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

Percentage Accurate: 99.1% → 98.5%

Time: 9.9s

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, 0.8× speedup

Math

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

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 (/ 1.0 (/ (- y z) (/ x (- t y))))))

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) / (x / (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 + (1.0d0 / ((y - z) / (x / (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 + (1.0 / ((y - z) / (x / (t - y))));
}

Python

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

Julia

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

Derivation

1. Initial program 98.8%

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

   1. *-commutative N/A

      \[\leadsto \mathsf{\_.f64}\left(1, \left(\frac{x}{\left(y - t\right) \cdot \color{blue}{\left(y - z\right)}}\right)\right) \]

   2. associate-/r* N/A

      \[\leadsto \mathsf{\_.f64}\left(1, \left(\frac{\frac{x}{y - t}}{\color{blue}{y - z}}\right)\right) \]

   3. clear-num N/A

      \[\leadsto \mathsf{\_.f64}\left(1, \left(\frac{1}{\color{blue}{\frac{y - z}{\frac{x}{y - t}}}}\right)\right) \]

   4. /-lowering-/.f64 N/A

      \[\leadsto \mathsf{\_.f64}\left(1, \mathsf{/.f64}\left(1, \color{blue}{\left(\frac{y - z}{\frac{x}{y - t}}\right)}\right)\right) \]

   5. /-lowering-/.f64 N/A

      \[\leadsto \mathsf{\_.f64}\left(1, \mathsf{/.f64}\left(1, \mathsf{/.f64}\left(\left(y - z\right), \color{blue}{\left(\frac{x}{y - t}\right)}\right)\right)\right) \]

   6. --lowering--.f64 N/A

      \[\leadsto \mathsf{\_.f64}\left(1, \mathsf{/.f64}\left(1, \mathsf{/.f64}\left(\mathsf{\_.f64}\left(y, z\right), \left(\frac{\color{blue}{x}}{y - t}\right)\right)\right)\right) \]

   7. /-lowering-/.f64 N/A

      \[\leadsto \mathsf{\_.f64}\left(1, \mathsf{/.f64}\left(1, \mathsf{/.f64}\left(\mathsf{\_.f64}\left(y, z\right), \mathsf{/.f64}\left(x, \color{blue}{\left(y - t\right)}\right)\right)\right)\right) \]

   8. --lowering--.f64 98.8%

      \[\leadsto \mathsf{\_.f64}\left(1, \mathsf{/.f64}\left(1, \mathsf{/.f64}\left(\mathsf{\_.f64}\left(y, z\right), \mathsf{/.f64}\left(x, \mathsf{\_.f64}\left(y, \color{blue}{t}\right)\right)\right)\right)\right) \]

4. Applied egg-rr 98.8%

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

5. Final simplification 98.8%

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

Alternative 2: 82.5% accurate, 0.4× speedup

Math

\[\begin{array}{l} [x, y, z, t] = \mathsf{sort}([x, y, z, t])\\ \\ \begin{array}{l} t_1 := 1 - \frac{x}{y \cdot y}\\ t_2 := 1 + \frac{\frac{x}{y - z}}{t}\\ \mathbf{if}\;t \leq -6.2 \cdot 10^{-222}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t \leq 1.45 \cdot 10^{-272}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 2 \cdot 10^{-197}:\\ \;\;\;\;1 + \frac{\frac{x}{y}}{z}\\ \mathbf{elif}\;t \leq 2.5 \cdot 10^{-102}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (- 1.0 (/ x (* y y)))) (t_2 (+ 1.0 (/ (/ x (- y z)) t))))
   (if (<= t -6.2e-222)
     t_2
     (if (<= t 1.45e-272)
       t_1
       (if (<= t 2e-197)
         (+ 1.0 (/ (/ x y) z))
         (if (<= t 2.5e-102) t_1 t_2))))))

C

assert(x < y && y < z && z < t);
double code(double x, double y, double z, double t) {
	double t_1 = 1.0 - (x / (y * y));
	double t_2 = 1.0 + ((x / (y - z)) / t);
	double tmp;
	if (t <= -6.2e-222) {
		tmp = t_2;
	} else if (t <= 1.45e-272) {
		tmp = t_1;
	} else if (t <= 2e-197) {
		tmp = 1.0 + ((x / y) / z);
	} else if (t <= 2.5e-102) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = 1.0d0 - (x / (y * y))
    t_2 = 1.0d0 + ((x / (y - z)) / t)
    if (t <= (-6.2d-222)) then
        tmp = t_2
    else if (t <= 1.45d-272) then
        tmp = t_1
    else if (t <= 2d-197) then
        tmp = 1.0d0 + ((x / y) / z)
    else if (t <= 2.5d-102) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t;
public static double code(double x, double y, double z, double t) {
	double t_1 = 1.0 - (x / (y * y));
	double t_2 = 1.0 + ((x / (y - z)) / t);
	double tmp;
	if (t <= -6.2e-222) {
		tmp = t_2;
	} else if (t <= 1.45e-272) {
		tmp = t_1;
	} else if (t <= 2e-197) {
		tmp = 1.0 + ((x / y) / z);
	} else if (t <= 2.5e-102) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

