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

Percentage Accurate: 99.2% → 99.2%

Time: 11.4s

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: 99.2% 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: 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]

Derivation

1. Initial program 99.2%

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

2. Final simplification 99.2%

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

Alternative 2: 77.9% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.32 \cdot 10^{-150}:\\ \;\;\;\;1 + \frac{\frac{x}{z}}{y - t}\\ \mathbf{elif}\;z \leq -5.1 \cdot 10^{-291}:\\ \;\;\;\;1 - \frac{\frac{x}{y}}{y}\\ \mathbf{elif}\;z \leq 3.25 \cdot 10^{-124}:\\ \;\;\;\;1 + \frac{\frac{x}{t}}{y}\\ \mathbf{else}:\\ \;\;\;\;1 + \frac{-1}{z \cdot \frac{t}{x}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -2.32e-150)
   (+ 1.0 (/ (/ x z) (- y t)))
   (if (<= z -5.1e-291)
     (- 1.0 (/ (/ x y) y))
     (if (<= z 3.25e-124)
       (+ 1.0 (/ (/ x t) y))
       (+ 1.0 (/ -1.0 (* z (/ t x))))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -2.32e-150) {
		tmp = 1.0 + ((x / z) / (y - t));
	} else if (z <= -5.1e-291) {
		tmp = 1.0 - ((x / y) / y);
	} else if (z <= 3.25e-124) {
		tmp = 1.0 + ((x / t) / y);
	} else {
		tmp = 1.0 + (-1.0 / (z * (t / x)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (z <= (-2.32d-150)) then
        tmp = 1.0d0 + ((x / z) / (y - t))
    else if (z <= (-5.1d-291)) then
        tmp = 1.0d0 - ((x / y) / y)
    else if (z <= 3.25d-124) then
        tmp = 1.0d0 + ((x / t) / y)
    else
        tmp = 1.0d0 + ((-1.0d0) / (z * (t / x)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -2.32e-150) {
		tmp = 1.0 + ((x / z) / (y - t));
	} else if (z <= -5.1e-291) {
		tmp = 1.0 - ((x / y) / y);
	} else if (z <= 3.25e-124) {
		tmp = 1.0 + ((x / t) / y);
	} else {
		tmp = 1.0 + (-1.0 / (z * (t / x)));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -2.32e-150:
		tmp = 1.0 + ((x / z) / (y - t))
	elif z <= -5.1e-291:
		tmp = 1.0 - ((x / y) / y)
	elif z <= 3.25e-124:
		tmp = 1.0 + ((x / t) / y)
	else:
		tmp = 1.0 + (-1.0 / (z * (t / x)))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -2.32e-150)
		tmp = Float64(1.0 + Float64(Float64(x / z) / Float64(y - t)));
	elseif (z <= -5.1e-291)
		tmp = Float64(1.0 - Float64(Float64(x / y) / y));
	elseif (z <= 3.25e-124)
		tmp = Float64(1.0 + Float64(Float64(x / t) / y));
	else
		tmp = Float64(1.0 + Float64(-1.0 / Float64(z * Float64(t / x))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (z <= -2.32e-150)
		tmp = 1.0 + ((x / z) / (y - t));
	elseif (z <= -5.1e-291)
		tmp = 1.0 - ((x / y) / y);
	elseif (z <= 3.25e-124)
		tmp = 1.0 + ((x / t) / y);
	else
		tmp = 1.0 + (-1.0 / (z * (t / x)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -2.32e-150], N[(1.0 + N[(N[(x / z), $MachinePrecision] / N[(y - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -5.1e-291], N[(1.0 - N[(N[(x / y), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 3.25e-124], N[(1.0 + N[(N[(x / t), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], N[(1.0 + N[(-1.0 / N[(z * N[(t / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if z < -2.3200000000000001e-150

   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. distribute-frac-neg 100.0%

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

      3. *-lft-identity 100.0%

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

      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 96.4%

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

   if -2.3200000000000001e-150 < z < -5.1e-291

   1. Initial program 100.0%

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

      1. associate-/l/ 99.7%

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

      2. clear-num 99.8%

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

      3. inv-pow 99.8%

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

      4. div-inv 99.8%

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

      5. clear-num 99.9%

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

   3. Applied egg-rr 99.9%

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

      1. unpow-1 99.9%

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

   5. Simplified 99.9%

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

   6. Taylor expanded in z around 0 89.3%

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

      1. associate-/r* 89.1%

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

   8. Simplified 89.1%

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

   9. Taylor expanded in y around inf 68.6%

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

   if -5.1e-291 < z < 3.24999999999999994e-124

   1. Initial program 95.0%

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

      1. associate-/l/ 99.9%

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

      2. clear-num 99.8%

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

      3. inv-pow 99.8%

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

      4. div-inv 99.9%

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

      5. clear-num 99.9%

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

   3. Applied egg-rr 99.9%

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

      1. unpow-1 99.9%

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

   5. Simplified 99.9%

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

   6. Taylor expanded in z around 0 82.8%

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

      1. associate-/r* 85.3%

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

   8. Simplified 85.3%

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

   9. Taylor expanded in y around 0 68.0%

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

       1. associate-*r/ 68.0%

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

       2. neg-mul-1 68.0%

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

   11. Simplified 68.0%

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

   if 3.24999999999999994e-124 < z

   1. Initial program 99.8%

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

      1. associate-/l/ 98.7%

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

      2. clear-num 98.7%

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

      3. inv-pow 98.7%

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

      4. div-inv 98.7%

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

      5. clear-num 98.7%

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

   3. Applied egg-rr 98.7%

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

      1. unpow-1 98.7%

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

   5. Simplified 98.7%

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

   6. Taylor expanded in y around 0 69.5%

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

      1. *-commutative 69.5%

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

      2. associate-*r/ 68.3%

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

   8. Simplified 68.3%

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

4. Final simplification 79.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.32 \cdot 10^{-150}:\\ \;\;\;\;1 + \frac{\frac{x}{z}}{y - t}\\ \mathbf{elif}\;z \leq -5.1 \cdot 10^{-291}:\\ \;\;\;\;1 - \frac{\frac{x}{y}}{y}\\ \mathbf{elif}\;z \leq 3.25 \cdot 10^{-124}:\\ \;\;\;\;1 + \frac{\frac{x}{t}}{y}\\ \mathbf{else}:\\ \;\;\;\;1 + \frac{-1}{z \cdot \frac{t}{x}}\\ \end{array} \]

