Diagrams.Solve.Tridiagonal:solveTriDiagonal from diagrams-solve-0.1, B

Percentage Accurate: 95.8% → 98.9%

Time: 7.8s

Alternatives: 8

Speedup: 0.3×

Specification

Math

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

FPCore

(FPCore (x y z t) :precision binary64 (/ x (- y (* z t))))

C

double code(double x, double y, double z, double t) {
	return x / (y - (z * t));
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    code = x / (y - (z * t))
end function

Java

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

Python

def code(x, y, z, t):
	return x / (y - (z * t))

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 95.8% accurate, 1.0× speedup

Math

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

FPCore

(FPCore (x y z t) :precision binary64 (/ x (- y (* z t))))

C

double code(double x, double y, double z, double t) {
	return x / (y - (z * t));
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    code = x / (y - (z * t))
end function

Java

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

Python

def code(x, y, z, t):
	return x / (y - (z * t))

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 98.9% accurate, 0.3× speedup

Math

\[\begin{array}{l} [x, y, z, t] = \mathsf{sort}([x, y, z, t])\\ \\ \begin{array}{l} \mathbf{if}\;z \cdot t \leq -2 \cdot 10^{+191}:\\ \;\;\;\;\frac{\frac{x}{\frac{y}{t} - z}}{t}\\ \mathbf{elif}\;z \cdot t \leq 4 \cdot 10^{+150}:\\ \;\;\;\;\frac{x}{y - z \cdot t}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{-z}}{t}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
(FPCore (x y z t)
 :precision binary64
 (if (<= (* z t) -2e+191)
   (/ (/ x (- (/ y t) z)) t)
   (if (<= (* z t) 4e+150) (/ x (- y (* z t))) (/ (/ x (- z)) t))))

C

assert(x < y && y < z && z < t);
double code(double x, double y, double z, double t) {
	double tmp;
	if ((z * t) <= -2e+191) {
		tmp = (x / ((y / t) - z)) / t;
	} else if ((z * t) <= 4e+150) {
		tmp = x / (y - (z * t));
	} else {
		tmp = (x / -z) / t;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((z * t) <= (-2d+191)) then
        tmp = (x / ((y / t) - z)) / t
    else if ((z * t) <= 4d+150) then
        tmp = x / (y - (z * t))
    else
        tmp = (x / -z) / t
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t;
public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((z * t) <= -2e+191) {
		tmp = (x / ((y / t) - z)) / t;
	} else if ((z * t) <= 4e+150) {
		tmp = x / (y - (z * t));
	} else {
		tmp = (x / -z) / t;
	}
	return tmp;
}

Python

[x, y, z, t] = sort([x, y, z, t])
def code(x, y, z, t):
	tmp = 0
	if (z * t) <= -2e+191:
		tmp = (x / ((y / t) - z)) / t
	elif (z * t) <= 4e+150:
		tmp = x / (y - (z * t))
	else:
		tmp = (x / -z) / t
	return tmp

Julia

x, y, z, t = sort([x, y, z, t])
function code(x, y, z, t)
	tmp = 0.0
	if (Float64(z * t) <= -2e+191)
		tmp = Float64(Float64(x / Float64(Float64(y / t) - z)) / t);
	elseif (Float64(z * t) <= 4e+150)
		tmp = Float64(x / Float64(y - Float64(z * t)));
	else
		tmp = Float64(Float64(x / Float64(-z)) / t);
	end
	return tmp
end

MATLAB

x, y, z, t = num2cell(sort([x, y, z, t])){:}
function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z * t) <= -2e+191)
		tmp = (x / ((y / t) - z)) / t;
	elseif ((z * t) <= 4e+150)
		tmp = x / (y - (z * t));
	else
		tmp = (x / -z) / t;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_] := If[LessEqual[N[(z * t), $MachinePrecision], -2e+191], N[(N[(x / N[(N[(y / t), $MachinePrecision] - z), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision], If[LessEqual[N[(z * t), $MachinePrecision], 4e+150], N[(x / N[(y - N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x / (-z)), $MachinePrecision] / t), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 z t) < -2.00000000000000015e191

