Details

Time bar (total: 16.8s)

sample71.0ms

Algorithm
intervals
Results
36.0ms381×body80valid
7.0ms111×body80nan

simplify3.2s

Counts
1 → 1
Iterations

Useful iterations: 3 (21.0ms)

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

localize28.0ms

Local error

Found 4 expressions with local error:

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

rewrite93.0ms

Algorithm
rewrite-expression-head
Rules
19×add-exp-log
16×add-sqr-sqrt
11×add-cube-cbrt *-un-lft-identity add-cbrt-cube add-log-exp
7×associate-*r*
6×fma-def prod-exp
4×pow1 expm1-log1p-u unpow-prod-down div-exp sum-log log1p-expm1-u
3×flip3-+ times-frac associate-*l* associate-/r* flip-+ unswap-sqr
2×cbrt-undiv +-commutative pow-to-exp pow-exp associate-/r/ cbrt-unprod sqr-pow
1×associate-+l+ frac-2neg clear-num *-commutative div-inv associate-/l*
Counts
4 → 88
Calls
4 calls:
6.0ms
(+ 1.0 (* 10.0 k))
37.0ms
(+ (+ 1.0 (* 10.0 k)) (* k k))
12.0ms
(* a (pow k m))
36.0ms
(/ (* a (pow k m)) (+ (+ 1.0 (* 10.0 k)) (* k k)))

series376.0ms

Counts
4 → 12
Calls
4 calls:
46.0ms
(+ 1.0 (* 10.0 k))
35.0ms
(+ (+ 1.0 (* 10.0 k)) (* k k))
115.0ms
(* a (pow k m))
178.0ms
(/ (* a (pow k m)) (+ (+ 1.0 (* 10.0 k)) (* k k)))

simplify1.2s

Counts
100 → 100
Iterations

Useful iterations: done (1.2s)

IterNodesCost
01791340
14711136
21628982
done5000933

prune422.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.1b

localize23.0ms

Local error

Found 4 expressions with local error:

0.6b
(cbrt k)
0.6b
(cbrt k)
0.6b
(cbrt k)
2.1b
(/ (* (* a (pow (* (cbrt k) (cbrt k)) m)) (pow (cbrt k) m)) (+ (+ 1.0 (* 10.0 k)) (* k k)))

rewrite118.0ms

Algorithm
rewrite-expression-head
Rules
58×add-exp-log
30×prod-exp
16×div-exp
13×add-cbrt-cube
11×pow-exp
9×cbrt-prod add-sqr-sqrt add-cube-cbrt *-un-lft-identity
8×pow-to-exp
4×pow1 expm1-log1p-u log1p-expm1-u add-log-exp
3×cbrt-undiv times-frac pow1/3 associate-/r* cbrt-unprod
2×associate-/r/
1×frac-2neg flip3-+ clear-num flip-+ div-inv associate-/l*
Counts
4 → 79
Calls
4 calls:
2.0ms
(cbrt k)
2.0ms
(cbrt k)
2.0ms
(cbrt k)
108.0ms
(/ (* (* a (pow (* (cbrt k) (cbrt k)) m)) (pow (cbrt k) m)) (+ (+ 1.0 (* 10.0 k)) (* k k)))

series1.6s

Counts
4 → 12
Calls
4 calls:
348.0ms
(cbrt k)
329.0ms
(cbrt k)
301.0ms
(cbrt k)
624.0ms
(/ (* (* a (pow (* (cbrt k) (cbrt k)) m)) (pow (cbrt k) m)) (+ (+ 1.0 (* 10.0 k)) (* k k)))

simplify1.2s

Counts
91 → 91
Iterations

Useful iterations: done (1.2s)

IterNodesCost
01801717
14951486
220971234
done50001164

prune484.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.1b

localize32.0ms

Local error

Found 4 expressions with local error:

