Details

Time bar (total: 5.2s)

analyze41.0ms

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

sample54.0ms

Algorithm
intervals
Results
30.0ms256×body80valid
8.0ms256×pre80true

simplify26.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (24.0ms)

IterNodesCost
0523053

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: 46.5b

Counts
2 → 2

localize18.0ms

Local error

Found 4 expressions with local error:

0.0b
(* (/ i (+ alpha (+ beta (* i 2.0)))) (+ i (+ alpha beta)))
0.1b
(* (+ alpha (+ beta (* i 2.0))) (- (* (+ alpha (+ beta (* i 2.0))) (+ alpha (+ beta (* i 2.0)))) 1.0))
6.3b
(* (* (/ 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))))
45.2b
(/ (+ (* i (+ i (+ alpha beta))) (* alpha beta)) (* (+ alpha (+ beta (* i 2.0))) (- (* (+ alpha (+ beta (* i 2.0))) (+ alpha (+ beta (* i 2.0)))) 1.0)))

rewrite106.0ms

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:
18.0ms
(* (/ 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))
37.0ms
(* (* (/ 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))))
28.0ms
(/ (+ (* i (+ i (+ alpha beta))) (* alpha beta)) (* (+ alpha (+ beta (* i 2.0))) (- (* (+ alpha (+ beta (* i 2.0))) (+ alpha (+ beta (* i 2.0)))) 1.0)))

series536.0ms

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))
305.0ms
(* (* (/ 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))))
159.0ms
(/ (+ (* i (+ i (+ alpha beta))) (* alpha beta)) (* (+ alpha (+ beta (* i 2.0))) (- (* (+ alpha (+ beta (* i 2.0))) (+ alpha (+ beta (* i 2.0)))) 1.0)))

simplify78.0ms

Algorithm
egg-herbie
Counts
177 → 177
Iterations

Useful iterations: 0 (52.0ms)

IterNodesCost
050125739

prune368.0ms

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

6 alts after pruning (6 fresh and 0 done)

PrunedKeptTotal
New1725177
Fresh011
Picked101
Done000
Total1736179

Merged error: 34.6b

Counts
179 → 6

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 (+ 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)))
39.9b
(/ (+ (* i (+ i (+ alpha beta))) (* alpha beta)) (- (* (+ alpha (+ beta (* i 2.0))) (+ alpha (+ beta (* i 2.0)))) 1.0))

rewrite108.0ms

Algorithm
rewrite-expression-head
Rules
123×*-un-lft-identity
80×times-frac
69×add-sqr-sqrt
61×add-exp-log add-cbrt-cube
50×add-cube-cbrt
44×associate-*r*
41×distribute-lft-out
22×prod-exp cbrt-unprod
19×cbrt-undiv div-exp associate-*l*
11×pow1
10×associate-/r/
8×associate-/r* associate-/l*
7×difference-of-squares
6×frac-times associate-*l/
5×flip3-+ flip-+ div-inv
4×associate-*r/ pow-prod-down associate-/l/ add-log-exp unswap-sqr
2×flip3-- frac-2neg clear-num *-commutative flip--
Counts
4 → 204
Calls
4 calls:
29.0ms
(* (/ i (+ alpha (+ beta (* i 2.0)))) (/ (+ i (+ alpha beta)) (+ alpha (+ beta (* i 2.0)))))
11.0ms
(/ (+ i (+ alpha beta)) (+ alpha (+ beta (* i 2.0))))
38.0ms
(* (* (/ 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)))
21.0ms
(/ (+ (* i (+ i (+ alpha beta))) (* alpha beta)) (- (* (+ alpha (+ beta (* i 2.0))) (+ alpha (+ beta (* i 2.0)))) 1.0))

series391.0ms

Counts
4 → 12
Calls
4 calls:
23.0ms
(* (/ i (+ alpha (+ beta (* i 2.0)))) (/ (+ i (+ alpha beta)) (+ alpha (+ beta (* i 2.0)))))
13.0ms
(/ (+ i (+ alpha beta)) (+ alpha (+ beta (* i 2.0))))
305.0ms
(* (* (/ 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)))
51.0ms
(/ (+ (* i (+ i (+ alpha beta))) (* alpha beta)) (- (* (+ alpha (+ beta (* i 2.0))) (+ alpha (+ beta (* i 2.0)))) 1.0))

simplify65.0ms

Algorithm
egg-herbie
Counts
216 → 216
Iterations

Useful iterations: 0 (33.0ms)

