Details

sample703.0ms

Algorithm

intervals

Results

82.0ms	80×	body	1280	nan
74.0ms	117×	body	1280	valid
39.0ms	60×	body	640	nan
20.0ms	45×	body	640	valid
16.0ms	100×	body	80	overflowed
16.0ms	39×	body	320	nan
14.0ms	141×	body	80	valid
13.0ms	275×	body	80	nan
7.0ms	20×	body	320	valid
4.0ms	16×	body	160	nan
2.0ms	12×	body	160	valid

simplify34.0ms

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

prune3.0ms

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: 28.5b

Counts

2 → 1

localize8.0ms

Local error

Found 3 expressions with local error:

0.0b	(pow x (/ 1.0 n))
0.0b	(pow (+ x 1.0) (/ 1.0 n))
2.2b	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))

rewrite19.0ms

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))
8.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))

series68.0ms

Counts

3 → 9

Calls

3 calls:

11.0ms	(pow x (/ 1.0 n))
19.0ms	(pow (+ x 1.0) (/ 1.0 n))
37.0ms	(- (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

prune173.0ms

Filtered

88 candidates to 71 candidates (19.3%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	84	4	88
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	85	4	89

Merged error: 19.5b

Counts

89 → 4

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b	(pow (sqrt (+ x 1.0)) (/ 1.0 n))
0.0b	(pow (sqrt (+ x 1.0)) (/ 1.0 n))
0.0b	(* (+ (pow (sqrt (+ x 1.0)) (/ 1.0 n)) (pow (sqrt x) (/ 1.0 n))) (- (pow (sqrt (+ x 1.0)) (/ 1.0 n)) (pow (sqrt x) (/ 1.0 n))))
2.2b	(- (pow (sqrt (+ x 1.0)) (/ 1.0 n)) (pow (sqrt x) (/ 1.0 n)))

rewrite60.0ms

Algorithm

rewrite-expression-head

Rules

74×	`add-sqr-sqrt`
64×	`unpow-prod-down`
55×	`*-un-lft-identity`
36×	`sqrt-prod`
32×	`difference-of-squares`
26×	`pow-unpow`
24×	`add-cube-cbrt`
23×	`associate-r`
18×	`times-frac` `sqr-pow`
10×	`pow1`
9×	`distribute-lft-out`
8×	`add-exp-log` `distribute-lft-out--`
7×	`associate-l`
6×	`pow-pow` `add-cbrt-cube` `add-log-exp`
4×	`frac-times` `flip3--` `flip--`
3×	`sub-neg` `flip3-+` `flip-+`
2×	`distribute-rgt-in` `pow-to-exp` `distribute-lft-in` `sqrt-pow1` `pow1/2` `associate-r/` `associate-l/` `pow-exp` `sqrt-pow2` `div-inv`
1×	`diff-log` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `unswap-sqr`

Counts

4 → 154

Calls

4 calls:

6.0ms	(pow (sqrt (+ x 1.0)) (/ 1.0 n))
6.0ms	(pow (sqrt (+ x 1.0)) (/ 1.0 n))
29.0ms	(* (+ (pow (sqrt (+ x 1.0)) (/ 1.0 n)) (pow (sqrt x) (/ 1.0 n))) (- (pow (sqrt (+ x 1.0)) (/ 1.0 n)) (pow (sqrt x) (/ 1.0 n))))
14.0ms	(- (pow (sqrt (+ x 1.0)) (/ 1.0 n)) (pow (sqrt x) (/ 1.0 n)))

series350.0ms

Counts

4 → 12

Calls

4 calls:

31.0ms	(pow (sqrt (+ x 1.0)) (/ 1.0 n))
29.0ms	(pow (sqrt (+ x 1.0)) (/ 1.0 n))
187.0ms	(* (+ (pow (sqrt (+ x 1.0)) (/ 1.0 n)) (pow (sqrt x) (/ 1.0 n))) (- (pow (sqrt (+ x 1.0)) (/ 1.0 n)) (pow (sqrt x) (/ 1.0 n))))
102.0ms	(- (pow (sqrt (+ x 1.0)) (/ 1.0 n)) (pow (sqrt x) (/ 1.0 n)))

simplify90.0ms

Algorithm

egg-herbie

Counts

166 → 166

Iterations

Useful iterations: 2 (68.0ms)

Iter	Nodes	Cost
0	697	2349
1	3117	2202
2	5002	2186

prune470.0ms

Filtered

166 candidates to 114 candidates (31.3%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	164	2	166
Fresh	0	3	3
Picked	1	0	1
Done	0	0	0
Total	165	5	170

Merged error: 19.5b

Counts

170 → 5

localize17.0ms

Local error

Found 4 expressions with local error:

0.1b	(cbrt (- (pow (sqrt (+ x 1.0)) (/ 1.0 n)) (pow (sqrt x) (/ 1.0 n))))
2.2b	(- (pow (sqrt (+ x 1.0)) (/ 1.0 n)) (pow (sqrt x) (/ 1.0 n)))
2.2b	(- (pow (sqrt (+ x 1.0)) (/ 1.0 n)) (pow (sqrt x) (/ 1.0 n)))
2.2b	(- (pow (sqrt (+ x 1.0)) (/ 1.0 n)) (pow (sqrt x) (/ 1.0 n)))

rewrite57.0ms

Algorithm

rewrite-expression-head

Rules

101×	`add-sqr-sqrt`
88×	`unpow-prod-down`
64×	`difference-of-squares`
48×	`sqrt-prod`
41×	`*-un-lft-identity`
32×	`sqr-pow`
23×	`cbrt-prod`
16×	`distribute-lft-out--`
10×	`add-log-exp`
5×	`add-cube-cbrt`
4×	`pow1` `add-exp-log` `flip3--` `add-cbrt-cube` `flip--` `distribute-lft-out`
3×	`sub-neg` `diff-log`
2×	`cbrt-div`
1×	`pow1/3`

