Average Error: 0.0 → 0.2
Time: 4.2s
Precision: 64
\[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b\]
↓
\[\mathsf{fma}\left(1 - y, z, \mathsf{fma}\left(b, \left(y + t\right) - 2, x\right) - \left(\sqrt[3]{t - 1} \cdot \sqrt[3]{t - 1}\right) \cdot \left(\sqrt[3]{t - 1} \cdot a\right)\right)\]
\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(1 - y, z, \mathsf{fma}\left(b, \left(y + t\right) - 2, x\right) - \left(\sqrt[3]{t - 1} \cdot \sqrt[3]{t - 1}\right) \cdot \left(\sqrt[3]{t - 1} \cdot a\right)\right)
double f(double x, double y, double z, double t, double a, double b) {
        double r37078 = x;
        double r37079 = y;
        double r37080 = 1.0;
        double r37081 = r37079 - r37080;
        double r37082 = z;
        double r37083 = r37081 * r37082;
        double r37084 = r37078 - r37083;
        double r37085 = t;
        double r37086 = r37085 - r37080;
        double r37087 = a;
        double r37088 = r37086 * r37087;
        double r37089 = r37084 - r37088;
        double r37090 = r37079 + r37085;
        double r37091 = 2.0;
        double r37092 = r37090 - r37091;
        double r37093 = b;
        double r37094 = r37092 * r37093;
        double r37095 = r37089 + r37094;
        return r37095;
}
↓
double f(double x, double y, double z, double t, double a, double b) {
        double r37096 = 1.0;
        double r37097 = y;
        double r37098 = r37096 - r37097;
        double r37099 = z;
        double r37100 = b;
        double r37101 = t;
        double r37102 = r37097 + r37101;
        double r37103 = 2.0;
        double r37104 = r37102 - r37103;
        double r37105 = x;
        double r37106 = fma(r37100, r37104, r37105);
        double r37107 = r37101 - r37096;
        double r37108 = cbrt(r37107);
        double r37109 = r37108 * r37108;
        double r37110 = a;
        double r37111 = r37108 * r37110;
        double r37112 = r37109 * r37111;
        double r37113 = r37106 - r37112;
        double r37114 = fma(r37098, r37099, r37113);
        return r37114;
}

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-cbrt0.2

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

  5. Applied associate-*l*0.2

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

  6. Final simplification0.2

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

Reproduce

herbie shell --seed 2019346 +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)))