Average Error: 6.6 → 0.9
Time: 3.0s
Precision: 64
\[x + \frac{y \cdot \left(z - x\right)}{t}\]
↓
\[\begin{array}{l} \mathbf{if}\;x + \frac{y \cdot \left(z - x\right)}{t} = -\infty \lor \neg \left(x + \frac{y \cdot \left(z - x\right)}{t} \le 1.00293034486153361 \cdot 10^{296}\right):\\ \;\;\;\;x + y \cdot \frac{1}{\frac{t}{z - x}}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y \cdot \left(z - x\right)}{t}\\ \end{array}\]
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 1.00293034486153361 \cdot 10^{296}\right):\\
\;\;\;\;x + y \cdot \frac{1}{\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 r302445 = x;
        double r302446 = y;
        double r302447 = z;
        double r302448 = r302447 - r302445;
        double r302449 = r302446 * r302448;
        double r302450 = t;
        double r302451 = r302449 / r302450;
        double r302452 = r302445 + r302451;
        return r302452;
}
↓
double f(double x, double y, double z, double t) {
        double r302453 = x;
        double r302454 = y;
        double r302455 = z;
        double r302456 = r302455 - r302453;
        double r302457 = r302454 * r302456;
        double r302458 = t;
        double r302459 = r302457 / r302458;
        double r302460 = r302453 + r302459;
        double r302461 = -inf.0;
        bool r302462 = r302460 <= r302461;
        double r302463 = 1.0029303448615336e+296;
        bool r302464 = r302460 <= r302463;
        double r302465 = !r302464;
        bool r302466 = r302462 || r302465;
        double r302467 = 1.0;
        double r302468 = r302458 / r302456;
        double r302469 = r302467 / r302468;
        double r302470 = r302454 * r302469;
        double r302471 = r302453 + r302470;
        double r302472 = r302466 ? r302471 : r302460;
        return r302472;
}

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

Derivation

  1. Split input into 2 regimes

  2. if (+ x (/ (* y (- z x)) t)) < -inf.0 or 1.0029303448615336e+296 < (+ x (/ (* y (- z x)) t))

    1. Initial program 58.2

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

    3. Applied *-un-lft-identity58.2

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

    4. Applied times-frac2.8

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

    5. Simplified2.8

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

    7. Applied clear-num2.8

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

    if -inf.0 < (+ x (/ (* y (- z x)) t)) < 1.0029303448615336e+296

    1. Initial program 0.7

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

  4. Final simplification0.9

    \[\leadsto \begin{array}{l} \mathbf{if}\;x + \frac{y \cdot \left(z - x\right)}{t} = -\infty \lor \neg \left(x + \frac{y \cdot \left(z - x\right)}{t} \le 1.00293034486153361 \cdot 10^{296}\right):\\ \;\;\;\;x + y \cdot \frac{1}{\frac{t}{z - x}}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y \cdot \left(z - x\right)}{t}\\ \end{array}\]

Reproduce

herbie shell --seed 2020057 +o rules:numerics
(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)))