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

Percentage Accurate: 95.7% → 97.7%

Time: 8.3s

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: 95.7% 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: 97.7% accurate, 0.5× speedup

Math

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

FPCore

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

C

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

Java

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

Python

[x, y, z, t] = sort([x, y, z, t])
def code(x, y, z, t):
	tmp = 0
	if (z * t) <= -math.inf:
		tmp = (-x / z) / t
	else:
		tmp = x / (y - (z * t))
	return tmp

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Split input into 2 regimes

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

   1. Initial program 59.2%

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

   3. Taylor expanded in y around 0 59.2%

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

      1. associate-*r/ 59.2%

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

      2. neg-mul-1 59.2%

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

      3. *-commutative 59.2%

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

      4. associate-/r* 99.8%

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

   5. Simplified 99.8%

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

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

   1. Initial program 98.3%

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

4. Final simplification 98.4%

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

Alternative 2: 78.5% accurate, 0.3× speedup

Math

\[\begin{array}{l} [x, y, z, t] = \mathsf{sort}([x, y, z, t])\\ \\ \begin{array}{l} \mathbf{if}\;z \cdot t \leq -\infty:\\ \;\;\;\;\frac{\frac{x}{t}}{-z}\\ \mathbf{elif}\;z \cdot t \leq -5 \cdot 10^{+26} \lor \neg \left(z \cdot t \leq 5 \cdot 10^{-97}\right):\\ \;\;\;\;\frac{-x}{z \cdot t}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y}\\ \end{array} \end{array} \]

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 (<= (* z t) (- INFINITY))
   (/ (/ x t) (- z))
   (if (or (<= (* z t) -5e+26) (not (<= (* z t) 5e-97)))
     (/ (- 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) <= -((double) INFINITY)) {
		tmp = (x / t) / -z;
	} else if (((z * t) <= -5e+26) || !((z * t) <= 5e-97)) {
		tmp = -x / (z * t);
	} else {
		tmp = x / y;
	}
	return tmp;
}

Java

assert x < y && y < z && z < t;
public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((z * t) <= -Double.POSITIVE_INFINITY) {
		tmp = (x / t) / -z;
	} else if (((z * t) <= -5e+26) || !((z * t) <= 5e-97)) {
		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) <= -math.inf:
		tmp = (x / t) / -z
	elif ((z * t) <= -5e+26) or not ((z * t) <= 5e-97):
		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) <= Float64(-Inf))
		tmp = Float64(Float64(x / t) / Float64(-z));
	elseif ((Float64(z * t) <= -5e+26) || !(Float64(z * t) <= 5e-97))
		tmp = Float64(Float64(-x) / Float64(z * t));
	else
		tmp = Float64(x / y);
	end
	return tmp
end

MATLAB

x, y, z, t = num2cell(sort([x, y, z, t])){:}
function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z * t) <= -Inf)
		tmp = (x / t) / -z;
	elseif (((z * t) <= -5e+26) || ~(((z * t) <= 5e-97)))
		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[LessEqual[N[(z * t), $MachinePrecision], (-Infinity)], N[(N[(x / t), $MachinePrecision] / (-z)), $MachinePrecision], If[Or[LessEqual[N[(z * t), $MachinePrecision], -5e+26], N[Not[LessEqual[N[(z * t), $MachinePrecision], 5e-97]], $MachinePrecision]], N[((-x) / N[(z * t), $MachinePrecision]), $MachinePrecision], N[(x / y), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

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

   1. Initial program 59.2%

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

   3. Taylor expanded in y around 0 59.2%

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

      1. associate-*r/ 59.2%

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

      2. neg-mul-1 59.2%

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

      3. *-commutative 59.2%

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

      4. associate-/r* 99.8%

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

   5. Simplified 99.8%

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

      1. associate-/r* 59.2%

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

      2. neg-mul-1 59.2%

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

      3. times-frac 99.7%

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

   7. Applied egg-rr 99.7%

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

      1. *-commutative 99.7%

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

      2. frac-2neg 99.7%

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

      3. metadata-eval 99.7%

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

      4. un-div-inv 99.9%

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

   9. Applied egg-rr 99.9%

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

   if -inf.0 < (*.f64 z t) < -5.0000000000000001e26 or 4.9999999999999995e-97 < (*.f64 z t)

