Details

Time bar (total: 6.9s)

analyze43.0ms (0.6%)

Algorithm
1×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

sample34.0ms (0.5%)

Algorithm
1×intervals
Results
19.0ms256×body80valid
5.0ms256×pre80true

simplify26.0ms (0.4%)

Algorithm
1×egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (24.0ms)

IterNodesCost
0523053

prune12.0ms (0.2%)

Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022

Merged error: 47.8b

Counts
2 → 2

localize21.0ms (0.3%)

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))
5.0b
(* (* (/ 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))))
47.0b
(/ (+ (* i (+ i (+ alpha beta))) (* alpha beta)) (* (+ alpha (+ beta (* i 2.0))) (- (* (+ alpha (+ beta (* i 2.0))) (+ alpha (+ beta (* i 2.0)))) 1.0)))

rewrite107.0ms (1.6%)

Algorithm
1×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:

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))))
26.0ms
(/ (+ (* i (+ i (+ alpha beta))) (* alpha beta)) (* (+ alpha (+ beta (* i 2.0))) (- (* (+ alpha (+ beta (* i 2.0))) (+ alpha (+ beta (* i 2.0)))) 1.0)))
22.0ms
(* (+ alpha (+ beta (* i 2.0))) (- (* (+ alpha (+ beta (* i 2.0))) (+ alpha (+ beta (* i 2.0)))) 1.0))
14.0ms
(* (/ i (+ alpha (+ beta (* i 2.0)))) (+ i (+ alpha beta)))

series545.0ms (7.9%)

Counts
4 → 12
Calls

4 calls:

308.0ms
(* (* (/ 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))))
165.0ms
(/ (+ (* i (+ i (+ alpha beta))) (* alpha beta)) (* (+ alpha (+ beta (* i 2.0))) (- (* (+ alpha (+ beta (* i 2.0))) (+ alpha (+ beta (* i 2.0)))) 1.0)))
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)))

simplify77.0ms (1.1%)

Algorithm
1×egg-herbie
Counts
177 → 177
Iterations

Useful iterations: 0 (51.0ms)

IterNodesCost
050125739

prune462.0ms (6.7%)

Pruning

5 alts after pruning (5 fresh and 0 done)

PrunedKeptTotal
New1725177
Fresh101
Picked101
Done000
Total1745179

Merged error: 36.7b

Counts
179 → 5

localize18.0ms (0.3%)

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)))
41.1b
(/ (+ (* i (+ i (+ alpha beta))) (* alpha beta)) (- (* (+ alpha (+ beta (* i 2.0))) (+ alpha (+ beta (* i 2.0)))) 1.0))

rewrite104.0ms (1.5%)

Algorithm
1×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:

40.0ms
(* (* (/ 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 (+ alpha (+ beta (* i 2.0)))) (/ (+ i (+ alpha beta)) (+ alpha (+ beta (* i 2.0)))))
21.0ms
(/ (+ (* i (+ i (+ alpha beta))) (* alpha beta)) (- (* (+ alpha (+ beta (* i 2.0))) (+ alpha (+ beta (* i 2.0)))) 1.0))
11.0ms
(/ (+ i (+ alpha beta)) (+ alpha (+ beta (* i 2.0))))

series394.0ms (5.7%)

Counts
4 → 12
Calls

4 calls:

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)))
50.0ms
(/ (+ (* i (+ i (+ alpha beta))) (* alpha beta)) (- (* (+ alpha (+ beta (* i 2.0))) (+ alpha (+ beta (* i 2.0)))) 1.0))
23.0ms
(* (/ i (+ alpha (+ beta (* i 2.0)))) (/ (+ i (+ alpha beta)) (+ alpha (+ beta (* i 2.0)))))
15.0ms
(/ (+ i (+ alpha beta)) (+ alpha (+ beta (* i 2.0))))

simplify63.0ms (0.9%)

Algorithm
1×egg-herbie
Counts
216 → 216
Iterations

Useful iterations: 0 (33.0ms)

IterNodesCost
050206791

prune601.0ms (8.7%)

