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

Percentage Accurate: 99.8% → 99.8%

Time: 14.5s

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, 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]

Derivation

1. Initial program 99.8%

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

2. Final simplification 99.8%

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

Alternative 2: 85.8% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -11000 \lor \neg \left(x \leq 2.25 \cdot 10^{-132}\right):\\ \;\;\;\;x \cdot \sin y + z\\ \mathbf{else}:\\ \;\;\;\;z \cdot \cos y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -11000.0) (not (<= x 2.25e-132)))
   (+ (* x (sin y)) z)
   (* z (cos y))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -11000.0) || !(x <= 2.25e-132)) {
		tmp = (x * sin(y)) + z;
	} else {
		tmp = z * 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 ((x <= (-11000.0d0)) .or. (.not. (x <= 2.25d-132))) then
        tmp = (x * sin(y)) + z
    else
        tmp = z * cos(y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((x <= -11000.0) || !(x <= 2.25e-132)) {
		tmp = (x * Math.sin(y)) + z;
	} else {
		tmp = z * Math.cos(y);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -11000.0) or not (x <= 2.25e-132):
		tmp = (x * math.sin(y)) + z
	else:
		tmp = z * math.cos(y)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -11000.0) || !(x <= 2.25e-132))
		tmp = Float64(Float64(x * sin(y)) + z);
	else
		tmp = Float64(z * cos(y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((x <= -11000.0) || ~((x <= 2.25e-132)))
		tmp = (x * sin(y)) + z;
	else
		tmp = z * cos(y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -11000.0], N[Not[LessEqual[x, 2.25e-132]], $MachinePrecision]], N[(N[(x * N[Sin[y], $MachinePrecision]), $MachinePrecision] + z), $MachinePrecision], N[(z * N[Cos[y], $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -11000 or 2.25e-132 < x

   1. Initial program 99.8%

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

   2. Taylor expanded in y around 0 87.7%

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

   if -11000 < x < 2.25e-132

   1. Initial program 99.8%

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

      1. +-commutative 99.8%

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

      2. add-sqr-sqrt 75.1%

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

      3. associate-*r* 75.1%

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

      4. fma-def 75.1%

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

   3. Applied egg-rr 75.1%

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

   4. Taylor expanded in y around 0 65.8%

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

   5. Taylor expanded in z around inf 89.1%

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

4. Final simplification 88.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -11000 \lor \neg \left(x \leq 2.25 \cdot 10^{-132}\right):\\ \;\;\;\;x \cdot \sin y + z\\ \mathbf{else}:\\ \;\;\;\;z \cdot \cos y\\ \end{array} \]

Alternative 3: 74.4% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.9 \cdot 10^{-8} \lor \neg \left(y \leq 6000\right):\\ \;\;\;\;z \cdot \cos y\\ \mathbf{else}:\\ \;\;\;\;z + x \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -1.9e-8) (not (<= y 6000.0))) (* z (cos y)) (+ z (* x y))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -1.9e-8) || !(y <= 6000.0)) {
		tmp = z * cos(y);
	} else {
		tmp = z + (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 ((y <= (-1.9d-8)) .or. (.not. (y <= 6000.0d0))) then
        tmp = z * cos(y)
    else
        tmp = z + (x * y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((y <= -1.9e-8) || !(y <= 6000.0)) {
		tmp = z * Math.cos(y);
	} else {
		tmp = z + (x * y);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -1.9e-8) or not (y <= 6000.0):
		tmp = z * math.cos(y)
	else:
		tmp = z + (x * y)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -1.9e-8) || !(y <= 6000.0))
		tmp = Float64(z * cos(y));
	else
		tmp = Float64(z + Float64(x * y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((y <= -1.9e-8) || ~((y <= 6000.0)))
		tmp = z * cos(y);
	else
		tmp = z + (x * y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -1.9e-8], N[Not[LessEqual[y, 6000.0]], $MachinePrecision]], N[(z * N[Cos[y], $MachinePrecision]), $MachinePrecision], N[(z + N[(x * y), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -1.90000000000000014e-8 or 6e3 < y

