Details

sample251.0ms

Algorithm

intervals

Results

72.0ms	129×	body	1280	valid
47.0ms	45×	body	1280	nan
32.0ms	59×	body	640	valid
18.0ms	124×	body	80	overflowed
17.0ms	25×	body	640	nan
12.0ms	118×	body	80	valid
10.0ms	221×	body	80	nan
6.0ms	20×	body	320	valid
5.0ms	12×	body	320	nan
2.0ms	13×	body	160	valid
2.0ms	10×	body	160	nan

simplify33.0ms

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

prune4.0ms

Filtered

1 candidates to 0 candidates (100.0%)

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: 29.6b

Counts

2 → 1

localize8.0ms

Local error

Found 2 expressions with local error:

0.0b	(pow x (/ 1.0 n))
1.3b	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))

rewrite14.0ms

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)))

series56.0ms

Counts

2 → 6

Calls

2 calls:

12.0ms	(pow x (/ 1.0 n))
44.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))

simplify46.0ms

Algorithm

egg-herbie

Counts

57 → 57

Iterations

Useful iterations: 2 (39.0ms)

Iter	Nodes	Cost
0	476	520
1	1648	503
2	5001	478

prune256.0ms

Filtered

57 candidates to 47 candidates (17.5%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	53	4	57
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	54	4	58

Merged error: 19.6b

Counts

58 → 4

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b	(pow x (/ 1.0 n))
0.0b	(log (- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n))))
0.0b	(exp (log (- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))))
1.3b	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))

rewrite36.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 106

Calls

4 calls:

3.0ms	(pow x (/ 1.0 n))
9.0ms	(log (- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n))))
10.0ms	(exp (log (- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))))
9.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))

series178.0ms

Counts

4 → 12

Calls

4 calls:

12.0ms	(pow x (/ 1.0 n))
88.0ms	(log (- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n))))
37.0ms	(exp (log (- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))))
41.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))

simplify65.0ms

Algorithm

egg-herbie

Counts

118 → 118

Iterations

Useful iterations: 2 (49.0ms)

Iter	Nodes	Cost
0	657	1395
1	2228	1330
2	5001	1309

prune860.0ms

Filtered

118 candidates to 92 candidates (22.0%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	116	2	118
Fresh	1	2	3
Picked	0	1	1
Done	0	0	0
Total	117	5	122

Merged error: 19.6b

Counts

122 → 5

localize22.0ms

Local error

Found 4 expressions with local error:

0.6b	(/ (log (/ 1 x)) (* x (pow n 2)))
3.5b	(+ (/ (/ 1.0 n) x) (* 1.0 (- 0 (/ (log (/ 1 x)) (* x (pow n 2))))))
7.7b	(/ (/ 0.5 n) (pow x 2))
8.5b	(* x (pow n 2))

rewrite44.0ms

Algorithm

rewrite-expression-head

Rules

191×	`times-frac`
106×	`add-sqr-sqrt`
100×	`add-cube-cbrt` `*-un-lft-identity`
46×	`unpow-prod-down`
32×	`add-exp-log`
19×	`associate-/l*`
16×	`add-cbrt-cube` `unpow2` `sqr-pow`
13×	`div-exp`
11×	`div-inv`
9×	`associate-/r*`
8×	`pow1` `associate-r`
6×	`associate-+r+` `prod-exp` `log-pow` `add-log-exp`
5×	`cbrt-undiv`
4×	`pow-to-exp` `pow-exp` `unswap-sqr`
3×	`distribute-rgt-in` `log-div` `distribute-lft-in` `div-sub` `associate-l`
2×	`sub-neg` `pow-flip` `frac-2neg` `sub0-neg` `associate-*r/` `frac-add` `clear-num` `distribute-rgt-neg-out` `cbrt-unprod` `inv-pow` `associate--r-`
1×	`+-commutative` `flip3--` `flip3-+` `distribute-frac-neg` `unsub-neg` `log-rec` `sum-log` `*-commutative` `flip--` `flip-+` `associate-/l/`

Counts

4 → 223

Calls

4 calls:

7.0ms	(/ (log (/ 1 x)) (* x (pow n 2)))
13.0ms	(+ (/ (/ 1.0 n) x) (* 1.0 (- 0 (/ (log (/ 1 x)) (* x (pow n 2))))))
8.0ms	(/ (/ 0.5 n) (pow x 2))
6.0ms	(* x (pow n 2))

series42.0ms

Counts

4 → 12

Calls

4 calls:

13.0ms	(/ (log (/ 1 x)) (* x (pow n 2)))
17.0ms	(+ (/ (/ 1.0 n) x) (* 1.0 (- 0 (/ (log (/ 1 x)) (* x (pow n 2))))))
6.0ms	(/ (/ 0.5 n) (pow x 2))
7.0ms	(* x (pow n 2))

simplify151.0ms

Algorithm

egg-herbie

Counts

235 → 235

Iterations

Useful iterations: 2 (130.0ms)

