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

Percentage Accurate: 99.1% → 98.8%

Time: 7.5s

Alternatives: 11

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: 98.8% 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 99.6%

   \[1 - \frac{x}{\left(y - z\right) \cdot \left(y - t\right)} \]
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 99.2

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

4. Applied rewrites 99.2%

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

Alternative 2: 89.3% accurate, 0.2× speedup

Math

\[\begin{array}{l} [x, y, z, t] = \mathsf{sort}([x, y, z, t])\\ \\ \begin{array}{l} t_1 := \frac{x}{\left(y - z\right) \cdot \left(y - t\right)}\\ t_2 := \frac{-x}{\left(z - y\right) \cdot t}\\ \mathbf{if}\;t\_1 \leq -20000000:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_1 \leq 20000:\\ \;\;\;\;1\\ \mathbf{elif}\;t\_1 \leq 2 \cdot 10^{+110}:\\ \;\;\;\;\frac{x}{\left(z - y\right) \cdot y}\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

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 (* (- y z) (- y t)))) (t_2 (/ (- x) (* (- z y) t))))
   (if (<= t_1 -20000000.0)
     t_2
     (if (<= t_1 20000.0) 1.0 (if (<= t_1 2e+110) (/ x (* (- z y) y)) t_2)))))

C

assert(x < y && y < z && z < t);
double code(double x, double y, double z, double t) {
	double t_1 = x / ((y - z) * (y - t));
	double t_2 = -x / ((z - y) * t);
	double tmp;
	if (t_1 <= -20000000.0) {
		tmp = t_2;
	} else if (t_1 <= 20000.0) {
		tmp = 1.0;
	} else if (t_1 <= 2e+110) {
		tmp = x / ((z - y) * y);
	} 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 / ((y - z) * (y - t))
    t_2 = -x / ((z - y) * t)
    if (t_1 <= (-20000000.0d0)) then
        tmp = t_2
    else if (t_1 <= 20000.0d0) then
        tmp = 1.0d0
    else if (t_1 <= 2d+110) then
        tmp = x / ((z - y) * y)
    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 / ((y - z) * (y - t));
	double t_2 = -x / ((z - y) * t);
	double tmp;
	if (t_1 <= -20000000.0) {
		tmp = t_2;
	} else if (t_1 <= 20000.0) {
		tmp = 1.0;
	} else if (t_1 <= 2e+110) {
		tmp = x / ((z - y) * y);
	} 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 / ((y - z) * (y - t))
	t_2 = -x / ((z - y) * t)
	tmp = 0
	if t_1 <= -20000000.0:
		tmp = t_2
	elif t_1 <= 20000.0:
		tmp = 1.0
	elif t_1 <= 2e+110:
		tmp = x / ((z - y) * y)
	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(y - z) * Float64(y - t)))
	t_2 = Float64(Float64(-x) / Float64(Float64(z - y) * t))
	tmp = 0.0
	if (t_1 <= -20000000.0)
		tmp = t_2;
	elseif (t_1 <= 20000.0)
		tmp = 1.0;
	elseif (t_1 <= 2e+110)
		tmp = Float64(x / Float64(Float64(z - y) * y));
	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 / ((y - z) * (y - t));
	t_2 = -x / ((z - y) * t);
	tmp = 0.0;
	if (t_1 <= -20000000.0)
		tmp = t_2;
	elseif (t_1 <= 20000.0)
		tmp = 1.0;
	elseif (t_1 <= 2e+110)
		tmp = x / ((z - y) * y);
	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[(y - z), $MachinePrecision] * N[(y - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[((-x) / N[(N[(z - y), $MachinePrecision] * t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -20000000.0], t$95$2, If[LessEqual[t$95$1, 20000.0], 1.0, If[LessEqual[t$95$1, 2e+110], N[(x / N[(N[(z - y), $MachinePrecision] * y), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 x (*.f64 (-.f64 y z) (-.f64 y t))) < -2e7 or 2e110 < (/.f64 x (*.f64 (-.f64 y z) (-.f64 y t)))

