Details

Time bar (total: 5.4s)

analyze67.0ms

Algorithm
search
Search
TrueOtherFalseIter
0%14%86%0
0%14%86%1
0%14%86%2
0%14%86%3
0%14%86%4
0%14%86%5
0%14%86%6
8.1%5.9%86%7
10.3%3.7%86%8
12.6%1.5%86%9
13.9%0.1%86%10
14%0%86%11
14%0%86%12
14%0%86%13
14%0%86%14

sample58.0ms

Algorithm
intervals
Results
33.0ms256×body80valid
13.0ms256×pre80true

simplify30.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (28.0ms)

IterNodesCost
0477653
1477653

prune11.0ms

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: 54.4b

Counts
2 → 2

localize16.0ms

Local error

Found 4 expressions with local error:

0.0b
(* (+ alpha (+ beta (* i 2.0))) (+ alpha (+ beta (* i 2.0))))
0.0b
(* (+ alpha (+ beta (* i 2.0))) (- (* (+ alpha (+ beta (* i 2.0))) (+ alpha (+ beta (* i 2.0)))) 1.0))
40.7b
(* (* i (+ i (+ alpha beta))) (/ (+ (* i (+ i (+ alpha beta))) (* alpha beta)) (* (+ alpha (+ beta (* i 2.0))) (* (+ alpha (+ beta (* i 2.0))) (- (* (+ alpha (+ beta (* i 2.0))) (+ alpha (+ beta (* i 2.0)))) 1.0)))))
50.4b
(/ (+ (* i (+ i (+ alpha beta))) (* alpha beta)) (* (+ alpha (+ beta (* i 2.0))) (* (+ alpha (+ beta (* i 2.0))) (- (* (+ alpha (+ beta (* i 2.0))) (+ alpha (+ beta (* i 2.0)))) 1.0))))

rewrite105.0ms

Algorithm
rewrite-expression-head
Rules
66×frac-times
52×associate-/r/
49×add-exp-log add-cbrt-cube
48×flip3-+ flip-+
41×associate-*r*
37×associate-*r/
30×*-un-lft-identity
23×prod-exp cbrt-unprod
22×associate-*l/
21×flip3-- flip--
19×add-sqr-sqrt
18×pow1
14×add-cube-cbrt
9×cbrt-undiv div-exp associate-*l*
7×distribute-lft-out
6×distribute-rgt-in distribute-lft-in times-frac swap-sqr
5×pow-prod-down
4×associate--l+ add-log-exp
3×*-commutative associate-/l*
2×sub-neg div-inv associate-/l/ unswap-sqr
1×pow2 frac-2neg pow-plus clear-num associate-/r* pow-sqr pow-prod-up difference-of-squares
Counts
4 → 190
Calls
4 calls:
10.0ms
(* (+ alpha (+ beta (* i 2.0))) (+ alpha (+ beta (* i 2.0))))
16.0ms
(* (+ alpha (+ beta (* i 2.0))) (- (* (+ alpha (+ beta (* i 2.0))) (+ alpha (+ beta (* i 2.0)))) 1.0))
36.0ms
(* (* i (+ i (+ alpha beta))) (/ (+ (* i (+ i (+ alpha beta))) (* alpha beta)) (* (+ alpha (+ beta (* i 2.0))) (* (+ alpha (+ beta (* i 2.0))) (- (* (+ alpha (+ beta (* i 2.0))) (+ alpha (+ beta (* i 2.0)))) 1.0)))))
31.0ms
(/ (+ (* i (+ i (+ alpha beta))) (* alpha beta)) (* (+ alpha (+ beta (* i 2.0))) (* (+ alpha (+ beta (* i 2.0))) (- (* (+ alpha (+ beta (* i 2.0))) (+ alpha (+ beta (* i 2.0)))) 1.0))))

series495.0ms

Counts
4 → 12
Calls
4 calls:
12.0ms
(* (+ alpha (+ beta (* i 2.0))) (+ alpha (+ beta (* i 2.0))))
56.0ms
(* (+ alpha (+ beta (* i 2.0))) (- (* (+ alpha (+ beta (* i 2.0))) (+ alpha (+ beta (* i 2.0)))) 1.0))
315.0ms
(* (* i (+ i (+ alpha beta))) (/ (+ (* i (+ i (+ alpha beta))) (* alpha beta)) (* (+ alpha (+ beta (* i 2.0))) (* (+ alpha (+ beta (* i 2.0))) (- (* (+ alpha (+ beta (* i 2.0))) (+ alpha (+ beta (* i 2.0)))) 1.0)))))
113.0ms
(/ (+ (* i (+ i (+ alpha beta))) (* alpha beta)) (* (+ alpha (+ beta (* i 2.0))) (* (+ alpha (+ beta (* i 2.0))) (- (* (+ alpha (+ beta (* i 2.0))) (+ alpha (+ beta (* i 2.0)))) 1.0))))

