Details

sample232.0ms

Algorithm

intervals

Results

75.0ms	128×	body	1280	valid
33.0ms	28×	body	1280	nan
26.0ms	55×	body	640	valid
18.0ms	26×	body	640	nan
18.0ms	113×	body	80	overflowed
11.0ms	33×	body	320	valid
10.0ms	192×	body	80	nan
9.0ms	90×	body	80	valid
5.0ms	12×	body	320	nan
3.0ms	14×	body	160	valid
1.0ms	5×	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

prune3.0ms

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: 33.2b

Counts

2 → 1

localize8.0ms

Local error

Found 3 expressions with local error:

0.0b	(pow x (/ 1.0 n))
0.1b	(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))
17.0ms	(pow (+ x 1.0) (/ 1.0 n))
42.0ms	(- (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

prune187.0ms

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: 22.2b

Counts

89 → 6

localize12.0ms

Local error

Found 4 expressions with local error:

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))))
0.1b	(pow (sqrt (+ x 1.0)) (/ 1.0 n))
0.1b	(pow (sqrt (+ x 1.0)) (/ 1.0 n))
2.0b	(- (pow (sqrt (+ x 1.0)) (/ 1.0 n)) (pow (sqrt x) (/ 1.0 n)))

rewrite64.0ms

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:

33.0ms	(* (+ (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))))
6.0ms	(pow (sqrt (+ x 1.0)) (/ 1.0 n))
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)))

series360.0ms

Counts

4 → 12

Calls

4 calls:

194.0ms	(* (+ (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))))
31.0ms	(pow (sqrt (+ x 1.0)) (/ 1.0 n))
30.0ms	(pow (sqrt (+ x 1.0)) (/ 1.0 n))
104.0ms	(- (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 (70.0ms)

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

prune476.0ms

Filtered

114 candidates to 166 candidates (-45.6%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	165	1	166
Fresh	0	5	5
Picked	1	0	1
Done	0	0	0
Total	166	6	172

Merged error: 22.2b

Counts

172 → 6

localize18.0ms

Local error

Found 4 expressions with local error:

0.1b	(pow (sqrt (+ x 1.0)) (/ 1.0 n))
0.1b	(pow (sqrt (+ x 1.0)) (/ 1.0 n))
0.1b	(pow (sqrt (+ x 1.0)) (/ 1.0 n))
2.0b	(- (pow (sqrt (+ x 1.0)) (/ 1.0 n)) (pow (sqrt x) (/ 1.0 n)))

rewrite36.0ms

Algorithm

rewrite-expression-head

Rules

55×	`add-sqr-sqrt`
46×	`*-un-lft-identity`
43×	`unpow-prod-down`
39×	`pow-unpow`
31×	`add-cube-cbrt`
27×	`times-frac`
24×	`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` `distribute-lft-out--`
3×	`pow-to-exp` `sqrt-pow1` `pow1/2` `pow-exp` `sqrt-pow2` `div-inv`
1×	`sub-neg` `flip3--` `diff-log` `flip--`

Counts

4 → 134

Calls

4 calls:

6.0ms	(pow (sqrt (+ x 1.0)) (/ 1.0 n))
6.0ms	(pow (sqrt (+ x 1.0)) (/ 1.0 n))
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)))

series198.0ms

Counts

4 → 12

Calls

4 calls:

30.0ms	(pow (sqrt (+ x 1.0)) (/ 1.0 n))
30.0ms	(pow (sqrt (+ x 1.0)) (/ 1.0 n))
32.0ms	(pow (sqrt (+ x 1.0)) (/ 1.0 n))
106.0ms	(- (pow (sqrt (+ x 1.0)) (/ 1.0 n)) (pow (sqrt x) (/ 1.0 n)))

simplify50.0ms

Algorithm

egg-herbie

Counts

146 → 146

Iterations

Useful iterations: 2 (35.0ms)

Iter	Nodes	Cost
0	440	1314
1	1601	1267
2	5001	1247

prune554.0ms

Filtered

102 candidates to 146 candidates (-43.1%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	145	1	146
Fresh	0	5	5
Picked	1	0	1
Done	0	0	0
Total	146	6	152

Merged error: 22.2b

Counts

152 → 6

localize22.0ms

Local error

Found 4 expressions with local error:

0.1b	(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)))

rewrite53.0ms

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)))
15.0ms	(- (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)))

series347.0ms

Counts

4 → 12

Calls

4 calls:

31.0ms	(pow (sqrt (+ x 1.0)) (/ 1.0 n))
106.0ms	(- (pow (sqrt (+ x 1.0)) (/ 1.0 n)) (pow (sqrt x) (/ 1.0 n)))
105.0ms	(- (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)))

simplify55.0ms

Algorithm

egg-herbie

Counts

142 → 142

Iterations

Useful iterations: 2 (36.0ms)

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

prune997.0ms

Filtered

98 candidates to 142 candidates (-44.9%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	138	4	142
Fresh	1	4	5
Picked	1	0	1
Done	0	0	0
Total	140	8	148

Merged error: 22.2b

Counts

148 → 8

regimes469.0ms

Accuracy

83% (1.9b remaining)

Error of 23.8b against oracle of 22.0b and baseline of 32.9b

bsearch1.0ms

simplify3.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	77	93
1	79	93
2	79	93

end0.0ms

sample7.4s

Algorithm

intervals

Results

2.2s	3917×	body	1280	valid
1.2s	1108×	body	1280	nan
835.0ms	1778×	body	640	valid
652.0ms	929×	body	640	nan
606.0ms	4068×	body	80	overflowed
325.0ms	6205×	body	80	nan
323.0ms	3110×	body	80	valid
294.0ms	897×	body	320	valid
189.0ms	446×	body	320	nan
97.0ms	480×	body	160	valid
52.0ms	236×	body	160	nan

Details

sample232.0ms

simplify33.0ms

prune3.0ms

localize8.0ms

rewrite20.0ms

series71.0ms

simplify49.0ms

prune187.0ms

localize12.0ms

rewrite64.0ms

series360.0ms

simplify90.0ms

prune476.0ms

localize18.0ms

rewrite36.0ms

series198.0ms

simplify50.0ms

prune554.0ms

localize22.0ms

rewrite53.0ms

series347.0ms

simplify55.0ms

prune997.0ms

regimes469.0ms

bsearch1.0ms

simplify3.0ms

end0.0ms

sample7.4s

Profiling