

Compiler

Compiled 122 to 95 computations (22.1% saved)

simplify35.0ms (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

27.1b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	27.1b	(.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))

Compiler

Compiled 128 to 88 computations (31.3% saved)

localize17.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	5.9b	(.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))
✓	10.4b	(fma.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2) (*.f64 (/.f64 h l) -1/2) 1)
✓	11.6b	(sqrt.f64 (/.f64 d h))
✓	14.1b	(sqrt.f64 (/.f64 d l))

series229.0ms (1.7%)

Counts

4 → 92

Calls

4 calls:

139.0ms	(.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))
66.0ms	(fma.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2) (*.f64 (/.f64 h l) -1/2) 1)
12.0ms	(sqrt.f64 (/.f64 d l))
12.0ms	(sqrt.f64 (/.f64 d h))

rewrite73.0ms (0.6%)

Algorithm

1×	batch-egg-rewrite

Rules

224×	`add-sqr-sqrt_binary64`
210×	`log1p-expm1-u_binary64`
210×	`expm1-log1p-u_binary64`
209×	`add-log-exp_binary64`
208×	`add-cbrt-cube_binary64`

Counts

4 → 86

Calls

4 calls:

70.0ms	(.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)
70.0ms	(sqrt.f64 (/.f64 d h))
70.0ms	(sqrt.f64 (/.f64 d l))

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	22	72
1	465	71
2	4917	71
3	5040	71

simplify82.0ms (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

178 → 101

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

prune121.0ms (0.9%)

Pruning

16 alts after pruning (16 fresh and 0 done)

	Pruned	Kept	Total
New	85	16	101
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	86	16	102

Error

12.6b

Counts

102 → 16

Alt Table

Status	Error	Program
	41.2b	(.f64 (.f64 (sqrt.f64 (/.f64 d h)) (.f64 (sqrt.f64 d) (sqrt.f64 (/.f64 1 l)))) (fma.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2) (.f64 (/.f64 h l) -1/2) 1))
	42.4b	(.f64 (sqrt.f64 (/.f64 1 (.f64 l h))) d)
	32.4b	(.f64 (.f64 (sqrt.f64 (/.f64 d h)) (sqrt.f64 (/.f64 d l))) 1)
	27.5b	(.f64 (.f64 (pow.f64 (cbrt.f64 (sqrt.f64 (/.f64 d h))) 3) (sqrt.f64 (/.f64 d l))) (fma.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2) (*.f64 (/.f64 h l) -1/2) 1))
	38.7b	(pow.f64 (cbrt.f64 (.f64 (fma.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2) (.f64 (/.f64 h l) -1/2) 1) (/.f64 d (*.f64 (sqrt.f64 l) (sqrt.f64 h))))) 3)
	43.2b	(.f64 (.f64 (/.f64 (sqrt.f64 (neg.f64 d)) (sqrt.f64 (neg.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))
	42.2b	(.f64 (.f64 (.f64 (sqrt.f64 d) (sqrt.f64 (/.f64 1 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))
	27.2b	(.f64 (.f64 (pow.f64 (pow.f64 (/.f64 d h) 1/4) 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))
	38.4b	(pow.f64 (.f64 (fma.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2) (.f64 (/.f64 h l) -1/2) 1) (/.f64 d (*.f64 (sqrt.f64 l) (sqrt.f64 h)))) 1)
	27.1b	(.f64 (.f64 (sqrt.f64 (/.f64 d h)) (pow.f64 (pow.f64 (/.f64 d l) 1/4) 2)) (fma.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2) (*.f64 (/.f64 h l) -1/2) 1))
▶	27.1b	(.f64 (.f64 (/.f64 1 (sqrt.f64 (/.f64 h d))) (sqrt.f64 (/.f64 d l))) (fma.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2) (*.f64 (/.f64 h l) -1/2) 1))
	34.7b	(.f64 (.f64 (sqrt.f64 (/.f64 d h)) (cbrt.f64 (pow.f64 (/.f64 d l) 3/2))) (fma.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2) (*.f64 (/.f64 h l) -1/2) 1))
	27.2b	(.f64 (.f64 (.f64 (sqrt.f64 (pow.f64 (cbrt.f64 (/.f64 d h)) 2)) (sqrt.f64 (cbrt.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))
	43.5b	(.f64 (.f64 (sqrt.f64 (/.f64 d h)) (sqrt.f64 (/.f64 d l))) (fma.f64 (/.f64 (.f64 (.f64 D D) (.f64 (.f64 M M) h)) (.f64 (.f64 d d) l)) -1/8 1))
	42.4b	(pow.f64 (sqrt.f64 (.f64 (fma.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2) (.f64 (/.f64 h l) -1/2) 1) (/.f64 d (*.f64 (sqrt.f64 l) (sqrt.f64 h))))) 2)
	44.6b	(.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))

