Details

Time bar (total: 7.1s)

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

sample66.0ms

Algorithm
intervals
Results
19.0ms256×body80valid

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: 45.6b

Counts
2 → 2

localize18.0ms

Local error

Found 4 expressions with local error:

0.1b
(* (/ 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))
4.1b
(* (* (/ 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))))
44.9b
(/ (+ (* 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))
36.0ms
(* (* (/ 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)))

series575.0ms

Counts
4 → 12
Calls
4 calls:
16.0ms
(* (/ i (+ alpha (+ beta (* i 2.0)))) (+ i (+ alpha beta)))
78.0ms
(* (+ alpha (+ beta (* i 2.0))) (- (* (+ alpha (+ beta (* i 2.0))) (+ alpha (+ beta (* i 2.0)))) 1.0))
317.0ms
(* (* (/ 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)))

simplify78.0ms

Algorithm
egg-herbie
Counts
177 → 177
Iterations

Useful iterations: 0 (52.0ms)

IterNodesCost
050125739

prune386.0ms

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

6 alts after pruning (6 fresh and 0 done)

PrunedKeptTotal
New1716177
Fresh101
Picked101
Done000
Total1736179

Merged error: 35.3b

Counts
179 → 6

localize19.0ms

Local error

Found 4 expressions with local error:

0.0b
(/ (+ i (+ alpha beta)) (+ alpha (+ beta (* i 2.0))))
0.0b
(/ i (+ 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)))
39.0b
(/ (+ (* 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
86×*-un-lft-identity
56×times-frac
51×add-exp-log add-cbrt-cube
48×add-sqr-sqrt
41×add-cube-cbrt
25×distribute-lft-out
18×associate-*r* prod-exp cbrt-unprod
16×cbrt-undiv div-exp
12×associate-/r*
11×associate-/l*
9×pow1
8×associate-/r/
7×difference-of-squares
5×frac-times associate-*l/
4×flip3-+ flip-+ div-inv associate-/l/ add-log-exp
3×frac-2neg associate-*r/ pow-prod-down clear-num
2×flip3-- flip--
1×associate-*l* *-commutative
Counts
4 → 169
Calls
4 calls:
11.0ms
(/ (+ i (+ alpha beta)) (+ alpha (+ beta (* i 2.0))))
6.0ms
(/ i (+ 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))

series405.0ms

Counts
4 → 12
Calls
4 calls:
16.0ms
(/ (+ i (+ alpha beta)) (+ alpha (+ beta (* i 2.0))))
14.0ms
(/ i (+ alpha (+ beta (* i 2.0))))
320.0ms
(* (* (/ 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)))
55.0ms
(/ (+ (* i (+ i (+ alpha beta))) (* alpha beta)) (- (* (+ alpha (+ beta (* i 2.0))) (+ alpha (+ beta (* i 2.0)))) 1.0))

simplify60.0ms

Algorithm
egg-herbie
Counts
181 → 181
Iterations

Useful iterations: 0 (34.0ms)

IterNodesCost
050365620

prune310.0ms

Filtered
117 candidates to 181 candidates (-54.7%)
Pruning

8 alts after pruning (8 fresh and 0 done)

PrunedKeptTotal
New1765181
Fresh235
Picked101
Done000
Total1798187

Merged error: 32.5b

Counts
187 → 8

localize33.0ms

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))))))
32.4b
(sqrt (+ (* i (+ i (+ alpha beta))) (* alpha beta)))
32.4b
(sqrt (+ (* i (+ i (+ alpha beta))) (* alpha beta)))

rewrite137.0ms

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:
53.0ms
(* (* (/ 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)))))))
55.0ms
(* (/ (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)))

series517.0ms

Counts
4 → 12
Calls
4 calls:
397.0ms
(* (* (/ 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)))))))
51.0ms
(* (/ (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))))))
32.0ms
(sqrt (+ (* i (+ i (+ alpha beta))) (* alpha beta)))
36.0ms
(sqrt (+ (* i (+ i (+ alpha beta))) (* alpha beta)))

simplify114.0ms

Algorithm
egg-herbie
Counts
222 → 222
Iterations

Useful iterations: 0 (69.0ms)

IterNodesCost
050349612

prune358.0ms

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

9 alts after pruning (8 fresh and 1 done)

PrunedKeptTotal
New2202222
Fresh167
Picked011
Done000
Total2219230

Merged error: 32.5b

Counts
230 → 9

localize23.0ms

Local error

Found 4 expressions with local error:

0.0b
(/ (+ i (+ alpha beta)) (+ alpha (+ beta (* i 2.0))))
0.0b
(/ i (+ 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) (sqrt 1.0))))) (- (+ alpha (+ beta (* i 2.0))) (sqrt 1.0))))
32.5b
(/ (+ (* i (+ i (+ alpha beta))) (* alpha beta)) (+ alpha (+ beta (+ (* i 2.0) (sqrt 1.0)))))

rewrite122.0ms

Algorithm
rewrite-expression-head
Rules
394×*-un-lft-identity
299×times-frac
203×add-sqr-sqrt
153×associate-*r*
121×distribute-lft-out
119×add-cube-cbrt
79×add-exp-log add-cbrt-cube
42×distribute-lft-out-- difference-of-squares
30×cbrt-undiv div-exp
27×prod-exp cbrt-unprod
22×associate-/r/
21×sqrt-prod
13×associate-/r*
12×flip3-+ flip-+
11×div-inv associate-/l*
9×pow1
5×frac-times associate-*l/
4×associate-/l/ add-log-exp
3×frac-2neg associate-*r/ pow-prod-down clear-num
1×flip3-- associate-*l* *-commutative flip--
Counts
4 → 318
Calls
4 calls:
11.0ms
(/ (+ i (+ alpha beta)) (+ alpha (+ beta (* i 2.0))))
6.0ms
(/ i (+ alpha (+ beta (* i 2.0))))
62.0ms
(* (* (/ 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))))
17.0ms
(/ (+ (* i (+ i (+ alpha beta))) (* alpha beta)) (+ alpha (+ beta (+ (* i 2.0) (sqrt 1.0)))))

series460.0ms

Counts
4 → 12
Calls
4 calls:
13.0ms
(/ (+ i (+ alpha beta)) (+ alpha (+ beta (* i 2.0))))
14.0ms
(/ i (+ alpha (+ beta (* i 2.0))))
402.0ms
(* (* (/ 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))))
30.0ms
(/ (+ (* i (+ i (+ alpha beta))) (* alpha beta)) (+ alpha (+ beta (+ (* i 2.0) (sqrt 1.0)))))

simplify117.0ms

Algorithm
egg-herbie
Counts
330 → 330
Iterations

Useful iterations: 0 (59.0ms)

IterNodesCost
0502813515

prune685.0ms

Filtered
157 candidates to 330 candidates (-110.2%)
Pruning

9 alts after pruning (8 fresh and 1 done)

PrunedKeptTotal
New3273330
Fresh257
Picked011
Done101
Total3309339

Merged error: 6.7b

Counts
339 → 9

regimes265.0ms

Accuracy

55.5% (2.7b remaining)

Error of 10.2b against oracle of 7.5b and baseline of 13.5b

bsearch26.0ms

Steps
ItersRangePoint
6
1.2264841720228282e+130
6.954701252439524e+130
1.418460281924807e+130

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
084110
184110

end0.0ms

sample2.0s

Algorithm
intervals
Results
630.0ms8000×body80valid

Profiling

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