Details

Time bar (total: 16.3s)

sample22.0ms

Algorithm
intervals
Results
6.0ms190×body80valid
3.0ms26×body640valid
2.0ms13×body1280valid
1.0ms15×body320valid
1.0ms12×body160valid

simplify1.3s

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: 19.8b

localize8.0ms

Local error

Found 3 expressions with local error:

0.0b
(* (- 1.0 x) y)
3.0b
(- 1.0 (/ (* (- 1.0 x) y) (+ y 1.0)))
4.2b
(/ (* (- 1.0 x) y) (+ y 1.0))

rewrite75.0ms

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:
22.0ms
(* (- 1.0 x) y)
19.0ms
(- 1.0 (/ (* (- 1.0 x) y) (+ y 1.0)))
30.0ms
(/ (* (- 1.0 x) y) (+ y 1.0))

series179.0ms

Counts
3 → 9
Calls
3 calls:
41.0ms
(* (- 1.0 x) y)
92.0ms
(- 1.0 (/ (* (- 1.0 x) y) (+ y 1.0)))
46.0ms
(/ (* (- 1.0 x) y) (+ y 1.0))

simplify1.4s

Counts
72 → 72
Iterations

Useful iterations: done (1.4s)

IterNodesCost
0128885
1347828
22051752
done5002746

prune188.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.1b

localize12.0ms

Local error

Found 3 expressions with local error:

0.0b
(/ y (+ y 1.0))
0.0b
(* (- 1.0 x) (/ y (+ y 1.0)))
3.0b
(- 1.0 (* (- 1.0 x) (/ y (+ y 1.0))))

rewrite90.0ms

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:
18.0ms
(/ y (+ y 1.0))
55.0ms
(* (- 1.0 x) (/ y (+ y 1.0)))
10.0ms
(- 1.0 (* (- 1.0 x) (/ y (+ y 1.0))))

series200.0ms

Counts
3 → 9
Calls
3 calls:
47.0ms
(/ y (+ y 1.0))
58.0ms
(* (- 1.0 x) (/ y (+ y 1.0)))
95.0ms
(- 1.0 (* (- 1.0 x) (/ y (+ y 1.0))))

simplify1.6s

Counts
97 → 97
Iterations

Useful iterations: 2 (399.0ms)

IterNodesCost
01571229
14241152
224931056
done50001056

prune207.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.1b

localize28.0ms

Local error

Found 4 expressions with local error:

0.1b
(* (* (- 1.0 x) (/ y (+ y 1.0))) (+ 1.0 (* (- 1.0 x) (/ y (+ y 1.0)))))
0.2b
(pow (* (- 1.0 x) (/ y (+ y 1.0))) 3)
3.0b
(- (pow 1.0 3) (pow (* (- 1.0 x) (/ y (+ y 1.0))) 3))
11.8b
(/ (- (pow 1.0 3) (pow (* (- 1.0 x) (/ y (+ y 1.0))) 3)) (+ (* 1.0 1.0) (* (* (- 1.0 x) (/ y (+ y 1.0))) (+ 1.0 (* (- 1.0 x) (/ y (+ y 1.0)))))))