Compiler

Compiled 3867 to 2106 computations (45.5% saved)

localize20.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	5.9b	(.f64 (.f64 (/.f64 1 (sqrt.f64 (/.f64 h d))) (sqrt.f64 (/.f64 d l))) (fma.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2) (*.f64 (/.f64 h l) -1/2) 1))
	10.4b	(fma.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2) (*.f64 (/.f64 h l) -1/2) 1)
✓	12.0b	(sqrt.f64 (/.f64 h d))
	14.1b	(sqrt.f64 (/.f64 d l))

series148.0ms (1.1%)

Counts

2 → 33

Calls

2 calls:

136.0ms	(.f64 (.f64 (/.f64 1 (sqrt.f64 (/.f64 h d))) (sqrt.f64 (/.f64 d l))) (fma.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2) (*.f64 (/.f64 h l) -1/2) 1))
12.0ms	(sqrt.f64 (/.f64 h d))

rewrite65.0ms (0.5%)

Algorithm

1×	batch-egg-rewrite

Rules

236×	`add-sqr-sqrt_binary64`
221×	`log1p-expm1-u_binary64`
221×	`expm1-log1p-u_binary64`
220×	`add-log-exp_binary64`
219×	`add-cbrt-cube_binary64`

Counts

2 → 42

Calls

2 calls:

64.0ms	(.f64 (.f64 (/.f64 1 (sqrt.f64 (/.f64 h d))) (sqrt.f64 (/.f64 d l))) (fma.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2) (*.f64 (/.f64 h l) -1/2) 1))
64.0ms	(sqrt.f64 (/.f64 h d))

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	23	45
1	490	43
2	4872	43
3	5023	43

simplify67.0ms (0.5%)

Algorithm

1×	egg-herbie

Rules

575×	`associate-/l/_binary64`
540×	`distribute-rgt-neg-in_binary64`
500×	`distribute-lft-neg-in_binary64`
492×	`associate-r_binary64`
429×	`associate-l_binary64`

Counts

75 → 50

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	30	1164
1	72	1116
2	179	1116
3	563	1116
4	2480	1116
5	4834	1116
6	4971	1116

prune126.0ms (1%)

Pruning

18 alts after pruning (18 fresh and 0 done)

	Pruned	Kept	Total
New	95	8	103
Fresh	5	10	15
Picked	1	0	1
Done	0	0	0
Total	101	18	119

