Details

Time bar (total: 6.6s)

analyze46.0ms

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

sample34.0ms

Algorithm
intervals
Results
20.0ms256×body80valid
5.0ms256×pre80true

simplify26.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (24.0ms)

IterNodesCost
0523053

prune14.0ms

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: 47.3b

Counts
2 → 2

localize17.0ms

Local error

Found 4 expressions with local error:

0.0b
(* (/ i (+ alpha (+ beta (* i 2.0)))) (+ i (+ alpha beta)))
0.0b
(* (+ alpha (+ beta (* i 2.0))) (- (* (+ alpha (+ beta (* i 2.0))) (+ alpha (+ beta (* i 2.0)))) 1.0))
4.5b
(* (* (/ i (+ alpha (+ beta (* i 2.0)))) (+ i (+ alpha beta))) (/ (+ (* i (+ i (+ alpha beta))) (* alpha beta)) (* (+ alpha (+ beta (* i 2.0))) (- (* (+ alpha (+ beta (* i 2.0))) (+ alpha (+ beta (* i 2.0)))) 1.0))))
46.1b
(/ (+ (* i (+ i (+ alpha beta))) (* alpha beta)) (* (+ alpha (+ beta (* i 2.0))) (- (* (+ alpha (+ beta (* i 2.0))) (+ alpha (+ beta (* i 2.0)))) 1.0)))

rewrite105.0ms

Algorithm
rewrite-expression-head
Rules
52×add-exp-log add-cbrt-cube
32×*-un-lft-identity
27×add-sqr-sqrt
24×associate-*r*
23×frac-times associate-*l*
22×prod-exp cbrt-unprod
19×add-cube-cbrt times-frac
18×associate-/r/
17×flip3-+ flip-+
14×associate-*l/
13×pow1 associate-*r/
12×cbrt-undiv div-exp
9×flip3-- flip--
7×distribute-lft-out
6×distribute-rgt-in distribute-lft-in
5×pow-prod-down
4×associate--l+ add-log-exp
3×*-commutative div-inv associate-/l* unswap-sqr
2×sub-neg associate-/l/
1×frac-2neg clear-num associate-/r* difference-of-squares
Counts
4 → 165
Calls
4 calls:
14.0ms
(* (/ i (+ alpha (+ beta (* i 2.0)))) (+ i (+ alpha beta)))
18.0ms
(* (+ alpha (+ beta (* i 2.0))) (- (* (+ alpha (+ beta (* i 2.0))) (+ alpha (+ beta (* i 2.0)))) 1.0))
41.0ms
(* (* (/ i (+ alpha (+ beta (* i 2.0)))) (+ i (+ alpha beta))) (/ (+ (* i (+ i (+ alpha beta))) (* alpha beta)) (* (+ alpha (+ beta (* i 2.0))) (- (* (+ alpha (+ beta (* i 2.0))) (+ alpha (+ beta (* i 2.0)))) 1.0))))
26.0ms
(/ (+ (* i (+ i (+ alpha beta))) (* alpha beta)) (* (+ alpha (+ beta (* i 2.0))) (- (* (+ alpha (+ beta (* i 2.0))) (+ alpha (+ beta (* i 2.0)))) 1.0)))

series732.0ms

Counts
4 → 12
Calls
4 calls:
15.0ms
(* (/ i (+ alpha (+ beta (* i 2.0)))) (+ i (+ alpha beta)))
56.0ms
(* (+ alpha (+ beta (* i 2.0))) (- (* (+ alpha (+ beta (* i 2.0))) (+ alpha (+ beta (* i 2.0)))) 1.0))
308.0ms
(* (* (/ i (+ alpha (+ beta (* i 2.0)))) (+ i (+ alpha beta))) (/ (+ (* i (+ i (+ alpha beta))) (* alpha beta)) (* (+ alpha (+ beta (* i 2.0))) (- (* (+ alpha (+ beta (* i 2.0))) (+ alpha (+ beta (* i 2.0)))) 1.0))))
353.0ms
(/ (+ (* i (+ i (+ alpha beta))) (* alpha beta)) (* (+ alpha (+ beta (* i 2.0))) (- (* (+ alpha (+ beta (* i 2.0))) (+ alpha (+ beta (* i 2.0)))) 1.0)))

simplify80.0ms

Algorithm
egg-herbie
Counts
177 → 177
Iterations

Useful iterations: 0 (53.0ms)