   1. Initial program 96.8%

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

   3. Taylor expanded in y around 0 80.1%

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

      1. associate-*r/ 80.1%

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

      2. neg-mul-1 80.1%

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

   5. Simplified 80.1%

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

   if -5.0000000000000001e26 < (*.f64 z t) < 4.9999999999999995e-97

   1. Initial program 99.9%

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

   3. Taylor expanded in y around inf 89.9%

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

4. Final simplification 85.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \cdot t \leq -\infty:\\ \;\;\;\;\frac{\frac{x}{t}}{-z}\\ \mathbf{elif}\;z \cdot t \leq -5 \cdot 10^{+26} \lor \neg \left(z \cdot t \leq 5 \cdot 10^{-97}\right):\\ \;\;\;\;\frac{-x}{z \cdot t}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 76.5% accurate, 0.3× speedup

Math

\[\begin{array}{l} [x, y, z, t] = \mathsf{sort}([x, y, z, t])\\ \\ \begin{array}{l} \mathbf{if}\;z \cdot t \leq -5 \cdot 10^{+26} \lor \neg \left(z \cdot t \leq 5 \cdot 10^{-97}\right):\\ \;\;\;\;\frac{-x}{z \cdot t}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y}\\ \end{array} \end{array} \]

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+26) (not (<= (* z t) 5e-97)))
   (/ (- 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+26) || !((z * t) <= 5e-97)) {
		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+26)) .or. (.not. ((z * t) <= 5d-97))) 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+26) || !((z * t) <= 5e-97)) {
		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+26) or not ((z * t) <= 5e-97):
		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+26) || !(Float64(z * t) <= 5e-97))
		tmp = Float64(Float64(-x) / Float64(z * t));
	else
		tmp = Float64(x / y);
	end
	return tmp
end

MATLAB

x, y, z, t = num2cell(sort([x, y, z, t])){:}
function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (((z * t) <= -5e+26) || ~(((z * t) <= 5e-97)))
		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+26], N[Not[LessEqual[N[(z * t), $MachinePrecision], 5e-97]], $MachinePrecision]], N[((-x) / N[(z * t), $MachinePrecision]), $MachinePrecision], N[(x / y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 z t) < -5.0000000000000001e26 or 4.9999999999999995e-97 < (*.f64 z t)

   1. Initial program 93.1%

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

   3. Taylor expanded in y around 0 78.0%

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

      1. associate-*r/ 78.0%

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

      2. neg-mul-1 78.0%

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

   5. Simplified 78.0%

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

   if -5.0000000000000001e26 < (*.f64 z t) < 4.9999999999999995e-97

   1. Initial program 99.9%

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

   3. Taylor expanded in y around inf 89.9%

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

4. Final simplification 83.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \cdot t \leq -5 \cdot 10^{+26} \lor \neg \left(z \cdot t \leq 5 \cdot 10^{-97}\right):\\ \;\;\;\;\frac{-x}{z \cdot t}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 78.5% accurate, 0.3× speedup

Math

\[\begin{array}{l} [x, y, z, t] = \mathsf{sort}([x, y, z, t])\\ \\ \begin{array}{l} \mathbf{if}\;z \cdot t \leq -5 \cdot 10^{+26} \lor \neg \left(z \cdot t \leq 5 \cdot 10^{-97}\right):\\ \;\;\;\;\frac{\frac{-x}{z}}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y}\\ \end{array} \end{array} \]

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+26) (not (<= (* z t) 5e-97)))
   (/ (/ (- 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+26) || !((z * t) <= 5e-97)) {
		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+26)) .or. (.not. ((z * t) <= 5d-97))) 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+26) || !((z * t) <= 5e-97)) {
		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+26) or not ((z * t) <= 5e-97):
		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+26) || !(Float64(z * t) <= 5e-97))
		tmp = Float64(Float64(Float64(-x) / 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+26) || ~(((z * t) <= 5e-97)))
		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+26], N[Not[LessEqual[N[(z * t), $MachinePrecision], 5e-97]], $MachinePrecision]], N[(N[((-x) / z), $MachinePrecision] / t), $MachinePrecision], N[(x / y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 z t) < -5.0000000000000001e26 or 4.9999999999999995e-97 < (*.f64 z t)

   1. Initial program 93.1%

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

   3. Taylor expanded in y around 0 78.0%

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

      1. associate-*r/ 78.0%

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

      2. neg-mul-1 78.0%

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

      3. *-commutative 78.0%

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

      4. associate-/r* 79.9%

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

   5. Simplified 79.9%

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

   if -5.0000000000000001e26 < (*.f64 z t) < 4.9999999999999995e-97

   1. Initial program 99.9%

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

   3. Taylor expanded in y around inf 89.9%

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

4. Final simplification 84.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \cdot t \leq -5 \cdot 10^{+26} \lor \neg \left(z \cdot t \leq 5 \cdot 10^{-97}\right):\\ \;\;\;\;\frac{\frac{-x}{z}}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 63.1% accurate, 0.4× speedup