0.0b
(+ (+ 1.0 (* 10.0 k)) (* k k))
0.0b
(* (* a (pow k (/ m 2))) (pow k (/ m 2)))
0.0b
(* a (pow k (/ m 2)))
2.1b
(/ (* (* a (pow k (/ m 2))) (pow k (/ m 2))) (+ (+ 1.0 (* 10.0 k)) (* k k)))

rewrite183.0ms

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×add-cube-cbrt *-un-lft-identity
9×add-log-exp
7×unpow-prod-down cbrt-unprod
4×pow1 expm1-log1p-u associate-*l* log1p-expm1-u
3×cbrt-undiv fma-def times-frac associate-/r* sum-log unswap-sqr sqr-pow
2×flip3-+ associate-/r/ *-commutative flip-+
1×+-commutative associate-+l+ frac-2neg clear-num div-inv associate-/l*
Counts
4 → 114
Calls
4 calls:
29.0ms
(+ (+ 1.0 (* 10.0 k)) (* k k))
43.0ms
(* (* a (pow k (/ m 2))) (pow k (/ m 2)))
14.0ms
(* a (pow k (/ m 2)))
92.0ms
(/ (* (* a (pow k (/ m 2))) (pow k (/ m 2))) (+ (+ 1.0 (* 10.0 k)) (* k k)))

series456.0ms

Counts
4 → 12
Calls
4 calls:
26.0ms
(+ (+ 1.0 (* 10.0 k)) (* k k))
113.0ms
(* (* a (pow k (/ m 2))) (pow k (/ m 2)))
105.0ms
(* a (pow k (/ m 2)))
210.0ms
(/ (* (* a (pow k (/ m 2))) (pow k (/ m 2))) (+ (+ 1.0 (* 10.0 k)) (* k k)))

simplify1.2s

Counts
126 → 126
Iterations

Useful iterations: done (1.2s)

IterNodesCost
02012456
15401932
221191623
done50011608

prune530.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0.1b

localize41.0ms

Local error

Found 4 expressions with local error:

0.0b
(* a (pow k (* 2 (/ m 2))))
0.0b
(pow (* a (pow k (* 2 (/ m 2)))) 3)
2.1b
(/ (cbrt (pow (* a (pow k (* 2 (/ m 2)))) 3)) (+ (+ 1.0 (* 10.0 k)) (* k k)))
15.4b
(cbrt (pow (* a (pow k (* 2 (/ m 2)))) 3))

rewrite102.0ms

Algorithm
rewrite-expression-head
Rules
40×cbrt-prod
34×add-sqr-sqrt
33×times-frac
29×add-cube-cbrt *-un-lft-identity
17×add-exp-log
11×associate-/l*
10×unpow-prod-down add-cbrt-cube
8×sqr-pow
7×associate-*r*
6×cube-mult unpow3 cube-prod pow-exp prod-exp
5×pow1
4×expm1-log1p-u log1p-expm1-u add-log-exp
3×pow-to-exp pow-unpow associate-*l* associate-/r* unswap-sqr
2×associate-/r/ cbrt-unprod rem-cube-cbrt
1×cbrt-undiv pow-pow frac-2neg flip3-+ pow1/3 div-exp clear-num *-commutative rem-cbrt-cube flip-+ div-inv
Counts
4 → 134
Calls
4 calls:
17.0ms
(* a (pow k (* 2 (/ m 2))))
17.0ms
(pow (* a (pow k (* 2 (/ m 2)))) 3)
55.0ms
(/ (cbrt (pow (* a (pow k (* 2 (/ m 2)))) 3)) (+ (+ 1.0 (* 10.0 k)) (* k k)))
9.0ms
(cbrt (pow (* a (pow k (* 2 (/ m 2)))) 3))

series525.0ms

Counts
4 → 12
Calls
4 calls:
84.0ms
(* a (pow k (* 2 (/ m 2))))
120.0ms
(pow (* a (pow k (* 2 (/ m 2)))) 3)
212.0ms
(/ (cbrt (pow (* a (pow k (* 2 (/ m 2)))) 3)) (+ (+ 1.0 (* 10.0 k)) (* k k)))
109.0ms
(cbrt (pow (* a (pow k (* 2 (/ m 2)))) 3))

simplify1.3s

Counts
146 → 146
Iterations

Useful iterations: done (1.3s)

IterNodesCost
02473635
15283103
219512800
done50002658

prune682.0ms

Pruning

4 alts after pruning (1 fresh and 3 done)

Merged error: 0.1b

regimes127.0ms

Accuracy

98.6% (0.0b remaining)

Error of 0.1b against oracle of 0.1b and baseline of 2.3b

bsearch84.0ms

Steps
ItersRangePoint
7
2.3568880196050932e+137
3.236469685930235e+139
5.978361395410556e+138

simplify9.0ms

Iterations

Useful iterations: 1 (5.0ms)

IterNodesCost
03560
14256
done4256

end0.0ms

sample2.7s

Algorithm
intervals
Results
1.5s11757×body80valid
412.0ms4170×body80nan