Average Error: 6.0 → 6.0
Time: 11.1s
Precision: 64
\[x \cdot x - \left(y \cdot 4\right) \cdot \left(z \cdot z - t\right)\]
↓
\[x \cdot x - \left(y \cdot 4\right) \cdot \left(z \cdot z - t\right)\]
x \cdot x - \left(y \cdot 4\right) \cdot \left(z \cdot z - t\right)
↓
x \cdot x - \left(y \cdot 4\right) \cdot \left(z \cdot z - t\right)
double f(double x, double y, double z, double t) {
        double r565521 = x;
        double r565522 = r565521 * r565521;
        double r565523 = y;
        double r565524 = 4.0;
        double r565525 = r565523 * r565524;
        double r565526 = z;
        double r565527 = r565526 * r565526;
        double r565528 = t;
        double r565529 = r565527 - r565528;
        double r565530 = r565525 * r565529;
        double r565531 = r565522 - r565530;
        return r565531;
}
↓
double f(double x, double y, double z, double t) {
        double r565532 = x;
        double r565533 = r565532 * r565532;
        double r565534 = y;
        double r565535 = 4.0;
        double r565536 = r565534 * r565535;
        double r565537 = z;
        double r565538 = r565537 * r565537;
        double r565539 = t;
        double r565540 = r565538 - r565539;
        double r565541 = r565536 * r565540;
        double r565542 = r565533 - r565541;
        return r565542;
}

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

Enter valid numbers for all inputs

Target

Original6.0
Target6.0
Herbie6.0
\[x \cdot x - 4 \cdot \left(y \cdot \left(z \cdot z - t\right)\right)\]

Derivation

  1. Initial program 6.0

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

  3. Applied sub-neg6.0

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

  4. Applied distribute-lft-in6.0

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

  6. Applied associate-*r*0.1

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

  7. Final simplification6.0

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

Reproduce

herbie shell --seed 2019298 
(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))))