Average Error: 0.0 → 0.0
Time: 14.4s
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 r1324544 = 1.0;
        double r1324545 = x;
        double r1324546 = r1324545 * r1324545;
        double r1324547 = r1324544 - r1324546;
        double r1324548 = -r1324547;
        double r1324549 = exp(r1324548);
        return r1324549;
}
↓
double f(double x) {
        double r1324550 = x;
        double r1324551 = r1324550 * r1324550;
        double r1324552 = exp(r1324551);
        double r1324553 = 1.0;
        double r1324554 = exp(r1324553);
        double r1324555 = r1324552 / r1324554;
        return r1324555;
}

Error

Bits error versus x

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Your Program's Arguments

Results

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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 +o rules:numerics
(FPCore (x)
  :name "exp neg sub"
  (exp (- (- 1.0 (* x x)))))