Average Error: 0.5 → 0.7
Time: 19.1s
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 r1217181 = x;
        double r1217182 = 1.0;
        double r1217183 = r1217181 - r1217182;
        double r1217184 = sqrt(r1217183);
        double r1217185 = sqrt(r1217181);
        double r1217186 = r1217184 * r1217185;
        return r1217186;
}
↓
double f(double x) {
        double r1217187 = x;
        double r1217188 = sqrt(r1217187);
        double r1217189 = sqrt(r1217188);
        double r1217190 = 1.0;
        double r1217191 = r1217187 - r1217190;
        double r1217192 = sqrt(r1217191);
        double r1217193 = r1217192 * r1217189;
        double r1217194 = r1217189 * r1217193;
        return r1217194;
}

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-sqrt0.5

    \[\leadsto \sqrt{x - 1} \cdot \sqrt{\color{blue}{\sqrt{x} \cdot \sqrt{x}}}\]

  4. Applied sqrt-prod0.7

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

  5. Applied associate-*r*0.7

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

  6. Final simplification0.7

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

Reproduce

herbie shell --seed 2019162 
(FPCore (x)
  :name "sqrt times"
  (* (sqrt (- x 1)) (sqrt x)))