Average Error: 5.9 → 0.1
Time: 4.2s
Precision: 64
\[x \cdot x - \left(y \cdot 4\right) \cdot \left(z \cdot z - t\right)\]
↓
\[x \cdot x - \left(\left(\left(y \cdot 4\right) \cdot z\right) \cdot z + \left(y \cdot 4\right) \cdot \left(-t\right)\right)\]
x \cdot x - \left(y \cdot 4\right) \cdot \left(z \cdot z - t\right)
↓
x \cdot x - \left(\left(\left(y \cdot 4\right) \cdot z\right) \cdot z + \left(y \cdot 4\right) \cdot \left(-t\right)\right)
double f(double x, double y, double z, double t) {
        double r735328 = x;
        double r735329 = r735328 * r735328;
        double r735330 = y;
        double r735331 = 4.0;
        double r735332 = r735330 * r735331;
        double r735333 = z;
        double r735334 = r735333 * r735333;
        double r735335 = t;
        double r735336 = r735334 - r735335;
        double r735337 = r735332 * r735336;
        double r735338 = r735329 - r735337;
        return r735338;
}
↓
double f(double x, double y, double z, double t) {
        double r735339 = x;
        double r735340 = r735339 * r735339;
        double r735341 = y;
        double r735342 = 4.0;
        double r735343 = r735341 * r735342;
        double r735344 = z;
        double r735345 = r735343 * r735344;
        double r735346 = r735345 * r735344;
        double r735347 = t;
        double r735348 = -r735347;
        double r735349 = r735343 * r735348;
        double r735350 = r735346 + r735349;
        double r735351 = r735340 - r735350;
        return r735351;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Bits error versus t

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Results

Enter valid numbers for all inputs

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-lft-in5.9

    \[\leadsto x \cdot x - \color{blue}{\left(\left(y \cdot 4\right) \cdot \left(z \cdot z\right) + \left(y \cdot 4\right) \cdot \left(-t\right)\right)}\]
  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 simplification0.1

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

Reproduce

herbie shell --seed 2020001 
(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))))