Details

Time bar (total: 14.9s)

sample30.0ms

Algorithm
intervals
Results
14.0ms256×body80valid

simplify2.0s

Counts
1 → 1
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0917
13617
215217
349917
4203317
done500117

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 21.5b

localize10.0ms

Local error

Found 3 expressions with local error:

0.0b
(* (+ x y) (+ x y))
0.1b
(* (* (+ x y) (+ x y)) (+ (+ x y) 1.0))
21.3b
(/ (* x y) (* (* (+ x y) (+ x y)) (+ (+ x y) 1.0)))

rewrite345.0ms

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:
49.0ms
(* (+ x y) (+ x y))
195.0ms
(* (* (+ x y) (+ x y)) (+ (+ x y) 1.0))
92.0ms
(/ (* x y) (* (* (+ x y) (+ x y)) (+ (+ x y) 1.0)))

series339.0ms

Counts
3 → 9
Calls
3 calls:
24.0ms
(* (+ x y) (+ x y))
68.0ms
(* (* (+ x y) (+ x y)) (+ (+ x y) 1.0))
248.0ms
(/ (* 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

prune502.0ms

Pruning

16 alts after pruning (15 fresh and 1 done)

Merged error: 10.0b

localize20.0ms

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))
1.0b
(+ (* x x) (* y (+ (* 2 x) y)))
21.3b
(/ (* x y) (* (+ (* x x) (* y (+ (* 2 x) y))) (+ (+ x y) 1.0)))

rewrite205.0ms

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:
34.0ms
(* y (+ (* 2 x) y))
115.0ms
(* (+ (* x x) (* y (+ (* 2 x) y))) (+ (+ x y) 1.0))
9.0ms
(+ (* x x) (* y (+ (* 2 x) y)))
43.0ms
(/ (* x y) (* (+ (* x x) (* y (+ (* 2 x) y))) (+ (+ x y) 1.0)))

series454.0ms

Counts
4 → 12
Calls
4 calls:
72.0ms
(* y (+ (* 2 x) y))
89.0ms
(* (+ (* x x) (* y (+ (* 2 x) y))) (+ (+ x y) 1.0))
28.0ms
(+ (* x x) (* y (+ (* 2 x) y)))
265.0ms
(/ (* x y) (* (+ (* x x) (* y (+ (* 2 x) y))) (+ (+ x y) 1.0)))

simplify1.7s

Counts
106 → 106
Iterations

Useful iterations: 2 (655.0ms)

IterNodesCost
01792395
16292312
231571938
done50001938

prune406.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 6.7b

localize23.0ms

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)))
1.0b
(+ (* x x) (* y (+ (* 2 x) y)))
17.6b
(/ x (+ (* x x) (* y (+ (* 2 x) y))))

rewrite187.0ms

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:
36.0ms
(/ y (+ (+ x y) 1.0))
111.0ms
(* (/ x (+ (* x x) (* y (+ (* 2 x) y)))) (/ y (+ (+ x y) 1.0)))
15.0ms
(+ (* x x) (* y (+ (* 2 x) y)))
19.0ms
(/ x (+ (* x x) (* y (+ (* 2 x) y))))

series366.0ms

Counts
4 → 12
Calls
4 calls:
60.0ms
(/ y (+ (+ x y) 1.0))
190.0ms
(* (/ 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))))

simplify1.2s

Counts
151 → 151
Iterations

Useful iterations: done (1.2s)

IterNodesCost
01993059
15662960
219762616
done50012612

prune475.0ms

Pruning

11 alts after pruning (9 fresh and 2 done)

Merged error: 6.6b

localize36.0ms

Local error

Found 4 expressions with local error:

1.0b
(+ (* x x) (* y (+ (* 2 x) y)))
1.0b
(+ (* x x) (* y (+ (* 2 x) y)))
27.4b
(sqrt (+ (* x x) (* y (+ (* 2 x) y))))
27.4b
(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:
16.0ms
(+ (* x x) (* y (+ (* 2 x) y)))
9.0ms
(+ (* x x) (* y (+ (* 2 x) y)))
13.0ms
(sqrt (+ (* x x) (* y (+ (* 2 x) y))))
16.0ms
(sqrt (+ (* x x) (* y (+ (* 2 x) y))))

series230.0ms

Counts
4 → 12
Calls
4 calls:
37.0ms
(+ (* x x) (* y (+ (* 2 x) y)))
33.0ms
(+ (* x x) (* y (+ (* 2 x) y)))
83.0ms
(sqrt (+ (* x x) (* y (+ (* 2 x) y))))
77.0ms
(sqrt (+ (* x x) (* y (+ (* 2 x) y))))

simplify2.2s

Counts
68 → 68
Iterations

Useful iterations: 2 (127.0ms)

IterNodesCost
0571168
11471062
2518950
32803950
done5001950

prune342.0ms

Pruning

11 alts after pruning (9 fresh and 2 done)

Merged error: 6.6b

regimes175.0ms

Accuracy

82.8% (0.3b remaining)

Error of 8.0b against oracle of 7.7b and baseline of 9.2b

bsearch3.0ms

simplify4.0ms

Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
02242
13142
done3142

end0.0ms

sample730.0ms

Algorithm
intervals
Results
470.0ms8000×body80valid