simplify86.0ms

Algorithm
egg-herbie
Counts
202 → 202
Iterations

Useful iterations: 0 (54.0ms)

IterNodesCost
050336966

prune503.0ms

Filtered
134 candidates to 202 candidates (-50.7%)
Pruning

10 alts after pruning (10 fresh and 0 done)

PrunedKeptTotal
New19210202
Fresh101
Picked101
Done000
Total19410204

Merged error: 46.2b

Counts
204 → 10

localize16.0ms

Local error

Found 4 expressions with local error:

0.0b
(* (+ alpha (+ beta (* i 2.0))) (- (* (+ alpha (+ beta (* i 2.0))) (+ alpha (+ beta (* i 2.0)))) 1.0))
4.5b
(* (/ (* i (+ i (+ alpha beta))) (+ alpha (+ beta (* i 2.0)))) (/ (+ (* i (+ i (+ alpha beta))) (* alpha beta)) (* (+ alpha (+ beta (* i 2.0))) (- (* (+ alpha (+ beta (* i 2.0))) (+ alpha (+ beta (* i 2.0)))) 1.0))))
35.6b
(/ (* i (+ i (+ alpha beta))) (+ alpha (+ beta (* i 2.0))))
48.9b
(/ (+ (* i (+ i (+ alpha beta))) (* alpha beta)) (* (+ alpha (+ beta (* i 2.0))) (- (* (+ alpha (+ beta (* i 2.0))) (+ alpha (+ beta (* i 2.0)))) 1.0)))

rewrite94.0ms

Algorithm
rewrite-expression-head
Rules
52×add-exp-log add-cbrt-cube
22×*-un-lft-identity
20×associate-/r/
19×add-sqr-sqrt associate-*r*
18×prod-exp cbrt-unprod
16×cbrt-undiv div-exp
14×add-cube-cbrt times-frac associate-*l*
13×frac-times flip3-+ flip-+
9×flip3-- associate-*r/ flip--
8×pow1
7×associate-*l/
5×distribute-rgt-in distribute-lft-in associate-/r*
4×associate--l+ div-inv associate-/l/ distribute-lft-out associate-/l* add-log-exp
2×sub-neg frac-2neg pow-prod-down clear-num *-commutative unswap-sqr
1×difference-of-squares
Counts
4 → 148
Calls
4 calls:
16.0ms
(* (+ alpha (+ beta (* i 2.0))) (- (* (+ alpha (+ beta (* i 2.0))) (+ alpha (+ beta (* i 2.0)))) 1.0))
35.0ms
(* (/ (* i (+ i (+ alpha beta))) (+ alpha (+ beta (* i 2.0)))) (/ (+ (* i (+ i (+ alpha beta))) (* alpha beta)) (* (+ alpha (+ beta (* i 2.0))) (- (* (+ alpha (+ beta (* i 2.0))) (+ alpha (+ beta (* i 2.0)))) 1.0))))
11.0ms
(/ (* i (+ i (+ alpha beta))) (+ alpha (+ beta (* i 2.0))))
25.0ms
(/ (+ (* i (+ i (+ alpha beta))) (* alpha beta)) (* (+ alpha (+ beta (* i 2.0))) (- (* (+ alpha (+ beta (* i 2.0))) (+ alpha (+ beta (* i 2.0)))) 1.0)))

