Details

sample214.0ms

Algorithm

intervals

Results

67.0ms	134×	body	1280	valid
29.0ms	30×	body	1280	nan
23.0ms	57×	body	640	valid
20.0ms	114×	body	80	overflowed
15.0ms	22×	body	640	nan
8.0ms	29×	body	320	valid
8.0ms	83×	body	80	valid
7.0ms	165×	body	80	nan
6.0ms	15×	body	320	nan
3.0ms	14×	body	160	valid
1.0ms	7×	body	160	nan

simplify33.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	17	6
1	34	6
2	80	6
3	236	6
4	868	6
5	5001	6

prune7.0ms

Filtered

1 candidates to 0 candidates (100.0%)

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: 32.3b

Counts

2 → 1

localize9.0ms

Local error

Found 3 expressions with local error:

0.0b	(pow x (/ 1.0 n))
0.2b	(pow (+ x 1.0) (/ 1.0 n))
0.9b	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))

rewrite20.0ms

Algorithm

rewrite-expression-head

Rules

31×	`add-sqr-sqrt`
28×	`*-un-lft-identity`
26×	`pow-unpow`
19×	`add-cube-cbrt`
18×	`times-frac`
17×	`unpow-prod-down`
9×	`difference-of-squares`
8×	`sqr-pow`
5×	`pow1` `add-exp-log` `add-log-exp`
3×	`add-cbrt-cube` `distribute-lft-out--`
2×	`pow-to-exp` `pow-pow` `pow-exp` `div-inv` `distribute-lft-out`
1×	`sub-neg` `flip3--` `diff-log` `flip--`

Counts

3 → 79

Calls

3 calls:

3.0ms	(pow x (/ 1.0 n))
5.0ms	(pow (+ x 1.0) (/ 1.0 n))
9.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))

series580.0ms

Counts

3 → 9

Calls

3 calls:

67.0ms	(pow x (/ 1.0 n))
181.0ms	(pow (+ x 1.0) (/ 1.0 n))
332.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))

simplify48.0ms

Algorithm

egg-herbie

Counts

88 → 88

Iterations

Useful iterations: 2 (34.0ms)

Iter	Nodes	Cost
0	476	639
1	1600	623
2	5001	609

prune439.0ms

Filtered

88 candidates to 70 candidates (20.5%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	81	7	88
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	82	7	89

Merged error: 21.4b

Counts

89 → 7

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b	(pow x (/ 1.0 n))
0.2b	(pow (sqrt (+ x 1.0)) (/ 1.0 n))
0.2b	(pow (sqrt (+ x 1.0)) (/ 1.0 n))
2.1b	(- (pow (sqrt (+ x 1.0)) (/ 1.0 n)) (sqrt (pow x (/ 1.0 n))))

rewrite31.0ms

Algorithm

rewrite-expression-head

Rules

54×	`add-sqr-sqrt`
39×	`pow-unpow`
36×	`*-un-lft-identity`
30×	`add-cube-cbrt`
29×	`unpow-prod-down`
27×	`times-frac`
24×	`sqrt-prod`
16×	`difference-of-squares`
11×	`sqr-pow`
9×	`pow1`
7×	`add-exp-log` `pow-pow`
6×	`add-log-exp`
4×	`add-cbrt-cube`
3×	`pow-to-exp` `pow-exp` `div-inv`
2×	`sqrt-pow1` `pow1/2` `sqrt-pow2` `distribute-lft-out`
1×	`sub-neg` `flip3--` `diff-log` `flip--` `distribute-lft-out--`

Counts

4 → 124

Calls

4 calls:

3.0ms	(pow x (/ 1.0 n))
6.0ms	(pow (sqrt (+ x 1.0)) (/ 1.0 n))
6.0ms	(pow (sqrt (+ x 1.0)) (/ 1.0 n))
12.0ms	(- (pow (sqrt (+ x 1.0)) (/ 1.0 n)) (sqrt (pow x (/ 1.0 n))))

series2.0s

Counts

4 → 12

Calls

4 calls:

65.0ms	(pow x (/ 1.0 n))
505.0ms	(pow (sqrt (+ x 1.0)) (/ 1.0 n))
501.0ms	(pow (sqrt (+ x 1.0)) (/ 1.0 n))
901.0ms	(- (pow (sqrt (+ x 1.0)) (/ 1.0 n)) (sqrt (pow x (/ 1.0 n))))

simplify55.0ms

Algorithm

egg-herbie

Counts

136 → 136

Iterations

Useful iterations: 2 (38.0ms)

Iter	Nodes	Cost
0	570	1199
1	1887	1156
2	5002	1145

prune934.0ms

Filtered

136 candidates to 97 candidates (28.7%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	132	4	136
Fresh	2	4	6
Picked	1	0	1
Done	0	0	0
Total	135	8	143

Merged error: 21.4b

Counts

143 → 8

localize15.0ms

Local error

Found 4 expressions with local error:

0.0b	(pow x (/ 1.0 n))
0.2b	(pow (sqrt (+ x 1.0)) (/ 1.0 n))
0.2b	(pow (sqrt (+ x 1.0)) (/ 1.0 n))
2.1b	(- (pow (sqrt (+ x 1.0)) (/ 1.0 n)) (sqrt (pow x (/ 1.0 n))))

rewrite34.0ms

Algorithm

rewrite-expression-head

Rules

54×	`add-sqr-sqrt`
39×	`pow-unpow`
36×	`*-un-lft-identity`
30×	`add-cube-cbrt`
29×	`unpow-prod-down`
27×	`times-frac`
24×	`sqrt-prod`
16×	`difference-of-squares`
11×	`sqr-pow`
9×	`pow1`
7×	`add-exp-log` `pow-pow`
6×	`add-log-exp`
4×	`add-cbrt-cube`
3×	`pow-to-exp` `pow-exp` `div-inv`
2×	`sqrt-pow1` `pow1/2` `sqrt-pow2` `distribute-lft-out`
1×	`sub-neg` `flip3--` `diff-log` `flip--` `distribute-lft-out--`

