Details

Time bar (total: 2.5min)

analyze129.0ms

Algorithm
search
Search
TrueOtherFalseIter
0%28.1%71.9%0
0%28.1%71.9%1
0%28.1%71.9%2
0%28.1%71.9%3
3.5%24.6%71.9%4
5.3%22.8%71.9%5
10.5%17.5%71.9%6
14%14%71.9%7
19.1%9%71.9%8
24.6%3.5%71.9%9
25.1%3%71.9%10
25.8%2.3%71.9%11
26.3%1.8%71.9%12
26.6%1.5%71.9%13
26.9%1.2%71.9%14

sample40.0ms

Algorithm
intervals
Results
12.0ms204×body80valid
5.0ms19×body1280valid
5.0ms256×pre80true
4.0ms16×body640valid
2.0ms12×body320valid
1.0ms5×body160valid

simplify53.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (51.0ms)

IterNodesCost
0502029

prune10.0ms

Filtered
1 candidates to 1 candidates (0.0%)
Pruning

1 alts after pruning (1 fresh and 0 done)

PrunedKeptTotal
New011
Fresh101
Picked000
Done000
Total112

Merged error: 18.6b

Counts
2 → 1

localize17.0ms

Local error

Found 4 expressions with local error:

0.0b
(* (+ alpha (+ beta (* 2.0 i))) (+ alpha (+ beta (+ 2.0 (* 2.0 i)))))
2.2b
(+ (* (+ alpha beta) (/ (- beta alpha) (* (+ alpha (+ beta (* 2.0 i))) (+ alpha (+ beta (+ 2.0 (* 2.0 i))))))) 1.0)
3.1b
(* (+ alpha beta) (/ (- beta alpha) (* (+ alpha (+ beta (* 2.0 i))) (+ alpha (+ beta (+ 2.0 (* 2.0 i)))))))
17.1b
(/ (- beta alpha) (* (+ alpha (+ beta (* 2.0 i))) (+ alpha (+ beta (+ 2.0 (* 2.0 i))))))

rewrite78.0ms

Algorithm
rewrite-expression-head
Rules
26×*-un-lft-identity
22×associate-*r*
21×add-sqr-sqrt flip3-+ flip-+
20×add-exp-log add-cbrt-cube
16×associate-/r/
14×frac-times
11×add-cube-cbrt
10×times-frac
8×pow1 associate-*l* associate-*l/
7×associate-*r/
6×prod-exp cbrt-unprod add-log-exp
5×distribute-lft-out associate-/l*
4×cbrt-undiv div-exp
3×distribute-lft-out-- difference-of-squares
2×pow-prod-down *-commutative div-inv associate-/l/ unswap-sqr
1×+-commutative distribute-rgt-in flip3-- frac-2neg distribute-lft-in div-sub clear-num associate-/r* sum-log flip--
Counts
4 → 120
Calls
4 calls:
13.0ms
(* (+ alpha (+ beta (* 2.0 i))) (+ alpha (+ beta (+ 2.0 (* 2.0 i)))))
20.0ms
(+ (* (+ alpha beta) (/ (- beta alpha) (* (+ alpha (+ beta (* 2.0 i))) (+ alpha (+ beta (+ 2.0 (* 2.0 i))))))) 1.0)
22.0ms
(* (+ alpha beta) (/ (- beta alpha) (* (+ alpha (+ beta (* 2.0 i))) (+ alpha (+ beta (+ 2.0 (* 2.0 i)))))))
18.0ms
(/ (- beta alpha) (* (+ alpha (+ beta (* 2.0 i))) (+ alpha (+ beta (+ 2.0 (* 2.0 i))))))

series200.0ms

Counts
4 → 12
Calls
4 calls:
19.0ms
(* (+ alpha (+ beta (* 2.0 i))) (+ alpha (+ beta (+ 2.0 (* 2.0 i)))))
80.0ms
(+ (* (+ alpha beta) (/ (- beta alpha) (* (+ alpha (+ beta (* 2.0 i))) (+ alpha (+ beta (+ 2.0 (* 2.0 i))))))) 1.0)
60.0ms
(* (+ alpha beta) (/ (- beta alpha) (* (+ alpha (+ beta (* 2.0 i))) (+ alpha (+ beta (+ 2.0 (* 2.0 i)))))))
40.0ms
(/ (- beta alpha) (* (+ alpha (+ beta (* 2.0 i))) (+ alpha (+ beta (+ 2.0 (* 2.0 i))))))

simplify64.0ms

Algorithm
egg-herbie
Counts
132 → 132
Iterations

Useful iterations: 0 (48.0ms)

