Details

analyze2.2s (13.7%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.8%	0.2%	0
0%	99.8%	0.2%	1
0%	99.8%	0.2%	2
0%	99.8%	0.2%	3
0%	99.8%	0.2%	4
0%	99.8%	0.2%	5
0%	99.8%	0.2%	6
0%	81.1%	18.9%	7
0%	68.6%	31.4%	8
0%	59.2%	40.8%	9
0%	59.2%	40.8%	10
0%	59.2%	40.8%	11
0.4%	49.5%	50.1%	12
0.8%	44.4%	54.8%	13
1.4%	39.9%	58.7%	14

Compiler

Compiled 41 to 32 computations (22% saved)

sample5.7s (36.1%)

Results

3.5s	13800×	body	128	invalid
2.2s	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)

simplify17.0ms (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

prune8.0ms (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

23.2b

Counts

3 → 2

Alt Table

Status	Error	Program
▶	23.5b	(.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))))
	24.0b	(.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

▶

23.5b

(*.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))))

24.0b

(*.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
✓	6.8b	(.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))))
✓	8.0b	(pow.f64 (/.f64 d h) (/.f64 1 2))
✓	10.9b	(pow.f64 (/.f64 d l) (/.f64 1 2))
✓	13.0b	(.f64 (.f64 (/.f64 1 2) (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2)) (/.f64 h l))

series1.0s (6.5%)

Counts

4 → 144

Calls

42 calls:

63.0ms	(pow.f64 (/.f64 d h) (/.f64 1 2))	d	-inf
63.0ms	(pow.f64 (/.f64 d l) (/.f64 1 2))	d	-inf
63.0ms	(pow.f64 (/.f64 d l) (/.f64 1 2))	d	0
57.0ms	(pow.f64 (/.f64 d h) (/.f64 1 2))	h	-inf
57.0ms	(pow.f64 (/.f64 d l) (/.f64 1 2))	d	inf

rewrite38.0ms (0.2%)

Algorithm

1×	batch-egg-rewrite

Rules

242×	`add-sqr-sqrt_binary64`
232×	`log1p-expm1-u_binary64`
232×	`expm1-log1p-u_binary64`
228×	`add-cbrt-cube_binary64`
226×	`add-cube-cbrt_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	24	74
1	510	73

Stop Event

1×	node limit

Counts

4 → 65

simplify85.0ms (0.5%)

Algorithm

1×	egg-herbie

Rules

633×	`associate-/l/_binary64`
225×	`associate-/l*_binary64`
225×	`times-frac_binary64`
147×	`associate-r_binary64`
130×	`fma-def_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	91	3502
1	231	3448
2	623	3384
3	2831	3112

Stop Event

1×	node limit

Counts

209 → 90

prune156.0ms (1%)

Pruning

17 alts after pruning (17 fresh and 0 done)

	Pruned	Kept	Total
New	74	16	90
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	75	17	92

