Data.Random.Distribution.Triangular:triangularCDF from random-fu-0.2.6.2, A

Percentage Accurate: 99.2% → 98.5%

Time: 11.0s

Alternatives: 11

Speedup: N/A×

Specification

Math

\[\begin{array}{l} \\ 1 - \frac{x}{\left(y - z\right) \cdot \left(y - t\right)} \end{array} \]

FPCore

(FPCore (x y z t) :precision binary64 (- 1.0 (/ x (* (- y z) (- y t)))))

C

double code(double x, double y, double z, double t) {
	return 1.0 - (x / ((y - z) * (y - 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 = 1.0d0 - (x / ((y - z) * (y - t)))
end function

Java

public static double code(double x, double y, double z, double t) {
	return 1.0 - (x / ((y - z) * (y - t)));
}

Python

def code(x, y, z, t):
	return 1.0 - (x / ((y - z) * (y - t)))

Julia

function code(x, y, z, t)
	return Float64(1.0 - Float64(x / Float64(Float64(y - z) * Float64(y - t))))
end

MATLAB

function tmp = code(x, y, z, t)
	tmp = 1.0 - (x / ((y - z) * (y - t)));
end

Wolfram

code[x_, y_, z_, t_] := N[(1.0 - N[(x / N[(N[(y - z), $MachinePrecision] * N[(y - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Initial Program: 99.2% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ 1 - \frac{x}{\left(y - z\right) \cdot \left(y - t\right)} \end{array} \]

FPCore

(FPCore (x y z t) :precision binary64 (- 1.0 (/ x (* (- y z) (- y t)))))

C

double code(double x, double y, double z, double t) {
	return 1.0 - (x / ((y - z) * (y - 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 = 1.0d0 - (x / ((y - z) * (y - t)))
end function

Java

public static double code(double x, double y, double z, double t) {
	return 1.0 - (x / ((y - z) * (y - t)));
}

Python

def code(x, y, z, t):
	return 1.0 - (x / ((y - z) * (y - t)))

Julia

function code(x, y, z, t)
	return Float64(1.0 - Float64(x / Float64(Float64(y - z) * Float64(y - t))))
end

MATLAB

function tmp = code(x, y, z, t)
	tmp = 1.0 - (x / ((y - z) * (y - t)));
end

Wolfram

code[x_, y_, z_, t_] := N[(1.0 - N[(x / N[(N[(y - z), $MachinePrecision] * N[(y - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Alternative 1: 98.5% accurate, 1.0× speedup

Math

\[\begin{array}{l} [x, y, z, t] = \mathsf{sort}([x, y, z, t])\\ \\ 1 + \frac{\frac{x}{z - y}}{y - t} \end{array} \]

FPCore

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
(FPCore (x y z t) :precision binary64 (+ 1.0 (/ (/ x (- z y)) (- y t))))

C

assert(x < y && y < z && z < t);
double code(double x, double y, double z, double t) {
	return 1.0 + ((x / (z - y)) / (y - t));
}

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 = 1.0d0 + ((x / (z - y)) / (y - t))
end function

Java

assert x < y && y < z && z < t;
public static double code(double x, double y, double z, double t) {
	return 1.0 + ((x / (z - y)) / (y - t));
}

Python

[x, y, z, t] = sort([x, y, z, t])
def code(x, y, z, t):
	return 1.0 + ((x / (z - y)) / (y - t))

Julia

x, y, z, t = sort([x, y, z, t])
function code(x, y, z, t)
	return Float64(1.0 + Float64(Float64(x / Float64(z - y)) / Float64(y - t)))
end

MATLAB

x, y, z, t = num2cell(sort([x, y, z, t])){:}
function tmp = code(x, y, z, t)
	tmp = 1.0 + ((x / (z - y)) / (y - t));
end

Wolfram

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_] := N[(1.0 + N[(N[(x / N[(z - y), $MachinePrecision]), $MachinePrecision] / N[(y - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 98.8%

   \[1 - \frac{x}{\left(y - z\right) \cdot \left(y - t\right)} \]
2. Step-by-step derivation

   1. sub-neg 98.8%

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

   2. neg-mul-1 98.8%

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

   3. *-commutative 98.8%

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

   4. *-commutative 98.8%

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

   5. associate-/r* 98.8%

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

   6. associate-*r/ 98.8%

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

   7. metadata-eval 98.8%

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

   8. times-frac 98.8%

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

   9. *-lft-identity 98.8%

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

   10. neg-mul-1 98.8%

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

   11. sub-neg 98.8%

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

   12. +-commutative 98.8%

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

   13. distribute-neg-out 98.8%

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

   14. remove-double-neg 98.8%

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

   15. sub-neg 98.8%

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

3. Simplified 98.8%

   \[\leadsto \color{blue}{1 + \frac{\frac{x}{z - y}}{y - t}} \]
4. Add Preprocessing

5. Final simplification 98.8%

   \[\leadsto 1 + \frac{\frac{x}{z - y}}{y - t} \]
6. Add Preprocessing

Alternative 2: 73.3% accurate, 0.4× speedup

Math

\[\begin{array}{l} [x, y, z, t] = \mathsf{sort}([x, y, z, t])\\ \\ \begin{array}{l} t_1 := 1 - \frac{x}{z \cdot t}\\ t_2 := 1 + \frac{x}{z \cdot y}\\ \mathbf{if}\;z \leq -3.9 \cdot 10^{+18}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;z \leq -3.2 \cdot 10^{-50}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -3 \cdot 10^{-71}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;z \leq 1.45 \cdot 10^{-155}:\\ \;\;\;\;1 + \frac{x}{y \cdot t}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

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 (/ x (* z t)))) (t_2 (+ 1.0 (/ x (* z y)))))
   (if (<= z -3.9e+18)
     t_2
     (if (<= z -3.2e-50)
       t_1
       (if (<= z -3e-71)
         t_2
         (if (<= z 1.45e-155) (+ 1.0 (/ x (* y t))) 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 - (x / (z * t));
	double t_2 = 1.0 + (x / (z * y));
	double tmp;
	if (z <= -3.9e+18) {
		tmp = t_2;
	} else if (z <= -3.2e-50) {
		tmp = t_1;
	} else if (z <= -3e-71) {
		tmp = t_2;
	} else if (z <= 1.45e-155) {
		tmp = 1.0 + (x / (y * t));
	} 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) :: t_2
    real(8) :: tmp
    t_1 = 1.0d0 - (x / (z * t))
    t_2 = 1.0d0 + (x / (z * y))
    if (z <= (-3.9d+18)) then
        tmp = t_2
    else if (z <= (-3.2d-50)) then
        tmp = t_1
    else if (z <= (-3d-71)) then
        tmp = t_2
    else if (z <= 1.45d-155) then
        tmp = 1.0d0 + (x / (y * t))
    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 = 1.0 - (x / (z * t));
	double t_2 = 1.0 + (x / (z * y));
	double tmp;
	if (z <= -3.9e+18) {
		tmp = t_2;
	} else if (z <= -3.2e-50) {
		tmp = t_1;
	} else if (z <= -3e-71) {
		tmp = t_2;
	} else if (z <= 1.45e-155) {
		tmp = 1.0 + (x / (y * t));
	} 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 - (x / (z * t))
	t_2 = 1.0 + (x / (z * y))
	tmp = 0
	if z <= -3.9e+18:
		tmp = t_2
	elif z <= -3.2e-50:
		tmp = t_1
	elif z <= -3e-71:
		tmp = t_2
	elif z <= 1.45e-155:
		tmp = 1.0 + (x / (y * t))
	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(x / Float64(z * t)))
	t_2 = Float64(1.0 + Float64(x / Float64(z * y)))
	tmp = 0.0
	if (z <= -3.9e+18)
		tmp = t_2;
	elseif (z <= -3.2e-50)
		tmp = t_1;
	elseif (z <= -3e-71)
		tmp = t_2;
	elseif (z <= 1.45e-155)
		tmp = Float64(1.0 + Float64(x / Float64(y * t)));
	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 - (x / (z * t));
	t_2 = 1.0 + (x / (z * y));
	tmp = 0.0;
	if (z <= -3.9e+18)
		tmp = t_2;
	elseif (z <= -3.2e-50)
		tmp = t_1;
	elseif (z <= -3e-71)
		tmp = t_2;
	elseif (z <= 1.45e-155)
		tmp = 1.0 + (x / (y * t));
	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[(x / N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(1.0 + N[(x / N[(z * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -3.9e+18], t$95$2, If[LessEqual[z, -3.2e-50], t$95$1, If[LessEqual[z, -3e-71], t$95$2, If[LessEqual[z, 1.45e-155], N[(1.0 + N[(x / N[(y * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -3.9e18 or -3.2e-50 < z < -3.0000000000000001e-71

