Diagrams.Solve.Tridiagonal:solveCyclicTriDiagonal from diagrams-solve-0.1, A

Percentage Accurate: 92.1% → 99.4%

Time: 2.9s

Alternatives: 6

Speedup: 1.0×

Specification

Math

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

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(Float64(x * y) / z)
end

MATLAB

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

Wolfram

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

Initial Program: 92.1% accurate, 1.0× speedup

Math

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

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(Float64(x * y) / z)
end

MATLAB

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

Wolfram

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

Alternative 1: 99.4% accurate, 0.2× speedup

Math

\[\begin{array}{l} [x, y] = \mathsf{sort}([x, y])\\ \\ \begin{array}{l} t_0 := \frac{x \cdot y}{z}\\ \mathbf{if}\;x \cdot y \leq -2 \cdot 10^{+221}:\\ \;\;\;\;\frac{\frac{y}{z}}{\frac{1}{x}}\\ \mathbf{elif}\;x \cdot y \leq -2 \cdot 10^{-205}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;x \cdot y \leq 10^{-169}:\\ \;\;\;\;\frac{x}{\frac{z}{y}}\\ \mathbf{elif}\;x \cdot y \leq 10^{+230}:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \end{array} \end{array} \]

FPCore

NOTE: x and y should be sorted in increasing order before calling this function.
(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (/ (* x y) z)))
   (if (<= (* x y) -2e+221)
     (/ (/ y z) (/ 1.0 x))
     (if (<= (* x y) -2e-205)
       t_0
       (if (<= (* x y) 1e-169)
         (/ x (/ z y))
         (if (<= (* x y) 1e+230) t_0 (* x (/ y z))))))))

C

assert(x < y);
double code(double x, double y, double z) {
	double t_0 = (x * y) / z;
	double tmp;
	if ((x * y) <= -2e+221) {
		tmp = (y / z) / (1.0 / x);
	} else if ((x * y) <= -2e-205) {
		tmp = t_0;
	} else if ((x * y) <= 1e-169) {
		tmp = x / (z / y);
	} else if ((x * y) <= 1e+230) {
		tmp = t_0;
	} else {
		tmp = x * (y / z);
	}
	return tmp;
}

Fortran

NOTE: x and y should be sorted in increasing order before calling this function.
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 = (x * y) / z
    if ((x * y) <= (-2d+221)) then
        tmp = (y / z) / (1.0d0 / x)
    else if ((x * y) <= (-2d-205)) then
        tmp = t_0
    else if ((x * y) <= 1d-169) then
        tmp = x / (z / y)
    else if ((x * y) <= 1d+230) then
        tmp = t_0
    else
        tmp = x * (y / z)
    end if
    code = tmp
end function

Java

assert x < y;
public static double code(double x, double y, double z) {
	double t_0 = (x * y) / z;
	double tmp;
	if ((x * y) <= -2e+221) {
		tmp = (y / z) / (1.0 / x);
	} else if ((x * y) <= -2e-205) {
		tmp = t_0;
	} else if ((x * y) <= 1e-169) {
		tmp = x / (z / y);
	} else if ((x * y) <= 1e+230) {
		tmp = t_0;
	} else {
		tmp = x * (y / z);
	}
	return tmp;
}

Python

[x, y] = sort([x, y])
def code(x, y, z):
	t_0 = (x * y) / z
	tmp = 0
	if (x * y) <= -2e+221:
		tmp = (y / z) / (1.0 / x)
	elif (x * y) <= -2e-205:
		tmp = t_0
	elif (x * y) <= 1e-169:
		tmp = x / (z / y)
	elif (x * y) <= 1e+230:
		tmp = t_0
	else:
		tmp = x * (y / z)
	return tmp

Julia

x, y = sort([x, y])
function code(x, y, z)
	t_0 = Float64(Float64(x * y) / z)
	tmp = 0.0
	if (Float64(x * y) <= -2e+221)
		tmp = Float64(Float64(y / z) / Float64(1.0 / x));
	elseif (Float64(x * y) <= -2e-205)
		tmp = t_0;
	elseif (Float64(x * y) <= 1e-169)
		tmp = Float64(x / Float64(z / y));
	elseif (Float64(x * y) <= 1e+230)
		tmp = t_0;
	else
		tmp = Float64(x * Float64(y / z));
	end
	return tmp
end