[x, y, z, t] = sort([x, y, z, t])
def code(x, y, z, t):
	t_1 = 1.0 - (x / (y * y))
	t_2 = 1.0 + ((x / (y - z)) / t)
	tmp = 0
	if t <= -6.2e-222:
		tmp = t_2
	elif t <= 1.45e-272:
		tmp = t_1
	elif t <= 2e-197:
		tmp = 1.0 + ((x / y) / z)
	elif t <= 2.5e-102:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

x, y, z, t = sort([x, y, z, t])
function code(x, y, z, t)
	t_1 = Float64(1.0 - Float64(x / Float64(y * y)))
	t_2 = Float64(1.0 + Float64(Float64(x / Float64(y - z)) / t))
	tmp = 0.0
	if (t <= -6.2e-222)
		tmp = t_2;
	elseif (t <= 1.45e-272)
		tmp = t_1;
	elseif (t <= 2e-197)
		tmp = Float64(1.0 + Float64(Float64(x / y) / z));
	elseif (t <= 2.5e-102)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

x, y, z, t = num2cell(sort([x, y, z, t])){:}
function tmp_2 = code(x, y, z, t)
	t_1 = 1.0 - (x / (y * y));
	t_2 = 1.0 + ((x / (y - z)) / t);
	tmp = 0.0;
	if (t <= -6.2e-222)
		tmp = t_2;
	elseif (t <= 1.45e-272)
		tmp = t_1;
	elseif (t <= 2e-197)
		tmp = 1.0 + ((x / y) / z);
	elseif (t <= 2.5e-102)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_] := Block[{t$95$1 = N[(1.0 - N[(x / N[(y * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(1.0 + N[(N[(x / N[(y - z), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -6.2e-222], t$95$2, If[LessEqual[t, 1.45e-272], t$95$1, If[LessEqual[t, 2e-197], N[(1.0 + N[(N[(x / y), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 2.5e-102], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if t < -6.19999999999999959e-222 or 2.50000000000000013e-102 < t

   1. Initial program 98.9%

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

   3. Taylor expanded in t around inf

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

      1. remove-double-neg N/A

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

      2. mul-1-neg N/A

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

      3. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(1, \color{blue}{\left(\mathsf{neg}\left(-1 \cdot \frac{x}{t \cdot \left(y - z\right)}\right)\right)}\right) \]

      4. mul-1-neg N/A

         \[\leadsto \mathsf{+.f64}\left(1, \left(\mathsf{neg}\left(\left(\mathsf{neg}\left(\frac{x}{t \cdot \left(y - z\right)}\right)\right)\right)\right)\right) \]

      5. remove-double-neg N/A

         \[\leadsto \mathsf{+.f64}\left(1, \left(\frac{x}{\color{blue}{t \cdot \left(y - z\right)}}\right)\right) \]

      6. associate-/l/ N/A

         \[\leadsto \mathsf{+.f64}\left(1, \left(\frac{\frac{x}{y - z}}{\color{blue}{t}}\right)\right) \]

      7. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(1, \mathsf{/.f64}\left(\left(\frac{x}{y - z}\right), \color{blue}{t}\right)\right) \]

      8. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(1, \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, \left(y - z\right)\right), t\right)\right) \]

      9. --lowering--.f64 89.1%

         \[\leadsto \mathsf{+.f64}\left(1, \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, \mathsf{\_.f64}\left(y, z\right)\right), t\right)\right) \]

   5. Simplified 89.1%

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

   if -6.19999999999999959e-222 < t < 1.44999999999999997e-272 or 2e-197 < t < 2.50000000000000013e-102

   1. Initial program 100.0%

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

   3. Taylor expanded in y around inf

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

      1. mul-1-neg N/A

         \[\leadsto 1 + \left(\mathsf{neg}\left(\frac{x}{{y}^{2}}\right)\right) \]

      2. unsub-neg N/A

         \[\leadsto 1 - \color{blue}{\frac{x}{{y}^{2}}} \]

      3. --lowering--.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(1, \color{blue}{\left(\frac{x}{{y}^{2}}\right)}\right) \]

      4. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(1, \mathsf{/.f64}\left(x, \color{blue}{\left({y}^{2}\right)}\right)\right) \]

      5. unpow2 N/A

         \[\leadsto \mathsf{\_.f64}\left(1, \mathsf{/.f64}\left(x, \left(y \cdot \color{blue}{y}\right)\right)\right) \]

      6. *-lowering-*.f64 87.2%

         \[\leadsto \mathsf{\_.f64}\left(1, \mathsf{/.f64}\left(x, \mathsf{*.f64}\left(y, \color{blue}{y}\right)\right)\right) \]

   5. Simplified 87.2%

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

   if 1.44999999999999997e-272 < t < 2e-197

   1. Initial program 91.9%

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

   3. Taylor expanded in y around inf

      \[\leadsto \mathsf{\_.f64}\left(1, \mathsf{/.f64}\left(x, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(y, z\right), \color{blue}{y}\right)\right)\right) \]
   4. Step-by-step derivation

   5. Simplified 83.6%

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

   6. Taylor expanded in z around inf

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

      1. remove-double-neg N/A

         \[\leadsto 1 + \left(\mathsf{neg}\left(\left(\mathsf{neg}\left(\frac{x}{y \cdot z}\right)\right)\right)\right) \]

      2. mul-1-neg N/A

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

      3. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(1, \color{blue}{\left(\mathsf{neg}\left(-1 \cdot \frac{x}{y \cdot z}\right)\right)}\right) \]

      4. mul-1-neg N/A

         \[\leadsto \mathsf{+.f64}\left(1, \left(\mathsf{neg}\left(\left(\mathsf{neg}\left(\frac{x}{y \cdot z}\right)\right)\right)\right)\right) \]

