Average Error: 0.1 → 0.0
Time: 9.9s
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
Target0.1
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
Error15.1
Cost1112
\[\begin{array}{l} t_0 := z \cdot \left(5 + x\right)\\ t_1 := x \cdot \left(z + y\right)\\ \mathbf{if}\;z \leq -8.769300275088442 \cdot 10^{-39}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq -8.33109499931419 \cdot 10^{-72}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -1.6515784804322487 \cdot 10^{-158}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq 1.2120149042996737 \cdot 10^{-139}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 3.0912240133643773 \cdot 10^{-27}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq 2.0579989441732522 \cdot 10^{+35}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \]
Alternative 2
Error15.1
Cost1112
\[\begin{array}{l} t_0 := z \cdot \left(5 + x\right)\\ t_1 := x \cdot \left(z + y\right)\\ \mathbf{if}\;z \leq -8.769300275088442 \cdot 10^{-39}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq -8.33109499931419 \cdot 10^{-72}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -1.6515784804322487 \cdot 10^{-158}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq 1.2120149042996737 \cdot 10^{-139}:\\ \;\;\;\;x \cdot y + z \cdot x\\ \mathbf{elif}\;z \leq 3.0912240133643773 \cdot 10^{-27}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq 2.0579989441732522 \cdot 10^{+35}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \]
Alternative 3
Error24.2
Cost720
\[\begin{array}{l} \mathbf{if}\;x \leq -1.9779842853003014 \cdot 10^{-11}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;x \leq 3.1351164851748682 \cdot 10^{-21}:\\ \;\;\;\;z \cdot 5\\ \mathbf{elif}\;x \leq 1.15 \cdot 10^{+201}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;x \leq 3.9 \cdot 10^{+289}:\\ \;\;\;\;z \cdot x\\ \mathbf{else}:\\ \;\;\;\;x \cdot y\\ \end{array} \]
Alternative 4
Error0.9
Cost712
\[\begin{array}{l} \mathbf{if}\;x \leq -116.54562991485636:\\ \;\;\;\;x \cdot y + z \cdot x\\ \mathbf{elif}\;x \leq 1.7949474361456739:\\ \;\;\;\;z \cdot 5 + x \cdot y\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(z + y\right)\\ \end{array} \]
Alternative 5
Error12.6
Cost584
\[\begin{array}{l} t_0 := x \cdot \left(z + y\right)\\ \mathbf{if}\;x \leq -1.9779842853003014 \cdot 10^{-11}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;x \leq 2.669105297775152 \cdot 10^{-34}:\\ \;\;\;\;z \cdot 5\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \]
Alternative 6
Error0.1
Cost576
\[x \cdot y + z \cdot \left(5 + x\right) \]
Alternative 7
Error0.1
Cost576
\[z \cdot 5 + x \cdot \left(z + y\right) \]
Alternative 8
Error36.9
Cost456
\[\begin{array}{l} \mathbf{if}\;z \leq -9.764260802913955 \cdot 10^{+99}:\\ \;\;\;\;z \cdot x\\ \mathbf{elif}\;z \leq 1.5531585901703365 \cdot 10^{+76}:\\ \;\;\;\;x \cdot y\\ \mathbf{else}:\\ \;\;\;\;z \cdot x\\ \end{array} \]
Alternative 9
Error51.0
Cost192
\[z \cdot x \]

Error

Reproduce

herbie shell --seed 2022317 
(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)))