Average Error: 22.9 → 0.3
Time: 3.0s
Precision: 64
\[1 - \frac{\left(1 - x\right) \cdot y}{y + 1}\]
↓
\[\begin{array}{l} \mathbf{if}\;\frac{\left(1 - x\right) \cdot y}{y + 1} \le 0.55294491994513906 \lor \neg \left(\frac{\left(1 - x\right) \cdot y}{y + 1} \le 1.00000753751841365\right):\\ \;\;\;\;1 - \left(1 - x\right) \cdot \frac{y}{y + 1}\\ \mathbf{else}:\\ \;\;\;\;1 \cdot \left(\frac{1}{y} - \frac{x}{y}\right) + x\\ \end{array}\]
1 - \frac{\left(1 - x\right) \cdot y}{y + 1}
↓
\begin{array}{l}
\mathbf{if}\;\frac{\left(1 - x\right) \cdot y}{y + 1} \le 0.55294491994513906 \lor \neg \left(\frac{\left(1 - x\right) \cdot y}{y + 1} \le 1.00000753751841365\right):\\
\;\;\;\;1 - \left(1 - x\right) \cdot \frac{y}{y + 1}\\

\mathbf{else}:\\
\;\;\;\;1 \cdot \left(\frac{1}{y} - \frac{x}{y}\right) + x\\

\end{array}
double code(double x, double y) {
	return (1.0 - (((1.0 - x) * y) / (y + 1.0)));
}
↓
double code(double x, double y) {
	double VAR;
	if ((((((1.0 - x) * y) / (y + 1.0)) <= 0.5529449199451391) || !((((1.0 - x) * y) / (y + 1.0)) <= 1.0000075375184136))) {
		VAR = (1.0 - ((1.0 - x) * (y / (y + 1.0))));
	} else {
		VAR = ((1.0 * ((1.0 / y) - (x / y))) + x);
	}
	return VAR;
}

Error

Bits error versus x

Bits error versus y

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original22.9
Target0.2
Herbie0.3
\[\begin{array}{l} \mathbf{if}\;y \lt -3693.84827882972468:\\ \;\;\;\;\frac{1}{y} - \left(\frac{x}{y} - x\right)\\ \mathbf{elif}\;y \lt 6799310503.41891003:\\ \;\;\;\;1 - \frac{\left(1 - x\right) \cdot y}{y + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{y} - \left(\frac{x}{y} - x\right)\\ \end{array}\]

Derivation

  1. Split input into 2 regimes

  2. if (/ (* (- 1.0 x) y) (+ y 1.0)) < 0.5529449199451391 or 1.0000075375184136 < (/ (* (- 1.0 x) y) (+ y 1.0))

    1. Initial program 11.1

      \[1 - \frac{\left(1 - x\right) \cdot y}{y + 1}\]
    2. Using strategy rm

    3. Applied *-un-lft-identity11.1

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

    4. Applied times-frac0.1

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

    5. Simplified0.1

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

    if 0.5529449199451391 < (/ (* (- 1.0 x) y) (+ y 1.0)) < 1.0000075375184136

    1. Initial program 58.4

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

    2. Taylor expanded around inf 0.9

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

    3. Simplified0.9

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

  4. Final simplification0.3

    \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{\left(1 - x\right) \cdot y}{y + 1} \le 0.55294491994513906 \lor \neg \left(\frac{\left(1 - x\right) \cdot y}{y + 1} \le 1.00000753751841365\right):\\ \;\;\;\;1 - \left(1 - x\right) \cdot \frac{y}{y + 1}\\ \mathbf{else}:\\ \;\;\;\;1 \cdot \left(\frac{1}{y} - \frac{x}{y}\right) + x\\ \end{array}\]

Reproduce

herbie shell --seed 2020102 
(FPCore (x y)
  :name "Diagrams.Trail:splitAtParam  from diagrams-lib-1.3.0.3, D"
  :precision binary64

  :herbie-target
  (if (< y -3693.8482788297247) (- (/ 1 y) (- (/ x y) x)) (if (< y 6799310503.41891) (- 1 (/ (* (- 1 x) y) (+ y 1))) (- (/ 1 y) (- (/ x y) x))))

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