      5. remove-double-neg N/A

         \[\leadsto \mathsf{+.f64}\left(1, \left(\frac{x}{\color{blue}{y \cdot z}}\right)\right) \]

      6. associate-/r* N/A

         \[\leadsto \mathsf{+.f64}\left(1, \left(\frac{\frac{x}{y}}{\color{blue}{z}}\right)\right) \]

      7. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(1, \mathsf{/.f64}\left(\left(\frac{x}{y}\right), \color{blue}{z}\right)\right) \]

      8. /-lowering-/.f64 75.1%

         \[\leadsto \mathsf{+.f64}\left(1, \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, y\right), z\right)\right) \]

   8. Simplified 75.1%

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

Alternative 3: 90.5% accurate, 0.5× speedup

Math

\[\begin{array}{l} [x, y, z, t] = \mathsf{sort}([x, y, z, t])\\ \\ \begin{array}{l} t_1 := 1 + \frac{\frac{1}{t}}{\frac{y - z}{x}}\\ \mathbf{if}\;t \leq -4.4 \cdot 10^{-78}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 7 \cdot 10^{-101}:\\ \;\;\;\;1 + \frac{\frac{x}{z - y}}{y}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (+ 1.0 (/ (/ 1.0 t) (/ (- y z) x)))))
   (if (<= t -4.4e-78)
     t_1
     (if (<= t 7e-101) (+ 1.0 (/ (/ x (- z y)) y)) t_1))))

C

assert(x < y && y < z && z < t);
double code(double x, double y, double z, double t) {
	double t_1 = 1.0 + ((1.0 / t) / ((y - z) / x));
	double tmp;
	if (t <= -4.4e-78) {
		tmp = t_1;
	} else if (t <= 7e-101) {
		tmp = 1.0 + ((x / (z - y)) / y);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = 1.0d0 + ((1.0d0 / t) / ((y - z) / x))
    if (t <= (-4.4d-78)) then
        tmp = t_1
    else if (t <= 7d-101) then
        tmp = 1.0d0 + ((x / (z - y)) / y)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t;
public static double code(double x, double y, double z, double t) {
	double t_1 = 1.0 + ((1.0 / t) / ((y - z) / x));
	double tmp;
	if (t <= -4.4e-78) {
		tmp = t_1;
	} else if (t <= 7e-101) {
		tmp = 1.0 + ((x / (z - y)) / y);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

[x, y, z, t] = sort([x, y, z, t])
def code(x, y, z, t):
	t_1 = 1.0 + ((1.0 / t) / ((y - z) / x))
	tmp = 0
	if t <= -4.4e-78:
		tmp = t_1
	elif t <= 7e-101:
		tmp = 1.0 + ((x / (z - y)) / y)
	else:
		tmp = t_1
	return tmp

Julia

x, y, z, t = sort([x, y, z, t])
function code(x, y, z, t)
	t_1 = Float64(1.0 + Float64(Float64(1.0 / t) / Float64(Float64(y - z) / x)))
	tmp = 0.0
	if (t <= -4.4e-78)
		tmp = t_1;
	elseif (t <= 7e-101)
		tmp = Float64(1.0 + Float64(Float64(x / Float64(z - y)) / y));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

x, y, z, t = num2cell(sort([x, y, z, t])){:}
function tmp_2 = code(x, y, z, t)
	t_1 = 1.0 + ((1.0 / t) / ((y - z) / x));
	tmp = 0.0;
	if (t <= -4.4e-78)
		tmp = t_1;
	elseif (t <= 7e-101)
		tmp = 1.0 + ((x / (z - y)) / y);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_] := Block[{t$95$1 = N[(1.0 + N[(N[(1.0 / t), $MachinePrecision] / N[(N[(y - z), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -4.4e-78], t$95$1, If[LessEqual[t, 7e-101], N[(1.0 + N[(N[(x / N[(z - y), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if t < -4.3999999999999998e-78 or 6.99999999999999989e-101 < t

   1. Initial program 99.9%

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

   3. Taylor expanded in t around inf

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

      1. remove-double-neg N/A

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

      2. mul-1-neg N/A

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

      3. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(1, \color{blue}{\left(\mathsf{neg}\left(-1 \cdot \frac{x}{t \cdot \left(y - z\right)}\right)\right)}\right) \]

      4. mul-1-neg N/A

         \[\leadsto \mathsf{+.f64}\left(1, \left(\mathsf{neg}\left(\left(\mathsf{neg}\left(\frac{x}{t \cdot \left(y - z\right)}\right)\right)\right)\right)\right) \]

      5. remove-double-neg N/A

         \[\leadsto \mathsf{+.f64}\left(1, \left(\frac{x}{\color{blue}{t \cdot \left(y - z\right)}}\right)\right) \]

      6. associate-/l/ N/A

         \[\leadsto \mathsf{+.f64}\left(1, \left(\frac{\frac{x}{y - z}}{\color{blue}{t}}\right)\right) \]

      7. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(1, \mathsf{/.f64}\left(\left(\frac{x}{y - z}\right), \color{blue}{t}\right)\right) \]

      8. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(1, \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, \left(y - z\right)\right), t\right)\right) \]

      9. --lowering--.f64 95.6%

         \[\leadsto \mathsf{+.f64}\left(1, \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, \mathsf{\_.f64}\left(y, z\right)\right), t\right)\right) \]

