Average Error: 7.7 → 0.2
Time: 3.0s
Precision: binary64
\[\frac{x + y}{1 - \frac{y}{z}}\]
↓
\[\begin{array}{l} \mathbf{if}\;y \leq -1.5895385369056823 \cdot 10^{+22} \lor \neg \left(y \leq 5.988031705976441 \cdot 10^{-14}\right):\\ \;\;\;\;\frac{1}{\frac{1}{y + x} + \frac{y}{y + x} \cdot \frac{-1}{z}}\\ \mathbf{else}:\\ \;\;\;\;\frac{y + x}{1 - \frac{y}{z}}\\ \end{array}\]
\frac{x + y}{1 - \frac{y}{z}}
↓
\begin{array}{l}
\mathbf{if}\;y \leq -1.5895385369056823 \cdot 10^{+22} \lor \neg \left(y \leq 5.988031705976441 \cdot 10^{-14}\right):\\
\;\;\;\;\frac{1}{\frac{1}{y + x} + \frac{y}{y + x} \cdot \frac{-1}{z}}\\

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

\end{array}
(FPCore (x y z) :precision binary64 (/ (+ x y) (- 1.0 (/ y z))))
↓
(FPCore (x y z)
 :precision binary64
 (if (or (<= y -1.5895385369056823e+22) (not (<= y 5.988031705976441e-14)))
   (/ 1.0 (+ (/ 1.0 (+ y x)) (* (/ y (+ y x)) (/ -1.0 z))))
   (/ (+ y x) (- 1.0 (/ y z)))))
double code(double x, double y, double z) {
	return (((double) (x + y)) / ((double) (1.0 - (y / z))));
}
↓
double code(double x, double y, double z) {
	double VAR;
	if (((y <= -1.5895385369056823e+22) || !(y <= 5.988031705976441e-14))) {
		VAR = (1.0 / ((double) ((1.0 / ((double) (y + x))) + ((double) ((y / ((double) (y + x))) * (-1.0 / z))))));
	} else {
		VAR = (((double) (y + x)) / ((double) (1.0 - (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
Target3.7
Herbie0.2
\[\begin{array}{l} \mathbf{if}\;y < -3.7429310762689856 \cdot 10^{+171}:\\ \;\;\;\;\frac{y + x}{-y} \cdot z\\ \mathbf{elif}\;y < 3.5534662456086734 \cdot 10^{+168}:\\ \;\;\;\;\frac{x + y}{1 - \frac{y}{z}}\\ \mathbf{else}:\\ \;\;\;\;\frac{y + x}{-y} \cdot z\\ \end{array}\]

Derivation

  1. Split input into 2 regimes

  2. if y < -1.58953853690568235e22 or 5.9880317059764411e-14 < y

    1. Initial program 15.5

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

    3. Applied clear-num15.7

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

    5. Applied div-sub15.7

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

    6. Simplified15.7

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

    7. Simplified9.6

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

    9. Applied *-un-lft-identity9.6

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

    10. Applied times-frac0.2

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

    if -1.58953853690568235e22 < y < 5.9880317059764411e-14

    1. Initial program 0.1

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

  4. Final simplification0.2

    \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.5895385369056823 \cdot 10^{+22} \lor \neg \left(y \leq 5.988031705976441 \cdot 10^{-14}\right):\\ \;\;\;\;\frac{1}{\frac{1}{y + x} + \frac{y}{y + x} \cdot \frac{-1}{z}}\\ \mathbf{else}:\\ \;\;\;\;\frac{y + x}{1 - \frac{y}{z}}\\ \end{array}\]

Reproduce

herbie shell --seed 2020198 
(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) (- 1.0 (/ y z))) (* (/ (+ y x) (- y)) z)))

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