   1. Initial program 83.9%

      \[\frac{x}{y - z \cdot t} \]
   2. Add Preprocessing

   3. Taylor expanded in t around inf 84.0%

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

      1. *-un-lft-identity 84.0%

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

      2. times-frac 97.1%

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

   5. Applied egg-rr 97.1%

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

      1. associate-*l/ 97.1%

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

      2. *-lft-identity 97.1%

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

   7. Simplified 97.1%

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

   if -2.00000000000000015e191 < (*.f64 z t) < 3.99999999999999992e150

   1. Initial program 99.8%

      \[\frac{x}{y - z \cdot t} \]
   2. Add Preprocessing

   if 3.99999999999999992e150 < (*.f64 z t)

   1. Initial program 86.6%

      \[\frac{x}{y - z \cdot t} \]
   2. Add Preprocessing

   3. Taylor expanded in t around inf 86.6%

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

      1. *-un-lft-identity 86.6%

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

      2. times-frac 99.8%

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

   5. Applied egg-rr 99.8%

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

      1. associate-*l/ 99.9%

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

      2. *-lft-identity 99.9%

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

   7. Simplified 99.9%

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

   8. Taylor expanded in y around 0 99.9%

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

      1. mul-1-neg 99.9%

         \[\leadsto \frac{\color{blue}{-\frac{x}{z}}}{t} \]

      2. distribute-neg-frac2 99.9%

         \[\leadsto \frac{\color{blue}{\frac{x}{-z}}}{t} \]

   10. Simplified 99.9%

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

4. Final simplification 99.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \cdot t \leq -2 \cdot 10^{+191}:\\ \;\;\;\;\frac{\frac{x}{\frac{y}{t} - z}}{t}\\ \mathbf{elif}\;z \cdot t \leq 4 \cdot 10^{+150}:\\ \;\;\;\;\frac{x}{y - z \cdot t}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{-z}}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 99.0% accurate, 0.3× speedup

Math

\[\begin{array}{l} [x, y, z, t] = \mathsf{sort}([x, y, z, t])\\ \\ \begin{array}{l} \mathbf{if}\;z \cdot t \leq -\infty \lor \neg \left(z \cdot t \leq 4 \cdot 10^{+150}\right):\\ \;\;\;\;\frac{\frac{x}{-z}}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y - z \cdot t}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
(FPCore (x y z t)
 :precision binary64
 (if (or (<= (* z t) (- INFINITY)) (not (<= (* z t) 4e+150)))
   (/ (/ x (- z)) t)
   (/ x (- y (* z t)))))

C

assert(x < y && y < z && z < t);
double code(double x, double y, double z, double t) {
	double tmp;
	if (((z * t) <= -((double) INFINITY)) || !((z * t) <= 4e+150)) {
		tmp = (x / -z) / t;
	} else {
		tmp = x / (y - (z * t));
	}
	return tmp;
}

Java

assert x < y && y < z && z < t;
public static double code(double x, double y, double z, double t) {
	double tmp;
	if (((z * t) <= -Double.POSITIVE_INFINITY) || !((z * t) <= 4e+150)) {
		tmp = (x / -z) / t;
	} else {
		tmp = x / (y - (z * t));
	}
	return tmp;
}

Python

[x, y, z, t] = sort([x, y, z, t])
def code(x, y, z, t):
	tmp = 0
	if ((z * t) <= -math.inf) or not ((z * t) <= 4e+150):
		tmp = (x / -z) / t
	else:
		tmp = x / (y - (z * t))
	return tmp

Julia

x, y, z, t = sort([x, y, z, t])
function code(x, y, z, t)
	tmp = 0.0
	if ((Float64(z * t) <= Float64(-Inf)) || !(Float64(z * t) <= 4e+150))
		tmp = Float64(Float64(x / Float64(-z)) / t);
	else
		tmp = Float64(x / Float64(y - Float64(z * t)));
	end
	return tmp
end

