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

Percentage Accurate: 99.8% → 99.8%

Time: 9.1s

Alternatives: 10

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 99.8%

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

3. Simplified 99.8%

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

5. Final simplification 99.8%

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

Alternative 2: 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 3: 73.7% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x \cdot \sin y\\ t_1 := z \cdot \cos y\\ \mathbf{if}\;x \leq -4.4 \cdot 10^{+111}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;x \leq -2.05 \cdot 10^{+79}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq -1.9 \cdot 10^{+56}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;x \leq -1.32 \cdot 10^{-21}:\\ \;\;\;\;z + x \cdot y\\ \mathbf{elif}\;x \leq 0.3:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq 65000000000000 \lor \neg \left(x \leq 2.6 \cdot 10^{+96}\right):\\ \;\;\;\;t\_0\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{t\_1}{x}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* x (sin y))) (t_1 (* z (cos y))))
   (if (<= x -4.4e+111)
     t_0
     (if (<= x -2.05e+79)
       t_1
       (if (<= x -1.9e+56)
         t_0
         (if (<= x -1.32e-21)
           (+ z (* x y))
           (if (<= x 0.3)
             t_1
             (if (or (<= x 65000000000000.0) (not (<= x 2.6e+96)))
               t_0
               (* x (/ t_1 x))))))))))

C

double code(double x, double y, double z) {
	double t_0 = x * sin(y);
	double t_1 = z * cos(y);
	double tmp;
	if (x <= -4.4e+111) {
		tmp = t_0;
	} else if (x <= -2.05e+79) {
		tmp = t_1;
	} else if (x <= -1.9e+56) {
		tmp = t_0;
	} else if (x <= -1.32e-21) {
		tmp = z + (x * y);
	} else if (x <= 0.3) {
		tmp = t_1;
	} else if ((x <= 65000000000000.0) || !(x <= 2.6e+96)) {
		tmp = t_0;
	} else {
		tmp = x * (t_1 / 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) :: t_0
    real(8) :: t_1
    real(8) :: tmp
    t_0 = x * sin(y)
    t_1 = z * cos(y)
    if (x <= (-4.4d+111)) then
        tmp = t_0
    else if (x <= (-2.05d+79)) then
        tmp = t_1
    else if (x <= (-1.9d+56)) then
        tmp = t_0
    else if (x <= (-1.32d-21)) then
        tmp = z + (x * y)
    else if (x <= 0.3d0) then
        tmp = t_1
    else if ((x <= 65000000000000.0d0) .or. (.not. (x <= 2.6d+96))) then
        tmp = t_0
    else
        tmp = x * (t_1 / x)
    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 (x <= -4.4e+111) {
		tmp = t_0;
	} else if (x <= -2.05e+79) {
		tmp = t_1;
	} else if (x <= -1.9e+56) {
		tmp = t_0;
	} else if (x <= -1.32e-21) {
		tmp = z + (x * y);
	} else if (x <= 0.3) {
		tmp = t_1;
	} else if ((x <= 65000000000000.0) || !(x <= 2.6e+96)) {
		tmp = t_0;
	} else {
		tmp = x * (t_1 / x);
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = x * math.sin(y)
	t_1 = z * math.cos(y)
	tmp = 0
	if x <= -4.4e+111:
		tmp = t_0
	elif x <= -2.05e+79:
		tmp = t_1
	elif x <= -1.9e+56:
		tmp = t_0
	elif x <= -1.32e-21:
		tmp = z + (x * y)
	elif x <= 0.3:
		tmp = t_1
	elif (x <= 65000000000000.0) or not (x <= 2.6e+96):
		tmp = t_0
	else:
		tmp = x * (t_1 / x)
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(x * sin(y))
	t_1 = Float64(z * cos(y))
	tmp = 0.0
	if (x <= -4.4e+111)
		tmp = t_0;
	elseif (x <= -2.05e+79)
		tmp = t_1;
	elseif (x <= -1.9e+56)
		tmp = t_0;
	elseif (x <= -1.32e-21)
		tmp = Float64(z + Float64(x * y));
	elseif (x <= 0.3)
		tmp = t_1;
	elseif ((x <= 65000000000000.0) || !(x <= 2.6e+96))
		tmp = t_0;
	else
		tmp = Float64(x * Float64(t_1 / x));
	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 (x <= -4.4e+111)
		tmp = t_0;
	elseif (x <= -2.05e+79)
		tmp = t_1;
	elseif (x <= -1.9e+56)
		tmp = t_0;
	elseif (x <= -1.32e-21)
		tmp = z + (x * y);
	elseif (x <= 0.3)
		tmp = t_1;
	elseif ((x <= 65000000000000.0) || ~((x <= 2.6e+96)))
		tmp = t_0;
	else
		tmp = x * (t_1 / x);
	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[x, -4.4e+111], t$95$0, If[LessEqual[x, -2.05e+79], t$95$1, If[LessEqual[x, -1.9e+56], t$95$0, If[LessEqual[x, -1.32e-21], N[(z + N[(x * y), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 0.3], t$95$1, If[Or[LessEqual[x, 65000000000000.0], N[Not[LessEqual[x, 2.6e+96]], $MachinePrecision]], t$95$0, N[(x * N[(t$95$1 / x), $MachinePrecision]), $MachinePrecision]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if x < -4.39999999999999997e111 or -2.05e79 < x < -1.89999999999999998e56 or 0.299999999999999989 < x < 6.5e13 or 2.6e96 < x