series531.0ms

Counts
4 → 12
Calls
4 calls:
56.0ms
(* (+ alpha (+ beta (* i 2.0))) (- (* (+ alpha (+ beta (* i 2.0))) (+ alpha (+ beta (* i 2.0)))) 1.0))
301.0ms
(* (/ (* i (+ i (+ alpha beta))) (+ alpha (+ beta (* i 2.0)))) (/ (+ (* i (+ i (+ alpha beta))) (* alpha beta)) (* (+ alpha (+ beta (* i 2.0))) (- (* (+ alpha (+ beta (* i 2.0))) (+ alpha (+ beta (* i 2.0)))) 1.0))))
18.0ms
(/ (* i (+ i (+ alpha beta))) (+ alpha (+ beta (* i 2.0))))
156.0ms
(/ (+ (* i (+ i (+ alpha beta))) (* alpha beta)) (* (+ alpha (+ beta (* i 2.0))) (- (* (+ alpha (+ beta (* i 2.0))) (+ alpha (+ beta (* i 2.0)))) 1.0)))

simplify58.0ms

Algorithm
egg-herbie
Counts
160 → 160
Iterations

Useful iterations: 0 (35.0ms)

IterNodesCost
051315824

prune297.0ms

Filtered
113 candidates to 160 candidates (-41.6%)
Pruning

8 alts after pruning (8 fresh and 0 done)

PrunedKeptTotal
New1555160
Fresh639
Picked101
Done000
Total1628170

Merged error: 37.5b

Counts
170 → 8

localize21.0ms

Local error

Found 4 expressions with local error:

0.1b
(* (/ i (* (+ alpha (+ beta (* i 2.0))) (/ (+ alpha (+ beta (* i 2.0))) (+ i (+ alpha beta))))) (/ (+ (* i (+ i (+ alpha beta))) (* alpha beta)) (- (* (+ alpha (+ beta (* i 2.0))) (+ alpha (+ beta (* i 2.0)))) 1.0)))
0.3b
(/ i (* (+ alpha (+ beta (* i 2.0))) (/ (+ alpha (+ beta (* i 2.0))) (+ i (+ alpha beta)))))
0.3b
(/ (+ alpha (+ beta (* i 2.0))) (+ i (+ alpha beta)))
41.6b
(/ (+ (* i (+ i (+ alpha beta))) (* alpha beta)) (- (* (+ alpha (+ beta (* i 2.0))) (+ alpha (+ beta (* i 2.0)))) 1.0))

rewrite88.0ms

Algorithm
rewrite-expression-head
Rules
73×*-un-lft-identity
51×times-frac
49×add-exp-log add-cbrt-cube
48×add-sqr-sqrt
36×add-cube-cbrt
21×distribute-lft-out
18×cbrt-undiv div-exp associate-*r*
16×associate-/r/
14×prod-exp cbrt-unprod
12×associate-*l*
10×associate-/r* associate-/l*
7×flip3-+ flip-+ difference-of-squares
6×pow1
5×frac-times associate-*l/ div-inv
4×associate-/l/ add-log-exp
3×frac-2neg associate-*r/ clear-num
2×flip3-- flip-- unswap-sqr
1×pow-prod-down *-commutative
Counts
4 → 168
Calls
4 calls:
39.0ms
(* (/ i (* (+ alpha (+ beta (* i 2.0))) (/ (+ alpha (+ beta (* i 2.0))) (+ i (+ alpha beta))))) (/ (+ (* i (+ i (+ alpha beta))) (* alpha beta)) (- (* (+ alpha (+ beta (* i 2.0))) (+ alpha (+ beta (* i 2.0)))) 1.0)))
15.0ms
(/ i (* (+ alpha (+ beta (* i 2.0))) (/ (+ alpha (+ beta (* i 2.0))) (+ i (+ alpha beta)))))
10.0ms
(/ (+ alpha (+ beta (* i 2.0))) (+ i (+ alpha beta)))
18.0ms
(/ (+ (* i (+ i (+ alpha beta))) (* alpha beta)) (- (* (+ alpha (+ beta (* i 2.0))) (+ alpha (+ beta (* i 2.0)))) 1.0))

series404.0ms

Counts
4 → 12
Calls
4 calls:
319.0ms
(* (/ i (* (+ alpha (+ beta (* i 2.0))) (/ (+ alpha (+ beta (* i 2.0))) (+ i (+ alpha beta))))) (/ (+ (* i (+ i (+ alpha beta))) (* alpha beta)) (- (* (+ alpha (+ beta (* i 2.0))) (+ alpha (+ beta (* i 2.0)))) 1.0)))
24.0ms
(/ i (* (+ alpha (+ beta (* i 2.0))) (/ (+ alpha (+ beta (* i 2.0))) (+ i (+ alpha beta)))))
14.0ms
(/ (+ alpha (+ beta (* i 2.0))) (+ i (+ alpha beta)))
46.0ms
(/ (+ (* i (+ i (+ alpha beta))) (* alpha beta)) (- (* (+ alpha (+ beta (* i 2.0))) (+ alpha (+ beta (* i 2.0)))) 1.0))

simplify60.0ms

Algorithm
egg-herbie
Counts
180 → 180
Iterations

Useful iterations: 0 (32.0ms)

