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

Percentage Accurate: 88.6% → 97.1%

Time: 9.1s

Alternatives: 9

Speedup: 0.8×

Specification

Math

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

FPCore

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

C

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

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 = x / ((y - z) * (t - z))
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 88.6% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

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 = x / ((y - z) * (t - z))
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 97.1% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \frac{\frac{x}{t - z}}{y - z} \end{array} \]

FPCore

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

C

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

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 = (x / (t - z)) / (y - z)
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 88.6%

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

   1. lift-/.f64 N/A

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

   2. lift-*.f64 N/A

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

   3. associate-/l/ N/A

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

   4. lower-/.f64 N/A

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

   5. lower-/.f64 97.0

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

4. Applied rewrites 97.0%

   \[\leadsto \color{blue}{\frac{\frac{x}{t - z}}{y - z}} \]
5. Add Preprocessing

Alternative 2: 68.3% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{z \cdot z}\\ \mathbf{if}\;z \leq -6.8 \cdot 10^{+31}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -1.55 \cdot 10^{-78}:\\ \;\;\;\;\frac{x}{\left(-z\right) \cdot y}\\ \mathbf{elif}\;z \leq 10^{+58}:\\ \;\;\;\;\frac{x}{\left(y - z\right) \cdot t}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ x (* z z))))
   (if (<= z -6.8e+31)
     t_1
     (if (<= z -1.55e-78)
       (/ x (* (- z) y))
       (if (<= z 1e+58) (/ x (* (- y z) t)) t_1)))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x / (z * z);
	double tmp;
	if (z <= -6.8e+31) {
		tmp = t_1;
	} else if (z <= -1.55e-78) {
		tmp = x / (-z * y);
	} else if (z <= 1e+58) {
		tmp = x / ((y - 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 = x / (z * z)
    if (z <= (-6.8d+31)) then
        tmp = t_1
    else if (z <= (-1.55d-78)) then
        tmp = x / (-z * y)
    else if (z <= 1d+58) then
        tmp = x / ((y - 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 = x / (z * z);
	double tmp;
	if (z <= -6.8e+31) {
		tmp = t_1;
	} else if (z <= -1.55e-78) {
		tmp = x / (-z * y);
	} else if (z <= 1e+58) {
		tmp = x / ((y - z) * t);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x / (z * z)
	tmp = 0
	if z <= -6.8e+31:
		tmp = t_1
	elif z <= -1.55e-78:
		tmp = x / (-z * y)
	elif z <= 1e+58:
		tmp = x / ((y - z) * t)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x / Float64(z * z))
	tmp = 0.0
	if (z <= -6.8e+31)
		tmp = t_1;
	elseif (z <= -1.55e-78)
		tmp = Float64(x / Float64(Float64(-z) * y));
	elseif (z <= 1e+58)
		tmp = Float64(x / Float64(Float64(y - z) * t));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x / (z * z);
	tmp = 0.0;
	if (z <= -6.8e+31)
		tmp = t_1;
	elseif (z <= -1.55e-78)
		tmp = x / (-z * y);
	elseif (z <= 1e+58)
		tmp = x / ((y - z) * t);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x / N[(z * z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -6.8e+31], t$95$1, If[LessEqual[z, -1.55e-78], N[(x / N[((-z) * y), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1e+58], N[(x / N[(N[(y - z), $MachinePrecision] * t), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if z < -6.7999999999999996e31 or 9.99999999999999944e57 < z

