Details

Time bar (total: 5.5s)

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
16.0ms256×body80valid
4.0ms256×pre80true

simplify109.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (107.0ms)

IterNodesCost
0724835

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: 4.5b

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))
4.3b
(/ (+ (+ (+ 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:
8.0ms
(+ (+ (+ 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)))
39.0ms
(/ (/ (/ (+ (+ (+ 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)))

series60.0ms

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

simplify148.0ms

Algorithm
egg-herbie
Counts
477 → 477
Iterations

Useful iterations: 0 (49.0ms)

IterNodesCost
0507324241

prune1.6s

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: 1.6b

Counts
479 → 7

localize18.0ms

Local error

Found 4 expressions with local error:

0.1b
(* (sqrt (+ alpha (+ beta (+ (* alpha beta) 1.0)))) (/ (sqrt (+ alpha (+ beta (+ (* alpha beta) 1.0)))) (+ alpha (+ beta (* 1.0 2.0)))))
0.2b
(/ (sqrt (+ alpha (+ beta (+ (* alpha beta) 1.0)))) (+ alpha (+ beta (* 1.0 2.0))))
4.2b
(sqrt (+ alpha (+ beta (+ (* alpha beta) 1.0))))
4.2b
(sqrt (+ alpha (+ beta (+ (* alpha beta) 1.0))))

rewrite63.0ms

Algorithm
rewrite-expression-head
Rules
138×*-un-lft-identity
68×times-frac
65×sqrt-prod
62×add-sqr-sqrt
53×distribute-lft-out
44×add-cube-cbrt
38×associate-*r*
11×add-exp-log add-cbrt-cube
10×sqrt-div
8×pow1 associate-*l* associate-/l*
7×flip3-+ flip-+
6×unswap-sqr
4×associate-/r* associate-/r/ add-log-exp
2×cbrt-undiv frac-times rem-sqrt-square sqrt-pow1 pow1/2 div-exp associate-*l/ prod-exp cbrt-unprod div-inv associate-/l/
1×frac-2neg associate-*r/ pow-prod-down clear-num *-commutative
Counts
4 → 164
Calls
4 calls:
28.0ms
(* (sqrt (+ alpha (+ beta (+ (* alpha beta) 1.0)))) (/ (sqrt (+ alpha (+ beta (+ (* alpha beta) 1.0)))) (+ alpha (+ beta (* 1.0 2.0)))))
15.0ms
(/ (sqrt (+ alpha (+ beta (+ (* alpha beta) 1.0)))) (+ alpha (+ beta (* 1.0 2.0))))
7.0ms
(sqrt (+ alpha (+ beta (+ (* alpha beta) 1.0))))
7.0ms
(sqrt (+ alpha (+ beta (+ (* alpha beta) 1.0))))

series72.0ms

Counts
4 → 12
Calls
4 calls:
11.0ms
(* (sqrt (+ alpha (+ beta (+ (* alpha beta) 1.0)))) (/ (sqrt (+ alpha (+ beta (+ (* alpha beta) 1.0)))) (+ alpha (+ beta (* 1.0 2.0)))))
44.0ms
(/ (sqrt (+ alpha (+ beta (+ (* alpha beta) 1.0)))) (+ alpha (+ beta (* 1.0 2.0))))
9.0ms
(sqrt (+ alpha (+ beta (+ (* alpha beta) 1.0))))
9.0ms
(sqrt (+ alpha (+ beta (+ (* alpha beta) 1.0))))

simplify64.0ms

Algorithm
egg-herbie
Counts
176 → 176
Iterations

Useful iterations: 0 (44.0ms)

IterNodesCost
051724022

prune371.0ms

Filtered
102 candidates to 176 candidates (-72.5%)
Pruning

7 alts after pruning (6 fresh and 1 done)

PrunedKeptTotal
New1751176
Fresh156
Picked011
Done000
Total1767183

Merged error: 1.6b

Counts
183 → 7

localize20.0ms

Local error

Found 4 expressions with local error:

0.5b
(* (+ alpha (+ beta (+ 1.0 (* 1.0 2.0)))) (sqrt (+ alpha (+ beta (* 1.0 2.0)))))
3.3b
(/ (sqrt (/ (+ alpha (+ beta (+ (* alpha beta) 1.0))) (+ alpha (+ beta (* 1.0 2.0))))) (* (+ alpha (+ beta (+ 1.0 (* 1.0 2.0)))) (sqrt (+ alpha (+ beta (* 1.0 2.0))))))
4.3b
(/ (+ alpha (+ beta (+ (* alpha beta) 1.0))) (+ alpha (+ beta (* 1.0 2.0))))
4.3b
(/ (+ alpha (+ beta (+ (* alpha beta) 1.0))) (+ alpha (+ beta (* 1.0 2.0))))

rewrite79.0ms

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-*r*
6×pow1
5×associate-*l* 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×pow-prod-down *-commutative
Counts
4 → 205
Calls
4 calls:
14.0ms
(* (+ alpha (+ beta (+ 1.0 (* 1.0 2.0)))) (sqrt (+ alpha (+ beta (* 1.0 2.0)))))
29.0ms
(/ (sqrt (/ (+ alpha (+ beta (+ (* alpha beta) 1.0))) (+ alpha (+ beta (* 1.0 2.0))))) (* (+ alpha (+ beta (+ 1.0 (* 1.0 2.0)))) (sqrt (+ alpha (+ beta (* 1.0 2.0))))))
13.0ms
(/ (+ alpha (+ beta (+ (* alpha beta) 1.0))) (+ alpha (+ beta (* 1.0 2.0))))
14.0ms
(/ (+ alpha (+ beta (+ (* alpha beta) 1.0))) (+ alpha (+ beta (* 1.0 2.0))))

