Details

sample227.0ms

Algorithm

intervals

Results

59.0ms	121×	body	1280	valid
39.0ms	71×	body	1280	nan
37.0ms	54×	body	10240	exit
22.0ms	69×	body	640	valid
20.0ms	56×	body	640	nan
8.0ms	181×	body	80	nan
8.0ms	30×	body	320	nan
6.0ms	27×	body	320	valid
5.0ms	105×	body	80	valid
2.0ms	15×	body	160	nan
1.0ms	9×	body	160	valid

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

Filtered

1 candidates to 0 candidates (100.0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Kept	Total
New	1	1
Fresh	1	1
Picked	0	0
Done	0	0
Total	2	2

Merged error: 29.9b

Counts

2 → 1

localize8.0ms

Local error

Found 3 expressions with local error:

0.0b	(pow (+ x 1.0) (/ 1.0 n))
0.0b	(pow x (/ 1.0 n))
1.2b	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))

rewrite26.0ms

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))
3.0ms	(pow x (/ 1.0 n))
12.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))

series510.0ms

Counts

3 → 9

Calls

3 calls:

154.0ms	(pow (+ x 1.0) (/ 1.0 n))
65.0ms	(pow x (/ 1.0 n))
291.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))

simplify67.0ms

Algorithm

egg-herbie

Counts

158 → 158

Iterations

Useful iterations: 2 (47.0ms)

Iter	Nodes	Cost
0	654	2164
1	2154	1642
2	5001	1637

prune266.0ms

Filtered

158 candidates to 95 candidates (39.9%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	153	5	158
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	154	5	159

Merged error: 19.1b

Counts

159 → 5

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b	(pow (sqrt (+ x 1.0)) (/ 1.0 n))
0.0b	(pow x (/ (/ 1.0 n) 2))
0.0b	(pow x (/ (/ 1.0 n) 2))
1.2b	(- (pow (sqrt (+ x 1.0)) (/ 1.0 n)) (pow x (/ (/ 1.0 n) 2)))

rewrite50.0ms

Algorithm

rewrite-expression-head

Rules

151×	`*-un-lft-identity`
148×	`add-sqr-sqrt`
141×	`times-frac`
131×	`add-cube-cbrt`
112×	`unpow-prod-down`
99×	`pow-unpow`
77×	`prod-diff`
39×	`sqrt-prod`
29×	`sqr-pow`
12×	`difference-of-squares`
11×	`fma-neg`
9×	`div-inv` `distribute-lft-out`
8×	`pow1`
7×	`add-exp-log`
6×	`add-log-exp`
5×	`pow-pow`
4×	`expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u`
3×	`pow-to-exp` `pow-exp`
1×	`sub-neg` `flip3--` `sqrt-pow1` `pow1/2` `diff-log` `sqrt-pow2` `flip--` `distribute-lft-out--`

Counts

4 → 269

Calls

4 calls:

5.0ms	(pow (sqrt (+ x 1.0)) (/ 1.0 n))
9.0ms	(pow x (/ (/ 1.0 n) 2))
6.0ms	(pow x (/ (/ 1.0 n) 2))
14.0ms	(- (pow (sqrt (+ x 1.0)) (/ 1.0 n)) (pow x (/ (/ 1.0 n) 2)))

series976.0ms

Counts

4 → 12

Calls

4 calls:

373.0ms	(pow (sqrt (+ x 1.0)) (/ 1.0 n))
64.0ms	(pow x (/ (/ 1.0 n) 2))
58.0ms	(pow x (/ (/ 1.0 n) 2))
480.0ms	(- (pow (sqrt (+ x 1.0)) (/ 1.0 n)) (pow x (/ (/ 1.0 n) 2)))

simplify104.0ms

Algorithm

egg-herbie

Counts

281 → 281

Iterations

Useful iterations: 2 (68.0ms)

Iter	Nodes	Cost
0	958	4123
1	3393	3178
2	5002	3169

prune693.0ms

Filtered

281 candidates to 181 candidates (35.6%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	281	0	281
Fresh	0	4	4
Picked	0	1	1
Done	0	0	0
Total	281	5	286

