Average Error: 6.5 → 0.7
Time: 21.0s
Precision: 64
\[x + \frac{y \cdot \left(z - x\right)}{t}\]
↓
\[\begin{array}{l} \mathbf{if}\;x + \frac{\left(z - x\right) \cdot y}{t} = -\infty \lor \neg \left(x + \frac{\left(z - x\right) \cdot y}{t} \le 1.736602043278335244176392881295697323332 \cdot 10^{303}\right):\\ \;\;\;\;\mathsf{fma}\left(z - x, \frac{y}{t}, x\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{\left(z - x\right) \cdot y}{t}\\ \end{array}\]
x + \frac{y \cdot \left(z - x\right)}{t}
↓
\begin{array}{l}
\mathbf{if}\;x + \frac{\left(z - x\right) \cdot y}{t} = -\infty \lor \neg \left(x + \frac{\left(z - x\right) \cdot y}{t} \le 1.736602043278335244176392881295697323332 \cdot 10^{303}\right):\\
\;\;\;\;\mathsf{fma}\left(z - x, \frac{y}{t}, x\right)\\

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

\end{array}
double f(double x, double y, double z, double t) {
        double r186153 = x;
        double r186154 = y;
        double r186155 = z;
        double r186156 = r186155 - r186153;
        double r186157 = r186154 * r186156;
        double r186158 = t;
        double r186159 = r186157 / r186158;
        double r186160 = r186153 + r186159;
        return r186160;
}
↓
double f(double x, double y, double z, double t) {
        double r186161 = x;
        double r186162 = z;
        double r186163 = r186162 - r186161;
        double r186164 = y;
        double r186165 = r186163 * r186164;
        double r186166 = t;
        double r186167 = r186165 / r186166;
        double r186168 = r186161 + r186167;
        double r186169 = -inf.0;
        bool r186170 = r186168 <= r186169;
        double r186171 = 1.7366020432783352e+303;
        bool r186172 = r186168 <= r186171;
        double r186173 = !r186172;
        bool r186174 = r186170 || r186173;
        double r186175 = r186164 / r186166;
        double r186176 = fma(r186163, r186175, r186161);
        double r186177 = r186174 ? r186176 : r186168;
        return r186177;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Bits error versus t

Target

Original6.5
Target2.1
Herbie0.7
\[x - \left(x \cdot \frac{y}{t} + \left(-z\right) \cdot \frac{y}{t}\right)\]

Derivation

  1. Split input into 2 regimes

  2. if (+ x (/ (* y (- z x)) t)) < -inf.0 or 1.7366020432783352e+303 < (+ x (/ (* y (- z x)) t))

    1. Initial program 60.7

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

    2. Simplified0.6

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

    if -inf.0 < (+ x (/ (* y (- z x)) t)) < 1.7366020432783352e+303

    1. Initial program 0.7

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

  4. Final simplification0.7

    \[\leadsto \begin{array}{l} \mathbf{if}\;x + \frac{\left(z - x\right) \cdot y}{t} = -\infty \lor \neg \left(x + \frac{\left(z - x\right) \cdot y}{t} \le 1.736602043278335244176392881295697323332 \cdot 10^{303}\right):\\ \;\;\;\;\mathsf{fma}\left(z - x, \frac{y}{t}, x\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{\left(z - x\right) \cdot y}{t}\\ \end{array}\]

Reproduce

herbie shell --seed 2019194 +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)))