Details

Time bar (total: 3.8s)

sample18.0ms

Algorithm
intervals
Results
5.0ms195×body80valid
2.0ms24×body640valid
1.0ms11×body1280valid
1.0ms12×body320valid
1.0ms14×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

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 24.6b

localize6.0ms

Local error

Found 2 expressions with local error:

3.5b
(- 1.0 (/ (* (- 1.0 x) y) (+ y 1.0)))
9.6b
(/ (* (- 1.0 x) y) (+ y 1.0))

rewrite46.0ms

Algorithm
rewrite-expression-head
Rules
10×*-un-lft-identity
7×add-exp-log add-cbrt-cube
6×add-sqr-sqrt
4×add-cube-cbrt times-frac associate-/r* add-log-exp
2×pow1 cbrt-undiv flip3-- div-exp associate-*l/ associate-/r/ flip-- associate-/l/ distribute-lft-out
1×sub-neg frac-2neg flip3-+ diff-log prod-exp clear-num cbrt-unprod flip-+ div-inv associate-/l* distribute-lft-out-- difference-of-squares
Counts
2 → 41
Calls
2 calls:
21.0ms
(- 1.0 (/ (* (- 1.0 x) y) (+ y 1.0)))
23.0ms
(/ (* (- 1.0 x) y) (+ y 1.0))

series311.0ms

Counts
2 → 6
Calls
2 calls:
272.0ms
(- 1.0 (/ (* (- 1.0 x) y) (+ y 1.0)))
39.0ms
(/ (* (- 1.0 x) y) (+ y 1.0))

simplify39.0ms

Algorithm
egg-herbie
Counts
47 → 47
Iterations

Useful iterations: 2 (34.0ms)

IterNodesCost
0287314
11151281
25001280

prune97.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.3b

localize6.0ms

Local error

Found 3 expressions with local error:

0.0b
(* (- 1.0 x) (/ y (+ y 1.0)))
0.0b
(/ y (+ y 1.0))
3.5b
(- 1.0 (* (- 1.0 x) (/ y (+ y 1.0))))

rewrite65.0ms

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:
45.0ms
(* (- 1.0 x) (/ y (+ y 1.0)))
11.0ms
(/ y (+ y 1.0))
6.0ms
(- 1.0 (* (- 1.0 x) (/ y (+ y 1.0))))

series132.0ms

Counts
3 → 9
Calls
3 calls:
40.0ms
(* (- 1.0 x) (/ y (+ y 1.0)))
30.0ms
(/ y (+ y 1.0))
61.0ms
(- 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

prune164.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.3b

localize10.0ms

Local error

Found 4 expressions with local error:

0.1b
(* (- 1.0 x) (/ y (- (* y y) (* 1.0 1.0))))
0.1b
(* (* (- 1.0 x) (/ y (- (* y y) (* 1.0 1.0)))) (- y 1.0))
5.0b
(- 1.0 (* (* (- 1.0 x) (/ y (- (* y y) (* 1.0 1.0)))) (- y 1.0)))
17.0b
(/ y (- (* y y) (* 1.0 1.0)))

rewrite159.0ms

Algorithm
rewrite-expression-head
Rules
32×add-sqr-sqrt
27×*-un-lft-identity
25×times-frac
23×add-cube-cbrt associate-*r*
20×add-exp-log add-cbrt-cube
18×frac-times
17×flip3-- flip--
13×associate-*l/
11×pow1
9×difference-of-squares
7×prod-exp cbrt-unprod
6×associate-*r/ associate-*l* add-log-exp
5×sub-neg
4×distribute-rgt-in distribute-lft-in pow-prod-down associate-/r* associate-/r/ associate--r+
3×cbrt-undiv div-exp associate-/l*
2×*-commutative div-inv distribute-lft-out-- unswap-sqr
1×frac-2neg diff-log clear-num
Counts
4 → 135
Calls
4 calls:
52.0ms
(* (- 1.0 x) (/ y (- (* y y) (* 1.0 1.0))))
80.0ms
(* (* (- 1.0 x) (/ y (- (* y y) (* 1.0 1.0)))) (- y 1.0))
6.0ms
(- 1.0 (* (* (- 1.0 x) (/ y (- (* y y) (* 1.0 1.0)))) (- y 1.0)))
15.0ms
(/ y (- (* y y) (* 1.0 1.0)))

