Details

analyze2.1s (14.6%)

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)

sample5.4s (37.2%)

Results

3.3s	13813×	body	128	invalid
2.1s	8256×	body	128	valid

Compiler

Compiled 82 to 64 computations (22% saved)

preprocess41.0ms (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

25.6b

Counts

3 → 2

Alt Table

Status	Error	Program
▶	25.9b	(.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 D) (.f64 2 d)) 2)) (/.f64 h l))))
	26.7b	(.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)))

Status

Error

Program

▶

25.9b

(*.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 D) (*.f64 2 d)) 2)) (/.f64 h l))))

26.7b

(*.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)))

Compiler

Compiled 208 to 151 computations (27.4% saved)

localize24.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	6.7b	(/.f64 (.f64 M D) (.f64 2 d))
✓	11.3b	(pow.f64 (/.f64 d l) (/.f64 1 2))
✓	11.4b	(pow.f64 (/.f64 d h) (/.f64 1 2))
✓	12.2b	(.f64 (.f64 (/.f64 1 2) (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2)) (/.f64 h l))

series210.0ms (1.4%)

Counts

4 → 96

Calls

36 calls:

14.0ms	(.f64 (.f64 (/.f64 1 2) (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2)) (/.f64 h l))	h	-inf
14.0ms	(.f64 (.f64 (/.f64 1 2) (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2)) (/.f64 h l))	M	-inf
14.0ms	(.f64 (.f64 (/.f64 1 2) (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2)) (/.f64 h l))	D	-inf
14.0ms	(.f64 (.f64 (/.f64 1 2) (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2)) (/.f64 h l))	h	0
13.0ms	(.f64 (.f64 (/.f64 1 2) (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2)) (/.f64 h l))	l	-inf

rewrite38.0ms (0.3%)

Algorithm

1×	batch-egg-rewrite

Rules

203×	`add-sqr-sqrt_binary64`
193×	`log1p-expm1-u_binary64`
193×	`expm1-log1p-u_binary64`
189×	`add-cbrt-cube_binary64`
189×	`add-log-exp_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	21	44
1	431	44

Stop Event

1×	node limit

Counts

4 → 112

simplify112.0ms (0.8%)

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

208 → 119

prune269.0ms (1.8%)

Pruning

21 alts after pruning (21 fresh and 0 done)

	Pruned	Kept	Total
New	98	21	119
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	100	21	121

Error

13.1b

Counts

121 → 21

Alt Table

Status	Error	Program
	41.7b	(.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))))
	26.0b	(.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))))
	36.1b	(.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 (log.f64 (pow.f64 (exp.f64 (/.f64 M 2)) (/.f64 D d))) 2)) (/.f64 h l))))
	43.3b	(.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))))
	43.4b	(.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))))
	26.0b	(.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))))
	26.2b	(.f64 (.f64 (.f64 (cbrt.f64 (/.f64 d h)) (cbrt.f64 (sqrt.f64 (/.f64 d 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))))
	32.0b	(.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))))
	29.0b	(.f64 (.f64 (pow.f64 (/.f64 d h) (/.f64 1 2)) (pow.f64 (/.f64 d l) (/.f64 1 2))) (-.f64 1 (cbrt.f64 (pow.f64 (.f64 1/2 (.f64 (pow.f64 (*.f64 (/.f64 M 2) (/.f64 D d)) 2) (/.f64 h l))) 3))))
	41.4b	(.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))))
▶	25.4b	(.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 2) (/.f64 D d)) 2)) h) l)))
	27.1b	(.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 (cbrt.f64 (pow.f64 (.f64 M D) 2)) 2) (/.f64 (cbrt.f64 (*.f64 M D)) d)) 2)) (/.f64 h l))))
	43.4b	(.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))))
	25.7b	(.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 2) (/.f64 D d)) 2)) (/.f64 l h))))
	25.9b	(.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))))
	43.3b	(.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))))
	26.2b	(.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))))
	33.6b	(.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 2) (/.f64 D d)) 2))))))
	25.5b	(.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 2) (/.f64 D d)) (sqrt.f64 1/2))) 2)))
	25.7b	(.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))))
	35.4b	(.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))))

