Average Error: 0.0 → 0.0
Time: 1.5s
Precision: binary64
\[x \cdot y + z \cdot \left(1 - y\right) \]
↓
\[\mathsf{fma}\left(y, x - z, z\right) \]
(FPCore (x y z) :precision binary64 (+ (* x y) (* z (- 1.0 y))))
↓
(FPCore (x y z) :precision binary64 (fma y (- x z) z))
double code(double x, double y, double z) {
	return (x * y) + (z * (1.0 - y));
}
↓
double code(double x, double y, double z) {
	return fma(y, (x - z), z);
}

function code(x, y, z)
	return Float64(Float64(x * y) + Float64(z * Float64(1.0 - y)))
end
↓
function code(x, y, z)
	return fma(y, Float64(x - z), z)
end

code[x_, y_, z_] := N[(N[(x * y), $MachinePrecision] + N[(z * N[(1.0 - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]
↓
code[x_, y_, z_] := N[(y * N[(x - z), $MachinePrecision] + z), $MachinePrecision]

x \cdot y + z \cdot \left(1 - y\right)
↓
\mathsf{fma}\left(y, x - z, z\right)

Error

Bits error versus x

Bits error versus y

Bits error versus z

Target

Original0.0
Target0.0
Herbie0.0
\[z - \left(z - x\right) \cdot y \]

Derivation

  1. Initial program 0.0

    \[x \cdot y + z \cdot \left(1 - y\right) \]

  2. Simplified0.0

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

  3. Final simplification0.0

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

Reproduce

herbie shell --seed 2022160 
(FPCore (x y z)
  :name "Diagrams.TwoD.Segment:bezierClip from diagrams-lib-1.3.0.3"
  :precision binary64

  :herbie-target
  (- z (* (- z x) y))

  (+ (* x y) (* z (- 1.0 y))))