Average Error: 14.5 → 1.7
Time: 3.9s
Precision: binary64
\[x \cdot \frac{\frac{y}{z} \cdot t}{t}\]
↓
\[\begin{array}{l} \mathbf{if}\;\frac{y}{z} \le -1.4405578742777392 \cdot 10^{-157} \lor \neg \left(\frac{y}{z} \le 1.76874034144091951 \cdot 10^{-306}\right):\\ \;\;\;\;\left(x \cdot \left(\sqrt[3]{y} \cdot \frac{\sqrt[3]{y}}{\sqrt[3]{z} \cdot \sqrt[3]{z}}\right)\right) \cdot \frac{\sqrt[3]{y}}{\sqrt[3]{z}}\\ \mathbf{else}:\\ \;\;\;\;\frac{y \cdot x}{z}\\ \end{array}\]
x \cdot \frac{\frac{y}{z} \cdot t}{t}
↓
\begin{array}{l}
\mathbf{if}\;\frac{y}{z} \le -1.4405578742777392 \cdot 10^{-157} \lor \neg \left(\frac{y}{z} \le 1.76874034144091951 \cdot 10^{-306}\right):\\
\;\;\;\;\left(x \cdot \left(\sqrt[3]{y} \cdot \frac{\sqrt[3]{y}}{\sqrt[3]{z} \cdot \sqrt[3]{z}}\right)\right) \cdot \frac{\sqrt[3]{y}}{\sqrt[3]{z}}\\

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

\end{array}
double code(double x, double y, double z, double t) {
	return ((double) (x * ((double) (((double) (((double) (y / z)) * t)) / t))));
}
↓
double code(double x, double y, double z, double t) {
	double VAR;
	if (((((double) (y / z)) <= -1.4405578742777392e-157) || !(((double) (y / z)) <= 1.7687403414409195e-306))) {
		VAR = ((double) (((double) (x * ((double) (((double) cbrt(y)) * ((double) (((double) cbrt(y)) / ((double) (((double) cbrt(z)) * ((double) cbrt(z)))))))))) * ((double) (((double) cbrt(y)) / ((double) cbrt(z))))));
	} else {
		VAR = ((double) (((double) (y * x)) / z));
	}
	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

Original14.5
Target1.5
Herbie1.7
\[\begin{array}{l} \mathbf{if}\;\frac{\frac{y}{z} \cdot t}{t} \lt -1.20672205123045005 \cdot 10^{245}:\\ \;\;\;\;\frac{y}{\frac{z}{x}}\\ \mathbf{elif}\;\frac{\frac{y}{z} \cdot t}{t} \lt -5.90752223693390633 \cdot 10^{-275}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \mathbf{elif}\;\frac{\frac{y}{z} \cdot t}{t} \lt 5.65895442315341522 \cdot 10^{-65}:\\ \;\;\;\;\frac{y}{\frac{z}{x}}\\ \mathbf{elif}\;\frac{\frac{y}{z} \cdot t}{t} \lt 2.0087180502407133 \cdot 10^{217}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{y \cdot x}{z}\\ \end{array}\]

Derivation

  1. Split input into 2 regimes

  2. if (/ y z) < -1.4405578742777392e-157 or 1.76874034144091951e-306 < (/ y z)

    1. Initial program 13.3

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

    2. Simplified4.2

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

    4. Applied add-cube-cbrt5.2

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

    5. Applied add-cube-cbrt5.4

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

    6. Applied times-frac5.4

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

    7. Applied associate-*r*2.0

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

    8. Simplified2.0

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

    if -1.4405578742777392e-157 < (/ y z) < 1.76874034144091951e-306

    1. Initial program 18.2

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

    2. Simplified11.9

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

    4. Applied associate-*r/0.9

      \[\leadsto \color{blue}{\frac{x \cdot y}{z}}\]
  3. Recombined 2 regimes into one program.

  4. Final simplification1.7

    \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{y}{z} \le -1.4405578742777392 \cdot 10^{-157} \lor \neg \left(\frac{y}{z} \le 1.76874034144091951 \cdot 10^{-306}\right):\\ \;\;\;\;\left(x \cdot \left(\sqrt[3]{y} \cdot \frac{\sqrt[3]{y}}{\sqrt[3]{z} \cdot \sqrt[3]{z}}\right)\right) \cdot \frac{\sqrt[3]{y}}{\sqrt[3]{z}}\\ \mathbf{else}:\\ \;\;\;\;\frac{y \cdot x}{z}\\ \end{array}\]

Reproduce

herbie shell --seed 2020185 
(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)))