MATLAB

x, y = num2cell(sort([x, y])){:}
function tmp_2 = code(x, y, z)
	t_0 = (x * y) / z;
	tmp = 0.0;
	if ((x * y) <= -2e+221)
		tmp = (y / z) / (1.0 / x);
	elseif ((x * y) <= -2e-205)
		tmp = t_0;
	elseif ((x * y) <= 1e-169)
		tmp = x / (z / y);
	elseif ((x * y) <= 1e+230)
		tmp = t_0;
	else
		tmp = x * (y / z);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x and y should be sorted in increasing order before calling this function.
code[x_, y_, z_] := Block[{t$95$0 = N[(N[(x * y), $MachinePrecision] / z), $MachinePrecision]}, If[LessEqual[N[(x * y), $MachinePrecision], -2e+221], N[(N[(y / z), $MachinePrecision] / N[(1.0 / x), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], -2e-205], t$95$0, If[LessEqual[N[(x * y), $MachinePrecision], 1e-169], N[(x / N[(z / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], 1e+230], t$95$0, N[(x * N[(y / z), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if (*.f64 x y) < -2.0000000000000001e221

   1. Initial program 84.0%

      \[\frac{x \cdot y}{z} \]
   2. Step-by-step derivation

      1. associate-/l* 99.8%

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

   3. Simplified 99.8%

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

      1. *-un-lft-identity 99.8%

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

      2. div-inv 99.8%

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

      3. times-frac 84.1%

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

   5. Applied egg-rr 84.1%

      \[\leadsto \color{blue}{\frac{1}{z} \cdot \frac{x}{\frac{1}{y}}} \]
   6. Step-by-step derivation

      1. frac-times 99.8%

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

      2. *-un-lft-identity 99.8%

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

      3. un-div-inv 99.8%

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

      4. associate-/l* 84.0%

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

      5. *-commutative 84.0%

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

      6. associate-*l/ 99.8%

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

      7. associate-/r/ 99.8%

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

      8. div-inv 99.7%

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

      9. associate-/r* 99.8%

         \[\leadsto \color{blue}{\frac{\frac{y}{z}}{\frac{1}{x}}} \]

   7. Applied egg-rr 99.8%

      \[\leadsto \color{blue}{\frac{\frac{y}{z}}{\frac{1}{x}}} \]

   if -2.0000000000000001e221 < (*.f64 x y) < -2e-205 or 1.00000000000000002e-169 < (*.f64 x y) < 1.0000000000000001e230

   1. Initial program 99.6%

      \[\frac{x \cdot y}{z} \]

   if -2e-205 < (*.f64 x y) < 1.00000000000000002e-169

   1. Initial program 86.1%

      \[\frac{x \cdot y}{z} \]
   2. Step-by-step derivation

      1. associate-/l* 99.9%

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

   3. Simplified 99.9%

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

   if 1.0000000000000001e230 < (*.f64 x y)

   1. Initial program 73.7%

      \[\frac{x \cdot y}{z} \]
   2. Step-by-step derivation

      1. associate-*r/ 99.8%

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

   3. Simplified 99.8%

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

4. Final simplification 99.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -2 \cdot 10^{+221}:\\ \;\;\;\;\frac{\frac{y}{z}}{\frac{1}{x}}\\ \mathbf{elif}\;x \cdot y \leq -2 \cdot 10^{-205}:\\ \;\;\;\;\frac{x \cdot y}{z}\\ \mathbf{elif}\;x \cdot y \leq 10^{-169}:\\ \;\;\;\;\frac{x}{\frac{z}{y}}\\ \mathbf{elif}\;x \cdot y \leq 10^{+230}:\\ \;\;\;\;\frac{x \cdot y}{z}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \end{array} \]

Alternative 2: 99.0% accurate, 0.2× speedup

Math

\[\begin{array}{l} [x, y] = \mathsf{sort}([x, y])\\ \\ \begin{array}{l} t_0 := \frac{x}{\frac{z}{y}}\\ t_1 := \frac{x \cdot y}{z}\\ \mathbf{if}\;x \cdot y \leq -1 \cdot 10^{+125}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;x \cdot y \leq -2 \cdot 10^{-205}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \cdot y \leq 10^{-169}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;x \cdot y \leq 10^{+230}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \end{array} \end{array} \]