IterNodesCost
057136072

prune391.0ms

Filtered
125 candidates to 180 candidates (-44.0%)
Pruning

9 alts after pruning (9 fresh and 0 done)

PrunedKeptTotal
New1737180
Fresh527
Picked101
Done000
Total1799188

Merged error: 35.1b

Counts
188 → 9

localize29.0ms

Local error

Found 4 expressions with local error:

0.3b
(/ (sqrt (+ (* i (+ i (+ alpha beta))) (* alpha beta))) (+ alpha (+ beta (+ (* i 2.0) (sqrt 1.0)))))
0.3b
(/ (sqrt (+ (* i (+ i (+ alpha beta))) (* alpha beta))) (+ alpha (+ beta (- (* i 2.0) (sqrt 1.0)))))
35.9b
(sqrt (+ (* i (+ i (+ alpha beta))) (* alpha beta)))
35.9b
(sqrt (+ (* i (+ i (+ alpha beta))) (* alpha beta)))

rewrite49.0ms

Algorithm
rewrite-expression-head
Rules
114×*-un-lft-identity
60×times-frac
46×add-sqr-sqrt
44×add-cube-cbrt
42×sqrt-prod distribute-lft-out
12×associate-/l*
10×associate-/r*
8×add-exp-log sqrt-div 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 → 144
Calls
4 calls:
15.0ms
(/ (sqrt (+ (* i (+ i (+ alpha beta))) (* alpha beta))) (+ alpha (+ beta (+ (* i 2.0) (sqrt 1.0)))))
15.0ms
(/ (sqrt (+ (* i (+ i (+ alpha beta))) (* alpha beta))) (+ alpha (+ beta (- (* i 2.0) (sqrt 1.0)))))
7.0ms
(sqrt (+ (* i (+ i (+ alpha beta))) (* alpha beta)))
7.0ms
(sqrt (+ (* i (+ i (+ alpha beta))) (* alpha beta)))

series161.0ms

Counts
4 → 12
Calls
4 calls:
48.0ms
(/ (sqrt (+ (* i (+ i (+ alpha beta))) (* alpha beta))) (+ alpha (+ beta (+ (* i 2.0) (sqrt 1.0)))))
49.0ms
(/ (sqrt (+ (* i (+ i (+ alpha beta))) (* alpha beta))) (+ alpha (+ beta (- (* i 2.0) (sqrt 1.0)))))
29.0ms
(sqrt (+ (* i (+ i (+ alpha beta))) (* alpha beta)))
33.0ms
(sqrt (+ (* i (+ i (+ alpha beta))) (* alpha beta)))

simplify40.0ms

Algorithm
egg-herbie
Counts
156 → 156
Iterations

Useful iterations: 0 (20.0ms)

IterNodesCost
050874580

prune287.0ms

Filtered
98 candidates to 156 candidates (-59.2%)
Pruning

10 alts after pruning (9 fresh and 1 done)

PrunedKeptTotal
New1542156
Fresh178
Picked011
Done000
Total15510165

Merged error: 35.1b

Counts
165 → 10

regimes259.0ms

Accuracy

33.2% (2.5b remaining)

Error of 36.4b against oracle of 33.9b and baseline of 37.6b

bsearch249.0ms

Steps
ItersRangePoint
8
5.28533136982728e+195
7.386511456253822e+198
5.380345921875369e+195

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
04876
14876

end0.0ms

analyze39.0ms

Algorithm
search
Search
TrueOtherFalseIter
0%14%86%0
0%14%86%1
0%14%86%2
0%14%86%3
0%14%86%4
0%14%86%5
0%14%86%6
8.1%5.9%86%7
10.3%3.7%86%8
12.6%1.5%86%9
13.9%0.1%86%10
14%0%86%11
14%0%86%12
14%0%86%13
14%0%86%14

sample966.0ms

Algorithm
intervals
Results
628.0ms8000×body80valid
164.0ms8000×pre80true

Profiling

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