Alternative 3: 77.9% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.6 \cdot 10^{-150}:\\ \;\;\;\;1 + \frac{\frac{x}{z}}{y - t}\\ \mathbf{elif}\;z \leq -2.9 \cdot 10^{-294}:\\ \;\;\;\;1 + \frac{-1}{\frac{y \cdot y}{x}}\\ \mathbf{elif}\;z \leq 3.4 \cdot 10^{-124}:\\ \;\;\;\;1 + \frac{\frac{x}{t}}{y}\\ \mathbf{else}:\\ \;\;\;\;1 + \frac{-1}{z \cdot \frac{t}{x}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -1.6e-150)
   (+ 1.0 (/ (/ x z) (- y t)))
   (if (<= z -2.9e-294)
     (+ 1.0 (/ -1.0 (/ (* y y) x)))
     (if (<= z 3.4e-124)
       (+ 1.0 (/ (/ x t) y))
       (+ 1.0 (/ -1.0 (* z (/ t x))))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -1.6e-150) {
		tmp = 1.0 + ((x / z) / (y - t));
	} else if (z <= -2.9e-294) {
		tmp = 1.0 + (-1.0 / ((y * y) / x));
	} else if (z <= 3.4e-124) {
		tmp = 1.0 + ((x / t) / y);
	} else {
		tmp = 1.0 + (-1.0 / (z * (t / x)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (z <= (-1.6d-150)) then
        tmp = 1.0d0 + ((x / z) / (y - t))
    else if (z <= (-2.9d-294)) then
        tmp = 1.0d0 + ((-1.0d0) / ((y * y) / x))
    else if (z <= 3.4d-124) then
        tmp = 1.0d0 + ((x / t) / y)
    else
        tmp = 1.0d0 + ((-1.0d0) / (z * (t / x)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -1.6e-150) {
		tmp = 1.0 + ((x / z) / (y - t));
	} else if (z <= -2.9e-294) {
		tmp = 1.0 + (-1.0 / ((y * y) / x));
	} else if (z <= 3.4e-124) {
		tmp = 1.0 + ((x / t) / y);
	} else {
		tmp = 1.0 + (-1.0 / (z * (t / x)));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -1.6e-150:
		tmp = 1.0 + ((x / z) / (y - t))
	elif z <= -2.9e-294:
		tmp = 1.0 + (-1.0 / ((y * y) / x))
	elif z <= 3.4e-124:
		tmp = 1.0 + ((x / t) / y)
	else:
		tmp = 1.0 + (-1.0 / (z * (t / x)))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -1.6e-150)
		tmp = Float64(1.0 + Float64(Float64(x / z) / Float64(y - t)));
	elseif (z <= -2.9e-294)
		tmp = Float64(1.0 + Float64(-1.0 / Float64(Float64(y * y) / x)));
	elseif (z <= 3.4e-124)
		tmp = Float64(1.0 + Float64(Float64(x / t) / y));
	else
		tmp = Float64(1.0 + Float64(-1.0 / Float64(z * Float64(t / x))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (z <= -1.6e-150)
		tmp = 1.0 + ((x / z) / (y - t));
	elseif (z <= -2.9e-294)
		tmp = 1.0 + (-1.0 / ((y * y) / x));
	elseif (z <= 3.4e-124)
		tmp = 1.0 + ((x / t) / y);
	else
		tmp = 1.0 + (-1.0 / (z * (t / x)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -1.6e-150], N[(1.0 + N[(N[(x / z), $MachinePrecision] / N[(y - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -2.9e-294], N[(1.0 + N[(-1.0 / N[(N[(y * y), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 3.4e-124], N[(1.0 + N[(N[(x / t), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], N[(1.0 + N[(-1.0 / N[(z * N[(t / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if z < -1.5999999999999999e-150

   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. distribute-frac-neg 100.0%

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

      3. *-lft-identity 100.0%

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

      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 96.4%

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

   if -1.5999999999999999e-150 < z < -2.9000000000000001e-294

   1. Initial program 100.0%

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

      1. associate-/l/ 99.8%

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

      2. clear-num 99.8%

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

      3. inv-pow 99.8%

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

      4. div-inv 99.8%

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

      5. clear-num 99.9%

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

   3. Applied egg-rr 99.9%

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

      1. unpow-1 99.9%

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

   5. Simplified 99.9%

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

   6. Taylor expanded in y around inf 67.7%

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

      1. unpow2 67.7%

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

   8. Simplified 67.7%

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

   if -2.9000000000000001e-294 < z < 3.4000000000000001e-124

   1. Initial program 94.7%

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

      1. associate-/l/ 99.9%

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

      2. clear-num 99.8%

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

      3. inv-pow 99.8%

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

      4. div-inv 99.9%

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

      5. clear-num 99.9%

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

   3. Applied egg-rr 99.9%

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

      1. unpow-1 99.9%

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

   5. Simplified 99.9%

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

   6. Taylor expanded in z around 0 81.8%

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

      1. associate-/r* 84.5%

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

   8. Simplified 84.5%

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

   9. Taylor expanded in y around 0 68.9%

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

       1. associate-*r/ 68.9%

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

       2. neg-mul-1 68.9%

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

   11. Simplified 68.9%

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

   if 3.4000000000000001e-124 < z

   1. Initial program 99.8%

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

      1. associate-/l/ 98.7%

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

      2. clear-num 98.7%

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

      3. inv-pow 98.7%

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

      4. div-inv 98.7%

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

      5. clear-num 98.7%

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

   3. Applied egg-rr 98.7%

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

      1. unpow-1 98.7%

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

   5. Simplified 98.7%

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

   6. Taylor expanded in y around 0 69.5%

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

      1. *-commutative 69.5%

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

      2. associate-*r/ 68.3%

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

   8. Simplified 68.3%

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

4. Final simplification 79.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.6 \cdot 10^{-150}:\\ \;\;\;\;1 + \frac{\frac{x}{z}}{y - t}\\ \mathbf{elif}\;z \leq -2.9 \cdot 10^{-294}:\\ \;\;\;\;1 + \frac{-1}{\frac{y \cdot y}{x}}\\ \mathbf{elif}\;z \leq 3.4 \cdot 10^{-124}:\\ \;\;\;\;1 + \frac{\frac{x}{t}}{y}\\ \mathbf{else}:\\ \;\;\;\;1 + \frac{-1}{z \cdot \frac{t}{x}}\\ \end{array} \]

