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

Percentage Accurate: 99.1% → 99.1%

Time: 8.1s

Alternatives: 10

Speedup: 1.0×

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 99.1% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 99.1% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.9%

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

3. Final simplification 99.9%

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

Alternative 2: 88.5% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := 1 - \frac{x}{\left(z - y\right) \cdot \left(t - y\right)}\\ \mathbf{if}\;t\_1 \leq -100:\\ \;\;\;\;1 - \frac{x}{\left(t - y\right) \cdot z}\\ \mathbf{elif}\;t\_1 \leq 2:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\left(z - y\right) \cdot y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (- 1.0 (/ x (* (- z y) (- t y))))))
   (if (<= t_1 -100.0)
     (- 1.0 (/ x (* (- t y) z)))
     (if (<= t_1 2.0) 1.0 (/ x (* (- z y) y))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = 1.0 - (x / ((z - y) * (t - y)));
	double tmp;
	if (t_1 <= -100.0) {
		tmp = 1.0 - (x / ((t - y) * z));
	} else if (t_1 <= 2.0) {
		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 = 1.0d0 - (x / ((z - y) * (t - y)))
    if (t_1 <= (-100.0d0)) then
        tmp = 1.0d0 - (x / ((t - y) * z))
    else if (t_1 <= 2.0d0) 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 = 1.0 - (x / ((z - y) * (t - y)));
	double tmp;
	if (t_1 <= -100.0) {
		tmp = 1.0 - (x / ((t - y) * z));
	} else if (t_1 <= 2.0) {
		tmp = 1.0;
	} else {
		tmp = x / ((z - y) * y);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = 1.0 - (x / ((z - y) * (t - y)))
	tmp = 0
	if t_1 <= -100.0:
		tmp = 1.0 - (x / ((t - y) * z))
	elif t_1 <= 2.0:
		tmp = 1.0
	else:
		tmp = x / ((z - y) * y)
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(1.0 - Float64(x / Float64(Float64(z - y) * Float64(t - y))))
	tmp = 0.0
	if (t_1 <= -100.0)
		tmp = Float64(1.0 - Float64(x / Float64(Float64(t - y) * z)));
	elseif (t_1 <= 2.0)
		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 = 1.0 - (x / ((z - y) * (t - y)));
	tmp = 0.0;
	if (t_1 <= -100.0)
		tmp = 1.0 - (x / ((t - y) * z));
	elseif (t_1 <= 2.0)
		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[(1.0 - N[(x / N[(N[(z - y), $MachinePrecision] * N[(t - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -100.0], N[(1.0 - N[(x / N[(N[(t - y), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 2.0], 1.0, N[(x / N[(N[(z - y), $MachinePrecision] * y), $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)))) < -100

