Details

Time bar (total: 10.2s)

analyze9.0ms

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

sample29.0ms

Algorithm
intervals
Results
16.0ms256×body80valid
4.0ms256×pre80true

simplify89.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
03317
111417
256317
3416417
4500217

prune3.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022

Merged error: 3.1b

Counts
2 → 1

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b
(+ (+ alpha beta) (* beta alpha))
0.1b
(/ (/ (+ (+ (+ 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))
2.9b
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

rewrite115.0ms

Algorithm
rewrite-expression-head
Rules
804×times-frac
584×*-un-lft-identity
340×add-sqr-sqrt add-cube-cbrt
122×distribute-lft-out
82×associate-/l*
54×associate-/r/
29×flip3-+ flip-+
27×div-inv
20×add-exp-log add-cbrt-cube
10×cbrt-undiv div-exp associate-/r*
9×add-log-exp
4×pow1 associate-/l/
3×frac-2neg clear-num sum-log
1×+-commutative associate-+l+
Counts
4 → 463
Calls
4 calls:
6.0ms
(+ (+ alpha beta) (* beta alpha))
19.0ms
(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0)))
40.0ms
(/ (/ (/ (+ (+ (+ 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)))

series57.0ms

Counts
4 → 12
Calls
4 calls:
4.0ms
(+ (+ alpha beta) (* beta alpha))
19.0ms
(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0)))
22.0ms
(/ (/ (/ (+ (+ (+ 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)))

simplify149.0ms

Algorithm
egg-herbie
Counts
475 → 475
Iterations

Useful iterations: 1 (31.0ms)

IterNodesCost
0151213008
1500112540

prune1.5s

Filtered
280 candidates to 475 candidates (-69.6%)
Pruning

7 alts after pruning (7 fresh and 0 done)

PrunedKeptTotal
New4687475
Fresh000
Picked101
Done000
Total4697476

Merged error: 1.2b

Counts
476 → 7

localize15.0ms

Local error

Found 4 expressions with local error:

0.1b
(* (sqrt (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0)))) (/ (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)))
0.1b
(/ (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))
2.9b
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))
2.9b
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

rewrite450.0ms

Algorithm
rewrite-expression-head
Rules
1471×times-frac
1040×*-un-lft-identity
673×add-sqr-sqrt
627×sqrt-prod
590×add-cube-cbrt
258×associate-*r*
225×distribute-lft-out
88×associate-/r/
71×associate-/l*
63×associate-*l*
46×flip3-+ flip-+
44×div-inv
20×unswap-sqr
15×add-exp-log add-cbrt-cube
10×associate-/r*
6×pow1
5×associate-/l/
4×cbrt-undiv div-exp add-log-exp
3×frac-2neg sqrt-div clear-num
2×prod-exp cbrt-unprod
1×frac-times associate-*r/ pow-prod-down associate-*l/ *-commutative
Counts
4 → 761
Calls
4 calls:
290.0ms
(* (sqrt (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0)))) (/ (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)))
40.0ms
(/ (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))
14.0ms
(/ (+ (+ (+ 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)))

series80.0ms

Counts
4 → 12
Calls
4 calls:
24.0ms
(* (sqrt (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0)))) (/ (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)))
26.0ms
(/ (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))
15.0ms
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))
14.0ms
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

simplify256.0ms

Algorithm
egg-herbie
Counts
773 → 773
Iterations

Useful iterations: 1 (39.0ms)

IterNodesCost
0195324980
1500124018

prune5.0s

Filtered
494 candidates to 773 candidates (-56.5%)
Pruning

7 alts after pruning (6 fresh and 1 done)

PrunedKeptTotal
New7730773
Fresh066
Picked011
Done000
Total7737780

Merged error: 1.2b

Counts
780 → 7

localize17.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (* (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (- (* (+ alpha beta) (+ alpha beta)) (* (* 2.0 1.0) (* 2.0 1.0)))) (- (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0)))
0.1b
(/ (/ (* (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (- (* (+ alpha beta) (+ alpha beta)) (* (* 2.0 1.0) (* 2.0 1.0)))) (- (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0))
0.1b
(* (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (- (* (+ alpha beta) (+ alpha beta)) (* (* 2.0 1.0) (* 2.0 1.0)))) (- (+ alpha beta) (* 2.0 1.0)))
16.1b
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (- (* (+ alpha beta) (+ alpha beta)) (* (* 2.0 1.0) (* 2.0 1.0))))

