Details

Time bar (total: 17.8s)

sample71.0ms

Algorithm
intervals
Results
34.0ms369×body80valid
8.0ms133×body80nan

simplify3.1s

Counts
1 → 1
Iterations

Useful iterations: 3 (21.0ms)

IterNodesCost
01215
12415
25313
310712
425412
573512
6272912
done500112

prune23.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 1.4b

localize25.0ms

Local error

Found 3 expressions with local error:

0.0b
(+ 1.0 (* 10.0 k))
0.0b
(+ (+ 1.0 (* 10.0 k)) (* k k))
1.4b
(/ (* a (pow k m)) (+ (+ 1.0 (* 10.0 k)) (* k k)))

rewrite99.0ms

Algorithm
rewrite-expression-head
Rules
13×add-exp-log
10×add-log-exp
8×add-cbrt-cube
7×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
6×fma-def
4×div-exp sum-log
3×pow1 expm1-log1p-u flip3-+ times-frac prod-exp associate-/r* flip-+ log1p-expm1-u
2×cbrt-undiv +-commutative associate-/r/
1×pow-to-exp associate-+l+ frac-2neg pow-exp clear-num cbrt-unprod div-inv associate-/l*
Counts
3 → 61
Calls
3 calls:
6.0ms
(+ 1.0 (* 10.0 k))
53.0ms
(+ (+ 1.0 (* 10.0 k)) (* k k))
38.0ms
(/ (* a (pow k m)) (+ (+ 1.0 (* 10.0 k)) (* k k)))

series301.0ms

Counts
3 → 9
Calls
3 calls:
57.0ms
(+ 1.0 (* 10.0 k))
34.0ms
(+ (+ 1.0 (* 10.0 k)) (* k k))
210.0ms
(/ (* a (pow k m)) (+ (+ 1.0 (* 10.0 k)) (* k k)))

simplify1.1s

Counts
70 → 70
Iterations

Useful iterations: done (1.1s)

IterNodesCost
01471091
1416904
21528765
done5001721

prune345.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.0b

localize12.0ms

Local error

Found 2 expressions with local error:

0.2b
(/ 1 (fma k (+ 10.0 k) 1.0))
1.2b
(* (* a (pow k m)) (/ 1 (fma k (+ 10.0 k) 1.0)))

rewrite61.0ms

Algorithm
rewrite-expression-head
Rules
50×add-exp-log
28×prod-exp
18×times-frac
17×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
16×add-cbrt-cube
13×associate-*r*
10×div-exp
6×cbrt-unprod
5×pow1 rec-exp 1-exp
4×pow-to-exp pow-exp
3×cbrt-undiv associate-/r* associate-/l*
2×expm1-log1p-u log1p-expm1-u div-inv add-log-exp
1×pow-flip frac-2neg associate-*r/ associate-*l* pow-prod-down clear-num un-div-inv *-commutative inv-pow
Counts
2 → 80
Calls
2 calls:
10.0ms
(/ 1 (fma k (+ 10.0 k) 1.0))
49.0ms
(* (* a (pow k m)) (/ 1 (fma k (+ 10.0 k) 1.0)))

series199.0ms

Counts
2 → 6
Calls
2 calls:
38.0ms
(/ 1 (fma k (+ 10.0 k) 1.0))
161.0ms
(* (* a (pow k m)) (/ 1 (fma k (+ 10.0 k) 1.0)))

simplify2.0s

Counts
86 → 86
Iterations

Useful iterations: done (2.0s)

IterNodesCost
01641472
14131266
213171098
done50001067

prune309.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.0b

localize27.0ms

Local error

Found 4 expressions with local error:

0.0b
(log1p (expm1 (/ 1 (fma k (+ 10.0 k) 1.0))))
0.2b
(/ 1 (fma k (+ 10.0 k) 1.0))
0.5b
(expm1 (/ 1 (fma k (+ 10.0 k) 1.0)))
1.2b
(* (* a (pow k m)) (log1p (expm1 (/ 1 (fma k (+ 10.0 k) 1.0)))))

