Details

sample191.0ms

Algorithm

intervals

Results

63.0ms	133×	body	1280	valid
34.0ms	60×	body	1280	nan
19.0ms	50×	body	640	nan
17.0ms	51×	body	640	valid
13.0ms	28×	body	10240	exit
8.0ms	187×	body	80	nan
7.0ms	30×	body	320	nan
6.0ms	24×	body	320	valid
4.0ms	93×	body	80	valid
2.0ms	14×	body	160	nan
2.0ms	13×	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

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: 32.4b

Counts

2 → 1

localize14.0ms

Local error

Found 2 expressions with local error:

0.0b	(pow x (/ 1.0 n))
1.9b	(- (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)))

series336.0ms

Counts

2 → 6

Calls

2 calls:

61.0ms	(pow x (/ 1.0 n))
275.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))

simplify63.0ms

Algorithm

egg-herbie

Counts

125 → 125

Iterations

Useful iterations: 2 (45.0ms)

Iter	Nodes	Cost
0	587	1993
1	1958	1473
2	5002	1469

prune247.0ms

Filtered

125 candidates to 69 candidates (55.2%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	121	4	125
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	122	4	126

Merged error: 22.3b

Counts

126 → 4

localize11.0ms

Local error

Found 3 expressions with local error:

0.0b	(pow x (/ 1.0 n))
1.8b	(log (exp (- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))))
1.9b	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))

rewrite46.0ms

Algorithm

rewrite-expression-head

Rules

131×	`unpow-prod-down`
119×	`*-un-lft-identity`
112×	`prod-diff`
99×	`add-sqr-sqrt`
75×	`add-cube-cbrt`
61×	`log-prod`
58×	`exp-sum`
44×	`sqr-pow`
18×	`difference-of-squares`
17×	`distribute-lft-out`
16×	`log-pow`
15×	`exp-prod`
13×	`pow-unpow`
9×	`times-frac`
8×	`fma-neg`
6×	`distribute-lft-out--`
5×	`pow1` `add-log-exp`
4×	`add-exp-log`
3×	`expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u`
2×	`sub-neg`
1×	`pow-to-exp` `log-div` `flip3--` `pow-pow` `exp-diff` `diff-log` `rem-log-exp` `pow-exp` `flip--` `div-inv`

Counts

3 → 207

Calls

3 calls:

4.0ms	(pow x (/ 1.0 n))
16.0ms	(log (exp (- (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)))

series611.0ms

Counts

3 → 9

Calls

3 calls:

63.0ms	(pow x (/ 1.0 n))
272.0ms	(log (exp (- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))))
275.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))

simplify82.0ms

Algorithm

egg-herbie

Counts

216 → 216

Iterations

Useful iterations: 2 (51.0ms)

Iter	Nodes	Cost
0	768	3764
1	2271	2716
2	5001	2312

prune428.0ms

Filtered

216 candidates to 108 candidates (50.0%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	214	2	216
Fresh	1	2	3
Picked	0	1	1
Done	0	0	0
Total	215	5	220

Merged error: 22.3b

Counts

220 → 5

localize13.0ms

Local error

Found 3 expressions with local error:

0.0b

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

0.0b

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

1.9b

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

rewrite77.0ms

Algorithm

rewrite-expression-head

Rules

206×	`unpow-prod-down`
134×	`*-un-lft-identity`
124×	`add-sqr-sqrt`
113×	`sqrt-prod`
110×	`prod-diff`
74×	`add-cube-cbrt`
39×	`sqr-pow`
32×	`difference-of-squares`
24×	`distribute-lft-out`
23×	`associate-l`
11×	`fma-def` `fma-neg`
8×	`distribute-lft-out--`
7×	`associate-r` `add-log-exp`
5×	`pow1` `add-exp-log` `add-cbrt-cube`
4×	`frac-times` `flip3--` `flip3-+` `flip--` `flip-+`
3×	`expm1-log1p-u` `log1p-expm1-u`
2×	`associate-r/` `associate-l/`
1×	`+-commutative` `distribute-rgt-in` `sub-neg` `distribute-lft-in` `diff-log` `pow-prod-down` `prod-exp` `sum-log` `*-commutative` `cbrt-unprod` `unswap-sqr`

Counts

3 → 237

Calls

3 calls:

12.0ms

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

31.0ms

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

20.0ms

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

series2.8s

Counts

3 → 9

Calls

3 calls:

541.0ms

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

1.5s

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

735.0ms

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

simplify125.0ms

Algorithm

egg-herbie

Counts

246 → 246

Iterations

Useful iterations: 2 (82.0ms)

Iter	Nodes	Cost
0	759	6013
1	3031	4545
2	5001	4522

prune574.0ms

Filtered

246 candidates to 118 candidates (48.0%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	244	2	246
Fresh	0	3	3
Picked	1	0	1
Done	0	1	1
Total	245	6	251

Merged error: 22.3b

Counts

251 → 6

localize16.0ms

Local error

Found 4 expressions with local error:

0.0b	(cbrt (- (pow (sqrt (+ x 1.0)) (/ 1.0 n)) (pow (sqrt x) (/ 1.0 n))))
1.9b	(- (pow (sqrt (+ x 1.0)) (/ 1.0 n)) (pow (sqrt x) (/ 1.0 n)))
1.9b	(- (pow (sqrt (+ x 1.0)) (/ 1.0 n)) (pow (sqrt x) (/ 1.0 n)))
1.9b	(- (pow (sqrt (+ x 1.0)) (/ 1.0 n)) (pow (sqrt x) (/ 1.0 n)))

rewrite102.0ms

Algorithm

rewrite-expression-head

Rules

517×	`unpow-prod-down`
330×	`prod-diff`
305×	`*-un-lft-identity`
299×	`add-sqr-sqrt`
279×	`sqrt-prod`
203×	`add-cube-cbrt`
98×	`sqr-pow`
64×	`difference-of-squares`
37×	`distribute-lft-out`
33×	`fma-neg`
23×	`cbrt-prod`
16×	`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 → 500

Calls

4 calls:

12.0ms	(cbrt (- (pow (sqrt (+ x 1.0)) (/ 1.0 n)) (pow (sqrt x) (/ 1.0 n))))
16.0ms	(- (pow (sqrt (+ x 1.0)) (/ 1.0 n)) (pow (sqrt x) (/ 1.0 n)))
16.0ms	(- (pow (sqrt (+ x 1.0)) (/ 1.0 n)) (pow (sqrt x) (/ 1.0 n)))
20.0ms	(- (pow (sqrt (+ x 1.0)) (/ 1.0 n)) (pow (sqrt x) (/ 1.0 n)))

series5.6s

Counts

4 → 12

Calls

4 calls:

3.2s	(cbrt (- (pow (sqrt (+ x 1.0)) (/ 1.0 n)) (pow (sqrt x) (/ 1.0 n))))
743.0ms	(- (pow (sqrt (+ x 1.0)) (/ 1.0 n)) (pow (sqrt x) (/ 1.0 n)))
940.0ms	(- (pow (sqrt (+ x 1.0)) (/ 1.0 n)) (pow (sqrt x) (/ 1.0 n)))
749.0ms	(- (pow (sqrt (+ x 1.0)) (/ 1.0 n)) (pow (sqrt x) (/ 1.0 n)))

simplify160.0ms

Algorithm

egg-herbie

Counts

512 → 512

Iterations

Useful iterations: 2 (48.0ms)

Iter	Nodes	Cost
0	646	14351
1	1742	10286
2	5001	10246

prune1.1s

Filtered

512 candidates to 187 candidates (36.5%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	508	4	512
Fresh	2	2	4
Picked	1	0	1
Done	1	0	1
Total	512	6	518

Merged error: 22.3b

Counts

518 → 6

regimes222.0ms

Accuracy

84.2% (1.6b remaining)

Error of 23.8b against oracle of 22.2b and baseline of 32.2b

bsearch1.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	57	106
1	57	106

end0.0ms

sample6.4s

Algorithm

intervals

Results

1.8s	3926×	body	1280	valid
1.3s	2181×	body	1280	nan
714.0ms	1799×	body	640	nan
586.0ms	1762×	body	640	valid
577.0ms	1410×	body	10240	exit
256.0ms	6260×	body	80	nan
229.0ms	868×	body	320	nan
189.0ms	861×	body	320	valid
160.0ms	3228×	body	80	valid
66.0ms	430×	body	160	nan
63.0ms	462×	body	160	valid