Average Error: 39.0 → 0.0
Time: 5.7s
Precision: 64
\[\left(x + 1\right) \cdot \left(x + 1\right) - 1\]
↓
\[x \cdot \left(2 + x\right)\]
\left(x + 1\right) \cdot \left(x + 1\right) - 1
↓
x \cdot \left(2 + x\right)
double f(double x) {
        double r11220 = x;
        double r11221 = 1.0;
        double r11222 = r11220 + r11221;
        double r11223 = r11222 * r11222;
        double r11224 = r11223 - r11221;
        return r11224;
}
↓
double f(double x) {
        double r11225 = x;
        double r11226 = 2.0;
        double r11227 = r11226 + r11225;
        double r11228 = r11225 * r11227;
        return r11228;
}

Error

Bits error versus x

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Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 39.0

    \[\left(x + 1\right) \cdot \left(x + 1\right) - 1\]

  2. Taylor expanded around 0 0.0

    \[\leadsto \color{blue}{2 \cdot x + {x}^{2}}\]

  3. Simplified0.0

    \[\leadsto \color{blue}{x \cdot \left(2 + x\right)}\]

  4. Final simplification0.0

    \[\leadsto x \cdot \left(2 + x\right)\]

Reproduce

herbie shell --seed 2019195 +o rules:numerics
(FPCore (x)
  :name "Expanding a square"
  (- (* (+ x 1.0) (+ x 1.0)) 1.0))