Average Error: 0.5 → 0.8
Time: 17.2s
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 r674306 = x;
        double r674307 = 1.0;
        double r674308 = r674306 - r674307;
        double r674309 = sqrt(r674308);
        double r674310 = sqrt(r674306);
        double r674311 = r674309 * r674310;
        return r674311;
}
↓
double f(double x) {
        double r674312 = x;
        double r674313 = sqrt(r674312);
        double r674314 = 1.0;
        double r674315 = r674312 - r674314;
        double r674316 = cbrt(r674315);
        double r674317 = sqrt(r674316);
        double r674318 = r674313 * r674317;
        double r674319 = r674316 * r674316;
        double r674320 = sqrt(r674319);
        double r674321 = r674318 * r674320;
        return r674321;
}

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)))