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

Percentage Accurate: 89.0% → 96.9%

Time: 6.8s

Alternatives: 11

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: 89.0% 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: 96.9% 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 88.9%

   \[\frac{x}{\left(y - z\right) \cdot \left(t - z\right)} \]
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. *-commutative N/A

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

   4. associate-/r* N/A

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

   5. lower-/.f64 N/A

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

   6. lower-/.f64 97.7

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

4. Applied rewrites 97.7%

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

Alternative 2: 93.5% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(y - z\right) \cdot \left(t - z\right)\\ t_2 := \frac{x}{t - z}\\ \mathbf{if}\;t\_1 \leq -\infty:\\ \;\;\;\;\frac{t\_2}{y}\\ \mathbf{elif}\;t\_1 \leq 5 \cdot 10^{+286}:\\ \;\;\;\;\frac{x}{t\_1}\\ \mathbf{else}:\\ \;\;\;\;\frac{t\_2}{-z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* (- y z) (- t z))) (t_2 (/ x (- t z))))
   (if (<= t_1 (- INFINITY))
     (/ t_2 y)
     (if (<= t_1 5e+286) (/ x t_1) (/ t_2 (- z))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (y - z) * (t - z);
	double t_2 = x / (t - z);
	double tmp;
	if (t_1 <= -((double) INFINITY)) {
		tmp = t_2 / y;
	} else if (t_1 <= 5e+286) {
		tmp = x / t_1;
	} else {
		tmp = t_2 / -z;
	}
	return tmp;
}

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = (y - z) * (t - z);
	double t_2 = x / (t - z);
	double tmp;
	if (t_1 <= -Double.POSITIVE_INFINITY) {
		tmp = t_2 / y;
	} else if (t_1 <= 5e+286) {
		tmp = x / t_1;
	} else {
		tmp = t_2 / -z;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (y - z) * (t - z)
	t_2 = x / (t - z)
	tmp = 0
	if t_1 <= -math.inf:
		tmp = t_2 / y
	elif t_1 <= 5e+286:
		tmp = x / t_1
	else:
		tmp = t_2 / -z
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(y - z) * Float64(t - z))
	t_2 = Float64(x / Float64(t - z))
	tmp = 0.0
	if (t_1 <= Float64(-Inf))
		tmp = Float64(t_2 / y);
	elseif (t_1 <= 5e+286)
		tmp = Float64(x / t_1);
	else
		tmp = Float64(t_2 / Float64(-z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (y - z) * (t - z);
	t_2 = x / (t - z);
	tmp = 0.0;
	if (t_1 <= -Inf)
		tmp = t_2 / y;
	elseif (t_1 <= 5e+286)
		tmp = x / t_1;
	else
		tmp = t_2 / -z;
	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]}, Block[{t$95$2 = N[(x / N[(t - z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, (-Infinity)], N[(t$95$2 / y), $MachinePrecision], If[LessEqual[t$95$1, 5e+286], N[(x / t$95$1), $MachinePrecision], N[(t$95$2 / (-z)), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 (-.f64 y z) (-.f64 t z)) < -inf.0

   1. Initial program 63.0%

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

   3. Taylor expanded in y around inf

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

      1. *-commutative N/A

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

      2. associate-/r* N/A

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

      3. lower-/.f64 N/A

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

      4. lower-/.f64 N/A

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

      5. lower--.f64 95.5

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

   5. Applied rewrites 95.5%

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

   if -inf.0 < (*.f64 (-.f64 y z) (-.f64 t z)) < 5.0000000000000004e286

   1. Initial program 95.6%

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

   if 5.0000000000000004e286 < (*.f64 (-.f64 y z) (-.f64 t z))

   1. Initial program 81.7%

      \[\frac{x}{\left(y - z\right) \cdot \left(t - z\right)} \]
   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. *-commutative N/A