Counts

4 → 129

Calls

4 calls:

12.0ms	(cbrt (- (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)))
14.0ms	(- (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)))

series752.0ms

Counts

4 → 12

Calls

4 calls:

443.0ms	(cbrt (- (pow (sqrt (+ x 1.0)) (/ 1.0 n)) (pow (sqrt x) (/ 1.0 n))))
103.0ms	(- (pow (sqrt (+ x 1.0)) (/ 1.0 n)) (pow (sqrt x) (/ 1.0 n)))
102.0ms	(- (pow (sqrt (+ x 1.0)) (/ 1.0 n)) (pow (sqrt x) (/ 1.0 n)))
103.0ms	(- (pow (sqrt (+ x 1.0)) (/ 1.0 n)) (pow (sqrt x) (/ 1.0 n)))

simplify69.0ms

Algorithm

egg-herbie

Counts

141 → 141

Iterations

Useful iterations: 2 (45.0ms)

Iter	Nodes	Cost
0	554	2652
1	2016	2567
2	5001	2524

prune785.0ms

Filtered

141 candidates to 96 candidates (31.9%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	139	2	141
Fresh	1	3	4
Picked	1	0	1
Done	0	0	0
Total	141	5	146

Merged error: 19.5b

Counts

146 → 5

localize24.0ms

Local error

Found 4 expressions with local error:

2.2b	(- (pow (sqrt (+ x 1.0)) (/ 1.0 n)) (pow (sqrt x) (/ 1.0 n)))
2.2b	(- (pow (sqrt (+ x 1.0)) (/ 1.0 n)) (pow (sqrt x) (/ 1.0 n)))
2.2b	(- (pow (sqrt (+ x 1.0)) (/ 1.0 n)) (pow (sqrt x) (/ 1.0 n)))
2.2b	(- (pow (sqrt (+ x 1.0)) (/ 1.0 n)) (pow (sqrt x) (/ 1.0 n)))

rewrite55.0ms

Algorithm

rewrite-expression-head

Rules

100×	`add-sqr-sqrt`
88×	`unpow-prod-down`
64×	`difference-of-squares`
48×	`sqrt-prod`
40×	`*-un-lft-identity`
32×	`sqr-pow`
16×	`distribute-lft-out--`
12×	`add-log-exp`
4×	`pow1` `add-exp-log` `add-cube-cbrt` `sub-neg` `flip3--` `diff-log` `add-cbrt-cube` `flip--` `distribute-lft-out`

Counts

4 → 128

Calls

4 calls:

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)))
12.0ms	(- (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)))

series407.0ms

Counts

4 → 12

Calls

4 calls:

101.0ms	(- (pow (sqrt (+ x 1.0)) (/ 1.0 n)) (pow (sqrt x) (/ 1.0 n)))
101.0ms	(- (pow (sqrt (+ x 1.0)) (/ 1.0 n)) (pow (sqrt x) (/ 1.0 n)))
101.0ms	(- (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)))

simplify165.0ms

Algorithm

egg-herbie

Counts

140 → 140

Iterations

Useful iterations: 2 (29.0ms)

Iter	Nodes	Cost
0	280	2376
1	961	2296
2	4702	2264
3	5003	2264

prune1.2s

Filtered

140 candidates to 96 candidates (31.4%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	140	0	140
Fresh	0	4	4
Picked	0	1	1
Done	0	0	0
Total	140	5	145

Merged error: 19.5b

Counts

145 → 5

regimes313.0ms

Accuracy

86% (1.5b remaining)

Error of 22.8b against oracle of 21.4b and baseline of 31.9b

bsearch155.0ms

Steps

Iters	Range		Point
11	8.67208259622753e-23	15420789.458085801	5036922.014807805
9	-22570177679.430683	-12722.186881915235	-177055548.10463205

simplify3.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	61	76
1	63	76
2	63	76

end0.0ms

sample9.2s

Algorithm

intervals

Results

2.1s	2091×	body	1280	nan
2.0s	3729×	body	1280	valid
1.2s	1726×	body	640	nan
690.0ms	1558×	body	640	valid
423.0ms	3910×	body	80	valid
415.0ms	2601×	body	80	overflowed
383.0ms	7919×	body	80	nan
365.0ms	881×	body	320	nan
237.0ms	769×	body	320	valid
98.0ms	442×	body	160	nan
70.0ms	363×	body	160	valid

Details

sample703.0ms

simplify34.0ms

prune3.0ms

localize8.0ms

rewrite19.0ms

series68.0ms

simplify49.0ms

prune173.0ms

localize13.0ms

rewrite60.0ms

series350.0ms

simplify90.0ms

prune470.0ms

localize17.0ms

rewrite57.0ms

series752.0ms

simplify69.0ms

prune785.0ms

localize24.0ms

rewrite55.0ms

series407.0ms

simplify165.0ms

prune1.2s

regimes313.0ms

bsearch155.0ms

simplify3.0ms

end0.0ms

sample9.2s

Profiling