Details

analyze2.2s (15.7%)

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)

sample5.9s (42.7%)

Symmetry

(sort M D)

Results

3.3s	13476×	body	128	invalid
2.5s	8256×	body	128	valid

Compiler

Compiled 122 to 95 computations (22.1% saved)

simplify33.0ms (0.2%)

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

28.9b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	28.9b	(.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))

Compiler

Compiled 128 to 88 computations (31.3% saved)

localize18.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	7.2b	(.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)
✓	13.0b	(sqrt.f64 (/.f64 d h))
✓	13.3b	(sqrt.f64 (/.f64 d l))

series283.0ms (2.1%)

Counts

4 → 92

Calls

4 calls:

146.0ms	(.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))
112.0ms	(fma.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2) (*.f64 (/.f64 h l) -1/2) 1)
13.0ms	(sqrt.f64 (/.f64 d l))
11.0ms	(sqrt.f64 (/.f64 d h))

rewrite74.0ms (0.5%)

Algorithm

2×	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 → 90

Calls

4 calls:

71.0ms	(.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))
71.0ms	(fma.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2) (*.f64 (/.f64 h l) -1/2) 1)
71.0ms	(sqrt.f64 (/.f64 d h))
71.0ms	(sqrt.f64 (/.f64 d l))

Iterations

Useful iterations: 0 (0.0ms)

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

simplify148.0ms (1.1%)

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

182 → 105

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

prune141.0ms (1%)

Pruning

19 alts after pruning (19 fresh and 0 done)

	Pruned	Kept	Total
New	86	19	105
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	87	19	106

Error

13.6b

Counts

106 → 19

Alt Table

Status	Error	Program
	61.7b	(.f64 (.f64 (sqrt.f64 (/.f64 d h)) (sqrt.f64 (/.f64 d l))) (.f64 -1/8 (/.f64 (.f64 (pow.f64 D 2) (.f64 (pow.f64 M 2) h)) (.f64 (pow.f64 d 2) l))))
	36.1b	(.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))
	60.8b	(.f64 -1/8 (.f64 (/.f64 (*.f64 (pow.f64 D 2) (pow.f64 M 2)) d) (sqrt.f64 (/.f64 h (pow.f64 l 3)))))
	42.8b	(.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))
	41.5b	(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)
	44.9b	(.f64 (.f64 (sqrt.f64 (/.f64 d h)) (/.f64 (sqrt.f64 d) (sqrt.f64 l))) (fma.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2) (*.f64 (/.f64 h l) -1/2) 1))
	29.0b	(.f64 (.f64 (sqrt.f64 (/.f64 d h)) (sqrt.f64 (/.f64 d l))) (pow.f64 (cbrt.f64 (fma.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2) (*.f64 (/.f64 h l) -1/2) 1)) 3))
	43.3b	(.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))
	34.5b	(.f64 (.f64 (sqrt.f64 (/.f64 d h)) (sqrt.f64 (/.f64 d l))) 1)
	30.9b	(.f64 (.f64 (sqrt.f64 (/.f64 d h)) (exp.f64 (log.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))
	45.6b	(.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))
	29.4b	(.f64 (.f64 (sqrt.f64 (/.f64 d h)) (pow.f64 (cbrt.f64 (sqrt.f64 (/.f64 d l))) 3)) (fma.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2) (*.f64 (/.f64 h l) -1/2) 1))
▶	28.5b	(.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))
	29.2b	(.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))
	43.4b	(.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))
	41.1b	(.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))))
	55.4b	(cbrt.f64 (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)))) 3))
	29.2b	(.f64 (.f64 (.f64 (cbrt.f64 (/.f64 d h)) (cbrt.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))
	45.7b	(.f64 (sqrt.f64 (/.f64 1 (.f64 l h))) d)

Compiler

Compiled 4143 to 2268 computations (45.3% saved)

localize22.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	7.2b	(.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)
✓	12.8b	(sqrt.f64 (/.f64 h d))
	13.3b	(sqrt.f64 (/.f64 d l))

series153.0ms (1.1%)

Counts

2 → 33

Calls

2 calls:

140.0ms	(.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))
13.0ms	(sqrt.f64 (/.f64 h d))

rewrite63.0ms (0.5%)

Algorithm

2×	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 → 44

Calls

2 calls:

62.0ms	(.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))
62.0ms	(sqrt.f64 (/.f64 h d))

Iterations

Useful iterations: 0 (0.0ms)

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

simplify69.0ms (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

77 → 52

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

prune120.0ms (0.9%)

Pruning

22 alts after pruning (22 fresh and 0 done)

	Pruned	Kept	Total
New	98	9	107
Fresh	5	13	18
Picked	1	0	1
Done	0	0	0
Total	104	22	126

