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

Percentage Accurate: 99.0% → 99.0%

Time: 6.7s

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: 99.0% 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: 99.0% 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]

Derivation

1. Initial program 99.9%

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

Alternative 2: 87.3% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -4.2 \cdot 10^{-116}:\\ \;\;\;\;\mathsf{fma}\left({\left(\left(y - t\right) \cdot z\right)}^{-1}, x, 1\right)\\ \mathbf{elif}\;t \leq 8.2 \cdot 10^{-134}:\\ \;\;\;\;1 - \frac{x}{\left(y - z\right) \cdot y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\left(y - z\right) \cdot t} + 1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= t -4.2e-116)
   (fma (pow (* (- y t) z) -1.0) x 1.0)
   (if (<= t 8.2e-134)
     (- 1.0 (/ x (* (- y z) y)))
     (+ (/ x (* (- y z) t)) 1.0))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= -4.2e-116) {
		tmp = fma(pow(((y - t) * z), -1.0), x, 1.0);
	} else if (t <= 8.2e-134) {
		tmp = 1.0 - (x / ((y - z) * y));
	} else {
		tmp = (x / ((y - z) * t)) + 1.0;
	}
	return tmp;
}

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (t <= -4.2e-116)
		tmp = fma((Float64(Float64(y - t) * z) ^ -1.0), x, 1.0);
	elseif (t <= 8.2e-134)
		tmp = Float64(1.0 - Float64(x / Float64(Float64(y - z) * y)));
	else
		tmp = Float64(Float64(x / Float64(Float64(y - z) * t)) + 1.0);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[t, -4.2e-116], N[(N[Power[N[(N[(y - t), $MachinePrecision] * z), $MachinePrecision], -1.0], $MachinePrecision] * x + 1.0), $MachinePrecision], If[LessEqual[t, 8.2e-134], N[(1.0 - N[(x / N[(N[(y - z), $MachinePrecision] * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x / N[(N[(y - z), $MachinePrecision] * t), $MachinePrecision]), $MachinePrecision] + 1.0), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -4.1999999999999998e-116

   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

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

      1. +-commutative N/A

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

      2. lower-+.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. *-commutative N/A

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

      5. lower-*.f64 N/A

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

      6. lower--.f64 82.0

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

   5. Applied rewrites 82.0%

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

   7. Applied rewrites 81.9%

      \[\leadsto \frac{\frac{x}{z}}{y - t} + 1 \]

   8. Taylor expanded in x around inf

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

   10. Applied rewrites 82.0%

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

   if -4.1999999999999998e-116 < t < 8.2000000000000004e-134

   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 91.2

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

   5. Applied rewrites 91.2%

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

   if 8.2000000000000004e-134 < 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

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

      1. +-commutative N/A

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

      2. lower-+.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. *-commutative N/A

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

      5. lower-*.f64 N/A

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

      6. lower--.f64 94.2

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

   5. Applied rewrites 94.2%

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

4. Final simplification 88.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -4.2 \cdot 10^{-116}:\\ \;\;\;\;\mathsf{fma}\left({\left(\left(y - t\right) \cdot z\right)}^{-1}, x, 1\right)\\ \mathbf{elif}\;t \leq 8.2 \cdot 10^{-134}:\\ \;\;\;\;1 - \frac{x}{\left(y - z\right) \cdot y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\left(y - z\right) \cdot t} + 1\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 89.7% accurate, 0.3× speedup

Math

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

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ x (* (- y z) (- y t)))))
   (if (or (<= t_1 -5e-10) (not (<= t_1 5e-10)))
     (+ (/ x (* (- y t) z)) 1.0)
     1.0)))