IterNodesCost
050173338

prune293.0ms

Filtered
106 candidates to 132 candidates (-24.5%)
Pruning

7 alts after pruning (7 fresh and 0 done)

PrunedKeptTotal
New1257132
Fresh000
Picked101
Done000
Total1267133

Merged error: 5.4b

Counts
133 → 7

localize17.0ms

Local error

Found 4 expressions with local error:

0.1b
(* (+ beta (+ alpha (* 2.0 i))) (/ (+ beta (+ alpha (+ 2.0 (* 2.0 i)))) (- beta alpha)))
0.3b
(/ 1 (* (+ beta (+ alpha (* 2.0 i))) (/ (+ beta (+ alpha (+ 2.0 (* 2.0 i)))) (- beta alpha))))
2.2b
(+ (* (+ alpha beta) (/ 1 (* (+ beta (+ alpha (* 2.0 i))) (/ (+ beta (+ alpha (+ 2.0 (* 2.0 i)))) (- beta alpha))))) 1.0)
3.1b
(* (+ alpha beta) (/ 1 (* (+ beta (+ alpha (* 2.0 i))) (/ (+ beta (+ alpha (+ 2.0 (* 2.0 i)))) (- beta alpha)))))

rewrite94.0ms

Algorithm
rewrite-expression-head
Rules
62×add-exp-log
60×*-un-lft-identity
43×associate-*r*
38×add-sqr-sqrt
32×times-frac add-cbrt-cube
24×prod-exp
21×add-cube-cbrt
19×div-exp
17×distribute-lft-out
12×associate-/r/
11×pow1
10×cbrt-unprod
9×cbrt-undiv flip3-+ flip-+
8×frac-times associate-*l* associate-*l/
6×rec-exp 1-exp add-log-exp
5×distribute-lft-out-- difference-of-squares
4×associate-*r/
3×pow-prod-down div-inv associate-/l* unswap-sqr
2×pow-flip *-commutative
1×+-commutative flip3-- frac-2neg clear-num associate-/r* sum-log un-div-inv flip-- inv-pow
Counts
4 → 149
Calls
4 calls:
21.0ms
(* (+ beta (+ alpha (* 2.0 i))) (/ (+ beta (+ alpha (+ 2.0 (* 2.0 i)))) (- beta alpha)))
17.0ms
(/ 1 (* (+ beta (+ alpha (* 2.0 i))) (/ (+ beta (+ alpha (+ 2.0 (* 2.0 i)))) (- beta alpha))))
23.0ms
(+ (* (+ alpha beta) (/ 1 (* (+ beta (+ alpha (* 2.0 i))) (/ (+ beta (+ alpha (+ 2.0 (* 2.0 i)))) (- beta alpha))))) 1.0)
27.0ms
(* (+ alpha beta) (/ 1 (* (+ beta (+ alpha (* 2.0 i))) (/ (+ beta (+ alpha (+ 2.0 (* 2.0 i)))) (- beta alpha)))))

series214.0ms

Counts
4 → 12
Calls
4 calls:
31.0ms
(* (+ beta (+ alpha (* 2.0 i))) (/ (+ beta (+ alpha (+ 2.0 (* 2.0 i)))) (- beta alpha)))
38.0ms
(/ 1 (* (+ beta (+ alpha (* 2.0 i))) (/ (+ beta (+ alpha (+ 2.0 (* 2.0 i)))) (- beta alpha))))
80.0ms
(+ (* (+ alpha beta) (/ 1 (* (+ beta (+ alpha (* 2.0 i))) (/ (+ beta (+ alpha (+ 2.0 (* 2.0 i)))) (- beta alpha))))) 1.0)
64.0ms
(* (+ alpha beta) (/ 1 (* (+ beta (+ alpha (* 2.0 i))) (/ (+ beta (+ alpha (+ 2.0 (* 2.0 i)))) (- beta alpha)))))

simplify86.0ms

Algorithm
egg-herbie
Counts
161 → 161
Iterations

Useful iterations: 0 (67.0ms)

