Details

Time bar (total: 5.7s)

analyze40.0ms

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
23.0ms256×body80valid
5.0ms256×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: 48.6b

Counts
2 → 2

localize17.0ms

Local error

Found 4 expressions with local error:

0.0b
(* (+ 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)))
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))))
47.8b
(/ (+ (* 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:
19.0ms
(* (+ 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)))
39.0ms
(* (* (/ 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)))

series553.0ms

Counts
4 → 12
Calls
4 calls:
56.0ms
(* (+ alpha (+ beta (* i 2.0))) (- (* (+ alpha (+ beta (* i 2.0))) (+ alpha (+ beta (* i 2.0)))) 1.0))
16.0ms
(* (/ i (+ alpha (+ beta (* i 2.0)))) (+ i (+ alpha beta)))
314.0ms
(* (* (/ 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)))

simplify78.0ms

Algorithm
egg-herbie
Counts
177 → 177
Iterations

Useful iterations: 0 (52.0ms)

IterNodesCost
050125739

prune369.0ms

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: 33.0b

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)))) (/ (+ 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))

rewrite101.0ms

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:
10.0ms
(/ (+ i (+ alpha beta)) (+ alpha (+ beta (* i 2.0))))
26.0ms
(* (/ i (+ alpha (+ beta (* i 2.0)))) (/ (+ i (+ alpha beta)) (+ alpha (+ beta (* i 2.0)))))
36.0ms
(* (* (/ 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)))
20.0ms
(/ (+ (* i (+ i (+ alpha beta))) (* alpha beta)) (- (* (+ alpha (+ beta (* i 2.0))) (+ alpha (+ beta (* i 2.0)))) 1.0))

series395.0ms

Counts
4 → 12
Calls
4 calls:
13.0ms
(/ (+ i (+ alpha beta)) (+ alpha (+ beta (* i 2.0))))
24.0ms
(* (/ i (+ alpha (+ beta (* i 2.0)))) (/ (+ i (+ alpha beta)) (+ alpha (+ beta (* i 2.0)))))
310.0ms
(* (* (/ 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)))
48.0ms
(/ (+ (* 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 (33.0ms)

IterNodesCost
050206791

prune348.0ms

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

6 alts after pruning (6 fresh and 0 done)

PrunedKeptTotal
New2124216
Fresh325
Picked101
Done000
Total2166222

Merged error: 30.0b

Counts
222 → 6

localize26.0ms

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))))))
32.2b
(sqrt (+ (* i (+ i (+ alpha beta))) (* alpha beta)))
32.2b
(sqrt (+ (* i (+ i (+ alpha beta))) (* alpha beta)))

rewrite134.0ms

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)))))))
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))))))
8.0ms
(sqrt (+ (* i (+ i (+ alpha beta))) (* alpha beta)))
8.0ms
(sqrt (+ (* i (+ i (+ alpha beta))) (* alpha beta)))

series502.0ms

Counts
4 → 12
Calls
4 calls:
388.0ms
(* (* (/ 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)))))))
48.0ms
(* (/ (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))))))
35.0ms
(sqrt (+ (* i (+ i (+ alpha beta))) (* alpha beta)))
31.0ms
(sqrt (+ (* i (+ i (+ alpha beta))) (* alpha beta)))

simplify109.0ms

Algorithm
egg-herbie
Counts
222 → 222
Iterations

Useful iterations: 0 (68.0ms)

IterNodesCost
050349612

prune341.0ms

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

5 alts after pruning (5 fresh and 0 done)

PrunedKeptTotal
New2202222
Fresh235
Picked101
Done000
Total2235228

Merged error: 30.0b

Counts
228 → 5

localize25.0ms

Local error

Found 4 expressions with local error:

0.0b
(* (/ i (+ alpha (+ beta (* i 2.0)))) (/ (+ i (+ alpha beta)) (+ alpha (+ beta (* i 2.0)))))
0.1b
(* (* (/ 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))))))
32.4b
(/ (+ (* i (+ i (+ alpha beta))) (* alpha beta)) (+ alpha (+ beta (- (* i 2.0) (sqrt 1.0)))))

rewrite140.0ms

Algorithm
rewrite-expression-head
Rules
272×add-exp-log
160×add-cbrt-cube
138×*-un-lft-identity
133×prod-exp
89×div-exp
88×times-frac
79×add-sqr-sqrt
73×cbrt-unprod
50×add-cube-cbrt distribute-lft-out
49×cbrt-undiv
48×associate-*r*
40×associate-*l*
20×pow1
19×frac-times
13×associate-*r/ associate-*l/
12×rec-exp 1-exp
10×pow-prod-down associate-/r/ unswap-sqr
6×flip3-+ flip-+
5×associate-/r* div-inv
4×add-log-exp
3×*-commutative associate-/l*
2×associate-/l/
1×frac-2neg clear-num
Counts
4 → 278
Calls
4 calls:
28.0ms
(* (/ i (+ alpha (+ beta (* i 2.0)))) (/ (+ 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)))))))
35.0ms
(* (/ 1 (+ alpha (+ beta (+ (* i 2.0) (sqrt 1.0))))) (/ (+ (* i (+ i (+ alpha beta))) (* alpha beta)) (+ alpha (+ beta (- (* i 2.0) (sqrt 1.0))))))
16.0ms
(/ (+ (* i (+ i (+ alpha beta))) (* alpha beta)) (+ alpha (+ beta (- (* i 2.0) (sqrt 1.0)))))

series523.0ms

Counts
4 → 12
Calls
4 calls:
23.0ms
(* (/ i (+ alpha (+ beta (* i 2.0)))) (/ (+ i (+ alpha beta)) (+ alpha (+ beta (* i 2.0)))))
385.0ms
(* (* (/ 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)))))))
84.0ms
(* (/ 1 (+ alpha (+ beta (+ (* i 2.0) (sqrt 1.0))))) (/ (+ (* i (+ i (+ alpha beta))) (* alpha beta)) (+ alpha (+ beta (- (* i 2.0) (sqrt 1.0))))))
30.0ms
(/ (+ (* i (+ i (+ alpha beta))) (* alpha beta)) (+ alpha (+ beta (- (* i 2.0) (sqrt 1.0)))))

simplify95.0ms

Algorithm
egg-herbie
Counts
290 → 290
Iterations

Useful iterations: 0 (46.0ms)

IterNodesCost
0508211225

prune464.0ms

Filtered
138 candidates to 290 candidates (-110.1%)
Pruning

5 alts after pruning (4 fresh and 1 done)

PrunedKeptTotal
New2891290
Fresh134
Picked011
Done000
Total2905295

Merged error: 7.9b

Counts
295 → 5

regimes190.0ms

Accuracy

44.2% (3.1b remaining)

Error of 10.7b against oracle of 7.5b and baseline of 13.1b

bsearch20.0ms

Steps
ItersRangePoint
7
7.980353456022975e+117
3.284496336173573e+119
2.673640569294421e+119

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
075114
175114

end0.0ms

sample957.0ms

Algorithm
intervals
Results
619.0ms8000×body80valid
168.0ms8000×pre80true

Profiling

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