Details

sample169.0ms

Algorithm

intervals

Results

54.0ms	107×	body	1280	valid
22.0ms	52×	body	10240	exit
21.0ms	52×	body	640	valid
13.0ms	153×	body	80	valid
13.0ms	21×	body	1280	nan
12.0ms	196×	body	80	nan
7.0ms	27×	body	320	valid
6.0ms	15×	body	640	nan
2.0ms	13×	body	160	valid
2.0ms	8×	body	320	nan
1.0ms	5×	body	160	nan

simplify35.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	17	6
1	35	6
2	85	6
3	249	6
4	911	6
5	5001	6

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 33.0b

localize8.0ms

Local error

Found 3 expressions with local error:

0.8b	(pow x (/ 1.0 n))
1.5b	(pow (+ x 1.0) (/ 1.0 n))
2.5b	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))

rewrite66.0ms

Algorithm

rewrite-expression-head

Rules

76×	`*-un-lft-identity`
73×	`unpow-prod-down`
63×	`add-sqr-sqrt`
56×	`prod-diff`
51×	`add-cube-cbrt`
26×	`pow-unpow`
24×	`sqr-pow`
18×	`times-frac`
10×	`distribute-lft-out`
9×	`difference-of-squares`
8×	`fma-neg`
5×	`pow1` `add-exp-log` `add-log-exp`
3×	`expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u` `distribute-lft-out--`
2×	`pow-to-exp` `pow-pow` `pow-exp` `div-inv`
1×	`sub-neg` `flip3--` `diff-log` `flip--`

Counts

3 → 149

Calls

3 calls:

2.0ms	(pow x (/ 1.0 n))
5.0ms	(pow (+ x 1.0) (/ 1.0 n))
52.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))

series481.0ms

Counts

3 → 9

Calls

3 calls:

60.0ms	(pow x (/ 1.0 n))
148.0ms	(pow (+ x 1.0) (/ 1.0 n))
272.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))

simplify65.0ms

Algorithm

egg-herbie

Counts

158 → 158

Iterations

Useful iterations: 2 (47.0ms)

Iter	Nodes	Cost
0	654	2164
1	2164	1642
2	5002	1637

prune336.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 25.2b

localize10.0ms

Local error

Found 4 expressions with local error:

0.8b	(pow x (/ 1.0 n))
1.5b	(pow (+ x 1.0) (/ 1.0 n))
2.5b	(log (exp (- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))))
2.5b	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))

rewrite173.0ms

Algorithm

rewrite-expression-head

Rules

135×	`unpow-prod-down`
130×	`*-un-lft-identity`
112×	`prod-diff`
108×	`add-sqr-sqrt`
84×	`add-cube-cbrt`
61×	`log-prod`
58×	`exp-sum`
45×	`sqr-pow`
26×	`pow-unpow`
18×	`times-frac` `distribute-lft-out` `difference-of-squares`
16×	`log-pow`
15×	`exp-prod`
8×	`fma-neg`
7×	`pow1`
6×	`add-exp-log` `distribute-lft-out--` `add-log-exp`
4×	`expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u`
2×	`pow-to-exp` `sub-neg` `pow-pow` `pow-exp` `div-inv`
1×	`log-div` `flip3--` `exp-diff` `diff-log` `rem-log-exp` `flip--`

Counts

4 → 237

Calls

4 calls:

2.0ms	(pow x (/ 1.0 n))
5.0ms	(pow (+ x 1.0) (/ 1.0 n))
102.0ms	(log (exp (- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))))
51.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))

series763.0ms

Counts

4 → 12

Calls

4 calls:

56.0ms	(pow x (/ 1.0 n))
149.0ms	(pow (+ x 1.0) (/ 1.0 n))
276.0ms	(log (exp (- (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)))

simplify88.0ms

Algorithm

egg-herbie

Counts

249 → 249

Iterations

Useful iterations: 2 (50.0ms)

Iter	Nodes	Cost
0	835	3935
1	2477	2885
2	5001	2880

prune527.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 25.2b

localize17.0ms

Local error

Found 4 expressions with local error:

0.8b	(pow x (/ (/ 1.0 n) 2))
1.5b	(pow (+ x 1.0) (/ 1.0 n))
1.5b	(pow (+ x 1.0) (/ 1.0 n))
2.8b	(- (sqrt (pow (+ x 1.0) (/ 1.0 n))) (pow x (/ (/ 1.0 n) 2)))

rewrite84.0ms

Algorithm

rewrite-expression-head

Rules

124×	`*-un-lft-identity`
119×	`add-sqr-sqrt`
102×	`add-cube-cbrt`
84×	`times-frac`
83×	`unpow-prod-down`
77×	`prod-diff`
73×	`sqrt-prod`
69×	`pow-unpow`
29×	`sqr-pow`
12×	`difference-of-squares`
11×	`fma-neg`
10×	`distribute-lft-out`
7×	`pow1` `add-exp-log`
6×	`div-inv` `add-log-exp`
4×	`expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u`
3×	`pow-to-exp` `pow-pow` `pow-exp`
1×	`sub-neg` `flip3--` `diff-log` `flip--` `distribute-lft-out--`

