Numeric.SpecFunctions:invIncompleteBetaWorker from math-functions-0.1.5.2, C

Percentage Accurate: 94.6% → 94.0%

Time: 6.4s

Alternatives: 12

Speedup: N/A×

• 20.1% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

double code(double x, double y, double z, double t) {
	return x * ((y / z) - (t / (1.0 - 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 / (1.0d0 - z)))
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 94.6% accurate, 1.0× speedup

Math

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

FPCore

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

C

double code(double x, double y, double z, double t) {
	return x * ((y / z) - (t / (1.0 - 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 / (1.0d0 - z)))
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 94.0% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq 4 \cdot 10^{+258}:\\ \;\;\;\;x \cdot \left(\frac{y}{z} - \frac{t}{1 - z}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{\frac{z}{x \cdot \left(y + t\right)}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z 4e+258)
   (* x (- (/ y z) (/ t (- 1.0 z))))
   (/ 1.0 (/ z (* x (+ y t))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= 4e+258) {
		tmp = x * ((y / z) - (t / (1.0 - z)));
	} else {
		tmp = 1.0 / (z / (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 <= 4d+258) then
        tmp = x * ((y / z) - (t / (1.0d0 - z)))
    else
        tmp = 1.0d0 / (z / (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 <= 4e+258) {
		tmp = x * ((y / z) - (t / (1.0 - z)));
	} else {
		tmp = 1.0 / (z / (x * (y + t)));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= 4e+258:
		tmp = x * ((y / z) - (t / (1.0 - z)))
	else:
		tmp = 1.0 / (z / (x * (y + t)))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= 4e+258)
		tmp = Float64(x * Float64(Float64(y / z) - Float64(t / Float64(1.0 - z))));
	else
		tmp = Float64(1.0 / Float64(z / Float64(x * Float64(y + t))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (z <= 4e+258)
		tmp = x * ((y / z) - (t / (1.0 - z)));
	else
		tmp = 1.0 / (z / (x * (y + t)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, 4e+258], N[(x * N[(N[(y / z), $MachinePrecision] - N[(t / N[(1.0 - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(1.0 / N[(z / N[(x * N[(y + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < 4.00000000000000023e258

   1. Initial program 96.0%

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

   if 4.00000000000000023e258 < z

   1. Initial program 64.9%

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

   2. Taylor expanded in z around inf 100.0%

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

      1. associate-/l* 60.5%

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

      2. neg-mul-1 60.5%

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

   4. Simplified 60.5%

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

      1. clear-num 60.5%

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

      2. associate-/r/ 60.5%

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

      3. clear-num 64.9%

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

      4. sub-neg 64.9%

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

      5. remove-double-neg 64.9%

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

   6. Applied egg-rr 64.9%

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

      1. associate-*l/ 100.0%

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

      2. clear-num 99.7%

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

   8. Applied egg-rr 99.7%

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

4. Final simplification 96.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq 4 \cdot 10^{+258}:\\ \;\;\;\;x \cdot \left(\frac{y}{z} - \frac{t}{1 - z}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{\frac{z}{x \cdot \left(y + t\right)}}\\ \end{array} \]

Alternative 2: 93.0% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \frac{y + t}{z}\\ \mathbf{if}\;z \leq -61000:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 0.000142:\\ \;\;\;\;x \cdot \left(\frac{y}{z} - t\right)\\ \mathbf{elif}\;z \leq 3.1 \cdot 10^{+259}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{\frac{z}{x \cdot \left(y + t\right)}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* x (/ (+ y t) z))))
   (if (<= z -61000.0)
     t_1
     (if (<= z 0.000142)
       (* x (- (/ y z) t))
       (if (<= z 3.1e+259) t_1 (/ 1.0 (/ z (* x (+ y t)))))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x * ((y + t) / z);
	double tmp;
	if (z <= -61000.0) {
		tmp = t_1;
	} else if (z <= 0.000142) {
		tmp = x * ((y / z) - t);
	} else if (z <= 3.1e+259) {
		tmp = t_1;
	} else {
		tmp = 1.0 / (z / (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) :: t_1
    real(8) :: tmp
    t_1 = x * ((y + t) / z)
    if (z <= (-61000.0d0)) then
        tmp = t_1
    else if (z <= 0.000142d0) then
        tmp = x * ((y / z) - t)
    else if (z <= 3.1d+259) then
        tmp = t_1
    else
        tmp = 1.0d0 / (z / (x * (y + 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) / z);
	double tmp;
	if (z <= -61000.0) {
		tmp = t_1;
	} else if (z <= 0.000142) {
		tmp = x * ((y / z) - t);
	} else if (z <= 3.1e+259) {
		tmp = t_1;
	} else {
		tmp = 1.0 / (z / (x * (y + t)));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x * ((y + t) / z)
	tmp = 0
	if z <= -61000.0:
		tmp = t_1
	elif z <= 0.000142:
		tmp = x * ((y / z) - t)
	elif z <= 3.1e+259:
		tmp = t_1
	else:
		tmp = 1.0 / (z / (x * (y + t)))
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x * Float64(Float64(y + t) / z))
	tmp = 0.0
	if (z <= -61000.0)
		tmp = t_1;
	elseif (z <= 0.000142)
		tmp = Float64(x * Float64(Float64(y / z) - t));
	elseif (z <= 3.1e+259)
		tmp = t_1;
	else
		tmp = Float64(1.0 / Float64(z / Float64(x * Float64(y + t))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x * ((y + t) / z);
	tmp = 0.0;
	if (z <= -61000.0)
		tmp = t_1;
	elseif (z <= 0.000142)
		tmp = x * ((y / z) - t);
	elseif (z <= 3.1e+259)
		tmp = t_1;
	else
		tmp = 1.0 / (z / (x * (y + t)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x * N[(N[(y + t), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -61000.0], t$95$1, If[LessEqual[z, 0.000142], N[(x * N[(N[(y / z), $MachinePrecision] - t), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 3.1e+259], t$95$1, N[(1.0 / N[(z / N[(x * N[(y + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -61000 or 1.42000000000000009e-4 < z < 3.1000000000000003e259