Error

12.4b

Counts

119 → 18

Alt Table

Status	Error	Program
	41.4b	(.f64 (.f64 (/.f64 1 (sqrt.f64 (/.f64 h d))) (.f64 (sqrt.f64 d) (sqrt.f64 (/.f64 1 l)))) (fma.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2) (.f64 (/.f64 h l) -1/2) 1))
	59.9b	(log.f64 (pow.f64 (exp.f64 (sqrt.f64 (/.f64 (/.f64 d l) (/.f64 h d)))) (fma.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2) (*.f64 (/.f64 h l) -1/2) 1)))
	30.4b	(.f64 (.f64 (/.f64 1 (sqrt.f64 (/.f64 h d))) (sqrt.f64 (/.f64 d l))) (cbrt.f64 (pow.f64 (fma.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2) (*.f64 (/.f64 h l) -1/2) 1) 3)))
	34.7b	(.f64 (.f64 (sqrt.f64 (/.f64 d h)) (cbrt.f64 (pow.f64 (/.f64 d l) 3/2))) (fma.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2) (*.f64 (/.f64 h l) -1/2) 1))
	42.4b	(.f64 (sqrt.f64 (/.f64 1 (.f64 l h))) d)
▶	27.1b	(.f64 (.f64 (/.f64 1 (sqrt.f64 (/.f64 h d))) (/.f64 1 (sqrt.f64 (/.f64 l d)))) (fma.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2) (*.f64 (/.f64 h l) -1/2) 1))
	59.5b	(neg.f64 (/.f64 d (*.f64 h l)))
	27.5b	(.f64 (.f64 (pow.f64 (cbrt.f64 (sqrt.f64 (/.f64 d h))) 3) (sqrt.f64 (/.f64 d l))) (fma.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2) (*.f64 (/.f64 h l) -1/2) 1))
	43.2b	(.f64 (.f64 (/.f64 (sqrt.f64 (neg.f64 d)) (sqrt.f64 (neg.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))
	42.2b	(.f64 (.f64 (.f64 (sqrt.f64 d) (sqrt.f64 (/.f64 1 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))
	27.2b	(.f64 (.f64 (pow.f64 (pow.f64 (/.f64 d h) 1/4) 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))
	38.4b	(pow.f64 (.f64 (fma.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2) (.f64 (/.f64 h l) -1/2) 1) (/.f64 d (*.f64 (sqrt.f64 l) (sqrt.f64 h)))) 1)
	27.2b	(.f64 (.f64 (.f64 (sqrt.f64 (pow.f64 (cbrt.f64 (/.f64 d h)) 2)) (sqrt.f64 (cbrt.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))
	43.3b	(.f64 (.f64 (/.f64 1 (sqrt.f64 (/.f64 h d))) (sqrt.f64 (/.f64 d l))) (fma.f64 (/.f64 (.f64 (.f64 D D) (.f64 (.f64 M M) h)) (.f64 (.f64 d d) l)) -1/8 1))
	42.4b	(pow.f64 (sqrt.f64 (.f64 (fma.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2) (.f64 (/.f64 h l) -1/2) 1) (/.f64 d (*.f64 (sqrt.f64 l) (sqrt.f64 h))))) 2)
	44.5b	(.f64 (.f64 (/.f64 1 (sqrt.f64 (/.f64 h d))) (/.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))
	36.4b	(pow.f64 (cbrt.f64 (.f64 (sqrt.f64 (/.f64 (/.f64 d l) (/.f64 h d))) (fma.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2) (.f64 (/.f64 h l) -1/2) 1))) 3)
	44.6b	(.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))

Compiler

Compiled 4199 to 2404 computations (42.7% saved)

localize20.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	5.9b	(.f64 (.f64 (/.f64 1 (sqrt.f64 (/.f64 h d))) (/.f64 1 (sqrt.f64 (/.f64 l d)))) (fma.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2) (*.f64 (/.f64 h l) -1/2) 1))
	10.4b	(fma.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2) (*.f64 (/.f64 h l) -1/2) 1)
	12.0b	(sqrt.f64 (/.f64 h d))
✓	13.9b	(sqrt.f64 (/.f64 l d))

series160.0ms (1.2%)

Counts

2 → 32

Calls

2 calls:

149.0ms	(.f64 (.f64 (/.f64 1 (sqrt.f64 (/.f64 h d))) (/.f64 1 (sqrt.f64 (/.f64 l d)))) (fma.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2) (*.f64 (/.f64 h l) -1/2) 1))
11.0ms	(sqrt.f64 (/.f64 l d))

rewrite59.0ms (0.4%)

Algorithm

1×	batch-egg-rewrite

Rules

250×	`add-sqr-sqrt_binary64`
234×	`log1p-expm1-u_binary64`
234×	`expm1-log1p-u_binary64`
233×	`add-log-exp_binary64`
232×	`add-cbrt-cube_binary64`

Counts

2 → 35

Calls

2 calls:

58.0ms	(.f64 (.f64 (/.f64 1 (sqrt.f64 (/.f64 h d))) (/.f64 1 (sqrt.f64 (/.f64 l d)))) (fma.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2) (*.f64 (/.f64 h l) -1/2) 1))
58.0ms	(sqrt.f64 (/.f64 l d))

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	24	48
1	519	46
2	4902	46
3	5102	46

simplify80.0ms (0.6%)

Algorithm

1×	egg-herbie

Rules

569×	`associate-/l/_binary64`
540×	`distribute-rgt-neg-in_binary64`
500×	`distribute-lft-neg-in_binary64`
492×	`associate-r_binary64`
429×	`associate-l_binary64`

