Details

Time bar (total: 6.3s)

analyze4.0ms

Algorithm
search
Search
TrueOtherFalseIter
0%56.2%43.8%0
0%56.2%43.8%1
0%56.2%43.8%2
42.1%14%43.8%3
42.1%14%43.8%4
52.7%3.5%43.8%5
56.2%0%43.8%6

sample28.0ms

Algorithm
intervals
Results
15.0ms256×body80valid
4.0ms256×pre80true

simplify116.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (114.0ms)

IterNodesCost
0494935
1494935

prune10.0ms

Filtered
1 candidates to 1 candidates (0.0%)
Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022

Merged error: 2.8b

Counts
2 → 2

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))
2.6b
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

rewrite122.0ms

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:
9.0ms
(+ (+ (+ 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)))
41.0ms
(/ (/ (/ (+ (+ (+ 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))
14.0ms
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

series58.0ms

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)))
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))
12.0ms
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

simplify190.0ms

Algorithm
egg-herbie
Counts
477 → 477
Iterations

Useful iterations: 0 (87.0ms)

IterNodesCost
0497323485
1497323485

prune1.6s

Filtered
288 candidates to 477 candidates (-65.6%)
Pruning

8 alts after pruning (8 fresh and 0 done)

PrunedKeptTotal
New4698477
Fresh101
Picked101
Done000
Total4718479

Merged error: 0.4b

Counts
479 → 8

localize16.0ms

Local error

Found 4 expressions with local error:

0.0b
(/ 1 (+ alpha (+ beta (* 1.0 2.0))))
0.0b
(/ (/ (+ alpha (+ beta (+ (* alpha beta) 1.0))) (+ alpha (+ beta (* 1.0 2.0)))) (+ alpha (+ beta (+ 1.0 (* 1.0 2.0)))))
0.1b
(* (/ 1 (+ alpha (+ beta (* 1.0 2.0)))) (/ (/ (+ alpha (+ beta (+ (* alpha beta) 1.0))) (+ alpha (+ beta (* 1.0 2.0)))) (+ alpha (+ beta (+ 1.0 (* 1.0 2.0))))))
2.6b
(/ (+ alpha (+ beta (+ (* alpha beta) 1.0))) (+ alpha (+ beta (* 1.0 2.0))))

rewrite158.0ms

Algorithm
rewrite-expression-head
Rules
845×*-un-lft-identity
539×times-frac
374×distribute-lft-out
226×add-sqr-sqrt
196×add-cube-cbrt
136×associate-*r*
54×add-exp-log
34×add-cbrt-cube associate-/l*
32×associate-/r/
24×div-exp
18×associate-*l*
17×flip3-+ flip-+
16×div-inv
14×cbrt-undiv
13×associate-/r*
12×prod-exp
9×unswap-sqr
7×pow1
6×cbrt-unprod
4×rec-exp 1-exp add-log-exp
3×frac-2neg clear-num associate-/l/
1×frac-times pow-flip associate-*r/ pow-prod-down associate-*l/ *-commutative inv-pow
Counts
4 → 453
Calls
4 calls:
6.0ms
(/ 1 (+ alpha (+ beta (* 1.0 2.0))))
24.0ms
(/ (/ (+ alpha (+ beta (+ (* alpha beta) 1.0))) (+ alpha (+ beta (* 1.0 2.0)))) (+ alpha (+ beta (+ 1.0 (* 1.0 2.0)))))
82.0ms
(* (/ 1 (+ alpha (+ beta (* 1.0 2.0)))) (/ (/ (+ alpha (+ beta (+ (* alpha beta) 1.0))) (+ alpha (+ beta (* 1.0 2.0)))) (+ alpha (+ beta (+ 1.0 (* 1.0 2.0))))))
14.0ms
(/ (+ alpha (+ beta (+ (* alpha beta) 1.0))) (+ alpha (+ beta (* 1.0 2.0))))

series66.0ms

Counts
4 → 12
Calls
4 calls:
5.0ms
(/ 1 (+ alpha (+ beta (* 1.0 2.0))))
18.0ms
(/ (/ (+ alpha (+ beta (+ (* alpha beta) 1.0))) (+ alpha (+ beta (* 1.0 2.0)))) (+ alpha (+ beta (+ 1.0 (* 1.0 2.0)))))
23.0ms
(* (/ 1 (+ alpha (+ beta (* 1.0 2.0)))) (/ (/ (+ alpha (+ beta (+ (* alpha beta) 1.0))) (+ alpha (+ beta (* 1.0 2.0)))) (+ alpha (+ beta (+ 1.0 (* 1.0 2.0))))))
19.0ms
(/ (+ alpha (+ beta (+ (* alpha beta) 1.0))) (+ alpha (+ beta (* 1.0 2.0))))

simplify169.0ms

Algorithm
egg-herbie
Counts
465 → 465
Iterations

Useful iterations: 0 (96.0ms)

IterNodesCost
0496715714
1496715714

prune886.0ms

Filtered
202 candidates to 465 candidates (-130.2%)
Pruning

8 alts after pruning (7 fresh and 1 done)

