Average Error: 0.0 → 0.0
Time: 1.6s
Precision: 64
\[e^{-\left(1 - x \cdot x\right)}\]
↓
\[\frac{1}{\frac{e^{1}}{e^{x \cdot x}}}\]
e^{-\left(1 - x \cdot x\right)}
↓
\frac{1}{\frac{e^{1}}{e^{x \cdot x}}}
double f(double x) {
        double r20950 = 1.0;
        double r20951 = x;
        double r20952 = r20951 * r20951;
        double r20953 = r20950 - r20952;
        double r20954 = -r20953;
        double r20955 = exp(r20954);
        return r20955;
}
↓
double f(double x) {
        double r20956 = 1.0;
        double r20957 = 1.0;
        double r20958 = exp(r20957);
        double r20959 = x;
        double r20960 = r20959 * r20959;
        double r20961 = exp(r20960);
        double r20962 = r20958 / r20961;
        double r20963 = r20956 / r20962;
        return r20963;
}

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. Final simplification0.0

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

Reproduce

herbie shell --seed 2020100 
(FPCore (x)
  :name "exp neg sub"
  :precision binary64
  (exp (- (- 1 (* x x)))))