Average Error: 0.0 → 0.0
Time: 39.0s
Precision: 64
\[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b\]
↓
\[\left(\left(\left(t + y\right) - 2\right) \cdot b + \mathsf{fma}\left(-a, t - 1, \left(t - 1\right) \cdot a\right)\right) + \mathsf{fma}\left(1, x - z \cdot \left(y - 1\right), \left(-a\right) \cdot \left(t - 1\right)\right)\]
\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
↓
\left(\left(\left(t + y\right) - 2\right) \cdot b + \mathsf{fma}\left(-a, t - 1, \left(t - 1\right) \cdot a\right)\right) + \mathsf{fma}\left(1, x - z \cdot \left(y - 1\right), \left(-a\right) \cdot \left(t - 1\right)\right)
double f(double x, double y, double z, double t, double a, double b) {
        double r2083011 = x;
        double r2083012 = y;
        double r2083013 = 1.0;
        double r2083014 = r2083012 - r2083013;
        double r2083015 = z;
        double r2083016 = r2083014 * r2083015;
        double r2083017 = r2083011 - r2083016;
        double r2083018 = t;
        double r2083019 = r2083018 - r2083013;
        double r2083020 = a;
        double r2083021 = r2083019 * r2083020;
        double r2083022 = r2083017 - r2083021;
        double r2083023 = r2083012 + r2083018;
        double r2083024 = 2.0;
        double r2083025 = r2083023 - r2083024;
        double r2083026 = b;
        double r2083027 = r2083025 * r2083026;
        double r2083028 = r2083022 + r2083027;
        return r2083028;
}
↓
double f(double x, double y, double z, double t, double a, double b) {
        double r2083029 = t;
        double r2083030 = y;
        double r2083031 = r2083029 + r2083030;
        double r2083032 = 2.0;
        double r2083033 = r2083031 - r2083032;
        double r2083034 = b;
        double r2083035 = r2083033 * r2083034;
        double r2083036 = a;
        double r2083037 = -r2083036;
        double r2083038 = 1.0;
        double r2083039 = r2083029 - r2083038;
        double r2083040 = r2083039 * r2083036;
        double r2083041 = fma(r2083037, r2083039, r2083040);
        double r2083042 = r2083035 + r2083041;
        double r2083043 = 1.0;
        double r2083044 = x;
        double r2083045 = z;
        double r2083046 = r2083030 - r2083038;
        double r2083047 = r2083045 * r2083046;
        double r2083048 = r2083044 - r2083047;
        double r2083049 = r2083037 * r2083039;
        double r2083050 = fma(r2083043, r2083048, r2083049);
        double r2083051 = r2083042 + r2083050;
        return r2083051;
}

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. Using strategy rm

  3. Applied *-un-lft-identity0.0

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

  4. Applied prod-diff0.0

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

  5. Applied associate-+l+0.0

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

  6. Final simplification0.0

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

Reproduce

herbie shell --seed 2019200 +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)))