Details

Time bar (total: 8.6s)

sample37.0ms

Algorithm
intervals
Results
8.0ms193×body80valid
7.0ms256×pre80true
5.0ms25×body1280valid
3.0ms19×body640valid
2.0ms14×body320valid
0.0ms5×body160valid

simplify508.0ms

Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
01529
13129
210129
341329
4146429
done500129

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 25.1b

localize13.0ms

Local error

Found 3 expressions with local error:

0.1b
(/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
1.6b
(+ (/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) 1.0)
21.8b
(/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i)))

rewrite408.0ms

Algorithm
rewrite-expression-head
Rules
54×times-frac
47×*-un-lft-identity
25×add-sqr-sqrt add-cube-cbrt
17×add-exp-log add-cbrt-cube
14×associate-/r/
11×flip3-+ flip-+ distribute-lft-out
10×associate-/l*
9×associate-/l/
7×cbrt-undiv div-exp associate-/r* div-inv
5×add-log-exp
4×frac-times
3×pow1 flip3-- flip--
2×frac-2neg associate-*r/ associate-*l/ prod-exp clear-num cbrt-unprod
1×+-commutative sum-log
Counts
3 → 111
Calls
3 calls:
89.0ms
(/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
291.0ms
(+ (/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) 1.0)
23.0ms
(/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i)))

series589.0ms

Counts
3 → 9
Calls
3 calls:
233.0ms
(/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
275.0ms
(+ (/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) 1.0)
80.0ms
(/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i)))

simplify949.0ms

Counts
120 → 120
Iterations

Useful iterations: 2 (226.0ms)

IterNodesCost
02254035
16953821
232893577
done50003577

prune356.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 8.5b

localize16.0ms

Local error

Found 4 expressions with local error:

0.0b
(/ (+ (+ alpha beta) (* 2.0 i)) (- beta alpha))
0.1b
(/ (/ (+ alpha beta) (/ (+ (+ alpha beta) (* 2.0 i)) (- beta alpha))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
0.1b
(/ (+ alpha beta) (/ (+ (+ alpha beta) (* 2.0 i)) (- beta alpha)))
1.6b
(+ (/ (/ (+ alpha beta) (/ (+ (+ alpha beta) (* 2.0 i)) (- beta alpha))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) 1.0)

rewrite717.0ms

Algorithm
rewrite-expression-head
Rules
1250×times-frac
1055×*-un-lft-identity
619×add-sqr-sqrt
461×add-cube-cbrt
218×distribute-lft-out
96×associate-/l*
79×distribute-lft-out-- difference-of-squares
60×associate-/r/
33×div-inv
30×associate-/r*
26×flip3-- flip--
20×add-exp-log add-cbrt-cube
10×cbrt-undiv div-exp
6×add-log-exp
5×associate-/l/
4×pow1 flip3-+ flip-+
3×frac-2neg clear-num
1×+-commutative sum-log
Counts
4 → 645
Calls
4 calls:
36.0ms
(/ (+ (+ alpha beta) (* 2.0 i)) (- beta alpha))
117.0ms
(/ (/ (+ alpha beta) (/ (+ (+ alpha beta) (* 2.0 i)) (- beta alpha))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
31.0ms
(/ (+ alpha beta) (/ (+ (+ alpha beta) (* 2.0 i)) (- beta alpha)))
476.0ms
(+ (/ (/ (+ alpha beta) (/ (+ (+ alpha beta) (* 2.0 i)) (- beta alpha))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) 1.0)

series715.0ms

Counts
4 → 12
Calls
4 calls:
123.0ms
(/ (+ (+ alpha beta) (* 2.0 i)) (- beta alpha))
228.0ms
(/ (/ (+ alpha beta) (/ (+ (+ alpha beta) (* 2.0 i)) (- beta alpha))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
81.0ms
(/ (+ alpha beta) (/ (+ (+ alpha beta) (* 2.0 i)) (- beta alpha)))
283.0ms
(+ (/ (/ (+ alpha beta) (/ (+ (+ alpha beta) (* 2.0 i)) (- beta alpha))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) 1.0)

simplify536.0ms

Counts
657 → 657
Iterations

Useful iterations: 1 (183.0ms)

IterNodesCost
070527143
1179926008
done500026008

prune1.5s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 8.5b

localize16.0ms

Local error

Found 4 expressions with local error:

0.1b
(exp (log (+ (/ (/ (+ alpha beta) (/ (+ (+ alpha beta) (* 2.0 i)) (- beta alpha))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) 1.0)))
0.1b
(/ (+ alpha beta) (/ (+ (+ alpha beta) (* 2.0 i)) (- beta alpha)))
1.6b
(+ (/ (/ (+ alpha beta) (/ (+ (+ alpha beta) (* 2.0 i)) (- beta alpha))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) 1.0)
1.7b
(log (+ (/ (/ (+ alpha beta) (/ (+ (+ alpha beta) (* 2.0 i)) (- beta alpha))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) 1.0))

rewrite1.1s

Algorithm
rewrite-expression-head
Rules
159×times-frac
154×*-un-lft-identity
104×add-sqr-sqrt
74×add-cube-cbrt
25×distribute-lft-out
21×associate-/r*
15×distribute-lft-out-- difference-of-squares
11×associate-/r/
10×add-exp-log
9×add-cbrt-cube
8×log-prod
6×pow1 div-inv add-log-exp
5×flip3-- flip--
4×log-div exp-prod flip3-+ exp-sum flip-+ associate-/l*
3×cbrt-undiv div-exp
2×exp-diff log-pow associate-/l/
1×+-commutative frac-2neg rem-log-exp clear-num sum-log rem-exp-log
Counts
4 → 171
Calls
4 calls:
300.0ms
(exp (log (+ (/ (/ (+ alpha beta) (/ (+ (+ alpha beta) (* 2.0 i)) (- beta alpha))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) 1.0)))
31.0ms
(/ (+ alpha beta) (/ (+ (+ alpha beta) (* 2.0 i)) (- beta alpha)))
469.0ms
(+ (/ (/ (+ alpha beta) (/ (+ (+ alpha beta) (* 2.0 i)) (- beta alpha))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) 1.0)
305.0ms
(log (+ (/ (/ (+ alpha beta) (/ (+ (+ alpha beta) (* 2.0 i)) (- beta alpha))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) 1.0))

series913.0ms

Counts
4 → 12
Calls
4 calls:
274.0ms
(exp (log (+ (/ (/ (+ alpha beta) (/ (+ (+ alpha beta) (* 2.0 i)) (- beta alpha))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) 1.0)))
81.0ms
(/ (+ alpha beta) (/ (+ (+ alpha beta) (* 2.0 i)) (- beta alpha)))
279.0ms
(+ (/ (/ (+ alpha beta) (/ (+ (+ alpha beta) (* 2.0 i)) (- beta alpha))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) 1.0)
278.0ms
(log (+ (/ (/ (+ alpha beta) (/ (+ (+ alpha beta) (* 2.0 i)) (- beta alpha))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) 1.0))

simplify208.0ms

Iterations

Useful iterations: 1 (65.0ms)

IterNodesCost
03145910
17335700