Average Error: 7.7 → 0.9
Time: 3.4s
Precision: binary64
\[\frac{x + y}{1 - \frac{y}{z}}\]
↓
\[\begin{array}{l} \mathbf{if}\;y \le -3.7828738445874092 \cdot 10^{138} \lor \neg \left(y \le 6.2255204369876334 \cdot 10^{43}\right):\\ \;\;\;\;\frac{1}{\frac{1}{y + x} - \frac{1}{z} \cdot \frac{y}{y + x}}\\ \mathbf{else}:\\ \;\;\;\;\frac{y + x}{1 - \frac{y}{z}}\\ \end{array}\]
\frac{x + y}{1 - \frac{y}{z}}
↓
\begin{array}{l}
\mathbf{if}\;y \le -3.7828738445874092 \cdot 10^{138} \lor \neg \left(y \le 6.2255204369876334 \cdot 10^{43}\right):\\
\;\;\;\;\frac{1}{\frac{1}{y + x} - \frac{1}{z} \cdot \frac{y}{y + x}}\\

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

\end{array}
double code(double x, double y, double z) {
	return ((double) (((double) (x + y)) / ((double) (1.0 - ((double) (y / z))))));
}
↓
double code(double x, double y, double z) {
	double VAR;
	if (((y <= -3.782873844587409e+138) || !(y <= 6.225520436987633e+43))) {
		VAR = ((double) (1.0 / ((double) (((double) (1.0 / ((double) (y + x)))) - ((double) (((double) (1.0 / z)) * ((double) (y / ((double) (y + x))))))))));
	} else {
		VAR = ((double) (((double) (y + x)) / ((double) (1.0 - ((double) (y / z))))));
	}
	return VAR;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original7.7
Target3.9
Herbie0.9
\[\begin{array}{l} \mathbf{if}\;y \lt -3.74293107626898565 \cdot 10^{171}:\\ \;\;\;\;\frac{y + x}{-y} \cdot z\\ \mathbf{elif}\;y \lt 3.55346624560867344 \cdot 10^{168}:\\ \;\;\;\;\frac{x + y}{1 - \frac{y}{z}}\\ \mathbf{else}:\\ \;\;\;\;\frac{y + x}{-y} \cdot z\\ \end{array}\]

Derivation

  1. Split input into 2 regimes

  2. if y < -3.7828738445874092e138 or 6.2255204369876334e43 < y

    1. Initial program 19.5

      \[\frac{x + y}{1 - \frac{y}{z}}\]
    2. Using strategy rm

    3. Applied clear-num19.6

      \[\leadsto \color{blue}{\frac{1}{\frac{1 - \frac{y}{z}}{x + y}}}\]
    4. Using strategy rm

    5. Applied div-sub19.6

      \[\leadsto \frac{1}{\color{blue}{\frac{1}{x + y} - \frac{\frac{y}{z}}{x + y}}}\]

    6. Simplified19.6

      \[\leadsto \frac{1}{\color{blue}{\frac{1}{y + x}} - \frac{\frac{y}{z}}{x + y}}\]

    7. Simplified12.6

      \[\leadsto \frac{1}{\frac{1}{y + x} - \color{blue}{\frac{y}{z \cdot \left(y + x\right)}}}\]
    8. Using strategy rm

    9. Applied *-un-lft-identity12.6

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

    10. Applied times-frac0.2

      \[\leadsto \frac{1}{\frac{1}{y + x} - \color{blue}{\frac{1}{z} \cdot \frac{y}{y + x}}}\]

    if -3.7828738445874092e138 < y < 6.2255204369876334e43

    1. Initial program 1.3

      \[\frac{x + y}{1 - \frac{y}{z}}\]
  3. Recombined 2 regimes into one program.

  4. Final simplification0.9

    \[\leadsto \begin{array}{l} \mathbf{if}\;y \le -3.7828738445874092 \cdot 10^{138} \lor \neg \left(y \le 6.2255204369876334 \cdot 10^{43}\right):\\ \;\;\;\;\frac{1}{\frac{1}{y + x} - \frac{1}{z} \cdot \frac{y}{y + x}}\\ \mathbf{else}:\\ \;\;\;\;\frac{y + x}{1 - \frac{y}{z}}\\ \end{array}\]

Reproduce

herbie shell --seed 2020181 
(FPCore (x y z)
  :name "Graphics.Rendering.Chart.Backend.Diagrams:calcFontMetrics from Chart-diagrams-1.5.1, A"
  :precision binary64

  :herbie-target
  (if (< y -3.7429310762689856e+171) (* (/ (+ y x) (neg y)) z) (if (< y 3.5534662456086734e+168) (/ (+ x y) (- 1.0 (/ y z))) (* (/ (+ y x) (neg y)) z)))

  (/ (+ x y) (- 1.0 (/ y z))))