Average Error: 0.0 → 0.0
Time: 15.6s
Precision: 64
\[e^{-\left(1 - x \cdot x\right)}\]
↓
\[e^{\left(1 + x\right) \cdot \left(x - 1\right)}\]
e^{-\left(1 - x \cdot x\right)}
↓
e^{\left(1 + x\right) \cdot \left(x - 1\right)}
double f(double x) {
        double r1504075 = 1.0;
        double r1504076 = x;
        double r1504077 = r1504076 * r1504076;
        double r1504078 = r1504075 - r1504077;
        double r1504079 = -r1504078;
        double r1504080 = exp(r1504079);
        return r1504080;
}
↓
double f(double x) {
        double r1504081 = 1.0;
        double r1504082 = x;
        double r1504083 = r1504081 + r1504082;
        double r1504084 = r1504082 - r1504081;
        double r1504085 = r1504083 * r1504084;
        double r1504086 = exp(r1504085);
        return r1504086;
}

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 *-un-lft-identity0.0

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

  5. Applied difference-of-squares0.0

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

  6. Final simplification0.0

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

Reproduce

herbie shell --seed 2019163 
(FPCore (x)
  :name "exp neg sub"
  (exp (- (- 1 (* x x)))))