Average Error: 0.1 → 0.1
Time: 8.9s
Precision: binary64
Cost: 19584
\[x \cdot \cos y - z \cdot \sin y \]
↓
\[\mathsf{fma}\left(\sin y, -z, x \cdot \cos y\right) \]
(FPCore (x y z) :precision binary64 (- (* x (cos y)) (* z (sin y))))
↓
(FPCore (x y z) :precision binary64 (fma (sin y) (- z) (* x (cos y))))
double code(double x, double y, double z) {
	return (x * cos(y)) - (z * sin(y));
}
↓
double code(double x, double y, double z) {
	return fma(sin(y), -z, (x * cos(y)));
}

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

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

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

Error

Derivation

  1. Initial program 0.1

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

  2. Applied egg-rr0.1

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

  3. Final simplification0.1

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

Alternatives

Alternative 1
Error0.1
Cost13248
\[x \cdot \cos y - \sin y \cdot z \]
Alternative 2
Error10.0
Cost7248
\[\begin{array}{l} t_0 := x - \sin y \cdot z\\ t_1 := x \cdot \cos y\\ \mathbf{if}\;z \leq -7 \cdot 10^{-164}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq 8.1 \cdot 10^{-140}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 4 \cdot 10^{-55}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq 1.2 \cdot 10^{+27}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \]
Alternative 3
Error16.3
Cost7184
\[\begin{array}{l} t_0 := z \cdot \left(-\sin y\right)\\ \mathbf{if}\;y \leq -7.5 \cdot 10^{+202}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y \leq -9.4 \cdot 10^{+154}:\\ \;\;\;\;x \cdot \cos y\\ \mathbf{elif}\;y \leq -0.0033:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y \leq 1.7 \cdot 10^{-19}:\\ \;\;\;\;x + y \cdot \left(y \cdot \left(x \cdot -0.5\right) - z\right)\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \]
Alternative 4
Error15.8
Cost6856
\[\begin{array}{l} t_0 := x \cdot \cos y\\ \mathbf{if}\;y \leq -1.45:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y \leq 0.0085:\\ \;\;\;\;x + y \cdot \left(y \cdot \left(x \cdot -0.5\right) - z\right)\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \]
Alternative 5
Error37.5
Cost520
\[\begin{array}{l} \mathbf{if}\;x \leq -2.6 \cdot 10^{-272}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 1.45 \cdot 10^{-122}:\\ \;\;\;\;z \cdot \left(-y\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
Alternative 6
Error30.4
Cost320
\[x - y \cdot z \]
Alternative 7
Error39.2
Cost64
\[x \]

Error

Reproduce

herbie shell --seed 2022338 
(FPCore (x y z)
  :name "Diagrams.ThreeD.Transform:aboutX from diagrams-lib-1.3.0.3, A"
  :precision binary64
  (- (* x (cos y)) (* z (sin y))))