Details

Time bar (total: 4.7s)

sample32.0ms

Algorithm
intervals
Results
9.0ms29×body640valid
9.0ms185×body80valid
3.0ms20×body320valid
3.0ms12×body1280valid
1.0ms10×body160valid

simplify66.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (2.0ms)

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: 22.1b

localize7.0ms

Local error

Found 3 expressions with local error:

0.0b
(* (- 1.0 x) y)
2.4b
(- 1.0 (/ (* (- 1.0 x) y) (+ y 1.0)))
5.2b
(/ (* (- 1.0 x) y) (+ y 1.0))

rewrite30.0ms

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

series148.0ms

Counts
3 → 9
Calls
3 calls:
35.0ms
(* (- 1.0 x) y)
66.0ms
(- 1.0 (/ (* (- 1.0 x) y) (+ y 1.0)))
48.0ms
(/ (* (- 1.0 x) y) (+ y 1.0))

simplify47.0ms

Algorithm
egg-herbie
Counts
72 → 72
Iterations

Useful iterations: 1 (10.0ms)

IterNodesCost
0338401
11456359
25001359

prune145.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.2b

localize11.0ms

Local error

Found 4 expressions with local error:

5.2b
(/ (* (- 1.0 x) y) (+ y 1.0))
5.2b
(/ (* (- 1.0 x) y) (+ y 1.0))
5.2b
(/ (* (- 1.0 x) y) (+ y 1.0))
7.4b
(/ (- (* 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))))

rewrite61.0ms

Algorithm
rewrite-expression-head
Rules
42×*-un-lft-identity
28×times-frac
21×add-exp-log add-cbrt-cube
20×add-sqr-sqrt add-cube-cbrt
16×associate-/r*
11×distribute-lft-out
8×associate-/r/ associate-/l/
7×cbrt-undiv div-exp associate-/l*
6×associate-*l/
5×difference-of-squares
4×pow1 flip3-- frac-2neg flip3-+ clear-num flip-- flip-+ div-inv add-log-exp
3×prod-exp cbrt-unprod
1×div-sub
Counts
4 → 122
Calls
4 calls:
14.0ms
(/ (* (- 1.0 x) y) (+ y 1.0))
9.0ms
(/ (* (- 1.0 x) y) (+ y 1.0))
9.0ms
(/ (* (- 1.0 x) y) (+ y 1.0))
26.0ms
(/ (- (* 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))))

series544.0ms

Counts
4 → 12
Calls
4 calls:
49.0ms
(/ (* (- 1.0 x) y) (+ y 1.0))
43.0ms
(/ (* (- 1.0 x) y) (+ y 1.0))
48.0ms
(/ (* (- 1.0 x) y) (+ y 1.0))
405.0ms
(/ (- (* 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))))

simplify65.0ms

Algorithm
egg-herbie
Counts
134 → 134
Iterations

Useful iterations: 1 (12.0ms)

IterNodesCost
04311543
120191406
250011406

prune284.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.2b

localize16.0ms

Local error

Found 4 expressions with local error:

0.0b
(+ (* y y) (- (* 1.0 1.0) (* y 1.0)))
5.3b
(- 1.0 (* (/ (* (- 1.0 x) y) (+ (pow y 3) (pow 1.0 3))) (+ (* y y) (- (* 1.0 1.0) (* y 1.0)))))
9.7b
(/ (* (- 1.0 x) y) (+ (pow y 3) (pow 1.0 3)))
16.6b
(* (/ (* (- 1.0 x) y) (+ (pow y 3) (pow 1.0 3))) (+ (* y y) (- (* 1.0 1.0) (* y 1.0))))

rewrite125.0ms

Algorithm
rewrite-expression-head
Rules
39×*-un-lft-identity
18×add-exp-log times-frac add-cbrt-cube
15×associate-*l* distribute-lft-out
12×unpow-prod-down cube-prod
11×add-sqr-sqrt add-log-exp
9×add-cube-cbrt associate-/r*
6×pow1
5×flip3-+ prod-exp cbrt-unprod flip-+
4×cbrt-undiv div-exp associate-/r/
3×associate-*r* associate-*l/ sum-cubes
2×distribute-rgt-in frac-times sub-neg associate-+r+ flip3-- distribute-lft-in diff-log associate-*r/ sum-log flip-- div-inv associate-/l/ associate--r+
1×+-commutative associate-+r- frac-2neg pow-prod-down clear-num *-commutative associate-/l* unswap-sqr
Counts
4 → 107
Calls
4 calls:
7.0ms
(+ (* y y) (- (* 1.0 1.0) (* y 1.0)))
2.0ms
(- 1.0 (* (/ (* (- 1.0 x) y) (+ (pow y 3) (pow 1.0 3))) (+ (* y y) (- (* 1.0 1.0) (* y 1.0)))))
27.0ms
(/ (* (- 1.0 x) y) (+ (pow y 3) (pow 1.0 3)))
85.0ms
(* (/ (* (- 1.0 x) y) (+ (pow y 3) (pow 1.0 3))) (+ (* y y) (- (* 1.0 1.0) (* y 1.0))))

