Details

sample159.0ms

Algorithm

intervals

Results

56.0ms	96×	body	1280	valid
28.0ms	60×	body	640	valid
11.0ms	144×	body	80	valid
10.0ms	32×	body	320	valid
10.0ms	152×	body	80	nan
9.0ms	13×	body	1280	nan
5.0ms	20×	body	320	nan
5.0ms	13×	body	640	nan
3.0ms	16×	body	160	valid
3.0ms	35×	body	80	overflowed
1.0ms	6×	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: 31.8b

localize13.0ms

Local error

Found 3 expressions with local error:

0.2b	(pow x (/ 1.0 n))
0.7b	(pow (+ x 1.0) (/ 1.0 n))
1.7b	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))

rewrite67.0ms

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))
49.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))

series455.0ms

Counts

3 → 9

Calls

3 calls:

57.0ms	(pow x (/ 1.0 n))
137.0ms	(pow (+ x 1.0) (/ 1.0 n))
261.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))

simplify66.0ms

Algorithm

egg-herbie

Counts

158 → 158

Iterations

Useful iterations: 2 (47.0ms)

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

prune330.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 22.4b

localize11.0ms

Local error

Found 4 expressions with local error:

0.2b	(pow x (/ 1.0 n))
0.7b	(pow (+ x 1.0) (/ 1.0 n))
1.7b	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
1.7b	(log (exp (- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))))

rewrite177.0ms

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))
49.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
105.0ms	(log (exp (- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))))

series751.0ms

Counts

4 → 12

Calls

4 calls:

55.0ms	(pow x (/ 1.0 n))
147.0ms	(pow (+ x 1.0) (/ 1.0 n))
276.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
273.0ms	(log (exp (- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))))

simplify90.0ms

Algorithm

egg-herbie

Counts

249 → 249

Iterations

Useful iterations: 2 (51.0ms)

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

prune517.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 22.4b

localize19.0ms

Local error

Found 4 expressions with local error:

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

rewrite222.0ms

Algorithm

rewrite-expression-head

Rules

236×	`unpow-prod-down`
224×	`prod-diff`
206×	`*-un-lft-identity`
156×	`add-sqr-sqrt`
132×	`add-cube-cbrt`
128×	`log-prod`
122×	`cbrt-prod`
116×	`exp-sum`
74×	`sqr-pow`
32×	`distribute-lft-out`
18×	`difference-of-squares`
16×	`fma-neg`
8×	`add-log-exp`
6×	`pow1` `add-exp-log` `distribute-lft-out--`
4×	`expm1-log1p-u` `sub-neg` `log-pow` `add-cbrt-cube` `log1p-expm1-u`
2×	`log-div` `cbrt-div` `flip3--` `exp-diff` `pow1/3` `diff-log` `rem-log-exp` `flip--`

Counts

4 → 334

Calls

4 calls:

51.0ms	(- (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)))
49.0ms	(log (cbrt (exp (- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n))))))
47.0ms	(log (cbrt (exp (- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n))))))

series1.4s

Counts

4 → 12

Calls

4 calls:

276.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
274.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
443.0ms	(log (cbrt (exp (- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n))))))
454.0ms	(log (cbrt (exp (- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n))))))

simplify97.0ms

Algorithm

egg-herbie

Counts

346 → 346

Iterations

Useful iterations: 2 (39.0ms)

Iter	Nodes	Cost
0	665	7966
1	1642	6298
2	5001	5480

prune917.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 22.3b

localize17.0ms

Local error

Found 4 expressions with local error:

0.7b	(pow (+ x 1.0) (/ 1.0 n))
1.7b	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
1.7b	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
1.7b	(log (cbrt (exp (- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n))))))

rewrite172.0ms

Algorithm

rewrite-expression-head

Rules

188×	`unpow-prod-down`
170×	`*-un-lft-identity`
168×	`prod-diff`
132×	`add-sqr-sqrt`
108×	`add-cube-cbrt`
64×	`log-prod`
61×	`cbrt-prod`
60×	`sqr-pow`
58×	`exp-sum`
26×	`distribute-lft-out`
18×	`difference-of-squares`
16×	`fma-neg`
13×	`pow-unpow`
9×	`times-frac`
8×	`add-log-exp`
6×	`pow1` `add-exp-log` `distribute-lft-out--`
4×	`expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u`
3×	`sub-neg`
2×	`flip3--` `diff-log` `log-pow` `flip--`
1×	`pow-to-exp` `log-div` `cbrt-div` `pow-pow` `exp-diff` `pow1/3` `rem-log-exp` `pow-exp` `div-inv`

Counts

4 → 287

Calls

4 calls:

6.0ms	(pow (+ x 1.0) (/ 1.0 n))
51.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
48.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
49.0ms	(log (cbrt (exp (- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n))))))

series1.1s

Counts

4 → 12

Calls

4 calls:

147.0ms	(pow (+ x 1.0) (/ 1.0 n))
274.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
269.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
451.0ms	(log (cbrt (exp (- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n))))))

simplify98.0ms

Algorithm

egg-herbie

Counts

299 → 299

Iterations

Useful iterations: 2 (50.0ms)

Iter	Nodes	Cost
0	794	5994
1	2158	4638
2	5002	4234

prune784.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 22.3b

regimes310.0ms

Accuracy

78% (1.8b remaining)

Error of 23.1b against oracle of 21.3b and baseline of 29.6b

bsearch2.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	47	54
1	47	54

end0.0ms

sample5.0s

Algorithm

intervals

Results

1.9s	3115×	body	1280	valid
747.0ms	1602×	body	640	valid
388.0ms	4811×	body	80	valid
346.0ms	601×	body	1280	nan
323.0ms	5106×	body	80	nan
283.0ms	896×	body	320	valid
249.0ms	573×	body	640	nan
99.0ms	1284×	body	80	overflowed
98.0ms	363×	body	320	nan
89.0ms	440×	body	160	valid
36.0ms	207×	body	160	nan