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

Percentage Accurate: 99.2% → 98.9%

Time: 7.3s

Alternatives: 8

Speedup: 1.0×

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 99.2% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 98.9% accurate, 0.8× speedup

Math

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

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 (fma (- y z) (- t) (* (- y z) y)))))

C

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

Julia

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

Derivation

1. Initial program 99.9%

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

   1. lift-*.f64 N/A

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

   2. lift--.f64 N/A

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

   3. sub-neg N/A

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

   4. +-commutative N/A

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

   5. distribute-lft-in N/A

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

   6. lower-fma.f64 N/A

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

   7. lower-neg.f64 N/A

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

   8. lower-*.f64 99.9

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

4. Applied rewrites 99.9%

   \[\leadsto 1 - \frac{x}{\color{blue}{\mathsf{fma}\left(y - z, -t, \left(y - z\right) \cdot y\right)}} \]
5. Add Preprocessing

Alternative 2: 90.1% accurate, 0.3× speedup

Math

\[\begin{array}{l} [x, y, z, t] = \mathsf{sort}([x, y, z, t])\\ \\ \begin{array}{l} t_1 := \frac{x}{\left(t - y\right) \cdot \left(z - y\right)}\\ t_2 := 1 - \frac{x}{\left(t - y\right) \cdot z}\\ \mathbf{if}\;t\_1 \leq -4 \cdot 10^{-8}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_1 \leq 5 \cdot 10^{-24}:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

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 (/ x (* (- t y) (- z y)))) (t_2 (- 1.0 (/ x (* (- t y) z)))))
   (if (<= t_1 -4e-8) t_2 (if (<= t_1 5e-24) 1.0 t_2))))

C

assert(x < y && y < z && z < t);
double code(double x, double y, double z, double t) {
	double t_1 = x / ((t - y) * (z - y));
	double t_2 = 1.0 - (x / ((t - y) * z));
	double tmp;
	if (t_1 <= -4e-8) {
		tmp = t_2;
	} else if (t_1 <= 5e-24) {
		tmp = 1.0;
	} 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 = x / ((t - y) * (z - y))
    t_2 = 1.0d0 - (x / ((t - y) * z))
    if (t_1 <= (-4d-8)) then
        tmp = t_2
    else if (t_1 <= 5d-24) then
        tmp = 1.0d0
    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 = x / ((t - y) * (z - y));
	double t_2 = 1.0 - (x / ((t - y) * z));
	double tmp;
	if (t_1 <= -4e-8) {
		tmp = t_2;
	} else if (t_1 <= 5e-24) {
		tmp = 1.0;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

[x, y, z, t] = sort([x, y, z, t])
def code(x, y, z, t):
	t_1 = x / ((t - y) * (z - y))
	t_2 = 1.0 - (x / ((t - y) * z))
	tmp = 0
	if t_1 <= -4e-8:
		tmp = t_2
	elif t_1 <= 5e-24:
		tmp = 1.0
	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(x / Float64(Float64(t - y) * Float64(z - y)))
	t_2 = Float64(1.0 - Float64(x / Float64(Float64(t - y) * z)))
	tmp = 0.0
	if (t_1 <= -4e-8)
		tmp = t_2;
	elseif (t_1 <= 5e-24)
		tmp = 1.0;
	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 = x / ((t - y) * (z - y));
	t_2 = 1.0 - (x / ((t - y) * z));
	tmp = 0.0;
	if (t_1 <= -4e-8)
		tmp = t_2;
	elseif (t_1 <= 5e-24)
		tmp = 1.0;
	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[(x / N[(N[(t - y), $MachinePrecision] * N[(z - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(1.0 - N[(x / N[(N[(t - y), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -4e-8], t$95$2, If[LessEqual[t$95$1, 5e-24], 1.0, t$95$2]]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 x (*.f64 (-.f64 y z) (-.f64 y t))) < -4.0000000000000001e-8 or 4.9999999999999998e-24 < (/.f64 x (*.f64 (-.f64 y z) (-.f64 y t)))

