Details

Time bar (total: 58.9s)

sample32.0ms

Algorithm
intervals
Results
17.0ms256×body80valid
4.0ms256×pre80true

simplify111.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (109.0ms)

IterNodesCost
0494935
1494935

prune9.0ms

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: 4.1b

Counts
2 → 2

localize16.0ms

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)))

rewrite106.0ms

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)
19.0ms
(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0)))
35.0ms
(/ (/ (/ (+ (+ (+ 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)))

series61.0ms

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

simplify169.0ms

Algorithm
egg-herbie
Counts
477 → 477
Iterations

Useful iterations: 0 (71.0ms)

IterNodesCost
0561323485

prune1.5s

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

10 alts after pruning (10 fresh and 0 done)

PrunedKeptTotal
New4689477
Fresh011
Picked101
Done000
Total46910479

Merged error: 1.6b

Counts
479 → 10

localize13.0ms

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 3.0)))
3.8b
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

rewrite116.0ms

Algorithm
rewrite-expression-head
Rules
954×times-frac
828×*-un-lft-identity
383×add-sqr-sqrt add-cube-cbrt
253×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-+l+
Counts
4 → 524
Calls
4 calls:
5.0ms
(+ (+ alpha beta) (* beta alpha))
19.0ms
(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0)))
38.0ms
(/ (/ (/ (+ (+ (+ 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)))

series56.0ms

Counts
4 → 12
Calls
4 calls:
4.0ms
(+ (+ alpha beta) (* beta alpha))
20.0ms
(/ (/ (+ (+ (+ 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 3.0)))
11.0ms
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

simplify221.0ms

Algorithm
egg-herbie
Counts
536 → 536
Iterations

Useful iterations: 0 (113.0ms)

IterNodesCost
0498423327
1498423327

prune1.2s

Filtered
284 candidates to 536 candidates (-88.7%)
Pruning

9 alts after pruning (8 fresh and 1 done)

PrunedKeptTotal
New5333536
Fresh459
Picked011
Done000
Total5379546

Merged error: 1.6b

Counts
546 → 9

localize23.0ms

Local error

Found 4 expressions with local error:

0.1b
(pow (/ (+ alpha (+ beta (+ (* alpha beta) 1.0))) (+ alpha (+ beta (* 1.0 2.0)))) 3)
0.1b
(/ (/ (cbrt (pow (/ (+ alpha (+ beta (+ (* alpha beta) 1.0))) (+ alpha (+ beta (* 1.0 2.0)))) 3)) (+ (+ alpha beta) (* 2.0 1.0))) (+ alpha (+ beta 3.0)))
3.6b
(cbrt (pow (/ (+ alpha (+ beta (+ (* alpha beta) 1.0))) (+ alpha (+ beta (* 1.0 2.0)))) 3))
3.8b
(/ (+ alpha (+ beta (+ (* alpha beta) 1.0))) (+ alpha (+ beta (* 1.0 2.0))))

rewrite455.0ms

Algorithm
rewrite-expression-head
Rules
3202×*-un-lft-identity
2863×times-frac
1271×distribute-lft-out
1102×cbrt-prod
1015×add-sqr-sqrt add-cube-cbrt
520×unpow-prod-down cube-prod
194×associate-/l*
96×associate-/r/
49×flip3-+ flip-+
48×div-inv
20×cube-mult unpow3 sqr-pow
14×add-exp-log
13×add-cbrt-cube
9×associate-/r*
5×pow1 cbrt-undiv div-exp
4×add-log-exp
3×pow-unpow associate-/l/
2×cube-div frac-2neg pow-exp clear-num rem-cube-cbrt
1×pow-to-exp cbrt-div pow-pow pow1/3 rem-cbrt-cube
Counts
4 → 1341
Calls
4 calls:
15.0ms
(pow (/ (+ alpha (+ beta (+ (* alpha beta) 1.0))) (+ alpha (+ beta (* 1.0 2.0)))) 3)
73.0ms
(/ (/ (cbrt (pow (/ (+ alpha (+ beta (+ (* alpha beta) 1.0))) (+ alpha (+ beta (* 1.0 2.0)))) 3)) (+ (+ alpha beta) (* 2.0 1.0))) (+ alpha (+ beta 3.0)))
15.0ms
(cbrt (pow (/ (+ alpha (+ beta (+ (* alpha beta) 1.0))) (+ alpha (+ beta (* 1.0 2.0)))) 3))
13.0ms
(/ (+ alpha (+ beta (+ (* alpha beta) 1.0))) (+ alpha (+ beta (* 1.0 2.0))))

series84.0ms

Counts
4 → 12
Calls
4 calls:
34.0ms
(pow (/ (+ alpha (+ beta (+ (* alpha beta) 1.0))) (+ alpha (+ beta (* 1.0 2.0)))) 3)
27.0ms
(/ (/ (cbrt (pow (/ (+ alpha (+ beta (+ (* alpha beta) 1.0))) (+ alpha (+ beta (* 1.0 2.0)))) 3)) (+ (+ alpha beta) (* 2.0 1.0))) (+ alpha (+ beta 3.0)))
11.0ms
(cbrt (pow (/ (+ alpha (+ beta (+ (* alpha beta) 1.0))) (+ alpha (+ beta (* 1.0 2.0)))) 3))
11.0ms
(/ (+ alpha (+ beta (+ (* alpha beta) 1.0))) (+ alpha (+ beta (* 1.0 2.0))))

simplify459.0ms

Algorithm
egg-herbie
Counts
1353 → 1353
Iterations

Useful iterations: 0 (157.0ms)