   1. Initial program 100.0%

      \[1 - \frac{x}{\left(y - z\right) \cdot \left(y - t\right)} \]
   2. Step-by-step derivation

      1. sub-neg 100.0%

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

      2. neg-mul-1 100.0%

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

      3. *-commutative 100.0%

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

      4. *-commutative 100.0%

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

      5. associate-/r* 100.0%

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

      6. associate-*r/ 100.0%

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

      7. metadata-eval 100.0%

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

      8. times-frac 100.0%

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

      9. *-lft-identity 100.0%

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

      10. neg-mul-1 100.0%

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

      11. sub-neg 100.0%

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

      12. +-commutative 100.0%

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

      13. distribute-neg-out 100.0%

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

      14. remove-double-neg 100.0%

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

      15. sub-neg 100.0%

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

   3. Simplified 100.0%

      \[\leadsto \color{blue}{1 + \frac{\frac{x}{z - y}}{y - t}} \]
   4. Add Preprocessing

   5. Taylor expanded in z around inf 97.4%

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

      1. associate-/r* 97.4%

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

   7. Simplified 97.4%

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

   8. Taylor expanded in y around inf 82.8%

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

      1. *-commutative 82.8%

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

   10. Simplified 82.8%

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

   if -3.9e18 < z < -3.2e-50 or 1.45000000000000005e-155 < z

   1. Initial program 99.9%

      \[1 - \frac{x}{\left(y - z\right) \cdot \left(y - t\right)} \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0 73.9%

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

   if -3.0000000000000001e-71 < z < 1.45000000000000005e-155

   1. Initial program 95.9%

      \[1 - \frac{x}{\left(y - z\right) \cdot \left(y - t\right)} \]
   2. Step-by-step derivation

      1. sub-neg 95.9%

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

      2. neg-mul-1 95.9%

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

      3. *-commutative 95.9%

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

      4. *-commutative 95.9%

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

      5. associate-/r* 95.8%

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

      6. associate-*r/ 95.8%

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

      7. metadata-eval 95.8%

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

      8. times-frac 95.8%

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

      9. *-lft-identity 95.8%

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

      10. neg-mul-1 95.8%

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

      11. sub-neg 95.8%

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

      12. +-commutative 95.8%

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

      13. distribute-neg-out 95.8%

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

      14. remove-double-neg 95.8%

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

      15. sub-neg 95.8%

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

   3. Simplified 95.8%

      \[\leadsto \color{blue}{1 + \frac{\frac{x}{z - y}}{y - t}} \]
   4. Add Preprocessing

   5. Taylor expanded in t around inf 73.5%

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

      1. associate-*r/ 73.5%

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

      2. neg-mul-1 73.5%

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

      3. associate-/r* 76.2%

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

   7. Simplified 76.2%

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

   8. Taylor expanded in z around 0 67.7%

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

4. Final simplification 74.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.9 \cdot 10^{+18}:\\ \;\;\;\;1 + \frac{x}{z \cdot y}\\ \mathbf{elif}\;z \leq -3.2 \cdot 10^{-50}:\\ \;\;\;\;1 - \frac{x}{z \cdot t}\\ \mathbf{elif}\;z \leq -3 \cdot 10^{-71}:\\ \;\;\;\;1 + \frac{x}{z \cdot y}\\ \mathbf{elif}\;z \leq 1.45 \cdot 10^{-155}:\\ \;\;\;\;1 + \frac{x}{y \cdot t}\\ \mathbf{else}:\\ \;\;\;\;1 - \frac{x}{z \cdot t}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 73.3% accurate, 0.4× speedup

Math

\[\begin{array}{l} [x, y, z, t] = \mathsf{sort}([x, y, z, t])\\ \\ \begin{array}{l} t_1 := 1 + \frac{x}{z \cdot y}\\ \mathbf{if}\;z \leq -3.6 \cdot 10^{+18}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -3 \cdot 10^{-50}:\\ \;\;\;\;1 - \frac{x}{z \cdot t}\\ \mathbf{elif}\;z \leq -3.3 \cdot 10^{-71}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 2.8 \cdot 10^{-155}:\\ \;\;\;\;1 + \frac{x}{y \cdot t}\\ \mathbf{else}:\\ \;\;\;\;1 - \frac{\frac{x}{t}}{z}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (+ 1.0 (/ x (* z y)))))
   (if (<= z -3.6e+18)
     t_1
     (if (<= z -3e-50)
       (- 1.0 (/ x (* z t)))
       (if (<= z -3.3e-71)
         t_1
         (if (<= z 2.8e-155) (+ 1.0 (/ x (* y t))) (- 1.0 (/ (/ x t) z))))))))

C

assert(x < y && y < z && z < t);
double code(double x, double y, double z, double t) {
	double t_1 = 1.0 + (x / (z * y));
	double tmp;
	if (z <= -3.6e+18) {
		tmp = t_1;
	} else if (z <= -3e-50) {
		tmp = 1.0 - (x / (z * t));
	} else if (z <= -3.3e-71) {
		tmp = t_1;
	} else if (z <= 2.8e-155) {
		tmp = 1.0 + (x / (y * t));
	} else {
		tmp = 1.0 - ((x / t) / z);
	}
	return tmp;
}

Fortran

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = 1.0d0 + (x / (z * y))
    if (z <= (-3.6d+18)) then
        tmp = t_1
    else if (z <= (-3d-50)) then
        tmp = 1.0d0 - (x / (z * t))
    else if (z <= (-3.3d-71)) then
        tmp = t_1
    else if (z <= 2.8d-155) then
        tmp = 1.0d0 + (x / (y * t))
    else
        tmp = 1.0d0 - ((x / t) / z)
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t;
public static double code(double x, double y, double z, double t) {
	double t_1 = 1.0 + (x / (z * y));
	double tmp;
	if (z <= -3.6e+18) {
		tmp = t_1;
	} else if (z <= -3e-50) {
		tmp = 1.0 - (x / (z * t));
	} else if (z <= -3.3e-71) {
		tmp = t_1;
	} else if (z <= 2.8e-155) {
		tmp = 1.0 + (x / (y * t));
	} else {
		tmp = 1.0 - ((x / t) / z);
	}
	return tmp;
}

Python

[x, y, z, t] = sort([x, y, z, t])
def code(x, y, z, t):
	t_1 = 1.0 + (x / (z * y))
	tmp = 0
	if z <= -3.6e+18:
		tmp = t_1
	elif z <= -3e-50:
		tmp = 1.0 - (x / (z * t))
	elif z <= -3.3e-71:
		tmp = t_1
	elif z <= 2.8e-155:
		tmp = 1.0 + (x / (y * t))
	else:
		tmp = 1.0 - ((x / t) / z)
	return tmp

Julia

x, y, z, t = sort([x, y, z, t])
function code(x, y, z, t)
	t_1 = Float64(1.0 + Float64(x / Float64(z * y)))
	tmp = 0.0
	if (z <= -3.6e+18)
		tmp = t_1;
	elseif (z <= -3e-50)
		tmp = Float64(1.0 - Float64(x / Float64(z * t)));
	elseif (z <= -3.3e-71)
		tmp = t_1;
	elseif (z <= 2.8e-155)
		tmp = Float64(1.0 + Float64(x / Float64(y * t)));
	else
		tmp = Float64(1.0 - Float64(Float64(x / t) / z));
	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 + (x / (z * y));
	tmp = 0.0;
	if (z <= -3.6e+18)
		tmp = t_1;
	elseif (z <= -3e-50)
		tmp = 1.0 - (x / (z * t));
	elseif (z <= -3.3e-71)
		tmp = t_1;
	elseif (z <= 2.8e-155)
		tmp = 1.0 + (x / (y * t));
	else
		tmp = 1.0 - ((x / t) / z);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_] := Block[{t$95$1 = N[(1.0 + N[(x / N[(z * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -3.6e+18], t$95$1, If[LessEqual[z, -3e-50], N[(1.0 - N[(x / N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -3.3e-71], t$95$1, If[LessEqual[z, 2.8e-155], N[(1.0 + N[(x / N[(y * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(1.0 - N[(N[(x / t), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -3.6e18 or -2.9999999999999999e-50 < z < -3.3000000000000002e-71

