Average Error: 6.2 → 0.7
Time: 5.2s
Precision: 64
\[x + \frac{y \cdot \left(z - x\right)}{t}\]
↓
\[\begin{array}{l} \mathbf{if}\;x + \frac{y \cdot \left(z - x\right)}{t} = -\infty \lor \neg \left(x + \frac{y \cdot \left(z - x\right)}{t} \le 1.83014942255142419 \cdot 10^{297}\right):\\ \;\;\;\;x + \frac{y}{\frac{t}{z - x}}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y \cdot \left(z - x\right)}{t}\\ \end{array}\]
x + \frac{y \cdot \left(z - x\right)}{t}
↓
\begin{array}{l}
\mathbf{if}\;x + \frac{y \cdot \left(z - x\right)}{t} = -\infty \lor \neg \left(x + \frac{y \cdot \left(z - x\right)}{t} \le 1.83014942255142419 \cdot 10^{297}\right):\\
\;\;\;\;x + \frac{y}{\frac{t}{z - x}}\\

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

\end{array}
double f(double x, double y, double z, double t) {
        double r376982 = x;
        double r376983 = y;
        double r376984 = z;
        double r376985 = r376984 - r376982;
        double r376986 = r376983 * r376985;
        double r376987 = t;
        double r376988 = r376986 / r376987;
        double r376989 = r376982 + r376988;
        return r376989;
}
↓
double f(double x, double y, double z, double t) {
        double r376990 = x;
        double r376991 = y;
        double r376992 = z;
        double r376993 = r376992 - r376990;
        double r376994 = r376991 * r376993;
        double r376995 = t;
        double r376996 = r376994 / r376995;
        double r376997 = r376990 + r376996;
        double r376998 = -inf.0;
        bool r376999 = r376997 <= r376998;
        double r377000 = 1.8301494225514242e+297;
        bool r377001 = r376997 <= r377000;
        double r377002 = !r377001;
        bool r377003 = r376999 || r377002;
        double r377004 = r376995 / r376993;
        double r377005 = r376991 / r377004;
        double r377006 = r376990 + r377005;
        double r377007 = r377003 ? r377006 : r376997;
        return r377007;
}

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

Original6.2
Target2.0
Herbie0.7
\[x - \left(x \cdot \frac{y}{t} + \left(-z\right) \cdot \frac{y}{t}\right)\]

Derivation

  1. Split input into 2 regimes

  2. if (+ x (/ (* y (- z x)) t)) < -inf.0 or 1.8301494225514242e+297 < (+ x (/ (* y (- z x)) t))

    1. Initial program 58.1

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

    3. Applied associate-/l*1.7

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

    if -inf.0 < (+ x (/ (* y (- z x)) t)) < 1.8301494225514242e+297

    1. Initial program 0.6

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

  4. Final simplification0.7

    \[\leadsto \begin{array}{l} \mathbf{if}\;x + \frac{y \cdot \left(z - x\right)}{t} = -\infty \lor \neg \left(x + \frac{y \cdot \left(z - x\right)}{t} \le 1.83014942255142419 \cdot 10^{297}\right):\\ \;\;\;\;x + \frac{y}{\frac{t}{z - x}}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y \cdot \left(z - x\right)}{t}\\ \end{array}\]

Reproduce

herbie shell --seed 2020046 
(FPCore (x y z t)
  :name "Optimisation.CirclePacking:place from circle-packing-0.1.0.4, D"
  :precision binary64

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

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