Average Error: 0.0 → 0.3
Time: 4.8s
Precision: 64
\[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b\]
↓
\[\mathsf{fma}\left(1 - y, z, \mathsf{fma}\left(b, \left(y + t\right) - 2, x\right) - \left(\sqrt[3]{\left(t - 1\right) \cdot a} \cdot \sqrt[3]{\left(t - 1\right) \cdot a}\right) \cdot \sqrt[3]{\left(t - 1\right) \cdot a}\right)\]
\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(1 - y, z, \mathsf{fma}\left(b, \left(y + t\right) - 2, x\right) - \left(\sqrt[3]{\left(t - 1\right) \cdot a} \cdot \sqrt[3]{\left(t - 1\right) \cdot a}\right) \cdot \sqrt[3]{\left(t - 1\right) \cdot a}\right)
double f(double x, double y, double z, double t, double a, double b) {
        double r21147 = x;
        double r21148 = y;
        double r21149 = 1.0;
        double r21150 = r21148 - r21149;
        double r21151 = z;
        double r21152 = r21150 * r21151;
        double r21153 = r21147 - r21152;
        double r21154 = t;
        double r21155 = r21154 - r21149;
        double r21156 = a;
        double r21157 = r21155 * r21156;
        double r21158 = r21153 - r21157;
        double r21159 = r21148 + r21154;
        double r21160 = 2.0;
        double r21161 = r21159 - r21160;
        double r21162 = b;
        double r21163 = r21161 * r21162;
        double r21164 = r21158 + r21163;
        return r21164;
}
↓
double f(double x, double y, double z, double t, double a, double b) {
        double r21165 = 1.0;
        double r21166 = y;
        double r21167 = r21165 - r21166;
        double r21168 = z;
        double r21169 = b;
        double r21170 = t;
        double r21171 = r21166 + r21170;
        double r21172 = 2.0;
        double r21173 = r21171 - r21172;
        double r21174 = x;
        double r21175 = fma(r21169, r21173, r21174);
        double r21176 = r21170 - r21165;
        double r21177 = a;
        double r21178 = r21176 * r21177;
        double r21179 = cbrt(r21178);
        double r21180 = r21179 * r21179;
        double r21181 = r21180 * r21179;
        double r21182 = r21175 - r21181;
        double r21183 = fma(r21167, r21168, r21182);
        return r21183;
}

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

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

  4. Applied add-cube-cbrt0.3

    \[\leadsto \mathsf{fma}\left(1 - y, z, \mathsf{fma}\left(b, \left(y + t\right) - 2, x\right) - \color{blue}{\left(\sqrt[3]{\left(t - 1\right) \cdot a} \cdot \sqrt[3]{\left(t - 1\right) \cdot a}\right) \cdot \sqrt[3]{\left(t - 1\right) \cdot a}}\right)\]

  5. Final simplification0.3

    \[\leadsto \mathsf{fma}\left(1 - y, z, \mathsf{fma}\left(b, \left(y + t\right) - 2, x\right) - \left(\sqrt[3]{\left(t - 1\right) \cdot a} \cdot \sqrt[3]{\left(t - 1\right) \cdot a}\right) \cdot \sqrt[3]{\left(t - 1\right) \cdot a}\right)\]

Reproduce

herbie shell --seed 2020027 +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)))