Details

Time bar (total: 4.2s)

sample17.0ms

Algorithm
intervals
Results
5.0ms192×body80valid
2.0ms28×body640valid
1.0ms19×body320valid
1.0ms11×body1280valid
0.0ms6×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: 22.0b

localize6.0ms

Local error

Found 3 expressions with local error:

0.0b
(* (- 1.0 x) y)
1.8b
(- 1.0 (/ (* (- 1.0 x) y) (+ y 1.0)))
6.4b
(/ (* (- 1.0 x) y) (+ y 1.0))

rewrite33.0ms

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:
11.0ms
(* (- 1.0 x) y)
10.0ms
(- 1.0 (/ (* (- 1.0 x) y) (+ y 1.0)))
10.0ms
(/ (* (- 1.0 x) y) (+ y 1.0))

series150.0ms

Counts
3 → 9
Calls
3 calls:
30.0ms
(* (- 1.0 x) y)
73.0ms
(- 1.0 (/ (* (- 1.0 x) y) (+ y 1.0)))
47.0ms
(/ (* (- 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

prune141.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.1b

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)))
1.8b
(- 1.0 (* (- 1.0 x) (/ y (+ y 1.0))))

rewrite36.0ms

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:
6.0ms
(/ y (+ y 1.0))
24.0ms
(* (- 1.0 x) (/ y (+ y 1.0)))
3.0ms
(- 1.0 (* (- 1.0 x) (/ y (+ y 1.0))))

series154.0ms

Counts
3 → 9
Calls
3 calls:
35.0ms
(/ y (+ y 1.0))
48.0ms
(* (- 1.0 x) (/ y (+ y 1.0)))
71.0ms
(- 1.0 (* (- 1.0 x) (/ y (+ y 1.0))))

simplify54.0ms

Algorithm
egg-herbie
Counts
97 → 97
Iterations

Useful iterations: 1 (12.0ms)

IterNodesCost
0400572
11790526
25002526

prune188.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.1b

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b
(* (- 1.0 x) y)
0.1b
(* (/ (* (- 1.0 x) y) (- (* y y) (* 1.0 1.0))) (- y 1.0))
3.7b
(- 1.0 (* (/ (* (- 1.0 x) y) (- (* y y) (* 1.0 1.0))) (- y 1.0)))
16.6b
(/ (* (- 1.0 x) y) (- (* y y) (* 1.0 1.0)))

rewrite65.0ms

Algorithm
rewrite-expression-head
Rules
20×add-exp-log add-cbrt-cube
19×add-sqr-sqrt
15×*-un-lft-identity associate-*l*
11×add-cube-cbrt
8×pow1 times-frac associate-*r*
7×flip3-- flip--
6×prod-exp cbrt-unprod add-log-exp
5×sub-neg associate-*l/ difference-of-squares
4×cbrt-undiv distribute-rgt-in distribute-lft-in div-exp associate-/r* associate-/r/ associate--r+
2×frac-times associate-*r/ pow-prod-down *-commutative div-inv associate-/l/ distribute-lft-out-- unswap-sqr
1×frac-2neg diff-log clear-num associate-/l*
Counts
4 → 105
Calls
4 calls:
14.0ms
(* (- 1.0 x) y)
34.0ms
(* (/ (* (- 1.0 x) y) (- (* y y) (* 1.0 1.0))) (- y 1.0))
3.0ms
(- 1.0 (* (/ (* (- 1.0 x) y) (- (* y y) (* 1.0 1.0))) (- y 1.0)))
10.0ms
(/ (* (- 1.0 x) y) (- (* y y) (* 1.0 1.0)))

series374.0ms

Counts
4 → 12
Calls
4 calls:
35.0ms
(* (- 1.0 x) y)
82.0ms
(* (/ (* (- 1.0 x) y) (- (* y y) (* 1.0 1.0))) (- y 1.0))
163.0ms
(- 1.0 (* (/ (* (- 1.0 x) y) (- (* y y) (* 1.0 1.0))) (- y 1.0)))
94.0ms
(/ (* (- 1.0 x) y) (- (* y y) (* 1.0 1.0)))

simplify85.0ms

Algorithm
egg-herbie
Counts
117 → 117
Iterations

Useful iterations: 1 (17.0ms)

IterNodesCost
05671027
13078900
25001900

prune435.0ms

Pruning

4 alts after pruning (2 fresh and 2 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 x) (/ y (+ y 1.0))) 1.0))
0.1b
(pow (* (- 1.0 x) (/ y (+ y 1.0))) 3)
1.7b
(- (pow 1.0 3) (pow (* (- 1.0 x) (/ y (+ y 1.0))) 3))
13.7b
(/ (- (pow 1.0 3) (pow (* (- 1.0 x) (/ y (+ y 1.0))) 3)) (+ (* (* (- 1.0 x) (/ y (+ y 1.0))) (+ (* (- 1.0 x) (/ y (+ y 1.0))) 1.0)) (* 1.0 1.0)))

rewrite203.0ms

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:
59.0ms
(* (* (- 1.0 x) (/ y (+ y 1.0))) (+ (* (- 1.0 x) (/ y (+ y 1.0))) 1.0))
9.0ms
(pow (* (- 1.0 x) (/ y (+ y 1.0))) 3)
13.0ms
(- (pow 1.0 3) (pow (* (- 1.0 x) (/ y (+ y 1.0))) 3))
114.0ms
(/ (- (pow 1.0 3) (pow (* (- 1.0 x) (/ y (+ y 1.0))) 3)) (+ (* (* (- 1.0 x) (/ y (+ y 1.0))) (+ (* (- 1.0 x) (/ y (+ y 1.0))) 1.0)) (* 1.0 1.0)))

series912.0ms

Counts
4 → 12
Calls
4 calls:
123.0ms
(* (* (- 1.0 x) (/ y (+ y 1.0))) (+ (* (- 1.0 x) (/ y (+ y 1.0))) 1.0))
91.0ms
(pow (* (- 1.0 x) (/ y (+ y 1.0))) 3)
146.0ms
(- (pow 1.0 3) (pow (* (- 1.0 x) (/ y (+ y 1.0))) 3))
552.0ms
(/ (- (pow 1.0 3) (pow (* (- 1.0 x) (/ y (+ y 1.0))) 3)) (+ (* (* (- 1.0 x) (/ y (+ y 1.0))) (+ (* (- 1.0 x) (/ y (+ y 1.0))) 1.0)) (* 1.0 1.0)))

simplify61.0ms

Algorithm
egg-herbie
Counts
174 → 174
Iterations

Useful iterations: 1 (25.0ms)

IterNodesCost
010053719
150023556

prune499.0ms

Pruning

5 alts after pruning (2 fresh and 3 done)

Merged error: 0.1b

regimes113.0ms

Accuracy

99.9% (0.0b remaining)

Error of 0.2b against oracle of 0.2b and baseline of 14.0b

bsearch92.0ms

Steps
ItersRangePoint
10
0.003064448021395057
556939279.5099251
179306177.53728765
9
-15640006985.087824
-457.59610972879165
-111259902.92763877

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
03515
13515

end0.0ms

sample420.0ms

Algorithm
intervals
Results
145.0ms6156×body80valid
64.0ms709×body640valid
39.0ms371×body1280valid
31.0ms489×body320valid
15.0ms275×body160valid