Details

sample137.0ms

Algorithm

intervals

Results

43.0ms	83×	body	1280	valid
20.0ms	55×	body	640	valid
17.0ms	26×	body	10240	exit
10.0ms	171×	body	80	valid
8.0ms	19×	body	1280	nan
5.0ms	18×	body	640	nan
5.0ms	144×	body	80	nan
5.0ms	25×	body	320	valid
3.0ms	13×	body	320	nan
1.0ms	11×	body	160	valid
0.0ms	2×	body	160	nan

simplify35.0ms

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: 30.2b

localize9.0ms

Local error

Found 3 expressions with local error:

0.5b	(pow x (/ 1.0 n))
1.5b	(pow (+ x 1.0) (/ 1.0 n))
2.0b	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))

rewrite99.0ms

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))
81.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))

series479.0ms

Counts

3 → 9

Calls

3 calls:

58.0ms	(pow x (/ 1.0 n))
148.0ms	(pow (+ x 1.0) (/ 1.0 n))
273.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))

simplify47.0ms

Algorithm

egg-herbie

Counts

88 → 88

Iterations

Useful iterations: 2 (37.0ms)

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

prune229.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 22.3b

localize11.0ms

Local error

Found 4 expressions with local error:

0.5b	(pow x (/ 1.0 n))
1.5b	(pow (+ x 1.0) (/ 1.0 n))
2.0b	(log (exp (- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))))
2.0b	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))

rewrite276.0ms

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))
13.0ms	(pow (+ x 1.0) (/ 1.0 n))
171.0ms	(log (exp (- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))))
83.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))

series759.0ms

Counts

4 → 12

Calls

4 calls:

62.0ms	(pow x (/ 1.0 n))
145.0ms	(pow (+ x 1.0) (/ 1.0 n))
277.0ms	(log (exp (- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))))
276.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))

simplify48.0ms

Algorithm

egg-herbie

Counts

121 → 121

Iterations

Useful iterations: 2 (38.0ms)

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

prune354.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 22.3b

localize16.0ms

Local error

Found 4 expressions with local error:

2.0b	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
2.0b	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
2.0b	(log (sqrt (exp (- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n))))))
2.0b	(log (sqrt (exp (- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n))))))

rewrite523.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 118

Calls

4 calls:

80.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
80.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
177.0ms	(log (sqrt (exp (- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n))))))
178.0ms	(log (sqrt (exp (- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n))))))

series1.5s

Counts

4 → 12

Calls

4 calls:

287.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
281.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
460.0ms	(log (sqrt (exp (- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n))))))
451.0ms	(log (sqrt (exp (- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n))))))

simplify118.0ms

Algorithm

egg-herbie

Counts

130 → 130

Iterations

Useful iterations: 2 (25.0ms)

Iter	Nodes	Cost
0	349	1482
1	940	1394
2	4101	1370
3	5001	1370

prune553.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 22.3b

localize27.0ms

Local error

Found 4 expressions with local error:

2.0b	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
2.0b	(log (sqrt (exp (- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n))))))
2.5b	(log (sqrt (exp (* (+ (pow (+ x 1.0) (/ (/ 1.0 n) 2)) (sqrt (pow x (/ 1.0 n)))) (- (pow (+ x 1.0) (/ (/ 1.0 n) 2)) (sqrt (pow x (/ 1.0 n))))))))
2.8b	(- (pow (+ x 1.0) (/ (/ 1.0 n) 2)) (sqrt (pow x (/ 1.0 n))))

rewrite414.0ms

Algorithm

rewrite-expression-head

Rules

50×	`add-sqr-sqrt`
30×	`difference-of-squares`
27×	`unpow-prod-down`
25×	`*-un-lft-identity`
24×	`log-pow`
21×	`sqrt-prod`
20×	`sqrt-pow1`
19×	`sqr-pow`
18×	`log-prod`
16×	`exp-prod`
11×	`add-log-exp`
9×	`add-cube-cbrt`
8×	`pow1`
7×	`distribute-lft-out--`
6×	`add-exp-log` `exp-sum`
5×	`sub-neg`
4×	`add-cbrt-cube`
2×	`distribute-rgt-in` `flip3--` `exp-to-pow` `distribute-lft-in` `pow1/2` `diff-log` `rem-log-exp` `flip--` `distribute-lft-out`
1×	`log-div` `exp-diff` `sqrt-div` `sum-log`

Counts

4 → 108

Calls

4 calls:

83.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
178.0ms	(log (sqrt (exp (- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n))))))
64.0ms	(log (sqrt (exp (* (+ (pow (+ x 1.0) (/ (/ 1.0 n) 2)) (sqrt (pow x (/ 1.0 n)))) (- (pow (+ x 1.0) (/ (/ 1.0 n) 2)) (sqrt (pow x (/ 1.0 n))))))))
85.0ms	(- (pow (+ x 1.0) (/ (/ 1.0 n) 2)) (sqrt (pow x (/ 1.0 n))))

series3.4s

Counts

4 → 12

Calls

4 calls:

285.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
467.0ms	(log (sqrt (exp (- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n))))))
2.3s	(log (sqrt (exp (* (+ (pow (+ x 1.0) (/ (/ 1.0 n) 2)) (sqrt (pow x (/ 1.0 n)))) (- (pow (+ x 1.0) (/ (/ 1.0 n) 2)) (sqrt (pow x (/ 1.0 n))))))))
351.0ms	(- (pow (+ x 1.0) (/ (/ 1.0 n) 2)) (sqrt (pow x (/ 1.0 n))))

simplify52.0ms

Algorithm

egg-herbie

Counts

120 → 120

Iterations

Useful iterations: 2 (37.0ms)

Iter	Nodes	Cost
0	563	1630
1	1521	1535
2	5002	1518

prune576.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 22.3b

regimes246.0ms

Accuracy

85% (1.3b remaining)

Error of 22.8b against oracle of 21.4b and baseline of 30.2b

bsearch1.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	52	79
1	52	79

end0.0ms

sample4.2s

Algorithm

intervals

Results

1.4s	3129×	body	1280	valid
585.0ms	1680×	body	640	valid
423.0ms	1075×	body	10240	exit
304.0ms	663×	body	1280	nan
253.0ms	4723×	body	80	valid
212.0ms	654×	body	640	nan
191.0ms	5045×	body	80	nan
185.0ms	847×	body	320	valid
64.0ms	343×	body	320	nan
61.0ms	446×	body	160	valid
20.0ms	185×	body	160	nan