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

Percentage Accurate: 99.0% → 99.7%

Time: 7.9s

Alternatives: 13

Speedup: 1.0×

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: 99.0% 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: 99.7% accurate, 0.8× speedup

Math

\[\begin{array}{l} [z, t] = \mathsf{sort}([z, t])\\ \\ \begin{array}{l} \mathbf{if}\;t \leq 5.2 \cdot 10^{+70}:\\ \;\;\;\;1 + \frac{\frac{x}{z - y}}{y - t}\\ \mathbf{else}:\\ \;\;\;\;1 + \frac{\frac{x}{t}}{y - z}\\ \end{array} \end{array} \]

FPCore

NOTE: z and t should be sorted in increasing order before calling this function.
(FPCore (x y z t)
 :precision binary64
 (if (<= t 5.2e+70)
   (+ 1.0 (/ (/ x (- z y)) (- y t)))
   (+ 1.0 (/ (/ x t) (- y z)))))

C

assert(z < t);
double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= 5.2e+70) {
		tmp = 1.0 + ((x / (z - y)) / (y - t));
	} else {
		tmp = 1.0 + ((x / t) / (y - z));
	}
	return tmp;
}

Fortran

NOTE: 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 <= 5.2d+70) then
        tmp = 1.0d0 + ((x / (z - y)) / (y - t))
    else
        tmp = 1.0d0 + ((x / t) / (y - z))
    end if
    code = tmp
end function

Java

assert z < t;
public static double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= 5.2e+70) {
		tmp = 1.0 + ((x / (z - y)) / (y - t));
	} else {
		tmp = 1.0 + ((x / t) / (y - z));
	}
	return tmp;
}

Python

[z, t] = sort([z, t])
def code(x, y, z, t):
	tmp = 0
	if t <= 5.2e+70:
		tmp = 1.0 + ((x / (z - y)) / (y - t))
	else:
		tmp = 1.0 + ((x / t) / (y - z))
	return tmp

Julia

z, t = sort([z, t])
function code(x, y, z, t)
	tmp = 0.0
	if (t <= 5.2e+70)
		tmp = Float64(1.0 + Float64(Float64(x / Float64(z - y)) / Float64(y - t)));
	else
		tmp = Float64(1.0 + Float64(Float64(x / t) / Float64(y - z)));
	end
	return tmp
end

MATLAB

z, t = num2cell(sort([z, t])){:}
function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (t <= 5.2e+70)
		tmp = 1.0 + ((x / (z - y)) / (y - t));
	else
		tmp = 1.0 + ((x / t) / (y - z));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: z and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_] := If[LessEqual[t, 5.2e+70], N[(1.0 + N[(N[(x / N[(z - y), $MachinePrecision]), $MachinePrecision] / N[(y - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(1.0 + N[(N[(x / t), $MachinePrecision] / N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < 5.2000000000000001e70

   1. Initial program 98.5%

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

      1. sub-neg 98.5%

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

      2. distribute-frac-neg 98.5%

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

      3. *-lft-identity 98.5%

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

      4. associate-/r* 99.0%

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

      5. associate-*r/ 99.0%

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

      6. metadata-eval 99.0%

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

      7. times-frac 99.0%

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

      8. neg-mul-1 99.0%

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

      9. remove-double-neg 99.0%

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

      10. neg-mul-1 99.0%

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

      11. sub-neg 99.0%

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

      12. +-commutative 99.0%

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

      13. distribute-neg-out 99.0%

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

      14. remove-double-neg 99.0%

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

      15. sub-neg 99.0%

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

   3. Simplified 99.0%

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

   if 5.2000000000000001e70 < t

   1. Initial program 100.0%

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

   2. Taylor expanded in t around inf 100.0%

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

      1. mul-1-neg 100.0%

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

      2. associate-/r* 100.0%

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

      3. distribute-neg-frac 100.0%

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

      4. distribute-frac-neg 100.0%

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

   4. Simplified 100.0%

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

4. Final simplification 99.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq 5.2 \cdot 10^{+70}:\\ \;\;\;\;1 + \frac{\frac{x}{z - y}}{y - t}\\ \mathbf{else}:\\ \;\;\;\;1 + \frac{\frac{x}{t}}{y - z}\\ \end{array} \]

Alternative 2: 87.3% accurate, 0.8× speedup

Math

\[\begin{array}{l} [z, t] = \mathsf{sort}([z, t])\\ \\ \begin{array}{l} \mathbf{if}\;y \leq -5 \cdot 10^{-40}:\\ \;\;\;\;1 - \frac{\frac{x}{y}}{y}\\ \mathbf{elif}\;y \leq 4.6 \cdot 10^{+20}:\\ \;\;\;\;1 + \frac{x}{\left(y - t\right) \cdot z}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

NOTE: z and t should be sorted in increasing order before calling this function.
(FPCore (x y z t)
 :precision binary64
 (if (<= y -5e-40)
   (- 1.0 (/ (/ x y) y))
   (if (<= y 4.6e+20) (+ 1.0 (/ x (* (- y t) z))) 1.0)))

C

assert(z < t);
double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -5e-40) {
		tmp = 1.0 - ((x / y) / y);
	} else if (y <= 4.6e+20) {
		tmp = 1.0 + (x / ((y - t) * z));
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Fortran

NOTE: 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 (y <= (-5d-40)) then
        tmp = 1.0d0 - ((x / y) / y)
    else if (y <= 4.6d+20) then
        tmp = 1.0d0 + (x / ((y - t) * z))
    else
        tmp = 1.0d0
    end if
    code = tmp
end function

Java

assert z < t;
public static double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -5e-40) {
		tmp = 1.0 - ((x / y) / y);
	} else if (y <= 4.6e+20) {
		tmp = 1.0 + (x / ((y - t) * z));
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Python

[z, t] = sort([z, t])
def code(x, y, z, t):
	tmp = 0
	if y <= -5e-40:
		tmp = 1.0 - ((x / y) / y)
	elif y <= 4.6e+20:
		tmp = 1.0 + (x / ((y - t) * z))
	else:
		tmp = 1.0
	return tmp

