Average Error: 14.6 → 1.1
Time: 3.6s
Precision: binary64
\[x \cdot \frac{\frac{y}{z} \cdot t}{t}\]
↓
\[\begin{array}{l} \mathbf{if}\;\frac{y}{z} \leq -9.718469549340153 \cdot 10^{+143}:\\ \;\;\;\;\frac{y \cdot x}{z}\\ \mathbf{elif}\;\frac{y}{z} \leq -3.63917652177614 \cdot 10^{-103} \lor \neg \left(\frac{y}{z} \leq 5.893930391846604 \cdot 10^{-162}\right) \land \frac{y}{z} \leq 1.1673693186349219 \cdot 10^{+216}:\\ \;\;\;\;\frac{y}{z} \cdot x\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{x}{z}\\ \end{array}\]
x \cdot \frac{\frac{y}{z} \cdot t}{t}
↓
\begin{array}{l}
\mathbf{if}\;\frac{y}{z} \leq -9.718469549340153 \cdot 10^{+143}:\\
\;\;\;\;\frac{y \cdot x}{z}\\

\mathbf{elif}\;\frac{y}{z} \leq -3.63917652177614 \cdot 10^{-103} \lor \neg \left(\frac{y}{z} \leq 5.893930391846604 \cdot 10^{-162}\right) \land \frac{y}{z} \leq 1.1673693186349219 \cdot 10^{+216}:\\
\;\;\;\;\frac{y}{z} \cdot x\\

\mathbf{else}:\\
\;\;\;\;y \cdot \frac{x}{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) -9.718469549340153e+143)
   (/ (* y x) z)
   (if (or (<= (/ y z) -3.63917652177614e-103)
           (and (not (<= (/ y z) 5.893930391846604e-162))
                (<= (/ y z) 1.1673693186349219e+216)))
     (* (/ y z) x)
     (* y (/ x z)))))
double code(double x, double y, double z, double t) {
	return ((double) (x * (((double) ((y / z) * t)) / t)));
}
↓
double code(double x, double y, double z, double t) {
	double tmp;
	if (((y / z) <= -9.718469549340153e+143)) {
		tmp = (((double) (y * x)) / z);
	} else {
		double tmp_1;
		if ((((y / z) <= -3.63917652177614e-103) || (!((y / z) <= 5.893930391846604e-162) && ((y / z) <= 1.1673693186349219e+216)))) {
			tmp_1 = ((double) ((y / z) * x));
		} else {
			tmp_1 = ((double) (y * (x / z)));
		}
		tmp = tmp_1;
	}
	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

Original14.6
Target1.4
Herbie1.1
\[\begin{array}{l} \mathbf{if}\;\frac{\frac{y}{z} \cdot t}{t} < -1.20672205123045 \cdot 10^{+245}:\\ \;\;\;\;\frac{y}{\frac{z}{x}}\\ \mathbf{elif}\;\frac{\frac{y}{z} \cdot t}{t} < -5.907522236933906 \cdot 10^{-275}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \mathbf{elif}\;\frac{\frac{y}{z} \cdot t}{t} < 5.658954423153415 \cdot 10^{-65}:\\ \;\;\;\;\frac{y}{\frac{z}{x}}\\ \mathbf{elif}\;\frac{\frac{y}{z} \cdot t}{t} < 2.0087180502407133 \cdot 10^{+217}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{y \cdot x}{z}\\ \end{array}\]

Derivation

  1. Split input into 3 regimes

  2. if (/.f64 y z) < -9.71846954934015296e143

    1. Initial program 34.1

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

    2. Simplified17.7

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

    4. Applied associate-*r/_binary643.1

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

    if -9.71846954934015296e143 < (/.f64 y z) < -3.63917652177614002e-103 or 5.89393039184660396e-162 < (/.f64 y z) < 1.16736931863492192e216

    1. Initial program 7.1

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

    2. Simplified0.2

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

    if -3.63917652177614002e-103 < (/.f64 y z) < 5.89393039184660396e-162 or 1.16736931863492192e216 < (/.f64 y z)

    1. Initial program 18.9

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

    2. Simplified10.2

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

    4. Applied add-cube-cbrt_binary6410.7

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

    5. Applied *-un-lft-identity_binary6410.7

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

    6. Applied times-frac_binary6410.7

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

    7. Applied associate-*r*_binary643.7

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

    8. Simplified3.7

      \[\leadsto \color{blue}{\frac{x}{\sqrt[3]{z} \cdot \sqrt[3]{z}}} \cdot \frac{y}{\sqrt[3]{z}}\]

    9. Taylor expanded around 0 1.9

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

    10. Simplified1.6

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

  4. Final simplification1.1

    \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{y}{z} \leq -9.718469549340153 \cdot 10^{+143}:\\ \;\;\;\;\frac{y \cdot x}{z}\\ \mathbf{elif}\;\frac{y}{z} \leq -3.63917652177614 \cdot 10^{-103} \lor \neg \left(\frac{y}{z} \leq 5.893930391846604 \cdot 10^{-162}\right) \land \frac{y}{z} \leq 1.1673693186349219 \cdot 10^{+216}:\\ \;\;\;\;\frac{y}{z} \cdot x\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{x}{z}\\ \end{array}\]

Reproduce

herbie shell --seed 2020205 
(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)))