Average Error: 0.0 → 0.0
Time: 10.3s
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 r1707870 = 1.0;
        double r1707871 = x;
        double r1707872 = r1707871 * r1707871;
        double r1707873 = r1707870 - r1707872;
        double r1707874 = -r1707873;
        double r1707875 = exp(r1707874);
        return r1707875;
}
↓
double f(double x) {
        double r1707876 = x;
        double r1707877 = r1707876 * r1707876;
        double r1707878 = 1.0;
        double r1707879 = r1707877 - r1707878;
        double r1707880 = exp(r1707879);
        return r1707880;
}

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 2019174 +o rules:numerics
(FPCore (x)
  :name "exp neg sub"
  (exp (- (- 1.0 (* x x)))))