   1. Initial program 99.7%

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

   3. Taylor expanded in z around inf

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

      1. *-commutative N/A

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

      2. associate-*r* N/A

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

      3. lower-*.f64 N/A

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

      4. mul-1-neg N/A

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

      5. sub-neg N/A

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

      6. mul-1-neg N/A

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

      7. +-commutative N/A

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

      8. distribute-neg-in N/A

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

      9. unsub-neg N/A

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

      10. mul-1-neg N/A

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

      11. remove-double-neg N/A

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

      12. lower--.f64 62.5

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

   5. Applied rewrites 62.5%

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

   if -4.0000000000000001e-8 < (/.f64 x (*.f64 (-.f64 y z) (-.f64 y t))) < 4.9999999999999998e-24

   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. Applied rewrites 100.0%

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

4. Final simplification 89.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x}{\left(t - y\right) \cdot \left(z - y\right)} \leq -4 \cdot 10^{-8}:\\ \;\;\;\;1 - \frac{x}{\left(t - y\right) \cdot z}\\ \mathbf{elif}\;\frac{x}{\left(t - y\right) \cdot \left(z - y\right)} \leq 5 \cdot 10^{-24}:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;1 - \frac{x}{\left(t - y\right) \cdot z}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 83.9% accurate, 0.3× speedup

Math

\[\begin{array}{l} [x, y, z, t] = \mathsf{sort}([x, y, z, t])\\ \\ \begin{array}{l} t_1 := \frac{x}{\left(t - y\right) \cdot \left(z - y\right)}\\ \mathbf{if}\;t\_1 \leq -50000:\\ \;\;\;\;1 - \frac{x}{t \cdot z}\\ \mathbf{elif}\;t\_1 \leq 2 \cdot 10^{-6}:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;1 - \frac{x}{y \cdot y}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ x (* (- t y) (- z y)))))
   (if (<= t_1 -50000.0)
     (- 1.0 (/ x (* t z)))
     (if (<= t_1 2e-6) 1.0 (- 1.0 (/ x (* y y)))))))

C

assert(x < y && y < z && z < t);
double code(double x, double y, double z, double t) {
	double t_1 = x / ((t - y) * (z - y));
	double tmp;
	if (t_1 <= -50000.0) {
		tmp = 1.0 - (x / (t * z));
	} else if (t_1 <= 2e-6) {
		tmp = 1.0;
	} 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) :: t_1
    real(8) :: tmp
    t_1 = x / ((t - y) * (z - y))
    if (t_1 <= (-50000.0d0)) then
        tmp = 1.0d0 - (x / (t * z))
    else if (t_1 <= 2d-6) then
        tmp = 1.0d0
    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 t_1 = x / ((t - y) * (z - y));
	double tmp;
	if (t_1 <= -50000.0) {
		tmp = 1.0 - (x / (t * z));
	} else if (t_1 <= 2e-6) {
		tmp = 1.0;
	} 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):
	t_1 = x / ((t - y) * (z - y))
	tmp = 0
	if t_1 <= -50000.0:
		tmp = 1.0 - (x / (t * z))
	elif t_1 <= 2e-6:
		tmp = 1.0
	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)
	t_1 = Float64(x / Float64(Float64(t - y) * Float64(z - y)))
	tmp = 0.0
	if (t_1 <= -50000.0)
		tmp = Float64(1.0 - Float64(x / Float64(t * z)));
	elseif (t_1 <= 2e-6)
		tmp = 1.0;
	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)
	t_1 = x / ((t - y) * (z - y));
	tmp = 0.0;
	if (t_1 <= -50000.0)
		tmp = 1.0 - (x / (t * z));
	elseif (t_1 <= 2e-6)
		tmp = 1.0;
	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_] := Block[{t$95$1 = N[(x / N[(N[(t - y), $MachinePrecision] * N[(z - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -50000.0], N[(1.0 - N[(x / N[(t * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 2e-6], 1.0, N[(1.0 - N[(x / N[(y * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 x (*.f64 (-.f64 y z) (-.f64 y t))) < -5e4

   1. Initial program 99.8%

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

   3. Taylor expanded in y around 0

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

      1. lower-*.f64 62.0

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

   5. Applied rewrites 62.0%

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

   if -5e4 < (/.f64 x (*.f64 (-.f64 y z) (-.f64 y t))) < 1.99999999999999991e-6

   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. Applied rewrites 97.9%

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

   if 1.99999999999999991e-6 < (/.f64 x (*.f64 (-.f64 y z) (-.f64 y t)))

