Average Error: 0.0 → 0.0
Time: 12.1s
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 r1795953 = 1.0;
        double r1795954 = x;
        double r1795955 = r1795954 * r1795954;
        double r1795956 = r1795953 - r1795955;
        double r1795957 = -r1795956;
        double r1795958 = exp(r1795957);
        return r1795958;
}
↓
double f(double x) {
        double r1795959 = x;
        double r1795960 = r1795959 * r1795959;
        double r1795961 = 1.0;
        double r1795962 = r1795960 - r1795961;
        double r1795963 = exp(r1795962);
        return r1795963;
}

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 2019158 
(FPCore (x)
  :name "exp neg sub"
  (exp (- (- 1 (* x x)))))