Details

Time bar (total: 4.7s)

sample56.0ms

Algorithm
intervals
Results
34.0ms372×body80valid
7.0ms103×body80nan

simplify106.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 2 (5.0ms)

IterNodesCost
0247
1487
2966
32566
48916
539636
650026

prune6.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 3.8b

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))
0.2b
(* a (pow k m))
3.7b
(/ (* a (pow k m)) (+ (+ 1.0 (* 10.0 k)) (* k k)))

rewrite35.0ms

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:
5.0ms
(+ 1.0 (* 10.0 k))
9.0ms
(+ (+ 1.0 (* 10.0 k)) (* k k))
5.0ms
(* a (pow k m))
13.0ms
(/ (* a (pow k m)) (+ (+ 1.0 (* 10.0 k)) (* k k)))

series225.0ms

Counts
4 → 12
Calls
4 calls:
31.0ms
(+ 1.0 (* 10.0 k))
23.0ms
(+ (+ 1.0 (* 10.0 k)) (* k k))
56.0ms
(* a (pow k m))
114.0ms
(/ (* a (pow k m)) (+ (+ 1.0 (* 10.0 k)) (* k k)))

simplify57.0ms

Algorithm
egg-herbie
Counts
86 → 86
Iterations

Useful iterations: 2 (50.0ms)

IterNodesCost
0457599
12146533
25001526

prune216.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 3.7b

localize16.0ms

Local error

Found 4 expressions with local error:

0.0b
(* a (pow k (/ m 2)))
0.0b
(+ 1.0 (* 10.0 k))
0.0b
(+ (+ 1.0 (* 10.0 k)) (* k k))
3.7b
(/ (* (* a (pow k (/ m 2))) (pow k (/ m 2))) (+ (+ 1.0 (* 10.0 k)) (* k k)))

rewrite38.0ms

Algorithm
rewrite-expression-head
Rules
49×add-exp-log
24×prod-exp
15×add-cbrt-cube
14×add-sqr-sqrt
13×div-exp
11×add-log-exp
9×add-cube-cbrt *-un-lft-identity
8×pow-to-exp pow-exp
7×associate-*r*
4×pow1 unpow-prod-down sum-log cbrt-unprod
3×cbrt-undiv flip3-+ times-frac associate-*l* associate-/r* flip-+ unswap-sqr
2×+-commutative associate-/r/ sqr-pow
1×associate-+l+ frac-2neg clear-num *-commutative div-inv associate-/l*
Counts
4 → 84
Calls
4 calls:
5.0ms
(* a (pow k (/ m 2)))
2.0ms
(+ 1.0 (* 10.0 k))
9.0ms
(+ (+ 1.0 (* 10.0 k)) (* k k))
20.0ms
(/ (* (* a (pow k (/ m 2))) (pow k (/ m 2))) (+ (+ 1.0 (* 10.0 k)) (* k k)))

series254.0ms

Counts
4 → 12
Calls
4 calls:
67.0ms
(* a (pow k (/ m 2)))
31.0ms
(+ 1.0 (* 10.0 k))
17.0ms
(+ (+ 1.0 (* 10.0 k)) (* k k))
138.0ms
(/ (* (* a (pow k (/ m 2))) (pow k (/ m 2))) (+ (+ 1.0 (* 10.0 k)) (* k k)))

simplify68.0ms

Algorithm
egg-herbie
Counts
96 → 96
Iterations

Useful iterations: 2 (59.0ms)

IterNodesCost
0553886
12696760
25001731

prune243.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 3.7b

localize15.0ms

Local error

Found 4 expressions with local error:

0.0b
(* (sqrt (+ (+ 1.0 (* 10.0 k)) (* k k))) (sqrt (+ (+ 1.0 (* 10.0 k)) (* k k))))
3.7b
(/ (* (* a (pow k (/ m 2))) (pow k (/ m 2))) (* (sqrt (+ (+ 1.0 (* 10.0 k)) (* k k))) (sqrt (+ (+ 1.0 (* 10.0 k)) (* k k)))))
12.4b
(sqrt (+ (+ 1.0 (* 10.0 k)) (* k k)))
12.4b
(sqrt (+ (+ 1.0 (* 10.0 k)) (* k k)))

rewrite287.0ms

Algorithm
rewrite-expression-head
Rules
99×add-exp-log
56×prod-exp
28×add-sqr-sqrt sqrt-div
27×add-cbrt-cube
26×div-exp
24×sqrt-prod
21×pow1
14×pow-to-exp add-cube-cbrt *-un-lft-identity flip3-+ pow-exp flip-+
10×sqrt-pow1 pow1/2 cbrt-unprod
8×frac-times swap-sqr associate-/r/
6×cbrt-undiv associate-*r* associate-*l*
5×pow-prod-up
4×associate-*r/ associate-*l/ add-log-exp unswap-sqr
3×pow-prod-down pow-sqr
2×rem-sqrt-square
1×pow2 frac-2neg times-frac pow-plus sqrt-unprod clear-num associate-/r* rem-square-sqrt *-commutative div-inv associate-/l*
Counts
4 → 140
Calls
4 calls:
46.0ms
(* (sqrt (+ (+ 1.0 (* 10.0 k)) (* k k))) (sqrt (+ (+ 1.0 (* 10.0 k)) (* k k))))
215.0ms
(/ (* (* a (pow k (/ m 2))) (pow k (/ m 2))) (* (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)))

series247.0ms

Counts
4 → 12
Calls
4 calls:
18.0ms
(* (sqrt (+ (+ 1.0 (* 10.0 k)) (* k k))) (sqrt (+ (+ 1.0 (* 10.0 k)) (* k k))))
133.0ms
(/ (* (* a (pow k (/ m 2))) (pow k (/ m 2))) (* (sqrt (+ (+ 1.0 (* 10.0 k)) (* k k))) (sqrt (+ (+ 1.0 (* 10.0 k)) (* k k)))))
46.0ms
(sqrt (+ (+ 1.0 (* 10.0 k)) (* k k)))
50.0ms
(sqrt (+ (+ 1.0 (* 10.0 k)) (* k k)))

simplify91.0ms

Algorithm
egg-herbie
Counts
152 → 152
Iterations

Useful iterations: 2 (73.0ms)

IterNodesCost
06381991
132041645
250011504

prune337.0ms

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 3.7b

localize19.0ms

Local error

Found 4 expressions with local error:

12.4b
(sqrt (+ (+ 1.0 (* 10.0 k)) (* k k)))
12.4b
(sqrt (+ (+ 1.0 (* 10.0 k)) (* k k)))
12.4b
(sqrt (+ (+ 1.0 (* 10.0 k)) (* k k)))
12.4b
(sqrt (+ (+ 1.0 (* 10.0 k)) (* k k)))

rewrite44.0ms

Algorithm
rewrite-expression-head
Rules
12×add-sqr-sqrt sqrt-prod
8×pow1 add-cube-cbrt *-un-lft-identity sqrt-div
4×add-exp-log rem-sqrt-square sqrt-pow1 flip3-+ pow1/2 add-cbrt-cube flip-+ add-log-exp
Counts
4 → 60
Calls
4 calls:
10.0ms
(sqrt (+ (+ 1.0 (* 10.0 k)) (* k k)))
12.0ms
(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)))

series196.0ms

Counts
4 → 12
Calls
4 calls:
46.0ms
(sqrt (+ (+ 1.0 (* 10.0 k)) (* k k)))
52.0ms
(sqrt (+ (+ 1.0 (* 10.0 k)) (* k k)))
51.0ms
(sqrt (+ (+ 1.0 (* 10.0 k)) (* k k)))
47.0ms
(sqrt (+ (+ 1.0 (* 10.0 k)) (* k k)))

simplify61.0ms

Algorithm
egg-herbie
Counts
72 → 72
Iterations

Useful iterations: 3 (54.0ms)

IterNodesCost
0145576
1515560
21983544
35002540

prune333.0ms

Pruning

2 alts after pruning (0 fresh and 2 done)

Merged error: 3.7b

regimes49.0ms

Accuracy

0% (0.0b remaining)

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

bsearch0.0ms

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
02218
12218

end0.0ms

sample1.7s

Algorithm
intervals
Results
1.0s11987×body80valid
280.0ms4270×body80nan