Details

Time bar (total: 5.6m)

sample41.0ms

Algorithm
intervals
Results
22.0ms256×body80valid
7.0ms256×pre80true

simplify966.0ms

Counts
1 → 1

prune9.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 2.8b

localize24.0ms

Local error

Found 4 expressions with local error:

2.7b
(/ (+ 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))

rewrite671.0ms

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
241.0ms
(/ (/ (/ (+ 1.0 (+ (* alpha beta) (+ beta alpha))) (+ 2 (+ beta alpha))) (+ 2 (+ beta alpha))) (+ (+ 1.0 (+ beta alpha)) 2))
197.0ms
(/ (/ (+ 1.0 (+ (* alpha beta) (+ beta alpha))) (+ 2 (+ beta alpha))) (+ 2 (+ beta alpha)))
159.0ms
(/ (+ 1.0 (+ (* alpha beta) (+ beta alpha))) (+ 2 (+ beta alpha)))
13.0ms
(+ (* alpha beta) (+ beta alpha))

series426.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
170.0ms
(/ (/ (/ (+ 1.0 (+ (* alpha beta) (+ beta alpha))) (+ 2 (+ beta alpha))) (+ 2 (+ beta alpha))) (+ (+ 1.0 (+ beta alpha)) 2))
137.0ms
(/ (/ (+ 1.0 (+ (* alpha beta) (+ beta alpha))) (+ 2 (+ beta alpha))) (+ 2 (+ beta alpha)))
101.0ms
(/ (+ 1.0 (+ (* alpha beta) (+ beta alpha))) (+ 2 (+ beta alpha)))
17.0ms
(+ (* alpha beta) (+ beta alpha))

simplify1.3s

Counts
1229 → 1229

prune13.9s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.6b

localize49.0ms

Local error

Found 4 expressions with local error:

2.7b
(/ (+ 1.0 (+ (* alpha beta) (+ beta alpha))) (+ 2 (+ beta alpha)))
0.1b
(/ (/ 1 (/ (+ 2 (+ beta alpha)) (/ (+ 1.0 (+ (* alpha beta) (+ beta alpha))) (+ 2 (+ beta alpha))))) (+ (+ 1.0 (+ beta alpha)) 2))
0.0b
(/ 1 (/ (+ 2 (+ beta alpha)) (/ (+ 1.0 (+ (* alpha beta) (+ beta alpha))) (+ 2 (+ beta alpha)))))
0.0b
(/ (+ 2 (+ beta alpha)) (/ (+ 1.0 (+ (* alpha beta) (+ beta alpha))) (+ 2 (+ beta alpha))))

rewrite1.6s

Algorithm
rewrite-expression-head
Rules
14577×*-un-lft-identity
11720×times-frac
6745×distribute-lft-out
3526×add-sqr-sqrt add-cube-cbrt
422×associate-/l*
300×associate-/r/
172×associate-/r*
167×div-inv
135×flip3-+ flip-+
64×add-exp-log
44×div-exp
34×add-cbrt-cube
20×cbrt-undiv
6×rec-exp 1-exp
5×pow1 associate-/l/
4×clear-num frac-2neg insert-posit16 add-log-exp
1×pow-flip inv-pow
Counts
4 → 3698
Calls
4 calls:
Slowest
294.0ms
(/ (/ 1 (/ (+ 2 (+ beta alpha)) (/ (+ 1.0 (+ (* alpha beta) (+ beta alpha))) (+ 2 (+ beta alpha))))) (+ (+ 1.0 (+ beta alpha)) 2))
224.0ms
(/ (+ 1.0 (+ (* alpha beta) (+ beta alpha))) (+ 2 (+ beta alpha)))
157.0ms
(/ (+ 2 (+ beta alpha)) (/ (+ 1.0 (+ (* alpha beta) (+ beta alpha))) (+ 2 (+ beta alpha))))
145.0ms
(/ 1 (/ (+ 2 (+ beta alpha)) (/ (+ 1.0 (+ (* alpha beta) (+ beta alpha))) (+ 2 (+ beta alpha)))))

