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

Percentage Accurate: 96.0% → 98.7%

Time: 7.9s

Alternatives: 7

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: 96.0% 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: 98.7% accurate, 0.3× speedup

Math

\[\begin{array}{l} [x, y, z, t] = \mathsf{sort}([x, y, z, t])\\ \\ \begin{array}{l} \mathbf{if}\;z \cdot t \leq -1 \cdot 10^{+272}:\\ \;\;\;\;\frac{\frac{x}{z}}{-t}\\ \mathbf{elif}\;z \cdot t \leq 2 \cdot 10^{+135}:\\ \;\;\;\;\frac{x}{y - z \cdot t}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{t}}{-z}\\ \end{array} \end{array} \]

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 t) -1e+272)
   (/ (/ x z) (- t))
   (if (<= (* z t) 2e+135) (/ x (- y (* z t))) (/ (/ 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 * t) <= -1e+272) {
		tmp = (x / z) / -t;
	} else if ((z * t) <= 2e+135) {
		tmp = x / (y - (z * t));
	} 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 * t) <= (-1d+272)) then
        tmp = (x / z) / -t
    else if ((z * t) <= 2d+135) then
        tmp = x / (y - (z * t))
    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 * t) <= -1e+272) {
		tmp = (x / z) / -t;
	} else if ((z * t) <= 2e+135) {
		tmp = x / (y - (z * t));
	} 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 * t) <= -1e+272:
		tmp = (x / z) / -t
	elif (z * t) <= 2e+135:
		tmp = x / (y - (z * t))
	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 (Float64(z * t) <= -1e+272)
		tmp = Float64(Float64(x / z) / Float64(-t));
	elseif (Float64(z * t) <= 2e+135)
		tmp = Float64(x / Float64(y - Float64(z * t)));
	else
		tmp = Float64(Float64(x / 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 ((z * t) <= -1e+272)
		tmp = (x / z) / -t;
	elseif ((z * t) <= 2e+135)
		tmp = x / (y - (z * t));
	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[N[(z * t), $MachinePrecision], -1e+272], N[(N[(x / z), $MachinePrecision] / (-t)), $MachinePrecision], If[LessEqual[N[(z * t), $MachinePrecision], 2e+135], N[(x / N[(y - N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x / t), $MachinePrecision] / (-z)), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 z t) < -1.0000000000000001e272

   1. Initial program 70.6%

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

      1. clear-num 70.7%

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

      2. inv-pow 70.7%

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

   4. Applied egg-rr 70.7%

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

   5. Taylor expanded in y around 0 70.7%

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

      1. mul-1-neg 70.7%

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

      2. associate-*l/ 97.5%

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

      3. *-commutative 97.5%

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

      4. distribute-rgt-neg-in 97.5%

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

      5. mul-1-neg 97.5%

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

      6. associate-*r/ 97.5%

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

      7. neg-mul-1 97.5%

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

   7. Simplified 97.5%

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

      1. unpow-prod-down 99.9%

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

      2. inv-pow 99.9%

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

      3. unpow-1 99.9%

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

      4. clear-num 99.9%

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

      5. add-sqr-sqrt 42.9%

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

      6. sqrt-unprod 66.0%

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

      7. sqr-neg 66.0%

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

      8. sqrt-unprod 22.8%

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

      9. add-sqr-sqrt 61.1%

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

      10. times-frac 61.6%

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

      11. *-un-lft-identity 61.6%

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

      12. frac-2neg 61.6%

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

      13. distribute-rgt-neg-in 61.6%

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

      14. add-sqr-sqrt 38.3%

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

      15. sqrt-unprod 70.6%

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

      16. sqr-neg 70.6%

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

      17. sqrt-unprod 32.3%

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

      18. add-sqr-sqrt 70.6%

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

   9. Applied egg-rr 70.6%

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

   10. Taylor expanded in x around 0 70.6%

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

       1. mul-1-neg 70.6%

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

       2. associate-/r* 99.9%

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

       3. associate-/l/ 70.6%

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

       4. associate-/r* 99.9%

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

       5. distribute-frac-neg2 99.9%

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

   12. Simplified 99.9%

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

   if -1.0000000000000001e272 < (*.f64 z t) < 1.99999999999999992e135

   1. Initial program 99.9%

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

   if 1.99999999999999992e135 < (*.f64 z t)

