Average Error: 28.4 → 0.2
Time: 18.4s
Precision: 64
\[\frac{\left(x \cdot x + y \cdot y\right) - z \cdot z}{y \cdot 2}\]
↓
\[\frac{y - \left(z + x\right) \cdot \frac{z - x}{y}}{2}\]
\frac{\left(x \cdot x + y \cdot y\right) - z \cdot z}{y \cdot 2}
↓
\frac{y - \left(z + x\right) \cdot \frac{z - x}{y}}{2}
double f(double x, double y, double z) {
        double r441054 = x;
        double r441055 = r441054 * r441054;
        double r441056 = y;
        double r441057 = r441056 * r441056;
        double r441058 = r441055 + r441057;
        double r441059 = z;
        double r441060 = r441059 * r441059;
        double r441061 = r441058 - r441060;
        double r441062 = 2.0;
        double r441063 = r441056 * r441062;
        double r441064 = r441061 / r441063;
        return r441064;
}
↓
double f(double x, double y, double z) {
        double r441065 = y;
        double r441066 = z;
        double r441067 = x;
        double r441068 = r441066 + r441067;
        double r441069 = r441066 - r441067;
        double r441070 = r441069 / r441065;
        double r441071 = r441068 * r441070;
        double r441072 = r441065 - r441071;
        double r441073 = 2.0;
        double r441074 = r441072 / r441073;
        return r441074;
}

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

Original28.4
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 28.4

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

  2. Simplified12.6

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

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

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

  5. Applied difference-of-squares12.6

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

  6. Applied times-frac0.2

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

  7. Simplified0.2

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

  8. Final simplification0.2

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

Reproduce

herbie shell --seed 2019303 
(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)))