Julia

z, t = sort([z, t])
function code(x, y, z, t)
	tmp = 0.0
	if (y <= -5e-40)
		tmp = Float64(1.0 - Float64(Float64(x / y) / y));
	elseif (y <= 4.6e+20)
		tmp = Float64(1.0 + Float64(x / Float64(Float64(y - t) * z)));
	else
		tmp = 1.0;
	end
	return tmp
end

MATLAB

z, t = num2cell(sort([z, t])){:}
function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= -5e-40)
		tmp = 1.0 - ((x / y) / y);
	elseif (y <= 4.6e+20)
		tmp = 1.0 + (x / ((y - t) * z));
	else
		tmp = 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: z and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_] := If[LessEqual[y, -5e-40], N[(1.0 - N[(N[(x / y), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 4.6e+20], N[(1.0 + N[(x / N[(N[(y - t), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], 1.0]]

Derivation

1. Split input into 3 regimes

2. if y < -4.99999999999999965e-40

   1. Initial program 100.0%

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

      1. clear-num 100.0%

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

      2. associate-/r/ 100.0%

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

      3. *-commutative 100.0%

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

      4. associate-/r* 100.0%

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

   3. Applied egg-rr 100.0%

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

   4. Taylor expanded in z around 0 97.2%

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

      1. associate-/r* 97.2%

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

   6. Simplified 97.2%

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

   7. Taylor expanded in y around inf 97.2%

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

   if -4.99999999999999965e-40 < y < 4.6e20

   1. Initial program 97.6%

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

      1. sub-neg 97.6%

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

      2. distribute-frac-neg 97.6%

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

      3. *-lft-identity 97.6%

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

      4. associate-/r* 98.5%

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

      5. associate-*r/ 98.5%

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

      6. metadata-eval 98.5%

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

      7. times-frac 98.5%

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

      8. neg-mul-1 98.5%

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

      9. remove-double-neg 98.5%

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

      10. neg-mul-1 98.5%

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

      11. sub-neg 98.5%

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

      12. +-commutative 98.5%

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

      13. distribute-neg-out 98.5%

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

      14. remove-double-neg 98.5%

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

      15. sub-neg 98.5%

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

   3. Simplified 98.5%

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

   4. Taylor expanded in z around inf 80.8%

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

   if 4.6e20 < y

   1. Initial program 100.0%

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

   2. Taylor expanded in y around 0 60.2%

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

      1. add-sqr-sqrt 36.3%

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

      2. sqrt-unprod 53.6%

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

      3. sqr-neg 53.6%

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

      4. sqrt-unprod 23.1%

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

      5. add-sqr-sqrt 59.0%

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

      6. distribute-frac-neg 59.0%

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

   4. Applied egg-rr 59.0%

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

   5. Taylor expanded in x around 0 98.0%

      \[\leadsto \color{blue}{1} \]
3. Recombined 3 regimes into one program.

4. Final simplification 88.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -5 \cdot 10^{-40}:\\ \;\;\;\;1 - \frac{\frac{x}{y}}{y}\\ \mathbf{elif}\;y \leq 4.6 \cdot 10^{+20}:\\ \;\;\;\;1 + \frac{x}{\left(y - t\right) \cdot z}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]

Alternative 3: 91.0% accurate, 0.8× speedup

Math

\[\begin{array}{l} [z, t] = \mathsf{sort}([z, t])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -1.36 \cdot 10^{-76}:\\ \;\;\;\;1 + \frac{x}{\left(y - t\right) \cdot z}\\ \mathbf{elif}\;z \leq 1.45 \cdot 10^{-177}:\\ \;\;\;\;1 - \frac{x}{y \cdot \left(y - t\right)}\\ \mathbf{else}:\\ \;\;\;\;1 + \frac{\frac{x}{y - t}}{z}\\ \end{array} \end{array} \]

FPCore

NOTE: z and t should be sorted in increasing order before calling this function.
(FPCore (x y z t)
 :precision binary64
 (if (<= z -1.36e-76)
   (+ 1.0 (/ x (* (- y t) z)))
   (if (<= z 1.45e-177)
     (- 1.0 (/ x (* y (- y t))))
     (+ 1.0 (/ (/ x (- y t)) z)))))

C

assert(z < t);
double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -1.36e-76) {
		tmp = 1.0 + (x / ((y - t) * z));
	} else if (z <= 1.45e-177) {
		tmp = 1.0 - (x / (y * (y - t)));
	} else {
		tmp = 1.0 + ((x / (y - t)) / z);
	}
	return tmp;
}

Fortran

NOTE: 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 <= (-1.36d-76)) then
        tmp = 1.0d0 + (x / ((y - t) * z))
    else if (z <= 1.45d-177) then
        tmp = 1.0d0 - (x / (y * (y - t)))
    else
        tmp = 1.0d0 + ((x / (y - t)) / z)
    end if
    code = tmp
end function

Java

assert z < t;
public static double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -1.36e-76) {
		tmp = 1.0 + (x / ((y - t) * z));
	} else if (z <= 1.45e-177) {
		tmp = 1.0 - (x / (y * (y - t)));
	} else {
		tmp = 1.0 + ((x / (y - t)) / z);
	}
	return tmp;
}

Python

[z, t] = sort([z, t])
def code(x, y, z, t):
	tmp = 0
	if z <= -1.36e-76:
		tmp = 1.0 + (x / ((y - t) * z))
	elif z <= 1.45e-177:
		tmp = 1.0 - (x / (y * (y - t)))
	else:
		tmp = 1.0 + ((x / (y - t)) / z)
	return tmp

Julia

z, t = sort([z, t])
function code(x, y, z, t)
	tmp = 0.0
	if (z <= -1.36e-76)
		tmp = Float64(1.0 + Float64(x / Float64(Float64(y - t) * z)));
	elseif (z <= 1.45e-177)
		tmp = Float64(1.0 - Float64(x / Float64(y * Float64(y - t))));
	else
		tmp = Float64(1.0 + Float64(Float64(x / Float64(y - t)) / z));
	end
	return tmp
end

