Details

Time bar (total: 21.4s)

sample35.0ms

Algorithm
intervals
sampling

Space saved by range analysis: 43.768318%

Space saved by search: 43.768318%

Guaranteed chance to sample good point: 100%

Results
15.0ms256×body80valid
4.0ms256×pre80true

simplify81.0ms

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: 3.9b

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))
3.6b
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

rewrite115.0ms

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)))

series59.0ms

Counts
4 → 12
Calls
4 calls:
3.0ms
(+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0)
21.0ms
(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0)))
23.0ms
(/ (/ (/ (+ (+ (+ 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)))

simplify144.0ms

Algorithm
egg-herbie
Counts
477 → 477
Iterations

Useful iterations: 1 (30.0ms)

IterNodesCost
0149213034
1500212552

prune1.4s

Filtered
281 candidates to 477 candidates (-69.8%)
Pruning

8 alts after pruning (8 fresh and 0 done)

PrunedKeptTotal
New4698477
Fresh000
Picked101
Done000
Total4708478

Merged error: 0.9b

Counts
478 → 8

localize14.0ms

Local error

Found 4 expressions with local error:

0.0b
(+ alpha (+ beta 3.0))
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 3.0)))
3.6b
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

rewrite119.0ms

Algorithm
rewrite-expression-head
Rules
954×times-frac
833×*-un-lft-identity
383×add-sqr-sqrt add-cube-cbrt
256×distribute-lft-out
82×associate-/l*
62×associate-/r/
33×flip3-+ flip-+
31×div-inv
20×add-exp-log add-cbrt-cube
11×associate-/r*
10×cbrt-undiv div-exp
9×add-log-exp
4×pow1 associate-/l/
3×frac-2neg clear-num sum-log
1×+-commutative associate-+r+
Counts
4 → 526
Calls
4 calls:
5.0ms
(+ alpha (+ beta 3.0))
19.0ms
(/ (/ (+ (+ (+ 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 3.0)))
13.0ms
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

series62.0ms

Counts
4 → 12
Calls
4 calls:
3.0ms
(+ alpha (+ beta 3.0))
25.0ms
(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0)))
23.0ms
(/ (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0))) (+ alpha (+ beta 3.0)))
12.0ms
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

simplify151.0ms

Algorithm
egg-herbie
Counts
538 → 538
Iterations

Useful iterations: 1 (32.0ms)

IterNodesCost
0149013810
1500113245

prune1.3s

Filtered
281 candidates to 538 candidates (-91.5%)
Pruning

7 alts after pruning (7 fresh and 0 done)

PrunedKeptTotal
New5362538
Fresh257
Picked101
Done000
Total5397546

Merged error: 0.9b

Counts
546 → 7

localize19.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (sqrt (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))) (sqrt (+ (+ alpha beta) (* 2.0 1.0))))
0.1b
(/ (sqrt (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))) (sqrt (+ (+ alpha beta) (* 2.0 1.0))))
3.6b
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))
3.6b
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

rewrite96.0ms

Algorithm
rewrite-expression-head
Rules
444×times-frac
384×sqrt-prod
336×*-un-lft-identity
236×add-sqr-sqrt add-cube-cbrt
50×distribute-lft-out associate-/l*
36×associate-/r/
20×flip3-+ flip-+
18×associate-/r* div-inv
12×add-exp-log add-cbrt-cube
6×sqrt-div associate-/l/
4×pow1 cbrt-undiv frac-2neg div-exp clear-num add-log-exp
2×sqrt-undiv
Counts
4 → 408
Calls
4 calls:
21.0ms
(/ (sqrt (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))) (sqrt (+ (+ alpha beta) (* 2.0 1.0))))
20.0ms
(/ (sqrt (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))) (sqrt (+ (+ alpha beta) (* 2.0 1.0))))
13.0ms
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))
13.0ms
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

series116.0ms

Counts
4 → 12
Calls
4 calls:
43.0ms
(/ (sqrt (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))) (sqrt (+ (+ alpha beta) (* 2.0 1.0))))
48.0ms
(/ (sqrt (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))) (sqrt (+ (+ 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)))

simplify139.0ms

Algorithm
egg-herbie
Counts
420 → 420
Iterations

Useful iterations: 2 (54.0ms)

