Details

Time bar (total: 18.0s)

sample91.0ms

Algorithm
intervals
Results
37.0ms386×body80valid
12.0ms152×body80nan

simplify1.4s

Counts
1 → 1
Iterations

Useful iterations: 3 (29.0ms)

IterNodesCost
01215
12415
25313
310812
427412
5147512
done500112

prune23.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 1.7b

localize37.0ms

Local error

Found 3 expressions with local error:

0.0b
(+ (+ 1.0 (* 10.0 k)) (* k k))
0.0b
(* a (pow k m))
1.7b
(/ (* a (pow k m)) (+ (+ 1.0 (* 10.0 k)) (* k k)))

rewrite77.0ms

Algorithm
rewrite-expression-head
Rules
18×add-exp-log
14×add-sqr-sqrt
10×add-cbrt-cube
9×*-un-lft-identity add-cube-cbrt
8×add-log-exp
7×associate-*r*
6×prod-exp
4×unpow-prod-down div-exp
3×expm1-log1p-u pow1 associate-/r* sum-log fma-def times-frac associate-*l* log1p-expm1-u unswap-sqr
2×pow-to-exp cbrt-undiv flip3-+ pow-exp associate-/r/ cbrt-unprod flip-+ sqr-pow
1×+-commutative associate-+l+ clear-num frac-2neg *-commutative div-inv associate-/l*
Counts
3 → 72
Calls
3 calls:
32.0ms
(+ (+ 1.0 (* 10.0 k)) (* k k))
10.0ms
(* a (pow k m))
32.0ms
(/ (* a (pow k m)) (+ (+ 1.0 (* 10.0 k)) (* k k)))

series269.0ms

Counts
3 → 9
Calls
3 calls:
27.0ms
(+ (+ 1.0 (* 10.0 k)) (* k k))
87.0ms
(* a (pow k m))
155.0ms
(/ (* a (pow k m)) (+ (+ 1.0 (* 10.0 k)) (* k k)))

simplify1.7s

Counts
81 → 81
Iterations

Useful iterations: done (1.7s)

IterNodesCost
01601204
14391146
22257929
done5001876

prune475.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.0b

localize29.0ms

Local error

Found 4 expressions with local error:

0.0b
(+ (+ 1.0 (* 10.0 k)) (* k k))
0.0b
(* a (pow k (/ m 2)))
0.0b
(* (* a (pow k (/ m 2))) (pow k (/ m 2)))
1.7b
(/ (* (* a (pow k (/ m 2))) (pow k (/ m 2))) (+ (+ 1.0 (* 10.0 k)) (* k k)))

rewrite171.0ms

Algorithm
rewrite-expression-head
Rules
75×add-exp-log
45×prod-exp
20×add-cbrt-cube
17×add-sqr-sqrt
15×pow-to-exp pow-exp
14×associate-*r*
13×div-exp
12×*-un-lft-identity add-cube-cbrt
9×add-log-exp
7×unpow-prod-down cbrt-unprod
4×expm1-log1p-u pow1 associate-*l* log1p-expm1-u
3×cbrt-undiv associate-/r* sum-log fma-def times-frac unswap-sqr sqr-pow
2×flip3-+ associate-/r/ *-commutative flip-+
1×+-commutative associate-+l+ clear-num frac-2neg div-inv associate-/l*
Counts
4 → 114
Calls
4 calls:
40.0ms
(+ (+ 1.0 (* 10.0 k)) (* k k))
19.0ms
(* a (pow k (/ m 2)))
29.0ms
(* (* a (pow k (/ m 2))) (pow k (/ m 2)))
76.0ms
(/ (* (* a (pow k (/ m 2))) (pow k (/ m 2))) (+ (+ 1.0 (* 10.0 k)) (* k k)))

series511.0ms

Counts
4 → 12
Calls
4 calls:
36.0ms
(+ (+ 1.0 (* 10.0 k)) (* k k))
109.0ms
(* a (pow k (/ m 2)))
136.0ms
(* (* a (pow k (/ m 2))) (pow k (/ m 2)))
230.0ms
(/ (* (* a (pow k (/ m 2))) (pow k (/ m 2))) (+ (+ 1.0 (* 10.0 k)) (* k k)))

simplify2.3s

Counts
126 → 126
Iterations

Useful iterations: done (2.3s)

IterNodesCost
02002456
15732063
238171701
done50011636

prune679.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.0b

localize44.0ms

Local error

Found 4 expressions with local error:

