Average Error: 1.9 → 1.9
Time: 4.9s
Precision: 64
\[x + \left(y - x\right) \cdot \frac{z}{t}\]
↓
\[\begin{array}{l} \mathbf{if}\;x \le -6.34892836660075745 \cdot 10^{-104} \lor \neg \left(x \le 3.87544783988843796 \cdot 10^{-103}\right):\\ \;\;\;\;x + \left(y - x\right) \cdot \frac{z}{t}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y - x}{\sqrt[3]{t} \cdot \sqrt[3]{t}} \cdot \frac{z}{\sqrt[3]{t}}\\ \end{array}\]
x + \left(y - x\right) \cdot \frac{z}{t}
↓
\begin{array}{l}
\mathbf{if}\;x \le -6.34892836660075745 \cdot 10^{-104} \lor \neg \left(x \le 3.87544783988843796 \cdot 10^{-103}\right):\\
\;\;\;\;x + \left(y - x\right) \cdot \frac{z}{t}\\

\mathbf{else}:\\
\;\;\;\;x + \frac{y - x}{\sqrt[3]{t} \cdot \sqrt[3]{t}} \cdot \frac{z}{\sqrt[3]{t}}\\

\end{array}
double f(double x, double y, double z, double t) {
        double r535994 = x;
        double r535995 = y;
        double r535996 = r535995 - r535994;
        double r535997 = z;
        double r535998 = t;
        double r535999 = r535997 / r535998;
        double r536000 = r535996 * r535999;
        double r536001 = r535994 + r536000;
        return r536001;
}
↓
double f(double x, double y, double z, double t) {
        double r536002 = x;
        double r536003 = -6.348928366600757e-104;
        bool r536004 = r536002 <= r536003;
        double r536005 = 3.875447839888438e-103;
        bool r536006 = r536002 <= r536005;
        double r536007 = !r536006;
        bool r536008 = r536004 || r536007;
        double r536009 = y;
        double r536010 = r536009 - r536002;
        double r536011 = z;
        double r536012 = t;
        double r536013 = r536011 / r536012;
        double r536014 = r536010 * r536013;
        double r536015 = r536002 + r536014;
        double r536016 = cbrt(r536012);
        double r536017 = r536016 * r536016;
        double r536018 = r536010 / r536017;
        double r536019 = r536011 / r536016;
        double r536020 = r536018 * r536019;
        double r536021 = r536002 + r536020;
        double r536022 = r536008 ? r536015 : r536021;
        return r536022;
}

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
Herbie1.9
\[\begin{array}{l} \mathbf{if}\;\left(y - x\right) \cdot \frac{z}{t} \lt -1013646692435.887:\\ \;\;\;\;x + \frac{y - x}{\frac{t}{z}}\\ \mathbf{elif}\;\left(y - x\right) \cdot \frac{z}{t} \lt -0.0:\\ \;\;\;\;x + \frac{\left(y - x\right) \cdot z}{t}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y - x}{\frac{t}{z}}\\ \end{array}\]

Derivation

  1. Split input into 2 regimes

  2. if x < -6.348928366600757e-104 or 3.875447839888438e-103 < x

    1. Initial program 0.5

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

    if -6.348928366600757e-104 < x < 3.875447839888438e-103

    1. Initial program 4.2

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

    3. Applied add-cube-cbrt4.9

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

    4. Applied *-un-lft-identity4.9

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

    5. Applied times-frac4.9

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

    6. Applied associate-*r*4.1

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

    7. Simplified4.1

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

  4. Final simplification1.9

    \[\leadsto \begin{array}{l} \mathbf{if}\;x \le -6.34892836660075745 \cdot 10^{-104} \lor \neg \left(x \le 3.87544783988843796 \cdot 10^{-103}\right):\\ \;\;\;\;x + \left(y - x\right) \cdot \frac{z}{t}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y - x}{\sqrt[3]{t} \cdot \sqrt[3]{t}} \cdot \frac{z}{\sqrt[3]{t}}\\ \end{array}\]

Reproduce

herbie shell --seed 2020081 
(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))))