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

Percentage Accurate: 95.9% → 97.8%

Time: 8.9s

Alternatives: 6

Speedup: 0.5×

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 95.9% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 97.8% accurate, 0.5× speedup

Math

\[\begin{array}{l} [x, y, z, t] = \mathsf{sort}([x, y, z, t])\\ \\ \begin{array}{l} \mathbf{if}\;z \cdot t \leq 10^{+231}:\\ \;\;\;\;\frac{x}{y - z \cdot t}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{t}}{-z}\\ \end{array} \end{array} \]

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+231) (/ 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+231) {
		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+231) 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+231) {
		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+231:
		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+231)
		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+231)
		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+231], N[(x / N[(y - N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x / t), $MachinePrecision] / (-z)), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 z t) < 1.0000000000000001e231

   1. Initial program 98.7%

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

   if 1.0000000000000001e231 < (*.f64 z t)

   1. Initial program 60.1%

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

      1. clear-num 60.1%

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

      2. associate-/r/ 60.1%

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

   4. Applied egg-rr 60.1%

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

   5. Taylor expanded in y around 0 60.1%

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

      1. associate-/r* 65.6%

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

   7. Simplified 65.6%

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

      1. associate-*l/ 99.7%

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

      2. frac-2neg 99.7%

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

      3. associate-*l/ 99.8%

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

      4. neg-mul-1 99.8%

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

      5. add-sqr-sqrt 37.8%

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

      6. sqrt-unprod 58.1%

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

      7. sqr-neg 58.1%

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

      8. sqrt-unprod 25.7%

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

      9. add-sqr-sqrt 45.8%

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

      10. distribute-frac-neg 45.8%

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

      11. add-sqr-sqrt 20.1%

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

      12. sqrt-unprod 53.9%

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

      13. sqr-neg 53.9%

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

      14. sqrt-unprod 61.5%

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

      15. add-sqr-sqrt 99.8%

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

   9. Applied egg-rr 99.8%

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

Alternative 2: 77.2% accurate, 0.3× speedup

Math

\[\begin{array}{l} [x, y, z, t] = \mathsf{sort}([x, y, z, t])\\ \\ \begin{array}{l} \mathbf{if}\;z \cdot t \leq -5 \cdot 10^{-70} \lor \neg \left(z \cdot t \leq 10^{+39}\right):\\ \;\;\;\;\frac{x}{t \cdot \left(-z\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y}\\ \end{array} \end{array} \]

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-70) (not (<= (* z t) 1e+39)))
   (/ 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-70) || !((z * t) <= 1e+39)) {
		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-70)) .or. (.not. ((z * t) <= 1d+39))) 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-70) || !((z * t) <= 1e+39)) {
		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-70) or not ((z * t) <= 1e+39):
		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-70) || !(Float64(z * t) <= 1e+39))
		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-70) || ~(((z * t) <= 1e+39)))
		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-70], N[Not[LessEqual[N[(z * t), $MachinePrecision], 1e+39]], $MachinePrecision]], N[(x / N[(t * (-z)), $MachinePrecision]), $MachinePrecision], N[(x / y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 z t) < -4.9999999999999998e-70 or 9.9999999999999994e38 < (*.f64 z t)

   1. Initial program 90.3%

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

   3. Taylor expanded in y around 0 72.4%

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

      1. associate-*r/ 72.4%

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

      2. neg-mul-1 72.4%

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

   5. Simplified 72.4%

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

   if -4.9999999999999998e-70 < (*.f64 z t) < 9.9999999999999994e38

   1. Initial program 99.9%

      \[\frac{x}{y - z \cdot t} \]
   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 77.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \cdot t \leq -5 \cdot 10^{-70} \lor \neg \left(z \cdot t \leq 10^{+39}\right):\\ \;\;\;\;\frac{x}{t \cdot \left(-z\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 78.7% accurate, 0.3× speedup

Math

\[\begin{array}{l} [x, y, z, t] = \mathsf{sort}([x, y, z, t])\\ \\ \begin{array}{l} \mathbf{if}\;z \cdot t \leq -5 \cdot 10^{-70}:\\ \;\;\;\;\frac{x}{t \cdot \left(-z\right)}\\ \mathbf{elif}\;z \cdot t \leq 10^{+39}:\\ \;\;\;\;\frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{z}}{-t}\\ \end{array} \end{array} \]

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-70)
   (/ x (* t (- z)))
   (if (<= (* z t) 1e+39) (/ 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-70) {
		tmp = x / (t * -z);
	} else if ((z * t) <= 1e+39) {
		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-70)) then
        tmp = x / (t * -z)
    else if ((z * t) <= 1d+39) 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-70) {
		tmp = x / (t * -z);
	} else if ((z * t) <= 1e+39) {
		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-70:
		tmp = x / (t * -z)
	elif (z * t) <= 1e+39:
		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-70)
		tmp = Float64(x / Float64(t * Float64(-z)));
	elseif (Float64(z * t) <= 1e+39)
		tmp = Float64(x / y);
	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) <= -5e-70)
		tmp = x / (t * -z);
	elseif ((z * t) <= 1e+39)
		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-70], N[(x / N[(t * (-z)), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(z * t), $MachinePrecision], 1e+39], N[(x / y), $MachinePrecision], N[(N[(x / z), $MachinePrecision] / (-t)), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 z t) < -4.9999999999999998e-70

