Details

analyze1.2s (28.3%)

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%	99.8%	0.2%	7
0%	99.8%	0.2%	8
5.8%	94%	0.2%	9
7.6%	92.2%	0.2%	10
11.6%	88.2%	0.2%	11
18.5%	81.3%	0.2%	12
32.3%	66.9%	0.8%	13
37%	62.2%	0.8%	14

Compiler

Compiled 14 to 9 computations (35.7% saved)

sample1.3s (30.4%)

Results

1.1s	8256×	body	128	valid
171.0ms	1611×	body	128	invalid

Compiler

Compiled 28 to 18 computations (35.7% saved)

preprocess12.0ms (0.3%)

Algorithm

2×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	32	91
0	4	4

Stop Event

1×	saturated
1×	saturated

Compiler

Compiled 13 to 8 computations (38.5% saved)

simplify6.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	13

Stop Event

1×

saturated

Counts

1 → 1

prune1.0ms (0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

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

Error

13.4b

Counts

2 → 1

Alt Table

Status	Error	Program
▶	13.4b	(.f64 x (/.f64 (.f64 (/.f64 y z) t) t))

Compiler

Compiled 39 to 24 computations (38.5% saved)

localize6.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	4.0b	(.f64 x (/.f64 (.f64 (/.f64 y z) t) t))
✓	5.0b	(*.f64 (/.f64 y z) t)
✓	10.1b	(/.f64 (*.f64 (/.f64 y z) t) t)

series35.0ms (0.8%)

Counts

3 → 120

Calls

30 calls:

2.0ms	(.f64 x (/.f64 (.f64 (/.f64 y z) t) t))	y	inf
2.0ms	(/.f64 (*.f64 (/.f64 y z) t) t)	t	inf
2.0ms	(.f64 x (/.f64 (.f64 (/.f64 y z) t) t))	y	-inf
1.0ms	(*.f64 (/.f64 y z) t)	y	-inf
1.0ms	(.f64 x (/.f64 (.f64 (/.f64 y z) t) t))	x	-inf

rewrite39.0ms (0.9%)

Algorithm

1×	batch-egg-rewrite

Rules

660×	`log1p-expm1-u_binary64`
660×	`expm1-log1p-u_binary64`
222×	`log-prod_binary64`
173×	`log-pow_binary64`
163×	`expm1-udef_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	30
1	163	30
2	1726	30

Stop Event

1×	node limit

Counts

3 → 52

simplify13.0ms (0.3%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	732

Stop Event

1×

saturated

Counts

172 → 55

prune34.0ms (0.8%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	48	7	55
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	49	7	56

Error

0.1b

Counts

56 → 7

Alt Table

Status	Error	Program
	33.6b	(pow.f64 (sqrt.f64 (.f64 (/.f64 (.f64 (/.f64 y z) t) t) x)) 2)
	37.4b	(.f64 x (/.f64 (cbrt.f64 (pow.f64 (.f64 (/.f64 y z) t) 3)) t))
	34.3b	(.f64 x (pow.f64 (sqrt.f64 (/.f64 (.f64 (/.f64 y z) t) t)) 2))
	6.9b	(/.f64 (*.f64 y x) z)
	19.3b	(.f64 x (/.f64 (/.f64 (.f64 y t) z) t))
▶	4.2b	(*.f64 x (/.f64 y z))
	37.6b	(cbrt.f64 (pow.f64 (.f64 (/.f64 (.f64 (/.f64 y z) t) t) x) 3))

Compiler

Compiled 960 to 355 computations (63% saved)

localize3.0ms (0.1%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	4.0b	(*.f64 x (/.f64 y z))

series12.0ms (0.3%)

Counts

1 → 36

Calls

9 calls:

2.0ms	(*.f64 x (/.f64 y z))	z	-inf
2.0ms	(*.f64 x (/.f64 y z))	y	-inf
1.0ms	(*.f64 x (/.f64 y z))	x	-inf
1.0ms	(*.f64 x (/.f64 y z))	x	0
1.0ms	(*.f64 x (/.f64 y z))	x	inf

rewrite28.0ms (0.7%)

Algorithm

1×	batch-egg-rewrite

Rules

442×	`log1p-expm1-u_binary64`
442×	`expm1-log1p-u_binary64`
424×	`pow1_binary64`
167×	`unpow-prod-down_binary64`
150×	`pow2_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	7
1	109	7
2	1154	7

Stop Event

1×	node limit

Counts

1 → 20

simplify7.0ms (0.2%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	252

Stop Event

1×

saturated

Counts

56 → 21

prune18.0ms (0.4%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	18	3	21
Fresh	2	4	6
Picked	0	1	1
Done	0	0	0
Total	20	8	28

