Average Error: 0.0 → 0.0
Time: 4.9s
Precision: 64
\[\left(x \cdot 2 + x \cdot x\right) + y \cdot y\]
↓
\[y \cdot y + \left(2 \cdot x + x \cdot x\right)\]
\left(x \cdot 2 + x \cdot x\right) + y \cdot y
↓
y \cdot y + \left(2 \cdot x + x \cdot x\right)
double f(double x, double y) {
        double r502940 = x;
        double r502941 = 2.0;
        double r502942 = r502940 * r502941;
        double r502943 = r502940 * r502940;
        double r502944 = r502942 + r502943;
        double r502945 = y;
        double r502946 = r502945 * r502945;
        double r502947 = r502944 + r502946;
        return r502947;
}
↓
double f(double x, double y) {
        double r502948 = y;
        double r502949 = r502948 * r502948;
        double r502950 = 2.0;
        double r502951 = x;
        double r502952 = r502950 * r502951;
        double r502953 = r502951 * r502951;
        double r502954 = r502952 + r502953;
        double r502955 = r502949 + r502954;
        return r502955;
}

Error

Bits error versus x

Bits error versus y

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Your Program's Arguments

Results

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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. Using strategy rm

  4. Applied distribute-lft-in0.0

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

  5. Simplified0.0

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

  6. Final simplification0.0

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

Reproduce

herbie shell --seed 2020045 
(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)))