Average Error: 6.6 → 0.9
Time: 3.7s
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 r432413 = x;
        double r432414 = y;
        double r432415 = z;
        double r432416 = r432415 - r432413;
        double r432417 = r432414 * r432416;
        double r432418 = t;
        double r432419 = r432417 / r432418;
        double r432420 = r432413 + r432419;
        return r432420;
}
↓
double f(double x, double y, double z, double t) {
        double r432421 = x;
        double r432422 = y;
        double r432423 = z;
        double r432424 = r432423 - r432421;
        double r432425 = r432422 * r432424;
        double r432426 = t;
        double r432427 = r432425 / r432426;
        double r432428 = r432421 + r432427;
        double r432429 = -inf.0;
        bool r432430 = r432428 <= r432429;
        double r432431 = 1.0029303448615336e+296;
        bool r432432 = r432428 <= r432431;
        double r432433 = !r432432;
        bool r432434 = r432430 || r432433;
        double r432435 = 1.0;
        double r432436 = r432426 / r432424;
        double r432437 = r432435 / r432436;
        double r432438 = r432422 * r432437;
        double r432439 = r432421 + r432438;
        double r432440 = r432434 ? r432439 : r432428;
        return r432440;
}

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 
(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)))