   1. Initial program 99.7%

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

   3. Taylor expanded in z around inf

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

      1. *-commutative N/A

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

      2. associate-*r* N/A

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

      3. lower-*.f64 N/A

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

      4. mul-1-neg N/A

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

      5. sub-neg N/A

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

      6. mul-1-neg N/A

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

      7. +-commutative N/A

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

      8. distribute-neg-in N/A

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

      9. unsub-neg N/A

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

      10. mul-1-neg N/A

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

      11. remove-double-neg N/A

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

      12. lower--.f64 54.2

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

   5. Applied rewrites 54.2%

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

   if -100 < (-.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 t around inf

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

   5. Applied rewrites 99.3%

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

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

   1. Initial program 99.7%

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

   3. Taylor expanded in x around inf

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

      1. associate-/r* N/A

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

      2. associate-*r/ N/A

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

      3. lower-/.f64 N/A

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

      4. mul-1-neg N/A

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

      5. distribute-neg-frac2 N/A

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

      6. mul-1-neg N/A

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

      7. lower-/.f64 N/A

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

      8. mul-1-neg N/A

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

      9. sub-neg N/A

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

      10. mul-1-neg N/A

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

      11. +-commutative N/A

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

      12. distribute-neg-in N/A

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

      13. unsub-neg N/A

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

      14. mul-1-neg N/A

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

      15. remove-double-neg N/A

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

      16. lower--.f64 N/A

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

      17. lower--.f64 93.6

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

   5. Applied rewrites 93.6%

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

   6. Taylor expanded in t around 0

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

   8. Applied rewrites 51.4%

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

4. Final simplification 88.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;1 - \frac{x}{\left(z - y\right) \cdot \left(t - y\right)} \leq -100:\\ \;\;\;\;1 - \frac{x}{\left(t - y\right) \cdot z}\\ \mathbf{elif}\;1 - \frac{x}{\left(z - y\right) \cdot \left(t - y\right)} \leq 2:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\left(z - y\right) \cdot y}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 90.1% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{t \cdot \left(y - z\right)}\\ t_2 := 1 - \frac{x}{\left(z - y\right) \cdot \left(t - y\right)}\\ \mathbf{if}\;t\_2 \leq -100:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_2 \leq 20000000:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ x (* t (- y z)))) (t_2 (- 1.0 (/ x (* (- z y) (- t y))))))
   (if (<= t_2 -100.0) t_1 (if (<= t_2 20000000.0) 1.0 t_1))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x / (t * (y - z));
	double t_2 = 1.0 - (x / ((z - y) * (t - y)));
	double tmp;
	if (t_2 <= -100.0) {
		tmp = t_1;
	} else if (t_2 <= 20000000.0) {
		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 * (y - z))
    t_2 = 1.0d0 - (x / ((z - y) * (t - y)))
    if (t_2 <= (-100.0d0)) then
        tmp = t_1
    else if (t_2 <= 20000000.0d0) 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 * (y - z));
	double t_2 = 1.0 - (x / ((z - y) * (t - y)));
	double tmp;
	if (t_2 <= -100.0) {
		tmp = t_1;
	} else if (t_2 <= 20000000.0) {
		tmp = 1.0;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x / (t * (y - z))
	t_2 = 1.0 - (x / ((z - y) * (t - y)))
	tmp = 0
	if t_2 <= -100.0:
		tmp = t_1
	elif t_2 <= 20000000.0:
		tmp = 1.0
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x / Float64(t * Float64(y - z)))
	t_2 = Float64(1.0 - Float64(x / Float64(Float64(z - y) * Float64(t - y))))
	tmp = 0.0
	if (t_2 <= -100.0)
		tmp = t_1;
	elseif (t_2 <= 20000000.0)
		tmp = 1.0;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x / (t * (y - z));
	t_2 = 1.0 - (x / ((z - y) * (t - y)));
	tmp = 0.0;
	if (t_2 <= -100.0)
		tmp = t_1;
	elseif (t_2 <= 20000000.0)
		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 * N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(1.0 - N[(x / N[(N[(z - y), $MachinePrecision] * N[(t - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, -100.0], t$95$1, If[LessEqual[t$95$2, 20000000.0], 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)))) < -100 or 2e7 < (-.f64 #s(literal 1 binary64) (/.f64 x (*.f64 (-.f64 y z) (-.f64 y t))))

   1. Initial program 99.7%

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

   3. Taylor expanded in x around inf

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

      1. associate-/r* N/A

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

      2. associate-*r/ N/A

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

      3. lower-/.f64 N/A

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

      4. mul-1-neg N/A

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

      5. distribute-neg-frac2 N/A

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

      6. mul-1-neg N/A

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

      7. lower-/.f64 N/A

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

      8. mul-1-neg N/A

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

      9. sub-neg N/A

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

      10. mul-1-neg N/A

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

      11. +-commutative N/A

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

      12. distribute-neg-in N/A

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

      13. unsub-neg N/A

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

      14. mul-1-neg N/A

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

      15. remove-double-neg N/A

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

      16. lower--.f64 N/A

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

      17. lower--.f64 95.5

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

   5. Applied rewrites 95.5%

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

   6. Taylor expanded in y around inf

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

   8. Applied rewrites 31.5%

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

   9. Taylor expanded in t around inf

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

   11. Applied rewrites 63.4%

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

   if -100 < (-.f64 #s(literal 1 binary64) (/.f64 x (*.f64 (-.f64 y z) (-.f64 y t)))) < 2e7

