Average Error: 15.1 → 0.0
Time: 17.7s
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 r13070009 = x;
        double r13070010 = y;
        double r13070011 = r13070009 - r13070010;
        double r13070012 = 2.0;
        double r13070013 = r13070009 * r13070012;
        double r13070014 = r13070013 * r13070010;
        double r13070015 = r13070011 / r13070014;
        return r13070015;
}
↓
double f(double x, double y) {
        double r13070016 = 0.5;
        double r13070017 = y;
        double r13070018 = r13070016 / r13070017;
        double r13070019 = x;
        double r13070020 = r13070016 / r13070019;
        double r13070021 = r13070018 - r13070020;
        return r13070021;
}

Error

Bits error versus x

Bits error versus y

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Your Program's Arguments

Results

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Target

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

Derivation

  1. Initial program 15.1

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

  2. Taylor expanded around 0 0.0

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

  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 2019179 
(FPCore (x y)
  :name "Linear.Projection:inversePerspective from linear-1.19.1.3, B"

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

  (/ (- x y) (* (* x 2.0) y)))