Compiler

Compiled 6156 to 4111 computations (33.2% saved)

localize22.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	6.2b	(/.f64 (.f64 (.f64 1/2 (pow.f64 (*.f64 (/.f64 M 2) (/.f64 D d)) 2)) h) l)
✓	6.6b	(.f64 (.f64 1/2 (pow.f64 (*.f64 (/.f64 M 2) (/.f64 D d)) 2)) h)
	11.3b	(pow.f64 (/.f64 d l) (/.f64 1 2))
	11.4b	(pow.f64 (/.f64 d h) (/.f64 1 2))

series282.0ms (1.9%)

Counts

2 → 108

Calls

27 calls:

14.0ms	(/.f64 (.f64 (.f64 1/2 (pow.f64 (*.f64 (/.f64 M 2) (/.f64 D d)) 2)) h) l)	h	0
13.0ms	(/.f64 (.f64 (.f64 1/2 (pow.f64 (*.f64 (/.f64 M 2) (/.f64 D d)) 2)) h) l)	l	inf
13.0ms	(/.f64 (.f64 (.f64 1/2 (pow.f64 (*.f64 (/.f64 M 2) (/.f64 D d)) 2)) h) l)	h	inf
13.0ms	(/.f64 (.f64 (.f64 1/2 (pow.f64 (*.f64 (/.f64 M 2) (/.f64 D d)) 2)) h) l)	M	0
13.0ms	(/.f64 (.f64 (.f64 1/2 (pow.f64 (*.f64 (/.f64 M 2) (/.f64 D d)) 2)) h) l)	l	0

rewrite61.0ms (0.4%)

Algorithm

1×	batch-egg-rewrite

Rules

292×	`log1p-udef_binary64`
163×	`add-sqr-sqrt_binary64`
155×	`log1p-expm1-u_binary64`
155×	`expm1-log1p-u_binary64`
153×	`add-cube-cbrt_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	15	41
1	332	41
2	4519	41

Stop Event

1×	node limit

Counts

2 → 62

simplify142.0ms (1%)

Algorithm

1×	egg-herbie

Rules

623×	`associate-/l/_binary64`
595×	`associate-/r/_binary64`
440×	`unswap-sqr_binary64`
356×	`*-commutative_binary64`
231×	`times-frac_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	29	2556
1	87	2556
2	261	2556
3	1626	2556
4	3724	2556
5	3952	2556
6	4637	2556
7	4719	2556
8	4816	2556
9	4942	2556

Stop Event

1×	node limit

Counts

170 → 70

prune278.0ms (1.9%)

Pruning

27 alts after pruning (27 fresh and 0 done)

	Pruned	Kept	Total
New	95	17	112
Fresh	10	10	20
Picked	1	0	1
Done	0	0	0
Total	106	27	133

