Average Error: 32.4 → 0
Time: 6.1s
Precision: 64
\[\frac{x}{x} - \frac{1}{x} \cdot \sqrt{x \cdot x}\]
↓
\[1 - 1 \cdot \frac{\left|x\right|}{x}\]
\frac{x}{x} - \frac{1}{x} \cdot \sqrt{x \cdot x}
↓
1 - 1 \cdot \frac{\left|x\right|}{x}
double f(double x) {
        double r5138961 = x;
        double r5138962 = r5138961 / r5138961;
        double r5138963 = 1.0;
        double r5138964 = r5138963 / r5138961;
        double r5138965 = r5138961 * r5138961;
        double r5138966 = sqrt(r5138965);
        double r5138967 = r5138964 * r5138966;
        double r5138968 = r5138962 - r5138967;
        return r5138968;
}
↓
double f(double x) {
        double r5138969 = 1.0;
        double r5138970 = 1.0;
        double r5138971 = x;
        double r5138972 = fabs(r5138971);
        double r5138973 = r5138972 / r5138971;
        double r5138974 = r5138970 * r5138973;
        double r5138975 = r5138969 - r5138974;
        return r5138975;
}

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. Simplified4.7

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

  4. Applied div-inv4.7

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

  5. Applied associate-*l*4.7

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

  6. Simplified0

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

  7. Final simplification0

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

Reproduce

herbie shell --seed 2019170 +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)))))