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

      4. associate-/r* N/A

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

      5. lower-/.f64 N/A

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

      6. lower-/.f64 99.9

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

   4. Applied rewrites 99.9%

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

   5. Taylor expanded in y around 0

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

      1. mul-1-neg N/A

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

      2. lower-neg.f64 90.8

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

   7. Applied rewrites 90.8%

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

Alternative 3: 66.2% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{\left(z + y\right) \cdot t}\\ \mathbf{if}\;t \leq -1.02 \cdot 10^{-81}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 1.75 \cdot 10^{-22}:\\ \;\;\;\;\frac{x}{\left(z - y\right) \cdot z}\\ \mathbf{elif}\;t \leq 6.9 \cdot 10^{+33} \lor \neg \left(t \leq 1.06 \cdot 10^{+119}\right):\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\left(-z\right) \cdot t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ x (* (+ z y) t))))
   (if (<= t -1.02e-81)
     t_1
     (if (<= t 1.75e-22)
       (/ x (* (- z y) z))
       (if (or (<= t 6.9e+33) (not (<= t 1.06e+119)))
         t_1
         (/ x (* (- z) t)))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x / ((z + y) * t);
	double tmp;
	if (t <= -1.02e-81) {
		tmp = t_1;
	} else if (t <= 1.75e-22) {
		tmp = x / ((z - y) * z);
	} else if ((t <= 6.9e+33) || !(t <= 1.06e+119)) {
		tmp = t_1;
	} else {
		tmp = 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 / ((z + y) * t)
    if (t <= (-1.02d-81)) then
        tmp = t_1
    else if (t <= 1.75d-22) then
        tmp = x / ((z - y) * z)
    else if ((t <= 6.9d+33) .or. (.not. (t <= 1.06d+119))) then
        tmp = t_1
    else
        tmp = 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 / ((z + y) * t);
	double tmp;
	if (t <= -1.02e-81) {
		tmp = t_1;
	} else if (t <= 1.75e-22) {
		tmp = x / ((z - y) * z);
	} else if ((t <= 6.9e+33) || !(t <= 1.06e+119)) {
		tmp = t_1;
	} else {
		tmp = x / (-z * t);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x / ((z + y) * t)
	tmp = 0
	if t <= -1.02e-81:
		tmp = t_1
	elif t <= 1.75e-22:
		tmp = x / ((z - y) * z)
	elif (t <= 6.9e+33) or not (t <= 1.06e+119):
		tmp = t_1
	else:
		tmp = x / (-z * t)
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x / Float64(Float64(z + y) * t))
	tmp = 0.0
	if (t <= -1.02e-81)
		tmp = t_1;
	elseif (t <= 1.75e-22)
		tmp = Float64(x / Float64(Float64(z - y) * z));
	elseif ((t <= 6.9e+33) || !(t <= 1.06e+119))
		tmp = t_1;
	else
		tmp = Float64(x / Float64(Float64(-z) * t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x / ((z + y) * t);
	tmp = 0.0;
	if (t <= -1.02e-81)
		tmp = t_1;
	elseif (t <= 1.75e-22)
		tmp = x / ((z - y) * z);
	elseif ((t <= 6.9e+33) || ~((t <= 1.06e+119)))
		tmp = t_1;
	else
		tmp = x / (-z * t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x / N[(N[(z + y), $MachinePrecision] * t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -1.02e-81], t$95$1, If[LessEqual[t, 1.75e-22], N[(x / N[(N[(z - y), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[t, 6.9e+33], N[Not[LessEqual[t, 1.06e+119]], $MachinePrecision]], t$95$1, N[(x / N[((-z) * t), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if t < -1.01999999999999998e-81 or 1.75000000000000003e-22 < t < 6.8999999999999995e33 or 1.0599999999999999e119 < t

   1. Initial program 86.3%

      \[\frac{x}{\left(y - z\right) \cdot \left(t - z\right)} \]
   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. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 77.2

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

   5. Applied rewrites 77.2%

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

   7. Applied rewrites 63.7%

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

   if -1.01999999999999998e-81 < t < 1.75000000000000003e-22

   1. Initial program 90.3%

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

   3. Taylor expanded in t around 0

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

      1. associate-*r* N/A

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

      2. lower-*.f64 N/A

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

      3. mul-1-neg N/A

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

      4. lower-neg.f64 N/A

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

      5. lower--.f64 77.5

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

   5. Applied rewrites 77.5%

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

   6. Taylor expanded in y around 0

      \[\leadsto \frac{x}{-1 \cdot \left(y \cdot z\right) + \color{blue}{{z}^{2}}} \]
   7. Step-by-step derivation

   8. Applied rewrites 77.5%

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

   if 6.8999999999999995e33 < t < 1.0599999999999999e119

   1. Initial program 99.7%

      \[\frac{x}{\left(y - z\right) \cdot \left(t - z\right)} \]
   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. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 85.3

