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

Percentage Accurate: 99.2% → 99.2%

Time: 7.8s

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: 99.2% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 99.2% 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 99.2%

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

3. Final simplification 99.2%

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

Alternative 2: 87.7% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{\left(t - y\right) \cdot \left(z - y\right)}\\ t_2 := \frac{x}{t \cdot \left(y - z\right)}\\ \mathbf{if}\;t\_1 \leq -5 \cdot 10^{+32}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_1 \leq 500000000000:\\ \;\;\;\;1\\ \mathbf{elif}\;t\_1 \leq 10^{+103}:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\left(t - y\right) \cdot y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ x (* (- t y) (- z y)))) (t_2 (/ x (* t (- y z)))))
   (if (<= t_1 -5e+32)
     t_2
     (if (<= t_1 500000000000.0)
       1.0
       (if (<= t_1 1e+103) t_2 (/ x (* (- t y) y)))))))

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 - z));
	double tmp;
	if (t_1 <= -5e+32) {
		tmp = t_2;
	} else if (t_1 <= 500000000000.0) {
		tmp = 1.0;
	} else if (t_1 <= 1e+103) {
		tmp = t_2;
	} else {
		tmp = x / ((t - y) * y);
	}
	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 - z))
    if (t_1 <= (-5d+32)) then
        tmp = t_2
    else if (t_1 <= 500000000000.0d0) then
        tmp = 1.0d0
    else if (t_1 <= 1d+103) then
        tmp = t_2
    else
        tmp = x / ((t - y) * y)
    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 - z));
	double tmp;
	if (t_1 <= -5e+32) {
		tmp = t_2;
	} else if (t_1 <= 500000000000.0) {
		tmp = 1.0;
	} else if (t_1 <= 1e+103) {
		tmp = t_2;
	} else {
		tmp = x / ((t - y) * y);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x / ((t - y) * (z - y))
	t_2 = x / (t * (y - z))
	tmp = 0
	if t_1 <= -5e+32:
		tmp = t_2
	elif t_1 <= 500000000000.0:
		tmp = 1.0
	elif t_1 <= 1e+103:
		tmp = t_2
	else:
		tmp = x / ((t - y) * y)
	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 * Float64(y - z)))
	tmp = 0.0
	if (t_1 <= -5e+32)
		tmp = t_2;
	elseif (t_1 <= 500000000000.0)
		tmp = 1.0;
	elseif (t_1 <= 1e+103)
		tmp = t_2;
	else
		tmp = Float64(x / Float64(Float64(t - y) * y));
	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 - z));
	tmp = 0.0;
	if (t_1 <= -5e+32)
		tmp = t_2;
	elseif (t_1 <= 500000000000.0)
		tmp = 1.0;
	elseif (t_1 <= 1e+103)
		tmp = t_2;
	else
		tmp = x / ((t - y) * y);
	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 * N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -5e+32], t$95$2, If[LessEqual[t$95$1, 500000000000.0], 1.0, If[LessEqual[t$95$1, 1e+103], t$95$2, N[(x / N[(N[(t - y), $MachinePrecision] * y), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 x (*.f64 (-.f64 y z) (-.f64 y t))) < -4.9999999999999997e32 or 5e11 < (/.f64 x (*.f64 (-.f64 y z) (-.f64 y t))) < 1e103

   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 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 90.8

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

   5. Applied rewrites 90.8%

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

   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 62.8%

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

   if -4.9999999999999997e32 < (/.f64 x (*.f64 (-.f64 y z) (-.f64 y t))) < 5e11

   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 97.8%

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

   if 1e103 < (/.f64 x (*.f64 (-.f64 y z) (-.f64 y t)))

   1. Initial program 91.5%

      \[1 - \frac{x}{\left(y - z\right) \cdot \left(y - t\right)} \]
   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 95.5

