Diagrams.ThreeD.Transform:aboutY from diagrams-lib-1.3.0.3

Percentage Accurate: 99.8% → 99.8%

Time: 8.7s

Alternatives: 7

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, 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]

Derivation

1. Initial program 99.8%

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

2. Final simplification 99.8%

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

Alternative 2: 74.9% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x \cdot \cos y\\ \mathbf{if}\;x \leq -1.85 \cdot 10^{-28}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;x \leq 1.5 \cdot 10^{-131}:\\ \;\;\;\;z \cdot \sin y\\ \mathbf{elif}\;x \leq 2.75 \cdot 10^{-64}:\\ \;\;\;\;t_0 + y \cdot z\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* x (cos y))))
   (if (<= x -1.85e-28)
     t_0
     (if (<= x 1.5e-131)
       (* z (sin y))
       (if (<= x 2.75e-64) (+ t_0 (* y z)) t_0)))))

C

double code(double x, double y, double z) {
	double t_0 = x * cos(y);
	double tmp;
	if (x <= -1.85e-28) {
		tmp = t_0;
	} else if (x <= 1.5e-131) {
		tmp = z * sin(y);
	} else if (x <= 2.75e-64) {
		tmp = t_0 + (y * z);
	} 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) :: tmp
    t_0 = x * cos(y)
    if (x <= (-1.85d-28)) then
        tmp = t_0
    else if (x <= 1.5d-131) then
        tmp = z * sin(y)
    else if (x <= 2.75d-64) then
        tmp = t_0 + (y * z)
    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 tmp;
	if (x <= -1.85e-28) {
		tmp = t_0;
	} else if (x <= 1.5e-131) {
		tmp = z * Math.sin(y);
	} else if (x <= 2.75e-64) {
		tmp = t_0 + (y * z);
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = x * math.cos(y)
	tmp = 0
	if x <= -1.85e-28:
		tmp = t_0
	elif x <= 1.5e-131:
		tmp = z * math.sin(y)
	elif x <= 2.75e-64:
		tmp = t_0 + (y * z)
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(x * cos(y))
	tmp = 0.0
	if (x <= -1.85e-28)
		tmp = t_0;
	elseif (x <= 1.5e-131)
		tmp = Float64(z * sin(y));
	elseif (x <= 2.75e-64)
		tmp = Float64(t_0 + Float64(y * z));
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = x * cos(y);
	tmp = 0.0;
	if (x <= -1.85e-28)
		tmp = t_0;
	elseif (x <= 1.5e-131)
		tmp = z * sin(y);
	elseif (x <= 2.75e-64)
		tmp = t_0 + (y * z);
	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]}, If[LessEqual[x, -1.85e-28], t$95$0, If[LessEqual[x, 1.5e-131], N[(z * N[Sin[y], $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 2.75e-64], N[(t$95$0 + N[(y * z), $MachinePrecision]), $MachinePrecision], t$95$0]]]]

Derivation

1. Split input into 3 regimes

2. if x < -1.8500000000000001e-28 or 2.7499999999999999e-64 < x

   1. Initial program 99.8%

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

   2. Taylor expanded in x around inf 84.8%

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

   if -1.8500000000000001e-28 < x < 1.49999999999999998e-131

   1. Initial program 99.8%

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

   2. Taylor expanded in x around 0 79.1%

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

   if 1.49999999999999998e-131 < x < 2.7499999999999999e-64

   1. Initial program 99.9%

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

   2. Taylor expanded in y around 0 88.7%

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

4. Final simplification 83.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.85 \cdot 10^{-28}:\\ \;\;\;\;x \cdot \cos y\\ \mathbf{elif}\;x \leq 1.5 \cdot 10^{-131}:\\ \;\;\;\;z \cdot \sin y\\ \mathbf{elif}\;x \leq 2.75 \cdot 10^{-64}:\\ \;\;\;\;x \cdot \cos y + y \cdot z\\ \mathbf{else}:\\ \;\;\;\;x \cdot \cos y\\ \end{array} \]