C

double code(double x, double y, double z, double t) {
	double t_1 = x / ((y - z) * (y - t));
	double tmp;
	if ((t_1 <= -5e-10) || !(t_1 <= 5e-10)) {
		tmp = (x / ((y - t) * z)) + 1.0;
	} else {
		tmp = 1.0;
	}
	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 / ((y - z) * (y - t))
    if ((t_1 <= (-5d-10)) .or. (.not. (t_1 <= 5d-10))) then
        tmp = (x / ((y - t) * z)) + 1.0d0
    else
        tmp = 1.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = x / ((y - z) * (y - t));
	double tmp;
	if ((t_1 <= -5e-10) || !(t_1 <= 5e-10)) {
		tmp = (x / ((y - t) * z)) + 1.0;
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x / ((y - z) * (y - t))
	tmp = 0
	if (t_1 <= -5e-10) or not (t_1 <= 5e-10):
		tmp = (x / ((y - t) * z)) + 1.0
	else:
		tmp = 1.0
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x / Float64(Float64(y - z) * Float64(y - t)))
	tmp = 0.0
	if ((t_1 <= -5e-10) || !(t_1 <= 5e-10))
		tmp = Float64(Float64(x / Float64(Float64(y - t) * z)) + 1.0);
	else
		tmp = 1.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x / ((y - z) * (y - t));
	tmp = 0.0;
	if ((t_1 <= -5e-10) || ~((t_1 <= 5e-10)))
		tmp = (x / ((y - t) * z)) + 1.0;
	else
		tmp = 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x / N[(N[(y - z), $MachinePrecision] * N[(y - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[t$95$1, -5e-10], N[Not[LessEqual[t$95$1, 5e-10]], $MachinePrecision]], N[(N[(x / N[(N[(y - t), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision] + 1.0), $MachinePrecision], 1.0]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 x (*.f64 (-.f64 y z) (-.f64 y t))) < -5.00000000000000031e-10 or 5.00000000000000031e-10 < (/.f64 x (*.f64 (-.f64 y z) (-.f64 y t)))

   1. Initial program 99.7%

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

   3. Taylor expanded in z around inf

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

      1. +-commutative N/A

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

      2. lower-+.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. *-commutative N/A

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

      5. lower-*.f64 N/A

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

      6. lower--.f64 61.9

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

   5. Applied rewrites 61.9%

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

   if -5.00000000000000031e-10 < (/.f64 x (*.f64 (-.f64 y z) (-.f64 y t))) < 5.00000000000000031e-10

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0

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

   5. Applied rewrites 99.8%

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

4. Final simplification 89.4%

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

Alternative 4: 85.5% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{\left(y - z\right) \cdot \left(y - t\right)}\\ \mathbf{if}\;t\_1 \leq -2 \cdot 10^{-7} \lor \neg \left(t\_1 \leq 5 \cdot 10^{-10}\right):\\ \;\;\;\;1 - \frac{x}{t \cdot z}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ x (* (- y z) (- y t)))))
   (if (or (<= t_1 -2e-7) (not (<= t_1 5e-10))) (- 1.0 (/ x (* t z))) 1.0)))

C

double code(double x, double y, double z, double t) {
	double t_1 = x / ((y - z) * (y - t));
	double tmp;
	if ((t_1 <= -2e-7) || !(t_1 <= 5e-10)) {
		tmp = 1.0 - (x / (t * z));
	} else {
		tmp = 1.0;
	}
	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 / ((y - z) * (y - t))
    if ((t_1 <= (-2d-7)) .or. (.not. (t_1 <= 5d-10))) then
        tmp = 1.0d0 - (x / (t * z))
    else
        tmp = 1.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = x / ((y - z) * (y - t));
	double tmp;
	if ((t_1 <= -2e-7) || !(t_1 <= 5e-10)) {
		tmp = 1.0 - (x / (t * z));
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x / ((y - z) * (y - t))
	tmp = 0
	if (t_1 <= -2e-7) or not (t_1 <= 5e-10):
		tmp = 1.0 - (x / (t * z))
	else:
		tmp = 1.0
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x / Float64(Float64(y - z) * Float64(y - t)))
	tmp = 0.0
	if ((t_1 <= -2e-7) || !(t_1 <= 5e-10))
		tmp = Float64(1.0 - Float64(x / Float64(t * z)));
	else
		tmp = 1.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x / ((y - z) * (y - t));
	tmp = 0.0;
	if ((t_1 <= -2e-7) || ~((t_1 <= 5e-10)))
		tmp = 1.0 - (x / (t * z));
	else
		tmp = 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x / N[(N[(y - z), $MachinePrecision] * N[(y - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[t$95$1, -2e-7], N[Not[LessEqual[t$95$1, 5e-10]], $MachinePrecision]], N[(1.0 - N[(x / N[(t * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], 1.0]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 x (*.f64 (-.f64 y z) (-.f64 y t))) < -1.9999999999999999e-7 or 5.00000000000000031e-10 < (/.f64 x (*.f64 (-.f64 y z) (-.f64 y t)))

