Details

Time bar (total: 25.4s)

sample46.0ms

Algorithm
intervals
Results
14.0ms220×body80valid
6.0ms256×pre80true
6.0ms17×body1280valid
2.0ms10×body640valid
1.0ms6×body320valid
0.0ms3×body160valid

simplify2.2s

Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
01529
13129
210229
345229
4209029
done500129

prune6.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 20.3b

localize32.0ms

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))
1.3b
(+ (/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) 1.0)
18.0b
(/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i)))

rewrite1.2s

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:
282.0ms
(/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
852.0ms
(+ (/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) 1.0)
88.0ms
(/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i)))

series878.0ms

Counts
3 → 9
Calls
3 calls:
342.0ms
(/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
420.0ms
(+ (/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) 1.0)
116.0ms
(/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i)))

simplify1.7s

Counts
120 → 120
Iterations

Useful iterations: 2 (547.0ms)

IterNodesCost
02254035
16753821
229493577
done50003577

prune556.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 2.0b

localize31.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
0.1b
(/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i)))
2.1b
(+ (* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) 1.0)
2.2b
(* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))

rewrite1.2s

Algorithm
rewrite-expression-head
Rules
321×times-frac
290×*-un-lft-identity
211×add-sqr-sqrt
140×add-cube-cbrt
90×associate-*r*
44×distribute-lft-out
31×distribute-lft-out-- difference-of-squares
26×associate-/l*
24×associate-/r/
20×add-exp-log add-cbrt-cube
15×flip3-+ flip-+
12×div-inv
7×cbrt-undiv div-exp associate-/r*
6×pow1 add-log-exp
4×associate-*l*
3×div-sub prod-exp cbrt-unprod associate-/l/ unswap-sqr
2×frac-times frac-2neg associate-*l/ clear-num
1×+-commutative flip3-- associate-*r/ pow-prod-down sum-log *-commutative flip--
Counts
4 → 295
Calls
4 calls:
297.0ms
(/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
72.0ms
(/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i)))
149.0ms
(+ (* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) 1.0)
634.0ms
(* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))

series1.1s

Counts
4 → 12
Calls
4 calls:
239.0ms
(/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
112.0ms
(/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i)))
395.0ms
(+ (* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) 1.0)
341.0ms
(* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))

simplify2.8s

Counts
307 → 307
Iterations

Useful iterations: done (2.8s)

IterNodesCost
03859712
110519275
246158911
done50018909

prune1.3s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 2.0b

localize38.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i)))
2.1b
(+ (* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) 1.0)
2.1b
(log (exp (+ (* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) 1.0)))
2.2b
(* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))

rewrite1.4s

Algorithm
rewrite-expression-head
Rules
162×times-frac
151×*-un-lft-identity
116×add-sqr-sqrt
90×associate-*r*
75×add-cube-cbrt
22×distribute-lft-out
16×distribute-lft-out-- difference-of-squares
15×add-exp-log add-cbrt-cube
12×associate-/r/
9×flip3-+ flip-+
7×pow1
6×div-inv add-log-exp
5×associate-/l*
4×cbrt-undiv log-prod div-exp associate-*l* log-pow
3×exp-prod prod-exp associate-/r* cbrt-unprod unswap-sqr
2×frac-times associate-*l/ associate-/l/
1×+-commutative flip3-- frac-2neg div-sub associate-*r/ rem-log-exp exp-sum pow-prod-down clear-num sum-log *-commutative flip--
Counts
4 → 184
Calls
4 calls:
63.0ms
(/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i)))
130.0ms
(+ (* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) 1.0)
570.0ms
(log (exp (+ (* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) 1.0)))
616.0ms
(* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))

series1.3s

Counts
4 → 12
Calls
4 calls:
118.0ms
(/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i)))
402.0ms
(+ (* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) 1.0)
401.0ms
(log (exp (+ (* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) 1.0)))
356.0ms
(* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))

simplify2.3s

Counts
196 → 196
Iterations

Useful iterations: done (2.3s)

IterNodesCost
03255447
18935140
239604794
done50014792

prune1.3s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 2.0b

localize40.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (- beta alpha) (/ 1 (+ (+ alpha beta) (* 2.0 i))))
2.1b
(+ (* (+ alpha beta) (/ (* (- beta alpha) (/ 1 (+ (+ alpha beta) (* 2.0 i)))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) 1.0)
2.1b
(log (exp (+ (* (+ alpha beta) (/ (* (- beta alpha) (/ 1 (+ (+ alpha beta) (* 2.0 i)))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) 1.0)))
2.2b
(* (+ alpha beta) (/ (* (- beta alpha) (/ 1 (+ (+ alpha beta) (* 2.0 i)))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))

rewrite1.8s

Algorithm
rewrite-expression-head
Rules
35×add-exp-log
28×add-sqr-sqrt
25×associate-*r*
24×*-un-lft-identity
23×add-cbrt-cube
17×add-cube-cbrt
15×times-frac
14×prod-exp
9×pow1 div-exp associate-*l*
8×cbrt-unprod
6×add-log-exp
5×cbrt-undiv flip3-+ flip-+
4×frac-times log-prod associate-*l/ associate-/r/ log-pow unswap-sqr
3×exp-prod
2×rec-exp flip3-- 1-exp associate-*r/ pow-prod-down *-commutative flip-- div-inv distribute-lft-out
1×+-commutative rem-log-exp exp-sum sum-log un-div-inv distribute-lft-out-- difference-of-squares
Counts
4 → 110
Calls
4 calls:
121.0ms
(* (- beta alpha) (/ 1 (+ (+ alpha beta) (* 2.0 i))))
217.0ms
(+ (* (+ alpha beta) (/ (* (- beta alpha) (/ 1 (+ (+ alpha beta) (* 2.0 i)))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) 1.0)
822.0ms
(log (exp (+ (* (+ alpha beta) (/ (* (- beta alpha) (/ 1 (+ (+ alpha beta) (* 2.0 i)))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) 1.0)))
646.0ms
(* (+ alpha beta) (/ (* (- beta alpha) (/ 1 (+ (+ alpha beta) (* 2.0 i)))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))

series1.4s

Counts
4 → 12
Calls
4 calls:
134.0ms
(* (- beta alpha) (/ 1 (+ (+ alpha beta) (* 2.0 i))))
449.0ms
(+ (* (+ alpha beta) (/ (* (- beta alpha) (/ 1 (+ (+ alpha beta) (* 2.0 i)))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) 1.0)
443.0ms
(log (exp (+ (* (+ alpha beta) (/ (* (- beta alpha) (/ 1 (+ (+ alpha beta) (* 2.0 i)))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) 1.0)))
374.0ms
(* (+ alpha beta) (/ (* (- beta alpha) (/ 1 (+ (+ alpha beta) (* 2.0 i)))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))

simplify2.1s

Counts
122 → 122
Iterations

Useful iterations: 2 (703.0ms)

IterNodesCost
02513505
16843077
228792663
done50022663

prune631.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 2.0b

regimes11.0ms