   1. Initial program 99.7%

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

      1. +-commutative 99.7%

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

      2. add-sqr-sqrt 55.7%

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

      3. associate-*r* 55.7%

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

      4. fma-def 55.7%

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

   3. Applied egg-rr 55.7%

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

   4. Taylor expanded in y around 0 21.7%

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

   5. Taylor expanded in z around inf 51.9%

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

   if -1.90000000000000014e-8 < y < 6e3

   1. Initial program 100.0%

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

   2. Taylor expanded in y around 0 97.7%

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

4. Final simplification 73.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.9 \cdot 10^{-8} \lor \neg \left(y \leq 6000\right):\\ \;\;\;\;z \cdot \cos y\\ \mathbf{else}:\\ \;\;\;\;z + x \cdot y\\ \end{array} \]

Alternative 4: 73.3% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.5 \cdot 10^{+22} \lor \neg \left(x \leq 3.8 \cdot 10^{+147}\right):\\ \;\;\;\;x \cdot \sin y\\ \mathbf{else}:\\ \;\;\;\;z \cdot \cos y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -1.5e+22) (not (<= x 3.8e+147))) (* x (sin y)) (* z (cos y))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -1.5e+22) || !(x <= 3.8e+147)) {
		tmp = x * sin(y);
	} else {
		tmp = z * 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 ((x <= (-1.5d+22)) .or. (.not. (x <= 3.8d+147))) then
        tmp = x * sin(y)
    else
        tmp = z * cos(y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((x <= -1.5e+22) || !(x <= 3.8e+147)) {
		tmp = x * Math.sin(y);
	} else {
		tmp = z * Math.cos(y);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -1.5e+22) or not (x <= 3.8e+147):
		tmp = x * math.sin(y)
	else:
		tmp = z * math.cos(y)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -1.5e+22) || !(x <= 3.8e+147))
		tmp = Float64(x * sin(y));
	else
		tmp = Float64(z * cos(y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((x <= -1.5e+22) || ~((x <= 3.8e+147)))
		tmp = x * sin(y);
	else
		tmp = z * cos(y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -1.5e+22], N[Not[LessEqual[x, 3.8e+147]], $MachinePrecision]], N[(x * N[Sin[y], $MachinePrecision]), $MachinePrecision], N[(z * N[Cos[y], $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -1.5e22 or 3.7999999999999997e147 < x

   1. Initial program 99.8%

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

      1. +-commutative 99.8%

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

      2. *-commutative 99.8%

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

      3. add-cube-cbrt 99.7%

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

      4. associate-*l* 99.8%

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

      5. fma-def 99.8%

         \[\leadsto \color{blue}{\mathsf{fma}\left(\sqrt[3]{\cos y} \cdot \sqrt[3]{\cos y}, \sqrt[3]{\cos y} \cdot z, x \cdot \sin y\right)} \]

      6. pow2 99.8%

         \[\leadsto \mathsf{fma}\left(\color{blue}{{\left(\sqrt[3]{\cos y}\right)}^{2}}, \sqrt[3]{\cos y} \cdot z, x \cdot \sin y\right) \]

   3. Applied egg-rr 99.8%

      \[\leadsto \color{blue}{\mathsf{fma}\left({\left(\sqrt[3]{\cos y}\right)}^{2}, \sqrt[3]{\cos y} \cdot z, x \cdot \sin y\right)} \]

   4. Taylor expanded in y around inf 99.8%

      \[\leadsto \mathsf{fma}\left(\color{blue}{{\left({\cos y}^{2}\right)}^{0.3333333333333333}}, \sqrt[3]{\cos y} \cdot z, x \cdot \sin y\right) \]

   5. Taylor expanded in z around 0 74.6%

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

   if -1.5e22 < x < 3.7999999999999997e147

   1. Initial program 99.8%

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

      1. +-commutative 99.8%

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

      2. add-sqr-sqrt 77.7%

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

      3. associate-*r* 77.7%

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

      4. fma-def 77.7%

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

   3. Applied egg-rr 77.7%

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

   4. Taylor expanded in y around 0 64.6%

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

   5. Taylor expanded in z around inf 81.2%

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

4. Final simplification 78.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.5 \cdot 10^{+22} \lor \neg \left(x \leq 3.8 \cdot 10^{+147}\right):\\ \;\;\;\;x \cdot \sin y\\ \mathbf{else}:\\ \;\;\;\;z \cdot \cos y\\ \end{array} \]

