Average Error: 6.2 → 0.8
Time: 12.0s
Precision: 64
\[x + \frac{y \cdot \left(z - x\right)}{t}\]
↓
\[\begin{array}{l} \mathbf{if}\;x + \frac{y \cdot \left(z - x\right)}{t} \le -3.57164337169283755 \cdot 10^{297}:\\ \;\;\;\;x + \frac{z - x}{\frac{t}{y}}\\ \mathbf{elif}\;x + \frac{y \cdot \left(z - x\right)}{t} \le 1.83014942255142419 \cdot 10^{297}:\\ \;\;\;\;x + \frac{y \cdot \left(z - x\right)}{t}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{t}{z - x}}\\ \end{array}\]
x + \frac{y \cdot \left(z - x\right)}{t}
↓
\begin{array}{l}
\mathbf{if}\;x + \frac{y \cdot \left(z - x\right)}{t} \le -3.57164337169283755 \cdot 10^{297}:\\
\;\;\;\;x + \frac{z - x}{\frac{t}{y}}\\

\mathbf{elif}\;x + \frac{y \cdot \left(z - x\right)}{t} \le 1.83014942255142419 \cdot 10^{297}:\\
\;\;\;\;x + \frac{y \cdot \left(z - x\right)}{t}\\

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

\end{array}
double f(double x, double y, double z, double t) {
        double r362305 = x;
        double r362306 = y;
        double r362307 = z;
        double r362308 = r362307 - r362305;
        double r362309 = r362306 * r362308;
        double r362310 = t;
        double r362311 = r362309 / r362310;
        double r362312 = r362305 + r362311;
        return r362312;
}
↓
double f(double x, double y, double z, double t) {
        double r362313 = x;
        double r362314 = y;
        double r362315 = z;
        double r362316 = r362315 - r362313;
        double r362317 = r362314 * r362316;
        double r362318 = t;
        double r362319 = r362317 / r362318;
        double r362320 = r362313 + r362319;
        double r362321 = -3.5716433716928375e+297;
        bool r362322 = r362320 <= r362321;
        double r362323 = r362318 / r362314;
        double r362324 = r362316 / r362323;
        double r362325 = r362313 + r362324;
        double r362326 = 1.8301494225514242e+297;
        bool r362327 = r362320 <= r362326;
        double r362328 = r362318 / r362316;
        double r362329 = r362314 / r362328;
        double r362330 = r362313 + r362329;
        double r362331 = r362327 ? r362320 : r362330;
        double r362332 = r362322 ? r362325 : r362331;
        return r362332;
}

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

Original6.2
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)) < -3.5716433716928375e+297

    1. Initial program 51.7

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

    2. Taylor expanded around 0 51.7

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

    3. Simplified1.4

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

    if -3.5716433716928375e+297 < (+ x (/ (* y (- z x)) t)) < 1.8301494225514242e+297

    1. Initial program 0.6

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

    if 1.8301494225514242e+297 < (+ x (/ (* y (- z x)) t))

    1. Initial program 53.1

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

    3. Applied associate-/l*3.0

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

  4. Final simplification0.8

    \[\leadsto \begin{array}{l} \mathbf{if}\;x + \frac{y \cdot \left(z - x\right)}{t} \le -3.57164337169283755 \cdot 10^{297}:\\ \;\;\;\;x + \frac{z - x}{\frac{t}{y}}\\ \mathbf{elif}\;x + \frac{y \cdot \left(z - x\right)}{t} \le 1.83014942255142419 \cdot 10^{297}:\\ \;\;\;\;x + \frac{y \cdot \left(z - x\right)}{t}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{t}{z - x}}\\ \end{array}\]

Reproduce

herbie shell --seed 2020046 
(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)))