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

Percentage Accurate: 99.8% → 99.8%

Time: 6.7s

Alternatives: 10

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

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

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1. Add Preprocessing

Alternative 2: 99.8% accurate, 0.7× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

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1. Add Preprocessing

Alternative 3: 99.8% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

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1. Add Preprocessing

Alternative 4: 74.8% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \cos y \cdot z\\ t_1 := x \cdot \sin y\\ \mathbf{if}\;y \leq -2.8 \cdot 10^{+176}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y \leq -3 \cdot 10^{+106}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -6.2 \cdot 10^{-5}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y \leq 4.2 \cdot 10^{-6}:\\ \;\;\;\;z + y \cdot x\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* (cos y) z)) (t_1 (* x (sin y))))
   (if (<= y -2.8e+176)
     t_0
     (if (<= y -3e+106)
       t_1
       (if (<= y -6.2e-5) t_0 (if (<= y 4.2e-6) (+ z (* y x)) t_1))))))

C

double code(double x, double y, double z) {
	double t_0 = cos(y) * z;
	double t_1 = x * sin(y);
	double tmp;
	if (y <= -2.8e+176) {
		tmp = t_0;
	} else if (y <= -3e+106) {
		tmp = t_1;
	} else if (y <= -6.2e-5) {
		tmp = t_0;
	} else if (y <= 4.2e-6) {
		tmp = z + (y * x);
	} else {
		tmp = t_1;
	}
	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 = cos(y) * z
    t_1 = x * sin(y)
    if (y <= (-2.8d+176)) then
        tmp = t_0
    else if (y <= (-3d+106)) then
        tmp = t_1
    else if (y <= (-6.2d-5)) then
        tmp = t_0
    else if (y <= 4.2d-6) then
        tmp = z + (y * x)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = Math.cos(y) * z;
	double t_1 = x * Math.sin(y);
	double tmp;
	if (y <= -2.8e+176) {
		tmp = t_0;
	} else if (y <= -3e+106) {
		tmp = t_1;
	} else if (y <= -6.2e-5) {
		tmp = t_0;
	} else if (y <= 4.2e-6) {
		tmp = z + (y * x);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = math.cos(y) * z
	t_1 = x * math.sin(y)
	tmp = 0
	if y <= -2.8e+176:
		tmp = t_0
	elif y <= -3e+106:
		tmp = t_1
	elif y <= -6.2e-5:
		tmp = t_0
	elif y <= 4.2e-6:
		tmp = z + (y * x)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(cos(y) * z)
	t_1 = Float64(x * sin(y))
	tmp = 0.0
	if (y <= -2.8e+176)
		tmp = t_0;
	elseif (y <= -3e+106)
		tmp = t_1;
	elseif (y <= -6.2e-5)
		tmp = t_0;
	elseif (y <= 4.2e-6)
		tmp = Float64(z + Float64(y * x));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = cos(y) * z;
	t_1 = x * sin(y);
	tmp = 0.0;
	if (y <= -2.8e+176)
		tmp = t_0;
	elseif (y <= -3e+106)
		tmp = t_1;
	elseif (y <= -6.2e-5)
		tmp = t_0;
	elseif (y <= 4.2e-6)
		tmp = z + (y * x);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(N[Cos[y], $MachinePrecision] * z), $MachinePrecision]}, Block[{t$95$1 = N[(x * N[Sin[y], $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -2.8e+176], t$95$0, If[LessEqual[y, -3e+106], t$95$1, If[LessEqual[y, -6.2e-5], t$95$0, If[LessEqual[y, 4.2e-6], N[(z + N[(y * x), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]

Derivation

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1. Add Preprocessing

Alternative 5: 74.8% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \cos y \cdot z\\ t_1 := x \cdot \sin y\\ \mathbf{if}\;y \leq -6.6 \cdot 10^{+176}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y \leq -1.5 \cdot 10^{+106}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -9.8 \cdot 10^{-5}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y \leq 4.2 \cdot 10^{-6}:\\ \;\;\;\;\mathsf{fma}\left(y, x, z\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* (cos y) z)) (t_1 (* x (sin y))))
   (if (<= y -6.6e+176)
     t_0
     (if (<= y -1.5e+106)
       t_1
       (if (<= y -9.8e-5) t_0 (if (<= y 4.2e-6) (fma y x z) t_1))))))

C

double code(double x, double y, double z) {
	double t_0 = cos(y) * z;
	double t_1 = x * sin(y);
	double tmp;
	if (y <= -6.6e+176) {
		tmp = t_0;
	} else if (y <= -1.5e+106) {
		tmp = t_1;
	} else if (y <= -9.8e-5) {
		tmp = t_0;
	} else if (y <= 4.2e-6) {
		tmp = fma(y, x, z);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z)
	t_0 = Float64(cos(y) * z)
	t_1 = Float64(x * sin(y))
	tmp = 0.0
	if (y <= -6.6e+176)
		tmp = t_0;
	elseif (y <= -1.5e+106)
		tmp = t_1;
	elseif (y <= -9.8e-5)
		tmp = t_0;
	elseif (y <= 4.2e-6)
		tmp = fma(y, x, z);
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(N[Cos[y], $MachinePrecision] * z), $MachinePrecision]}, Block[{t$95$1 = N[(x * N[Sin[y], $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -6.6e+176], t$95$0, If[LessEqual[y, -1.5e+106], t$95$1, If[LessEqual[y, -9.8e-5], t$95$0, If[LessEqual[y, 4.2e-6], N[(y * x + z), $MachinePrecision], t$95$1]]]]]]