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

   5. Applied rewrites 95.5%

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

   6. Taylor expanded in y around inf

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

   8. Applied rewrites 54.3%

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

   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 68.8%

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

4. Final simplification 89.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x}{\left(t - y\right) \cdot \left(z - y\right)} \leq -5 \cdot 10^{+32}:\\ \;\;\;\;\frac{x}{t \cdot \left(y - z\right)}\\ \mathbf{elif}\;\frac{x}{\left(t - y\right) \cdot \left(z - y\right)} \leq 500000000000:\\ \;\;\;\;1\\ \mathbf{elif}\;\frac{x}{\left(t - y\right) \cdot \left(z - y\right)} \leq 10^{+103}:\\ \;\;\;\;\frac{x}{t \cdot \left(y - z\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\left(t - y\right) \cdot y}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 89.8% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{\left(y - t\right) \cdot z}\\ t_2 := 1 - \frac{x}{\left(t - y\right) \cdot \left(z - y\right)}\\ \mathbf{if}\;t\_2 \leq -400000000000:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_2 \leq 2:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ x (* (- y t) z))) (t_2 (- 1.0 (/ x (* (- t y) (- z y))))))
   (if (<= t_2 -400000000000.0) t_1 (if (<= t_2 2.0) 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 = 1.0 - (x / ((t - y) * (z - y)));
	double tmp;
	if (t_2 <= -400000000000.0) {
		tmp = t_1;
	} else if (t_2 <= 2.0) {
		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 = 1.0d0 - (x / ((t - y) * (z - y)))
    if (t_2 <= (-400000000000.0d0)) then
        tmp = t_1
    else if (t_2 <= 2.0d0) 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 = 1.0 - (x / ((t - y) * (z - y)));
	double tmp;
	if (t_2 <= -400000000000.0) {
		tmp = t_1;
	} else if (t_2 <= 2.0) {
		tmp = 1.0;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x / ((y - t) * z)
	t_2 = 1.0 - (x / ((t - y) * (z - y)))
	tmp = 0
	if t_2 <= -400000000000.0:
		tmp = t_1
	elif t_2 <= 2.0:
		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(1.0 - Float64(x / Float64(Float64(t - y) * Float64(z - y))))
	tmp = 0.0
	if (t_2 <= -400000000000.0)
		tmp = t_1;
	elseif (t_2 <= 2.0)
		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 = 1.0 - (x / ((t - y) * (z - y)));
	tmp = 0.0;
	if (t_2 <= -400000000000.0)
		tmp = t_1;
	elseif (t_2 <= 2.0)
		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[(1.0 - N[(x / N[(N[(t - y), $MachinePrecision] * N[(z - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, -400000000000.0], t$95$1, If[LessEqual[t$95$2, 2.0], 1.0, t$95$1]]]]

Derivation

1. Split input into 2 regimes

2. if (-.f64 #s(literal 1 binary64) (/.f64 x (*.f64 (-.f64 y z) (-.f64 y t)))) < -4e11 or 2 < (-.f64 #s(literal 1 binary64) (/.f64 x (*.f64 (-.f64 y z) (-.f64 y t))))

   1. Initial program 97.0%

      \[1 - \frac{x}{\left(y - z\right) \cdot \left(y - t\right)} \]
   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 91.3

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

   5. Applied rewrites 91.3%

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

   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 55.5%

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

   if -4e11 < (-.f64 #s(literal 1 binary64) (/.f64 x (*.f64 (-.f64 y z) (-.f64 y t)))) < 2

