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

Percentage Accurate: 99.0% → 98.8%

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: 99.0% 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: 98.8% accurate, 0.9× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 99.5%

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

   1. lift--.f64 N/A

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

   2. sub-neg N/A

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

   3. +-commutative N/A

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

   4. lift-/.f64 N/A

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

   5. distribute-neg-frac2 N/A

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

   6. div-inv N/A

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

   7. lower-fma.f64 N/A

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

   8. frac-2neg N/A

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

   9. metadata-eval N/A

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

   10. remove-double-neg N/A

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

   11. lower-/.f64 99.5

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

   12. lift-*.f64 N/A

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

   13. *-commutative N/A

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

   14. lower-*.f64 99.5

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

4. Applied rewrites 99.5%

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

5. Final simplification 99.5%

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

Alternative 2: 84.5% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := 1 - \frac{x}{z \cdot t}\\ t_2 := 1 - \frac{x}{\left(z - y\right) \cdot \left(t - y\right)}\\ \mathbf{if}\;t\_2 \leq -5000000000:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_2 \leq 2:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (- 1.0 (/ x (* z t)))) (t_2 (- 1.0 (/ x (* (- z y) (- t y))))))
   (if (<= t_2 -5000000000.0) t_1 (if (<= t_2 2.0) 1.0 t_1))))

C

double code(double x, double y, double z, double t) {
	double t_1 = 1.0 - (x / (z * t));
	double t_2 = 1.0 - (x / ((z - y) * (t - y)));
	double tmp;
	if (t_2 <= -5000000000.0) {
		tmp = t_1;
	} else if (t_2 <= 2.0) {
		tmp = 1.0;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = 1.0d0 - (x / (z * t))
    t_2 = 1.0d0 - (x / ((z - y) * (t - y)))
    if (t_2 <= (-5000000000.0d0)) then
        tmp = t_1
    else if (t_2 <= 2.0d0) then
        tmp = 1.0d0
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = 1.0 - (x / (z * t));
	double t_2 = 1.0 - (x / ((z - y) * (t - y)));
	double tmp;
	if (t_2 <= -5000000000.0) {
		tmp = t_1;
	} else if (t_2 <= 2.0) {
		tmp = 1.0;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = 1.0 - (x / (z * t))
	t_2 = 1.0 - (x / ((z - y) * (t - y)))
	tmp = 0
	if t_2 <= -5000000000.0:
		tmp = t_1
	elif t_2 <= 2.0:
		tmp = 1.0
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(1.0 - Float64(x / Float64(z * t)))
	t_2 = Float64(1.0 - Float64(x / Float64(Float64(z - y) * Float64(t - y))))
	tmp = 0.0
	if (t_2 <= -5000000000.0)
		tmp = t_1;
	elseif (t_2 <= 2.0)
		tmp = 1.0;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = 1.0 - (x / (z * t));
	t_2 = 1.0 - (x / ((z - y) * (t - y)));
	tmp = 0.0;
	if (t_2 <= -5000000000.0)
		tmp = t_1;
	elseif (t_2 <= 2.0)
		tmp = 1.0;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(1.0 - N[(x / N[(z * t), $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, -5000000000.0], t$95$1, If[LessEqual[t$95$2, 2.0], 1.0, t$95$1]]]]

Derivation

1. Split input into 2 regimes

2. if (-.f64 #s(literal 1 binary64) (/.f64 x (*.f64 (-.f64 y z) (-.f64 y t)))) < -5e9 or 2 < (-.f64 #s(literal 1 binary64) (/.f64 x (*.f64 (-.f64 y z) (-.f64 y t))))

   1. Initial program 98.4%

      \[1 - \frac{x}{\left(y - z\right) \cdot \left(y - t\right)} \]
   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 45.2

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

   5. Applied rewrites 45.2%

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

   if -5e9 < (-.f64 #s(literal 1 binary64) (/.f64 x (*.f64 (-.f64 y z) (-.f64 y t)))) < 2