IterNodesCost
050125739

prune359.0ms

Filtered
129 candidates to 177 candidates (-37.2%)
Pruning

4 alts after pruning (4 fresh and 0 done)

PrunedKeptTotal
New1734177
Fresh101
Picked101
Done000
Total1754179

Merged error: 37.2b

Counts
179 → 4

localize17.0ms

Local error

Found 4 expressions with local error:

0.0b
(/ i (+ alpha (+ beta (* i 2.0))))
0.0b
(* (/ i (+ alpha (+ beta (* i 2.0)))) (/ (+ i (+ alpha beta)) (+ alpha (+ beta (* i 2.0)))))
0.1b
(* (* (/ i (+ alpha (+ beta (* i 2.0)))) (/ (+ i (+ alpha beta)) (+ alpha (+ beta (* i 2.0))))) (/ (+ (* i (+ i (+ alpha beta))) (* alpha beta)) (- (* (+ alpha (+ beta (* i 2.0))) (+ alpha (+ beta (* i 2.0)))) 1.0)))
40.3b
(/ (+ (* i (+ i (+ alpha beta))) (* alpha beta)) (- (* (+ alpha (+ beta (* i 2.0))) (+ alpha (+ beta (* i 2.0)))) 1.0))

rewrite99.0ms

Algorithm
rewrite-expression-head
Rules
92×*-un-lft-identity
72×times-frac
67×add-sqr-sqrt
61×add-exp-log add-cbrt-cube
48×add-cube-cbrt
44×associate-*r*
24×distribute-lft-out
22×prod-exp cbrt-unprod
19×cbrt-undiv div-exp associate-*l*
11×pow1
10×associate-/r/
8×associate-/r*
7×difference-of-squares
6×frac-times associate-*l/ associate-/l*
5×div-inv
4×flip3-+ associate-*r/ pow-prod-down flip-+ add-log-exp unswap-sqr
2×flip3-- frac-2neg clear-num *-commutative flip-- associate-/l/
Counts
4 → 192
Calls
4 calls:
6.0ms
(/ i (+ alpha (+ beta (* i 2.0))))
25.0ms
(* (/ i (+ alpha (+ beta (* i 2.0)))) (/ (+ i (+ alpha beta)) (+ alpha (+ beta (* i 2.0)))))
37.0ms
(* (* (/ i (+ alpha (+ beta (* i 2.0)))) (/ (+ i (+ alpha beta)) (+ alpha (+ beta (* i 2.0))))) (/ (+ (* i (+ i (+ alpha beta))) (* alpha beta)) (- (* (+ alpha (+ beta (* i 2.0))) (+ alpha (+ beta (* i 2.0)))) 1.0)))
23.0ms
(/ (+ (* i (+ i (+ alpha beta))) (* alpha beta)) (- (* (+ alpha (+ beta (* i 2.0))) (+ alpha (+ beta (* i 2.0)))) 1.0))

series400.0ms

Counts
4 → 12
Calls
4 calls:
12.0ms
(/ i (+ alpha (+ beta (* i 2.0))))
22.0ms
(* (/ i (+ alpha (+ beta (* i 2.0)))) (/ (+ i (+ alpha beta)) (+ alpha (+ beta (* i 2.0)))))
317.0ms
(* (* (/ i (+ alpha (+ beta (* i 2.0)))) (/ (+ i (+ alpha beta)) (+ alpha (+ beta (* i 2.0))))) (/ (+ (* i (+ i (+ alpha beta))) (* alpha beta)) (- (* (+ alpha (+ beta (* i 2.0))) (+ alpha (+ beta (* i 2.0)))) 1.0)))
48.0ms
(/ (+ (* i (+ i (+ alpha beta))) (* alpha beta)) (- (* (+ alpha (+ beta (* i 2.0))) (+ alpha (+ beta (* i 2.0)))) 1.0))

simplify71.0ms

Algorithm
egg-herbie
Counts
204 → 204
Iterations

Useful iterations: 0 (45.0ms)

IterNodesCost
050286381

prune315.0ms

Filtered
131 candidates to 204 candidates (-55.7%)
Pruning

8 alts after pruning (7 fresh and 1 done)

PrunedKeptTotal
New2004204
Fresh033
Picked011
Done000
Total2008208

Merged error: 34.6b

Counts
208 → 8

localize21.0ms

Local error

Found 4 expressions with local error:

0.0b
(* (/ i (+ alpha (+ beta (* i 2.0)))) (/ (+ i (+ alpha beta)) (+ alpha (+ beta (* i 2.0)))))
0.0b
(/ (/ (+ (* i (+ i (+ alpha beta))) (* alpha beta)) (+ alpha (+ beta (+ (* i 2.0) (sqrt 1.0))))) (- (+ alpha (+ beta (* i 2.0))) (sqrt 1.0)))
0.1b
(* (* (/ i (+ alpha (+ beta (* i 2.0)))) (/ (+ i (+ alpha beta)) (+ alpha (+ beta (* i 2.0))))) (/ (/ (+ (* i (+ i (+ alpha beta))) (* alpha beta)) (+ alpha (+ beta (+ (* i 2.0) (sqrt 1.0))))) (- (+ alpha (+ beta (* i 2.0))) (sqrt 1.0))))
34.4b
(/ (+ (* i (+ i (+ alpha beta))) (* alpha beta)) (+ alpha (+ beta (+ (* i 2.0) (sqrt 1.0)))))

rewrite176.0ms

Algorithm
rewrite-expression-head
Rules
707×*-un-lft-identity
570×times-frac
395×add-sqr-sqrt
211×add-cube-cbrt
210×distribute-lft-out
179×associate-*r*
92×add-exp-log add-cbrt-cube
86×distribute-lft-out-- difference-of-squares
43×sqrt-prod
40×associate-/r/
35×cbrt-undiv div-exp
31×prod-exp cbrt-unprod
24×associate-/l*
20×div-inv
19×flip3-+ associate-*l* flip-+
12×associate-/r*
11×pow1
6×frac-times associate-*l/
4×associate-*r/ pow-prod-down add-log-exp unswap-sqr
3×associate-/l/
2×flip3-- frac-2neg clear-num *-commutative flip--
Counts
4 → 500
Calls
4 calls:
25.0ms
(* (/ i (+ alpha (+ beta (* i 2.0)))) (/ (+ i (+ alpha beta)) (+ alpha (+ beta (* i 2.0)))))
32.0ms
(/ (/ (+ (* i (+ i (+ alpha beta))) (* alpha beta)) (+ alpha (+ beta (+ (* i 2.0) (sqrt 1.0))))) (- (+ alpha (+ beta (* i 2.0))) (sqrt 1.0)))
60.0ms
(* (* (/ i (+ alpha (+ beta (* i 2.0)))) (/ (+ i (+ alpha beta)) (+ alpha (+ beta (* i 2.0))))) (/ (/ (+ (* i (+ i (+ alpha beta))) (* alpha beta)) (+ alpha (+ beta (+ (* i 2.0) (sqrt 1.0))))) (- (+ alpha (+ beta (* i 2.0))) (sqrt 1.0))))
18.0ms
(/ (+ (* i (+ i (+ alpha beta))) (* alpha beta)) (+ alpha (+ beta (+ (* i 2.0) (sqrt 1.0)))))

series466.0ms

Counts
4 → 12
Calls
4 calls:
22.0ms
(* (/ i (+ alpha (+ beta (* i 2.0)))) (/ (+ i (+ alpha beta)) (+ alpha (+ beta (* i 2.0)))))
44.0ms
(/ (/ (+ (* i (+ i (+ alpha beta))) (* alpha beta)) (+ alpha (+ beta (+ (* i 2.0) (sqrt 1.0))))) (- (+ alpha (+ beta (* i 2.0))) (sqrt 1.0)))
373.0ms
(* (* (/ i (+ alpha (+ beta (* i 2.0)))) (/ (+ i (+ alpha beta)) (+ alpha (+ beta (* i 2.0))))) (/ (/ (+ (* i (+ i (+ alpha beta))) (* alpha beta)) (+ alpha (+ beta (+ (* i 2.0) (sqrt 1.0))))) (- (+ alpha (+ beta (* i 2.0))) (sqrt 1.0))))
27.0ms
(/ (+ (* i (+ i (+ alpha beta))) (* alpha beta)) (+ alpha (+ beta (+ (* i 2.0) (sqrt 1.0)))))

simplify157.0ms

Algorithm
egg-herbie
Counts
512 → 512
Iterations

Useful iterations: 0 (58.0ms)

IterNodesCost
0504124337

prune1.2s

Filtered
232 candidates to 512 candidates (-120.7%)
Pruning

9 alts after pruning (7 fresh and 2 done)

PrunedKeptTotal
New5093512
Fresh246
Picked011
Done011
Total5119520

Merged error: 7.0b

Counts
520 → 9

localize20.0ms

Local error

Found 4 expressions with local error:

0.0b
(/ i (+ alpha (+ beta (* i 2.0))))
0.0b
(* (/ i (+ alpha (+ beta (* i 2.0)))) (/ (+ i (+ alpha beta)) (+ alpha (+ beta (* i 2.0)))))
0.0b
(/ (+ (* i 0.5) (- (* 0.125 (/ 1.0 i)) (* (sqrt 1.0) 0.25))) (- (+ alpha (+ beta (* i 2.0))) (sqrt 1.0)))
0.1b
(* (* (/ i (+ alpha (+ beta (* i 2.0)))) (/ (+ i (+ alpha beta)) (+ alpha (+ beta (* i 2.0))))) (/ (+ (* i 0.5) (- (* 0.125 (/ 1.0 i)) (* (sqrt 1.0) 0.25))) (- (+ alpha (+ beta (* i 2.0))) (sqrt 1.0))))

rewrite93.0ms

Algorithm
rewrite-expression-head
Rules
133×*-un-lft-identity
94×add-sqr-sqrt
90×times-frac
61×add-exp-log add-cbrt-cube
54×add-cube-cbrt
53×associate-*r*
31×distribute-lft-out
22×prod-exp cbrt-unprod
19×cbrt-undiv div-exp associate-*l*
14×distribute-lft-out-- difference-of-squares
11×pow1 associate-/r*
10×associate-/r/
7×sqrt-prod
6×frac-times associate-*l/ associate-/l*
5×div-inv
4×flip3-+ associate-*r/ pow-prod-down flip-+ add-log-exp unswap-sqr
2×flip3-- frac-2neg clear-num *-commutative flip-- associate-/l/
1×associate-+r- div-sub
Counts
4 → 214
Calls
4 calls:
6.0ms
(/ i (+ alpha (+ beta (* i 2.0))))
25.0ms
(* (/ i (+ alpha (+ beta (* i 2.0)))) (/ (+ i (+ alpha beta)) (+ alpha (+ beta (* i 2.0)))))
18.0ms
(/ (+ (* i 0.5) (- (* 0.125 (/ 1.0 i)) (* (sqrt 1.0) 0.25))) (- (+ alpha (+ beta (* i 2.0))) (sqrt 1.0)))
35.0ms
(* (* (/ i (+ alpha (+ beta (* i 2.0)))) (/ (+ i (+ alpha beta)) (+ alpha (+ beta (* i 2.0))))) (/ (+ (* i 0.5) (- (* 0.125 (/ 1.0 i)) (* (sqrt 1.0) 0.25))) (- (+ alpha (+ beta (* i 2.0))) (sqrt 1.0))))

series119.0ms

Counts
4 → 12
Calls
4 calls:
12.0ms
(/ i (+ alpha (+ beta (* i 2.0))))
23.0ms
(* (/ i (+ alpha (+ beta (* i 2.0)))) (/ (+ i (+ alpha beta)) (+ alpha (+ beta (* i 2.0)))))
20.0ms
(/ (+ (* i 0.5) (- (* 0.125 (/ 1.0 i)) (* (sqrt 1.0) 0.25))) (- (+ alpha (+ beta (* i 2.0))) (sqrt 1.0)))
63.0ms
(* (* (/ i (+ alpha (+ beta (* i 2.0)))) (/ (+ i (+ alpha beta)) (+ alpha (+ beta (* i 2.0))))) (/ (+ (* i 0.5) (- (* 0.125 (/ 1.0 i)) (* (sqrt 1.0) 0.25))) (- (+ alpha (+ beta (* i 2.0))) (sqrt 1.0))))

simplify63.0ms

Algorithm
egg-herbie
Counts
226 → 226
Iterations

Useful iterations: 0 (33.0ms)

IterNodesCost
053467111

prune532.0ms

Filtered
134 candidates to 226 candidates (-68.7%)
Pruning

20 alts after pruning (18 fresh and 2 done)

PrunedKeptTotal
New21412226
Fresh066
Picked101
Done022
Total21520235

Merged error: 7.0b

Counts
235 → 20

regimes423.0ms

Accuracy

48.8% (3.0b remaining)

Error of 10.4b against oracle of 7.4b and baseline of 13.2b

bsearch16.0ms

Steps
ItersRangePoint
5
5.025118953569102e+119
1.0539265021819178e+120
9.562673361052236e+119

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
095162
195162

end0.0ms

sample956.0ms

Algorithm
intervals
Results
630.0ms8000×body80valid
168.0ms8000×pre80true

Profiling

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