Average Error: 32.4 → 0
Time: 1.6s
Precision: 64
\[\frac{x}{x} - \frac{1}{x} \cdot \sqrt{x \cdot x}\]
↓
\[1 + \left(-\frac{1 \cdot \left|x\right|}{x}\right)\]
\frac{x}{x} - \frac{1}{x} \cdot \sqrt{x \cdot x}
↓
1 + \left(-\frac{1 \cdot \left|x\right|}{x}\right)
double f(double x) {
        double r133178 = x;
        double r133179 = r133178 / r133178;
        double r133180 = 1.0;
        double r133181 = r133180 / r133178;
        double r133182 = r133178 * r133178;
        double r133183 = sqrt(r133182);
        double r133184 = r133181 * r133183;
        double r133185 = r133179 - r133184;
        return r133185;
}
↓
double f(double x) {
        double r133186 = 1.0;
        double r133187 = 1.0;
        double r133188 = x;
        double r133189 = fabs(r133188);
        double r133190 = r133187 * r133189;
        double r133191 = r133190 / r133188;
        double r133192 = -r133191;
        double r133193 = r133186 + r133192;
        return r133193;
}

Error

Bits error versus x

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original32.4
Target0
Herbie0
\[\begin{array}{l} \mathbf{if}\;x \lt 0.0:\\ \;\;\;\;2\\ \mathbf{else}:\\ \;\;\;\;0.0\\ \end{array}\]

Derivation

  1. Initial program 32.4

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

  2. Simplified0

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

  3. Final simplification0

    \[\leadsto 1 + \left(-\frac{1 \cdot \left|x\right|}{x}\right)\]

Reproduce

herbie shell --seed 2020034 
(FPCore (x)
  :name "sqrt sqr"
  :precision binary64

  :herbie-target
  (if (< x 0.0) 2 0.0)

  (- (/ x x) (* (/ 1 x) (sqrt (* x x)))))