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

Percentage Accurate: 99.8% → 99.8%

Time: 8.2s

Alternatives: 8

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: 73.9% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x \cdot \cos y\\ t_1 := z \cdot \sin y\\ \mathbf{if}\;y \leq -1.1 \cdot 10^{+67}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y \leq -5.5 \cdot 10^{-8}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 0.00095:\\ \;\;\;\;x + y \cdot z\\ \mathbf{elif}\;y \leq 2.65 \cdot 10^{+88}:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* x (cos y))) (t_1 (* z (sin y))))
   (if (<= y -1.1e+67)
     t_0
     (if (<= y -5.5e-8)
       t_1
       (if (<= y 0.00095) (+ x (* y z)) (if (<= y 2.65e+88) t_0 t_1))))))

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 <= -1.1e+67) {
		tmp = t_0;
	} else if (y <= -5.5e-8) {
		tmp = t_1;
	} else if (y <= 0.00095) {
		tmp = x + (y * z);
	} else if (y <= 2.65e+88) {
		tmp = t_0;
	} else {
		tmp = t_1;
	}
	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 <= (-1.1d+67)) then
        tmp = t_0
    else if (y <= (-5.5d-8)) then
        tmp = t_1
    else if (y <= 0.00095d0) then
        tmp = x + (y * z)
    else if (y <= 2.65d+88) then
        tmp = t_0
    else
        tmp = t_1
    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 <= -1.1e+67) {
		tmp = t_0;
	} else if (y <= -5.5e-8) {
		tmp = t_1;
	} else if (y <= 0.00095) {
		tmp = x + (y * z);
	} else if (y <= 2.65e+88) {
		tmp = t_0;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = x * math.cos(y)
	t_1 = z * math.sin(y)
	tmp = 0
	if y <= -1.1e+67:
		tmp = t_0
	elif y <= -5.5e-8:
		tmp = t_1
	elif y <= 0.00095:
		tmp = x + (y * z)
	elif y <= 2.65e+88:
		tmp = t_0
	else:
		tmp = t_1
	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 <= -1.1e+67)
		tmp = t_0;
	elseif (y <= -5.5e-8)
		tmp = t_1;
	elseif (y <= 0.00095)
		tmp = Float64(x + Float64(y * z));
	elseif (y <= 2.65e+88)
		tmp = t_0;
	else
		tmp = t_1;
	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 <= -1.1e+67)
		tmp = t_0;
	elseif (y <= -5.5e-8)
		tmp = t_1;
	elseif (y <= 0.00095)
		tmp = x + (y * z);
	elseif (y <= 2.65e+88)
		tmp = t_0;
	else
		tmp = t_1;
	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, -1.1e+67], t$95$0, If[LessEqual[y, -5.5e-8], t$95$1, If[LessEqual[y, 0.00095], N[(x + N[(y * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 2.65e+88], t$95$0, t$95$1]]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.1e67 or 9.49999999999999998e-4 < y < 2.64999999999999994e88

   1. Initial program 99.7%

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

   2. Taylor expanded in x around inf 63.4%

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

   if -1.1e67 < y < -5.5000000000000003e-8 or 2.64999999999999994e88 < y

   1. Initial program 99.7%

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

   2. Taylor expanded in x around 0 65.9%

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

   if -5.5000000000000003e-8 < y < 9.49999999999999998e-4

   1. Initial program 100.0%

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

   2. Taylor expanded in y around 0 99.6%

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

4. Final simplification 82.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.1 \cdot 10^{+67}:\\ \;\;\;\;x \cdot \cos y\\ \mathbf{elif}\;y \leq -5.5 \cdot 10^{-8}:\\ \;\;\;\;z \cdot \sin y\\ \mathbf{elif}\;y \leq 0.00095:\\ \;\;\;\;x + y \cdot z\\ \mathbf{elif}\;y \leq 2.65 \cdot 10^{+88}:\\ \;\;\;\;x \cdot \cos y\\ \mathbf{else}:\\ \;\;\;\;z \cdot \sin y\\ \end{array} \]

