Details

analyze2.1s (16.8%)

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)

sample5.5s (43.6%)

Results

3.2s	13324×	body	128	invalid
2.2s	8256×	body	128	valid

Compiler

Compiled 82 to 64 computations (22% saved)

preprocess43.0ms (0.3%)

Algorithm

2×	egg-herbie

Rules

775×	`associate-*r/_binary64`
448×	`*-commutative_binary64`
230×	`associate-/l*_binary64`
205×	`distribute-rgt-neg-in_binary64`
185×	`distribute-lft-neg-in_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	122	451
1	419	451
2	1543	429
0	5	5
1	5	5

Stop Event

1×	unsound
1×	node limit

Symmetry

(sort M D)

Compiler

Compiled 40 to 31 computations (22.5% saved)

simplify15.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

425×	`associate-/l*_binary64`
398×	`*-commutative_binary64`
236×	`associate-/l/_binary64`
214×	`associate-/r/_binary64`
203×	`associate-/r*_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	24	41
1	62	41
2	195	39
3	1309	39

Stop Event

1×	node limit

Counts

1 → 2

prune5.0ms (0%)

Pruning

3 alts after pruning (3 fresh and 0 done)

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

Error

23.7b

Counts

3 → 2

Alt Table

Status	Error	Program
	24.4b	(.f64 (sqrt.f64 (/.f64 d h)) (.f64 (sqrt.f64 (/.f64 d l)) (fma.f64 (/.f64 h l) (.f64 (pow.f64 (.f64 M (/.f64 (/.f64 D d) 2)) 2) -1/2) 1)))
▶	24.1b	(.f64 (.f64 (pow.f64 (/.f64 d h) (/.f64 1 2)) (pow.f64 (/.f64 d l) (/.f64 1 2))) (-.f64 1 (.f64 (.f64 (/.f64 1 2) (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2)) (/.f64 h l))))

Status

Error

Program

24.4b

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

▶

24.1b

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

Compiler

Compiled 208 to 151 computations (27.4% saved)

localize25.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	6.5b	(/.f64 (.f64 M D) (.f64 2 d))
✓	9.7b	(pow.f64 (/.f64 d l) (/.f64 1 2))
✓	10.2b	(pow.f64 (/.f64 d h) (/.f64 1 2))
✓	11.1b	(.f64 (.f64 (/.f64 1 2) (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2)) (/.f64 h l))

series278.0ms (2.2%)

Counts

4 → 96

Calls

36 calls:

36.0ms	(.f64 (.f64 (/.f64 1 2) (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2)) (/.f64 h l))	l	0
29.0ms	(.f64 (.f64 (/.f64 1 2) (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2)) (/.f64 h l))	M	0
24.0ms	(.f64 (.f64 (/.f64 1 2) (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2)) (/.f64 h l))	D	0
19.0ms	(.f64 (.f64 (/.f64 1 2) (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2)) (/.f64 h l))	h	0
17.0ms	(.f64 (.f64 (/.f64 1 2) (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2)) (/.f64 h l))	d	inf

rewrite40.0ms (0.3%)

Algorithm

1×	batch-egg-rewrite

Rules

207×	`add-sqr-sqrt_binary64`
205×	`pow1_binary64`
202×	`*-un-lft-identity_binary64`
193×	`add-log-exp_binary64`
193×	`log1p-expm1-u_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	21	44
1	434	44

Stop Event

1×	node limit

Counts

4 → 115

simplify119.0ms (1%)

Algorithm

1×	egg-herbie

Rules

680×	`unswap-sqr_binary64`
535×	`associate-/l/_binary64`
493×	`associate-/r/_binary64`
349×	`*-commutative_binary64`
216×	`times-frac_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	29	1860
1	87	1860
2	261	1860
3	1579	1860
4	3428	1860
5	3704	1860
6	4815	1860
7	4897	1860
8	4996	1860

Stop Event

1×	node limit

Counts

211 → 122

prune330.0ms (2.6%)

Pruning

23 alts after pruning (23 fresh and 0 done)

	Pruned	Kept	Total
New	100	22	122
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	101	23	124

