Average Error: 10.8 → 0.5
Time: 17.0s
Precision: 64
\[x + \frac{y \cdot \left(z - t\right)}{z - a}\]
↓
\[\begin{array}{l} \mathbf{if}\;y \le -4.293463962714998493379525507428593936827 \cdot 10^{-60} \lor \neg \left(y \le 1.812839748984545334595059911175536357052 \cdot 10^{-103}\right):\\ \;\;\;\;x + \frac{y}{\frac{z - a}{z - t}}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{1}{z - a} \cdot \left(y \cdot \left(z - t\right)\right)\\ \end{array}\]
x + \frac{y \cdot \left(z - t\right)}{z - a}
↓
\begin{array}{l}
\mathbf{if}\;y \le -4.293463962714998493379525507428593936827 \cdot 10^{-60} \lor \neg \left(y \le 1.812839748984545334595059911175536357052 \cdot 10^{-103}\right):\\
\;\;\;\;x + \frac{y}{\frac{z - a}{z - t}}\\

\mathbf{else}:\\
\;\;\;\;x + \frac{1}{z - a} \cdot \left(y \cdot \left(z - t\right)\right)\\

\end{array}
double f(double x, double y, double z, double t, double a) {
        double r409918 = x;
        double r409919 = y;
        double r409920 = z;
        double r409921 = t;
        double r409922 = r409920 - r409921;
        double r409923 = r409919 * r409922;
        double r409924 = a;
        double r409925 = r409920 - r409924;
        double r409926 = r409923 / r409925;
        double r409927 = r409918 + r409926;
        return r409927;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r409928 = y;
        double r409929 = -4.2934639627149985e-60;
        bool r409930 = r409928 <= r409929;
        double r409931 = 1.8128397489845453e-103;
        bool r409932 = r409928 <= r409931;
        double r409933 = !r409932;
        bool r409934 = r409930 || r409933;
        double r409935 = x;
        double r409936 = z;
        double r409937 = a;
        double r409938 = r409936 - r409937;
        double r409939 = t;
        double r409940 = r409936 - r409939;
        double r409941 = r409938 / r409940;
        double r409942 = r409928 / r409941;
        double r409943 = r409935 + r409942;
        double r409944 = 1.0;
        double r409945 = r409944 / r409938;
        double r409946 = r409928 * r409940;
        double r409947 = r409945 * r409946;
        double r409948 = r409935 + r409947;
        double r409949 = r409934 ? r409943 : r409948;
        return r409949;
}

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

Original10.8
Target1.2
Herbie0.5
\[x + \frac{y}{\frac{z - a}{z - t}}\]

Derivation

  1. Split input into 2 regimes

  2. if y < -4.2934639627149985e-60 or 1.8128397489845453e-103 < y

    1. Initial program 18.2

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

    3. Applied associate-/l*0.5

      \[\leadsto x + \color{blue}{\frac{y}{\frac{z - a}{z - t}}}\]
    4. Using strategy rm

    5. Applied pow10.5

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

    if -4.2934639627149985e-60 < y < 1.8128397489845453e-103

    1. Initial program 0.5

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

    3. Applied associate-/l*2.2

      \[\leadsto x + \color{blue}{\frac{y}{\frac{z - a}{z - t}}}\]
    4. Using strategy rm

    5. Applied pow12.2

      \[\leadsto \color{blue}{{\left(x + \frac{y}{\frac{z - a}{z - t}}\right)}^{1}}\]
    6. Using strategy rm

    7. Applied div-inv2.3

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

    8. Applied *-un-lft-identity2.3

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

    9. Applied times-frac0.5

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

    10. Simplified0.5

      \[\leadsto {\left(x + \frac{1}{z - a} \cdot \color{blue}{\left(y \cdot \left(z - t\right)\right)}\right)}^{1}\]
  3. Recombined 2 regimes into one program.

  4. Final simplification0.5

    \[\leadsto \begin{array}{l} \mathbf{if}\;y \le -4.293463962714998493379525507428593936827 \cdot 10^{-60} \lor \neg \left(y \le 1.812839748984545334595059911175536357052 \cdot 10^{-103}\right):\\ \;\;\;\;x + \frac{y}{\frac{z - a}{z - t}}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{1}{z - a} \cdot \left(y \cdot \left(z - t\right)\right)\\ \end{array}\]

Reproduce

herbie shell --seed 2019208 
(FPCore (x y z t a)
  :name "Graphics.Rendering.Plot.Render.Plot.Axis:renderAxisTicks from plot-0.2.3.4, A"
  :precision binary64

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

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