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0

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

   5. Applied rewrites 99.5%

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

4. Final simplification 83.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;1 - \frac{x}{\left(z - y\right) \cdot \left(t - y\right)} \leq -5000000000:\\ \;\;\;\;1 - \frac{x}{z \cdot t}\\ \mathbf{elif}\;1 - \frac{x}{\left(z - y\right) \cdot \left(t - y\right)} \leq 2:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;1 - \frac{x}{z \cdot t}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 80.0% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{t \cdot y} + 1\\ t_2 := 1 - \frac{x}{\left(z - y\right) \cdot \left(t - y\right)}\\ \mathbf{if}\;t\_2 \leq 0.9995:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_2 \leq 10^{+48}:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (+ (/ x (* t y)) 1.0)) (t_2 (- 1.0 (/ x (* (- z y) (- t y))))))
   (if (<= t_2 0.9995) t_1 (if (<= t_2 1e+48) 1.0 t_1))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (x / (t * y)) + 1.0;
	double t_2 = 1.0 - (x / ((z - y) * (t - y)));
	double tmp;
	if (t_2 <= 0.9995) {
		tmp = t_1;
	} else if (t_2 <= 1e+48) {
		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)) + 1.0d0
    t_2 = 1.0d0 - (x / ((z - y) * (t - y)))
    if (t_2 <= 0.9995d0) then
        tmp = t_1
    else if (t_2 <= 1d+48) 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)) + 1.0;
	double t_2 = 1.0 - (x / ((z - y) * (t - y)));
	double tmp;
	if (t_2 <= 0.9995) {
		tmp = t_1;
	} else if (t_2 <= 1e+48) {
		tmp = 1.0;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (x / (t * y)) + 1.0
	t_2 = 1.0 - (x / ((z - y) * (t - y)))
	tmp = 0
	if t_2 <= 0.9995:
		tmp = t_1
	elif t_2 <= 1e+48:
		tmp = 1.0
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(x / Float64(t * y)) + 1.0)
	t_2 = Float64(1.0 - Float64(x / Float64(Float64(z - y) * Float64(t - y))))
	tmp = 0.0
	if (t_2 <= 0.9995)
		tmp = t_1;
	elseif (t_2 <= 1e+48)
		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)) + 1.0;
	t_2 = 1.0 - (x / ((z - y) * (t - y)));
	tmp = 0.0;
	if (t_2 <= 0.9995)
		tmp = t_1;
	elseif (t_2 <= 1e+48)
		tmp = 1.0;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(x / N[(t * y), $MachinePrecision]), $MachinePrecision] + 1.0), $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, 0.9995], t$95$1, If[LessEqual[t$95$2, 1e+48], 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)))) < 0.99950000000000006 or 1.00000000000000004e48 < (-.f64 #s(literal 1 binary64) (/.f64 x (*.f64 (-.f64 y z) (-.f64 y t))))

   1. Initial program 98.3%

      \[1 - \frac{x}{\left(y - z\right) \cdot \left(y - t\right)} \]
   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 57.0

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

   5. Applied rewrites 57.0%

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

   6. Taylor expanded in y around inf

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

   8. Applied rewrites 26.8%

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

   if 0.99950000000000006 < (-.f64 #s(literal 1 binary64) (/.f64 x (*.f64 (-.f64 y z) (-.f64 y t)))) < 1.00000000000000004e48

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0

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

   5. Applied rewrites 96.9%

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

4. Final simplification 77.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;1 - \frac{x}{\left(z - y\right) \cdot \left(t - y\right)} \leq 0.9995:\\ \;\;\;\;\frac{x}{t \cdot y} + 1\\ \mathbf{elif}\;1 - \frac{x}{\left(z - y\right) \cdot \left(t - y\right)} \leq 10^{+48}:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{t \cdot y} + 1\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 80.3% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{z \cdot y} + 1\\ t_2 := 1 - \frac{x}{\left(z - y\right) \cdot \left(t - y\right)}\\ \mathbf{if}\;t\_2 \leq -2 \cdot 10^{+20}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_2 \leq 5 \cdot 10^{+48}:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (+ (/ x (* z y)) 1.0)) (t_2 (- 1.0 (/ x (* (- z y) (- t y))))))
   (if (<= t_2 -2e+20) t_1 (if (<= t_2 5e+48) 1.0 t_1))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (x / (z * y)) + 1.0;
	double t_2 = 1.0 - (x / ((z - y) * (t - y)));
	double tmp;
	if (t_2 <= -2e+20) {
		tmp = t_1;
	} else if (t_2 <= 5e+48) {
		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 / (z * y)) + 1.0d0
    t_2 = 1.0d0 - (x / ((z - y) * (t - y)))
    if (t_2 <= (-2d+20)) then
        tmp = t_1
    else if (t_2 <= 5d+48) 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 / (z * y)) + 1.0;
	double t_2 = 1.0 - (x / ((z - y) * (t - y)));
	double tmp;
	if (t_2 <= -2e+20) {
		tmp = t_1;
	} else if (t_2 <= 5e+48) {
		tmp = 1.0;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (x / (z * y)) + 1.0
	t_2 = 1.0 - (x / ((z - y) * (t - y)))
	tmp = 0
	if t_2 <= -2e+20:
		tmp = t_1
	elif t_2 <= 5e+48:
		tmp = 1.0
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(x / Float64(z * y)) + 1.0)
	t_2 = Float64(1.0 - Float64(x / Float64(Float64(z - y) * Float64(t - y))))
	tmp = 0.0
	if (t_2 <= -2e+20)
		tmp = t_1;
	elseif (t_2 <= 5e+48)
		tmp = 1.0;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (x / (z * y)) + 1.0;
	t_2 = 1.0 - (x / ((z - y) * (t - y)));
	tmp = 0.0;
	if (t_2 <= -2e+20)
		tmp = t_1;
	elseif (t_2 <= 5e+48)
		tmp = 1.0;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(x / N[(z * y), $MachinePrecision]), $MachinePrecision] + 1.0), $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, -2e+20], t$95$1, If[LessEqual[t$95$2, 5e+48], 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)))) < -2e20 or 4.99999999999999973e48 < (-.f64 #s(literal 1 binary64) (/.f64 x (*.f64 (-.f64 y z) (-.f64 y t))))

