Details

Time bar (total: 7.9m)

sample59.0ms

Algorithm
intervals
Results
36.0ms256×body80valid
9.0ms256×pre80true

simplify131.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
130.0ms
(/ (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2 1))) (+ (+ alpha beta) (* 2 1))) (+ (+ (+ alpha beta) (* 2 1)) 1.0))

prune17.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 3.3b

localize53.0ms

Local error

Found 4 expressions with local error:

3.1b
(/ (+ 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)))
0.0b
(+ (+ 1.0 (+ beta alpha)) 2)

rewrite944.0ms

Algorithm
rewrite-expression-head
Rules
4332×*-un-lft-identity
2696×times-frac
2173×distribute-lft-out
778×add-sqr-sqrt add-cube-cbrt
166×associate-/l*
102×associate-/r/
53×flip3-+ flip-+
51×div-inv
20×add-cbrt-cube add-exp-log
16×associate-/r*
13×add-log-exp
10×cbrt-undiv div-exp
6×sum-log
4×pow1 insert-posit16 associate-/l/
3×clear-num frac-2neg
1×+-commutative associate-+l+
Counts
4 → 1221
Calls
4 calls:
Slowest
364.0ms
(/ (/ (/ (+ 1.0 (+ (* alpha beta) (+ beta alpha))) (+ 2 (+ beta alpha))) (+ 2 (+ beta alpha))) (+ (+ 1.0 (+ beta alpha)) 2))
212.0ms
(/ (/ (+ 1.0 (+ (* alpha beta) (+ beta alpha))) (+ 2 (+ beta alpha))) (+ 2 (+ beta alpha)))
150.0ms
(/ (+ 1.0 (+ (* alpha beta) (+ beta alpha))) (+ 2 (+ beta alpha)))
113.0ms
(+ (+ 1.0 (+ beta alpha)) 2)

series639.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
251.0ms
(/ (/ (/ (+ 1.0 (+ (* alpha beta) (+ beta alpha))) (+ 2 (+ beta alpha))) (+ 2 (+ beta alpha))) (+ (+ 1.0 (+ beta alpha)) 2))
233.0ms
(/ (/ (+ 1.0 (+ (* alpha beta) (+ beta alpha))) (+ 2 (+ beta alpha))) (+ 2 (+ beta alpha)))
130.0ms
(/ (+ 1.0 (+ (* alpha beta) (+ beta alpha))) (+ 2 (+ beta alpha)))
25.0ms
(+ (+ 1.0 (+ beta alpha)) 2)

simplify7.5m

Counts
2150 → 1233
Calls
2150 calls:
Slowest
1.0s
(/ (/ (/ (+ 1.0 (+ (* alpha beta) (+ beta alpha))) (sqrt (+ 2 (+ beta alpha)))) (+ 2 (+ beta alpha))) (+ (+ 1.0 (+ beta alpha)) 2))
1.0s
(/ (* (* (+ 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))))
976.0ms
(/ (/ (/ (+ 1.0 (+ (* alpha beta) (+ beta alpha))) (- (* 2 2) (* (+ beta alpha) (+ beta alpha)))) (sqrt (+ 2 (+ beta alpha)))) (sqrt (+ (+ 1.0 (+ beta alpha)) 2)))
910.0ms
(/ (/ (/ (+ 1.0 (+ (* alpha beta) (+ beta alpha))) (sqrt (+ 2 (+ beta alpha)))) (+ 2 (+ beta alpha))) (+ (+ 1.0 (+ beta alpha)) 2))
900.0ms
(/ (/ (/ (+ 1.0 (+ (* alpha beta) (+ beta alpha))) (+ 2 (+ beta alpha))) (+ 2 (+ beta alpha))) (sqrt (+ (+ 1.0 (+ beta alpha)) 2)))

prune14.6s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.9b

localize35.0ms

Local error

Found 4 expressions with local error:

3.1b
(/ (+ 1.0 (+ (* alpha beta) (+ beta alpha))) (+ 2 (+ beta alpha)))
3.1b
(/ (+ 1.0 (+ (* alpha beta) (+ 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))
0.1b
(* (/ (sqrt (/ (/ (+ 1.0 (+ (* alpha beta) (+ beta alpha))) (+ 2 (+ beta alpha))) (+ 2 (+ beta alpha)))) 1) (/ (sqrt (/ (/ (+ 1.0 (+ (* alpha beta) (+ beta alpha))) (+ 2 (+ beta alpha))) (+ 2 (+ beta alpha)))) (+ (+ 1.0 (+ beta alpha)) 2)))

rewrite1.8s

Algorithm
rewrite-expression-head
Rules
8779×*-un-lft-identity
5938×times-frac
4324×distribute-lft-out
2233×sqrt-prod
1897×add-sqr-sqrt
1694×add-cube-cbrt
840×associate-*r*
421×associate-*l*
200×associate-/r/
147×associate-/l*
102×flip3-+ flip-+
101×div-inv
45×unswap-sqr
27×add-exp-log
22×add-cbrt-cube
16×associate-/r*
10×div-exp
7×cbrt-undiv
6×pow1 prod-exp
5×associate-/l/
4×cbrt-unprod insert-posit16 add-log-exp
3×clear-num frac-2neg
2×1-exp
1×frac-times sqrt-div pow-prod-down associate-*l/ associate-*r/ *-commutative
Counts
4 → 2416
Calls
4 calls:
Slowest
988.0ms
(* (/ (sqrt (/ (/ (+ 1.0 (+ (* alpha beta) (+ beta alpha))) (+ 2 (+ beta alpha))) (+ 2 (+ beta alpha)))) 1) (/ (sqrt (/ (/ (+ 1.0 (+ (* alpha beta) (+ beta alpha))) (+ 2 (+ beta alpha))) (+ 2 (+ beta alpha)))) (+ (+ 1.0 (+ beta alpha)) 2)))
315.0ms
(/ (sqrt (/ (/ (+ 1.0 (+ (* alpha beta) (+ beta alpha))) (+ 2 (+ beta alpha))) (+ 2 (+ beta alpha)))) (+ (+ 1.0 (+ beta alpha)) 2))
172.0ms
(/ (+ 1.0 (+ (* alpha beta) (+ beta alpha))) (+ 2 (+ beta alpha)))
132.0ms
(/ (+ 1.0 (+ (* alpha beta) (+ beta alpha))) (+ 2 (+ beta alpha)))

series650.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
229.0ms
(* (/ (sqrt (/ (/ (+ 1.0 (+ (* alpha beta) (+ beta alpha))) (+ 2 (+ beta alpha))) (+ 2 (+ beta alpha)))) 1) (/ (sqrt (/ (/ (+ 1.0 (+ (* alpha beta) (+ beta alpha))) (+ 2 (+ beta alpha))) (+ 2 (+ beta alpha)))) (+ (+ 1.0 (+ beta alpha)) 2)))
166.0ms
(/ (sqrt (/ (/ (+ 1.0 (+ (* alpha beta) (+ beta alpha))) (+ 2 (+ beta alpha))) (+ 2 (+ beta alpha)))) (+ (+ 1.0 (+ beta alpha)) 2))
142.0ms
(/ (+ 1.0 (+ (* alpha beta) (+ beta alpha))) (+ 2 (+ beta alpha)))
113.0ms
(/ (+ 1.0 (+ (* alpha beta) (+ beta alpha))) (+ 2 (+ beta alpha)))