Average Error: 6.6 → 6.6
Time: 5.4s
Precision: 64
\[x + \frac{y \cdot \left(z - x\right)}{t}\]
↓
\[x - \left(\frac{x \cdot y}{t} - \frac{y \cdot z}{t}\right)\]
x + \frac{y \cdot \left(z - x\right)}{t}
↓
x - \left(\frac{x \cdot y}{t} - \frac{y \cdot z}{t}\right)
double f(double x, double y, double z, double t) {
        double r234870 = x;
        double r234871 = y;
        double r234872 = z;
        double r234873 = r234872 - r234870;
        double r234874 = r234871 * r234873;
        double r234875 = t;
        double r234876 = r234874 / r234875;
        double r234877 = r234870 + r234876;
        return r234877;
}
↓
double f(double x, double y, double z, double t) {
        double r234878 = x;
        double r234879 = y;
        double r234880 = r234878 * r234879;
        double r234881 = t;
        double r234882 = r234880 / r234881;
        double r234883 = z;
        double r234884 = r234879 * r234883;
        double r234885 = r234884 / r234881;
        double r234886 = r234882 - r234885;
        double r234887 = r234878 - r234886;
        return r234887;
}

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

Original6.6
Target2.1
Herbie6.6
\[x - \left(x \cdot \frac{y}{t} + \left(-z\right) \cdot \frac{y}{t}\right)\]

Derivation

  1. Initial program 6.6

    \[x + \frac{y \cdot \left(z - x\right)}{t}\]
  2. Using strategy rm

  3. Applied associate-/l*6.0

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

  5. Applied associate-/r/2.1

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

  7. Applied add-cube-cbrt2.6

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

  8. Applied add-cube-cbrt2.8

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

  9. Applied times-frac2.8

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

  10. Applied associate-*l*1.0

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

  11. Final simplification6.6

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

Reproduce

herbie shell --seed 1978988140 
(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)))