Details

Time bar (total: 9.8s)

sample31.0ms

Algorithm
intervals
Results
10.0ms256×body80valid
3.0ms74×body80nan

simplify4.0ms

Counts
1 → 1
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
056
166
done66

prune12.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 19.8b

localize12.0ms

Local error

Found 1 expressions with local error:

18.4b
(sqrt (+ (* x x) y))

rewrite23.0ms

Algorithm
rewrite-expression-head
Rules
3×add-sqr-sqrt sqrt-prod
2×pow1 add-cube-cbrt *-un-lft-identity sqrt-div
1×add-exp-log rem-sqrt-square sqrt-pow1 flip3-+ pow1/2 add-cbrt-cube flip-+ add-log-exp
Counts
1 → 15
Calls
1 calls:
22.0ms
(sqrt (+ (* x x) y))

series64.0ms

Counts
1 → 3
Calls
1 calls:
64.0ms
(sqrt (+ (* x x) y))

simplify2.0s

Counts
18 → 18
Iterations

Useful iterations: 3 (706.0ms)

IterNodesCost
051195
1122173
2448157
32399154
done5003154

prune59.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0b

localize24.0ms

Local error

Found 4 expressions with local error:

0.1b
(sqrt (sqrt (+ (* x x) y)))
0.6b
(* (sqrt (sqrt (+ (* x x) y))) (sqrt (sqrt (+ (* x x) y))))
18.4b
(sqrt (+ (* x x) y))
18.4b
(sqrt (+ (* x x) y))

rewrite154.0ms

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:
14.0ms
(sqrt (sqrt (+ (* x x) y)))
95.0ms
(* (sqrt (sqrt (+ (* x x) y))) (sqrt (sqrt (+ (* x x) y))))
19.0ms
(sqrt (+ (* x x) y))
19.0ms
(sqrt (+ (* x x) y))

series252.0ms

Counts
4 → 12
Calls
4 calls:
80.0ms
(sqrt (sqrt (+ (* x x) y)))
64.0ms
(* (sqrt (sqrt (+ (* x x) y))) (sqrt (sqrt (+ (* x x) y))))
58.0ms
(sqrt (+ (* x x) y))
50.0ms
(sqrt (+ (* x x) y))

simplify1.1s

Counts
146 → 146
Iterations

Useful iterations: done (1.1s)

IterNodesCost
01382475
13081579
213341419
done50001396

prune518.0ms

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
(+ 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)))

series30.0ms

Counts
1 → 3
Calls
1 calls:
30.0ms
(+ x (* 1/2 (/ y x)))

simplify3.2s

Counts
14 → 14
Iterations

Useful iterations: 2 (50.0ms)

IterNodesCost
027166
186157
2302143
31157143
44751143
done5001143

prune47.0ms

Pruning

4 alts after pruning (1 fresh and 3 done)

Merged error: 0b

localize10.0ms

Local error

Found 1 expressions with local error:

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

rewrite23.0ms

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:
23.0ms
(- (* (/ y x) -1/2) x)

series78.0ms

Counts
1 → 3
Calls
1 calls:
78.0ms
(- (* (/ y x) -1/2) x)

simplify1.0s

Counts
15 → 15
Iterations

Useful iterations: 3 (238.0ms)

IterNodesCost
032173
182166
2235149
31297147
done5000147

prune45.0ms

Pruning

4 alts after pruning (0 fresh and 4 done)

Merged error: 0b

regimes218.0ms

Accuracy

99.4% (0.1b remaining)

Error of 0.1b against oracle of 0.0b and baseline of 21.4b

bsearch61.0ms

Steps
ItersRangePoint
7
8.459134100805035e+109
3.638681240743296e+111
3.588070708117172e+111
10
-9.986183728447351e+162
-1.6363070093370384e+150
-1.3649655464070602e+154

simplify4.0ms

Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
01828
12228
done2228

end0.0ms

sample734.0ms

Algorithm
intervals
Results
274.0ms8000×body80valid
72.0ms2603×body80nan