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

   5. Applied rewrites 85.3%

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

   6. Taylor expanded in y around 0

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

   8. Applied rewrites 56.3%

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

4. Final simplification 69.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.02 \cdot 10^{-81}:\\ \;\;\;\;\frac{x}{\left(z + y\right) \cdot t}\\ \mathbf{elif}\;t \leq 1.75 \cdot 10^{-22}:\\ \;\;\;\;\frac{x}{\left(z - y\right) \cdot z}\\ \mathbf{elif}\;t \leq 6.9 \cdot 10^{+33} \lor \neg \left(t \leq 1.06 \cdot 10^{+119}\right):\\ \;\;\;\;\frac{x}{\left(z + y\right) \cdot t}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\left(-z\right) \cdot t}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 60.3% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{z \cdot z}\\ t_2 := \frac{x}{\left(-z\right) \cdot t}\\ \mathbf{if}\;z \leq -3.4 \cdot 10^{+68}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -1.6 \cdot 10^{-137}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;z \leq 2.15 \cdot 10^{-49}:\\ \;\;\;\;\frac{x}{t \cdot y}\\ \mathbf{elif}\;z \leq 0.55:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ x (* z z))) (t_2 (/ x (* (- z) t))))
   (if (<= z -3.4e+68)
     t_1
     (if (<= z -1.6e-137)
       t_2
       (if (<= z 2.15e-49) (/ x (* t y)) (if (<= z 0.55) t_2 t_1))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x / (z * z);
	double t_2 = x / (-z * t);
	double tmp;
	if (z <= -3.4e+68) {
		tmp = t_1;
	} else if (z <= -1.6e-137) {
		tmp = t_2;
	} else if (z <= 2.15e-49) {
		tmp = x / (t * y);
	} else if (z <= 0.55) {
		tmp = t_2;
	} 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 * z)
    t_2 = x / (-z * t)
    if (z <= (-3.4d+68)) then
        tmp = t_1
    else if (z <= (-1.6d-137)) then
        tmp = t_2
    else if (z <= 2.15d-49) then
        tmp = x / (t * y)
    else if (z <= 0.55d0) then
        tmp = t_2
    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 t_2 = x / (-z * t);
	double tmp;
	if (z <= -3.4e+68) {
		tmp = t_1;
	} else if (z <= -1.6e-137) {
		tmp = t_2;
	} else if (z <= 2.15e-49) {
		tmp = x / (t * y);
	} else if (z <= 0.55) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x / (z * z)
	t_2 = x / (-z * t)
	tmp = 0
	if z <= -3.4e+68:
		tmp = t_1
	elif z <= -1.6e-137:
		tmp = t_2
	elif z <= 2.15e-49:
		tmp = x / (t * y)
	elif z <= 0.55:
		tmp = t_2
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x / Float64(z * z))
	t_2 = Float64(x / Float64(Float64(-z) * t))
	tmp = 0.0
	if (z <= -3.4e+68)
		tmp = t_1;
	elseif (z <= -1.6e-137)
		tmp = t_2;
	elseif (z <= 2.15e-49)
		tmp = Float64(x / Float64(t * y));
	elseif (z <= 0.55)
		tmp = t_2;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x / (z * z);
	t_2 = x / (-z * t);
	tmp = 0.0;
	if (z <= -3.4e+68)
		tmp = t_1;
	elseif (z <= -1.6e-137)
		tmp = t_2;
	elseif (z <= 2.15e-49)
		tmp = x / (t * y);
	elseif (z <= 0.55)
		tmp = t_2;
	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]}, Block[{t$95$2 = N[(x / N[((-z) * t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -3.4e+68], t$95$1, If[LessEqual[z, -1.6e-137], t$95$2, If[LessEqual[z, 2.15e-49], N[(x / N[(t * y), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 0.55], t$95$2, t$95$1]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -3.40000000000000015e68 or 0.55000000000000004 < z

   1. Initial program 87.3%

      \[\frac{x}{\left(y - z\right) \cdot \left(t - z\right)} \]
   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 76.9

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

   5. Applied rewrites 76.9%

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

   if -3.40000000000000015e68 < z < -1.60000000000000011e-137 or 2.15000000000000008e-49 < z < 0.55000000000000004

   1. Initial program 92.1%

      \[\frac{x}{\left(y - z\right) \cdot \left(t - z\right)} \]
   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. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 48.1

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

   5. Applied rewrites 48.1%

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

   6. Taylor expanded in y around 0

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

   8. Applied rewrites 34.1%

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

   if -1.60000000000000011e-137 < z < 2.15000000000000008e-49

   1. Initial program 88.5%

      \[\frac{x}{\left(y - z\right) \cdot \left(t - z\right)} \]
   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 58.7