Alternative 5: 42.0% accurate, 29.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -4.2 \cdot 10^{+116}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;x \leq 3.6 \cdot 10^{+145}:\\ \;\;\;\;z\\ \mathbf{else}:\\ \;\;\;\;x \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -4.2e+116) (* x y) (if (<= x 3.6e+145) z (* x y))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -4.2e+116) {
		tmp = x * y;
	} else if (x <= 3.6e+145) {
		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 <= (-4.2d+116)) then
        tmp = x * y
    else if (x <= 3.6d+145) 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 <= -4.2e+116) {
		tmp = x * y;
	} else if (x <= 3.6e+145) {
		tmp = z;
	} else {
		tmp = x * y;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= -4.2e+116:
		tmp = x * y
	elif x <= 3.6e+145:
		tmp = z
	else:
		tmp = x * y
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -4.2e+116)
		tmp = Float64(x * y);
	elseif (x <= 3.6e+145)
		tmp = z;
	else
		tmp = Float64(x * y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (x <= -4.2e+116)
		tmp = x * y;
	elseif (x <= 3.6e+145)
		tmp = z;
	else
		tmp = x * y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -4.2e+116], N[(x * y), $MachinePrecision], If[LessEqual[x, 3.6e+145], z, N[(x * y), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if x < -4.2000000000000002e116 or 3.59999999999999974e145 < x

   1. Initial program 99.8%

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

   2. Taylor expanded in y around 0 46.0%

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

   3. Taylor expanded in y around inf 33.3%

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

   if -4.2000000000000002e116 < x < 3.59999999999999974e145

   1. Initial program 99.8%

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

      1. +-commutative 99.8%

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

      2. *-commutative 99.8%

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

      3. add-cube-cbrt 99.2%

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

      4. associate-*l* 99.2%

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

      5. fma-def 99.2%

         \[\leadsto \color{blue}{\mathsf{fma}\left(\sqrt[3]{\cos y} \cdot \sqrt[3]{\cos y}, \sqrt[3]{\cos y} \cdot z, x \cdot \sin y\right)} \]

      6. pow2 99.2%

         \[\leadsto \mathsf{fma}\left(\color{blue}{{\left(\sqrt[3]{\cos y}\right)}^{2}}, \sqrt[3]{\cos y} \cdot z, x \cdot \sin y\right) \]

   3. Applied egg-rr 99.2%

      \[\leadsto \color{blue}{\mathsf{fma}\left({\left(\sqrt[3]{\cos y}\right)}^{2}, \sqrt[3]{\cos y} \cdot z, x \cdot \sin y\right)} \]

   4. Taylor expanded in y around inf 99.6%

      \[\leadsto \mathsf{fma}\left(\color{blue}{{\left({\cos y}^{2}\right)}^{0.3333333333333333}}, \sqrt[3]{\cos y} \cdot z, x \cdot \sin y\right) \]

   5. Taylor expanded in y around 0 48.2%

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

4. Final simplification 43.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -4.2 \cdot 10^{+116}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;x \leq 3.6 \cdot 10^{+145}:\\ \;\;\;\;z\\ \mathbf{else}:\\ \;\;\;\;x \cdot y\\ \end{array} \]

Alternative 6: 52.8% 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. Taylor expanded in y around 0 50.7%

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

3. Final simplification 50.7%

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

Alternative 7: 39.6% 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. Step-by-step derivation

   1. +-commutative 99.8%

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

   2. *-commutative 99.8%

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

   3. add-cube-cbrt 99.3%

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

   4. associate-*l* 99.3%

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

   5. fma-def 99.3%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\sqrt[3]{\cos y} \cdot \sqrt[3]{\cos y}, \sqrt[3]{\cos y} \cdot z, x \cdot \sin y\right)} \]

   6. pow2 99.3%

      \[\leadsto \mathsf{fma}\left(\color{blue}{{\left(\sqrt[3]{\cos y}\right)}^{2}}, \sqrt[3]{\cos y} \cdot z, x \cdot \sin y\right) \]

3. Applied egg-rr 99.3%

   \[\leadsto \color{blue}{\mathsf{fma}\left({\left(\sqrt[3]{\cos y}\right)}^{2}, \sqrt[3]{\cos y} \cdot z, x \cdot \sin y\right)} \]

4. Taylor expanded in y around inf 99.6%

   \[\leadsto \mathsf{fma}\left(\color{blue}{{\left({\cos y}^{2}\right)}^{0.3333333333333333}}, \sqrt[3]{\cos y} \cdot z, x \cdot \sin y\right) \]

5. Taylor expanded in y around 0 38.7%

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

6. Final simplification 38.7%

   \[\leadsto z \]

Reproduce

herbie shell --seed 2023278 
(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))))