series350.0ms

Counts
4 → 12
Calls
4 calls:
80.0ms
(* (- 1.0 x) (/ y (- (* y y) (* 1.0 1.0))))
69.0ms
(* (* (- 1.0 x) (/ y (- (* y y) (* 1.0 1.0)))) (- y 1.0))
137.0ms
(- 1.0 (* (* (- 1.0 x) (/ y (- (* y y) (* 1.0 1.0)))) (- y 1.0)))
64.0ms
(/ y (- (* y y) (* 1.0 1.0)))

simplify107.0ms

Algorithm
egg-herbie
Counts
147 → 147
Iterations

Useful iterations: 2 (92.0ms)

IterNodesCost
07141438
138671306
250011304

prune320.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.3b

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b
(/ y (+ y 1.0))
0.1b
(* (* (- 1.0 x) (/ y (+ y 1.0))) (* (- 1.0 x) (/ y (+ y 1.0))))
3.5b
(- (* 1.0 1.0) (* (* (- 1.0 x) (/ y (+ y 1.0))) (* (- 1.0 x) (/ y (+ y 1.0)))))
11.0b
(/ (- (* 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)))))

rewrite165.0ms

Algorithm
rewrite-expression-head
Rules
49×frac-times
44×add-exp-log add-cbrt-cube
43×pow1
30×*-un-lft-identity
29×associate-*l/
26×flip3-- flip--
24×times-frac
22×add-sqr-sqrt add-cube-cbrt
21×prod-exp cbrt-unprod
17×associate-*r/ pow-prod-down
8×cbrt-undiv div-exp
7×associate-/r* associate-/l*
6×add-log-exp
5×difference-of-squares
4×associate-/r/ pow-sqr pow-prod-up distribute-lft-out
2×frac-2neg flip3-+ pow-plus clear-num flip-+ div-inv associate-/l/
1×pow2 sub-neg diff-log div-sub swap-sqr associate-*r* associate-*l* *-commutative
Counts
4 → 161
Calls
4 calls:
11.0ms
(/ y (+ y 1.0))
106.0ms
(* (* (- 1.0 x) (/ y (+ y 1.0))) (* (- 1.0 x) (/ y (+ y 1.0))))
10.0ms
(- (* 1.0 1.0) (* (* (- 1.0 x) (/ y (+ y 1.0))) (* (- 1.0 x) (/ y (+ y 1.0)))))
31.0ms
(/ (- (* 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)))))

series519.0ms

Counts
4 → 12
Calls
4 calls:
31.0ms
(/ y (+ y 1.0))
50.0ms
(* (* (- 1.0 x) (/ y (+ y 1.0))) (* (- 1.0 x) (/ y (+ y 1.0))))
81.0ms
(- (* 1.0 1.0) (* (* (- 1.0 x) (/ y (+ y 1.0))) (* (- 1.0 x) (/ y (+ y 1.0)))))
358.0ms
(/ (- (* 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)))))

simplify126.0ms

Algorithm
egg-herbie
Counts
173 → 173
Iterations

Useful iterations: 1 (25.0ms)

IterNodesCost
08752285
146311991
250021991

prune301.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.3b

regimes188.0ms

Accuracy

99.9% (0.0b remaining)

Error of 0.2b against oracle of 0.2b and baseline of 22.2b

bsearch60.0ms

Steps
ItersRangePoint
8
227507829.52260175
202115485668.4307
240320796.85121965
7
-1557293340.659962
-28256763.0897718
-119383534.45748925

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
03314
13314

end0.0ms

sample485.0ms

Algorithm
intervals
Results
154.0ms6066×body80valid
63.0ms744×body640valid
42.0ms384×body1280valid
36.0ms510×body320valid
16.0ms296×body160valid