Details

sample216.0ms

Algorithm

intervals

Results

57.0ms	122×	body	1280	valid
40.0ms	69×	body	1280	nan
26.0ms	66×	body	640	valid
22.0ms	55×	body	640	nan
22.0ms	30×	body	10240	exit
9.0ms	35×	body	320	nan
8.0ms	190×	body	80	nan
6.0ms	30×	body	320	valid
4.0ms	92×	body	80	valid
1.0ms	10×	body	160	nan
1.0ms	8×	body	160	valid

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: 34.6b

localize9.0ms

Local error

Found 3 expressions with local error:

0.0b	(pow (+ x 1.0) (/ 1.0 n))
0.0b	(pow x (/ 1.0 n))
1.5b	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))

rewrite27.0ms

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) (/ 1.0 n))
4.0ms	(pow x (/ 1.0 n))
12.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))

series475.0ms

Counts

3 → 9

Calls

3 calls:

145.0ms	(pow (+ x 1.0) (/ 1.0 n))
55.0ms	(pow x (/ 1.0 n))
275.0ms	(- (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

prune462.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 22.2b

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b	(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	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))

rewrite57.0ms

Algorithm

rewrite-expression-head

Rules

201×	`unpow-prod-down`
177×	`*-un-lft-identity`
168×	`prod-diff`
144×	`add-sqr-sqrt`
108×	`add-cube-cbrt`
67×	`sqr-pow`
27×	`distribute-lft-out` `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 → 299

Calls

4 calls:

4.0ms	(pow x (/ 1.0 n))
14.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
12.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
12.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))

series857.0ms

Counts

4 → 12

Calls

4 calls:

55.0ms	(pow x (/ 1.0 n))
270.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
265.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
266.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))

simplify94.0ms

Algorithm

egg-herbie

Counts

311 → 311

Iterations

Useful iterations: 2 (45.0ms)

Iter	Nodes	Cost
0	587	5673
1	1958	4113
2	5002	4107

prune729.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 22.2b

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b	(pow (+ x 1.0) (/ 1.0 n))
0.0b	(pow x (/ 1.0 n))
0.0b	(expm1 (log1p (pow x (/ 1.0 n))))
42.0b	(- (pow (+ x 1.0) (/ 1.0 n)) (expm1 (log1p (pow x (/ 1.0 n)))))

rewrite23.0ms

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:

6.0ms	(pow (+ x 1.0) (/ 1.0 n))
4.0ms	(pow x (/ 1.0 n))
1.0ms	(expm1 (log1p (pow x (/ 1.0 n))))
9.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (expm1 (log1p (pow x (/ 1.0 n)))))

series604.0ms

Counts

4 → 12

Calls

4 calls:

142.0ms	(pow (+ x 1.0) (/ 1.0 n))
61.0ms	(pow x (/ 1.0 n))
88.0ms	(expm1 (log1p (pow x (/ 1.0 n))))
314.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (expm1 (log1p (pow x (/ 1.0 n)))))

simplify62.0ms

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: 22.2b

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)))))

rewrite79.0ms

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:

12.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
12.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
15.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
18.0ms	(log (exp (- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))))

series1.1s

Counts

4 → 12

Calls

4 calls:

274.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
277.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
284.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
279.0ms	(log (exp (- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))))

simplify96.0ms

Algorithm

egg-herbie

Counts

370 → 370

Iterations

Useful iterations: 2 (36.0ms)

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

prune907.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 22.2b

regimes204.0ms

Accuracy

83.5% (1.6b remaining)

Error of 24.3b against oracle of 22.6b and baseline of 32.6b

bsearch1.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	52	51
1	52	51

end0.0ms

sample6.4s

Algorithm

intervals

Results

1.8s	3892×	body	1280	valid
1.2s	2167×	body	1280	nan
723.0ms	1801×	body	640	nan
607.0ms	1803×	body	640	valid
591.0ms	1437×	body	10240	exit
267.0ms	6260×	body	80	nan
213.0ms	871×	body	320	nan
203.0ms	881×	body	320	valid
160.0ms	3147×	body	80	valid
65.0ms	468×	body	160	valid
62.0ms	434×	body	160	nan