rewrite295.0ms

Algorithm
rewrite-expression-head
Rules
74×add-sqr-sqrt
40×difference-of-squares
39×times-frac
34×*-un-lft-identity
31×sqr-pow
24×add-cube-cbrt
21×add-exp-log add-cbrt-cube
18×frac-times
13×associate-*l/ associate-/l*
12×pow1
11×unpow-prod-down cube-prod
10×flip3-- flip--
7×flip3-+ prod-exp cbrt-unprod flip-+
6×associate-*r/ add-log-exp
5×difference-cubes cube-div distribute-lft-out--
4×pow-prod-down
3×cbrt-undiv pow-unpow div-exp associate-*r* pow-exp associate-/r* rem-cube-cbrt
2×pow-pow associate-/r/ associate-/l/
1×distribute-rgt-in cube-mult pow-to-exp sub-neg frac-2neg distribute-lft-in diff-log unpow3 div-sub associate-*l* clear-num *-commutative div-inv
Counts
4 → 162
Calls
4 calls:
127.0ms
(* (* (- 1.0 x) (/ y (+ y 1.0))) (+ 1.0 (* (- 1.0 x) (/ y (+ y 1.0)))))
20.0ms
(pow (* (- 1.0 x) (/ y (+ y 1.0))) 3)
30.0ms
(- (pow 1.0 3) (pow (* (- 1.0 x) (/ y (+ y 1.0))) 3))
103.0ms
(/ (- (pow 1.0 3) (pow (* (- 1.0 x) (/ y (+ y 1.0))) 3)) (+ (* 1.0 1.0) (* (* (- 1.0 x) (/ y (+ y 1.0))) (+ 1.0 (* (- 1.0 x) (/ y (+ y 1.0)))))))

series1.1s

Counts
4 → 12
Calls
4 calls:
134.0ms
(* (* (- 1.0 x) (/ y (+ y 1.0))) (+ 1.0 (* (- 1.0 x) (/ y (+ y 1.0)))))
70.0ms
(pow (* (- 1.0 x) (/ y (+ y 1.0))) 3)
220.0ms
(- (pow 1.0 3) (pow (* (- 1.0 x) (/ y (+ y 1.0))) 3))
633.0ms
(/ (- (pow 1.0 3) (pow (* (- 1.0 x) (/ y (+ y 1.0))) 3)) (+ (* 1.0 1.0) (* (* (- 1.0 x) (/ y (+ y 1.0))) (+ 1.0 (* (- 1.0 x) (/ y (+ y 1.0)))))))

simplify655.0ms

Counts
174 → 174
Iterations

Useful iterations: done (643.0ms)

IterNodesCost
03187831
111027379
done50017027

prune644.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.1b

localize53.0ms

Local error

Found 4 expressions with local error:

3.0b
(- (pow 1.0 3) (pow (* (- 1.0 x) (/ y (+ y 1.0))) 3))
4.2b
(/ (* (- 1.0 x) y) (+ y 1.0))
8.1b
(* (/ (- (pow 1.0 3) (pow (* (- 1.0 x) (/ y (+ y 1.0))) 3)) (- (* 1.0 (pow 1.0 3)) (* (pow (/ (* (- 1.0 x) y) (+ y 1.0)) (* 2 1)) (* (+ 1.0 (* (- 1.0 x) (/ y (+ y 1.0)))) (+ 1.0 (* (- 1.0 x) (/ y (+ y 1.0)))))))) (- (* 1.0 1.0) (* (* (- 1.0 x) (/ y (+ y 1.0))) (+ 1.0 (* (- 1.0 x) (/ y (+ y 1.0)))))))
14.1b
(/ (- (pow 1.0 3) (pow (* (- 1.0 x) (/ y (+ y 1.0))) 3)) (- (* 1.0 (pow 1.0 3)) (* (pow (/ (* (- 1.0 x) y) (+ y 1.0)) (* 2 1)) (* (+ 1.0 (* (- 1.0 x) (/ y (+ y 1.0)))) (+ 1.0 (* (- 1.0 x) (/ y (+ y 1.0))))))))

