Average Error: 0.0 → 0.0
Time: 2.4s
Precision: binary64
Cost: 6720
\[200 \cdot \left(x - y\right) \]
↓
\[\mathsf{fma}\left(x, 200, -200 \cdot y\right) \]
(FPCore (x y) :precision binary64 (* 200.0 (- x y)))
↓
(FPCore (x y) :precision binary64 (fma x 200.0 (* -200.0 y)))
double code(double x, double y) {
	return 200.0 * (x - y);
}
↓
double code(double x, double y) {
	return fma(x, 200.0, (-200.0 * y));
}

function code(x, y)
	return Float64(200.0 * Float64(x - y))
end
↓
function code(x, y)
	return fma(x, 200.0, Float64(-200.0 * y))
end

code[x_, y_] := N[(200.0 * N[(x - y), $MachinePrecision]), $MachinePrecision]
↓
code[x_, y_] := N[(x * 200.0 + N[(-200.0 * y), $MachinePrecision]), $MachinePrecision]

200 \cdot \left(x - y\right)
↓
\mathsf{fma}\left(x, 200, -200 \cdot y\right)

Error

Derivation

  1. Initial program 0.0

    \[200 \cdot \left(x - y\right) \]

  2. Taylor expanded in x around 0 0.0

    \[\leadsto \color{blue}{200 \cdot x + -200 \cdot y} \]

  3. Applied egg-rr0.0

    \[\leadsto \color{blue}{\mathsf{fma}\left(x, 200, -200 \cdot y\right)} \]

  4. Final simplification0.0

    \[\leadsto \mathsf{fma}\left(x, 200, -200 \cdot y\right) \]

Alternatives

Alternative 1
Error0.0
Cost6720
\[\mathsf{fma}\left(-200, y, x \cdot 200\right) \]
Alternative 2
Error16.8
Cost720
\[\begin{array}{l} \mathbf{if}\;y \leq -7 \cdot 10^{+73}:\\ \;\;\;\;-200 \cdot y\\ \mathbf{elif}\;y \leq 5.2 \cdot 10^{-59}:\\ \;\;\;\;x \cdot 200\\ \mathbf{elif}\;y \leq 6 \cdot 10^{+25}:\\ \;\;\;\;-200 \cdot y\\ \mathbf{elif}\;y \leq 3.5 \cdot 10^{+61}:\\ \;\;\;\;x \cdot 200\\ \mathbf{else}:\\ \;\;\;\;-200 \cdot y\\ \end{array} \]
Alternative 3
Error0.0
Cost448
\[-200 \cdot y + x \cdot 200 \]
Alternative 4
Error0.0
Cost320
\[200 \cdot \left(x - y\right) \]
Alternative 5
Error31.2
Cost192
\[-200 \cdot y \]

Error

Reproduce

herbie shell --seed 2022337 
(FPCore (x y)
  :name "Data.Colour.CIE:cieLABView from colour-2.3.3, C"
  :precision binary64
  (* 200.0 (- x y)))