Derivation

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1. Add Preprocessing

Alternative 6: 85.7% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -2.5 \cdot 10^{-85} \lor \neg \left(x \leq 3.7 \cdot 10^{-139}\right):\\ \;\;\;\;z + x \cdot \sin y\\ \mathbf{else}:\\ \;\;\;\;\cos y \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -2.5e-85) (not (<= x 3.7e-139)))
   (+ z (* x (sin y)))
   (* (cos y) z)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -2.5e-85) || !(x <= 3.7e-139)) {
		tmp = z + (x * sin(y));
	} else {
		tmp = cos(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 ((x <= (-2.5d-85)) .or. (.not. (x <= 3.7d-139))) then
        tmp = z + (x * sin(y))
    else
        tmp = cos(y) * z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((x <= -2.5e-85) || !(x <= 3.7e-139)) {
		tmp = z + (x * Math.sin(y));
	} else {
		tmp = Math.cos(y) * z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -2.5e-85) or not (x <= 3.7e-139):
		tmp = z + (x * math.sin(y))
	else:
		tmp = math.cos(y) * z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -2.5e-85) || !(x <= 3.7e-139))
		tmp = Float64(z + Float64(x * sin(y)));
	else
		tmp = Float64(cos(y) * z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((x <= -2.5e-85) || ~((x <= 3.7e-139)))
		tmp = z + (x * sin(y));
	else
		tmp = cos(y) * z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -2.5e-85], N[Not[LessEqual[x, 3.7e-139]], $MachinePrecision]], N[(z + N[(x * N[Sin[y], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[Cos[y], $MachinePrecision] * z), $MachinePrecision]]

Derivation

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1. Add Preprocessing

Alternative 7: 74.4% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -650000000 \lor \neg \left(y \leq 4.2 \cdot 10^{-6}\right):\\ \;\;\;\;x \cdot \sin y\\ \mathbf{else}:\\ \;\;\;\;z + y \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -650000000.0) (not (<= y 4.2e-6))) (* x (sin y)) (+ z (* y x))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -650000000.0) || !(y <= 4.2e-6)) {
		tmp = x * sin(y);
	} else {
		tmp = z + (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 ((y <= (-650000000.0d0)) .or. (.not. (y <= 4.2d-6))) then
        tmp = x * sin(y)
    else
        tmp = z + (y * x)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((y <= -650000000.0) || !(y <= 4.2e-6)) {
		tmp = x * Math.sin(y);
	} else {
		tmp = z + (y * x);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -650000000.0) or not (y <= 4.2e-6):
		tmp = x * math.sin(y)
	else:
		tmp = z + (y * x)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -650000000.0) || !(y <= 4.2e-6))
		tmp = Float64(x * sin(y));
	else
		tmp = Float64(z + Float64(y * x));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((y <= -650000000.0) || ~((y <= 4.2e-6)))
		tmp = x * sin(y);
	else
		tmp = z + (y * x);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -650000000.0], N[Not[LessEqual[y, 4.2e-6]], $MachinePrecision]], N[(x * N[Sin[y], $MachinePrecision]), $MachinePrecision], N[(z + N[(y * x), $MachinePrecision]), $MachinePrecision]]

Derivation

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1. Add Preprocessing

Alternative 8: 42.2% accurate, 29.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -5.1 \cdot 10^{-165}:\\ \;\;\;\;z\\ \mathbf{elif}\;z \leq 1.46 \cdot 10^{-154}:\\ \;\;\;\;y \cdot x\\ \mathbf{else}:\\ \;\;\;\;z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -5.1e-165) z (if (<= z 1.46e-154) (* y x) z)))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -5.1e-165) {
		tmp = z;
	} else if (z <= 1.46e-154) {
		tmp = y * x;
	} 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 <= (-5.1d-165)) then
        tmp = z
    else if (z <= 1.46d-154) then
        tmp = y * x
    else
        tmp = z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (z <= -5.1e-165) {
		tmp = z;
	} else if (z <= 1.46e-154) {
		tmp = y * x;
	} else {
		tmp = z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -5.1e-165:
		tmp = z
	elif z <= 1.46e-154:
		tmp = y * x
	else:
		tmp = z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -5.1e-165)
		tmp = z;
	elseif (z <= 1.46e-154)
		tmp = Float64(y * x);
	else
		tmp = z;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= -5.1e-165)
		tmp = z;
	elseif (z <= 1.46e-154)
		tmp = y * x;
	else
		tmp = z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -5.1e-165], z, If[LessEqual[z, 1.46e-154], N[(y * x), $MachinePrecision], z]]

Derivation

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1. Add Preprocessing

Alternative 9: 52.8% accurate, 41.4× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

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1. Add Preprocessing

Alternative 10: 39.4% 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 2023364 
(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))))