Details

Time bar (total: 3.2s)

sample20.0ms

Algorithm
intervals
Results
4.0ms191×body80valid
4.0ms18×body640valid
2.0ms15×body1280valid
1.0ms21×body320valid
0.0ms11×body160valid

simplify65.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
0165
1355
2745
31285
42525
53745
65145
76425
87775
910105
1016865
1150015

prune2.0ms

Filtered
1 candidates to 0 candidates (0.0%)
Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 24.9b

localize7.0ms

Local error

Found 3 expressions with local error:

0.0b
(* (- 1.0 x) y)
2.6b
(- 1.0 (/ (* (- 1.0 x) y) (+ y 1.0)))
9.1b
(/ (* (- 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)))
10.0ms
(/ (* (- 1.0 x) y) (+ y 1.0))

series144.0ms

Counts
3 → 9
Calls
3 calls:
31.0ms
(* (- 1.0 x) y)
66.0ms
(- 1.0 (/ (* (- 1.0 x) y) (+ y 1.0)))
46.0ms
(/ (* (- 1.0 x) y) (+ y 1.0))

simplify44.0ms

Algorithm
egg-herbie
Counts
72 → 72
Iterations

Useful iterations: 1 (9.0ms)

IterNodesCost
0338401
11456359
25001359

prune142.0ms

Filtered
72 candidates to 51 candidates (70.8%)
Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.2b

localize6.0ms

Local error

Found 3 expressions with local error:

0.0b
(/ y (+ y 1.0))
0.0b
(* (- 1.0 x) (/ y (+ y 1.0)))
2.6b
(- 1.0 (* (- 1.0 x) (/ y (+ y 1.0))))

rewrite34.0ms

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:
5.0ms
(/ y (+ y 1.0))
23.0ms
(* (- 1.0 x) (/ y (+ y 1.0)))
2.0ms
(- 1.0 (* (- 1.0 x) (/ y (+ y 1.0))))

series151.0ms

Counts
3 → 9
Calls
3 calls:
37.0ms
(/ y (+ y 1.0))
43.0ms
(* (- 1.0 x) (/ y (+ y 1.0)))
70.0ms
(- 1.0 (* (- 1.0 x) (/ y (+ y 1.0))))

simplify52.0ms

Algorithm
egg-herbie
Counts
97 → 97
Iterations

Useful iterations: 1 (12.0ms)

IterNodesCost
0400572
11790526
25002526

prune177.0ms

Filtered
97 candidates to 70 candidates (72.2%)
Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.2b

localize8.0ms

Local error

Found 4 expressions with local error:

0.0b
(* (- 1.0 x) y)
0.2b
(/ 1 (/ (+ y 1.0) (* (- 1.0 x) y)))
2.6b
(- 1.0 (/ 1 (/ (+ y 1.0) (* (- 1.0 x) y))))
9.2b
(/ (+ y 1.0) (* (- 1.0 x) y))

rewrite64.0ms

Algorithm
rewrite-expression-head
Rules
52×times-frac
45×*-un-lft-identity
38×add-sqr-sqrt
32×add-exp-log
27×add-cube-cbrt
20×add-cbrt-cube
14×div-exp
12×associate-*l/
11×associate-/r* associate-/r/
7×pow1 cbrt-undiv flip3-- flip-- div-inv associate-/l*
6×distribute-lft-out add-log-exp
5×associate-*l* prod-exp
4×difference-of-squares
3×rec-exp 1-exp associate-*r* cbrt-unprod distribute-lft-out--
2×frac-2neg clear-num associate-/l/
1×sub-neg pow-flip flip3-+ diff-log pow-prod-down *-commutative flip-+ inv-pow unswap-sqr
Counts
4 → 134
Calls
4 calls:
10.0ms
(* (- 1.0 x) y)
15.0ms
(/ 1 (/ (+ y 1.0) (* (- 1.0 x) y)))
21.0ms
(- 1.0 (/ 1 (/ (+ y 1.0) (* (- 1.0 x) y))))
11.0ms
(/ (+ y 1.0) (* (- 1.0 x) y))

