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

Percentage Accurate: 99.8% → 99.8%

Time: 8.8s

Alternatives: 6

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: 84.7% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -5.2 \cdot 10^{+205} \lor \neg \left(x \leq -4.6 \cdot 10^{+161} \lor \neg \left(x \leq -1000000000000\right) \land x \leq 52\right):\\ \;\;\;\;x \cdot \cos y\\ \mathbf{else}:\\ \;\;\;\;x - z \cdot \sin y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -5.2e+205)
         (not
          (or (<= x -4.6e+161)
              (and (not (<= x -1000000000000.0)) (<= x 52.0)))))
   (* x (cos y))
   (- x (* z (sin y)))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -5.2e+205) || !((x <= -4.6e+161) || (!(x <= -1000000000000.0) && (x <= 52.0)))) {
		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 <= (-5.2d+205)) .or. (.not. (x <= (-4.6d+161)) .or. (.not. (x <= (-1000000000000.0d0))) .and. (x <= 52.0d0))) 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 <= -5.2e+205) || !((x <= -4.6e+161) || (!(x <= -1000000000000.0) && (x <= 52.0)))) {
		tmp = x * Math.cos(y);
	} else {
		tmp = x - (z * Math.sin(y));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -5.2e+205) or not ((x <= -4.6e+161) or (not (x <= -1000000000000.0) and (x <= 52.0))):
		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 <= -5.2e+205) || !((x <= -4.6e+161) || (!(x <= -1000000000000.0) && (x <= 52.0))))
		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 <= -5.2e+205) || ~(((x <= -4.6e+161) || (~((x <= -1000000000000.0)) && (x <= 52.0)))))
		tmp = x * cos(y);
	else
		tmp = x - (z * sin(y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -5.2e+205], N[Not[Or[LessEqual[x, -4.6e+161], And[N[Not[LessEqual[x, -1000000000000.0]], $MachinePrecision], LessEqual[x, 52.0]]]], $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 < -5.1999999999999998e205 or -4.5999999999999999e161 < x < -1e12 or 52 < x

   1. Initial program 99.7%

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

   2. Taylor expanded in x around 0 99.7%

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

      1. mul-1-neg 99.7%

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

      2. distribute-rgt-neg-out 99.7%

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

      3. +-commutative 99.7%

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

      4. fma-udef 99.7%

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

      5. distribute-rgt-neg-out 99.7%

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

      6. *-commutative 99.7%

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

      7. distribute-rgt-neg-in 99.7%

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

   4. Simplified 99.7%

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

   5. Taylor expanded in x around inf 88.7%

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

   if -5.1999999999999998e205 < x < -4.5999999999999999e161 or -1e12 < x < 52

   1. Initial program 99.8%

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

   2. Taylor expanded in y around 0 92.4%

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

4. Final simplification 90.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -5.2 \cdot 10^{+205} \lor \neg \left(x \leq -4.6 \cdot 10^{+161} \lor \neg \left(x \leq -1000000000000\right) \land x \leq 52\right):\\ \;\;\;\;x \cdot \cos y\\ \mathbf{else}:\\ \;\;\;\;x - z \cdot \sin y\\ \end{array} \]

Alternative 3: 73.4% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x \cdot \cos y\\ \mathbf{if}\;x \leq -2.5 \cdot 10^{-35}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;x \leq -5.2 \cdot 10^{-187}:\\ \;\;\;\;x - y \cdot z\\ \mathbf{elif}\;x \leq 1.15 \cdot 10^{-11}:\\ \;\;\;\;z \cdot \left(-\sin y\right)\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* x (cos y))))
   (if (<= x -2.5e-35)
     t_0
     (if (<= x -5.2e-187)
       (- x (* y z))
       (if (<= x 1.15e-11) (* z (- (sin y))) t_0)))))

C

double code(double x, double y, double z) {
	double t_0 = x * cos(y);
	double tmp;
	if (x <= -2.5e-35) {
		tmp = t_0;
	} else if (x <= -5.2e-187) {
		tmp = x - (y * z);
	} else if (x <= 1.15e-11) {
		tmp = z * -sin(y);
	} 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 <= (-2.5d-35)) then
        tmp = t_0
    else if (x <= (-5.2d-187)) then
        tmp = x - (y * z)
    else if (x <= 1.15d-11) then
        tmp = z * -sin(y)
    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 <= -2.5e-35) {
		tmp = t_0;
	} else if (x <= -5.2e-187) {
		tmp = x - (y * z);
	} else if (x <= 1.15e-11) {
		tmp = z * -Math.sin(y);
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = x * math.cos(y)
	tmp = 0
	if x <= -2.5e-35:
		tmp = t_0
	elif x <= -5.2e-187:
		tmp = x - (y * z)
	elif x <= 1.15e-11:
		tmp = z * -math.sin(y)
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(x * cos(y))
	tmp = 0.0
	if (x <= -2.5e-35)
		tmp = t_0;
	elseif (x <= -5.2e-187)
		tmp = Float64(x - Float64(y * z));
	elseif (x <= 1.15e-11)
		tmp = Float64(z * Float64(-sin(y)));
	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 <= -2.5e-35)
		tmp = t_0;
	elseif (x <= -5.2e-187)
		tmp = x - (y * z);
	elseif (x <= 1.15e-11)
		tmp = z * -sin(y);
	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, -2.5e-35], t$95$0, If[LessEqual[x, -5.2e-187], N[(x - N[(y * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 1.15e-11], N[(z * (-N[Sin[y], $MachinePrecision])), $MachinePrecision], t$95$0]]]]

