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

Percentage Accurate: 94.6% → 97.3%

Time: 13.2s

Alternatives: 12

Speedup: 0.2×

• 21.1% 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: 97.3% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(\frac{y}{z} - \frac{t}{1 - z}\right)\\ \mathbf{if}\;t_1 \leq -\infty:\\ \;\;\;\;\frac{y \cdot \left(1 - z\right) - z \cdot t}{\frac{z \cdot \left(1 - z\right)}{x}}\\ \mathbf{elif}\;t_1 \leq -1 \cdot 10^{-240} \lor \neg \left(t_1 \leq 0\right):\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot \left(y + t\right)}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* x (- (/ y z) (/ t (- 1.0 z))))))
   (if (<= t_1 (- INFINITY))
     (/ (- (* y (- 1.0 z)) (* z t)) (/ (* z (- 1.0 z)) x))
     (if (or (<= t_1 -1e-240) (not (<= t_1 0.0))) t_1 (/ (* x (+ y t)) z)))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x * ((y / z) - (t / (1.0 - z)));
	double tmp;
	if (t_1 <= -((double) INFINITY)) {
		tmp = ((y * (1.0 - z)) - (z * t)) / ((z * (1.0 - z)) / x);
	} else if ((t_1 <= -1e-240) || !(t_1 <= 0.0)) {
		tmp = t_1;
	} else {
		tmp = (x * (y + t)) / z;
	}
	return tmp;
}

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = x * ((y / z) - (t / (1.0 - z)));
	double tmp;
	if (t_1 <= -Double.POSITIVE_INFINITY) {
		tmp = ((y * (1.0 - z)) - (z * t)) / ((z * (1.0 - z)) / x);
	} else if ((t_1 <= -1e-240) || !(t_1 <= 0.0)) {
		tmp = t_1;
	} else {
		tmp = (x * (y + t)) / z;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x * ((y / z) - (t / (1.0 - z)))
	tmp = 0
	if t_1 <= -math.inf:
		tmp = ((y * (1.0 - z)) - (z * t)) / ((z * (1.0 - z)) / x)
	elif (t_1 <= -1e-240) or not (t_1 <= 0.0):
		tmp = t_1
	else:
		tmp = (x * (y + t)) / z
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x * Float64(Float64(y / z) - Float64(t / Float64(1.0 - z))))
	tmp = 0.0
	if (t_1 <= Float64(-Inf))
		tmp = Float64(Float64(Float64(y * Float64(1.0 - z)) - Float64(z * t)) / Float64(Float64(z * Float64(1.0 - z)) / x));
	elseif ((t_1 <= -1e-240) || !(t_1 <= 0.0))
		tmp = t_1;
	else
		tmp = Float64(Float64(x * Float64(y + t)) / z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x * ((y / z) - (t / (1.0 - z)));
	tmp = 0.0;
	if (t_1 <= -Inf)
		tmp = ((y * (1.0 - z)) - (z * t)) / ((z * (1.0 - z)) / x);
	elseif ((t_1 <= -1e-240) || ~((t_1 <= 0.0)))
		tmp = t_1;
	else
		tmp = (x * (y + t)) / z;
	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 - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, (-Infinity)], N[(N[(N[(y * N[(1.0 - z), $MachinePrecision]), $MachinePrecision] - N[(z * t), $MachinePrecision]), $MachinePrecision] / N[(N[(z * N[(1.0 - z), $MachinePrecision]), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[t$95$1, -1e-240], N[Not[LessEqual[t$95$1, 0.0]], $MachinePrecision]], t$95$1, N[(N[(x * N[(y + t), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 x (-.f64 (/.f64 y z) (/.f64 t (-.f64 1 z)))) < -inf.0

   1. Initial program 75.1%

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

      1. *-commutative 75.1%

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

      2. frac-sub 75.1%

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

      3. associate-*l/ 100.0%

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

      4. associate-/l* 100.0%

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

   3. Applied egg-rr 100.0%

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

   if -inf.0 < (*.f64 x (-.f64 (/.f64 y z) (/.f64 t (-.f64 1 z)))) < -9.9999999999999997e-241 or -0.0 < (*.f64 x (-.f64 (/.f64 y z) (/.f64 t (-.f64 1 z))))

   1. Initial program 98.3%

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

   if -9.9999999999999997e-241 < (*.f64 x (-.f64 (/.f64 y z) (/.f64 t (-.f64 1 z)))) < -0.0

