Details

sample139.0ms

Algorithm

intervals

Results

50.0ms	106×	body	1280	valid
19.0ms	38×	body	10240	exit
18.0ms	55×	body	640	valid
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

simplify34.0ms

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: 32.3b

localize12.0ms

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))

rewrite116.0ms

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:

4.0ms	(pow x (/ 1.0 n))
93.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
10.0ms	(pow (+ x 1.0) (/ 1.0 n))

series463.0ms

Counts

3 → 9

Calls

3 calls:

60.0ms	(pow x (/ 1.0 n))
263.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
140.0ms	(pow (+ x 1.0) (/ 1.0 n))

simplify64.0ms

Algorithm

egg-herbie

Counts

158 → 158

Iterations

Useful iterations: 2 (47.0ms)

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

prune321.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 22.2b

localize15.0ms

Local error

Found 4 expressions with local error:

0.0b	(expm1 (log1p (pow x (/ 1.0 n))))
0.8b	(pow x (/ 1.0 n))
1.7b	(pow (+ x 1.0) (/ 1.0 n))
34.9b	(- (pow (+ x 1.0) (/ 1.0 n)) (expm1 (log1p (pow x (/ 1.0 n)))))

rewrite107.0ms

Algorithm

rewrite-expression-head

Rules

48×	`*-un-lft-identity`
41×	`add-sqr-sqrt`
36×	`add-cube-cbrt`
26×	`pow-unpow`
24×	`unpow-prod-down` `prod-diff`
18×	`times-frac`
8×	`fma-neg`
7×	`sqr-pow`
6×	`pow1` `add-exp-log` `add-log-exp`
5×	`distribute-lft-out`
4×	`expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u`
3×	`difference-of-squares`
2×	`pow-to-exp` `pow-pow` `pow-exp` `div-inv` `expm1-udef`
1×	`sub-neg` `expm1-log1p` `flip3--` `diff-log` `flip--` `distribute-lft-out--` `associate--r-`

Counts

4 → 121

Calls

4 calls:

0.0ms	(expm1 (log1p (pow x (/ 1.0 n))))
4.0ms	(pow x (/ 1.0 n))
10.0ms	(pow (+ x 1.0) (/ 1.0 n))
88.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (expm1 (log1p (pow x (/ 1.0 n)))))

series596.0ms

Counts

4 → 12

Calls

4 calls:

89.0ms	(expm1 (log1p (pow x (/ 1.0 n))))
63.0ms	(pow x (/ 1.0 n))
138.0ms	(pow (+ x 1.0) (/ 1.0 n))
306.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (expm1 (log1p (pow x (/ 1.0 n)))))

simplify57.0ms

Algorithm

egg-herbie

Counts

133 → 133

Iterations

Useful iterations: 2 (44.0ms)

Iter	Nodes	Cost
0	556	1604
1	1971	1009
2	5003	997

prune339.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 22.2b

localize21.0ms

Local error

Found 4 expressions with local error:

1.7b	(pow (+ x 1.0) (/ 1.0 n))
34.9b	(- (pow (+ x 1.0) (/ 1.0 n)) (expm1 (log1p (pow x (/ 1.0 n)))))
34.9b	(- (pow (+ x 1.0) (/ 1.0 n)) (expm1 (log1p (pow x (/ 1.0 n)))))
34.9b	(- (pow (+ x 1.0) (/ 1.0 n)) (expm1 (log1p (pow x (/ 1.0 n)))))

rewrite287.0ms

Algorithm

rewrite-expression-head

Rules

92×	`*-un-lft-identity`
75×	`add-sqr-sqrt`
72×	`prod-diff`
60×	`add-cube-cbrt`
55×	`unpow-prod-down`
24×	`fma-neg`
16×	`sqr-pow`
13×	`pow-unpow` `distribute-lft-out`
10×	`add-log-exp`
9×	`times-frac` `difference-of-squares`
5×	`pow1` `add-exp-log`
4×	`expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u`
3×	`sub-neg` `flip3--` `diff-log` `flip--` `distribute-lft-out--` `expm1-udef` `associate--r-`
1×	`pow-to-exp` `pow-pow` `pow-exp` `div-inv`