Error

8.5b

Counts

133 → 27

Alt Table

Status	Error	Program
	41.7b	(.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))))
	36.1b	(.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 (log.f64 (pow.f64 (exp.f64 (/.f64 M 2)) (/.f64 D d))) 2)) (/.f64 h l))))
	43.3b	(.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))))
	25.7b	(.f64 (.f64 (.f64 (cbrt.f64 (/.f64 d h)) (cbrt.f64 (sqrt.f64 (/.f64 d h)))) (pow.f64 (/.f64 d l) (/.f64 1 2))) (-.f64 1 (/.f64 (.f64 (.f64 1/2 (pow.f64 (.f64 (/.f64 M 2) (/.f64 D d)) 2)) h) l)))
	34.7b	(.f64 (.f64 (pow.f64 (/.f64 d h) (/.f64 1 2)) (pow.f64 (/.f64 d l) (/.f64 1 2))) (-.f64 1 (.f64 1/8 (.f64 D (.f64 (/.f64 D (.f64 d l)) (.f64 (.f64 M M) (/.f64 h d)))))))
	41.9b	(.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 2) (/.f64 D d)) 2)) h) l)))
	33.1b	(.f64 (.f64 (pow.f64 (/.f64 d h) (/.f64 1 2)) (pow.f64 (/.f64 d l) (/.f64 1 2))) (-.f64 1 (/.f64 (.f64 1/8 (.f64 D (.f64 (/.f64 D d) (.f64 (*.f64 M M) (/.f64 h d))))) l)))
	25.7b	(.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 (/.f64 (.f64 (.f64 1/2 (pow.f64 (.f64 (/.f64 M 2) (/.f64 D d)) 2)) h) l)))
	25.5b	(.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 2) (/.f64 D d)) 2)) h) l)))
	40.6b	(.f64 (.f64 (pow.f64 (/.f64 d h) (/.f64 1 2)) (pow.f64 (/.f64 d l) (/.f64 1 2))) (-.f64 1 (/.f64 (.f64 1/8 (/.f64 (.f64 (pow.f64 D 2) (*.f64 (pow.f64 M 2) h)) (pow.f64 d 2))) l)))
	29.0b	(.f64 (.f64 (pow.f64 (/.f64 d h) (/.f64 1 2)) (pow.f64 (/.f64 d l) (/.f64 1 2))) (-.f64 1 (cbrt.f64 (pow.f64 (.f64 1/2 (.f64 (pow.f64 (*.f64 (/.f64 M 2) (/.f64 D d)) 2) (/.f64 h l))) 3))))
	42.6b	(.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 2) (/.f64 D d)) 2)) h) l)))
▶	24.0b	(.f64 (.f64 (pow.f64 (/.f64 d h) (/.f64 1 2)) (pow.f64 (/.f64 d l) (/.f64 1 2))) (-.f64 1 (pow.f64 (/.f64 (.f64 (/.f64 (.f64 M (*.f64 1/2 D)) d) (sqrt.f64 1/2)) (sqrt.f64 (/.f64 l h))) 2)))
	33.6b	(.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 2) (/.f64 D d)) 2))))))
	25.5b	(.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 2) (/.f64 D d)) 2)) h) l)))
	41.9b	(.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 2) (/.f64 D d)) 2)) h) l)))
	25.4b	(.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 2) (/.f64 D d)) 2)) h) l)))
	40.9b	(.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 2) (/.f64 D d)) 2)) h) l)))
	41.4b	(.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))))
	42.6b	(.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 2) (/.f64 D d)) 2)) h) l)))
	27.1b	(.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 (cbrt.f64 (pow.f64 (.f64 M D) 2)) 2) (/.f64 (cbrt.f64 (*.f64 M D)) d)) 2)) (/.f64 h l))))
	25.7b	(.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 2) (/.f64 D d)) 2)) (/.f64 l h))))
	41.3b	(.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 2) (/.f64 D d)) 2)) h) l)))
	44.0b	(.f64 (.f64 (pow.f64 (/.f64 d h) (/.f64 1 2)) (pow.f64 (/.f64 d l) (/.f64 1 2))) (-.f64 1 (/.f64 (pow.f64 (.f64 (sqrt.f64 h) (.f64 (/.f64 (.f64 M (.f64 1/2 D)) d) (sqrt.f64 1/2))) 2) l)))
	25.7b	(.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))))
	31.7b	(.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 2) (/.f64 D d)) 2)) h) l)))
	35.4b	(.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))))

Compiler

Compiled 6236 to 4244 computations (31.9% saved)

localize25.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	6.7b	(/.f64 (.f64 M (.f64 1/2 D)) d)
	11.3b	(pow.f64 (/.f64 d l) (/.f64 1 2))
	11.4b	(pow.f64 (/.f64 d h) (/.f64 1 2))
✓	15.3b	(sqrt.f64 (/.f64 l h))

series26.0ms (0.2%)

