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

Percentage Accurate: 99.8% → 99.8%

Time: 13.6s

Alternatives: 7

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-define 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. Add Preprocessing

5. Final simplification 99.8%

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

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. Add Preprocessing

3. Final simplification 99.8%

   \[\leadsto z \cdot \cos y + x \cdot \sin y \]
4. Add Preprocessing

Alternative 3: 75.2% accurate, 1.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := z \cdot \cos y\\ t_1 := x \cdot \sin y\\ \mathbf{if}\;y \leq -9.5 \cdot 10^{+202}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;y \leq -540:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 0.105:\\ \;\;\;\;z + y \cdot \left(x + y \cdot \left(z \cdot -0.5 + y \cdot \left(x \cdot -0.16666666666666666 + 0.041666666666666664 \cdot \left(y \cdot z\right)\right)\right)\right)\\ \mathbf{elif}\;y \leq 2.25 \cdot 10^{+236}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* z (cos y))) (t_1 (* x (sin y))))
   (if (<= y -9.5e+202)
     t_0
     (if (<= y -540.0)
       t_1
       (if (<= y 0.105)
         (+
          z
          (*
           y
           (+
            x
            (*
             y
             (+
              (* z -0.5)
              (*
               y
               (+
                (* x -0.16666666666666666)
                (* 0.041666666666666664 (* y z)))))))))
         (if (<= y 2.25e+236) t_1 t_0))))))

C

double code(double x, double y, double z) {
	double t_0 = z * cos(y);
	double t_1 = x * sin(y);
	double tmp;
	if (y <= -9.5e+202) {
		tmp = t_0;
	} else if (y <= -540.0) {
		tmp = t_1;
	} else if (y <= 0.105) {
		tmp = z + (y * (x + (y * ((z * -0.5) + (y * ((x * -0.16666666666666666) + (0.041666666666666664 * (y * z))))))));
	} else if (y <= 2.25e+236) {
		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 = z * cos(y)
    t_1 = x * sin(y)
    if (y <= (-9.5d+202)) then
        tmp = t_0
    else if (y <= (-540.0d0)) then
        tmp = t_1
    else if (y <= 0.105d0) then
        tmp = z + (y * (x + (y * ((z * (-0.5d0)) + (y * ((x * (-0.16666666666666666d0)) + (0.041666666666666664d0 * (y * z))))))))
    else if (y <= 2.25d+236) 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 = z * Math.cos(y);
	double t_1 = x * Math.sin(y);
	double tmp;
	if (y <= -9.5e+202) {
		tmp = t_0;
	} else if (y <= -540.0) {
		tmp = t_1;
	} else if (y <= 0.105) {
		tmp = z + (y * (x + (y * ((z * -0.5) + (y * ((x * -0.16666666666666666) + (0.041666666666666664 * (y * z))))))));
	} else if (y <= 2.25e+236) {
		tmp = t_1;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = z * math.cos(y)
	t_1 = x * math.sin(y)
	tmp = 0
	if y <= -9.5e+202:
		tmp = t_0
	elif y <= -540.0:
		tmp = t_1
	elif y <= 0.105:
		tmp = z + (y * (x + (y * ((z * -0.5) + (y * ((x * -0.16666666666666666) + (0.041666666666666664 * (y * z))))))))
	elif y <= 2.25e+236:
		tmp = t_1
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(z * cos(y))
	t_1 = Float64(x * sin(y))
	tmp = 0.0
	if (y <= -9.5e+202)
		tmp = t_0;
	elseif (y <= -540.0)
		tmp = t_1;
	elseif (y <= 0.105)
		tmp = Float64(z + Float64(y * Float64(x + Float64(y * Float64(Float64(z * -0.5) + Float64(y * Float64(Float64(x * -0.16666666666666666) + Float64(0.041666666666666664 * Float64(y * z)))))))));
	elseif (y <= 2.25e+236)
		tmp = t_1;
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = z * cos(y);
	t_1 = x * sin(y);
	tmp = 0.0;
	if (y <= -9.5e+202)
		tmp = t_0;
	elseif (y <= -540.0)
		tmp = t_1;
	elseif (y <= 0.105)
		tmp = z + (y * (x + (y * ((z * -0.5) + (y * ((x * -0.16666666666666666) + (0.041666666666666664 * (y * z))))))));
	elseif (y <= 2.25e+236)
		tmp = t_1;
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(z * N[Cos[y], $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(x * N[Sin[y], $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -9.5e+202], t$95$0, If[LessEqual[y, -540.0], t$95$1, If[LessEqual[y, 0.105], N[(z + N[(y * N[(x + N[(y * N[(N[(z * -0.5), $MachinePrecision] + N[(y * N[(N[(x * -0.16666666666666666), $MachinePrecision] + N[(0.041666666666666664 * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 2.25e+236], t$95$1, t$95$0]]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -9.50000000000000059e202 or 2.25000000000000009e236 < y

