Average Error: 0.5 → 0.7
Time: 16.5s
Precision: 64
\[\sqrt{x - 1} \cdot \sqrt{x}\]
↓
\[\sqrt{\sqrt{x}} \cdot \left(\sqrt{x - 1} \cdot \sqrt{\sqrt{x}}\right)\]
\sqrt{x - 1} \cdot \sqrt{x}
↓
\sqrt{\sqrt{x}} \cdot \left(\sqrt{x - 1} \cdot \sqrt{\sqrt{x}}\right)
double f(double x) {
        double r369866 = x;
        double r369867 = 1.0;
        double r369868 = r369866 - r369867;
        double r369869 = sqrt(r369868);
        double r369870 = sqrt(r369866);
        double r369871 = r369869 * r369870;
        return r369871;
}
↓
double f(double x) {
        double r369872 = x;
        double r369873 = sqrt(r369872);
        double r369874 = sqrt(r369873);
        double r369875 = 1.0;
        double r369876 = r369872 - r369875;
        double r369877 = sqrt(r369876);
        double r369878 = r369877 * r369874;
        double r369879 = r369874 * r369878;
        return r369879;
}

Error

Bits error versus x

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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-sqr-sqrt0.7

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

  4. Applied associate-*r*0.7

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

  5. Final simplification0.7

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

Reproduce

herbie shell --seed 2019139 +o rules:numerics
(FPCore (x)
  :name "sqrt times"
  (* (sqrt (- x 1)) (sqrt x)))