Details

Time bar (total: 8.8m)

sample67.0ms

Algorithm
intervals
Results
45.0ms256×body80valid
10.0ms256×pre80true

simplify130.0ms

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: 2.6b

localize32.0ms

Local error

Found 4 expressions with local error:

2.4b
(/ (+ 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)

rewrite995.0ms

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
372.0ms
(/ (/ (/ (+ 1.0 (+ (* alpha beta) (+ beta alpha))) (+ 2 (+ beta alpha))) (+ 2 (+ beta alpha))) (+ (+ 1.0 (+ beta alpha)) 2))
216.0ms
(/ (/ (+ 1.0 (+ (* alpha beta) (+ beta alpha))) (+ 2 (+ beta alpha))) (+ 2 (+ beta alpha)))
206.0ms
(/ (+ 1.0 (+ (* alpha beta) (+ beta alpha))) (+ 2 (+ beta alpha)))
118.0ms
(+ (+ 1.0 (+ beta alpha)) 2)

series559.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
237.0ms
(/ (/ (/ (+ 1.0 (+ (* alpha beta) (+ beta alpha))) (+ 2 (+ beta alpha))) (+ 2 (+ beta alpha))) (+ (+ 1.0 (+ beta alpha)) 2))
193.0ms
(/ (/ (+ 1.0 (+ (* alpha beta) (+ beta alpha))) (+ 2 (+ beta alpha))) (+ 2 (+ beta alpha)))
112.0ms
(/ (+ 1.0 (+ (* alpha beta) (+ beta alpha))) (+ 2 (+ beta alpha)))
17.0ms
(+ (+ 1.0 (+ beta alpha)) 2)

simplify7.4m

Counts
2150 → 1233
Calls
2150 calls:
Slowest
1.1s
(/ (/ (/ (+ 1.0 (+ (* alpha beta) (+ beta alpha))) (sqrt (+ 2 (+ beta alpha)))) (+ 2 (+ beta alpha))) (+ (+ 1.0 (+ beta alpha)) 2))
931.0ms
(/ (/ (/ (+ 1.0 (+ (* alpha beta) (+ beta alpha))) (cbrt (+ 2 (+ beta alpha)))) (+ 2 (+ beta alpha))) (+ (+ 1.0 (+ beta alpha)) 2))
922.0ms
(/ (/ (/ (sqrt (+ 1.0 (+ (* alpha beta) (+ beta alpha)))) (+ 2 (+ beta alpha))) (sqrt (+ 2 (+ beta alpha)))) (+ (+ 1.0 (+ beta alpha)) 2))
904.0ms
(/ (/ (+ 1.0 (+ (* alpha beta) (+ beta alpha))) (- (* 2 2) (* (+ beta alpha) (+ beta alpha)))) (* (cbrt (+ 2 (+ beta alpha))) (cbrt (+ 2 (+ beta alpha)))))
849.0ms
(/ (/ (/ (cbrt (+ 1.0 (+ (* alpha beta) (+ beta alpha)))) (+ 2 (+ beta alpha))) (+ 2 (+ beta alpha))) (sqrt (+ (+ 1.0 (+ beta alpha)) 2)))

prune14.1s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 1.2b

localize62.0ms

Local error

Found 4 expressions with local error:

2.4b
(sqrt (+ 1.0 (+ (* alpha beta) (+ beta alpha))))
2.4b
(sqrt (+ 1.0 (+ (* alpha beta) (+ beta alpha))))
0.5b
(/ (sqrt (+ 1.0 (+ (* alpha beta) (+ beta alpha)))) (sqrt (+ 2 (+ beta alpha))))
0.5b
(/ (sqrt (+ 1.0 (+ (* alpha beta) (+ beta alpha)))) (sqrt (+ 2 (+ beta alpha))))

rewrite469.0ms

Algorithm
rewrite-expression-head
Rules
194×*-un-lft-identity
160×sqrt-prod
112×times-frac
76×add-sqr-sqrt
74×add-cube-cbrt
68×distribute-lft-out
16×associate-/r*
14×associate-/l*
12×sqrt-div
8×add-cbrt-cube add-exp-log
6×pow1 flip3-+ flip-+
4×associate-/r/ insert-posit16 add-log-exp associate-/l/
2×cbrt-undiv rem-sqrt-square sqrt-undiv clear-num frac-2neg sqrt-pow1 pow1/2 div-exp div-inv
Counts
4 → 212
Calls
4 calls:
Slowest
168.0ms
(/ (sqrt (+ 1.0 (+ (* alpha beta) (+ beta alpha)))) (sqrt (+ 2 (+ beta alpha))))
127.0ms
(/ (sqrt (+ 1.0 (+ (* alpha beta) (+ beta alpha)))) (sqrt (+ 2 (+ beta alpha))))
84.0ms
(sqrt (+ 1.0 (+ (* alpha beta) (+ beta alpha))))
82.0ms
(sqrt (+ 1.0 (+ (* alpha beta) (+ beta alpha))))

