Details

Time bar (total: 8.0m)

sample70.0ms

Algorithm
intervals
Results
40.0ms256×body80valid
11.0ms256×pre80true

simplify100.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
100.0ms
(/ (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2 1))) (+ (+ alpha beta) (* 2 1))) (+ (+ (+ alpha beta) (* 2 1)) 1.0))

prune9.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 3.1b

localize42.0ms

Local error

Found 4 expressions with local error:

2.9b
(/ (+ 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
(+ (* alpha beta) (+ beta alpha))

rewrite722.0ms

Algorithm
rewrite-expression-head
Rules
4323×*-un-lft-identity
2696×times-frac
2167×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*
10×cbrt-undiv div-exp
9×add-log-exp
4×pow1 insert-posit16 associate-/l/
3×clear-num sum-log frac-2neg
1×+-commutative associate-+r+
Counts
4 → 1217
Calls
4 calls:
Slowest
254.0ms
(/ (/ (/ (+ 1.0 (+ (* alpha beta) (+ beta alpha))) (+ 2 (+ beta alpha))) (+ 2 (+ beta alpha))) (+ (+ 1.0 (+ beta alpha)) 2))
222.0ms
(/ (/ (+ 1.0 (+ (* alpha beta) (+ beta alpha))) (+ 2 (+ beta alpha))) (+ 2 (+ beta alpha)))
141.0ms
(/ (+ 1.0 (+ (* alpha beta) (+ beta alpha))) (+ 2 (+ beta alpha)))
23.0ms
(+ (* alpha beta) (+ beta alpha))

series501.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
197.0ms
(/ (/ (/ (+ 1.0 (+ (* alpha beta) (+ beta alpha))) (+ 2 (+ beta alpha))) (+ 2 (+ beta alpha))) (+ (+ 1.0 (+ beta alpha)) 2))
168.0ms
(/ (/ (+ 1.0 (+ (* alpha beta) (+ beta alpha))) (+ 2 (+ beta alpha))) (+ 2 (+ beta alpha)))
119.0ms
(/ (+ 1.0 (+ (* alpha beta) (+ beta alpha))) (+ 2 (+ beta alpha)))
17.0ms
(+ (* alpha beta) (+ beta alpha))

simplify7.2m

Counts
2146 → 1229
Calls
2146 calls:
Slowest
995.0ms
(/ (/ (sqrt (/ (+ 1.0 (+ (* alpha beta) (+ beta alpha))) (+ 2 (+ beta alpha)))) (+ 2 (+ beta alpha))) (+ (+ 1.0 (+ beta alpha)) 2))
982.0ms
(/ (/ (/ (+ 1.0 (+ (* alpha beta) (+ beta alpha))) (sqrt (+ 2 (+ beta alpha)))) (+ 2 (+ beta alpha))) (+ (+ 1.0 (+ beta alpha)) 2))
917.0ms
(/ (/ (/ (+ 1.0 (+ (* alpha beta) (+ beta alpha))) (cbrt (+ 2 (+ beta alpha)))) (+ 2 (+ beta alpha))) (+ (+ 1.0 (+ beta alpha)) 2))
862.0ms
(/ (/ (/ (+ 1.0 (+ (* alpha beta) (+ beta alpha))) (+ 2 (+ beta alpha))) (sqrt (+ 2 (+ beta alpha)))) (+ (+ 1.0 (+ beta alpha)) 2))
861.0ms
(/ (/ (/ (cbrt (+ 1.0 (+ (* alpha beta) (+ beta alpha)))) (+ 2 (+ beta alpha))) (+ 2 (+ beta alpha))) (sqrt (+ (+ 1.0 (+ beta alpha)) 2)))

prune14.0s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 1.2b

localize45.0ms

Local error

Found 4 expressions with local error:

2.8b
(sqrt (+ 1.0 (+ (* alpha beta) (+ beta alpha))))
2.8b
(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))))

rewrite453.0ms

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
143.0ms
(/ (sqrt (+ 1.0 (+ (* alpha beta) (+ beta alpha)))) (sqrt (+ 2 (+ beta alpha))))
136.0ms
(/ (sqrt (+ 1.0 (+ (* alpha beta) (+ beta alpha)))) (sqrt (+ 2 (+ beta alpha))))
86.0ms
(sqrt (+ 1.0 (+ (* alpha beta) (+ beta alpha))))
83.0ms
(sqrt (+ 1.0 (+ (* alpha beta) (+ beta alpha))))

