Average Error: 14.8 → 0.4
Time: 2.6s
Precision: binary64
\[x \cdot \frac{\frac{y}{z} \cdot t}{t}\]
↓
\[\begin{array}{l} \mathbf{if}\;\frac{y}{z} \leq -\infty:\\ \;\;\;\;\frac{y \cdot x}{z}\\ \mathbf{elif}\;\frac{y}{z} \leq -2.7857673698474565 \cdot 10^{-307}:\\ \;\;\;\;\frac{y}{z} \cdot x\\ \mathbf{elif}\;\frac{y}{z} \leq 0:\\ \;\;\;\;\left(y \cdot x\right) \cdot \frac{1}{z}\\ \mathbf{elif}\;\frac{y}{z} \leq 3.7409640787884874 \cdot 10^{+230}:\\ \;\;\;\;\frac{x}{\frac{z}{y}}\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{\frac{\frac{z}{x}}{y}}\\ \end{array}\]
x \cdot \frac{\frac{y}{z} \cdot t}{t}
↓
\begin{array}{l}
\mathbf{if}\;\frac{y}{z} \leq -\infty:\\
\;\;\;\;\frac{y \cdot x}{z}\\

\mathbf{elif}\;\frac{y}{z} \leq -2.7857673698474565 \cdot 10^{-307}:\\
\;\;\;\;\frac{y}{z} \cdot x\\

\mathbf{elif}\;\frac{y}{z} \leq 0:\\
\;\;\;\;\left(y \cdot x\right) \cdot \frac{1}{z}\\

\mathbf{elif}\;\frac{y}{z} \leq 3.7409640787884874 \cdot 10^{+230}:\\
\;\;\;\;\frac{x}{\frac{z}{y}}\\

\mathbf{else}:\\
\;\;\;\;\frac{1}{\frac{\frac{z}{x}}{y}}\\

\end{array}
(FPCore (x y z t) :precision binary64 (* x (/ (* (/ y z) t) t)))
↓
(FPCore (x y z t)
 :precision binary64
 (if (<= (/ y z) (- INFINITY))
   (/ (* y x) z)
   (if (<= (/ y z) -2.7857673698474565e-307)
     (* (/ y z) x)
     (if (<= (/ y z) 0.0)
       (* (* y x) (/ 1.0 z))
       (if (<= (/ y z) 3.7409640787884874e+230)
         (/ x (/ z y))
         (/ 1.0 (/ (/ z x) y)))))))
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) <= -((double) INFINITY)) {
		tmp = (y * x) / z;
	} else if ((y / z) <= -2.7857673698474565e-307) {
		tmp = (y / z) * x;
	} else if ((y / z) <= 0.0) {
		tmp = (y * x) * (1.0 / z);
	} else if ((y / z) <= 3.7409640787884874e+230) {
		tmp = x / (z / y);
	} else {
		tmp = 1.0 / ((z / x) / y);
	}
	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

Original14.8
Target1.6
Herbie0.4
\[\begin{array}{l} \mathbf{if}\;\frac{\frac{y}{z} \cdot t}{t} < -1.20672205123045 \cdot 10^{+245}:\\ \;\;\;\;\frac{y}{\frac{z}{x}}\\ \mathbf{elif}\;\frac{\frac{y}{z} \cdot t}{t} < -5.907522236933906 \cdot 10^{-275}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \mathbf{elif}\;\frac{\frac{y}{z} \cdot t}{t} < 5.658954423153415 \cdot 10^{-65}:\\ \;\;\;\;\frac{y}{\frac{z}{x}}\\ \mathbf{elif}\;\frac{\frac{y}{z} \cdot t}{t} < 2.0087180502407133 \cdot 10^{+217}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{y \cdot x}{z}\\ \end{array}\]

Derivation

  1. Split input into 5 regimes

  2. if (/.f64 y z) < -inf.0

    1. Initial program 64.0

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

    2. Simplified64.0

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

    4. Applied associate-*r/_binary640.2

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

    if -inf.0 < (/.f64 y z) < -2.78576736984745653e-307

    1. Initial program 10.3

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

    2. Simplified0.2

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

    if -2.78576736984745653e-307 < (/.f64 y z) < 0.0

    1. Initial program 21.7

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

    2. Simplified21.4

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

    4. Applied div-inv_binary6421.4

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

    5. Applied associate-*r*_binary640.1

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

    if 0.0 < (/.f64 y z) < 3.74096407878848741e230

    1. Initial program 9.5

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

    2. Simplified0.4

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

    4. Applied associate-*r/_binary648.1

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

    6. Applied associate-/l*_binary640.7

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

    if 3.74096407878848741e230 < (/.f64 y z)

    1. Initial program 45.4

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

    2. Simplified33.9

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

    4. Applied associate-*r/_binary640.6

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

    6. Applied clear-num_binary640.6

      \[\leadsto \color{blue}{\frac{1}{\frac{z}{x \cdot y}}}\]
    7. Using strategy rm

    8. Applied associate-/r*_binary640.6

      \[\leadsto \frac{1}{\color{blue}{\frac{\frac{z}{x}}{y}}}\]
  3. Recombined 5 regimes into one program.

  4. Final simplification0.4

    \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{y}{z} \leq -\infty:\\ \;\;\;\;\frac{y \cdot x}{z}\\ \mathbf{elif}\;\frac{y}{z} \leq -2.7857673698474565 \cdot 10^{-307}:\\ \;\;\;\;\frac{y}{z} \cdot x\\ \mathbf{elif}\;\frac{y}{z} \leq 0:\\ \;\;\;\;\left(y \cdot x\right) \cdot \frac{1}{z}\\ \mathbf{elif}\;\frac{y}{z} \leq 3.7409640787884874 \cdot 10^{+230}:\\ \;\;\;\;\frac{x}{\frac{z}{y}}\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{\frac{\frac{z}{x}}{y}}\\ \end{array}\]

Reproduce

herbie shell --seed 2020260 
(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)))