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

Percentage Accurate: 99.8% → 99.8%

Time: 9.5s

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: 75.0% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := z \cdot \left(-\sin y\right)\\ t_1 := x \cdot \cos y\\ \mathbf{if}\;y \leq -1.2 \cdot 10^{+181}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y \leq -0.002:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 0.0014:\\ \;\;\;\;x - y \cdot z\\ \mathbf{elif}\;y \leq 2.2 \cdot 10^{+78} \lor \neg \left(y \leq 1.25 \cdot 10^{+211}\right):\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* z (- (sin y)))) (t_1 (* x (cos y))))
   (if (<= y -1.2e+181)
     t_0
     (if (<= y -0.002)
       t_1
       (if (<= y 0.0014)
         (- x (* y z))
         (if (or (<= y 2.2e+78) (not (<= y 1.25e+211))) t_1 t_0))))))

C

double code(double x, double y, double z) {
	double t_0 = z * -sin(y);
	double t_1 = x * cos(y);
	double tmp;
	if (y <= -1.2e+181) {
		tmp = t_0;
	} else if (y <= -0.002) {
		tmp = t_1;
	} else if (y <= 0.0014) {
		tmp = x - (y * z);
	} else if ((y <= 2.2e+78) || !(y <= 1.25e+211)) {
		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 * -sin(y)
    t_1 = x * cos(y)
    if (y <= (-1.2d+181)) then
        tmp = t_0
    else if (y <= (-0.002d0)) then
        tmp = t_1
    else if (y <= 0.0014d0) then
        tmp = x - (y * z)
    else if ((y <= 2.2d+78) .or. (.not. (y <= 1.25d+211))) 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.sin(y);
	double t_1 = x * Math.cos(y);
	double tmp;
	if (y <= -1.2e+181) {
		tmp = t_0;
	} else if (y <= -0.002) {
		tmp = t_1;
	} else if (y <= 0.0014) {
		tmp = x - (y * z);
	} else if ((y <= 2.2e+78) || !(y <= 1.25e+211)) {
		tmp = t_1;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = z * -math.sin(y)
	t_1 = x * math.cos(y)
	tmp = 0
	if y <= -1.2e+181:
		tmp = t_0
	elif y <= -0.002:
		tmp = t_1
	elif y <= 0.0014:
		tmp = x - (y * z)
	elif (y <= 2.2e+78) or not (y <= 1.25e+211):
		tmp = t_1
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(z * Float64(-sin(y)))
	t_1 = Float64(x * cos(y))
	tmp = 0.0
	if (y <= -1.2e+181)
		tmp = t_0;
	elseif (y <= -0.002)
		tmp = t_1;
	elseif (y <= 0.0014)
		tmp = Float64(x - Float64(y * z));
	elseif ((y <= 2.2e+78) || !(y <= 1.25e+211))
		tmp = t_1;
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = z * -sin(y);
	t_1 = x * cos(y);
	tmp = 0.0;
	if (y <= -1.2e+181)
		tmp = t_0;
	elseif (y <= -0.002)
		tmp = t_1;
	elseif (y <= 0.0014)
		tmp = x - (y * z);
	elseif ((y <= 2.2e+78) || ~((y <= 1.25e+211)))
		tmp = t_1;
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(z * (-N[Sin[y], $MachinePrecision])), $MachinePrecision]}, Block[{t$95$1 = N[(x * N[Cos[y], $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -1.2e+181], t$95$0, If[LessEqual[y, -0.002], t$95$1, If[LessEqual[y, 0.0014], N[(x - N[(y * z), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[y, 2.2e+78], N[Not[LessEqual[y, 1.25e+211]], $MachinePrecision]], t$95$1, t$95$0]]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.20000000000000001e181 or 2.20000000000000014e78 < y < 1.2499999999999999e211

   1. Initial program 99.6%

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

   2. Taylor expanded in x around 0 64.5%

      \[\leadsto \color{blue}{-1 \cdot \left(z \cdot \sin y\right)} \]
   3. Step-by-step derivation