Error

12.3b

Counts

92 → 17

Alt Table

Status	Error	Program
	23.8b	(.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))))
	43.7b	(*.f64 d (sqrt.f64 (/.f64 (pow.f64 h -1) l)))
	44.5b	(.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))))
	43.7b	(.f64 (sqrt.f64 (/.f64 1 (.f64 l h))) d)
	24.0b	(.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)))
	41.8b	(.f64 (.f64 (.f64 (pow.f64 (cbrt.f64 (pow.f64 (/.f64 d h) 2)) 1/2) (pow.f64 (cbrt.f64 (/.f64 d h)) 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))))
	23.7b	(.f64 (.f64 (pow.f64 (/.f64 d h) (/.f64 1 2)) (pow.f64 (/.f64 d l) (/.f64 1 2))) (-.f64 1 (pow.f64 (sqrt.f64 (.f64 1/2 (.f64 (pow.f64 (*.f64 (/.f64 M 2) (/.f64 D d)) 2) (/.f64 h l)))) 2)))
	31.9b	(.f64 (.f64 (pow.f64 (/.f64 d h) (/.f64 1 2)) (pow.f64 (/.f64 d l) (/.f64 1 2))) (-.f64 1 (.f64 (.f64 (/.f64 D d) (/.f64 D d)) (/.f64 (.f64 (.f64 M M) 1/8) (/.f64 l h)))))
	35.1b	(pow.f64 (.f64 (sqrt.f64 (.f64 (/.f64 d h) (/.f64 d l))) (-.f64 1 (.f64 1/2 (.f64 (pow.f64 (*.f64 (/.f64 M 2) (/.f64 D d)) 2) (/.f64 h l))))) 1)
	39.8b	(.f64 (.f64 (pow.f64 (/.f64 d h) (/.f64 1 2)) (.f64 (sqrt.f64 d) (pow.f64 (/.f64 1 l) 1/2))) (-.f64 1 (.f64 (.f64 (/.f64 1 2) (pow.f64 (/.f64 (.f64 M D) (*.f64 2 d)) 2)) (/.f64 h l))))
▶	22.6b	(.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)))
	39.9b	(.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))))))
	45.8b	(fma.f64 d (sqrt.f64 (/.f64 (pow.f64 h -1) l)) (.f64 -1/8 (/.f64 (sqrt.f64 (/.f64 h (pow.f64 l 3))) (/.f64 (/.f64 d M) (.f64 D (*.f64 D M))))))
	44.1b	(.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))))
	39.9b	(.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 D) (.f64 2 d)) 2)) (/.f64 h l))))
	61.0b	(log.f64 (pow.f64 (exp.f64 (sqrt.f64 (.f64 (/.f64 d h) (/.f64 d l)))) (-.f64 1 (.f64 1/2 (.f64 (pow.f64 (.f64 (/.f64 M 2) (/.f64 D d)) 2) (/.f64 h l))))))
	23.6b	(.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 (.f64 (.f64 (/.f64 1 2) (pow.f64 (/.f64 (.f64 M D) (*.f64 2 d)) 2)) (/.f64 h l))))

Compiler

Compiled 4241 to 2743 computations (35.3% saved)

localize24.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	6.8b	(.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)))
	8.0b	(pow.f64 (/.f64 d h) (/.f64 1 2))
✓	8.0b	(/.f64 (.f64 (.f64 1/2 (pow.f64 (*.f64 (/.f64 M 2) (/.f64 D d)) 2)) h) l)
	10.9b	(pow.f64 (/.f64 d l) (/.f64 1 2))

series361.0ms (2.3%)

Counts

2 → 96

Calls

30 calls:

17.0ms	(.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)))	d	-inf
17.0ms	(.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)))	M	inf
15.0ms	(/.f64 (.f64 (.f64 1/2 (pow.f64 (*.f64 (/.f64 M 2) (/.f64 D d)) 2)) h) l)	h	-inf
15.0ms	(/.f64 (.f64 (.f64 1/2 (pow.f64 (*.f64 (/.f64 M 2) (/.f64 D d)) 2)) h) l)	h	0
15.0ms	(/.f64 (.f64 (.f64 1/2 (pow.f64 (*.f64 (/.f64 M 2) (/.f64 D d)) 2)) h) l)	l	-inf

rewrite30.0ms (0.2%)

Algorithm

1×	batch-egg-rewrite

Rules

243×	`add-sqr-sqrt_binary64`
235×	`log1p-expm1-u_binary64`
235×	`expm1-log1p-u_binary64`
231×	`add-cbrt-cube_binary64`
229×	`add-cube-cbrt_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	24	62
1	516	61

Stop Event

1×	node limit

Counts

2 → 31

simplify83.0ms (0.5%)

Algorithm

1×	egg-herbie

Rules

703×	`associate-/r/_binary64`
609×	`associate-/l/_binary64`
434×	`*-commutative_binary64`
250×	`fma-def_binary64`
225×	`associate-/l*_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	42	2790
1	122	2736
2	359	2736
3	2102	2736
4	4915	2736

Stop Event

1×	node limit

Counts

127 → 42

prune136.0ms (0.9%)

Pruning

20 alts after pruning (20 fresh and 0 done)

	Pruned	Kept	Total
New	82	10	92
Fresh	6	10	16
Picked	1	0	1
Done	0	0	0
Total	89	20	109

