Details

analyze1.2s

Algorithm: search

sample226.0ms

Algorithm

intervals

Results

66.0ms	121×	body	1280	valid
49.0ms	44×	body	1280	nan
20.0ms	28×	body	640	nan
17.0ms	42×	body	640	valid
15.0ms	86×	body	80	overflowed
8.0ms	19×	body	320	nan
8.0ms	6×	body	1280	invalid
8.0ms	23×	body	320	valid
5.0ms	56×	body	80	valid
5.0ms	7×	body	640	invalid
3.0ms	14×	body	160	valid
2.0ms	6×	body	320	invalid
1.0ms	5×	body	160	invalid
1.0ms	17×	body	80	nan
1.0ms	4×	body	160	nan
1.0ms	5×	body	80	invalid

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

prune6.0ms

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: 32.8b

Counts

2 → 1

localize10.0ms

Local error

Found 3 expressions with local error:

0.0b	(pow x (/ 1.0 n))
0.3b	(pow (+ x 1.0) (/ 1.0 n))
2.0b	(- (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)))

series71.0ms

Counts

3 → 9

Calls

3 calls:

12.0ms	(pow x (/ 1.0 n))
20.0ms	(pow (+ x 1.0) (/ 1.0 n))
39.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))

simplify49.0ms

Algorithm

egg-herbie

Counts

88 → 88

Iterations

Useful iterations: 2 (40.0ms)

Iter	Nodes	Cost
0	552	688
1	1885	669
2	5002	641

prune197.0ms

Filtered

71 candidates to 88 candidates (-23.9%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	82	6	88
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	83	6	89

Merged error: 20.9b

Counts

89 → 6

localize15.0ms

Local error

Found 4 expressions with local error:

0.3b	(cbrt (+ x 1.0))
0.3b	(cbrt (+ x 1.0))
0.3b	(cbrt (+ x 1.0))
4.9b	(- (* (pow (* (cbrt (+ x 1.0)) (cbrt (+ x 1.0))) (/ 1.0 n)) (pow (cbrt (+ x 1.0)) (/ 1.0 n))) (pow x (/ 1.0 n)))

rewrite20.0ms

Algorithm

rewrite-expression-head

Rules

13×	`*-un-lft-identity`
12×	`cbrt-prod`
7×	`add-sqr-sqrt` `add-cube-cbrt`
6×	`cbrt-div` `add-log-exp`
4×	`pow1` `add-exp-log` `add-cbrt-cube`
3×	`flip3-+` `pow1/3` `flip-+` `distribute-lft-out`
1×	`sub-neg` `flip3--` `diff-log` `flip--`

Counts

4 → 54

Calls

4 calls:

3.0ms	(cbrt (+ x 1.0))
3.0ms	(cbrt (+ x 1.0))
3.0ms	(cbrt (+ x 1.0))
10.0ms	(- (* (pow (* (cbrt (+ x 1.0)) (cbrt (+ x 1.0))) (/ 1.0 n)) (pow (cbrt (+ x 1.0)) (/ 1.0 n))) (pow x (/ 1.0 n)))

series113.0ms

Counts

4 → 12

Calls

4 calls:

6.0ms	(cbrt (+ x 1.0))
6.0ms	(cbrt (+ x 1.0))
6.0ms	(cbrt (+ x 1.0))
96.0ms	(- (* (pow (* (cbrt (+ x 1.0)) (cbrt (+ x 1.0))) (/ 1.0 n)) (pow (cbrt (+ x 1.0)) (/ 1.0 n))) (pow x (/ 1.0 n)))

simplify43.0ms

Algorithm

egg-herbie

Counts

66 → 66

Iterations

Useful iterations: 2 (35.0ms)

Iter	Nodes	Cost
0	433	788
1	1424	727
2	5001	672

prune224.0ms

Filtered

55 candidates to 66 candidates (-20.0%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	63	3	66
Fresh	0	5	5
Picked	1	0	1
Done	0	0	0
Total	64	8	72

Merged error: 20.7b

Counts

72 → 8

localize16.0ms

Local error

Found 4 expressions with local error:

0.0b	(pow (sqrt x) (/ 1.0 n))
0.3b	(pow (sqrt (+ x 1.0)) (/ 1.0 n))
0.3b	(pow (sqrt (+ x 1.0)) (/ 1.0 n))
2.0b	(- (pow (sqrt (+ x 1.0)) (/ 1.0 n)) (pow (sqrt x) (/ 1.0 n)))

rewrite32.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 133

Calls

4 calls:

4.0ms	(pow (sqrt 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)) (pow (sqrt x) (/ 1.0 n)))

series186.0ms

Counts

4 → 12

Calls

4 calls:

22.0ms	(pow (sqrt x) (/ 1.0 n))
30.0ms	(pow (sqrt (+ x 1.0)) (/ 1.0 n))
31.0ms	(pow (sqrt (+ x 1.0)) (/ 1.0 n))
103.0ms	(- (pow (sqrt (+ x 1.0)) (/ 1.0 n)) (pow (sqrt x) (/ 1.0 n)))

simplify52.0ms

Algorithm

egg-herbie

Counts

145 → 145

Iterations

Useful iterations: 2 (38.0ms)