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

   5. Applied rewrites 58.7%

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

Alternative 5: 90.5% accurate, 0.5× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(y - z) * Float64(t - z))
	tmp = 0.0
	if (t_1 <= Float64(-Inf))
		tmp = Float64(Float64(x / Float64(t - z)) / y);
	else
		tmp = Float64(x / 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 (t_1 <= -Inf)
		tmp = (x / (t - z)) / y;
	else
		tmp = x / 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[LessEqual[t$95$1, (-Infinity)], N[(N[(x / N[(t - z), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], N[(x / t$95$1), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 (-.f64 y z) (-.f64 t z)) < -inf.0

   1. Initial program 63.0%

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

   3. Taylor expanded in y around inf

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

      1. *-commutative N/A

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

      2. associate-/r* N/A

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

      3. lower-/.f64 N/A

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

      4. lower-/.f64 N/A

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

      5. lower--.f64 95.5

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

   5. Applied rewrites 95.5%

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

   if -inf.0 < (*.f64 (-.f64 y z) (-.f64 t z))

   1. Initial program 91.3%

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

Alternative 6: 89.0% accurate, 0.6× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(y - z) * Float64(t - z))
	tmp = 0.0
	if (t_1 <= Float64(-Inf))
		tmp = Float64(Float64(x / y) / t);
	else
		tmp = Float64(x / 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 (t_1 <= -Inf)
		tmp = (x / y) / t;
	else
		tmp = x / 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[LessEqual[t$95$1, (-Infinity)], N[(N[(x / y), $MachinePrecision] / t), $MachinePrecision], N[(x / t$95$1), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 (-.f64 y z) (-.f64 t z)) < -inf.0

   1. Initial program 63.0%

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

   3. Taylor expanded in t around inf

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

      1. *-commutative N/A

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

      2. associate-/r* N/A

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

      3. lower-/.f64 N/A

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

      4. lower-/.f64 N/A

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

      5. lower--.f64 86.8

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

   5. Applied rewrites 86.8%

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

   6. Taylor expanded in y around inf

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

   8. Applied rewrites 78.3%

      \[\leadsto \frac{\frac{x}{y}}{t} \]

   if -inf.0 < (*.f64 (-.f64 y z) (-.f64 t z))

   1. Initial program 91.3%

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

Alternative 7: 72.6% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3.7 \cdot 10^{-87} \lor \neg \left(z \leq 3 \cdot 10^{-8}\right):\\ \;\;\;\;\frac{x}{\left(z - y\right) \cdot z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\left(t - z\right) \cdot y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -3.7e-87) (not (<= z 3e-8)))
   (/ x (* (- z y) z))
   (/ x (* (- t z) y))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -3.7e-87) || !(z <= 3e-8)) {
		tmp = x / ((z - y) * z);
	} else {
		tmp = x / ((t - z) * y);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((z <= (-3.7d-87)) .or. (.not. (z <= 3d-8))) then
        tmp = x / ((z - y) * z)
    else
        tmp = x / ((t - z) * y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -3.7e-87) || !(z <= 3e-8)) {
		tmp = x / ((z - y) * z);
	} else {
		tmp = x / ((t - z) * y);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -3.7e-87) or not (z <= 3e-8):
		tmp = x / ((z - y) * z)
	else:
		tmp = x / ((t - z) * y)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -3.7e-87) || !(z <= 3e-8))
		tmp = Float64(x / Float64(Float64(z - y) * z));
	else
		tmp = Float64(x / Float64(Float64(t - z) * y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z <= -3.7e-87) || ~((z <= 3e-8)))
		tmp = x / ((z - y) * z);
	else
		tmp = x / ((t - z) * y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -3.7e-87], N[Not[LessEqual[z, 3e-8]], $MachinePrecision]], N[(x / N[(N[(z - y), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision], N[(x / N[(N[(t - z), $MachinePrecision] * y), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -3.7000000000000002e-87 or 2.99999999999999973e-8 < z

   1. Initial program 87.3%

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

   3. Taylor expanded in t around 0

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

      1. associate-*r* N/A

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

      2. lower-*.f64 N/A

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

      3. mul-1-neg N/A

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

      4. lower-neg.f64 N/A

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

      5. lower--.f64 73.0

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

   5. Applied rewrites 73.0%

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

   6. Taylor expanded in y around 0

      \[\leadsto \frac{x}{-1 \cdot \left(y \cdot z\right) + \color{blue}{{z}^{2}}} \]
   7. Step-by-step derivation

