Average Error: 6.5 → 0.9
Time: 5.1s
Precision: 64
\[x + \frac{y \cdot \left(z - x\right)}{t}\]
↓
\[\begin{array}{l} \mathbf{if}\;x + \frac{y \cdot \left(z - x\right)}{t} = -\infty \lor \neg \left(x + \frac{y \cdot \left(z - x\right)}{t} \le 4.596907320351968711623976426577643448601 \cdot 10^{299}\right):\\ \;\;\;\;x + y \cdot \frac{z - x}{t}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y \cdot \left(z - x\right)}{t}\\ \end{array}\]
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 4.596907320351968711623976426577643448601 \cdot 10^{299}\right):\\
\;\;\;\;x + y \cdot \frac{z - x}{t}\\

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

\end{array}
double f(double x, double y, double z, double t) {
        double r295173 = x;
        double r295174 = y;
        double r295175 = z;
        double r295176 = r295175 - r295173;
        double r295177 = r295174 * r295176;
        double r295178 = t;
        double r295179 = r295177 / r295178;
        double r295180 = r295173 + r295179;
        return r295180;
}
↓
double f(double x, double y, double z, double t) {
        double r295181 = x;
        double r295182 = y;
        double r295183 = z;
        double r295184 = r295183 - r295181;
        double r295185 = r295182 * r295184;
        double r295186 = t;
        double r295187 = r295185 / r295186;
        double r295188 = r295181 + r295187;
        double r295189 = -inf.0;
        bool r295190 = r295188 <= r295189;
        double r295191 = 4.596907320351969e+299;
        bool r295192 = r295188 <= r295191;
        double r295193 = !r295192;
        bool r295194 = r295190 || r295193;
        double r295195 = r295184 / r295186;
        double r295196 = r295182 * r295195;
        double r295197 = r295181 + r295196;
        double r295198 = r295194 ? r295197 : r295188;
        return r295198;
}

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

Original6.5
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)) < -inf.0 or 4.596907320351969e+299 < (+ 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

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

    if -inf.0 < (+ x (/ (* y (- z x)) t)) < 4.596907320351969e+299

    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

    \[\leadsto \begin{array}{l} \mathbf{if}\;x + \frac{y \cdot \left(z - x\right)}{t} = -\infty \lor \neg \left(x + \frac{y \cdot \left(z - x\right)}{t} \le 4.596907320351968711623976426577643448601 \cdot 10^{299}\right):\\ \;\;\;\;x + y \cdot \frac{z - x}{t}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y \cdot \left(z - x\right)}{t}\\ \end{array}\]

Reproduce

herbie shell --seed 2019353 
(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)))