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

Percentage Accurate: 99.3% → 99.3%

Time: 7.5s

Alternatives: 10

Speedup: 1.0×

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 99.3% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 99.3% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

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 / ((t - y) * (z - y)))
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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 99.1%

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

3. Final simplification 99.1%

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

Alternative 2: 89.4% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{\left(t - y\right) \cdot \left(z - y\right)}\\ \mathbf{if}\;t\_1 \leq -5 \cdot 10^{+191}:\\ \;\;\;\;\frac{x}{\left(t - y\right) \cdot y}\\ \mathbf{elif}\;t\_1 \leq -40000000:\\ \;\;\;\;1 - \frac{x}{\left(t - y\right) \cdot z}\\ \mathbf{elif}\;t\_1 \leq 0.002:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{t \cdot \left(y - z\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ x (* (- t y) (- z y)))))
   (if (<= t_1 -5e+191)
     (/ x (* (- t y) y))
     (if (<= t_1 -40000000.0)
       (- 1.0 (/ x (* (- t y) z)))
       (if (<= t_1 0.002) 1.0 (/ x (* t (- y z))))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x / ((t - y) * (z - y));
	double tmp;
	if (t_1 <= -5e+191) {
		tmp = x / ((t - y) * y);
	} else if (t_1 <= -40000000.0) {
		tmp = 1.0 - (x / ((t - y) * z));
	} else if (t_1 <= 0.002) {
		tmp = 1.0;
	} else {
		tmp = x / (t * (y - z));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x / ((t - y) * (z - y))
    if (t_1 <= (-5d+191)) then
        tmp = x / ((t - y) * y)
    else if (t_1 <= (-40000000.0d0)) then
        tmp = 1.0d0 - (x / ((t - y) * z))
    else if (t_1 <= 0.002d0) then
        tmp = 1.0d0
    else
        tmp = x / (t * (y - z))
    end if
    code = tmp
end function

Java

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 <= -5e+191) {
		tmp = x / ((t - y) * y);
	} else if (t_1 <= -40000000.0) {
		tmp = 1.0 - (x / ((t - y) * z));
	} else if (t_1 <= 0.002) {
		tmp = 1.0;
	} else {
		tmp = x / (t * (y - z));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x / ((t - y) * (z - y))
	tmp = 0
	if t_1 <= -5e+191:
		tmp = x / ((t - y) * y)
	elif t_1 <= -40000000.0:
		tmp = 1.0 - (x / ((t - y) * z))
	elif t_1 <= 0.002:
		tmp = 1.0
	else:
		tmp = x / (t * (y - z))
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x / Float64(Float64(t - y) * Float64(z - y)))
	tmp = 0.0
	if (t_1 <= -5e+191)
		tmp = Float64(x / Float64(Float64(t - y) * y));
	elseif (t_1 <= -40000000.0)
		tmp = Float64(1.0 - Float64(x / Float64(Float64(t - y) * z)));
	elseif (t_1 <= 0.002)
		tmp = 1.0;
	else
		tmp = Float64(x / Float64(t * Float64(y - z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x / ((t - y) * (z - y));
	tmp = 0.0;
	if (t_1 <= -5e+191)
		tmp = x / ((t - y) * y);
	elseif (t_1 <= -40000000.0)
		tmp = 1.0 - (x / ((t - y) * z));
	elseif (t_1 <= 0.002)
		tmp = 1.0;
	else
		tmp = x / (t * (y - z));
	end
	tmp_2 = tmp;
end

Wolfram

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, -5e+191], N[(x / N[(N[(t - y), $MachinePrecision] * y), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, -40000000.0], N[(1.0 - N[(x / N[(N[(t - y), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 0.002], 1.0, N[(x / N[(t * N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 4 regimes

2. if (/.f64 x (*.f64 (-.f64 y z) (-.f64 y t))) < -5.0000000000000002e191

   1. Initial program 94.2%

      \[1 - \frac{x}{\left(y - z\right) \cdot \left(y - t\right)} \]
   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. associate-*r/ N/A

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

      2. *-commutative N/A

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

      3. associate-/r* N/A

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

      4. associate-*r/ N/A

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

      5. lower-/.f64 N/A

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

      6. mul-1-neg N/A

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

      7. distribute-neg-frac2 N/A

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

      8. mul-1-neg N/A

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

      9. lower-/.f64 N/A

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

      10. mul-1-neg N/A

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

      11. sub-neg N/A

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

      12. mul-1-neg N/A

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

      13. +-commutative N/A

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

      14. distribute-neg-in N/A

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

      15. unsub-neg N/A

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

      16. mul-1-neg N/A

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

      17. remove-double-neg N/A

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

      18. lower--.f64 N/A

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

      19. lower--.f64 89.0

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

   5. Applied rewrites 89.0%

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

   6. Taylor expanded in y around inf

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

   8. Applied rewrites 49.1%

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

   9. Taylor expanded in z around 0

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

   11. Applied rewrites 54.4%

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

   if -5.0000000000000002e191 < (/.f64 x (*.f64 (-.f64 y z) (-.f64 y t))) < -4e7

   1. Initial program 99.0%

      \[1 - \frac{x}{\left(y - z\right) \cdot \left(y - t\right)} \]
   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 69.3