   5. Simplified 95.6%

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

      1. div-inv N/A

         \[\leadsto \mathsf{+.f64}\left(1, \left(\frac{x}{y - z} \cdot \color{blue}{\frac{1}{t}}\right)\right) \]

      2. clear-num N/A

         \[\leadsto \mathsf{+.f64}\left(1, \left(\frac{1}{\frac{y - z}{x}} \cdot \frac{\color{blue}{1}}{t}\right)\right) \]

      3. associate-*l/ N/A

         \[\leadsto \mathsf{+.f64}\left(1, \left(\frac{1 \cdot \frac{1}{t}}{\color{blue}{\frac{y - z}{x}}}\right)\right) \]

      4. div-inv N/A

         \[\leadsto \mathsf{+.f64}\left(1, \left(\frac{\frac{1}{t}}{\frac{\color{blue}{y - z}}{x}}\right)\right) \]

      5. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(1, \mathsf{/.f64}\left(\left(\frac{1}{t}\right), \color{blue}{\left(\frac{y - z}{x}\right)}\right)\right) \]

      6. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(1, \mathsf{/.f64}\left(\mathsf{/.f64}\left(1, t\right), \left(\frac{\color{blue}{y - z}}{x}\right)\right)\right) \]

      7. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(1, \mathsf{/.f64}\left(\mathsf{/.f64}\left(1, t\right), \mathsf{/.f64}\left(\left(y - z\right), \color{blue}{x}\right)\right)\right) \]

      8. --lowering--.f64 95.5%

         \[\leadsto \mathsf{+.f64}\left(1, \mathsf{/.f64}\left(\mathsf{/.f64}\left(1, t\right), \mathsf{/.f64}\left(\mathsf{\_.f64}\left(y, z\right), x\right)\right)\right) \]

   7. Applied egg-rr 95.5%

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

   if -4.3999999999999998e-78 < t < 6.99999999999999989e-101

   1. Initial program 96.8%

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

   3. Taylor expanded in t around 0

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

      1. --lowering--.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(1, \color{blue}{\left(\frac{x}{y \cdot \left(y - z\right)}\right)}\right) \]

      2. *-commutative N/A

         \[\leadsto \mathsf{\_.f64}\left(1, \left(\frac{x}{\left(y - z\right) \cdot \color{blue}{y}}\right)\right) \]

      3. associate-/r* N/A

         \[\leadsto \mathsf{\_.f64}\left(1, \left(\frac{\frac{x}{y - z}}{\color{blue}{y}}\right)\right) \]

      4. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(1, \mathsf{/.f64}\left(\left(\frac{x}{y - z}\right), \color{blue}{y}\right)\right) \]

      5. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(1, \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, \left(y - z\right)\right), y\right)\right) \]

      6. --lowering--.f64 92.5%

         \[\leadsto \mathsf{\_.f64}\left(1, \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, \mathsf{\_.f64}\left(y, z\right)\right), y\right)\right) \]

   5. Simplified 92.5%

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

4. Final simplification 94.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -4.4 \cdot 10^{-78}:\\ \;\;\;\;1 + \frac{\frac{1}{t}}{\frac{y - z}{x}}\\ \mathbf{elif}\;t \leq 7 \cdot 10^{-101}:\\ \;\;\;\;1 + \frac{\frac{x}{z - y}}{y}\\ \mathbf{else}:\\ \;\;\;\;1 + \frac{\frac{1}{t}}{\frac{y - z}{x}}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 90.4% accurate, 0.6× speedup

Math

\[\begin{array}{l} [x, y, z, t] = \mathsf{sort}([x, y, z, t])\\ \\ \begin{array}{l} t_1 := 1 + \frac{\frac{x}{y - z}}{t}\\ \mathbf{if}\;t \leq -5.1 \cdot 10^{-70}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 7 \cdot 10^{-101}:\\ \;\;\;\;1 + \frac{\frac{x}{z - y}}{y}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (+ 1.0 (/ (/ x (- y z)) t))))
   (if (<= t -5.1e-70)
     t_1
     (if (<= t 7e-101) (+ 1.0 (/ (/ x (- z y)) y)) t_1))))

C

assert(x < y && y < z && z < t);
double code(double x, double y, double z, double t) {
	double t_1 = 1.0 + ((x / (y - z)) / t);
	double tmp;
	if (t <= -5.1e-70) {
		tmp = t_1;
	} else if (t <= 7e-101) {
		tmp = 1.0 + ((x / (z - y)) / y);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = 1.0d0 + ((x / (y - z)) / t)
    if (t <= (-5.1d-70)) then
        tmp = t_1
    else if (t <= 7d-101) then
        tmp = 1.0d0 + ((x / (z - y)) / y)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t;
public static double code(double x, double y, double z, double t) {
	double t_1 = 1.0 + ((x / (y - z)) / t);
	double tmp;
	if (t <= -5.1e-70) {
		tmp = t_1;
	} else if (t <= 7e-101) {
		tmp = 1.0 + ((x / (z - y)) / y);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

[x, y, z, t] = sort([x, y, z, t])
def code(x, y, z, t):
	t_1 = 1.0 + ((x / (y - z)) / t)
	tmp = 0
	if t <= -5.1e-70:
		tmp = t_1
	elif t <= 7e-101:
		tmp = 1.0 + ((x / (z - y)) / y)
	else:
		tmp = t_1
	return tmp

