Details

Time bar (total: 38.1s)

sample64.0ms

Algorithm
intervals
Results
26.0ms416×body80valid
8.0ms156×body80nan

simplify20.2s

Counts
1 → 1
Iterations

Useful iterations: 3 (690.0ms)

IterNodesCost
01215
13815
220413
3158212
done500012

prune6.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 2.1b

localize10.0ms

Local error

Found 2 expressions with local error:

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

rewrite45.0ms

Algorithm
rewrite-expression-head
Rules
17×add-exp-log
12×add-sqr-sqrt
9×add-cbrt-cube
7×add-cube-cbrt *-un-lft-identity associate-*r*
6×prod-exp
4×unpow-prod-down div-exp
3×times-frac associate-*l* associate-/r* unswap-sqr
2×pow1 cbrt-undiv expm1-log1p-u pow-to-exp pow-exp cbrt-unprod log1p-expm1-u add-log-exp sqr-pow
1×frac-2neg clear-num *-commutative div-inv associate-/l*
Counts
2 → 52
Calls
2 calls:
28.0ms
(* a (pow k m))
13.0ms
(/ (* a (pow k m)) (fma k (+ 10.0 k) 1.0))

series287.0ms

Counts
2 → 6
Calls
2 calls:
88.0ms
(* a (pow k m))
198.0ms
(/ (* a (pow k m)) (fma k (+ 10.0 k) 1.0))

simplify5.1s

Counts
58 → 58
Iterations

Useful iterations: done (5.1s)

IterNodesCost
0134808
13205767
done5001678

prune306.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.0b

localize21.0ms

Local error

Found 3 expressions with local error:

0.0b
(* a (pow k m))
0.1b
(/ 1 (/ (fma k (+ 10.0 k) 1.0) (* a (pow k m))))
2.1b
(/ (fma k (+ 10.0 k) 1.0) (* a (pow k m)))

rewrite83.0ms

Algorithm
rewrite-expression-head
Rules
56×add-exp-log
36×times-frac
29×add-sqr-sqrt
26×div-exp
24×add-cube-cbrt *-un-lft-identity
19×add-cbrt-cube
15×prod-exp
8×associate-/r*
7×cbrt-undiv associate-*r*
6×div-inv associate-/l*
5×pow-to-exp rec-exp 1-exp pow-exp
4×pow1 unpow-prod-down
3×expm1-log1p-u associate-*l* cbrt-unprod log1p-expm1-u add-log-exp unswap-sqr
2×frac-2neg clear-num sqr-pow
1×pow-flip associate-/r/ *-commutative inv-pow
Counts
3 → 116
Calls
3 calls:
18.0ms
(* a (pow k m))
37.0ms
(/ 1 (/ (fma k (+ 10.0 k) 1.0) (* a (pow k m))))
19.0ms
(/ (fma k (+ 10.0 k) 1.0) (* a (pow k m)))

series426.0ms

Counts
3 → 9
Calls
3 calls:
102.0ms
(* a (pow k m))
150.0ms
(/ 1 (/ (fma k (+ 10.0 k) 1.0) (* a (pow k m))))
173.0ms
(/ (fma k (+ 10.0 k) 1.0) (* a (pow k m)))

simplify705.0ms

Counts
125 → 125
Iterations

Useful iterations: done (700.0ms)

IterNodesCost
02302256
done50002137

prune511.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.0b

localize18.0ms

Local error

Found 4 expressions with local error:

0.0b
(* (cbrt (pow k m)) (cbrt (pow k m)))
0.0b
(* (* a (* (cbrt (pow k m)) (cbrt (pow k m)))) (cbrt (pow k m)))
0.1b
(/ 1 (/ (fma k (+ 10.0 k) 1.0) (* (* a (* (cbrt (pow k m)) (cbrt (pow k m)))) (cbrt (pow k m)))))
2.1b
(/ (fma k (+ 10.0 k) 1.0) (* (* a (* (cbrt (pow k m)) (cbrt (pow k m)))) (cbrt (pow k m))))

