Average Error: 0.0 → 0.0
Time: 7.6s
Precision: 64
\[e^{-\left(1 - x \cdot x\right)}\]
↓
\[{\left(e^{x}\right)}^{x} \cdot e^{-1}\]
e^{-\left(1 - x \cdot x\right)}
↓
{\left(e^{x}\right)}^{x} \cdot e^{-1}
double f(double x) {
        double r33507 = 1.0;
        double r33508 = x;
        double r33509 = r33508 * r33508;
        double r33510 = r33507 - r33509;
        double r33511 = -r33510;
        double r33512 = exp(r33511);
        return r33512;
}
↓
double f(double x) {
        double r33513 = x;
        double r33514 = exp(r33513);
        double r33515 = pow(r33514, r33513);
        double r33516 = 1.0;
        double r33517 = -r33516;
        double r33518 = exp(r33517);
        double r33519 = r33515 * r33518;
        return r33519;
}

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 sub-neg0.0

    \[\leadsto e^{\color{blue}{x \cdot x + \left(-1\right)}}\]

  5. Applied exp-sum0.0

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

  6. Simplified0.0

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

  7. Final simplification0.0

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

Reproduce

herbie shell --seed 2019194 
(FPCore (x)
  :name "exp neg sub"
  (exp (- (- 1.0 (* x x)))))