Details

Time bar (total: 1.7s)

sample16.0ms

Algorithm
intervals
Results
5.0ms256×body80valid
1.0ms87×body80nan

simplify3.0ms

Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
063
163
done63

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 24.1b

localize7.0ms

Local error

Found 2 expressions with local error:

0.0b
(+ (* x x) y)
22.5b
(sqrt (+ (* x x) y))

rewrite17.0ms

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:
7.0ms
(+ (* x x) y)
9.0ms
(sqrt (+ (* x x) y))

series59.0ms

Counts
2 → 6
Calls
2 calls:
19.0ms
(+ (* x x) y)
40.0ms
(sqrt (+ (* x x) y))

simplify51.0ms

Counts
32 → 32
Iterations

Useful iterations: 3 (46.0ms)

IterNodesCost
0141152
1475139
21515138
35002136
done5002136

prune66.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0b

localize7.0ms

Local error

Found 4 expressions with local error:

0.0b
(sqrt (sqrt (+ (* x x) y)))
0.5b
(* (sqrt (sqrt (+ (* x x) y))) (sqrt (sqrt (+ (* x x) y))))
22.5b
(sqrt (+ (* x x) y))
22.5b
(sqrt (+ (* x x) y))

rewrite94.0ms

Algorithm
rewrite-expression-head
Rules
82×sqrt-prod
54×add-sqr-sqrt
38×sqrt-pow1
32×sqrt-div
31×pow1
20×add-cube-cbrt *-un-lft-identity pow1/2
15×swap-sqr
9×flip3-+ associate-*r* associate-*l* pow-prod-up flip-+ unswap-sqr
6×add-exp-log add-cbrt-cube
5×pow-prod-down pow-sqr
4×frac-times rem-sqrt-square add-log-exp
2×associate-*r/ associate-*l/
1×pow2 pow-plus sqrt-unprod prod-exp rem-square-sqrt *-commutative cbrt-unprod
Counts
4 → 134
Calls
4 calls:
10.0ms
(sqrt (sqrt (+ (* x x) y)))
59.0ms
(* (sqrt (sqrt (+ (* x x) y))) (sqrt (sqrt (+ (* x x) y))))
9.0ms
(sqrt (+ (* x x) y))
9.0ms
(sqrt (+ (* x x) y))

series204.0ms

Counts
4 → 12
Calls
4 calls:
76.0ms
(sqrt (sqrt (+ (* x x) y)))
46.0ms
(* (sqrt (sqrt (+ (* x x) y))) (sqrt (sqrt (+ (* x x) y))))
40.0ms
(sqrt (+ (* x x) y))
40.0ms
(sqrt (+ (* x x) y))

simplify47.0ms

Counts
146 → 146
Iterations

Useful iterations: 2 (37.0ms)

IterNodesCost
0264901
11062835
25001816
done5001816

prune228.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0b

localize5.0ms

Local error

Found 1 expressions with local error:

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

rewrite6.0ms

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:
6.0ms
(+ x (* 1/2 (/ y x)))

series24.0ms

Counts
1 → 3
Calls
1 calls:
24.0ms
(+ x (* 1/2 (/ y x)))

simplify109.0ms

Counts
14 → 14
Iterations

Useful iterations: 1 (4.0ms)

IterNodesCost
08376
129769
2110169
3389169
4500169
done500169

prune24.0ms

Pruning

4 alts after pruning (1 fresh and 3 done)

Merged error: 0b

localize6.0ms

Local error

Found 1 expressions with local error:

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

rewrite6.0ms

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:
5.0ms
(+ x (* 1/2 (/ y x)))

series23.0ms

Counts
1 → 3
Calls
1 calls:
23.0ms
(+ x (* 1/2 (/ y x)))

simplify105.0ms

Counts
14 → 14
Iterations

Useful iterations: 1 (4.0ms)

IterNodesCost
08376
129769
2110169
3389169
4500169
done500169

prune23.0ms

Pruning

4 alts after pruning (0 fresh and 4 done)

Merged error: 0b

regimes141.0ms

Accuracy

99.9% (0.0b remaining)

Error of 0.0b against oracle of 0.0b and baseline of 21.8b

bsearch46.0ms

Steps
ItersRangePoint
9
8.224203313001901e+127
3.439700743057548e+134
1.4479473348721725e+133
9
-2.4426674496164293e+154
-1.2333471528461792e+149
-1.358575356778545e+154

simplify2.0ms

Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
02210
12910
23110
33110
done3110

end0.0ms

sample420.0ms

Algorithm
intervals
Results
152.0ms8000×body80valid
42.0ms2610×body80nan