Diagrams.ThreeD.Transform:aboutX from diagrams-lib-1.3.0.3, B

Average Error: 0.1 → 0.1

Time: 12.9s

Precision: binary64

Cost: 13248

Math

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

↓

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

FPCore

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

↓

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

Python

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

↓

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

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(x * sin(y)) + Float64(z * cos(y)))
end

MATLAB

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

↓

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

Derivation

1. Initial program 0.1

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

2. Final simplification 0.1

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

Alternatives

Alternative 1
Error	16.2
Cost	7252

\[\begin{array}{l} t_0 := \cos y \cdot z\\ t_1 := \sin y \cdot x\\ \mathbf{if}\;y \leq -3.5 \cdot 10^{+189}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y \leq -5.8 \cdot 10^{+79}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -0.000225:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y \leq 0.007:\\ \;\;\;\;y \cdot x + z\\ \mathbf{elif}\;y \leq 5.4 \cdot 10^{+190}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \]

Alternative 2
Error	9.6
Cost	7236

\[\begin{array}{l} \mathbf{if}\;x \leq -2.9 \cdot 10^{-91}:\\ \;\;\;\;0.5 \cdot \left(z + \left(z + \sin y \cdot \left(x \cdot 2\right)\right)\right)\\ \mathbf{elif}\;x \leq 6 \cdot 10^{+61}:\\ \;\;\;\;\cos y \cdot z\\ \mathbf{else}:\\ \;\;\;\;x \cdot \sin y + z\\ \end{array} \]

Alternative 3
Error	9.6
Cost	6984

\[\begin{array}{l} t_0 := x \cdot \sin y + z\\ \mathbf{if}\;x \leq -5.4 \cdot 10^{-93}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;x \leq 5.1 \cdot 10^{+61}:\\ \;\;\;\;\cos y \cdot z\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \]

Alternative 4
Error	17.1
Cost	6856

\[\begin{array}{l} t_0 := \cos y \cdot z\\ \mathbf{if}\;y \leq -0.00029:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y \leq 6.2 \cdot 10^{-14}:\\ \;\;\;\;y \cdot x + z\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \]

Alternative 5
Error	37.9
Cost	456

\[\begin{array}{l} \mathbf{if}\;z \leq -1.5 \cdot 10^{-186}:\\ \;\;\;\;z\\ \mathbf{elif}\;z \leq 1.22 \cdot 10^{-162}:\\ \;\;\;\;y \cdot x\\ \mathbf{else}:\\ \;\;\;\;z\\ \end{array} \]

Alternative 6
Error	31.2
Cost	320

\[y \cdot x + z \]

Alternative 7
Error	39.7
Cost	64

\[z \]

Reproduce

herbie shell --seed 2023075 
(FPCore (x y z)
  :name "Diagrams.ThreeD.Transform:aboutX from diagrams-lib-1.3.0.3, B"
  :precision binary64
  (+ (* x (sin y)) (* z (cos y))))