MATLAB

x, y, z, t = num2cell(sort([x, y, z, t])){:}
function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (((z * t) <= -Inf) || ~(((z * t) <= 4e+150)))
		tmp = (x / -z) / t;
	else
		tmp = x / (y - (z * t));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_] := If[Or[LessEqual[N[(z * t), $MachinePrecision], (-Infinity)], N[Not[LessEqual[N[(z * t), $MachinePrecision], 4e+150]], $MachinePrecision]], N[(N[(x / (-z)), $MachinePrecision] / t), $MachinePrecision], N[(x / N[(y - N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 z t) < -inf.0 or 3.99999999999999992e150 < (*.f64 z t)

   1. Initial program 81.5%

      \[\frac{x}{y - z \cdot t} \]
   2. Add Preprocessing

   3. Taylor expanded in t around inf 81.5%

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

      1. *-un-lft-identity 81.5%

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

      2. times-frac 99.9%

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

   5. Applied egg-rr 99.9%

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

      1. associate-*l/ 99.9%

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

      2. *-lft-identity 99.9%

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

   7. Simplified 99.9%

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

   8. Taylor expanded in y around 0 99.9%

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

      1. mul-1-neg 99.9%

         \[\leadsto \frac{\color{blue}{-\frac{x}{z}}}{t} \]

      2. distribute-neg-frac2 99.9%

         \[\leadsto \frac{\color{blue}{\frac{x}{-z}}}{t} \]

   10. Simplified 99.9%

       \[\leadsto \frac{\color{blue}{\frac{x}{-z}}}{t} \]

   if -inf.0 < (*.f64 z t) < 3.99999999999999992e150

   1. Initial program 99.8%

      \[\frac{x}{y - z \cdot t} \]
   2. Add Preprocessing
3. Recombined 2 regimes into one program.

4. Final simplification 99.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \cdot t \leq -\infty \lor \neg \left(z \cdot t \leq 4 \cdot 10^{+150}\right):\\ \;\;\;\;\frac{\frac{x}{-z}}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y - z \cdot t}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 72.5% accurate, 0.4× speedup

Math

\[\begin{array}{l} [x, y, z, t] = \mathsf{sort}([x, y, z, t])\\ \\ \begin{array}{l} \mathbf{if}\;y \leq -1.05 \cdot 10^{-66} \lor \neg \left(y \leq 3 \cdot 10^{-31}\right):\\ \;\;\;\;\frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{t \cdot \left(-z\right)}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
(FPCore (x y z t)
 :precision binary64
 (if (or (<= y -1.05e-66) (not (<= y 3e-31))) (/ x y) (/ x (* t (- z)))))

C

assert(x < y && y < z && z < t);
double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -1.05e-66) || !(y <= 3e-31)) {
		tmp = x / y;
	} else {
		tmp = x / (t * -z);
	}
	return tmp;
}

Fortran

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((y <= (-1.05d-66)) .or. (.not. (y <= 3d-31))) then
        tmp = x / y
    else
        tmp = x / (t * -z)
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t;
public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -1.05e-66) || !(y <= 3e-31)) {
		tmp = x / y;
	} else {
		tmp = x / (t * -z);
	}
	return tmp;
}

Python

[x, y, z, t] = sort([x, y, z, t])
def code(x, y, z, t):
	tmp = 0
	if (y <= -1.05e-66) or not (y <= 3e-31):
		tmp = x / y
	else:
		tmp = x / (t * -z)
	return tmp

Julia

x, y, z, t = sort([x, y, z, t])
function code(x, y, z, t)
	tmp = 0.0
	if ((y <= -1.05e-66) || !(y <= 3e-31))
		tmp = Float64(x / y);
	else
		tmp = Float64(x / Float64(t * Float64(-z)));
	end
	return tmp
end

MATLAB

x, y, z, t = num2cell(sort([x, y, z, t])){:}
function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((y <= -1.05e-66) || ~((y <= 3e-31)))
		tmp = x / y;
	else
		tmp = x / (t * -z);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_] := If[Or[LessEqual[y, -1.05e-66], N[Not[LessEqual[y, 3e-31]], $MachinePrecision]], N[(x / y), $MachinePrecision], N[(x / N[(t * (-z)), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -1.05e-66 or 2.99999999999999981e-31 < y

   1. Initial program 96.7%

      \[\frac{x}{y - z \cdot t} \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf 75.5%

