Average Error: 0.3 → 0.3
Time: 8.7s
Precision: 64
\[\frac{1}{\sqrt{x}}\]
\[\sqrt{\frac{\frac{1}{\sqrt{x}} \cdot 1}{\sqrt{x}}}\]
\frac{1}{\sqrt{x}}
\sqrt{\frac{\frac{1}{\sqrt{x}} \cdot 1}{\sqrt{x}}}
double f(double x) {
        double r1617375 = 1.0;
        double r1617376 = x;
        double r1617377 = sqrt(r1617376);
        double r1617378 = r1617375 / r1617377;
        return r1617378;
}

double f(double x) {
        double r1617379 = 1.0;
        double r1617380 = x;
        double r1617381 = sqrt(r1617380);
        double r1617382 = r1617379 / r1617381;
        double r1617383 = r1617382 * r1617379;
        double r1617384 = r1617383 / r1617381;
        double r1617385 = sqrt(r1617384);
        return r1617385;
}

Error

Bits error versus x

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Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 0.3

    \[\frac{1}{\sqrt{x}}\]
  2. Using strategy rm
  3. Applied add-sqr-sqrt0.6

    \[\leadsto \color{blue}{\sqrt{\frac{1}{\sqrt{x}}} \cdot \sqrt{\frac{1}{\sqrt{x}}}}\]
  4. Using strategy rm
  5. Applied sqrt-unprod0.3

    \[\leadsto \color{blue}{\sqrt{\frac{1}{\sqrt{x}} \cdot \frac{1}{\sqrt{x}}}}\]
  6. Simplified0.3

    \[\leadsto \sqrt{\color{blue}{\frac{\frac{1}{\sqrt{x}} \cdot 1}{\sqrt{x}}}}\]
  7. Final simplification0.3

    \[\leadsto \sqrt{\frac{\frac{1}{\sqrt{x}} \cdot 1}{\sqrt{x}}}\]

Reproduce

herbie shell --seed 1 
(FPCore (x)
  :name "1/sqrt(x)"
  :precision binary64
  (/ 1 (sqrt x)))