Error

10.8b

Counts

124 → 23

Alt Table

Status	Error	Program
	43.9b	(.f64 (.f64 (pow.f64 (/.f64 d h) (/.f64 1 2)) (pow.f64 (/.f64 d l) (/.f64 1 2))) (-.f64 1 (.f64 1/8 (/.f64 (.f64 (pow.f64 D 2) (.f64 (pow.f64 M 2) h)) (.f64 l (pow.f64 d 2))))))
	44.6b	(.f64 (.f64 (/.f64 (sqrt.f64 d) (sqrt.f64 h)) (pow.f64 (/.f64 d l) (/.f64 1 2))) (-.f64 1 (.f64 (.f64 (/.f64 1 2) (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2)) (/.f64 h l))))
	41.3b	(.f64 (.f64 (pow.f64 (/.f64 d h) (/.f64 1 2)) (pow.f64 (/.f64 d l) (/.f64 1 2))) (-.f64 1 (.f64 (.f64 (/.f64 1 2) (pow.f64 (log.f64 (pow.f64 (pow.f64 (exp.f64 M) D) (/.f64 1/2 d))) 2)) (/.f64 h l))))
	32.1b	(.f64 (.f64 (pow.f64 (/.f64 d h) (/.f64 1 2)) (pow.f64 (/.f64 d l) (/.f64 1 2))) (-.f64 1 (log.f64 (pow.f64 (exp.f64 (/.f64 h l)) (.f64 1/2 (pow.f64 (.f64 (/.f64 M (*.f64 2 d)) D) 2))))))
	24.2b	(.f64 (.f64 (.f64 (pow.f64 (/.f64 d h) 1/4) (pow.f64 (/.f64 d h) 1/4)) (pow.f64 (/.f64 d l) (/.f64 1 2))) (-.f64 1 (.f64 (.f64 (/.f64 1 2) (pow.f64 (/.f64 (.f64 M D) (*.f64 2 d)) 2)) (/.f64 h l))))
▶	22.4b	(.f64 (.f64 (pow.f64 (/.f64 d h) (/.f64 1 2)) (pow.f64 (/.f64 d l) (/.f64 1 2))) (-.f64 1 (pow.f64 (.f64 (sqrt.f64 (/.f64 h l)) (.f64 (.f64 (/.f64 M (.f64 2 d)) D) (sqrt.f64 1/2))) 2)))
	23.9b	(.f64 (.f64 (pow.f64 (/.f64 d h) (/.f64 1 2)) (pow.f64 (/.f64 d l) (/.f64 1 2))) (-.f64 1 (.f64 (.f64 (/.f64 1 2) (pow.f64 (.f64 (.f64 M 1/2) (/.f64 D d)) 2)) (/.f64 h l))))
	44.6b	(.f64 (.f64 (.f64 (sqrt.f64 d) (sqrt.f64 (/.f64 1 h))) (pow.f64 (/.f64 d l) (/.f64 1 2))) (-.f64 1 (.f64 (.f64 (/.f64 1 2) (pow.f64 (/.f64 (.f64 M D) (*.f64 2 d)) 2)) (/.f64 h l))))
	33.7b	(.f64 (.f64 (pow.f64 (/.f64 d h) (/.f64 1 2)) (cbrt.f64 (pow.f64 (/.f64 d l) 3/2))) (-.f64 1 (.f64 (.f64 (/.f64 1 2) (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2)) (/.f64 h l))))
	45.7b	(.f64 (.f64 (pow.f64 (/.f64 d h) (/.f64 1 2)) (/.f64 (sqrt.f64 d) (sqrt.f64 l))) (-.f64 1 (.f64 (.f64 (/.f64 1 2) (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2)) (/.f64 h l))))
	38.5b	(.f64 (.f64 (pow.f64 (/.f64 d h) (/.f64 1 2)) (/.f64 (sqrt.f64 (neg.f64 d)) (sqrt.f64 (neg.f64 l)))) (-.f64 1 (.f64 (.f64 (/.f64 1 2) (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2)) (/.f64 h l))))
	38.6b	(.f64 (.f64 (/.f64 (sqrt.f64 (neg.f64 d)) (sqrt.f64 (neg.f64 h))) (pow.f64 (/.f64 d l) (/.f64 1 2))) (-.f64 1 (.f64 (.f64 (/.f64 1 2) (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2)) (/.f64 h l))))
	24.4b	(.f64 (sqrt.f64 (/.f64 d h)) (.f64 (sqrt.f64 (/.f64 d l)) (fma.f64 (/.f64 h l) (.f64 (pow.f64 (.f64 M (/.f64 (/.f64 D d) 2)) 2) -1/2) 1)))
	24.3b	(.f64 (.f64 (pow.f64 (/.f64 d h) (/.f64 1 2)) (.f64 (cbrt.f64 (/.f64 d l)) (cbrt.f64 (sqrt.f64 (/.f64 d l))))) (-.f64 1 (.f64 (.f64 (/.f64 1 2) (pow.f64 (/.f64 (.f64 M D) (*.f64 2 d)) 2)) (/.f64 h l))))
	24.6b	(.f64 (.f64 (pow.f64 (/.f64 d h) (/.f64 1 2)) (pow.f64 (/.f64 d l) (/.f64 1 2))) (-.f64 1 (-.f64 (exp.f64 (log1p.f64 (.f64 1/2 (.f64 (pow.f64 (.f64 (/.f64 M (.f64 2 d)) D) 2) (/.f64 h l))))) 1)))
	33.7b	(.f64 (.f64 (cbrt.f64 (pow.f64 (/.f64 d h) 3/2)) (pow.f64 (/.f64 d l) (/.f64 1 2))) (-.f64 1 (.f64 (.f64 (/.f64 1 2) (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2)) (/.f64 h l))))
	23.6b	(.f64 (.f64 (/.f64 1 (sqrt.f64 (/.f64 h d))) (pow.f64 (/.f64 d l) (/.f64 1 2))) (-.f64 1 (.f64 (.f64 (/.f64 1 2) (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2)) (/.f64 h l))))
	24.2b	(.f64 (.f64 (pow.f64 (/.f64 d h) (/.f64 1 2)) (/.f64 1 (sqrt.f64 (/.f64 l d)))) (-.f64 1 (.f64 (.f64 (/.f64 1 2) (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2)) (/.f64 h l))))
	24.2b	(.f64 (.f64 (pow.f64 (/.f64 d h) (/.f64 1 2)) (pow.f64 (/.f64 d l) (/.f64 1 2))) (-.f64 1 (.f64 (.f64 (/.f64 1 2) (pow.f64 (.f64 1/2 (.f64 D (/.f64 M d))) 2)) (/.f64 h l))))
	45.7b	(.f64 (.f64 (pow.f64 (/.f64 d h) (/.f64 1 2)) (.f64 (sqrt.f64 d) (sqrt.f64 (/.f64 1 l)))) (-.f64 1 (.f64 (.f64 (/.f64 1 2) (pow.f64 (/.f64 (.f64 M D) (*.f64 2 d)) 2)) (/.f64 h l))))
	23.9b	(.f64 (.f64 (pow.f64 (/.f64 d h) (/.f64 1 2)) (pow.f64 (/.f64 d l) (/.f64 1 2))) (-.f64 1 (/.f64 (.f64 1/2 (pow.f64 (.f64 (/.f64 M (*.f64 2 d)) D) 2)) (/.f64 l h))))
	23.9b	(.f64 (.f64 (pow.f64 (/.f64 d h) (/.f64 1 2)) (pow.f64 (/.f64 d l) (/.f64 1 2))) (-.f64 1 (/.f64 1 (/.f64 l (.f64 (.f64 1/2 (pow.f64 (.f64 (/.f64 M (.f64 2 d)) D) 2)) h)))))
	24.2b	(.f64 (.f64 (pow.f64 (/.f64 d h) (/.f64 1 2)) (.f64 (pow.f64 (/.f64 d l) 1/4) (pow.f64 (/.f64 d l) 1/4))) (-.f64 1 (.f64 (.f64 (/.f64 1 2) (pow.f64 (/.f64 (.f64 M D) (*.f64 2 d)) 2)) (/.f64 h l))))

Compiler

Compiled 6389 to 4326 computations (32.3% saved)

localize25.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	6.5b	(.f64 (.f64 (pow.f64 (/.f64 d h) (/.f64 1 2)) (pow.f64 (/.f64 d l) (/.f64 1 2))) (-.f64 1 (pow.f64 (.f64 (sqrt.f64 (/.f64 h l)) (.f64 (.f64 (/.f64 M (.f64 2 d)) D) (sqrt.f64 1/2))) 2)))
	9.7b	(pow.f64 (/.f64 d l) (/.f64 1 2))
	10.2b	(pow.f64 (/.f64 d h) (/.f64 1 2))
✓	13.0b	(sqrt.f64 (/.f64 h l))

series271.0ms (2.2%)

