Average Error: 14.0 → 3.2
Time: 2.7s
Precision: 64
\[x \cdot \frac{\frac{y}{z} \cdot t}{t}\]
↓
\[\begin{array}{l} \mathbf{if}\;\frac{y}{z} \le -1.16452267223055705 \cdot 10^{-227}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \mathbf{elif}\;\frac{y}{z} \le 0.0:\\ \;\;\;\;\frac{x \cdot y}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\frac{z}{y}}\\ \end{array}\]
x \cdot \frac{\frac{y}{z} \cdot t}{t}
↓
\begin{array}{l}
\mathbf{if}\;\frac{y}{z} \le -1.16452267223055705 \cdot 10^{-227}:\\
\;\;\;\;x \cdot \frac{y}{z}\\

\mathbf{elif}\;\frac{y}{z} \le 0.0:\\
\;\;\;\;\frac{x \cdot y}{z}\\

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

\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) <= -1.164522672230557e-227)) {
		VAR = (x * (y / z));
	} else {
		double VAR_1;
		if (((y / z) <= 0.0)) {
			VAR_1 = ((x * y) / z);
		} else {
			VAR_1 = (x / (z / y));
		}
		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

Derivation

  1. Split input into 3 regimes

  2. if (/ y z) < -1.164522672230557e-227

    1. Initial program 12.7

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

    2. Simplified3.9

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

    if -1.164522672230557e-227 < (/ y z) < 0.0

    1. Initial program 17.6

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

    2. Simplified13.6

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

    4. Applied associate-*r/0.2

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

    if 0.0 < (/ y z)

    1. Initial program 13.7

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

    2. Simplified4.1

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

    4. Applied associate-*r/7.4

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

    6. Applied associate-/l*3.9

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

  4. Final simplification3.2

    \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{y}{z} \le -1.16452267223055705 \cdot 10^{-227}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \mathbf{elif}\;\frac{y}{z} \le 0.0:\\ \;\;\;\;\frac{x \cdot y}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\frac{z}{y}}\\ \end{array}\]

Reproduce

herbie shell --seed 2020102 +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)))