Average Error: 0.0 → 0.0
Time: 3.2s
Precision: 64
\[\left(x \cdot 2 + x \cdot x\right) + y \cdot y\]
↓
\[y \cdot y + x \cdot \left(2 + x\right)\]
\left(x \cdot 2 + x \cdot x\right) + y \cdot y
↓
y \cdot y + x \cdot \left(2 + x\right)
double f(double x, double y) {
        double r401136 = x;
        double r401137 = 2.0;
        double r401138 = r401136 * r401137;
        double r401139 = r401136 * r401136;
        double r401140 = r401138 + r401139;
        double r401141 = y;
        double r401142 = r401141 * r401141;
        double r401143 = r401140 + r401142;
        return r401143;
}
↓
double f(double x, double y) {
        double r401144 = y;
        double r401145 = r401144 * r401144;
        double r401146 = x;
        double r401147 = 2.0;
        double r401148 = r401147 + r401146;
        double r401149 = r401146 * r401148;
        double r401150 = r401145 + r401149;
        return r401150;
}

Error

Bits error versus x

Bits error versus y

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original0.0
Target0.0
Herbie0.0
\[y \cdot y + \left(2 \cdot x + x \cdot x\right)\]

Derivation

  1. Initial program 0.0

    \[\left(x \cdot 2 + x \cdot x\right) + y \cdot y\]

  2. Simplified0.0

    \[\leadsto \color{blue}{y \cdot y + x \cdot \left(2 + x\right)}\]

  3. Final simplification0.0

    \[\leadsto y \cdot y + x \cdot \left(2 + x\right)\]

Reproduce

herbie shell --seed 2020003 
(FPCore (x y)
  :name "Numeric.Log:$clog1p from log-domain-0.10.2.1, A"
  :precision binary64

  :herbie-target
  (+ (* y y) (+ (* 2 x) (* x x)))

  (+ (+ (* x 2) (* x x)) (* y y)))