0.6b
(cbrt k)
0.6b
(cbrt k)
0.6b
(cbrt k)
1.7b
(/ (* (* (* a (pow (* (cbrt k) (cbrt k)) (/ m 2))) (pow (cbrt k) (/ m 2))) (pow k (/ m 2))) (+ (+ 1.0 (* 10.0 k)) (* k k)))

rewrite123.0ms

Algorithm
rewrite-expression-head
Rules
200×add-exp-log
138×prod-exp
49×div-exp pow-exp
40×pow-to-exp
18×add-cbrt-cube
9×cbrt-prod add-sqr-sqrt *-un-lft-identity add-cube-cbrt
6×cbrt-unprod
4×expm1-log1p-u pow1 cbrt-undiv log1p-expm1-u add-log-exp
3×associate-/r* times-frac pow1/3
2×associate-/r/
1×clear-num frac-2neg flip3-+ flip-+ div-inv associate-/l*
Counts
4 → 113
Calls
4 calls:
1.0ms
(cbrt k)
1.0ms
(cbrt k)
1.0ms
(cbrt k)
108.0ms
(/ (* (* (* a (pow (* (cbrt k) (cbrt k)) (/ m 2))) (pow (cbrt k) (/ m 2))) (pow k (/ m 2))) (+ (+ 1.0 (* 10.0 k)) (* k k)))

series1.5s

Counts
4 → 12
Calls
4 calls:
235.0ms
(cbrt k)
291.0ms
(cbrt k)
204.0ms
(cbrt k)
719.0ms
(/ (* (* (* a (pow (* (cbrt k) (cbrt k)) (/ m 2))) (pow (cbrt k) (/ m 2))) (pow k (/ m 2))) (+ (+ 1.0 (* 10.0 k)) (* k k)))

simplify1.6s

Counts
125 → 125
Iterations

Useful iterations: done (1.6s)

IterNodesCost
02473690
16973326
237292745
done50012532

prune704.0ms

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0.0b

localize53.0ms

Local error

Found 4 expressions with local error:

0.0b
(/ (* (/ a (sqrt (fma (+ 10.0 k) k 1.0))) (pow k m)) (sqrt (+ (+ 1.0 (* 10.0 k)) (* k k))))
0.0b
(/ a (sqrt (fma (+ 10.0 k) k 1.0)))
15.4b
(sqrt (fma (+ 10.0 k) k 1.0))
15.4b
(sqrt (+ (+ 1.0 (* 10.0 k)) (* k k)))

rewrite106.0ms

Algorithm
rewrite-expression-head
Rules
28×add-sqr-sqrt
27×add-exp-log
25×*-un-lft-identity add-cube-cbrt
24×times-frac sqrt-prod
15×add-cbrt-cube
12×associate-/r*
11×div-exp
6×pow1 prod-exp
5×cbrt-undiv
4×expm1-log1p-u sqrt-div log1p-expm1-u associate-/l* add-log-exp
2×pow-to-exp rem-sqrt-square clear-num frac-2neg sqrt-pow1 flip3-+ pow1/2 pow-exp associate-/r/ cbrt-unprod flip-+ div-inv
1×associate-*l/ hypot-def associate-/l/
Counts
4 → 112
Calls
4 calls:
43.0ms
(/ (* (/ a (sqrt (fma (+ 10.0 k) k 1.0))) (pow k m)) (sqrt (+ (+ 1.0 (* 10.0 k)) (* k k))))
10.0ms
(/ a (sqrt (fma (+ 10.0 k) k 1.0)))
2.0ms
(sqrt (fma (+ 10.0 k) k 1.0))
48.0ms
(sqrt (+ (+ 1.0 (* 10.0 k)) (* k k)))

series584.0ms

Counts
4 → 12
Calls
4 calls:
290.0ms
(/ (* (/ a (sqrt (fma (+ 10.0 k) k 1.0))) (pow k m)) (sqrt (+ (+ 1.0 (* 10.0 k)) (* k k))))
146.0ms
(/ a (sqrt (fma (+ 10.0 k) k 1.0)))
84.0ms
(sqrt (fma (+ 10.0 k) k 1.0))
65.0ms
(sqrt (+ (+ 1.0 (* 10.0 k)) (* k k)))

simplify1.6s

Counts
124 → 124
Iterations

Useful iterations: done (1.6s)

IterNodesCost
02482645
16272411
229802095
done50012028

prune883.0ms

Pruning

5 alts after pruning (2 fresh and 3 done)

Merged error: 0.0b

regimes237.0ms

Accuracy

94.8% (0.1b remaining)

Error of 0.2b against oracle of 0.0b and baseline of 2.1b

bsearch104.0ms

Steps
ItersRangePoint
6
5.172846739179762e+122
3.935844582495948e+123
9.32143918529101e+122

simplify10.0ms

Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
04279
15479
26079
36679
done6679

end0.0ms

sample2.7s

Algorithm
intervals
Results
1.2s11894×body80valid
731.0ms4343×body80nan