Counts

67 → 41

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	27	1155
1	63	1107
2	150	1107
3	508	1107
4	2397	1107
5	4746	1107
6	4996	1107
7	4949	1107

prune117.0ms (0.9%)

Pruning

20 alts after pruning (19 fresh and 1 done)

	Pruned	Kept	Total
New	91	3	94
Fresh	1	16	17
Picked	0	1	1
Done	0	0	0
Total	92	20	112

Error

12.3b

Counts

112 → 20

Alt Table

Status	Error	Program
▶	27.0b	(pow.f64 (.f64 (/.f64 (pow.f64 (/.f64 h d) -1/2) (sqrt.f64 (/.f64 l d))) (fma.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2) (.f64 (/.f64 h l) -1/2) 1)) 1)
	41.4b	(.f64 (.f64 (/.f64 1 (sqrt.f64 (/.f64 h d))) (.f64 (sqrt.f64 d) (sqrt.f64 (/.f64 1 l)))) (fma.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2) (.f64 (/.f64 h l) -1/2) 1))
	59.9b	(log.f64 (pow.f64 (exp.f64 (sqrt.f64 (/.f64 (/.f64 d l) (/.f64 h d)))) (fma.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2) (*.f64 (/.f64 h l) -1/2) 1)))
	30.4b	(.f64 (.f64 (/.f64 1 (sqrt.f64 (/.f64 h d))) (sqrt.f64 (/.f64 d l))) (cbrt.f64 (pow.f64 (fma.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2) (*.f64 (/.f64 h l) -1/2) 1) 3)))
	34.7b	(.f64 (.f64 (sqrt.f64 (/.f64 d h)) (cbrt.f64 (pow.f64 (/.f64 d l) 3/2))) (fma.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2) (*.f64 (/.f64 h l) -1/2) 1))
	42.2b	(.f64 (.f64 (/.f64 1 (/.f64 (sqrt.f64 h) (sqrt.f64 d))) (/.f64 1 (sqrt.f64 (/.f64 l d)))) (fma.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2) (*.f64 (/.f64 h l) -1/2) 1))
	42.4b	(.f64 (sqrt.f64 (/.f64 1 (.f64 l h))) d)
✓	27.1b	(.f64 (.f64 (/.f64 1 (sqrt.f64 (/.f64 h d))) (/.f64 1 (sqrt.f64 (/.f64 l d)))) (fma.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2) (*.f64 (/.f64 h l) -1/2) 1))
	59.5b	(neg.f64 (/.f64 d (*.f64 h l)))
	27.5b	(.f64 (.f64 (pow.f64 (cbrt.f64 (sqrt.f64 (/.f64 d h))) 3) (sqrt.f64 (/.f64 d l))) (fma.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2) (*.f64 (/.f64 h l) -1/2) 1))
	27.2b	(.f64 (.f64 (pow.f64 (pow.f64 (/.f64 d h) 1/4) 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))
	38.4b	(pow.f64 (.f64 (fma.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2) (.f64 (/.f64 h l) -1/2) 1) (/.f64 d (*.f64 (sqrt.f64 l) (sqrt.f64 h)))) 1)
	27.2b	(.f64 (.f64 (.f64 (sqrt.f64 (pow.f64 (cbrt.f64 (/.f64 d h)) 2)) (sqrt.f64 (cbrt.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))
	43.3b	(.f64 (.f64 (/.f64 1 (sqrt.f64 (/.f64 h d))) (sqrt.f64 (/.f64 d l))) (fma.f64 (/.f64 (.f64 (.f64 D D) (.f64 (.f64 M M) h)) (.f64 (.f64 d d) l)) -1/8 1))
	42.4b	(pow.f64 (sqrt.f64 (.f64 (fma.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2) (.f64 (/.f64 h l) -1/2) 1) (/.f64 d (*.f64 (sqrt.f64 l) (sqrt.f64 h))))) 2)
	44.5b	(.f64 (.f64 (/.f64 1 (sqrt.f64 (/.f64 h d))) (/.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))
	43.2b	(.f64 (.f64 (/.f64 (sqrt.f64 (neg.f64 d)) (sqrt.f64 (neg.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))
	36.4b	(pow.f64 (cbrt.f64 (.f64 (sqrt.f64 (/.f64 (/.f64 d l) (/.f64 h d))) (fma.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2) (.f64 (/.f64 h l) -1/2) 1))) 3)
	44.6b	(.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))
	32.2b	(.f64 (.f64 (/.f64 1 (sqrt.f64 (/.f64 h d))) (/.f64 1 (sqrt.f64 (/.f64 l d)))) 1)

