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

Percentage Accurate: 95.9% → 97.9%

Time: 7.9s

Alternatives: 8

Speedup: 0.5×

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: 95.9% 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: 97.9% accurate, 0.5× speedup

Math

\[\begin{array}{l} [x, y, z, t] = \mathsf{sort}([x, y, z, t])\\ \\ \begin{array}{l} \mathbf{if}\;z \cdot t \leq -5 \cdot 10^{+298}:\\ \;\;\;\;\frac{-1}{t \cdot \frac{z}{x}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y - z \cdot t}\\ \end{array} \end{array} \]

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 (<= (* z t) -5e+298) (/ -1.0 (* t (/ z x))) (/ 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) <= -5e+298) {
		tmp = -1.0 / (t * (z / x));
	} else {
		tmp = x / (y - (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) <= (-5d+298)) then
        tmp = (-1.0d0) / (t * (z / x))
    else
        tmp = x / (y - (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) <= -5e+298) {
		tmp = -1.0 / (t * (z / x));
	} 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) <= -5e+298:
		tmp = -1.0 / (t * (z / x))
	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) <= -5e+298)
		tmp = Float64(-1.0 / Float64(t * Float64(z / x)));
	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) <= -5e+298)
		tmp = -1.0 / (t * (z / x));
	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[LessEqual[N[(z * t), $MachinePrecision], -5e+298], N[(-1.0 / N[(t * N[(z / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x / N[(y - N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 z t) < -5.0000000000000003e298

   1. Initial program 77.4%

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

   3. Taylor expanded in z around inf 77.4%

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

      1. clear-num 77.4%

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

      2. inv-pow 77.4%

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

   5. Applied egg-rr 77.4%

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

      1. unpow-1 77.4%

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

      2. associate-/l* 99.9%

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

   7. Simplified 99.9%

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

   8. Taylor expanded in z around inf 77.4%

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

      1. mul-1-neg 77.4%

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

      2. associate-/l* 99.9%

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

      3. distribute-lft-neg-in 99.9%

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

   10. Simplified 99.9%

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

   if -5.0000000000000003e298 < (*.f64 z t)

   1. Initial program 99.1%

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

4. Final simplification 99.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \cdot t \leq -5 \cdot 10^{+298}:\\ \;\;\;\;\frac{-1}{t \cdot \frac{z}{x}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y - z \cdot t}\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 76.2% accurate, 0.2× speedup

Math

\[\begin{array}{l} [x, y, z, t] = \mathsf{sort}([x, y, z, t])\\ \\ \begin{array}{l} \mathbf{if}\;z \cdot t \leq -1 \cdot 10^{-26} \lor \neg \left(z \cdot t \leq 5 \cdot 10^{-133} \lor \neg \left(z \cdot t \leq 4 \cdot 10^{-72}\right) \land z \cdot t \leq 2 \cdot 10^{+27}\right):\\ \;\;\;\;\frac{-x}{z \cdot t}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y}\\ \end{array} \end{array} \]

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 t) -1e-26)
         (not
          (or (<= (* z t) 5e-133)
              (and (not (<= (* z t) 4e-72)) (<= (* z t) 2e+27)))))
   (/ (- 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 * t) <= -1e-26) || !(((z * t) <= 5e-133) || (!((z * t) <= 4e-72) && ((z * t) <= 2e+27)))) {
		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 * t) <= (-1d-26)) .or. (.not. ((z * t) <= 5d-133) .or. (.not. ((z * t) <= 4d-72)) .and. ((z * t) <= 2d+27))) 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 * t) <= -1e-26) || !(((z * t) <= 5e-133) || (!((z * t) <= 4e-72) && ((z * t) <= 2e+27)))) {
		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 * t) <= -1e-26) or not (((z * t) <= 5e-133) or (not ((z * t) <= 4e-72) and ((z * t) <= 2e+27))):
		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 ((Float64(z * t) <= -1e-26) || !((Float64(z * t) <= 5e-133) || (!(Float64(z * t) <= 4e-72) && (Float64(z * t) <= 2e+27))))
		tmp = Float64(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 * t) <= -1e-26) || ~((((z * t) <= 5e-133) || (~(((z * t) <= 4e-72)) && ((z * t) <= 2e+27)))))
		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[N[(z * t), $MachinePrecision], -1e-26], N[Not[Or[LessEqual[N[(z * t), $MachinePrecision], 5e-133], And[N[Not[LessEqual[N[(z * t), $MachinePrecision], 4e-72]], $MachinePrecision], LessEqual[N[(z * t), $MachinePrecision], 2e+27]]]], $MachinePrecision]], N[((-x) / N[(z * t), $MachinePrecision]), $MachinePrecision], N[(x / y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 z t) < -1e-26 or 4.9999999999999999e-133 < (*.f64 z t) < 3.9999999999999999e-72 or 2e27 < (*.f64 z t)

