Average Error: 0.0 → 0.0
Time: 6.2s
Precision: binary64
Cost: 6720
\[x + \left(y - x\right) \cdot z \]
↓
\[\mathsf{fma}\left(y - x, z, x\right) \]
(FPCore (x y z) :precision binary64 (+ x (* (- y x) z)))
↓
(FPCore (x y z) :precision binary64 (fma (- y x) z x))
double code(double x, double y, double z) {
	return x + ((y - x) * z);
}
↓
double code(double x, double y, double z) {
	return fma((y - x), z, x);
}

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

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

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

Error

Derivation

  1. Initial program 0.0

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

  2. Simplified0.0

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

    [Start]0.0

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

    +-commutative [=>]0.0

    \[ \color{blue}{\left(y - x\right) \cdot z + x} \]

    fma-def [=>]0.0

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

  3. Final simplification0.0

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

Alternatives

Alternative 1
Error23.6
Cost916
\[\begin{array}{l} t_0 := z \cdot \left(-x\right)\\ \mathbf{if}\;z \leq -1.85 \cdot 10^{+94}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;z \leq -0.0138:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq 3.7 \cdot 10^{-50}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 10^{+33}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;z \leq 1.85 \cdot 10^{+92}:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;y \cdot z\\ \end{array} \]
Alternative 2
Error15.9
Cost850
\[\begin{array}{l} \mathbf{if}\;x \leq -7.6 \cdot 10^{-178} \lor \neg \left(x \leq 2.45 \cdot 10^{-120}\right) \land \left(x \leq 8.8 \cdot 10^{-99} \lor \neg \left(x \leq 6 \cdot 10^{-93}\right)\right):\\ \;\;\;\;x \cdot \left(1 - z\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot z\\ \end{array} \]
Alternative 3
Error12.5
Cost848
\[\begin{array}{l} t_0 := \left(y - x\right) \cdot z\\ t_1 := x \cdot \left(1 - z\right)\\ \mathbf{if}\;z \leq -800000000000:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq 3.8 \cdot 10^{-50}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 1.95 \cdot 10^{-18}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;z \leq 14.2:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \]
Alternative 4
Error0.8
Cost585
\[\begin{array}{l} \mathbf{if}\;z \leq -1 \lor \neg \left(z \leq 0.0022\right):\\ \;\;\;\;\left(y - x\right) \cdot z\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot z\\ \end{array} \]
Alternative 5
Error0.0
Cost576
\[\left(x + y \cdot z\right) - x \cdot z \]
Alternative 6
Error23.1
Cost456
\[\begin{array}{l} \mathbf{if}\;z \leq -9 \cdot 10^{-6}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;z \leq 3.9 \cdot 10^{-50}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y \cdot z\\ \end{array} \]
Alternative 7
Error0.0
Cost448
\[x + \left(y - x\right) \cdot z \]
Alternative 8
Error34.4
Cost64
\[x \]

Error

Reproduce

herbie shell --seed 2022364 
(FPCore (x y z)
  :name "Diagrams.ThreeD.Shapes:frustum from diagrams-lib-1.3.0.3, B"
  :precision binary64
  (+ x (* (- y x) z)))