Average Error: 26.3 → 0.1
Time: 19.4s
Precision: 64
\[\frac{\left(x \cdot x + y \cdot y\right) - z \cdot z}{y \cdot 2.0}\]
↓
\[\frac{y + \frac{x - z}{\frac{y}{z + x}}}{2.0}\]
\frac{\left(x \cdot x + y \cdot y\right) - z \cdot z}{y \cdot 2.0}
↓
\frac{y + \frac{x - z}{\frac{y}{z + x}}}{2.0}
double f(double x, double y, double z) {
        double r24980167 = x;
        double r24980168 = r24980167 * r24980167;
        double r24980169 = y;
        double r24980170 = r24980169 * r24980169;
        double r24980171 = r24980168 + r24980170;
        double r24980172 = z;
        double r24980173 = r24980172 * r24980172;
        double r24980174 = r24980171 - r24980173;
        double r24980175 = 2.0;
        double r24980176 = r24980169 * r24980175;
        double r24980177 = r24980174 / r24980176;
        return r24980177;
}
↓
double f(double x, double y, double z) {
        double r24980178 = y;
        double r24980179 = x;
        double r24980180 = z;
        double r24980181 = r24980179 - r24980180;
        double r24980182 = r24980180 + r24980179;
        double r24980183 = r24980178 / r24980182;
        double r24980184 = r24980181 / r24980183;
        double r24980185 = r24980178 + r24980184;
        double r24980186 = 2.0;
        double r24980187 = r24980185 / r24980186;
        return r24980187;
}

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

Original26.3
Target0.2
Herbie0.1
\[y \cdot 0.5 - \left(\frac{0.5}{y} \cdot \left(z + x\right)\right) \cdot \left(z - x\right)\]

Derivation

  1. Initial program 26.3

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

  2. Simplified0.1

    \[\leadsto \color{blue}{\frac{\frac{x - z}{\frac{y}{z + x}} + y}{2.0}}\]

  3. Final simplification0.1

    \[\leadsto \frac{y + \frac{x - z}{\frac{y}{z + x}}}{2.0}\]

Reproduce

herbie shell --seed 2019162 +o rules:numerics
(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)))