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

Percentage Accurate: 99.8% → 99.8%

Time: 10.4s

Alternatives: 7

Speedup: 1.0×

Specification

Math

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

FPCore

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

C

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

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    code = (x * sin(y)) + (z * cos(y))
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 99.8% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    code = (x * sin(y)) + (z * cos(y))
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 99.8% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    code = (x * sin(y)) + (z * cos(y))
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.8%

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

Alternative 2: 80.3% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := z \cdot \cos y\\ t_1 := z \cdot \left(1 + x \cdot \frac{\sin y}{z}\right)\\ \mathbf{if}\;z \leq -1.12 \cdot 10^{+110}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;z \leq -1.55 \cdot 10^{-181}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 3.2 \cdot 10^{-227}:\\ \;\;\;\;x \cdot \sin y\\ \mathbf{elif}\;z \leq 2.5 \cdot 10^{+59}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* z (cos y))) (t_1 (* z (+ 1.0 (* x (/ (sin y) z))))))
   (if (<= z -1.12e+110)
     t_0
     (if (<= z -1.55e-181)
       t_1
       (if (<= z 3.2e-227) (* x (sin y)) (if (<= z 2.5e+59) 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 <= -1.12e+110) {
		tmp = t_0;
	} else if (z <= -1.55e-181) {
		tmp = t_1;
	} else if (z <= 3.2e-227) {
		tmp = x * sin(y);
	} else if (z <= 2.5e+59) {
		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 <= (-1.12d+110)) then
        tmp = t_0
    else if (z <= (-1.55d-181)) then
        tmp = t_1
    else if (z <= 3.2d-227) then
        tmp = x * sin(y)
    else if (z <= 2.5d+59) 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 <= -1.12e+110) {
		tmp = t_0;
	} else if (z <= -1.55e-181) {
		tmp = t_1;
	} else if (z <= 3.2e-227) {
		tmp = x * Math.sin(y);
	} else if (z <= 2.5e+59) {
		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 <= -1.12e+110:
		tmp = t_0
	elif z <= -1.55e-181:
		tmp = t_1
	elif z <= 3.2e-227:
		tmp = x * math.sin(y)
	elif z <= 2.5e+59:
		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 <= -1.12e+110)
		tmp = t_0;
	elseif (z <= -1.55e-181)
		tmp = t_1;
	elseif (z <= 3.2e-227)
		tmp = Float64(x * sin(y));
	elseif (z <= 2.5e+59)
		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 <= -1.12e+110)
		tmp = t_0;
	elseif (z <= -1.55e-181)
		tmp = t_1;
	elseif (z <= 3.2e-227)
		tmp = x * sin(y);
	elseif (z <= 2.5e+59)
		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, -1.12e+110], t$95$0, If[LessEqual[z, -1.55e-181], t$95$1, If[LessEqual[z, 3.2e-227], N[(x * N[Sin[y], $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 2.5e+59], t$95$1, t$95$0]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.1200000000000001e110 or 2.4999999999999999e59 < z

   1. Initial program 99.8%

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

   3. Taylor expanded in x around 0 88.8%

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

   if -1.1200000000000001e110 < z < -1.55000000000000011e-181 or 3.2000000000000001e-227 < z < 2.4999999999999999e59

   1. Initial program 99.7%

      \[x \cdot \sin y + z \cdot \cos y \]
   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 z around inf 98.3%

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

      1. associate-/l* 98.1%

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

   7. Simplified 98.1%

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

   8. Taylor expanded in y around 0 80.2%

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

   if -1.55000000000000011e-181 < z < 3.2000000000000001e-227

   1. Initial program 99.8%

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

   3. Taylor expanded in x around inf 93.7%

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

Alternative 3: 86.1% accurate, 1.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3.8 \cdot 10^{+109} \lor \neg \left(z \leq 1.7 \cdot 10^{+59}\right):\\ \;\;\;\;z \cdot \cos y\\ \mathbf{else}:\\ \;\;\;\;z + x \cdot \left(z \cdot \frac{\sin y}{z}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -3.8e+109) (not (<= z 1.7e+59)))
   (* z (cos y))
   (+ z (* x (* z (/ (sin y) z))))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -3.8e+109) || !(z <= 1.7e+59)) {
		tmp = z * cos(y);
	} else {
		tmp = z + (x * (z * (sin(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 ((z <= (-3.8d+109)) .or. (.not. (z <= 1.7d+59))) then
        tmp = z * cos(y)
    else
        tmp = z + (x * (z * (sin(y) / z)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((z <= -3.8e+109) || !(z <= 1.7e+59)) {
		tmp = z * Math.cos(y);
	} else {
		tmp = z + (x * (z * (Math.sin(y) / z)));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -3.8e+109) or not (z <= 1.7e+59):
		tmp = z * math.cos(y)
	else:
		tmp = z + (x * (z * (math.sin(y) / z)))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -3.8e+109) || !(z <= 1.7e+59))
		tmp = Float64(z * cos(y));
	else
		tmp = Float64(z + Float64(x * Float64(z * Float64(sin(y) / z))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((z <= -3.8e+109) || ~((z <= 1.7e+59)))
		tmp = z * cos(y);
	else
		tmp = z + (x * (z * (sin(y) / z)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -3.8e+109], N[Not[LessEqual[z, 1.7e+59]], $MachinePrecision]], N[(z * N[Cos[y], $MachinePrecision]), $MachinePrecision], N[(z + N[(x * N[(z * N[(N[Sin[y], $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -3.80000000000000039e109 or 1.70000000000000003e59 < z