Merged error: 19.1b

Counts

286 → 5

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b	(exp (- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n))))
0.0b	(pow x (/ 1.0 n))
1.2b	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
1.2b	(log (exp (- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))))

rewrite71.0ms

Algorithm

rewrite-expression-head

Rules

193×	`unpow-prod-down`
172×	`*-un-lft-identity`
168×	`prod-diff`
143×	`add-sqr-sqrt`
116×	`exp-sum`
107×	`add-cube-cbrt`
65×	`sqr-pow`
61×	`log-prod`
30×	`exp-prod`
27×	`difference-of-squares`
25×	`distribute-lft-out`
16×	`log-pow`
13×	`pow-unpow`
9×	`times-frac` `distribute-lft-out--` `add-log-exp`
8×	`fma-neg`
6×	`pow1` `add-exp-log`
4×	`expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u`
3×	`sub-neg`
2×	`exp-diff` `diff-log` `rem-log-exp` `rem-exp-log`
1×	`pow-to-exp` `log-div` `flip3--` `pow-pow` `pow-exp` `flip--` `div-inv`

Counts

4 → 293

Calls

4 calls:

20.0ms	(exp (- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n))))
3.0ms	(pow x (/ 1.0 n))
12.0ms	(- (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)))))

series1.3s

Counts

4 → 12

Calls

4 calls:

477.0ms	(exp (- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n))))
66.0ms	(pow x (/ 1.0 n))
510.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
294.0ms	(log (exp (- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))))

simplify103.0ms

Algorithm

egg-herbie

Counts

305 → 305

Iterations

Useful iterations: 2 (52.0ms)

Iter	Nodes	Cost
0	787	5600
1	2324	4244
2	5001	3441

prune448.0ms

Filtered

305 candidates to 143 candidates (53.1%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	303	2	305
Fresh	0	3	3
Picked	1	0	1
Done	0	1	1
Total	304	6	310

Merged error: 19.1b

Counts

310 → 6

localize13.0ms

Local error

Found 4 expressions with local error:

1.2b	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
1.2b	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
1.2b	(log (sqrt (exp (- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n))))))
1.2b	(log (sqrt (exp (- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n))))))

rewrite98.0ms

Algorithm

rewrite-expression-head

Rules

256×	`unpow-prod-down`
224×	`prod-diff`
222×	`*-un-lft-identity`
182×	`add-sqr-sqrt`
134×	`add-cube-cbrt`
128×	`log-prod`
122×	`sqrt-prod`
116×	`exp-sum`
86×	`sqr-pow`
36×	`log-pow` `difference-of-squares`
34×	`distribute-lft-out`
32×	`sqrt-pow1`
30×	`exp-prod`
16×	`fma-neg`
12×	`distribute-lft-out--`
8×	`pow1` `add-log-exp`
6×	`add-exp-log`
4×	`expm1-log1p-u` `sub-neg` `add-cbrt-cube` `log1p-expm1-u`
2×	`log-div` `flip3--` `pow1/2` `exp-diff` `sqrt-div` `diff-log` `rem-log-exp` `flip--`

Counts

4 → 366

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)))
23.0ms	(log (sqrt (exp (- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n))))))
21.0ms	(log (sqrt (exp (- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n))))))

series1.6s

Counts

4 → 12

Calls

4 calls:

294.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
310.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
481.0ms	(log (sqrt (exp (- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n))))))
475.0ms	(log (sqrt (exp (- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n))))))

simplify123.0ms

Algorithm

egg-herbie

Counts

378 → 378

Iterations

Useful iterations: 2 (48.0ms)

Iter	Nodes	Cost
0	709	8170
1	1694	6502
2	5001	5684

prune819.0ms

Filtered

378 candidates to 172 candidates (54.5%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	377	1	378
Fresh	0	4	4
Picked	1	0	1
Done	0	1	1
Total	378	6	384

Merged error: 19.1b

Counts

384 → 6

regimes204.0ms

Accuracy

84.6% (1.6b remaining)

Error of 24.4b against oracle of 22.8b and baseline of 33.2b

bsearch1.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	57	69
1	57	69

end0.0ms

sample6.5s

Algorithm

intervals

Results

1.9s	3888×	body	1280	valid
1.3s	2107×	body	1280	nan
687.0ms	1655×	body	640	nan
657.0ms	1912×	body	640	valid
612.0ms	1416×	body	10240	exit
274.0ms	6166×	body	80	nan
237.0ms	928×	body	320	nan
188.0ms	849×	body	320	valid
148.0ms	3089×	body	80	valid
68.0ms	468×	body	160	nan
57.0ms	417×	body	160	valid