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

Percentage Accurate: 95.7% → 99.7%

Time: 8.4s

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: 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: 99.7% accurate, 0.3× speedup

Math

\[\begin{array}{l} [x, y, z, t] = \mathsf{sort}([x, y, z, t])\\ \\ \begin{array}{l} \mathbf{if}\;z \cdot t \leq -\infty:\\ \;\;\;\;\frac{-1}{t \cdot \frac{z}{x}}\\ \mathbf{elif}\;z \cdot t \leq 5 \cdot 10^{+286}:\\ \;\;\;\;\frac{x}{y - z \cdot t}\\ \mathbf{else}:\\ \;\;\;\;\frac{-1}{z \cdot \frac{t}{x}}\\ \end{array} \end{array} \]

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))
   (/ -1.0 (* t (/ z x)))
   (if (<= (* z t) 5e+286) (/ x (- y (* z t))) (/ -1.0 (* z (/ t x))))))

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 = -1.0 / (t * (z / x));
	} else if ((z * t) <= 5e+286) {
		tmp = x / (y - (z * t));
	} else {
		tmp = -1.0 / (z * (t / x));
	}
	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 = -1.0 / (t * (z / x));
	} else if ((z * t) <= 5e+286) {
		tmp = x / (y - (z * t));
	} else {
		tmp = -1.0 / (z * (t / x));
	}
	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 = -1.0 / (t * (z / x))
	elif (z * t) <= 5e+286:
		tmp = x / (y - (z * t))
	else:
		tmp = -1.0 / (z * (t / x))
	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(-1.0 / Float64(t * Float64(z / x)));
	elseif (Float64(z * t) <= 5e+286)
		tmp = Float64(x / Float64(y - Float64(z * t)));
	else
		tmp = Float64(-1.0 / Float64(z * Float64(t / x)));
	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 = -1.0 / (t * (z / x));
	elseif ((z * t) <= 5e+286)
		tmp = x / (y - (z * t));
	else
		tmp = -1.0 / (z * (t / x));
	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[(-1.0 / N[(t * N[(z / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(z * t), $MachinePrecision], 5e+286], N[(x / N[(y - N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(-1.0 / N[(z * N[(t / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

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

   1. Initial program 58.6%

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

      1. clear-num 58.6%

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

      2. associate-/r/ 58.6%

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

   4. Applied egg-rr 58.6%

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

      1. associate-/r/ 58.6%

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

   6. Applied egg-rr 58.6%

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

   7. Taylor expanded in y around 0 58.6%

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

      1. mul-1-neg 58.6%

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

      2. associate-/l* 99.9%

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

      3. distribute-lft-neg-in 99.9%

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

   9. Simplified 99.9%

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

   if -inf.0 < (*.f64 z t) < 5.0000000000000004e286

   1. Initial program 99.8%

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

   if 5.0000000000000004e286 < (*.f64 z t)

