Average Error: 0.0 → 0.0
Time: 832.0ms
Precision: 64
\[x \cdot \left(1 - x \cdot 0.5\right)\]
↓
\[x \cdot 1 + x \cdot \left(-x \cdot 0.5\right)\]
x \cdot \left(1 - x \cdot 0.5\right)
↓
x \cdot 1 + x \cdot \left(-x \cdot 0.5\right)
double f(double x) {
        double r37368 = x;
        double r37369 = 1.0;
        double r37370 = 0.5;
        double r37371 = r37368 * r37370;
        double r37372 = r37369 - r37371;
        double r37373 = r37368 * r37372;
        return r37373;
}
↓
double f(double x) {
        double r37374 = x;
        double r37375 = 1.0;
        double r37376 = r37374 * r37375;
        double r37377 = 0.5;
        double r37378 = r37374 * r37377;
        double r37379 = -r37378;
        double r37380 = r37374 * r37379;
        double r37381 = r37376 + r37380;
        return r37381;
}

Error

Bits error versus x

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 0.0

    \[x \cdot \left(1 - x \cdot 0.5\right)\]
  2. Using strategy rm

  3. Applied sub-neg0.0

    \[\leadsto x \cdot \color{blue}{\left(1 + \left(-x \cdot 0.5\right)\right)}\]

  4. Applied distribute-lft-in0.0

    \[\leadsto \color{blue}{x \cdot 1 + x \cdot \left(-x \cdot 0.5\right)}\]

  5. Final simplification0.0

    \[\leadsto x \cdot 1 + x \cdot \left(-x \cdot 0.5\right)\]

Reproduce

herbie shell --seed 2020065 +o rules:numerics
(FPCore (x)
  :name "Numeric.SpecFunctions:log1p from math-functions-0.1.5.2, B"
  :precision binary64
  (* x (- 1 (* x 0.5))))