Details

Time bar (total: 22.9s)

sample104.0ms

Algorithm
intervals
Results
19.0ms27×body1280valid
16.0ms35×body640valid
15.0ms195×body80valid
6.0ms101×body80nan
5.0ms17×body320valid
2.0ms12×body160valid

simplify1.9s

Counts
1 → 1
Iterations

Useful iterations: 2 (7.0ms)

IterNodesCost
01013
11813
22711
35211
410811
524411
657711
7185011
done500011

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 6.4b

localize10.0ms

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)

rewrite106.0ms

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:
74.0ms
(+ x (/ (pow (/ y (+ z y)) y) y))
11.0ms
(/ y (+ z y))
18.0ms
(pow (/ y (+ z y)) y)

series526.0ms

Counts
3 → 9
Calls
3 calls:
104.0ms
(+ x (/ (pow (/ y (+ z y)) y) y))
72.0ms
(/ y (+ z y))
349.0ms
(pow (/ y (+ z y)) y)

simplify1.8s

Counts
87 → 87
Iterations

Useful iterations: 3 (846.0ms)

IterNodesCost
01581091
13901024
2976970
32786964
done5002964

prune267.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.5b

localize50.0ms

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)

rewrite98.0ms

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)
27.0ms
(pow (/ (cbrt y) (cbrt (+ z y))) y)
63.0ms
(pow (/ (* (cbrt y) (cbrt y)) (* (cbrt (+ z y)) (cbrt (+ z y)))) y)

series1.6s

Counts
4 → 12
Calls
4 calls:
304.0ms
(cbrt y)
545.0ms
(cbrt y)
389.0ms
(pow (/ (cbrt y) (cbrt (+ z y))) y)
341.0ms
(pow (/ (* (cbrt y) (cbrt y)) (* (cbrt (+ z y)) (cbrt (+ z y)))) y)

simplify2.9s

Counts
128 → 128
Iterations

Useful iterations: 3 (1.4s)

IterNodesCost
02952319
16782162
214681952
342441927
done50001927

prune658.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.0b

localize35.0ms

Local error

Found 4 expressions with local error:

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

rewrite36.0ms

Algorithm
rewrite-expression-head
Rules
54×unpow-prod-down
49×*-un-lft-identity
48×cbrt-prod
42×times-frac
37×add-sqr-sqrt add-cube-cbrt
9×add-exp-log pow-unpow
7×pow1
6×distribute-lft-out
4×pow-exp add-cbrt-cube add-log-exp
3×pow-to-exp pow-pow sqr-pow
2×cbrt-div associate-/r/
1×flip3-+ pow1/3 div-exp flip-+ div-inv
Counts
4 → 108
Calls
4 calls:
1.0ms
(cbrt y)
20.0ms
(pow (/ (cbrt y) (cbrt (+ z y))) y)
5.0ms
(pow (fabs (/ (cbrt y) (cbrt (+ z y)))) y)
5.0ms
(pow (fabs (/ (cbrt y) (cbrt (+ z y)))) y)

series774.0ms

Counts
4 → 12
Calls
4 calls:
300.0ms
(cbrt y)
376.0ms
(pow (/ (cbrt y) (cbrt (+ z y))) y)
47.0ms
(pow (fabs (/ (cbrt y) (cbrt (+ z y)))) y)
51.0ms
(pow (fabs (/ (cbrt y) (cbrt (+ z y)))) y)

simplify2.3s

Counts
120 → 120
Iterations

Useful iterations: done (2.3s)

IterNodesCost
02411988
15271853
210881794
328331778
done50001774

prune720.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.0b

localize21.0ms

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)

rewrite741.0ms

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:
674.0ms
(* (cbrt (+ x (/ (pow (/ y (+ z y)) y) y))) (cbrt (+ x (/ (pow (/ y (+ z y)) y) y))))
28.0ms
(pow (/ y (+ z y)) y)
14.0ms
(pow (/ y (+ z y)) y)
19.0ms
(pow (/ y (+ z y)) y)

series1.5s

Counts
4 → 12
Calls
4 calls:
402.0ms
(* (cbrt (+ x (/ (pow (/ y (+ z y)) y) y))) (cbrt (+ x (/ (pow (/ y (+ z y)) y) y))))
349.0ms
(pow (/ y (+ z y)) y)
366.0ms
(pow (/ y (+ z y)) y)
380.0ms
(pow (/ y (+ z y)) y)

simplify2.6s

Counts
164 → 164
Iterations

Useful iterations: done (2.6s)

IterNodesCost
02123468
14853170
212082980
336112719
done50002707

prune699.0ms

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0b

regimes153.0ms

Accuracy

-103.3% (1.8b remaining)

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

bsearch161.0ms

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
030104
13970
done3970

end0.0ms

sample3.2s

Algorithm
intervals
Results
1.1s799×body1280valid
624.0ms6551×body80valid
410.0ms898×body640valid
212.0ms3160×body80nan
208.0ms598×body320valid
100.0ms308×body160valid