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

Percentage Accurate: 95.5% → 99.4%

Time: 7.2s

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: 95.5% 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: 99.4% accurate, 0.3× speedup

Math

\[\begin{array}{l} [x, y, z, t] = \mathsf{sort}([x, y, z, t])\\ \\ \begin{array}{l} \mathbf{if}\;z \cdot t \leq -2 \cdot 10^{+192}:\\ \;\;\;\;\frac{\frac{-x}{t}}{z}\\ \mathbf{elif}\;z \cdot t \leq 2 \cdot 10^{+291}:\\ \;\;\;\;\frac{x}{y - z \cdot t}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{z}}{-t}\\ \end{array} \end{array} \]

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+192)
   (/ (/ (- x) t) z)
   (if (<= (* z t) 2e+291) (/ 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+192) {
		tmp = (-x / t) / z;
	} else if ((z * t) <= 2e+291) {
		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+192)) then
        tmp = (-x / t) / z
    else if ((z * t) <= 2d+291) 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+192) {
		tmp = (-x / t) / z;
	} else if ((z * t) <= 2e+291) {
		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+192:
		tmp = (-x / t) / z
	elif (z * t) <= 2e+291:
		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+192)
		tmp = Float64(Float64(Float64(-x) / t) / z);
	elseif (Float64(z * t) <= 2e+291)
		tmp = Float64(x / Float64(y - Float64(z * t)));
	else
		tmp = Float64(Float64(x / z) / Float64(-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+192)
		tmp = (-x / t) / z;
	elseif ((z * t) <= 2e+291)
		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+192], N[(N[((-x) / t), $MachinePrecision] / z), $MachinePrecision], If[LessEqual[N[(z * t), $MachinePrecision], 2e+291], 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) < -2.00000000000000008e192

   1. Initial program 77.2%

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

      1. clear-num 77.1%

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

      2. associate-/r/ 77.2%

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

   4. Applied egg-rr 77.2%

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

   5. Taylor expanded in y around 0 77.2%

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

      1. mul-1-neg 77.2%

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

      2. associate-/r* 99.6%

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

      3. distribute-frac-neg2 99.6%

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

   7. Simplified 99.6%

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

   if -2.00000000000000008e192 < (*.f64 z t) < 1.9999999999999999e291

   1. Initial program 99.9%

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

   if 1.9999999999999999e291 < (*.f64 z t)

   1. Initial program 68.6%

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

      1. clear-num 68.6%

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

      2. inv-pow 68.6%

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

   4. Applied egg-rr 68.6%

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

   5. Taylor expanded in y around inf 68.4%

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

      1. +-commutative 68.4%

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

      2. mul-1-neg 68.4%

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

      3. unsub-neg 68.4%

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

      4. associate-/l* 79.9%

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

   7. Simplified 79.9%

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

   8. Taylor expanded in y around 0 68.6%

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

      1. neg-mul-1 68.6%

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

      2. associate-/l/ 99.9%

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

      3. distribute-frac-neg2 99.9%

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

   10. Simplified 99.9%

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

4. Final simplification 99.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \cdot t \leq -2 \cdot 10^{+192}:\\ \;\;\;\;\frac{\frac{-x}{t}}{z}\\ \mathbf{elif}\;z \cdot t \leq 2 \cdot 10^{+291}:\\ \;\;\;\;\frac{x}{y - z \cdot t}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{z}}{-t}\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 70.6% accurate, 0.4× speedup

Math

\[\begin{array}{l} [x, y, z, t] = \mathsf{sort}([x, y, z, t])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -2.9 \cdot 10^{-63} \lor \neg \left(z \leq 3 \cdot 10^{-137}\right):\\ \;\;\;\;\frac{\frac{-x}{t}}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y}\\ \end{array} \end{array} \]

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 (<= z -2.9e-63) (not (<= z 3e-137))) (/ (/ (- 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 ((z <= -2.9e-63) || !(z <= 3e-137)) {
		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 ((z <= (-2.9d-63)) .or. (.not. (z <= 3d-137))) 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 ((z <= -2.9e-63) || !(z <= 3e-137)) {
		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 (z <= -2.9e-63) or not (z <= 3e-137):
		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 ((z <= -2.9e-63) || !(z <= 3e-137))
		tmp = Float64(Float64(Float64(-x) / t) / 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 ((z <= -2.9e-63) || ~((z <= 3e-137)))
		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[z, -2.9e-63], N[Not[LessEqual[z, 3e-137]], $MachinePrecision]], N[(N[((-x) / t), $MachinePrecision] / z), $MachinePrecision], N[(x / y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -2.89999999999999975e-63 or 2.9999999999999998e-137 < z