Alternative 4: 77.6% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -6.2 \cdot 10^{-65}:\\ \;\;\;\;1 + \frac{\frac{x}{z}}{y - t}\\ \mathbf{elif}\;z \leq -4.9 \cdot 10^{-290}:\\ \;\;\;\;1 - \frac{x}{y \cdot \left(y - z\right)}\\ \mathbf{elif}\;z \leq 1.65 \cdot 10^{-124}:\\ \;\;\;\;1 + \frac{\frac{x}{t}}{y}\\ \mathbf{else}:\\ \;\;\;\;1 + \frac{-1}{z \cdot \frac{t}{x}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -6.2e-65)
   (+ 1.0 (/ (/ x z) (- y t)))
   (if (<= z -4.9e-290)
     (- 1.0 (/ x (* y (- y z))))
     (if (<= z 1.65e-124)
       (+ 1.0 (/ (/ x t) y))
       (+ 1.0 (/ -1.0 (* z (/ t x))))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -6.2e-65) {
		tmp = 1.0 + ((x / z) / (y - t));
	} else if (z <= -4.9e-290) {
		tmp = 1.0 - (x / (y * (y - z)));
	} else if (z <= 1.65e-124) {
		tmp = 1.0 + ((x / t) / y);
	} else {
		tmp = 1.0 + (-1.0 / (z * (t / x)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (z <= (-6.2d-65)) then
        tmp = 1.0d0 + ((x / z) / (y - t))
    else if (z <= (-4.9d-290)) then
        tmp = 1.0d0 - (x / (y * (y - z)))
    else if (z <= 1.65d-124) then
        tmp = 1.0d0 + ((x / t) / y)
    else
        tmp = 1.0d0 + ((-1.0d0) / (z * (t / x)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -6.2e-65) {
		tmp = 1.0 + ((x / z) / (y - t));
	} else if (z <= -4.9e-290) {
		tmp = 1.0 - (x / (y * (y - z)));
	} else if (z <= 1.65e-124) {
		tmp = 1.0 + ((x / t) / y);
	} else {
		tmp = 1.0 + (-1.0 / (z * (t / x)));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -6.2e-65:
		tmp = 1.0 + ((x / z) / (y - t))
	elif z <= -4.9e-290:
		tmp = 1.0 - (x / (y * (y - z)))
	elif z <= 1.65e-124:
		tmp = 1.0 + ((x / t) / y)
	else:
		tmp = 1.0 + (-1.0 / (z * (t / x)))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -6.2e-65)
		tmp = Float64(1.0 + Float64(Float64(x / z) / Float64(y - t)));
	elseif (z <= -4.9e-290)
		tmp = Float64(1.0 - Float64(x / Float64(y * Float64(y - z))));
	elseif (z <= 1.65e-124)
		tmp = Float64(1.0 + Float64(Float64(x / t) / y));
	else
		tmp = Float64(1.0 + Float64(-1.0 / Float64(z * Float64(t / x))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (z <= -6.2e-65)
		tmp = 1.0 + ((x / z) / (y - t));
	elseif (z <= -4.9e-290)
		tmp = 1.0 - (x / (y * (y - z)));
	elseif (z <= 1.65e-124)
		tmp = 1.0 + ((x / t) / y);
	else
		tmp = 1.0 + (-1.0 / (z * (t / x)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -6.2e-65], N[(1.0 + N[(N[(x / z), $MachinePrecision] / N[(y - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -4.9e-290], N[(1.0 - N[(x / N[(y * N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.65e-124], N[(1.0 + N[(N[(x / t), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], N[(1.0 + N[(-1.0 / N[(z * N[(t / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if z < -6.20000000000000032e-65

   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. distribute-frac-neg 100.0%

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

      3. *-lft-identity 100.0%

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

      4. associate-/r* 99.9%

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

      5. associate-*r/ 99.9%

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

      6. metadata-eval 99.9%

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

      7. times-frac 99.9%

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

      8. neg-mul-1 99.9%

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

      9. remove-double-neg 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. Taylor expanded in z around inf 98.9%

