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

Percentage Accurate: 99.8% → 99.8%

Time: 9.6s

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, 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]

Derivation

1. Initial program 99.8%

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

2. Final simplification 99.8%

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

Alternative 2: 74.5% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := z \cdot \sin y\\ \mathbf{if}\;y \leq -66000000000:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y \leq 0.3:\\ \;\;\;\;x + y \cdot \left(z + y \cdot \left(x \cdot -0.5\right)\right)\\ \mathbf{elif}\;y \leq 2.85 \cdot 10^{+190} \lor \neg \left(y \leq 7.8 \cdot 10^{+238}\right):\\ \;\;\;\;x \cdot \cos y\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* z (sin y))))
   (if (<= y -66000000000.0)
     t_0
     (if (<= y 0.3)
       (+ x (* y (+ z (* y (* x -0.5)))))
       (if (or (<= y 2.85e+190) (not (<= y 7.8e+238))) (* x (cos y)) t_0)))))

C

double code(double x, double y, double z) {
	double t_0 = z * sin(y);
	double tmp;
	if (y <= -66000000000.0) {
		tmp = t_0;
	} else if (y <= 0.3) {
		tmp = x + (y * (z + (y * (x * -0.5))));
	} else if ((y <= 2.85e+190) || !(y <= 7.8e+238)) {
		tmp = x * cos(y);
	} 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) :: tmp
    t_0 = z * sin(y)
    if (y <= (-66000000000.0d0)) then
        tmp = t_0
    else if (y <= 0.3d0) then
        tmp = x + (y * (z + (y * (x * (-0.5d0)))))
    else if ((y <= 2.85d+190) .or. (.not. (y <= 7.8d+238))) then
        tmp = x * cos(y)
    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.sin(y);
	double tmp;
	if (y <= -66000000000.0) {
		tmp = t_0;
	} else if (y <= 0.3) {
		tmp = x + (y * (z + (y * (x * -0.5))));
	} else if ((y <= 2.85e+190) || !(y <= 7.8e+238)) {
		tmp = x * Math.cos(y);
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = z * math.sin(y)
	tmp = 0
	if y <= -66000000000.0:
		tmp = t_0
	elif y <= 0.3:
		tmp = x + (y * (z + (y * (x * -0.5))))
	elif (y <= 2.85e+190) or not (y <= 7.8e+238):
		tmp = x * math.cos(y)
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(z * sin(y))
	tmp = 0.0
	if (y <= -66000000000.0)
		tmp = t_0;
	elseif (y <= 0.3)
		tmp = Float64(x + Float64(y * Float64(z + Float64(y * Float64(x * -0.5)))));
	elseif ((y <= 2.85e+190) || !(y <= 7.8e+238))
		tmp = Float64(x * cos(y));
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = z * sin(y);
	tmp = 0.0;
	if (y <= -66000000000.0)
		tmp = t_0;
	elseif (y <= 0.3)
		tmp = x + (y * (z + (y * (x * -0.5))));
	elseif ((y <= 2.85e+190) || ~((y <= 7.8e+238)))
		tmp = x * cos(y);
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(z * N[Sin[y], $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -66000000000.0], t$95$0, If[LessEqual[y, 0.3], N[(x + N[(y * N[(z + N[(y * N[(x * -0.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[y, 2.85e+190], N[Not[LessEqual[y, 7.8e+238]], $MachinePrecision]], N[(x * N[Cos[y], $MachinePrecision]), $MachinePrecision], t$95$0]]]]

Derivation

1. Split input into 3 regimes

2. if y < -6.6e10 or 2.84999999999999993e190 < y < 7.79999999999999986e238

   1. Initial program 99.8%

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

   2. Taylor expanded in x around 0 62.9%

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

   if -6.6e10 < y < 0.299999999999999989

   1. Initial program 100.0%

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

   2. Taylor expanded in y around 0 98.1%

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

      1. +-commutative 98.1%

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

      2. *-commutative 98.1%

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

      3. associate-*r* 98.1%

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

      4. unpow2 98.1%

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

      5. associate-*r* 98.1%

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

      6. distribute-rgt-out 98.1%

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

      7. *-commutative 98.1%

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

   4. Simplified 98.1%

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

   if 0.299999999999999989 < y < 2.84999999999999993e190 or 7.79999999999999986e238 < y

   1. Initial program 99.5%

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

   2. Taylor expanded in x around inf 69.1%

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

4. Final simplification 83.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -66000000000:\\ \;\;\;\;z \cdot \sin y\\ \mathbf{elif}\;y \leq 0.3:\\ \;\;\;\;x + y \cdot \left(z + y \cdot \left(x \cdot -0.5\right)\right)\\ \mathbf{elif}\;y \leq 2.85 \cdot 10^{+190} \lor \neg \left(y \leq 7.8 \cdot 10^{+238}\right):\\ \;\;\;\;x \cdot \cos y\\ \mathbf{else}:\\ \;\;\;\;z \cdot \sin y\\ \end{array} \]