   1. Initial program 99.7%

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

   2. Taylor expanded in z around inf 90.3%

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

      1. associate-/l* 99.6%

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

      2. neg-mul-1 99.6%

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

   4. Simplified 99.6%

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

      1. clear-num 99.0%

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

      2. associate-/r/ 99.7%

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

      3. clear-num 99.7%

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

      4. sub-neg 99.7%

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

      5. remove-double-neg 99.7%

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

   6. Applied egg-rr 99.7%

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

   if -61000 < z < 1.42000000000000009e-4

   1. Initial program 93.0%

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

   2. Taylor expanded in z around 0 86.7%

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

      1. +-commutative 86.7%

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

      2. mul-1-neg 86.7%

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

      3. unsub-neg 86.7%

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

      4. *-commutative 86.7%

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

      5. associate-*r/ 84.6%

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

      6. distribute-lft-out-- 90.6%

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

   4. Simplified 90.6%

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

   if 3.1000000000000003e259 < z

   1. Initial program 64.9%

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

   2. Taylor expanded in z around inf 100.0%

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

      1. associate-/l* 60.5%

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

      2. neg-mul-1 60.5%

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

   4. Simplified 60.5%

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

      1. clear-num 60.5%

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

      2. associate-/r/ 60.5%

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

      3. clear-num 64.9%

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

      4. sub-neg 64.9%

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

      5. remove-double-neg 64.9%

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

   6. Applied egg-rr 64.9%

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

      1. associate-*l/ 100.0%

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

      2. clear-num 99.7%

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

   8. Applied egg-rr 99.7%

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

4. Final simplification 94.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -61000:\\ \;\;\;\;x \cdot \frac{y + t}{z}\\ \mathbf{elif}\;z \leq 0.000142:\\ \;\;\;\;x \cdot \left(\frac{y}{z} - t\right)\\ \mathbf{elif}\;z \leq 3.1 \cdot 10^{+259}:\\ \;\;\;\;x \cdot \frac{y + t}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{\frac{z}{x \cdot \left(y + t\right)}}\\ \end{array} \]

Alternative 3: 93.0% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -61000:\\ \;\;\;\;x \cdot \frac{y + t}{z}\\ \mathbf{elif}\;z \leq 0.000142:\\ \;\;\;\;x \cdot \left(\frac{y}{z} - t\right)\\ \mathbf{elif}\;z \leq 4 \cdot 10^{+258}:\\ \;\;\;\;x \cdot \left(\frac{y}{z} + \frac{t}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{\frac{z}{x \cdot \left(y + t\right)}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -61000.0)
   (* x (/ (+ y t) z))
   (if (<= z 0.000142)
     (* x (- (/ y z) t))
     (if (<= z 4e+258)
       (* x (+ (/ y z) (/ t z)))
       (/ 1.0 (/ z (* x (+ y t))))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -61000.0) {
		tmp = x * ((y + t) / z);
	} else if (z <= 0.000142) {
		tmp = x * ((y / z) - t);
	} else if (z <= 4e+258) {
		tmp = x * ((y / z) + (t / z));
	} else {
		tmp = 1.0 / (z / (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 <= (-61000.0d0)) then
        tmp = x * ((y + t) / z)
    else if (z <= 0.000142d0) then
        tmp = x * ((y / z) - t)
    else if (z <= 4d+258) then
        tmp = x * ((y / z) + (t / z))
    else
        tmp = 1.0d0 / (z / (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 <= -61000.0) {
		tmp = x * ((y + t) / z);
	} else if (z <= 0.000142) {
		tmp = x * ((y / z) - t);
	} else if (z <= 4e+258) {
		tmp = x * ((y / z) + (t / z));
	} else {
		tmp = 1.0 / (z / (x * (y + t)));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -61000.0:
		tmp = x * ((y + t) / z)
	elif z <= 0.000142:
		tmp = x * ((y / z) - t)
	elif z <= 4e+258:
		tmp = x * ((y / z) + (t / z))
	else:
		tmp = 1.0 / (z / (x * (y + t)))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -61000.0)
		tmp = Float64(x * Float64(Float64(y + t) / z));
	elseif (z <= 0.000142)
		tmp = Float64(x * Float64(Float64(y / z) - t));
	elseif (z <= 4e+258)
		tmp = Float64(x * Float64(Float64(y / z) + Float64(t / z)));
	else
		tmp = Float64(1.0 / Float64(z / Float64(x * Float64(y + t))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (z <= -61000.0)
		tmp = x * ((y + t) / z);
	elseif (z <= 0.000142)
		tmp = x * ((y / z) - t);
	elseif (z <= 4e+258)
		tmp = x * ((y / z) + (t / z));
	else
		tmp = 1.0 / (z / (x * (y + t)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -61000.0], N[(x * N[(N[(y + t), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 0.000142], N[(x * N[(N[(y / z), $MachinePrecision] - t), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 4e+258], N[(x * N[(N[(y / z), $MachinePrecision] + N[(t / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(1.0 / N[(z / N[(x * N[(y + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if z < -61000