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

   if -6.20000000000000032e-65 < z < -4.9000000000000001e-290

   1. Initial program 100.0%

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

   2. Taylor expanded in t around 0 71.6%

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

   if -4.9000000000000001e-290 < z < 1.64999999999999992e-124

   1. Initial program 95.0%

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

      1. associate-/l/ 99.9%

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

      2. clear-num 99.8%

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

      3. inv-pow 99.8%

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

      4. div-inv 99.9%

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

      5. clear-num 99.9%

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

   3. Applied egg-rr 99.9%

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

      1. unpow-1 99.9%

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

   5. Simplified 99.9%

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

   6. Taylor expanded in z around 0 82.8%

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

      1. associate-/r* 85.3%

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

   8. Simplified 85.3%

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

   9. Taylor expanded in y around 0 68.0%

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

       1. associate-*r/ 68.0%

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

       2. neg-mul-1 68.0%

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

   11. Simplified 68.0%

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

   if 1.64999999999999992e-124 < z

   1. Initial program 99.8%

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

      1. associate-/l/ 98.7%

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

      2. clear-num 98.7%

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

      3. inv-pow 98.7%

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

      4. div-inv 98.7%

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

      5. clear-num 98.7%

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

   3. Applied egg-rr 98.7%

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

      1. unpow-1 98.7%

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

   5. Simplified 98.7%

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

   6. Taylor expanded in y around 0 69.5%

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

      1. *-commutative 69.5%

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

      2. associate-*r/ 68.3%

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

   8. Simplified 68.3%

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

4. Final simplification 79.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -6.2 \cdot 10^{-65}:\\ \;\;\;\;1 + \frac{\frac{x}{z}}{y - t}\\ \mathbf{elif}\;z \leq -4.9 \cdot 10^{-290}:\\ \;\;\;\;1 - \frac{x}{y \cdot \left(y - z\right)}\\ \mathbf{elif}\;z \leq 1.65 \cdot 10^{-124}:\\ \;\;\;\;1 + \frac{\frac{x}{t}}{y}\\ \mathbf{else}:\\ \;\;\;\;1 + \frac{-1}{z \cdot \frac{t}{x}}\\ \end{array} \]

Alternative 5: 77.8% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.75 \cdot 10^{-150}:\\ \;\;\;\;1 + \frac{\frac{x}{z}}{y - t}\\ \mathbf{elif}\;z \leq -5 \cdot 10^{-290}:\\ \;\;\;\;1 - \frac{\frac{x}{y}}{y}\\ \mathbf{elif}\;z \leq 3.4 \cdot 10^{-124}:\\ \;\;\;\;1 + \frac{\frac{x}{t}}{y}\\ \mathbf{else}:\\ \;\;\;\;1 - \frac{\frac{x}{t}}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -1.75e-150)
   (+ 1.0 (/ (/ x z) (- y t)))
   (if (<= z -5e-290)
     (- 1.0 (/ (/ x y) y))
     (if (<= z 3.4e-124) (+ 1.0 (/ (/ x t) y)) (- 1.0 (/ (/ x t) z))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -1.75e-150) {
		tmp = 1.0 + ((x / z) / (y - t));
	} else if (z <= -5e-290) {
		tmp = 1.0 - ((x / y) / y);
	} else if (z <= 3.4e-124) {
		tmp = 1.0 + ((x / t) / y);
	} else {
		tmp = 1.0 - ((x / t) / z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (z <= (-1.75d-150)) then
        tmp = 1.0d0 + ((x / z) / (y - t))
    else if (z <= (-5d-290)) then
        tmp = 1.0d0 - ((x / y) / y)
    else if (z <= 3.4d-124) then
        tmp = 1.0d0 + ((x / t) / y)
    else
        tmp = 1.0d0 - ((x / t) / z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -1.75e-150) {
		tmp = 1.0 + ((x / z) / (y - t));
	} else if (z <= -5e-290) {
		tmp = 1.0 - ((x / y) / y);
	} else if (z <= 3.4e-124) {
		tmp = 1.0 + ((x / t) / y);
	} else {
		tmp = 1.0 - ((x / t) / z);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -1.75e-150:
		tmp = 1.0 + ((x / z) / (y - t))
	elif z <= -5e-290:
		tmp = 1.0 - ((x / y) / y)
	elif z <= 3.4e-124:
		tmp = 1.0 + ((x / t) / y)
	else:
		tmp = 1.0 - ((x / t) / z)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -1.75e-150)
		tmp = Float64(1.0 + Float64(Float64(x / z) / Float64(y - t)));
	elseif (z <= -5e-290)
		tmp = Float64(1.0 - Float64(Float64(x / y) / y));
	elseif (z <= 3.4e-124)
		tmp = Float64(1.0 + Float64(Float64(x / t) / y));
	else
		tmp = Float64(1.0 - Float64(Float64(x / t) / z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (z <= -1.75e-150)
		tmp = 1.0 + ((x / z) / (y - t));
	elseif (z <= -5e-290)
		tmp = 1.0 - ((x / y) / y);
	elseif (z <= 3.4e-124)
		tmp = 1.0 + ((x / t) / y);
	else
		tmp = 1.0 - ((x / t) / z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -1.75e-150], N[(1.0 + N[(N[(x / z), $MachinePrecision] / N[(y - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -5e-290], N[(1.0 - N[(N[(x / y), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 3.4e-124], 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 < -1.7499999999999999e-150

   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. distribute-frac-neg 100.0%

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

      3. *-lft-identity 100.0%

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

      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 96.4%

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

   if -1.7499999999999999e-150 < z < -5.0000000000000001e-290

   1. Initial program 100.0%

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

      1. associate-/l/ 99.7%

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

      2. clear-num 99.8%

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

      3. inv-pow 99.8%

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

      4. div-inv 99.8%

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

      5. clear-num 99.9%

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

   3. Applied egg-rr 99.9%

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

      1. unpow-1 99.9%

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

   5. Simplified 99.9%

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

   6. Taylor expanded in z around 0 89.3%

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

      1. associate-/r* 89.1%

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

   8. Simplified 89.1%

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

   9. Taylor expanded in y around inf 68.6%

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

   if -5.0000000000000001e-290 < z < 3.4000000000000001e-124

   1. Initial program 95.0%

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

      1. associate-/l/ 99.9%

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

      2. clear-num 99.8%

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

      3. inv-pow 99.8%

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

      4. div-inv 99.9%

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

      5. clear-num 99.9%

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

   3. Applied egg-rr 99.9%

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

      1. unpow-1 99.9%

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

   5. Simplified 99.9%

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

   6. Taylor expanded in z around 0 82.8%

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

      1. associate-/r* 85.3%

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

   8. Simplified 85.3%

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

   9. Taylor expanded in y around 0 68.0%

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

       1. associate-*r/ 68.0%

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

       2. neg-mul-1 68.0%

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

   11. Simplified 68.0%

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

   if 3.4000000000000001e-124 < z

   1. Initial program 99.8%

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

      1. associate-/l/ 98.7%

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

      2. clear-num 98.7%

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

      3. inv-pow 98.7%

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

      4. div-inv 98.7%

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

      5. clear-num 98.7%

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

   3. Applied egg-rr 98.7%

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

      1. unpow-1 98.7%

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

   5. Simplified 98.7%

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

   6. Taylor expanded in y around 0 69.5%

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

      1. associate-/r* 68.4%

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

   8. Simplified 68.4%

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

4. Final simplification 79.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.75 \cdot 10^{-150}:\\ \;\;\;\;1 + \frac{\frac{x}{z}}{y - t}\\ \mathbf{elif}\;z \leq -5 \cdot 10^{-290}:\\ \;\;\;\;1 - \frac{\frac{x}{y}}{y}\\ \mathbf{elif}\;z \leq 3.4 \cdot 10^{-124}:\\ \;\;\;\;1 + \frac{\frac{x}{t}}{y}\\ \mathbf{else}:\\ \;\;\;\;1 - \frac{\frac{x}{t}}{z}\\ \end{array} \]