Compiler

Compiled 4222 to 2532 computations (40% saved)

localize24.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	5.9b	(.f64 (/.f64 (pow.f64 (/.f64 h d) -1/2) (sqrt.f64 (/.f64 l d))) (fma.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2) (.f64 (/.f64 h l) -1/2) 1))
	10.4b	(fma.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2) (*.f64 (/.f64 h l) -1/2) 1)
✓	12.0b	(pow.f64 (/.f64 h d) -1/2)
	13.9b	(sqrt.f64 (/.f64 l d))

series506.0ms (3.8%)

Counts

2 → 57

Calls

2 calls:

352.0ms	(pow.f64 (/.f64 h d) -1/2)
154.0ms	(.f64 (/.f64 (pow.f64 (/.f64 h d) -1/2) (sqrt.f64 (/.f64 l d))) (fma.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2) (.f64 (/.f64 h l) -1/2) 1))

rewrite35.0ms (0.3%)

Algorithm

1×	batch-egg-rewrite

Rules

232×	`add-sqr-sqrt_binary64`
218×	`log1p-expm1-u_binary64`
218×	`expm1-log1p-u_binary64`
216×	`add-log-exp_binary64`
215×	`add-cbrt-cube_binary64`

Counts

2 → 33

Calls

2 calls:

34.0ms	(.f64 (/.f64 (pow.f64 (/.f64 h d) -1/2) (sqrt.f64 (/.f64 l d))) (fma.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2) (.f64 (/.f64 h l) -1/2) 1))
34.0ms	(pow.f64 (/.f64 h d) -1/2)

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	22	47
1	475	47
2	4993	47

simplify117.0ms (0.9%)

Algorithm

1×	egg-herbie

Rules

625×	`fma-def_binary64`
503×	`associate-r_binary64`
438×	`associate-l_binary64`
357×	`div-sub_binary64`
299×	`fma-neg_binary64`

Counts

90 → 47

Iterations

Useful iterations: 5 (0.0ms)

Iter	Nodes	Cost
0	58	1476
1	135	1428
2	301	1428
3	919	1284
4	3390	1284
5	4783	1260
6	4626	1260
7	4891	1260
8	4961	1260

prune135.0ms (1%)

Pruning

19 alts after pruning (18 fresh and 1 done)

	Pruned	Kept	Total
New	93	1	94
Fresh	1	17	18
Picked	1	0	1
Done	0	1	1
Total	95	19	114

