Average Error: 0.0 → 0.0
Time: 47.4s
Precision: 64
\[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b\]
↓
\[\mathsf{fma}\left(\left(y + t\right) - 2, b, \mathsf{fma}\left(a, 1 - t, \mathsf{fma}\left(z, 1 - y, x\right)\right)\right)\]
\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(\left(y + t\right) - 2, b, \mathsf{fma}\left(a, 1 - t, \mathsf{fma}\left(z, 1 - y, x\right)\right)\right)
double f(double x, double y, double z, double t, double a, double b) {
        double r2160321 = x;
        double r2160322 = y;
        double r2160323 = 1.0;
        double r2160324 = r2160322 - r2160323;
        double r2160325 = z;
        double r2160326 = r2160324 * r2160325;
        double r2160327 = r2160321 - r2160326;
        double r2160328 = t;
        double r2160329 = r2160328 - r2160323;
        double r2160330 = a;
        double r2160331 = r2160329 * r2160330;
        double r2160332 = r2160327 - r2160331;
        double r2160333 = r2160322 + r2160328;
        double r2160334 = 2.0;
        double r2160335 = r2160333 - r2160334;
        double r2160336 = b;
        double r2160337 = r2160335 * r2160336;
        double r2160338 = r2160332 + r2160337;
        return r2160338;
}
↓
double f(double x, double y, double z, double t, double a, double b) {
        double r2160339 = y;
        double r2160340 = t;
        double r2160341 = r2160339 + r2160340;
        double r2160342 = 2.0;
        double r2160343 = r2160341 - r2160342;
        double r2160344 = b;
        double r2160345 = a;
        double r2160346 = 1.0;
        double r2160347 = r2160346 - r2160340;
        double r2160348 = z;
        double r2160349 = r2160346 - r2160339;
        double r2160350 = x;
        double r2160351 = fma(r2160348, r2160349, r2160350);
        double r2160352 = fma(r2160345, r2160347, r2160351);
        double r2160353 = fma(r2160343, r2160344, r2160352);
        return r2160353;
}

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

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

  3. Final simplification0.0

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

Reproduce

herbie shell --seed 2019168 +o rules:numerics
(FPCore (x y z t a b)
  :name "Statistics.Distribution.Beta:$centropy from math-functions-0.1.5.2"
  (+ (- (- x (* (- y 1.0) z)) (* (- t 1.0) a)) (* (- (+ y t) 2.0) b)))