Details

sample227.0ms

Algorithm

intervals

Results

67.0ms	123×	body	1280	valid
35.0ms	31×	body	1280	nan
27.0ms	58×	body	640	valid
18.0ms	121×	body	80	overflowed
17.0ms	25×	body	640	nan
12.0ms	39×	body	320	valid
10.0ms	205×	body	80	nan
9.0ms	93×	body	80	valid
6.0ms	14×	body	320	nan
2.0ms	10×	body	160	valid
1.0ms	4×	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

Filtered

1 candidates to 0 candidates (0.0%)

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: 33.1b

Counts

2 → 1

localize13.0ms

Local error

Found 1 expressions with local error:

2.2b	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))

rewrite16.0ms

Algorithm

rewrite-expression-head

Rules

66×	`unpow-prod-down`
56×	`*-un-lft-identity` `prod-diff`
45×	`add-sqr-sqrt`
33×	`add-cube-cbrt`
22×	`sqr-pow`
9×	`distribute-lft-out` `difference-of-squares`
8×	`fma-neg`
3×	`distribute-lft-out--` `add-log-exp`
1×	`pow1` `add-exp-log` `expm1-log1p-u` `sub-neg` `flip3--` `diff-log` `add-cbrt-cube` `flip--` `log1p-expm1-u`

Counts

1 → 90

Calls

1 calls:

11.0ms

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

series275.0ms

Counts

1 → 3

Calls

1 calls:

274.0ms

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

simplify51.0ms

Algorithm

egg-herbie

Counts

93 → 93

Iterations

Useful iterations: 2 (35.0ms)

Iter	Nodes	Cost
0	413	1840
1	1182	1320
2	5002	1316

prune142.0ms

Filtered

93 candidates to 44 candidates (47.3%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	90	3	93
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	91	3	94

Merged error: 22.0b

Counts

94 → 3

localize14.0ms

Local error

Found 3 expressions with local error:

0.1b	(exp (log (- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))))
0.5b	(log (- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n))))
2.2b	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))

rewrite42.0ms

Algorithm

rewrite-expression-head

Rules

86×	`unpow-prod-down`
75×	`*-un-lft-identity`
74×	`add-sqr-sqrt`
56×	`prod-diff`
38×	`add-cube-cbrt`
34×	`sqr-pow`
30×	`log-prod`
27×	`difference-of-squares`
15×	`exp-sum`
11×	`distribute-lft-out`
9×	`distribute-lft-out--`
8×	`fma-neg`
5×	`pow1` `add-log-exp`
4×	`add-exp-log` `log-div` `exp-prod`
3×	`expm1-log1p-u` `flip3--` `add-cbrt-cube` `flip--` `log1p-expm1-u`
2×	`exp-diff` `log-pow`
1×	`sub-neg` `diff-log` `rem-log-exp` `rem-exp-log`

Counts

3 → 149

Calls

3 calls:

11.0ms	(exp (log (- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))))
12.0ms	(log (- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n))))
11.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))

series997.0ms

Counts

3 → 9

Calls

3 calls:

279.0ms	(exp (log (- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))))
445.0ms	(log (- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n))))
273.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))

simplify63.0ms

Algorithm

egg-herbie

Counts

158 → 158

Iterations

Useful iterations: 2 (40.0ms)

Iter	Nodes	Cost
0	557	2664
1	1523	2102
2	5002	2079

prune319.0ms

Filtered

158 candidates to 94 candidates (59.5%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	155	3	158
Fresh	1	1	2
Picked	1	0	1
Done	0	0	0
Total	157	4	161

Merged error: 22.0b

Counts

161 → 4

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b	(pow (log (- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))) 3)
0.1b	(exp (cbrt (pow (log (- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))) 3)))
0.5b	(log (- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n))))
2.2b	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))

rewrite39.0ms

Algorithm

rewrite-expression-head

Rules

84×	`unpow-prod-down`
74×	`*-un-lft-identity`
68×	`add-sqr-sqrt`
56×	`prod-diff`
44×	`add-cube-cbrt`
30×	`sqr-pow`
18×	`difference-of-squares`
17×	`exp-prod`
15×	`log-prod`
14×	`cbrt-prod`
10×	`pow1` `distribute-lft-out`
8×	`fma-neg` `cube-prod`
7×	`add-log-exp`
6×	`add-exp-log` `distribute-lft-out--`
5×	`log-pow` `add-cbrt-cube`
4×	`expm1-log1p-u` `log1p-expm1-u`
3×	`pow-unpow`
2×	`cube-mult` `log-div` `flip3--` `unpow3` `flip--`
1×	`pow-to-exp` `sub-neg` `pow-pow` `diff-log` `rem-log-exp` `pow-exp` `rem-exp-log` `rem-cube-cbrt`

