Details

Time bar (total: 8.3m)

sample49.0ms

Algorithm
intervals
Results
27.0ms256×body80valid
8.0ms256×pre80true

simplify142.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
141.0ms
(/ (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2 1))) (+ (+ alpha beta) (* 2 1))) (+ (+ (+ alpha beta) (* 2 1)) 1.0))

prune22.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 4.3b

localize44.0ms

Local error

Found 4 expressions with local error:

4.1b
(/ (+ 1.0 (fma beta alpha (+ beta alpha))) (+ 2 (+ beta alpha)))
0.1b
(/ (/ (/ (+ 1.0 (fma beta alpha (+ beta alpha))) (+ 2 (+ beta alpha))) (+ 2 (+ beta alpha))) (+ (+ 1.0 (+ beta alpha)) 2))
0.0b
(/ (/ (+ 1.0 (fma beta alpha (+ beta alpha))) (+ 2 (+ beta alpha))) (+ 2 (+ beta alpha)))
0.0b
(+ (+ 1.0 (+ beta alpha)) 2)

rewrite524.0ms

Algorithm
rewrite-expression-head
Rules
4338×*-un-lft-identity
2696×times-frac
2176×distribute-lft-out
779×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
5×fma-def
4×expm1-log1p-u pow1 insert-posit16 log1p-expm1-u associate-/l/
3×clear-num frac-2neg
1×+-commutative associate-+l+
Counts
4 → 1234
Calls
4 calls:
Slowest
174.0ms
(/ (/ (/ (+ 1.0 (fma beta alpha (+ beta alpha))) (+ 2 (+ beta alpha))) (+ 2 (+ beta alpha))) (+ (+ 1.0 (+ beta alpha)) 2))
125.0ms
(+ (+ 1.0 (+ beta alpha)) 2)
80.0ms
(/ (/ (+ 1.0 (fma beta alpha (+ beta alpha))) (+ 2 (+ beta alpha))) (+ 2 (+ beta alpha)))
38.0ms
(/ (+ 1.0 (fma beta alpha (+ beta alpha))) (+ 2 (+ beta alpha)))

series619.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
255.0ms
(/ (/ (/ (+ 1.0 (fma beta alpha (+ beta alpha))) (+ 2 (+ beta alpha))) (+ 2 (+ beta alpha))) (+ (+ 1.0 (+ beta alpha)) 2))
214.0ms
(/ (/ (+ 1.0 (fma beta alpha (+ beta alpha))) (+ 2 (+ beta alpha))) (+ 2 (+ beta alpha)))
127.0ms
(/ (+ 1.0 (fma beta alpha (+ beta alpha))) (+ 2 (+ beta alpha)))
23.0ms
(+ (+ 1.0 (+ beta alpha)) 2)

simplify8.0m

Counts
2152 → 1246
Calls
2152 calls:
Slowest
1.2s
(/ (/ (/ (cbrt (+ 1.0 (fma beta alpha (+ beta alpha)))) (cbrt (+ 2 (+ beta alpha)))) (+ 2 (+ beta alpha))) (+ (+ 1.0 (+ beta alpha)) 2))
1.1s
(/ (/ (/ (sqrt (+ 1.0 (fma beta alpha (+ beta alpha)))) (sqrt (+ 2 (+ beta alpha)))) (+ 2 (+ beta alpha))) (+ (+ 1.0 (+ beta alpha)) 2))
1.1s
(/ (/ (/ (cbrt (+ 1.0 (fma beta alpha (+ beta alpha)))) (sqrt (+ 2 (+ beta alpha)))) (+ 2 (+ beta alpha))) (+ (+ 1.0 (+ beta alpha)) 2))
1.1s
(/ (/ (/ (+ 1.0 (fma beta alpha (+ beta alpha))) (sqrt (+ 2 (+ beta alpha)))) (+ 2 (+ beta alpha))) (+ (+ 1.0 (+ beta alpha)) 2))
1.1s
(/ (/ (sqrt (/ (+ 1.0 (fma beta alpha (+ beta alpha))) (+ 2 (+ beta alpha)))) (+ 2 (+ beta alpha))) (+ (+ 1.0 (+ beta alpha)) 2))

prune14.0s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 1.5b

localize57.0ms

Local error

Found 4 expressions with local error:

4.1b
(/ (+ 1.0 (fma beta alpha (+ beta alpha))) (+ 2 (+ beta alpha)))
0.1b
(/ (/ 1 (/ (+ 2 (+ beta alpha)) (/ (+ 1.0 (fma beta alpha (+ beta alpha))) (+ 2 (+ beta alpha))))) (+ (+ 1.0 (+ beta alpha)) 2))
0.0b
(/ 1 (/ (+ 2 (+ beta alpha)) (/ (+ 1.0 (fma beta alpha (+ beta alpha))) (+ 2 (+ beta alpha)))))
0.0b
(/ (+ 2 (+ beta alpha)) (/ (+ 1.0 (fma beta alpha (+ beta alpha))) (+ 2 (+ beta alpha))))

rewrite611.0ms

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×expm1-log1p-u clear-num frac-2neg insert-posit16 log1p-expm1-u add-log-exp
1×pow-flip inv-pow
Counts
4 → 3706
Calls
4 calls:
Slowest
172.0ms
(/ (/ 1 (/ (+ 2 (+ beta alpha)) (/ (+ 1.0 (fma beta alpha (+ beta alpha))) (+ 2 (+ beta alpha))))) (+ (+ 1.0 (+ beta alpha)) 2))
59.0ms
(/ (+ 2 (+ beta alpha)) (/ (+ 1.0 (fma beta alpha (+ beta alpha))) (+ 2 (+ beta alpha))))
46.0ms
(/ 1 (/ (+ 2 (+ beta alpha)) (/ (+ 1.0 (fma beta alpha (+ beta alpha))) (+ 2 (+ beta alpha)))))
35.0ms
(/ (+ 1.0 (fma beta alpha (+ beta alpha))) (+ 2 (+ beta alpha)))

series694.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
220.0ms
(/ 1 (/ (+ 2 (+ beta alpha)) (/ (+ 1.0 (fma beta alpha (+ beta alpha))) (+ 2 (+ beta alpha)))))
186.0ms
(/ (/ 1 (/ (+ 2 (+ beta alpha)) (/ (+ 1.0 (fma beta alpha (+ beta alpha))) (+ 2 (+ beta alpha))))) (+ (+ 1.0 (+ beta alpha)) 2))
176.0ms
(/ (+ 2 (+ beta alpha)) (/ (+ 1.0 (fma beta alpha (+ beta alpha))) (+ 2 (+ beta alpha))))
112.0ms
(/ (+ 1.0 (fma beta alpha (+ beta alpha))) (+ 2 (+ beta alpha)))