Details

sample140.0ms

Algorithm

intervals

Results

48.0ms	106×	body	1280	valid
20.0ms	55×	body	640	valid
19.0ms	38×	body	10240	exit
7.0ms	137×	body	80	valid
6.0ms	30×	body	320	valid
6.0ms	20×	body	640	nan
5.0ms	137×	body	80	nan
4.0ms	10×	body	1280	nan
2.0ms	16×	body	160	valid
2.0ms	9×	body	320	nan
1.0ms	8×	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: 32.3b

localize8.0ms

Local error

Found 3 expressions with local error:

0.8b	(pow x (/ 1.0 n))
1.4b	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
1.7b	(pow (+ x 1.0) (/ 1.0 n))

rewrite95.0ms

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:

5.0ms	(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))

series423.0ms

Counts

3 → 9

Calls

3 calls:

53.0ms	(pow x (/ 1.0 n))
241.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
129.0ms	(pow (+ x 1.0) (/ 1.0 n))

simplify43.0ms

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: 21.8b

localize13.0ms

Local error

Found 4 expressions with local error:

0.8b	(pow x (/ 1.0 n))
1.4b	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
1.6b	(log (exp (- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))))
1.7b	(pow (+ x 1.0) (/ 1.0 n))

rewrite257.0ms

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))
75.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
163.0ms	(log (exp (- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))))
10.0ms	(pow (+ x 1.0) (/ 1.0 n))

series657.0ms

Counts

4 → 12

Calls

4 calls:

54.0ms	(pow x (/ 1.0 n))
239.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
239.0ms	(log (exp (- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))))
126.0ms	(pow (+ x 1.0) (/ 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

prune349.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 21.8b

localize17.0ms

Local error

Found 4 expressions with local error:

1.5b	(log (cbrt (exp (- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n))))))
1.5b	(log (cbrt (exp (- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n))))))
1.7b	(pow (+ x 1.0) (/ 1.0 n))
1.7b	(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))))))
65.0ms	(log (cbrt (exp (- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n))))))
10.0ms	(pow (+ x 1.0) (/ 1.0 n))
11.0ms	(pow (+ x 1.0) (/ 1.0 n))

series1.1s

Counts

4 → 12

Calls

4 calls:

411.0ms	(log (cbrt (exp (- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n))))))
410.0ms	(log (cbrt (exp (- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n))))))
128.0ms	(pow (+ x 1.0) (/ 1.0 n))
129.0ms	(pow (+ x 1.0) (/ 1.0 n))

simplify37.0ms

Algorithm

egg-herbie

Counts

106 → 106

Iterations

Useful iterations: 2 (27.0ms)

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

prune474.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 21.8b

localize22.0ms

Local error

Found 4 expressions with local error:

1.5b	(log (cbrt (exp (- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n))))))
1.7b	(pow (+ x 1.0) (/ 1.0 n))
1.7b	(pow (+ x 1.0) (/ 1.0 n))
1.7b	(pow (+ x 1.0) (/ 1.0 n))

rewrite101.0ms

Algorithm

rewrite-expression-head

Rules

39×	`pow-unpow`
36×	`*-un-lft-identity`
30×	`add-sqr-sqrt` `add-cube-cbrt`
27×	`times-frac`
12×	`unpow-prod-down`
8×	`pow1` `add-exp-log` `log-prod`
5×	`cbrt-prod`
4×	`add-cbrt-cube` `add-log-exp`
3×	`pow-to-exp` `pow-pow` `pow-exp` `div-inv` `distribute-lft-out` `sqr-pow`
2×	`exp-sum` `log-pow`
1×	`sub-neg` `log-div` `cbrt-div` `exp-diff` `pow1/3` `rem-log-exp`

Counts

4 → 103

Calls

4 calls:

66.0ms	(log (cbrt (exp (- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n))))))
10.0ms	(pow (+ x 1.0) (/ 1.0 n))
11.0ms	(pow (+ x 1.0) (/ 1.0 n))
10.0ms	(pow (+ x 1.0) (/ 1.0 n))

series826.0ms

Counts

4 → 12

Calls

4 calls:

421.0ms	(log (cbrt (exp (- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n))))))
135.0ms	(pow (+ x 1.0) (/ 1.0 n))
131.0ms	(pow (+ x 1.0) (/ 1.0 n))
139.0ms	(pow (+ x 1.0) (/ 1.0 n))

simplify38.0ms

Algorithm

egg-herbie

Counts

115 → 115

Iterations

Useful iterations: 2 (28.0ms)

Iter	Nodes	Cost
0	321	817
1	1037	770
2	5001	759

prune568.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 21.8b

regimes178.0ms

Accuracy

81.4% (1.7b remaining)

Error of 22.2b against oracle of 20.5b and baseline of 29.7b

bsearch122.0ms

Steps

Iters	Range		Point
7	2.3561478261553777e+24	7.622267412949973e+25	2.37986048177438e+24
5	-6.846532700157587	-1.9233913688650928	-3.5791419874615427

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	35	20
1	35	20

end0.0ms

sample4.1s

Algorithm

intervals

Results

1.4s	3146×	body	1280	valid
527.0ms	1610×	body	640	valid
436.0ms	1106×	body	10240	exit
279.0ms	612×	body	1280	nan
251.0ms	4664×	body	80	valid
186.0ms	586×	body	640	nan
184.0ms	860×	body	320	valid
177.0ms	4907×	body	80	nan
63.0ms	342×	body	320	nan
58.0ms	440×	body	160	valid
21.0ms	167×	body	160	nan