   1. Initial program 92.3%

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

      1. clear-num 91.6%

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

      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 58.7%

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

      1. mul-1-neg 58.7%

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

      2. associate-/r* 63.5%

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

      3. distribute-frac-neg2 63.5%

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

   7. Simplified 63.5%

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

   if -2.89999999999999975e-63 < z < 2.9999999999999998e-137

   1. Initial program 100.0%

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

   3. Taylor expanded in y around inf 81.9%

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

4. Final simplification 69.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.9 \cdot 10^{-63} \lor \neg \left(z \leq 3 \cdot 10^{-137}\right):\\ \;\;\;\;\frac{\frac{-x}{t}}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 68.4% accurate, 0.4× speedup

Math

\[\begin{array}{l} [x, y, z, t] = \mathsf{sort}([x, y, z, t])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -1.05 \cdot 10^{-62} \lor \neg \left(z \leq 1.18 \cdot 10^{-122}\right):\\ \;\;\;\;\frac{-x}{z \cdot t}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y}\\ \end{array} \end{array} \]

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 -1.05e-62) (not (<= z 1.18e-122))) (/ (- 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 <= -1.05e-62) || !(z <= 1.18e-122)) {
		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 <= (-1.05d-62)) .or. (.not. (z <= 1.18d-122))) 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 <= -1.05e-62) || !(z <= 1.18e-122)) {
		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 <= -1.05e-62) or not (z <= 1.18e-122):
		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 <= -1.05e-62) || !(z <= 1.18e-122))
		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 <= -1.05e-62) || ~((z <= 1.18e-122)))
		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, -1.05e-62], N[Not[LessEqual[z, 1.18e-122]], $MachinePrecision]], N[((-x) / N[(z * t), $MachinePrecision]), $MachinePrecision], N[(x / y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.05e-62 or 1.17999999999999998e-122 < z

   1. Initial program 92.2%

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

   3. Taylor expanded in y around 0 59.0%

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

      1. associate-*r/ 59.0%

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

      2. neg-mul-1 59.0%

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

   5. Simplified 59.0%

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

   if -1.05e-62 < z < 1.17999999999999998e-122

   1. Initial program 100.0%

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

   3. Taylor expanded in y around inf 82.1%

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

4. Final simplification 66.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.05 \cdot 10^{-62} \lor \neg \left(z \leq 1.18 \cdot 10^{-122}\right):\\ \;\;\;\;\frac{-x}{z \cdot t}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 71.8% accurate, 0.4× speedup

Math

\[\begin{array}{l} [x, y, z, t] = \mathsf{sort}([x, y, z, t])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -6.8 \cdot 10^{-63}:\\ \;\;\;\;\frac{\frac{x}{z}}{-t}\\ \mathbf{elif}\;z \leq 3.4 \cdot 10^{-136}:\\ \;\;\;\;\frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{-x}{t}}{z}\\ \end{array} \end{array} \]

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 -6.8e-63)
   (/ (/ x z) (- t))
   (if (<= z 3.4e-136) (/ 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 (z <= -6.8e-63) {
		tmp = (x / z) / -t;
	} else if (z <= 3.4e-136) {
		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 (z <= (-6.8d-63)) then
        tmp = (x / z) / -t
    else if (z <= 3.4d-136) 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 (z <= -6.8e-63) {
		tmp = (x / z) / -t;
	} else if (z <= 3.4e-136) {
		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 z <= -6.8e-63:
		tmp = (x / z) / -t
	elif z <= 3.4e-136:
		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 (z <= -6.8e-63)
		tmp = Float64(Float64(x / z) / Float64(-t));
	elseif (z <= 3.4e-136)
		tmp = Float64(x / y);
	else
		tmp = Float64(Float64(Float64(-x) / t) / 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 (z <= -6.8e-63)
		tmp = (x / z) / -t;
	elseif (z <= 3.4e-136)
		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[LessEqual[z, -6.8e-63], N[(N[(x / z), $MachinePrecision] / (-t)), $MachinePrecision], If[LessEqual[z, 3.4e-136], N[(x / y), $MachinePrecision], N[(N[((-x) / t), $MachinePrecision] / z), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -6.79999999999999997e-63

