Average Error: 5.9 → 0.1
Time: 18.8s
Precision: 64
\[x \cdot x - \left(y \cdot 4\right) \cdot \left(z \cdot z - t\right)\]
↓
\[\left(x \cdot x - z \cdot \left(z \cdot \left(4 \cdot y\right)\right)\right) + \left(4 \cdot y\right) \cdot t\]
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 r34723164 = x;
        double r34723165 = r34723164 * r34723164;
        double r34723166 = y;
        double r34723167 = 4.0;
        double r34723168 = r34723166 * r34723167;
        double r34723169 = z;
        double r34723170 = r34723169 * r34723169;
        double r34723171 = t;
        double r34723172 = r34723170 - r34723171;
        double r34723173 = r34723168 * r34723172;
        double r34723174 = r34723165 - r34723173;
        return r34723174;
}
↓
double f(double x, double y, double z, double t) {
        double r34723175 = x;
        double r34723176 = r34723175 * r34723175;
        double r34723177 = z;
        double r34723178 = 4.0;
        double r34723179 = y;
        double r34723180 = r34723178 * r34723179;
        double r34723181 = r34723177 * r34723180;
        double r34723182 = r34723177 * r34723181;
        double r34723183 = r34723176 - r34723182;
        double r34723184 = t;
        double r34723185 = r34723180 * r34723184;
        double r34723186 = r34723183 + r34723185;
        return r34723186;
}

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

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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. Taylor expanded around inf 5.9

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

  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 2019169 
(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))))