Counts

2 → 36

Calls

15 calls:

3.0ms	(/.f64 (.f64 M (.f64 1/2 D)) d)	D	inf
2.0ms	(sqrt.f64 (/.f64 l h))	l	0
2.0ms	(sqrt.f64 (/.f64 l h))	h	-inf
2.0ms	(sqrt.f64 (/.f64 l h))	h	inf
2.0ms	(sqrt.f64 (/.f64 l h))	l	-inf

rewrite51.0ms (0.4%)

Algorithm

1×	batch-egg-rewrite

Rules

704×	`log-prod_binary64`
228×	`expm1-udef_binary64`
228×	`log1p-udef_binary64`
209×	`log-pow_binary64`
140×	`log-div_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	16
1	252	16
2	3377	16

Stop Event

1×	node limit

Counts

2 → 84

simplify16.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

15×	`associate-/l*_binary64`
14×	`*-commutative_binary64`
11×	`associate-/r/_binary64`
10×	`associate-r_binary64`
8×	`associate-l_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	360
1	14	360
2	29	360
3	55	360
4	85	360
5	96	360

Stop Event

1×

saturated

Counts

120 → 86

prune322.0ms (2.2%)

Pruning

27 alts after pruning (27 fresh and 0 done)

	Pruned	Kept	Total
New	122	6	128
Fresh	5	21	26
Picked	1	0	1
Done	0	0	0
Total	128	27	155

