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

Percentage Accurate: 99.8% → 99.8%

Time: 9.3s

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, 0.7× speedup

Math

\[\begin{array}{l} \\ \mathsf{fma}\left(\cos y, x, z \cdot \left(-\sin y\right)\right) \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 (fma (cos y) x (* z (- (sin y)))))

C

double code(double x, double y, double z) {
	return fma(cos(y), x, (z * -sin(y)));
}

Julia

function code(x, y, z)
	return fma(cos(y), x, Float64(z * Float64(-sin(y))))
end

Wolfram

code[x_, y_, z_] := N[(N[Cos[y], $MachinePrecision] * x + N[(z * (-N[Sin[y], $MachinePrecision])), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 99.8%

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

   1. *-commutative 99.8%

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

   2. fma-neg 99.8%

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

   3. distribute-rgt-neg-in 99.8%

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

4. Applied egg-rr 99.8%

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

5. Final simplification 99.8%

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

Alternative 2: 99.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \cos y \cdot x - z \cdot \sin y \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 (- (* (cos y) x) (* z (sin y))))

C

double code(double x, double y, double z) {
	return (cos(y) * x) - (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 = (cos(y) * x) - (z * sin(y))
end function

Java

public static double code(double x, double y, double z) {
	return (Math.cos(y) * x) - (z * Math.sin(y));
}

Python

def code(x, y, z):
	return (math.cos(y) * x) - (z * math.sin(y))

Julia

function code(x, y, z)
	return Float64(Float64(cos(y) * x) - Float64(z * sin(y)))
end

MATLAB

function tmp = code(x, y, z)
	tmp = (cos(y) * x) - (z * sin(y));
end

Wolfram

code[x_, y_, z_] := N[(N[(N[Cos[y], $MachinePrecision] * x), $MachinePrecision] - N[(z * N[Sin[y], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 99.8%

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

3. Final simplification 99.8%

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

Alternative 3: 75.4% accurate, 1.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := z \cdot \left(-\sin y\right)\\ \mathbf{if}\;y \leq -64000:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;y \leq 0.0108:\\ \;\;\;\;x + y \cdot \left(y \cdot \left(x \cdot -0.5\right) - z\right)\\ \mathbf{elif}\;y \leq 7.8 \cdot 10^{+93} \lor \neg \left(y \leq 1.35 \cdot 10^{+256}\right):\\ \;\;\;\;\cos y \cdot x\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* z (- (sin y)))))
   (if (<= y -64000.0)
     t_0
     (if (<= y 0.0108)
       (+ x (* y (- (* y (* x -0.5)) z)))
       (if (or (<= y 7.8e+93) (not (<= y 1.35e+256))) (* (cos y) x) t_0)))))

C

double code(double x, double y, double z) {
	double t_0 = z * -sin(y);
	double tmp;
	if (y <= -64000.0) {
		tmp = t_0;
	} else if (y <= 0.0108) {
		tmp = x + (y * ((y * (x * -0.5)) - z));
	} else if ((y <= 7.8e+93) || !(y <= 1.35e+256)) {
		tmp = cos(y) * x;
	} 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 = z * -sin(y)
    if (y <= (-64000.0d0)) then
        tmp = t_0
    else if (y <= 0.0108d0) then
        tmp = x + (y * ((y * (x * (-0.5d0))) - z))
    else if ((y <= 7.8d+93) .or. (.not. (y <= 1.35d+256))) then
        tmp = cos(y) * x
    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 tmp;
	if (y <= -64000.0) {
		tmp = t_0;
	} else if (y <= 0.0108) {
		tmp = x + (y * ((y * (x * -0.5)) - z));
	} else if ((y <= 7.8e+93) || !(y <= 1.35e+256)) {
		tmp = Math.cos(y) * x;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = z * -math.sin(y)
	tmp = 0
	if y <= -64000.0:
		tmp = t_0
	elif y <= 0.0108:
		tmp = x + (y * ((y * (x * -0.5)) - z))
	elif (y <= 7.8e+93) or not (y <= 1.35e+256):
		tmp = math.cos(y) * x
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(z * Float64(-sin(y)))
	tmp = 0.0
	if (y <= -64000.0)
		tmp = t_0;
	elseif (y <= 0.0108)
		tmp = Float64(x + Float64(y * Float64(Float64(y * Float64(x * -0.5)) - z)));
	elseif ((y <= 7.8e+93) || !(y <= 1.35e+256))
		tmp = Float64(cos(y) * x);
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = z * -sin(y);
	tmp = 0.0;
	if (y <= -64000.0)
		tmp = t_0;
	elseif (y <= 0.0108)
		tmp = x + (y * ((y * (x * -0.5)) - z));
	elseif ((y <= 7.8e+93) || ~((y <= 1.35e+256)))
		tmp = cos(y) * x;
	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]}, If[LessEqual[y, -64000.0], t$95$0, If[LessEqual[y, 0.0108], N[(x + N[(y * N[(N[(y * N[(x * -0.5), $MachinePrecision]), $MachinePrecision] - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[y, 7.8e+93], N[Not[LessEqual[y, 1.35e+256]], $MachinePrecision]], N[(N[Cos[y], $MachinePrecision] * x), $MachinePrecision], t$95$0]]]]