   1. Initial program 73.8%

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

      1. clear-num 73.8%

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

      2. inv-pow 73.8%

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

   4. Applied egg-rr 73.8%

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

   5. Taylor expanded in y around 0 73.8%

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

      1. mul-1-neg 73.8%

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

      2. associate-*l/ 99.9%

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

      3. *-commutative 99.9%

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

      4. distribute-rgt-neg-in 99.9%

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

      5. mul-1-neg 99.9%

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

      6. associate-*r/ 99.9%

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

      7. neg-mul-1 99.9%

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

   7. Simplified 99.9%

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

      1. unpow-1 99.9%

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

      2. frac-2neg 99.9%

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

      3. metadata-eval 99.9%

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

      4. associate-*r/ 73.8%

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

      5. add-sqr-sqrt 45.5%

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

      6. times-frac 60.9%

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

      7. add-sqr-sqrt 27.6%

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

      8. sqrt-unprod 45.5%

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

      9. sqr-neg 45.5%

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

      10. sqrt-unprod 27.9%

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

      11. add-sqr-sqrt 45.2%

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

      12. times-frac 45.5%

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

      13. add-sqr-sqrt 68.4%

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

      14. clear-num 68.4%

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

      15. associate-/l/ 67.9%

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

      16. clear-num 67.9%

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

      17. div-inv 67.9%

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

      18. clear-num 67.9%

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

      19. distribute-rgt-neg-out 67.9%

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

      20. distribute-frac-neg 67.9%

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

      21. associate-*r/ 68.4%

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

      22. add-sqr-sqrt 45.5%

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

   9. Applied egg-rr 99.9%

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

4. Final simplification 99.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \cdot t \leq -\infty:\\ \;\;\;\;\frac{-1}{t \cdot \frac{z}{x}}\\ \mathbf{elif}\;z \cdot t \leq 5 \cdot 10^{+286}:\\ \;\;\;\;\frac{x}{y - z \cdot t}\\ \mathbf{else}:\\ \;\;\;\;\frac{-1}{z \cdot \frac{t}{x}}\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 79.4% accurate, 0.2× speedup

Math

\[\begin{array}{l} [x, y, z, t] = \mathsf{sort}([x, y, z, t])\\ \\ \begin{array}{l} t_1 := \frac{-1}{z \cdot \frac{t}{x}}\\ \mathbf{if}\;z \cdot t \leq -\infty:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \cdot t \leq -4 \cdot 10^{-95}:\\ \;\;\;\;\frac{x}{-z \cdot t}\\ \mathbf{elif}\;z \cdot t \leq 5 \cdot 10^{+39}:\\ \;\;\;\;\frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ -1.0 (* z (/ t x)))))
   (if (<= (* z t) (- INFINITY))
     t_1
     (if (<= (* z t) -4e-95)
       (/ x (- (* z t)))
       (if (<= (* z t) 5e+39) (/ x y) t_1)))))

C

assert(x < y && y < z && z < t);
double code(double x, double y, double z, double t) {
	double t_1 = -1.0 / (z * (t / x));
	double tmp;
	if ((z * t) <= -((double) INFINITY)) {
		tmp = t_1;
	} else if ((z * t) <= -4e-95) {
		tmp = x / -(z * t);
	} else if ((z * t) <= 5e+39) {
		tmp = x / y;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Java

assert x < y && y < z && z < t;
public static double code(double x, double y, double z, double t) {
	double t_1 = -1.0 / (z * (t / x));
	double tmp;
	if ((z * t) <= -Double.POSITIVE_INFINITY) {
		tmp = t_1;
	} else if ((z * t) <= -4e-95) {
		tmp = x / -(z * t);
	} else if ((z * t) <= 5e+39) {
		tmp = x / y;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

[x, y, z, t] = sort([x, y, z, t])
def code(x, y, z, t):
	t_1 = -1.0 / (z * (t / x))
	tmp = 0
	if (z * t) <= -math.inf:
		tmp = t_1
	elif (z * t) <= -4e-95:
		tmp = x / -(z * t)
	elif (z * t) <= 5e+39:
		tmp = x / y
	else:
		tmp = t_1
	return tmp

Julia

x, y, z, t = sort([x, y, z, t])
function code(x, y, z, t)
	t_1 = Float64(-1.0 / Float64(z * Float64(t / x)))
	tmp = 0.0
	if (Float64(z * t) <= Float64(-Inf))
		tmp = t_1;
	elseif (Float64(z * t) <= -4e-95)
		tmp = Float64(x / Float64(-Float64(z * t)));
	elseif (Float64(z * t) <= 5e+39)
		tmp = Float64(x / y);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

x, y, z, t = num2cell(sort([x, y, z, t])){:}
function tmp_2 = code(x, y, z, t)
	t_1 = -1.0 / (z * (t / x));
	tmp = 0.0;
	if ((z * t) <= -Inf)
		tmp = t_1;
	elseif ((z * t) <= -4e-95)
		tmp = x / -(z * t);
	elseif ((z * t) <= 5e+39)
		tmp = x / y;
	else
		tmp = t_1;
	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_] := Block[{t$95$1 = N[(-1.0 / N[(z * N[(t / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(z * t), $MachinePrecision], (-Infinity)], t$95$1, If[LessEqual[N[(z * t), $MachinePrecision], -4e-95], N[(x / (-N[(z * t), $MachinePrecision])), $MachinePrecision], If[LessEqual[N[(z * t), $MachinePrecision], 5e+39], N[(x / y), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 z t) < -inf.0 or 5.00000000000000015e39 < (*.f64 z t)

