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

Percentage Accurate: 99.8% → 99.8%

Time: 9.0s

Alternatives: 8

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. Add Preprocessing
3. Add Preprocessing

Alternative 2: 79.7% accurate, 1.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.6 \cdot 10^{-99}:\\ \;\;\;\;z \cdot \left(1 + x \cdot \frac{\sin y}{z}\right)\\ \mathbf{elif}\;x \leq 2.5 \cdot 10^{-53}:\\ \;\;\;\;z \cdot \cos y\\ \mathbf{elif}\;x \leq 3.5 \cdot 10^{+223}:\\ \;\;\;\;z \cdot \left(1 + \frac{x}{\frac{z}{\sin y}}\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \sin y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -1.6e-99)
   (* z (+ 1.0 (* x (/ (sin y) z))))
   (if (<= x 2.5e-53)
     (* z (cos y))
     (if (<= x 3.5e+223) (* z (+ 1.0 (/ x (/ z (sin y))))) (* x (sin y))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -1.6e-99) {
		tmp = z * (1.0 + (x * (sin(y) / z)));
	} else if (x <= 2.5e-53) {
		tmp = z * cos(y);
	} else if (x <= 3.5e+223) {
		tmp = z * (1.0 + (x / (z / sin(y))));
	} else {
		tmp = x * 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 <= (-1.6d-99)) then
        tmp = z * (1.0d0 + (x * (sin(y) / z)))
    else if (x <= 2.5d-53) then
        tmp = z * cos(y)
    else if (x <= 3.5d+223) then
        tmp = z * (1.0d0 + (x / (z / sin(y))))
    else
        tmp = x * sin(y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (x <= -1.6e-99) {
		tmp = z * (1.0 + (x * (Math.sin(y) / z)));
	} else if (x <= 2.5e-53) {
		tmp = z * Math.cos(y);
	} else if (x <= 3.5e+223) {
		tmp = z * (1.0 + (x / (z / Math.sin(y))));
	} else {
		tmp = x * Math.sin(y);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= -1.6e-99:
		tmp = z * (1.0 + (x * (math.sin(y) / z)))
	elif x <= 2.5e-53:
		tmp = z * math.cos(y)
	elif x <= 3.5e+223:
		tmp = z * (1.0 + (x / (z / math.sin(y))))
	else:
		tmp = x * math.sin(y)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -1.6e-99)
		tmp = Float64(z * Float64(1.0 + Float64(x * Float64(sin(y) / z))));
	elseif (x <= 2.5e-53)
		tmp = Float64(z * cos(y));
	elseif (x <= 3.5e+223)
		tmp = Float64(z * Float64(1.0 + Float64(x / Float64(z / sin(y)))));
	else
		tmp = Float64(x * sin(y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (x <= -1.6e-99)
		tmp = z * (1.0 + (x * (sin(y) / z)));
	elseif (x <= 2.5e-53)
		tmp = z * cos(y);
	elseif (x <= 3.5e+223)
		tmp = z * (1.0 + (x / (z / sin(y))));
	else
		tmp = x * sin(y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -1.6e-99], N[(z * N[(1.0 + N[(x * N[(N[Sin[y], $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 2.5e-53], N[(z * N[Cos[y], $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 3.5e+223], N[(z * N[(1.0 + N[(x / N[(z / N[Sin[y], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x * N[Sin[y], $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if x < -1.6e-99

   1. Initial program 99.8%

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

      1. expm1-log1p-u 99.7%

         \[\leadsto x \cdot \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(\sin y\right)\right)} + z \cdot \cos y \]

   4. Applied egg-rr 99.7%

      \[\leadsto x \cdot \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(\sin y\right)\right)} + z \cdot \cos y \]

   5. Taylor expanded in y around 0 83.7%

      \[\leadsto x \cdot \mathsf{expm1}\left(\mathsf{log1p}\left(\sin y\right)\right) + \color{blue}{z} \]

   6. Taylor expanded in z around inf 74.4%

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

      1. associate-/l* 74.4%

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

   8. Simplified 74.4%

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

   if -1.6e-99 < x < 2.5e-53

   1. Initial program 99.9%

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

   3. Taylor expanded in x around 0 90.9%

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

   if 2.5e-53 < x < 3.5000000000000001e223

   1. Initial program 99.8%

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

      1. expm1-log1p-u 99.8%

         \[\leadsto x \cdot \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(\sin y\right)\right)} + z \cdot \cos y \]

