Details

sample171.0ms

Algorithm

intervals

Results

54.0ms	107×	body	1280	valid
21.0ms	52×	body	10240	exit
20.0ms	52×	body	640	valid
13.0ms	153×	body	80	valid
12.0ms	196×	body	80	nan
10.0ms	21×	body	1280	nan
9.0ms	15×	body	640	nan
7.0ms	27×	body	320	valid
2.0ms	13×	body	160	valid
2.0ms	8×	body	320	nan
1.0ms	5×	body	160	nan

simplify34.0ms

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

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 33.0b

localize9.0ms

Local error

Found 3 expressions with local error:

0.8b	(pow x (/ 1.0 n))
1.5b	(pow (+ x 1.0) (/ 1.0 n))
2.5b	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))

rewrite52.0ms

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:

2.0ms	(pow x (/ 1.0 n))
5.0ms	(pow (+ x 1.0) (/ 1.0 n))
39.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))

series476.0ms

Counts

3 → 9

Calls

3 calls:

60.0ms	(pow x (/ 1.0 n))
140.0ms	(pow (+ x 1.0) (/ 1.0 n))
275.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))

simplify44.0ms

Algorithm

egg-herbie

Counts

88 → 88

Iterations

Useful iterations: 2 (36.0ms)

Iter	Nodes	Cost
0	476	639
1	1600	623
2	5001	609

prune236.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 24.9b

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b	(pow (pow (+ x 1.0) (/ 1.0 n)) 3)
0.8b	(pow x (/ 1.0 n))
1.5b	(pow (+ x 1.0) (/ 1.0 n))
2.5b	(- (cbrt (pow (pow (+ x 1.0) (/ 1.0 n)) 3)) (pow x (/ 1.0 n)))

rewrite123.0ms

Algorithm

rewrite-expression-head

Rules

61×	`add-sqr-sqrt`
47×	`unpow-prod-down`
33×	`*-un-lft-identity`
29×	`pow-unpow`
27×	`difference-of-squares`
25×	`add-cube-cbrt`
24×	`cbrt-prod`
23×	`sqr-pow`
18×	`times-frac`
17×	`cube-prod`
8×	`add-exp-log`
6×	`pow1` `pow-exp` `add-log-exp`
5×	`add-cbrt-cube`
4×	`pow-to-exp`
3×	`pow-pow` `distribute-lft-out`
2×	`div-inv`
1×	`cube-mult` `sub-neg` `flip3--` `diff-log` `unpow3` `flip--` `distribute-lft-out--` `rem-cube-cbrt`

Counts

4 → 130

Calls

4 calls:

9.0ms	(pow (pow (+ x 1.0) (/ 1.0 n)) 3)
2.0ms	(pow x (/ 1.0 n))
5.0ms	(pow (+ x 1.0) (/ 1.0 n))
102.0ms	(- (cbrt (pow (pow (+ x 1.0) (/ 1.0 n)) 3)) (pow x (/ 1.0 n)))

series844.0ms

Counts

4 → 12

Calls

4 calls:

371.0ms	(pow (pow (+ x 1.0) (/ 1.0 n)) 3)
55.0ms	(pow x (/ 1.0 n))
146.0ms	(pow (+ x 1.0) (/ 1.0 n))
271.0ms	(- (cbrt (pow (pow (+ x 1.0) (/ 1.0 n)) 3)) (pow x (/ 1.0 n)))

simplify66.0ms

Algorithm

egg-herbie

Counts

142 → 142

Iterations

Useful iterations: 2 (52.0ms)

Iter	Nodes	Cost
0	655	1232
1	2377	1182
2	5001	1171

prune340.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 24.8b

localize11.0ms

Local error

Found 4 expressions with local error:

0.8b	(pow x (/ 1.0 n))
1.5b	(pow (+ x 1.0) (/ 1.0 n))
2.5b	(log (exp (- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))))
2.5b	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))

rewrite146.0ms

Algorithm

rewrite-expression-head

Rules

46×	`add-sqr-sqrt`
38×	`*-un-lft-identity`
27×	`unpow-prod-down`
26×	`pow-unpow`
22×	`add-cube-cbrt`
18×	`times-frac` `difference-of-squares`
16×	`log-pow`
15×	`exp-prod`
14×	`sqr-pow`
7×	`pow1`
6×	`add-exp-log` `distribute-lft-out--` `add-log-exp`
5×	`log-prod`
4×	`add-cbrt-cube`
3×	`distribute-lft-out`
2×	`pow-to-exp` `sub-neg` `pow-pow` `exp-sum` `pow-exp` `div-inv`
1×	`log-div` `flip3--` `exp-diff` `diff-log` `rem-log-exp` `flip--`

Counts

4 → 109

Calls

4 calls:

2.0ms	(pow x (/ 1.0 n))
5.0ms	(pow (+ x 1.0) (/ 1.0 n))
92.0ms	(log (exp (- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))))
42.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))

series753.0ms

Counts

4 → 12

Calls

4 calls:

62.0ms	(pow x (/ 1.0 n))
148.0ms	(pow (+ x 1.0) (/ 1.0 n))
274.0ms	(log (exp (- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))))
269.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))

simplify49.0ms

Algorithm

egg-herbie

Counts

121 → 121

Iterations

Useful iterations: 2 (38.0ms)

Iter	Nodes	Cost
0	541	922
1	1758	884
2	5002	863

prune363.0ms

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 24.8b

localize15.0ms

Local error

Found 4 expressions with local error:

2.3b	(log (cbrt (exp (- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n))))))
2.3b	(log (cbrt (exp (- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n))))))
2.5b	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
2.5b	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))

rewrite156.0ms

Algorithm

rewrite-expression-head

Rules

32×	`add-sqr-sqrt`
22×	`*-un-lft-identity`
20×	`unpow-prod-down`
18×	`difference-of-squares`
16×	`log-prod`
12×	`sqr-pow`
10×	`cbrt-prod`
8×	`add-cube-cbrt` `add-log-exp`
6×	`pow1` `add-exp-log` `distribute-lft-out--`
4×	`sub-neg` `exp-sum` `log-pow` `add-cbrt-cube`
2×	`log-div` `cbrt-div` `flip3--` `exp-diff` `pow1/3` `diff-log` `rem-log-exp` `flip--` `distribute-lft-out`

Counts

4 → 86

Calls

4 calls:

35.0ms	(log (cbrt (exp (- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n))))))
37.0ms	(log (cbrt (exp (- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n))))))
42.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
39.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))

series1.5s

Counts

4 → 12

Calls

4 calls:

451.0ms	(log (cbrt (exp (- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n))))))
456.0ms	(log (cbrt (exp (- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n))))))
278.0ms	(- (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)))

simplify107.0ms

Algorithm

egg-herbie

Counts

98 → 98

Iterations

Useful iterations: 2 (23.0ms)

Iter	Nodes	Cost
0	300	1278
1	805	1194
2	3713	1170
3	5001	1170

prune431.0ms

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 24.7b

regimes268.0ms

Accuracy

81.9% (1.6b remaining)

Error of 22.8b against oracle of 21.2b and baseline of 30.1b

bsearch1.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	36	22
1	36	22

end0.0ms

sample4.9s

Algorithm

intervals

Results

1.6s	3185×	body	1280	valid
614.0ms	1597×	body	640	valid
531.0ms	1118×	body	10240	exit
411.0ms	4708×	body	80	valid
329.0ms	640×	body	1280	nan
313.0ms	5176×	body	80	nan
254.0ms	639×	body	640	nan
225.0ms	863×	body	320	valid
85.0ms	350×	body	320	nan
85.0ms	473×	body	160	valid
26.0ms	169×	body	160	nan