Average Error: 2.1 → 0.7
Time: 18.8s
Precision: 64
\[x + \left(y - x\right) \cdot \frac{z}{t}\]
↓
\[\begin{array}{l} \mathbf{if}\;\frac{z}{t} = -\infty:\\ \;\;\;\;x + \left(\left(y - x\right) \cdot z\right) \cdot \frac{1}{t}\\ \mathbf{elif}\;\frac{z}{t} \le -8.834662634358639897139141015869877498875 \cdot 10^{-218} \lor \neg \left(\frac{z}{t} \le 0.0\right):\\ \;\;\;\;x + \left(y - x\right) \cdot \frac{z}{t}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{\left(y - x\right) \cdot z}{t}\\ \end{array}\]
x + \left(y - x\right) \cdot \frac{z}{t}
↓
\begin{array}{l}
\mathbf{if}\;\frac{z}{t} = -\infty:\\
\;\;\;\;x + \left(\left(y - x\right) \cdot z\right) \cdot \frac{1}{t}\\

\mathbf{elif}\;\frac{z}{t} \le -8.834662634358639897139141015869877498875 \cdot 10^{-218} \lor \neg \left(\frac{z}{t} \le 0.0\right):\\
\;\;\;\;x + \left(y - x\right) \cdot \frac{z}{t}\\

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

\end{array}
double f(double x, double y, double z, double t) {
        double r374773 = x;
        double r374774 = y;
        double r374775 = r374774 - r374773;
        double r374776 = z;
        double r374777 = t;
        double r374778 = r374776 / r374777;
        double r374779 = r374775 * r374778;
        double r374780 = r374773 + r374779;
        return r374780;
}
↓
double f(double x, double y, double z, double t) {
        double r374781 = z;
        double r374782 = t;
        double r374783 = r374781 / r374782;
        double r374784 = -inf.0;
        bool r374785 = r374783 <= r374784;
        double r374786 = x;
        double r374787 = y;
        double r374788 = r374787 - r374786;
        double r374789 = r374788 * r374781;
        double r374790 = 1.0;
        double r374791 = r374790 / r374782;
        double r374792 = r374789 * r374791;
        double r374793 = r374786 + r374792;
        double r374794 = -8.83466263435864e-218;
        bool r374795 = r374783 <= r374794;
        double r374796 = 0.0;
        bool r374797 = r374783 <= r374796;
        double r374798 = !r374797;
        bool r374799 = r374795 || r374798;
        double r374800 = r374788 * r374783;
        double r374801 = r374786 + r374800;
        double r374802 = r374789 / r374782;
        double r374803 = r374786 + r374802;
        double r374804 = r374799 ? r374801 : r374803;
        double r374805 = r374785 ? r374793 : r374804;
        return r374805;
}

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
Herbie0.7
\[\begin{array}{l} \mathbf{if}\;\left(y - x\right) \cdot \frac{z}{t} \lt -1013646692435.88671875:\\ \;\;\;\;x + \frac{y - x}{\frac{t}{z}}\\ \mathbf{elif}\;\left(y - x\right) \cdot \frac{z}{t} \lt -0.0:\\ \;\;\;\;x + \frac{\left(y - x\right) \cdot z}{t}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y - x}{\frac{t}{z}}\\ \end{array}\]

Derivation

  1. Split input into 3 regimes

  2. if (/ z t) < -inf.0

    1. Initial program 64.0

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

    3. Applied div-inv64.0

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

    4. Applied associate-*r*0.3

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

    if -inf.0 < (/ z t) < -8.83466263435864e-218 or 0.0 < (/ z t)

    1. Initial program 1.1

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

    if -8.83466263435864e-218 < (/ z t) < 0.0

    1. Initial program 1.9

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

    3. Applied associate-*r/0.3

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

  4. Final simplification0.7

    \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{z}{t} = -\infty:\\ \;\;\;\;x + \left(\left(y - x\right) \cdot z\right) \cdot \frac{1}{t}\\ \mathbf{elif}\;\frac{z}{t} \le -8.834662634358639897139141015869877498875 \cdot 10^{-218} \lor \neg \left(\frac{z}{t} \le 0.0\right):\\ \;\;\;\;x + \left(y - x\right) \cdot \frac{z}{t}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{\left(y - x\right) \cdot z}{t}\\ \end{array}\]

Reproduce

herbie shell --seed 2019325 
(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))))