   4. Applied egg-rr 99.8%

      \[\leadsto x \cdot \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(\sin y\right)\right)} + z \cdot \cos y \]

   5. Taylor expanded in y around 0 82.0%

      \[\leadsto x \cdot \mathsf{expm1}\left(\mathsf{log1p}\left(\sin y\right)\right) + \color{blue}{z} \]

   6. Taylor expanded in z around inf 80.0%

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

      1. associate-/l* 79.8%

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

   8. Simplified 79.8%

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

      1. clear-num 79.8%

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

      2. un-div-inv 79.9%

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

   10. Applied egg-rr 79.9%

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

   if 3.5000000000000001e223 < x

   1. Initial program 99.7%

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

   3. Taylor expanded in x around inf 89.0%

      \[\leadsto \color{blue}{x \cdot \sin y} \]
3. Recombined 4 regimes into one program.
4. Add Preprocessing

Alternative 3: 79.7% accurate, 1.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := z \cdot \left(1 + x \cdot \frac{\sin y}{z}\right)\\ \mathbf{if}\;x \leq -5.5 \cdot 10^{-99}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;x \leq 4.8 \cdot 10^{-50}:\\ \;\;\;\;z \cdot \cos y\\ \mathbf{elif}\;x \leq 8.5 \cdot 10^{+212}:\\ \;\;\;\;t\_0\\ \mathbf{else}:\\ \;\;\;\;x \cdot \sin y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* z (+ 1.0 (* x (/ (sin y) z))))))
   (if (<= x -5.5e-99)
     t_0
     (if (<= x 4.8e-50)
       (* z (cos y))
       (if (<= x 8.5e+212) t_0 (* x (sin y)))))))

C

double code(double x, double y, double z) {
	double t_0 = z * (1.0 + (x * (sin(y) / z)));
	double tmp;
	if (x <= -5.5e-99) {
		tmp = t_0;
	} else if (x <= 4.8e-50) {
		tmp = z * cos(y);
	} else if (x <= 8.5e+212) {
		tmp = t_0;
	} else {
		tmp = x * 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) :: t_0
    real(8) :: tmp
    t_0 = z * (1.0d0 + (x * (sin(y) / z)))
    if (x <= (-5.5d-99)) then
        tmp = t_0
    else if (x <= 4.8d-50) then
        tmp = z * cos(y)
    else if (x <= 8.5d+212) then
        tmp = t_0
    else
        tmp = x * sin(y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = z * (1.0 + (x * (Math.sin(y) / z)));
	double tmp;
	if (x <= -5.5e-99) {
		tmp = t_0;
	} else if (x <= 4.8e-50) {
		tmp = z * Math.cos(y);
	} else if (x <= 8.5e+212) {
		tmp = t_0;
	} else {
		tmp = x * Math.sin(y);
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = z * (1.0 + (x * (math.sin(y) / z)))
	tmp = 0
	if x <= -5.5e-99:
		tmp = t_0
	elif x <= 4.8e-50:
		tmp = z * math.cos(y)
	elif x <= 8.5e+212:
		tmp = t_0
	else:
		tmp = x * math.sin(y)
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(z * Float64(1.0 + Float64(x * Float64(sin(y) / z))))
	tmp = 0.0
	if (x <= -5.5e-99)
		tmp = t_0;
	elseif (x <= 4.8e-50)
		tmp = Float64(z * cos(y));
	elseif (x <= 8.5e+212)
		tmp = t_0;
	else
		tmp = Float64(x * sin(y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = z * (1.0 + (x * (sin(y) / z)));
	tmp = 0.0;
	if (x <= -5.5e-99)
		tmp = t_0;
	elseif (x <= 4.8e-50)
		tmp = z * cos(y);
	elseif (x <= 8.5e+212)
		tmp = t_0;
	else
		tmp = x * sin(y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(z * N[(1.0 + N[(x * N[(N[Sin[y], $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -5.5e-99], t$95$0, If[LessEqual[x, 4.8e-50], N[(z * N[Cos[y], $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 8.5e+212], t$95$0, N[(x * N[Sin[y], $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if x < -5.49999999999999991e-99 or 4.80000000000000004e-50 < x < 8.49999999999999979e212

