Details

Time bar (total: 4.3s)

sample50.0ms

Algorithm
intervals
Results
27.0ms366×body80valid
7.0ms133×body80nan

simplify106.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 2 (5.0ms)

IterNodesCost
0247
1487
2966
32566
48916
539636
650026

prune7.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 1.8b

localize14.0ms

Local error

Found 3 expressions with local error:

0.0b
(* a (pow k m))
0.0b
(+ (+ 1.0 (* 10.0 k)) (* k k))
1.8b
(/ (* a (pow k m)) (+ (+ 1.0 (* 10.0 k)) (* k k)))

rewrite29.0ms

Algorithm
rewrite-expression-head
Rules
18×add-exp-log
13×add-sqr-sqrt
10×add-cbrt-cube
8×add-cube-cbrt *-un-lft-identity add-log-exp
7×associate-*r*
6×prod-exp
4×unpow-prod-down div-exp
3×pow1 times-frac associate-*l* associate-/r* sum-log unswap-sqr
2×cbrt-undiv pow-to-exp flip3-+ pow-exp associate-/r/ cbrt-unprod flip-+ sqr-pow
1×+-commutative associate-+l+ frac-2neg clear-num *-commutative div-inv associate-/l*
Counts
3 → 63
Calls
3 calls:
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)))

series198.0ms

Counts
3 → 9
Calls
3 calls:
63.0ms
(* 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)))

simplify55.0ms

Algorithm
egg-herbie
Counts
72 → 72
Iterations

Useful iterations: 2 (48.0ms)

IterNodesCost
0405548
11965482
25001475

prune198.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 1.8b

localize9.0ms

Local error

Found 3 expressions with local error:

0.0b
(* a (pow k m))
0.0b
(* k (+ 10.0 k))
1.8b
(/ (* a (pow k m)) (+ 1.0 (* k (+ 10.0 k))))

rewrite22.0ms

Algorithm
rewrite-expression-head
Rules
20×add-exp-log
17×add-sqr-sqrt
12×*-un-lft-identity add-cbrt-cube
11×associate-*r*
10×add-cube-cbrt
7×prod-exp
6×associate-*l*
5×pow1
4×unpow-prod-down div-exp unswap-sqr
3×times-frac associate-/r* cbrt-unprod add-log-exp
2×cbrt-undiv pow-to-exp flip3-+ associate-*r/ pow-exp associate-/r/ *-commutative flip-+ sqr-pow
1×distribute-rgt-in frac-2neg distribute-lft-in pow-prod-down clear-num div-inv distribute-lft-out associate-/l*
Counts
3 → 73
Calls
3 calls:
5.0ms
(* a (pow k m))
9.0ms
(* k (+ 10.0 k))
6.0ms
(/ (* a (pow k m)) (+ 1.0 (* k (+ 10.0 k))))

series227.0ms

Counts
3 → 9
Calls
3 calls:
63.0ms
(* a (pow k m))
42.0ms
(* k (+ 10.0 k))
123.0ms
(/ (* a (pow k m)) (+ 1.0 (* k (+ 10.0 k))))

simplify60.0ms

Algorithm
egg-herbie
Counts
82 → 82
Iterations

Useful iterations: 2 (54.0ms)

IterNodesCost
0446493
12226441
25001440

prune206.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 1.8b

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b
(* k (+ 10.0 k))
0.0b
(* a (pow k (/ m 2)))
0.0b
(* (* a (pow k (/ m 2))) (pow k (/ m 2)))
1.8b
(/ (* (* a (pow k (/ m 2))) (pow k (/ m 2))) (+ 1.0 (* k (+ 10.0 k))))