Alternative 6: 84.2% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.9 \cdot 10^{-90}:\\ \;\;\;\;1 + \frac{\frac{x}{z}}{y - t}\\ \mathbf{elif}\;z \leq 3.4 \cdot 10^{-124}:\\ \;\;\;\;1 - \frac{x}{y \cdot \left(y - t\right)}\\ \mathbf{else}:\\ \;\;\;\;1 + \frac{-1}{z \cdot \frac{t}{x}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -2.9e-90)
   (+ 1.0 (/ (/ x z) (- y t)))
   (if (<= z 3.4e-124)
     (- 1.0 (/ x (* y (- y t))))
     (+ 1.0 (/ -1.0 (* z (/ t x)))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -2.9e-90) {
		tmp = 1.0 + ((x / z) / (y - t));
	} else if (z <= 3.4e-124) {
		tmp = 1.0 - (x / (y * (y - t)));
	} else {
		tmp = 1.0 + (-1.0 / (z * (t / x)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (z <= (-2.9d-90)) then
        tmp = 1.0d0 + ((x / z) / (y - t))
    else if (z <= 3.4d-124) then
        tmp = 1.0d0 - (x / (y * (y - t)))
    else
        tmp = 1.0d0 + ((-1.0d0) / (z * (t / x)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -2.9e-90) {
		tmp = 1.0 + ((x / z) / (y - t));
	} else if (z <= 3.4e-124) {
		tmp = 1.0 - (x / (y * (y - t)));
	} else {
		tmp = 1.0 + (-1.0 / (z * (t / x)));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -2.9e-90:
		tmp = 1.0 + ((x / z) / (y - t))
	elif z <= 3.4e-124:
		tmp = 1.0 - (x / (y * (y - t)))
	else:
		tmp = 1.0 + (-1.0 / (z * (t / x)))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -2.9e-90)
		tmp = Float64(1.0 + Float64(Float64(x / z) / Float64(y - t)));
	elseif (z <= 3.4e-124)
		tmp = Float64(1.0 - Float64(x / Float64(y * Float64(y - t))));
	else
		tmp = Float64(1.0 + Float64(-1.0 / Float64(z * Float64(t / x))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (z <= -2.9e-90)
		tmp = 1.0 + ((x / z) / (y - t));
	elseif (z <= 3.4e-124)
		tmp = 1.0 - (x / (y * (y - t)));
	else
		tmp = 1.0 + (-1.0 / (z * (t / x)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -2.9e-90], N[(1.0 + N[(N[(x / z), $MachinePrecision] / N[(y - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 3.4e-124], N[(1.0 - N[(x / N[(y * N[(y - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(1.0 + N[(-1.0 / N[(z * N[(t / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -2.89999999999999983e-90

   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. distribute-frac-neg 100.0%

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

      3. *-lft-identity 100.0%

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

      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 98.2%

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

   if -2.89999999999999983e-90 < z < 3.4000000000000001e-124

   1. Initial program 97.5%

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

   2. Taylor expanded in z around 0 86.4%

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

   if 3.4000000000000001e-124 < z

   1. Initial program 99.8%

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

      1. associate-/l/ 98.7%

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

      2. clear-num 98.7%

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

      3. inv-pow 98.7%

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

      4. div-inv 98.7%

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

      5. clear-num 98.7%

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

   3. Applied egg-rr 98.7%

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

      1. unpow-1 98.7%

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

   5. Simplified 98.7%

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

   6. Taylor expanded in y around 0 69.5%

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

      1. *-commutative 69.5%

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

      2. associate-*r/ 68.3%

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

   8. Simplified 68.3%

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

4. Final simplification 85.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.9 \cdot 10^{-90}:\\ \;\;\;\;1 + \frac{\frac{x}{z}}{y - t}\\ \mathbf{elif}\;z \leq 3.4 \cdot 10^{-124}:\\ \;\;\;\;1 - \frac{x}{y \cdot \left(y - t\right)}\\ \mathbf{else}:\\ \;\;\;\;1 + \frac{-1}{z \cdot \frac{t}{x}}\\ \end{array} \]