   1. Initial program 100.0%

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

   3. Taylor expanded in t around inf

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

   5. Applied rewrites 98.4%

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

4. Final simplification 90.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;1 - \frac{x}{\left(z - y\right) \cdot \left(t - y\right)} \leq -100:\\ \;\;\;\;\frac{x}{t \cdot \left(y - z\right)}\\ \mathbf{elif}\;1 - \frac{x}{\left(z - y\right) \cdot \left(t - y\right)} \leq 20000000:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{t \cdot \left(y - z\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 86.0% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := 1 - \frac{x}{\left(z - y\right) \cdot \left(t - y\right)}\\ \mathbf{if}\;t\_1 \leq -100:\\ \;\;\;\;\frac{-x}{t \cdot z}\\ \mathbf{elif}\;t\_1 \leq 2:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\left(t - y\right) \cdot y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (- 1.0 (/ x (* (- z y) (- t y))))))
   (if (<= t_1 -100.0)
     (/ (- x) (* t z))
     (if (<= t_1 2.0) 1.0 (/ x (* (- t y) y))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = 1.0 - (x / ((z - y) * (t - y)));
	double tmp;
	if (t_1 <= -100.0) {
		tmp = -x / (t * z);
	} else if (t_1 <= 2.0) {
		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 = 1.0d0 - (x / ((z - y) * (t - y)))
    if (t_1 <= (-100.0d0)) then
        tmp = -x / (t * z)
    else if (t_1 <= 2.0d0) 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 = 1.0 - (x / ((z - y) * (t - y)));
	double tmp;
	if (t_1 <= -100.0) {
		tmp = -x / (t * z);
	} else if (t_1 <= 2.0) {
		tmp = 1.0;
	} else {
		tmp = x / ((t - y) * y);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = 1.0 - (x / ((z - y) * (t - y)))
	tmp = 0
	if t_1 <= -100.0:
		tmp = -x / (t * z)
	elif t_1 <= 2.0:
		tmp = 1.0
	else:
		tmp = x / ((t - y) * y)
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(1.0 - Float64(x / Float64(Float64(z - y) * Float64(t - y))))
	tmp = 0.0
	if (t_1 <= -100.0)
		tmp = Float64(Float64(-x) / Float64(t * z));
	elseif (t_1 <= 2.0)
		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 = 1.0 - (x / ((z - y) * (t - y)));
	tmp = 0.0;
	if (t_1 <= -100.0)
		tmp = -x / (t * z);
	elseif (t_1 <= 2.0)
		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[(1.0 - N[(x / N[(N[(z - y), $MachinePrecision] * N[(t - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -100.0], N[((-x) / N[(t * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 2.0], 1.0, N[(x / N[(N[(t - y), $MachinePrecision] * y), $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)))) < -100

