Details

sample176.0ms

Algorithm

intervals

Results

62.0ms	100×	body	1280	valid
25.0ms	52×	body	640	valid
15.0ms	140×	body	80	valid
13.0ms	164×	body	80	nan
13.0ms	17×	body	1280	nan
8.0ms	27×	body	320	valid
8.0ms	19×	body	640	nan
7.0ms	10×	body	320	nan
4.0ms	16×	body	160	valid
3.0ms	31×	body	80	overflowed
2.0ms	10×	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

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 29.4b

localize8.0ms

Local error

Found 3 expressions with local error:

0.5b	(pow x (/ 1.0 n))
1.0b	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
1.7b	(pow (+ x 1.0) (/ 1.0 n))

rewrite67.0ms

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))
49.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
9.0ms	(pow (+ x 1.0) (/ 1.0 n))

series484.0ms

Counts

3 → 9

Calls

3 calls:

60.0ms	(pow x (/ 1.0 n))
275.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
149.0ms	(pow (+ x 1.0) (/ 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

prune339.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 20.9b

localize11.0ms

Local error

Found 4 expressions with local error:

0.1b	(log (- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n))))
0.5b	(pow x (/ 1.0 n))
1.0b	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
1.7b	(pow (+ x 1.0) (/ 1.0 n))

rewrite96.0ms

Algorithm

rewrite-expression-head

Rules

85×	`*-un-lft-identity`
83×	`unpow-prod-down`
77×	`add-sqr-sqrt`
56×	`prod-diff`
53×	`add-cube-cbrt`
30×	`sqr-pow`
26×	`pow-unpow`
18×	`times-frac` `difference-of-squares`
15×	`log-prod`
11×	`distribute-lft-out`
8×	`fma-neg`
7×	`pow1` `add-exp-log`
6×	`distribute-lft-out--` `add-log-exp`
4×	`expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u`
2×	`pow-to-exp` `log-div` `flip3--` `pow-pow` `pow-exp` `flip--` `div-inv`
1×	`sub-neg` `diff-log` `rem-log-exp` `log-pow`

Counts

4 → 177

Calls

4 calls:

27.0ms	(log (- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n))))
2.0ms	(pow x (/ 1.0 n))
53.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
6.0ms	(pow (+ x 1.0) (/ 1.0 n))

series969.0ms

Counts

4 → 12

Calls

4 calls:

468.0ms	(log (- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n))))
64.0ms	(pow x (/ 1.0 n))
281.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
156.0ms	(pow (+ x 1.0) (/ 1.0 n))

simplify77.0ms

Algorithm

egg-herbie

Counts

189 → 189

Iterations

Useful iterations: 2 (54.0ms)

Iter	Nodes	Cost
0	741	2591
1	2415	2042
2	5001	2037

prune510.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 20.4b

localize15.0ms

Local error

Found 4 expressions with local error:

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

rewrite79.0ms

Algorithm

rewrite-expression-head

Rules

89×	`*-un-lft-identity`
78×	`unpow-prod-down`
72×	`add-sqr-sqrt`
60×	`add-cube-cbrt`
56×	`prod-diff`
39×	`pow-unpow`
27×	`times-frac`
25×	`sqr-pow`
12×	`distribute-lft-out`
9×	`difference-of-squares`
8×	`fma-neg`
7×	`pow1` `add-exp-log`
6×	`add-log-exp`
4×	`expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u`
3×	`pow-to-exp` `pow-pow` `pow-exp` `div-inv` `distribute-lft-out--`
1×	`sub-neg` `flip3--` `diff-log` `flip--`

Counts

4 → 180

Calls

4 calls:

50.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
6.0ms	(pow (+ x 1.0) (/ 1.0 n))
10.0ms	(pow (+ x 1.0) (/ 1.0 n))
6.0ms	(pow (+ x 1.0) (/ 1.0 n))

series750.0ms

Counts

4 → 12

Calls

4 calls:

284.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
156.0ms	(pow (+ x 1.0) (/ 1.0 n))
156.0ms	(pow (+ x 1.0) (/ 1.0 n))
153.0ms	(pow (+ x 1.0) (/ 1.0 n))

simplify64.0ms

Algorithm

egg-herbie

Counts

192 → 192

Iterations

Useful iterations: 2 (43.0ms)

Iter	Nodes	Cost
0	542	2353
1	1694	1827
2	5001	1826

prune669.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 20.4b

localize30.0ms

Local error

Found 4 expressions with local error:

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

rewrite26.0ms

Algorithm

rewrite-expression-head

Rules

52×	`pow-unpow`
44×	`*-un-lft-identity`
36×	`add-sqr-sqrt` `add-cube-cbrt` `times-frac`
16×	`unpow-prod-down`
8×	`pow1` `add-exp-log`
4×	`expm1-log1p-u` `pow-to-exp` `pow-pow` `pow-exp` `add-cbrt-cube` `log1p-expm1-u` `div-inv` `distribute-lft-out` `add-log-exp` `sqr-pow`

Counts

4 → 120

Calls

4 calls:

5.0ms	(pow (+ x 1.0) (/ 1.0 n))
5.0ms	(pow (+ x 1.0) (/ 1.0 n))
5.0ms	(pow (+ x 1.0) (/ 1.0 n))
6.0ms	(pow (+ x 1.0) (/ 1.0 n))

series595.0ms

Counts

4 → 12

Calls

4 calls:

150.0ms	(pow (+ x 1.0) (/ 1.0 n))
150.0ms	(pow (+ x 1.0) (/ 1.0 n))
141.0ms	(pow (+ x 1.0) (/ 1.0 n))
154.0ms	(pow (+ x 1.0) (/ 1.0 n))

simplify72.0ms

Algorithm

egg-herbie

Counts

132 → 132

Iterations

Useful iterations: 3 (63.0ms)

Iter	Nodes	Cost
0	203	700
1	659	676
2	2664	672
3	5001	664

prune693.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 20.4b

regimes214.0ms

Accuracy

79.2% (1.9b remaining)

Error of 22.7b against oracle of 20.8b and baseline of 29.8b

bsearch282.0ms

Steps

Iters	Range		Point
9	36901638985.00122	4.914394902755447e+18	52298366200.24001
10	-1.5980559511733492e+31	-1.2929377546055754e+19	-1.3110305152567192e+19

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	70	64
1	71	64
2	71	64

end0.0ms

sample5.4s

Algorithm

intervals

Results

2.0s	3170×	body	1280	valid
753.0ms	1574×	body	640	valid
512.0ms	4747×	body	80	valid
405.0ms	5172×	body	80	nan
377.0ms	609×	body	1280	nan
316.0ms	939×	body	320	valid
289.0ms	630×	body	640	nan
132.0ms	1316×	body	80	overflowed
104.0ms	448×	body	160	valid
99.0ms	342×	body	320	nan
28.0ms	154×	body	160	nan