Details

Time bar (total: 15.9s)

sample87.0ms

Algorithm
intervals
Results
44.0ms382×body80valid
9.0ms131×body80nan

simplify1.4s

Counts
1 → 1
Iterations

Useful iterations: 2 (13.0ms)

IterNodesCost
01215
12415
24813
39613
425613
5140813
done500013

prune12.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 2.5b

localize26.0ms

Local error

Found 4 expressions with local error:

0.0b
(+ 1.0 (* 10.0 k))
0.0b
(* a (pow k m))
0.0b
(+ (+ 1.0 (* 10.0 k)) (* k k))
2.5b
(/ (* a (pow k m)) (+ (+ 1.0 (* 10.0 k)) (* k k)))

rewrite146.0ms

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:
6.0ms
(+ 1.0 (* 10.0 k))
16.0ms
(* a (pow k m))
46.0ms
(+ (+ 1.0 (* 10.0 k)) (* k k))
76.0ms
(/ (* a (pow k m)) (+ (+ 1.0 (* 10.0 k)) (* k k)))

series352.0ms

Counts
4 → 12
Calls
4 calls:
50.0ms
(+ 1.0 (* 10.0 k))
87.0ms
(* a (pow k m))
39.0ms
(+ (+ 1.0 (* 10.0 k)) (* k k))
176.0ms
(/ (* a (pow k m)) (+ (+ 1.0 (* 10.0 k)) (* k k)))

simplify1.2s

Counts
86 → 86
Iterations

Useful iterations: done (1.2s)

IterNodesCost
01711264
14781188
22327988
done5000984

prune324.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 2.5b

localize43.0ms

Local error

Found 4 expressions with local error:

0.6b
(cbrt k)
0.6b
(cbrt k)
0.6b
(cbrt k)
2.5b
(/ (* (* a (pow (* (cbrt k) (cbrt k)) m)) (pow (cbrt k) m)) (+ (+ 1.0 (* 10.0 k)) (* k k)))

rewrite90.0ms

Algorithm
rewrite-expression-head
Rules
58×add-exp-log
30×prod-exp
16×div-exp
13×add-cbrt-cube
11×pow-exp
9×cbrt-prod add-sqr-sqrt add-cube-cbrt *-un-lft-identity
8×pow-to-exp
4×pow1 add-log-exp
3×cbrt-undiv times-frac pow1/3 associate-/r* cbrt-unprod
2×associate-/r/
1×frac-2neg flip3-+ clear-num flip-+ div-inv associate-/l*
Counts
4 → 71
Calls
4 calls:
1.0ms
(cbrt k)
1.0ms
(cbrt k)
1.0ms
(cbrt k)
85.0ms
(/ (* (* a (pow (* (cbrt k) (cbrt k)) m)) (pow (cbrt k) m)) (+ (+ 1.0 (* 10.0 k)) (* k k)))

series1.3s

Counts
4 → 12
Calls
4 calls:
239.0ms
(cbrt k)
244.0ms
(cbrt k)
272.0ms
(cbrt k)
509.0ms
(/ (* (* a (pow (* (cbrt k) (cbrt k)) m)) (pow (cbrt k) m)) (+ (+ 1.0 (* 10.0 k)) (* k k)))

simplify1.3s

Counts
83 → 83
Iterations

Useful iterations: done (1.3s)

IterNodesCost
01761649
15221463
230131185
done50011176

prune381.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 2.5b

localize11.0ms

Local error

Found 3 expressions with local error:

0.0b
(* k (+ 10.0 k))
0.5b
(/ (pow k m) (+ 1.0 (* k (+ 10.0 k))))
1.9b
(* a (/ (pow k m) (+ 1.0 (* k (+ 10.0 k)))))

rewrite106.0ms

Algorithm
rewrite-expression-head
Rules
48×add-sqr-sqrt
45×times-frac
38×*-un-lft-identity
36×add-cube-cbrt
31×associate-*r*
22×unpow-prod-down
20×add-exp-log
12×add-cbrt-cube
8×sqr-pow
7×pow1 associate-/l*
6×div-exp associate-*l*
5×prod-exp unswap-sqr
4×associate-/r/
3×flip3-+ associate-*r/ associate-/r* cbrt-unprod flip-+ add-log-exp
2×cbrt-undiv pow-to-exp pow-prod-down pow-exp *-commutative div-inv
1×distribute-rgt-in frac-2neg distribute-lft-in clear-num distribute-lft-out
Counts
3 → 120
Calls
3 calls:
26.0ms
(* k (+ 10.0 k))
16.0ms
(/ (pow k m) (+ 1.0 (* k (+ 10.0 k))))
56.0ms
(* a (/ (pow k m) (+ 1.0 (* k (+ 10.0 k)))))

series357.0ms

Counts
3 → 9
Calls
3 calls:
59.0ms
(* k (+ 10.0 k))
108.0ms
(/ (pow k m) (+ 1.0 (* k (+ 10.0 k))))
190.0ms
(* a (/ (pow k m) (+ 1.0 (* k (+ 10.0 k)))))

simplify1.8s

Counts
129 → 129
Iterations

Useful iterations: done (1.8s)

IterNodesCost
02402271
16532178
230802046
done50022040

prune595.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 2.5b

localize27.0ms

Local error

Found 4 expressions with local error:

0.0b
(* a (pow k m))
0.0b
(* k (+ 10.0 k))
0.2b
(/ 1 (/ (+ 1.0 (* k (+ 10.0 k))) (* a (pow k m))))
2.4b
(/ (+ 1.0 (* k (+ 10.0 k))) (* a (pow k m)))

rewrite133.0ms

Algorithm
rewrite-expression-head
Rules
59×add-exp-log
36×times-frac
34×add-sqr-sqrt
29×*-un-lft-identity
27×add-cube-cbrt
26×div-exp
22×add-cbrt-cube
16×prod-exp
11×associate-*r*
8×associate-/r*
7×pow1 cbrt-undiv
6×associate-*l* div-inv associate-/l*
5×pow-to-exp rec-exp 1-exp pow-exp
4×unpow-prod-down cbrt-unprod add-log-exp unswap-sqr
2×frac-2neg flip3-+ associate-*r/ clear-num *-commutative flip-+ associate-/l/ sqr-pow
1×distribute-rgt-in pow-flip distribute-lft-in pow-prod-down associate-/r/ distribute-lft-out inv-pow
Counts
4 → 135
Calls
4 calls:
19.0ms
(* a (pow k m))
25.0ms
(* k (+ 10.0 k))
35.0ms
(/ 1 (/ (+ 1.0 (* k (+ 10.0 k))) (* a (pow k m))))
44.0ms
(/ (+ 1.0 (* k (+ 10.0 k))) (* a (pow k m)))

series534.0ms

Counts
4 → 12
Calls
4 calls:
97.0ms
(* a (pow k m))
81.0ms
(* k (+ 10.0 k))
189.0ms
(/ 1 (/ (+ 1.0 (* k (+ 10.0 k))) (* a (pow k m))))
167.0ms
(/ (+ 1.0 (* k (+ 10.0 k))) (* a (pow k m)))

simplify2.2s

Counts
147 → 147
Iterations

Useful iterations: done (2.2s)

IterNodesCost
02642543
17392340
237742132
done50002111

prune487.0ms

Pruning

5 alts after pruning (2 fresh and 3 done)

Merged error: 0.2b

regimes100.0ms

Accuracy

97.8% (0.0b remaining)

Error of 0.1b against oracle of 0.1b and baseline of 2.2b

bsearch88.0ms

Steps
ItersRangePoint
5
1.6321848072006352e+139
5.467748683075901e+139
4.3880472092866065e+139

simplify10.0ms

Iterations

Useful iterations: 0 (2.0ms)

IterNodesCost
03970
15170
done5170

end0.0ms

sample2.8s

Algorithm
intervals
Results
1.7s12027×body80valid
352.0ms4253×body80nan