Average Error: 32.6 → 0
Time: 6.0s
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 r5529938 = x;
        double r5529939 = r5529938 / r5529938;
        double r5529940 = 1.0;
        double r5529941 = r5529940 / r5529938;
        double r5529942 = r5529938 * r5529938;
        double r5529943 = sqrt(r5529942);
        double r5529944 = r5529941 * r5529943;
        double r5529945 = r5529939 - r5529944;
        return r5529945;
}
↓
double f(double x) {
        double r5529946 = 1.0;
        double r5529947 = 1.0;
        double r5529948 = x;
        double r5529949 = fabs(r5529948);
        double r5529950 = r5529947 * r5529949;
        double r5529951 = r5529950 / r5529948;
        double r5529952 = r5529946 - r5529951;
        return r5529952;
}

Error

Bits error versus x

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original32.6
Target0
Herbie0
\[\begin{array}{l} \mathbf{if}\;x \lt 0.0:\\ \;\;\;\;2\\ \mathbf{else}:\\ \;\;\;\;0.0\\ \end{array}\]

Derivation

  1. Initial program 32.6

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

  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

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

Reproduce

herbie shell --seed 2019174 +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)))))