MATLAB

z, t = num2cell(sort([z, t])){:}
function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (z <= -1.36e-76)
		tmp = 1.0 + (x / ((y - t) * z));
	elseif (z <= 1.45e-177)
		tmp = 1.0 - (x / (y * (y - t)));
	else
		tmp = 1.0 + ((x / (y - t)) / z);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: z and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_] := If[LessEqual[z, -1.36e-76], N[(1.0 + N[(x / N[(N[(y - t), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.45e-177], N[(1.0 - N[(x / N[(y * N[(y - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(1.0 + N[(N[(x / N[(y - t), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.35999999999999993e-76

   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. distribute-frac-neg 99.9%

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

      3. *-lft-identity 99.9%

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

      4. associate-/r* 100.0%

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

      5. associate-*r/ 100.0%

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

      6. metadata-eval 100.0%

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

      7. times-frac 100.0%

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

      8. neg-mul-1 100.0%

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

      9. remove-double-neg 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. Taylor expanded in z around inf 95.1%

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

   if -1.35999999999999993e-76 < z < 1.44999999999999999e-177

   1. Initial program 97.3%

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

   2. Taylor expanded in z around 0 87.1%

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

   if 1.44999999999999999e-177 < z

   1. Initial program 99.0%

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

      1. sub-neg 99.0%

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

      2. distribute-frac-neg 99.0%

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

      3. *-lft-identity 99.0%

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

      4. associate-/r* 99.0%

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

      5. associate-*r/ 99.0%

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

      6. metadata-eval 99.0%

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

      7. times-frac 99.0%

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

      8. neg-mul-1 99.0%

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

      9. remove-double-neg 99.0%

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

      10. neg-mul-1 99.0%

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

      11. sub-neg 99.0%

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

      12. +-commutative 99.0%

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

      13. distribute-neg-out 99.0%

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

      14. remove-double-neg 99.0%

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

      15. sub-neg 99.0%

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

   3. Simplified 99.0%

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

   4. Taylor expanded in z around inf 92.0%

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

   5. Taylor expanded in x around 0 91.1%

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

      1. associate-/r* 84.1%

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

   7. Simplified 84.1%

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

4. Final simplification 88.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.36 \cdot 10^{-76}:\\ \;\;\;\;1 + \frac{x}{\left(y - t\right) \cdot z}\\ \mathbf{elif}\;z \leq 1.45 \cdot 10^{-177}:\\ \;\;\;\;1 - \frac{x}{y \cdot \left(y - t\right)}\\ \mathbf{else}:\\ \;\;\;\;1 + \frac{\frac{x}{y - t}}{z}\\ \end{array} \]

Alternative 4: 91.4% accurate, 0.8× speedup

Math

\[\begin{array}{l} [z, t] = \mathsf{sort}([z, t])\\ \\ \begin{array}{l} t_1 := \frac{x}{y - t}\\ \mathbf{if}\;z \leq -1.36 \cdot 10^{-76}:\\ \;\;\;\;1 + \frac{x}{\left(y - t\right) \cdot z}\\ \mathbf{elif}\;z \leq 1.5 \cdot 10^{-177}:\\ \;\;\;\;1 - \frac{t_1}{y}\\ \mathbf{else}:\\ \;\;\;\;1 + \frac{t_1}{z}\\ \end{array} \end{array} \]

FPCore

NOTE: z and t should be sorted in increasing order before calling this function.
(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ x (- y t))))
   (if (<= z -1.36e-76)
     (+ 1.0 (/ x (* (- y t) z)))
     (if (<= z 1.5e-177) (- 1.0 (/ t_1 y)) (+ 1.0 (/ t_1 z))))))

C

assert(z < t);
double code(double x, double y, double z, double t) {
	double t_1 = x / (y - t);
	double tmp;
	if (z <= -1.36e-76) {
		tmp = 1.0 + (x / ((y - t) * z));
	} else if (z <= 1.5e-177) {
		tmp = 1.0 - (t_1 / y);
	} else {
		tmp = 1.0 + (t_1 / z);
	}
	return tmp;
}

Fortran

NOTE: z and t should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x / (y - t)
    if (z <= (-1.36d-76)) then
        tmp = 1.0d0 + (x / ((y - t) * z))
    else if (z <= 1.5d-177) then
        tmp = 1.0d0 - (t_1 / y)
    else
        tmp = 1.0d0 + (t_1 / z)
    end if
    code = tmp
end function

Java

assert z < t;
public static double code(double x, double y, double z, double t) {
	double t_1 = x / (y - t);
	double tmp;
	if (z <= -1.36e-76) {
		tmp = 1.0 + (x / ((y - t) * z));
	} else if (z <= 1.5e-177) {
		tmp = 1.0 - (t_1 / y);
	} else {
		tmp = 1.0 + (t_1 / z);
	}
	return tmp;
}

Python

[z, t] = sort([z, t])
def code(x, y, z, t):
	t_1 = x / (y - t)
	tmp = 0
	if z <= -1.36e-76:
		tmp = 1.0 + (x / ((y - t) * z))
	elif z <= 1.5e-177:
		tmp = 1.0 - (t_1 / y)
	else:
		tmp = 1.0 + (t_1 / z)
	return tmp

Julia

z, t = sort([z, t])
function code(x, y, z, t)
	t_1 = Float64(x / Float64(y - t))
	tmp = 0.0
	if (z <= -1.36e-76)
		tmp = Float64(1.0 + Float64(x / Float64(Float64(y - t) * z)));
	elseif (z <= 1.5e-177)
		tmp = Float64(1.0 - Float64(t_1 / y));
	else
		tmp = Float64(1.0 + Float64(t_1 / z));
	end
	return tmp
end