   1. Initial program 97.4%

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

   3. Taylor expanded in x around inf

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

      1. mul-1-neg N/A

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

      2. associate-/r* N/A

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

      3. distribute-neg-frac2 N/A

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

      4. mul-1-neg N/A

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

      5. lower-/.f64 N/A

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

      6. lower-/.f64 N/A

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

      7. lower--.f64 N/A

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

      8. mul-1-neg N/A

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

      9. sub-neg N/A

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

      10. mul-1-neg N/A

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

      11. +-commutative N/A

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

      12. distribute-neg-in N/A

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

      13. unsub-neg N/A

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

      14. mul-1-neg N/A

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

      15. remove-double-neg N/A

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

      16. lower--.f64 91.8

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

   5. Applied rewrites 91.8%

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

   6. Taylor expanded in t around inf

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

   8. Applied rewrites 64.7%

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

   if -2e7 < (/.f64 x (*.f64 (-.f64 y z) (-.f64 y t))) < 2e4

   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 98.4%

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

   if 2e4 < (/.f64 x (*.f64 (-.f64 y z) (-.f64 y t))) < 2e110

   1. Initial program 99.8%

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

   3. Taylor expanded in x around inf

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

      1. mul-1-neg N/A

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

      2. associate-/r* N/A

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

      3. distribute-neg-frac2 N/A

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

      4. mul-1-neg N/A

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

      5. lower-/.f64 N/A

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

      6. lower-/.f64 N/A

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

      7. lower--.f64 N/A

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

      8. mul-1-neg N/A

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

      9. sub-neg N/A

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

      10. mul-1-neg N/A

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

      11. +-commutative N/A

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

      12. distribute-neg-in N/A

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

      13. unsub-neg N/A

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

      14. mul-1-neg N/A

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

      15. remove-double-neg N/A

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

      16. lower--.f64 95.7

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

   5. Applied rewrites 95.7%

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

   6. Taylor expanded in t around 0

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

   8. Applied rewrites 58.5%

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

Alternative 3: 89.6% accurate, 0.3× speedup

Math

\[\begin{array}{l} [x, y, z, t] = \mathsf{sort}([x, y, z, t])\\ \\ \begin{array}{l} t_1 := \frac{x}{\left(y - z\right) \cdot \left(y - t\right)}\\ \mathbf{if}\;t\_1 \leq -20000000:\\ \;\;\;\;\frac{-x}{\left(z - y\right) \cdot t}\\ \mathbf{elif}\;t\_1 \leq 5 \cdot 10^{-30}:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;1 - \frac{x}{\left(t - y\right) \cdot z}\\ \end{array} \end{array} \]

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 (* (- y z) (- y t)))))
   (if (<= t_1 -20000000.0)
     (/ (- x) (* (- z y) t))
     (if (<= t_1 5e-30) 1.0 (- 1.0 (/ x (* (- t y) z)))))))

C

assert(x < y && y < z && z < t);
double code(double x, double y, double z, double t) {
	double t_1 = x / ((y - z) * (y - t));
	double tmp;
	if (t_1 <= -20000000.0) {
		tmp = -x / ((z - y) * t);
	} else if (t_1 <= 5e-30) {
		tmp = 1.0;
	} else {
		tmp = 1.0 - (x / ((t - y) * z));
	}
	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 / ((y - z) * (y - t))
    if (t_1 <= (-20000000.0d0)) then
        tmp = -x / ((z - y) * t)
    else if (t_1 <= 5d-30) then
        tmp = 1.0d0
    else
        tmp = 1.0d0 - (x / ((t - y) * z))
    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 / ((y - z) * (y - t));
	double tmp;
	if (t_1 <= -20000000.0) {
		tmp = -x / ((z - y) * t);
	} else if (t_1 <= 5e-30) {
		tmp = 1.0;
	} else {
		tmp = 1.0 - (x / ((t - y) * z));
	}
	return tmp;
}

Python

[x, y, z, t] = sort([x, y, z, t])
def code(x, y, z, t):
	t_1 = x / ((y - z) * (y - t))
	tmp = 0
	if t_1 <= -20000000.0:
		tmp = -x / ((z - y) * t)
	elif t_1 <= 5e-30:
		tmp = 1.0
	else:
		tmp = 1.0 - (x / ((t - y) * z))
	return tmp

Julia

x, y, z, t = sort([x, y, z, t])
function code(x, y, z, t)
	t_1 = Float64(x / Float64(Float64(y - z) * Float64(y - t)))
	tmp = 0.0
	if (t_1 <= -20000000.0)
		tmp = Float64(Float64(-x) / Float64(Float64(z - y) * t));
	elseif (t_1 <= 5e-30)
		tmp = 1.0;
	else
		tmp = Float64(1.0 - Float64(x / Float64(Float64(t - y) * z)));
	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 / ((y - z) * (y - t));
	tmp = 0.0;
	if (t_1 <= -20000000.0)
		tmp = -x / ((z - y) * t);
	elseif (t_1 <= 5e-30)
		tmp = 1.0;
	else
		tmp = 1.0 - (x / ((t - y) * z));
	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[(y - z), $MachinePrecision] * N[(y - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -20000000.0], N[((-x) / N[(N[(z - y), $MachinePrecision] * t), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 5e-30], 1.0, N[(1.0 - N[(x / N[(N[(t - y), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 x (*.f64 (-.f64 y z) (-.f64 y t))) < -2e7