   1. Initial program 99.7%

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

   3. Taylor expanded in y around 0

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

      1. lower-*.f64 46.9

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

   5. Applied rewrites 46.9%

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

   if -1.9999999999999999e-7 < (/.f64 x (*.f64 (-.f64 y z) (-.f64 y t))) < 5.00000000000000031e-10

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0

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

   5. Applied rewrites 99.6%

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

4. Final simplification 85.4%

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

Alternative 5: 81.1% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{\left(y - z\right) \cdot \left(y - t\right)}\\ \mathbf{if}\;t\_1 \leq -5 \cdot 10^{+23} \lor \neg \left(t\_1 \leq 0.001\right):\\ \;\;\;\;\frac{x}{z \cdot y} + 1\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ x (* (- y z) (- y t)))))
   (if (or (<= t_1 -5e+23) (not (<= t_1 0.001))) (+ (/ x (* z y)) 1.0) 1.0)))

C

double code(double x, double y, double z, double t) {
	double t_1 = x / ((y - z) * (y - t));
	double tmp;
	if ((t_1 <= -5e+23) || !(t_1 <= 0.001)) {
		tmp = (x / (z * y)) + 1.0;
	} else {
		tmp = 1.0;
	}
	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 / ((y - z) * (y - t))
    if ((t_1 <= (-5d+23)) .or. (.not. (t_1 <= 0.001d0))) then
        tmp = (x / (z * y)) + 1.0d0
    else
        tmp = 1.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = x / ((y - z) * (y - t));
	double tmp;
	if ((t_1 <= -5e+23) || !(t_1 <= 0.001)) {
		tmp = (x / (z * y)) + 1.0;
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x / ((y - z) * (y - t))
	tmp = 0
	if (t_1 <= -5e+23) or not (t_1 <= 0.001):
		tmp = (x / (z * y)) + 1.0
	else:
		tmp = 1.0
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x / Float64(Float64(y - z) * Float64(y - t)))
	tmp = 0.0
	if ((t_1 <= -5e+23) || !(t_1 <= 0.001))
		tmp = Float64(Float64(x / Float64(z * y)) + 1.0);
	else
		tmp = 1.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x / ((y - z) * (y - t));
	tmp = 0.0;
	if ((t_1 <= -5e+23) || ~((t_1 <= 0.001)))
		tmp = (x / (z * y)) + 1.0;
	else
		tmp = 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x / N[(N[(y - z), $MachinePrecision] * N[(y - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[t$95$1, -5e+23], N[Not[LessEqual[t$95$1, 0.001]], $MachinePrecision]], N[(N[(x / N[(z * y), $MachinePrecision]), $MachinePrecision] + 1.0), $MachinePrecision], 1.0]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 x (*.f64 (-.f64 y z) (-.f64 y t))) < -4.9999999999999999e23 or 1e-3 < (/.f64 x (*.f64 (-.f64 y z) (-.f64 y t)))

   1. Initial program 99.7%

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

   3. Taylor expanded in z around inf

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

      1. +-commutative N/A

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

      2. lower-+.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. *-commutative N/A

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

      5. lower-*.f64 N/A

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

      6. lower--.f64 62.3

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

   5. Applied rewrites 62.3%

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

   6. Taylor expanded in y around inf

      \[\leadsto \frac{x}{y \cdot z} + 1 \]
   7. Step-by-step derivation

   8. Applied rewrites 28.2%

      \[\leadsto \frac{x}{z \cdot y} + 1 \]