Math

\[\begin{array}{l} [x, y, z, t] = \mathsf{sort}([x, y, z, t])\\ \\ \begin{array}{l} \mathbf{if}\;z \cdot t \leq -5 \cdot 10^{+154} \lor \neg \left(z \cdot t \leq 2 \cdot 10^{+102}\right):\\ \;\;\;\;\frac{x}{z \cdot t}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y}\\ \end{array} \end{array} \]

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+154) (not (<= (* z t) 2e+102)))
   (/ 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+154) || !((z * t) <= 2e+102)) {
		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+154)) .or. (.not. ((z * t) <= 2d+102))) 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+154) || !((z * t) <= 2e+102)) {
		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+154) or not ((z * t) <= 2e+102):
		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+154) || !(Float64(z * t) <= 2e+102))
		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+154) || ~(((z * t) <= 2e+102)))
		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+154], N[Not[LessEqual[N[(z * t), $MachinePrecision], 2e+102]], $MachinePrecision]], N[(x / N[(z * t), $MachinePrecision]), $MachinePrecision], N[(x / y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 z t) < -5.00000000000000004e154 or 1.99999999999999995e102 < (*.f64 z t)

   1. Initial program 87.5%

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

   3. Taylor expanded in y around 0 82.7%

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

      1. associate-*r/ 82.7%

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

      2. neg-mul-1 82.7%

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

      3. *-commutative 82.7%

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

      4. associate-/r* 92.6%

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

   5. Simplified 92.6%

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

      1. expm1-log1p-u 89.8%

         \[\leadsto \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(\frac{\frac{-x}{z}}{t}\right)\right)} \]

      2. expm1-udef 53.2%

         \[\leadsto \color{blue}{e^{\mathsf{log1p}\left(\frac{\frac{-x}{z}}{t}\right)} - 1} \]

      3. div-inv 53.2%

         \[\leadsto e^{\mathsf{log1p}\left(\frac{\color{blue}{\left(-x\right) \cdot \frac{1}{z}}}{t}\right)} - 1 \]

      4. div-inv 53.2%

         \[\leadsto e^{\mathsf{log1p}\left(\frac{\color{blue}{\frac{-x}{z}}}{t}\right)} - 1 \]

      5. add-sqr-sqrt 27.1%

         \[\leadsto e^{\mathsf{log1p}\left(\frac{\frac{\color{blue}{\sqrt{-x} \cdot \sqrt{-x}}}{z}}{t}\right)} - 1 \]

      6. sqrt-unprod 48.9%

         \[\leadsto e^{\mathsf{log1p}\left(\frac{\frac{\color{blue}{\sqrt{\left(-x\right) \cdot \left(-x\right)}}}{z}}{t}\right)} - 1 \]

      7. sqr-neg 48.9%

         \[\leadsto e^{\mathsf{log1p}\left(\frac{\frac{\sqrt{\color{blue}{x \cdot x}}}{z}}{t}\right)} - 1 \]

      8. sqrt-unprod 23.7%

         \[\leadsto e^{\mathsf{log1p}\left(\frac{\frac{\color{blue}{\sqrt{x} \cdot \sqrt{x}}}{z}}{t}\right)} - 1 \]

      9. add-sqr-sqrt 49.6%

         \[\leadsto e^{\mathsf{log1p}\left(\frac{\frac{\color{blue}{x}}{z}}{t}\right)} - 1 \]

   7. Applied egg-rr 49.6%

      \[\leadsto \color{blue}{e^{\mathsf{log1p}\left(\frac{\frac{x}{z}}{t}\right)} - 1} \]
   8. Step-by-step derivation

      1. expm1-def 47.7%

         \[\leadsto \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(\frac{\frac{x}{z}}{t}\right)\right)} \]

      2. expm1-log1p 47.7%

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

      3. associate-/l/ 47.9%

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

   9. Simplified 47.9%

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

   if -5.00000000000000004e154 < (*.f64 z t) < 1.99999999999999995e102

   1. Initial program 99.9%

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

   3. Taylor expanded in y around inf 68.4%

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

4. Final simplification 62.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \cdot t \leq -5 \cdot 10^{+154} \lor \neg \left(z \cdot t \leq 2 \cdot 10^{+102}\right):\\ \;\;\;\;\frac{x}{z \cdot t}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 53.4% accurate, 2.3× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 96.2%

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

3. Taylor expanded in y around inf 53.1%

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

4. Final simplification 53.1%

   \[\leadsto \frac{x}{y} \]
5. 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 2024019 
(FPCore (x y z t)
  :name "Diagrams.Solve.Tridiagonal:solveTriDiagonal from diagrams-solve-0.1, B"
  :precision binary64

  :herbie-target
  (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))))