Details

Time bar (total: 17.0s)

sample73.0ms

Algorithm
intervals
Results
31.0ms363×body80valid
10.0ms129×body80nan

simplify3.2s

Counts
1 → 1
Iterations

Useful iterations: 2 (7.0ms)

IterNodesCost
01215
12415
24813
39513
423913
571813
6274513
done500013

prune10.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 1.8b

localize24.0ms

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)))

rewrite130.0ms

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))
23.0ms
(* a (pow k m))
49.0ms
(+ (+ 1.0 (* 10.0 k)) (* k k))
42.0ms
(/ (* a (pow k m)) (+ (+ 1.0 (* 10.0 k)) (* k k)))

series317.0ms

Counts
4 → 12
Calls
4 calls:
59.0ms
(+ 1.0 (* 10.0 k))
65.0ms
(* a (pow k m))
24.0ms
(+ (+ 1.0 (* 10.0 k)) (* k k))
169.0ms
(/ (* 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

prune336.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 1.7b

localize38.0ms

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))))

rewrite191.0ms

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:
49.0ms
(+ (+ 1.0 (* 10.0 k)) (* k k))
79.0ms
(/ (/ (* a (pow k m)) (sqrt (+ 1.0 (* k (+ 10.0 k))))) (sqrt (+ (+ 1.0 (* 10.0 k)) (* k k))))
45.0ms
(sqrt (+ (+ 1.0 (* 10.0 k)) (* k k)))
10.0ms
(sqrt (+ 1.0 (* k (+ 10.0 k))))

series362.0ms

Counts
4 → 12
Calls
4 calls:
40.0ms
(+ (+ 1.0 (* 10.0 k)) (* k k))
189.0ms
(/ (/ (* a (pow k m)) (sqrt (+ 1.0 (* k (+ 10.0 k))))) (sqrt (+ (+ 1.0 (* 10.0 k)) (* k k))))
50.0ms
(sqrt (+ (+ 1.0 (* 10.0 k)) (* k k)))
83.0ms
(sqrt (+ 1.0 (* k (+ 10.0 k))))

simplify1.5s

Counts
166 → 166
Iterations

Useful iterations: done (1.5s)

IterNodesCost
03115835
17834686
224944359
done50014226

prune674.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 1.7b

localize17.0ms

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 (+ 1.0 (* (+ 10.0 k) k))))
16.3b
(sqrt (+ 1.0 (* (+ 10.0 k) k)))
16.3b
(sqrt (+ 1.0 (* k (+ 10.0 k))))

rewrite114.0ms

Algorithm
rewrite-expression-head
Rules
120×times-frac
72×sqrt-prod
59×add-sqr-sqrt
57×add-cube-cbrt *-un-lft-identity
30×add-exp-log
22×sqrt-div
18×associate-/r/ add-cbrt-cube
13×div-exp associate-/l*
12×associate-/r*
11×flip3-+ flip-+
9×div-inv
7×cbrt-undiv
6×pow1 prod-exp
4×add-log-exp
2×pow-to-exp rem-sqrt-square frac-2neg sqrt-pow1 pow1/2 pow-exp clear-num cbrt-unprod
1×associate-/l/
Counts
4 → 172
Calls
4 calls:
35.0ms
(/ (* a (pow k m)) (sqrt (+ 1.0 (* k (+ 10.0 k)))))
51.0ms
(/ (/ (* a (pow k m)) (sqrt (+ 1.0 (* k (+ 10.0 k))))) (sqrt (+ 1.0 (* (+ 10.0 k) k))))
5.0ms
(sqrt (+ 1.0 (* (+ 10.0 k) k)))
6.0ms
(sqrt (+ 1.0 (* k (+ 10.0 k))))

series568.0ms

Counts
4 → 12
Calls
4 calls:
215.0ms
(/ (* a (pow k m)) (sqrt (+ 1.0 (* k (+ 10.0 k)))))
200.0ms
(/ (/ (* a (pow k m)) (sqrt (+ 1.0 (* k (+ 10.0 k))))) (sqrt (+ 1.0 (* (+ 10.0 k) k))))
60.0ms
(sqrt (+ 1.0 (* (+ 10.0 k) k)))
92.0ms
(sqrt (+ 1.0 (* k (+ 10.0 k))))

simplify1.4s

Counts
184 → 184
Iterations

Useful iterations: done (1.4s)

IterNodesCost
03205936
18225181
223944817
done50004681

prune723.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0.0b

localize46.0ms

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))))

rewrite37.0ms

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:
10.0ms
(/ 1 (fabs (cbrt (+ 1.0 (* k (+ 10.0 k))))))
10.0ms
(sqrt (+ 1.0 (* k (+ 10.0 k))))
6.0ms
(cbrt (+ 1.0 (* k (+ 10.0 k))))
6.0ms
(cbrt (+ 1.0 (* k (+ 10.0 k))))

series428.0ms

Counts
4 → 12
Calls
4 calls:
31.0ms
(/ 1 (fabs (cbrt (+ 1.0 (* k (+ 10.0 k))))))
65.0ms
(sqrt (+ 1.0 (* k (+ 10.0 k))))
173.0ms
(cbrt (+ 1.0 (* k (+ 10.0 k))))
159.0ms
(cbrt (+ 1.0 (* k (+ 10.0 k))))

simplify2.4s

Counts
84 → 84
Iterations

Useful iterations: 3 (877.0ms)

IterNodesCost
01541409
13251293
28111189
326231172
done50011172

prune532.0ms

Pruning

4 alts after pruning (1 fresh and 3 done)

Merged error: 0.0b

regimes163.0ms

Accuracy

97.6% (0.0b remaining)

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

bsearch91.0ms

Steps
ItersRangePoint
9
5.026229641937241e+135
1.4970672528079013e+142
1.4423024704689428e+138

simplify9.0ms

Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
03561
14661
done4661

end0.0ms

sample2.4s

Algorithm
intervals
Results
1.2s11970×body80valid
400.0ms4494×body80nan