Counts

4 → 124

Calls

4 calls:

3.0ms	(pow x (/ 1.0 n))
8.0ms	(pow (sqrt (+ x 1.0)) (/ 1.0 n))
6.0ms	(pow (sqrt (+ x 1.0)) (/ 1.0 n))
12.0ms	(- (pow (sqrt (+ x 1.0)) (/ 1.0 n)) (sqrt (pow x (/ 1.0 n))))

series1.8s

Counts

4 → 12

Calls

4 calls:

68.0ms	(pow x (/ 1.0 n))
503.0ms	(pow (sqrt (+ x 1.0)) (/ 1.0 n))
500.0ms	(pow (sqrt (+ x 1.0)) (/ 1.0 n))
717.0ms	(- (pow (sqrt (+ x 1.0)) (/ 1.0 n)) (sqrt (pow x (/ 1.0 n))))

simplify51.0ms

Algorithm

egg-herbie

Counts

136 → 136

Iterations

Useful iterations: 2 (38.0ms)

Iter	Nodes	Cost
0	570	1199
1	1887	1156
2	5002	1145

prune1.4s

Filtered

136 candidates to 97 candidates (28.7%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	135	1	136
Fresh	1	6	7
Picked	1	0	1
Done	0	0	0
Total	137	7	144

Merged error: 21.4b

Counts

144 → 7

localize23.0ms

Local error

Found 4 expressions with local error:

0.1b	(pow (sqrt (sqrt (+ x 1.0))) (/ 1.0 n))
0.1b	(pow (sqrt (sqrt (+ x 1.0))) (/ 1.0 n))
0.2b	(pow (sqrt (+ x 1.0)) (/ 1.0 n))
1.2b	(- (pow (sqrt (sqrt (+ x 1.0))) (/ 1.0 n)) (sqrt (pow (sqrt x) (/ 1.0 n))))

rewrite45.0ms

Algorithm

rewrite-expression-head

Rules

73×	`add-sqr-sqrt`
66×	`sqrt-prod`
52×	`unpow-prod-down`
41×	`*-un-lft-identity`
39×	`pow-unpow`
33×	`add-cube-cbrt`
27×	`times-frac`
25×	`difference-of-squares`
13×	`pow-pow` `sqr-pow`
12×	`pow1`
9×	`sqrt-pow1`
7×	`add-exp-log`
6×	`add-log-exp`
5×	`pow1/2`
4×	`add-cbrt-cube`
3×	`pow-to-exp` `pow-exp` `sqrt-pow2` `div-inv` `distribute-lft-out`
1×	`sub-neg` `flip3--` `diff-log` `flip--` `distribute-lft-out--`

Counts

4 → 150

Calls

4 calls:

7.0ms	(pow (sqrt (sqrt (+ x 1.0))) (/ 1.0 n))
7.0ms	(pow (sqrt (sqrt (+ x 1.0))) (/ 1.0 n))
6.0ms	(pow (sqrt (+ x 1.0)) (/ 1.0 n))
19.0ms	(- (pow (sqrt (sqrt (+ x 1.0))) (/ 1.0 n)) (sqrt (pow (sqrt x) (/ 1.0 n))))

series2.7s

Counts

4 → 12

Calls

4 calls:

502.0ms	(pow (sqrt (sqrt (+ x 1.0))) (/ 1.0 n))
493.0ms	(pow (sqrt (sqrt (+ x 1.0))) (/ 1.0 n))
508.0ms	(pow (sqrt (+ x 1.0)) (/ 1.0 n))
1.2s	(- (pow (sqrt (sqrt (+ x 1.0))) (/ 1.0 n)) (sqrt (pow (sqrt x) (/ 1.0 n))))

simplify56.0ms

Algorithm

egg-herbie

Counts

162 → 162

Iterations

Useful iterations: 2 (39.0ms)

Iter	Nodes	Cost
0	608	1765
1	1934	1699
2	5001	1692

prune1.2s

Filtered

162 candidates to 104 candidates (35.8%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	160	2	162
Fresh	0	6	6
Picked	1	0	1
Done	0	0	0
Total	161	8	169

Merged error: 21.4b

Counts

169 → 8

regimes402.0ms

Accuracy

85.8% (1.5b remaining)

Error of 23.8b against oracle of 22.2b and baseline of 33.1b

bsearch2.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	56	72
1	56	72

end0.0ms

sample7.1s

Algorithm

intervals

Results

2.0s	3865×	body	1280	valid
1.2s	1127×	body	1280	nan
817.0ms	1857×	body	640	valid
632.0ms	959×	body	640	nan
601.0ms	4229×	body	80	overflowed
296.0ms	3118×	body	80	valid
281.0ms	926×	body	320	valid
277.0ms	6176×	body	80	nan
175.0ms	448×	body	320	nan
83.0ms	450×	body	160	valid
48.0ms	236×	body	160	nan

Details

sample214.0ms

simplify33.0ms

prune7.0ms

localize9.0ms

rewrite20.0ms

series580.0ms

simplify48.0ms

prune439.0ms

localize13.0ms

rewrite31.0ms

series2.0s

simplify55.0ms

prune934.0ms

localize15.0ms

rewrite34.0ms

series1.8s

simplify51.0ms

prune1.4s

localize23.0ms

rewrite45.0ms

series2.7s

simplify56.0ms

prune1.2s

regimes402.0ms

bsearch2.0ms

simplify2.0ms

end0.0ms

sample7.1s

Profiling