Details

sample207.0ms

Algorithm

intervals

Results

66.0ms	133×	body	1280	valid
41.0ms	60×	body	1280	nan
20.0ms	50×	body	640	nan
18.0ms	51×	body	640	valid
14.0ms	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

simplify34.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	17	6
1	34	6
2	80	6
3	236	6
4	868	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

localize8.0ms

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)))

rewrite15.0ms

Algorithm

rewrite-expression-head

Rules

22×	`add-sqr-sqrt`
17×	`*-un-lft-identity`
13×	`unpow-prod-down` `pow-unpow`
10×	`add-cube-cbrt`
9×	`times-frac` `difference-of-squares`
7×	`sqr-pow`
4×	`add-log-exp`
3×	`pow1` `add-exp-log` `distribute-lft-out--`
2×	`add-cbrt-cube`
1×	`pow-to-exp` `sub-neg` `flip3--` `pow-pow` `diff-log` `pow-exp` `flip--` `div-inv` `distribute-lft-out`

Counts

2 → 51

Calls

2 calls:

3.0ms	(pow x (/ 1.0 n))
9.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))

series329.0ms

Counts

2 → 6

Calls

2 calls:

61.0ms	(pow x (/ 1.0 n))
268.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))

simplify40.0ms

Algorithm

egg-herbie

Counts

57 → 57

Iterations

Useful iterations: 2 (33.0ms)

Iter	Nodes	Cost
0	404	475
1	1391	461
2	5001	449

prune155.0ms

Filtered

57 candidates to 46 candidates (80.7%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	54	3	57
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	55	3	58

Merged error: 21.6b

Counts

58 → 3

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)))

rewrite31.0ms

Algorithm

rewrite-expression-head

Rules

37×	`add-sqr-sqrt`
27×	`*-un-lft-identity`
23×	`unpow-prod-down`
18×	`difference-of-squares`
16×	`log-pow`
15×	`exp-prod`
13×	`add-cube-cbrt` `pow-unpow` `sqr-pow`
9×	`times-frac`
6×	`distribute-lft-out--`
5×	`pow1` `log-prod` `add-log-exp`
4×	`add-exp-log`
3×	`add-cbrt-cube`
2×	`sub-neg` `exp-sum` `distribute-lft-out`
1×	`pow-to-exp` `log-div` `flip3--` `pow-pow` `exp-diff` `diff-log` `rem-log-exp` `pow-exp` `flip--` `div-inv`

Counts

3 → 81

Calls

3 calls:

4.0ms	(pow x (/ 1.0 n))
11.0ms	(log (exp (- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))))
10.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))

series612.0ms

Counts

3 → 9

Calls

3 calls:

61.0ms	(pow x (/ 1.0 n))
276.0ms	(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)))

simplify45.0ms

Algorithm

egg-herbie

Counts

90 → 90

Iterations

Useful iterations: 2 (35.0ms)

Iter	Nodes	Cost
0	469	758
1	1549	722
2	5001	703

prune258.0ms

Filtered

90 candidates to 71 candidates (78.9%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	89	1	90
Fresh	0	2	2
Picked	0	1	1
Done	0	0	0
Total	89	4	93

Merged error: 21.6b

Counts

93 → 4

localize15.0ms

Local error

Found 4 expressions with local error:

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

rewrite44.0ms

Algorithm

rewrite-expression-head

Rules

32×	`add-sqr-sqrt`
22×	`*-un-lft-identity`
20×	`unpow-prod-down`
18×	`difference-of-squares`
16×	`log-prod`
12×	`sqr-pow`
10×	`cbrt-prod`
8×	`add-cube-cbrt` `add-log-exp`
6×	`pow1` `add-exp-log` `distribute-lft-out--`
4×	`sub-neg` `exp-sum` `log-pow` `add-cbrt-cube`
2×	`log-div` `cbrt-div` `flip3--` `exp-diff` `pow1/3` `diff-log` `rem-log-exp` `flip--` `distribute-lft-out`

Counts

4 → 86

Calls

4 calls:

10.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
10.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
10.0ms	(log (cbrt (exp (- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n))))))
10.0ms	(log (cbrt (exp (- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n))))))

series1.5s

Counts

4 → 12

Calls

4 calls:

281.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
277.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
455.0ms	(log (cbrt (exp (- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n))))))
457.0ms	(log (cbrt (exp (- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n))))))

simplify106.0ms

Algorithm

egg-herbie

Counts

98 → 98

Iterations

Useful iterations: 2 (23.0ms)

Iter	Nodes	Cost
0	300	1278
1	805	1194
2	3713	1170
3	5001	1170

prune443.0ms

Filtered

98 candidates to 82 candidates (83.7%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	96	2	98
Fresh	0	2	2
Picked	1	0	1
Done	0	1	1
Total	97	5	102

Merged error: 21.4b

Counts

102 → 5

localize18.0ms

Local error

Found 4 expressions with local error:

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

rewrite47.0ms

Algorithm

rewrite-expression-head

Rules

24×	`log-prod`
22×	`add-sqr-sqrt`
17×	`*-un-lft-identity`
15×	`cbrt-prod`
10×	`add-cube-cbrt` `unpow-prod-down`
9×	`difference-of-squares`
7×	`pow1` `add-exp-log`
6×	`exp-sum` `log-pow` `add-log-exp` `sqr-pow`
4×	`sub-neg` `add-cbrt-cube`
3×	`log-div` `cbrt-div` `exp-diff` `pow1/3` `rem-log-exp` `distribute-lft-out--`
1×	`flip3--` `diff-log` `flip--` `distribute-lft-out`

Counts

4 → 81

Calls

4 calls:

13.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
10.0ms	(log (cbrt (exp (- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n))))))
10.0ms	(log (cbrt (exp (- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n))))))
10.0ms	(log (cbrt (exp (- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n))))))

series1.6s

Counts

4 → 12

Calls

4 calls:

285.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
449.0ms	(log (cbrt (exp (- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n))))))
445.0ms	(log (cbrt (exp (- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n))))))
449.0ms	(log (cbrt (exp (- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n))))))

simplify109.0ms

Algorithm

egg-herbie

Counts

93 → 93

Iterations

Useful iterations: 2 (24.0ms)

Iter	Nodes	Cost
0	300	1265
1	805	1165
2	3713	1141
3	5001	1141

prune440.0ms

Filtered

93 candidates to 77 candidates (82.8%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	92	1	93
Fresh	1	2	3
Picked	1	0	1
Done	0	1	1
Total	94	4	98

Merged error: 21.4b

Counts

98 → 4

regimes160.0ms

Accuracy

83.3% (1.8b remaining)

Error of 23.4b against oracle of 21.6b and baseline of 32.2b

bsearch1.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	42	38
1	42	38

end0.0ms

sample6.7s

Algorithm

intervals

Results

1.9s	3926×	body	1280	valid
1.3s	2181×	body	1280	nan
739.0ms	1799×	body	640	nan
633.0ms	1410×	body	10240	exit
614.0ms	1762×	body	640	valid
277.0ms	6260×	body	80	nan
219.0ms	868×	body	320	nan
191.0ms	861×	body	320	valid
163.0ms	3228×	body	80	valid
67.0ms	462×	body	160	valid
64.0ms	430×	body	160	nan