Details

Time bar (total: 8.5s)

sample59.0ms

Algorithm
intervals
Results
22.0ms54×body1280valid
11.0ms51×body640valid
6.0ms149×body80valid
4.0ms28×body320valid
2.0ms87×body80nan
1.0ms8×body160valid

simplify116.0ms

Counts
1 → 1
Iterations

Useful iterations: 4 (7.0ms)

IterNodesCost
0156
1246
2516
31066
43044
57744
641424
750014
done50014

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 10.0b

localize8.0ms

Local error

Found 3 expressions with local error:

0.0b
(/ x (+ x y))
0.1b
(* x (log (/ x (+ x y))))
7.7b
(log (/ x (+ x y)))

rewrite44.0ms

Algorithm
rewrite-expression-head
Rules
64×*-un-lft-identity
54×log-prod
48×times-frac
40×add-sqr-sqrt
38×add-cube-cbrt
18×distribute-rgt-in distribute-lft-in
13×distribute-lft-out
10×add-exp-log
8×associate-/r/
7×pow1 add-cbrt-cube
4×flip3-+ associate-*r* associate-/r* flip-+ div-inv
3×associate-*l* associate-/l* add-log-exp
2×div-exp rem-log-exp log-pow
1×cbrt-undiv log-div frac-2neg pow-prod-down prod-exp clear-num *-commutative cbrt-unprod unswap-sqr
Counts
3 → 117
Calls
3 calls:
10.0ms
(/ x (+ x y))
23.0ms
(* x (log (/ x (+ x y))))
6.0ms
(log (/ x (+ x y)))

series170.0ms

Counts
3 → 9
Calls
3 calls:
44.0ms
(/ x (+ x y))
74.0ms
(* x (log (/ x (+ x y))))
52.0ms
(log (/ x (+ x y)))

simplify100.0ms

Counts
126 → 126
Iterations

Useful iterations: 2 (30.0ms)

IterNodesCost
0293850
11237789
24806759
35001759
done5001759

prune241.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.9b

localize13.0ms

Local error

Found 4 expressions with local error:

0.6b
(cbrt (+ x y))
0.6b
(cbrt (+ x y))
3.0b
(log (/ (cbrt x) (cbrt (+ x y))))
3.0b
(log (/ (cbrt x) (cbrt (+ x y))))

rewrite31.0ms

Algorithm
rewrite-expression-head
Rules
98×cbrt-prod
96×log-prod
88×*-un-lft-identity
84×times-frac
60×add-sqr-sqrt add-cube-cbrt
14×distribute-lft-out
10×add-exp-log
8×cbrt-div
6×pow1
4×flip3-+ rem-log-exp associate-/r/ add-cbrt-cube flip-+ add-log-exp
2×log-div pow1/3 div-exp log-pow div-inv
Counts
4 → 146
Calls
4 calls:
4.0ms
(cbrt (+ x y))
4.0ms
(cbrt (+ x y))
8.0ms
(log (/ (cbrt x) (cbrt (+ x y))))
9.0ms
(log (/ (cbrt x) (cbrt (+ x y))))

series410.0ms

Counts
4 → 12
Calls
4 calls:
132.0ms
(cbrt (+ x y))
128.0ms
(cbrt (+ x y))
74.0ms
(log (/ (cbrt x) (cbrt (+ x y))))
75.0ms
(log (/ (cbrt x) (cbrt (+ x y))))

simplify134.0ms

Counts
158 → 158
Iterations

Useful iterations: 2 (23.0ms)

IterNodesCost
03541566
19331516
239241484
350021484
done50021484

prune613.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.7b

localize21.0ms

Local error

Found 4 expressions with local error:

0.6b
(cbrt (cbrt (+ x y)))
0.6b
(cbrt (cbrt (+ x y)))
3.0b
(log (/ (cbrt x) (cbrt (+ x y))))
29.0b
(log (/ (cbrt x) (* (* (cbrt (cbrt (+ x y))) (cbrt (cbrt (+ x y)))) (cbrt (cbrt (+ x y))))))

