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

Percentage Accurate: 99.8% → 99.8%

Time: 9.0s

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 99.8%

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

   1. fma-define 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. Add Preprocessing
5. Add Preprocessing

Alternative 2: 86.5% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -7 \cdot 10^{-71} \lor \neg \left(x \leq 1.46 \cdot 10^{-75}\right):\\ \;\;\;\;\mathsf{fma}\left(x, \sin y, z\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \cos y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -7e-71) (not (<= x 1.46e-75))) (fma x (sin y) z) (* z (cos y))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -7e-71) || !(x <= 1.46e-75)) {
		tmp = fma(x, sin(y), z);
	} else {
		tmp = z * cos(y);
	}
	return tmp;
}

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -7e-71) || !(x <= 1.46e-75))
		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, -7e-71], N[Not[LessEqual[x, 1.46e-75]], $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 < -6.9999999999999998e-71 or 1.45999999999999991e-75 < x

   1. Initial program 99.8%

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

      1. fma-define 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. Add Preprocessing

   5. Taylor expanded in y around 0 91.4%

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

   if -6.9999999999999998e-71 < x < 1.45999999999999991e-75

   1. Initial program 99.9%

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

      1. fma-define 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. Add Preprocessing

   5. Taylor expanded in x around 0 90.0%

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

4. Final simplification 90.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -7 \cdot 10^{-71} \lor \neg \left(x \leq 1.46 \cdot 10^{-75}\right):\\ \;\;\;\;\mathsf{fma}\left(x, \sin y, z\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \cos y\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 99.8% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.8%

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

3. Final simplification 99.8%

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

Alternative 4: 74.5% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x \cdot \sin y\\ t_1 := z \cdot \cos y\\ \mathbf{if}\;y \leq -5.5 \cdot 10^{+111}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;y \leq -5.4 \cdot 10^{+23}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq -0.022:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;y \leq 0.32:\\ \;\;\;\;z + y \cdot \left(x + y \cdot \left(z \cdot -0.5 + -0.16666666666666666 \cdot \left(x \cdot y\right)\right)\right)\\ \mathbf{elif}\;y \leq 1.95 \cdot 10^{+149}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* x (sin y))) (t_1 (* z (cos y))))
   (if (<= y -5.5e+111)
     t_0
     (if (<= y -5.4e+23)
       t_1
       (if (<= y -0.022)
         t_0
         (if (<= y 0.32)
           (+
            z
            (* y (+ x (* y (+ (* z -0.5) (* -0.16666666666666666 (* x y)))))))
           (if (<= y 1.95e+149) t_1 t_0)))))))

