Average Error: 3.5 → 3.5
Time: 4.9s
Precision: 64
\[x \cdot \left(1 - y \cdot z\right)\]
↓
\[\left(1 - y \cdot z\right) \cdot x\]
x \cdot \left(1 - y \cdot z\right)
↓
\left(1 - y \cdot z\right) \cdot x
double f(double x, double y, double z) {
        double r201982 = x;
        double r201983 = 1.0;
        double r201984 = y;
        double r201985 = z;
        double r201986 = r201984 * r201985;
        double r201987 = r201983 - r201986;
        double r201988 = r201982 * r201987;
        return r201988;
}
↓
double f(double x, double y, double z) {
        double r201989 = 1.0;
        double r201990 = y;
        double r201991 = z;
        double r201992 = r201990 * r201991;
        double r201993 = r201989 - r201992;
        double r201994 = x;
        double r201995 = r201993 * r201994;
        return r201995;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Split input into 2 regimes

  2. if (* y z) < -inf.0 or 6.519152385092011e+168 < (* y z)

    1. Initial program 32.7

      \[x \cdot \left(1 - y \cdot z\right)\]
    2. Using strategy rm

    3. Applied sub-neg32.7

      \[\leadsto x \cdot \color{blue}{\left(1 + \left(-y \cdot z\right)\right)}\]

    4. Applied distribute-lft-in32.7

      \[\leadsto \color{blue}{x \cdot 1 + x \cdot \left(-y \cdot z\right)}\]
    5. Using strategy rm

    6. Applied add-cube-cbrt33.3

      \[\leadsto x \cdot 1 + \color{blue}{\left(\left(\sqrt[3]{x} \cdot \sqrt[3]{x}\right) \cdot \sqrt[3]{x}\right)} \cdot \left(-y \cdot z\right)\]

    7. Applied associate-*l*33.3

      \[\leadsto x \cdot 1 + \color{blue}{\left(\sqrt[3]{x} \cdot \sqrt[3]{x}\right) \cdot \left(\sqrt[3]{x} \cdot \left(-y \cdot z\right)\right)}\]
    8. Using strategy rm

    9. Applied distribute-lft-neg-in33.3

      \[\leadsto x \cdot 1 + \left(\sqrt[3]{x} \cdot \sqrt[3]{x}\right) \cdot \left(\sqrt[3]{x} \cdot \color{blue}{\left(\left(-y\right) \cdot z\right)}\right)\]

    10. Applied associate-*r*18.9

      \[\leadsto x \cdot 1 + \left(\sqrt[3]{x} \cdot \sqrt[3]{x}\right) \cdot \color{blue}{\left(\left(\sqrt[3]{x} \cdot \left(-y\right)\right) \cdot z\right)}\]
    11. Using strategy rm

    12. Applied associate-*r*2.6

      \[\leadsto x \cdot 1 + \color{blue}{\left(\left(\sqrt[3]{x} \cdot \sqrt[3]{x}\right) \cdot \left(\sqrt[3]{x} \cdot \left(-y\right)\right)\right) \cdot z}\]

    13. Simplified1.4

      \[\leadsto x \cdot 1 + \color{blue}{\left(\left(-x\right) \cdot y\right)} \cdot z\]

    if -inf.0 < (* y z) < 6.519152385092011e+168

    1. Initial program 0.1

      \[x \cdot \left(1 - y \cdot z\right)\]
    2. Using strategy rm

    3. Applied sub-neg0.1

      \[\leadsto x \cdot \color{blue}{\left(1 + \left(-y \cdot z\right)\right)}\]

    4. Applied distribute-lft-in0.1

      \[\leadsto \color{blue}{x \cdot 1 + x \cdot \left(-y \cdot z\right)}\]
  3. Recombined 2 regimes into one program.

  4. Final simplification3.5

    \[\leadsto \left(1 - y \cdot z\right) \cdot x\]

Reproduce

herbie shell --seed 2019308 
(FPCore (x y z)
  :name "Data.Colour.RGBSpace.HSV:hsv from colour-2.3.3, I"
  :precision binary64
  (* x (- 1 (* y z))))