Details

Time bar (total: 3.5s)

sample17.0ms

Algorithm
intervals
Results
5.0ms198×body80valid
2.0ms24×body640valid
1.0ms11×body1280valid
1.0ms15×body320valid
0.0ms8×body160valid

simplify60.0ms

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

Filtered
1 candidates to 0 candidates (0.0%)
Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 23.0b

localize7.0ms

Local error

Found 3 expressions with local error:

0.0b
(* (- 1.0 x) y)
2.6b
(- 1.0 (/ (* (- 1.0 x) y) (+ y 1.0)))
8.4b
(/ (* (- 1.0 x) y) (+ y 1.0))

rewrite22.0ms

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:
6.0ms
(* (- 1.0 x) y)
7.0ms
(- 1.0 (/ (* (- 1.0 x) y) (+ y 1.0)))
8.0ms
(/ (* (- 1.0 x) y) (+ y 1.0))

series146.0ms

Counts
3 → 9
Calls
3 calls:
29.0ms
(* (- 1.0 x) y)
70.0ms
(- 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

prune144.0ms

Filtered
72 candidates to 51 candidates (70.8%)
Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.2b

localize8.0ms

Local error

Found 4 expressions with local error:

0.0b
(* (- 1.0 x) y)
0.0b
(/ 1 (+ y 1.0))
4.1b
(- 1.0 (* (* (- 1.0 x) y) (/ 1 (+ y 1.0))))
8.5b
(* (* (- 1.0 x) y) (/ 1 (+ y 1.0)))

rewrite31.0ms

Algorithm
rewrite-expression-head
Rules
39×*-un-lft-identity
32×add-exp-log
27×add-sqr-sqrt
24×times-frac
23×add-cube-cbrt
21×associate-*r*
20×add-cbrt-cube
13×prod-exp
12×pow1
8×associate-*l/
7×cbrt-unprod distribute-lft-out
6×div-exp associate-*l* add-log-exp
4×flip3-- pow-prod-down associate-/r* associate-/r/ flip--
3×cbrt-undiv rec-exp 1-exp associate-/l*
2×frac-times flip3-+ *-commutative flip-+ div-inv
1×sub-neg pow-flip frac-2neg diff-log associate-*r/ clear-num un-div-inv distribute-lft-out-- inv-pow difference-of-squares unswap-sqr
Counts
4 → 118
Calls
4 calls:
6.0ms
(* (- 1.0 x) y)
5.0ms
(/ 1 (+ y 1.0))
3.0ms
(- 1.0 (* (* (- 1.0 x) y) (/ 1 (+ y 1.0))))
13.0ms
(* (* (- 1.0 x) y) (/ 1 (+ y 1.0)))

series171.0ms

Counts
4 → 12
Calls
4 calls:
29.0ms
(* (- 1.0 x) y)
27.0ms
(/ 1 (+ y 1.0))
66.0ms
(- 1.0 (* (* (- 1.0 x) y) (/ 1 (+ y 1.0))))
48.0ms
(* (* (- 1.0 x) y) (/ 1 (+ y 1.0)))

simplify70.0ms

Algorithm
egg-herbie
Counts
130 → 130
Iterations

Useful iterations: 2 (61.0ms)

IterNodesCost
0509737
12631636
25001599

prune208.0ms

Filtered
130 candidates to 74 candidates (56.9%)
Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.2b

localize9.0ms

Local error

Found 4 expressions with local error:

0.0b
(* (/ (- 1.0 x) (sqrt (+ y 1.0))) (/ y (sqrt (+ y 1.0))))
0.1b
(/ (- 1.0 x) (sqrt (+ y 1.0)))
0.1b
(/ y (sqrt (+ y 1.0)))
3.8b
(- 1.0 (* (/ (- 1.0 x) (sqrt (+ y 1.0))) (/ y (sqrt (+ y 1.0)))))

rewrite61.0ms

Algorithm
rewrite-expression-head
Rules
138×*-un-lft-identity
132×add-sqr-sqrt
124×times-frac
78×sqrt-prod
72×add-cube-cbrt
41×associate-*l*
27×associate-*r*
20×add-exp-log add-cbrt-cube
18×distribute-lft-out
15×distribute-lft-out-- difference-of-squares
14×associate-/r*
9×unswap-sqr
8×sqrt-div associate-/r/ associate-/l*
6×pow1 cbrt-undiv div-exp add-log-exp
4×flip3-+ prod-exp cbrt-unprod flip-+ div-inv
2×flip3-- frac-2neg clear-num flip-- associate-/l/
1×frac-times sub-neg diff-log div-sub associate-*r/ pow-prod-down associate-*l/ *-commutative
Counts
4 → 218
Calls
4 calls:
34.0ms
(* (/ (- 1.0 x) (sqrt (+ y 1.0))) (/ y (sqrt (+ y 1.0))))
8.0ms
(/ (- 1.0 x) (sqrt (+ y 1.0)))
6.0ms
(/ y (sqrt (+ y 1.0)))
3.0ms
(- 1.0 (* (/ (- 1.0 x) (sqrt (+ y 1.0))) (/ y (sqrt (+ y 1.0)))))

series295.0ms

Counts
4 → 12
Calls
4 calls:
43.0ms
(* (/ (- 1.0 x) (sqrt (+ y 1.0))) (/ y (sqrt (+ y 1.0))))
67.0ms
(/ (- 1.0 x) (sqrt (+ y 1.0)))
113.0ms
(/ y (sqrt (+ y 1.0)))
71.0ms
(- 1.0 (* (/ (- 1.0 x) (sqrt (+ y 1.0))) (/ y (sqrt (+ y 1.0)))))

simplify91.0ms

Algorithm
egg-herbie
Counts
230 → 230
Iterations

Useful iterations: 2 (66.0ms)

IterNodesCost
07902194
130802034
250011931

prune430.0ms

Filtered
230 candidates to 137 candidates (59.6%)
Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0.2b

localize14.0ms

Local error

Found 4 expressions with local error:

8.4b
(/ (* (- 1.0 x) y) (+ y 1.0))
8.4b
(/ (* (- 1.0 x) y) (+ y 1.0))
8.4b
(/ (* (- 1.0 x) y) (+ y 1.0))
10.3b
(/ (- (* 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))))

rewrite41.0ms

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))
12.0ms
(/ (- (* 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))))

series534.0ms

Counts
4 → 12
Calls
4 calls:
44.0ms
(/ (* (- 1.0 x) y) (+ y 1.0))
46.0ms
(/ (* (- 1.0 x) y) (+ y 1.0))
43.0ms
(/ (* (- 1.0 x) y) (+ y 1.0))
400.0ms
(/ (- (* 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))))

simplify63.0ms

Algorithm
egg-herbie
Counts
134 → 134
Iterations

Useful iterations: 1 (11.0ms)

IterNodesCost
04311543
120191406
250011406

prune273.0ms

Filtered
134 candidates to 98 candidates (73.1%)
Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 0.1b

regimes251.0ms

Accuracy

99.6% (0.1b remaining)

Error of 0.3b against oracle of 0.2b and baseline of 22.0b

bsearch79.0ms

Steps
ItersRangePoint
8
24048332.968690775
1128751172469.6636
227113532.89233634
10
-1.0296308640320476e+26
-7509027891406199.0
-7583054551493676.0

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
03111
13111

end0.0ms

sample443.0ms

Algorithm
intervals
Results
155.0ms6141×body80valid
65.0ms708×body640valid
39.0ms356×body1280valid
35.0ms483×body320valid
14.0ms312×body160valid