   1. Initial program 82.6%

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

      1. clear-num 82.4%

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

      2. inv-pow 82.4%

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

   4. Applied egg-rr 82.4%

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

   5. Taylor expanded in y around 0 82.4%

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

      1. mul-1-neg 82.4%

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

      2. associate-*l/ 99.5%

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

      3. *-commutative 99.5%

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

      4. distribute-rgt-neg-in 99.5%

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

      5. mul-1-neg 99.5%

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

      6. associate-*r/ 99.5%

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

      7. neg-mul-1 99.5%

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

   7. Simplified 99.5%

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

      1. *-commutative 99.5%

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

      2. unpow-prod-down 99.7%

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

      3. unpow-1 99.7%

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

      4. clear-num 99.7%

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

      5. add-sqr-sqrt 44.5%

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

      6. sqrt-unprod 64.9%

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

      7. sqr-neg 64.9%

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

      8. sqrt-unprod 29.9%

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

      9. add-sqr-sqrt 52.0%

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

      10. inv-pow 52.0%

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

      11. div-inv 52.0%

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

      12. frac-2neg 52.0%

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

      13. distribute-frac-neg2 52.0%

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

      14. add-sqr-sqrt 22.1%

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

      15. sqrt-unprod 70.1%

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

      16. sqr-neg 70.1%

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

      17. sqrt-unprod 55.0%

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

      18. add-sqr-sqrt 99.8%

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

   9. Applied egg-rr 99.8%

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

Alternative 2: 77.6% accurate, 0.3× speedup

Math

\[\begin{array}{l} [x, y, z, t] = \mathsf{sort}([x, y, z, t])\\ \\ \begin{array}{l} \mathbf{if}\;z \cdot t \leq -5 \cdot 10^{+124} \lor \neg \left(z \cdot t \leq 4 \cdot 10^{+25}\right):\\ \;\;\;\;\frac{\frac{x}{t}}{-z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y}\\ \end{array} \end{array} \]

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 t) -5e+124) (not (<= (* z t) 4e+25)))
   (/ (/ 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 * t) <= -5e+124) || !((z * t) <= 4e+25)) {
		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 * t) <= (-5d+124)) .or. (.not. ((z * t) <= 4d+25))) 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 * t) <= -5e+124) || !((z * t) <= 4e+25)) {
		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 * t) <= -5e+124) or not ((z * t) <= 4e+25):
		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 ((Float64(z * t) <= -5e+124) || !(Float64(z * t) <= 4e+25))
		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 (((z * t) <= -5e+124) || ~(((z * t) <= 4e+25)))
		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[N[(z * t), $MachinePrecision], -5e+124], N[Not[LessEqual[N[(z * t), $MachinePrecision], 4e+25]], $MachinePrecision]], N[(N[(x / t), $MachinePrecision] / (-z)), $MachinePrecision], N[(x / y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 z t) < -4.9999999999999996e124 or 4.00000000000000036e25 < (*.f64 z t)