   1. Initial program 95.8%

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

   3. Taylor expanded in x around inf

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

      1. mul-1-neg N/A

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

      2. associate-/r* N/A

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

      3. distribute-neg-frac2 N/A

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

      4. mul-1-neg N/A

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

      5. lower-/.f64 N/A

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

      6. lower-/.f64 N/A

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

      7. lower--.f64 N/A

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

      8. mul-1-neg N/A

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

      9. sub-neg N/A

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

      10. mul-1-neg N/A

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

      11. +-commutative N/A

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

      12. distribute-neg-in N/A

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

      13. unsub-neg N/A

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

      14. mul-1-neg N/A

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

      15. remove-double-neg N/A

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

      16. lower--.f64 93.9

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

   5. Applied rewrites 93.9%

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

   6. Taylor expanded in t around inf

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

   8. Applied rewrites 63.9%

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

   if -2e7 < (/.f64 x (*.f64 (-.f64 y z) (-.f64 y t))) < 4.99999999999999972e-30

   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 99.4%

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

   if 4.99999999999999972e-30 < (/.f64 x (*.f64 (-.f64 y z) (-.f64 y t)))

   1. Initial program 99.8%

      \[1 - \frac{x}{\left(y - z\right) \cdot \left(y - t\right)} \]
   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 66.0

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

   5. Applied rewrites 66.0%

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

Alternative 4: 88.5% accurate, 0.3× speedup

Math

\[\begin{array}{l} [x, y, z, t] = \mathsf{sort}([x, y, z, t])\\ \\ \begin{array}{l} t_1 := \frac{x}{\left(y - z\right) \cdot \left(y - t\right)}\\ \mathbf{if}\;t\_1 \leq -1 \cdot 10^{+54} \lor \neg \left(t\_1 \leq 2 \cdot 10^{-7}\right):\\ \;\;\;\;\frac{x}{\left(y - t\right) \cdot z}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ x (* (- y z) (- y t)))))
   (if (or (<= t_1 -1e+54) (not (<= t_1 2e-7))) (/ x (* (- y t) z)) 1.0)))

C

assert(x < y && y < z && z < t);
double code(double x, double y, double z, double t) {
	double t_1 = x / ((y - z) * (y - t));
	double tmp;
	if ((t_1 <= -1e+54) || !(t_1 <= 2e-7)) {
		tmp = x / ((y - t) * z);
	} 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) :: t_1
    real(8) :: tmp
    t_1 = x / ((y - z) * (y - t))
    if ((t_1 <= (-1d+54)) .or. (.not. (t_1 <= 2d-7))) then
        tmp = x / ((y - t) * z)
    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 t_1 = x / ((y - z) * (y - t));
	double tmp;
	if ((t_1 <= -1e+54) || !(t_1 <= 2e-7)) {
		tmp = x / ((y - t) * z);
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Python

[x, y, z, t] = sort([x, y, z, t])
def code(x, y, z, t):
	t_1 = x / ((y - z) * (y - t))
	tmp = 0
	if (t_1 <= -1e+54) or not (t_1 <= 2e-7):
		tmp = x / ((y - t) * z)
	else:
		tmp = 1.0
	return tmp

Julia

x, y, z, t = sort([x, y, z, t])
function code(x, y, z, t)
	t_1 = Float64(x / Float64(Float64(y - z) * Float64(y - t)))
	tmp = 0.0
	if ((t_1 <= -1e+54) || !(t_1 <= 2e-7))
		tmp = Float64(x / Float64(Float64(y - t) * z));
	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)
	t_1 = x / ((y - z) * (y - t));
	tmp = 0.0;
	if ((t_1 <= -1e+54) || ~((t_1 <= 2e-7)))
		tmp = x / ((y - t) * z);
	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_] := Block[{t$95$1 = N[(x / N[(N[(y - z), $MachinePrecision] * N[(y - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[t$95$1, -1e+54], N[Not[LessEqual[t$95$1, 2e-7]], $MachinePrecision]], N[(x / N[(N[(y - t), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision], 1.0]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 x (*.f64 (-.f64 y z) (-.f64 y t))) < -1.0000000000000001e54 or 1.9999999999999999e-7 < (/.f64 x (*.f64 (-.f64 y z) (-.f64 y t)))

