Details

Time bar (total: 15.9s)

sample60.0ms

Algorithm
intervals
Results
24.0ms382×body80valid
7.0ms131×body80nan

simplify1.5s

Counts
1 → 1
Iterations

Useful iterations: 3 (20.0ms)

IterNodesCost
01215
12415
25313
310812
427012
5144212
done500112

prune14.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 2.5b

localize14.0ms

Local error

Found 4 expressions with local error:

0.0b
(+ 1.0 (* 10.0 k))
0.0b
(* a (pow k m))
0.0b
(+ (+ 1.0 (* 10.0 k)) (* k k))
2.5b
(/ (* a (pow k m)) (+ (+ 1.0 (* 10.0 k)) (* k k)))

rewrite136.0ms

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:
12.0ms
(+ 1.0 (* 10.0 k))
24.0ms
(* a (pow k m))
33.0ms
(+ (+ 1.0 (* 10.0 k)) (* k k))
61.0ms
(/ (* a (pow k m)) (+ (+ 1.0 (* 10.0 k)) (* k k)))

series351.0ms

Counts
4 → 12
Calls
4 calls:
61.0ms
(+ 1.0 (* 10.0 k))
95.0ms
(* a (pow k m))
34.0ms
(+ (+ 1.0 (* 10.0 k)) (* k k))
161.0ms
(/ (* a (pow k m)) (+ (+ 1.0 (* 10.0 k)) (* k k)))

simplify1.8s

Counts
100 → 100
Iterations

Useful iterations: done (1.8s)

IterNodesCost
01791340
14991186
22549990
done5000977

prune454.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.2b

localize18.0ms

Local error

Found 4 expressions with local error:

0.0b
(* a (pow k (/ m 2)))
0.0b
(* (* a (pow k (/ m 2))) (pow k (/ m 2)))
0.0b
(+ (+ 1.0 (* 10.0 k)) (* k k))
2.5b
(/ (* (* a (pow k (/ m 2))) (pow k (/ m 2))) (+ (+ 1.0 (* 10.0 k)) (* k k)))

rewrite165.0ms

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:
14.0ms
(* a (pow k (/ m 2)))
32.0ms
(* (* a (pow k (/ m 2))) (pow k (/ m 2)))
33.0ms
(+ (+ 1.0 (* 10.0 k)) (* k k))
81.0ms
(/ (* (* a (pow k (/ m 2))) (pow k (/ m 2))) (+ (+ 1.0 (* 10.0 k)) (* k k)))

series476.0ms

Counts
4 → 12
Calls
4 calls:
120.0ms
(* a (pow k (/ m 2)))
145.0ms
(* (* a (pow k (/ m 2))) (pow k (/ m 2)))
22.0ms
(+ (+ 1.0 (* 10.0 k)) (* k k))
189.0ms
(/ (* (* a (pow k (/ m 2))) (pow k (/ m 2))) (+ (+ 1.0 (* 10.0 k)) (* k k)))

simplify3.1s

Counts
126 → 126
Iterations

Useful iterations: done (3.1s)

IterNodesCost
02012456
15762055
236021647
done50011614

prune510.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0b

localize26.0ms

Local error

Found 4 expressions with local error:

0.0b
(fma k (+ 10.0 k) 1.0)
0.0b
(* (pow k (/ m 2)) a)
0.5b
(/ (pow k (/ m 2)) (fma k (+ 10.0 k) 1.0))
1.9b
(* (* (pow k (/ m 2)) a) (/ (pow k (/ m 2)) (fma k (+ 10.0 k) 1.0)))

