?

Average Error: 0.2% → 0.19%
Time: 10.3s
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 0.2

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

  2. Simplified0.19

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

    [Start]0.2

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

    fma-def [=>]0.19

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

  3. Final simplification0.19

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

Alternatives

Alternative 1
Error0.2%
Cost13248
\[z \cdot \cos y + x \cdot \sin y \]
Alternative 2
Error26.25%
Cost6988
\[\begin{array}{l} t_0 := x \cdot \sin y\\ \mathbf{if}\;y \leq -0.00058:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y \leq 1.8 \cdot 10^{+23}:\\ \;\;\;\;z + x \cdot y\\ \mathbf{elif}\;y \leq 1.3 \cdot 10^{+186}:\\ \;\;\;\;z \cdot \cos y\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \]
Alternative 3
Error26.29%
Cost6988
\[\begin{array}{l} t_0 := x \cdot \sin y\\ \mathbf{if}\;y \leq -0.00285:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y \leq 1.8 \cdot 10^{+23}:\\ \;\;\;\;\mathsf{fma}\left(y, x, z\right)\\ \mathbf{elif}\;y \leq 3.3 \cdot 10^{+185}:\\ \;\;\;\;z \cdot \cos y\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \]
Alternative 4
Error14.69%
Cost6985
\[\begin{array}{l} \mathbf{if}\;x \leq -1.6 \cdot 10^{-5} \lor \neg \left(x \leq 1.72 \cdot 10^{-137}\right):\\ \;\;\;\;z + x \cdot \sin y\\ \mathbf{else}:\\ \;\;\;\;z \cdot \cos y\\ \end{array} \]
Alternative 5
Error26.25%
Cost6857
\[\begin{array}{l} \mathbf{if}\;y \leq -240000000000 \lor \neg \left(y \leq 1.8 \cdot 10^{+23}\right):\\ \;\;\;\;z \cdot \cos y\\ \mathbf{else}:\\ \;\;\;\;z + x \cdot y\\ \end{array} \]
Alternative 6
Error58.71%
Cost456
\[\begin{array}{l} \mathbf{if}\;z \leq -4 \cdot 10^{-129}:\\ \;\;\;\;z\\ \mathbf{elif}\;z \leq 8.5 \cdot 10^{-109}:\\ \;\;\;\;x \cdot y\\ \mathbf{else}:\\ \;\;\;\;z\\ \end{array} \]
Alternative 7
Error48.04%
Cost320
\[z + x \cdot y \]
Alternative 8
Error60.48%
Cost64
\[z \]

Error

Reproduce?

herbie shell --seed 2023088 
(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))))