   1. Initial program 97.9%

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

   3. Taylor expanded in x around inf

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

      1. mul-1-neg N/A

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

      2. associate-/r* N/A

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

      3. distribute-neg-frac2 N/A

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

      4. mul-1-neg N/A

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

      5. lower-/.f64 N/A

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

      6. lower-/.f64 N/A

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

      7. lower--.f64 N/A

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

      8. mul-1-neg N/A

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

      9. sub-neg N/A

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

      10. mul-1-neg N/A

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

      11. +-commutative N/A

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

      12. distribute-neg-in N/A

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

      13. unsub-neg N/A

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

      14. mul-1-neg N/A

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

      15. remove-double-neg N/A

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

      16. lower--.f64 92.0

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

   5. Applied rewrites 92.0%

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

   6. Taylor expanded in z around inf

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

   8. Applied rewrites 58.1%

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

   if -1.0000000000000001e54 < (/.f64 x (*.f64 (-.f64 y z) (-.f64 y t))) < 1.9999999999999999e-7

   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 97.1%

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

4. Final simplification 89.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x}{\left(y - z\right) \cdot \left(y - t\right)} \leq -1 \cdot 10^{+54} \lor \neg \left(\frac{x}{\left(y - z\right) \cdot \left(y - t\right)} \leq 2 \cdot 10^{-7}\right):\\ \;\;\;\;\frac{x}{\left(y - t\right) \cdot z}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 87.6% accurate, 0.3× speedup

Math

\[\begin{array}{l} [x, y, z, t] = \mathsf{sort}([x, y, z, t])\\ \\ \begin{array}{l} t_1 := \frac{x}{\left(y - z\right) \cdot \left(y - t\right)}\\ \mathbf{if}\;t\_1 \leq -20000000:\\ \;\;\;\;\frac{-x}{\left(y - t\right) \cdot y}\\ \mathbf{elif}\;t\_1 \leq 2 \cdot 10^{-7}:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\left(y - t\right) \cdot z}\\ \end{array} \end{array} \]

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 (* (- y z) (- y t)))))
   (if (<= t_1 -20000000.0)
     (/ (- x) (* (- y t) y))
     (if (<= t_1 2e-7) 1.0 (/ x (* (- y t) z))))))

C

assert(x < y && y < z && z < t);
double code(double x, double y, double z, double t) {
	double t_1 = x / ((y - z) * (y - t));
	double tmp;
	if (t_1 <= -20000000.0) {
		tmp = -x / ((y - t) * y);
	} else if (t_1 <= 2e-7) {
		tmp = 1.0;
	} else {
		tmp = x / ((y - t) * z);
	}
	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 / ((y - z) * (y - t))
    if (t_1 <= (-20000000.0d0)) then
        tmp = -x / ((y - t) * y)
    else if (t_1 <= 2d-7) then
        tmp = 1.0d0
    else
        tmp = x / ((y - t) * z)
    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 / ((y - z) * (y - t));
	double tmp;
	if (t_1 <= -20000000.0) {
		tmp = -x / ((y - t) * y);
	} else if (t_1 <= 2e-7) {
		tmp = 1.0;
	} else {
		tmp = x / ((y - t) * z);
	}
	return tmp;
}

Python

[x, y, z, t] = sort([x, y, z, t])
def code(x, y, z, t):
	t_1 = x / ((y - z) * (y - t))
	tmp = 0
	if t_1 <= -20000000.0:
		tmp = -x / ((y - t) * y)
	elif t_1 <= 2e-7:
		tmp = 1.0
	else:
		tmp = x / ((y - t) * z)
	return tmp

Julia

x, y, z, t = sort([x, y, z, t])
function code(x, y, z, t)
	t_1 = Float64(x / Float64(Float64(y - z) * Float64(y - t)))
	tmp = 0.0
	if (t_1 <= -20000000.0)
		tmp = Float64(Float64(-x) / Float64(Float64(y - t) * y));
	elseif (t_1 <= 2e-7)
		tmp = 1.0;
	else
		tmp = Float64(x / Float64(Float64(y - t) * z));
	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 / ((y - z) * (y - t));
	tmp = 0.0;
	if (t_1 <= -20000000.0)
		tmp = -x / ((y - t) * y);
	elseif (t_1 <= 2e-7)
		tmp = 1.0;
	else
		tmp = x / ((y - t) * z);
	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[(y - z), $MachinePrecision] * N[(y - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -20000000.0], N[((-x) / N[(N[(y - t), $MachinePrecision] * y), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 2e-7], 1.0, N[(x / N[(N[(y - t), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 x (*.f64 (-.f64 y z) (-.f64 y t))) < -2e7

