Details

Time bar (total: 1.2s)

sample34.0ms

Algorithm
intervals
Results
8.0ms193×body80valid
5.0ms25×body1280valid
4.0ms256×pre80true
3.0ms19×body640valid
2.0ms14×body320valid
0.0ms5×body160valid

simplify580.0ms

Counts
1 → 1
Iterations

Useful iterations: 3 (28.0ms)

IterNodesCost
01529
13129
210527
343826
4162026
done500026

prune11.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 14.5b

localize12.0ms

Local error

Found 3 expressions with local error:

0.0b
(/ (+ alpha beta) (+ (fma 2.0 i (+ alpha beta)) 2.0))
0.1b
(/ (- beta alpha) (fma 2.0 i (+ alpha beta)))
1.7b
(fma (/ (+ alpha beta) (+ (fma 2.0 i (+ alpha beta)) 2.0)) (/ (- beta alpha) (fma 2.0 i (+ alpha beta))) 1.0)

rewrite22.0ms

Algorithm
rewrite-expression-head
Rules
51×*-un-lft-identity
31×add-sqr-sqrt times-frac
23×add-cube-cbrt
10×distribute-lft-out
9×associate-/l*
7×add-exp-log associate-/r* add-cbrt-cube
4×associate-/l/ distribute-lft-out-- difference-of-squares
3×pow1 expm1-log1p-u log1p-expm1-u add-log-exp
2×cbrt-undiv frac-2neg flip3-+ div-exp clear-num associate-/r/ flip-+ div-inv
1×flip3-- div-sub flip-- fma-udef
Counts
3 → 92
Calls
3 calls:
11.0ms
(/ (+ alpha beta) (+ (fma 2.0 i (+ alpha beta)) 2.0))
8.0ms
(/ (- beta alpha) (fma 2.0 i (+ alpha beta)))
0.0ms
(fma (/ (+ alpha beta) (+ (fma 2.0 i (+ alpha beta)) 2.0)) (/ (- beta alpha) (fma 2.0 i (+ alpha beta))) 1.0)

series394.0ms

Counts
3 → 9
Calls
3 calls:
74.0ms
(/ (+ alpha beta) (+ (fma 2.0 i (+ alpha beta)) 2.0))
77.0ms
(/ (- beta alpha) (fma 2.0 i (+ alpha beta)))
243.0ms
(fma (/ (+ alpha beta) (+ (fma 2.0 i (+ alpha beta)) 2.0)) (/ (- beta alpha) (fma 2.0 i (+ alpha beta))) 1.0)

simplify104.0ms

Iterations

Useful iterations: 1 (34.0ms)

IterNodesCost
01761908
13951852