Average Error: 15.1 → 3.7
Time: 10.6s
Precision: 64
\[x \cdot \frac{\frac{y}{z} \cdot t}{t}\]
↓
\[\begin{array}{l} \mathbf{if}\;\frac{y}{z} \le -1.63086994211637596483956921546385031623 \cdot 10^{66}:\\ \;\;\;\;\frac{y \cdot x}{z}\\ \mathbf{elif}\;\frac{y}{z} \le -6.545487680777495021156682531032583832353 \cdot 10^{-230}:\\ \;\;\;\;\frac{y}{z} \cdot x\\ \mathbf{elif}\;\frac{y}{z} \le 4.814036022956164419199695264571075550494 \cdot 10^{-12}:\\ \;\;\;\;\frac{y \cdot x}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{\frac{z}{x}}\\ \end{array}\]
x \cdot \frac{\frac{y}{z} \cdot t}{t}
↓
\begin{array}{l}
\mathbf{if}\;\frac{y}{z} \le -1.63086994211637596483956921546385031623 \cdot 10^{66}:\\
\;\;\;\;\frac{y \cdot x}{z}\\

\mathbf{elif}\;\frac{y}{z} \le -6.545487680777495021156682531032583832353 \cdot 10^{-230}:\\
\;\;\;\;\frac{y}{z} \cdot x\\

\mathbf{elif}\;\frac{y}{z} \le 4.814036022956164419199695264571075550494 \cdot 10^{-12}:\\
\;\;\;\;\frac{y \cdot x}{z}\\

\mathbf{else}:\\
\;\;\;\;\frac{y}{\frac{z}{x}}\\

\end{array}
double f(double x, double y, double z, double t) {
        double r62994 = x;
        double r62995 = y;
        double r62996 = z;
        double r62997 = r62995 / r62996;
        double r62998 = t;
        double r62999 = r62997 * r62998;
        double r63000 = r62999 / r62998;
        double r63001 = r62994 * r63000;
        return r63001;
}
↓
double f(double x, double y, double z, double __attribute__((unused)) t) {
        double r63002 = y;
        double r63003 = z;
        double r63004 = r63002 / r63003;
        double r63005 = -1.630869942116376e+66;
        bool r63006 = r63004 <= r63005;
        double r63007 = x;
        double r63008 = r63002 * r63007;
        double r63009 = r63008 / r63003;
        double r63010 = -6.545487680777495e-230;
        bool r63011 = r63004 <= r63010;
        double r63012 = r63004 * r63007;
        double r63013 = 4.8140360229561644e-12;
        bool r63014 = r63004 <= r63013;
        double r63015 = r63003 / r63007;
        double r63016 = r63002 / r63015;
        double r63017 = r63014 ? r63009 : r63016;
        double r63018 = r63011 ? r63012 : r63017;
        double r63019 = r63006 ? r63009 : r63018;
        return r63019;
}

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

Derivation

  1. Split input into 3 regimes

  2. if (/ y z) < -1.630869942116376e+66 or -6.545487680777495e-230 < (/ y z) < 4.8140360229561644e-12

    1. Initial program 17.6

      \[x \cdot \frac{\frac{y}{z} \cdot t}{t}\]

    2. Simplified3.9

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

    if -1.630869942116376e+66 < (/ y z) < -6.545487680777495e-230

    1. Initial program 6.5

      \[x \cdot \frac{\frac{y}{z} \cdot t}{t}\]

    2. Simplified9.8

      \[\leadsto \color{blue}{\frac{y \cdot x}{z}}\]
    3. Using strategy rm

    4. Applied associate-/l*9.1

      \[\leadsto \color{blue}{\frac{y}{\frac{z}{x}}}\]
    5. Using strategy rm

    6. Applied associate-/r/0.2

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

    if 4.8140360229561644e-12 < (/ y z)

    1. Initial program 18.7

      \[x \cdot \frac{\frac{y}{z} \cdot t}{t}\]

    2. Simplified8.3

      \[\leadsto \color{blue}{\frac{y \cdot x}{z}}\]
    3. Using strategy rm

    4. Applied associate-/l*7.3

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

  4. Final simplification3.7

    \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{y}{z} \le -1.63086994211637596483956921546385031623 \cdot 10^{66}:\\ \;\;\;\;\frac{y \cdot x}{z}\\ \mathbf{elif}\;\frac{y}{z} \le -6.545487680777495021156682531032583832353 \cdot 10^{-230}:\\ \;\;\;\;\frac{y}{z} \cdot x\\ \mathbf{elif}\;\frac{y}{z} \le 4.814036022956164419199695264571075550494 \cdot 10^{-12}:\\ \;\;\;\;\frac{y \cdot x}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{\frac{z}{x}}\\ \end{array}\]

Reproduce

herbie shell --seed 2019208 
(FPCore (x y z t)
  :name "Graphics.Rendering.Chart.Backend.Diagrams:calcFontMetrics from Chart-diagrams-1.5.1"
  :precision binary64
  (* x (/ (* (/ y z) t) t)))