Average Error: 0.0 → 0.0
Time: 3.9s
Precision: binary64
Cost: 6976
\[ \begin{array}{c}[x, y] = \mathsf{sort}([x, y])\\ \end{array} \]
\[\left(x + y\right) \cdot \left(z + 1\right) \]
↓
\[\mathsf{fma}\left(z + 1, x, \left(z + 1\right) \cdot y\right) \]
(FPCore (x y z) :precision binary64 (* (+ x y) (+ z 1.0)))
↓
(FPCore (x y z) :precision binary64 (fma (+ z 1.0) x (* (+ z 1.0) y)))
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), x, ((z + 1.0) * y));
}

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), x, Float64(Float64(z + 1.0) * y))
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] * x + N[(N[(z + 1.0), $MachinePrecision] * y), $MachinePrecision]), $MachinePrecision]

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

Error

Derivation

  1. Initial program 0.0

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

  2. Applied egg-rr0.0

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

  3. Final simplification0.0

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

Alternatives

Alternative 1
Error32.6
Cost1116
\[\begin{array}{l} \mathbf{if}\;z \leq -9.8 \cdot 10^{+238}:\\ \;\;\;\;z \cdot x\\ \mathbf{elif}\;z \leq -1:\\ \;\;\;\;z \cdot y\\ \mathbf{elif}\;z \leq 1.25 \cdot 10^{-241}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 3 \cdot 10^{-156}:\\ \;\;\;\;y\\ \mathbf{elif}\;z \leq 1.4 \cdot 10^{-113}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 0.048:\\ \;\;\;\;y\\ \mathbf{elif}\;z \leq 2.4 \cdot 10^{+61}:\\ \;\;\;\;z \cdot y\\ \mathbf{else}:\\ \;\;\;\;z \cdot x\\ \end{array} \]
Alternative 2
Error33.1
Cost852
\[\begin{array}{l} \mathbf{if}\;z \leq -1.3 \cdot 10^{-10}:\\ \;\;\;\;z \cdot x\\ \mathbf{elif}\;z \leq 2.9 \cdot 10^{-239}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 3 \cdot 10^{-156}:\\ \;\;\;\;y\\ \mathbf{elif}\;z \leq 2.15 \cdot 10^{-109}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 0.026:\\ \;\;\;\;y\\ \mathbf{else}:\\ \;\;\;\;z \cdot x\\ \end{array} \]
Alternative 3
Error12.8
Cost848
\[\begin{array}{l} t_0 := \left(z + 1\right) \cdot y\\ \mathbf{if}\;z \leq -2.7 \cdot 10^{+230}:\\ \;\;\;\;z \cdot x\\ \mathbf{elif}\;z \leq -1.3 \cdot 10^{-10}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq 1.52 \cdot 10^{-21}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;z \leq 8.2 \cdot 10^{+61}:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;z \cdot x\\ \end{array} \]
Alternative 4
Error13.0
Cost720
\[\begin{array}{l} \mathbf{if}\;z \leq -9.8 \cdot 10^{+235}:\\ \;\;\;\;z \cdot x\\ \mathbf{elif}\;z \leq -1:\\ \;\;\;\;z \cdot y\\ \mathbf{elif}\;z \leq 23:\\ \;\;\;\;x + y\\ \mathbf{elif}\;z \leq 8.5 \cdot 10^{+61}:\\ \;\;\;\;z \cdot y\\ \mathbf{else}:\\ \;\;\;\;z \cdot x\\ \end{array} \]
Alternative 5
Error0.0
Cost704
\[\left(z + 1\right) \cdot y + \left(z + 1\right) \cdot x \]
Alternative 6
Error1.6
Cost584
\[\begin{array}{l} t_0 := z \cdot \left(x + y\right)\\ \mathbf{if}\;z \leq -1:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq 1:\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \]
Alternative 7
Error0.0
Cost448
\[\left(z + 1\right) \cdot \left(x + y\right) \]
Alternative 8
Error30.6
Cost196
\[\begin{array}{l} \mathbf{if}\;y \leq 1.08 \cdot 10^{-69}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \]
Alternative 9
Error43.5
Cost64
\[x \]

Error

Reproduce

herbie shell --seed 2022325 
(FPCore (x y z)
  :name "Optimisation.CirclePacking:place from circle-packing-0.1.0.4, G"
  :precision binary64
  (* (+ x y) (+ z 1.0)))