MATLAB

z, t = num2cell(sort([z, t])){:}
function tmp_2 = code(x, y, z, t)
	t_1 = x / (y - t);
	tmp = 0.0;
	if (z <= -1.36e-76)
		tmp = 1.0 + (x / ((y - t) * z));
	elseif (z <= 1.5e-177)
		tmp = 1.0 - (t_1 / y);
	else
		tmp = 1.0 + (t_1 / z);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: z and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x / N[(y - t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.36e-76], N[(1.0 + N[(x / N[(N[(y - t), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.5e-177], N[(1.0 - N[(t$95$1 / y), $MachinePrecision]), $MachinePrecision], N[(1.0 + N[(t$95$1 / z), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.35999999999999993e-76

   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. distribute-frac-neg 99.9%

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

      3. *-lft-identity 99.9%

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

      4. associate-/r* 100.0%

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

      5. associate-*r/ 100.0%

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

      6. metadata-eval 100.0%

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

      7. times-frac 100.0%

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

      8. neg-mul-1 100.0%

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

      9. remove-double-neg 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. Taylor expanded in z around inf 95.1%

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

   if -1.35999999999999993e-76 < z < 1.50000000000000004e-177

   1. Initial program 97.3%

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

      1. clear-num 97.3%

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

      2. associate-/r/ 97.3%

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

      3. *-commutative 97.3%

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

      4. associate-/r* 97.3%

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

   3. Applied egg-rr 97.3%

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

   4. Taylor expanded in z around 0 87.1%

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

      1. associate-/r* 88.4%

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

   6. Simplified 88.4%

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

   if 1.50000000000000004e-177 < z

   1. Initial program 99.0%

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

      1. sub-neg 99.0%

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

      2. distribute-frac-neg 99.0%

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

      3. *-lft-identity 99.0%

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

      4. associate-/r* 99.0%

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

      5. associate-*r/ 99.0%

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

      6. metadata-eval 99.0%

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

      7. times-frac 99.0%

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

      8. neg-mul-1 99.0%

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

      9. remove-double-neg 99.0%

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

      10. neg-mul-1 99.0%

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

      11. sub-neg 99.0%

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

      12. +-commutative 99.0%

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

      13. distribute-neg-out 99.0%

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

      14. remove-double-neg 99.0%

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

      15. sub-neg 99.0%

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

   3. Simplified 99.0%

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

   4. Taylor expanded in z around inf 92.0%

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

   5. Taylor expanded in x around 0 91.1%

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

      1. associate-/r* 84.1%

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

   7. Simplified 84.1%

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

4. Final simplification 88.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.36 \cdot 10^{-76}:\\ \;\;\;\;1 + \frac{x}{\left(y - t\right) \cdot z}\\ \mathbf{elif}\;z \leq 1.5 \cdot 10^{-177}:\\ \;\;\;\;1 - \frac{\frac{x}{y - t}}{y}\\ \mathbf{else}:\\ \;\;\;\;1 + \frac{\frac{x}{y - t}}{z}\\ \end{array} \]

Alternative 5: 92.3% accurate, 0.8× speedup

Math

\[\begin{array}{l} [z, t] = \mathsf{sort}([z, t])\\ \\ \begin{array}{l} \mathbf{if}\;t \leq -1 \cdot 10^{-261}:\\ \;\;\;\;1 + \frac{\frac{x}{z}}{y - t}\\ \mathbf{elif}\;t \leq 1.9 \cdot 10^{-73}:\\ \;\;\;\;1 - \frac{\frac{x}{y}}{y - z}\\ \mathbf{else}:\\ \;\;\;\;1 + \frac{\frac{x}{t}}{y - z}\\ \end{array} \end{array} \]

FPCore

NOTE: z and t should be sorted in increasing order before calling this function.
(FPCore (x y z t)
 :precision binary64
 (if (<= t -1e-261)
   (+ 1.0 (/ (/ x z) (- y t)))
   (if (<= t 1.9e-73)
     (- 1.0 (/ (/ x y) (- y z)))
     (+ 1.0 (/ (/ x t) (- y z))))))

C

assert(z < t);
double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= -1e-261) {
		tmp = 1.0 + ((x / z) / (y - t));
	} else if (t <= 1.9e-73) {
		tmp = 1.0 - ((x / y) / (y - z));
	} else {
		tmp = 1.0 + ((x / t) / (y - z));
	}
	return tmp;
}

Fortran

NOTE: 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 <= (-1d-261)) then
        tmp = 1.0d0 + ((x / z) / (y - t))
    else if (t <= 1.9d-73) then
        tmp = 1.0d0 - ((x / y) / (y - z))
    else
        tmp = 1.0d0 + ((x / t) / (y - z))
    end if
    code = tmp
end function

Java

assert z < t;
public static double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= -1e-261) {
		tmp = 1.0 + ((x / z) / (y - t));
	} else if (t <= 1.9e-73) {
		tmp = 1.0 - ((x / y) / (y - z));
	} else {
		tmp = 1.0 + ((x / t) / (y - z));
	}
	return tmp;
}

Python

[z, t] = sort([z, t])
def code(x, y, z, t):
	tmp = 0
	if t <= -1e-261:
		tmp = 1.0 + ((x / z) / (y - t))
	elif t <= 1.9e-73:
		tmp = 1.0 - ((x / y) / (y - z))
	else:
		tmp = 1.0 + ((x / t) / (y - z))
	return tmp

Julia

z, t = sort([z, t])
function code(x, y, z, t)
	tmp = 0.0
	if (t <= -1e-261)
		tmp = Float64(1.0 + Float64(Float64(x / z) / Float64(y - t)));
	elseif (t <= 1.9e-73)
		tmp = Float64(1.0 - Float64(Float64(x / y) / Float64(y - z)));
	else
		tmp = Float64(1.0 + Float64(Float64(x / t) / Float64(y - z)));
	end
	return tmp
end