Error

0.1b

Counts

28 → 8

Alt Table

Status	Error	Program
▶	5.1b	(pow.f64 (cbrt.f64 (*.f64 x (/.f64 y z))) 3)
	6.9b	(/.f64 (*.f64 y x) z)
	37.4b	(.f64 x (/.f64 (cbrt.f64 (pow.f64 (.f64 (/.f64 y z) t) 3)) t))
	34.3b	(.f64 x (pow.f64 (sqrt.f64 (/.f64 (.f64 (/.f64 y z) t) t)) 2))
	33.4b	(cbrt.f64 (pow.f64 (*.f64 x (/.f64 y z)) 3))
	29.4b	(pow.f64 (sqrt.f64 (*.f64 x (/.f64 y z))) 2)
	19.3b	(.f64 x (/.f64 (/.f64 (.f64 y t) z) t))
✓	4.2b	(*.f64 x (/.f64 y z))

Compiler

Compiled 388 to 207 computations (46.6% saved)

localize7.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.6b	(pow.f64 (cbrt.f64 (*.f64 x (/.f64 y z))) 3)
	4.0b	(*.f64 x (/.f64 y z))
✓	11.2b	(cbrt.f64 (*.f64 x (/.f64 y z)))

series115.0ms (2.7%)

Counts

2 → 0

Calls

18 calls:

21.0ms	(pow.f64 (cbrt.f64 (*.f64 x (/.f64 y z))) 3)	z	-inf
20.0ms	(pow.f64 (cbrt.f64 (*.f64 x (/.f64 y z))) 3)	x	-inf
18.0ms	(pow.f64 (cbrt.f64 (*.f64 x (/.f64 y z))) 3)	y	-inf
10.0ms	(cbrt.f64 (*.f64 x (/.f64 y z)))	y	-inf
8.0ms	(cbrt.f64 (*.f64 x (/.f64 y z)))	z	-inf

rewrite33.0ms (0.8%)

Algorithm

1×	batch-egg-rewrite

Rules

600×	`log1p-expm1-u_binary64`
600×	`expm1-log1p-u_binary64`
192×	`pow2_binary64`
192×	`log-prod_binary64`
143×	`log-pow_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	16
1	169	16
2	1616	16

Stop Event

1×	node limit

Counts

2 → 39

simplify5.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	0	0

Stop Event

1×

saturated

Counts

39 → 39

prune48.0ms (1.1%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	55	5	60
Fresh	1	5	6
Picked	1	0	1
Done	0	1	1
Total	57	11	68

Error

0.0b

Counts

68 → 11

Alt Table

Status	Error	Program
	29.4b	(pow.f64 (sqrt.f64 (*.f64 x (/.f64 y z))) 2)
▶	5.1b	(.f64 (cbrt.f64 (.f64 x (/.f64 y z))) (pow.f64 (cbrt.f64 (*.f64 x (/.f64 y z))) 2))
	6.9b	(/.f64 (*.f64 y x) z)
	5.3b	(pow.f64 (*.f64 (cbrt.f64 (/.f64 y z)) (cbrt.f64 x)) 3)
	37.4b	(.f64 x (/.f64 (cbrt.f64 (pow.f64 (.f64 (/.f64 y z) t) 3)) t))
	33.4b	(cbrt.f64 (pow.f64 (*.f64 x (/.f64 y z)) 3))
	19.3b	(.f64 x (/.f64 (/.f64 (.f64 y t) z) t))
✓	4.2b	(*.f64 x (/.f64 y z))
	7.8b	(pow.f64 (cbrt.f64 (/.f64 (*.f64 y x) z)) 3)
	5.3b	(pow.f64 (cbrt.f64 (pow.f64 (cbrt.f64 (*.f64 x (/.f64 y z))) 3)) 3)
	18.0b	(pow.f64 (cbrt.f64 (expm1.f64 (log1p.f64 (*.f64 x (/.f64 y z))))) 3)

Compiler

Compiled 984 to 471 computations (52.1% saved)

localize7.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.3b	(.f64 (cbrt.f64 (.f64 x (/.f64 y z))) (pow.f64 (cbrt.f64 (*.f64 x (/.f64 y z))) 2))
✓	0.5b	(pow.f64 (cbrt.f64 (*.f64 x (/.f64 y z))) 2)
	4.0b	(*.f64 x (/.f64 y z))
	11.2b	(cbrt.f64 (*.f64 x (/.f64 y z)))

series239.0ms (5.6%)

Counts

2 → 36

Calls

18 calls:

55.0ms	(.f64 (cbrt.f64 (.f64 x (/.f64 y z))) (pow.f64 (cbrt.f64 (*.f64 x (/.f64 y z))) 2))	x	-inf
54.0ms	(.f64 (cbrt.f64 (.f64 x (/.f64 y z))) (pow.f64 (cbrt.f64 (*.f64 x (/.f64 y z))) 2))	z	-inf
50.0ms	(.f64 (cbrt.f64 (.f64 x (/.f64 y z))) (pow.f64 (cbrt.f64 (*.f64 x (/.f64 y z))) 2))	y	-inf
22.0ms	(pow.f64 (cbrt.f64 (*.f64 x (/.f64 y z))) 2)	x	-inf
19.0ms	(pow.f64 (cbrt.f64 (*.f64 x (/.f64 y z))) 2)	y	-inf

rewrite35.0ms (0.8%)