series444.0ms

Counts
4 → 12
Calls
4 calls:
21.0ms
(+ (* y y) (- (* 1.0 1.0) (* y 1.0)))
226.0ms
(- 1.0 (* (/ (* (- 1.0 x) y) (+ (pow y 3) (pow 1.0 3))) (+ (* y y) (- (* 1.0 1.0) (* y 1.0)))))
88.0ms
(/ (* (- 1.0 x) y) (+ (pow y 3) (pow 1.0 3)))
109.0ms
(* (/ (* (- 1.0 x) y) (+ (pow y 3) (pow 1.0 3))) (+ (* y y) (- (* 1.0 1.0) (* y 1.0))))

simplify94.0ms

Algorithm
egg-herbie
Counts
119 → 119
Iterations

Useful iterations: 2 (81.0ms)

IterNodesCost
06451335
135761152
250011147

prune330.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0.2b

localize18.0ms

Local error

Found 4 expressions with local error:

0.0b
(* (+ (* 1.0 (- 1.0 y)) (pow y 2)) (/ y (+ y 1.0)))
2.6b
(/ (- 1.0 x) (+ (* y y) (- (* 1.0 1.0) (* y 1.0))))
4.6b
(- 1.0 (* (/ (- 1.0 x) (+ (* y y) (- (* 1.0 1.0) (* y 1.0)))) (* (+ (* 1.0 (- 1.0 y)) (pow y 2)) (/ y (+ y 1.0)))))
16.6b
(* (/ (- 1.0 x) (+ (* y y) (- (* 1.0 1.0) (* y 1.0)))) (* (+ (* 1.0 (- 1.0 y)) (pow y 2)) (/ y (+ y 1.0))))

rewrite140.0ms

Algorithm
rewrite-expression-head
Rules
52×*-un-lft-identity
51×add-sqr-sqrt
43×times-frac
32×add-exp-log add-cube-cbrt add-cbrt-cube
24×associate-*l*
19×associate-*r*
12×prod-exp cbrt-unprod
11×pow1 frac-times
9×flip3-+ flip-+
8×associate-*r/
7×cbrt-undiv div-exp associate-*l/ distribute-lft-out-- difference-of-squares
6×associate-/r/ add-log-exp
5×associate-/l*
4×pow-prod-down
3×associate-/r* div-inv distribute-lft-out
2×flip3-- *-commutative flip-- associate-/l/ unswap-sqr
1×sub-neg frac-2neg diff-log div-sub clear-num
Counts
4 → 148
Calls
4 calls:
36.0ms
(* (+ (* 1.0 (- 1.0 y)) (pow y 2)) (/ y (+ y 1.0)))
20.0ms
(/ (- 1.0 x) (+ (* y y) (- (* 1.0 1.0) (* y 1.0))))
2.0ms
(- 1.0 (* (/ (- 1.0 x) (+ (* y y) (- (* 1.0 1.0) (* y 1.0)))) (* (+ (* 1.0 (- 1.0 y)) (pow y 2)) (/ y (+ y 1.0)))))
76.0ms
(* (/ (- 1.0 x) (+ (* y y) (- (* 1.0 1.0) (* y 1.0)))) (* (+ (* 1.0 (- 1.0 y)) (pow y 2)) (/ y (+ y 1.0))))

series237.0ms

Counts
4 → 12
Calls
4 calls:
71.0ms
(* (+ (* 1.0 (- 1.0 y)) (pow y 2)) (/ y (+ y 1.0)))
45.0ms
(/ (- 1.0 x) (+ (* y y) (- (* 1.0 1.0) (* y 1.0))))
72.0ms
(- 1.0 (* (/ (- 1.0 x) (+ (* y y) (- (* 1.0 1.0) (* y 1.0)))) (* (+ (* 1.0 (- 1.0 y)) (pow y 2)) (/ y (+ y 1.0)))))
48.0ms
(* (/ (- 1.0 x) (+ (* y y) (- (* 1.0 1.0) (* y 1.0)))) (* (+ (* 1.0 (- 1.0 y)) (pow y 2)) (/ y (+ y 1.0))))

simplify127.0ms

Algorithm
egg-herbie
Counts
160 → 160
Iterations

Useful iterations: 2 (107.0ms)

IterNodesCost
08792400
148031886
250011783

prune451.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0.2b

regimes392.0ms

Accuracy

99.7% (0.1b remaining)

Error of 0.2b against oracle of 0.1b and baseline of 22.9b

bsearch90.0ms

Steps
ItersRangePoint
9
363928.4733812492
249936452872729.84
57260141.12847787
7
-1450154140655066.2
-31027174625110.03
-85111338363411.1

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
04225
14225

end0.0ms

sample760.0ms

Algorithm
intervals
Results
310.0ms6115×body80valid
136.0ms734×body640valid
86.0ms368×body1280valid
70.0ms507×body320valid
26.0ms276×body160valid