Details

analyze2.2s (14.9%)

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)

sample6.5s (43.8%)

Symmetry

(sort M D)

Results

3.6s	13306×	body	128	invalid
2.8s	8256×	body	128	valid

Compiler

Compiled 122 to 95 computations (22.1% saved)

simplify37.0ms (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

prune5.0ms (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)

localize21.0ms (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))

series348.0ms (2.4%)

Counts

4 → 92

Calls

4 calls:

222.0ms	(.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))
88.0ms	(fma.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2) (*.f64 (/.f64 h l) -1/2) 1)
19.0ms	(sqrt.f64 (/.f64 d l))
18.0ms	(sqrt.f64 (/.f64 d h))

rewrite75.0ms (0.5%)

Algorithm

2×	batch-egg-rewrite

Rules

86× egg-rr

Counts

4 → 86

Calls

2 calls:

73.0ms

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

0.0ms

()

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

simplify86.0ms (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

prune123.0ms (0.8%)

Pruning

18 alts after pruning (18 fresh and 0 done)

	Pruned	Kept	Total
New	83	18	101
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	84	18	102

Error

11.4b

Counts

102 → 18

Alt Table

Status	Error	Program
	40.6b	(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)
	42.9b	(.f64 (sqrt.f64 (/.f64 1 (.f64 l h))) d)
	40.3b	(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)
	29.9b	(.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))
	31.7b	(.f64 (.f64 (exp.f64 (log.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))
	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)))))
	33.9b	(.f64 (.f64 (sqrt.f64 (/.f64 d h)) (sqrt.f64 (/.f64 d l))) 1)
▶	29.8b	(.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))
	29.8b	(.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))
	30.1b	(.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))
	30.2b	(.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))
	43.7b	(.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))
	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))
	47.4b	(.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))
	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))
	29.9b	(.f64 (.f64 (sqrt.f64 (/.f64 d h)) (.f64 (sqrt.f64 (pow.f64 (cbrt.f64 (/.f64 d l)) 2)) (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))
	29.9b	(.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))
	29.9b	(.f64 (.f64 (sqrt.f64 (/.f64 d h)) (.f64 (cbrt.f64 (/.f64 d l)) (cbrt.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 4007 to 2196 computations (45.2% saved)

localize20.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	6.1b	(.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))
	10.7b	(fma.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2) (*.f64 (/.f64 h l) -1/2) 1)
✓	12.3b	(pow.f64 (/.f64 d h) 1/4)
	15.1b	(sqrt.f64 (/.f64 d l))

series702.0ms (4.8%)

Counts

2 → 56

Calls

2 calls:

421.0ms	(pow.f64 (/.f64 d h) 1/4)
281.0ms	(.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))

rewrite64.0ms (0.4%)

Algorithm

2×	batch-egg-rewrite

Rules

33× egg-rr

Counts

2 → 33

Calls

2 calls:

64.0ms	((pow.f64 (/.f64 d h) 1/4) (.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)))
0.0ms	()

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	24	47
1	512	45
2	4690	45
3	5523	45
0	0	0
1	0	0

simplify103.0ms (0.7%)

Algorithm

1×	egg-herbie

Rules

752×	`div-sub_binary64`
503×	`associate-r_binary64`
501×	`fma-def_binary64`
438×	`associate-l_binary64`
286×	`unswap-sqr_binary64`

Counts

89 → 45

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	56	1467
1	127	1419
2	273	1419
3	864	1275
4	3310	1275
5	4642	1275
6	4762	1275
7	5290	1275

prune201.0ms (1.4%)

Pruning

20 alts after pruning (20 fresh and 0 done)

	Pruned	Kept	Total
New	92	6	98
Fresh	3	14	17
Picked	1	0	1
Done	0	0	0
Total	96	20	116

Error

11.4b

Counts

116 → 20

Alt Table

Status	Error	Program
	59.9b	(log.f64 (pow.f64 (exp.f64 (pow.f64 (.f64 (/.f64 d h) (/.f64 d l)) 1/2)) (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))
	39.2b	(pow.f64 (.f64 (pow.f64 (.f64 (/.f64 d h) (/.f64 d l)) 1/2) (fma.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2) (*.f64 (/.f64 h l) -1/2) 1)) 1)
	40.6b	(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)
	42.9b	(.f64 (sqrt.f64 (/.f64 1 (.f64 l h))) d)
	31.7b	(.f64 (.f64 (pow.f64 (exp.f64 (.f64 1/4 (log.f64 (/.f64 d h)))) 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))
	40.3b	(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)
	29.9b	(.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))
	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)))))
	33.9b	(.f64 (.f64 (sqrt.f64 (/.f64 d h)) (sqrt.f64 (/.f64 d l))) 1)
	42.8b	(.f64 (.f64 (pow.f64 (.f64 (pow.f64 d 1/4) (pow.f64 (/.f64 1 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))
	29.9b	(.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))
	30.0b	(.f64 (.f64 (pow.f64 (pow.f64 (/.f64 d h) 1/4) 2) (.f64 (cbrt.f64 (/.f64 d l)) (cbrt.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))
	29.9b	(.f64 (.f64 (sqrt.f64 (/.f64 d h)) (.f64 (cbrt.f64 (/.f64 d l)) (cbrt.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))
	30.1b	(.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))
	30.2b	(.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))
	43.7b	(.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))
	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))
	29.9b	(.f64 (.f64 (sqrt.f64 (/.f64 d h)) (.f64 (sqrt.f64 (pow.f64 (cbrt.f64 (/.f64 d l)) 2)) (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))
▶	29.8b	(.f64 (.f64 (pow.f64 (pow.f64 (/.f64 d h) 1/4) 2) (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))