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0

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

   5. Applied rewrites 98.7%

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

4. Final simplification 87.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;1 - \frac{x}{\left(t - y\right) \cdot \left(z - y\right)} \leq -400000000000:\\ \;\;\;\;\frac{x}{\left(y - t\right) \cdot z}\\ \mathbf{elif}\;1 - \frac{x}{\left(t - y\right) \cdot \left(z - y\right)} \leq 2:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\left(y - t\right) \cdot z}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 84.0% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := 1 - \frac{x}{\left(t - y\right) \cdot \left(z - y\right)}\\ \mathbf{if}\;t\_1 \leq -400000000000:\\ \;\;\;\;\frac{-x}{y \cdot y}\\ \mathbf{elif}\;t\_1 \leq 2000:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;\frac{-x}{t \cdot z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (- 1.0 (/ x (* (- t y) (- z y))))))
   (if (<= t_1 -400000000000.0)
     (/ (- x) (* y y))
     (if (<= t_1 2000.0) 1.0 (/ (- x) (* t z))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = 1.0 - (x / ((t - y) * (z - y)));
	double tmp;
	if (t_1 <= -400000000000.0) {
		tmp = -x / (y * y);
	} else if (t_1 <= 2000.0) {
		tmp = 1.0;
	} else {
		tmp = -x / (t * 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 = 1.0d0 - (x / ((t - y) * (z - y)))
    if (t_1 <= (-400000000000.0d0)) then
        tmp = -x / (y * y)
    else if (t_1 <= 2000.0d0) then
        tmp = 1.0d0
    else
        tmp = -x / (t * z)
    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 - y)));
	double tmp;
	if (t_1 <= -400000000000.0) {
		tmp = -x / (y * y);
	} else if (t_1 <= 2000.0) {
		tmp = 1.0;
	} else {
		tmp = -x / (t * z);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = 1.0 - (x / ((t - y) * (z - y)))
	tmp = 0
	if t_1 <= -400000000000.0:
		tmp = -x / (y * y)
	elif t_1 <= 2000.0:
		tmp = 1.0
	else:
		tmp = -x / (t * z)
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(1.0 - Float64(x / Float64(Float64(t - y) * Float64(z - y))))
	tmp = 0.0
	if (t_1 <= -400000000000.0)
		tmp = Float64(Float64(-x) / Float64(y * y));
	elseif (t_1 <= 2000.0)
		tmp = 1.0;
	else
		tmp = Float64(Float64(-x) / Float64(t * z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = 1.0 - (x / ((t - y) * (z - y)));
	tmp = 0.0;
	if (t_1 <= -400000000000.0)
		tmp = -x / (y * y);
	elseif (t_1 <= 2000.0)
		tmp = 1.0;
	else
		tmp = -x / (t * z);
	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] * N[(z - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -400000000000.0], N[((-x) / N[(y * y), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 2000.0], 1.0, N[((-x) / N[(t * z), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (-.f64 #s(literal 1 binary64) (/.f64 x (*.f64 (-.f64 y z) (-.f64 y t)))) < -4e11

   1. Initial program 94.5%

      \[1 - \frac{x}{\left(y - z\right) \cdot \left(y - t\right)} \]
   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 96.4

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

   5. Applied rewrites 96.4%

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

   6. Taylor expanded in y around inf

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

   8. Applied rewrites 40.0%

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

   if -4e11 < (-.f64 #s(literal 1 binary64) (/.f64 x (*.f64 (-.f64 y z) (-.f64 y t)))) < 2e3

   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 98.3%

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

   if 2e3 < (-.f64 #s(literal 1 binary64) (/.f64 x (*.f64 (-.f64 y z) (-.f64 y t))))

   1. Initial program 99.6%

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

   3. Taylor expanded in 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 87.5

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

   5. Applied rewrites 87.5%

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

   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 63.8%

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

   9. Taylor expanded in y around 0

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

   11. Applied rewrites 39.4%

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

4. Final simplification 82.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;1 - \frac{x}{\left(t - y\right) \cdot \left(z - y\right)} \leq -400000000000:\\ \;\;\;\;\frac{-x}{y \cdot y}\\ \mathbf{elif}\;1 - \frac{x}{\left(t - y\right) \cdot \left(z - y\right)} \leq 2000:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;\frac{-x}{t \cdot z}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 85.7% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{-x}{t \cdot z}\\ t_2 := 1 - \frac{x}{\left(t - y\right) \cdot \left(z - y\right)}\\ \mathbf{if}\;t\_2 \leq -2 \cdot 10^{+16}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_2 \leq 2000:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ (- x) (* t z))) (t_2 (- 1.0 (/ x (* (- t y) (- z y))))))
   (if (<= t_2 -2e+16) t_1 (if (<= t_2 2000.0) 1.0 t_1))))

C

double code(double x, double y, double z, double t) {
	double t_1 = -x / (t * z);
	double t_2 = 1.0 - (x / ((t - y) * (z - y)));
	double tmp;
	if (t_2 <= -2e+16) {
		tmp = t_1;
	} else if (t_2 <= 2000.0) {
		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 / (t * z)
    t_2 = 1.0d0 - (x / ((t - y) * (z - y)))
    if (t_2 <= (-2d+16)) then
        tmp = t_1
    else if (t_2 <= 2000.0d0) 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 / (t * z);
	double t_2 = 1.0 - (x / ((t - y) * (z - y)));
	double tmp;
	if (t_2 <= -2e+16) {
		tmp = t_1;
	} else if (t_2 <= 2000.0) {
		tmp = 1.0;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = -x / (t * z)
	t_2 = 1.0 - (x / ((t - y) * (z - y)))
	tmp = 0
	if t_2 <= -2e+16:
		tmp = t_1
	elif t_2 <= 2000.0:
		tmp = 1.0
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(-x) / Float64(t * z))
	t_2 = Float64(1.0 - Float64(x / Float64(Float64(t - y) * Float64(z - y))))
	tmp = 0.0
	if (t_2 <= -2e+16)
		tmp = t_1;
	elseif (t_2 <= 2000.0)
		tmp = 1.0;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = -x / (t * z);
	t_2 = 1.0 - (x / ((t - y) * (z - y)));
	tmp = 0.0;
	if (t_2 <= -2e+16)
		tmp = t_1;
	elseif (t_2 <= 2000.0)
		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[(t * z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(1.0 - N[(x / N[(N[(t - y), $MachinePrecision] * N[(z - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, -2e+16], t$95$1, If[LessEqual[t$95$2, 2000.0], 1.0, t$95$1]]]]

