Details

Time bar (total: 28.8s)

sample67.0ms

Algorithm
intervals
Results
27.0ms371×body80valid
9.0ms133×body80nan

simplify3.9s

Counts
1 → 1
Iterations

Useful iterations: 2 (14.0ms)

IterNodesCost
01215
12415
24813
39513
423913
571813
6274513
done500013

prune12.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 2.2b

localize10.0ms

Local error

Found 3 expressions with local error:

0.0b
(/ (+ (* k (+ 10.0 k)) 1.0) (pow k m))
0.0b
(* k (+ 10.0 k))
2.2b
(/ a (/ (+ (* k (+ 10.0 k)) 1.0) (pow k m)))

rewrite142.0ms

Algorithm
rewrite-expression-head
Rules
180×times-frac
105×add-sqr-sqrt *-un-lft-identity
103×add-cube-cbrt
48×unpow-prod-down
32×associate-/r*
20×add-exp-log
16×sqr-pow
12×add-cbrt-cube
10×div-exp
6×div-inv associate-/l*
5×pow1
4×cbrt-undiv associate-*r*
3×associate-*l* add-log-exp
2×pow-to-exp frac-2neg flip3-+ associate-*r/ pow-exp clear-num flip-+ associate-/l/
1×distribute-rgt-in distribute-lft-in pow-prod-down prod-exp associate-/r/ *-commutative cbrt-unprod distribute-lft-out unswap-sqr
Counts
3 → 190
Calls
3 calls:
63.0ms
(/ (+ (* k (+ 10.0 k)) 1.0) (pow k m))
24.0ms
(* k (+ 10.0 k))
45.0ms
(/ a (/ (+ (* k (+ 10.0 k)) 1.0) (pow k m)))

series338.0ms

Counts
3 → 9
Calls
3 calls:
94.0ms
(/ (+ (* k (+ 10.0 k)) 1.0) (pow k m))
57.0ms
(* k (+ 10.0 k))
186.0ms
(/ a (/ (+ (* k (+ 10.0 k)) 1.0) (pow k m)))

simplify2.0s

Counts
199 → 199
Iterations

Useful iterations: done (1.9s)

IterNodesCost
03664560
18404341
228514178
done50014148

prune753.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 2.2b

localize33.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (sqrt (+ (* k (+ 10.0 k)) 1.0)) (/ (pow k m) (sqrt (+ (* k (+ 10.0 k)) 1.0))))
2.2b
(/ a (/ (sqrt (+ (* k (+ 10.0 k)) 1.0)) (/ (pow k m) (sqrt (+ (* k (+ 10.0 k)) 1.0)))))
14.7b
(sqrt (+ (* k (+ 10.0 k)) 1.0))
14.7b
(sqrt (+ (* k (+ 10.0 k)) 1.0))

rewrite582.0ms

Algorithm
rewrite-expression-head
Rules
3621×times-frac
1625×add-sqr-sqrt
1623×add-cube-cbrt *-un-lft-identity
1380×sqrt-prod
558×unpow-prod-down
341×associate-/r*
186×sqr-pow
68×sqrt-div associate-/r/
37×div-inv
34×flip3-+ flip-+
30×add-exp-log
19×div-exp
18×add-cbrt-cube
9×cbrt-undiv associate-/l*
6×pow1
4×add-log-exp
2×pow-to-exp rem-sqrt-square frac-2neg sqrt-pow1 pow1/2 pow-exp clear-num associate-/l/
Counts
4 → 1585
Calls
4 calls:
76.0ms
(/ (sqrt (+ (* k (+ 10.0 k)) 1.0)) (/ (pow k m) (sqrt (+ (* k (+ 10.0 k)) 1.0))))
141.0ms
(/ a (/ (sqrt (+ (* k (+ 10.0 k)) 1.0)) (/ (pow k m) (sqrt (+ (* k (+ 10.0 k)) 1.0)))))
31.0ms
(sqrt (+ (* k (+ 10.0 k)) 1.0))
31.0ms
(sqrt (+ (* k (+ 10.0 k)) 1.0))

series414.0ms

Counts
4 → 12
Calls
4 calls:
104.0ms
(/ (sqrt (+ (* k (+ 10.0 k)) 1.0)) (/ (pow k m) (sqrt (+ (* k (+ 10.0 k)) 1.0))))
173.0ms
(/ a (/ (sqrt (+ (* k (+ 10.0 k)) 1.0)) (/ (pow k m) (sqrt (+ (* k (+ 10.0 k)) 1.0)))))
66.0ms
(sqrt (+ (* k (+ 10.0 k)) 1.0))
71.0ms
(sqrt (+ (* k (+ 10.0 k)) 1.0))

simplify4.1s

Counts
1597 → 1597
Iterations

Useful iterations: done (3.9s)

