Average Error: 0.0 → 0.0
Time: 1.6s
Precision: 64
\[2 \cdot \left(x \cdot x - x \cdot y\right)\]
↓
\[\mathsf{fma}\left({x}^{1}, {x}^{1}, x \cdot \left(-y\right)\right) \cdot 2\]
2 \cdot \left(x \cdot x - x \cdot y\right)
↓
\mathsf{fma}\left({x}^{1}, {x}^{1}, x \cdot \left(-y\right)\right) \cdot 2
double code(double x, double y) {
	return (2.0 * ((x * x) - (x * y)));
}
↓
double code(double x, double y) {
	return (fma(pow(x, 1.0), pow(x, 1.0), (x * -y)) * 2.0);
}

Error

Bits error versus x

Bits error versus y

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Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

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

Derivation

  1. Initial program 0.0

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

  2. Simplified0.0

    \[\leadsto \color{blue}{\left(x \cdot \left(x - y\right)\right) \cdot 2}\]
  3. Using strategy rm

  4. Applied sub-neg0.0

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

  5. Applied distribute-lft-in0.0

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

  6. Simplified0.0

    \[\leadsto \left(\color{blue}{{x}^{2}} + x \cdot \left(-y\right)\right) \cdot 2\]
  7. Using strategy rm

  8. Applied sqr-pow0.0

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

  9. Applied fma-def0.0

    \[\leadsto \color{blue}{\mathsf{fma}\left({x}^{\left(\frac{2}{2}\right)}, {x}^{\left(\frac{2}{2}\right)}, x \cdot \left(-y\right)\right)} \cdot 2\]

  10. Final simplification0.0

    \[\leadsto \mathsf{fma}\left({x}^{1}, {x}^{1}, x \cdot \left(-y\right)\right) \cdot 2\]

Reproduce

herbie shell --seed 2020075 +o rules:numerics
(FPCore (x y)
  :name "Linear.Matrix:fromQuaternion from linear-1.19.1.3, A"
  :precision binary64

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

  (* 2 (- (* x x) (* x y))))