Alternative 7: 84.4% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.15 \cdot 10^{-94}:\\ \;\;\;\;1 + \frac{\frac{x}{z}}{y - t}\\ \mathbf{elif}\;z \leq 3.7 \cdot 10^{-125}:\\ \;\;\;\;1 - \frac{\frac{x}{y - t}}{y}\\ \mathbf{else}:\\ \;\;\;\;1 + \frac{-1}{z \cdot \frac{t}{x}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -1.15e-94)
   (+ 1.0 (/ (/ x z) (- y t)))
   (if (<= z 3.7e-125)
     (- 1.0 (/ (/ x (- y t)) y))
     (+ 1.0 (/ -1.0 (* z (/ t x)))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -1.15e-94) {
		tmp = 1.0 + ((x / z) / (y - t));
	} else if (z <= 3.7e-125) {
		tmp = 1.0 - ((x / (y - t)) / y);
	} else {
		tmp = 1.0 + (-1.0 / (z * (t / x)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (z <= (-1.15d-94)) then
        tmp = 1.0d0 + ((x / z) / (y - t))
    else if (z <= 3.7d-125) then
        tmp = 1.0d0 - ((x / (y - t)) / y)
    else
        tmp = 1.0d0 + ((-1.0d0) / (z * (t / x)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -1.15e-94) {
		tmp = 1.0 + ((x / z) / (y - t));
	} else if (z <= 3.7e-125) {
		tmp = 1.0 - ((x / (y - t)) / y);
	} else {
		tmp = 1.0 + (-1.0 / (z * (t / x)));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -1.15e-94:
		tmp = 1.0 + ((x / z) / (y - t))
	elif z <= 3.7e-125:
		tmp = 1.0 - ((x / (y - t)) / y)
	else:
		tmp = 1.0 + (-1.0 / (z * (t / x)))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -1.15e-94)
		tmp = Float64(1.0 + Float64(Float64(x / z) / Float64(y - t)));
	elseif (z <= 3.7e-125)
		tmp = Float64(1.0 - Float64(Float64(x / Float64(y - t)) / y));
	else
		tmp = Float64(1.0 + Float64(-1.0 / Float64(z * Float64(t / x))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (z <= -1.15e-94)
		tmp = 1.0 + ((x / z) / (y - t));
	elseif (z <= 3.7e-125)
		tmp = 1.0 - ((x / (y - t)) / y);
	else
		tmp = 1.0 + (-1.0 / (z * (t / x)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -1.15e-94], N[(1.0 + N[(N[(x / z), $MachinePrecision] / N[(y - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 3.7e-125], N[(1.0 - N[(N[(x / N[(y - t), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], N[(1.0 + N[(-1.0 / N[(z * N[(t / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.15e-94

   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. distribute-frac-neg 100.0%

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

      3. *-lft-identity 100.0%

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

      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 98.2%

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

   if -1.15e-94 < z < 3.6999999999999999e-125

   1. Initial program 97.5%

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

      1. associate-/l/ 99.8%

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

      2. clear-num 99.8%

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

      3. inv-pow 99.8%

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

      4. div-inv 99.8%

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

      5. clear-num 99.9%

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

   3. Applied egg-rr 99.9%

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

      1. unpow-1 99.9%

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

   5. Simplified 99.9%

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

   6. Taylor expanded in z around 0 86.4%

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

      1. associate-/r* 87.6%

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

   8. Simplified 87.6%

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

   if 3.6999999999999999e-125 < z

   1. Initial program 99.8%

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

      1. associate-/l/ 98.7%

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

      2. clear-num 98.7%

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

      3. inv-pow 98.7%

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

      4. div-inv 98.7%

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

      5. clear-num 98.7%

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

   3. Applied egg-rr 98.7%

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

      1. unpow-1 98.7%

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

   5. Simplified 98.7%

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

   6. Taylor expanded in y around 0 69.5%

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

      1. *-commutative 69.5%

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

      2. associate-*r/ 68.3%

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

   8. Simplified 68.3%

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

4. Final simplification 85.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.15 \cdot 10^{-94}:\\ \;\;\;\;1 + \frac{\frac{x}{z}}{y - t}\\ \mathbf{elif}\;z \leq 3.7 \cdot 10^{-125}:\\ \;\;\;\;1 - \frac{\frac{x}{y - t}}{y}\\ \mathbf{else}:\\ \;\;\;\;1 + \frac{-1}{z \cdot \frac{t}{x}}\\ \end{array} \]

Alternative 8: 86.7% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.2 \cdot 10^{-191}:\\ \;\;\;\;1 + \frac{\frac{x}{z}}{y - t}\\ \mathbf{elif}\;t \leq 1.12 \cdot 10^{-63}:\\ \;\;\;\;1 - \frac{x}{y \cdot \left(y - z\right)}\\ \mathbf{else}:\\ \;\;\;\;1 + \frac{\frac{x}{t}}{y - z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= t -1.2e-191)
   (+ 1.0 (/ (/ x z) (- y t)))
   (if (<= t 1.12e-63)
     (- 1.0 (/ x (* y (- y z))))
     (+ 1.0 (/ (/ x t) (- y z))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= -1.2e-191) {
		tmp = 1.0 + ((x / z) / (y - t));
	} else if (t <= 1.12e-63) {
		tmp = 1.0 - (x / (y * (y - z)));
	} else {
		tmp = 1.0 + ((x / t) / (y - z));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (t <= (-1.2d-191)) then
        tmp = 1.0d0 + ((x / z) / (y - t))
    else if (t <= 1.12d-63) then
        tmp = 1.0d0 - (x / (y * (y - z)))
    else
        tmp = 1.0d0 + ((x / t) / (y - z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= -1.2e-191) {
		tmp = 1.0 + ((x / z) / (y - t));
	} else if (t <= 1.12e-63) {
		tmp = 1.0 - (x / (y * (y - z)));
	} else {
		tmp = 1.0 + ((x / t) / (y - z));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if t <= -1.2e-191:
		tmp = 1.0 + ((x / z) / (y - t))
	elif t <= 1.12e-63:
		tmp = 1.0 - (x / (y * (y - z)))
	else:
		tmp = 1.0 + ((x / t) / (y - z))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (t <= -1.2e-191)
		tmp = Float64(1.0 + Float64(Float64(x / z) / Float64(y - t)));
	elseif (t <= 1.12e-63)
		tmp = Float64(1.0 - Float64(x / Float64(y * Float64(y - z))));
	else
		tmp = Float64(1.0 + Float64(Float64(x / t) / Float64(y - z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (t <= -1.2e-191)
		tmp = 1.0 + ((x / z) / (y - t));
	elseif (t <= 1.12e-63)
		tmp = 1.0 - (x / (y * (y - z)));
	else
		tmp = 1.0 + ((x / t) / (y - z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[t, -1.2e-191], N[(1.0 + N[(N[(x / z), $MachinePrecision] / N[(y - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.12e-63], N[(1.0 - N[(x / N[(y * N[(y - z), $MachinePrecision]), $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 < -1.2e-191

