Average Error: 7.4 → 0.1
Time: 4.1s
Precision: 64
\[\frac{x + y}{1 - \frac{y}{z}}\]
↓
\[\begin{array}{l} \mathbf{if}\;\frac{x + y}{1 - \frac{y}{z}} \le -2.847567984179807 \cdot 10^{-300} \lor \neg \left(\frac{x + y}{1 - \frac{y}{z}} \le 0.0\right):\\ \;\;\;\;\frac{x + y}{1 - \frac{y}{z}}\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{\frac{1}{x + y} - y \cdot \frac{\frac{1}{z}}{x + y}}\\ \end{array}\]
\frac{x + y}{1 - \frac{y}{z}}
↓
\begin{array}{l}
\mathbf{if}\;\frac{x + y}{1 - \frac{y}{z}} \le -2.847567984179807 \cdot 10^{-300} \lor \neg \left(\frac{x + y}{1 - \frac{y}{z}} \le 0.0\right):\\
\;\;\;\;\frac{x + y}{1 - \frac{y}{z}}\\

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

\end{array}
double code(double x, double y, double z) {
	return ((x + y) / (1.0 - (y / z)));
}
↓
double code(double x, double y, double z) {
	double VAR;
	if (((((x + y) / (1.0 - (y / z))) <= -2.847567984179807e-300) || !(((x + y) / (1.0 - (y / z))) <= 0.0))) {
		VAR = ((x + y) / (1.0 - (y / z)));
	} else {
		VAR = (1.0 / ((1.0 / (x + y)) - (y * ((1.0 / z) / (x + y)))));
	}
	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

Original7.4
Target3.9
Herbie0.1
\[\begin{array}{l} \mathbf{if}\;y \lt -3.74293107626898565 \cdot 10^{171}:\\ \;\;\;\;\frac{y + x}{-y} \cdot z\\ \mathbf{elif}\;y \lt 3.55346624560867344 \cdot 10^{168}:\\ \;\;\;\;\frac{x + y}{1 - \frac{y}{z}}\\ \mathbf{else}:\\ \;\;\;\;\frac{y + x}{-y} \cdot z\\ \end{array}\]

Derivation

  1. Split input into 2 regimes

  2. if (/ (+ x y) (- 1.0 (/ y z))) < -2.847567984179807e-300 or 0.0 < (/ (+ x y) (- 1.0 (/ y z)))

    1. Initial program 0.1

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

    if -2.847567984179807e-300 < (/ (+ x y) (- 1.0 (/ y z))) < 0.0

    1. Initial program 59.8

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

    3. Applied clear-num59.8

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

    5. Applied div-sub59.8

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

    7. Applied *-un-lft-identity59.8

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

    8. Applied div-inv59.8

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

    9. Applied times-frac0.4

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

    10. Simplified0.4

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

  4. Final simplification0.1

    \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x + y}{1 - \frac{y}{z}} \le -2.847567984179807 \cdot 10^{-300} \lor \neg \left(\frac{x + y}{1 - \frac{y}{z}} \le 0.0\right):\\ \;\;\;\;\frac{x + y}{1 - \frac{y}{z}}\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{\frac{1}{x + y} - y \cdot \frac{\frac{1}{z}}{x + y}}\\ \end{array}\]

Reproduce

herbie shell --seed 2020100 
(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) (- y)) z) (if (< y 3.5534662456086734e+168) (/ (+ x y) (- 1 (/ y z))) (* (/ (+ y x) (- y)) z)))

  (/ (+ x y) (- 1 (/ y z))))