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

Percentage Accurate: 95.4% → 97.6%

Time: 10.0s

Alternatives: 6

Speedup: 0.6×

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: 95.4% 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: 97.6% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \cdot t \leq -1 \cdot 10^{+266}:\\ \;\;\;\;\frac{\frac{x}{t}}{-z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y - z \cdot t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= (* z t) -1e+266) (/ (/ x t) (- z)) (/ x (- y (* z t)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z * t) <= -1e+266) {
		tmp = (x / t) / -z;
	} else {
		tmp = x / (y - (z * t));
	}
	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) :: tmp
    if ((z * t) <= (-1d+266)) then
        tmp = (x / t) / -z
    else
        tmp = x / (y - (z * t))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((z * t) <= -1e+266) {
		tmp = (x / t) / -z;
	} else {
		tmp = x / (y - (z * t));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z * t) <= -1e+266:
		tmp = (x / t) / -z
	else:
		tmp = x / (y - (z * t))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (Float64(z * t) <= -1e+266)
		tmp = Float64(Float64(x / t) / Float64(-z));
	else
		tmp = Float64(x / Float64(y - Float64(z * t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z * t) <= -1e+266)
		tmp = (x / t) / -z;
	else
		tmp = x / (y - (z * t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[N[(z * t), $MachinePrecision], -1e+266], N[(N[(x / t), $MachinePrecision] / (-z)), $MachinePrecision], N[(x / N[(y - N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 z t) < -1e266

   1. Initial program 76.9%

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

      1. clear-num 76.9%

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

      2. associate-/r/ 76.9%

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

   3. Applied egg-rr 76.9%

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

   4. Taylor expanded in y around 0 76.9%

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

      1. associate-*l/ 76.9%

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

      2. neg-mul-1 76.9%

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

      3. associate-/r* 99.9%

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

      4. frac-2neg 99.9%

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

      5. add-sqr-sqrt 42.3%

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

      6. sqrt-unprod 57.3%

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

      7. sqr-neg 57.3%

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

      8. sqrt-unprod 22.8%

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

      9. add-sqr-sqrt 50.5%

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

      10. distribute-frac-neg 50.5%

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

      11. add-sqr-sqrt 27.7%

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

      12. sqrt-unprod 69.9%

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

      13. sqr-neg 69.9%

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

      14. sqrt-unprod 57.3%

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

      15. add-sqr-sqrt 99.9%

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

   6. Applied egg-rr 99.9%

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

   if -1e266 < (*.f64 z t)

   1. Initial program 98.2%

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

4. Final simplification 98.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \cdot t \leq -1 \cdot 10^{+266}:\\ \;\;\;\;\frac{\frac{x}{t}}{-z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y - z \cdot t}\\ \end{array} \]

Alternative 2: 78.8% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \cdot t \leq -1 \cdot 10^{-87}:\\ \;\;\;\;\frac{\frac{x}{t}}{-z}\\ \mathbf{elif}\;z \cdot t \leq 5 \cdot 10^{-42}:\\ \;\;\;\;\frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{-1}{t} \cdot \frac{x}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= (* z t) -1e-87)
   (/ (/ x t) (- z))
   (if (<= (* z t) 5e-42) (/ x y) (* (/ -1.0 t) (/ x z)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z * t) <= -1e-87) {
		tmp = (x / t) / -z;
	} else if ((z * t) <= 5e-42) {
		tmp = x / y;
	} else {
		tmp = (-1.0 / t) * (x / z);
	}
	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) :: tmp
    if ((z * t) <= (-1d-87)) then
        tmp = (x / t) / -z
    else if ((z * t) <= 5d-42) then
        tmp = x / y
    else
        tmp = ((-1.0d0) / t) * (x / z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((z * t) <= -1e-87) {
		tmp = (x / t) / -z;
	} else if ((z * t) <= 5e-42) {
		tmp = x / y;
	} else {
		tmp = (-1.0 / t) * (x / z);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z * t) <= -1e-87:
		tmp = (x / t) / -z
	elif (z * t) <= 5e-42:
		tmp = x / y
	else:
		tmp = (-1.0 / t) * (x / z)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (Float64(z * t) <= -1e-87)
		tmp = Float64(Float64(x / t) / Float64(-z));
	elseif (Float64(z * t) <= 5e-42)
		tmp = Float64(x / y);
	else
		tmp = Float64(Float64(-1.0 / t) * Float64(x / z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z * t) <= -1e-87)
		tmp = (x / t) / -z;
	elseif ((z * t) <= 5e-42)
		tmp = x / y;
	else
		tmp = (-1.0 / t) * (x / z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[N[(z * t), $MachinePrecision], -1e-87], N[(N[(x / t), $MachinePrecision] / (-z)), $MachinePrecision], If[LessEqual[N[(z * t), $MachinePrecision], 5e-42], N[(x / y), $MachinePrecision], N[(N[(-1.0 / t), $MachinePrecision] * N[(x / z), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 z t) < -1.00000000000000002e-87

