Average Error: 0.1 → 0.1
Time: 17.4s
Precision: 64
\[x \cdot \left(1 - x \cdot y\right)\]
↓
\[x \cdot \left(1 - y \cdot x\right)\]
x \cdot \left(1 - x \cdot y\right)
↓
x \cdot \left(1 - y \cdot x\right)
double f(double x, double y) {
        double r3514950 = x;
        double r3514951 = 1.0;
        double r3514952 = y;
        double r3514953 = r3514950 * r3514952;
        double r3514954 = r3514951 - r3514953;
        double r3514955 = r3514950 * r3514954;
        return r3514955;
}
↓
double f(double x, double y) {
        double r3514956 = x;
        double r3514957 = 1.0;
        double r3514958 = y;
        double r3514959 = r3514958 * r3514956;
        double r3514960 = r3514957 - r3514959;
        double r3514961 = r3514956 * r3514960;
        return r3514961;
}

Error

Bits error versus x

Bits error versus y

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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 *-commutative0.1

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

  4. Final simplification0.1

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

Reproduce

herbie shell --seed 2019169 
(FPCore (x y)
  :name "Numeric.SpecFunctions:log1p from math-functions-0.1.5.2, A"
  (* x (- 1.0 (* x y))))