Average Error: 6.5 → 1.0
Time: 31.6s
Precision: 64
\[x + \frac{y \cdot \left(z - x\right)}{t}\]
↓
\[\begin{array}{l} \mathbf{if}\;x + \frac{y \cdot \left(z - x\right)}{t} = -\infty:\\ \;\;\;\;x + \frac{y}{\frac{t}{z - x}}\\ \mathbf{elif}\;x + \frac{y \cdot \left(z - x\right)}{t} \le 5.79683763111968270393952416527987892058 \cdot 10^{292}:\\ \;\;\;\;x + \frac{y \cdot \left(z - x\right)}{t}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{z - x}{t}\\ \end{array}\]
x + \frac{y \cdot \left(z - x\right)}{t}
↓
\begin{array}{l}
\mathbf{if}\;x + \frac{y \cdot \left(z - x\right)}{t} = -\infty:\\
\;\;\;\;x + \frac{y}{\frac{t}{z - x}}\\

\mathbf{elif}\;x + \frac{y \cdot \left(z - x\right)}{t} \le 5.79683763111968270393952416527987892058 \cdot 10^{292}:\\
\;\;\;\;x + \frac{y \cdot \left(z - x\right)}{t}\\

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

\end{array}
double f(double x, double y, double z, double t) {
        double r66334008 = x;
        double r66334009 = y;
        double r66334010 = z;
        double r66334011 = r66334010 - r66334008;
        double r66334012 = r66334009 * r66334011;
        double r66334013 = t;
        double r66334014 = r66334012 / r66334013;
        double r66334015 = r66334008 + r66334014;
        return r66334015;
}
↓
double f(double x, double y, double z, double t) {
        double r66334016 = x;
        double r66334017 = y;
        double r66334018 = z;
        double r66334019 = r66334018 - r66334016;
        double r66334020 = r66334017 * r66334019;
        double r66334021 = t;
        double r66334022 = r66334020 / r66334021;
        double r66334023 = r66334016 + r66334022;
        double r66334024 = -inf.0;
        bool r66334025 = r66334023 <= r66334024;
        double r66334026 = r66334021 / r66334019;
        double r66334027 = r66334017 / r66334026;
        double r66334028 = r66334016 + r66334027;
        double r66334029 = 5.796837631119683e+292;
        bool r66334030 = r66334023 <= r66334029;
        double r66334031 = r66334019 / r66334021;
        double r66334032 = r66334017 * r66334031;
        double r66334033 = r66334016 + r66334032;
        double r66334034 = r66334030 ? r66334023 : r66334033;
        double r66334035 = r66334025 ? r66334028 : r66334034;
        return r66334035;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Bits error versus t

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original6.5
Target2.3
Herbie1.0
\[x - \left(x \cdot \frac{y}{t} + \left(-z\right) \cdot \frac{y}{t}\right)\]

Derivation

  1. Split input into 3 regimes

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

    1. Initial program 64.0

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

    3. Applied associate-/l*0.2

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

    if -inf.0 < (+ x (/ (* y (- z x)) t)) < 5.796837631119683e+292

    1. Initial program 0.7

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

    if 5.796837631119683e+292 < (+ x (/ (* y (- z x)) t))

    1. Initial program 47.6

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

    3. Applied *-un-lft-identity47.6

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

    4. Applied times-frac5.9

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

    5. Simplified5.9

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

  4. Final simplification1.0

    \[\leadsto \begin{array}{l} \mathbf{if}\;x + \frac{y \cdot \left(z - x\right)}{t} = -\infty:\\ \;\;\;\;x + \frac{y}{\frac{t}{z - x}}\\ \mathbf{elif}\;x + \frac{y \cdot \left(z - x\right)}{t} \le 5.79683763111968270393952416527987892058 \cdot 10^{292}:\\ \;\;\;\;x + \frac{y \cdot \left(z - x\right)}{t}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{z - x}{t}\\ \end{array}\]

Reproduce

herbie shell --seed 2019173 
(FPCore (x y z t)
  :name "Optimisation.CirclePacking:place from circle-packing-0.1.0.4, D"

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

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