   1. Initial program 95.8%

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

   3. Taylor expanded in x around inf

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

      1. mul-1-neg N/A

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

      2. associate-/r* N/A

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

      3. distribute-neg-frac2 N/A

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

      4. mul-1-neg N/A

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

      5. lower-/.f64 N/A

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

      6. lower-/.f64 N/A

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

      7. lower--.f64 N/A

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

      8. mul-1-neg N/A

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

      9. sub-neg N/A

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

      10. mul-1-neg N/A

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

      11. +-commutative N/A

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

      12. distribute-neg-in N/A

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

      13. unsub-neg N/A

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

      14. mul-1-neg N/A

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

      15. remove-double-neg N/A

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

      16. lower--.f64 93.9

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

   5. Applied rewrites 93.9%

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

   6. Taylor expanded in z around 0

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

   8. Applied rewrites 61.2%

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

   if -2e7 < (/.f64 x (*.f64 (-.f64 y z) (-.f64 y t))) < 1.9999999999999999e-7

   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 98.9%

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

   if 1.9999999999999999e-7 < (/.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 x around inf

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

      1. mul-1-neg N/A

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

      2. associate-/r* N/A

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

      3. distribute-neg-frac2 N/A

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

      4. mul-1-neg N/A

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

      5. lower-/.f64 N/A

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

      6. lower-/.f64 N/A

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

      7. lower--.f64 N/A

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

      8. mul-1-neg N/A

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

      9. sub-neg N/A

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

      10. mul-1-neg N/A

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

      11. +-commutative N/A

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

      12. distribute-neg-in N/A

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

      13. unsub-neg N/A

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

      14. mul-1-neg N/A

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

      15. remove-double-neg N/A

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

      16. lower--.f64 90.0

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

   5. Applied rewrites 90.0%

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

   6. Taylor expanded in z around inf

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

   8. Applied rewrites 63.6%

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

Alternative 6: 87.3% accurate, 0.3× speedup

Math

\[\begin{array}{l} [x, y, z, t] = \mathsf{sort}([x, y, z, t])\\ \\ \begin{array}{l} t_1 := \frac{x}{\left(y - z\right) \cdot \left(y - t\right)}\\ \mathbf{if}\;t\_1 \leq -20000000:\\ \;\;\;\;\frac{x}{\left(z - y\right) \cdot y}\\ \mathbf{elif}\;t\_1 \leq 2 \cdot 10^{-7}:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\left(y - t\right) \cdot z}\\ \end{array} \end{array} \]

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 (* (- y z) (- y t)))))
   (if (<= t_1 -20000000.0)
     (/ x (* (- z y) y))
     (if (<= t_1 2e-7) 1.0 (/ x (* (- y t) z))))))

C

assert(x < y && y < z && z < t);
double code(double x, double y, double z, double t) {
	double t_1 = x / ((y - z) * (y - t));
	double tmp;
	if (t_1 <= -20000000.0) {
		tmp = x / ((z - y) * y);
	} else if (t_1 <= 2e-7) {
		tmp = 1.0;
	} else {
		tmp = x / ((y - t) * z);
	}
	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 / ((y - z) * (y - t))
    if (t_1 <= (-20000000.0d0)) then
        tmp = x / ((z - y) * y)
    else if (t_1 <= 2d-7) then
        tmp = 1.0d0
    else
        tmp = x / ((y - t) * z)
    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 / ((y - z) * (y - t));
	double tmp;
	if (t_1 <= -20000000.0) {
		tmp = x / ((z - y) * y);
	} else if (t_1 <= 2e-7) {
		tmp = 1.0;
	} else {
		tmp = x / ((y - t) * z);
	}
	return tmp;
}

Python

[x, y, z, t] = sort([x, y, z, t])
def code(x, y, z, t):
	t_1 = x / ((y - z) * (y - t))
	tmp = 0
	if t_1 <= -20000000.0:
		tmp = x / ((z - y) * y)
	elif t_1 <= 2e-7:
		tmp = 1.0
	else:
		tmp = x / ((y - t) * z)
	return tmp

