Average Error: 32.4 → 0
Time: 1.5s
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 r157067 = x;
        double r157068 = r157067 / r157067;
        double r157069 = 1.0;
        double r157070 = r157069 / r157067;
        double r157071 = r157067 * r157067;
        double r157072 = sqrt(r157071);
        double r157073 = r157070 * r157072;
        double r157074 = r157068 - r157073;
        return r157074;
}
↓
double f(double x) {
        double r157075 = 1.0;
        double r157076 = 1.0;
        double r157077 = x;
        double r157078 = fabs(r157077);
        double r157079 = r157076 * r157078;
        double r157080 = r157079 / r157077;
        double r157081 = -r157080;
        double r157082 = r157075 + r157081;
        return r157082;
}

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 2020100 
(FPCore (x)
  :name "sqrt sqr"
  :precision binary64

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

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