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

   5. Applied rewrites 69.3%

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

   if -4e7 < (/.f64 x (*.f64 (-.f64 y z) (-.f64 y t))) < 2e-3

   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%

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

   if 2e-3 < (/.f64 x (*.f64 (-.f64 y z) (-.f64 y t)))

   1. Initial program 96.7%

      \[1 - \frac{x}{\left(y - z\right) \cdot \left(y - t\right)} \]
   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. associate-*r/ N/A

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

      2. *-commutative N/A

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

      3. associate-/r* N/A

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

      4. associate-*r/ N/A

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

      5. lower-/.f64 N/A

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

      6. mul-1-neg N/A

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

      7. distribute-neg-frac2 N/A

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

      8. mul-1-neg N/A

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

      9. lower-/.f64 N/A

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

      10. mul-1-neg N/A

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

      11. sub-neg N/A

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

      12. mul-1-neg N/A

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

      13. +-commutative N/A

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

      14. distribute-neg-in N/A

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

      15. unsub-neg N/A

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

      16. mul-1-neg N/A

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

      17. remove-double-neg N/A

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

      18. lower--.f64 N/A

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

      19. lower--.f64 90.1

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

   5. Applied rewrites 90.1%

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

   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 69.9%

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

4. Final simplification 89.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x}{\left(t - y\right) \cdot \left(z - y\right)} \leq -5 \cdot 10^{+191}:\\ \;\;\;\;\frac{x}{\left(t - y\right) \cdot y}\\ \mathbf{elif}\;\frac{x}{\left(t - y\right) \cdot \left(z - y\right)} \leq -40000000:\\ \;\;\;\;1 - \frac{x}{\left(t - y\right) \cdot z}\\ \mathbf{elif}\;\frac{x}{\left(t - y\right) \cdot \left(z - y\right)} \leq 0.002:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{t \cdot \left(y - z\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 89.4% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{\left(t - y\right) \cdot \left(z - y\right)}\\ \mathbf{if}\;t\_1 \leq -5 \cdot 10^{+191}:\\ \;\;\;\;\frac{x}{\left(t - y\right) \cdot y}\\ \mathbf{elif}\;t\_1 \leq -40000000:\\ \;\;\;\;\frac{x}{\left(y - t\right) \cdot z}\\ \mathbf{elif}\;t\_1 \leq 0.002:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{t \cdot \left(y - z\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ x (* (- t y) (- z y)))))
   (if (<= t_1 -5e+191)
     (/ x (* (- t y) y))
     (if (<= t_1 -40000000.0)
       (/ x (* (- y t) z))
       (if (<= t_1 0.002) 1.0 (/ x (* t (- y z))))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x / ((t - y) * (z - y));
	double tmp;
	if (t_1 <= -5e+191) {
		tmp = x / ((t - y) * y);
	} else if (t_1 <= -40000000.0) {
		tmp = x / ((y - t) * z);
	} else if (t_1 <= 0.002) {
		tmp = 1.0;
	} else {
		tmp = x / (t * (y - z));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x / ((t - y) * (z - y))
    if (t_1 <= (-5d+191)) then
        tmp = x / ((t - y) * y)
    else if (t_1 <= (-40000000.0d0)) then
        tmp = x / ((y - t) * z)
    else if (t_1 <= 0.002d0) then
        tmp = 1.0d0
    else
        tmp = x / (t * (y - z))
    end if
    code = tmp
end function

Java

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 <= -5e+191) {
		tmp = x / ((t - y) * y);
	} else if (t_1 <= -40000000.0) {
		tmp = x / ((y - t) * z);
	} else if (t_1 <= 0.002) {
		tmp = 1.0;
	} else {
		tmp = x / (t * (y - z));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x / ((t - y) * (z - y))
	tmp = 0
	if t_1 <= -5e+191:
		tmp = x / ((t - y) * y)
	elif t_1 <= -40000000.0:
		tmp = x / ((y - t) * z)
	elif t_1 <= 0.002:
		tmp = 1.0
	else:
		tmp = x / (t * (y - z))
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x / Float64(Float64(t - y) * Float64(z - y)))
	tmp = 0.0
	if (t_1 <= -5e+191)
		tmp = Float64(x / Float64(Float64(t - y) * y));
	elseif (t_1 <= -40000000.0)
		tmp = Float64(x / Float64(Float64(y - t) * z));
	elseif (t_1 <= 0.002)
		tmp = 1.0;
	else
		tmp = Float64(x / Float64(t * Float64(y - z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x / ((t - y) * (z - y));
	tmp = 0.0;
	if (t_1 <= -5e+191)
		tmp = x / ((t - y) * y);
	elseif (t_1 <= -40000000.0)
		tmp = x / ((y - t) * z);
	elseif (t_1 <= 0.002)
		tmp = 1.0;
	else
		tmp = x / (t * (y - z));
	end
	tmp_2 = tmp;
end

