Average Error: 0.0 → 0
Time: 1.9s
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(Float64(-y), 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-rr32.5

    \[\leadsto \color{blue}{{\left(\sqrt{x - y \cdot z}\right)}^{2}} \]

  3. Taylor expanded in x around 0 27.9

    \[\leadsto \color{blue}{{\left(\sqrt{-y \cdot z}\right)}^{2} + x} \]

  4. Applied egg-rr0

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

  5. Final simplification0

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

Reproduce

herbie shell --seed 2022156 
(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)))