Average Error: 0.5 → 0.8
Time: 4.9s
Precision: 64
\[\sqrt{x - 1} \cdot \sqrt{x}\]
↓
\[\sqrt{\sqrt[3]{x - 1} \cdot \sqrt[3]{x - 1}} \cdot \left(\sqrt{\sqrt[3]{x - 1}} \cdot \sqrt{x}\right)\]
\sqrt{x - 1} \cdot \sqrt{x}
↓
\sqrt{\sqrt[3]{x - 1} \cdot \sqrt[3]{x - 1}} \cdot \left(\sqrt{\sqrt[3]{x - 1}} \cdot \sqrt{x}\right)
double f(double x) {
        double r22623 = x;
        double r22624 = 1.0;
        double r22625 = r22623 - r22624;
        double r22626 = sqrt(r22625);
        double r22627 = sqrt(r22623);
        double r22628 = r22626 * r22627;
        return r22628;
}
↓
double f(double x) {
        double r22629 = x;
        double r22630 = 1.0;
        double r22631 = r22629 - r22630;
        double r22632 = cbrt(r22631);
        double r22633 = r22632 * r22632;
        double r22634 = sqrt(r22633);
        double r22635 = sqrt(r22632);
        double r22636 = sqrt(r22629);
        double r22637 = r22635 * r22636;
        double r22638 = r22634 * r22637;
        return r22638;
}

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

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

Reproduce

herbie shell --seed 2019318 
(FPCore (x)
  :name "sqrt times"
  :precision binary64
  (* (sqrt (- x 1)) (sqrt x)))