Average Error: 5.9 → 0.1
Time: 5.2s
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 r1347941 = x;
        double r1347942 = r1347941 * r1347941;
        double r1347943 = y;
        double r1347944 = 4.0;
        double r1347945 = r1347943 * r1347944;
        double r1347946 = z;
        double r1347947 = r1347946 * r1347946;
        double r1347948 = t;
        double r1347949 = r1347947 - r1347948;
        double r1347950 = r1347945 * r1347949;
        double r1347951 = r1347942 - r1347950;
        return r1347951;
}
↓
double f(double x, double y, double z, double t) {
        double r1347952 = x;
        double r1347953 = r1347952 * r1347952;
        double r1347954 = y;
        double r1347955 = 4.0;
        double r1347956 = r1347954 * r1347955;
        double r1347957 = z;
        double r1347958 = r1347956 * r1347957;
        double r1347959 = r1347958 * r1347957;
        double r1347960 = t;
        double r1347961 = -r1347960;
        double r1347962 = r1347956 * r1347961;
        double r1347963 = r1347959 + r1347962;
        double r1347964 = r1347953 - r1347963;
        return r1347964;
}

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

Original5.9
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 2020034 +o rules:numerics
(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))))