   if -4.9999999999999999e23 < (/.f64 x (*.f64 (-.f64 y z) (-.f64 y t))) < 1e-3

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0

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

   5. Applied rewrites 97.4%

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

4. Final simplification 80.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x}{\left(y - z\right) \cdot \left(y - t\right)} \leq -5 \cdot 10^{+23} \lor \neg \left(\frac{x}{\left(y - z\right) \cdot \left(y - t\right)} \leq 0.001\right):\\ \;\;\;\;\frac{x}{z \cdot y} + 1\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 81.1% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{\left(y - z\right) \cdot \left(y - t\right)}\\ \mathbf{if}\;t\_1 \leq -50000000000000:\\ \;\;\;\;\frac{x}{t \cdot y} + 1\\ \mathbf{elif}\;t\_1 \leq 0.001:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{z \cdot y} + 1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ x (* (- y z) (- y t)))))
   (if (<= t_1 -50000000000000.0)
     (+ (/ x (* t y)) 1.0)
     (if (<= t_1 0.001) 1.0 (+ (/ x (* z y)) 1.0)))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x / ((y - z) * (y - t));
	double tmp;
	if (t_1 <= -50000000000000.0) {
		tmp = (x / (t * y)) + 1.0;
	} else if (t_1 <= 0.001) {
		tmp = 1.0;
	} else {
		tmp = (x / (z * y)) + 1.0;
	}
	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 / ((y - z) * (y - t))
    if (t_1 <= (-50000000000000.0d0)) then
        tmp = (x / (t * y)) + 1.0d0
    else if (t_1 <= 0.001d0) then
        tmp = 1.0d0
    else
        tmp = (x / (z * y)) + 1.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = x / ((y - z) * (y - t));
	double tmp;
	if (t_1 <= -50000000000000.0) {
		tmp = (x / (t * y)) + 1.0;
	} else if (t_1 <= 0.001) {
		tmp = 1.0;
	} else {
		tmp = (x / (z * y)) + 1.0;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x / ((y - z) * (y - t))
	tmp = 0
	if t_1 <= -50000000000000.0:
		tmp = (x / (t * y)) + 1.0
	elif t_1 <= 0.001:
		tmp = 1.0
	else:
		tmp = (x / (z * y)) + 1.0
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x / Float64(Float64(y - z) * Float64(y - t)))
	tmp = 0.0
	if (t_1 <= -50000000000000.0)
		tmp = Float64(Float64(x / Float64(t * y)) + 1.0);
	elseif (t_1 <= 0.001)
		tmp = 1.0;
	else
		tmp = Float64(Float64(x / Float64(z * y)) + 1.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x / ((y - z) * (y - t));
	tmp = 0.0;
	if (t_1 <= -50000000000000.0)
		tmp = (x / (t * y)) + 1.0;
	elseif (t_1 <= 0.001)
		tmp = 1.0;
	else
		tmp = (x / (z * y)) + 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x / N[(N[(y - z), $MachinePrecision] * N[(y - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -50000000000000.0], N[(N[(x / N[(t * y), $MachinePrecision]), $MachinePrecision] + 1.0), $MachinePrecision], If[LessEqual[t$95$1, 0.001], 1.0, N[(N[(x / N[(z * y), $MachinePrecision]), $MachinePrecision] + 1.0), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 x (*.f64 (-.f64 y z) (-.f64 y t))) < -5e13

   1. Initial program 99.6%

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

   3. Taylor expanded in t around inf

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

      1. +-commutative N/A

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

      2. lower-+.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. *-commutative N/A

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

      5. lower-*.f64 N/A

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

      6. lower--.f64 62.6

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

   5. Applied rewrites 62.6%

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

   6. Taylor expanded in y around inf

      \[\leadsto \frac{x}{t \cdot y} + 1 \]
   7. Step-by-step derivation

   8. Applied rewrites 21.1%

      \[\leadsto \frac{x}{t \cdot y} + 1 \]

   if -5e13 < (/.f64 x (*.f64 (-.f64 y z) (-.f64 y t))) < 1e-3

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0

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

   5. Applied rewrites 98.3%

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

   if 1e-3 < (/.f64 x (*.f64 (-.f64 y z) (-.f64 y t)))

   1. Initial program 99.7%

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

   3. Taylor expanded in z around inf

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

      1. +-commutative N/A

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

      2. lower-+.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. *-commutative N/A