Pruning

8 alts after pruning (7 fresh and 1 done)

PrunedKeptTotal
New2106216
Fresh314
Picked011
Done000
Total2138221

Merged error: 34.1b

Counts
221 → 8

localize30.0ms (0.4%)

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))))))
34.9b
(sqrt (+ (* i (+ i (+ alpha beta))) (* alpha beta)))
34.9b
(sqrt (+ (* i (+ i (+ alpha beta))) (* alpha beta)))

rewrite138.0ms (2%)

Algorithm
1×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:

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

series495.0ms (7.2%)

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)))))))
46.0ms
(* (/ (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)))

simplify110.0ms (1.6%)

Algorithm
1×egg-herbie
Counts
222 → 222
Iterations

Useful iterations: 0 (66.0ms)

IterNodesCost
050349612

prune785.0ms (11.4%)

Pruning

7 alts after pruning (5 fresh and 2 done)

PrunedKeptTotal
New2211222
Fresh246
Picked011
Done011
Total2237230

Merged error: 34.1b

Counts
230 → 7

localize24.0ms (0.4%)

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 (+ 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)))))
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))))))
35.1b
(/ (+ (* i (+ i (+ alpha beta))) (* alpha beta)) (+ alpha (+ beta (+ (* i 2.0) (sqrt 1.0)))))

rewrite136.0ms (2%)

Algorithm
1×rewrite-expression-head
Rules
124×*-un-lft-identity
112×add-exp-log add-cbrt-cube
71×times-frac
55×add-sqr-sqrt
47×distribute-lft-out
43×add-cube-cbrt
42×cbrt-undiv div-exp
40×prod-exp cbrt-unprod
39×associate-*l*
27×associate-*r*
11×pow1 frac-times associate-*r/
10×associate-/r* associate-/r/
9×associate-/l/
7×associate-*l/
6×flip3-+ flip-+
5×div-inv
4×pow-prod-down associate-/l* add-log-exp unswap-sqr
2×frac-2neg clear-num *-commutative
Counts
4 → 218
Calls

4 calls:

42.0ms
(/ (* (/ (+ (* 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)))))
37.0ms
(* (/ (+ (* 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))))))
30.0ms
(* (/ i (+ alpha (+ beta (* i 2.0)))) (/ (+ i (+ alpha beta)) (+ alpha (+ beta (* i 2.0)))))
16.0ms
(/ (+ (* i (+ i (+ alpha beta))) (* alpha beta)) (+ alpha (+ beta (+ (* i 2.0) (sqrt 1.0)))))

series559.0ms (8.1%)

Counts
4 → 12
Calls

4 calls:

396.0ms
(/ (* (/ (+ (* 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)))))
109.0ms
(* (/ (+ (* 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))))))
29.0ms
(/ (+ (* i (+ i (+ alpha beta))) (* alpha beta)) (+ alpha (+ beta (+ (* i 2.0) (sqrt 1.0)))))
24.0ms
(* (/ i (+ alpha (+ beta (* i 2.0)))) (/ (+ i (+ alpha beta)) (+ alpha (+ beta (* i 2.0)))))

simplify80.0ms (1.2%)

Algorithm
1×egg-herbie
Counts
230 → 230
Iterations

Useful iterations: 0 (40.0ms)

IterNodesCost
049848459
149848459

prune800.0ms (11.6%)

Pruning

7 alts after pruning (4 fresh and 3 done)

PrunedKeptTotal
New2291230
Fresh134
Picked011
Done022
Total2307237

Merged error: 6.9b

Counts
237 → 7

regimes229.0ms (3.3%)

Accuracy

Total 2.6b remaining (27%)

Threshold costs 0b (0%)

bsearch10.0ms (0.1%)

Steps
ItersRangePoint
3
4.759807116599614e+112
5.76175194432539e+112
4.947671771798196e+112

simplify2.0ms (0%)

Algorithm
1×egg-herbie
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
091124
191124

end0.0ms (0%)

sample971.0ms (14.1%)

Algorithm
1×intervals
Results
632.0ms8000×body80valid
167.0ms8000×pre80true

Profiling

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