Julia

x, y, z, t = sort([x, y, z, t])
function code(x, y, z, t)
	t_1 = Float64(x / Float64(Float64(y - z) * Float64(y - t)))
	tmp = 0.0
	if (t_1 <= -20000000.0)
		tmp = Float64(x / Float64(Float64(z - y) * y));
	elseif (t_1 <= 2e-7)
		tmp = 1.0;
	else
		tmp = Float64(x / Float64(Float64(y - t) * z));
	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 / ((y - z) * (y - t));
	tmp = 0.0;
	if (t_1 <= -20000000.0)
		tmp = x / ((z - y) * y);
	elseif (t_1 <= 2e-7)
		tmp = 1.0;
	else
		tmp = x / ((y - t) * z);
	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[(y - z), $MachinePrecision] * N[(y - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -20000000.0], N[(x / N[(N[(z - y), $MachinePrecision] * y), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 2e-7], 1.0, N[(x / N[(N[(y - t), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 x (*.f64 (-.f64 y z) (-.f64 y t))) < -2e7

   1. Initial program 95.8%

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

   3. Taylor expanded in x around inf

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

      1. mul-1-neg N/A

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

      2. associate-/r* N/A

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

      3. distribute-neg-frac2 N/A

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

      4. mul-1-neg N/A

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

      5. lower-/.f64 N/A

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

      6. lower-/.f64 N/A

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

      7. lower--.f64 N/A

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

      8. mul-1-neg N/A

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

      9. sub-neg N/A

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

      10. mul-1-neg N/A

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

      11. +-commutative N/A

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

      12. distribute-neg-in N/A

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

      13. unsub-neg N/A

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

      14. mul-1-neg N/A

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

      15. remove-double-neg N/A

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

      16. lower--.f64 93.9

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

   5. Applied rewrites 93.9%

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

   6. Taylor expanded in t around 0

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

   8. Applied rewrites 45.7%

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

   if -2e7 < (/.f64 x (*.f64 (-.f64 y z) (-.f64 y t))) < 1.9999999999999999e-7

   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 98.9%

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

   if 1.9999999999999999e-7 < (/.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 x around inf

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

      1. mul-1-neg N/A

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

      2. associate-/r* N/A

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

      3. distribute-neg-frac2 N/A

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

      4. mul-1-neg N/A

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

      5. lower-/.f64 N/A

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

      6. lower-/.f64 N/A

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

      7. lower--.f64 N/A

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

      8. mul-1-neg N/A

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

      9. sub-neg N/A

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

      10. mul-1-neg N/A

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

      11. +-commutative N/A

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

      12. distribute-neg-in N/A

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

      13. unsub-neg N/A

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

      14. mul-1-neg N/A

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

      15. remove-double-neg N/A

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

      16. lower--.f64 90.0

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

   5. Applied rewrites 90.0%

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

   6. Taylor expanded in z around inf

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

   8. Applied rewrites 63.6%

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

Alternative 7: 85.1% accurate, 0.3× speedup

Math

\[\begin{array}{l} [x, y, z, t] = \mathsf{sort}([x, y, z, t])\\ \\ \begin{array}{l} t_1 := \frac{x}{\left(y - z\right) \cdot \left(y - t\right)}\\ \mathbf{if}\;t\_1 \leq -1 \cdot 10^{+54} \lor \neg \left(t\_1 \leq 2 \cdot 10^{-7}\right):\\ \;\;\;\;\frac{-x}{t \cdot z}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ x (* (- y z) (- y t)))))
   (if (or (<= t_1 -1e+54) (not (<= t_1 2e-7))) (/ (- x) (* t z)) 1.0)))

C

assert(x < y && y < z && z < t);
double code(double x, double y, double z, double t) {
	double t_1 = x / ((y - z) * (y - t));
	double tmp;
	if ((t_1 <= -1e+54) || !(t_1 <= 2e-7)) {
		tmp = -x / (t * z);
	} 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) :: t_1
    real(8) :: tmp
    t_1 = x / ((y - z) * (y - t))
    if ((t_1 <= (-1d+54)) .or. (.not. (t_1 <= 2d-7))) then
        tmp = -x / (t * z)
    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 t_1 = x / ((y - z) * (y - t));
	double tmp;
	if ((t_1 <= -1e+54) || !(t_1 <= 2e-7)) {
		tmp = -x / (t * z);
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Python

[x, y, z, t] = sort([x, y, z, t])
def code(x, y, z, t):
	t_1 = x / ((y - z) * (y - t))
	tmp = 0
	if (t_1 <= -1e+54) or not (t_1 <= 2e-7):
		tmp = -x / (t * z)
	else:
		tmp = 1.0
	return tmp

