Details

Time bar (total: 3.8s)

sample18.0ms

Algorithm
intervals
Results
5.0ms202×body80valid
2.0ms22×body640valid
1.0ms11×body1280valid
1.0ms15×body320valid
0.0ms6×body160valid

simplify76.0ms

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: 19.9b

localize7.0ms

Local error

Found 3 expressions with local error:

0.0b
(* (- 1.0 x) y)
2.5b
(- 1.0 (/ (* (- 1.0 x) y) (+ y 1.0)))
6.6b
(/ (* (- 1.0 x) y) (+ y 1.0))

rewrite67.0ms

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:
21.0ms
(* (- 1.0 x) y)
22.0ms
(- 1.0 (/ (* (- 1.0 x) y) (+ y 1.0)))
23.0ms
(/ (* (- 1.0 x) y) (+ y 1.0))

series143.0ms

Counts
3 → 9
Calls
3 calls:
30.0ms
(* (- 1.0 x) y)
70.0ms
(- 1.0 (/ (* (- 1.0 x) y) (+ y 1.0)))
43.0ms
(/ (* (- 1.0 x) y) (+ y 1.0))

simplify54.0ms

Algorithm
egg-herbie
Counts
72 → 72
Iterations

Useful iterations: 1 (11.0ms)

IterNodesCost
0338401
11456359
25001359

prune140.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.2b

localize7.0ms

Local error

Found 3 expressions with local error:

0.0b
(/ y (+ y 1.0))
0.0b
(* (- 1.0 x) (/ y (+ y 1.0)))
2.5b
(- 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:
11.0ms
(/ y (+ y 1.0))
45.0ms
(* (- 1.0 x) (/ y (+ y 1.0)))
6.0ms
(- 1.0 (* (- 1.0 x) (/ y (+ y 1.0))))

series151.0ms

Counts
3 → 9
Calls
3 calls:
32.0ms
(/ y (+ y 1.0))
48.0ms
(* (- 1.0 x) (/ y (+ y 1.0)))
71.0ms
(- 1.0 (* (- 1.0 x) (/ y (+ y 1.0))))

simplify56.0ms

Algorithm
egg-herbie
Counts
97 → 97
Iterations

Useful iterations: 1 (13.0ms)

IterNodesCost
0400572
11790526
25002526

prune193.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.2b

localize11.0ms

Local error

Found 4 expressions with local error:

0.1b
(* (* (- 1.0 x) (/ y (- (* y y) (* 1.0 1.0)))) (- y 1.0))
0.1b
(* (- 1.0 x) (/ y (- (* y y) (* 1.0 1.0))))
3.8b
(- 1.0 (* (* (- 1.0 x) (/ y (- (* y y) (* 1.0 1.0)))) (- y 1.0)))
10.2b
(/ y (- (* y y) (* 1.0 1.0)))

rewrite153.0ms

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:
77.0ms
(* (* (- 1.0 x) (/ y (- (* y y) (* 1.0 1.0)))) (- y 1.0))
52.0ms
(* (- 1.0 x) (/ y (- (* y y) (* 1.0 1.0))))
6.0ms
(- 1.0 (* (* (- 1.0 x) (/ y (- (* y y) (* 1.0 1.0)))) (- y 1.0)))
13.0ms
(/ y (- (* y y) (* 1.0 1.0)))

series402.0ms

Counts
4 → 12
Calls
4 calls:
75.0ms
(* (* (- 1.0 x) (/ y (- (* y y) (* 1.0 1.0)))) (- y 1.0))
90.0ms
(* (- 1.0 x) (/ y (- (* y y) (* 1.0 1.0))))
166.0ms
(- 1.0 (* (* (- 1.0 x) (/ y (- (* y y) (* 1.0 1.0)))) (- y 1.0)))
71.0ms
(/ y (- (* y y) (* 1.0 1.0)))

simplify111.0ms

Algorithm
egg-herbie
Counts
147 → 147
Iterations

Useful iterations: 2 (92.0ms)

IterNodesCost
07141438
138671306
250011304

prune316.0ms

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0.2b

localize15.0ms

Local error

Found 4 expressions with local error:

0.0b
(+ 1.0 (* (- 1.0 x) (/ y (+ y 1.0))))
0.1b
(* (* (- 1.0 x) (/ y (+ y 1.0))) (* (- 1.0 x) (/ y (+ y 1.0))))
2.5b
(- (* 1.0 1.0) (* (* (- 1.0 x) (/ y (+ y 1.0))) (* (- 1.0 x) (/ y (+ y 1.0)))))
10.2b
(/ (- (* 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)))))

rewrite151.0ms

Algorithm
rewrite-expression-head
Rules
49×frac-times
43×pow1
42×add-exp-log add-cbrt-cube
29×associate-*l/
26×flip3-- flip--
21×prod-exp cbrt-unprod
17×associate-*r/ pow-prod-down
13×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
12×times-frac
8×add-log-exp
7×cbrt-undiv div-exp
5×difference-of-squares
4×pow-sqr pow-prod-up associate-/l*
3×associate-/r*
2×flip3-+ pow-plus associate-/r/ flip-+ associate-/l/
1×+-commutative pow2 sub-neg frac-2neg diff-log div-sub swap-sqr associate-*r* associate-*l* clear-num sum-log *-commutative div-inv
Counts
4 → 139
Calls
4 calls:
7.0ms
(+ 1.0 (* (- 1.0 x) (/ y (+ y 1.0))))
102.0ms
(* (* (- 1.0 x) (/ y (+ y 1.0))) (* (- 1.0 x) (/ y (+ y 1.0))))
9.0ms
(- (* 1.0 1.0) (* (* (- 1.0 x) (/ y (+ y 1.0))) (* (- 1.0 x) (/ y (+ y 1.0)))))
27.0ms
(/ (- (* 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)))))

series608.0ms

Counts
4 → 12
Calls
4 calls:
50.0ms
(+ 1.0 (* (- 1.0 x) (/ y (+ y 1.0))))
58.0ms
(* (* (- 1.0 x) (/ y (+ y 1.0))) (* (- 1.0 x) (/ y (+ y 1.0))))
96.0ms
(- (* 1.0 1.0) (* (* (- 1.0 x) (/ y (+ y 1.0))) (* (- 1.0 x) (/ y (+ y 1.0)))))
404.0ms
(/ (- (* 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)))))

simplify113.0ms

Algorithm
egg-herbie
Counts
151 → 151
Iterations

Useful iterations: 2 (94.0ms)

IterNodesCost
08272225
141901935
250021931

prune257.0ms

Pruning

7 alts after pruning (4 fresh and 3 done)

Merged error: 0.1b

regimes105.0ms

Accuracy

99.9% (0.0b remaining)

Error of 0.1b against oracle of 0.1b and baseline of 14.7b

bsearch82.0ms

Steps
ItersRangePoint
10
0.01509307947529729
651559680696848.9
99278016.70606303
9
-8425493960980.196
-11523406.719001934
-86808837.13671295

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
03314
13314

end0.0ms

sample497.0ms

Algorithm
intervals
Results
159.0ms6053×body80valid
65.0ms742×body640valid
43.0ms536×body320valid
40.0ms365×body1280valid
14.0ms304×body160valid