Details

analyze2.1s (16.6%)

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)

sample6.0s (47%)

Symmetry

(sort M D)

Results

3.6s	13319×	body	128	invalid
2.4s	8256×	body	128	valid

Compiler

Compiled 122 to 95 computations (22.1% saved)

simplify32.0ms (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`

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

Stop Event

1×	node limit

Counts

1 → 2

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

24.9b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	24.9b	(.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
✓	6.0b	(.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))
✓	8.0b	(fma.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2) (*.f64 (/.f64 h l) -1/2) 1)
✓	12.7b	(sqrt.f64 (/.f64 d l))
✓	12.8b	(sqrt.f64 (/.f64 d h))

series235.0ms (1.8%)

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))
68.0ms	(fma.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2) (*.f64 (/.f64 h l) -1/2) 1)
14.0ms	(sqrt.f64 (/.f64 d h))
13.0ms	(sqrt.f64 (/.f64 d l))

rewrite62.0ms (0.5%)

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`

Iterations

Useful iterations: 1 (0.0ms)

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

Stop Event

1×	node limit

Counts

4 → 86

Calls

4 calls:

60.0ms	(.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))
60.0ms	(fma.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2) (*.f64 (/.f64 h l) -1/2) 1)
60.0ms	(sqrt.f64 (/.f64 d l))
60.0ms	(sqrt.f64 (/.f64 d h))

simplify80.0ms (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`

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

Stop Event

1×	node limit

Counts

178 → 101

prune123.0ms (1%)

Pruning

14 alts after pruning (14 fresh and 0 done)

	Pruned	Kept	Total
New	87	14	101
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	88	14	102

Error

10.2b

Counts

102 → 14

Alt Table

Status	Error	Program
▶	24.1b	(.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))
	40.4b	(.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))
	41.2b	(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 h) (sqrt.f64 l))))) 3)
	41.7b	(.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))
	25.2b	(.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))
	40.9b	(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 h) (sqrt.f64 l)))) 1)
	42.9b	(.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))
	29.2b	(.f64 (.f64 (sqrt.f64 (/.f64 d h)) (sqrt.f64 (/.f64 d l))) 1)
	25.5b	(.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))
	43.3b	(.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))
	25.2b	(.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))
	43.3b	(.f64 (sqrt.f64 (/.f64 1 (.f64 l h))) d)
	59.0b	(.f64 -1/8 (.f64 (/.f64 (*.f64 (pow.f64 D 2) (pow.f64 M 2)) d) (sqrt.f64 (/.f64 h (pow.f64 l 3)))))
	40.0b	(.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))

Compiler

Compiled 3713 to 1988 computations (46.5% saved)

localize18.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	6.0b	(.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))
	8.0b	(fma.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2) (*.f64 (/.f64 h l) -1/2) 1)
✓	12.3b	(sqrt.f64 (/.f64 h d))
	12.7b	(sqrt.f64 (/.f64 d l))

series149.0ms (1.2%)

Counts

2 → 33

Calls

2 calls:

137.0ms	(.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))

rewrite53.0ms (0.4%)

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`

Iterations

Useful iterations: 1 (0.0ms)

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

Stop Event

1×	node limit

Counts

2 → 42

Calls

2 calls:

52.0ms	(.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))
52.0ms	(sqrt.f64 (/.f64 h d))

simplify63.0ms (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`

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

Stop Event

1×	node limit

Counts

75 → 50

prune117.0ms (0.9%)

Pruning

18 alts after pruning (18 fresh and 0 done)

	Pruned	Kept	Total
New	95	8	103
Fresh	3	10	13
Picked	1	0	1
Done	0	0	0
Total	99	18	117

