?

Average Error: 0.1% → 0.03%
Time: 7.9s
Precision: binary64
Cost: 6848

?

\[x \cdot \left(y + z\right) + z \cdot 5 \]
↓
\[\mathsf{fma}\left(z, 5, x \cdot \left(z + y\right)\right) \]
(FPCore (x y z) :precision binary64 (+ (* x (+ y z)) (* z 5.0)))
↓
(FPCore (x y z) :precision binary64 (fma z 5.0 (* x (+ z y))))
double code(double x, double y, double z) {
	return (x * (y + z)) + (z * 5.0);
}
↓
double code(double x, double y, double z) {
	return fma(z, 5.0, (x * (z + y)));
}

function code(x, y, z)
	return Float64(Float64(x * Float64(y + z)) + Float64(z * 5.0))
end
↓
function code(x, y, z)
	return fma(z, 5.0, Float64(x * Float64(z + y)))
end

code[x_, y_, z_] := N[(N[(x * N[(y + z), $MachinePrecision]), $MachinePrecision] + N[(z * 5.0), $MachinePrecision]), $MachinePrecision]
↓
code[x_, y_, z_] := N[(z * 5.0 + N[(x * N[(z + y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

x \cdot \left(y + z\right) + z \cdot 5
↓
\mathsf{fma}\left(z, 5, x \cdot \left(z + y\right)\right)

Error?

Target

Original0.1%
Target0.09%
Herbie0.03%
\[\left(x + 5\right) \cdot z + x \cdot y \]

Derivation?

  1. Initial program 0.1

    \[x \cdot \left(y + z\right) + z \cdot 5 \]

  2. Applied egg-rr0.03

    \[\leadsto \color{blue}{\mathsf{fma}\left(z, 5, x \cdot \left(y + z\right)\right)} \]

  3. Final simplification0.03

    \[\leadsto \mathsf{fma}\left(z, 5, x \cdot \left(z + y\right)\right) \]

Alternatives

Alternative 1
Error0.08%
Cost6848
\[\mathsf{fma}\left(x, y, z \cdot \left(5 + x\right)\right) \]
Alternative 2
Error23.72%
Cost850
\[\begin{array}{l} \mathbf{if}\;z \leq -1.65 \cdot 10^{-26} \lor \neg \left(z \leq 6.5 \cdot 10^{-189} \lor \neg \left(z \leq 1.8 \cdot 10^{+59}\right) \land z \leq 2.2 \cdot 10^{+84}\right):\\ \;\;\;\;z \cdot \left(5 + x\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(z + y\right)\\ \end{array} \]
Alternative 3
Error37.05%
Cost720
\[\begin{array}{l} \mathbf{if}\;x \leq -8.2 \cdot 10^{+70}:\\ \;\;\;\;z \cdot x\\ \mathbf{elif}\;x \leq -6 \cdot 10^{-34}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;x \leq 6.8 \cdot 10^{-17}:\\ \;\;\;\;z \cdot 5\\ \mathbf{elif}\;x \leq 1.7 \cdot 10^{+180}:\\ \;\;\;\;x \cdot y\\ \mathbf{else}:\\ \;\;\;\;z \cdot x\\ \end{array} \]
Alternative 4
Error1.38%
Cost713
\[\begin{array}{l} \mathbf{if}\;x \leq -5 \lor \neg \left(x \leq 5\right):\\ \;\;\;\;x \cdot \left(z + y\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot y + z \cdot 5\\ \end{array} \]
Alternative 5
Error1.38%
Cost712
\[\begin{array}{l} \mathbf{if}\;x \leq -5:\\ \;\;\;\;x \cdot y + z \cdot x\\ \mathbf{elif}\;x \leq 5:\\ \;\;\;\;x \cdot y + z \cdot 5\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(z + y\right)\\ \end{array} \]
Alternative 6
Error26.45%
Cost585
\[\begin{array}{l} \mathbf{if}\;z \leq -6.7 \cdot 10^{-49} \lor \neg \left(z \leq 1.6 \cdot 10^{-189}\right):\\ \;\;\;\;z \cdot \left(5 + x\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot y\\ \end{array} \]
Alternative 7
Error0.1%
Cost576
\[z \cdot 5 + x \cdot \left(z + y\right) \]
Alternative 8
Error0.09%
Cost576
\[z \cdot \left(5 + x\right) + x \cdot y \]
Alternative 9
Error37.38%
Cost456
\[\begin{array}{l} \mathbf{if}\;x \leq -2.2 \cdot 10^{-33}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;x \leq 4.2 \cdot 10^{-17}:\\ \;\;\;\;z \cdot 5\\ \mathbf{else}:\\ \;\;\;\;x \cdot y\\ \end{array} \]
Alternative 10
Error61.43%
Cost192
\[x \cdot y \]

Error

Reproduce?

herbie shell --seed 2023121 
(FPCore (x y z)
  :name "Graphics.Rendering.Plot.Render.Plot.Legend:renderLegendOutside from plot-0.2.3.4, C"
  :precision binary64

  :herbie-target
  (+ (* (+ x 5.0) z) (* x y))

  (+ (* x (+ y z)) (* z 5.0)))