Average Error: 32.4 → 0
Time: 4.5s
Precision: 64
\[\frac{x}{x} - \frac{1}{x} \cdot \sqrt{x \cdot x}\]
↓
\[1 - \frac{1 \cdot \left|x\right|}{x}\]
\frac{x}{x} - \frac{1}{x} \cdot \sqrt{x \cdot x}
↓
1 - \frac{1 \cdot \left|x\right|}{x}
double f(double x) {
        double r92249 = x;
        double r92250 = r92249 / r92249;
        double r92251 = 1.0;
        double r92252 = r92251 / r92249;
        double r92253 = r92249 * r92249;
        double r92254 = sqrt(r92253);
        double r92255 = r92252 * r92254;
        double r92256 = r92250 - r92255;
        return r92256;
}
↓
double f(double x) {
        double r92257 = 1.0;
        double r92258 = 1.0;
        double r92259 = x;
        double r92260 = fabs(r92259);
        double r92261 = r92258 * r92260;
        double r92262 = r92261 / r92259;
        double r92263 = r92257 - r92262;
        return r92263;
}

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. Simplified4.8

    \[\leadsto \color{blue}{1 - \frac{1}{x} \cdot \left|x\right|}\]
  3. Using strategy rm

  4. Applied associate-*l/0

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

  5. Final simplification0

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

Reproduce

herbie shell --seed 2019195 
(FPCore (x)
  :name "sqrt sqr"

  :herbie-target
  (if (< x 0.0) 2.0 0.0)

  (- (/ x x) (* (/ 1.0 x) (sqrt (* x x)))))