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

Percentage Accurate: 89.3% → 98.2%

Time: 13.1s

Alternatives: 25

Speedup: 1.0×

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: 89.3% 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: 98.2% accurate, 0.4× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Split input into 2 regimes

2. if (/.f64 x (*.f64 (-.f64 y z) (-.f64 t z))) < -0.0

   1. Initial program 84.0%

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

      1. associate-/l/ 98.8%

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

   3. Simplified 98.8%

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

   if -0.0 < (/.f64 x (*.f64 (-.f64 y z) (-.f64 t z)))

   1. Initial program 98.2%

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

4. Final simplification 98.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x}{\left(y - z\right) \cdot \left(t - z\right)} \leq 0:\\ \;\;\;\;\frac{\frac{x}{t - z}}{y - z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\left(y - z\right) \cdot \left(t - z\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 49.0% accurate, 0.0× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 87.6%

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

   1. add-sqr-sqrt 45.7%

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

   2. times-frac 49.1%

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

4. Applied egg-rr 49.1%

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

5. Final simplification 49.1%

   \[\leadsto \frac{\sqrt{x}}{y - z} \cdot \frac{\sqrt{x}}{t - z} \]
6. Add Preprocessing

Alternative 3: 46.8% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{y \cdot t}\\ \mathbf{if}\;t \leq -9.5 \cdot 10^{-86}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 2.1 \cdot 10^{-116}:\\ \;\;\;\;\frac{x}{y \cdot \left(-z\right)}\\ \mathbf{elif}\;t \leq 1.8 \cdot 10^{+20} \lor \neg \left(t \leq 1.95 \cdot 10^{+174}\right) \land t \leq 2.2 \cdot 10^{+239}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{z \cdot \left(-t\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ x (* y t))))
   (if (<= t -9.5e-86)
     t_1
     (if (<= t 2.1e-116)
       (/ x (* y (- z)))
       (if (or (<= t 1.8e+20) (and (not (<= t 1.95e+174)) (<= t 2.2e+239)))
         t_1
         (/ x (* z (- t))))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x / (y * t);
	double tmp;
	if (t <= -9.5e-86) {
		tmp = t_1;
	} else if (t <= 2.1e-116) {
		tmp = x / (y * -z);
	} else if ((t <= 1.8e+20) || (!(t <= 1.95e+174) && (t <= 2.2e+239))) {
		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 / (y * t)
    if (t <= (-9.5d-86)) then
        tmp = t_1
    else if (t <= 2.1d-116) then
        tmp = x / (y * -z)
    else if ((t <= 1.8d+20) .or. (.not. (t <= 1.95d+174)) .and. (t <= 2.2d+239)) 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 / (y * t);
	double tmp;
	if (t <= -9.5e-86) {
		tmp = t_1;
	} else if (t <= 2.1e-116) {
		tmp = x / (y * -z);
	} else if ((t <= 1.8e+20) || (!(t <= 1.95e+174) && (t <= 2.2e+239))) {
		tmp = t_1;
	} else {
		tmp = x / (z * -t);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x / (y * t)
	tmp = 0
	if t <= -9.5e-86:
		tmp = t_1
	elif t <= 2.1e-116:
		tmp = x / (y * -z)
	elif (t <= 1.8e+20) or (not (t <= 1.95e+174) and (t <= 2.2e+239)):
		tmp = t_1
	else:
		tmp = x / (z * -t)
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x / Float64(y * t))
	tmp = 0.0
	if (t <= -9.5e-86)
		tmp = t_1;
	elseif (t <= 2.1e-116)
		tmp = Float64(x / Float64(y * Float64(-z)));
	elseif ((t <= 1.8e+20) || (!(t <= 1.95e+174) && (t <= 2.2e+239)))
		tmp = t_1;
	else
		tmp = Float64(x / Float64(z * Float64(-t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x / (y * t);
	tmp = 0.0;
	if (t <= -9.5e-86)
		tmp = t_1;
	elseif (t <= 2.1e-116)
		tmp = x / (y * -z);
	elseif ((t <= 1.8e+20) || (~((t <= 1.95e+174)) && (t <= 2.2e+239)))
		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[(y * t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -9.5e-86], t$95$1, If[LessEqual[t, 2.1e-116], N[(x / N[(y * (-z)), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[t, 1.8e+20], And[N[Not[LessEqual[t, 1.95e+174]], $MachinePrecision], LessEqual[t, 2.2e+239]]], t$95$1, N[(x / N[(z * (-t)), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if t < -9.4999999999999996e-86 or 2.0999999999999999e-116 < t < 1.8e20 or 1.9499999999999999e174 < t < 2.20000000000000005e239

   1. Initial program 88.2%

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

   3. Taylor expanded in z around 0 49.8%

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

   if -9.4999999999999996e-86 < t < 2.0999999999999999e-116

   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. add-sqr-sqrt 38.4%

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

      2. times-frac 43.4%

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

   4. Applied egg-rr 43.4%

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

   5. Taylor expanded in t around 0 78.3%

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

      1. associate-*r/ 78.3%

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

      2. neg-mul-1 78.3%

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

   7. Simplified 78.3%

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

   8. Taylor expanded in z around 0 52.5%

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

      1. *-commutative 52.5%

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

   10. Simplified 52.5%

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

   if 1.8e20 < t < 1.9499999999999999e174 or 2.20000000000000005e239 < t

   1. Initial program 85.1%

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

      1. associate-/l/ 98.2%

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

   3. Simplified 98.2%

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

   5. Taylor expanded in t around inf 84.7%

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

   6. Taylor expanded in y around 0 55.4%

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

      1. associate-*r/ 55.4%

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

      2. neg-mul-1 55.4%

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

   8. Simplified 55.4%

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

4. Final simplification 51.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -9.5 \cdot 10^{-86}:\\ \;\;\;\;\frac{x}{y \cdot t}\\ \mathbf{elif}\;t \leq 2.1 \cdot 10^{-116}:\\ \;\;\;\;\frac{x}{y \cdot \left(-z\right)}\\ \mathbf{elif}\;t \leq 1.8 \cdot 10^{+20} \lor \neg \left(t \leq 1.95 \cdot 10^{+174}\right) \land t \leq 2.2 \cdot 10^{+239}:\\ \;\;\;\;\frac{x}{y \cdot t}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{z \cdot \left(-t\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 47.5% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{y \cdot t}\\ \mathbf{if}\;t \leq -4.1 \cdot 10^{-86}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 4.1 \cdot 10^{-116}:\\ \;\;\;\;\frac{x}{y \cdot \left(-z\right)}\\ \mathbf{elif}\;t \leq 2.05 \cdot 10^{+20}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 4.1 \cdot 10^{+173}:\\ \;\;\;\;\frac{x}{z \cdot \left(-t\right)}\\ \mathbf{elif}\;t \leq 1.85 \cdot 10^{+239}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{-t}}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ x (* y t))))
   (if (<= t -4.1e-86)
     t_1
     (if (<= t 4.1e-116)
       (/ x (* y (- z)))
       (if (<= t 2.05e+20)
         t_1
         (if (<= t 4.1e+173)
           (/ x (* z (- t)))
           (if (<= t 1.85e+239) t_1 (/ (/ x (- t)) z))))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x / (y * t);
	double tmp;
	if (t <= -4.1e-86) {
		tmp = t_1;
	} else if (t <= 4.1e-116) {
		tmp = x / (y * -z);
	} else if (t <= 2.05e+20) {
		tmp = t_1;
	} else if (t <= 4.1e+173) {
		tmp = x / (z * -t);
	} else if (t <= 1.85e+239) {
		tmp = t_1;
	} else {
		tmp = (x / -t) / 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) :: t_1
    real(8) :: tmp
    t_1 = x / (y * t)
    if (t <= (-4.1d-86)) then
        tmp = t_1
    else if (t <= 4.1d-116) then
        tmp = x / (y * -z)
    else if (t <= 2.05d+20) then
        tmp = t_1
    else if (t <= 4.1d+173) then
        tmp = x / (z * -t)
    else if (t <= 1.85d+239) then
        tmp = t_1
    else
        tmp = (x / -t) / z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = x / (y * t);
	double tmp;
	if (t <= -4.1e-86) {
		tmp = t_1;
	} else if (t <= 4.1e-116) {
		tmp = x / (y * -z);
	} else if (t <= 2.05e+20) {
		tmp = t_1;
	} else if (t <= 4.1e+173) {
		tmp = x / (z * -t);
	} else if (t <= 1.85e+239) {
		tmp = t_1;
	} else {
		tmp = (x / -t) / z;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x / (y * t)
	tmp = 0
	if t <= -4.1e-86:
		tmp = t_1
	elif t <= 4.1e-116:
		tmp = x / (y * -z)
	elif t <= 2.05e+20:
		tmp = t_1
	elif t <= 4.1e+173:
		tmp = x / (z * -t)
	elif t <= 1.85e+239:
		tmp = t_1
	else:
		tmp = (x / -t) / z
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x / Float64(y * t))
	tmp = 0.0
	if (t <= -4.1e-86)
		tmp = t_1;
	elseif (t <= 4.1e-116)
		tmp = Float64(x / Float64(y * Float64(-z)));
	elseif (t <= 2.05e+20)
		tmp = t_1;
	elseif (t <= 4.1e+173)
		tmp = Float64(x / Float64(z * Float64(-t)));
	elseif (t <= 1.85e+239)
		tmp = t_1;
	else
		tmp = Float64(Float64(x / Float64(-t)) / z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x / (y * t);
	tmp = 0.0;
	if (t <= -4.1e-86)
		tmp = t_1;
	elseif (t <= 4.1e-116)
		tmp = x / (y * -z);
	elseif (t <= 2.05e+20)
		tmp = t_1;
	elseif (t <= 4.1e+173)
		tmp = x / (z * -t);
	elseif (t <= 1.85e+239)
		tmp = t_1;
	else
		tmp = (x / -t) / z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x / N[(y * t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -4.1e-86], t$95$1, If[LessEqual[t, 4.1e-116], N[(x / N[(y * (-z)), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 2.05e+20], t$95$1, If[LessEqual[t, 4.1e+173], N[(x / N[(z * (-t)), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.85e+239], t$95$1, N[(N[(x / (-t)), $MachinePrecision] / z), $MachinePrecision]]]]]]]

Derivation

1. Split input into 4 regimes

2. if t < -4.09999999999999979e-86 or 4.0999999999999999e-116 < t < 2.05e20 or 4.09999999999999976e173 < t < 1.84999999999999999e239

   1. Initial program 88.2%

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

   3. Taylor expanded in z around 0 49.8%

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

   if -4.09999999999999979e-86 < t < 4.0999999999999999e-116

   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. add-sqr-sqrt 38.4%

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

      2. times-frac 43.4%

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

   4. Applied egg-rr 43.4%

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

   5. Taylor expanded in t around 0 78.3%

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

      1. associate-*r/ 78.3%

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

      2. neg-mul-1 78.3%

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

   7. Simplified 78.3%

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

   8. Taylor expanded in z around 0 52.5%

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

      1. *-commutative 52.5%

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

   10. Simplified 52.5%

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

   if 2.05e20 < t < 4.09999999999999976e173

   1. Initial program 88.8%

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

      1. associate-/l/ 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in t around inf 83.8%

