Average Error: 32.2 → 0
Time: 4.1s
Precision: 64
\[\frac{x}{x} - \frac{1}{x} \cdot \sqrt{x \cdot x}\]
↓
\[1 - \frac{\left|x\right|}{x}\]
\frac{x}{x} - \frac{1}{x} \cdot \sqrt{x \cdot x}
↓
1 - \frac{\left|x\right|}{x}
double f(double x) {
        double r20253024 = x;
        double r20253025 = r20253024 / r20253024;
        double r20253026 = 1.0;
        double r20253027 = r20253026 / r20253024;
        double r20253028 = r20253024 * r20253024;
        double r20253029 = sqrt(r20253028);
        double r20253030 = r20253027 * r20253029;
        double r20253031 = r20253025 - r20253030;
        return r20253031;
}
↓
double f(double x) {
        double r20253032 = 1.0;
        double r20253033 = x;
        double r20253034 = fabs(r20253033);
        double r20253035 = r20253034 / r20253033;
        double r20253036 = r20253032 - r20253035;
        return r20253036;
}

Error

Bits error versus x

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original32.2
Target0
Herbie0
\[\begin{array}{l} \mathbf{if}\;x \lt 0:\\ \;\;\;\;2\\ \mathbf{else}:\\ \;\;\;\;0\\ \end{array}\]

Derivation

  1. Initial program 32.2

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

  2. Simplified0

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

  3. Final simplification0

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

Reproduce

herbie shell --seed 2019112 +o rules:numerics
(FPCore (x)
  :name "sqrt sqr"

  :herbie-target
  (if (< x 0) 2 0)

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