   1. Initial program 99.8%

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

   3. Taylor expanded in x around inf 83.4%

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

   if -4.39999999999999997e111 < x < -2.05e79 or -1.32e-21 < x < 0.299999999999999989

   1. Initial program 99.8%

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

   3. Taylor expanded in x around 0 89.4%

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

   if -1.89999999999999998e56 < x < -1.32e-21

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 76.0%

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

      1. *-commutative 76.0%

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

   5. Simplified 76.0%

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

   if 6.5e13 < x < 2.6e96

   1. Initial program 99.8%

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

      1. add-cbrt-cube 52.4%

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

      2. pow3 52.3%

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

   4. Applied egg-rr 52.3%

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

   5. Taylor expanded in y around 0 29.2%

      \[\leadsto \color{blue}{x \cdot y} + \sqrt[3]{{\left(z \cdot \cos y\right)}^{3}} \]
   6. Step-by-step derivation

      1. *-commutative 29.2%

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

   7. Simplified 29.2%

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

   8. Taylor expanded in x around inf 44.8%

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

   9. Taylor expanded in z around inf 63.0%

      \[\leadsto x \cdot \color{blue}{\frac{z \cdot \cos y}{x}} \]
3. Recombined 4 regimes into one program.

4. Final simplification 84.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -4.4 \cdot 10^{+111}:\\ \;\;\;\;x \cdot \sin y\\ \mathbf{elif}\;x \leq -2.05 \cdot 10^{+79}:\\ \;\;\;\;z \cdot \cos y\\ \mathbf{elif}\;x \leq -1.9 \cdot 10^{+56}:\\ \;\;\;\;x \cdot \sin y\\ \mathbf{elif}\;x \leq -1.32 \cdot 10^{-21}:\\ \;\;\;\;z + x \cdot y\\ \mathbf{elif}\;x \leq 0.3:\\ \;\;\;\;z \cdot \cos y\\ \mathbf{elif}\;x \leq 65000000000000 \lor \neg \left(x \leq 2.6 \cdot 10^{+96}\right):\\ \;\;\;\;x \cdot \sin y\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{z \cdot \cos y}{x}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 73.5% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x \cdot \sin y\\ t_1 := z \cdot \cos y\\ \mathbf{if}\;x \leq -6.6 \cdot 10^{+112}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;x \leq -1.1 \cdot 10^{+79}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq -1.3 \cdot 10^{+55}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;x \leq -2.3 \cdot 10^{-23}:\\ \;\;\;\;z + x \cdot y\\ \mathbf{elif}\;x \leq 0.03 \lor \neg \left(x \leq 60000000000000\right) \land x \leq 4.5 \cdot 10^{+94}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* x (sin y))) (t_1 (* z (cos y))))
