Average Error: 6.7 → 0.9
Time: 22.7s
Precision: 64
\[x + \frac{y \cdot \left(z - x\right)}{t}\]
↓
\[\begin{array}{l} \mathbf{if}\;x + \frac{\left(z - x\right) \cdot y}{t} \le -4.015242760717319860347263184406053785305 \cdot 10^{305}:\\ \;\;\;\;x + \frac{y}{\frac{t}{z - x}}\\ \mathbf{elif}\;x + \frac{\left(z - x\right) \cdot y}{t} \le 2.038097847986346269413799617144504707187 \cdot 10^{304}:\\ \;\;\;\;x + \frac{\left(z - x\right) \cdot y}{t}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{t}{z - x}}\\ \end{array}\]
x + \frac{y \cdot \left(z - x\right)}{t}
↓
\begin{array}{l}
\mathbf{if}\;x + \frac{\left(z - x\right) \cdot y}{t} \le -4.015242760717319860347263184406053785305 \cdot 10^{305}:\\
\;\;\;\;x + \frac{y}{\frac{t}{z - x}}\\

\mathbf{elif}\;x + \frac{\left(z - x\right) \cdot y}{t} \le 2.038097847986346269413799617144504707187 \cdot 10^{304}:\\
\;\;\;\;x + \frac{\left(z - x\right) \cdot y}{t}\\

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

\end{array}
double f(double x, double y, double z, double t) {
        double r17331285 = x;
        double r17331286 = y;
        double r17331287 = z;
        double r17331288 = r17331287 - r17331285;
        double r17331289 = r17331286 * r17331288;
        double r17331290 = t;
        double r17331291 = r17331289 / r17331290;
        double r17331292 = r17331285 + r17331291;
        return r17331292;
}
↓
double f(double x, double y, double z, double t) {
        double r17331293 = x;
        double r17331294 = z;
        double r17331295 = r17331294 - r17331293;
        double r17331296 = y;
        double r17331297 = r17331295 * r17331296;
        double r17331298 = t;
        double r17331299 = r17331297 / r17331298;
        double r17331300 = r17331293 + r17331299;
        double r17331301 = -4.01524276071732e+305;
        bool r17331302 = r17331300 <= r17331301;
        double r17331303 = r17331298 / r17331295;
        double r17331304 = r17331296 / r17331303;
        double r17331305 = r17331293 + r17331304;
        double r17331306 = 2.0380978479863463e+304;
        bool r17331307 = r17331300 <= r17331306;
        double r17331308 = r17331307 ? r17331300 : r17331305;
        double r17331309 = r17331302 ? r17331305 : r17331308;
        return r17331309;
}

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

Original6.7
Target2.1
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)) < -4.01524276071732e+305 or 2.0380978479863463e+304 < (+ x (/ (* y (- z x)) t))

    1. Initial program 60.1

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

    3. Applied associate-/l*1.3

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

    if -4.01524276071732e+305 < (+ x (/ (* y (- z x)) t)) < 2.0380978479863463e+304

    1. Initial program 0.8

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

  4. Final simplification0.9

    \[\leadsto \begin{array}{l} \mathbf{if}\;x + \frac{\left(z - x\right) \cdot y}{t} \le -4.015242760717319860347263184406053785305 \cdot 10^{305}:\\ \;\;\;\;x + \frac{y}{\frac{t}{z - x}}\\ \mathbf{elif}\;x + \frac{\left(z - x\right) \cdot y}{t} \le 2.038097847986346269413799617144504707187 \cdot 10^{304}:\\ \;\;\;\;x + \frac{\left(z - x\right) \cdot y}{t}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{t}{z - x}}\\ \end{array}\]

Reproduce

herbie shell --seed 2019172 
(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)))