Average Error: 0.0 → 0.0
Time: 3.2s
Precision: 64
\[e^{-\left(1 - x \cdot x\right)}\]
↓
\[e^{x \cdot x + -1}\]
e^{-\left(1 - x \cdot x\right)}
↓
e^{x \cdot x + -1}
double f(double x) {
        double r406176 = 1.0;
        double r406177 = x;
        double r406178 = r406177 * r406177;
        double r406179 = r406176 - r406178;
        double r406180 = -r406179;
        double r406181 = exp(r406180);
        return r406181;
}
↓
double f(double x) {
        double r406182 = x;
        double r406183 = r406182 * r406182;
        double r406184 = -1.0;
        double r406185 = r406183 + r406184;
        double r406186 = exp(r406185);
        return r406186;
}

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. Final simplification0.0

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

Reproduce

herbie shell --seed 2019156 
(FPCore (x)
  :name "exp neg sub"
  (exp (- (- 1 (* x x)))))