Details

Time bar (total: 45.8s)

sample84.0ms

Algorithm
intervals
Results
49.0ms416×body80valid
9.0ms156×body80nan

simplify3.1s

Counts
1 → 1
Iterations

Useful iterations: 3 (27.0ms)

IterNodesCost
01215
12415
25313
310712
425412
573512
6272912
done500112

prune6.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 2.1b

localize21.0ms

Local error

Found 2 expressions with local error:

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

rewrite80.0ms

Algorithm
rewrite-expression-head
Rules
180×times-frac
100×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
48×unpow-prod-down
32×associate-/r*
17×add-exp-log
16×sqr-pow
10×div-exp
9×add-cbrt-cube
6×div-inv associate-/l*
4×cbrt-undiv
2×pow1 expm1-log1p-u pow-to-exp frac-2neg pow-exp clear-num log1p-expm1-u add-log-exp
1×associate-/r/
Counts
2 → 169
Calls
2 calls:
15.0ms
(/ (fma k (+ 10.0 k) 1.0) (pow k m))
38.0ms
(/ a (/ (fma k (+ 10.0 k) 1.0) (pow k m)))

series279.0ms

Counts
2 → 6
Calls
2 calls:
90.0ms
(/ (fma k (+ 10.0 k) 1.0) (pow k m))
189.0ms
(/ a (/ (fma k (+ 10.0 k) 1.0) (pow k m)))

simplify2.0s

Counts
175 → 175
Iterations

Useful iterations: done (2.0s)

IterNodesCost
03314107
17133899
223573762
done50003717

prune725.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.0b

localize28.0ms

Local error

Found 4 expressions with local error:

0.0b
(/ a (sqrt (/ (fma k (+ 10.0 k) 1.0) (pow k m))))
0.0b
(/ (/ a (sqrt (/ (fma k (+ 10.0 k) 1.0) (pow k m)))) (sqrt (/ (fma k (+ 10.0 k) 1.0) (pow k m))))
9.3b
(sqrt (/ (fma k (+ 10.0 k) 1.0) (pow k m)))
9.3b
(sqrt (/ (fma k (+ 10.0 k) 1.0) (pow k m)))

rewrite793.0ms

Algorithm
rewrite-expression-head
Rules
8861×times-frac
4575×sqrt-prod
3629×add-sqr-sqrt
3617×add-cube-cbrt *-un-lft-identity
1649×unpow-prod-down
551×sqr-pow
214×div-inv
92×associate-/l*
56×associate-/r*
33×sqrt-div
31×associate-/r/
11×add-exp-log add-cbrt-cube
8×rem-sqrt-square
6×pow1
4×cbrt-undiv expm1-log1p-u div-exp log1p-expm1-u add-log-exp
2×frac-2neg sqrt-pow1 pow1/2 clear-num
1×associate-/l/
Counts
4 → 2839
Calls
4 calls:
20.0ms
(/ a (sqrt (/ (fma k (+ 10.0 k) 1.0) (pow k m))))
189.0ms
(/ (/ a (sqrt (/ (fma k (+ 10.0 k) 1.0) (pow k m)))) (sqrt (/ (fma k (+ 10.0 k) 1.0) (pow k m))))
17.0ms
(sqrt (/ (fma k (+ 10.0 k) 1.0) (pow k m)))
17.0ms
(sqrt (/ (fma k (+ 10.0 k) 1.0) (pow k m)))

series711.0ms

Counts
4 → 12
Calls
4 calls:
228.0ms
(/ a (sqrt (/ (fma k (+ 10.0 k) 1.0) (pow k m))))
165.0ms
(/ (/ a (sqrt (/ (fma k (+ 10.0 k) 1.0) (pow k m)))) (sqrt (/ (fma k (+ 10.0 k) 1.0) (pow k m))))
152.0ms
(sqrt (/ (fma k (+ 10.0 k) 1.0) (pow k m)))
167.0ms
(sqrt (/ (fma k (+ 10.0 k) 1.0) (pow k m)))

simplify2.9s

Counts
2851 → 2851
Iterations

Useful iterations: done (2.5s)

IterNodesCost
04294157609
done5001152028

prune20.7s

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.0b

localize49.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (/ a (sqrt (/ (fma k (+ 10.0 k) 1.0) (pow k m)))) (sqrt (/ (sqrt (fma k (+ 10.0 k) 1.0)) (* (cbrt (pow k m)) (cbrt (pow k m))))))
9.3b
(sqrt (/ (fma k (+ 10.0 k) 1.0) (pow k m)))
16.4b
(sqrt (fma k (+ 10.0 k) 1.0))
16.4b
(sqrt (fma k (+ 10.0 k) 1.0))

