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

Percentage Accurate: 99.1% → 98.5%

Time: 8.7s

Alternatives: 10

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: 99.1% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    code = 1.0d0 - (x / ((y - z) * (y - t)))
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 98.5% accurate, 0.1× speedup

Math

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

FPCore

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

C

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

Fortran

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    code = 1.0d0 - (((y - z) * ((y - t) / x)) ** (-1.0d0))
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.2%

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

   1. clear-num 99.1%

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

   2. inv-pow 99.1%

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

   3. associate-/l* 98.9%

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

4. Applied egg-rr 98.9%

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

5. Final simplification 98.9%

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

Alternative 2: 84.8% accurate, 0.6× speedup

Math

\[\begin{array}{l} [x, y, z, t] = \mathsf{sort}([x, y, z, t])\\ \\ \begin{array}{l} \mathbf{if}\;y \leq -4.4 \cdot 10^{-58} \lor \neg \left(y \leq 5.2 \cdot 10^{-34}\right):\\ \;\;\;\;1 + \frac{x}{y \cdot \left(t - y\right)}\\ \mathbf{else}:\\ \;\;\;\;1 - \frac{\frac{x}{z}}{t}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
(FPCore (x y z t)
 :precision binary64
 (if (or (<= y -4.4e-58) (not (<= y 5.2e-34)))
   (+ 1.0 (/ x (* y (- t y))))
   (- 1.0 (/ (/ x z) t))))

C

assert(x < y && y < z && z < t);
double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -4.4e-58) || !(y <= 5.2e-34)) {
		tmp = 1.0 + (x / (y * (t - y)));
	} else {
		tmp = 1.0 - ((x / z) / t);
	}
	return tmp;
}

Fortran

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((y <= (-4.4d-58)) .or. (.not. (y <= 5.2d-34))) then
        tmp = 1.0d0 + (x / (y * (t - y)))
    else
        tmp = 1.0d0 - ((x / z) / t)
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t;
public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -4.4e-58) || !(y <= 5.2e-34)) {
		tmp = 1.0 + (x / (y * (t - y)));
	} else {
		tmp = 1.0 - ((x / z) / t);
	}
	return tmp;
}

Python

[x, y, z, t] = sort([x, y, z, t])
def code(x, y, z, t):
	tmp = 0
	if (y <= -4.4e-58) or not (y <= 5.2e-34):
		tmp = 1.0 + (x / (y * (t - y)))
	else:
		tmp = 1.0 - ((x / z) / t)
	return tmp

Julia

x, y, z, t = sort([x, y, z, t])
function code(x, y, z, t)
	tmp = 0.0
	if ((y <= -4.4e-58) || !(y <= 5.2e-34))
		tmp = Float64(1.0 + Float64(x / Float64(y * Float64(t - y))));
	else
		tmp = Float64(1.0 - Float64(Float64(x / z) / t));
	end
	return tmp
end

MATLAB

x, y, z, t = num2cell(sort([x, y, z, t])){:}
function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((y <= -4.4e-58) || ~((y <= 5.2e-34)))
		tmp = 1.0 + (x / (y * (t - y)));
	else
		tmp = 1.0 - ((x / z) / t);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_] := If[Or[LessEqual[y, -4.4e-58], N[Not[LessEqual[y, 5.2e-34]], $MachinePrecision]], N[(1.0 + N[(x / N[(y * N[(t - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(1.0 - N[(N[(x / z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -4.40000000000000011e-58 or 5.1999999999999999e-34 < y

   1. Initial program 99.9%

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

   3. Taylor expanded in z around 0 91.6%

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

   if -4.40000000000000011e-58 < y < 5.1999999999999999e-34

   1. Initial program 98.1%

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

      1. clear-num 98.1%

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

      2. inv-pow 98.1%

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

      3. associate-/l* 97.5%

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

   4. Applied egg-rr 97.5%

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

   5. Taylor expanded in y around 0 81.2%

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

      1. *-commutative 81.2%

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

      2. associate-/r* 81.3%

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

   7. Simplified 81.3%

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

4. Final simplification 87.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4.4 \cdot 10^{-58} \lor \neg \left(y \leq 5.2 \cdot 10^{-34}\right):\\ \;\;\;\;1 + \frac{x}{y \cdot \left(t - y\right)}\\ \mathbf{else}:\\ \;\;\;\;1 - \frac{\frac{x}{z}}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 83.4% accurate, 0.6× speedup

