Average Error: 6.0 → 0.1
Time: 21.9s
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 r33825295 = x;
        double r33825296 = r33825295 * r33825295;
        double r33825297 = y;
        double r33825298 = 4.0;
        double r33825299 = r33825297 * r33825298;
        double r33825300 = z;
        double r33825301 = r33825300 * r33825300;
        double r33825302 = t;
        double r33825303 = r33825301 - r33825302;
        double r33825304 = r33825299 * r33825303;
        double r33825305 = r33825296 - r33825304;
        return r33825305;
}
↓
double f(double x, double y, double z, double t) {
        double r33825306 = x;
        double r33825307 = r33825306 * r33825306;
        double r33825308 = z;
        double r33825309 = 4.0;
        double r33825310 = y;
        double r33825311 = r33825309 * r33825310;
        double r33825312 = r33825308 * r33825311;
        double r33825313 = r33825308 * r33825312;
        double r33825314 = r33825307 - r33825313;
        double r33825315 = t;
        double r33825316 = r33825311 * r33825315;
        double r33825317 = r33825314 + r33825316;
        return r33825317;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Bits error versus t

Try it out

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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))))