Details

Time bar (total: 9.6m)

sample92.0ms

Algorithm
intervals
Results
27.0ms198×body80valid
11.0ms22×body640valid
11.0ms17×body1280valid
11.0ms256×pre80true
10.0ms11×body320valid
2.0ms8×body160valid

simplify167.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
166.0ms
(/ (+ (/ (/ (* (+ 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: 27.2b

localize61.0ms

Local error

Found 3 expressions with local error:

23.1b
(/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2 i)))
2.5b
(+ (/ (/ (* (+ 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))

rewrite683.0ms

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
473.0ms
(+ (/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0)) 1.0)
160.0ms
(/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0))
49.0ms
(/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2 i)))

series825.0ms

Counts
3 → 9
Calls
3 calls:
Slowest
386.0ms
(+ (/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0)) 1.0)
333.0ms
(/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0))
106.0ms
(/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2 i)))

simplify24.9s

Counts
128 → 123
Calls
128 calls:
Slowest
1.1s
(/ (* (* (/ (* (+ 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)))
696.0ms
(/ (* (* (* (+ alpha beta) (- beta alpha)) (* (+ alpha beta) (- beta alpha))) (* (+ alpha beta) (- beta alpha))) (* (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i))) (+ (+ alpha beta) (* 2 i))))
641.0ms
(/ (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0))
638.0ms
(/ (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0))
601.0ms
(/ (/ 1 (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0))

prune1.4s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 5.1b

localize45.0ms

Local error

Found 4 expressions with local error:

2.5b
(+ (/ (/ (+ 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))

rewrite980.0ms

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
657.0ms
(+ (/ (/ (+ alpha beta) (/ (+ (+ alpha beta) (* 2 i)) (- beta alpha))) (+ (+ (+ alpha beta) (* 2 i)) 2.0)) 1.0)
169.0ms
(/ (/ (+ alpha beta) (/ (+ (+ alpha beta) (* 2 i)) (- beta alpha))) (+ (+ (+ alpha beta) (* 2 i)) 2.0))
78.0ms
(/ (+ (+ alpha beta) (* 2 i)) (- beta alpha))
47.0ms
(/ (+ alpha beta) (/ (+ (+ alpha beta) (* 2 i)) (- beta alpha)))

series961.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
369.0ms
(+ (/ (/ (+ alpha beta) (/ (+ (+ alpha beta) (* 2 i)) (- beta alpha))) (+ (+ (+ alpha beta) (* 2 i)) 2.0)) 1.0)
318.0ms
(/ (/ (+ alpha beta) (/ (+ (+ alpha beta) (* 2 i)) (- beta alpha))) (+ (+ (+ alpha beta) (* 2 i)) 2.0))
148.0ms
(/ (+ (+ alpha beta) (* 2 i)) (- beta alpha))
125.0ms
(/ (+ alpha beta) (/ (+ (+ alpha beta) (* 2 i)) (- beta alpha)))

simplify3.2m

Counts
1068 → 661
Calls
1068 calls:
Slowest
1.1s
(/ (/ (sqrt (+ alpha beta)) (+ (* beta beta) (+ (* alpha alpha) (* beta alpha)))) (+ (+ (+ alpha beta) (* 2 i)) 2.0))
834.0ms
(/ (/ (sqrt (+ alpha beta)) (/ (* (cbrt (+ (+ alpha beta) (* 2 i))) (cbrt (+ (+ alpha beta) (* 2 i)))) (* (cbrt (- beta alpha)) (cbrt (- beta alpha))))) 1)
777.0ms
(/ (/ (cbrt (+ alpha beta)) (+ (* beta beta) (+ (* alpha alpha) (* beta alpha)))) (+ (+ (+ alpha beta) (* 2 i)) 2.0))
772.0ms
(/ (/ (+ alpha beta) (+ (* beta beta) (+ (* alpha alpha) (* beta alpha)))) (+ (+ (+ alpha beta) (* 2 i)) 2.0))
759.0ms
(/ (/ (sqrt (+ alpha beta)) (+ (* beta beta) (+ (* alpha alpha) (* beta alpha)))) (+ (+ (+ alpha beta) (* 2 i)) 2.0))

prune8.8s

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 5.1b

localize95.0ms

Local error

Found 4 expressions with local error:

2.5b
(+ (pow (/ (/ (+ alpha beta) (/ (+ (+ alpha beta) (* 2 i)) (- beta alpha))) (+ (+ (+ alpha beta) (* 2 i)) 2.0)) 3) (pow 1.0 3))
1.7b
(- (* 1.0 1.0) (* (/ (/ (+ alpha beta) (/ (+ (+ alpha beta) (* 2 i)) (- beta alpha))) (+ (+ (+ alpha beta) (* 2 i)) 2.0)) 1.0))
0.1b
(pow (/ (/ (+ alpha beta) (/ (+ (+ alpha beta) (* 2 i)) (- beta alpha))) (+ (+ (+ alpha beta) (* 2 i)) 2.0)) 3)
0.1b
(/ (+ alpha beta) (/ (+ (+ alpha beta) (* 2 i)) (- beta alpha)))

rewrite1.5s

Algorithm
rewrite-expression-head
Rules
2023×times-frac
1684×*-un-lft-identity
938×add-sqr-sqrt
716×add-cube-cbrt
373×distribute-lft-out
366×unpow-prod-down cube-prod
111×distribute-lft-out-- difference-of-squares
87×associate-/r/
48×div-inv
38×flip3-- flip--
21×associate-/r*
19×add-cbrt-cube add-exp-log
9×cbrt-undiv div-exp
8×add-log-exp
5×pow1
4×flip3-+ pow-exp flip-+ insert-posit16 associate-/l* rem-cube-cbrt
3×pow-unpow
2×associate-/l/
1×cube-div cube-mult pow-to-exp +-commutative clear-num sum-log sub-neg pow-pow frac-2neg distribute-rgt-out-- diff-log unpow3 sum-cubes sqr-pow
Counts
4 → 908
Calls
4 calls:
Slowest
1.2s
(+ (pow (/ (/ (+ alpha beta) (/ (+ (+ alpha beta) (* 2 i)) (- beta alpha))) (+ (+ (+ alpha beta) (* 2 i)) 2.0)) 3) (pow 1.0 3))
149.0ms
(pow (/ (/ (+ alpha beta) (/ (+ (+ alpha beta) (* 2 i)) (- beta alpha))) (+ (+ (+ alpha beta) (* 2 i)) 2.0)) 3)
64.0ms
(/ (+ alpha beta) (/ (+ (+ alpha beta) (* 2 i)) (- beta alpha)))
7.0ms
(- (* 1.0 1.0) (* (/ (/ (+ alpha beta) (/ (+ (+ alpha beta) (* 2 i)) (- beta alpha))) (+ (+ (+ alpha beta) (* 2 i)) 2.0)) 1.0))

series11.3s

Counts
4 → 12
Calls
4 calls:
Slowest
7.4s
(+ (pow (/ (/ (+ alpha beta) (/ (+ (+ alpha beta) (* 2 i)) (- beta alpha))) (+ (+ (+ alpha beta) (* 2 i)) 2.0)) 3) (pow 1.0 3))
3.6s
(pow (/ (/ (+ alpha beta) (/ (+ (+ alpha beta) (* 2 i)) (- beta alpha))) (+ (+ (+ alpha beta) (* 2 i)) 2.0)) 3)
236.0ms
(- (* 1.0 1.0) (* (/ (/ (+ alpha beta) (/ (+ (+ alpha beta) (* 2 i)) (- beta alpha))) (+ (+ (+ alpha beta) (* 2 i)) 2.0)) 1.0))
134.0ms
(/ (+ alpha beta) (/ (+ (+ alpha beta) (* 2 i)) (- beta alpha)))

simplify4.9m

Counts
960 → 920
Calls
960 calls:
Slowest
1.5s
(pow (/ (/ (* (cbrt (+ alpha beta)) (cbrt (+ alpha beta))) (/ (* (cbrt (+ (+ alpha beta) (* 2 i))) (cbrt (+ (+ alpha beta) (* 2 i)))) 1)) 1) 3)
1.2s
(pow (/ (+ alpha beta) (/ (+ (+ alpha beta) (* 2 i)) (- beta alpha))) 3)
1.2s
(pow (/ (/ (* (cbrt (+ alpha beta)) (cbrt (+ alpha beta))) (* (cbrt (/ (+ (+ alpha beta) (* 2 i)) (- beta alpha))) (cbrt (/ (+ (+ alpha beta) (* 2 i)) (- beta alpha))))) 1) 3)
1.2s
(pow (/ (/ (* (cbrt (+ alpha beta)) (cbrt (+ alpha beta))) (/ (* (cbrt (+ (+ alpha beta) (* 2 i))) (cbrt (+ (+ alpha beta) (* 2 i)))) 1)) 1) 3)
1.1s
(pow (/ (/ 1 (/ (* (cbrt (+ (+ alpha beta) (* 2 i))) (cbrt (+ (+ alpha beta) (* 2 i)))) 1)) (sqrt (+ (+ (+ alpha beta) (* 2 i)) 2.0))) 3)

prune20.8s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 5.0b

localize123.0ms

Local error

Found 4 expressions with local error:

