Average Error: 0.0 → 0.1
Time: 17.7s
Precision: 64
\[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b\]
↓
\[\left(\left(x - \left(z \cdot \sqrt[3]{y - 1}\right) \cdot \left(\sqrt[3]{y - 1} \cdot \sqrt[3]{y - 1}\right)\right) - \left(t - 1\right) \cdot a\right) + \left(\left(t + y\right) - 2\right) \cdot b\]
\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(x - \left(z \cdot \sqrt[3]{y - 1}\right) \cdot \left(\sqrt[3]{y - 1} \cdot \sqrt[3]{y - 1}\right)\right) - \left(t - 1\right) \cdot a\right) + \left(\left(t + y\right) - 2\right) \cdot b
double f(double x, double y, double z, double t, double a, double b) {
        double r41771 = x;
        double r41772 = y;
        double r41773 = 1.0;
        double r41774 = r41772 - r41773;
        double r41775 = z;
        double r41776 = r41774 * r41775;
        double r41777 = r41771 - r41776;
        double r41778 = t;
        double r41779 = r41778 - r41773;
        double r41780 = a;
        double r41781 = r41779 * r41780;
        double r41782 = r41777 - r41781;
        double r41783 = r41772 + r41778;
        double r41784 = 2.0;
        double r41785 = r41783 - r41784;
        double r41786 = b;
        double r41787 = r41785 * r41786;
        double r41788 = r41782 + r41787;
        return r41788;
}
↓
double f(double x, double y, double z, double t, double a, double b) {
        double r41789 = x;
        double r41790 = z;
        double r41791 = y;
        double r41792 = 1.0;
        double r41793 = r41791 - r41792;
        double r41794 = cbrt(r41793);
        double r41795 = r41790 * r41794;
        double r41796 = r41794 * r41794;
        double r41797 = r41795 * r41796;
        double r41798 = r41789 - r41797;
        double r41799 = t;
        double r41800 = r41799 - r41792;
        double r41801 = a;
        double r41802 = r41800 * r41801;
        double r41803 = r41798 - r41802;
        double r41804 = r41799 + r41791;
        double r41805 = 2.0;
        double r41806 = r41804 - r41805;
        double r41807 = b;
        double r41808 = r41806 * r41807;
        double r41809 = r41803 + r41808;
        return r41809;
}

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

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

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

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

  4. Applied add-cube-cbrt0.1

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

  5. Applied associate-*l*0.1

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

  6. Final simplification0.1

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

Reproduce

herbie shell --seed 2019196 
(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)))