Details

Time bar (total: 4.3s)

sample18.0ms

Algorithm
intervals
Results
5.0ms193×body80valid
2.0ms26×body640valid
2.0ms14×body1280valid
1.0ms15×body320valid
0.0ms8×body160valid

simplify74.0ms

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: 24.8b

localize7.0ms

Local error

Found 3 expressions with local error:

0.0b
(* (- 1.0 x) y)
2.3b
(- 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)
9.0ms
(- 1.0 (/ (* (- 1.0 x) y) (+ y 1.0)))
9.0ms
(/ (* (- 1.0 x) y) (+ y 1.0))

series144.0ms

Counts
3 → 9
Calls
3 calls:
29.0ms
(* (- 1.0 x) y)
68.0ms
(- 1.0 (/ (* (- 1.0 x) y) (+ y 1.0)))
46.0ms
(/ (* (- 1.0 x) y) (+ y 1.0))

simplify49.0ms

Algorithm
egg-herbie
Counts
72 → 72
Iterations

Useful iterations: 1 (11.0ms)

IterNodesCost
0338401
11456359
25001359

prune144.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.1b

localize11.0ms

Local error

Found 4 expressions with local error:

0.3b
(cbrt (+ y 1.0))
3.7b
(/ (/ (* (- 1.0 x) y) (* (cbrt (+ y 1.0)) (cbrt (+ y 1.0)))) (cbrt (+ y 1.0)))
5.5b
(/ (* (- 1.0 x) y) (* (cbrt (+ y 1.0)) (cbrt (+ y 1.0))))
11.0b
(- 1.0 (/ (/ (* (- 1.0 x) y) (* (cbrt (+ y 1.0)) (cbrt (+ y 1.0)))) (cbrt (+ y 1.0))))

rewrite93.0ms

Algorithm
rewrite-expression-head
Rules
112×cbrt-div
102×times-frac
74×associate-/r/
73×*-un-lft-identity
61×cbrt-prod
56×flip3-+ flip-+
49×add-sqr-sqrt
41×add-cube-cbrt
36×frac-times
34×add-exp-log
21×add-cbrt-cube
20×associate-*l/
18×associate-*r/
15×distribute-lft-out
14×associate-/l*
13×cbrt-undiv div-exp
10×div-inv
8×prod-exp associate-/r* cbrt-unprod
6×add-log-exp
4×pow1
3×associate-/l/ difference-of-squares
2×flip3-- frac-2neg clear-num flip--
1×sub-neg pow1/3 diff-log distribute-lft-out--
Counts
4 → 195
Calls
4 calls:
2.0ms
(cbrt (+ y 1.0))
24.0ms
(/ (/ (* (- 1.0 x) y) (* (cbrt (+ y 1.0)) (cbrt (+ y 1.0)))) (cbrt (+ y 1.0)))
13.0ms
(/ (* (- 1.0 x) y) (* (cbrt (+ y 1.0)) (cbrt (+ y 1.0))))
42.0ms
(- 1.0 (/ (/ (* (- 1.0 x) y) (* (cbrt (+ y 1.0)) (cbrt (+ y 1.0)))) (cbrt (+ y 1.0))))

series352.0ms

Counts
4 → 12
Calls
4 calls:
88.0ms
(cbrt (+ y 1.0))
43.0ms
(/ (/ (* (- 1.0 x) y) (* (cbrt (+ y 1.0)) (cbrt (+ y 1.0)))) (cbrt (+ y 1.0)))
150.0ms
(/ (* (- 1.0 x) y) (* (cbrt (+ y 1.0)) (cbrt (+ y 1.0))))
70.0ms
(- 1.0 (/ (/ (* (- 1.0 x) y) (* (cbrt (+ y 1.0)) (cbrt (+ y 1.0)))) (cbrt (+ y 1.0))))

simplify113.0ms

Algorithm
egg-herbie
Counts
207 → 207
Iterations

Useful iterations: 2 (80.0ms)

IterNodesCost
09473492
139923239
250033136

prune489.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.1b

localize17.0ms

Local error

Found 4 expressions with local error:

0.0b
(* (- 1.0 x) y)
5.7b
(- 1.0 (* (/ (* (- 1.0 x) y) (+ (pow y 3) (pow 1.0 3))) (+ (* y y) (- (* 1.0 1.0) (* y 1.0)))))
15.4b
(* (/ (* (- 1.0 x) y) (+ (pow y 3) (pow 1.0 3))) (+ (* y y) (- (* 1.0 1.0) (* y 1.0))))
15.5b
(/ (* (- 1.0 x) y) (+ (pow y 3) (pow 1.0 3)))

rewrite132.0ms

Algorithm
rewrite-expression-head
Rules
43×*-un-lft-identity
20×add-exp-log associate-*l* add-cbrt-cube
18×times-frac
17×add-sqr-sqrt
15×distribute-lft-out
12×unpow-prod-down cube-prod
11×add-cube-cbrt
9×associate-/r*
8×pow1
6×associate-*r* prod-exp cbrt-unprod add-log-exp
5×associate-*l/
4×cbrt-undiv flip3-+ div-exp associate-/r/ flip-+
3×flip3-- sum-cubes flip--
2×distribute-rgt-in frac-times distribute-lft-in associate-*r/ pow-prod-down *-commutative div-inv associate-/l/ associate--r+ unswap-sqr
1×sub-neg frac-2neg diff-log clear-num associate-/l* distribute-lft-out-- difference-of-squares
Counts
4 → 114
Calls
4 calls:
11.0ms
(* (- 1.0 x) y)
2.0ms
(- 1.0 (* (/ (* (- 1.0 x) y) (+ (pow y 3) (pow 1.0 3))) (+ (* y y) (- (* 1.0 1.0) (* y 1.0)))))
86.0ms
(* (/ (* (- 1.0 x) y) (+ (pow y 3) (pow 1.0 3))) (+ (* y y) (- (* 1.0 1.0) (* y 1.0))))
29.0ms
(/ (* (- 1.0 x) y) (+ (pow y 3) (pow 1.0 3)))

series466.0ms

Counts
4 → 12
Calls
4 calls:
34.0ms
(* (- 1.0 x) y)
235.0ms
(- 1.0 (* (/ (* (- 1.0 x) y) (+ (pow y 3) (pow 1.0 3))) (+ (* y y) (- (* 1.0 1.0) (* y 1.0)))))
107.0ms
(* (/ (* (- 1.0 x) y) (+ (pow y 3) (pow 1.0 3))) (+ (* y y) (- (* 1.0 1.0) (* y 1.0))))
90.0ms
(/ (* (- 1.0 x) y) (+ (pow y 3) (pow 1.0 3)))

simplify104.0ms

Algorithm
egg-herbie
Counts
126 → 126
Iterations

Useful iterations: 2 (90.0ms)

IterNodesCost
06751296
138591122
250011120

prune331.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0.1b

localize12.0ms

Local error

Found 4 expressions with local error:

9.1b
(/ (* (- 1.0 x) y) (+ y 1.0))
9.1b
(/ (* (- 1.0 x) y) (+ y 1.0))
9.1b
(/ (* (- 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))))

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:
9.0ms
(/ (* (- 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))))

series554.0ms

Counts
4 → 12
Calls
4 calls:
49.0ms
(/ (* (- 1.0 x) y) (+ y 1.0))
45.0ms
(/ (* (- 1.0 x) y) (+ y 1.0))
50.0ms
(/ (* (- 1.0 x) y) (+ y 1.0))
408.0ms
(/ (- (* 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))))

simplify67.0ms

Algorithm
egg-herbie
Counts
134 → 134
Iterations

Useful iterations: 1 (12.0ms)

IterNodesCost
04311543
120191406
250011406

prune289.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0.1b

regimes168.0ms

Accuracy

99.9% (0.0b remaining)

Error of 0.2b against oracle of 0.2b and baseline of 22.4b

bsearch90.0ms

Steps
ItersRangePoint
9
89650.56729712563
29561296481055.625
68276704.36136045
9
-852931462.9897757
-2046.7894046871118
-133725111.24277952

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
04118
14118

end0.0ms

sample434.0ms

Algorithm
intervals
Results
147.0ms6147×body80valid
64.0ms723×body640valid
39.0ms367×body1280valid
32.0ms498×body320valid
12.0ms265×body160valid