Julia

x, y, z, t = sort([x, y, z, t])
function code(x, y, z, t)
	t_1 = Float64(x / Float64(Float64(y - z) * Float64(y - t)))
	tmp = 0.0
	if ((t_1 <= -1e+54) || !(t_1 <= 2e-7))
		tmp = Float64(Float64(-x) / Float64(t * z));
	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)
	t_1 = x / ((y - z) * (y - t));
	tmp = 0.0;
	if ((t_1 <= -1e+54) || ~((t_1 <= 2e-7)))
		tmp = -x / (t * z);
	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_] := Block[{t$95$1 = N[(x / N[(N[(y - z), $MachinePrecision] * N[(y - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[t$95$1, -1e+54], N[Not[LessEqual[t$95$1, 2e-7]], $MachinePrecision]], N[((-x) / N[(t * z), $MachinePrecision]), $MachinePrecision], 1.0]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 x (*.f64 (-.f64 y z) (-.f64 y t))) < -1.0000000000000001e54 or 1.9999999999999999e-7 < (/.f64 x (*.f64 (-.f64 y z) (-.f64 y t)))

   1. Initial program 97.9%

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

   3. Taylor expanded in x around inf

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

      1. mul-1-neg N/A

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

      2. associate-/r* N/A

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

      3. distribute-neg-frac2 N/A

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

      4. mul-1-neg N/A

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

      5. lower-/.f64 N/A

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

      6. lower-/.f64 N/A

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

      7. lower--.f64 N/A

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

      8. mul-1-neg N/A

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

      9. sub-neg N/A

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

      10. mul-1-neg N/A

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

      11. +-commutative N/A

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

      12. distribute-neg-in N/A

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

      13. unsub-neg N/A

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

      14. mul-1-neg N/A

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

      15. remove-double-neg N/A

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

      16. lower--.f64 92.0

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

   5. Applied rewrites 92.0%

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

   6. Taylor expanded in y around 0

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

   8. Applied rewrites 40.5%

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

   if -1.0000000000000001e54 < (/.f64 x (*.f64 (-.f64 y z) (-.f64 y t))) < 1.9999999999999999e-7

   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 97.1%

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

4. Final simplification 85.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x}{\left(y - z\right) \cdot \left(y - t\right)} \leq -1 \cdot 10^{+54} \lor \neg \left(\frac{x}{\left(y - z\right) \cdot \left(y - t\right)} \leq 2 \cdot 10^{-7}\right):\\ \;\;\;\;\frac{-x}{t \cdot z}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 91.5% accurate, 0.7× speedup

Math

\[\begin{array}{l} [x, y, z, t] = \mathsf{sort}([x, y, z, t])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -2.7 \cdot 10^{-47} \lor \neg \left(z \leq 3.9 \cdot 10^{-116}\right):\\ \;\;\;\;1 - \frac{x}{\left(t - y\right) \cdot z}\\ \mathbf{else}:\\ \;\;\;\;1 - \frac{x}{\left(y - t\right) \cdot y}\\ \end{array} \end{array} \]

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 (or (<= z -2.7e-47) (not (<= z 3.9e-116)))
   (- 1.0 (/ x (* (- t y) z)))
   (- 1.0 (/ x (* (- y t) y)))))

C

assert(x < y && y < z && z < t);
double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -2.7e-47) || !(z <= 3.9e-116)) {
		tmp = 1.0 - (x / ((t - y) * z));
	} else {
		tmp = 1.0 - (x / ((y - t) * y));
	}
	return tmp;
}

Fortran

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((z <= (-2.7d-47)) .or. (.not. (z <= 3.9d-116))) then
        tmp = 1.0d0 - (x / ((t - y) * z))
    else
        tmp = 1.0d0 - (x / ((y - t) * y))
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t;
public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -2.7e-47) || !(z <= 3.9e-116)) {
		tmp = 1.0 - (x / ((t - y) * z));
	} else {
		tmp = 1.0 - (x / ((y - t) * y));
	}
	return tmp;
}

Python

[x, y, z, t] = sort([x, y, z, t])
def code(x, y, z, t):
	tmp = 0
	if (z <= -2.7e-47) or not (z <= 3.9e-116):
		tmp = 1.0 - (x / ((t - y) * z))
	else:
		tmp = 1.0 - (x / ((y - t) * y))
	return tmp

Julia

x, y, z, t = sort([x, y, z, t])
function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -2.7e-47) || !(z <= 3.9e-116))
		tmp = Float64(1.0 - Float64(x / Float64(Float64(t - y) * z)));
	else
		tmp = Float64(1.0 - Float64(x / Float64(Float64(y - t) * y)));
	end
	return tmp
end