   1. Initial program 78.4%

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

   2. Taylor expanded in z around inf 99.9%

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

4. Final simplification 98.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot \left(\frac{y}{z} - \frac{t}{1 - z}\right) \leq -\infty:\\ \;\;\;\;\frac{y \cdot \left(1 - z\right) - z \cdot t}{\frac{z \cdot \left(1 - z\right)}{x}}\\ \mathbf{elif}\;x \cdot \left(\frac{y}{z} - \frac{t}{1 - z}\right) \leq -1 \cdot 10^{-240} \lor \neg \left(x \cdot \left(\frac{y}{z} - \frac{t}{1 - z}\right) \leq 0\right):\\ \;\;\;\;x \cdot \left(\frac{y}{z} - \frac{t}{1 - z}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot \left(y + t\right)}{z}\\ \end{array} \]

Alternative 2: 95.5% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(\frac{y}{z} - \frac{t}{1 - z}\right)\\ \mathbf{if}\;t_1 \leq -5 \cdot 10^{+301}:\\ \;\;\;\;\frac{y + t}{\frac{z}{x}}\\ \mathbf{elif}\;t_1 \leq -1 \cdot 10^{-240} \lor \neg \left(t_1 \leq 0\right):\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot \left(y + t\right)}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* x (- (/ y z) (/ t (- 1.0 z))))))
   (if (<= t_1 -5e+301)
     (/ (+ y t) (/ z x))
     (if (or (<= t_1 -1e-240) (not (<= t_1 0.0))) t_1 (/ (* x (+ y t)) z)))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x * ((y / z) - (t / (1.0 - z)));
	double tmp;
	if (t_1 <= -5e+301) {
		tmp = (y + t) / (z / x);
	} else if ((t_1 <= -1e-240) || !(t_1 <= 0.0)) {
		tmp = t_1;
	} else {
		tmp = (x * (y + 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 / z) - (t / (1.0d0 - z)))
    if (t_1 <= (-5d+301)) then
        tmp = (y + t) / (z / x)
    else if ((t_1 <= (-1d-240)) .or. (.not. (t_1 <= 0.0d0))) then
        tmp = t_1
    else
        tmp = (x * (y + 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 / z) - (t / (1.0 - z)));
	double tmp;
	if (t_1 <= -5e+301) {
		tmp = (y + t) / (z / x);
	} else if ((t_1 <= -1e-240) || !(t_1 <= 0.0)) {
		tmp = t_1;
	} else {
		tmp = (x * (y + t)) / z;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x * ((y / z) - (t / (1.0 - z)))
	tmp = 0
	if t_1 <= -5e+301:
		tmp = (y + t) / (z / x)
	elif (t_1 <= -1e-240) or not (t_1 <= 0.0):
		tmp = t_1
	else:
		tmp = (x * (y + t)) / z
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x * Float64(Float64(y / z) - Float64(t / Float64(1.0 - z))))
	tmp = 0.0
	if (t_1 <= -5e+301)
		tmp = Float64(Float64(y + t) / Float64(z / x));
	elseif ((t_1 <= -1e-240) || !(t_1 <= 0.0))
		tmp = t_1;
	else
		tmp = Float64(Float64(x * Float64(y + t)) / z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x * ((y / z) - (t / (1.0 - z)));
	tmp = 0.0;
	if (t_1 <= -5e+301)
		tmp = (y + t) / (z / x);
	elseif ((t_1 <= -1e-240) || ~((t_1 <= 0.0)))
		tmp = t_1;
	else
		tmp = (x * (y + t)) / z;
	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 - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -5e+301], N[(N[(y + t), $MachinePrecision] / N[(z / x), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[t$95$1, -1e-240], N[Not[LessEqual[t$95$1, 0.0]], $MachinePrecision]], t$95$1, N[(N[(x * N[(y + t), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 x (-.f64 (/.f64 y z) (/.f64 t (-.f64 1 z)))) < -5.0000000000000004e301

   1. Initial program 77.1%

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

      1. add-cube-cbrt 76.9%

         \[\leadsto x \cdot \color{blue}{\left(\left(\sqrt[3]{\frac{y}{z} - \frac{t}{1 - z}} \cdot \sqrt[3]{\frac{y}{z} - \frac{t}{1 - z}}\right) \cdot \sqrt[3]{\frac{y}{z} - \frac{t}{1 - z}}\right)} \]

      2. pow3 77.0%

         \[\leadsto x \cdot \color{blue}{{\left(\sqrt[3]{\frac{y}{z} - \frac{t}{1 - z}}\right)}^{3}} \]

   3. Applied egg-rr 77.0%

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

      1. rem-cube-cbrt 77.1%

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

      2. frac-sub 69.8%

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

      3. associate-*r/ 92.6%

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

   5. Applied egg-rr 92.6%

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

      1. *-commutative 92.6%

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

      2. associate-/l* 92.7%

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

      3. *-commutative 92.7%

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

      4. *-commutative 92.7%

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

      5. *-commutative 92.7%

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

      6. associate-/l* 93.0%

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

   7. Simplified 93.0%

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

   8. Taylor expanded in z around -inf 90.3%

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

      1. *-commutative 90.3%

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

      2. associate-/l* 97.3%

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

      3. mul-1-neg 97.3%

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

      4. sub-neg 97.3%

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

      5. remove-double-neg 97.3%

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

   10. Simplified 97.3%

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

   if -5.0000000000000004e301 < (*.f64 x (-.f64 (/.f64 y z) (/.f64 t (-.f64 1 z)))) < -9.9999999999999997e-241 or -0.0 < (*.f64 x (-.f64 (/.f64 y z) (/.f64 t (-.f64 1 z))))