Alternative 3: 73.9% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x \cdot \cos y\\ t_1 := z \cdot \sin y\\ \mathbf{if}\;y \leq -3.8 \cdot 10^{+66}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y \leq -5.5 \cdot 10^{-8}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 0.00135:\\ \;\;\;\;\mathsf{fma}\left(y, z, x\right)\\ \mathbf{elif}\;y \leq 3.2 \cdot 10^{+88}:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* x (cos y))) (t_1 (* z (sin y))))
   (if (<= y -3.8e+66)
     t_0
     (if (<= y -5.5e-8)
       t_1
       (if (<= y 0.00135) (fma y z x) (if (<= y 3.2e+88) t_0 t_1))))))

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 <= -3.8e+66) {
		tmp = t_0;
	} else if (y <= -5.5e-8) {
		tmp = t_1;
	} else if (y <= 0.00135) {
		tmp = fma(y, z, x);
	} else if (y <= 3.2e+88) {
		tmp = t_0;
	} else {
		tmp = t_1;
	}
	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 <= -3.8e+66)
		tmp = t_0;
	elseif (y <= -5.5e-8)
		tmp = t_1;
	elseif (y <= 0.00135)
		tmp = fma(y, z, x);
	elseif (y <= 3.2e+88)
		tmp = t_0;
	else
		tmp = t_1;
	end
	return 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, -3.8e+66], t$95$0, If[LessEqual[y, -5.5e-8], t$95$1, If[LessEqual[y, 0.00135], N[(y * z + x), $MachinePrecision], If[LessEqual[y, 3.2e+88], t$95$0, t$95$1]]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -3.8000000000000002e66 or 0.0013500000000000001 < y < 3.1999999999999999e88

   1. Initial program 99.7%

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

   2. Taylor expanded in x around inf 63.4%

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

   if -3.8000000000000002e66 < y < -5.5000000000000003e-8 or 3.1999999999999999e88 < y

   1. Initial program 99.7%

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

   2. Taylor expanded in x around 0 65.9%

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

   if -5.5000000000000003e-8 < y < 0.0013500000000000001

   1. Initial program 100.0%

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

   2. Taylor expanded in y around 0 99.6%

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

      1. +-commutative 99.6%

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

      2. fma-def 99.6%

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

   4. Simplified 99.6%

      \[\leadsto \color{blue}{\mathsf{fma}\left(y, z, x\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification 82.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.8 \cdot 10^{+66}:\\ \;\;\;\;x \cdot \cos y\\ \mathbf{elif}\;y \leq -5.5 \cdot 10^{-8}:\\ \;\;\;\;z \cdot \sin y\\ \mathbf{elif}\;y \leq 0.00135:\\ \;\;\;\;\mathsf{fma}\left(y, z, x\right)\\ \mathbf{elif}\;y \leq 3.2 \cdot 10^{+88}:\\ \;\;\;\;x \cdot \cos y\\ \mathbf{else}:\\ \;\;\;\;z \cdot \sin y\\ \end{array} \]

Alternative 4: 85.5% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -6.3 \cdot 10^{-114} \lor \neg \left(z \leq 6.5 \cdot 10^{-160}\right):\\ \;\;\;\;x + z \cdot \sin y\\ \mathbf{else}:\\ \;\;\;\;x \cdot \cos y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -6.3e-114) (not (<= z 6.5e-160)))
   (+ x (* z (sin y)))
   (* x (cos y))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -6.3e-114) || !(z <= 6.5e-160)) {
		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 <= (-6.3d-114)) .or. (.not. (z <= 6.5d-160))) 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 <= -6.3e-114) || !(z <= 6.5e-160)) {
		tmp = x + (z * Math.sin(y));
	} else {
		tmp = x * Math.cos(y);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -6.3e-114) or not (z <= 6.5e-160):
		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 <= -6.3e-114) || !(z <= 6.5e-160))
		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 <= -6.3e-114) || ~((z <= 6.5e-160)))
		tmp = x + (z * sin(y));
	else
		tmp = x * cos(y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -6.3e-114], N[Not[LessEqual[z, 6.5e-160]], $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 < -6.30000000000000014e-114 or 6.4999999999999996e-160 < z

