Details

Time bar (total: 10.2s)

sample33.0ms

Algorithm
intervals
Results
11.0ms256×body80valid
4.0ms85×body80nan

simplify4.0ms

Counts
1 → 1
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
056
166
done66

prune11.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 22.8b

localize12.0ms

Local error

Found 2 expressions with local error:

0.0b
(+ (* x x) y)
21.2b
(sqrt (+ (* x x) y))

rewrite37.0ms

Algorithm
rewrite-expression-head
Rules
4×add-sqr-sqrt add-log-exp
3×pow1 add-cube-cbrt *-un-lft-identity sqrt-prod
2×add-exp-log flip3-+ sqrt-div add-cbrt-cube flip-+
1×+-commutative rem-sqrt-square sqrt-pow1 pow1/2 sum-log
Counts
2 → 26
Calls
2 calls:
16.0ms
(+ (* x x) y)
20.0ms
(sqrt (+ (* x x) y))

series110.0ms

Counts
2 → 6
Calls
2 calls:
40.0ms
(+ (* x x) y)
70.0ms
(sqrt (+ (* x x) y))

simplify675.0ms

Counts
32 → 32
Iterations

Useful iterations: done (674.0ms)

IterNodesCost
059319
1154294
2700258
done5000255

prune112.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0b

localize11.0ms

Local error

Found 4 expressions with local error:

0.1b
(sqrt (cbrt (+ (* x x) y)))
0.3b
(* (fabs (cbrt (+ (* x x) y))) (sqrt (cbrt (+ (* x x) y))))
22.0b
(cbrt (+ (* x x) y))
22.0b
(cbrt (+ (* x x) y))

rewrite63.0ms

Algorithm
rewrite-expression-head
Rules
20×add-sqr-sqrt
14×cbrt-prod sqrt-prod
12×add-cube-cbrt *-un-lft-identity
9×associate-*r*
8×cbrt-div
7×pow1
6×add-exp-log add-cbrt-cube
4×flip3-+ sqrt-div flip-+ add-log-exp
3×pow1/3 associate-*l* unswap-sqr
2×rem-sqrt-square sqrt-pow1 associate-*r/
1×pow1/2 pow-prod-down prod-exp *-commutative cbrt-unprod
Counts
4 → 74
Calls
4 calls:
11.0ms
(sqrt (cbrt (+ (* x x) y)))
38.0ms
(* (fabs (cbrt (+ (* x x) y))) (sqrt (cbrt (+ (* x x) y))))
6.0ms
(cbrt (+ (* x x) y))
6.0ms
(cbrt (+ (* x x) y))

series539.0ms

Counts
4 → 12
Calls
4 calls:
143.0ms
(sqrt (cbrt (+ (* x x) y)))
157.0ms
(* (fabs (cbrt (+ (* x x) y))) (sqrt (cbrt (+ (* x x) y))))
106.0ms
(cbrt (+ (* x x) y))
133.0ms
(cbrt (+ (* x x) y))

simplify2.8s

Counts
86 → 86
Iterations

Useful iterations: 3 (1.2s)

IterNodesCost
01221272
12721193
210231062
348181056
done50011056

prune321.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0b

localize6.0ms

Local error

Found 1 expressions with local error:

0.0b
(- (* (/ y x) -1/2) x)

rewrite12.0ms

Algorithm
rewrite-expression-head
Rules
3×add-log-exp
1×pow1 add-exp-log add-sqr-sqrt add-cube-cbrt sub-neg flip3-- *-un-lft-identity diff-log add-cbrt-cube flip--
Counts
1 → 12
Calls
1 calls:
11.0ms
(- (* (/ y x) -1/2) x)

series54.0ms

Counts
1 → 3
Calls
1 calls:
54.0ms
(- (* (/ y x) -1/2) x)

simplify1.1s

Counts
15 → 15
Iterations

Useful iterations: 3 (261.0ms)

IterNodesCost
032173
182166
2235149
31297147
done5000147

prune47.0ms

Pruning

4 alts after pruning (1 fresh and 3 done)

Merged error: 0b

localize11.0ms

Local error

Found 1 expressions with local error:

0.0b
(+ x (* 1/2 (/ y x)))

rewrite19.0ms

Algorithm
rewrite-expression-head
Rules
3×add-log-exp
1×pow1 add-exp-log +-commutative add-sqr-sqrt add-cube-cbrt *-un-lft-identity flip3-+ sum-log add-cbrt-cube flip-+
Counts
1 → 11
Calls
1 calls:
19.0ms
(+ x (* 1/2 (/ y x)))

series36.0ms

Counts
1 → 3
Calls
1 calls:
36.0ms
(+ x (* 1/2 (/ y x)))

simplify3.3s

Counts
14 → 14
Iterations

Useful iterations: 2 (46.0ms)

IterNodesCost
027166
186157
2302143
31157143
44751143
done5001143

prune31.0ms

Pruning

4 alts after pruning (0 fresh and 4 done)

Merged error: 0b

regimes189.0ms

Accuracy

99% (0.2b remaining)

Error of 0.2b against oracle of 0.0b and baseline of 21.7b

bsearch46.0ms

Steps
ItersRangePoint
3
6.598426988503463e+95
8.73093819312065e+95
8.331092342254927e+95
10
-7.015537041391403e+155
-1.2785578264641574e+145
-1.3300132858515627e+154

simplify2.0ms

Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01828
12228
done2228

end0.0ms

sample679.0ms

Algorithm
intervals
Results
264.0ms8000×body80valid
94.0ms2706×body80nan