Counts

4 → 234

Calls

4 calls:

7.0ms	(pow x (/ (/ 1.0 n) 2))
5.0ms	(pow (+ x 1.0) (/ 1.0 n))
5.0ms	(pow (+ x 1.0) (/ 1.0 n))
55.0ms	(- (sqrt (pow (+ x 1.0) (/ 1.0 n))) (pow x (/ (/ 1.0 n) 2)))

series757.0ms

Counts

4 → 12

Calls

4 calls:

56.0ms	(pow x (/ (/ 1.0 n) 2))
151.0ms	(pow (+ x 1.0) (/ 1.0 n))
151.0ms	(pow (+ x 1.0) (/ 1.0 n))
399.0ms	(- (sqrt (pow (+ x 1.0) (/ 1.0 n))) (pow x (/ (/ 1.0 n) 2)))

simplify97.0ms

Algorithm

egg-herbie

Counts

246 → 246

Iterations

Useful iterations: 2 (61.0ms)

Iter	Nodes	Cost
0	980	3839
1	3461	2852
2	5002	2817

prune764.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 24.8b

localize16.0ms

Local error

Found 4 expressions with local error:

1.5b	(pow (+ x 1.0) (/ 1.0 n))
1.5b	(pow (+ x 1.0) (/ 1.0 n))
2.8b	(- (sqrt (pow (+ x 1.0) (/ 1.0 n))) (pow x (/ (/ 1.0 n) 2)))
2.8b	(log (exp (- (sqrt (pow (+ x 1.0) (/ 1.0 n))) (pow x (/ (/ 1.0 n) 2)))))

rewrite206.0ms

Algorithm

rewrite-expression-head

Rules

154×	`prod-diff`
149×	`*-un-lft-identity`
148×	`unpow-prod-down`
145×	`add-sqr-sqrt`
138×	`sqrt-prod`
111×	`add-cube-cbrt`
82×	`log-prod`
79×	`exp-sum`
53×	`sqr-pow`
26×	`pow-unpow`
24×	`difference-of-squares`
18×	`times-frac`
17×	`log-pow` `distribute-lft-out`
16×	`exp-prod`
11×	`fma-neg`
7×	`pow1`
6×	`add-exp-log` `add-log-exp`
4×	`expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u`
2×	`pow-to-exp` `sub-neg` `pow-pow` `pow-exp` `div-inv` `distribute-lft-out--`
1×	`log-div` `flip3--` `exp-diff` `diff-log` `rem-log-exp` `flip--`

Counts

4 → 285

Calls

4 calls:

6.0ms	(pow (+ x 1.0) (/ 1.0 n))
5.0ms	(pow (+ x 1.0) (/ 1.0 n))
56.0ms	(- (sqrt (pow (+ x 1.0) (/ 1.0 n))) (pow x (/ (/ 1.0 n) 2)))
121.0ms	(log (exp (- (sqrt (pow (+ x 1.0) (/ 1.0 n))) (pow x (/ (/ 1.0 n) 2)))))

series1.1s

Counts

4 → 12

Calls

4 calls:

159.0ms	(pow (+ x 1.0) (/ 1.0 n))
160.0ms	(pow (+ x 1.0) (/ 1.0 n))
413.0ms	(- (sqrt (pow (+ x 1.0) (/ 1.0 n))) (pow x (/ (/ 1.0 n) 2)))
415.0ms	(log (exp (- (sqrt (pow (+ x 1.0) (/ 1.0 n))) (pow x (/ (/ 1.0 n) 2)))))

simplify96.0ms

Algorithm

egg-herbie

Counts

297 → 297

Iterations

Useful iterations: 2 (49.0ms)

Iter	Nodes	Cost
0	814	6456
1	2195	4496
2	5001	3769

prune770.0ms

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 24.8b

regimes299.0ms

Accuracy

82.2% (1.6b remaining)

Error of 22.9b against oracle of 21.3b and baseline of 30.1b

bsearch1.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	51	51
1	51	51

end0.0ms

sample4.9s

Algorithm

intervals

Results

1.6s	3185×	body	1280	valid
613.0ms	1597×	body	640	valid
539.0ms	1118×	body	10240	exit
404.0ms	4708×	body	80	valid
334.0ms	640×	body	1280	nan
331.0ms	5176×	body	80	nan
251.0ms	639×	body	640	nan
230.0ms	863×	body	320	valid
89.0ms	473×	body	160	valid
88.0ms	350×	body	320	nan
26.0ms	169×	body	160	nan