Average Error: 1.3 → 1.2
Time: 18.3s
Precision: 64
\[x + y \cdot \frac{z - t}{z - a}\]
↓
\[\begin{array}{l} \mathbf{if}\;z \le -3.019015469284913797565702456939618742875 \cdot 10^{-136} \lor \neg \left(z \le 3.320401513850043595539041976707631052552 \cdot 10^{-256}\right):\\ \;\;\;\;y \cdot \frac{z - t}{z - a} + x\\ \mathbf{else}:\\ \;\;\;\;\left(\sqrt[3]{y} \cdot \sqrt[3]{y}\right) \cdot \frac{\sqrt[3]{y} \cdot \left(z - t\right)}{z - a} + x\\ \end{array}\]
x + y \cdot \frac{z - t}{z - a}
↓
\begin{array}{l}
\mathbf{if}\;z \le -3.019015469284913797565702456939618742875 \cdot 10^{-136} \lor \neg \left(z \le 3.320401513850043595539041976707631052552 \cdot 10^{-256}\right):\\
\;\;\;\;y \cdot \frac{z - t}{z - a} + x\\

\mathbf{else}:\\
\;\;\;\;\left(\sqrt[3]{y} \cdot \sqrt[3]{y}\right) \cdot \frac{\sqrt[3]{y} \cdot \left(z - t\right)}{z - a} + x\\

\end{array}
double f(double x, double y, double z, double t, double a) {
        double r523155 = x;
        double r523156 = y;
        double r523157 = z;
        double r523158 = t;
        double r523159 = r523157 - r523158;
        double r523160 = a;
        double r523161 = r523157 - r523160;
        double r523162 = r523159 / r523161;
        double r523163 = r523156 * r523162;
        double r523164 = r523155 + r523163;
        return r523164;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r523165 = z;
        double r523166 = -3.0190154692849138e-136;
        bool r523167 = r523165 <= r523166;
        double r523168 = 3.3204015138500436e-256;
        bool r523169 = r523165 <= r523168;
        double r523170 = !r523169;
        bool r523171 = r523167 || r523170;
        double r523172 = y;
        double r523173 = t;
        double r523174 = r523165 - r523173;
        double r523175 = a;
        double r523176 = r523165 - r523175;
        double r523177 = r523174 / r523176;
        double r523178 = r523172 * r523177;
        double r523179 = x;
        double r523180 = r523178 + r523179;
        double r523181 = cbrt(r523172);
        double r523182 = r523181 * r523181;
        double r523183 = r523181 * r523174;
        double r523184 = r523183 / r523176;
        double r523185 = r523182 * r523184;
        double r523186 = r523185 + r523179;
        double r523187 = r523171 ? r523180 : r523186;
        return r523187;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Bits error versus t

Bits error versus a

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original1.3
Target1.2
Herbie1.2
\[x + \frac{y}{\frac{z - a}{z - t}}\]

Derivation

  1. Split input into 2 regimes

  2. if z < -3.0190154692849138e-136 or 3.3204015138500436e-256 < z

    1. Initial program 0.8

      \[x + y \cdot \frac{z - t}{z - a}\]

    if -3.0190154692849138e-136 < z < 3.3204015138500436e-256

    1. Initial program 3.8

      \[x + y \cdot \frac{z - t}{z - a}\]
    2. Using strategy rm

    3. Applied add-cube-cbrt4.2

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

    4. Applied associate-*l*4.2

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

    5. Simplified3.1

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

  4. Final simplification1.2

    \[\leadsto \begin{array}{l} \mathbf{if}\;z \le -3.019015469284913797565702456939618742875 \cdot 10^{-136} \lor \neg \left(z \le 3.320401513850043595539041976707631052552 \cdot 10^{-256}\right):\\ \;\;\;\;y \cdot \frac{z - t}{z - a} + x\\ \mathbf{else}:\\ \;\;\;\;\left(\sqrt[3]{y} \cdot \sqrt[3]{y}\right) \cdot \frac{\sqrt[3]{y} \cdot \left(z - t\right)}{z - a} + x\\ \end{array}\]

Reproduce

herbie shell --seed 2019194 
(FPCore (x y z t a)
  :name "Graphics.Rendering.Plot.Render.Plot.Axis:renderAxisLine from plot-0.2.3.4, A"

  :herbie-target
  (+ x (/ y (/ (- z a) (- z t))))

  (+ x (* y (/ (- z t) (- z a)))))