Graphics.Rasterific.Svg.PathConverter:segmentToBezier from rasterific-svg-0.2.3.1, B

Average Error: 0.08% → 0.08%

Time: 9.3s

Precision: binary64

Cost: 19584

Math

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

↓

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

FPCore

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

↓

(FPCore (x y z) :precision binary64 (fma (sin y) (- z) (+ x (cos y))))

C

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

↓

double code(double x, double y, double z) {
	return fma(sin(y), -z, (x + cos(y)));
}

Julia

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

↓

function code(x, y, z)
	return fma(sin(y), Float64(-z), Float64(x + cos(y)))
end

Wolfram

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

↓

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

Derivation

1. Initial program 0.08

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

2. Simplified 0.08

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

   [Start] 0.08	\[ \left(x + \cos y\right) - z \cdot \sin y \]
   cancel-sign-sub-inv [=>] 0.08	\[ \color{blue}{\left(x + \cos y\right) + \left(-z\right) \cdot \sin y} \]
   +-commutative [=>] 0.08	\[ \color{blue}{\left(-z\right) \cdot \sin y + \left(x + \cos y\right)} \]
   *-commutative [=>] 0.08	\[ \color{blue}{\sin y \cdot \left(-z\right)} + \left(x + \cos y\right) \]
   fma-def [=>] 0.08	\[ \color{blue}{\mathsf{fma}\left(\sin y, -z, x + \cos y\right)} \]

3. Final simplification 0.08

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

Alternatives

Alternative 1
Error	9.95%
Cost	13385

\[\begin{array}{l} \mathbf{if}\;x \leq -19000000 \lor \neg \left(x \leq 0.029\right):\\ \;\;\;\;x + \cos y\\ \mathbf{else}:\\ \;\;\;\;\cos y - \sin y \cdot z\\ \end{array} \]

Alternative 2
Error	0.08%
Cost	13248

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

Alternative 3
Error	18.05%
Cost	6921

\[\begin{array}{l} \mathbf{if}\;z \leq -2.5 \cdot 10^{+96} \lor \neg \left(z \leq 5 \cdot 10^{+101}\right):\\ \;\;\;\;\sin y \cdot \left(-z\right)\\ \mathbf{else}:\\ \;\;\;\;x + \cos y\\ \end{array} \]

Alternative 4
Error	18.85%
Cost	6857

\[\begin{array}{l} \mathbf{if}\;y \leq -1750 \lor \neg \left(y \leq 4.4 \cdot 10^{+18}\right):\\ \;\;\;\;x + \cos y\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(y \cdot -0.5 - z\right) + \left(x + 1\right)\\ \end{array} \]

Alternative 5
Error	29.13%
Cost	968

\[\begin{array}{l} \mathbf{if}\;y \leq -29000:\\ \;\;\;\;x + 1\\ \mathbf{elif}\;y \leq 6.2 \cdot 10^{+18}:\\ \;\;\;\;y \cdot \left(y \cdot -0.5 - z\right) + \left(x + 1\right)\\ \mathbf{else}:\\ \;\;\;\;x + 1\\ \end{array} \]

Alternative 6
Error	29.14%
Cost	712

\[\begin{array}{l} \mathbf{if}\;y \leq -3500000:\\ \;\;\;\;x + 1\\ \mathbf{elif}\;y \leq 9 \cdot 10^{+19}:\\ \;\;\;\;\left(x + 1\right) - y \cdot z\\ \mathbf{else}:\\ \;\;\;\;x + 1\\ \end{array} \]

Alternative 7
Error	37.89%
Cost	388

\[\begin{array}{l} \mathbf{if}\;z \leq -3.1 \cdot 10^{+197}:\\ \;\;\;\;y \cdot \left(-z\right)\\ \mathbf{else}:\\ \;\;\;\;x + 1\\ \end{array} \]

Alternative 8
Error	38.18%
Cost	192

\[x + 1 \]

Alternative 9
Error	56.95%
Cost	64

\[x \]

Reproduce

herbie shell --seed 2023121 
(FPCore (x y z)
  :name "Graphics.Rasterific.Svg.PathConverter:segmentToBezier from rasterific-svg-0.2.3.1, B"
  :precision binary64
  (- (+ x (cos y)) (* z (sin y))))