Average Error: 1.3 → 1.2
Time: 17.4s
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 r473555 = x;
        double r473556 = y;
        double r473557 = z;
        double r473558 = t;
        double r473559 = r473557 - r473558;
        double r473560 = a;
        double r473561 = r473557 - r473560;
        double r473562 = r473559 / r473561;
        double r473563 = r473556 * r473562;
        double r473564 = r473555 + r473563;
        return r473564;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r473565 = z;
        double r473566 = -3.0190154692849138e-136;
        bool r473567 = r473565 <= r473566;
        double r473568 = 3.3204015138500436e-256;
        bool r473569 = r473565 <= r473568;
        double r473570 = !r473569;
        bool r473571 = r473567 || r473570;
        double r473572 = y;
        double r473573 = t;
        double r473574 = r473565 - r473573;
        double r473575 = a;
        double r473576 = r473565 - r473575;
        double r473577 = r473574 / r473576;
        double r473578 = r473572 * r473577;
        double r473579 = x;
        double r473580 = r473578 + r473579;
        double r473581 = cbrt(r473572);
        double r473582 = r473581 * r473581;
        double r473583 = r473581 * r473574;
        double r473584 = r473583 / r473576;
        double r473585 = r473582 * r473584;
        double r473586 = r473585 + r473579;
        double r473587 = r473571 ? r473580 : r473586;
        return r473587;
}

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)))))