Average Error: 0.0 → 0.0
Time: 22.5s
Precision: 64
\[e^{-\left(1 - x \cdot x\right)}\]
↓
\[\frac{1}{\sqrt{e^{1}}} \cdot \frac{e^{x \cdot x}}{\sqrt{e^{1}}}\]
e^{-\left(1 - x \cdot x\right)}
↓
\frac{1}{\sqrt{e^{1}}} \cdot \frac{e^{x \cdot x}}{\sqrt{e^{1}}}
double f(double x) {
        double r2006915 = 1.0;
        double r2006916 = x;
        double r2006917 = r2006916 * r2006916;
        double r2006918 = r2006915 - r2006917;
        double r2006919 = -r2006918;
        double r2006920 = exp(r2006919);
        return r2006920;
}
↓
double f(double x) {
        double r2006921 = 1.0;
        double r2006922 = 1.0;
        double r2006923 = exp(r2006922);
        double r2006924 = sqrt(r2006923);
        double r2006925 = r2006921 / r2006924;
        double r2006926 = x;
        double r2006927 = r2006926 * r2006926;
        double r2006928 = exp(r2006927);
        double r2006929 = r2006928 / r2006924;
        double r2006930 = r2006925 * r2006929;
        return r2006930;
}

Error

Bits error versus x

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Results

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Derivation

  1. Initial program 0.0

    \[e^{-\left(1 - x \cdot x\right)}\]

  2. Simplified0.0

    \[\leadsto \color{blue}{e^{x \cdot x - 1}}\]
  3. Using strategy rm

  4. Applied exp-diff0.0

    \[\leadsto \color{blue}{\frac{e^{x \cdot x}}{e^{1}}}\]
  5. Using strategy rm

  6. Applied add-sqr-sqrt1.0

    \[\leadsto \frac{e^{x \cdot x}}{\color{blue}{\sqrt{e^{1}} \cdot \sqrt{e^{1}}}}\]

  7. Applied *-un-lft-identity1.0

    \[\leadsto \frac{\color{blue}{1 \cdot e^{x \cdot x}}}{\sqrt{e^{1}} \cdot \sqrt{e^{1}}}\]

  8. Applied times-frac0.0

    \[\leadsto \color{blue}{\frac{1}{\sqrt{e^{1}}} \cdot \frac{e^{x \cdot x}}{\sqrt{e^{1}}}}\]

  9. Final simplification0.0

    \[\leadsto \frac{1}{\sqrt{e^{1}}} \cdot \frac{e^{x \cdot x}}{\sqrt{e^{1}}}\]

Reproduce

herbie shell --seed 2019168 
(FPCore (x)
  :name "exp neg sub"
  (exp (- (- 1.0 (* x x)))))