Average Error: 0.5 → 0.8
Time: 15.9s
Precision: 64
\[\sqrt{x - 1} \cdot \sqrt{x}\]
↓
\[\left(\sqrt{x} \cdot \sqrt{\sqrt[3]{x - 1}}\right) \cdot \sqrt{\sqrt[3]{x - 1} \cdot \sqrt[3]{x - 1}}\]
\sqrt{x - 1} \cdot \sqrt{x}
↓
\left(\sqrt{x} \cdot \sqrt{\sqrt[3]{x - 1}}\right) \cdot \sqrt{\sqrt[3]{x - 1} \cdot \sqrt[3]{x - 1}}
double f(double x) {
        double r788763 = x;
        double r788764 = 1.0;
        double r788765 = r788763 - r788764;
        double r788766 = sqrt(r788765);
        double r788767 = sqrt(r788763);
        double r788768 = r788766 * r788767;
        return r788768;
}
↓
double f(double x) {
        double r788769 = x;
        double r788770 = sqrt(r788769);
        double r788771 = 1.0;
        double r788772 = r788769 - r788771;
        double r788773 = cbrt(r788772);
        double r788774 = sqrt(r788773);
        double r788775 = r788770 * r788774;
        double r788776 = r788773 * r788773;
        double r788777 = sqrt(r788776);
        double r788778 = r788775 * r788777;
        return r788778;
}

Error

Bits error versus x

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 0.5

    \[\sqrt{x - 1} \cdot \sqrt{x}\]
  2. Using strategy rm

  3. Applied add-cube-cbrt0.9

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

  4. Applied sqrt-prod0.8

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

  5. Applied associate-*l*0.8

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

  6. Final simplification0.8

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

Reproduce

herbie shell --seed 2019163 +o rules:numerics
(FPCore (x)
  :name "sqrt times"
  (* (sqrt (- x 1)) (sqrt x)))