   1. Initial program 99.9%

      \[x \cdot \sin y + z \cdot \cos y \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0 69.6%

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

   if -9.50000000000000059e202 < y < -540 or 0.104999999999999996 < y < 2.25000000000000009e236

   1. Initial program 99.6%

      \[x \cdot \sin y + z \cdot \cos y \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf 58.7%

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

   if -540 < y < 0.104999999999999996

   1. Initial program 100.0%

      \[x \cdot \sin y + z \cdot \cos y \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0 98.4%

      \[\leadsto \color{blue}{z + y \cdot \left(x + y \cdot \left(-0.5 \cdot z + y \cdot \left(-0.16666666666666666 \cdot x + 0.041666666666666664 \cdot \left(y \cdot z\right)\right)\right)\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification 80.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -9.5 \cdot 10^{+202}:\\ \;\;\;\;z \cdot \cos y\\ \mathbf{elif}\;y \leq -540:\\ \;\;\;\;x \cdot \sin y\\ \mathbf{elif}\;y \leq 0.105:\\ \;\;\;\;z + y \cdot \left(x + y \cdot \left(z \cdot -0.5 + y \cdot \left(x \cdot -0.16666666666666666 + 0.041666666666666664 \cdot \left(y \cdot z\right)\right)\right)\right)\\ \mathbf{elif}\;y \leq 2.25 \cdot 10^{+236}:\\ \;\;\;\;x \cdot \sin y\\ \mathbf{else}:\\ \;\;\;\;z \cdot \cos y\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 74.2% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -540 \lor \neg \left(y \leq 0.025\right):\\ \;\;\;\;x \cdot \sin y\\ \mathbf{else}:\\ \;\;\;\;z + y \cdot \left(x + y \cdot \left(z \cdot -0.5 + y \cdot \left(x \cdot -0.16666666666666666 + 0.041666666666666664 \cdot \left(y \cdot z\right)\right)\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -540.0) (not (<= y 0.025)))
   (* x (sin y))
   (+
    z
    (*
     y
     (+
      x
      (*
       y
       (+
        (* z -0.5)
        (*
         y
         (+
          (* x -0.16666666666666666)
          (* 0.041666666666666664 (* y z)))))))))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -540.0) || !(y <= 0.025)) {
		tmp = x * sin(y);
	} else {
		tmp = z + (y * (x + (y * ((z * -0.5) + (y * ((x * -0.16666666666666666) + (0.041666666666666664 * (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 <= (-540.0d0)) .or. (.not. (y <= 0.025d0))) then
        tmp = x * sin(y)
    else
        tmp = z + (y * (x + (y * ((z * (-0.5d0)) + (y * ((x * (-0.16666666666666666d0)) + (0.041666666666666664d0 * (y * z))))))))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((y <= -540.0) || !(y <= 0.025)) {
		tmp = x * Math.sin(y);
	} else {
		tmp = z + (y * (x + (y * ((z * -0.5) + (y * ((x * -0.16666666666666666) + (0.041666666666666664 * (y * z))))))));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -540.0) or not (y <= 0.025):
		tmp = x * math.sin(y)
	else:
		tmp = z + (y * (x + (y * ((z * -0.5) + (y * ((x * -0.16666666666666666) + (0.041666666666666664 * (y * z))))))))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -540.0) || !(y <= 0.025))
		tmp = Float64(x * sin(y));
	else
		tmp = Float64(z + Float64(y * Float64(x + Float64(y * Float64(Float64(z * -0.5) + Float64(y * Float64(Float64(x * -0.16666666666666666) + Float64(0.041666666666666664 * Float64(y * z)))))))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((y <= -540.0) || ~((y <= 0.025)))
		tmp = x * sin(y);
	else
		tmp = z + (y * (x + (y * ((z * -0.5) + (y * ((x * -0.16666666666666666) + (0.041666666666666664 * (y * z))))))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -540.0], N[Not[LessEqual[y, 0.025]], $MachinePrecision]], N[(x * N[Sin[y], $MachinePrecision]), $MachinePrecision], N[(z + N[(y * N[(x + N[(y * N[(N[(z * -0.5), $MachinePrecision] + N[(y * N[(N[(x * -0.16666666666666666), $MachinePrecision] + N[(0.041666666666666664 * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -540 or 0.025000000000000001 < y