   1. Initial program 87.8%

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

      1. clear-num 86.9%

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

      2. inv-pow 86.9%

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

   4. Applied egg-rr 86.9%

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

   5. Taylor expanded in y around 0 79.7%

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

      1. mul-1-neg 79.7%

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

      2. associate-*l/ 88.2%

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

      3. *-commutative 88.2%

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

      4. distribute-rgt-neg-in 88.2%

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

      5. mul-1-neg 88.2%

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

      6. associate-*r/ 88.2%

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

      7. neg-mul-1 88.2%

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

   7. Simplified 88.2%

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

      1. *-commutative 88.2%

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

      2. unpow-prod-down 88.5%

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

      3. unpow-1 88.5%

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

      4. clear-num 89.9%

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

      5. add-sqr-sqrt 45.0%

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

      6. sqrt-unprod 60.8%

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

      7. sqr-neg 60.8%

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

      8. sqrt-unprod 20.1%

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

      9. add-sqr-sqrt 45.7%

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

      10. inv-pow 45.7%

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

      11. div-inv 45.7%

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

      12. frac-2neg 45.7%

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

      13. distribute-frac-neg2 45.7%

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

      14. add-sqr-sqrt 25.5%

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

      15. sqrt-unprod 61.1%

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

      16. sqr-neg 61.1%

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

      17. sqrt-unprod 44.7%

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

      18. add-sqr-sqrt 90.0%

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

   9. Applied egg-rr 90.0%

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

   if -4.9999999999999996e124 < (*.f64 z t) < 4.00000000000000036e25

   1. Initial program 99.9%

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

   3. Taylor expanded in y around inf 78.4%

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

4. Final simplification 83.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \cdot t \leq -5 \cdot 10^{+124} \lor \neg \left(z \cdot t \leq 4 \cdot 10^{+25}\right):\\ \;\;\;\;\frac{\frac{x}{t}}{-z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 76.5% accurate, 0.3× speedup

Math

\[\begin{array}{l} [x, y, z, t] = \mathsf{sort}([x, y, z, t])\\ \\ \begin{array}{l} \mathbf{if}\;z \cdot t \leq -5 \cdot 10^{+34} \lor \neg \left(z \cdot t \leq 4 \cdot 10^{+25}\right):\\ \;\;\;\;\frac{x}{t \cdot \left(-z\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y}\\ \end{array} \end{array} \]

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+34) (not (<= (* z t) 4e+25)))
   (/ 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 * t) <= -5e+34) || !((z * t) <= 4e+25)) {
		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 * t) <= (-5d+34)) .or. (.not. ((z * t) <= 4d+25))) 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 * t) <= -5e+34) || !((z * t) <= 4e+25)) {
		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 * t) <= -5e+34) or not ((z * t) <= 4e+25):
		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 ((Float64(z * t) <= -5e+34) || !(Float64(z * t) <= 4e+25))
		tmp = Float64(x / Float64(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 (((z * t) <= -5e+34) || ~(((z * t) <= 4e+25)))
		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[N[(z * t), $MachinePrecision], -5e+34], N[Not[LessEqual[N[(z * t), $MachinePrecision], 4e+25]], $MachinePrecision]], N[(x / N[(t * (-z)), $MachinePrecision]), $MachinePrecision], N[(x / y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 z t) < -4.9999999999999998e34 or 4.00000000000000036e25 < (*.f64 z t)

   1. Initial program 89.1%

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

   3. Taylor expanded in y around 0 77.5%

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

      1. associate-*r/ 77.5%

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

      2. neg-mul-1 77.5%

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

   5. Simplified 77.5%

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

   if -4.9999999999999998e34 < (*.f64 z t) < 4.00000000000000036e25

   1. Initial program 99.9%

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

   3. Taylor expanded in y around inf 81.3%

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

4. Final simplification 79.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \cdot t \leq -5 \cdot 10^{+34} \lor \neg \left(z \cdot t \leq 4 \cdot 10^{+25}\right):\\ \;\;\;\;\frac{x}{t \cdot \left(-z\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 77.7% accurate, 0.3× speedup

Math

\[\begin{array}{l} [x, y, z, t] = \mathsf{sort}([x, y, z, t])\\ \\ \begin{array}{l} \mathbf{if}\;z \cdot t \leq -5 \cdot 10^{+112}:\\ \;\;\;\;\frac{\frac{x}{z}}{-t}\\ \mathbf{elif}\;z \cdot t \leq 4 \cdot 10^{+25}:\\ \;\;\;\;\frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{t}}{-z}\\ \end{array} \end{array} \]