rewrite115.0ms

Algorithm
rewrite-expression-head
Rules
62×add-exp-log
42×add-sqr-sqrt times-frac
37×add-cube-cbrt *-un-lft-identity
31×prod-exp
28×associate-*r*
25×unpow-prod-down
20×add-cbrt-cube
15×div-exp
10×pow-to-exp pow-exp
9×sqr-pow
8×associate-*l*
7×cbrt-unprod associate-/l*
6×pow1
4×expm1-log1p-u log1p-expm1-u add-log-exp
3×cbrt-undiv associate-/r* unswap-sqr
2×*-commutative div-inv
1×frac-2neg associate-*r/ pow-prod-down clear-num fma-udef
Counts
4 → 142
Calls
4 calls:
1.0ms
(fma k (+ 10.0 k) 1.0)
29.0ms
(* (pow k (/ m 2)) a)
21.0ms
(/ (pow k (/ m 2)) (fma k (+ 10.0 k) 1.0))
54.0ms
(* (* (pow k (/ m 2)) a) (/ (pow k (/ m 2)) (fma k (+ 10.0 k) 1.0)))

series483.0ms

Counts
4 → 12
Calls
4 calls:
23.0ms
(fma k (+ 10.0 k) 1.0)
150.0ms
(* (pow k (/ m 2)) a)
100.0ms
(/ (pow k (/ m 2)) (fma k (+ 10.0 k) 1.0))
209.0ms
(* (* (pow k (/ m 2)) a) (/ (pow k (/ m 2)) (fma k (+ 10.0 k) 1.0)))

simplify364.0ms

Counts
154 → 154
Iterations

Useful iterations: done (359.0ms)

IterNodesCost
02483185
16713005
done50012742

prune725.0ms

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0b

localize16.0ms

Local error

Found 4 expressions with local error:

0.0b
(* 2 (/ m 2))
0.0b
(* a (pow k (* 2 (/ m 2))))
0.2b
(/ 1 (/ (fma k (+ 10.0 k) 1.0) (* a (pow k (* 2 (/ m 2))))))
2.4b
(/ (fma k (+ 10.0 k) 1.0) (* a (pow k (* 2 (/ m 2)))))

rewrite110.0ms

Algorithm
rewrite-expression-head
Rules
62×add-exp-log
46×times-frac
43×add-sqr-sqrt
33×add-cube-cbrt *-un-lft-identity
27×div-exp
25×add-cbrt-cube
20×associate-*r*
17×prod-exp
8×cbrt-undiv associate-/r*
7×pow1 div-inv
6×associate-*l* associate-/l*
5×pow-to-exp rec-exp 1-exp pow-exp cbrt-unprod unswap-sqr
4×expm1-log1p-u unpow-prod-down log1p-expm1-u add-log-exp
2×frac-2neg clear-num *-commutative sqr-pow
1×pow-flip associate-*r/ pow-prod-down associate-/r/ inv-pow
Counts
4 → 150
Calls
4 calls:
25.0ms
(* 2 (/ m 2))
24.0ms
(* a (pow k (* 2 (/ m 2))))
28.0ms
(/ 1 (/ (fma k (+ 10.0 k) 1.0) (* a (pow k (* 2 (/ m 2))))))
22.0ms
(/ (fma k (+ 10.0 k) 1.0) (* a (pow k (* 2 (/ m 2)))))

series456.0ms

Counts
4 → 12
Calls
4 calls:
13.0ms
(* 2 (/ m 2))
86.0ms
(* a (pow k (* 2 (/ m 2))))
154.0ms
(/ 1 (/ (fma k (+ 10.0 k) 1.0) (* a (pow k (* 2 (/ m 2))))))
204.0ms
(/ (fma k (+ 10.0 k) 1.0) (* a (pow k (* 2 (/ m 2)))))

simplify1.8s

Counts
162 → 162
Iterations

Useful iterations: done (1.8s)

IterNodesCost
02903093
17612838
231562580
done50002571

prune686.0ms

Pruning

5 alts after pruning (2 fresh and 3 done)

Merged error: 0b

regimes140.0ms

Accuracy

96.5% (0.1b remaining)

Error of 0.1b against oracle of 0.0b and baseline of 2.2b

bsearch52.0ms

Steps
ItersRangePoint
6
44039.89650146889
517946.10598021303
510508.1455585844

simplify6.0ms

Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
03977
14977
done4977

end0.0ms

sample2.3s

Algorithm
intervals
Results
1.1s12027×body80valid
403.0ms4253×body80nan