   1. Initial program 99.7%

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

   3. Taylor expanded in x around inf

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

      1. associate-/r* N/A

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

      2. associate-*r/ N/A

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

      3. lower-/.f64 N/A

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

      4. mul-1-neg N/A

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

      5. distribute-neg-frac2 N/A

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

      6. mul-1-neg N/A

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

      7. lower-/.f64 N/A

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

      8. mul-1-neg N/A

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

      9. sub-neg N/A

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

      10. mul-1-neg N/A

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

      11. +-commutative N/A

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

      12. distribute-neg-in N/A

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

      13. unsub-neg N/A

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

      14. mul-1-neg N/A

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

      15. remove-double-neg N/A

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

      16. lower--.f64 N/A

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

      17. lower--.f64 93.9

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

   5. Applied rewrites 93.9%

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

   6. Taylor expanded in y around 0

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

   8. Applied rewrites 42.6%

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

   if -100 < (-.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 t around inf

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

   5. Applied rewrites 99.3%

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

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

   1. Initial program 99.7%

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

   3. Taylor expanded in x around inf

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

      1. associate-/r* N/A

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

      2. associate-*r/ N/A

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

      3. lower-/.f64 N/A

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

      4. mul-1-neg N/A

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

      5. distribute-neg-frac2 N/A

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

      6. mul-1-neg N/A

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

      7. lower-/.f64 N/A

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

      8. mul-1-neg N/A

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

      9. sub-neg N/A

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

      10. mul-1-neg N/A

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

      11. +-commutative N/A

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

      12. distribute-neg-in N/A

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

      13. unsub-neg N/A

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

      14. mul-1-neg N/A

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

      15. remove-double-neg N/A

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

      16. lower--.f64 N/A

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

      17. lower--.f64 93.6

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

   5. Applied rewrites 93.6%

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

   6. Taylor expanded in z around 0

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

   8. Applied rewrites 55.5%

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

4. Final simplification 87.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;1 - \frac{x}{\left(z - y\right) \cdot \left(t - y\right)} \leq -100:\\ \;\;\;\;\frac{-x}{t \cdot z}\\ \mathbf{elif}\;1 - \frac{x}{\left(z - y\right) \cdot \left(t - y\right)} \leq 2:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\left(t - y\right) \cdot y}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 86.1% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{-x}{t \cdot z}\\ t_2 := 1 - \frac{x}{\left(z - y\right) \cdot \left(t - y\right)}\\ \mathbf{if}\;t\_2 \leq -100:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_2 \leq 4 \cdot 10^{+22}:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ (- x) (* t z))) (t_2 (- 1.0 (/ x (* (- z y) (- t y))))))
   (if (<= t_2 -100.0) t_1 (if (<= t_2 4e+22) 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 / ((z - y) * (t - y)));
	double tmp;
	if (t_2 <= -100.0) {
		tmp = t_1;
	} else if (t_2 <= 4e+22) {
		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 / ((z - y) * (t - y)))
    if (t_2 <= (-100.0d0)) then
        tmp = t_1
    else if (t_2 <= 4d+22) 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 / ((z - y) * (t - y)));
	double tmp;
	if (t_2 <= -100.0) {
		tmp = t_1;
	} else if (t_2 <= 4e+22) {
		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 / ((z - y) * (t - y)))
	tmp = 0
	if t_2 <= -100.0:
		tmp = t_1
	elif t_2 <= 4e+22:
		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(z - y) * Float64(t - y))))
	tmp = 0.0
	if (t_2 <= -100.0)
		tmp = t_1;
	elseif (t_2 <= 4e+22)
		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 / ((z - y) * (t - y)));
	tmp = 0.0;
	if (t_2 <= -100.0)
		tmp = t_1;
	elseif (t_2 <= 4e+22)
		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[(z - y), $MachinePrecision] * N[(t - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, -100.0], t$95$1, If[LessEqual[t$95$2, 4e+22], 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)))) < -100 or 4e22 < (-.f64 #s(literal 1 binary64) (/.f64 x (*.f64 (-.f64 y z) (-.f64 y t))))

   1. Initial program 99.7%

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

   3. Taylor expanded in x around inf

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

      1. associate-/r* N/A

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

      2. associate-*r/ N/A

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

      3. lower-/.f64 N/A

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

      4. mul-1-neg N/A

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

      5. distribute-neg-frac2 N/A

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

      6. mul-1-neg N/A

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

      7. lower-/.f64 N/A

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

      8. mul-1-neg N/A

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

      9. sub-neg N/A

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

      10. mul-1-neg N/A

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

      11. +-commutative N/A

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

      12. distribute-neg-in N/A

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

      13. unsub-neg N/A

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

      14. mul-1-neg N/A

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

      15. remove-double-neg N/A

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

      16. lower--.f64 N/A

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

      17. lower--.f64 95.5

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

   5. Applied rewrites 95.5%

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

   6. Taylor expanded in y around 0

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

   8. Applied rewrites 44.7%

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

   if -100 < (-.f64 #s(literal 1 binary64) (/.f64 x (*.f64 (-.f64 y z) (-.f64 y t)))) < 4e22