      1. mul-1-neg 64.5%

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

      2. *-commutative 64.5%

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

      3. distribute-rgt-neg-in 64.5%

         \[\leadsto \color{blue}{\sin y \cdot \left(-z\right)} \]

   4. Simplified 64.5%

      \[\leadsto \color{blue}{\sin y \cdot \left(-z\right)} \]

   if -1.20000000000000001e181 < y < -2e-3 or 0.00139999999999999999 < y < 2.20000000000000014e78 or 1.2499999999999999e211 < y

   1. Initial program 99.6%

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

   2. Taylor expanded in y around 0 48.2%

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

   3. Taylor expanded in x around inf 69.0%

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

   if -2e-3 < y < 0.00139999999999999999

   1. Initial program 100.0%

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

   2. Taylor expanded in y around 0 99.8%

      \[\leadsto \color{blue}{-1 \cdot \left(y \cdot z\right) + x} \]
   3. Step-by-step derivation

      1. +-commutative 99.8%

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

      2. mul-1-neg 99.8%

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

      3. unsub-neg 99.8%

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

   4. Simplified 99.8%

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

4. Final simplification 84.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.2 \cdot 10^{+181}:\\ \;\;\;\;z \cdot \left(-\sin y\right)\\ \mathbf{elif}\;y \leq -0.002:\\ \;\;\;\;x \cdot \cos y\\ \mathbf{elif}\;y \leq 0.0014:\\ \;\;\;\;x - y \cdot z\\ \mathbf{elif}\;y \leq 2.2 \cdot 10^{+78} \lor \neg \left(y \leq 1.25 \cdot 10^{+211}\right):\\ \;\;\;\;x \cdot \cos y\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(-\sin y\right)\\ \end{array} \]

Alternative 3: 85.7% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -0.021 \lor \neg \left(x \leq 4.7 \cdot 10^{+115}\right):\\ \;\;\;\;x \cdot \cos y\\ \mathbf{else}:\\ \;\;\;\;x - z \cdot \sin y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -0.021) (not (<= x 4.7e+115)))
   (* x (cos y))
   (- x (* z (sin y)))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -0.021) || !(x <= 4.7e+115)) {
		tmp = x * cos(y);
	} else {
		tmp = x - (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 <= (-0.021d0)) .or. (.not. (x <= 4.7d+115))) then
        tmp = x * cos(y)
    else
        tmp = x - (z * sin(y))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((x <= -0.021) || !(x <= 4.7e+115)) {
		tmp = x * Math.cos(y);
	} else {
		tmp = x - (z * Math.sin(y));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -0.021) or not (x <= 4.7e+115):
		tmp = x * math.cos(y)
	else:
		tmp = x - (z * math.sin(y))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -0.021) || !(x <= 4.7e+115))
		tmp = Float64(x * cos(y));
	else
		tmp = Float64(x - Float64(z * sin(y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((x <= -0.021) || ~((x <= 4.7e+115)))
		tmp = x * cos(y);
	else
		tmp = x - (z * sin(y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -0.021], N[Not[LessEqual[x, 4.7e+115]], $MachinePrecision]], N[(x * N[Cos[y], $MachinePrecision]), $MachinePrecision], N[(x - N[(z * N[Sin[y], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -0.0210000000000000013 or 4.6999999999999996e115 < x

   1. Initial program 99.8%

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

   2. Taylor expanded in y around 0 79.6%

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

   3. Taylor expanded in x around inf 92.2%

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

   if -0.0210000000000000013 < x < 4.6999999999999996e115

   1. Initial program 99.8%

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

   2. Taylor expanded in y around 0 88.8%

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

4. Final simplification 90.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -0.021 \lor \neg \left(x \leq 4.7 \cdot 10^{+115}\right):\\ \;\;\;\;x \cdot \cos y\\ \mathbf{else}:\\ \;\;\;\;x - z \cdot \sin y\\ \end{array} \]