   (if (<= x -6.6e+112)
     t_0
     (if (<= x -1.1e+79)
       t_1
       (if (<= x -1.3e+55)
         t_0
         (if (<= x -2.3e-23)
           (+ z (* x y))
           (if (or (<= x 0.03)
                   (and (not (<= x 60000000000000.0)) (<= x 4.5e+94)))
             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 (x <= -6.6e+112) {
		tmp = t_0;
	} else if (x <= -1.1e+79) {
		tmp = t_1;
	} else if (x <= -1.3e+55) {
		tmp = t_0;
	} else if (x <= -2.3e-23) {
		tmp = z + (x * y);
	} else if ((x <= 0.03) || (!(x <= 60000000000000.0) && (x <= 4.5e+94))) {
		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 (x <= (-6.6d+112)) then
        tmp = t_0
    else if (x <= (-1.1d+79)) then
        tmp = t_1
    else if (x <= (-1.3d+55)) then
        tmp = t_0
    else if (x <= (-2.3d-23)) then
        tmp = z + (x * y)
    else if ((x <= 0.03d0) .or. (.not. (x <= 60000000000000.0d0)) .and. (x <= 4.5d+94)) 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 (x <= -6.6e+112) {
		tmp = t_0;
	} else if (x <= -1.1e+79) {
		tmp = t_1;
	} else if (x <= -1.3e+55) {
		tmp = t_0;
	} else if (x <= -2.3e-23) {
		tmp = z + (x * y);
	} else if ((x <= 0.03) || (!(x <= 60000000000000.0) && (x <= 4.5e+94))) {
		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 x <= -6.6e+112:
		tmp = t_0
	elif x <= -1.1e+79:
		tmp = t_1
	elif x <= -1.3e+55:
		tmp = t_0
	elif x <= -2.3e-23:
		tmp = z + (x * y)
	elif (x <= 0.03) or (not (x <= 60000000000000.0) and (x <= 4.5e+94)):
		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 (x <= -6.6e+112)
		tmp = t_0;
	elseif (x <= -1.1e+79)
		tmp = t_1;
	elseif (x <= -1.3e+55)
		tmp = t_0;
	elseif (x <= -2.3e-23)
		tmp = Float64(z + Float64(x * y));
	elseif ((x <= 0.03) || (!(x <= 60000000000000.0) && (x <= 4.5e+94)))
		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 (x <= -6.6e+112)
		tmp = t_0;
	elseif (x <= -1.1e+79)
		tmp = t_1;
	elseif (x <= -1.3e+55)
		tmp = t_0;
	elseif (x <= -2.3e-23)
		tmp = z + (x * y);
	elseif ((x <= 0.03) || (~((x <= 60000000000000.0)) && (x <= 4.5e+94)))
		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[x, -6.6e+112], t$95$0, If[LessEqual[x, -1.1e+79], t$95$1, If[LessEqual[x, -1.3e+55], t$95$0, If[LessEqual[x, -2.3e-23], N[(z + N[(x * y), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[x, 0.03], And[N[Not[LessEqual[x, 60000000000000.0]], $MachinePrecision], LessEqual[x, 4.5e+94]]], t$95$1, t$95$0]]]]]]]

Derivation

1. Split input into 3 regimes

2. if x < -6.5999999999999998e112 or -1.0999999999999999e79 < x < -1.3e55 or 0.029999999999999999 < x < 6e13 or 4.49999999999999972e94 < x

   1. Initial program 99.8%

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

   3. Taylor expanded in x around inf 83.4%

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

   if -6.5999999999999998e112 < x < -1.0999999999999999e79 or -2.3000000000000001e-23 < x < 0.029999999999999999 or 6e13 < x < 4.49999999999999972e94

