Details

Time bar (total: 6.3s)

sample47.0ms

Algorithm
intervals
Results
21.0ms256×body80valid
8.0ms256×pre80true

simplify26.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (24.0ms)

IterNodesCost
0523053

prune12.0ms

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: 47.2b

Counts
2 → 2

localize17.0ms

Local error

Found 4 expressions with local error:

0.0b
(* (/ i (+ alpha (+ beta (* i 2.0)))) (+ i (+ alpha beta)))
0.1b
(* (+ alpha (+ beta (* i 2.0))) (- (* (+ alpha (+ beta (* i 2.0))) (+ alpha (+ beta (* i 2.0)))) 1.0))
5.4b
(* (* (/ 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))))
46.4b
(/ (+ (* i (+ i (+ alpha beta))) (* alpha beta)) (* (+ alpha (+ beta (* i 2.0))) (- (* (+ alpha (+ beta (* i 2.0))) (+ alpha (+ beta (* i 2.0)))) 1.0)))

rewrite108.0ms

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-rgt-in distribute-lft-in distribute-lft-out
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 → 167
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))
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)))

series549.0ms

Counts
4 → 12
Calls
4 calls:
16.0ms
(* (/ i (+ alpha (+ beta (* i 2.0)))) (+ i (+ alpha beta)))
58.0ms
(* (+ alpha (+ beta (* i 2.0))) (- (* (+ alpha (+ beta (* i 2.0))) (+ alpha (+ beta (* i 2.0)))) 1.0))
316.0ms
(* (* (/ 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)))

simplify81.0ms

Algorithm
egg-herbie
Counts
179 → 179
Iterations

Useful iterations: 0 (54.0ms)

IterNodesCost
050125777

prune396.0ms

Filtered
129 candidates to 179 candidates (-38.8%)
Pruning

7 alts after pruning (7 fresh and 0 done)

PrunedKeptTotal
New1727179
Fresh101
Picked101
Done000
Total1747181

Merged error: 35.1b

Counts
181 → 7

localize17.0ms

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)))
39.4b
(/ (+ (* i (+ i (+ alpha beta))) (* alpha beta)) (- (* (+ alpha (+ beta (* i 2.0))) (+ alpha (+ beta (* i 2.0)))) 1.0))

rewrite91.0ms

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:
10.0ms
(* (+ alpha (+ beta (* i 2.0))) (+ 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)))
24.0ms
(/ (+ (* 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:
15.0ms
(* (+ alpha (+ beta (* i 2.0))) (+ 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)))
52.0ms
(/ (+ (* i (+ i (+ alpha beta))) (* alpha beta)) (- (* (+ alpha (+ beta (* i 2.0))) (+ alpha (+ beta (* i 2.0)))) 1.0))

simplify78.0ms

Algorithm
egg-herbie
Counts
188 → 188
Iterations

Useful iterations: 0 (53.0ms)

IterNodesCost
050175171

prune342.0ms

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

8 alts after pruning (7 fresh and 1 done)

PrunedKeptTotal
New1853188
Fresh246
Picked011
Done000
Total1878195

Merged error: 33.1b

Counts
195 → 8

localize29.0ms

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

rewrite98.0ms

Algorithm
rewrite-expression-head
Rules
154×*-un-lft-identity
102×times-frac
91×add-sqr-sqrt
60×sqrt-prod
59×add-cube-cbrt
57×distribute-lft-out
36×associate-*r* associate-*l*
18×add-exp-log add-cbrt-cube
9×unswap-sqr
8×pow1
6×flip3-+ sqrt-div associate-/r/ flip-+ associate-/l*
5×cbrt-undiv div-exp associate-/r*
4×prod-exp cbrt-unprod add-log-exp
3×div-inv
2×rem-sqrt-square sqrt-pow1 pow1/2 associate-/l/
1×frac-times frac-2neg associate-*r/ pow-prod-down associate-*l/ clear-num *-commutative
Counts
4 → 188
Calls
4 calls:
17.0ms
(/ (sqrt (+ (* i (+ i (+ alpha beta))) (* alpha beta))) (+ alpha (+ beta (+ (* i 2.0) (sqrt 1.0)))))
57.0ms
(* (/ (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)))

series161.0ms

Counts
4 → 12
Calls
4 calls:
51.0ms
(/ (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)))
34.0ms
(sqrt (+ (* i (+ i (+ alpha beta))) (* alpha beta)))

simplify94.0ms

Algorithm
egg-herbie
Counts
200 → 200
Iterations

Useful iterations: 0 (60.0ms)

