Average Error: 14.2 → 2.9
Time: 6.2s
Precision: binary64
\[[x, y]=\mathsf{sort}([x, y])\]
\[x \cdot \frac{\frac{y}{z} \cdot t}{t}\]
↓
\[\begin{array}{l} \mathbf{if}\;\frac{y}{z} \leq -4.3368341188513626 \cdot 10^{+45} \lor \neg \left(\frac{y}{z} \leq -1.0508213286859204 \cdot 10^{-148}\right) \land \frac{y}{z} \leq 4.9952376169741 \cdot 10^{-312}:\\ \;\;\;\;\frac{y \cdot x}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{z} \cdot x\\ \end{array}\]
x \cdot \frac{\frac{y}{z} \cdot t}{t}
↓
\begin{array}{l}
\mathbf{if}\;\frac{y}{z} \leq -4.3368341188513626 \cdot 10^{+45} \lor \neg \left(\frac{y}{z} \leq -1.0508213286859204 \cdot 10^{-148}\right) \land \frac{y}{z} \leq 4.9952376169741 \cdot 10^{-312}:\\
\;\;\;\;\frac{y \cdot x}{z}\\

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

\end{array}
(FPCore (x y z t) :precision binary64 (* x (/ (* (/ y z) t) t)))
↓
(FPCore (x y z t)
 :precision binary64
 (if (or (<= (/ y z) -4.3368341188513626e+45)
         (and (not (<= (/ y z) -1.0508213286859204e-148))
              (<= (/ y z) 4.9952376169741e-312)))
   (/ (* y x) z)
   (* (/ y z) x)))
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) <= -4.3368341188513626e+45) || (!((y / z) <= -1.0508213286859204e-148) && ((y / z) <= 4.9952376169741e-312))) {
		tmp = (y * x) / z;
	} else {
		tmp = (y / z) * x;
	}
	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

Original14.2
Target1.5
Herbie2.9
\[\begin{array}{l} \mathbf{if}\;\frac{\frac{y}{z} \cdot t}{t} < -1.20672205123045 \cdot 10^{+245}:\\ \;\;\;\;\frac{y}{\frac{z}{x}}\\ \mathbf{elif}\;\frac{\frac{y}{z} \cdot t}{t} < -5.907522236933906 \cdot 10^{-275}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \mathbf{elif}\;\frac{\frac{y}{z} \cdot t}{t} < 5.658954423153415 \cdot 10^{-65}:\\ \;\;\;\;\frac{y}{\frac{z}{x}}\\ \mathbf{elif}\;\frac{\frac{y}{z} \cdot t}{t} < 2.0087180502407133 \cdot 10^{+217}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{y \cdot x}{z}\\ \end{array}\]

Derivation

  1. Split input into 2 regimes

  2. if (/.f64 y z) < -4.3368341188513626e45 or -1.05082132868592043e-148 < (/.f64 y z) < 4.9952376169741e-312

    1. Initial program 18.9

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

    2. Simplified10.5

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

    3. Taylor expanded around 0 3.1

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

    if -4.3368341188513626e45 < (/.f64 y z) < -1.05082132868592043e-148 or 4.9952376169741e-312 < (/.f64 y z)

    1. Initial program 11.0

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

    2. Simplified2.8

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

  4. Final simplification2.9

    \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{y}{z} \leq -4.3368341188513626 \cdot 10^{+45} \lor \neg \left(\frac{y}{z} \leq -1.0508213286859204 \cdot 10^{-148}\right) \land \frac{y}{z} \leq 4.9952376169741 \cdot 10^{-312}:\\ \;\;\;\;\frac{y \cdot x}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{z} \cdot x\\ \end{array}\]

Reproduce

herbie shell --seed 2021044 
(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)))