Details

Time bar (total: 54.4s)

analyze3.0ms

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

sample27.0ms

Algorithm
intervals
Results
15.0ms256×body80valid
4.0ms256×pre80true

simplify114.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (112.0ms)

IterNodesCost
0494935
1494935

prune13.0ms

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: 1.6b

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))
1.5b
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

rewrite108.0ms

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)
22.0ms
(/ (/ (+ (+ (+ 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))
14.0ms
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

series60.0ms

Counts
4 → 12
Calls
4 calls:
3.0ms
(+ (+ (+ 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)))
26.0ms
(/ (/ (/ (+ (+ (+ 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)))

simplify159.0ms

Algorithm
egg-herbie
Counts
477 → 477
Iterations

Useful iterations: 0 (64.0ms)

IterNodesCost
0501623485

prune1.4s

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

7 alts after pruning (7 fresh and 0 done)

PrunedKeptTotal
New4707477
Fresh101
Picked101
Done000
Total4727479

Merged error: 0.5b

Counts
479 → 7

localize13.0ms

Local error

Found 3 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))) (+ alpha (+ beta 3.0)))
1.5b
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

rewrite111.0ms

Algorithm
rewrite-expression-head
Rules
954×times-frac
827×*-un-lft-identity
382×add-sqr-sqrt add-cube-cbrt
253×distribute-lft-out
82×associate-/l*
62×associate-/r/
32×flip3-+ flip-+
31×div-inv
19×add-exp-log add-cbrt-cube
11×associate-/r*
10×cbrt-undiv div-exp
4×associate-/l/
3×pow1 frac-2neg clear-num add-log-exp
Counts
3 → 511
Calls
3 calls:
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 3.0)))
16.0ms
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

series59.0ms

Counts
3 → 9
Calls
3 calls:
25.0ms
(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0)))
22.0ms
(/ (/ (/ (+ (+ (+ 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)))

simplify212.0ms

Algorithm
egg-herbie
Counts
520 → 520
Iterations

Useful iterations: 0 (113.0ms)

IterNodesCost
0500223836

prune1.2s

Filtered
274 candidates to 520 candidates (-89.8%)
Pruning

7 alts after pruning (6 fresh and 1 done)

PrunedKeptTotal
New5200520
Fresh066
Picked011
Done000
Total5207527

Merged error: 0.5b

Counts
527 → 7

localize21.0ms

Local error

Found 4 expressions with local error:

0.5b
(* (sqrt (+ alpha (+ beta (* 1.0 2.0)))) (+ alpha (+ beta (+ 1.0 (* 1.0 2.0)))))
1.1b
(/ (sqrt (/ (+ alpha (+ beta (+ (* alpha beta) 1.0))) (+ alpha (+ beta (* 1.0 2.0))))) (* (sqrt (+ alpha (+ beta (* 1.0 2.0)))) (+ alpha (+ beta (+ 1.0 (* 1.0 2.0))))))
1.5b
(/ (+ alpha (+ beta (+ (* alpha beta) 1.0))) (+ alpha (+ beta (* 1.0 2.0))))
1.5b
(/ (+ alpha (+ beta (+ (* alpha beta) 1.0))) (+ alpha (+ beta (* 1.0 2.0))))

