Details

Time bar (total: 2.7m)

sample88.0ms

Algorithm
intervals
Results
56.0ms256×body80valid
12.0ms256×pre80true

simplify110.0ms

Calls
1 calls:
Slowest
110.0ms
(/ (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2 1))) (+ (+ alpha beta) (* 2 1))) (+ (+ (+ alpha beta) (* 2 1)) 1.0))

prune15.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 2.3b

localize26.0ms

Local error

Found 3 expressions with local error:

2.2b
(/ (+ 1.0 (+ (* alpha beta) (+ beta alpha))) (+ 2 (+ beta alpha)))
0.1b
(/ (/ (/ (+ 1.0 (+ (* alpha beta) (+ beta alpha))) (+ 2 (+ beta alpha))) (+ 2 (+ beta alpha))) (+ (+ 1.0 (+ beta alpha)) 2))
0.0b
(/ (/ (+ 1.0 (+ (* alpha beta) (+ beta alpha))) (+ 2 (+ beta alpha))) (+ 2 (+ beta alpha)))

rewrite86.0ms

Algorithm
rewrite-expression-head
Rules
531×times-frac
255×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
69×associate-/l*
46×associate-/r/
24×flip3-+ flip-+
23×div-inv
19×add-cbrt-cube add-exp-log
10×cbrt-undiv div-exp
9×associate-/r*
4×associate-/l/
3×pow1 clear-num frac-2neg insert-posit16 add-log-exp
Calls
3 calls:
Slowest
28.0ms
(/ (/ (/ (+ 1.0 (+ (* alpha beta) (+ beta alpha))) (+ 2 (+ beta alpha))) (+ 2 (+ beta alpha))) (+ (+ 1.0 (+ beta alpha)) 2))
26.0ms
(/ (+ 1.0 (+ (* alpha beta) (+ beta alpha))) (+ 2 (+ beta alpha)))
19.0ms
(/ (/ (+ 1.0 (+ (* alpha beta) (+ beta alpha))) (+ 2 (+ beta alpha))) (+ 2 (+ beta alpha)))

series225.0ms

Calls
3 calls:
Slowest
95.0ms
(/ (/ (/ (+ 1.0 (+ (* alpha beta) (+ beta alpha))) (+ 2 (+ beta alpha))) (+ 2 (+ beta alpha))) (+ (+ 1.0 (+ beta alpha)) 2))
69.0ms
(/ (+ 1.0 (+ (* alpha beta) (+ beta alpha))) (+ 2 (+ beta alpha)))
61.0ms
(/ (/ (+ 1.0 (+ (* alpha beta) (+ beta alpha))) (+ 2 (+ beta alpha))) (+ 2 (+ beta alpha)))

simplify1.7m

Calls
520 calls:
Slowest
975.0ms
(+ (pow 1.0 3) (pow (+ (* alpha beta) (+ beta alpha)) 3))
680.0ms
(/ (/ (* (* (+ 1.0 (+ (* alpha beta) (+ beta alpha))) (+ 1.0 (+ (* alpha beta) (+ beta alpha)))) (+ 1.0 (+ (* alpha beta) (+ beta alpha)))) (* (* (+ 2 (+ beta alpha)) (+ 2 (+ beta alpha))) (+ 2 (+ beta alpha)))) (* (* (+ 2 (+ beta alpha)) (+ 2 (+ beta alpha))) (+ 2 (+ beta alpha))))
656.0ms
(- (- (log (/ (+ 1.0 (+ (* alpha beta) (+ beta alpha))) (+ 2 (+ beta alpha)))) (log (+ 2 (+ beta alpha)))) (log (+ (+ 1.0 (+ beta alpha)) 2)))
641.0ms
(/ (* (* (/ (/ (+ 1.0 (+ (* alpha beta) (+ beta alpha))) (+ 2 (+ beta alpha))) (+ 2 (+ beta alpha))) (/ (/ (+ 1.0 (+ (* alpha beta) (+ beta alpha))) (+ 2 (+ beta alpha))) (+ 2 (+ beta alpha)))) (/ (/ (+ 1.0 (+ (* alpha beta) (+ beta alpha))) (+ 2 (+ beta alpha))) (+ 2 (+ beta alpha)))) (* (* (+ (+ 1.0 (+ beta alpha)) 2) (+ (+ 1.0 (+ beta alpha)) 2)) (+ (+ 1.0 (+ beta alpha)) 2)))
640.0ms
(/ (/ (sqrt (/ (+ 1.0 (+ (* alpha beta) (+ beta alpha))) (+ 2 (+ beta alpha)))) (+ 2 (+ beta alpha))) (+ (+ 1.0 (+ beta alpha)) 2))

prune4.2s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.8b

localize12.0ms

Local error

Found 4 expressions with local error:

2.2b
(/ (+ 2 (+ beta alpha)) (+ 1.0 (+ (* alpha beta) (+ beta alpha))))
0.1b
(/ (/ (/ 1 (/ (+ 2 (+ beta alpha)) (+ 1.0 (+ (* alpha beta) (+ beta alpha))))) (+ 2 (+ beta alpha))) (+ (+ 1.0 (+ beta alpha)) 2))
0.0b
(/ 1 (/ (+ 2 (+ beta alpha)) (+ 1.0 (+ (* alpha beta) (+ beta alpha)))))
0.0b
(/ (/ 1 (/ (+ 2 (+ beta alpha)) (+ 1.0 (+ (* alpha beta) (+ beta alpha))))) (+ 2 (+ beta alpha)))

rewrite49.0ms

Algorithm
rewrite-expression-head
Rules
156×times-frac
87×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
33×associate-/r/
29×associate-/l*
28×add-exp-log
25×div-inv
24×associate-/r*
14×div-exp
13×add-cbrt-cube
9×flip3-+ flip-+
6×rec-exp
5×pow1 cbrt-undiv
4×clear-num frac-2neg insert-posit16 add-log-exp associate-/l/
1×pow-flip inv-pow
Calls
4 calls:
Slowest
22.0ms
(/ (/ (/ 1 (/ (+ 2 (+ beta alpha)) (+ 1.0 (+ (* alpha beta) (+ beta alpha))))) (+ 2 (+ beta alpha))) (+ (+ 1.0 (+ beta alpha)) 2))
13.0ms
(/ (+ 2 (+ beta alpha)) (+ 1.0 (+ (* alpha beta) (+ beta alpha))))
8.0ms
(/ (/ 1 (/ (+ 2 (+ beta alpha)) (+ 1.0 (+ (* alpha beta) (+ beta alpha))))) (+ 2 (+ beta alpha)))
3.0ms
(/ 1 (/ (+ 2 (+ beta alpha)) (+ 1.0 (+ (* alpha beta) (+ beta alpha)))))

series300.0ms

Calls
4 calls:
Slowest
104.0ms
(/ (/ (/ 1 (/ (+ 2 (+ beta alpha)) (+ 1.0 (+ (* alpha beta) (+ beta alpha))))) (+ 2 (+ beta alpha))) (+ (+ 1.0 (+ beta alpha)) 2))
72.0ms
(/ (+ 2 (+ beta alpha)) (+ 1.0 (+ (* alpha beta) (+ beta alpha))))
72.0ms
(/ (/ 1 (/ (+ 2 (+ beta alpha)) (+ 1.0 (+ (* alpha beta) (+ beta alpha))))) (+ 2 (+ beta alpha)))
52.0ms
(/ 1 (/ (+ 2 (+ beta alpha)) (+ 1.0 (+ (* alpha beta) (+ beta alpha)))))

simplify49.0s

Calls
258 calls:
Slowest
768.0ms
(/ (* (* (/ (/ 1 (/ (+ 2 (+ beta alpha)) (+ 1.0 (+ (* alpha beta) (+ beta alpha))))) (+ 2 (+ beta alpha))) (/ (/ 1 (/ (+ 2 (+ beta alpha)) (+ 1.0 (+ (* alpha beta) (+ beta alpha))))) (+ 2 (+ beta alpha)))) (/ (/ 1 (/ (+ 2 (+ beta alpha)) (+ 1.0 (+ (* alpha beta) (+ beta alpha))))) (+ 2 (+ beta alpha)))) (* (* (+ (+ 1.0 (+ beta alpha)) 2) (+ (+ 1.0 (+ beta alpha)) 2)) (+ (+ 1.0 (+ beta alpha)) 2)))
573.0ms
(/ (* (* (/ 1 (/ (+ 2 (+ beta alpha)) (+ 1.0 (+ (* alpha beta) (+ beta alpha))))) (/ 1 (/ (+ 2 (+ beta alpha)) (+ 1.0 (+ (* alpha beta) (+ beta alpha)))))) (/ 1 (/ (+ 2 (+ beta alpha)) (+ 1.0 (+ (* alpha beta) (+ beta alpha)))))) (* (* (+ 2 (+ beta alpha)) (+ 2 (+ beta alpha))) (+ 2 (+ beta alpha))))
568.0ms
(/ (/ (cbrt (/ 1 (/ (+ 2 (+ beta alpha)) (+ 1.0 (+ (* alpha beta) (+ beta alpha)))))) (cbrt (+ 2 (+ beta alpha)))) (cbrt (+ (+ 1.0 (+ beta alpha)) 2)))
537.0ms
(+ (pow 2 3) (pow (+ beta alpha) 3))
515.0ms
(/ (/ (/ 1 (/ (+ 2 (+ beta alpha)) (+ 1.0 (+ (* alpha beta) (+ beta alpha))))) (- (* 2 2) (* (+ beta alpha) (+ beta alpha)))) 1)

