Average Error: 0.5 → 0.5
Time: 5.0s
Precision: 64
\[\sqrt{x - 1} \cdot \sqrt{x}\]
↓
\[\sqrt{1} \cdot \left(\sqrt{x - 1} \cdot \sqrt{x}\right)\]
\sqrt{x - 1} \cdot \sqrt{x}
↓
\sqrt{1} \cdot \left(\sqrt{x - 1} \cdot \sqrt{x}\right)
double f(double x) {
        double r21110 = x;
        double r21111 = 1.0;
        double r21112 = r21110 - r21111;
        double r21113 = sqrt(r21112);
        double r21114 = sqrt(r21110);
        double r21115 = r21113 * r21114;
        return r21115;
}
↓
double f(double x) {
        double r21116 = 1.0;
        double r21117 = sqrt(r21116);
        double r21118 = x;
        double r21119 = 1.0;
        double r21120 = r21118 - r21119;
        double r21121 = sqrt(r21120);
        double r21122 = sqrt(r21118);
        double r21123 = r21121 * r21122;
        double r21124 = r21117 * r21123;
        return r21124;
}

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 *-un-lft-identity0.5

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

  4. Applied sqrt-prod0.5

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

  5. Applied associate-*l*0.5

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

  6. Final simplification0.5

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

Reproduce

herbie shell --seed 2020035 
(FPCore (x)
  :name "sqrt times"
  :precision binary64
  (* (sqrt (- x 1)) (sqrt x)))