Details

Time bar (total: 9.9s)

sample14.0ms

Algorithm
intervals
Results
5.0ms256×body80valid

simplify145.0ms

Counts
1 → 1
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
079
1179
2289
3419
4549
5659
6779
7899
8969
91049
101059
111079
121089
done1089

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.0b

localize6.0ms

Local error

Found 1 expressions with local error:

0.0b
(/ (- x y) (- 2.0 (+ x y)))

rewrite45.0ms

Algorithm
rewrite-expression-head
Rules
58×*-un-lft-identity
40×add-sqr-sqrt
30×times-frac
19×distribute-lft-out--
14×add-cube-cbrt
13×difference-of-squares
6×associate-/r* distribute-lft-out
5×associate-/l*
3×add-exp-log add-cbrt-cube
2×flip3-- associate-/r/ flip-- associate-/l/
1×pow1 cbrt-undiv expm1-log1p-u frac-2neg div-sub div-exp clear-num log1p-expm1-u div-inv add-log-exp
Counts
1 → 60
Calls
1 calls:
43.0ms
(/ (- x y) (- 2.0 (+ x y)))

series54.0ms

Counts
1 → 3
Calls
1 calls:
54.0ms
(/ (- x y) (- 2.0 (+ x y)))

simplify1.2s

Counts
63 → 63
Iterations

Useful iterations: 3 (416.0ms)

IterNodesCost
01141010
1284965
2745923
32060921
done5000921

prune110.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0b

localize7.0ms

Local error

Found 3 expressions with local error:

0.0b
(- (/ x (- 2.0 (+ x y))) (/ y (- 2.0 (+ x y))))
0.0b
(/ y (- 2.0 (+ x y)))
0.0b
(/ x (- 2.0 (+ x y)))

rewrite393.0ms

Algorithm
rewrite-expression-head
Rules
1352×*-un-lft-identity
946×times-frac
843×add-sqr-sqrt
576×prod-diff
517×add-cube-cbrt
335×distribute-lft-out--
161×distribute-lft-out difference-of-squares
106×associate-/r/
54×flip3-- flip--
53×div-inv
24×fma-neg
12×associate-/r*
7×add-exp-log add-cbrt-cube
6×associate-/l*
5×add-log-exp
3×pow1 expm1-log1p-u distribute-rgt-out-- log1p-expm1-u
2×cbrt-undiv frac-2neg div-exp clear-num
1×sub-neg diff-log frac-sub sub-div
Counts
3 → 722
Calls
3 calls:
249.0ms
(- (/ x (- 2.0 (+ x y))) (/ y (- 2.0 (+ x y))))
30.0ms
(/ y (- 2.0 (+ x y)))
28.0ms
(/ x (- 2.0 (+ x y)))

series172.0ms

Counts
3 → 9
Calls
3 calls:
70.0ms
(- (/ x (- 2.0 (+ x y))) (/ y (- 2.0 (+ x y))))
52.0ms
(/ y (- 2.0 (+ x y)))
49.0ms
(/ x (- 2.0 (+ x y)))

simplify2.0s

Counts
731 → 731
Iterations

Useful iterations: done (1.9s)

IterNodesCost
058044551
1129639894
2283530752
done500122997

prune594.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0b

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b
(/ y (- (- 2.0 x) y))
0.0b
(/ x (- 2.0 (+ x y)))
0.3b
(pow (cbrt (/ x (- 2.0 (+ x y)))) 3)
7.2b
(cbrt (/ x (- 2.0 (+ x y))))