   1. Initial program 94.5%

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

   3. Taylor expanded in y around 0 72.3%

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

      1. associate-*r/ 72.3%

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

      2. neg-mul-1 72.3%

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

   5. Simplified 72.3%

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

   if -1e-26 < (*.f64 z t) < 4.9999999999999999e-133 or 3.9999999999999999e-72 < (*.f64 z t) < 2e27

   1. Initial program 99.9%

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

   3. Taylor expanded in y around inf 91.6%

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

4. Final simplification 81.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \cdot t \leq -1 \cdot 10^{-26} \lor \neg \left(z \cdot t \leq 5 \cdot 10^{-133} \lor \neg \left(z \cdot t \leq 4 \cdot 10^{-72}\right) \land z \cdot t \leq 2 \cdot 10^{+27}\right):\\ \;\;\;\;\frac{-x}{z \cdot t}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 77.0% accurate, 0.2× speedup

Math

\[\begin{array}{l} [x, y, z, t] = \mathsf{sort}([x, y, z, t])\\ \\ \begin{array}{l} \mathbf{if}\;z \cdot t \leq -1 \cdot 10^{-26}:\\ \;\;\;\;\frac{\frac{x}{t}}{-z}\\ \mathbf{elif}\;z \cdot t \leq 5 \cdot 10^{-133} \lor \neg \left(z \cdot t \leq 4 \cdot 10^{-72}\right) \land z \cdot t \leq 2 \cdot 10^{+27}:\\ \;\;\;\;\frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{-x}{z \cdot t}\\ \end{array} \end{array} \]

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 t) -1e-26)
   (/ (/ x t) (- z))
   (if (or (<= (* z t) 5e-133)
           (and (not (<= (* z t) 4e-72)) (<= (* z t) 2e+27)))
     (/ 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 * t) <= -1e-26) {
		tmp = (x / t) / -z;
	} else if (((z * t) <= 5e-133) || (!((z * t) <= 4e-72) && ((z * t) <= 2e+27))) {
		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 * t) <= (-1d-26)) then
        tmp = (x / t) / -z
    else if (((z * t) <= 5d-133) .or. (.not. ((z * t) <= 4d-72)) .and. ((z * t) <= 2d+27)) 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 * t) <= -1e-26) {
		tmp = (x / t) / -z;
	} else if (((z * t) <= 5e-133) || (!((z * t) <= 4e-72) && ((z * t) <= 2e+27))) {
		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 * t) <= -1e-26:
		tmp = (x / t) / -z
	elif ((z * t) <= 5e-133) or (not ((z * t) <= 4e-72) and ((z * t) <= 2e+27)):
		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 (Float64(z * t) <= -1e-26)
		tmp = Float64(Float64(x / t) / Float64(-z));
	elseif ((Float64(z * t) <= 5e-133) || (!(Float64(z * t) <= 4e-72) && (Float64(z * t) <= 2e+27)))
		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 ((z * t) <= -1e-26)
		tmp = (x / t) / -z;
	elseif (((z * t) <= 5e-133) || (~(((z * t) <= 4e-72)) && ((z * t) <= 2e+27)))
		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[N[(z * t), $MachinePrecision], -1e-26], N[(N[(x / t), $MachinePrecision] / (-z)), $MachinePrecision], If[Or[LessEqual[N[(z * t), $MachinePrecision], 5e-133], And[N[Not[LessEqual[N[(z * t), $MachinePrecision], 4e-72]], $MachinePrecision], LessEqual[N[(z * t), $MachinePrecision], 2e+27]]], N[(x / y), $MachinePrecision], N[((-x) / N[(z * t), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 z t) < -1e-26

   1. Initial program 93.0%

      \[\frac{x}{y - z \cdot t} \]
   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/ 92.9%

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

   4. Applied egg-rr 92.9%

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

   5. Taylor expanded in y around 0 69.8%

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

      1. mul-1-neg 69.8%

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

      2. associate-/r* 71.3%

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

      3. distribute-neg-frac2 71.3%

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

   7. Simplified 71.3%

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

   if -1e-26 < (*.f64 z t) < 4.9999999999999999e-133 or 3.9999999999999999e-72 < (*.f64 z t) < 2e27