   1. Initial program 98.3%

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

   if -9.9999999999999997e-241 < (*.f64 x (-.f64 (/.f64 y z) (/.f64 t (-.f64 1 z)))) < -0.0

   1. Initial program 78.4%

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

   2. Taylor expanded in z around inf 99.9%

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

4. Final simplification 98.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot \left(\frac{y}{z} - \frac{t}{1 - z}\right) \leq -5 \cdot 10^{+301}:\\ \;\;\;\;\frac{y + t}{\frac{z}{x}}\\ \mathbf{elif}\;x \cdot \left(\frac{y}{z} - \frac{t}{1 - z}\right) \leq -1 \cdot 10^{-240} \lor \neg \left(x \cdot \left(\frac{y}{z} - \frac{t}{1 - z}\right) \leq 0\right):\\ \;\;\;\;x \cdot \left(\frac{y}{z} - \frac{t}{1 - z}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot \left(y + t\right)}{z}\\ \end{array} \]

Alternative 3: 97.3% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(\frac{y}{z} - \frac{t}{1 - z}\right)\\ \mathbf{if}\;t_1 \leq -\infty:\\ \;\;\;\;\frac{x \cdot \left(y \cdot \left(1 - z\right) - z \cdot t\right)}{z \cdot \left(1 - z\right)}\\ \mathbf{elif}\;t_1 \leq -1 \cdot 10^{-240} \lor \neg \left(t_1 \leq 0\right):\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot \left(y + t\right)}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* x (- (/ y z) (/ t (- 1.0 z))))))
   (if (<= t_1 (- INFINITY))
     (/ (* x (- (* y (- 1.0 z)) (* z t))) (* z (- 1.0 z)))
     (if (or (<= t_1 -1e-240) (not (<= t_1 0.0))) t_1 (/ (* x (+ y t)) z)))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x * ((y / z) - (t / (1.0 - z)));
	double tmp;
	if (t_1 <= -((double) INFINITY)) {
		tmp = (x * ((y * (1.0 - z)) - (z * t))) / (z * (1.0 - z));
	} else if ((t_1 <= -1e-240) || !(t_1 <= 0.0)) {
		tmp = t_1;
	} else {
		tmp = (x * (y + t)) / z;
	}
	return tmp;
}

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = x * ((y / z) - (t / (1.0 - z)));
	double tmp;
	if (t_1 <= -Double.POSITIVE_INFINITY) {
		tmp = (x * ((y * (1.0 - z)) - (z * t))) / (z * (1.0 - z));
	} else if ((t_1 <= -1e-240) || !(t_1 <= 0.0)) {
		tmp = t_1;
	} else {
		tmp = (x * (y + t)) / z;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x * ((y / z) - (t / (1.0 - z)))
	tmp = 0
	if t_1 <= -math.inf:
		tmp = (x * ((y * (1.0 - z)) - (z * t))) / (z * (1.0 - z))
	elif (t_1 <= -1e-240) or not (t_1 <= 0.0):
		tmp = t_1
	else:
		tmp = (x * (y + t)) / z
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x * Float64(Float64(y / z) - Float64(t / Float64(1.0 - z))))
	tmp = 0.0
	if (t_1 <= Float64(-Inf))
		tmp = Float64(Float64(x * Float64(Float64(y * Float64(1.0 - z)) - Float64(z * t))) / Float64(z * Float64(1.0 - z)));
	elseif ((t_1 <= -1e-240) || !(t_1 <= 0.0))
		tmp = t_1;
	else
		tmp = Float64(Float64(x * Float64(y + t)) / z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x * ((y / z) - (t / (1.0 - z)));
	tmp = 0.0;
	if (t_1 <= -Inf)
		tmp = (x * ((y * (1.0 - z)) - (z * t))) / (z * (1.0 - z));
	elseif ((t_1 <= -1e-240) || ~((t_1 <= 0.0)))
		tmp = t_1;
	else
		tmp = (x * (y + t)) / z;
	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 - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, (-Infinity)], N[(N[(x * N[(N[(y * N[(1.0 - z), $MachinePrecision]), $MachinePrecision] - N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(z * N[(1.0 - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[t$95$1, -1e-240], N[Not[LessEqual[t$95$1, 0.0]], $MachinePrecision]], t$95$1, N[(N[(x * N[(y + t), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 x (-.f64 (/.f64 y z) (/.f64 t (-.f64 1 z)))) < -inf.0

