Details

Time bar (total: 13.7s)

sample26.0ms

Algorithm
intervals
Results
13.0ms256×body80valid

simplify1.8s

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: 18.1b

localize13.0ms

Local error

Found 3 expressions with local error:

0.0b
(* (+ x y) (+ x y))
0.1b
(* (* (+ x y) (+ x y)) (+ (+ x y) 1.0))
18.0b
(/ (* x y) (* (* (+ x y) (+ x y)) (+ (+ x y) 1.0)))

rewrite302.0ms

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:
51.0ms
(* (+ x y) (+ x y))
150.0ms
(* (* (+ x y) (+ x y)) (+ (+ x y) 1.0))
91.0ms
(/ (* x y) (* (* (+ x y) (+ x y)) (+ (+ x y) 1.0)))

series295.0ms

Counts
3 → 9
Calls
3 calls:
28.0ms
(* (+ x y) (+ x y))
54.0ms
(* (* (+ x y) (+ x y)) (+ (+ x y) 1.0))
213.0ms
(/ (* x y) (* (* (+ x y) (+ x y)) (+ (+ x y) 1.0)))

simplify2.8s

Counts
149 → 149
Iterations

Useful iterations: done (2.8s)

IterNodesCost
02183333
18633063
248742795
done50012697

prune470.0ms

Pruning

17 alts after pruning (17 fresh and 0 done)

Merged error: 9.5b

localize25.0ms

Local error

Found 4 expressions with local error:

0.0b
(* y (+ (* 2 x) y))
0.1b
(* (+ (* x x) (* y (+ (* 2 x) y))) (+ (+ x y) 1.0))
1.2b
(+ (* x x) (* y (+ (* 2 x) y)))
18.0b
(/ (* x y) (* (+ (* x x) (* y (+ (* 2 x) y))) (+ (+ x y) 1.0)))

rewrite241.0ms

Algorithm
rewrite-expression-head
Rules
20×add-exp-log add-cbrt-cube
14×flip3-+ flip-+
13×*-un-lft-identity
12×add-sqr-sqrt
8×pow1 frac-times add-cube-cbrt associate-*r* associate-/r/
6×associate-*r/ associate-*l* prod-exp cbrt-unprod add-log-exp
4×cbrt-undiv div-exp associate-*l/
3×distribute-rgt-in distribute-lft-in distribute-lft-out
2×associate-+r+ pow-prod-down *-commutative unswap-sqr
1×+-commutative frac-2neg times-frac clear-num associate-/r* sum-log div-inv associate-/l*
Counts
4 → 94
Calls
4 calls:
39.0ms
(* y (+ (* 2 x) y))
135.0ms
(* (+ (* x x) (* y (+ (* 2 x) y))) (+ (+ x y) 1.0))
12.0ms
(+ (* x x) (* y (+ (* 2 x) y)))
50.0ms
(/ (* x y) (* (+ (* x x) (* y (+ (* 2 x) y))) (+ (+ x y) 1.0)))

series401.0ms

Counts
4 → 12
Calls
4 calls:
45.0ms
(* y (+ (* 2 x) y))
71.0ms
(* (+ (* x x) (* y (+ (* 2 x) y))) (+ (+ x y) 1.0))
37.0ms
(+ (* x x) (* y (+ (* 2 x) y)))
247.0ms
(/ (* x y) (* (+ (* x x) (* y (+ (* 2 x) y))) (+ (+ x y) 1.0)))

simplify1.5s

Counts
106 → 106
Iterations

Useful iterations: 2 (588.0ms)

IterNodesCost
01792395
16292312
231571938
done50001938

prune386.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 6.1b

localize28.0ms

Local error

Found 4 expressions with local error:

0.0b
(* y (+ (* 2 x) y))
0.1b
(* (/ x (+ (* x x) (* y (+ (* 2 x) y)))) (/ y (+ (+ x y) 1.0)))
1.2b
(+ (* x x) (* y (+ (* 2 x) y)))
17.8b
(/ x (+ (* x x) (* y (+ (* 2 x) y))))

rewrite231.0ms

Algorithm
rewrite-expression-head
Rules
45×*-un-lft-identity
44×add-sqr-sqrt
37×times-frac
30×add-cube-cbrt
24×associate-*r*
20×add-exp-log add-cbrt-cube
18×associate-*l*
9×distribute-lft-out
8×pow1
6×associate-/r/ add-log-exp
5×cbrt-undiv flip3-+ div-exp prod-exp cbrt-unprod flip-+ unswap-sqr
3×associate-*r/ associate-/r* div-inv associate-/l*
2×distribute-rgt-in associate-+r+ distribute-lft-in pow-prod-down *-commutative
1×+-commutative frac-times frac-2neg associate-*l/ clear-num sum-log
Counts
4 → 124
Calls
4 calls:
34.0ms
(* y (+ (* 2 x) y))
158.0ms
(* (/ x (+ (* x x) (* y (+ (* 2 x) y)))) (/ y (+ (+ x y) 1.0)))
14.0ms
(+ (* x x) (* y (+ (* 2 x) y)))
18.0ms
(/ x (+ (* x x) (* y (+ (* 2 x) y))))

series428.0ms

Counts
4 → 12
Calls
4 calls:
41.0ms
(* y (+ (* 2 x) y))
228.0ms
(* (/ x (+ (* x x) (* y (+ (* 2 x) y)))) (/ y (+ (+ x y) 1.0)))
36.0ms
(+ (* x x) (* y (+ (* 2 x) y)))
123.0ms
(/ x (+ (* x x) (* y (+ (* 2 x) y))))

simplify1.2s

Counts
136 → 136
Iterations

Useful iterations: 2 (488.0ms)

IterNodesCost
02052840
16252737
222352417
done50012417

prune348.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 6.1b

localize28.0ms

Local error

Found 4 expressions with local error:

1.2b
(+ (* x x) (* y (+ (* 2 x) y)))
1.2b
(+ (* x x) (* y (+ (* 2 x) y)))
28.5b
(sqrt (+ (* x x) (* y (+ (* 2 x) y))))
28.5b
(sqrt (+ (* x x) (* y (+ (* 2 x) y))))

rewrite55.0ms

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:
13.0ms
(+ (* x x) (* y (+ (* 2 x) y)))
14.0ms
(+ (* x x) (* y (+ (* 2 x) y)))
12.0ms
(sqrt (+ (* x x) (* y (+ (* 2 x) y))))
12.0ms
(sqrt (+ (* x x) (* y (+ (* 2 x) y))))

series241.0ms

Counts
4 → 12
Calls
4 calls:
31.0ms
(+ (* x x) (* y (+ (* 2 x) y)))
38.0ms
(+ (* x x) (* y (+ (* 2 x) y)))
84.0ms
(sqrt (+ (* x x) (* y (+ (* 2 x) y))))
87.0ms
(sqrt (+ (* x x) (* y (+ (* 2 x) y))))

simplify1.9s

Counts
68 → 68
Iterations

Useful iterations: 2 (103.0ms)

IterNodesCost
0571168
11471062
2518950
32803950
done5001950

prune231.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 6.1b

regimes102.0ms

Accuracy

0% (1.7b remaining)

Error of 9.4b against oracle of 7.7b and baseline of 9.4b

bsearch0.0ms

simplify2.0ms

Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01421
12121
done2121

end0.0ms

sample679.0ms

Algorithm
intervals
Results
449.0ms8000×body80valid