Details

sample170.0ms

Algorithm

intervals

Results

69.0ms	112×	body	1280	valid
27.0ms	59×	body	640	valid
12.0ms	17×	body	1280	nan
12.0ms	150×	body	80	valid
10.0ms	22×	body	640	nan
9.0ms	161×	body	80	nan
5.0ms	18×	body	320	valid
3.0ms	40×	body	80	overflowed
2.0ms	10×	body	160	nan
2.0ms	8×	body	320	nan
1.0ms	7×	body	160	valid

simplify35.0ms

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

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 28.5b

localize8.0ms

Local error

Found 3 expressions with local error:

0.3b	(pow x (/ 1.0 n))
0.5b	(pow (+ x 1.0) (/ 1.0 n))
0.6b	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))

rewrite63.0ms

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))
5.0ms	(pow (+ x 1.0) (/ 1.0 n))
49.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))

series474.0ms

Counts

3 → 9

Calls

3 calls:

55.0ms	(pow x (/ 1.0 n))
148.0ms	(pow (+ x 1.0) (/ 1.0 n))
271.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))

simplify72.0ms

Algorithm

egg-herbie

Counts

158 → 158

Iterations

Useful iterations: 2 (47.0ms)

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

prune324.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 20.0b

localize14.0ms

Local error

Found 4 expressions with local error:

0.3b	(pow x (/ 1.0 n))
0.5b	(pow (+ x 1.0) (/ 1.0 n))
0.6b	(log (exp (- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))))
0.6b	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))

rewrite165.0ms

Algorithm

rewrite-expression-head

Rules

135×	`unpow-prod-down`
130×	`*-un-lft-identity`
112×	`prod-diff`
108×	`add-sqr-sqrt`
84×	`add-cube-cbrt`
61×	`log-prod`
58×	`exp-sum`
45×	`sqr-pow`
26×	`pow-unpow`
18×	`times-frac` `distribute-lft-out` `difference-of-squares`
16×	`log-pow`
15×	`exp-prod`
8×	`fma-neg`
7×	`pow1`
6×	`add-exp-log` `distribute-lft-out--` `add-log-exp`
4×	`expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u`
2×	`pow-to-exp` `sub-neg` `pow-pow` `pow-exp` `div-inv`
1×	`log-div` `flip3--` `exp-diff` `diff-log` `rem-log-exp` `flip--`

Counts

4 → 237

Calls

4 calls:

2.0ms	(pow x (/ 1.0 n))
5.0ms	(pow (+ x 1.0) (/ 1.0 n))
98.0ms	(log (exp (- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))))
47.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))

series759.0ms

Counts

4 → 12

Calls

4 calls:

63.0ms	(pow x (/ 1.0 n))
148.0ms	(pow (+ x 1.0) (/ 1.0 n))
272.0ms	(log (exp (- (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)))

simplify85.0ms

Algorithm

egg-herbie

Counts

249 → 249

Iterations

Useful iterations: 2 (52.0ms)

Iter	Nodes	Cost
0	835	3935
1	2477	2885
2	5001	2880

prune514.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 20.0b

localize12.0ms

Local error

Found 4 expressions with local error:

0.5b	(pow (+ x 1.0) (/ 1.0 n))
0.6b	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
0.6b	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
0.6b	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))

rewrite170.0ms

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:

5.0ms	(pow (+ x 1.0) (/ 1.0 n))
47.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
49.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
51.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))

series977.0ms

Counts

4 → 12

Calls

4 calls:

150.0ms	(pow (+ x 1.0) (/ 1.0 n))
274.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
273.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
279.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))

simplify94.0ms

Algorithm

egg-herbie

Counts

312 → 312

Iterations

Useful iterations: 2 (45.0ms)

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

prune794.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 20.0b

localize22.0ms

Local error

Found 4 expressions with local error:

0.5b	(pow (+ x 1.0) (/ 1.0 n))
0.6b	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
0.6b	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
0.6b	(- (pow (+ x 1.0) (/ (/ 1.0 n) 2)) (pow x (/ (/ 1.0 n) 2)))

rewrite171.0ms

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:

5.0ms	(pow (+ x 1.0) (/ 1.0 n))
47.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
49.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
52.0ms	(- (pow (+ x 1.0) (/ (/ 1.0 n) 2)) (pow x (/ (/ 1.0 n) 2)))

series995.0ms

Counts

4 → 12

Calls

4 calls:

153.0ms	(pow (+ x 1.0) (/ 1.0 n))
280.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
279.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
283.0ms	(- (pow (+ x 1.0) (/ (/ 1.0 n) 2)) (pow x (/ (/ 1.0 n) 2)))

simplify126.0ms

Algorithm

egg-herbie

Counts

312 → 312

Iterations

Useful iterations: 2 (70.0ms)

Iter	Nodes	Cost
0	867	6070
1	2705	4345
2	5001	4341

prune967.0ms

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 20.0b

regimes308.0ms

Accuracy

82.9% (1.4b remaining)

Error of 22.3b against oracle of 20.9b and baseline of 29.0b

bsearch2.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	61	86
1	61	86

end0.0ms

sample5.2s

Algorithm

intervals

Results

1.9s	3182×	body	1280	valid
749.0ms	1645×	body	640	valid
595.0ms	637×	body	1280	nan
382.0ms	4691×	body	80	valid
284.0ms	4954×	body	80	nan
270.0ms	610×	body	640	nan
245.0ms	779×	body	320	valid
95.0ms	354×	body	320	nan
94.0ms	1220×	body	80	overflowed
90.0ms	445×	body	160	valid
30.0ms	183×	body	160	nan