Average Error: 12.4 → 0.0
Time: 1.5s
Precision: 64
\[\left(\left(x \cdot y - y \cdot y\right) + y \cdot y\right) - y \cdot z\]
↓
\[\mathsf{fma}\left(x, y, y \cdot \left(-z\right)\right)\]
\left(\left(x \cdot y - y \cdot y\right) + y \cdot y\right) - y \cdot z
↓
\mathsf{fma}\left(x, y, y \cdot \left(-z\right)\right)
double code(double x, double y, double z) {
	return ((double) (((double) (((double) (((double) (x * y)) - ((double) (y * y)))) + ((double) (y * y)))) - ((double) (y * z))));
}
↓
double code(double x, double y, double z) {
	return ((double) fma(x, y, ((double) (y * ((double) -(z))))));
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original12.4
Target0.0
Herbie0.0
\[\left(x - z\right) \cdot y\]

Derivation

  1. Initial program 12.4

    \[\left(\left(x \cdot y - y \cdot y\right) + y \cdot y\right) - y \cdot z\]

  2. Simplified0.0

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

  4. Applied sub-neg0.0

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

  5. Applied distribute-lft-in0.0

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

  7. Applied *-commutative0.0

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

  8. Applied fma-def0.0

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

  9. Final simplification0.0

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

Reproduce

herbie shell --seed 2020113 +o rules:numerics
(FPCore (x y z)
  :name "Linear.Quaternion:$c/ from linear-1.19.1.3, D"
  :precision binary64

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

  (- (+ (- (* x y) (* y y)) (* y y)) (* y z)))