   1. Initial program 99.9%

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

   2. Taylor expanded in y around 0 85.6%

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

   if -6.30000000000000014e-114 < z < 6.4999999999999996e-160

   1. Initial program 99.8%

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

   2. Taylor expanded in x around inf 94.3%

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

4. Final simplification 88.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -6.3 \cdot 10^{-114} \lor \neg \left(z \leq 6.5 \cdot 10^{-160}\right):\\ \;\;\;\;x + z \cdot \sin y\\ \mathbf{else}:\\ \;\;\;\;x \cdot \cos y\\ \end{array} \]

Alternative 5: 73.9% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -42000 \lor \neg \left(y \leq 0.00105\right):\\ \;\;\;\;x \cdot \cos y\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -42000.0) (not (<= y 0.00105))) (* x (cos y)) (+ x (* y z))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -42000.0) || !(y <= 0.00105)) {
		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 <= (-42000.0d0)) .or. (.not. (y <= 0.00105d0))) 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 <= -42000.0) || !(y <= 0.00105)) {
		tmp = x * Math.cos(y);
	} else {
		tmp = x + (y * z);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -42000.0) or not (y <= 0.00105):
		tmp = x * math.cos(y)
	else:
		tmp = x + (y * z)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -42000.0) || !(y <= 0.00105))
		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 <= -42000.0) || ~((y <= 0.00105)))
		tmp = x * cos(y);
	else
		tmp = x + (y * z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -42000.0], N[Not[LessEqual[y, 0.00105]], $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 < -42000 or 0.00104999999999999994 < y

   1. Initial program 99.7%

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

   2. Taylor expanded in x around inf 52.0%

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

   if -42000 < y < 0.00104999999999999994

   1. Initial program 100.0%

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

   2. Taylor expanded in y around 0 97.9%

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

4. Final simplification 76.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -42000 \lor \neg \left(y \leq 0.00105\right):\\ \;\;\;\;x \cdot \cos y\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot z\\ \end{array} \]

Alternative 6: 38.5% accurate, 40.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq 2.8 \cdot 10^{+27}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 (if (<= z 2.8e+27) x (* y z)))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= 2.8e+27) {
		tmp = x;
	} else {
		tmp = 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 <= 2.8d+27) then
        tmp = x
    else
        tmp = y * z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (z <= 2.8e+27) {
		tmp = x;
	} else {
		tmp = y * z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= 2.8e+27:
		tmp = x
	else:
		tmp = y * z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= 2.8e+27)
		tmp = x;
	else
		tmp = Float64(y * z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= 2.8e+27)
		tmp = x;
	else
		tmp = y * z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, 2.8e+27], x, N[(y * z), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < 2.7999999999999999e27

   1. Initial program 99.8%

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

   2. Taylor expanded in y around 0 58.4%

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

   3. Taylor expanded in x around inf 48.5%

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

   if 2.7999999999999999e27 < z

   1. Initial program 99.8%

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

   2. Taylor expanded in y around 0 38.5%

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

   3. Taylor expanded in x around 0 26.8%

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

      1. *-commutative 26.8%

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

   5. Simplified 26.8%

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

4. Final simplification 44.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq 2.8 \cdot 10^{+27}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y \cdot z\\ \end{array} \]

Alternative 7: 51.8% 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 54.3%

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

3. Final simplification 54.3%

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

Alternative 8: 38.6% 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. Taylor expanded in y around 0 54.3%

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

3. Taylor expanded in x around inf 41.7%

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

4. Final simplification 41.7%

   \[\leadsto x \]

Reproduce

herbie shell --seed 2023311 
(FPCore (x y z)
  :name "Diagrams.ThreeD.Transform:aboutY from diagrams-lib-1.3.0.3"
  :precision binary64
  (+ (* x (cos y)) (* z (sin y))))