FPCore

NOTE: x and y should be sorted in increasing order before calling this function.
(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (/ x (/ z y))) (t_1 (/ (* x y) z)))
   (if (<= (* x y) -1e+125)
     t_0
     (if (<= (* x y) -2e-205)
       t_1
       (if (<= (* x y) 1e-169)
         t_0
         (if (<= (* x y) 1e+230) t_1 (* x (/ y z))))))))

C

assert(x < y);
double code(double x, double y, double z) {
	double t_0 = x / (z / y);
	double t_1 = (x * y) / z;
	double tmp;
	if ((x * y) <= -1e+125) {
		tmp = t_0;
	} else if ((x * y) <= -2e-205) {
		tmp = t_1;
	} else if ((x * y) <= 1e-169) {
		tmp = t_0;
	} else if ((x * y) <= 1e+230) {
		tmp = t_1;
	} else {
		tmp = x * (y / z);
	}
	return tmp;
}

Fortran

NOTE: x and y should be sorted in increasing order before calling this function.
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 / (z / y)
    t_1 = (x * y) / z
    if ((x * y) <= (-1d+125)) then
        tmp = t_0
    else if ((x * y) <= (-2d-205)) then
        tmp = t_1
    else if ((x * y) <= 1d-169) then
        tmp = t_0
    else if ((x * y) <= 1d+230) then
        tmp = t_1
    else
        tmp = x * (y / z)
    end if
    code = tmp
end function

Java

assert x < y;
public static double code(double x, double y, double z) {
	double t_0 = x / (z / y);
	double t_1 = (x * y) / z;
	double tmp;
	if ((x * y) <= -1e+125) {
		tmp = t_0;
	} else if ((x * y) <= -2e-205) {
		tmp = t_1;
	} else if ((x * y) <= 1e-169) {
		tmp = t_0;
	} else if ((x * y) <= 1e+230) {
		tmp = t_1;
	} else {
		tmp = x * (y / z);
	}
	return tmp;
}

Python

[x, y] = sort([x, y])
def code(x, y, z):
	t_0 = x / (z / y)
	t_1 = (x * y) / z
	tmp = 0
	if (x * y) <= -1e+125:
		tmp = t_0
	elif (x * y) <= -2e-205:
		tmp = t_1
	elif (x * y) <= 1e-169:
		tmp = t_0
	elif (x * y) <= 1e+230:
		tmp = t_1
	else:
		tmp = x * (y / z)
	return tmp

Julia

x, y = sort([x, y])
function code(x, y, z)
	t_0 = Float64(x / Float64(z / y))
	t_1 = Float64(Float64(x * y) / z)
	tmp = 0.0
	if (Float64(x * y) <= -1e+125)
		tmp = t_0;
	elseif (Float64(x * y) <= -2e-205)
		tmp = t_1;
	elseif (Float64(x * y) <= 1e-169)
		tmp = t_0;
	elseif (Float64(x * y) <= 1e+230)
		tmp = t_1;
	else
		tmp = Float64(x * Float64(y / z));
	end
	return tmp
end

MATLAB

x, y = num2cell(sort([x, y])){:}
function tmp_2 = code(x, y, z)
	t_0 = x / (z / y);
	t_1 = (x * y) / z;
	tmp = 0.0;
	if ((x * y) <= -1e+125)
		tmp = t_0;
	elseif ((x * y) <= -2e-205)
		tmp = t_1;
	elseif ((x * y) <= 1e-169)
		tmp = t_0;
	elseif ((x * y) <= 1e+230)
		tmp = t_1;
	else
		tmp = x * (y / z);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x and y should be sorted in increasing order before calling this function.
code[x_, y_, z_] := Block[{t$95$0 = N[(x / N[(z / y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(N[(x * y), $MachinePrecision] / z), $MachinePrecision]}, If[LessEqual[N[(x * y), $MachinePrecision], -1e+125], t$95$0, If[LessEqual[N[(x * y), $MachinePrecision], -2e-205], t$95$1, If[LessEqual[N[(x * y), $MachinePrecision], 1e-169], t$95$0, If[LessEqual[N[(x * y), $MachinePrecision], 1e+230], t$95$1, N[(x * N[(y / z), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 x y) < -9.9999999999999992e124 or -2e-205 < (*.f64 x y) < 1.00000000000000002e-169

   1. Initial program 87.4%

      \[\frac{x \cdot y}{z} \]
   2. Step-by-step derivation

      1. associate-/l* 99.7%

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

   3. Simplified 99.7%

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

   if -9.9999999999999992e124 < (*.f64 x y) < -2e-205 or 1.00000000000000002e-169 < (*.f64 x y) < 1.0000000000000001e230