Counts

2 → 36

Calls

21 calls:

41.0ms	(.f64 (.f64 (pow.f64 (/.f64 d h) (/.f64 1 2)) (pow.f64 (/.f64 d l) (/.f64 1 2))) (-.f64 1 (pow.f64 (.f64 (sqrt.f64 (/.f64 h l)) (.f64 (.f64 (/.f64 M (.f64 2 d)) D) (sqrt.f64 1/2))) 2)))	h	-inf
21.0ms	(.f64 (.f64 (pow.f64 (/.f64 d h) (/.f64 1 2)) (pow.f64 (/.f64 d l) (/.f64 1 2))) (-.f64 1 (pow.f64 (.f64 (sqrt.f64 (/.f64 h l)) (.f64 (.f64 (/.f64 M (.f64 2 d)) D) (sqrt.f64 1/2))) 2)))	D	-inf
19.0ms	(.f64 (.f64 (pow.f64 (/.f64 d h) (/.f64 1 2)) (pow.f64 (/.f64 d l) (/.f64 1 2))) (-.f64 1 (pow.f64 (.f64 (sqrt.f64 (/.f64 h l)) (.f64 (.f64 (/.f64 M (.f64 2 d)) D) (sqrt.f64 1/2))) 2)))	D	inf
18.0ms	(.f64 (.f64 (pow.f64 (/.f64 d h) (/.f64 1 2)) (pow.f64 (/.f64 d l) (/.f64 1 2))) (-.f64 1 (pow.f64 (.f64 (sqrt.f64 (/.f64 h l)) (.f64 (.f64 (/.f64 M (.f64 2 d)) D) (sqrt.f64 1/2))) 2)))	d	0
18.0ms	(.f64 (.f64 (pow.f64 (/.f64 d h) (/.f64 1 2)) (pow.f64 (/.f64 d l) (/.f64 1 2))) (-.f64 1 (pow.f64 (.f64 (sqrt.f64 (/.f64 h l)) (.f64 (.f64 (/.f64 M (.f64 2 d)) D) (sqrt.f64 1/2))) 2)))	D	0

rewrite31.0ms (0.2%)

Algorithm

1×	batch-egg-rewrite

Rules

263×	`add-sqr-sqrt_binary64`
260×	`pow1_binary64`
257×	`*-un-lft-identity_binary64`
244×	`add-log-exp_binary64`
244×	`log1p-expm1-u_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	26	50
1	548	48

Stop Event

1×	node limit

Counts

2 → 30

simplify39.0ms (0.3%)

Algorithm

1×	egg-herbie

Rules

616×	`associate-/l*_binary64`
543×	`associate-/r/_binary64`
417×	`associate-/r*_binary64`
237×	`unswap-sqr_binary64`
176×	`distribute-rgt-neg-in_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	38	1546
1	99	1236
2	301	1236
3	1432	1236

Stop Event

1×	node limit

Counts

66 → 38

prune160.0ms (1.3%)

Pruning

22 alts after pruning (22 fresh and 0 done)

	Pruned	Kept	Total
New	67	13	80
Fresh	13	9	22
Picked	1	0	1
Done	0	0	0
Total	81	22	103