Counts

4 → 172

Calls

4 calls:

3.0ms	(pow (log (- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))) 3)
4.0ms	(exp (cbrt (pow (log (- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))) 3)))
12.0ms	(log (- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n))))
11.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))

series2.1s

Counts

4 → 12

Calls

4 calls:

1.1s	(pow (log (- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))) 3)
286.0ms	(exp (cbrt (pow (log (- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))) 3)))
457.0ms	(log (- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n))))
276.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))

simplify129.0ms

Algorithm

egg-herbie

Counts

184 → 184

Iterations

Useful iterations: 2 (95.0ms)

Iter	Nodes	Cost
0	1202	3166
1	4560	2559
2	5001	2558

prune472.0ms

Filtered

184 candidates to 105 candidates (57.1%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	182	2	184
Fresh	1	2	3
Picked	1	0	1
Done	0	0	0
Total	184	4	188

Merged error: 22.0b

Counts

188 → 4

localize14.0ms

Local error

Found 4 expressions with local error:

0.0b	(pow (log (- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))) 3)
0.1b	(pow E (cbrt (pow (log (- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))) 3)))
0.5b	(log (- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n))))
2.2b	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))

rewrite38.0ms

Algorithm

rewrite-expression-head

Rules

87×	`unpow-prod-down`
75×	`*-un-lft-identity`
69×	`add-sqr-sqrt`
56×	`prod-diff`
45×	`add-cube-cbrt`
31×	`sqr-pow`
20×	`pow-unpow`
18×	`difference-of-squares`
15×	`log-prod`
14×	`cbrt-prod`
11×	`pow1`
10×	`distribute-lft-out`
8×	`fma-neg` `cube-prod`
7×	`add-exp-log`
6×	`distribute-lft-out--` `add-log-exp`
5×	`log-pow` `add-cbrt-cube`
4×	`expm1-log1p-u` `log1p-expm1-u`
3×	`pow-exp`
2×	`cube-mult` `pow-to-exp` `log-div` `flip3--` `pow-pow` `unpow3` `flip--`
1×	`sub-neg` `e-exp-1` `diff-log` `rem-log-exp` `rem-cube-cbrt`

Counts

4 → 179

Calls

4 calls:

3.0ms	(pow (log (- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))) 3)
4.0ms	(pow E (cbrt (pow (log (- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))) 3)))
12.0ms	(log (- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n))))
11.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))

series2.2s

Counts

4 → 12

Calls

4 calls:

1.1s	(pow (log (- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))) 3)
427.0ms	(pow E (cbrt (pow (log (- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))) 3)))
447.0ms	(log (- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n))))
278.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))

simplify65.0ms

Algorithm

egg-herbie

Counts

191 → 191

Iterations

Useful iterations: 1 (29.0ms)

Iter	Nodes	Cost
0	1330	3345
1	5001	2707

prune474.0ms

Filtered

191 candidates to 110 candidates (57.6%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	190	1	191
Fresh	1	2	3
Picked	0	1	1
Done	0	0	0
Total	191	4	195

Merged error: 22.0b

Counts

195 → 4

regimes244.0ms

Accuracy

86.5% (1.4b remaining)

Error of 24.2b against oracle of 22.8b and baseline of 33.1b

bsearch224.0ms

Steps

Iters	Range		Point
9	932939.2879875953	25160700273564.105	54666412.879635885
10	-114621340556398.55	-6.784177417847745e-05	-46.92585733952256

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	48	24
1	48	24

end0.0ms

sample7.3s

Algorithm

intervals

Results

2.3s	3879×	body	1280	valid
1.2s	1067×	body	1280	nan
828.0ms	1775×	body	640	valid
644.0ms	900×	body	640	nan
621.0ms	4045×	body	80	overflowed
324.0ms	3137×	body	80	valid
310.0ms	6208×	body	80	nan
282.0ms	898×	body	320	valid
191.0ms	439×	body	320	nan
82.0ms	424×	body	160	valid
55.0ms	233×	body	160	nan