   1. Initial program 98.2%

      \[1 - \frac{x}{\left(y - z\right) \cdot \left(y - t\right)} \]
   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 64.6

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

   5. Applied rewrites 64.6%

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

   6. Taylor expanded in y around inf

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

   8. Applied rewrites 32.4%

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

   if -2e20 < (-.f64 #s(literal 1 binary64) (/.f64 x (*.f64 (-.f64 y z) (-.f64 y t)))) < 4.99999999999999973e48

   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 95.1%

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

4. Final simplification 78.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;1 - \frac{x}{\left(z - y\right) \cdot \left(t - y\right)} \leq -2 \cdot 10^{+20}:\\ \;\;\;\;\frac{x}{z \cdot y} + 1\\ \mathbf{elif}\;1 - \frac{x}{\left(z - y\right) \cdot \left(t - y\right)} \leq 5 \cdot 10^{+48}:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{z \cdot y} + 1\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 89.0% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := 1 - \frac{x}{\left(y - z\right) \cdot y}\\ \mathbf{if}\;y \leq -3.05 \cdot 10^{-31}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 7.5 \cdot 10^{-39}:\\ \;\;\;\;\frac{x}{\left(y - z\right) \cdot t} + 1\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (- 1.0 (/ x (* (- y z) y)))))
   (if (<= y -3.05e-31)
     t_1
     (if (<= y 7.5e-39) (+ (/ x (* (- y z) t)) 1.0) 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 <= -3.05e-31) {
		tmp = t_1;
	} else if (y <= 7.5e-39) {
		tmp = (x / ((y - z) * t)) + 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) :: tmp
    t_1 = 1.0d0 - (x / ((y - z) * y))
    if (y <= (-3.05d-31)) then
        tmp = t_1
    else if (y <= 7.5d-39) then
        tmp = (x / ((y - z) * t)) + 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 = 1.0 - (x / ((y - z) * y));
	double tmp;
	if (y <= -3.05e-31) {
		tmp = t_1;
	} else if (y <= 7.5e-39) {
		tmp = (x / ((y - z) * t)) + 1.0;
	} 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 <= -3.05e-31:
		tmp = t_1
	elif y <= 7.5e-39:
		tmp = (x / ((y - z) * t)) + 1.0
	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 <= -3.05e-31)
		tmp = t_1;
	elseif (y <= 7.5e-39)
		tmp = Float64(Float64(x / Float64(Float64(y - z) * t)) + 1.0);
	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 <= -3.05e-31)
		tmp = t_1;
	elseif (y <= 7.5e-39)
		tmp = (x / ((y - z) * t)) + 1.0;
	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, -3.05e-31], t$95$1, If[LessEqual[y, 7.5e-39], N[(N[(x / N[(N[(y - z), $MachinePrecision] * t), $MachinePrecision]), $MachinePrecision] + 1.0), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if y < -3.0499999999999999e-31 or 7.49999999999999971e-39 < 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 95.8

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

   5. Applied rewrites 95.8%

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

   if -3.0499999999999999e-31 < y < 7.49999999999999971e-39

   1. Initial program 99.1%

      \[1 - \frac{x}{\left(y - z\right) \cdot \left(y - t\right)} \]
   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 82.3