   1. Initial program 99.8%

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

   3. Taylor expanded in x around 0 86.3%

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

   if -1.3e55 < x < -2.3000000000000001e-23

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 76.0%

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

      1. *-commutative 76.0%

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

   5. Simplified 76.0%

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

4. Final simplification 84.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -6.6 \cdot 10^{+112}:\\ \;\;\;\;x \cdot \sin y\\ \mathbf{elif}\;x \leq -1.1 \cdot 10^{+79}:\\ \;\;\;\;z \cdot \cos y\\ \mathbf{elif}\;x \leq -1.3 \cdot 10^{+55}:\\ \;\;\;\;x \cdot \sin y\\ \mathbf{elif}\;x \leq -2.3 \cdot 10^{-23}:\\ \;\;\;\;z + x \cdot y\\ \mathbf{elif}\;x \leq 0.03 \lor \neg \left(x \leq 60000000000000\right) \land x \leq 4.5 \cdot 10^{+94}:\\ \;\;\;\;z \cdot \cos y\\ \mathbf{else}:\\ \;\;\;\;x \cdot \sin y\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 79.1% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := z \cdot \cos y\\ t_1 := z \cdot \left(1 + x \cdot \frac{\sin y}{z}\right)\\ \mathbf{if}\;z \leq -9 \cdot 10^{+107}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;z \leq -3.4 \cdot 10^{-186}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 2.1 \cdot 10^{-248}:\\ \;\;\;\;x \cdot \sin y\\ \mathbf{elif}\;z \leq 6.4 \cdot 10^{-15}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* z (cos y))) (t_1 (* z (+ 1.0 (* x (/ (sin y) z))))))
   (if (<= z -9e+107)
     t_0
     (if (<= z -3.4e-186)
       t_1
       (if (<= z 2.1e-248) (* x (sin y)) (if (<= z 6.4e-15) t_1 t_0))))))

C

double code(double x, double y, double z) {
	double t_0 = z * cos(y);
	double t_1 = z * (1.0 + (x * (sin(y) / z)));
	double tmp;
	if (z <= -9e+107) {
		tmp = t_0;
	} else if (z <= -3.4e-186) {
		tmp = t_1;
	} else if (z <= 2.1e-248) {
		tmp = x * sin(y);
	} else if (z <= 6.4e-15) {
		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 = z * cos(y)
    t_1 = z * (1.0d0 + (x * (sin(y) / z)))
    if (z <= (-9d+107)) then
        tmp = t_0
    else if (z <= (-3.4d-186)) then
        tmp = t_1
    else if (z <= 2.1d-248) then
        tmp = x * sin(y)
    else if (z <= 6.4d-15) 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 = z * Math.cos(y);
	double t_1 = z * (1.0 + (x * (Math.sin(y) / z)));
	double tmp;
	if (z <= -9e+107) {
		tmp = t_0;
	} else if (z <= -3.4e-186) {
		tmp = t_1;
	} else if (z <= 2.1e-248) {
		tmp = x * Math.sin(y);
	} else if (z <= 6.4e-15) {
		tmp = t_1;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = z * math.cos(y)
	t_1 = z * (1.0 + (x * (math.sin(y) / z)))
	tmp = 0
	if z <= -9e+107:
		tmp = t_0
	elif z <= -3.4e-186:
		tmp = t_1
	elif z <= 2.1e-248:
		tmp = x * math.sin(y)
	elif z <= 6.4e-15:
		tmp = t_1
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(z * cos(y))
	t_1 = Float64(z * Float64(1.0 + Float64(x * Float64(sin(y) / z))))
	tmp = 0.0
	if (z <= -9e+107)
		tmp = t_0;
	elseif (z <= -3.4e-186)
		tmp = t_1;
	elseif (z <= 2.1e-248)
		tmp = Float64(x * sin(y));
	elseif (z <= 6.4e-15)
		tmp = t_1;
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = z * cos(y);
	t_1 = z * (1.0 + (x * (sin(y) / z)));
	tmp = 0.0;
	if (z <= -9e+107)
		tmp = t_0;
	elseif (z <= -3.4e-186)
		tmp = t_1;
	elseif (z <= 2.1e-248)
		tmp = x * sin(y);
	elseif (z <= 6.4e-15)
		tmp = t_1;
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(z * N[Cos[y], $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(z * N[(1.0 + N[(x * N[(N[Sin[y], $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -9e+107], t$95$0, If[LessEqual[z, -3.4e-186], t$95$1, If[LessEqual[z, 2.1e-248], N[(x * N[Sin[y], $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 6.4e-15], t$95$1, t$95$0]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -9e107 or 6.3999999999999999e-15 < z