rewrite41.0ms

Algorithm
rewrite-expression-head
Rules
18×add-exp-log
13×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
11×add-cbrt-cube
9×times-frac
7×pow1 prod-exp
5×log1p-expm1-u
4×expm1-log1p-u add-log-exp
3×associate-*r* associate-/r* cbrt-unprod associate-/l*
2×div-exp
1×cbrt-undiv pow-to-exp rec-exp log1p-udef expm1-log1p pow-flip frac-2neg 1-exp log1p-expm1 associate-*l* pow-prod-down pow-exp clear-num *-commutative div-inv inv-pow expm1-udef
Counts
4 → 76
Calls
4 calls:
0.0ms
(log1p (expm1 (/ 1 (fma k (+ 10.0 k) 1.0))))
6.0ms
(/ 1 (fma k (+ 10.0 k) 1.0))
0.0ms
(expm1 (/ 1 (fma k (+ 10.0 k) 1.0)))
33.0ms
(* (* a (pow k m)) (log1p (expm1 (/ 1 (fma k (+ 10.0 k) 1.0)))))

series670.0ms

Counts
4 → 12
Calls
4 calls:
252.0ms
(log1p (expm1 (/ 1 (fma k (+ 10.0 k) 1.0))))
67.0ms
(/ 1 (fma k (+ 10.0 k) 1.0))
104.0ms
(expm1 (/ 1 (fma k (+ 10.0 k) 1.0)))
246.0ms
(* (* a (pow k m)) (log1p (expm1 (/ 1 (fma k (+ 10.0 k) 1.0)))))

simplify4.3s

Counts
88 → 88
Iterations

Useful iterations: done (4.3s)

IterNodesCost
01761454
13961297
211901094
345831057
done50001053

prune320.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.0b

localize25.0ms

Local error

Found 4 expressions with local error:

0.5b
(expm1 (/ (/ 1 (sqrt (fma k (+ 10.0 k) 1.0))) (sqrt (fma k (+ 10.0 k) 1.0))))
1.2b
(* (* a (pow k m)) (log1p (expm1 (/ (/ 1 (sqrt (fma k (+ 10.0 k) 1.0))) (sqrt (fma k (+ 10.0 k) 1.0))))))
13.2b
(sqrt (fma k (+ 10.0 k) 1.0))
13.2b
(sqrt (fma k (+ 10.0 k) 1.0))

rewrite53.0ms

Algorithm
rewrite-expression-head
Rules
14×add-exp-log
9×add-sqr-sqrt add-cbrt-cube
8×pow1
7×add-cube-cbrt *-un-lft-identity prod-exp
6×sqrt-prod
5×log1p-expm1-u
4×expm1-log1p-u add-log-exp
3×associate-*r* cbrt-unprod
2×rem-sqrt-square sqrt-pow1 pow1/2
1×pow-to-exp expm1-log1p associate-*l* pow-prod-down pow-exp *-commutative expm1-udef
Counts
4 → 62
Calls
4 calls:
1.0ms
(expm1 (/ (/ 1 (sqrt (fma k (+ 10.0 k) 1.0))) (sqrt (fma k (+ 10.0 k) 1.0))))
43.0ms
(* (* a (pow k m)) (log1p (expm1 (/ (/ 1 (sqrt (fma k (+ 10.0 k) 1.0))) (sqrt (fma k (+ 10.0 k) 1.0))))))
3.0ms
(sqrt (fma k (+ 10.0 k) 1.0))
3.0ms
(sqrt (fma k (+ 10.0 k) 1.0))

series536.0ms

Counts
4 → 12
Calls
4 calls:
133.0ms
(expm1 (/ (/ 1 (sqrt (fma k (+ 10.0 k) 1.0))) (sqrt (fma k (+ 10.0 k) 1.0))))
249.0ms
(* (* a (pow k m)) (log1p (expm1 (/ (/ 1 (sqrt (fma k (+ 10.0 k) 1.0))) (sqrt (fma k (+ 10.0 k) 1.0))))))
74.0ms
(sqrt (fma k (+ 10.0 k) 1.0))
79.0ms
(sqrt (fma k (+ 10.0 k) 1.0))

simplify1.4s

Counts
74 → 74
Iterations

Useful iterations: done (1.4s)

IterNodesCost
01571526
13781043
21247880
done5000837

prune295.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0b

regimes110.0ms

Accuracy

98.5% (0.0b remaining)

Error of 0.1b against oracle of 0.1b and baseline of 1.9b

bsearch76.0ms

Steps
ItersRangePoint
8
6.078647819315964e+130
2.9949035539067785e+135
3.8587532980234343e+133

simplify8.0ms

Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
03252
14052
done4052

end0.0ms

sample2.3s

Algorithm
intervals
Results
1.1s11910×body80valid
410.0ms4225×body80nan