   1. Initial program 99.6%

      \[\frac{x \cdot y}{z} \]

   if 1.0000000000000001e230 < (*.f64 x y)

   1. Initial program 73.7%

      \[\frac{x \cdot y}{z} \]
   2. Step-by-step derivation

      1. associate-*r/ 99.8%

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

   3. Simplified 99.8%

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

4. Final simplification 99.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -1 \cdot 10^{+125}:\\ \;\;\;\;\frac{x}{\frac{z}{y}}\\ \mathbf{elif}\;x \cdot y \leq -2 \cdot 10^{-205}:\\ \;\;\;\;\frac{x \cdot y}{z}\\ \mathbf{elif}\;x \cdot y \leq 10^{-169}:\\ \;\;\;\;\frac{x}{\frac{z}{y}}\\ \mathbf{elif}\;x \cdot y \leq 10^{+230}:\\ \;\;\;\;\frac{x \cdot y}{z}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \end{array} \]

Alternative 3: 92.0% accurate, 0.7× speedup

Math

\[\begin{array}{l} [x, y] = \mathsf{sort}([x, y])\\ \\ \begin{array}{l} \mathbf{if}\;x \leq -1.7 \cdot 10^{+205}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{x}{z}\\ \end{array} \end{array} \]

FPCore

NOTE: x and y should be sorted in increasing order before calling this function.
(FPCore (x y z)
 :precision binary64
 (if (<= x -1.7e+205) (* x (/ y z)) (* y (/ x z))))

C

assert(x < y);
double code(double x, double y, double z) {
	double tmp;
	if (x <= -1.7e+205) {
		tmp = x * (y / z);
	} else {
		tmp = y * (x / z);
	}
	return tmp;
}

Fortran

NOTE: x and y should be sorted in increasing order before calling this function.
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 <= (-1.7d+205)) then
        tmp = x * (y / z)
    else
        tmp = y * (x / z)
    end if
    code = tmp
end function

Java

assert x < y;
public static double code(double x, double y, double z) {
	double tmp;
	if (x <= -1.7e+205) {
		tmp = x * (y / z);
	} else {
		tmp = y * (x / z);
	}
	return tmp;
}

Python

[x, y] = sort([x, y])
def code(x, y, z):
	tmp = 0
	if x <= -1.7e+205:
		tmp = x * (y / z)
	else:
		tmp = y * (x / z)
	return tmp

Julia

x, y = sort([x, y])
function code(x, y, z)
	tmp = 0.0
	if (x <= -1.7e+205)
		tmp = Float64(x * Float64(y / z));
	else
		tmp = Float64(y * Float64(x / z));
	end
	return tmp
end

MATLAB

x, y = num2cell(sort([x, y])){:}
function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (x <= -1.7e+205)
		tmp = x * (y / z);
	else
		tmp = y * (x / z);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x and y should be sorted in increasing order before calling this function.
code[x_, y_, z_] := If[LessEqual[x, -1.7e+205], N[(x * N[(y / z), $MachinePrecision]), $MachinePrecision], N[(y * N[(x / z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -1.7e205

   1. Initial program 85.2%

      \[\frac{x \cdot y}{z} \]
   2. Step-by-step derivation

      1. associate-*r/ 99.9%

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

   3. Simplified 99.9%

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

   if -1.7e205 < x

   1. Initial program 92.8%

      \[\frac{x \cdot y}{z} \]
   2. Step-by-step derivation

      1. associate-*l/ 89.4%

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

   3. Simplified 89.4%

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

4. Final simplification 90.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.7 \cdot 10^{+205}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{x}{z}\\ \end{array} \]

Alternative 4: 91.8% accurate, 0.7× speedup

Math

\[\begin{array}{l} [x, y] = \mathsf{sort}([x, y])\\ \\ \begin{array}{l} \mathbf{if}\;x \leq -5.2 \cdot 10^{+203}:\\ \;\;\;\;\frac{x}{\frac{z}{y}}\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{x}{z}\\ \end{array} \end{array} \]

FPCore

NOTE: x and y should be sorted in increasing order before calling this function.
(FPCore (x y z)
 :precision binary64
 (if (<= x -5.2e+203) (/ x (/ z y)) (* y (/ x z))))

C

assert(x < y);
double code(double x, double y, double z) {
	double tmp;
	if (x <= -5.2e+203) {
		tmp = x / (z / y);
	} else {
		tmp = y * (x / z);
	}
	return tmp;
}

