Details

Time bar (total: 1.5m)

sample27.0ms

Algorithm
intervals
Results
11.0ms256×body80valid
4.0ms256×pre80true

simplify83.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
03317
111417
256317
3416417
4500217

prune2.0ms

Filtered
1 candidates to 0 candidates (0.0%)
Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022

Merged error: 3.6b

Counts
2 → 1

localize18.0ms

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))
3.4b
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

rewrite130.0ms

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:
8.0ms
(+ (+ (+ 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)))
43.0ms
(/ (/ (/ (+ (+ (+ 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)))

series362.0ms

Counts
4 → 12
Calls
4 calls:
13.0ms
(+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0)
134.0ms
(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0)))
144.0ms
(/ (/ (/ (+ (+ (+ 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))
71.0ms
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

simplify140.0ms

Algorithm
egg-herbie
Counts
477 → 477
Iterations

Useful iterations: 1 (31.0ms)

IterNodesCost
0149213034
1500212552

prune963.0ms

Filtered
477 candidates to 281 candidates (58.9%)
Pruning

8 alts after pruning (8 fresh and 0 done)

PrunedKeptTotal
New4698477
Fresh000
Picked101
Done000
Total4708478

Merged error: 1.1b

Counts
478 → 8

localize16.0ms

Local error

Found 4 expressions with local error:

3.4b
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))
3.4b
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))
14.0b
(sqrt (/ (/ (/ (+ (+ (+ 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)))
14.0b
(sqrt (/ (/ (/ (+ (+ (+ 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)))

rewrite212.0ms

Algorithm
rewrite-expression-head
Rules
1236×times-frac
888×*-un-lft-identity
508×add-sqr-sqrt
492×sqrt-prod
488×add-cube-cbrt
200×distribute-lft-out
72×associate-/r/
38×flip3-+ flip-+
36×div-inv
8×add-exp-log rem-sqrt-square add-cbrt-cube associate-/l*
6×pow1 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 → 590
Calls
4 calls:
19.0ms
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))
15.0ms
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))
53.0ms
(sqrt (/ (/ (/ (+ (+ (+ 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)))
57.0ms
(sqrt (/ (/ (/ (+ (+ (+ 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)))

series711.0ms

Counts
4 → 12
Calls
4 calls:
75.0ms
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))
75.0ms
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))
282.0ms
(sqrt (/ (/ (/ (+ (+ (+ 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)))
279.0ms
(sqrt (/ (/ (/ (+ (+ (+ 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)))

simplify211.0ms

Algorithm
egg-herbie
Counts
602 → 602
Iterations

Useful iterations: 1 (34.0ms)

IterNodesCost
0158020724
1500120206

prune1.6s

Filtered
602 candidates to 320 candidates (53.2%)
Pruning

8 alts after pruning (7 fresh and 1 done)

PrunedKeptTotal
New6020602
Fresh077
Picked011
Done000
Total6028610

Merged error: 1.1b

Counts
610 → 8

localize18.0ms

Local error

Found 4 expressions with local error:

0.0b
(+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0)
0.0b
(* (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))
1.7b
(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (* (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))))
3.4b
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

rewrite75.0ms

Algorithm
rewrite-expression-head
Rules
55×*-un-lft-identity
54×times-frac
33×add-sqr-sqrt
31×add-cube-cbrt
22×associate-/l*
20×add-exp-log add-cbrt-cube
17×flip3-+ flip-+
14×associate-/r/
13×add-log-exp
12×distribute-lft-out
8×frac-times
7×cbrt-undiv div-exp
6×pow1 sum-log
4×associate-*r/ associate-*l* associate-*l/ associate-/r* div-inv
3×associate-*r* prod-exp cbrt-unprod associate-/l/
2×frac-2neg clear-num
1×+-commutative distribute-rgt-in associate-+l+ distribute-lft-in pow-prod-down *-commutative unswap-sqr
Counts
4 → 143
Calls
4 calls:
8.0ms
(+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0)
16.0ms
(* (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))
29.0ms
(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (* (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))))
15.0ms
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

series272.0ms

Counts
4 → 12
Calls
4 calls:
13.0ms
(+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0)
28.0ms
(* (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))
153.0ms
(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (* (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))))
77.0ms
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

simplify120.0ms

Algorithm
egg-herbie
Counts
155 → 155
Iterations

Useful iterations: 1 (20.0ms)

IterNodesCost
07322482
139192257
250012257

prune351.0ms

Filtered
155 candidates to 113 candidates (72.9%)
Pruning

8 alts after pruning (6 fresh and 2 done)

PrunedKeptTotal
New1541155
Fresh156
Picked011
Done011
Total1558163

Merged error: 1.1b

Counts
163 → 8

localize17.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0) (/ (sqrt (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))) (+ (+ alpha beta) (* 2.0 1.0))))
1.9b
(/ (/ (sqrt (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))) 1) (/ (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0) (/ (sqrt (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))) (+ (+ alpha beta) (* 2.0 1.0)))))
3.4b
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))
3.4b
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

rewrite5.6s

Algorithm
rewrite-expression-head
Rules
93236×times-frac
51845×*-un-lft-identity
32243×add-sqr-sqrt add-cube-cbrt
30186×sqrt-prod
9801×distribute-lft-out
3982×associate-/r/
2308×div-inv
1959×flip3-+ flip-+
356×associate-/r*
79×associate-/l*
43×add-exp-log
34×add-cbrt-cube
29×div-exp
20×cbrt-undiv
7×associate-/l/
4×pow1 frac-2neg clear-num add-log-exp
3×1-exp
Counts
4 → 19638
Calls
4 calls:
62.0ms
(/ (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0) (/ (sqrt (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))) (+ (+ alpha beta) (* 2.0 1.0))))
535.0ms
(/ (/ (sqrt (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))) 1) (/ (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0) (/ (sqrt (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))) (+ (+ alpha beta) (* 2.0 1.0)))))
16.0ms
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))
15.0ms
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

series1.7s

Counts
4 → 12
Calls
4 calls:
1.4s
(/ (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0) (/ (sqrt (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))) (+ (+ alpha beta) (* 2.0 1.0))))
152.0ms
(/ (/ (sqrt (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))) 1) (/ (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0) (/ (sqrt (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))) (+ (+ alpha beta) (* 2.0 1.0)))))
73.0ms
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))
76.0ms
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

simplify11.1s

Algorithm
egg-herbie
Counts
19650 → 19650
Iterations

Useful iterations: 0 (274.0ms)

IterNodesCost
0180451252303

prune1.1m

Filtered
19650 candidates to 10253 candidates (52.2%)
Pruning

8 alts after pruning (5 fresh and 3 done)

PrunedKeptTotal
New19650019650
Fresh055
Picked011
Done022
Total19650819658

Merged error: 1.1b

Counts
19658 → 8

regimes114.0ms

Accuracy

91.5% (0.2b remaining)

Error of 1.5b against oracle of 1.2b and baseline of 3.8b

bsearch2.0ms

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
04069
14069

end0.0ms

sample858.0ms

Algorithm
intervals
Results
592.0ms8000×body80valid
122.0ms8000×pre80true

Profiling

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