   1. Initial program 99.9%

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

   3. Taylor expanded in y around inf 91.6%

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

   if 4.9999999999999999e-133 < (*.f64 z t) < 3.9999999999999999e-72 or 2e27 < (*.f64 z t)

   1. Initial program 96.6%

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

   3. Taylor expanded in y around 0 75.7%

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

      1. associate-*r/ 75.7%

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

      2. neg-mul-1 75.7%

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

   5. Simplified 75.7%

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

4. Final simplification 81.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \cdot t \leq -1 \cdot 10^{-26}:\\ \;\;\;\;\frac{\frac{x}{t}}{-z}\\ \mathbf{elif}\;z \cdot t \leq 5 \cdot 10^{-133} \lor \neg \left(z \cdot t \leq 4 \cdot 10^{-72}\right) \land z \cdot t \leq 2 \cdot 10^{+27}:\\ \;\;\;\;\frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{-x}{z \cdot t}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 77.0% accurate, 0.2× speedup

Math

\[\begin{array}{l} [x, y, z, t] = \mathsf{sort}([x, y, z, t])\\ \\ \begin{array}{l} \mathbf{if}\;z \cdot t \leq -1 \cdot 10^{-26}:\\ \;\;\;\;\frac{\frac{x}{t}}{-z}\\ \mathbf{elif}\;z \cdot t \leq 5 \cdot 10^{-133}:\\ \;\;\;\;\frac{x}{y}\\ \mathbf{elif}\;z \cdot t \leq 4 \cdot 10^{-72}:\\ \;\;\;\;x \cdot \frac{\frac{-1}{t}}{z}\\ \mathbf{elif}\;z \cdot t \leq 2 \cdot 10^{+27}:\\ \;\;\;\;\frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{-x}{z \cdot t}\\ \end{array} \end{array} \]

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 t) -1e-26)
   (/ (/ x t) (- z))
   (if (<= (* z t) 5e-133)
     (/ x y)
     (if (<= (* z t) 4e-72)
       (* x (/ (/ -1.0 t) z))
       (if (<= (* z t) 2e+27) (/ 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 * t) <= -1e-26) {
		tmp = (x / t) / -z;
	} else if ((z * t) <= 5e-133) {
		tmp = x / y;
	} else if ((z * t) <= 4e-72) {
		tmp = x * ((-1.0 / t) / z);
	} else if ((z * t) <= 2e+27) {
		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 * t) <= (-1d-26)) then
        tmp = (x / t) / -z
    else if ((z * t) <= 5d-133) then
        tmp = x / y
    else if ((z * t) <= 4d-72) then
        tmp = x * (((-1.0d0) / t) / z)
    else if ((z * t) <= 2d+27) 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 * t) <= -1e-26) {
		tmp = (x / t) / -z;
	} else if ((z * t) <= 5e-133) {
		tmp = x / y;
	} else if ((z * t) <= 4e-72) {
		tmp = x * ((-1.0 / t) / z);
	} else if ((z * t) <= 2e+27) {
		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 * t) <= -1e-26:
		tmp = (x / t) / -z
	elif (z * t) <= 5e-133:
		tmp = x / y
	elif (z * t) <= 4e-72:
		tmp = x * ((-1.0 / t) / z)
	elif (z * t) <= 2e+27:
		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 (Float64(z * t) <= -1e-26)
		tmp = Float64(Float64(x / t) / Float64(-z));
	elseif (Float64(z * t) <= 5e-133)
		tmp = Float64(x / y);
	elseif (Float64(z * t) <= 4e-72)
		tmp = Float64(x * Float64(Float64(-1.0 / t) / z));
	elseif (Float64(z * t) <= 2e+27)
		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 ((z * t) <= -1e-26)
		tmp = (x / t) / -z;
	elseif ((z * t) <= 5e-133)
		tmp = x / y;
	elseif ((z * t) <= 4e-72)
		tmp = x * ((-1.0 / t) / z);
	elseif ((z * t) <= 2e+27)
		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[N[(z * t), $MachinePrecision], -1e-26], N[(N[(x / t), $MachinePrecision] / (-z)), $MachinePrecision], If[LessEqual[N[(z * t), $MachinePrecision], 5e-133], N[(x / y), $MachinePrecision], If[LessEqual[N[(z * t), $MachinePrecision], 4e-72], N[(x * N[(N[(-1.0 / t), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(z * t), $MachinePrecision], 2e+27], N[(x / y), $MachinePrecision], N[((-x) / N[(z * t), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 4 regimes

2. if (*.f64 z t) < -1e-26

   1. Initial program 93.0%

      \[\frac{x}{y - z \cdot t} \]
   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/ 92.9%

