Average Error: 0.0 → 0.0
Time: 11.6s
Precision: 64
\[e^{-\left(1 - x \cdot x\right)}\]
↓
\[\frac{1}{\sqrt{e}} \cdot \frac{e^{x \cdot x}}{\sqrt{e}}\]
e^{-\left(1 - x \cdot x\right)}
↓
\frac{1}{\sqrt{e}} \cdot \frac{e^{x \cdot x}}{\sqrt{e}}
double f(double x) {
        double r1893564 = 1.0;
        double r1893565 = x;
        double r1893566 = r1893565 * r1893565;
        double r1893567 = r1893564 - r1893566;
        double r1893568 = -r1893567;
        double r1893569 = exp(r1893568);
        return r1893569;
}
↓
double f(double x) {
        double r1893570 = 1.0;
        double r1893571 = exp(1.0);
        double r1893572 = sqrt(r1893571);
        double r1893573 = r1893570 / r1893572;
        double r1893574 = x;
        double r1893575 = r1893574 * r1893574;
        double r1893576 = exp(r1893575);
        double r1893577 = r1893576 / r1893572;
        double r1893578 = r1893573 * r1893577;
        return r1893578;
}

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. Simplified0.0

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

  7. Applied add-sqr-sqrt1.0

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

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

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

  9. Applied times-frac0.0

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

  10. Final simplification0.0

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

Reproduce

herbie shell --seed 2019168 
(FPCore (x)
  :name "exp neg sub"
  (exp (- (- 1 (* x x)))))