Error

8.0b

Counts

155 → 27

Alt Table

Status	Error	Program
	41.7b	(.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))))
	42.1b	(.f64 (.f64 (pow.f64 (/.f64 d h) (/.f64 1 2)) (/.f64 (sqrt.f64 d) (sqrt.f64 l))) (-.f64 1 (pow.f64 (/.f64 (.f64 (/.f64 (.f64 M (*.f64 1/2 D)) d) (sqrt.f64 1/2)) (sqrt.f64 (/.f64 l h))) 2)))
	36.1b	(.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 (log.f64 (pow.f64 (exp.f64 (/.f64 M 2)) (/.f64 D d))) 2)) (/.f64 h l))))
	40.5b	(.f64 (.f64 (pow.f64 (/.f64 d h) (/.f64 1 2)) (/.f64 (sqrt.f64 (neg.f64 d)) (sqrt.f64 (neg.f64 l)))) (-.f64 1 (pow.f64 (/.f64 (.f64 (/.f64 (.f64 M (*.f64 1/2 D)) d) (sqrt.f64 1/2)) (sqrt.f64 (/.f64 l h))) 2)))
	44.0b	(.f64 (.f64 (pow.f64 (/.f64 d h) (/.f64 1 2)) (pow.f64 (/.f64 d l) (/.f64 1 2))) (-.f64 1 (/.f64 (pow.f64 (.f64 (sqrt.f64 h) (.f64 (/.f64 (.f64 M (.f64 1/2 D)) d) (sqrt.f64 1/2))) 2) l)))
	43.3b	(.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))))
	25.7b	(.f64 (.f64 (.f64 (cbrt.f64 (/.f64 d h)) (cbrt.f64 (sqrt.f64 (/.f64 d h)))) (pow.f64 (/.f64 d l) (/.f64 1 2))) (-.f64 1 (/.f64 (.f64 (.f64 1/2 (pow.f64 (.f64 (/.f64 M 2) (/.f64 D d)) 2)) h) l)))
	34.4b	(.f64 (.f64 (pow.f64 (/.f64 d h) (/.f64 1 2)) (cbrt.f64 (pow.f64 (/.f64 d l) 3/2))) (-.f64 1 (pow.f64 (/.f64 (.f64 (/.f64 (.f64 M (*.f64 1/2 D)) d) (sqrt.f64 1/2)) (sqrt.f64 (/.f64 l h))) 2)))
	34.7b	(.f64 (.f64 (pow.f64 (/.f64 d h) (/.f64 1 2)) (pow.f64 (/.f64 d l) (/.f64 1 2))) (-.f64 1 (.f64 1/8 (.f64 D (.f64 (/.f64 D (.f64 d l)) (.f64 (.f64 M M) (/.f64 h d)))))))
	41.9b	(.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 2) (/.f64 D d)) 2)) h) l)))
	33.1b	(.f64 (.f64 (pow.f64 (/.f64 d h) (/.f64 1 2)) (pow.f64 (/.f64 d l) (/.f64 1 2))) (-.f64 1 (/.f64 (.f64 1/8 (.f64 D (.f64 (/.f64 D d) (.f64 (*.f64 M M) (/.f64 h d))))) l)))
	25.7b	(.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 (/.f64 (.f64 (.f64 1/2 (pow.f64 (.f64 (/.f64 M 2) (/.f64 D d)) 2)) h) l)))
	25.5b	(.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 2) (/.f64 D d)) 2)) h) l)))
	40.6b	(.f64 (.f64 (pow.f64 (/.f64 d h) (/.f64 1 2)) (pow.f64 (/.f64 d l) (/.f64 1 2))) (-.f64 1 (/.f64 (.f64 1/8 (/.f64 (.f64 (pow.f64 D 2) (*.f64 (pow.f64 M 2) h)) (pow.f64 d 2))) l)))
	29.0b	(.f64 (.f64 (pow.f64 (/.f64 d h) (/.f64 1 2)) (pow.f64 (/.f64 d l) (/.f64 1 2))) (-.f64 1 (cbrt.f64 (pow.f64 (.f64 1/2 (.f64 (pow.f64 (*.f64 (/.f64 M 2) (/.f64 D d)) 2) (/.f64 h l))) 3))))
	42.6b	(.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 2) (/.f64 D d)) 2)) h) l)))
	33.6b	(.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 2) (/.f64 D d)) 2))))))
	25.5b	(.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 2) (/.f64 D d)) 2)) h) l)))
	41.9b	(.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 2) (/.f64 D d)) 2)) h) l)))
	40.4b	(.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 (.f64 (/.f64 (.f64 M (*.f64 1/2 D)) d) (sqrt.f64 1/2)) (sqrt.f64 (/.f64 l h))) 2)))
▶	25.4b	(.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 2) (/.f64 D d)) 2)) h) l)))
	40.9b	(.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 2) (/.f64 D d)) 2)) h) l)))
	41.3b	(.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 2) (/.f64 D d)) 2)) h) l)))
	30.1b	(.f64 (.f64 (cbrt.f64 (pow.f64 (/.f64 d h) 3/2)) (pow.f64 (/.f64 d l) (/.f64 1 2))) (-.f64 1 (pow.f64 (/.f64 (.f64 (/.f64 (.f64 M (*.f64 1/2 D)) d) (sqrt.f64 1/2)) (sqrt.f64 (/.f64 l h))) 2)))
	27.1b	(.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 (cbrt.f64 (pow.f64 (.f64 M D) 2)) 2) (/.f64 (cbrt.f64 (*.f64 M D)) d)) 2)) (/.f64 h l))))
	25.7b	(.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))))
	26.2b	(.f64 (.f64 (exp.f64 (log.f64 (sqrt.f64 (/.f64 d h)))) (pow.f64 (/.f64 d l) (/.f64 1 2))) (-.f64 1 (pow.f64 (/.f64 (.f64 (/.f64 (.f64 M (*.f64 1/2 D)) d) (sqrt.f64 1/2)) (sqrt.f64 (/.f64 l h))) 2)))

Compiler

Compiled 7077 to 4702 computations (33.6% saved)

localize23.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
	6.2b	(/.f64 (.f64 (.f64 1/2 (pow.f64 (*.f64 (/.f64 M 2) (/.f64 D d)) 2)) h) l)
	6.6b	(.f64 (.f64 1/2 (pow.f64 (*.f64 (/.f64 M 2) (/.f64 D d)) 2)) h)
	11.4b	(pow.f64 (/.f64 d h) (/.f64 1 2))
✓	11.6b	(sqrt.f64 (/.f64 l d))

series11.0ms (0.1%)