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

   5. Applied rewrites 82.3%

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

Alternative 6: 86.0% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := 1 - \frac{x}{y \cdot y}\\ \mathbf{if}\;y \leq -5.8 \cdot 10^{-31}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 1.75 \cdot 10^{+20}:\\ \;\;\;\;\frac{x}{\left(y - z\right) \cdot t} + 1\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (- 1.0 (/ x (* y y)))))
   (if (<= y -5.8e-31)
     t_1
     (if (<= y 1.75e+20) (+ (/ x (* (- y z) t)) 1.0) t_1))))

C

double code(double x, double y, double z, double t) {
	double t_1 = 1.0 - (x / (y * y));
	double tmp;
	if (y <= -5.8e-31) {
		tmp = t_1;
	} else if (y <= 1.75e+20) {
		tmp = (x / ((y - z) * t)) + 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) :: tmp
    t_1 = 1.0d0 - (x / (y * y))
    if (y <= (-5.8d-31)) then
        tmp = t_1
    else if (y <= 1.75d+20) then
        tmp = (x / ((y - z) * t)) + 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 = 1.0 - (x / (y * y));
	double tmp;
	if (y <= -5.8e-31) {
		tmp = t_1;
	} else if (y <= 1.75e+20) {
		tmp = (x / ((y - z) * t)) + 1.0;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = 1.0 - (x / (y * y))
	tmp = 0
	if y <= -5.8e-31:
		tmp = t_1
	elif y <= 1.75e+20:
		tmp = (x / ((y - z) * t)) + 1.0
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(1.0 - Float64(x / Float64(y * y)))
	tmp = 0.0
	if (y <= -5.8e-31)
		tmp = t_1;
	elseif (y <= 1.75e+20)
		tmp = Float64(Float64(x / Float64(Float64(y - z) * t)) + 1.0);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = 1.0 - (x / (y * y));
	tmp = 0.0;
	if (y <= -5.8e-31)
		tmp = t_1;
	elseif (y <= 1.75e+20)
		tmp = (x / ((y - z) * t)) + 1.0;
	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[(y * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -5.8e-31], t$95$1, If[LessEqual[y, 1.75e+20], N[(N[(x / N[(N[(y - z), $MachinePrecision] * t), $MachinePrecision]), $MachinePrecision] + 1.0), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if y < -5.8000000000000001e-31 or 1.75e20 < 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 y around inf

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

      1. unpow2 N/A

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

      2. lower-*.f64 92.0

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

   5. Applied rewrites 92.0%

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

   if -5.8000000000000001e-31 < y < 1.75e20

   1. Initial program 99.1%

      \[1 - \frac{x}{\left(y - z\right) \cdot \left(y - t\right)} \]
   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 82.1

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

   5. Applied rewrites 82.1%

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

Alternative 7: 86.9% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := 1 - \frac{x}{y \cdot y}\\ \mathbf{if}\;y \leq -7.4 \cdot 10^{-31}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 1.75 \cdot 10^{+20}:\\ \;\;\;\;\frac{x}{z \cdot \left(y - t\right)} + 1\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (- 1.0 (/ x (* y y)))))
   (if (<= y -7.4e-31)
     t_1
     (if (<= y 1.75e+20) (+ (/ x (* z (- y t))) 1.0) t_1))))

C

double code(double x, double y, double z, double t) {
	double t_1 = 1.0 - (x / (y * y));
	double tmp;
	if (y <= -7.4e-31) {
		tmp = t_1;
	} else if (y <= 1.75e+20) {
		tmp = (x / (z * (y - t))) + 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) :: tmp
    t_1 = 1.0d0 - (x / (y * y))
    if (y <= (-7.4d-31)) then
        tmp = t_1
    else if (y <= 1.75d+20) then
        tmp = (x / (z * (y - t))) + 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 = 1.0 - (x / (y * y));
	double tmp;
	if (y <= -7.4e-31) {
		tmp = t_1;
	} else if (y <= 1.75e+20) {
		tmp = (x / (z * (y - t))) + 1.0;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = 1.0 - (x / (y * y))
	tmp = 0
	if y <= -7.4e-31:
		tmp = t_1
	elif y <= 1.75e+20:
		tmp = (x / (z * (y - t))) + 1.0
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(1.0 - Float64(x / Float64(y * y)))
	tmp = 0.0
	if (y <= -7.4e-31)
		tmp = t_1;
	elseif (y <= 1.75e+20)
		tmp = Float64(Float64(x / Float64(z * Float64(y - t))) + 1.0);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = 1.0 - (x / (y * y));
	tmp = 0.0;
	if (y <= -7.4e-31)
		tmp = t_1;
	elseif (y <= 1.75e+20)
		tmp = (x / (z * (y - t))) + 1.0;
	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[(y * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -7.4e-31], t$95$1, If[LessEqual[y, 1.75e+20], N[(N[(x / N[(z * N[(y - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + 1.0), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if y < -7.3999999999999996e-31 or 1.75e20 < 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 y around inf