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

   6. Taylor expanded in y around 0 53.4%

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

      1. associate-*r/ 53.4%

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

      2. neg-mul-1 53.4%

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

   8. Simplified 53.4%

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

   if 1.84999999999999999e239 < t

   1. Initial program 75.2%

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

      1. associate-/l/ 93.5%

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

   3. Simplified 93.5%

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

   5. Taylor expanded in t around inf 87.4%

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

   6. Taylor expanded in y around 0 61.0%

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

      1. associate-*r/ 61.0%

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

      2. neg-mul-1 61.0%

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

   8. Simplified 61.0%

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

   9. Taylor expanded in x around 0 61.0%

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

       1. mul-1-neg 61.0%

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

       2. associate-/r* 55.5%

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

       3. distribute-neg-frac2 55.5%

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

   11. Simplified 55.5%

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

4. Final simplification 51.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -4.1 \cdot 10^{-86}:\\ \;\;\;\;\frac{x}{y \cdot t}\\ \mathbf{elif}\;t \leq 4.1 \cdot 10^{-116}:\\ \;\;\;\;\frac{x}{y \cdot \left(-z\right)}\\ \mathbf{elif}\;t \leq 2.05 \cdot 10^{+20}:\\ \;\;\;\;\frac{x}{y \cdot t}\\ \mathbf{elif}\;t \leq 4.1 \cdot 10^{+173}:\\ \;\;\;\;\frac{x}{z \cdot \left(-t\right)}\\ \mathbf{elif}\;t \leq 1.85 \cdot 10^{+239}:\\ \;\;\;\;\frac{x}{y \cdot t}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{-t}}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 48.6% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{y \cdot t}\\ \mathbf{if}\;t \leq -6.1 \cdot 10^{-86}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 3.5 \cdot 10^{-116}:\\ \;\;\;\;\frac{\frac{x}{-z}}{y}\\ \mathbf{elif}\;t \leq 6.2 \cdot 10^{+19}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 1.1 \cdot 10^{+174}:\\ \;\;\;\;\frac{x}{z \cdot \left(-t\right)}\\ \mathbf{elif}\;t \leq 3.3 \cdot 10^{+239}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{-t}}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ x (* y t))))
   (if (<= t -6.1e-86)
     t_1
     (if (<= t 3.5e-116)
       (/ (/ x (- z)) y)
       (if (<= t 6.2e+19)
         t_1
         (if (<= t 1.1e+174)
           (/ x (* z (- t)))
           (if (<= t 3.3e+239) t_1 (/ (/ x (- t)) z))))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x / (y * t);
	double tmp;
	if (t <= -6.1e-86) {
		tmp = t_1;
	} else if (t <= 3.5e-116) {
		tmp = (x / -z) / y;
	} else if (t <= 6.2e+19) {
		tmp = t_1;
	} else if (t <= 1.1e+174) {
		tmp = x / (z * -t);
	} else if (t <= 3.3e+239) {
		tmp = t_1;
	} else {
		tmp = (x / -t) / 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) :: t_1
    real(8) :: tmp
    t_1 = x / (y * t)
    if (t <= (-6.1d-86)) then
        tmp = t_1
    else if (t <= 3.5d-116) then
        tmp = (x / -z) / y
    else if (t <= 6.2d+19) then
        tmp = t_1
    else if (t <= 1.1d+174) then
        tmp = x / (z * -t)
    else if (t <= 3.3d+239) then
        tmp = t_1
    else
        tmp = (x / -t) / z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = x / (y * t);
	double tmp;
	if (t <= -6.1e-86) {
		tmp = t_1;
	} else if (t <= 3.5e-116) {
		tmp = (x / -z) / y;
	} else if (t <= 6.2e+19) {
		tmp = t_1;
	} else if (t <= 1.1e+174) {
		tmp = x / (z * -t);
	} else if (t <= 3.3e+239) {
		tmp = t_1;
	} else {
		tmp = (x / -t) / z;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x / (y * t)
	tmp = 0
	if t <= -6.1e-86:
		tmp = t_1
	elif t <= 3.5e-116:
		tmp = (x / -z) / y
	elif t <= 6.2e+19:
		tmp = t_1
	elif t <= 1.1e+174:
		tmp = x / (z * -t)
	elif t <= 3.3e+239:
		tmp = t_1
	else:
		tmp = (x / -t) / z
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x / Float64(y * t))
	tmp = 0.0
	if (t <= -6.1e-86)
		tmp = t_1;
	elseif (t <= 3.5e-116)
		tmp = Float64(Float64(x / Float64(-z)) / y);
	elseif (t <= 6.2e+19)
		tmp = t_1;
	elseif (t <= 1.1e+174)
		tmp = Float64(x / Float64(z * Float64(-t)));
	elseif (t <= 3.3e+239)
		tmp = t_1;
	else
		tmp = Float64(Float64(x / Float64(-t)) / z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x / (y * t);
	tmp = 0.0;
	if (t <= -6.1e-86)
		tmp = t_1;
	elseif (t <= 3.5e-116)
		tmp = (x / -z) / y;
	elseif (t <= 6.2e+19)
		tmp = t_1;
	elseif (t <= 1.1e+174)
		tmp = x / (z * -t);
	elseif (t <= 3.3e+239)
		tmp = t_1;
	else
		tmp = (x / -t) / z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x / N[(y * t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -6.1e-86], t$95$1, If[LessEqual[t, 3.5e-116], N[(N[(x / (-z)), $MachinePrecision] / y), $MachinePrecision], If[LessEqual[t, 6.2e+19], t$95$1, If[LessEqual[t, 1.1e+174], N[(x / N[(z * (-t)), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 3.3e+239], t$95$1, N[(N[(x / (-t)), $MachinePrecision] / z), $MachinePrecision]]]]]]]

Derivation

1. Split input into 4 regimes

2. if t < -6.10000000000000032e-86 or 3.49999999999999984e-116 < t < 6.2e19 or 1.1000000000000001e174 < t < 3.2999999999999998e239

   1. Initial program 88.2%

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

   3. Taylor expanded in z around 0 49.8%

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

   if -6.10000000000000032e-86 < t < 3.49999999999999984e-116

   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. add-sqr-sqrt 38.4%

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

      2. times-frac 43.4%

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

   4. Applied egg-rr 43.4%

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

   5. Taylor expanded in t around 0 78.3%

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

      1. associate-*r/ 78.3%

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

      2. neg-mul-1 78.3%

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

   7. Simplified 78.3%

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

   8. Taylor expanded in z around 0 52.5%

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

      1. mul-1-neg 52.5%

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

      2. associate-/r* 53.1%

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

      3. distribute-neg-frac2 53.1%

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

   10. Simplified 53.1%

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

   11. Taylor expanded in x around 0 52.5%

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

       1. associate-/l/ 58.6%

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

       2. associate-*r/ 58.6%

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

       3. associate-*r/ 58.6%

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

       4. neg-mul-1 58.6%

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

   13. Simplified 58.6%

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

   if 6.2e19 < t < 1.1000000000000001e174

   1. Initial program 88.8%

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

      1. associate-/l/ 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in t around inf 83.8%

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

   6. Taylor expanded in y around 0 53.4%

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

      1. associate-*r/ 53.4%

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

      2. neg-mul-1 53.4%

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

   8. Simplified 53.4%

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

   if 3.2999999999999998e239 < t

   1. Initial program 75.2%

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

      1. associate-/l/ 93.5%

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

   3. Simplified 93.5%

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

   5. Taylor expanded in t around inf 87.4%

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

   6. Taylor expanded in y around 0 61.0%

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

      1. associate-*r/ 61.0%

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

      2. neg-mul-1 61.0%

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

   8. Simplified 61.0%

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

   9. Taylor expanded in x around 0 61.0%

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

       1. mul-1-neg 61.0%

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

       2. associate-/r* 55.5%

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

       3. distribute-neg-frac2 55.5%

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

   11. Simplified 55.5%

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

4. Final simplification 53.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -6.1 \cdot 10^{-86}:\\ \;\;\;\;\frac{x}{y \cdot t}\\ \mathbf{elif}\;t \leq 3.5 \cdot 10^{-116}:\\ \;\;\;\;\frac{\frac{x}{-z}}{y}\\ \mathbf{elif}\;t \leq 6.2 \cdot 10^{+19}:\\ \;\;\;\;\frac{x}{y \cdot t}\\ \mathbf{elif}\;t \leq 1.1 \cdot 10^{+174}:\\ \;\;\;\;\frac{x}{z \cdot \left(-t\right)}\\ \mathbf{elif}\;t \leq 3.3 \cdot 10^{+239}:\\ \;\;\;\;\frac{x}{y \cdot t}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{-t}}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 72.8% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{y - z}\\ \mathbf{if}\;y \leq -0.0017:\\ \;\;\;\;\frac{\frac{x}{y}}{t - z}\\ \mathbf{elif}\;y \leq -2.8 \cdot 10^{-24}:\\ \;\;\;\;t\_1 \cdot \frac{-1}{z}\\ \mathbf{elif}\;y \leq -8.5 \cdot 10^{-84}:\\ \;\;\;\;\frac{t\_1}{t}\\ \mathbf{elif}\;y \leq 6.5 \cdot 10^{-188}:\\ \;\;\;\;\frac{\frac{x}{z}}{z - t}\\ \mathbf{else}:\\ \;\;\;\;\frac{-1}{\frac{t}{x} \cdot \left(z - y\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ x (- y z))))
   (if (<= y -0.0017)
     (/ (/ x y) (- t z))
     (if (<= y -2.8e-24)
       (* t_1 (/ -1.0 z))
       (if (<= y -8.5e-84)
         (/ t_1 t)
         (if (<= y 6.5e-188)
           (/ (/ x z) (- z t))
           (/ -1.0 (* (/ t x) (- z y)))))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x / (y - z);
	double tmp;
	if (y <= -0.0017) {
		tmp = (x / y) / (t - z);
	} else if (y <= -2.8e-24) {
		tmp = t_1 * (-1.0 / z);
	} else if (y <= -8.5e-84) {
		tmp = t_1 / t;
	} else if (y <= 6.5e-188) {
		tmp = (x / z) / (z - t);
	} else {
		tmp = -1.0 / ((t / x) * (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) :: t_1
    real(8) :: tmp
    t_1 = x / (y - z)
    if (y <= (-0.0017d0)) then
        tmp = (x / y) / (t - z)
    else if (y <= (-2.8d-24)) then
        tmp = t_1 * ((-1.0d0) / z)
    else if (y <= (-8.5d-84)) then
        tmp = t_1 / t
    else if (y <= 6.5d-188) then
        tmp = (x / z) / (z - t)
    else
        tmp = (-1.0d0) / ((t / x) * (z - y))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = x / (y - z);
	double tmp;
	if (y <= -0.0017) {
		tmp = (x / y) / (t - z);
	} else if (y <= -2.8e-24) {
		tmp = t_1 * (-1.0 / z);
	} else if (y <= -8.5e-84) {
		tmp = t_1 / t;
	} else if (y <= 6.5e-188) {
		tmp = (x / z) / (z - t);
	} else {
		tmp = -1.0 / ((t / x) * (z - y));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x / (y - z)
	tmp = 0
	if y <= -0.0017:
		tmp = (x / y) / (t - z)
	elif y <= -2.8e-24:
		tmp = t_1 * (-1.0 / z)
	elif y <= -8.5e-84:
		tmp = t_1 / t
	elif y <= 6.5e-188:
		tmp = (x / z) / (z - t)
	else:
		tmp = -1.0 / ((t / x) * (z - y))
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x / Float64(y - z))
	tmp = 0.0
	if (y <= -0.0017)
		tmp = Float64(Float64(x / y) / Float64(t - z));
	elseif (y <= -2.8e-24)
		tmp = Float64(t_1 * Float64(-1.0 / z));
	elseif (y <= -8.5e-84)
		tmp = Float64(t_1 / t);
	elseif (y <= 6.5e-188)
		tmp = Float64(Float64(x / z) / Float64(z - t));
	else
		tmp = Float64(-1.0 / Float64(Float64(t / x) * Float64(z - y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x / (y - z);
	tmp = 0.0;
	if (y <= -0.0017)
		tmp = (x / y) / (t - z);
	elseif (y <= -2.8e-24)
		tmp = t_1 * (-1.0 / z);
	elseif (y <= -8.5e-84)
		tmp = t_1 / t;
	elseif (y <= 6.5e-188)
		tmp = (x / z) / (z - t);
	else
		tmp = -1.0 / ((t / x) * (z - y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x / N[(y - z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -0.0017], N[(N[(x / y), $MachinePrecision] / N[(t - z), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -2.8e-24], N[(t$95$1 * N[(-1.0 / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -8.5e-84], N[(t$95$1 / t), $MachinePrecision], If[LessEqual[y, 6.5e-188], N[(N[(x / z), $MachinePrecision] / N[(z - t), $MachinePrecision]), $MachinePrecision], N[(-1.0 / N[(N[(t / x), $MachinePrecision] * N[(z - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 5 regimes

2. if y < -0.00169999999999999991

   1. Initial program 84.7%

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

      1. add-sqr-sqrt 42.1%

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

      2. times-frac 49.1%

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

   4. Applied egg-rr 49.1%

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

   5. Taylor expanded in y around inf 82.9%

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

      1. associate-/r* 84.4%

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

   7. Simplified 84.4%

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

   if -0.00169999999999999991 < y < -2.8000000000000002e-24

   1. Initial program 80.7%

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

      1. associate-/r* 99.7%

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

      2. div-inv 100.0%

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

   4. Applied egg-rr 100.0%

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

   5. Taylor expanded in t around 0 99.7%

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

   if -2.8000000000000002e-24 < y < -8.4999999999999994e-84

   1. Initial program 94.1%

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

      1. add-sqr-sqrt 41.1%

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

      2. times-frac 46.8%

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

   4. Applied egg-rr 46.8%

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

      1. frac-times 41.1%

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

      2. add-sqr-sqrt 94.1%

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

      3. *-rgt-identity 94.1%

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

      4. frac-times 99.8%

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

      5. clear-num 99.8%

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

      6. associate-*l/ 99.4%

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

      7. *-un-lft-identity 99.4%

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

   6. Applied egg-rr 99.4%

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

   7. Taylor expanded in t around inf 65.9%

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

      1. associate-/l/ 77.1%

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

   9. Simplified 77.1%

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

   if -8.4999999999999994e-84 < y < 6.4999999999999998e-188

   1. Initial program 91.9%

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

   3. Taylor expanded in x around 0 91.9%

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

      1. associate-/l/ 91.1%

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

   5. Simplified 91.1%

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

   6. Taylor expanded in y around 0 79.4%

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

      1. mul-1-neg 79.4%

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

   8. Simplified 79.4%

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

   if 6.4999999999999998e-188 < y

   1. Initial program 85.4%

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

      1. associate-/l/ 96.8%

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

   3. Simplified 96.8%

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

   5. Taylor expanded in t around inf 54.7%

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

      1. clear-num 54.6%

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

      2. inv-pow 54.6%

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

      3. div-inv 54.6%

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

      4. clear-num 54.6%

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

   7. Applied egg-rr 54.6%

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

      1. unpow-1 54.6%

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

   9. Simplified 54.6%

      \[\leadsto \color{blue}{\frac{1}{\left(y - z\right) \cdot \frac{t}{x}}} \]
3. Recombined 5 regimes into one program.