   1. Initial program 100.0%

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

   3. Taylor expanded in t around inf

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

   5. Applied rewrites 97.6%

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

4. Final simplification 85.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;1 - \frac{x}{\left(z - y\right) \cdot \left(t - y\right)} \leq -100:\\ \;\;\;\;\frac{-x}{t \cdot z}\\ \mathbf{elif}\;1 - \frac{x}{\left(z - y\right) \cdot \left(t - y\right)} \leq 4 \cdot 10^{+22}:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;\frac{-x}{t \cdot z}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 87.6% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{\left(z - y\right) \cdot \left(t - y\right)}\\ \mathbf{if}\;t\_1 \leq -10:\\ \;\;\;\;\frac{x}{\left(z - y\right) \cdot y}\\ \mathbf{elif}\;t\_1 \leq 4 \cdot 10^{-26}:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\left(y - t\right) \cdot z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ x (* (- z y) (- t y)))))
   (if (<= t_1 -10.0)
     (/ x (* (- z y) y))
     (if (<= t_1 4e-26) 1.0 (/ x (* (- y t) z))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x / ((z - y) * (t - y));
	double tmp;
	if (t_1 <= -10.0) {
		tmp = x / ((z - y) * y);
	} else if (t_1 <= 4e-26) {
		tmp = 1.0;
	} else {
		tmp = x / ((y - 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 = x / ((z - y) * (t - y))
    if (t_1 <= (-10.0d0)) then
        tmp = x / ((z - y) * y)
    else if (t_1 <= 4d-26) then
        tmp = 1.0d0
    else
        tmp = x / ((y - t) * z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = x / ((z - y) * (t - y));
	double tmp;
	if (t_1 <= -10.0) {
		tmp = x / ((z - y) * y);
	} else if (t_1 <= 4e-26) {
		tmp = 1.0;
	} else {
		tmp = x / ((y - t) * z);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x / ((z - y) * (t - y))
	tmp = 0
	if t_1 <= -10.0:
		tmp = x / ((z - y) * y)
	elif t_1 <= 4e-26:
		tmp = 1.0
	else:
		tmp = x / ((y - t) * z)
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x / Float64(Float64(z - y) * Float64(t - y)))
	tmp = 0.0
	if (t_1 <= -10.0)
		tmp = Float64(x / Float64(Float64(z - y) * y));
	elseif (t_1 <= 4e-26)
		tmp = 1.0;
	else
		tmp = Float64(x / Float64(Float64(y - t) * z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x / ((z - y) * (t - y));
	tmp = 0.0;
	if (t_1 <= -10.0)
		tmp = x / ((z - y) * y);
	elseif (t_1 <= 4e-26)
		tmp = 1.0;
	else
		tmp = x / ((y - t) * z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x / N[(N[(z - y), $MachinePrecision] * N[(t - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -10.0], N[(x / N[(N[(z - y), $MachinePrecision] * y), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 4e-26], 1.0, N[(x / N[(N[(y - t), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 x (*.f64 (-.f64 y z) (-.f64 y t))) < -10

   1. Initial program 99.7%

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

   3. Taylor expanded in x around inf

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

      1. associate-/r* N/A

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

      2. associate-*r/ N/A

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

      3. lower-/.f64 N/A

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

      4. mul-1-neg N/A

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

      5. distribute-neg-frac2 N/A

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

      6. mul-1-neg N/A

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

      7. lower-/.f64 N/A

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

      8. mul-1-neg N/A

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

      9. sub-neg N/A

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

      10. mul-1-neg N/A

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

      11. +-commutative N/A

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

      12. distribute-neg-in N/A

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

      13. unsub-neg N/A

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

      14. mul-1-neg N/A

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

      15. remove-double-neg N/A

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

      16. lower--.f64 N/A

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

      17. lower--.f64 93.6

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

   5. Applied rewrites 93.6%

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

   6. Taylor expanded in t around 0

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

   8. Applied rewrites 51.4%

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

   if -10 < (/.f64 x (*.f64 (-.f64 y z) (-.f64 y t))) < 4.0000000000000002e-26

   1. Initial program 100.0%

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

   3. Taylor expanded in t around inf

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

   5. Applied rewrites 99.3%

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

   if 4.0000000000000002e-26 < (/.f64 x (*.f64 (-.f64 y z) (-.f64 y t)))

