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

Percentage Accurate: 99.8% → 99.8%

Time: 8.4s

Alternatives: 10

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

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

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1. Add Preprocessing

Alternative 2: 85.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.45 \cdot 10^{-26} \lor \neg \left(x \leq 8.2 \cdot 10^{+91}\right):\\ \;\;\;\;x \cdot \cos y\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\sin y, -z, x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -1.45e-26) (not (<= x 8.2e+91)))
   (* x (cos y))
   (fma (sin y) (- z) x)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -1.45e-26) || !(x <= 8.2e+91)) {
		tmp = x * cos(y);
	} else {
		tmp = fma(sin(y), -z, x);
	}
	return tmp;
}

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -1.45e-26) || !(x <= 8.2e+91))
		tmp = Float64(x * cos(y));
	else
		tmp = fma(sin(y), Float64(-z), x);
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -1.45e-26], N[Not[LessEqual[x, 8.2e+91]], $MachinePrecision]], N[(x * N[Cos[y], $MachinePrecision]), $MachinePrecision], N[(N[Sin[y], $MachinePrecision] * (-z) + x), $MachinePrecision]]

Derivation

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1. Add Preprocessing

Alternative 3: 99.8% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

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1. Add Preprocessing

Alternative 4: 74.2% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x \cdot \cos y\\ t_1 := z \cdot \left(-\sin y\right)\\ \mathbf{if}\;y \leq -1.7 \cdot 10^{+205}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y \leq -6.7 \cdot 10^{+97}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -16500:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y \leq 2.35 \cdot 10^{-8}:\\ \;\;\;\;x - y \cdot z\\ \mathbf{elif}\;y \leq 1.7 \cdot 10^{+170}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* x (cos y))) (t_1 (* z (- (sin y)))))
   (if (<= y -1.7e+205)
     t_0
     (if (<= y -6.7e+97)
       t_1
       (if (<= y -16500.0)
         t_0
         (if (<= y 2.35e-8) (- x (* y z)) (if (<= y 1.7e+170) t_1 t_0)))))))

C

double code(double x, double y, double z) {
	double t_0 = x * cos(y);
	double t_1 = z * -sin(y);
	double tmp;
	if (y <= -1.7e+205) {
		tmp = t_0;
	} else if (y <= -6.7e+97) {
		tmp = t_1;
	} else if (y <= -16500.0) {
		tmp = t_0;
	} else if (y <= 2.35e-8) {
		tmp = x - (y * z);
	} else if (y <= 1.7e+170) {
		tmp = t_1;
	} 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 * cos(y)
    t_1 = z * -sin(y)
    if (y <= (-1.7d+205)) then
        tmp = t_0
    else if (y <= (-6.7d+97)) then
        tmp = t_1
    else if (y <= (-16500.0d0)) then
        tmp = t_0
    else if (y <= 2.35d-8) then
        tmp = x - (y * z)
    else if (y <= 1.7d+170) then
        tmp = t_1
    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.cos(y);
	double t_1 = z * -Math.sin(y);
	double tmp;
	if (y <= -1.7e+205) {
		tmp = t_0;
	} else if (y <= -6.7e+97) {
		tmp = t_1;
	} else if (y <= -16500.0) {
		tmp = t_0;
	} else if (y <= 2.35e-8) {
		tmp = x - (y * z);
	} else if (y <= 1.7e+170) {
		tmp = t_1;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = x * math.cos(y)
	t_1 = z * -math.sin(y)
	tmp = 0
	if y <= -1.7e+205:
		tmp = t_0
	elif y <= -6.7e+97:
		tmp = t_1
	elif y <= -16500.0:
		tmp = t_0
	elif y <= 2.35e-8:
		tmp = x - (y * z)
	elif y <= 1.7e+170:
		tmp = t_1
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(x * cos(y))
	t_1 = Float64(z * Float64(-sin(y)))
	tmp = 0.0
	if (y <= -1.7e+205)
		tmp = t_0;
	elseif (y <= -6.7e+97)
		tmp = t_1;
	elseif (y <= -16500.0)
		tmp = t_0;
	elseif (y <= 2.35e-8)
		tmp = Float64(x - Float64(y * z));
	elseif (y <= 1.7e+170)
		tmp = t_1;
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = x * cos(y);
	t_1 = z * -sin(y);
	tmp = 0.0;
	if (y <= -1.7e+205)
		tmp = t_0;
	elseif (y <= -6.7e+97)
		tmp = t_1;
	elseif (y <= -16500.0)
		tmp = t_0;
	elseif (y <= 2.35e-8)
		tmp = x - (y * z);
	elseif (y <= 1.7e+170)
		tmp = t_1;
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(x * N[Cos[y], $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(z * (-N[Sin[y], $MachinePrecision])), $MachinePrecision]}, If[LessEqual[y, -1.7e+205], t$95$0, If[LessEqual[y, -6.7e+97], t$95$1, If[LessEqual[y, -16500.0], t$95$0, If[LessEqual[y, 2.35e-8], N[(x - N[(y * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.7e+170], t$95$1, t$95$0]]]]]]]

