Details

sample229.0ms

Algorithm

intervals

Results

74.0ms	139×	body	1280	valid
45.0ms	78×	body	1280	nan
23.0ms	47×	body	10240	exit
21.0ms	54×	body	640	nan
17.0ms	49×	body	640	valid
8.0ms	213×	body	80	nan
7.0ms	26×	body	320	nan
6.0ms	25×	body	320	valid
5.0ms	90×	body	80	valid
2.0ms	17×	body	160	nan
1.0ms	12×	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: 30.9b

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))
2.0b	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))

rewrite27.0ms

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)))

series479.0ms

Counts

3 → 9

Calls

3 calls:

148.0ms	(pow (+ x 1.0) (/ 1.0 n))
61.0ms	(pow x (/ 1.0 n))
269.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))

simplify68.0ms

Algorithm

egg-herbie

Counts

158 → 158

Iterations

Useful iterations: 2 (49.0ms)

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: 22.1b

Counts

159 → 7

localize11.0ms

Local error

Found 4 expressions with local error:

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

rewrite13.0ms

Algorithm

rewrite-expression-head

Rules

20×	`add-sqr-sqrt`
18×	`*-un-lft-identity`
14×	`add-cube-cbrt`
13×	`pow-unpow`
9×	`times-frac`
8×	`sqrt-prod`
7×	`pow1`
5×	`add-exp-log`
4×	`expm1-log1p-u` `sqrt-div` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`
3×	`unpow-prod-down`
2×	`rem-sqrt-square` `sqrt-pow1` `flip3-+` `pow1/2` `flip-+` `hypot-def` `distribute-lft-out`
1×	`pow-to-exp` `pow-pow` `pow-exp` `fma-udef` `div-inv` `sqr-pow`

Counts

4 → 77

Calls

4 calls:

3.0ms	(sqrt (+ x 1.0))
3.0ms	(sqrt (+ x 1.0))
4.0ms	(pow x (/ 1.0 n))
1.0ms	(fma (pow (sqrt (+ x 1.0)) (/ 1.0 n)) (pow (sqrt (+ x 1.0)) (/ 1.0 n)) (- (pow x (/ 1.0 n))))

series802.0ms

Counts

4 → 12

Calls

4 calls:

28.0ms	(sqrt (+ x 1.0))
29.0ms	(sqrt (+ x 1.0))
60.0ms	(pow x (/ 1.0 n))
684.0ms	(fma (pow (sqrt (+ x 1.0)) (/ 1.0 n)) (pow (sqrt (+ x 1.0)) (/ 1.0 n)) (- (pow x (/ 1.0 n))))

simplify45.0ms

Algorithm

egg-herbie

Counts

89 → 89

Iterations

Useful iterations: 2 (37.0ms)

Iter	Nodes	Cost
0	459	584
1	1627	532
2	5001	515

prune257.0ms

Filtered

89 candidates to 72 candidates (80.9%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	88	1	89
Fresh	1	5	6
Picked	0	1	1
Done	0	0	0
Total	89	7	96

Merged error: 22.1b

Counts

96 → 7

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b	(pow (- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n))) 3)
0.0b	(pow x (/ 1.0 n))
0.0b	(cbrt (pow (- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n))) 3))
2.0b	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))

rewrite51.0ms

Algorithm

rewrite-expression-head

Rules

139×	`unpow-prod-down`
110×	`add-sqr-sqrt`
101×	`*-un-lft-identity`
56×	`prod-diff`
50×	`add-cube-cbrt`
49×	`sqr-pow`
45×	`difference-of-squares`
36×	`cbrt-prod`
30×	`cube-prod`
16×	`pow-unpow`
15×	`distribute-lft-out--`
13×	`distribute-lft-out`
9×	`times-frac`
8×	`fma-neg`
6×	`pow1` `add-exp-log` `add-log-exp`
5×	`add-cbrt-cube`
4×	`cube-div` `expm1-log1p-u` `log1p-expm1-u`
3×	`flip3--` `flip--`
2×	`cube-mult` `pow-to-exp` `cbrt-div` `pow-pow` `unpow3` `pow-exp`
1×	`sub-neg` `pow1/3` `diff-log` `rem-cbrt-cube` `div-inv` `rem-cube-cbrt`

