Average Error: 14.5 → 0.0
Time: 11.0s
Precision: 64
\[\frac{x - y}{\left(x \cdot 2.0\right) \cdot y}\]
↓
\[\frac{0.5}{y} - \frac{0.5}{x}\]
\frac{x - y}{\left(x \cdot 2.0\right) \cdot y}
↓
\frac{0.5}{y} - \frac{0.5}{x}
double f(double x, double y) {
        double r23460110 = x;
        double r23460111 = y;
        double r23460112 = r23460110 - r23460111;
        double r23460113 = 2.0;
        double r23460114 = r23460110 * r23460113;
        double r23460115 = r23460114 * r23460111;
        double r23460116 = r23460112 / r23460115;
        return r23460116;
}
↓
double f(double x, double y) {
        double r23460117 = 0.5;
        double r23460118 = y;
        double r23460119 = r23460117 / r23460118;
        double r23460120 = x;
        double r23460121 = r23460117 / r23460120;
        double r23460122 = r23460119 - r23460121;
        return r23460122;
}

Error

Bits error versus x

Bits error versus y

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original14.5
Target0.0
Herbie0.0
\[\frac{0.5}{y} - \frac{0.5}{x}\]

Derivation

  1. Initial program 14.5

    \[\frac{x - y}{\left(x \cdot 2.0\right) \cdot y}\]

  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 2019162 +o rules:numerics
(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)))