   1. Initial program 99.7%

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

   2. Taylor expanded in z around inf 92.2%

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

      1. associate-/l* 99.6%

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

      2. neg-mul-1 99.6%

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

   4. Simplified 99.6%

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

      1. clear-num 98.9%

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

      2. associate-/r/ 99.7%

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

      3. clear-num 99.7%

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

      4. sub-neg 99.7%

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

      5. remove-double-neg 99.7%

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

   6. Applied egg-rr 99.7%

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

   if -61000 < z < 1.42000000000000009e-4

   1. Initial program 93.0%

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

   2. Taylor expanded in z around 0 86.7%

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

      1. +-commutative 86.7%

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

      2. mul-1-neg 86.7%

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

      3. unsub-neg 86.7%

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

      4. *-commutative 86.7%

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

      5. associate-*r/ 84.6%

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

      6. distribute-lft-out-- 90.6%

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

   4. Simplified 90.6%

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

   if 1.42000000000000009e-4 < z < 4.00000000000000023e258

   1. Initial program 99.7%

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

   2. Taylor expanded in z around inf 99.7%

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

      1. associate-*r/ 99.7%

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

      2. neg-mul-1 99.7%

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

   4. Simplified 99.7%

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

   if 4.00000000000000023e258 < z

   1. Initial program 64.9%

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

   2. Taylor expanded in z around inf 100.0%

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

      1. associate-/l* 60.5%

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

      2. neg-mul-1 60.5%

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

   4. Simplified 60.5%

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

      1. clear-num 60.5%

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

      2. associate-/r/ 60.5%

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

      3. clear-num 64.9%

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

      4. sub-neg 64.9%

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

      5. remove-double-neg 64.9%

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

   6. Applied egg-rr 64.9%

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

      1. associate-*l/ 100.0%

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

      2. clear-num 99.7%

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

   8. Applied egg-rr 99.7%

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

4. Final simplification 94.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -61000:\\ \;\;\;\;x \cdot \frac{y + t}{z}\\ \mathbf{elif}\;z \leq 0.000142:\\ \;\;\;\;x \cdot \left(\frac{y}{z} - t\right)\\ \mathbf{elif}\;z \leq 4 \cdot 10^{+258}:\\ \;\;\;\;x \cdot \left(\frac{y}{z} + \frac{t}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{\frac{z}{x \cdot \left(y + t\right)}}\\ \end{array} \]

Alternative 4: 93.3% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \frac{y + t}{z}\\ \mathbf{if}\;z \leq -61000:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 0.000142:\\ \;\;\;\;x \cdot \left(\frac{y}{z} - t\right)\\ \mathbf{elif}\;z \leq 1.09 \cdot 10^{+276}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;\left(y + t\right) \cdot \frac{x}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* x (/ (+ y t) z))))
   (if (<= z -61000.0)
     t_1
     (if (<= z 0.000142)
       (* x (- (/ y z) t))
       (if (<= z 1.09e+276) t_1 (* (+ y t) (/ x z)))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x * ((y + t) / z);
	double tmp;
	if (z <= -61000.0) {
		tmp = t_1;
	} else if (z <= 0.000142) {
		tmp = x * ((y / z) - t);
	} else if (z <= 1.09e+276) {
		tmp = t_1;
	} else {
		tmp = (y + t) * (x / 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) / z)
    if (z <= (-61000.0d0)) then
        tmp = t_1
    else if (z <= 0.000142d0) then
        tmp = x * ((y / z) - t)
    else if (z <= 1.09d+276) then
        tmp = t_1
    else
        tmp = (y + t) * (x / 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) / z);
	double tmp;
	if (z <= -61000.0) {
		tmp = t_1;
	} else if (z <= 0.000142) {
		tmp = x * ((y / z) - t);
	} else if (z <= 1.09e+276) {
		tmp = t_1;
	} else {
		tmp = (y + t) * (x / z);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x * ((y + t) / z)
	tmp = 0
	if z <= -61000.0:
		tmp = t_1
	elif z <= 0.000142:
		tmp = x * ((y / z) - t)
	elif z <= 1.09e+276:
		tmp = t_1
	else:
		tmp = (y + t) * (x / z)
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x * Float64(Float64(y + t) / z))
	tmp = 0.0
	if (z <= -61000.0)
		tmp = t_1;
	elseif (z <= 0.000142)
		tmp = Float64(x * Float64(Float64(y / z) - t));
	elseif (z <= 1.09e+276)
		tmp = t_1;
	else
		tmp = Float64(Float64(y + t) * Float64(x / z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x * ((y + t) / z);
	tmp = 0.0;
	if (z <= -61000.0)
		tmp = t_1;
	elseif (z <= 0.000142)
		tmp = x * ((y / z) - t);
	elseif (z <= 1.09e+276)
		tmp = t_1;
	else
		tmp = (y + t) * (x / z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x * N[(N[(y + t), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -61000.0], t$95$1, If[LessEqual[z, 0.000142], N[(x * N[(N[(y / z), $MachinePrecision] - t), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.09e+276], t$95$1, N[(N[(y + t), $MachinePrecision] * N[(x / z), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -61000 or 1.42000000000000009e-4 < z < 1.09e276

   1. Initial program 99.7%

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

   2. Taylor expanded in z around inf 90.6%

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

      1. associate-/l* 99.6%

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

      2. neg-mul-1 99.6%

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

   4. Simplified 99.6%

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

      1. clear-num 99.0%

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

      2. associate-/r/ 99.7%

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

      3. clear-num 99.7%

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

      4. sub-neg 99.7%

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

      5. remove-double-neg 99.7%

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

   6. Applied egg-rr 99.7%

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

   if -61000 < z < 1.42000000000000009e-4

   1. Initial program 93.0%

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

   2. Taylor expanded in z around 0 86.7%

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

      1. +-commutative 86.7%

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

      2. mul-1-neg 86.7%

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

      3. unsub-neg 86.7%

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

      4. *-commutative 86.7%

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

      5. associate-*r/ 84.6%

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

      6. distribute-lft-out-- 90.6%

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

   4. Simplified 90.6%

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

   if 1.09e276 < z

   1. Initial program 53.1%

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

   2. Taylor expanded in z around inf 100.0%

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

      1. associate-/l* 47.3%

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

      2. associate-/r/ 99.7%

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

      3. cancel-sign-sub-inv 99.7%

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

      4. metadata-eval 99.7%

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

      5. *-lft-identity 99.7%

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

      6. +-commutative 99.7%

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

   4. Simplified 99.7%

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

4. Final simplification 94.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -61000:\\ \;\;\;\;x \cdot \frac{y + t}{z}\\ \mathbf{elif}\;z \leq 0.000142:\\ \;\;\;\;x \cdot \left(\frac{y}{z} - t\right)\\ \mathbf{elif}\;z \leq 1.09 \cdot 10^{+276}:\\ \;\;\;\;x \cdot \frac{y + t}{z}\\ \mathbf{else}:\\ \;\;\;\;\left(y + t\right) \cdot \frac{x}{z}\\ \end{array} \]

