Details

analyze13.0ms

Algorithm

Search

True	Other	False	Iter
0%	25%	75%	0
0%	25%	75%	1
0%	12.5%	87.5%	2
0%	6.3%	93.7%	3
0%	3.1%	96.9%	4
0%	1.6%	98.4%	5
0%	0.8%	99.2%	6
0%	0.4%	99.6%	7
0%	0.2%	99.8%	8
0.1%	0.1%	99.8%	9
0.1%	0%	99.9%	10
0.1%	0%	99.9%	11
0.1%	0%	99.9%	12
0.1%	0%	99.9%	13
0.1%	0%	99.9%	14

sample69.0ms

Algorithm

intervals

Results

55.0ms	256×	body	80	valid
3.0ms	260×	pre	80	true
1.0ms	4×	body	80	invalid

simplify75.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 2 (21.0ms)

Iter	Nodes	Cost
0	90	61
1	389	58
2	2115	36
3	5001	36

prune16.0ms

Filtered

1 candidates to 1 candidates (0.0%)

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

Merged error: 2.6b

Counts

2 → 2

localize29.0ms

Local error

Found 4 expressions with local error:

0.5b	(* (/ 1.0 (fabs x)) (/ 1.0 (fabs x)))
0.5b	(* (/ 1.0 (fabs x)) (/ 1.0 (fabs x)))
1.0b	(sqrt PI)
2.4b	(exp (* (fabs x) (fabs x)))

rewrite30.0ms

Algorithm

rewrite-expression-head

Rules

86×	`add-sqr-sqrt`
80×	`times-frac`
61×	`add-cube-cbrt` `*-un-lft-identity`
28×	`add-exp-log` `add-cbrt-cube`
26×	`swap-sqr` `associate-r` `associate-l`
19×	`pow1`
8×	`cbrt-undiv` `div-exp` `prod-exp` `cbrt-unprod` `div-inv` `unswap-sqr`
6×	`add-log-exp`
3×	`sqrt-prod`
2×	`pow2` `frac-times` `pow-plus` `associate-r/` `pow-prod-down` `associate-l/` `pow-sqr` `*-commutative` `pow-prod-up`
1×	`rem-sqrt-square` `exp-prod` `exp-to-pow` `sqrt-pow1` `pow1/2` `rem-exp-log`

Counts

4 → 157

Calls

4 calls:

10.0ms	(* (/ 1.0 (fabs x)) (/ 1.0 (fabs x)))
10.0ms	(* (/ 1.0 (fabs x)) (/ 1.0 (fabs x)))
1.0ms	(sqrt PI)
2.0ms	(exp (* (fabs x) (fabs x)))

series33.0ms

Counts

4 → 10

Calls

4 calls:

10.0ms	(* (/ 1.0 (fabs x)) (/ 1.0 (fabs x)))
9.0ms	(* (/ 1.0 (fabs x)) (/ 1.0 (fabs x)))
0.0ms	(sqrt PI)
13.0ms	(exp (* (fabs x) (fabs x)))

simplify70.0ms

Algorithm

egg-herbie

Counts

167 → 167

Iterations

Useful iterations: 2 (57.0ms)

Iter	Nodes	Cost
0	437	1271
1	2104	1091
2	5001	993

prune762.0ms

Filtered

109 candidates to 167 candidates (-53.2%)

Pruning

14 alts after pruning (14 fresh and 0 done)

	Pruned	Kept	Total
New	154	13	167
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	155	14	169

Merged error: 0.8b

Counts

169 → 14

localize35.0ms

Local error

Found 4 expressions with local error:

0.5b	(* (/ 1.0 (fabs x)) (/ 1.0 (fabs x)))
0.5b	(* (/ 1.0 (fabs x)) (/ 1.0 (fabs x)))
1.0b	(pow (exp (fabs x)) (fabs x))
1.0b	(sqrt PI)

rewrite36.0ms

Algorithm

rewrite-expression-head

Rules

89×	`add-sqr-sqrt`
80×	`times-frac`
64×	`add-cube-cbrt` `*-un-lft-identity`
28×	`add-exp-log` `add-cbrt-cube`
26×	`swap-sqr` `associate-r` `associate-l`
20×	`pow1`
8×	`cbrt-undiv` `div-exp` `prod-exp` `cbrt-unprod` `div-inv` `unswap-sqr`
4×	`pow-pow` `add-log-exp`
3×	`unpow-prod-down` `pow-unpow` `exp-prod` `sqrt-prod`
2×	`pow2` `frac-times` `pow-plus` `associate-r/` `pow-prod-down` `associate-l/` `pow-sqr` `*-commutative` `pow-prod-up`
1×	`pow-to-exp` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `pow-exp` `sqr-pow`

Counts

4 → 167

Calls

4 calls:

11.0ms	(* (/ 1.0 (fabs x)) (/ 1.0 (fabs x)))
13.0ms	(* (/ 1.0 (fabs x)) (/ 1.0 (fabs x)))
3.0ms	(pow (exp (fabs x)) (fabs x))
1.0ms	(sqrt PI)

series49.0ms

Counts

4 → 10

Calls

4 calls:

10.0ms	(* (/ 1.0 (fabs x)) (/ 1.0 (fabs x)))
10.0ms	(* (/ 1.0 (fabs x)) (/ 1.0 (fabs x)))
29.0ms	(pow (exp (fabs x)) (fabs x))
0.0ms	(sqrt PI)

simplify67.0ms

Algorithm

egg-herbie

Counts

177 → 177

Iterations

Useful iterations: 2 (53.0ms)

Iter	Nodes	Cost
0	413	1275
1	2257	1097
2	5001	1015

prune875.0ms

Filtered

115 candidates to 177 candidates (-53.9%)

Pruning

23 alts after pruning (23 fresh and 0 done)

	Pruned	Kept	Total
New	163	14	177
Fresh	4	9	13
Picked	1	0	1
Done	0	0	0
Total	168	23	191

Merged error: 0.5b

Counts

191 → 23

localize136.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt (fabs x))
0.6b	(cbrt (fabs x))
1.0b	(pow (exp (fabs x)) (fabs x))
1.0b	(sqrt PI)

rewrite10.0ms

Algorithm

rewrite-expression-head

Rules

11×	`add-sqr-sqrt`
10×	`add-cube-cbrt` `*-un-lft-identity`
6×	`pow1` `cbrt-prod`
4×	`add-exp-log` `pow-pow` `add-cbrt-cube` `add-log-exp`
3×	`unpow-prod-down` `pow-unpow` `exp-prod` `sqrt-prod`
2×	`pow1/3`
1×	`pow-to-exp` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `pow-exp` `sqr-pow`

Counts

4 → 55

Calls

4 calls:

1.0ms	(cbrt (fabs x))
1.0ms	(cbrt (fabs x))
4.0ms	(pow (exp (fabs x)) (fabs x))
2.0ms	(sqrt PI)

series114.0ms

Counts

4 → 10

Calls

4 calls:

29.0ms	(cbrt (fabs x))
38.0ms	(cbrt (fabs x))
46.0ms	(pow (exp (fabs x)) (fabs x))
0.0ms	(sqrt PI)

simplify34.0ms

Algorithm

egg-herbie

Counts

65 → 65

Iterations

Useful iterations: 2 (29.0ms)

Iter	Nodes	Cost
0	216	340
1	956	316
2	5001	274

prune405.0ms

Filtered

47 candidates to 65 candidates (-38.3%)

Pruning

24 alts after pruning (23 fresh and 1 done)

	Pruned	Kept	Total
New	63	2	65
Fresh	1	21	22
Picked	0	1	1
Done	0	0	0
Total	64	24	88