Wolfram

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, -5e+191], N[(x / N[(N[(t - y), $MachinePrecision] * y), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, -40000000.0], N[(x / N[(N[(y - t), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 0.002], 1.0, N[(x / N[(t * N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 4 regimes

2. if (/.f64 x (*.f64 (-.f64 y z) (-.f64 y t))) < -5.0000000000000002e191

   1. Initial program 94.2%

      \[1 - \frac{x}{\left(y - z\right) \cdot \left(y - t\right)} \]
   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. associate-*r/ N/A

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

      2. *-commutative N/A

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

      3. associate-/r* N/A

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

      4. associate-*r/ N/A

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

      5. lower-/.f64 N/A

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

      6. mul-1-neg N/A

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

      7. distribute-neg-frac2 N/A

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

      8. mul-1-neg N/A

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

      9. lower-/.f64 N/A

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

      10. mul-1-neg N/A

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

      11. sub-neg N/A

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

      12. mul-1-neg N/A

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

      13. +-commutative N/A

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

      14. distribute-neg-in N/A

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

      15. unsub-neg N/A

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

      16. mul-1-neg N/A

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

      17. remove-double-neg N/A

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

      18. lower--.f64 N/A

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

      19. lower--.f64 89.0

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

   5. Applied rewrites 89.0%

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

   6. Taylor expanded in y around inf

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

   8. Applied rewrites 49.1%

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

   9. Taylor expanded in z around 0

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

   11. Applied rewrites 54.4%

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

   if -5.0000000000000002e191 < (/.f64 x (*.f64 (-.f64 y z) (-.f64 y t))) < -4e7

   1. Initial program 99.0%

      \[1 - \frac{x}{\left(y - z\right) \cdot \left(y - t\right)} \]
   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. associate-*r/ N/A

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

      2. *-commutative N/A

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

      3. associate-/r* N/A

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

      4. associate-*r/ N/A

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

      5. lower-/.f64 N/A

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

      6. mul-1-neg N/A

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

      7. distribute-neg-frac2 N/A

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

      8. mul-1-neg N/A

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

      9. lower-/.f64 N/A

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

      10. mul-1-neg N/A

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

      11. sub-neg N/A

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

      12. mul-1-neg N/A

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

      13. +-commutative N/A

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

      14. distribute-neg-in N/A

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

      15. unsub-neg N/A

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

      16. mul-1-neg N/A

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

      17. remove-double-neg N/A

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

      18. lower--.f64 N/A

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

      19. lower--.f64 92.3

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

   5. Applied rewrites 92.3%

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

   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 67.2%

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

   if -4e7 < (/.f64 x (*.f64 (-.f64 y z) (-.f64 y t))) < 2e-3

   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%

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

   if 2e-3 < (/.f64 x (*.f64 (-.f64 y z) (-.f64 y t)))

   1. Initial program 96.7%

      \[1 - \frac{x}{\left(y - z\right) \cdot \left(y - t\right)} \]
   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. associate-*r/ N/A