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

   4. Applied egg-rr 92.9%

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

   5. Taylor expanded in y around 0 69.8%

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

      1. mul-1-neg 69.8%

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

      2. associate-/r* 71.3%

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

      3. distribute-neg-frac2 71.3%

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

   7. Simplified 71.3%

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

   if -1e-26 < (*.f64 z t) < 4.9999999999999999e-133 or 3.9999999999999999e-72 < (*.f64 z t) < 2e27

   1. Initial program 99.9%

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

   3. Taylor expanded in y around inf 91.6%

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

   if 4.9999999999999999e-133 < (*.f64 z t) < 3.9999999999999999e-72

   1. Initial program 99.5%

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

      1. clear-num 99.5%

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

      2. associate-/r/ 99.2%

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

   4. Applied egg-rr 99.2%

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

   5. Taylor expanded in y around 0 68.9%

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

      1. associate-/r* 69.2%

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

   7. Simplified 69.2%

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

   if 2e27 < (*.f64 z t)

   1. Initial program 95.9%

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

   3. Taylor expanded in y around 0 77.1%

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

      1. associate-*r/ 77.1%

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

      2. neg-mul-1 77.1%

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

   5. Simplified 77.1%

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

4. Final simplification 81.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \cdot t \leq -1 \cdot 10^{-26}:\\ \;\;\;\;\frac{\frac{x}{t}}{-z}\\ \mathbf{elif}\;z \cdot t \leq 5 \cdot 10^{-133}:\\ \;\;\;\;\frac{x}{y}\\ \mathbf{elif}\;z \cdot t \leq 4 \cdot 10^{-72}:\\ \;\;\;\;x \cdot \frac{\frac{-1}{t}}{z}\\ \mathbf{elif}\;z \cdot t \leq 2 \cdot 10^{+27}:\\ \;\;\;\;\frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{-x}{z \cdot t}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 62.4% accurate, 0.4× speedup

Math

\[\begin{array}{l} [x, y, z, t] = \mathsf{sort}([x, y, z, t])\\ \\ \begin{array}{l} \mathbf{if}\;z \cdot t \leq -5 \cdot 10^{+272} \lor \neg \left(z \cdot t \leq 10^{+197}\right):\\ \;\;\;\;\frac{x}{z \cdot t}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y}\\ \end{array} \end{array} \]

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 t) -5e+272) (not (<= (* z t) 1e+197)))
   (/ 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 * t) <= -5e+272) || !((z * t) <= 1e+197)) {
		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 * t) <= (-5d+272)) .or. (.not. ((z * t) <= 1d+197))) 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 * t) <= -5e+272) || !((z * t) <= 1e+197)) {
		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 * t) <= -5e+272) or not ((z * t) <= 1e+197):
		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 ((Float64(z * t) <= -5e+272) || !(Float64(z * t) <= 1e+197))
		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 * t) <= -5e+272) || ~(((z * t) <= 1e+197)))
		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[N[(z * t), $MachinePrecision], -5e+272], N[Not[LessEqual[N[(z * t), $MachinePrecision], 1e+197]], $MachinePrecision]], N[(x / N[(z * t), $MachinePrecision]), $MachinePrecision], N[(x / y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 z t) < -4.99999999999999973e272 or 9.9999999999999995e196 < (*.f64 z t)

   1. Initial program 84.2%

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

      1. clear-num 82.7%

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

      2. associate-/r/ 84.2%

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

   4. Applied egg-rr 84.2%

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

   5. Taylor expanded in y around 0 84.2%

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

      1. associate-/r* 85.9%

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

   7. Simplified 85.9%

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

      1. *-commutative 85.9%

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

      2. associate-/l/ 84.2%

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

      3. frac-2neg 84.2%

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

      4. metadata-eval 84.2%

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

      5. distribute-lft-neg-out 84.2%

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

      6. div-inv 84.2%

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

      7. add-sqr-sqrt 46.5%

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

      8. sqrt-unprod 75.0%

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

      9. sqr-neg 75.0%

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

      10. sqrt-unprod 32.0%

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

      11. add-sqr-sqrt 67.0%

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

   9. Applied egg-rr 67.0%

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

   if -4.99999999999999973e272 < (*.f64 z t) < 9.9999999999999995e196

   1. Initial program 99.9%

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

   3. Taylor expanded in y around inf 68.5%

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

4. Final simplification 68.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \cdot t \leq -5 \cdot 10^{+272} \lor \neg \left(z \cdot t \leq 10^{+197}\right):\\ \;\;\;\;\frac{x}{z \cdot t}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 97.9% accurate, 0.5× speedup