Error

9.0b

Counts

103 → 22

Alt Table

Status	Error	Program
	23.9b	(.f64 (.f64 (pow.f64 (/.f64 d h) (/.f64 1 2)) (pow.f64 (/.f64 d l) (/.f64 1 2))) (-.f64 1 (.f64 (.f64 (/.f64 1 2) (pow.f64 (.f64 (.f64 M 1/2) (/.f64 D d)) 2)) (/.f64 h l))))
	44.6b	(.f64 (.f64 (.f64 (sqrt.f64 d) (sqrt.f64 (/.f64 1 h))) (pow.f64 (/.f64 d l) (/.f64 1 2))) (-.f64 1 (.f64 (.f64 (/.f64 1 2) (pow.f64 (/.f64 (.f64 M D) (*.f64 2 d)) 2)) (/.f64 h l))))
	38.5b	(.f64 (.f64 (pow.f64 (/.f64 d h) (/.f64 1 2)) (/.f64 (sqrt.f64 (neg.f64 d)) (sqrt.f64 (neg.f64 l)))) (-.f64 1 (.f64 (.f64 (/.f64 1 2) (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2)) (/.f64 h l))))
	43.6b	(.f64 (.f64 (/.f64 (sqrt.f64 d) (sqrt.f64 h)) (pow.f64 (/.f64 d l) (/.f64 1 2))) (-.f64 1 (pow.f64 (.f64 (sqrt.f64 (/.f64 h l)) (.f64 (.f64 (/.f64 M (.f64 2 d)) D) (sqrt.f64 1/2))) 2)))
	22.5b	(.f64 (.f64 (pow.f64 (/.f64 d h) (/.f64 1 2)) (pow.f64 (/.f64 d l) (/.f64 1 2))) (-.f64 1 (pow.f64 (.f64 (pow.f64 (cbrt.f64 (sqrt.f64 (/.f64 h l))) 3) (.f64 (.f64 (/.f64 M (.f64 2 d)) D) (sqrt.f64 1/2))) 2)))
	60.3b	(.f64 (sqrt.f64 (/.f64 h (pow.f64 l 3))) (.f64 (/.f64 -1/8 d) (.f64 D (.f64 D (*.f64 M M)))))
	22.7b	(.f64 (.f64 (pow.f64 (/.f64 d h) (/.f64 1 2)) (.f64 (cbrt.f64 (/.f64 d l)) (cbrt.f64 (sqrt.f64 (/.f64 d l))))) (-.f64 1 (pow.f64 (.f64 (sqrt.f64 (/.f64 h l)) (.f64 (.f64 (/.f64 M (*.f64 2 d)) D) (sqrt.f64 1/2))) 2)))
	45.9b	(.f64 (.f64 (pow.f64 (/.f64 d h) (/.f64 1 2)) (pow.f64 (/.f64 d l) (/.f64 1 2))) (-.f64 1 (pow.f64 (.f64 (/.f64 (sqrt.f64 h) (sqrt.f64 l)) (.f64 (.f64 (/.f64 M (.f64 2 d)) D) (sqrt.f64 1/2))) 2)))
	23.9b	(.f64 (.f64 (pow.f64 (/.f64 d h) (/.f64 1 2)) (pow.f64 (/.f64 d l) (/.f64 1 2))) (-.f64 1 (/.f64 1 (/.f64 l (.f64 (.f64 1/2 (pow.f64 (.f64 (/.f64 M (.f64 2 d)) D) 2)) h)))))
	24.4b	(.f64 (sqrt.f64 (/.f64 d h)) (.f64 (sqrt.f64 (/.f64 d l)) (fma.f64 (/.f64 h l) (.f64 (pow.f64 (.f64 M (/.f64 (/.f64 D d) 2)) 2) -1/2) 1)))
	22.6b	(.f64 (.f64 (pow.f64 (/.f64 d h) (/.f64 1 2)) (.f64 (pow.f64 (/.f64 d l) 1/4) (pow.f64 (/.f64 d l) 1/4))) (-.f64 1 (pow.f64 (.f64 (sqrt.f64 (/.f64 h l)) (.f64 (.f64 (/.f64 M (*.f64 2 d)) D) (sqrt.f64 1/2))) 2)))
	32.7b	(.f64 (.f64 (cbrt.f64 (pow.f64 (/.f64 d h) 3/2)) (pow.f64 (/.f64 d l) (/.f64 1 2))) (-.f64 1 (pow.f64 (.f64 (sqrt.f64 (/.f64 h l)) (.f64 (.f64 (/.f64 M (.f64 2 d)) D) (sqrt.f64 1/2))) 2)))
	44.4b	(.f64 (.f64 (pow.f64 (/.f64 d h) (/.f64 1 2)) (/.f64 (sqrt.f64 d) (sqrt.f64 l))) (-.f64 1 (pow.f64 (.f64 (sqrt.f64 (/.f64 h l)) (.f64 (.f64 (/.f64 M (.f64 2 d)) D) (sqrt.f64 1/2))) 2)))
	24.2b	(.f64 (.f64 (pow.f64 (/.f64 d h) (/.f64 1 2)) (/.f64 1 (sqrt.f64 (/.f64 l d)))) (-.f64 1 (.f64 (.f64 (/.f64 1 2) (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2)) (/.f64 h l))))
	45.4b	(.f64 (sqrt.f64 (/.f64 1 (.f64 l h))) d)
	34.4b	(pow.f64 (.f64 (pow.f64 (.f64 (/.f64 d h) (/.f64 d l)) 1/2) (-.f64 1 (.f64 (/.f64 h l) (pow.f64 (.f64 (.f64 (/.f64 M (.f64 d 2)) D) (sqrt.f64 1/2)) 2)))) 1)
	32.1b	(.f64 (.f64 (pow.f64 (/.f64 d h) (/.f64 1 2)) (pow.f64 (/.f64 d l) (/.f64 1 2))) (-.f64 1 (log.f64 (pow.f64 (exp.f64 (/.f64 h l)) (.f64 1/2 (pow.f64 (.f64 (/.f64 M (*.f64 2 d)) D) 2))))))
	24.2b	(.f64 (.f64 (.f64 (pow.f64 (/.f64 d h) 1/4) (pow.f64 (/.f64 d h) 1/4)) (pow.f64 (/.f64 d l) (/.f64 1 2))) (-.f64 1 (.f64 (.f64 (/.f64 1 2) (pow.f64 (/.f64 (.f64 M D) (*.f64 2 d)) 2)) (/.f64 h l))))
▶	22.4b	(.f64 (.f64 (pow.f64 (/.f64 d h) (/.f64 1 2)) (pow.f64 (/.f64 d l) (/.f64 1 2))) (-.f64 1 (pow.f64 (.f64 (pow.f64 (sqrt.f64 (sqrt.f64 (/.f64 h l))) 2) (.f64 (.f64 (/.f64 M (.f64 2 d)) D) (sqrt.f64 1/2))) 2)))
	37.7b	(.f64 (.f64 (/.f64 (sqrt.f64 (neg.f64 d)) (sqrt.f64 (neg.f64 h))) (pow.f64 (/.f64 d l) (/.f64 1 2))) (-.f64 1 (pow.f64 (.f64 (sqrt.f64 (/.f64 h l)) (.f64 (.f64 (/.f64 M (.f64 2 d)) D) (sqrt.f64 1/2))) 2)))
	24.2b	(.f64 (.f64 (pow.f64 (/.f64 d h) (/.f64 1 2)) (.f64 (pow.f64 (/.f64 d l) 1/4) (pow.f64 (/.f64 d l) 1/4))) (-.f64 1 (.f64 (.f64 (/.f64 1 2) (pow.f64 (/.f64 (.f64 M D) (*.f64 2 d)) 2)) (/.f64 h l))))
	39.9b	(pow.f64 (sqrt.f64 (.f64 (pow.f64 (.f64 (/.f64 d h) (/.f64 d l)) 1/2) (-.f64 1 (.f64 (/.f64 h l) (pow.f64 (.f64 (.f64 (/.f64 M (.f64 d 2)) D) (sqrt.f64 1/2)) 2))))) 2)

Compiler

Compiled 4411 to 2953 computations (33.1% saved)

localize26.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	6.5b	(.f64 (.f64 (pow.f64 (/.f64 d h) (/.f64 1 2)) (pow.f64 (/.f64 d l) (/.f64 1 2))) (-.f64 1 (pow.f64 (.f64 (pow.f64 (sqrt.f64 (sqrt.f64 (/.f64 h l))) 2) (.f64 (.f64 (/.f64 M (.f64 2 d)) D) (sqrt.f64 1/2))) 2)))
	9.7b	(pow.f64 (/.f64 d l) (/.f64 1 2))
	10.2b	(pow.f64 (/.f64 d h) (/.f64 1 2))
	13.0b	(sqrt.f64 (/.f64 h l))

series259.0ms (2.1%)

Counts

1 → 36

Calls

15 calls:

43.0ms	(.f64 (.f64 (pow.f64 (/.f64 d h) (/.f64 1 2)) (pow.f64 (/.f64 d l) (/.f64 1 2))) (-.f64 1 (pow.f64 (.f64 (pow.f64 (sqrt.f64 (sqrt.f64 (/.f64 h l))) 2) (.f64 (.f64 (/.f64 M (.f64 2 d)) D) (sqrt.f64 1/2))) 2)))	h	-inf
19.0ms	(.f64 (.f64 (pow.f64 (/.f64 d h) (/.f64 1 2)) (pow.f64 (/.f64 d l) (/.f64 1 2))) (-.f64 1 (pow.f64 (.f64 (pow.f64 (sqrt.f64 (sqrt.f64 (/.f64 h l))) 2) (.f64 (.f64 (/.f64 M (.f64 2 d)) D) (sqrt.f64 1/2))) 2)))	D	inf
18.0ms	(.f64 (.f64 (pow.f64 (/.f64 d h) (/.f64 1 2)) (pow.f64 (/.f64 d l) (/.f64 1 2))) (-.f64 1 (pow.f64 (.f64 (pow.f64 (sqrt.f64 (sqrt.f64 (/.f64 h l))) 2) (.f64 (.f64 (/.f64 M (.f64 2 d)) D) (sqrt.f64 1/2))) 2)))	l	-inf
18.0ms	(.f64 (.f64 (pow.f64 (/.f64 d h) (/.f64 1 2)) (pow.f64 (/.f64 d l) (/.f64 1 2))) (-.f64 1 (pow.f64 (.f64 (pow.f64 (sqrt.f64 (sqrt.f64 (/.f64 h l))) 2) (.f64 (.f64 (/.f64 M (.f64 2 d)) D) (sqrt.f64 1/2))) 2)))	M	inf
17.0ms	(.f64 (.f64 (pow.f64 (/.f64 d h) (/.f64 1 2)) (pow.f64 (/.f64 d l) (/.f64 1 2))) (-.f64 1 (pow.f64 (.f64 (pow.f64 (sqrt.f64 (sqrt.f64 (/.f64 h l))) 2) (.f64 (.f64 (/.f64 M (.f64 2 d)) D) (sqrt.f64 1/2))) 2)))	d	0

rewrite26.0ms (0.2%)

Algorithm

1×	batch-egg-rewrite

Rules

272×	`add-sqr-sqrt_binary64`
270×	`pow1_binary64`
266×	`*-un-lft-identity_binary64`
253×	`add-log-exp_binary64`
253×	`log1p-expm1-u_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	28	44
1	592	44

Stop Event

1×	node limit

Counts

1 → 9

simplify40.0ms (0.3%)

Algorithm

1×	egg-herbie

Rules

616×	`associate-/l*_binary64`
543×	`associate-/r/_binary64`
417×	`associate-/r*_binary64`
237×	`unswap-sqr_binary64`
176×	`distribute-rgt-neg-in_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	38	1546
1	99	1236
2	301	1236
3	1432	1236

Stop Event

1×	node limit

Counts

45 → 17

prune140.0ms (1.1%)

Pruning

22 alts after pruning (21 fresh and 1 done)

	Pruned	Kept	Total
New	77	1	78
Fresh	1	20	21
Picked	0	1	1
Done	0	0	0
Total	78	22	100

