Average Error: 0.0 → 0.0
Time: 15.7s
Precision: 64
\[e^{-\left(1 - x \cdot x\right)}\]
↓
\[e^{-1} \cdot e^{x \cdot x}\]
e^{-\left(1 - x \cdot x\right)}
↓
e^{-1} \cdot e^{x \cdot x}
double f(double x) {
        double r1429722 = 1.0;
        double r1429723 = x;
        double r1429724 = r1429723 * r1429723;
        double r1429725 = r1429722 - r1429724;
        double r1429726 = -r1429725;
        double r1429727 = exp(r1429726);
        return r1429727;
}
↓
double f(double x) {
        double r1429728 = 1.0;
        double r1429729 = -r1429728;
        double r1429730 = exp(r1429729);
        double r1429731 = x;
        double r1429732 = r1429731 * r1429731;
        double r1429733 = exp(r1429732);
        double r1429734 = r1429730 * r1429733;
        return r1429734;
}

Error

Bits error versus x

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Your Program's Arguments

Results

Enter valid numbers for all inputs

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. Using strategy rm

  4. Applied sub-neg0.0

    \[\leadsto e^{\color{blue}{x \cdot x + \left(-1\right)}}\]

  5. Applied exp-sum0.0

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

  6. Final simplification0.0

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

Reproduce

herbie shell --seed 2019200 
(FPCore (x)
  :name "exp neg sub"
  (exp (- (- 1.0 (* x x)))))