Average Error: 1.4 → 2.8
Time: 7.2s
Precision: 64
\[x + y \cdot \frac{z - t}{z - a}\]
↓
\[\left(x + \frac{z}{\frac{z - a}{y}}\right) - \frac{t}{\frac{z - a}{y}}\]
x + y \cdot \frac{z - t}{z - a}
↓
\left(x + \frac{z}{\frac{z - a}{y}}\right) - \frac{t}{\frac{z - a}{y}}
double f(double x, double y, double z, double t, double a) {
        double r376097 = x;
        double r376098 = y;
        double r376099 = z;
        double r376100 = t;
        double r376101 = r376099 - r376100;
        double r376102 = a;
        double r376103 = r376099 - r376102;
        double r376104 = r376101 / r376103;
        double r376105 = r376098 * r376104;
        double r376106 = r376097 + r376105;
        return r376106;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r376107 = x;
        double r376108 = z;
        double r376109 = a;
        double r376110 = r376108 - r376109;
        double r376111 = y;
        double r376112 = r376110 / r376111;
        double r376113 = r376108 / r376112;
        double r376114 = r376107 + r376113;
        double r376115 = t;
        double r376116 = r376115 / r376112;
        double r376117 = r376114 - r376116;
        return r376117;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Bits error versus t

Bits error versus a

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original1.4
Target1.3
Herbie2.8
\[x + \frac{y}{\frac{z - a}{z - t}}\]

Derivation

  1. Initial program 1.4

    \[x + y \cdot \frac{z - t}{z - a}\]
  2. Using strategy rm

  3. Applied add-cube-cbrt1.9

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

  4. Applied add-cube-cbrt1.8

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

  5. Applied times-frac1.8

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

  6. Applied associate-*r*0.6

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

  7. Final simplification2.8

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

Reproduce

herbie shell --seed 1978988140 
(FPCore (x y z t a)
  :name "Graphics.Rendering.Plot.Render.Plot.Axis:renderAxisLine from plot-0.2.3.4, A"
  :precision binary64

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

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