Average Error: 2.1 → 2.4
Time: 4.0s
Precision: 64
\[\frac{x}{y} \cdot \left(z - t\right) + t\]
↓
\[\left(\sqrt[3]{z \cdot \frac{x}{y}} \cdot \sqrt[3]{z \cdot \frac{x}{y}}\right) \cdot \sqrt[3]{z \cdot \frac{x}{y}} + \left(t - t \cdot \frac{x}{y}\right)\]
\frac{x}{y} \cdot \left(z - t\right) + t
↓
\left(\sqrt[3]{z \cdot \frac{x}{y}} \cdot \sqrt[3]{z \cdot \frac{x}{y}}\right) \cdot \sqrt[3]{z \cdot \frac{x}{y}} + \left(t - t \cdot \frac{x}{y}\right)
double f(double x, double y, double z, double t) {
        double r561913 = x;
        double r561914 = y;
        double r561915 = r561913 / r561914;
        double r561916 = z;
        double r561917 = t;
        double r561918 = r561916 - r561917;
        double r561919 = r561915 * r561918;
        double r561920 = r561919 + r561917;
        return r561920;
}
↓
double f(double x, double y, double z, double t) {
        double r561921 = z;
        double r561922 = x;
        double r561923 = y;
        double r561924 = r561922 / r561923;
        double r561925 = r561921 * r561924;
        double r561926 = cbrt(r561925);
        double r561927 = r561926 * r561926;
        double r561928 = r561927 * r561926;
        double r561929 = t;
        double r561930 = r561929 * r561924;
        double r561931 = r561929 - r561930;
        double r561932 = r561928 + r561931;
        return r561932;
}

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
Target2.3
Herbie2.4
\[\begin{array}{l} \mathbf{if}\;z \lt 2.759456554562692182563154937894909044548 \cdot 10^{-282}:\\ \;\;\;\;\frac{x}{y} \cdot \left(z - t\right) + t\\ \mathbf{elif}\;z \lt 2.32699445087443595687739933019129648094 \cdot 10^{-110}:\\ \;\;\;\;x \cdot \frac{z - t}{y} + t\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y} \cdot \left(z - t\right) + t\\ \end{array}\]

Derivation

  1. Initial program 2.1

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

  3. Applied sub-neg2.1

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

  4. Applied distribute-rgt-in2.1

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

  5. Applied associate-+l+2.1

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

  6. Simplified2.1

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

  8. Applied add-cube-cbrt2.4

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

  9. Final simplification2.4

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

Reproduce

herbie shell --seed 2020001 
(FPCore (x y z t)
  :name "Numeric.Signal.Multichannel:$cget from hsignal-0.2.7.1"
  :precision binary64

  :herbie-target
  (if (< z 2.759456554562692e-282) (+ (* (/ x y) (- z t)) t) (if (< z 2.326994450874436e-110) (+ (* x (/ (- z t) y)) t) (+ (* (/ x y) (- z t)) t)))

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