?

Average Error: 0.1 → 0.1
Time: 1.4min
Precision: binary64
Cost: 19520

?

\[x \cdot \sin y + z \cdot \cos y \]
↓
\[\mathsf{fma}\left(x, \sin y, z \cdot \cos y\right) \]
(FPCore (x y z) :precision binary64 (+ (* x (sin y)) (* z (cos y))))
↓
(FPCore (x y z) :precision binary64 (fma x (sin y) (* z (cos y))))
double code(double x, double y, double z) {
	return (x * sin(y)) + (z * cos(y));
}
↓
double code(double x, double y, double z) {
	return fma(x, sin(y), (z * cos(y)));
}

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

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

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

Error?

Derivation?

  1. Initial program 0.1

    \[x \cdot \sin y + z \cdot \cos y \]

  2. Simplified0.1

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

Alternatives

Alternative 1
Error0.1
Cost13248
\[x \cdot \sin y + z \cdot \cos y \]
Alternative 2
Error15.9
Cost7120
\[\begin{array}{l} t_0 := \cos y \cdot z\\ \mathbf{if}\;y \leq -1.8 \cdot 10^{+90}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y \leq -5.2 \cdot 10^{+17}:\\ \;\;\;\;\sin y \cdot x\\ \mathbf{elif}\;y \leq -6.8 \cdot 10^{-8}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y \leq 1.4 \cdot 10^{-7}:\\ \;\;\;\;y \cdot x + z\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \]
Alternative 3
Error16.2
Cost6856
\[\begin{array}{l} t_0 := \cos y \cdot z\\ \mathbf{if}\;y \leq -6.8 \cdot 10^{-8}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y \leq 1.4 \cdot 10^{-7}:\\ \;\;\;\;y \cdot x + z\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \]
Alternative 4
Error37.5
Cost456
\[\begin{array}{l} \mathbf{if}\;z \leq -6.6 \cdot 10^{-233}:\\ \;\;\;\;z\\ \mathbf{elif}\;z \leq 4 \cdot 10^{-126}:\\ \;\;\;\;y \cdot x\\ \mathbf{else}:\\ \;\;\;\;z\\ \end{array} \]
Alternative 5
Error30.6
Cost320
\[y \cdot x + z \]
Alternative 6
Error38.7
Cost64
\[z \]

Error

Reproduce?

herbie shell --seed 2023033 
(FPCore (x y z)
  :name "Diagrams.ThreeD.Transform:aboutX from diagrams-lib-1.3.0.3, B"
  :precision binary64
  (+ (* x (sin y)) (* z (cos y))))