   1. Initial program 100.0%

      \[1 - \frac{x}{\left(y - z\right) \cdot \left(y - t\right)} \]
   2. Step-by-step derivation

      1. sub-neg 100.0%

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

      2. neg-mul-1 100.0%

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

      3. *-commutative 100.0%

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

      4. *-commutative 100.0%

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

      5. associate-/r* 100.0%

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

      6. associate-*r/ 100.0%

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

      7. metadata-eval 100.0%

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

      8. times-frac 100.0%

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

      9. *-lft-identity 100.0%

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

      10. neg-mul-1 100.0%

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

      11. sub-neg 100.0%

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

      12. +-commutative 100.0%

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

      13. distribute-neg-out 100.0%

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

      14. remove-double-neg 100.0%

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

      15. sub-neg 100.0%

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

   3. Simplified 100.0%

      \[\leadsto \color{blue}{1 + \frac{\frac{x}{z - y}}{y - t}} \]
   4. Add Preprocessing

   5. Taylor expanded in z around inf 97.4%

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

      1. associate-/r* 97.4%

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

   7. Simplified 97.4%

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

   8. Taylor expanded in y around inf 82.8%

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

      1. *-commutative 82.8%

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

   10. Simplified 82.8%

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

   if -3.6e18 < z < -2.9999999999999999e-50

   1. Initial program 100.0%

      \[1 - \frac{x}{\left(y - z\right) \cdot \left(y - t\right)} \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0 68.4%

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

   if -3.3000000000000002e-71 < z < 2.8e-155

   1. Initial program 95.9%

      \[1 - \frac{x}{\left(y - z\right) \cdot \left(y - t\right)} \]
   2. Step-by-step derivation

      1. sub-neg 95.9%

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

      2. neg-mul-1 95.9%

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

      3. *-commutative 95.9%

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

      4. *-commutative 95.9%

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

      5. associate-/r* 95.8%

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

      6. associate-*r/ 95.8%

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

      7. metadata-eval 95.8%

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

      8. times-frac 95.8%

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

      9. *-lft-identity 95.8%

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

      10. neg-mul-1 95.8%

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

      11. sub-neg 95.8%

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

      12. +-commutative 95.8%

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

      13. distribute-neg-out 95.8%

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

      14. remove-double-neg 95.8%

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

      15. sub-neg 95.8%

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

   3. Simplified 95.8%

      \[\leadsto \color{blue}{1 + \frac{\frac{x}{z - y}}{y - t}} \]
   4. Add Preprocessing

   5. Taylor expanded in t around inf 73.5%

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

      1. associate-*r/ 73.5%

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

      2. neg-mul-1 73.5%

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

      3. associate-/r* 76.2%

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

   7. Simplified 76.2%

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

   8. Taylor expanded in z around 0 67.7%

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

   if 2.8e-155 < z

   1. Initial program 99.9%

      \[1 - \frac{x}{\left(y - z\right) \cdot \left(y - t\right)} \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. clear-num 99.9%

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

      2. associate-/r/ 99.9%

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

      3. *-commutative 99.9%

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

      4. associate-/r* 99.9%

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

   4. Applied egg-rr 99.9%

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

   5. Taylor expanded in y around 0 74.7%

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

      1. associate-/r* 74.4%

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

   7. Simplified 74.4%

      \[\leadsto 1 - \color{blue}{\frac{\frac{x}{t}}{z}} \]
3. Recombined 4 regimes into one program.

4. Final simplification 74.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.6 \cdot 10^{+18}:\\ \;\;\;\;1 + \frac{x}{z \cdot y}\\ \mathbf{elif}\;z \leq -3 \cdot 10^{-50}:\\ \;\;\;\;1 - \frac{x}{z \cdot t}\\ \mathbf{elif}\;z \leq -3.3 \cdot 10^{-71}:\\ \;\;\;\;1 + \frac{x}{z \cdot y}\\ \mathbf{elif}\;z \leq 2.8 \cdot 10^{-155}:\\ \;\;\;\;1 + \frac{x}{y \cdot t}\\ \mathbf{else}:\\ \;\;\;\;1 - \frac{\frac{x}{t}}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 73.4% accurate, 0.4× speedup

Math

\[\begin{array}{l} [x, y, z, t] = \mathsf{sort}([x, y, z, t])\\ \\ \begin{array}{l} t_1 := 1 + \frac{x}{z \cdot y}\\ \mathbf{if}\;z \leq -3.8 \cdot 10^{+18}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -3.2 \cdot 10^{-50}:\\ \;\;\;\;1 - \frac{x}{z \cdot t}\\ \mathbf{elif}\;z \leq -3.3 \cdot 10^{-71}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 8.6 \cdot 10^{-155}:\\ \;\;\;\;1 + \frac{\frac{x}{t}}{y}\\ \mathbf{else}:\\ \;\;\;\;1 - \frac{\frac{x}{t}}{z}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (+ 1.0 (/ x (* z y)))))
   (if (<= z -3.8e+18)
     t_1
     (if (<= z -3.2e-50)
       (- 1.0 (/ x (* z t)))
       (if (<= z -3.3e-71)
         t_1
         (if (<= z 8.6e-155) (+ 1.0 (/ (/ x t) y)) (- 1.0 (/ (/ x t) z))))))))

C

assert(x < y && y < z && z < t);
double code(double x, double y, double z, double t) {
	double t_1 = 1.0 + (x / (z * y));
	double tmp;
	if (z <= -3.8e+18) {
		tmp = t_1;
	} else if (z <= -3.2e-50) {
		tmp = 1.0 - (x / (z * t));
	} else if (z <= -3.3e-71) {
		tmp = t_1;
	} else if (z <= 8.6e-155) {
		tmp = 1.0 + ((x / t) / y);
	} else {
		tmp = 1.0 - ((x / t) / z);
	}
	return tmp;
}

Fortran

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = 1.0d0 + (x / (z * y))
    if (z <= (-3.8d+18)) then
        tmp = t_1
    else if (z <= (-3.2d-50)) then
        tmp = 1.0d0 - (x / (z * t))
    else if (z <= (-3.3d-71)) then
        tmp = t_1
    else if (z <= 8.6d-155) then
        tmp = 1.0d0 + ((x / t) / y)
    else
        tmp = 1.0d0 - ((x / t) / z)
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t;
public static double code(double x, double y, double z, double t) {
	double t_1 = 1.0 + (x / (z * y));
	double tmp;
	if (z <= -3.8e+18) {
		tmp = t_1;
	} else if (z <= -3.2e-50) {
		tmp = 1.0 - (x / (z * t));
	} else if (z <= -3.3e-71) {
		tmp = t_1;
	} else if (z <= 8.6e-155) {
		tmp = 1.0 + ((x / t) / y);
	} else {
		tmp = 1.0 - ((x / t) / z);
	}
	return tmp;
}

Python

[x, y, z, t] = sort([x, y, z, t])
def code(x, y, z, t):
	t_1 = 1.0 + (x / (z * y))
	tmp = 0
	if z <= -3.8e+18:
		tmp = t_1
	elif z <= -3.2e-50:
		tmp = 1.0 - (x / (z * t))
	elif z <= -3.3e-71:
		tmp = t_1
	elif z <= 8.6e-155:
		tmp = 1.0 + ((x / t) / y)
	else:
		tmp = 1.0 - ((x / t) / z)
	return tmp