   1. Initial program 99.7%

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

   3. Taylor expanded in x around inf

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

      1. associate-/r* N/A

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

      2. associate-*r/ N/A

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

      3. lower-/.f64 N/A

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

      4. mul-1-neg N/A

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

      5. distribute-neg-frac2 N/A

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

      6. mul-1-neg N/A

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

      7. lower-/.f64 N/A

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

      8. mul-1-neg N/A

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

      9. sub-neg N/A

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

      10. mul-1-neg N/A

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

      11. +-commutative N/A

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

      12. distribute-neg-in N/A

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

      13. unsub-neg N/A

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

      14. mul-1-neg N/A

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

      15. remove-double-neg N/A

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

      16. lower--.f64 N/A

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

      17. lower--.f64 93.9

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

   5. Applied rewrites 93.9%

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

   6. Taylor expanded in z around inf

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

   8. Applied rewrites 51.7%

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

4. Final simplification 87.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x}{\left(z - y\right) \cdot \left(t - y\right)} \leq -10:\\ \;\;\;\;\frac{x}{\left(z - y\right) \cdot y}\\ \mathbf{elif}\;\frac{x}{\left(z - y\right) \cdot \left(t - y\right)} \leq 4 \cdot 10^{-26}:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\left(y - t\right) \cdot z}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 89.4% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{\left(z - y\right) \cdot \left(t - y\right)}\\ \mathbf{if}\;t\_1 \leq -1 \cdot 10^{+14}:\\ \;\;\;\;\frac{x}{t \cdot \left(y - z\right)}\\ \mathbf{elif}\;t\_1 \leq 4 \cdot 10^{-26}:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\left(y - t\right) \cdot z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ x (* (- z y) (- t y)))))
   (if (<= t_1 -1e+14)
     (/ x (* t (- y z)))
     (if (<= t_1 4e-26) 1.0 (/ x (* (- y t) z))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x / ((z - y) * (t - y));
	double tmp;
	if (t_1 <= -1e+14) {
		tmp = x / (t * (y - z));
	} else if (t_1 <= 4e-26) {
		tmp = 1.0;
	} else {
		tmp = x / ((y - 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 = x / ((z - y) * (t - y))
    if (t_1 <= (-1d+14)) then
        tmp = x / (t * (y - z))
    else if (t_1 <= 4d-26) then
        tmp = 1.0d0
    else
        tmp = x / ((y - t) * z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = x / ((z - y) * (t - y));
	double tmp;
	if (t_1 <= -1e+14) {
		tmp = x / (t * (y - z));
	} else if (t_1 <= 4e-26) {
		tmp = 1.0;
	} else {
		tmp = x / ((y - t) * z);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x / ((z - y) * (t - y))
	tmp = 0
	if t_1 <= -1e+14:
		tmp = x / (t * (y - z))
	elif t_1 <= 4e-26:
		tmp = 1.0
	else:
		tmp = x / ((y - t) * z)
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x / Float64(Float64(z - y) * Float64(t - y)))
	tmp = 0.0
	if (t_1 <= -1e+14)
		tmp = Float64(x / Float64(t * Float64(y - z)));
	elseif (t_1 <= 4e-26)
		tmp = 1.0;
	else
		tmp = Float64(x / Float64(Float64(y - t) * z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x / ((z - y) * (t - y));
	tmp = 0.0;
	if (t_1 <= -1e+14)
		tmp = x / (t * (y - z));
	elseif (t_1 <= 4e-26)
		tmp = 1.0;
	else
		tmp = x / ((y - t) * z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x / N[(N[(z - y), $MachinePrecision] * N[(t - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -1e+14], N[(x / N[(t * N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 4e-26], 1.0, N[(x / N[(N[(y - t), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 x (*.f64 (-.f64 y z) (-.f64 y t))) < -1e14