Alternative 5: 64.5% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{t}{\frac{z}{x}}\\ \mathbf{if}\;t \leq -1.9 \cdot 10^{+33}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -7.7 \cdot 10^{-268}:\\ \;\;\;\;y \cdot \frac{x}{z}\\ \mathbf{elif}\;t \leq 1.4 \cdot 10^{+175}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ t (/ z x))))
   (if (<= t -1.9e+33)
     t_1
     (if (<= t -7.7e-268)
       (* y (/ x z))
       (if (<= t 1.4e+175) (* x (/ y z)) t_1)))))

C

double code(double x, double y, double z, double t) {
	double t_1 = t / (z / x);
	double tmp;
	if (t <= -1.9e+33) {
		tmp = t_1;
	} else if (t <= -7.7e-268) {
		tmp = y * (x / z);
	} else if (t <= 1.4e+175) {
		tmp = x * (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 = t / (z / x)
    if (t <= (-1.9d+33)) then
        tmp = t_1
    else if (t <= (-7.7d-268)) then
        tmp = y * (x / z)
    else if (t <= 1.4d+175) then
        tmp = x * (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 = t / (z / x);
	double tmp;
	if (t <= -1.9e+33) {
		tmp = t_1;
	} else if (t <= -7.7e-268) {
		tmp = y * (x / z);
	} else if (t <= 1.4e+175) {
		tmp = x * (y / z);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = t / (z / x)
	tmp = 0
	if t <= -1.9e+33:
		tmp = t_1
	elif t <= -7.7e-268:
		tmp = y * (x / z)
	elif t <= 1.4e+175:
		tmp = x * (y / z)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(t / Float64(z / x))
	tmp = 0.0
	if (t <= -1.9e+33)
		tmp = t_1;
	elseif (t <= -7.7e-268)
		tmp = Float64(y * Float64(x / z));
	elseif (t <= 1.4e+175)
		tmp = Float64(x * Float64(y / z));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = t / (z / x);
	tmp = 0.0;
	if (t <= -1.9e+33)
		tmp = t_1;
	elseif (t <= -7.7e-268)
		tmp = y * (x / z);
	elseif (t <= 1.4e+175)
		tmp = x * (y / z);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(t / N[(z / x), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -1.9e+33], t$95$1, If[LessEqual[t, -7.7e-268], N[(y * N[(x / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.4e+175], N[(x * N[(y / z), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if t < -1.90000000000000001e33 or 1.4000000000000001e175 < t

   1. Initial program 95.3%

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

   2. Taylor expanded in z around inf 68.8%

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

      1. associate-/l* 70.9%

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

      2. neg-mul-1 70.9%

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

   4. Simplified 70.9%

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

   5. Taylor expanded in y around 0 55.6%

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

      1. associate-/l* 53.3%

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

   7. Simplified 53.3%

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

   if -1.90000000000000001e33 < t < -7.70000000000000001e-268

   1. Initial program 89.5%

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

   2. Taylor expanded in y around inf 77.8%

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

      1. associate-/l* 79.0%

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

      2. associate-/r/ 87.1%

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

   4. Applied egg-rr 87.1%

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

   if -7.70000000000000001e-268 < t < 1.4000000000000001e175

   1. Initial program 97.2%

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

   2. Taylor expanded in y around inf 74.3%

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

      1. associate-*r/ 77.7%

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

   4. Simplified 77.7%

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

4. Final simplification 72.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.9 \cdot 10^{+33}:\\ \;\;\;\;\frac{t}{\frac{z}{x}}\\ \mathbf{elif}\;t \leq -7.7 \cdot 10^{-268}:\\ \;\;\;\;y \cdot \frac{x}{z}\\ \mathbf{elif}\;t \leq 1.4 \cdot 10^{+175}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{\frac{z}{x}}\\ \end{array} \]

Alternative 6: 67.3% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{\frac{z}{t}}\\ \mathbf{if}\;t \leq -1 \cdot 10^{+33}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -8.2 \cdot 10^{-268}:\\ \;\;\;\;y \cdot \frac{x}{z}\\ \mathbf{elif}\;t \leq 2.8 \cdot 10^{+173}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ x (/ z t))))
   (if (<= t -1e+33)
     t_1
     (if (<= t -8.2e-268)
       (* y (/ x z))
       (if (<= t 2.8e+173) (* x (/ y z)) t_1)))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x / (z / t);
	double tmp;
	if (t <= -1e+33) {
		tmp = t_1;
	} else if (t <= -8.2e-268) {
		tmp = y * (x / z);
	} else if (t <= 2.8e+173) {
		tmp = x * (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 / (z / t)
    if (t <= (-1d+33)) then
        tmp = t_1
    else if (t <= (-8.2d-268)) then
        tmp = y * (x / z)
    else if (t <= 2.8d+173) then
        tmp = x * (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 / (z / t);
	double tmp;
	if (t <= -1e+33) {
		tmp = t_1;
	} else if (t <= -8.2e-268) {
		tmp = y * (x / z);
	} else if (t <= 2.8e+173) {
		tmp = x * (y / z);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x / (z / t)
	tmp = 0
	if t <= -1e+33:
		tmp = t_1
	elif t <= -8.2e-268:
		tmp = y * (x / z)
	elif t <= 2.8e+173:
		tmp = x * (y / z)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x / Float64(z / t))
	tmp = 0.0
	if (t <= -1e+33)
		tmp = t_1;
	elseif (t <= -8.2e-268)
		tmp = Float64(y * Float64(x / z));
	elseif (t <= 2.8e+173)
		tmp = Float64(x * Float64(y / z));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x / (z / t);
	tmp = 0.0;
	if (t <= -1e+33)
		tmp = t_1;
	elseif (t <= -8.2e-268)
		tmp = y * (x / z);
	elseif (t <= 2.8e+173)
		tmp = x * (y / z);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x / N[(z / t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -1e+33], t$95$1, If[LessEqual[t, -8.2e-268], N[(y * N[(x / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 2.8e+173], N[(x * N[(y / z), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if t < -9.9999999999999995e32 or 2.79999999999999982e173 < t

