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

Average Error: 0.1 → 0.1

Time: 8.3s

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	17.4
Cost	7648

\[\begin{array}{l} t_0 := x \cdot \cos y\\ t_1 := z \cdot \sin y\\ \mathbf{if}\;z \leq -2.2721934532230194 \cdot 10^{+217}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -2.784487020553269 \cdot 10^{+191}:\\ \;\;\;\;x + y \cdot z\\ \mathbf{elif}\;z \leq -3.0844967116570647 \cdot 10^{+97}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 1.3343980466546453 \cdot 10^{+111}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq 1.2367901634640969 \cdot 10^{+122}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 8.044793878156357 \cdot 10^{+126}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq 7.266274041986495 \cdot 10^{+147}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 1.0320190436123988 \cdot 10^{+189}:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 2
Error	16.8
Cost	6856

\[\begin{array}{l} t_0 := z \cdot \sin y\\ \mathbf{if}\;y \leq -901.760773367421:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y \leq 0.011147630301063862:\\ \;\;\;\;x + y \cdot z\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \]

Alternative 3
Error	37.9
Cost	456

\[\begin{array}{l} \mathbf{if}\;z \leq -3.0050395976929094 \cdot 10^{+221}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;z \leq 1.7624802837630254 \cdot 10^{+193}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y \cdot z\\ \end{array} \]

Alternative 4
Error	31.4
Cost	320

\[x + y \cdot z \]

Alternative 5
Error	39.5
Cost	64

\[x \]

Reproduce

herbie shell --seed 2022325 
(FPCore (x y z)
  :name "Diagrams.ThreeD.Transform:aboutY from diagrams-lib-1.3.0.3"
  :precision binary64
  (+ (* x (cos y)) (* z (sin y))))