Average Error: 7.5 → 0.4
Time: 3.3s
Precision: binary64
\[\frac{x + y}{1 - \frac{y}{z}}\]
↓
\[\begin{array}{l} \mathbf{if}\;y \le -3.28620844561740035 \cdot 10^{51} \lor \neg \left(y \le 1.37223536616252467 \cdot 10^{-69}\right):\\ \;\;\;\;\frac{1}{\frac{1}{y + x} + \frac{y}{y + x} \cdot \frac{-1}{z}}\\ \mathbf{else}:\\ \;\;\;\;\left(y + x\right) \cdot \frac{1}{1 - \frac{y}{z}}\\ \end{array}\]
\frac{x + y}{1 - \frac{y}{z}}
↓
\begin{array}{l}
\mathbf{if}\;y \le -3.28620844561740035 \cdot 10^{51} \lor \neg \left(y \le 1.37223536616252467 \cdot 10^{-69}\right):\\
\;\;\;\;\frac{1}{\frac{1}{y + x} + \frac{y}{y + x} \cdot \frac{-1}{z}}\\

\mathbf{else}:\\
\;\;\;\;\left(y + x\right) \cdot \frac{1}{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 <= -3.2862084456174004e+51) || !(y <= 1.3722353661625247e-69))) {
		VAR = ((double) (1.0 / ((double) (((double) (1.0 / ((double) (y + x)))) + ((double) (((double) (y / ((double) (y + x)))) * ((double) (-1.0 / z))))))));
	} else {
		VAR = ((double) (((double) (y + x)) * ((double) (1.0 / ((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

Original7.5
Target4.2
Herbie0.4
\[\begin{array}{l} \mathbf{if}\;y \lt -3.74293107626898565 \cdot 10^{171}:\\ \;\;\;\;\frac{y + x}{-y} \cdot z\\ \mathbf{elif}\;y \lt 3.55346624560867344 \cdot 10^{168}:\\ \;\;\;\;\frac{x + y}{1 - \frac{y}{z}}\\ \mathbf{else}:\\ \;\;\;\;\frac{y + x}{-y} \cdot z\\ \end{array}\]

Derivation

  1. Split input into 2 regimes

  2. if y < -3.28620844561740035e51 or 1.37223536616252467e-69 < y

    1. Initial program 14.1

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

    3. Applied clear-num14.2

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

    5. Applied div-sub14.2

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

    6. Simplified14.2

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

    7. Simplified9.1

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

    9. Applied *-un-lft-identity9.1

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

    10. Applied times-frac0.4

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

    if -3.28620844561740035e51 < y < 1.37223536616252467e-69

    1. Initial program 0.2

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

    3. Applied div-inv0.3

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

  4. Final simplification0.4

    \[\leadsto \begin{array}{l} \mathbf{if}\;y \le -3.28620844561740035 \cdot 10^{51} \lor \neg \left(y \le 1.37223536616252467 \cdot 10^{-69}\right):\\ \;\;\;\;\frac{1}{\frac{1}{y + x} + \frac{y}{y + x} \cdot \frac{-1}{z}}\\ \mathbf{else}:\\ \;\;\;\;\left(y + x\right) \cdot \frac{1}{1 - \frac{y}{z}}\\ \end{array}\]

Reproduce

herbie shell --seed 2020185 
(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))))