Details

Time bar (total: 18.5s)

sample64.0ms

Algorithm
intervals
Results
28.0ms381×body80valid
7.0ms111×body80nan

simplify3.8s

Counts
1 → 1
Iterations

Useful iterations: 2 (14.0ms)

IterNodesCost
01215
12415
24813
39513
423913
571813
6274513
done500013

prune10.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 2.1b

localize27.0ms

Local error

Found 4 expressions with local error:

0.0b
(+ 1.0 (* 10.0 k))
0.0b
(+ (+ 1.0 (* 10.0 k)) (* k k))
0.0b
(* a (pow k m))
2.1b
(/ (* a (pow k m)) (+ (+ 1.0 (* 10.0 k)) (* k k)))

rewrite137.0ms

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))
29.0ms
(+ (+ 1.0 (* 10.0 k)) (* k k))
25.0ms
(* a (pow k m))
75.0ms
(/ (* a (pow k m)) (+ (+ 1.0 (* 10.0 k)) (* k k)))

series337.0ms

Counts
4 → 12
Calls
4 calls:
46.0ms
(+ 1.0 (* 10.0 k))
22.0ms
(+ (+ 1.0 (* 10.0 k)) (* k k))
82.0ms
(* a (pow k m))
187.0ms
(/ (* a (pow k m)) (+ (+ 1.0 (* 10.0 k)) (* k k)))

simplify1.1s

Counts
86 → 86
Iterations

Useful iterations: done (1.1s)

IterNodesCost
01711264
14511098
21536988
done5001938

prune312.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 2.1b

localize32.0ms

Local error

Found 4 expressions with local error:

0.6b
(cbrt k)
0.6b
(cbrt k)
0.6b
(cbrt k)
2.1b
(/ (* (* a (pow (* (cbrt k) (cbrt k)) m)) (pow (cbrt k) m)) (+ (+ 1.0 (* 10.0 k)) (* k k)))

rewrite78.0ms

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)
73.0ms
(/ (* (* a (pow (* (cbrt k) (cbrt k)) m)) (pow (cbrt k) m)) (+ (+ 1.0 (* 10.0 k)) (* k k)))

series1.4s

Counts
4 → 12
Calls
4 calls:
298.0ms
(cbrt k)
316.0ms
(cbrt k)
267.0ms
(cbrt k)
534.0ms
(/ (* (* a (pow (* (cbrt k) (cbrt k)) m)) (pow (cbrt k) m)) (+ (+ 1.0 (* 10.0 k)) (* k k)))

simplify1.2s

Counts
83 → 83
Iterations

Useful iterations: done (1.2s)

IterNodesCost
01761649
14871424
220391179
done50011170

prune353.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 2.1b

localize16.0ms

Local error

Found 4 expressions with local error:

0.0b
(+ (+ 1.0 (* 10.0 k)) (* k k))
0.0b
(* (* a (pow k (/ m 2))) (pow k (/ m 2)))
0.0b
(* a (pow k (/ m 2)))
2.1b
(/ (* (* a (pow k (/ m 2))) (pow k (/ m 2))) (+ (+ 1.0 (* 10.0 k)) (* k k)))

rewrite176.0ms

Algorithm
rewrite-expression-head
Rules
75×add-exp-log
45×prod-exp
20×add-cbrt-cube
16×add-sqr-sqrt
15×pow-to-exp pow-exp
14×associate-*r*
13×div-exp
11×add-cube-cbrt *-un-lft-identity
9×add-log-exp
7×unpow-prod-down cbrt-unprod
4×pow1 associate-*l*
3×cbrt-undiv times-frac associate-/r* sum-log unswap-sqr sqr-pow
2×flip3-+ associate-/r/ *-commutative flip-+
1×+-commutative associate-+l+ frac-2neg clear-num div-inv associate-/l*
Counts
4 → 103
Calls
4 calls:
35.0ms
(+ (+ 1.0 (* 10.0 k)) (* k k))
38.0ms
(* (* a (pow k (/ m 2))) (pow k (/ m 2)))
27.0ms
(* a (pow k (/ m 2)))
69.0ms
(/ (* (* a (pow k (/ m 2))) (pow k (/ m 2))) (+ (+ 1.0 (* 10.0 k)) (* k k)))