Fortran

NOTE: x and y should be sorted in increasing order before calling this function.
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+203)) then
        tmp = x / (z / y)
    else
        tmp = y * (x / z)
    end if
    code = tmp
end function

Java

assert x < y;
public static double code(double x, double y, double z) {
	double tmp;
	if (x <= -5.2e+203) {
		tmp = x / (z / y);
	} else {
		tmp = y * (x / z);
	}
	return tmp;
}

Python

[x, y] = sort([x, y])
def code(x, y, z):
	tmp = 0
	if x <= -5.2e+203:
		tmp = x / (z / y)
	else:
		tmp = y * (x / z)
	return tmp

Julia

x, y = sort([x, y])
function code(x, y, z)
	tmp = 0.0
	if (x <= -5.2e+203)
		tmp = Float64(x / Float64(z / y));
	else
		tmp = Float64(y * Float64(x / z));
	end
	return tmp
end

MATLAB

x, y = num2cell(sort([x, y])){:}
function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (x <= -5.2e+203)
		tmp = x / (z / y);
	else
		tmp = y * (x / z);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x and y should be sorted in increasing order before calling this function.
code[x_, y_, z_] := If[LessEqual[x, -5.2e+203], N[(x / N[(z / y), $MachinePrecision]), $MachinePrecision], N[(y * N[(x / z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -5.1999999999999997e203

   1. Initial program 86.0%

      \[\frac{x \cdot y}{z} \]
   2. Step-by-step derivation

      1. associate-/l* 99.8%

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

   3. Simplified 99.8%

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

   if -5.1999999999999997e203 < x

   1. Initial program 92.7%

      \[\frac{x \cdot y}{z} \]
   2. Step-by-step derivation

      1. associate-*l/ 89.4%

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

   3. Simplified 89.4%

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

4. Final simplification 90.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -5.2 \cdot 10^{+203}:\\ \;\;\;\;\frac{x}{\frac{z}{y}}\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{x}{z}\\ \end{array} \]

Alternative 5: 91.9% accurate, 0.7× speedup

Math

\[\begin{array}{l} [x, y] = \mathsf{sort}([x, y])\\ \\ \begin{array}{l} \mathbf{if}\;x \leq -3.4 \cdot 10^{+204}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{\frac{z}{x}}\\ \end{array} \end{array} \]

FPCore

NOTE: x and y should be sorted in increasing order before calling this function.
(FPCore (x y z)
 :precision binary64
 (if (<= x -3.4e+204) (* x (/ y z)) (/ y (/ z x))))

C

assert(x < y);
double code(double x, double y, double z) {
	double tmp;
	if (x <= -3.4e+204) {
		tmp = x * (y / z);
	} else {
		tmp = y / (z / x);
	}
	return tmp;
}

Fortran

NOTE: x and y should be sorted in increasing order before calling this function.
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 <= (-3.4d+204)) then
        tmp = x * (y / z)
    else
        tmp = y / (z / x)
    end if
    code = tmp
end function

Java

assert x < y;
public static double code(double x, double y, double z) {
	double tmp;
	if (x <= -3.4e+204) {
		tmp = x * (y / z);
	} else {
		tmp = y / (z / x);
	}
	return tmp;
}

Python

[x, y] = sort([x, y])
def code(x, y, z):
	tmp = 0
	if x <= -3.4e+204:
		tmp = x * (y / z)
	else:
		tmp = y / (z / x)
	return tmp

Julia

x, y = sort([x, y])
function code(x, y, z)
	tmp = 0.0
	if (x <= -3.4e+204)
		tmp = Float64(x * Float64(y / z));
	else
		tmp = Float64(y / Float64(z / x));
	end
	return tmp
end

MATLAB

x, y = num2cell(sort([x, y])){:}
function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (x <= -3.4e+204)
		tmp = x * (y / z);
	else
		tmp = y / (z / x);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x and y should be sorted in increasing order before calling this function.
code[x_, y_, z_] := If[LessEqual[x, -3.4e+204], N[(x * N[(y / z), $MachinePrecision]), $MachinePrecision], N[(y / N[(z / x), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -3.4000000000000001e204