Julia

x, y, z, t = sort([x, y, z, t])
function code(x, y, z, t)
	t_1 = Float64(1.0 + Float64(x / Float64(z * y)))
	tmp = 0.0
	if (z <= -3.8e+18)
		tmp = t_1;
	elseif (z <= -3.2e-50)
		tmp = Float64(1.0 - Float64(x / Float64(z * t)));
	elseif (z <= -3.3e-71)
		tmp = t_1;
	elseif (z <= 8.6e-155)
		tmp = Float64(1.0 + Float64(Float64(x / t) / y));
	else
		tmp = Float64(1.0 - Float64(Float64(x / t) / z));
	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 + (x / (z * y));
	tmp = 0.0;
	if (z <= -3.8e+18)
		tmp = t_1;
	elseif (z <= -3.2e-50)
		tmp = 1.0 - (x / (z * t));
	elseif (z <= -3.3e-71)
		tmp = t_1;
	elseif (z <= 8.6e-155)
		tmp = 1.0 + ((x / t) / y);
	else
		tmp = 1.0 - ((x / t) / z);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_] := Block[{t$95$1 = N[(1.0 + N[(x / N[(z * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -3.8e+18], t$95$1, If[LessEqual[z, -3.2e-50], N[(1.0 - N[(x / N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -3.3e-71], t$95$1, If[LessEqual[z, 8.6e-155], N[(1.0 + N[(N[(x / t), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], N[(1.0 - N[(N[(x / t), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -3.8e18 or -3.2e-50 < z < -3.3000000000000002e-71

   1. Initial program 100.0%

      \[1 - \frac{x}{\left(y - z\right) \cdot \left(y - t\right)} \]
   2. Step-by-step derivation

      1. sub-neg 100.0%

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

      2. neg-mul-1 100.0%

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

      3. *-commutative 100.0%

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

      4. *-commutative 100.0%

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

      5. associate-/r* 100.0%

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

      6. associate-*r/ 100.0%

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

      7. metadata-eval 100.0%

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

      8. times-frac 100.0%

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

      9. *-lft-identity 100.0%

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

      10. neg-mul-1 100.0%

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

      11. sub-neg 100.0%

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

      12. +-commutative 100.0%

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

      13. distribute-neg-out 100.0%

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

      14. remove-double-neg 100.0%

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

      15. sub-neg 100.0%

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

   3. Simplified 100.0%

      \[\leadsto \color{blue}{1 + \frac{\frac{x}{z - y}}{y - t}} \]
   4. Add Preprocessing

   5. Taylor expanded in z around inf 97.4%

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

      1. associate-/r* 97.4%

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

   7. Simplified 97.4%

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

   8. Taylor expanded in y around inf 82.8%

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

      1. *-commutative 82.8%

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

   10. Simplified 82.8%

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

   if -3.8e18 < z < -3.2e-50

   1. Initial program 100.0%

      \[1 - \frac{x}{\left(y - z\right) \cdot \left(y - t\right)} \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0 68.4%

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

   if -3.3000000000000002e-71 < z < 8.60000000000000016e-155

   1. Initial program 95.9%

      \[1 - \frac{x}{\left(y - z\right) \cdot \left(y - t\right)} \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. clear-num 95.8%

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

      2. associate-/r/ 95.8%

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

      3. *-commutative 95.8%

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

      4. associate-/r* 95.8%

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

   4. Applied egg-rr 95.8%

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

   5. Taylor expanded in z around 0 89.0%

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

      1. associate-/r* 85.4%

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

   7. Simplified 85.4%

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

   8. Taylor expanded in y around 0 67.7%

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

      1. mul-1-neg 67.7%

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

      2. associate-/r* 68.0%

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

      3. distribute-neg-frac 68.0%

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

   10. Simplified 68.0%

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

   if 8.60000000000000016e-155 < z

   1. Initial program 99.9%

      \[1 - \frac{x}{\left(y - z\right) \cdot \left(y - t\right)} \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. clear-num 99.9%

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

      2. associate-/r/ 99.9%

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

      3. *-commutative 99.9%

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

      4. associate-/r* 99.9%

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

   4. Applied egg-rr 99.9%

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

   5. Taylor expanded in y around 0 74.7%

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

      1. associate-/r* 74.4%

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

   7. Simplified 74.4%

      \[\leadsto 1 - \color{blue}{\frac{\frac{x}{t}}{z}} \]
3. Recombined 4 regimes into one program.

4. Final simplification 74.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.8 \cdot 10^{+18}:\\ \;\;\;\;1 + \frac{x}{z \cdot y}\\ \mathbf{elif}\;z \leq -3.2 \cdot 10^{-50}:\\ \;\;\;\;1 - \frac{x}{z \cdot t}\\ \mathbf{elif}\;z \leq -3.3 \cdot 10^{-71}:\\ \;\;\;\;1 + \frac{x}{z \cdot y}\\ \mathbf{elif}\;z \leq 8.6 \cdot 10^{-155}:\\ \;\;\;\;1 + \frac{\frac{x}{t}}{y}\\ \mathbf{else}:\\ \;\;\;\;1 - \frac{\frac{x}{t}}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 85.8% accurate, 0.6× speedup

Math

\[\begin{array}{l} [x, y, z, t] = \mathsf{sort}([x, y, z, t])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -2.85 \cdot 10^{-195} \lor \neg \left(z \leq 4.5 \cdot 10^{-159}\right):\\ \;\;\;\;1 + \frac{\frac{x}{z}}{y - t}\\ \mathbf{else}:\\ \;\;\;\;1 + \frac{\frac{x}{t}}{y}\\ \end{array} \end{array} \]

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 -2.85e-195) (not (<= z 4.5e-159)))
   (+ 1.0 (/ (/ x z) (- y t)))
   (+ 1.0 (/ (/ x t) y))))

C

assert(x < y && y < z && z < t);
double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -2.85e-195) || !(z <= 4.5e-159)) {
		tmp = 1.0 + ((x / z) / (y - t));
	} else {
		tmp = 1.0 + ((x / t) / 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 <= (-2.85d-195)) .or. (.not. (z <= 4.5d-159))) then
        tmp = 1.0d0 + ((x / z) / (y - t))
    else
        tmp = 1.0d0 + ((x / t) / 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 <= -2.85e-195) || !(z <= 4.5e-159)) {
		tmp = 1.0 + ((x / z) / (y - t));
	} else {
		tmp = 1.0 + ((x / t) / y);
	}
	return tmp;
}

Python

[x, y, z, t] = sort([x, y, z, t])
def code(x, y, z, t):
	tmp = 0
	if (z <= -2.85e-195) or not (z <= 4.5e-159):
		tmp = 1.0 + ((x / z) / (y - t))
	else:
		tmp = 1.0 + ((x / t) / y)
	return tmp

Julia

x, y, z, t = sort([x, y, z, t])
function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -2.85e-195) || !(z <= 4.5e-159))
		tmp = Float64(1.0 + Float64(Float64(x / z) / Float64(y - t)));
	else
		tmp = Float64(1.0 + Float64(Float64(x / t) / 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 <= -2.85e-195) || ~((z <= 4.5e-159)))
		tmp = 1.0 + ((x / z) / (y - t));
	else
		tmp = 1.0 + ((x / t) / 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[z, -2.85e-195], N[Not[LessEqual[z, 4.5e-159]], $MachinePrecision]], N[(1.0 + N[(N[(x / z), $MachinePrecision] / N[(y - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(1.0 + N[(N[(x / t), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -2.85e-195 or 4.49999999999999989e-159 < z

   1. Initial program 99.9%

      \[1 - \frac{x}{\left(y - z\right) \cdot \left(y - t\right)} \]
   2. Step-by-step derivation

      1. sub-neg 99.9%

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

      2. neg-mul-1 99.9%

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

      3. *-commutative 99.9%

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

      4. *-commutative 99.9%

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

      5. associate-/r* 99.9%

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

      6. associate-*r/ 99.9%

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

      7. metadata-eval 99.9%

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

      8. times-frac 99.9%

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

      9. *-lft-identity 99.9%

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

      10. neg-mul-1 99.9%

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

      11. sub-neg 99.9%

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

      12. +-commutative 99.9%

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

      13. distribute-neg-out 99.9%

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

      14. remove-double-neg 99.9%

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

      15. sub-neg 99.9%

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

   3. Simplified 99.9%

      \[\leadsto \color{blue}{1 + \frac{\frac{x}{z - y}}{y - t}} \]
   4. Add Preprocessing

