Details

Time bar (total: 8.3m)

sample45.0ms

Algorithm
intervals
Results
25.0ms256×body80valid
7.0ms256×pre80true

simplify151.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
150.0ms
(/ (/ (/ (+ (+ (+ 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: 2.3b

localize54.0ms

Local error

Found 3 expressions with local error:

2.2b
(/ (+ 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)))

rewrite422.0ms

Algorithm
rewrite-expression-head
Rules
4322×*-un-lft-identity
2696×times-frac
2167×distribute-lft-out
777×add-sqr-sqrt add-cube-cbrt
166×associate-/l*
102×associate-/r/
52×flip3-+ flip-+
51×div-inv
19×add-cbrt-cube add-exp-log
16×associate-/r*
10×cbrt-undiv div-exp
4×associate-/l/
3×expm1-log1p-u pow1 clear-num frac-2neg insert-posit16 log1p-expm1-u add-log-exp
Counts
3 → 1209
Calls
3 calls:
Slowest
218.0ms
(/ (/ (/ (+ 1.0 (fma beta alpha (+ beta alpha))) (+ 2 (+ beta alpha))) (+ 2 (+ beta alpha))) (+ (+ 1.0 (+ beta alpha)) 2))
81.0ms
(/ (/ (+ 1.0 (fma beta alpha (+ beta alpha))) (+ 2 (+ beta alpha))) (+ 2 (+ beta alpha)))
56.0ms
(/ (+ 1.0 (fma beta alpha (+ beta alpha))) (+ 2 (+ beta alpha)))

series1.1s

Counts
3 → 9
Calls
3 calls:
Slowest
700.0ms
(/ (/ (/ (+ 1.0 (fma beta alpha (+ beta alpha))) (+ 2 (+ beta alpha))) (+ 2 (+ beta alpha))) (+ (+ 1.0 (+ beta alpha)) 2))
227.0ms
(/ (/ (+ 1.0 (fma beta alpha (+ beta alpha))) (+ 2 (+ beta alpha))) (+ 2 (+ beta alpha)))
150.0ms
(/ (+ 1.0 (fma beta alpha (+ beta alpha))) (+ 2 (+ beta alpha)))

simplify8.0m

Counts
2141 → 1218
Calls
2141 calls:
Slowest
1.2s
(/ (/ (/ (sqrt (+ 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))) (cbrt (+ 2 (+ beta alpha)))) (+ 2 (+ beta alpha))) (+ (+ 1.0 (+ beta alpha)) 2))
1.0s
(/ (/ (- 2 (+ beta alpha)) (+ 2 (+ beta alpha))) (+ (+ 1.0 (+ beta alpha)) 2))
999.0ms
(/ (/ (cbrt (/ (+ 1.0 (fma beta alpha (+ beta alpha))) (+ 2 (+ beta alpha)))) (+ 2 (+ beta alpha))) (+ (+ 1.0 (+ beta alpha)) 2))
995.0ms
(/ (/ (/ (+ 1.0 (fma beta alpha (+ beta alpha))) (sqrt (+ 2 (+ beta alpha)))) (+ 2 (+ beta alpha))) (+ (+ 1.0 (+ beta alpha)) 2))

prune14.4s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 1.4b

localize71.0ms

Local error

Found 4 expressions with local error:

2.2b
(/ (+ 1.0 (fma beta alpha (+ beta alpha))) (+ 2 (+ beta alpha)))
2.2b
(/ (+ 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))))

rewrite649.0ms

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
467.0ms
(/ (sqrt (/ (+ 1.0 (fma beta alpha (+ beta alpha))) (+ 2 (+ beta alpha)))) (sqrt (+ 2 (+ beta alpha))))
80.0ms
(/ (sqrt (/ (+ 1.0 (fma beta alpha (+ beta alpha))) (+ 2 (+ beta alpha)))) (sqrt (+ 2 (+ beta alpha))))
36.0ms
(/ (+ 1.0 (fma beta alpha (+ beta alpha))) (+ 2 (+ beta alpha)))
32.0ms
(/ (+ 1.0 (fma beta alpha (+ beta alpha))) (+ 2 (+ beta alpha)))

series738.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
256.0ms
(/ (sqrt (/ (+ 1.0 (fma beta alpha (+ beta alpha))) (+ 2 (+ beta alpha)))) (sqrt (+ 2 (+ beta alpha))))
229.0ms
(/ (sqrt (/ (+ 1.0 (fma beta alpha (+ beta alpha))) (+ 2 (+ beta alpha)))) (sqrt (+ 2 (+ beta alpha))))
137.0ms
(/ (+ 1.0 (fma beta alpha (+ beta alpha))) (+ 2 (+ beta alpha)))
115.0ms
(/ (+ 1.0 (fma beta alpha (+ beta alpha))) (+ 2 (+ beta alpha)))