Error

10.7b

Counts

109 → 20

Alt Table

Status	Error	Program
	22.9b	(.f64 (.f64 (pow.f64 (/.f64 d h) (/.f64 1 2)) (.f64 (pow.f64 (pow.f64 (cbrt.f64 (/.f64 d l)) 2) 1/2) (pow.f64 (cbrt.f64 (/.f64 d l)) 1/2))) (-.f64 1 (/.f64 (.f64 (.f64 1/2 (pow.f64 (.f64 (/.f64 M 2) (/.f64 D d)) 2)) h) l)))
▶	22.6b	(.f64 (.f64 (pow.f64 (/.f64 d h) (/.f64 1 2)) (pow.f64 (/.f64 d l) (/.f64 1 2))) (-.f64 1 (.f64 (.f64 1/2 (.f64 (pow.f64 (.f64 (*.f64 M 1/2) (/.f64 D d)) 2) h)) (/.f64 1 l))))
	45.8b	(fma.f64 d (sqrt.f64 (/.f64 (pow.f64 h -1) l)) (.f64 -1/8 (/.f64 (sqrt.f64 (/.f64 h (pow.f64 l 3))) (/.f64 (/.f64 d M) (.f64 D (*.f64 D M))))))
	40.4b	(.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 2) (/.f64 D d)) 2)) h) l)))
	41.9b	(.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)))
	42.1b	(.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)))
	33.6b	(.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 2) (/.f64 D d)) 2)) h) l)))
	23.7b	(.f64 (.f64 (pow.f64 (/.f64 d h) (/.f64 1 2)) (pow.f64 (/.f64 d l) (/.f64 1 2))) (-.f64 1 (pow.f64 (sqrt.f64 (.f64 1/2 (.f64 (pow.f64 (*.f64 (/.f64 M 2) (/.f64 D d)) 2) (/.f64 h l)))) 2)))
	31.9b	(.f64 (.f64 (pow.f64 (/.f64 d h) (/.f64 1 2)) (pow.f64 (/.f64 d l) (/.f64 1 2))) (-.f64 1 (.f64 (.f64 (/.f64 D d) (/.f64 D d)) (/.f64 (.f64 (.f64 M M) 1/8) (/.f64 l h)))))
	34.8b	(pow.f64 (.f64 (sqrt.f64 (.f64 (/.f64 d h) (/.f64 d l))) (-.f64 1 (/.f64 (.f64 1/2 (pow.f64 (.f64 (*.f64 M 1/2) (/.f64 D d)) 2)) (/.f64 l h)))) 1)
	39.8b	(.f64 (.f64 (pow.f64 (/.f64 d h) (/.f64 1 2)) (.f64 (sqrt.f64 d) (pow.f64 (/.f64 1 l) 1/2))) (-.f64 1 (.f64 (.f64 (/.f64 1 2) (pow.f64 (/.f64 (.f64 M D) (*.f64 2 d)) 2)) (/.f64 h l))))
	39.9b	(.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))))))
	43.7b	(*.f64 d (sqrt.f64 (/.f64 (pow.f64 h -1) l)))
	43.7b	(.f64 (sqrt.f64 (/.f64 1 (.f64 l h))) d)
	23.0b	(.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)))
	40.3b	(.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 2) (/.f64 D d)) 2)) h) l)))
	60.0b	(.f64 (.f64 (log.f64 (exp.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)))
	41.8b	(.f64 (.f64 (.f64 (pow.f64 (cbrt.f64 (pow.f64 (/.f64 d h) 2)) 1/2) (pow.f64 (cbrt.f64 (/.f64 d h)) 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))))
	61.0b	(log.f64 (pow.f64 (exp.f64 (sqrt.f64 (.f64 (/.f64 d h) (/.f64 d l)))) (-.f64 1 (.f64 1/2 (.f64 (pow.f64 (.f64 (/.f64 M 2) (/.f64 D d)) 2) (/.f64 h l))))))
	23.6b	(.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 (.f64 (.f64 (/.f64 1 2) (pow.f64 (/.f64 (.f64 M D) (*.f64 2 d)) 2)) (/.f64 h l))))