Error

13.3b

Counts

126 → 22

Alt Table

Status	Error	Program
▶	29.0b	(.f64 (.f64 (/.f64 1 (sqrt.f64 (/.f64 h d))) (pow.f64 (cbrt.f64 (sqrt.f64 (/.f64 d l))) 3)) (fma.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2) (*.f64 (/.f64 h l) -1/2) 1))
	36.1b	(.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))
	60.8b	(.f64 -1/8 (.f64 (/.f64 (*.f64 (pow.f64 D 2) (pow.f64 M 2)) d) (sqrt.f64 (/.f64 h (pow.f64 l 3)))))
	42.8b	(.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))
	41.5b	(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)
	44.9b	(.f64 (.f64 (sqrt.f64 (/.f64 d h)) (/.f64 (sqrt.f64 d) (sqrt.f64 l))) (fma.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2) (*.f64 (/.f64 h l) -1/2) 1))
	29.0b	(.f64 (.f64 (sqrt.f64 (/.f64 d h)) (sqrt.f64 (/.f64 d l))) (pow.f64 (cbrt.f64 (fma.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2) (*.f64 (/.f64 h l) -1/2) 1)) 3))
	43.3b	(.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))
	61.3b	(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)))
	55.4b	(cbrt.f64 (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)))) 3))
	36.4b	(.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))
	42.8b	(.f64 (.f64 (/.f64 1 (/.f64 (sqrt.f64 (neg.f64 h)) (sqrt.f64 (neg.f64 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))
	43.3b	(.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))
	60.5b	(neg.f64 (/.f64 d (*.f64 h l)))
	45.7b	(.f64 (sqrt.f64 (/.f64 1 (.f64 l h))) d)
	45.6b	(.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))
	34.0b	(.f64 (.f64 (/.f64 1 (sqrt.f64 (/.f64 h d))) (sqrt.f64 (/.f64 d l))) 1)
	43.4b	(.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))
	41.1b	(.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))))
	29.2b	(.f64 (.f64 (.f64 (cbrt.f64 (/.f64 d h)) (cbrt.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))
	36.8b	(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)
	29.3b	(.f64 (.f64 (/.f64 1 (expm1.f64 (log1p.f64 (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))

Compiler

Compiled 4496 to 2591 computations (42.4% saved)

localize21.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	7.2b	(.f64 (.f64 (/.f64 1 (sqrt.f64 (/.f64 h d))) (pow.f64 (cbrt.f64 (sqrt.f64 (/.f64 d l))) 3)) (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)
	12.8b	(sqrt.f64 (/.f64 h d))
	13.3b	(sqrt.f64 (/.f64 d l))

series147.0ms (1.1%)

Counts

1 → 33

Calls

1 calls:

147.0ms

(*.f64 (*.f64 (/.f64 1 (sqrt.f64 (/.f64 h d))) (pow.f64 (cbrt.f64 (sqrt.f64 (/.f64 d l))) 3)) (fma.f64 (pow.f64 (/.f64 (*.f64 M D) (*.f64 d 2)) 2) (*.f64 (/.f64 h l) -1/2) 1))

rewrite60.0ms (0.4%)

Algorithm

2×	batch-egg-rewrite

Rules

253×	`add-sqr-sqrt_binary64`
241×	`log1p-expm1-u_binary64`
241×	`expm1-log1p-u_binary64`
237×	`add-cbrt-cube_binary64`
237×	`add-log-exp_binary64`

Counts

1 → 15

Calls

1 calls:

59.0ms

(*.f64 (*.f64 (/.f64 1 (sqrt.f64 (/.f64 h d))) (pow.f64 (cbrt.f64 (sqrt.f64 (/.f64 d l))) 3)) (fma.f64 (pow.f64 (/.f64 (*.f64 M D) (*.f64 d 2)) 2) (*.f64 (/.f64 h l) -1/2) 1))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	26	39
1	537	39
2	4959	39
3	5069	39
0	0	0
1	0	0

simplify72.0ms (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

48 → 23

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

prune112.0ms (0.8%)

Pruning

22 alts after pruning (21 fresh and 1 done)

	Pruned	Kept	Total
New	103	3	106
Fresh	3	18	21
Picked	0	1	1
Done	0	0	0
Total	106	22	128