rewrite41.0ms

Algorithm
rewrite-expression-head
Rules
77×add-exp-log
46×prod-exp
22×add-cbrt-cube
20×add-sqr-sqrt
18×associate-*r*
15×pow-to-exp *-un-lft-identity pow-exp
13×add-cube-cbrt div-exp
8×cbrt-unprod
7×unpow-prod-down associate-*l*
6×pow1
4×add-log-exp unswap-sqr
3×cbrt-undiv times-frac associate-/r* *-commutative sqr-pow
2×flip3-+ associate-*r/ associate-/r/ flip-+
1×distribute-rgt-in frac-2neg distribute-lft-in pow-prod-down clear-num div-inv distribute-lft-out associate-/l*
Counts
4 → 113
Calls
4 calls:
9.0ms
(* k (+ 10.0 k))
5.0ms
(* a (pow k (/ m 2)))
11.0ms
(* (* a (pow k (/ m 2))) (pow k (/ m 2)))
13.0ms
(/ (* (* a (pow k (/ m 2))) (pow k (/ m 2))) (+ 1.0 (* k (+ 10.0 k))))

series334.0ms

Counts
4 → 12
Calls
4 calls:
48.0ms
(* k (+ 10.0 k))
62.0ms
(* a (pow k (/ m 2)))
80.0ms
(* (* a (pow k (/ m 2))) (pow k (/ m 2)))
143.0ms
(/ (* (* a (pow k (/ m 2))) (pow k (/ m 2))) (+ 1.0 (* k (+ 10.0 k))))

simplify84.0ms

Algorithm
egg-herbie
Counts
125 → 125
Iterations

Useful iterations: 2 (73.0ms)

IterNodesCost
05781023
13128849
25003841

prune275.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 1.8b

localize17.0ms

Local error

Found 4 expressions with local error:

0.0b
(+ (+ 1.0 (* 10.0 k)) (* k k))
0.1b
(/ (/ (* a (pow k m)) (sqrt (+ (+ 1.0 (* 10.0 k)) (* k k)))) (sqrt (+ (+ 1.0 (* 10.0 k)) (* k k))))
13.8b
(sqrt (+ (+ 1.0 (* 10.0 k)) (* k k)))
13.8b
(sqrt (+ (+ 1.0 (* 10.0 k)) (* k k)))

rewrite69.0ms

Algorithm
rewrite-expression-head
Rules
114×times-frac
66×sqrt-prod
55×add-sqr-sqrt
53×add-cube-cbrt *-un-lft-identity
20×add-exp-log sqrt-div
16×associate-/r/
13×add-cbrt-cube
12×associate-/l*
11×flip3-+ flip-+
9×div-exp add-log-exp
8×div-inv
6×pow1 associate-/r*
5×cbrt-undiv
3×prod-exp sum-log
2×rem-sqrt-square sqrt-pow1 pow1/2
1×+-commutative pow-to-exp associate-+l+ frac-2neg pow-exp clear-num cbrt-unprod associate-/l/
Counts
4 → 154
Calls
4 calls:
9.0ms
(+ (+ 1.0 (* 10.0 k)) (* k k))
33.0ms
(/ (/ (* a (pow k m)) (sqrt (+ (+ 1.0 (* 10.0 k)) (* k k)))) (sqrt (+ (+ 1.0 (* 10.0 k)) (* k k))))
10.0ms
(sqrt (+ (+ 1.0 (* 10.0 k)) (* k k)))
10.0ms
(sqrt (+ (+ 1.0 (* 10.0 k)) (* k k)))

series239.0ms

Counts
4 → 12
Calls
4 calls:
18.0ms
(+ (+ 1.0 (* 10.0 k)) (* k k))
115.0ms
(/ (/ (* a (pow k m)) (sqrt (+ (+ 1.0 (* 10.0 k)) (* k k)))) (sqrt (+ (+ 1.0 (* 10.0 k)) (* k k))))
53.0ms
(sqrt (+ (+ 1.0 (* 10.0 k)) (* k k)))
52.0ms
(sqrt (+ (+ 1.0 (* 10.0 k)) (* k k)))

simplify84.0ms

Algorithm
egg-herbie
Counts
166 → 166
Iterations

Useful iterations: 2 (59.0ms)

IterNodesCost
07283106
132152772
250022769

prune429.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 1.8b

regimes66.0ms

Accuracy

0% (0.1b remaining)

Error of 1.9b against oracle of 1.8b and baseline of 1.9b

bsearch0.0ms

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01910
11910

end0.0ms

sample1.5s

Algorithm
intervals
Results
901.0ms11961×body80valid
239.0ms4294×body80nan