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

Average Accuracy: 99.9% → 99.9%

Time: 9.3s

Precision: binary64

Cost: 19520

Math

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

↓

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

FPCore

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

↓

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

C

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

↓

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

Julia

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

↓

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

Wolfram

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

↓

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

Derivation

1. Initial program 99.9%

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

2. Simplified 100.0%

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

   [Start] 99.9	\[ \left(x + \sin y\right) + z \cdot \cos y \]
   +-commutative [=>] 99.9	\[ \color{blue}{z \cdot \cos y + \left(x + \sin y\right)} \]
   fma-def [=>] 100.0	\[ \color{blue}{\mathsf{fma}\left(z, \cos y, x + \sin y\right)} \]

3. Final simplification 100.0%

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

Alternatives

Alternative 1
Accuracy	89.0%
Cost	13384

\[\begin{array}{l} \mathbf{if}\;x \leq -6.5 \cdot 10^{-18}:\\ \;\;\;\;z + x\\ \mathbf{elif}\;x \leq 2.8 \cdot 10^{+36}:\\ \;\;\;\;\sin y + z \cdot \cos y\\ \mathbf{else}:\\ \;\;\;\;z + x\\ \end{array} \]

Alternative 2
Accuracy	99.9%
Cost	13248

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

Alternative 3
Accuracy	84.2%
Cost	7244

\[\begin{array}{l} t_0 := z \cdot \cos y\\ t_1 := t_0 + \left(y + x\right)\\ \mathbf{if}\;z \leq -4400:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 1.26 \cdot 10^{+33}:\\ \;\;\;\;x + \sin y\\ \mathbf{elif}\;z \leq 2.3 \cdot 10^{+104}:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 4
Accuracy	81.9%
Cost	7121

\[\begin{array}{l} t_0 := z \cdot \cos y\\ \mathbf{if}\;z \leq -1.5 \cdot 10^{+222}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq -1.56 \cdot 10^{+106}:\\ \;\;\;\;z + x\\ \mathbf{elif}\;z \leq -2600000 \lor \neg \left(z \leq 2.45 \cdot 10^{+33}\right):\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;x + \sin y\\ \end{array} \]

Alternative 5
Accuracy	70.2%
Cost	7120

\[\begin{array}{l} t_0 := z \cdot \cos y\\ \mathbf{if}\;z \leq -1.3 \cdot 10^{+222}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq 5 \cdot 10^{-174}:\\ \;\;\;\;z + x\\ \mathbf{elif}\;z \leq 1.25 \cdot 10^{-131}:\\ \;\;\;\;\sin y\\ \mathbf{elif}\;z \leq 6.2 \cdot 10^{+33}:\\ \;\;\;\;z + x\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \]

Alternative 6
Accuracy	70.1%
Cost	6860

\[\begin{array}{l} \mathbf{if}\;y \leq -1 \cdot 10^{+20}:\\ \;\;\;\;z + x\\ \mathbf{elif}\;y \leq 5.1 \cdot 10^{+38}:\\ \;\;\;\;y + \left(z + x\right)\\ \mathbf{elif}\;y \leq 3.1 \cdot 10^{+119}:\\ \;\;\;\;\sin y\\ \mathbf{else}:\\ \;\;\;\;z + x\\ \end{array} \]

Alternative 7
Accuracy	70.5%
Cost	584

\[\begin{array}{l} \mathbf{if}\;y \leq -9.5 \cdot 10^{+18}:\\ \;\;\;\;z + x\\ \mathbf{elif}\;y \leq 2.6 \cdot 10^{-30}:\\ \;\;\;\;y + \left(z + x\right)\\ \mathbf{else}:\\ \;\;\;\;z + x\\ \end{array} \]

Alternative 8
Accuracy	68.4%
Cost	456

\[\begin{array}{l} \mathbf{if}\;x \leq -2.8 \cdot 10^{-110}:\\ \;\;\;\;z + x\\ \mathbf{elif}\;x \leq 6.9 \cdot 10^{-220}:\\ \;\;\;\;z + y\\ \mathbf{else}:\\ \;\;\;\;z + x\\ \end{array} \]

Alternative 9
Accuracy	44.8%
Cost	328

\[\begin{array}{l} \mathbf{if}\;x \leq -4.2 \cdot 10^{-91}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 1.3 \cdot 10^{-218}:\\ \;\;\;\;y\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 10
Accuracy	54.6%
Cost	328

\[\begin{array}{l} \mathbf{if}\;x \leq -5.2 \cdot 10^{-45}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 2.7 \cdot 10^{-72}:\\ \;\;\;\;z\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 11
Accuracy	66.6%
Cost	192

\[z + x \]

Alternative 12
Accuracy	42.7%
Cost	64

\[x \]

Reproduce

herbie shell --seed 2023159 
(FPCore (x y z)
  :name "Graphics.Rasterific.Svg.PathConverter:segmentToBezier from rasterific-svg-0.2.3.1, C"
  :precision binary64
  (+ (+ x (sin y)) (* z (cos y))))