Details

sample231.0ms

Algorithm

intervals

Results

80.0ms	143×	body	1280	valid
26.0ms	26×	body	1280	nan
24.0ms	56×	body	640	valid
22.0ms	149×	body	80	overflowed
17.0ms	24×	body	640	nan
11.0ms	215×	body	80	nan
11.0ms	18×	body	320	nan
9.0ms	89×	body	80	valid
7.0ms	23×	body	320	valid
3.0ms	17×	body	160	valid
1.0ms	4×	body	160	nan

simplify35.0ms

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: 33.3b

Counts

2 → 1

localize8.0ms

Local error

Found 1 expressions with local error:

2.4b	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))

rewrite11.0ms

Algorithm

rewrite-expression-head

Rules

13×	`add-sqr-sqrt`
10×	`unpow-prod-down`
9×	`difference-of-squares`
8×	`*-un-lft-identity`
6×	`sqr-pow`
3×	`distribute-lft-out--` `add-log-exp`
1×	`pow1` `add-exp-log` `add-cube-cbrt` `sub-neg` `flip3--` `diff-log` `add-cbrt-cube` `flip--` `distribute-lft-out`

Counts

1 → 24

Calls

1 calls:

9.0ms

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

series274.0ms

Counts

1 → 3

Calls

1 calls:

274.0ms

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

simplify75.0ms

Algorithm

egg-herbie

Counts

27 → 27

Iterations

Useful iterations: 2 (18.0ms)

Iter	Nodes	Cost
0	222	326
1	594	313
2	2745	307
3	5003	307

prune89.0ms

Filtered

27 candidates to 23 candidates (85.2%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	23	4	27
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	24	4	28

Merged error: 22.6b

Counts

28 → 4

localize11.0ms

Local error

Found 2 expressions with local error:

2.4b	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
2.4b	(log (exp (- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))))

rewrite23.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

2 → 54

Calls

2 calls:

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

series556.0ms

Counts

2 → 6

Calls

2 calls:

280.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
275.0ms	(log (exp (- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))))

simplify89.0ms

Algorithm

egg-herbie

Counts

60 → 60

Iterations

Useful iterations: 2 (21.0ms)

Iter	Nodes	Cost
0	290	609
1	797	574
2	3273	562
3	5001	562

prune164.0ms

Filtered

60 candidates to 48 candidates (80.0%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	58	2	60
Fresh	0	3	3
Picked	1	0	1
Done	0	0	0
Total	59	5	64

Merged error: 22.6b

Counts

64 → 5

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt (+ x 1.0))
0.0b	(sqrt (+ x 1.0))
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))))
2.4b	(- (pow (sqrt (+ x 1.0)) (/ 1.0 n)) (pow (sqrt x) (/ 1.0 n)))

rewrite62.0ms

Algorithm

rewrite-expression-head

Rules

60×	`add-sqr-sqrt`
50×	`unpow-prod-down`
39×	`*-un-lft-identity`
36×	`sqrt-prod`
32×	`difference-of-squares`
23×	`associate-r`
16×	`sqr-pow`
9×	`distribute-lft-out`
8×	`pow1` `add-cube-cbrt` `distribute-lft-out--`
7×	`associate-l`
6×	`add-exp-log` `add-cbrt-cube` `add-log-exp`
5×	`flip3-+` `flip-+`
4×	`frac-times` `flip3--` `sqrt-div` `flip--`
3×	`sub-neg`
2×	`distribute-rgt-in` `rem-sqrt-square` `distribute-lft-in` `sqrt-pow1` `pow1/2` `associate-r/` `associate-l/`
1×	`diff-log` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `unswap-sqr`

Counts

4 → 118

Calls

4 calls:

3.0ms	(sqrt (+ x 1.0))
3.0ms	(sqrt (+ x 1.0))
36.0ms	(* (+ (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))))
14.0ms	(- (pow (sqrt (+ x 1.0)) (/ 1.0 n)) (pow (sqrt x) (/ 1.0 n)))

series2.3s

Counts

4 → 12

Calls

4 calls:

36.0ms	(sqrt (+ x 1.0))
30.0ms	(sqrt (+ x 1.0))
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))))
717.0ms	(- (pow (sqrt (+ x 1.0)) (/ 1.0 n)) (pow (sqrt x) (/ 1.0 n)))

simplify69.0ms

Algorithm

egg-herbie

Counts

130 → 130

Iterations

Useful iterations: 2 (50.0ms)

