Average Error: 14.5 → 0.6
Time: 17.5s
Precision: 64
\[x \cdot \frac{\frac{y}{z} \cdot t}{t}\]
↓
\[\begin{array}{l} \mathbf{if}\;\frac{y}{z} \le -5.088450935899302 \cdot 10^{+226}:\\ \;\;\;\;y \cdot \frac{x}{z}\\ \mathbf{elif}\;\frac{y}{z} \le -2.5749346451873716 \cdot 10^{-156}:\\ \;\;\;\;\frac{y}{z} \cdot x\\ \mathbf{elif}\;\frac{y}{z} \le 4.6204979673822 \cdot 10^{-317}:\\ \;\;\;\;\frac{x \cdot y}{z}\\ \mathbf{elif}\;\frac{y}{z} \le 4.2714341334416977 \cdot 10^{+201}:\\ \;\;\;\;\frac{x}{\frac{z}{y}}\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{x}{z}\\ \end{array}\]
x \cdot \frac{\frac{y}{z} \cdot t}{t}
↓
\begin{array}{l}
\mathbf{if}\;\frac{y}{z} \le -5.088450935899302 \cdot 10^{+226}:\\
\;\;\;\;y \cdot \frac{x}{z}\\

\mathbf{elif}\;\frac{y}{z} \le -2.5749346451873716 \cdot 10^{-156}:\\
\;\;\;\;\frac{y}{z} \cdot x\\

\mathbf{elif}\;\frac{y}{z} \le 4.6204979673822 \cdot 10^{-317}:\\
\;\;\;\;\frac{x \cdot y}{z}\\

\mathbf{elif}\;\frac{y}{z} \le 4.2714341334416977 \cdot 10^{+201}:\\
\;\;\;\;\frac{x}{\frac{z}{y}}\\

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

\end{array}
double f(double x, double y, double z, double t) {
        double r23894059 = x;
        double r23894060 = y;
        double r23894061 = z;
        double r23894062 = r23894060 / r23894061;
        double r23894063 = t;
        double r23894064 = r23894062 * r23894063;
        double r23894065 = r23894064 / r23894063;
        double r23894066 = r23894059 * r23894065;
        return r23894066;
}
↓
double f(double x, double y, double z, double __attribute__((unused)) t) {
        double r23894067 = y;
        double r23894068 = z;
        double r23894069 = r23894067 / r23894068;
        double r23894070 = -5.088450935899302e+226;
        bool r23894071 = r23894069 <= r23894070;
        double r23894072 = x;
        double r23894073 = r23894072 / r23894068;
        double r23894074 = r23894067 * r23894073;
        double r23894075 = -2.5749346451873716e-156;
        bool r23894076 = r23894069 <= r23894075;
        double r23894077 = r23894069 * r23894072;
        double r23894078 = 4.6204979673822e-317;
        bool r23894079 = r23894069 <= r23894078;
        double r23894080 = r23894072 * r23894067;
        double r23894081 = r23894080 / r23894068;
        double r23894082 = 4.2714341334416977e+201;
        bool r23894083 = r23894069 <= r23894082;
        double r23894084 = r23894068 / r23894067;
        double r23894085 = r23894072 / r23894084;
        double r23894086 = r23894083 ? r23894085 : r23894074;
        double r23894087 = r23894079 ? r23894081 : r23894086;
        double r23894088 = r23894076 ? r23894077 : r23894087;
        double r23894089 = r23894071 ? r23894074 : r23894088;
        return r23894089;
}

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

Original14.5
Target1.5
Herbie0.6
\[\begin{array}{l} \mathbf{if}\;\frac{\frac{y}{z} \cdot t}{t} \lt -1.20672205123045 \cdot 10^{+245}:\\ \;\;\;\;\frac{y}{\frac{z}{x}}\\ \mathbf{elif}\;\frac{\frac{y}{z} \cdot t}{t} \lt -5.907522236933906 \cdot 10^{-275}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \mathbf{elif}\;\frac{\frac{y}{z} \cdot t}{t} \lt 5.658954423153415 \cdot 10^{-65}:\\ \;\;\;\;\frac{y}{\frac{z}{x}}\\ \mathbf{elif}\;\frac{\frac{y}{z} \cdot t}{t} \lt 2.0087180502407133 \cdot 10^{+217}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{y \cdot x}{z}\\ \end{array}\]

Derivation

  1. Split input into 4 regimes

  2. if (/ y z) < -5.088450935899302e+226 or 4.2714341334416977e+201 < (/ y z)

    1. Initial program 41.2

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

    2. Simplified0.9

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

    if -5.088450935899302e+226 < (/ y z) < -2.5749346451873716e-156

    1. Initial program 8.0

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

    2. Simplified9.6

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

    3. Taylor expanded around 0 9.2

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

    5. Applied *-un-lft-identity9.2

      \[\leadsto \frac{x \cdot y}{\color{blue}{1 \cdot z}}\]

    6. Applied times-frac0.3

      \[\leadsto \color{blue}{\frac{x}{1} \cdot \frac{y}{z}}\]

    7. Simplified0.3

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

    if -2.5749346451873716e-156 < (/ y z) < 4.6204979673822e-317

    1. Initial program 17.5

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

    2. Simplified0.6

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

    3. Taylor expanded around 0 0.9

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

    if 4.6204979673822e-317 < (/ y z) < 4.2714341334416977e+201

    1. Initial program 9.0

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

    2. Simplified7.7

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

    3. Taylor expanded around 0 8.2

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

    5. Applied associate-/l*0.5

      \[\leadsto \color{blue}{\frac{x}{\frac{z}{y}}}\]
  3. Recombined 4 regimes into one program.

  4. Final simplification0.6

    \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{y}{z} \le -5.088450935899302 \cdot 10^{+226}:\\ \;\;\;\;y \cdot \frac{x}{z}\\ \mathbf{elif}\;\frac{y}{z} \le -2.5749346451873716 \cdot 10^{-156}:\\ \;\;\;\;\frac{y}{z} \cdot x\\ \mathbf{elif}\;\frac{y}{z} \le 4.6204979673822 \cdot 10^{-317}:\\ \;\;\;\;\frac{x \cdot y}{z}\\ \mathbf{elif}\;\frac{y}{z} \le 4.2714341334416977 \cdot 10^{+201}:\\ \;\;\;\;\frac{x}{\frac{z}{y}}\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{x}{z}\\ \end{array}\]

Reproduce

herbie shell --seed 2019164 +o rules:numerics
(FPCore (x y z t)
  :name "Graphics.Rendering.Chart.Backend.Diagrams:calcFontMetrics from Chart-diagrams-1.5.1, B"

  :herbie-target
  (if (< (/ (* (/ y z) t) t) -1.20672205123045e+245) (/ y (/ z x)) (if (< (/ (* (/ y z) t) t) -5.907522236933906e-275) (* x (/ y z)) (if (< (/ (* (/ y z) t) t) 5.658954423153415e-65) (/ y (/ z x)) (if (< (/ (* (/ y z) t) t) 2.0087180502407133e+217) (* x (/ y z)) (/ (* y x) z)))))

  (* x (/ (* (/ y z) t) t)))