Average Error: 12.9 → 0.0
Time: 5.9s
Precision: binary64
Cost: 6784
\[\left(\left(x \cdot y - y \cdot y\right) + y \cdot y\right) - y \cdot z \]
↓
\[\mathsf{fma}\left(y, x, y \cdot \left(-z\right)\right) \]
(FPCore (x y z)
 :precision binary64
 (- (+ (- (* x y) (* y y)) (* y y)) (* y z)))
↓
(FPCore (x y z) :precision binary64 (fma y x (* y (- z))))
double code(double x, double y, double z) {
	return (((x * y) - (y * y)) + (y * y)) - (y * z);
}
↓
double code(double x, double y, double z) {
	return fma(y, x, (y * -z));
}

function code(x, y, z)
	return Float64(Float64(Float64(Float64(x * y) - Float64(y * y)) + Float64(y * y)) - Float64(y * z))
end
↓
function code(x, y, z)
	return fma(y, x, Float64(y * Float64(-z)))
end

code[x_, y_, z_] := N[(N[(N[(N[(x * y), $MachinePrecision] - N[(y * y), $MachinePrecision]), $MachinePrecision] + N[(y * y), $MachinePrecision]), $MachinePrecision] - N[(y * z), $MachinePrecision]), $MachinePrecision]
↓
code[x_, y_, z_] := N[(y * x + N[(y * (-z)), $MachinePrecision]), $MachinePrecision]

\left(\left(x \cdot y - y \cdot y\right) + y \cdot y\right) - y \cdot z
↓
\mathsf{fma}\left(y, x, y \cdot \left(-z\right)\right)

Error

Target

Original12.9
Target0.0
Herbie0.0
\[\left(x - z\right) \cdot y \]

Derivation

  1. Initial program 12.9

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

  2. Applied egg-rr0.0

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

  3. Final simplification0.0

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

Alternatives

Alternative 1
Error15.5
Cost784
\[\begin{array}{l} t_0 := y \cdot \left(-z\right)\\ \mathbf{if}\;z \leq -4.3660531790651035 \cdot 10^{-31}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq 1.600760303331691 \cdot 10^{-74}:\\ \;\;\;\;y \cdot x\\ \mathbf{elif}\;z \leq 1.1354328350781584 \cdot 10^{-37}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq 12324.076275452126:\\ \;\;\;\;y \cdot x\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \]
Alternative 2
Error0.0
Cost448
\[y \cdot x - y \cdot z \]
Alternative 3
Error0.0
Cost320
\[y \cdot \left(x - z\right) \]
Alternative 4
Error29.9
Cost192
\[y \cdot x \]

Error

Reproduce

herbie shell --seed 2022291 
(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)))