Average Error: 6.5 → 1.0
Time: 25.0s
Precision: 64
\[x + \frac{y \cdot \left(z - x\right)}{t}\]
↓
\[\begin{array}{l} \mathbf{if}\;x + \frac{y \cdot \left(z - x\right)}{t} = -\infty:\\ \;\;\;\;\mathsf{fma}\left(\frac{y}{t}, z - x, x\right)\\ \mathbf{elif}\;x + \frac{y \cdot \left(z - x\right)}{t} \le 1.182849089073599646632869886806705569477 \cdot 10^{250}:\\ \;\;\;\;x + \frac{y \cdot \left(z - x\right)}{t}\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\frac{y}{t}, z - x, x\right)\\ \end{array}\]
x + \frac{y \cdot \left(z - x\right)}{t}
↓
\begin{array}{l}
\mathbf{if}\;x + \frac{y \cdot \left(z - x\right)}{t} = -\infty:\\
\;\;\;\;\mathsf{fma}\left(\frac{y}{t}, z - x, x\right)\\

\mathbf{elif}\;x + \frac{y \cdot \left(z - x\right)}{t} \le 1.182849089073599646632869886806705569477 \cdot 10^{250}:\\
\;\;\;\;x + \frac{y \cdot \left(z - x\right)}{t}\\

\mathbf{else}:\\
\;\;\;\;\mathsf{fma}\left(\frac{y}{t}, z - x, x\right)\\

\end{array}
double f(double x, double y, double z, double t) {
        double r40332092 = x;
        double r40332093 = y;
        double r40332094 = z;
        double r40332095 = r40332094 - r40332092;
        double r40332096 = r40332093 * r40332095;
        double r40332097 = t;
        double r40332098 = r40332096 / r40332097;
        double r40332099 = r40332092 + r40332098;
        return r40332099;
}
↓
double f(double x, double y, double z, double t) {
        double r40332100 = x;
        double r40332101 = y;
        double r40332102 = z;
        double r40332103 = r40332102 - r40332100;
        double r40332104 = r40332101 * r40332103;
        double r40332105 = t;
        double r40332106 = r40332104 / r40332105;
        double r40332107 = r40332100 + r40332106;
        double r40332108 = -inf.0;
        bool r40332109 = r40332107 <= r40332108;
        double r40332110 = r40332101 / r40332105;
        double r40332111 = fma(r40332110, r40332103, r40332100);
        double r40332112 = 1.1828490890735996e+250;
        bool r40332113 = r40332107 <= r40332112;
        double r40332114 = r40332113 ? r40332107 : r40332111;
        double r40332115 = r40332109 ? r40332111 : r40332114;
        return r40332115;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Bits error versus t

Target

Original6.5
Target2.3
Herbie1.0
\[x - \left(x \cdot \frac{y}{t} + \left(-z\right) \cdot \frac{y}{t}\right)\]

Derivation

  1. Split input into 2 regimes

  2. if (+ x (/ (* y (- z x)) t)) < -inf.0 or 1.1828490890735996e+250 < (+ x (/ (* y (- z x)) t))

    1. Initial program 39.9

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

    2. Simplified2.3

      \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{y}{t}, z - x, x\right)}\]

    if -inf.0 < (+ x (/ (* y (- z x)) t)) < 1.1828490890735996e+250

    1. Initial program 0.8

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

  4. Final simplification1.0

    \[\leadsto \begin{array}{l} \mathbf{if}\;x + \frac{y \cdot \left(z - x\right)}{t} = -\infty:\\ \;\;\;\;\mathsf{fma}\left(\frac{y}{t}, z - x, x\right)\\ \mathbf{elif}\;x + \frac{y \cdot \left(z - x\right)}{t} \le 1.182849089073599646632869886806705569477 \cdot 10^{250}:\\ \;\;\;\;x + \frac{y \cdot \left(z - x\right)}{t}\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\frac{y}{t}, z - x, x\right)\\ \end{array}\]

Reproduce

herbie shell --seed 2019173 +o rules:numerics
(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)))