Average Error: 6.0 → 0.1
Time: 22.1s
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 r31243106 = x;
        double r31243107 = r31243106 * r31243106;
        double r31243108 = y;
        double r31243109 = 4.0;
        double r31243110 = r31243108 * r31243109;
        double r31243111 = z;
        double r31243112 = r31243111 * r31243111;
        double r31243113 = t;
        double r31243114 = r31243112 - r31243113;
        double r31243115 = r31243110 * r31243114;
        double r31243116 = r31243107 - r31243115;
        return r31243116;
}
↓
double f(double x, double y, double z, double t) {
        double r31243117 = x;
        double r31243118 = r31243117 * r31243117;
        double r31243119 = z;
        double r31243120 = 4.0;
        double r31243121 = y;
        double r31243122 = r31243120 * r31243121;
        double r31243123 = r31243119 * r31243122;
        double r31243124 = r31243119 * r31243123;
        double r31243125 = r31243118 - r31243124;
        double r31243126 = t;
        double r31243127 = r31243122 * r31243126;
        double r31243128 = r31243125 + r31243127;
        return r31243128;
}

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

Original6.0
Target6.0
Herbie0.1
\[x \cdot x - 4 \cdot \left(y \cdot \left(z \cdot z - t\right)\right)\]

Derivation

  1. Initial program 6.0

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

  2. Taylor expanded around inf 6.0

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

  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 2019172 
(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))))