Average Error: 5.8 → 0.1
Time: 19.2s
Precision: 64
\[x \cdot x - \left(y \cdot 4\right) \cdot \left(z \cdot z - t\right)\]
↓
\[\left(x \cdot x - z \cdot \left(z \cdot \left(4 \cdot y\right)\right)\right) + \left(4 \cdot y\right) \cdot t\]
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(4 \cdot y\right)\right)\right) + \left(4 \cdot y\right) \cdot t
double f(double x, double y, double z, double t) {
        double r34006462 = x;
        double r34006463 = r34006462 * r34006462;
        double r34006464 = y;
        double r34006465 = 4.0;
        double r34006466 = r34006464 * r34006465;
        double r34006467 = z;
        double r34006468 = r34006467 * r34006467;
        double r34006469 = t;
        double r34006470 = r34006468 - r34006469;
        double r34006471 = r34006466 * r34006470;
        double r34006472 = r34006463 - r34006471;
        return r34006472;
}
↓
double f(double x, double y, double z, double t) {
        double r34006473 = x;
        double r34006474 = r34006473 * r34006473;
        double r34006475 = z;
        double r34006476 = 4.0;
        double r34006477 = y;
        double r34006478 = r34006476 * r34006477;
        double r34006479 = r34006475 * r34006478;
        double r34006480 = r34006475 * r34006479;
        double r34006481 = r34006474 - r34006480;
        double r34006482 = t;
        double r34006483 = r34006478 * r34006482;
        double r34006484 = r34006481 + r34006483;
        return r34006484;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Bits error versus t

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original5.8
Target5.8
Herbie0.1
\[x \cdot x - 4 \cdot \left(y \cdot \left(z \cdot z - t\right)\right)\]

Derivation

  1. Initial program 5.8

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

  2. Taylor expanded around inf 5.8

    \[\leadsto \color{blue}{\left(4 \cdot \left(t \cdot y\right) + {x}^{2}\right) - 4 \cdot \left({z}^{2} \cdot y\right)}\]

  3. Simplified0.1

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

  4. Final simplification0.1

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

Reproduce

herbie shell --seed 2019171 
(FPCore (x y z t)
  :name "Graphics.Rasterific.Shading:$sradialGradientWithFocusShader from Rasterific-0.6.1, B"

  :herbie-target
  (- (* x x) (* 4.0 (* y (- (* z z) t))))

  (- (* x x) (* (* y 4.0) (- (* z z) t))))