Error

9.0b

Counts

100 → 22

Alt Table

Status	Error	Program
	33.4b	(pow.f64 (.f64 (pow.f64 (.f64 (/.f64 d h) (/.f64 d l)) 1/2) (-.f64 1 (pow.f64 (.f64 (sqrt.f64 (/.f64 h l)) (.f64 (/.f64 M (.f64 d 2)) (.f64 D (sqrt.f64 1/2)))) 2))) 1)
	32.1b	(.f64 (.f64 (pow.f64 (/.f64 d h) (/.f64 1 2)) (pow.f64 (/.f64 d l) (/.f64 1 2))) (-.f64 1 (log.f64 (pow.f64 (exp.f64 (/.f64 h l)) (.f64 1/2 (pow.f64 (.f64 (/.f64 M (*.f64 2 d)) D) 2))))))
	23.9b	(.f64 (.f64 (pow.f64 (/.f64 d h) (/.f64 1 2)) (pow.f64 (/.f64 d l) (/.f64 1 2))) (-.f64 1 (.f64 (.f64 (/.f64 1 2) (pow.f64 (.f64 (.f64 M 1/2) (/.f64 D d)) 2)) (/.f64 h l))))
	44.6b	(.f64 (.f64 (.f64 (sqrt.f64 d) (sqrt.f64 (/.f64 1 h))) (pow.f64 (/.f64 d l) (/.f64 1 2))) (-.f64 1 (.f64 (.f64 (/.f64 1 2) (pow.f64 (/.f64 (.f64 M D) (*.f64 2 d)) 2)) (/.f64 h l))))
	38.5b	(.f64 (.f64 (pow.f64 (/.f64 d h) (/.f64 1 2)) (/.f64 (sqrt.f64 (neg.f64 d)) (sqrt.f64 (neg.f64 l)))) (-.f64 1 (.f64 (.f64 (/.f64 1 2) (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2)) (/.f64 h l))))
	43.6b	(.f64 (.f64 (/.f64 (sqrt.f64 d) (sqrt.f64 h)) (pow.f64 (/.f64 d l) (/.f64 1 2))) (-.f64 1 (pow.f64 (.f64 (sqrt.f64 (/.f64 h l)) (.f64 (.f64 (/.f64 M (.f64 2 d)) D) (sqrt.f64 1/2))) 2)))
▶	22.5b	(.f64 (.f64 (pow.f64 (/.f64 d h) (/.f64 1 2)) (pow.f64 (/.f64 d l) (/.f64 1 2))) (-.f64 1 (pow.f64 (.f64 (pow.f64 (cbrt.f64 (sqrt.f64 (/.f64 h l))) 3) (.f64 (.f64 (/.f64 M (.f64 2 d)) D) (sqrt.f64 1/2))) 2)))
	60.3b	(.f64 (sqrt.f64 (/.f64 h (pow.f64 l 3))) (.f64 (/.f64 -1/8 d) (.f64 D (.f64 D (*.f64 M M)))))
	22.7b	(.f64 (.f64 (pow.f64 (/.f64 d h) (/.f64 1 2)) (.f64 (cbrt.f64 (/.f64 d l)) (cbrt.f64 (sqrt.f64 (/.f64 d l))))) (-.f64 1 (pow.f64 (.f64 (sqrt.f64 (/.f64 h l)) (.f64 (.f64 (/.f64 M (*.f64 2 d)) D) (sqrt.f64 1/2))) 2)))
	45.9b	(.f64 (.f64 (pow.f64 (/.f64 d h) (/.f64 1 2)) (pow.f64 (/.f64 d l) (/.f64 1 2))) (-.f64 1 (pow.f64 (.f64 (/.f64 (sqrt.f64 h) (sqrt.f64 l)) (.f64 (.f64 (/.f64 M (.f64 2 d)) D) (sqrt.f64 1/2))) 2)))
	23.9b	(.f64 (.f64 (pow.f64 (/.f64 d h) (/.f64 1 2)) (pow.f64 (/.f64 d l) (/.f64 1 2))) (-.f64 1 (/.f64 1 (/.f64 l (.f64 (.f64 1/2 (pow.f64 (.f64 (/.f64 M (.f64 2 d)) D) 2)) h)))))
	24.4b	(.f64 (sqrt.f64 (/.f64 d h)) (.f64 (sqrt.f64 (/.f64 d l)) (fma.f64 (/.f64 h l) (.f64 (pow.f64 (.f64 M (/.f64 (/.f64 D d) 2)) 2) -1/2) 1)))
	32.7b	(.f64 (.f64 (cbrt.f64 (pow.f64 (/.f64 d h) 3/2)) (pow.f64 (/.f64 d l) (/.f64 1 2))) (-.f64 1 (pow.f64 (.f64 (sqrt.f64 (/.f64 h l)) (.f64 (.f64 (/.f64 M (.f64 2 d)) D) (sqrt.f64 1/2))) 2)))
	44.4b	(.f64 (.f64 (pow.f64 (/.f64 d h) (/.f64 1 2)) (/.f64 (sqrt.f64 d) (sqrt.f64 l))) (-.f64 1 (pow.f64 (.f64 (sqrt.f64 (/.f64 h l)) (.f64 (.f64 (/.f64 M (.f64 2 d)) D) (sqrt.f64 1/2))) 2)))
	24.2b	(.f64 (.f64 (pow.f64 (/.f64 d h) (/.f64 1 2)) (/.f64 1 (sqrt.f64 (/.f64 l d)))) (-.f64 1 (.f64 (.f64 (/.f64 1 2) (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2)) (/.f64 h l))))
	45.4b	(.f64 (sqrt.f64 (/.f64 1 (.f64 l h))) d)
	34.4b	(pow.f64 (.f64 (pow.f64 (.f64 (/.f64 d h) (/.f64 d l)) 1/2) (-.f64 1 (.f64 (/.f64 h l) (pow.f64 (.f64 (.f64 (/.f64 M (.f64 d 2)) D) (sqrt.f64 1/2)) 2)))) 1)
	24.2b	(.f64 (.f64 (.f64 (pow.f64 (/.f64 d h) 1/4) (pow.f64 (/.f64 d h) 1/4)) (pow.f64 (/.f64 d l) (/.f64 1 2))) (-.f64 1 (.f64 (.f64 (/.f64 1 2) (pow.f64 (/.f64 (.f64 M D) (*.f64 2 d)) 2)) (/.f64 h l))))
✓	22.4b	(.f64 (.f64 (pow.f64 (/.f64 d h) (/.f64 1 2)) (pow.f64 (/.f64 d l) (/.f64 1 2))) (-.f64 1 (pow.f64 (.f64 (pow.f64 (sqrt.f64 (sqrt.f64 (/.f64 h l))) 2) (.f64 (.f64 (/.f64 M (.f64 2 d)) D) (sqrt.f64 1/2))) 2)))
	37.7b	(.f64 (.f64 (/.f64 (sqrt.f64 (neg.f64 d)) (sqrt.f64 (neg.f64 h))) (pow.f64 (/.f64 d l) (/.f64 1 2))) (-.f64 1 (pow.f64 (.f64 (sqrt.f64 (/.f64 h l)) (.f64 (.f64 (/.f64 M (.f64 2 d)) D) (sqrt.f64 1/2))) 2)))
	24.2b	(.f64 (.f64 (pow.f64 (/.f64 d h) (/.f64 1 2)) (.f64 (pow.f64 (/.f64 d l) 1/4) (pow.f64 (/.f64 d l) 1/4))) (-.f64 1 (.f64 (.f64 (/.f64 1 2) (pow.f64 (/.f64 (.f64 M D) (*.f64 2 d)) 2)) (/.f64 h l))))
	39.9b	(pow.f64 (sqrt.f64 (.f64 (pow.f64 (.f64 (/.f64 d h) (/.f64 d l)) 1/2) (-.f64 1 (.f64 (/.f64 h l) (pow.f64 (.f64 (.f64 (/.f64 M (.f64 d 2)) D) (sqrt.f64 1/2)) 2))))) 2)

Compiler

Compiled 4481 to 3013 computations (32.8% saved)

localize25.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	6.5b	(.f64 (.f64 (pow.f64 (/.f64 d h) (/.f64 1 2)) (pow.f64 (/.f64 d l) (/.f64 1 2))) (-.f64 1 (pow.f64 (.f64 (pow.f64 (cbrt.f64 (sqrt.f64 (/.f64 h l))) 3) (.f64 (.f64 (/.f64 M (.f64 2 d)) D) (sqrt.f64 1/2))) 2)))
	9.7b	(pow.f64 (/.f64 d l) (/.f64 1 2))
	10.2b	(pow.f64 (/.f64 d h) (/.f64 1 2))
	13.0b	(sqrt.f64 (/.f64 h l))

series294.0ms (2.3%)

Counts

1 → 36

Calls

15 calls:

49.0ms	(.f64 (.f64 (pow.f64 (/.f64 d h) (/.f64 1 2)) (pow.f64 (/.f64 d l) (/.f64 1 2))) (-.f64 1 (pow.f64 (.f64 (pow.f64 (cbrt.f64 (sqrt.f64 (/.f64 h l))) 3) (.f64 (.f64 (/.f64 M (.f64 2 d)) D) (sqrt.f64 1/2))) 2)))	h	0
35.0ms	(.f64 (.f64 (pow.f64 (/.f64 d h) (/.f64 1 2)) (pow.f64 (/.f64 d l) (/.f64 1 2))) (-.f64 1 (pow.f64 (.f64 (pow.f64 (cbrt.f64 (sqrt.f64 (/.f64 h l))) 3) (.f64 (.f64 (/.f64 M (.f64 2 d)) D) (sqrt.f64 1/2))) 2)))	h	-inf
22.0ms	(.f64 (.f64 (pow.f64 (/.f64 d h) (/.f64 1 2)) (pow.f64 (/.f64 d l) (/.f64 1 2))) (-.f64 1 (pow.f64 (.f64 (pow.f64 (cbrt.f64 (sqrt.f64 (/.f64 h l))) 3) (.f64 (.f64 (/.f64 M (.f64 2 d)) D) (sqrt.f64 1/2))) 2)))	d	0
18.0ms	(.f64 (.f64 (pow.f64 (/.f64 d h) (/.f64 1 2)) (pow.f64 (/.f64 d l) (/.f64 1 2))) (-.f64 1 (pow.f64 (.f64 (pow.f64 (cbrt.f64 (sqrt.f64 (/.f64 h l))) 3) (.f64 (.f64 (/.f64 M (.f64 2 d)) D) (sqrt.f64 1/2))) 2)))	D	inf
18.0ms	(.f64 (.f64 (pow.f64 (/.f64 d h) (/.f64 1 2)) (pow.f64 (/.f64 d l) (/.f64 1 2))) (-.f64 1 (pow.f64 (.f64 (pow.f64 (cbrt.f64 (sqrt.f64 (/.f64 h l))) 3) (.f64 (.f64 (/.f64 M (.f64 2 d)) D) (sqrt.f64 1/2))) 2)))	l	-inf

rewrite27.0ms (0.2%)

Algorithm

1×	batch-egg-rewrite

Rules

282×	`add-sqr-sqrt_binary64`
277×	`pow1_binary64`
273×	`*-un-lft-identity_binary64`
263×	`add-log-exp_binary64`
263×	`log1p-expm1-u_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	29	44
1	616	44

Stop Event

1×	node limit

Counts

1 → 8

simplify38.0ms (0.3%)

Algorithm

1×	egg-herbie

Rules

616×	`associate-/l*_binary64`
543×	`associate-/r/_binary64`
417×	`associate-/r*_binary64`
237×	`unswap-sqr_binary64`
176×	`distribute-rgt-neg-in_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	38	1546
1	99	1236
2	301	1236
3	1432	1236

Stop Event

1×	node limit

Counts

44 → 16

prune125.0ms (1%)

Pruning

21 alts after pruning (20 fresh and 1 done)

	Pruned	Kept	Total
New	76	1	77
Fresh	1	19	20
Picked	1	0	1
Done	0	1	1
Total	78	21	99