C

double code(double x, double y, double z) {
	double t_0 = x * sin(y);
	double t_1 = z * cos(y);
	double tmp;
	if (y <= -5.5e+111) {
		tmp = t_0;
	} else if (y <= -5.4e+23) {
		tmp = t_1;
	} else if (y <= -0.022) {
		tmp = t_0;
	} else if (y <= 0.32) {
		tmp = z + (y * (x + (y * ((z * -0.5) + (-0.16666666666666666 * (x * y))))));
	} else if (y <= 1.95e+149) {
		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 = x * sin(y)
    t_1 = z * cos(y)
    if (y <= (-5.5d+111)) then
        tmp = t_0
    else if (y <= (-5.4d+23)) then
        tmp = t_1
    else if (y <= (-0.022d0)) then
        tmp = t_0
    else if (y <= 0.32d0) then
        tmp = z + (y * (x + (y * ((z * (-0.5d0)) + ((-0.16666666666666666d0) * (x * y))))))
    else if (y <= 1.95d+149) 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 = x * Math.sin(y);
	double t_1 = z * Math.cos(y);
	double tmp;
	if (y <= -5.5e+111) {
		tmp = t_0;
	} else if (y <= -5.4e+23) {
		tmp = t_1;
	} else if (y <= -0.022) {
		tmp = t_0;
	} else if (y <= 0.32) {
		tmp = z + (y * (x + (y * ((z * -0.5) + (-0.16666666666666666 * (x * y))))));
	} else if (y <= 1.95e+149) {
		tmp = t_1;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = x * math.sin(y)
	t_1 = z * math.cos(y)
	tmp = 0
	if y <= -5.5e+111:
		tmp = t_0
	elif y <= -5.4e+23:
		tmp = t_1
	elif y <= -0.022:
		tmp = t_0
	elif y <= 0.32:
		tmp = z + (y * (x + (y * ((z * -0.5) + (-0.16666666666666666 * (x * y))))))
	elif y <= 1.95e+149:
		tmp = t_1
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(x * sin(y))
	t_1 = Float64(z * cos(y))
	tmp = 0.0
	if (y <= -5.5e+111)
		tmp = t_0;
	elseif (y <= -5.4e+23)
		tmp = t_1;
	elseif (y <= -0.022)
		tmp = t_0;
	elseif (y <= 0.32)
		tmp = Float64(z + Float64(y * Float64(x + Float64(y * Float64(Float64(z * -0.5) + Float64(-0.16666666666666666 * Float64(x * y)))))));
	elseif (y <= 1.95e+149)
		tmp = t_1;
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = x * sin(y);
	t_1 = z * cos(y);
	tmp = 0.0;
	if (y <= -5.5e+111)
		tmp = t_0;
	elseif (y <= -5.4e+23)
		tmp = t_1;
	elseif (y <= -0.022)
		tmp = t_0;
	elseif (y <= 0.32)
		tmp = z + (y * (x + (y * ((z * -0.5) + (-0.16666666666666666 * (x * y))))));
	elseif (y <= 1.95e+149)
		tmp = t_1;
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(x * N[Sin[y], $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(z * N[Cos[y], $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -5.5e+111], t$95$0, If[LessEqual[y, -5.4e+23], t$95$1, If[LessEqual[y, -0.022], t$95$0, If[LessEqual[y, 0.32], N[(z + N[(y * N[(x + N[(y * N[(N[(z * -0.5), $MachinePrecision] + N[(-0.16666666666666666 * N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.95e+149], t$95$1, t$95$0]]]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -5.4999999999999998e111 or -5.3999999999999997e23 < y < -0.021999999999999999 or 1.95e149 < y

   1. Initial program 99.7%

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

      1. fma-define 99.7%

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

   3. Simplified 99.7%

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

   5. Taylor expanded in x around inf 70.8%

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

   if -5.4999999999999998e111 < y < -5.3999999999999997e23 or 0.320000000000000007 < y < 1.95e149

   1. Initial program 99.7%

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

      1. fma-define 99.7%

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

   3. Simplified 99.7%

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

   5. Taylor expanded in x around 0 67.4%

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

   if -0.021999999999999999 < y < 0.320000000000000007

   1. Initial program 100.0%

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

      1. fma-define 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in y around 0 99.5%

      \[\leadsto \color{blue}{z + y \cdot \left(x + y \cdot \left(-0.5 \cdot z + -0.16666666666666666 \cdot \left(x \cdot y\right)\right)\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification 84.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -5.5 \cdot 10^{+111}:\\ \;\;\;\;x \cdot \sin y\\ \mathbf{elif}\;y \leq -5.4 \cdot 10^{+23}:\\ \;\;\;\;z \cdot \cos y\\ \mathbf{elif}\;y \leq -0.022:\\ \;\;\;\;x \cdot \sin y\\ \mathbf{elif}\;y \leq 0.32:\\ \;\;\;\;z + y \cdot \left(x + y \cdot \left(z \cdot -0.5 + -0.16666666666666666 \cdot \left(x \cdot y\right)\right)\right)\\ \mathbf{elif}\;y \leq 1.95 \cdot 10^{+149}:\\ \;\;\;\;z \cdot \cos y\\ \mathbf{else}:\\ \;\;\;\;x \cdot \sin y\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 86.5% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.65 \cdot 10^{-69} \lor \neg \left(x \leq 1.15 \cdot 10^{-75}\right):\\ \;\;\;\;z + x \cdot \sin y\\ \mathbf{else}:\\ \;\;\;\;z \cdot \cos y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -1.65e-69) (not (<= x 1.15e-75)))
   (+ z (* x (sin y)))
   (* z (cos y))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -1.65e-69) || !(x <= 1.15e-75)) {
		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 <= (-1.65d-69)) .or. (.not. (x <= 1.15d-75))) 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 <= -1.65e-69) || !(x <= 1.15e-75)) {
		tmp = z + (x * Math.sin(y));
	} else {
		tmp = z * Math.cos(y);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -1.65e-69) or not (x <= 1.15e-75):
		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 <= -1.65e-69) || !(x <= 1.15e-75))
		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 <= -1.65e-69) || ~((x <= 1.15e-75)))
		tmp = z + (x * sin(y));
	else
		tmp = z * cos(y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -1.65e-69], N[Not[LessEqual[x, 1.15e-75]], $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 < -1.65e-69 or 1.15e-75 < x