series463.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
147.0ms
(/ (sqrt (+ 1.0 (+ (* alpha beta) (+ beta alpha)))) (sqrt (+ 2 (+ beta alpha))))
139.0ms
(/ (sqrt (+ 1.0 (+ (* alpha beta) (+ beta alpha)))) (sqrt (+ 2 (+ beta alpha))))
88.0ms
(sqrt (+ 1.0 (+ (* alpha beta) (+ beta alpha))))
88.0ms
(sqrt (+ 1.0 (+ (* alpha beta) (+ beta alpha))))

simplify29.8s

Counts
294 → 224
Calls
294 calls:
Slowest
327.0ms
(sqrt (+ (* 2 2) (- (* (+ beta alpha) (+ beta alpha)) (* 2 (+ beta alpha)))))
297.0ms
(sqrt (+ (* 2 2) (- (* (+ beta alpha) (+ beta alpha)) (* 2 (+ beta alpha)))))
271.0ms
(/ (* (* (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)))))
263.0ms
(/ (* (* (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)))))
198.0ms
(/ (sqrt (sqrt (+ 1.0 (+ (* alpha beta) (+ beta alpha))))) (* (cbrt (sqrt (+ 2 (+ beta alpha)))) (cbrt (sqrt (+ 2 (+ beta alpha))))))

prune3.3s

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 1.2b

localize73.0ms

Local error

Found 4 expressions with local error:

16.5b
(sqrt (/ (/ (/ (+ 1.0 (+ (* alpha beta) (+ beta alpha))) (+ 2 (+ beta alpha))) (+ 2 (+ beta alpha))) (+ (+ 1.0 (+ beta alpha)) 2)))
16.5b
(sqrt (/ (/ (/ (+ 1.0 (+ (* alpha beta) (+ beta alpha))) (+ 2 (+ beta alpha))) (+ 2 (+ beta alpha))) (+ (+ 1.0 (+ beta alpha)) 2)))
2.9b
(/ (+ 1.0 (+ (* alpha beta) (+ beta alpha))) (+ 2 (+ beta alpha)))
2.9b
(/ (+ 1.0 (+ (* alpha beta) (+ beta alpha))) (+ 2 (+ beta alpha)))

rewrite1.0s

Algorithm
rewrite-expression-head
Rules
7106×*-un-lft-identity
4444×times-frac
3630×distribute-lft-out
1644×sqrt-prod
1244×add-sqr-sqrt
1224×add-cube-cbrt
152×associate-/r/
78×flip3-+ flip-+
76×div-inv
10×associate-/r*
8×rem-sqrt-square add-cbrt-cube add-exp-log associate-/l*
6×pow1
4×insert-posit16 add-log-exp associate-/l/
2×cbrt-undiv clear-num frac-2neg sqrt-pow1 pow1/2 sqrt-div div-exp
Counts
4 → 1766
Calls
4 calls:
Slowest
254.0ms
(sqrt (/ (/ (/ (+ 1.0 (+ (* alpha beta) (+ beta alpha))) (+ 2 (+ beta alpha))) (+ 2 (+ beta alpha))) (+ (+ 1.0 (+ beta alpha)) 2)))
195.0ms
(/ (+ 1.0 (+ (* alpha beta) (+ beta alpha))) (+ 2 (+ beta alpha)))
184.0ms
(/ (+ 1.0 (+ (* alpha beta) (+ beta alpha))) (+ 2 (+ beta alpha)))
184.0ms
(sqrt (/ (/ (/ (+ 1.0 (+ (* alpha beta) (+ beta alpha))) (+ 2 (+ beta alpha))) (+ 2 (+ beta alpha))) (+ (+ 1.0 (+ beta alpha)) 2)))

series1.1s

Counts
4 → 12
Calls
4 calls:
Slowest
422.0ms
(sqrt (/ (/ (/ (+ 1.0 (+ (* alpha beta) (+ beta alpha))) (+ 2 (+ beta alpha))) (+ 2 (+ beta alpha))) (+ (+ 1.0 (+ beta alpha)) 2)))
401.0ms
(sqrt (/ (/ (/ (+ 1.0 (+ (* alpha beta) (+ beta alpha))) (+ 2 (+ beta alpha))) (+ 2 (+ beta alpha))) (+ (+ 1.0 (+ beta alpha)) 2)))
124.0ms
(/ (+ 1.0 (+ (* alpha beta) (+ beta alpha))) (+ 2 (+ beta alpha)))
110.0ms
(/ (+ 1.0 (+ (* alpha beta) (+ beta alpha))) (+ 2 (+ beta alpha)))