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

   if -1.05e-66 < y < 2.99999999999999981e-31

   1. Initial program 94.6%

      \[\frac{x}{y - z \cdot t} \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0 75.0%

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

      1. associate-*r/ 75.0%

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

      2. neg-mul-1 75.0%

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

   5. Simplified 75.0%

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

4. Final simplification 75.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.05 \cdot 10^{-66} \lor \neg \left(y \leq 3 \cdot 10^{-31}\right):\\ \;\;\;\;\frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{t \cdot \left(-z\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 74.0% accurate, 0.4× speedup

Math

\[\begin{array}{l} [x, y, z, t] = \mathsf{sort}([x, y, z, t])\\ \\ \begin{array}{l} \mathbf{if}\;t \leq -4.3 \cdot 10^{-60} \lor \neg \left(t \leq 1800000\right):\\ \;\;\;\;\frac{\frac{x}{t}}{-z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
(FPCore (x y z t)
 :precision binary64
 (if (or (<= t -4.3e-60) (not (<= t 1800000.0))) (/ (/ x t) (- z)) (/ x y)))

C

assert(x < y && y < z && z < t);
double code(double x, double y, double z, double t) {
	double tmp;
	if ((t <= -4.3e-60) || !(t <= 1800000.0)) {
		tmp = (x / t) / -z;
	} else {
		tmp = x / y;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((t <= (-4.3d-60)) .or. (.not. (t <= 1800000.0d0))) then
        tmp = (x / t) / -z
    else
        tmp = x / y
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t;
public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((t <= -4.3e-60) || !(t <= 1800000.0)) {
		tmp = (x / t) / -z;
	} else {
		tmp = x / y;
	}
	return tmp;
}

Python

[x, y, z, t] = sort([x, y, z, t])
def code(x, y, z, t):
	tmp = 0
	if (t <= -4.3e-60) or not (t <= 1800000.0):
		tmp = (x / t) / -z
	else:
		tmp = x / y
	return tmp

Julia

x, y, z, t = sort([x, y, z, t])
function code(x, y, z, t)
	tmp = 0.0
	if ((t <= -4.3e-60) || !(t <= 1800000.0))
		tmp = Float64(Float64(x / t) / Float64(-z));
	else
		tmp = Float64(x / y);
	end
	return tmp
end

MATLAB

x, y, z, t = num2cell(sort([x, y, z, t])){:}
function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((t <= -4.3e-60) || ~((t <= 1800000.0)))
		tmp = (x / t) / -z;
	else
		tmp = x / y;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_] := If[Or[LessEqual[t, -4.3e-60], N[Not[LessEqual[t, 1800000.0]], $MachinePrecision]], N[(N[(x / t), $MachinePrecision] / (-z)), $MachinePrecision], N[(x / y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -4.3000000000000001e-60 or 1.8e6 < t

   1. Initial program 91.8%

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

      1. clear-num 91.1%

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

      2. associate-/r/ 91.7%

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

   4. Applied egg-rr 91.7%

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

   5. Taylor expanded in y around 0 68.9%

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

      1. mul-1-neg 68.9%

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

      2. associate-/r* 75.2%

         \[\leadsto -\color{blue}{\frac{\frac{x}{t}}{z}} \]

      3. distribute-neg-frac2 75.2%

         \[\leadsto \color{blue}{\frac{\frac{x}{t}}{-z}} \]

   7. Simplified 75.2%

      \[\leadsto \color{blue}{\frac{\frac{x}{t}}{-z}} \]

   if -4.3000000000000001e-60 < t < 1.8e6

   1. Initial program 99.9%

      \[\frac{x}{y - z \cdot t} \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf 77.1%

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

4. Final simplification 76.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -4.3 \cdot 10^{-60} \lor \neg \left(t \leq 1800000\right):\\ \;\;\;\;\frac{\frac{x}{t}}{-z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 72.6% accurate, 0.4× speedup