rewrite134.0ms

Algorithm
rewrite-expression-head
Rules
87×times-frac
84×*-un-lft-identity
51×add-sqr-sqrt
46×add-cube-cbrt
34×add-exp-log add-cbrt-cube
22×associate-*l*
19×distribute-lft-out
18×associate-/r/
14×cbrt-undiv div-exp associate-/l*
11×associate-/r*
9×div-inv difference-of-squares
8×flip3-+ flip-+ associate-/l/
6×pow1 flip3-- prod-exp flip-- cbrt-unprod
4×frac-times associate-*r/ add-log-exp
3×distribute-rgt-in frac-2neg distribute-lft-in associate-*r* clear-num
2×sub-neg associate-*l/ associate--l+ unswap-sqr
1×pow-prod-down *-commutative
Counts
4 → 191
Calls
4 calls:
32.0ms
(/ (* (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (- (* (+ alpha beta) (+ alpha beta)) (* (* 2.0 1.0) (* 2.0 1.0)))) (- (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0)))
47.0ms
(/ (/ (* (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (- (* (+ alpha beta) (+ alpha beta)) (* (* 2.0 1.0) (* 2.0 1.0)))) (- (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0))
28.0ms
(* (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (- (* (+ alpha beta) (+ alpha beta)) (* (* 2.0 1.0) (* 2.0 1.0)))) (- (+ alpha beta) (* 2.0 1.0)))
19.0ms
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (- (* (+ alpha beta) (+ alpha beta)) (* (* 2.0 1.0) (* 2.0 1.0))))

series114.0ms

Counts
4 → 12
Calls
4 calls:
39.0ms
(/ (* (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (- (* (+ alpha beta) (+ alpha beta)) (* (* 2.0 1.0) (* 2.0 1.0)))) (- (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0)))
34.0ms
(/ (/ (* (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (- (* (+ alpha beta) (+ alpha beta)) (* (* 2.0 1.0) (* 2.0 1.0)))) (- (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0))
20.0ms
(* (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (- (* (+ alpha beta) (+ alpha beta)) (* (* 2.0 1.0) (* 2.0 1.0)))) (- (+ alpha beta) (* 2.0 1.0)))
20.0ms
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (- (* (+ alpha beta) (+ alpha beta)) (* (* 2.0 1.0) (* 2.0 1.0))))

simplify78.0ms

Algorithm
egg-herbie
Counts
203 → 203
Iterations

Useful iterations: 1 (25.0ms)

IterNodesCost
09185092
150024559

prune584.0ms

Filtered
143 candidates to 203 candidates (-42.0%)
Pruning

7 alts after pruning (5 fresh and 2 done)

PrunedKeptTotal
New2030203
Fresh055
Picked011
Done011
Total2037210

Merged error: 1.2b

Counts
210 → 7

localize14.0ms

Local error

Found 4 expressions with local error:

0.0b
(+ (+ alpha beta) (* beta alpha))
0.0b
(* (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))
1.9b
(/ (/ (+ (+ (+ 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))))
2.9b
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

rewrite79.0ms

Algorithm
rewrite-expression-head
Rules
54×times-frac
53×*-un-lft-identity
33×add-sqr-sqrt
31×add-cube-cbrt
22×associate-/l*
20×add-exp-log add-cbrt-cube
17×flip3-+ flip-+
14×associate-/r/
11×distribute-lft-out
9×add-log-exp
8×frac-times
7×cbrt-undiv div-exp
6×pow1
4×associate-*r/ associate-*l* associate-*l/ associate-/r* div-inv
3×associate-*r* prod-exp sum-log 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 → 141
Calls
4 calls:
6.0ms
(+ (+ alpha beta) (* beta alpha))
19.0ms
(* (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))
33.0ms
(/ (/ (+ (+ (+ 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))))
16.0ms
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

series62.0ms

Counts
4 → 12
Calls
4 calls:
4.0ms
(+ (+ alpha beta) (* beta alpha))
7.0ms
(* (+ (+ (+ alpha beta) (* 2.0 1.0)) 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)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))))
13.0ms
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

simplify126.0ms

Algorithm
egg-herbie
Counts
153 → 153
Iterations

Useful iterations: 1 (22.0ms)

IterNodesCost
07652456
142412233
250012233

prune272.0ms

Filtered
112 candidates to 153 candidates (-36.6%)
Pruning

7 alts after pruning (4 fresh and 3 done)

PrunedKeptTotal
New1530153
Fresh044
Picked011
Done022
Total1537160

Merged error: 1.2b

Counts
160 → 7

regimes201.0ms

Accuracy

55.9% (1.1b remaining)

Error of 2.3b against oracle of 1.2b and baseline of 3.7b

bsearch20.0ms

Steps
ItersRangePoint
3
3.063599342505731e+167
4.0275996522547463e+167
3.2443494005836714e+167

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
04348
14348

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

sample761.0ms

Algorithm
intervals
Results
488.0ms8000×body80valid
134.0ms8000×pre80true

Profiling

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