Average Error: 14.2 → 0.4
Time: 3.6s
Precision: 64
\[x \cdot \frac{\frac{y}{z} \cdot t}{t}\]
↓
\[\begin{array}{l} \mathbf{if}\;\frac{y}{z} \le -5.77198757729635198 \cdot 10^{244}:\\ \;\;\;\;y \cdot \frac{x}{z}\\ \mathbf{elif}\;\frac{y}{z} \le -2.09577494757252 \cdot 10^{-174}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \mathbf{elif}\;\frac{y}{z} \le 1.2250350955876178 \cdot 10^{-236}:\\ \;\;\;\;\frac{x \cdot y}{z}\\ \mathbf{elif}\;\frac{y}{z} \le 3.34650733303407685 \cdot 10^{227}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;\left(x \cdot y\right) \cdot \frac{1}{z}\\ \end{array}\]
x \cdot \frac{\frac{y}{z} \cdot t}{t}
↓
\begin{array}{l}
\mathbf{if}\;\frac{y}{z} \le -5.77198757729635198 \cdot 10^{244}:\\
\;\;\;\;y \cdot \frac{x}{z}\\

\mathbf{elif}\;\frac{y}{z} \le -2.09577494757252 \cdot 10^{-174}:\\
\;\;\;\;x \cdot \frac{y}{z}\\

\mathbf{elif}\;\frac{y}{z} \le 1.2250350955876178 \cdot 10^{-236}:\\
\;\;\;\;\frac{x \cdot y}{z}\\

\mathbf{elif}\;\frac{y}{z} \le 3.34650733303407685 \cdot 10^{227}:\\
\;\;\;\;x \cdot \frac{y}{z}\\

\mathbf{else}:\\
\;\;\;\;\left(x \cdot y\right) \cdot \frac{1}{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 VAR;
	if (((y / z) <= -5.771987577296352e+244)) {
		VAR = (y * (x / z));
	} else {
		double VAR_1;
		if (((y / z) <= -2.09577494757252e-174)) {
			VAR_1 = (x * (y / z));
		} else {
			double VAR_2;
			if (((y / z) <= 1.2250350955876178e-236)) {
				VAR_2 = ((x * y) / z);
			} else {
				double VAR_3;
				if (((y / z) <= 3.346507333034077e+227)) {
					VAR_3 = (x * (y / z));
				} else {
					VAR_3 = ((x * y) * (1.0 / z));
				}
				VAR_2 = VAR_3;
			}
			VAR_1 = VAR_2;
		}
		VAR = VAR_1;
	}
	return VAR;
}

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

Original14.2
Target1.6
Herbie0.4
\[\begin{array}{l} \mathbf{if}\;\frac{\frac{y}{z} \cdot t}{t} \lt -1.20672205123045005 \cdot 10^{245}:\\ \;\;\;\;\frac{y}{\frac{z}{x}}\\ \mathbf{elif}\;\frac{\frac{y}{z} \cdot t}{t} \lt -5.90752223693390633 \cdot 10^{-275}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \mathbf{elif}\;\frac{\frac{y}{z} \cdot t}{t} \lt 5.65895442315341522 \cdot 10^{-65}:\\ \;\;\;\;\frac{y}{\frac{z}{x}}\\ \mathbf{elif}\;\frac{\frac{y}{z} \cdot t}{t} \lt 2.0087180502407133 \cdot 10^{217}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{y \cdot x}{z}\\ \end{array}\]

Derivation

  1. Split input into 4 regimes

  2. if (/ y z) < -5.771987577296352e+244

    1. Initial program 49.3

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

    2. Simplified35.0

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

    4. Applied *-un-lft-identity35.0

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

    5. Applied add-cube-cbrt35.5

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

    6. Applied times-frac35.5

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

    7. Applied associate-*r*8.7

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

    8. Simplified8.7

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

    10. Applied associate-*l*9.0

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

    11. Taylor expanded around 0 0.5

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

    12. Simplified0.6

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

    if -5.771987577296352e+244 < (/ y z) < -2.09577494757252e-174 or 1.2250350955876178e-236 < (/ y z) < 3.346507333034077e+227

    1. Initial program 8.5

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

    2. Simplified0.2

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

    if -2.09577494757252e-174 < (/ y z) < 1.2250350955876178e-236

    1. Initial program 16.1

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

    2. Simplified10.1

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

    4. Applied associate-*r/0.6

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

    if 3.346507333034077e+227 < (/ y z)

    1. Initial program 46.5

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

    2. Simplified32.2

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

    4. Applied div-inv32.3

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

    5. Applied associate-*r*1.0

      \[\leadsto \color{blue}{\left(x \cdot y\right) \cdot \frac{1}{z}}\]
  3. Recombined 4 regimes into one program.

  4. Final simplification0.4

    \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{y}{z} \le -5.77198757729635198 \cdot 10^{244}:\\ \;\;\;\;y \cdot \frac{x}{z}\\ \mathbf{elif}\;\frac{y}{z} \le -2.09577494757252 \cdot 10^{-174}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \mathbf{elif}\;\frac{y}{z} \le 1.2250350955876178 \cdot 10^{-236}:\\ \;\;\;\;\frac{x \cdot y}{z}\\ \mathbf{elif}\;\frac{y}{z} \le 3.34650733303407685 \cdot 10^{227}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;\left(x \cdot y\right) \cdot \frac{1}{z}\\ \end{array}\]

Reproduce

herbie shell --seed 2020075 
(FPCore (x y z t)
  :name "Graphics.Rendering.Chart.Backend.Diagrams:calcFontMetrics from Chart-diagrams-1.5.1, B"
  :precision binary64

  :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)))