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

Percentage Accurate: 99.2% → 99.2%

Time: 9.9s

Alternatives: 8

Speedup: 1.0×

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 99.2% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 99.2% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.2%

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

3. Final simplification 99.2%

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

Alternative 2: 90.3% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := 1 + \frac{x}{z \cdot \left(y - t\right)}\\ t_2 := 1 + \frac{x}{\left(y - z\right) \cdot \left(t - y\right)}\\ \mathbf{if}\;t\_2 \leq -2:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_2 \leq 1.1:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (+ 1.0 (/ x (* z (- y t)))))
        (t_2 (+ 1.0 (/ x (* (- y z) (- t y))))))
   (if (<= t_2 -2.0) t_1 (if (<= t_2 1.1) 1.0 t_1))))

C

double code(double x, double y, double z, double t) {
	double t_1 = 1.0 + (x / (z * (y - t)));
	double t_2 = 1.0 + (x / ((y - z) * (t - y)));
	double tmp;
	if (t_2 <= -2.0) {
		tmp = t_1;
	} else if (t_2 <= 1.1) {
		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 * (y - t)))
    t_2 = 1.0d0 + (x / ((y - z) * (t - y)))
    if (t_2 <= (-2.0d0)) then
        tmp = t_1
    else if (t_2 <= 1.1d0) 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 * (y - t)));
	double t_2 = 1.0 + (x / ((y - z) * (t - y)));
	double tmp;
	if (t_2 <= -2.0) {
		tmp = t_1;
	} else if (t_2 <= 1.1) {
		tmp = 1.0;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = 1.0 + (x / (z * (y - t)))
	t_2 = 1.0 + (x / ((y - z) * (t - y)))
	tmp = 0
	if t_2 <= -2.0:
		tmp = t_1
	elif t_2 <= 1.1:
		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 * Float64(y - t))))
	t_2 = Float64(1.0 + Float64(x / Float64(Float64(y - z) * Float64(t - y))))
	tmp = 0.0
	if (t_2 <= -2.0)
		tmp = t_1;
	elseif (t_2 <= 1.1)
		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 * (y - t)));
	t_2 = 1.0 + (x / ((y - z) * (t - y)));
	tmp = 0.0;
	if (t_2 <= -2.0)
		tmp = t_1;
	elseif (t_2 <= 1.1)
		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 * N[(y - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(1.0 + N[(x / N[(N[(y - z), $MachinePrecision] * N[(t - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, -2.0], t$95$1, If[LessEqual[t$95$2, 1.1], 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)))) < -2 or 1.1000000000000001 < (-.f64 #s(literal 1 binary64) (/.f64 x (*.f64 (-.f64 y z) (-.f64 y t))))

   1. Initial program 96.9%

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

   3. Taylor expanded in z around inf

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

      1. mul-1-neg N/A

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

      2. distribute-neg-frac2 N/A

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

      3. mul-1-neg N/A

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

      4. lower-/.f64 N/A

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

      5. mul-1-neg N/A

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

      6. distribute-rgt-neg-in N/A

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

      7. mul-1-neg N/A

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

      8. lower-*.f64 N/A

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

      9. mul-1-neg N/A

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

      10. sub-neg N/A

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

      11. mul-1-neg N/A

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

      12. +-commutative N/A

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

      13. distribute-neg-in N/A

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

      14. unsub-neg N/A

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

      15. mul-1-neg N/A

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

      16. remove-double-neg N/A

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

      17. lower--.f64 71.9

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

   5. Applied rewrites 71.9%

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

   if -2 < (-.f64 #s(literal 1 binary64) (/.f64 x (*.f64 (-.f64 y z) (-.f64 y t)))) < 1.1000000000000001