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

      2. *-commutative N/A

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

      3. associate-/r* N/A

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

      4. associate-*r/ N/A

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

      5. lower-/.f64 N/A

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

      6. mul-1-neg N/A

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

      7. distribute-neg-frac2 N/A

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

      8. mul-1-neg N/A

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

      9. lower-/.f64 N/A

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

      10. mul-1-neg N/A

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

      11. sub-neg N/A

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

      12. mul-1-neg N/A

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

      13. +-commutative N/A

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

      14. distribute-neg-in N/A

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

      15. unsub-neg N/A

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

      16. mul-1-neg N/A

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

      17. remove-double-neg N/A

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

      18. lower--.f64 N/A

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

      19. lower--.f64 90.1

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

   5. Applied rewrites 90.1%

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

   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 69.9%

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

4. Final simplification 89.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x}{\left(t - y\right) \cdot \left(z - y\right)} \leq -5 \cdot 10^{+191}:\\ \;\;\;\;\frac{x}{\left(t - y\right) \cdot y}\\ \mathbf{elif}\;\frac{x}{\left(t - y\right) \cdot \left(z - y\right)} \leq -40000000:\\ \;\;\;\;\frac{x}{\left(y - t\right) \cdot z}\\ \mathbf{elif}\;\frac{x}{\left(t - y\right) \cdot \left(z - y\right)} \leq 0.002:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{t \cdot \left(y - z\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 88.9% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{\left(y - t\right) \cdot z}\\ t_2 := \frac{x}{\left(t - y\right) \cdot \left(z - y\right)}\\ \mathbf{if}\;t\_2 \leq -5 \cdot 10^{+191}:\\ \;\;\;\;\frac{x}{\left(t - y\right) \cdot y}\\ \mathbf{elif}\;t\_2 \leq -40000000:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_2 \leq 20000:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ x (* (- y t) z))) (t_2 (/ x (* (- t y) (- z y)))))
   (if (<= t_2 -5e+191)
     (/ x (* (- t y) y))
     (if (<= t_2 -40000000.0) t_1 (if (<= t_2 20000.0) 1.0 t_1)))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x / ((y - t) * z);
	double t_2 = x / ((t - y) * (z - y));
	double tmp;
	if (t_2 <= -5e+191) {
		tmp = x / ((t - y) * y);
	} else if (t_2 <= -40000000.0) {
		tmp = t_1;
	} else if (t_2 <= 20000.0) {
		tmp = 1.0;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = x / ((y - t) * z)
    t_2 = x / ((t - y) * (z - y))
    if (t_2 <= (-5d+191)) then
        tmp = x / ((t - y) * y)
    else if (t_2 <= (-40000000.0d0)) then
        tmp = t_1
    else if (t_2 <= 20000.0d0) then
        tmp = 1.0d0
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = x / ((y - t) * z);
	double t_2 = x / ((t - y) * (z - y));
	double tmp;
	if (t_2 <= -5e+191) {
		tmp = x / ((t - y) * y);
	} else if (t_2 <= -40000000.0) {
		tmp = t_1;
	} else if (t_2 <= 20000.0) {
		tmp = 1.0;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x / ((y - t) * z)
	t_2 = x / ((t - y) * (z - y))
	tmp = 0
	if t_2 <= -5e+191:
		tmp = x / ((t - y) * y)
	elif t_2 <= -40000000.0:
		tmp = t_1
	elif t_2 <= 20000.0:
		tmp = 1.0
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x / Float64(Float64(y - t) * z))
	t_2 = Float64(x / Float64(Float64(t - y) * Float64(z - y)))
	tmp = 0.0
	if (t_2 <= -5e+191)
		tmp = Float64(x / Float64(Float64(t - y) * y));
	elseif (t_2 <= -40000000.0)
		tmp = t_1;
	elseif (t_2 <= 20000.0)
		tmp = 1.0;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x / ((y - t) * z);
	t_2 = x / ((t - y) * (z - y));
	tmp = 0.0;
	if (t_2 <= -5e+191)
		tmp = x / ((t - y) * y);
	elseif (t_2 <= -40000000.0)
		tmp = t_1;
	elseif (t_2 <= 20000.0)
		tmp = 1.0;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x / N[(N[(y - t), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x / N[(N[(t - y), $MachinePrecision] * N[(z - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, -5e+191], N[(x / N[(N[(t - y), $MachinePrecision] * y), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$2, -40000000.0], t$95$1, If[LessEqual[t$95$2, 20000.0], 1.0, t$95$1]]]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 x (*.f64 (-.f64 y z) (-.f64 y t))) < -5.0000000000000002e191

   1. Initial program 94.2%

      \[1 - \frac{x}{\left(y - z\right) \cdot \left(y - t\right)} \]
   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. associate-*r/ N/A

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

      2. *-commutative N/A

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

      3. associate-/r* N/A

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

      4. associate-*r/ N/A

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

      5. lower-/.f64 N/A

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

      6. mul-1-neg N/A

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

      7. distribute-neg-frac2 N/A

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

      8. mul-1-neg N/A

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

      9. lower-/.f64 N/A

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

      10. mul-1-neg N/A

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

      11. sub-neg N/A

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

      12. mul-1-neg N/A

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

      13. +-commutative N/A

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

      14. distribute-neg-in N/A

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

      15. unsub-neg N/A

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

      16. mul-1-neg N/A

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

      17. remove-double-neg N/A

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

      18. lower--.f64 N/A

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

      19. lower--.f64 89.0

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

   5. Applied rewrites 89.0%

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

   6. Taylor expanded in y around inf

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

   8. Applied rewrites 49.1%

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

   9. Taylor expanded in z around 0

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

   11. Applied rewrites 54.4%

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

   if -5.0000000000000002e191 < (/.f64 x (*.f64 (-.f64 y z) (-.f64 y t))) < -4e7 or 2e4 < (/.f64 x (*.f64 (-.f64 y z) (-.f64 y t)))