Counts

1 → 0

Calls

6 calls:

2.0ms	(sqrt.f64 (/.f64 l d))	l	0
2.0ms	(sqrt.f64 (/.f64 l d))	d	-inf
2.0ms	(sqrt.f64 (/.f64 l d))	d	inf
2.0ms	(sqrt.f64 (/.f64 l d))	l	-inf
2.0ms	(sqrt.f64 (/.f64 l d))	l	inf

rewrite34.0ms (0.2%)

Algorithm

1×	batch-egg-rewrite

Rules

505×	`log1p-expm1-u_binary64`
505×	`expm1-log1p-u_binary64`
420×	`unpow-prod-down_binary64`
265×	`log-prod_binary64`
136×	`pow2_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	5	6
1	105	6
2	1379	6

Stop Event

1×	node limit

Counts

1 → 60

simplify6.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	0	0

Stop Event

1×

saturated

Counts

60 → 60

prune281.0ms (1.9%)

Pruning

28 alts after pruning (28 fresh and 0 done)

	Pruned	Kept	Total
New	142	9	151
Fresh	7	19	26
Picked	1	0	1
Done	0	0	0
Total	150	28	178

Error

7.9b

Counts

178 → 28

Alt Table

Status	Error	Program
	41.7b	(.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))))
	40.3b	(.f64 (.f64 (pow.f64 (/.f64 d h) (/.f64 1 2)) (/.f64 1 (sqrt.f64 (/.f64 l d)))) (-.f64 1 (/.f64 (.f64 1/8 (/.f64 (.f64 (pow.f64 D 2) (*.f64 h (pow.f64 M 2))) (pow.f64 d 2))) l)))
	41.1b	(.f64 (.f64 (/.f64 (sqrt.f64 (neg.f64 d)) (sqrt.f64 (neg.f64 h))) (/.f64 1 (sqrt.f64 (/.f64 l d)))) (-.f64 1 (/.f64 (.f64 (.f64 1/2 (pow.f64 (*.f64 (/.f64 M 2) (/.f64 D d)) 2)) h) l)))
	42.1b	(.f64 (.f64 (pow.f64 (/.f64 d h) (/.f64 1 2)) (/.f64 (sqrt.f64 d) (sqrt.f64 l))) (-.f64 1 (pow.f64 (/.f64 (.f64 (/.f64 (.f64 M (*.f64 1/2 D)) d) (sqrt.f64 1/2)) (sqrt.f64 (/.f64 l h))) 2)))
	36.1b	(.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 (log.f64 (pow.f64 (exp.f64 (/.f64 M 2)) (/.f64 D d))) 2)) (/.f64 h l))))
	43.3b	(.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))))
	34.7b	(.f64 (.f64 (pow.f64 (/.f64 d h) (/.f64 1 2)) (pow.f64 (/.f64 d l) (/.f64 1 2))) (-.f64 1 (.f64 1/8 (.f64 D (.f64 (/.f64 D (.f64 d l)) (.f64 (.f64 M M) (/.f64 h d)))))))
	41.9b	(.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 2) (/.f64 D d)) 2)) h) l)))
	33.1b	(.f64 (.f64 (pow.f64 (/.f64 d h) (/.f64 1 2)) (pow.f64 (/.f64 d l) (/.f64 1 2))) (-.f64 1 (/.f64 (.f64 1/8 (.f64 D (.f64 (/.f64 D d) (.f64 (*.f64 M M) (/.f64 h d))))) l)))
	29.0b	(.f64 (.f64 (pow.f64 (/.f64 d h) (/.f64 1 2)) (pow.f64 (/.f64 d l) (/.f64 1 2))) (-.f64 1 (cbrt.f64 (pow.f64 (.f64 1/2 (.f64 (pow.f64 (*.f64 (/.f64 M 2) (/.f64 D d)) 2) (/.f64 h l))) 3))))
	42.6b	(.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 2) (/.f64 D d)) 2)) h) l)))
	33.6b	(.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 2) (/.f64 D d)) 2))))))
	25.5b	(.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 2) (/.f64 D d)) 2)) h) l)))
