Details

sample239.0ms

Algorithm

intervals

Results

74.0ms	133×	body	1280	valid
40.0ms	40×	body	1280	nan
23.0ms	51×	body	640	valid
21.0ms	24×	body	640	nan
20.0ms	137×	body	80	overflowed
11.0ms	218×	body	80	nan
11.0ms	33×	body	320	valid
9.0ms	93×	body	80	valid
6.0ms	14×	body	320	nan
3.0ms	13×	body	160	valid
1.0ms	4×	body	160	nan

simplify36.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	17	6
1	35	6
2	85	6
3	249	6
4	911	6
5	5001	6

prune2.0ms

Filtered

1 candidates to 0 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: 32.2b

Counts

2 → 1

localize9.0ms

Local error

Found 3 expressions with local error:

0.1b	(pow x (/ 1.0 n))
0.1b	(pow (+ x 1.0) (/ 1.0 n))
2.1b	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))

rewrite27.0ms

Algorithm

rewrite-expression-head

Rules

76×	`*-un-lft-identity`
73×	`unpow-prod-down`
63×	`add-sqr-sqrt`
56×	`prod-diff`
51×	`add-cube-cbrt`
26×	`pow-unpow`
24×	`sqr-pow`
18×	`times-frac`
10×	`distribute-lft-out`
9×	`difference-of-squares`
8×	`fma-neg`
5×	`pow1` `add-exp-log` `add-log-exp`
3×	`expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u` `distribute-lft-out--`
2×	`pow-to-exp` `pow-pow` `pow-exp` `div-inv`
1×	`sub-neg` `flip3--` `diff-log` `flip--`

Counts

3 → 149

Calls

3 calls:

3.0ms	(pow x (/ 1.0 n))
6.0ms	(pow (+ x 1.0) (/ 1.0 n))
11.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))

series469.0ms

Counts

3 → 9

Calls

3 calls:

60.0ms	(pow x (/ 1.0 n))
140.0ms	(pow (+ x 1.0) (/ 1.0 n))
269.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))

simplify68.0ms

Algorithm

egg-herbie

Counts

158 → 158

Iterations

Useful iterations: 2 (48.0ms)

Iter	Nodes	Cost
0	654	2164
1	2164	1642
2	5002	1637

prune283.0ms

Filtered

158 candidates to 95 candidates (60.1%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	151	7	158
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	152	7	159

Merged error: 23.9b

Counts

159 → 7

localize13.0ms

Local error

Found 4 expressions with local error:

0.1b	(pow (+ x 1.0) (/ 1.0 n))
2.1b	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
2.1b	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
2.1b	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))

rewrite58.0ms

Algorithm

rewrite-expression-head

Rules

202×	`unpow-prod-down`
179×	`*-un-lft-identity`
168×	`prod-diff`
144×	`add-sqr-sqrt`
108×	`add-cube-cbrt`
67×	`sqr-pow`
28×	`distribute-lft-out`
27×	`difference-of-squares`
24×	`fma-neg`
13×	`pow-unpow`
10×	`add-log-exp`
9×	`times-frac` `distribute-lft-out--`
5×	`pow1` `add-exp-log`
4×	`expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u`
3×	`sub-neg` `flip3--` `diff-log` `flip--`
1×	`pow-to-exp` `pow-pow` `pow-exp` `div-inv`

Counts

4 → 300

Calls

4 calls:

9.0ms	(pow (+ x 1.0) (/ 1.0 n))
11.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
11.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
11.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))

series966.0ms

Counts

4 → 12

Calls

4 calls:

148.0ms	(pow (+ x 1.0) (/ 1.0 n))
273.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
270.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
275.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))

simplify101.0ms

Algorithm

egg-herbie

Counts

312 → 312

Iterations

Useful iterations: 2 (48.0ms)

Iter	Nodes	Cost
0	542	5691
1	1694	4129
2	5001	4126

prune626.0ms

Filtered

312 candidates to 158 candidates (50.6%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	311	1	312
Fresh	0	6	6
Picked	0	1	1
Done	0	0	0
Total	311	8	319

Merged error: 23.9b

Counts

319 → 8

localize28.0ms

Local error

Found 4 expressions with local error:

0.1b	(pow (+ x 1.0) (/ 1.0 n))
2.1b	(- (pow (sqrt (+ x 1.0)) (/ 1.0 n)) (pow (sqrt x) (/ 1.0 n)))
2.1b	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
2.1b	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))

rewrite71.0ms

Algorithm

rewrite-expression-head

Rules

301×	`unpow-prod-down`
222×	`prod-diff`
221×	`*-un-lft-identity`
190×	`add-sqr-sqrt`
142×	`add-cube-cbrt`
89×	`sqrt-prod`
75×	`sqr-pow`
34×	`difference-of-squares`
31×	`distribute-lft-out`
27×	`fma-neg`
13×	`pow-unpow`
10×	`distribute-lft-out--` `add-log-exp`
9×	`times-frac`
5×	`pow1` `add-exp-log`
4×	`expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u`
3×	`sub-neg` `flip3--` `diff-log` `flip--`
1×	`pow-to-exp` `pow-pow` `pow-exp` `div-inv`

