Details

Time bar (total: 16.6s)

sample64.0ms

Algorithm
intervals
Results
30.0ms363×body80valid
10.0ms129×body80nan

simplify3.3s

Counts
1 → 1
Iterations

Useful iterations: 2 (6.0ms)

IterNodesCost
01215
12415
24813
39513
423913
571813
6274513
done500013

prune11.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 1.8b

localize20.0ms

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))
1.7b
(/ (* a (pow k m)) (+ (+ 1.0 (* 10.0 k)) (* k k)))

rewrite116.0ms

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:
11.0ms
(+ 1.0 (* 10.0 k))
21.0ms
(* a (pow k m))
25.0ms
(+ (+ 1.0 (* 10.0 k)) (* k k))
56.0ms
(/ (* a (pow k m)) (+ (+ 1.0 (* 10.0 k)) (* k k)))

series337.0ms

Counts
4 → 12
Calls
4 calls:
38.0ms
(+ 1.0 (* 10.0 k))
69.0ms
(* a (pow k m))
35.0ms
(+ (+ 1.0 (* 10.0 k)) (* k k))
195.0ms
(/ (* a (pow k m)) (+ (+ 1.0 (* 10.0 k)) (* k k)))

simplify1.2s

Counts
86 → 86
Iterations

Useful iterations: done (1.2s)

IterNodesCost
01711264
14511098
21536988
done5001938

prune445.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 1.7b

localize41.0ms

Local error

Found 4 expressions with local error:

0.0b
(+ (+ 1.0 (* 10.0 k)) (* k k))
0.0b
(/ (/ (* a (pow k m)) (sqrt (+ 1.0 (* k (+ 10.0 k))))) (sqrt (+ (+ 1.0 (* 10.0 k)) (* k k))))
16.3b
(sqrt (+ (+ 1.0 (* 10.0 k)) (* k k)))
16.3b
(sqrt (+ 1.0 (* k (+ 10.0 k))))

rewrite135.0ms

Algorithm
rewrite-expression-head
Rules
114×times-frac
66×sqrt-prod
55×add-sqr-sqrt
53×add-cube-cbrt *-un-lft-identity
20×add-exp-log sqrt-div
16×associate-/r/
13×add-cbrt-cube
12×associate-/l*
11×flip3-+ flip-+
9×div-exp add-log-exp
8×div-inv
6×pow1 associate-/r*
5×cbrt-undiv
3×prod-exp sum-log
2×rem-sqrt-square sqrt-pow1 pow1/2
1×+-commutative pow-to-exp associate-+l+ frac-2neg pow-exp clear-num cbrt-unprod associate-/l/
Counts
4 → 154
Calls
4 calls:
22.0ms
(+ (+ 1.0 (* 10.0 k)) (* k k))
70.0ms
(/ (/ (* a (pow k m)) (sqrt (+ 1.0 (* k (+ 10.0 k))))) (sqrt (+ (+ 1.0 (* 10.0 k)) (* k k))))
22.0ms
(sqrt (+ (+ 1.0 (* 10.0 k)) (* k k)))
8.0ms
(sqrt (+ 1.0 (* k (+ 10.0 k))))

series328.0ms

Counts
4 → 12
Calls
4 calls:
22.0ms
(+ (+ 1.0 (* 10.0 k)) (* k k))
191.0ms
(/ (/ (* a (pow k m)) (sqrt (+ 1.0 (* k (+ 10.0 k))))) (sqrt (+ (+ 1.0 (* 10.0 k)) (* k k))))
67.0ms
(sqrt (+ (+ 1.0 (* 10.0 k)) (* k k)))
49.0ms
(sqrt (+ 1.0 (* k (+ 10.0 k))))

simplify1.3s

Counts
166 → 166
Iterations

Useful iterations: done (1.3s)

IterNodesCost
03115835
17834686
224944359
done50014226

prune608.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 1.7b

localize30.0ms

Local error

Found 4 expressions with local error:

0.0b
(/ (* a (pow k m)) (sqrt (+ 1.0 (* k (+ 10.0 k)))))
0.0b
(/ (/ (* a (pow k m)) (sqrt (+ 1.0 (* k (+ 10.0 k))))) (sqrt (pow (+ (+ 1.0 (* 10.0 k)) (* k k)) 1)))
16.3b
(sqrt (pow (+ (+ 1.0 (* 10.0 k)) (* k k)) 1))
16.3b
(sqrt (+ 1.0 (* k (+ 10.0 k))))

rewrite249.0ms

Algorithm
rewrite-expression-head
Rules
192×times-frac
140×sqrt-prod
86×add-sqr-sqrt
83×add-cube-cbrt *-un-lft-identity
43×unpow-prod-down
30×add-exp-log
26×sqrt-div
24×associate-/r/
18×add-cbrt-cube
16×associate-/r*
15×sqr-pow
13×flip3-+ div-exp flip-+ div-inv associate-/l*
7×cbrt-undiv
6×prod-exp
5×pow1
4×rem-sqrt-square add-log-exp
2×pow-to-exp frac-2neg sqrt-pow1 pow1/2 pow-exp clear-num cbrt-unprod
1×associate-/l/
Counts
4 → 226
Calls
4 calls:
18.0ms
(/ (* a (pow k m)) (sqrt (+ 1.0 (* k (+ 10.0 k)))))
119.0ms
(/ (/ (* a (pow k m)) (sqrt (+ 1.0 (* k (+ 10.0 k))))) (sqrt (pow (+ (+ 1.0 (* 10.0 k)) (* k k)) 1)))
89.0ms
(sqrt (pow (+ (+ 1.0 (* 10.0 k)) (* k k)) 1))
11.0ms
(sqrt (+ 1.0 (* k (+ 10.0 k))))

series556.0ms

Counts
4 → 12
Calls
4 calls:
235.0ms
(/ (* a (pow k m)) (sqrt (+ 1.0 (* k (+ 10.0 k)))))
167.0ms
(/ (/ (* a (pow k m)) (sqrt (+ 1.0 (* k (+ 10.0 k))))) (sqrt (pow (+ (+ 1.0 (* 10.0 k)) (* k k)) 1)))
76.0ms
(sqrt (pow (+ (+ 1.0 (* 10.0 k)) (* k k)) 1))
78.0ms
(sqrt (+ 1.0 (* k (+ 10.0 k))))

simplify1.6s

Counts
238 → 238
Iterations

Useful iterations: done (1.6s)

IterNodesCost
03969540
18947253
225006743
done50006523

prune833.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 1.7b

localize38.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ 1 (fabs (cbrt (+ 1.0 (* k (+ 10.0 k))))))
16.3b
(sqrt (+ 1.0 (* k (+ 10.0 k))))
16.8b
(cbrt (+ 1.0 (* k (+ 10.0 k))))
16.8b
(cbrt (+ 1.0 (* k (+ 10.0 k))))

rewrite23.0ms

Algorithm
rewrite-expression-head
Rules
16×add-sqr-sqrt
15×add-cube-cbrt *-un-lft-identity
9×times-frac
8×add-exp-log
6×pow1 cbrt-prod add-cbrt-cube
4×cbrt-div add-log-exp
3×flip3-+ associate-/r* sqrt-prod flip-+ associate-/l*
2×pow1/3 sqrt-div div-exp
1×cbrt-undiv rem-sqrt-square rec-exp pow-flip frac-2neg sqrt-pow1 pow1/2 1-exp clear-num div-inv inv-pow
Counts
4 → 72
Calls
4 calls:
8.0ms
(/ 1 (fabs (cbrt (+ 1.0 (* k (+ 10.0 k))))))
5.0ms
(sqrt (+ 1.0 (* k (+ 10.0 k))))
3.0ms
(cbrt (+ 1.0 (* k (+ 10.0 k))))
3.0ms
(cbrt (+ 1.0 (* k (+ 10.0 k))))

series358.0ms

Counts
4 → 12
Calls
4 calls:
26.0ms
(/ 1 (fabs (cbrt (+ 1.0 (* k (+ 10.0 k))))))
54.0ms
(sqrt (+ 1.0 (* k (+ 10.0 k))))
146.0ms
(cbrt (+ 1.0 (* k (+ 10.0 k))))
132.0ms
(cbrt (+ 1.0 (* k (+ 10.0 k))))

simplify1.7s

Counts
84 → 84
Iterations

Useful iterations: 3 (696.0ms)

IterNodesCost
01541409
13251293
28111189
326231172
done50011172

prune505.0ms

Pruning

3 alts after pruning (0 fresh and 3 done)

Merged error: 1.7b

regimes154.0ms

Accuracy

0% (0.0b remaining)

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

bsearch0.0ms

simplify3.0ms

Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01215
11615
done1615

end0.0ms

sample2.7s

Algorithm
intervals
Results
1.8s11970×body80valid
356.0ms4494×body80nan