Details

Time bar (total: 5.9s)

analyze44.0ms

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

sample35.0ms

Algorithm
intervals
Results
20.0ms256×body80valid
5.0ms256×pre80true

simplify25.0ms

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: 48.4b

Counts
2 → 2

localize19.0ms

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))
3.9b
(* (* (/ 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))))
46.9b
(/ (+ (* i (+ i (+ alpha beta))) (* alpha beta)) (* (+ alpha (+ beta (* i 2.0))) (- (* (+ alpha (+ beta (* i 2.0))) (+ alpha (+ beta (* i 2.0)))) 1.0)))

rewrite104.0ms

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))
40.0ms
(* (* (/ 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))))
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)))

series537.0ms

Counts
4 → 12
Calls
4 calls:
15.0ms
(* (/ i (+ alpha (+ beta (* i 2.0)))) (+ i (+ alpha beta)))
57.0ms
(* (+ alpha (+ beta (* i 2.0))) (- (* (+ alpha (+ beta (* i 2.0))) (+ alpha (+ beta (* i 2.0)))) 1.0))
302.0ms
(* (* (/ 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))))
163.0ms
(/ (+ (* i (+ i (+ alpha beta))) (* alpha beta)) (* (+ alpha (+ beta (* i 2.0))) (- (* (+ alpha (+ beta (* i 2.0))) (+ alpha (+ beta (* i 2.0)))) 1.0)))

simplify79.0ms

Algorithm
egg-herbie
Counts
177 → 177
Iterations

Useful iterations: 0 (52.0ms)

IterNodesCost
050125739

prune378.0ms

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

5 alts after pruning (5 fresh and 0 done)

PrunedKeptTotal
New1725177
Fresh101
Picked101
Done000
Total1745179

Merged error: 33.2b

Counts
179 → 5

localize19.0ms

Local error

Found 4 expressions with local error:

0.0b
(* (+ alpha (+ beta (* i 2.0))) (+ 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)))
37.4b
(/ (+ (* i (+ i (+ alpha beta))) (* alpha beta)) (- (* (+ alpha (+ beta (* i 2.0))) (+ alpha (+ beta (* i 2.0)))) 1.0))

rewrite93.0ms

Algorithm
rewrite-expression-head
Rules
87×*-un-lft-identity
51×add-exp-log add-cbrt-cube
45×add-sqr-sqrt
44×times-frac
36×add-cube-cbrt
27×distribute-lft-out
22×associate-*r*
19×prod-exp cbrt-unprod
16×pow1
15×cbrt-undiv div-exp
9×frac-times flip3-+ flip-+
8×associate-/r* associate-/l*
7×associate-*l/ difference-of-squares
6×swap-sqr associate-/r/
5×associate-*r/ associate-*l*
4×pow-prod-down associate-/l/ add-log-exp
3×div-inv
2×flip3-- frac-2neg clear-num *-commutative flip--
1×pow2 distribute-rgt-in distribute-lft-in pow-plus pow-sqr pow-prod-up unswap-sqr
Counts
4 → 176
Calls
4 calls:
11.0ms
(* (+ alpha (+ beta (* i 2.0))) (+ alpha (+ beta (* i 2.0))))
11.0ms
(/ (+ i (+ alpha beta)) (+ alpha (+ beta (* i 2.0))))
39.0ms
(* (* (/ 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)))
25.0ms
(/ (+ (* i (+ i (+ alpha beta))) (* alpha beta)) (- (* (+ alpha (+ beta (* i 2.0))) (+ alpha (+ beta (* i 2.0)))) 1.0))

series384.0ms

Counts
4 → 12
Calls
4 calls:
12.0ms
(* (+ alpha (+ beta (* i 2.0))) (+ alpha (+ beta (* i 2.0))))
15.0ms
(/ (+ i (+ alpha beta)) (+ alpha (+ beta (* i 2.0))))
306.0ms
(* (* (/ 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))

simplify76.0ms

Algorithm
egg-herbie
Counts
188 → 188
Iterations

Useful iterations: 0 (51.0ms)

IterNodesCost
050175171

prune540.0ms

Filtered
117 candidates to 188 candidates (-60.7%)
Pruning

7 alts after pruning (7 fresh and 0 done)

PrunedKeptTotal
New1844188
Fresh134
Picked101
Done000
Total1867193

Merged error: 30.3b

Counts
193 → 7

localize27.0ms

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)))))))
0.1b
(* (/ (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))))))
31.1b
(sqrt (+ (* i (+ i (+ alpha beta))) (* alpha beta)))
31.1b
(sqrt (+ (* i (+ i (+ alpha beta))) (* alpha beta)))

rewrite139.0ms

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:
56.0ms
(* (* (/ 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))))))
8.0ms
(sqrt (+ (* i (+ i (+ alpha beta))) (* alpha beta)))
8.0ms
(sqrt (+ (* i (+ i (+ alpha beta))) (* alpha beta)))

series489.0ms

Counts
4 → 12
Calls
4 calls:
382.0ms
(* (* (/ 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)))))))
44.0ms
(* (/ (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))))))
33.0ms
(sqrt (+ (* i (+ i (+ alpha beta))) (* alpha beta)))
30.0ms
(sqrt (+ (* i (+ i (+ alpha beta))) (* alpha beta)))

simplify112.0ms

Algorithm
egg-herbie
Counts
222 → 222
Iterations

Useful iterations: 0 (71.0ms)

