Details

sample156.0ms

Algorithm

intervals

Results

47.0ms	98×	body	1280	valid
24.0ms	23×	body	10240	exit
20.0ms	56×	body	640	valid
15.0ms	28×	body	1280	nan
8.0ms	152×	body	80	valid
6.0ms	28×	body	320	valid
6.0ms	18×	body	640	nan
6.0ms	160×	body	80	nan
3.0ms	17×	body	320	nan
1.0ms	9×	body	160	valid
0.0ms	4×	body	160	nan

simplify37.0ms

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: 28.1b

localize9.0ms

Local error

Found 3 expressions with local error:

0.3b	(pow x (/ 1.0 n))
0.5b	(pow (+ x 1.0) (/ 1.0 n))
1.5b	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))

rewrite71.0ms

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:

5.0ms	(pow x (/ 1.0 n))
6.0ms	(pow (+ x 1.0) (/ 1.0 n))
53.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))

series483.0ms

Counts

3 → 9

Calls

3 calls:

56.0ms	(pow x (/ 1.0 n))
147.0ms	(pow (+ x 1.0) (/ 1.0 n))
280.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))

simplify75.0ms

Algorithm

egg-herbie

Counts

158 → 158

Iterations

Useful iterations: 2 (49.0ms)

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

prune330.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 20.6b

localize13.0ms

Local error

Found 4 expressions with local error:

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

rewrite318.0ms

Algorithm

rewrite-expression-head

Rules

202×	`unpow-prod-down`
179×	`*-un-lft-identity`
168×	`prod-diff`
144×	`add-sqr-sqrt`
108×	`add-cube-cbrt`
67×	`sqr-pow`
28×	`distribute-lft-out`
27×	`difference-of-squares`
24×	`fma-neg`
13×	`pow-unpow`
10×	`add-log-exp`
9×	`times-frac` `distribute-lft-out--`
5×	`pow1` `add-exp-log`
4×	`expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u`
3×	`sub-neg` `flip3--` `diff-log` `flip--`
1×	`pow-to-exp` `pow-pow` `pow-exp` `div-inv`

Counts

4 → 300

Calls

4 calls:

8.0ms	(pow (+ x 1.0) (/ 1.0 n))
53.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
56.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
186.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))

series960.0ms

Counts

4 → 12

Calls

4 calls:

148.0ms	(pow (+ x 1.0) (/ 1.0 n))
272.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
272.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
268.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))

simplify100.0ms

Algorithm

egg-herbie

Counts

312 → 312

Iterations

Useful iterations: 2 (43.0ms)

Iter	Nodes	Cost
0	542	5691
1	1694	4129
2	5001	4126

prune715.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 20.5b

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b	(expm1 (log1p (pow x (/ 1.0 n))))
0.3b	(pow x (/ 1.0 n))
0.5b	(pow (+ x 1.0) (/ 1.0 n))
34.5b	(- (pow (+ x 1.0) (/ 1.0 n)) (expm1 (log1p (pow x (/ 1.0 n)))))

rewrite65.0ms

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))))
2.0ms	(pow x (/ 1.0 n))
6.0ms	(pow (+ x 1.0) (/ 1.0 n))
52.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (expm1 (log1p (pow x (/ 1.0 n)))))

series606.0ms

Counts

4 → 12

Calls

4 calls:

88.0ms	(expm1 (log1p (pow x (/ 1.0 n))))
55.0ms	(pow x (/ 1.0 n))
149.0ms	(pow (+ x 1.0) (/ 1.0 n))
313.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (expm1 (log1p (pow x (/ 1.0 n)))))

simplify59.0ms

Algorithm

egg-herbie

Counts

133 → 133

Iterations

Useful iterations: 2 (44.0ms)

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

prune346.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 20.5b

localize17.0ms

Local error

Found 4 expressions with local error:

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

rewrite295.0ms

Algorithm

rewrite-expression-head

Rules

260×	`unpow-prod-down`
224×	`prod-diff`
222×	`*-un-lft-identity`
180×	`add-sqr-sqrt`
132×	`add-cube-cbrt`
87×	`sqr-pow`
61×	`log-prod`
58×	`exp-sum`
36×	`difference-of-squares`
35×	`distribute-lft-out`
24×	`fma-neg`
16×	`log-pow`
15×	`exp-prod`
12×	`distribute-lft-out--`
10×	`add-log-exp`
5×	`pow1`
4×	`add-exp-log` `expm1-log1p-u` `sub-neg` `add-cbrt-cube` `log1p-expm1-u`
3×	`flip3--` `diff-log` `flip--`
1×	`log-div` `exp-diff` `rem-log-exp`

Counts

4 → 358

Calls

4 calls:

54.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
55.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
52.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
112.0ms	(log (exp (- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))))

series1.1s

Counts

4 → 12

Calls

4 calls:

279.0ms	(- (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)))
282.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
280.0ms	(log (exp (- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))))

simplify106.0ms

Algorithm

egg-herbie

Counts

370 → 370

Iterations

Useful iterations: 2 (36.0ms)

Iter	Nodes	Cost
0	594	7291
1	1493	5203
2	5002	4228

prune895.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 20.5b

regimes198.0ms

Accuracy

83.3% (1.4b remaining)

Error of 22.7b against oracle of 21.3b and baseline of 29.4b

bsearch1.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	52	51
1	52	51

end0.0ms

sample4.3s

Algorithm

intervals

Results

1.5s	3180×	body	1280	valid
580.0ms	1614×	body	640	valid
490.0ms	1152×	body	10240	exit
300.0ms	627×	body	1280	nan
267.0ms	4669×	body	80	valid
232.0ms	654×	body	640	nan
202.0ms	5087×	body	80	nan
197.0ms	832×	body	320	valid
75.0ms	363×	body	320	nan
67.0ms	458×	body	160	valid
23.0ms	188×	body	160	nan