   1. Initial program 93.3%

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

      1. clear-num 93.2%

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

      2. associate-/r/ 93.2%

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

   3. Applied egg-rr 93.2%

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

   4. Taylor expanded in y around 0 78.2%

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

      1. associate-*l/ 78.2%

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

      2. neg-mul-1 78.2%

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

      3. associate-/r* 82.6%

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

      4. frac-2neg 82.6%

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

      5. add-sqr-sqrt 37.0%

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

      6. sqrt-unprod 46.9%

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

      7. sqr-neg 46.9%

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

      8. sqrt-unprod 19.0%

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

      9. add-sqr-sqrt 32.2%

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

      10. distribute-frac-neg 32.2%

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

      11. add-sqr-sqrt 13.2%

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

      12. sqrt-unprod 50.5%

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

      13. sqr-neg 50.5%

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

      14. sqrt-unprod 45.3%

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

      15. add-sqr-sqrt 82.6%

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

   6. Applied egg-rr 82.6%

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

   if -1.00000000000000002e-87 < (*.f64 z t) < 5.00000000000000003e-42

   1. Initial program 99.9%

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

   2. Taylor expanded in y around inf 87.9%

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

   if 5.00000000000000003e-42 < (*.f64 z t)

   1. Initial program 93.8%

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

      1. clear-num 93.7%

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

      2. associate-/r/ 93.8%

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

   3. Applied egg-rr 93.8%

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

      1. associate-/r/ 93.7%

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

      2. div-inv 93.7%

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

      3. associate-/r* 93.7%

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

   5. Applied egg-rr 93.7%

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

   6. Taylor expanded in y around 0 81.8%

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

      1. associate-/l/ 81.8%

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

      2. associate-*l/ 81.8%

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

      3. *-un-lft-identity 81.8%

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

      4. associate-/l* 81.8%

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

      5. times-frac 83.2%

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

   8. Applied egg-rr 83.2%

      \[\leadsto \color{blue}{\frac{-1}{t} \cdot \frac{x}{z}} \]
3. Recombined 3 regimes into one program.

4. Final simplification 84.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \cdot t \leq -1 \cdot 10^{-87}:\\ \;\;\;\;\frac{\frac{x}{t}}{-z}\\ \mathbf{elif}\;z \cdot t \leq 5 \cdot 10^{-42}:\\ \;\;\;\;\frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{-1}{t} \cdot \frac{x}{z}\\ \end{array} \]

