Graphics.Rendering.Plot.Render.Plot.Legend:renderLegendOutside from plot-0.2.3.4, C

Average Error: 0.1 → 0.0

Time: 6.8s

Precision: binary64

Cost: 6848

Math

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

↓

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

FPCore

(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))))

C

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)));
}

Julia

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

Wolfram

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]

Target

Original	0.1
Target	0.1
Herbie	0.0

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

Derivation

1. Initial program 0.1

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

2. Applied egg-rr 0.0

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

3. Final simplification 0.0

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

Alternatives

Alternative 1
Error	0.0
Cost	6848

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

Alternative 2
Error	23.5
Cost	720

\[\begin{array}{l} \mathbf{if}\;x \leq -3.7644105263790963 \cdot 10^{+34}:\\ \;\;\;\;z \cdot x\\ \mathbf{elif}\;x \leq -2.956768271475151 \cdot 10^{-56}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;x \leq 2.368437938656694 \cdot 10^{-33}:\\ \;\;\;\;z \cdot 5\\ \mathbf{elif}\;x \leq 2.35 \cdot 10^{+117}:\\ \;\;\;\;x \cdot y\\ \mathbf{else}:\\ \;\;\;\;z \cdot x\\ \end{array} \]

Alternative 3
Error	13.4
Cost	712

\[\begin{array}{l} t_0 := z \cdot 5 + z \cdot x\\ \mathbf{if}\;z \leq -1.6950565496523817 \cdot 10^{-14}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq 3.772754161080676 \cdot 10^{-49}:\\ \;\;\;\;x \cdot \left(z + y\right)\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \]

Alternative 4
Error	16.6
Cost	584

\[\begin{array}{l} t_0 := z \cdot \left(5 + x\right)\\ \mathbf{if}\;z \leq -2.72546431864727 \cdot 10^{-180}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq 3.1983772000709783 \cdot 10^{-190}:\\ \;\;\;\;x \cdot y\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \]

Alternative 5
Error	13.4
Cost	584

\[\begin{array}{l} t_0 := z \cdot \left(5 + x\right)\\ \mathbf{if}\;z \leq -1.6950565496523817 \cdot 10^{-14}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq 3.772754161080676 \cdot 10^{-49}:\\ \;\;\;\;x \cdot \left(z + y\right)\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \]

Alternative 6
Error	0.1
Cost	576

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

Alternative 7
Error	35.9
Cost	456

\[\begin{array}{l} \mathbf{if}\;y \leq -2.7833487649445906 \cdot 10^{-81}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;y \leq 5.470923883743339 \cdot 10^{-218}:\\ \;\;\;\;z \cdot x\\ \mathbf{else}:\\ \;\;\;\;x \cdot y\\ \end{array} \]

Alternative 8
Error	50.7
Cost	192

\[z \cdot x \]

Reproduce

herbie shell --seed 2022318 
(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)))