Details

Time bar (total: 31.2s)

sample16.0ms

Algorithm
intervals
Results
7.0ms255×body80valid
0.0ms1×body1280valid

simplify136.0ms

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)))

rewrite47.0ms

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 frac-2neg div-sub div-exp clear-num div-inv add-log-exp
Counts
1 → 58
Calls
1 calls:
45.0ms
(/ (- x y) (- 2.0 (+ x y)))

series51.0ms

Counts
1 → 3
Calls
1 calls:
51.0ms
(/ (- x y) (- 2.0 (+ x y)))

simplify1.2s

Counts
61 → 61
Iterations

Useful iterations: 3 (400.0ms)

IterNodesCost
0112990
1276951
2712905
31924903
done5000903

prune123.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.0b

localize18.0ms

Local error

Found 4 expressions with local error:

0.4b
(/ 1 (* (cbrt (- 2.0 (+ x y))) (cbrt (- 2.0 (+ x y)))))
0.6b
(cbrt (- 2.0 (+ x y)))
0.6b
(cbrt (- 2.0 (+ x y)))
0.6b
(cbrt (- 2.0 (+ x y)))

rewrite159.0ms

Algorithm
rewrite-expression-head
Rules
24×*-un-lft-identity
18×cbrt-prod cbrt-div
15×add-exp-log add-sqr-sqrt
12×pow1
9×add-cube-cbrt flip3-- pow-flip pow1/3 flip--
8×associate-/r/
7×add-cbrt-cube
6×distribute-lft-out--
4×frac-times div-exp add-log-exp
3×times-frac prod-exp distribute-lft-out associate-/l* difference-of-squares
2×cbrt-undiv rec-exp 1-exp associate-*r/ pow-prod-down associate-*l/ pow-sqr pow-prod-up
1×pow2 frac-2neg pow-plus clear-num associate-/r* cbrt-unprod div-inv inv-pow
Counts
4 → 91
Calls
4 calls:
97.0ms
(/ 1 (* (cbrt (- 2.0 (+ x y))) (cbrt (- 2.0 (+ x y)))))
17.0ms
(cbrt (- 2.0 (+ x y)))
18.0ms
(cbrt (- 2.0 (+ x y)))
23.0ms
(cbrt (- 2.0 (+ x y)))

series423.0ms

Counts
4 → 12
Calls
4 calls:
107.0ms
(/ 1 (* (cbrt (- 2.0 (+ x y))) (cbrt (- 2.0 (+ x y)))))
106.0ms
(cbrt (- 2.0 (+ x y)))
103.0ms
(cbrt (- 2.0 (+ x y)))
106.0ms
(cbrt (- 2.0 (+ x y)))

simplify1.3s

Counts
103 → 103
Iterations

Useful iterations: done (1.3s)

IterNodesCost
01651587
13751443
27811332
318721253
done50001235

prune377.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0.0b

localize16.0ms

Local error

Found 3 expressions with local error:

0.0b
(* (- 2.0 (+ x y)) (+ x y))
3.8b
(- (* x x) (* y y))
28.8b
(/ (- (* x x) (* y y)) (* (- 2.0 (+ x y)) (+ x y)))

rewrite193.0ms

Algorithm
rewrite-expression-head
Rules
14×*-un-lft-identity
11×add-sqr-sqrt
10×add-exp-log add-cbrt-cube
8×frac-times flip3-- associate-/r/ flip--
7×add-cube-cbrt
6×flip3-+ associate-*l* flip-+
5×pow1 add-log-exp
4×times-frac associate-*r/ associate-*r* associate-*l/ associate-/l* difference-of-squares
2×cbrt-undiv div-exp prod-exp cbrt-unprod associate-/l/ distribute-lft-out distribute-lft-out--
1×distribute-rgt-in sub-neg frac-2neg distribute-lft-in diff-log div-sub pow-prod-down clear-num associate-/r* *-commutative div-inv unswap-sqr
Counts
3 → 79
Calls
3 calls:
125.0ms
(* (- 2.0 (+ x y)) (+ x y))
11.0ms
(- (* x x) (* y y))
53.0ms
(/ (- (* x x) (* y y)) (* (- 2.0 (+ x y)) (+ x y)))

series235.0ms

Counts
3 → 9
Calls
3 calls:
50.0ms
(* (- 2.0 (+ x y)) (+ x y))
48.0ms
(- (* x x) (* y y))
136.0ms
(/ (- (* x x) (* y y)) (* (- 2.0 (+ x y)) (+ x y)))

simplify2.1s

Counts
88 → 88
Iterations

Useful iterations: done (2.1s)

IterNodesCost
01601573
15121522
223181352
done50001215

prune264.0ms

Pruning

4 alts after pruning (1 fresh and 3 done)

Merged error: 0.0b

localize24.0ms

Local error

Found 4 expressions with local error:

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

rewrite576.0ms

Algorithm
rewrite-expression-head
Rules
421×*-un-lft-identity
384×sqrt-prod
342×add-sqr-sqrt
268×times-frac
108×add-cube-cbrt
102×difference-of-squares
89×distribute-lft-out
86×associate-*r*
85×distribute-lft-out--
54×associate-*l*
20×add-exp-log add-cbrt-cube
16×associate-/r* associate-/l*
9×unswap-sqr
8×associate-/r/
6×pow1 cbrt-undiv div-exp add-log-exp
4×flip3-- sqrt-div prod-exp flip-- cbrt-unprod div-inv associate-/l/
3×flip3-+ flip-+
2×frac-2neg clear-num
1×+-commutative frac-times associate-*r/ pow-prod-down associate-*l/ sum-log *-commutative
Counts
4 → 375
Calls
4 calls:
18.0ms
(+ (sqrt 2.0) (sqrt (+ x y)))
57.0ms
(/ (sqrt (- x y)) (- (sqrt 2.0) (sqrt (+ x y))))
73.0ms
(/ (sqrt (- x y)) (+ (sqrt 2.0) (sqrt (+ x y))))
398.0ms
(* (/ (sqrt (- x y)) (+ (sqrt 2.0) (sqrt (+ x y)))) (/ (sqrt (- x y)) (- (sqrt 2.0) (sqrt (+ x y)))))

series20.1s

Counts
4 → 12
Calls
4 calls:
73.0ms
(+ (sqrt 2.0) (sqrt (+ x y)))
2.1s
(/ (sqrt (- x y)) (- (sqrt 2.0) (sqrt (+ x y))))
2.1s
(/ (sqrt (- x y)) (+ (sqrt 2.0) (sqrt (+ x y))))
15.7s
(* (/ (sqrt (- x y)) (+ (sqrt 2.0) (sqrt (+ x y)))) (/ (sqrt (- x y)) (- (sqrt 2.0) (sqrt (+ x y)))))

simplify2.3s

Counts
387 → 387
Iterations

Useful iterations: done (2.2s)

IterNodesCost
040810660
111059507
233638828
done50008765

prune893.0ms

Pruning

4 alts after pruning (0 fresh and 4 done)

Merged error: 0.0b

regimes70.0ms

Accuracy

0% (0.0b remaining)

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

bsearch0.0ms

simplify2.0ms

Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
079
189
done89

end0.0ms

sample658.0ms

Algorithm
intervals
Results
387.0ms7996×body80valid
1.0ms3×body1280valid
0.0ms1×body320valid