Average Error: 0.0 → 0.0
Time: 12.9s
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 r1075195 = 1.0;
        double r1075196 = x;
        double r1075197 = r1075196 * r1075196;
        double r1075198 = r1075195 - r1075197;
        double r1075199 = -r1075198;
        double r1075200 = exp(r1075199);
        return r1075200;
}
↓
double f(double x) {
        double r1075201 = -1.0;
        double r1075202 = exp(r1075201);
        double r1075203 = x;
        double r1075204 = r1075203 * r1075203;
        double r1075205 = exp(r1075204);
        double r1075206 = r1075202 * r1075205;
        return r1075206;
}

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

    \[\leadsto \color{blue}{e^{\mathsf{fma}\left(x, x, -1\right)}}\]
  3. Using strategy rm

  4. Applied fma-udef0.0

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

  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 2019144 +o rules:numerics
(FPCore (x)
  :name "exp neg sub"
  (exp (- (- 1 (* x x)))))