   1. Initial program 97.5%

      \[1 - \frac{x}{\left(y - z\right) \cdot \left(y - t\right)} \]
   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. associate-*r/ N/A

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

      2. *-commutative N/A

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

      3. associate-/r* N/A

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

      4. associate-*r/ N/A

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

      5. lower-/.f64 N/A

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

      6. mul-1-neg N/A

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

      7. distribute-neg-frac2 N/A

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

      8. mul-1-neg N/A

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

      9. lower-/.f64 N/A

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

      10. mul-1-neg N/A

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

      11. sub-neg N/A

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

      12. mul-1-neg N/A

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

      13. +-commutative N/A

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

      14. distribute-neg-in N/A

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

      15. unsub-neg N/A

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

      16. mul-1-neg N/A

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

      17. remove-double-neg N/A

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

      18. lower--.f64 N/A

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

      19. lower--.f64 91.8

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

   5. Applied rewrites 91.8%

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

   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 65.4%

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

   if -4e7 < (/.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 98.2%

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

4. Final simplification 88.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x}{\left(t - y\right) \cdot \left(z - y\right)} \leq -5 \cdot 10^{+191}:\\ \;\;\;\;\frac{x}{\left(t - y\right) \cdot y}\\ \mathbf{elif}\;\frac{x}{\left(t - y\right) \cdot \left(z - y\right)} \leq -40000000:\\ \;\;\;\;\frac{x}{\left(y - t\right) \cdot z}\\ \mathbf{elif}\;\frac{x}{\left(t - y\right) \cdot \left(z - y\right)} \leq 20000:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\left(y - t\right) \cdot z}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 89.3% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{\left(t - y\right) \cdot \left(z - y\right)}\\ t_2 := \frac{x}{\left(y - t\right) \cdot z}\\ \mathbf{if}\;t\_1 \leq -40000000:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_1 \leq 20000:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ x (* (- t y) (- z y)))) (t_2 (/ x (* (- y t) z))))
   (if (<= t_1 -40000000.0) t_2 (if (<= t_1 20000.0) 1.0 t_2))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x / ((t - y) * (z - y));
	double t_2 = x / ((y - t) * z);
	double tmp;
	if (t_1 <= -40000000.0) {
		tmp = t_2;
	} else if (t_1 <= 20000.0) {
		tmp = 1.0;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = x / ((t - y) * (z - y))
    t_2 = x / ((y - t) * z)
    if (t_1 <= (-40000000.0d0)) then
        tmp = t_2
    else if (t_1 <= 20000.0d0) then
        tmp = 1.0d0
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = x / ((t - y) * (z - y));
	double t_2 = x / ((y - t) * z);
	double tmp;
	if (t_1 <= -40000000.0) {
		tmp = t_2;
	} else if (t_1 <= 20000.0) {
		tmp = 1.0;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x / ((t - y) * (z - y))
	t_2 = x / ((y - t) * z)
	tmp = 0
	if t_1 <= -40000000.0:
		tmp = t_2
	elif t_1 <= 20000.0:
		tmp = 1.0
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x / Float64(Float64(t - y) * Float64(z - y)))
	t_2 = Float64(x / Float64(Float64(y - t) * z))
	tmp = 0.0
	if (t_1 <= -40000000.0)
		tmp = t_2;
	elseif (t_1 <= 20000.0)
		tmp = 1.0;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x / ((t - y) * (z - y));
	t_2 = x / ((y - t) * z);
	tmp = 0.0;
	if (t_1 <= -40000000.0)
		tmp = t_2;
	elseif (t_1 <= 20000.0)
		tmp = 1.0;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

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[(x / N[(N[(y - t), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -40000000.0], t$95$2, If[LessEqual[t$95$1, 20000.0], 1.0, t$95$2]]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 x (*.f64 (-.f64 y z) (-.f64 y t))) < -4e7 or 2e4 < (/.f64 x (*.f64 (-.f64 y z) (-.f64 y t)))

   1. Initial program 96.7%

      \[1 - \frac{x}{\left(y - z\right) \cdot \left(y - t\right)} \]
   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. associate-*r/ N/A

