Details

Time bar (total: 5.3s)

analyze3.0ms

Algorithm
search
sampling

Space saved by range analysis: 43.823218%

Space saved by search: 43.823218%

Guaranteed chance to sample good point: 100%

sample31.0ms

Algorithm
intervals
Results
19.0ms256×body80valid
4.0ms256×pre80true

simplify78.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
03317
111417
256317
3416417
4500217

prune3.0ms

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

rewrite103.0ms

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:
5.0ms
(+ (+ alpha beta) (* beta alpha))
18.0ms
(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0)))
37.0ms
(/ (/ (/ (+ (+ (+ 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)))

series62.0ms

Counts
4 → 12
Calls
4 calls:
4.0ms
(+ (+ alpha beta) (* beta alpha))
19.0ms
(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0)))
21.0ms
(/ (/ (/ (+ (+ (+ 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))
17.0ms
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

simplify140.0ms

Algorithm
egg-herbie
Counts
475 → 475
Iterations

Useful iterations: 1 (29.0ms)

IterNodesCost
0151213008
1500112540

prune1.3s

Filtered
280 candidates to 475 candidates (-69.6%)
Pruning

8 alts after pruning (7 fresh and 1 done)

PrunedKeptTotal
New4687475
Fresh000
Picked011
Done000
Total4688476

Merged error: 0.6b

Counts
476 → 8

localize15.0ms

Local error

Found 4 expressions with local error:

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

rewrite79.0ms

Algorithm
rewrite-expression-head
Rules
210×times-frac
160×*-un-lft-identity
120×add-sqr-sqrt sqrt-prod
108×add-cube-cbrt
26×distribute-lft-out
20×associate-/r/
12×flip3-+ flip-+
10×div-inv
8×add-exp-log add-cbrt-cube associate-/l*
6×pow1 rem-sqrt-square associate-/r*
4×associate-/l/ add-log-exp
2×cbrt-undiv frac-2neg sqrt-pow1 pow1/2 sqrt-div div-exp clear-num
Counts
4 → 216
Calls
4 calls:
22.0ms
(sqrt (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0))))
20.0ms
(sqrt (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0))))
13.0ms
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))
14.0ms
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

series114.0ms

Counts
4 → 12
Calls
4 calls:
43.0ms
(sqrt (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0))))
47.0ms
(sqrt (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0))))
12.0ms
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))
12.0ms
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

simplify97.0ms

Algorithm
egg-herbie
Counts
228 → 228
Iterations

Useful iterations: 2 (54.0ms)

IterNodesCost
06534806
124174538
250024386

prune767.0ms

Filtered
158 candidates to 228 candidates (-44.3%)
Pruning

8 alts after pruning (6 fresh and 2 done)

PrunedKeptTotal
New2280228
Fresh066
Picked011
Done011
Total2288236

Merged error: 0.6b

Counts
236 → 8

localize15.0ms

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))

rewrite60.0ms

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:
15.0ms
(/ (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (+ (+ alpha beta) (* 2.0 1.0)))
26.0ms
(* (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))

series77.0ms

Counts
4 → 12
Calls
4 calls:
47.0ms
(/ (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (+ (+ alpha beta) (* 2.0 1.0)))
12.0ms
(* (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))
9.0ms
(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))

simplify73.0ms

Algorithm
egg-herbie
Counts
149 → 149
Iterations

Useful iterations: 2 (52.0ms)

IterNodesCost
05362171
122441957
250021889

prune311.0ms

Filtered
101 candidates to 149 candidates (-47.5%)
Pruning

8 alts after pruning (5 fresh and 3 done)

PrunedKeptTotal
New1490149
Fresh055
Picked011
Done022
Total1498157

Merged error: 0.6b

Counts
157 → 8

localize22.0ms

Local error

Found 4 expressions with local error:

4.2b
(cbrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
4.2b
(cbrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
4.2b
(cbrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
8.3b
(/ (* (cbrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (cbrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))) (* (* (cbrt (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0)) (cbrt (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0))) (sqrt (+ (+ alpha beta) (* 2.0 1.0)))))

rewrite69.0ms

Algorithm
rewrite-expression-head
Rules
54×cbrt-div
36×flip3-+ flip-+
32×frac-times
26×associate-/r/
25×add-exp-log
18×sqrt-div
16×associate-*l/
15×add-cbrt-cube
13×*-un-lft-identity
12×cbrt-prod
10×associate-*r/
9×prod-exp cbrt-unprod
8×associate-/l/
7×add-sqr-sqrt add-cube-cbrt
6×cbrt-undiv div-exp
4×pow1 add-log-exp
3×pow1/3 distribute-lft-out
1×frac-2neg times-frac clear-num associate-/r* div-inv associate-/l*
Counts
4 → 101
Calls
4 calls:
7.0ms
(cbrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
7.0ms
(cbrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
7.0ms
(cbrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
44.0ms
(/ (* (cbrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (cbrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))) (* (* (cbrt (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0)) (cbrt (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0))) (sqrt (+ (+ alpha beta) (* 2.0 1.0)))))

series160.0ms

Counts
4 → 12
Calls
4 calls:
14.0ms
(cbrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
15.0ms
(cbrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
14.0ms
(cbrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
116.0ms
(/ (* (cbrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (cbrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))) (* (* (cbrt (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0)) (cbrt (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0))) (sqrt (+ (+ alpha beta) (* 2.0 1.0)))))

simplify92.0ms

Algorithm
egg-herbie
Counts
113 → 113
Iterations

Useful iterations: 2 (68.0ms)

IterNodesCost
09492856
135292578
250012553

prune570.0ms

Filtered
89 candidates to 113 candidates (-27.0%)
Pruning

8 alts after pruning (4 fresh and 4 done)

PrunedKeptTotal
New1130113
Fresh044
Picked011
Done033
Total1138121

Merged error: 0.6b

Counts
121 → 8

regimes203.0ms

Accuracy

91.7% (0.2b remaining)

Error of 1.4b against oracle of 1.2b and baseline of 3.5b

bsearch1.0ms

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
02534
12534

end0.0ms

analyze3.0ms

Algorithm
search
sampling

Space saved by range analysis: 43.823218%

Space saved by search: 43.823218%

Guaranteed chance to sample good point: 100%

sample754.0ms

Algorithm
intervals
Results
490.0ms8000×body80valid
132.0ms8000×pre80true

Profiling

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