Details

Time bar (total: 14.4s)

sample39.0ms

Algorithm
intervals
Results
15.0ms387×body80valid
4.0ms135×body80nan

simplify2.1s

Counts
1 → 1
Iterations

Useful iterations: 2 (6.0ms)

IterNodesCost
01215
12415
24813
39513
423913
571813
6274513
done500013

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 2.6b

localize9.0ms

Local error

Found 3 expressions with local error:

0.0b
(/ (+ (* k (+ 10.0 k)) 1.0) (pow k m))
0.0b
(* k (+ 10.0 k))
2.6b
(/ a (/ (+ (* k (+ 10.0 k)) 1.0) (pow k m)))

rewrite92.0ms

Algorithm
rewrite-expression-head
Rules
180×times-frac
105×add-sqr-sqrt *-un-lft-identity
103×add-cube-cbrt
48×unpow-prod-down
32×associate-/r*
20×add-exp-log
16×sqr-pow
12×add-cbrt-cube
10×div-exp
6×div-inv associate-/l*
5×pow1
4×cbrt-undiv associate-*r*
3×associate-*l* add-log-exp
2×pow-to-exp frac-2neg flip3-+ associate-*r/ pow-exp clear-num flip-+ associate-/l/
1×distribute-rgt-in distribute-lft-in pow-prod-down prod-exp associate-/r/ *-commutative cbrt-unprod distribute-lft-out unswap-sqr
Counts
3 → 190
Calls
3 calls:
35.0ms
(/ (+ (* k (+ 10.0 k)) 1.0) (pow k m))
19.0ms
(* k (+ 10.0 k))
30.0ms
(/ a (/ (+ (* k (+ 10.0 k)) 1.0) (pow k m)))

series237.0ms

Counts
3 → 9
Calls
3 calls:
67.0ms
(/ (+ (* k (+ 10.0 k)) 1.0) (pow k m))
48.0ms
(* k (+ 10.0 k))
123.0ms
(/ a (/ (+ (* k (+ 10.0 k)) 1.0) (pow k m)))

simplify1.5s

Counts
199 → 199
Iterations

Useful iterations: done (1.5s)

IterNodesCost
03664560
18404341
228514178
done50014148

prune505.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 2.6b

localize9.0ms

Local error

Found 3 expressions with local error:

0.0b
(* k (+ 10.0 k))
0.3b
(/ (pow k m) (+ (* k (+ 10.0 k)) 1.0))
2.4b
(* a (/ (pow k m) (+ (* k (+ 10.0 k)) 1.0)))

rewrite102.0ms

Algorithm
rewrite-expression-head
Rules
48×add-sqr-sqrt
45×times-frac
38×*-un-lft-identity
36×add-cube-cbrt
31×associate-*r*
22×unpow-prod-down
20×add-exp-log
12×add-cbrt-cube
8×sqr-pow
7×pow1 associate-/l*
6×div-exp associate-*l*
5×prod-exp unswap-sqr
4×associate-/r/
3×flip3-+ associate-*r/ associate-/r* cbrt-unprod flip-+ add-log-exp
2×cbrt-undiv pow-to-exp pow-prod-down pow-exp *-commutative div-inv
1×distribute-rgt-in frac-2neg distribute-lft-in clear-num distribute-lft-out
Counts
3 → 120
Calls
3 calls:
20.0ms
(* k (+ 10.0 k))
22.0ms
(/ (pow k m) (+ (* k (+ 10.0 k)) 1.0))
54.0ms
(* a (/ (pow k m) (+ (* k (+ 10.0 k)) 1.0)))

series231.0ms

Counts
3 → 9
Calls
3 calls:
42.0ms
(* k (+ 10.0 k))
70.0ms
(/ (pow k m) (+ (* k (+ 10.0 k)) 1.0))
119.0ms
(* a (/ (pow k m) (+ (* k (+ 10.0 k)) 1.0)))

simplify903.0ms

Counts
129 → 129
Iterations

Useful iterations: done (899.0ms)

IterNodesCost
02402271
15872164
217952038
done50001984

prune319.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.0b

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b
(/ (/ (pow k m) (sqrt (+ (* k (+ 10.0 k)) 1.0))) (sqrt (+ (* k (+ 10.0 k)) 1.0)))
2.4b
(* a (/ (/ (pow k m) (sqrt (+ (* k (+ 10.0 k)) 1.0))) (sqrt (+ (* k (+ 10.0 k)) 1.0))))
15.0b
(sqrt (+ (* k (+ 10.0 k)) 1.0))
15.0b
(sqrt (+ (* k (+ 10.0 k)) 1.0))