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

      5. lower-*.f64 N/A

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

      6. lower--.f64 60.6

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

   5. Applied rewrites 60.6%

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

   6. Taylor expanded in y around inf

      \[\leadsto \frac{x}{y \cdot z} + 1 \]
   7. Step-by-step derivation

   8. Applied rewrites 30.9%

      \[\leadsto \frac{x}{z \cdot y} + 1 \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 7: 89.5% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.45 \cdot 10^{-16} \lor \neg \left(y \leq 5 \cdot 10^{-52}\right):\\ \;\;\;\;1 - \frac{x}{\left(y - t\right) \cdot y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\left(y - z\right) \cdot t} + 1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= y -1.45e-16) (not (<= y 5e-52)))
   (- 1.0 (/ x (* (- y t) y)))
   (+ (/ x (* (- y z) t)) 1.0)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -1.45e-16) || !(y <= 5e-52)) {
		tmp = 1.0 - (x / ((y - t) * y));
	} else {
		tmp = (x / ((y - z) * t)) + 1.0;
	}
	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 ((y <= (-1.45d-16)) .or. (.not. (y <= 5d-52))) then
        tmp = 1.0d0 - (x / ((y - t) * y))
    else
        tmp = (x / ((y - z) * t)) + 1.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -1.45e-16) || !(y <= 5e-52)) {
		tmp = 1.0 - (x / ((y - t) * y));
	} else {
		tmp = (x / ((y - z) * t)) + 1.0;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (y <= -1.45e-16) or not (y <= 5e-52):
		tmp = 1.0 - (x / ((y - t) * y))
	else:
		tmp = (x / ((y - z) * t)) + 1.0
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((y <= -1.45e-16) || !(y <= 5e-52))
		tmp = Float64(1.0 - Float64(x / Float64(Float64(y - t) * y)));
	else
		tmp = Float64(Float64(x / Float64(Float64(y - z) * t)) + 1.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((y <= -1.45e-16) || ~((y <= 5e-52)))
		tmp = 1.0 - (x / ((y - t) * y));
	else
		tmp = (x / ((y - z) * t)) + 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[y, -1.45e-16], N[Not[LessEqual[y, 5e-52]], $MachinePrecision]], N[(1.0 - N[(x / N[(N[(y - t), $MachinePrecision] * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x / N[(N[(y - z), $MachinePrecision] * t), $MachinePrecision]), $MachinePrecision] + 1.0), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -1.4499999999999999e-16 or 5e-52 < y

   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 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 94.3

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

   5. Applied rewrites 94.3%

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

   if -1.4499999999999999e-16 < y < 5e-52

   1. Initial program 99.8%

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

   3. Taylor expanded in t around inf

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

      1. +-commutative N/A

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

      2. lower-+.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. *-commutative N/A

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

      5. lower-*.f64 N/A

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

      6. lower--.f64 86.7

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

   5. Applied rewrites 86.7%

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

4. Final simplification 91.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.45 \cdot 10^{-16} \lor \neg \left(y \leq 5 \cdot 10^{-52}\right):\\ \;\;\;\;1 - \frac{x}{\left(y - t\right) \cdot y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\left(y - z\right) \cdot t} + 1\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 87.3% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -4.2 \cdot 10^{-116}:\\ \;\;\;\;\frac{x}{\left(y - t\right) \cdot z} + 1\\ \mathbf{elif}\;t \leq 8.2 \cdot 10^{-134}:\\ \;\;\;\;1 - \frac{x}{\left(y - z\right) \cdot y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\left(y - z\right) \cdot t} + 1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= t -4.2e-116)
   (+ (/ x (* (- y t) z)) 1.0)
   (if (<= t 8.2e-134)
     (- 1.0 (/ x (* (- y z) y)))
     (+ (/ x (* (- y z) t)) 1.0))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= -4.2e-116) {
		tmp = (x / ((y - t) * z)) + 1.0;
	} else if (t <= 8.2e-134) {
		tmp = 1.0 - (x / ((y - z) * y));
	} else {
		tmp = (x / ((y - z) * t)) + 1.0;
	}
	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 <= (-4.2d-116)) then
        tmp = (x / ((y - t) * z)) + 1.0d0
    else if (t <= 8.2d-134) then
        tmp = 1.0d0 - (x / ((y - z) * y))
    else
        tmp = (x / ((y - z) * t)) + 1.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= -4.2e-116) {
		tmp = (x / ((y - t) * z)) + 1.0;
	} else if (t <= 8.2e-134) {
		tmp = 1.0 - (x / ((y - z) * y));
	} else {
		tmp = (x / ((y - z) * t)) + 1.0;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if t <= -4.2e-116:
		tmp = (x / ((y - t) * z)) + 1.0
	elif t <= 8.2e-134:
		tmp = 1.0 - (x / ((y - z) * y))
	else:
		tmp = (x / ((y - z) * t)) + 1.0
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (t <= -4.2e-116)
		tmp = Float64(Float64(x / Float64(Float64(y - t) * z)) + 1.0);
	elseif (t <= 8.2e-134)
		tmp = Float64(1.0 - Float64(x / Float64(Float64(y - z) * y)));
	else
		tmp = Float64(Float64(x / Float64(Float64(y - z) * t)) + 1.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (t <= -4.2e-116)
		tmp = (x / ((y - t) * z)) + 1.0;
	elseif (t <= 8.2e-134)
		tmp = 1.0 - (x / ((y - z) * y));
	else
		tmp = (x / ((y - z) * t)) + 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[t, -4.2e-116], N[(N[(x / N[(N[(y - t), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision] + 1.0), $MachinePrecision], If[LessEqual[t, 8.2e-134], N[(1.0 - N[(x / N[(N[(y - z), $MachinePrecision] * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x / N[(N[(y - z), $MachinePrecision] * t), $MachinePrecision]), $MachinePrecision] + 1.0), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -4.1999999999999998e-116