Compiler

Compiled 4482 to 2941 computations (34.4% saved)

localize26.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	6.8b	(.f64 (.f64 (pow.f64 (/.f64 d h) (/.f64 1 2)) (pow.f64 (/.f64 d l) (/.f64 1 2))) (-.f64 1 (.f64 (.f64 1/2 (.f64 (pow.f64 (.f64 (*.f64 M 1/2) (/.f64 D d)) 2) h)) (/.f64 1 l))))
	8.0b	(pow.f64 (/.f64 d h) (/.f64 1 2))
✓	8.1b	(.f64 (.f64 1/2 (.f64 (pow.f64 (.f64 (*.f64 M 1/2) (/.f64 D d)) 2) h)) (/.f64 1 l))
	10.9b	(pow.f64 (/.f64 d l) (/.f64 1 2))

series354.0ms (2.2%)

Counts

2 → 96

Calls

30 calls:

16.0ms	(.f64 (.f64 (pow.f64 (/.f64 d h) (/.f64 1 2)) (pow.f64 (/.f64 d l) (/.f64 1 2))) (-.f64 1 (.f64 (.f64 1/2 (.f64 (pow.f64 (.f64 (*.f64 M 1/2) (/.f64 D d)) 2) h)) (/.f64 1 l))))	M	-inf
15.0ms	(.f64 (.f64 (pow.f64 (/.f64 d h) (/.f64 1 2)) (pow.f64 (/.f64 d l) (/.f64 1 2))) (-.f64 1 (.f64 (.f64 1/2 (.f64 (pow.f64 (.f64 (*.f64 M 1/2) (/.f64 D d)) 2) h)) (/.f64 1 l))))	D	-inf
15.0ms	(.f64 (.f64 (pow.f64 (/.f64 d h) (/.f64 1 2)) (pow.f64 (/.f64 d l) (/.f64 1 2))) (-.f64 1 (.f64 (.f64 1/2 (.f64 (pow.f64 (.f64 (*.f64 M 1/2) (/.f64 D d)) 2) h)) (/.f64 1 l))))	M	inf
15.0ms	(.f64 (.f64 1/2 (.f64 (pow.f64 (.f64 (*.f64 M 1/2) (/.f64 D d)) 2) h)) (/.f64 1 l))	h	0
15.0ms	(.f64 (.f64 (pow.f64 (/.f64 d h) (/.f64 1 2)) (pow.f64 (/.f64 d l) (/.f64 1 2))) (-.f64 1 (.f64 (.f64 1/2 (.f64 (pow.f64 (.f64 (*.f64 M 1/2) (/.f64 D d)) 2) h)) (/.f64 1 l))))	D	inf

rewrite30.0ms (0.2%)

Algorithm

1×	batch-egg-rewrite

Rules

250×	`add-sqr-sqrt_binary64`
241×	`log1p-expm1-u_binary64`
241×	`expm1-log1p-u_binary64`
237×	`add-cbrt-cube_binary64`
234×	`add-cube-cbrt_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	25	62
1	533	61

Stop Event

1×	node limit

Counts

2 → 28

simplify81.0ms (0.5%)

Algorithm

1×	egg-herbie

Rules

703×	`associate-/r/_binary64`
609×	`associate-/l/_binary64`
434×	`*-commutative_binary64`
250×	`fma-def_binary64`
225×	`associate-/l*_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	42	2790
1	122	2736
2	359	2736
3	2102	2736
4	4915	2736

Stop Event

1×	node limit

Counts

124 → 39

prune130.0ms (0.8%)

Pruning

17 alts after pruning (17 fresh and 0 done)

	Pruned	Kept	Total
New	86	3	89
Fresh	5	14	19
Picked	1	0	1
Done	0	0	0
Total	92	17	109