   1. Initial program 75.1%

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

      1. *-commutative 75.1%

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

      2. frac-sub 75.1%

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

      3. associate-*l/ 100.0%

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

   3. Applied egg-rr 100.0%

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

   if -inf.0 < (*.f64 x (-.f64 (/.f64 y z) (/.f64 t (-.f64 1 z)))) < -9.9999999999999997e-241 or -0.0 < (*.f64 x (-.f64 (/.f64 y z) (/.f64 t (-.f64 1 z))))

   1. Initial program 98.3%

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

   if -9.9999999999999997e-241 < (*.f64 x (-.f64 (/.f64 y z) (/.f64 t (-.f64 1 z)))) < -0.0

   1. Initial program 78.4%

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

   2. Taylor expanded in z around inf 99.9%

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

4. Final simplification 98.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot \left(\frac{y}{z} - \frac{t}{1 - z}\right) \leq -\infty:\\ \;\;\;\;\frac{x \cdot \left(y \cdot \left(1 - z\right) - z \cdot t\right)}{z \cdot \left(1 - z\right)}\\ \mathbf{elif}\;x \cdot \left(\frac{y}{z} - \frac{t}{1 - z}\right) \leq -1 \cdot 10^{-240} \lor \neg \left(x \cdot \left(\frac{y}{z} - \frac{t}{1 - z}\right) \leq 0\right):\\ \;\;\;\;x \cdot \left(\frac{y}{z} - \frac{t}{1 - z}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot \left(y + t\right)}{z}\\ \end{array} \]

Alternative 4: 73.5% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(\frac{y}{z} - t\right)\\ \mathbf{if}\;z \leq -2 \cdot 10^{+42}:\\ \;\;\;\;\frac{x}{\frac{z}{t}}\\ \mathbf{elif}\;z \leq -7.5 \cdot 10^{-198}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 2.15 \cdot 10^{-259}:\\ \;\;\;\;\frac{x \cdot y}{z}\\ \mathbf{elif}\;z \leq 820000000000:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 5 \cdot 10^{+90}:\\ \;\;\;\;x \cdot \frac{t}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\frac{z}{y}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* x (- (/ y z) t))))
   (if (<= z -2e+42)
     (/ x (/ z t))
     (if (<= z -7.5e-198)
       t_1
       (if (<= z 2.15e-259)
         (/ (* x y) z)
         (if (<= z 820000000000.0)
           t_1
           (if (<= z 5e+90) (* x (/ t z)) (/ x (/ z y)))))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x * ((y / z) - t);
	double tmp;
	if (z <= -2e+42) {
		tmp = x / (z / t);
	} else if (z <= -7.5e-198) {
		tmp = t_1;
	} else if (z <= 2.15e-259) {
		tmp = (x * y) / z;
	} else if (z <= 820000000000.0) {
		tmp = t_1;
	} else if (z <= 5e+90) {
		tmp = x * (t / z);
	} 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) :: t_1
    real(8) :: tmp
    t_1 = x * ((y / z) - t)
    if (z <= (-2d+42)) then
        tmp = x / (z / t)
    else if (z <= (-7.5d-198)) then
        tmp = t_1
    else if (z <= 2.15d-259) then
        tmp = (x * y) / z
    else if (z <= 820000000000.0d0) then
        tmp = t_1
    else if (z <= 5d+90) then
        tmp = x * (t / z)
    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 t_1 = x * ((y / z) - t);
	double tmp;
	if (z <= -2e+42) {
		tmp = x / (z / t);
	} else if (z <= -7.5e-198) {
		tmp = t_1;
	} else if (z <= 2.15e-259) {
		tmp = (x * y) / z;
	} else if (z <= 820000000000.0) {
		tmp = t_1;
	} else if (z <= 5e+90) {
		tmp = x * (t / z);
	} else {
		tmp = x / (z / y);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x * ((y / z) - t)
	tmp = 0
	if z <= -2e+42:
		tmp = x / (z / t)
	elif z <= -7.5e-198:
		tmp = t_1
	elif z <= 2.15e-259:
		tmp = (x * y) / z
	elif z <= 820000000000.0:
		tmp = t_1
	elif z <= 5e+90:
		tmp = x * (t / z)
	else:
		tmp = x / (z / y)
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x * Float64(Float64(y / z) - t))
	tmp = 0.0
	if (z <= -2e+42)
		tmp = Float64(x / Float64(z / t));
	elseif (z <= -7.5e-198)
		tmp = t_1;
	elseif (z <= 2.15e-259)
		tmp = Float64(Float64(x * y) / z);
	elseif (z <= 820000000000.0)
		tmp = t_1;
	elseif (z <= 5e+90)
		tmp = Float64(x * Float64(t / z));
	else
		tmp = Float64(x / Float64(z / y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x * ((y / z) - t);
	tmp = 0.0;
	if (z <= -2e+42)
		tmp = x / (z / t);
	elseif (z <= -7.5e-198)
		tmp = t_1;
	elseif (z <= 2.15e-259)
		tmp = (x * y) / z;
	elseif (z <= 820000000000.0)
		tmp = t_1;
	elseif (z <= 5e+90)
		tmp = x * (t / z);
	else
		tmp = x / (z / y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x * N[(N[(y / z), $MachinePrecision] - t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -2e+42], N[(x / N[(z / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -7.5e-198], t$95$1, If[LessEqual[z, 2.15e-259], N[(N[(x * y), $MachinePrecision] / z), $MachinePrecision], If[LessEqual[z, 820000000000.0], t$95$1, If[LessEqual[z, 5e+90], N[(x * N[(t / z), $MachinePrecision]), $MachinePrecision], N[(x / N[(z / y), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 5 regimes

