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

Average Error: 0.1 → 0.0

Time: 17.5s

Precision: binary64

Cost: 6848

Math

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

↓

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

FPCore

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

↓

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

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, (0.5 * x), (-0.125 * z));
}

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(0.5 * x), Float64(-0.125 * z))
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[(0.5 * x), $MachinePrecision] + N[(-0.125 * z), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 0.1

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

2. Applied egg-rr 0.0

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

Alternatives

Alternative 1
Error	16.3
Cost	716

\[\begin{array}{l} t_0 := \left(0.5 \cdot y\right) \cdot x\\ \mathbf{if}\;z \leq -1.02 \cdot 10^{-47}:\\ \;\;\;\;-0.125 \cdot z\\ \mathbf{elif}\;z \leq 1.2 \cdot 10^{-44}:\\ \;\;\;\;\begin{array}{l} \mathbf{if}\;y \ne 0:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array}\\ \mathbf{else}:\\ \;\;\;\;-0.125 \cdot z\\ \end{array} \]

Alternative 2
Error	0.1
Cost	576

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

Alternative 3
Error	27.2
Cost	192

\[-0.125 \cdot z \]

Reproduce

herbie shell --seed 2023033 
(FPCore (x y z)
  :name "Diagrams.Solve.Polynomial:quartForm  from diagrams-solve-0.1, D"
  :precision binary64
  (- (/ (* x y) 2.0) (/ z 8.0)))