Average Error: 15.1 → 0.0
Time: 7.3s
Precision: 64
\[\frac{x + y}{\left(x \cdot 2\right) \cdot y}\]
↓
\[\frac{0.5}{y} + \frac{0.5}{x}\]
\frac{x + y}{\left(x \cdot 2\right) \cdot y}
↓
\frac{0.5}{y} + \frac{0.5}{x}
double f(double x, double y) {
        double r18958227 = x;
        double r18958228 = y;
        double r18958229 = r18958227 + r18958228;
        double r18958230 = 2.0;
        double r18958231 = r18958227 * r18958230;
        double r18958232 = r18958231 * r18958228;
        double r18958233 = r18958229 / r18958232;
        return r18958233;
}
↓
double f(double x, double y) {
        double r18958234 = 0.5;
        double r18958235 = y;
        double r18958236 = r18958234 / r18958235;
        double r18958237 = x;
        double r18958238 = r18958234 / r18958237;
        double r18958239 = r18958236 + r18958238;
        return r18958239;
}

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

Original15.1
Target0.0
Herbie0.0
\[\frac{0.5}{x} + \frac{0.5}{y}\]

Derivation

  1. Initial program 15.1

    \[\frac{x + y}{\left(x \cdot 2\right) \cdot y}\]

  2. Taylor expanded around 0 0.0

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

  3. Simplified0.0

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

  4. Final simplification0.0

    \[\leadsto \frac{0.5}{y} + \frac{0.5}{x}\]

Reproduce

herbie shell --seed 2019174 +o rules:numerics
(FPCore (x y)
  :name "Linear.Projection:inversePerspective from linear-1.19.1.3, C"

  :herbie-target
  (+ (/ 0.5 x) (/ 0.5 y))

  (/ (+ x y) (* (* x 2.0) y)))