   1. Initial program 83.4%

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

      1. clear-num 83.3%

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

      2. inv-pow 83.3%

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

   4. Applied egg-rr 83.3%

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

   5. Taylor expanded in y around 0 71.4%

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

      1. mul-1-neg 71.4%

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

      2. associate-*l/ 86.5%

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

      3. *-commutative 86.5%

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

      4. distribute-rgt-neg-in 86.5%

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

      5. mul-1-neg 86.5%

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

      6. associate-*r/ 86.5%

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

      7. neg-mul-1 86.5%

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

   7. Simplified 86.5%

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

      1. unpow-1 86.5%

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

      2. frac-2neg 86.5%

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

      3. metadata-eval 86.5%

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

      4. associate-*r/ 71.4%

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

      5. add-sqr-sqrt 34.5%

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

      6. times-frac 41.3%

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

      7. add-sqr-sqrt 16.2%

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

      8. sqrt-unprod 25.8%

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

      9. sqr-neg 25.8%

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

      10. sqrt-unprod 15.2%

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

      11. add-sqr-sqrt 21.6%

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

      12. times-frac 21.7%

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

      13. add-sqr-sqrt 39.1%

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

      14. clear-num 39.1%

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

      15. associate-/l/ 38.8%

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

      16. clear-num 38.8%

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

      17. div-inv 38.8%

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

      18. clear-num 38.8%

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

      19. distribute-rgt-neg-out 38.8%

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

      20. distribute-frac-neg 38.8%

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

      21. associate-*r/ 39.1%

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

      22. add-sqr-sqrt 21.7%

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

   9. Applied egg-rr 86.5%

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

   if -inf.0 < (*.f64 z t) < -3.99999999999999996e-95

   1. Initial program 99.8%

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

   3. Taylor expanded in y around 0 76.0%

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

      1. associate-*r/ 76.0%

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

      2. neg-mul-1 76.0%

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

   5. Simplified 76.0%

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

   if -3.99999999999999996e-95 < (*.f64 z t) < 5.00000000000000015e39

   1. Initial program 99.9%

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

   3. Taylor expanded in y around inf 79.9%

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

4. Final simplification 80.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \cdot t \leq -\infty:\\ \;\;\;\;\frac{-1}{z \cdot \frac{t}{x}}\\ \mathbf{elif}\;z \cdot t \leq -4 \cdot 10^{-95}:\\ \;\;\;\;\frac{x}{-z \cdot t}\\ \mathbf{elif}\;z \cdot t \leq 5 \cdot 10^{+39}:\\ \;\;\;\;\frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{-1}{z \cdot \frac{t}{x}}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 79.6% accurate, 0.3× speedup

Math

\[\begin{array}{l} [x, y, z, t] = \mathsf{sort}([x, y, z, t])\\ \\ \begin{array}{l} t_1 := \frac{\frac{-x}{t}}{z}\\ \mathbf{if}\;z \cdot t \leq -2 \cdot 10^{+242}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \cdot t \leq -4 \cdot 10^{-95}:\\ \;\;\;\;\frac{x}{-z \cdot t}\\ \mathbf{elif}\;z \cdot t \leq 5 \cdot 10^{+39}:\\ \;\;\;\;\frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ (/ (- x) t) z)))
   (if (<= (* z t) -2e+242)
     t_1
     (if (<= (* z t) -4e-95)
       (/ x (- (* z t)))
       (if (<= (* z t) 5e+39) (/ x y) t_1)))))

C

assert(x < y && y < z && z < t);
double code(double x, double y, double z, double t) {
	double t_1 = (-x / t) / z;
	double tmp;
	if ((z * t) <= -2e+242) {
		tmp = t_1;
	} else if ((z * t) <= -4e-95) {
		tmp = x / -(z * t);
	} else if ((z * t) <= 5e+39) {
		tmp = x / y;
	} else {
		tmp = t_1;
	}
	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) :: t_1
    real(8) :: tmp
    t_1 = (-x / t) / z
    if ((z * t) <= (-2d+242)) then
        tmp = t_1
    else if ((z * t) <= (-4d-95)) then
        tmp = x / -(z * t)
    else if ((z * t) <= 5d+39) then
        tmp = x / y
    else
        tmp = t_1
    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 t_1 = (-x / t) / z;
	double tmp;
	if ((z * t) <= -2e+242) {
		tmp = t_1;
	} else if ((z * t) <= -4e-95) {
		tmp = x / -(z * t);
	} else if ((z * t) <= 5e+39) {
		tmp = x / y;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

