Average Error: 15.2 → 2.1
Time: 2.9s
Precision: 64
\[x \cdot \frac{\frac{y}{z} \cdot t}{t}\]
↓
\[\begin{array}{l} \mathbf{if}\;\frac{y}{z} = -\infty:\\ \;\;\;\;\left(x \cdot y\right) \cdot \frac{1}{z}\\ \mathbf{elif}\;\frac{y}{z} \le -3.69264767565036338 \cdot 10^{-178}:\\ \;\;\;\;\frac{x}{\frac{z}{y}}\\ \mathbf{elif}\;\frac{y}{z} \le 8.1313930047618145 \cdot 10^{-276}:\\ \;\;\;\;\left(x \cdot y\right) \cdot \frac{1}{z}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \end{array}\]
x \cdot \frac{\frac{y}{z} \cdot t}{t}
↓
\begin{array}{l}
\mathbf{if}\;\frac{y}{z} = -\infty:\\
\;\;\;\;\left(x \cdot y\right) \cdot \frac{1}{z}\\

\mathbf{elif}\;\frac{y}{z} \le -3.69264767565036338 \cdot 10^{-178}:\\
\;\;\;\;\frac{x}{\frac{z}{y}}\\

\mathbf{elif}\;\frac{y}{z} \le 8.1313930047618145 \cdot 10^{-276}:\\
\;\;\;\;\left(x \cdot y\right) \cdot \frac{1}{z}\\

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

\end{array}
double code(double x, double y, double z, double t) {
	return (x * (((y / z) * t) / t));
}
↓
double code(double x, double y, double z, double t) {
	double temp;
	if (((y / z) <= -inf.0)) {
		temp = ((x * y) * (1.0 / z));
	} else {
		double temp_1;
		if (((y / z) <= -3.6926476756503634e-178)) {
			temp_1 = (x / (z / y));
		} else {
			double temp_2;
			if (((y / z) <= 8.131393004761814e-276)) {
				temp_2 = ((x * y) * (1.0 / z));
			} else {
				temp_2 = (x * (y / z));
			}
			temp_1 = temp_2;
		}
		temp = temp_1;
	}
	return temp;
}

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) < -inf.0 or -3.6926476756503634e-178 < (/ y z) < 8.131393004761814e-276

    1. Initial program 22.5

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

    2. Simplified17.3

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

    4. Applied *-un-lft-identity17.3

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

    5. Applied add-cube-cbrt17.5

      \[\leadsto x \cdot \frac{\color{blue}{\left(\sqrt[3]{y} \cdot \sqrt[3]{y}\right) \cdot \sqrt[3]{y}}}{1 \cdot z}\]

    6. Applied times-frac17.5

      \[\leadsto x \cdot \color{blue}{\left(\frac{\sqrt[3]{y} \cdot \sqrt[3]{y}}{1} \cdot \frac{\sqrt[3]{y}}{z}\right)}\]

    7. Applied associate-*r*4.1

      \[\leadsto \color{blue}{\left(x \cdot \frac{\sqrt[3]{y} \cdot \sqrt[3]{y}}{1}\right) \cdot \frac{\sqrt[3]{y}}{z}}\]

    8. Simplified4.1

      \[\leadsto \color{blue}{\left(x \cdot \left(\sqrt[3]{y} \cdot \sqrt[3]{y}\right)\right)} \cdot \frac{\sqrt[3]{y}}{z}\]
    9. Using strategy rm

    10. Applied div-inv4.1

      \[\leadsto \left(x \cdot \left(\sqrt[3]{y} \cdot \sqrt[3]{y}\right)\right) \cdot \color{blue}{\left(\sqrt[3]{y} \cdot \frac{1}{z}\right)}\]

    11. Applied associate-*r*1.1

      \[\leadsto \color{blue}{\left(\left(x \cdot \left(\sqrt[3]{y} \cdot \sqrt[3]{y}\right)\right) \cdot \sqrt[3]{y}\right) \cdot \frac{1}{z}}\]

    12. Simplified0.6

      \[\leadsto \color{blue}{\left(x \cdot y\right)} \cdot \frac{1}{z}\]

    if -inf.0 < (/ y z) < -3.6926476756503634e-178

    1. Initial program 9.9

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

    2. Simplified0.2

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

    4. Applied clear-num0.3

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

    5. Applied un-div-inv0.2

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

    if 8.131393004761814e-276 < (/ y z)

    1. Initial program 14.5

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

    2. Simplified4.5

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

  4. Final simplification2.1

    \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{y}{z} = -\infty:\\ \;\;\;\;\left(x \cdot y\right) \cdot \frac{1}{z}\\ \mathbf{elif}\;\frac{y}{z} \le -3.69264767565036338 \cdot 10^{-178}:\\ \;\;\;\;\frac{x}{\frac{z}{y}}\\ \mathbf{elif}\;\frac{y}{z} \le 8.1313930047618145 \cdot 10^{-276}:\\ \;\;\;\;\left(x \cdot y\right) \cdot \frac{1}{z}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \end{array}\]

Reproduce

herbie shell --seed 2020066 +o rules:numerics
(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)))