Average Error: 27.7 → 0.2
Time: 12.8s
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 r700143 = x;
        double r700144 = r700143 * r700143;
        double r700145 = y;
        double r700146 = r700145 * r700145;
        double r700147 = r700144 + r700146;
        double r700148 = z;
        double r700149 = r700148 * r700148;
        double r700150 = r700147 - r700149;
        double r700151 = 2.0;
        double r700152 = r700145 * r700151;
        double r700153 = r700150 / r700152;
        return r700153;
}
↓
double f(double x, double y, double z) {
        double r700154 = y;
        double r700155 = z;
        double r700156 = x;
        double r700157 = r700155 + r700156;
        double r700158 = r700155 - r700156;
        double r700159 = r700158 / r700154;
        double r700160 = r700157 * r700159;
        double r700161 = r700154 - r700160;
        double r700162 = 2.0;
        double r700163 = r700161 / r700162;
        return r700163;
}

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

Original27.7
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 27.7

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

  2. Simplified12.4

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

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

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

  5. Applied difference-of-squares12.4

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

  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 2019350 
(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)))