   1. Initial program 81.3%

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

   3. Taylor expanded in z around inf

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

      1. unpow2 N/A

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

      2. lower-*.f64 72.6

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

   5. Applied rewrites 72.6%

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

   if -6.7999999999999996e31 < z < -1.55000000000000009e-78

   1. Initial program 99.4%

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

   3. Taylor expanded in z around 0

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

      1. +-commutative N/A

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

      2. *-commutative N/A

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

      3. lower-fma.f64 N/A

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

      4. +-commutative N/A

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

      5. mul-1-neg N/A

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

      6. unsub-neg N/A

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

      7. lower--.f64 N/A

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

      8. mul-1-neg N/A

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

      9. lower-neg.f64 N/A

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

      10. lower-*.f64 74.5

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

   5. Applied rewrites 74.5%

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

   6. Taylor expanded in t around 0

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

   8. Applied rewrites 39.7%

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

   if -1.55000000000000009e-78 < z < 9.99999999999999944e57

   1. Initial program 91.7%

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

   3. Taylor expanded in t around inf

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

      1. lower-*.f64 N/A

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

      2. lower--.f64 70.1

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

   5. Applied rewrites 70.1%

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

4. Final simplification 68.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -6.8 \cdot 10^{+31}:\\ \;\;\;\;\frac{x}{z \cdot z}\\ \mathbf{elif}\;z \leq -1.55 \cdot 10^{-78}:\\ \;\;\;\;\frac{x}{\left(-z\right) \cdot y}\\ \mathbf{elif}\;z \leq 10^{+58}:\\ \;\;\;\;\frac{x}{\left(y - z\right) \cdot t}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{z \cdot z}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 62.0% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{z \cdot z}\\ \mathbf{if}\;z \leq -6.8 \cdot 10^{+31}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -1.75 \cdot 10^{-84}:\\ \;\;\;\;\frac{x}{\left(-z\right) \cdot y}\\ \mathbf{elif}\;z \leq 2.7 \cdot 10^{-15}:\\ \;\;\;\;\frac{x}{y \cdot t}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ x (* z z))))
   (if (<= z -6.8e+31)
     t_1
     (if (<= z -1.75e-84)
       (/ x (* (- z) y))
       (if (<= z 2.7e-15) (/ x (* y t)) t_1)))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x / (z * z);
	double tmp;
	if (z <= -6.8e+31) {
		tmp = t_1;
	} else if (z <= -1.75e-84) {
		tmp = x / (-z * y);
	} else if (z <= 2.7e-15) {
		tmp = x / (y * 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 = x / (z * z)
    if (z <= (-6.8d+31)) then
        tmp = t_1
    else if (z <= (-1.75d-84)) then
        tmp = x / (-z * y)
    else if (z <= 2.7d-15) then
        tmp = x / (y * 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 = x / (z * z);
	double tmp;
	if (z <= -6.8e+31) {
		tmp = t_1;
	} else if (z <= -1.75e-84) {
		tmp = x / (-z * y);
	} else if (z <= 2.7e-15) {
		tmp = x / (y * t);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x / (z * z)
	tmp = 0
	if z <= -6.8e+31:
		tmp = t_1
	elif z <= -1.75e-84:
		tmp = x / (-z * y)
	elif z <= 2.7e-15:
		tmp = x / (y * t)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x / Float64(z * z))
	tmp = 0.0
	if (z <= -6.8e+31)
		tmp = t_1;
	elseif (z <= -1.75e-84)
		tmp = Float64(x / Float64(Float64(-z) * y));
	elseif (z <= 2.7e-15)
		tmp = Float64(x / Float64(y * t));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x / (z * z);
	tmp = 0.0;
	if (z <= -6.8e+31)
		tmp = t_1;
	elseif (z <= -1.75e-84)
		tmp = x / (-z * y);
	elseif (z <= 2.7e-15)
		tmp = x / (y * t);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x / N[(z * z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -6.8e+31], t$95$1, If[LessEqual[z, -1.75e-84], N[(x / N[((-z) * y), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 2.7e-15], N[(x / N[(y * t), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if z < -6.7999999999999996e31 or 2.70000000000000009e-15 < z

