Details

sample132.0ms

Algorithm

intervals

Results

52.0ms	113×	body	1280	valid
15.0ms	51×	body	640	valid
10.0ms	24×	body	1280	nan
9.0ms	35×	body	10240	exit
7.0ms	131×	body	80	valid
6.0ms	19×	body	640	nan
5.0ms	153×	body	80	nan
5.0ms	23×	body	320	valid
2.0ms	15×	body	160	valid
2.0ms	9×	body	320	nan
1.0ms	5×	body	160	nan

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: 30.3b

localize8.0ms

Local error

Found 3 expressions with local error:

0.3b	(pow x (/ 1.0 n))
1.0b	(pow (+ x 1.0) (/ 1.0 n))
2.1b	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))

rewrite92.0ms

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:

4.0ms	(pow x (/ 1.0 n))
11.0ms	(pow (+ x 1.0) (/ 1.0 n))
74.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))

series444.0ms

Counts

3 → 9

Calls

3 calls:

57.0ms	(pow x (/ 1.0 n))
133.0ms	(pow (+ x 1.0) (/ 1.0 n))
253.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))

simplify42.0ms

Algorithm

egg-herbie

Counts

88 → 88

Iterations

Useful iterations: 2 (34.0ms)

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

prune243.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 22.7b

localize11.0ms

Local error

Found 4 expressions with local error:

0.3b	(pow x (/ 1.0 n))
1.0b	(pow (+ x 1.0) (/ 1.0 n))
2.1b	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
2.1b	(log (exp (- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))))

rewrite247.0ms

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:

4.0ms	(pow x (/ 1.0 n))
10.0ms	(pow (+ x 1.0) (/ 1.0 n))
71.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
157.0ms	(log (exp (- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))))

series708.0ms

Counts

4 → 12

Calls

4 calls:

58.0ms	(pow x (/ 1.0 n))
133.0ms	(pow (+ x 1.0) (/ 1.0 n))
259.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
257.0ms	(log (exp (- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))))

simplify46.0ms

Algorithm

egg-herbie

Counts

121 → 121

Iterations

Useful iterations: 2 (35.0ms)

Iter	Nodes	Cost
0	541	922
1	1760	884
2	5001	863

prune359.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 22.7b

localize13.0ms

Local error

Found 4 expressions with local error:

0.3b	(pow x (/ 1.0 n))
1.0b	(pow (+ x 1.0) (/ 1.0 n))
1.0b	(pow (+ x 1.0) (/ 1.0 n))
2.1b	(- (sqrt (pow (+ x 1.0) (/ 1.0 n))) (sqrt (pow x (/ 1.0 n))))

rewrite110.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 115

Calls

4 calls:

4.0ms	(pow x (/ 1.0 n))
10.0ms	(pow (+ x 1.0) (/ 1.0 n))
11.0ms	(pow (+ x 1.0) (/ 1.0 n))
82.0ms	(- (sqrt (pow (+ x 1.0) (/ 1.0 n))) (sqrt (pow x (/ 1.0 n))))

series669.0ms

Counts

4 → 12

Calls

4 calls:

53.0ms	(pow x (/ 1.0 n))
140.0ms	(pow (+ x 1.0) (/ 1.0 n))
133.0ms	(pow (+ x 1.0) (/ 1.0 n))
343.0ms	(- (sqrt (pow (+ x 1.0) (/ 1.0 n))) (sqrt (pow x (/ 1.0 n))))

simplify46.0ms

Algorithm

egg-herbie

Counts

127 → 127

Iterations

Useful iterations: 2 (36.0ms)

Iter	Nodes	Cost
0	502	1033
1	1683	997
2	5002	986

prune459.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 22.7b

localize18.0ms

Local error

Found 4 expressions with local error:

1.9b	(log (cbrt (exp (- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n))))))
1.9b	(log (cbrt (exp (- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n))))))
2.1b	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
2.1b	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))

rewrite271.0ms

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:

61.0ms	(log (cbrt (exp (- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n))))))
61.0ms	(log (cbrt (exp (- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n))))))
72.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
74.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))

series1.4s

Counts

4 → 12

Calls

4 calls:

429.0ms	(log (cbrt (exp (- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n))))))
429.0ms	(log (cbrt (exp (- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n))))))
255.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
264.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))

simplify103.0ms

Algorithm

egg-herbie

Counts

98 → 98

Iterations

Useful iterations: 2 (22.0ms)

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

prune430.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 22.7b

regimes261.0ms

Accuracy

82.2% (1.6b remaining)

Error of 22.5b against oracle of 20.9b and baseline of 29.7b

bsearch1.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	35	22
1	35	22

end0.0ms

sample4.1s

Algorithm

intervals

Results

1.4s	3138×	body	1280	valid
541.0ms	1627×	body	640	valid
439.0ms	1100×	body	10240	exit
284.0ms	645×	body	1280	nan
237.0ms	4707×	body	80	valid
198.0ms	643×	body	640	nan
180.0ms	853×	body	320	valid
173.0ms	4912×	body	80	nan
63.0ms	455×	body	160	valid
61.0ms	340×	body	320	nan
21.0ms	198×	body	160	nan