Average Error: 2.0 → 3.2
Time: 3.3s
Precision: 64
\[\frac{x}{y} \cdot \left(z - t\right) + t\]
↓
\[\frac{x}{\sqrt[3]{y} \cdot \sqrt[3]{y}} \cdot \frac{z - t}{\sqrt[3]{y}} + t\]
\frac{x}{y} \cdot \left(z - t\right) + t
↓
\frac{x}{\sqrt[3]{y} \cdot \sqrt[3]{y}} \cdot \frac{z - t}{\sqrt[3]{y}} + t
double f(double x, double y, double z, double t) {
        double r437629 = x;
        double r437630 = y;
        double r437631 = r437629 / r437630;
        double r437632 = z;
        double r437633 = t;
        double r437634 = r437632 - r437633;
        double r437635 = r437631 * r437634;
        double r437636 = r437635 + r437633;
        return r437636;
}
↓
double f(double x, double y, double z, double t) {
        double r437637 = x;
        double r437638 = y;
        double r437639 = cbrt(r437638);
        double r437640 = r437639 * r437639;
        double r437641 = r437637 / r437640;
        double r437642 = z;
        double r437643 = t;
        double r437644 = r437642 - r437643;
        double r437645 = r437644 / r437639;
        double r437646 = r437641 * r437645;
        double r437647 = r437646 + r437643;
        return r437647;
}

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

Original2.0
Target2.3
Herbie3.2
\[\begin{array}{l} \mathbf{if}\;z \lt 2.7594565545626922 \cdot 10^{-282}:\\ \;\;\;\;\frac{x}{y} \cdot \left(z - t\right) + t\\ \mathbf{elif}\;z \lt 2.326994450874436 \cdot 10^{-110}:\\ \;\;\;\;x \cdot \frac{z - t}{y} + t\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y} \cdot \left(z - t\right) + t\\ \end{array}\]

Derivation

  1. Initial program 2.0

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

  3. Applied div-inv2.1

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

  4. Applied associate-*l*6.6

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

  5. Simplified6.6

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

  7. Applied add-cube-cbrt7.1

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

  8. Applied *-un-lft-identity7.1

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

  9. Applied times-frac7.1

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

  10. Applied associate-*r*3.2

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

  11. Simplified3.2

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

  12. Final simplification3.2

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

Reproduce

herbie shell --seed 2020047 
(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))