   1. Initial program 90.6%

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

      1. clear-num 89.2%

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

      2. inv-pow 89.2%

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

   4. Applied egg-rr 89.2%

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

   5. Taylor expanded in y around inf 73.8%

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

      1. +-commutative 73.8%

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

      2. mul-1-neg 73.8%

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

      3. unsub-neg 73.8%

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

      4. associate-/l* 72.4%

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

   7. Simplified 72.4%

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

   8. Taylor expanded in y around 0 68.0%

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

      1. neg-mul-1 68.0%

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

      2. associate-/l/ 76.1%

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

      3. distribute-frac-neg2 76.1%

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

   10. Simplified 76.1%

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

   if -6.79999999999999997e-63 < z < 3.4e-136

   1. Initial program 100.0%

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

   3. Taylor expanded in y around inf 81.9%

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

   if 3.4e-136 < z

   1. Initial program 93.5%

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

      1. clear-num 93.2%

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

      2. associate-/r/ 93.2%

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

   4. Applied egg-rr 93.2%

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

   5. Taylor expanded in y around 0 52.2%

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

      1. mul-1-neg 52.2%

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

      2. associate-/r* 58.4%

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

      3. distribute-frac-neg2 58.4%

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

   7. Simplified 58.4%

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

4. Final simplification 70.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -6.8 \cdot 10^{-63}:\\ \;\;\;\;\frac{\frac{x}{z}}{-t}\\ \mathbf{elif}\;z \leq 3.4 \cdot 10^{-136}:\\ \;\;\;\;\frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{-x}{t}}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 56.9% accurate, 0.5× speedup

Math

\[\begin{array}{l} [x, y, z, t] = \mathsf{sort}([x, y, z, t])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -1.1 \cdot 10^{+151} \lor \neg \left(z \leq 2.7 \cdot 10^{+72}\right):\\ \;\;\;\;\frac{x}{z \cdot t}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y}\\ \end{array} \end{array} \]

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 -1.1e+151) (not (<= z 2.7e+72))) (/ 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 <= -1.1e+151) || !(z <= 2.7e+72)) {
		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 <= (-1.1d+151)) .or. (.not. (z <= 2.7d+72))) 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 <= -1.1e+151) || !(z <= 2.7e+72)) {
		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 <= -1.1e+151) or not (z <= 2.7e+72):
		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 <= -1.1e+151) || !(z <= 2.7e+72))
		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 <= -1.1e+151) || ~((z <= 2.7e+72)))
		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, -1.1e+151], N[Not[LessEqual[z, 2.7e+72]], $MachinePrecision]], N[(x / N[(z * t), $MachinePrecision]), $MachinePrecision], N[(x / y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.10000000000000003e151 or 2.7000000000000001e72 < z

   1. Initial program 90.9%

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

      1. clear-num 90.4%

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

      2. associate-/r/ 90.8%

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

   4. Applied egg-rr 90.8%

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

   5. Taylor expanded in y around 0 63.2%

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

      1. metadata-eval 63.2%

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

      2. *-commutative 63.2%

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

      3. distribute-neg-frac 63.2%

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

      4. associate-/r* 63.9%

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

      5. distribute-neg-frac 63.9%

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

      6. distribute-neg-frac 63.9%

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

      7. metadata-eval 63.9%

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

   7. Simplified 63.9%

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

      1. associate-/l/ 63.2%

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

      2. associate-*l/ 63.3%

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

      3. neg-mul-1 63.3%

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

      4. add-sqr-sqrt 31.8%

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

      5. sqrt-unprod 38.6%

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

      6. sqr-neg 38.6%

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

      7. sqrt-unprod 14.3%

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

      8. add-sqr-sqrt 31.3%

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

   9. Applied egg-rr 31.3%

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

   if -1.10000000000000003e151 < z < 2.7000000000000001e72

   1. Initial program 96.9%

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

   3. Taylor expanded in y around inf 64.0%

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

4. Final simplification 51.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.1 \cdot 10^{+151} \lor \neg \left(z \leq 2.7 \cdot 10^{+72}\right):\\ \;\;\;\;\frac{x}{z \cdot t}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 57.6% accurate, 0.5× speedup

