Details

Time bar (total: 48.4s)

sample80.0ms

Algorithm
intervals
Results
30.0ms416×body80valid
16.0ms156×body80nan

simplify3.4s

Counts
1 → 1
Iterations

Useful iterations: 3 (33.0ms)

IterNodesCost
01215
12415
25313
310712
425412
573512
6272912
done500112

prune10.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 2.1b

localize22.0ms

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)))

rewrite64.0ms

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:
17.0ms
(/ (fma k (+ 10.0 k) 1.0) (pow k m))
29.0ms
(/ a (/ (fma k (+ 10.0 k) 1.0) (pow k m)))

series260.0ms

Counts
2 → 6
Calls
2 calls:
94.0ms
(/ (fma k (+ 10.0 k) 1.0) (pow k m))
166.0ms
(/ a (/ (fma k (+ 10.0 k) 1.0) (pow k m)))

simplify1.9s

Counts
175 → 175
Iterations

Useful iterations: done (1.9s)

IterNodesCost
03314107
17133899
223573762
done50003717

prune831.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.0b

localize27.0ms

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)))

rewrite785.0ms

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:
38.0ms
(/ a (sqrt (/ (fma k (+ 10.0 k) 1.0) (pow k m))))
120.0ms
(/ (/ a (sqrt (/ (fma k (+ 10.0 k) 1.0) (pow k m)))) (sqrt (/ (fma k (+ 10.0 k) 1.0) (pow k m))))
14.0ms
(sqrt (/ (fma k (+ 10.0 k) 1.0) (pow k m)))
13.0ms
(sqrt (/ (fma k (+ 10.0 k) 1.0) (pow k m)))

series764.0ms

Counts
4 → 12
Calls
4 calls:
260.0ms
(/ a (sqrt (/ (fma k (+ 10.0 k) 1.0) (pow k m))))
150.0ms
(/ (/ a (sqrt (/ (fma k (+ 10.0 k) 1.0) (pow k m)))) (sqrt (/ (fma k (+ 10.0 k) 1.0) (pow k m))))
168.0ms
(sqrt (/ (fma k (+ 10.0 k) 1.0) (pow k m)))
185.0ms
(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

prune20.5s

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0.0b

localize68.0ms

Local error

Found 4 expressions with local error:

16.4b
(sqrt (fma k (+ 10.0 k) 1.0))
16.9b
(cbrt (fma k (+ 10.0 k) 1.0))
16.9b
(cbrt (fma k (+ 10.0 k) 1.0))
16.9b
(cbrt (fma k (+ 10.0 k) 1.0))

rewrite5.0ms

Algorithm
rewrite-expression-head
Rules
9×cbrt-prod add-sqr-sqrt
8×add-cube-cbrt *-un-lft-identity
5×pow1
4×add-exp-log expm1-log1p-u add-cbrt-cube log1p-expm1-u add-log-exp
3×pow1/3 sqrt-prod
1×rem-sqrt-square sqrt-pow1 pow1/2
Counts
4 → 54
Calls
4 calls:
1.0ms
(sqrt (fma k (+ 10.0 k) 1.0))
1.0ms
(cbrt (fma k (+ 10.0 k) 1.0))
1.0ms
(cbrt (fma k (+ 10.0 k) 1.0))
1.0ms
(cbrt (fma k (+ 10.0 k) 1.0))

series634.0ms

Counts
4 → 12
Calls
4 calls:
95.0ms
(sqrt (fma k (+ 10.0 k) 1.0))
203.0ms
(cbrt (fma k (+ 10.0 k) 1.0))
141.0ms
(cbrt (fma k (+ 10.0 k) 1.0))
195.0ms
(cbrt (fma k (+ 10.0 k) 1.0))

simplify3.5s

Counts
66 → 66
Iterations

Useful iterations: 4 (2.0s)

