Details

sample207.0ms

Algorithm

intervals

Results

59.0ms	133×	body	1280	valid
37.0ms	59×	body	1280	nan
26.0ms	67×	body	640	nan
20.0ms	57×	body	10240	exit
15.0ms	47×	body	640	valid
9.0ms	27×	body	320	nan
8.0ms	192×	body	80	nan
6.0ms	31×	body	320	valid
4.0ms	91×	body	80	valid
2.0ms	14×	body	160	nan
2.0ms	14×	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: 33.1b

localize8.0ms

Local error

Found 3 expressions with local error:

0.0b	(pow x (/ 1.0 n))
0.0b	(pow (+ x 1.0) (/ 1.0 n))
2.7b	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))

rewrite26.0ms

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:

3.0ms	(pow x (/ 1.0 n))
6.0ms	(pow (+ x 1.0) (/ 1.0 n))
14.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))

series458.0ms

Counts

3 → 9

Calls

3 calls:

54.0ms	(pow x (/ 1.0 n))
140.0ms	(pow (+ x 1.0) (/ 1.0 n))
264.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))

simplify43.0ms

Algorithm

egg-herbie

Counts

88 → 88

Iterations

Useful iterations: 2 (34.0ms)

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

prune245.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 20.0b

localize14.0ms

Local error

Found 4 expressions with local error:

0.0b	(pow (+ x 1.0) (/ 1.0 n))
0.0b	(log (exp (pow (+ x 1.0) (/ 1.0 n))))
0.0b	(exp (pow (+ x 1.0) (/ 1.0 n)))
3.0b	(- (log (exp (pow (+ x 1.0) (/ 1.0 n)))) (pow x (/ 1.0 n)))

rewrite30.0ms

Algorithm

rewrite-expression-head

Rules

27×	`*-un-lft-identity`
23×	`add-sqr-sqrt`
18×	`add-cube-cbrt`
16×	`exp-prod`
13×	`unpow-prod-down` `pow-unpow`
10×	`log-pow`
9×	`times-frac`
7×	`pow1`
6×	`log-prod` `add-log-exp`
5×	`add-exp-log`
4×	`add-cbrt-cube` `sqr-pow`
3×	`associate--l+` `distribute-lft-out` `difference-of-squares`
2×	`distribute-lft-out--`
1×	`pow-to-exp` `sub-neg` `flip3--` `pow-pow` `diff-log` `rem-log-exp` `pow-exp` `flip--` `div-inv` `rem-exp-log`

Counts

4 → 84

Calls

4 calls:

5.0ms	(pow (+ x 1.0) (/ 1.0 n))
5.0ms	(log (exp (pow (+ x 1.0) (/ 1.0 n))))
5.0ms	(exp (pow (+ x 1.0) (/ 1.0 n)))
12.0ms	(- (log (exp (pow (+ x 1.0) (/ 1.0 n)))) (pow x (/ 1.0 n)))

series839.0ms

Counts

4 → 12

Calls

4 calls:

147.0ms	(pow (+ x 1.0) (/ 1.0 n))
145.0ms	(log (exp (pow (+ x 1.0) (/ 1.0 n))))
282.0ms	(exp (pow (+ x 1.0) (/ 1.0 n)))
265.0ms	(- (log (exp (pow (+ x 1.0) (/ 1.0 n)))) (pow x (/ 1.0 n)))

simplify40.0ms

Algorithm

egg-herbie

Counts

96 → 96

Iterations

Useful iterations: 2 (32.0ms)

Iter	Nodes	Cost
0	432	696
1	1368	626
2	5002	614

prune276.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 19.8b

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b	(pow x (/ 1.0 n))
0.0b	(pow (+ x 1.0) (/ 1.0 n))
2.7b	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
2.7b	(log (exp (- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))))

rewrite33.0ms

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))
6.0ms	(pow (+ x 1.0) (/ 1.0 n))
9.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
10.0ms	(log (exp (- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))))

series759.0ms

Counts

4 → 12

Calls

4 calls:

57.0ms	(pow x (/ 1.0 n))
152.0ms	(pow (+ x 1.0) (/ 1.0 n))
275.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
275.0ms	(log (exp (- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))))

simplify49.0ms

Algorithm

egg-herbie

Counts

121 → 121

Iterations

Useful iterations: 2 (37.0ms)

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

prune381.0ms

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 19.8b

localize15.0ms

Local error

Found 4 expressions with local error:

2.7b	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
2.7b	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
2.8b	(log (cbrt (exp (- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n))))))
2.8b	(log (cbrt (exp (- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n))))))

rewrite46.0ms

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:

9.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
14.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
10.0ms	(log (cbrt (exp (- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n))))))
10.0ms	(log (cbrt (exp (- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n))))))

series1.5s

Counts

4 → 12

Calls

4 calls:

282.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
279.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
454.0ms	(log (cbrt (exp (- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n))))))
453.0ms	(log (cbrt (exp (- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n))))))

simplify113.0ms

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

prune462.0ms

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 19.8b

regimes280.0ms

Accuracy

84.4% (1.8b remaining)

Error of 23.5b against oracle of 21.8b and baseline of 33.2b

bsearch1.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	40	37
1	40	37

end0.0ms

sample6.5s

Algorithm

intervals

Results

1.8s	3981×	body	1280	valid
1.3s	2166×	body	1280	nan
720.0ms	1811×	body	640	nan
617.0ms	1839×	body	640	valid
614.0ms	1428×	body	10240	exit
260.0ms	6185×	body	80	nan
221.0ms	896×	body	320	nan
189.0ms	872×	body	320	valid
140.0ms	2985×	body	80	valid
67.0ms	453×	body	160	valid
63.0ms	447×	body	160	nan