Average Error: 0.0 → 0.0
Time: 18.3s
Precision: 64
\[e^{-\left(1 - x \cdot x\right)}\]
↓
\[\frac{1}{e^{1 - x \cdot x}}\]
e^{-\left(1 - x \cdot x\right)}
↓
\frac{1}{e^{1 - x \cdot x}}
double f(double x) {
        double r1626523 = 1.0;
        double r1626524 = x;
        double r1626525 = r1626524 * r1626524;
        double r1626526 = r1626523 - r1626525;
        double r1626527 = -r1626526;
        double r1626528 = exp(r1626527);
        return r1626528;
}
↓
double f(double x) {
        double r1626529 = 1.0;
        double r1626530 = x;
        double r1626531 = r1626530 * r1626530;
        double r1626532 = r1626529 - r1626531;
        double r1626533 = exp(r1626532);
        double r1626534 = r1626529 / r1626533;
        return r1626534;
}

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 add-log-exp0.0

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

  4. Applied neg-log0.0

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

  5. Applied rem-exp-log0.0

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

  6. Final simplification0.0

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

Reproduce

herbie shell --seed 2019142 
(FPCore (x)
  :name "exp neg sub"
  (exp (- (- 1 (* x x)))))