Details

Time bar (total: 3.8s)

sample35.0ms

Algorithm
intervals
Results
15.0ms362×body80valid
4.0ms136×body80nan

simplify102.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 2 (4.0ms)

IterNodesCost
0247
1487
2966
32566
48916
539636
650026

prune6.0ms

Filtered
1 candidates to 1 candidates (100.0%)
Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 1.7b

localize10.0ms

Local error

Found 3 expressions with local error:

0.0b
(+ 1.0 (* 10.0 k))
0.0b
(+ (+ 1.0 (* 10.0 k)) (* k k))
1.7b
(/ (* a (pow k m)) (+ (+ 1.0 (* 10.0 k)) (* k k)))

rewrite27.0ms

Algorithm
rewrite-expression-head
Rules
13×add-exp-log
10×add-log-exp
8×add-cbrt-cube
5×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
4×div-exp sum-log
3×pow1 flip3-+ times-frac prod-exp associate-/r* flip-+
2×cbrt-undiv +-commutative associate-/r/
1×pow-to-exp associate-+l+ frac-2neg pow-exp clear-num cbrt-unprod div-inv associate-/l*
Counts
3 → 49
Calls
3 calls:
2.0ms
(+ 1.0 (* 10.0 k))
9.0ms
(+ (+ 1.0 (* 10.0 k)) (* k k))
14.0ms
(/ (* a (pow k m)) (+ (+ 1.0 (* 10.0 k)) (* k k)))

series175.0ms

Counts
3 → 9
Calls
3 calls:
33.0ms
(+ 1.0 (* 10.0 k))
19.0ms
(+ (+ 1.0 (* 10.0 k)) (* k k))
123.0ms
(/ (* a (pow k m)) (+ (+ 1.0 (* 10.0 k)) (* k k)))

simplify50.0ms

Algorithm
egg-herbie
Counts
58 → 58
Iterations

Useful iterations: 2 (43.0ms)

IterNodesCost
0404484
11787427
25001418

prune141.0ms

Filtered
58 candidates to 41 candidates (70.7%)
Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 1.7b

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b
(+ (+ 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)))

rewrite75.0ms

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))
36.0ms
(/ (/ (* 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)))
13.0ms
(sqrt (+ (+ 1.0 (* 10.0 k)) (* k k)))

series237.0ms

Counts
4 → 12
Calls
4 calls:
19.0ms
(+ (+ 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))))
51.0ms
(sqrt (+ (+ 1.0 (* 10.0 k)) (* k k)))
51.0ms
(sqrt (+ (+ 1.0 (* 10.0 k)) (* k k)))

simplify87.0ms

Algorithm
egg-herbie
Counts
166 → 166
Iterations

Useful iterations: 2 (61.0ms)

IterNodesCost
07283104
132212772
250012769

prune423.0ms

Filtered
166 candidates to 103 candidates (62.0%)
Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 1.7b

localize10.0ms

Local error

Found 3 expressions with local error:

0.0b
(* k (+ 10.0 k))
0.1b
(/ 1 (/ (+ 1.0 (* k (+ 10.0 k))) (* a (pow k m))))
1.7b
(/ (+ 1.0 (* k (+ 10.0 k))) (* a (pow k m)))

rewrite34.0ms

Algorithm
rewrite-expression-head
Rules
53×add-exp-log
36×times-frac
26×div-exp
25×add-sqr-sqrt *-un-lft-identity
23×add-cube-cbrt
19×add-cbrt-cube
13×prod-exp
8×associate-/r*
7×cbrt-undiv
6×pow1 div-inv associate-/l*
5×rec-exp 1-exp
4×pow-to-exp associate-*r* pow-exp
3×associate-*l* cbrt-unprod add-log-exp
2×frac-2neg flip3-+ associate-*r/ clear-num flip-+ associate-/l/
1×distribute-rgt-in pow-flip distribute-lft-in pow-prod-down associate-/r/ *-commutative distribute-lft-out inv-pow unswap-sqr
Counts
3 → 110
Calls
3 calls:
10.0ms
(* k (+ 10.0 k))
10.0ms
(/ 1 (/ (+ 1.0 (* k (+ 10.0 k))) (* a (pow k m))))
10.0ms
(/ (+ 1.0 (* k (+ 10.0 k))) (* a (pow k m)))

series259.0ms

Counts
3 → 9
Calls
3 calls:
46.0ms
(* k (+ 10.0 k))
106.0ms
(/ 1 (/ (+ 1.0 (* k (+ 10.0 k))) (* a (pow k m))))
107.0ms
(/ (+ 1.0 (* k (+ 10.0 k))) (* a (pow k m)))

simplify78.0ms

Algorithm
egg-herbie
Counts
119 → 119
Iterations

Useful iterations: 2 (67.0ms)

IterNodesCost
06231117
13103987
25001947

prune225.0ms

Filtered
119 candidates to 65 candidates (54.6%)
Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 1.7b

localize24.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ 2 (* (fabs (cbrt (+ (+ 1.0 (* 10.0 k)) (* k k)))) 2))
14.9b
(sqrt (+ (+ 1.0 (* 10.0 k)) (* k k)))
15.5b
(cbrt (+ (+ 1.0 (* 10.0 k)) (* k k)))
15.5b
(cbrt (+ (+ 1.0 (* 10.0 k)) (* k k)))

rewrite26.0ms

Algorithm
rewrite-expression-head
Rules
10×add-sqr-sqrt
9×add-exp-log add-cube-cbrt *-un-lft-identity add-cbrt-cube
6×cbrt-prod
5×pow1
4×cbrt-div add-log-exp
3×flip3-+ times-frac sqrt-prod flip-+ associate-/l*
2×cbrt-undiv pow1/3 sqrt-div div-exp
1×rem-sqrt-square frac-2neg sqrt-pow1 pow1/2 prod-exp clear-num associate-/r* cbrt-unprod div-inv
Counts
4 → 62
Calls
4 calls:
3.0ms
(/ 2 (* (fabs (cbrt (+ (+ 1.0 (* 10.0 k)) (* k k)))) 2))
10.0ms
(sqrt (+ (+ 1.0 (* 10.0 k)) (* k k)))
6.0ms
(cbrt (+ (+ 1.0 (* 10.0 k)) (* k k)))
6.0ms
(cbrt (+ (+ 1.0 (* 10.0 k)) (* k k)))

series292.0ms

Counts
4 → 12
Calls
4 calls:
21.0ms
(/ 2 (* (fabs (cbrt (+ (+ 1.0 (* 10.0 k)) (* k k)))) 2))
49.0ms
(sqrt (+ (+ 1.0 (* 10.0 k)) (* k k)))
114.0ms
(cbrt (+ (+ 1.0 (* 10.0 k)) (* k k)))
108.0ms
(cbrt (+ (+ 1.0 (* 10.0 k)) (* k k)))

simplify41.0ms

Algorithm
egg-herbie
Counts
74 → 74
Iterations

Useful iterations: 2 (33.0ms)

IterNodesCost
0351747
11326667
25002648

prune361.0ms

Filtered
74 candidates to 64 candidates (86.5%)
Pruning

5 alts after pruning (2 fresh and 3 done)

Merged error: 1.7b

regimes76.0ms

Accuracy

0% (0.1b remaining)

Error of 2.2b against oracle of 2.1b and baseline of 2.2b

bsearch0.0ms

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01814
11814

end0.0ms

sample982.0ms

Algorithm
intervals
Results
488.0ms11793×body80valid
142.0ms4206×body80nan