   1. Initial program 99.7%

      \[x \cdot \sin y + z \cdot \cos y \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf 52.1%

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

   if -540 < y < 0.025000000000000001

   1. Initial program 100.0%

      \[x \cdot \sin y + z \cdot \cos y \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0 98.4%

      \[\leadsto \color{blue}{z + y \cdot \left(x + y \cdot \left(-0.5 \cdot z + y \cdot \left(-0.16666666666666666 \cdot x + 0.041666666666666664 \cdot \left(y \cdot z\right)\right)\right)\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 76.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -540 \lor \neg \left(y \leq 0.025\right):\\ \;\;\;\;x \cdot \sin y\\ \mathbf{else}:\\ \;\;\;\;z + y \cdot \left(x + y \cdot \left(z \cdot -0.5 + y \cdot \left(x \cdot -0.16666666666666666 + 0.041666666666666664 \cdot \left(y \cdot z\right)\right)\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 39.7% accurate, 25.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq 1.4 \cdot 10^{+194}:\\ \;\;\;\;z\\ \mathbf{else}:\\ \;\;\;\;x \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 (if (<= x 1.4e+194) z (* x y)))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= 1.4e+194) {
		tmp = z;
	} else {
		tmp = 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 (x <= 1.4d+194) then
        tmp = z
    else
        tmp = x * y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (x <= 1.4e+194) {
		tmp = z;
	} else {
		tmp = x * y;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= 1.4e+194:
		tmp = z
	else:
		tmp = x * y
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= 1.4e+194)
		tmp = z;
	else
		tmp = Float64(x * y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (x <= 1.4e+194)
		tmp = z;
	else
		tmp = x * y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, 1.4e+194], z, N[(x * y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < 1.40000000000000005e194

   1. Initial program 99.9%

      \[x \cdot \sin y + z \cdot \cos y \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf 94.6%

      \[\leadsto \color{blue}{z \cdot \left(\cos y + \frac{x \cdot \sin y}{z}\right)} \]
   4. Step-by-step derivation

      1. associate-/l* 94.5%

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

   5. Simplified 94.5%

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

   6. Taylor expanded in y around 0 49.3%

      \[\leadsto z \cdot \color{blue}{\left(1 + y \cdot \left(-0.5 \cdot y + \frac{x}{z}\right)\right)} \]

   7. Taylor expanded in y around 0 42.8%

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

   if 1.40000000000000005e194 < x

   1. Initial program 99.7%

      \[x \cdot \sin y + z \cdot \cos y \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0 50.8%

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

      1. +-commutative 50.8%

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

   5. Simplified 50.8%

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

   6. Taylor expanded in x around inf 39.3%

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

      1. *-commutative 39.3%

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

   8. Simplified 39.3%

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

4. Final simplification 42.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq 1.4 \cdot 10^{+194}:\\ \;\;\;\;z\\ \mathbf{else}:\\ \;\;\;\;x \cdot y\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 52.0% 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

1. Initial program 99.8%

   \[x \cdot \sin y + z \cdot \cos y \]
2. Add Preprocessing

3. Taylor expanded in y around 0 53.9%

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

   1. +-commutative 53.9%

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

5. Simplified 53.9%

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

6. Final simplification 53.9%

   \[\leadsto z + x \cdot y \]
7. Add Preprocessing

Alternative 7: 38.4% 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. Add Preprocessing

3. Taylor expanded in z around inf 92.8%

   \[\leadsto \color{blue}{z \cdot \left(\cos y + \frac{x \cdot \sin y}{z}\right)} \]
4. Step-by-step derivation

   1. associate-/l* 92.7%

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

5. Simplified 92.7%

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

6. Taylor expanded in y around 0 47.9%

   \[\leadsto z \cdot \color{blue}{\left(1 + y \cdot \left(-0.5 \cdot y + \frac{x}{z}\right)\right)} \]

7. Taylor expanded in y around 0 40.5%

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

8. Final simplification 40.5%

   \[\leadsto z \]
9. Add Preprocessing

Reproduce

herbie shell --seed 2024055 
(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))))