Average Error: 0.1 → 0.0
Time: 4.2s
Precision: binary64
\[\left(x + \sin y\right) + z \cdot \cos y \]
↓
\[x + \mathsf{fma}\left(z, \cos y, \sin y\right) \]
(FPCore (x y z) :precision binary64 (+ (+ x (sin y)) (* z (cos y))))
↓
(FPCore (x y z) :precision binary64 (+ x (fma z (cos y) (sin 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 x + fma(z, cos(y), sin(y));
}

function code(x, y, z)
	return Float64(Float64(x + sin(y)) + Float64(z * cos(y)))
end
↓
function code(x, y, z)
	return Float64(x + fma(z, cos(y), sin(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[(z * N[Cos[y], $MachinePrecision] + N[Sin[y], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

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

Error

Derivation

  1. Initial program 0.1

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

  2. Applied egg-rr0.5

    \[\leadsto \color{blue}{\mathsf{fma}\left(\cos y \cdot {\left(\sqrt[3]{z}\right)}^{2}, \sqrt[3]{z}, x + \sin y\right)} \]

  3. Taylor expanded in y around inf 0.1

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

  4. Simplified0.0

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

  5. Final simplification0.0

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

Reproduce

herbie shell --seed 2022192 
(FPCore (x y z)
  :name "Graphics.Rasterific.Svg.PathConverter:segmentToBezier from rasterific-svg-0.2.3.1, C"
  :precision binary64
  (+ (+ x (sin y)) (* z (cos y))))