Details

sample224.0ms

Algorithm

intervals

Results

60.0ms	113×	body	1280	valid
43.0ms	41×	body	1280	nan
30.0ms	58×	body	640	valid
22.0ms	33×	body	640	nan
18.0ms	116×	body	80	overflowed
10.0ms	104×	body	80	valid
8.0ms	176×	body	80	nan
7.0ms	24×	body	320	valid
4.0ms	21×	body	160	valid
2.0ms	5×	body	320	nan
1.0ms	5×	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

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: 30.6b

Counts

2 → 1

localize9.0ms

Local error

Found 1 expressions with local error:

2.7b	(- (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)))

series282.0ms

Counts

1 → 3

Calls

1 calls:

282.0ms

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

simplify58.0ms

Algorithm

egg-herbie

Counts

93 → 93

Iterations

Useful iterations: 2 (36.0ms)

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

prune154.0ms

Filtered

93 candidates to 44 candidates (47.3%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	89	4	93
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	90	4	94

Merged error: 20.5b

Counts

94 → 4

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b	(cbrt (- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n))))
2.7b	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
2.7b	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
2.7b	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))

rewrite62.0ms

Algorithm

rewrite-expression-head

Rules

208×	`unpow-prod-down`
177×	`*-un-lft-identity`
168×	`prod-diff`
149×	`add-sqr-sqrt`
101×	`add-cube-cbrt`
72×	`sqr-pow`
36×	`difference-of-squares`
28×	`distribute-lft-out`
24×	`fma-neg`
15×	`cbrt-prod`
12×	`distribute-lft-out--`
10×	`add-log-exp`
4×	`pow1` `add-exp-log` `expm1-log1p-u` `flip3--` `add-cbrt-cube` `flip--` `log1p-expm1-u`
3×	`sub-neg` `diff-log`
2×	`cbrt-div`
1×	`pow1/3`

Counts

4 → 297

Calls

4 calls:

9.0ms	(cbrt (- (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)))
14.0ms	(- (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)))

series1.4s

Counts

4 → 12

Calls

4 calls:

581.0ms	(cbrt (- (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)))
283.0ms	(- (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)))

simplify98.0ms

Algorithm

egg-herbie

Counts

309 → 309

Iterations

Useful iterations: 2 (43.0ms)

Iter	Nodes	Cost
0	554	5996
1	1534	4421
2	5001	4401

prune644.0ms

Filtered

309 candidates to 157 candidates (50.8%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	307	2	309
Fresh	0	3	3
Picked	0	1	1
Done	0	0	0
Total	307	6	313

Merged error: 20.5b

Counts

313 → 6

localize35.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt x)
2.7b	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
2.7b	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
5.1b	(fma (* (cbrt (pow (+ x 1.0) (/ 1.0 n))) (cbrt (pow (+ x 1.0) (/ 1.0 n)))) (cbrt (pow (+ x 1.0) (/ 1.0 n))) (- (* (pow (cbrt x) (/ 1.0 n)) (pow (* (cbrt x) (cbrt x)) (/ 1.0 n)))))

rewrite36.0ms

Algorithm

rewrite-expression-head

Rules

132×	`unpow-prod-down`
115×	`*-un-lft-identity`
112×	`prod-diff`
93×	`add-sqr-sqrt`
69×	`add-cube-cbrt`
44×	`sqr-pow`
18×	`distribute-lft-out` `difference-of-squares`
16×	`fma-neg`
8×	`add-log-exp`
6×	`distribute-lft-out--`
4×	`pow1` `add-exp-log` `expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u`
3×	`cbrt-prod`
2×	`sub-neg` `flip3--` `diff-log` `flip--`
1×	`pow1/3` `fma-udef`

Counts

4 → 203

Calls

4 calls:

1.0ms	(cbrt x)
11.0ms	(- (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)))
1.0ms	(fma (* (cbrt (pow (+ x 1.0) (/ 1.0 n))) (cbrt (pow (+ x 1.0) (/ 1.0 n)))) (cbrt (pow (+ x 1.0) (/ 1.0 n))) (- (* (pow (cbrt x) (/ 1.0 n)) (pow (* (cbrt x) (cbrt x)) (/ 1.0 n)))))

series1.6s

Counts

4 → 12

Calls

4 calls:

181.0ms	(cbrt x)
286.0ms	(- (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)))
839.0ms	(fma (* (cbrt (pow (+ x 1.0) (/ 1.0 n))) (cbrt (pow (+ x 1.0) (/ 1.0 n)))) (cbrt (pow (+ x 1.0) (/ 1.0 n))) (- (* (pow (cbrt x) (/ 1.0 n)) (pow (* (cbrt x) (cbrt x)) (/ 1.0 n)))))

simplify95.0ms

Algorithm

egg-herbie

Counts

215 → 215

Iterations

Useful iterations: 2 (55.0ms)