   1. Initial program 99.8%

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

   3. Taylor expanded in x around 0 88.3%

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

   if -9e107 < z < -3.3999999999999999e-186 or 2.1e-248 < z < 6.3999999999999999e-15

   1. Initial program 99.8%

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

      1. add-sqr-sqrt 47.6%

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

      2. associate-*r* 47.7%

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

      3. fma-define 47.7%

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

   4. Applied egg-rr 47.7%

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

   5. Taylor expanded in y around 0 44.7%

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

   6. Taylor expanded in z around inf 80.6%

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

      1. associate-/l* 80.5%

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

   8. Simplified 80.5%

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

   if -3.3999999999999999e-186 < z < 2.1e-248

   1. Initial program 99.8%

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

   3. Taylor expanded in x around inf 81.5%

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

4. Final simplification 84.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -9 \cdot 10^{+107}:\\ \;\;\;\;z \cdot \cos y\\ \mathbf{elif}\;z \leq -3.4 \cdot 10^{-186}:\\ \;\;\;\;z \cdot \left(1 + x \cdot \frac{\sin y}{z}\right)\\ \mathbf{elif}\;z \leq 2.1 \cdot 10^{-248}:\\ \;\;\;\;x \cdot \sin y\\ \mathbf{elif}\;z \leq 6.4 \cdot 10^{-15}:\\ \;\;\;\;z \cdot \left(1 + x \cdot \frac{\sin y}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \cos y\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 74.3% accurate, 1.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x \cdot \sin y\\ t_1 := z \cdot \cos y\\ \mathbf{if}\;x \leq -4.2 \cdot 10^{+111}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;x \leq -2.5 \cdot 10^{+47}:\\ \;\;\;\;x \cdot \frac{t\_1}{x}\\ \mathbf{elif}\;x \leq -3.05 \cdot 10^{-21}:\\ \;\;\;\;x \cdot \left(y + \cos y \cdot \frac{z}{x}\right)\\ \mathbf{elif}\;x \leq 7.8 \cdot 10^{+93}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* x (sin y))) (t_1 (* z (cos y))))
   (if (<= x -4.2e+111)
     t_0
     (if (<= x -2.5e+47)
       (* x (/ t_1 x))
       (if (<= x -3.05e-21)
         (* x (+ y (* (cos y) (/ z x))))
         (if (<= x 7.8e+93) 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 (x <= -4.2e+111) {
		tmp = t_0;
	} else if (x <= -2.5e+47) {
		tmp = x * (t_1 / x);
	} else if (x <= -3.05e-21) {
		tmp = x * (y + (cos(y) * (z / x)));
	} else if (x <= 7.8e+93) {
		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 (x <= (-4.2d+111)) then
        tmp = t_0
    else if (x <= (-2.5d+47)) then
        tmp = x * (t_1 / x)
    else if (x <= (-3.05d-21)) then
        tmp = x * (y + (cos(y) * (z / x)))
    else if (x <= 7.8d+93) 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 (x <= -4.2e+111) {
		tmp = t_0;
	} else if (x <= -2.5e+47) {
		tmp = x * (t_1 / x);
	} else if (x <= -3.05e-21) {
		tmp = x * (y + (Math.cos(y) * (z / x)));
	} else if (x <= 7.8e+93) {
		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 x <= -4.2e+111:
		tmp = t_0
	elif x <= -2.5e+47:
		tmp = x * (t_1 / x)
	elif x <= -3.05e-21:
		tmp = x * (y + (math.cos(y) * (z / x)))
	elif x <= 7.8e+93:
		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 (x <= -4.2e+111)
		tmp = t_0;
	elseif (x <= -2.5e+47)
		tmp = Float64(x * Float64(t_1 / x));
	elseif (x <= -3.05e-21)
		tmp = Float64(x * Float64(y + Float64(cos(y) * Float64(z / x))));
	elseif (x <= 7.8e+93)
		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 (x <= -4.2e+111)
		tmp = t_0;
	elseif (x <= -2.5e+47)
		tmp = x * (t_1 / x);
	elseif (x <= -3.05e-21)
		tmp = x * (y + (cos(y) * (z / x)));
	elseif (x <= 7.8e+93)
		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[x, -4.2e+111], t$95$0, If[LessEqual[x, -2.5e+47], N[(x * N[(t$95$1 / x), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, -3.05e-21], N[(x * N[(y + N[(N[Cos[y], $MachinePrecision] * N[(z / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 7.8e+93], t$95$1, t$95$0]]]]]]