   1. Initial program 82.1%

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

   3. Taylor expanded in z around inf

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

      1. unpow2 N/A

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

      2. lower-*.f64 67.6

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

   5. Applied rewrites 67.6%

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

   if -6.7999999999999996e31 < z < -1.7500000000000001e-84

   1. Initial program 99.4%

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

   3. Taylor expanded in z around 0

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

      1. +-commutative N/A

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

      2. *-commutative N/A

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

      3. lower-fma.f64 N/A

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

      4. +-commutative N/A

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

      5. mul-1-neg N/A

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

      6. unsub-neg N/A

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

      7. lower--.f64 N/A

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

      8. mul-1-neg N/A

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

      9. lower-neg.f64 N/A

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

      10. lower-*.f64 74.5

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

   5. Applied rewrites 74.5%

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

   6. Taylor expanded in t around 0

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

   8. Applied rewrites 39.7%

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

   if -1.7500000000000001e-84 < z < 2.70000000000000009e-15

   1. Initial program 92.3%

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

   3. Taylor expanded in z around 0

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

      1. lower-*.f64 63.8

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

   5. Applied rewrites 63.8%

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

4. Final simplification 63.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -6.8 \cdot 10^{+31}:\\ \;\;\;\;\frac{x}{z \cdot z}\\ \mathbf{elif}\;z \leq -1.75 \cdot 10^{-84}:\\ \;\;\;\;\frac{x}{\left(-z\right) \cdot y}\\ \mathbf{elif}\;z \leq 2.7 \cdot 10^{-15}:\\ \;\;\;\;\frac{x}{y \cdot t}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{z \cdot z}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 92.8% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.8 \cdot 10^{+109}:\\ \;\;\;\;\frac{\frac{x}{z}}{z - y}\\ \mathbf{elif}\;z \leq 3.8 \cdot 10^{+144}:\\ \;\;\;\;\frac{x}{\left(y - z\right) \cdot \left(t - z\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{z}}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -1.8e+109)
   (/ (/ x z) (- z y))
   (if (<= z 3.8e+144) (/ x (* (- y z) (- t z))) (/ (/ x z) z))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -1.8e+109) {
		tmp = (x / z) / (z - y);
	} else if (z <= 3.8e+144) {
		tmp = x / ((y - z) * (t - z));
	} else {
		tmp = (x / z) / z;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (z <= (-1.8d+109)) then
        tmp = (x / z) / (z - y)
    else if (z <= 3.8d+144) then
        tmp = x / ((y - z) * (t - z))
    else
        tmp = (x / z) / z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -1.8e+109) {
		tmp = (x / z) / (z - y);
	} else if (z <= 3.8e+144) {
		tmp = x / ((y - z) * (t - z));
	} else {
		tmp = (x / z) / z;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -1.8e+109:
		tmp = (x / z) / (z - y)
	elif z <= 3.8e+144:
		tmp = x / ((y - z) * (t - z))
	else:
		tmp = (x / z) / z
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -1.8e+109)
		tmp = Float64(Float64(x / z) / Float64(z - y));
	elseif (z <= 3.8e+144)
		tmp = Float64(x / Float64(Float64(y - z) * Float64(t - z)));
	else
		tmp = Float64(Float64(x / z) / z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (z <= -1.8e+109)
		tmp = (x / z) / (z - y);
	elseif (z <= 3.8e+144)
		tmp = x / ((y - z) * (t - z));
	else
		tmp = (x / z) / z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -1.8e+109], N[(N[(x / z), $MachinePrecision] / N[(z - y), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 3.8e+144], N[(x / N[(N[(y - z), $MachinePrecision] * N[(t - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x / z), $MachinePrecision] / z), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.8e109

   1. Initial program 78.8%

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

   3. Taylor expanded in t around 0

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

      1. mul-1-neg N/A

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

      2. associate-/r* N/A

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

      3. distribute-neg-frac2 N/A

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

      4. mul-1-neg N/A

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

      5. lower-/.f64 N/A

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

      6. lower-/.f64 N/A

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

      7. mul-1-neg N/A

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

      8. sub-neg N/A

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

      9. +-commutative N/A

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

      10. distribute-neg-in N/A

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

      11. unsub-neg N/A

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

      12. remove-double-neg N/A

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

      13. lower--.f64 87.2

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

   5. Applied rewrites 87.2%

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

   if -1.8e109 < z < 3.80000000000000026e144

   1. Initial program 92.4%

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

   if 3.80000000000000026e144 < z

   1. Initial program 78.1%

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

      1. lift-/.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. associate-/l/ N/A