Math

\[\begin{array}{l} [x, y, z, t] = \mathsf{sort}([x, y, z, t])\\ \\ \begin{array}{l} \mathbf{if}\;y \leq -2.6 \cdot 10^{-64}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq 5.5 \cdot 10^{-33}:\\ \;\;\;\;1 - \frac{x}{z \cdot t}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
(FPCore (x y z t)
 :precision binary64
 (if (<= y -2.6e-64) 1.0 (if (<= y 5.5e-33) (- 1.0 (/ x (* z t))) 1.0)))

C

assert(x < y && y < z && z < t);
double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -2.6e-64) {
		tmp = 1.0;
	} else if (y <= 5.5e-33) {
		tmp = 1.0 - (x / (z * t));
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (y <= (-2.6d-64)) then
        tmp = 1.0d0
    else if (y <= 5.5d-33) then
        tmp = 1.0d0 - (x / (z * t))
    else
        tmp = 1.0d0
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t;
public static double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -2.6e-64) {
		tmp = 1.0;
	} else if (y <= 5.5e-33) {
		tmp = 1.0 - (x / (z * t));
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Python

[x, y, z, t] = sort([x, y, z, t])
def code(x, y, z, t):
	tmp = 0
	if y <= -2.6e-64:
		tmp = 1.0
	elif y <= 5.5e-33:
		tmp = 1.0 - (x / (z * t))
	else:
		tmp = 1.0
	return tmp

Julia

x, y, z, t = sort([x, y, z, t])
function code(x, y, z, t)
	tmp = 0.0
	if (y <= -2.6e-64)
		tmp = 1.0;
	elseif (y <= 5.5e-33)
		tmp = Float64(1.0 - Float64(x / Float64(z * t)));
	else
		tmp = 1.0;
	end
	return tmp
end

MATLAB

x, y, z, t = num2cell(sort([x, y, z, t])){:}
function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= -2.6e-64)
		tmp = 1.0;
	elseif (y <= 5.5e-33)
		tmp = 1.0 - (x / (z * t));
	else
		tmp = 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_] := If[LessEqual[y, -2.6e-64], 1.0, If[LessEqual[y, 5.5e-33], N[(1.0 - N[(x / N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], 1.0]]

Derivation

1. Split input into 2 regimes

2. if y < -2.6e-64 or 5.5e-33 < y

   1. Initial program 99.9%

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

   3. Taylor expanded in y around 0 55.9%

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

      1. associate-/r* 55.9%

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

      2. div-inv 55.9%

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

   5. Applied egg-rr 55.9%

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

      1. *-commutative 55.9%

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

      2. frac-2neg 55.9%

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

      3. associate-*r/ 55.9%

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

      4. add-sqr-sqrt 27.3%

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

      5. sqrt-unprod 55.2%

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

      6. sqr-neg 55.2%

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

      7. sqrt-unprod 27.5%

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

      8. add-sqr-sqrt 54.5%

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

      9. associate-/r/ 54.5%

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

      10. clear-num 54.5%

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

   7. Applied egg-rr 54.5%

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

   8. Taylor expanded in x around 0 86.3%

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

   if -2.6e-64 < y < 5.5e-33

   1. Initial program 98.1%

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

   3. Taylor expanded in y around 0 81.6%

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

4. Final simplification 84.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.6 \cdot 10^{-64}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq 5.5 \cdot 10^{-33}:\\ \;\;\;\;1 - \frac{x}{z \cdot t}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 82.8% accurate, 0.6× speedup

Math

\[\begin{array}{l} [x, y, z, t] = \mathsf{sort}([x, y, z, t])\\ \\ \begin{array}{l} \mathbf{if}\;y \leq -3.9 \cdot 10^{-64}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq 5.5 \cdot 10^{-34}:\\ \;\;\;\;1 - \frac{\frac{x}{z}}{t}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
(FPCore (x y z t)
 :precision binary64
 (if (<= y -3.9e-64) 1.0 (if (<= y 5.5e-34) (- 1.0 (/ (/ x z) t)) 1.0)))