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

      2. *-commutative N/A

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

      3. associate-/r* N/A

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

      4. associate-*r/ N/A

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

      5. lower-/.f64 N/A

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

      6. mul-1-neg N/A

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

      7. distribute-neg-frac2 N/A

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

      8. mul-1-neg N/A

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

      9. lower-/.f64 N/A

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

      10. mul-1-neg N/A

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

      11. sub-neg N/A

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

      12. mul-1-neg N/A

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

      13. +-commutative N/A

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

      14. distribute-neg-in N/A

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

      15. unsub-neg N/A

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

      16. mul-1-neg N/A

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

      17. remove-double-neg N/A

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

      18. lower--.f64 N/A

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

      19. lower--.f64 91.1

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

   5. Applied rewrites 91.1%

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

   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 60.2%

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

   if -4e7 < (/.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 98.2%

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

4. Final simplification 87.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x}{\left(t - y\right) \cdot \left(z - y\right)} \leq -40000000:\\ \;\;\;\;\frac{x}{\left(y - t\right) \cdot z}\\ \mathbf{elif}\;\frac{x}{\left(t - y\right) \cdot \left(z - y\right)} \leq 20000:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\left(y - t\right) \cdot z}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 85.3% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{\left(t - y\right) \cdot \left(z - y\right)}\\ t_2 := \frac{-x}{t \cdot z}\\ \mathbf{if}\;t\_1 \leq -40000000:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_1 \leq 2 \cdot 10^{+32}:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ x (* (- t y) (- z y)))) (t_2 (/ (- x) (* t z))))
   (if (<= t_1 -40000000.0) t_2 (if (<= t_1 2e+32) 1.0 t_2))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x / ((t - y) * (z - y));
	double t_2 = -x / (t * z);
	double tmp;
	if (t_1 <= -40000000.0) {
		tmp = t_2;
	} else if (t_1 <= 2e+32) {
		tmp = 1.0;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = x / ((t - y) * (z - y))
    t_2 = -x / (t * z)
    if (t_1 <= (-40000000.0d0)) then
        tmp = t_2
    else if (t_1 <= 2d+32) then
        tmp = 1.0d0
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = x / ((t - y) * (z - y));
	double t_2 = -x / (t * z);
	double tmp;
	if (t_1 <= -40000000.0) {
		tmp = t_2;
	} else if (t_1 <= 2e+32) {
		tmp = 1.0;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x / ((t - y) * (z - y))
	t_2 = -x / (t * z)
	tmp = 0
	if t_1 <= -40000000.0:
		tmp = t_2
	elif t_1 <= 2e+32:
		tmp = 1.0
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x / Float64(Float64(t - y) * Float64(z - y)))
	t_2 = Float64(Float64(-x) / Float64(t * z))
	tmp = 0.0
	if (t_1 <= -40000000.0)
		tmp = t_2;
	elseif (t_1 <= 2e+32)
		tmp = 1.0;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x / ((t - y) * (z - y));
	t_2 = -x / (t * z);
	tmp = 0.0;
	if (t_1 <= -40000000.0)
		tmp = t_2;
	elseif (t_1 <= 2e+32)
		tmp = 1.0;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

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[((-x) / N[(t * z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -40000000.0], t$95$2, If[LessEqual[t$95$1, 2e+32], 1.0, t$95$2]]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 x (*.f64 (-.f64 y z) (-.f64 y t))) < -4e7 or 2.00000000000000011e32 < (/.f64 x (*.f64 (-.f64 y z) (-.f64 y t)))

   1. Initial program 96.7%

      \[1 - \frac{x}{\left(y - z\right) \cdot \left(y - t\right)} \]
   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. associate-*r/ N/A

