Average Error: 15.1 → 7.8
Time: 3.2s
Precision: 64
\[\frac{\left(x \cdot 2\right) \cdot y}{x - y}\]
↓
\[\frac{x \cdot 2}{\frac{x - y}{y}}\]
\frac{\left(x \cdot 2\right) \cdot y}{x - y}
↓
\frac{x \cdot 2}{\frac{x - y}{y}}
double f(double x, double y) {
        double r554983 = x;
        double r554984 = 2.0;
        double r554985 = r554983 * r554984;
        double r554986 = y;
        double r554987 = r554985 * r554986;
        double r554988 = r554983 - r554986;
        double r554989 = r554987 / r554988;
        return r554989;
}
↓
double f(double x, double y) {
        double r554990 = x;
        double r554991 = 2.0;
        double r554992 = r554990 * r554991;
        double r554993 = y;
        double r554994 = r554990 - r554993;
        double r554995 = r554994 / r554993;
        double r554996 = r554992 / r554995;
        return r554996;
}

Error

Bits error versus x

Bits error versus y

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original15.1
Target0.3
Herbie7.8
\[\begin{array}{l} \mathbf{if}\;x \lt -1.721044263414944729490876394165887012892 \cdot 10^{81}:\\ \;\;\;\;\frac{2 \cdot x}{x - y} \cdot y\\ \mathbf{elif}\;x \lt 83645045635564432:\\ \;\;\;\;\frac{x \cdot 2}{\frac{x - y}{y}}\\ \mathbf{else}:\\ \;\;\;\;\frac{2 \cdot x}{x - y} \cdot y\\ \end{array}\]

Derivation

  1. Split input into 2 regimes

  2. if y < -5.573191811409158e+49 or 1797816337.0316365 < y

    1. Initial program 17.9

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

    3. Applied associate-/l*0.1

      \[\leadsto \color{blue}{\frac{x \cdot 2}{\frac{x - y}{y}}}\]
    4. Using strategy rm

    5. Applied clear-num0.2

      \[\leadsto \color{blue}{\frac{1}{\frac{\frac{x - y}{y}}{x \cdot 2}}}\]

    if -5.573191811409158e+49 < y < 1797816337.0316365

    1. Initial program 12.7

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

    3. Applied associate-/l*14.3

      \[\leadsto \color{blue}{\frac{x \cdot 2}{\frac{x - y}{y}}}\]
    4. Using strategy rm

    5. Applied div-inv14.4

      \[\leadsto \frac{x \cdot 2}{\color{blue}{\left(x - y\right) \cdot \frac{1}{y}}}\]

    6. Applied times-frac0.3

      \[\leadsto \color{blue}{\frac{x}{x - y} \cdot \frac{2}{\frac{1}{y}}}\]

    7. Simplified0.1

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

  4. Final simplification7.8

    \[\leadsto \frac{x \cdot 2}{\frac{x - y}{y}}\]

Reproduce

herbie shell --seed 1978988140 
(FPCore (x y)
  :name "Linear.Projection:perspective from linear-1.19.1.3, B"
  :precision binary64

  :herbie-target
  (if (< x -1.7210442634149447e81) (* (/ (* 2 x) (- x y)) y) (if (< x 83645045635564432) (/ (* x 2) (/ (- x y) y)) (* (/ (* 2 x) (- x y)) y)))

  (/ (* (* x 2) y) (- x y)))