Details

Time bar (total: 14.4s)

sample42.0ms

Algorithm
intervals
Results
15.0ms391×body80valid
5.0ms168×body80nan

simplify2.1s

Counts
1 → 1
Iterations

Useful iterations: 2 (7.0ms)

IterNodesCost
01215
12415
24813
39513
423913
571813
6274513
done500013

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 2.3b

localize9.0ms

Local error

Found 3 expressions with local error:

0.0b
(* k (+ 10.0 k))
0.0b
(/ (+ (* k (+ 10.0 k)) 1.0) (pow k m))
2.3b
(/ a (/ (+ (* k (+ 10.0 k)) 1.0) (pow k m)))

rewrite90.0ms

Algorithm
rewrite-expression-head
Rules
180×times-frac
105×add-sqr-sqrt *-un-lft-identity
103×add-cube-cbrt
48×unpow-prod-down
32×associate-/r*
20×add-exp-log
16×sqr-pow
12×add-cbrt-cube
10×div-exp
6×div-inv associate-/l*
5×pow1
4×cbrt-undiv associate-*r*
3×associate-*l* add-log-exp
2×pow-to-exp frac-2neg flip3-+ associate-*r/ pow-exp clear-num flip-+ associate-/l/
1×distribute-rgt-in distribute-lft-in pow-prod-down prod-exp associate-/r/ *-commutative cbrt-unprod distribute-lft-out unswap-sqr
Counts
3 → 190
Calls
3 calls:
18.0ms
(* k (+ 10.0 k))
34.0ms
(/ (+ (* k (+ 10.0 k)) 1.0) (pow k m))
28.0ms
(/ a (/ (+ (* k (+ 10.0 k)) 1.0) (pow k m)))

series235.0ms

Counts
3 → 9
Calls
3 calls:
43.0ms
(* k (+ 10.0 k))
70.0ms
(/ (+ (* k (+ 10.0 k)) 1.0) (pow k m))
122.0ms
(/ a (/ (+ (* k (+ 10.0 k)) 1.0) (pow k m)))

simplify1.3s

Counts
199 → 199
Iterations

Useful iterations: done (1.3s)

IterNodesCost
03664560
18404341
228474178
done50014148

prune527.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.0b

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b
(/ a (sqrt (+ (* k (+ 10.0 k)) 1.0)))
0.0b
(/ (/ a (sqrt (+ (* k (+ 10.0 k)) 1.0))) (/ (sqrt (+ (* k (+ 10.0 k)) 1.0)) (pow k m)))
12.1b
(sqrt (+ (* k (+ 10.0 k)) 1.0))
12.1b
(sqrt (+ (* k (+ 10.0 k)) 1.0))

rewrite267.0ms

Algorithm
rewrite-expression-head
Rules
3018×times-frac
1309×add-sqr-sqrt
1307×add-cube-cbrt *-un-lft-identity
966×sqrt-prod
450×unpow-prod-down
150×sqr-pow
100×sqrt-div
97×associate-/r/
74×div-inv
52×associate-/r*
50×flip3-+ flip-+
30×add-exp-log
27×associate-/l*
19×div-exp
18×add-cbrt-cube
9×cbrt-undiv
6×pow1
4×add-log-exp
2×pow-to-exp rem-sqrt-square frac-2neg sqrt-pow1 pow1/2 pow-exp clear-num
1×associate-/l/
Counts
4 → 1269
Calls
4 calls:
22.0ms
(/ a (sqrt (+ (* k (+ 10.0 k)) 1.0)))
83.0ms
(/ (/ a (sqrt (+ (* k (+ 10.0 k)) 1.0))) (/ (sqrt (+ (* k (+ 10.0 k)) 1.0)) (pow k m)))
15.0ms
(sqrt (+ (* k (+ 10.0 k)) 1.0))
17.0ms
(sqrt (+ (* k (+ 10.0 k)) 1.0))

series333.0ms

Counts
4 → 12
Calls
4 calls:
109.0ms
(/ a (sqrt (+ (* k (+ 10.0 k)) 1.0)))
121.0ms
(/ (/ a (sqrt (+ (* k (+ 10.0 k)) 1.0))) (/ (sqrt (+ (* k (+ 10.0 k)) 1.0)) (pow k m)))
55.0ms
(sqrt (+ (* k (+ 10.0 k)) 1.0))
48.0ms
(sqrt (+ (* k (+ 10.0 k)) 1.0))

simplify2.0s

Counts
1281 → 1281
Iterations

Useful iterations: done (2.0s)