series463.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
158.0ms
(/ (sqrt (+ 1.0 (+ (* alpha beta) (+ beta alpha)))) (sqrt (+ 2 (+ beta alpha))))
158.0ms
(/ (sqrt (+ 1.0 (+ (* alpha beta) (+ beta alpha)))) (sqrt (+ 2 (+ beta alpha))))
75.0ms
(sqrt (+ 1.0 (+ (* alpha beta) (+ beta alpha))))
72.0ms
(sqrt (+ 1.0 (+ (* alpha beta) (+ beta alpha))))

simplify31.3s

Counts
294 → 224
Calls
294 calls:
Slowest
510.0ms
(- (log (sqrt (+ 1.0 (+ (* alpha beta) (+ beta alpha))))) (log (sqrt (+ 2 (+ beta alpha)))))
298.0ms
(sqrt (+ (* 2 2) (- (* (+ beta alpha) (+ beta alpha)) (* 2 (+ beta alpha)))))
293.0ms
(/ (* (* (sqrt (+ 1.0 (+ (* alpha beta) (+ beta alpha)))) (sqrt (+ 1.0 (+ (* alpha beta) (+ beta alpha))))) (sqrt (+ 1.0 (+ (* alpha beta) (+ beta alpha))))) (* (* (sqrt (+ 2 (+ beta alpha))) (sqrt (+ 2 (+ beta alpha)))) (sqrt (+ 2 (+ beta alpha)))))
282.0ms
(/ (* (* (sqrt (+ 1.0 (+ (* alpha beta) (+ beta alpha)))) (sqrt (+ 1.0 (+ (* alpha beta) (+ beta alpha))))) (sqrt (+ 1.0 (+ (* alpha beta) (+ beta alpha))))) (* (* (sqrt (+ 2 (+ beta alpha))) (sqrt (+ 2 (+ beta alpha)))) (sqrt (+ 2 (+ beta alpha)))))
274.0ms
(sqrt (+ (* 2 2) (- (* (+ beta alpha) (+ beta alpha)) (* 2 (+ beta alpha)))))

prune3.1s

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 1.2b

localize67.0ms

Local error

Found 4 expressions with local error:

2.4b
(/ (+ 1.0 (+ (* alpha beta) (+ beta alpha))) (+ 2 (+ beta alpha)))
2.4b
(/ (+ 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) (sqrt (/ (/ (+ 1.0 (+ (* alpha beta) (+ beta alpha))) (+ 2 (+ 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)))))

rewrite27.8s

Algorithm
rewrite-expression-head
Rules
800186×*-un-lft-identity
622265×times-frac
392623×distribute-lft-out
229432×sqrt-prod
151352×add-sqr-sqrt add-cube-cbrt
20390×associate-/r/
10266×div-inv
10127×flip3-+ flip-+
988×associate-/r*
153×associate-/l*
142×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
Counts
4 → 118703
Calls
4 calls:
Slowest
1.6s
(/ (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))))))
429.0ms
(/ (+ (+ 1.0 (+ beta alpha)) 2) (sqrt (/ (/ (+ 1.0 (+ (* alpha beta) (+ beta alpha))) (+ 2 (+ beta alpha))) (+ 2 (+ beta alpha)))))
237.0ms
(/ (+ 1.0 (+ (* alpha beta) (+ beta alpha))) (+ 2 (+ beta alpha)))
234.0ms
(/ (+ 1.0 (+ (* alpha beta) (+ beta alpha))) (+ 2 (+ beta alpha)))

series907.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
414.0ms
(/ (+ (+ 1.0 (+ beta alpha)) 2) (sqrt (/ (/ (+ 1.0 (+ (* alpha beta) (+ beta alpha))) (+ 2 (+ beta alpha))) (+ 2 (+ beta alpha)))))
212.0ms
(/ (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))))))
148.0ms
(/ (+ 1.0 (+ (* alpha beta) (+ beta alpha))) (+ 2 (+ beta alpha)))
132.0ms
(/ (+ 1.0 (+ (* alpha beta) (+ beta alpha))) (+ 2 (+ beta alpha)))