4. Final simplification 72.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -0.0017:\\ \;\;\;\;\frac{\frac{x}{y}}{t - z}\\ \mathbf{elif}\;y \leq -2.8 \cdot 10^{-24}:\\ \;\;\;\;\frac{x}{y - z} \cdot \frac{-1}{z}\\ \mathbf{elif}\;y \leq -8.5 \cdot 10^{-84}:\\ \;\;\;\;\frac{\frac{x}{y - z}}{t}\\ \mathbf{elif}\;y \leq 6.5 \cdot 10^{-188}:\\ \;\;\;\;\frac{\frac{x}{z}}{z - t}\\ \mathbf{else}:\\ \;\;\;\;\frac{-1}{\frac{t}{x} \cdot \left(z - y\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 73.1% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{\frac{x}{z}}{z - t}\\ \mathbf{if}\;y \leq -8.2 \cdot 10^{-6}:\\ \;\;\;\;\frac{\frac{x}{y}}{t - z}\\ \mathbf{elif}\;y \leq -2.6 \cdot 10^{-24}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq -2.9 \cdot 10^{-84}:\\ \;\;\;\;\frac{\frac{x}{y - z}}{t}\\ \mathbf{elif}\;y \leq 6.2 \cdot 10^{-170}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{t}}{y - z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ (/ x z) (- z t))))
   (if (<= y -8.2e-6)
     (/ (/ x y) (- t z))
     (if (<= y -2.6e-24)
       t_1
       (if (<= y -2.9e-84)
         (/ (/ x (- y z)) t)
         (if (<= y 6.2e-170) t_1 (/ (/ x t) (- y z))))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (x / z) / (z - t);
	double tmp;
	if (y <= -8.2e-6) {
		tmp = (x / y) / (t - z);
	} else if (y <= -2.6e-24) {
		tmp = t_1;
	} else if (y <= -2.9e-84) {
		tmp = (x / (y - z)) / t;
	} else if (y <= 6.2e-170) {
		tmp = t_1;
	} else {
		tmp = (x / t) / (y - 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) :: t_1
    real(8) :: tmp
    t_1 = (x / z) / (z - t)
    if (y <= (-8.2d-6)) then
        tmp = (x / y) / (t - z)
    else if (y <= (-2.6d-24)) then
        tmp = t_1
    else if (y <= (-2.9d-84)) then
        tmp = (x / (y - z)) / t
    else if (y <= 6.2d-170) then
        tmp = t_1
    else
        tmp = (x / t) / (y - z)
    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 - t);
	double tmp;
	if (y <= -8.2e-6) {
		tmp = (x / y) / (t - z);
	} else if (y <= -2.6e-24) {
		tmp = t_1;
	} else if (y <= -2.9e-84) {
		tmp = (x / (y - z)) / t;
	} else if (y <= 6.2e-170) {
		tmp = t_1;
	} else {
		tmp = (x / t) / (y - z);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (x / z) / (z - t)
	tmp = 0
	if y <= -8.2e-6:
		tmp = (x / y) / (t - z)
	elif y <= -2.6e-24:
		tmp = t_1
	elif y <= -2.9e-84:
		tmp = (x / (y - z)) / t
	elif y <= 6.2e-170:
		tmp = t_1
	else:
		tmp = (x / t) / (y - z)
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(x / z) / Float64(z - t))
	tmp = 0.0
	if (y <= -8.2e-6)
		tmp = Float64(Float64(x / y) / Float64(t - z));
	elseif (y <= -2.6e-24)
		tmp = t_1;
	elseif (y <= -2.9e-84)
		tmp = Float64(Float64(x / Float64(y - z)) / t);
	elseif (y <= 6.2e-170)
		tmp = t_1;
	else
		tmp = Float64(Float64(x / t) / Float64(y - z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (x / z) / (z - t);
	tmp = 0.0;
	if (y <= -8.2e-6)
		tmp = (x / y) / (t - z);
	elseif (y <= -2.6e-24)
		tmp = t_1;
	elseif (y <= -2.9e-84)
		tmp = (x / (y - z)) / t;
	elseif (y <= 6.2e-170)
		tmp = t_1;
	else
		tmp = (x / t) / (y - z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(x / z), $MachinePrecision] / N[(z - t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -8.2e-6], N[(N[(x / y), $MachinePrecision] / N[(t - z), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -2.6e-24], t$95$1, If[LessEqual[y, -2.9e-84], N[(N[(x / N[(y - z), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision], If[LessEqual[y, 6.2e-170], t$95$1, N[(N[(x / t), $MachinePrecision] / N[(y - z), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -8.1999999999999994e-6

   1. Initial program 84.9%

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

      1. add-sqr-sqrt 41.5%

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

      2. times-frac 48.3%

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

   4. Applied egg-rr 48.3%

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

   5. Taylor expanded in y around inf 83.1%

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

      1. associate-/r* 84.6%

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

   7. Simplified 84.6%

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

   if -8.1999999999999994e-6 < y < -2.6e-24 or -2.90000000000000019e-84 < y < 6.19999999999999971e-170

   1. Initial program 91.4%

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

   3. Taylor expanded in x around 0 91.4%

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

      1. associate-/l/ 91.8%

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

   5. Simplified 91.8%

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

   6. Taylor expanded in y around 0 80.1%

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

      1. mul-1-neg 80.1%

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

   8. Simplified 80.1%

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

   if -2.6e-24 < y < -2.90000000000000019e-84

   1. Initial program 94.1%

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

      1. add-sqr-sqrt 41.1%

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

      2. times-frac 46.8%

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

   4. Applied egg-rr 46.8%

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

      1. frac-times 41.1%

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

      2. add-sqr-sqrt 94.1%

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

      3. *-rgt-identity 94.1%

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

      4. frac-times 99.8%

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

      5. clear-num 99.8%

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

      6. associate-*l/ 99.4%

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

      7. *-un-lft-identity 99.4%

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

   6. Applied egg-rr 99.4%

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

   7. Taylor expanded in t around inf 65.9%

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

      1. associate-/l/ 77.1%

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

   9. Simplified 77.1%

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

   if 6.19999999999999971e-170 < y

   1. Initial program 84.9%

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

      1. associate-/l/ 96.7%

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

   3. Simplified 96.7%

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

   5. Taylor expanded in t around inf 55.3%

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

4. Final simplification 72.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -8.2 \cdot 10^{-6}:\\ \;\;\;\;\frac{\frac{x}{y}}{t - z}\\ \mathbf{elif}\;y \leq -2.6 \cdot 10^{-24}:\\ \;\;\;\;\frac{\frac{x}{z}}{z - t}\\ \mathbf{elif}\;y \leq -2.9 \cdot 10^{-84}:\\ \;\;\;\;\frac{\frac{x}{y - z}}{t}\\ \mathbf{elif}\;y \leq 6.2 \cdot 10^{-170}:\\ \;\;\;\;\frac{\frac{x}{z}}{z - t}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{t}}{y - z}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 73.1% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{y - z}\\ \mathbf{if}\;y \leq -0.0028:\\ \;\;\;\;\frac{\frac{x}{y}}{t - z}\\ \mathbf{elif}\;y \leq -4.5 \cdot 10^{-24}:\\ \;\;\;\;t\_1 \cdot \frac{-1}{z}\\ \mathbf{elif}\;y \leq -7.9 \cdot 10^{-84}:\\ \;\;\;\;\frac{t\_1}{t}\\ \mathbf{elif}\;y \leq 7.5 \cdot 10^{-170}:\\ \;\;\;\;\frac{\frac{x}{z}}{z - t}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{t}}{y - z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ x (- y z))))
   (if (<= y -0.0028)
     (/ (/ x y) (- t z))
     (if (<= y -4.5e-24)
       (* t_1 (/ -1.0 z))
       (if (<= y -7.9e-84)
         (/ t_1 t)
         (if (<= y 7.5e-170) (/ (/ x z) (- z t)) (/ (/ x t) (- y z))))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x / (y - z);
	double tmp;
	if (y <= -0.0028) {
		tmp = (x / y) / (t - z);
	} else if (y <= -4.5e-24) {
		tmp = t_1 * (-1.0 / z);
	} else if (y <= -7.9e-84) {
		tmp = t_1 / t;
	} else if (y <= 7.5e-170) {
		tmp = (x / z) / (z - t);
	} else {
		tmp = (x / t) / (y - 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) :: t_1
    real(8) :: tmp
    t_1 = x / (y - z)
    if (y <= (-0.0028d0)) then
        tmp = (x / y) / (t - z)
    else if (y <= (-4.5d-24)) then
        tmp = t_1 * ((-1.0d0) / z)
    else if (y <= (-7.9d-84)) then
        tmp = t_1 / t
    else if (y <= 7.5d-170) then
        tmp = (x / z) / (z - t)
    else
        tmp = (x / t) / (y - z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = x / (y - z);
	double tmp;
	if (y <= -0.0028) {
		tmp = (x / y) / (t - z);
	} else if (y <= -4.5e-24) {
		tmp = t_1 * (-1.0 / z);
	} else if (y <= -7.9e-84) {
		tmp = t_1 / t;
	} else if (y <= 7.5e-170) {
		tmp = (x / z) / (z - t);
	} else {
		tmp = (x / t) / (y - z);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x / (y - z)
	tmp = 0
	if y <= -0.0028:
		tmp = (x / y) / (t - z)
	elif y <= -4.5e-24:
		tmp = t_1 * (-1.0 / z)
	elif y <= -7.9e-84:
		tmp = t_1 / t
	elif y <= 7.5e-170:
		tmp = (x / z) / (z - t)
	else:
		tmp = (x / t) / (y - z)
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x / Float64(y - z))
	tmp = 0.0
	if (y <= -0.0028)
		tmp = Float64(Float64(x / y) / Float64(t - z));
	elseif (y <= -4.5e-24)
		tmp = Float64(t_1 * Float64(-1.0 / z));
	elseif (y <= -7.9e-84)
		tmp = Float64(t_1 / t);
	elseif (y <= 7.5e-170)
		tmp = Float64(Float64(x / z) / Float64(z - t));
	else
		tmp = Float64(Float64(x / t) / Float64(y - z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x / (y - z);
	tmp = 0.0;
	if (y <= -0.0028)
		tmp = (x / y) / (t - z);
	elseif (y <= -4.5e-24)
		tmp = t_1 * (-1.0 / z);
	elseif (y <= -7.9e-84)
		tmp = t_1 / t;
	elseif (y <= 7.5e-170)
		tmp = (x / z) / (z - t);
	else
		tmp = (x / t) / (y - z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x / N[(y - z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -0.0028], N[(N[(x / y), $MachinePrecision] / N[(t - z), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -4.5e-24], N[(t$95$1 * N[(-1.0 / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -7.9e-84], N[(t$95$1 / t), $MachinePrecision], If[LessEqual[y, 7.5e-170], N[(N[(x / z), $MachinePrecision] / N[(z - t), $MachinePrecision]), $MachinePrecision], N[(N[(x / t), $MachinePrecision] / N[(y - z), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 5 regimes

2. if y < -0.00279999999999999997

   1. Initial program 84.7%

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

      1. add-sqr-sqrt 42.1%

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

      2. times-frac 49.1%

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

   4. Applied egg-rr 49.1%

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

   5. Taylor expanded in y around inf 82.9%

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

      1. associate-/r* 84.4%

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

   7. Simplified 84.4%

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

   if -0.00279999999999999997 < y < -4.4999999999999997e-24

   1. Initial program 80.7%

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

      1. associate-/r* 99.7%

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

      2. div-inv 100.0%

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

   4. Applied egg-rr 100.0%

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

   5. Taylor expanded in t around 0 99.7%

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

   if -4.4999999999999997e-24 < y < -7.89999999999999991e-84

   1. Initial program 94.1%

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

      1. add-sqr-sqrt 41.1%

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

      2. times-frac 46.8%

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

   4. Applied egg-rr 46.8%

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

      1. frac-times 41.1%

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

      2. add-sqr-sqrt 94.1%

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

      3. *-rgt-identity 94.1%

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

      4. frac-times 99.8%

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

      5. clear-num 99.8%

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

      6. associate-*l/ 99.4%

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

      7. *-un-lft-identity 99.4%

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

   6. Applied egg-rr 99.4%

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

   7. Taylor expanded in t around inf 65.9%

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

      1. associate-/l/ 77.1%

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

   9. Simplified 77.1%

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

   if -7.89999999999999991e-84 < y < 7.4999999999999998e-170

   1. Initial program 92.2%

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

   3. Taylor expanded in x around 0 92.2%

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

      1. associate-/l/ 91.4%

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

   5. Simplified 91.4%

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

   6. Taylor expanded in y around 0 79.1%

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

      1. mul-1-neg 79.1%

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

   8. Simplified 79.1%

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

   if 7.4999999999999998e-170 < y

   1. Initial program 84.9%

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

      1. associate-/l/ 96.7%

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

   3. Simplified 96.7%

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

   5. Taylor expanded in t around inf 55.3%

      \[\leadsto \frac{\color{blue}{\frac{x}{t}}}{y - z} \]
3. Recombined 5 regimes into one program.