   1. Initial program 99.7%

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

   3. Taylor expanded in x around inf

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

      1. associate-/r* N/A

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

      2. associate-*r/ N/A

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

      3. lower-/.f64 N/A

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

      4. mul-1-neg N/A

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

      5. distribute-neg-frac2 N/A

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

      6. mul-1-neg N/A

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

      7. lower-/.f64 N/A

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

      8. mul-1-neg N/A

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

      9. sub-neg N/A

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

      10. mul-1-neg N/A

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

      11. +-commutative N/A

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

      12. distribute-neg-in N/A

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

      13. unsub-neg N/A

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

      14. mul-1-neg N/A

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

      15. remove-double-neg N/A

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

      16. lower--.f64 N/A

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

      17. lower--.f64 96.7

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

   5. Applied rewrites 96.7%

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

   6. Taylor expanded in y around inf

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

   8. Applied rewrites 38.3%

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

   9. Taylor expanded in t around inf

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

   11. Applied rewrites 55.8%

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

   if -1e14 < (/.f64 x (*.f64 (-.f64 y z) (-.f64 y t))) < 4.0000000000000002e-26

   1. Initial program 100.0%

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

   3. Taylor expanded in t around inf

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

   5. Applied rewrites 98.4%

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

   if 4.0000000000000002e-26 < (/.f64 x (*.f64 (-.f64 y z) (-.f64 y t)))

   1. Initial program 99.7%

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

   3. Taylor expanded in x around inf

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

      1. associate-/r* N/A

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

      2. associate-*r/ N/A

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

      3. lower-/.f64 N/A

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

      4. mul-1-neg N/A

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

      5. distribute-neg-frac2 N/A

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

      6. mul-1-neg N/A

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

      7. lower-/.f64 N/A

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

      8. mul-1-neg N/A

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

      9. sub-neg N/A

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

      10. mul-1-neg N/A

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

      11. +-commutative N/A

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

      12. distribute-neg-in N/A

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

      13. unsub-neg N/A

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

      14. mul-1-neg N/A

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

      15. remove-double-neg N/A

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

      16. lower--.f64 N/A

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

      17. lower--.f64 93.9

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

   5. Applied rewrites 93.9%

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

   6. Taylor expanded in z around inf

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

   8. Applied rewrites 51.7%

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

4. Final simplification 88.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x}{\left(z - y\right) \cdot \left(t - y\right)} \leq -1 \cdot 10^{+14}:\\ \;\;\;\;\frac{x}{t \cdot \left(y - z\right)}\\ \mathbf{elif}\;\frac{x}{\left(z - y\right) \cdot \left(t - y\right)} \leq 4 \cdot 10^{-26}:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\left(y - t\right) \cdot z}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 86.7% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -6.5 \cdot 10^{-233}:\\ \;\;\;\;1 - \frac{x}{\left(t - y\right) \cdot z}\\ \mathbf{elif}\;t \leq 3 \cdot 10^{-34}:\\ \;\;\;\;1 - \frac{x}{\left(y - z\right) \cdot y}\\ \mathbf{else}:\\ \;\;\;\;1 - \frac{x}{\left(z - y\right) \cdot t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= t -6.5e-233)
   (- 1.0 (/ x (* (- t y) z)))
   (if (<= t 3e-34) (- 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 <= -6.5e-233) {
		tmp = 1.0 - (x / ((t - y) * z));
	} else if (t <= 3e-34) {
		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 <= (-6.5d-233)) then
        tmp = 1.0d0 - (x / ((t - y) * z))
    else if (t <= 3d-34) 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 <= -6.5e-233) {
		tmp = 1.0 - (x / ((t - y) * z));
	} else if (t <= 3e-34) {
		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 <= -6.5e-233:
		tmp = 1.0 - (x / ((t - y) * z))
	elif t <= 3e-34:
		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 <= -6.5e-233)
		tmp = Float64(1.0 - Float64(x / Float64(Float64(t - y) * z)));
	elseif (t <= 3e-34)
		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 <= -6.5e-233)
		tmp = 1.0 - (x / ((t - y) * z));
	elseif (t <= 3e-34)
		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, -6.5e-233], N[(1.0 - N[(x / N[(N[(t - y), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 3e-34], N[(1.0 - N[(x / N[(N[(y - z), $MachinePrecision] * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(1.0 - N[(x / N[(N[(z - y), $MachinePrecision] * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -6.49999999999999989e-233

