Average Error: 0.0 → 0.0
Time: 12.5s
Precision: 64
\[e^{-\left(1 - x \cdot x\right)}\]
↓
\[\sqrt{e^{x \cdot x - 1}} \cdot \sqrt{e^{x \cdot x - 1}}\]
e^{-\left(1 - x \cdot x\right)}
↓
\sqrt{e^{x \cdot x - 1}} \cdot \sqrt{e^{x \cdot x - 1}}
double f(double x) {
        double r44240 = 1.0;
        double r44241 = x;
        double r44242 = r44241 * r44241;
        double r44243 = r44240 - r44242;
        double r44244 = -r44243;
        double r44245 = exp(r44244);
        return r44245;
}
↓
double f(double x) {
        double r44246 = x;
        double r44247 = r44246 * r44246;
        double r44248 = 1.0;
        double r44249 = r44247 - r44248;
        double r44250 = exp(r44249);
        double r44251 = sqrt(r44250);
        double r44252 = r44251 * r44251;
        return r44252;
}

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 add-sqr-sqrt0.0

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

  5. Final simplification0.0

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

Reproduce

herbie shell --seed 2020047 
(FPCore (x)
  :name "exp neg sub"
  :precision binary64
  (exp (- (- 1 (* x x)))))