Details

Time bar (total: 11.7s)

sample44.0ms

Algorithm
intervals
Results
15.0ms256×body80valid
7.0ms256×pre80true

simplify2.2s

Counts
1 → 1
Iterations
IterNodes
done5000
73699
6840
5403
4208
3103
248
122
09

prune17.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 20.7b

localize18.0ms

Local error

Found 3 expressions with local error:

0.0b
(+ (* x x) (* y y))
0.0b
(/ (- x y) (/ (+ (* x x) (* y y)) (+ y x)))
19.9b
(/ (+ (* x x) (* y y)) (+ y x))

rewrite103.0ms

Algorithm
rewrite-expression-head
Rules
174×times-frac
161×*-un-lft-identity
117×add-sqr-sqrt
79×add-cube-cbrt
22×associate-/r* distribute-lft-out
19×distribute-lft-out-- difference-of-squares
15×associate-/r/
10×add-cbrt-cube add-exp-log
9×flip3-+ flip-+
8×div-inv associate-/l*
5×add-log-exp
4×cbrt-undiv div-exp associate-/l/
3×pow1
2×clear-num frac-2neg
1×+-commutative sum-log flip3-- div-sub flip--
Counts
3 → 177
Calls
3 calls:
6.0ms
(+ (* x x) (* y y))
47.0ms
(/ (- x y) (/ (+ (* x x) (* y y)) (+ y x)))
41.0ms
(/ (+ (* x x) (* y y)) (+ y x))

series205.0ms

Counts
3 → 9
Calls
3 calls:
47.0ms
(+ (* x x) (* y y))
80.0ms
(/ (- x y) (/ (+ (* x x) (* y y)) (+ y x)))
78.0ms
(/ (+ (* x x) (* y y)) (+ y x))

simplify1.5s

Counts
186 → 186
Iterations
IterNodes
done5001
24896
1814
0248

prune814.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.7b

localize7.0ms

rewrite0.0ms

Algorithm
rewrite-expression-head
Rules
Counts
0 → 0

series0.0ms

Counts
0 → 0

simplify0.0ms

Counts
0 → 0
Iterations
IterNodes
done0
00

prune21.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.7b

localize39.0ms

Local error

Found 4 expressions with local error:

0.0b
(/ (- x y) (sqrt (+ (* y y) (* x x))))
0.0b
(/ (sqrt (+ (* x x) (* y y))) (+ y x))
19.8b
(sqrt (+ (* x x) (* y y)))
19.8b
(sqrt (+ (* y y) (* x x)))

rewrite83.0ms

Algorithm
rewrite-expression-head
Rules
70×*-un-lft-identity
58×add-sqr-sqrt
54×times-frac
42×add-cube-cbrt
39×sqrt-prod
11×associate-/l*
10×associate-/r*
8×add-cbrt-cube sqrt-div add-exp-log
7×distribute-lft-out distribute-lft-out-- difference-of-squares
6×pow1
5×flip3-+ flip-+
4×associate-/r/ add-log-exp associate-/l/
2×cbrt-undiv rem-sqrt-square clear-num frac-2neg sqrt-pow1 pow1/2 div-exp div-inv
1×flip3-- div-sub flip--
Counts
4 → 138
Calls
4 calls:
28.0ms
(/ (- x y) (sqrt (+ (* y y) (* x x))))
23.0ms
(/ (sqrt (+ (* x x) (* y y))) (+ y x))
12.0ms
(sqrt (+ (* x x) (* y y)))
12.0ms
(sqrt (+ (* y y) (* x x)))

series358.0ms

Counts
4 → 12
Calls
4 calls:
127.0ms
(/ (- x y) (sqrt (+ (* y y) (* x x))))
116.0ms
(/ (sqrt (+ (* x x) (* y y))) (+ y x))
55.0ms
(sqrt (+ (* x x) (* y y)))
60.0ms
(sqrt (+ (* y y) (* x x)))

simplify1.2s

Counts
150 → 150
Iterations
IterNodes
done5001
21934
1427
0195

prune717.0ms

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0.7b

localize64.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (+ x y) (/ (- x y) (+ (* y y) (* x x))))
20.0b
(/ (- x y) (+ (* y y) (* x x)))
20.0b
(/ (- x y) (+ (* y y) (* x x)))
20.0b
(/ (- x y) (+ (* y y) (* x x)))

rewrite150.0ms

Algorithm
rewrite-expression-head
Rules
79×add-sqr-sqrt
76×*-un-lft-identity
61×times-frac
44×add-cube-cbrt
21×associate-*r*
15×add-cbrt-cube add-exp-log associate-/l* distribute-lft-out-- difference-of-squares
9×associate-/r*
8×associate-/r/
6×pow1 flip3-+ flip-+ associate-/l/
4×cbrt-undiv div-exp associate-*l* div-inv add-log-exp
3×clear-num frac-2neg flip3-- div-sub flip--
2×frac-times associate-*l/ prod-exp cbrt-unprod unswap-sqr
1×pow-prod-down associate-*r/ *-commutative distribute-lft-out
Counts
4 → 165
Calls
4 calls:
71.0ms
(* (+ x y) (/ (- x y) (+ (* y y) (* x x))))
29.0ms
(/ (- x y) (+ (* y y) (* x x)))
18.0ms
(/ (- x y) (+ (* y y) (* x x)))
20.0ms
(/ (- x y) (+ (* y y) (* x x)))

series322.0ms

Counts
4 → 12
Calls
4 calls:
104.0ms
(* (+ x y) (/ (- x y) (+ (* y y) (* x x))))
61.0ms
(/ (- x y) (+ (* y y) (* x x)))
62.0ms
(/ (- x y) (+ (* y y) (* x x)))
95.0ms
(/ (- x y) (+ (* y y) (* x x)))

simplify1.3s

Counts
177 → 177
Iterations
IterNodes
done5000
22667
1401
0134

prune1.1s

Pruning

5 alts after pruning (2 fresh and 3 done)

Merged error: 0.7b

regimes131.0ms

Accuracy

77.5% (4.7b remaining)

Error of 5.2b against oracle of 0.5b and baseline of 21.5b

bsearch173.0ms

Steps
ItersRangePoint
8
6.407984111669537e-169
7.540032000890206e-165
7.425329178057677e-165
8
-9.89376127309662e-187
-2.6494694123937767e-189
-9.739334495050349e-187
8
-9.53817991064458e-160
-5.549334443309092e-163
-7.512106064144896e-163
7
-9.685109581380507e+154
-1.5171851739610474e+153
-1.3662083597641618e+154

simplify4.0ms

Iterations
IterNodes
done36
136
030

end0.0ms

sample1.2s

Algorithm
intervals
Results
616.0ms8000×body80valid
247.0ms8000×pre80true