Math

\[\begin{array}{l} [x, y, z, t] = \mathsf{sort}([x, y, z, t])\\ \\ \begin{array}{l} \mathbf{if}\;t \leq -8 \cdot 10^{-58}:\\ \;\;\;\;\frac{\frac{x}{t}}{-z}\\ \mathbf{elif}\;t \leq 2000000:\\ \;\;\;\;\frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{-z}}{t}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
(FPCore (x y z t)
 :precision binary64
 (if (<= t -8e-58)
   (/ (/ x t) (- z))
   (if (<= t 2000000.0) (/ x y) (/ (/ x (- z)) t))))

C

assert(x < y && y < z && z < t);
double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= -8e-58) {
		tmp = (x / t) / -z;
	} else if (t <= 2000000.0) {
		tmp = x / y;
	} else {
		tmp = (x / -z) / t;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (t <= (-8d-58)) then
        tmp = (x / t) / -z
    else if (t <= 2000000.0d0) then
        tmp = x / y
    else
        tmp = (x / -z) / t
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t;
public static double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= -8e-58) {
		tmp = (x / t) / -z;
	} else if (t <= 2000000.0) {
		tmp = x / y;
	} else {
		tmp = (x / -z) / t;
	}
	return tmp;
}

Python

[x, y, z, t] = sort([x, y, z, t])
def code(x, y, z, t):
	tmp = 0
	if t <= -8e-58:
		tmp = (x / t) / -z
	elif t <= 2000000.0:
		tmp = x / y
	else:
		tmp = (x / -z) / t
	return tmp

Julia

x, y, z, t = sort([x, y, z, t])
function code(x, y, z, t)
	tmp = 0.0
	if (t <= -8e-58)
		tmp = Float64(Float64(x / t) / Float64(-z));
	elseif (t <= 2000000.0)
		tmp = Float64(x / y);
	else
		tmp = Float64(Float64(x / Float64(-z)) / t);
	end
	return tmp
end

MATLAB

x, y, z, t = num2cell(sort([x, y, z, t])){:}
function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (t <= -8e-58)
		tmp = (x / t) / -z;
	elseif (t <= 2000000.0)
		tmp = x / y;
	else
		tmp = (x / -z) / t;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_] := If[LessEqual[t, -8e-58], N[(N[(x / t), $MachinePrecision] / (-z)), $MachinePrecision], If[LessEqual[t, 2000000.0], N[(x / y), $MachinePrecision], N[(N[(x / (-z)), $MachinePrecision] / t), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -8.0000000000000002e-58

   1. Initial program 92.1%

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

      1. clear-num 91.4%

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

      2. associate-/r/ 92.1%

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

   4. Applied egg-rr 92.1%

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

   5. Taylor expanded in y around 0 64.4%

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

      1. mul-1-neg 64.4%

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

      2. associate-/r* 72.8%

         \[\leadsto -\color{blue}{\frac{\frac{x}{t}}{z}} \]

      3. distribute-neg-frac2 72.8%

         \[\leadsto \color{blue}{\frac{\frac{x}{t}}{-z}} \]

   7. Simplified 72.8%

      \[\leadsto \color{blue}{\frac{\frac{x}{t}}{-z}} \]

   if -8.0000000000000002e-58 < t < 2e6

   1. Initial program 99.9%

      \[\frac{x}{y - z \cdot t} \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf 77.3%

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

   if 2e6 < t

   1. Initial program 91.2%

      \[\frac{x}{y - z \cdot t} \]
   2. Add Preprocessing

   3. Taylor expanded in t around inf 91.2%

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

      1. *-un-lft-identity 91.2%

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

      2. times-frac 94.6%

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

   5. Applied egg-rr 94.6%

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

      1. associate-*l/ 94.7%

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

      2. *-lft-identity 94.7%

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

   7. Simplified 94.7%

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

   8. Taylor expanded in y around 0 82.6%

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

      1. mul-1-neg 82.6%

         \[\leadsto \frac{\color{blue}{-\frac{x}{z}}}{t} \]

      2. distribute-neg-frac2 82.6%

         \[\leadsto \frac{\color{blue}{\frac{x}{-z}}}{t} \]

   10. Simplified 82.6%

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

4. Final simplification 77.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -8 \cdot 10^{-58}:\\ \;\;\;\;\frac{\frac{x}{t}}{-z}\\ \mathbf{elif}\;t \leq 2000000:\\ \;\;\;\;\frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{-z}}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 58.3% accurate, 0.5× speedup