prune2.4s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0b

localize9.0ms

Local error

Found 4 expressions with local error:

2.2b
(/ (+ 1.0 (+ (* alpha beta) (+ beta alpha))) (+ 2 (+ beta alpha)))
2.2b
(/ (+ 1.0 (+ (* alpha beta) (+ beta alpha))) (+ 2 (+ beta alpha)))
0.1b
(/ (+ (+ 1.0 (+ beta alpha)) 2) (sqrt (/ (/ (+ 1.0 (+ (* alpha beta) (+ beta alpha))) (+ 2 (+ beta alpha))) (+ 2 (+ beta alpha)))))
0.1b
(/ (sqrt (/ (/ (+ 1.0 (+ (* alpha beta) (+ beta alpha))) (+ 2 (+ beta alpha))) (+ 2 (+ beta alpha)))) (/ (+ (+ 1.0 (+ beta alpha)) 2) (sqrt (/ (/ (+ 1.0 (+ (* alpha beta) (+ beta alpha))) (+ 2 (+ beta alpha))) (+ 2 (+ beta alpha))))))

rewrite1.5s

Algorithm
rewrite-expression-head
Rules
42372×times-frac
17187×sqrt-prod
15906×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
2757×associate-/r/
1407×div-inv
1353×flip3-+ flip-+
227×associate-/r*
63×associate-/l*
57×sqrt-div
15×add-cbrt-cube add-exp-log
7×associate-/l/
6×cbrt-undiv div-exp
4×pow1 clear-num frac-2neg insert-posit16 add-log-exp
Calls
4 calls:
Slowest
62.0ms
(/ (sqrt (/ (/ (+ 1.0 (+ (* alpha beta) (+ beta alpha))) (+ 2 (+ beta alpha))) (+ 2 (+ beta alpha)))) (/ (+ (+ 1.0 (+ beta alpha)) 2) (sqrt (/ (/ (+ 1.0 (+ (* alpha beta) (+ beta alpha))) (+ 2 (+ beta alpha))) (+ 2 (+ beta alpha))))))
26.0ms
(/ (+ (+ 1.0 (+ beta alpha)) 2) (sqrt (/ (/ (+ 1.0 (+ (* alpha beta) (+ beta alpha))) (+ 2 (+ beta alpha))) (+ 2 (+ beta alpha)))))
25.0ms
(/ (+ 1.0 (+ (* alpha beta) (+ beta alpha))) (+ 2 (+ beta alpha)))
15.0ms
(/ (+ 1.0 (+ (* alpha beta) (+ beta alpha))) (+ 2 (+ beta alpha)))

series388.0ms

Calls
4 calls:
Slowest
179.0ms
(/ (+ (+ 1.0 (+ beta alpha)) 2) (sqrt (/ (/ (+ 1.0 (+ (* alpha beta) (+ beta alpha))) (+ 2 (+ beta alpha))) (+ 2 (+ beta alpha)))))
104.0ms
(/ (sqrt (/ (/ (+ 1.0 (+ (* alpha beta) (+ beta alpha))) (+ 2 (+ beta alpha))) (+ 2 (+ beta alpha)))) (/ (+ (+ 1.0 (+ beta alpha)) 2) (sqrt (/ (/ (+ 1.0 (+ (* alpha beta) (+ beta alpha))) (+ 2 (+ beta alpha))) (+ 2 (+ beta alpha))))))
55.0ms
(/ (+ 1.0 (+ (* alpha beta) (+ beta alpha))) (+ 2 (+ beta alpha)))
50.0ms
(/ (+ 1.0 (+ (* alpha beta) (+ beta alpha))) (+ 2 (+ beta alpha)))