Average Error: 1.4 → 1.5
Time: 4.5s
Precision: 64
\[x + y \cdot \frac{z - t}{a - t}\]
↓
\[\begin{array}{l} \mathbf{if}\;t \le -1.0071455594193599 \cdot 10^{-271} \lor \neg \left(t \le 7.46702847266602817 \cdot 10^{-71}\right):\\ \;\;\;\;x + y \cdot \left(\frac{z}{a - t} - \frac{t}{a - t}\right)\\ \mathbf{else}:\\ \;\;\;\;x + \left(\left(z - t\right) \cdot y\right) \cdot \frac{1}{a - t}\\ \end{array}\]
x + y \cdot \frac{z - t}{a - t}
↓
\begin{array}{l}
\mathbf{if}\;t \le -1.0071455594193599 \cdot 10^{-271} \lor \neg \left(t \le 7.46702847266602817 \cdot 10^{-71}\right):\\
\;\;\;\;x + y \cdot \left(\frac{z}{a - t} - \frac{t}{a - t}\right)\\

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

\end{array}
double f(double x, double y, double z, double t, double a) {
        double r577916 = x;
        double r577917 = y;
        double r577918 = z;
        double r577919 = t;
        double r577920 = r577918 - r577919;
        double r577921 = a;
        double r577922 = r577921 - r577919;
        double r577923 = r577920 / r577922;
        double r577924 = r577917 * r577923;
        double r577925 = r577916 + r577924;
        return r577925;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r577926 = t;
        double r577927 = -1.0071455594193599e-271;
        bool r577928 = r577926 <= r577927;
        double r577929 = 7.467028472666028e-71;
        bool r577930 = r577926 <= r577929;
        double r577931 = !r577930;
        bool r577932 = r577928 || r577931;
        double r577933 = x;
        double r577934 = y;
        double r577935 = z;
        double r577936 = a;
        double r577937 = r577936 - r577926;
        double r577938 = r577935 / r577937;
        double r577939 = r577926 / r577937;
        double r577940 = r577938 - r577939;
        double r577941 = r577934 * r577940;
        double r577942 = r577933 + r577941;
        double r577943 = r577935 - r577926;
        double r577944 = r577943 * r577934;
        double r577945 = 1.0;
        double r577946 = r577945 / r577937;
        double r577947 = r577944 * r577946;
        double r577948 = r577933 + r577947;
        double r577949 = r577932 ? r577942 : r577948;
        return r577949;
}

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

Original1.4
Target0.5
Herbie1.5
\[\begin{array}{l} \mathbf{if}\;y \lt -8.50808486055124107 \cdot 10^{-17}:\\ \;\;\;\;x + y \cdot \frac{z - t}{a - t}\\ \mathbf{elif}\;y \lt 2.8944268627920891 \cdot 10^{-49}:\\ \;\;\;\;x + \left(y \cdot \left(z - t\right)\right) \cdot \frac{1}{a - t}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{z - t}{a - t}\\ \end{array}\]

Derivation

  1. Split input into 2 regimes

  2. if t < -1.0071455594193599e-271 or 7.467028472666028e-71 < t

    1. Initial program 0.9

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

    3. Applied div-sub0.8

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

    if -1.0071455594193599e-271 < t < 7.467028472666028e-71

    1. Initial program 3.5

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

    3. Applied *-un-lft-identity3.5

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

    4. Applied add-cube-cbrt3.9

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

    5. Applied times-frac3.9

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

    6. Applied associate-*r*2.9

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

    7. Simplified2.9

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

    9. Applied div-inv2.9

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

    10. Applied associate-*r*4.2

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

    11. Simplified3.9

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

  4. Final simplification1.5

    \[\leadsto \begin{array}{l} \mathbf{if}\;t \le -1.0071455594193599 \cdot 10^{-271} \lor \neg \left(t \le 7.46702847266602817 \cdot 10^{-71}\right):\\ \;\;\;\;x + y \cdot \left(\frac{z}{a - t} - \frac{t}{a - t}\right)\\ \mathbf{else}:\\ \;\;\;\;x + \left(\left(z - t\right) \cdot y\right) \cdot \frac{1}{a - t}\\ \end{array}\]

Reproduce

herbie shell --seed 2020056 
(FPCore (x y z t a)
  :name "Graphics.Rendering.Plot.Render.Plot.Axis:renderAxisLine from plot-0.2.3.4, B"
  :precision binary64

  :herbie-target
  (if (< y -8.508084860551241e-17) (+ x (* y (/ (- z t) (- a t)))) (if (< y 2.894426862792089e-49) (+ x (* (* y (- z t)) (/ 1 (- a t)))) (+ x (* y (/ (- z t) (- a t))))))

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