   1. Initial program 99.8%

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

   3. Taylor expanded in y around 0 91.4%

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

   if -1.65e-69 < x < 1.15e-75

   1. Initial program 99.9%

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

      1. fma-define 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. Add Preprocessing

   5. Taylor expanded in x around 0 90.0%

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

4. Final simplification 90.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.65 \cdot 10^{-69} \lor \neg \left(x \leq 1.15 \cdot 10^{-75}\right):\\ \;\;\;\;z + x \cdot \sin y\\ \mathbf{else}:\\ \;\;\;\;z \cdot \cos y\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 74.6% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -0.045 \lor \neg \left(y \leq 2.1 \cdot 10^{-6}\right):\\ \;\;\;\;x \cdot \sin y\\ \mathbf{else}:\\ \;\;\;\;z + y \cdot \left(x + y \cdot \left(z \cdot -0.5 + -0.16666666666666666 \cdot \left(x \cdot y\right)\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -0.045) (not (<= y 2.1e-6)))
   (* x (sin y))
   (+ z (* y (+ x (* y (+ (* z -0.5) (* -0.16666666666666666 (* x y)))))))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -0.045) || !(y <= 2.1e-6)) {
		tmp = x * sin(y);
	} else {
		tmp = z + (y * (x + (y * ((z * -0.5) + (-0.16666666666666666 * (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 <= (-0.045d0)) .or. (.not. (y <= 2.1d-6))) then
        tmp = x * sin(y)
    else
        tmp = z + (y * (x + (y * ((z * (-0.5d0)) + ((-0.16666666666666666d0) * (x * y))))))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((y <= -0.045) || !(y <= 2.1e-6)) {
		tmp = x * Math.sin(y);
	} else {
		tmp = z + (y * (x + (y * ((z * -0.5) + (-0.16666666666666666 * (x * y))))));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -0.045) or not (y <= 2.1e-6):
		tmp = x * math.sin(y)
	else:
		tmp = z + (y * (x + (y * ((z * -0.5) + (-0.16666666666666666 * (x * y))))))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -0.045) || !(y <= 2.1e-6))
		tmp = Float64(x * sin(y));
	else
		tmp = Float64(z + Float64(y * Float64(x + Float64(y * Float64(Float64(z * -0.5) + Float64(-0.16666666666666666 * Float64(x * y)))))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((y <= -0.045) || ~((y <= 2.1e-6)))
		tmp = x * sin(y);
	else
		tmp = z + (y * (x + (y * ((z * -0.5) + (-0.16666666666666666 * (x * y))))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -0.045], N[Not[LessEqual[y, 2.1e-6]], $MachinePrecision]], N[(x * N[Sin[y], $MachinePrecision]), $MachinePrecision], N[(z + N[(y * N[(x + N[(y * N[(N[(z * -0.5), $MachinePrecision] + N[(-0.16666666666666666 * N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -0.044999999999999998 or 2.0999999999999998e-6 < y

