Average Error: 15.3 → 1.5
Time: 12.5s
Precision: binary64
\[[x, y]=\mathsf{sort}([x, y])\]
\[x \cdot \frac{\frac{y}{z} \cdot t}{t} \]
↓
\[\begin{array}{l} \mathbf{if}\;\frac{y}{z} \leq -2.2357824457939506 \cdot 10^{+126}:\\ \;\;\;\;\frac{y}{\frac{z}{x}}\\ \mathbf{elif}\;\frac{y}{z} \leq -1.419433575819517 \cdot 10^{-271}:\\ \;\;\;\;\frac{y}{z} \cdot x\\ \mathbf{else}:\\ \;\;\;\;\left(x \cdot \frac{{\left(\sqrt[3]{y}\right)}^{2}}{\sqrt[3]{z} \cdot \sqrt[3]{z}}\right) \cdot \frac{\sqrt[3]{y}}{\sqrt[3]{z}}\\ \end{array} \]
x \cdot \frac{\frac{y}{z} \cdot t}{t}
↓
\begin{array}{l}
\mathbf{if}\;\frac{y}{z} \leq -2.2357824457939506 \cdot 10^{+126}:\\
\;\;\;\;\frac{y}{\frac{z}{x}}\\

\mathbf{elif}\;\frac{y}{z} \leq -1.419433575819517 \cdot 10^{-271}:\\
\;\;\;\;\frac{y}{z} \cdot x\\

\mathbf{else}:\\
\;\;\;\;\left(x \cdot \frac{{\left(\sqrt[3]{y}\right)}^{2}}{\sqrt[3]{z} \cdot \sqrt[3]{z}}\right) \cdot \frac{\sqrt[3]{y}}{\sqrt[3]{z}}\\


\end{array}

(FPCore (x y z t) :precision binary64 (* x (/ (* (/ y z) t) t)))
↓
(FPCore (x y z t)
 :precision binary64
 (if (<= (/ y z) -2.2357824457939506e+126)
   (/ y (/ z x))
   (if (<= (/ y z) -1.419433575819517e-271)
     (* (/ y z) x)
     (*
      (* x (/ (pow (cbrt y) 2.0) (* (cbrt z) (cbrt z))))
      (/ (cbrt y) (cbrt z))))))
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 tmp;
	if ((y / z) <= -2.2357824457939506e+126) {
		tmp = y / (z / x);
	} else if ((y / z) <= -1.419433575819517e-271) {
		tmp = (y / z) * x;
	} else {
		tmp = (x * (pow(cbrt(y), 2.0) / (cbrt(z) * cbrt(z)))) * (cbrt(y) / cbrt(z));
	}
	return tmp;
}

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

Original15.3
Target1.4
Herbie1.5
\[\begin{array}{l} \mathbf{if}\;\frac{\frac{y}{z} \cdot t}{t} < -1.20672205123045 \cdot 10^{+245}:\\ \;\;\;\;\frac{y}{\frac{z}{x}}\\ \mathbf{elif}\;\frac{\frac{y}{z} \cdot t}{t} < -5.907522236933906 \cdot 10^{-275}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \mathbf{elif}\;\frac{\frac{y}{z} \cdot t}{t} < 5.658954423153415 \cdot 10^{-65}:\\ \;\;\;\;\frac{y}{\frac{z}{x}}\\ \mathbf{elif}\;\frac{\frac{y}{z} \cdot t}{t} < 2.0087180502407133 \cdot 10^{+217}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{y \cdot x}{z}\\ \end{array} \]

Derivation

  1. Split input into 3 regimes

  2. if (/.f64 y z) < -2.23578244579395063e126

    1. Initial program 33.7

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

    2. Simplified17.1

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

    3. Taylor expanded in x around 0 3.5

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

    4. Applied associate-/l*_binary642.7

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

    if -2.23578244579395063e126 < (/.f64 y z) < -1.419433575819517e-271

    1. Initial program 8.1

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

    2. Simplified0.2

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

    if -1.419433575819517e-271 < (/.f64 y z)

    1. Initial program 15.9

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

    2. Simplified7.7

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

    3. Applied add-cube-cbrt_binary648.4

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

    4. Applied add-cube-cbrt_binary648.5

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

    5. Applied times-frac_binary648.6

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

    6. Applied associate-*r*_binary642.0

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

    7. Applied pow2_binary642.0

      \[\leadsto \left(x \cdot \frac{\color{blue}{{\left(\sqrt[3]{y}\right)}^{2}}}{\sqrt[3]{z} \cdot \sqrt[3]{z}}\right) \cdot \frac{\sqrt[3]{y}}{\sqrt[3]{z}} \]
  3. Recombined 3 regimes into one program.

  4. Final simplification1.5

    \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{y}{z} \leq -2.2357824457939506 \cdot 10^{+126}:\\ \;\;\;\;\frac{y}{\frac{z}{x}}\\ \mathbf{elif}\;\frac{y}{z} \leq -1.419433575819517 \cdot 10^{-271}:\\ \;\;\;\;\frac{y}{z} \cdot x\\ \mathbf{else}:\\ \;\;\;\;\left(x \cdot \frac{{\left(\sqrt[3]{y}\right)}^{2}}{\sqrt[3]{z} \cdot \sqrt[3]{z}}\right) \cdot \frac{\sqrt[3]{y}}{\sqrt[3]{z}}\\ \end{array} \]

Reproduce

herbie shell --seed 2021275 
(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)))