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

Average Error: 0.2% → 0.2%

Time: 7.7s

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 0.2

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

2. Final simplification 0.2

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

Alternatives

Alternative 1
Error	13.66%
Cost	6985

\[\begin{array}{l} \mathbf{if}\;x \leq -1.85 \cdot 10^{-16} \lor \neg \left(x \leq 3.4 \cdot 10^{-49}\right):\\ \;\;\;\;x \cdot \sin y + z\\ \mathbf{else}:\\ \;\;\;\;z \cdot \cos y\\ \end{array} \]

Alternative 2
Error	25.81%
Cost	6857

\[\begin{array}{l} \mathbf{if}\;y \leq -14 \lor \neg \left(y \leq 1.44 \cdot 10^{-8}\right):\\ \;\;\;\;z \cdot \cos y\\ \mathbf{else}:\\ \;\;\;\;z + x \cdot y\\ \end{array} \]

Alternative 3
Error	57.3%
Cost	456

\[\begin{array}{l} \mathbf{if}\;z \leq -1.22 \cdot 10^{-172}:\\ \;\;\;\;z\\ \mathbf{elif}\;z \leq 4.9 \cdot 10^{-205}:\\ \;\;\;\;x \cdot y\\ \mathbf{else}:\\ \;\;\;\;z\\ \end{array} \]

Alternative 4
Error	47.7%
Cost	320

\[z + x \cdot y \]

Alternative 5
Error	60.41%
Cost	64

\[z \]

Reproduce

herbie shell --seed 2023090 
(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))))