Average Error: 0.0 → 0.0
Time: 3.3s
Precision: binary64
Cost: 6720
\[\left(1 - x\right) \cdot y + x \cdot z \]
↓
\[\mathsf{fma}\left(x, z - y, y\right) \]
(FPCore (x y z) :precision binary64 (+ (* (- 1.0 x) y) (* x z)))
↓
(FPCore (x y z) :precision binary64 (fma x (- z y) y))
double code(double x, double y, double z) {
	return ((1.0 - x) * y) + (x * z);
}
↓
double code(double x, double y, double z) {
	return fma(x, (z - y), y);
}

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

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

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

Error

Target

Original0.0
Target0.0
Herbie0.0
\[y - x \cdot \left(y - z\right) \]

Derivation

  1. Initial program 0.0

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

  2. Simplified0.0

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

  3. Final simplification0.0

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

Alternatives

Alternative 1
Error15.9
Cost848
\[\begin{array}{l} t_0 := y \cdot \left(1 - x\right)\\ \mathbf{if}\;y \leq -3.0491365115771048 \cdot 10^{-117}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y \leq -9.726890206674207 \cdot 10^{-178}:\\ \;\;\;\;x \cdot z\\ \mathbf{elif}\;y \leq -4.4178891406936545 \cdot 10^{-194}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y \leq 3.2186848096096415 \cdot 10^{-93}:\\ \;\;\;\;x \cdot z\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \]
Alternative 2
Error15.9
Cost848
\[\begin{array}{l} t_0 := y \cdot \left(1 - x\right)\\ \mathbf{if}\;y \leq -3.0491365115771048 \cdot 10^{-117}:\\ \;\;\;\;y - x \cdot y\\ \mathbf{elif}\;y \leq -9.726890206674207 \cdot 10^{-178}:\\ \;\;\;\;x \cdot z\\ \mathbf{elif}\;y \leq -4.4178891406936545 \cdot 10^{-194}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y \leq 3.2186848096096415 \cdot 10^{-93}:\\ \;\;\;\;x \cdot z\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \]
Alternative 3
Error23.6
Cost784
\[\begin{array}{l} t_0 := x \cdot \left(-y\right)\\ \mathbf{if}\;x \leq -1.9 \cdot 10^{+88}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;x \leq -117400125672067660:\\ \;\;\;\;x \cdot z\\ \mathbf{elif}\;x \leq 4.9548887232214546 \cdot 10^{-36}:\\ \;\;\;\;y\\ \mathbf{elif}\;x \leq 4.2 \cdot 10^{+28}:\\ \;\;\;\;x \cdot z\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \]
Alternative 4
Error12.4
Cost584
\[\begin{array}{l} t_0 := x \cdot \left(z - y\right)\\ \mathbf{if}\;x \leq -117400125672067660:\\ \;\;\;\;t_0\\ \mathbf{elif}\;x \leq 4.9548887232214546 \cdot 10^{-36}:\\ \;\;\;\;y - x \cdot y\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \]
Alternative 5
Error0.0
Cost576
\[x \cdot z + y \cdot \left(1 - x\right) \]
Alternative 6
Error24.6
Cost456
\[\begin{array}{l} \mathbf{if}\;x \leq -117400125672067660:\\ \;\;\;\;x \cdot z\\ \mathbf{elif}\;x \leq 4.9548887232214546 \cdot 10^{-36}:\\ \;\;\;\;y\\ \mathbf{else}:\\ \;\;\;\;x \cdot z\\ \end{array} \]
Alternative 7
Error34.9
Cost64
\[y \]

Error

Reproduce

herbie shell --seed 2022325 
(FPCore (x y z)
  :name "Diagrams.Color.HSV:lerp  from diagrams-contrib-1.3.0.5"
  :precision binary64

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

  (+ (* (- 1.0 x) y) (* x z)))