   1. Initial program 99.6%

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

   3. Taylor expanded in y around inf

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

      1. unpow2 N/A

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

      2. lower-*.f64 32.2

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

   5. Applied rewrites 32.2%

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

4. Final simplification 86.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x}{\left(t - y\right) \cdot \left(z - y\right)} \leq -50000:\\ \;\;\;\;1 - \frac{x}{t \cdot z}\\ \mathbf{elif}\;\frac{x}{\left(t - y\right) \cdot \left(z - y\right)} \leq 2 \cdot 10^{-6}:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;1 - \frac{x}{y \cdot y}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 85.7% accurate, 0.3× speedup

Math

\[\begin{array}{l} [x, y, z, t] = \mathsf{sort}([x, y, z, t])\\ \\ \begin{array}{l} t_1 := \frac{x}{\left(t - y\right) \cdot \left(z - y\right)}\\ t_2 := 1 - \frac{x}{t \cdot z}\\ \mathbf{if}\;t\_1 \leq -50000:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_1 \leq 2 \cdot 10^{-11}:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

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 (/ x (* (- t y) (- z y)))) (t_2 (- 1.0 (/ x (* t z)))))
   (if (<= t_1 -50000.0) t_2 (if (<= t_1 2e-11) 1.0 t_2))))

C

assert(x < y && y < z && z < t);
double code(double x, double y, double z, double t) {
	double t_1 = x / ((t - y) * (z - y));
	double t_2 = 1.0 - (x / (t * z));
	double tmp;
	if (t_1 <= -50000.0) {
		tmp = t_2;
	} else if (t_1 <= 2e-11) {
		tmp = 1.0;
	} 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 = x / ((t - y) * (z - y))
    t_2 = 1.0d0 - (x / (t * z))
    if (t_1 <= (-50000.0d0)) then
        tmp = t_2
    else if (t_1 <= 2d-11) then
        tmp = 1.0d0
    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 = x / ((t - y) * (z - y));
	double t_2 = 1.0 - (x / (t * z));
	double tmp;
	if (t_1 <= -50000.0) {
		tmp = t_2;
	} else if (t_1 <= 2e-11) {
		tmp = 1.0;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

[x, y, z, t] = sort([x, y, z, t])
def code(x, y, z, t):
	t_1 = x / ((t - y) * (z - y))
	t_2 = 1.0 - (x / (t * z))
	tmp = 0
	if t_1 <= -50000.0:
		tmp = t_2
	elif t_1 <= 2e-11:
		tmp = 1.0
	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(x / Float64(Float64(t - y) * Float64(z - y)))
	t_2 = Float64(1.0 - Float64(x / Float64(t * z)))
	tmp = 0.0
	if (t_1 <= -50000.0)
		tmp = t_2;
	elseif (t_1 <= 2e-11)
		tmp = 1.0;
	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 = x / ((t - y) * (z - y));
	t_2 = 1.0 - (x / (t * z));
	tmp = 0.0;
	if (t_1 <= -50000.0)
		tmp = t_2;
	elseif (t_1 <= 2e-11)
		tmp = 1.0;
	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[(x / N[(N[(t - y), $MachinePrecision] * N[(z - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(1.0 - N[(x / N[(t * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -50000.0], t$95$2, If[LessEqual[t$95$1, 2e-11], 1.0, t$95$2]]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 x (*.f64 (-.f64 y z) (-.f64 y t))) < -5e4 or 1.99999999999999988e-11 < (/.f64 x (*.f64 (-.f64 y z) (-.f64 y t)))

   1. Initial program 99.7%

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

   3. Taylor expanded in y around 0

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

      1. lower-*.f64 48.3

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

   5. Applied rewrites 48.3%

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

   if -5e4 < (/.f64 x (*.f64 (-.f64 y z) (-.f64 y t))) < 1.99999999999999988e-11

   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. Applied rewrites 98.7%

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

4. Final simplification 85.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x}{\left(t - y\right) \cdot \left(z - y\right)} \leq -50000:\\ \;\;\;\;1 - \frac{x}{t \cdot z}\\ \mathbf{elif}\;\frac{x}{\left(t - y\right) \cdot \left(z - y\right)} \leq 2 \cdot 10^{-11}:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;1 - \frac{x}{t \cdot z}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 93.1% accurate, 0.7× speedup

