Average Error: 6.6 → 1.7
Time: 12.7s
Precision: 64
\[x + \frac{y \cdot \left(z - x\right)}{t}\]
↓
\[\begin{array}{l} \mathbf{if}\;t \le -5631930325664136519745536:\\ \;\;\;\;x + \frac{y}{\frac{t}{z - x}}\\ \mathbf{elif}\;t \le 1.313456436383683786127876557812595999187 \cdot 10^{-110}:\\ \;\;\;\;\left(\frac{y \cdot z}{t} - \frac{x \cdot y}{t}\right) + x\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{t}{z - x}}\\ \end{array}\]
x + \frac{y \cdot \left(z - x\right)}{t}
↓
\begin{array}{l}
\mathbf{if}\;t \le -5631930325664136519745536:\\
\;\;\;\;x + \frac{y}{\frac{t}{z - x}}\\

\mathbf{elif}\;t \le 1.313456436383683786127876557812595999187 \cdot 10^{-110}:\\
\;\;\;\;\left(\frac{y \cdot z}{t} - \frac{x \cdot y}{t}\right) + x\\

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

\end{array}
double f(double x, double y, double z, double t) {
        double r11890913 = x;
        double r11890914 = y;
        double r11890915 = z;
        double r11890916 = r11890915 - r11890913;
        double r11890917 = r11890914 * r11890916;
        double r11890918 = t;
        double r11890919 = r11890917 / r11890918;
        double r11890920 = r11890913 + r11890919;
        return r11890920;
}
↓
double f(double x, double y, double z, double t) {
        double r11890921 = t;
        double r11890922 = -5.631930325664137e+24;
        bool r11890923 = r11890921 <= r11890922;
        double r11890924 = x;
        double r11890925 = y;
        double r11890926 = z;
        double r11890927 = r11890926 - r11890924;
        double r11890928 = r11890921 / r11890927;
        double r11890929 = r11890925 / r11890928;
        double r11890930 = r11890924 + r11890929;
        double r11890931 = 1.3134564363836838e-110;
        bool r11890932 = r11890921 <= r11890931;
        double r11890933 = r11890925 * r11890926;
        double r11890934 = r11890933 / r11890921;
        double r11890935 = r11890924 * r11890925;
        double r11890936 = r11890935 / r11890921;
        double r11890937 = r11890934 - r11890936;
        double r11890938 = r11890937 + r11890924;
        double r11890939 = r11890932 ? r11890938 : r11890930;
        double r11890940 = r11890923 ? r11890930 : r11890939;
        return r11890940;
}

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

Original6.6
Target2.0
Herbie1.7
\[x - \left(x \cdot \frac{y}{t} + \left(-z\right) \cdot \frac{y}{t}\right)\]

Derivation

  1. Split input into 2 regimes

  2. if t < -5.631930325664137e+24 or 1.3134564363836838e-110 < t

    1. Initial program 8.9

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

    3. Applied associate-/l*1.6

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

    if -5.631930325664137e+24 < t < 1.3134564363836838e-110

    1. Initial program 1.9

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

    2. Taylor expanded around 0 1.9

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

  4. Final simplification1.7

    \[\leadsto \begin{array}{l} \mathbf{if}\;t \le -5631930325664136519745536:\\ \;\;\;\;x + \frac{y}{\frac{t}{z - x}}\\ \mathbf{elif}\;t \le 1.313456436383683786127876557812595999187 \cdot 10^{-110}:\\ \;\;\;\;\left(\frac{y \cdot z}{t} - \frac{x \cdot y}{t}\right) + x\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{t}{z - x}}\\ \end{array}\]

Reproduce

herbie shell --seed 2019171 +o rules:numerics
(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)))