Average Error: 2.3 → 1.9
Time: 4.6s
Precision: 64
\[x + \left(y - x\right) \cdot \frac{z}{t}\]
↓
\[\begin{array}{l} \mathbf{if}\;t \le -5.710194955151591629493346688798012753313 \cdot 10^{144}:\\ \;\;\;\;x + \frac{y - x}{\sqrt[3]{t} \cdot \sqrt[3]{t}} \cdot \frac{z}{\sqrt[3]{t}}\\ \mathbf{elif}\;t \le 206588178.7833076417446136474609375:\\ \;\;\;\;x + \frac{\left(y - x\right) \cdot z}{t}\\ \mathbf{else}:\\ \;\;\;\;x + \left(y - x\right) \cdot \frac{z}{t}\\ \end{array}\]
x + \left(y - x\right) \cdot \frac{z}{t}
↓
\begin{array}{l}
\mathbf{if}\;t \le -5.710194955151591629493346688798012753313 \cdot 10^{144}:\\
\;\;\;\;x + \frac{y - x}{\sqrt[3]{t} \cdot \sqrt[3]{t}} \cdot \frac{z}{\sqrt[3]{t}}\\

\mathbf{elif}\;t \le 206588178.7833076417446136474609375:\\
\;\;\;\;x + \frac{\left(y - x\right) \cdot z}{t}\\

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

\end{array}
double f(double x, double y, double z, double t) {
        double r534710 = x;
        double r534711 = y;
        double r534712 = r534711 - r534710;
        double r534713 = z;
        double r534714 = t;
        double r534715 = r534713 / r534714;
        double r534716 = r534712 * r534715;
        double r534717 = r534710 + r534716;
        return r534717;
}
↓
double f(double x, double y, double z, double t) {
        double r534718 = t;
        double r534719 = -5.7101949551515916e+144;
        bool r534720 = r534718 <= r534719;
        double r534721 = x;
        double r534722 = y;
        double r534723 = r534722 - r534721;
        double r534724 = cbrt(r534718);
        double r534725 = r534724 * r534724;
        double r534726 = r534723 / r534725;
        double r534727 = z;
        double r534728 = r534727 / r534724;
        double r534729 = r534726 * r534728;
        double r534730 = r534721 + r534729;
        double r534731 = 206588178.78330764;
        bool r534732 = r534718 <= r534731;
        double r534733 = r534723 * r534727;
        double r534734 = r534733 / r534718;
        double r534735 = r534721 + r534734;
        double r534736 = r534727 / r534718;
        double r534737 = r534723 * r534736;
        double r534738 = r534721 + r534737;
        double r534739 = r534732 ? r534735 : r534738;
        double r534740 = r534720 ? r534730 : r534739;
        return r534740;
}

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

Original2.3
Target2.3
Herbie1.9
\[\begin{array}{l} \mathbf{if}\;\left(y - x\right) \cdot \frac{z}{t} \lt -1013646692435.88671875:\\ \;\;\;\;x + \frac{y - x}{\frac{t}{z}}\\ \mathbf{elif}\;\left(y - x\right) \cdot \frac{z}{t} \lt -0.0:\\ \;\;\;\;x + \frac{\left(y - x\right) \cdot z}{t}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y - x}{\frac{t}{z}}\\ \end{array}\]

Derivation

  1. Split input into 3 regimes

  2. if t < -5.7101949551515916e+144

    1. Initial program 1.1

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

    3. Applied add-cube-cbrt1.3

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

    4. Applied *-un-lft-identity1.3

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

    5. Applied times-frac1.3

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

    6. Applied associate-*r*1.0

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

    7. Simplified1.0

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

    if -5.7101949551515916e+144 < t < 206588178.78330764

    1. Initial program 3.3

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

    3. Applied associate-*r/2.6

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

    if 206588178.78330764 < t

    1. Initial program 1.2

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

  4. Final simplification1.9

    \[\leadsto \begin{array}{l} \mathbf{if}\;t \le -5.710194955151591629493346688798012753313 \cdot 10^{144}:\\ \;\;\;\;x + \frac{y - x}{\sqrt[3]{t} \cdot \sqrt[3]{t}} \cdot \frac{z}{\sqrt[3]{t}}\\ \mathbf{elif}\;t \le 206588178.7833076417446136474609375:\\ \;\;\;\;x + \frac{\left(y - x\right) \cdot z}{t}\\ \mathbf{else}:\\ \;\;\;\;x + \left(y - x\right) \cdot \frac{z}{t}\\ \end{array}\]

Reproduce

herbie shell --seed 2019353 
(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))))