Details

Time bar (total: 29.2s)

sample83.0ms

Algorithm
intervals
Results
46.0ms384×body80valid
15.0ms136×body80nan

simplify1.4s

Counts
1 → 1
Iterations
IterNodes
done2000
62000
5639
4204
387
247
126
012

prune13.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 1.2b

localize18.0ms

Local error

Found 3 expressions with local error:

0.0b
(+ (+ 1 (* 10 k)) (* k k))
0.0b
(* a (pow k m))
1.2b
(/ (* a (pow k m)) (+ (+ 1 (* 10 k)) (* k k)))

rewrite64.0ms

Algorithm
rewrite-expression-head
Rules
18×add-exp-log
13×add-sqr-sqrt
10×add-cbrt-cube
8×*-un-lft-identity add-cube-cbrt add-log-exp
7×associate-*r*
6×prod-exp
4×unpow-prod-down div-exp
3×pow1 associate-/r* sum-log times-frac associate-*l* insert-posit16 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 → 66
Calls
3 calls:
29.0ms
(+ (+ 1 (* 10 k)) (* k k))
8.0ms
(* a (pow k m))
26.0ms
(/ (* a (pow k m)) (+ (+ 1 (* 10 k)) (* k k)))

series248.0ms

Counts
3 → 9
Calls
3 calls:
29.0ms
(+ (+ 1 (* 10 k)) (* k k))
72.0ms
(* a (pow k m))
147.0ms
(/ (* a (pow k m)) (+ (+ 1 (* 10 k)) (* k k)))

simplify1.2s

Counts
75 → 75
Iterations
IterNodes
done2014
32014
21447
1408
0153

prune755.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.0b

localize22.0ms

Local error

Found 4 expressions with local error:

0.0b
(/ (/ (+ 1 (* (+ 10 k) k)) a) (pow k m))
0.0b
(* (+ 10 k) k)
0.3b
(/ 1 (/ (/ (+ 1 (* (+ 10 k) k)) a) (pow k m)))
3.6b
(/ (+ 1 (* (+ 10 k) k)) a)

rewrite144.0ms

Algorithm
rewrite-expression-head
Rules
1073×times-frac
500×add-sqr-sqrt *-un-lft-identity
498×add-cube-cbrt
198×unpow-prod-down
105×associate-/r*
70×add-exp-log
66×sqr-pow
51×div-exp
43×div-inv
22×add-cbrt-cube
19×associate-/l*
10×cbrt-undiv
8×pow-to-exp pow-exp
7×pow1 rec-exp 1-exp
4×associate-*l* insert-posit16 add-log-exp
3×clear-num frac-2neg associate-*r* associate-/l/
2×flip3-+ associate-*l/ flip-+
1×pow-prod-down prod-exp associate-/r/ *-commutative cbrt-unprod pow-flip distribute-lft-out inv-pow unswap-sqr
Counts
4 → 604
Calls
4 calls:
30.0ms
(/ (/ (+ 1 (* (+ 10 k) k)) a) (pow k m))
31.0ms
(* (+ 10 k) k)
27.0ms
(/ 1 (/ (/ (+ 1 (* (+ 10 k) k)) a) (pow k m)))
35.0ms
(/ (+ 1 (* (+ 10 k) k)) a)

series370.0ms

Counts
4 → 12
Calls
4 calls:
146.0ms
(/ (/ (+ 1 (* (+ 10 k) k)) a) (pow k m))
43.0ms
(* (+ 10 k) k)
128.0ms
(/ 1 (/ (/ (+ 1 (* (+ 10 k) k)) a) (pow k m)))
52.0ms
(/ (+ 1 (* (+ 10 k) k)) a)

simplify1.9s

Counts
616 → 616
Iterations
IterNodes
done2000
12000
0895

prune7.9s

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0.0b

localize39.0ms

Local error

Found 4 expressions with local error:

3.6b
(/ (+ 1 (* (+ 10 k) k)) a)
3.6b
(/ (+ 1 (* (+ 10 k) k)) a)
3.6b
(/ (+ 1 (* (+ 10 k) k)) a)
14.6b
(cbrt (* (* (/ 1 (/ (/ (+ 1 (* (+ 10 k) k)) a) (pow k m))) (/ 1 (/ (/ (+ 1 (* (+ 10 k) k)) a) (pow k m)))) (/ 1 (/ (/ (+ 1 (* (+ 10 k) k)) a) (pow k m)))))

