Average Error: 1.5 → 1.0
Time: 25.8s
Precision: 64
\[x + y \cdot \frac{z - t}{z - a}\]
↓
\[\begin{array}{l} \mathbf{if}\;y \le -2.212645841190267324612631053459760197997 \cdot 10^{-233}:\\ \;\;\;\;x + y \cdot \frac{z - t}{z - a}\\ \mathbf{elif}\;y \le 1.119067119670475321537633852374314219182 \cdot 10^{-184}:\\ \;\;\;\;x + \frac{y \cdot \left(z - t\right)}{z - a}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{\frac{z - a}{z - t}} + x\\ \end{array}\]
x + y \cdot \frac{z - t}{z - a}
↓
\begin{array}{l}
\mathbf{if}\;y \le -2.212645841190267324612631053459760197997 \cdot 10^{-233}:\\
\;\;\;\;x + y \cdot \frac{z - t}{z - a}\\

\mathbf{elif}\;y \le 1.119067119670475321537633852374314219182 \cdot 10^{-184}:\\
\;\;\;\;x + \frac{y \cdot \left(z - t\right)}{z - a}\\

\mathbf{else}:\\
\;\;\;\;\frac{y}{\frac{z - a}{z - t}} + x\\

\end{array}
double f(double x, double y, double z, double t, double a) {
        double r82537999 = x;
        double r82538000 = y;
        double r82538001 = z;
        double r82538002 = t;
        double r82538003 = r82538001 - r82538002;
        double r82538004 = a;
        double r82538005 = r82538001 - r82538004;
        double r82538006 = r82538003 / r82538005;
        double r82538007 = r82538000 * r82538006;
        double r82538008 = r82537999 + r82538007;
        return r82538008;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r82538009 = y;
        double r82538010 = -2.2126458411902673e-233;
        bool r82538011 = r82538009 <= r82538010;
        double r82538012 = x;
        double r82538013 = z;
        double r82538014 = t;
        double r82538015 = r82538013 - r82538014;
        double r82538016 = a;
        double r82538017 = r82538013 - r82538016;
        double r82538018 = r82538015 / r82538017;
        double r82538019 = r82538009 * r82538018;
        double r82538020 = r82538012 + r82538019;
        double r82538021 = 1.1190671196704753e-184;
        bool r82538022 = r82538009 <= r82538021;
        double r82538023 = r82538009 * r82538015;
        double r82538024 = r82538023 / r82538017;
        double r82538025 = r82538012 + r82538024;
        double r82538026 = r82538017 / r82538015;
        double r82538027 = r82538009 / r82538026;
        double r82538028 = r82538027 + r82538012;
        double r82538029 = r82538022 ? r82538025 : r82538028;
        double r82538030 = r82538011 ? r82538020 : r82538029;
        return r82538030;
}

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
Herbie1.0
\[x + \frac{y}{\frac{z - a}{z - t}}\]

Derivation

  1. Split input into 3 regimes

  2. if y < -2.2126458411902673e-233

    1. Initial program 1.1

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

    if -2.2126458411902673e-233 < y < 1.1190671196704753e-184

    1. Initial program 3.0

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

    3. Applied associate-*r/0.4

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

    if 1.1190671196704753e-184 < y

    1. Initial program 1.3

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

    3. Applied add-cube-cbrt1.9

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

    4. Applied associate-*l*1.9

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

    6. Applied pow11.9

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

    7. Applied pow11.9

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

    8. Applied pow-prod-down1.9

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

    9. Applied pow11.9

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

    10. Applied pow11.9

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

    11. Applied pow-prod-down1.9

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

    12. Applied pow-prod-down1.9

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

    13. Simplified1.2

      \[\leadsto x + {\color{blue}{\left(\frac{y}{\frac{z - a}{z - t}}\right)}}^{1}\]
  3. Recombined 3 regimes into one program.

  4. Final simplification1.0

    \[\leadsto \begin{array}{l} \mathbf{if}\;y \le -2.212645841190267324612631053459760197997 \cdot 10^{-233}:\\ \;\;\;\;x + y \cdot \frac{z - t}{z - a}\\ \mathbf{elif}\;y \le 1.119067119670475321537633852374314219182 \cdot 10^{-184}:\\ \;\;\;\;x + \frac{y \cdot \left(z - t\right)}{z - a}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{\frac{z - a}{z - t}} + x\\ \end{array}\]

Reproduce

herbie shell --seed 2019173 +o rules:numerics
(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)))))