series190.0ms

Counts
4 → 12
Calls
4 calls:
32.0ms
(* (- 1.0 x) y)
34.0ms
(/ 1 (/ (+ y 1.0) (* (- 1.0 x) y)))
85.0ms
(- 1.0 (/ 1 (/ (+ y 1.0) (* (- 1.0 x) y))))
39.0ms
(/ (+ y 1.0) (* (- 1.0 x) y))

simplify67.0ms

Algorithm
egg-herbie
Counts
146 → 146
Iterations

Useful iterations: 2 (54.0ms)

IterNodesCost
05481077
12591907
25001895

prune211.0ms

Filtered
146 candidates to 84 candidates (57.5%)
Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0.2b

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b
(* (- 1.0 x) (/ y (+ y 1.0)))
0.1b
(* (* (- 1.0 x) (/ y (+ y 1.0))) (* (- 1.0 x) (/ y (+ y 1.0))))
2.6b
(- (* 1.0 1.0) (* (* (- 1.0 x) (/ y (+ y 1.0))) (* (- 1.0 x) (/ y (+ y 1.0)))))
10.1b
(/ (- (* 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)))))

rewrite97.0ms

Algorithm
rewrite-expression-head
Rules
51×frac-times
47×add-exp-log add-cbrt-cube
45×pow1
31×associate-*l/
30×*-un-lft-identity
29×add-sqr-sqrt
28×flip3-- flip--
25×times-frac
23×prod-exp cbrt-unprod
22×add-cube-cbrt
19×associate-*r*
18×associate-*r/ pow-prod-down
8×cbrt-undiv div-exp
6×associate-*l* add-log-exp difference-of-squares
4×associate-/r/ pow-sqr pow-prod-up associate-/l*
3×associate-/r* distribute-lft-out
2×flip3-+ pow-plus *-commutative flip-+ div-inv associate-/l/ unswap-sqr
1×pow2 sub-neg frac-2neg diff-log div-sub swap-sqr clear-num distribute-lft-out--
Counts
4 → 171
Calls
4 calls:
22.0ms
(* (- 1.0 x) (/ y (+ y 1.0)))
52.0ms
(* (* (- 1.0 x) (/ y (+ y 1.0))) (* (- 1.0 x) (/ y (+ y 1.0))))
3.0ms
(- (* 1.0 1.0) (* (* (- 1.0 x) (/ y (+ y 1.0))) (* (- 1.0 x) (/ y (+ y 1.0)))))
11.0ms
(/ (- (* 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)))))

series577.0ms

Counts
4 → 12
Calls
4 calls:
46.0ms
(* (- 1.0 x) (/ y (+ y 1.0)))
52.0ms
(* (* (- 1.0 x) (/ y (+ y 1.0))) (* (- 1.0 x) (/ y (+ y 1.0))))
85.0ms
(- (* 1.0 1.0) (* (* (- 1.0 x) (/ y (+ y 1.0))) (* (- 1.0 x) (/ y (+ y 1.0)))))
393.0ms
(/ (- (* 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)))))

simplify136.0ms

Algorithm
egg-herbie
Counts
183 → 183
Iterations

Useful iterations: 1 (26.0ms)

IterNodesCost
09252382
149522083
250012083

prune319.0ms

Filtered
183 candidates to 108 candidates (59.0%)
Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0.2b

regimes117.0ms

Accuracy

99.9% (0.0b remaining)

Error of 0.2b against oracle of 0.2b and baseline of 14.3b

bsearch67.0ms

Steps
ItersRangePoint
9
19555.519105776155
5849697155433.691
360844840.9089586
7
-195151873765.63306
-4240874295.0135207
-4286551152.90639

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
02910
12910

end0.0ms

sample420.0ms

Algorithm
intervals
Results
139.0ms6101×body80valid
64.0ms723×body640valid
39.0ms363×body1280valid
35.0ms512×body320valid
17.0ms301×body160valid