   5. Taylor expanded in z around inf 88.6%

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

      1. associate-/r* 88.6%

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

   7. Simplified 88.6%

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

   if -2.85e-195 < z < 4.49999999999999989e-159

   1. Initial program 94.4%

      \[1 - \frac{x}{\left(y - z\right) \cdot \left(y - t\right)} \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. clear-num 94.4%

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

      2. associate-/r/ 94.4%

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

      3. *-commutative 94.4%

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

      4. associate-/r* 94.4%

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

   4. Applied egg-rr 94.4%

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

   5. Taylor expanded in z around 0 90.1%

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

      1. associate-/r* 85.2%

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

   7. Simplified 85.2%

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

   8. Taylor expanded in y around 0 70.5%

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

      1. mul-1-neg 70.5%

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

      2. associate-/r* 70.9%

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

      3. distribute-neg-frac 70.9%

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

   10. Simplified 70.9%

       \[\leadsto 1 - \color{blue}{\frac{-\frac{x}{t}}{y}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 85.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.85 \cdot 10^{-195} \lor \neg \left(z \leq 4.5 \cdot 10^{-159}\right):\\ \;\;\;\;1 + \frac{\frac{x}{z}}{y - t}\\ \mathbf{else}:\\ \;\;\;\;1 + \frac{\frac{x}{t}}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 91.3% accurate, 0.6× speedup

Math

\[\begin{array}{l} [x, y, z, t] = \mathsf{sort}([x, y, z, t])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -3.3 \cdot 10^{-62} \lor \neg \left(z \leq 9.8 \cdot 10^{-155}\right):\\ \;\;\;\;1 + \frac{\frac{x}{z}}{y - t}\\ \mathbf{else}:\\ \;\;\;\;1 - \frac{x}{y \cdot \left(y - t\right)}\\ \end{array} \end{array} \]

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 -3.3e-62) (not (<= z 9.8e-155)))
   (+ 1.0 (/ (/ x z) (- y t)))
   (- 1.0 (/ x (* y (- y t))))))

C

assert(x < y && y < z && z < t);
double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -3.3e-62) || !(z <= 9.8e-155)) {
		tmp = 1.0 + ((x / z) / (y - t));
	} else {
		tmp = 1.0 - (x / (y * (y - t)));
	}
	return tmp;
}

Fortran

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((z <= (-3.3d-62)) .or. (.not. (z <= 9.8d-155))) then
        tmp = 1.0d0 + ((x / z) / (y - t))
    else
        tmp = 1.0d0 - (x / (y * (y - t)))
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t;
public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -3.3e-62) || !(z <= 9.8e-155)) {
		tmp = 1.0 + ((x / z) / (y - t));
	} else {
		tmp = 1.0 - (x / (y * (y - t)));
	}
	return tmp;
}

Python

[x, y, z, t] = sort([x, y, z, t])
def code(x, y, z, t):
	tmp = 0
	if (z <= -3.3e-62) or not (z <= 9.8e-155):
		tmp = 1.0 + ((x / z) / (y - t))
	else:
		tmp = 1.0 - (x / (y * (y - t)))
	return tmp

Julia

x, y, z, t = sort([x, y, z, t])
function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -3.3e-62) || !(z <= 9.8e-155))
		tmp = Float64(1.0 + Float64(Float64(x / z) / Float64(y - t)));
	else
		tmp = Float64(1.0 - Float64(x / Float64(y * Float64(y - 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 <= -3.3e-62) || ~((z <= 9.8e-155)))
		tmp = 1.0 + ((x / z) / (y - t));
	else
		tmp = 1.0 - (x / (y * (y - 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[z, -3.3e-62], N[Not[LessEqual[z, 9.8e-155]], $MachinePrecision]], N[(1.0 + N[(N[(x / z), $MachinePrecision] / N[(y - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(1.0 - N[(x / N[(y * N[(y - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -3.30000000000000004e-62 or 9.80000000000000026e-155 < z

   1. Initial program 99.9%

      \[1 - \frac{x}{\left(y - z\right) \cdot \left(y - t\right)} \]
   2. Step-by-step derivation

      1. sub-neg 99.9%

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

      2. neg-mul-1 99.9%

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

      3. *-commutative 99.9%

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

      4. *-commutative 99.9%

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

      5. associate-/r* 100.0%

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

      6. associate-*r/ 100.0%

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

      7. metadata-eval 100.0%

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

      8. times-frac 100.0%

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

      9. *-lft-identity 100.0%

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

      10. neg-mul-1 100.0%

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

      11. sub-neg 100.0%

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

      12. +-commutative 100.0%

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

      13. distribute-neg-out 100.0%

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

      14. remove-double-neg 100.0%

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

      15. sub-neg 100.0%

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

   3. Simplified 100.0%

      \[\leadsto \color{blue}{1 + \frac{\frac{x}{z - y}}{y - t}} \]
   4. Add Preprocessing

   5. Taylor expanded in z around inf 93.7%

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

      1. associate-/r* 93.7%

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

   7. Simplified 93.7%

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

   if -3.30000000000000004e-62 < z < 9.80000000000000026e-155

   1. Initial program 96.0%

      \[1 - \frac{x}{\left(y - z\right) \cdot \left(y - t\right)} \]
   2. Add Preprocessing

   3. Taylor expanded in z around 0 89.3%

      \[\leadsto 1 - \color{blue}{\frac{x}{y \cdot \left(y - t\right)}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 92.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.3 \cdot 10^{-62} \lor \neg \left(z \leq 9.8 \cdot 10^{-155}\right):\\ \;\;\;\;1 + \frac{\frac{x}{z}}{y - t}\\ \mathbf{else}:\\ \;\;\;\;1 - \frac{x}{y \cdot \left(y - t\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 91.1% accurate, 0.6× speedup

Math

\[\begin{array}{l} [x, y, z, t] = \mathsf{sort}([x, y, z, t])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -2.2 \cdot 10^{-60} \lor \neg \left(z \leq 9.8 \cdot 10^{-155}\right):\\ \;\;\;\;1 + \frac{\frac{x}{z}}{y - t}\\ \mathbf{else}:\\ \;\;\;\;1 - \frac{\frac{x}{y}}{y - t}\\ \end{array} \end{array} \]

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 -2.2e-60) (not (<= z 9.8e-155)))
   (+ 1.0 (/ (/ x z) (- y t)))
   (- 1.0 (/ (/ x y) (- y t)))))

C

assert(x < y && y < z && z < t);
double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -2.2e-60) || !(z <= 9.8e-155)) {
		tmp = 1.0 + ((x / z) / (y - t));
	} else {
		tmp = 1.0 - ((x / y) / (y - t));
	}
	return tmp;
}

Fortran

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((z <= (-2.2d-60)) .or. (.not. (z <= 9.8d-155))) then
        tmp = 1.0d0 + ((x / z) / (y - t))
    else
        tmp = 1.0d0 - ((x / y) / (y - t))
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t;
public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -2.2e-60) || !(z <= 9.8e-155)) {
		tmp = 1.0 + ((x / z) / (y - t));
	} else {
		tmp = 1.0 - ((x / y) / (y - t));
	}
	return tmp;
}

Python

[x, y, z, t] = sort([x, y, z, t])
def code(x, y, z, t):
	tmp = 0
	if (z <= -2.2e-60) or not (z <= 9.8e-155):
		tmp = 1.0 + ((x / z) / (y - t))
	else:
		tmp = 1.0 - ((x / y) / (y - t))
	return tmp

Julia

x, y, z, t = sort([x, y, z, t])
function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -2.2e-60) || !(z <= 9.8e-155))
		tmp = Float64(1.0 + Float64(Float64(x / z) / Float64(y - t)));
	else
		tmp = Float64(1.0 - Float64(Float64(x / y) / Float64(y - 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 <= -2.2e-60) || ~((z <= 9.8e-155)))
		tmp = 1.0 + ((x / z) / (y - t));
	else
		tmp = 1.0 - ((x / y) / (y - 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[z, -2.2e-60], N[Not[LessEqual[z, 9.8e-155]], $MachinePrecision]], N[(1.0 + N[(N[(x / z), $MachinePrecision] / N[(y - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(1.0 - N[(N[(x / y), $MachinePrecision] / N[(y - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -2.1999999999999999e-60 or 9.80000000000000026e-155 < z

