Average Error: 27.9 → 0.2
Time: 24.3s
Precision: 64
\[\frac{\left(x \cdot x + y \cdot y\right) - z \cdot z}{y \cdot 2}\]
↓
\[\frac{y - \frac{z + x}{\frac{y}{z - x}}}{2}\]
\frac{\left(x \cdot x + y \cdot y\right) - z \cdot z}{y \cdot 2}
↓
\frac{y - \frac{z + x}{\frac{y}{z - x}}}{2}
double f(double x, double y, double z) {
        double r190688044 = x;
        double r190688045 = r190688044 * r190688044;
        double r190688046 = y;
        double r190688047 = r190688046 * r190688046;
        double r190688048 = r190688045 + r190688047;
        double r190688049 = z;
        double r190688050 = r190688049 * r190688049;
        double r190688051 = r190688048 - r190688050;
        double r190688052 = 2.0;
        double r190688053 = r190688046 * r190688052;
        double r190688054 = r190688051 / r190688053;
        return r190688054;
}
↓
double f(double x, double y, double z) {
        double r190688055 = y;
        double r190688056 = z;
        double r190688057 = x;
        double r190688058 = r190688056 + r190688057;
        double r190688059 = r190688056 - r190688057;
        double r190688060 = r190688055 / r190688059;
        double r190688061 = r190688058 / r190688060;
        double r190688062 = r190688055 - r190688061;
        double r190688063 = 2.0;
        double r190688064 = r190688062 / r190688063;
        return r190688064;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original27.9
Target0.2
Herbie0.2
\[y \cdot 0.5 - \left(\frac{0.5}{y} \cdot \left(z + x\right)\right) \cdot \left(z - x\right)\]

Derivation

  1. Initial program 27.9

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

  2. Simplified12.3

    \[\leadsto \color{blue}{\frac{y - \frac{z \cdot z - x \cdot x}{y}}{2}}\]
  3. Using strategy rm

  4. Applied difference-of-squares12.3

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

  5. Applied associate-/l*0.2

    \[\leadsto \frac{y - \color{blue}{\frac{z + x}{\frac{y}{z - x}}}}{2}\]

  6. Final simplification0.2

    \[\leadsto \frac{y - \frac{z + x}{\frac{y}{z - x}}}{2}\]

Reproduce

herbie shell --seed 2019173 
(FPCore (x y z)
  :name "Diagrams.TwoD.Apollonian:initialConfig from diagrams-contrib-1.3.0.5, A"

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

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