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

      2. *-commutative N/A

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

      3. associate-/r* N/A

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

      4. associate-*r/ N/A

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

      5. lower-/.f64 N/A

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

      6. mul-1-neg N/A

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

      7. distribute-neg-frac2 N/A

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

      8. mul-1-neg N/A

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

      9. lower-/.f64 N/A

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

      10. mul-1-neg N/A

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

      11. sub-neg N/A

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

      12. mul-1-neg N/A

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

      13. +-commutative N/A

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

      14. distribute-neg-in N/A

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

      15. unsub-neg N/A

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

      16. mul-1-neg N/A

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

      17. remove-double-neg N/A

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

      18. lower--.f64 N/A

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

      19. lower--.f64 91.0

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

   5. Applied rewrites 91.0%

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

   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 67.8%

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

   9. Taylor expanded in y around 0

      \[\leadsto \frac{-x}{t \cdot z} \]
   10. Step-by-step derivation

   11. Applied rewrites 50.8%

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

   if -4e7 < (/.f64 x (*.f64 (-.f64 y z) (-.f64 y t))) < 2.00000000000000011e32

   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 97.7%

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

4. Final simplification 84.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x}{\left(t - y\right) \cdot \left(z - y\right)} \leq -40000000:\\ \;\;\;\;\frac{-x}{t \cdot z}\\ \mathbf{elif}\;\frac{x}{\left(t - y\right) \cdot \left(z - y\right)} \leq 2 \cdot 10^{+32}:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;\frac{-x}{t \cdot z}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 81.3% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{\left(t - y\right) \cdot \left(z - y\right)}\\ t_2 := \frac{x}{t \cdot y}\\ \mathbf{if}\;t\_1 \leq -2 \cdot 10^{+76}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_1 \leq 0.002:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ x (* (- t y) (- z y)))) (t_2 (/ x (* t y))))
   (if (<= t_1 -2e+76) t_2 (if (<= t_1 0.002) 1.0 t_2))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x / ((t - y) * (z - y));
	double t_2 = x / (t * y);
	double tmp;
	if (t_1 <= -2e+76) {
		tmp = t_2;
	} else if (t_1 <= 0.002) {
		tmp = 1.0;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = x / ((t - y) * (z - y))
    t_2 = x / (t * y)
    if (t_1 <= (-2d+76)) then
        tmp = t_2
    else if (t_1 <= 0.002d0) then
        tmp = 1.0d0
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = x / ((t - y) * (z - y));
	double t_2 = x / (t * y);
	double tmp;
	if (t_1 <= -2e+76) {
		tmp = t_2;
	} else if (t_1 <= 0.002) {
		tmp = 1.0;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x / ((t - y) * (z - y))
	t_2 = x / (t * y)
	tmp = 0
	if t_1 <= -2e+76:
		tmp = t_2
	elif t_1 <= 0.002:
		tmp = 1.0
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x / Float64(Float64(t - y) * Float64(z - y)))
	t_2 = Float64(x / Float64(t * y))
	tmp = 0.0
	if (t_1 <= -2e+76)
		tmp = t_2;
	elseif (t_1 <= 0.002)
		tmp = 1.0;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x / ((t - y) * (z - y));
	t_2 = x / (t * y);
	tmp = 0.0;
	if (t_1 <= -2e+76)
		tmp = t_2;
	elseif (t_1 <= 0.002)
		tmp = 1.0;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

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[(x / N[(t * y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -2e+76], t$95$2, If[LessEqual[t$95$1, 0.002], 1.0, t$95$2]]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 x (*.f64 (-.f64 y z) (-.f64 y t))) < -2.0000000000000001e76 or 2e-3 < (/.f64 x (*.f64 (-.f64 y z) (-.f64 y t)))

   1. Initial program 96.4%

      \[1 - \frac{x}{\left(y - z\right) \cdot \left(y - t\right)} \]
   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. associate-*r/ N/A

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

      2. *-commutative N/A

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

      3. associate-/r* N/A

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

      4. associate-*r/ N/A

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

      5. lower-/.f64 N/A

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

      6. mul-1-neg N/A

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

      7. distribute-neg-frac2 N/A

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

      8. mul-1-neg N/A

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

      9. lower-/.f64 N/A

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

      10. mul-1-neg N/A

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

      11. sub-neg N/A

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

      12. mul-1-neg N/A

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

      13. +-commutative N/A

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

      14. distribute-neg-in N/A

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

      15. unsub-neg N/A

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

      16. mul-1-neg N/A

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

      17. remove-double-neg N/A

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

      18. lower--.f64 N/A

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

      19. lower--.f64 91.2

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

   5. Applied rewrites 91.2%

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

   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 66.0%

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

   9. Taylor expanded in y around inf

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

   11. Applied rewrites 30.4%

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

   if -2.0000000000000001e76 < (/.f64 x (*.f64 (-.f64 y z) (-.f64 y t))) < 2e-3

   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 94.0%

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

4. Final simplification 78.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x}{\left(t - y\right) \cdot \left(z - y\right)} \leq -2 \cdot 10^{+76}:\\ \;\;\;\;\frac{x}{t \cdot y}\\ \mathbf{elif}\;\frac{x}{\left(t - y\right) \cdot \left(z - y\right)} \leq 0.002:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{t \cdot y}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 86.3% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.02 \cdot 10^{-100}:\\ \;\;\;\;1 - \frac{x}{\left(t - y\right) \cdot z}\\ \mathbf{elif}\;z \leq 1.08 \cdot 10^{-262}:\\ \;\;\;\;1 - \frac{x}{\left(y - t\right) \cdot y}\\ \mathbf{else}:\\ \;\;\;\;1 - \frac{x}{\left(z - y\right) \cdot t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -1.02e-100)
   (- 1.0 (/ x (* (- t y) z)))
   (if (<= z 1.08e-262)
     (- 1.0 (/ x (* (- y t) y)))
     (- 1.0 (/ x (* (- z y) t))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -1.02e-100) {
		tmp = 1.0 - (x / ((t - y) * z));
	} else if (z <= 1.08e-262) {
		tmp = 1.0 - (x / ((y - t) * y));
	} else {
		tmp = 1.0 - (x / ((z - y) * t));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (z <= (-1.02d-100)) then
        tmp = 1.0d0 - (x / ((t - y) * z))
    else if (z <= 1.08d-262) then
        tmp = 1.0d0 - (x / ((y - t) * y))
    else
        tmp = 1.0d0 - (x / ((z - y) * t))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -1.02e-100) {
		tmp = 1.0 - (x / ((t - y) * z));
	} else if (z <= 1.08e-262) {
		tmp = 1.0 - (x / ((y - t) * y));
	} else {
		tmp = 1.0 - (x / ((z - y) * t));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -1.02e-100:
		tmp = 1.0 - (x / ((t - y) * z))
	elif z <= 1.08e-262:
		tmp = 1.0 - (x / ((y - t) * y))
	else:
		tmp = 1.0 - (x / ((z - y) * t))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -1.02e-100)
		tmp = Float64(1.0 - Float64(x / Float64(Float64(t - y) * z)));
	elseif (z <= 1.08e-262)
		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

