Average Error: 0.0 → 0.0
Time: 4.9s
Precision: binary64
Cost: 6848
\[x \cdot y + \left(1 - x\right) \cdot z \]
↓
\[\mathsf{fma}\left(y, x, \left(1 - x\right) \cdot z\right) \]
(FPCore (x y z) :precision binary64 (+ (* x y) (* (- 1.0 x) z)))
↓
(FPCore (x y z) :precision binary64 (fma y x (* (- 1.0 x) z)))
double code(double x, double y, double z) {
	return (x * y) + ((1.0 - x) * z);
}
↓
double code(double x, double y, double z) {
	return fma(y, x, ((1.0 - x) * z));
}

function code(x, y, z)
	return Float64(Float64(x * y) + Float64(Float64(1.0 - x) * z))
end
↓
function code(x, y, z)
	return fma(y, x, Float64(Float64(1.0 - x) * z))
end

code[x_, y_, z_] := N[(N[(x * y), $MachinePrecision] + N[(N[(1.0 - x), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision]
↓
code[x_, y_, z_] := N[(y * x + N[(N[(1.0 - x), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision]

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

Error

Derivation

  1. Initial program 0.0

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

  2. Applied egg-rr0.0

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

  3. Final simplification0.0

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

Alternatives

Alternative 1
Error0.0
Cost6720
\[\mathsf{fma}\left(x, y - z, z\right) \]
Alternative 2
Error16.6
Cost848
\[\begin{array}{l} t_0 := z - x \cdot z\\ \mathbf{if}\;z \leq -6.0713097400873816 \cdot 10^{-161}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq 1.96275473269512 \cdot 10^{-208}:\\ \;\;\;\;y \cdot x\\ \mathbf{elif}\;z \leq 1.0312400925926484 \cdot 10^{-193}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq 4.739239133975398 \cdot 10^{-128}:\\ \;\;\;\;y \cdot x\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \]
Alternative 3
Error24.1
Cost784
\[\begin{array}{l} t_0 := z \cdot \left(-x\right)\\ \mathbf{if}\;x \leq -3.3 \cdot 10^{+137}:\\ \;\;\;\;y \cdot x\\ \mathbf{elif}\;x \leq -5.2047775308356974 \cdot 10^{-14}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;x \leq 1.4974919964123157 \cdot 10^{-45}:\\ \;\;\;\;z\\ \mathbf{elif}\;x \leq 1.0378715465507266 \cdot 10^{+26}:\\ \;\;\;\;y \cdot x\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \]
Alternative 4
Error2.3
Cost712
\[\begin{array}{l} t_0 := y \cdot x - x \cdot z\\ \mathbf{if}\;x \leq -309565389.64855254:\\ \;\;\;\;t_0\\ \mathbf{elif}\;x \leq 1.4974919964123157 \cdot 10^{-45}:\\ \;\;\;\;z + y \cdot x\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \]
Alternative 5
Error14.3
Cost584
\[\begin{array}{l} t_0 := z - x \cdot z\\ \mathbf{if}\;z \leq -6.0713097400873816 \cdot 10^{-161}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq 8.520865919400332 \cdot 10^{-34}:\\ \;\;\;\;x \cdot \left(y - z\right)\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \]
Alternative 6
Error2.3
Cost584
\[\begin{array}{l} t_0 := x \cdot \left(y - z\right)\\ \mathbf{if}\;x \leq -309565389.64855254:\\ \;\;\;\;t_0\\ \mathbf{elif}\;x \leq 1.4974919964123157 \cdot 10^{-45}:\\ \;\;\;\;z + y \cdot x\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \]
Alternative 7
Error0.0
Cost576
\[\left(1 - x\right) \cdot z + y \cdot x \]
Alternative 8
Error25.9
Cost456
\[\begin{array}{l} \mathbf{if}\;z \leq -6.0713097400873816 \cdot 10^{-161}:\\ \;\;\;\;z\\ \mathbf{elif}\;z \leq 8.520865919400332 \cdot 10^{-34}:\\ \;\;\;\;y \cdot x\\ \mathbf{else}:\\ \;\;\;\;z\\ \end{array} \]
Alternative 9
Error0.0
Cost448
\[z + x \cdot \left(y - z\right) \]
Alternative 10
Error35.0
Cost64
\[z \]

Error

Reproduce

herbie shell --seed 2022302 
(FPCore (x y z)
  :name "Diagrams.Backend.Rasterific:$crender from diagrams-rasterific-1.3.1.3"
  :precision binary64
  (+ (* x y) (* (- 1.0 x) z)))