   8. Applied rewrites 73.0%

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

   if -3.7000000000000002e-87 < z < 2.99999999999999973e-8

   1. Initial program 91.0%

      \[\frac{x}{\left(y - z\right) \cdot \left(t - z\right)} \]
   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 76.9

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

   5. Applied rewrites 76.9%

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

4. Final simplification 74.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.7 \cdot 10^{-87} \lor \neg \left(z \leq 3 \cdot 10^{-8}\right):\\ \;\;\;\;\frac{x}{\left(z - y\right) \cdot z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\left(t - z\right) \cdot y}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 69.6% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -9 \cdot 10^{-218}:\\ \;\;\;\;\frac{x}{\left(t - z\right) \cdot y}\\ \mathbf{elif}\;t \leq 1.06 \cdot 10^{-55}:\\ \;\;\;\;\frac{x}{\left(z - y\right) \cdot z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\left(y - z\right) \cdot t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= t -9e-218)
   (/ x (* (- t z) y))
   (if (<= t 1.06e-55) (/ x (* (- z y) z)) (/ x (* (- y z) t)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= -9e-218) {
		tmp = x / ((t - z) * y);
	} else if (t <= 1.06e-55) {
		tmp = x / ((z - y) * 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 (t <= (-9d-218)) then
        tmp = x / ((t - z) * y)
    else if (t <= 1.06d-55) then
        tmp = x / ((z - y) * 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 (t <= -9e-218) {
		tmp = x / ((t - z) * y);
	} else if (t <= 1.06e-55) {
		tmp = x / ((z - y) * z);
	} else {
		tmp = x / ((y - z) * t);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if t <= -9e-218:
		tmp = x / ((t - z) * y)
	elif t <= 1.06e-55:
		tmp = x / ((z - y) * z)
	else:
		tmp = x / ((y - z) * t)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (t <= -9e-218)
		tmp = Float64(x / Float64(Float64(t - z) * y));
	elseif (t <= 1.06e-55)
		tmp = Float64(x / Float64(Float64(z - y) * 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 (t <= -9e-218)
		tmp = x / ((t - z) * y);
	elseif (t <= 1.06e-55)
		tmp = x / ((z - y) * z);
	else
		tmp = x / ((y - z) * t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[t, -9e-218], N[(x / N[(N[(t - z), $MachinePrecision] * y), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.06e-55], N[(x / N[(N[(z - y), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision], N[(x / N[(N[(y - z), $MachinePrecision] * t), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -8.99999999999999953e-218

   1. Initial program 89.9%

      \[\frac{x}{\left(y - z\right) \cdot \left(t - z\right)} \]
   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 56.6

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

   5. Applied rewrites 56.6%

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

   if -8.99999999999999953e-218 < t < 1.06e-55

   1. Initial program 87.4%

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

   3. Taylor expanded in t around 0

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

      1. associate-*r* N/A

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

      2. lower-*.f64 N/A

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

      3. mul-1-neg N/A

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

      4. lower-neg.f64 N/A

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

      5. lower--.f64 76.3

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

   5. Applied rewrites 76.3%

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

   6. Taylor expanded in y around 0

      \[\leadsto \frac{x}{-1 \cdot \left(y \cdot z\right) + \color{blue}{{z}^{2}}} \]
   7. Step-by-step derivation

   8. Applied rewrites 76.3%

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

   if 1.06e-55 < t

   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. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 82.3

