Details

Time bar (total: 6.0s)

analyze49.0ms

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

sample38.0ms

Algorithm
intervals
Results
22.0ms256×body80valid
6.0ms256×pre80true

simplify26.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (24.0ms)

IterNodesCost
0523053

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: 45.7b

Counts
2 → 2

localize21.0ms

Local error

Found 4 expressions with local error:

0.1b
(* (+ alpha (+ beta (* i 2.0))) (- (* (+ alpha (+ beta (* i 2.0))) (+ alpha (+ beta (* i 2.0)))) 1.0))
0.1b
(* (/ i (+ alpha (+ beta (* i 2.0)))) (+ i (+ alpha beta)))
2.3b
(* (* (/ 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))))
44.7b
(/ (+ (* i (+ i (+ alpha beta))) (* alpha beta)) (* (+ alpha (+ beta (* i 2.0))) (- (* (+ alpha (+ beta (* i 2.0))) (+ alpha (+ beta (* i 2.0)))) 1.0)))

rewrite109.0ms

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
(* (+ alpha (+ beta (* i 2.0))) (- (* (+ alpha (+ beta (* i 2.0))) (+ alpha (+ beta (* i 2.0)))) 1.0))
19.0ms
(* (/ i (+ alpha (+ beta (* i 2.0)))) (+ i (+ alpha beta)))
38.0ms
(* (* (/ 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))))
27.0ms
(/ (+ (* i (+ i (+ alpha beta))) (* alpha beta)) (* (+ alpha (+ beta (* i 2.0))) (- (* (+ alpha (+ beta (* i 2.0))) (+ alpha (+ beta (* i 2.0)))) 1.0)))

series546.0ms

Counts
4 → 12
Calls
4 calls:
57.0ms
(* (+ alpha (+ beta (* i 2.0))) (- (* (+ alpha (+ beta (* i 2.0))) (+ alpha (+ beta (* i 2.0)))) 1.0))
15.0ms
(* (/ i (+ alpha (+ beta (* i 2.0)))) (+ i (+ alpha beta)))
309.0ms
(* (* (/ 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))))
166.0ms
(/ (+ (* i (+ i (+ alpha beta))) (* alpha beta)) (* (+ alpha (+ beta (* i 2.0))) (- (* (+ alpha (+ beta (* i 2.0))) (+ alpha (+ beta (* i 2.0)))) 1.0)))

simplify76.0ms

Algorithm
egg-herbie
Counts
177 → 177
Iterations

Useful iterations: 0 (52.0ms)

IterNodesCost
050125739

prune376.0ms

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

8 alts after pruning (8 fresh and 0 done)

PrunedKeptTotal
New1698177
Fresh101
Picked101
Done000
Total1718179

Merged error: 33.8b

Counts
179 → 8

localize18.0ms

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)))
39.6b
(/ (+ (* 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:
25.0ms
(* (/ 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)))
23.0ms
(/ (+ (* i (+ i (+ alpha beta))) (* alpha beta)) (- (* (+ alpha (+ beta (* i 2.0))) (+ alpha (+ beta (* i 2.0)))) 1.0))

series393.0ms

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))))
311.0ms
(* (* (/ 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)))
47.0ms
(/ (+ (* i (+ i (+ alpha beta))) (* alpha beta)) (- (* (+ alpha (+ beta (* i 2.0))) (+ alpha (+ beta (* i 2.0)))) 1.0))

simplify64.0ms

Algorithm
egg-herbie
Counts
216 → 216
Iterations

Useful iterations: 0 (32.0ms)

IterNodesCost
050206791

prune387.0ms

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

9 alts after pruning (8 fresh and 1 done)

PrunedKeptTotal
New2133216
Fresh257
Picked011
Done000
Total2159224

Merged error: 32.1b

Counts
224 → 9

localize28.0ms

Local error

Found 4 expressions with local error:

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))))) (* (/ 1 (+ alpha (+ beta (+ (* i 2.0) (sqrt 1.0))))) (/ (+ (* i (+ i (+ alpha beta))) (* alpha beta)) (+ alpha (+ beta (- (* i 2.0) (sqrt 1.0)))))))
0.2b
(* (/ 1 (+ alpha (+ beta (+ (* i 2.0) (sqrt 1.0))))) (/ (+ (* i (+ i (+ alpha beta))) (* alpha beta)) (+ alpha (+ beta (- (* i 2.0) (sqrt 1.0))))))
34.5b
(/ (+ (* i (+ i (+ alpha beta))) (* alpha beta)) (+ alpha (+ beta (- (* i 2.0) (sqrt 1.0)))))

rewrite127.0ms

Algorithm
rewrite-expression-head
Rules
262×add-exp-log
150×add-cbrt-cube
132×*-un-lft-identity
129×prod-exp
86×div-exp
72×times-frac
69×cbrt-unprod
60×add-sqr-sqrt
51×distribute-lft-out
46×cbrt-undiv
43×add-cube-cbrt
22×associate-*r* associate-*l*
18×pow1 frac-times
12×rec-exp 1-exp associate-*r/ associate-*l/
9×pow-prod-down associate-/r*
8×associate-/r/ associate-/l*
6×flip3-+ flip-+ unswap-sqr
4×div-inv associate-/l/ add-log-exp
2×frac-2neg clear-num *-commutative
Counts
4 → 255
Calls
4 calls:
11.0ms
(/ (+ i (+ alpha beta)) (+ alpha (+ beta (* i 2.0))))
45.0ms
(* (* (/ i (+ alpha (+ beta (* i 2.0)))) (/ (+ i (+ alpha beta)) (+ alpha (+ beta (* i 2.0))))) (* (/ 1 (+ alpha (+ beta (+ (* i 2.0) (sqrt 1.0))))) (/ (+ (* i (+ i (+ alpha beta))) (* alpha beta)) (+ alpha (+ beta (- (* i 2.0) (sqrt 1.0)))))))
38.0ms
(* (/ 1 (+ alpha (+ beta (+ (* i 2.0) (sqrt 1.0))))) (/ (+ (* i (+ i (+ alpha beta))) (* alpha beta)) (+ alpha (+ beta (- (* i 2.0) (sqrt 1.0))))))
17.0ms
(/ (+ (* i (+ i (+ alpha beta))) (* alpha beta)) (+ alpha (+ beta (- (* i 2.0) (sqrt 1.0)))))

series509.0ms

Counts
4 → 12
Calls
4 calls:
16.0ms
(/ (+ i (+ alpha beta)) (+ alpha (+ beta (* i 2.0))))
386.0ms
(* (* (/ i (+ alpha (+ beta (* i 2.0)))) (/ (+ i (+ alpha beta)) (+ alpha (+ beta (* i 2.0))))) (* (/ 1 (+ alpha (+ beta (+ (* i 2.0) (sqrt 1.0))))) (/ (+ (* i (+ i (+ alpha beta))) (* alpha beta)) (+ alpha (+ beta (- (* i 2.0) (sqrt 1.0)))))))
79.0ms
(* (/ 1 (+ alpha (+ beta (+ (* i 2.0) (sqrt 1.0))))) (/ (+ (* i (+ i (+ alpha beta))) (* alpha beta)) (+ alpha (+ beta (- (* i 2.0) (sqrt 1.0))))))
28.0ms
(/ (+ (* i (+ i (+ alpha beta))) (* alpha beta)) (+ alpha (+ beta (- (* i 2.0) (sqrt 1.0)))))

simplify92.0ms

Algorithm
egg-herbie
Counts
267 → 267
Iterations

Useful iterations: 0 (48.0ms)

IterNodesCost
0508210440

prune461.0ms

Filtered
124 candidates to 267 candidates (-115.3%)
Pruning

8 alts after pruning (6 fresh and 2 done)

