Details

Time bar (total: 4.6s)

sample31.0ms

Algorithm
intervals
Results
15.0ms256×body80valid
4.0ms256×pre80true

simplify79.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
03317
111417
256317
3416417
4500217

prune3.0ms

Filtered
1 candidates to 0 candidates (100.0%)
Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022

Merged error: 4.1b

Counts
2 → 1

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b
(+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0)
0.0b
(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0)))
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))
3.8b
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

rewrite112.0ms

Algorithm
rewrite-expression-head
Rules
804×times-frac
586×*-un-lft-identity
340×add-sqr-sqrt add-cube-cbrt
123×distribute-lft-out
82×associate-/l*
54×associate-/r/
29×flip3-+ flip-+
27×div-inv
20×add-exp-log add-cbrt-cube
13×add-log-exp
10×cbrt-undiv div-exp associate-/r*
6×sum-log
4×pow1 associate-/l/
3×frac-2neg clear-num
1×+-commutative associate-+l+
Counts
4 → 465
Calls
4 calls:
7.0ms
(+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0)
18.0ms
(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0)))
38.0ms
(/ (/ (/ (+ (+ (+ 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))
13.0ms
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

series60.0ms

Counts
4 → 12
Calls
4 calls:
3.0ms
(+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0)
20.0ms
(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0)))
24.0ms
(/ (/ (/ (+ (+ (+ 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))
13.0ms
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

simplify143.0ms

Algorithm
egg-herbie
Counts
477 → 477
Iterations

Useful iterations: 1 (29.0ms)

IterNodesCost
0149213034
1500212552

prune1.4s

Filtered
477 candidates to 281 candidates (41.1%)
Pruning

8 alts after pruning (8 fresh and 0 done)

PrunedKeptTotal
New4698477
Fresh000
Picked101
Done000
Total4708478

Merged error: 1.7b

Counts
478 → 8

localize17.0ms

Local error

Found 4 expressions with local error:

0.0b
(/ 1 (+ (+ alpha beta) (* 2.0 1.0)))
0.0b
(+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0)
0.2b
(* (/ 1 (+ (+ alpha beta) (* 2.0 1.0))) (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0)))
3.8b
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

rewrite91.0ms

Algorithm
rewrite-expression-head
Rules
165×times-frac
152×*-un-lft-identity
109×add-sqr-sqrt
79×add-cube-cbrt
78×associate-*r*
49×add-exp-log
35×distribute-lft-out
29×add-cbrt-cube
21×div-exp
16×associate-/r/
15×associate-*l*
13×add-log-exp
12×prod-exp
11×cbrt-undiv
10×flip3-+ flip-+
9×unswap-sqr
8×div-inv
7×pow1 associate-/l*
6×associate-/r* sum-log cbrt-unprod
4×rec-exp 1-exp
2×frac-2neg clear-num associate-/l/
1×+-commutative frac-times associate-+l+ pow-flip associate-*r/ pow-prod-down associate-*l/ *-commutative inv-pow
Counts
4 → 215
Calls
4 calls:
9.0ms
(/ 1 (+ (+ alpha beta) (* 2.0 1.0)))
8.0ms
(+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0)
50.0ms
(* (/ 1 (+ (+ alpha beta) (* 2.0 1.0))) (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0)))
14.0ms
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

series44.0ms

Counts
4 → 12
Calls
4 calls:
5.0ms
(/ 1 (+ (+ alpha beta) (* 2.0 1.0)))
3.0ms
(+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0)
23.0ms
(* (/ 1 (+ (+ alpha beta) (* 2.0 1.0))) (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0)))
12.0ms
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

simplify63.0ms

Algorithm
egg-herbie
Counts
227 → 227
Iterations

Useful iterations: 1 (26.0ms)

IterNodesCost
010593694
150023337

prune447.0ms

Filtered
227 candidates to 142 candidates (37.4%)
Pruning

8 alts after pruning (7 fresh and 1 done)

PrunedKeptTotal
New2270227
Fresh077
Picked011
Done000
Total2278235

Merged error: 1.7b

Counts
235 → 8

localize17.0ms

Local error

Found 4 expressions with local error:

0.2b
(/ (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (+ (+ alpha beta) (* 2.0 1.0)))
0.2b
(* (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (/ (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (+ (+ alpha beta) (* 2.0 1.0))))
3.8b
(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
3.8b
(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))

rewrite58.0ms

Algorithm
rewrite-expression-head
Rules
58×*-un-lft-identity
56×add-sqr-sqrt
46×times-frac
45×sqrt-prod
38×add-cube-cbrt
27×associate-*r*
11×add-exp-log add-cbrt-cube
10×sqrt-div distribute-lft-out
8×pow1
7×flip3-+ associate-*l* flip-+ associate-/l*
6×unswap-sqr
4×associate-/r/ add-log-exp
3×associate-/r*
2×cbrt-undiv frac-times rem-sqrt-square sqrt-pow1 pow1/2 div-exp associate-*l/ prod-exp cbrt-unprod div-inv associate-/l/
1×frac-2neg associate-*r/ pow-prod-down clear-num *-commutative
Counts
4 → 137
Calls
4 calls:
13.0ms
(/ (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (+ (+ alpha beta) (* 2.0 1.0)))
25.0ms
(* (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (/ (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (+ (+ alpha beta) (* 2.0 1.0))))
7.0ms
(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
7.0ms
(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))

series79.0ms

Counts
4 → 12
Calls
4 calls:
44.0ms
(/ (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (+ (+ alpha beta) (* 2.0 1.0)))
16.0ms
(* (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (/ (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (+ (+ alpha beta) (* 2.0 1.0))))
9.0ms
(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
10.0ms
(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))

simplify70.0ms

Algorithm
egg-herbie
Counts
149 → 149
Iterations

Useful iterations: 2 (51.0ms)

IterNodesCost
05362171
122441957
250021889

prune319.0ms

Filtered
149 candidates to 101 candidates (32.2%)
Pruning

8 alts after pruning (6 fresh and 2 done)

PrunedKeptTotal
New1481149
Fresh156
Picked011
Done011
Total1498157

Merged error: 1.7b

Counts
157 → 8

localize18.0ms

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)))
0.4b
(/ (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))

rewrite52.0ms

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:
16.0ms
(/ (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0) (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)))
15.0ms
(/ (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (sqrt (+ (+ alpha beta) (* 2.0 1.0))))
7.0ms
(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
7.0ms
(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))

series105.0ms

Counts
4 → 12
Calls
4 calls:
69.0ms
(/ (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0) (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)))
17.0ms
(/ (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (sqrt (+ (+ alpha beta) (* 2.0 1.0))))
10.0ms
(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
9.0ms
(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))

simplify67.0ms

Algorithm
egg-herbie
Counts
171 → 171
Iterations

Useful iterations: 2 (44.0ms)

IterNodesCost
05512625
120872476
250012422

prune404.0ms

Filtered
171 candidates to 103 candidates (39.8%)
Pruning

8 alts after pruning (5 fresh and 3 done)

PrunedKeptTotal
New1710171
Fresh055
Picked011
Done022
Total1718179

Merged error: 1.7b

Counts
179 → 8

regimes127.0ms

Accuracy

54.2% (1.1b remaining)

Error of 2.1b against oracle of 1.0b and baseline of 3.5b

bsearch20.0ms

Steps
ItersRangePoint
8
3.7677946908776397e+140
5.071052486296128e+143
4.992383245033972e+143

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
03933
13933

end0.0ms

sample838.0ms

Algorithm
intervals
Results
494.0ms8000×body80valid
121.0ms8000×pre80true

Profiling

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