Details

Time bar (total: 14.9s)

sample20.0ms

Algorithm
intervals
Results
9.0ms256×body80valid

simplify1.7s

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

localize14.0ms

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)))

rewrite340.0ms

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:
53.0ms
(* (+ x y) (+ x y))
188.0ms
(* (* (+ x y) (+ x y)) (+ (+ x y) 1.0))
86.0ms
(/ (* x y) (* (* (+ x y) (+ x y)) (+ (+ x y) 1.0)))

series252.0ms

Counts
3 → 9
Calls
3 calls:
17.0ms
(* (+ x y) (+ x y))
45.0ms
(* (* (+ x y) (+ x y)) (+ (+ x y) 1.0))
191.0ms
(/ (* 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

prune481.0ms

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 10.9b

localize25.0ms

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)))

rewrite160.0ms

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:
101.0ms
(* (+ (* x x) (* y (+ (* 2 x) y))) (+ (+ x y) 1.0))
10.0ms
(+ (* x x) (* y (+ (* 2 x) y)))
45.0ms
(/ (* x y) (* (+ (* x x) (* y (+ (* 2 x) y))) (+ (+ x y) 1.0)))

series397.0ms

Counts
3 → 9
Calls
3 calls:
86.0ms
(* (+ (* x x) (* y (+ (* 2 x) y))) (+ (+ x y) 1.0))
42.0ms
(+ (* x x) (* y (+ (* 2 x) y)))
269.0ms
(/ (* x y) (* (+ (* x x) (* y (+ (* 2 x) y))) (+ (+ x y) 1.0)))

simplify1.7s

Counts
81 → 81
Iterations

Useful iterations: 2 (493.0ms)

IterNodesCost
01522142
15382086
228641724
done50011724

prune308.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 8.4b

localize22.0ms

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))))

rewrite286.0ms

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:
70.0ms
(/ y (+ (+ x y) 1.0))
179.0ms
(* (/ x (+ (* x x) (* y (+ (* 2 x) y)))) (/ y (+ (+ x y) 1.0)))
10.0ms
(+ (* x x) (* y (+ (* 2 x) y)))
13.0ms
(/ x (+ (* x x) (* y (+ (* 2 x) y))))

series439.0ms

Counts
4 → 12
Calls
4 calls:
50.0ms
(/ y (+ (+ x y) 1.0))
235.0ms
(* (/ x (+ (* x x) (* y (+ (* 2 x) y)))) (/ y (+ (+ x y) 1.0)))
39.0ms
(+ (* x x) (* y (+ (* 2 x) y)))
114.0ms
(/ x (+ (* x x) (* y (+ (* 2 x) y))))

simplify1.3s

Counts
151 → 151
Iterations

Useful iterations: done (1.3s)

IterNodesCost
01993059
15662960
219762616
done50012612

prune626.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 8.4b

localize21.0ms

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))))

rewrite53.0ms

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:
10.0ms
(+ (* x x) (* y (+ (* 2 x) y)))
10.0ms
(+ (* x x) (* y (+ (* 2 x) y)))
14.0ms
(sqrt (+ (* x x) (* y (+ (* 2 x) y))))
17.0ms
(sqrt (+ (* x x) (* y (+ (* 2 x) y))))

series258.0ms

Counts
4 → 12
Calls
4 calls:
42.0ms
(+ (* x x) (* y (+ (* 2 x) y)))
43.0ms
(+ (* x x) (* y (+ (* 2 x) y)))
97.0ms
(sqrt (+ (* x x) (* y (+ (* 2 x) y))))
76.0ms
(sqrt (+ (* x x) (* y (+ (* 2 x) y))))

simplify2.5s

Counts
68 → 68
Iterations

Useful iterations: 2 (146.0ms)

IterNodesCost
0571168
11471062
2518950
32803950
done5001950

prune317.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 8.4b

regimes76.0ms

Accuracy

0% (1.6b remaining)

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

bsearch0.0ms

simplify3.0ms

Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01421
12121
done2121

end0.0ms

sample1.0s

Algorithm
intervals
Results
678.0ms8000×body80valid