4. Final simplification 72.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -0.0028:\\ \;\;\;\;\frac{\frac{x}{y}}{t - z}\\ \mathbf{elif}\;y \leq -4.5 \cdot 10^{-24}:\\ \;\;\;\;\frac{x}{y - z} \cdot \frac{-1}{z}\\ \mathbf{elif}\;y \leq -7.9 \cdot 10^{-84}:\\ \;\;\;\;\frac{\frac{x}{y - z}}{t}\\ \mathbf{elif}\;y \leq 7.5 \cdot 10^{-170}:\\ \;\;\;\;\frac{\frac{x}{z}}{z - t}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{t}}{y - z}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 67.5% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -6 \cdot 10^{-50}:\\ \;\;\;\;\frac{\frac{x}{y}}{t - z}\\ \mathbf{elif}\;y \leq -5.5 \cdot 10^{-235} \lor \neg \left(y \leq 1.45 \cdot 10^{-304}\right):\\ \;\;\;\;\frac{\frac{x}{y - z}}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{z \cdot \left(z + t\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -6e-50)
   (/ (/ x y) (- t z))
   (if (or (<= y -5.5e-235) (not (<= y 1.45e-304)))
     (/ (/ x (- y z)) t)
     (/ x (* z (+ z t))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -6e-50) {
		tmp = (x / y) / (t - z);
	} else if ((y <= -5.5e-235) || !(y <= 1.45e-304)) {
		tmp = (x / (y - z)) / t;
	} else {
		tmp = x / (z * (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 <= (-6d-50)) then
        tmp = (x / y) / (t - z)
    else if ((y <= (-5.5d-235)) .or. (.not. (y <= 1.45d-304))) then
        tmp = (x / (y - z)) / t
    else
        tmp = x / (z * (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 <= -6e-50) {
		tmp = (x / y) / (t - z);
	} else if ((y <= -5.5e-235) || !(y <= 1.45e-304)) {
		tmp = (x / (y - z)) / t;
	} else {
		tmp = x / (z * (z + t));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -6e-50:
		tmp = (x / y) / (t - z)
	elif (y <= -5.5e-235) or not (y <= 1.45e-304):
		tmp = (x / (y - z)) / t
	else:
		tmp = x / (z * (z + t))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -6e-50)
		tmp = Float64(Float64(x / y) / Float64(t - z));
	elseif ((y <= -5.5e-235) || !(y <= 1.45e-304))
		tmp = Float64(Float64(x / Float64(y - z)) / t);
	else
		tmp = Float64(x / Float64(z * Float64(z + t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= -6e-50)
		tmp = (x / y) / (t - z);
	elseif ((y <= -5.5e-235) || ~((y <= 1.45e-304)))
		tmp = (x / (y - z)) / t;
	else
		tmp = x / (z * (z + t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -6e-50], N[(N[(x / y), $MachinePrecision] / N[(t - z), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[y, -5.5e-235], N[Not[LessEqual[y, 1.45e-304]], $MachinePrecision]], N[(N[(x / N[(y - z), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision], N[(x / N[(z * N[(z + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -5.99999999999999981e-50

   1. Initial program 84.7%

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

      1. add-sqr-sqrt 45.3%

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

      2. times-frac 53.5%

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

   4. Applied egg-rr 53.5%

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

   5. Taylor expanded in y around inf 79.6%

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

      1. associate-/r* 80.9%

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

   7. Simplified 80.9%

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

   if -5.99999999999999981e-50 < y < -5.4999999999999998e-235 or 1.45e-304 < y

   1. Initial program 87.8%

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

      1. add-sqr-sqrt 45.7%

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

      2. times-frac 48.3%

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

   4. Applied egg-rr 48.3%

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

      1. frac-times 45.7%

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

      2. add-sqr-sqrt 87.8%

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

      3. *-rgt-identity 87.8%

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

      4. frac-times 95.9%

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

      5. clear-num 95.8%

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

      6. associate-*l/ 96.4%

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

      7. *-un-lft-identity 96.4%

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

   6. Applied egg-rr 96.4%

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

   7. Taylor expanded in t around inf 59.4%

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

      1. associate-/l/ 63.4%

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

   9. Simplified 63.4%

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

   if -5.4999999999999998e-235 < y < 1.45e-304

   1. Initial program 99.5%

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

   3. Taylor expanded in x around 0 99.5%

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

      1. associate-/l/ 72.2%

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

   5. Simplified 72.2%

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

   6. Taylor expanded in y around 0 65.6%

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

      1. mul-1-neg 65.6%

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

   8. Simplified 65.6%

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

      1. add-sqr-sqrt 40.8%

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

      2. sqrt-unprod 45.2%

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

      3. sqr-neg 45.2%

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

      4. sqrt-unprod 18.2%

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

      5. add-sqr-sqrt 28.7%

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

      6. *-un-lft-identity 28.7%

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

      7. associate-/l/ 28.8%

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

      8. sub-neg 28.8%

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

      9. add-sqr-sqrt 19.0%

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

      10. sqrt-unprod 40.3%

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

      11. sqr-neg 40.3%

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

      12. sqrt-unprod 21.4%

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

      13. add-sqr-sqrt 51.6%

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

   10. Applied egg-rr 51.6%

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

       1. *-lft-identity 51.6%

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

       2. *-commutative 51.6%

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

       3. +-commutative 51.6%

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

   12. Simplified 51.6%

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

4. Final simplification 68.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -6 \cdot 10^{-50}:\\ \;\;\;\;\frac{\frac{x}{y}}{t - z}\\ \mathbf{elif}\;y \leq -5.5 \cdot 10^{-235} \lor \neg \left(y \leq 1.45 \cdot 10^{-304}\right):\\ \;\;\;\;\frac{\frac{x}{y - z}}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{z \cdot \left(z + t\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 52.2% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.05 \cdot 10^{+127}:\\ \;\;\;\;\frac{\frac{x}{-z}}{y}\\ \mathbf{elif}\;z \leq -2000000000000:\\ \;\;\;\;\frac{\frac{x}{-t}}{z}\\ \mathbf{elif}\;z \leq 3.8 \cdot 10^{+72}:\\ \;\;\;\;\frac{x}{y} \cdot \frac{1}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{z}}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -1.05e+127)
   (/ (/ x (- z)) y)
   (if (<= z -2000000000000.0)
     (/ (/ x (- t)) z)
     (if (<= z 3.8e+72) (* (/ x y) (/ 1.0 t)) (/ (/ x z) t)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -1.05e+127) {
		tmp = (x / -z) / y;
	} else if (z <= -2000000000000.0) {
		tmp = (x / -t) / z;
	} else if (z <= 3.8e+72) {
		tmp = (x / y) * (1.0 / t);
	} 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 (z <= (-1.05d+127)) then
        tmp = (x / -z) / y
    else if (z <= (-2000000000000.0d0)) then
        tmp = (x / -t) / z
    else if (z <= 3.8d+72) then
        tmp = (x / y) * (1.0d0 / t)
    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 (z <= -1.05e+127) {
		tmp = (x / -z) / y;
	} else if (z <= -2000000000000.0) {
		tmp = (x / -t) / z;
	} else if (z <= 3.8e+72) {
		tmp = (x / y) * (1.0 / t);
	} else {
		tmp = (x / z) / t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -1.05e+127:
		tmp = (x / -z) / y
	elif z <= -2000000000000.0:
		tmp = (x / -t) / z
	elif z <= 3.8e+72:
		tmp = (x / y) * (1.0 / t)
	else:
		tmp = (x / z) / t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -1.05e+127)
		tmp = Float64(Float64(x / Float64(-z)) / y);
	elseif (z <= -2000000000000.0)
		tmp = Float64(Float64(x / Float64(-t)) / z);
	elseif (z <= 3.8e+72)
		tmp = Float64(Float64(x / y) * Float64(1.0 / t));
	else
		tmp = Float64(Float64(x / z) / t);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (z <= -1.05e+127)
		tmp = (x / -z) / y;
	elseif (z <= -2000000000000.0)
		tmp = (x / -t) / z;
	elseif (z <= 3.8e+72)
		tmp = (x / y) * (1.0 / t);
	else
		tmp = (x / z) / t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -1.05e+127], N[(N[(x / (-z)), $MachinePrecision] / y), $MachinePrecision], If[LessEqual[z, -2000000000000.0], N[(N[(x / (-t)), $MachinePrecision] / z), $MachinePrecision], If[LessEqual[z, 3.8e+72], N[(N[(x / y), $MachinePrecision] * N[(1.0 / t), $MachinePrecision]), $MachinePrecision], N[(N[(x / z), $MachinePrecision] / t), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if z < -1.04999999999999996e127

   1. Initial program 83.3%

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

      1. add-sqr-sqrt 39.0%

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

      2. times-frac 46.2%

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

   4. Applied egg-rr 46.2%

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

   5. Taylor expanded in t around 0 83.3%

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

      1. associate-*r/ 83.3%

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

      2. neg-mul-1 83.3%

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

   7. Simplified 83.3%

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

   8. Taylor expanded in z around 0 48.8%

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

      1. mul-1-neg 48.8%

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

      2. associate-/r* 46.2%

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

      3. distribute-neg-frac2 46.2%

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

   10. Simplified 46.2%

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

   11. Taylor expanded in x around 0 48.8%

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

       1. associate-/l/ 55.9%

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

       2. associate-*r/ 55.9%

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

       3. associate-*r/ 55.9%

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

       4. neg-mul-1 55.9%

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

   13. Simplified 55.9%

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

   if -1.04999999999999996e127 < z < -2e12

   1. Initial program 88.0%

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

      1. associate-/l/ 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in t around inf 48.5%

