Average Error: 2.1 → 1.5
Time: 17.7s
Precision: 64
\[\frac{x}{y} \cdot \left(z - t\right) + t\]
↓
\[\begin{array}{l} \mathbf{if}\;\frac{x}{y} \le -3.43872422120508929 \cdot 10^{-224} \lor \neg \left(\frac{x}{y} \le 7.5728756396099922 \cdot 10^{-286}\right):\\ \;\;\;\;\left(z \cdot \frac{x}{y} + \left(-t\right) \cdot \frac{x}{y}\right) + t\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{z - t}{y} + t\\ \end{array}\]
\frac{x}{y} \cdot \left(z - t\right) + t
↓
\begin{array}{l}
\mathbf{if}\;\frac{x}{y} \le -3.43872422120508929 \cdot 10^{-224} \lor \neg \left(\frac{x}{y} \le 7.5728756396099922 \cdot 10^{-286}\right):\\
\;\;\;\;\left(z \cdot \frac{x}{y} + \left(-t\right) \cdot \frac{x}{y}\right) + t\\

\mathbf{else}:\\
\;\;\;\;x \cdot \frac{z - t}{y} + t\\

\end{array}
double f(double x, double y, double z, double t) {
        double r310763 = x;
        double r310764 = y;
        double r310765 = r310763 / r310764;
        double r310766 = z;
        double r310767 = t;
        double r310768 = r310766 - r310767;
        double r310769 = r310765 * r310768;
        double r310770 = r310769 + r310767;
        return r310770;
}
↓
double f(double x, double y, double z, double t) {
        double r310771 = x;
        double r310772 = y;
        double r310773 = r310771 / r310772;
        double r310774 = -3.4387242212050893e-224;
        bool r310775 = r310773 <= r310774;
        double r310776 = 7.572875639609992e-286;
        bool r310777 = r310773 <= r310776;
        double r310778 = !r310777;
        bool r310779 = r310775 || r310778;
        double r310780 = z;
        double r310781 = r310780 * r310773;
        double r310782 = t;
        double r310783 = -r310782;
        double r310784 = r310783 * r310773;
        double r310785 = r310781 + r310784;
        double r310786 = r310785 + r310782;
        double r310787 = r310780 - r310782;
        double r310788 = r310787 / r310772;
        double r310789 = r310771 * r310788;
        double r310790 = r310789 + r310782;
        double r310791 = r310779 ? r310786 : r310790;
        return r310791;
}

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
Target2.4
Herbie1.5
\[\begin{array}{l} \mathbf{if}\;z \lt 2.7594565545626922 \cdot 10^{-282}:\\ \;\;\;\;\frac{x}{y} \cdot \left(z - t\right) + t\\ \mathbf{elif}\;z \lt 2.326994450874436 \cdot 10^{-110}:\\ \;\;\;\;x \cdot \frac{z - t}{y} + t\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y} \cdot \left(z - t\right) + t\\ \end{array}\]

Derivation

  1. Split input into 2 regimes

  2. if (/ x y) < -3.4387242212050893e-224 or 7.572875639609992e-286 < (/ x y)

    1. Initial program 1.9

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

    3. Applied sub-neg1.9

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

    4. Applied distribute-lft-in1.9

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

    5. Simplified1.9

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

    6. Simplified1.9

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

    if -3.4387242212050893e-224 < (/ x y) < 7.572875639609992e-286

    1. Initial program 2.6

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

    3. Applied div-inv2.6

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

    4. Applied associate-*l*0.2

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

    5. Simplified0.2

      \[\leadsto x \cdot \color{blue}{\frac{z - t}{y}} + t\]
  3. Recombined 2 regimes into one program.

  4. Final simplification1.5

    \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x}{y} \le -3.43872422120508929 \cdot 10^{-224} \lor \neg \left(\frac{x}{y} \le 7.5728756396099922 \cdot 10^{-286}\right):\\ \;\;\;\;\left(z \cdot \frac{x}{y} + \left(-t\right) \cdot \frac{x}{y}\right) + t\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{z - t}{y} + t\\ \end{array}\]

Reproduce

herbie shell --seed 2019198 
(FPCore (x y z t)
  :name "Numeric.Signal.Multichannel:$cget from hsignal-0.2.7.1"

  :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))