Details

sample195.0ms

Algorithm

intervals

Results

58.0ms	126×	body	1280	valid
38.0ms	74×	body	1280	nan
17.0ms	47×	body	640	valid
16.0ms	43×	body	640	nan
11.0ms	41×	body	10240	exit
10.0ms	29×	body	320	valid
8.0ms	200×	body	80	nan
8.0ms	33×	body	320	nan
5.0ms	104×	body	80	valid
3.0ms	20×	body	160	valid
2.0ms	12×	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: 31.6b

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))
3.2b	(- (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))
11.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))

series459.0ms

Counts

3 → 9

Calls

3 calls:

138.0ms	(pow (+ x 1.0) (/ 1.0 n))
57.0ms	(pow x (/ 1.0 n))
264.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))

simplify68.0ms

Algorithm

egg-herbie

Counts

158 → 158

Iterations

Useful iterations: 2 (48.0ms)

Iter	Nodes	Cost
0	654	2164
1	2164	1642
2	5002	1637

prune284.0ms

Filtered

158 candidates to 95 candidates (60.1%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	151	7	158
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	152	7	159

Merged error: 23.8b

Counts

159 → 7

localize13.0ms

Local error

Found 4 expressions with local error:

0.1b	(cbrt (- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n))))
3.2b	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
3.2b	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
3.2b	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))

rewrite60.0ms

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)))
11.0ms	(- (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)))

series1.3s

Counts

4 → 12

Calls

4 calls:

556.0ms	(cbrt (- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n))))
268.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
265.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
260.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))

simplify90.0ms

Algorithm

egg-herbie

Counts

309 → 309

Iterations

Useful iterations: 2 (42.0ms)

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

prune607.0ms

Filtered

309 candidates to 157 candidates (50.8%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	308	1	309
Fresh	1	5	6
Picked	0	1	1
Done	0	0	0
Total	309	7	316

Merged error: 23.8b

Counts

316 → 7

localize15.0ms

Local error

Found 4 expressions with local error:

0.3b	(cbrt (+ x 1.0))
0.3b	(cbrt (+ x 1.0))
0.3b	(cbrt (+ x 1.0))
4.9b	(fma (pow (* (cbrt (+ x 1.0)) (cbrt (+ x 1.0))) (/ 1.0 n)) (pow (cbrt (+ x 1.0)) (/ 1.0 n)) (- (pow x (/ 1.0 n))))

rewrite11.0ms

Algorithm

rewrite-expression-head

Rules

13×	`*-un-lft-identity`
12×	`cbrt-prod`
7×	`add-sqr-sqrt` `add-cube-cbrt`
6×	`cbrt-div`
4×	`pow1` `add-exp-log` `expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`
3×	`flip3-+` `pow1/3` `flip-+` `distribute-lft-out`
1×	`fma-udef`

Counts

4 → 58

Calls

4 calls:

3.0ms	(cbrt (+ x 1.0))
3.0ms	(cbrt (+ x 1.0))
3.0ms	(cbrt (+ x 1.0))
1.0ms	(fma (pow (* (cbrt (+ x 1.0)) (cbrt (+ x 1.0))) (/ 1.0 n)) (pow (cbrt (+ x 1.0)) (/ 1.0 n)) (- (pow x (/ 1.0 n))))

series1.1s

Counts

4 → 12

Calls

4 calls:

87.0ms	(cbrt (+ x 1.0))
86.0ms	(cbrt (+ x 1.0))
86.0ms	(cbrt (+ x 1.0))
834.0ms	(fma (pow (* (cbrt (+ x 1.0)) (cbrt (+ x 1.0))) (/ 1.0 n)) (pow (cbrt (+ x 1.0)) (/ 1.0 n)) (- (pow x (/ 1.0 n))))

simplify45.0ms

Algorithm

egg-herbie

Counts

70 → 70

Iterations

Useful iterations: 2 (36.0ms)

Iter	Nodes	Cost
0	465	701
1	1620	644
2	5001	634

prune297.0ms

Filtered

70 candidates to 64 candidates (91.4%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	67	3	70
Fresh	0	5	5
Picked	1	0	1
Done	1	0	1
Total	69	8	77