rewrite625.0ms

Algorithm
rewrite-expression-head
Rules
79×add-exp-log
61×add-sqr-sqrt
59×cbrt-prod
37×add-cube-cbrt *-un-lft-identity
36×times-frac
32×add-cbrt-cube
31×prod-exp
26×div-exp
23×unpow-prod-down
21×pow1
20×associate-*r*
19×cbrt-unprod
16×unswap-sqr
13×cbrt-undiv sqr-pow
11×associate-*l*
10×swap-sqr
8×pow-prod-down associate-/r*
6×pow1/3 div-inv associate-/l*
5×rec-exp 1-exp
4×expm1-log1p-u log1p-expm1-u add-log-exp
2×frac-2neg clear-num pow-sqr *-commutative pow-prod-up
1×pow2 pow-flip pow-plus associate-/r/ inv-pow
Counts
4 → 189
Calls
4 calls:
36.0ms
(* (cbrt (pow k m)) (cbrt (pow k m)))
183.0ms
(* (* a (* (cbrt (pow k m)) (cbrt (pow k m)))) (cbrt (pow k m)))
277.0ms
(/ 1 (/ (fma k (+ 10.0 k) 1.0) (* (* a (* (cbrt (pow k m)) (cbrt (pow k m)))) (cbrt (pow k m)))))
120.0ms
(/ (fma k (+ 10.0 k) 1.0) (* (* a (* (cbrt (pow k m)) (cbrt (pow k m)))) (cbrt (pow k m))))

series629.0ms

Counts
4 → 12
Calls
4 calls:
169.0ms
(* (cbrt (pow k m)) (cbrt (pow k m)))
118.0ms
(* (* a (* (cbrt (pow k m)) (cbrt (pow k m)))) (cbrt (pow k m)))
170.0ms
(/ 1 (/ (fma k (+ 10.0 k) 1.0) (* (* a (* (cbrt (pow k m)) (cbrt (pow k m)))) (cbrt (pow k m)))))
171.0ms
(/ (fma k (+ 10.0 k) 1.0) (* (* a (* (cbrt (pow k m)) (cbrt (pow k m)))) (cbrt (pow k m))))

simplify634.0ms

Counts
201 → 201
Iterations

Useful iterations: done (625.0ms)

IterNodesCost
03195055
done50004833

prune1.1s

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0.0b

localize17.0ms

Local error

Found 4 expressions with local error:

2.1b
(/ (fma k (+ 10.0 k) 1.0) (* a (pow k m)))
2.1b
(/ (fma k (+ 10.0 k) 1.0) (* a (pow k m)))
9.8b
(sqrt (/ 1 (/ (fma k (+ 10.0 k) 1.0) (* a (pow k m)))))
9.8b
(sqrt (/ 1 (/ (fma k (+ 10.0 k) 1.0) (* a (pow k m)))))

rewrite111.0ms

Algorithm
rewrite-expression-head
Rules
70×times-frac
52×sqrt-prod
44×add-sqr-sqrt
38×*-un-lft-identity
36×add-cube-cbrt
24×add-exp-log
14×add-cbrt-cube
10×div-inv
8×pow1 div-exp
6×rem-sqrt-square sqrt-pow1 prod-exp associate-/l*
4×cbrt-undiv expm1-log1p-u log1p-expm1-u add-log-exp
2×pow-to-exp pow-flip frac-2neg pow1/2 sqrt-div pow-exp clear-num associate-/r* associate-/r/ cbrt-unprod inv-pow
Counts
4 → 136
Calls
4 calls:
18.0ms
(/ (fma k (+ 10.0 k) 1.0) (* a (pow k m)))
19.0ms
(/ (fma k (+ 10.0 k) 1.0) (* a (pow k m)))
40.0ms
(sqrt (/ 1 (/ (fma k (+ 10.0 k) 1.0) (* a (pow k m)))))
24.0ms
(sqrt (/ 1 (/ (fma k (+ 10.0 k) 1.0) (* a (pow k m)))))

series1.1s

Counts
4 → 12
Calls
4 calls:
186.0ms
(/ (fma k (+ 10.0 k) 1.0) (* a (pow k m)))
143.0ms
(/ (fma k (+ 10.0 k) 1.0) (* a (pow k m)))
366.0ms
(sqrt (/ 1 (/ (fma k (+ 10.0 k) 1.0) (* a (pow k m)))))
371.0ms
(sqrt (/ 1 (/ (fma k (+ 10.0 k) 1.0) (* a (pow k m)))))

simplify2.5s

Counts
148 → 148
Iterations

Useful iterations: done (2.5s)

IterNodesCost
02373274
120732952
done50002702

prune741.0ms

Pruning

5 alts after pruning (2 fresh and 3 done)

Merged error: 0.0b

regimes134.0ms

Accuracy

97.9% (0.0b remaining)

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

bsearch16.0ms

Steps
ItersRangePoint
2
9.669451620439698e+25
1.0657150563594859e+26
1.0039838724122883e+26

simplify4.0ms

Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
03157
13857
done3857

end0.0ms

sample2.8s

Algorithm
intervals
Results
1.2s11904×body80valid
828.0ms4108×body80nan