IterNodesCost
050033670

prune257.0ms

Filtered
102 candidates to 161 candidates (-57.8%)
Pruning

8 alts after pruning (7 fresh and 1 done)

PrunedKeptTotal
New1583161
Fresh246
Picked011
Done000
Total1608168

Merged error: 5.4b

Counts
168 → 8

localize31.0ms

Local error

Found 4 expressions with local error:

0.6b
(cbrt (+ alpha (+ beta (+ 2.0 (* 2.0 i)))))
0.6b
(cbrt (+ alpha (+ beta (+ 2.0 (* 2.0 i)))))
3.1b
(* (+ alpha beta) (/ 1 (* (* (+ alpha (+ beta (* 2.0 i))) (* (cbrt (+ alpha (+ beta (+ 2.0 (* 2.0 i))))) (/ (cbrt (+ alpha (+ beta (+ 2.0 (* 2.0 i))))) (* (cbrt (- beta alpha)) (cbrt (- beta alpha)))))) (/ (cbrt (+ beta (+ alpha (+ 2.0 (* 2.0 i))))) (cbrt (- beta alpha))))))
5.3b
(+ (* (+ alpha beta) (/ 1 (* (* (+ alpha (+ beta (* 2.0 i))) (* (cbrt (+ alpha (+ beta (+ 2.0 (* 2.0 i))))) (/ (cbrt (+ alpha (+ beta (+ 2.0 (* 2.0 i))))) (* (cbrt (- beta alpha)) (cbrt (- beta alpha)))))) (/ (cbrt (+ beta (+ alpha (+ 2.0 (* 2.0 i))))) (cbrt (- beta alpha)))))) 1.0)

rewrite337.0ms

Algorithm
rewrite-expression-head
Rules
188×add-exp-log
112×prod-exp
51×frac-times
50×add-cbrt-cube
49×div-exp
42×associate-*r*
38×cbrt-unprod
35×associate-*l/ associate-/r/
29×flip3-+ flip-+
28×cbrt-div
21×*-un-lft-identity
20×cbrt-undiv
18×associate-*r/
11×add-sqr-sqrt rec-exp 1-exp
10×cbrt-prod
9×add-cube-cbrt
7×distribute-lft-out
6×pow1 add-log-exp
4×associate-*l*
3×times-frac
2×pow1/3
1×+-commutative pow-prod-down sum-log un-div-inv *-commutative div-inv unswap-sqr
Counts
4 → 149
Calls
4 calls:
6.0ms
(cbrt (+ alpha (+ beta (+ 2.0 (* 2.0 i)))))
7.0ms
(cbrt (+ alpha (+ beta (+ 2.0 (* 2.0 i)))))
256.0ms
(* (+ alpha beta) (/ 1 (* (* (+ alpha (+ beta (* 2.0 i))) (* (cbrt (+ alpha (+ beta (+ 2.0 (* 2.0 i))))) (/ (cbrt (+ alpha (+ beta (+ 2.0 (* 2.0 i))))) (* (cbrt (- beta alpha)) (cbrt (- beta alpha)))))) (/ (cbrt (+ beta (+ alpha (+ 2.0 (* 2.0 i))))) (cbrt (- beta alpha))))))
57.0ms
(+ (* (+ alpha beta) (/ 1 (* (* (+ alpha (+ beta (* 2.0 i))) (* (cbrt (+ alpha (+ beta (+ 2.0 (* 2.0 i))))) (/ (cbrt (+ alpha (+ beta (+ 2.0 (* 2.0 i))))) (* (cbrt (- beta alpha)) (cbrt (- beta alpha)))))) (/ (cbrt (+ beta (+ alpha (+ 2.0 (* 2.0 i))))) (cbrt (- beta alpha)))))) 1.0)

series2.5min

Calls
1 calls:
2.5s
(+ (* (+ alpha beta) (/ 1 (* (* (+ alpha (+ beta (* 2.0 i))) (* (cbrt (+ alpha (+ beta (+ 2.0 (* 2.0 i))))) (/ (cbrt (+ alpha (+ beta (+ 2.0 (* 2.0 i))))) (* (cbrt (- beta alpha)) (cbrt (- beta alpha)))))) (/ (cbrt (+ beta (+ alpha (+ 2.0 (* 2.0 i))))) (cbrt (- beta alpha)))))) 1.0)

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