series63.0ms

Counts
4 → 12
Calls
4 calls:
15.0ms
(* (+ alpha (+ beta (+ 1.0 (* 1.0 2.0)))) (sqrt (+ alpha (+ beta (* 1.0 2.0)))))
25.0ms
(/ (sqrt (/ (+ alpha (+ beta (+ (* alpha beta) 1.0))) (+ alpha (+ beta (* 1.0 2.0))))) (* (+ alpha (+ beta (+ 1.0 (* 1.0 2.0)))) (sqrt (+ alpha (+ beta (* 1.0 2.0))))))
11.0ms
(/ (+ alpha (+ beta (+ (* alpha beta) 1.0))) (+ alpha (+ beta (* 1.0 2.0))))
11.0ms
(/ (+ alpha (+ beta (+ (* alpha beta) 1.0))) (+ alpha (+ beta (* 1.0 2.0))))

simplify71.0ms

Algorithm
egg-herbie
Counts
217 → 217
Iterations

Useful iterations: 0 (41.0ms)

IterNodesCost
050236693

prune996.0ms

Filtered
136 candidates to 217 candidates (-59.6%)
Pruning

7 alts after pruning (5 fresh and 2 done)

PrunedKeptTotal
New2170217
Fresh055
Picked011
Done011
Total2177224

Merged error: 1.6b

Counts
224 → 7

localize16.0ms

Local error

Found 4 expressions with local error:

0.0b
(+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0)
0.0b
(* (+ alpha (+ beta (* 1.0 2.0))) (+ alpha (+ beta (* 1.0 2.0))))
0.1b
(/ (/ (+ alpha (+ beta (+ (* alpha beta) 1.0))) (* (+ alpha (+ beta (* 1.0 2.0))) (+ alpha (+ beta (* 1.0 2.0))))) (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0))
18.7b
(/ (+ alpha (+ beta (+ (* alpha beta) 1.0))) (* (+ alpha (+ beta (* 1.0 2.0))) (+ alpha (+ beta (* 1.0 2.0)))))

rewrite74.0ms

Algorithm
rewrite-expression-head
Rules
125×*-un-lft-identity
98×times-frac
50×associate-/r/
46×distribute-lft-out
45×flip3-+ flip-+
40×add-sqr-sqrt
38×add-cube-cbrt
28×frac-times
22×associate-/l*
20×add-exp-log add-cbrt-cube
14×associate-*r/ associate-*l/
13×add-log-exp
11×pow1
7×cbrt-undiv div-exp div-inv
6×swap-sqr sum-log
5×associate-/r*
4×associate-*r* associate-*l*
3×prod-exp cbrt-unprod associate-/l/
2×frac-2neg clear-num
1×+-commutative pow2 distribute-rgt-in associate-+l+ distribute-lft-in pow-plus pow-prod-down pow-sqr *-commutative pow-prod-up unswap-sqr
Counts
4 → 198
Calls
4 calls:
8.0ms
(+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0)
12.0ms
(* (+ alpha (+ beta (* 1.0 2.0))) (+ alpha (+ beta (* 1.0 2.0))))
27.0ms
(/ (/ (+ alpha (+ beta (+ (* alpha beta) 1.0))) (* (+ alpha (+ beta (* 1.0 2.0))) (+ alpha (+ beta (* 1.0 2.0))))) (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0))
18.0ms
(/ (+ alpha (+ beta (+ (* alpha beta) 1.0))) (* (+ alpha (+ beta (* 1.0 2.0))) (+ alpha (+ beta (* 1.0 2.0)))))

series49.0ms

Counts
4 → 12
Calls
4 calls:
3.0ms
(+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0)
5.0ms
(* (+ alpha (+ beta (* 1.0 2.0))) (+ alpha (+ beta (* 1.0 2.0))))
22.0ms
(/ (/ (+ alpha (+ beta (+ (* alpha beta) 1.0))) (* (+ alpha (+ beta (* 1.0 2.0))) (+ alpha (+ beta (* 1.0 2.0))))) (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0))
19.0ms
(/ (+ alpha (+ beta (+ (* alpha beta) 1.0))) (* (+ alpha (+ beta (* 1.0 2.0))) (+ alpha (+ beta (* 1.0 2.0)))))

simplify80.0ms

Algorithm
egg-herbie
Counts
210 → 210
Iterations

Useful iterations: 0 (46.0ms)

IterNodesCost
050137097

prune428.0ms

Filtered
128 candidates to 210 candidates (-64.1%)
Pruning

7 alts after pruning (4 fresh and 3 done)

PrunedKeptTotal
New2100210
Fresh044
Picked011
Done022
Total2107217

Merged error: 1.6b

Counts
217 → 7

regimes126.0ms

Accuracy

54% (1.1b remaining)

Error of 2.4b against oracle of 1.3b and baseline of 3.7b

bsearch16.0ms

Steps
ItersRangePoint
7
1.9160160055064062e+171
5.890348504278836e+172
6.102135130455812e+171

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
08152
18152

end0.0ms

sample774.0ms

Algorithm
intervals
Results
496.0ms8000×body80valid
135.0ms8000×pre80true

Profiling

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