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

      4. lower-/.f64 N/A

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

      5. lower-/.f64 100.0

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

   4. Applied rewrites 100.0%

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

   5. Taylor expanded in z around inf

      \[\leadsto \color{blue}{\frac{x}{{z}^{2}}} \]
   6. Step-by-step derivation

      1. unpow2 N/A

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

      2. associate-/r* N/A

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

      3. lower-/.f64 N/A

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

      4. lower-/.f64 100.0

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

   7. Applied rewrites 100.0%

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

Alternative 5: 68.6% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.5 \cdot 10^{-61}:\\ \;\;\;\;\frac{x}{y \cdot \left(t - z\right)}\\ \mathbf{elif}\;y \leq 1.35 \cdot 10^{-207}:\\ \;\;\;\;\frac{x}{\left(z - t\right) \cdot z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\left(y - z\right) \cdot t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -2.5e-61)
   (/ x (* y (- t z)))
   (if (<= y 1.35e-207) (/ x (* (- z t) z)) (/ x (* (- y z) t)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -2.5e-61) {
		tmp = x / (y * (t - z));
	} else if (y <= 1.35e-207) {
		tmp = x / ((z - t) * z);
	} else {
		tmp = x / ((y - 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) :: tmp
    if (y <= (-2.5d-61)) then
        tmp = x / (y * (t - z))
    else if (y <= 1.35d-207) then
        tmp = x / ((z - t) * z)
    else
        tmp = x / ((y - z) * t)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -2.5e-61) {
		tmp = x / (y * (t - z));
	} else if (y <= 1.35e-207) {
		tmp = x / ((z - t) * z);
	} else {
		tmp = x / ((y - z) * t);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -2.5e-61:
		tmp = x / (y * (t - z))
	elif y <= 1.35e-207:
		tmp = x / ((z - t) * z)
	else:
		tmp = x / ((y - z) * t)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -2.5e-61)
		tmp = Float64(x / Float64(y * Float64(t - z)));
	elseif (y <= 1.35e-207)
		tmp = Float64(x / Float64(Float64(z - t) * z));
	else
		tmp = Float64(x / Float64(Float64(y - z) * t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= -2.5e-61)
		tmp = x / (y * (t - z));
	elseif (y <= 1.35e-207)
		tmp = x / ((z - t) * z);
	else
		tmp = x / ((y - z) * t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -2.5e-61], N[(x / N[(y * N[(t - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.35e-207], N[(x / N[(N[(z - t), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision], N[(x / N[(N[(y - z), $MachinePrecision] * t), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -2.4999999999999999e-61

   1. Initial program 89.0%

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

   3. Taylor expanded in y around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 85.9

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

   5. Applied rewrites 85.9%

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

   if -2.4999999999999999e-61 < y < 1.35e-207

   1. Initial program 87.2%

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

   3. Taylor expanded in y around 0

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

      1. *-commutative N/A

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

      2. associate-*r* N/A

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

      3. lower-*.f64 N/A

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

      4. mul-1-neg N/A

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

      5. sub-neg N/A

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

      6. +-commutative N/A

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

      7. distribute-neg-in N/A

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

      8. remove-double-neg N/A

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

      9. unsub-neg N/A

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

      10. lower--.f64 73.1

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

   5. Applied rewrites 73.1%

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

   if 1.35e-207 < y

   1. Initial program 89.1%

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

   3. Taylor expanded in t around inf

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

      1. lower-*.f64 N/A

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

      2. lower--.f64 53.9

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

   5. Applied rewrites 53.9%

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

4. Final simplification 70.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.5 \cdot 10^{-61}:\\ \;\;\;\;\frac{x}{y \cdot \left(t - z\right)}\\ \mathbf{elif}\;y \leq 1.35 \cdot 10^{-207}:\\ \;\;\;\;\frac{x}{\left(z - t\right) \cdot z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\left(y - z\right) \cdot t}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 62.5% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -3.9 \cdot 10^{-62}:\\ \;\;\;\;\frac{x}{y \cdot \left(t - z\right)}\\ \mathbf{elif}\;y \leq -1.52 \cdot 10^{-187}:\\ \;\;\;\;\frac{x}{z \cdot z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\left(y - z\right) \cdot t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -3.9e-62)
   (/ x (* y (- t z)))
   (if (<= y -1.52e-187) (/ x (* z z)) (/ x (* (- y z) t)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -3.9e-62) {
		tmp = x / (y * (t - z));
	} else if (y <= -1.52e-187) {
		tmp = x / (z * z);
	} else {
		tmp = x / ((y - 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) :: tmp
    if (y <= (-3.9d-62)) then
        tmp = x / (y * (t - z))
    else if (y <= (-1.52d-187)) then
        tmp = x / (z * z)
    else
        tmp = x / ((y - z) * t)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -3.9e-62) {
		tmp = x / (y * (t - z));
	} else if (y <= -1.52e-187) {
		tmp = x / (z * z);
	} else {
		tmp = x / ((y - z) * t);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -3.9e-62:
		tmp = x / (y * (t - z))
	elif y <= -1.52e-187:
		tmp = x / (z * z)
	else:
		tmp = x / ((y - z) * t)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -3.9e-62)
		tmp = Float64(x / Float64(y * Float64(t - z)));
	elseif (y <= -1.52e-187)
		tmp = Float64(x / Float64(z * z));
	else
		tmp = Float64(x / Float64(Float64(y - z) * t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= -3.9e-62)
		tmp = x / (y * (t - z));
	elseif (y <= -1.52e-187)
		tmp = x / (z * z);
	else
		tmp = x / ((y - z) * t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -3.9e-62], N[(x / N[(y * N[(t - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -1.52e-187], N[(x / N[(z * z), $MachinePrecision]), $MachinePrecision], N[(x / N[(N[(y - z), $MachinePrecision] * t), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -3.9000000000000003e-62

