Details

Time bar (total: 12.3s)

sample24.0ms

Algorithm
intervals
Results
6.0ms188×body80valid
3.0ms27×body640valid
2.0ms16×body1280valid
1.0ms15×body320valid
1.0ms10×body160valid

simplify1.1s

Counts
1 → 1
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0811
11611
23511
37411
415311
541311
6166211
done500111

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 23.1b

localize8.0ms

Local error

Found 3 expressions with local error:

0.0b
(* (- 1.0 x) y)
2.9b
(- 1.0 (/ (* (- 1.0 x) y) (+ y 1.0)))
6.8b
(/ (* (- 1.0 x) y) (+ y 1.0))

rewrite76.0ms

Algorithm
rewrite-expression-head
Rules
15×*-un-lft-identity
13×add-sqr-sqrt
10×add-exp-log add-cbrt-cube
7×add-cube-cbrt
5×pow1 associate-*l* add-log-exp
4×times-frac associate-*l/ associate-/r*
3×flip3-- associate-*r* flip--
2×cbrt-undiv div-exp prod-exp associate-/r/ cbrt-unprod associate-/l/ distribute-lft-out distribute-lft-out-- difference-of-squares
1×sub-neg frac-2neg flip3-+ diff-log pow-prod-down clear-num *-commutative flip-+ div-inv associate-/l* unswap-sqr
Counts
3 → 63
Calls
3 calls:
28.0ms
(* (- 1.0 x) y)
22.0ms
(- 1.0 (/ (* (- 1.0 x) y) (+ y 1.0)))
24.0ms
(/ (* (- 1.0 x) y) (+ y 1.0))

series225.0ms

Counts
3 → 9
Calls
3 calls:
56.0ms
(* (- 1.0 x) y)
121.0ms
(- 1.0 (/ (* (- 1.0 x) y) (+ y 1.0)))
47.0ms
(/ (* (- 1.0 x) y) (+ y 1.0))

simplify1.3s

Counts
72 → 72
Iterations

Useful iterations: done (1.3s)

IterNodesCost
0128885
1347828
22051752
done5002746

prune270.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.3b

localize8.0ms

Local error

Found 3 expressions with local error:

0.0b
(/ y (+ y 1.0))
0.0b
(* (- 1.0 x) (/ y (+ y 1.0)))
2.9b
(- 1.0 (* (- 1.0 x) (/ y (+ y 1.0))))

rewrite132.0ms

Algorithm
rewrite-expression-head
Rules
37×*-un-lft-identity
28×add-sqr-sqrt
25×times-frac
21×add-cube-cbrt
18×associate-*r*
10×add-exp-log add-cbrt-cube
7×distribute-lft-out
5×pow1 associate-*l* add-log-exp
4×associate-/r* associate-/r/
3×flip3-- flip-- associate-/l*
2×cbrt-undiv frac-times flip3-+ div-exp associate-*l/ prod-exp cbrt-unprod flip-+ div-inv unswap-sqr
1×sub-neg frac-2neg diff-log associate-*r/ pow-prod-down clear-num *-commutative distribute-lft-out-- difference-of-squares
Counts
3 → 88
Calls
3 calls:
23.0ms
(/ y (+ y 1.0))
97.0ms
(* (- 1.0 x) (/ y (+ y 1.0)))
7.0ms
(- 1.0 (* (- 1.0 x) (/ y (+ y 1.0))))

series261.0ms

Counts
3 → 9
Calls
3 calls:
53.0ms
(/ y (+ y 1.0))
79.0ms
(* (- 1.0 x) (/ y (+ y 1.0)))
129.0ms
(- 1.0 (* (- 1.0 x) (/ y (+ y 1.0))))

simplify2.0s

Counts
97 → 97
Iterations

Useful iterations: 2 (478.0ms)

IterNodesCost
01571229
14241152
224931056
done50001056

prune338.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.3b

localize33.0ms

Local error

Found 4 expressions with local error:

0.0b
(+ 1.0 (* (- 1.0 x) (/ y (+ y 1.0))))
0.1b
(* (* (- 1.0 x) (/ y (+ y 1.0))) (* (- 1.0 x) (/ y (+ y 1.0))))
2.9b
(- (* 1.0 1.0) (* (* (- 1.0 x) (/ y (+ y 1.0))) (* (- 1.0 x) (/ y (+ y 1.0)))))
8.5b
(/ (- (* 1.0 1.0) (* (* (- 1.0 x) (/ y (+ y 1.0))) (* (- 1.0 x) (/ y (+ y 1.0))))) (+ 1.0 (* (- 1.0 x) (/ y (+ y 1.0)))))

rewrite288.0ms

Algorithm
rewrite-expression-head
Rules
49×frac-times
43×pow1
42×add-exp-log add-cbrt-cube
29×associate-*l/
26×flip3-- flip--
21×prod-exp cbrt-unprod
17×associate-*r/ pow-prod-down
13×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
12×times-frac
8×add-log-exp
7×cbrt-undiv div-exp
5×difference-of-squares
4×pow-sqr pow-prod-up associate-/l*
3×associate-/r*
2×flip3-+ pow-plus associate-/r/ flip-+ associate-/l/
1×+-commutative pow2 sub-neg frac-2neg diff-log div-sub swap-sqr associate-*r* associate-*l* clear-num sum-log *-commutative div-inv
Counts
4 → 139
Calls
4 calls:
16.0ms
(+ 1.0 (* (- 1.0 x) (/ y (+ y 1.0))))
199.0ms
(* (* (- 1.0 x) (/ y (+ y 1.0))) (* (- 1.0 x) (/ y (+ y 1.0))))
18.0ms
(- (* 1.0 1.0) (* (* (- 1.0 x) (/ y (+ y 1.0))) (* (- 1.0 x) (/ y (+ y 1.0)))))
42.0ms
(/ (- (* 1.0 1.0) (* (* (- 1.0 x) (/ y (+ y 1.0))) (* (- 1.0 x) (/ y (+ y 1.0))))) (+ 1.0 (* (- 1.0 x) (/ y (+ y 1.0)))))

