Average Error: 0.0 → 0.0
Time: 4.1s
Precision: 64
\[e^{-\left(1 - x \cdot x\right)}\]
↓
\[\frac{\sqrt{{\left(e^{x}\right)}^{x}}}{\frac{e^{1}}{\sqrt{{\left(e^{x}\right)}^{x}}}}\]
e^{-\left(1 - x \cdot x\right)}
↓
\frac{\sqrt{{\left(e^{x}\right)}^{x}}}{\frac{e^{1}}{\sqrt{{\left(e^{x}\right)}^{x}}}}
double f(double x) {
        double r29529 = 1.0;
        double r29530 = x;
        double r29531 = r29530 * r29530;
        double r29532 = r29529 - r29531;
        double r29533 = -r29532;
        double r29534 = exp(r29533);
        return r29534;
}
↓
double f(double x) {
        double r29535 = x;
        double r29536 = exp(r29535);
        double r29537 = pow(r29536, r29535);
        double r29538 = sqrt(r29537);
        double r29539 = 1.0;
        double r29540 = exp(r29539);
        double r29541 = r29540 / r29538;
        double r29542 = r29538 / r29541;
        return r29542;
}

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 add-log-exp0.0

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

  4. Applied add-log-exp0.0

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

  5. Applied diff-log0.0

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

  6. Applied neg-log0.0

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

  7. Applied rem-exp-log0.0

    \[\leadsto \color{blue}{\frac{1}{\frac{e^{1}}{e^{x \cdot x}}}}\]
  8. Using strategy rm

  9. Applied add-log-exp0.0

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

  10. Applied exp-to-pow0.0

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

  12. Applied add-sqr-sqrt0.0

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

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

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

  14. Applied times-frac0.0

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

  15. Applied associate-/r*0.0

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

  16. Simplified0.0

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

  17. Final simplification0.0

    \[\leadsto \frac{\sqrt{{\left(e^{x}\right)}^{x}}}{\frac{e^{1}}{\sqrt{{\left(e^{x}\right)}^{x}}}}\]

Reproduce

herbie shell --seed 2020035 
(FPCore (x)
  :name "exp neg sub"
  :precision binary64
  (exp (- (- 1 (* x x)))))