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

Percentage Accurate: 99.8% → 99.8%

Time: 7.9s

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

1. Initial program 99.8%

   \[x \cdot \sin y + z \cdot \cos y \]
2. Step-by-step derivation

   1. fma-def 99.8%

      \[\leadsto \color{blue}{\mathsf{fma}\left(x, \sin y, z \cdot \cos y\right)} \]

3. Simplified 99.8%

   \[\leadsto \color{blue}{\mathsf{fma}\left(x, \sin y, z \cdot \cos y\right)} \]

4. Final simplification 99.8%

   \[\leadsto \mathsf{fma}\left(x, \sin y, z \cdot \cos y\right) \]

Alternative 2: 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

1. Initial program 99.8%

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

2. Final simplification 99.8%

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

Alternative 3: 73.1% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := z \cdot \cos y\\ \mathbf{if}\;z \leq -2.9 \cdot 10^{-44}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq -8.8 \cdot 10^{-86}:\\ \;\;\;\;z + x \cdot y\\ \mathbf{elif}\;z \leq -5.8 \cdot 10^{-133} \lor \neg \left(z \leq 1.45 \cdot 10^{-44}\right):\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;x \cdot \sin y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* z (cos y))))
   (if (<= z -2.9e-44)
     t_0
     (if (<= z -8.8e-86)
       (+ z (* x y))
       (if (or (<= z -5.8e-133) (not (<= z 1.45e-44))) t_0 (* x (sin y)))))))

C

double code(double x, double y, double z) {
	double t_0 = z * cos(y);
	double tmp;
	if (z <= -2.9e-44) {
		tmp = t_0;
	} else if (z <= -8.8e-86) {
		tmp = z + (x * y);
	} else if ((z <= -5.8e-133) || !(z <= 1.45e-44)) {
		tmp = t_0;
	} else {
		tmp = x * sin(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) :: t_0
    real(8) :: tmp
    t_0 = z * cos(y)
    if (z <= (-2.9d-44)) then
        tmp = t_0
    else if (z <= (-8.8d-86)) then
        tmp = z + (x * y)
    else if ((z <= (-5.8d-133)) .or. (.not. (z <= 1.45d-44))) then
        tmp = t_0
    else
        tmp = x * sin(y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = z * Math.cos(y);
	double tmp;
	if (z <= -2.9e-44) {
		tmp = t_0;
	} else if (z <= -8.8e-86) {
		tmp = z + (x * y);
	} else if ((z <= -5.8e-133) || !(z <= 1.45e-44)) {
		tmp = t_0;
	} else {
		tmp = x * Math.sin(y);
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = z * math.cos(y)
	tmp = 0
	if z <= -2.9e-44:
		tmp = t_0
	elif z <= -8.8e-86:
		tmp = z + (x * y)
	elif (z <= -5.8e-133) or not (z <= 1.45e-44):
		tmp = t_0
	else:
		tmp = x * math.sin(y)
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(z * cos(y))
	tmp = 0.0
	if (z <= -2.9e-44)
		tmp = t_0;
	elseif (z <= -8.8e-86)
		tmp = Float64(z + Float64(x * y));
	elseif ((z <= -5.8e-133) || !(z <= 1.45e-44))
		tmp = t_0;
	else
		tmp = Float64(x * sin(y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = z * cos(y);
	tmp = 0.0;
	if (z <= -2.9e-44)
		tmp = t_0;
	elseif (z <= -8.8e-86)
		tmp = z + (x * y);
	elseif ((z <= -5.8e-133) || ~((z <= 1.45e-44)))
		tmp = t_0;
	else
		tmp = x * sin(y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(z * N[Cos[y], $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -2.9e-44], t$95$0, If[LessEqual[z, -8.8e-86], N[(z + N[(x * y), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[z, -5.8e-133], N[Not[LessEqual[z, 1.45e-44]], $MachinePrecision]], t$95$0, N[(x * N[Sin[y], $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -2.9000000000000001e-44 or -8.8000000000000006e-86 < z < -5.7999999999999997e-133 or 1.4500000000000001e-44 < z

   1. Initial program 99.8%

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

   2. Taylor expanded in x around 0 85.3%

      \[\leadsto \color{blue}{z \cdot \cos y} \]

   if -2.9000000000000001e-44 < z < -8.8000000000000006e-86

   1. Initial program 99.7%

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

   2. Taylor expanded in y around 0 85.1%

      \[\leadsto \color{blue}{z + x \cdot y} \]
   3. Step-by-step derivation

      1. +-commutative 85.1%

         \[\leadsto \color{blue}{x \cdot y + z} \]

   4. Simplified 85.1%

      \[\leadsto \color{blue}{x \cdot y + z} \]

   if -5.7999999999999997e-133 < z < 1.4500000000000001e-44

   1. Initial program 99.8%

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

   2. Taylor expanded in x around inf 75.9%

      \[\leadsto \color{blue}{x \cdot \sin y} \]
3. Recombined 3 regimes into one program.