Error

12.3b

Counts

114 → 19

Alt Table

Status	Error	Program
	41.4b	(.f64 (.f64 (/.f64 1 (sqrt.f64 (/.f64 h d))) (.f64 (sqrt.f64 d) (sqrt.f64 (/.f64 1 l)))) (fma.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2) (.f64 (/.f64 h l) -1/2) 1))
	59.9b	(log.f64 (pow.f64 (exp.f64 (sqrt.f64 (/.f64 (/.f64 d l) (/.f64 h d)))) (fma.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2) (*.f64 (/.f64 h l) -1/2) 1)))
	34.7b	(.f64 (.f64 (sqrt.f64 (/.f64 d h)) (cbrt.f64 (pow.f64 (/.f64 d l) 3/2))) (fma.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2) (*.f64 (/.f64 h l) -1/2) 1))
	42.2b	(.f64 (.f64 (/.f64 1 (/.f64 (sqrt.f64 h) (sqrt.f64 d))) (/.f64 1 (sqrt.f64 (/.f64 l d)))) (fma.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2) (*.f64 (/.f64 h l) -1/2) 1))
	42.4b	(.f64 (sqrt.f64 (/.f64 1 (.f64 l h))) d)
✓	27.1b	(.f64 (.f64 (/.f64 1 (sqrt.f64 (/.f64 h d))) (/.f64 1 (sqrt.f64 (/.f64 l d)))) (fma.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2) (*.f64 (/.f64 h l) -1/2) 1))
	59.5b	(neg.f64 (/.f64 d (*.f64 h l)))
	27.5b	(.f64 (.f64 (pow.f64 (cbrt.f64 (sqrt.f64 (/.f64 d h))) 3) (sqrt.f64 (/.f64 d l))) (fma.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2) (*.f64 (/.f64 h l) -1/2) 1))
	44.6b	(.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))
	27.0b	(pow.f64 (/.f64 (.f64 (pow.f64 (/.f64 h d) -1/2) (fma.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2) (.f64 -1/2 (/.f64 h l)) 1)) (sqrt.f64 (/.f64 l d))) 1)
	27.2b	(.f64 (.f64 (pow.f64 (pow.f64 (/.f64 d h) 1/4) 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))
	38.4b	(pow.f64 (.f64 (fma.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2) (.f64 (/.f64 h l) -1/2) 1) (/.f64 d (*.f64 (sqrt.f64 l) (sqrt.f64 h)))) 1)
	27.2b	(.f64 (.f64 (.f64 (sqrt.f64 (pow.f64 (cbrt.f64 (/.f64 d h)) 2)) (sqrt.f64 (cbrt.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))
	43.3b	(.f64 (.f64 (/.f64 1 (sqrt.f64 (/.f64 h d))) (sqrt.f64 (/.f64 d l))) (fma.f64 (/.f64 (.f64 (.f64 D D) (.f64 (.f64 M M) h)) (.f64 (.f64 d d) l)) -1/8 1))
	42.4b	(pow.f64 (sqrt.f64 (.f64 (fma.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2) (.f64 (/.f64 h l) -1/2) 1) (/.f64 d (*.f64 (sqrt.f64 l) (sqrt.f64 h))))) 2)
	44.5b	(.f64 (.f64 (/.f64 1 (sqrt.f64 (/.f64 h d))) (/.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))
	43.2b	(.f64 (.f64 (/.f64 (sqrt.f64 (neg.f64 d)) (sqrt.f64 (neg.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))
	36.4b	(pow.f64 (cbrt.f64 (.f64 (sqrt.f64 (/.f64 (/.f64 d l) (/.f64 h d))) (fma.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2) (.f64 (/.f64 h l) -1/2) 1))) 3)
	32.2b	(.f64 (.f64 (/.f64 1 (sqrt.f64 (/.f64 h d))) (/.f64 1 (sqrt.f64 (/.f64 l d)))) 1)

Compiler

Compiled 3522 to 2089 computations (40.7% saved)

regimes1.2s (9%)

Accuracy

Total 5.0b remaining (28.7%)

Threshold costs 0b (0%)

Counts

89 → 3

Compiler

Compiled 20246 to 14670 computations (27.5% saved)

bsearch717.0ms (5.4%)

Steps

Iters	Range		Point
10	-2.3460650882530407e-298	4.619434787473256e-303	-1.8608481929594e-310
10	-3.002508392220107e-47	-1.1387991585092574e-59	-1.1166493905219246e-54

Compiler

Compiled 6 to 5 computations (16.7% saved)

simplify5.0ms (0%)

Algorithm

1×	egg-herbie

Rules

12×	`*-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	45	138
1	63	138
2	69	138
3	72	138
4	71	138

end598.0ms (4.5%)

Remove: (sort M D)
Compiler: Compiled 973 to 678 computations (30.3% saved)

Details

analyze2.2s (16.5%)

sample6.3s (47.6%)

simplify35.0ms (0.3%)

prune4.0ms (0%)

localize17.0ms (0.1%)

series229.0ms (1.7%)

rewrite73.0ms (0.6%)

simplify82.0ms (0.6%)

prune121.0ms (0.9%)

localize20.0ms (0.1%)

series148.0ms (1.1%)

rewrite65.0ms (0.5%)

simplify67.0ms (0.5%)

prune126.0ms (1%)

localize20.0ms (0.2%)

series160.0ms (1.2%)

rewrite59.0ms (0.4%)

simplify80.0ms (0.6%)

prune117.0ms (0.9%)

localize24.0ms (0.2%)

series506.0ms (3.8%)

rewrite35.0ms (0.3%)

simplify117.0ms (0.9%)

prune135.0ms (1%)

regimes1.2s (9%)

bsearch717.0ms (5.4%)

simplify5.0ms (0%)

end598.0ms (4.5%)

Profiling