Details

Time bar (total: 1.8s)

sample15.0ms

Algorithm
intervals
Results
4.0ms256×body80valid
1.0ms87×body80nan

simplify5.0ms

Counts
1 → 1
Iterations

Useful iterations: 0 (2.0ms)

IterNodesCost
073
173
done73

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 24.1b

localize4.0ms

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
add-sqr-sqrt
add-log-exp
pow1 add-cube-cbrt *-un-lft-identity sqrt-prod
add-exp-log expm1-log1p-u flip3-+ sqrt-div add-cbrt-cube flip-+ log1p-expm1-u
+-commutative rem-sqrt-square fma-def sqrt-pow1 pow1/2 sum-log hypot-def
Counts
2 → 32
Calls
2 calls:
7.0ms
(+ (* x x) y)
9.0ms
(sqrt (+ (* x x) y))

series66.0ms

Counts
2 → 6
Calls
2 calls:
20.0ms
(+ (* x x) y)
46.0ms
(sqrt (+ (* x x) y))

simplify56.0ms

Counts
38 → 38
Iterations

Useful iterations: 3 (53.0ms)

IterNodesCost
0153160
1518146
21716138
35002136
done5002136

prune86.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0b

localize10.0ms

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))

rewrite95.0ms

Algorithm
rewrite-expression-head
Rules
82×sqrt-prod
56×add-sqr-sqrt
38×sqrt-pow1
32×sqrt-div
31×pow1
20×add-cube-cbrt *-un-lft-identity pow1/2
15×swap-sqr
flip3-+ associate-*r* associate-*l* pow-prod-up flip-+ unswap-sqr
add-exp-log add-cbrt-cube
pow-prod-down pow-sqr
expm1-log1p-u frac-times rem-sqrt-square log1p-expm1-u add-log-exp
associate-*r/ associate-*l/ hypot-def
pow2 pow-plus sqrt-unprod prod-exp rem-square-sqrt *-commutative cbrt-unprod
Counts
4 → 144
Calls
4 calls:
10.0ms
(sqrt (sqrt (+ (* x x) y)))
60.0ms
(* (sqrt (sqrt (+ (* x x) y))) (sqrt (sqrt (+ (* x x) y))))
9.0ms
(sqrt (+ (* x x) y))
10.0ms
(sqrt (+ (* x x) y))

series205.0ms

Counts
4 → 12
Calls
4 calls:
78.0ms
(sqrt (sqrt (+ (* x x) y)))
40.0ms
(* (sqrt (sqrt (+ (* x x) y))) (sqrt (sqrt (+ (* x x) y))))
40.0ms
(sqrt (+ (* x x) y))
47.0ms
(sqrt (+ (* x x) y))

simplify50.0ms

Counts
156 → 156
Iterations

Useful iterations: 2 (39.0ms)

IterNodesCost
0279927
11130856
25001822
done5001822

prune294.0ms

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
(fma 1/2 (/ y x) x)

rewrite1.0ms

Algorithm
rewrite-expression-head
Rules
pow1 add-exp-log add-sqr-sqrt expm1-log1p-u add-cube-cbrt *-un-lft-identity add-cbrt-cube fma-udef log1p-expm1-u add-log-exp
Counts
1 → 10
Calls
1 calls:
0.0ms
(fma 1/2 (/ y x) x)

series38.0ms

Counts
1 → 3
Calls
1 calls:
38.0ms
(fma 1/2 (/ y x) x)

simplify80.0ms

Counts
13 → 13
Iterations

Useful iterations: 1 (4.0ms)

IterNodesCost
02144
14839
215639
358539
4278439
5500139
done500139

prune23.0ms

Pruning

4 alts after pruning (1 fresh and 3 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
fma-def add-log-exp
add-sqr-sqrt add-cube-cbrt *-un-lft-identity
pow1 add-exp-log +-commutative expm1-log1p-u flip3-+ sum-log add-cbrt-cube flip-+ log1p-expm1-u
Counts
1 → 16
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)))

simplify121.0ms

Counts
19 → 19
Iterations

Useful iterations: 1 (5.0ms)

IterNodesCost
08884
132270
2125370
3455270
4500170
done500170

prune33.0ms

Pruning

4 alts after pruning (0 fresh and 4 done)

Merged error: 0b

regimes152.0ms

Accuracy

99.9% (0.0b remaining)

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

bsearch44.0ms

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

simplify7.0ms

Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
0239
1309
2329
3329
done329

end0.0ms

sample395.0ms

Algorithm
intervals
Results
140.0ms8000×body80valid
40.0ms2610×body80nan