Details

Time bar (total: 7.3m)

sample84.0ms

Algorithm
intervals
Results
50.0ms256×body80valid
12.0ms256×pre80true

simplify130.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
129.0ms
(/ (/ (/ (+ (+ (+ 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: 2.1b

localize59.0ms

Local error

Found 4 expressions with local error:

1.9b
(/ (+ 1.0 (+ (* alpha beta) (+ beta alpha))) (+ 2 (+ beta alpha)))
0.0b
(/ (/ (/ (+ 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)

rewrite813.0ms

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
276.0ms
(/ (/ (/ (+ 1.0 (+ (* alpha beta) (+ beta alpha))) (+ 2 (+ beta alpha))) (+ 2 (+ beta alpha))) (+ (+ 1.0 (+ beta alpha)) 2))
234.0ms
(/ (/ (+ 1.0 (+ (* alpha beta) (+ beta alpha))) (+ 2 (+ beta alpha))) (+ 2 (+ beta alpha)))
193.0ms
(/ (+ 1.0 (+ (* alpha beta) (+ beta alpha))) (+ 2 (+ beta alpha)))
54.0ms
(+ (+ 1.0 (+ beta alpha)) 2)

series535.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
207.0ms
(/ (/ (/ (+ 1.0 (+ (* alpha beta) (+ beta alpha))) (+ 2 (+ beta alpha))) (+ 2 (+ beta alpha))) (+ (+ 1.0 (+ beta alpha)) 2))
196.0ms
(/ (/ (+ 1.0 (+ (* alpha beta) (+ beta alpha))) (+ 2 (+ beta alpha))) (+ 2 (+ beta alpha)))
108.0ms
(/ (+ 1.0 (+ (* alpha beta) (+ beta alpha))) (+ 2 (+ beta alpha)))
24.0ms
(+ (+ 1.0 (+ beta alpha)) 2)

simplify7.0m

Counts
2150 → 1233
Calls
2150 calls:
Slowest
993.0ms
(/ (/ (/ (+ 1.0 (+ (* alpha beta) (+ beta alpha))) (sqrt (+ 2 (+ beta alpha)))) (+ 2 (+ beta alpha))) (+ (+ 1.0 (+ beta alpha)) 2))
848.0ms
(/ (/ (/ (+ 1.0 (+ (* alpha beta) (+ beta alpha))) (+ 2 (+ beta alpha))) (+ 2 (+ beta alpha))) (sqrt (+ (+ 1.0 (+ beta alpha)) 2)))
831.0ms
(/ (/ (/ (sqrt (+ 1.0 (+ (* alpha beta) (+ beta alpha)))) (+ 2 (+ beta alpha))) (+ 2 (+ beta alpha))) (cbrt (+ (+ 1.0 (+ beta alpha)) 2)))
791.0ms
(/ (/ (/ (* (cbrt (+ 1.0 (+ (* alpha beta) (+ beta alpha)))) (cbrt (+ 1.0 (+ (* alpha beta) (+ beta alpha))))) (sqrt (+ 2 (+ beta alpha)))) 1) (* (cbrt (+ (+ 1.0 (+ beta alpha)) 2)) (cbrt (+ (+ 1.0 (+ beta alpha)) 2))))
785.0ms
(/ (/ (/ 1 (+ 2 (+ beta alpha))) (+ 2 (+ beta alpha))) (cbrt (+ (+ 1.0 (+ beta alpha)) 2)))

prune14.2s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.2b

localize59.0ms

Local error

Found 4 expressions with local error:

1.9b
(/ (+ (+ (* beta alpha) (+ alpha beta)) 1.0) (+ 2 (+ alpha beta)))
0.1b
(/ (/ (/ (+ (+ (* beta alpha) (+ alpha beta)) 1.0) (+ 2 (+ alpha beta))) (+ 1.0 (+ 2 (+ alpha beta)))) (+ 2 (+ alpha beta)))
0.0b
(/ (/ (+ (+ (* beta alpha) (+ alpha beta)) 1.0) (+ 2 (+ alpha beta))) (+ 1.0 (+ 2 (+ alpha beta))))
0.0b
(+ 1.0 (+ 2 (+ alpha beta)))

rewrite1.1s

Algorithm
rewrite-expression-head
Rules
4595×*-un-lft-identity
2782×times-frac
2345×distribute-lft-out
797×add-sqr-sqrt add-cube-cbrt
192×associate-/l*
104×associate-/r/
54×flip3-+ flip-+
52×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-+r+
Counts
4 → 1267
Calls
4 calls:
Slowest
439.0ms
(/ (/ (/ (+ (+ (* beta alpha) (+ alpha beta)) 1.0) (+ 2 (+ alpha beta))) (+ 1.0 (+ 2 (+ alpha beta)))) (+ 2 (+ alpha beta)))
331.0ms
(/ (/ (+ (+ (* beta alpha) (+ alpha beta)) 1.0) (+ 2 (+ alpha beta))) (+ 1.0 (+ 2 (+ alpha beta))))
239.0ms
(/ (+ (+ (* beta alpha) (+ alpha beta)) 1.0) (+ 2 (+ alpha beta)))
27.0ms
(+ 1.0 (+ 2 (+ alpha beta)))

series566.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
252.0ms
(/ (/ (/ (+ (+ (* beta alpha) (+ alpha beta)) 1.0) (+ 2 (+ alpha beta))) (+ 1.0 (+ 2 (+ alpha beta)))) (+ 2 (+ alpha beta)))
191.0ms
(/ (/ (+ (+ (* beta alpha) (+ alpha beta)) 1.0) (+ 2 (+ alpha beta))) (+ 1.0 (+ 2 (+ alpha beta))))
101.0ms
(/ (+ (+ (* beta alpha) (+ alpha beta)) 1.0) (+ 2 (+ alpha beta)))
21.0ms
(+ 1.0 (+ 2 (+ alpha beta)))