IterNodesCost
062210308
122849702
250029548

prune1.6s

Filtered
246 candidates to 420 candidates (-70.7%)
Pruning

7 alts after pruning (6 fresh and 1 done)

PrunedKeptTotal
New4200420
Fresh066
Picked011
Done000
Total4207427

Merged error: 0.9b

Counts
427 → 7

localize18.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0))) (/ (- (* alpha alpha) (* (+ beta 3.0) (+ beta 3.0))) (- alpha (+ beta 3.0))))
1.3b
(- (* alpha alpha) (* (+ beta 3.0) (+ beta 3.0)))
3.6b
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))
18.5b
(/ (- (* alpha alpha) (* (+ beta 3.0) (+ beta 3.0))) (- alpha (+ beta 3.0)))

rewrite345.0ms

Algorithm
rewrite-expression-head
Rules
6090×times-frac
3840×*-un-lft-identity
2527×add-sqr-sqrt
2029×add-cube-cbrt
623×difference-of-squares
532×distribute-lft-out
498×distribute-lft-out--
375×associate-/r/
188×div-inv
126×flip3-+ flip-+
68×associate-/l*
64×flip3-- flip--
39×associate-/r*
29×add-exp-log add-cbrt-cube
17×cbrt-undiv div-exp
6×add-log-exp
5×associate-/l/
4×pow1
3×frac-2neg clear-num
2×associate--r+
1×distribute-rgt-in sub-neg distribute-lft-in diff-log div-sub
Counts
4 → 2015
Calls
4 calls:
68.0ms
(/ (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0))) (/ (- (* alpha alpha) (* (+ beta 3.0) (+ beta 3.0))) (- alpha (+ beta 3.0))))
3.0ms
(- (* alpha alpha) (* (+ beta 3.0) (+ beta 3.0)))
13.0ms
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))
10.0ms
(/ (- (* alpha alpha) (* (+ beta 3.0) (+ beta 3.0))) (- alpha (+ beta 3.0)))

series64.0ms

Counts
4 → 12
Calls
4 calls:
34.0ms
(/ (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0))) (/ (- (* alpha alpha) (* (+ beta 3.0) (+ beta 3.0))) (- alpha (+ beta 3.0))))
7.0ms
(- (* alpha alpha) (* (+ beta 3.0) (+ beta 3.0)))
12.0ms
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))
11.0ms
(/ (- (* alpha alpha) (* (+ beta 3.0) (+ beta 3.0))) (- alpha (+ beta 3.0)))

simplify725.0ms

Algorithm
egg-herbie
Counts
2027 → 2027
Iterations

Useful iterations: 0 (34.0ms)

IterNodesCost
0500183178

prune13.7s

Filtered
1157 candidates to 2027 candidates (-75.2%)
Pruning

7 alts after pruning (5 fresh and 2 done)

PrunedKeptTotal
New202702027
Fresh055
Picked011
Done011
Total202772034

Merged error: 0.9b

Counts
2034 → 7

regimes119.0ms

Accuracy

12.2% (2.5b remaining)

Error of 3.8b against oracle of 1.3b and baseline of 4.1b

bsearch39.0ms

Steps
ItersRangePoint
9
6.587050653076561e+123
2.3363145794199297e+133
2.2685932503789918e+133

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
02934
12934

end0.0ms

sample888.0ms

Algorithm
intervals
sampling

Space saved by range analysis: 43.768318%

Space saved by search: 43.768318%

Guaranteed chance to sample good point: 100%

Results
509.0ms8000×body80valid
146.0ms8000×pre80true

Profiling

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