   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 99.9%

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

4. Final simplification 92.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;1 + \frac{x}{\left(y - z\right) \cdot \left(t - y\right)} \leq -2:\\ \;\;\;\;1 + \frac{x}{z \cdot \left(y - t\right)}\\ \mathbf{elif}\;1 + \frac{x}{\left(y - z\right) \cdot \left(t - y\right)} \leq 1.1:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;1 + \frac{x}{z \cdot \left(y - t\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 89.9% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{z \cdot \left(y - t\right)}\\ t_2 := 1 + \frac{x}{\left(y - z\right) \cdot \left(t - y\right)}\\ \mathbf{if}\;t\_2 \leq -2:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_2 \leq 500:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ x (* z (- y t)))) (t_2 (+ 1.0 (/ x (* (- y z) (- t y))))))
   (if (<= t_2 -2.0) t_1 (if (<= t_2 500.0) 1.0 t_1))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x / (z * (y - t));
	double t_2 = 1.0 + (x / ((y - z) * (t - y)));
	double tmp;
	if (t_2 <= -2.0) {
		tmp = t_1;
	} else if (t_2 <= 500.0) {
		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 / (z * (y - t))
    t_2 = 1.0d0 + (x / ((y - z) * (t - y)))
    if (t_2 <= (-2.0d0)) then
        tmp = t_1
    else if (t_2 <= 500.0d0) 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 / (z * (y - t));
	double t_2 = 1.0 + (x / ((y - z) * (t - y)));
	double tmp;
	if (t_2 <= -2.0) {
		tmp = t_1;
	} else if (t_2 <= 500.0) {
		tmp = 1.0;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x / (z * (y - t))
	t_2 = 1.0 + (x / ((y - z) * (t - y)))
	tmp = 0
	if t_2 <= -2.0:
		tmp = t_1
	elif t_2 <= 500.0:
		tmp = 1.0
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x / Float64(z * Float64(y - t)))
	t_2 = Float64(1.0 + Float64(x / Float64(Float64(y - z) * Float64(t - y))))
	tmp = 0.0
	if (t_2 <= -2.0)
		tmp = t_1;
	elseif (t_2 <= 500.0)
		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 - t));
	t_2 = 1.0 + (x / ((y - z) * (t - y)));
	tmp = 0.0;
	if (t_2 <= -2.0)
		tmp = t_1;
	elseif (t_2 <= 500.0)
		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[(z * N[(y - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(1.0 + N[(x / N[(N[(y - z), $MachinePrecision] * N[(t - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, -2.0], t$95$1, If[LessEqual[t$95$2, 500.0], 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)))) < -2 or 500 < (-.f64 #s(literal 1 binary64) (/.f64 x (*.f64 (-.f64 y z) (-.f64 y t))))

   1. Initial program 96.7%

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

   3. Taylor expanded in z around inf

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

      1. mul-1-neg N/A

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

      2. distribute-neg-frac2 N/A

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

      3. mul-1-neg N/A

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

      4. lower-/.f64 N/A

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

      5. mul-1-neg N/A

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

      6. distribute-rgt-neg-in N/A

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

      7. mul-1-neg N/A

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

      8. lower-*.f64 N/A

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

      9. mul-1-neg N/A

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

      10. sub-neg N/A

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

      11. mul-1-neg N/A

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

      12. +-commutative N/A

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

      13. distribute-neg-in N/A

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

      14. unsub-neg N/A

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

      15. mul-1-neg N/A

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

      16. remove-double-neg N/A

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

      17. lower--.f64 70.5

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

   5. Applied rewrites 70.5%

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

   6. Taylor expanded in x around inf

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

      1. associate-*r/ N/A

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

      2. mul-1-neg N/A

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

      3. sub-neg N/A

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

      4. mul-1-neg N/A

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

      5. lower-/.f64 N/A

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

      6. lower-neg.f64 N/A

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

      7. lower-*.f64 N/A

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

      8. mul-1-neg N/A

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

      9. sub-neg N/A

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

      10. lower--.f64 69.1

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

   8. Applied rewrites 69.1%

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

   if -2 < (-.f64 #s(literal 1 binary64) (/.f64 x (*.f64 (-.f64 y z) (-.f64 y t)))) < 500