Derivation

1. Split input into 3 regimes

2. if y < -64000 or 7.8000000000000005e93 < y < 1.34999999999999997e256

   1. Initial program 99.6%

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

   3. Taylor expanded in x around 0 59.6%

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

      1. mul-1-neg 59.6%

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

      2. *-commutative 59.6%

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

      3. distribute-rgt-neg-in 59.6%

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

   5. Simplified 59.6%

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

   if -64000 < y < 0.010800000000000001

   1. Initial program 100.0%

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

      1. *-commutative 100.0%

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

      2. fma-neg 100.0%

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

      3. distribute-rgt-neg-in 100.0%

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

   4. Applied egg-rr 100.0%

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

   5. Taylor expanded in y around 0 98.4%

      \[\leadsto \color{blue}{x + \left(-1 \cdot \left(y \cdot z\right) + -0.5 \cdot \left(x \cdot {y}^{2}\right)\right)} \]
   6. Step-by-step derivation

      1. +-commutative 98.4%

         \[\leadsto x + \color{blue}{\left(-0.5 \cdot \left(x \cdot {y}^{2}\right) + -1 \cdot \left(y \cdot z\right)\right)} \]

      2. mul-1-neg 98.4%

         \[\leadsto x + \left(-0.5 \cdot \left(x \cdot {y}^{2}\right) + \color{blue}{\left(-y \cdot z\right)}\right) \]

      3. unsub-neg 98.4%

         \[\leadsto x + \color{blue}{\left(-0.5 \cdot \left(x \cdot {y}^{2}\right) - y \cdot z\right)} \]

      4. associate-*r* 98.4%

         \[\leadsto x + \left(\color{blue}{\left(-0.5 \cdot x\right) \cdot {y}^{2}} - y \cdot z\right) \]

      5. unpow2 98.4%

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

      6. associate-*r* 98.4%

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

      7. *-commutative 98.4%

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

      8. distribute-rgt-out-- 98.4%

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

      9. *-commutative 98.4%

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

   7. Simplified 98.4%

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

   if 0.010800000000000001 < y < 7.8000000000000005e93 or 1.34999999999999997e256 < y

