Details

sample53.0ms

Algorithm

intervals

Results

27.0ms	382×	body	80	valid
9.0ms	141×	body	80	nan

simplify104.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 2 (5.0ms)

Iter	Nodes	Cost
0	24	7
1	48	7
2	96	6
3	256	6
4	891	6
5	3963	6
6	5002	6

prune6.0ms

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: 2.8b

Counts

2 → 2

localize10.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ 1.0 (* 10.0 k))
0.0b	(* a (pow k m))
0.0b	(+ (+ 1.0 (* 10.0 k)) (* k k))
2.8b	(/ (* a (pow k m)) (+ (+ 1.0 (* 10.0 k)) (* k k)))

rewrite22.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 74

Calls

4 calls:

2.0ms	(+ 1.0 (* 10.0 k))
5.0ms	(* a (pow k m))
5.0ms	(+ (+ 1.0 (* 10.0 k)) (* k k))
8.0ms	(/ (* a (pow k m)) (+ (+ 1.0 (* 10.0 k)) (* k k)))

series232.0ms

Counts

4 → 12

Calls

4 calls:

38.0ms	(+ 1.0 (* 10.0 k))
55.0ms	(* a (pow k m))
24.0ms	(+ (+ 1.0 (* 10.0 k)) (* k k))
114.0ms	(/ (* a (pow k m)) (+ (+ 1.0 (* 10.0 k)) (* k k)))

simplify59.0ms

Algorithm

egg-herbie

Counts

86 → 86

Iterations

Useful iterations: 2 (51.0ms)

Iter	Nodes	Cost
0	457	599
1	2146	533
2	5001	526

prune185.0ms

Filtered

86 candidates to 63 candidates (73.3%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	82	4	86
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	83	5	88

Merged error: 2.7b

Counts

88 → 5

localize14.0ms

Local error

Found 4 expressions with local error:

0.7b	(cbrt (+ 1.0 (* 10.0 k)))
0.7b	(cbrt (+ 1.0 (* 10.0 k)))
0.7b	(cbrt (+ 1.0 (* 10.0 k)))
2.8b	(/ (* a (pow k m)) (+ (* (* (cbrt (+ 1.0 (* 10.0 k))) (cbrt (+ 1.0 (* 10.0 k)))) (cbrt (+ 1.0 (* 10.0 k)))) (* k k)))

rewrite27.0ms

Algorithm

rewrite-expression-head

Rules

14×	`add-exp-log`
9×	`cbrt-prod` `add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity` `add-cbrt-cube`
6×	`cbrt-div`
4×	`pow1` `flip3-+` `div-exp` `flip-+` `add-log-exp`
3×	`times-frac` `pow1/3` `prod-exp` `associate-/r*`
2×	`cbrt-undiv` `associate-/r/`
1×	`pow-to-exp` `frac-2neg` `pow-exp` `clear-num` `cbrt-unprod` `div-inv` `associate-/l*`

Counts

4 → 64

Calls

4 calls:

2.0ms	(cbrt (+ 1.0 (* 10.0 k)))
2.0ms	(cbrt (+ 1.0 (* 10.0 k)))
2.0ms	(cbrt (+ 1.0 (* 10.0 k)))
19.0ms	(/ (* a (pow k m)) (+ (* (* (cbrt (+ 1.0 (* 10.0 k))) (cbrt (+ 1.0 (* 10.0 k)))) (cbrt (+ 1.0 (* 10.0 k)))) (* k k)))

series497.0ms

Counts

4 → 12

Calls

4 calls:

122.0ms	(cbrt (+ 1.0 (* 10.0 k)))
129.0ms	(cbrt (+ 1.0 (* 10.0 k)))
127.0ms	(cbrt (+ 1.0 (* 10.0 k)))
119.0ms	(/ (* a (pow k m)) (+ (* (* (cbrt (+ 1.0 (* 10.0 k))) (cbrt (+ 1.0 (* 10.0 k)))) (cbrt (+ 1.0 (* 10.0 k)))) (* k k)))

simplify59.0ms

Algorithm

egg-herbie

Counts

76 → 76

Iterations

Useful iterations: 2 (47.0ms)

Iter	Nodes	Cost
0	503	1204
1	2122	1045
2	5001	1030

prune262.0ms

Filtered

76 candidates to 66 candidates (86.8%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	76	0	76
Fresh	0	4	4
Picked	0	1	1
Done	0	0	0
Total	76	5	81

Merged error: 2.7b

Counts

81 → 5

localize9.0ms

Local error

Found 3 expressions with local error:

0.0b	(* k (+ 10.0 k))
0.2b	(/ (pow k m) (+ (* k (+ 10.0 k)) 1.0))
2.6b	(* (/ (pow k m) (+ (* k (+ 10.0 k)) 1.0)) a)

rewrite38.0ms

Algorithm

rewrite-expression-head

Rules

48×	`add-sqr-sqrt`
45×	`times-frac`
38×	`*-un-lft-identity`
36×	`add-cube-cbrt`
30×	`associate-l`
22×	`unpow-prod-down`
20×	`add-exp-log`
12×	`add-cbrt-cube`
8×	`sqr-pow`
7×	`pow1` `associate-r` `associate-/l*`
6×	`div-exp`
5×	`prod-exp` `unswap-sqr`
4×	`associate-/r/`
3×	`flip3-+` `associate-/r*` `cbrt-unprod` `flip-+` `add-log-exp`
2×	`cbrt-undiv` `pow-to-exp` `associate-r/` `pow-prod-down` `pow-exp` `-commutative` `div-inv`
1×	`distribute-rgt-in` `frac-2neg` `distribute-lft-in` `associate-*l/` `clear-num` `distribute-lft-out`

Counts

3 → 120

Calls

3 calls:

6.0ms	(* k (+ 10.0 k))
14.0ms	(/ (pow k m) (+ (* k (+ 10.0 k)) 1.0))
13.0ms	(* (/ (pow k m) (+ (* k (+ 10.0 k)) 1.0)) a)

series216.0ms

Counts

3 → 9

Calls

3 calls:

48.0ms	(* k (+ 10.0 k))
63.0ms	(/ (pow k m) (+ (* k (+ 10.0 k)) 1.0))
105.0ms	(* (/ (pow k m) (+ (* k (+ 10.0 k)) 1.0)) a)

simplify74.0ms

Algorithm

egg-herbie

Counts

129 → 129

Iterations

Useful iterations: 2 (62.0ms)

Iter	Nodes	Cost
0	608	1105
1	2523	1041
2	5001	1035

prune274.0ms

Filtered

129 candidates to 98 candidates (76.0%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	129	0	129
Fresh	0	3	3
Picked	0	1	1
Done	0	1	1
Total	129	5	134

Merged error: 2.7b

Counts

134 → 5

localize19.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (pow k m) (sqrt (+ (+ 1.0 (* 10.0 k)) (* k k))))
0.1b	(* (/ a (sqrt (+ (+ 1.0 (* 10.0 k)) (* k k)))) (/ (pow k m) (sqrt (+ (+ 1.0 (* 10.0 k)) (* k k)))))
14.5b	(sqrt (+ (+ 1.0 (* 10.0 k)) (* k k)))
14.5b	(sqrt (+ (+ 1.0 (* 10.0 k)) (* k k)))

rewrite62.0ms

Algorithm

rewrite-expression-head

Rules

146×	`add-sqr-sqrt`
134×	`times-frac`
76×	`add-cube-cbrt` `*-un-lft-identity` `sqrt-prod`
48×	`associate-r`
45×	`unpow-prod-down`
33×	`add-exp-log`
24×	`associate-l`
21×	`unswap-sqr`
19×	`sqr-pow`
18×	`add-cbrt-cube`
13×	`div-exp`
10×	`sqrt-div`
8×	`pow1` `prod-exp`
7×	`associate-/l*`
6×	`associate-/r*` `associate-/r/`
5×	`cbrt-undiv` `flip3-+` `flip-+`
4×	`cbrt-unprod` `add-log-exp`
3×	`pow-to-exp` `pow-exp` `div-inv`
2×	`rem-sqrt-square` `sqrt-pow1` `pow1/2`
1×	`frac-times` `frac-2neg` `associate-r/` `pow-prod-down` `associate-l/` `clear-num` `*-commutative`

Counts

4 → 218

Calls

4 calls:

9.0ms	(/ (pow k m) (sqrt (+ (+ 1.0 (* 10.0 k)) (* k k))))
34.0ms	(* (/ a (sqrt (+ (+ 1.0 (* 10.0 k)) (* k k)))) (/ (pow k m) (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)))

series338.0ms

Counts

4 → 12

Calls

4 calls:

115.0ms	(/ (pow k m) (sqrt (+ (+ 1.0 (* 10.0 k)) (* k k))))
116.0ms	(* (/ a (sqrt (+ (+ 1.0 (* 10.0 k)) (* k k)))) (/ (pow k m) (sqrt (+ (+ 1.0 (* 10.0 k)) (* k k)))))
54.0ms	(sqrt (+ (+ 1.0 (* 10.0 k)) (* k k)))
53.0ms	(sqrt (+ (+ 1.0 (* 10.0 k)) (* k k)))

simplify120.0ms

Algorithm

egg-herbie

Counts

230 → 230

Iterations

Useful iterations: 2 (81.0ms)

Iter	Nodes	Cost
0	899	3695
1	3999	3453
2	5002	3348

prune502.0ms

Filtered

230 candidates to 148 candidates (64.3%)

Pruning

5 alts after pruning (2 fresh and 3 done)

	Pruned	Kept	Total
New	230	0	230
Fresh	0	2	2
Picked	0	1	1
Done	0	2	2
Total	230	5	235

Merged error: 2.7b

Counts

235 → 5

regimes75.0ms

Accuracy

0% (0.1b remaining)

Error of 2.1b against oracle of 2.0b and baseline of 2.1b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	20	16
1	20	16

end0.0ms

sample1.4s

Algorithm

intervals

Results

864.0ms	11882×	body	80	valid
200.0ms	4295×	body	80	nan