	40.4b	(.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 (.f64 (/.f64 (.f64 M (*.f64 1/2 D)) d) (sqrt.f64 1/2)) (sqrt.f64 (/.f64 l h))) 2)))
	25.5b	(.f64 (.f64 (.f64 (pow.f64 (/.f64 d h) 1/4) (pow.f64 (/.f64 d h) 1/4)) (/.f64 1 (sqrt.f64 (/.f64 l d)))) (-.f64 1 (/.f64 (.f64 (.f64 1/2 (pow.f64 (.f64 (/.f64 M 2) (/.f64 D d)) 2)) h) l)))
	21.1b	(.f64 (.f64 (pow.f64 (/.f64 d h) (/.f64 1 2)) (/.f64 1 (.f64 (pow.f64 (/.f64 1 (pow.f64 (cbrt.f64 d) 2)) 1/2) (pow.f64 (/.f64 l (cbrt.f64 d)) 1/2)))) (-.f64 1 (/.f64 (.f64 (.f64 1/2 (pow.f64 (.f64 (/.f64 M 2) (/.f64 D d)) 2)) h) l)))
	41.3b	(.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 2) (/.f64 D d)) 2)) h) l)))
	30.1b	(.f64 (.f64 (cbrt.f64 (pow.f64 (/.f64 d h) 3/2)) (pow.f64 (/.f64 d l) (/.f64 1 2))) (-.f64 1 (pow.f64 (/.f64 (.f64 (/.f64 (.f64 M (*.f64 1/2 D)) d) (sqrt.f64 1/2)) (sqrt.f64 (/.f64 l h))) 2)))
	25.7b	(.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))))
	41.3b	(.f64 (.f64 (pow.f64 (/.f64 d h) (/.f64 1 2)) (/.f64 1 (.f64 (sqrt.f64 (neg.f64 l)) (pow.f64 (/.f64 1 (neg.f64 d)) 1/2)))) (-.f64 1 (/.f64 (.f64 (.f64 1/2 (pow.f64 (.f64 (/.f64 M 2) (/.f64 D d)) 2)) h) l)))
	25.7b	(.f64 (.f64 (pow.f64 (/.f64 d h) (/.f64 1 2)) (/.f64 1 (.f64 (sqrt.f64 (cbrt.f64 (/.f64 l d))) (cbrt.f64 (/.f64 l d))))) (-.f64 1 (/.f64 (.f64 (.f64 1/2 (pow.f64 (.f64 (/.f64 M 2) (/.f64 D d)) 2)) h) l)))
	26.2b	(.f64 (.f64 (exp.f64 (log.f64 (sqrt.f64 (/.f64 d h)))) (pow.f64 (/.f64 d l) (/.f64 1 2))) (-.f64 1 (pow.f64 (/.f64 (.f64 (/.f64 (.f64 M (*.f64 1/2 D)) d) (sqrt.f64 1/2)) (sqrt.f64 (/.f64 l h))) 2)))
	40.5b	(.f64 (.f64 (pow.f64 (/.f64 d h) (/.f64 1 2)) (/.f64 (sqrt.f64 (neg.f64 d)) (sqrt.f64 (neg.f64 l)))) (-.f64 1 (pow.f64 (/.f64 (.f64 (/.f64 (.f64 M (*.f64 1/2 D)) d) (sqrt.f64 1/2)) (sqrt.f64 (/.f64 l h))) 2)))
	43.8b	(.f64 (.f64 (pow.f64 (/.f64 d h) (/.f64 1 2)) (/.f64 1 (sqrt.f64 (/.f64 l d)))) (-.f64 1 (/.f64 (pow.f64 (.f64 (sqrt.f64 h) (.f64 (/.f64 (.f64 M (.f64 1/2 D)) d) (sqrt.f64 1/2))) 2) l)))
	25.7b	(.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 (/.f64 (.f64 (.f64 1/2 (pow.f64 (.f64 (/.f64 M 2) (/.f64 D d)) 2)) h) l)))
	27.1b	(.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 (cbrt.f64 (pow.f64 (.f64 M D) 2)) 2) (/.f64 (cbrt.f64 (*.f64 M D)) d)) 2)) (/.f64 h l))))
	25.7b	(.f64 (.f64 (.f64 (sqrt.f64 (pow.f64 (cbrt.f64 (/.f64 d h)) 2)) (sqrt.f64 (cbrt.f64 (/.f64 d h)))) (/.f64 1 (sqrt.f64 (/.f64 l d)))) (-.f64 1 (/.f64 (.f64 (.f64 1/2 (pow.f64 (.f64 (/.f64 M 2) (/.f64 D d)) 2)) h) l)))
	41.8b	(.f64 (.f64 (/.f64 (sqrt.f64 d) (sqrt.f64 h)) (/.f64 1 (sqrt.f64 (/.f64 l d)))) (-.f64 1 (/.f64 (.f64 (.f64 1/2 (pow.f64 (*.f64 (/.f64 M 2) (/.f64 D d)) 2)) h) l)))

