Details

Time bar (total: 7.4s)

sample32.0ms

Algorithm
intervals
Results
15.0ms256×body80valid

simplify212.0ms

Counts
1 → 1
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0919
11719
23519
36719
411419
516619
619519
719919
done19919

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 30.1b

localize12.0ms

Local error

Found 2 expressions with local error:

3.3b
(- (* x x) (* (* y 4.0) y))
29.6b
(/ (- (* x x) (* (* y 4.0) y)) (+ (* x x) (* (* y 4.0) y)))

rewrite46.0ms

Algorithm
rewrite-expression-head
Rules
10×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
9×times-frac
4×add-exp-log add-cbrt-cube add-log-exp
3×associate-/r* associate-/l*
2×pow1 flip3-- associate-/r/ flip-- associate-/l/
1×cbrt-undiv sub-neg frac-2neg flip3-+ diff-log div-sub div-exp clear-num flip-+ div-inv
Counts
2 → 44
Calls
2 calls:
8.0ms
(- (* x x) (* (* y 4.0) y))
36.0ms
(/ (- (* x x) (* (* y 4.0) y)) (+ (* x x) (* (* y 4.0) y)))

series161.0ms

Counts
2 → 6
Calls
2 calls:
63.0ms
(- (* x x) (* (* y 4.0) y))
98.0ms
(/ (- (* x x) (* (* y 4.0) y)) (+ (* x x) (* (* y 4.0) y)))

simplify745.0ms

Counts
50 → 50
Iterations

Useful iterations: done (742.0ms)

IterNodesCost
0821196
12371174
211631062
done50011060

prune260.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.3b

localize27.0ms

Local error

Found 3 expressions with local error:

0.0b
(- (/ (* x x) (+ (* x x) (* (* y 4.0) y))) (/ (* (* y 4.0) y) (+ (* x x) (* (* y 4.0) y))))
21.2b
(/ (* (* y 4.0) y) (+ (* x x) (* (* y 4.0) y)))
24.0b
(/ (* x x) (+ (* x x) (* (* y 4.0) y)))

rewrite194.0ms

Algorithm
rewrite-expression-head
Rules
17×add-exp-log add-cbrt-cube
11×add-sqr-sqrt
9×*-un-lft-identity
8×associate-/r/
7×add-cube-cbrt times-frac
6×associate-/r*
5×cbrt-undiv div-exp add-log-exp
4×flip3-+ prod-exp cbrt-unprod flip-+ div-inv
3×pow1 distribute-rgt-out--
2×frac-2neg clear-num associate-/l* difference-of-squares
1×sub-neg flip3-- diff-log frac-sub flip-- distribute-lft-out-- sub-div
Counts
3 → 68
Calls
3 calls:
119.0ms
(- (/ (* x x) (+ (* x x) (* (* y 4.0) y))) (/ (* (* y 4.0) y) (+ (* x x) (* (* y 4.0) y))))
53.0ms
(/ (* (* y 4.0) y) (+ (* x x) (* (* y 4.0) y)))
18.0ms
(/ (* x x) (+ (* x x) (* (* y 4.0) y)))

series291.0ms

Counts
3 → 9
Calls
3 calls:
111.0ms
(- (/ (* x x) (+ (* x x) (* (* y 4.0) y))) (/ (* (* y 4.0) y) (+ (* x x) (* (* y 4.0) y))))
91.0ms
(/ (* (* y 4.0) y) (+ (* x x) (* (* y 4.0) y)))
88.0ms
(/ (* x x) (+ (* x x) (* (* y 4.0) y)))

simplify2.5s

Counts
77 → 77
Iterations

Useful iterations: done (2.5s)

IterNodesCost
01301924
14071818
227761606
done50011602

prune241.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.3b

localize21.0ms

Local error

Found 4 expressions with local error:

0.0b
(- (/ (* x x) (+ (* x x) (* (* y 4.0) y))) (/ 1 (/ (+ (* x x) (* (* y 4.0) y)) (* (* y 4.0) y))))
0.4b
(/ 1 (/ (+ (* x x) (* (* y 4.0) y)) (* (* y 4.0) y)))
20.9b
(/ (+ (* x x) (* (* y 4.0) y)) (* (* y 4.0) y))
24.0b
(/ (* x x) (+ (* x x) (* (* y 4.0) y)))

rewrite265.0ms

Algorithm
rewrite-expression-head
Rules
52×add-exp-log
46×times-frac
38×add-sqr-sqrt
32×add-cbrt-cube
29×*-un-lft-identity
24×add-cube-cbrt
22×div-exp
13×prod-exp
12×cbrt-undiv
11×associate-/r*
8×div-inv
7×cbrt-unprod associate-/l*
6×add-log-exp difference-of-squares
5×pow1
4×rec-exp 1-exp
3×frac-2neg clear-num associate-/r/
2×flip3-+ flip-+ associate-/l/ distribute-lft-out--
1×sub-neg flip3-- pow-flip diff-log frac-sub flip-- inv-pow
Counts
4 → 129
Calls
4 calls:
140.0ms
(- (/ (* x x) (+ (* x x) (* (* y 4.0) y))) (/ 1 (/ (+ (* x x) (* (* y 4.0) y)) (* (* y 4.0) y))))
52.0ms
(/ 1 (/ (+ (* x x) (* (* y 4.0) y)) (* (* y 4.0) y)))
45.0ms
(/ (+ (* x x) (* (* y 4.0) y)) (* (* y 4.0) y))
19.0ms
(/ (* x x) (+ (* x x) (* (* y 4.0) y)))

series347.0ms

Counts
4 → 12
Calls
4 calls:
103.0ms
(- (/ (* x x) (+ (* x x) (* (* y 4.0) y))) (/ 1 (/ (+ (* x x) (* (* y 4.0) y)) (* (* y 4.0) y))))
93.0ms
(/ 1 (/ (+ (* x x) (* (* y 4.0) y)) (* (* y 4.0) y)))
83.0ms
(/ (+ (* x x) (* (* y 4.0) y)) (* (* y 4.0) y))
69.0ms
(/ (* x x) (+ (* x x) (* (* y 4.0) y)))

simplify400.0ms

Counts
141 → 141
Iterations

Useful iterations: done (394.0ms)

IterNodesCost
02203773
16633503
done50003187

prune499.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0.3b

localize1.0ms

rewrite0.0ms

Algorithm
rewrite-expression-head
Rules
Counts
0 → 0

series0.0ms

Counts
0 → 0

simplify0.0ms

Counts
0 → 0
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
000
done00

prune0.0ms

Pruning

4 alts after pruning (1 fresh and 3 done)

Merged error: 0.3b

regimes257.0ms

Accuracy

53.7% (14.3b remaining)

Error of 14.7b against oracle of 0.4b and baseline of 31.3b

bsearch142.0ms

Steps
ItersRangePoint
10
5.167486607436607e+189
1.579909217741876e+200
2.6000500965086023e+199
7
4.9870422886920376e+101
3.527056463873254e+103
5.054706620732832e+101
7
3.190648122733064e-18
7.485433461213294e-17
2.080267309844611e-17
8
2.5170704355541145e-165
3.3521330590547855e-162
1.89336738182365e-164
9
4.618542844504654e-202
3.093253510056225e-194
8.146242059652438e-197
0
0.0
4.9406564584125e-324
0.0

simplify8.0ms

Iterations

Useful iterations: 0 (2.0ms)

IterNodesCost
034142
139142
done39142

end0.0ms

sample815.0ms

Algorithm
intervals
Results
530.0ms8000×body80valid