Counts

4 → 183

Calls

4 calls:

10.0ms	(pow (+ x 1.0) (/ 1.0 n))
90.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (expm1 (log1p (pow x (/ 1.0 n)))))
90.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (expm1 (log1p (pow x (/ 1.0 n)))))
89.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (expm1 (log1p (pow x (/ 1.0 n)))))

series1.1s

Counts

4 → 12

Calls

4 calls:

153.0ms	(pow (+ x 1.0) (/ 1.0 n))
313.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (expm1 (log1p (pow x (/ 1.0 n)))))
311.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (expm1 (log1p (pow x (/ 1.0 n)))))
317.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (expm1 (log1p (pow x (/ 1.0 n)))))

simplify63.0ms

Algorithm

egg-herbie

Counts

195 → 195

Iterations

Useful iterations: 2 (39.0ms)

Iter	Nodes	Cost
0	420	3765
1	1410	2050
2	5002	1995

prune628.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 22.2b

localize20.0ms

Local error

Found 4 expressions with local error:

34.9b	(- (pow (+ x 1.0) (/ 1.0 n)) (expm1 (log1p (pow x (/ 1.0 n)))))
34.9b	(- (pow (+ x 1.0) (/ 1.0 n)) (expm1 (log1p (pow x (/ 1.0 n)))))
34.9b	(- (pow (+ x 1.0) (/ 1.0 n)) (expm1 (log1p (pow x (/ 1.0 n)))))
34.9b	(- (pow (+ x 1.0) (/ 1.0 n)) (expm1 (log1p (pow x (/ 1.0 n)))))

rewrite366.0ms

Algorithm

rewrite-expression-head

Rules

108×	`*-un-lft-identity`
96×	`prod-diff`
88×	`add-sqr-sqrt`
68×	`add-cube-cbrt` `unpow-prod-down`
32×	`fma-neg`
20×	`sqr-pow`
16×	`distribute-lft-out`
12×	`add-log-exp` `difference-of-squares`
4×	`pow1` `add-exp-log` `expm1-log1p-u` `sub-neg` `flip3--` `diff-log` `add-cbrt-cube` `flip--` `log1p-expm1-u` `distribute-lft-out--` `expm1-udef` `associate--r-`

Counts

4 → 204

Calls

4 calls:

90.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (expm1 (log1p (pow x (/ 1.0 n)))))
88.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (expm1 (log1p (pow x (/ 1.0 n)))))
90.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (expm1 (log1p (pow x (/ 1.0 n)))))
89.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (expm1 (log1p (pow x (/ 1.0 n)))))

series1.2s

Counts

4 → 12

Calls

4 calls:

312.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (expm1 (log1p (pow x (/ 1.0 n)))))
308.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (expm1 (log1p (pow x (/ 1.0 n)))))
313.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (expm1 (log1p (pow x (/ 1.0 n)))))
314.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (expm1 (log1p (pow x (/ 1.0 n)))))

simplify66.0ms

Algorithm

egg-herbie

Counts

216 → 216

Iterations

Useful iterations: 2 (29.0ms)

Iter	Nodes	Cost
0	291	4792
1	906	2508
2	5001	2444

prune686.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 22.2b

regimes218.0ms

Accuracy

81.5% (1.6b remaining)

Error of 22.5b against oracle of 20.9b and baseline of 29.6b

bsearch1.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	57	67
1	57	67

end0.0ms

sample4.2s

Algorithm

intervals

Results

1.4s	3146×	body	1280	valid
543.0ms	1610×	body	640	valid
448.0ms	1106×	body	10240	exit
284.0ms	612×	body	1280	nan
249.0ms	4664×	body	80	valid
196.0ms	860×	body	320	valid
186.0ms	586×	body	640	nan
183.0ms	4907×	body	80	nan
64.0ms	342×	body	320	nan
60.0ms	440×	body	160	valid
18.0ms	167×	body	160	nan