rewrite90.0ms

Algorithm
rewrite-expression-head
Rules
118×cbrt-div
84×log-prod
70×cbrt-prod
54×*-un-lft-identity
48×times-frac
38×add-sqr-sqrt add-cube-cbrt
30×flip3-+ flip-+
28×frac-times associate-/r/
17×add-exp-log
14×associate-*l/
8×associate-*r/ distribute-lft-out
6×pow1 rem-log-exp
4×div-exp add-cbrt-cube add-log-exp
3×prod-exp
2×log-div pow1/3 log-pow div-inv
Counts
4 → 142
Calls
4 calls:
4.0ms
(cbrt (cbrt (+ x y)))
4.0ms
(cbrt (cbrt (+ x y)))
8.0ms
(log (/ (cbrt x) (cbrt (+ x y))))
65.0ms
(log (/ (cbrt x) (* (* (cbrt (cbrt (+ x y))) (cbrt (cbrt (+ x y)))) (cbrt (cbrt (+ x y))))))

series610.0ms

Counts
4 → 12
Calls
4 calls:
198.0ms
(cbrt (cbrt (+ x y)))
260.0ms
(cbrt (cbrt (+ x y)))
76.0ms
(log (/ (cbrt x) (cbrt (+ x y))))
75.0ms
(log (/ (cbrt x) (* (* (cbrt (cbrt (+ x y))) (cbrt (cbrt (+ x y)))) (cbrt (cbrt (+ x y))))))

simplify157.0ms

Counts
154 → 154
Iterations

Useful iterations: 2 (31.0ms)

IterNodesCost
06412153
113602045
248571813
350021813
done50021813

prune644.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.7b

localize34.0ms

Local error

Found 4 expressions with local error:

0.6b
(cbrt (* (cbrt (+ x y)) (cbrt (+ x y))))
0.6b
(cbrt (cbrt (* (cbrt (+ x y)) (cbrt (+ x y)))))
3.0b
(log (/ (cbrt x) (cbrt (+ x y))))
26.3b
(log (/ (cbrt x) (* (* (cbrt (cbrt (+ x y))) (cbrt (cbrt (+ x y)))) (* (cbrt (cbrt (* (cbrt (+ x y)) (cbrt (+ x y))))) (cbrt (cbrt (cbrt (+ x y))))))))

rewrite245.0ms

Algorithm
rewrite-expression-head
Rules
1940×cbrt-div
576×frac-times
418×flip3-+ flip-+
300×log-prod
244×associate-/r/
192×associate-*l/
156×associate-*r/
54×cbrt-prod
48×times-frac
47×*-un-lft-identity
35×add-sqr-sqrt add-cube-cbrt
26×add-exp-log
8×rem-log-exp prod-exp
6×pow1 div-exp distribute-lft-out
4×add-cbrt-cube add-log-exp
2×log-div pow1/3 log-pow div-inv
Counts
4 → 363
Calls
4 calls:
12.0ms
(cbrt (* (cbrt (+ x y)) (cbrt (+ x y))))
5.0ms
(cbrt (cbrt (* (cbrt (+ x y)) (cbrt (+ x y)))))
8.0ms
(log (/ (cbrt x) (cbrt (+ x y))))
144.0ms
(log (/ (cbrt x) (* (* (cbrt (cbrt (+ x y))) (cbrt (cbrt (+ x y)))) (* (cbrt (cbrt (* (cbrt (+ x y)) (cbrt (+ x y))))) (cbrt (cbrt (cbrt (+ x y))))))))

series665.0ms

Counts
4 → 12
Calls
4 calls:
262.0ms
(cbrt (* (cbrt (+ x y)) (cbrt (+ x y))))
257.0ms
(cbrt (cbrt (* (cbrt (+ x y)) (cbrt (+ x y)))))
68.0ms
(log (/ (cbrt x) (cbrt (+ x y))))
78.0ms
(log (/ (cbrt x) (* (* (cbrt (cbrt (+ x y))) (cbrt (cbrt (+ x y)))) (* (cbrt (cbrt (* (cbrt (+ x y)) (cbrt (+ x y))))) (cbrt (cbrt (cbrt (+ x y))))))))

simplify139.0ms

Counts
375 → 375
Iterations

Useful iterations: 1 (39.0ms)

IterNodesCost
0358314166
1500114013
done500114013

prune2.1s

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0.7b

regimes51.0ms

Accuracy

35.8% (2.8b remaining)

Error of 4.1b against oracle of 1.3b and baseline of 5.7b

bsearch57.0ms

Steps
ItersRangePoint
7
2.9747277857311056e+25
1.4945517842790262e+27
3.0175644937213605e+25

simplify1.0ms

Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
04048
14048
done4048

end0.0ms

sample1.7s

Algorithm
intervals
Results
621.0ms1481×body1280valid
351.0ms1490×body640valid
192.0ms4783×body80valid
127.0ms836×body320valid
94.0ms2967×body80nan
45.0ms472×body160valid