   1. Initial program 95.7%

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

   3. Taylor expanded in y around 0 74.7%

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

      1. associate-*r/ 74.7%

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

      2. neg-mul-1 74.7%

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

   5. Simplified 74.7%

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

   if -4.9999999999999998e-70 < (*.f64 z t) < 9.9999999999999994e38

   1. Initial program 99.9%

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

   3. Taylor expanded in y around inf 82.1%

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

   if 9.9999999999999994e38 < (*.f64 z t)

   1. Initial program 82.7%

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

      1. clear-num 80.1%

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

      2. associate-/r/ 82.7%

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

   4. Applied egg-rr 82.7%

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

   5. Taylor expanded in y around 0 69.2%

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

      1. associate-/r* 71.4%

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

   7. Simplified 71.4%

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

      1. associate-*l/ 82.7%

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

      2. frac-2neg 82.7%

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

      3. associate-*l/ 82.8%

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

      4. neg-mul-1 82.8%

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

      5. add-sqr-sqrt 42.9%

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

      6. sqrt-unprod 56.8%

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

      7. sqr-neg 56.8%

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

      8. sqrt-unprod 16.3%

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

      9. add-sqr-sqrt 31.8%

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

      10. distribute-frac-neg 31.8%

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

      11. add-sqr-sqrt 15.5%

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

      12. sqrt-unprod 39.3%

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

      13. sqr-neg 39.3%

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

      14. sqrt-unprod 39.5%

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

      15. add-sqr-sqrt 82.8%

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

   9. Applied egg-rr 82.8%

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

   10. Taylor expanded in x around 0 69.1%

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

       1. mul-1-neg 69.1%

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

       2. associate-/l/ 85.0%

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

       3. distribute-neg-frac2 85.0%

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

   12. Simplified 85.0%

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

4. Final simplification 80.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \cdot t \leq -5 \cdot 10^{-70}:\\ \;\;\;\;\frac{x}{t \cdot \left(-z\right)}\\ \mathbf{elif}\;z \cdot t \leq 10^{+39}:\\ \;\;\;\;\frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{z}}{-t}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 78.7% accurate, 0.3× speedup

Math

\[\begin{array}{l} [x, y, z, t] = \mathsf{sort}([x, y, z, t])\\ \\ \begin{array}{l} \mathbf{if}\;z \cdot t \leq -5 \cdot 10^{-70}:\\ \;\;\;\;\frac{x}{t \cdot \left(-z\right)}\\ \mathbf{elif}\;z \cdot t \leq 10^{+39}:\\ \;\;\;\;\frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{t}}{-z}\\ \end{array} \end{array} \]

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-70)
   (/ x (* t (- z)))
   (if (<= (* z t) 1e+39) (/ 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-70) {
		tmp = x / (t * -z);
	} else if ((z * t) <= 1e+39) {
		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-70)) then
        tmp = x / (t * -z)
    else if ((z * t) <= 1d+39) 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-70) {
		tmp = x / (t * -z);
	} else if ((z * t) <= 1e+39) {
		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-70:
		tmp = x / (t * -z)
	elif (z * t) <= 1e+39:
		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-70)
		tmp = Float64(x / Float64(t * Float64(-z)));
	elseif (Float64(z * t) <= 1e+39)
		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-70)
		tmp = x / (t * -z);
	elseif ((z * t) <= 1e+39)
		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-70], N[(x / N[(t * (-z)), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(z * t), $MachinePrecision], 1e+39], N[(x / y), $MachinePrecision], N[(N[(x / t), $MachinePrecision] / (-z)), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 z t) < -4.9999999999999998e-70

   1. Initial program 95.7%

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

   3. Taylor expanded in y around 0 74.7%

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

      1. associate-*r/ 74.7%

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

      2. neg-mul-1 74.7%

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

   5. Simplified 74.7%

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

   if -4.9999999999999998e-70 < (*.f64 z t) < 9.9999999999999994e38

   1. Initial program 99.9%

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

   3. Taylor expanded in y around inf 82.1%

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

   if 9.9999999999999994e38 < (*.f64 z t)

