Details

Time bar (total: 6.6m)

sample46.0ms

Algorithm
intervals
Results
26.0ms256×body80valid
8.0ms256×pre80true

simplify139.0ms

Calls
1 calls:
Slowest
139.0ms
(/ (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2 1))) (+ (+ alpha beta) (* 2 1))) (+ (+ (+ alpha beta) (* 2 1)) 1.0))

prune16.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 2.6b

localize34.0ms

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)

rewrite104.0ms

Algorithm
rewrite-expression-head
Rules
531×times-frac
256×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
69×associate-/l*
46×associate-/r/
25×flip3-+ flip-+
23×div-inv
20×add-cbrt-cube add-exp-log
10×cbrt-undiv div-exp
9×associate-/r*
4×pow1 insert-posit16 add-log-exp associate-/l/
3×clear-num frac-2neg
1×+-commutative associate-+l+
Calls
4 calls:
Slowest
36.0ms
(/ (/ (/ (+ 1.0 (+ (* alpha beta) (+ beta alpha))) (+ 2 (+ beta alpha))) (+ 2 (+ beta alpha))) (+ (+ 1.0 (+ beta alpha)) 2))
30.0ms
(/ (+ 1.0 (+ (* alpha beta) (+ beta alpha))) (+ 2 (+ beta alpha)))
26.0ms
(/ (/ (+ 1.0 (+ (* alpha beta) (+ beta alpha))) (+ 2 (+ beta alpha))) (+ 2 (+ beta alpha)))
5.0ms
(+ (+ 1.0 (+ beta alpha)) 2)

series529.0ms

Calls
4 calls:
Slowest
203.0ms
(/ (/ (/ (+ 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)))
110.0ms
(/ (+ 1.0 (+ (* alpha beta) (+ beta alpha))) (+ 2 (+ beta alpha)))
23.0ms
(+ (+ 1.0 (+ beta alpha)) 2)

simplify1.8m

Calls
523 calls:
Slowest
1.1s
(+ (pow 1.0 3) (pow (+ (* alpha beta) (+ beta alpha)) 3))
638.0ms
(/ (/ (/ (+ 1.0 (+ (* alpha beta) (+ beta alpha))) (cbrt (+ 2 (+ beta alpha)))) (+ 2 (+ beta alpha))) (+ (+ 1.0 (+ beta alpha)) 2))
632.0ms
(/ (/ (+ 1.0 (+ (* alpha beta) (+ beta alpha))) (- (* 2 2) (* (+ beta alpha) (+ beta alpha)))) 1)
624.0ms
(/ (/ (/ (+ 1.0 (+ (* alpha beta) (+ beta alpha))) (sqrt (+ 2 (+ beta alpha)))) (+ 2 (+ beta alpha))) (+ (+ 1.0 (+ beta alpha)) 2))
605.0ms
(/ (/ (sqrt (/ (+ 1.0 (+ (* alpha beta) (+ beta alpha))) (+ 2 (+ beta alpha)))) (* (cbrt (+ 2 (+ beta alpha))) (cbrt (+ 2 (+ beta alpha))))) (sqrt (+ (+ 1.0 (+ beta alpha)) 2)))

prune3.9s

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0.9b

localize32.0ms

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))))
0.9b
(* (/ (/ (/ (sqrt (+ 1.0 (+ (* alpha beta) (+ beta alpha)))) (sqrt (+ 2 (+ beta alpha)))) 1) 1) (/ (/ (/ (sqrt (+ 1.0 (+ (* alpha beta) (+ beta alpha)))) (sqrt (+ 2 (+ beta alpha)))) (+ 2 (+ beta alpha))) (+ (+ 1.0 (+ beta alpha)) 2)))
0.5b
(/ (/ (/ (sqrt (+ 1.0 (+ (* alpha beta) (+ beta alpha)))) (sqrt (+ 2 (+ beta alpha)))) (+ 2 (+ beta alpha))) (+ (+ 1.0 (+ beta alpha)) 2))