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

   6. Taylor expanded in y around 0 33.5%

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

      1. associate-*r/ 33.5%

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

      2. neg-mul-1 33.5%

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

   8. Simplified 33.5%

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

   9. Taylor expanded in x around 0 33.5%

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

       1. mul-1-neg 33.5%

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

       2. associate-/r* 33.5%

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

       3. distribute-neg-frac2 33.5%

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

   11. Simplified 33.5%

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

   if -2e12 < z < 3.80000000000000006e72

   1. Initial program 93.9%

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

   3. Taylor expanded in z around 0 57.5%

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

      1. *-un-lft-identity 57.5%

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

      2. times-frac 59.2%

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

   5. Applied egg-rr 59.2%

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

   if 3.80000000000000006e72 < z

   1. Initial program 74.5%

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

      1. associate-/l/ 99.7%

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

   3. Simplified 99.7%

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

   5. Taylor expanded in t around inf 35.2%

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

   6. Taylor expanded in y around 0 33.5%

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

      1. associate-*r/ 33.5%

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

      2. neg-mul-1 33.5%

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

   8. Simplified 33.5%

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

      1. div-inv 33.5%

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

      2. add-sqr-sqrt 11.3%

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

      3. sqrt-unprod 36.2%

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

      4. sqr-neg 36.2%

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

      5. sqrt-unprod 20.4%

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

      6. add-sqr-sqrt 31.3%

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

      7. associate-/r* 29.6%

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

   10. Applied egg-rr 29.6%

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

       1. *-commutative 29.6%

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

       2. associate-*l/ 25.7%

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

       3. associate-*r/ 35.0%

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

       4. associate-*l/ 35.0%

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

       5. *-lft-identity 35.0%

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

   12. Simplified 35.0%

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

4. Final simplification 50.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.05 \cdot 10^{+127}:\\ \;\;\;\;\frac{\frac{x}{-z}}{y}\\ \mathbf{elif}\;z \leq -2000000000000:\\ \;\;\;\;\frac{\frac{x}{-t}}{z}\\ \mathbf{elif}\;z \leq 3.8 \cdot 10^{+72}:\\ \;\;\;\;\frac{x}{y} \cdot \frac{1}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{z}}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 52.6% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.4 \cdot 10^{+122}:\\ \;\;\;\;\frac{\frac{x}{-z}}{y}\\ \mathbf{elif}\;z \leq -29000000000000:\\ \;\;\;\;\frac{\frac{x}{-t}}{z}\\ \mathbf{elif}\;z \leq 2.55 \cdot 10^{+72}:\\ \;\;\;\;\frac{x}{y} \cdot \frac{1}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{t \cdot \frac{z}{x}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -2.4e+122)
   (/ (/ x (- z)) y)
   (if (<= z -29000000000000.0)
     (/ (/ x (- t)) z)
     (if (<= z 2.55e+72) (* (/ x y) (/ 1.0 t)) (/ 1.0 (* t (/ z x)))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -2.4e+122) {
		tmp = (x / -z) / y;
	} else if (z <= -29000000000000.0) {
		tmp = (x / -t) / z;
	} else if (z <= 2.55e+72) {
		tmp = (x / y) * (1.0 / t);
	} else {
		tmp = 1.0 / (t * (z / x));
	}
	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 <= (-2.4d+122)) then
        tmp = (x / -z) / y
    else if (z <= (-29000000000000.0d0)) then
        tmp = (x / -t) / z
    else if (z <= 2.55d+72) then
        tmp = (x / y) * (1.0d0 / t)
    else
        tmp = 1.0d0 / (t * (z / x))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -2.4e+122) {
		tmp = (x / -z) / y;
	} else if (z <= -29000000000000.0) {
		tmp = (x / -t) / z;
	} else if (z <= 2.55e+72) {
		tmp = (x / y) * (1.0 / t);
	} else {
		tmp = 1.0 / (t * (z / x));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -2.4e+122:
		tmp = (x / -z) / y
	elif z <= -29000000000000.0:
		tmp = (x / -t) / z
	elif z <= 2.55e+72:
		tmp = (x / y) * (1.0 / t)
	else:
		tmp = 1.0 / (t * (z / x))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -2.4e+122)
		tmp = Float64(Float64(x / Float64(-z)) / y);
	elseif (z <= -29000000000000.0)
		tmp = Float64(Float64(x / Float64(-t)) / z);
	elseif (z <= 2.55e+72)
		tmp = Float64(Float64(x / y) * Float64(1.0 / t));
	else
		tmp = Float64(1.0 / Float64(t * Float64(z / x)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (z <= -2.4e+122)
		tmp = (x / -z) / y;
	elseif (z <= -29000000000000.0)
		tmp = (x / -t) / z;
	elseif (z <= 2.55e+72)
		tmp = (x / y) * (1.0 / t);
	else
		tmp = 1.0 / (t * (z / x));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -2.4e+122], N[(N[(x / (-z)), $MachinePrecision] / y), $MachinePrecision], If[LessEqual[z, -29000000000000.0], N[(N[(x / (-t)), $MachinePrecision] / z), $MachinePrecision], If[LessEqual[z, 2.55e+72], N[(N[(x / y), $MachinePrecision] * N[(1.0 / t), $MachinePrecision]), $MachinePrecision], N[(1.0 / N[(t * N[(z / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if z < -2.4000000000000002e122

   1. Initial program 83.3%

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

      1. add-sqr-sqrt 39.0%

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

      2. times-frac 46.2%

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

   4. Applied egg-rr 46.2%

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

   5. Taylor expanded in t around 0 83.3%

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

      1. associate-*r/ 83.3%

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

      2. neg-mul-1 83.3%

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

   7. Simplified 83.3%

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

   8. Taylor expanded in z around 0 48.8%

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

      1. mul-1-neg 48.8%

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

      2. associate-/r* 46.2%

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

      3. distribute-neg-frac2 46.2%

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

   10. Simplified 46.2%

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

   11. Taylor expanded in x around 0 48.8%

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

       1. associate-/l/ 55.9%

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

       2. associate-*r/ 55.9%

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

       3. associate-*r/ 55.9%

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

       4. neg-mul-1 55.9%

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

   13. Simplified 55.9%

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

   if -2.4000000000000002e122 < z < -2.9e13

   1. Initial program 88.0%

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

      1. associate-/l/ 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in t around inf 48.5%

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

   6. Taylor expanded in y around 0 33.5%

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

      1. associate-*r/ 33.5%

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

      2. neg-mul-1 33.5%

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

   8. Simplified 33.5%

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

   9. Taylor expanded in x around 0 33.5%

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

       1. mul-1-neg 33.5%

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

       2. associate-/r* 33.5%

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

       3. distribute-neg-frac2 33.5%

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

   11. Simplified 33.5%

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

   if -2.9e13 < z < 2.54999999999999989e72

   1. Initial program 93.9%

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

   3. Taylor expanded in z around 0 57.5%

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

      1. *-un-lft-identity 57.5%

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

      2. times-frac 59.2%

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

   5. Applied egg-rr 59.2%

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

   if 2.54999999999999989e72 < z

   1. Initial program 74.5%

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

      1. associate-/l/ 99.7%

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

   3. Simplified 99.7%

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

   5. Taylor expanded in t around inf 35.2%

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

   6. Taylor expanded in y around 0 33.5%

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

      1. associate-*r/ 33.5%

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

      2. neg-mul-1 33.5%

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

   8. Simplified 33.5%

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

      1. clear-num 33.5%

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

      2. inv-pow 33.5%

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

      3. associate-/l* 40.9%

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

      4. add-sqr-sqrt 11.3%

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

      5. sqrt-unprod 40.1%

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

      6. sqr-neg 40.1%

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

      7. sqrt-unprod 25.8%

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

      8. add-sqr-sqrt 36.8%

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

   10. Applied egg-rr 36.8%

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

       1. unpow-1 36.8%

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

   12. Simplified 36.8%

       \[\leadsto \color{blue}{\frac{1}{t \cdot \frac{z}{x}}} \]
3. Recombined 4 regimes into one program.

4. Final simplification 50.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.4 \cdot 10^{+122}:\\ \;\;\;\;\frac{\frac{x}{-z}}{y}\\ \mathbf{elif}\;z \leq -29000000000000:\\ \;\;\;\;\frac{\frac{x}{-t}}{z}\\ \mathbf{elif}\;z \leq 2.55 \cdot 10^{+72}:\\ \;\;\;\;\frac{x}{y} \cdot \frac{1}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{t \cdot \frac{z}{x}}\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 63.5% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq 2.7 \cdot 10^{-196}:\\ \;\;\;\;\frac{x}{y \cdot \left(t - z\right)}\\ \mathbf{elif}\;t \leq 1.22 \cdot 10^{-110}:\\ \;\;\;\;\frac{x}{z \cdot \left(z + t\right)}\\ \mathbf{elif}\;t \leq 3.3 \cdot 10^{+207}:\\ \;\;\;\;\frac{x}{\left(y - z\right) \cdot t}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{t}}{y - z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= t 2.7e-196)
   (/ x (* y (- t z)))
   (if (<= t 1.22e-110)
     (/ x (* z (+ z t)))
     (if (<= t 3.3e+207) (/ x (* (- y z) t)) (/ (/ x t) (- y z))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= 2.7e-196) {
		tmp = x / (y * (t - z));
	} else if (t <= 1.22e-110) {
		tmp = x / (z * (z + t));
	} else if (t <= 3.3e+207) {
		tmp = x / ((y - z) * t);
	} else {
		tmp = (x / t) / (y - 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 (t <= 2.7d-196) then
        tmp = x / (y * (t - z))
    else if (t <= 1.22d-110) then
        tmp = x / (z * (z + t))
    else if (t <= 3.3d+207) then
        tmp = x / ((y - z) * t)
    else
        tmp = (x / t) / (y - z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= 2.7e-196) {
		tmp = x / (y * (t - z));
	} else if (t <= 1.22e-110) {
		tmp = x / (z * (z + t));
	} else if (t <= 3.3e+207) {
		tmp = x / ((y - z) * t);
	} else {
		tmp = (x / t) / (y - z);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if t <= 2.7e-196:
		tmp = x / (y * (t - z))
	elif t <= 1.22e-110:
		tmp = x / (z * (z + t))
	elif t <= 3.3e+207:
		tmp = x / ((y - z) * t)
	else:
		tmp = (x / t) / (y - z)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (t <= 2.7e-196)
		tmp = Float64(x / Float64(y * Float64(t - z)));
	elseif (t <= 1.22e-110)
		tmp = Float64(x / Float64(z * Float64(z + t)));
	elseif (t <= 3.3e+207)
		tmp = Float64(x / Float64(Float64(y - z) * t));
	else
		tmp = Float64(Float64(x / t) / Float64(y - z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (t <= 2.7e-196)
		tmp = x / (y * (t - z));
	elseif (t <= 1.22e-110)
		tmp = x / (z * (z + t));
	elseif (t <= 3.3e+207)
		tmp = x / ((y - z) * t);
	else
		tmp = (x / t) / (y - z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[t, 2.7e-196], N[(x / N[(y * N[(t - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.22e-110], N[(x / N[(z * N[(z + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 3.3e+207], N[(x / N[(N[(y - z), $MachinePrecision] * t), $MachinePrecision]), $MachinePrecision], N[(N[(x / t), $MachinePrecision] / N[(y - z), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if t < 2.69999999999999982e-196

   1. Initial program 90.2%

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

   3. Taylor expanded in y around inf 59.2%

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

      1. *-commutative 59.2%

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

   5. Simplified 59.2%

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

   if 2.69999999999999982e-196 < t < 1.22e-110

   1. Initial program 84.0%

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

   3. Taylor expanded in x around 0 84.0%

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

      1. associate-/l/ 94.7%

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

   5. Simplified 94.7%

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

   6. Taylor expanded in y around 0 61.3%

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

      1. mul-1-neg 61.3%

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

   8. Simplified 61.3%

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

      1. add-sqr-sqrt 33.5%

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

      2. sqrt-unprod 50.9%

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

      3. sqr-neg 50.9%

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

      4. sqrt-unprod 34.0%

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

      5. add-sqr-sqrt 52.2%

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

      6. *-un-lft-identity 52.2%

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

      7. associate-/l/ 52.5%

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

      8. sub-neg 52.5%

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

      9. add-sqr-sqrt 17.8%

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

      10. sqrt-unprod 52.2%

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

      11. sqr-neg 52.2%

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

      12. sqrt-unprod 34.4%

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

      13. add-sqr-sqrt 62.4%

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

   10. Applied egg-rr 62.4%

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

       1. *-lft-identity 62.4%

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

       2. *-commutative 62.4%

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

       3. +-commutative 62.4%

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

   12. Simplified 62.4%

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

   if 1.22e-110 < t < 3.3e207

   1. Initial program 85.8%

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

   3. Taylor expanded in t around inf 68.7%

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

   if 3.3e207 < t

   1. Initial program 79.3%

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

      1. associate-/l/ 94.6%

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

   3. Simplified 94.6%

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

   5. Taylor expanded in t around inf 89.5%

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

4. Final simplification 64.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq 2.7 \cdot 10^{-196}:\\ \;\;\;\;\frac{x}{y \cdot \left(t - z\right)}\\ \mathbf{elif}\;t \leq 1.22 \cdot 10^{-110}:\\ \;\;\;\;\frac{x}{z \cdot \left(z + t\right)}\\ \mathbf{elif}\;t \leq 3.3 \cdot 10^{+207}:\\ \;\;\;\;\frac{x}{\left(y - z\right) \cdot t}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{t}}{y - z}\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 49.3% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -4.4 \cdot 10^{+181}:\\ \;\;\;\;\frac{x}{y \cdot z}\\ \mathbf{elif}\;z \leq -230000000:\\ \;\;\;\;\frac{x}{z \cdot \left(-t\right)}\\ \mathbf{elif}\;z \leq 7.1 \cdot 10^{+71}:\\ \;\;\;\;\frac{x}{y \cdot t}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{z}}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -4.4e+181)
   (/ x (* y z))
   (if (<= z -230000000.0)
     (/ x (* z (- t)))
     (if (<= z 7.1e+71) (/ x (* y t)) (/ (/ x z) t)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -4.4e+181) {
		tmp = x / (y * z);
	} else if (z <= -230000000.0) {
		tmp = x / (z * -t);
	} else if (z <= 7.1e+71) {
		tmp = x / (y * t);
	} 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 (z <= (-4.4d+181)) then
        tmp = x / (y * z)
    else if (z <= (-230000000.0d0)) then
        tmp = x / (z * -t)
    else if (z <= 7.1d+71) then
        tmp = x / (y * t)
    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 (z <= -4.4e+181) {
		tmp = x / (y * z);
	} else if (z <= -230000000.0) {
		tmp = x / (z * -t);
	} else if (z <= 7.1e+71) {
		tmp = x / (y * t);
	} else {
		tmp = (x / z) / t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -4.4e+181:
		tmp = x / (y * z)
	elif z <= -230000000.0:
		tmp = x / (z * -t)
	elif z <= 7.1e+71:
		tmp = x / (y * t)
	else:
		tmp = (x / z) / t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -4.4e+181)
		tmp = Float64(x / Float64(y * z));
	elseif (z <= -230000000.0)
		tmp = Float64(x / Float64(z * Float64(-t)));
	elseif (z <= 7.1e+71)
		tmp = Float64(x / Float64(y * t));
	else
		tmp = Float64(Float64(x / z) / t);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (z <= -4.4e+181)
		tmp = x / (y * z);
	elseif (z <= -230000000.0)
		tmp = x / (z * -t);
	elseif (z <= 7.1e+71)
		tmp = x / (y * t);
	else
		tmp = (x / z) / t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -4.4e+181], N[(x / N[(y * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -230000000.0], N[(x / N[(z * (-t)), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 7.1e+71], N[(x / N[(y * t), $MachinePrecision]), $MachinePrecision], N[(N[(x / z), $MachinePrecision] / t), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if z < -4.4000000000000002e181

