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

Percentage Accurate: 99.8% → 99.8%

Time: 6.6s

Alternatives: 9

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, 0.7× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 99.9%

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

   1. fma-def 99.9%

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

3. Simplified 99.9%

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

4. Final simplification 99.9%

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

Alternative 2: 84.7% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.95 \cdot 10^{-181} \lor \neg \left(x \leq 2.7 \cdot 10^{-16}\right):\\ \;\;\;\;\mathsf{fma}\left(x, \sin y, z\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \cos y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -1.95e-181) (not (<= x 2.7e-16)))
   (fma x (sin y) z)
   (* z (cos y))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -1.95e-181) || !(x <= 2.7e-16)) {
		tmp = fma(x, sin(y), z);
	} else {
		tmp = z * cos(y);
	}
	return tmp;
}

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -1.95e-181) || !(x <= 2.7e-16))
		tmp = fma(x, sin(y), z);
	else
		tmp = Float64(z * cos(y));
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -1.95e-181], N[Not[LessEqual[x, 2.7e-16]], $MachinePrecision]], N[(x * N[Sin[y], $MachinePrecision] + z), $MachinePrecision], N[(z * N[Cos[y], $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -1.95e-181 or 2.69999999999999999e-16 < x

   1. Initial program 99.9%

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

      1. fma-def 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in y around 0 86.5%

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

   if -1.95e-181 < x < 2.69999999999999999e-16

   1. Initial program 99.9%

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

      1. add-sqr-sqrt 51.7%

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

      2. associate-*r* 51.7%

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

      3. fma-def 51.7%

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

   3. Applied egg-rr 51.7%

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

   4. Taylor expanded in x around 0 90.6%

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

4. Final simplification 87.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.95 \cdot 10^{-181} \lor \neg \left(x \leq 2.7 \cdot 10^{-16}\right):\\ \;\;\;\;\mathsf{fma}\left(x, \sin y, z\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \cos y\\ \end{array} \]

Alternative 3: 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 99.9%

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

2. Final simplification 99.9%

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

Alternative 4: 84.7% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -4.9 \cdot 10^{-181} \lor \neg \left(x \leq 2.25 \cdot 10^{-13}\right):\\ \;\;\;\;z + x \cdot \sin y\\ \mathbf{else}:\\ \;\;\;\;z \cdot \cos y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -4.9e-181) (not (<= x 2.25e-13)))
   (+ z (* x (sin y)))
   (* z (cos y))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -4.9e-181) || !(x <= 2.25e-13)) {
		tmp = z + (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 <= (-4.9d-181)) .or. (.not. (x <= 2.25d-13))) then
        tmp = z + (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 <= -4.9e-181) || !(x <= 2.25e-13)) {
		tmp = z + (x * Math.sin(y));
	} else {
		tmp = z * Math.cos(y);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -4.9e-181) or not (x <= 2.25e-13):
		tmp = z + (x * math.sin(y))
	else:
		tmp = z * math.cos(y)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -4.9e-181) || !(x <= 2.25e-13))
		tmp = Float64(z + 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 <= -4.9e-181) || ~((x <= 2.25e-13)))
		tmp = z + (x * sin(y));
	else
		tmp = z * cos(y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -4.9e-181], N[Not[LessEqual[x, 2.25e-13]], $MachinePrecision]], N[(z + N[(x * N[Sin[y], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(z * N[Cos[y], $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -4.89999999999999963e-181 or 2.25e-13 < x

   1. Initial program 99.9%

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

   2. Taylor expanded in y around 0 86.5%

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

   if -4.89999999999999963e-181 < x < 2.25e-13

   1. Initial program 99.9%

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

      1. add-sqr-sqrt 51.7%

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

      2. associate-*r* 51.7%

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

      3. fma-def 51.7%

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

   3. Applied egg-rr 51.7%

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

   4. Taylor expanded in x around 0 90.6%

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

4. Final simplification 87.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -4.9 \cdot 10^{-181} \lor \neg \left(x \leq 2.25 \cdot 10^{-13}\right):\\ \;\;\;\;z + x \cdot \sin y\\ \mathbf{else}:\\ \;\;\;\;z \cdot \cos y\\ \end{array} \]

Alternative 5: 74.4% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.8 \cdot 10^{-5} \lor \neg \left(y \leq 0.0027\right):\\ \;\;\;\;z \cdot \cos y\\ \mathbf{else}:\\ \;\;\;\;z + x \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -1.8e-5) (not (<= y 0.0027))) (* z (cos y)) (+ z (* x y))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -1.8e-5) || !(y <= 0.0027)) {
		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 <= (-1.8d-5)) .or. (.not. (y <= 0.0027d0))) 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 <= -1.8e-5) || !(y <= 0.0027)) {
		tmp = z * Math.cos(y);
	} else {
		tmp = z + (x * y);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -1.8e-5) or not (y <= 0.0027):
		tmp = z * math.cos(y)
	else:
		tmp = z + (x * y)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -1.8e-5) || !(y <= 0.0027))
		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 <= -1.8e-5) || ~((y <= 0.0027)))
		tmp = z * cos(y);
	else
		tmp = z + (x * y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -1.8e-5], N[Not[LessEqual[y, 0.0027]], $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 < -1.80000000000000005e-5 or 0.0027000000000000001 < y

