Average Error: 0.0 → 0.0
Time: 28.5s
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 r1758592 = 1.0;
        double r1758593 = x;
        double r1758594 = r1758593 * r1758593;
        double r1758595 = r1758592 - r1758594;
        double r1758596 = -r1758595;
        double r1758597 = exp(r1758596);
        return r1758597;
}
↓
double f(double x) {
        double r1758598 = x;
        double r1758599 = r1758598 * r1758598;
        double r1758600 = -1.0;
        double r1758601 = r1758599 + r1758600;
        double r1758602 = exp(r1758601);
        return r1758602;
}

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 2019138 
(FPCore (x)
  :name "exp neg sub"
  (exp (- (- 1 (* x x)))))