   1. Initial program 98.9%

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

      1. sub-neg 98.9%

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

      2. distribute-frac-neg 98.9%

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

      3. *-lft-identity 98.9%

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

      4. associate-/r* 95.8%

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

      5. associate-*r/ 95.8%

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

      6. metadata-eval 95.8%

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

      7. times-frac 95.8%

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

      8. neg-mul-1 95.8%

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

      9. remove-double-neg 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. Taylor expanded in z around inf 79.0%

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

   if -1.2e-191 < t < 1.12000000000000002e-63

   1. Initial program 98.7%

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

   2. Taylor expanded in t around 0 89.6%

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

   if 1.12000000000000002e-63 < t

   1. Initial program 99.9%

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

   2. Taylor expanded in t around inf 98.8%

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

      1. mul-1-neg 98.8%

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

      2. associate-/r* 98.8%

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

      3. distribute-neg-frac 98.8%

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

      4. distribute-frac-neg 98.8%

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

   4. Simplified 98.8%

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

4. Final simplification 88.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.2 \cdot 10^{-191}:\\ \;\;\;\;1 + \frac{\frac{x}{z}}{y - t}\\ \mathbf{elif}\;t \leq 1.12 \cdot 10^{-63}:\\ \;\;\;\;1 - \frac{x}{y \cdot \left(y - z\right)}\\ \mathbf{else}:\\ \;\;\;\;1 + \frac{\frac{x}{t}}{y - z}\\ \end{array} \]

Alternative 9: 71.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -4.6 \cdot 10^{-75} \lor \neg \left(t \leq 8 \cdot 10^{-43}\right):\\ \;\;\;\;1 - \frac{x}{z \cdot t}\\ \mathbf{else}:\\ \;\;\;\;1 + \frac{x}{y \cdot z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= t -4.6e-75) (not (<= t 8e-43)))
   (- 1.0 (/ x (* z t)))
   (+ 1.0 (/ x (* y z)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((t <= -4.6e-75) || !(t <= 8e-43)) {
		tmp = 1.0 - (x / (z * t));
	} else {
		tmp = 1.0 + (x / (y * z));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((t <= (-4.6d-75)) .or. (.not. (t <= 8d-43))) then
        tmp = 1.0d0 - (x / (z * t))
    else
        tmp = 1.0d0 + (x / (y * z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((t <= -4.6e-75) || !(t <= 8e-43)) {
		tmp = 1.0 - (x / (z * t));
	} else {
		tmp = 1.0 + (x / (y * z));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (t <= -4.6e-75) or not (t <= 8e-43):
		tmp = 1.0 - (x / (z * t))
	else:
		tmp = 1.0 + (x / (y * z))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((t <= -4.6e-75) || !(t <= 8e-43))
		tmp = Float64(1.0 - Float64(x / Float64(z * t)));
	else
		tmp = Float64(1.0 + Float64(x / Float64(y * z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((t <= -4.6e-75) || ~((t <= 8e-43)))
		tmp = 1.0 - (x / (z * t));
	else
		tmp = 1.0 + (x / (y * z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[t, -4.6e-75], N[Not[LessEqual[t, 8e-43]], $MachinePrecision]], N[(1.0 - N[(x / N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(1.0 + N[(x / N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -4.6e-75 or 8.00000000000000062e-43 < 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 80.8%

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

   if -4.6e-75 < t < 8.00000000000000062e-43

   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* 99.9%

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

      5. associate-*r/ 99.9%

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

      6. metadata-eval 99.9%

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

      7. times-frac 99.9%

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

      8. neg-mul-1 99.9%

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

      9. remove-double-neg 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. Taylor expanded in z around inf 73.5%

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

   5. Taylor expanded in y around inf 66.2%

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

4. Final simplification 74.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -4.6 \cdot 10^{-75} \lor \neg \left(t \leq 8 \cdot 10^{-43}\right):\\ \;\;\;\;1 - \frac{x}{z \cdot t}\\ \mathbf{else}:\\ \;\;\;\;1 + \frac{x}{y \cdot z}\\ \end{array} \]

Alternative 10: 83.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -3.5 \cdot 10^{-54} \lor \neg \left(y \leq 9.6 \cdot 10^{-29}\right):\\ \;\;\;\;1 - \frac{x}{y \cdot y}\\ \mathbf{else}:\\ \;\;\;\;1 - \frac{x}{z \cdot t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= y -3.5e-54) (not (<= y 9.6e-29)))
   (- 1.0 (/ x (* y y)))
   (- 1.0 (/ x (* z t)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -3.5e-54) || !(y <= 9.6e-29)) {
		tmp = 1.0 - (x / (y * y));
	} else {
		tmp = 1.0 - (x / (z * t));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((y <= (-3.5d-54)) .or. (.not. (y <= 9.6d-29))) then
        tmp = 1.0d0 - (x / (y * y))
    else
        tmp = 1.0d0 - (x / (z * t))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -3.5e-54) || !(y <= 9.6e-29)) {
		tmp = 1.0 - (x / (y * y));
	} else {
		tmp = 1.0 - (x / (z * t));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (y <= -3.5e-54) or not (y <= 9.6e-29):
		tmp = 1.0 - (x / (y * y))
	else:
		tmp = 1.0 - (x / (z * t))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((y <= -3.5e-54) || !(y <= 9.6e-29))
		tmp = Float64(1.0 - Float64(x / Float64(y * y)));
	else
		tmp = Float64(1.0 - Float64(x / Float64(z * t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((y <= -3.5e-54) || ~((y <= 9.6e-29)))
		tmp = 1.0 - (x / (y * y));
	else
		tmp = 1.0 - (x / (z * t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[y, -3.5e-54], N[Not[LessEqual[y, 9.6e-29]], $MachinePrecision]], N[(1.0 - N[(x / N[(y * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(1.0 - N[(x / N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -3.49999999999999982e-54 or 9.59999999999999968e-29 < y

