Details

Time bar (total: 4.2m)

sample117.0ms

Algorithm
intervals
Results
45.0ms207×body80valid
17.0ms18×body1280valid
14.0ms256×pre80true
14.0ms19×body640valid
4.0ms7×body320valid
2.0ms5×body160valid

simplify139.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
138.0ms
(/ (+ (/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0)) 1.0) 2.0)

prune12.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 23.3b

localize64.0ms

Local error

Found 3 expressions with local error:

22.8b
(/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2 i)))
1.5b
(+ (/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0)) 1.0)
0.1b
(/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0))

rewrite807.0ms

Algorithm
rewrite-expression-head
Rules
54×times-frac
47×*-un-lft-identity
25×add-sqr-sqrt add-cube-cbrt
17×add-cbrt-cube add-exp-log
14×associate-/r/
11×flip3-+ flip-+ distribute-lft-out
10×associate-/l*
9×associate-/l/
7×cbrt-undiv associate-/r* div-exp div-inv
5×add-log-exp
4×frac-times
3×pow1 flip3-- insert-posit16 flip--
2×clear-num frac-2neg associate-*l/ prod-exp associate-*r/ cbrt-unprod
1×+-commutative sum-log
Counts
3 → 114
Calls
3 calls:
Slowest
546.0ms
(+ (/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0)) 1.0)
189.0ms
(/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0))
69.0ms
(/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2 i)))

series837.0ms

Counts
3 → 9
Calls
3 calls:
Slowest
410.0ms
(+ (/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0)) 1.0)
318.0ms
(/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0))
108.0ms
(/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2 i)))

simplify26.6s

Counts
128 → 123
Calls
128 calls:
Slowest
722.0ms
(/ (/ 1 (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0))
720.0ms
(/ (* (* (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2 i))) (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2 i)))) (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2 i)))) (* (* (+ (+ (+ alpha beta) (* 2 i)) 2.0) (+ (+ (+ alpha beta) (* 2 i)) 2.0)) (+ (+ (+ alpha beta) (* 2 i)) 2.0)))
678.0ms
(/ (* (* (* (+ alpha beta) (- beta alpha)) (* (+ alpha beta) (- beta alpha))) (* (+ alpha beta) (- beta alpha))) (* (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i))) (+ (+ alpha beta) (* 2 i))))
663.0ms
(/ (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0))
634.0ms
(/ (/ 1 (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0))

prune1.5s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 5.2b

localize44.0ms

Local error

Found 4 expressions with local error:

1.5b
(+ (/ (/ (+ alpha beta) (/ (+ (+ alpha beta) (* 2 i)) (- beta alpha))) (+ (+ (+ alpha beta) (* 2 i)) 2.0)) 1.0)
0.1b
(/ (+ alpha beta) (/ (+ (+ alpha beta) (* 2 i)) (- beta alpha)))
0.1b
(/ (/ (+ alpha beta) (/ (+ (+ alpha beta) (* 2 i)) (- beta alpha))) (+ (+ (+ alpha beta) (* 2 i)) 2.0))
0.0b
(/ (+ (+ alpha beta) (* 2 i)) (- beta alpha))

rewrite970.0ms

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-cbrt-cube add-exp-log
10×cbrt-undiv div-exp
6×add-log-exp
5×associate-/l/
4×pow1 flip3-+ flip-+ insert-posit16
3×clear-num frac-2neg
1×+-commutative sum-log
Counts
4 → 649
Calls
4 calls:
Slowest
617.0ms
(+ (/ (/ (+ alpha beta) (/ (+ (+ alpha beta) (* 2 i)) (- beta alpha))) (+ (+ (+ alpha beta) (* 2 i)) 2.0)) 1.0)
191.0ms
(/ (/ (+ alpha beta) (/ (+ (+ alpha beta) (* 2 i)) (- beta alpha))) (+ (+ (+ alpha beta) (* 2 i)) 2.0))
83.0ms
(/ (+ (+ alpha beta) (* 2 i)) (- beta alpha))
58.0ms
(/ (+ alpha beta) (/ (+ (+ alpha beta) (* 2 i)) (- beta alpha)))

series1.1s

Counts
4 → 12
Calls
4 calls:
Slowest
418.0ms
(+ (/ (/ (+ alpha beta) (/ (+ (+ alpha beta) (* 2 i)) (- beta alpha))) (+ (+ (+ alpha beta) (* 2 i)) 2.0)) 1.0)
325.0ms
(/ (/ (+ alpha beta) (/ (+ (+ alpha beta) (* 2 i)) (- beta alpha))) (+ (+ (+ alpha beta) (* 2 i)) 2.0))
204.0ms
(/ (+ (+ alpha beta) (* 2 i)) (- beta alpha))
106.0ms
(/ (+ alpha beta) (/ (+ (+ alpha beta) (* 2 i)) (- beta alpha)))