rewrite133.0ms

Algorithm
rewrite-expression-head
Rules
2430×times-frac
1101×add-sqr-sqrt
1099×*-un-lft-identity add-cube-cbrt
762×sqrt-prod
402×associate-*r*
132×associate-/l*
60×associate-/r/
46×sqrt-div
32×flip3-+ flip-+
31×div-inv
27×add-cbrt-cube add-exp-log
12×cbrt-undiv div-exp
6×pow1
4×associate-*l* prod-exp cbrt-unprod insert-posit16 add-log-exp
3×associate-/r*
2×rem-sqrt-square pow1/2
1×frac-times clear-num frac-2neg pow-prod-down associate-*l/ associate-*r/ *-commutative associate-/l/
Calls
4 calls:
Slowest
52.0ms
(* (/ (/ (/ (sqrt (+ 1.0 (+ (* alpha beta) (+ beta alpha)))) (sqrt (+ 2 (+ beta alpha)))) 1) 1) (/ (/ (/ (sqrt (+ 1.0 (+ (* alpha beta) (+ beta alpha)))) (sqrt (+ 2 (+ beta alpha)))) (+ 2 (+ beta alpha))) (+ (+ 1.0 (+ beta alpha)) 2)))
25.0ms
(/ (/ (/ (sqrt (+ 1.0 (+ (* alpha beta) (+ beta alpha)))) (sqrt (+ 2 (+ beta alpha)))) (+ 2 (+ beta alpha))) (+ (+ 1.0 (+ beta alpha)) 2))
4.0ms
(sqrt (+ 1.0 (+ (* alpha beta) (+ beta alpha))))
3.0ms
(sqrt (+ 1.0 (+ (* alpha beta) (+ beta alpha))))

series940.0ms

Calls
4 calls:
Slowest
556.0ms
(/ (/ (/ (sqrt (+ 1.0 (+ (* alpha beta) (+ beta alpha)))) (sqrt (+ 2 (+ beta alpha)))) (+ 2 (+ beta alpha))) (+ (+ 1.0 (+ beta alpha)) 2))
248.0ms
(* (/ (/ (/ (sqrt (+ 1.0 (+ (* alpha beta) (+ beta alpha)))) (sqrt (+ 2 (+ beta alpha)))) 1) 1) (/ (/ (/ (sqrt (+ 1.0 (+ (* alpha beta) (+ beta alpha)))) (sqrt (+ 2 (+ beta alpha)))) (+ 2 (+ beta alpha))) (+ (+ 1.0 (+ beta alpha)) 2)))
71.0ms
(sqrt (+ 1.0 (+ (* alpha beta) (+ beta alpha))))
65.0ms
(sqrt (+ 1.0 (+ (* alpha beta) (+ beta alpha))))

simplify4.4m

Calls
1377 calls:
Slowest
1.1s
(* (* (* (/ (/ (/ (sqrt (+ 1.0 (+ (* alpha beta) (+ beta alpha)))) (sqrt (+ 2 (+ beta alpha)))) 1) 1) (/ (/ (/ (sqrt (+ 1.0 (+ (* alpha beta) (+ beta alpha)))) (sqrt (+ 2 (+ beta alpha)))) 1) 1)) (/ (/ (/ (sqrt (+ 1.0 (+ (* alpha beta) (+ beta alpha)))) (sqrt (+ 2 (+ beta alpha)))) 1) 1)) (/ (* (* (/ (/ (sqrt (+ 1.0 (+ (* alpha beta) (+ beta alpha)))) (sqrt (+ 2 (+ beta alpha)))) (+ 2 (+ beta alpha))) (/ (/ (sqrt (+ 1.0 (+ (* alpha beta) (+ beta alpha)))) (sqrt (+ 2 (+ beta alpha)))) (+ 2 (+ beta alpha)))) (/ (/ (sqrt (+ 1.0 (+ (* alpha beta) (+ beta alpha)))) (sqrt (+ 2 (+ beta alpha)))) (+ 2 (+ beta alpha)))) (* (* (+ (+ 1.0 (+ beta alpha)) 2) (+ (+ 1.0 (+ beta alpha)) 2)) (+ (+ 1.0 (+ beta alpha)) 2))))
894.0ms
(sqrt (+ (pow 1.0 3) (pow (+ (* alpha beta) (+ beta alpha)) 3)))
883.0ms
(sqrt (+ (pow 1.0 3) (pow (+ (* alpha beta) (+ beta alpha)) 3)))
696.0ms
(/ (/ (/ (sqrt (+ 1.0 (+ (* alpha beta) (+ beta alpha)))) (sqrt (+ 2 (+ beta alpha)))) (cbrt (+ 2 (+ beta alpha)))) (cbrt (+ (+ 1.0 (+ beta alpha)) 2)))
695.0ms
(/ (/ (/ (* (cbrt (sqrt (+ 1.0 (+ (* alpha beta) (+ beta alpha))))) (cbrt (sqrt (+ 1.0 (+ (* alpha beta) (+ beta alpha)))))) (sqrt 1)) 1) (* (cbrt (+ (+ 1.0 (+ beta alpha)) 2)) (cbrt (+ (+ 1.0 (+ beta alpha)) 2))))

