?

Average Error: 0.1 → 0.1
Time: 8.5s
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

    [Start]0.1

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

    fma-def [=>]0.1

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

  3. Final simplification0.1

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

Alternatives

Alternative 1
Error0.1
Cost13248
\[z \cdot \cos y + x \cdot \sin y \]
Alternative 2
Error15.9
Cost6988
\[\begin{array}{l} t_0 := x \cdot \sin y\\ \mathbf{if}\;y \leq -2.25 \cdot 10^{-5}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y \leq 0.00013:\\ \;\;\;\;z + x \cdot y\\ \mathbf{elif}\;y \leq 1.9 \cdot 10^{+204}:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;z \cdot \cos y\\ \end{array} \]
Alternative 3
Error15.9
Cost6988
\[\begin{array}{l} t_0 := x \cdot \sin y\\ \mathbf{if}\;y \leq -1.35 \cdot 10^{-5}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y \leq 0.0038:\\ \;\;\;\;\mathsf{fma}\left(y, x, z\right)\\ \mathbf{elif}\;y \leq 3.8 \cdot 10^{+204}:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;z \cdot \cos y\\ \end{array} \]
Alternative 4
Error9.2
Cost6985
\[\begin{array}{l} \mathbf{if}\;x \leq -3.1 \cdot 10^{-46} \lor \neg \left(x \leq 6.8 \cdot 10^{-153}\right):\\ \;\;\;\;z + x \cdot \sin y\\ \mathbf{else}:\\ \;\;\;\;z \cdot \cos y\\ \end{array} \]
Alternative 5
Error16.8
Cost6857
\[\begin{array}{l} \mathbf{if}\;y \leq -5.7 \cdot 10^{+31} \lor \neg \left(y \leq 0.027\right):\\ \;\;\;\;z \cdot \cos y\\ \mathbf{else}:\\ \;\;\;\;z + x \cdot y\\ \end{array} \]
Alternative 6
Error37.0
Cost456
\[\begin{array}{l} \mathbf{if}\;x \leq -3 \cdot 10^{+161}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;x \leq 3.4 \cdot 10^{+106}:\\ \;\;\;\;z\\ \mathbf{else}:\\ \;\;\;\;x \cdot y\\ \end{array} \]
Alternative 7
Error30.4
Cost320
\[z + x \cdot y \]
Alternative 8
Error38.4
Cost64
\[z \]

Error

Reproduce?

herbie shell --seed 2023041 
(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))))