   1. Initial program 99.7%

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

      1. fma-define 99.7%

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

   3. Simplified 99.7%

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

   5. Taylor expanded in x around inf 56.7%

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

   if -0.044999999999999998 < y < 2.0999999999999998e-6

   1. Initial program 100.0%

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

      1. fma-define 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in y around 0 99.9%

      \[\leadsto \color{blue}{z + y \cdot \left(x + y \cdot \left(-0.5 \cdot z + -0.16666666666666666 \cdot \left(x \cdot y\right)\right)\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 77.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -0.045 \lor \neg \left(y \leq 2.1 \cdot 10^{-6}\right):\\ \;\;\;\;x \cdot \sin y\\ \mathbf{else}:\\ \;\;\;\;z + y \cdot \left(x + y \cdot \left(z \cdot -0.5 + -0.16666666666666666 \cdot \left(x \cdot y\right)\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 34.7% accurate, 13.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.5 \cdot 10^{+86} \lor \neg \left(x \leq 2.8 \cdot 10^{+206}\right):\\ \;\;\;\;x \cdot y\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{z}{x}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -1.5e+86) (not (<= x 2.8e+206))) (* x y) (* x (/ z x))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -1.5e+86) || !(x <= 2.8e+206)) {
		tmp = x * y;
	} else {
		tmp = x * (z / 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 <= (-1.5d+86)) .or. (.not. (x <= 2.8d+206))) then
        tmp = x * y
    else
        tmp = x * (z / x)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((x <= -1.5e+86) || !(x <= 2.8e+206)) {
		tmp = x * y;
	} else {
		tmp = x * (z / x);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -1.5e+86) or not (x <= 2.8e+206):
		tmp = x * y
	else:
		tmp = x * (z / x)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -1.5e+86) || !(x <= 2.8e+206))
		tmp = Float64(x * y);
	else
		tmp = Float64(x * Float64(z / x));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((x <= -1.5e+86) || ~((x <= 2.8e+206)))
		tmp = x * y;
	else
		tmp = x * (z / x);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -1.5e+86], N[Not[LessEqual[x, 2.8e+206]], $MachinePrecision]], N[(x * y), $MachinePrecision], N[(x * N[(z / x), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -1.49999999999999988e86 or 2.7999999999999998e206 < x

   1. Initial program 99.8%

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

      1. fma-define 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in y around 0 54.5%

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

      1. +-commutative 54.5%

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

   7. Simplified 54.5%

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

   8. Taylor expanded in x around inf 42.6%

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

      1. *-commutative 42.6%

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

   10. Simplified 42.6%

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

   if -1.49999999999999988e86 < x < 2.7999999999999998e206

   1. Initial program 99.9%

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

      1. fma-define 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. Add Preprocessing

   5. Taylor expanded in y around 0 50.1%

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

      1. +-commutative 50.1%

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

   7. Simplified 50.1%

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

   8. Taylor expanded in x around inf 44.5%

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

   9. Taylor expanded in y around 0 38.7%

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

4. Final simplification 40.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.5 \cdot 10^{+86} \lor \neg \left(x \leq 2.8 \cdot 10^{+206}\right):\\ \;\;\;\;x \cdot y\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{z}{x}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 51.9% 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. Step-by-step derivation

   1. fma-define 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. Add Preprocessing

5. Taylor expanded in y around 0 51.6%

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

   1. +-commutative 51.6%

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

7. Simplified 51.6%

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

8. Final simplification 51.6%

   \[\leadsto z + x \cdot y \]
9. Add Preprocessing

Alternative 9: 16.5% accurate, 69.0× speedup

Math

\[\begin{array}{l} \\ x \cdot y \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 (* x y))

C

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

Java

public static double code(double x, double y, double z) {
	return x * y;
}

Python

def code(x, y, z):
	return x * y

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.8%

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

   1. fma-define 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. Add Preprocessing

5. Taylor expanded in y around 0 51.6%

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

   1. +-commutative 51.6%

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

7. Simplified 51.6%

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

8. Taylor expanded in x around inf 20.2%

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

   1. *-commutative 20.2%

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

10. Simplified 20.2%

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

11. Final simplification 20.2%

    \[\leadsto x \cdot y \]
12. Add Preprocessing

Reproduce

herbie shell --seed 2024144 
(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))))