Average Error: 0.0 → 0.0
Time: 9.7s
Precision: 64
\[e^{-\left(1 - x \cdot x\right)}\]
↓
\[e^{x \cdot x} \cdot \frac{1}{e}\]
e^{-\left(1 - x \cdot x\right)}
↓
e^{x \cdot x} \cdot \frac{1}{e}
double f(double x) {
        double r1631258 = 1.0;
        double r1631259 = x;
        double r1631260 = r1631259 * r1631259;
        double r1631261 = r1631258 - r1631260;
        double r1631262 = -r1631261;
        double r1631263 = exp(r1631262);
        return r1631263;
}
↓
double f(double x) {
        double r1631264 = x;
        double r1631265 = r1631264 * r1631264;
        double r1631266 = exp(r1631265);
        double r1631267 = 1.0;
        double r1631268 = exp(1.0);
        double r1631269 = r1631267 / r1631268;
        double r1631270 = r1631266 * r1631269;
        return r1631270;
}

Error

Bits error versus x

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Your Program's Arguments

Results

Enter valid numbers for all inputs

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

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

  7. Final simplification0.0

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

Reproduce

herbie shell --seed 2019162 
(FPCore (x)
  :name "exp neg sub"
  (exp (- (- 1 (* x x)))))