Average Error: 22.5 → 0.4
Time: 3.1s
Precision: 64
\[1 - \frac{\left(1 - x\right) \cdot y}{y + 1}\]
↓
\[\begin{array}{l} \mathbf{if}\;\frac{\left(1 - x\right) \cdot y}{y + 1} \le 0.991865807491388085 \lor \neg \left(\frac{\left(1 - x\right) \cdot y}{y + 1} \le 1\right):\\ \;\;\;\;1 - \left(1 - x\right) \cdot \frac{y}{y + 1}\\ \mathbf{else}:\\ \;\;\;\;1 \cdot \left(\frac{1}{y} - \frac{x}{y}\right) + x\\ \end{array}\]
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 0.991865807491388085 \lor \neg \left(\frac{\left(1 - x\right) \cdot y}{y + 1} \le 1\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 ((double) (1.0 - ((double) (((double) (((double) (1.0 - x)) * y)) / ((double) (y + 1.0))))));
}
↓
double code(double x, double y) {
	double VAR;
	if (((((double) (((double) (((double) (1.0 - x)) * y)) / ((double) (y + 1.0)))) <= 0.9918658074913881) || !(((double) (((double) (((double) (1.0 - x)) * y)) / ((double) (y + 1.0)))) <= 1.0))) {
		VAR = ((double) (1.0 - ((double) (((double) (1.0 - x)) * ((double) (y / ((double) (y + 1.0))))))));
	} else {
		VAR = ((double) (((double) (1.0 * ((double) (((double) (1.0 / y)) - ((double) (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

Original22.5
Target0.2
Herbie0.4
\[\begin{array}{l} \mathbf{if}\;y \lt -3693.84827882972468:\\ \;\;\;\;\frac{1}{y} - \left(\frac{x}{y} - x\right)\\ \mathbf{elif}\;y \lt 6799310503.41891003:\\ \;\;\;\;1 - \frac{\left(1 - x\right) \cdot y}{y + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{y} - \left(\frac{x}{y} - x\right)\\ \end{array}\]

Derivation

  1. Split input into 2 regimes

  2. if (/ (* (- 1.0 x) y) (+ y 1.0)) < 0.9918658074913881 or 1.0 < (/ (* (- 1.0 x) y) (+ y 1.0))

    1. Initial program 11.0

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

    3. Applied *-un-lft-identity11.0

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

    4. Applied times-frac0.4

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

    5. Simplified0.4

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

    if 0.9918658074913881 < (/ (* (- 1.0 x) y) (+ y 1.0)) < 1.0

    1. Initial program 59.8

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

    2. Taylor expanded around inf 0.5

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

    3. Simplified0.5

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

  4. Final simplification0.4

    \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{\left(1 - x\right) \cdot y}{y + 1} \le 0.991865807491388085 \lor \neg \left(\frac{\left(1 - x\right) \cdot y}{y + 1} \le 1\right):\\ \;\;\;\;1 - \left(1 - x\right) \cdot \frac{y}{y + 1}\\ \mathbf{else}:\\ \;\;\;\;1 \cdot \left(\frac{1}{y} - \frac{x}{y}\right) + x\\ \end{array}\]

Reproduce

herbie shell --seed 2020126 
(FPCore (x y)
  :name "Diagrams.Trail:splitAtParam  from diagrams-lib-1.3.0.3, D"
  :precision binary64

  :herbie-target
  (if (< y -3693.8482788297247) (- (/ 1.0 y) (- (/ x y) x)) (if (< y 6799310503.41891) (- 1.0 (/ (* (- 1.0 x) y) (+ y 1.0))) (- (/ 1.0 y) (- (/ x y) x))))

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