Average Error: 0.1 → 0.0
Time: 8.2s
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
Target0.1
Herbie0.0
\[\left(x + 5\right) \cdot z + x \cdot y \]

Derivation

  1. Initial program 0.1

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

  2. Applied egg-rr0.0

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

  3. Final simplification0.0

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

Alternatives

Alternative 1
Error0.1
Cost6848
\[\mathsf{fma}\left(y, x, z \cdot \left(5 + x\right)\right) \]
Alternative 2
Error0.1
Cost1088
\[\left(x \cdot y + \left(2 \cdot \left(z \cdot x\right) + z \cdot 5\right)\right) - z \cdot x \]
Alternative 3
Error25.9
Cost984
\[\begin{array}{l} \mathbf{if}\;z \leq -4.610884478440135 \cdot 10^{-83}:\\ \;\;\;\;z \cdot 5\\ \mathbf{elif}\;z \leq 4.57788388618739 \cdot 10^{-149}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;z \leq 7.981206814387478 \cdot 10^{-82}:\\ \;\;\;\;z \cdot 5\\ \mathbf{elif}\;z \leq 1645020192140757.5:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;z \leq 5.042928892730777 \cdot 10^{+70}:\\ \;\;\;\;z \cdot 5\\ \mathbf{elif}\;z \leq 1.15 \cdot 10^{+88}:\\ \;\;\;\;z \cdot x\\ \mathbf{else}:\\ \;\;\;\;z \cdot 5\\ \end{array} \]
Alternative 4
Error14.6
Cost976
\[\begin{array}{l} t_0 := x \cdot \left(z + y\right)\\ \mathbf{if}\;z \leq -4.610884478440135 \cdot 10^{-83}:\\ \;\;\;\;z \cdot \left(5 + x\right)\\ \mathbf{elif}\;z \leq 4.57788388618739 \cdot 10^{-149}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq 5.755836129014734 \cdot 10^{-84}:\\ \;\;\;\;z \cdot 5\\ \mathbf{elif}\;z \leq 1645020192140757.5:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;z \cdot x + z \cdot 5\\ \end{array} \]
Alternative 5
Error16.0
Cost848
\[\begin{array}{l} t_0 := z \cdot \left(5 + x\right)\\ \mathbf{if}\;z \leq -4.610884478440135 \cdot 10^{-83}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq -5.6131545876545796 \cdot 10^{-108}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;z \leq -2.2024825167068496 \cdot 10^{-144}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq 4.57788388618739 \cdot 10^{-149}:\\ \;\;\;\;x \cdot y\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \]
Alternative 6
Error14.6
Cost848
\[\begin{array}{l} t_0 := z \cdot \left(5 + x\right)\\ t_1 := x \cdot \left(z + y\right)\\ \mathbf{if}\;z \leq -4.610884478440135 \cdot 10^{-83}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq 4.57788388618739 \cdot 10^{-149}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 5.755836129014734 \cdot 10^{-84}:\\ \;\;\;\;z \cdot 5\\ \mathbf{elif}\;z \leq 1645020192140757.5:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \]
Alternative 7
Error0.9
Cost840
\[\begin{array}{l} t_0 := x \cdot \left(\left(y + z \cdot 2\right) - z\right)\\ \mathbf{if}\;x \leq -195.2286821300134:\\ \;\;\;\;t_0\\ \mathbf{elif}\;x \leq 0.29720739973434707:\\ \;\;\;\;x \cdot y + z \cdot 5\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \]
Alternative 8
Error0.9
Cost712
\[\begin{array}{l} t_0 := x \cdot \left(z + y\right)\\ \mathbf{if}\;x \leq -195.2286821300134:\\ \;\;\;\;t_0\\ \mathbf{elif}\;x \leq 0.29720739973434707:\\ \;\;\;\;x \cdot y + z \cdot 5\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \]
Alternative 9
Error0.1
Cost576
\[z \cdot 5 + x \cdot \left(z + y\right) \]
Alternative 10
Error24.5
Cost456
\[\begin{array}{l} \mathbf{if}\;x \leq -195.2286821300134:\\ \;\;\;\;z \cdot x\\ \mathbf{elif}\;x \leq 0.29720739973434707:\\ \;\;\;\;z \cdot 5\\ \mathbf{else}:\\ \;\;\;\;z \cdot x\\ \end{array} \]
Alternative 11
Error51.1
Cost192
\[z \cdot x \]

Error

Reproduce

herbie shell --seed 2022291 
(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)))