Details

Time bar (total: 4.7s)

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

sample29.0ms

Algorithm
intervals
Results
16.0ms256×body80valid
4.0ms256×pre80true

simplify115.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (113.0ms)

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: 3.1b

Counts
2 → 2

localize12.0ms

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

rewrite103.0ms

Algorithm
rewrite-expression-head
Rules
804×times-frac
583×*-un-lft-identity
339×add-sqr-sqrt add-cube-cbrt
122×distribute-lft-out
82×associate-/l*
54×associate-/r/
28×flip3-+ flip-+
27×div-inv
19×add-exp-log add-cbrt-cube
10×cbrt-undiv div-exp associate-/r*
4×associate-/l/
3×pow1 frac-2neg clear-num add-log-exp
Counts
3 → 450
Calls
3 calls:
22.0ms
(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0)))
36.0ms
(/ (/ (/ (+ (+ (+ 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)))

series61.0ms

Counts
3 → 9
Calls
3 calls:
20.0ms
(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0)))
28.0ms
(/ (/ (/ (+ (+ (+ 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)))

simplify157.0ms

Algorithm
egg-herbie
Counts
459 → 459
Iterations

Useful iterations: 0 (63.0ms)

IterNodesCost
0552223282

prune1.4s

Filtered
275 candidates to 459 candidates (-66.9%)
Pruning

10 alts after pruning (10 fresh and 0 done)

PrunedKeptTotal
New44910459
Fresh101
Picked101
Done000
Total45110461

Merged error: 1.3b

Counts
461 → 10

localize18.0ms

Local error

Found 4 expressions with local error:

0.0b
(/ (* (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (/ 1 (+ alpha (+ beta (* 1.0 2.0))))) (+ (+ alpha beta) (* 2.0 1.0)))
0.0b
(/ 1 (+ alpha (+ beta (* 1.0 2.0))))
0.1b
(/ (/ (* (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (/ 1 (+ alpha (+ beta (* 1.0 2.0))))) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0))
2.9b
(* (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (/ 1 (+ alpha (+ beta (* 1.0 2.0)))))

rewrite82.0ms

Algorithm
rewrite-expression-head
Rules
81×*-un-lft-identity
80×times-frac
54×add-exp-log
51×add-sqr-sqrt
44×add-cube-cbrt
34×add-cbrt-cube
24×div-exp
18×associate-*r* associate-/r/ distribute-lft-out
14×cbrt-undiv
13×flip3-+ flip-+ associate-/l*
12×prod-exp
11×associate-/r*
9×div-inv
7×pow1 associate-/l/
6×cbrt-unprod
4×frac-times rec-exp 1-exp associate-*l* associate-*l/ add-log-exp
3×frac-2neg clear-num unswap-sqr
2×associate-*r/ un-div-inv
1×pow-flip pow-prod-down *-commutative inv-pow
Counts
4 → 188
Calls
4 calls:
24.0ms
(/ (* (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (/ 1 (+ alpha (+ beta (* 1.0 2.0))))) (+ (+ alpha beta) (* 2.0 1.0)))
6.0ms
(/ 1 (+ alpha (+ beta (* 1.0 2.0))))
27.0ms
(/ (/ (* (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (/ 1 (+ alpha (+ beta (* 1.0 2.0))))) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0))
18.0ms
(* (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (/ 1 (+ alpha (+ beta (* 1.0 2.0)))))

series62.0ms

Counts
4 → 12
Calls
4 calls:
21.0ms
(/ (* (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (/ 1 (+ alpha (+ beta (* 1.0 2.0))))) (+ (+ alpha beta) (* 2.0 1.0)))
5.0ms
(/ 1 (+ alpha (+ beta (* 1.0 2.0))))
23.0ms
(/ (/ (* (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (/ 1 (+ alpha (+ beta (* 1.0 2.0))))) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0))
12.0ms
(* (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (/ 1 (+ alpha (+ beta (* 1.0 2.0)))))

simplify78.0ms

Algorithm
egg-herbie
Counts
200 → 200
Iterations

Useful iterations: 0 (49.0ms)

IterNodesCost
049775617
149775617

prune437.0ms

Filtered
132 candidates to 200 candidates (-51.5%)
Pruning

10 alts after pruning (9 fresh and 1 done)

PrunedKeptTotal
New2000200
Fresh099
Picked011
Done000
Total20010210

Merged error: 1.3b

Counts
210 → 10

localize20.0ms

Local error

Found 4 expressions with local error:

0.2b
(/ (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))))
2.9b
(sqrt (+ alpha (+ beta (+ (* alpha beta) 1.0))))
2.9b
(sqrt (+ alpha (+ beta (+ (* alpha beta) 1.0))))

rewrite46.0ms

Algorithm
rewrite-expression-head
Rules
140×*-un-lft-identity
64×times-frac
60×sqrt-prod
54×distribute-lft-out
46×add-sqr-sqrt
44×add-cube-cbrt
16×associate-/l*
8×add-exp-log sqrt-div associate-/r* add-cbrt-cube
6×pow1 flip3-+ flip-+
4×associate-/r/ associate-/l/ add-log-exp
2×cbrt-undiv rem-sqrt-square frac-2neg sqrt-pow1 pow1/2 div-exp clear-num div-inv
Counts
4 → 154
Calls
4 calls:
13.0ms
(/ (sqrt (+ alpha (+ beta (+ (* alpha beta) 1.0)))) (+ alpha (+ beta (* 1.0 2.0))))
13.0ms
(/ (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))))

series111.0ms

Counts
4 → 12
Calls
4 calls:
45.0ms
(/ (sqrt (+ alpha (+ beta (+ (* alpha beta) 1.0)))) (+ alpha (+ beta (* 1.0 2.0))))
47.0ms
(/ (sqrt (+ alpha (+ beta (+ (* alpha beta) 1.0)))) (+ alpha (+ beta (* 1.0 2.0))))
9.0ms
(sqrt (+ alpha (+ beta (+ (* alpha beta) 1.0))))
10.0ms
(sqrt (+ alpha (+ beta (+ (* alpha beta) 1.0))))

simplify56.0ms

Algorithm
egg-herbie
Counts
166 → 166
Iterations

Useful iterations: 0 (33.0ms)

IterNodesCost
050933988

prune409.0ms

Filtered
98 candidates to 166 candidates (-69.4%)
Pruning

10 alts after pruning (8 fresh and 2 done)

PrunedKeptTotal
New1651166
Fresh178
Picked011
Done011
Total16610176

Merged error: 1.3b

Counts
176 → 10

localize18.0ms

Local error

Found 3 expressions with local error:

0.0b
(* (+ alpha (+ beta (* 1.0 2.0))) (+ alpha (+ beta (+ 1.0 (* 1.0 2.0)))))
2.1b
(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (* (+ alpha (+ beta (* 1.0 2.0))) (+ alpha (+ beta (+ 1.0 (* 1.0 2.0))))))
2.9b
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

rewrite59.0ms

Algorithm
rewrite-expression-head
Rules
57×*-un-lft-identity
54×times-frac
32×add-sqr-sqrt
30×add-cube-cbrt
22×associate-/l*
19×add-exp-log add-cbrt-cube
16×flip3-+ flip-+
14×associate-/r/ distribute-lft-out
8×frac-times
7×cbrt-undiv div-exp
5×pow1 associate-*r*
4×associate-*r/ associate-*l* associate-*l/ associate-/r* div-inv
3×prod-exp cbrt-unprod associate-/l/ add-log-exp
2×frac-2neg clear-num
1×distribute-rgt-in distribute-lft-in pow-prod-down *-commutative unswap-sqr
Counts
3 → 130
Calls
3 calls:
13.0ms
(* (+ alpha (+ beta (* 1.0 2.0))) (+ alpha (+ beta (+ 1.0 (* 1.0 2.0)))))
28.0ms
(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (* (+ alpha (+ beta (* 1.0 2.0))) (+ alpha (+ beta (+ 1.0 (* 1.0 2.0))))))
14.0ms
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

series42.0ms

Counts
3 → 9
Calls
3 calls:
6.0ms
(* (+ alpha (+ beta (* 1.0 2.0))) (+ alpha (+ beta (+ 1.0 (* 1.0 2.0)))))
23.0ms
(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (* (+ alpha (+ beta (* 1.0 2.0))) (+ alpha (+ beta (+ 1.0 (* 1.0 2.0))))))
12.0ms
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

simplify60.0ms

Algorithm
egg-herbie
Counts
139 → 139
Iterations

Useful iterations: 0 (36.0ms)

IterNodesCost
056094301

prune301.0ms

Filtered
102 candidates to 139 candidates (-36.3%)
Pruning

10 alts after pruning (7 fresh and 3 done)

PrunedKeptTotal
New1381139
Fresh167
Picked011
Done022
Total13910149

Merged error: 1.3b

Counts
149 → 10

regimes153.0ms

Accuracy

0% (2.8b remaining)

Error of 4.0b against oracle of 1.2b and baseline of 4.0b

bsearch0.0ms

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
02937
12937

end0.0ms

sample797.0ms

Algorithm
intervals
Results
510.0ms8000×body80valid
141.0ms8000×pre80true

Profiling

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