Details

Time bar (total: 23.3s)

sample92.0ms

Algorithm
intervals
Results
21.0ms27×body1280valid
17.0ms195×body80valid
15.0ms35×body640valid
6.0ms101×body80nan
5.0ms17×body320valid
2.0ms12×body160valid

simplify1.7s

Counts
1 → 1
Iterations

Useful iterations: 2 (8.0ms)

IterNodesCost
01013
11813
22711
35211
410811
524411
657711
7185011
done500011

prune7.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 6.4b

localize20.0ms

Local error

Found 3 expressions with local error:

0.0b
(+ x (/ (pow (/ y (+ z y)) y) y))
0.0b
(/ y (+ z y))
6.4b
(pow (/ y (+ z y)) y)

rewrite137.0ms

Algorithm
rewrite-expression-head
Rules
37×*-un-lft-identity
24×times-frac
21×add-sqr-sqrt add-cube-cbrt
18×unpow-prod-down
8×add-exp-log distribute-lft-out
5×add-cbrt-cube add-log-exp
4×pow1 associate-/r* associate-/r/
3×pow-unpow flip3-+ flip-+ associate-/l*
2×div-exp pow-exp div-inv
1×cbrt-undiv +-commutative pow-to-exp pow-pow frac-2neg clear-num sum-log sqr-pow
Counts
3 → 78
Calls
3 calls:
92.0ms
(+ x (/ (pow (/ y (+ z y)) y) y))
18.0ms
(/ y (+ z y))
22.0ms
(pow (/ y (+ z y)) y)

series479.0ms

Counts
3 → 9
Calls
3 calls:
121.0ms
(+ x (/ (pow (/ y (+ z y)) y) y))
43.0ms
(/ y (+ z y))
315.0ms
(pow (/ y (+ z y)) y)

simplify1.8s

Counts
87 → 87
Iterations

Useful iterations: 3 (925.0ms)

IterNodesCost
01581091
13901024
2976970
32786964
done5002964

prune231.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.5b

localize23.0ms

Local error

Found 4 expressions with local error:

0.6b
(cbrt y)
0.6b
(cbrt y)
1.8b
(pow (/ (cbrt y) (cbrt (+ z y))) y)
2.8b
(pow (/ (* (cbrt y) (cbrt y)) (* (cbrt (+ z y)) (cbrt (+ z y)))) y)

rewrite71.0ms

Algorithm
rewrite-expression-head
Rules
61×unpow-prod-down
51×cbrt-prod
48×*-un-lft-identity
43×times-frac
36×add-sqr-sqrt add-cube-cbrt
20×add-exp-log
14×cbrt-div
10×associate-/r/
7×flip3-+ pow-exp flip-+
6×pow1 pow-unpow distribute-lft-out
5×div-exp
4×frac-times prod-exp add-cbrt-cube add-log-exp
2×pow-to-exp pow-pow pow1/3 associate-*r/ associate-*l/ div-inv sqr-pow
Counts
4 → 116
Calls
4 calls:
1.0ms
(cbrt y)
1.0ms
(cbrt y)
26.0ms
(pow (/ (cbrt y) (cbrt (+ z y))) y)
38.0ms
(pow (/ (* (cbrt y) (cbrt y)) (* (cbrt (+ z y)) (cbrt (+ z y)))) y)

series1.2s

Counts
4 → 12
Calls
4 calls:
256.0ms
(cbrt y)
291.0ms
(cbrt y)
351.0ms
(pow (/ (cbrt y) (cbrt (+ z y))) y)
337.0ms
(pow (/ (* (cbrt y) (cbrt y)) (* (cbrt (+ z y)) (cbrt (+ z y)))) y)

simplify2.6s

Counts
128 → 128
Iterations

Useful iterations: 3 (1.2s)

IterNodesCost
02952319
16782162
214681952
342441927
done50001927

prune592.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.0b

localize21.0ms

Local error

Found 4 expressions with local error:

0.6b
(cbrt y)
1.8b
(pow (/ (cbrt y) (cbrt (+ z y))) y)
1.8b
(pow (/ (cbrt y) (cbrt (+ z y))) y)
1.8b
(pow (/ (cbrt y) (cbrt (+ z y))) y)

rewrite122.0ms

Algorithm
rewrite-expression-head
Rules
144×unpow-prod-down
138×cbrt-prod
126×times-frac
125×*-un-lft-identity
89×add-sqr-sqrt add-cube-cbrt
18×distribute-lft-out
13×add-exp-log
9×pow-unpow
7×pow1
6×cbrt-div pow-exp associate-/r/
4×add-cbrt-cube add-log-exp
3×pow-to-exp pow-pow flip3-+ div-exp flip-+ div-inv sqr-pow
1×pow1/3
Counts
4 → 200
Calls
4 calls:
2.0ms
(cbrt y)
39.0ms
(pow (/ (cbrt y) (cbrt (+ z y))) y)
45.0ms
(pow (/ (cbrt y) (cbrt (+ z y))) y)
21.0ms
(pow (/ (cbrt y) (cbrt (+ z y))) y)

series1.5s

Counts
4 → 12
Calls
4 calls:
304.0ms
(cbrt y)
383.0ms
(pow (/ (cbrt y) (cbrt (+ z y))) y)
378.0ms
(pow (/ (cbrt y) (cbrt (+ z y))) y)
385.0ms
(pow (/ (cbrt y) (cbrt (+ z y))) y)

simplify2.0s

Counts
212 → 212
Iterations

Useful iterations: done (2.0s)

IterNodesCost
02083938
14593679
29343592
324003562
done50003550

prune1.1s

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.0b

localize33.0ms

Local error

Found 4 expressions with local error:

0.5b
(* (cbrt (+ x (/ (pow (/ y (+ z y)) y) y))) (cbrt (+ x (/ (pow (/ y (+ z y)) y) y))))
6.4b
(pow (/ y (+ z y)) y)
6.4b
(pow (/ y (+ z y)) y)
6.4b
(pow (/ y (+ z y)) y)

rewrite821.0ms

Algorithm
rewrite-expression-head
Rules
71×*-un-lft-identity
54×unpow-prod-down
47×add-sqr-sqrt
39×add-cube-cbrt
36×times-frac
24×cbrt-prod
15×add-exp-log distribute-lft-out
14×pow1
12×cbrt-div
9×pow-unpow flip3-+ swap-sqr flip-+
7×associate-*r* associate-*l*
6×pow1/3 pow-exp associate-/r/
4×frac-times add-cbrt-cube add-log-exp unswap-sqr
3×pow-to-exp pow-pow div-exp div-inv sqr-pow
2×associate-*r/ pow-prod-down associate-*l/ pow-sqr pow-prod-up
1×pow2 pow-plus prod-exp *-commutative cbrt-unprod
Counts
4 → 152
Calls
4 calls:
723.0ms
(* (cbrt (+ x (/ (pow (/ y (+ z y)) y) y))) (cbrt (+ x (/ (pow (/ y (+ z y)) y) y))))
37.0ms
(pow (/ y (+ z y)) y)
28.0ms
(pow (/ y (+ z y)) y)
27.0ms
(pow (/ y (+ z y)) y)

series1.4s

Counts
4 → 12
Calls
4 calls:
405.0ms
(* (cbrt (+ x (/ (pow (/ y (+ z y)) y) y))) (cbrt (+ x (/ (pow (/ y (+ z y)) y) y))))
369.0ms
(pow (/ y (+ z y)) y)
353.0ms
(pow (/ y (+ z y)) y)
319.0ms
(pow (/ y (+ z y)) y)

simplify2.9s

Counts
164 → 164
Iterations

Useful iterations: done (2.9s)

IterNodesCost
02123468
14853170
212082980
336112719
done50002707

prune737.0ms

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0b

regimes135.0ms

Accuracy

-103.3% (1.8b remaining)

Error of 2.0b against oracle of 0.2b and baseline of 1.1b

bsearch178.0ms

Steps
ItersRangePoint
9
4.677893477719556e+118
2.9580431597534113e+125
4.7668968669307006e+118
8
4.861077116233833e+20
3.339550470087394e+24
2.7983300664584073e+24

simplify8.0ms

Iterations

Useful iterations: 1 (5.0ms)

IterNodesCost
028100
13768
done3768

end0.0ms

sample3.5s

Algorithm
intervals
Results
922.0ms898×body640valid
804.0ms6551×body80valid
628.0ms799×body1280valid
246.0ms3160×body80nan
173.0ms598×body320valid
56.0ms308×body160valid