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

Percentage Accurate: 99.8% → 99.8%

Time: 8.4s

Alternatives: 8

Speedup: 1.0×

Specification

Math

\[\begin{array}{l} \\ x \cdot \cos y - z \cdot \sin y \end{array} \]

FPCore

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

C

double code(double x, double y, double z) {
	return (x * cos(y)) - (z * sin(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

Java

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

Python

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

Julia

function code(x, y, z)
	return Float64(Float64(x * cos(y)) - Float64(z * sin(y)))
end

MATLAB

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

Wolfram

code[x_, y_, z_] := N[(N[(x * N[Cos[y], $MachinePrecision]), $MachinePrecision] - N[(z * N[Sin[y], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Initial Program: 99.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ x \cdot \cos y - z \cdot \sin y \end{array} \]

FPCore

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

C

double code(double x, double y, double z) {
	return (x * cos(y)) - (z * sin(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

Java

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

Python

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

Julia

function code(x, y, z)
	return Float64(Float64(x * cos(y)) - Float64(z * sin(y)))
end

MATLAB

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

Wolfram

code[x_, y_, z_] := N[(N[(x * N[Cos[y], $MachinePrecision]), $MachinePrecision] - N[(z * N[Sin[y], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Alternative 1: 99.8% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \mathsf{fma}\left(\cos y, x, z \cdot \left(-\sin y\right)\right) \end{array} \]

FPCore

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

C

double code(double x, double y, double z) {
	return fma(cos(y), x, (z * -sin(y)));
}

Julia

function code(x, y, z)
	return fma(cos(y), x, Float64(z * Float64(-sin(y))))
end

Wolfram

code[x_, y_, z_] := N[(N[Cos[y], $MachinePrecision] * x + N[(z * (-N[Sin[y], $MachinePrecision])), $MachinePrecision]), $MachinePrecision]

Derivation

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1. Add Preprocessing

Alternative 2: 99.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \cos y \cdot x - z \cdot \sin y \end{array} \]

FPCore

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

C

double code(double x, double y, double z) {
	return (cos(y) * x) - (z * sin(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 = (cos(y) * x) - (z * sin(y))
end function

Java

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

Python

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

Julia

function code(x, y, z)
	return Float64(Float64(cos(y) * x) - Float64(z * sin(y)))
end

MATLAB

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

Wolfram

code[x_, y_, z_] := N[(N[(N[Cos[y], $MachinePrecision] * x), $MachinePrecision] - N[(z * N[Sin[y], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

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Alternative 3: 85.7% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.7 \cdot 10^{-8} \lor \neg \left(z \leq 7 \cdot 10^{-87}\right):\\ \;\;\;\;x - z \cdot \sin y\\ \mathbf{else}:\\ \;\;\;\;\cos y \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -1.7e-8) (not (<= z 7e-87))) (- x (* z (sin y))) (* (cos y) x)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -1.7e-8) || !(z <= 7e-87)) {
		tmp = x - (z * sin(y));
	} else {
		tmp = cos(y) * x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if ((z <= (-1.7d-8)) .or. (.not. (z <= 7d-87))) then
        tmp = x - (z * sin(y))
    else
        tmp = cos(y) * x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((z <= -1.7e-8) || !(z <= 7e-87)) {
		tmp = x - (z * Math.sin(y));
	} else {
		tmp = Math.cos(y) * x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -1.7e-8) or not (z <= 7e-87):
		tmp = x - (z * math.sin(y))
	else:
		tmp = math.cos(y) * x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -1.7e-8) || !(z <= 7e-87))
		tmp = Float64(x - Float64(z * sin(y)));
	else
		tmp = Float64(cos(y) * x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((z <= -1.7e-8) || ~((z <= 7e-87)))
		tmp = x - (z * sin(y));
	else
		tmp = cos(y) * x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -1.7e-8], N[Not[LessEqual[z, 7e-87]], $MachinePrecision]], N[(x - N[(z * N[Sin[y], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[Cos[y], $MachinePrecision] * x), $MachinePrecision]]

Derivation

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1. Add Preprocessing

Alternative 4: 74.7% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.05 \cdot 10^{+70} \lor \neg \left(z \leq 2.2 \cdot 10^{+105}\right):\\ \;\;\;\;z \cdot \left(-\sin y\right)\\ \mathbf{else}:\\ \;\;\;\;\cos y \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -2.05e+70) (not (<= z 2.2e+105)))
   (* z (- (sin y)))
   (* (cos y) x)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -2.05e+70) || !(z <= 2.2e+105)) {
		tmp = z * -sin(y);
	} else {
		tmp = cos(y) * x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if ((z <= (-2.05d+70)) .or. (.not. (z <= 2.2d+105))) then
        tmp = z * -sin(y)
    else
        tmp = cos(y) * x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((z <= -2.05e+70) || !(z <= 2.2e+105)) {
		tmp = z * -Math.sin(y);
	} else {
		tmp = Math.cos(y) * x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -2.05e+70) or not (z <= 2.2e+105):
		tmp = z * -math.sin(y)
	else:
		tmp = math.cos(y) * x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -2.05e+70) || !(z <= 2.2e+105))
		tmp = Float64(z * Float64(-sin(y)));
	else
		tmp = Float64(cos(y) * x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((z <= -2.05e+70) || ~((z <= 2.2e+105)))
		tmp = z * -sin(y);
	else
		tmp = cos(y) * x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -2.05e+70], N[Not[LessEqual[z, 2.2e+105]], $MachinePrecision]], N[(z * (-N[Sin[y], $MachinePrecision])), $MachinePrecision], N[(N[Cos[y], $MachinePrecision] * x), $MachinePrecision]]