Julia

x, y, z, t = sort([x, y, z, t])
function code(x, y, z, t)
	t_1 = Float64(1.0 + Float64(Float64(x / Float64(y - z)) / t))
	tmp = 0.0
	if (t <= -5.1e-70)
		tmp = t_1;
	elseif (t <= 7e-101)
		tmp = Float64(1.0 + Float64(Float64(x / Float64(z - y)) / y));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

x, y, z, t = num2cell(sort([x, y, z, t])){:}
function tmp_2 = code(x, y, z, t)
	t_1 = 1.0 + ((x / (y - z)) / t);
	tmp = 0.0;
	if (t <= -5.1e-70)
		tmp = t_1;
	elseif (t <= 7e-101)
		tmp = 1.0 + ((x / (z - y)) / y);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_] := Block[{t$95$1 = N[(1.0 + N[(N[(x / N[(y - z), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -5.1e-70], t$95$1, If[LessEqual[t, 7e-101], N[(1.0 + N[(N[(x / N[(z - y), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if t < -5.10000000000000025e-70 or 6.99999999999999989e-101 < t

   1. Initial program 99.9%

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

   3. Taylor expanded in t around inf

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

      1. remove-double-neg N/A

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

      2. mul-1-neg N/A

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

      3. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(1, \color{blue}{\left(\mathsf{neg}\left(-1 \cdot \frac{x}{t \cdot \left(y - z\right)}\right)\right)}\right) \]

      4. mul-1-neg N/A

         \[\leadsto \mathsf{+.f64}\left(1, \left(\mathsf{neg}\left(\left(\mathsf{neg}\left(\frac{x}{t \cdot \left(y - z\right)}\right)\right)\right)\right)\right) \]

      5. remove-double-neg N/A

         \[\leadsto \mathsf{+.f64}\left(1, \left(\frac{x}{\color{blue}{t \cdot \left(y - z\right)}}\right)\right) \]

      6. associate-/l/ N/A

         \[\leadsto \mathsf{+.f64}\left(1, \left(\frac{\frac{x}{y - z}}{\color{blue}{t}}\right)\right) \]

      7. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(1, \mathsf{/.f64}\left(\left(\frac{x}{y - z}\right), \color{blue}{t}\right)\right) \]

      8. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(1, \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, \left(y - z\right)\right), t\right)\right) \]

      9. --lowering--.f64 95.6%

         \[\leadsto \mathsf{+.f64}\left(1, \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, \mathsf{\_.f64}\left(y, z\right)\right), t\right)\right) \]

   5. Simplified 95.6%

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

   if -5.10000000000000025e-70 < t < 6.99999999999999989e-101

   1. Initial program 96.8%

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

   3. Taylor expanded in t around 0

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

      1. --lowering--.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(1, \color{blue}{\left(\frac{x}{y \cdot \left(y - z\right)}\right)}\right) \]

      2. *-commutative N/A

         \[\leadsto \mathsf{\_.f64}\left(1, \left(\frac{x}{\left(y - z\right) \cdot \color{blue}{y}}\right)\right) \]

      3. associate-/r* N/A

         \[\leadsto \mathsf{\_.f64}\left(1, \left(\frac{\frac{x}{y - z}}{\color{blue}{y}}\right)\right) \]

      4. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(1, \mathsf{/.f64}\left(\left(\frac{x}{y - z}\right), \color{blue}{y}\right)\right) \]

      5. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(1, \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, \left(y - z\right)\right), y\right)\right) \]

      6. --lowering--.f64 92.5%

         \[\leadsto \mathsf{\_.f64}\left(1, \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, \mathsf{\_.f64}\left(y, z\right)\right), y\right)\right) \]

   5. Simplified 92.5%

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

4. Final simplification 94.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -5.1 \cdot 10^{-70}:\\ \;\;\;\;1 + \frac{\frac{x}{y - z}}{t}\\ \mathbf{elif}\;t \leq 7 \cdot 10^{-101}:\\ \;\;\;\;1 + \frac{\frac{x}{z - y}}{y}\\ \mathbf{else}:\\ \;\;\;\;1 + \frac{\frac{x}{y - z}}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 90.1% accurate, 0.6× speedup

Math

\[\begin{array}{l} [x, y, z, t] = \mathsf{sort}([x, y, z, t])\\ \\ \begin{array}{l} t_1 := 1 + \frac{\frac{x}{y - z}}{t}\\ \mathbf{if}\;t \leq -4.3 \cdot 10^{-82}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 2.75 \cdot 10^{-101}:\\ \;\;\;\;1 + \frac{x}{y \cdot \left(z - y\right)}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (+ 1.0 (/ (/ x (- y z)) t))))
   (if (<= t -4.3e-82)
     t_1
     (if (<= t 2.75e-101) (+ 1.0 (/ x (* y (- z y)))) t_1))))

C

assert(x < y && y < z && z < t);
double code(double x, double y, double z, double t) {
	double t_1 = 1.0 + ((x / (y - z)) / t);
	double tmp;
	if (t <= -4.3e-82) {
		tmp = t_1;
	} else if (t <= 2.75e-101) {
		tmp = 1.0 + (x / (y * (z - y)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = 1.0d0 + ((x / (y - z)) / t)
    if (t <= (-4.3d-82)) then
        tmp = t_1
    else if (t <= 2.75d-101) then
        tmp = 1.0d0 + (x / (y * (z - y)))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t;
public static double code(double x, double y, double z, double t) {
	double t_1 = 1.0 + ((x / (y - z)) / t);
	double tmp;
	if (t <= -4.3e-82) {
		tmp = t_1;
	} else if (t <= 2.75e-101) {
		tmp = 1.0 + (x / (y * (z - y)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