   1. Initial program 89.0%

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

   3. Taylor expanded in y around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 85.9

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

   5. Applied rewrites 85.9%

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

   if -3.9000000000000003e-62 < y < -1.52e-187

   1. Initial program 90.1%

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

   3. Taylor expanded in z around inf

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

      1. unpow2 N/A

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

      2. lower-*.f64 59.5

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

   5. Applied rewrites 59.5%

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

   if -1.52e-187 < y

   1. Initial program 88.0%

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

   3. Taylor expanded in t around inf

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

      1. lower-*.f64 N/A

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

      2. lower--.f64 54.4

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

   5. Applied rewrites 54.4%

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

4. Final simplification 66.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.9 \cdot 10^{-62}:\\ \;\;\;\;\frac{x}{y \cdot \left(t - z\right)}\\ \mathbf{elif}\;y \leq -1.52 \cdot 10^{-187}:\\ \;\;\;\;\frac{x}{z \cdot z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\left(y - z\right) \cdot t}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 61.0% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{z \cdot z}\\ \mathbf{if}\;z \leq -1.95 \cdot 10^{-86}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 2.7 \cdot 10^{-15}:\\ \;\;\;\;\frac{x}{y \cdot t}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ x (* z z))))
   (if (<= z -1.95e-86) t_1 (if (<= z 2.7e-15) (/ x (* y t)) t_1))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x / (z * z);
	double tmp;
	if (z <= -1.95e-86) {
		tmp = t_1;
	} else if (z <= 2.7e-15) {
		tmp = x / (y * 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 = x / (z * z)
    if (z <= (-1.95d-86)) then
        tmp = t_1
    else if (z <= 2.7d-15) then
        tmp = x / (y * 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 = x / (z * z);
	double tmp;
	if (z <= -1.95e-86) {
		tmp = t_1;
	} else if (z <= 2.7e-15) {
		tmp = x / (y * t);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x / (z * z)
	tmp = 0
	if z <= -1.95e-86:
		tmp = t_1
	elif z <= 2.7e-15:
		tmp = x / (y * t)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x / Float64(z * z))
	tmp = 0.0
	if (z <= -1.95e-86)
		tmp = t_1;
	elseif (z <= 2.7e-15)
		tmp = Float64(x / Float64(y * t));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x / (z * z);
	tmp = 0.0;
	if (z <= -1.95e-86)
		tmp = t_1;
	elseif (z <= 2.7e-15)
		tmp = x / (y * t);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x / N[(z * z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.95e-86], t$95$1, If[LessEqual[z, 2.7e-15], N[(x / N[(y * t), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if z < -1.9500000000000001e-86 or 2.70000000000000009e-15 < z