   1. Initial program 79.4%

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

      1. add-sqr-sqrt 41.5%

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

      2. times-frac 51.9%

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

   4. Applied egg-rr 51.9%

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

   5. Taylor expanded in t around 0 79.4%

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

      1. associate-*r/ 79.4%

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

      2. neg-mul-1 79.4%

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

   7. Simplified 79.4%

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

   8. Taylor expanded in z around 0 50.6%

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

      1. mul-1-neg 50.6%

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

      2. associate-/r* 46.9%

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

      3. distribute-neg-frac2 46.9%

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

   10. Simplified 46.9%

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

       1. div-inv 46.9%

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

       2. *-un-lft-identity 46.9%

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

       3. associate-*l/ 53.8%

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

       4. div-inv 53.8%

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

       5. add-sqr-sqrt 53.8%

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

       6. sqrt-unprod 79.4%

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

       7. sqr-neg 79.4%

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

       8. sqrt-unprod 0.0%

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

       9. add-sqr-sqrt 53.9%

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

   12. Applied egg-rr 53.9%

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

       1. *-lft-identity 53.9%

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

       2. associate-/l/ 50.6%

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

       3. *-commutative 50.6%

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

   14. Simplified 50.6%

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

   if -4.4000000000000002e181 < z < -2.3e8

   1. Initial program 89.1%

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

      1. associate-/l/ 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in t around inf 45.3%

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

   6. Taylor expanded in y around 0 34.3%

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

      1. associate-*r/ 34.3%

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

      2. neg-mul-1 34.3%

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

   8. Simplified 34.3%

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

   if -2.3e8 < z < 7.09999999999999986e71

   1. Initial program 93.9%

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

   3. Taylor expanded in z around 0 57.5%

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

   if 7.09999999999999986e71 < z

   1. Initial program 74.5%

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

      1. associate-/l/ 99.7%

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

   3. Simplified 99.7%

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

   5. Taylor expanded in t around inf 35.2%

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

   6. Taylor expanded in y around 0 33.5%

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

      1. associate-*r/ 33.5%

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

      2. neg-mul-1 33.5%

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

   8. Simplified 33.5%

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

      1. div-inv 33.5%

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

      2. add-sqr-sqrt 11.3%

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

      3. sqrt-unprod 36.2%

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

      4. sqr-neg 36.2%

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

      5. sqrt-unprod 20.4%

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

      6. add-sqr-sqrt 31.3%

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

      7. associate-/r* 29.6%

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

   10. Applied egg-rr 29.6%

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

       1. *-commutative 29.6%

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

       2. associate-*l/ 25.7%

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

       3. associate-*r/ 35.0%

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

       4. associate-*l/ 35.0%

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

       5. *-lft-identity 35.0%

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

   12. Simplified 35.0%

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

4. Final simplification 48.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.4 \cdot 10^{+181}:\\ \;\;\;\;\frac{x}{y \cdot z}\\ \mathbf{elif}\;z \leq -230000000:\\ \;\;\;\;\frac{x}{z \cdot \left(-t\right)}\\ \mathbf{elif}\;z \leq 7.1 \cdot 10^{+71}:\\ \;\;\;\;\frac{x}{y \cdot t}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{z}}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 93.6% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.8 \cdot 10^{+152}:\\ \;\;\;\;\frac{\frac{x}{z}}{z - y}\\ \mathbf{elif}\;z \leq 3.2 \cdot 10^{+93}:\\ \;\;\;\;\frac{x}{\left(y - z\right) \cdot \left(t - z\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y - z} \cdot \frac{-1}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -2.8e+152)
   (/ (/ x z) (- z y))
   (if (<= z 3.2e+93) (/ x (* (- y z) (- t z))) (* (/ x (- y z)) (/ -1.0 z)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -2.8e+152) {
		tmp = (x / z) / (z - y);
	} else if (z <= 3.2e+93) {
		tmp = x / ((y - z) * (t - z));
	} else {
		tmp = (x / (y - z)) * (-1.0 / 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 <= (-2.8d+152)) then
        tmp = (x / z) / (z - y)
    else if (z <= 3.2d+93) then
        tmp = x / ((y - z) * (t - z))
    else
        tmp = (x / (y - z)) * ((-1.0d0) / z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -2.8e+152) {
		tmp = (x / z) / (z - y);
	} else if (z <= 3.2e+93) {
		tmp = x / ((y - z) * (t - z));
	} else {
		tmp = (x / (y - z)) * (-1.0 / z);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -2.8e+152:
		tmp = (x / z) / (z - y)
	elif z <= 3.2e+93:
		tmp = x / ((y - z) * (t - z))
	else:
		tmp = (x / (y - z)) * (-1.0 / z)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -2.8e+152)
		tmp = Float64(Float64(x / z) / Float64(z - y));
	elseif (z <= 3.2e+93)
		tmp = Float64(x / Float64(Float64(y - z) * Float64(t - z)));
	else
		tmp = Float64(Float64(x / Float64(y - z)) * Float64(-1.0 / z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (z <= -2.8e+152)
		tmp = (x / z) / (z - y);
	elseif (z <= 3.2e+93)
		tmp = x / ((y - z) * (t - z));
	else
		tmp = (x / (y - z)) * (-1.0 / z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -2.8e+152], N[(N[(x / z), $MachinePrecision] / N[(z - y), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 3.2e+93], N[(x / N[(N[(y - z), $MachinePrecision] * N[(t - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x / N[(y - z), $MachinePrecision]), $MachinePrecision] * N[(-1.0 / z), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -2.8000000000000002e152

   1. Initial program 79.7%

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

      1. associate-/l/ 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in t around 0 99.4%

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

      1. associate-*r/ 99.4%

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

      2. neg-mul-1 99.4%

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

   7. Simplified 99.4%

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

   if -2.8000000000000002e152 < z < 3.2000000000000001e93

   1. Initial program 92.8%

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

   if 3.2000000000000001e93 < z

   1. Initial program 72.7%

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

      1. associate-/r* 99.8%

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

      2. div-inv 99.8%

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

   4. Applied egg-rr 99.8%

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

   5. Taylor expanded in t around 0 93.4%

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

4. Final simplification 93.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.8 \cdot 10^{+152}:\\ \;\;\;\;\frac{\frac{x}{z}}{z - y}\\ \mathbf{elif}\;z \leq 3.2 \cdot 10^{+93}:\\ \;\;\;\;\frac{x}{\left(y - z\right) \cdot \left(t - z\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y - z} \cdot \frac{-1}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 93.6% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.05 \cdot 10^{+153}:\\ \;\;\;\;\frac{\frac{x}{z}}{z - y}\\ \mathbf{elif}\;z \leq 1.6 \cdot 10^{+94}:\\ \;\;\;\;\frac{x}{\left(y - z\right) \cdot \left(t - z\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{-1}{z}}{\frac{y - z}{x}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -1.05e+153)
   (/ (/ x z) (- z y))
   (if (<= z 1.6e+94) (/ x (* (- y z) (- t z))) (/ (/ -1.0 z) (/ (- y z) x)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -1.05e+153) {
		tmp = (x / z) / (z - y);
	} else if (z <= 1.6e+94) {
		tmp = x / ((y - z) * (t - z));
	} else {
		tmp = (-1.0 / z) / ((y - z) / x);
	}
	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 <= (-1.05d+153)) then
        tmp = (x / z) / (z - y)
    else if (z <= 1.6d+94) then
        tmp = x / ((y - z) * (t - z))
    else
        tmp = ((-1.0d0) / z) / ((y - z) / x)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -1.05e+153) {
		tmp = (x / z) / (z - y);
	} else if (z <= 1.6e+94) {
		tmp = x / ((y - z) * (t - z));
	} else {
		tmp = (-1.0 / z) / ((y - z) / x);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -1.05e+153:
		tmp = (x / z) / (z - y)
	elif z <= 1.6e+94:
		tmp = x / ((y - z) * (t - z))
	else:
		tmp = (-1.0 / z) / ((y - z) / x)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -1.05e+153)
		tmp = Float64(Float64(x / z) / Float64(z - y));
	elseif (z <= 1.6e+94)
		tmp = Float64(x / Float64(Float64(y - z) * Float64(t - z)));
	else
		tmp = Float64(Float64(-1.0 / z) / Float64(Float64(y - z) / x));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (z <= -1.05e+153)
		tmp = (x / z) / (z - y);
	elseif (z <= 1.6e+94)
		tmp = x / ((y - z) * (t - z));
	else
		tmp = (-1.0 / z) / ((y - z) / x);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -1.05e+153], N[(N[(x / z), $MachinePrecision] / N[(z - y), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.6e+94], N[(x / N[(N[(y - z), $MachinePrecision] * N[(t - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(-1.0 / z), $MachinePrecision] / N[(N[(y - z), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.05000000000000008e153

   1. Initial program 79.7%

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

      1. associate-/l/ 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in t around 0 99.4%

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

      1. associate-*r/ 99.4%

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

      2. neg-mul-1 99.4%

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

   7. Simplified 99.4%

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

   if -1.05000000000000008e153 < z < 1.60000000000000007e94

   1. Initial program 92.8%

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

   if 1.60000000000000007e94 < z

   1. Initial program 72.1%

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

      1. add-sqr-sqrt 39.6%

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

      2. times-frac 54.4%

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

   4. Applied egg-rr 54.4%

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

      1. frac-times 39.6%

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

      2. add-sqr-sqrt 72.1%

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

      3. *-rgt-identity 72.1%

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

      4. frac-times 99.8%

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

      5. clear-num 99.8%

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

      6. associate-*l/ 99.8%

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

      7. *-un-lft-identity 99.8%

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

   6. Applied egg-rr 99.8%

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

   7. Taylor expanded in t around 0 93.3%

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

4. Final simplification 93.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.05 \cdot 10^{+153}:\\ \;\;\;\;\frac{\frac{x}{z}}{z - y}\\ \mathbf{elif}\;z \leq 1.6 \cdot 10^{+94}:\\ \;\;\;\;\frac{x}{\left(y - z\right) \cdot \left(t - z\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{-1}{z}}{\frac{y - z}{x}}\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 66.1% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -3.3 \cdot 10^{-83} \lor \neg \left(t \leq 1.8 \cdot 10^{-118}\right):\\ \;\;\;\;\frac{x}{\left(y - z\right) \cdot t}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{-z}}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= t -3.3e-83) (not (<= t 1.8e-118)))
   (/ x (* (- y z) t))
   (/ (/ x (- z)) y)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((t <= -3.3e-83) || !(t <= 1.8e-118)) {
		tmp = x / ((y - z) * t);
	} else {
		tmp = (x / -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 ((t <= (-3.3d-83)) .or. (.not. (t <= 1.8d-118))) then
        tmp = x / ((y - z) * t)
    else
        tmp = (x / -z) / y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((t <= -3.3e-83) || !(t <= 1.8e-118)) {
		tmp = x / ((y - z) * t);
	} else {
		tmp = (x / -z) / y;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (t <= -3.3e-83) or not (t <= 1.8e-118):
		tmp = x / ((y - z) * t)
	else:
		tmp = (x / -z) / y
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((t <= -3.3e-83) || !(t <= 1.8e-118))
		tmp = Float64(x / Float64(Float64(y - z) * t));
	else
		tmp = Float64(Float64(x / Float64(-z)) / y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((t <= -3.3e-83) || ~((t <= 1.8e-118)))
		tmp = x / ((y - z) * t);
	else
		tmp = (x / -z) / y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[t, -3.3e-83], N[Not[LessEqual[t, 1.8e-118]], $MachinePrecision]], N[(x / N[(N[(y - z), $MachinePrecision] * t), $MachinePrecision]), $MachinePrecision], N[(N[(x / (-z)), $MachinePrecision] / y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -3.2999999999999999e-83 or 1.8000000000000001e-118 < t