Math

\[\begin{array}{l} [x, y, z, t] = \mathsf{sort}([x, y, z, t])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -2.65 \cdot 10^{+219} \lor \neg \left(z \leq 9 \cdot 10^{-21}\right):\\ \;\;\;\;\frac{x}{z \cdot t}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -2.65e+219) (not (<= z 9e-21))) (/ x (* z t)) (/ x y)))

C

assert(x < y && y < z && z < t);
double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -2.65e+219) || !(z <= 9e-21)) {
		tmp = x / (z * t);
	} else {
		tmp = x / y;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((z <= (-2.65d+219)) .or. (.not. (z <= 9d-21))) then
        tmp = x / (z * t)
    else
        tmp = x / y
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t;
public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -2.65e+219) || !(z <= 9e-21)) {
		tmp = x / (z * t);
	} else {
		tmp = x / y;
	}
	return tmp;
}

Python

[x, y, z, t] = sort([x, y, z, t])
def code(x, y, z, t):
	tmp = 0
	if (z <= -2.65e+219) or not (z <= 9e-21):
		tmp = x / (z * t)
	else:
		tmp = x / y
	return tmp

Julia

x, y, z, t = sort([x, y, z, t])
function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -2.65e+219) || !(z <= 9e-21))
		tmp = Float64(x / Float64(z * t));
	else
		tmp = Float64(x / y);
	end
	return tmp
end

MATLAB

x, y, z, t = num2cell(sort([x, y, z, t])){:}
function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z <= -2.65e+219) || ~((z <= 9e-21)))
		tmp = x / (z * t);
	else
		tmp = x / y;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_] := If[Or[LessEqual[z, -2.65e+219], N[Not[LessEqual[z, 9e-21]], $MachinePrecision]], N[(x / N[(z * t), $MachinePrecision]), $MachinePrecision], N[(x / y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -2.64999999999999992e219 or 8.99999999999999936e-21 < z

   1. Initial program 92.3%

      \[\frac{x}{y - z \cdot t} \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0 69.4%

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

      1. associate-*r/ 69.4%

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

      2. neg-mul-1 69.4%

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

   5. Simplified 69.4%

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

      1. div-inv 69.4%

         \[\leadsto \color{blue}{\left(-x\right) \cdot \frac{1}{t \cdot z}} \]

      2. add-sqr-sqrt 28.6%

         \[\leadsto \color{blue}{\left(\sqrt{-x} \cdot \sqrt{-x}\right)} \cdot \frac{1}{t \cdot z} \]

      3. sqrt-unprod 41.9%

         \[\leadsto \color{blue}{\sqrt{\left(-x\right) \cdot \left(-x\right)}} \cdot \frac{1}{t \cdot z} \]

      4. sqr-neg 41.9%

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

      5. sqrt-unprod 17.2%

         \[\leadsto \color{blue}{\left(\sqrt{x} \cdot \sqrt{x}\right)} \cdot \frac{1}{t \cdot z} \]

      6. add-sqr-sqrt 39.1%

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

      7. *-commutative 39.1%

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

      8. associate-/r* 39.1%

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

   7. Applied egg-rr 39.1%

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

      1. associate-/l/ 39.1%

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

      2. associate-*r/ 39.1%

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

      3. *-rgt-identity 39.1%

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

   9. Simplified 39.1%

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

   if -2.64999999999999992e219 < z < 8.99999999999999936e-21

   1. Initial program 98.0%

      \[\frac{x}{y - z \cdot t} \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf 67.4%

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

4. Final simplification 56.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.65 \cdot 10^{+219} \lor \neg \left(z \leq 9 \cdot 10^{-21}\right):\\ \;\;\;\;\frac{x}{z \cdot t}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 58.6% accurate, 0.5× speedup

Math

\[\begin{array}{l} [x, y, z, t] = \mathsf{sort}([x, y, z, t])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -2.2 \cdot 10^{+221}:\\ \;\;\;\;\frac{\frac{x}{z}}{t}\\ \mathbf{elif}\;z \leq 9 \cdot 10^{-21}:\\ \;\;\;\;\frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{z \cdot t}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
(FPCore (x y z t)
 :precision binary64
 (if (<= z -2.2e+221) (/ (/ x z) t) (if (<= z 9e-21) (/ x y) (/ x (* z t)))))