   1. Initial program 99.7%

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

      1. add-sqr-sqrt 45.2%

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

      2. associate-*r* 45.3%

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

      3. fma-def 45.3%

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

   3. Applied egg-rr 45.3%

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

   4. Taylor expanded in x around 0 54.8%

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

   if -1.80000000000000005e-5 < y < 0.0027000000000000001

   1. Initial program 100.0%

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

   2. Taylor expanded in y around 0 99.9%

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

4. Final simplification 78.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.8 \cdot 10^{-5} \lor \neg \left(y \leq 0.0027\right):\\ \;\;\;\;z \cdot \cos y\\ \mathbf{else}:\\ \;\;\;\;z + x \cdot y\\ \end{array} \]

Alternative 6: 74.4% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.4 \cdot 10^{-5} \lor \neg \left(y \leq 0.00021\right):\\ \;\;\;\;z \cdot \cos y\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(y, x, z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -2.4e-5) (not (<= y 0.00021))) (* z (cos y)) (fma y x z)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -2.4e-5) || !(y <= 0.00021)) {
		tmp = z * cos(y);
	} else {
		tmp = fma(y, x, z);
	}
	return tmp;
}

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -2.4e-5) || !(y <= 0.00021))
		tmp = Float64(z * cos(y));
	else
		tmp = fma(y, x, z);
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -2.4e-5], N[Not[LessEqual[y, 0.00021]], $MachinePrecision]], N[(z * N[Cos[y], $MachinePrecision]), $MachinePrecision], N[(y * x + z), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -2.4000000000000001e-5 or 2.1000000000000001e-4 < y

   1. Initial program 99.7%

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

      1. add-sqr-sqrt 45.2%

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

      2. associate-*r* 45.3%

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

      3. fma-def 45.3%

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

   3. Applied egg-rr 45.3%

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

   4. Taylor expanded in x around 0 54.8%

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

   if -2.4000000000000001e-5 < y < 2.1000000000000001e-4

   1. Initial program 100.0%

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

   2. Taylor expanded in y around 0 99.9%

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

      1. fma-def 99.9%

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

   4. Simplified 99.9%

      \[\leadsto \color{blue}{\mathsf{fma}\left(y, x, z\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 78.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.4 \cdot 10^{-5} \lor \neg \left(y \leq 0.00021\right):\\ \;\;\;\;z \cdot \cos y\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(y, x, z\right)\\ \end{array} \]

Alternative 7: 42.1% accurate, 29.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.9 \cdot 10^{-137}:\\ \;\;\;\;z\\ \mathbf{elif}\;z \leq 4.4 \cdot 10^{-204}:\\ \;\;\;\;x \cdot y\\ \mathbf{else}:\\ \;\;\;\;z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -1.9e-137) z (if (<= z 4.4e-204) (* x y) z)))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -1.9e-137) {
		tmp = z;
	} else if (z <= 4.4e-204) {
		tmp = x * y;
	} else {
		tmp = 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 (z <= (-1.9d-137)) then
        tmp = z
    else if (z <= 4.4d-204) then
        tmp = x * y
    else
        tmp = z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (z <= -1.9e-137) {
		tmp = z;
	} else if (z <= 4.4e-204) {
		tmp = x * y;
	} else {
		tmp = z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -1.9e-137:
		tmp = z
	elif z <= 4.4e-204:
		tmp = x * y
	else:
		tmp = z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -1.9e-137)
		tmp = z;
	elseif (z <= 4.4e-204)
		tmp = Float64(x * y);
	else
		tmp = z;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= -1.9e-137)
		tmp = z;
	elseif (z <= 4.4e-204)
		tmp = x * y;
	else
		tmp = z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -1.9e-137], z, If[LessEqual[z, 4.4e-204], N[(x * y), $MachinePrecision], z]]

Derivation

1. Split input into 2 regimes

2. if z < -1.89999999999999999e-137 or 4.3999999999999997e-204 < z

   1. Initial program 99.9%

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

   2. Taylor expanded in y around 0 55.8%

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

   3. Taylor expanded in y around 0 48.5%

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

   if -1.89999999999999999e-137 < z < 4.3999999999999997e-204

   1. Initial program 99.8%

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

   2. Taylor expanded in y around 0 54.8%

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

   3. Taylor expanded in y around inf 47.1%

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

4. Final simplification 48.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.9 \cdot 10^{-137}:\\ \;\;\;\;z\\ \mathbf{elif}\;z \leq 4.4 \cdot 10^{-204}:\\ \;\;\;\;x \cdot y\\ \mathbf{else}:\\ \;\;\;\;z\\ \end{array} \]

Alternative 8: 52.2% 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 99.9%

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

2. Taylor expanded in y around 0 55.6%

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

3. Final simplification 55.6%

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

Alternative 9: 39.2% 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 99.9%

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

2. Taylor expanded in y around 0 55.6%

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

3. Taylor expanded in y around 0 40.2%

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

4. Final simplification 40.2%

   \[\leadsto z \]

Reproduce

herbie shell --seed 2023221 
(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))))