C

assert(x < y && y < z && z < t);
double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -3.9e-64) {
		tmp = 1.0;
	} else if (y <= 5.5e-34) {
		tmp = 1.0 - ((x / z) / t);
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (y <= (-3.9d-64)) then
        tmp = 1.0d0
    else if (y <= 5.5d-34) then
        tmp = 1.0d0 - ((x / z) / t)
    else
        tmp = 1.0d0
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t;
public static double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -3.9e-64) {
		tmp = 1.0;
	} else if (y <= 5.5e-34) {
		tmp = 1.0 - ((x / z) / t);
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Python

[x, y, z, t] = sort([x, y, z, t])
def code(x, y, z, t):
	tmp = 0
	if y <= -3.9e-64:
		tmp = 1.0
	elif y <= 5.5e-34:
		tmp = 1.0 - ((x / z) / t)
	else:
		tmp = 1.0
	return tmp

Julia

x, y, z, t = sort([x, y, z, t])
function code(x, y, z, t)
	tmp = 0.0
	if (y <= -3.9e-64)
		tmp = 1.0;
	elseif (y <= 5.5e-34)
		tmp = Float64(1.0 - Float64(Float64(x / z) / t));
	else
		tmp = 1.0;
	end
	return tmp
end

MATLAB

x, y, z, t = num2cell(sort([x, y, z, t])){:}
function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= -3.9e-64)
		tmp = 1.0;
	elseif (y <= 5.5e-34)
		tmp = 1.0 - ((x / z) / t);
	else
		tmp = 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_] := If[LessEqual[y, -3.9e-64], 1.0, If[LessEqual[y, 5.5e-34], N[(1.0 - N[(N[(x / z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision], 1.0]]

Derivation

1. Split input into 2 regimes

2. if y < -3.8999999999999997e-64 or 5.50000000000000014e-34 < y

   1. Initial program 99.9%

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

   3. Taylor expanded in y around 0 55.9%

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

      1. associate-/r* 55.9%

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

      2. div-inv 55.9%

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

   5. Applied egg-rr 55.9%

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

      1. *-commutative 55.9%

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

      2. frac-2neg 55.9%

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

      3. associate-*r/ 55.9%

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

      4. add-sqr-sqrt 27.3%

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

      5. sqrt-unprod 55.2%

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

      6. sqr-neg 55.2%

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

      7. sqrt-unprod 27.5%

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

      8. add-sqr-sqrt 54.5%

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

      9. associate-/r/ 54.5%

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

      10. clear-num 54.5%

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

   7. Applied egg-rr 54.5%

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

   8. Taylor expanded in x around 0 86.3%

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

   if -3.8999999999999997e-64 < y < 5.50000000000000014e-34

   1. Initial program 98.1%

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

      1. clear-num 98.0%

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

      2. inv-pow 98.0%

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

      3. associate-/l* 97.4%

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

   4. Applied egg-rr 97.4%

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

   5. Taylor expanded in y around 0 81.6%

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

      1. *-commutative 81.6%

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

      2. associate-/r* 81.7%

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

   7. Simplified 81.7%

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

4. Final simplification 84.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.9 \cdot 10^{-64}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq 5.5 \cdot 10^{-34}:\\ \;\;\;\;1 - \frac{\frac{x}{z}}{t}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 89.7% accurate, 0.7× speedup

Math

\[\begin{array}{l} [x, y, z, t] = \mathsf{sort}([x, y, z, t])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -9 \cdot 10^{-43}:\\ \;\;\;\;1 - \frac{x}{z \cdot \left(t - y\right)}\\ \mathbf{else}:\\ \;\;\;\;1 + \frac{1}{\frac{y}{x} \cdot \left(t - y\right)}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
(FPCore (x y z t)
 :precision binary64
 (if (<= z -9e-43)
   (- 1.0 (/ x (* z (- t y))))
   (+ 1.0 (/ 1.0 (* (/ y x) (- t y))))))