Compiler

Compiled 6737 to 4298 computations (36.2% saved)

regimes3.1s (21.2%)

Accuracy

Total 6.9b remaining (45.1%)

Threshold costs 0b (0%)

Counts

171 → 4

Compiler

Compiled 48776 to 37115 computations (23.9% saved)

bsearch824.0ms (5.7%)

Algorithm

3×	binary-search

Calls

3 calls:

412.0ms	d
279.0ms	d
123.0ms	d

Steps

Iters	Point		Range
3.8e+19	∈ [	2.216891818828465e+19	,	1.7970597579082522e+21	]
0.0	∈ [	-5.433679355272953e-306	,	1.946412183473344e-302	]
-1.35e+52	∈ [	-4.088152873346991e+52	,	-4.665354514458615e+50	]

Compiler

Compiled 6 to 5 computations (16.7% saved)

simplify8.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

22×	`*-commutative_binary64`
10×	`+-commutative_binary64`
10×	`sub-neg_binary64`
8×	`neg-sub0_binary64`
8×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	64	214
1	90	214
2	104	214
3	118	214
4	131	214
5	136	214
6	139	214
7	140	214

Stop Event

1×

saturated

end813.0ms (5.6%)

Stop Event

1×

fuel

Compiler

Compiled 1703 to 1231 computations (27.7% saved)

Details

analyze2.1s (14.6%)

sample5.4s (37.2%)

preprocess41.0ms (0.3%)

simplify15.0ms (0.1%)

prune5.0ms (0%)

localize24.0ms (0.2%)

series210.0ms (1.4%)

rewrite38.0ms (0.3%)

simplify112.0ms (0.8%)

prune269.0ms (1.8%)

localize22.0ms (0.2%)

series282.0ms (1.9%)

rewrite61.0ms (0.4%)

simplify142.0ms (1%)

prune278.0ms (1.9%)

localize25.0ms (0.2%)

series26.0ms (0.2%)

rewrite51.0ms (0.4%)

simplify16.0ms (0.1%)

prune322.0ms (2.2%)

localize23.0ms (0.2%)

series11.0ms (0.1%)

rewrite34.0ms (0.2%)

simplify6.0ms (0%)

prune281.0ms (1.9%)

regimes3.1s (21.2%)

bsearch824.0ms (5.7%)

simplify8.0ms (0.1%)

end813.0ms (5.6%)

Profiling