Alternative 3: 86.4% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.45 \cdot 10^{-98} \lor \neg \left(z \leq 5.6 \cdot 10^{-25}\right):\\ \;\;\;\;x + z \cdot \left(3 \cdot \left(\sin y \cdot 0.3333333333333333\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \cos y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -1.45e-98) (not (<= z 5.6e-25)))
   (+ x (* z (* 3.0 (* (sin y) 0.3333333333333333))))
   (* x (cos y))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -1.45e-98) || !(z <= 5.6e-25)) {
		tmp = x + (z * (3.0 * (sin(y) * 0.3333333333333333)));
	} else {
		tmp = x * 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 ((z <= (-1.45d-98)) .or. (.not. (z <= 5.6d-25))) then
        tmp = x + (z * (3.0d0 * (sin(y) * 0.3333333333333333d0)))
    else
        tmp = x * cos(y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((z <= -1.45e-98) || !(z <= 5.6e-25)) {
		tmp = x + (z * (3.0 * (Math.sin(y) * 0.3333333333333333)));
	} else {
		tmp = x * Math.cos(y);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -1.45e-98) or not (z <= 5.6e-25):
		tmp = x + (z * (3.0 * (math.sin(y) * 0.3333333333333333)))
	else:
		tmp = x * math.cos(y)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -1.45e-98) || !(z <= 5.6e-25))
		tmp = Float64(x + Float64(z * Float64(3.0 * Float64(sin(y) * 0.3333333333333333))));
	else
		tmp = Float64(x * cos(y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((z <= -1.45e-98) || ~((z <= 5.6e-25)))
		tmp = x + (z * (3.0 * (sin(y) * 0.3333333333333333)));
	else
		tmp = x * cos(y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -1.45e-98], N[Not[LessEqual[z, 5.6e-25]], $MachinePrecision]], N[(x + N[(z * N[(3.0 * N[(N[Sin[y], $MachinePrecision] * 0.3333333333333333), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x * N[Cos[y], $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.45e-98 or 5.59999999999999976e-25 < z

   1. Initial program 99.8%

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

      1. log1p-expm1-u 99.7%

         \[\leadsto x \cdot \cos y + z \cdot \color{blue}{\mathsf{log1p}\left(\mathsf{expm1}\left(\sin y\right)\right)} \]

   3. Applied egg-rr 99.7%

      \[\leadsto x \cdot \cos y + z \cdot \color{blue}{\mathsf{log1p}\left(\mathsf{expm1}\left(\sin y\right)\right)} \]
   4. Step-by-step derivation

      1. log1p-expm1-u 99.8%

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

      2. add-log-exp 80.7%

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

      3. add-cube-cbrt 80.0%

         \[\leadsto x \cdot \cos y + z \cdot \log \color{blue}{\left(\left(\sqrt[3]{e^{\sin y}} \cdot \sqrt[3]{e^{\sin y}}\right) \cdot \sqrt[3]{e^{\sin y}}\right)} \]

      4. pow3 79.9%

         \[\leadsto x \cdot \cos y + z \cdot \log \color{blue}{\left({\left(\sqrt[3]{e^{\sin y}}\right)}^{3}\right)} \]

      5. log-pow 80.0%

         \[\leadsto x \cdot \cos y + z \cdot \color{blue}{\left(3 \cdot \log \left(\sqrt[3]{e^{\sin y}}\right)\right)} \]

      6. pow1/3 80.2%

         \[\leadsto x \cdot \cos y + z \cdot \left(3 \cdot \log \color{blue}{\left({\left(e^{\sin y}\right)}^{0.3333333333333333}\right)}\right) \]

      7. log-pow 80.7%

         \[\leadsto x \cdot \cos y + z \cdot \left(3 \cdot \color{blue}{\left(0.3333333333333333 \cdot \log \left(e^{\sin y}\right)\right)}\right) \]

      8. add-log-exp 99.6%

         \[\leadsto x \cdot \cos y + z \cdot \left(3 \cdot \left(0.3333333333333333 \cdot \color{blue}{\sin y}\right)\right) \]

   5. Applied egg-rr 99.6%

      \[\leadsto x \cdot \cos y + z \cdot \color{blue}{\left(3 \cdot \left(0.3333333333333333 \cdot \sin y\right)\right)} \]

   6. Taylor expanded in y around 0 88.8%

      \[\leadsto \color{blue}{x} + z \cdot \left(3 \cdot \left(0.3333333333333333 \cdot \sin y\right)\right) \]

   if -1.45e-98 < z < 5.59999999999999976e-25

   1. Initial program 99.8%

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

   2. Taylor expanded in x around inf 88.0%

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

4. Final simplification 88.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.45 \cdot 10^{-98} \lor \neg \left(z \leq 5.6 \cdot 10^{-25}\right):\\ \;\;\;\;x + z \cdot \left(3 \cdot \left(\sin y \cdot 0.3333333333333333\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \cos y\\ \end{array} \]