   1. Initial program 99.9%

      \[1 - \frac{x}{\left(y - z\right) \cdot \left(y - t\right)} \]
   2. Step-by-step derivation

      1. sub-neg 99.9%

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

      2. neg-mul-1 99.9%

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

      3. *-commutative 99.9%

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

      4. *-commutative 99.9%

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

      5. associate-/r* 100.0%

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

      6. associate-*r/ 100.0%

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

      7. metadata-eval 100.0%

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

      8. times-frac 100.0%

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

      9. *-lft-identity 100.0%

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

      10. neg-mul-1 100.0%

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

      11. sub-neg 100.0%

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

      12. +-commutative 100.0%

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

      13. distribute-neg-out 100.0%

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

      14. remove-double-neg 100.0%

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

      15. sub-neg 100.0%

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

   3. Simplified 100.0%

      \[\leadsto \color{blue}{1 + \frac{\frac{x}{z - y}}{y - t}} \]
   4. Add Preprocessing

   5. Taylor expanded in z around inf 93.7%

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

      1. associate-/r* 93.7%

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

   7. Simplified 93.7%

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

   if -2.1999999999999999e-60 < z < 9.80000000000000026e-155

   1. Initial program 96.0%

      \[1 - \frac{x}{\left(y - z\right) \cdot \left(y - t\right)} \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. clear-num 96.0%

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

      2. associate-/r/ 96.0%

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

      3. *-commutative 96.0%

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

      4. associate-/r* 96.0%

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

   4. Applied egg-rr 96.0%

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

   5. Taylor expanded in z around 0 89.3%

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

      1. associate-/r* 85.8%

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

   7. Simplified 85.8%

      \[\leadsto 1 - \color{blue}{\frac{\frac{x}{y}}{y - t}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 91.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.2 \cdot 10^{-60} \lor \neg \left(z \leq 9.8 \cdot 10^{-155}\right):\\ \;\;\;\;1 + \frac{\frac{x}{z}}{y - t}\\ \mathbf{else}:\\ \;\;\;\;1 - \frac{\frac{x}{y}}{y - t}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 67.7% accurate, 0.6× speedup

Math

\[\begin{array}{l} [x, y, z, t] = \mathsf{sort}([x, y, z, t])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -8.8 \cdot 10^{-28} \lor \neg \left(z \leq 9 \cdot 10^{-54}\right):\\ \;\;\;\;1 + \frac{x}{z \cdot t}\\ \mathbf{else}:\\ \;\;\;\;1 + \frac{x}{y \cdot t}\\ \end{array} \end{array} \]

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 -8.8e-28) (not (<= z 9e-54)))
   (+ 1.0 (/ x (* z t)))
   (+ 1.0 (/ x (* y t)))))

C

assert(x < y && y < z && z < t);
double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -8.8e-28) || !(z <= 9e-54)) {
		tmp = 1.0 + (x / (z * t));
	} else {
		tmp = 1.0 + (x / (y * t));
	}
	return tmp;
}

Fortran

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((z <= (-8.8d-28)) .or. (.not. (z <= 9d-54))) then
        tmp = 1.0d0 + (x / (z * t))
    else
        tmp = 1.0d0 + (x / (y * t))
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t;
public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -8.8e-28) || !(z <= 9e-54)) {
		tmp = 1.0 + (x / (z * t));
	} else {
		tmp = 1.0 + (x / (y * t));
	}
	return tmp;
}

Python

[x, y, z, t] = sort([x, y, z, t])
def code(x, y, z, t):
	tmp = 0
	if (z <= -8.8e-28) or not (z <= 9e-54):
		tmp = 1.0 + (x / (z * t))
	else:
		tmp = 1.0 + (x / (y * t))
	return tmp

Julia

x, y, z, t = sort([x, y, z, t])
function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -8.8e-28) || !(z <= 9e-54))
		tmp = Float64(1.0 + Float64(x / Float64(z * t)));
	else
		tmp = Float64(1.0 + Float64(x / Float64(y * 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 <= -8.8e-28) || ~((z <= 9e-54)))
		tmp = 1.0 + (x / (z * t));
	else
		tmp = 1.0 + (x / (y * 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[z, -8.8e-28], N[Not[LessEqual[z, 9e-54]], $MachinePrecision]], N[(1.0 + N[(x / N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(1.0 + N[(x / N[(y * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -8.79999999999999984e-28 or 8.9999999999999997e-54 < z

   1. Initial program 99.9%

      \[1 - \frac{x}{\left(y - z\right) \cdot \left(y - t\right)} \]
   2. Step-by-step derivation

      1. sub-neg 99.9%

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

      2. neg-mul-1 99.9%

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

      3. *-commutative 99.9%

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

      4. *-commutative 99.9%

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

      5. associate-/r* 100.0%

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

      6. associate-*r/ 100.0%

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

      7. metadata-eval 100.0%

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

      8. times-frac 100.0%

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

      9. *-lft-identity 100.0%

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

      10. neg-mul-1 100.0%

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

      11. sub-neg 100.0%

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

      12. +-commutative 100.0%

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

      13. distribute-neg-out 100.0%

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

      14. remove-double-neg 100.0%

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

      15. sub-neg 100.0%

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

   3. Simplified 100.0%

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

      1. clear-num 99.9%

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

      2. inv-pow 99.9%

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

      3. div-inv 99.9%

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

      4. clear-num 99.9%

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

   6. Applied egg-rr 99.9%

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

      1. unpow-1 99.9%

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

      2. associate-/r* 99.9%

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

   8. Simplified 99.9%

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

   9. Taylor expanded in y around 0 77.5%

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

       1. mul-1-neg 77.5%

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

       2. associate-/l/ 77.5%

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

       3. distribute-neg-frac 77.5%

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

       4. distribute-neg-frac 77.5%

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

   11. Simplified 77.5%

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

       1. expm1-log1p-u 75.3%

          \[\leadsto 1 + \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(\frac{\frac{-x}{z}}{t}\right)\right)} \]

       2. expm1-udef 75.3%

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

       3. add-cbrt-cube 74.6%

          \[\leadsto 1 + \left(e^{\mathsf{log1p}\left(\color{blue}{\sqrt[3]{\left(\frac{\frac{-x}{z}}{t} \cdot \frac{\frac{-x}{z}}{t}\right) \cdot \frac{\frac{-x}{z}}{t}}}\right)} - 1\right) \]

       4. add-cbrt-cube 75.3%

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

       5. frac-2neg 75.3%

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

       6. remove-double-neg 75.3%

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

       7. associate-/l/ 75.3%

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

       8. frac-2neg 75.3%

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

       9. add-sqr-sqrt 33.3%

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

       10. sqrt-unprod 67.0%

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

       11. sqr-neg 67.0%

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

       12. sqrt-unprod 40.7%

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

       13. add-sqr-sqrt 73.2%

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

       14. distribute-rgt-neg-out 73.2%

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

       15. remove-double-neg 73.2%

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

   13. Applied egg-rr 73.2%

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

       1. expm1-def 73.2%

          \[\leadsto 1 + \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(\frac{x}{t \cdot z}\right)\right)} \]

       2. expm1-log1p 75.5%

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

       3. *-commutative 75.5%

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

   15. Simplified 75.5%

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

   if -8.79999999999999984e-28 < z < 8.9999999999999997e-54

   1. Initial program 97.3%

      \[1 - \frac{x}{\left(y - z\right) \cdot \left(y - t\right)} \]
   2. Step-by-step derivation

      1. sub-neg 97.3%

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

      2. neg-mul-1 97.3%

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

      3. *-commutative 97.3%

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

      4. *-commutative 97.3%

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

      5. associate-/r* 97.2%

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

      6. associate-*r/ 97.2%

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

      7. metadata-eval 97.2%

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

      8. times-frac 97.2%

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

      9. *-lft-identity 97.2%

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

      10. neg-mul-1 97.2%

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

      11. sub-neg 97.2%

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

      12. +-commutative 97.2%

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

      13. distribute-neg-out 97.2%

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

      14. remove-double-neg 97.2%

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

      15. sub-neg 97.2%

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

   3. Simplified 97.2%

      \[\leadsto \color{blue}{1 + \frac{\frac{x}{z - y}}{y - t}} \]
   4. Add Preprocessing

