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

Average Accuracy: 99.8% → 99.8%

Time: 15.6s

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 99.8%

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

2. Final simplification 99.8%

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

Alternatives

Alternative 1
Accuracy	72.5%
Cost	7384

\[\begin{array}{l} t_0 := z \cdot \sin y\\ t_1 := x \cdot \cos y\\ t_2 := x + y \cdot z\\ \mathbf{if}\;x \leq -6.5 \cdot 10^{+43}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq -160000000:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq -850:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq -2.3 \cdot 10^{-99}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;x \leq -5.3 \cdot 10^{-129}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq 2.65 \cdot 10^{-117}:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 2
Accuracy	72.4%
Cost	7384

\[\begin{array}{l} t_0 := z \cdot \sin y\\ t_1 := x \cdot \cos y\\ \mathbf{if}\;x \leq -5.2 \cdot 10^{+43}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq -1500000000:\\ \;\;\;\;\mathsf{fma}\left(z, y, x\right)\\ \mathbf{elif}\;x \leq -860:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq -4.6 \cdot 10^{-99}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;x \leq -1.6 \cdot 10^{-124}:\\ \;\;\;\;\mathsf{fma}\left(z, y, x\right)\\ \mathbf{elif}\;x \leq 6.5 \cdot 10^{-113}:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 3
Accuracy	75.1%
Cost	6857

\[\begin{array}{l} \mathbf{if}\;y \leq -40 \lor \neg \left(y \leq 0.0039\right):\\ \;\;\;\;z \cdot \sin y\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot z\\ \end{array} \]

Alternative 4
Accuracy	41.5%
Cost	324

\[\begin{array}{l} \mathbf{if}\;z \leq 3.2 \cdot 10^{+125}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y \cdot z\\ \end{array} \]

Alternative 5
Accuracy	53.0%
Cost	320

\[x + y \cdot z \]

Alternative 6
Accuracy	39.9%
Cost	64

\[x \]

Reproduce

herbie shell --seed 2023136 
(FPCore (x y z)
  :name "Diagrams.ThreeD.Transform:aboutY from diagrams-lib-1.3.0.3"
  :precision binary64
  (+ (* x (cos y)) (* z (sin y))))