Average Error: 28.6 → 0.1
Time: 13.5s
Precision: 64
\[\frac{\left(x \cdot x + y \cdot y\right) - z \cdot z}{y \cdot 2}\]
↓
\[\frac{y + \frac{x + z}{y} \cdot \left(x - z\right)}{2}\]
\frac{\left(x \cdot x + y \cdot y\right) - z \cdot z}{y \cdot 2}
↓
\frac{y + \frac{x + z}{y} \cdot \left(x - z\right)}{2}
double f(double x, double y, double z) {
        double r1377200 = x;
        double r1377201 = r1377200 * r1377200;
        double r1377202 = y;
        double r1377203 = r1377202 * r1377202;
        double r1377204 = r1377201 + r1377203;
        double r1377205 = z;
        double r1377206 = r1377205 * r1377205;
        double r1377207 = r1377204 - r1377206;
        double r1377208 = 2.0;
        double r1377209 = r1377202 * r1377208;
        double r1377210 = r1377207 / r1377209;
        return r1377210;
}
↓
double f(double x, double y, double z) {
        double r1377211 = y;
        double r1377212 = x;
        double r1377213 = z;
        double r1377214 = r1377212 + r1377213;
        double r1377215 = r1377214 / r1377211;
        double r1377216 = r1377212 - r1377213;
        double r1377217 = r1377215 * r1377216;
        double r1377218 = r1377211 + r1377217;
        double r1377219 = 2.0;
        double r1377220 = r1377218 / r1377219;
        return r1377220;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

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Your Program's Arguments

Results

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Target

Original28.6
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 28.6

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

  2. Simplified12.7

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

  4. Applied difference-of-squares12.7

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

  5. Applied associate-/l*0.1

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

  7. Applied associate-/r/0.1

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

  8. Final simplification0.1

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

Reproduce

herbie shell --seed 2019198 
(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)))