rewrite345.0ms

Algorithm
rewrite-expression-head
Rules
3779×times-frac
2251×sqrt-prod
1424×add-sqr-sqrt
1416×add-cube-cbrt *-un-lft-identity
388×unpow-prod-down
148×div-inv
130×sqr-pow
89×associate-/l*
16×sqrt-div
15×associate-/r/
13×associate-/r*
9×add-exp-log add-cbrt-cube
7×pow1
6×rem-sqrt-square
4×expm1-log1p-u log1p-expm1-u add-log-exp
3×cbrt-undiv sqrt-pow1 pow1/2 div-exp
1×frac-2neg clear-num associate-/l/
Counts
4 → 1348
Calls
4 calls:
105.0ms
(/ (/ a (sqrt (/ (fma k (+ 10.0 k) 1.0) (pow k m)))) (sqrt (/ (sqrt (fma k (+ 10.0 k) 1.0)) (* (cbrt (pow k m)) (cbrt (pow k m))))))
8.0ms
(sqrt (/ (fma k (+ 10.0 k) 1.0) (pow k m)))
2.0ms
(sqrt (fma k (+ 10.0 k) 1.0))
2.0ms
(sqrt (fma k (+ 10.0 k) 1.0))

series755.0ms

Counts
4 → 12
Calls
4 calls:
463.0ms
(/ (/ a (sqrt (/ (fma k (+ 10.0 k) 1.0) (pow k m)))) (sqrt (/ (sqrt (fma k (+ 10.0 k) 1.0)) (* (cbrt (pow k m)) (cbrt (pow k m))))))
141.0ms
(sqrt (/ (fma k (+ 10.0 k) 1.0) (pow k m)))
61.0ms
(sqrt (fma k (+ 10.0 k) 1.0))
90.0ms
(sqrt (fma k (+ 10.0 k) 1.0))

simplify3.0s

Counts
1360 → 1360
Iterations

Useful iterations: done (2.9s)

IterNodesCost
0207281984
1452176582
done500175736

prune5.5s

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0.0b

localize17.0ms

Local error

Found 4 expressions with local error:

0.0b
(/ (/ a (sqrt (/ (fma k (+ 10.0 k) 1.0) (pow k m)))) (cbrt (* (/ (fma k (+ 10.0 k) 1.0) (pow k m)) (sqrt (/ (fma k (+ 10.0 k) 1.0) (pow k m))))))
9.3b
(sqrt (/ (fma k (+ 10.0 k) 1.0) (pow k m)))
9.3b
(sqrt (/ (fma k (+ 10.0 k) 1.0) (pow k m)))
12.7b
(cbrt (* (/ (fma k (+ 10.0 k) 1.0) (pow k m)) (sqrt (/ (fma k (+ 10.0 k) 1.0) (pow k m)))))

rewrite132.0ms

Algorithm
rewrite-expression-head
Rules
1139×times-frac
505×add-sqr-sqrt
492×add-cube-cbrt *-un-lft-identity
425×sqrt-prod
155×unpow-prod-down
91×cbrt-prod
89×associate-/l*
53×sqr-pow
23×div-inv
11×sqrt-div
9×add-exp-log
8×rem-sqrt-square associate-/r/
7×add-cbrt-cube
6×pow1 cbrt-div
4×expm1-log1p-u associate-/r* log1p-expm1-u add-log-exp
3×cbrt-undiv div-exp
2×frac-times sqrt-pow1 pow1/2 associate-*r/ associate-*l/
1×frac-2neg pow1/3 pow3 clear-num rem-cbrt-cube associate-/l/
Counts
4 → 566
Calls
4 calls:
52.0ms
(/ (/ a (sqrt (/ (fma k (+ 10.0 k) 1.0) (pow k m)))) (cbrt (* (/ (fma k (+ 10.0 k) 1.0) (pow k m)) (sqrt (/ (fma k (+ 10.0 k) 1.0) (pow k m))))))
8.0ms
(sqrt (/ (fma k (+ 10.0 k) 1.0) (pow k m)))
8.0ms
(sqrt (/ (fma k (+ 10.0 k) 1.0) (pow k m)))
14.0ms
(cbrt (* (/ (fma k (+ 10.0 k) 1.0) (pow k m)) (sqrt (/ (fma k (+ 10.0 k) 1.0) (pow k m)))))

series469.0ms

Counts
4 → 12
Calls
4 calls:
119.0ms
(/ (/ a (sqrt (/ (fma k (+ 10.0 k) 1.0) (pow k m)))) (cbrt (* (/ (fma k (+ 10.0 k) 1.0) (pow k m)) (sqrt (/ (fma k (+ 10.0 k) 1.0) (pow k m))))))
112.0ms
(sqrt (/ (fma k (+ 10.0 k) 1.0) (pow k m)))
119.0ms
(sqrt (/ (fma k (+ 10.0 k) 1.0) (pow k m)))
118.0ms
(cbrt (* (/ (fma k (+ 10.0 k) 1.0) (pow k m)) (sqrt (/ (fma k (+ 10.0 k) 1.0) (pow k m)))))

simplify1.2s

Counts
578 → 578
Iterations

Useful iterations: done (1.2s)

IterNodesCost
0107333874
1229532973
done500026476

prune2.8s

Pruning

4 alts after pruning (1 fresh and 3 done)

Merged error: 0.0b

regimes87.0ms

bsearch2.0ms