rewrite293.0ms

Algorithm
rewrite-expression-head
Rules
28×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
27×times-frac
10×cbrt-div add-cbrt-cube add-exp-log
9×associate-/r* associate-/l*
6×frac-times associate-*l/ associate-/l/
4×pow1 insert-posit16 add-log-exp
3×cbrt-undiv clear-num frac-2neg flip3-+ div-exp associate-*r/ un-div-inv flip-+ div-inv
1×cbrt-prod pow1/3 pow3 rem-cbrt-cube
Counts
4 → 111
Calls
4 calls:
43.0ms
(/ (+ 1 (* (+ 10 k) k)) a)
41.0ms
(/ (+ 1 (* (+ 10 k) k)) a)
42.0ms
(/ (+ 1 (* (+ 10 k) k)) a)
165.0ms
(cbrt (* (* (/ 1 (/ (/ (+ 1 (* (+ 10 k) k)) a) (pow k m))) (/ 1 (/ (/ (+ 1 (* (+ 10 k) k)) a) (pow k m)))) (/ 1 (/ (/ (+ 1 (* (+ 10 k) k)) a) (pow k m)))))

series296.0ms

Counts
4 → 12
Calls
4 calls:
40.0ms
(/ (+ 1 (* (+ 10 k) k)) a)
53.0ms
(/ (+ 1 (* (+ 10 k) k)) a)
47.0ms
(/ (+ 1 (* (+ 10 k) k)) a)
156.0ms
(cbrt (* (* (/ 1 (/ (/ (+ 1 (* (+ 10 k) k)) a) (pow k m))) (/ 1 (/ (/ (+ 1 (* (+ 10 k) k)) a) (pow k m)))) (/ 1 (/ (/ (+ 1 (* (+ 10 k) k)) a) (pow k m)))))

simplify1.4s

Counts
123 → 123
Iterations
IterNodes
done2000
32000
21039
1356
0152

prune1.7s

Pruning

4 alts after pruning (1 fresh and 3 done)

Merged error: 0.0b

localize84.0ms

Local error

Found 4 expressions with local error:

3.5b
(* (/ (pow (/ 1 k) (- m)) k) (/ a k))
8.6b
(- (* (/ 99 (* k k)) (* (/ (pow (/ 1 k) (- m)) k) (/ a k))) (/ (* (* 10 a) (pow (/ 1 k) (- m))) (* k (* k k))))
8.9b
(* (/ 99 (* k k)) (* (/ (pow (/ 1 k) (- m)) k) (/ a k)))
13.2b
(/ (* (* 10 a) (pow (/ 1 k) (- m))) (* k (* k k)))

rewrite225.0ms

Algorithm
rewrite-expression-head
Rules
456×add-exp-log
209×prod-exp
173×div-exp
121×add-cbrt-cube
111×times-frac
95×add-sqr-sqrt
62×associate-*l*
57×*-un-lft-identity
56×pow-exp
55×add-cube-cbrt
54×cbrt-unprod
45×unpow-prod-down
35×cbrt-undiv
14×pow-to-exp rec-exp 1-exp associate-*r*
13×associate-*r/
12×unswap-sqr
11×frac-times pow1
7×associate-*l/ frac-sub div-inv
6×add-log-exp
5×sqr-pow
4×pow-prod-down insert-posit16
3×associate-/l/
2×pow-neg *-commutative
1×neg-sub0 clear-num associate-/r* sub-neg frac-2neg flip3-- diff-log un-div-inv flip-- associate-/l* pow-sub
Counts
4 → 282
Calls
4 calls:
40.0ms
(* (/ (pow (/ 1 k) (- m)) k) (/ a k))
66.0ms
(- (* (/ 99 (* k k)) (* (/ (pow (/ 1 k) (- m)) k) (/ a k))) (/ (* (* 10 a) (pow (/ 1 k) (- m))) (* k (* k k))))
50.0ms
(* (/ 99 (* k k)) (* (/ (pow (/ 1 k) (- m)) k) (/ a k)))
56.0ms
(/ (* (* 10 a) (pow (/ 1 k) (- m))) (* k (* k k)))

series772.0ms

Counts
4 → 12
Calls
4 calls:
178.0ms
(* (/ (pow (/ 1 k) (- m)) k) (/ a k))
271.0ms
(- (* (/ 99 (* k k)) (* (/ (pow (/ 1 k) (- m)) k) (/ a k))) (/ (* (* 10 a) (pow (/ 1 k) (- m))) (* k (* k k))))
195.0ms
(* (/ 99 (* k k)) (* (/ (pow (/ 1 k) (- m)) k) (/ a k)))
128.0ms
(/ (* (* 10 a) (pow (/ 1 k) (- m))) (* k (* k k)))

simplify1.5s

Counts
294 → 294
Iterations
IterNodes
done2008
22008
11578
0526

prune5.0s

Pruning

4 alts after pruning (0 fresh and 4 done)

Merged error: 0.0b

regimes255.0ms

Accuracy

97% (0.1b remaining)

Error of 0.1b against oracle of 0.0b and baseline of 2.0b

bsearch122.0ms

Steps
ItersRangePoint
9
1.1545712148288017e+146
4.1427324963373916e+152
3.442415825498342e+150

simplify12.0ms

Iterations
IterNodes
done42
142
030

end0.0ms

sample3.3s

Algorithm
intervals
Results
2.2s11956×body80valid
626.0ms4252×body80nan