Derivation

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1. Add Preprocessing

Alternative 5: 75.0% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -0.00017 \lor \neg \left(y \leq 0.0005\right):\\ \;\;\;\;\cos y \cdot x\\ \mathbf{else}:\\ \;\;\;\;x - y \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -0.00017) (not (<= y 0.0005))) (* (cos y) x) (- x (* y z))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -0.00017) || !(y <= 0.0005)) {
		tmp = cos(y) * x;
	} else {
		tmp = x - (y * z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if ((y <= (-0.00017d0)) .or. (.not. (y <= 0.0005d0))) then
        tmp = cos(y) * x
    else
        tmp = x - (y * z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((y <= -0.00017) || !(y <= 0.0005)) {
		tmp = Math.cos(y) * x;
	} else {
		tmp = x - (y * z);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -0.00017) or not (y <= 0.0005):
		tmp = math.cos(y) * x
	else:
		tmp = x - (y * z)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -0.00017) || !(y <= 0.0005))
		tmp = Float64(cos(y) * x);
	else
		tmp = Float64(x - Float64(y * z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((y <= -0.00017) || ~((y <= 0.0005)))
		tmp = cos(y) * x;
	else
		tmp = x - (y * z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -0.00017], N[Not[LessEqual[y, 0.0005]], $MachinePrecision]], N[(N[Cos[y], $MachinePrecision] * x), $MachinePrecision], N[(x - N[(y * z), $MachinePrecision]), $MachinePrecision]]

Derivation

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1. Add Preprocessing

Alternative 6: 41.9% accurate, 25.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.35 \cdot 10^{+159} \lor \neg \left(z \leq 5.5 \cdot 10^{+156}\right):\\ \;\;\;\;y \cdot \left(-z\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -1.35e+159) (not (<= z 5.5e+156))) (* y (- z)) x))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -1.35e+159) || !(z <= 5.5e+156)) {
		tmp = y * -z;
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if ((z <= (-1.35d+159)) .or. (.not. (z <= 5.5d+156))) then
        tmp = y * -z
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((z <= -1.35e+159) || !(z <= 5.5e+156)) {
		tmp = y * -z;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -1.35e+159) or not (z <= 5.5e+156):
		tmp = y * -z
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -1.35e+159) || !(z <= 5.5e+156))
		tmp = Float64(y * Float64(-z));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((z <= -1.35e+159) || ~((z <= 5.5e+156)))
		tmp = y * -z;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -1.35e+159], N[Not[LessEqual[z, 5.5e+156]], $MachinePrecision]], N[(y * (-z)), $MachinePrecision], x]

Derivation

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1. Add Preprocessing

Alternative 7: 52.3% accurate, 41.4× speedup

Math

\[\begin{array}{l} \\ x - y \cdot z \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 (- x (* y z)))

C

double code(double x, double y, double z) {
	return x - (y * z);
}

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 - (y * z)
end function

Java

public static double code(double x, double y, double z) {
	return x - (y * z);
}

Python

def code(x, y, z):
	return x - (y * z)

Julia

function code(x, y, z)
	return Float64(x - Float64(y * z))
end

MATLAB

function tmp = code(x, y, z)
	tmp = x - (y * z);
end

Wolfram

code[x_, y_, z_] := N[(x - N[(y * z), $MachinePrecision]), $MachinePrecision]

Derivation

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Alternative 8: 39.4% accurate, 207.0× speedup

Math

\[\begin{array}{l} \\ x \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 x)

C

double code(double x, double y, double z) {
	return x;
}

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
end function

Java

public static double code(double x, double y, double z) {
	return x;
}

Python

def code(x, y, z):
	return x

Julia

function code(x, y, z)
	return x
end

MATLAB

function tmp = code(x, y, z)
	tmp = x;
end

Wolfram

code[x_, y_, z_] := x

Derivation

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1. Add Preprocessing

Reproduce

herbie shell --seed 2023347 
(FPCore (x y z)
  :name "Diagrams.ThreeD.Transform:aboutX from diagrams-lib-1.3.0.3, A"
  :precision binary64
  (- (* x (cos y)) (* z (sin y))))