Average Error: 2.4 → 0
Time: 5.4s
Precision: 64
\[e^{\alpha \cdot \left(\left(1 - x\right) - 1\right)}\]
\[e^{\left(-x\right) \cdot \alpha}\]
e^{\alpha \cdot \left(\left(1 - x\right) - 1\right)}
e^{\left(-x\right) \cdot \alpha}
double f(double alpha, double x) {
        double r539485 = alpha;
        double r539486 = 1.0;
        double r539487 = x;
        double r539488 = r539486 - r539487;
        double r539489 = r539488 - r539486;
        double r539490 = r539485 * r539489;
        double r539491 = exp(r539490);
        return r539491;
}

double f(double alpha, double x) {
        double r539492 = x;
        double r539493 = -r539492;
        double r539494 = alpha;
        double r539495 = r539493 * r539494;
        double r539496 = exp(r539495);
        return r539496;
}

Error

Bits error versus alpha

Bits error versus x

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 2.4

    \[e^{\alpha \cdot \left(\left(1 - x\right) - 1\right)}\]
  2. Simplified0

    \[\leadsto \color{blue}{e^{\left(-x\right) \cdot \alpha}}\]
  3. Final simplification0

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

Reproduce

herbie shell --seed 1 
(FPCore (alpha x)
  :name "exp(alpha*(1 - x - 1))"
  :precision binary32
  (exp (* alpha (- (- 1 x) 1))))