Average Error: 0.1 → 0.2
Time: 10.8s
Precision: 64
\[\left(\sqrt{x} - e^{x \cdot 0.1000000000000000055511151231257827021182}\right) \cdot 0.1000000000000000055511151231257827021182\]
\[\frac{\frac{x \cdot x - e^{\left(x \cdot 0.1000000000000000055511151231257827021182\right) \cdot 4}}{x + e^{2 \cdot \left(x \cdot 0.1000000000000000055511151231257827021182\right)}}}{\sqrt{x} + e^{x \cdot 0.1000000000000000055511151231257827021182}} \cdot 0.1000000000000000055511151231257827021182\]
\left(\sqrt{x} - e^{x \cdot 0.1000000000000000055511151231257827021182}\right) \cdot 0.1000000000000000055511151231257827021182
\frac{\frac{x \cdot x - e^{\left(x \cdot 0.1000000000000000055511151231257827021182\right) \cdot 4}}{x + e^{2 \cdot \left(x \cdot 0.1000000000000000055511151231257827021182\right)}}}{\sqrt{x} + e^{x \cdot 0.1000000000000000055511151231257827021182}} \cdot 0.1000000000000000055511151231257827021182
double f(double x) {
        double r2265284 = x;
        double r2265285 = sqrt(r2265284);
        double r2265286 = 0.1;
        double r2265287 = r2265284 * r2265286;
        double r2265288 = exp(r2265287);
        double r2265289 = r2265285 - r2265288;
        double r2265290 = r2265289 * r2265286;
        return r2265290;
}

double f(double x) {
        double r2265291 = x;
        double r2265292 = r2265291 * r2265291;
        double r2265293 = 0.1;
        double r2265294 = r2265291 * r2265293;
        double r2265295 = 4.0;
        double r2265296 = r2265294 * r2265295;
        double r2265297 = exp(r2265296);
        double r2265298 = r2265292 - r2265297;
        double r2265299 = 2.0;
        double r2265300 = r2265299 * r2265294;
        double r2265301 = exp(r2265300);
        double r2265302 = r2265291 + r2265301;
        double r2265303 = r2265298 / r2265302;
        double r2265304 = sqrt(r2265291);
        double r2265305 = exp(r2265294);
        double r2265306 = r2265304 + r2265305;
        double r2265307 = r2265303 / r2265306;
        double r2265308 = r2265307 * r2265293;
        return r2265308;
}

Error

Bits error versus x

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 0.1

    \[\left(\sqrt{x} - e^{x \cdot 0.1000000000000000055511151231257827021182}\right) \cdot 0.1000000000000000055511151231257827021182\]
  2. Using strategy rm
  3. Applied flip--0.2

    \[\leadsto \color{blue}{\frac{\sqrt{x} \cdot \sqrt{x} - e^{x \cdot 0.1000000000000000055511151231257827021182} \cdot e^{x \cdot 0.1000000000000000055511151231257827021182}}{\sqrt{x} + e^{x \cdot 0.1000000000000000055511151231257827021182}}} \cdot 0.1000000000000000055511151231257827021182\]
  4. Simplified0.2

    \[\leadsto \frac{\color{blue}{x - e^{2 \cdot \left(x \cdot 0.1000000000000000055511151231257827021182\right)}}}{\sqrt{x} + e^{x \cdot 0.1000000000000000055511151231257827021182}} \cdot 0.1000000000000000055511151231257827021182\]
  5. Using strategy rm
  6. Applied flip--0.2

    \[\leadsto \frac{\color{blue}{\frac{x \cdot x - e^{2 \cdot \left(x \cdot 0.1000000000000000055511151231257827021182\right)} \cdot e^{2 \cdot \left(x \cdot 0.1000000000000000055511151231257827021182\right)}}{x + e^{2 \cdot \left(x \cdot 0.1000000000000000055511151231257827021182\right)}}}}{\sqrt{x} + e^{x \cdot 0.1000000000000000055511151231257827021182}} \cdot 0.1000000000000000055511151231257827021182\]
  7. Simplified0.2

    \[\leadsto \frac{\frac{\color{blue}{x \cdot x - e^{\left(x \cdot 0.1000000000000000055511151231257827021182\right) \cdot 4}}}{x + e^{2 \cdot \left(x \cdot 0.1000000000000000055511151231257827021182\right)}}}{\sqrt{x} + e^{x \cdot 0.1000000000000000055511151231257827021182}} \cdot 0.1000000000000000055511151231257827021182\]
  8. Final simplification0.2

    \[\leadsto \frac{\frac{x \cdot x - e^{\left(x \cdot 0.1000000000000000055511151231257827021182\right) \cdot 4}}{x + e^{2 \cdot \left(x \cdot 0.1000000000000000055511151231257827021182\right)}}}{\sqrt{x} + e^{x \cdot 0.1000000000000000055511151231257827021182}} \cdot 0.1000000000000000055511151231257827021182\]

Reproduce

herbie shell --seed 1 
(FPCore (x)
  :name "(sqrt(x) - exp(x*0.1))*0.1"
  :precision binary64
  (* (- (sqrt x) (exp (* x 0.10000000000000001))) 0.10000000000000001))