simplify3.3m

Counts
1068 → 661
Calls
1068 calls:
Slowest
1.0s
(/ (/ 1 (/ (* (cbrt (+ (+ alpha beta) (* 2 i))) (cbrt (+ (+ alpha beta) (* 2 i)))) (+ (sqrt beta) (sqrt alpha)))) 1)
784.0ms
(/ (* (* (/ (+ alpha beta) (/ (+ (+ alpha beta) (* 2 i)) (- beta alpha))) (/ (+ alpha beta) (/ (+ (+ alpha beta) (* 2 i)) (- beta alpha)))) (/ (+ alpha beta) (/ (+ (+ alpha beta) (* 2 i)) (- beta alpha)))) (* (* (+ (+ (+ alpha beta) (* 2 i)) 2.0) (+ (+ (+ alpha beta) (* 2 i)) 2.0)) (+ (+ (+ alpha beta) (* 2 i)) 2.0)))
777.0ms
(/ (/ (cbrt (+ alpha beta)) (+ (* beta beta) (+ (* alpha alpha) (* beta alpha)))) (+ (+ (+ alpha beta) (* 2 i)) 2.0))
756.0ms
(/ (/ (+ alpha beta) (+ (* beta beta) (+ (* alpha alpha) (* beta alpha)))) (+ (+ (+ alpha beta) (* 2 i)) 2.0))
753.0ms
(/ (/ (cbrt (+ alpha beta)) (+ (* beta beta) (+ (* alpha alpha) (* beta alpha)))) (+ (+ (+ alpha beta) (* 2 i)) 2.0))

prune8.8s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 5.2b

localize99.0ms

Local error

Found 4 expressions with local error:

2.1b
(- (* 1.0 1.0) (* (/ (/ (+ alpha beta) (/ (+ (+ alpha beta) (* 2 i)) (- beta alpha))) (+ (+ (+ alpha beta) (* 2 i)) 2.0)) 1.0))
1.5b
(+ (pow (/ (/ (+ alpha beta) (/ (+ (+ alpha beta) (* 2 i)) (- beta alpha))) (+ (+ (+ alpha beta) (* 2 i)) 2.0)) 3) (pow 1.0 3))
0.1b
(* (/ (/ (+ alpha beta) (/ (+ (+ alpha beta) (* 2 i)) (- beta alpha))) (+ (+ (+ alpha beta) (* 2 i)) 2.0)) (/ (/ (+ alpha beta) (/ (+ (+ alpha beta) (* 2 i)) (- beta alpha))) (+ (+ (+ alpha beta) (* 2 i)) 2.0)))
0.1b
(/ (+ alpha beta) (/ (+ (+ alpha beta) (* 2 i)) (- beta alpha)))

rewrite2.3s

Algorithm
rewrite-expression-head
Rules
7531×times-frac
7517×*-un-lft-identity
2913×add-sqr-sqrt
2179×add-cube-cbrt
1689×distribute-lft-out
1008×swap-sqr
543×distribute-lft-out--
362×associate-*r* associate-*l*
327×difference-of-squares
247×associate-/r/
134×div-inv
110×flip3-- flip--
89×add-cbrt-cube add-exp-log
51×cbrt-undiv div-exp
21×associate-/r*
16×prod-exp cbrt-unprod unswap-sqr
11×pow1
8×add-log-exp
6×flip3-+ flip-+
4×unpow-prod-down cube-prod insert-posit16 associate-/l*
2×associate-/l/
1×pow2 frac-times +-commutative clear-num sum-log sub-neg frac-2neg pow-plus distribute-rgt-out-- diff-log pow-prod-down associate-*l/ associate-*r/ pow-sqr sum-cubes *-commutative pow-prod-up
Counts
4 → 1956
Calls
4 calls:
Slowest
1.3s
(+ (pow (/ (/ (+ alpha beta) (/ (+ (+ alpha beta) (* 2 i)) (- beta alpha))) (+ (+ (+ alpha beta) (* 2 i)) 2.0)) 3) (pow 1.0 3))
801.0ms
(* (/ (/ (+ alpha beta) (/ (+ (+ alpha beta) (* 2 i)) (- beta alpha))) (+ (+ (+ alpha beta) (* 2 i)) 2.0)) (/ (/ (+ alpha beta) (/ (+ (+ alpha beta) (* 2 i)) (- beta alpha))) (+ (+ (+ alpha beta) (* 2 i)) 2.0)))
56.0ms
(/ (+ alpha beta) (/ (+ (+ alpha beta) (* 2 i)) (- beta alpha)))
14.0ms
(- (* 1.0 1.0) (* (/ (/ (+ alpha beta) (/ (+ (+ alpha beta) (* 2 i)) (- beta alpha))) (+ (+ (+ alpha beta) (* 2 i)) 2.0)) 1.0))

series10.8s

Counts
4 → 12
Calls
4 calls:
Slowest
8.3s
(+ (pow (/ (/ (+ alpha beta) (/ (+ (+ alpha beta) (* 2 i)) (- beta alpha))) (+ (+ (+ alpha beta) (* 2 i)) 2.0)) 3) (pow 1.0 3))
2.1s
(* (/ (/ (+ alpha beta) (/ (+ (+ alpha beta) (* 2 i)) (- beta alpha))) (+ (+ (+ alpha beta) (* 2 i)) 2.0)) (/ (/ (+ alpha beta) (/ (+ (+ alpha beta) (* 2 i)) (- beta alpha))) (+ (+ (+ alpha beta) (* 2 i)) 2.0)))
276.0ms
(- (* 1.0 1.0) (* (/ (/ (+ alpha beta) (/ (+ (+ alpha beta) (* 2 i)) (- beta alpha))) (+ (+ (+ alpha beta) (* 2 i)) 2.0)) 1.0))
135.0ms
(/ (+ alpha beta) (/ (+ (+ alpha beta) (* 2 i)) (- beta alpha)))