Average Error: 0.0 → 0.0
Time: 11.8s
Precision: 64
\[e^{-\left(1 - x \cdot x\right)}\]
↓
\[e^{x \cdot x - 1}\]
e^{-\left(1 - x \cdot x\right)}
↓
e^{x \cdot x - 1}
double f(double x) {
        double r39370 = 1.0;
        double r39371 = x;
        double r39372 = r39371 * r39371;
        double r39373 = r39370 - r39372;
        double r39374 = -r39373;
        double r39375 = exp(r39374);
        return r39375;
}
↓
double f(double x) {
        double r39376 = x;
        double r39377 = r39376 * r39376;
        double r39378 = 1.0;
        double r39379 = r39377 - r39378;
        double r39380 = exp(r39379);
        return r39380;
}

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. Using strategy rm

  3. Applied sub-neg0.0

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

  4. Applied distribute-neg-in0.0

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

  5. Applied exp-sum0.0

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

  6. Simplified0.0

    \[\leadsto e^{-1} \cdot \color{blue}{{\left(e^{x}\right)}^{x}}\]
  7. Using strategy rm

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

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

  9. Applied associate-*l*0.0

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

  10. Simplified0.0

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

  11. Final simplification0.0

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

Reproduce

herbie shell --seed 2019174 
(FPCore (x)
  :name "exp neg sub"
  (exp (- (- 1.0 (* x x)))))