   1. Initial program 95.3%

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

   2. Taylor expanded in z around inf 68.8%

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

      1. associate-/l* 70.9%

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

      2. neg-mul-1 70.9%

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

   4. Simplified 70.9%

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

   5. Taylor expanded in y around 0 60.3%

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

   if -9.9999999999999995e32 < t < -8.1999999999999998e-268

   1. Initial program 89.5%

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

   2. Taylor expanded in y around inf 77.8%

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

      1. associate-/l* 79.0%

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

      2. associate-/r/ 87.1%

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

   4. Applied egg-rr 87.1%

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

   if -8.1999999999999998e-268 < t < 2.79999999999999982e173

   1. Initial program 97.2%

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

   2. Taylor expanded in y around inf 74.3%

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

      1. associate-*r/ 77.7%

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

   4. Simplified 77.7%

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

4. Final simplification 74.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1 \cdot 10^{+33}:\\ \;\;\;\;\frac{x}{\frac{z}{t}}\\ \mathbf{elif}\;t \leq -8.2 \cdot 10^{-268}:\\ \;\;\;\;y \cdot \frac{x}{z}\\ \mathbf{elif}\;t \leq 2.8 \cdot 10^{+173}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\frac{z}{t}}\\ \end{array} \]

Alternative 7: 73.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -9 \cdot 10^{+23}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \mathbf{elif}\;z \leq 4.3 \cdot 10^{+92}:\\ \;\;\;\;x \cdot \left(\frac{y}{z} - t\right)\\ \mathbf{elif}\;z \leq 6.8 \cdot 10^{+244}:\\ \;\;\;\;\frac{x}{\frac{z}{t}}\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{x}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -9e+23)
   (* x (/ y z))
   (if (<= z 4.3e+92)
     (* x (- (/ y z) t))
     (if (<= z 6.8e+244) (/ x (/ z t)) (* y (/ x z))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -9e+23) {
		tmp = x * (y / z);
	} else if (z <= 4.3e+92) {
		tmp = x * ((y / z) - t);
	} else if (z <= 6.8e+244) {
		tmp = x / (z / t);
	} else {
		tmp = y * (x / 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 <= (-9d+23)) then
        tmp = x * (y / z)
    else if (z <= 4.3d+92) then
        tmp = x * ((y / z) - t)
    else if (z <= 6.8d+244) then
        tmp = x / (z / t)
    else
        tmp = y * (x / z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -9e+23) {
		tmp = x * (y / z);
	} else if (z <= 4.3e+92) {
		tmp = x * ((y / z) - t);
	} else if (z <= 6.8e+244) {
		tmp = x / (z / t);
	} else {
		tmp = y * (x / z);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -9e+23:
		tmp = x * (y / z)
	elif z <= 4.3e+92:
		tmp = x * ((y / z) - t)
	elif z <= 6.8e+244:
		tmp = x / (z / t)
	else:
		tmp = y * (x / z)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -9e+23)
		tmp = Float64(x * Float64(y / z));
	elseif (z <= 4.3e+92)
		tmp = Float64(x * Float64(Float64(y / z) - t));
	elseif (z <= 6.8e+244)
		tmp = Float64(x / Float64(z / t));
	else
		tmp = Float64(y * Float64(x / z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (z <= -9e+23)
		tmp = x * (y / z);
	elseif (z <= 4.3e+92)
		tmp = x * ((y / z) - t);
	elseif (z <= 6.8e+244)
		tmp = x / (z / t);
	else
		tmp = y * (x / z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -9e+23], N[(x * N[(y / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 4.3e+92], N[(x * N[(N[(y / z), $MachinePrecision] - t), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 6.8e+244], N[(x / N[(z / t), $MachinePrecision]), $MachinePrecision], N[(y * N[(x / z), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if z < -8.99999999999999958e23

   1. Initial program 99.7%

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

   2. Taylor expanded in y around inf 62.0%

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

      1. associate-*r/ 65.9%

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

   4. Simplified 65.9%

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

   if -8.99999999999999958e23 < z < 4.2999999999999998e92

   1. Initial program 94.0%

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

   2. Taylor expanded in z around 0 81.4%

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

      1. +-commutative 81.4%

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

      2. mul-1-neg 81.4%

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

      3. unsub-neg 81.4%

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

      4. *-commutative 81.4%

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

      5. associate-*r/ 80.7%

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

      6. distribute-lft-out-- 85.8%

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

   4. Simplified 85.8%

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

   if 4.2999999999999998e92 < z < 6.8000000000000002e244

   1. Initial program 99.9%

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

   2. Taylor expanded in z around inf 88.7%

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

      1. associate-/l* 99.7%

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

      2. neg-mul-1 99.7%

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

   4. Simplified 99.7%

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

   5. Taylor expanded in y around 0 78.3%

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

   if 6.8000000000000002e244 < z

   1. Initial program 69.9%

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

   2. Taylor expanded in y around inf 79.7%

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

      1. associate-/l* 66.1%

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

      2. associate-/r/ 83.1%

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

   4. Applied egg-rr 83.1%

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

4. Final simplification 80.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -9 \cdot 10^{+23}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \mathbf{elif}\;z \leq 4.3 \cdot 10^{+92}:\\ \;\;\;\;x \cdot \left(\frac{y}{z} - t\right)\\ \mathbf{elif}\;z \leq 6.8 \cdot 10^{+244}:\\ \;\;\;\;\frac{x}{\frac{z}{t}}\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{x}{z}\\ \end{array} \]

