Average Error: 1.9 → 1.3
Time: 23.4s
Precision: 64
\[x + \left(y - x\right) \cdot \frac{z}{t}\]
↓
\[\begin{array}{l} \mathbf{if}\;z \le 4.680081952247758434360845558331483175442 \cdot 10^{-308}:\\ \;\;\;\;x + \left(y - x\right) \cdot \frac{z}{t}\\ \mathbf{else}:\\ \;\;\;\;x + \left(\left(y - x\right) \cdot \frac{\sqrt{z}}{\sqrt[3]{t} \cdot \sqrt[3]{t}}\right) \cdot \frac{\sqrt{z}}{\sqrt[3]{t}}\\ \end{array}\]
x + \left(y - x\right) \cdot \frac{z}{t}
↓
\begin{array}{l}
\mathbf{if}\;z \le 4.680081952247758434360845558331483175442 \cdot 10^{-308}:\\
\;\;\;\;x + \left(y - x\right) \cdot \frac{z}{t}\\

\mathbf{else}:\\
\;\;\;\;x + \left(\left(y - x\right) \cdot \frac{\sqrt{z}}{\sqrt[3]{t} \cdot \sqrt[3]{t}}\right) \cdot \frac{\sqrt{z}}{\sqrt[3]{t}}\\

\end{array}
double f(double x, double y, double z, double t) {
        double r350763 = x;
        double r350764 = y;
        double r350765 = r350764 - r350763;
        double r350766 = z;
        double r350767 = t;
        double r350768 = r350766 / r350767;
        double r350769 = r350765 * r350768;
        double r350770 = r350763 + r350769;
        return r350770;
}
↓
double f(double x, double y, double z, double t) {
        double r350771 = z;
        double r350772 = 4.680081952247758e-308;
        bool r350773 = r350771 <= r350772;
        double r350774 = x;
        double r350775 = y;
        double r350776 = r350775 - r350774;
        double r350777 = t;
        double r350778 = r350771 / r350777;
        double r350779 = r350776 * r350778;
        double r350780 = r350774 + r350779;
        double r350781 = sqrt(r350771);
        double r350782 = cbrt(r350777);
        double r350783 = r350782 * r350782;
        double r350784 = r350781 / r350783;
        double r350785 = r350776 * r350784;
        double r350786 = r350781 / r350782;
        double r350787 = r350785 * r350786;
        double r350788 = r350774 + r350787;
        double r350789 = r350773 ? r350780 : r350788;
        return r350789;
}

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

Original1.9
Target2.2
Herbie1.3
\[\begin{array}{l} \mathbf{if}\;\left(y - x\right) \cdot \frac{z}{t} \lt -1013646692435.88671875:\\ \;\;\;\;x + \frac{y - x}{\frac{t}{z}}\\ \mathbf{elif}\;\left(y - x\right) \cdot \frac{z}{t} \lt -0.0:\\ \;\;\;\;x + \frac{\left(y - x\right) \cdot z}{t}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y - x}{\frac{t}{z}}\\ \end{array}\]

Derivation

  1. Split input into 2 regimes

  2. if z < 4.680081952247758e-308

    1. Initial program 1.5

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

    if 4.680081952247758e-308 < z

    1. Initial program 2.3

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

    3. Applied add-cube-cbrt2.8

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

    4. Applied add-sqr-sqrt2.8

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

    5. Applied times-frac2.8

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

    6. Applied associate-*r*1.1

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

  4. Final simplification1.3

    \[\leadsto \begin{array}{l} \mathbf{if}\;z \le 4.680081952247758434360845558331483175442 \cdot 10^{-308}:\\ \;\;\;\;x + \left(y - x\right) \cdot \frac{z}{t}\\ \mathbf{else}:\\ \;\;\;\;x + \left(\left(y - x\right) \cdot \frac{\sqrt{z}}{\sqrt[3]{t} \cdot \sqrt[3]{t}}\right) \cdot \frac{\sqrt{z}}{\sqrt[3]{t}}\\ \end{array}\]

Reproduce

herbie shell --seed 2019303 
(FPCore (x y z t)
  :name "Graphics.Rendering.Plot.Render.Plot.Axis:tickPosition from plot-0.2.3.4"
  :precision binary64

  :herbie-target
  (if (< (* (- y x) (/ z t)) -1013646692435.887) (+ x (/ (- y x) (/ t z))) (if (< (* (- y x) (/ z t)) -0.0) (+ x (/ (* (- y x) z) t)) (+ x (/ (- y x) (/ t z)))))

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