IterNodesCost
049647089
149647089

prune416.0ms

Filtered
119 candidates to 200 candidates (-68.1%)
Pruning

8 alts after pruning (7 fresh and 1 done)

PrunedKeptTotal
New1991200
Fresh066
Picked011
Done101
Total2008208

Merged error: 33.1b

Counts
208 → 8

localize22.0ms

Local error

Found 4 expressions with local error:

0.0b
(/ (+ 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))))
34.6b
(/ (+ (* i (+ i (+ alpha beta))) (* alpha beta)) (+ alpha (+ beta (+ (* i 2.0) (sqrt 1.0)))))

rewrite158.0ms

Algorithm
rewrite-expression-head
Rules
701×*-un-lft-identity
554×times-frac
376×add-sqr-sqrt
211×distribute-lft-out
204×add-cube-cbrt
153×associate-*r*
86×distribute-lft-out-- difference-of-squares
82×add-exp-log add-cbrt-cube
43×sqrt-prod
38×associate-/r/
32×cbrt-undiv div-exp
29×associate-/l*
27×prod-exp cbrt-unprod
19×flip3-+ flip-+ div-inv
16×associate-/r*
9×pow1
5×frac-times associate-*l/ associate-/l/
4×add-log-exp
3×frac-2neg associate-*r/ pow-prod-down clear-num
2×flip3-- flip--
1×associate-*l* *-commutative
Counts
4 → 477
Calls
4 calls:
11.0ms
(/ (+ i (+ alpha beta)) (+ alpha (+ beta (* i 2.0))))
34.0ms
(/ (/ (+ (* i (+ i (+ alpha beta))) (* alpha beta)) (+ alpha (+ beta (+ (* i 2.0) (sqrt 1.0))))) (- (+ 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 (+ i (+ alpha beta))) (* alpha beta)) (+ alpha (+ beta (+ (* i 2.0) (sqrt 1.0))))) (- (+ alpha (+ beta (* i 2.0))) (sqrt 1.0))))
16.0ms
(/ (+ (* i (+ i (+ alpha beta))) (* alpha beta)) (+ alpha (+ beta (+ (* i 2.0) (sqrt 1.0)))))

series487.0ms

Counts
4 → 12
Calls
4 calls:
13.0ms
(/ (+ i (+ alpha beta)) (+ alpha (+ beta (* i 2.0))))
47.0ms
(/ (/ (+ (* i (+ i (+ alpha beta))) (* alpha beta)) (+ alpha (+ beta (+ (* i 2.0) (sqrt 1.0))))) (- (+ alpha (+ beta (* i 2.0))) (sqrt 1.0)))
391.0ms
(* (* (/ 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))))
35.0ms
(/ (+ (* i (+ i (+ alpha beta))) (* alpha beta)) (+ alpha (+ beta (+ (* i 2.0) (sqrt 1.0)))))

simplify155.0ms

Algorithm
egg-herbie
Counts
489 → 489
Iterations

Useful iterations: 0 (61.0ms)

IterNodesCost
0503723524

prune1.2s

Filtered
219 candidates to 489 candidates (-123.3%)
Pruning

7 alts after pruning (6 fresh and 1 done)

PrunedKeptTotal
New4863489
Fresh336
Picked101
Done011
Total4907497

Merged error: 6.3b

Counts
497 → 7

regimes234.0ms

Accuracy

48.5% (3.1b remaining)

Error of 10.2b against oracle of 7.1b and baseline of 13.1b

bsearch20.0ms

Steps
ItersRangePoint
6
9.85832843349007e+99
4.4680879213569435e+100
3.3078638610239012e+100

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
094124
194124

end0.0ms

sample1.1s

Algorithm
intervals
Results
625.0ms8000×body80valid
164.0ms8000×pre80true

Profiling

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