Average Error: 28.9 → 0.2
Time: 12.0s
Precision: 64
\[\frac{\left(x \cdot x + y \cdot y\right) - z \cdot z}{y \cdot 2}\]
↓
\[\frac{y + \left(z + x\right) \cdot \frac{x - z}{y}}{2}\]
\frac{\left(x \cdot x + y \cdot y\right) - z \cdot z}{y \cdot 2}
↓
\frac{y + \left(z + x\right) \cdot \frac{x - z}{y}}{2}
double f(double x, double y, double z) {
        double r384654 = x;
        double r384655 = r384654 * r384654;
        double r384656 = y;
        double r384657 = r384656 * r384656;
        double r384658 = r384655 + r384657;
        double r384659 = z;
        double r384660 = r384659 * r384659;
        double r384661 = r384658 - r384660;
        double r384662 = 2.0;
        double r384663 = r384656 * r384662;
        double r384664 = r384661 / r384663;
        return r384664;
}
↓
double f(double x, double y, double z) {
        double r384665 = y;
        double r384666 = z;
        double r384667 = x;
        double r384668 = r384666 + r384667;
        double r384669 = r384667 - r384666;
        double r384670 = r384669 / r384665;
        double r384671 = r384668 * r384670;
        double r384672 = r384665 + r384671;
        double r384673 = 2.0;
        double r384674 = r384672 / r384673;
        return r384674;
}

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

Original28.9
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 28.9

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

  2. Simplified12.7

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

  4. Applied *-un-lft-identity12.7

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

  5. Applied difference-of-squares12.7

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

  6. Applied times-frac0.2

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

  7. Simplified0.2

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

  8. Final simplification0.2

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

Reproduce

herbie shell --seed 2020042 
(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)))