Average Error: 0.1 → 0.1
Time: 3.0s
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 r77150 = x;
        double r77151 = 1.0;
        double r77152 = y;
        double r77153 = r77150 * r77152;
        double r77154 = r77151 - r77153;
        double r77155 = r77150 * r77154;
        return r77155;
}
↓
double f(double x, double y) {
        double r77156 = x;
        double r77157 = 1.0;
        double r77158 = r77156 * r77157;
        double r77159 = y;
        double r77160 = r77156 * r77159;
        double r77161 = -r77160;
        double r77162 = r77156 * r77161;
        double r77163 = r77158 + r77162;
        return r77163;
}

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 2020064 
(FPCore (x y)
  :name "Numeric.SpecFunctions:log1p from math-functions-0.1.5.2, A"
  :precision binary64
  (* x (- 1 (* x y))))