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 t) -5e+112)
   (/ (/ x z) (- t))
   (if (<= (* z t) 4e+25) (/ 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 * t) <= -5e+112) {
		tmp = (x / z) / -t;
	} else if ((z * t) <= 4e+25) {
		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 * t) <= (-5d+112)) then
        tmp = (x / z) / -t
    else if ((z * t) <= 4d+25) 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 * t) <= -5e+112) {
		tmp = (x / z) / -t;
	} else if ((z * t) <= 4e+25) {
		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 * t) <= -5e+112:
		tmp = (x / z) / -t
	elif (z * t) <= 4e+25:
		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 (Float64(z * t) <= -5e+112)
		tmp = Float64(Float64(x / z) / Float64(-t));
	elseif (Float64(z * t) <= 4e+25)
		tmp = Float64(x / y);
	else
		tmp = Float64(Float64(x / 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 ((z * t) <= -5e+112)
		tmp = (x / z) / -t;
	elseif ((z * t) <= 4e+25)
		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[N[(z * t), $MachinePrecision], -5e+112], N[(N[(x / z), $MachinePrecision] / (-t)), $MachinePrecision], If[LessEqual[N[(z * t), $MachinePrecision], 4e+25], N[(x / y), $MachinePrecision], N[(N[(x / t), $MachinePrecision] / (-z)), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 z t) < -5e112

   1. Initial program 86.0%

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

      1. clear-num 84.2%

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

      2. inv-pow 84.2%

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

   4. Applied egg-rr 84.2%

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

   5. Taylor expanded in y around 0 82.0%

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

      1. mul-1-neg 82.0%

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

      2. associate-*l/ 92.7%

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

      3. *-commutative 92.7%

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

      4. distribute-rgt-neg-in 92.7%

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

      5. mul-1-neg 92.7%

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

      6. associate-*r/ 92.7%

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

      7. neg-mul-1 92.7%

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

   7. Simplified 92.7%

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

      1. unpow-prod-down 94.5%

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

      2. inv-pow 94.5%

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

      3. unpow-1 94.5%

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

      4. clear-num 95.9%

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

      5. add-sqr-sqrt 56.7%

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

      6. sqrt-unprod 75.9%

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

      7. sqr-neg 75.9%

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

      8. sqrt-unprod 19.4%

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

      9. add-sqr-sqrt 55.8%

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

      10. times-frac 56.0%

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

      11. *-un-lft-identity 56.0%

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

      12. frac-2neg 56.0%

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

      13. distribute-rgt-neg-in 56.0%

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

      14. add-sqr-sqrt 36.4%

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

      15. sqrt-unprod 60.3%

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

      16. sqr-neg 60.3%

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

      17. sqrt-unprod 29.1%

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

      18. add-sqr-sqrt 83.7%

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

   9. Applied egg-rr 83.7%

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

   10. Taylor expanded in x around 0 83.7%

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

       1. mul-1-neg 83.7%

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

       2. associate-/r* 95.9%

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

       3. associate-/l/ 83.7%

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

       4. associate-/r* 95.5%

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

       5. distribute-frac-neg2 95.5%

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

   12. Simplified 95.5%

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

   if -5e112 < (*.f64 z t) < 4.00000000000000036e25

   1. Initial program 99.9%

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

   3. Taylor expanded in y around inf 79.3%

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

   if 4.00000000000000036e25 < (*.f64 z t)