Derivation

1. Split input into 2 regimes

2. if (-.f64 #s(literal 1 binary64) (/.f64 x (*.f64 (-.f64 y z) (-.f64 y t)))) < -2e16 or 2e3 < (-.f64 #s(literal 1 binary64) (/.f64 x (*.f64 (-.f64 y z) (-.f64 y t))))

   1. Initial program 96.9%

      \[1 - \frac{x}{\left(y - z\right) \cdot \left(y - t\right)} \]
   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. 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 92.4

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

   5. Applied rewrites 92.4%

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

   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 55.6%

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

   9. Taylor expanded in y around 0

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

   11. Applied rewrites 35.4%

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

   if -2e16 < (-.f64 #s(literal 1 binary64) (/.f64 x (*.f64 (-.f64 y z) (-.f64 y t)))) < 2e3

   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 97.8%

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

4. Final simplification 81.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;1 - \frac{x}{\left(t - y\right) \cdot \left(z - y\right)} \leq -2 \cdot 10^{+16}:\\ \;\;\;\;\frac{-x}{t \cdot z}\\ \mathbf{elif}\;1 - \frac{x}{\left(t - y\right) \cdot \left(z - y\right)} \leq 2000:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;\frac{-x}{t \cdot z}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 80.7% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{t \cdot y}\\ t_2 := 1 - \frac{x}{\left(t - y\right) \cdot \left(z - y\right)}\\ \mathbf{if}\;t\_2 \leq -4 \cdot 10^{+24}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_2 \leq 10^{+38}:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ x (* t y))) (t_2 (- 1.0 (/ x (* (- t y) (- z y))))))
   (if (<= t_2 -4e+24) t_1 (if (<= t_2 1e+38) 1.0 t_1))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x / (t * y);
	double t_2 = 1.0 - (x / ((t - y) * (z - y)));
	double tmp;
	if (t_2 <= -4e+24) {
		tmp = t_1;
	} else if (t_2 <= 1e+38) {
		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 / (t * y)
    t_2 = 1.0d0 - (x / ((t - y) * (z - y)))
    if (t_2 <= (-4d+24)) then
        tmp = t_1
    else if (t_2 <= 1d+38) 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 / (t * y);
	double t_2 = 1.0 - (x / ((t - y) * (z - y)));
	double tmp;
	if (t_2 <= -4e+24) {
		tmp = t_1;
	} else if (t_2 <= 1e+38) {
		tmp = 1.0;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x / (t * y)
	t_2 = 1.0 - (x / ((t - y) * (z - y)))
	tmp = 0
	if t_2 <= -4e+24:
		tmp = t_1
	elif t_2 <= 1e+38:
		tmp = 1.0
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x / Float64(t * y))
	t_2 = Float64(1.0 - Float64(x / Float64(Float64(t - y) * Float64(z - y))))
	tmp = 0.0
	if (t_2 <= -4e+24)
		tmp = t_1;
	elseif (t_2 <= 1e+38)
		tmp = 1.0;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x / (t * y);
	t_2 = 1.0 - (x / ((t - y) * (z - y)));
	tmp = 0.0;
	if (t_2 <= -4e+24)
		tmp = t_1;
	elseif (t_2 <= 1e+38)
		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[(t * y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(1.0 - N[(x / N[(N[(t - y), $MachinePrecision] * N[(z - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, -4e+24], t$95$1, If[LessEqual[t$95$2, 1e+38], 1.0, t$95$1]]]]

Derivation

1. Split input into 2 regimes

2. if (-.f64 #s(literal 1 binary64) (/.f64 x (*.f64 (-.f64 y z) (-.f64 y t)))) < -3.9999999999999999e24 or 9.99999999999999977e37 < (-.f64 #s(literal 1 binary64) (/.f64 x (*.f64 (-.f64 y z) (-.f64 y t))))

