Average Error: 10.6 → 0.4
Time: 4.2s
Precision: 64
\[x + \frac{y \cdot \left(z - t\right)}{a - t}\]
↓
\[\begin{array}{l} \mathbf{if}\;y \le -8.06916043366223524 \cdot 10^{-64}:\\ \;\;\;\;x + \frac{y}{\frac{a - t}{z - t}}\\ \mathbf{elif}\;y \le 5.4933827527075371 \cdot 10^{24}:\\ \;\;\;\;x + 1 \cdot \frac{\left(z - t\right) \cdot y}{a - t}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{z - t}{a - t}\\ \end{array}\]
x + \frac{y \cdot \left(z - t\right)}{a - t}
↓
\begin{array}{l}
\mathbf{if}\;y \le -8.06916043366223524 \cdot 10^{-64}:\\
\;\;\;\;x + \frac{y}{\frac{a - t}{z - t}}\\

\mathbf{elif}\;y \le 5.4933827527075371 \cdot 10^{24}:\\
\;\;\;\;x + 1 \cdot \frac{\left(z - t\right) \cdot y}{a - t}\\

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

\end{array}
double f(double x, double y, double z, double t, double a) {
        double r545960 = x;
        double r545961 = y;
        double r545962 = z;
        double r545963 = t;
        double r545964 = r545962 - r545963;
        double r545965 = r545961 * r545964;
        double r545966 = a;
        double r545967 = r545966 - r545963;
        double r545968 = r545965 / r545967;
        double r545969 = r545960 + r545968;
        return r545969;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r545970 = y;
        double r545971 = -8.069160433662235e-64;
        bool r545972 = r545970 <= r545971;
        double r545973 = x;
        double r545974 = a;
        double r545975 = t;
        double r545976 = r545974 - r545975;
        double r545977 = z;
        double r545978 = r545977 - r545975;
        double r545979 = r545976 / r545978;
        double r545980 = r545970 / r545979;
        double r545981 = r545973 + r545980;
        double r545982 = 5.493382752707537e+24;
        bool r545983 = r545970 <= r545982;
        double r545984 = 1.0;
        double r545985 = r545978 * r545970;
        double r545986 = r545985 / r545976;
        double r545987 = r545984 * r545986;
        double r545988 = r545973 + r545987;
        double r545989 = r545978 / r545976;
        double r545990 = r545970 * r545989;
        double r545991 = r545973 + r545990;
        double r545992 = r545983 ? r545988 : r545991;
        double r545993 = r545972 ? r545981 : r545992;
        return r545993;
}

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

Original10.6
Target1.1
Herbie0.4
\[x + \frac{y}{\frac{a - t}{z - t}}\]

Derivation

  1. Split input into 3 regimes

  2. if y < -8.069160433662235e-64

    1. Initial program 17.7

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

    3. Applied associate-/l*0.6

      \[\leadsto x + \color{blue}{\frac{y}{\frac{a - t}{z - t}}}\]

    if -8.069160433662235e-64 < y < 5.493382752707537e+24

    1. Initial program 0.4

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

    3. Applied associate-/l*1.7

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

    5. Applied div-inv1.8

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

    6. Applied add-cube-cbrt2.0

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

    7. Applied times-frac2.6

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

    8. Simplified2.6

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

    10. Applied *-un-lft-identity2.6

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

    11. Applied associate-*l*2.6

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

    12. Simplified0.4

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

    if 5.493382752707537e+24 < y

    1. Initial program 25.9

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

    3. Applied *-un-lft-identity25.9

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

    4. Applied times-frac0.4

      \[\leadsto x + \color{blue}{\frac{y}{1} \cdot \frac{z - t}{a - t}}\]

    5. Simplified0.4

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

  4. Final simplification0.4

    \[\leadsto \begin{array}{l} \mathbf{if}\;y \le -8.06916043366223524 \cdot 10^{-64}:\\ \;\;\;\;x + \frac{y}{\frac{a - t}{z - t}}\\ \mathbf{elif}\;y \le 5.4933827527075371 \cdot 10^{24}:\\ \;\;\;\;x + 1 \cdot \frac{\left(z - t\right) \cdot y}{a - t}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{z - t}{a - t}\\ \end{array}\]

Reproduce

herbie shell --seed 2020062 
(FPCore (x y z t a)
  :name "Graphics.Rendering.Plot.Render.Plot.Axis:renderAxisTicks from plot-0.2.3.4, B"
  :precision binary64

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

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