Average Error: 6.1 → 0.1
Time: 18.2s
Precision: 64
\[x \cdot x - \left(y \cdot 4\right) \cdot \left(z \cdot z - t\right)\]
↓
\[\left(x \cdot x - \left(\left(y \cdot 4\right) \cdot z\right) \cdot z\right) - \left(-t\right) \cdot \left(y \cdot 4\right)\]
x \cdot x - \left(y \cdot 4\right) \cdot \left(z \cdot z - t\right)
↓
\left(x \cdot x - \left(\left(y \cdot 4\right) \cdot z\right) \cdot z\right) - \left(-t\right) \cdot \left(y \cdot 4\right)
double f(double x, double y, double z, double t) {
        double r481457 = x;
        double r481458 = r481457 * r481457;
        double r481459 = y;
        double r481460 = 4.0;
        double r481461 = r481459 * r481460;
        double r481462 = z;
        double r481463 = r481462 * r481462;
        double r481464 = t;
        double r481465 = r481463 - r481464;
        double r481466 = r481461 * r481465;
        double r481467 = r481458 - r481466;
        return r481467;
}
↓
double f(double x, double y, double z, double t) {
        double r481468 = x;
        double r481469 = r481468 * r481468;
        double r481470 = y;
        double r481471 = 4.0;
        double r481472 = r481470 * r481471;
        double r481473 = z;
        double r481474 = r481472 * r481473;
        double r481475 = r481474 * r481473;
        double r481476 = r481469 - r481475;
        double r481477 = t;
        double r481478 = -r481477;
        double r481479 = r481478 * r481472;
        double r481480 = r481476 - r481479;
        return r481480;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Bits error versus t

Try it out

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Results

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Target

Original6.1
Target6.1
Herbie0.1
\[x \cdot x - 4 \cdot \left(y \cdot \left(z \cdot z - t\right)\right)\]

Derivation

  1. Initial program 6.1

    \[x \cdot x - \left(y \cdot 4\right) \cdot \left(z \cdot z - t\right)\]
  2. Using strategy rm

  3. Applied sub-neg6.1

    \[\leadsto x \cdot x - \left(y \cdot 4\right) \cdot \color{blue}{\left(z \cdot z + \left(-t\right)\right)}\]

  4. Applied distribute-rgt-in6.1

    \[\leadsto x \cdot x - \color{blue}{\left(\left(z \cdot z\right) \cdot \left(y \cdot 4\right) + \left(-t\right) \cdot \left(y \cdot 4\right)\right)}\]

  5. Applied associate--r+6.1

    \[\leadsto \color{blue}{\left(x \cdot x - \left(z \cdot z\right) \cdot \left(y \cdot 4\right)\right) - \left(-t\right) \cdot \left(y \cdot 4\right)}\]

  6. Simplified6.1

    \[\leadsto \color{blue}{\left(x \cdot x - \left(y \cdot 4\right) \cdot \left(z \cdot z\right)\right)} - \left(-t\right) \cdot \left(y \cdot 4\right)\]
  7. Using strategy rm

  8. Applied associate-*r*0.1

    \[\leadsto \left(x \cdot x - \color{blue}{\left(\left(y \cdot 4\right) \cdot z\right) \cdot z}\right) - \left(-t\right) \cdot \left(y \cdot 4\right)\]

  9. Final simplification0.1

    \[\leadsto \left(x \cdot x - \left(\left(y \cdot 4\right) \cdot z\right) \cdot z\right) - \left(-t\right) \cdot \left(y \cdot 4\right)\]

Reproduce

herbie shell --seed 2019323 
(FPCore (x y z t)
  :name "Graphics.Rasterific.Shading:$sradialGradientWithFocusShader from Rasterific-0.6.1, B"
  :precision binary64

  :herbie-target
  (- (* x x) (* 4 (* y (- (* z z) t))))

  (- (* x x) (* (* y 4) (- (* z z) t))))