C

assert(x < y && y < z && z < t);
double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -2.2e+221) {
		tmp = (x / z) / t;
	} else if (z <= 9e-21) {
		tmp = x / y;
	} else {
		tmp = x / (z * t);
	}
	return tmp;
}

Fortran

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (z <= (-2.2d+221)) then
        tmp = (x / z) / t
    else if (z <= 9d-21) then
        tmp = x / y
    else
        tmp = x / (z * t)
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t;
public static double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -2.2e+221) {
		tmp = (x / z) / t;
	} else if (z <= 9e-21) {
		tmp = x / y;
	} else {
		tmp = x / (z * t);
	}
	return tmp;
}

Python

[x, y, z, t] = sort([x, y, z, t])
def code(x, y, z, t):
	tmp = 0
	if z <= -2.2e+221:
		tmp = (x / z) / t
	elif z <= 9e-21:
		tmp = x / y
	else:
		tmp = x / (z * t)
	return tmp

Julia

x, y, z, t = sort([x, y, z, t])
function code(x, y, z, t)
	tmp = 0.0
	if (z <= -2.2e+221)
		tmp = Float64(Float64(x / z) / t);
	elseif (z <= 9e-21)
		tmp = Float64(x / y);
	else
		tmp = Float64(x / Float64(z * t));
	end
	return tmp
end

MATLAB

x, y, z, t = num2cell(sort([x, y, z, t])){:}
function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (z <= -2.2e+221)
		tmp = (x / z) / t;
	elseif (z <= 9e-21)
		tmp = x / y;
	else
		tmp = x / (z * t);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_] := If[LessEqual[z, -2.2e+221], N[(N[(x / z), $MachinePrecision] / t), $MachinePrecision], If[LessEqual[z, 9e-21], N[(x / y), $MachinePrecision], N[(x / N[(z * t), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -2.1999999999999999e221

   1. Initial program 89.5%

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

      1. clear-num 88.0%

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

      2. associate-/r/ 89.3%

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

   4. Applied egg-rr 89.3%

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

   5. Taylor expanded in y around 0 75.1%

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

      1. associate-*l/ 75.2%

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

      2. *-commutative 75.2%

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

      3. neg-mul-1 75.2%

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

      4. add-sqr-sqrt 34.2%

         \[\leadsto \frac{\color{blue}{\sqrt{-x} \cdot \sqrt{-x}}}{z \cdot t} \]

      5. sqrt-unprod 42.0%

         \[\leadsto \frac{\color{blue}{\sqrt{\left(-x\right) \cdot \left(-x\right)}}}{z \cdot t} \]

      6. sqr-neg 42.0%

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

      7. sqrt-unprod 22.0%

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

      8. add-sqr-sqrt 45.6%

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

      9. associate-/r* 45.9%

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

   7. Applied egg-rr 45.9%

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

   if -2.1999999999999999e221 < z < 8.99999999999999936e-21

   1. Initial program 98.0%

      \[\frac{x}{y - z \cdot t} \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf 67.4%

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

   if 8.99999999999999936e-21 < z

   1. Initial program 93.4%

      \[\frac{x}{y - z \cdot t} \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0 67.2%

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

      1. associate-*r/ 67.2%

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

      2. neg-mul-1 67.2%

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

   5. Simplified 67.2%

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

      1. div-inv 67.3%

         \[\leadsto \color{blue}{\left(-x\right) \cdot \frac{1}{t \cdot z}} \]

      2. add-sqr-sqrt 26.6%

         \[\leadsto \color{blue}{\left(\sqrt{-x} \cdot \sqrt{-x}\right)} \cdot \frac{1}{t \cdot z} \]

      3. sqrt-unprod 41.8%

         \[\leadsto \color{blue}{\sqrt{\left(-x\right) \cdot \left(-x\right)}} \cdot \frac{1}{t \cdot z} \]

