Diagrams.Solve.Polynomial:cubForm from diagrams-solve-0.1, B

Average Error: 0.2 → 0.1

Time: 2.0s

Precision: binary64

\[ \begin{array}{c}[x, y] = \mathsf{sort}([x, y])\\ \end{array} \]

Math

\[\left(x \cdot 3\right) \cdot y - z \]

↓

\[-\mathsf{fma}\left(x, y \cdot -3, z\right) \]

FPCore

(FPCore (x y z) :precision binary64 (- (* (* x 3.0) y) z))

↓

(FPCore (x y z) :precision binary64 (- (fma x (* y -3.0) z)))

C

double code(double x, double y, double z) {
	return ((x * 3.0) * y) - z;
}

↓

double code(double x, double y, double z) {
	return -fma(x, (y * -3.0), z);
}

Julia

function code(x, y, z)
	return Float64(Float64(Float64(x * 3.0) * y) - z)
end

↓

function code(x, y, z)
	return Float64(-fma(x, Float64(y * -3.0), z))
end

Wolfram

code[x_, y_, z_] := N[(N[(N[(x * 3.0), $MachinePrecision] * y), $MachinePrecision] - z), $MachinePrecision]

↓

code[x_, y_, z_] := (-N[(x * N[(y * -3.0), $MachinePrecision] + z), $MachinePrecision])

Target

Original	0.2
Target	0.1
Herbie	0.1

\[x \cdot \left(3 \cdot y\right) - z \]

Derivation

1. Initial program 0.2

   \[\left(x \cdot 3\right) \cdot y - z \]

2. Simplified 0.1

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

3. Final simplification 0.1

   \[\leadsto -\mathsf{fma}\left(x, y \cdot -3, z\right) \]

Reproduce

herbie shell --seed 2022211 
(FPCore (x y z)
  :name "Diagrams.Solve.Polynomial:cubForm  from diagrams-solve-0.1, B"
  :precision binary64

  :herbie-target
  (- (* x (* 3.0 y)) z)

  (- (* (* x 3.0) y) z))