IterNodesCost
089873
1200816
2515758
31403737
44412730
done5000730

prune646.0ms

Pruning

4 alts after pruning (1 fresh and 3 done)

Merged error: 0.0b

localize28.0ms

Local error

Found 4 expressions with local error:

0.8b
(fma (/ (pow (exp m) (+ 0 (log k))) k) (/ a k) (* (/ (pow (exp m) (+ 0 (log k))) (/ (pow k 2) a)) (- (/ 99.0 (pow k 2)) (/ 10.0 k))))
2.3b
(* (/ (pow (exp m) (+ 0 (log k))) (/ (pow k 2) a)) (- (/ 99.0 (pow k 2)) (/ 10.0 k)))
2.3b
(/ (pow (exp m) (+ 0 (log k))) (/ (pow k 2) a))
6.5b
(/ (pow k 2) a)

rewrite717.0ms

Algorithm
rewrite-expression-head
Rules
2050×times-frac
1251×add-sqr-sqrt
1180×*-un-lft-identity
1174×add-cube-cbrt
728×prod-diff
580×unpow-prod-down
366×distribute-rgt-in distribute-lft-in
229×associate-*l*
200×sqr-pow
138×unpow2
102×div-inv
67×add-exp-log
57×unpow-prod-up
45×div-exp
31×associate-/r*
20×add-cbrt-cube
16×associate-/l* unswap-sqr
15×pow-to-exp associate-*r* pow-exp
13×prod-exp
10×difference-of-squares
7×cbrt-undiv
6×pow1
4×expm1-log1p-u log1p-expm1-u add-log-exp
3×frac-times associate-*r/ cbrt-unprod
2×sub-neg flip3-- frac-2neg clear-num associate-/r/ frac-sub flip-- distribute-lft-out--
1×pow-prod-down associate-*l/ *-commutative fma-udef
Counts
4 → 1374
Calls
4 calls:
0.0ms
(fma (/ (pow (exp m) (+ 0 (log k))) k) (/ a k) (* (/ (pow (exp m) (+ 0 (log k))) (/ (pow k 2) a)) (- (/ 99.0 (pow k 2)) (/ 10.0 k))))
478.0ms
(* (/ (pow (exp m) (+ 0 (log k))) (/ (pow k 2) a)) (- (/ 99.0 (pow k 2)) (/ 10.0 k)))
36.0ms
(/ (pow (exp m) (+ 0 (log k))) (/ (pow k 2) a))
8.0ms
(/ (pow k 2) a)

series964.0ms

Counts
4 → 12
Calls
4 calls:
351.0ms
(fma (/ (pow (exp m) (+ 0 (log k))) k) (/ a k) (* (/ (pow (exp m) (+ 0 (log k))) (/ (pow k 2) a)) (- (/ 99.0 (pow k 2)) (/ 10.0 k))))
362.0ms
(* (/ (pow (exp m) (+ 0 (log k))) (/ (pow k 2) a)) (- (/ 99.0 (pow k 2)) (/ 10.0 k)))
213.0ms
(/ (pow (exp m) (+ 0 (log k))) (/ (pow k 2) a))
37.0ms
(/ (pow k 2) a)

simplify3.1s

Counts
1386 → 1386
Iterations

Useful iterations: done (2.9s)

IterNodesCost
0212073010
1488262364
done500060893

prune5.6s

Pruning

5 alts after pruning (1 fresh and 4 done)

Merged error: 0.0b

regimes99.0ms

Accuracy

98.1% (0.0b remaining)

Error of 0.1b against oracle of 0.0b and baseline of 2.0b

bsearch55.0ms

Steps
ItersRangePoint
7
3.169316652691789e+110
2.502942302693858e+112
3.7123001813996137e+111

simplify4.0ms

Iterations

Useful iterations: 1 (2.0ms)

IterNodesCost
03052
13348
done3348

end0.0ms

sample1.6s

Algorithm
intervals
Results
756.0ms11904×body80valid
309.0ms4108×body80nan