Diagrams.Solve.Polynomial:quartForm from diagrams-solve-0.1, D

Average Error: 0.0 → 0.0

Time: 4.1s

Precision: binary64

Cost: 6848

Math

\[\frac{x \cdot y}{2} - \frac{z}{8} \]

↓

\[\mathsf{fma}\left(y, x \cdot 0.5, z \cdot -0.125\right) \]

FPCore

(FPCore (x y z) :precision binary64 (- (/ (* x y) 2.0) (/ z 8.0)))

↓

(FPCore (x y z) :precision binary64 (fma y (* x 0.5) (* z -0.125)))

C

double code(double x, double y, double z) {
	return ((x * y) / 2.0) - (z / 8.0);
}

↓

double code(double x, double y, double z) {
	return fma(y, (x * 0.5), (z * -0.125));
}

Julia

function code(x, y, z)
	return Float64(Float64(Float64(x * y) / 2.0) - Float64(z / 8.0))
end

↓

function code(x, y, z)
	return fma(y, Float64(x * 0.5), Float64(z * -0.125))
end

Wolfram

code[x_, y_, z_] := N[(N[(N[(x * y), $MachinePrecision] / 2.0), $MachinePrecision] - N[(z / 8.0), $MachinePrecision]), $MachinePrecision]

↓

code[x_, y_, z_] := N[(y * N[(x * 0.5), $MachinePrecision] + N[(z * -0.125), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 0.0

   \[\frac{x \cdot y}{2} - \frac{z}{8} \]

2. Applied egg-rr 0.0

   \[\leadsto \color{blue}{\mathsf{fma}\left(y, x \cdot 0.5, z \cdot -0.125\right)} \]

Alternatives

Alternative 1
Error	16.0
Cost	716

\[\begin{array}{l} t_0 := \left(x \cdot 0.5\right) \cdot y\\ \mathbf{if}\;z \leq -1.9 \cdot 10^{-28}:\\ \;\;\;\;-0.125 \cdot z\\ \mathbf{elif}\;z \leq 1.9 \cdot 10^{-52}:\\ \;\;\;\;\begin{array}{l} \mathbf{if}\;y \ne 0:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array}\\ \mathbf{else}:\\ \;\;\;\;-0.125 \cdot z\\ \end{array} \]

Alternative 2
Error	0.0
Cost	576

\[\frac{x \cdot y}{2} - \frac{z}{8} \]

Alternative 3
Error	26.8
Cost	192

\[-0.125 \cdot z \]

Reproduce

herbie shell --seed 2023010 
(FPCore (x y z)
  :name "Diagrams.Solve.Polynomial:quartForm  from diagrams-solve-0.1, D"
  :precision binary64
  (- (/ (* x y) 2.0) (/ z 8.0)))