rewrite340.0ms

Algorithm
rewrite-expression-head
Rules
1148×times-frac
607×add-sqr-sqrt
583×sqrt-prod
553×add-cube-cbrt *-un-lft-identity
294×associate-*r*
238×unpow-prod-down
82×sqr-pow
48×associate-/l*
34×sqrt-div
30×add-exp-log associate-/r/
18×add-cbrt-cube
17×flip3-+ flip-+
15×div-inv unswap-sqr
14×div-exp
8×pow1
6×cbrt-undiv associate-/r*
5×prod-exp
4×add-log-exp
3×associate-*l* cbrt-unprod
2×pow-to-exp rem-sqrt-square sqrt-pow1 pow1/2 pow-exp
1×frac-2neg associate-*r/ pow-prod-down clear-num *-commutative associate-/l/
Counts
4 → 721
Calls
4 calls:
70.0ms
(/ (/ (pow k m) (sqrt (+ (* k (+ 10.0 k)) 1.0))) (sqrt (+ (* k (+ 10.0 k)) 1.0)))
178.0ms
(* a (/ (/ (pow k m) (sqrt (+ (* k (+ 10.0 k)) 1.0))) (sqrt (+ (* k (+ 10.0 k)) 1.0))))
15.0ms
(sqrt (+ (* k (+ 10.0 k)) 1.0))
15.0ms
(sqrt (+ (* k (+ 10.0 k)) 1.0))

series279.0ms

Counts
4 → 12
Calls
4 calls:
65.0ms
(/ (/ (pow k m) (sqrt (+ (* k (+ 10.0 k)) 1.0))) (sqrt (+ (* k (+ 10.0 k)) 1.0)))
119.0ms
(* a (/ (/ (pow k m) (sqrt (+ (* k (+ 10.0 k)) 1.0))) (sqrt (+ (* k (+ 10.0 k)) 1.0))))
48.0ms
(sqrt (+ (* k (+ 10.0 k)) 1.0))
46.0ms
(sqrt (+ (* k (+ 10.0 k)) 1.0))

simplify1.9s

Counts
733 → 733
Iterations

Useful iterations: done (1.8s)

IterNodesCost
080126276
1185822521
2441620830
done500020040

prune1.2s

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.0b

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b
(/ (/ (pow k (/ m 2)) (sqrt (+ (* k (+ 10.0 k)) 1.0))) (sqrt (+ (* k (+ 10.0 k)) 1.0)))
2.4b
(* (* a (pow k (/ m 2))) (/ (/ (pow k (/ m 2)) (sqrt (+ (* k (+ 10.0 k)) 1.0))) (sqrt (+ (* k (+ 10.0 k)) 1.0))))
15.0b
(sqrt (+ (* k (+ 10.0 k)) 1.0))
15.0b
(sqrt (+ (* k (+ 10.0 k)) 1.0))

rewrite305.0ms

Algorithm
rewrite-expression-head
Rules
1122×times-frac
570×sqrt-prod
554×add-sqr-sqrt
552×add-cube-cbrt *-un-lft-identity
294×associate-*r*
234×unpow-prod-down
88×add-exp-log
78×sqr-pow
48×associate-/l*
35×div-exp prod-exp
34×sqrt-div
30×associate-/r/ add-cbrt-cube
17×flip3-+ flip-+
15×div-inv
10×pow-to-exp pow-exp
9×cbrt-undiv cbrt-unprod
8×pow1
6×associate-/r*
4×add-log-exp
2×rem-sqrt-square sqrt-pow1 pow1/2
1×frac-2neg associate-*r/ associate-*l* pow-prod-down clear-num *-commutative associate-/l/
Counts
4 → 722
Calls
4 calls:
66.0ms
(/ (/ (pow k (/ m 2)) (sqrt (+ (* k (+ 10.0 k)) 1.0))) (sqrt (+ (* k (+ 10.0 k)) 1.0)))
149.0ms
(* (* a (pow k (/ m 2))) (/ (/ (pow k (/ m 2)) (sqrt (+ (* k (+ 10.0 k)) 1.0))) (sqrt (+ (* k (+ 10.0 k)) 1.0))))
15.0ms
(sqrt (+ (* k (+ 10.0 k)) 1.0))
15.0ms
(sqrt (+ (* k (+ 10.0 k)) 1.0))

series301.0ms

Counts
4 → 12
Calls
4 calls:
66.0ms
(/ (/ (pow k (/ m 2)) (sqrt (+ (* k (+ 10.0 k)) 1.0))) (sqrt (+ (* k (+ 10.0 k)) 1.0)))
139.0ms
(* (* a (pow k (/ m 2))) (/ (/ (pow k (/ m 2)) (sqrt (+ (* k (+ 10.0 k)) 1.0))) (sqrt (+ (* k (+ 10.0 k)) 1.0))))
45.0ms
(sqrt (+ (* k (+ 10.0 k)) 1.0))
52.0ms
(sqrt (+ (* k (+ 10.0 k)) 1.0))

simplify1.1s

Counts
734 → 734
Iterations

Useful iterations: done (1.1s)

IterNodesCost
081730090
1222425632
done500024065

prune1.6s

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0.0b

regimes68.0ms

Accuracy

98.4% (0.0b remaining)

Error of 0.1b against oracle of 0.0b and baseline of 2.1b

bsearch54.0ms

Steps
ItersRangePoint
8
4.3686855948509866e+58
2.0359353864836098e+63
5.955206810537291e+60

simplify4.0ms

Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
03058
13658
done3658

end0.0ms

sample1.1s

Algorithm
intervals
Results
482.0ms11812×body80valid
139.0ms4093×body80nan