Average Error: 28.4 → 0.2
Time: 15.7s
Precision: 64
\[\frac{\left(x \cdot x + y \cdot y\right) - z \cdot z}{y \cdot 2}\]
↓
\[\frac{y + \frac{x - z}{\frac{y}{z + x}}}{2}\]
\frac{\left(x \cdot x + y \cdot y\right) - z \cdot z}{y \cdot 2}
↓
\frac{y + \frac{x - z}{\frac{y}{z + x}}}{2}
double f(double x, double y, double z) {
        double r461752 = x;
        double r461753 = r461752 * r461752;
        double r461754 = y;
        double r461755 = r461754 * r461754;
        double r461756 = r461753 + r461755;
        double r461757 = z;
        double r461758 = r461757 * r461757;
        double r461759 = r461756 - r461758;
        double r461760 = 2.0;
        double r461761 = r461754 * r461760;
        double r461762 = r461759 / r461761;
        return r461762;
}
↓
double f(double x, double y, double z) {
        double r461763 = y;
        double r461764 = x;
        double r461765 = z;
        double r461766 = r461764 - r461765;
        double r461767 = r461765 + r461764;
        double r461768 = r461763 / r461767;
        double r461769 = r461766 / r461768;
        double r461770 = r461763 + r461769;
        double r461771 = 2.0;
        double r461772 = r461770 / r461771;
        return r461772;
}

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. Simplified12.5

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

  4. Applied *-un-lft-identity12.5

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

  5. Applied difference-of-squares12.5

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

  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. Using strategy rm

  9. Applied sub-neg0.2

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

  10. Simplified0.2

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

  11. Final simplification0.2

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

Reproduce

herbie shell --seed 2019306 
(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)))