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0

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

   5. Applied rewrites 98.7%

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

4. Final simplification 91.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;1 + \frac{x}{\left(y - z\right) \cdot \left(t - y\right)} \leq -2:\\ \;\;\;\;\frac{x}{z \cdot \left(y - t\right)}\\ \mathbf{elif}\;1 + \frac{x}{\left(y - z\right) \cdot \left(t - y\right)} \leq 500:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{z \cdot \left(y - t\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 80.8% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{y \cdot z}\\ t_2 := 1 + \frac{x}{\left(y - z\right) \cdot \left(t - y\right)}\\ \mathbf{if}\;t\_2 \leq -4 \cdot 10^{+44}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_2 \leq 500:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ x (* y z))) (t_2 (+ 1.0 (/ x (* (- y z) (- t y))))))
   (if (<= t_2 -4e+44) t_1 (if (<= t_2 500.0) 1.0 t_1))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x / (y * z);
	double t_2 = 1.0 + (x / ((y - z) * (t - y)));
	double tmp;
	if (t_2 <= -4e+44) {
		tmp = t_1;
	} else if (t_2 <= 500.0) {
		tmp = 1.0;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = x / (y * z)
    t_2 = 1.0d0 + (x / ((y - z) * (t - y)))
    if (t_2 <= (-4d+44)) then
        tmp = t_1
    else if (t_2 <= 500.0d0) then
        tmp = 1.0d0
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = x / (y * z);
	double t_2 = 1.0 + (x / ((y - z) * (t - y)));
	double tmp;
	if (t_2 <= -4e+44) {
		tmp = t_1;
	} else if (t_2 <= 500.0) {
		tmp = 1.0;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x / (y * z)
	t_2 = 1.0 + (x / ((y - z) * (t - y)))
	tmp = 0
	if t_2 <= -4e+44:
		tmp = t_1
	elif t_2 <= 500.0:
		tmp = 1.0
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x / Float64(y * z))
	t_2 = Float64(1.0 + Float64(x / Float64(Float64(y - z) * Float64(t - y))))
	tmp = 0.0
	if (t_2 <= -4e+44)
		tmp = t_1;
	elseif (t_2 <= 500.0)
		tmp = 1.0;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x / (y * z);
	t_2 = 1.0 + (x / ((y - z) * (t - y)));
	tmp = 0.0;
	if (t_2 <= -4e+44)
		tmp = t_1;
	elseif (t_2 <= 500.0)
		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[(y * z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(1.0 + N[(x / N[(N[(y - z), $MachinePrecision] * N[(t - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, -4e+44], t$95$1, If[LessEqual[t$95$2, 500.0], 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)))) < -4.0000000000000004e44 or 500 < (-.f64 #s(literal 1 binary64) (/.f64 x (*.f64 (-.f64 y z) (-.f64 y t))))

   1. Initial program 96.4%

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

   3. Taylor expanded in z around inf

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

      1. mul-1-neg N/A

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

      2. distribute-neg-frac2 N/A

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

      3. mul-1-neg N/A

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

      4. lower-/.f64 N/A

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

      5. mul-1-neg N/A

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

      6. distribute-rgt-neg-in N/A

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

      7. mul-1-neg N/A

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

      8. lower-*.f64 N/A

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

      9. mul-1-neg N/A

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

      10. sub-neg N/A

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

      11. mul-1-neg N/A

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

      12. +-commutative N/A

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

      13. distribute-neg-in N/A

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

      14. unsub-neg N/A

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

      15. mul-1-neg N/A

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

      16. remove-double-neg N/A

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

      17. lower--.f64 68.0

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

   5. Applied rewrites 68.0%

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

   6. Taylor expanded in x around inf

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

      1. associate-*r/ N/A

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

      2. mul-1-neg N/A

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

      3. sub-neg N/A

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

      4. mul-1-neg N/A

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

      5. lower-/.f64 N/A

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

      6. lower-neg.f64 N/A

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

      7. lower-*.f64 N/A

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

      8. mul-1-neg N/A

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

      9. sub-neg N/A

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

      10. lower--.f64 68.0

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

   8. Applied rewrites 68.0%

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

   9. Taylor expanded in t around 0

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

       1. lower-/.f64 N/A

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

       2. lower-*.f64 30.6

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

   11. Applied rewrites 30.6%

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

   if -4.0000000000000004e44 < (-.f64 #s(literal 1 binary64) (/.f64 x (*.f64 (-.f64 y z) (-.f64 y t)))) < 500