   1. Initial program 87.0%

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

   3. Taylor expanded in t around inf 73.6%

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

   if -3.2999999999999999e-83 < t < 1.8000000000000001e-118

   1. Initial program 89.0%

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

      1. add-sqr-sqrt 40.7%

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

      2. times-frac 45.6%

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

   4. Applied egg-rr 45.6%

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

   5. Taylor expanded in t around 0 77.8%

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

      1. associate-*r/ 77.8%

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

      2. neg-mul-1 77.8%

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

   7. Simplified 77.8%

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

   8. Taylor expanded in z around 0 50.6%

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

      1. mul-1-neg 50.6%

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

      2. associate-/r* 51.1%

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

      3. distribute-neg-frac2 51.1%

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

   10. Simplified 51.1%

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

   11. Taylor expanded in x around 0 50.6%

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

       1. associate-/l/ 56.5%

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

       2. associate-*r/ 56.5%

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

       3. associate-*r/ 56.5%

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

       4. neg-mul-1 56.5%

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

   13. Simplified 56.5%

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

4. Final simplification 68.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -3.3 \cdot 10^{-83} \lor \neg \left(t \leq 1.8 \cdot 10^{-118}\right):\\ \;\;\;\;\frac{x}{\left(y - z\right) \cdot t}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{-z}}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 17: 69.2% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -5.3 \cdot 10^{+119} \lor \neg \left(z \leq 6.2 \cdot 10^{+79}\right):\\ \;\;\;\;\frac{x}{z \cdot \left(z + t\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\left(y - z\right) \cdot t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -5.3e+119) (not (<= z 6.2e+79)))
   (/ x (* z (+ z t)))
   (/ x (* (- y z) t))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -5.3e+119) || !(z <= 6.2e+79)) {
		tmp = x / (z * (z + t));
	} 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 ((z <= (-5.3d+119)) .or. (.not. (z <= 6.2d+79))) then
        tmp = x / (z * (z + t))
    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 ((z <= -5.3e+119) || !(z <= 6.2e+79)) {
		tmp = x / (z * (z + t));
	} else {
		tmp = x / ((y - z) * t);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -5.3e+119) or not (z <= 6.2e+79):
		tmp = x / (z * (z + t))
	else:
		tmp = x / ((y - z) * t)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -5.3e+119) || !(z <= 6.2e+79))
		tmp = Float64(x / Float64(z * Float64(z + t)));
	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 ((z <= -5.3e+119) || ~((z <= 6.2e+79)))
		tmp = x / (z * (z + t));
	else
		tmp = x / ((y - z) * t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -5.3e+119], N[Not[LessEqual[z, 6.2e+79]], $MachinePrecision]], N[(x / N[(z * N[(z + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x / N[(N[(y - z), $MachinePrecision] * t), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -5.29999999999999972e119 or 6.1999999999999998e79 < z

   1. Initial program 77.6%

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

   3. Taylor expanded in x around 0 77.6%

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

      1. associate-/l/ 99.8%

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

   5. Simplified 99.8%

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

   6. Taylor expanded in y around 0 92.6%

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

      1. mul-1-neg 92.6%

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

   8. Simplified 92.6%

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

      1. add-sqr-sqrt 56.0%

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

      2. sqrt-unprod 78.3%

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

      3. sqr-neg 78.3%

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

      4. sqrt-unprod 50.7%

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

      5. add-sqr-sqrt 65.3%

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

      6. *-un-lft-identity 65.3%

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

      7. associate-/l/ 66.7%

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

      8. sub-neg 66.7%

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

      9. add-sqr-sqrt 35.8%

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

      10. sqrt-unprod 75.5%

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

      11. sqr-neg 75.5%

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

      12. sqrt-unprod 39.7%

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

      13. add-sqr-sqrt 76.6%

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

   10. Applied egg-rr 76.6%

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

       1. *-lft-identity 76.6%

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

       2. *-commutative 76.6%

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

       3. +-commutative 76.6%

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

   12. Simplified 76.6%

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

   if -5.29999999999999972e119 < z < 6.1999999999999998e79

   1. Initial program 92.9%

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

   3. Taylor expanded in t around inf 68.3%

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

4. Final simplification 71.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5.3 \cdot 10^{+119} \lor \neg \left(z \leq 6.2 \cdot 10^{+79}\right):\\ \;\;\;\;\frac{x}{z \cdot \left(z + t\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\left(y - z\right) \cdot t}\\ \end{array} \]
5. Add Preprocessing

Alternative 18: 62.6% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq 1.3 \cdot 10^{-203}:\\ \;\;\;\;\frac{x}{y \cdot \left(t - z\right)}\\ \mathbf{elif}\;t \leq 9.2 \cdot 10^{-111}:\\ \;\;\;\;\frac{x}{z \cdot \left(z + t\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\left(y - z\right) \cdot t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= t 1.3e-203)
   (/ x (* y (- t z)))
   (if (<= t 9.2e-111) (/ x (* z (+ z t))) (/ x (* (- y z) t)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= 1.3e-203) {
		tmp = x / (y * (t - z));
	} else if (t <= 9.2e-111) {
		tmp = x / (z * (z + t));
	} 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 <= 1.3d-203) then
        tmp = x / (y * (t - z))
    else if (t <= 9.2d-111) then
        tmp = x / (z * (z + t))
    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 <= 1.3e-203) {
		tmp = x / (y * (t - z));
	} else if (t <= 9.2e-111) {
		tmp = x / (z * (z + t));
	} else {
		tmp = x / ((y - z) * t);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if t <= 1.3e-203:
		tmp = x / (y * (t - z))
	elif t <= 9.2e-111:
		tmp = x / (z * (z + t))
	else:
		tmp = x / ((y - z) * t)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (t <= 1.3e-203)
		tmp = Float64(x / Float64(y * Float64(t - z)));
	elseif (t <= 9.2e-111)
		tmp = Float64(x / Float64(z * Float64(z + t)));
	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 <= 1.3e-203)
		tmp = x / (y * (t - z));
	elseif (t <= 9.2e-111)
		tmp = x / (z * (z + t));
	else
		tmp = x / ((y - z) * t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[t, 1.3e-203], N[(x / N[(y * N[(t - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 9.2e-111], N[(x / N[(z * N[(z + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x / N[(N[(y - z), $MachinePrecision] * t), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < 1.29999999999999988e-203

   1. Initial program 90.2%

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

   3. Taylor expanded in y around inf 59.2%

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

      1. *-commutative 59.2%

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

   5. Simplified 59.2%

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

   if 1.29999999999999988e-203 < t < 9.2e-111

   1. Initial program 84.0%

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

   3. Taylor expanded in x around 0 84.0%

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

      1. associate-/l/ 94.7%

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

   5. Simplified 94.7%

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

   6. Taylor expanded in y around 0 61.3%

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

      1. mul-1-neg 61.3%

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

   8. Simplified 61.3%

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

      1. add-sqr-sqrt 33.5%

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

      2. sqrt-unprod 50.9%

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

      3. sqr-neg 50.9%

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

      4. sqrt-unprod 34.0%

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

      5. add-sqr-sqrt 52.2%

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

      6. *-un-lft-identity 52.2%

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

      7. associate-/l/ 52.5%

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

      8. sub-neg 52.5%

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

      9. add-sqr-sqrt 17.8%

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

      10. sqrt-unprod 52.2%

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

      11. sqr-neg 52.2%

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

      12. sqrt-unprod 34.4%

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

      13. add-sqr-sqrt 62.4%

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

   10. Applied egg-rr 62.4%

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

       1. *-lft-identity 62.4%

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

       2. *-commutative 62.4%

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

       3. +-commutative 62.4%

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

   12. Simplified 62.4%

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

   if 9.2e-111 < t

   1. Initial program 84.6%

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

   3. Taylor expanded in t around inf 70.7%

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

4. Final simplification 63.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq 1.3 \cdot 10^{-203}:\\ \;\;\;\;\frac{x}{y \cdot \left(t - z\right)}\\ \mathbf{elif}\;t \leq 9.2 \cdot 10^{-111}:\\ \;\;\;\;\frac{x}{z \cdot \left(z + t\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\left(y - z\right) \cdot t}\\ \end{array} \]
5. Add Preprocessing

Alternative 19: 63.8% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq 3 \cdot 10^{-207}:\\ \;\;\;\;\frac{\frac{x}{y}}{t - z}\\ \mathbf{elif}\;t \leq 1.24 \cdot 10^{-110}:\\ \;\;\;\;\frac{x}{z \cdot \left(z + t\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{t}}{y - z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= t 3e-207)
   (/ (/ x y) (- t z))
   (if (<= t 1.24e-110) (/ x (* z (+ z t))) (/ (/ x t) (- y z)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= 3e-207) {
		tmp = (x / y) / (t - z);
	} else if (t <= 1.24e-110) {
		tmp = x / (z * (z + t));
	} else {
		tmp = (x / t) / (y - 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 (t <= 3d-207) then
        tmp = (x / y) / (t - z)
    else if (t <= 1.24d-110) then
        tmp = x / (z * (z + t))
    else
        tmp = (x / t) / (y - z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= 3e-207) {
		tmp = (x / y) / (t - z);
	} else if (t <= 1.24e-110) {
		tmp = x / (z * (z + t));
	} else {
		tmp = (x / t) / (y - z);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if t <= 3e-207:
		tmp = (x / y) / (t - z)
	elif t <= 1.24e-110:
		tmp = x / (z * (z + t))
	else:
		tmp = (x / t) / (y - z)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (t <= 3e-207)
		tmp = Float64(Float64(x / y) / Float64(t - z));
	elseif (t <= 1.24e-110)
		tmp = Float64(x / Float64(z * Float64(z + t)));
	else
		tmp = Float64(Float64(x / t) / Float64(y - z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (t <= 3e-207)
		tmp = (x / y) / (t - z);
	elseif (t <= 1.24e-110)
		tmp = x / (z * (z + t));
	else
		tmp = (x / t) / (y - z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[t, 3e-207], N[(N[(x / y), $MachinePrecision] / N[(t - z), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.24e-110], N[(x / N[(z * N[(z + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x / t), $MachinePrecision] / N[(y - z), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < 2.9999999999999999e-207

   1. Initial program 90.2%

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

      1. add-sqr-sqrt 46.6%

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

      2. times-frac 49.6%

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

   4. Applied egg-rr 49.6%

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

   5. Taylor expanded in y around inf 59.2%

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

      1. associate-/r* 59.2%

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

   7. Simplified 59.2%

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

   if 2.9999999999999999e-207 < t < 1.24000000000000006e-110

   1. Initial program 84.0%

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

   3. Taylor expanded in x around 0 84.0%

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

      1. associate-/l/ 94.7%

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

   5. Simplified 94.7%

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

   6. Taylor expanded in y around 0 61.3%

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

      1. mul-1-neg 61.3%

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

   8. Simplified 61.3%

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

      1. add-sqr-sqrt 33.5%

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

      2. sqrt-unprod 50.9%

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

      3. sqr-neg 50.9%

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

      4. sqrt-unprod 34.0%

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

      5. add-sqr-sqrt 52.2%

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

      6. *-un-lft-identity 52.2%

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

      7. associate-/l/ 52.5%

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

      8. sub-neg 52.5%

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

      9. add-sqr-sqrt 17.8%

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

      10. sqrt-unprod 52.2%

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

      11. sqr-neg 52.2%

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

      12. sqrt-unprod 34.4%

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

      13. add-sqr-sqrt 62.4%

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

   10. Applied egg-rr 62.4%

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

       1. *-lft-identity 62.4%

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

       2. *-commutative 62.4%

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

       3. +-commutative 62.4%

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

   12. Simplified 62.4%

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

   if 1.24000000000000006e-110 < t

   1. Initial program 84.6%

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

      1. associate-/l/ 97.0%

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

   3. Simplified 97.0%

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

   5. Taylor expanded in t around inf 72.4%

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

4. Final simplification 64.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq 3 \cdot 10^{-207}:\\ \;\;\;\;\frac{\frac{x}{y}}{t - z}\\ \mathbf{elif}\;t \leq 1.24 \cdot 10^{-110}:\\ \;\;\;\;\frac{x}{z \cdot \left(z + t\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{t}}{y - z}\\ \end{array} \]
5. Add Preprocessing

Alternative 20: 72.4% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.15 \cdot 10^{-60}:\\ \;\;\;\;\frac{\frac{x}{y}}{t - z}\\ \mathbf{elif}\;y \leq 8.5 \cdot 10^{-247}:\\ \;\;\;\;\frac{x}{z \cdot \left(z - t\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{y - z}}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -1.15e-60)
   (/ (/ x y) (- t z))
   (if (<= y 8.5e-247) (/ x (* z (- z t))) (/ (/ x (- y z)) t))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -1.15e-60) {
		tmp = (x / y) / (t - z);
	} else if (y <= 8.5e-247) {
		tmp = x / (z * (z - t));
	} 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 <= (-1.15d-60)) then
        tmp = (x / y) / (t - z)
    else if (y <= 8.5d-247) then
        tmp = x / (z * (z - t))
    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 <= -1.15e-60) {
		tmp = (x / y) / (t - z);
	} else if (y <= 8.5e-247) {
		tmp = x / (z * (z - t));
	} else {
		tmp = (x / (y - z)) / t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -1.15e-60:
		tmp = (x / y) / (t - z)
	elif y <= 8.5e-247:
		tmp = x / (z * (z - t))
	else:
		tmp = (x / (y - z)) / t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -1.15e-60)
		tmp = Float64(Float64(x / y) / Float64(t - z));
	elseif (y <= 8.5e-247)
		tmp = Float64(x / Float64(z * Float64(z - t)));
	else
		tmp = Float64(Float64(x / Float64(y - z)) / t);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= -1.15e-60)
		tmp = (x / y) / (t - z);
	elseif (y <= 8.5e-247)
		tmp = x / (z * (z - t));
	else
		tmp = (x / (y - z)) / t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -1.15e-60], N[(N[(x / y), $MachinePrecision] / N[(t - z), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 8.5e-247], N[(x / N[(z * N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x / N[(y - z), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.1500000000000001e-60