Error

10.0b

Counts

117 → 18

Alt Table

Status	Error	Program
	41.2b	(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 h) (sqrt.f64 l))))) 3)
	41.7b	(.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))
	25.2b	(.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))
	28.4b	(.f64 (.f64 (/.f64 1 (sqrt.f64 (/.f64 h d))) (sqrt.f64 (/.f64 d l))) 1)
	40.9b	(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 h) (sqrt.f64 l)))) 1)
	42.9b	(.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))
	32.8b	(pow.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)) 1)
	43.3b	(.f64 (sqrt.f64 (/.f64 1 (.f64 l h))) d)
▶	24.0b	(.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))
	58.6b	(neg.f64 (/.f64 d (*.f64 h l)))
	42.5b	(.f64 (.f64 (/.f64 1 (sqrt.f64 (/.f64 h d))) (/.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))
	40.0b	(.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))
	25.5b	(.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))
	43.3b	(.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))
	39.5b	(.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))
	37.7b	(pow.f64 (sqrt.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))) 2)
	40.0b	(.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))
	59.0b	(.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 4131 to 2354 computations (43% saved)

localize20.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	6.0b	(.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))
	8.0b	(fma.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2) (*.f64 (/.f64 h l) -1/2) 1)
	12.3b	(sqrt.f64 (/.f64 h d))
✓	12.9b	(sqrt.f64 (/.f64 l d))

series169.0ms (1.3%)

Counts

2 → 32

Calls

2 calls:

158.0ms	(.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))

rewrite55.0ms (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`

Iterations

Useful iterations: 1 (0.0ms)

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

Stop Event

1×	node limit

Counts

2 → 35

Calls

2 calls:

54.0ms	(.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))
54.0ms	(sqrt.f64 (/.f64 l d))

simplify76.0ms (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`

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

Stop Event

1×	node limit

Counts

67 → 41

prune112.0ms (0.9%)

Pruning

17 alts after pruning (17 fresh and 0 done)

	Pruned	Kept	Total
New	90	4	94
Fresh	4	13	17
Picked	1	0	1
Done	0	0	0
Total	95	17	112

Error

9.9b

Counts

112 → 17

Alt Table

Status	Error	Program
	41.2b	(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 h) (sqrt.f64 l))))) 3)
	28.2b	(.f64 (.f64 (/.f64 1 (sqrt.f64 (/.f64 h d))) (/.f64 1 (sqrt.f64 (/.f64 l d)))) 1)
	41.7b	(.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))
	40.9b	(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 h) (sqrt.f64 l)))) 1)
	42.9b	(.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))
	32.8b	(pow.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)) 1)
	43.3b	(.f64 (sqrt.f64 (/.f64 1 (.f64 l h))) d)
	42.5b	(.f64 (.f64 (/.f64 1 (sqrt.f64 (/.f64 h d))) (/.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))
	40.0b	(.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))
	25.5b	(.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))
	43.3b	(.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))
	39.5b	(.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))
	39.9b	(.f64 (.f64 (/.f64 1 (/.f64 (sqrt.f64 (neg.f64 h)) (sqrt.f64 (neg.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))
	29.9b	(pow.f64 (sqrt.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))) 2)
▶	23.9b	(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)
	59.0b	(.f64 -1/8 (.f64 (/.f64 (*.f64 (pow.f64 D 2) (pow.f64 M 2)) d) (sqrt.f64 (/.f64 h (pow.f64 l 3)))))
	58.6b	(neg.f64 (/.f64 d (*.f64 h l)))

Compiler

Compiled 4007 to 2378 computations (40.7% saved)

localize19.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	6.0b	(.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))
	8.0b	(fma.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2) (*.f64 (/.f64 h l) -1/2) 1)
✓	12.3b	(pow.f64 (/.f64 h d) -1/2)
	12.9b	(sqrt.f64 (/.f64 l d))

series556.0ms (4.3%)

Counts

2 → 57

Calls

2 calls:

380.0ms	(pow.f64 (/.f64 h d) -1/2)
176.0ms	(.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))

rewrite31.0ms (0.2%)

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`

Iterations

Useful iterations: 0 (0.0ms)

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

Stop Event

1×	node limit

Counts

2 → 33

Calls

2 calls:

31.0ms	(.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))
30.0ms	(pow.f64 (/.f64 h d) -1/2)

simplify108.0ms (0.8%)

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`

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

Stop Event

1×	node limit

Counts

90 → 47

prune107.0ms (0.8%)

Pruning

17 alts after pruning (16 fresh and 1 done)

	Pruned	Kept	Total
New	94	0	94
Fresh	0	16	16
Picked	0	1	1
Done	0	0	0
Total	94	17	111

Error

9.9b

Counts

111 → 17

Alt Table

Status	Error	Program
	41.2b	(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 h) (sqrt.f64 l))))) 3)
	28.2b	(.f64 (.f64 (/.f64 1 (sqrt.f64 (/.f64 h d))) (/.f64 1 (sqrt.f64 (/.f64 l d)))) 1)
	41.7b	(.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))
	40.9b	(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 h) (sqrt.f64 l)))) 1)
	42.9b	(.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))
	32.8b	(pow.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)) 1)
	43.3b	(.f64 (sqrt.f64 (/.f64 1 (.f64 l h))) d)
	42.5b	(.f64 (.f64 (/.f64 1 (sqrt.f64 (/.f64 h d))) (/.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))
	40.0b	(.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))
	25.5b	(.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))
	43.3b	(.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))
	39.5b	(.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))
	39.9b	(.f64 (.f64 (/.f64 1 (/.f64 (sqrt.f64 (neg.f64 h)) (sqrt.f64 (neg.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))
	29.9b	(pow.f64 (sqrt.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))) 2)
✓	23.9b	(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)
	59.0b	(.f64 -1/8 (.f64 (/.f64 (*.f64 (pow.f64 D 2) (pow.f64 M 2)) d) (sqrt.f64 (/.f64 h (pow.f64 l 3)))))
	58.6b	(neg.f64 (/.f64 d (*.f64 h l)))

Compiler

Compiled 3433 to 2026 computations (41% saved)

regimes1.4s (10.7%)

Accuracy

Total 6.8b remaining (35.7%)

Threshold costs 0b (0%)

Counts

90 → 3

Compiler

Compiled 20757 to 15139 computations (27.1% saved)

bsearch779.0ms (6.1%)

Steps

Iters	Range		Point
9	1.3385571678944242e+215	6.6858651901748974e+221	3.8e+215
8	-1.009830194643337e-289	-2.632640713727445e-293	-2.7e-293

Compiler

Compiled 6 to 5 computations (16.7% saved)

simplify5.0ms (0%)

Algorithm

1×	egg-herbie

Rules

11×	`*-commutative_binary64`
2×	`+-commutative_binary64`
2×	`sub-neg_binary64`
2×	`neg-sub0_binary64`
2×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	44	111
1	60	111
2	64	111
3	66	111
4	65	111

Stop Event

1×

saturated

end317.0ms (2.5%)

Remove: (sort M D)
Compiler: Compiled 816 to 587 computations (28.1% saved)

Details

analyze2.1s (16.6%)

sample6.0s (47%)

simplify32.0ms (0.2%)

prune4.0ms (0%)

localize18.0ms (0.1%)

series235.0ms (1.8%)

rewrite62.0ms (0.5%)

simplify80.0ms (0.6%)

prune123.0ms (1%)

localize18.0ms (0.1%)

series149.0ms (1.2%)

rewrite53.0ms (0.4%)

simplify63.0ms (0.5%)

prune117.0ms (0.9%)

localize20.0ms (0.2%)

series169.0ms (1.3%)

rewrite55.0ms (0.4%)

simplify76.0ms (0.6%)

prune112.0ms (0.9%)

localize19.0ms (0.1%)

series556.0ms (4.3%)

rewrite31.0ms (0.2%)

simplify108.0ms (0.8%)

prune107.0ms (0.8%)

regimes1.4s (10.7%)

bsearch779.0ms (6.1%)

simplify5.0ms (0%)

end317.0ms (2.5%)

Profiling