   1. Initial program 96.8%

      \[1 - \frac{x}{\left(y - z\right) \cdot \left(y - t\right)} \]
   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. 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 92.0

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

   5. Applied rewrites 92.0%

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

   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 55.0%

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

   9. Taylor expanded in y around inf

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

   11. Applied rewrites 27.9%

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

   if -3.9999999999999999e24 < (-.f64 #s(literal 1 binary64) (/.f64 x (*.f64 (-.f64 y z) (-.f64 y t)))) < 9.99999999999999977e37

   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 96.3%

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

4. Final simplification 79.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;1 - \frac{x}{\left(t - y\right) \cdot \left(z - y\right)} \leq -4 \cdot 10^{+24}:\\ \;\;\;\;\frac{x}{t \cdot y}\\ \mathbf{elif}\;1 - \frac{x}{\left(t - y\right) \cdot \left(z - y\right)} \leq 10^{+38}:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{t \cdot y}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 87.7% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{\left(t - y\right) \cdot \left(z - y\right)}\\ \mathbf{if}\;t\_1 \leq -1000:\\ \;\;\;\;\frac{x}{\left(y - t\right) \cdot z}\\ \mathbf{elif}\;t\_1 \leq 2 \cdot 10^{-5}:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\left(t - y\right) \cdot y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ x (* (- t y) (- z y)))))
   (if (<= t_1 -1000.0)
     (/ x (* (- y t) z))
     (if (<= t_1 2e-5) 1.0 (/ x (* (- t y) y))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x / ((t - y) * (z - y));
	double tmp;
	if (t_1 <= -1000.0) {
		tmp = x / ((y - t) * z);
	} else if (t_1 <= 2e-5) {
		tmp = 1.0;
	} else {
		tmp = x / ((t - y) * y);
	}
	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 <= (-1000.0d0)) then
        tmp = x / ((y - t) * z)
    else if (t_1 <= 2d-5) then
        tmp = 1.0d0
    else
        tmp = x / ((t - y) * y)
    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 <= -1000.0) {
		tmp = x / ((y - t) * z);
	} else if (t_1 <= 2e-5) {
		tmp = 1.0;
	} else {
		tmp = x / ((t - y) * y);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x / ((t - y) * (z - y))
	tmp = 0
	if t_1 <= -1000.0:
		tmp = x / ((y - t) * z)
	elif t_1 <= 2e-5:
		tmp = 1.0
	else:
		tmp = x / ((t - y) * y)
	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 <= -1000.0)
		tmp = Float64(x / Float64(Float64(y - t) * z));
	elseif (t_1 <= 2e-5)
		tmp = 1.0;
	else
		tmp = Float64(x / Float64(Float64(t - y) * y));
	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 <= -1000.0)
		tmp = x / ((y - t) * z);
	elseif (t_1 <= 2e-5)
		tmp = 1.0;
	else
		tmp = x / ((t - y) * y);
	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, -1000.0], N[(x / N[(N[(y - t), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 2e-5], 1.0, N[(x / N[(N[(t - y), $MachinePrecision] * y), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 x (*.f64 (-.f64 y z) (-.f64 y t))) < -1e3

   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 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 85.9

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

   5. Applied rewrites 85.9%

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

   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 58.4%

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

   if -1e3 < (/.f64 x (*.f64 (-.f64 y z) (-.f64 y t))) < 2.00000000000000016e-5

   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 2.00000000000000016e-5 < (/.f64 x (*.f64 (-.f64 y z) (-.f64 y t)))

   1. Initial program 94.5%

      \[1 - \frac{x}{\left(y - z\right) \cdot \left(y - t\right)} \]
   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 96.4

