Average Error: 6.1 → 0.1
Time: 3.8s
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 r876588 = x;
        double r876589 = r876588 * r876588;
        double r876590 = y;
        double r876591 = 4.0;
        double r876592 = r876590 * r876591;
        double r876593 = z;
        double r876594 = r876593 * r876593;
        double r876595 = t;
        double r876596 = r876594 - r876595;
        double r876597 = r876592 * r876596;
        double r876598 = r876589 - r876597;
        return r876598;
}
↓
double f(double x, double y, double z, double t) {
        double r876599 = x;
        double r876600 = r876599 * r876599;
        double r876601 = z;
        double r876602 = y;
        double r876603 = 4.0;
        double r876604 = r876602 * r876603;
        double r876605 = r876601 * r876604;
        double r876606 = r876601 * r876605;
        double r876607 = r876600 - r876606;
        double r876608 = t;
        double r876609 = -r876608;
        double r876610 = r876609 * r876604;
        double r876611 = r876607 - r876610;
        return r876611;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Bits error versus t

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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. 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 2020057 
(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))))