Alternative 4: 75.0% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -0.00088 \lor \neg \left(y \leq 0.0015\right):\\ \;\;\;\;x \cdot \cos y\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -0.00088) (not (<= y 0.0015))) (* x (cos y)) (+ x (* y z))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -0.00088) || !(y <= 0.0015)) {
		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 <= (-0.00088d0)) .or. (.not. (y <= 0.0015d0))) 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 <= -0.00088) || !(y <= 0.0015)) {
		tmp = x * Math.cos(y);
	} else {
		tmp = x + (y * z);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -0.00088) or not (y <= 0.0015):
		tmp = x * math.cos(y)
	else:
		tmp = x + (y * z)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -0.00088) || !(y <= 0.0015))
		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 <= -0.00088) || ~((y <= 0.0015)))
		tmp = x * cos(y);
	else
		tmp = x + (y * z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -0.00088], N[Not[LessEqual[y, 0.0015]], $MachinePrecision]], N[(x * N[Cos[y], $MachinePrecision]), $MachinePrecision], N[(x + N[(y * z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -8.80000000000000031e-4 or 0.0015 < y

   1. Initial program 99.6%

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

   2. Taylor expanded in x around inf 51.1%

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

   if -8.80000000000000031e-4 < y < 0.0015

   1. Initial program 100.0%

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

   2. Taylor expanded in y around 0 98.7%

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

      1. +-commutative 98.7%

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

   4. Simplified 98.7%

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

4. Final simplification 75.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -0.00088 \lor \neg \left(y \leq 0.0015\right):\\ \;\;\;\;x \cdot \cos y\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot z\\ \end{array} \]

Alternative 5: 74.4% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -2.2 \cdot 10^{-28} \lor \neg \left(x \leq 1.45 \cdot 10^{-126}\right):\\ \;\;\;\;x \cdot \cos y\\ \mathbf{else}:\\ \;\;\;\;z \cdot \sin y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -2.2e-28) (not (<= x 1.45e-126))) (* x (cos y)) (* z (sin y))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -2.2e-28) || !(x <= 1.45e-126)) {
		tmp = x * cos(y);
	} else {
		tmp = z * 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) :: tmp
    if ((x <= (-2.2d-28)) .or. (.not. (x <= 1.45d-126))) then
        tmp = x * cos(y)
    else
        tmp = z * sin(y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((x <= -2.2e-28) || !(x <= 1.45e-126)) {
		tmp = x * Math.cos(y);
	} else {
		tmp = z * Math.sin(y);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -2.2e-28) or not (x <= 1.45e-126):
		tmp = x * math.cos(y)
	else:
		tmp = z * math.sin(y)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -2.2e-28) || !(x <= 1.45e-126))
		tmp = Float64(x * cos(y));
	else
		tmp = Float64(z * sin(y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((x <= -2.2e-28) || ~((x <= 1.45e-126)))
		tmp = x * cos(y);
	else
		tmp = z * sin(y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -2.2e-28], N[Not[LessEqual[x, 1.45e-126]], $MachinePrecision]], N[(x * N[Cos[y], $MachinePrecision]), $MachinePrecision], N[(z * N[Sin[y], $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -2.19999999999999996e-28 or 1.44999999999999994e-126 < x

   1. Initial program 99.8%

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

   2. Taylor expanded in x around inf 82.8%

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

   if -2.19999999999999996e-28 < x < 1.44999999999999994e-126

   1. Initial program 99.8%

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

   2. Taylor expanded in x around 0 78.5%

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

4. Final simplification 81.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.2 \cdot 10^{-28} \lor \neg \left(x \leq 1.45 \cdot 10^{-126}\right):\\ \;\;\;\;x \cdot \cos y\\ \mathbf{else}:\\ \;\;\;\;z \cdot \sin y\\ \end{array} \]

Alternative 6: 53.2% 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

1. Initial program 99.8%

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

2. Taylor expanded in y around 0 53.6%

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

   1. +-commutative 53.6%

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

4. Simplified 53.6%

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

5. Final simplification 53.6%

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

Alternative 7: 39.7% 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

1. Initial program 99.8%

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

2. Taylor expanded in y around 0 53.6%

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

   1. +-commutative 53.6%

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

4. Simplified 53.6%

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

5. Taylor expanded in y around 0 41.6%

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

6. Final simplification 41.6%

   \[\leadsto x \]

Reproduce

herbie shell --seed 2023275 
(FPCore (x y z)
  :name "Diagrams.ThreeD.Transform:aboutY from diagrams-lib-1.3.0.3"
  :precision binary64
  (+ (* x (cos y)) (* z (sin y))))