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

Average Accuracy: 99.9% → 99.9%

Time: 8.7s

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 99.9%

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

   [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 [=>] 99.9	\[ \color{blue}{\mathsf{fma}\left(z, \cos y, x + \sin y\right)} \]

3. Final simplification 99.9%

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

Alternatives

Alternative 1
Accuracy	88.7%
Cost	13384

\[\begin{array}{l} t_0 := z \cdot \cos y\\ \mathbf{if}\;x \leq -14000000000000:\\ \;\;\;\;z + x\\ \mathbf{elif}\;x \leq 2.4 \cdot 10^{-27}:\\ \;\;\;\;\sin y + t_0\\ \mathbf{elif}\;x \leq 8.5 \cdot 10^{+55}:\\ \;\;\;\;t_0 + \left(y + x\right)\\ \mathbf{else}:\\ \;\;\;\;z + x\\ \end{array} \]

Alternative 2
Accuracy	99.9%
Cost	13248

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

Alternative 3
Accuracy	69.6%
Cost	7516

\[\begin{array}{l} t_0 := z \cdot \cos y\\ \mathbf{if}\;x \leq -8 \cdot 10^{-65}:\\ \;\;\;\;z + x\\ \mathbf{elif}\;x \leq -6.8 \cdot 10^{-175}:\\ \;\;\;\;\sin y\\ \mathbf{elif}\;x \leq -1.6 \cdot 10^{-277}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;x \leq 2.8 \cdot 10^{-280}:\\ \;\;\;\;\sin y\\ \mathbf{elif}\;x \leq 7.4 \cdot 10^{-224}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;x \leq 5.3 \cdot 10^{-192}:\\ \;\;\;\;\sin y\\ \mathbf{elif}\;x \leq 9 \cdot 10^{-78}:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;z + x\\ \end{array} \]

Alternative 4
Accuracy	85.3%
Cost	7120

\[\begin{array}{l} t_0 := z \cdot \cos y\\ \mathbf{if}\;z \leq -1.4 \cdot 10^{+112}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq -8.5 \cdot 10^{-29}:\\ \;\;\;\;z + x\\ \mathbf{elif}\;z \leq 7 \cdot 10^{-27}:\\ \;\;\;\;x + \sin y\\ \mathbf{elif}\;z \leq 8.2 \cdot 10^{+210}:\\ \;\;\;\;z + x\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \]

Alternative 5
Accuracy	84.5%
Cost	7113

\[\begin{array}{l} \mathbf{if}\;z \leq -6 \cdot 10^{-29} \lor \neg \left(z \leq 1.6 \cdot 10^{-57}\right):\\ \;\;\;\;z \cdot \cos y + \left(y + x\right)\\ \mathbf{else}:\\ \;\;\;\;x + \sin y\\ \end{array} \]

Alternative 6
Accuracy	65.1%
Cost	6992

\[\begin{array}{l} \mathbf{if}\;x \leq -1.4 \cdot 10^{-65}:\\ \;\;\;\;z + x\\ \mathbf{elif}\;x \leq 6.8 \cdot 10^{-288}:\\ \;\;\;\;\sin y\\ \mathbf{elif}\;x \leq 1.95 \cdot 10^{-222}:\\ \;\;\;\;z\\ \mathbf{elif}\;x \leq 4.7 \cdot 10^{-192}:\\ \;\;\;\;\sin y\\ \mathbf{else}:\\ \;\;\;\;z + x\\ \end{array} \]

Alternative 7
Accuracy	55.0%
Cost	592

\[\begin{array}{l} \mathbf{if}\;x \leq -8:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 105:\\ \;\;\;\;z\\ \mathbf{elif}\;x \leq 9.8 \cdot 10^{+28}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 9.2 \cdot 10^{+55}:\\ \;\;\;\;z\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 8
Accuracy	70.4%
Cost	584

\[\begin{array}{l} \mathbf{if}\;y \leq -3.5 \cdot 10^{+69}:\\ \;\;\;\;z + x\\ \mathbf{elif}\;y \leq 1.25 \cdot 10^{-6}:\\ \;\;\;\;x + \left(z + y\right)\\ \mathbf{else}:\\ \;\;\;\;z + x\\ \end{array} \]

Alternative 9
Accuracy	68.0%
Cost	456

\[\begin{array}{l} \mathbf{if}\;x \leq -4 \cdot 10^{-67}:\\ \;\;\;\;z + x\\ \mathbf{elif}\;x \leq 3.8 \cdot 10^{-164}:\\ \;\;\;\;z + y\\ \mathbf{else}:\\ \;\;\;\;z + x\\ \end{array} \]

Alternative 10
Accuracy	44.5%
Cost	328

\[\begin{array}{l} \mathbf{if}\;x \leq -4.8 \cdot 10^{-53}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 2.6 \cdot 10^{-145}:\\ \;\;\;\;y\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 11
Accuracy	66.6%
Cost	192

\[z + x \]

Alternative 12
Accuracy	42.8%
Cost	64

\[x \]

Reproduce

herbie shell --seed 2023147 
(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))))