   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 96.2%

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

4. Final simplification 81.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;1 + \frac{x}{\left(y - z\right) \cdot \left(t - y\right)} \leq -4 \cdot 10^{+44}:\\ \;\;\;\;\frac{x}{y \cdot z}\\ \mathbf{elif}\;1 + \frac{x}{\left(y - z\right) \cdot \left(t - y\right)} \leq 500:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y \cdot z}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 89.0% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{\left(y - z\right) \cdot \left(y - t\right)}\\ t_2 := \frac{x}{\left(y - z\right) \cdot t}\\ \mathbf{if}\;t\_1 \leq -400:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_1 \leq 4 \cdot 10^{-13}:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ x (* (- y z) (- y t)))) (t_2 (/ x (* (- y z) t))))
   (if (<= t_1 -400.0) t_2 (if (<= t_1 4e-13) 1.0 t_2))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x / ((y - z) * (y - t));
	double t_2 = x / ((y - z) * t);
	double tmp;
	if (t_1 <= -400.0) {
		tmp = t_2;
	} else if (t_1 <= 4e-13) {
		tmp = 1.0;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = x / ((y - z) * (y - t))
    t_2 = x / ((y - z) * t)
    if (t_1 <= (-400.0d0)) then
        tmp = t_2
    else if (t_1 <= 4d-13) then
        tmp = 1.0d0
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = x / ((y - z) * (y - t));
	double t_2 = x / ((y - z) * t);
	double tmp;
	if (t_1 <= -400.0) {
		tmp = t_2;
	} else if (t_1 <= 4e-13) {
		tmp = 1.0;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x / ((y - z) * (y - t))
	t_2 = x / ((y - z) * t)
	tmp = 0
	if t_1 <= -400.0:
		tmp = t_2
	elif t_1 <= 4e-13:
		tmp = 1.0
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x / Float64(Float64(y - z) * Float64(y - t)))
	t_2 = Float64(x / Float64(Float64(y - z) * t))
	tmp = 0.0
	if (t_1 <= -400.0)
		tmp = t_2;
	elseif (t_1 <= 4e-13)
		tmp = 1.0;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x / ((y - z) * (y - t));
	t_2 = x / ((y - z) * t);
	tmp = 0.0;
	if (t_1 <= -400.0)
		tmp = t_2;
	elseif (t_1 <= 4e-13)
		tmp = 1.0;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x / N[(N[(y - z), $MachinePrecision] * N[(y - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x / N[(N[(y - z), $MachinePrecision] * t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -400.0], t$95$2, If[LessEqual[t$95$1, 4e-13], 1.0, t$95$2]]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 x (*.f64 (-.f64 y z) (-.f64 y t))) < -400 or 4.0000000000000001e-13 < (/.f64 x (*.f64 (-.f64 y z) (-.f64 y t)))