series922.0ms

Counts
4 → 12
Calls
4 calls:
78.0ms
(+ 1.0 (* (- 1.0 x) (/ y (+ y 1.0))))
76.0ms
(* (* (- 1.0 x) (/ y (+ y 1.0))) (* (- 1.0 x) (/ y (+ y 1.0))))
137.0ms
(- (* 1.0 1.0) (* (* (- 1.0 x) (/ y (+ y 1.0))) (* (- 1.0 x) (/ y (+ y 1.0)))))
630.0ms
(/ (- (* 1.0 1.0) (* (* (- 1.0 x) (/ y (+ y 1.0))) (* (- 1.0 x) (/ y (+ y 1.0))))) (+ 1.0 (* (- 1.0 x) (/ y (+ y 1.0)))))

simplify563.0ms

Counts
151 → 151
Iterations

Useful iterations: done (555.0ms)

IterNodesCost
02514985
18584495
done50004025

prune471.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.3b

localize46.0ms

Local error

Found 4 expressions with local error:

0.1b
(* (* (- 1.0 x) (/ y (+ y 1.0))) (* (- 1.0 x) y))
1.9b
(/ (* (* (- 1.0 x) (/ y (+ y 1.0))) (* (- 1.0 x) y)) (+ y 1.0))
2.9b
(- (* 1.0 1.0) (/ (* (* (- 1.0 x) (/ y (+ y 1.0))) (* (- 1.0 x) y)) (+ y 1.0)))
8.5b
(/ (- (* 1.0 1.0) (/ (* (* (- 1.0 x) (/ y (+ y 1.0))) (* (- 1.0 x) y)) (+ y 1.0))) (+ 1.0 (* (- 1.0 x) (/ y (+ y 1.0)))))

rewrite873.0ms

Algorithm
rewrite-expression-head
Rules
56×add-exp-log add-cbrt-cube
46×associate-*l/
32×frac-times
26×flip3-- prod-exp flip-- cbrt-unprod
20×add-sqr-sqrt
19×*-un-lft-identity associate-/l/
16×pow1 times-frac
15×add-cube-cbrt
12×cbrt-undiv div-exp
10×associate-*r/
8×pow-prod-down
7×associate-/r*
6×add-log-exp
5×associate-/l* difference-of-squares
4×associate-/r/
2×frac-2neg flip3-+ clear-num flip-+ div-inv distribute-lft-out
1×sub-neg diff-log div-sub associate-*r* associate-*l* *-commutative
Counts
4 → 144
Calls
4 calls:
159.0ms
(* (* (- 1.0 x) (/ y (+ y 1.0))) (* (- 1.0 x) y))
175.0ms
(/ (* (* (- 1.0 x) (/ y (+ y 1.0))) (* (- 1.0 x) y)) (+ y 1.0))
41.0ms
(- (* 1.0 1.0) (/ (* (* (- 1.0 x) (/ y (+ y 1.0))) (* (- 1.0 x) y)) (+ y 1.0)))
483.0ms
(/ (- (* 1.0 1.0) (/ (* (* (- 1.0 x) (/ y (+ y 1.0))) (* (- 1.0 x) y)) (+ y 1.0))) (+ 1.0 (* (- 1.0 x) (/ y (+ y 1.0)))))

series909.0ms

Counts
4 → 12
Calls
4 calls:
88.0ms
(* (* (- 1.0 x) (/ y (+ y 1.0))) (* (- 1.0 x) y))
67.0ms
(/ (* (* (- 1.0 x) (/ y (+ y 1.0))) (* (- 1.0 x) y)) (+ y 1.0))
144.0ms
(- (* 1.0 1.0) (/ (* (* (- 1.0 x) (/ y (+ y 1.0))) (* (- 1.0 x) y)) (+ y 1.0)))
610.0ms
(/ (- (* 1.0 1.0) (/ (* (* (- 1.0 x) (/ y (+ y 1.0))) (* (- 1.0 x) y)) (+ y 1.0))) (+ 1.0 (* (- 1.0 x) (/ y (+ y 1.0)))))

simplify655.0ms

Counts
156 → 156
Iterations

Useful iterations: done (643.0ms)

IterNodesCost
02725108
19274823
done50004299

prune580.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.2b

regimes133.0ms

Accuracy

99.9% (0.0b remaining)

Error of 0.2b against oracle of 0.2b and baseline of 14.2b

bsearch101.0ms

Steps
ItersRangePoint
9
6123.270275452558
293663098603.6372
228723108.99904495
8
-517858925.4294923
-28361.394281441724
-124109135.66881044

simplify3.0ms

Iterations

Useful iterations: 1 (2.0ms)

IterNodesCost
01941
12631
done2631

end0.0ms

sample1.1s

Algorithm
intervals
Results
443.0ms6110×body80valid
125.0ms730×body640valid
95.0ms504×body320valid
71.0ms339×body1280valid
67.0ms317×body160valid