Details

sample134.0ms

Algorithm

intervals

Results

48.0ms	105×	body	1280	valid
16.0ms	44×	body	640	valid
13.0ms	22×	body	1280	nan
9.0ms	172×	body	80	valid
9.0ms	31×	body	10240	exit
7.0ms	24×	body	640	nan
6.0ms	172×	body	80	nan
5.0ms	22×	body	320	valid
2.0ms	9×	body	320	nan
2.0ms	14×	body	160	valid
0.0ms	4×	body	160	nan

simplify40.0ms

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

1 alts after pruning (1 fresh and 0 done)

Merged error: 27.9b

localize8.0ms

Local error

Found 3 expressions with local error:

1.0b	(pow x (/ 1.0 n))
1.7b	(pow (+ x 1.0) (/ 1.0 n))
2.2b	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))

rewrite69.0ms

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:

2.0ms	(pow x (/ 1.0 n))
6.0ms	(pow (+ x 1.0) (/ 1.0 n))
52.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))

series472.0ms

Counts

3 → 9

Calls

3 calls:

55.0ms	(pow x (/ 1.0 n))
144.0ms	(pow (+ x 1.0) (/ 1.0 n))
273.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))

simplify66.0ms

Algorithm

egg-herbie

Counts

158 → 158

Iterations

Useful iterations: 2 (47.0ms)

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

prune332.0ms

Filtered

158 candidates to 95 candidates (60.1%)

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 21.3b

localize12.0ms

Local error

Found 4 expressions with local error:

1.7b	(pow (+ x 1.0) (/ 1.0 n))
2.2b	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
2.2b	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
2.2b	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))

rewrite186.0ms

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:

6.0ms	(pow (+ x 1.0) (/ 1.0 n))
52.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
54.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
56.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))

series976.0ms

Counts

4 → 12

Calls

4 calls:

150.0ms	(pow (+ x 1.0) (/ 1.0 n))
275.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
277.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
274.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))

simplify94.0ms

Algorithm

egg-herbie

Counts

312 → 312

Iterations

Useful iterations: 2 (42.0ms)

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

prune755.0ms

Filtered

312 candidates to 158 candidates (50.6%)

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 21.2b

localize33.0ms

Local error

Found 4 expressions with local error:

1.7b	(pow (+ x 1.0) (/ 1.0 n))
2.2b	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
2.2b	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
4.1b	(fma (* (cbrt (pow (+ x 1.0) (/ 1.0 n))) (cbrt (pow (+ x 1.0) (/ 1.0 n)))) (cbrt (pow (+ x 1.0) (/ 1.0 n))) (- (* (pow (cbrt x) (/ 1.0 n)) (pow (* (cbrt x) (cbrt x)) (/ 1.0 n)))))

rewrite128.0ms

Algorithm

rewrite-expression-head

Rules

136×	`unpow-prod-down`
124×	`*-un-lft-identity`
112×	`prod-diff`
100×	`add-sqr-sqrt`
76×	`add-cube-cbrt`
45×	`sqr-pow`
19×	`distribute-lft-out`
18×	`difference-of-squares`
16×	`fma-neg`
13×	`pow-unpow`
9×	`times-frac`
8×	`add-log-exp`
6×	`distribute-lft-out--`
5×	`pow1` `add-exp-log`
4×	`expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u`
2×	`sub-neg` `flip3--` `diff-log` `flip--`
1×	`pow-to-exp` `pow-pow` `pow-exp` `fma-udef` `div-inv`

Counts

4 → 220

Calls

4 calls:

6.0ms	(pow (+ x 1.0) (/ 1.0 n))
55.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
56.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
0.0ms	(fma (* (cbrt (pow (+ x 1.0) (/ 1.0 n))) (cbrt (pow (+ x 1.0) (/ 1.0 n)))) (cbrt (pow (+ x 1.0) (/ 1.0 n))) (- (* (pow (cbrt x) (/ 1.0 n)) (pow (* (cbrt x) (cbrt x)) (/ 1.0 n)))))

series1.7s

Counts

4 → 12

Calls

4 calls:

