Average Error: 0.0 → 0.0
Time: 820.0ms
Precision: 64
\[e^{-\left(1 - x \cdot x\right)}\]
↓
\[{\left(e^{-1}\right)}^{\left(1 - x \cdot x\right)}\]
e^{-\left(1 - x \cdot x\right)}
↓
{\left(e^{-1}\right)}^{\left(1 - x \cdot x\right)}
double f(double x) {
        double r31553 = 1.0;
        double r31554 = x;
        double r31555 = r31554 * r31554;
        double r31556 = r31553 - r31555;
        double r31557 = -r31556;
        double r31558 = exp(r31557);
        return r31558;
}
↓
double f(double x) {
        double r31559 = -1.0;
        double r31560 = exp(r31559);
        double r31561 = 1.0;
        double r31562 = x;
        double r31563 = r31562 * r31562;
        double r31564 = r31561 - r31563;
        double r31565 = pow(r31560, r31564);
        return r31565;
}

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. Using strategy rm

  3. Applied neg-mul-10.0

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

  4. Applied exp-prod0.0

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

  5. Final simplification0.0

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

Reproduce

herbie shell --seed 2020064 
(FPCore (x)
  :name "exp neg sub"
  :precision binary64
  (exp (- (- 1 (* x x)))))