[x, y, z, t] = sort([x, y, z, t])
def code(x, y, z, t):
	t_1 = (-x / t) / z
	tmp = 0
	if (z * t) <= -2e+242:
		tmp = t_1
	elif (z * t) <= -4e-95:
		tmp = x / -(z * t)
	elif (z * t) <= 5e+39:
		tmp = x / y
	else:
		tmp = t_1
	return tmp

Julia

x, y, z, t = sort([x, y, z, t])
function code(x, y, z, t)
	t_1 = Float64(Float64(Float64(-x) / t) / z)
	tmp = 0.0
	if (Float64(z * t) <= -2e+242)
		tmp = t_1;
	elseif (Float64(z * t) <= -4e-95)
		tmp = Float64(x / Float64(-Float64(z * t)));
	elseif (Float64(z * t) <= 5e+39)
		tmp = Float64(x / y);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

x, y, z, t = num2cell(sort([x, y, z, t])){:}
function tmp_2 = code(x, y, z, t)
	t_1 = (-x / t) / z;
	tmp = 0.0;
	if ((z * t) <= -2e+242)
		tmp = t_1;
	elseif ((z * t) <= -4e-95)
		tmp = x / -(z * t);
	elseif ((z * t) <= 5e+39)
		tmp = x / y;
	else
		tmp = t_1;
	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_] := Block[{t$95$1 = N[(N[((-x) / t), $MachinePrecision] / z), $MachinePrecision]}, If[LessEqual[N[(z * t), $MachinePrecision], -2e+242], t$95$1, If[LessEqual[N[(z * t), $MachinePrecision], -4e-95], N[(x / (-N[(z * t), $MachinePrecision])), $MachinePrecision], If[LessEqual[N[(z * t), $MachinePrecision], 5e+39], N[(x / y), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 z t) < -2.0000000000000001e242 or 5.00000000000000015e39 < (*.f64 z t)

   1. Initial program 85.5%

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

      1. clear-num 85.4%

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

      2. associate-/r/ 85.5%

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

   4. Applied egg-rr 85.5%

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

      1. associate-/r/ 85.4%

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

   6. Applied egg-rr 85.4%

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

   7. Taylor expanded in y around 0 75.1%

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

      1. mul-1-neg 75.1%

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

      2. associate-/r* 88.2%

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

      3. distribute-frac-neg2 88.2%

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

   9. Simplified 88.2%

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

   if -2.0000000000000001e242 < (*.f64 z t) < -3.99999999999999996e-95

   1. Initial program 99.8%

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

   3. Taylor expanded in y around 0 72.3%

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

      1. associate-*r/ 72.3%

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

      2. neg-mul-1 72.3%

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

   5. Simplified 72.3%

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

   if -3.99999999999999996e-95 < (*.f64 z t) < 5.00000000000000015e39

   1. Initial program 99.9%

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

   3. Taylor expanded in y around inf 79.9%

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

4. Final simplification 80.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \cdot t \leq -2 \cdot 10^{+242}:\\ \;\;\;\;\frac{\frac{-x}{t}}{z}\\ \mathbf{elif}\;z \cdot t \leq -4 \cdot 10^{-95}:\\ \;\;\;\;\frac{x}{-z \cdot t}\\ \mathbf{elif}\;z \cdot t \leq 5 \cdot 10^{+39}:\\ \;\;\;\;\frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{-x}{t}}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 99.7% accurate, 0.3× speedup

