Details

Time bar (total: 12.6s)

sample18.0ms

Algorithm
intervals
Results
5.0ms199×body80valid
2.0ms26×body640valid
1.0ms18×body320valid
1.0ms10×body1280valid
0.0ms3×body160valid

simplify3.3s

Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
0811
11611
23511
37011
413011
521311
625611
727211
829911
936811
1042011
1142611
1244111
1347711
1456711
1579911
16107811
17150911
18193311
19196811
done196811

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 21.3b

localize7.0ms

Local error

Found 3 expressions with local error:

0.0b
(* (- 1.0 x) y)
1.4b
(- 1.0 (/ (* (- 1.0 x) y) (+ y 1.0)))
7.1b
(/ (* (- 1.0 x) y) (+ y 1.0))

rewrite31.0ms

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:
10.0ms
(* (- 1.0 x) y)
10.0ms
(- 1.0 (/ (* (- 1.0 x) y) (+ y 1.0)))
9.0ms
(/ (* (- 1.0 x) y) (+ y 1.0))

series140.0ms

Counts
3 → 9
Calls
3 calls:
31.0ms
(* (- 1.0 x) y)
63.0ms
(- 1.0 (/ (* (- 1.0 x) y) (+ y 1.0)))
46.0ms
(/ (* (- 1.0 x) y) (+ y 1.0))

simplify879.0ms

Counts
72 → 72
Iterations

Useful iterations: done (877.0ms)

IterNodesCost
0128885
1336828
21226746
done5000744

prune148.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.1b

localize7.0ms

Local error

Found 1 expressions with local error:

1.4b
(- 1.0 (* (- 1.0 x) (/ y (+ y 1.0))))

rewrite2.0ms

Algorithm
rewrite-expression-head
Rules
3×add-log-exp
1×pow1 add-exp-log add-sqr-sqrt add-cube-cbrt sub-neg flip3-- *-un-lft-identity diff-log add-cbrt-cube flip--
Counts
1 → 12
Calls
1 calls:
2.0ms
(- 1.0 (* (- 1.0 x) (/ y (+ y 1.0))))

series67.0ms

Counts
1 → 3
Calls
1 calls:
67.0ms
(- 1.0 (* (- 1.0 x) (/ y (+ y 1.0))))

simplify1.1s

Counts
15 → 15
Iterations

Useful iterations: done (1.1s)

IterNodesCost
042274
1113263
2342237
31263235
done5000229

prune36.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.1b

localize15.0ms

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)))))
0.1b
(pow (* (- 1.0 x) (/ y (+ y 1.0))) 3)
1.3b
(- (pow 1.0 3) (pow (* (- 1.0 x) (/ y (+ y 1.0))) 3))
12.3b
(/ (- (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)))))))

rewrite95.0ms

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:
31.0ms
(* (* (- 1.0 x) (/ y (+ y 1.0))) (+ 1.0 (* (- 1.0 x) (/ y (+ y 1.0)))))
8.0ms
(pow (* (- 1.0 x) (/ y (+ y 1.0))) 3)
12.0ms
(- (pow 1.0 3) (pow (* (- 1.0 x) (/ y (+ y 1.0))) 3))
37.0ms
(/ (- (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)))))))

series855.0ms

Counts
4 → 12
Calls
4 calls:
130.0ms
(* (* (- 1.0 x) (/ y (+ y 1.0))) (+ 1.0 (* (- 1.0 x) (/ y (+ y 1.0)))))
58.0ms
(pow (* (- 1.0 x) (/ y (+ y 1.0))) 3)
146.0ms
(- (pow 1.0 3) (pow (* (- 1.0 x) (/ y (+ y 1.0))) 3))
521.0ms
(/ (- (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)))))))

simplify1.8s

Counts
174 → 174
Iterations

Useful iterations: 2 (745.0ms)

IterNodesCost
03187831
110017379
246706999
done50006999

prune544.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.1b

localize6.0ms

Local error

Found 2 expressions with local error:

0.0b
(+ (* (/ 1.0 y) (- 1 x)) x)
0.2b
(* (/ 1.0 y) (- 1 x))

rewrite25.0ms

Algorithm
rewrite-expression-head
Rules
18×add-sqr-sqrt
13×*-un-lft-identity associate-*l*
10×add-cube-cbrt times-frac
7×add-exp-log add-cbrt-cube
6×associate-*r*
4×pow1 distribute-rgt-in sub-neg associate-+l+ distribute-lft-in add-log-exp
2×frac-times flip3-- associate-*r/ prod-exp flip-- cbrt-unprod difference-of-squares unswap-sqr
1×cbrt-undiv +-commutative flip3-+ div-exp pow-prod-down associate-*l/ sum-log *-commutative flip-+ div-inv distribute-lft-out--
Counts
2 → 58
Calls
2 calls:
7.0ms
(+ (* (/ 1.0 y) (- 1 x)) x)
16.0ms
(* (/ 1.0 y) (- 1 x))

series69.0ms

Counts
2 → 6
Calls
2 calls:
28.0ms
(+ (* (/ 1.0 y) (- 1 x)) x)
40.0ms
(* (/ 1.0 y) (- 1 x))

simplify2.6s

Counts
64 → 64
Iterations

Useful iterations: 3 (1.4s)

IterNodesCost
0119735
1317678
21059614
34245608
done5000608

prune112.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0.1b

regimes84.0ms

Accuracy

100% (0.0b remaining)

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

bsearch79.0ms

Steps
ItersRangePoint
8
28638621.607503247
50024088429.266525
212488777.89840698
10
-7.884632933156152e+16
-925426.909356872
-104628043.80156818

simplify2.0ms

Iterations

Useful iterations: 1 (1.0ms)

IterNodesCost
01937
12829
done2829

end0.0ms

sample442.0ms

Algorithm
intervals
Results
156.0ms6133×body80valid
64.0ms719×body640valid
39.0ms347×body1280valid
35.0ms515×body320valid
16.0ms286×body160valid