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

Percentage Accurate: 99.8% → 99.8%

Time: 7.1s

Alternatives: 9

Speedup: 1.0×

Specification

Math

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

FPCore

(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));
}

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

Java

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))

Julia

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

Wolfram

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

Initial Program: 99.8% accurate, 1.0× speedup

Math

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

FPCore

(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));
}

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

Java

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))

Julia

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

Wolfram

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

Alternative 1: 99.8% accurate, 0.7× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

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1. Add Preprocessing

Alternative 2: 85.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -5.9 \cdot 10^{-31} \lor \neg \left(x \leq 3 \cdot 10^{-75}\right):\\ \;\;\;\;\mathsf{fma}\left(x, \sin y, z\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \cos y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -5.9e-31) (not (<= x 3e-75))) (fma x (sin y) z) (* z (cos y))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -5.9e-31) || !(x <= 3e-75)) {
		tmp = fma(x, sin(y), z);
	} else {
		tmp = z * cos(y);
	}
	return tmp;
}

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -5.9e-31) || !(x <= 3e-75))
		tmp = fma(x, sin(y), z);
	else
		tmp = Float64(z * cos(y));
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -5.9e-31], N[Not[LessEqual[x, 3e-75]], $MachinePrecision]], N[(x * N[Sin[y], $MachinePrecision] + z), $MachinePrecision], N[(z * N[Cos[y], $MachinePrecision]), $MachinePrecision]]

Derivation

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1. Add Preprocessing

Alternative 3: 99.8% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

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Alternative 4: 72.6% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x \cdot \sin y\\ t_1 := z \cdot \cos y\\ \mathbf{if}\;x \leq -8 \cdot 10^{+55}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;x \leq -3.4 \cdot 10^{+23}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq -0.0275:\\ \;\;\;\;t_0\\ \mathbf{elif}\;x \leq 8000000:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 10^{+137}:\\ \;\;\;\;z + x \cdot y\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* x (sin y))) (t_1 (* z (cos y))))
   (if (<= x -8e+55)
     t_0
     (if (<= x -3.4e+23)
       t_1
       (if (<= x -0.0275)
         t_0
         (if (<= x 8000000.0) t_1 (if (<= x 1e+137) (+ z (* x y)) t_0)))))))

C

double code(double x, double y, double z) {
	double t_0 = x * sin(y);
	double t_1 = z * cos(y);
	double tmp;
	if (x <= -8e+55) {
		tmp = t_0;
	} else if (x <= -3.4e+23) {
		tmp = t_1;
	} else if (x <= -0.0275) {
		tmp = t_0;
	} else if (x <= 8000000.0) {
		tmp = t_1;
	} else if (x <= 1e+137) {
		tmp = z + (x * y);
	} else {
		tmp = t_0;
	}
	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) :: t_0
    real(8) :: t_1
    real(8) :: tmp
    t_0 = x * sin(y)
    t_1 = z * cos(y)
    if (x <= (-8d+55)) then
        tmp = t_0
    else if (x <= (-3.4d+23)) then
        tmp = t_1
    else if (x <= (-0.0275d0)) then
        tmp = t_0
    else if (x <= 8000000.0d0) then
        tmp = t_1
    else if (x <= 1d+137) then
        tmp = z + (x * y)
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = x * Math.sin(y);
	double t_1 = z * Math.cos(y);
	double tmp;
	if (x <= -8e+55) {
		tmp = t_0;
	} else if (x <= -3.4e+23) {
		tmp = t_1;
	} else if (x <= -0.0275) {
		tmp = t_0;
	} else if (x <= 8000000.0) {
		tmp = t_1;
	} else if (x <= 1e+137) {
		tmp = z + (x * y);
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = x * math.sin(y)
	t_1 = z * math.cos(y)
	tmp = 0
	if x <= -8e+55:
		tmp = t_0
	elif x <= -3.4e+23:
		tmp = t_1
	elif x <= -0.0275:
		tmp = t_0
	elif x <= 8000000.0:
		tmp = t_1
	elif x <= 1e+137:
		tmp = z + (x * y)
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(x * sin(y))
	t_1 = Float64(z * cos(y))
	tmp = 0.0
	if (x <= -8e+55)
		tmp = t_0;
	elseif (x <= -3.4e+23)
		tmp = t_1;
	elseif (x <= -0.0275)
		tmp = t_0;
	elseif (x <= 8000000.0)
		tmp = t_1;
	elseif (x <= 1e+137)
		tmp = Float64(z + Float64(x * y));
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = x * sin(y);
	t_1 = z * cos(y);
	tmp = 0.0;
	if (x <= -8e+55)
		tmp = t_0;
	elseif (x <= -3.4e+23)
		tmp = t_1;
	elseif (x <= -0.0275)
		tmp = t_0;
	elseif (x <= 8000000.0)
		tmp = t_1;
	elseif (x <= 1e+137)
		tmp = z + (x * y);
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(x * N[Sin[y], $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(z * N[Cos[y], $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -8e+55], t$95$0, If[LessEqual[x, -3.4e+23], t$95$1, If[LessEqual[x, -0.0275], t$95$0, If[LessEqual[x, 8000000.0], t$95$1, If[LessEqual[x, 1e+137], N[(z + N[(x * y), $MachinePrecision]), $MachinePrecision], t$95$0]]]]]]]

