Average Error: 28.2 → 0.2
Time: 12.1s
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 r1264577 = x;
        double r1264578 = r1264577 * r1264577;
        double r1264579 = y;
        double r1264580 = r1264579 * r1264579;
        double r1264581 = r1264578 + r1264580;
        double r1264582 = z;
        double r1264583 = r1264582 * r1264582;
        double r1264584 = r1264581 - r1264583;
        double r1264585 = 2.0;
        double r1264586 = r1264579 * r1264585;
        double r1264587 = r1264584 / r1264586;
        return r1264587;
}
↓
double f(double x, double y, double z) {
        double r1264588 = y;
        double r1264589 = z;
        double r1264590 = x;
        double r1264591 = r1264589 + r1264590;
        double r1264592 = r1264590 - r1264589;
        double r1264593 = r1264592 / r1264588;
        double r1264594 = r1264591 * r1264593;
        double r1264595 = r1264588 + r1264594;
        double r1264596 = 2.0;
        double r1264597 = r1264595 / r1264596;
        return r1264597;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Try it out

Your Program's Arguments

Results

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Target

Original28.2
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 28.2

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

  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 2020047 
(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)))