Alternative 3: 85.3% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -2.6 \cdot 10^{+47} \lor \neg \left(x \leq 4.2 \cdot 10^{+138}\right):\\ \;\;\;\;x \cdot \cos y\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \sin y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -2.6e+47) (not (<= x 4.2e+138)))
   (* x (cos y))
   (+ x (* z (sin y)))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -2.6e+47) || !(x <= 4.2e+138)) {
		tmp = x * cos(y);
	} else {
		tmp = x + (z * 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 <= (-2.6d+47)) .or. (.not. (x <= 4.2d+138))) then
        tmp = x * cos(y)
    else
        tmp = x + (z * sin(y))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((x <= -2.6e+47) || !(x <= 4.2e+138)) {
		tmp = x * Math.cos(y);
	} else {
		tmp = x + (z * Math.sin(y));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -2.6e+47) or not (x <= 4.2e+138):
		tmp = x * math.cos(y)
	else:
		tmp = x + (z * math.sin(y))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -2.6e+47) || !(x <= 4.2e+138))
		tmp = Float64(x * cos(y));
	else
		tmp = Float64(x + Float64(z * sin(y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((x <= -2.6e+47) || ~((x <= 4.2e+138)))
		tmp = x * cos(y);
	else
		tmp = x + (z * sin(y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -2.6e+47], N[Not[LessEqual[x, 4.2e+138]], $MachinePrecision]], N[(x * N[Cos[y], $MachinePrecision]), $MachinePrecision], N[(x + N[(z * N[Sin[y], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -2.60000000000000003e47 or 4.20000000000000014e138 < x

   1. Initial program 99.8%

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

   2. Taylor expanded in x around inf 93.5%

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

   if -2.60000000000000003e47 < x < 4.20000000000000014e138

   1. Initial program 99.9%

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

   2. Taylor expanded in y around 0 92.5%

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

4. Final simplification 92.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.6 \cdot 10^{+47} \lor \neg \left(x \leq 4.2 \cdot 10^{+138}\right):\\ \;\;\;\;x \cdot \cos y\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \sin y\\ \end{array} \]

Alternative 4: 74.5% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -0.0032 \lor \neg \left(y \leq 0.28\right):\\ \;\;\;\;x \cdot \cos y\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -0.0032) (not (<= y 0.28))) (* x (cos y)) (+ x (* y z))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -0.0032) || !(y <= 0.28)) {
		tmp = x * cos(y);
	} else {
		tmp = x + (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 <= (-0.0032d0)) .or. (.not. (y <= 0.28d0))) then
        tmp = x * cos(y)
    else
        tmp = x + (y * z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((y <= -0.0032) || !(y <= 0.28)) {
		tmp = x * Math.cos(y);
	} else {
		tmp = x + (y * z);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -0.0032) or not (y <= 0.28):
		tmp = x * math.cos(y)
	else:
		tmp = x + (y * z)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -0.0032) || !(y <= 0.28))
		tmp = Float64(x * cos(y));
	else
		tmp = Float64(x + Float64(y * z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((y <= -0.0032) || ~((y <= 0.28)))
		tmp = x * cos(y);
	else
		tmp = x + (y * z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -0.0032], N[Not[LessEqual[y, 0.28]], $MachinePrecision]], N[(x * N[Cos[y], $MachinePrecision]), $MachinePrecision], N[(x + N[(y * z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -0.00320000000000000015 or 0.28000000000000003 < y

   1. Initial program 99.7%

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

   2. Taylor expanded in x around inf 51.5%

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

   if -0.00320000000000000015 < y < 0.28000000000000003

   1. Initial program 100.0%

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

   2. Taylor expanded in y around 0 98.9%

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

      1. +-commutative 98.9%

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

   4. Simplified 98.9%

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

4. Final simplification 77.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -0.0032 \lor \neg \left(y \leq 0.28\right):\\ \;\;\;\;x \cdot \cos y\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot z\\ \end{array} \]

Alternative 5: 42.1% accurate, 29.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -5.2 \cdot 10^{-116}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 8 \cdot 10^{-111}:\\ \;\;\;\;y \cdot z\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -5.2e-116) x (if (<= x 8e-111) (* y z) x)))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -5.2e-116) {
		tmp = x;
	} else if (x <= 8e-111) {
		tmp = y * z;
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (x <= (-5.2d-116)) then
        tmp = x
    else if (x <= 8d-111) then
        tmp = y * z
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (x <= -5.2e-116) {
		tmp = x;
	} else if (x <= 8e-111) {
		tmp = y * z;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= -5.2e-116:
		tmp = x
	elif x <= 8e-111:
		tmp = y * z
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -5.2e-116)
		tmp = x;
	elseif (x <= 8e-111)
		tmp = Float64(y * z);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (x <= -5.2e-116)
		tmp = x;
	elseif (x <= 8e-111)
		tmp = y * z;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -5.2e-116], x, If[LessEqual[x, 8e-111], N[(y * z), $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if x < -5.2000000000000001e-116 or 8.00000000000000071e-111 < x

