Average Error: 32.9 → 0
Time: 1.4s
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 r119013 = x;
        double r119014 = r119013 / r119013;
        double r119015 = 1.0;
        double r119016 = r119015 / r119013;
        double r119017 = r119013 * r119013;
        double r119018 = sqrt(r119017);
        double r119019 = r119016 * r119018;
        double r119020 = r119014 - r119019;
        return r119020;
}
↓
double f(double x) {
        double r119021 = 1.0;
        double r119022 = 1.0;
        double r119023 = x;
        double r119024 = fabs(r119023);
        double r119025 = r119022 * r119024;
        double r119026 = r119025 / r119023;
        double r119027 = -r119026;
        double r119028 = r119021 + r119027;
        return r119028;
}

Error

Bits error versus x

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original32.9
Target0
Herbie0
\[\begin{array}{l} \mathbf{if}\;x \lt 0.0:\\ \;\;\;\;2\\ \mathbf{else}:\\ \;\;\;\;0.0\\ \end{array}\]

Derivation

  1. Initial program 32.9

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

  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 2020083 
(FPCore (x)
  :name "sqrt sqr"
  :precision binary64

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

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