Derivation

1. Split input into 3 regimes

2. if x < -2.49999999999999982e-35 or 1.15000000000000007e-11 < x

   1. Initial program 99.7%

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

   2. Taylor expanded in x around 0 99.7%

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

      1. mul-1-neg 99.7%

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

      2. distribute-rgt-neg-out 99.7%

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

      3. +-commutative 99.7%

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

      4. fma-udef 99.7%

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

      5. distribute-rgt-neg-out 99.7%

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

      6. *-commutative 99.7%

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

      7. distribute-rgt-neg-in 99.7%

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

   4. Simplified 99.7%

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

   5. Taylor expanded in x around inf 84.0%

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

   if -2.49999999999999982e-35 < x < -5.1999999999999999e-187

   1. Initial program 100.0%

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

   2. Taylor expanded in y around 0 69.8%

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

      1. +-commutative 69.8%

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

      2. mul-1-neg 69.8%

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

      3. unsub-neg 69.8%

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

   4. Simplified 69.8%

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

   if -5.1999999999999999e-187 < x < 1.15000000000000007e-11

   1. Initial program 99.8%

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

   2. Taylor expanded in x around 0 80.9%

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

      1. mul-1-neg 80.9%

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

      2. *-commutative 80.9%

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

      3. distribute-rgt-neg-in 80.9%

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

   4. Simplified 80.9%

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

4. Final simplification 81.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.5 \cdot 10^{-35}:\\ \;\;\;\;x \cdot \cos y\\ \mathbf{elif}\;x \leq -5.2 \cdot 10^{-187}:\\ \;\;\;\;x - y \cdot z\\ \mathbf{elif}\;x \leq 1.15 \cdot 10^{-11}:\\ \;\;\;\;z \cdot \left(-\sin y\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \cos y\\ \end{array} \]

Alternative 4: 73.5% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -0.0055 \lor \neg \left(y \leq 0.35\right):\\ \;\;\;\;x \cdot \cos y\\ \mathbf{else}:\\ \;\;\;\;x - y \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -0.0055) (not (<= y 0.35))) (* x (cos y)) (- x (* y z))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -0.0055) || !(y <= 0.35)) {
		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 <= (-0.0055d0)) .or. (.not. (y <= 0.35d0))) 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 <= -0.0055) || !(y <= 0.35)) {
		tmp = x * Math.cos(y);
	} else {
		tmp = x - (y * z);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -0.0055) or not (y <= 0.35):
		tmp = x * math.cos(y)
	else:
		tmp = x - (y * z)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -0.0055) || !(y <= 0.35))
		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 <= -0.0055) || ~((y <= 0.35)))
		tmp = x * cos(y);
	else
		tmp = x - (y * z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -0.0055], N[Not[LessEqual[y, 0.35]], $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 < -0.0054999999999999997 or 0.34999999999999998 < y

   1. Initial program 99.6%

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

   2. Taylor expanded in x around 0 99.6%

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

      1. mul-1-neg 99.6%

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

      2. distribute-rgt-neg-out 99.6%

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

      3. +-commutative 99.6%

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

      4. fma-udef 99.6%

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

      5. distribute-rgt-neg-out 99.6%

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

      6. *-commutative 99.6%

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

      7. distribute-rgt-neg-in 99.6%

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

   4. Simplified 99.6%

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

   5. Taylor expanded in x around inf 51.7%

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

   if -0.0054999999999999997 < y < 0.34999999999999998

   1. Initial program 100.0%

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

   2. Taylor expanded in y around 0 98.5%

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

      1. +-commutative 98.5%

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

      2. mul-1-neg 98.5%

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

      3. unsub-neg 98.5%

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

   4. Simplified 98.5%

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

4. Final simplification 74.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -0.0055 \lor \neg \left(y \leq 0.35\right):\\ \;\;\;\;x \cdot \cos y\\ \mathbf{else}:\\ \;\;\;\;x - y \cdot z\\ \end{array} \]

Alternative 5: 51.2% 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 51.0%

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

   1. +-commutative 51.0%

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

   2. mul-1-neg 51.0%

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

   3. unsub-neg 51.0%

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

4. Simplified 51.0%

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

5. Final simplification 51.0%

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

Alternative 6: 38.5% 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 x around 0 99.8%

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

   1. mul-1-neg 99.8%

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

   2. distribute-rgt-neg-out 99.8%

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

   3. +-commutative 99.8%

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

   4. fma-udef 99.8%

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

   5. distribute-rgt-neg-out 99.8%

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

   6. *-commutative 99.8%

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

   7. distribute-rgt-neg-in 99.8%

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

4. Simplified 99.8%

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

5. Taylor expanded in y around 0 35.6%

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

6. Final simplification 35.6%

   \[\leadsto x \]

Reproduce

herbie shell --seed 2023202 
(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))))