      4. sqr-neg 41.8%

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

      5. sqrt-unprod 15.5%

         \[\leadsto \color{blue}{\left(\sqrt{x} \cdot \sqrt{x}\right)} \cdot \frac{1}{t \cdot z} \]

      6. add-sqr-sqrt 36.7%

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

      7. *-commutative 36.7%

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

      8. associate-/r* 36.6%

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

   7. Applied egg-rr 36.6%

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

      1. associate-/l/ 36.7%

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

      2. associate-*r/ 36.7%

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

      3. *-rgt-identity 36.7%

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

   9. Simplified 36.7%

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

4. Final simplification 56.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.2 \cdot 10^{+221}:\\ \;\;\;\;\frac{\frac{x}{z}}{t}\\ \mathbf{elif}\;z \leq 9 \cdot 10^{-21}:\\ \;\;\;\;\frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{z \cdot t}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 53.8% accurate, 2.3× speedup

Math

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

FPCore

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

C

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

Fortran

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    code = x / y
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 95.8%

   \[\frac{x}{y - z \cdot t} \]
2. Add Preprocessing

3. Taylor expanded in y around inf 54.1%

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

4. Final simplification 54.1%

   \[\leadsto \frac{x}{y} \]
5. Add Preprocessing

Developer target: 96.3% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{1}{\frac{y}{x} - \frac{z}{x} \cdot t}\\ \mathbf{if}\;x < -1.618195973607049 \cdot 10^{+50}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x < 2.1378306434876444 \cdot 10^{+131}:\\ \;\;\;\;\frac{x}{y - z \cdot t}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ 1.0 (- (/ y x) (* (/ z x) t)))))
   (if (< x -1.618195973607049e+50)
     t_1
     (if (< x 2.1378306434876444e+131) (/ x (- y (* z t))) t_1))))

C

double code(double x, double y, double z, double t) {
	double t_1 = 1.0 / ((y / x) - ((z / x) * t));
	double tmp;
	if (x < -1.618195973607049e+50) {
		tmp = t_1;
	} else if (x < 2.1378306434876444e+131) {
		tmp = x / (y - (z * t));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = 1.0d0 / ((y / x) - ((z / x) * t))
    if (x < (-1.618195973607049d+50)) then
        tmp = t_1
    else if (x < 2.1378306434876444d+131) then
        tmp = x / (y - (z * t))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = 1.0 / ((y / x) - ((z / x) * t));
	double tmp;
	if (x < -1.618195973607049e+50) {
		tmp = t_1;
	} else if (x < 2.1378306434876444e+131) {
		tmp = x / (y - (z * t));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = 1.0 / ((y / x) - ((z / x) * t))
	tmp = 0
	if x < -1.618195973607049e+50:
		tmp = t_1
	elif x < 2.1378306434876444e+131:
		tmp = x / (y - (z * t))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(1.0 / Float64(Float64(y / x) - Float64(Float64(z / x) * t)))
	tmp = 0.0
	if (x < -1.618195973607049e+50)
		tmp = t_1;
	elseif (x < 2.1378306434876444e+131)
		tmp = Float64(x / Float64(y - Float64(z * t)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = 1.0 / ((y / x) - ((z / x) * t));
	tmp = 0.0;
	if (x < -1.618195973607049e+50)
		tmp = t_1;
	elseif (x < 2.1378306434876444e+131)
		tmp = x / (y - (z * t));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(1.0 / N[(N[(y / x), $MachinePrecision] - N[(N[(z / x), $MachinePrecision] * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[Less[x, -1.618195973607049e+50], t$95$1, If[Less[x, 2.1378306434876444e+131], N[(x / N[(y - N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Reproduce

herbie shell --seed 2024080 
(FPCore (x y z t)
  :name "Diagrams.Solve.Tridiagonal:solveTriDiagonal from diagrams-solve-0.1, B"
  :precision binary64

  :alt
  (if (< x -1.618195973607049e+50) (/ 1.0 (- (/ y x) (* (/ z x) t))) (if (< x 2.1378306434876444e+131) (/ x (- y (* z t))) (/ 1.0 (- (/ y x) (* (/ z x) t)))))

  (/ x (- y (* z t))))