Average Error: 1.9 → 0.8
Time: 4.1s
Precision: 64
\[x + \left(y - x\right) \cdot \frac{z}{t}\]
↓
\[\begin{array}{l} \mathbf{if}\;\frac{z}{t} \le -1.1750164074185684 \cdot 10^{201} \lor \neg \left(\frac{z}{t} \le -3.5698471343657757 \cdot 10^{-249} \lor \neg \left(\frac{z}{t} \le 0.0\right)\right):\\ \;\;\;\;x + \left(\left(y - x\right) \cdot z\right) \cdot \frac{1}{t}\\ \mathbf{else}:\\ \;\;\;\;x + \left(y - x\right) \cdot \frac{z}{t}\\ \end{array}\]
x + \left(y - x\right) \cdot \frac{z}{t}
↓
\begin{array}{l}
\mathbf{if}\;\frac{z}{t} \le -1.1750164074185684 \cdot 10^{201} \lor \neg \left(\frac{z}{t} \le -3.5698471343657757 \cdot 10^{-249} \lor \neg \left(\frac{z}{t} \le 0.0\right)\right):\\
\;\;\;\;x + \left(\left(y - x\right) \cdot z\right) \cdot \frac{1}{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 r492638 = x;
        double r492639 = y;
        double r492640 = r492639 - r492638;
        double r492641 = z;
        double r492642 = t;
        double r492643 = r492641 / r492642;
        double r492644 = r492640 * r492643;
        double r492645 = r492638 + r492644;
        return r492645;
}
↓
double f(double x, double y, double z, double t) {
        double r492646 = z;
        double r492647 = t;
        double r492648 = r492646 / r492647;
        double r492649 = -1.1750164074185684e+201;
        bool r492650 = r492648 <= r492649;
        double r492651 = -3.5698471343657757e-249;
        bool r492652 = r492648 <= r492651;
        double r492653 = 0.0;
        bool r492654 = r492648 <= r492653;
        double r492655 = !r492654;
        bool r492656 = r492652 || r492655;
        double r492657 = !r492656;
        bool r492658 = r492650 || r492657;
        double r492659 = x;
        double r492660 = y;
        double r492661 = r492660 - r492659;
        double r492662 = r492661 * r492646;
        double r492663 = 1.0;
        double r492664 = r492663 / r492647;
        double r492665 = r492662 * r492664;
        double r492666 = r492659 + r492665;
        double r492667 = r492661 * r492648;
        double r492668 = r492659 + r492667;
        double r492669 = r492658 ? r492666 : r492668;
        return r492669;
}

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

Original1.9
Target2.0
Herbie0.8
\[\begin{array}{l} \mathbf{if}\;\left(y - x\right) \cdot \frac{z}{t} \lt -1013646692435.887:\\ \;\;\;\;x + \frac{y - x}{\frac{t}{z}}\\ \mathbf{elif}\;\left(y - x\right) \cdot \frac{z}{t} \lt -0.0:\\ \;\;\;\;x + \frac{\left(y - x\right) \cdot z}{t}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y - x}{\frac{t}{z}}\\ \end{array}\]

Derivation

  1. Split input into 2 regimes

  2. if (/ z t) < -1.1750164074185684e+201 or -3.5698471343657757e-249 < (/ z t) < 0.0

    1. Initial program 6.0

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

    3. Applied div-inv6.0

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

    4. Applied associate-*r*0.7

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

    if -1.1750164074185684e+201 < (/ z t) < -3.5698471343657757e-249 or 0.0 < (/ z t)

    1. Initial program 1.1

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

  4. Final simplification0.8

    \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{z}{t} \le -1.1750164074185684 \cdot 10^{201} \lor \neg \left(\frac{z}{t} \le -3.5698471343657757 \cdot 10^{-249} \lor \neg \left(\frac{z}{t} \le 0.0\right)\right):\\ \;\;\;\;x + \left(\left(y - x\right) \cdot z\right) \cdot \frac{1}{t}\\ \mathbf{else}:\\ \;\;\;\;x + \left(y - x\right) \cdot \frac{z}{t}\\ \end{array}\]

Reproduce

herbie shell --seed 2020021 
(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))))