Diagrams.ThreeD.Transform:aboutY from diagrams-lib-1.3.0.3

Percentage Accurate: 99.8% → 99.8%

Time: 7.4s

Alternatives: 7

Speedup: 1.0×

Specification

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 99.8% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 99.8% accurate, 0.7× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 99.8%

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

   1. fma-def 99.8%

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

3. Simplified 99.8%

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

4. Final simplification 99.8%

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

Alternative 2: 99.8% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.8%

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

2. Final simplification 99.8%

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

Alternative 3: 75.0% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x \cdot \cos y\\ t_1 := z \cdot \sin y\\ \mathbf{if}\;y \leq -5.5 \cdot 10^{+230}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y \leq -4 \cdot 10^{+207}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -3.2 \cdot 10^{+125}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y \leq -4.7 \cdot 10^{+58}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -7.5 \cdot 10^{+18}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y \leq -0.0245 \lor \neg \left(y \leq 0.0025\right):\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \left(z + y \cdot \left(x \cdot -0.5\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* x (cos y))) (t_1 (* z (sin y))))
   (if (<= y -5.5e+230)
     t_0
     (if (<= y -4e+207)
       t_1
       (if (<= y -3.2e+125)
         t_0
         (if (<= y -4.7e+58)
           t_1
           (if (<= y -7.5e+18)
             t_0
             (if (or (<= y -0.0245) (not (<= y 0.0025)))
               t_1
               (+ x (* y (+ z (* y (* x -0.5)))))))))))))

C

double code(double x, double y, double z) {
	double t_0 = x * cos(y);
	double t_1 = z * sin(y);
	double tmp;
	if (y <= -5.5e+230) {
		tmp = t_0;
	} else if (y <= -4e+207) {
		tmp = t_1;
	} else if (y <= -3.2e+125) {
		tmp = t_0;
	} else if (y <= -4.7e+58) {
		tmp = t_1;
	} else if (y <= -7.5e+18) {
		tmp = t_0;
	} else if ((y <= -0.0245) || !(y <= 0.0025)) {
		tmp = t_1;
	} else {
		tmp = x + (y * (z + (y * (x * -0.5))));
	}
	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 * cos(y)
    t_1 = z * sin(y)
    if (y <= (-5.5d+230)) then
        tmp = t_0
    else if (y <= (-4d+207)) then
        tmp = t_1
    else if (y <= (-3.2d+125)) then
        tmp = t_0
    else if (y <= (-4.7d+58)) then
        tmp = t_1
    else if (y <= (-7.5d+18)) then
        tmp = t_0
    else if ((y <= (-0.0245d0)) .or. (.not. (y <= 0.0025d0))) then
        tmp = t_1
    else
        tmp = x + (y * (z + (y * (x * (-0.5d0)))))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = x * Math.cos(y);
	double t_1 = z * Math.sin(y);
	double tmp;
	if (y <= -5.5e+230) {
		tmp = t_0;
	} else if (y <= -4e+207) {
		tmp = t_1;
	} else if (y <= -3.2e+125) {
		tmp = t_0;
	} else if (y <= -4.7e+58) {
		tmp = t_1;
	} else if (y <= -7.5e+18) {
		tmp = t_0;
	} else if ((y <= -0.0245) || !(y <= 0.0025)) {
		tmp = t_1;
	} else {
		tmp = x + (y * (z + (y * (x * -0.5))));
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = x * math.cos(y)
	t_1 = z * math.sin(y)
	tmp = 0
	if y <= -5.5e+230:
		tmp = t_0
	elif y <= -4e+207:
		tmp = t_1
	elif y <= -3.2e+125:
		tmp = t_0
	elif y <= -4.7e+58:
		tmp = t_1
	elif y <= -7.5e+18:
		tmp = t_0
	elif (y <= -0.0245) or not (y <= 0.0025):
		tmp = t_1
	else:
		tmp = x + (y * (z + (y * (x * -0.5))))
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(x * cos(y))
	t_1 = Float64(z * sin(y))
	tmp = 0.0
	if (y <= -5.5e+230)
		tmp = t_0;
	elseif (y <= -4e+207)
		tmp = t_1;
	elseif (y <= -3.2e+125)
		tmp = t_0;
	elseif (y <= -4.7e+58)
		tmp = t_1;
	elseif (y <= -7.5e+18)
		tmp = t_0;
	elseif ((y <= -0.0245) || !(y <= 0.0025))
		tmp = t_1;
	else
		tmp = Float64(x + Float64(y * Float64(z + Float64(y * Float64(x * -0.5)))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = x * cos(y);
	t_1 = z * sin(y);
	tmp = 0.0;
	if (y <= -5.5e+230)
		tmp = t_0;
	elseif (y <= -4e+207)
		tmp = t_1;
	elseif (y <= -3.2e+125)
		tmp = t_0;
	elseif (y <= -4.7e+58)
		tmp = t_1;
	elseif (y <= -7.5e+18)
		tmp = t_0;
	elseif ((y <= -0.0245) || ~((y <= 0.0025)))
		tmp = t_1;
	else
		tmp = x + (y * (z + (y * (x * -0.5))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(x * N[Cos[y], $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(z * N[Sin[y], $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -5.5e+230], t$95$0, If[LessEqual[y, -4e+207], t$95$1, If[LessEqual[y, -3.2e+125], t$95$0, If[LessEqual[y, -4.7e+58], t$95$1, If[LessEqual[y, -7.5e+18], t$95$0, If[Or[LessEqual[y, -0.0245], N[Not[LessEqual[y, 0.0025]], $MachinePrecision]], t$95$1, N[(x + N[(y * N[(z + N[(y * N[(x * -0.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -5.49999999999999979e230 or -4.0000000000000002e207 < y < -3.19999999999999983e125 or -4.69999999999999972e58 < y < -7.5e18

