Details

sample147.0ms

Algorithm

intervals

Results

53.0ms	118×	body	1280	valid
22.0ms	34×	body	10240	exit
13.0ms	45×	body	640	valid
10.0ms	22×	body	1280	nan
8.0ms	154×	body	80	valid
7.0ms	20×	body	640	nan
6.0ms	166×	body	80	nan
4.0ms	19×	body	320	valid
2.0ms	14×	body	160	valid
2.0ms	8×	body	320	nan
0.0ms	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: 31.0b

localize12.0ms

Local error

Found 3 expressions with local error:

0.7b	(pow x (/ 1.0 n))
1.4b	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
1.5b	(pow (+ x 1.0) (/ 1.0 n))

rewrite90.0ms

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))
73.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
10.0ms	(pow (+ x 1.0) (/ 1.0 n))

series438.0ms

Counts

3 → 9

Calls

3 calls:

52.0ms	(pow x (/ 1.0 n))
253.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
134.0ms	(pow (+ x 1.0) (/ 1.0 n))

simplify44.0ms

Algorithm

egg-herbie

Counts

88 → 88

Iterations

Useful iterations: 2 (35.0ms)

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

prune235.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 21.2b

localize11.0ms

Local error

Found 4 expressions with local error:

0.7b	(pow x (/ 1.0 n))
1.4b	(log (exp (- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))))
1.4b	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
1.5b	(pow (+ x 1.0) (/ 1.0 n))

rewrite253.0ms

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))
158.0ms	(log (exp (- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))))
76.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
10.0ms	(pow (+ x 1.0) (/ 1.0 n))

series704.0ms

Counts

4 → 12

Calls

4 calls:

52.0ms	(pow x (/ 1.0 n))
259.0ms	(log (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)))
137.0ms	(pow (+ x 1.0) (/ 1.0 n))

simplify48.0ms

Algorithm

egg-herbie

Counts

121 → 121

Iterations

Useful iterations: 2 (37.0ms)

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

prune353.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 21.2b

localize15.0ms

Local error

Found 4 expressions with local error:

1.4b	(log (cbrt (exp (- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n))))))
1.4b	(log (cbrt (exp (- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n))))))
1.5b	(pow (+ x 1.0) (/ 1.0 n))
1.5b	(pow (+ x 1.0) (/ 1.0 n))

rewrite152.0ms

Algorithm

rewrite-expression-head

Rules

28×	`*-un-lft-identity`
26×	`pow-unpow`
24×	`add-sqr-sqrt` `add-cube-cbrt`
18×	`times-frac`
16×	`log-prod`
10×	`cbrt-prod`
8×	`pow1` `add-exp-log` `unpow-prod-down`
4×	`exp-sum` `log-pow` `add-cbrt-cube` `add-log-exp`
2×	`pow-to-exp` `sub-neg` `log-div` `cbrt-div` `pow-pow` `exp-diff` `pow1/3` `rem-log-exp` `pow-exp` `div-inv` `distribute-lft-out` `sqr-pow`

Counts

4 → 94

Calls

4 calls:

63.0ms	(log (cbrt (exp (- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n))))))
63.0ms	(log (cbrt (exp (- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n))))))
14.0ms	(pow (+ x 1.0) (/ 1.0 n))
10.0ms	(pow (+ x 1.0) (/ 1.0 n))

series1.1s

Counts

4 → 12

Calls

4 calls:

424.0ms	(log (cbrt (exp (- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n))))))
425.0ms	(log (cbrt (exp (- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n))))))
134.0ms	(pow (+ x 1.0) (/ 1.0 n))
141.0ms	(pow (+ x 1.0) (/ 1.0 n))

simplify43.0ms

Algorithm

egg-herbie

Counts

106 → 106

Iterations

Useful iterations: 2 (27.0ms)

Iter	Nodes	Cost
0	321	962
1	1037	892
2	5001	878

prune463.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 21.1b

localize20.0ms

Local error

Found 4 expressions with local error:

1.4b	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
1.4b	(log (cbrt (exp (- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n))))))
1.5b	(pow (+ x 1.0) (/ 1.0 n))
1.5b	(pow (+ x 1.0) (/ 1.0 n))

rewrite162.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 99

Calls

4 calls:

74.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
63.0ms	(log (cbrt (exp (- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n))))))
11.0ms	(pow (+ x 1.0) (/ 1.0 n))
11.0ms	(pow (+ x 1.0) (/ 1.0 n))

series971.0ms

Counts

4 → 12

Calls

4 calls:

262.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
426.0ms	(log (cbrt (exp (- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n))))))
143.0ms	(pow (+ x 1.0) (/ 1.0 n))
140.0ms	(pow (+ x 1.0) (/ 1.0 n))

simplify45.0ms

Algorithm

egg-herbie

Counts

111 → 111

Iterations

Useful iterations: 2 (34.0ms)

Iter	Nodes	Cost
0	437	967
1	1366	921
2	5001	905

prune439.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 21.1b

regimes283.0ms

Accuracy

80.8% (1.8b remaining)

Error of 21.9b against oracle of 20.1b and baseline of 29.4b

bsearch1.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	51	65
1	51	65

end0.0ms

sample4.2s

Algorithm

intervals

Results

1.4s	3151×	body	1280	valid
546.0ms	1640×	body	640	valid
488.0ms	1186×	body	10240	exit
275.0ms	627×	body	1280	nan
258.0ms	4753×	body	80	valid
208.0ms	645×	body	640	nan
185.0ms	833×	body	320	valid
181.0ms	5039×	body	80	nan
69.0ms	368×	body	320	nan
57.0ms	426×	body	160	valid
20.0ms	174×	body	160	nan