Alternative 3: 76.6% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \cdot t \leq -1 \cdot 10^{-87} \lor \neg \left(z \cdot t \leq 5 \cdot 10^{-52}\right):\\ \;\;\;\;\frac{-x}{z \cdot t}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= (* z t) -1e-87) (not (<= (* z t) 5e-52)))
   (/ (- x) (* z t))
   (/ x y)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (((z * t) <= -1e-87) || !((z * t) <= 5e-52)) {
		tmp = -x / (z * t);
	} else {
		tmp = x / y;
	}
	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) :: tmp
    if (((z * t) <= (-1d-87)) .or. (.not. ((z * t) <= 5d-52))) then
        tmp = -x / (z * t)
    else
        tmp = x / y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (((z * t) <= -1e-87) || !((z * t) <= 5e-52)) {
		tmp = -x / (z * t);
	} else {
		tmp = x / y;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if ((z * t) <= -1e-87) or not ((z * t) <= 5e-52):
		tmp = -x / (z * t)
	else:
		tmp = x / y
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((Float64(z * t) <= -1e-87) || !(Float64(z * t) <= 5e-52))
		tmp = Float64(Float64(-x) / Float64(z * t));
	else
		tmp = Float64(x / y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (((z * t) <= -1e-87) || ~(((z * t) <= 5e-52)))
		tmp = -x / (z * t);
	else
		tmp = x / y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[N[(z * t), $MachinePrecision], -1e-87], N[Not[LessEqual[N[(z * t), $MachinePrecision], 5e-52]], $MachinePrecision]], N[((-x) / N[(z * t), $MachinePrecision]), $MachinePrecision], N[(x / y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 z t) < -1.00000000000000002e-87 or 5e-52 < (*.f64 z t)

   1. Initial program 93.6%

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

   2. Taylor expanded in y around 0 79.3%

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

      1. associate-*r/ 79.3%

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

      2. neg-mul-1 79.3%

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

   4. Simplified 79.3%

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

   if -1.00000000000000002e-87 < (*.f64 z t) < 5e-52

   1. Initial program 99.9%

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

   2. Taylor expanded in y around inf 88.7%

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

4. Final simplification 82.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \cdot t \leq -1 \cdot 10^{-87} \lor \neg \left(z \cdot t \leq 5 \cdot 10^{-52}\right):\\ \;\;\;\;\frac{-x}{z \cdot t}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y}\\ \end{array} \]

Alternative 4: 78.4% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \cdot t \leq -1 \cdot 10^{-87} \lor \neg \left(z \cdot t \leq 5 \cdot 10^{-52}\right):\\ \;\;\;\;\frac{\frac{x}{t}}{-z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= (* z t) -1e-87) (not (<= (* z t) 5e-52)))
   (/ (/ x t) (- z))
   (/ x y)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (((z * t) <= -1e-87) || !((z * t) <= 5e-52)) {
		tmp = (x / t) / -z;
	} else {
		tmp = x / y;
	}
	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) :: tmp
    if (((z * t) <= (-1d-87)) .or. (.not. ((z * t) <= 5d-52))) then
        tmp = (x / t) / -z
    else
        tmp = x / y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (((z * t) <= -1e-87) || !((z * t) <= 5e-52)) {
		tmp = (x / t) / -z;
	} else {
		tmp = x / y;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if ((z * t) <= -1e-87) or not ((z * t) <= 5e-52):
		tmp = (x / t) / -z
	else:
		tmp = x / y
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((Float64(z * t) <= -1e-87) || !(Float64(z * t) <= 5e-52))
		tmp = Float64(Float64(x / t) / Float64(-z));
	else
		tmp = Float64(x / y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (((z * t) <= -1e-87) || ~(((z * t) <= 5e-52)))
		tmp = (x / t) / -z;
	else
		tmp = x / y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[N[(z * t), $MachinePrecision], -1e-87], N[Not[LessEqual[N[(z * t), $MachinePrecision], 5e-52]], $MachinePrecision]], N[(N[(x / t), $MachinePrecision] / (-z)), $MachinePrecision], N[(x / y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 z t) < -1.00000000000000002e-87 or 5e-52 < (*.f64 z t)

