Average Error: 2.1 → 1.7
Time: 3.6s
Precision: 64
\[x + \left(y - x\right) \cdot \frac{z}{t}\]
↓
\[\begin{array}{l} \mathbf{if}\;\frac{z}{t} \le -8.51976868513873936 \cdot 10^{-131} \lor \neg \left(\frac{z}{t} \le -0.0\right):\\ \;\;\;\;x + \left(y - x\right) \cdot \frac{z}{t}\\ \mathbf{else}:\\ \;\;\;\;x + \left(z \cdot \left(y - x\right)\right) \cdot \frac{1}{t}\\ \end{array}\]
x + \left(y - x\right) \cdot \frac{z}{t}
↓
\begin{array}{l}
\mathbf{if}\;\frac{z}{t} \le -8.51976868513873936 \cdot 10^{-131} \lor \neg \left(\frac{z}{t} \le -0.0\right):\\
\;\;\;\;x + \left(y - x\right) \cdot \frac{z}{t}\\

\mathbf{else}:\\
\;\;\;\;x + \left(z \cdot \left(y - x\right)\right) \cdot \frac{1}{t}\\

\end{array}
double f(double x, double y, double z, double t) {
        double r633720 = x;
        double r633721 = y;
        double r633722 = r633721 - r633720;
        double r633723 = z;
        double r633724 = t;
        double r633725 = r633723 / r633724;
        double r633726 = r633722 * r633725;
        double r633727 = r633720 + r633726;
        return r633727;
}
↓
double f(double x, double y, double z, double t) {
        double r633728 = z;
        double r633729 = t;
        double r633730 = r633728 / r633729;
        double r633731 = -8.519768685138739e-131;
        bool r633732 = r633730 <= r633731;
        double r633733 = -0.0;
        bool r633734 = r633730 <= r633733;
        double r633735 = !r633734;
        bool r633736 = r633732 || r633735;
        double r633737 = x;
        double r633738 = y;
        double r633739 = r633738 - r633737;
        double r633740 = r633739 * r633730;
        double r633741 = r633737 + r633740;
        double r633742 = r633728 * r633739;
        double r633743 = 1.0;
        double r633744 = r633743 / r633729;
        double r633745 = r633742 * r633744;
        double r633746 = r633737 + r633745;
        double r633747 = r633736 ? r633741 : r633746;
        return r633747;
}

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
Herbie1.7
\[\begin{array}{l} \mathbf{if}\;\left(y - x\right) \cdot \frac{z}{t} \lt -1013646692435.887:\\ \;\;\;\;x + \frac{y - x}{\frac{t}{z}}\\ \mathbf{elif}\;\left(y - x\right) \cdot \frac{z}{t} \lt -0.0:\\ \;\;\;\;x + \frac{\left(y - x\right) \cdot z}{t}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y - x}{\frac{t}{z}}\\ \end{array}\]

Derivation

  1. Split input into 2 regimes

  2. if (/ z t) < -8.519768685138739e-131 or -0.0 < (/ z t)

    1. Initial program 2.0

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

    if -8.519768685138739e-131 < (/ z t) < -0.0

    1. Initial program 2.3

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

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

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

    4. Applied add-cube-cbrt2.4

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

    5. Applied times-frac2.4

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

    6. Applied associate-*r*1.2

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

    7. Simplified1.2

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

    9. Applied div-inv1.2

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

    10. Applied associate-*r*1.3

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

    11. Simplified1.1

      \[\leadsto x + \color{blue}{\left(z \cdot \left(y - x\right)\right)} \cdot \frac{1}{t}\]
  3. Recombined 2 regimes into one program.

  4. Final simplification1.7

    \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{z}{t} \le -8.51976868513873936 \cdot 10^{-131} \lor \neg \left(\frac{z}{t} \le -0.0\right):\\ \;\;\;\;x + \left(y - x\right) \cdot \frac{z}{t}\\ \mathbf{else}:\\ \;\;\;\;x + \left(z \cdot \left(y - x\right)\right) \cdot \frac{1}{t}\\ \end{array}\]

Reproduce

herbie shell --seed 2020035 
(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))))