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (z <= -1.02e-100)
		tmp = 1.0 - (x / ((t - y) * z));
	elseif (z <= 1.08e-262)
		tmp = 1.0 - (x / ((y - t) * y));
	else
		tmp = 1.0 - (x / ((z - y) * t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -1.02e-100], N[(1.0 - N[(x / N[(N[(t - y), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.08e-262], 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 < -1.02e-100

   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 91.6

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

   5. Applied rewrites 91.6%

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

   if -1.02e-100 < z < 1.08000000000000001e-262

   1. Initial program 97.2%

      \[1 - \frac{x}{\left(y - z\right) \cdot \left(y - t\right)} \]
   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 90.4

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

   5. Applied rewrites 90.4%

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

   if 1.08000000000000001e-262 < z

   1. Initial program 99.5%

      \[1 - \frac{x}{\left(y - z\right) \cdot \left(y - t\right)} \]
   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 85.5

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

   5. Applied rewrites 85.5%

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

Alternative 9: 90.4% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := 1 - \frac{x}{\left(t - y\right) \cdot z}\\ \mathbf{if}\;z \leq -1.02 \cdot 10^{-100}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 3.4 \cdot 10^{-179}:\\ \;\;\;\;1 - \frac{x}{\left(y - t\right) \cdot y}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (- 1.0 (/ x (* (- t y) z)))))
   (if (<= z -1.02e-100)
     t_1
     (if (<= z 3.4e-179) (- 1.0 (/ x (* (- y t) y))) t_1))))

C

double code(double x, double y, double z, double t) {
	double t_1 = 1.0 - (x / ((t - y) * z));
	double tmp;
	if (z <= -1.02e-100) {
		tmp = t_1;
	} else if (z <= 3.4e-179) {
		tmp = 1.0 - (x / ((y - t) * y));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = 1.0d0 - (x / ((t - y) * z))
    if (z <= (-1.02d-100)) then
        tmp = t_1
    else if (z <= 3.4d-179) then
        tmp = 1.0d0 - (x / ((y - t) * y))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

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 <= -1.02e-100) {
		tmp = t_1;
	} else if (z <= 3.4e-179) {
		tmp = 1.0 - (x / ((y - t) * y));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = 1.0 - (x / ((t - y) * z))
	tmp = 0
	if z <= -1.02e-100:
		tmp = t_1
	elif z <= 3.4e-179:
		tmp = 1.0 - (x / ((y - t) * y))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(1.0 - Float64(x / Float64(Float64(t - y) * z)))
	tmp = 0.0
	if (z <= -1.02e-100)
		tmp = t_1;
	elseif (z <= 3.4e-179)
		tmp = Float64(1.0 - Float64(x / Float64(Float64(y - t) * y)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = 1.0 - (x / ((t - y) * z));
	tmp = 0.0;
	if (z <= -1.02e-100)
		tmp = t_1;
	elseif (z <= 3.4e-179)
		tmp = 1.0 - (x / ((y - t) * y));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

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, -1.02e-100], t$95$1, If[LessEqual[z, 3.4e-179], 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 < -1.02e-100 or 3.3999999999999997e-179 < 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 93.2

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

   5. Applied rewrites 93.2%

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

   if -1.02e-100 < z < 3.3999999999999997e-179

   1. Initial program 97.3%

      \[1 - \frac{x}{\left(y - z\right) \cdot \left(y - t\right)} \]
   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 91.4

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

   5. Applied rewrites 91.4%

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

Alternative 10: 75.2% accurate, 26.0× speedup

Math

\[\begin{array}{l} \\ 1 \end{array} \]

FPCore

(FPCore (x y z t) :precision binary64 1.0)

C

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

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
end function

Java

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

Python

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

Julia

function code(x, y, z, t)
	return 1.0
end

MATLAB

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

Wolfram

code[x_, y_, z_, t_] := 1.0

Derivation

1. Initial program 99.1%

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

3. Taylor expanded in x around 0

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

5. Applied rewrites 71.8%

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

Reproduce

herbie shell --seed 2024331 
(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)))))