Math

\[\begin{array}{l} [x, y, z, t] = \mathsf{sort}([x, y, z, t])\\ \\ \begin{array}{l} \mathbf{if}\;t \leq -4 \cdot 10^{-161}:\\ \;\;\;\;1 - \frac{x}{\left(t - y\right) \cdot z}\\ \mathbf{elif}\;t \leq 1.6 \cdot 10^{-57}:\\ \;\;\;\;1 - \frac{x}{\left(y - z\right) \cdot y}\\ \mathbf{else}:\\ \;\;\;\;1 - \frac{x}{\left(z - y\right) \cdot t}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
(FPCore (x y z t)
 :precision binary64
 (if (<= t -4e-161)
   (- 1.0 (/ x (* (- t y) z)))
   (if (<= t 1.6e-57)
     (- 1.0 (/ x (* (- y z) y)))
     (- 1.0 (/ x (* (- z y) t))))))

C

assert(x < y && y < z && z < t);
double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= -4e-161) {
		tmp = 1.0 - (x / ((t - y) * z));
	} else if (t <= 1.6e-57) {
		tmp = 1.0 - (x / ((y - z) * y));
	} else {
		tmp = 1.0 - (x / ((z - y) * t));
	}
	return tmp;
}

Fortran

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (t <= (-4d-161)) then
        tmp = 1.0d0 - (x / ((t - y) * z))
    else if (t <= 1.6d-57) then
        tmp = 1.0d0 - (x / ((y - z) * y))
    else
        tmp = 1.0d0 - (x / ((z - y) * t))
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t;
public static double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= -4e-161) {
		tmp = 1.0 - (x / ((t - y) * z));
	} else if (t <= 1.6e-57) {
		tmp = 1.0 - (x / ((y - z) * y));
	} else {
		tmp = 1.0 - (x / ((z - y) * t));
	}
	return tmp;
}

Python

[x, y, z, t] = sort([x, y, z, t])
def code(x, y, z, t):
	tmp = 0
	if t <= -4e-161:
		tmp = 1.0 - (x / ((t - y) * z))
	elif t <= 1.6e-57:
		tmp = 1.0 - (x / ((y - z) * y))
	else:
		tmp = 1.0 - (x / ((z - y) * t))
	return tmp

Julia

x, y, z, t = sort([x, y, z, t])
function code(x, y, z, t)
	tmp = 0.0
	if (t <= -4e-161)
		tmp = Float64(1.0 - Float64(x / Float64(Float64(t - y) * z)));
	elseif (t <= 1.6e-57)
		tmp = Float64(1.0 - Float64(x / Float64(Float64(y - z) * y)));
	else
		tmp = Float64(1.0 - Float64(x / Float64(Float64(z - y) * t)));
	end
	return tmp
end

MATLAB

x, y, z, t = num2cell(sort([x, y, z, t])){:}
function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (t <= -4e-161)
		tmp = 1.0 - (x / ((t - y) * z));
	elseif (t <= 1.6e-57)
		tmp = 1.0 - (x / ((y - z) * y));
	else
		tmp = 1.0 - (x / ((z - y) * t));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_] := If[LessEqual[t, -4e-161], N[(1.0 - N[(x / N[(N[(t - y), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.6e-57], N[(1.0 - N[(x / N[(N[(y - z), $MachinePrecision] * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(1.0 - N[(x / N[(N[(z - y), $MachinePrecision] * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -4.00000000000000011e-161

