Average Error: 0.0 → 0.0
Time: 2.0s
Precision: 64
\[\left(x \cdot x\right) \cdot 2 - 1\]
↓
\[2 \cdot \left(x \cdot x\right) - 1\]
\left(x \cdot x\right) \cdot 2 - 1
↓
2 \cdot \left(x \cdot x\right) - 1
double f(double x) {
        double r20629 = x;
        double r20630 = r20629 * r20629;
        double r20631 = 2.0;
        double r20632 = r20630 * r20631;
        double r20633 = 1.0;
        double r20634 = r20632 - r20633;
        return r20634;
}
↓
double f(double x) {
        double r20635 = 2.0;
        double r20636 = x;
        double r20637 = r20636 * r20636;
        double r20638 = r20635 * r20637;
        double r20639 = 1.0;
        double r20640 = r20638 - r20639;
        return r20640;
}

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

    \[\left(x \cdot x\right) \cdot 2 - 1\]

  2. Simplified0.0

    \[\leadsto \color{blue}{2 \cdot \left(x \cdot x\right) - 1}\]

  3. Final simplification0.0

    \[\leadsto 2 \cdot \left(x \cdot x\right) - 1\]

Reproduce

herbie shell --seed 2019196 +o rules:numerics
(FPCore (x)
  :name "Numeric.SpecFunctions:logGammaCorrection from math-functions-0.1.5.2"
  (- (* (* x x) 2.0) 1.0))