Iter	Nodes	Cost
0	509	1263
1	1779	1221
2	5001	1203

prune388.0ms

Filtered

102 candidates to 145 candidates (-42.2%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	143	2	145
Fresh	0	7	7
Picked	1	0	1
Done	0	0	0
Total	144	9	153

Merged error: 20.7b

Counts

153 → 9

localize22.0ms

Local error

Found 4 expressions with local error:

0.3b	(pow (sqrt (+ x 1.0)) (/ 1.0 n))
2.0b	(- (pow (sqrt (+ x 1.0)) (/ 1.0 n)) (pow (sqrt x) (/ 1.0 n)))
2.0b	(- (pow (sqrt (+ x 1.0)) (/ 1.0 n)) (pow (sqrt x) (/ 1.0 n)))
2.0b	(- (pow (sqrt (+ x 1.0)) (/ 1.0 n)) (pow (sqrt x) (/ 1.0 n)))

rewrite49.0ms

Algorithm

rewrite-expression-head

Rules

85×	`add-sqr-sqrt`
73×	`unpow-prod-down`
48×	`difference-of-squares`
42×	`*-un-lft-identity`
40×	`sqrt-prod`
25×	`sqr-pow`
13×	`add-cube-cbrt` `pow-unpow`
12×	`distribute-lft-out--`
10×	`add-log-exp`
9×	`times-frac`
6×	`pow1`
5×	`add-exp-log`
4×	`add-cbrt-cube` `distribute-lft-out`
3×	`sub-neg` `flip3--` `pow-pow` `diff-log` `flip--`
1×	`pow-to-exp` `sqrt-pow1` `pow1/2` `pow-exp` `sqrt-pow2` `div-inv`

Counts

4 → 130

Calls

4 calls:

6.0ms	(pow (sqrt (+ x 1.0)) (/ 1.0 n))
13.0ms	(- (pow (sqrt (+ x 1.0)) (/ 1.0 n)) (pow (sqrt x) (/ 1.0 n)))
12.0ms	(- (pow (sqrt (+ x 1.0)) (/ 1.0 n)) (pow (sqrt x) (/ 1.0 n)))
13.0ms	(- (pow (sqrt (+ x 1.0)) (/ 1.0 n)) (pow (sqrt x) (/ 1.0 n)))

series341.0ms

Counts

4 → 12

Calls

4 calls:

29.0ms	(pow (sqrt (+ x 1.0)) (/ 1.0 n))
102.0ms	(- (pow (sqrt (+ x 1.0)) (/ 1.0 n)) (pow (sqrt x) (/ 1.0 n)))
104.0ms	(- (pow (sqrt (+ x 1.0)) (/ 1.0 n)) (pow (sqrt x) (/ 1.0 n)))
106.0ms	(- (pow (sqrt (+ x 1.0)) (/ 1.0 n)) (pow (sqrt x) (/ 1.0 n)))

simplify57.0ms

Algorithm

egg-herbie

Counts

142 → 142

Iterations

Useful iterations: 2 (36.0ms)

Iter	Nodes	Cost
0	440	2022
1	1601	1953
2	5001	1925

prune722.0ms

Filtered

98 candidates to 142 candidates (-44.9%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	140	2	142
Fresh	1	7	8
Picked	1	0	1
Done	0	0	0
Total	142	9	151

Merged error: 20.7b

Counts

151 → 9

regimes387.0ms

Accuracy

84.5% (1.6b remaining)

Error of 23.7b against oracle of 22.1b and baseline of 32.6b

bsearch139.0ms

Steps

Iters	Range		Point
6	207880946.17776674	1339344633.7650335	651939305.9106334
8	-96.06284289880654	-0.01993022418852686	-94.53466195227803

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	70	70
1	72	70
2	72	70

end0.0ms

analyze1.1s

Algorithm: search

sample6.7s

Algorithm

intervals

Results

2.1s	3781×	body	1280	valid
1.3s	1163×	body	1280	nan
677.0ms	1528×	body	640	valid
636.0ms	894×	body	640	nan
487.0ms	2764×	body	80	overflowed
235.0ms	739×	body	320	valid
186.0ms	442×	body	320	nan
181.0ms	254×	body	640	invalid
150.0ms	1611×	body	80	valid
131.0ms	101×	body	1280	invalid
75.0ms	185×	body	320	invalid
72.0ms	341×	body	160	valid
58.0ms	243×	body	160	nan
32.0ms	521×	body	80	nan
28.0ms	225×	body	80	invalid
18.0ms	75×	body	160	invalid

Details

analyze1.2s

sample226.0ms

simplify33.0ms

prune6.0ms

localize10.0ms

rewrite20.0ms

series71.0ms

simplify49.0ms

prune197.0ms

localize15.0ms

rewrite20.0ms

series113.0ms

simplify43.0ms

prune224.0ms

localize16.0ms

rewrite32.0ms

series186.0ms

simplify52.0ms

prune388.0ms

localize22.0ms

rewrite49.0ms

series341.0ms

simplify57.0ms

prune722.0ms

regimes387.0ms

bsearch139.0ms

simplify2.0ms

end0.0ms

analyze1.1s

sample6.7s

Profiling