   1. Initial program 99.9%

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

      1. flip3-+ 40.2%

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

      2. clear-num 40.1%

         \[\leadsto \color{blue}{\frac{1}{\frac{\left(x \cdot \cos y\right) \cdot \left(x \cdot \cos y\right) + \left(\left(z \cdot \sin y\right) \cdot \left(z \cdot \sin y\right) - \left(x \cdot \cos y\right) \cdot \left(z \cdot \sin y\right)\right)}{{\left(x \cdot \cos y\right)}^{3} + {\left(z \cdot \sin y\right)}^{3}}}} \]

      3. clear-num 40.1%

         \[\leadsto \frac{1}{\color{blue}{\frac{1}{\frac{{\left(x \cdot \cos y\right)}^{3} + {\left(z \cdot \sin y\right)}^{3}}{\left(x \cdot \cos y\right) \cdot \left(x \cdot \cos y\right) + \left(\left(z \cdot \sin y\right) \cdot \left(z \cdot \sin y\right) - \left(x \cdot \cos y\right) \cdot \left(z \cdot \sin y\right)\right)}}}} \]

      4. flip3-+ 99.5%

         \[\leadsto \frac{1}{\frac{1}{\color{blue}{x \cdot \cos y + z \cdot \sin y}}} \]

      5. +-commutative 99.5%

         \[\leadsto \frac{1}{\frac{1}{\color{blue}{z \cdot \sin y + x \cdot \cos y}}} \]

      6. fma-def 99.5%

         \[\leadsto \frac{1}{\frac{1}{\color{blue}{\mathsf{fma}\left(z, \sin y, x \cdot \cos y\right)}}} \]

   3. Applied egg-rr 99.5%

      \[\leadsto \color{blue}{\frac{1}{\frac{1}{\mathsf{fma}\left(z, \sin y, x \cdot \cos y\right)}}} \]

   4. Taylor expanded in y around 0 53.3%

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

   if -5.2000000000000001e-116 < x < 8.00000000000000071e-111

   1. Initial program 99.8%

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

   2. Taylor expanded in y around 0 51.4%

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

      1. +-commutative 51.4%

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

   4. Simplified 51.4%

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

   5. Taylor expanded in y around inf 33.8%

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

4. Final simplification 47.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -5.2 \cdot 10^{-116}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 8 \cdot 10^{-111}:\\ \;\;\;\;y \cdot z\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 6: 52.7% 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 58.1%

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

   1. +-commutative 58.1%

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

4. Simplified 58.1%

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

5. Final simplification 58.1%

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

Alternative 7: 38.4% accurate, 207.0× speedup

Math

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

FPCore

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

C

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

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
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_] := x

Derivation

1. Initial program 99.8%

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

   1. flip3-+ 38.0%

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

   2. clear-num 37.9%

      \[\leadsto \color{blue}{\frac{1}{\frac{\left(x \cdot \cos y\right) \cdot \left(x \cdot \cos y\right) + \left(\left(z \cdot \sin y\right) \cdot \left(z \cdot \sin y\right) - \left(x \cdot \cos y\right) \cdot \left(z \cdot \sin y\right)\right)}{{\left(x \cdot \cos y\right)}^{3} + {\left(z \cdot \sin y\right)}^{3}}}} \]

   3. clear-num 37.9%

      \[\leadsto \frac{1}{\color{blue}{\frac{1}{\frac{{\left(x \cdot \cos y\right)}^{3} + {\left(z \cdot \sin y\right)}^{3}}{\left(x \cdot \cos y\right) \cdot \left(x \cdot \cos y\right) + \left(\left(z \cdot \sin y\right) \cdot \left(z \cdot \sin y\right) - \left(x \cdot \cos y\right) \cdot \left(z \cdot \sin y\right)\right)}}}} \]

   4. flip3-+ 99.5%

      \[\leadsto \frac{1}{\frac{1}{\color{blue}{x \cdot \cos y + z \cdot \sin y}}} \]

   5. +-commutative 99.5%

      \[\leadsto \frac{1}{\frac{1}{\color{blue}{z \cdot \sin y + x \cdot \cos y}}} \]

   6. fma-def 99.5%

      \[\leadsto \frac{1}{\frac{1}{\color{blue}{\mathsf{fma}\left(z, \sin y, x \cdot \cos y\right)}}} \]

3. Applied egg-rr 99.5%

   \[\leadsto \color{blue}{\frac{1}{\frac{1}{\mathsf{fma}\left(z, \sin y, x \cdot \cos y\right)}}} \]

4. Taylor expanded in y around 0 43.3%

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

5. Final simplification 43.3%

   \[\leadsto x \]

Reproduce

herbie shell --seed 2023301 
(FPCore (x y z)
  :name "Diagrams.ThreeD.Transform:aboutY from diagrams-lib-1.3.0.3"
  :precision binary64
  (+ (* x (cos y)) (* z (sin y))))