Average Error: 0.1 → 0.1
Time: 3.3s
Precision: 64
\[x \cdot \left(1 - x \cdot y\right)\]
↓
\[x \cdot 1 + x \cdot \left(-x \cdot y\right)\]
x \cdot \left(1 - x \cdot y\right)
↓
x \cdot 1 + x \cdot \left(-x \cdot y\right)
double f(double x, double y) {
        double r58147 = x;
        double r58148 = 1.0;
        double r58149 = y;
        double r58150 = r58147 * r58149;
        double r58151 = r58148 - r58150;
        double r58152 = r58147 * r58151;
        return r58152;
}
↓
double f(double x, double y) {
        double r58153 = x;
        double r58154 = 1.0;
        double r58155 = r58153 * r58154;
        double r58156 = y;
        double r58157 = r58153 * r58156;
        double r58158 = -r58157;
        double r58159 = r58153 * r58158;
        double r58160 = r58155 + r58159;
        return r58160;
}

Error

Bits error versus x

Bits error versus y

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 0.1

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

  3. Applied sub-neg0.1

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

  4. Applied distribute-lft-in0.1

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

  5. Final simplification0.1

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

Reproduce

herbie shell --seed 2020100 
(FPCore (x y)
  :name "Numeric.SpecFunctions:log1p from math-functions-0.1.5.2, A"
  :precision binary64
  (* x (- 1 (* x y))))