Details

sample167.0ms

Algorithm

intervals

Results

68.0ms	112×	body	1280	valid
26.0ms	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

simplify33.0ms

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: 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)))

rewrite50.0ms

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))
40.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))

series472.0ms

Counts

3 → 9

Calls

3 calls:

59.0ms	(pow x (/ 1.0 n))
140.0ms	(pow (+ x 1.0) (/ 1.0 n))
272.0ms	(- (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

prune252.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 19.2b

localize10.0ms

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)))

rewrite148.0ms

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))
93.0ms	(log (exp (- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))))
43.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))

series741.0ms

Counts

4 → 12

Calls

4 calls:

60.0ms	(pow x (/ 1.0 n))
139.0ms	(pow (+ x 1.0) (/ 1.0 n))
275.0ms	(log (exp (- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))))
267.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))

simplify46.0ms

Algorithm

egg-herbie

Counts

121 → 121

Iterations

Useful iterations: 2 (36.0ms)

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

prune371.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 19.2b

localize10.0ms

Local error

Found 4 expressions with local error:

0.3b	(pow x (/ 1.0 n))
0.5b	(pow (+ x 1.0) (/ 1.0 n))
0.5b	(pow (+ x 1.0) (/ 1.0 n))
1.6b	(- (* (sqrt (pow (+ x 1.0) (/ 1.0 n))) (sqrt (pow (+ x 1.0) (/ 1.0 n)))) (pow x (/ 1.0 n)))

rewrite32.0ms

Algorithm

rewrite-expression-head

Rules

39×	`pow-unpow`
32×	`*-un-lft-identity`
30×	`add-sqr-sqrt`
28×	`add-cube-cbrt`
27×	`times-frac`
12×	`unpow-prod-down`
7×	`pow1` `add-exp-log`
6×	`add-log-exp`
4×	`add-cbrt-cube` `sqr-pow`
3×	`pow-to-exp` `pow-pow` `pow-exp` `div-inv` `difference-of-squares`
2×	`distribute-lft-out`
1×	`sub-neg` `flip3--` `diff-log` `flip--`

Counts

4 → 98

Calls

4 calls:

2.0ms	(pow x (/ 1.0 n))
6.0ms	(pow (+ x 1.0) (/ 1.0 n))
5.0ms	(pow (+ x 1.0) (/ 1.0 n))
16.0ms	(- (* (sqrt (pow (+ x 1.0) (/ 1.0 n))) (sqrt (pow (+ x 1.0) (/ 1.0 n)))) (pow x (/ 1.0 n)))

series620.0ms

Counts

4 → 12

Calls

4 calls:

60.0ms	(pow x (/ 1.0 n))
146.0ms	(pow (+ x 1.0) (/ 1.0 n))
140.0ms	(pow (+ x 1.0) (/ 1.0 n))
274.0ms	(- (* (sqrt (pow (+ x 1.0) (/ 1.0 n))) (sqrt (pow (+ x 1.0) (/ 1.0 n)))) (pow x (/ 1.0 n)))

simplify45.0ms

Algorithm

egg-herbie

Counts

110 → 110

Iterations

Useful iterations: 2 (36.0ms)

Iter	Nodes	Cost
0	467	787
1	1617	714
2	5002	697

prune362.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 19.1b

localize19.0ms

Local error

Found 4 expressions with local error:

0.5b	(pow (+ x 1.0) (/ 1.0 n))
1.6b	(- (* (sqrt (pow (+ x 1.0) (/ 1.0 n))) (sqrt (pow (+ x 1.0) (/ 1.0 n)))) (pow x (/ 1.0 n)))
1.6b	(- (* (sqrt (pow (+ x 1.0) (/ 1.0 n))) (sqrt (pow (+ x 1.0) (/ 1.0 n)))) (pow x (/ 1.0 n)))
1.6b	(- (* (sqrt (pow (+ x 1.0) (/ 1.0 n))) (sqrt (pow (+ x 1.0) (/ 1.0 n)))) (pow x (/ 1.0 n)))

rewrite57.0ms

Algorithm

rewrite-expression-head

Rules

18×	`add-sqr-sqrt`
14×	`*-un-lft-identity`
13×	`pow-unpow`
12×	`add-cube-cbrt`
10×	`add-log-exp`
9×	`times-frac` `difference-of-squares`
7×	`unpow-prod-down`
5×	`pow1` `add-exp-log`
4×	`add-cbrt-cube` `sqr-pow`
3×	`sub-neg` `flip3--` `diff-log` `flip--`
1×	`pow-to-exp` `pow-pow` `pow-exp` `div-inv` `distribute-lft-out`

Counts

4 → 73

Calls

4 calls:

5.0ms	(pow (+ x 1.0) (/ 1.0 n))
16.0ms	(- (* (sqrt (pow (+ x 1.0) (/ 1.0 n))) (sqrt (pow (+ x 1.0) (/ 1.0 n)))) (pow x (/ 1.0 n)))
16.0ms	(- (* (sqrt (pow (+ x 1.0) (/ 1.0 n))) (sqrt (pow (+ x 1.0) (/ 1.0 n)))) (pow x (/ 1.0 n)))
16.0ms	(- (* (sqrt (pow (+ x 1.0) (/ 1.0 n))) (sqrt (pow (+ x 1.0) (/ 1.0 n)))) (pow x (/ 1.0 n)))

series985.0ms

Counts

4 → 12

Calls

4 calls:

151.0ms	(pow (+ x 1.0) (/ 1.0 n))
280.0ms	(- (* (sqrt (pow (+ x 1.0) (/ 1.0 n))) (sqrt (pow (+ x 1.0) (/ 1.0 n)))) (pow x (/ 1.0 n)))
277.0ms	(- (* (sqrt (pow (+ x 1.0) (/ 1.0 n))) (sqrt (pow (+ x 1.0) (/ 1.0 n)))) (pow x (/ 1.0 n)))
277.0ms	(- (* (sqrt (pow (+ x 1.0) (/ 1.0 n))) (sqrt (pow (+ x 1.0) (/ 1.0 n)))) (pow x (/ 1.0 n)))

simplify42.0ms

Algorithm

egg-herbie

Counts

85 → 85

Iterations

Useful iterations: 2 (32.0ms)

Iter	Nodes	Cost
0	350	1074
1	1158	888
2	5002	862

prune376.0ms

Pruning

11 alts after pruning (9 fresh and 2 done)

Merged error: 19.1b

regimes334.0ms

Accuracy

84.1% (1.4b remaining)

Error of 21.8b against oracle of 20.5b and baseline of 29.0b

bsearch163.0ms

Steps

Iters	Range		Point
3	5702493.407928515	6835871.788935939	6765035.640122974
9	-8.752539455896483e+21	-1018083199604230.8	-1030752291146602.5

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	48	58
1	48	58

end0.0ms

sample4.8s

Algorithm

intervals

Results

1.9s	3182×	body	1280	valid
738.0ms	1645×	body	640	valid
380.0ms	637×	body	1280	nan
378.0ms	4691×	body	80	valid
284.0ms	4954×	body	80	nan
259.0ms	610×	body	640	nan
237.0ms	779×	body	320	valid
95.0ms	354×	body	320	nan
92.0ms	445×	body	160	valid
88.0ms	1220×	body	80	overflowed
29.0ms	183×	body	160	nan