Error

13.3b

Counts

128 → 22

Alt Table

Status	Error	Program
✓	29.0b	(.f64 (.f64 (/.f64 1 (sqrt.f64 (/.f64 h d))) (pow.f64 (cbrt.f64 (sqrt.f64 (/.f64 d l))) 3)) (fma.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2) (*.f64 (/.f64 h l) -1/2) 1))
	36.1b	(.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))
	43.6b	(.f64 (.f64 (/.f64 1 (sqrt.f64 (/.f64 h d))) (pow.f64 (cbrt.f64 (/.f64 (sqrt.f64 (neg.f64 d)) (sqrt.f64 (neg.f64 l)))) 3)) (fma.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2) (*.f64 (/.f64 h l) -1/2) 1))
	34.0b	(.f64 (.f64 (/.f64 1 (sqrt.f64 (/.f64 h d))) (sqrt.f64 (/.f64 d l))) 1)
	28.9b	(pow.f64 (cbrt.f64 (.f64 (/.f64 (sqrt.f64 (/.f64 d l)) (sqrt.f64 (/.f64 h d))) (fma.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2) (.f64 (/.f64 h l) -1/2) 1))) 3)
	43.4b	(.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))
▶	28.5b	(.f64 (/.f64 (sqrt.f64 (/.f64 d l)) (sqrt.f64 (/.f64 h d))) (fma.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2) (.f64 (/.f64 h l) -1/2) 1))
	41.5b	(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)
	44.9b	(.f64 (.f64 (sqrt.f64 (/.f64 d h)) (/.f64 (sqrt.f64 d) (sqrt.f64 l))) (fma.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2) (*.f64 (/.f64 h l) -1/2) 1))
	29.0b	(.f64 (.f64 (sqrt.f64 (/.f64 d h)) (sqrt.f64 (/.f64 d l))) (pow.f64 (cbrt.f64 (fma.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2) (*.f64 (/.f64 h l) -1/2) 1)) 3))
	43.3b	(.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))
	36.4b	(.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))
	42.8b	(.f64 (.f64 (/.f64 1 (/.f64 (sqrt.f64 (neg.f64 h)) (sqrt.f64 (neg.f64 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))
	43.3b	(.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))
	60.5b	(neg.f64 (/.f64 d (*.f64 h l)))
	45.7b	(.f64 (sqrt.f64 (/.f64 1 (.f64 l h))) d)
	45.6b	(.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))
	60.8b	(.f64 -1/8 (.f64 (/.f64 (*.f64 (pow.f64 D 2) (pow.f64 M 2)) d) (sqrt.f64 (/.f64 h (pow.f64 l 3)))))
	41.1b	(.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))))
	61.3b	(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)))
	29.2b	(.f64 (.f64 (.f64 (cbrt.f64 (/.f64 d h)) (cbrt.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))
	36.8b	(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)

Compiler

Compiled 4702 to 2747 computations (41.6% saved)

localize18.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	7.2b	(.f64 (/.f64 (sqrt.f64 (/.f64 d l)) (sqrt.f64 (/.f64 h 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)
	12.8b	(sqrt.f64 (/.f64 h d))
	13.3b	(sqrt.f64 (/.f64 d l))

series147.0ms (1.1%)

Counts

1 → 33

Calls

1 calls:

147.0ms

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

rewrite36.0ms (0.3%)

Algorithm

2×	batch-egg-rewrite

Rules

228×	`add-sqr-sqrt_binary64`
214×	`log1p-expm1-u_binary64`
214×	`expm1-log1p-u_binary64`
213×	`add-log-exp_binary64`
212×	`add-cbrt-cube_binary64`

Counts

1 → 18

Calls

1 calls:

35.0ms

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	22	37
1	471	37
2	4981	37
0	0	0
1	0	0

simplify73.0ms (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

51 → 26

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

prune117.0ms (0.9%)

Pruning

25 alts after pruning (25 fresh and 0 done)

	Pruned	Kept	Total
New	102	7	109
Fresh	2	18	20
Picked	1	0	1
Done	1	0	1
Total	106	25	131