rewrite303.0ms

Algorithm
rewrite-expression-head
Rules
127×add-sqr-sqrt
83×times-frac
64×difference-of-squares
62×*-un-lft-identity
48×sqr-pow
45×associate-*l*
42×add-cube-cbrt
16×add-exp-log unpow-prod-down cube-prod add-cbrt-cube
14×associate-/l*
8×difference-cubes distribute-lft-out--
7×flip3-- associate-/r* flip--
6×pow1 associate-/r/ add-log-exp
4×cbrt-undiv div-exp associate-/l/
3×sub-neg associate-*r* associate-*l/ prod-exp cbrt-unprod div-inv
2×distribute-rgt-in frac-times frac-2neg distribute-lft-in associate-*r/ clear-num distribute-lft-out unswap-sqr
1×flip3-+ diff-log div-sub pow-prod-down *-commutative flip-+
Counts
4 → 193
Calls
4 calls:
24.0ms
(- (pow 1.0 3) (pow (* (- 1.0 x) (/ y (+ y 1.0))) 3))
34.0ms
(/ (* (- 1.0 x) y) (+ y 1.0))
151.0ms
(* (/ (- (pow 1.0 3) (pow (* (- 1.0 x) (/ y (+ y 1.0))) 3)) (- (* 1.0 (pow 1.0 3)) (* (pow (/ (* (- 1.0 x) y) (+ y 1.0)) (* 2 1)) (* (+ 1.0 (* (- 1.0 x) (/ y (+ y 1.0)))) (+ 1.0 (* (- 1.0 x) (/ y (+ y 1.0)))))))) (- (* 1.0 1.0) (* (* (- 1.0 x) (/ y (+ y 1.0))) (+ 1.0 (* (- 1.0 x) (/ y (+ y 1.0)))))))
75.0ms
(/ (- (pow 1.0 3) (pow (* (- 1.0 x) (/ y (+ y 1.0))) 3)) (- (* 1.0 (pow 1.0 3)) (* (pow (/ (* (- 1.0 x) y) (+ y 1.0)) (* 2 1)) (* (+ 1.0 (* (- 1.0 x) (/ y (+ y 1.0)))) (+ 1.0 (* (- 1.0 x) (/ y (+ y 1.0))))))))

series4.5s

Counts
4 → 12
Calls
4 calls:
212.0ms
(- (pow 1.0 3) (pow (* (- 1.0 x) (/ y (+ y 1.0))) 3))
65.0ms
(/ (* (- 1.0 x) y) (+ y 1.0))
3.0s
(* (/ (- (pow 1.0 3) (pow (* (- 1.0 x) (/ y (+ y 1.0))) 3)) (- (* 1.0 (pow 1.0 3)) (* (pow (/ (* (- 1.0 x) y) (+ y 1.0)) (* 2 1)) (* (+ 1.0 (* (- 1.0 x) (/ y (+ y 1.0)))) (+ 1.0 (* (- 1.0 x) (/ y (+ y 1.0)))))))) (- (* 1.0 1.0) (* (* (- 1.0 x) (/ y (+ y 1.0))) (+ 1.0 (* (- 1.0 x) (/ y (+ y 1.0)))))))
1.2s
(/ (- (pow 1.0 3) (pow (* (- 1.0 x) (/ y (+ y 1.0))) 3)) (- (* 1.0 (pow 1.0 3)) (* (pow (/ (* (- 1.0 x) y) (+ y 1.0)) (* 2 1)) (* (+ 1.0 (* (- 1.0 x) (/ y (+ y 1.0)))) (+ 1.0 (* (- 1.0 x) (/ y (+ y 1.0))))))))

simplify670.0ms

Counts
205 → 205
Iterations

Useful iterations: done (654.0ms)

IterNodesCost
035015747
1105314977
done500014119

prune1.5s

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.1b

regimes172.0ms

Accuracy

100% (0.0b remaining)

Error of 0.1b against oracle of 0.1b and baseline of 14.7b

bsearch123.0ms

Steps
ItersRangePoint
9
388.37859194422595
403275480.5297131
186543853.31569508
9
-7479483537821808.0
-2823503834.9923654
-2868269604.961125

simplify6.0ms

Iterations

Useful iterations: 1 (3.0ms)

IterNodesCost
01941
12631
done2631

end0.0ms

sample1.0s

Algorithm
intervals
Results
383.0ms6045×body80valid
218.0ms765×body640valid
84.0ms398×body1280valid
61.0ms505×body320valid
25.0ms287×body160valid