Average Error: 39.6 → 0.0
Time: 6.0s
Precision: 64
\[\left(x + 1\right) \cdot \left(x + 1\right) - 1\]
↓
\[2 \cdot x + x \cdot x\]
\left(x + 1\right) \cdot \left(x + 1\right) - 1
↓
2 \cdot x + x \cdot x
double f(double x) {
        double r11278 = x;
        double r11279 = 1.0;
        double r11280 = r11278 + r11279;
        double r11281 = r11280 * r11280;
        double r11282 = r11281 - r11279;
        return r11282;
}
↓
double f(double x) {
        double r11283 = 2.0;
        double r11284 = x;
        double r11285 = r11283 * r11284;
        double r11286 = r11284 * r11284;
        double r11287 = r11285 + r11286;
        return r11287;
}

Error

Bits error versus x

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Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 39.6

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

  2. Taylor expanded around 0 0.0

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

  3. Simplified0.0

    \[\leadsto \color{blue}{x \cdot \left(2 + x\right)}\]
  4. Using strategy rm

  5. Applied distribute-rgt-in0.0

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

  6. Final simplification0.0

    \[\leadsto 2 \cdot x + x \cdot x\]

Reproduce

herbie shell --seed 2019208 +o rules:numerics
(FPCore (x)
  :name "Expanding a square"
  :precision binary64
  (- (* (+ x 1) (+ x 1)) 1))