Details

Time bar (total: 12.9s)

sample57.0ms

Algorithm
intervals
Results
20.0ms256×body80valid
18.0ms256×pre80true

simplify4.2s

Counts
1 → 1
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0915
12215
24815
310115
418815
534615
657915
787515
8227115
done500015

prune17.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 21.8b

localize10.0ms

Local error

Found 2 expressions with local error:

0.0b
(+ (* x x) (* y y))
21.8b
(/ (* (- x y) (+ x y)) (+ (* x x) (* y y)))

rewrite51.0ms

Algorithm
rewrite-expression-head
Rules
8×associate-/l/
7×add-exp-log add-cbrt-cube
5×flip3-+ flip-+
4×add-sqr-sqrt frac-times add-cube-cbrt *-un-lft-identity add-log-exp
3×flip3-- times-frac associate-/r* flip--
2×pow1 cbrt-undiv associate-*r/ div-exp associate-*l/ associate-/r/
1×+-commutative frac-2neg prod-exp clear-num sum-log cbrt-unprod div-inv associate-/l*
Counts
2 → 42
Calls
2 calls:
13.0ms
(+ (* x x) (* y y))
37.0ms
(/ (* (- x y) (+ x y)) (+ (* x x) (* y y)))

series161.0ms

Counts
2 → 6
Calls
2 calls:
53.0ms
(+ (* x x) (* y y))
108.0ms
(/ (* (- x y) (+ x y)) (+ (* x x) (* y y)))

simplify1.1s

Counts
48 → 48
Iterations

Useful iterations: done (1.1s)

IterNodesCost
091826
1303802
21443662
done5000655

prune197.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.5b

localize20.0ms

Local error

Found 3 expressions with local error:

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

rewrite159.0ms

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-exp-log add-cbrt-cube
9×flip3-+ flip-+
8×div-inv associate-/l*
5×add-log-exp
4×cbrt-undiv div-exp associate-/l/
3×pow1
2×frac-2neg clear-num
1×+-commutative flip3-- div-sub sum-log flip--
Counts
3 → 177
Calls
3 calls:
8.0ms
(+ (* x x) (* y y))
68.0ms
(/ (- x y) (/ (+ (* x x) (* y y)) (+ x y)))
73.0ms
(/ (+ (* x x) (* y y)) (+ x y))

series200.0ms

Counts
3 → 9
Calls
3 calls:
45.0ms
(+ (* x x) (* y y))
83.0ms
(/ (- x y) (/ (+ (* x x) (* y y)) (+ x y)))
69.0ms
(/ (+ (* x x) (* y y)) (+ x y))

simplify1.9s

Counts
186 → 186
Iterations

Useful iterations: done (1.9s)

IterNodesCost
02454688
16974481
225064301
done50004282

prune545.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.4b

localize29.0ms

Local error

Found 4 expressions with local error:

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

rewrite569.0ms

Algorithm
rewrite-expression-head
Rules
228×times-frac
213×*-un-lft-identity
129×add-sqr-sqrt
93×add-cube-cbrt
32×distribute-lft-out
26×associate-/r*
25×distribute-lft-out--
19×associate-/r/
13×add-exp-log add-cbrt-cube
11×div-inv
10×flip3-+ flip-+
9×associate-/l* difference-of-squares
6×add-log-exp
5×cbrt-undiv div-exp
4×pow1 associate-/l/
3×frac-2neg clear-num
2×distribute-rgt-out--
1×sub-neg flip3-- diff-log frac-sub flip-- sub-div
Counts
4 → 210
Calls
4 calls:
421.0ms
(- (/ x (/ (+ (* x x) (* y y)) (+ x y))) (/ y (/ (+ (* x x) (* y y)) (+ x y))))
34.0ms
(/ y (/ (+ (* x x) (* y y)) (+ x y)))
50.0ms
(/ (+ (* x x) (* y y)) (+ x y))
48.0ms
(/ (+ (* x x) (* y y)) (+ x y))

series298.0ms

Counts
4 → 12
Calls
4 calls:
87.0ms
(- (/ x (/ (+ (* x x) (* y y)) (+ x y))) (/ y (/ (+ (* x x) (* y y)) (+ x y))))
70.0ms
(/ y (/ (+ (* x x) (* y y)) (+ x y)))
75.0ms
(/ (+ (* x x) (* y y)) (+ x y))
66.0ms
(/ (+ (* x x) (* y y)) (+ x y))

simplify1.3s

Counts
222 → 222
Iterations

Useful iterations: done (1.3s)

IterNodesCost
02675448
16185246
220714876
done50004860

prune803.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0.4b

localize0.0ms

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: 0.4b

regimes84.0ms

Accuracy

73.7% (5.2b remaining)

Error of 5.7b against oracle of 0.5b and baseline of 20.2b

bsearch142.0ms

Steps
ItersRangePoint
6
2.9279685249567416e-168
2.6375677437861027e-167
3.401055982211938e-168
8
9.824641264729823e-205
2.911049425072326e-200
2.835103494848979e-200
9
-4.5014022528895856e-160
-1.9657628581050384e-165
-4.057021676631311e-160
9
-6291016968.746921
-7465.585501010854
-6208632077.041414

simplify3.0ms

Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
02349
12749
done2749

end0.0ms

sample1.0s

Algorithm
intervals
Results
657.0ms8000×body80valid
184.0ms8000×pre80true