series440.0ms

Counts
4 → 12
Calls
4 calls:
25.0ms
(+ (+ 1.0 (* 10.0 k)) (* k k))
98.0ms
(* (* a (pow k (/ m 2))) (pow k (/ m 2)))
98.0ms
(* a (pow k (/ m 2)))
219.0ms
(/ (* (* a (pow k (/ m 2))) (pow k (/ m 2))) (+ (+ 1.0 (* 10.0 k)) (* k k)))

simplify1.6s

Counts
115 → 115
Iterations

Useful iterations: done (1.6s)

IterNodesCost
01932344
15221850
220421604
done50001575

prune443.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 2.1b

localize29.0ms

Local error

Found 4 expressions with local error:

0.0b
(/ (* (pow k (/ m 2)) a) (sqrt (+ 1.0 (* k (+ 10.0 k)))))
0.0b
(* (/ (* (pow k (/ m 2)) a) (sqrt (+ 1.0 (* k (+ 10.0 k))))) (/ (pow k (/ m 2)) (sqrt (+ 1.0 (* k (+ 10.0 k))))))
15.2b
(sqrt (+ 1.0 (* k (+ 10.0 k))))
15.2b
(sqrt (+ 1.0 (* k (+ 10.0 k))))

rewrite199.0ms

Algorithm
rewrite-expression-head
Rules
88×add-exp-log
60×add-sqr-sqrt times-frac
48×associate-*r*
40×add-cube-cbrt *-un-lft-identity
39×sqrt-prod
35×div-exp prod-exp
30×add-cbrt-cube
20×unpow-prod-down
12×associate-*l*
10×pow-to-exp sqrt-div pow-exp
9×cbrt-undiv cbrt-unprod
8×pow1 sqr-pow
7×unswap-sqr
6×associate-/r* associate-/r/
5×flip3-+ flip-+
4×add-log-exp
3×div-inv
2×rem-sqrt-square sqrt-pow1 pow1/2
1×frac-times frac-2neg associate-*r/ pow-prod-down associate-*l/ clear-num *-commutative associate-/l*
Counts
4 → 166
Calls
4 calls:
33.0ms
(/ (* (pow k (/ m 2)) a) (sqrt (+ 1.0 (* k (+ 10.0 k)))))
147.0ms
(* (/ (* (pow k (/ m 2)) a) (sqrt (+ 1.0 (* k (+ 10.0 k))))) (/ (pow k (/ m 2)) (sqrt (+ 1.0 (* k (+ 10.0 k))))))
5.0ms
(sqrt (+ 1.0 (* k (+ 10.0 k))))
6.0ms
(sqrt (+ 1.0 (* k (+ 10.0 k))))

series643.0ms

Counts
4 → 12
Calls
4 calls:
352.0ms
(/ (* (pow k (/ m 2)) a) (sqrt (+ 1.0 (* k (+ 10.0 k)))))
185.0ms
(* (/ (* (pow k (/ m 2)) a) (sqrt (+ 1.0 (* k (+ 10.0 k))))) (/ (pow k (/ m 2)) (sqrt (+ 1.0 (* k (+ 10.0 k))))))
50.0ms
(sqrt (+ 1.0 (* k (+ 10.0 k))))
56.0ms
(sqrt (+ 1.0 (* k (+ 10.0 k))))

simplify2.8s

Counts
178 → 178
Iterations

Useful iterations: done (2.8s)

IterNodesCost
03205639
19115167
234814213
done50014157

prune844.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 2.1b

regimes73.0ms

Accuracy

0% (0.0b remaining)

Error of 2.3b against oracle of 2.3b and baseline of 2.3b

bsearch0.0ms

simplify3.0ms

Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
01624
12124
done2124

end0.0ms

sample2.4s

Algorithm
intervals
Results
1.1s11757×body80valid
446.0ms4170×body80nan