Average Error: 0.0 → 0.0
Time: 12.7s
Precision: 64
\[e^{-\left(1 - x \cdot x\right)}\]
↓
\[\frac{e^{x \cdot x}}{e^{1}}\]
e^{-\left(1 - x \cdot x\right)}
↓
\frac{e^{x \cdot x}}{e^{1}}
double f(double x) {
        double r1443526 = 1.0;
        double r1443527 = x;
        double r1443528 = r1443527 * r1443527;
        double r1443529 = r1443526 - r1443528;
        double r1443530 = -r1443529;
        double r1443531 = exp(r1443530);
        return r1443531;
}
↓
double f(double x) {
        double r1443532 = x;
        double r1443533 = r1443532 * r1443532;
        double r1443534 = exp(r1443533);
        double r1443535 = 1.0;
        double r1443536 = exp(r1443535);
        double r1443537 = r1443534 / r1443536;
        return r1443537;
}

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. Simplified0.0

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

  4. Applied exp-diff0.0

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

  5. Final simplification0.0

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

Reproduce

herbie shell --seed 2019169 
(FPCore (x)
  :name "exp neg sub"
  (exp (- (- 1.0 (* x x)))))