Details

Time bar (total: 5.2s)

sample52.0ms

Algorithm
intervals
Results
29.0ms387×body80valid
6.0ms148×body80nan

simplify106.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 2 (4.0ms)

IterNodesCost
0247
1487
2966
32566
48916
539636
650026

prune5.0ms

Filtered
1 candidates to 1 candidates (100.0%)
Pruning

1 alts after pruning (1 fresh and 0 done)

PrunedKeptTotal
New101
Fresh011
Picked000
Done000
Total112

Merged error: 2.7b

Counts
2 → 1

localize10.0ms

Local error

Found 4 expressions with local error:

0.0b
(+ (+ 1.0 (* 10.0 k)) (* k k))
0.0b
(+ 1.0 (* 10.0 k))
0.0b
(* a (pow k m))
2.7b
(/ (* 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:
5.0ms
(+ (+ 1.0 (* 10.0 k)) (* k k))
3.0ms
(+ 1.0 (* 10.0 k))
5.0ms
(* a (pow k m))
8.0ms
(/ (* a (pow k m)) (+ (+ 1.0 (* 10.0 k)) (* k k)))

series227.0ms

Counts
4 → 12
Calls
4 calls:
18.0ms
(+ (+ 1.0 (* 10.0 k)) (* k k))
36.0ms
(+ 1.0 (* 10.0 k))
60.0ms
(* a (pow k m))
113.0ms
(/ (* 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

prune186.0ms

Filtered
86 candidates to 63 candidates (73.3%)
Pruning

5 alts after pruning (4 fresh and 1 done)

PrunedKeptTotal
New82486
Fresh000
Picked011
Done000
Total82587

Merged error: 2.7b

Counts
87 → 5

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b
(/ (* a (pow k m)) (sqrt (+ (+ 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))))
15.9b
(sqrt (+ (+ 1.0 (* 10.0 k)) (* k k)))
15.9b
(sqrt (+ (+ 1.0 (* 10.0 k)) (* k k)))

rewrite47.0ms

Algorithm
rewrite-expression-head
Rules
120×times-frac
72×sqrt-prod
59×add-sqr-sqrt
57×add-cube-cbrt *-un-lft-identity
30×add-exp-log
22×sqrt-div
18×associate-/r/ add-cbrt-cube
13×div-exp associate-/l*
12×associate-/r*
11×flip3-+ flip-+
9×div-inv
7×cbrt-undiv
6×pow1 prod-exp
4×add-log-exp
2×pow-to-exp rem-sqrt-square frac-2neg sqrt-pow1 pow1/2 pow-exp clear-num cbrt-unprod
1×associate-/l/
Counts
4 → 172
Calls
4 calls:
10.0ms
(/ (* a (pow k m)) (sqrt (+ (+ 1.0 (* 10.0 k)) (* k k))))
16.0ms
(/ (/ (* a (pow k m)) (sqrt (+ (+ 1.0 (* 10.0 k)) (* k k)))) (sqrt (+ (+ 1.0 (* 10.0 k)) (* k k))))
4.0ms
(sqrt (+ (+ 1.0 (* 10.0 k)) (* k k)))
4.0ms
(sqrt (+ (+ 1.0 (* 10.0 k)) (* k k)))

series372.0ms

Counts
4 → 12
Calls
4 calls:
160.0ms
(/ (* a (pow k m)) (sqrt (+ (+ 1.0 (* 10.0 k)) (* k k))))
113.0ms
(/ (/ (* a (pow k m)) (sqrt (+ (+ 1.0 (* 10.0 k)) (* k k)))) (sqrt (+ (+ 1.0 (* 10.0 k)) (* k k))))
52.0ms
(sqrt (+ (+ 1.0 (* 10.0 k)) (* k k)))
47.0ms
(sqrt (+ (+ 1.0 (* 10.0 k)) (* k k)))

simplify91.0ms

Algorithm
egg-herbie
Counts
184 → 184
Iterations

Useful iterations: 1 (18.0ms)

IterNodesCost
07563435
132823085
250013085

prune381.0ms

Filtered
184 candidates to 114 candidates (62.0%)
Pruning

6 alts after pruning (4 fresh and 2 done)

PrunedKeptTotal
New1831184
Fresh033
Picked011
Done011
Total1836189

Merged error: 2.7b

Counts
189 → 6

localize14.0ms

Local error

Found 4 expressions with local error:

2.7b
(/ (* a (pow k m)) (* (* (cbrt (+ (+ 1.0 (* 10.0 k)) (* k k))) (cbrt (+ (+ 1.0 (* 10.0 k)) (* k k)))) (cbrt (+ (+ 1.0 (* 10.0 k)) (* k k)))))
16.4b
(cbrt (+ (+ 1.0 (* 10.0 k)) (* k k)))
16.4b
(cbrt (+ (+ 1.0 (* 10.0 k)) (* k k)))
16.4b
(cbrt (+ (+ 1.0 (* 10.0 k)) (* k k)))