Iter	Nodes	Cost
0	1037	1834
1	4830	1606
2	5001	1605

prune2.4s

Filtered

235 candidates to 147 candidates (37.4%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	231	4	235
Fresh	0	3	3
Picked	1	0	1
Done	0	1	1
Total	232	8	240

Merged error: 19.4b

Counts

240 → 8

localize21.0ms

Local error

Found 4 expressions with local error:

0.6b	(/ (log (/ 1 x)) (* x (pow n 2)))
3.5b	(+ (/ (/ 1.0 n) x) (* 1.0 (- 0 (/ (log (/ 1 x)) (* x (pow n 2))))))
7.7b	(/ (/ 0.5 n) (pow x 2))
8.5b	(* x (pow n 2))

rewrite47.0ms

Algorithm

rewrite-expression-head

Rules

191×	`times-frac`
106×	`add-sqr-sqrt`
100×	`add-cube-cbrt` `*-un-lft-identity`
46×	`unpow-prod-down`
32×	`add-exp-log`
19×	`associate-/l*`
16×	`add-cbrt-cube` `unpow2` `sqr-pow`
13×	`div-exp`
11×	`div-inv`
9×	`associate-/r*`
8×	`pow1` `associate-r`
6×	`associate-+r+` `prod-exp` `log-pow` `add-log-exp`
5×	`cbrt-undiv`
4×	`pow-to-exp` `pow-exp` `unswap-sqr`
3×	`distribute-rgt-in` `log-div` `distribute-lft-in` `div-sub` `associate-l`
2×	`sub-neg` `pow-flip` `frac-2neg` `sub0-neg` `associate-*r/` `frac-add` `clear-num` `distribute-rgt-neg-out` `cbrt-unprod` `inv-pow` `associate--r-`
1×	`+-commutative` `flip3--` `flip3-+` `distribute-frac-neg` `unsub-neg` `log-rec` `sum-log` `*-commutative` `flip--` `flip-+` `associate-/l/`

Counts

4 → 223

Calls

4 calls:

7.0ms	(/ (log (/ 1 x)) (* x (pow n 2)))
14.0ms	(+ (/ (/ 1.0 n) x) (* 1.0 (- 0 (/ (log (/ 1 x)) (* x (pow n 2))))))
8.0ms	(/ (/ 0.5 n) (pow x 2))
5.0ms	(* x (pow n 2))

series39.0ms

Counts

4 → 12

Calls

4 calls:

13.0ms	(/ (log (/ 1 x)) (* x (pow n 2)))
13.0ms	(+ (/ (/ 1.0 n) x) (* 1.0 (- 0 (/ (log (/ 1 x)) (* x (pow n 2))))))
6.0ms	(/ (/ 0.5 n) (pow x 2))
7.0ms	(* x (pow n 2))

simplify139.0ms

Algorithm

egg-herbie

Counts

235 → 235

Iterations

Useful iterations: 2 (117.0ms)

Iter	Nodes	Cost
0	1038	1902
1	4874	1613
2	5001	1612

prune3.2s

Filtered

235 candidates to 148 candidates (37.0%)

Pruning

11 alts after pruning (9 fresh and 2 done)

	Pruned	Kept	Total
New	231	4	235
Fresh	1	5	6
Picked	0	1	1
Done	0	1	1
Total	232	11	243

Merged error: 19.4b

Counts

243 → 11

regimes489.0ms

Accuracy

81.8% (2.1b remaining)

Error of 23.9b against oracle of 21.8b and baseline of 33.5b

bsearch179.0ms

Steps

Iters	Range		Point
4	7916476625122.62	14502975650822.773	8033134678603.644
11	-2621393.439199732	-3.9048216217793476e-19	-85.39147387860265

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	66	43
1	73	43
2	76	43
3	76	43

end0.0ms

sample7.0s

Algorithm

intervals

Results

2.1s	4038×	body	1280	valid
1.2s	1086×	body	1280	nan
776.0ms	1751×	body	640	valid
624.0ms	914×	body	640	nan
582.0ms	4120×	body	80	overflowed
292.0ms	3074×	body	80	valid
276.0ms	6262×	body	80	nan
252.0ms	846×	body	320	valid
180.0ms	462×	body	320	nan
88.0ms	458×	body	160	valid
44.0ms	217×	body	160	nan

Details

sample251.0ms

simplify33.0ms

prune4.0ms

localize8.0ms

rewrite14.0ms

series56.0ms

simplify46.0ms

prune256.0ms

localize11.0ms

rewrite36.0ms

series178.0ms

simplify65.0ms

prune860.0ms

localize22.0ms

rewrite44.0ms

series42.0ms

simplify151.0ms

prune2.4s

localize21.0ms

rewrite47.0ms

series39.0ms

simplify139.0ms

prune3.2s

regimes489.0ms

bsearch179.0ms

simplify2.0ms

end0.0ms

sample7.0s

Profiling