prune10.7s

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 0.9b

localize31.0ms

Local error

Found 4 expressions with local error:

2.6b
(cbrt (+ 1.0 (+ (* alpha beta) (+ beta alpha))))
2.6b
(cbrt (+ 1.0 (+ (* alpha beta) (+ beta alpha))))
2.6b
(cbrt (+ 1.0 (+ (* alpha beta) (+ beta alpha))))
1.0b
(/ (/ (/ (* (cbrt (+ 1.0 (+ (* alpha beta) (+ beta alpha)))) (cbrt (+ 1.0 (+ (* alpha beta) (+ beta alpha))))) 1) 1) (* (cbrt (+ (+ 1.0 (+ beta alpha)) 2)) (cbrt (+ (+ 1.0 (+ beta alpha)) 2))))

rewrite28.0ms

Algorithm
rewrite-expression-head
Rules
18×cbrt-div
9×cbrt-prod add-sqr-sqrt *-un-lft-identity flip3-+ add-exp-log add-cube-cbrt flip-+
8×associate-/r/
7×add-cbrt-cube
4×frac-times pow1 times-frac insert-posit16 associate-/l* add-log-exp
3×pow1/3 div-inv
2×cbrt-undiv div-exp associate-*l/ associate-*r/
1×clear-num associate-/r* frac-2neg prod-exp cbrt-unprod associate-/l/
Calls
4 calls:
Slowest
21.0ms
(/ (/ (/ (* (cbrt (+ 1.0 (+ (* alpha beta) (+ beta alpha)))) (cbrt (+ 1.0 (+ (* alpha beta) (+ beta alpha))))) 1) 1) (* (cbrt (+ (+ 1.0 (+ beta alpha)) 2)) (cbrt (+ (+ 1.0 (+ beta alpha)) 2))))
2.0ms
(cbrt (+ 1.0 (+ (* alpha beta) (+ beta alpha))))
2.0ms
(cbrt (+ 1.0 (+ (* alpha beta) (+ beta alpha))))
2.0ms
(cbrt (+ 1.0 (+ (* alpha beta) (+ beta alpha))))

series332.0ms

Calls
4 calls:
Slowest
146.0ms
(/ (/ (/ (* (cbrt (+ 1.0 (+ (* alpha beta) (+ beta alpha)))) (cbrt (+ 1.0 (+ (* alpha beta) (+ beta alpha))))) 1) 1) (* (cbrt (+ (+ 1.0 (+ beta alpha)) 2)) (cbrt (+ (+ 1.0 (+ beta alpha)) 2))))
65.0ms
(cbrt (+ 1.0 (+ (* alpha beta) (+ beta alpha))))
63.0ms
(cbrt (+ 1.0 (+ (* alpha beta) (+ beta alpha))))
59.0ms
(cbrt (+ 1.0 (+ (* alpha beta) (+ beta alpha))))

