Average Error: 6.3 → 0.7
Time: 3.6s
Precision: 64
\[x + \frac{y \cdot \left(z - x\right)}{t}\]
↓
\[\begin{array}{l} \mathbf{if}\;x + \frac{y \cdot \left(z - x\right)}{t} = -\infty:\\ \;\;\;\;x + \frac{y}{\frac{t}{z - x}}\\ \mathbf{elif}\;x + \frac{y \cdot \left(z - x\right)}{t} \le 2.6466639631087562 \cdot 10^{300}:\\ \;\;\;\;x + \frac{y \cdot \left(z - x\right)}{t}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{t} \cdot \left(z - x\right)\\ \end{array}\]
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 2.6466639631087562 \cdot 10^{300}:\\
\;\;\;\;x + \frac{y \cdot \left(z - x\right)}{t}\\

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

\end{array}
double f(double x, double y, double z, double t) {
        double r348916 = x;
        double r348917 = y;
        double r348918 = z;
        double r348919 = r348918 - r348916;
        double r348920 = r348917 * r348919;
        double r348921 = t;
        double r348922 = r348920 / r348921;
        double r348923 = r348916 + r348922;
        return r348923;
}
↓
double f(double x, double y, double z, double t) {
        double r348924 = x;
        double r348925 = y;
        double r348926 = z;
        double r348927 = r348926 - r348924;
        double r348928 = r348925 * r348927;
        double r348929 = t;
        double r348930 = r348928 / r348929;
        double r348931 = r348924 + r348930;
        double r348932 = -inf.0;
        bool r348933 = r348931 <= r348932;
        double r348934 = r348929 / r348927;
        double r348935 = r348925 / r348934;
        double r348936 = r348924 + r348935;
        double r348937 = 2.6466639631087562e+300;
        bool r348938 = r348931 <= r348937;
        double r348939 = r348925 / r348929;
        double r348940 = r348939 * r348927;
        double r348941 = r348924 + r348940;
        double r348942 = r348938 ? r348931 : r348941;
        double r348943 = r348933 ? r348936 : r348942;
        return r348943;
}

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

Original6.3
Target1.9
Herbie0.7
\[x - \left(x \cdot \frac{y}{t} + \left(-z\right) \cdot \frac{y}{t}\right)\]

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)) < 2.6466639631087562e+300

    1. Initial program 0.7

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

    if 2.6466639631087562e+300 < (+ x (/ (* y (- z x)) t))

    1. Initial program 53.1

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

    3. Applied associate-/l*3.4

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

    5. Applied associate-/r/1.3

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

  4. Final simplification0.7

    \[\leadsto \begin{array}{l} \mathbf{if}\;x + \frac{y \cdot \left(z - x\right)}{t} = -\infty:\\ \;\;\;\;x + \frac{y}{\frac{t}{z - x}}\\ \mathbf{elif}\;x + \frac{y \cdot \left(z - x\right)}{t} \le 2.6466639631087562 \cdot 10^{300}:\\ \;\;\;\;x + \frac{y \cdot \left(z - x\right)}{t}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{t} \cdot \left(z - x\right)\\ \end{array}\]

Reproduce

herbie shell --seed 2020003 
(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)))