Merged error: 0.5b

Counts

88 → 24

localize48.0ms

Local error

Found 4 expressions with local error:

0.5b	(cbrt (/ 1.0 (fabs x)))
0.9b	(pow (cbrt (/ 1.0 (fabs x))) 4)
1.0b	(pow (exp (fabs x)) (fabs x))
1.0b	(sqrt PI)

rewrite15.0ms

Algorithm

rewrite-expression-head

Rules

26×	`cbrt-prod`
25×	`add-sqr-sqrt`
24×	`add-cube-cbrt` `*-un-lft-identity`
19×	`unpow-prod-down`
18×	`times-frac`
7×	`pow1`
6×	`pow-unpow` `pow-pow`
5×	`add-exp-log`
4×	`add-cbrt-cube` `add-log-exp`
3×	`exp-prod` `sqrt-prod`
2×	`pow-to-exp` `pow1/3` `pow-exp` `div-inv` `sqr-pow`
1×	`rem-sqrt-square` `cbrt-div` `sqrt-pow1` `pow1/2`

Counts

4 → 86

Calls

4 calls:

2.0ms	(cbrt (/ 1.0 (fabs x)))
5.0ms	(pow (cbrt (/ 1.0 (fabs x))) 4)
3.0ms	(pow (exp (fabs x)) (fabs x))
1.0ms	(sqrt PI)

series101.0ms

Counts

4 → 10

Calls

4 calls:

27.0ms	(cbrt (/ 1.0 (fabs x)))
43.0ms	(pow (cbrt (/ 1.0 (fabs x))) 4)
30.0ms	(pow (exp (fabs x)) (fabs x))
0.0ms	(sqrt PI)

simplify49.0ms

Algorithm

egg-herbie

Counts

96 → 96

Iterations

Useful iterations: 2 (40.0ms)

Iter	Nodes	Cost
0	380	655
1	1463	626
2	5001	590

prune465.0ms

Filtered

71 candidates to 96 candidates (-35.2%)

Pruning

23 alts after pruning (22 fresh and 1 done)

	Pruned	Kept	Total
New	92	4	96
Fresh	4	18	22
Picked	1	0	1
Done	0	1	1
Total	97	23	120

Merged error: 0.5b

Counts

120 → 23

regimes401.0ms

Accuracy

0% (0.8b remaining)

Error of 1.4b against oracle of 0.6b and baseline of 1.4b

bsearch0.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	68	78
1	68	78

end0.0ms

analyze7.0ms

Algorithm

Search

True	Other	False	Iter
0%	25%	75%	0
0%	25%	75%	1
0%	12.5%	87.5%	2
0%	6.3%	93.7%	3
0%	3.1%	96.9%	4
0%	1.6%	98.4%	5
0%	0.8%	99.2%	6
0%	0.4%	99.6%	7
0%	0.2%	99.8%	8
0.1%	0.1%	99.8%	9
0.1%	0%	99.9%	10
0.1%	0%	99.9%	11
0.1%	0%	99.9%	12
0.1%	0%	99.9%	13
0.1%	0%	99.9%	14

sample1.8s

Algorithm

intervals

Results

1.6s	8000×	body	80	valid
97.0ms	8114×	pre	80	true
22.0ms	114×	body	80	invalid

Details

analyze13.0ms

sample69.0ms

simplify75.0ms

prune16.0ms

localize29.0ms

rewrite30.0ms

series33.0ms

simplify70.0ms

prune762.0ms

localize35.0ms

rewrite36.0ms

series49.0ms

simplify67.0ms

prune875.0ms

localize136.0ms

rewrite10.0ms

series114.0ms

simplify34.0ms

prune405.0ms

localize48.0ms

rewrite15.0ms

series101.0ms

simplify49.0ms

prune465.0ms

regimes401.0ms

bsearch0.0ms

simplify2.0ms

end0.0ms

analyze7.0ms

sample1.8s

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