   1. Initial program 99.9%

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

   2. Taylor expanded in y around inf 89.1%

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

      1. unpow2 89.1%

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

   4. Simplified 89.1%

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

   if -3.49999999999999982e-54 < y < 9.59999999999999968e-29

   1. Initial program 98.2%

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

   2. Taylor expanded in y around 0 74.7%

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

4. Final simplification 82.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.5 \cdot 10^{-54} \lor \neg \left(y \leq 9.6 \cdot 10^{-29}\right):\\ \;\;\;\;1 - \frac{x}{y \cdot y}\\ \mathbf{else}:\\ \;\;\;\;1 - \frac{x}{z \cdot t}\\ \end{array} \]

Alternative 11: 83.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -3.2 \cdot 10^{-53}:\\ \;\;\;\;1 - \frac{x}{y \cdot y}\\ \mathbf{elif}\;y \leq 1.85 \cdot 10^{-28}:\\ \;\;\;\;1 - \frac{x}{z \cdot t}\\ \mathbf{else}:\\ \;\;\;\;1 - \frac{\frac{x}{y}}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -3.2e-53)
   (- 1.0 (/ x (* y y)))
   (if (<= y 1.85e-28) (- 1.0 (/ x (* z t))) (- 1.0 (/ (/ x y) y)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -3.2e-53) {
		tmp = 1.0 - (x / (y * y));
	} else if (y <= 1.85e-28) {
		tmp = 1.0 - (x / (z * t));
	} else {
		tmp = 1.0 - ((x / y) / y);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (y <= (-3.2d-53)) then
        tmp = 1.0d0 - (x / (y * y))
    else if (y <= 1.85d-28) then
        tmp = 1.0d0 - (x / (z * t))
    else
        tmp = 1.0d0 - ((x / y) / y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -3.2e-53) {
		tmp = 1.0 - (x / (y * y));
	} else if (y <= 1.85e-28) {
		tmp = 1.0 - (x / (z * t));
	} else {
		tmp = 1.0 - ((x / y) / y);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -3.2e-53:
		tmp = 1.0 - (x / (y * y))
	elif y <= 1.85e-28:
		tmp = 1.0 - (x / (z * t))
	else:
		tmp = 1.0 - ((x / y) / y)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -3.2e-53)
		tmp = Float64(1.0 - Float64(x / Float64(y * y)));
	elseif (y <= 1.85e-28)
		tmp = Float64(1.0 - Float64(x / Float64(z * t)));
	else
		tmp = Float64(1.0 - Float64(Float64(x / y) / y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= -3.2e-53)
		tmp = 1.0 - (x / (y * y));
	elseif (y <= 1.85e-28)
		tmp = 1.0 - (x / (z * t));
	else
		tmp = 1.0 - ((x / y) / y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -3.2e-53], N[(1.0 - N[(x / N[(y * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.85e-28], N[(1.0 - N[(x / N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(1.0 - N[(N[(x / y), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -3.2000000000000001e-53

   1. Initial program 100.0%

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

   2. Taylor expanded in y around inf 88.7%

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

      1. unpow2 88.7%

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

   4. Simplified 88.7%

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

   if -3.2000000000000001e-53 < y < 1.8500000000000001e-28

   1. Initial program 98.2%

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

   2. Taylor expanded in y around 0 74.7%

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

   if 1.8500000000000001e-28 < y

   1. Initial program 99.9%

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

      1. associate-/l/ 100.0%

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

      2. clear-num 100.0%

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

      3. inv-pow 100.0%

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

      4. div-inv 99.9%

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

      5. clear-num 100.0%

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

   3. Applied egg-rr 100.0%

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

      1. unpow-1 100.0%

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

   5. Simplified 100.0%

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

   6. Taylor expanded in z around 0 97.3%

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

      1. associate-/r* 97.3%

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

   8. Simplified 97.3%

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

   9. Taylor expanded in y around inf 89.5%

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

4. Final simplification 82.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.2 \cdot 10^{-53}:\\ \;\;\;\;1 - \frac{x}{y \cdot y}\\ \mathbf{elif}\;y \leq 1.85 \cdot 10^{-28}:\\ \;\;\;\;1 - \frac{x}{z \cdot t}\\ \mathbf{else}:\\ \;\;\;\;1 - \frac{\frac{x}{y}}{y}\\ \end{array} \]

Alternative 12: 98.6% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ 1 + \frac{\frac{x}{z - y}}{y - t} \end{array} \]

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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 99.2%

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

   1. sub-neg 99.2%

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

   2. distribute-frac-neg 99.2%

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

   3. *-lft-identity 99.2%

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

   4. associate-/r* 97.7%

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

   5. associate-*r/ 97.7%

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

   6. metadata-eval 97.7%

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

   7. times-frac 97.7%

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

   8. neg-mul-1 97.7%

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

   9. remove-double-neg 97.7%

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

   10. neg-mul-1 97.7%

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

   11. sub-neg 97.7%

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

   12. +-commutative 97.7%

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

   13. distribute-neg-out 97.7%

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

   14. remove-double-neg 97.7%

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

   15. sub-neg 97.7%

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

3. Simplified 97.7%

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

4. Final simplification 97.7%

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

Alternative 13: 57.9% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ 1 + \frac{x}{y \cdot z} \end{array} \]

FPCore

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

C

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

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))
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.2%

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

   1. sub-neg 99.2%

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

   2. distribute-frac-neg 99.2%

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

   3. *-lft-identity 99.2%

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

   4. associate-/r* 97.7%

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

   5. associate-*r/ 97.7%

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

   6. metadata-eval 97.7%

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

   7. times-frac 97.7%

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

   8. neg-mul-1 97.7%

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

   9. remove-double-neg 97.7%

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

   10. neg-mul-1 97.7%

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

   11. sub-neg 97.7%

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

   12. +-commutative 97.7%

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

   13. distribute-neg-out 97.7%

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

   14. remove-double-neg 97.7%

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

   15. sub-neg 97.7%

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

3. Simplified 97.7%

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

4. Taylor expanded in z around inf 78.0%

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

5. Taylor expanded in y around inf 59.0%

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

6. Final simplification 59.0%

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

Reproduce

herbie shell --seed 2023274 
(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)))))