IterNodesCost
050206791

prune370.0ms

Filtered
134 candidates to 216 candidates (-61.2%)
Pruning

8 alts after pruning (8 fresh and 0 done)

PrunedKeptTotal
New2097216
Fresh415
Picked101
Done000
Total2148222

Merged error: 31.6b

Counts
222 → 8

localize28.0ms

Local error

Found 4 expressions with local error:

0.1b
(* (* (/ i (+ alpha (+ beta (* i 2.0)))) (/ (+ i (+ alpha beta)) (+ alpha (+ beta (* i 2.0))))) (* (/ (sqrt (+ (* i (+ i (+ alpha beta))) (* alpha beta))) (+ alpha (+ beta (+ (* i 2.0) (sqrt 1.0))))) (/ (sqrt (+ (* i (+ i (+ alpha beta))) (* alpha beta))) (+ alpha (+ beta (- (* i 2.0) (sqrt 1.0)))))))
0.2b
(* (/ (sqrt (+ (* i (+ i (+ alpha beta))) (* alpha beta))) (+ alpha (+ beta (+ (* i 2.0) (sqrt 1.0))))) (/ (sqrt (+ (* i (+ i (+ alpha beta))) (* alpha beta))) (+ alpha (+ beta (- (* i 2.0) (sqrt 1.0))))))
32.5b
(sqrt (+ (* i (+ i (+ alpha beta))) (* alpha beta)))
32.5b
(sqrt (+ (* i (+ i (+ alpha beta))) (* alpha beta)))

rewrite142.0ms

Algorithm
rewrite-expression-head
Rules
146×add-exp-log add-cbrt-cube
100×*-un-lft-identity
72×add-sqr-sqrt times-frac
69×prod-exp cbrt-unprod
44×cbrt-undiv div-exp
42×sqrt-prod
40×add-cube-cbrt
37×associate-*r* associate-*l*
36×distribute-lft-out
20×pow1
18×frac-times
12×associate-*r/ associate-*l/
9×pow-prod-down unswap-sqr
4×flip3-+ sqrt-div associate-/r/ flip-+ add-log-exp
2×rem-sqrt-square sqrt-pow1 pow1/2 *-commutative div-inv
Counts
4 → 210
Calls
4 calls:
58.0ms
(* (* (/ i (+ alpha (+ beta (* i 2.0)))) (/ (+ i (+ alpha beta)) (+ alpha (+ beta (* i 2.0))))) (* (/ (sqrt (+ (* i (+ i (+ alpha beta))) (* alpha beta))) (+ alpha (+ beta (+ (* i 2.0) (sqrt 1.0))))) (/ (sqrt (+ (* i (+ i (+ alpha beta))) (* alpha beta))) (+ alpha (+ beta (- (* i 2.0) (sqrt 1.0)))))))
54.0ms
(* (/ (sqrt (+ (* i (+ i (+ alpha beta))) (* alpha beta))) (+ alpha (+ beta (+ (* i 2.0) (sqrt 1.0))))) (/ (sqrt (+ (* i (+ i (+ alpha beta))) (* alpha beta))) (+ alpha (+ beta (- (* i 2.0) (sqrt 1.0))))))
9.0ms
(sqrt (+ (* i (+ i (+ alpha beta))) (* alpha beta)))
8.0ms
(sqrt (+ (* i (+ i (+ alpha beta))) (* alpha beta)))

series496.0ms

Counts
4 → 12
Calls
4 calls:
384.0ms
(* (* (/ i (+ alpha (+ beta (* i 2.0)))) (/ (+ i (+ alpha beta)) (+ alpha (+ beta (* i 2.0))))) (* (/ (sqrt (+ (* i (+ i (+ alpha beta))) (* alpha beta))) (+ alpha (+ beta (+ (* i 2.0) (sqrt 1.0))))) (/ (sqrt (+ (* i (+ i (+ alpha beta))) (* alpha beta))) (+ alpha (+ beta (- (* i 2.0) (sqrt 1.0)))))))
45.0ms
(* (/ (sqrt (+ (* i (+ i (+ alpha beta))) (* alpha beta))) (+ alpha (+ beta (+ (* i 2.0) (sqrt 1.0))))) (/ (sqrt (+ (* i (+ i (+ alpha beta))) (* alpha beta))) (+ alpha (+ beta (- (* i 2.0) (sqrt 1.0))))))
30.0ms
(sqrt (+ (* i (+ i (+ alpha beta))) (* alpha beta)))
36.0ms
(sqrt (+ (* i (+ i (+ alpha beta))) (* alpha beta)))