Error

10.7b

Counts

109 → 17

Alt Table

Status	Error	Program
	41.9b	(.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 1/2 (.f64 (pow.f64 (.f64 (*.f64 M 1/2) (/.f64 D d)) 2) h)) (/.f64 1 l))))
	45.8b	(fma.f64 d (sqrt.f64 (/.f64 (pow.f64 h -1) l)) (.f64 -1/8 (/.f64 (sqrt.f64 (/.f64 h (pow.f64 l 3))) (/.f64 (/.f64 d M) (.f64 D (*.f64 D M))))))
	33.7b	(pow.f64 (.f64 (sqrt.f64 (.f64 (/.f64 d h) (/.f64 d l))) (-.f64 1 (/.f64 (.f64 1/2 (.f64 (pow.f64 (.f64 M (.f64 1/2 (/.f64 D d))) 2) h)) l))) 1)
▶	23.6b	(.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 (.f64 (.f64 (/.f64 1 2) (pow.f64 (/.f64 (.f64 M D) (*.f64 2 d)) 2)) (/.f64 h l))))
	23.7b	(.f64 (.f64 (pow.f64 (/.f64 d h) (/.f64 1 2)) (pow.f64 (/.f64 d l) (/.f64 1 2))) (-.f64 1 (pow.f64 (sqrt.f64 (.f64 1/2 (.f64 (pow.f64 (*.f64 (/.f64 M 2) (/.f64 D d)) 2) (/.f64 h l)))) 2)))
	31.9b	(.f64 (.f64 (pow.f64 (/.f64 d h) (/.f64 1 2)) (pow.f64 (/.f64 d l) (/.f64 1 2))) (-.f64 1 (.f64 (.f64 (/.f64 D d) (/.f64 D d)) (/.f64 (.f64 (.f64 M M) 1/8) (/.f64 l h)))))
	34.8b	(pow.f64 (.f64 (sqrt.f64 (.f64 (/.f64 d h) (/.f64 d l))) (-.f64 1 (/.f64 (.f64 1/2 (pow.f64 (.f64 (*.f64 M 1/2) (/.f64 D d)) 2)) (/.f64 l h)))) 1)
	39.8b	(.f64 (.f64 (pow.f64 (/.f64 d h) (/.f64 1 2)) (.f64 (sqrt.f64 d) (pow.f64 (/.f64 1 l) 1/2))) (-.f64 1 (.f64 (.f64 (/.f64 1 2) (pow.f64 (/.f64 (.f64 M D) (*.f64 2 d)) 2)) (/.f64 h l))))
	39.9b	(.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))))))
	43.7b	(.f64 (sqrt.f64 (/.f64 1 (.f64 l h))) d)
	33.6b	(.f64 (.f64 (pow.f64 (/.f64 d h) (/.f64 1 2)) (cbrt.f64 (pow.f64 (/.f64 d l) 3/2))) (-.f64 1 (.f64 (.f64 1/2 (.f64 (pow.f64 (.f64 (*.f64 M 1/2) (/.f64 D d)) 2) h)) (/.f64 1 l))))
	40.3b	(.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 2) (/.f64 D d)) 2)) h) l)))
	40.4b	(.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 2) (/.f64 D d)) 2)) h) l)))
	42.1b	(.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)))
	60.0b	(.f64 (.f64 (log.f64 (exp.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)))
	41.8b	(.f64 (.f64 (.f64 (pow.f64 (cbrt.f64 (pow.f64 (/.f64 d h) 2)) 1/2) (pow.f64 (cbrt.f64 (/.f64 d h)) 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))))
	61.0b	(log.f64 (pow.f64 (exp.f64 (sqrt.f64 (.f64 (/.f64 d h) (/.f64 d l)))) (-.f64 1 (.f64 1/2 (.f64 (pow.f64 (.f64 (/.f64 M 2) (/.f64 D d)) 2) (/.f64 h l))))))

Compiler

Compiled 4243 to 2830 computations (33.3% saved)

localize24.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	6.8b	(.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))))
	8.0b	(pow.f64 (/.f64 d h) (/.f64 1 2))
✓	11.0b	(pow.f64 (/.f64 d l) 1/4)
	13.0b	(.f64 (.f64 (/.f64 1 2) (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2)) (/.f64 h l))

series572.0ms (3.6%)

Counts

2 → 56

Calls

21 calls:

81.0ms	(pow.f64 (/.f64 d l) 1/4)	l	inf
70.0ms	(pow.f64 (/.f64 d l) 1/4)	d	inf
64.0ms	(pow.f64 (/.f64 d l) 1/4)	d	-inf
60.0ms	(pow.f64 (/.f64 d l) 1/4)	d	0
56.0ms	(pow.f64 (/.f64 d l) 1/4)	l	-inf

rewrite41.0ms (0.3%)

Algorithm

1×	batch-egg-rewrite

Rules

257×	`add-sqr-sqrt_binary64`
249×	`log1p-expm1-u_binary64`
249×	`expm1-log1p-u_binary64`
244×	`add-cbrt-cube_binary64`
242×	`add-cube-cbrt_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	26	49
1	553	47

Stop Event

1×	node limit

Counts

2 → 30

simplify53.0ms (0.3%)

Algorithm

1×	egg-herbie

Rules

478×	`associate-r_binary64`
460×	`fma-def_binary64`
435×	`associate-l_binary64`
251×	`associate-/l*_binary64`
155×	`associate-/r/_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	56	1511
1	129	1463
2	311	1451
3	1041	1319
4	4710	1319

Stop Event

1×	node limit

Counts

86 → 44

prune188.0ms (1.2%)

Pruning

21 alts after pruning (21 fresh and 0 done)

	Pruned	Kept	Total
New	105	7	112
Fresh	2	14	16
Picked	1	0	1
Done	0	0	0
Total	108	21	129

Error

10.7b

Counts

129 → 21

Alt Table

Status	Error	Program
	23.7b	(.f64 (.f64 (pow.f64 (/.f64 d h) (/.f64 1 2)) (.f64 (pow.f64 (/.f64 d l) 1/4) (.f64 (pow.f64 (pow.f64 (cbrt.f64 (/.f64 d l)) 2) 1/4) (pow.f64 (cbrt.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))))
	43.7b	(.f64 (sqrt.f64 (/.f64 1 (.f64 l h))) d)
	41.9b	(.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 1/2 (.f64 (pow.f64 (.f64 (*.f64 M 1/2) (/.f64 D d)) 2) h)) (/.f64 1 l))))
	45.8b	(fma.f64 d (sqrt.f64 (/.f64 (pow.f64 h -1) l)) (.f64 -1/8 (/.f64 (sqrt.f64 (/.f64 h (pow.f64 l 3))) (/.f64 (/.f64 d M) (.f64 D (*.f64 D M))))))
	44.1b	(.f64 (.f64 (/.f64 (sqrt.f64 (neg.f64 d)) (sqrt.f64 (neg.f64 h))) (.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))))
	23.7b	(.f64 (.f64 (pow.f64 (/.f64 d h) (/.f64 1 2)) (pow.f64 (/.f64 d l) (/.f64 1 2))) (-.f64 1 (pow.f64 (sqrt.f64 (.f64 1/2 (.f64 (pow.f64 (*.f64 (/.f64 M 2) (/.f64 D d)) 2) (/.f64 h l)))) 2)))
	31.9b	(.f64 (.f64 (pow.f64 (/.f64 d h) (/.f64 1 2)) (pow.f64 (/.f64 d l) (/.f64 1 2))) (-.f64 1 (.f64 (.f64 (/.f64 D d) (/.f64 D d)) (/.f64 (.f64 (.f64 M M) 1/8) (/.f64 l h)))))
	40.0b	(.f64 (.f64 (/.f64 (sqrt.f64 d) (sqrt.f64 h)) (.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	(.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))))))
	39.8b	(.f64 (.f64 (pow.f64 (/.f64 d h) (/.f64 1 2)) (.f64 (sqrt.f64 d) (pow.f64 (/.f64 1 l) 1/2))) (-.f64 1 (.f64 (.f64 (/.f64 1 2) (pow.f64 (/.f64 (.f64 M D) (*.f64 2 d)) 2)) (/.f64 h l))))
	23.7b	(.f64 (.f64 (pow.f64 (/.f64 d h) (/.f64 1 2)) (.f64 (pow.f64 (/.f64 d l) 1/4) (cbrt.f64 (pow.f64 (/.f64 d l) 3/4)))) (-.f64 1 (.f64 (.f64 (/.f64 1 2) (pow.f64 (/.f64 (.f64 M D) (*.f64 2 d)) 2)) (/.f64 h l))))
	23.6b	(.f64 (.f64 (pow.f64 (/.f64 d h) (/.f64 1 2)) (.f64 (pow.f64 (/.f64 d l) 1/4) (.f64 (pow.f64 (/.f64 d l) 1/8) (pow.f64 (/.f64 d l) 1/8)))) (-.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 (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)))
	40.4b	(.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 2) (/.f64 D d)) 2)) h) l)))
	42.1b	(.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)))
	60.0b	(.f64 (.f64 (log.f64 (exp.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)))
	41.8b	(.f64 (.f64 (.f64 (pow.f64 (cbrt.f64 (pow.f64 (/.f64 d h) 2)) 1/2) (pow.f64 (cbrt.f64 (/.f64 d h)) 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))))
	23.8b	(.f64 (.f64 (.f64 (cbrt.f64 (/.f64 d h)) (cbrt.f64 (sqrt.f64 (/.f64 d h)))) (.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))))
	35.1b	(pow.f64 (.f64 (pow.f64 (.f64 (/.f64 d l) (/.f64 d h)) 1/2) (-.f64 1 (.f64 1/2 (.f64 (pow.f64 (*.f64 (/.f64 M 2) (/.f64 D d)) 2) (/.f64 h l))))) 1)
	61.0b	(log.f64 (pow.f64 (exp.f64 (sqrt.f64 (.f64 (/.f64 d h) (/.f64 d l)))) (-.f64 1 (.f64 1/2 (.f64 (pow.f64 (.f64 (/.f64 M 2) (/.f64 D d)) 2) (/.f64 h l))))))
	33.7b	(pow.f64 (.f64 (sqrt.f64 (.f64 (/.f64 d h) (/.f64 d l))) (-.f64 1 (/.f64 (.f64 1/2 (.f64 (pow.f64 (.f64 M (.f64 1/2 (/.f64 D d))) 2) h)) l))) 1)