rewrite74.0ms

Algorithm
rewrite-expression-head
Rules
192×*-un-lft-identity
109×times-frac
80×distribute-lft-out
57×sqrt-prod
55×add-sqr-sqrt
51×add-cube-cbrt
39×associate-/l*
18×flip3-+ flip-+
16×associate-/r/
15×add-exp-log add-cbrt-cube
13×sqrt-div
9×associate-/r*
8×frac-times
7×associate-*l*
6×pow1
5×associate-*r* div-inv associate-/l/
4×cbrt-undiv associate-*r/ div-exp associate-*l/ add-log-exp
3×frac-2neg clear-num
2×prod-exp cbrt-unprod unswap-sqr
1×distribute-rgt-in distribute-lft-in pow-prod-down *-commutative
Counts
4 → 207
Calls
4 calls:
13.0ms
(* (sqrt (+ alpha (+ beta (* 1.0 2.0)))) (+ alpha (+ beta (+ 1.0 (* 1.0 2.0)))))
26.0ms
(/ (sqrt (/ (+ alpha (+ beta (+ (* alpha beta) 1.0))) (+ alpha (+ beta (* 1.0 2.0))))) (* (sqrt (+ alpha (+ beta (* 1.0 2.0)))) (+ alpha (+ beta (+ 1.0 (* 1.0 2.0))))))
13.0ms
(/ (+ alpha (+ beta (+ (* alpha beta) 1.0))) (+ alpha (+ beta (* 1.0 2.0))))
13.0ms
(/ (+ alpha (+ beta (+ (* alpha beta) 1.0))) (+ alpha (+ beta (* 1.0 2.0))))

series64.0ms

Counts
4 → 12
Calls
4 calls:
16.0ms
(* (sqrt (+ alpha (+ beta (* 1.0 2.0)))) (+ alpha (+ beta (+ 1.0 (* 1.0 2.0)))))
22.0ms
(/ (sqrt (/ (+ alpha (+ beta (+ (* alpha beta) 1.0))) (+ alpha (+ beta (* 1.0 2.0))))) (* (sqrt (+ alpha (+ beta (* 1.0 2.0)))) (+ alpha (+ beta (+ 1.0 (* 1.0 2.0))))))
11.0ms
(/ (+ alpha (+ beta (+ (* alpha beta) 1.0))) (+ alpha (+ beta (* 1.0 2.0))))
15.0ms
(/ (+ alpha (+ beta (+ (* alpha beta) 1.0))) (+ alpha (+ beta (* 1.0 2.0))))

simplify93.0ms

Algorithm
egg-herbie
Counts
219 → 219
Iterations

Useful iterations: 0 (59.0ms)

IterNodesCost
049946744
149946744

prune756.0ms

Filtered
136 candidates to 219 candidates (-61.0%)
Pruning

7 alts after pruning (5 fresh and 2 done)

PrunedKeptTotal
New2190219
Fresh055
Picked011
Done011
Total2197226

Merged error: 0.5b

Counts
226 → 7

localize22.0ms

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))
0.8b
(/ (/ (+ alpha (+ beta (+ (* alpha beta) 1.0))) (sqrt (+ alpha (+ beta (* 1.0 2.0))))) (sqrt (+ (+ alpha beta) (* 2.0 1.0))))
1.4b
(/ (+ alpha (+ beta (+ (* alpha beta) 1.0))) (sqrt (+ alpha (+ beta (* 1.0 2.0)))))

rewrite1.1s

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:
83.0ms
(/ (/ (/ (+ 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)))
203.0ms
(/ (/ (/ (/ (+ 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))))
14.0ms
(/ (+ alpha (+ beta (+ (* alpha beta) 1.0))) (sqrt (+ alpha (+ beta (* 1.0 2.0)))))

series95.0ms

Counts
4 → 12
Calls
4 calls:
30.0ms
(/ (/ (/ (+ 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)))
36.0ms
(/ (/ (/ (/ (+ 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)))))

simplify2.1s

Algorithm
egg-herbie
Counts
5250 → 5250
Iterations

Useful iterations: 0 (211.0ms)

IterNodesCost
05586376911

prune45.9s

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

7 alts after pruning (4 fresh and 3 done)

PrunedKeptTotal
New524915250
Fresh134
Picked011
Done022
Total525075257

Merged error: 0.5b

Counts
5257 → 7

regimes118.0ms

Accuracy

0% (2.5b remaining)

Error of 3.6b against oracle of 1.1b and baseline of 3.6b

bsearch0.0ms

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
02431
12431

end0.0ms

analyze3.0ms

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

sample740.0ms

Algorithm
intervals
Results
486.0ms8000×body80valid
124.0ms8000×pre80true

Profiling

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