Average Error: 2.1 → 2.1
Time: 4.1s
Precision: 64
\[\frac{x - y}{z - y} \cdot t\]
↓
\[\frac{t}{\frac{z - y}{x - y}} \cdot \left(\sqrt[3]{1} \cdot \sqrt[3]{1}\right)\]
\frac{x - y}{z - y} \cdot t
↓
\frac{t}{\frac{z - y}{x - y}} \cdot \left(\sqrt[3]{1} \cdot \sqrt[3]{1}\right)
double f(double x, double y, double z, double t) {
        double r430867 = x;
        double r430868 = y;
        double r430869 = r430867 - r430868;
        double r430870 = z;
        double r430871 = r430870 - r430868;
        double r430872 = r430869 / r430871;
        double r430873 = t;
        double r430874 = r430872 * r430873;
        return r430874;
}
↓
double f(double x, double y, double z, double t) {
        double r430875 = t;
        double r430876 = z;
        double r430877 = y;
        double r430878 = r430876 - r430877;
        double r430879 = x;
        double r430880 = r430879 - r430877;
        double r430881 = r430878 / r430880;
        double r430882 = r430875 / r430881;
        double r430883 = 1.0;
        double r430884 = cbrt(r430883);
        double r430885 = r430884 * r430884;
        double r430886 = r430882 * r430885;
        return r430886;
}

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
Herbie2.1
\[\frac{t}{\frac{z - y}{x - y}}\]

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 *-un-lft-identity2.3

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

  6. Applied *-un-lft-identity2.3

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

  7. Applied times-frac2.3

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

  8. Applied add-cube-cbrt2.3

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

  9. Applied times-frac2.3

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

  10. Applied associate-*l*2.3

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

  11. Simplified2.1

    \[\leadsto \frac{\sqrt[3]{1} \cdot \sqrt[3]{1}}{\frac{1}{1}} \cdot \color{blue}{\frac{t}{\frac{z - y}{x - y}}}\]

  12. Final simplification2.1

    \[\leadsto \frac{t}{\frac{z - y}{x - y}} \cdot \left(\sqrt[3]{1} \cdot \sqrt[3]{1}\right)\]

Reproduce

herbie shell --seed 2020100 
(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))