rewrite45.0ms

Algorithm
rewrite-expression-head
Rules
60×cbrt-div
46×add-exp-log
30×flip3-+ flip-+
28×frac-times
26×associate-/r/
21×prod-exp
17×add-cbrt-cube
14×associate-*l/
12×div-exp
9×cbrt-prod cbrt-unprod
8×associate-*r/
7×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
6×cbrt-undiv
4×pow1 add-log-exp
3×pow-to-exp pow1/3 pow-exp
1×frac-2neg times-frac clear-num associate-/r* div-inv associate-/l*
Counts
4 → 96
Calls
4 calls:
24.0ms
(/ (* a (pow k m)) (* (* (cbrt (+ (+ 1.0 (* 10.0 k)) (* k k))) (cbrt (+ (+ 1.0 (* 10.0 k)) (* k k)))) (cbrt (+ (+ 1.0 (* 10.0 k)) (* k k)))))
8.0ms
(cbrt (+ (+ 1.0 (* 10.0 k)) (* k k)))
4.0ms
(cbrt (+ (+ 1.0 (* 10.0 k)) (* k k)))
4.0ms
(cbrt (+ (+ 1.0 (* 10.0 k)) (* k k)))

series620.0ms

Counts
4 → 12
Calls
4 calls:
113.0ms
(/ (* a (pow k m)) (* (* (cbrt (+ (+ 1.0 (* 10.0 k)) (* k k))) (cbrt (+ (+ 1.0 (* 10.0 k)) (* k k)))) (cbrt (+ (+ 1.0 (* 10.0 k)) (* k k)))))
293.0ms
(cbrt (+ (+ 1.0 (* 10.0 k)) (* k k)))
107.0ms
(cbrt (+ (+ 1.0 (* 10.0 k)) (* k k)))
107.0ms
(cbrt (+ (+ 1.0 (* 10.0 k)) (* k k)))

simplify73.0ms

Algorithm
egg-herbie
Counts
108 → 108
Iterations

Useful iterations: 2 (56.0ms)

IterNodesCost
07212092
128691692
250011608

prune305.0ms

Filtered
108 candidates to 77 candidates (71.3%)
Pruning

6 alts after pruning (3 fresh and 3 done)

PrunedKeptTotal
New1080108
Fresh033
Picked011
Done022
Total1086114

Merged error: 2.7b

Counts
114 → 6

localize16.0ms

Local error

Found 4 expressions with local error:

0.0b
(/ (/ (* a (pow k m)) (sqrt (+ (+ 1.0 (* 10.0 k)) (* k k)))) (cbrt (pow (sqrt (+ (+ 1.0 (* 10.0 k)) (* k k))) 3)))
15.9b
(sqrt (+ (+ 1.0 (* 10.0 k)) (* k k)))
15.9b
(sqrt (+ (+ 1.0 (* 10.0 k)) (* k k)))
20.1b
(cbrt (pow (sqrt (+ (+ 1.0 (* 10.0 k)) (* k k))) 3))

rewrite64.0ms

Algorithm
rewrite-expression-head
Rules
384×times-frac
252×cbrt-prod
157×add-sqr-sqrt
156×sqrt-prod
155×add-cube-cbrt *-un-lft-identity
84×unpow-prod-down cube-prod
52×sqrt-div
46×associate-/r/
26×flip3-+ flip-+
23×div-inv
21×associate-/r*
20×add-exp-log
14×cube-mult unpow3 sqr-pow
12×associate-/l*
10×add-cbrt-cube
9×div-exp
6×pow1
5×cbrt-undiv
4×cube-div cbrt-div add-log-exp
3×prod-exp
2×rem-sqrt-square sqrt-pow1 pow1/2
1×pow-to-exp frac-2neg pow1/3 pow-exp clear-num rem-cbrt-cube cbrt-unprod associate-/l/
Counts
4 → 365
Calls
4 calls:
26.0ms
(/ (/ (* a (pow k m)) (sqrt (+ (+ 1.0 (* 10.0 k)) (* k k)))) (cbrt (pow (sqrt (+ (+ 1.0 (* 10.0 k)) (* k k))) 3)))
4.0ms
(sqrt (+ (+ 1.0 (* 10.0 k)) (* k k)))
4.0ms
(sqrt (+ (+ 1.0 (* 10.0 k)) (* k k)))
6.0ms
(cbrt (pow (sqrt (+ (+ 1.0 (* 10.0 k)) (* k k))) 3))

series256.0ms

Counts
4 → 12
Calls
4 calls:
111.0ms
(/ (/ (* a (pow k m)) (sqrt (+ (+ 1.0 (* 10.0 k)) (* k k)))) (cbrt (pow (sqrt (+ (+ 1.0 (* 10.0 k)) (* k k))) 3)))
48.0ms
(sqrt (+ (+ 1.0 (* 10.0 k)) (* k k)))
45.0ms
(sqrt (+ (+ 1.0 (* 10.0 k)) (* k k)))
52.0ms
(cbrt (pow (sqrt (+ (+ 1.0 (* 10.0 k)) (* k k))) 3))

simplify170.0ms

Algorithm
egg-herbie
Counts
377 → 377
Iterations

Useful iterations: 1 (25.0ms)

IterNodesCost
011649157
149677724
250027724

prune530.0ms

Filtered
377 candidates to 143 candidates (37.9%)
Pruning

6 alts after pruning (2 fresh and 4 done)

PrunedKeptTotal
New3770377
Fresh022
Picked011
Done033
Total3776383

Merged error: 2.7b

Counts
383 → 6

regimes107.0ms

Accuracy

0% (0.0b remaining)

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

bsearch0.0ms

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0167
1167

end0.0ms

sample1.4s

Algorithm
intervals
Results
832.0ms11995×body80valid
189.0ms4174×body80nan

Profiling

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