Error

13.3b

Counts

131 → 25

Alt Table

Status	Error	Program
	60.8b	(.f64 -1/8 (.f64 (/.f64 (*.f64 (pow.f64 D 2) (pow.f64 M 2)) d) (sqrt.f64 (/.f64 h (pow.f64 l 3)))))
	47.4b	(.f64 (/.f64 (sqrt.f64 (/.f64 d l)) (-.f64 (exp.f64 (log1p.f64 (sqrt.f64 (/.f64 h d)))) 1)) (fma.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2) (.f64 (/.f64 h l) -1/2) 1))
	43.6b	(.f64 (.f64 (/.f64 1 (sqrt.f64 (/.f64 h d))) (pow.f64 (cbrt.f64 (/.f64 (sqrt.f64 (neg.f64 d)) (sqrt.f64 (neg.f64 l)))) 3)) (fma.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2) (*.f64 (/.f64 h l) -1/2) 1))
	34.0b	(.f64 (.f64 (/.f64 1 (sqrt.f64 (/.f64 h d))) (sqrt.f64 (/.f64 d l))) 1)
	28.9b	(pow.f64 (cbrt.f64 (.f64 (/.f64 (sqrt.f64 (/.f64 d l)) (sqrt.f64 (/.f64 h d))) (fma.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2) (.f64 (/.f64 h l) -1/2) 1))) 3)
	43.4b	(.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))
	43.2b	(.f64 (/.f64 (sqrt.f64 (/.f64 d l)) (/.f64 (sqrt.f64 h) (sqrt.f64 d))) (fma.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2) (.f64 (/.f64 h l) -1/2) 1))
	44.9b	(.f64 (.f64 (sqrt.f64 (/.f64 d h)) (/.f64 (sqrt.f64 d) (sqrt.f64 l))) (fma.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2) (*.f64 (/.f64 h l) -1/2) 1))
	44.5b	(.f64 (/.f64 (.f64 (sqrt.f64 d) (sqrt.f64 (/.f64 1 l))) (sqrt.f64 (/.f64 h d))) (fma.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2) (*.f64 (/.f64 h l) -1/2) 1))
	41.1b	(.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))))
	42.8b	(.f64 (/.f64 (sqrt.f64 (/.f64 d l)) (/.f64 (sqrt.f64 (neg.f64 h)) (sqrt.f64 (neg.f64 d)))) (fma.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2) (.f64 (/.f64 h l) -1/2) 1))
	29.0b	(.f64 (.f64 (sqrt.f64 (/.f64 d h)) (sqrt.f64 (/.f64 d l))) (pow.f64 (cbrt.f64 (fma.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2) (*.f64 (/.f64 h l) -1/2) 1)) 3))
	43.3b	(.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))
	61.3b	(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)))
	43.3b	(.f64 (/.f64 (/.f64 (sqrt.f64 (neg.f64 d)) (sqrt.f64 (neg.f64 l))) (sqrt.f64 (/.f64 h d))) (fma.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2) (.f64 (/.f64 h l) -1/2) 1))
	29.0b	(.f64 (/.f64 (pow.f64 (cbrt.f64 (sqrt.f64 (/.f64 d l))) 3) (sqrt.f64 (/.f64 h d))) (fma.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2) (.f64 (/.f64 h l) -1/2) 1))
	29.2b	(.f64 (.f64 (.f64 (cbrt.f64 (/.f64 d h)) (cbrt.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))
	36.4b	(.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))
	42.8b	(.f64 (.f64 (/.f64 1 (/.f64 (sqrt.f64 (neg.f64 h)) (sqrt.f64 (neg.f64 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))
	60.5b	(neg.f64 (/.f64 d (*.f64 h l)))
	45.7b	(.f64 (sqrt.f64 (/.f64 1 (.f64 l h))) d)
	36.1b	(.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))
	45.6b	(.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))
	28.8b	(.f64 (/.f64 (sqrt.f64 (/.f64 d l)) (.f64 (cbrt.f64 (/.f64 h d)) (cbrt.f64 (sqrt.f64 (/.f64 h d))))) (fma.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2) (*.f64 (/.f64 h l) -1/2) 1))
	36.8b	(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)

Compiler

Compiled 3825 to 2010 computations (47.5% saved)

regimes1.9s (13.6%)

Accuracy

Total 5.7b remaining (32.6%)

Threshold costs 0b (0%)

Counts

106 → 3

Compiler

Compiled 24292 to 17596 computations (27.6% saved)

bsearch1.3s (9.6%)

Steps

Iters	Range		Point
11	-6.197465600324314e-292	7.312371962382711e-304	-3.39784574529724e-310
9	-9.672149082018834e-86	-4.027968113736697e-91	-8.370385366690261e-91

Compiler

Compiled 6 to 5 computations (16.7% saved)

simplify32.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

10×	`*-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	44	138
1	60	138
2	66	138
3	69	138
4	68	138

end571.0ms (4.2%)

Remove: (sort M D)
Compiler: Compiled 1155 to 807 computations (30.1% saved)

Details

analyze2.2s (15.7%)

sample5.9s (42.7%)

simplify33.0ms (0.2%)

prune4.0ms (0%)

localize18.0ms (0.1%)

series283.0ms (2.1%)

rewrite74.0ms (0.5%)

simplify148.0ms (1.1%)

prune141.0ms (1%)

localize22.0ms (0.2%)

series153.0ms (1.1%)

rewrite63.0ms (0.5%)

simplify69.0ms (0.5%)

prune120.0ms (0.9%)

localize21.0ms (0.2%)

series147.0ms (1.1%)

rewrite60.0ms (0.4%)

simplify72.0ms (0.5%)

prune112.0ms (0.8%)

localize18.0ms (0.1%)

series147.0ms (1.1%)

rewrite36.0ms (0.3%)

simplify73.0ms (0.5%)

prune117.0ms (0.9%)

regimes1.9s (13.6%)

bsearch1.3s (9.6%)

simplify32.0ms (0.2%)

end571.0ms (4.2%)

Profiling