Average Error: 0.0 → 0.0
Time: 2.2s
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 r461384 = x;
        double r461385 = 2.0;
        double r461386 = r461384 * r461385;
        double r461387 = r461384 * r461384;
        double r461388 = r461386 + r461387;
        double r461389 = y;
        double r461390 = r461389 * r461389;
        double r461391 = r461388 + r461390;
        return r461391;
}
↓
double f(double x, double y) {
        double r461392 = y;
        double r461393 = r461392 * r461392;
        double r461394 = x;
        double r461395 = 2.0;
        double r461396 = r461395 + r461394;
        double r461397 = r461394 * r461396;
        double r461398 = r461393 + r461397;
        return r461398;
}

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. Final simplification0.0

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

Reproduce

herbie shell --seed 2019322 
(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)))