Graphics.Rendering.Chart.Drawing:drawTextsR from Chart-1.5.3

Average Error: 0.0 → 0.0

Time: 47.3s

Precision: binary64

Cost: 6848

Math

\[x \cdot y + \left(x - 1\right) \cdot z \]

↓

\[\mathsf{fma}\left(x, y, \left(-1 + x\right) \cdot z\right) \]

FPCore

(FPCore (x y z) :precision binary64 (+ (* x y) (* (- x 1.0) z)))

↓

(FPCore (x y z) :precision binary64 (fma x y (* (+ -1.0 x) z)))

C

double code(double x, double y, double z) {
	return (x * y) + ((x - 1.0) * z);
}

↓

double code(double x, double y, double z) {
	return fma(x, y, ((-1.0 + x) * z));
}

Julia

function code(x, y, z)
	return Float64(Float64(x * y) + Float64(Float64(x - 1.0) * z))
end

↓

function code(x, y, z)
	return fma(x, y, Float64(Float64(-1.0 + x) * z))
end

Wolfram

code[x_, y_, z_] := N[(N[(x * y), $MachinePrecision] + N[(N[(x - 1.0), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision]

↓

code[x_, y_, z_] := N[(x * y + N[(N[(-1.0 + x), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 0.0

   \[x \cdot y + \left(x - 1\right) \cdot z \]

2. Simplified 0.0

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

Alternatives

Alternative 1
Error	24.4
Cost	852

\[\begin{array}{l} \mathbf{if}\;x \leq -2.5 \cdot 10^{+118}:\\ \;\;\;\;z \cdot x\\ \mathbf{elif}\;x \leq -8.3 \cdot 10^{+92}:\\ \;\;\;\;y \cdot x\\ \mathbf{elif}\;x \leq -1 \cdot 10^{+24}:\\ \;\;\;\;z \cdot x\\ \mathbf{elif}\;x \leq -2.45 \cdot 10^{-88}:\\ \;\;\;\;y \cdot x\\ \mathbf{elif}\;x \leq 1:\\ \;\;\;\;-z\\ \mathbf{else}:\\ \;\;\;\;z \cdot x\\ \end{array} \]

Alternative 2
Error	12.7
Cost	584

\[\begin{array}{l} t_0 := \left(y + z\right) \cdot x\\ \mathbf{if}\;x \leq -1.2 \cdot 10^{-87}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;x \leq 1.3 \cdot 10^{-10}:\\ \;\;\;\;-z\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \]

Alternative 3
Error	12.7
Cost	584

\[\begin{array}{l} t_0 := \left(y + z\right) \cdot x\\ \mathbf{if}\;x \leq -1.2 \cdot 10^{-87}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;x \leq 0.00155:\\ \;\;\;\;\left(x - 1\right) \cdot z\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \]

Alternative 4
Error	1.4
Cost	584

\[\begin{array}{l} t_0 := \left(y + z\right) \cdot x\\ \mathbf{if}\;x \leq -7.6 \cdot 10^{+23}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;x \leq 1:\\ \;\;\;\;y \cdot x - z\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \]

Alternative 5
Error	24.5
Cost	456

\[\begin{array}{l} \mathbf{if}\;x \leq -1.45 \cdot 10^{-87}:\\ \;\;\;\;y \cdot x\\ \mathbf{elif}\;x \leq 3.8 \cdot 10^{-12}:\\ \;\;\;\;-z\\ \mathbf{else}:\\ \;\;\;\;y \cdot x\\ \end{array} \]

Alternative 6
Error	0.0
Cost	448

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

Alternative 7
Error	35.4
Cost	128

\[-z \]

Reproduce

herbie shell --seed 2023033 
(FPCore (x y z)
  :name "Graphics.Rendering.Chart.Drawing:drawTextsR from Chart-1.5.3"
  :precision binary64
  (+ (* x y) (* (- x 1.0) z)))