Compiler

Compiled 4361 to 2648 computations (39.3% saved)

localize80.0ms (0.5%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	6.1b	(.f64 (.f64 (pow.f64 (pow.f64 (/.f64 d h) 1/4) 2) (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))
	10.7b	(fma.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2) (*.f64 (/.f64 h l) -1/2) 1)
	12.3b	(pow.f64 (/.f64 d h) 1/4)
✓	15.4b	(pow.f64 (/.f64 d l) 1/4)

series775.0ms (5.3%)

Counts

2 → 60

Calls

2 calls:

539.0ms	(pow.f64 (/.f64 d l) 1/4)
235.0ms	(.f64 (.f64 (pow.f64 (pow.f64 (/.f64 d h) 1/4) 2) (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))

rewrite65.0ms (0.4%)

Algorithm

2×	batch-egg-rewrite

Rules

30× egg-rr

Counts

2 → 30

Calls

2 calls:

64.0ms

((pow.f64 (/.f64 d l) 1/4) (*.f64 (*.f64 (pow.f64 (pow.f64 (/.f64 d h) 1/4) 2) (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)))

0.0ms

()

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	25	48
1	540	45
2	4894	45
3	4987	45
0	0	0
1	0	0

simplify154.0ms (1%)

Algorithm

1×	egg-herbie

Rules

752×	`div-sub_binary64`
505×	`fma-def_binary64`
503×	`associate-r_binary64`
438×	`associate-l_binary64`
286×	`unswap-sqr_binary64`

Counts

90 → 42

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	56	1602
1	126	1548
2	273	1548
3	864	1404
4	3310	1404
5	4644	1404
6	4774	1404
7	5305	1404

prune131.0ms (0.9%)

Pruning

19 alts after pruning (19 fresh and 0 done)

	Pruned	Kept	Total
New	88	4	92
Fresh	4	15	19
Picked	1	0	1
Done	0	0	0
Total	93	19	112

Error

11.4b

Counts

112 → 19

Alt Table

Status	Error	Program
	59.9b	(log.f64 (pow.f64 (exp.f64 (pow.f64 (.f64 (/.f64 d h) (/.f64 d l)) 1/2)) (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))
	39.2b	(pow.f64 (.f64 (pow.f64 (.f64 (/.f64 d h) (/.f64 d l)) 1/2) (fma.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2) (*.f64 (/.f64 h l) -1/2) 1)) 1)
	40.6b	(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)
	42.9b	(.f64 (sqrt.f64 (/.f64 1 (.f64 l h))) d)
	30.0b	(.f64 (.f64 (pow.f64 (pow.f64 (/.f64 d h) 1/4) 2) (pow.f64 (cbrt.f64 (pow.f64 (/.f64 d l) 3/4)) 2)) (fma.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2) (*.f64 (/.f64 h l) -1/2) 1))
	40.3b	(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)
	29.9b	(.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))
	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)))))
	33.9b	(.f64 (.f64 (sqrt.f64 (/.f64 d h)) (sqrt.f64 (/.f64 d l))) 1)
	45.7b	(.f64 (.f64 (pow.f64 (pow.f64 (/.f64 d h) 1/4) 2) (pow.f64 (exp.f64 (.f64 1/4 (-.f64 (log.f64 d) (log.f64 l)))) 2)) (fma.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2) (.f64 (/.f64 h l) -1/2) 1))
▶	29.9b	(.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))
	43.7b	(.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))
	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))
	29.9b	(.f64 (.f64 (sqrt.f64 (/.f64 d h)) (.f64 (sqrt.f64 (pow.f64 (cbrt.f64 (/.f64 d l)) 2)) (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))
	30.0b	(.f64 (.f64 (pow.f64 (pow.f64 (/.f64 d h) 1/4) 2) (pow.f64 (.f64 (pow.f64 (/.f64 d l) 1/8) (pow.f64 (/.f64 d l) 1/8)) 2)) (fma.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2) (.f64 (/.f64 h l) -1/2) 1))
	29.9b	(.f64 (.f64 (sqrt.f64 (/.f64 d h)) (.f64 (cbrt.f64 (/.f64 d l)) (cbrt.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))
	42.8b	(.f64 (.f64 (pow.f64 (.f64 (pow.f64 d 1/4) (pow.f64 (/.f64 1 h) 1/4)) 2) (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))
	30.2b	(.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))

