Average Error: 2.2 → 3.3
Time: 7.0s
Precision: 64
\[x + \left(y - x\right) \cdot \frac{z}{t}\]
↓
\[\begin{array}{l} \mathbf{if}\;x \le -2.83245230970383374 \cdot 10^{-70}:\\ \;\;\;\;x + \left(y - x\right) \cdot \frac{z}{t}\\ \mathbf{elif}\;x \le -2.07809484407539427 \cdot 10^{-240}:\\ \;\;\;\;x + \left(\frac{z \cdot y}{t} - \frac{x \cdot z}{t}\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y - x}{\sqrt[3]{t} \cdot \sqrt[3]{t}} \cdot \frac{z}{\sqrt[3]{t}}\\ \end{array}\]
x + \left(y - x\right) \cdot \frac{z}{t}
↓
\begin{array}{l}
\mathbf{if}\;x \le -2.83245230970383374 \cdot 10^{-70}:\\
\;\;\;\;x + \left(y - x\right) \cdot \frac{z}{t}\\

\mathbf{elif}\;x \le -2.07809484407539427 \cdot 10^{-240}:\\
\;\;\;\;x + \left(\frac{z \cdot y}{t} - \frac{x \cdot z}{t}\right)\\

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

\end{array}
double f(double x, double y, double z, double t) {
        double r571799 = x;
        double r571800 = y;
        double r571801 = r571800 - r571799;
        double r571802 = z;
        double r571803 = t;
        double r571804 = r571802 / r571803;
        double r571805 = r571801 * r571804;
        double r571806 = r571799 + r571805;
        return r571806;
}
↓
double f(double x, double y, double z, double t) {
        double r571807 = x;
        double r571808 = -2.8324523097038337e-70;
        bool r571809 = r571807 <= r571808;
        double r571810 = y;
        double r571811 = r571810 - r571807;
        double r571812 = z;
        double r571813 = t;
        double r571814 = r571812 / r571813;
        double r571815 = r571811 * r571814;
        double r571816 = r571807 + r571815;
        double r571817 = -2.0780948440753943e-240;
        bool r571818 = r571807 <= r571817;
        double r571819 = r571812 * r571810;
        double r571820 = r571819 / r571813;
        double r571821 = r571807 * r571812;
        double r571822 = r571821 / r571813;
        double r571823 = r571820 - r571822;
        double r571824 = r571807 + r571823;
        double r571825 = cbrt(r571813);
        double r571826 = r571825 * r571825;
        double r571827 = r571811 / r571826;
        double r571828 = r571812 / r571825;
        double r571829 = r571827 * r571828;
        double r571830 = r571807 + r571829;
        double r571831 = r571818 ? r571824 : r571830;
        double r571832 = r571809 ? r571816 : r571831;
        return r571832;
}

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

Original2.2
Target2.4
Herbie3.3
\[\begin{array}{l} \mathbf{if}\;\left(y - x\right) \cdot \frac{z}{t} \lt -1013646692435.887:\\ \;\;\;\;x + \frac{y - x}{\frac{t}{z}}\\ \mathbf{elif}\;\left(y - x\right) \cdot \frac{z}{t} \lt -0.0:\\ \;\;\;\;x + \frac{\left(y - x\right) \cdot z}{t}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y - x}{\frac{t}{z}}\\ \end{array}\]

Derivation

  1. Split input into 3 regimes

  2. if x < -2.8324523097038337e-70

    1. Initial program 0.4

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

    if -2.8324523097038337e-70 < x < -2.0780948440753943e-240

    1. Initial program 4.4

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

    3. Applied add-cube-cbrt5.0

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

    4. Applied *-un-lft-identity5.0

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

    5. Applied times-frac5.0

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

    6. Applied associate-*r*3.4

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

    7. Simplified3.4

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

    8. Taylor expanded around 0 3.5

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

    if -2.0780948440753943e-240 < x

    1. Initial program 2.4

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

    3. Applied add-cube-cbrt3.0

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

    4. Applied *-un-lft-identity3.0

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

    5. Applied times-frac3.0

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

    6. Applied associate-*r*4.7

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

    7. Simplified4.7

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

  4. Final simplification3.3

    \[\leadsto \begin{array}{l} \mathbf{if}\;x \le -2.83245230970383374 \cdot 10^{-70}:\\ \;\;\;\;x + \left(y - x\right) \cdot \frac{z}{t}\\ \mathbf{elif}\;x \le -2.07809484407539427 \cdot 10^{-240}:\\ \;\;\;\;x + \left(\frac{z \cdot y}{t} - \frac{x \cdot z}{t}\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y - x}{\sqrt[3]{t} \cdot \sqrt[3]{t}} \cdot \frac{z}{\sqrt[3]{t}}\\ \end{array}\]

Reproduce

herbie shell --seed 2020047 +o rules:numerics
(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))))