Details

Time bar (total: 30.8s)

sample20.0ms

Algorithm
intervals
Results
8.0ms255×body80valid
0.0ms1×body1280valid

simplify204.0ms

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

localize10.0ms

Local error

Found 1 expressions with local error:

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

rewrite76.0ms

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:
71.0ms
(/ (- x y) (- 2.0 (+ x y)))

series80.0ms

Counts
1 → 3
Calls
1 calls:
79.0ms
(/ (- x y) (- 2.0 (+ x y)))

simplify1.6s

Counts
63 → 63
Iterations

Useful iterations: 3 (523.0ms)

IterNodesCost
01141010
1284965
2745923
32060921
done5000921

prune155.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.0b

localize25.0ms

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)))

rewrite139.0ms

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×expm1-log1p-u frac-times div-exp log1p-expm1-u 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 → 99
Calls
4 calls:
78.0ms
(/ 1 (* (cbrt (- 2.0 (+ x y))) (cbrt (- 2.0 (+ x y)))))
18.0ms
(cbrt (- 2.0 (+ x y)))
19.0ms
(cbrt (- 2.0 (+ x y)))
20.0ms
(cbrt (- 2.0 (+ x y)))

series553.0ms

Counts
4 → 12
Calls
4 calls:
156.0ms
(/ 1 (* (cbrt (- 2.0 (+ x y))) (cbrt (- 2.0 (+ x y)))))
145.0ms
(cbrt (- 2.0 (+ x y)))
137.0ms
(cbrt (- 2.0 (+ x y)))
115.0ms
(cbrt (- 2.0 (+ x y)))

simplify1.4s

Counts
111 → 111
Iterations

Useful iterations: done (1.4s)

IterNodesCost
01691661
13881503
28371390
320691313
done50001295

prune306.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0.0b

localize14.0ms

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)))

rewrite192.0ms

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
3×expm1-log1p-u log1p-expm1-u
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 fma-neg diff-log div-sub prod-diff pow-prod-down clear-num associate-/r* *-commutative div-inv unswap-sqr
Counts
3 → 87
Calls
3 calls:
118.0ms
(* (- 2.0 (+ x y)) (+ x y))
12.0ms
(- (* x x) (* y y))
57.0ms
(/ (- (* x x) (* y y)) (* (- 2.0 (+ x y)) (+ x y)))

series228.0ms

Counts
3 → 9
Calls
3 calls:
44.0ms
(* (- 2.0 (+ x y)) (+ x y))
50.0ms
(- (* x x) (* y y))
134.0ms
(/ (- (* x x) (* y y)) (* (- 2.0 (+ x y)) (+ x y)))

simplify1.4s

Counts
96 → 96
Iterations

Useful iterations: done (1.4s)

IterNodesCost
01691663
15341597
224421428
done50021422

prune284.0ms

Pruning

4 alts after pruning (1 fresh and 3 done)

Merged error: 0.0b

localize15.0ms

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)))))

rewrite504.0ms

Algorithm
rewrite-expression-head
Rules
423×*-un-lft-identity
387×sqrt-prod
344×add-sqr-sqrt
268×times-frac
110×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 fma-def div-exp add-log-exp
4×expm1-log1p-u flip3-- sqrt-div prod-exp flip-- cbrt-unprod log1p-expm1-u 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 → 389
Calls
4 calls:
29.0ms
(+ (sqrt 2.0) (sqrt (+ x y)))
78.0ms
(/ (sqrt (- x y)) (- (sqrt 2.0) (sqrt (+ x y))))
71.0ms
(/ (sqrt (- x y)) (+ (sqrt 2.0) (sqrt (+ x y))))
284.0ms
(* (/ (sqrt (- x y)) (+ (sqrt 2.0) (sqrt (+ x y)))) (/ (sqrt (- x y)) (- (sqrt 2.0) (sqrt (+ x y)))))

series19.7s

Counts
4 → 12
Calls
4 calls:
60.0ms
(+ (sqrt 2.0) (sqrt (+ x y)))
2.2s
(/ (sqrt (- x y)) (- (sqrt 2.0) (sqrt (+ x y))))
2.4s
(/ (sqrt (- x y)) (+ (sqrt 2.0) (sqrt (+ x y))))
15.0s
(* (/ (sqrt (- x y)) (+ (sqrt 2.0) (sqrt (+ x y)))) (/ (sqrt (- x y)) (- (sqrt 2.0) (sqrt (+ x y)))))

simplify2.2s

Counts
401 → 401
Iterations

Useful iterations: done (2.2s)

IterNodesCost
041610780
111479611
234848910
done50018801

prune1.0s

Pruning

4 alts after pruning (0 fresh and 4 done)

Merged error: 0.0b

regimes54.0ms

Accuracy

0% (0.0b remaining)

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

bsearch0.0ms

simplify1.0ms

Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
079
189
done89

end0.0ms

sample580.0ms

Algorithm
intervals
Results
351.0ms7996×body80valid
0.0ms3×body1280valid
0.0ms1×body320valid