[x, y, z, t] = sort([x, y, z, t])
def code(x, y, z, t):
	t_1 = 1.0 + ((x / (y - z)) / t)
	tmp = 0
	if t <= -4.3e-82:
		tmp = t_1
	elif t <= 2.75e-101:
		tmp = 1.0 + (x / (y * (z - y)))
	else:
		tmp = t_1
	return tmp

Julia

x, y, z, t = sort([x, y, z, t])
function code(x, y, z, t)
	t_1 = Float64(1.0 + Float64(Float64(x / Float64(y - z)) / t))
	tmp = 0.0
	if (t <= -4.3e-82)
		tmp = t_1;
	elseif (t <= 2.75e-101)
		tmp = Float64(1.0 + Float64(x / Float64(y * Float64(z - y))));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

x, y, z, t = num2cell(sort([x, y, z, t])){:}
function tmp_2 = code(x, y, z, t)
	t_1 = 1.0 + ((x / (y - z)) / t);
	tmp = 0.0;
	if (t <= -4.3e-82)
		tmp = t_1;
	elseif (t <= 2.75e-101)
		tmp = 1.0 + (x / (y * (z - y)));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_] := Block[{t$95$1 = N[(1.0 + N[(N[(x / N[(y - z), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -4.3e-82], t$95$1, If[LessEqual[t, 2.75e-101], N[(1.0 + N[(x / N[(y * N[(z - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if t < -4.30000000000000019e-82 or 2.74999999999999986e-101 < t

   1. Initial program 99.9%

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

   3. Taylor expanded in t around inf

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

      1. remove-double-neg N/A

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

      2. mul-1-neg N/A

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

      3. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(1, \color{blue}{\left(\mathsf{neg}\left(-1 \cdot \frac{x}{t \cdot \left(y - z\right)}\right)\right)}\right) \]

      4. mul-1-neg N/A

         \[\leadsto \mathsf{+.f64}\left(1, \left(\mathsf{neg}\left(\left(\mathsf{neg}\left(\frac{x}{t \cdot \left(y - z\right)}\right)\right)\right)\right)\right) \]

      5. remove-double-neg N/A

         \[\leadsto \mathsf{+.f64}\left(1, \left(\frac{x}{\color{blue}{t \cdot \left(y - z\right)}}\right)\right) \]

      6. associate-/l/ N/A

         \[\leadsto \mathsf{+.f64}\left(1, \left(\frac{\frac{x}{y - z}}{\color{blue}{t}}\right)\right) \]

      7. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(1, \mathsf{/.f64}\left(\left(\frac{x}{y - z}\right), \color{blue}{t}\right)\right) \]

      8. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(1, \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, \left(y - z\right)\right), t\right)\right) \]

      9. --lowering--.f64 95.0%

         \[\leadsto \mathsf{+.f64}\left(1, \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, \mathsf{\_.f64}\left(y, z\right)\right), t\right)\right) \]

   5. Simplified 95.0%

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

   if -4.30000000000000019e-82 < t < 2.74999999999999986e-101

   1. Initial program 96.8%

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

   3. Taylor expanded in y around inf

      \[\leadsto \mathsf{\_.f64}\left(1, \mathsf{/.f64}\left(x, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(y, z\right), \color{blue}{y}\right)\right)\right) \]
   4. Step-by-step derivation

   5. Simplified 91.4%

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

4. Final simplification 93.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -4.3 \cdot 10^{-82}:\\ \;\;\;\;1 + \frac{\frac{x}{y - z}}{t}\\ \mathbf{elif}\;t \leq 2.75 \cdot 10^{-101}:\\ \;\;\;\;1 + \frac{x}{y \cdot \left(z - y\right)}\\ \mathbf{else}:\\ \;\;\;\;1 + \frac{\frac{x}{y - z}}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 81.1% accurate, 0.6× speedup

Math

\[\begin{array}{l} [x, y, z, t] = \mathsf{sort}([x, y, z, t])\\ \\ \begin{array}{l} \mathbf{if}\;y \leq -2.65 \cdot 10^{-142}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq 2.55 \cdot 10^{-83}:\\ \;\;\;\;1 - \frac{\frac{x}{t}}{z}\\ \mathbf{else}:\\ \;\;\;\;1 - \frac{x}{y \cdot y}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
(FPCore (x y z t)
 :precision binary64
 (if (<= y -2.65e-142)
   1.0
   (if (<= y 2.55e-83) (- 1.0 (/ (/ x t) z)) (- 1.0 (/ x (* y y))))))

C

assert(x < y && y < z && z < t);
double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -2.65e-142) {
		tmp = 1.0;
	} else if (y <= 2.55e-83) {
		tmp = 1.0 - ((x / t) / z);
	} else {
		tmp = 1.0 - (x / (y * 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 (y <= (-2.65d-142)) then
        tmp = 1.0d0
    else if (y <= 2.55d-83) then
        tmp = 1.0d0 - ((x / t) / z)
    else
        tmp = 1.0d0 - (x / (y * 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 (y <= -2.65e-142) {
		tmp = 1.0;
	} else if (y <= 2.55e-83) {
		tmp = 1.0 - ((x / t) / z);
	} else {
		tmp = 1.0 - (x / (y * y));
	}
	return tmp;
}

Python

[x, y, z, t] = sort([x, y, z, t])
def code(x, y, z, t):
	tmp = 0
	if y <= -2.65e-142:
		tmp = 1.0
	elif y <= 2.55e-83:
		tmp = 1.0 - ((x / t) / z)
	else:
		tmp = 1.0 - (x / (y * y))
	return tmp