simplify7.4s

Calls
52 calls:
Slowest
858.0ms
(cbrt (+ (pow 1.0 3) (pow (+ (* alpha beta) (+ beta alpha)) 3)))
607.0ms
(cbrt (+ (pow 1.0 3) (pow (+ (* alpha beta) (+ beta alpha)) 3)))
605.0ms
(cbrt (+ (pow 1.0 3) (pow (+ (* alpha beta) (+ beta alpha)) 3)))
272.0ms
(/ (* (* (/ (/ (* (cbrt (+ 1.0 (+ (* alpha beta) (+ beta alpha)))) (cbrt (+ 1.0 (+ (* alpha beta) (+ beta alpha))))) 1) 1) (/ (/ (* (cbrt (+ 1.0 (+ (* alpha beta) (+ beta alpha)))) (cbrt (+ 1.0 (+ (* alpha beta) (+ beta alpha))))) 1) 1)) (/ (/ (* (cbrt (+ 1.0 (+ (* alpha beta) (+ beta alpha)))) (cbrt (+ 1.0 (+ (* alpha beta) (+ beta alpha))))) 1) 1)) (* (* (* (cbrt (+ (+ 1.0 (+ beta alpha)) 2)) (cbrt (+ (+ 1.0 (+ beta alpha)) 2))) (* (cbrt (+ (+ 1.0 (+ beta alpha)) 2)) (cbrt (+ (+ 1.0 (+ beta alpha)) 2)))) (* (cbrt (+ (+ 1.0 (+ beta alpha)) 2)) (cbrt (+ (+ 1.0 (+ beta alpha)) 2)))))
247.0ms
(- (log (/ (/ (* (cbrt (+ 1.0 (+ (* alpha beta) (+ beta alpha)))) (cbrt (+ 1.0 (+ (* alpha beta) (+ beta alpha))))) 1) 1)) (+ (log (cbrt (+ (+ 1.0 (+ beta alpha)) 2))) (log (cbrt (+ (+ 1.0 (+ beta alpha)) 2)))))

prune868.0ms

Pruning

6 alts after pruning (3 fresh and 3 done)

Merged error: 0.9b

localize16.0ms

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))) (- (* 2 2) (* (+ beta alpha) (+ beta alpha))))
0.0b
(/ (/ (/ (+ 1.0 (+ (* alpha beta) (+ beta alpha))) (+ 2 (+ beta alpha))) (- (* 2 2) (* (+ beta alpha) (+ beta alpha)))) (/ (+ (+ 1.0 (+ beta alpha)) 2) (- 2 (+ beta alpha))))
0.0b
(* (+ beta alpha) (+ beta alpha))

rewrite113.0ms

Algorithm
rewrite-expression-head
Rules
3243×times-frac
1238×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
309×associate-/r/
256×difference-of-squares
155×div-inv
84×flip3-- flip-- associate-/l*
77×flip3-+ flip-+
34×add-cbrt-cube add-exp-log
22×associate-/r*
19×cbrt-undiv div-exp
9×pow1
4×frac-times insert-posit16 add-log-exp associate-/l/
3×clear-num frac-2neg associate-*r* associate-*l*
2×associate-*l/ associate-*r/
1×pow2 distribute-rgt-in distribute-lft-in pow-plus pow-prod-down prod-exp *-commutative pow-prod-up cbrt-unprod
Calls
4 calls:
Slowest
32.0ms
(/ (/ (/ (+ 1.0 (+ (* alpha beta) (+ beta alpha))) (+ 2 (+ beta alpha))) (- (* 2 2) (* (+ beta alpha) (+ beta alpha)))) (/ (+ (+ 1.0 (+ beta alpha)) 2) (- 2 (+ beta alpha))))
20.0ms
(/ (/ (+ 1.0 (+ (* alpha beta) (+ beta alpha))) (+ 2 (+ beta alpha))) (- (* 2 2) (* (+ beta alpha) (+ beta alpha))))
18.0ms
(/ (+ 1.0 (+ (* alpha beta) (+ beta alpha))) (+ 2 (+ beta alpha)))
4.0ms
(* (+ beta alpha) (+ beta alpha))

series442.0ms

Calls
4 calls:
Slowest
193.0ms
(/ (/ (/ (+ 1.0 (+ (* alpha beta) (+ beta alpha))) (+ 2 (+ beta alpha))) (- (* 2 2) (* (+ beta alpha) (+ beta alpha)))) (/ (+ (+ 1.0 (+ beta alpha)) 2) (- 2 (+ beta alpha))))
145.0ms
(/ (/ (+ 1.0 (+ (* alpha beta) (+ beta alpha))) (+ 2 (+ beta alpha))) (- (* 2 2) (* (+ beta alpha) (+ beta alpha))))
89.0ms
(/ (+ 1.0 (+ (* alpha beta) (+ beta alpha))) (+ 2 (+ beta alpha)))
16.0ms
(* (+ beta alpha) (+ beta alpha))