   1. Initial program 100.0%

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

   3. Taylor expanded in z around inf

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

      1. *-commutative N/A

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

      2. associate-*r* N/A

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

      3. lower-*.f64 N/A

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

      4. mul-1-neg N/A

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

      5. sub-neg N/A

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

      6. mul-1-neg N/A

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

      7. +-commutative N/A

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

      8. distribute-neg-in N/A

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

      9. unsub-neg N/A

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

      10. mul-1-neg N/A

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

      11. remove-double-neg N/A

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

      12. lower--.f64 80.9

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

   5. Applied rewrites 80.9%

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

   if -4.00000000000000011e-161 < t < 1.6e-57

   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 0

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 95.0

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

   5. Applied rewrites 95.0%

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

   if 1.6e-57 < 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

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

      1. *-commutative N/A

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

      2. associate-*r* N/A

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

      3. lower-*.f64 N/A

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

      4. mul-1-neg N/A

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

      5. sub-neg N/A

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

      6. mul-1-neg N/A

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

      7. +-commutative N/A

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

      8. distribute-neg-in N/A

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

      9. unsub-neg N/A

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

      10. mul-1-neg N/A

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

      11. remove-double-neg N/A

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

      12. lower--.f64 98.8

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

   5. Applied rewrites 98.8%

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

Alternative 6: 90.8% accurate, 0.7× speedup

Math

\[\begin{array}{l} [x, y, z, t] = \mathsf{sort}([x, y, z, t])\\ \\ \begin{array}{l} t_1 := 1 - \frac{x}{\left(t - y\right) \cdot z}\\ \mathbf{if}\;z \leq -22000000:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 3 \cdot 10^{-138}:\\ \;\;\;\;1 - \frac{x}{\left(y - t\right) \cdot y}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

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 (* (- t y) z)))))
   (if (<= z -22000000.0)
     t_1
     (if (<= z 3e-138) (- 1.0 (/ x (* (- y t) 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 / ((t - y) * z));
	double tmp;
	if (z <= -22000000.0) {
		tmp = t_1;
	} else if (z <= 3e-138) {
		tmp = 1.0 - (x / ((y - t) * 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 / ((t - y) * z))
    if (z <= (-22000000.0d0)) then
        tmp = t_1
    else if (z <= 3d-138) then
        tmp = 1.0d0 - (x / ((y - t) * 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 / ((t - y) * z));
	double tmp;
	if (z <= -22000000.0) {
		tmp = t_1;
	} else if (z <= 3e-138) {
		tmp = 1.0 - (x / ((y - t) * 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 / ((t - y) * z))
	tmp = 0
	if z <= -22000000.0:
		tmp = t_1
	elif z <= 3e-138:
		tmp = 1.0 - (x / ((y - t) * 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(x / Float64(Float64(t - y) * z)))
	tmp = 0.0
	if (z <= -22000000.0)
		tmp = t_1;
	elseif (z <= 3e-138)
		tmp = Float64(1.0 - Float64(x / Float64(Float64(y - t) * 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 / ((t - y) * z));
	tmp = 0.0;
	if (z <= -22000000.0)
		tmp = t_1;
	elseif (z <= 3e-138)
		tmp = 1.0 - (x / ((y - t) * 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[(x / N[(N[(t - y), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -22000000.0], t$95$1, If[LessEqual[z, 3e-138], N[(1.0 - N[(x / N[(N[(y - t), $MachinePrecision] * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if z < -2.2e7 or 3.0000000000000001e-138 < z

   1. Initial program 99.9%

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

   3. Taylor expanded in z around inf

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

      1. *-commutative N/A

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

      2. associate-*r* N/A

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

      3. lower-*.f64 N/A

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

      4. mul-1-neg N/A

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

      5. sub-neg N/A

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

      6. mul-1-neg N/A

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

      7. +-commutative N/A

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

      8. distribute-neg-in N/A

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

      9. unsub-neg N/A

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

      10. mul-1-neg N/A

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

      11. remove-double-neg N/A

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

      12. lower--.f64 94.7

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

   5. Applied rewrites 94.7%

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

   if -2.2e7 < z < 3.0000000000000001e-138

   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

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 88.7

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

   5. Applied rewrites 88.7%

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

Alternative 7: 99.2% accurate, 1.0× speedup

Math

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

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 (* (- t y) (- z y)))))

C

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

Python

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

Derivation

1. Initial program 99.9%

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

3. Final simplification 99.9%

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

Alternative 8: 75.5% accurate, 26.0× 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 99.9%

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

3. Taylor expanded in x around 0

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

5. Applied rewrites 75.4%

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

Reproduce

herbie shell --seed 2024294 
(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)))))