Julia

x, y, z, t = sort([x, y, z, t])
function code(x, y, z, t)
	tmp = 0.0
	if (y <= -2.65e-142)
		tmp = 1.0;
	elseif (y <= 2.55e-83)
		tmp = Float64(1.0 - Float64(Float64(x / t) / z));
	else
		tmp = Float64(1.0 - Float64(x / Float64(y * 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 (y <= -2.65e-142)
		tmp = 1.0;
	elseif (y <= 2.55e-83)
		tmp = 1.0 - ((x / t) / z);
	else
		tmp = 1.0 - (x / (y * 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[y, -2.65e-142], 1.0, If[LessEqual[y, 2.55e-83], N[(1.0 - N[(N[(x / t), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], N[(1.0 - N[(x / N[(y * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -2.6499999999999999e-142

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0

      \[\leadsto \color{blue}{1} \]
   4. Step-by-step derivation

   5. Simplified 85.9%

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

   if -2.6499999999999999e-142 < y < 2.55000000000000018e-83

   1. Initial program 96.2%

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

   3. Taylor expanded in y around 0

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

      1. --lowering--.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(1, \color{blue}{\left(\frac{x}{t \cdot z}\right)}\right) \]

      2. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(1, \mathsf{/.f64}\left(x, \color{blue}{\left(t \cdot z\right)}\right)\right) \]

      3. *-lowering-*.f64 75.4%

         \[\leadsto \mathsf{\_.f64}\left(1, \mathsf{/.f64}\left(x, \mathsf{*.f64}\left(t, \color{blue}{z}\right)\right)\right) \]

   5. Simplified 75.4%

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

      1. associate-/r* N/A

         \[\leadsto \mathsf{\_.f64}\left(1, \left(\frac{\frac{x}{t}}{\color{blue}{z}}\right)\right) \]

      2. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(1, \mathsf{/.f64}\left(\left(\frac{x}{t}\right), \color{blue}{z}\right)\right) \]

      3. /-lowering-/.f64 76.6%

         \[\leadsto \mathsf{\_.f64}\left(1, \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, t\right), z\right)\right) \]

   7. Applied egg-rr 76.6%

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

   if 2.55000000000000018e-83 < 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 inf

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

      1. mul-1-neg N/A

         \[\leadsto 1 + \left(\mathsf{neg}\left(\frac{x}{{y}^{2}}\right)\right) \]

      2. unsub-neg N/A

         \[\leadsto 1 - \color{blue}{\frac{x}{{y}^{2}}} \]

      3. --lowering--.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(1, \color{blue}{\left(\frac{x}{{y}^{2}}\right)}\right) \]

      4. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(1, \mathsf{/.f64}\left(x, \color{blue}{\left({y}^{2}\right)}\right)\right) \]

      5. unpow2 N/A

         \[\leadsto \mathsf{\_.f64}\left(1, \mathsf{/.f64}\left(x, \left(y \cdot \color{blue}{y}\right)\right)\right) \]

      6. *-lowering-*.f64 86.2%

         \[\leadsto \mathsf{\_.f64}\left(1, \mathsf{/.f64}\left(x, \mathsf{*.f64}\left(y, \color{blue}{y}\right)\right)\right) \]

   5. Simplified 86.2%

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

Alternative 7: 81.4% accurate, 0.6× speedup

Math

\[\begin{array}{l} [x, y, z, t] = \mathsf{sort}([x, y, z, t])\\ \\ \begin{array}{l} \mathbf{if}\;y \leq -1.05 \cdot 10^{-142}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq 3.7 \cdot 10^{-84}:\\ \;\;\;\;1 - \frac{x}{z \cdot t}\\ \mathbf{else}:\\ \;\;\;\;1 - \frac{x}{y \cdot y}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
(FPCore (x y z t)
 :precision binary64
 (if (<= y -1.05e-142)
   1.0
   (if (<= y 3.7e-84) (- 1.0 (/ x (* z t))) (- 1.0 (/ x (* y y))))))

C

assert(x < y && y < z && z < t);
double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -1.05e-142) {
		tmp = 1.0;
	} else if (y <= 3.7e-84) {
		tmp = 1.0 - (x / (z * t));
	} else {
		tmp = 1.0 - (x / (y * 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 (y <= (-1.05d-142)) then
        tmp = 1.0d0
    else if (y <= 3.7d-84) then
        tmp = 1.0d0 - (x / (z * t))
    else
        tmp = 1.0d0 - (x / (y * 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 (y <= -1.05e-142) {
		tmp = 1.0;
	} else if (y <= 3.7e-84) {
		tmp = 1.0 - (x / (z * t));
	} else {
		tmp = 1.0 - (x / (y * y));
	}
	return tmp;
}

Python

[x, y, z, t] = sort([x, y, z, t])
def code(x, y, z, t):
	tmp = 0
	if y <= -1.05e-142:
		tmp = 1.0
	elif y <= 3.7e-84:
		tmp = 1.0 - (x / (z * t))
	else:
		tmp = 1.0 - (x / (y * y))
	return tmp