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

   5. Applied rewrites 82.3%

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

Alternative 9: 60.4% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.02 \cdot 10^{-81}:\\ \;\;\;\;\frac{x}{t \cdot y}\\ \mathbf{elif}\;t \leq 6 \cdot 10^{+14}:\\ \;\;\;\;\frac{x}{\left(z - y\right) \cdot z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\left(-z\right) \cdot t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= t -1.02e-81)
   (/ x (* t y))
   (if (<= t 6e+14) (/ x (* (- z y) z)) (/ x (* (- z) t)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= -1.02e-81) {
		tmp = x / (t * y);
	} else if (t <= 6e+14) {
		tmp = x / ((z - y) * z);
	} else {
		tmp = 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) :: tmp
    if (t <= (-1.02d-81)) then
        tmp = x / (t * y)
    else if (t <= 6d+14) then
        tmp = x / ((z - y) * z)
    else
        tmp = x / (-z * t)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= -1.02e-81) {
		tmp = x / (t * y);
	} else if (t <= 6e+14) {
		tmp = x / ((z - y) * z);
	} else {
		tmp = x / (-z * t);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if t <= -1.02e-81:
		tmp = x / (t * y)
	elif t <= 6e+14:
		tmp = x / ((z - y) * z)
	else:
		tmp = x / (-z * t)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (t <= -1.02e-81)
		tmp = Float64(x / Float64(t * y));
	elseif (t <= 6e+14)
		tmp = Float64(x / Float64(Float64(z - y) * z));
	else
		tmp = Float64(x / Float64(Float64(-z) * t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (t <= -1.02e-81)
		tmp = x / (t * y);
	elseif (t <= 6e+14)
		tmp = x / ((z - y) * z);
	else
		tmp = x / (-z * t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[t, -1.02e-81], N[(x / N[(t * y), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 6e+14], N[(x / N[(N[(z - y), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision], N[(x / N[((-z) * t), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -1.01999999999999998e-81

   1. Initial program 87.3%

      \[\frac{x}{\left(y - z\right) \cdot \left(t - z\right)} \]
   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 49.9

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

   5. Applied rewrites 49.9%

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

   if -1.01999999999999998e-81 < t < 6e14

   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 0

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

      1. associate-*r* N/A

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

      2. lower-*.f64 N/A

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

      3. mul-1-neg N/A

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

      4. lower-neg.f64 N/A

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

      5. lower--.f64 75.3

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

   5. Applied rewrites 75.3%

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

   6. Taylor expanded in y around 0

      \[\leadsto \frac{x}{-1 \cdot \left(y \cdot z\right) + \color{blue}{{z}^{2}}} \]
   7. Step-by-step derivation

   8. Applied rewrites 75.3%

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

   if 6e14 < t

   1. Initial program 90.2%

      \[\frac{x}{\left(y - z\right) \cdot \left(t - z\right)} \]
   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. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 85.3

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

   5. Applied rewrites 85.3%

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

   6. Taylor expanded in y around 0

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

   8. Applied rewrites 56.9%

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

Alternative 10: 60.9% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -42000000 \lor \neg \left(z \leq 3 \cdot 10^{-8}\right):\\ \;\;\;\;\frac{x}{z \cdot z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{t \cdot y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -42000000.0) (not (<= z 3e-8))) (/ x (* z z)) (/ x (* t y))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -42000000.0) || !(z <= 3e-8)) {
		tmp = x / (z * z);
	} else {
		tmp = x / (t * y);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((z <= (-42000000.0d0)) .or. (.not. (z <= 3d-8))) then
        tmp = x / (z * z)
    else
        tmp = x / (t * y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -42000000.0) || !(z <= 3e-8)) {
		tmp = x / (z * z);
	} else {
		tmp = x / (t * y);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -42000000.0) or not (z <= 3e-8):
		tmp = x / (z * z)
	else:
		tmp = x / (t * y)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -42000000.0) || !(z <= 3e-8))
		tmp = Float64(x / Float64(z * z));
	else
		tmp = Float64(x / Float64(t * y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z <= -42000000.0) || ~((z <= 3e-8)))
		tmp = x / (z * z);
	else
		tmp = x / (t * y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -42000000.0], N[Not[LessEqual[z, 3e-8]], $MachinePrecision]], N[(x / N[(z * z), $MachinePrecision]), $MachinePrecision], N[(x / N[(t * y), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -4.2e7 or 2.99999999999999973e-8 < z

   1. Initial program 87.4%

      \[\frac{x}{\left(y - z\right) \cdot \left(t - z\right)} \]
   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 70.0

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

   5. Applied rewrites 70.0%

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

   if -4.2e7 < z < 2.99999999999999973e-8

   1. Initial program 90.3%

      \[\frac{x}{\left(y - z\right) \cdot \left(t - z\right)} \]
   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 49.7

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

   5. Applied rewrites 49.7%

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

4. Final simplification 59.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -42000000 \lor \neg \left(z \leq 3 \cdot 10^{-8}\right):\\ \;\;\;\;\frac{x}{z \cdot z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{t \cdot y}\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 39.1% accurate, 1.4× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 88.9%

   \[\frac{x}{\left(y - z\right) \cdot \left(t - z\right)} \]
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 35.2

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

5. Applied rewrites 35.2%

   \[\leadsto \frac{x}{\color{blue}{t \cdot y}} \]
6. Add Preprocessing

Developer Target 1: 87.9% 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 2024320 
(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))))