Average Error: 3.2 → 3.2
Time: 11.0s
Precision: 64
\[x \cdot \left(1 - y \cdot z\right)\]
↓
\[x \cdot \left(1 - y \cdot z\right)\]
x \cdot \left(1 - y \cdot z\right)
↓
x \cdot \left(1 - y \cdot z\right)
double f(double x, double y, double z) {
        double r190392 = x;
        double r190393 = 1.0;
        double r190394 = y;
        double r190395 = z;
        double r190396 = r190394 * r190395;
        double r190397 = r190393 - r190396;
        double r190398 = r190392 * r190397;
        return r190398;
}
↓
double f(double x, double y, double z) {
        double r190399 = x;
        double r190400 = 1.0;
        double r190401 = y;
        double r190402 = z;
        double r190403 = r190401 * r190402;
        double r190404 = r190400 - r190403;
        double r190405 = r190399 * r190404;
        return r190405;
}

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. Initial program 3.2

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

  3. Applied add-cube-cbrt4.4

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

  4. Applied associate-*l*4.4

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

  6. Applied sub-neg4.4

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

  7. Applied distribute-lft-in4.4

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

  8. Applied distribute-lft-in4.4

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

  9. Simplified3.6

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

  10. Simplified3.2

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

  11. Final simplification3.2

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

Reproduce

herbie shell --seed 2019297 
(FPCore (x y z)
  :name "Data.Colour.RGBSpace.HSV:hsv from colour-2.3.3, I"
  :precision binary64
  (* x (- 1 (* y z))))