Average Error: 0.0 → 0.0
Time: 4.9s
Precision: binary64
Cost: 6976
\[ \begin{array}{c}[x, y] = \mathsf{sort}([x, y])\\ \end{array} \]
\[\left(x + y\right) \cdot \left(z + 1\right) \]
↓
\[\mathsf{fma}\left(z + 1, y, \left(z + 1\right) \cdot x\right) \]
(FPCore (x y z) :precision binary64 (* (+ x y) (+ z 1.0)))
↓
(FPCore (x y z) :precision binary64 (fma (+ z 1.0) y (* (+ z 1.0) x)))
double code(double x, double y, double z) {
	return (x + y) * (z + 1.0);
}
↓
double code(double x, double y, double z) {
	return fma((z + 1.0), y, ((z + 1.0) * x));
}

function code(x, y, z)
	return Float64(Float64(x + y) * Float64(z + 1.0))
end
↓
function code(x, y, z)
	return fma(Float64(z + 1.0), y, Float64(Float64(z + 1.0) * x))
end

code[x_, y_, z_] := N[(N[(x + y), $MachinePrecision] * N[(z + 1.0), $MachinePrecision]), $MachinePrecision]
↓
code[x_, y_, z_] := N[(N[(z + 1.0), $MachinePrecision] * y + N[(N[(z + 1.0), $MachinePrecision] * x), $MachinePrecision]), $MachinePrecision]

\left(x + y\right) \cdot \left(z + 1\right)
↓
\mathsf{fma}\left(z + 1, y, \left(z + 1\right) \cdot x\right)

Error

Derivation

  1. Initial program 0.0

    \[\left(x + y\right) \cdot \left(z + 1\right) \]

  2. Applied egg-rr0.0

    \[\leadsto \color{blue}{\mathsf{fma}\left(z + 1, y, \left(z + 1\right) \cdot x\right)} \]

  3. Final simplification0.0

    \[\leadsto \mathsf{fma}\left(z + 1, y, \left(z + 1\right) \cdot x\right) \]

Alternatives

Alternative 1
Error32.7
Cost1380
\[\begin{array}{l} \mathbf{if}\;z \leq -1.6 \cdot 10^{+75}:\\ \;\;\;\;z \cdot y\\ \mathbf{elif}\;z \leq -2.15 \cdot 10^{+42}:\\ \;\;\;\;z \cdot x\\ \mathbf{elif}\;z \leq -1:\\ \;\;\;\;z \cdot y\\ \mathbf{elif}\;z \leq -3.2 \cdot 10^{-219}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 9.6 \cdot 10^{-302}:\\ \;\;\;\;y\\ \mathbf{elif}\;z \leq 1.75 \cdot 10^{-185}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 1.2 \cdot 10^{-104}:\\ \;\;\;\;y\\ \mathbf{elif}\;z \leq 1.1 \cdot 10^{-22}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 1:\\ \;\;\;\;y\\ \mathbf{else}:\\ \;\;\;\;z \cdot y\\ \end{array} \]
Alternative 2
Error31.5
Cost1360
\[\begin{array}{l} t_0 := z + 1 \leq 1\\ t_1 := \left(z + 1\right) \cdot y\\ \mathbf{if}\;z + 1 \leq -5 \cdot 10^{+75}:\\ \;\;\;\;z \cdot y\\ \mathbf{elif}\;z + 1 \leq -2 \cdot 10^{+43}:\\ \;\;\;\;z \cdot x\\ \mathbf{elif}\;t_0:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t_0:\\ \;\;\;\;y + x\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]
Alternative 3
Error32.7
Cost1116
\[\begin{array}{l} \mathbf{if}\;z \leq -0.39:\\ \;\;\;\;z \cdot x\\ \mathbf{elif}\;z \leq -2.5 \cdot 10^{-219}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 9.6 \cdot 10^{-302}:\\ \;\;\;\;y\\ \mathbf{elif}\;z \leq 1.1 \cdot 10^{-184}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 8.5 \cdot 10^{-104}:\\ \;\;\;\;y\\ \mathbf{elif}\;z \leq 8.5 \cdot 10^{-24}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 2.1:\\ \;\;\;\;y\\ \mathbf{else}:\\ \;\;\;\;z \cdot x\\ \end{array} \]
Alternative 4
Error13.8
Cost980
\[\begin{array}{l} t_0 := \left(z + 1\right) \cdot x\\ t_1 := \left(z + 1\right) \cdot y\\ \mathbf{if}\;x \leq -170000000:\\ \;\;\;\;t_0\\ \mathbf{elif}\;x \leq -3.3 \cdot 10^{-90}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq -2.55 \cdot 10^{-113}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;x \leq -9.6 \cdot 10^{-132}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq -7 \cdot 10^{-185}:\\ \;\;\;\;y + x\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]
Alternative 5
Error1.6
Cost840
\[\begin{array}{l} t_0 := z \cdot \left(y + x\right)\\ \mathbf{if}\;z + 1 \leq -5:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z + 1 \leq 2:\\ \;\;\;\;y + x\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \]
Alternative 6
Error13.3
Cost720
\[\begin{array}{l} \mathbf{if}\;z \leq -4.4 \cdot 10^{+75}:\\ \;\;\;\;z \cdot y\\ \mathbf{elif}\;z \leq -2.05 \cdot 10^{+43}:\\ \;\;\;\;z \cdot x\\ \mathbf{elif}\;z \leq -1:\\ \;\;\;\;z \cdot y\\ \mathbf{elif}\;z \leq 850000000000:\\ \;\;\;\;y + x\\ \mathbf{else}:\\ \;\;\;\;z \cdot y\\ \end{array} \]
Alternative 7
Error0.0
Cost704
\[\left(z + 1\right) \cdot x + \left(z + 1\right) \cdot y \]
Alternative 8
Error31.9
Cost460
\[\begin{array}{l} \mathbf{if}\;x \leq -13500000000000:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq -2.06 \cdot 10^{-81}:\\ \;\;\;\;y\\ \mathbf{elif}\;x \leq -6.8 \cdot 10^{-114}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \]
Alternative 9
Error0.0
Cost448
\[\left(z + 1\right) \cdot \left(y + x\right) \]
Alternative 10
Error43.6
Cost64
\[x \]

Error

Reproduce

herbie shell --seed 2022337 
(FPCore (x y z)
  :name "Optimisation.CirclePacking:place from circle-packing-0.1.0.4, G"
  :precision binary64
  (* (+ x y) (+ z 1.0)))