   1. Initial program 89.6%

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

      1. clear-num 89.4%

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

      2. inv-pow 89.4%

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

   4. Applied egg-rr 89.4%

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

   5. Taylor expanded in y around 0 77.5%

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

      1. mul-1-neg 77.5%

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

      2. associate-*l/ 84.2%

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

      3. *-commutative 84.2%

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

      4. distribute-rgt-neg-in 84.2%

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

      5. mul-1-neg 84.2%

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

      6. associate-*r/ 84.2%

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

      7. neg-mul-1 84.2%

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

   7. Simplified 84.2%

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

      1. *-commutative 84.2%

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

      2. unpow-prod-down 83.4%

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

      3. unpow-1 83.4%

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

      4. clear-num 84.7%

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

      5. add-sqr-sqrt 37.9%

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

      6. sqrt-unprod 50.5%

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

      7. sqr-neg 50.5%

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

      8. sqrt-unprod 19.8%

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

      9. add-sqr-sqrt 38.3%

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

      10. inv-pow 38.3%

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

      11. div-inv 38.3%

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

      12. frac-2neg 38.3%

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

      13. distribute-frac-neg2 38.3%

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

      14. add-sqr-sqrt 18.5%

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

      15. sqrt-unprod 58.2%

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

      16. sqr-neg 58.2%

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

      17. sqrt-unprod 46.6%

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

      18. add-sqr-sqrt 84.8%

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

   9. Applied egg-rr 84.8%

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

Alternative 5: 62.4% accurate, 0.4× speedup

Math

\[\begin{array}{l} [x, y, z, t] = \mathsf{sort}([x, y, z, t])\\ \\ \begin{array}{l} \mathbf{if}\;z \cdot t \leq -5 \cdot 10^{+112} \lor \neg \left(z \cdot t \leq 2 \cdot 10^{+100}\right):\\ \;\;\;\;\frac{x}{z \cdot t}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y}\\ \end{array} \end{array} \]

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+112) (not (<= (* z t) 2e+100)))
   (/ 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+112) || !((z * t) <= 2e+100)) {
		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+112)) .or. (.not. ((z * t) <= 2d+100))) 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+112) || !((z * t) <= 2e+100)) {
		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+112) or not ((z * t) <= 2e+100):
		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+112) || !(Float64(z * t) <= 2e+100))
		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+112) || ~(((z * t) <= 2e+100)))
		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+112], N[Not[LessEqual[N[(z * t), $MachinePrecision], 2e+100]], $MachinePrecision]], N[(x / N[(z * t), $MachinePrecision]), $MachinePrecision], N[(x / y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 z t) < -5e112 or 2.00000000000000003e100 < (*.f64 z t)

   1. Initial program 85.6%

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

      1. clear-num 84.7%

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

      2. inv-pow 84.7%

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

   4. Applied egg-rr 84.7%

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

   5. Taylor expanded in y around 0 83.6%

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

      1. mul-1-neg 83.6%

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

      2. associate-*l/ 96.2%

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

      3. *-commutative 96.2%

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

      4. distribute-rgt-neg-in 96.2%

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

      5. mul-1-neg 96.2%

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

      6. associate-*r/ 96.2%

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

      7. neg-mul-1 96.2%

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

   7. Simplified 96.2%

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

      1. unpow-prod-down 97.2%

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

      2. inv-pow 97.2%

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

      3. unpow-1 97.2%

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

      4. clear-num 97.8%

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

      5. add-sqr-sqrt 52.6%

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

      6. sqrt-unprod 71.0%

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

      7. sqr-neg 71.0%

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

      8. sqrt-unprod 23.6%

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

      9. add-sqr-sqrt 54.5%

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

      10. times-frac 54.3%

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

      11. *-un-lft-identity 54.3%

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

   9. Applied egg-rr 54.3%

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

   if -5e112 < (*.f64 z t) < 2.00000000000000003e100

   1. Initial program 99.9%

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

   3. Taylor expanded in y around inf 75.3%

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

4. Final simplification 68.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \cdot t \leq -5 \cdot 10^{+112} \lor \neg \left(z \cdot t \leq 2 \cdot 10^{+100}\right):\\ \;\;\;\;\frac{x}{z \cdot t}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 62.5% accurate, 0.4× speedup

Math

\[\begin{array}{l} [x, y, z, t] = \mathsf{sort}([x, y, z, t])\\ \\ \begin{array}{l} \mathbf{if}\;z \cdot t \leq -5 \cdot 10^{+112}:\\ \;\;\;\;\frac{x}{z \cdot t}\\ \mathbf{elif}\;z \cdot t \leq 2 \cdot 10^{+100}:\\ \;\;\;\;\frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{z}}{t}\\ \end{array} \end{array} \]