4. Final simplification 82.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.9 \cdot 10^{-44}:\\ \;\;\;\;z \cdot \cos y\\ \mathbf{elif}\;z \leq -8.8 \cdot 10^{-86}:\\ \;\;\;\;z + x \cdot y\\ \mathbf{elif}\;z \leq -5.8 \cdot 10^{-133} \lor \neg \left(z \leq 1.45 \cdot 10^{-44}\right):\\ \;\;\;\;z \cdot \cos y\\ \mathbf{else}:\\ \;\;\;\;x \cdot \sin y\\ \end{array} \]

Alternative 4: 73.2% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := z \cdot \cos y\\ \mathbf{if}\;z \leq -2.9 \cdot 10^{-44}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq -1.4 \cdot 10^{-83}:\\ \;\;\;\;\mathsf{fma}\left(x, y, z\right)\\ \mathbf{elif}\;z \leq -3.8 \cdot 10^{-129} \lor \neg \left(z \leq 9.6 \cdot 10^{-39}\right):\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;x \cdot \sin y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* z (cos y))))
   (if (<= z -2.9e-44)
     t_0
     (if (<= z -1.4e-83)
       (fma x y z)
       (if (or (<= z -3.8e-129) (not (<= z 9.6e-39))) t_0 (* x (sin y)))))))

C

double code(double x, double y, double z) {
	double t_0 = z * cos(y);
	double tmp;
	if (z <= -2.9e-44) {
		tmp = t_0;
	} else if (z <= -1.4e-83) {
		tmp = fma(x, y, z);
	} else if ((z <= -3.8e-129) || !(z <= 9.6e-39)) {
		tmp = t_0;
	} else {
		tmp = x * sin(y);
	}
	return tmp;
}

Julia

function code(x, y, z)
	t_0 = Float64(z * cos(y))
	tmp = 0.0
	if (z <= -2.9e-44)
		tmp = t_0;
	elseif (z <= -1.4e-83)
		tmp = fma(x, y, z);
	elseif ((z <= -3.8e-129) || !(z <= 9.6e-39))
		tmp = t_0;
	else
		tmp = Float64(x * sin(y));
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(z * N[Cos[y], $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -2.9e-44], t$95$0, If[LessEqual[z, -1.4e-83], N[(x * y + z), $MachinePrecision], If[Or[LessEqual[z, -3.8e-129], N[Not[LessEqual[z, 9.6e-39]], $MachinePrecision]], t$95$0, N[(x * N[Sin[y], $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -2.9000000000000001e-44 or -1.4e-83 < z < -3.79999999999999985e-129 or 9.60000000000000063e-39 < z

   1. Initial program 99.8%

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

   2. Taylor expanded in x around 0 85.3%

      \[\leadsto \color{blue}{z \cdot \cos y} \]

   if -2.9000000000000001e-44 < z < -1.4e-83

   1. Initial program 99.7%

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

   2. Taylor expanded in y around 0 85.1%

      \[\leadsto \color{blue}{z + x \cdot y} \]
   3. Step-by-step derivation

      1. +-commutative 85.1%

         \[\leadsto \color{blue}{x \cdot y + z} \]

      2. fma-def 85.2%

         \[\leadsto \color{blue}{\mathsf{fma}\left(x, y, z\right)} \]

   4. Simplified 85.2%

      \[\leadsto \color{blue}{\mathsf{fma}\left(x, y, z\right)} \]

   if -3.79999999999999985e-129 < z < 9.60000000000000063e-39

   1. Initial program 99.8%

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

   2. Taylor expanded in x around inf 75.9%

      \[\leadsto \color{blue}{x \cdot \sin y} \]
3. Recombined 3 regimes into one program.

