Average Error: 10.5 → 0.5
Time: 29.3s
Precision: 64
\[x + \frac{\left(y - z\right) \cdot t}{a - z}\]
↓
\[\begin{array}{l} \mathbf{if}\;\frac{\left(y - z\right) \cdot t}{a - z} = -\infty:\\ \;\;\;\;x + \frac{y - z}{\frac{a - z}{t}}\\ \mathbf{elif}\;\frac{\left(y - z\right) \cdot t}{a - z} \le 2.304130805788302065283561126237878159374 \cdot 10^{260}:\\ \;\;\;\;x + \frac{\left(y - z\right) \cdot t}{a - z}\\ \mathbf{else}:\\ \;\;\;\;x + \left(y - z\right) \cdot \frac{t}{a - z}\\ \end{array}\]
x + \frac{\left(y - z\right) \cdot t}{a - z}
↓
\begin{array}{l}
\mathbf{if}\;\frac{\left(y - z\right) \cdot t}{a - z} = -\infty:\\
\;\;\;\;x + \frac{y - z}{\frac{a - z}{t}}\\

\mathbf{elif}\;\frac{\left(y - z\right) \cdot t}{a - z} \le 2.304130805788302065283561126237878159374 \cdot 10^{260}:\\
\;\;\;\;x + \frac{\left(y - z\right) \cdot t}{a - z}\\

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

\end{array}
double f(double x, double y, double z, double t, double a) {
        double r109322712 = x;
        double r109322713 = y;
        double r109322714 = z;
        double r109322715 = r109322713 - r109322714;
        double r109322716 = t;
        double r109322717 = r109322715 * r109322716;
        double r109322718 = a;
        double r109322719 = r109322718 - r109322714;
        double r109322720 = r109322717 / r109322719;
        double r109322721 = r109322712 + r109322720;
        return r109322721;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r109322722 = y;
        double r109322723 = z;
        double r109322724 = r109322722 - r109322723;
        double r109322725 = t;
        double r109322726 = r109322724 * r109322725;
        double r109322727 = a;
        double r109322728 = r109322727 - r109322723;
        double r109322729 = r109322726 / r109322728;
        double r109322730 = -inf.0;
        bool r109322731 = r109322729 <= r109322730;
        double r109322732 = x;
        double r109322733 = r109322728 / r109322725;
        double r109322734 = r109322724 / r109322733;
        double r109322735 = r109322732 + r109322734;
        double r109322736 = 2.304130805788302e+260;
        bool r109322737 = r109322729 <= r109322736;
        double r109322738 = r109322732 + r109322729;
        double r109322739 = r109322725 / r109322728;
        double r109322740 = r109322724 * r109322739;
        double r109322741 = r109322732 + r109322740;
        double r109322742 = r109322737 ? r109322738 : r109322741;
        double r109322743 = r109322731 ? r109322735 : r109322742;
        return r109322743;
}

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

Original10.5
Target0.6
Herbie0.5
\[\begin{array}{l} \mathbf{if}\;t \lt -1.068297449017406694366747246993994850729 \cdot 10^{-39}:\\ \;\;\;\;x + \frac{y - z}{a - z} \cdot t\\ \mathbf{elif}\;t \lt 3.911094988758637497591020599238553861375 \cdot 10^{-141}:\\ \;\;\;\;x + \frac{\left(y - z\right) \cdot t}{a - z}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y - z}{a - z} \cdot t\\ \end{array}\]

Derivation

  1. Split input into 3 regimes

  2. if (/ (* (- y z) t) (- a z)) < -inf.0

    1. Initial program 64.0

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

    3. Applied associate-/l*0.2

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

    if -inf.0 < (/ (* (- y z) t) (- a z)) < 2.304130805788302e+260

    1. Initial program 0.2

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

    if 2.304130805788302e+260 < (/ (* (- y z) t) (- a z))

    1. Initial program 55.9

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

    3. Applied *-un-lft-identity55.9

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

    4. Applied times-frac3.1

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

    5. Simplified3.1

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

  4. Final simplification0.5

    \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{\left(y - z\right) \cdot t}{a - z} = -\infty:\\ \;\;\;\;x + \frac{y - z}{\frac{a - z}{t}}\\ \mathbf{elif}\;\frac{\left(y - z\right) \cdot t}{a - z} \le 2.304130805788302065283561126237878159374 \cdot 10^{260}:\\ \;\;\;\;x + \frac{\left(y - z\right) \cdot t}{a - z}\\ \mathbf{else}:\\ \;\;\;\;x + \left(y - z\right) \cdot \frac{t}{a - z}\\ \end{array}\]

Reproduce

herbie shell --seed 2019173 
(FPCore (x y z t a)
  :name "Graphics.Rendering.Plot.Render.Plot.Axis:renderAxisTick from plot-0.2.3.4, A"

  :herbie-target
  (if (< t -1.0682974490174067e-39) (+ x (* (/ (- y z) (- a z)) t)) (if (< t 3.9110949887586375e-141) (+ x (/ (* (- y z) t) (- a z))) (+ x (* (/ (- y z) (- a z)) t))))

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