Average Error: 32.2 → 0
Time: 5.6s
Precision: 64
\[\frac{x}{x} - \frac{1}{x} \cdot \sqrt{x \cdot x}\]
↓
\[1 - \frac{\left|x\right| \cdot 1}{x}\]
\frac{x}{x} - \frac{1}{x} \cdot \sqrt{x \cdot x}
↓
1 - \frac{\left|x\right| \cdot 1}{x}
double f(double x) {
        double r3472133 = x;
        double r3472134 = r3472133 / r3472133;
        double r3472135 = 1.0;
        double r3472136 = r3472135 / r3472133;
        double r3472137 = r3472133 * r3472133;
        double r3472138 = sqrt(r3472137);
        double r3472139 = r3472136 * r3472138;
        double r3472140 = r3472134 - r3472139;
        return r3472140;
}
↓
double f(double x) {
        double r3472141 = 1.0;
        double r3472142 = x;
        double r3472143 = fabs(r3472142);
        double r3472144 = 1.0;
        double r3472145 = r3472143 * r3472144;
        double r3472146 = r3472145 / r3472142;
        double r3472147 = r3472141 - r3472146;
        return r3472147;
}

Error

Bits error versus x

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

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

Derivation

  1. Initial program 32.2

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

  2. Simplified4.9

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

  4. Applied associate-*l/0

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

  5. Final simplification0

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

Reproduce

herbie shell --seed 2019192 +o rules:numerics
(FPCore (x)
  :name "sqrt sqr"

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

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