   1. Initial program 85.4%

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

   3. Taylor expanded in z around inf

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

      1. unpow2 N/A

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

      2. lower-*.f64 59.6

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

   5. Applied rewrites 59.6%

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

   if -1.9500000000000001e-86 < z < 2.70000000000000009e-15

   1. Initial program 92.2%

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

   3. Taylor expanded in z around 0

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

      1. lower-*.f64 64.3

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

   5. Applied rewrites 64.3%

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

4. Final simplification 61.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.95 \cdot 10^{-86}:\\ \;\;\;\;\frac{x}{z \cdot z}\\ \mathbf{elif}\;z \leq 2.7 \cdot 10^{-15}:\\ \;\;\;\;\frac{x}{y \cdot t}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{z \cdot z}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 90.3% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq 3.8 \cdot 10^{+144}:\\ \;\;\;\;\frac{x}{\left(y - z\right) \cdot \left(t - z\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{z}}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z 3.8e+144) (/ x (* (- y z) (- t z))) (/ (/ x z) z)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= 3.8e+144) {
		tmp = x / ((y - z) * (t - z));
	} else {
		tmp = (x / z) / z;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (z <= 3.8d+144) then
        tmp = x / ((y - z) * (t - z))
    else
        tmp = (x / z) / z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= 3.8e+144) {
		tmp = x / ((y - z) * (t - z));
	} else {
		tmp = (x / z) / z;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= 3.8e+144:
		tmp = x / ((y - z) * (t - z))
	else:
		tmp = (x / z) / z
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= 3.8e+144)
		tmp = Float64(x / Float64(Float64(y - z) * Float64(t - z)));
	else
		tmp = Float64(Float64(x / z) / z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (z <= 3.8e+144)
		tmp = x / ((y - z) * (t - z));
	else
		tmp = (x / z) / z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, 3.8e+144], N[(x / N[(N[(y - z), $MachinePrecision] * N[(t - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x / z), $MachinePrecision] / z), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < 3.80000000000000026e144

   1. Initial program 90.2%

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

   if 3.80000000000000026e144 < z

   1. Initial program 78.1%

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

      1. lift-/.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. associate-/l/ N/A

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

      4. lower-/.f64 N/A

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

      5. lower-/.f64 100.0

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

   4. Applied rewrites 100.0%

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

   5. Taylor expanded in z around inf

      \[\leadsto \color{blue}{\frac{x}{{z}^{2}}} \]
   6. Step-by-step derivation

      1. unpow2 N/A

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

      2. associate-/r* N/A

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

      3. lower-/.f64 N/A

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

      4. lower-/.f64 100.0

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

   7. Applied rewrites 100.0%

      \[\leadsto \color{blue}{\frac{\frac{x}{z}}{z}} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 9: 39.4% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \frac{x}{y \cdot t} \end{array} \]

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 88.6%

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

3. Taylor expanded in z around 0

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

   1. lower-*.f64 40.3

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

5. Applied rewrites 40.3%

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

6. Final simplification 40.3%

   \[\leadsto \frac{x}{y \cdot t} \]
7. Add Preprocessing

Developer Target 1: 87.7% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(y - z\right) \cdot \left(t - z\right)\\ \mathbf{if}\;\frac{x}{t\_1} < 0:\\ \;\;\;\;\frac{\frac{x}{y - z}}{t - z}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{1}{t\_1}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* (- y z) (- t z))))
   (if (< (/ x t_1) 0.0) (/ (/ x (- y z)) (- t z)) (* x (/ 1.0 t_1)))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (y - z) * (t - z);
	double tmp;
	if ((x / t_1) < 0.0) {
		tmp = (x / (y - z)) / (t - z);
	} else {
		tmp = x * (1.0 / 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 = (y - z) * (t - z)
    if ((x / t_1) < 0.0d0) then
        tmp = (x / (y - z)) / (t - z)
    else
        tmp = x * (1.0d0 / t_1)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = (y - z) * (t - z);
	double tmp;
	if ((x / t_1) < 0.0) {
		tmp = (x / (y - z)) / (t - z);
	} else {
		tmp = x * (1.0 / t_1);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (y - z) * (t - z)
	tmp = 0
	if (x / t_1) < 0.0:
		tmp = (x / (y - z)) / (t - z)
	else:
		tmp = x * (1.0 / t_1)
	return tmp

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(y - z), $MachinePrecision] * N[(t - z), $MachinePrecision]), $MachinePrecision]}, If[Less[N[(x / t$95$1), $MachinePrecision], 0.0], N[(N[(x / N[(y - z), $MachinePrecision]), $MachinePrecision] / N[(t - z), $MachinePrecision]), $MachinePrecision], N[(x * N[(1.0 / t$95$1), $MachinePrecision]), $MachinePrecision]]]

Reproduce

herbie shell --seed 2024243 
(FPCore (x y z t)
  :name "Data.Random.Distribution.Triangular:triangularCDF from random-fu-0.2.6.2, B"
  :precision binary64

  :alt
  (! :herbie-platform default (if (< (/ x (* (- y z) (- t z))) 0) (/ (/ x (- y z)) (- t z)) (* x (/ 1 (* (- y z) (- t z))))))

  (/ x (* (- y z) (- t z))))