Derivation

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1. Add Preprocessing

Alternative 5: 74.2% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x \cdot \cos y\\ t_1 := z \cdot \left(-\sin y\right)\\ \mathbf{if}\;y \leq -4.1 \cdot 10^{+204}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y \leq -1.9 \cdot 10^{+98}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -16500:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y \leq 2.35 \cdot 10^{-8}:\\ \;\;\;\;\mathsf{fma}\left(y, -z, x\right)\\ \mathbf{elif}\;y \leq 1.25 \cdot 10^{+169}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* x (cos y))) (t_1 (* z (- (sin y)))))
   (if (<= y -4.1e+204)
     t_0
     (if (<= y -1.9e+98)
       t_1
       (if (<= y -16500.0)
         t_0
         (if (<= y 2.35e-8) (fma y (- z) x) (if (<= y 1.25e+169) t_1 t_0)))))))

C

double code(double x, double y, double z) {
	double t_0 = x * cos(y);
	double t_1 = z * -sin(y);
	double tmp;
	if (y <= -4.1e+204) {
		tmp = t_0;
	} else if (y <= -1.9e+98) {
		tmp = t_1;
	} else if (y <= -16500.0) {
		tmp = t_0;
	} else if (y <= 2.35e-8) {
		tmp = fma(y, -z, x);
	} else if (y <= 1.25e+169) {
		tmp = t_1;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Julia

function code(x, y, z)
	t_0 = Float64(x * cos(y))
	t_1 = Float64(z * Float64(-sin(y)))
	tmp = 0.0
	if (y <= -4.1e+204)
		tmp = t_0;
	elseif (y <= -1.9e+98)
		tmp = t_1;
	elseif (y <= -16500.0)
		tmp = t_0;
	elseif (y <= 2.35e-8)
		tmp = fma(y, Float64(-z), x);
	elseif (y <= 1.25e+169)
		tmp = t_1;
	else
		tmp = t_0;
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(x * N[Cos[y], $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(z * (-N[Sin[y], $MachinePrecision])), $MachinePrecision]}, If[LessEqual[y, -4.1e+204], t$95$0, If[LessEqual[y, -1.9e+98], t$95$1, If[LessEqual[y, -16500.0], t$95$0, If[LessEqual[y, 2.35e-8], N[(y * (-z) + x), $MachinePrecision], If[LessEqual[y, 1.25e+169], t$95$1, t$95$0]]]]]]]

