Average Error: 3.6 → 3.5
Time: 25.5s
Precision: 64
\[x \cdot \left(1 - y \cdot z\right)\]
↓
\[x \cdot 1 + \left(-x \cdot \left(z \cdot y\right)\right)\]
x \cdot \left(1 - y \cdot z\right)
↓
x \cdot 1 + \left(-x \cdot \left(z \cdot y\right)\right)
double f(double x, double y, double z) {
        double r229567 = x;
        double r229568 = 1.0;
        double r229569 = y;
        double r229570 = z;
        double r229571 = r229569 * r229570;
        double r229572 = r229568 - r229571;
        double r229573 = r229567 * r229572;
        return r229573;
}
↓
double f(double x, double y, double z) {
        double r229574 = x;
        double r229575 = 1.0;
        double r229576 = r229574 * r229575;
        double r229577 = z;
        double r229578 = y;
        double r229579 = r229577 * r229578;
        double r229580 = r229574 * r229579;
        double r229581 = -r229580;
        double r229582 = r229576 + r229581;
        return r229582;
}

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 3.6

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

  3. Applied add-cube-cbrt4.8

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

  4. Applied associate-*l*4.8

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

  6. Applied sub-neg4.8

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

  7. Applied distribute-lft-in4.8

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

  8. Applied distribute-lft-in4.8

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

  9. Simplified3.9

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

  10. Simplified3.5

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

  11. Final simplification3.5

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

Reproduce

herbie shell --seed 2019199 +o rules:numerics
(FPCore (x y z)
  :name "Data.Colour.RGBSpace.HSV:hsv from colour-2.3.3, I"
  (* x (- 1.0 (* y z))))