Details

sample40.0ms

Algorithm

intervals

Results

19.0ms	371×	body	80	valid
5.0ms	131×	body	80	nan

simplify105.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 1 (3.0ms)

Iter	Nodes	Cost
0	24	7
1	53	5
2	106	5
3	269	5
4	904	5
5	3976	5
6	5001	5

prune11.0ms

Filtered

1 candidates to 1 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: 2.1b

Counts

2 → 2

localize10.0ms

Local error

Found 2 expressions with local error:

0.0b	(* a (pow k m))
2.1b	(/ (* a (pow k m)) (+ (+ 1.0 (* 10.0 k)) (* k k)))

rewrite15.0ms

Algorithm

rewrite-expression-head

Rules

17×	`add-exp-log`
12×	`add-sqr-sqrt`
9×	`add-cbrt-cube`
7×	`add-cube-cbrt` `-un-lft-identity` `associate-r*`
6×	`prod-exp`
4×	`unpow-prod-down` `div-exp`
3×	`times-frac` `associate-l` `associate-/r*` `unswap-sqr`
2×	`pow1` `cbrt-undiv` `expm1-log1p-u` `pow-to-exp` `pow-exp` `associate-/r/` `cbrt-unprod` `log1p-expm1-u` `add-log-exp` `sqr-pow`
1×	`frac-2neg` `flip3-+` `clear-num` `-commutative` `flip-+` `div-inv` `associate-/l`

Counts

2 → 54

Calls

2 calls:

5.0ms	(* a (pow k m))
8.0ms	(/ (* a (pow k m)) (+ (+ 1.0 (* 10.0 k)) (* k k)))

series174.0ms

Counts

2 → 6

Calls

2 calls:

59.0ms	(* a (pow k m))
115.0ms	(/ (* a (pow k m)) (+ (+ 1.0 (* 10.0 k)) (* k k)))

simplify50.0ms

Algorithm

egg-herbie

Counts

60 → 60

Iterations

Useful iterations: 2 (44.0ms)

Iter	Nodes	Cost
0	371	469
1	1892	408
2	5001	391

prune142.0ms

Filtered

60 candidates to 46 candidates (76.7%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	57	3	60
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	59	3	62

Merged error: 0.0b

Counts

62 → 3

localize10.0ms

Local error

Found 2 expressions with local error:

0.2b	(/ (pow k m) (+ (+ 1.0 (* 10.0 k)) (* k k)))
2.1b	(* a (/ (pow k m) (+ (+ 1.0 (* 10.0 k)) (* k k))))

rewrite27.0ms

Algorithm

rewrite-expression-head

Rules

45×	`times-frac`
43×	`add-sqr-sqrt`
33×	`add-cube-cbrt` `*-un-lft-identity`
27×	`associate-r`
22×	`unpow-prod-down`
17×	`add-exp-log`
9×	`add-cbrt-cube`
8×	`sqr-pow`
7×	`associate-/l*`
6×	`div-exp`
4×	`pow1` `prod-exp` `associate-/r/` `unswap-sqr`
3×	`associate-l` `associate-/r*`
2×	`cbrt-undiv` `expm1-log1p-u` `pow-to-exp` `flip3-+` `pow-exp` `cbrt-unprod` `flip-+` `log1p-expm1-u` `div-inv` `add-log-exp`
1×	`frac-2neg` `associate-r/` `pow-prod-down` `clear-num` `-commutative`

Counts

2 → 101

Calls

2 calls:

11.0ms	(/ (pow k m) (+ (+ 1.0 (* 10.0 k)) (* k k)))
13.0ms	(* a (/ (pow k m) (+ (+ 1.0 (* 10.0 k)) (* k k))))

series177.0ms

Counts

2 → 6

Calls

2 calls:

66.0ms	(/ (pow k m) (+ (+ 1.0 (* 10.0 k)) (* k k)))
112.0ms	(* a (/ (pow k m) (+ (+ 1.0 (* 10.0 k)) (* k k))))

simplify65.0ms

Algorithm

egg-herbie

Counts

107 → 107

Iterations

Useful iterations: 2 (53.0ms)

Iter	Nodes	Cost
0	530	1198
1	2562	1092
2	5001	1068

prune262.0ms

Filtered

107 candidates to 86 candidates (80.4%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	107	0	107
Fresh	0	2	2
Picked	0	1	1
Done	0	0	0
Total	107	3	110

Merged error: 0.0b

Counts

110 → 3

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (* a (pow k m)) (sqrt (+ (+ 1.0 (* 10.0 k)) (* k k))))
0.0b	(/ (/ (* a (pow k m)) (sqrt (+ (+ 1.0 (* 10.0 k)) (* k k)))) (sqrt (+ (+ 1.0 (* 10.0 k)) (* k k))))
14.9b	(sqrt (+ (+ 1.0 (* 10.0 k)) (* k k)))
14.9b	(sqrt (+ (+ 1.0 (* 10.0 k)) (* k k)))

rewrite41.0ms

Algorithm

rewrite-expression-head

Rules

120×	`times-frac`
72×	`sqrt-prod`
61×	`add-sqr-sqrt`
57×	`add-cube-cbrt` `*-un-lft-identity`
30×	`add-exp-log`
22×	`sqrt-div`
18×	`associate-/r/` `add-cbrt-cube`
13×	`div-exp` `associate-/l*`
12×	`associate-/r*`
11×	`flip3-+` `flip-+`
9×	`div-inv`
7×	`cbrt-undiv`
6×	`pow1` `prod-exp`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
2×	`pow-to-exp` `rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `pow-exp` `clear-num` `cbrt-unprod` `hypot-def`
1×	`associate-/l/`