IterNodesCost
0178873920
1388066023
done500065251

prune5.2s

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 2.2b

localize18.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (pow k m) (sqrt (sqrt (+ (* k (+ 10.0 k)) 1.0))))
14.7b
(sqrt (+ (* k (+ 10.0 k)) 1.0))
14.7b
(sqrt (+ (* k (+ 10.0 k)) 1.0))
14.7b
(sqrt (+ (* k (+ 10.0 k)) 1.0))

rewrite145.0ms

Algorithm
rewrite-expression-head
Rules
81×sqrt-prod
63×times-frac
54×add-sqr-sqrt
51×add-cube-cbrt *-un-lft-identity
30×unpow-prod-down
10×sqrt-div sqr-pow
9×add-exp-log associate-/r*
7×pow1 associate-/l*
6×add-cbrt-cube
4×flip3-+ flip-+ add-log-exp
3×rem-sqrt-square sqrt-pow1 pow1/2 div-exp
2×associate-/r/
1×cbrt-undiv pow-to-exp frac-2neg pow-exp clear-num div-inv
Counts
4 → 140
Calls
4 calls:
54.0ms
(/ (pow k m) (sqrt (sqrt (+ (* k (+ 10.0 k)) 1.0))))
33.0ms
(sqrt (+ (* k (+ 10.0 k)) 1.0))
18.0ms
(sqrt (+ (* k (+ 10.0 k)) 1.0))
30.0ms
(sqrt (+ (* k (+ 10.0 k)) 1.0))

series464.0ms

Counts
4 → 12
Calls
4 calls:
227.0ms
(/ (pow k m) (sqrt (sqrt (+ (* k (+ 10.0 k)) 1.0))))
70.0ms
(sqrt (+ (* k (+ 10.0 k)) 1.0))
81.0ms
(sqrt (+ (* k (+ 10.0 k)) 1.0))
86.0ms
(sqrt (+ (* k (+ 10.0 k)) 1.0))

simplify2.8s

Counts
152 → 152
Iterations

Useful iterations: done (2.8s)

IterNodesCost
02373372
14503034
212182953
341272882
done50012876

prune784.0ms

Pruning

5 alts after pruning (2 fresh and 3 done)

Merged error: 2.2b

localize26.0ms

Local error

Found 3 expressions with local error:

0.0b
(- (+ (* 10.0 k) 1.0) (* 1.0 (* m (log k))))
0.2b
(* m (log k))
0.3b
(/ a (- (+ (* 10.0 k) 1.0) (* 1.0 (* m (log k)))))

rewrite189.0ms

Algorithm
rewrite-expression-head
Rules
21×add-sqr-sqrt
19×add-cube-cbrt *-un-lft-identity
18×log-prod
15×distribute-rgt-in distribute-lft-in
12×associate--r+
9×times-frac
8×add-log-exp
7×add-exp-log add-cbrt-cube
6×pow1
4×associate-*r*
3×associate-*l* associate-/r* associate-/l*
2×flip3-- diff-log associate-/r/ flip--
1×cbrt-undiv sub-neg frac-2neg div-exp pow-prod-down prod-exp associate--l+ clear-num sum-log log-pow *-commutative cbrt-unprod div-inv unswap-sqr
Counts
3 → 80
Calls
3 calls:
63.0ms
(- (+ (* 10.0 k) 1.0) (* 1.0 (* m (log k))))
17.0ms
(* m (log k))
106.0ms
(/ a (- (+ (* 10.0 k) 1.0) (* 1.0 (* m (log k)))))

series274.0ms

Counts
3 → 9
Calls
3 calls:
62.0ms
(- (+ (* 10.0 k) 1.0) (* 1.0 (* m (log k))))
70.0ms
(* m (log k))
141.0ms
(/ a (- (+ (* 10.0 k) 1.0) (* 1.0 (* m (log k)))))

simplify3.6s

Counts
89 → 89
Iterations

Useful iterations: 3 (1.3s)

IterNodesCost
01751389
14171346
210681226
336511207
done50011207

prune368.0ms

Pruning

6 alts after pruning (3 fresh and 3 done)

Merged error: 2.2b

regimes122.0ms

Accuracy

0% (0.0b remaining)

Error of 2.1b against oracle of 2.0b and baseline of 2.1b

bsearch0.0ms

simplify2.0ms

Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01113
11413
done1413

end0.0ms

sample2.6s

Algorithm
intervals
Results
1.4s11875×body80valid
397.0ms4247×body80nan