Average Error: 0.0 → 0.0
Time: 7.0s
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 r1071104 = x;
        double r1071105 = 2.0;
        double r1071106 = r1071104 * r1071105;
        double r1071107 = r1071104 * r1071104;
        double r1071108 = r1071106 + r1071107;
        double r1071109 = y;
        double r1071110 = r1071109 * r1071109;
        double r1071111 = r1071108 + r1071110;
        return r1071111;
}
↓
double f(double x, double y) {
        double r1071112 = y;
        double r1071113 = r1071112 * r1071112;
        double r1071114 = x;
        double r1071115 = 2.0;
        double r1071116 = r1071115 + r1071114;
        double r1071117 = r1071114 * r1071116;
        double r1071118 = r1071113 + r1071117;
        return r1071118;
}

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 2020047 
(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)))