Average Error: 15.2 → 0.2
Time: 29.1s
Precision: 64
\[\frac{\left(x \cdot 2\right) \cdot y}{x - y}\]
↓
\[\frac{1}{\frac{0.5}{y} - \frac{0.5}{x}}\]
\frac{\left(x \cdot 2\right) \cdot y}{x - y}
↓
\frac{1}{\frac{0.5}{y} - \frac{0.5}{x}}
double f(double x, double y) {
        double r399200 = x;
        double r399201 = 2.0;
        double r399202 = r399200 * r399201;
        double r399203 = y;
        double r399204 = r399202 * r399203;
        double r399205 = r399200 - r399203;
        double r399206 = r399204 / r399205;
        return r399206;
}
↓
double f(double x, double y) {
        double r399207 = 1.0;
        double r399208 = 0.5;
        double r399209 = y;
        double r399210 = r399208 / r399209;
        double r399211 = x;
        double r399212 = r399208 / r399211;
        double r399213 = r399210 - r399212;
        double r399214 = r399207 / r399213;
        return r399214;
}

Error

Bits error versus x

Bits error versus y

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Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original15.2
Target0.3
Herbie0.2
\[\begin{array}{l} \mathbf{if}\;x \lt -1.721044263414944729490876394165887012892 \cdot 10^{81}:\\ \;\;\;\;\frac{2 \cdot x}{x - y} \cdot y\\ \mathbf{elif}\;x \lt 83645045635564432:\\ \;\;\;\;\frac{x \cdot 2}{\frac{x - y}{y}}\\ \mathbf{else}:\\ \;\;\;\;\frac{2 \cdot x}{x - y} \cdot y\\ \end{array}\]

Derivation

  1. Initial program 15.2

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

  3. Applied clear-num15.3

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

  4. Taylor expanded around 0 0.2

    \[\leadsto \frac{1}{\color{blue}{0.5 \cdot \frac{1}{y} - 0.5 \cdot \frac{1}{x}}}\]

  5. Simplified0.2

    \[\leadsto \frac{1}{\color{blue}{\frac{0.5}{y} - \frac{0.5}{x}}}\]

  6. Final simplification0.2

    \[\leadsto \frac{1}{\frac{0.5}{y} - \frac{0.5}{x}}\]

Reproduce

herbie shell --seed 2019209 
(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)))