Iter	Nodes	Cost
0	491	1966
1	2033	1807
2	5003	1795

prune382.0ms

Filtered

130 candidates to 88 candidates (67.7%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	128	2	130
Fresh	0	4	4
Picked	1	0	1
Done	0	0	0
Total	129	6	135

Merged error: 22.6b

Counts

135 → 6

localize17.0ms

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))) (- (pow (sqrt (+ x 1.0)) (/ 1.0 n)) (pow (sqrt x) (/ 1.0 n)))))
2.4b	(- (pow (sqrt (+ x 1.0)) (/ 1.0 n)) (pow (sqrt x) (/ 1.0 n)))
2.4b	(- (pow (sqrt (+ x 1.0)) (/ 1.0 n)) (pow (sqrt x) (/ 1.0 n)))
2.4b	(- (pow (sqrt (+ x 1.0)) (/ 1.0 n)) (pow (sqrt x) (/ 1.0 n)))

rewrite79.0ms

Algorithm

rewrite-expression-head

Rules

76×	`add-sqr-sqrt`
66×	`unpow-prod-down`
48×	`difference-of-squares`
36×	`sqrt-prod`
31×	`*-un-lft-identity`
24×	`sqr-pow`
12×	`distribute-lft-out--`
10×	`add-log-exp`
8×	`cbrt-div`
6×	`flip3--` `flip--`
4×	`pow1` `add-exp-log` `frac-times` `add-cube-cbrt` `add-cbrt-cube`
3×	`sub-neg` `flip3-+` `diff-log` `flip-+` `distribute-lft-out`
2×	`associate-r/` `associate-l/`
1×	`cbrt-prod` `pow1/3`

Counts

4 → 113

Calls

4 calls:

27.0ms	(cbrt (* (+ (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)))))
14.0ms	(- (pow (sqrt (+ x 1.0)) (/ 1.0 n)) (pow (sqrt x) (/ 1.0 n)))
18.0ms	(- (pow (sqrt (+ x 1.0)) (/ 1.0 n)) (pow (sqrt x) (/ 1.0 n)))
14.0ms	(- (pow (sqrt (+ x 1.0)) (/ 1.0 n)) (pow (sqrt x) (/ 1.0 n)))

series17.4s

Counts

4 → 12

Calls

4 calls:

15.2s	(cbrt (* (+ (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)))))
747.0ms	(- (pow (sqrt (+ x 1.0)) (/ 1.0 n)) (pow (sqrt x) (/ 1.0 n)))
737.0ms	(- (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)))

simplify56.0ms

Algorithm

egg-herbie

Counts

125 → 125

Iterations

Useful iterations: 2 (34.0ms)

Iter	Nodes	Cost
0	399	2394
1	1260	2280
2	5001	2265

prune479.0ms

Filtered

125 candidates to 89 candidates (71.2%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	124	1	125
Fresh	0	5	5
Picked	1	0	1
Done	0	0	0
Total	125	6	131

Merged error: 22.6b

Counts

131 → 6

regimes249.0ms

Accuracy

85.5% (1.6b remaining)

Error of 24.1b against oracle of 22.4b and baseline of 33.8b

bsearch2.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	55	51
1	55	51

end0.0ms

sample7.3s

Algorithm

intervals

Results

2.2s	4032×	body	1280	valid
1.2s	1034×	body	1280	nan
850.0ms	1805×	body	640	valid
636.0ms	890×	body	640	nan
624.0ms	4066×	body	80	overflowed
313.0ms	6225×	body	80	nan
311.0ms	3004×	body	80	valid
281.0ms	890×	body	320	valid
196.0ms	467×	body	320	nan
89.0ms	448×	body	160	valid
51.0ms	231×	body	160	nan

Details

sample231.0ms

simplify35.0ms

prune2.0ms

localize8.0ms

rewrite11.0ms

series274.0ms

simplify75.0ms

prune89.0ms

localize11.0ms

rewrite23.0ms

series556.0ms

simplify89.0ms

prune164.0ms

localize12.0ms

rewrite62.0ms

series2.3s

simplify69.0ms

prune382.0ms

localize17.0ms

rewrite79.0ms

series17.4s

simplify56.0ms

prune479.0ms

regimes249.0ms

bsearch2.0ms

simplify2.0ms

end0.0ms

sample7.3s

Profiling