   1. Initial program 99.6%

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

   3. Taylor expanded in x around inf 76.8%

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

4. Final simplification 82.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -64000:\\ \;\;\;\;z \cdot \left(-\sin y\right)\\ \mathbf{elif}\;y \leq 0.0108:\\ \;\;\;\;x + y \cdot \left(y \cdot \left(x \cdot -0.5\right) - z\right)\\ \mathbf{elif}\;y \leq 7.8 \cdot 10^{+93} \lor \neg \left(y \leq 1.35 \cdot 10^{+256}\right):\\ \;\;\;\;\cos y \cdot x\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(-\sin y\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 84.2% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.22 \cdot 10^{-27} \lor \neg \left(x \leq 2.2 \cdot 10^{+203}\right):\\ \;\;\;\;\cos y \cdot x\\ \mathbf{else}:\\ \;\;\;\;x - z \cdot \sin y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -1.22e-27) (not (<= x 2.2e+203)))
   (* (cos y) x)
   (- x (* z (sin y)))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -1.22e-27) || !(x <= 2.2e+203)) {
		tmp = cos(y) * x;
	} 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 <= (-1.22d-27)) .or. (.not. (x <= 2.2d+203))) then
        tmp = cos(y) * x
    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 <= -1.22e-27) || !(x <= 2.2e+203)) {
		tmp = Math.cos(y) * x;
	} else {
		tmp = x - (z * Math.sin(y));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -1.22e-27) or not (x <= 2.2e+203):
		tmp = math.cos(y) * x
	else:
		tmp = x - (z * math.sin(y))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -1.22e-27) || !(x <= 2.2e+203))
		tmp = Float64(cos(y) * x);
	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 <= -1.22e-27) || ~((x <= 2.2e+203)))
		tmp = cos(y) * x;
	else
		tmp = x - (z * sin(y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -1.22e-27], N[Not[LessEqual[x, 2.2e+203]], $MachinePrecision]], N[(N[Cos[y], $MachinePrecision] * x), $MachinePrecision], N[(x - N[(z * N[Sin[y], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -1.22e-27 or 2.20000000000000004e203 < x

   1. Initial program 99.8%

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

   3. Taylor expanded in x around inf 91.1%

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

   if -1.22e-27 < x < 2.20000000000000004e203

   1. Initial program 99.8%

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

   3. 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 89.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.22 \cdot 10^{-27} \lor \neg \left(x \leq 2.2 \cdot 10^{+203}\right):\\ \;\;\;\;\cos y \cdot x\\ \mathbf{else}:\\ \;\;\;\;x - z \cdot \sin y\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 75.3% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -7.2 \cdot 10^{-8} \lor \neg \left(y \leq 0.007\right):\\ \;\;\;\;\cos y \cdot x\\ \mathbf{else}:\\ \;\;\;\;x - y \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -7.2e-8) (not (<= y 0.007))) (* (cos y) x) (- x (* y z))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -7.2e-8) || !(y <= 0.007)) {
		tmp = cos(y) * x;
	} 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 <= (-7.2d-8)) .or. (.not. (y <= 0.007d0))) then
        tmp = cos(y) * x
    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 <= -7.2e-8) || !(y <= 0.007)) {
		tmp = Math.cos(y) * x;
	} else {
		tmp = x - (y * z);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -7.2e-8) or not (y <= 0.007):
		tmp = math.cos(y) * x
	else:
		tmp = x - (y * z)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -7.2e-8) || !(y <= 0.007))
		tmp = Float64(cos(y) * x);
	else
		tmp = Float64(x - Float64(y * z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((y <= -7.2e-8) || ~((y <= 0.007)))
		tmp = cos(y) * x;
	else
		tmp = x - (y * z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -7.2e-8], N[Not[LessEqual[y, 0.007]], $MachinePrecision]], N[(N[Cos[y], $MachinePrecision] * x), $MachinePrecision], N[(x - N[(y * z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -7.19999999999999962e-8 or 0.00700000000000000015 < y

   1. Initial program 99.6%

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

   3. Taylor expanded in x around inf 53.0%

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

   if -7.19999999999999962e-8 < y < 0.00700000000000000015

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 99.3%

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

      1. mul-1-neg 99.3%

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

      2. unsub-neg 99.3%

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

   5. Simplified 99.3%

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

4. Final simplification 76.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -7.2 \cdot 10^{-8} \lor \neg \left(y \leq 0.007\right):\\ \;\;\;\;\cos y \cdot x\\ \mathbf{else}:\\ \;\;\;\;x - y \cdot z\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 53.5% 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. Add Preprocessing

3. Taylor expanded in y around 0 54.8%

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

   1. mul-1-neg 54.8%

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

   2. unsub-neg 54.8%

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

5. Simplified 54.8%

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

6. Final simplification 54.8%

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

Alternative 7: 39.9% 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. Add Preprocessing
3. Step-by-step derivation

   1. *-commutative 99.8%

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

   2. fma-neg 99.8%

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

   3. distribute-rgt-neg-in 99.8%

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

4. Applied egg-rr 99.8%

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

5. Taylor expanded in y around 0 39.5%

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

6. Final simplification 39.5%

   \[\leadsto x \]
7. Add Preprocessing

Reproduce

herbie shell --seed 2024031 
(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))))