Math

\[\begin{array}{l} [x, y, z, t] = \mathsf{sort}([x, y, z, t])\\ \\ \begin{array}{l} \mathbf{if}\;z \cdot t \leq -\infty \lor \neg \left(z \cdot t \leq 5 \cdot 10^{+286}\right):\\ \;\;\;\;\frac{-1}{z \cdot \frac{t}{x}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y - z \cdot t}\\ \end{array} \end{array} \]

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 (or (<= (* z t) (- INFINITY)) (not (<= (* z t) 5e+286)))
   (/ -1.0 (* z (/ t x)))
   (/ 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)) || !((z * t) <= 5e+286)) {
		tmp = -1.0 / (z * (t / x));
	} 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) || !((z * t) <= 5e+286)) {
		tmp = -1.0 / (z * (t / x));
	} 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) or not ((z * t) <= 5e+286):
		tmp = -1.0 / (z * (t / x))
	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)) || !(Float64(z * t) <= 5e+286))
		tmp = Float64(-1.0 / Float64(z * Float64(t / x)));
	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) || ~(((z * t) <= 5e+286)))
		tmp = -1.0 / (z * (t / x));
	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[Or[LessEqual[N[(z * t), $MachinePrecision], (-Infinity)], N[Not[LessEqual[N[(z * t), $MachinePrecision], 5e+286]], $MachinePrecision]], N[(-1.0 / N[(z * N[(t / x), $MachinePrecision]), $MachinePrecision]), $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 or 5.0000000000000004e286 < (*.f64 z t)

   1. Initial program 66.7%

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

      1. clear-num 66.7%

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

      2. inv-pow 66.7%

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

   4. Applied egg-rr 66.7%

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

   5. Taylor expanded in y around 0 66.7%

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

      1. mul-1-neg 66.7%

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

      2. associate-*l/ 99.9%

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

      3. *-commutative 99.9%

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

      4. distribute-rgt-neg-in 99.9%

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

      5. mul-1-neg 99.9%

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

      6. associate-*r/ 99.9%

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

      7. neg-mul-1 99.9%

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

   7. Simplified 99.9%

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

      1. unpow-1 99.9%

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

      2. frac-2neg 99.9%

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

      3. metadata-eval 99.9%

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

      4. associate-*r/ 66.7%

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

      5. add-sqr-sqrt 39.3%

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

      6. times-frac 55.7%

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

      7. add-sqr-sqrt 20.5%

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

      8. sqrt-unprod 39.3%

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

      9. sqr-neg 39.3%

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

      10. sqrt-unprod 26.8%

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

      11. add-sqr-sqrt 39.1%

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

      12. times-frac 39.3%

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

      13. add-sqr-sqrt 63.8%

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

      14. clear-num 63.8%

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

      15. associate-/l/ 63.2%

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

      16. clear-num 63.2%

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

      17. div-inv 63.2%

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

      18. clear-num 63.2%

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

      19. distribute-rgt-neg-out 63.2%

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

      20. distribute-frac-neg 63.2%

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

      21. associate-*r/ 63.8%

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

      22. add-sqr-sqrt 39.3%

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

   9. Applied egg-rr 99.9%

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

   if -inf.0 < (*.f64 z t) < 5.0000000000000004e286

   1. Initial program 99.8%

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

4. Final simplification 99.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \cdot t \leq -\infty \lor \neg \left(z \cdot t \leq 5 \cdot 10^{+286}\right):\\ \;\;\;\;\frac{-1}{z \cdot \frac{t}{x}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y - z \cdot t}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 76.0% accurate, 0.3× speedup

Math

\[\begin{array}{l} [x, y, z, t] = \mathsf{sort}([x, y, z, t])\\ \\ \begin{array}{l} \mathbf{if}\;z \cdot t \leq -4 \cdot 10^{-95} \lor \neg \left(z \cdot t \leq 5 \cdot 10^{+39}\right):\\ \;\;\;\;\frac{x}{-z \cdot t}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y}\\ \end{array} \end{array} \]

