Details

sample53.0ms

Algorithm

intervals

Results

31.0ms	361×	body	80	valid
7.0ms	116×	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

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 2.8b

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)))

rewrite31.0ms

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))
9.0ms	(+ (+ 1.0 (* 10.0 k)) (* k k))
13.0ms	(/ (* a (pow k m)) (+ (+ 1.0 (* 10.0 k)) (* k k)))

series228.0ms

Counts

4 → 12

Calls

4 calls:

37.0ms	(+ 1.0 (* 10.0 k))
56.0ms	(* a (pow k m))
18.0ms	(+ (+ 1.0 (* 10.0 k)) (* k k))
117.0ms	(/ (* 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

prune211.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 2.8b

localize10.0ms

Local error

Found 4 expressions with local error:

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

rewrite63.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 191

Calls

4 calls:

2.0ms	(+ 1.0 (* 10.0 k))
24.0ms	(/ (+ (+ 1.0 (* 10.0 k)) (* k k)) (pow k m))
9.0ms	(+ (+ 1.0 (* 10.0 k)) (* k k))
20.0ms	(/ a (/ (+ (+ 1.0 (* 10.0 k)) (* k k)) (pow k m)))

series234.0ms

Counts

4 → 12

Calls

4 calls:

37.0ms	(+ 1.0 (* 10.0 k))
62.0ms	(/ (+ (+ 1.0 (* 10.0 k)) (* k k)) (pow k m))
23.0ms	(+ (+ 1.0 (* 10.0 k)) (* k k))
112.0ms	(/ a (/ (+ (+ 1.0 (* 10.0 k)) (* k k)) (pow k m)))

simplify106.0ms

Algorithm

egg-herbie

Counts

203 → 203

Iterations

Useful iterations: 2 (82.0ms)

Iter	Nodes	Cost
0	884	2613
1	4188	2490
2	5001	2481

prune561.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 2.8b

localize17.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (+ 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)))))
16.8b	(sqrt (+ (+ 1.0 (* 10.0 k)) (* k k)))
16.8b	(sqrt (+ (+ 1.0 (* 10.0 k)) (* k k)))

rewrite119.0ms

Algorithm

rewrite-expression-head

Rules

116×	`add-sqr-sqrt`
92×	`times-frac`
52×	`sqrt-prod`
48×	`associate-r`
46×	`add-cube-cbrt` `*-un-lft-identity`
28×	`add-exp-log`
24×	`unpow-prod-down` `associate-l`
21×	`unswap-sqr`
16×	`add-cbrt-cube`
12×	`sqr-pow`
10×	`div-exp`
9×	`add-log-exp`
8×	`pow1` `sqrt-div` `prod-exp`
5×	`flip3-+` `flip-+`
4×	`cbrt-undiv` `associate-/r/` `cbrt-unprod`
3×	`sum-log`
2×	`pow-to-exp` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `pow-exp` `div-inv`
1×	`+-commutative` `frac-times` `associate-+l+` `associate-r/` `pow-prod-down` `associate-l/` `*-commutative`

Counts

4 → 160

Calls

4 calls:

9.0ms	(+ (+ 1.0 (* 10.0 k)) (* k k))
81.0ms	(* (/ a (sqrt (+ (+ 1.0 (* 10.0 k)) (* k k)))) (/ (pow k m) (sqrt (+ (+ 1.0 (* 10.0 k)) (* k k)))))
11.0ms	(sqrt (+ (+ 1.0 (* 10.0 k)) (* k k)))
10.0ms	(sqrt (+ (+ 1.0 (* 10.0 k)) (* k k)))

series237.0ms

Counts

4 → 12

Calls

4 calls:

18.0ms	(+ (+ 1.0 (* 10.0 k)) (* k k))
121.0ms	(* (/ a (sqrt (+ (+ 1.0 (* 10.0 k)) (* k k)))) (/ (pow k m) (sqrt (+ (+ 1.0 (* 10.0 k)) (* k k)))))
46.0ms	(sqrt (+ (+ 1.0 (* 10.0 k)) (* k k)))
52.0ms	(sqrt (+ (+ 1.0 (* 10.0 k)) (* k k)))

simplify92.0ms

Algorithm

egg-herbie

Counts

172 → 172

Iterations

Useful iterations: 2 (70.0ms)

Iter	Nodes	Cost
0	859	2730
1	3871	2549
2	5001	2435

prune465.0ms

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 2.8b

localize19.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (pow k (/ m 2)) (sqrt (cbrt (+ (+ 1.0 (* 10.0 k)) (* k k)))))
16.8b	(sqrt (+ (+ 1.0 (* 10.0 k)) (* k k)))
17.4b	(cbrt (+ (+ 1.0 (* 10.0 k)) (* k k)))
17.4b	(cbrt (+ (+ 1.0 (* 10.0 k)) (* k k)))

rewrite46.0ms

Algorithm

rewrite-expression-head

Rules

63×	`times-frac`
52×	`add-sqr-sqrt`
51×	`add-cube-cbrt` `*-un-lft-identity` `sqrt-prod`
30×	`cbrt-prod` `unpow-prod-down`
10×	`sqr-pow`
9×	`add-exp-log` `associate-/r*`
7×	`associate-/l*`
6×	`cbrt-div` `add-cbrt-cube`
5×	`pow1`
4×	`flip3-+` `sqrt-div` `flip-+` `add-log-exp`
3×	`div-exp`
2×	`pow1/3` `associate-/r/`
1×	`cbrt-undiv` `pow-to-exp` `rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `pow-exp` `clear-num` `div-inv`

Counts

4 → 136

Calls

4 calls:

16.0ms	(/ (pow k (/ m 2)) (sqrt (cbrt (+ (+ 1.0 (* 10.0 k)) (* k k)))))
13.0ms	(sqrt (+ (+ 1.0 (* 10.0 k)) (* k k)))
6.0ms	(cbrt (+ (+ 1.0 (* 10.0 k)) (* k k)))
5.0ms	(cbrt (+ (+ 1.0 (* 10.0 k)) (* k k)))

series429.0ms

Counts

4 → 12

Calls

4 calls:

159.0ms	(/ (pow k (/ m 2)) (sqrt (cbrt (+ (+ 1.0 (* 10.0 k)) (* k k)))))
53.0ms	(sqrt (+ (+ 1.0 (* 10.0 k)) (* k k)))
108.0ms	(cbrt (+ (+ 1.0 (* 10.0 k)) (* k k)))
109.0ms	(cbrt (+ (+ 1.0 (* 10.0 k)) (* k k)))

simplify64.0ms

Algorithm

egg-herbie

Counts

148 → 148

Iterations

Useful iterations: 2 (44.0ms)

Iter	Nodes	Cost
0	578	2279
1	2046	2148
2	5001	2112

prune672.0ms

Pruning

5 alts after pruning (2 fresh and 3 done)

Merged error: 2.8b

regimes74.0ms

Accuracy

0% (0.1b remaining)

Error of 2.3b against oracle of 2.2b and baseline of 2.3b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	15	7
1	15	7

end0.0ms

sample1.5s

Algorithm

intervals

Results

920.0ms	11841×	body	80	valid
241.0ms	4270×	body	80	nan