   1. Initial program 99.8%

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

   3. Taylor expanded in x around 0 88.8%

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

   if -3.80000000000000039e109 < z < 1.70000000000000003e59

   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 z around inf 91.9%

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

      1. associate-/l* 91.8%

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

   7. Simplified 91.8%

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

      1. distribute-rgt-in 91.8%

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

      2. *-commutative 91.8%

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

      3. associate-*l* 99.7%

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

   9. Applied egg-rr 99.7%

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

   10. Taylor expanded in y around 0 85.9%

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

4. Final simplification 86.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.8 \cdot 10^{+109} \lor \neg \left(z \leq 1.7 \cdot 10^{+59}\right):\\ \;\;\;\;z \cdot \cos y\\ \mathbf{else}:\\ \;\;\;\;z + x \cdot \left(z \cdot \frac{\sin y}{z}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 74.9% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.5 \cdot 10^{+90}:\\ \;\;\;\;z \cdot \cos y\\ \mathbf{elif}\;y \leq -0.014 \lor \neg \left(y \leq 50000000000\right):\\ \;\;\;\;x \cdot \sin y\\ \mathbf{else}:\\ \;\;\;\;z + y \cdot \left(x + y \cdot \left(x \cdot \left(y \cdot -0.16666666666666666\right)\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -1.5e+90)
   (* z (cos y))
   (if (or (<= y -0.014) (not (<= y 50000000000.0)))
     (* x (sin y))
     (+ z (* y (+ x (* y (* x (* y -0.16666666666666666)))))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -1.5e+90) {
		tmp = z * cos(y);
	} else if ((y <= -0.014) || !(y <= 50000000000.0)) {
		tmp = x * sin(y);
	} else {
		tmp = z + (y * (x + (y * (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 <= (-1.5d+90)) then
        tmp = z * cos(y)
    else if ((y <= (-0.014d0)) .or. (.not. (y <= 50000000000.0d0))) then
        tmp = x * sin(y)
    else
        tmp = z + (y * (x + (y * (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 <= -1.5e+90) {
		tmp = z * Math.cos(y);
	} else if ((y <= -0.014) || !(y <= 50000000000.0)) {
		tmp = x * Math.sin(y);
	} else {
		tmp = z + (y * (x + (y * (x * (y * -0.16666666666666666)))));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -1.5e+90:
		tmp = z * math.cos(y)
	elif (y <= -0.014) or not (y <= 50000000000.0):
		tmp = x * math.sin(y)
	else:
		tmp = z + (y * (x + (y * (x * (y * -0.16666666666666666)))))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -1.5e+90)
		tmp = Float64(z * cos(y));
	elseif ((y <= -0.014) || !(y <= 50000000000.0))
		tmp = Float64(x * sin(y));
	else
		tmp = Float64(z + Float64(y * Float64(x + Float64(y * Float64(x * Float64(y * -0.16666666666666666))))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= -1.5e+90)
		tmp = z * cos(y);
	elseif ((y <= -0.014) || ~((y <= 50000000000.0)))
		tmp = x * sin(y);
	else
		tmp = z + (y * (x + (y * (x * (y * -0.16666666666666666)))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -1.5e+90], N[(z * N[Cos[y], $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[y, -0.014], N[Not[LessEqual[y, 50000000000.0]], $MachinePrecision]], N[(x * N[Sin[y], $MachinePrecision]), $MachinePrecision], N[(z + N[(y * N[(x + N[(y * N[(x * N[(y * -0.16666666666666666), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.49999999999999989e90

   1. Initial program 99.7%

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

   3. Taylor expanded in x around 0 64.6%

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

   if -1.49999999999999989e90 < y < -0.0140000000000000003 or 5e10 < y

   1. Initial program 99.5%

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

   3. Taylor expanded in x around inf 60.5%

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

   if -0.0140000000000000003 < y < 5e10

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 98.4%

      \[\leadsto \color{blue}{z + y \cdot \left(x + y \cdot \left(-0.5 \cdot z + -0.16666666666666666 \cdot \left(x \cdot y\right)\right)\right)} \]