Counts

4 → 365

Calls

4 calls:

6.0ms	(pow (+ x 1.0) (/ 1.0 n))
17.0ms	(- (pow (sqrt (+ x 1.0)) (/ 1.0 n)) (pow (sqrt x) (/ 1.0 n)))
12.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
12.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))

series1.4s

Counts

4 → 12

Calls

4 calls:

143.0ms	(pow (+ x 1.0) (/ 1.0 n))
717.0ms	(- (pow (sqrt (+ x 1.0)) (/ 1.0 n)) (pow (sqrt x) (/ 1.0 n)))
273.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
276.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))

simplify145.0ms

Algorithm

egg-herbie

Counts

377 → 377

Iterations

Useful iterations: 2 (74.0ms)

Iter	Nodes	Cost
0	973	8393
1	2949	5988
2	5001	5957

prune1.0s

Filtered

377 candidates to 168 candidates (44.6%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	375	2	377
Fresh	0	6	6
Picked	1	0	1
Done	1	0	1
Total	377	8	385

Merged error: 23.8b

Counts

385 → 8

localize21.0ms

Local error

Found 4 expressions with local error:

0.1b	(pow (sqrt x) (* 2 (/ 1.0 n)))
0.1b	(pow (+ x 1.0) (/ 1.0 n))
2.1b	(- (pow (+ x 1.0) (/ 1.0 n)) (pow (sqrt x) (* 2 (/ 1.0 n))))
4.1b	(fma (pow (sqrt x) (/ 1.0 n)) (- (pow (sqrt x) (/ 1.0 n))) (pow (sqrt x) (* 2 (/ 1.0 n))))

rewrite31.0ms

Algorithm

rewrite-expression-head

Rules

112×	`unpow-prod-down`
86×	`*-un-lft-identity`
80×	`prod-diff`
77×	`add-sqr-sqrt`
60×	`add-cube-cbrt`
30×	`sqrt-prod`
28×	`sqr-pow`
14×	`pow-unpow`
12×	`distribute-lft-out` `difference-of-squares`
9×	`times-frac`
8×	`fma-neg`
7×	`pow1`
6×	`add-exp-log` `add-log-exp`
4×	`expm1-log1p-u` `pow-pow` `add-cbrt-cube` `log1p-expm1-u`
2×	`pow-to-exp` `pow-exp`
1×	`sub-neg` `flip3--` `sqrt-pow1` `pow1/2` `diff-log` `sqrt-pow2` `flip--` `fma-udef` `div-inv` `distribute-lft-out--`

Counts

4 → 178

Calls

4 calls:

3.0ms	(pow (sqrt x) (* 2 (/ 1.0 n)))
5.0ms	(pow (+ x 1.0) (/ 1.0 n))
13.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow (sqrt x) (* 2 (/ 1.0 n))))
1.0ms	(fma (pow (sqrt x) (/ 1.0 n)) (- (pow (sqrt x) (/ 1.0 n))) (pow (sqrt x) (* 2 (/ 1.0 n))))

series1.9s

Counts

4 → 12

Calls

4 calls:

212.0ms	(pow (sqrt x) (* 2 (/ 1.0 n)))
152.0ms	(pow (+ x 1.0) (/ 1.0 n))
448.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow (sqrt x) (* 2 (/ 1.0 n))))
1.1s	(fma (pow (sqrt x) (/ 1.0 n)) (- (pow (sqrt x) (/ 1.0 n))) (pow (sqrt x) (* 2 (/ 1.0 n))))

simplify106.0ms

Algorithm

egg-herbie

Counts

190 → 190

Iterations

Useful iterations: 2 (66.0ms)

Iter	Nodes	Cost
0	775	4136
1	2778	2972
2	5001	2949

prune424.0ms

Filtered

190 candidates to 101 candidates (53.2%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	187	3	190
Fresh	2	5	7
Picked	1	0	1
Done	0	0	0
Total	190	8	198

Merged error: 23.8b

Counts

198 → 8

regimes231.0ms

Accuracy

82.6% (1.8b remaining)

Error of 24.4b against oracle of 22.6b and baseline of 32.9b

bsearch1.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	65	71
1	65	71

end0.0ms

sample7.2s

Algorithm

intervals

Results

2.1s	3910×	body	1280	valid
1.2s	1115×	body	1280	nan
827.0ms	1813×	body	640	valid
634.0ms	908×	body	640	nan
613.0ms	4125×	body	80	overflowed
312.0ms	3100×	body	80	valid
307.0ms	6269×	body	80	nan
288.0ms	923×	body	320	valid
183.0ms	436×	body	320	nan
89.0ms	452×	body	160	valid
53.0ms	231×	body	160	nan