Average Error: 0.0 → 0.0
Time: 3.4s
Precision: 64
\[\frac{x - y}{x + y}\]
↓
\[\log \left(\sqrt{e^{\frac{x - y}{x + y}}}\right) + \frac{1}{2} \cdot \frac{x - y}{x + y}\]
\frac{x - y}{x + y}
↓
\log \left(\sqrt{e^{\frac{x - y}{x + y}}}\right) + \frac{1}{2} \cdot \frac{x - y}{x + y}
double f(double x, double y) {
        double r858246 = x;
        double r858247 = y;
        double r858248 = r858246 - r858247;
        double r858249 = r858246 + r858247;
        double r858250 = r858248 / r858249;
        return r858250;
}
↓
double f(double x, double y) {
        double r858251 = x;
        double r858252 = y;
        double r858253 = r858251 - r858252;
        double r858254 = r858251 + r858252;
        double r858255 = r858253 / r858254;
        double r858256 = exp(r858255);
        double r858257 = sqrt(r858256);
        double r858258 = log(r858257);
        double r858259 = 0.5;
        double r858260 = r858259 * r858255;
        double r858261 = r858258 + r858260;
        return r858261;
}

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

Original0.0
Target0.0
Herbie0.0
\[\frac{x}{x + y} - \frac{y}{x + y}\]

Derivation

  1. Initial program 0.0

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

  3. Applied add-log-exp0.0

    \[\leadsto \color{blue}{\log \left(e^{\frac{x - y}{x + y}}\right)}\]
  4. Using strategy rm

  5. Applied add-sqr-sqrt0.0

    \[\leadsto \log \color{blue}{\left(\sqrt{e^{\frac{x - y}{x + y}}} \cdot \sqrt{e^{\frac{x - y}{x + y}}}\right)}\]

  6. Applied log-prod0.0

    \[\leadsto \color{blue}{\log \left(\sqrt{e^{\frac{x - y}{x + y}}}\right) + \log \left(\sqrt{e^{\frac{x - y}{x + y}}}\right)}\]
  7. Using strategy rm

  8. Applied pow10.0

    \[\leadsto \log \left(\sqrt{e^{\frac{x - y}{x + y}}}\right) + \log \left(\sqrt{\color{blue}{{\left(e^{\frac{x - y}{x + y}}\right)}^{1}}}\right)\]

  9. Applied sqrt-pow10.0

    \[\leadsto \log \left(\sqrt{e^{\frac{x - y}{x + y}}}\right) + \log \color{blue}{\left({\left(e^{\frac{x - y}{x + y}}\right)}^{\left(\frac{1}{2}\right)}\right)}\]

  10. Applied log-pow0.0

    \[\leadsto \log \left(\sqrt{e^{\frac{x - y}{x + y}}}\right) + \color{blue}{\frac{1}{2} \cdot \log \left(e^{\frac{x - y}{x + y}}\right)}\]

  11. Simplified0.0

    \[\leadsto \log \left(\sqrt{e^{\frac{x - y}{x + y}}}\right) + \frac{1}{2} \cdot \color{blue}{\frac{x - y}{x + y}}\]

  12. Final simplification0.0

    \[\leadsto \log \left(\sqrt{e^{\frac{x - y}{x + y}}}\right) + \frac{1}{2} \cdot \frac{x - y}{x + y}\]

Reproduce

herbie shell --seed 2020001 
(FPCore (x y)
  :name "Data.Colour.RGB:hslsv from colour-2.3.3, D"
  :precision binary64

  :herbie-target
  (- (/ x (+ x y)) (/ y (+ x y)))

  (/ (- x y) (+ x y)))