   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 77.2

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

   5. Applied rewrites 77.2%

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

   if -6.49999999999999989e-233 < t < 3e-34

   1. Initial program 99.9%

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

   3. Taylor expanded in t around 0

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 87.1

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

   5. Applied rewrites 87.1%

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

   if 3e-34 < t

   1. Initial program 100.0%

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

   3. Taylor expanded in t around inf

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

      1. *-commutative N/A

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

      2. associate-*r* N/A

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

      3. lower-*.f64 N/A

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

      4. mul-1-neg N/A

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

      5. sub-neg N/A

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

      6. mul-1-neg N/A

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

      7. +-commutative N/A

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

      8. distribute-neg-in N/A

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

      9. unsub-neg N/A

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

      10. mul-1-neg N/A

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

      11. remove-double-neg N/A

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

      12. lower--.f64 95.8

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

   5. Applied rewrites 95.8%

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

Alternative 9: 89.8% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := 1 - \frac{x}{\left(y - z\right) \cdot y}\\ \mathbf{if}\;y \leq -3.6 \cdot 10^{-109}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 1.04 \cdot 10^{-22}:\\ \;\;\;\;1 - \frac{x}{\left(t - y\right) \cdot z}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (- 1.0 (/ x (* (- y z) y)))))
   (if (<= y -3.6e-109)
     t_1
     (if (<= y 1.04e-22) (- 1.0 (/ x (* (- t y) z))) t_1))))

C

double code(double x, double y, double z, double t) {
	double t_1 = 1.0 - (x / ((y - z) * y));
	double tmp;
	if (y <= -3.6e-109) {
		tmp = t_1;
	} else if (y <= 1.04e-22) {
		tmp = 1.0 - (x / ((t - y) * z));
	} 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 / ((y - z) * y))
    if (y <= (-3.6d-109)) then
        tmp = t_1
    else if (y <= 1.04d-22) then
        tmp = 1.0d0 - (x / ((t - y) * z))
    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 / ((y - z) * y));
	double tmp;
	if (y <= -3.6e-109) {
		tmp = t_1;
	} else if (y <= 1.04e-22) {
		tmp = 1.0 - (x / ((t - y) * z));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = 1.0 - (x / ((y - z) * y))
	tmp = 0
	if y <= -3.6e-109:
		tmp = t_1
	elif y <= 1.04e-22:
		tmp = 1.0 - (x / ((t - y) * z))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(1.0 - Float64(x / Float64(Float64(y - z) * y)))
	tmp = 0.0
	if (y <= -3.6e-109)
		tmp = t_1;
	elseif (y <= 1.04e-22)
		tmp = Float64(1.0 - Float64(x / Float64(Float64(t - y) * z)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = 1.0 - (x / ((y - z) * y));
	tmp = 0.0;
	if (y <= -3.6e-109)
		tmp = t_1;
	elseif (y <= 1.04e-22)
		tmp = 1.0 - (x / ((t - y) * z));
	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[(y - z), $MachinePrecision] * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -3.6e-109], t$95$1, If[LessEqual[y, 1.04e-22], N[(1.0 - N[(x / N[(N[(t - y), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if y < -3.6000000000000001e-109 or 1.04e-22 < y

   1. Initial program 99.9%

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

   3. Taylor expanded in 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 93.9

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

   5. Applied rewrites 93.9%

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

   if -3.6000000000000001e-109 < y < 1.04e-22

   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 83.8

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

   5. Applied rewrites 83.8%

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

Alternative 10: 76.4% 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 99.9%

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

3. Taylor expanded in t around inf

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

5. Applied rewrites 76.2%

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

Reproduce

herbie shell --seed 2024255 
(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)))))