Average Error: 0.0 → 0.0
Time: 9.0s
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 r842702 = 1.0;
        double r842703 = x;
        double r842704 = r842703 * r842703;
        double r842705 = r842702 - r842704;
        double r842706 = -r842705;
        double r842707 = exp(r842706);
        return r842707;
}
↓
double f(double x) {
        double r842708 = x;
        double r842709 = r842708 * r842708;
        double r842710 = 1.0;
        double r842711 = r842709 - r842710;
        double r842712 = exp(r842711);
        return r842712;
}

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 2019172 
(FPCore (x)
  :name "exp neg sub"
  (exp (- (- 1.0 (* x x)))))