IterNodesCost
0159564605
1440757982
done500056490

prune2.8s

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.0b

localize10.0ms

Local error

Found 4 expressions with local error:

0.0b
(* (pow k m) a)
0.0b
(* k (+ 10.0 k))
0.3b
(/ 1 (+ (* k (+ 10.0 k)) 1.0))
2.1b
(* (/ 1 (+ (* k (+ 10.0 k)) 1.0)) (* (pow k m) a))

rewrite121.0ms

Algorithm
rewrite-expression-head
Rules
59×add-exp-log
32×prod-exp
31×add-sqr-sqrt
26×*-un-lft-identity
25×associate-*l*
24×add-cube-cbrt
22×add-cbrt-cube
18×times-frac
10×div-exp
9×pow1
8×associate-*r* cbrt-unprod
5×pow-to-exp rec-exp 1-exp pow-exp
4×unpow-prod-down associate-/r/ add-log-exp unswap-sqr
3×cbrt-undiv flip3-+ associate-/r* *-commutative flip-+ associate-/l*
2×associate-*r/ pow-prod-down div-inv sqr-pow
1×distribute-rgt-in pow-flip frac-2neg distribute-lft-in associate-*l/ clear-num distribute-lft-out inv-pow
Counts
4 → 127
Calls
4 calls:
11.0ms
(* (pow k m) a)
19.0ms
(* k (+ 10.0 k))
21.0ms
(/ 1 (+ (* k (+ 10.0 k)) 1.0))
66.0ms
(* (/ 1 (+ (* k (+ 10.0 k)) 1.0)) (* (pow k m) a))

series283.0ms

Counts
4 → 12
Calls
4 calls:
97.0ms
(* (pow k m) a)
42.0ms
(* k (+ 10.0 k))
34.0ms
(/ 1 (+ (* k (+ 10.0 k)) 1.0))
109.0ms
(* (/ 1 (+ (* k (+ 10.0 k)) 1.0)) (* (pow k m) a))

simplify835.0ms

Counts
139 → 139
Iterations

Useful iterations: done (832.0ms)

IterNodesCost
02312006
15971783
219191581
done50011539

prune285.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.0b

localize29.0ms

Local error

Found 4 expressions with local error:

12.1b
(sqrt (+ (* k (+ 10.0 k)) 1.0))
12.1b
(sqrt (+ (* k (+ 10.0 k)) 1.0))
12.6b
(cbrt (+ (* k (+ 10.0 k)) 1.0))
12.6b
(cbrt (+ (* k (+ 10.0 k)) 1.0))

rewrite51.0ms

Algorithm
rewrite-expression-head
Rules
10×add-sqr-sqrt
8×add-cube-cbrt *-un-lft-identity
6×pow1 cbrt-prod sqrt-prod
4×add-exp-log cbrt-div flip3-+ sqrt-div add-cbrt-cube flip-+ add-log-exp
2×rem-sqrt-square sqrt-pow1 pow1/2 pow1/3
Counts
4 → 56
Calls
4 calls:
18.0ms
(sqrt (+ (* k (+ 10.0 k)) 1.0))
15.0ms
(sqrt (+ (* k (+ 10.0 k)) 1.0))
8.0ms
(cbrt (+ (* k (+ 10.0 k)) 1.0))
9.0ms
(cbrt (+ (* k (+ 10.0 k)) 1.0))

series305.0ms

Counts
4 → 12
Calls
4 calls:
47.0ms
(sqrt (+ (* k (+ 10.0 k)) 1.0))
52.0ms
(sqrt (+ (* k (+ 10.0 k)) 1.0))
102.0ms
(cbrt (+ (* k (+ 10.0 k)) 1.0))
103.0ms
(cbrt (+ (* k (+ 10.0 k)) 1.0))

simplify1.1s

Counts
68 → 68
Iterations

Useful iterations: done (1.1s)

IterNodesCost
01041082
12471012
2669954
32156914
done5000912

prune408.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0.0b

regimes85.0ms

Accuracy

95.1% (0.1b remaining)

Error of 0.2b against oracle of 0.1b and baseline of 2.1b

bsearch61.0ms

Steps
ItersRangePoint
9
6.524589428332346e+47
1.6525700559986095e+56
4.3724534202259655e+54

simplify10.0ms

Iterations

Useful iterations: 1 (2.0ms)

IterNodesCost
03764
15058
done5058

end0.0ms

sample1.1s

Algorithm
intervals
Results
466.0ms11914×body80valid
136.0ms4329×body80nan