C

assert(x < y && y < z && z < t);
double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -9e-43) {
		tmp = 1.0 - (x / (z * (t - y)));
	} else {
		tmp = 1.0 + (1.0 / ((y / x) * (t - y)));
	}
	return tmp;
}

Fortran

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (z <= (-9d-43)) then
        tmp = 1.0d0 - (x / (z * (t - y)))
    else
        tmp = 1.0d0 + (1.0d0 / ((y / x) * (t - y)))
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t;
public static double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -9e-43) {
		tmp = 1.0 - (x / (z * (t - y)));
	} else {
		tmp = 1.0 + (1.0 / ((y / x) * (t - y)));
	}
	return tmp;
}

Python

[x, y, z, t] = sort([x, y, z, t])
def code(x, y, z, t):
	tmp = 0
	if z <= -9e-43:
		tmp = 1.0 - (x / (z * (t - y)))
	else:
		tmp = 1.0 + (1.0 / ((y / x) * (t - y)))
	return tmp

Julia

x, y, z, t = sort([x, y, z, t])
function code(x, y, z, t)
	tmp = 0.0
	if (z <= -9e-43)
		tmp = Float64(1.0 - Float64(x / Float64(z * Float64(t - y))));
	else
		tmp = Float64(1.0 + Float64(1.0 / Float64(Float64(y / x) * Float64(t - y))));
	end
	return tmp
end

MATLAB

x, y, z, t = num2cell(sort([x, y, z, t])){:}
function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (z <= -9e-43)
		tmp = 1.0 - (x / (z * (t - y)));
	else
		tmp = 1.0 + (1.0 / ((y / x) * (t - y)));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_] := If[LessEqual[z, -9e-43], N[(1.0 - N[(x / N[(z * N[(t - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(1.0 + N[(1.0 / N[(N[(y / x), $MachinePrecision] * N[(t - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -9.0000000000000005e-43

   1. Initial program 99.9%

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

   3. Taylor expanded in z around inf 96.3%

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

      1. associate-*r/ 96.3%

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

      2. neg-mul-1 96.3%

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

      3. *-commutative 96.3%

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

   5. Simplified 96.3%

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

   if -9.0000000000000005e-43 < z

   1. Initial program 98.8%

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

   3. Taylor expanded in z around 0 78.2%

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

      1. associate-/r* 78.8%

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

   5. Simplified 78.8%

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

      1. clear-num 78.8%

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

      2. inv-pow 78.8%

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

      3. div-inv 78.8%

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

      4. clear-num 78.8%

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

   7. Applied egg-rr 78.8%

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

      1. unpow-1 78.8%

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

   9. Simplified 78.8%

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

4. Final simplification 84.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -9 \cdot 10^{-43}:\\ \;\;\;\;1 - \frac{x}{z \cdot \left(t - y\right)}\\ \mathbf{else}:\\ \;\;\;\;1 + \frac{1}{\frac{y}{x} \cdot \left(t - y\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 90.1% accurate, 0.8× speedup

Math

\[\begin{array}{l} [x, y, z, t] = \mathsf{sort}([x, y, z, t])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -4 \cdot 10^{-43}:\\ \;\;\;\;1 - \frac{x}{z \cdot \left(t - y\right)}\\ \mathbf{else}:\\ \;\;\;\;1 + \frac{x}{y \cdot \left(t - y\right)}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
(FPCore (x y z t)
 :precision binary64
 (if (<= z -4e-43) (- 1.0 (/ x (* z (- t y)))) (+ 1.0 (/ x (* y (- t y))))))

C

assert(x < y && y < z && z < t);
double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -4e-43) {
		tmp = 1.0 - (x / (z * (t - y)));
	} else {
		tmp = 1.0 + (x / (y * (t - y)));
	}
	return tmp;
}

Fortran

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (z <= (-4d-43)) then
        tmp = 1.0d0 - (x / (z * (t - y)))
    else
        tmp = 1.0d0 + (x / (y * (t - y)))
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t;
public static double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -4e-43) {
		tmp = 1.0 - (x / (z * (t - y)));
	} else {
		tmp = 1.0 + (x / (y * (t - y)));
	}
	return tmp;
}