simplify128.0ms

Algorithm
egg-herbie
Counts
222 → 222
Iterations

Useful iterations: 0 (84.0ms)

IterNodesCost
050349612

prune362.0ms

Filtered
108 candidates to 222 candidates (-105.6%)
Pruning

7 alts after pruning (7 fresh and 0 done)

PrunedKeptTotal
New2202222
Fresh257
Picked101
Done000
Total2237230

Merged error: 31.6b

Counts
230 → 7

localize28.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (sqrt (+ (* i (+ i (+ alpha beta))) (* alpha beta))) (+ alpha (+ beta (+ (* i 2.0) (sqrt 1.0)))))
0.1b
(/ (sqrt (+ (* i (+ i (+ alpha beta))) (* alpha beta))) (- (+ alpha (+ beta (* i 2.0))) (sqrt 1.0)))
32.5b
(sqrt (+ (* i (+ i (+ alpha beta))) (* alpha beta)))
32.5b
(sqrt (+ (* i (+ i (+ alpha beta))) (* alpha beta)))

rewrite56.0ms

Algorithm
rewrite-expression-head
Rules
118×*-un-lft-identity
78×add-sqr-sqrt
72×times-frac
55×sqrt-prod
48×add-cube-cbrt
28×distribute-lft-out
14×distribute-lft-out-- difference-of-squares
12×associate-/r* associate-/l*
8×add-exp-log sqrt-div add-cbrt-cube
6×pow1
5×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
1×flip3-- flip--
Counts
4 → 158
Calls
4 calls:
17.0ms
(/ (sqrt (+ (* i (+ i (+ alpha beta))) (* alpha beta))) (+ alpha (+ beta (+ (* i 2.0) (sqrt 1.0)))))
17.0ms
(/ (sqrt (+ (* i (+ i (+ alpha beta))) (* alpha beta))) (- (+ alpha (+ beta (* i 2.0))) (sqrt 1.0)))
8.0ms
(sqrt (+ (* i (+ i (+ alpha beta))) (* alpha beta)))
8.0ms
(sqrt (+ (* i (+ i (+ alpha beta))) (* alpha beta)))

series162.0ms

Counts
4 → 12
Calls
4 calls:
48.0ms
(/ (sqrt (+ (* i (+ i (+ alpha beta))) (* alpha beta))) (+ alpha (+ beta (+ (* i 2.0) (sqrt 1.0)))))
50.0ms
(/ (sqrt (+ (* i (+ i (+ alpha beta))) (* alpha beta))) (- (+ alpha (+ beta (* i 2.0))) (sqrt 1.0)))
30.0ms
(sqrt (+ (* i (+ i (+ alpha beta))) (* alpha beta)))
34.0ms
(sqrt (+ (* i (+ i (+ alpha beta))) (* alpha beta)))

simplify78.0ms

Algorithm
egg-herbie
Counts
170 → 170
Iterations

Useful iterations: 0 (52.0ms)

IterNodesCost
051365222

prune309.0ms

Filtered
104 candidates to 170 candidates (-63.5%)
Pruning

7 alts after pruning (6 fresh and 1 done)

PrunedKeptTotal
New1700170
Fresh066
Picked011
Done000
Total1707177

Merged error: 31.6b

Counts
177 → 7

regimes222.0ms

Accuracy

34% (2.3b remaining)

Error of 35.8b against oracle of 33.5b and baseline of 37.0b

bsearch22.0ms

Steps
ItersRangePoint
8
5.837724927607128e+212
3.0128089446176277e+215
5.8969926040431975e+212

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
05376
15376

end0.0ms

sample971.0ms

Algorithm
intervals
Results
623.0ms8000×body80valid
174.0ms8000×pre80true

Profiling

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