Alternative 4: 74.8% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -0.00145 \lor \neg \left(y \leq 0.0142\right):\\ \;\;\;\;x \cdot \cos y\\ \mathbf{else}:\\ \;\;\;\;x - y \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -0.00145) (not (<= y 0.0142))) (* x (cos y)) (- x (* y z))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -0.00145) || !(y <= 0.0142)) {
		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 <= (-0.00145d0)) .or. (.not. (y <= 0.0142d0))) 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 <= -0.00145) || !(y <= 0.0142)) {
		tmp = x * Math.cos(y);
	} else {
		tmp = x - (y * z);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -0.00145) or not (y <= 0.0142):
		tmp = x * math.cos(y)
	else:
		tmp = x - (y * z)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -0.00145) || !(y <= 0.0142))
		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 <= -0.00145) || ~((y <= 0.0142)))
		tmp = x * cos(y);
	else
		tmp = x - (y * z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -0.00145], N[Not[LessEqual[y, 0.0142]], $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 < -0.00145 or 0.014200000000000001 < y

   1. Initial program 99.6%

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

   2. Taylor expanded in y around 0 34.3%

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

   3. Taylor expanded in x around inf 52.7%

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

   if -0.00145 < y < 0.014200000000000001

   1. Initial program 100.0%

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

   2. Taylor expanded in y around 0 99.8%

      \[\leadsto \color{blue}{-1 \cdot \left(y \cdot z\right) + x} \]
   3. Step-by-step derivation

      1. +-commutative 99.8%

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

      2. mul-1-neg 99.8%

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

      3. unsub-neg 99.8%

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

   4. Simplified 99.8%

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

4. Final simplification 78.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -0.00145 \lor \neg \left(y \leq 0.0142\right):\\ \;\;\;\;x \cdot \cos y\\ \mathbf{else}:\\ \;\;\;\;x - y \cdot z\\ \end{array} \]

Alternative 5: 40.5% accurate, 25.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -8.4 \cdot 10^{-134}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq -8.2 \cdot 10^{-294}:\\ \;\;\;\;y \cdot \left(-z\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -8.4e-134) x (if (<= x -8.2e-294) (* y (- z)) x)))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -8.4e-134) {
		tmp = x;
	} else if (x <= -8.2e-294) {
		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 <= (-8.4d-134)) then
        tmp = x
    else if (x <= (-8.2d-294)) 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 <= -8.4e-134) {
		tmp = x;
	} else if (x <= -8.2e-294) {
		tmp = y * -z;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= -8.4e-134:
		tmp = x
	elif x <= -8.2e-294:
		tmp = y * -z
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -8.4e-134)
		tmp = x;
	elseif (x <= -8.2e-294)
		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 <= -8.4e-134)
		tmp = x;
	elseif (x <= -8.2e-294)
		tmp = y * -z;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -8.4e-134], x, If[LessEqual[x, -8.2e-294], N[(y * (-z)), $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if x < -8.3999999999999996e-134 or -8.1999999999999998e-294 < x

   1. Initial program 99.8%

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

   2. Taylor expanded in y around 0 70.0%

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

   3. Taylor expanded in y around 0 46.0%

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

   if -8.3999999999999996e-134 < x < -8.1999999999999998e-294

   1. Initial program 99.9%

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

   2. Taylor expanded in y around 0 71.0%

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

   3. Taylor expanded in x around 0 51.0%

      \[\leadsto \color{blue}{-1 \cdot \left(y \cdot z\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 46.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -8.4 \cdot 10^{-134}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq -8.2 \cdot 10^{-294}:\\ \;\;\;\;y \cdot \left(-z\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 6: 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

1. Initial program 99.8%

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

2. Taylor expanded in y around 0 57.2%

   \[\leadsto \color{blue}{-1 \cdot \left(y \cdot z\right) + x} \]
3. Step-by-step derivation

   1. +-commutative 57.2%

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

   2. mul-1-neg 57.2%

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

   3. unsub-neg 57.2%

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

4. Simplified 57.2%

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

5. Final simplification 57.2%

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

Alternative 7: 39.1% 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 70.1%

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

3. Taylor expanded in y around 0 43.0%

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

4. Final simplification 43.0%

   \[\leadsto x \]

Reproduce

herbie shell --seed 2023263 
(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))))