MATLAB

z, t = num2cell(sort([z, t])){:}
function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (t <= -1e-261)
		tmp = 1.0 + ((x / z) / (y - t));
	elseif (t <= 1.9e-73)
		tmp = 1.0 - ((x / y) / (y - z));
	else
		tmp = 1.0 + ((x / t) / (y - z));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: z and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_] := If[LessEqual[t, -1e-261], N[(1.0 + N[(N[(x / z), $MachinePrecision] / N[(y - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.9e-73], N[(1.0 - N[(N[(x / y), $MachinePrecision] / N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(1.0 + N[(N[(x / t), $MachinePrecision] / N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -9.99999999999999984e-262

   1. Initial program 99.1%

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

      1. sub-neg 99.1%

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

      2. distribute-frac-neg 99.1%

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

      3. *-lft-identity 99.1%

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

      4. associate-/r* 98.5%

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

      5. associate-*r/ 98.5%

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

      6. metadata-eval 98.5%

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

      7. times-frac 98.5%

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

      8. neg-mul-1 98.5%

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

      9. remove-double-neg 98.5%

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

      10. neg-mul-1 98.5%

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

      11. sub-neg 98.5%

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

      12. +-commutative 98.5%

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

      13. distribute-neg-out 98.5%

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

      14. remove-double-neg 98.5%

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

      15. sub-neg 98.5%

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

   3. Simplified 98.5%

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

   4. Taylor expanded in z around inf 84.1%

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

   if -9.99999999999999984e-262 < t < 1.9000000000000001e-73

   1. Initial program 96.4%

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

      1. *-commutative 96.4%

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

      2. associate-/r* 92.9%

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

   3. Simplified 92.9%

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

   4. Taylor expanded in y around inf 87.5%

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

   if 1.9000000000000001e-73 < t

   1. Initial program 100.0%

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

   2. Taylor expanded in t around inf 99.6%

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

      1. mul-1-neg 99.6%

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

      2. associate-/r* 99.6%

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

      3. distribute-neg-frac 99.6%

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

      4. distribute-frac-neg 99.6%

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

   4. Simplified 99.6%

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

4. Final simplification 89.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1 \cdot 10^{-261}:\\ \;\;\;\;1 + \frac{\frac{x}{z}}{y - t}\\ \mathbf{elif}\;t \leq 1.9 \cdot 10^{-73}:\\ \;\;\;\;1 - \frac{\frac{x}{y}}{y - z}\\ \mathbf{else}:\\ \;\;\;\;1 + \frac{\frac{x}{t}}{y - z}\\ \end{array} \]

Alternative 6: 98.9% accurate, 0.8× speedup

Math

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

FPCore

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

C

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

Fortran

NOTE: 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 - (((1.0d0 / (y - t)) / (y - z)) * x)
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 98.7%

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

   1. clear-num 98.7%

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

   2. associate-/r/ 98.7%

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

   3. *-commutative 98.7%

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

   4. associate-/r* 98.7%

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

3. Applied egg-rr 98.7%

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

4. Final simplification 98.7%

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

Alternative 7: 83.7% accurate, 1.0× speedup

Math

\[\begin{array}{l} [z, t] = \mathsf{sort}([z, t])\\ \\ \begin{array}{l} \mathbf{if}\;y \leq -5 \cdot 10^{-45}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq 2.1 \cdot 10^{-99}:\\ \;\;\;\;1 - \frac{x}{t \cdot z}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

NOTE: z and t should be sorted in increasing order before calling this function.
(FPCore (x y z t)
 :precision binary64
 (if (<= y -5e-45) 1.0 (if (<= y 2.1e-99) (- 1.0 (/ x (* t z))) 1.0)))

C

assert(z < t);
double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -5e-45) {
		tmp = 1.0;
	} else if (y <= 2.1e-99) {
		tmp = 1.0 - (x / (t * z));
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Fortran

NOTE: 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 (y <= (-5d-45)) then
        tmp = 1.0d0
    else if (y <= 2.1d-99) then
        tmp = 1.0d0 - (x / (t * z))
    else
        tmp = 1.0d0
    end if
    code = tmp
end function

Java

assert z < t;
public static double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -5e-45) {
		tmp = 1.0;
	} else if (y <= 2.1e-99) {
		tmp = 1.0 - (x / (t * z));
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Python

[z, t] = sort([z, t])
def code(x, y, z, t):
	tmp = 0
	if y <= -5e-45:
		tmp = 1.0
	elif y <= 2.1e-99:
		tmp = 1.0 - (x / (t * z))
	else:
		tmp = 1.0
	return tmp

Julia

z, t = sort([z, t])
function code(x, y, z, t)
	tmp = 0.0
	if (y <= -5e-45)
		tmp = 1.0;
	elseif (y <= 2.1e-99)
		tmp = Float64(1.0 - Float64(x / Float64(t * z)));
	else
		tmp = 1.0;
	end
	return tmp
end

MATLAB

z, t = num2cell(sort([z, t])){:}
function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= -5e-45)
		tmp = 1.0;
	elseif (y <= 2.1e-99)
		tmp = 1.0 - (x / (t * z));
	else
		tmp = 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: z and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_] := If[LessEqual[y, -5e-45], 1.0, If[LessEqual[y, 2.1e-99], N[(1.0 - N[(x / N[(t * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], 1.0]]

Derivation

1. Split input into 2 regimes

2. if y < -4.99999999999999976e-45 or 2.09999999999999984e-99 < y

   1. Initial program 100.0%

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

   2. Taylor expanded in y around 0 57.1%

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

      1. add-sqr-sqrt 35.9%

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

      2. sqrt-unprod 51.3%

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

      3. sqr-neg 51.3%

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

      4. sqrt-unprod 20.1%

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

      5. add-sqr-sqrt 54.5%

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

      6. distribute-frac-neg 54.5%

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

   4. Applied egg-rr 54.5%

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

   5. Taylor expanded in x around 0 87.1%

      \[\leadsto \color{blue}{1} \]

   if -4.99999999999999976e-45 < y < 2.09999999999999984e-99

   1. Initial program 96.9%

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

   2. Taylor expanded in y around 0 73.5%

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

4. Final simplification 81.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -5 \cdot 10^{-45}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq 2.1 \cdot 10^{-99}:\\ \;\;\;\;1 - \frac{x}{t \cdot z}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]