PrunedKeptTotal
New4650465
Fresh077
Picked011
Done000
Total4658473

Merged error: 0.4b

Counts
473 → 8

localize17.0ms

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)))
0.1b
(/ (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0))) (* (sqrt (+ alpha (+ beta (+ 1.0 (* 1.0 2.0))))) (sqrt (+ alpha (+ beta (+ 1.0 (* 1.0 2.0)))))))
0.7b
(* (sqrt (+ alpha (+ beta (+ 1.0 (* 1.0 2.0))))) (sqrt (+ alpha (+ beta (+ 1.0 (* 1.0 2.0))))))
2.6b
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

rewrite125.0ms

Algorithm
rewrite-expression-head
Rules
354×times-frac
270×*-un-lft-identity
170×add-sqr-sqrt
158×add-cube-cbrt
82×associate-/l*
58×distribute-lft-out
38×sqrt-prod
36×associate-/r/
34×add-exp-log add-cbrt-cube
27×flip3-+ flip-+
24×sqrt-div
19×pow1
16×cbrt-undiv swap-sqr div-exp
15×div-inv
8×frac-times sqrt-pow1 pow1/2 associate-*r* associate-*l*
7×associate-/r*
5×pow-prod-up
4×associate-*r/ associate-*l/ prod-exp cbrt-unprod associate-/l/ add-log-exp unswap-sqr
3×frac-2neg pow-prod-down clear-num pow-sqr
1×pow2 pow-plus sqrt-unprod rem-square-sqrt *-commutative
Counts
4 → 348
Calls
4 calls:
22.0ms
(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0)))
46.0ms
(/ (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0))) (* (sqrt (+ alpha (+ beta (+ 1.0 (* 1.0 2.0))))) (sqrt (+ alpha (+ beta (+ 1.0 (* 1.0 2.0)))))))
18.0ms
(* (sqrt (+ alpha (+ beta (+ 1.0 (* 1.0 2.0))))) (sqrt (+ alpha (+ beta (+ 1.0 (* 1.0 2.0))))))
15.0ms
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

series61.0ms

Counts
4 → 12
Calls
4 calls:
21.0ms
(/ (/ (+ (+ (+ 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))) (* (sqrt (+ alpha (+ beta (+ 1.0 (* 1.0 2.0))))) (sqrt (+ alpha (+ beta (+ 1.0 (* 1.0 2.0)))))))
3.0ms
(* (sqrt (+ alpha (+ beta (+ 1.0 (* 1.0 2.0))))) (sqrt (+ alpha (+ beta (+ 1.0 (* 1.0 2.0))))))
13.0ms
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

simplify144.0ms

Algorithm
egg-herbie
Counts
360 → 360
Iterations

Useful iterations: 0 (83.0ms)

IterNodesCost
0497512940
1497512940

prune1.2s

Filtered
227 candidates to 360 candidates (-58.6%)
Pruning

8 alts after pruning (6 fresh and 2 done)

PrunedKeptTotal
New3600360
Fresh066
Picked011
Done011
Total3608368

Merged error: 0.4b

Counts
368 → 8

localize19.0ms

Local error

Found 3 expressions with local error:

0.0b
(* (+ alpha (+ beta (* 1.0 2.0))) (+ alpha (+ beta (+ 1.0 (* 1.0 2.0)))))
1.6b
(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (* (+ alpha (+ beta (* 1.0 2.0))) (+ alpha (+ beta (+ 1.0 (* 1.0 2.0))))))
2.6b
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

rewrite59.0ms

Algorithm
rewrite-expression-head
Rules
57×*-un-lft-identity
54×times-frac
32×add-sqr-sqrt
30×add-cube-cbrt
22×associate-/l*
19×add-exp-log add-cbrt-cube
16×flip3-+ flip-+
14×associate-/r/ distribute-lft-out
8×frac-times
7×cbrt-undiv div-exp
5×pow1 associate-*r*
4×associate-*r/ associate-*l* associate-*l/ associate-/r* div-inv
3×prod-exp cbrt-unprod associate-/l/ add-log-exp
2×frac-2neg clear-num
1×distribute-rgt-in distribute-lft-in pow-prod-down *-commutative unswap-sqr
Counts
3 → 130
Calls
3 calls:
13.0ms
(* (+ alpha (+ beta (* 1.0 2.0))) (+ alpha (+ beta (+ 1.0 (* 1.0 2.0)))))
27.0ms
(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (* (+ alpha (+ beta (* 1.0 2.0))) (+ alpha (+ beta (+ 1.0 (* 1.0 2.0))))))
14.0ms
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

series45.0ms

Counts
3 → 9
Calls
3 calls:
7.0ms
(* (+ alpha (+ beta (* 1.0 2.0))) (+ alpha (+ beta (+ 1.0 (* 1.0 2.0)))))
27.0ms
(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (* (+ alpha (+ beta (* 1.0 2.0))) (+ alpha (+ beta (+ 1.0 (* 1.0 2.0))))))
12.0ms
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

simplify53.0ms

Algorithm
egg-herbie
Counts
139 → 139
Iterations

Useful iterations: 0 (33.0ms)

IterNodesCost
056094301

prune275.0ms

Filtered
103 candidates to 139 candidates (-35.0%)
Pruning

8 alts after pruning (5 fresh and 3 done)

PrunedKeptTotal
New1390139
Fresh055
Picked011
Done022
Total1398147

Merged error: 0.4b

Counts
147 → 8

regimes135.0ms

Accuracy

-9.1% (2.8b remaining)

Error of 3.9b against oracle of 1.1b and baseline of 3.7b

bsearch25.0ms

Steps
ItersRangePoint
3
4.035897511607625e+129
4.9094886450348696e+129
4.090496957446828e+129
8
5.483957153734187e+85
3.871782010829796e+89
3.681462720248197e+89

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
076121
176121

end0.0ms

sample753.0ms

Algorithm
intervals
Results
473.0ms8000×body80valid
139.0ms8000×pre80true

Profiling

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