Average Error: 0.5 → 0.8
Time: 14.4s
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 r820157 = x;
        double r820158 = 1.0;
        double r820159 = r820157 - r820158;
        double r820160 = sqrt(r820159);
        double r820161 = sqrt(r820157);
        double r820162 = r820160 * r820161;
        return r820162;
}
↓
double f(double x) {
        double r820163 = x;
        double r820164 = sqrt(r820163);
        double r820165 = 1.0;
        double r820166 = r820163 - r820165;
        double r820167 = cbrt(r820166);
        double r820168 = sqrt(r820167);
        double r820169 = r820164 * r820168;
        double r820170 = r820167 * r820167;
        double r820171 = sqrt(r820170);
        double r820172 = r820169 * r820171;
        return r820172;
}

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 
(FPCore (x)
  :name "sqrt times"
  (* (sqrt (- x 1)) (sqrt x)))