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

   5. Applied rewrites 96.4%

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

   6. Taylor expanded in y around inf

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

   8. Applied rewrites 40.0%

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

   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 51.6%

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

4. Final simplification 87.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x}{\left(t - y\right) \cdot \left(z - y\right)} \leq -1000:\\ \;\;\;\;\frac{x}{\left(y - t\right) \cdot z}\\ \mathbf{elif}\;\frac{x}{\left(t - y\right) \cdot \left(z - y\right)} \leq 2 \cdot 10^{-5}:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\left(t - y\right) \cdot y}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 87.8% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{\left(t - y\right) \cdot \left(z - y\right)}\\ \mathbf{if}\;t\_1 \leq -1000:\\ \;\;\;\;\frac{x}{\left(y - t\right) \cdot z}\\ \mathbf{elif}\;t\_1 \leq 2 \cdot 10^{-5}:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\left(z - y\right) \cdot y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ x (* (- t y) (- z y)))))
   (if (<= t_1 -1000.0)
     (/ x (* (- y t) z))
     (if (<= t_1 2e-5) 1.0 (/ x (* (- z y) y))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x / ((t - y) * (z - y));
	double tmp;
	if (t_1 <= -1000.0) {
		tmp = x / ((y - t) * z);
	} else if (t_1 <= 2e-5) {
		tmp = 1.0;
	} else {
		tmp = x / ((z - y) * y);
	}
	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 <= (-1000.0d0)) then
        tmp = x / ((y - t) * z)
    else if (t_1 <= 2d-5) then
        tmp = 1.0d0
    else
        tmp = x / ((z - y) * y)
    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 <= -1000.0) {
		tmp = x / ((y - t) * z);
	} else if (t_1 <= 2e-5) {
		tmp = 1.0;
	} else {
		tmp = x / ((z - y) * y);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x / ((t - y) * (z - y))
	tmp = 0
	if t_1 <= -1000.0:
		tmp = x / ((y - t) * z)
	elif t_1 <= 2e-5:
		tmp = 1.0
	else:
		tmp = x / ((z - y) * y)
	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 <= -1000.0)
		tmp = Float64(x / Float64(Float64(y - t) * z));
	elseif (t_1 <= 2e-5)
		tmp = 1.0;
	else
		tmp = Float64(x / Float64(Float64(z - y) * y));
	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 <= -1000.0)
		tmp = x / ((y - t) * z);
	elseif (t_1 <= 2e-5)
		tmp = 1.0;
	else
		tmp = x / ((z - y) * y);
	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, -1000.0], N[(x / N[(N[(y - t), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 2e-5], 1.0, N[(x / N[(N[(z - y), $MachinePrecision] * y), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 x (*.f64 (-.f64 y z) (-.f64 y t))) < -1e3

   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 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 85.9

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

   5. Applied rewrites 85.9%

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

   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 58.4%

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

   if -1e3 < (/.f64 x (*.f64 (-.f64 y z) (-.f64 y t))) < 2.00000000000000016e-5

   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 2.00000000000000016e-5 < (/.f64 x (*.f64 (-.f64 y z) (-.f64 y t)))

   1. Initial program 94.5%

      \[1 - \frac{x}{\left(y - z\right) \cdot \left(y - t\right)} \]
   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 96.4

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

   5. Applied rewrites 96.4%

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

   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 59.5%

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

4. Final simplification 88.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x}{\left(t - y\right) \cdot \left(z - y\right)} \leq -1000:\\ \;\;\;\;\frac{x}{\left(y - t\right) \cdot z}\\ \mathbf{elif}\;\frac{x}{\left(t - y\right) \cdot \left(z - y\right)} \leq 2 \cdot 10^{-5}:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\left(z - y\right) \cdot y}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 85.4% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -8.5 \cdot 10^{-47}:\\ \;\;\;\;1 - \frac{x}{\left(t - y\right) \cdot z}\\ \mathbf{elif}\;z \leq 4.4 \cdot 10^{-95}:\\ \;\;\;\;1 - \frac{x}{\left(y - t\right) \cdot y}\\ \mathbf{else}:\\ \;\;\;\;1 - \frac{x}{t \cdot z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -8.5e-47)
   (- 1.0 (/ x (* (- t y) z)))
   (if (<= z 4.4e-95) (- 1.0 (/ x (* (- y t) y))) (- 1.0 (/ x (* t z))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -8.5e-47) {
		tmp = 1.0 - (x / ((t - y) * z));
	} else if (z <= 4.4e-95) {
		tmp = 1.0 - (x / ((y - t) * y));
	} else {
		tmp = 1.0 - (x / (t * 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) :: tmp
    if (z <= (-8.5d-47)) then
        tmp = 1.0d0 - (x / ((t - y) * z))
    else if (z <= 4.4d-95) then
        tmp = 1.0d0 - (x / ((y - t) * y))
    else
        tmp = 1.0d0 - (x / (t * z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -8.5e-47) {
		tmp = 1.0 - (x / ((t - y) * z));
	} else if (z <= 4.4e-95) {
		tmp = 1.0 - (x / ((y - t) * y));
	} else {
		tmp = 1.0 - (x / (t * z));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -8.5e-47:
		tmp = 1.0 - (x / ((t - y) * z))
	elif z <= 4.4e-95:
		tmp = 1.0 - (x / ((y - t) * y))
	else:
		tmp = 1.0 - (x / (t * z))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -8.5e-47)
		tmp = Float64(1.0 - Float64(x / Float64(Float64(t - y) * z)));
	elseif (z <= 4.4e-95)
		tmp = Float64(1.0 - Float64(x / Float64(Float64(y - t) * y)));
	else
		tmp = Float64(1.0 - Float64(x / Float64(t * z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (z <= -8.5e-47)
		tmp = 1.0 - (x / ((t - y) * z));
	elseif (z <= 4.4e-95)
		tmp = 1.0 - (x / ((y - t) * y));
	else
		tmp = 1.0 - (x / (t * z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -8.5e-47], N[(1.0 - N[(x / N[(N[(t - y), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 4.4e-95], N[(1.0 - N[(x / N[(N[(y - t), $MachinePrecision] * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(1.0 - N[(x / N[(t * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -8.4999999999999999e-47