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

      1. unpow2 N/A

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

      2. lower-*.f64 92.0

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

   5. Applied rewrites 92.0%

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

   if -7.3999999999999996e-31 < y < 1.75e20

   1. Initial program 99.1%

      \[1 - \frac{x}{\left(y - z\right) \cdot \left(y - t\right)} \]
   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 88.9

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

   5. Applied rewrites 88.9%

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

4. Final simplification 90.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -7.4 \cdot 10^{-31}:\\ \;\;\;\;1 - \frac{x}{y \cdot y}\\ \mathbf{elif}\;y \leq 1.75 \cdot 10^{+20}:\\ \;\;\;\;\frac{x}{z \cdot \left(y - t\right)} + 1\\ \mathbf{else}:\\ \;\;\;\;1 - \frac{x}{y \cdot y}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 81.3% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := 1 - \frac{x}{y \cdot y}\\ \mathbf{if}\;y \leq -3.05 \cdot 10^{-31}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 1.1 \cdot 10^{+19}:\\ \;\;\;\;1 - \frac{x}{z \cdot t}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (- 1.0 (/ x (* y y)))))
   (if (<= y -3.05e-31) t_1 (if (<= y 1.1e+19) (- 1.0 (/ x (* z t))) t_1))))

C

double code(double x, double y, double z, double t) {
	double t_1 = 1.0 - (x / (y * y));
	double tmp;
	if (y <= -3.05e-31) {
		tmp = t_1;
	} else if (y <= 1.1e+19) {
		tmp = 1.0 - (x / (z * t));
	} 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 * y))
    if (y <= (-3.05d-31)) then
        tmp = t_1
    else if (y <= 1.1d+19) then
        tmp = 1.0d0 - (x / (z * t))
    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 * y));
	double tmp;
	if (y <= -3.05e-31) {
		tmp = t_1;
	} else if (y <= 1.1e+19) {
		tmp = 1.0 - (x / (z * t));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = 1.0 - (x / (y * y))
	tmp = 0
	if y <= -3.05e-31:
		tmp = t_1
	elif y <= 1.1e+19:
		tmp = 1.0 - (x / (z * t))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(1.0 - Float64(x / Float64(y * y)))
	tmp = 0.0
	if (y <= -3.05e-31)
		tmp = t_1;
	elseif (y <= 1.1e+19)
		tmp = Float64(1.0 - Float64(x / Float64(z * t)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = 1.0 - (x / (y * y));
	tmp = 0.0;
	if (y <= -3.05e-31)
		tmp = t_1;
	elseif (y <= 1.1e+19)
		tmp = 1.0 - (x / (z * t));
	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[(y * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -3.05e-31], t$95$1, If[LessEqual[y, 1.1e+19], N[(1.0 - N[(x / N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if y < -3.0499999999999999e-31 or 1.1e19 < 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 y around inf

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

      1. unpow2 N/A

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

      2. lower-*.f64 92.0

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

   5. Applied rewrites 92.0%

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

   if -3.0499999999999999e-31 < y < 1.1e19

   1. Initial program 99.1%

      \[1 - \frac{x}{\left(y - z\right) \cdot \left(y - t\right)} \]
   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 74.2

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

   5. Applied rewrites 74.2%

      \[\leadsto 1 - \frac{x}{\color{blue}{t \cdot z}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 83.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.05 \cdot 10^{-31}:\\ \;\;\;\;1 - \frac{x}{y \cdot y}\\ \mathbf{elif}\;y \leq 1.1 \cdot 10^{+19}:\\ \;\;\;\;1 - \frac{x}{z \cdot t}\\ \mathbf{else}:\\ \;\;\;\;1 - \frac{x}{y \cdot y}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 99.0% 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 99.5%

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

3. Final simplification 99.5%

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

Alternative 10: 74.3% 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 99.5%

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

3. Taylor expanded in x around 0

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

5. Applied rewrites 70.5%

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

Reproduce

herbie shell --seed 2024298 
(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)))))