Counts

4 → 182

Calls

4 calls:

9.0ms	(/ (* a (pow k m)) (sqrt (+ (+ 1.0 (* 10.0 k)) (* k k))))
16.0ms	(/ (/ (* a (pow k m)) (sqrt (+ (+ 1.0 (* 10.0 k)) (* k k)))) (sqrt (+ (+ 1.0 (* 10.0 k)) (* k k))))
4.0ms	(sqrt (+ (+ 1.0 (* 10.0 k)) (* k k)))
4.0ms	(sqrt (+ (+ 1.0 (* 10.0 k)) (* k k)))

series365.0ms

Counts

4 → 12

Calls

4 calls:

152.0ms	(/ (* a (pow k m)) (sqrt (+ (+ 1.0 (* 10.0 k)) (* k k))))
116.0ms	(/ (/ (* a (pow k m)) (sqrt (+ (+ 1.0 (* 10.0 k)) (* k k)))) (sqrt (+ (+ 1.0 (* 10.0 k)) (* k k))))
45.0ms	(sqrt (+ (+ 1.0 (* 10.0 k)) (* k k)))
51.0ms	(sqrt (+ (+ 1.0 (* 10.0 k)) (* k k)))

simplify96.0ms

Algorithm

egg-herbie

Counts

194 → 194

Iterations

Useful iterations: 2 (62.0ms)

Iter	Nodes	Cost
0	773	3506
1	3380	3103
2	5003	3090

prune422.0ms

Filtered

194 candidates to 123 candidates (63.4%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	193	1	194
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	193	4	197

Merged error: 0.0b

Counts

197 → 4

localize16.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ 1 (sqrt (sqrt (+ (+ 1.0 (* 10.0 k)) (* k k)))))
14.9b	(sqrt (+ (+ 1.0 (* 10.0 k)) (* k k)))
14.9b	(sqrt (+ (+ 1.0 (* 10.0 k)) (* k k)))
14.9b	(sqrt (+ (+ 1.0 (* 10.0 k)) (* k k)))

rewrite26.0ms

Algorithm

rewrite-expression-head

Rules

45×	`sqrt-prod`
35×	`add-sqr-sqrt`
29×	`add-cube-cbrt` `*-un-lft-identity`
27×	`times-frac`
10×	`pow1` `sqrt-div`
9×	`associate-/r*`
8×	`add-exp-log`
7×	`sqrt-pow1`
6×	`add-cbrt-cube`
5×	`pow-flip` `pow1/2`
4×	`expm1-log1p-u` `flip3-+` `flip-+` `log1p-expm1-u` `add-log-exp`
3×	`rem-sqrt-square` `hypot-def` `associate-/l*`
2×	`div-exp` `associate-/r/`
1×	`cbrt-undiv` `rec-exp` `frac-2neg` `1-exp` `clear-num` `div-inv` `inv-pow`

Counts

4 → 117

Calls

4 calls:

8.0ms	(/ 1 (sqrt (sqrt (+ (+ 1.0 (* 10.0 k)) (* k k)))))
5.0ms	(sqrt (+ (+ 1.0 (* 10.0 k)) (* k k)))
4.0ms	(sqrt (+ (+ 1.0 (* 10.0 k)) (* k k)))
5.0ms	(sqrt (+ (+ 1.0 (* 10.0 k)) (* k k)))

series272.0ms

Counts

4 → 12

Calls

4 calls:

121.0ms	(/ 1 (sqrt (sqrt (+ (+ 1.0 (* 10.0 k)) (* k k)))))
52.0ms	(sqrt (+ (+ 1.0 (* 10.0 k)) (* k k)))
46.0ms	(sqrt (+ (+ 1.0 (* 10.0 k)) (* k k)))
53.0ms	(sqrt (+ (+ 1.0 (* 10.0 k)) (* k k)))

simplify47.0ms

Algorithm

egg-herbie

Counts

129 → 129

Iterations

Useful iterations: 2 (34.0ms)

Iter	Nodes	Cost
0	372	1258
1	1423	1156
2	5002	1106

prune341.0ms

Filtered

129 candidates to 83 candidates (64.3%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	129	0	129
Fresh	0	1	1
Picked	0	1	1
Done	0	2	2
Total	129	4	133

Merged error: 0.0b

Counts

133 → 4

regimes78.0ms

Accuracy

97.7% (0.0b remaining)

Error of 0.1b against oracle of 0.1b and baseline of 1.9b

bsearch40.0ms

Steps

Iters	Range		Point
5	9.694562852154096e+135	2.3045760005517895e+136	1.3253131732275456e+136

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	48	34
1	54	34
2	54	34

end0.0ms

sample1.2s

Algorithm

intervals

Results

642.0ms	12026×	body	80	valid
178.0ms	4152×	body	80	nan