Alternative 8: 82.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} [z, t] = \mathsf{sort}([z, t])\\ \\ \begin{array}{l} \mathbf{if}\;y \leq -2.25 \cdot 10^{-42}:\\ \;\;\;\;1 - \frac{x}{y \cdot y}\\ \mathbf{elif}\;y \leq 3.3 \cdot 10^{-100}:\\ \;\;\;\;1 - \frac{x}{t \cdot z}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

NOTE: z and t should be sorted in increasing order before calling this function.
(FPCore (x y z t)
 :precision binary64
 (if (<= y -2.25e-42)
   (- 1.0 (/ x (* y y)))
   (if (<= y 3.3e-100) (- 1.0 (/ x (* t z))) 1.0)))

C

assert(z < t);
double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -2.25e-42) {
		tmp = 1.0 - (x / (y * y));
	} else if (y <= 3.3e-100) {
		tmp = 1.0 - (x / (t * z));
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Fortran

NOTE: 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 (y <= (-2.25d-42)) then
        tmp = 1.0d0 - (x / (y * y))
    else if (y <= 3.3d-100) then
        tmp = 1.0d0 - (x / (t * z))
    else
        tmp = 1.0d0
    end if
    code = tmp
end function

Java

assert z < t;
public static double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -2.25e-42) {
		tmp = 1.0 - (x / (y * y));
	} else if (y <= 3.3e-100) {
		tmp = 1.0 - (x / (t * z));
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Python

[z, t] = sort([z, t])
def code(x, y, z, t):
	tmp = 0
	if y <= -2.25e-42:
		tmp = 1.0 - (x / (y * y))
	elif y <= 3.3e-100:
		tmp = 1.0 - (x / (t * z))
	else:
		tmp = 1.0
	return tmp

Julia

z, t = sort([z, t])
function code(x, y, z, t)
	tmp = 0.0
	if (y <= -2.25e-42)
		tmp = Float64(1.0 - Float64(x / Float64(y * y)));
	elseif (y <= 3.3e-100)
		tmp = Float64(1.0 - Float64(x / Float64(t * z)));
	else
		tmp = 1.0;
	end
	return tmp
end

MATLAB

z, t = num2cell(sort([z, t])){:}
function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= -2.25e-42)
		tmp = 1.0 - (x / (y * y));
	elseif (y <= 3.3e-100)
		tmp = 1.0 - (x / (t * z));
	else
		tmp = 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: z and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_] := If[LessEqual[y, -2.25e-42], N[(1.0 - N[(x / N[(y * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 3.3e-100], N[(1.0 - N[(x / N[(t * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], 1.0]]

Derivation

1. Split input into 3 regimes

2. if y < -2.25e-42

   1. Initial program 100.0%

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

   2. Taylor expanded in y around inf 97.2%

      \[\leadsto 1 - \color{blue}{\frac{x}{{y}^{2}}} \]
   3. Step-by-step derivation

      1. unpow2 97.2%

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

   4. Simplified 97.2%

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

   if -2.25e-42 < y < 3.29999999999999996e-100

   1. Initial program 96.9%

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

   2. Taylor expanded in y around 0 73.5%

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

   if 3.29999999999999996e-100 < y

   1. Initial program 99.9%

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

   2. Taylor expanded in y around 0 57.3%

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

      1. add-sqr-sqrt 34.5%

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

      2. sqrt-unprod 49.5%

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

      3. sqr-neg 49.5%

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

      4. sqrt-unprod 19.7%

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

      5. add-sqr-sqrt 52.9%

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

      6. distribute-frac-neg 52.9%

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

   4. Applied egg-rr 52.9%

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

   5. Taylor expanded in x around 0 81.7%

      \[\leadsto \color{blue}{1} \]
3. Recombined 3 regimes into one program.

4. Final simplification 82.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.25 \cdot 10^{-42}:\\ \;\;\;\;1 - \frac{x}{y \cdot y}\\ \mathbf{elif}\;y \leq 3.3 \cdot 10^{-100}:\\ \;\;\;\;1 - \frac{x}{t \cdot z}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]

Alternative 9: 82.7% accurate, 1.0× speedup

Math

\[\begin{array}{l} [z, t] = \mathsf{sort}([z, t])\\ \\ \begin{array}{l} \mathbf{if}\;y \leq -5.2 \cdot 10^{-39}:\\ \;\;\;\;1 - \frac{x}{y \cdot y}\\ \mathbf{elif}\;y \leq 1.55 \cdot 10^{-97}:\\ \;\;\;\;1 - \frac{\frac{x}{t}}{z}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

NOTE: z and t should be sorted in increasing order before calling this function.
(FPCore (x y z t)
 :precision binary64
 (if (<= y -5.2e-39)
   (- 1.0 (/ x (* y y)))
   (if (<= y 1.55e-97) (- 1.0 (/ (/ x t) z)) 1.0)))

C

assert(z < t);
double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -5.2e-39) {
		tmp = 1.0 - (x / (y * y));
	} else if (y <= 1.55e-97) {
		tmp = 1.0 - ((x / t) / z);
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Fortran

NOTE: 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 (y <= (-5.2d-39)) then
        tmp = 1.0d0 - (x / (y * y))
    else if (y <= 1.55d-97) then
        tmp = 1.0d0 - ((x / t) / z)
    else
        tmp = 1.0d0
    end if
    code = tmp
end function

Java

assert z < t;
public static double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -5.2e-39) {
		tmp = 1.0 - (x / (y * y));
	} else if (y <= 1.55e-97) {
		tmp = 1.0 - ((x / t) / z);
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Python

[z, t] = sort([z, t])
def code(x, y, z, t):
	tmp = 0
	if y <= -5.2e-39:
		tmp = 1.0 - (x / (y * y))
	elif y <= 1.55e-97:
		tmp = 1.0 - ((x / t) / z)
	else:
		tmp = 1.0
	return tmp

