Average Error: 0.0 → 0
Time: 1.8s
Precision: binary64
\[x - y \cdot z \]
↓
\[\mathsf{fma}\left(y, -z, x\right) \]
(FPCore (x y z) :precision binary64 (- x (* y z)))
↓
(FPCore (x y z) :precision binary64 (fma y (- z) x))
double code(double x, double y, double z) {
	return x - (y * z);
}
↓
double code(double x, double y, double z) {
	return fma(y, -z, x);
}

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

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

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

Error

Bits error versus x

Bits error versus y

Bits error versus z

Target

Original0.0
Target0.0
Herbie0
\[\frac{x + y \cdot z}{\frac{x + y \cdot z}{x - y \cdot z}} \]

Derivation

  1. Initial program 0.0

    \[x - y \cdot z \]

  2. Applied egg-rr39.9

    \[\leadsto \color{blue}{\left({x}^{3} - {\left(y \cdot z\right)}^{3}\right) \cdot \frac{1}{\mathsf{fma}\left(x, x, \left(y \cdot z\right) \cdot \left(x + y \cdot z\right)\right)}} \]

  3. Taylor expanded in x around 0 0.0

    \[\leadsto \color{blue}{x - y \cdot z} \]

  4. Simplified0

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

  5. Final simplification0

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

Reproduce

herbie shell --seed 2022166 
(FPCore (x y z)
  :name "Diagrams.Solve.Tridiagonal:solveTriDiagonal from diagrams-solve-0.1, C"
  :precision binary64

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

  (- x (* y z)))