2. if z < -2.00000000000000009e42

   1. Initial program 92.5%

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

      1. flip-- 75.2%

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

      2. associate-*r/ 67.9%

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

      3. associate-/l* 75.2%

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

      4. *-un-lft-identity 75.2%

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

      5. associate-/l* 75.2%

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

      6. flip-- 91.7%

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

   3. Applied egg-rr 91.7%

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

   4. Taylor expanded in y around 0 69.7%

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

      1. associate-*r/ 69.7%

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

      2. neg-mul-1 69.7%

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

      3. neg-sub0 69.7%

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

      4. associate--r- 69.7%

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

      5. metadata-eval 69.7%

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

   6. Simplified 69.7%

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

   7. Taylor expanded in z around inf 69.7%

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

   if -2.00000000000000009e42 < z < -7.50000000000000064e-198 or 2.15e-259 < z < 8.2e11

   1. Initial program 95.0%

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

   2. Taylor expanded in z around 0 91.1%

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

   if -7.50000000000000064e-198 < z < 2.15e-259

   1. Initial program 83.1%

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

   2. Taylor expanded in y around inf 96.9%

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

   if 8.2e11 < z < 5.0000000000000004e90

   1. Initial program 99.7%

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

   2. Taylor expanded in y around 0 75.7%

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

      1. associate-*r/ 75.7%

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

      2. associate-*r* 75.7%

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

      3. mul-1-neg 75.7%

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

      4. associate-*l/ 75.8%

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

      5. *-commutative 75.8%

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

   4. Simplified 75.8%

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

   5. Taylor expanded in z around inf 75.8%

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

   if 5.0000000000000004e90 < z

   1. Initial program 92.1%

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

      1. flip-- 68.4%

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

      2. associate-*r/ 60.6%

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

      3. associate-/l* 68.3%

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

      4. *-un-lft-identity 68.3%

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

      5. associate-/l* 68.4%

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

      6. flip-- 91.5%

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

   3. Applied egg-rr 91.5%

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

   4. Taylor expanded in y around inf 59.0%

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

      1. associate-/l* 68.9%

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

   6. Simplified 68.9%

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

4. Final simplification 83.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2 \cdot 10^{+42}:\\ \;\;\;\;\frac{x}{\frac{z}{t}}\\ \mathbf{elif}\;z \leq -7.5 \cdot 10^{-198}:\\ \;\;\;\;x \cdot \left(\frac{y}{z} - t\right)\\ \mathbf{elif}\;z \leq 2.15 \cdot 10^{-259}:\\ \;\;\;\;\frac{x \cdot y}{z}\\ \mathbf{elif}\;z \leq 820000000000:\\ \;\;\;\;x \cdot \left(\frac{y}{z} - t\right)\\ \mathbf{elif}\;z \leq 5 \cdot 10^{+90}:\\ \;\;\;\;x \cdot \frac{t}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\frac{z}{y}}\\ \end{array} \]

