Details

sample209.0ms

Algorithm

intervals

Results

53.0ms	117×	body	1280	valid
51.0ms	83×	body	1280	nan
21.0ms	63×	body	640	valid
20.0ms	52×	body	640	nan
11.0ms	39×	body	10240	exit
9.0ms	209×	body	80	nan
7.0ms	30×	body	320	nan
6.0ms	27×	body	320	valid
5.0ms	103×	body	80	valid
3.0ms	20×	body	160	valid
2.0ms	16×	body	160	nan

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 (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: 34.7b

Counts

2 → 1

localize8.0ms

Local error

Found 2 expressions with local error:

0.0b	(pow x (/ 1.0 n))
3.1b	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))

rewrite21.0ms

Algorithm

rewrite-expression-head

Rules

69×	`unpow-prod-down`
65×	`*-un-lft-identity`
56×	`prod-diff`
54×	`add-sqr-sqrt`
42×	`add-cube-cbrt`
23×	`sqr-pow`
13×	`pow-unpow`
9×	`times-frac` `distribute-lft-out` `difference-of-squares`
8×	`fma-neg`
4×	`add-log-exp`
3×	`pow1` `add-exp-log` `distribute-lft-out--`
2×	`expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u`
1×	`pow-to-exp` `sub-neg` `flip3--` `pow-pow` `diff-log` `pow-exp` `flip--` `div-inv`

Counts

2 → 119

Calls

2 calls:

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

series344.0ms

Counts

2 → 6

Calls

2 calls:

61.0ms	(pow x (/ 1.0 n))
282.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))

simplify64.0ms

Algorithm

egg-herbie

Counts

125 → 125

Iterations

Useful iterations: 2 (46.0ms)

Iter	Nodes	Cost
0	586	1993
1	1944	1473
2	5002	1469

prune208.0ms

Filtered

125 candidates to 69 candidates (55.2%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	118	7	125
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	119	7	126

Merged error: 24.5b

Counts

126 → 7

localize12.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (cbrt (- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))) (cbrt (- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))))
3.1b	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
3.1b	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
3.1b	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))

rewrite92.0ms

Algorithm

rewrite-expression-head

Rules

246×	`unpow-prod-down`
221×	`*-un-lft-identity`
200×	`add-sqr-sqrt`
168×	`prod-diff`
108×	`add-cube-cbrt`
90×	`sqr-pow`
72×	`cbrt-prod`
63×	`difference-of-squares`
33×	`distribute-lft-out`
27×	`distribute-lft-out--`
24×	`fma-neg`
22×	`swap-sqr`
18×	`associate-r` `associate-l`
12×	`cbrt-div`
11×	`pow1`
10×	`add-log-exp`
9×	`flip3--` `flip--`
8×	`add-cbrt-cube`
6×	`add-exp-log` `pow1/3`
4×	`expm1-log1p-u` `frac-times` `cbrt-unprod` `log1p-expm1-u` `unswap-sqr`
3×	`sub-neg` `diff-log`
2×	`associate-r/` `pow-prod-down` `associate-l/` `pow-sqr` `pow-prod-up`
1×	`pow2` `pow-plus` `prod-exp` `*-commutative`

Counts

4 → 363

Calls

4 calls:

34.0ms	(* (cbrt (- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))) (cbrt (- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))))
13.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
13.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
13.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))

series2.3s

Counts

4 → 12

Calls

4 calls:

1.5s	(* (cbrt (- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))) (cbrt (- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))))
290.0ms	(- (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)))
281.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))

simplify128.0ms

Algorithm

egg-herbie

Counts

375 → 375

Iterations

Useful iterations: 2 (61.0ms)

Iter	Nodes	Cost
0	701	7579
1	2249	5888
2	5001	5677

prune801.0ms

Filtered

375 candidates to 195 candidates (52.0%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	367	8	375
Fresh	3	3	6
Picked	1	0	1
Done	0	0	0
Total	371	11	382

Merged error: 24.4b

Counts

382 → 11

localize31.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt x)
3.1b	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
3.1b	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
3.1b	(- (pow (+ x 1.0) (/ 1.0 n)) (* (pow (cbrt x) (/ 1.0 n)) (pow (* (cbrt x) (cbrt x)) (/ 1.0 n))))

rewrite223.0ms

Algorithm

rewrite-expression-head

Rules

1523×	`add-sqr-sqrt`
1447×	`unpow-prod-down`
832×	`prod-diff`
692×	`unswap-sqr`
600×	`*-un-lft-identity`
540×	`cbrt-prod`
363×	`add-cube-cbrt`
361×	`sqr-pow`
296×	`associate-r`
153×	`difference-of-squares`
136×	`swap-sqr`
131×	`associate-l`
110×	`distribute-lft-out`
60×	`*-commutative`
24×	`fma-neg`
10×	`distribute-lft-out--` `add-log-exp`
4×	`pow1` `add-exp-log` `expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u`
3×	`sub-neg` `flip3--` `diff-log` `flip--`
1×	`pow1/3`

Counts

4 → 1074

Calls

4 calls:

1.0ms	(cbrt x)
13.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
13.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
78.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (* (pow (cbrt x) (/ 1.0 n)) (pow (* (cbrt x) (cbrt x)) (/ 1.0 n))))

series1.2s

Counts

4 → 12

Calls

4 calls:

178.0ms	(cbrt x)
294.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
286.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
464.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (* (pow (cbrt x) (/ 1.0 n)) (pow (* (cbrt x) (cbrt x)) (/ 1.0 n))))

simplify479.0ms

Algorithm

egg-herbie

Counts

1086 → 1086

Iterations

Useful iterations: 1 (56.0ms)

Iter	Nodes	Cost
0	3254	54184
1	5001	48990

prune2.7s

Filtered

1086 candidates to 361 candidates (33.2%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	1081	5	1086
Fresh	6	4	10
Picked	1	0	1
Done	0	0	0
Total	1088	9	1097

Merged error: 24.4b

Counts

1097 → 9

localize45.0ms

Local error

Found 4 expressions with local error:

3.1b	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
3.1b	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
3.9b	(fma 1 (pow (+ x 1.0) (/ 1.0 n)) (- (* (* (pow (cbrt (cbrt x)) (/ 1.0 n)) (pow (* (cbrt x) (cbrt x)) (/ 1.0 n))) (pow (cbrt (* (cbrt x) (cbrt x))) (/ 1.0 n)))))
4.4b	(fma (- (* (pow (cbrt (cbrt x)) (/ 1.0 n)) (pow (* (cbrt x) (cbrt x)) (/ 1.0 n)))) (pow (cbrt (* (cbrt x) (cbrt x))) (/ 1.0 n)) (* (* (pow (cbrt (cbrt x)) (/ 1.0 n)) (pow (* (cbrt x) (cbrt x)) (/ 1.0 n))) (pow (cbrt (* (cbrt x) (cbrt x))) (/ 1.0 n))))

rewrite40.0ms

Algorithm

rewrite-expression-head

Rules

132×	`unpow-prod-down`
114×	`*-un-lft-identity`
112×	`prod-diff`
92×	`add-sqr-sqrt`
68×	`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`
2×	`sub-neg` `flip3--` `diff-log` `flip--` `fma-udef`

Counts

4 → 200

Calls

4 calls:

13.0ms	(- (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)))
1.0ms	(fma 1 (pow (+ x 1.0) (/ 1.0 n)) (- (* (* (pow (cbrt (cbrt x)) (/ 1.0 n)) (pow (* (cbrt x) (cbrt x)) (/ 1.0 n))) (pow (cbrt (* (cbrt x) (cbrt x))) (/ 1.0 n)))))
1.0ms	(fma (- (* (pow (cbrt (cbrt x)) (/ 1.0 n)) (pow (* (cbrt x) (cbrt x)) (/ 1.0 n)))) (pow (cbrt (* (cbrt x) (cbrt x))) (/ 1.0 n)) (* (* (pow (cbrt (cbrt x)) (/ 1.0 n)) (pow (* (cbrt x) (cbrt x)) (/ 1.0 n))) (pow (cbrt (* (cbrt x) (cbrt x))) (/ 1.0 n))))

series2.0s

Counts

4 → 12

Calls

4 calls:

298.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
299.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
776.0ms	(fma 1 (pow (+ x 1.0) (/ 1.0 n)) (- (* (* (pow (cbrt (cbrt x)) (/ 1.0 n)) (pow (* (cbrt x) (cbrt x)) (/ 1.0 n))) (pow (cbrt (* (cbrt x) (cbrt x))) (/ 1.0 n)))))
639.0ms	(fma (- (* (pow (cbrt (cbrt x)) (/ 1.0 n)) (pow (* (cbrt x) (cbrt x)) (/ 1.0 n)))) (pow (cbrt (* (cbrt x) (cbrt x))) (/ 1.0 n)) (* (* (pow (cbrt (cbrt x)) (/ 1.0 n)) (pow (* (cbrt x) (cbrt x)) (/ 1.0 n))) (pow (cbrt (* (cbrt x) (cbrt x))) (/ 1.0 n))))

simplify105.0ms

Algorithm

egg-herbie

Counts

212 → 212

Iterations

Useful iterations: 2 (67.0ms)

Iter	Nodes	Cost
0	890	4570
1	3166	3490
2	5001	3457

prune1.0s

Filtered

212 candidates to 112 candidates (52.8%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	209	3	212
Fresh	1	7	8
Picked	1	0	1
Done	0	0	0
Total	211	10	221

Merged error: 24.4b

Counts

221 → 10

regimes470.0ms

Accuracy

84.6% (1.6b remaining)

Error of 24.7b against oracle of 23.1b and baseline of 33.5b

bsearch2.0ms

simplify4.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	112	220
1	122	220
2	122	220

end0.0ms

sample6.6s

Algorithm

intervals

Results

1.8s	3895×	body	1280	valid
1.3s	2247×	body	1280	nan
736.0ms	1820×	body	640	nan
660.0ms	1416×	body	10240	exit
623.0ms	1809×	body	640	valid
257.0ms	6194×	body	80	nan
221.0ms	890×	body	320	nan
205.0ms	933×	body	320	valid
157.0ms	3187×	body	80	valid
65.0ms	458×	body	160	nan
61.0ms	441×	body	160	valid