Compiler

Compiled 4362 to 2809 computations (35.6% saved)

localize22.0ms (0.1%)

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))

series430.0ms (2.9%)

Counts

1 → 24

Calls

1 calls:

430.0ms

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

rewrite41.0ms (0.3%)

Algorithm

2×	batch-egg-rewrite

Rules

50× egg-rr

Counts

1 → 50

Calls

2 calls:

40.0ms	((cbrt.f64 (/.f64 d h)))
0.0ms	()

Iterations

Useful iterations: 0 (0.0ms)

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

simplify63.0ms (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

prune206.0ms (1.4%)

Pruning

18 alts after pruning (18 fresh and 0 done)

	Pruned	Kept	Total
New	135	1	136
Fresh	1	17	18
Picked	1	0	1
Done	0	0	0
Total	137	18	155

Error

11.4b

Counts

155 → 18

Alt Table

Status	Error	Program
	59.9b	(log.f64 (pow.f64 (exp.f64 (pow.f64 (.f64 (/.f64 d h) (/.f64 d l)) 1/2)) (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))
	39.2b	(pow.f64 (.f64 (pow.f64 (.f64 (/.f64 d h) (/.f64 d l)) 1/2) (fma.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2) (*.f64 (/.f64 h l) -1/2) 1)) 1)
	40.6b	(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)
	42.9b	(.f64 (sqrt.f64 (/.f64 1 (.f64 l h))) d)
	30.0b	(.f64 (.f64 (pow.f64 (pow.f64 (/.f64 d h) 1/4) 2) (pow.f64 (cbrt.f64 (pow.f64 (/.f64 d l) 3/4)) 2)) (fma.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2) (*.f64 (/.f64 h l) -1/2) 1))
	40.3b	(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)
	29.9b	(.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))
	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)))))
	33.9b	(.f64 (.f64 (sqrt.f64 (/.f64 d h)) (sqrt.f64 (/.f64 d l))) 1)
	43.7b	(.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))
	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))
	29.9b	(.f64 (.f64 (.f64 (cbrt.f64 (/.f64 d h)) (cbrt.f64 (sqrt.f64 (/.f64 d h)))) (/.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))
	30.0b	(.f64 (.f64 (pow.f64 (pow.f64 (/.f64 d h) 1/4) 2) (pow.f64 (.f64 (pow.f64 (/.f64 d l) 1/8) (pow.f64 (/.f64 d l) 1/8)) 2)) (fma.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2) (.f64 (/.f64 h l) -1/2) 1))
	45.7b	(.f64 (.f64 (pow.f64 (pow.f64 (/.f64 d h) 1/4) 2) (pow.f64 (exp.f64 (.f64 1/4 (-.f64 (log.f64 d) (log.f64 l)))) 2)) (fma.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2) (.f64 (/.f64 h l) -1/2) 1))
	29.9b	(.f64 (.f64 (sqrt.f64 (/.f64 d h)) (.f64 (cbrt.f64 (/.f64 d l)) (cbrt.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))
	42.8b	(.f64 (.f64 (pow.f64 (.f64 (pow.f64 d 1/4) (pow.f64 (/.f64 1 h) 1/4)) 2) (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))
	30.2b	(.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))

Compiler

Compiled 5543 to 2543 computations (54.1% saved)

regimes1.6s (10.9%)

Accuracy

Total 5.9b remaining (32.1%)

Threshold costs 0b (0%)

Counts

109 → 3

Compiler

Compiled 26994 to 19906 computations (26.3% saved)

bsearch348.0ms (2.4%)

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)

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

end380.0ms (2.6%)

Remove: (sort M D)
Compiler: Compiled 973 to 679 computations (30.2% saved)

Details

analyze2.2s (14.9%)

sample6.5s (43.8%)

simplify37.0ms (0.3%)

prune5.0ms (0%)

localize21.0ms (0.1%)

series348.0ms (2.4%)

rewrite75.0ms (0.5%)

simplify86.0ms (0.6%)

prune123.0ms (0.8%)

localize20.0ms (0.1%)

series702.0ms (4.8%)

rewrite64.0ms (0.4%)

simplify103.0ms (0.7%)

prune201.0ms (1.4%)

localize80.0ms (0.5%)

series775.0ms (5.3%)

rewrite65.0ms (0.4%)

simplify154.0ms (1%)

prune131.0ms (0.9%)

localize22.0ms (0.1%)

series430.0ms (2.9%)

rewrite41.0ms (0.3%)

simplify63.0ms (0.4%)

prune206.0ms (1.4%)

regimes1.6s (10.9%)

bsearch348.0ms (2.4%)

simplify5.0ms (0%)

end380.0ms (2.6%)

Profiling