Julia

z, t = sort([z, t])
function code(x, y, z, t)
	tmp = 0.0
	if (y <= -5.2e-39)
		tmp = Float64(1.0 - Float64(x / Float64(y * y)));
	elseif (y <= 1.55e-97)
		tmp = Float64(1.0 - Float64(Float64(x / t) / z));
	else
		tmp = 1.0;
	end
	return tmp
end

MATLAB

z, t = num2cell(sort([z, t])){:}
function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= -5.2e-39)
		tmp = 1.0 - (x / (y * y));
	elseif (y <= 1.55e-97)
		tmp = 1.0 - ((x / t) / z);
	else
		tmp = 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: z and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_] := If[LessEqual[y, -5.2e-39], N[(1.0 - N[(x / N[(y * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.55e-97], N[(1.0 - N[(N[(x / t), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], 1.0]]

Derivation

1. Split input into 3 regimes

2. if y < -5.2e-39

   1. Initial program 100.0%

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

   2. Taylor expanded in y around inf 97.2%

      \[\leadsto 1 - \color{blue}{\frac{x}{{y}^{2}}} \]
   3. Step-by-step derivation

      1. unpow2 97.2%

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

   4. Simplified 97.2%

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

   if -5.2e-39 < y < 1.55000000000000001e-97

   1. Initial program 96.9%

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

      1. clear-num 96.9%

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

      2. associate-/r/ 97.0%

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

      3. *-commutative 97.0%

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

      4. associate-/r* 97.0%

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

   3. Applied egg-rr 97.0%

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

   4. Taylor expanded in y around 0 73.5%

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

      1. associate-/r* 73.5%

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

   6. Simplified 73.5%

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

      1. *-commutative 73.5%

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

      2. associate-*r/ 70.6%

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

      3. div-inv 70.7%

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

   8. Applied egg-rr 70.7%

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

   if 1.55000000000000001e-97 < y

   1. Initial program 99.9%

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

   2. Taylor expanded in y around 0 57.3%

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

      1. add-sqr-sqrt 34.5%

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

      2. sqrt-unprod 49.5%

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

      3. sqr-neg 49.5%

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

      4. sqrt-unprod 19.7%

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

      5. add-sqr-sqrt 52.9%

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

      6. distribute-frac-neg 52.9%

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

   4. Applied egg-rr 52.9%

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

   5. Taylor expanded in x around 0 81.7%

      \[\leadsto \color{blue}{1} \]
3. Recombined 3 regimes into one program.

4. Final simplification 81.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -5.2 \cdot 10^{-39}:\\ \;\;\;\;1 - \frac{x}{y \cdot y}\\ \mathbf{elif}\;y \leq 1.55 \cdot 10^{-97}:\\ \;\;\;\;1 - \frac{\frac{x}{t}}{z}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]

Alternative 10: 82.7% accurate, 1.0× speedup

Math

\[\begin{array}{l} [z, t] = \mathsf{sort}([z, t])\\ \\ \begin{array}{l} \mathbf{if}\;y \leq -5.5 \cdot 10^{-41}:\\ \;\;\;\;1 - \frac{\frac{x}{y}}{y}\\ \mathbf{elif}\;y \leq 3.8 \cdot 10^{-96}:\\ \;\;\;\;1 - \frac{\frac{x}{t}}{z}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

NOTE: z and t should be sorted in increasing order before calling this function.
(FPCore (x y z t)
 :precision binary64
 (if (<= y -5.5e-41)
   (- 1.0 (/ (/ x y) y))
   (if (<= y 3.8e-96) (- 1.0 (/ (/ x t) z)) 1.0)))

C

assert(z < t);
double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -5.5e-41) {
		tmp = 1.0 - ((x / y) / y);
	} else if (y <= 3.8e-96) {
		tmp = 1.0 - ((x / t) / z);
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Fortran

NOTE: 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 (y <= (-5.5d-41)) then
        tmp = 1.0d0 - ((x / y) / y)
    else if (y <= 3.8d-96) then
        tmp = 1.0d0 - ((x / t) / z)
    else
        tmp = 1.0d0
    end if
    code = tmp
end function

Java

assert z < t;
public static double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -5.5e-41) {
		tmp = 1.0 - ((x / y) / y);
	} else if (y <= 3.8e-96) {
		tmp = 1.0 - ((x / t) / z);
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Python

[z, t] = sort([z, t])
def code(x, y, z, t):
	tmp = 0
	if y <= -5.5e-41:
		tmp = 1.0 - ((x / y) / y)
	elif y <= 3.8e-96:
		tmp = 1.0 - ((x / t) / z)
	else:
		tmp = 1.0
	return tmp

Julia

z, t = sort([z, t])
function code(x, y, z, t)
	tmp = 0.0
	if (y <= -5.5e-41)
		tmp = Float64(1.0 - Float64(Float64(x / y) / y));
	elseif (y <= 3.8e-96)
		tmp = Float64(1.0 - Float64(Float64(x / t) / z));
	else
		tmp = 1.0;
	end
	return tmp
end

MATLAB

z, t = num2cell(sort([z, t])){:}
function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= -5.5e-41)
		tmp = 1.0 - ((x / y) / y);
	elseif (y <= 3.8e-96)
		tmp = 1.0 - ((x / t) / z);
	else
		tmp = 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: z and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_] := If[LessEqual[y, -5.5e-41], N[(1.0 - N[(N[(x / y), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 3.8e-96], N[(1.0 - N[(N[(x / t), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], 1.0]]