Math

\[\begin{array}{l} [x, y, z, t] = \mathsf{sort}([x, y, z, t])\\ \\ \begin{array}{l} \mathbf{if}\;z \cdot t \leq -\infty:\\ \;\;\;\;\frac{-1}{z \cdot \frac{t}{x}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y - z \cdot t}\\ \end{array} \end{array} \]

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 (<= (* z t) (- INFINITY)) (/ -1.0 (* z (/ t x))) (/ 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)) {
		tmp = -1.0 / (z * (t / x));
	} 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) {
		tmp = -1.0 / (z * (t / x));
	} 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:
		tmp = -1.0 / (z * (t / x))
	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))
		tmp = Float64(-1.0 / Float64(z * Float64(t / x)));
	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)
		tmp = -1.0 / (z * (t / x));
	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[LessEqual[N[(z * t), $MachinePrecision], (-Infinity)], N[(-1.0 / N[(z * N[(t / x), $MachinePrecision]), $MachinePrecision]), $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

   1. Initial program 74.3%

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

      1. clear-num 74.3%

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

      2. associate-/r/ 74.3%

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

   4. Applied egg-rr 74.3%

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

   5. Taylor expanded in y around 0 74.3%

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

      1. associate-/r* 78.0%

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

   7. Simplified 78.0%

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

      1. *-commutative 78.0%

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

      2. associate-/l/ 74.3%

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

      3. frac-2neg 74.3%

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

      4. metadata-eval 74.3%

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

      5. distribute-lft-neg-out 74.3%

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

      6. div-inv 74.3%

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

      7. associate-/l/ 99.9%

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

      8. clear-num 99.9%

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

      9. frac-2neg 99.9%

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

      10. metadata-eval 99.9%

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

      11. add-sqr-sqrt 58.8%

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

      12. sqrt-unprod 78.4%

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

      13. sqr-neg 78.4%

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

      14. sqrt-unprod 36.5%

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

      15. add-sqr-sqrt 73.9%

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

      16. distribute-frac-neg 73.9%

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

      17. div-inv 73.9%

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

      18. add-sqr-sqrt 37.5%

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

      19. sqrt-unprod 78.7%

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

      20. sqr-neg 78.7%

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

      21. sqrt-unprod 40.9%

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

      22. add-sqr-sqrt 99.9%

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

      23. clear-num 99.9%

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

   9. Applied egg-rr 99.9%

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

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

   1. Initial program 99.1%

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

4. Final simplification 99.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \cdot t \leq -\infty:\\ \;\;\;\;\frac{-1}{z \cdot \frac{t}{x}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y - z \cdot t}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 53.8% accurate, 1.4× speedup

Math

\[\begin{array}{l} [x, y, z, t] = \mathsf{sort}([x, y, z, t])\\ \\ \frac{1}{\frac{y}{x}} \end{array} \]

FPCore

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
(FPCore (x y z t) :precision binary64 (/ 1.0 (/ y x)))

C

assert(x < y && y < z && z < t);
double code(double x, double y, double z, double t) {
	return 1.0 / (y / x);
}

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 = 1.0d0 / (y / x)
end function

Java

assert x < y && y < z && z < t;
public static double code(double x, double y, double z, double t) {
	return 1.0 / (y / x);
}

Python

[x, y, z, t] = sort([x, y, z, t])
def code(x, y, z, t):
	return 1.0 / (y / x)

Julia

x, y, z, t = sort([x, y, z, t])
function code(x, y, z, t)
	return Float64(1.0 / Float64(y / x))
end

MATLAB

x, y, z, t = num2cell(sort([x, y, z, t])){:}
function tmp = code(x, y, z, t)
	tmp = 1.0 / (y / x);
end

Wolfram

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_] := N[(1.0 / N[(y / x), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 96.9%

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

3. Taylor expanded in z around inf 89.5%

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

   1. clear-num 88.5%

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

   2. inv-pow 88.5%

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

5. Applied egg-rr 88.5%

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

   1. unpow-1 88.5%

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

   2. associate-/l* 83.7%

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

7. Simplified 83.7%

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

8. Taylor expanded in z around 0 58.4%

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

9. Final simplification 58.4%

   \[\leadsto \frac{1}{\frac{y}{x}} \]
10. Add Preprocessing

Alternative 8: 54.2% 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 96.9%

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

3. Taylor expanded in y around inf 58.3%

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

4. Final simplification 58.3%

   \[\leadsto \frac{x}{y} \]
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 2024060 
(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))))