   1. Initial program 82.7%

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

      1. clear-num 80.1%

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

      2. associate-/r/ 82.7%

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

   4. Applied egg-rr 82.7%

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

   5. Taylor expanded in y around 0 69.2%

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

      1. associate-/r* 71.4%

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

   7. Simplified 71.4%

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

      1. associate-*l/ 82.7%

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

      2. frac-2neg 82.7%

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

      3. associate-*l/ 82.8%

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

      4. neg-mul-1 82.8%

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

      5. add-sqr-sqrt 42.9%

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

      6. sqrt-unprod 56.8%

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

      7. sqr-neg 56.8%

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

      8. sqrt-unprod 16.3%

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

      9. add-sqr-sqrt 31.8%

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

      10. distribute-frac-neg 31.8%

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

      11. add-sqr-sqrt 15.5%

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

      12. sqrt-unprod 39.3%

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

      13. sqr-neg 39.3%

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

      14. sqrt-unprod 39.5%

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

      15. add-sqr-sqrt 82.8%

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

   9. Applied egg-rr 82.8%

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

4. Final simplification 80.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \cdot t \leq -5 \cdot 10^{-70}:\\ \;\;\;\;\frac{x}{t \cdot \left(-z\right)}\\ \mathbf{elif}\;z \cdot t \leq 10^{+39}:\\ \;\;\;\;\frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{t}}{-z}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 63.4% accurate, 0.4× speedup

Math

\[\begin{array}{l} [x, y, z, t] = \mathsf{sort}([x, y, z, t])\\ \\ \begin{array}{l} \mathbf{if}\;z \cdot t \leq -1 \cdot 10^{+202} \lor \neg \left(z \cdot t \leq 10^{+231}\right):\\ \;\;\;\;\frac{x}{z \cdot t}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
(FPCore (x y z t)
 :precision binary64
 (if (or (<= (* z t) -1e+202) (not (<= (* z t) 1e+231)))
   (/ x (* z t))
   (/ x y)))

C

assert(x < y && y < z && z < t);
double code(double x, double y, double z, double t) {
	double tmp;
	if (((z * t) <= -1e+202) || !((z * t) <= 1e+231)) {
		tmp = x / (z * t);
	} else {
		tmp = x / y;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (((z * t) <= (-1d+202)) .or. (.not. ((z * t) <= 1d+231))) then
        tmp = x / (z * t)
    else
        tmp = x / y
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t;
public static double code(double x, double y, double z, double t) {
	double tmp;
	if (((z * t) <= -1e+202) || !((z * t) <= 1e+231)) {
		tmp = x / (z * t);
	} else {
		tmp = x / y;
	}
	return tmp;
}

Python

[x, y, z, t] = sort([x, y, z, t])
def code(x, y, z, t):
	tmp = 0
	if ((z * t) <= -1e+202) or not ((z * t) <= 1e+231):
		tmp = x / (z * t)
	else:
		tmp = x / y
	return tmp

Julia

x, y, z, t = sort([x, y, z, t])
function code(x, y, z, t)
	tmp = 0.0
	if ((Float64(z * t) <= -1e+202) || !(Float64(z * t) <= 1e+231))
		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) <= -1e+202) || ~(((z * t) <= 1e+231)))
		tmp = x / (z * t);
	else
		tmp = x / y;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_] := If[Or[LessEqual[N[(z * t), $MachinePrecision], -1e+202], N[Not[LessEqual[N[(z * t), $MachinePrecision], 1e+231]], $MachinePrecision]], N[(x / N[(z * t), $MachinePrecision]), $MachinePrecision], N[(x / y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 z t) < -9.999999999999999e201 or 1.0000000000000001e231 < (*.f64 z t)

   1. Initial program 76.2%

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

      1. clear-num 76.3%

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

      2. associate-/r/ 76.3%

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

   4. Applied egg-rr 76.3%

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

   5. Taylor expanded in y around 0 76.3%

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

      1. associate-/r* 78.6%

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

   7. Simplified 78.6%

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

      1. associate-/l/ 76.3%

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

      2. associate-*l/ 76.2%

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

      3. neg-mul-1 76.2%

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

      4. add-sqr-sqrt 42.9%

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

      5. sqrt-unprod 60.9%

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

      6. sqr-neg 60.9%

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

      7. sqrt-unprod 21.1%

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

      8. add-sqr-sqrt 53.9%

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

   9. Applied egg-rr 53.9%

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

   if -9.999999999999999e201 < (*.f64 z t) < 1.0000000000000001e231

   1. Initial program 99.9%

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

   3. Taylor expanded in y around inf 66.4%

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

4. Final simplification 64.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \cdot t \leq -1 \cdot 10^{+202} \lor \neg \left(z \cdot t \leq 10^{+231}\right):\\ \;\;\;\;\frac{x}{z \cdot t}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 54.7% accurate, 2.3× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 95.5%

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

3. Taylor expanded in y around inf 56.4%

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

Developer Target 1: 96.8% 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 2024163 
(FPCore (x y z t)
  :name "Diagrams.Solve.Tridiagonal:solveTriDiagonal from diagrams-solve-0.1, B"
  :precision binary64

  :alt
  (! :herbie-platform default (if (< x -161819597360704900000000000000000000000000000000000) (/ 1 (- (/ y x) (* (/ z x) t))) (if (< x 213783064348764440000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000) (/ x (- y (* z t))) (/ 1 (- (/ y x) (* (/ z x) t))))))

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