Counts

4 → 219

Calls

4 calls:

11.0ms	(pow (- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n))) 3)
4.0ms	(pow x (/ 1.0 n))
12.0ms	(cbrt (pow (- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n))) 3))
15.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))

series1.1s

Counts

4 → 12

Calls

4 calls:

451.0ms	(pow (- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n))) 3)
56.0ms	(pow x (/ 1.0 n))
282.0ms	(cbrt (pow (- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n))) 3))
274.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))

simplify111.0ms

Algorithm

egg-herbie

Counts

231 → 231

Iterations

Useful iterations: 2 (80.0ms)

Iter	Nodes	Cost
0	915	3356
1	3725	2800
2	5001	2789

prune402.0ms

Filtered

231 candidates to 120 candidates (51.9%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	230	1	231
Fresh	0	5	5
Picked	0	1	1
Done	0	1	1
Total	230	8	238

Merged error: 22.1b

Counts

238 → 8

localize16.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt (+ x 1.0))
0.0b	(exp (pow x (/ 1.0 n)))
0.0b	(pow x (/ 1.0 n))
2.0b	(log (/ (exp (pow (sqrt (+ x 1.0)) (* 2 (/ 1.0 n)))) (exp (pow x (/ 1.0 n)))))

rewrite23.0ms

Algorithm

rewrite-expression-head

Rules

26×	`*-un-lft-identity`
25×	`add-sqr-sqrt`
22×	`add-cube-cbrt`
18×	`times-frac`
13×	`pow-unpow` `log-prod`
9×	`exp-prod`
7×	`pow1`
6×	`add-exp-log` `unpow-prod-down`
5×	`add-log-exp`
4×	`expm1-log1p-u` `sqrt-prod` `add-cbrt-cube` `log1p-expm1-u`
2×	`sqrt-div` `rem-log-exp` `log-pow` `div-inv` `sqr-pow`
1×	`pow-to-exp` `rem-sqrt-square` `log-div` `pow-pow` `sqrt-pow1` `flip3-+` `pow1/2` `div-exp` `pow-exp` `flip-+` `hypot-def` `rem-exp-log` `distribute-lft-out` `pow-div`

Counts

4 → 92

Calls

4 calls:

3.0ms	(sqrt (+ x 1.0))
3.0ms	(exp (pow x (/ 1.0 n)))
4.0ms	(pow x (/ 1.0 n))
10.0ms	(log (/ (exp (pow (sqrt (+ x 1.0)) (* 2 (/ 1.0 n)))) (exp (pow x (/ 1.0 n)))))

series848.0ms

Counts

4 → 12

Calls

4 calls:

30.0ms	(sqrt (+ x 1.0))
73.0ms	(exp (pow x (/ 1.0 n)))
62.0ms	(pow x (/ 1.0 n))
683.0ms	(log (/ (exp (pow (sqrt (+ x 1.0)) (* 2 (/ 1.0 n)))) (exp (pow x (/ 1.0 n)))))

simplify58.0ms

Algorithm

egg-herbie

Counts

104 → 104

Iterations

Useful iterations: 2 (48.0ms)

Iter	Nodes	Cost
0	670	911
1	2337	846
2	5001	839

prune340.0ms

Filtered

104 candidates to 85 candidates (81.7%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	101	3	104
Fresh	2	3	5
Picked	1	0	1
Done	1	1	2
Total	105	7	112

Merged error: 21.9b

Counts

112 → 7

regimes234.0ms

Accuracy

81.4% (2.0b remaining)

Error of 23.3b against oracle of 21.3b and baseline of 31.9b

bsearch2.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	51	46
1	51	46

end0.0ms

sample6.6s

Algorithm

intervals

Results

1.9s	3932×	body	1280	valid
1.3s	2165×	body	1280	nan
733.0ms	1804×	body	640	nan
622.0ms	1773×	body	640	valid
615.0ms	1477×	body	10240	exit
275.0ms	6191×	body	80	nan
221.0ms	875×	body	320	nan
207.0ms	919×	body	320	valid
157.0ms	3183×	body	80	valid
69.0ms	474×	body	160	nan
63.0ms	447×	body	160	valid