Details

Time bar (total: 8.9m)

sample56.0ms

Algorithm
intervals
Results
33.0ms256×body80valid
8.0ms256×pre80true

simplify118.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
118.0ms
(/ (/ (/ (+ (+ (+ 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: 3.3b

localize37.0ms

Local error

Found 4 expressions with local error:

3.1b
(/ (+ 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)

rewrite455.0ms

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
173.0ms
(/ (/ (/ (+ 1.0 (fma beta alpha (+ beta alpha))) (+ 2 (+ beta alpha))) (+ 2 (+ beta alpha))) (+ (+ 1.0 (+ beta alpha)) 2))
83.0ms
(+ (+ 1.0 (+ beta alpha)) 2)
67.0ms
(/ (/ (+ 1.0 (fma beta alpha (+ beta alpha))) (+ 2 (+ beta alpha))) (+ 2 (+ beta alpha)))
28.0ms
(/ (+ 1.0 (fma beta alpha (+ beta alpha))) (+ 2 (+ beta alpha)))

series530.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
211.0ms
(/ (/ (/ (+ 1.0 (fma beta alpha (+ beta alpha))) (+ 2 (+ beta alpha))) (+ 2 (+ beta alpha))) (+ (+ 1.0 (+ beta alpha)) 2))
175.0ms
(/ (/ (+ 1.0 (fma beta alpha (+ beta alpha))) (+ 2 (+ beta alpha))) (+ 2 (+ beta alpha)))
130.0ms
(/ (+ 1.0 (fma beta alpha (+ beta alpha))) (+ 2 (+ beta alpha)))
15.0ms
(+ (+ 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
(/ (/ (- 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))
1.1s
(/ (/ (/ (+ 1.0 (fma beta alpha (+ beta alpha))) (cbrt (+ 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))

prune15.1s

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0.9b

localize48.0ms

Local error

Found 4 expressions with local error:

3.1b
(sqrt (+ 1.0 (fma beta alpha (+ beta alpha))))
3.1b
(sqrt (+ 1.0 (fma beta alpha (+ beta alpha))))
0.4b
(/ (sqrt (+ 1.0 (fma beta alpha (+ beta alpha)))) (sqrt (+ 2 (+ beta alpha))))
0.4b
(/ (sqrt (+ 1.0 (fma beta alpha (+ beta alpha)))) (sqrt (+ 2 (+ beta alpha))))

rewrite81.0ms

Algorithm
rewrite-expression-head
Rules
194×*-un-lft-identity
160×sqrt-prod
112×times-frac
80×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×expm1-log1p-u associate-/r/ insert-posit16 log1p-expm1-u add-log-exp associate-/l/
2×cbrt-undiv rem-sqrt-square sqrt-undiv clear-num frac-2neg sqrt-pow1 pow1/2 div-exp hypot-def div-inv
Counts
4 → 222
Calls
4 calls:
Slowest
37.0ms
(/ (sqrt (+ 1.0 (fma beta alpha (+ beta alpha)))) (sqrt (+ 2 (+ beta alpha))))
30.0ms
(/ (sqrt (+ 1.0 (fma beta alpha (+ beta alpha)))) (sqrt (+ 2 (+ beta alpha))))
4.0ms
(sqrt (+ 1.0 (fma beta alpha (+ beta alpha))))
4.0ms
(sqrt (+ 1.0 (fma beta alpha (+ beta alpha))))

series490.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
192.0ms
(/ (sqrt (+ 1.0 (fma beta alpha (+ beta alpha)))) (sqrt (+ 2 (+ beta alpha))))
161.0ms
(/ (sqrt (+ 1.0 (fma beta alpha (+ beta alpha)))) (sqrt (+ 2 (+ beta alpha))))
69.0ms
(sqrt (+ 1.0 (fma beta alpha (+ beta alpha))))
67.0ms
(sqrt (+ 1.0 (fma beta alpha (+ beta alpha))))

simplify32.1s

Counts
296 → 234
Calls
296 calls:
Slowest
531.0ms
(/ (sqrt (sqrt (+ 1.0 (fma beta alpha (+ beta alpha))))) (sqrt (+ 2 (+ beta alpha))))
428.0ms
(sqrt (+ (* 2 2) (- (* (+ beta alpha) (+ beta alpha)) (* 2 (+ beta alpha)))))
364.0ms
(sqrt (+ (pow 1.0 3) (pow (fma beta alpha (+ beta alpha)) 3)))
361.0ms
(sqrt (+ (pow 1.0 3) (pow (fma beta alpha (+ beta alpha)) 3)))
359.0ms
(sqrt (+ (pow 1.0 3) (pow (fma beta alpha (+ beta alpha)) 3)))

prune3.3s

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 0.9b

localize51.0ms

Local error

Found 4 expressions with local error:

3.1b
(/ (+ 1.0 (fma beta alpha (+ beta alpha))) (+ 2 (+ beta alpha)))
3.1b
(/ (+ 1.0 (fma beta alpha (+ beta alpha))) (+ 2 (+ beta alpha)))
0.2b
(/ (sqrt (/ (+ 1.0 (fma beta alpha (+ beta alpha))) (+ 2 (+ beta alpha)))) (sqrt (+ 2 (+ beta alpha))))
0.2b
(/ (sqrt (/ (+ 1.0 (fma beta alpha (+ beta alpha))) (+ 2 (+ beta alpha)))) (sqrt (+ 2 (+ beta alpha))))

rewrite307.0ms

Algorithm
rewrite-expression-head
Rules
1258×*-un-lft-identity
864×times-frac
768×sqrt-prod
528×distribute-lft-out
344×add-sqr-sqrt add-cube-cbrt
66×associate-/l*
44×associate-/r/
26×associate-/r*
24×flip3-+ flip-+
22×div-inv
12×add-cbrt-cube add-exp-log
6×sqrt-div associate-/l/
4×expm1-log1p-u pow1 cbrt-undiv clear-num frac-2neg div-exp insert-posit16 log1p-expm1-u add-log-exp
2×sqrt-undiv
Counts
4 → 672
Calls
4 calls:
Slowest
99.0ms
(/ (sqrt (/ (+ 1.0 (fma beta alpha (+ beta alpha))) (+ 2 (+ beta alpha)))) (sqrt (+ 2 (+ beta alpha))))
76.0ms
(/ (sqrt (/ (+ 1.0 (fma beta alpha (+ beta alpha))) (+ 2 (+ beta alpha)))) (sqrt (+ 2 (+ beta alpha))))
49.0ms
(/ (+ 1.0 (fma beta alpha (+ beta alpha))) (+ 2 (+ beta alpha)))
46.0ms
(/ (+ 1.0 (fma beta alpha (+ beta alpha))) (+ 2 (+ beta alpha)))

series779.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
275.0ms
(/ (sqrt (/ (+ 1.0 (fma beta alpha (+ beta alpha))) (+ 2 (+ beta alpha)))) (sqrt (+ 2 (+ beta alpha))))
271.0ms
(/ (sqrt (/ (+ 1.0 (fma beta alpha (+ beta alpha))) (+ 2 (+ beta alpha)))) (sqrt (+ 2 (+ beta alpha))))
123.0ms
(/ (+ 1.0 (fma beta alpha (+ beta alpha))) (+ 2 (+ beta alpha)))
110.0ms
(/ (+ 1.0 (fma beta alpha (+ beta alpha))) (+ 2 (+ beta alpha)))