Derivation

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1. Add Preprocessing

Alternative 5: 85.8% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -6.1 \cdot 10^{-32} \lor \neg \left(x \leq 3.3 \cdot 10^{-71}\right):\\ \;\;\;\;z + x \cdot \sin y\\ \mathbf{else}:\\ \;\;\;\;z \cdot \cos y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -6.1e-32) (not (<= x 3.3e-71)))
   (+ z (* x (sin y)))
   (* z (cos y))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -6.1e-32) || !(x <= 3.3e-71)) {
		tmp = z + (x * sin(y));
	} else {
		tmp = z * cos(y);
	}
	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 ((x <= (-6.1d-32)) .or. (.not. (x <= 3.3d-71))) then
        tmp = z + (x * sin(y))
    else
        tmp = z * cos(y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((x <= -6.1e-32) || !(x <= 3.3e-71)) {
		tmp = z + (x * Math.sin(y));
	} else {
		tmp = z * Math.cos(y);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -6.1e-32) or not (x <= 3.3e-71):
		tmp = z + (x * math.sin(y))
	else:
		tmp = z * math.cos(y)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -6.1e-32) || !(x <= 3.3e-71))
		tmp = Float64(z + Float64(x * sin(y)));
	else
		tmp = Float64(z * cos(y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((x <= -6.1e-32) || ~((x <= 3.3e-71)))
		tmp = z + (x * sin(y));
	else
		tmp = z * cos(y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -6.1e-32], N[Not[LessEqual[x, 3.3e-71]], $MachinePrecision]], N[(z + N[(x * N[Sin[y], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(z * N[Cos[y], $MachinePrecision]), $MachinePrecision]]

Derivation

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1. Add Preprocessing

Alternative 6: 74.3% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -0.4 \lor \neg \left(y \leq 3.3 \cdot 10^{-18}\right):\\ \;\;\;\;x \cdot \sin y\\ \mathbf{else}:\\ \;\;\;\;z + x \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -0.4) (not (<= y 3.3e-18))) (* x (sin y)) (+ z (* x y))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -0.4) || !(y <= 3.3e-18)) {
		tmp = x * sin(y);
	} else {
		tmp = z + (x * y);
	}
	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 <= (-0.4d0)) .or. (.not. (y <= 3.3d-18))) then
        tmp = x * sin(y)
    else
        tmp = z + (x * y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((y <= -0.4) || !(y <= 3.3e-18)) {
		tmp = x * Math.sin(y);
	} else {
		tmp = z + (x * y);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -0.4) or not (y <= 3.3e-18):
		tmp = x * math.sin(y)
	else:
		tmp = z + (x * y)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -0.4) || !(y <= 3.3e-18))
		tmp = Float64(x * sin(y));
	else
		tmp = Float64(z + Float64(x * y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((y <= -0.4) || ~((y <= 3.3e-18)))
		tmp = x * sin(y);
	else
		tmp = z + (x * y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -0.4], N[Not[LessEqual[y, 3.3e-18]], $MachinePrecision]], N[(x * N[Sin[y], $MachinePrecision]), $MachinePrecision], N[(z + N[(x * y), $MachinePrecision]), $MachinePrecision]]

Derivation

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1. Add Preprocessing

Alternative 7: 42.4% accurate, 29.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -7.5 \cdot 10^{-95}:\\ \;\;\;\;z\\ \mathbf{elif}\;z \leq 2.35 \cdot 10^{-70}:\\ \;\;\;\;x \cdot y\\ \mathbf{else}:\\ \;\;\;\;z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -7.5e-95) z (if (<= z 2.35e-70) (* x y) z)))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -7.5e-95) {
		tmp = z;
	} else if (z <= 2.35e-70) {
		tmp = x * y;
	} else {
		tmp = 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 (z <= (-7.5d-95)) then
        tmp = z
    else if (z <= 2.35d-70) then
        tmp = x * y
    else
        tmp = z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (z <= -7.5e-95) {
		tmp = z;
	} else if (z <= 2.35e-70) {
		tmp = x * y;
	} else {
		tmp = z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -7.5e-95:
		tmp = z
	elif z <= 2.35e-70:
		tmp = x * y
	else:
		tmp = z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -7.5e-95)
		tmp = z;
	elseif (z <= 2.35e-70)
		tmp = Float64(x * y);
	else
		tmp = z;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= -7.5e-95)
		tmp = z;
	elseif (z <= 2.35e-70)
		tmp = x * y;
	else
		tmp = z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -7.5e-95], z, If[LessEqual[z, 2.35e-70], N[(x * y), $MachinePrecision], z]]

Derivation

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1. Add Preprocessing

Alternative 8: 53.0% accurate, 41.4× speedup

Math

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

FPCore

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

C

double code(double x, double y, double z) {
	return z + (x * 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 = z + (x * y)
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

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1. Add Preprocessing

Alternative 9: 39.7% accurate, 207.0× speedup

Math

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

FPCore

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

C

double code(double x, double y, double z) {
	return 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 = z
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_] := z

Derivation

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1. Add Preprocessing

Reproduce

herbie shell --seed 2023343 
(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))))