Derivation

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1. Add Preprocessing

Alternative 6: 85.7% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.15 \cdot 10^{-26} \lor \neg \left(x \leq 4.6 \cdot 10^{+86}\right):\\ \;\;\;\;x \cdot \cos y\\ \mathbf{else}:\\ \;\;\;\;x - \sin y \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -1.15e-26) (not (<= x 4.6e+86)))
   (* x (cos y))
   (- x (* (sin y) z))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -1.15e-26) || !(x <= 4.6e+86)) {
		tmp = x * cos(y);
	} else {
		tmp = x - (sin(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 <= (-1.15d-26)) .or. (.not. (x <= 4.6d+86))) then
        tmp = x * cos(y)
    else
        tmp = x - (sin(y) * z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((x <= -1.15e-26) || !(x <= 4.6e+86)) {
		tmp = x * Math.cos(y);
	} else {
		tmp = x - (Math.sin(y) * z);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -1.15e-26) or not (x <= 4.6e+86):
		tmp = x * math.cos(y)
	else:
		tmp = x - (math.sin(y) * z)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -1.15e-26) || !(x <= 4.6e+86))
		tmp = Float64(x * cos(y));
	else
		tmp = Float64(x - Float64(sin(y) * z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((x <= -1.15e-26) || ~((x <= 4.6e+86)))
		tmp = x * cos(y);
	else
		tmp = x - (sin(y) * z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -1.15e-26], N[Not[LessEqual[x, 4.6e+86]], $MachinePrecision]], N[(x * N[Cos[y], $MachinePrecision]), $MachinePrecision], N[(x - N[(N[Sin[y], $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision]]

Derivation

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1. Add Preprocessing

Alternative 7: 74.7% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -16500 \lor \neg \left(y \leq 1.05\right):\\ \;\;\;\;x \cdot \cos y\\ \mathbf{else}:\\ \;\;\;\;x - y \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -16500.0) (not (<= y 1.05))) (* x (cos y)) (- x (* y z))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -16500.0) || !(y <= 1.05)) {
		tmp = x * cos(y);
	} 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 <= (-16500.0d0)) .or. (.not. (y <= 1.05d0))) then
        tmp = x * cos(y)
    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 <= -16500.0) || !(y <= 1.05)) {
		tmp = x * Math.cos(y);
	} else {
		tmp = x - (y * z);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -16500.0) or not (y <= 1.05):
		tmp = x * math.cos(y)
	else:
		tmp = x - (y * z)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -16500.0) || !(y <= 1.05))
		tmp = Float64(x * cos(y));
	else
		tmp = Float64(x - Float64(y * z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((y <= -16500.0) || ~((y <= 1.05)))
		tmp = x * cos(y);
	else
		tmp = x - (y * z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -16500.0], N[Not[LessEqual[y, 1.05]], $MachinePrecision]], N[(x * N[Cos[y], $MachinePrecision]), $MachinePrecision], N[(x - N[(y * z), $MachinePrecision]), $MachinePrecision]]

Derivation

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1. Add Preprocessing

Alternative 8: 42.2% accurate, 25.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -6.4 \cdot 10^{-137}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 5.2 \cdot 10^{-203}:\\ \;\;\;\;y \cdot \left(-z\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -6.4e-137) x (if (<= x 5.2e-203) (* y (- z)) x)))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -6.4e-137) {
		tmp = x;
	} else if (x <= 5.2e-203) {
		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 (x <= (-6.4d-137)) then
        tmp = x
    else if (x <= 5.2d-203) 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 (x <= -6.4e-137) {
		tmp = x;
	} else if (x <= 5.2e-203) {
		tmp = y * -z;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= -6.4e-137:
		tmp = x
	elif x <= 5.2e-203:
		tmp = y * -z
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -6.4e-137)
		tmp = x;
	elseif (x <= 5.2e-203)
		tmp = Float64(y * Float64(-z));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (x <= -6.4e-137)
		tmp = x;
	elseif (x <= 5.2e-203)
		tmp = y * -z;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -6.4e-137], x, If[LessEqual[x, 5.2e-203], N[(y * (-z)), $MachinePrecision], x]]

Derivation

&prev;&pcontext;&pcontext2;&ctx;
1. Add Preprocessing

Alternative 9: 52.4% 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

&prev;&pcontext;&pcontext2;&ctx;
1. Add Preprocessing

Alternative 10: 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

&prev;&pcontext;&pcontext2;&ctx;
1. Add Preprocessing

Reproduce

herbie shell --seed 2023348 
(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))))