Average Error: 0.1 → 0.0
Time: 4.5s
Precision: binary64
\[\left(x + \sin y\right) + z \cdot \cos y \]
↓
\[\sin y + \mathsf{fma}\left(z, \cos y, x\right) \]
(FPCore (x y z) :precision binary64 (+ (+ x (sin y)) (* z (cos y))))
↓
(FPCore (x y z) :precision binary64 (+ (sin y) (fma z (cos y) x)))
double code(double x, double y, double z) {
	return (x + sin(y)) + (z * cos(y));
}
↓
double code(double x, double y, double z) {
	return sin(y) + fma(z, cos(y), x);
}

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

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

Error

Bits error versus x

Bits error versus y

Bits error versus z

Derivation

  1. Initial program 0.1

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

  2. Simplified0.0

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

  3. Final simplification0.0

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

Reproduce

herbie shell --seed 2022150 
(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))))