Derivation

1. Split input into 4 regimes

2. if x < -4.1999999999999999e111 or 7.8000000000000005e93 < x

   1. Initial program 99.8%

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

   3. Taylor expanded in x around inf 83.9%

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

   if -4.1999999999999999e111 < x < -2.50000000000000011e47

   1. Initial program 99.8%

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

      1. add-cbrt-cube 46.5%

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

      2. pow3 46.5%

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

   4. Applied egg-rr 46.5%

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

   5. Taylor expanded in y around 0 24.3%

      \[\leadsto \color{blue}{x \cdot y} + \sqrt[3]{{\left(z \cdot \cos y\right)}^{3}} \]
   6. Step-by-step derivation

      1. *-commutative 24.3%

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

   7. Simplified 24.3%

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

   8. Taylor expanded in x around inf 37.4%

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

   9. Taylor expanded in z around inf 72.0%

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

   if -2.50000000000000011e47 < x < -3.05000000000000007e-21

   1. Initial program 100.0%

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

      1. add-cbrt-cube 63.8%

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

      2. pow3 63.8%

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

   4. Applied egg-rr 63.8%

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

   5. Taylor expanded in y around 0 48.8%

      \[\leadsto \color{blue}{x \cdot y} + \sqrt[3]{{\left(z \cdot \cos y\right)}^{3}} \]
   6. Step-by-step derivation

      1. *-commutative 48.8%

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

   7. Simplified 48.8%

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

   8. Taylor expanded in x around inf 85.0%

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

      1. *-commutative 85.0%

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

      2. associate-/l* 85.0%

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

   10. Applied egg-rr 85.0%

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

   if -3.05000000000000007e-21 < x < 7.8000000000000005e93

   1. Initial program 99.8%

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

   3. Taylor expanded in x around 0 83.0%

      \[\leadsto \color{blue}{z \cdot \cos y} \]
3. Recombined 4 regimes into one program.

4. Final simplification 82.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -4.2 \cdot 10^{+111}:\\ \;\;\;\;x \cdot \sin y\\ \mathbf{elif}\;x \leq -2.5 \cdot 10^{+47}:\\ \;\;\;\;x \cdot \frac{z \cdot \cos y}{x}\\ \mathbf{elif}\;x \leq -3.05 \cdot 10^{-21}:\\ \;\;\;\;x \cdot \left(y + \cos y \cdot \frac{z}{x}\right)\\ \mathbf{elif}\;x \leq 7.8 \cdot 10^{+93}:\\ \;\;\;\;z \cdot \cos y\\ \mathbf{else}:\\ \;\;\;\;x \cdot \sin y\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 74.4% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -400 \lor \neg \left(y \leq 0.1\right):\\ \;\;\;\;x \cdot \sin y\\ \mathbf{else}:\\ \;\;\;\;z + y \cdot \left(x + y \cdot \left(z \cdot -0.5 + \left(x \cdot y\right) \cdot -0.16666666666666666\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -400.0) (not (<= y 0.1)))
   (* x (sin y))
   (+ z (* y (+ x (* y (+ (* z -0.5) (* (* x y) -0.16666666666666666))))))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -400.0) || !(y <= 0.1)) {
		tmp = x * sin(y);
	} else {
		tmp = z + (y * (x + (y * ((z * -0.5) + ((x * y) * -0.16666666666666666)))));
	}
	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 <= (-400.0d0)) .or. (.not. (y <= 0.1d0))) then
        tmp = x * sin(y)
    else
        tmp = z + (y * (x + (y * ((z * (-0.5d0)) + ((x * y) * (-0.16666666666666666d0))))))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((y <= -400.0) || !(y <= 0.1)) {
		tmp = x * Math.sin(y);
	} else {
		tmp = z + (y * (x + (y * ((z * -0.5) + ((x * y) * -0.16666666666666666)))));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -400.0) or not (y <= 0.1):
		tmp = x * math.sin(y)
	else:
		tmp = z + (y * (x + (y * ((z * -0.5) + ((x * y) * -0.16666666666666666)))))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -400.0) || !(y <= 0.1))
		tmp = Float64(x * sin(y));
	else
		tmp = Float64(z + Float64(y * Float64(x + Float64(y * Float64(Float64(z * -0.5) + Float64(Float64(x * y) * -0.16666666666666666))))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((y <= -400.0) || ~((y <= 0.1)))
		tmp = x * sin(y);
	else
		tmp = z + (y * (x + (y * ((z * -0.5) + ((x * y) * -0.16666666666666666)))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -400.0], N[Not[LessEqual[y, 0.1]], $MachinePrecision]], N[(x * N[Sin[y], $MachinePrecision]), $MachinePrecision], N[(z + N[(y * N[(x + N[(y * N[(N[(z * -0.5), $MachinePrecision] + N[(N[(x * y), $MachinePrecision] * -0.16666666666666666), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -400 or 0.10000000000000001 < y

