Average Error: 5.9 → 0.8
Time: 16.6s
Precision: 64
\[x + \frac{y \cdot \left(z - x\right)}{t}\]
↓
\[\begin{array}{l} \mathbf{if}\;x + \frac{\left(z - x\right) \cdot y}{t} = -\infty:\\ \;\;\;\;x + \frac{y}{\frac{t}{z - x}}\\ \mathbf{elif}\;x + \frac{\left(z - x\right) \cdot y}{t} \le 1.3995432143967562 \cdot 10^{+297}:\\ \;\;\;\;x + \frac{\left(z - x\right) \cdot y}{t}\\ \mathbf{else}:\\ \;\;\;\;x + \left(\left(-\frac{y}{t} \cdot x\right) + \frac{y}{t} \cdot z\right)\\ \end{array}\]
x + \frac{y \cdot \left(z - x\right)}{t}
↓
\begin{array}{l}
\mathbf{if}\;x + \frac{\left(z - x\right) \cdot y}{t} = -\infty:\\
\;\;\;\;x + \frac{y}{\frac{t}{z - x}}\\

\mathbf{elif}\;x + \frac{\left(z - x\right) \cdot y}{t} \le 1.3995432143967562 \cdot 10^{+297}:\\
\;\;\;\;x + \frac{\left(z - x\right) \cdot y}{t}\\

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

\end{array}
double f(double x, double y, double z, double t) {
        double r20650393 = x;
        double r20650394 = y;
        double r20650395 = z;
        double r20650396 = r20650395 - r20650393;
        double r20650397 = r20650394 * r20650396;
        double r20650398 = t;
        double r20650399 = r20650397 / r20650398;
        double r20650400 = r20650393 + r20650399;
        return r20650400;
}
↓
double f(double x, double y, double z, double t) {
        double r20650401 = x;
        double r20650402 = z;
        double r20650403 = r20650402 - r20650401;
        double r20650404 = y;
        double r20650405 = r20650403 * r20650404;
        double r20650406 = t;
        double r20650407 = r20650405 / r20650406;
        double r20650408 = r20650401 + r20650407;
        double r20650409 = -inf.0;
        bool r20650410 = r20650408 <= r20650409;
        double r20650411 = r20650406 / r20650403;
        double r20650412 = r20650404 / r20650411;
        double r20650413 = r20650401 + r20650412;
        double r20650414 = 1.3995432143967562e+297;
        bool r20650415 = r20650408 <= r20650414;
        double r20650416 = r20650404 / r20650406;
        double r20650417 = r20650416 * r20650401;
        double r20650418 = -r20650417;
        double r20650419 = r20650416 * r20650402;
        double r20650420 = r20650418 + r20650419;
        double r20650421 = r20650401 + r20650420;
        double r20650422 = r20650415 ? r20650408 : r20650421;
        double r20650423 = r20650410 ? r20650413 : r20650422;
        return r20650423;
}

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

Original5.9
Target2.0
Herbie0.8
\[x - \left(x \cdot \frac{y}{t} + \left(-z\right) \cdot \frac{y}{t}\right)\]

Derivation

  1. Split input into 3 regimes

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

    1. Initial program 60.2

      \[x + \frac{y \cdot \left(z - x\right)}{t}\]
    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)) < 1.3995432143967562e+297

    1. Initial program 0.8

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

    if 1.3995432143967562e+297 < (+ x (/ (* y (- z x)) t))

    1. Initial program 49.0

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

    2. Taylor expanded around 0 49.0

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

    3. Simplified1.5

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

    5. Applied sub-neg1.5

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

    6. Applied distribute-rgt-in1.5

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

  4. Final simplification0.8

    \[\leadsto \begin{array}{l} \mathbf{if}\;x + \frac{\left(z - x\right) \cdot y}{t} = -\infty:\\ \;\;\;\;x + \frac{y}{\frac{t}{z - x}}\\ \mathbf{elif}\;x + \frac{\left(z - x\right) \cdot y}{t} \le 1.3995432143967562 \cdot 10^{+297}:\\ \;\;\;\;x + \frac{\left(z - x\right) \cdot y}{t}\\ \mathbf{else}:\\ \;\;\;\;x + \left(\left(-\frac{y}{t} \cdot x\right) + \frac{y}{t} \cdot z\right)\\ \end{array}\]

Reproduce

herbie shell --seed 2019158 
(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)))