   1. Initial program 85.2%

      \[\frac{x \cdot y}{z} \]
   2. Step-by-step derivation

      1. associate-*r/ 99.9%

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

   3. Simplified 99.9%

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

   if -3.4000000000000001e204 < x

   1. Initial program 92.8%

      \[\frac{x \cdot y}{z} \]
   2. Step-by-step derivation

      1. associate-*r/ 91.0%

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

   3. Simplified 91.0%

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

      1. *-commutative 91.0%

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

      2. associate-*l/ 92.8%

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

      3. associate-/l* 90.3%

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

   5. Applied egg-rr 90.3%

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

4. Final simplification 91.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -3.4 \cdot 10^{+204}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{\frac{z}{x}}\\ \end{array} \]

Alternative 6: 92.4% accurate, 1.0× speedup

Math

\[\begin{array}{l} [x, y] = \mathsf{sort}([x, y])\\ \\ x \cdot \frac{y}{z} \end{array} \]

FPCore

NOTE: x and y should be sorted in increasing order before calling this function.
(FPCore (x y z) :precision binary64 (* x (/ y z)))

C

assert(x < y);
double code(double x, double y, double z) {
	return x * (y / z);
}

Fortran

NOTE: x and y should be sorted in increasing order before calling this function.
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

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

Python

[x, y] = sort([x, y])
def code(x, y, z):
	return x * (y / z)

Julia

x, y = sort([x, y])
function code(x, y, z)
	return Float64(x * Float64(y / z))
end

MATLAB

x, y = num2cell(sort([x, y])){:}
function tmp = code(x, y, z)
	tmp = x * (y / z);
end

Wolfram

NOTE: x and y should be sorted in increasing order before calling this function.
code[x_, y_, z_] := N[(x * N[(y / z), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 92.2%

   \[\frac{x \cdot y}{z} \]
2. Step-by-step derivation

   1. associate-*r/ 91.7%

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

3. Simplified 91.7%

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

4. Final simplification 91.7%

   \[\leadsto x \cdot \frac{y}{z} \]

Developer target: 91.8% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z < -4.262230790519429 \cdot 10^{-138}:\\ \;\;\;\;\frac{x \cdot y}{z}\\ \mathbf{elif}\;z < 1.7042130660650472 \cdot 10^{-164}:\\ \;\;\;\;\frac{x}{\frac{z}{y}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{z} \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (< z -4.262230790519429e-138)
   (/ (* x y) z)
   (if (< z 1.7042130660650472e-164) (/ x (/ z y)) (* (/ x z) y))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z < -4.262230790519429e-138) {
		tmp = (x * y) / z;
	} else if (z < 1.7042130660650472e-164) {
		tmp = x / (z / y);
	} else {
		tmp = (x / z) * 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 < (-4.262230790519429d-138)) then
        tmp = (x * y) / z
    else if (z < 1.7042130660650472d-164) then
        tmp = x / (z / y)
    else
        tmp = (x / z) * y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (z < -4.262230790519429e-138) {
		tmp = (x * y) / z;
	} else if (z < 1.7042130660650472e-164) {
		tmp = x / (z / y);
	} else {
		tmp = (x / z) * y;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z < -4.262230790519429e-138:
		tmp = (x * y) / z
	elif z < 1.7042130660650472e-164:
		tmp = x / (z / y)
	else:
		tmp = (x / z) * y
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z < -4.262230790519429e-138)
		tmp = Float64(Float64(x * y) / z);
	elseif (z < 1.7042130660650472e-164)
		tmp = Float64(x / Float64(z / y));
	else
		tmp = Float64(Float64(x / z) * y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z < -4.262230790519429e-138)
		tmp = (x * y) / z;
	elseif (z < 1.7042130660650472e-164)
		tmp = x / (z / y);
	else
		tmp = (x / z) * y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Less[z, -4.262230790519429e-138], N[(N[(x * y), $MachinePrecision] / z), $MachinePrecision], If[Less[z, 1.7042130660650472e-164], N[(x / N[(z / y), $MachinePrecision]), $MachinePrecision], N[(N[(x / z), $MachinePrecision] * y), $MachinePrecision]]]

Reproduce

herbie shell --seed 2023230 
(FPCore (x y z)
  :name "Diagrams.Solve.Tridiagonal:solveCyclicTriDiagonal from diagrams-solve-0.1, A"
  :precision binary64

  :herbie-target
  (if (< z -4.262230790519429e-138) (/ (* x y) z) (if (< z 1.7042130660650472e-164) (/ x (/ z y)) (* (/ x z) y)))

  (/ (* x y) z))