Details

Time bar (total: 9.2m)

sample83.0ms

Algorithm
intervals
Results
54.0ms256×body80valid
12.0ms256×pre80true

simplify115.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
115.0ms
(/ (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2 1))) (+ (+ alpha beta) (* 2 1))) (+ (+ (+ alpha beta) (* 2 1)) 1.0))

prune18.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 2.6b

localize45.0ms

Local error

Found 4 expressions with local error:

2.4b
(/ (+ 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)

rewrite414.0ms

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
186.0ms
(/ (/ (/ (+ 1.0 (fma beta alpha (+ beta alpha))) (+ 2 (+ beta alpha))) (+ 2 (+ beta alpha))) (+ (+ 1.0 (+ beta alpha)) 2))
75.0ms
(+ (+ 1.0 (+ beta alpha)) 2)
52.0ms
(/ (/ (+ 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)))

series534.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
221.0ms
(/ (/ (/ (+ 1.0 (fma beta alpha (+ beta alpha))) (+ 2 (+ beta alpha))) (+ 2 (+ beta alpha))) (+ (+ 1.0 (+ beta alpha)) 2))
177.0ms
(/ (/ (+ 1.0 (fma beta alpha (+ beta alpha))) (+ 2 (+ beta alpha))) (+ 2 (+ beta alpha)))
121.0ms
(/ (+ 1.0 (fma beta alpha (+ beta alpha))) (+ 2 (+ beta alpha)))
14.0ms
(+ (+ 1.0 (+ beta alpha)) 2)

simplify8.3m

Counts
2152 → 1246
Calls
2152 calls:
Slowest
1.2s
(/ (/ (/ (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))
1.0s
(/ (/ (/ (sqrt (+ 1.0 (fma beta alpha (+ beta alpha)))) (cbrt (+ 2 (+ beta alpha)))) (+ 2 (+ beta alpha))) (+ (+ 1.0 (+ beta alpha)) 2))
999.0ms
(/ (/ (/ (+ 1.0 (fma beta alpha (+ beta alpha))) (cbrt (+ 2 (+ beta alpha)))) (+ 2 (+ beta alpha))) (+ (+ 1.0 (+ beta alpha)) 2))

prune14.5s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 1.2b

localize45.0ms

Local error

Found 4 expressions with local error:

2.4b
(sqrt (+ 1.0 (fma beta alpha (+ beta alpha))))
2.4b
(sqrt (+ 1.0 (fma beta alpha (+ beta alpha))))
0.5b
(/ (sqrt (+ 1.0 (fma beta alpha (+ beta alpha)))) (sqrt (+ 2 (+ beta alpha))))
0.5b
(/ (sqrt (+ 1.0 (fma beta alpha (+ beta alpha)))) (sqrt (+ 2 (+ beta alpha))))

rewrite95.0ms

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
39.0ms
(/ (sqrt (+ 1.0 (fma beta alpha (+ beta alpha)))) (sqrt (+ 2 (+ beta alpha))))
31.0ms
(/ (sqrt (+ 1.0 (fma beta alpha (+ beta alpha)))) (sqrt (+ 2 (+ beta alpha))))
9.0ms
(sqrt (+ 1.0 (fma beta alpha (+ beta alpha))))
9.0ms
(sqrt (+ 1.0 (fma beta alpha (+ beta alpha))))

series426.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
151.0ms
(/ (sqrt (+ 1.0 (fma beta alpha (+ beta alpha)))) (sqrt (+ 2 (+ beta alpha))))
134.0ms
(/ (sqrt (+ 1.0 (fma beta alpha (+ beta alpha)))) (sqrt (+ 2 (+ beta alpha))))
71.0ms
(sqrt (+ 1.0 (fma beta alpha (+ beta alpha))))
70.0ms
(sqrt (+ 1.0 (fma beta alpha (+ beta alpha))))