   1. Initial program 99.7%

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

   2. Taylor expanded in x around inf 76.3%

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

   if -5.49999999999999979e230 < y < -4.0000000000000002e207 or -3.19999999999999983e125 < y < -4.69999999999999972e58 or -7.5e18 < y < -0.024500000000000001 or 0.00250000000000000005 < y

   1. Initial program 99.7%

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

   2. Taylor expanded in x around 0 73.3%

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

   if -0.024500000000000001 < y < 0.00250000000000000005

   1. Initial program 100.0%

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

   2. Taylor expanded in y around 0 99.7%

      \[\leadsto \color{blue}{x + \left(-0.5 \cdot \left(x \cdot {y}^{2}\right) + y \cdot z\right)} \]
   3. Step-by-step derivation

      1. associate-*r* 99.7%

         \[\leadsto x + \left(\color{blue}{\left(-0.5 \cdot x\right) \cdot {y}^{2}} + y \cdot z\right) \]

      2. unpow2 99.7%

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

      3. associate-*r* 99.7%

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

      4. *-commutative 99.7%

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

      5. distribute-rgt-out 99.7%

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

      6. *-commutative 99.7%

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

   4. Simplified 99.7%

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

4. Final simplification 86.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -5.5 \cdot 10^{+230}:\\ \;\;\;\;x \cdot \cos y\\ \mathbf{elif}\;y \leq -4 \cdot 10^{+207}:\\ \;\;\;\;z \cdot \sin y\\ \mathbf{elif}\;y \leq -3.2 \cdot 10^{+125}:\\ \;\;\;\;x \cdot \cos y\\ \mathbf{elif}\;y \leq -4.7 \cdot 10^{+58}:\\ \;\;\;\;z \cdot \sin y\\ \mathbf{elif}\;y \leq -7.5 \cdot 10^{+18}:\\ \;\;\;\;x \cdot \cos y\\ \mathbf{elif}\;y \leq -0.0245 \lor \neg \left(y \leq 0.0025\right):\\ \;\;\;\;z \cdot \sin y\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \left(z + y \cdot \left(x \cdot -0.5\right)\right)\\ \end{array} \]

Alternative 4: 85.0% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -4.8 \cdot 10^{-152} \lor \neg \left(z \leq 2.5 \cdot 10^{-64}\right):\\ \;\;\;\;x + z \cdot \sin y\\ \mathbf{else}:\\ \;\;\;\;x \cdot \cos y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -4.8e-152) (not (<= z 2.5e-64)))
   (+ x (* z (sin y)))
   (* x (cos y))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -4.8e-152) || !(z <= 2.5e-64)) {
		tmp = x + (z * sin(y));
	} else {
		tmp = x * 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 ((z <= (-4.8d-152)) .or. (.not. (z <= 2.5d-64))) then
        tmp = x + (z * sin(y))
    else
        tmp = x * cos(y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((z <= -4.8e-152) || !(z <= 2.5e-64)) {
		tmp = x + (z * Math.sin(y));
	} else {
		tmp = x * Math.cos(y);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -4.8e-152) or not (z <= 2.5e-64):
		tmp = x + (z * math.sin(y))
	else:
		tmp = x * math.cos(y)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -4.8e-152) || !(z <= 2.5e-64))
		tmp = Float64(x + Float64(z * sin(y)));
	else
		tmp = Float64(x * cos(y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((z <= -4.8e-152) || ~((z <= 2.5e-64)))
		tmp = x + (z * sin(y));
	else
		tmp = x * cos(y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -4.8e-152], N[Not[LessEqual[z, 2.5e-64]], $MachinePrecision]], N[(x + N[(z * N[Sin[y], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x * N[Cos[y], $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -4.8e-152 or 2.50000000000000017e-64 < z