Derivation

1. Split input into 3 regimes

2. if y < -5.50000000000000022e-41

   1. Initial program 100.0%

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

      1. clear-num 100.0%

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

      2. associate-/r/ 100.0%

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

      3. *-commutative 100.0%

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

      4. associate-/r* 100.0%

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

   3. Applied egg-rr 100.0%

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

   4. Taylor expanded in z around 0 97.2%

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

      1. associate-/r* 97.2%

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

   6. Simplified 97.2%

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

   7. Taylor expanded in y around inf 97.2%

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

   if -5.50000000000000022e-41 < y < 3.8000000000000001e-96

   1. Initial program 96.9%

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

      1. clear-num 96.9%

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

      2. associate-/r/ 97.0%

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

      3. *-commutative 97.0%

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

      4. associate-/r* 97.0%

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

   3. Applied egg-rr 97.0%

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

   4. Taylor expanded in y around 0 73.5%

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

      1. associate-/r* 73.5%

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

   6. Simplified 73.5%

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

      1. *-commutative 73.5%

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

      2. associate-*r/ 70.6%

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

      3. div-inv 70.7%

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

   8. Applied egg-rr 70.7%

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

   if 3.8000000000000001e-96 < y

   1. Initial program 99.9%

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

   2. Taylor expanded in y around 0 57.3%

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

      1. add-sqr-sqrt 34.5%

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

      2. sqrt-unprod 49.5%

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

      3. sqr-neg 49.5%

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

      4. sqrt-unprod 19.7%

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

      5. add-sqr-sqrt 52.9%

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

      6. distribute-frac-neg 52.9%

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

   4. Applied egg-rr 52.9%

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

   5. Taylor expanded in x around 0 81.7%

      \[\leadsto \color{blue}{1} \]
3. Recombined 3 regimes into one program.

4. Final simplification 81.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -5.5 \cdot 10^{-41}:\\ \;\;\;\;1 - \frac{\frac{x}{y}}{y}\\ \mathbf{elif}\;y \leq 3.8 \cdot 10^{-96}:\\ \;\;\;\;1 - \frac{\frac{x}{t}}{z}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]

Alternative 11: 99.0% accurate, 1.0× speedup

Math

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

FPCore

NOTE: 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) (- y z)))))

C

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

Fortran

NOTE: 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) * (y - z)))
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 98.7%

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

2. Final simplification 98.7%

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

Alternative 12: 75.9% accurate, 1.2× speedup

Math

\[\begin{array}{l} [z, t] = \mathsf{sort}([z, t])\\ \\ \begin{array}{l} \mathbf{if}\;t \leq 9.2 \cdot 10^{-153}:\\ \;\;\;\;1 + \frac{x}{y \cdot z}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

NOTE: z and t should be sorted in increasing order before calling this function.
(FPCore (x y z t)
 :precision binary64
 (if (<= t 9.2e-153) (+ 1.0 (/ x (* y z))) 1.0))

C

assert(z < t);
double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= 9.2e-153) {
		tmp = 1.0 + (x / (y * z));
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Fortran

NOTE: 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 <= 9.2d-153) then
        tmp = 1.0d0 + (x / (y * z))
    else
        tmp = 1.0d0
    end if
    code = tmp
end function

Java

assert z < t;
public static double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= 9.2e-153) {
		tmp = 1.0 + (x / (y * z));
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Python

[z, t] = sort([z, t])
def code(x, y, z, t):
	tmp = 0
	if t <= 9.2e-153:
		tmp = 1.0 + (x / (y * z))
	else:
		tmp = 1.0
	return tmp

Julia

z, t = sort([z, t])
function code(x, y, z, t)
	tmp = 0.0
	if (t <= 9.2e-153)
		tmp = Float64(1.0 + Float64(x / Float64(y * z)));
	else
		tmp = 1.0;
	end
	return tmp
end

MATLAB

z, t = num2cell(sort([z, t])){:}
function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (t <= 9.2e-153)
		tmp = 1.0 + (x / (y * z));
	else
		tmp = 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: z and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_] := If[LessEqual[t, 9.2e-153], N[(1.0 + N[(x / N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], 1.0]

Derivation

1. Split input into 2 regimes

2. if t < 9.19999999999999988e-153

   1. Initial program 98.2%

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

      1. sub-neg 98.2%

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

      2. distribute-frac-neg 98.2%

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

      3. *-lft-identity 98.2%

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

      4. associate-/r* 98.8%

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

      5. associate-*r/ 98.8%

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

      6. metadata-eval 98.8%

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

      7. times-frac 98.8%

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

      8. neg-mul-1 98.8%

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

      9. remove-double-neg 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. Taylor expanded in z around inf 82.3%

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

   5. Taylor expanded in y around inf 61.1%

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

      1. *-commutative 61.1%

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

   7. Simplified 61.1%

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

   if 9.19999999999999988e-153 < t

   1. Initial program 99.9%

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

   2. Taylor expanded in y around 0 70.9%

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

      1. add-sqr-sqrt 38.3%

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

      2. sqrt-unprod 61.7%

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

      3. sqr-neg 61.7%

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

      4. sqrt-unprod 27.1%

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

      5. add-sqr-sqrt 61.5%

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

      6. distribute-frac-neg 61.5%

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

   4. Applied egg-rr 61.5%

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

   5. Taylor expanded in x around 0 84.5%

      \[\leadsto \color{blue}{1} \]
3. Recombined 2 regimes into one program.

4. Final simplification 68.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq 9.2 \cdot 10^{-153}:\\ \;\;\;\;1 + \frac{x}{y \cdot z}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]

Alternative 13: 75.3% accurate, 11.0× speedup

Math

\[\begin{array}{l} [z, t] = \mathsf{sort}([z, t])\\ \\ 1 \end{array} \]

FPCore

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

C

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

Fortran

NOTE: 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
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

NOTE: z and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_] := 1.0

Derivation

1. Initial program 98.7%

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

2. Taylor expanded in y around 0 63.6%

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

   1. add-sqr-sqrt 36.7%

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

   2. sqrt-unprod 52.1%

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

   3. sqr-neg 52.1%

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

   4. sqrt-unprod 21.1%

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

   5. add-sqr-sqrt 50.5%

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

   6. distribute-frac-neg 50.5%

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

4. Applied egg-rr 50.5%

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

5. Taylor expanded in x around 0 68.6%

   \[\leadsto \color{blue}{1} \]

6. Final simplification 68.6%

   \[\leadsto 1 \]

Reproduce

herbie shell --seed 2023309 
(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)))))