Average Error: 2.1 → 2.2
Time: 21.3s
Precision: 64
\[x + \left(y - x\right) \cdot \frac{z}{t}\]
↓
\[\begin{array}{l} \mathbf{if}\;x \le -1877249882.573062:\\ \;\;\;\;x + \frac{z}{t} \cdot \left(y - x\right)\\ \mathbf{elif}\;x \le 2.6855686957563794 \cdot 10^{-288}:\\ \;\;\;\;\frac{\left(y - x\right) \cdot z}{t} + x\\ \mathbf{else}:\\ \;\;\;\;x + \frac{z}{t} \cdot \left(y - x\right)\\ \end{array}\]
x + \left(y - x\right) \cdot \frac{z}{t}
↓
\begin{array}{l}
\mathbf{if}\;x \le -1877249882.573062:\\
\;\;\;\;x + \frac{z}{t} \cdot \left(y - x\right)\\

\mathbf{elif}\;x \le 2.6855686957563794 \cdot 10^{-288}:\\
\;\;\;\;\frac{\left(y - x\right) \cdot z}{t} + 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 r26811787 = x;
        double r26811788 = y;
        double r26811789 = r26811788 - r26811787;
        double r26811790 = z;
        double r26811791 = t;
        double r26811792 = r26811790 / r26811791;
        double r26811793 = r26811789 * r26811792;
        double r26811794 = r26811787 + r26811793;
        return r26811794;
}
↓
double f(double x, double y, double z, double t) {
        double r26811795 = x;
        double r26811796 = -1877249882.573062;
        bool r26811797 = r26811795 <= r26811796;
        double r26811798 = z;
        double r26811799 = t;
        double r26811800 = r26811798 / r26811799;
        double r26811801 = y;
        double r26811802 = r26811801 - r26811795;
        double r26811803 = r26811800 * r26811802;
        double r26811804 = r26811795 + r26811803;
        double r26811805 = 2.6855686957563794e-288;
        bool r26811806 = r26811795 <= r26811805;
        double r26811807 = r26811802 * r26811798;
        double r26811808 = r26811807 / r26811799;
        double r26811809 = r26811808 + r26811795;
        double r26811810 = r26811806 ? r26811809 : r26811804;
        double r26811811 = r26811797 ? r26811804 : r26811810;
        return r26811811;
}

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
Herbie2.2
\[\begin{array}{l} \mathbf{if}\;\left(y - x\right) \cdot \frac{z}{t} \lt -1013646692435.8867:\\ \;\;\;\;x + \frac{y - x}{\frac{t}{z}}\\ \mathbf{elif}\;\left(y - x\right) \cdot \frac{z}{t} \lt -0.0:\\ \;\;\;\;x + \frac{\left(y - x\right) \cdot z}{t}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y - x}{\frac{t}{z}}\\ \end{array}\]

Derivation

  1. Split input into 2 regimes

  2. if x < -1877249882.573062 or 2.6855686957563794e-288 < x

    1. Initial program 1.2

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

    if -1877249882.573062 < x < 2.6855686957563794e-288

    1. Initial program 4.1

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

    3. Applied associate-*r/4.3

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

  4. Final simplification2.2

    \[\leadsto \begin{array}{l} \mathbf{if}\;x \le -1877249882.573062:\\ \;\;\;\;x + \frac{z}{t} \cdot \left(y - x\right)\\ \mathbf{elif}\;x \le 2.6855686957563794 \cdot 10^{-288}:\\ \;\;\;\;\frac{\left(y - x\right) \cdot z}{t} + x\\ \mathbf{else}:\\ \;\;\;\;x + \frac{z}{t} \cdot \left(y - x\right)\\ \end{array}\]

Reproduce

herbie shell --seed 2019158 
(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))))