Details

Time bar (total: 22.8s)

sample46.0ms

Algorithm
intervals
Results
20.0ms376×body80valid
6.0ms127×body80nan

simplify3.1s

Counts
1 → 1
Iterations
IterNodes
done5003
62078
5627
4203
385
245
124
012

prune11.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 2.5b

localize18.0ms

Local error

Found 3 expressions with local error:

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

rewrite72.0ms

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* 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 → 63
Calls
3 calls:
25.0ms
(+ (+ 1.0 (* 10.0 k)) (* k k))
9.0ms
(* a (pow k m))
35.0ms
(/ (* a (pow k m)) (+ (+ 1.0 (* 10.0 k)) (* k k)))

series298.0ms

Counts
3 → 9
Calls
3 calls:
27.0ms
(+ (+ 1.0 (* 10.0 k)) (* k k))
90.0ms
(* a (pow k m))
180.0ms
(/ (* a (pow k m)) (+ (+ 1.0 (* 10.0 k)) (* k k)))

simplify1.5s

Counts
72 → 72
Iterations
IterNodes
done5001
21422
1410
0154

prune449.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.0b

localize56.0ms

Local error

Found 4 expressions with local error:

0.0b
(* a (pow k m))
0.0b
(/ (/ (* a (pow k m)) (sqrt (+ (+ 1.0 (* 10.0 k)) (* k k)))) (sqrt (+ (+ 1.0 (* 10.0 k)) (* k k))))
16.3b
(sqrt (+ (+ 1.0 (* 10.0 k)) (* k k)))
16.3b
(sqrt (+ (+ 1.0 (* 10.0 k)) (* k k)))

rewrite230.0ms

Algorithm
rewrite-expression-head
Rules
114×times-frac
66×sqrt-prod
63×add-sqr-sqrt
56×*-un-lft-identity add-cube-cbrt
25×add-exp-log
20×sqrt-div
16×associate-/r/
15×add-cbrt-cube
12×associate-/l*
10×flip3-+ flip-+
9×div-exp
8×div-inv
7×associate-*r*
6×pow1 associate-/r* prod-exp
5×cbrt-undiv
4×unpow-prod-down add-log-exp
3×associate-*l* unswap-sqr
2×pow-to-exp rem-sqrt-square sqrt-pow1 pow1/2 pow-exp cbrt-unprod sqr-pow
1×clear-num frac-2neg *-commutative associate-/l/
Counts
4 → 166
Calls
4 calls:
20.0ms
(* a (pow k m))
127.0ms
(/ (/ (* a (pow k m)) (sqrt (+ (+ 1.0 (* 10.0 k)) (* k k)))) (sqrt (+ (+ 1.0 (* 10.0 k)) (* k k))))
35.0ms
(sqrt (+ (+ 1.0 (* 10.0 k)) (* k k)))
36.0ms
(sqrt (+ (+ 1.0 (* 10.0 k)) (* k k)))

series401.0ms

Counts
4 → 12
Calls
4 calls:
80.0ms
(* a (pow k m))
166.0ms
(/ (/ (* a (pow k m)) (sqrt (+ (+ 1.0 (* 10.0 k)) (* k k)))) (sqrt (+ (+ 1.0 (* 10.0 k)) (* k k))))
92.0ms
(sqrt (+ (+ 1.0 (* 10.0 k)) (* k k)))
63.0ms
(sqrt (+ (+ 1.0 (* 10.0 k)) (* k k)))

simplify2.8s

Counts
178 → 178
Iterations
IterNodes
done5010
22768
1734
0296

prune1.2s

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.0b

localize49.0ms

Local error

Found 4 expressions with local error:

0.6b
(cbrt k)
0.6b
(cbrt k)
0.6b
(cbrt k)
2.5b
(/ (* (* a (pow (* (cbrt k) (cbrt k)) m)) (pow (cbrt k) m)) (+ (+ 1.0 (* 10.0 k)) (* k k)))

rewrite60.0ms

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 *-un-lft-identity add-cube-cbrt
8×pow-to-exp
4×pow1 add-log-exp
3×cbrt-undiv associate-/r* times-frac pow1/3 cbrt-unprod
2×associate-/r/
1×clear-num frac-2neg flip3-+ flip-+ div-inv associate-/l*
Counts
4 → 71
Calls
4 calls:
1.0ms
(cbrt k)
1.0ms
(cbrt k)
1.0ms
(cbrt k)
56.0ms
(/ (* (* a (pow (* (cbrt k) (cbrt k)) m)) (pow (cbrt k) m)) (+ (+ 1.0 (* 10.0 k)) (* k k)))