   1. Initial program 96.8%

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

      1. lift--.f64 N/A

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

      2. lift--.f64 N/A

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

      3. lift-*.f64 N/A

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

      4. lift-/.f64 N/A

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

      5. *-lft-identity N/A

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

      6. cancel-sign-sub-inv N/A

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

      7. metadata-eval N/A

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

      8. neg-mul-1 N/A

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

      9. +-commutative N/A

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

      10. lift-/.f64 N/A

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

      11. clear-num N/A

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

      12. associate-/r/ N/A

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

      13. distribute-lft-neg-in N/A

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

      14. distribute-frac-neg2 N/A

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

      15. lower-fma.f64 N/A

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

   4. Applied rewrites 96.6%

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

   5. Taylor expanded in t around inf

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

      1. lower-/.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 64.7

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

   7. Applied rewrites 64.7%

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

   8. Taylor expanded in t around 0

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

      1. lower-/.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 63.3

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

   10. Applied rewrites 63.3%

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

   if -400 < (/.f64 x (*.f64 (-.f64 y z) (-.f64 y t))) < 4.0000000000000001e-13

   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 99.1%

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

4. Final simplification 90.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x}{\left(y - z\right) \cdot \left(y - t\right)} \leq -400:\\ \;\;\;\;\frac{x}{\left(y - z\right) \cdot t}\\ \mathbf{elif}\;\frac{x}{\left(y - z\right) \cdot \left(y - t\right)} \leq 4 \cdot 10^{-13}:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\left(y - z\right) \cdot t}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 85.3% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{\left(y - z\right) \cdot \left(y - t\right)}\\ \mathbf{if}\;t\_1 \leq -2 \cdot 10^{+29}:\\ \;\;\;\;\frac{-x}{z \cdot t}\\ \mathbf{elif}\;t\_1 \leq 4 \cdot 10^{-13}:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;1 - \frac{x}{z \cdot t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ x (* (- y z) (- y t)))))
   (if (<= t_1 -2e+29)
     (/ (- x) (* z t))
     (if (<= t_1 4e-13) 1.0 (- 1.0 (/ x (* z t)))))))

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+29) {
		tmp = -x / (z * t);
	} else if (t_1 <= 4e-13) {
		tmp = 1.0;
	} else {
		tmp = 1.0 - (x / (z * 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) :: t_1
    real(8) :: tmp
    t_1 = x / ((y - z) * (y - t))
    if (t_1 <= (-2d+29)) then
        tmp = -x / (z * t)
    else if (t_1 <= 4d-13) then
        tmp = 1.0d0
    else
        tmp = 1.0d0 - (x / (z * t))
    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+29) {
		tmp = -x / (z * t);
	} else if (t_1 <= 4e-13) {
		tmp = 1.0;
	} else {
		tmp = 1.0 - (x / (z * t));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x / ((y - z) * (y - t))
	tmp = 0
	if t_1 <= -2e+29:
		tmp = -x / (z * t)
	elif t_1 <= 4e-13:
		tmp = 1.0
	else:
		tmp = 1.0 - (x / (z * t))
	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+29)
		tmp = Float64(Float64(-x) / Float64(z * t));
	elseif (t_1 <= 4e-13)
		tmp = 1.0;
	else
		tmp = Float64(1.0 - Float64(x / Float64(z * t)));
	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+29)
		tmp = -x / (z * t);
	elseif (t_1 <= 4e-13)
		tmp = 1.0;
	else
		tmp = 1.0 - (x / (z * t));
	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, -2e+29], N[((-x) / N[(z * t), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 4e-13], 1.0, N[(1.0 - N[(x / N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 x (*.f64 (-.f64 y z) (-.f64 y t))) < -1.99999999999999983e29

   1. Initial program 99.8%

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

   3. Taylor expanded in y around 0

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

      1. lower--.f64 N/A

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

      2. lower-/.f64 N/A

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

      3. lower-*.f64 60.6

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

   5. Applied rewrites 60.6%

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

   6. Taylor expanded in x around inf

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

      1. associate-*r/ N/A

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

      2. lower-/.f64 N/A

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

      3. neg-mul-1 N/A

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

      4. lower-neg.f64 N/A

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

      5. lower-*.f64 60.6

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

   8. Applied rewrites 60.6%

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

   if -1.99999999999999983e29 < (/.f64 x (*.f64 (-.f64 y z) (-.f64 y t))) < 4.0000000000000001e-13

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0

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

   5. Applied rewrites 98.2%

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

   if 4.0000000000000001e-13 < (/.f64 x (*.f64 (-.f64 y z) (-.f64 y t)))