Algorithm

1×	batch-egg-rewrite

Rules

626×	`log1p-expm1-u_binary64`
626×	`expm1-log1p-u_binary64`
203×	`log-prod_binary64`
154×	`log-pow_binary64`
149×	`expm1-udef_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	10	35
1	186	19
2	1851	19

Stop Event

1×	node limit

Counts

2 → 33

simplify7.0ms (0.2%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	252

Stop Event

1×

saturated

Counts

69 → 34

prune78.0ms (1.8%)

Pruning

13 alts after pruning (12 fresh and 1 done)

	Pruned	Kept	Total
New	115	3	118
Fresh	0	9	9
Picked	1	0	1
Done	0	1	1
Total	116	13	129

Error

0.0b

Counts

129 → 13

Alt Table

Status	Error	Program
	6.9b	(/.f64 (*.f64 y x) z)
	5.3b	(pow.f64 (*.f64 (cbrt.f64 (/.f64 y z)) (cbrt.f64 x)) 3)
	7.8b	(pow.f64 (cbrt.f64 (/.f64 (*.f64 y x) z)) 3)
	5.0b	(.f64 (.f64 (cbrt.f64 x) (cbrt.f64 (/.f64 y z))) (pow.f64 (cbrt.f64 (*.f64 x (/.f64 y z))) 2))
	37.4b	(.f64 x (/.f64 (cbrt.f64 (pow.f64 (.f64 (/.f64 y z) t) 3)) t))
	25.1b	(.f64 (cbrt.f64 (.f64 x (/.f64 y z))) (cbrt.f64 (pow.f64 (*.f64 x (/.f64 y z)) 2)))
	33.4b	(cbrt.f64 (pow.f64 (*.f64 x (/.f64 y z)) 3))
	29.4b	(pow.f64 (sqrt.f64 (*.f64 x (/.f64 y z))) 2)
	19.3b	(.f64 x (/.f64 (/.f64 (.f64 y t) z) t))
✓	4.2b	(*.f64 x (/.f64 y z))
	5.3b	(pow.f64 (cbrt.f64 (pow.f64 (cbrt.f64 (*.f64 x (/.f64 y z))) 3)) 3)
	5.7b	(.f64 (cbrt.f64 (.f64 x (/.f64 y z))) (pow.f64 (pow.f64 (cbrt.f64 (cbrt.f64 (*.f64 x (/.f64 y z)))) 3) 2))
	18.0b	(pow.f64 (cbrt.f64 (expm1.f64 (log1p.f64 (*.f64 x (/.f64 y z))))) 3)

Compiler

Compiled 2332 to 783 computations (66.4% saved)

regimes805.0ms (19%)

Accuracy

Total 0.3b remaining (86.4%)

Threshold costs 0.3b (86.4%)

Counts

30 → 5

Compiler

Compiled 3957 to 2708 computations (31.6% saved)

bsearch1.0ms (0%)

Algorithm

4×	left-value

Calls

4 calls:

0.0ms	(/.f64 y z)
0.0ms	(/.f64 y z)
0.0ms	(/.f64 y z)
0.0ms	(/.f64 y z)

Steps

Iters	Point		Range
8.196600566113814e+219	∈ [	8.196600566113814e+219	,	2.7095045171415422e+222	]
2.0884440150511374e-185	∈ [	2.0884440150511374e-185	,	5.993858545605601e-171	]
-2.353714236473384e-302	∈ [	-2.353714236473384e-302	,	-1.02245687046e-313	]
-1.3512618534244792e+244	∈ [	-1.3512618534244792e+244	,	-1.2437481922790468e+239	]

Compiler

Compiled 7 to 5 computations (28.6% saved)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	21	71

Stop Event

1×

saturated

end153.0ms (3.6%)

Stop Event

1×

fuel

Compiler

Compiled 292 to 168 computations (42.5% saved)

Details

analyze1.2s (28.3%)

sample1.3s (30.4%)

preprocess12.0ms (0.3%)

simplify6.0ms (0.1%)

prune1.0ms (0%)

localize6.0ms (0.1%)

series35.0ms (0.8%)

rewrite39.0ms (0.9%)

simplify13.0ms (0.3%)

prune34.0ms (0.8%)

localize3.0ms (0.1%)

series12.0ms (0.3%)

rewrite28.0ms (0.7%)

simplify7.0ms (0.2%)

prune18.0ms (0.4%)

localize7.0ms (0.2%)

series115.0ms (2.7%)

rewrite33.0ms (0.8%)

simplify5.0ms (0.1%)

prune48.0ms (1.1%)

localize7.0ms (0.2%)

series239.0ms (5.6%)

rewrite35.0ms (0.8%)

simplify7.0ms (0.2%)

prune78.0ms (1.8%)

regimes805.0ms (19%)

bsearch1.0ms (0%)

simplify2.0ms (0%)

end153.0ms (3.6%)

Profiling