Details

Time bar (total: 18.6s)

sample34.0ms

Algorithm
intervals
Results
14.0ms367×body80valid
5.0ms141×body80nan

simplify1.6s

Counts
1 → 1
Iterations

Useful iterations: 2 (6.0ms)

IterNodesCost
01215
12415
24713
39313
423213
570213
6270013
done500113

prune8.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 1.5b

localize9.0ms

Local error

Found 3 expressions with local error:

0.0b
(* k (+ 10.0 k))
0.2b
(* (/ a (+ (* k (+ 10.0 k)) 1.0)) (pow k m))
3.3b
(/ a (+ (* k (+ 10.0 k)) 1.0))

rewrite51.0ms

Algorithm
rewrite-expression-head
Rules
37×add-sqr-sqrt
24×*-un-lft-identity
22×add-cube-cbrt
21×times-frac
20×add-exp-log
18×associate-*l*
12×add-cbrt-cube
11×associate-*r*
7×prod-exp unswap-sqr
5×pow1 unpow-prod-down
4×div-exp associate-/r/
3×flip3-+ associate-/r* cbrt-unprod flip-+ associate-/l* add-log-exp sqr-pow
2×cbrt-undiv pow-to-exp associate-*r/ pow-exp *-commutative div-inv
1×distribute-rgt-in frac-2neg distribute-lft-in pow-prod-down associate-*l/ clear-num distribute-lft-out
Counts
3 → 97
Calls
3 calls:
10.0ms
(* k (+ 10.0 k))
28.0ms
(* (/ a (+ (* k (+ 10.0 k)) 1.0)) (pow k m))
10.0ms
(/ a (+ (* k (+ 10.0 k)) 1.0))

series225.0ms

Counts
3 → 9
Calls
3 calls:
45.0ms
(* k (+ 10.0 k))
114.0ms
(* (/ a (+ (* k (+ 10.0 k)) 1.0)) (pow k m))
66.0ms
(/ a (+ (* k (+ 10.0 k)) 1.0))

simplify877.0ms

Counts
106 → 106
Iterations

Useful iterations: 2 (179.0ms)

IterNodesCost
02101673
15631610
222831490
done50011490

prune455.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 1.2b

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b
(* (/ a (+ (* k (+ 10.0 k)) 1.0)) (pow k (/ m 2)))
0.0b
(* (* (/ a (+ (* k (+ 10.0 k)) 1.0)) (pow k (/ m 2))) (pow k (/ m 2)))
0.0b
(* k (+ 10.0 k))
3.3b
(/ a (+ (* k (+ 10.0 k)) 1.0))

rewrite92.0ms

Algorithm
rewrite-expression-head
Rules
77×add-exp-log
46×prod-exp
40×add-sqr-sqrt
27×*-un-lft-identity
25×add-cube-cbrt
22×add-cbrt-cube
21×times-frac
19×associate-*l*
18×associate-*r*
15×pow-to-exp pow-exp
13×div-exp
8×unpow-prod-down cbrt-unprod
7×unswap-sqr
6×pow1
4×associate-/r/ add-log-exp sqr-pow
3×cbrt-undiv flip3-+ associate-*l/ associate-/r* *-commutative flip-+ associate-/l*
2×associate-*r/ div-inv
1×distribute-rgt-in frac-2neg distribute-lft-in pow-prod-down clear-num distribute-lft-out
Counts
4 → 138
Calls
4 calls:
28.0ms
(* (/ a (+ (* k (+ 10.0 k)) 1.0)) (pow k (/ m 2)))
35.0ms
(* (* (/ a (+ (* k (+ 10.0 k)) 1.0)) (pow k (/ m 2))) (pow k (/ m 2)))
10.0ms
(* k (+ 10.0 k))
12.0ms
(/ a (+ (* k (+ 10.0 k)) 1.0))

series359.0ms

Counts
4 → 12
Calls
4 calls:
120.0ms
(* (/ a (+ (* k (+ 10.0 k)) 1.0)) (pow k (/ m 2)))
134.0ms
(* (* (/ a (+ (* k (+ 10.0 k)) 1.0)) (pow k (/ m 2))) (pow k (/ m 2)))
43.0ms
(* k (+ 10.0 k))
63.0ms
(/ a (+ (* k (+ 10.0 k)) 1.0))

simplify1.3s

Counts
150 → 150
Iterations

Useful iterations: 2 (257.0ms)

