Average Error: 0.0 → 0.0
Time: 7.0s
Precision: 64
\[e^{-\left(1 - x \cdot x\right)}\]
↓
\[\frac{e^{x \cdot x}}{e}\]
e^{-\left(1 - x \cdot x\right)}
↓
\frac{e^{x \cdot x}}{e}
double f(double x) {
        double r772228 = 1.0;
        double r772229 = x;
        double r772230 = r772229 * r772229;
        double r772231 = r772228 - r772230;
        double r772232 = -r772231;
        double r772233 = exp(r772232);
        return r772233;
}
↓
double f(double x) {
        double r772234 = x;
        double r772235 = r772234 * r772234;
        double r772236 = exp(r772235);
        double r772237 = exp(1.0);
        double r772238 = r772236 / r772237;
        return r772238;
}

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-sum0.0

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

  5. Simplified0.0

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

  7. Applied un-div-inv0.0

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

  8. Final simplification0.0

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

Reproduce

herbie shell --seed 2019153 
(FPCore (x)
  :name "exp neg sub"
  (exp (- (- 1 (* x x)))))