Alternative 5: 86.5% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(\frac{y}{z} - t\right)\\ t_2 := \left(y + t\right) \cdot \frac{x}{z}\\ \mathbf{if}\;z \leq -4.15 \cdot 10^{+21}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq -6.5 \cdot 10^{-198}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 1.9 \cdot 10^{-259}:\\ \;\;\;\;\frac{x \cdot y}{z}\\ \mathbf{elif}\;z \leq 1.45 \cdot 10^{-14}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* x (- (/ y z) t))) (t_2 (* (+ y t) (/ x z))))
   (if (<= z -4.15e+21)
     t_2
     (if (<= z -6.5e-198)
       t_1
       (if (<= z 1.9e-259) (/ (* x y) z) (if (<= z 1.45e-14) t_1 t_2))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x * ((y / z) - t);
	double t_2 = (y + t) * (x / z);
	double tmp;
	if (z <= -4.15e+21) {
		tmp = t_2;
	} else if (z <= -6.5e-198) {
		tmp = t_1;
	} else if (z <= 1.9e-259) {
		tmp = (x * y) / z;
	} else if (z <= 1.45e-14) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = x * ((y / z) - t)
    t_2 = (y + t) * (x / z)
    if (z <= (-4.15d+21)) then
        tmp = t_2
    else if (z <= (-6.5d-198)) then
        tmp = t_1
    else if (z <= 1.9d-259) then
        tmp = (x * y) / z
    else if (z <= 1.45d-14) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = x * ((y / z) - t);
	double t_2 = (y + t) * (x / z);
	double tmp;
	if (z <= -4.15e+21) {
		tmp = t_2;
	} else if (z <= -6.5e-198) {
		tmp = t_1;
	} else if (z <= 1.9e-259) {
		tmp = (x * y) / z;
	} else if (z <= 1.45e-14) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x * ((y / z) - t)
	t_2 = (y + t) * (x / z)
	tmp = 0
	if z <= -4.15e+21:
		tmp = t_2
	elif z <= -6.5e-198:
		tmp = t_1
	elif z <= 1.9e-259:
		tmp = (x * y) / z
	elif z <= 1.45e-14:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x * Float64(Float64(y / z) - t))
	t_2 = Float64(Float64(y + t) * Float64(x / z))
	tmp = 0.0
	if (z <= -4.15e+21)
		tmp = t_2;
	elseif (z <= -6.5e-198)
		tmp = t_1;
	elseif (z <= 1.9e-259)
		tmp = Float64(Float64(x * y) / z);
	elseif (z <= 1.45e-14)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x * ((y / z) - t);
	t_2 = (y + t) * (x / z);
	tmp = 0.0;
	if (z <= -4.15e+21)
		tmp = t_2;
	elseif (z <= -6.5e-198)
		tmp = t_1;
	elseif (z <= 1.9e-259)
		tmp = (x * y) / z;
	elseif (z <= 1.45e-14)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x * N[(N[(y / z), $MachinePrecision] - t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(y + t), $MachinePrecision] * N[(x / z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -4.15e+21], t$95$2, If[LessEqual[z, -6.5e-198], t$95$1, If[LessEqual[z, 1.9e-259], N[(N[(x * y), $MachinePrecision] / z), $MachinePrecision], If[LessEqual[z, 1.45e-14], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -4.15e21 or 1.4500000000000001e-14 < z

   1. Initial program 93.9%

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

      1. add-cube-cbrt 92.4%

         \[\leadsto x \cdot \color{blue}{\left(\left(\sqrt[3]{\frac{y}{z} - \frac{t}{1 - z}} \cdot \sqrt[3]{\frac{y}{z} - \frac{t}{1 - z}}\right) \cdot \sqrt[3]{\frac{y}{z} - \frac{t}{1 - z}}\right)} \]

      2. pow3 92.5%

         \[\leadsto x \cdot \color{blue}{{\left(\sqrt[3]{\frac{y}{z} - \frac{t}{1 - z}}\right)}^{3}} \]

   3. Applied egg-rr 92.5%

      \[\leadsto x \cdot \color{blue}{{\left(\sqrt[3]{\frac{y}{z} - \frac{t}{1 - z}}\right)}^{3}} \]

   4. Taylor expanded in z around inf 86.0%

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

      1. associate-/l* 92.3%

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

      2. associate-/r/ 87.3%

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

      3. cancel-sign-sub-inv 87.3%

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

      4. metadata-eval 87.3%

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

      5. *-lft-identity 87.3%

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

      6. +-commutative 87.3%

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

   6. Simplified 87.3%

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

   if -4.15e21 < z < -6.5000000000000004e-198 or 1.9e-259 < z < 1.4500000000000001e-14

   1. Initial program 94.5%

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

   2. Taylor expanded in z around 0 93.8%

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

   if -6.5000000000000004e-198 < z < 1.9e-259

   1. Initial program 83.1%

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

   2. Taylor expanded in y around inf 96.9%

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

4. Final simplification 91.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.15 \cdot 10^{+21}:\\ \;\;\;\;\left(y + t\right) \cdot \frac{x}{z}\\ \mathbf{elif}\;z \leq -6.5 \cdot 10^{-198}:\\ \;\;\;\;x \cdot \left(\frac{y}{z} - t\right)\\ \mathbf{elif}\;z \leq 1.9 \cdot 10^{-259}:\\ \;\;\;\;\frac{x \cdot y}{z}\\ \mathbf{elif}\;z \leq 1.45 \cdot 10^{-14}:\\ \;\;\;\;x \cdot \left(\frac{y}{z} - t\right)\\ \mathbf{else}:\\ \;\;\;\;\left(y + t\right) \cdot \frac{x}{z}\\ \end{array} \]