Math

\[\begin{array}{l} [x, y, z, t] = \mathsf{sort}([x, y, z, t])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -1.7 \cdot 10^{+151}:\\ \;\;\;\;\frac{\frac{x}{z}}{t}\\ \mathbf{elif}\;z \leq 2.1 \cdot 10^{+75}:\\ \;\;\;\;\frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{z \cdot t}\\ \end{array} \end{array} \]

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 -1.7e+151) (/ (/ x z) t) (if (<= z 2.1e+75) (/ 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 <= -1.7e+151) {
		tmp = (x / z) / t;
	} else if (z <= 2.1e+75) {
		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 <= (-1.7d+151)) then
        tmp = (x / z) / t
    else if (z <= 2.1d+75) 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 <= -1.7e+151) {
		tmp = (x / z) / t;
	} else if (z <= 2.1e+75) {
		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 <= -1.7e+151:
		tmp = (x / z) / t
	elif z <= 2.1e+75:
		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 <= -1.7e+151)
		tmp = Float64(Float64(x / z) / t);
	elseif (z <= 2.1e+75)
		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 <= -1.7e+151)
		tmp = (x / z) / t;
	elseif (z <= 2.1e+75)
		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, -1.7e+151], N[(N[(x / z), $MachinePrecision] / t), $MachinePrecision], If[LessEqual[z, 2.1e+75], N[(x / y), $MachinePrecision], N[(x / N[(z * t), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.7e151

   1. Initial program 85.0%

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

   3. Taylor expanded in y around 0 75.8%

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

      1. associate-*r/ 75.8%

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

      2. neg-mul-1 75.8%

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

   5. Simplified 75.8%

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

      1. div-inv 75.8%

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

      2. add-sqr-sqrt 39.1%

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

      3. sqrt-unprod 47.8%

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

      4. sqr-neg 47.8%

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

      5. sqrt-unprod 18.1%

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

      6. add-sqr-sqrt 46.2%

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

      7. *-commutative 46.2%

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

      8. associate-/r* 46.2%

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

   7. Applied egg-rr 46.2%

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

      1. associate-*r/ 47.9%

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

      2. associate-*r/ 47.9%

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

      3. *-rgt-identity 47.9%

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

   9. Simplified 47.9%

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

   if -1.7e151 < z < 2.09999999999999999e75

   1. Initial program 97.0%

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

   3. Taylor expanded in y around inf 64.5%

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

   if 2.09999999999999999e75 < z

   1. Initial program 93.4%

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

      1. clear-num 93.2%

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

      2. associate-/r/ 93.3%

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

   4. Applied egg-rr 93.3%

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

   5. Taylor expanded in y around 0 59.6%

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

      1. metadata-eval 59.6%

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

      2. *-commutative 59.6%

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

      3. distribute-neg-frac 59.6%

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

      4. associate-/r* 60.6%

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

      5. distribute-neg-frac 60.6%

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

      6. distribute-neg-frac 60.6%

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

      7. metadata-eval 60.6%

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

   7. Simplified 60.6%

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

      1. associate-/l/ 59.6%

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

      2. associate-*l/ 59.7%

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

      3. neg-mul-1 59.7%

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

      4. add-sqr-sqrt 30.4%

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

      5. sqrt-unprod 36.7%

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

      6. sqr-neg 36.7%

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

      7. sqrt-unprod 13.3%

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

      8. add-sqr-sqrt 25.7%

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

   9. Applied egg-rr 25.7%

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

4. Final simplification 53.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.7 \cdot 10^{+151}:\\ \;\;\;\;\frac{\frac{x}{z}}{t}\\ \mathbf{elif}\;z \leq 2.1 \cdot 10^{+75}:\\ \;\;\;\;\frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{z \cdot t}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 53.2% 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 94.7%

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

   1. clear-num 94.2%

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

   2. associate-/r/ 94.5%

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

4. Applied egg-rr 94.5%

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

5. Taylor expanded in y around inf 52.6%

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

   1. associate-*l/ 52.7%

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

   2. *-un-lft-identity 52.7%

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

   3. clear-num 52.8%

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

7. Applied egg-rr 52.8%

   \[\leadsto \color{blue}{\frac{1}{\frac{y}{x}}} \]
8. Add Preprocessing

Alternative 8: 53.5% 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 94.7%

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

3. Taylor expanded in y around inf 52.7%

   \[\leadsto \color{blue}{\frac{x}{y}} \]
4. Add Preprocessing

Developer target: 96.2% 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 2024085 
(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))))