Details

sample217.0ms

Algorithm

intervals

Results

56.0ms	117×	body	1280	valid
48.0ms	83×	body	1280	nan
26.0ms	63×	body	640	valid
21.0ms	52×	body	640	nan
12.0ms	39×	body	10240	exit
9.0ms	209×	body	80	nan
7.0ms	30×	body	320	nan
6.0ms	103×	body	80	valid
6.0ms	27×	body	320	valid
3.0ms	20×	body	160	valid
2.0ms	16×	body	160	nan

simplify153.0ms

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	4996	6
6	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

localize9.0ms

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)))

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

series344.0ms

Counts

2 → 6

Calls

2 calls:

60.0ms	(pow x (/ 1.0 n))
283.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))

simplify39.0ms

Algorithm

egg-herbie

Counts

57 → 57

Iterations

Useful iterations: 2 (32.0ms)

Iter	Nodes	Cost
0	403	475
1	1384	461
2	5002	449

prune133.0ms

Filtered

57 candidates to 46 candidates (80.7%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	52	5	57
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	53	5	58

Merged error: 24.2b

Counts

58 → 5

localize12.0ms

Local error

Found 4 expressions with local error:

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

rewrite43.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 109

Calls

4 calls:

13.0ms	(exp (- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n))))
3.0ms	(pow x (/ 1.0 n))
13.0ms	(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)))

series1.1s

Counts

4 → 12

Calls

4 calls:

456.0ms	(exp (- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n))))
64.0ms	(pow x (/ 1.0 n))
280.0ms	(log (exp (- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))))
283.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))

simplify46.0ms

Algorithm

egg-herbie

Counts

121 → 121

Iterations

Useful iterations: 2 (35.0ms)

Iter	Nodes	Cost
0	485	991
1	1600	937
2	5001	918

prune283.0ms

Filtered

121 candidates to 92 candidates (76.0%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	118	3	121
Fresh	1	3	4
Picked	0	1	1
Done	0	0	0
Total	119	7	126

Merged error: 24.2b

Counts

126 → 7

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt (pow x (/ 1.0 n)))
0.0b	(sqrt (pow x (/ 1.0 n)))
0.0b	(* (- (pow (+ x 1.0) (/ (/ 1.0 n) 2)) (sqrt (pow x (/ 1.0 n)))) (+ (pow (+ x 1.0) (/ (/ 1.0 n) 2)) (sqrt (pow x (/ 1.0 n)))))
3.4b	(- (pow (+ x 1.0) (/ (/ 1.0 n) 2)) (sqrt (pow x (/ 1.0 n))))

rewrite70.0ms

Algorithm

rewrite-expression-head

Rules

64×	`add-sqr-sqrt`
32×	`sqrt-pow1` `sqrt-prod`
30×	`*-un-lft-identity`
26×	`pow-unpow`
24×	`add-cube-cbrt` `difference-of-squares`
22×	`unpow-prod-down`
18×	`times-frac` `sqr-pow`
16×	`associate-l`
10×	`pow1`
6×	`add-exp-log` `rem-sqrt-square` `add-cbrt-cube` `add-log-exp`
4×	`frac-times` `flip3--` `associate-r` `flip--`
3×	`flip3-+` `flip-+`
2×	`+-commutative` `distribute-rgt-in` `pow-pow` `distribute-lft-in` `pow1/2` `associate-r/` `associate-l/` `div-inv` `distribute-lft-out--`
1×	`sub-neg` `diff-log` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `distribute-lft-out` `unswap-sqr`

Counts

4 → 137

Calls

4 calls:

4.0ms	(sqrt (pow x (/ 1.0 n)))
5.0ms	(sqrt (pow x (/ 1.0 n)))
39.0ms	(* (- (pow (+ x 1.0) (/ (/ 1.0 n) 2)) (sqrt (pow x (/ 1.0 n)))) (+ (pow (+ x 1.0) (/ (/ 1.0 n) 2)) (sqrt (pow x (/ 1.0 n)))))
16.0ms	(- (pow (+ x 1.0) (/ (/ 1.0 n) 2)) (sqrt (pow x (/ 1.0 n))))

series1.2s

Counts

4 → 12

Calls

4 calls:

84.0ms	(sqrt (pow x (/ 1.0 n)))
84.0ms	(sqrt (pow x (/ 1.0 n)))
659.0ms	(* (- (pow (+ x 1.0) (/ (/ 1.0 n) 2)) (sqrt (pow x (/ 1.0 n)))) (+ (pow (+ x 1.0) (/ (/ 1.0 n) 2)) (sqrt (pow x (/ 1.0 n)))))
354.0ms	(- (pow (+ x 1.0) (/ (/ 1.0 n) 2)) (sqrt (pow x (/ 1.0 n))))

simplify72.0ms

Algorithm

egg-herbie

Counts

149 → 149

Iterations

Useful iterations: 2 (53.0ms)

Iter	Nodes	Cost
0	648	1856
1	2441	1724
2	5002	1718

prune448.0ms

Filtered

149 candidates to 123 candidates (82.6%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	145	4	149
Fresh	1	4	5
Picked	1	0	1
Done	1	0	1
Total	148	8	156

Merged error: 24.1b

Counts

156 → 8

localize18.0ms

Local error

Found 4 expressions with local error:

0.1b	(cbrt (- (pow (+ x 1.0) (/ (/ 1.0 n) 2)) (sqrt (pow x (/ 1.0 n)))))
3.4b	(- (pow (+ x 1.0) (/ (/ 1.0 n) 2)) (sqrt (pow x (/ 1.0 n))))
3.4b	(- (pow (+ x 1.0) (/ (/ 1.0 n) 2)) (sqrt (pow x (/ 1.0 n))))
3.4b	(- (pow (+ x 1.0) (/ (/ 1.0 n) 2)) (sqrt (pow x (/ 1.0 n))))

rewrite73.0ms

Algorithm

rewrite-expression-head

Rules

73×	`add-sqr-sqrt`
48×	`difference-of-squares`
36×	`sqrt-prod`
28×	`unpow-prod-down` `sqr-pow`
16×	`cbrt-prod`
13×	`*-un-lft-identity`
10×	`add-log-exp`
5×	`add-cube-cbrt`
4×	`pow1` `add-exp-log` `flip3--` `add-cbrt-cube` `flip--` `distribute-lft-out--`
3×	`sub-neg` `diff-log`
2×	`cbrt-div`
1×	`pow1/3`

Counts

4 → 101

Calls

4 calls:

16.0ms	(cbrt (- (pow (+ x 1.0) (/ (/ 1.0 n) 2)) (sqrt (pow x (/ 1.0 n)))))
17.0ms	(- (pow (+ x 1.0) (/ (/ 1.0 n) 2)) (sqrt (pow x (/ 1.0 n))))
16.0ms	(- (pow (+ x 1.0) (/ (/ 1.0 n) 2)) (sqrt (pow x (/ 1.0 n))))
20.0ms	(- (pow (+ x 1.0) (/ (/ 1.0 n) 2)) (sqrt (pow x (/ 1.0 n))))

series12.3s

Counts

4 → 12

Calls

4 calls:

11.2s	(cbrt (- (pow (+ x 1.0) (/ (/ 1.0 n) 2)) (sqrt (pow x (/ 1.0 n)))))
367.0ms	(- (pow (+ x 1.0) (/ (/ 1.0 n) 2)) (sqrt (pow x (/ 1.0 n))))
363.0ms	(- (pow (+ x 1.0) (/ (/ 1.0 n) 2)) (sqrt (pow x (/ 1.0 n))))
365.0ms	(- (pow (+ x 1.0) (/ (/ 1.0 n) 2)) (sqrt (pow x (/ 1.0 n))))

simplify212.0ms

Algorithm

egg-herbie

Counts

113 → 113

Iterations

Useful iterations: 1 (67.0ms)

Iter	Nodes	Cost
0	4041	8280
1	5002	8210

prune2.9s

Filtered

113 candidates to 91 candidates (80.5%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	112	1	113
Fresh	0	7	7
Picked	1	0	1
Done	0	0	0
Total	113	8	121

Merged error: 24.1b

Counts

121 → 8

regimes237.0ms

Accuracy

84.7% (1.7b remaining)

Error of 24.3b against oracle of 22.6b and baseline of 33.5b

bsearch1.0ms

simplify3.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	72	100
1	78	100
2	82	100
3	82	100

end0.0ms

sample6.8s

Algorithm

intervals

Results

1.9s	3895×	body	1280	valid
1.3s	2247×	body	1280	nan
768.0ms	1820×	body	640	nan
666.0ms	1416×	body	10240	exit
633.0ms	1809×	body	640	valid
276.0ms	6194×	body	80	nan
225.0ms	890×	body	320	nan
210.0ms	933×	body	320	valid
168.0ms	3187×	body	80	valid
66.0ms	458×	body	160	nan
63.0ms	441×	body	160	valid