Details

Time bar (total: 14.5s)

sample22.0ms

Algorithm
intervals
Results
10.0ms256×body80valid

simplify2.9s

Counts
1 → 1
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
079
1179
2289
3419
4559
51179
63169
710559
839199
done50009

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.0b

localize13.0ms

Local error

Found 1 expressions with local error:

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

rewrite83.0ms

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:
78.0ms
(/ (- x y) (- 2.0 (+ x y)))

series66.0ms

Counts
1 → 3
Calls
1 calls:
66.0ms
(/ (- x y) (- 2.0 (+ x y)))

simplify666.0ms

Counts
63 → 63
Iterations

Useful iterations: done (663.0ms)

IterNodesCost
01141010
1289965
21052925
done5000923

prune146.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0b

localize9.0ms

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)))

rewrite568.0ms

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:
382.0ms
(- (/ x (- 2.0 (+ x y))) (/ y (- 2.0 (+ x y))))
40.0ms
(/ y (- 2.0 (+ x y)))
32.0ms
(/ x (- 2.0 (+ x y)))

series212.0ms

Counts
3 → 9
Calls
3 calls:
88.0ms
(- (/ x (- 2.0 (+ x y))) (/ y (- 2.0 (+ x y))))
60.0ms
(/ y (- 2.0 (+ x y)))
64.0ms
(/ x (- 2.0 (+ x y)))

simplify2.1s

Counts
731 → 731
Iterations

Useful iterations: 2 (745.0ms)

IterNodesCost
058044551
1133939990
2435131496
done500031496

prune1.6s

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0b

localize20.0ms

Local error

Found 4 expressions with local error:

0.5b
(* (cbrt (- x y)) (cbrt (- x y)))
0.5b
(cbrt (- x y))
0.5b
(cbrt (- x y))
0.5b
(cbrt (- x y))

rewrite70.0ms

Algorithm
rewrite-expression-head
Rules
43×cbrt-prod
37×add-sqr-sqrt
35×*-un-lft-identity
18×cbrt-div
15×add-cube-cbrt
11×pow1
10×swap-sqr
9×flip3-- pow1/3 flip-- distribute-lft-out--
8×associate-*r* associate-*l*
7×difference-of-squares
6×add-exp-log
4×expm1-log1p-u frac-times add-cbrt-cube log1p-expm1-u add-log-exp unswap-sqr
2×associate-*r/ pow-prod-down associate-*l/ pow-sqr pow-prod-up
1×pow2 pow-plus prod-exp *-commutative cbrt-unprod
Counts
4 → 109
Calls
4 calls:
47.0ms
(* (cbrt (- x y)) (cbrt (- x y)))
6.0ms
(cbrt (- x y))
7.0ms
(cbrt (- x y))
7.0ms
(cbrt (- x y))

series808.0ms

Counts
4 → 12
Calls
4 calls:
170.0ms
(* (cbrt (- x y)) (cbrt (- x y)))
213.0ms
(cbrt (- x y))
211.0ms
(cbrt (- x y))
214.0ms
(cbrt (- x y))

simplify910.0ms

Counts
121 → 121
Iterations

Useful iterations: done (906.0ms)

IterNodesCost
01351434
12951320
210331262
done50001209

prune385.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0b

localize16.0ms

Local error

Found 4 expressions with local error:

0.0b
(/ y (- 2.0 (+ x y)))
0.1b
(* (/ y (- 2.0 (+ x y))) (/ y (- 2.0 (+ x y))))
0.1b
(* (/ x (- 2.0 (+ x y))) (/ x (- 2.0 (+ x y))))
3.5b
(/ (- (* (/ x (- 2.0 (+ x y))) (/ x (- 2.0 (+ x y)))) (* (/ y (- 2.0 (+ x y))) (/ y (- 2.0 (+ x y))))) (+ (/ y (- 2.0 (+ x y))) (/ x (- 2.0 (+ x y)))))

rewrite844.0ms

Algorithm
rewrite-expression-head
Rules
738×*-un-lft-identity
438×times-frac
254×add-sqr-sqrt
164×distribute-lft-out--
154×add-cube-cbrt
147×distribute-lft-out
84×swap-sqr
58×difference-of-squares
48×associate-*r* associate-*l*
41×associate-/r/
32×add-exp-log add-cbrt-cube
25×associate-/r*
20×flip3-- flip-- div-inv
18×pow1
16×associate-/l/
15×distribute-rgt-out
12×associate-*r/ associate-*l/
10×cbrt-undiv frac-times div-exp
9×frac-sub
8×prod-exp cbrt-unprod unswap-sqr
7×associate-/l*
5×sub-div
4×expm1-log1p-u log1p-expm1-u add-log-exp
2×pow2 frac-2neg pow-plus pow-prod-down clear-num pow-sqr *-commutative pow-prod-up
1×flip3-+ div-sub frac-add flip-+
Counts
4 → 416
Calls
4 calls:
31.0ms
(/ y (- 2.0 (+ x y)))
195.0ms
(* (/ y (- 2.0 (+ x y))) (/ y (- 2.0 (+ x y))))
155.0ms
(* (/ x (- 2.0 (+ x y))) (/ x (- 2.0 (+ x y))))
432.0ms
(/ (- (* (/ x (- 2.0 (+ x y))) (/ x (- 2.0 (+ x y)))) (* (/ y (- 2.0 (+ x y))) (/ y (- 2.0 (+ x y))))) (+ (/ y (- 2.0 (+ x y))) (/ x (- 2.0 (+ x y)))))

series367.0ms

Counts
4 → 12
Calls
4 calls:
59.0ms
(/ y (- 2.0 (+ x y)))
64.0ms
(* (/ y (- 2.0 (+ x y))) (/ y (- 2.0 (+ x y))))
68.0ms
(* (/ x (- 2.0 (+ x y))) (/ x (- 2.0 (+ x y))))
175.0ms
(/ (- (* (/ x (- 2.0 (+ x y))) (/ x (- 2.0 (+ x y)))) (* (/ y (- 2.0 (+ x y))) (/ y (- 2.0 (+ x y))))) (+ (/ y (- 2.0 (+ x y))) (/ x (- 2.0 (+ x y)))))

simplify1.2s

Counts
428 → 428
Iterations

Useful iterations: done (1.2s)

IterNodesCost
045914938
1157613936
done500013260

prune921.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0b

regimes39.0ms

Accuracy

0% (1.3b remaining)

Error of 1.3b against oracle of 0.0b and baseline of 1.3b

bsearch0.0ms

simplify1.0ms

Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01020
11120
done1120

end0.0ms

sample528.0ms

Algorithm
intervals
Results
311.0ms7999×body80valid
0.0ms1×body640valid