rewrite123.0ms

Algorithm
rewrite-expression-head
Rules
144×*-un-lft-identity
93×add-sqr-sqrt
90×times-frac
72×cbrt-prod
59×add-cube-cbrt
38×distribute-lft-out--
27×unpow-prod-down cube-prod
17×difference-of-squares
13×distribute-lft-out
12×associate-/r*
10×associate-/r/
9×add-exp-log
8×add-cbrt-cube
6×associate-/l*
5×pow1 flip3-- flip-- div-inv
4×expm1-log1p-u log1p-expm1-u add-log-exp
3×pow-unpow
2×cbrt-undiv cbrt-div pow-pow frac-2neg pow1/3 div-exp clear-num
1×cube-div cube-mult pow-to-exp unpow3 pow-exp rem-cube-cbrt sqr-pow
Counts
4 → 196
Calls
4 calls:
36.0ms
(/ y (- (- 2.0 x) y))
28.0ms
(/ x (- 2.0 (+ x y)))
35.0ms
(pow (cbrt (/ x (- 2.0 (+ x y)))) 3)
15.0ms
(cbrt (/ x (- 2.0 (+ x y))))

series453.0ms

Counts
4 → 12
Calls
4 calls:
49.0ms
(/ y (- (- 2.0 x) y))
55.0ms
(/ x (- 2.0 (+ x y)))
216.0ms
(pow (cbrt (/ x (- 2.0 (+ x y)))) 3)
134.0ms
(cbrt (/ x (- 2.0 (+ x y))))

simplify1.1s

Counts
208 → 208
Iterations

Useful iterations: done (1.1s)

IterNodesCost
03033343
17652799
220962616
done50002610

prune485.0ms

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0b

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b
(/ x (- 2.0 (+ x y)))
0.0b
(* (+ x y) (+ x y))
7.2b
(* (/ y (- (* 2.0 2.0) (* (+ x y) (+ x y)))) (+ 2.0 (+ x y)))
12.8b
(/ y (- (* 2.0 2.0) (* (+ x y) (+ x y))))

rewrite168.0ms

Algorithm
rewrite-expression-head
Rules
76×*-un-lft-identity
52×add-sqr-sqrt
43×times-frac
37×add-cube-cbrt
22×associate-*l*
15×add-exp-log add-cbrt-cube
13×pow1 distribute-lft-out
11×difference-of-squares
10×associate-/r*
9×associate-*r*
8×flip3-+ flip-+ distribute-lft-out--
6×frac-times swap-sqr associate-/r/ associate-/l*
4×expm1-log1p-u associate-*r/ log1p-expm1-u add-log-exp
3×cbrt-undiv flip3-- div-exp associate-*l/ prod-exp flip-- cbrt-unprod div-inv unswap-sqr
2×distribute-rgt-in frac-2neg distribute-lft-in pow-prod-down clear-num *-commutative
1×pow2 pow-plus pow-sqr pow-prod-up
Counts
4 → 167
Calls
4 calls:
28.0ms
(/ x (- 2.0 (+ x y)))
34.0ms
(* (+ x y) (+ x y))
83.0ms
(* (/ y (- (* 2.0 2.0) (* (+ x y) (+ x y)))) (+ 2.0 (+ x y)))
16.0ms
(/ y (- (* 2.0 2.0) (* (+ x y) (+ x y))))

series251.0ms

Counts
4 → 12
Calls
4 calls:
54.0ms
(/ x (- 2.0 (+ x y)))
16.0ms
(* (+ x y) (+ x y))
96.0ms
(* (/ y (- (* 2.0 2.0) (* (+ x y) (+ x y)))) (+ 2.0 (+ x y)))
86.0ms
(/ y (- (* 2.0 2.0) (* (+ x y) (+ x y))))

simplify1.8s

Counts
179 → 179
Iterations

Useful iterations: done (1.8s)

IterNodesCost
02712996
17922821
233252586
done50002469

prune496.0ms

Pruning

2 alts after pruning (0 fresh and 2 done)

Merged error: 0b

regimes29.0ms

Accuracy

0% (0.2b remaining)

Error of 0.2b against oracle of 0.0b and baseline of 0.2b

bsearch0.0ms

simplify2.0ms

Iterations

Useful iterations: 1 (1.0ms)

IterNodesCost
01520
11718
done1718

end0.0ms

sample333.0ms

Algorithm
intervals
Results
164.0ms7998×body80valid
0.0ms1×body1280valid
0.0ms1×body320valid