Iter	Nodes	Cost
0	739	4188
1	2432	2959
2	5002	2915

prune795.0ms

Filtered

215 candidates to 109 candidates (50.7%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	214	1	215
Fresh	0	4	4
Picked	1	0	1
Done	0	1	1
Total	215	6	221

Merged error: 20.5b

Counts

221 → 6

localize26.0ms

Local error

Found 4 expressions with local error:

0.0b	(cbrt (pow (+ x 1.0) (/ 1.0 n)))
0.0b	(* (cbrt (pow (+ x 1.0) (/ 1.0 n))) (cbrt (pow (+ x 1.0) (/ 1.0 n))))
5.4b	(- (* (* (cbrt (pow (+ x 1.0) (/ 1.0 n))) (cbrt (pow (+ x 1.0) (/ 1.0 n)))) (cbrt (pow (+ x 1.0) (/ 1.0 n)))) (pow (sqrt x) (* 2 (/ 1.0 n))))
6.0b	(fma (pow (sqrt x) (/ 1.0 n)) (- (pow (sqrt x) (/ 1.0 n))) (pow (sqrt x) (* 2 (/ 1.0 n))))

rewrite46.0ms

Algorithm

rewrite-expression-head

Rules

68×	`cbrt-prod`
45×	`add-sqr-sqrt`
38×	`unpow-prod-down`
37×	`*-un-lft-identity`
21×	`add-cube-cbrt`
16×	`unswap-sqr`
14×	`sqr-pow`
13×	`swap-sqr`
11×	`pow1` `associate-r` `associate-l`
10×	`prod-diff`
7×	`pow1/3` `distribute-lft-out`
6×	`add-exp-log` `add-log-exp`
4×	`expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u`
3×	`sqrt-prod`
2×	`pow-prod-down` `pow-sqr` `pow-prod-up`
1×	`pow2` `sub-neg` `flip3--` `pow-plus` `fma-neg` `diff-log` `prod-exp` `*-commutative` `flip--` `cbrt-unprod` `fma-udef`

Counts

4 → 124

Calls

4 calls:

4.0ms	(cbrt (pow (+ x 1.0) (/ 1.0 n)))
14.0ms	(* (cbrt (pow (+ x 1.0) (/ 1.0 n))) (cbrt (pow (+ x 1.0) (/ 1.0 n))))
21.0ms	(- (* (* (cbrt (pow (+ x 1.0) (/ 1.0 n))) (cbrt (pow (+ x 1.0) (/ 1.0 n)))) (cbrt (pow (+ x 1.0) (/ 1.0 n)))) (pow (sqrt x) (* 2 (/ 1.0 n))))
1.0ms	(fma (pow (sqrt x) (/ 1.0 n)) (- (pow (sqrt x) (/ 1.0 n))) (pow (sqrt x) (* 2 (/ 1.0 n))))

series2.2s

Counts

4 → 12

Calls

4 calls:

173.0ms	(cbrt (pow (+ x 1.0) (/ 1.0 n)))
267.0ms	(* (cbrt (pow (+ x 1.0) (/ 1.0 n))) (cbrt (pow (+ x 1.0) (/ 1.0 n))))
441.0ms	(- (* (* (cbrt (pow (+ x 1.0) (/ 1.0 n))) (cbrt (pow (+ x 1.0) (/ 1.0 n)))) (cbrt (pow (+ x 1.0) (/ 1.0 n)))) (pow (sqrt x) (* 2 (/ 1.0 n))))
1.3s	(fma (pow (sqrt x) (/ 1.0 n)) (- (pow (sqrt x) (/ 1.0 n))) (pow (sqrt x) (* 2 (/ 1.0 n))))

simplify77.0ms

Algorithm

egg-herbie

Counts

136 → 136

Iterations

Useful iterations: 2 (57.0ms)

Iter	Nodes	Cost
0	675	2235
1	2543	1825
2	5002	1678

prune437.0ms

Filtered

136 candidates to 94 candidates (69.1%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	135	1	136
Fresh	0	4	4
Picked	0	1	1
Done	0	1	1
Total	135	7	142

Merged error: 20.4b

Counts

142 → 7

regimes242.0ms

Accuracy

83.6% (1.7b remaining)

Error of 23.8b against oracle of 22.1b and baseline of 32.5b

bsearch1.0ms

simplify3.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	79	111
1	81	111
2	81	111

end0.0ms

sample7.1s

Algorithm

intervals

Results

2.1s	3915×	body	1280	valid
1.2s	1146×	body	1280	nan
774.0ms	1743×	body	640	valid
665.0ms	934×	body	640	nan
589.0ms	4016×	body	80	overflowed
318.0ms	3207×	body	80	valid
306.0ms	6364×	body	80	nan
286.0ms	933×	body	320	valid
194.0ms	466×	body	320	nan
84.0ms	446×	body	160	valid
44.0ms	210×	body	160	nan