Details

Time bar (total: 7.0s)

sample22.0ms

Algorithm
intervals
Results
9.0ms256×body80valid
3.0ms256×pre80true

simplify81.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
03317
111417
256317
3416417
4500217

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 4.1b

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b
(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0)))
0.0b
(+ (+ alpha beta) (* beta alpha))
0.1b
(/ (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0))
3.9b
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

rewrite650.0ms

Algorithm
rewrite-expression-head
Rules
804×times-frac
584×*-un-lft-identity
340×add-sqr-sqrt add-cube-cbrt
122×distribute-lft-out
82×associate-/l*
54×associate-/r/
29×flip3-+ flip-+
27×div-inv
20×add-exp-log add-cbrt-cube
10×cbrt-undiv div-exp associate-/r*
9×add-log-exp
4×pow1 associate-/l/
3×frac-2neg clear-num sum-log
1×+-commutative associate-+l+
Counts
4 → 463
Calls
4 calls:
181.0ms
(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0)))
14.0ms
(+ (+ alpha beta) (* beta alpha))
269.0ms
(/ (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0))
153.0ms
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

series377.0ms

Counts
4 → 12
Calls
4 calls:
136.0ms
(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0)))
14.0ms
(+ (+ alpha beta) (* beta alpha))
148.0ms
(/ (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0))
79.0ms
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

simplify134.0ms

Algorithm
egg-herbie
Counts
475 → 475
Iterations

Useful iterations: 1 (28.0ms)

IterNodesCost
0151213008
1500112540

prune933.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 1.1b

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b
(/ 1 (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0))
0.0b
(+ (+ alpha beta) (* beta alpha))
0.1b
(* (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0))) (/ 1 (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0)))
3.9b
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

rewrite644.0ms

Algorithm
rewrite-expression-head
Rules
141×times-frac
116×*-un-lft-identity
103×add-sqr-sqrt
73×add-cube-cbrt
60×associate-*l*
49×add-exp-log
29×add-cbrt-cube
21×div-exp
20×distribute-lft-out
18×associate-*r*
14×associate-/r/
12×prod-exp
11×cbrt-undiv
9×flip3-+ flip-+ add-log-exp unswap-sqr
7×pow1 associate-/r* div-inv associate-/l*
6×cbrt-unprod
4×rec-exp 1-exp
3×sum-log
2×frac-2neg clear-num associate-/l/
1×+-commutative frac-times associate-+l+ pow-flip associate-*r/ pow-prod-down associate-*l/ un-div-inv *-commutative inv-pow
Counts
4 → 203
Calls
4 calls:
67.0ms
(/ 1 (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0))
14.0ms
(+ (+ alpha beta) (* beta alpha))
403.0ms
(* (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0))) (/ 1 (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0)))
150.0ms
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

series274.0ms

Counts
4 → 12
Calls
4 calls:
38.0ms
(/ 1 (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0))
14.0ms
(+ (+ alpha beta) (* beta alpha))
146.0ms
(* (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0))) (/ 1 (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0)))
75.0ms
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

simplify120.0ms

Algorithm
egg-herbie
Counts
215 → 215
Iterations

Useful iterations: 1 (26.0ms)

IterNodesCost
010383476
148653031
250023031

prune461.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 1.1b

localize17.0ms

Local error

Found 4 expressions with local error:

0.3b
(/ (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0) (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)))
0.5b
(/ (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (sqrt (+ (+ alpha beta) (* 2.0 1.0))))
3.8b
(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
3.8b
(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))

rewrite450.0ms

Algorithm
rewrite-expression-head
Rules
98×*-un-lft-identity
80×sqrt-prod
70×times-frac
56×add-sqr-sqrt
54×add-cube-cbrt
22×distribute-lft-out
13×associate-/r*
11×associate-/l*
10×sqrt-div
8×add-exp-log add-cbrt-cube
6×pow1 flip3-+ flip-+
4×associate-/r/ associate-/l/ add-log-exp
2×cbrt-undiv rem-sqrt-square frac-2neg sqrt-pow1 pow1/2 div-exp clear-num div-inv
1×sqrt-undiv
Counts
4 → 159
Calls
4 calls:
200.0ms
(/ (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0) (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)))
115.0ms
(/ (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (sqrt (+ (+ alpha beta) (* 2.0 1.0))))
64.0ms
(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
64.0ms
(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))

series394.0ms

Counts
4 → 12
Calls
4 calls:
201.0ms
(/ (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0) (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)))
100.0ms
(/ (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (sqrt (+ (+ alpha beta) (* 2.0 1.0))))
48.0ms
(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
46.0ms
(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))

simplify65.0ms

Algorithm
egg-herbie
Counts
171 → 171
Iterations

Useful iterations: 2 (43.0ms)

IterNodesCost
05072617
119422448
250032394

prune416.0ms

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 1.1b

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b
(+ (+ alpha beta) (* beta alpha))
0.0b
(* (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))
2.3b
(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (* (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))))
3.9b
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

rewrite579.0ms

Algorithm
rewrite-expression-head
Rules
54×times-frac
53×*-un-lft-identity
33×add-sqr-sqrt
31×add-cube-cbrt
22×associate-/l*
20×add-exp-log add-cbrt-cube
17×flip3-+ flip-+
14×associate-/r/
11×distribute-lft-out
9×add-log-exp
8×frac-times
7×cbrt-undiv div-exp
6×pow1
4×associate-*r/ associate-*l* associate-*l/ associate-/r* div-inv
3×associate-*r* prod-exp sum-log cbrt-unprod associate-/l/
2×frac-2neg clear-num
1×+-commutative distribute-rgt-in associate-+l+ distribute-lft-in pow-prod-down *-commutative unswap-sqr
Counts
4 → 141
Calls
4 calls:
13.0ms
(+ (+ alpha beta) (* beta alpha))
200.0ms
(* (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))
209.0ms
(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (* (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))))
150.0ms
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

series264.0ms

Counts
4 → 12
Calls
4 calls:
14.0ms
(+ (+ alpha beta) (* beta alpha))
28.0ms
(* (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))
147.0ms
(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (* (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))))
75.0ms
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

simplify122.0ms

Algorithm
egg-herbie
Counts
153 → 153
Iterations

Useful iterations: 1 (21.0ms)

IterNodesCost
07652456
142412233
250012233

prune354.0ms

Pruning

5 alts after pruning (2 fresh and 3 done)

Merged error: 1.1b

regimes50.0ms

Accuracy

51.1% (1.3b remaining)

Error of 2.6b against oracle of 1.3b and baseline of 3.9b

bsearch44.0ms

Steps
ItersRangePoint
6
2.768519539735807e+141
2.4903735148463687e+142
1.1855871908403355e+142

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
04546
14546

end0.0ms

sample504.0ms

Algorithm
intervals
Results
280.0ms8000×body80valid
90.0ms8000×pre80true