Alternative 8: 89.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -61000 \lor \neg \left(z \leq 1\right):\\ \;\;\;\;\left(y + t\right) \cdot \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(\frac{y}{z} - t\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -61000.0) (not (<= z 1.0)))
   (* (+ y t) (/ x z))
   (* x (- (/ y z) t))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -61000.0) || !(z <= 1.0)) {
		tmp = (y + t) * (x / z);
	} else {
		tmp = x * ((y / z) - t);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((z <= (-61000.0d0)) .or. (.not. (z <= 1.0d0))) then
        tmp = (y + t) * (x / z)
    else
        tmp = x * ((y / z) - t)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -61000.0) || !(z <= 1.0)) {
		tmp = (y + t) * (x / z);
	} else {
		tmp = x * ((y / z) - t);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -61000.0) or not (z <= 1.0):
		tmp = (y + t) * (x / z)
	else:
		tmp = x * ((y / z) - t)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -61000.0) || !(z <= 1.0))
		tmp = Float64(Float64(y + t) * Float64(x / z));
	else
		tmp = Float64(x * Float64(Float64(y / z) - t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z <= -61000.0) || ~((z <= 1.0)))
		tmp = (y + t) * (x / z);
	else
		tmp = x * ((y / z) - t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -61000.0], N[Not[LessEqual[z, 1.0]], $MachinePrecision]], N[(N[(y + t), $MachinePrecision] * N[(x / z), $MachinePrecision]), $MachinePrecision], N[(x * N[(N[(y / z), $MachinePrecision] - t), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -61000 or 1 < z

   1. Initial program 96.2%

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

   2. Taylor expanded in z around inf 91.2%

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

      1. associate-/l* 95.7%

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

      2. associate-/r/ 89.3%

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

      3. cancel-sign-sub-inv 89.3%

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

      4. metadata-eval 89.3%

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

      5. *-lft-identity 89.3%

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

      6. +-commutative 89.3%

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

   4. Simplified 89.3%

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

   if -61000 < z < 1

   1. Initial program 93.1%

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

   2. Taylor expanded in z around 0 86.9%

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

      1. +-commutative 86.9%

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

      2. mul-1-neg 86.9%

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

      3. unsub-neg 86.9%

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

      4. *-commutative 86.9%

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

      5. associate-*r/ 84.9%

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

      6. distribute-lft-out-- 90.7%

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

   4. Simplified 90.7%

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

4. Final simplification 90.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -61000 \lor \neg \left(z \leq 1\right):\\ \;\;\;\;\left(y + t\right) \cdot \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(\frac{y}{z} - t\right)\\ \end{array} \]

Alternative 9: 71.5% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -4.1 \cdot 10^{-74}:\\ \;\;\;\;y \cdot \frac{x}{z}\\ \mathbf{elif}\;y \leq 6.4 \cdot 10^{-190}:\\ \;\;\;\;x \cdot \frac{t}{z + -1}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot y}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -4.1e-74)
   (* y (/ x z))
   (if (<= y 6.4e-190) (* x (/ t (+ z -1.0))) (/ (* x y) z))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -4.1e-74) {
		tmp = y * (x / z);
	} else if (y <= 6.4e-190) {
		tmp = x * (t / (z + -1.0));
	} else {
		tmp = (x * 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 (y <= (-4.1d-74)) then
        tmp = y * (x / z)
    else if (y <= 6.4d-190) then
        tmp = x * (t / (z + (-1.0d0)))
    else
        tmp = (x * y) / z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -4.1e-74) {
		tmp = y * (x / z);
	} else if (y <= 6.4e-190) {
		tmp = x * (t / (z + -1.0));
	} else {
		tmp = (x * y) / z;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -4.1e-74:
		tmp = y * (x / z)
	elif y <= 6.4e-190:
		tmp = x * (t / (z + -1.0))
	else:
		tmp = (x * y) / z
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -4.1e-74)
		tmp = Float64(y * Float64(x / z));
	elseif (y <= 6.4e-190)
		tmp = Float64(x * Float64(t / Float64(z + -1.0)));
	else
		tmp = Float64(Float64(x * y) / z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= -4.1e-74)
		tmp = y * (x / z);
	elseif (y <= 6.4e-190)
		tmp = x * (t / (z + -1.0));
	else
		tmp = (x * y) / z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -4.1e-74], N[(y * N[(x / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 6.4e-190], N[(x * N[(t / N[(z + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x * y), $MachinePrecision] / z), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -4.10000000000000032e-74

   1. Initial program 93.7%

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

   2. Taylor expanded in y around inf 79.5%

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

      1. associate-/l* 80.4%

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

      2. associate-/r/ 82.1%

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

   4. Applied egg-rr 82.1%

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

   if -4.10000000000000032e-74 < y < 6.4000000000000001e-190

   1. Initial program 98.2%

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

   2. Taylor expanded in y around 0 78.8%

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

      1. associate-*r/ 78.8%

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

      2. associate-*r* 78.8%

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

      3. neg-mul-1 78.8%

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

      4. associate-*l/ 80.4%

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

      5. *-commutative 80.4%

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

      6. distribute-frac-neg 80.4%

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

      7. neg-mul-1 80.4%

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

      8. metadata-eval 80.4%

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

      9. times-frac 80.4%

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

      10. *-lft-identity 80.4%

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

      11. neg-mul-1 80.4%

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

      12. neg-sub0 80.4%

          \[\leadsto x \cdot \frac{t}{\color{blue}{0 - \left(1 - z\right)}} \]

      13. associate--r- 80.4%

          \[\leadsto x \cdot \frac{t}{\color{blue}{\left(0 - 1\right) + z}} \]

      14. metadata-eval 80.4%

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

   4. Simplified 80.4%

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

   if 6.4000000000000001e-190 < y

   1. Initial program 91.6%

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

   2. Taylor expanded in y around inf 80.8%

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

4. Final simplification 81.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4.1 \cdot 10^{-74}:\\ \;\;\;\;y \cdot \frac{x}{z}\\ \mathbf{elif}\;y \leq 6.4 \cdot 10^{-190}:\\ \;\;\;\;x \cdot \frac{t}{z + -1}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot y}{z}\\ \end{array} \]

