Average Error: 0.0 → 0.0
Time: 13.0s
Precision: 64
\[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b\]
↓
\[\mathsf{fma}\left(b, \left(y + t\right) - 2, \mathsf{fma}\left(1 - y, z, \mathsf{fma}\left(a, 1 - t, x\right)\right)\right)\]
\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b
↓
\mathsf{fma}\left(b, \left(y + t\right) - 2, \mathsf{fma}\left(1 - y, z, \mathsf{fma}\left(a, 1 - t, x\right)\right)\right)
double f(double x, double y, double z, double t, double a, double b) {
        double r29315 = x;
        double r29316 = y;
        double r29317 = 1.0;
        double r29318 = r29316 - r29317;
        double r29319 = z;
        double r29320 = r29318 * r29319;
        double r29321 = r29315 - r29320;
        double r29322 = t;
        double r29323 = r29322 - r29317;
        double r29324 = a;
        double r29325 = r29323 * r29324;
        double r29326 = r29321 - r29325;
        double r29327 = r29316 + r29322;
        double r29328 = 2.0;
        double r29329 = r29327 - r29328;
        double r29330 = b;
        double r29331 = r29329 * r29330;
        double r29332 = r29326 + r29331;
        return r29332;
}
↓
double f(double x, double y, double z, double t, double a, double b) {
        double r29333 = b;
        double r29334 = y;
        double r29335 = t;
        double r29336 = r29334 + r29335;
        double r29337 = 2.0;
        double r29338 = r29336 - r29337;
        double r29339 = 1.0;
        double r29340 = r29339 - r29334;
        double r29341 = z;
        double r29342 = a;
        double r29343 = r29339 - r29335;
        double r29344 = x;
        double r29345 = fma(r29342, r29343, r29344);
        double r29346 = fma(r29340, r29341, r29345);
        double r29347 = fma(r29333, r29338, r29346);
        return r29347;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Bits error versus t

Bits error versus a

Bits error versus b

Derivation

  1. Initial program 0.0

    \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b\]

  2. Simplified0.0

    \[\leadsto \color{blue}{\mathsf{fma}\left(b, \left(y + t\right) - 2, \mathsf{fma}\left(1 - y, z, \mathsf{fma}\left(a, 1 - t, x\right)\right)\right)}\]

  3. Final simplification0.0

    \[\leadsto \mathsf{fma}\left(b, \left(y + t\right) - 2, \mathsf{fma}\left(1 - y, z, \mathsf{fma}\left(a, 1 - t, x\right)\right)\right)\]

Reproduce

herbie shell --seed 2019325 +o rules:numerics
(FPCore (x y z t a b)
  :name "Statistics.Distribution.Beta:$centropy from math-functions-0.1.5.2"
  :precision binary64
  (+ (- (- x (* (- y 1) z)) (* (- t 1) a)) (* (- (+ y t) 2) b)))