Average Error: 1.5 → 1.3
Time: 14.4s
Precision: 64
\[x + y \cdot \frac{z - t}{z - a}\]
↓
\[\begin{array}{l} \mathbf{if}\;z \le -6.964036638581209574726043986735525528163 \cdot 10^{-102} \lor \neg \left(z \le 9.403031276241487005540332044897243661846 \cdot 10^{-164}\right):\\ \;\;\;\;x + y \cdot \frac{z - t}{z - a}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\sqrt[3]{z - a} \cdot \sqrt[3]{z - a}} \cdot \frac{z - t}{\sqrt[3]{z - a}}\\ \end{array}\]
x + y \cdot \frac{z - t}{z - a}
↓
\begin{array}{l}
\mathbf{if}\;z \le -6.964036638581209574726043986735525528163 \cdot 10^{-102} \lor \neg \left(z \le 9.403031276241487005540332044897243661846 \cdot 10^{-164}\right):\\
\;\;\;\;x + y \cdot \frac{z - t}{z - a}\\

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

\end{array}
double f(double x, double y, double z, double t, double a) {
        double r382525 = x;
        double r382526 = y;
        double r382527 = z;
        double r382528 = t;
        double r382529 = r382527 - r382528;
        double r382530 = a;
        double r382531 = r382527 - r382530;
        double r382532 = r382529 / r382531;
        double r382533 = r382526 * r382532;
        double r382534 = r382525 + r382533;
        return r382534;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r382535 = z;
        double r382536 = -6.9640366385812096e-102;
        bool r382537 = r382535 <= r382536;
        double r382538 = 9.403031276241487e-164;
        bool r382539 = r382535 <= r382538;
        double r382540 = !r382539;
        bool r382541 = r382537 || r382540;
        double r382542 = x;
        double r382543 = y;
        double r382544 = t;
        double r382545 = r382535 - r382544;
        double r382546 = a;
        double r382547 = r382535 - r382546;
        double r382548 = r382545 / r382547;
        double r382549 = r382543 * r382548;
        double r382550 = r382542 + r382549;
        double r382551 = cbrt(r382547);
        double r382552 = r382551 * r382551;
        double r382553 = r382543 / r382552;
        double r382554 = r382545 / r382551;
        double r382555 = r382553 * r382554;
        double r382556 = r382542 + r382555;
        double r382557 = r382541 ? r382550 : r382556;
        return r382557;
}

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

Original1.5
Target1.4
Herbie1.3
\[x + \frac{y}{\frac{z - a}{z - t}}\]

Derivation

  1. Split input into 2 regimes

  2. if z < -6.9640366385812096e-102 or 9.403031276241487e-164 < z

    1. Initial program 0.5

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

    if -6.9640366385812096e-102 < z < 9.403031276241487e-164

    1. Initial program 4.4

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

    3. Applied add-cube-cbrt4.8

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

    4. Applied *-un-lft-identity4.8

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

    5. Applied times-frac4.8

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

    6. Applied associate-*r*3.5

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

    7. Simplified3.4

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

  4. Final simplification1.3

    \[\leadsto \begin{array}{l} \mathbf{if}\;z \le -6.964036638581209574726043986735525528163 \cdot 10^{-102} \lor \neg \left(z \le 9.403031276241487005540332044897243661846 \cdot 10^{-164}\right):\\ \;\;\;\;x + y \cdot \frac{z - t}{z - a}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\sqrt[3]{z - a} \cdot \sqrt[3]{z - a}} \cdot \frac{z - t}{\sqrt[3]{z - a}}\\ \end{array}\]

Reproduce

herbie shell --seed 2019306 
(FPCore (x y z t a)
  :name "Graphics.Rendering.Plot.Render.Plot.Axis:renderAxisLine from plot-0.2.3.4, A"
  :precision binary64

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

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