   1. Initial program 99.6%

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

   3. Taylor expanded in x around inf 45.8%

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

   if -400 < y < 0.10000000000000001

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 98.8%

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

4. Final simplification 71.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -400 \lor \neg \left(y \leq 0.1\right):\\ \;\;\;\;x \cdot \sin y\\ \mathbf{else}:\\ \;\;\;\;z + y \cdot \left(x + y \cdot \left(z \cdot -0.5 + \left(x \cdot y\right) \cdot -0.16666666666666666\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 40.2% accurate, 15.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -2.3 \cdot 10^{+113} \lor \neg \left(x \leq 24.5\right):\\ \;\;\;\;x \cdot y\\ \mathbf{else}:\\ \;\;\;\;z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -2.3e+113) (not (<= x 24.5))) (* x y) z))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -2.3e+113) || !(x <= 24.5)) {
		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 <= (-2.3d+113)) .or. (.not. (x <= 24.5d0))) 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 <= -2.3e+113) || !(x <= 24.5)) {
		tmp = x * y;
	} else {
		tmp = z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -2.3e+113) or not (x <= 24.5):
		tmp = x * y
	else:
		tmp = z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -2.3e+113) || !(x <= 24.5))
		tmp = Float64(x * y);
	else
		tmp = z;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((x <= -2.3e+113) || ~((x <= 24.5)))
		tmp = x * y;
	else
		tmp = z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -2.3e+113], N[Not[LessEqual[x, 24.5]], $MachinePrecision]], N[(x * y), $MachinePrecision], z]

Derivation

1. Split input into 2 regimes

2. if x < -2.29999999999999997e113 or 24.5 < x

   1. Initial program 99.8%

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

   3. Taylor expanded in y around 0 47.3%

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

      1. *-commutative 47.3%

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

   5. Simplified 47.3%

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

   6. Taylor expanded in y around inf 43.5%

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

   7. Taylor expanded in y around inf 35.9%

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

      1. *-commutative 35.9%

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

   9. Simplified 35.9%

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

   if -2.29999999999999997e113 < x < 24.5

   1. Initial program 99.8%

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

   3. Taylor expanded in y around 0 52.1%

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

      1. *-commutative 52.1%

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

   5. Simplified 52.1%

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

   6. Taylor expanded in z around inf 48.5%

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

4. Final simplification 43.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.3 \cdot 10^{+113} \lor \neg \left(x \leq 24.5\right):\\ \;\;\;\;x \cdot y\\ \mathbf{else}:\\ \;\;\;\;z\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 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. Add Preprocessing

3. Taylor expanded in y around 0 50.2%

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

   1. *-commutative 50.2%

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

5. Simplified 50.2%

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

6. Final simplification 50.2%

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

Alternative 10: 38.5% 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. Taylor expanded in y around 0 50.2%

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

   1. *-commutative 50.2%

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

5. Simplified 50.2%

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

6. Taylor expanded in z around inf 34.7%

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

7. Final simplification 34.7%

   \[\leadsto z \]
8. Add Preprocessing

Reproduce

herbie shell --seed 2024112 
(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))))