Average Error: 5.9 → 0.1
Time: 3.9s
Precision: 64
\[x \cdot x - \left(y \cdot 4\right) \cdot \left(z \cdot z - t\right)\]
↓
\[\left(x \cdot x - z \cdot \left(z \cdot \left(y \cdot 4\right)\right)\right) - \left(-t\right) \cdot \left(y \cdot 4\right)\]
x \cdot x - \left(y \cdot 4\right) \cdot \left(z \cdot z - t\right)
↓
\left(x \cdot x - z \cdot \left(z \cdot \left(y \cdot 4\right)\right)\right) - \left(-t\right) \cdot \left(y \cdot 4\right)
double f(double x, double y, double z, double t) {
        double r649417 = x;
        double r649418 = r649417 * r649417;
        double r649419 = y;
        double r649420 = 4.0;
        double r649421 = r649419 * r649420;
        double r649422 = z;
        double r649423 = r649422 * r649422;
        double r649424 = t;
        double r649425 = r649423 - r649424;
        double r649426 = r649421 * r649425;
        double r649427 = r649418 - r649426;
        return r649427;
}
↓
double f(double x, double y, double z, double t) {
        double r649428 = x;
        double r649429 = r649428 * r649428;
        double r649430 = z;
        double r649431 = y;
        double r649432 = 4.0;
        double r649433 = r649431 * r649432;
        double r649434 = r649430 * r649433;
        double r649435 = r649430 * r649434;
        double r649436 = r649429 - r649435;
        double r649437 = t;
        double r649438 = -r649437;
        double r649439 = r649438 * r649433;
        double r649440 = r649436 - r649439;
        return r649440;
}

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

Original5.9
Target5.9
Herbie0.1
\[x \cdot x - 4 \cdot \left(y \cdot \left(z \cdot z - t\right)\right)\]

Derivation

  1. Initial program 5.9

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

  3. Applied sub-neg5.9

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

  4. Applied distribute-rgt-in5.9

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

  5. Applied associate--r+5.9

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

  7. Applied associate-*l*0.1

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

  8. Final simplification0.1

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

Reproduce

herbie shell --seed 2020002 
(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))))