Average Error: 6.7 → 1.6
Time: 17.5s
Precision: 64
\[x + \frac{y \cdot \left(z - x\right)}{t}\]
↓
\[\left(y \cdot \frac{\sqrt[3]{z - x} \cdot \sqrt[3]{z - x}}{\sqrt[3]{t} \cdot \sqrt[3]{t}}\right) \cdot \frac{\sqrt[3]{z - x}}{\sqrt[3]{t}} + x\]
x + \frac{y \cdot \left(z - x\right)}{t}
↓
\left(y \cdot \frac{\sqrt[3]{z - x} \cdot \sqrt[3]{z - x}}{\sqrt[3]{t} \cdot \sqrt[3]{t}}\right) \cdot \frac{\sqrt[3]{z - x}}{\sqrt[3]{t}} + x
double f(double x, double y, double z, double t) {
        double r281813 = x;
        double r281814 = y;
        double r281815 = z;
        double r281816 = r281815 - r281813;
        double r281817 = r281814 * r281816;
        double r281818 = t;
        double r281819 = r281817 / r281818;
        double r281820 = r281813 + r281819;
        return r281820;
}
↓
double f(double x, double y, double z, double t) {
        double r281821 = y;
        double r281822 = z;
        double r281823 = x;
        double r281824 = r281822 - r281823;
        double r281825 = cbrt(r281824);
        double r281826 = r281825 * r281825;
        double r281827 = t;
        double r281828 = cbrt(r281827);
        double r281829 = r281828 * r281828;
        double r281830 = r281826 / r281829;
        double r281831 = r281821 * r281830;
        double r281832 = r281825 / r281828;
        double r281833 = r281831 * r281832;
        double r281834 = r281833 + r281823;
        return r281834;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Bits error versus t

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original6.7
Target2.0
Herbie1.6
\[x - \left(x \cdot \frac{y}{t} + \left(-z\right) \cdot \frac{y}{t}\right)\]

Derivation

  1. Initial program 6.7

    \[x + \frac{y \cdot \left(z - x\right)}{t}\]

  2. Simplified2.0

    \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{y}{t}, z - x, x\right)}\]
  3. Using strategy rm

  4. Applied fma-udef2.0

    \[\leadsto \color{blue}{\frac{y}{t} \cdot \left(z - x\right) + x}\]

  5. Simplified6.7

    \[\leadsto \color{blue}{y \cdot \frac{z - x}{t}} + x\]
  6. Using strategy rm

  7. Applied add-cube-cbrt7.1

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

  8. Applied add-cube-cbrt7.2

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

  9. Applied times-frac7.2

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

  10. Applied associate-*r*1.6

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

  11. Final simplification1.6

    \[\leadsto \left(y \cdot \frac{\sqrt[3]{z - x} \cdot \sqrt[3]{z - x}}{\sqrt[3]{t} \cdot \sqrt[3]{t}}\right) \cdot \frac{\sqrt[3]{z - x}}{\sqrt[3]{t}} + x\]

Reproduce

herbie shell --seed 2019209 +o rules:numerics
(FPCore (x y z t)
  :name "Optimisation.CirclePacking:place from circle-packing-0.1.0.4, D"
  :precision binary64

  :herbie-target
  (- x (+ (* x (/ y t)) (* (- z) (/ y t))))

  (+ x (/ (* y (- z x)) t)))