Average Error: 1.4 → 1.4
Time: 16.4s
Precision: 64
\[e^{\left(-\gamma\right) \cdot x} - 1\]
\[\frac{\frac{e^{\left(x \cdot \gamma\right) \cdot -9} - {\left({1}^{3}\right)}^{3}}{{1}^{3} \cdot \left(e^{\left(x \cdot \gamma\right) \cdot -3} + {1}^{3}\right) + {\left(e^{x \cdot \gamma}\right)}^{-6}}}{e^{\left(x \cdot \gamma\right) \cdot -2} + 1 \cdot \left(e^{\left(-\gamma\right) \cdot x} + 1\right)}\]
e^{\left(-\gamma\right) \cdot x} - 1
\frac{\frac{e^{\left(x \cdot \gamma\right) \cdot -9} - {\left({1}^{3}\right)}^{3}}{{1}^{3} \cdot \left(e^{\left(x \cdot \gamma\right) \cdot -3} + {1}^{3}\right) + {\left(e^{x \cdot \gamma}\right)}^{-6}}}{e^{\left(x \cdot \gamma\right) \cdot -2} + 1 \cdot \left(e^{\left(-\gamma\right) \cdot x} + 1\right)}
double f(double gamma, double x) {
        double r549248 = gamma;
        double r549249 = -r549248;
        double r549250 = x;
        double r549251 = r549249 * r549250;
        double r549252 = exp(r549251);
        double r549253 = 1.0;
        double r549254 = r549252 - r549253;
        return r549254;
}

double f(double gamma, double x) {
        double r549255 = x;
        double r549256 = gamma;
        double r549257 = r549255 * r549256;
        double r549258 = -9.0;
        double r549259 = r549257 * r549258;
        double r549260 = exp(r549259);
        double r549261 = 1.0;
        double r549262 = 3.0;
        double r549263 = pow(r549261, r549262);
        double r549264 = pow(r549263, r549262);
        double r549265 = r549260 - r549264;
        double r549266 = -3.0;
        double r549267 = r549257 * r549266;
        double r549268 = exp(r549267);
        double r549269 = r549268 + r549263;
        double r549270 = r549263 * r549269;
        double r549271 = exp(r549257);
        double r549272 = -6.0;
        double r549273 = pow(r549271, r549272);
        double r549274 = r549270 + r549273;
        double r549275 = r549265 / r549274;
        double r549276 = -2.0;
        double r549277 = r549257 * r549276;
        double r549278 = exp(r549277);
        double r549279 = -r549256;
        double r549280 = r549279 * r549255;
        double r549281 = exp(r549280);
        double r549282 = r549281 + r549261;
        double r549283 = r549261 * r549282;
        double r549284 = r549278 + r549283;
        double r549285 = r549275 / r549284;
        return r549285;
}

Error

Bits error versus gamma

Bits error versus x

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 1.4

    \[e^{\left(-\gamma\right) \cdot x} - 1\]
  2. Using strategy rm
  3. Applied flip3--1.4

    \[\leadsto \color{blue}{\frac{{\left(e^{\left(-\gamma\right) \cdot x}\right)}^{3} - {1}^{3}}{e^{\left(-\gamma\right) \cdot x} \cdot e^{\left(-\gamma\right) \cdot x} + \left(1 \cdot 1 + e^{\left(-\gamma\right) \cdot x} \cdot 1\right)}}\]
  4. Simplified1.4

    \[\leadsto \frac{\color{blue}{e^{\left(x \cdot \gamma\right) \cdot -3} - {1}^{3}}}{e^{\left(-\gamma\right) \cdot x} \cdot e^{\left(-\gamma\right) \cdot x} + \left(1 \cdot 1 + e^{\left(-\gamma\right) \cdot x} \cdot 1\right)}\]
  5. Simplified1.4

    \[\leadsto \frac{e^{\left(x \cdot \gamma\right) \cdot -3} - {1}^{3}}{\color{blue}{e^{\left(x \cdot \gamma\right) \cdot -2} + 1 \cdot \left(e^{\left(-\gamma\right) \cdot x} + 1\right)}}\]
  6. Using strategy rm
  7. Applied flip3--1.4

    \[\leadsto \frac{\color{blue}{\frac{{\left(e^{\left(x \cdot \gamma\right) \cdot -3}\right)}^{3} - {\left({1}^{3}\right)}^{3}}{e^{\left(x \cdot \gamma\right) \cdot -3} \cdot e^{\left(x \cdot \gamma\right) \cdot -3} + \left({1}^{3} \cdot {1}^{3} + e^{\left(x \cdot \gamma\right) \cdot -3} \cdot {1}^{3}\right)}}}{e^{\left(x \cdot \gamma\right) \cdot -2} + 1 \cdot \left(e^{\left(-\gamma\right) \cdot x} + 1\right)}\]
  8. Simplified1.4

    \[\leadsto \frac{\frac{\color{blue}{e^{\left(x \cdot \gamma\right) \cdot -9} - {\left({1}^{3}\right)}^{3}}}{e^{\left(x \cdot \gamma\right) \cdot -3} \cdot e^{\left(x \cdot \gamma\right) \cdot -3} + \left({1}^{3} \cdot {1}^{3} + e^{\left(x \cdot \gamma\right) \cdot -3} \cdot {1}^{3}\right)}}{e^{\left(x \cdot \gamma\right) \cdot -2} + 1 \cdot \left(e^{\left(-\gamma\right) \cdot x} + 1\right)}\]
  9. Simplified1.4

    \[\leadsto \frac{\frac{e^{\left(x \cdot \gamma\right) \cdot -9} - {\left({1}^{3}\right)}^{3}}{\color{blue}{{1}^{3} \cdot \left(e^{\left(x \cdot \gamma\right) \cdot -3} + {1}^{3}\right) + {\left(e^{x \cdot \gamma}\right)}^{-6}}}}{e^{\left(x \cdot \gamma\right) \cdot -2} + 1 \cdot \left(e^{\left(-\gamma\right) \cdot x} + 1\right)}\]
  10. Final simplification1.4

    \[\leadsto \frac{\frac{e^{\left(x \cdot \gamma\right) \cdot -9} - {\left({1}^{3}\right)}^{3}}{{1}^{3} \cdot \left(e^{\left(x \cdot \gamma\right) \cdot -3} + {1}^{3}\right) + {\left(e^{x \cdot \gamma}\right)}^{-6}}}{e^{\left(x \cdot \gamma\right) \cdot -2} + 1 \cdot \left(e^{\left(-\gamma\right) \cdot x} + 1\right)}\]

Reproduce

herbie shell --seed 1 
(FPCore (gamma x)
  :name "exp(-gamma*x) - 1"
  :precision binary32
  (- (exp (* (- gamma) x)) 1))