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 (<= (* z t) -5e+112)
   (/ x (* z t))
   (if (<= (* z t) 2e+100) (/ 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) <= -5e+112) {
		tmp = x / (z * t);
	} else if ((z * t) <= 2e+100) {
		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) <= (-5d+112)) then
        tmp = x / (z * t)
    else if ((z * t) <= 2d+100) 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) <= -5e+112) {
		tmp = x / (z * t);
	} else if ((z * t) <= 2e+100) {
		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) <= -5e+112:
		tmp = x / (z * t)
	elif (z * t) <= 2e+100:
		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) <= -5e+112)
		tmp = Float64(x / Float64(z * t));
	elseif (Float64(z * t) <= 2e+100)
		tmp = Float64(x / y);
	else
		tmp = Float64(Float64(x / 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+112)
		tmp = x / (z * t);
	elseif ((z * t) <= 2e+100)
		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], -5e+112], N[(x / N[(z * t), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(z * t), $MachinePrecision], 2e+100], N[(x / y), $MachinePrecision], N[(N[(x / z), $MachinePrecision] / t), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 z t) < -5e112

   1. Initial program 86.0%

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

      1. clear-num 84.2%

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

      2. inv-pow 84.2%

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

   4. Applied egg-rr 84.2%

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

   5. Taylor expanded in y around 0 82.0%

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

      1. mul-1-neg 82.0%

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

      2. associate-*l/ 92.7%

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

      3. *-commutative 92.7%

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

      4. distribute-rgt-neg-in 92.7%

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

      5. mul-1-neg 92.7%

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

      6. associate-*r/ 92.7%

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

      7. neg-mul-1 92.7%

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

   7. Simplified 92.7%

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

      1. unpow-prod-down 94.5%

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

      2. inv-pow 94.5%

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

      3. unpow-1 94.5%

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

      4. clear-num 95.9%

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

      5. add-sqr-sqrt 56.7%

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

      6. sqrt-unprod 75.9%

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

      7. sqr-neg 75.9%

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

      8. sqrt-unprod 19.4%

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

      9. add-sqr-sqrt 55.8%

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

      10. times-frac 56.0%

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

      11. *-un-lft-identity 56.0%

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

   9. Applied egg-rr 56.0%

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

   if -5e112 < (*.f64 z t) < 2.00000000000000003e100

   1. Initial program 99.9%

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

   3. Taylor expanded in y around inf 75.3%

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

   if 2.00000000000000003e100 < (*.f64 z t)

   1. Initial program 85.2%

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

      1. clear-num 85.1%

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

      2. associate-/r/ 85.1%

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

   4. Applied egg-rr 85.1%

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

   5. Taylor expanded in t around inf 86.5%

      \[\leadsto \color{blue}{\frac{-1 \cdot \frac{y}{t \cdot {z}^{2}} - \frac{1}{z}}{t}} \cdot x \]
   6. Step-by-step derivation

      1. associate-*r/ 86.5%

         \[\leadsto \frac{\color{blue}{\frac{-1 \cdot y}{t \cdot {z}^{2}}} - \frac{1}{z}}{t} \cdot x \]

      2. mul-1-neg 86.5%

         \[\leadsto \frac{\frac{\color{blue}{-y}}{t \cdot {z}^{2}} - \frac{1}{z}}{t} \cdot x \]

   7. Simplified 86.5%

      \[\leadsto \color{blue}{\frac{\frac{-y}{t \cdot {z}^{2}} - \frac{1}{z}}{t}} \cdot x \]

   8. Taylor expanded in y around 0 84.4%

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

      1. associate-/r* 87.9%

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

   10. Simplified 87.9%

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

       1. associate-/l/ 84.4%

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

       2. associate-*l/ 84.5%

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

       3. neg-mul-1 84.5%

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

       4. add-sqr-sqrt 41.5%

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

       5. sqrt-unprod 63.4%

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

       6. sqr-neg 63.4%

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

       7. sqrt-unprod 30.1%

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

       8. add-sqr-sqrt 52.7%

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

       9. associate-/r* 52.5%

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

   12. Applied egg-rr 52.5%

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

Alternative 7: 54.9% 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 94.9%

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

3. Taylor expanded in y around inf 56.6%

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

Developer target: 96.1% 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 2024091 
(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))))