PrunedKeptTotal
New2643267
Fresh437
Picked011
Done011
Total2688276

Merged error: 6.3b

Counts
276 → 8

localize27.0ms

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))))) (* (/ 1 (+ alpha (+ beta (+ (* i 2.0) (sqrt 1.0))))) (+ (* i 0.5) (+ (* (sqrt 1.0) 0.25) (* 0.125 (/ 1.0 i))))))
0.2b
(* (/ 1 (+ alpha (+ beta (+ (* i 2.0) (sqrt 1.0))))) (+ (* i 0.5) (+ (* (sqrt 1.0) 0.25) (* 0.125 (/ 1.0 i)))))

rewrite113.0ms

Algorithm
rewrite-expression-head
Rules
142×add-exp-log
132×*-un-lft-identity
92×add-cbrt-cube
73×times-frac prod-exp
62×add-sqr-sqrt
50×distribute-lft-out
43×add-cube-cbrt cbrt-unprod
40×associate-*l*
37×div-exp
32×frac-times
30×associate-*r*
23×cbrt-undiv
22×associate-*r/
20×pow1
15×flip3-+ associate-*l/ flip-+
10×pow-prod-down
8×associate-/r/
7×unswap-sqr
6×rec-exp 1-exp
5×distribute-rgt-in distribute-lft-in associate-/l*
4×associate-/r* div-inv add-log-exp
3×*-commutative
2×associate-/l/
1×frac-2neg clear-num
Counts
4 → 243
Calls
4 calls:
26.0ms
(* (/ i (+ alpha (+ beta (* i 2.0)))) (/ (+ i (+ alpha beta)) (+ alpha (+ beta (* i 2.0)))))
11.0ms
(/ (+ i (+ alpha beta)) (+ alpha (+ beta (* i 2.0))))
39.0ms
(* (* (/ i (+ alpha (+ beta (* i 2.0)))) (/ (+ i (+ alpha beta)) (+ alpha (+ beta (* i 2.0))))) (* (/ 1 (+ alpha (+ beta (+ (* i 2.0) (sqrt 1.0))))) (+ (* i 0.5) (+ (* (sqrt 1.0) 0.25) (* 0.125 (/ 1.0 i))))))
20.0ms
(* (/ 1 (+ alpha (+ beta (+ (* i 2.0) (sqrt 1.0))))) (+ (* i 0.5) (+ (* (sqrt 1.0) 0.25) (* 0.125 (/ 1.0 i)))))

series149.0ms

Counts
4 → 12
Calls
4 calls:
24.0ms
(* (/ i (+ alpha (+ beta (* i 2.0)))) (/ (+ i (+ alpha beta)) (+ alpha (+ beta (* i 2.0)))))
13.0ms
(/ (+ i (+ alpha beta)) (+ alpha (+ beta (* i 2.0))))
63.0ms
(* (* (/ i (+ alpha (+ beta (* i 2.0)))) (/ (+ i (+ alpha beta)) (+ alpha (+ beta (* i 2.0))))) (* (/ 1 (+ alpha (+ beta (+ (* i 2.0) (sqrt 1.0))))) (+ (* i 0.5) (+ (* (sqrt 1.0) 0.25) (* 0.125 (/ 1.0 i))))))
49.0ms
(* (/ 1 (+ alpha (+ beta (+ (* i 2.0) (sqrt 1.0))))) (+ (* i 0.5) (+ (* (sqrt 1.0) 0.25) (* 0.125 (/ 1.0 i)))))

simplify97.0ms

Algorithm
egg-herbie
Counts
255 → 255
Iterations

Useful iterations: 0 (55.0ms)

IterNodesCost
049978579
149978579

prune613.0ms

Filtered
142 candidates to 255 candidates (-79.6%)
Pruning

18 alts after pruning (16 fresh and 2 done)

PrunedKeptTotal
New24411255
Fresh055
Picked101
Done022
Total24518263

Merged error: 6.2b

Counts
263 → 18

regimes460.0ms

Accuracy

39.3% (3.5b remaining)

Error of 11.3b against oracle of 7.8b and baseline of 13.6b

bsearch19.0ms

Steps
ItersRangePoint
5
7.753952769943415e+71
2.89429095961775e+72
2.218615150937078e+72

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
078167
178167

end0.0ms

sample1.1s

Algorithm
intervals
Results
710.0ms8000×body80valid
189.0ms8000×pre80true

Profiling

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