Python

[x, y, z, t] = sort([x, y, z, t])
def code(x, y, z, t):
	tmp = 0
	if z <= -4e-43:
		tmp = 1.0 - (x / (z * (t - y)))
	else:
		tmp = 1.0 + (x / (y * (t - y)))
	return tmp

Julia

x, y, z, t = sort([x, y, z, t])
function code(x, y, z, t)
	tmp = 0.0
	if (z <= -4e-43)
		tmp = Float64(1.0 - Float64(x / Float64(z * Float64(t - y))));
	else
		tmp = Float64(1.0 + Float64(x / Float64(y * Float64(t - y))));
	end
	return tmp
end

MATLAB

x, y, z, t = num2cell(sort([x, y, z, t])){:}
function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (z <= -4e-43)
		tmp = 1.0 - (x / (z * (t - y)));
	else
		tmp = 1.0 + (x / (y * (t - y)));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_] := If[LessEqual[z, -4e-43], N[(1.0 - N[(x / N[(z * N[(t - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(1.0 + N[(x / N[(y * N[(t - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -4.00000000000000031e-43

   1. Initial program 99.9%

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

   3. Taylor expanded in z around inf 96.3%

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

      1. associate-*r/ 96.3%

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

      2. neg-mul-1 96.3%

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

      3. *-commutative 96.3%

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

   5. Simplified 96.3%

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

   if -4.00000000000000031e-43 < z

   1. Initial program 98.8%

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

   3. Taylor expanded in z around 0 78.2%

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

4. Final simplification 83.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4 \cdot 10^{-43}:\\ \;\;\;\;1 - \frac{x}{z \cdot \left(t - y\right)}\\ \mathbf{else}:\\ \;\;\;\;1 + \frac{x}{y \cdot \left(t - y\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 98.5% accurate, 0.8× speedup

Math

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

FPCore

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

C

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

Fortran

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    code = 1.0d0 + ((1.0d0 / (y - z)) / ((t - y) / x))
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.2%

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

   1. clear-num 99.1%

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

   2. inv-pow 99.1%

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

   3. associate-/l* 98.9%

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

4. Applied egg-rr 98.9%

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

   1. unpow-1 98.9%

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

   2. associate-/r* 98.9%

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

6. Applied egg-rr 98.9%

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

7. Final simplification 98.9%

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

Alternative 8: 99.1% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    code = 1.0d0 + (x / ((y - z) * (t - y)))
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.2%

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

3. Final simplification 99.2%

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

Alternative 9: 98.4% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    code = 1.0d0 + ((x / (y - t)) / (z - y))
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.2%

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

   1. clear-num 99.1%

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

   2. inv-pow 99.1%

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

   3. associate-/l* 98.9%

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

4. Applied egg-rr 98.9%

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

   1. unpow-1 98.9%

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

   2. *-commutative 98.9%

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

   3. associate-/r* 98.8%

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

   4. clear-num 98.8%

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

6. Applied egg-rr 98.8%

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

7. Final simplification 98.8%

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

Alternative 10: 75.3% accurate, 11.0× speedup

Math

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

FPCore

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

C

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

Fortran

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    code = 1.0d0
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.2%

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

3. Taylor expanded in y around 0 66.5%

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

   1. associate-/r* 66.2%

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

   2. div-inv 66.1%

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

5. Applied egg-rr 66.1%

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

   1. *-commutative 66.1%

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

   2. frac-2neg 66.1%

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

   3. associate-*r/ 66.5%

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

   4. add-sqr-sqrt 34.1%

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

   5. sqrt-unprod 57.4%

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

   6. sqr-neg 57.4%

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

   7. sqrt-unprod 26.4%

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

   8. add-sqr-sqrt 53.8%

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

   9. associate-/r/ 53.8%

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

   10. clear-num 53.8%

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

7. Applied egg-rr 53.8%

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

8. Taylor expanded in x around 0 72.4%

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

9. Final simplification 72.4%

   \[\leadsto 1 \]
10. Add Preprocessing

Reproduce

herbie shell --seed 2024074 
(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)))))