   1. Initial program 85.1%

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

      1. add-sqr-sqrt 45.4%

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

      2. times-frac 53.4%

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

   4. Applied egg-rr 53.4%

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

   5. Taylor expanded in y around inf 80.1%

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

      1. associate-/r* 81.3%

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

   7. Simplified 81.3%

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

   if -1.1500000000000001e-60 < y < 8.5000000000000003e-247

   1. Initial program 94.2%

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

   3. Taylor expanded in y around 0 83.1%

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

      1. associate-*r/ 83.1%

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

      2. neg-mul-1 83.1%

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

   5. Simplified 83.1%

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

   if 8.5000000000000003e-247 < y

   1. Initial program 85.5%

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

      1. add-sqr-sqrt 43.8%

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

      2. times-frac 47.6%

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

   4. Applied egg-rr 47.6%

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

      1. frac-times 43.8%

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

      2. add-sqr-sqrt 85.5%

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

      3. *-rgt-identity 85.5%

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

      4. frac-times 95.8%

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

      5. clear-num 95.7%

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

      6. associate-*l/ 96.5%

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

      7. *-un-lft-identity 96.5%

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

   6. Applied egg-rr 96.5%

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

   7. Taylor expanded in t around inf 55.8%

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

      1. associate-/l/ 60.1%

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

   9. Simplified 60.1%

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

4. Final simplification 72.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.15 \cdot 10^{-60}:\\ \;\;\;\;\frac{\frac{x}{y}}{t - z}\\ \mathbf{elif}\;y \leq 8.5 \cdot 10^{-247}:\\ \;\;\;\;\frac{x}{z \cdot \left(z - t\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{y - z}}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 21: 47.2% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.6 \cdot 10^{+105} \lor \neg \left(z \leq 2 \cdot 10^{+100}\right):\\ \;\;\;\;\frac{x}{z \cdot t}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y \cdot t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -2.6e+105) (not (<= z 2e+100))) (/ x (* z t)) (/ x (* y t))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -2.6e+105) || !(z <= 2e+100)) {
		tmp = x / (z * t);
	} else {
		tmp = x / (y * 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 ((z <= (-2.6d+105)) .or. (.not. (z <= 2d+100))) then
        tmp = x / (z * t)
    else
        tmp = x / (y * t)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -2.6e+105) || !(z <= 2e+100)) {
		tmp = x / (z * t);
	} else {
		tmp = x / (y * t);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -2.6e+105) or not (z <= 2e+100):
		tmp = x / (z * t)
	else:
		tmp = x / (y * t)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -2.6e+105) || !(z <= 2e+100))
		tmp = Float64(x / Float64(z * t));
	else
		tmp = Float64(x / Float64(y * t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z <= -2.6e+105) || ~((z <= 2e+100)))
		tmp = x / (z * t);
	else
		tmp = x / (y * t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -2.6e+105], N[Not[LessEqual[z, 2e+100]], $MachinePrecision]], N[(x / N[(z * t), $MachinePrecision]), $MachinePrecision], N[(x / N[(y * t), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -2.6000000000000002e105 or 2.00000000000000003e100 < z

   1. Initial program 77.9%

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

      1. associate-/l/ 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in t around inf 37.0%

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

   6. Taylor expanded in y around 0 38.3%

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

      1. associate-*r/ 38.3%

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

      2. neg-mul-1 38.3%

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

   8. Simplified 38.3%

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

      1. add-sqr-sqrt 18.2%

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

      2. sqrt-unprod 40.4%

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

      3. sqr-neg 40.4%

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

      4. sqrt-unprod 18.9%

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

      5. add-sqr-sqrt 37.1%

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

      6. *-un-lft-identity 37.1%

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

      7. associate-/r* 32.6%

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

   10. Applied egg-rr 32.6%

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

       1. *-lft-identity 32.6%

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

       2. associate-/l/ 37.1%

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

   12. Simplified 37.1%

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

   if -2.6000000000000002e105 < z < 2.00000000000000003e100

   1. Initial program 92.5%

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

   3. Taylor expanded in z around 0 50.0%

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

4. Final simplification 45.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.6 \cdot 10^{+105} \lor \neg \left(z \leq 2 \cdot 10^{+100}\right):\\ \;\;\;\;\frac{x}{z \cdot t}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y \cdot t}\\ \end{array} \]
5. Add Preprocessing

Alternative 22: 49.4% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.75 \cdot 10^{+105} \lor \neg \left(z \leq 1.35 \cdot 10^{+72}\right):\\ \;\;\;\;\frac{\frac{x}{z}}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y \cdot t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -1.75e+105) (not (<= z 1.35e+72))) (/ (/ x z) t) (/ x (* y t))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -1.75e+105) || !(z <= 1.35e+72)) {
		tmp = (x / z) / t;
	} else {
		tmp = x / (y * 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 ((z <= (-1.75d+105)) .or. (.not. (z <= 1.35d+72))) then
        tmp = (x / z) / t
    else
        tmp = x / (y * t)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -1.75e+105) || !(z <= 1.35e+72)) {
		tmp = (x / z) / t;
	} else {
		tmp = x / (y * t);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -1.75e+105) or not (z <= 1.35e+72):
		tmp = (x / z) / t
	else:
		tmp = x / (y * t)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -1.75e+105) || !(z <= 1.35e+72))
		tmp = Float64(Float64(x / z) / t);
	else
		tmp = Float64(x / Float64(y * t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z <= -1.75e+105) || ~((z <= 1.35e+72)))
		tmp = (x / z) / t;
	else
		tmp = x / (y * t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -1.75e+105], N[Not[LessEqual[z, 1.35e+72]], $MachinePrecision]], N[(N[(x / z), $MachinePrecision] / t), $MachinePrecision], N[(x / N[(y * t), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.74999999999999996e105 or 1.35e72 < z

   1. Initial program 78.6%

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

      1. associate-/l/ 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in t around inf 36.9%

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

   6. Taylor expanded in y around 0 36.1%

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

      1. associate-*r/ 36.1%

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

      2. neg-mul-1 36.1%

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

   8. Simplified 36.1%

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

      1. div-inv 36.1%

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

      2. add-sqr-sqrt 16.3%

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

      3. sqrt-unprod 39.7%

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

      4. sqr-neg 39.7%

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

      5. sqrt-unprod 17.8%

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

      6. add-sqr-sqrt 33.9%

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

      7. associate-/r* 32.9%

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

   10. Applied egg-rr 32.9%

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

       1. *-commutative 32.9%

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

       2. associate-*l/ 29.9%

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

       3. associate-*r/ 39.5%

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

       4. associate-*l/ 39.5%

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

       5. *-lft-identity 39.5%

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

   12. Simplified 39.5%

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

   if -1.74999999999999996e105 < z < 1.35e72

   1. Initial program 93.1%

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

   3. Taylor expanded in z around 0 52.3%

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

4. Final simplification 47.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.75 \cdot 10^{+105} \lor \neg \left(z \leq 1.35 \cdot 10^{+72}\right):\\ \;\;\;\;\frac{\frac{x}{z}}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y \cdot t}\\ \end{array} \]
5. Add Preprocessing

Alternative 23: 47.0% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.75 \cdot 10^{+118}:\\ \;\;\;\;\frac{x}{y \cdot z}\\ \mathbf{elif}\;z \leq 2.9 \cdot 10^{+100}:\\ \;\;\;\;\frac{x}{y \cdot t}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{z \cdot t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -2.75e+118)
   (/ x (* y z))
   (if (<= z 2.9e+100) (/ x (* y t)) (/ x (* z t)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -2.75e+118) {
		tmp = x / (y * z);
	} else if (z <= 2.9e+100) {
		tmp = x / (y * t);
	} 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 (z <= (-2.75d+118)) then
        tmp = x / (y * z)
    else if (z <= 2.9d+100) then
        tmp = x / (y * t)
    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 (z <= -2.75e+118) {
		tmp = x / (y * z);
	} else if (z <= 2.9e+100) {
		tmp = x / (y * t);
	} else {
		tmp = x / (z * t);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -2.75e+118:
		tmp = x / (y * z)
	elif z <= 2.9e+100:
		tmp = x / (y * t)
	else:
		tmp = x / (z * t)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -2.75e+118)
		tmp = Float64(x / Float64(y * z));
	elseif (z <= 2.9e+100)
		tmp = Float64(x / Float64(y * t));
	else
		tmp = Float64(x / Float64(z * t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (z <= -2.75e+118)
		tmp = x / (y * z);
	elseif (z <= 2.9e+100)
		tmp = x / (y * t);
	else
		tmp = x / (z * t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -2.75e+118], N[(x / N[(y * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 2.9e+100], N[(x / N[(y * t), $MachinePrecision]), $MachinePrecision], N[(x / N[(z * t), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -2.7500000000000002e118

   1. Initial program 83.7%

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

      1. add-sqr-sqrt 38.0%

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

      2. times-frac 45.0%

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

   4. Applied egg-rr 45.0%

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

   5. Taylor expanded in t around 0 83.7%

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

      1. associate-*r/ 83.7%

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

      2. neg-mul-1 83.7%

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

   7. Simplified 83.7%

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

   8. Taylor expanded in z around 0 50.1%

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

      1. mul-1-neg 50.1%

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

      2. associate-/r* 47.6%

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

      3. distribute-neg-frac2 47.6%

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

   10. Simplified 47.6%

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

       1. div-inv 47.6%

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

       2. *-un-lft-identity 47.6%

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

       3. associate-*l/ 57.0%

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

       4. div-inv 57.0%

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

       5. add-sqr-sqrt 57.0%

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

       6. sqrt-unprod 81.3%

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

       7. sqr-neg 81.3%

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

       8. sqrt-unprod 0.0%

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

       9. add-sqr-sqrt 54.3%

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

   12. Applied egg-rr 54.3%

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

       1. *-lft-identity 54.3%

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

       2. associate-/l/ 47.4%

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

       3. *-commutative 47.4%

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

   14. Simplified 47.4%

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

   if -2.7500000000000002e118 < z < 2.9e100

   1. Initial program 92.1%

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

   3. Taylor expanded in z around 0 48.6%

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

   if 2.9e100 < z

   1. Initial program 71.8%

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

      1. associate-/l/ 99.7%

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

   3. Simplified 99.7%

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

   5. Taylor expanded in t around inf 34.9%

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

   6. Taylor expanded in y around 0 37.4%

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

      1. associate-*r/ 37.4%

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

      2. neg-mul-1 37.4%

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

   8. Simplified 37.4%

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

      1. add-sqr-sqrt 14.0%

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

      2. sqrt-unprod 36.5%

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

      3. sqr-neg 36.5%

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

      4. sqrt-unprod 23.5%

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

      5. add-sqr-sqrt 37.3%

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

      6. *-un-lft-identity 37.3%

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

      7. associate-/r* 30.1%

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

   10. Applied egg-rr 30.1%

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

       1. *-lft-identity 30.1%

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

       2. associate-/l/ 37.3%

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

   12. Simplified 37.3%

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

4. Final simplification 46.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.75 \cdot 10^{+118}:\\ \;\;\;\;\frac{x}{y \cdot z}\\ \mathbf{elif}\;z \leq 2.9 \cdot 10^{+100}:\\ \;\;\;\;\frac{x}{y \cdot t}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{z \cdot t}\\ \end{array} \]
5. Add Preprocessing

Alternative 24: 97.0% accurate, 1.0× speedup

Math

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

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(Float64(x / 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[(N[(x / N[(y - z), $MachinePrecision]), $MachinePrecision] / N[(t - z), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 87.6%

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

3. Taylor expanded in x around 0 87.6%

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

   1. associate-/l/ 94.8%

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

5. Simplified 94.8%

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

6. Final simplification 94.8%

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

Alternative 25: 40.2% accurate, 1.8× 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 87.6%

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

3. Taylor expanded in z around 0 38.7%

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

4. Final simplification 38.7%

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

Developer target: 88.2% 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 2024077 
(FPCore (x y z t)
  :name "Data.Random.Distribution.Triangular:triangularCDF from random-fu-0.2.6.2, B"
  :precision binary64

  :alt
  (if (< (/ x (* (- y z) (- t z))) 0.0) (/ (/ x (- y z)) (- t z)) (* x (/ 1.0 (* (- y z) (- t z)))))

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