Merged error: 23.7b

Counts

77 → 8

localize21.0ms

Local error

Found 4 expressions with local error:

0.3b	(cbrt (+ x 1.0))
4.9b	(fma (pow (* (cbrt (+ x 1.0)) (cbrt (+ x 1.0))) (/ 1.0 n)) (pow (cbrt (+ x 1.0)) (/ 1.0 n)) (- (pow x (/ 1.0 n))))
4.9b	(fma (pow (* (cbrt (+ x 1.0)) (cbrt (+ x 1.0))) (/ 1.0 n)) (pow (cbrt (+ x 1.0)) (/ 1.0 n)) (- (pow x (/ 1.0 n))))
4.9b	(fma (pow (* (cbrt (+ x 1.0)) (cbrt (+ x 1.0))) (/ 1.0 n)) (pow (cbrt (+ x 1.0)) (/ 1.0 n)) (- (pow x (/ 1.0 n))))

rewrite6.0ms

Algorithm

rewrite-expression-head

Rules

7×	`*-un-lft-identity`
5×	`add-sqr-sqrt` `add-cube-cbrt`
4×	`pow1` `add-exp-log` `cbrt-prod` `expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`
3×	`fma-udef`
2×	`cbrt-div`
1×	`flip3-+` `pow1/3` `flip-+` `distribute-lft-out`

Counts

4 → 46

Calls

4 calls:

3.0ms	(cbrt (+ x 1.0))
1.0ms	(fma (pow (* (cbrt (+ x 1.0)) (cbrt (+ x 1.0))) (/ 1.0 n)) (pow (cbrt (+ x 1.0)) (/ 1.0 n)) (- (pow x (/ 1.0 n))))
1.0ms	(fma (pow (* (cbrt (+ x 1.0)) (cbrt (+ x 1.0))) (/ 1.0 n)) (pow (cbrt (+ x 1.0)) (/ 1.0 n)) (- (pow x (/ 1.0 n))))
1.0ms	(fma (pow (* (cbrt (+ x 1.0)) (cbrt (+ x 1.0))) (/ 1.0 n)) (pow (cbrt (+ x 1.0)) (/ 1.0 n)) (- (pow x (/ 1.0 n))))

series2.7s

Counts

4 → 12

Calls

4 calls:

96.0ms	(cbrt (+ x 1.0))
900.0ms	(fma (pow (* (cbrt (+ x 1.0)) (cbrt (+ x 1.0))) (/ 1.0 n)) (pow (cbrt (+ x 1.0)) (/ 1.0 n)) (- (pow x (/ 1.0 n))))
858.0ms	(fma (pow (* (cbrt (+ x 1.0)) (cbrt (+ x 1.0))) (/ 1.0 n)) (pow (cbrt (+ x 1.0)) (/ 1.0 n)) (- (pow x (/ 1.0 n))))
859.0ms	(fma (pow (* (cbrt (+ x 1.0)) (cbrt (+ x 1.0))) (/ 1.0 n)) (pow (cbrt (+ x 1.0)) (/ 1.0 n)) (- (pow x (/ 1.0 n))))

simplify47.0ms

Algorithm

egg-herbie

Counts

58 → 58

Iterations

Useful iterations: 2 (37.0ms)

Iter	Nodes	Cost
0	465	1095
1	1620	988
2	5001	982

prune317.0ms

Filtered

58 candidates to 56 candidates (96.6%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	58	0	58
Fresh	0	7	7
Picked	0	1	1
Done	0	0	0
Total	58	8	66

Merged error: 23.7b

Counts

66 → 8

regimes443.0ms

Accuracy

82.1% (1.9b remaining)

Error of 24.0b against oracle of 22.1b and baseline of 32.8b

bsearch1.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	58	88
1	58	88

end0.0ms

sample6.4s

Algorithm

intervals

Results

1.8s	3853×	body	1280	valid
1.2s	2135×	body	1280	nan
724.0ms	1817×	body	640	nan
641.0ms	1455×	body	10240	exit
626.0ms	1871×	body	640	valid
258.0ms	6303×	body	80	nan
206.0ms	841×	body	320	nan
188.0ms	862×	body	320	valid
151.0ms	3103×	body	80	valid
72.0ms	464×	body	160	nan
71.0ms	453×	body	160	valid