2.5b
(+ (log (exp (pow (/ (/ (+ alpha beta) (/ (+ (+ alpha beta) (* 2 i)) (- beta alpha))) (+ (+ (+ alpha beta) (* 2 i)) 2.0)) 3))) (pow 1.0 3))
1.7b
(- (* 1.0 1.0) (* (/ (/ (+ alpha beta) (/ (+ (+ alpha beta) (* 2 i)) (- beta alpha))) (+ (+ (+ alpha beta) (* 2 i)) 2.0)) 1.0))
1.0b
(log (exp (pow (/ (/ (+ alpha beta) (/ (+ (+ alpha beta) (* 2 i)) (- beta alpha))) (+ (+ (+ alpha beta) (* 2 i)) 2.0)) 3)))
0.1b
(pow (/ (/ (+ alpha beta) (/ (+ (+ alpha beta) (* 2 i)) (- beta alpha))) (+ (+ (+ alpha beta) (* 2 i)) 2.0)) 3)

rewrite4.5s

Algorithm
rewrite-expression-head
Rules
3728×times-frac
3067×*-un-lft-identity
1680×add-sqr-sqrt
1296×add-cube-cbrt
732×log-pow
730×exp-prod
724×unpow-prod-down cube-prod
694×distribute-lft-out
192×distribute-lft-out-- difference-of-squares
152×associate-/r/
84×div-inv
65×flip3-- flip--
14×add-cbrt-cube add-exp-log
7×pow1 add-log-exp
6×cbrt-undiv log-prod div-exp
5×flip3-+ flip-+
4×pow-exp insert-posit16 rem-cube-cbrt
3×pow-unpow associate-+l+
2×cube-mult unpow3 sqr-pow
1×cube-div pow-to-exp +-commutative sum-log sub-neg pow-pow distribute-rgt-out-- diff-log rem-log-exp
Counts
4 → 1523
Calls
4 calls:
Slowest
3.6s
(+ (log (exp (pow (/ (/ (+ alpha beta) (/ (+ (+ alpha beta) (* 2 i)) (- beta alpha))) (+ (+ (+ alpha beta) (* 2 i)) 2.0)) 3))) (pow 1.0 3))
642.0ms
(log (exp (pow (/ (/ (+ alpha beta) (/ (+ (+ alpha beta) (* 2 i)) (- beta alpha))) (+ (+ (+ alpha beta) (* 2 i)) 2.0)) 3)))
143.0ms
(pow (/ (/ (+ alpha beta) (/ (+ (+ alpha beta) (* 2 i)) (- beta alpha))) (+ (+ (+ alpha beta) (* 2 i)) 2.0)) 3)
13.0ms
(- (* 1.0 1.0) (* (/ (/ (+ alpha beta) (/ (+ (+ alpha beta) (* 2 i)) (- beta alpha))) (+ (+ (+ alpha beta) (* 2 i)) 2.0)) 1.0))

series14.9s

Counts
4 → 12
Calls
4 calls:
Slowest
7.4s
(+ (log (exp (pow (/ (/ (+ alpha beta) (/ (+ (+ alpha beta) (* 2 i)) (- beta alpha))) (+ (+ (+ alpha beta) (* 2 i)) 2.0)) 3))) (pow 1.0 3))
3.6s
(pow (/ (/ (+ alpha beta) (/ (+ (+ alpha beta) (* 2 i)) (- beta alpha))) (+ (+ (+ alpha beta) (* 2 i)) 2.0)) 3)
3.6s
(log (exp (pow (/ (/ (+ alpha beta) (/ (+ (+ alpha beta) (* 2 i)) (- beta alpha))) (+ (+ (+ alpha beta) (* 2 i)) 2.0)) 3)))
274.0ms
(- (* 1.0 1.0) (* (/ (/ (+ alpha beta) (/ (+ (+ alpha beta) (* 2 i)) (- beta alpha))) (+ (+ (+ alpha beta) (* 2 i)) 2.0)) 1.0))