   5. Taylor expanded in t around inf 74.6%

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

      1. associate-*r/ 74.6%

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

      2. neg-mul-1 74.6%

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

      3. associate-/r* 76.4%

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

   7. Simplified 76.4%

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

   8. Taylor expanded in z around 0 63.8%

      \[\leadsto 1 + \color{blue}{\frac{x}{t \cdot y}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 70.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -8.8 \cdot 10^{-28} \lor \neg \left(z \leq 9 \cdot 10^{-54}\right):\\ \;\;\;\;1 + \frac{x}{z \cdot t}\\ \mathbf{else}:\\ \;\;\;\;1 + \frac{x}{y \cdot t}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 73.0% accurate, 0.6× speedup

Math

\[\begin{array}{l} [x, y, z, t] = \mathsf{sort}([x, y, z, t])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -2 \cdot 10^{-71}:\\ \;\;\;\;1 + \frac{x}{z \cdot y}\\ \mathbf{elif}\;z \leq 2.7 \cdot 10^{-54}:\\ \;\;\;\;1 + \frac{x}{y \cdot t}\\ \mathbf{else}:\\ \;\;\;\;1 + \frac{x}{z \cdot t}\\ \end{array} \end{array} \]

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 -2e-71)
   (+ 1.0 (/ x (* z y)))
   (if (<= z 2.7e-54) (+ 1.0 (/ x (* y t))) (+ 1.0 (/ x (* z t))))))

C

assert(x < y && y < z && z < t);
double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -2e-71) {
		tmp = 1.0 + (x / (z * y));
	} else if (z <= 2.7e-54) {
		tmp = 1.0 + (x / (y * t));
	} else {
		tmp = 1.0 + (x / (z * t));
	}
	return tmp;
}

Fortran

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (z <= (-2d-71)) then
        tmp = 1.0d0 + (x / (z * y))
    else if (z <= 2.7d-54) then
        tmp = 1.0d0 + (x / (y * t))
    else
        tmp = 1.0d0 + (x / (z * t))
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t;
public static double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -2e-71) {
		tmp = 1.0 + (x / (z * y));
	} else if (z <= 2.7e-54) {
		tmp = 1.0 + (x / (y * t));
	} else {
		tmp = 1.0 + (x / (z * t));
	}
	return tmp;
}

Python

[x, y, z, t] = sort([x, y, z, t])
def code(x, y, z, t):
	tmp = 0
	if z <= -2e-71:
		tmp = 1.0 + (x / (z * y))
	elif z <= 2.7e-54:
		tmp = 1.0 + (x / (y * t))
	else:
		tmp = 1.0 + (x / (z * t))
	return tmp

Julia

x, y, z, t = sort([x, y, z, t])
function code(x, y, z, t)
	tmp = 0.0
	if (z <= -2e-71)
		tmp = Float64(1.0 + Float64(x / Float64(z * y)));
	elseif (z <= 2.7e-54)
		tmp = Float64(1.0 + Float64(x / Float64(y * t)));
	else
		tmp = Float64(1.0 + Float64(x / 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 <= -2e-71)
		tmp = 1.0 + (x / (z * y));
	elseif (z <= 2.7e-54)
		tmp = 1.0 + (x / (y * t));
	else
		tmp = 1.0 + (x / (z * t));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_] := If[LessEqual[z, -2e-71], N[(1.0 + N[(x / N[(z * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 2.7e-54], N[(1.0 + N[(x / N[(y * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(1.0 + N[(x / N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.9999999999999998e-71

   1. Initial program 100.0%

      \[1 - \frac{x}{\left(y - z\right) \cdot \left(y - t\right)} \]
   2. Step-by-step derivation

      1. sub-neg 100.0%

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

      2. neg-mul-1 100.0%

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

      3. *-commutative 100.0%

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

      4. *-commutative 100.0%

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

      5. associate-/r* 100.0%

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

      6. associate-*r/ 100.0%

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

      7. metadata-eval 100.0%

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

      8. times-frac 100.0%

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

      9. *-lft-identity 100.0%

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

      10. neg-mul-1 100.0%

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

      11. sub-neg 100.0%

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

      12. +-commutative 100.0%

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

      13. distribute-neg-out 100.0%

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

      14. remove-double-neg 100.0%

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

      15. sub-neg 100.0%

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

   3. Simplified 100.0%

      \[\leadsto \color{blue}{1 + \frac{\frac{x}{z - y}}{y - t}} \]
   4. Add Preprocessing

   5. Taylor expanded in z around inf 93.7%

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

      1. associate-/r* 93.6%

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

   7. Simplified 93.6%

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

   8. Taylor expanded in y around inf 78.4%

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

      1. *-commutative 78.4%

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

   10. Simplified 78.4%

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

   if -1.9999999999999998e-71 < z < 2.70000000000000026e-54

   1. Initial program 96.9%

      \[1 - \frac{x}{\left(y - z\right) \cdot \left(y - t\right)} \]
   2. Step-by-step derivation

      1. sub-neg 96.9%

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

      2. neg-mul-1 96.9%

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

      3. *-commutative 96.9%

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

      4. *-commutative 96.9%

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

      5. associate-/r* 96.8%

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

      6. associate-*r/ 96.8%

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

      7. metadata-eval 96.8%

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

      8. times-frac 96.8%

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

      9. *-lft-identity 96.8%

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

      10. neg-mul-1 96.8%

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

      11. sub-neg 96.8%

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

      12. +-commutative 96.8%

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

      13. distribute-neg-out 96.8%

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

      14. remove-double-neg 96.8%

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

      15. sub-neg 96.8%

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

   3. Simplified 96.8%

      \[\leadsto \color{blue}{1 + \frac{\frac{x}{z - y}}{y - t}} \]
   4. Add Preprocessing

   5. Taylor expanded in t around inf 73.7%

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

      1. associate-*r/ 73.7%

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

      2. neg-mul-1 73.7%

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

      3. associate-/r* 75.7%

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

   7. Simplified 75.7%

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

   8. Taylor expanded in z around 0 63.2%

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

   if 2.70000000000000026e-54 < z

   1. Initial program 99.9%

      \[1 - \frac{x}{\left(y - z\right) \cdot \left(y - t\right)} \]
   2. Step-by-step derivation

      1. sub-neg 99.9%

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

      2. neg-mul-1 99.9%

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

      3. *-commutative 99.9%

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

      4. *-commutative 99.9%

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

      5. associate-/r* 99.9%

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

      6. associate-*r/ 99.9%

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

      7. metadata-eval 99.9%

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

      8. times-frac 99.9%

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

      9. *-lft-identity 99.9%

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

      10. neg-mul-1 99.9%

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

      11. sub-neg 99.9%

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

      12. +-commutative 99.9%

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

      13. distribute-neg-out 99.9%

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

      14. remove-double-neg 99.9%

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

      15. sub-neg 99.9%

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

   3. Simplified 99.9%

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

      1. clear-num 99.9%

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

      2. inv-pow 99.9%

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

      3. div-inv 99.9%

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

      4. clear-num 99.9%

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

   6. Applied egg-rr 99.9%

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

      1. unpow-1 99.9%

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

      2. associate-/r* 99.9%

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

   8. Simplified 99.9%

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

   9. Taylor expanded in y around 0 78.5%

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

       1. mul-1-neg 78.5%

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

       2. associate-/l/ 78.5%

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

       3. distribute-neg-frac 78.5%

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

       4. distribute-neg-frac 78.5%

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

   11. Simplified 78.5%

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

       1. expm1-log1p-u 74.3%

          \[\leadsto 1 + \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(\frac{\frac{-x}{z}}{t}\right)\right)} \]

       2. expm1-udef 74.3%

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

       3. add-cbrt-cube 74.2%

          \[\leadsto 1 + \left(e^{\mathsf{log1p}\left(\color{blue}{\sqrt[3]{\left(\frac{\frac{-x}{z}}{t} \cdot \frac{\frac{-x}{z}}{t}\right) \cdot \frac{\frac{-x}{z}}{t}}}\right)} - 1\right) \]