Julia

x, y, z, t = sort([x, y, z, t])
function code(x, y, z, t)
	tmp = 0.0
	if (y <= -1.05e-142)
		tmp = 1.0;
	elseif (y <= 3.7e-84)
		tmp = Float64(1.0 - Float64(x / Float64(z * t)));
	else
		tmp = Float64(1.0 - Float64(x / Float64(y * 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 (y <= -1.05e-142)
		tmp = 1.0;
	elseif (y <= 3.7e-84)
		tmp = 1.0 - (x / (z * t));
	else
		tmp = 1.0 - (x / (y * 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[y, -1.05e-142], 1.0, If[LessEqual[y, 3.7e-84], N[(1.0 - N[(x / N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(1.0 - N[(x / N[(y * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.05e-142

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0

      \[\leadsto \color{blue}{1} \]
   4. Step-by-step derivation

   5. Simplified 85.9%

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

   if -1.05e-142 < y < 3.6999999999999999e-84

   1. Initial program 96.2%

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

   3. Taylor expanded in y around 0

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

      1. --lowering--.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(1, \color{blue}{\left(\frac{x}{t \cdot z}\right)}\right) \]

      2. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(1, \mathsf{/.f64}\left(x, \color{blue}{\left(t \cdot z\right)}\right)\right) \]

      3. *-lowering-*.f64 75.4%

         \[\leadsto \mathsf{\_.f64}\left(1, \mathsf{/.f64}\left(x, \mathsf{*.f64}\left(t, \color{blue}{z}\right)\right)\right) \]

   5. Simplified 75.4%

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

   if 3.6999999999999999e-84 < 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 inf

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

      1. mul-1-neg N/A

         \[\leadsto 1 + \left(\mathsf{neg}\left(\frac{x}{{y}^{2}}\right)\right) \]

      2. unsub-neg N/A

         \[\leadsto 1 - \color{blue}{\frac{x}{{y}^{2}}} \]

      3. --lowering--.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(1, \color{blue}{\left(\frac{x}{{y}^{2}}\right)}\right) \]

      4. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(1, \mathsf{/.f64}\left(x, \color{blue}{\left({y}^{2}\right)}\right)\right) \]

      5. unpow2 N/A

         \[\leadsto \mathsf{\_.f64}\left(1, \mathsf{/.f64}\left(x, \left(y \cdot \color{blue}{y}\right)\right)\right) \]

      6. *-lowering-*.f64 86.2%

         \[\leadsto \mathsf{\_.f64}\left(1, \mathsf{/.f64}\left(x, \mathsf{*.f64}\left(y, \color{blue}{y}\right)\right)\right) \]

   5. Simplified 86.2%

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

4. Final simplification 82.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.05 \cdot 10^{-142}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq 3.7 \cdot 10^{-84}:\\ \;\;\;\;1 - \frac{x}{z \cdot t}\\ \mathbf{else}:\\ \;\;\;\;1 - \frac{x}{y \cdot y}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 83.0% accurate, 0.6× speedup

Math

\[\begin{array}{l} [x, y, z, t] = \mathsf{sort}([x, y, z, t])\\ \\ \begin{array}{l} \mathbf{if}\;y \leq -2.65 \cdot 10^{-142}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq 1.95 \cdot 10^{-113}:\\ \;\;\;\;1 - \frac{x}{z \cdot t}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

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 -2.65e-142) 1.0 (if (<= y 1.95e-113) (- 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 <= -2.65e-142) {
		tmp = 1.0;
	} else if (y <= 1.95e-113) {
		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 <= (-2.65d-142)) then
        tmp = 1.0d0
    else if (y <= 1.95d-113) 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 <= -2.65e-142) {
		tmp = 1.0;
	} else if (y <= 1.95e-113) {
		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 <= -2.65e-142:
		tmp = 1.0
	elif y <= 1.95e-113:
		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 <= -2.65e-142)
		tmp = 1.0;
	elseif (y <= 1.95e-113)
		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 <= -2.65e-142)
		tmp = 1.0;
	elseif (y <= 1.95e-113)
		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, -2.65e-142], 1.0, If[LessEqual[y, 1.95e-113], N[(1.0 - N[(x / N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], 1.0]]

Derivation

1. Split input into 2 regimes

2. if y < -2.6499999999999999e-142 or 1.9499999999999999e-113 < y

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0

      \[\leadsto \color{blue}{1} \]
   4. Step-by-step derivation

   5. Simplified 84.9%

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

   if -2.6499999999999999e-142 < y < 1.9499999999999999e-113

   1. Initial program 95.8%

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

   3. Taylor expanded in y around 0

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

      1. --lowering--.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(1, \color{blue}{\left(\frac{x}{t \cdot z}\right)}\right) \]

      2. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(1, \mathsf{/.f64}\left(x, \color{blue}{\left(t \cdot z\right)}\right)\right) \]

      3. *-lowering-*.f64 74.8%

         \[\leadsto \mathsf{\_.f64}\left(1, \mathsf{/.f64}\left(x, \mathsf{*.f64}\left(t, \color{blue}{z}\right)\right)\right) \]

   5. Simplified 74.8%

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

4. Final simplification 82.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.65 \cdot 10^{-142}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq 1.95 \cdot 10^{-113}:\\ \;\;\;\;1 - \frac{x}{z \cdot t}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 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 98.8%

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

3. Final simplification 98.8%

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

Alternative 10: 74.5% 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 98.8%

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

3. Taylor expanded in x around 0

   \[\leadsto \color{blue}{1} \]
4. Step-by-step derivation

5. Simplified 74.7%

   \[\leadsto \color{blue}{1} \]
6. Add Preprocessing

Reproduce

herbie shell --seed 2024139 
(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)))))