Average Error: 6.5 → 1.9
Time: 12.7s
Precision: 64
\[x + \frac{y \cdot \left(z - x\right)}{t}\]
↓
\[\begin{array}{l} \mathbf{if}\;x \le -2.642592177827107676405494020606785260044 \cdot 10^{-268}:\\ \;\;\;\;x - \left(x - z\right) \cdot \frac{y}{t}\\ \mathbf{elif}\;x \le 4.817264783557647095538793580222919409807 \cdot 10^{-197}:\\ \;\;\;\;x - \frac{y}{\frac{t}{x - z}}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{x - z}{\frac{t}{y}}\\ \end{array}\]
x + \frac{y \cdot \left(z - x\right)}{t}
↓
\begin{array}{l}
\mathbf{if}\;x \le -2.642592177827107676405494020606785260044 \cdot 10^{-268}:\\
\;\;\;\;x - \left(x - z\right) \cdot \frac{y}{t}\\

\mathbf{elif}\;x \le 4.817264783557647095538793580222919409807 \cdot 10^{-197}:\\
\;\;\;\;x - \frac{y}{\frac{t}{x - z}}\\

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

\end{array}
double f(double x, double y, double z, double t) {
        double r271432 = x;
        double r271433 = y;
        double r271434 = z;
        double r271435 = r271434 - r271432;
        double r271436 = r271433 * r271435;
        double r271437 = t;
        double r271438 = r271436 / r271437;
        double r271439 = r271432 + r271438;
        return r271439;
}
↓
double f(double x, double y, double z, double t) {
        double r271440 = x;
        double r271441 = -2.6425921778271077e-268;
        bool r271442 = r271440 <= r271441;
        double r271443 = z;
        double r271444 = r271440 - r271443;
        double r271445 = y;
        double r271446 = t;
        double r271447 = r271445 / r271446;
        double r271448 = r271444 * r271447;
        double r271449 = r271440 - r271448;
        double r271450 = 4.817264783557647e-197;
        bool r271451 = r271440 <= r271450;
        double r271452 = r271446 / r271444;
        double r271453 = r271445 / r271452;
        double r271454 = r271440 - r271453;
        double r271455 = r271446 / r271445;
        double r271456 = r271444 / r271455;
        double r271457 = r271440 - r271456;
        double r271458 = r271451 ? r271454 : r271457;
        double r271459 = r271442 ? r271449 : r271458;
        return r271459;
}

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
Target2.1
Herbie1.9
\[x - \left(x \cdot \frac{y}{t} + \left(-z\right) \cdot \frac{y}{t}\right)\]

Derivation

  1. Split input into 3 regimes

  2. if x < -2.6425921778271077e-268

    1. Initial program 6.8

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

    2. Simplified6.8

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

    3. Taylor expanded around 0 6.8

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

    4. Simplified1.7

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

    6. Applied div-inv1.9

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

    7. Simplified1.8

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

    if -2.6425921778271077e-268 < x < 4.817264783557647e-197

    1. Initial program 5.2

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

    2. Simplified5.2

      \[\leadsto \color{blue}{x - \frac{y \cdot \left(x - z\right)}{t}}\]
    3. Using strategy rm

    4. Applied associate-/l*5.0

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

    if 4.817264783557647e-197 < x

    1. Initial program 6.7

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

    2. Simplified6.7

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

    3. Taylor expanded around 0 6.7

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

    4. Simplified1.1

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

  4. Final simplification1.9

    \[\leadsto \begin{array}{l} \mathbf{if}\;x \le -2.642592177827107676405494020606785260044 \cdot 10^{-268}:\\ \;\;\;\;x - \left(x - z\right) \cdot \frac{y}{t}\\ \mathbf{elif}\;x \le 4.817264783557647095538793580222919409807 \cdot 10^{-197}:\\ \;\;\;\;x - \frac{y}{\frac{t}{x - z}}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{x - z}{\frac{t}{y}}\\ \end{array}\]

Reproduce

herbie shell --seed 2019194 
(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)))