   1. Initial program 93.6%

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

      1. clear-num 93.5%

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

      2. associate-/r/ 93.5%

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

   3. Applied egg-rr 93.5%

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

   4. Taylor expanded in y around 0 79.3%

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

      1. associate-*l/ 79.3%

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

      2. neg-mul-1 79.3%

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

      3. associate-/r* 81.9%

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

      4. frac-2neg 81.9%

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

      5. add-sqr-sqrt 42.1%

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

      6. sqrt-unprod 51.1%

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

      7. sqr-neg 51.1%

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

      8. sqrt-unprod 17.4%

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

      9. add-sqr-sqrt 32.5%

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

      10. distribute-frac-neg 32.5%

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

      11. add-sqr-sqrt 15.1%

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

      12. sqrt-unprod 47.4%

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

      13. sqr-neg 47.4%

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

      14. sqrt-unprod 39.5%

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

      15. add-sqr-sqrt 81.9%

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

   6. Applied egg-rr 81.9%

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

   if -1.00000000000000002e-87 < (*.f64 z t) < 5e-52

   1. Initial program 99.9%

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

   2. Taylor expanded in y around inf 88.7%

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

4. Final simplification 84.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \cdot t \leq -1 \cdot 10^{-87} \lor \neg \left(z \cdot t \leq 5 \cdot 10^{-52}\right):\\ \;\;\;\;\frac{\frac{x}{t}}{-z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y}\\ \end{array} \]

Alternative 5: 63.3% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \cdot t \leq -5 \cdot 10^{+174} \lor \neg \left(z \cdot t \leq 2 \cdot 10^{+173}\right):\\ \;\;\;\;\frac{x}{z \cdot t}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= (* z t) -5e+174) (not (<= (* z t) 2e+173)))
   (/ x (* z t))
   (/ x y)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (((z * t) <= -5e+174) || !((z * t) <= 2e+173)) {
		tmp = x / (z * t);
	} else {
		tmp = x / y;
	}
	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) :: tmp
    if (((z * t) <= (-5d+174)) .or. (.not. ((z * t) <= 2d+173))) then
        tmp = x / (z * t)
    else
        tmp = x / y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (((z * t) <= -5e+174) || !((z * t) <= 2e+173)) {
		tmp = x / (z * t);
	} else {
		tmp = x / y;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if ((z * t) <= -5e+174) or not ((z * t) <= 2e+173):
		tmp = x / (z * t)
	else:
		tmp = x / y
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((Float64(z * t) <= -5e+174) || !(Float64(z * t) <= 2e+173))
		tmp = Float64(x / Float64(z * t));
	else
		tmp = Float64(x / y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (((z * t) <= -5e+174) || ~(((z * t) <= 2e+173)))
		tmp = x / (z * t);
	else
		tmp = x / y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[N[(z * t), $MachinePrecision], -5e+174], N[Not[LessEqual[N[(z * t), $MachinePrecision], 2e+173]], $MachinePrecision]], N[(x / N[(z * t), $MachinePrecision]), $MachinePrecision], N[(x / y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 z t) < -4.9999999999999997e174 or 2e173 < (*.f64 z t)

   1. Initial program 86.5%

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

      1. clear-num 86.5%

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

      2. associate-/r/ 86.5%

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

   3. Applied egg-rr 86.5%

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

   4. Taylor expanded in y around 0 85.2%

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

      1. associate-*l/ 85.2%

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

      2. *-commutative 85.2%

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

      3. neg-mul-1 85.2%

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

      4. add-sqr-sqrt 42.6%

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

      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 29.3%

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

      8. add-sqr-sqrt 54.8%

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

   6. Applied egg-rr 54.8%

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

   if -4.9999999999999997e174 < (*.f64 z t) < 2e173

   1. Initial program 99.8%

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

   2. Taylor expanded in y around inf 62.7%

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

4. Final simplification 60.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \cdot t \leq -5 \cdot 10^{+174} \lor \neg \left(z \cdot t \leq 2 \cdot 10^{+173}\right):\\ \;\;\;\;\frac{x}{z \cdot t}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y}\\ \end{array} \]

Alternative 6: 53.9% accurate, 2.3× speedup

Math

\[\begin{array}{l} \\ \frac{x}{y} \end{array} \]

FPCore

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

C

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

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
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 96.0%

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

2. Taylor expanded in y around inf 50.3%

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

3. Final simplification 50.3%

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

Developer target: 96.8% accurate, 0.5× 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 2023202 
(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))))