simplify34.4s

Counts
296 → 234
Calls
296 calls:
Slowest
527.0ms
(/ (sqrt (sqrt (+ 1.0 (fma beta alpha (+ beta alpha))))) (sqrt 1))
383.0ms
(sqrt (+ (pow 1.0 3) (pow (fma beta alpha (+ beta alpha)) 3)))
379.0ms
(sqrt (+ (pow 1.0 3) (pow (fma beta alpha (+ beta alpha)) 3)))
370.0ms
(sqrt (+ (pow 1.0 3) (pow (fma beta alpha (+ beta alpha)) 3)))
359.0ms
(sqrt (+ (* 2 2) (- (* (+ beta alpha) (+ beta alpha)) (* 2 (+ beta alpha)))))

prune3.4s

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 1.2b

localize50.0ms

Local error

Found 4 expressions with local error:

2.4b
(/ (+ 1.0 (fma beta alpha (+ beta alpha))) (+ 2 (+ beta alpha)))
1.5b
(/ (/ (+ 1.0 (fma beta alpha (+ beta alpha))) (+ 2 (+ beta alpha))) (- (* 2 2) (* (+ beta alpha) (+ beta alpha))))
0.0b
(/ (/ (/ (+ 1.0 (fma beta alpha (+ beta alpha))) (+ 2 (+ beta alpha))) (- (* 2 2) (* (+ beta alpha) (+ beta alpha)))) (/ (+ (+ 1.0 (+ beta alpha)) 2) (- 2 (+ beta alpha))))
0.0b
(/ (+ (+ 1.0 (+ beta alpha)) 2) (- 2 (+ beta alpha)))

rewrite976.0ms

Algorithm
rewrite-expression-head
Rules
19199×*-un-lft-identity
16788×times-frac
7741×distribute-lft-out
5776×add-sqr-sqrt
4430×add-cube-cbrt
1818×difference-of-squares
1346×distribute-lft-out--
669×associate-/r/
335×div-inv
180×flip3-+ flip-+
156×flip3-- flip--
146×associate-/l*
57×associate-/r*
34×add-cbrt-cube add-exp-log
20×cbrt-undiv div-exp
6×associate-/l/
4×expm1-log1p-u pow1 clear-num frac-2neg insert-posit16 log1p-expm1-u add-log-exp
Counts
4 → 5068
Calls
4 calls:
Slowest
206.0ms
(/ (+ (+ 1.0 (+ beta alpha)) 2) (- 2 (+ beta alpha)))
205.0ms
(/ (/ (/ (+ 1.0 (fma beta alpha (+ beta alpha))) (+ 2 (+ beta alpha))) (- (* 2 2) (* (+ beta alpha) (+ beta alpha)))) (/ (+ (+ 1.0 (+ beta alpha)) 2) (- 2 (+ beta alpha))))
85.0ms
(/ (/ (+ 1.0 (fma beta alpha (+ beta alpha))) (+ 2 (+ beta alpha))) (- (* 2 2) (* (+ beta alpha) (+ beta alpha))))
37.0ms
(/ (+ 1.0 (fma beta alpha (+ beta alpha))) (+ 2 (+ beta alpha)))

series775.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
313.0ms
(/ (/ (/ (+ 1.0 (fma beta alpha (+ beta alpha))) (+ 2 (+ beta alpha))) (- (* 2 2) (* (+ beta alpha) (+ beta alpha)))) (/ (+ (+ 1.0 (+ beta alpha)) 2) (- 2 (+ beta alpha))))
275.0ms
(/ (/ (+ 1.0 (fma beta alpha (+ beta alpha))) (+ 2 (+ beta alpha))) (- (* 2 2) (* (+ beta alpha) (+ beta alpha))))
116.0ms
(/ (+ 1.0 (fma beta alpha (+ beta alpha))) (+ 2 (+ beta alpha)))
70.0ms
(/ (+ (+ 1.0 (+ beta alpha)) 2) (- 2 (+ beta alpha)))