   4. Taylor expanded in z around 0 98.4%

      \[\leadsto z + y \cdot \left(x + y \cdot \color{blue}{\left(-0.16666666666666666 \cdot \left(x \cdot y\right)\right)}\right) \]
   5. Step-by-step derivation

      1. *-commutative 98.4%

         \[\leadsto z + y \cdot \left(x + y \cdot \color{blue}{\left(\left(x \cdot y\right) \cdot -0.16666666666666666\right)}\right) \]

      2. associate-*r* 98.4%

         \[\leadsto z + y \cdot \left(x + y \cdot \color{blue}{\left(x \cdot \left(y \cdot -0.16666666666666666\right)\right)}\right) \]

   6. Simplified 98.4%

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

4. Final simplification 78.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.5 \cdot 10^{+90}:\\ \;\;\;\;z \cdot \cos y\\ \mathbf{elif}\;y \leq -0.014 \lor \neg \left(y \leq 50000000000\right):\\ \;\;\;\;x \cdot \sin y\\ \mathbf{else}:\\ \;\;\;\;z + y \cdot \left(x + y \cdot \left(x \cdot \left(y \cdot -0.16666666666666666\right)\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 74.7% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -0.029 \lor \neg \left(y \leq 50000000000\right):\\ \;\;\;\;x \cdot \sin y\\ \mathbf{else}:\\ \;\;\;\;z + y \cdot \left(x + y \cdot \left(x \cdot \left(y \cdot -0.16666666666666666\right)\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -0.029) (not (<= y 50000000000.0)))
   (* x (sin y))
   (+ z (* y (+ x (* y (* x (* y -0.16666666666666666))))))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -0.029) || !(y <= 50000000000.0)) {
		tmp = x * sin(y);
	} else {
		tmp = z + (y * (x + (y * (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 <= (-0.029d0)) .or. (.not. (y <= 50000000000.0d0))) then
        tmp = x * sin(y)
    else
        tmp = z + (y * (x + (y * (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 <= -0.029) || !(y <= 50000000000.0)) {
		tmp = x * Math.sin(y);
	} else {
		tmp = z + (y * (x + (y * (x * (y * -0.16666666666666666)))));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -0.029) or not (y <= 50000000000.0):
		tmp = x * math.sin(y)
	else:
		tmp = z + (y * (x + (y * (x * (y * -0.16666666666666666)))))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -0.029) || !(y <= 50000000000.0))
		tmp = Float64(x * sin(y));
	else
		tmp = Float64(z + Float64(y * Float64(x + Float64(y * Float64(x * Float64(y * -0.16666666666666666))))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((y <= -0.029) || ~((y <= 50000000000.0)))
		tmp = x * sin(y);
	else
		tmp = z + (y * (x + (y * (x * (y * -0.16666666666666666)))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -0.029], N[Not[LessEqual[y, 50000000000.0]], $MachinePrecision]], N[(x * N[Sin[y], $MachinePrecision]), $MachinePrecision], N[(z + N[(y * N[(x + N[(y * N[(x * N[(y * -0.16666666666666666), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -0.0290000000000000015 or 5e10 < y

   1. Initial program 99.6%

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

   3. Taylor expanded in x around inf 52.5%

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

   if -0.0290000000000000015 < y < 5e10

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 98.4%

      \[\leadsto \color{blue}{z + y \cdot \left(x + y \cdot \left(-0.5 \cdot z + -0.16666666666666666 \cdot \left(x \cdot y\right)\right)\right)} \]

   4. Taylor expanded in z around 0 98.4%

      \[\leadsto z + y \cdot \left(x + y \cdot \color{blue}{\left(-0.16666666666666666 \cdot \left(x \cdot y\right)\right)}\right) \]
   5. Step-by-step derivation

      1. *-commutative 98.4%

         \[\leadsto z + y \cdot \left(x + y \cdot \color{blue}{\left(\left(x \cdot y\right) \cdot -0.16666666666666666\right)}\right) \]

      2. associate-*r* 98.4%

         \[\leadsto z + y \cdot \left(x + y \cdot \color{blue}{\left(x \cdot \left(y \cdot -0.16666666666666666\right)\right)}\right) \]

   6. Simplified 98.4%

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

4. Final simplification 73.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -0.029 \lor \neg \left(y \leq 50000000000\right):\\ \;\;\;\;x \cdot \sin y\\ \mathbf{else}:\\ \;\;\;\;z + y \cdot \left(x + y \cdot \left(x \cdot \left(y \cdot -0.16666666666666666\right)\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 52.1% 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 48.2%

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

   1. +-commutative 48.2%

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

5. Simplified 48.2%

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

6. Final simplification 48.2%

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

Alternative 7: 38.4% 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 99.7%

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

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 36.9%

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

Reproduce

herbie shell --seed 2024146 
(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))))