Average Error: 0.0 → 0.0
Time: 17.6s
Precision: 64
\[e^{-\left(1 - x \cdot x\right)}\]
↓
\[{e}^{\left(-1 + x \cdot x\right)}\]
e^{-\left(1 - x \cdot x\right)}
↓
{e}^{\left(-1 + x \cdot x\right)}
double f(double x) {
        double r1201021 = 1.0;
        double r1201022 = x;
        double r1201023 = r1201022 * r1201022;
        double r1201024 = r1201021 - r1201023;
        double r1201025 = -r1201024;
        double r1201026 = exp(r1201025);
        return r1201026;
}
↓
double f(double x) {
        double r1201027 = exp(1.0);
        double r1201028 = -1.0;
        double r1201029 = x;
        double r1201030 = r1201029 * r1201029;
        double r1201031 = r1201028 + r1201030;
        double r1201032 = pow(r1201027, r1201031);
        return r1201032;
}

Error

Bits error versus x

Try it out

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

    \[\leadsto \color{blue}{e^{-1 + x \cdot x}}\]
  3. Using strategy rm

  4. Applied *-un-lft-identity0.0

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

  5. Applied exp-prod0.0

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

  6. Simplified0.0

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

  7. Final simplification0.0

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

Reproduce

herbie shell --seed 2019132 
(FPCore (x)
  :name "exp neg sub"
  (exp (- (- 1 (* x x)))))