Details

Time bar (total: 8.5s)

sample32.0ms

Algorithm
intervals
Results
11.0ms256×body80valid
3.0ms68×body80nan

simplify4.0ms

Counts
1 → 1
Iterations
IterNodes
done6
16
05

prune7.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 24.9b

localize13.0ms

Local error

Found 1 expressions with local error:

23.2b
(sqrt (+ (* x x) y))

rewrite16.0ms

Algorithm
rewrite-expression-head
Rules
3×add-sqr-sqrt sqrt-prod
2×pow1 *-un-lft-identity sqrt-div add-cube-cbrt
1×rem-sqrt-square sqrt-pow1 flip3-+ add-cbrt-cube pow1/2 add-exp-log flip-+ add-log-exp
Counts
1 → 15
Calls
1 calls:
15.0ms
(sqrt (+ (* x x) y))

series79.0ms

Counts
1 → 3
Calls
1 calls:
79.0ms
(sqrt (+ (* x x) y))

simplify1.8s

Counts
18 → 18
Iterations
IterNodes
done5000
32548
2454
1122
051

prune143.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0b

localize21.0ms

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))))
23.2b
(sqrt (+ (* x x) y))
23.2b
(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×*-un-lft-identity pow1/2 add-cube-cbrt
15×swap-sqr
9×flip3-+ associate-*r* associate-*l* pow-prod-up flip-+ unswap-sqr
6×add-cbrt-cube add-exp-log
5×pow-prod-down pow-sqr
4×frac-times rem-sqrt-square add-log-exp
2×associate-*l/ associate-*r/
1×pow2 rem-square-sqrt pow-plus sqrt-unprod prod-exp *-commutative cbrt-unprod
Counts
4 → 134
Calls
4 calls:
9.0ms
(sqrt (sqrt (+ (* x x) y)))
65.0ms
(* (sqrt (sqrt (+ (* x x) y))) (sqrt (sqrt (+ (* x x) y))))
7.0ms
(sqrt (+ (* x x) y))
7.0ms
(sqrt (+ (* x x) y))

series255.0ms

Counts
4 → 12
Calls
4 calls:
88.0ms
(sqrt (sqrt (+ (* x x) y)))
60.0ms
(* (sqrt (sqrt (+ (* x x) y))) (sqrt (sqrt (+ (* x x) y))))
51.0ms
(sqrt (+ (* x x) y))
55.0ms
(sqrt (+ (* x x) y))

simplify1.1s

Counts
146 → 146
Iterations
IterNodes
done5000
21332
1308
0138

prune414.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0b

localize8.0ms

Local error

Found 1 expressions with local error:

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

rewrite23.0ms

Algorithm
rewrite-expression-head
Rules
14×add-sqr-sqrt
13×associate-*r*
10×times-frac
9×*-un-lft-identity add-cube-cbrt
6×add-cbrt-cube add-exp-log
3×pow1 associate-*l*
2×prod-exp cbrt-unprod unswap-sqr
1×cbrt-undiv div-exp pow-prod-down associate-*r/ *-commutative div-inv add-log-exp
Counts
1 → 32
Calls
1 calls:
21.0ms
(* 1/2 (/ y x))

series19.0ms

Counts
1 → 3
Calls
1 calls:
19.0ms
(* 1/2 (/ y x))

simplify1.7s

Counts
35 → 35
Iterations
IterNodes
done5000
32504
2572
1178
068

prune151.0ms

Pruning

4 alts after pruning (1 fresh and 3 done)

Merged error: 0b

localize14.0ms

Local error

Found 1 expressions with local error:

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

rewrite21.0ms

Algorithm
rewrite-expression-head
Rules
14×add-sqr-sqrt
13×associate-*r*
10×times-frac
9×*-un-lft-identity add-cube-cbrt
6×add-cbrt-cube add-exp-log
3×pow1 associate-*l*
2×prod-exp cbrt-unprod unswap-sqr
1×cbrt-undiv div-exp pow-prod-down associate-*r/ *-commutative div-inv add-log-exp
Counts
1 → 32
Calls
1 calls:
19.0ms
(* -1/2 (/ y x))

series28.0ms

Counts
1 → 3
Calls
1 calls:
28.0ms
(* -1/2 (/ y x))

simplify1.3s

Counts
35 → 35
Iterations
IterNodes
done5001
32505
2572
1178
068

prune98.0ms

Pruning

4 alts after pruning (0 fresh and 4 done)

Merged error: 0b

regimes358.0ms

Accuracy

100% (0.0b remaining)

Error of 0.0b against oracle of 0.0b and baseline of 21.5b

bsearch76.0ms

Steps
ItersRangePoint
7
3.6808033284981034e+145
9.595693332345167e+146
8.914808959129563e+145
8
-4.755519083684039e+154
-2.121197795503813e+151
-1.3527325623815516e+154

simplify5.0ms

Iterations
IterNodes
done22
122
018

end0.0ms

sample688.0ms

Algorithm
intervals
Results
308.0ms8000×body80valid
110.0ms2610×body80nan