Average Error: 1.8 → 2.3
Time: 50.9s
Precision: 64
\[x + \left(y - x\right) \cdot \frac{z}{t}\]
↓
\[\begin{array}{l} \mathbf{if}\;x \le -20778392.899190597236156463623046875:\\ \;\;\;\;x + \frac{z}{t} \cdot \left(y - x\right)\\ \mathbf{elif}\;x \le 1.709797410018517080639012525016209371533 \cdot 10^{-278}:\\ \;\;\;\;\left(\frac{z}{\frac{t}{y}} - \frac{z \cdot x}{t}\right) + x\\ \mathbf{else}:\\ \;\;\;\;x + \frac{z}{t} \cdot \left(y - x\right)\\ \end{array}\]
x + \left(y - x\right) \cdot \frac{z}{t}
↓
\begin{array}{l}
\mathbf{if}\;x \le -20778392.899190597236156463623046875:\\
\;\;\;\;x + \frac{z}{t} \cdot \left(y - x\right)\\

\mathbf{elif}\;x \le 1.709797410018517080639012525016209371533 \cdot 10^{-278}:\\
\;\;\;\;\left(\frac{z}{\frac{t}{y}} - \frac{z \cdot x}{t}\right) + x\\

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

\end{array}
double f(double x, double y, double z, double t) {
        double r28968003 = x;
        double r28968004 = y;
        double r28968005 = r28968004 - r28968003;
        double r28968006 = z;
        double r28968007 = t;
        double r28968008 = r28968006 / r28968007;
        double r28968009 = r28968005 * r28968008;
        double r28968010 = r28968003 + r28968009;
        return r28968010;
}
↓
double f(double x, double y, double z, double t) {
        double r28968011 = x;
        double r28968012 = -20778392.899190597;
        bool r28968013 = r28968011 <= r28968012;
        double r28968014 = z;
        double r28968015 = t;
        double r28968016 = r28968014 / r28968015;
        double r28968017 = y;
        double r28968018 = r28968017 - r28968011;
        double r28968019 = r28968016 * r28968018;
        double r28968020 = r28968011 + r28968019;
        double r28968021 = 1.709797410018517e-278;
        bool r28968022 = r28968011 <= r28968021;
        double r28968023 = r28968015 / r28968017;
        double r28968024 = r28968014 / r28968023;
        double r28968025 = r28968014 * r28968011;
        double r28968026 = r28968025 / r28968015;
        double r28968027 = r28968024 - r28968026;
        double r28968028 = r28968027 + r28968011;
        double r28968029 = r28968022 ? r28968028 : r28968020;
        double r28968030 = r28968013 ? r28968020 : r28968029;
        return r28968030;
}

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

Original1.8
Target2.1
Herbie2.3
\[\begin{array}{l} \mathbf{if}\;\left(y - x\right) \cdot \frac{z}{t} \lt -1013646692435.88671875:\\ \;\;\;\;x + \frac{y - x}{\frac{t}{z}}\\ \mathbf{elif}\;\left(y - x\right) \cdot \frac{z}{t} \lt -0.0:\\ \;\;\;\;x + \frac{\left(y - x\right) \cdot z}{t}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y - x}{\frac{t}{z}}\\ \end{array}\]

Derivation

  1. Split input into 2 regimes

  2. if x < -20778392.899190597 or 1.709797410018517e-278 < x

    1. Initial program 1.3

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

    if -20778392.899190597 < x < 1.709797410018517e-278

    1. Initial program 3.1

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

    2. Taylor expanded around 0 4.8

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

    4. Applied associate-/l*4.7

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

  4. Final simplification2.3

    \[\leadsto \begin{array}{l} \mathbf{if}\;x \le -20778392.899190597236156463623046875:\\ \;\;\;\;x + \frac{z}{t} \cdot \left(y - x\right)\\ \mathbf{elif}\;x \le 1.709797410018517080639012525016209371533 \cdot 10^{-278}:\\ \;\;\;\;\left(\frac{z}{\frac{t}{y}} - \frac{z \cdot x}{t}\right) + x\\ \mathbf{else}:\\ \;\;\;\;x + \frac{z}{t} \cdot \left(y - x\right)\\ \end{array}\]

Reproduce

herbie shell --seed 2019168 
(FPCore (x y z t)
  :name "Graphics.Rendering.Plot.Render.Plot.Axis:tickPosition from plot-0.2.3.4"

  :herbie-target
  (if (< (* (- y x) (/ z t)) -1013646692435.8867) (+ 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))))