Alternative 10: 63.9% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -2.8 \cdot 10^{+152} \lor \neg \left(t \leq 2.05 \cdot 10^{+165}\right):\\ \;\;\;\;x \cdot \left(-t\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= t -2.8e+152) (not (<= t 2.05e+165))) (* x (- t)) (* x (/ y z))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((t <= -2.8e+152) || !(t <= 2.05e+165)) {
		tmp = x * -t;
	} else {
		tmp = x * (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 <= (-2.8d+152)) .or. (.not. (t <= 2.05d+165))) then
        tmp = x * -t
    else
        tmp = x * (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 <= -2.8e+152) || !(t <= 2.05e+165)) {
		tmp = x * -t;
	} else {
		tmp = x * (y / z);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (t <= -2.8e+152) or not (t <= 2.05e+165):
		tmp = x * -t
	else:
		tmp = x * (y / z)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((t <= -2.8e+152) || !(t <= 2.05e+165))
		tmp = Float64(x * Float64(-t));
	else
		tmp = Float64(x * Float64(y / z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((t <= -2.8e+152) || ~((t <= 2.05e+165)))
		tmp = x * -t;
	else
		tmp = x * (y / z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[t, -2.8e+152], N[Not[LessEqual[t, 2.05e+165]], $MachinePrecision]], N[(x * (-t)), $MachinePrecision], N[(x * N[(y / z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -2.8000000000000002e152 or 2.0500000000000001e165 < t

   1. Initial program 95.1%

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

   2. Taylor expanded in y around 0 72.6%

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

      1. associate-*r/ 72.6%

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

      2. associate-*r* 72.6%

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

      3. neg-mul-1 72.6%

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

      4. associate-*l/ 78.8%

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

      5. *-commutative 78.8%

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

      6. distribute-frac-neg 78.8%

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

      7. neg-mul-1 78.8%

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

      8. metadata-eval 78.8%

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

      9. times-frac 78.8%

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

      10. *-lft-identity 78.8%

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

      11. neg-mul-1 78.8%

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

      12. neg-sub0 78.8%

          \[\leadsto x \cdot \frac{t}{\color{blue}{0 - \left(1 - z\right)}} \]

      13. associate--r- 78.8%

          \[\leadsto x \cdot \frac{t}{\color{blue}{\left(0 - 1\right) + z}} \]

      14. metadata-eval 78.8%

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

   4. Simplified 78.8%

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

   5. Taylor expanded in z around 0 42.2%

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

      1. mul-1-neg 42.2%

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

      2. *-commutative 42.2%

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

      3. distribute-rgt-neg-in 42.2%

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

   7. Simplified 42.2%

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

   if -2.8000000000000002e152 < t < 2.0500000000000001e165

   1. Initial program 94.4%

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

   2. Taylor expanded in y around inf 73.8%

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

      1. associate-*r/ 75.7%

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

   4. Simplified 75.7%

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

4. Final simplification 67.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.8 \cdot 10^{+152} \lor \neg \left(t \leq 2.05 \cdot 10^{+165}\right):\\ \;\;\;\;x \cdot \left(-t\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \end{array} \]

Alternative 11: 62.2% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -4.8 \cdot 10^{-268}:\\ \;\;\;\;y \cdot \frac{x}{z}\\ \mathbf{elif}\;t \leq 9.5 \cdot 10^{+163}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(-t\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= t -4.8e-268)
   (* y (/ x z))
   (if (<= t 9.5e+163) (* x (/ y z)) (* x (- t)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= -4.8e-268) {
		tmp = y * (x / z);
	} else if (t <= 9.5e+163) {
		tmp = x * (y / z);
	} else {
		tmp = x * -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 <= (-4.8d-268)) then
        tmp = y * (x / z)
    else if (t <= 9.5d+163) then
        tmp = x * (y / z)
    else
        tmp = x * -t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= -4.8e-268) {
		tmp = y * (x / z);
	} else if (t <= 9.5e+163) {
		tmp = x * (y / z);
	} else {
		tmp = x * -t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if t <= -4.8e-268:
		tmp = y * (x / z)
	elif t <= 9.5e+163:
		tmp = x * (y / z)
	else:
		tmp = x * -t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (t <= -4.8e-268)
		tmp = Float64(y * Float64(x / z));
	elseif (t <= 9.5e+163)
		tmp = Float64(x * Float64(y / z));
	else
		tmp = Float64(x * Float64(-t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (t <= -4.8e-268)
		tmp = y * (x / z);
	elseif (t <= 9.5e+163)
		tmp = x * (y / z);
	else
		tmp = x * -t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[t, -4.8e-268], N[(y * N[(x / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 9.5e+163], N[(x * N[(y / z), $MachinePrecision]), $MachinePrecision], N[(x * (-t)), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -4.7999999999999998e-268

   1. Initial program 91.4%

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

   2. Taylor expanded in y around inf 61.6%

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

      1. associate-/l* 60.0%

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

      2. associate-/r/ 66.7%

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

   4. Applied egg-rr 66.7%

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

   if -4.7999999999999998e-268 < t < 9.50000000000000053e163

   1. Initial program 97.1%

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

   2. Taylor expanded in y around inf 75.5%

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

      1. associate-*r/ 78.9%

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

   4. Simplified 78.9%

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

   if 9.50000000000000053e163 < t

   1. Initial program 99.8%

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

   2. Taylor expanded in y around 0 76.7%

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

      1. associate-*r/ 76.7%

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

      2. associate-*r* 76.7%

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

      3. neg-mul-1 76.7%

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

      4. associate-*l/ 84.1%

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

      5. *-commutative 84.1%

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

      6. distribute-frac-neg 84.1%

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

      7. neg-mul-1 84.1%

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

      8. metadata-eval 84.1%

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

      9. times-frac 84.1%

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

      10. *-lft-identity 84.1%

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

      11. neg-mul-1 84.1%

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

      12. neg-sub0 84.1%

          \[\leadsto x \cdot \frac{t}{\color{blue}{0 - \left(1 - z\right)}} \]

      13. associate--r- 84.1%

          \[\leadsto x \cdot \frac{t}{\color{blue}{\left(0 - 1\right) + z}} \]

      14. metadata-eval 84.1%

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

   4. Simplified 84.1%

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

   5. Taylor expanded in z around 0 47.1%

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

      1. mul-1-neg 47.1%

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

      2. *-commutative 47.1%

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

      3. distribute-rgt-neg-in 47.1%

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

   7. Simplified 47.1%

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

4. Final simplification 69.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -4.8 \cdot 10^{-268}:\\ \;\;\;\;y \cdot \frac{x}{z}\\ \mathbf{elif}\;t \leq 9.5 \cdot 10^{+163}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(-t\right)\\ \end{array} \]