IterNodesCost
050349612

prune372.0ms

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

7 alts after pruning (6 fresh and 1 done)

PrunedKeptTotal
New2202222
Fresh246
Picked011
Done000
Total2227229

Merged error: 30.3b

Counts
229 → 7

localize26.0ms

Local error

Found 4 expressions with local error:

0.0b
(/ (+ i (+ alpha beta)) (+ alpha (+ beta (* i 2.0))))
0.1b
(* (/ (+ (* i (+ i (+ alpha beta))) (* alpha beta)) (+ alpha (+ beta (+ (* i 2.0) (sqrt 1.0))))) (* (/ i (+ alpha (+ beta (* i 2.0)))) (/ (+ i (+ alpha beta)) (+ alpha (+ beta (* i 2.0))))))
0.1b
(/ (* (/ (+ (* i (+ i (+ alpha beta))) (* alpha beta)) (+ alpha (+ beta (+ (* i 2.0) (sqrt 1.0))))) (* (/ i (+ alpha (+ beta (* i 2.0)))) (/ (+ i (+ alpha beta)) (+ alpha (+ beta (* i 2.0)))))) (+ alpha (+ beta (- (* i 2.0) (sqrt 1.0)))))
31.2b
(/ (+ (* i (+ i (+ alpha beta))) (* alpha beta)) (+ alpha (+ beta (+ (* i 2.0) (sqrt 1.0)))))

rewrite122.0ms

Algorithm
rewrite-expression-head
Rules
118×*-un-lft-identity
102×add-exp-log add-cbrt-cube
55×times-frac
48×distribute-lft-out
39×cbrt-undiv div-exp
36×add-sqr-sqrt add-cube-cbrt prod-exp cbrt-unprod
21×associate-*l*
14×associate-/r*
11×associate-/l/
10×frac-times associate-*r/
9×pow1 associate-/l*
8×associate-/r/
6×flip3-+ associate-*l/ flip-+
4×div-inv add-log-exp
3×frac-2neg pow-prod-down clear-num
1×associate-*r* *-commutative
Counts
4 → 195
Calls
4 calls:
11.0ms
(/ (+ i (+ alpha beta)) (+ alpha (+ beta (* i 2.0))))
35.0ms
(* (/ (+ (* i (+ i (+ alpha beta))) (* alpha beta)) (+ alpha (+ beta (+ (* i 2.0) (sqrt 1.0))))) (* (/ i (+ alpha (+ beta (* i 2.0)))) (/ (+ i (+ alpha beta)) (+ alpha (+ beta (* i 2.0))))))
45.0ms
(/ (* (/ (+ (* i (+ i (+ alpha beta))) (* alpha beta)) (+ alpha (+ beta (+ (* i 2.0) (sqrt 1.0))))) (* (/ i (+ alpha (+ beta (* i 2.0)))) (/ (+ i (+ alpha beta)) (+ alpha (+ beta (* i 2.0)))))) (+ alpha (+ beta (- (* i 2.0) (sqrt 1.0)))))
17.0ms
(/ (+ (* i (+ i (+ alpha beta))) (* alpha beta)) (+ alpha (+ beta (+ (* i 2.0) (sqrt 1.0)))))

series537.0ms

Counts
4 → 12
Calls
4 calls:
13.0ms
(/ (+ i (+ alpha beta)) (+ alpha (+ beta (* i 2.0))))
108.0ms
(* (/ (+ (* i (+ i (+ alpha beta))) (* alpha beta)) (+ alpha (+ beta (+ (* i 2.0) (sqrt 1.0))))) (* (/ i (+ alpha (+ beta (* i 2.0)))) (/ (+ i (+ alpha beta)) (+ alpha (+ beta (* i 2.0))))))
386.0ms
(/ (* (/ (+ (* i (+ i (+ alpha beta))) (* alpha beta)) (+ alpha (+ beta (+ (* i 2.0) (sqrt 1.0))))) (* (/ i (+ alpha (+ beta (* i 2.0)))) (/ (+ i (+ alpha beta)) (+ alpha (+ beta (* i 2.0)))))) (+ alpha (+ beta (- (* i 2.0) (sqrt 1.0)))))
29.0ms
(/ (+ (* i (+ i (+ alpha beta))) (* alpha beta)) (+ alpha (+ beta (+ (* i 2.0) (sqrt 1.0)))))

simplify84.0ms

Algorithm
egg-herbie
Counts
207 → 207
Iterations

Useful iterations: 0 (51.0ms)

IterNodesCost
049777667
149777667

prune346.0ms

Filtered
115 candidates to 207 candidates (-80.0%)
Pruning

8 alts after pruning (6 fresh and 2 done)

PrunedKeptTotal
New2052207
Fresh145
Picked011
Done011
Total2068214

Merged error: 6.1b

Counts
214 → 8

regimes260.0ms

Accuracy

45.8% (3.2b remaining)

Error of 10.3b against oracle of 7.1b and baseline of 13.1b

bsearch21.0ms

Steps
ItersRangePoint
7
3.4121724945211734e+89
2.1652870885560225e+91
4.69796267948655e+90

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
088110
188110

end0.0ms

sample989.0ms

Algorithm
intervals
Results
643.0ms8000×body80valid
173.0ms8000×pre80true

Profiling

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