   1. Initial program 93.8%

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

   3. Taylor expanded in y around 0

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

      1. lower--.f64 N/A

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

      2. lower-/.f64 N/A

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

      3. lower-*.f64 52.1

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

   5. Applied rewrites 52.1%

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

4. Final simplification 88.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x}{\left(y - z\right) \cdot \left(y - t\right)} \leq -2 \cdot 10^{+29}:\\ \;\;\;\;\frac{-x}{z \cdot t}\\ \mathbf{elif}\;\frac{x}{\left(y - z\right) \cdot \left(y - t\right)} \leq 4 \cdot 10^{-13}:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;1 - \frac{x}{z \cdot t}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 84.9% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{\left(y - z\right) \cdot \left(y - t\right)}\\ t_2 := \frac{-x}{z \cdot t}\\ \mathbf{if}\;t\_1 \leq -2 \cdot 10^{+29}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_1 \leq 4 \cdot 10^{-13}:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ x (* (- y z) (- y t)))) (t_2 (/ (- x) (* z t))))
   (if (<= t_1 -2e+29) t_2 (if (<= t_1 4e-13) 1.0 t_2))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x / ((y - z) * (y - t));
	double t_2 = -x / (z * t);
	double tmp;
	if (t_1 <= -2e+29) {
		tmp = t_2;
	} else if (t_1 <= 4e-13) {
		tmp = 1.0;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = x / ((y - z) * (y - t))
    t_2 = -x / (z * t)
    if (t_1 <= (-2d+29)) then
        tmp = t_2
    else if (t_1 <= 4d-13) then
        tmp = 1.0d0
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = x / ((y - z) * (y - t));
	double t_2 = -x / (z * t);
	double tmp;
	if (t_1 <= -2e+29) {
		tmp = t_2;
	} else if (t_1 <= 4e-13) {
		tmp = 1.0;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x / ((y - z) * (y - t))
	t_2 = -x / (z * t)
	tmp = 0
	if t_1 <= -2e+29:
		tmp = t_2
	elif t_1 <= 4e-13:
		tmp = 1.0
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x / Float64(Float64(y - z) * Float64(y - t)))
	t_2 = Float64(Float64(-x) / Float64(z * t))
	tmp = 0.0
	if (t_1 <= -2e+29)
		tmp = t_2;
	elseif (t_1 <= 4e-13)
		tmp = 1.0;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x / ((y - z) * (y - t));
	t_2 = -x / (z * t);
	tmp = 0.0;
	if (t_1 <= -2e+29)
		tmp = t_2;
	elseif (t_1 <= 4e-13)
		tmp = 1.0;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x / N[(N[(y - z), $MachinePrecision] * N[(y - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[((-x) / N[(z * t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -2e+29], t$95$2, If[LessEqual[t$95$1, 4e-13], 1.0, t$95$2]]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 x (*.f64 (-.f64 y z) (-.f64 y t))) < -1.99999999999999983e29 or 4.0000000000000001e-13 < (/.f64 x (*.f64 (-.f64 y z) (-.f64 y t)))

   1. Initial program 96.7%

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

   3. Taylor expanded in y around 0

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

      1. lower--.f64 N/A

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

      2. lower-/.f64 N/A

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

      3. lower-*.f64 56.1

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

   5. Applied rewrites 56.1%

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

   6. Taylor expanded in x around inf

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

      1. associate-*r/ N/A

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

      2. lower-/.f64 N/A

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

      3. neg-mul-1 N/A

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

      4. lower-neg.f64 N/A

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

      5. lower-*.f64 54.7

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

   8. Applied rewrites 54.7%

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

   if -1.99999999999999983e29 < (/.f64 x (*.f64 (-.f64 y z) (-.f64 y t))) < 4.0000000000000001e-13

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0

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

   5. Applied rewrites 98.2%

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

4. Final simplification 87.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x}{\left(y - z\right) \cdot \left(y - t\right)} \leq -2 \cdot 10^{+29}:\\ \;\;\;\;\frac{-x}{z \cdot t}\\ \mathbf{elif}\;\frac{x}{\left(y - z\right) \cdot \left(y - t\right)} \leq 4 \cdot 10^{-13}:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;\frac{-x}{z \cdot t}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 74.8% accurate, 26.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.2%

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

3. Taylor expanded in x around 0

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

5. Applied rewrites 75.4%

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

Reproduce

herbie shell --seed 2024219 
(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)))))