IterNodesCost
02653042
17472747
232352471
done50002471

prune362.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 1.2b

localize12.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (/ a (sqrt (+ (* k (+ 10.0 k)) 1.0))) (sqrt (+ (* k (+ 10.0 k)) 1.0)))
0.2b
(* (/ (/ a (sqrt (+ (* k (+ 10.0 k)) 1.0))) (sqrt (+ (* k (+ 10.0 k)) 1.0))) (pow k m))
14.4b
(sqrt (+ (* k (+ 10.0 k)) 1.0))
14.4b
(sqrt (+ (* k (+ 10.0 k)) 1.0))

rewrite180.0ms

Algorithm
rewrite-expression-head
Rules
552×times-frac
343×add-sqr-sqrt
285×sqrt-prod
276×add-cube-cbrt *-un-lft-identity
150×associate-*l*
34×sqrt-div
33×add-exp-log
30×associate-/r/
24×associate-/l*
21×unswap-sqr
18×add-cbrt-cube
17×flip3-+ flip-+
15×div-inv
12×div-exp
10×unpow-prod-down
9×prod-exp
8×sqr-pow
7×associate-*r*
6×pow1 cbrt-undiv associate-/r*
4×add-log-exp
3×pow-to-exp pow-exp cbrt-unprod
2×rem-sqrt-square sqrt-pow1 pow1/2
1×frac-2neg associate-*l/ clear-num *-commutative associate-/l/
Counts
4 → 420
Calls
4 calls:
31.0ms
(/ (/ a (sqrt (+ (* k (+ 10.0 k)) 1.0))) (sqrt (+ (* k (+ 10.0 k)) 1.0)))
99.0ms
(* (/ (/ a (sqrt (+ (* k (+ 10.0 k)) 1.0))) (sqrt (+ (* k (+ 10.0 k)) 1.0))) (pow k m))
10.0ms
(sqrt (+ (* k (+ 10.0 k)) 1.0))
8.0ms
(sqrt (+ (* k (+ 10.0 k)) 1.0))

series277.0ms

Counts
4 → 12
Calls
4 calls:
66.0ms
(/ (/ a (sqrt (+ (* k (+ 10.0 k)) 1.0))) (sqrt (+ (* k (+ 10.0 k)) 1.0)))
113.0ms
(* (/ (/ a (sqrt (+ (* k (+ 10.0 k)) 1.0))) (sqrt (+ (* k (+ 10.0 k)) 1.0))) (pow k m))
46.0ms
(sqrt (+ (* k (+ 10.0 k)) 1.0))
52.0ms
(sqrt (+ (* k (+ 10.0 k)) 1.0))

simplify2.3s

Counts
432 → 432
Iterations

Useful iterations: 2 (419.0ms)

IterNodesCost
047713990
1122812445
2468711309
done500011309

prune1.1s

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 1.2b

localize14.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (/ (/ (/ a (sqrt (sqrt (+ (* k (+ 10.0 k)) 1.0)))) (sqrt (+ (* k (+ 10.0 k)) 1.0))) (sqrt (sqrt (+ (* k (+ 10.0 k)) 1.0)))) (pow k m))
14.4b
(sqrt (+ (* k (+ 10.0 k)) 1.0))
14.4b
(sqrt (+ (* k (+ 10.0 k)) 1.0))
14.4b
(sqrt (+ (* k (+ 10.0 k)) 1.0))

rewrite1.0s

Algorithm
rewrite-expression-head
Rules
5283×times-frac
4365×sqrt-prod
2601×add-sqr-sqrt
2251×add-cube-cbrt *-un-lft-identity
1842×associate-*l*
244×sqrt-div
128×associate-/r/
84×unswap-sqr
67×flip3-+ flip-+
64×div-inv
42×add-exp-log
31×unpow-prod-down
29×sqr-pow
18×div-exp add-cbrt-cube
12×prod-exp
7×pow1 associate-*r*
6×cbrt-undiv
4×pow-to-exp pow-exp cbrt-unprod add-log-exp
3×rem-sqrt-square sqrt-pow1 pow1/2
1×associate-*l/ *-commutative
Counts
4 → 2003
Calls
4 calls:
731.0ms
(* (/ (/ (/ a (sqrt (sqrt (+ (* k (+ 10.0 k)) 1.0)))) (sqrt (+ (* k (+ 10.0 k)) 1.0))) (sqrt (sqrt (+ (* k (+ 10.0 k)) 1.0)))) (pow k m))
10.0ms
(sqrt (+ (* k (+ 10.0 k)) 1.0))
8.0ms
(sqrt (+ (* k (+ 10.0 k)) 1.0))
8.0ms
(sqrt (+ (* k (+ 10.0 k)) 1.0))

series264.0ms

Counts
4 → 12
Calls
4 calls:
115.0ms
(* (/ (/ (/ a (sqrt (sqrt (+ (* k (+ 10.0 k)) 1.0)))) (sqrt (+ (* k (+ 10.0 k)) 1.0))) (sqrt (sqrt (+ (* k (+ 10.0 k)) 1.0)))) (pow k m))
50.0ms
(sqrt (+ (* k (+ 10.0 k)) 1.0))
46.0ms
(sqrt (+ (* k (+ 10.0 k)) 1.0))
53.0ms
(sqrt (+ (* k (+ 10.0 k)) 1.0))

simplify882.0ms

Counts
2015 → 2015
Iterations

Useful iterations: done (781.0ms)

IterNodesCost
0114876449
1293872501
done500171250

prune6.2s

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 1.2b

regimes80.0ms

Accuracy

0% (0.1b remaining)

Error of 2.0b against oracle of 1.9b and baseline of 2.0b

bsearch0.0ms

simplify2.0ms

Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01421
11921
done1921

end0.0ms

sample967.0ms

Algorithm
intervals
Results
472.0ms11825×body80valid
140.0ms4243×body80nan