Alternative 6: 91.4% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(\frac{y}{z} - t\right)\\ t_2 := \frac{x}{\frac{z}{y + t}}\\ \mathbf{if}\;z \leq -4.15 \cdot 10^{+21}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq -7 \cdot 10^{-198}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 1.9 \cdot 10^{-259}:\\ \;\;\;\;\frac{x \cdot y}{z}\\ \mathbf{elif}\;z \leq 1.45 \cdot 10^{-14}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* x (- (/ y z) t))) (t_2 (/ x (/ z (+ y t)))))
   (if (<= z -4.15e+21)
     t_2
     (if (<= z -7e-198)
       t_1
       (if (<= z 1.9e-259) (/ (* x y) z) (if (<= z 1.45e-14) t_1 t_2))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x * ((y / z) - t);
	double t_2 = x / (z / (y + t));
	double tmp;
	if (z <= -4.15e+21) {
		tmp = t_2;
	} else if (z <= -7e-198) {
		tmp = t_1;
	} else if (z <= 1.9e-259) {
		tmp = (x * y) / z;
	} else if (z <= 1.45e-14) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = x * ((y / z) - t)
    t_2 = x / (z / (y + t))
    if (z <= (-4.15d+21)) then
        tmp = t_2
    else if (z <= (-7d-198)) then
        tmp = t_1
    else if (z <= 1.9d-259) then
        tmp = (x * y) / z
    else if (z <= 1.45d-14) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = x * ((y / z) - t);
	double t_2 = x / (z / (y + t));
	double tmp;
	if (z <= -4.15e+21) {
		tmp = t_2;
	} else if (z <= -7e-198) {
		tmp = t_1;
	} else if (z <= 1.9e-259) {
		tmp = (x * y) / z;
	} else if (z <= 1.45e-14) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x * ((y / z) - t)
	t_2 = x / (z / (y + t))
	tmp = 0
	if z <= -4.15e+21:
		tmp = t_2
	elif z <= -7e-198:
		tmp = t_1
	elif z <= 1.9e-259:
		tmp = (x * y) / z
	elif z <= 1.45e-14:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x * Float64(Float64(y / z) - t))
	t_2 = Float64(x / Float64(z / Float64(y + t)))
	tmp = 0.0
	if (z <= -4.15e+21)
		tmp = t_2;
	elseif (z <= -7e-198)
		tmp = t_1;
	elseif (z <= 1.9e-259)
		tmp = Float64(Float64(x * y) / z);
	elseif (z <= 1.45e-14)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x * ((y / z) - t);
	t_2 = x / (z / (y + t));
	tmp = 0.0;
	if (z <= -4.15e+21)
		tmp = t_2;
	elseif (z <= -7e-198)
		tmp = t_1;
	elseif (z <= 1.9e-259)
		tmp = (x * y) / z;
	elseif (z <= 1.45e-14)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x * N[(N[(y / z), $MachinePrecision] - t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x / N[(z / N[(y + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -4.15e+21], t$95$2, If[LessEqual[z, -7e-198], t$95$1, If[LessEqual[z, 1.9e-259], N[(N[(x * y), $MachinePrecision] / z), $MachinePrecision], If[LessEqual[z, 1.45e-14], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -4.15e21 or 1.4500000000000001e-14 < z

   1. Initial program 93.9%

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

      1. add-cube-cbrt 92.4%

         \[\leadsto x \cdot \color{blue}{\left(\left(\sqrt[3]{\frac{y}{z} - \frac{t}{1 - z}} \cdot \sqrt[3]{\frac{y}{z} - \frac{t}{1 - z}}\right) \cdot \sqrt[3]{\frac{y}{z} - \frac{t}{1 - z}}\right)} \]

      2. pow3 92.5%

         \[\leadsto x \cdot \color{blue}{{\left(\sqrt[3]{\frac{y}{z} - \frac{t}{1 - z}}\right)}^{3}} \]

   3. Applied egg-rr 92.5%

      \[\leadsto x \cdot \color{blue}{{\left(\sqrt[3]{\frac{y}{z} - \frac{t}{1 - z}}\right)}^{3}} \]

   4. Taylor expanded in z around inf 86.0%

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

      1. associate-/l* 92.3%

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

      2. cancel-sign-sub-inv 92.3%

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

      3. metadata-eval 92.3%

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

      4. *-lft-identity 92.3%

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

   6. Simplified 92.3%

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

   if -4.15e21 < z < -7.0000000000000005e-198 or 1.9e-259 < z < 1.4500000000000001e-14