4. Final simplification 82.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.9 \cdot 10^{-44}:\\ \;\;\;\;z \cdot \cos y\\ \mathbf{elif}\;z \leq -1.4 \cdot 10^{-83}:\\ \;\;\;\;\mathsf{fma}\left(x, y, z\right)\\ \mathbf{elif}\;z \leq -3.8 \cdot 10^{-129} \lor \neg \left(z \leq 9.6 \cdot 10^{-39}\right):\\ \;\;\;\;z \cdot \cos y\\ \mathbf{else}:\\ \;\;\;\;x \cdot \sin y\\ \end{array} \]

Alternative 5: 86.2% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -7.3 \cdot 10^{-59} \lor \neg \left(x \leq 1.6 \cdot 10^{-98}\right):\\ \;\;\;\;z + x \cdot \sin y\\ \mathbf{else}:\\ \;\;\;\;z \cdot \cos y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -7.3e-59) (not (<= x 1.6e-98)))
   (+ z (* x (sin y)))
   (* z (cos y))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -7.3e-59) || !(x <= 1.6e-98)) {
		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 <= (-7.3d-59)) .or. (.not. (x <= 1.6d-98))) 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 <= -7.3e-59) || !(x <= 1.6e-98)) {
		tmp = z + (x * Math.sin(y));
	} else {
		tmp = z * Math.cos(y);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -7.3e-59) or not (x <= 1.6e-98):
		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 <= -7.3e-59) || !(x <= 1.6e-98))
		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 <= -7.3e-59) || ~((x <= 1.6e-98)))
		tmp = z + (x * sin(y));
	else
		tmp = z * cos(y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -7.3e-59], N[Not[LessEqual[x, 1.6e-98]], $MachinePrecision]], N[(z + N[(x * N[Sin[y], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(z * N[Cos[y], $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -7.3000000000000004e-59 or 1.6e-98 < x

   1. Initial program 99.8%

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

   2. Taylor expanded in y around 0 85.3%

      \[\leadsto x \cdot \sin y + \color{blue}{z} \]

   if -7.3000000000000004e-59 < x < 1.6e-98

   1. Initial program 99.9%

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

   2. Taylor expanded in x around 0 92.9%

      \[\leadsto \color{blue}{z \cdot \cos y} \]
3. Recombined 2 regimes into one program.

4. Final simplification 88.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -7.3 \cdot 10^{-59} \lor \neg \left(x \leq 1.6 \cdot 10^{-98}\right):\\ \;\;\;\;z + x \cdot \sin y\\ \mathbf{else}:\\ \;\;\;\;z \cdot \cos y\\ \end{array} \]

Alternative 6: 75.0% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -0.00146 \lor \neg \left(y \leq 0.053\right):\\ \;\;\;\;x \cdot \sin y\\ \mathbf{else}:\\ \;\;\;\;z + x \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -0.00146) (not (<= y 0.053))) (* x (sin y)) (+ z (* x y))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -0.00146) || !(y <= 0.053)) {
		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 <= (-0.00146d0)) .or. (.not. (y <= 0.053d0))) 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 <= -0.00146) || !(y <= 0.053)) {
		tmp = x * Math.sin(y);
	} else {
		tmp = z + (x * y);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -0.00146) or not (y <= 0.053):
		tmp = x * math.sin(y)
	else:
		tmp = z + (x * y)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -0.00146) || !(y <= 0.053))
		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 <= -0.00146) || ~((y <= 0.053)))
		tmp = x * sin(y);
	else
		tmp = z + (x * y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -0.00146], N[Not[LessEqual[y, 0.053]], $MachinePrecision]], N[(x * N[Sin[y], $MachinePrecision]), $MachinePrecision], N[(z + N[(x * y), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -0.0014599999999999999 or 0.0529999999999999985 < y

   1. Initial program 99.7%

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

   2. Taylor expanded in x around inf 44.8%

      \[\leadsto \color{blue}{x \cdot \sin y} \]

   if -0.0014599999999999999 < y < 0.0529999999999999985

   1. Initial program 100.0%

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

   2. Taylor expanded in y around 0 98.2%

      \[\leadsto \color{blue}{z + x \cdot y} \]
   3. Step-by-step derivation

      1. +-commutative 98.2%

         \[\leadsto \color{blue}{x \cdot y + z} \]

   4. Simplified 98.2%

      \[\leadsto \color{blue}{x \cdot y + z} \]
3. Recombined 2 regimes into one program.