   1. Initial program 99.8%

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

      1. expm1-log1p-u 99.8%

         \[\leadsto x \cdot \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(\sin y\right)\right)} + z \cdot \cos y \]

   4. Applied egg-rr 99.8%

      \[\leadsto x \cdot \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(\sin y\right)\right)} + z \cdot \cos y \]

   5. Taylor expanded in y around 0 82.9%

      \[\leadsto x \cdot \mathsf{expm1}\left(\mathsf{log1p}\left(\sin y\right)\right) + \color{blue}{z} \]

   6. Taylor expanded in z around inf 76.7%

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

      1. associate-/l* 76.6%

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

   8. Simplified 76.6%

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

   if -5.49999999999999991e-99 < x < 4.80000000000000004e-50

   1. Initial program 99.9%

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

   3. Taylor expanded in x around 0 90.9%

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

   if 8.49999999999999979e212 < x

   1. Initial program 99.7%

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

   3. Taylor expanded in x around inf 89.0%

      \[\leadsto \color{blue}{x \cdot \sin y} \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 4: 76.0% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -0.046 \lor \neg \left(y \leq 2.25 \cdot 10^{-8}\right):\\ \;\;\;\;z \cdot \cos y\\ \mathbf{else}:\\ \;\;\;\;z + y \cdot \left(x + y \cdot \left(z \cdot -0.5 + -0.16666666666666666 \cdot \left(x \cdot y\right)\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -0.046) (not (<= y 2.25e-8)))
   (* z (cos 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 <= -0.046) || !(y <= 2.25e-8)) {
		tmp = z * cos(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 <= (-0.046d0)) .or. (.not. (y <= 2.25d-8))) then
        tmp = z * cos(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 <= -0.046) || !(y <= 2.25e-8)) {
		tmp = z * Math.cos(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 <= -0.046) or not (y <= 2.25e-8):
		tmp = z * math.cos(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 <= -0.046) || !(y <= 2.25e-8))
		tmp = Float64(z * cos(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 <= -0.046) || ~((y <= 2.25e-8)))
		tmp = z * cos(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, -0.046], N[Not[LessEqual[y, 2.25e-8]], $MachinePrecision]], N[(z * N[Cos[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 < -0.045999999999999999 or 2.24999999999999996e-8 < y

   1. Initial program 99.6%

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

   3. Taylor expanded in x around 0 59.3%

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

   if -0.045999999999999999 < y < 2.24999999999999996e-8

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 99.4%

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

4. Final simplification 79.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -0.046 \lor \neg \left(y \leq 2.25 \cdot 10^{-8}\right):\\ \;\;\;\;z \cdot \cos y\\ \mathbf{else}:\\ \;\;\;\;z + y \cdot \left(x + y \cdot \left(z \cdot -0.5 + -0.16666666666666666 \cdot \left(x \cdot y\right)\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 74.8% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -0.032 \lor \neg \left(y \leq 0.26\right):\\ \;\;\;\;x \cdot \sin y\\ \mathbf{else}:\\ \;\;\;\;z + y \cdot \left(x + -0.5 \cdot \left(y \cdot z\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -0.032) (not (<= y 0.26)))
   (* x (sin y))
   (+ z (* y (+ x (* -0.5 (* y z)))))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -0.032) || !(y <= 0.26)) {
		tmp = x * sin(y);
	} else {
		tmp = z + (y * (x + (-0.5 * (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 <= (-0.032d0)) .or. (.not. (y <= 0.26d0))) then
        tmp = x * sin(y)
    else
        tmp = z + (y * (x + ((-0.5d0) * (y * z))))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((y <= -0.032) || !(y <= 0.26)) {
		tmp = x * Math.sin(y);
	} else {
		tmp = z + (y * (x + (-0.5 * (y * z))));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -0.032) or not (y <= 0.26):
		tmp = x * math.sin(y)
	else:
		tmp = z + (y * (x + (-0.5 * (y * z))))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -0.032) || !(y <= 0.26))
		tmp = Float64(x * sin(y));
	else
		tmp = Float64(z + Float64(y * Float64(x + Float64(-0.5 * Float64(y * z)))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((y <= -0.032) || ~((y <= 0.26)))
		tmp = x * sin(y);
	else
		tmp = z + (y * (x + (-0.5 * (y * z))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -0.032], N[Not[LessEqual[y, 0.26]], $MachinePrecision]], N[(x * N[Sin[y], $MachinePrecision]), $MachinePrecision], N[(z + N[(y * N[(x + N[(-0.5 * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -0.032000000000000001 or 0.26000000000000001 < y