Error

9.0b

Counts

99 → 21

Alt Table

Status	Error	Program
	33.4b	(pow.f64 (.f64 (pow.f64 (.f64 (/.f64 d h) (/.f64 d l)) 1/2) (-.f64 1 (pow.f64 (.f64 (sqrt.f64 (/.f64 h l)) (.f64 (/.f64 M (.f64 d 2)) (.f64 D (sqrt.f64 1/2)))) 2))) 1)
	32.1b	(.f64 (.f64 (pow.f64 (/.f64 d h) (/.f64 1 2)) (pow.f64 (/.f64 d l) (/.f64 1 2))) (-.f64 1 (log.f64 (pow.f64 (exp.f64 (/.f64 h l)) (.f64 1/2 (pow.f64 (.f64 (/.f64 M (*.f64 2 d)) D) 2))))))
	23.9b	(.f64 (.f64 (pow.f64 (/.f64 d h) (/.f64 1 2)) (pow.f64 (/.f64 d l) (/.f64 1 2))) (-.f64 1 (.f64 (.f64 (/.f64 1 2) (pow.f64 (.f64 (.f64 M 1/2) (/.f64 D d)) 2)) (/.f64 h l))))
	44.6b	(.f64 (.f64 (.f64 (sqrt.f64 d) (sqrt.f64 (/.f64 1 h))) (pow.f64 (/.f64 d l) (/.f64 1 2))) (-.f64 1 (.f64 (.f64 (/.f64 1 2) (pow.f64 (/.f64 (.f64 M D) (*.f64 2 d)) 2)) (/.f64 h l))))
	38.5b	(.f64 (.f64 (pow.f64 (/.f64 d h) (/.f64 1 2)) (/.f64 (sqrt.f64 (neg.f64 d)) (sqrt.f64 (neg.f64 l)))) (-.f64 1 (.f64 (.f64 (/.f64 1 2) (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2)) (/.f64 h l))))
	60.3b	(.f64 (sqrt.f64 (/.f64 h (pow.f64 l 3))) (.f64 (/.f64 -1/8 d) (.f64 D (.f64 D (*.f64 M M)))))
	22.7b	(.f64 (.f64 (pow.f64 (/.f64 d h) (/.f64 1 2)) (.f64 (cbrt.f64 (/.f64 d l)) (cbrt.f64 (sqrt.f64 (/.f64 d l))))) (-.f64 1 (pow.f64 (.f64 (sqrt.f64 (/.f64 h l)) (.f64 (.f64 (/.f64 M (*.f64 2 d)) D) (sqrt.f64 1/2))) 2)))
	45.9b	(.f64 (.f64 (pow.f64 (/.f64 d h) (/.f64 1 2)) (pow.f64 (/.f64 d l) (/.f64 1 2))) (-.f64 1 (pow.f64 (.f64 (/.f64 (sqrt.f64 h) (sqrt.f64 l)) (.f64 (.f64 (/.f64 M (.f64 2 d)) D) (sqrt.f64 1/2))) 2)))
	23.9b	(.f64 (.f64 (pow.f64 (/.f64 d h) (/.f64 1 2)) (pow.f64 (/.f64 d l) (/.f64 1 2))) (-.f64 1 (/.f64 1 (/.f64 l (.f64 (.f64 1/2 (pow.f64 (.f64 (/.f64 M (.f64 2 d)) D) 2)) h)))))
	24.4b	(.f64 (sqrt.f64 (/.f64 d h)) (.f64 (sqrt.f64 (/.f64 d l)) (fma.f64 (/.f64 h l) (.f64 (pow.f64 (.f64 M (/.f64 (/.f64 D d) 2)) 2) -1/2) 1)))
	32.7b	(.f64 (.f64 (cbrt.f64 (pow.f64 (/.f64 d h) 3/2)) (pow.f64 (/.f64 d l) (/.f64 1 2))) (-.f64 1 (pow.f64 (.f64 (sqrt.f64 (/.f64 h l)) (.f64 (.f64 (/.f64 M (.f64 2 d)) D) (sqrt.f64 1/2))) 2)))
	44.4b	(.f64 (.f64 (pow.f64 (/.f64 d h) (/.f64 1 2)) (/.f64 (sqrt.f64 d) (sqrt.f64 l))) (-.f64 1 (pow.f64 (.f64 (sqrt.f64 (/.f64 h l)) (.f64 (.f64 (/.f64 M (.f64 2 d)) D) (sqrt.f64 1/2))) 2)))
	24.2b	(.f64 (.f64 (pow.f64 (/.f64 d h) (/.f64 1 2)) (/.f64 1 (sqrt.f64 (/.f64 l d)))) (-.f64 1 (.f64 (.f64 (/.f64 1 2) (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2)) (/.f64 h l))))
	45.4b	(.f64 (sqrt.f64 (/.f64 1 (.f64 l h))) d)
	34.4b	(pow.f64 (.f64 (pow.f64 (.f64 (/.f64 d h) (/.f64 d l)) 1/2) (-.f64 1 (.f64 (/.f64 h l) (pow.f64 (.f64 (.f64 (/.f64 M (.f64 d 2)) D) (sqrt.f64 1/2)) 2)))) 1)
	43.7b	(.f64 (.f64 (/.f64 (sqrt.f64 d) (sqrt.f64 h)) (pow.f64 (/.f64 d l) (/.f64 1 2))) (-.f64 1 (pow.f64 (.f64 (pow.f64 (cbrt.f64 (sqrt.f64 (/.f64 h l))) 3) (.f64 (.f64 (/.f64 M (.f64 2 d)) D) (sqrt.f64 1/2))) 2)))
	24.2b	(.f64 (.f64 (.f64 (pow.f64 (/.f64 d h) 1/4) (pow.f64 (/.f64 d h) 1/4)) (pow.f64 (/.f64 d l) (/.f64 1 2))) (-.f64 1 (.f64 (.f64 (/.f64 1 2) (pow.f64 (/.f64 (.f64 M D) (*.f64 2 d)) 2)) (/.f64 h l))))
✓	22.4b	(.f64 (.f64 (pow.f64 (/.f64 d h) (/.f64 1 2)) (pow.f64 (/.f64 d l) (/.f64 1 2))) (-.f64 1 (pow.f64 (.f64 (pow.f64 (sqrt.f64 (sqrt.f64 (/.f64 h l))) 2) (.f64 (.f64 (/.f64 M (.f64 2 d)) D) (sqrt.f64 1/2))) 2)))
	37.7b	(.f64 (.f64 (/.f64 (sqrt.f64 (neg.f64 d)) (sqrt.f64 (neg.f64 h))) (pow.f64 (/.f64 d l) (/.f64 1 2))) (-.f64 1 (pow.f64 (.f64 (sqrt.f64 (/.f64 h l)) (.f64 (.f64 (/.f64 M (.f64 2 d)) D) (sqrt.f64 1/2))) 2)))
	24.2b	(.f64 (.f64 (pow.f64 (/.f64 d h) (/.f64 1 2)) (.f64 (pow.f64 (/.f64 d l) 1/4) (pow.f64 (/.f64 d l) 1/4))) (-.f64 1 (.f64 (.f64 (/.f64 1 2) (pow.f64 (/.f64 (.f64 M D) (*.f64 2 d)) 2)) (/.f64 h l))))
	39.9b	(pow.f64 (sqrt.f64 (.f64 (pow.f64 (.f64 (/.f64 d h) (/.f64 d l)) 1/2) (-.f64 1 (.f64 (/.f64 h l) (pow.f64 (.f64 (.f64 (/.f64 M (.f64 d 2)) D) (sqrt.f64 1/2)) 2))))) 2)

Compiler

Compiled 3684 to 2401 computations (34.8% saved)

regimes1.6s (13%)

Accuracy

Total 8.7b remaining (45.8%)

Threshold costs 0b (0%)

Counts

102 → 3

Compiler

Compiled 29506 to 22595 computations (23.4% saved)

bsearch471.0ms (3.8%)

Algorithm

2×	binary-search

Calls

2 calls:

310.0ms	l
156.0ms	l

Steps

Iters	Point		Range
4.8269720407177665e-122	∈ [	2.8762646973789087e-122	,	3.90813229773484e-121	]
-4.279388089894161e-103	∈ [	-1.615962288825501e-102	,	-9.111669870501434e-104	]

Compiler

Compiled 6 to 5 computations (16.7% saved)

simplify6.0ms (0%)

Algorithm

1×	egg-herbie

Rules

16×	`*-commutative_binary64`
6×	`+-commutative_binary64`
6×	`sub-neg_binary64`
4×	`neg-sub0_binary64`
4×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	51	158
1	74	158
2	86	158
3	92	158
4	94	158

Stop Event

1×

saturated

end475.0ms (3.8%)

Stop Event

1×

fuel

Remove

(sort M D)

Compiler

Compiled 1218 to 896 computations (26.4% saved)

Details

analyze2.1s (16.8%)

sample5.5s (43.6%)

preprocess43.0ms (0.3%)

simplify15.0ms (0.1%)

prune5.0ms (0%)

localize25.0ms (0.2%)

series278.0ms (2.2%)

rewrite40.0ms (0.3%)

simplify119.0ms (1%)

prune330.0ms (2.6%)

localize25.0ms (0.2%)

series271.0ms (2.2%)

rewrite31.0ms (0.2%)

simplify39.0ms (0.3%)

prune160.0ms (1.3%)

localize26.0ms (0.2%)

series259.0ms (2.1%)

rewrite26.0ms (0.2%)

simplify40.0ms (0.3%)

prune140.0ms (1.1%)

localize25.0ms (0.2%)

series294.0ms (2.3%)

rewrite27.0ms (0.2%)

simplify38.0ms (0.3%)

prune125.0ms (1%)

regimes1.6s (13%)

bsearch471.0ms (3.8%)

simplify6.0ms (0%)

end475.0ms (3.8%)

Profiling