Average Error: 2.0 → 2.4
Time: 6.4s
Precision: 64
\[x + \left(y - x\right) \cdot \frac{z}{t}\]
↓
\[\begin{array}{l} \mathbf{if}\;x \le -1.370918042146381127285332195867531032316 \cdot 10^{-76} \lor \neg \left(x \le 1.78843006131791689904510956091429861366 \cdot 10^{49}\right):\\ \;\;\;\;x + \left(y - x\right) \cdot \frac{z}{t}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{\left(y - x\right) \cdot z}{t}\\ \end{array}\]
x + \left(y - x\right) \cdot \frac{z}{t}
↓
\begin{array}{l}
\mathbf{if}\;x \le -1.370918042146381127285332195867531032316 \cdot 10^{-76} \lor \neg \left(x \le 1.78843006131791689904510956091429861366 \cdot 10^{49}\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 r741639 = x;
        double r741640 = y;
        double r741641 = r741640 - r741639;
        double r741642 = z;
        double r741643 = t;
        double r741644 = r741642 / r741643;
        double r741645 = r741641 * r741644;
        double r741646 = r741639 + r741645;
        return r741646;
}
↓
double f(double x, double y, double z, double t) {
        double r741647 = x;
        double r741648 = -1.3709180421463811e-76;
        bool r741649 = r741647 <= r741648;
        double r741650 = 1.788430061317917e+49;
        bool r741651 = r741647 <= r741650;
        double r741652 = !r741651;
        bool r741653 = r741649 || r741652;
        double r741654 = y;
        double r741655 = r741654 - r741647;
        double r741656 = z;
        double r741657 = t;
        double r741658 = r741656 / r741657;
        double r741659 = r741655 * r741658;
        double r741660 = r741647 + r741659;
        double r741661 = r741655 * r741656;
        double r741662 = r741661 / r741657;
        double r741663 = r741647 + r741662;
        double r741664 = r741653 ? r741660 : r741663;
        return r741664;
}

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

Original2.0
Target2.2
Herbie2.4
\[\begin{array}{l} \mathbf{if}\;\left(y - x\right) \cdot \frac{z}{t} \lt -1013646692435.88671875:\\ \;\;\;\;x + \frac{y - x}{\frac{t}{z}}\\ \mathbf{elif}\;\left(y - x\right) \cdot \frac{z}{t} \lt -0.0:\\ \;\;\;\;x + \frac{\left(y - x\right) \cdot z}{t}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y - x}{\frac{t}{z}}\\ \end{array}\]

Derivation

  1. Split input into 2 regimes

  2. if x < -1.3709180421463811e-76 or 1.788430061317917e+49 < x

    1. Initial program 0.2

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

    if -1.3709180421463811e-76 < x < 1.788430061317917e+49

    1. Initial program 3.6

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

    3. Applied add-cube-cbrt4.3

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

    4. Applied *-un-lft-identity4.3

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

    5. Applied times-frac4.3

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

    6. Applied associate-*r*3.8

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

    7. Simplified3.8

      \[\leadsto x + \color{blue}{\frac{y - x}{\sqrt[3]{t} \cdot \sqrt[3]{t}}} \cdot \frac{z}{\sqrt[3]{t}}\]
    8. Using strategy rm

    9. Applied frac-times5.1

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

    10. Simplified4.4

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

  4. Final simplification2.4

    \[\leadsto \begin{array}{l} \mathbf{if}\;x \le -1.370918042146381127285332195867531032316 \cdot 10^{-76} \lor \neg \left(x \le 1.78843006131791689904510956091429861366 \cdot 10^{49}\right):\\ \;\;\;\;x + \left(y - x\right) \cdot \frac{z}{t}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{\left(y - x\right) \cdot z}{t}\\ \end{array}\]

Reproduce

herbie shell --seed 2019362 
(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))))