Details

Time bar (total: 46.8s)

sample103.0ms

Algorithm
intervals
Results
39.0ms416×body80valid
20.0ms156×body80nan

simplify21.1s

Counts
1 → 1
Iterations

Useful iterations: 2 (36.0ms)

IterNodesCost
01215
13815
219913
3158313
done500113

prune7.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 2.1b

localize12.0ms

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))
2.1b
(/ (* a (pow k m)) (+ (+ 1.0 (* 10.0 k)) (* k k)))

rewrite119.0ms

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))
18.0ms
(* a (pow k m))
44.0ms
(+ (+ 1.0 (* 10.0 k)) (* k k))
48.0ms
(/ (* a (pow k m)) (+ (+ 1.0 (* 10.0 k)) (* k k)))

series329.0ms

Counts
4 → 12
Calls
4 calls:
40.0ms
(+ 1.0 (* 10.0 k))
108.0ms
(* a (pow k m))
25.0ms
(+ (+ 1.0 (* 10.0 k)) (* k k))
156.0ms
(/ (* a (pow k m)) (+ (+ 1.0 (* 10.0 k)) (* k k)))

simplify4.5s

Counts
86 → 86
Iterations

Useful iterations: done (4.5s)

IterNodesCost
01711264
136401104
done5000996

prune319.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 2.1b

localize27.0ms

Local error

Found 4 expressions with local error:

0.0b
(+ (+ 1.0 (* 10.0 k)) (* k k))
0.0b
(/ (* (/ a (sqrt (+ 1.0 (* k (+ 10.0 k))))) (pow k m)) (sqrt (+ (+ 1.0 (* 10.0 k)) (* k k))))
16.4b
(sqrt (+ (+ 1.0 (* 10.0 k)) (* k k)))
16.4b
(sqrt (+ 1.0 (* k (+ 10.0 k))))

rewrite136.0ms

Algorithm
rewrite-expression-head
Rules
25×add-exp-log
13×add-cbrt-cube
12×add-sqr-sqrt sqrt-prod
10×add-cube-cbrt *-un-lft-identity div-exp
9×add-log-exp
6×pow1 times-frac sqrt-div prod-exp associate-/r*
4×cbrt-undiv flip3-+ flip-+
3×sum-log
2×pow-to-exp rem-sqrt-square sqrt-pow1 pow1/2 pow-exp associate-/r/ cbrt-unprod
1×+-commutative associate-+l+ frac-2neg associate-*l/ clear-num div-inv associate-/l/ associate-/l*
Counts
4 → 79
Calls
4 calls:
26.0ms
(+ (+ 1.0 (* 10.0 k)) (* k k))
52.0ms
(/ (* (/ a (sqrt (+ 1.0 (* k (+ 10.0 k))))) (pow k m)) (sqrt (+ (+ 1.0 (* 10.0 k)) (* k k))))
40.0ms
(sqrt (+ (+ 1.0 (* 10.0 k)) (* k k)))
12.0ms
(sqrt (+ 1.0 (* k (+ 10.0 k))))

series335.0ms

Counts
4 → 12
Calls
4 calls:
32.0ms
(+ (+ 1.0 (* 10.0 k)) (* k k))
167.0ms
(/ (* (/ a (sqrt (+ 1.0 (* k (+ 10.0 k))))) (pow k m)) (sqrt (+ (+ 1.0 (* 10.0 k)) (* k k))))
67.0ms
(sqrt (+ (+ 1.0 (* 10.0 k)) (* k k)))
68.0ms
(sqrt (+ 1.0 (* k (+ 10.0 k))))

simplify7.3s

Counts
91 → 91
Iterations

Useful iterations: done (7.3s)

IterNodesCost
02062139
122931606
done50011439

prune481.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 2.1b

localize25.0ms

Local error

Found 4 expressions with local error:

0.0b
(/ (/ (+ 1.0 (* k (+ 10.0 k))) a) (pow k m))
0.0b
(* k (+ 10.0 k))
0.1b
(/ 1 (/ (/ (+ 1.0 (* k (+ 10.0 k))) a) (pow k m)))
3.8b
(/ (+ 1.0 (* k (+ 10.0 k))) a)

rewrite242.0ms

Algorithm
rewrite-expression-head
Rules
1073×times-frac
500×add-sqr-sqrt *-un-lft-identity
498×add-cube-cbrt
198×unpow-prod-down
105×associate-/r*
70×add-exp-log
66×sqr-pow
51×div-exp
43×div-inv
22×add-cbrt-cube
19×associate-/l*
10×cbrt-undiv
8×pow-to-exp pow-exp
7×pow1 rec-exp 1-exp
4×associate-*r* add-log-exp
3×frac-2neg associate-*l* clear-num associate-/l/
2×flip3-+ associate-*r/ flip-+
1×distribute-rgt-in pow-flip distribute-lft-in pow-prod-down prod-exp associate-/r/ *-commutative cbrt-unprod distribute-lft-out inv-pow unswap-sqr
Counts
4 → 602
Calls
4 calls:
42.0ms
(/ (/ (+ 1.0 (* k (+ 10.0 k))) a) (pow k m))
39.0ms
(* k (+ 10.0 k))
45.0ms
(/ 1 (/ (/ (+ 1.0 (* k (+ 10.0 k))) a) (pow k m)))
55.0ms
(/ (+ 1.0 (* k (+ 10.0 k))) a)

series430.0ms

Counts
4 → 12
Calls
4 calls:
173.0ms
(/ (/ (+ 1.0 (* k (+ 10.0 k))) a) (pow k m))
54.0ms
(* k (+ 10.0 k))
151.0ms
(/ 1 (/ (/ (+ 1.0 (* k (+ 10.0 k))) a) (pow k m)))
52.0ms
(/ (+ 1.0 (* k (+ 10.0 k))) a)

simplify1.1s

Counts
614 → 614
Iterations

Useful iterations: done (1.0s)

IterNodesCost
089817811
done500016919

prune2.9s

Pruning

5 alts after pruning (2 fresh and 3 done)

Merged error: 0.0b

localize30.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (/ a (sqrt (+ (* (+ 10.0 k) k) 1.0))) (fabs (cbrt (+ 1.0 (* k (+ 10.0 k))))))
16.4b
(sqrt (+ (* (+ 10.0 k) k) 1.0))
16.9b
(cbrt (+ 1.0 (* k (+ 10.0 k))))
16.9b
(cbrt (+ 1.0 (* k (+ 10.0 k))))

rewrite122.0ms

Algorithm
rewrite-expression-head
Rules
144×times-frac
85×add-sqr-sqrt
84×add-cube-cbrt *-un-lft-identity
39×sqrt-prod
24×associate-/l*
10×sqrt-div
9×add-exp-log add-cbrt-cube
8×associate-/r/
7×flip3-+ flip-+
6×cbrt-prod
5×pow1 div-inv
4×cbrt-div add-log-exp
3×cbrt-undiv div-exp associate-/r*
2×pow1/3
1×rem-sqrt-square frac-2neg sqrt-pow1 pow1/2 clear-num associate-/l/
Counts
4 → 155
Calls
4 calls:
66.0ms
(/ (/ a (sqrt (+ (* (+ 10.0 k) k) 1.0))) (fabs (cbrt (+ 1.0 (* k (+ 10.0 k))))))
31.0ms
(sqrt (+ (* (+ 10.0 k) k) 1.0))
6.0ms
(cbrt (+ 1.0 (* k (+ 10.0 k))))
6.0ms
(cbrt (+ 1.0 (* k (+ 10.0 k))))

series554.0ms

Counts
4 → 12
Calls
4 calls:
190.0ms
(/ (/ a (sqrt (+ (* (+ 10.0 k) k) 1.0))) (fabs (cbrt (+ 1.0 (* k (+ 10.0 k))))))
71.0ms
(sqrt (+ (* (+ 10.0 k) k) 1.0))
139.0ms
(cbrt (+ 1.0 (* k (+ 10.0 k))))
153.0ms
(cbrt (+ 1.0 (* k (+ 10.0 k))))

simplify2.5s

Counts
167 → 167
Iterations

Useful iterations: done (2.5s)

IterNodesCost
03495430
121835149
done50014977

prune1.2s

Pruning

5 alts after pruning (1 fresh and 4 done)

Merged error: 0.0b

regimes161.0ms

Accuracy

94.5% (0.1b remaining)

Error of 0.2b against oracle of 0.1b and baseline of 2.0b

bsearch21.0ms

Steps
ItersRangePoint
2
9.669451620439698e+25
1.0657150563594859e+26
1.0533688195700462e+26

simplify17.0ms

Iterations

Useful iterations: done (16.0ms)

IterNodesCost
03464
14364
done4358

end0.0ms

sample2.7s

Algorithm
intervals
Results
1.6s11904×body80valid
336.0ms4108×body80nan