Compiler

Compiled 5191 to 3221 computations (38% saved)

regimes2.8s (17.7%)

Accuracy

Total 8.7b remaining (46.5%)

Threshold costs 0b (0%)

Counts

180 → 3

Compiler

Compiled 52534 to 39283 computations (25.2% saved)

bsearch956.0ms (6%)

Algorithm

2×	binary-search

Calls

2 calls:

747.0ms	l
197.0ms	l

Steps

Iters	Point		Range
2.7932440493458067e-69	∈ [	2.736328770159259e-69	,	8.121305587837426e-69	]
-1.7821996346274e-310	∈ [	-2.763225821813567e-287	,	2.654092803449024e-288	]

Compiler

Compiled 6 to 5 computations (16.7% saved)

simplify14.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	54	152
1	82	152
2	108	152
3	129	152
4	147	152
5	156	152
6	160	152
7	161	152

Stop Event

1×

saturated

end644.0ms (4.1%)

Stop Event

1×

fuel

Compiler

Compiled 1243 to 896 computations (27.9% saved)

Details

analyze2.2s (13.7%)

sample5.7s (36.1%)

preprocess41.0ms (0.3%)

simplify17.0ms (0.1%)

prune8.0ms (0%)

localize24.0ms (0.2%)

series1.0s (6.5%)

rewrite38.0ms (0.2%)

simplify85.0ms (0.5%)

prune156.0ms (1%)

localize24.0ms (0.1%)

series361.0ms (2.3%)

rewrite30.0ms (0.2%)

simplify83.0ms (0.5%)

prune136.0ms (0.9%)

localize26.0ms (0.2%)

series354.0ms (2.2%)

rewrite30.0ms (0.2%)

simplify81.0ms (0.5%)

prune130.0ms (0.8%)

localize24.0ms (0.2%)

series572.0ms (3.6%)

rewrite41.0ms (0.3%)

simplify53.0ms (0.3%)

prune188.0ms (1.2%)

regimes2.8s (17.7%)

bsearch956.0ms (6%)

simplify14.0ms (0.1%)

end644.0ms (4.1%)

Profiling