MATLAB

x, y, z, t = num2cell(sort([x, y, z, t])){:}
function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z <= -2.7e-47) || ~((z <= 3.9e-116)))
		tmp = 1.0 - (x / ((t - y) * z));
	else
		tmp = 1.0 - (x / ((y - t) * y));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_] := If[Or[LessEqual[z, -2.7e-47], N[Not[LessEqual[z, 3.9e-116]], $MachinePrecision]], N[(1.0 - N[(x / N[(N[(t - y), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(1.0 - N[(x / N[(N[(y - t), $MachinePrecision] * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -2.6999999999999998e-47 or 3.9000000000000001e-116 < 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 96.3

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

   5. Applied rewrites 96.3%

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

   if -2.6999999999999998e-47 < z < 3.9000000000000001e-116

   1. Initial program 98.9%

      \[1 - \frac{x}{\left(y - z\right) \cdot \left(y - t\right)} \]
   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 91.6

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

   5. Applied rewrites 91.6%

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

4. Final simplification 94.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.7 \cdot 10^{-47} \lor \neg \left(z \leq 3.9 \cdot 10^{-116}\right):\\ \;\;\;\;1 - \frac{x}{\left(t - y\right) \cdot z}\\ \mathbf{else}:\\ \;\;\;\;1 - \frac{x}{\left(y - t\right) \cdot y}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 92.4% accurate, 0.7× speedup

Math

\[\begin{array}{l} [x, y, z, t] = \mathsf{sort}([x, y, z, t])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -2.7 \cdot 10^{-47}:\\ \;\;\;\;1 - \frac{x}{\left(t - y\right) \cdot z}\\ \mathbf{elif}\;z \leq 3.9 \cdot 10^{-116}:\\ \;\;\;\;1 - \frac{x}{\left(y - t\right) \cdot y}\\ \mathbf{else}:\\ \;\;\;\;1 - \frac{x}{\left(z - y\right) \cdot t}\\ \end{array} \end{array} \]

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 (<= z -2.7e-47)
   (- 1.0 (/ x (* (- t y) z)))
   (if (<= z 3.9e-116)
     (- 1.0 (/ x (* (- y t) 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 (z <= -2.7e-47) {
		tmp = 1.0 - (x / ((t - y) * z));
	} else if (z <= 3.9e-116) {
		tmp = 1.0 - (x / ((y - t) * 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 (z <= (-2.7d-47)) then
        tmp = 1.0d0 - (x / ((t - y) * z))
    else if (z <= 3.9d-116) then
        tmp = 1.0d0 - (x / ((y - t) * 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 (z <= -2.7e-47) {
		tmp = 1.0 - (x / ((t - y) * z));
	} else if (z <= 3.9e-116) {
		tmp = 1.0 - (x / ((y - t) * 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 z <= -2.7e-47:
		tmp = 1.0 - (x / ((t - y) * z))
	elif z <= 3.9e-116:
		tmp = 1.0 - (x / ((y - t) * 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 (z <= -2.7e-47)
		tmp = Float64(1.0 - Float64(x / Float64(Float64(t - y) * z)));
	elseif (z <= 3.9e-116)
		tmp = Float64(1.0 - Float64(x / Float64(Float64(y - t) * 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 (z <= -2.7e-47)
		tmp = 1.0 - (x / ((t - y) * z));
	elseif (z <= 3.9e-116)
		tmp = 1.0 - (x / ((y - t) * 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[z, -2.7e-47], N[(1.0 - N[(x / N[(N[(t - y), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 3.9e-116], N[(1.0 - N[(x / N[(N[(y - t), $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 z < -2.6999999999999998e-47

   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 97.9

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

   5. Applied rewrites 97.9%

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

   if -2.6999999999999998e-47 < z < 3.9000000000000001e-116

   1. Initial program 98.9%

      \[1 - \frac{x}{\left(y - z\right) \cdot \left(y - t\right)} \]
   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 91.6

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

   5. Applied rewrites 91.6%

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

   if 3.9000000000000001e-116 < z

   1. Initial program 100.0%

      \[1 - \frac{x}{\left(y - z\right) \cdot \left(y - t\right)} \]
   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 79.1

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

   5. Applied rewrites 79.1%

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

Alternative 10: 99.1% accurate, 1.0× speedup

Math

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

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) (- y t)))))

C

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

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) * (y - t)))
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) * (y - t)));
}

Python

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

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(y - t))))
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) * (y - t)));
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[(y - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 99.6%

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

Alternative 11: 75.6% 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 99.6%

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

3. Taylor expanded in x around 0

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

5. Applied rewrites 78.2%

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

Reproduce

herbie shell --seed 2024340 
(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)))))