Details

sample231.0ms

Algorithm

intervals

Results

62.0ms	120×	body	1280	valid
37.0ms	33×	body	1280	nan
30.0ms	55×	body	640	valid
18.0ms	118×	body	80	overflowed
17.0ms	26×	body	640	nan
10.0ms	100×	body	80	valid
9.0ms	32×	body	320	valid
8.0ms	162×	body	80	nan
6.0ms	15×	body	320	nan
3.0ms	17×	body	160	valid
2.0ms	9×	body	160	nan

simplify36.0ms

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: 30.6b

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))
2.8b	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))

rewrite20.0ms

Algorithm

rewrite-expression-head

Rules

31×	`add-sqr-sqrt`
28×	`*-un-lft-identity`
26×	`pow-unpow`
19×	`add-cube-cbrt`
18×	`times-frac`
17×	`unpow-prod-down`
9×	`difference-of-squares`
8×	`sqr-pow`
5×	`pow1` `add-exp-log` `add-log-exp`
3×	`add-cbrt-cube` `distribute-lft-out--`
2×	`pow-to-exp` `pow-pow` `pow-exp` `div-inv` `distribute-lft-out`
1×	`sub-neg` `flip3--` `diff-log` `flip--`

Counts

3 → 79

Calls

3 calls:

5.0ms	(pow (+ x 1.0) (/ 1.0 n))
3.0ms	(pow x (/ 1.0 n))
9.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))

series73.0ms

Counts

3 → 9

Calls

3 calls:

20.0ms	(pow (+ x 1.0) (/ 1.0 n))
12.0ms	(pow x (/ 1.0 n))
40.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))

simplify49.0ms

Algorithm

egg-herbie

Counts

88 → 88

Iterations

Useful iterations: 2 (40.0ms)

Iter	Nodes	Cost
0	552	688
1	1885	669
2	5002	641

prune457.0ms

Filtered

88 candidates to 71 candidates (19.3%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	84	4	88
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	85	4	89

Merged error: 20.8b

Counts

89 → 4

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt (pow x (/ 1.0 n)))
0.0b	(pow x (/ 1.0 n))
0.0b	(pow x (/ 1.0 n))
3.3b	(- (pow (sqrt (+ x 1.0)) (/ 1.0 n)) (sqrt (pow x (/ 1.0 n))))

rewrite28.0ms

Algorithm

rewrite-expression-head

Rules

48×	`add-sqr-sqrt`
26×	`pow-unpow`
24×	`*-un-lft-identity`
23×	`sqrt-prod`
22×	`add-cube-cbrt` `unpow-prod-down`
18×	`times-frac`
16×	`difference-of-squares`
12×	`sqr-pow`
6×	`pow1` `add-exp-log` `add-log-exp`
4×	`add-cbrt-cube`
3×	`rem-sqrt-square`
2×	`pow-to-exp` `pow-pow` `pow-exp` `div-inv`
1×	`sub-neg` `flip3--` `sqrt-pow1` `pow1/2` `diff-log` `flip--` `distribute-lft-out--`

Counts

4 → 102

Calls

4 calls:

2.0ms	(sqrt (pow x (/ 1.0 n)))
3.0ms	(pow x (/ 1.0 n))
3.0ms	(pow x (/ 1.0 n))
15.0ms	(- (pow (sqrt (+ x 1.0)) (/ 1.0 n)) (sqrt (pow x (/ 1.0 n))))

series104.0ms

Counts

4 → 12

Calls

4 calls:

16.0ms	(sqrt (pow x (/ 1.0 n)))
15.0ms	(pow x (/ 1.0 n))
12.0ms	(pow x (/ 1.0 n))
60.0ms	(- (pow (sqrt (+ x 1.0)) (/ 1.0 n)) (sqrt (pow x (/ 1.0 n))))

simplify53.0ms

Algorithm

egg-herbie

Counts

114 → 114

Iterations

Useful iterations: 2 (42.0ms)

Iter	Nodes	Cost
0	572	1081
1	2007	1049
2	5002	1000

prune833.0ms

Filtered

114 candidates to 88 candidates (22.8%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	113	1	114
Fresh	0	3	3
Picked	1	0	1
Done	0	0	0
Total	114	4	118

Merged error: 20.8b

Counts

118 → 4

localize18.0ms

Local error

Found 4 expressions with local error:

0.0b	(pow x (/ 1.0 n))
0.0b	(pow x (/ 1.0 n))
0.0b	(* (cbrt (pow x (/ 1.0 n))) (cbrt (pow x (/ 1.0 n))))
3.3b	(- (pow (sqrt (+ x 1.0)) (/ 1.0 n)) (sqrt (pow x (/ 1.0 n))))

rewrite37.0ms

Algorithm

rewrite-expression-head

Rules

80×	`add-sqr-sqrt`
52×	`cbrt-prod`
38×	`unpow-prod-down`
34×	`*-un-lft-identity`
32×	`add-cube-cbrt`
26×	`pow-unpow`
22×	`sqr-pow`
18×	`times-frac`
16×	`sqrt-prod` `difference-of-squares` `unswap-sqr`
13×	`pow1`
10×	`swap-sqr` `associate-r` `associate-l`
8×	`add-exp-log`
6×	`pow1/3` `add-log-exp`
4×	`add-cbrt-cube`
2×	`pow-to-exp` `pow-pow` `pow-prod-down` `pow-exp` `pow-sqr` `pow-prod-up` `div-inv`
1×	`pow2` `sub-neg` `flip3--` `pow-plus` `diff-log` `prod-exp` `*-commutative` `flip--` `cbrt-unprod` `distribute-lft-out--`

Counts

4 → 147

Calls

4 calls:

4.0ms	(pow x (/ 1.0 n))
3.0ms	(pow x (/ 1.0 n))
9.0ms	(* (cbrt (pow x (/ 1.0 n))) (cbrt (pow x (/ 1.0 n))))
14.0ms	(- (pow (sqrt (+ x 1.0)) (/ 1.0 n)) (sqrt (pow x (/ 1.0 n))))

series115.0ms

Counts

4 → 12

Calls

4 calls:

12.0ms	(pow x (/ 1.0 n))
12.0ms	(pow x (/ 1.0 n))
28.0ms	(* (cbrt (pow x (/ 1.0 n))) (cbrt (pow x (/ 1.0 n))))
62.0ms	(- (pow (sqrt (+ x 1.0)) (/ 1.0 n)) (sqrt (pow x (/ 1.0 n))))

simplify71.0ms

Algorithm

egg-herbie

Counts

159 → 159

Iterations

Useful iterations: 2 (55.0ms)

Iter	Nodes	Cost
0	719	1670
1	2688	1609
2	5001	1544

prune2.1s

Filtered

159 candidates to 113 candidates (28.9%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	159	0	159
Fresh	0	3	3
Picked	0	1	1
Done	0	0	0
Total	159	4	163

Merged error: 20.8b

Counts

163 → 4

localize20.0ms

Local error

Found 4 expressions with local error:

0.5b	(/ (neg 0.5) (* (pow x 2) n))
2.3b	(+ (* (/ 1.0 x) (+ (/ 1 n) 0)) (/ (* (log x) 1.0) (* x (pow n 2))))
8.5b	(* x (pow n 2))
10.3b	(* (pow x 2) n)

rewrite35.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 111

Calls

4 calls:

6.0ms	(/ (neg 0.5) (* (pow x 2) n))
13.0ms	(+ (* (/ 1.0 x) (+ (/ 1 n) 0)) (/ (* (log x) 1.0) (* x (pow n 2))))
7.0ms	(* x (pow n 2))
5.0ms	(* (pow x 2) n)

series39.0ms

Counts

4 → 12

Calls

4 calls:

4.0ms	(/ (neg 0.5) (* (pow x 2) n))
24.0ms	(+ (* (/ 1.0 x) (+ (/ 1 n) 0)) (/ (* (log x) 1.0) (* x (pow n 2))))
7.0ms	(* x (pow n 2))
4.0ms	(* (pow x 2) n)

simplify216.0ms

Algorithm

egg-herbie

Counts

123 → 123

Iterations

Useful iterations: 2 (206.0ms)

Iter	Nodes	Cost
0	667	781
1	3718	677
2	5002	674

prune711.0ms

Filtered

123 candidates to 87 candidates (29.3%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	116	7	123
Fresh	0	2	2
Picked	1	0	1
Done	0	1	1
Total	117	10	127

Merged error: 20.7b

Counts

127 → 10

regimes347.0ms

Accuracy

83.6% (1.7b remaining)

Error of 23.3b against oracle of 21.5b and baseline of 32.1b

bsearch2.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	60	45
1	62	45
2	62	45

end0.0ms

sample7.2s

Algorithm

intervals

Results

2.1s	3900×	body	1280	valid
1.2s	1064×	body	1280	nan
838.0ms	1820×	body	640	valid
636.0ms	916×	body	640	nan
591.0ms	3987×	body	80	overflowed
318.0ms	3110×	body	80	valid
294.0ms	6379×	body	80	nan
280.0ms	894×	body	320	valid
180.0ms	444×	body	320	nan
82.0ms	434×	body	160	valid
39.0ms	182×	body	160	nan

Details

sample231.0ms

simplify36.0ms

prune4.0ms

localize8.0ms

rewrite20.0ms

series73.0ms

simplify49.0ms

prune457.0ms

localize13.0ms

rewrite28.0ms

series104.0ms

simplify53.0ms

prune833.0ms

localize18.0ms

rewrite37.0ms

series115.0ms

simplify71.0ms

prune2.1s

localize20.0ms

rewrite35.0ms

series39.0ms

simplify216.0ms

prune711.0ms

regimes347.0ms

bsearch2.0ms

simplify2.0ms

end0.0ms

sample7.2s

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