   1. Initial program 100.0%

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

   3. Taylor expanded in z around inf

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

      1. *-commutative N/A

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

      2. associate-*r* N/A

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

      3. lower-*.f64 N/A

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

      4. mul-1-neg N/A

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

      5. sub-neg N/A

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

      6. mul-1-neg N/A

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

      7. +-commutative N/A

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

      8. distribute-neg-in N/A

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

      9. unsub-neg N/A

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

      10. mul-1-neg N/A

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

      11. remove-double-neg N/A

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

      12. lower--.f64 98.0

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

   5. Applied rewrites 98.0%

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

   if -8.4999999999999999e-47 < z < 4.3999999999999998e-95

   1. Initial program 98.3%

      \[1 - \frac{x}{\left(y - z\right) \cdot \left(y - t\right)} \]
   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 88.2

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

   5. Applied rewrites 88.2%

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

   if 4.3999999999999998e-95 < 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 y around 0

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

      1. lower-*.f64 80.5

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

   5. Applied rewrites 80.5%

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

Alternative 10: 82.2% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq 4.3 \cdot 10^{-90}:\\ \;\;\;\;1 - \frac{x}{\left(y - z\right) \cdot y}\\ \mathbf{else}:\\ \;\;\;\;1 - \frac{x}{\left(z - y\right) \cdot t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= t 4.3e-90) (- 1.0 (/ x (* (- y z) y))) (- 1.0 (/ x (* (- z y) t)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= 4.3e-90) {
		tmp = 1.0 - (x / ((y - z) * 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 (t <= 4.3d-90) then
        tmp = 1.0d0 - (x / ((y - z) * 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 (t <= 4.3e-90) {
		tmp = 1.0 - (x / ((y - z) * y));
	} else {
		tmp = 1.0 - (x / ((z - y) * t));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if t <= 4.3e-90:
		tmp = 1.0 - (x / ((y - z) * y))
	else:
		tmp = 1.0 - (x / ((z - y) * t))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (t <= 4.3e-90)
		tmp = Float64(1.0 - Float64(x / Float64(Float64(y - z) * y)));
	else
		tmp = Float64(1.0 - Float64(x / Float64(Float64(z - y) * t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (t <= 4.3e-90)
		tmp = 1.0 - (x / ((y - z) * y));
	else
		tmp = 1.0 - (x / ((z - y) * t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[t, 4.3e-90], N[(1.0 - N[(x / N[(N[(y - z), $MachinePrecision] * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(1.0 - N[(x / N[(N[(z - y), $MachinePrecision] * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < 4.3000000000000002e-90

   1. Initial program 99.3%

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

   3. Taylor expanded in t around 0

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 75.4

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

   5. Applied rewrites 75.4%

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

   if 4.3000000000000002e-90 < t

   1. Initial program 99.0%

      \[1 - \frac{x}{\left(y - z\right) \cdot \left(y - t\right)} \]
   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 96.0

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

   5. Applied rewrites 96.0%

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

Alternative 11: 75.0% 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 99.2%

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

3. Taylor expanded in x around 0

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

5. Applied rewrites 73.3%

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

Reproduce

herbie shell --seed 2024332 
(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)))))