Details

Time bar (total: 13.5s)

sample17.0ms

Algorithm
intervals
Results
9.0ms256×body80valid

simplify1.9s

Counts
1 → 1
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0917
13617
215217
349917
4203317
done500117

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 21.4b

localize16.0ms

Local error

Found 3 expressions with local error:

0.0b
(* (+ x y) (+ x y))
0.1b
(* (* (+ x y) (+ x y)) (+ (+ x y) 1.0))
21.2b
(/ (* x y) (* (* (+ x y) (+ x y)) (+ (+ x y) 1.0)))

rewrite338.0ms

Algorithm
rewrite-expression-head
Rules
60×frac-times flip3-+ flip-+
31×add-exp-log add-cbrt-cube
30×associate-*l/
27×*-un-lft-identity
26×associate-/r/
18×associate-*r/
15×pow1
13×prod-exp cbrt-unprod
11×add-sqr-sqrt
9×associate-*r* distribute-lft-out
8×add-cube-cbrt
6×cbrt-undiv swap-sqr div-exp
5×associate-*l*
4×pow-prod-down
3×add-log-exp
2×distribute-rgt-in distribute-lft-in *-commutative unswap-sqr
1×pow2 frac-2neg times-frac pow-plus clear-num associate-/r* pow-sqr pow-prod-up div-inv associate-/l*
Counts
3 → 140
Calls
3 calls:
36.0ms
(* (+ x y) (+ x y))
164.0ms
(* (* (+ x y) (+ x y)) (+ (+ x y) 1.0))
128.0ms
(/ (* x y) (* (* (+ x y) (+ x y)) (+ (+ x y) 1.0)))

series302.0ms

Counts
3 → 9
Calls
3 calls:
17.0ms
(* (+ x y) (+ x y))
68.0ms
(* (* (+ x y) (+ x y)) (+ (+ x y) 1.0))
217.0ms
(/ (* x y) (* (* (+ x y) (+ x y)) (+ (+ x y) 1.0)))

simplify2.6s

Counts
149 → 149
Iterations

Useful iterations: done (2.6s)

IterNodesCost
02183333
18633063
248742795
done50012697

prune424.0ms

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 10.9b

localize14.0ms

Local error

Found 3 expressions with local error:

0.1b
(* (+ (* x x) (* y (+ (* 2 x) y))) (+ (+ x y) 1.0))
1.6b
(+ (* x x) (* y (+ (* 2 x) y)))
21.2b
(/ (* x y) (* (+ (* x x) (* y (+ (* 2 x) y))) (+ (+ x y) 1.0)))

rewrite221.0ms

Algorithm
rewrite-expression-head
Rules
17×add-exp-log add-cbrt-cube
13×flip3-+ flip-+
10×*-un-lft-identity
8×frac-times associate-/r/
7×add-sqr-sqrt
5×pow1 add-cube-cbrt associate-*r* prod-exp cbrt-unprod add-log-exp
4×cbrt-undiv associate-*r/ div-exp associate-*l/
3×associate-*l* distribute-lft-out
2×distribute-rgt-in associate-+r+ distribute-lft-in
1×+-commutative frac-2neg times-frac pow-prod-down clear-num associate-/r* sum-log *-commutative div-inv associate-/l* unswap-sqr
Counts
3 → 72
Calls
3 calls:
143.0ms
(* (+ (* x x) (* y (+ (* 2 x) y))) (+ (+ x y) 1.0))
16.0ms
(+ (* x x) (* y (+ (* 2 x) y)))
58.0ms
(/ (* x y) (* (+ (* x x) (* y (+ (* 2 x) y))) (+ (+ x y) 1.0)))

series273.0ms

Counts
3 → 9
Calls
3 calls:
56.0ms
(* (+ (* x x) (* y (+ (* 2 x) y))) (+ (+ x y) 1.0))
25.0ms
(+ (* x x) (* y (+ (* 2 x) y)))
192.0ms
(/ (* x y) (* (+ (* x x) (* y (+ (* 2 x) y))) (+ (+ x y) 1.0)))

simplify1.5s

Counts
81 → 81
Iterations

Useful iterations: 2 (583.0ms)

IterNodesCost
01522142
15382086
228641724
done50011724

prune226.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 8.4b

localize19.0ms

Local error

Found 4 expressions with local error:

0.0b
(/ y (+ (+ x y) 1.0))
0.1b
(* (/ x (+ (* x x) (* y (+ (* 2 x) y)))) (/ y (+ (+ x y) 1.0)))
1.6b
(+ (* x x) (* y (+ (* 2 x) y)))
20.8b
(/ x (+ (* x x) (* y (+ (* 2 x) y))))

rewrite202.0ms

Algorithm
rewrite-expression-head
Rules
73×*-un-lft-identity
52×times-frac
50×add-sqr-sqrt
38×add-cube-cbrt
21×associate-*r* distribute-lft-out
20×add-exp-log add-cbrt-cube
15×associate-*l*
8×associate-/r* associate-/r/
6×pow1 cbrt-undiv div-exp associate-/l* add-log-exp
5×flip3-+ flip-+
4×prod-exp cbrt-unprod div-inv unswap-sqr
2×associate-+r+ frac-2neg clear-num
1×+-commutative distribute-rgt-in frac-times distribute-lft-in associate-*r/ pow-prod-down associate-*l/ sum-log *-commutative
Counts
4 → 139
Calls
4 calls:
37.0ms
(/ y (+ (+ x y) 1.0))
137.0ms
(* (/ x (+ (* x x) (* y (+ (* 2 x) y)))) (/ y (+ (+ x y) 1.0)))
9.0ms
(+ (* x x) (* y (+ (* 2 x) y)))
12.0ms
(/ x (+ (* x x) (* y (+ (* 2 x) y))))

series455.0ms

Counts
4 → 12
Calls
4 calls:
85.0ms
(/ y (+ (+ x y) 1.0))
253.0ms
(* (/ x (+ (* x x) (* y (+ (* 2 x) y)))) (/ y (+ (+ x y) 1.0)))
30.0ms
(+ (* x x) (* y (+ (* 2 x) y)))
86.0ms
(/ x (+ (* x x) (* y (+ (* 2 x) y))))

simplify1.1s

Counts
151 → 151
Iterations

Useful iterations: done (1.1s)

IterNodesCost
01993059
15662960
219762616
done50012612

prune410.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 8.4b

localize30.0ms

Local error

Found 4 expressions with local error:

1.6b
(+ (* x x) (* y (+ (* 2 x) y)))
1.6b
(+ (* x x) (* y (+ (* 2 x) y)))
32.7b
(sqrt (+ (* x x) (* y (+ (* 2 x) y))))
32.7b
(sqrt (+ (* x x) (* y (+ (* 2 x) y))))

rewrite38.0ms

Algorithm
rewrite-expression-head
Rules
8×add-sqr-sqrt add-log-exp
6×pow1 add-cube-cbrt *-un-lft-identity sqrt-prod
4×add-exp-log associate-+r+ flip3-+ sqrt-div add-cbrt-cube flip-+
2×+-commutative distribute-rgt-in rem-sqrt-square distribute-lft-in sqrt-pow1 pow1/2 sum-log
Counts
4 → 56
Calls
4 calls:
9.0ms
(+ (* x x) (* y (+ (* 2 x) y)))
11.0ms
(+ (* x x) (* y (+ (* 2 x) y)))
8.0ms
(sqrt (+ (* x x) (* y (+ (* 2 x) y))))
8.0ms
(sqrt (+ (* x x) (* y (+ (* 2 x) y))))

series201.0ms

Counts
4 → 12
Calls
4 calls:
25.0ms
(+ (* x x) (* y (+ (* 2 x) y)))
27.0ms
(+ (* x x) (* y (+ (* 2 x) y)))
70.0ms
(sqrt (+ (* x x) (* y (+ (* 2 x) y))))
79.0ms
(sqrt (+ (* x x) (* y (+ (* 2 x) y))))

simplify2.0s

Counts
68 → 68
Iterations

Useful iterations: 2 (106.0ms)

IterNodesCost
0571168
11471062
2518950
32803950
done5001950

prune279.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 8.4b

regimes83.0ms

Accuracy

0% (1.6b remaining)

Error of 9.1b against oracle of 7.4b and baseline of 9.1b

bsearch0.0ms

simplify4.0ms

Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
01421
12121
done2121

end0.0ms

sample845.0ms

Algorithm
intervals
Results
614.0ms8000×body80valid