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

Average Error: 0.0 → 0.0

Time: 7.2s

Precision: binary64

Cost: 13248

Math

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

↓

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

FPCore

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

↓

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

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 (sin(y) + (z * cos(y))) + x;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    code = (x + sin(y)) + (z * cos(y))
end function

↓

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    code = (sin(y) + (z * cos(y))) + x
end function

Java

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

↓

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

Python

def code(x, y, z):
	return (x + math.sin(y)) + (z * math.cos(y))

↓

def code(x, y, z):
	return (math.sin(y) + (z * math.cos(y))) + x

Julia

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

↓

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

MATLAB

function tmp = code(x, y, z)
	tmp = (x + sin(y)) + (z * cos(y));
end

↓

function tmp = code(x, y, z)
	tmp = (sin(y) + (z * cos(y))) + x;
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[(N[(N[Sin[y], $MachinePrecision] + N[(z * N[Cos[y], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + x), $MachinePrecision]

Derivation

1. Initial program 0.0

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

2. Simplified 0.0

   \[\leadsto \color{blue}{\mathsf{fma}\left(z, \cos y, x + \sin y\right)} \]
   Proof
   (fma.f64 z (cos.f64 y) (+.f64 x (sin.f64 y))): 0 points increase in error, 0 points decrease in error
   (Rewrite<= fma-def_binary64 (+.f64 (*.f64 z (cos.f64 y)) (+.f64 x (sin.f64 y)))): 1 points increase in error, 0 points decrease in error
   (Rewrite<= +-commutative_binary64 (+.f64 (+.f64 x (sin.f64 y)) (*.f64 z (cos.f64 y)))): 0 points increase in error, 0 points decrease in error

3. Applied egg-rr 0.0

   \[\leadsto \color{blue}{\left(z \cdot \cos y + \sin y\right) + x} \]

4. Final simplification 0.0

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

Alternatives

Alternative 1
Error	0.5
Cost	13256

\[\begin{array}{l} \mathbf{if}\;z \leq -5700000000000:\\ \;\;\;\;x + z \cdot \cos y\\ \mathbf{elif}\;z \leq 0.9:\\ \;\;\;\;x + \left(z + \sin y\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\cos y, z, x\right)\\ \end{array} \]

Alternative 2
Error	0.0
Cost	13248

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

Alternative 3
Error	18.3
Cost	7384

\[\begin{array}{l} t_0 := z \cdot \cos y\\ \mathbf{if}\;x \leq -2.7 \cdot 10^{-17}:\\ \;\;\;\;z + x\\ \mathbf{elif}\;x \leq -1.35 \cdot 10^{-174}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;x \leq -1.16 \cdot 10^{-233}:\\ \;\;\;\;\sin y\\ \mathbf{elif}\;x \leq 6 \cdot 10^{-124}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;x \leq 1.8 \cdot 10^{-50}:\\ \;\;\;\;\sin y\\ \mathbf{elif}\;x \leq 8.4 \cdot 10^{-20}:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;z + x\\ \end{array} \]

Alternative 4
Error	14.5
Cost	7120

\[\begin{array}{l} t_0 := z \cdot \cos y\\ \mathbf{if}\;x \leq -2.1 \cdot 10^{-15}:\\ \;\;\;\;z + x\\ \mathbf{elif}\;x \leq -3.5 \cdot 10^{-170}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;x \leq 2.45 \cdot 10^{-49}:\\ \;\;\;\;z + \sin y\\ \mathbf{elif}\;x \leq 1.2 \cdot 10^{-19}:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;z + x\\ \end{array} \]

Alternative 5
Error	9.8
Cost	7120

\[\begin{array}{l} t_0 := z \cdot \cos y\\ \mathbf{if}\;z \leq -6.5 \cdot 10^{+89}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq -1.9 \cdot 10^{-71}:\\ \;\;\;\;z + x\\ \mathbf{elif}\;z \leq 3.6 \cdot 10^{-24}:\\ \;\;\;\;\sin y + x\\ \mathbf{elif}\;z \leq 1.08 \cdot 10^{+202}:\\ \;\;\;\;z + x\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \]

Alternative 6
Error	3.1
Cost	6984

\[\begin{array}{l} t_0 := x + z \cdot \cos y\\ \mathbf{if}\;z \leq -1.9 \cdot 10^{-71}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq 1.3 \cdot 10^{-23}:\\ \;\;\;\;\sin y + x\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \]

Alternative 7
Error	0.5
Cost	6984

\[\begin{array}{l} t_0 := x + z \cdot \cos y\\ \mathbf{if}\;z \leq -5700000000000:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq 1.45:\\ \;\;\;\;z + \left(\sin y + x\right)\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \]

Alternative 8
Error	0.5
Cost	6984

\[\begin{array}{l} t_0 := x + z \cdot \cos y\\ \mathbf{if}\;z \leq -5700000000000:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq 1.75:\\ \;\;\;\;x + \left(z + \sin y\right)\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \]

Alternative 9
Error	18.9
Cost	6728

\[\begin{array}{l} \mathbf{if}\;y \leq -1.15 \cdot 10^{+21}:\\ \;\;\;\;z + x\\ \mathbf{elif}\;y \leq -7000:\\ \;\;\;\;\sin y\\ \mathbf{elif}\;y \leq 2.4 \cdot 10^{+25}:\\ \;\;\;\;z + \left(y + x\right)\\ \mathbf{else}:\\ \;\;\;\;z + x\\ \end{array} \]

Alternative 10
Error	18.8
Cost	584

\[\begin{array}{l} \mathbf{if}\;y \leq -5200000:\\ \;\;\;\;z + x\\ \mathbf{elif}\;y \leq 1.76 \cdot 10^{+25}:\\ \;\;\;\;z + \left(y + x\right)\\ \mathbf{else}:\\ \;\;\;\;z + x\\ \end{array} \]

Alternative 11
Error	28.1
Cost	328

\[\begin{array}{l} \mathbf{if}\;x \leq -2.4 \cdot 10^{-32}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 1400000000000:\\ \;\;\;\;z\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 12
Error	21.4
Cost	192

\[z + x \]

Alternative 13
Error	36.1
Cost	64

\[x \]

Reproduce

herbie shell --seed 2022329 
(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))))