IterNodesCost
0500267266

prune1.7s

Filtered
338 candidates to 1353 candidates (-300.3%)
Pruning

9 alts after pruning (7 fresh and 2 done)

PrunedKeptTotal
New135301353
Fresh077
Picked011
Done011
Total135391362

Merged error: 1.6b

Counts
1362 → 9

localize19.0ms

Local error

Found 4 expressions with local error:

0.0b
(/ (/ (/ (+ alpha (+ beta (+ (* alpha beta) 1.0))) (sqrt (+ alpha (+ beta (* 1.0 2.0))))) (sqrt (+ (+ alpha beta) (* 2.0 1.0)))) (+ (+ alpha beta) (* 2.0 1.0)))
0.1b
(/ (/ (/ (/ (+ alpha (+ beta (+ (* alpha beta) 1.0))) (sqrt (+ alpha (+ beta (* 1.0 2.0))))) (sqrt (+ (+ alpha beta) (* 2.0 1.0)))) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0))
1.7b
(/ (/ (+ alpha (+ beta (+ (* alpha beta) 1.0))) (sqrt (+ alpha (+ beta (* 1.0 2.0))))) (sqrt (+ (+ alpha beta) (* 2.0 1.0))))
2.7b
(/ (+ alpha (+ beta (+ (* alpha beta) 1.0))) (sqrt (+ alpha (+ beta (* 1.0 2.0)))))

rewrite1.0s

Algorithm
rewrite-expression-head
Rules
16774×times-frac
13167×*-un-lft-identity
6144×add-sqr-sqrt add-cube-cbrt
4907×sqrt-prod
3939×distribute-lft-out
1060×associate-/l*
298×associate-/r/
284×sqrt-div
150×flip3-+ flip-+
149×div-inv
34×add-exp-log add-cbrt-cube
20×cbrt-undiv div-exp associate-/r*
5×associate-/l/
4×pow1 frac-2neg clear-num add-log-exp
Counts
4 → 5238
Calls
4 calls:
78.0ms
(/ (/ (/ (+ alpha (+ beta (+ (* alpha beta) 1.0))) (sqrt (+ alpha (+ beta (* 1.0 2.0))))) (sqrt (+ (+ alpha beta) (* 2.0 1.0)))) (+ (+ alpha beta) (* 2.0 1.0)))
207.0ms
(/ (/ (/ (/ (+ alpha (+ beta (+ (* alpha beta) 1.0))) (sqrt (+ alpha (+ beta (* 1.0 2.0))))) (sqrt (+ (+ alpha beta) (* 2.0 1.0)))) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0))
27.0ms
(/ (/ (+ alpha (+ beta (+ (* alpha beta) 1.0))) (sqrt (+ alpha (+ beta (* 1.0 2.0))))) (sqrt (+ (+ alpha beta) (* 2.0 1.0))))
16.0ms
(/ (+ alpha (+ beta (+ (* alpha beta) 1.0))) (sqrt (+ alpha (+ beta (* 1.0 2.0)))))

series91.0ms

Counts
4 → 12
Calls
4 calls:
28.0ms
(/ (/ (/ (+ alpha (+ beta (+ (* alpha beta) 1.0))) (sqrt (+ alpha (+ beta (* 1.0 2.0))))) (sqrt (+ (+ alpha beta) (* 2.0 1.0)))) (+ (+ alpha beta) (* 2.0 1.0)))
34.0ms
(/ (/ (/ (/ (+ alpha (+ beta (+ (* alpha beta) 1.0))) (sqrt (+ alpha (+ beta (* 1.0 2.0))))) (sqrt (+ (+ alpha beta) (* 2.0 1.0)))) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0))
16.0ms
(/ (/ (+ alpha (+ beta (+ (* alpha beta) 1.0))) (sqrt (+ alpha (+ beta (* 1.0 2.0))))) (sqrt (+ (+ alpha beta) (* 2.0 1.0))))
13.0ms
(/ (+ alpha (+ beta (+ (* alpha beta) 1.0))) (sqrt (+ alpha (+ beta (* 1.0 2.0)))))

simplify1.8s

Algorithm
egg-herbie
Counts
5250 → 5250
Iterations

Useful iterations: 0 (219.0ms)

IterNodesCost
05586376911

prune48.4s

Filtered
1517 candidates to 5250 candidates (-246.1%)
Pruning

9 alts after pruning (6 fresh and 3 done)

PrunedKeptTotal
New524915250
Fresh156
Picked011
Done022
Total525095259

Merged error: 1.6b

Counts
5259 → 9

regimes133.0ms

Accuracy

35.7% (1.6b remaining)

Error of 2.9b against oracle of 1.3b and baseline of 3.8b

bsearch18.0ms

Steps
ItersRangePoint
6
2.469202528104227e+196
1.945526915707786e+197
1.9107204585361316e+197

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
05385
15385

end0.0ms

sample897.0ms

Algorithm
intervals
Results
541.0ms8000×body80valid
129.0ms8000×pre80true

Profiling

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