Average Error: 2.1 → 1.1
Time: 10.6s
Precision: 64
\[\frac{x - y}{z - y} \cdot t\]
↓
\[\frac{\frac{t}{\frac{\sqrt[3]{z - y} \cdot \sqrt[3]{z - y}}{\sqrt[3]{x - y} \cdot \sqrt[3]{x - y}}}}{\frac{\sqrt[3]{z - y}}{\sqrt[3]{x - y}}}\]
\frac{x - y}{z - y} \cdot t
↓
\frac{\frac{t}{\frac{\sqrt[3]{z - y} \cdot \sqrt[3]{z - y}}{\sqrt[3]{x - y} \cdot \sqrt[3]{x - y}}}}{\frac{\sqrt[3]{z - y}}{\sqrt[3]{x - y}}}
double f(double x, double y, double z, double t) {
        double r380601 = x;
        double r380602 = y;
        double r380603 = r380601 - r380602;
        double r380604 = z;
        double r380605 = r380604 - r380602;
        double r380606 = r380603 / r380605;
        double r380607 = t;
        double r380608 = r380606 * r380607;
        return r380608;
}
↓
double f(double x, double y, double z, double t) {
        double r380609 = t;
        double r380610 = z;
        double r380611 = y;
        double r380612 = r380610 - r380611;
        double r380613 = cbrt(r380612);
        double r380614 = r380613 * r380613;
        double r380615 = x;
        double r380616 = r380615 - r380611;
        double r380617 = cbrt(r380616);
        double r380618 = r380617 * r380617;
        double r380619 = r380614 / r380618;
        double r380620 = r380609 / r380619;
        double r380621 = r380613 / r380617;
        double r380622 = r380620 / r380621;
        return r380622;
}

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

Original2.1
Target2.1
Herbie1.1
\[\frac{t}{\frac{z - y}{x - y}}\]

Derivation

  1. Initial program 2.1

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

  3. Applied clear-num2.3

    \[\leadsto \color{blue}{\frac{1}{\frac{z - y}{x - y}}} \cdot t\]
  4. Using strategy rm

  5. Applied associate-*l/2.1

    \[\leadsto \color{blue}{\frac{1 \cdot t}{\frac{z - y}{x - y}}}\]

  6. Simplified2.1

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

  8. Applied add-cube-cbrt3.1

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

  9. Applied add-cube-cbrt2.8

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

  10. Applied times-frac2.8

    \[\leadsto \frac{t}{\color{blue}{\frac{\sqrt[3]{z - y} \cdot \sqrt[3]{z - y}}{\sqrt[3]{x - y} \cdot \sqrt[3]{x - y}} \cdot \frac{\sqrt[3]{z - y}}{\sqrt[3]{x - y}}}}\]

  11. Applied associate-/r*1.1

    \[\leadsto \color{blue}{\frac{\frac{t}{\frac{\sqrt[3]{z - y} \cdot \sqrt[3]{z - y}}{\sqrt[3]{x - y} \cdot \sqrt[3]{x - y}}}}{\frac{\sqrt[3]{z - y}}{\sqrt[3]{x - y}}}}\]

  12. Final simplification1.1

    \[\leadsto \frac{\frac{t}{\frac{\sqrt[3]{z - y} \cdot \sqrt[3]{z - y}}{\sqrt[3]{x - y} \cdot \sqrt[3]{x - y}}}}{\frac{\sqrt[3]{z - y}}{\sqrt[3]{x - y}}}\]

Reproduce

herbie shell --seed 2020045 
(FPCore (x y z t)
  :name "Numeric.Signal.Multichannel:$cput from hsignal-0.2.7.1"
  :precision binary64

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

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