       4. add-cbrt-cube 74.3%

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

       5. frac-2neg 74.3%

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

       6. remove-double-neg 74.3%

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

       7. associate-/l/ 74.3%

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

       8. frac-2neg 74.3%

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

       9. add-sqr-sqrt 33.9%

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

       10. sqrt-unprod 66.4%

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

       11. sqr-neg 66.4%

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

       12. sqrt-unprod 39.9%

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

       13. add-sqr-sqrt 73.7%

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

       14. distribute-rgt-neg-out 73.7%

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

       15. remove-double-neg 73.7%

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

   13. Applied egg-rr 73.7%

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

       1. expm1-def 73.7%

          \[\leadsto 1 + \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(\frac{x}{t \cdot z}\right)\right)} \]

       2. expm1-log1p 76.5%

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

       3. *-commutative 76.5%

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

   15. Simplified 76.5%

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

4. Final simplification 72.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2 \cdot 10^{-71}:\\ \;\;\;\;1 + \frac{x}{z \cdot y}\\ \mathbf{elif}\;z \leq 2.7 \cdot 10^{-54}:\\ \;\;\;\;1 + \frac{x}{y \cdot t}\\ \mathbf{else}:\\ \;\;\;\;1 + \frac{x}{z \cdot t}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 90.2% accurate, 0.8× speedup

Math

\[\begin{array}{l} [x, y, z, t] = \mathsf{sort}([x, y, z, t])\\ \\ \begin{array}{l} \mathbf{if}\;t \leq 9.8 \cdot 10^{-132}:\\ \;\;\;\;1 - \frac{x}{y \cdot \left(y - z\right)}\\ \mathbf{else}:\\ \;\;\;\;1 - \frac{\frac{x}{t}}{z - y}\\ \end{array} \end{array} \]

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 (<= t 9.8e-132) (- 1.0 (/ x (* y (- y z)))) (- 1.0 (/ (/ x t) (- z y)))))

C

assert(x < y && y < z && z < t);
double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= 9.8e-132) {
		tmp = 1.0 - (x / (y * (y - z)));
	} else {
		tmp = 1.0 - ((x / t) / (z - 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 (t <= 9.8d-132) then
        tmp = 1.0d0 - (x / (y * (y - z)))
    else
        tmp = 1.0d0 - ((x / t) / (z - 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 (t <= 9.8e-132) {
		tmp = 1.0 - (x / (y * (y - z)));
	} else {
		tmp = 1.0 - ((x / t) / (z - y));
	}
	return tmp;
}

Python

[x, y, z, t] = sort([x, y, z, t])
def code(x, y, z, t):
	tmp = 0
	if t <= 9.8e-132:
		tmp = 1.0 - (x / (y * (y - z)))
	else:
		tmp = 1.0 - ((x / t) / (z - y))
	return tmp

Julia

x, y, z, t = sort([x, y, z, t])
function code(x, y, z, t)
	tmp = 0.0
	if (t <= 9.8e-132)
		tmp = Float64(1.0 - Float64(x / Float64(y * Float64(y - z))));
	else
		tmp = Float64(1.0 - Float64(Float64(x / t) / Float64(z - 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 (t <= 9.8e-132)
		tmp = 1.0 - (x / (y * (y - z)));
	else
		tmp = 1.0 - ((x / t) / (z - 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[t, 9.8e-132], N[(1.0 - N[(x / N[(y * N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(1.0 - N[(N[(x / t), $MachinePrecision] / N[(z - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < 9.79999999999999961e-132

   1. Initial program 98.8%

      \[1 - \frac{x}{\left(y - z\right) \cdot \left(y - t\right)} \]
   2. Add Preprocessing

   3. Taylor expanded in t around 0 78.2%

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

   if 9.79999999999999961e-132 < t

   1. Initial program 98.8%

      \[1 - \frac{x}{\left(y - z\right) \cdot \left(y - t\right)} \]
   2. Step-by-step derivation

      1. sub-neg 98.8%

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

      2. neg-mul-1 98.8%

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

      3. *-commutative 98.8%

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

      4. *-commutative 98.8%

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

      5. associate-/r* 100.0%

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

      6. associate-*r/ 100.0%

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

      7. metadata-eval 100.0%

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

      8. times-frac 100.0%

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

      9. *-lft-identity 100.0%

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

      10. neg-mul-1 100.0%

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

      11. sub-neg 100.0%

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

      12. +-commutative 100.0%

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

      13. distribute-neg-out 100.0%

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

      14. remove-double-neg 100.0%

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

      15. sub-neg 100.0%

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

   3. Simplified 100.0%

      \[\leadsto \color{blue}{1 + \frac{\frac{x}{z - y}}{y - t}} \]
   4. Add Preprocessing

   5. Taylor expanded in t around inf 93.2%

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

      1. associate-*r/ 93.2%

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

      2. neg-mul-1 93.2%

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

      3. associate-/r* 94.3%

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

   7. Simplified 94.3%

      \[\leadsto 1 + \color{blue}{\frac{\frac{-x}{t}}{z - y}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 83.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq 9.8 \cdot 10^{-132}:\\ \;\;\;\;1 - \frac{x}{y \cdot \left(y - z\right)}\\ \mathbf{else}:\\ \;\;\;\;1 - \frac{\frac{x}{t}}{z - y}\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 58.0% accurate, 1.6× speedup

Math

\[\begin{array}{l} [x, y, z, t] = \mathsf{sort}([x, y, z, t])\\ \\ 1 + \frac{x}{y \cdot t} \end{array} \]

FPCore

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
(FPCore (x y z t) :precision binary64 (+ 1.0 (/ x (* y t))))

C

assert(x < y && y < z && z < t);
double code(double x, double y, double z, double t) {
	return 1.0 + (x / (y * t));
}

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 = 1.0d0 + (x / (y * t))
end function

Java

assert x < y && y < z && z < t;
public static double code(double x, double y, double z, double t) {
	return 1.0 + (x / (y * t));
}

Python

[x, y, z, t] = sort([x, y, z, t])
def code(x, y, z, t):
	return 1.0 + (x / (y * t))

Julia

x, y, z, t = sort([x, y, z, t])
function code(x, y, z, t)
	return Float64(1.0 + Float64(x / Float64(y * t)))
end

MATLAB

x, y, z, t = num2cell(sort([x, y, z, t])){:}
function tmp = code(x, y, z, t)
	tmp = 1.0 + (x / (y * t));
end

Wolfram

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_] := N[(1.0 + N[(x / N[(y * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 98.8%

   \[1 - \frac{x}{\left(y - z\right) \cdot \left(y - t\right)} \]
2. Step-by-step derivation

   1. sub-neg 98.8%

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

   2. neg-mul-1 98.8%

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

   3. *-commutative 98.8%

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

   4. *-commutative 98.8%

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

   5. associate-/r* 98.8%

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

   6. associate-*r/ 98.8%

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

   7. metadata-eval 98.8%

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

   8. times-frac 98.8%

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

   9. *-lft-identity 98.8%

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

   10. neg-mul-1 98.8%

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

   11. sub-neg 98.8%

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

   12. +-commutative 98.8%

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

   13. distribute-neg-out 98.8%

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

   14. remove-double-neg 98.8%

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

   15. sub-neg 98.8%

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

3. Simplified 98.8%

   \[\leadsto \color{blue}{1 + \frac{\frac{x}{z - y}}{y - t}} \]
4. Add Preprocessing

5. Taylor expanded in t around inf 78.3%

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

   1. associate-*r/ 78.3%

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

   2. neg-mul-1 78.3%

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

   3. associate-/r* 78.9%

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

7. Simplified 78.9%

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

8. Taylor expanded in z around 0 58.0%

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

9. Final simplification 58.0%

   \[\leadsto 1 + \frac{x}{y \cdot t} \]
10. Add Preprocessing

Reproduce

herbie shell --seed 2024031 
(FPCore (x y z t)
  :name "Data.Random.Distribution.Triangular:triangularCDF from random-fu-0.2.6.2, A"
  :precision binary64
  (- 1.0 (/ x (* (- y z) (- y t)))))