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) -4e-95) (not (<= (* z t) 5e+39)))
   (/ 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) <= -4e-95) || !((z * t) <= 5e+39)) {
		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) <= (-4d-95)) .or. (.not. ((z * t) <= 5d+39))) 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) <= -4e-95) || !((z * t) <= 5e+39)) {
		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) <= -4e-95) or not ((z * t) <= 5e+39):
		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) <= -4e-95) || !(Float64(z * t) <= 5e+39))
		tmp = Float64(x / Float64(-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) <= -4e-95) || ~(((z * t) <= 5e+39)))
		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], -4e-95], N[Not[LessEqual[N[(z * t), $MachinePrecision], 5e+39]], $MachinePrecision]], N[(x / (-N[(z * t), $MachinePrecision])), $MachinePrecision], N[(x / y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 z t) < -3.99999999999999996e-95 or 5.00000000000000015e39 < (*.f64 z t)

   1. Initial program 91.8%

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

   3. Taylor expanded in y around 0 73.9%

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

      1. associate-*r/ 73.9%

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

      2. neg-mul-1 73.9%

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

   5. Simplified 73.9%

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

   if -3.99999999999999996e-95 < (*.f64 z t) < 5.00000000000000015e39

   1. Initial program 99.9%

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

   3. Taylor expanded in y around inf 79.9%

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

4. Final simplification 76.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \cdot t \leq -4 \cdot 10^{-95} \lor \neg \left(z \cdot t \leq 5 \cdot 10^{+39}\right):\\ \;\;\;\;\frac{x}{-z \cdot t}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 63.1% accurate, 0.4× speedup

Math

\[\begin{array}{l} [x, y, z, t] = \mathsf{sort}([x, y, z, t])\\ \\ \begin{array}{l} \mathbf{if}\;z \cdot t \leq -1 \cdot 10^{+225} \lor \neg \left(z \cdot t \leq 2 \cdot 10^{+131}\right):\\ \;\;\;\;\frac{x}{z \cdot t}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y}\\ \end{array} \end{array} \]

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+225) (not (<= (* z t) 2e+131)))
   (/ 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+225) || !((z * t) <= 2e+131)) {
		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+225)) .or. (.not. ((z * t) <= 2d+131))) 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+225) || !((z * t) <= 2e+131)) {
		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+225) or not ((z * t) <= 2e+131):
		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+225) || !(Float64(z * t) <= 2e+131))
		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+225) || ~(((z * t) <= 2e+131)))
		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+225], N[Not[LessEqual[N[(z * t), $MachinePrecision], 2e+131]], $MachinePrecision]], N[(x / N[(z * t), $MachinePrecision]), $MachinePrecision], N[(x / y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 z t) < -9.99999999999999928e224 or 1.9999999999999998e131 < (*.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 82.5%

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

      2. inv-pow 82.5%

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

   4. Applied egg-rr 82.5%

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

   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/ 96.8%

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

      3. *-commutative 96.8%

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

      4. distribute-rgt-neg-in 96.8%

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

      5. mul-1-neg 96.8%

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

      6. associate-*r/ 96.8%

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

      7. neg-mul-1 96.8%

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

   7. Simplified 96.8%

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

      1. unpow-1 96.8%

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

      2. associate-*r/ 79.7%

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

      3. add-sqr-sqrt 38.4%

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

      4. times-frac 46.9%

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

      5. add-sqr-sqrt 18.1%

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

      6. sqrt-unprod 31.0%

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

      7. sqr-neg 31.0%

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

      8. sqrt-unprod 18.5%

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

      9. add-sqr-sqrt 26.7%

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

      10. times-frac 26.9%

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

      11. add-sqr-sqrt 49.4%

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

      12. clear-num 49.4%

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

      13. associate-/l/ 49.2%

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

      14. clear-num 49.2%

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

      15. clear-num 49.2%

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

      16. associate-/l/ 49.4%

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

   9. Applied egg-rr 49.4%

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

   if -9.99999999999999928e224 < (*.f64 z t) < 1.9999999999999998e131

   1. Initial program 99.9%

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

   3. Taylor expanded in y around inf 63.0%

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

4. Final simplification 59.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \cdot t \leq -1 \cdot 10^{+225} \lor \neg \left(z \cdot t \leq 2 \cdot 10^{+131}\right):\\ \;\;\;\;\frac{x}{z \cdot t}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 54.6% 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 95.4%

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

3. Taylor expanded in y around inf 50.2%

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

Developer target: 96.6% 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 2024089 
(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))))