Alternative 12: 23.1% accurate, 2.8× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 94.5%

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

2. Taylor expanded in y around 0 44.9%

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

   1. associate-*r/ 44.9%

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

   2. associate-*r* 44.9%

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

   3. neg-mul-1 44.9%

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

   4. associate-*l/ 45.8%

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

   5. *-commutative 45.8%

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

   6. distribute-frac-neg 45.8%

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

   7. neg-mul-1 45.8%

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

   8. metadata-eval 45.8%

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

   9. times-frac 45.8%

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

   10. *-lft-identity 45.8%

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

   11. neg-mul-1 45.8%

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

   12. neg-sub0 45.8%

       \[\leadsto x \cdot \frac{t}{\color{blue}{0 - \left(1 - z\right)}} \]

   13. associate--r- 45.8%

       \[\leadsto x \cdot \frac{t}{\color{blue}{\left(0 - 1\right) + z}} \]

   14. metadata-eval 45.8%

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

4. Simplified 45.8%

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

5. Taylor expanded in z around 0 25.3%

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

   1. mul-1-neg 25.3%

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

   2. *-commutative 25.3%

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

   3. distribute-rgt-neg-in 25.3%

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

7. Simplified 25.3%

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

8. Final simplification 25.3%

   \[\leadsto x \cdot \left(-t\right) \]

Developer target: 95.2% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(\frac{y}{z} - t \cdot \frac{1}{1 - z}\right)\\ t_2 := x \cdot \left(\frac{y}{z} - \frac{t}{1 - z}\right)\\ \mathbf{if}\;t_2 < -7.623226303312042 \cdot 10^{-196}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t_2 < 1.4133944927702302 \cdot 10^{-211}:\\ \;\;\;\;\frac{y \cdot x}{z} + \left(-\frac{t \cdot x}{1 - z}\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* x (- (/ y z) (* t (/ 1.0 (- 1.0 z))))))
        (t_2 (* x (- (/ y z) (/ t (- 1.0 z))))))
   (if (< t_2 -7.623226303312042e-196)
     t_1
     (if (< t_2 1.4133944927702302e-211)
       (+ (/ (* y x) z) (- (/ (* t x) (- 1.0 z))))
       t_1))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x * ((y / z) - (t * (1.0 / (1.0 - z))));
	double t_2 = x * ((y / z) - (t / (1.0 - z)));
	double tmp;
	if (t_2 < -7.623226303312042e-196) {
		tmp = t_1;
	} else if (t_2 < 1.4133944927702302e-211) {
		tmp = ((y * x) / z) + -((t * x) / (1.0 - 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) :: t_2
    real(8) :: tmp
    t_1 = x * ((y / z) - (t * (1.0d0 / (1.0d0 - z))))
    t_2 = x * ((y / z) - (t / (1.0d0 - z)))
    if (t_2 < (-7.623226303312042d-196)) then
        tmp = t_1
    else if (t_2 < 1.4133944927702302d-211) then
        tmp = ((y * x) / z) + -((t * x) / (1.0d0 - 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 * (1.0 / (1.0 - z))));
	double t_2 = x * ((y / z) - (t / (1.0 - z)));
	double tmp;
	if (t_2 < -7.623226303312042e-196) {
		tmp = t_1;
	} else if (t_2 < 1.4133944927702302e-211) {
		tmp = ((y * x) / z) + -((t * x) / (1.0 - z));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x * ((y / z) - (t * (1.0 / (1.0 - z))))
	t_2 = x * ((y / z) - (t / (1.0 - z)))
	tmp = 0
	if t_2 < -7.623226303312042e-196:
		tmp = t_1
	elif t_2 < 1.4133944927702302e-211:
		tmp = ((y * x) / z) + -((t * x) / (1.0 - z))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x * Float64(Float64(y / z) - Float64(t * Float64(1.0 / Float64(1.0 - z)))))
	t_2 = Float64(x * Float64(Float64(y / z) - Float64(t / Float64(1.0 - z))))
	tmp = 0.0
	if (t_2 < -7.623226303312042e-196)
		tmp = t_1;
	elseif (t_2 < 1.4133944927702302e-211)
		tmp = Float64(Float64(Float64(y * x) / z) + Float64(-Float64(Float64(t * x) / Float64(1.0 - z))));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x * ((y / z) - (t * (1.0 / (1.0 - z))));
	t_2 = x * ((y / z) - (t / (1.0 - z)));
	tmp = 0.0;
	if (t_2 < -7.623226303312042e-196)
		tmp = t_1;
	elseif (t_2 < 1.4133944927702302e-211)
		tmp = ((y * x) / z) + -((t * x) / (1.0 - 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 * N[(1.0 / N[(1.0 - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x * N[(N[(y / z), $MachinePrecision] - N[(t / N[(1.0 - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[Less[t$95$2, -7.623226303312042e-196], t$95$1, If[Less[t$95$2, 1.4133944927702302e-211], N[(N[(N[(y * x), $MachinePrecision] / z), $MachinePrecision] + (-N[(N[(t * x), $MachinePrecision] / N[(1.0 - z), $MachinePrecision]), $MachinePrecision])), $MachinePrecision], t$95$1]]]]

Reproduce

herbie shell --seed 2023293 
(FPCore (x y z t)
  :name "Numeric.SpecFunctions:invIncompleteBetaWorker from math-functions-0.1.5.2, C"
  :precision binary64

  :herbie-target
  (if (< (* x (- (/ y z) (/ t (- 1.0 z)))) -7.623226303312042e-196) (* x (- (/ y z) (* t (/ 1.0 (- 1.0 z))))) (if (< (* x (- (/ y z) (/ t (- 1.0 z)))) 1.4133944927702302e-211) (+ (/ (* y x) z) (- (/ (* t x) (- 1.0 z)))) (* x (- (/ y z) (* t (/ 1.0 (- 1.0 z)))))))

  (* x (- (/ y z) (/ t (- 1.0 z)))))