   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

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

      1. +-commutative N/A

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

      2. lower-+.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. *-commutative N/A

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

      5. lower-*.f64 N/A

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

      6. lower--.f64 82.0

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

   5. Applied rewrites 82.0%

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

   if -4.1999999999999998e-116 < t < 8.2000000000000004e-134

   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 91.2

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

   5. Applied rewrites 91.2%

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

   if 8.2000000000000004e-134 < 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

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

      1. +-commutative N/A

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

      2. lower-+.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. *-commutative N/A

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

      5. lower-*.f64 N/A

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

      6. lower--.f64 94.2

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

   5. Applied rewrites 94.2%

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

Alternative 9: 82.6% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq 1.35 \cdot 10^{-130}:\\ \;\;\;\;\frac{x}{\left(y - t\right) \cdot z} + 1\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\left(y - z\right) \cdot t} + 1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= t 1.35e-130) (+ (/ x (* (- y t) z)) 1.0) (+ (/ x (* (- y z) t)) 1.0)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= 1.35e-130) {
		tmp = (x / ((y - t) * z)) + 1.0;
	} else {
		tmp = (x / ((y - z) * t)) + 1.0;
	}
	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 <= 1.35d-130) then
        tmp = (x / ((y - t) * z)) + 1.0d0
    else
        tmp = (x / ((y - z) * t)) + 1.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= 1.35e-130) {
		tmp = (x / ((y - t) * z)) + 1.0;
	} else {
		tmp = (x / ((y - z) * t)) + 1.0;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if t <= 1.35e-130:
		tmp = (x / ((y - t) * z)) + 1.0
	else:
		tmp = (x / ((y - z) * t)) + 1.0
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (t <= 1.35e-130)
		tmp = Float64(Float64(x / Float64(Float64(y - t) * z)) + 1.0);
	else
		tmp = Float64(Float64(x / Float64(Float64(y - z) * t)) + 1.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (t <= 1.35e-130)
		tmp = (x / ((y - t) * z)) + 1.0;
	else
		tmp = (x / ((y - z) * t)) + 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[t, 1.35e-130], N[(N[(x / N[(N[(y - t), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision] + 1.0), $MachinePrecision], N[(N[(x / N[(N[(y - z), $MachinePrecision] * t), $MachinePrecision]), $MachinePrecision] + 1.0), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < 1.34999999999999996e-130

   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

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

      1. +-commutative N/A

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

      2. lower-+.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. *-commutative N/A

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

      5. lower-*.f64 N/A

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

      6. lower--.f64 80.5

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

   5. Applied rewrites 80.5%

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

   if 1.34999999999999996e-130 < 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

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

      1. +-commutative N/A

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

      2. lower-+.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. *-commutative N/A

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

      5. lower-*.f64 N/A

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

      6. lower--.f64 94.2

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

   5. Applied rewrites 94.2%

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

Alternative 10: 74.9% 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 x around 0

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

5. Applied rewrites 74.2%

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

Reproduce

herbie shell --seed 2024339 
(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)))))