153.0ms	(pow (+ x 1.0) (/ 1.0 n))
478.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
282.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
829.0ms	(fma (* (cbrt (pow (+ x 1.0) (/ 1.0 n))) (cbrt (pow (+ x 1.0) (/ 1.0 n)))) (cbrt (pow (+ x 1.0) (/ 1.0 n))) (- (* (pow (cbrt x) (/ 1.0 n)) (pow (* (cbrt x) (cbrt x)) (/ 1.0 n)))))

simplify99.0ms

Algorithm

egg-herbie

Counts

232 → 232

Iterations

Useful iterations: 2 (60.0ms)

Iter	Nodes	Cost
0	843	4316
1	2886	3088
2	5001	3047

prune977.0ms

Filtered

232 candidates to 121 candidates (52.2%)

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 21.2b

localize43.0ms

Local error

Found 4 expressions with local error:

1.7b	(pow (+ x 1.0) (/ 1.0 n))
2.2b	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
2.2b	(- (pow (+ x 1.0) (/ (/ 1.0 n) 2)) (pow x (/ (/ 1.0 n) 2)))
4.1b	(fma (* (cbrt (pow (+ x 1.0) (/ 1.0 n))) (cbrt (pow (+ x 1.0) (/ 1.0 n)))) (cbrt (pow (+ x 1.0) (/ 1.0 n))) (- (* (pow (cbrt x) (/ 1.0 n)) (pow (* (cbrt x) (cbrt x)) (/ 1.0 n)))))

rewrite127.0ms

Algorithm

rewrite-expression-head

Rules

136×	`unpow-prod-down`
124×	`*-un-lft-identity`
112×	`prod-diff`
100×	`add-sqr-sqrt`
76×	`add-cube-cbrt`
45×	`sqr-pow`
19×	`distribute-lft-out`
18×	`difference-of-squares`
16×	`fma-neg`
13×	`pow-unpow`
9×	`times-frac`
8×	`add-log-exp`
6×	`distribute-lft-out--`
5×	`pow1` `add-exp-log`
4×	`expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u`
2×	`sub-neg` `flip3--` `diff-log` `flip--`
1×	`pow-to-exp` `pow-pow` `pow-exp` `fma-udef` `div-inv`

Counts

4 → 220

Calls

4 calls:

6.0ms	(pow (+ x 1.0) (/ 1.0 n))
55.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
55.0ms	(- (pow (+ x 1.0) (/ (/ 1.0 n) 2)) (pow x (/ (/ 1.0 n) 2)))
0.0ms	(fma (* (cbrt (pow (+ x 1.0) (/ 1.0 n))) (cbrt (pow (+ x 1.0) (/ 1.0 n)))) (cbrt (pow (+ x 1.0) (/ 1.0 n))) (- (* (pow (cbrt x) (/ 1.0 n)) (pow (* (cbrt x) (cbrt x)) (/ 1.0 n)))))

series1.5s

Counts

4 → 12

Calls

4 calls:

151.0ms	(pow (+ x 1.0) (/ 1.0 n))
287.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
284.0ms	(- (pow (+ x 1.0) (/ (/ 1.0 n) 2)) (pow x (/ (/ 1.0 n) 2)))
824.0ms	(fma (* (cbrt (pow (+ x 1.0) (/ 1.0 n))) (cbrt (pow (+ x 1.0) (/ 1.0 n)))) (cbrt (pow (+ x 1.0) (/ 1.0 n))) (- (* (pow (cbrt x) (/ 1.0 n)) (pow (* (cbrt x) (cbrt x)) (/ 1.0 n)))))

simplify132.0ms

Algorithm

egg-herbie

Counts

232 → 232

Iterations

Useful iterations: 2 (86.0ms)

Iter	Nodes	Cost
0	1168	4695
1	3901	3367
2	5001	3348

prune1.2s

Filtered

232 candidates to 127 candidates (54.7%)

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 21.2b

regimes282.0ms

Accuracy

84.8% (1.3b remaining)

Error of 22.5b against oracle of 21.2b and baseline of 29.8b

bsearch2.0ms

simplify3.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	91	165
1	93	165
2	93	165

end0.0ms

sample4.3s

Algorithm

intervals

Results

1.5s	3227×	body	1280	valid
551.0ms	1581×	body	640	valid
521.0ms	1194×	body	10240	exit
304.0ms	658×	body	1280	nan
256.0ms	4751×	body	80	valid
219.0ms	657×	body	640	nan
201.0ms	5141×	body	80	nan
190.0ms	853×	body	320	valid
66.0ms	348×	body	320	nan
59.0ms	426×	body	160	valid
22.0ms	193×	body	160	nan