series689.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
231.0ms
(/ (+ 2 (+ beta alpha)) (/ (+ 1.0 (+ (* alpha beta) (+ beta alpha))) (+ 2 (+ beta alpha))))
183.0ms
(/ (/ 1 (/ (+ 2 (+ beta alpha)) (/ (+ 1.0 (+ (* alpha beta) (+ beta alpha))) (+ 2 (+ beta alpha))))) (+ (+ 1.0 (+ beta alpha)) 2))
152.0ms
(/ 1 (/ (+ 2 (+ beta alpha)) (/ (+ 1.0 (+ (* alpha beta) (+ beta alpha))) (+ 2 (+ beta alpha)))))
123.0ms
(/ (+ 1.0 (+ (* alpha beta) (+ beta alpha))) (+ 2 (+ beta alpha)))

simplify6.4s

Counts
3710 → 3710

prune48.5s

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0.0b

localize46.0ms

Local error

Found 4 expressions with local error:

2.7b
(/ (+ 1.0 (+ (* alpha beta) (+ beta alpha))) (+ 2 (+ beta alpha)))
2.7b
(/ (+ 1.0 (+ (* alpha beta) (+ beta alpha))) (+ 2 (+ beta alpha)))
0.1b
(/ (+ (+ 1.0 (+ beta alpha)) 2) (sqrt (/ 1 (/ (+ 2 (+ beta alpha)) (/ (+ 1.0 (+ (* alpha beta) (+ beta alpha))) (+ 2 (+ beta alpha)))))))
0.1b
(/ (sqrt (/ 1 (/ (+ 2 (+ beta alpha)) (/ (+ 1.0 (+ (* alpha beta) (+ beta alpha))) (+ 2 (+ beta alpha)))))) (/ (+ (+ 1.0 (+ beta alpha)) 2) (sqrt (/ 1 (/ (+ 2 (+ beta alpha)) (/ (+ 1.0 (+ (* alpha beta) (+ beta alpha))) (+ 2 (+ beta alpha))))))))

rewrite4.3m

Algorithm
rewrite-expression-head
Rules
7724274×*-un-lft-identity
7501514×times-frac
3461193×distribute-lft-out
2039750×sqrt-prod
2002636×add-sqr-sqrt add-cube-cbrt
169570×associate-/r/
94943×div-inv
74630×flip3-+ flip-+
2906×associate-/r*
427×associate-/l*
416×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 → 1031397
Calls
4 calls:
Slowest
10.7s
(/ (sqrt (/ 1 (/ (+ 2 (+ beta alpha)) (/ (+ 1.0 (+ (* alpha beta) (+ beta alpha))) (+ 2 (+ beta alpha)))))) (/ (+ (+ 1.0 (+ beta alpha)) 2) (sqrt (/ 1 (/ (+ 2 (+ beta alpha)) (/ (+ 1.0 (+ (* alpha beta) (+ beta alpha))) (+ 2 (+ beta alpha))))))))
387.0ms
(/ (+ (+ 1.0 (+ beta alpha)) 2) (sqrt (/ 1 (/ (+ 2 (+ beta alpha)) (/ (+ 1.0 (+ (* alpha beta) (+ beta alpha))) (+ 2 (+ beta alpha)))))))
171.0ms
(/ (+ 1.0 (+ (* alpha beta) (+ beta alpha))) (+ 2 (+ beta alpha)))
148.0ms
(/ (+ 1.0 (+ (* alpha beta) (+ beta alpha))) (+ 2 (+ beta alpha)))

series626.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
267.0ms
(/ (+ (+ 1.0 (+ beta alpha)) 2) (sqrt (/ 1 (/ (+ 2 (+ beta alpha)) (/ (+ 1.0 (+ (* alpha beta) (+ beta alpha))) (+ 2 (+ beta alpha)))))))
150.0ms
(/ (sqrt (/ 1 (/ (+ 2 (+ beta alpha)) (/ (+ 1.0 (+ (* alpha beta) (+ beta alpha))) (+ 2 (+ beta alpha)))))) (/ (+ (+ 1.0 (+ beta alpha)) 2) (sqrt (/ 1 (/ (+ 2 (+ beta alpha)) (/ (+ 1.0 (+ (* alpha beta) (+ beta alpha))) (+ 2 (+ beta alpha))))))))
106.0ms
(/ (+ 1.0 (+ (* alpha beta) (+ beta alpha))) (+ 2 (+ beta alpha)))
77.0ms
(/ (+ 1.0 (+ (* alpha beta) (+ beta alpha))) (+ 2 (+ beta alpha)))