   1. Initial program 99.6%

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

   3. Taylor expanded in x around inf 44.1%

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

   if -0.032000000000000001 < y < 0.26000000000000001

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 99.3%

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

4. Final simplification 71.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -0.032 \lor \neg \left(y \leq 0.26\right):\\ \;\;\;\;x \cdot \sin y\\ \mathbf{else}:\\ \;\;\;\;z + y \cdot \left(x + -0.5 \cdot \left(y \cdot z\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 41.5% accurate, 15.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -5.5 \cdot 10^{+70} \lor \neg \left(x \leq 6.5 \cdot 10^{+218}\right):\\ \;\;\;\;x \cdot y\\ \mathbf{else}:\\ \;\;\;\;z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -5.5e+70) (not (<= x 6.5e+218))) (* x y) z))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -5.5e+70) || !(x <= 6.5e+218)) {
		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 ((x <= (-5.5d+70)) .or. (.not. (x <= 6.5d+218))) 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 ((x <= -5.5e+70) || !(x <= 6.5e+218)) {
		tmp = x * y;
	} else {
		tmp = z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -5.5e+70) or not (x <= 6.5e+218):
		tmp = x * y
	else:
		tmp = z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -5.5e+70) || !(x <= 6.5e+218))
		tmp = Float64(x * y);
	else
		tmp = z;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((x <= -5.5e+70) || ~((x <= 6.5e+218)))
		tmp = x * y;
	else
		tmp = z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -5.5e+70], N[Not[LessEqual[x, 6.5e+218]], $MachinePrecision]], N[(x * y), $MachinePrecision], z]

Derivation

1. Split input into 2 regimes

2. if x < -5.49999999999999986e70 or 6.4999999999999999e218 < x

   1. Initial program 99.7%

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

   3. Taylor expanded in y around 0 51.1%

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

      1. +-commutative 51.1%

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

   5. Simplified 51.1%

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

   6. Taylor expanded in x around inf 51.0%

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

   7. Taylor expanded in x around inf 35.5%

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

      1. *-commutative 35.5%

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

   9. Simplified 35.5%

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

   if -5.49999999999999986e70 < x < 6.4999999999999999e218

   1. Initial program 99.8%

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

      1. expm1-log1p-u 99.8%

         \[\leadsto x \cdot \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(\sin y\right)\right)} + z \cdot \cos y \]

   4. Applied egg-rr 99.8%

      \[\leadsto x \cdot \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(\sin y\right)\right)} + z \cdot \cos y \]

   5. Taylor expanded in y around 0 49.9%

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

4. Final simplification 46.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -5.5 \cdot 10^{+70} \lor \neg \left(x \leq 6.5 \cdot 10^{+218}\right):\\ \;\;\;\;x \cdot y\\ \mathbf{else}:\\ \;\;\;\;z\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 53.4% 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. Add Preprocessing

3. Taylor expanded in y around 0 53.5%

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

   1. +-commutative 53.5%

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

5. Simplified 53.5%

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

6. Final simplification 53.5%

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

Alternative 8: 39.1% 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. Add Preprocessing
3. Step-by-step derivation

   1. expm1-log1p-u 99.8%

      \[\leadsto x \cdot \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(\sin y\right)\right)} + z \cdot \cos y \]

4. Applied egg-rr 99.8%

   \[\leadsto x \cdot \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(\sin y\right)\right)} + z \cdot \cos y \]

5. Taylor expanded in y around 0 42.9%

   \[\leadsto \color{blue}{z} \]
6. Add Preprocessing

Reproduce

herbie shell --seed 2024170 
(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))))