series1.4s

Counts
4 → 12
Calls
4 calls:
297.0ms
(cbrt k)
287.0ms
(cbrt k)
277.0ms
(cbrt k)
490.0ms
(/ (* (* a (pow (* (cbrt k) (cbrt k)) m)) (pow (cbrt k) m)) (+ (+ 1.0 (* 10.0 k)) (* k k)))

simplify2.3s

Counts
83 → 83
Iterations
IterNodes
done5000
21958
1498
0172

prune597.0ms

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0.0b

localize78.0ms

Local error

Found 4 expressions with local error:

1.2b
(* (/ (* a (pow k m)) (sqrt (sqrt (+ (+ 1.0 (* 10.0 k)) (* k k))))) (/ (/ 1 (sqrt (+ (+ 1.0 (* 10.0 k)) (* k k)))) (sqrt (sqrt (+ (+ 1.0 (* 10.0 k)) (* k k))))))
16.3b
(sqrt (+ (+ 1.0 (* 10.0 k)) (* k k)))
16.3b
(sqrt (+ (+ 1.0 (* 10.0 k)) (* k k)))
16.3b
(sqrt (+ (+ 1.0 (* 10.0 k)) (* k k)))

rewrite553.0ms

Algorithm
rewrite-expression-head
Rules
414×times-frac
336×sqrt-prod
257×add-sqr-sqrt
222×associate-*r*
207×*-un-lft-identity
201×add-cube-cbrt
109×add-exp-log
50×div-exp
40×add-cbrt-cube prod-exp
32×sqrt-div
22×associate-/r/
16×unswap-sqr
15×cbrt-undiv associate-*l*
14×flip3-+ flip-+
12×cbrt-unprod
11×div-inv
9×pow1
5×pow-to-exp rec-exp 1-exp pow-exp
4×add-log-exp
3×rem-sqrt-square sqrt-pow1 pow1/2
1×frac-times pow-prod-down associate-*l/ associate-*r/ *-commutative
Counts
4 → 344
Calls
4 calls:
408.0ms
(* (/ (* a (pow k m)) (sqrt (sqrt (+ (+ 1.0 (* 10.0 k)) (* k k))))) (/ (/ 1 (sqrt (+ (+ 1.0 (* 10.0 k)) (* k k)))) (sqrt (sqrt (+ (+ 1.0 (* 10.0 k)) (* k k))))))
31.0ms
(sqrt (+ (+ 1.0 (* 10.0 k)) (* k k)))
35.0ms
(sqrt (+ (+ 1.0 (* 10.0 k)) (* k k)))
33.0ms
(sqrt (+ (+ 1.0 (* 10.0 k)) (* k k)))

series407.0ms

Counts
4 → 12
Calls
4 calls:
201.0ms
(* (/ (* a (pow k m)) (sqrt (sqrt (+ (+ 1.0 (* 10.0 k)) (* k k))))) (/ (/ 1 (sqrt (+ (+ 1.0 (* 10.0 k)) (* k k)))) (sqrt (sqrt (+ (+ 1.0 (* 10.0 k)) (* k k))))))
86.0ms
(sqrt (+ (+ 1.0 (* 10.0 k)) (* k k)))
49.0ms
(sqrt (+ (+ 1.0 (* 10.0 k)) (* k k)))
70.0ms
(sqrt (+ (+ 1.0 (* 10.0 k)) (* k k)))

simplify2.5s

Counts
356 → 356
Iterations
IterNodes
done5000
11850
0533

prune2.4s

Pruning

5 alts after pruning (2 fresh and 3 done)

Merged error: 0.0b

regimes203.0ms

Accuracy

94.1% (0.1b remaining)

Error of 0.2b against oracle of 0.1b and baseline of 2.0b

bsearch64.0ms

Steps
ItersRangePoint
6
9.738155686380769e+38
9.363839846338779e+39
1.390911796383614e+39

simplify9.0ms

Iterations
IterNodes
done53
153
039

end0.0ms

sample2.1s

Algorithm
intervals
Results
1.3s12098×body80valid
340.0ms4310×body80nan