Average Error: 28.7 → 0.1
Time: 16.1s
Precision: 64
\[\frac{\left(x \cdot x + y \cdot y\right) - z \cdot z}{y \cdot 2}\]
↓
\[\frac{y + \left(x + z\right) \cdot \frac{x - z}{y}}{2}\]
\frac{\left(x \cdot x + y \cdot y\right) - z \cdot z}{y \cdot 2}
↓
\frac{y + \left(x + z\right) \cdot \frac{x - z}{y}}{2}
double f(double x, double y, double z) {
        double r450163 = x;
        double r450164 = r450163 * r450163;
        double r450165 = y;
        double r450166 = r450165 * r450165;
        double r450167 = r450164 + r450166;
        double r450168 = z;
        double r450169 = r450168 * r450168;
        double r450170 = r450167 - r450169;
        double r450171 = 2.0;
        double r450172 = r450165 * r450171;
        double r450173 = r450170 / r450172;
        return r450173;
}
↓
double f(double x, double y, double z) {
        double r450174 = y;
        double r450175 = x;
        double r450176 = z;
        double r450177 = r450175 + r450176;
        double r450178 = r450175 - r450176;
        double r450179 = r450178 / r450174;
        double r450180 = r450177 * r450179;
        double r450181 = r450174 + r450180;
        double r450182 = 2.0;
        double r450183 = r450181 / r450182;
        return r450183;
}

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

Original28.7
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 28.7

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

  2. Simplified12.6

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

  4. Applied *-un-lft-identity12.6

    \[\leadsto \frac{y + \frac{x \cdot x - z \cdot z}{\color{blue}{1 \cdot y}}}{2}\]

  5. Applied difference-of-squares12.6

    \[\leadsto \frac{y + \frac{\color{blue}{\left(x + z\right) \cdot \left(x - z\right)}}{1 \cdot y}}{2}\]

  6. Applied times-frac0.1

    \[\leadsto \frac{y + \color{blue}{\frac{x + z}{1} \cdot \frac{x - z}{y}}}{2}\]

  7. Simplified0.1

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

  8. Final simplification0.1

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

Reproduce

herbie shell --seed 2019235 
(FPCore (x y z)
  :name "Diagrams.TwoD.Apollonian:initialConfig from diagrams-contrib-1.3.0.5, A"
  :precision binary64

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

  (/ (- (+ (* x x) (* y y)) (* z z)) (* y 2)))