Diagrams.ThreeD.Transform:aboutY from diagrams-lib-1.3.0.3

Average Error: 0.1 → 0.1

Time: 10.4s

Precision: binary64

Cost: 13248

Math

\[x \cdot \cos y + z \cdot \sin y \]

↓

\[z \cdot \sin y + x \cdot \cos y \]

FPCore

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

↓

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

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 * cos(y)) + (z * sin(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 = (z * sin(y)) + (x * cos(y))
end function

Java

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

↓

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

Python

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

↓

def code(x, y, z):
	return (z * math.sin(y)) + (x * math.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 Float64(Float64(z * sin(y)) + Float64(x * cos(y)))
end

MATLAB

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

↓

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

Derivation

1. Initial program 0.1

   \[x \cdot \cos y + z \cdot \sin y \]

2. Final simplification 0.1

   \[\leadsto z \cdot \sin y + x \cdot \cos y \]

Alternatives

Alternative 1
Error	15.8
Cost	6988

\[\begin{array}{l} t_0 := z \cdot \sin y\\ \mathbf{if}\;y \leq -9.378164219909968 \cdot 10^{-6}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y \leq 5.25574909823934 \cdot 10^{-10}:\\ \;\;\;\;\mathsf{fma}\left(z, y, x\right)\\ \mathbf{elif}\;y \leq 1.1144058313615295 \cdot 10^{+223}:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;x \cdot \cos y\\ \end{array} \]

Alternative 2
Error	9.1
Cost	6984

\[\begin{array}{l} t_0 := x \cdot \cos y\\ \mathbf{if}\;x \leq -1.010597192887955 \cdot 10^{+130}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;x \leq 2.0354426856870493 \cdot 10^{+124}:\\ \;\;\;\;x + z \cdot \sin y\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \]

Alternative 3
Error	16.5
Cost	6856

\[\begin{array}{l} t_0 := x \cdot \cos y\\ \mathbf{if}\;y \leq -641368656.6932448:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y \leq 2.9304107160500146 \cdot 10^{-10}:\\ \;\;\;\;x + y \cdot z\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \]

Alternative 4
Error	16.5
Cost	6856

\[\begin{array}{l} t_0 := x \cdot \cos y\\ \mathbf{if}\;y \leq -641368656.6932448:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y \leq 2.9304107160500146 \cdot 10^{-10}:\\ \;\;\;\;\mathsf{fma}\left(z, y, x\right)\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \]

Alternative 5
Error	37.2
Cost	456

\[\begin{array}{l} \mathbf{if}\;x \leq -2.1313940557463502 \cdot 10^{-66}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 6.972927347465469 \cdot 10^{-177}:\\ \;\;\;\;y \cdot z\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 6
Error	30.3
Cost	320

\[x + y \cdot z \]

Alternative 7
Error	38.8
Cost	64

\[x \]

Reproduce

herbie shell --seed 2022294 
(FPCore (x y z)
  :name "Diagrams.ThreeD.Transform:aboutY from diagrams-lib-1.3.0.3"
  :precision binary64
  (+ (* x (cos y)) (* z (sin y))))