   1. Initial program 99.8%

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

   2. Taylor expanded in y around 0 90.1%

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

   if -4.8e-152 < z < 2.50000000000000017e-64

   1. Initial program 99.8%

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

   2. Taylor expanded in x around inf 90.1%

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

4. Final simplification 90.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.8 \cdot 10^{-152} \lor \neg \left(z \leq 2.5 \cdot 10^{-64}\right):\\ \;\;\;\;x + z \cdot \sin y\\ \mathbf{else}:\\ \;\;\;\;x \cdot \cos y\\ \end{array} \]

Alternative 5: 74.9% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -0.00205 \lor \neg \left(y \leq 420000\right):\\ \;\;\;\;x \cdot \cos y\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \left(z + y \cdot \left(x \cdot -0.5\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -0.00205) (not (<= y 420000.0)))
   (* x (cos y))
   (+ x (* y (+ z (* y (* x -0.5)))))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -0.00205) || !(y <= 420000.0)) {
		tmp = x * cos(y);
	} else {
		tmp = x + (y * (z + (y * (x * -0.5))));
	}
	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 <= (-0.00205d0)) .or. (.not. (y <= 420000.0d0))) then
        tmp = x * cos(y)
    else
        tmp = x + (y * (z + (y * (x * (-0.5d0)))))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((y <= -0.00205) || !(y <= 420000.0)) {
		tmp = x * Math.cos(y);
	} else {
		tmp = x + (y * (z + (y * (x * -0.5))));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -0.00205) or not (y <= 420000.0):
		tmp = x * math.cos(y)
	else:
		tmp = x + (y * (z + (y * (x * -0.5))))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -0.00205) || !(y <= 420000.0))
		tmp = Float64(x * cos(y));
	else
		tmp = Float64(x + Float64(y * Float64(z + Float64(y * Float64(x * -0.5)))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((y <= -0.00205) || ~((y <= 420000.0)))
		tmp = x * cos(y);
	else
		tmp = x + (y * (z + (y * (x * -0.5))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -0.00205], N[Not[LessEqual[y, 420000.0]], $MachinePrecision]], N[(x * N[Cos[y], $MachinePrecision]), $MachinePrecision], N[(x + N[(y * N[(z + N[(y * N[(x * -0.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -0.00205000000000000017 or 4.2e5 < y

   1. Initial program 99.7%

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

   2. Taylor expanded in x around inf 45.7%

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

   if -0.00205000000000000017 < y < 4.2e5

   1. Initial program 100.0%

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

   2. Taylor expanded in y around 0 97.1%

      \[\leadsto \color{blue}{x + \left(-0.5 \cdot \left(x \cdot {y}^{2}\right) + y \cdot z\right)} \]
   3. Step-by-step derivation

      1. associate-*r* 97.1%

         \[\leadsto x + \left(\color{blue}{\left(-0.5 \cdot x\right) \cdot {y}^{2}} + y \cdot z\right) \]

      2. unpow2 97.1%

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

      3. associate-*r* 97.1%

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

      4. *-commutative 97.1%

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

      5. distribute-rgt-out 97.1%

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

      6. *-commutative 97.1%

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

   4. Simplified 97.1%

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

4. Final simplification 71.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -0.00205 \lor \neg \left(y \leq 420000\right):\\ \;\;\;\;x \cdot \cos y\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \left(z + y \cdot \left(x \cdot -0.5\right)\right)\\ \end{array} \]

Alternative 6: 52.5% accurate, 41.4× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.8%

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

2. Taylor expanded in y around 0 51.2%

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

3. Final simplification 51.2%

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

Alternative 7: 17.2% accurate, 69.0× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.8%

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

2. Taylor expanded in y around 0 51.2%

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

3. Taylor expanded in x around 0 19.8%

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

4. Final simplification 19.8%

   \[\leadsto y \cdot z \]

Reproduce

herbie shell --seed 2023290 
(FPCore (x y z)
  :name "Diagrams.ThreeD.Transform:aboutY from diagrams-lib-1.3.0.3"
  :precision binary64
  (+ (* x (cos y)) (* z (sin y))))