4. Final simplification 71.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -0.00146 \lor \neg \left(y \leq 0.053\right):\\ \;\;\;\;x \cdot \sin y\\ \mathbf{else}:\\ \;\;\;\;z + x \cdot y\\ \end{array} \]

Alternative 7: 39.7% accurate, 40.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.6 \cdot 10^{+51}:\\ \;\;\;\;x \cdot y\\ \mathbf{else}:\\ \;\;\;\;z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 (if (<= x -1.6e+51) (* x y) z))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -1.6e+51) {
		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 (x <= (-1.6d+51)) 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 (x <= -1.6e+51) {
		tmp = x * y;
	} else {
		tmp = z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= -1.6e+51:
		tmp = x * y
	else:
		tmp = z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -1.6e+51)
		tmp = Float64(x * y);
	else
		tmp = z;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (x <= -1.6e+51)
		tmp = x * y;
	else
		tmp = z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -1.6e+51], N[(x * y), $MachinePrecision], z]

Derivation

1. Split input into 2 regimes

2. if x < -1.6000000000000001e51

   1. Initial program 99.8%

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

   2. Taylor expanded in x around inf 70.3%

      \[\leadsto \color{blue}{x \cdot \sin y} \]

   3. Taylor expanded in y around 0 36.9%

      \[\leadsto \color{blue}{x \cdot y} \]

   if -1.6000000000000001e51 < x

   1. Initial program 99.8%

      \[x \cdot \sin y + z \cdot \cos y \]
   2. Step-by-step derivation

      1. *-commutative 99.8%

         \[\leadsto \color{blue}{\sin y \cdot x} + z \cdot \cos y \]

      2. add-sqr-sqrt 62.4%

         \[\leadsto \sin y \cdot \color{blue}{\left(\sqrt{x} \cdot \sqrt{x}\right)} + z \cdot \cos y \]

      3. associate-*r* 62.4%

         \[\leadsto \color{blue}{\left(\sin y \cdot \sqrt{x}\right) \cdot \sqrt{x}} + z \cdot \cos y \]

      4. fma-def 62.4%

         \[\leadsto \color{blue}{\mathsf{fma}\left(\sin y \cdot \sqrt{x}, \sqrt{x}, z \cdot \cos y\right)} \]

   3. Applied egg-rr 62.4%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\sin y \cdot \sqrt{x}, \sqrt{x}, z \cdot \cos y\right)} \]

   4. Taylor expanded in y around 0 46.6%

      \[\leadsto \mathsf{fma}\left(\sin y \cdot \sqrt{x}, \sqrt{x}, \color{blue}{z}\right) \]

   5. Taylor expanded in y around 0 42.9%

      \[\leadsto \color{blue}{z} \]
3. Recombined 2 regimes into one program.

4. Final simplification 41.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.6 \cdot 10^{+51}:\\ \;\;\;\;x \cdot y\\ \mathbf{else}:\\ \;\;\;\;z\\ \end{array} \]

Alternative 8: 52.5% 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

1. Initial program 99.8%

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

2. Taylor expanded in y around 0 51.4%

   \[\leadsto \color{blue}{z + x \cdot y} \]
3. Step-by-step derivation

   1. +-commutative 51.4%

      \[\leadsto \color{blue}{x \cdot y + z} \]

4. Simplified 51.4%

   \[\leadsto \color{blue}{x \cdot y + z} \]

5. Final simplification 51.4%

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

Alternative 9: 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

1. Initial program 99.8%

   \[x \cdot \sin y + z \cdot \cos y \]
2. Step-by-step derivation

   1. *-commutative 99.8%

      \[\leadsto \color{blue}{\sin y \cdot x} + z \cdot \cos y \]

   2. add-sqr-sqrt 51.0%

      \[\leadsto \sin y \cdot \color{blue}{\left(\sqrt{x} \cdot \sqrt{x}\right)} + z \cdot \cos y \]

   3. associate-*r* 51.0%

      \[\leadsto \color{blue}{\left(\sin y \cdot \sqrt{x}\right) \cdot \sqrt{x}} + z \cdot \cos y \]

   4. fma-def 51.0%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\sin y \cdot \sqrt{x}, \sqrt{x}, z \cdot \cos y\right)} \]

3. Applied egg-rr 51.0%

   \[\leadsto \color{blue}{\mathsf{fma}\left(\sin y \cdot \sqrt{x}, \sqrt{x}, z \cdot \cos y\right)} \]

4. Taylor expanded in y around 0 38.0%

   \[\leadsto \mathsf{fma}\left(\sin y \cdot \sqrt{x}, \sqrt{x}, \color{blue}{z}\right) \]

5. Taylor expanded in y around 0 38.2%

   \[\leadsto \color{blue}{z} \]

6. Final simplification 38.2%

   \[\leadsto z \]

Reproduce

herbie shell --seed 2023290 
(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))))