   1. Initial program 94.5%

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

   2. Taylor expanded in z around 0 93.8%

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

   if -7.0000000000000005e-198 < z < 1.9e-259

   1. Initial program 83.1%

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

   2. Taylor expanded in y around inf 96.9%

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

4. Final simplification 93.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.15 \cdot 10^{+21}:\\ \;\;\;\;\frac{x}{\frac{z}{y + t}}\\ \mathbf{elif}\;z \leq -7 \cdot 10^{-198}:\\ \;\;\;\;x \cdot \left(\frac{y}{z} - t\right)\\ \mathbf{elif}\;z \leq 1.9 \cdot 10^{-259}:\\ \;\;\;\;\frac{x \cdot y}{z}\\ \mathbf{elif}\;z \leq 1.45 \cdot 10^{-14}:\\ \;\;\;\;x \cdot \left(\frac{y}{z} - t\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\frac{z}{y + t}}\\ \end{array} \]

Alternative 7: 42.3% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -4.15 \cdot 10^{+21} \lor \neg \left(z \leq -7.5 \cdot 10^{-187}\right) \land \left(z \leq 8.5 \cdot 10^{-280} \lor \neg \left(z \leq 7 \cdot 10^{-11}\right)\right):\\ \;\;\;\;t \cdot \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(-t\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -4.15e+21)
         (and (not (<= z -7.5e-187)) (or (<= z 8.5e-280) (not (<= z 7e-11)))))
   (* t (/ x z))
   (* x (- t))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -4.15e+21) || (!(z <= -7.5e-187) && ((z <= 8.5e-280) || !(z <= 7e-11)))) {
		tmp = t * (x / 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 ((z <= (-4.15d+21)) .or. (.not. (z <= (-7.5d-187))) .and. (z <= 8.5d-280) .or. (.not. (z <= 7d-11))) then
        tmp = t * (x / 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 ((z <= -4.15e+21) || (!(z <= -7.5e-187) && ((z <= 8.5e-280) || !(z <= 7e-11)))) {
		tmp = t * (x / z);
	} else {
		tmp = x * -t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -4.15e+21) or (not (z <= -7.5e-187) and ((z <= 8.5e-280) or not (z <= 7e-11))):
		tmp = t * (x / z)
	else:
		tmp = x * -t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -4.15e+21) || (!(z <= -7.5e-187) && ((z <= 8.5e-280) || !(z <= 7e-11))))
		tmp = Float64(t * Float64(x / z));
	else
		tmp = Float64(x * Float64(-t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z <= -4.15e+21) || (~((z <= -7.5e-187)) && ((z <= 8.5e-280) || ~((z <= 7e-11)))))
		tmp = t * (x / z);
	else
		tmp = x * -t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -4.15e+21], And[N[Not[LessEqual[z, -7.5e-187]], $MachinePrecision], Or[LessEqual[z, 8.5e-280], N[Not[LessEqual[z, 7e-11]], $MachinePrecision]]]], N[(t * N[(x / z), $MachinePrecision]), $MachinePrecision], N[(x * (-t)), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -4.15e21 or -7.5000000000000004e-187 < z < 8.50000000000000037e-280 or 7.00000000000000038e-11 < z

   1. Initial program 92.6%

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

      1. flip-- 63.2%

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

      2. associate-*r/ 56.5%

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

      3. associate-/l* 63.0%

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

      4. *-un-lft-identity 63.0%

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

      5. associate-/l* 63.1%

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

      6. flip-- 92.1%

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

   3. Applied egg-rr 92.1%

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

   4. Taylor expanded in y around 0 48.3%

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

      1. associate-*r/ 48.3%

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

      2. neg-mul-1 48.3%

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

      3. neg-sub0 48.3%

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

      4. associate--r- 48.3%

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

      5. metadata-eval 48.3%

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

   6. Simplified 48.3%

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

   7. Taylor expanded in z around inf 48.3%

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

      1. associate-*r/ 49.3%

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

   9. Simplified 49.3%

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

   if -4.15e21 < z < -7.5000000000000004e-187 or 8.50000000000000037e-280 < z < 7.00000000000000038e-11

   1. Initial program 92.9%

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

   2. Taylor expanded in y around 0 34.3%

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

      1. associate-*r/ 34.3%

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

      2. associate-*r* 34.3%

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

      3. mul-1-neg 34.3%

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

      4. associate-*l/ 34.3%

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

      5. *-commutative 34.3%

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

   4. Simplified 34.3%

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

   5. Taylor expanded in z around 0 33.6%

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

      1. associate-*r* 33.6%

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

      2. mul-1-neg 33.6%

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

   7. Simplified 33.6%

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

4. Final simplification 42.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.15 \cdot 10^{+21} \lor \neg \left(z \leq -7.5 \cdot 10^{-187}\right) \land \left(z \leq 8.5 \cdot 10^{-280} \lor \neg \left(z \leq 7 \cdot 10^{-11}\right)\right):\\ \;\;\;\;t \cdot \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(-t\right)\\ \end{array} \]

Alternative 8: 44.8% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \frac{t}{z}\\ t_2 := x \cdot \left(-t\right)\\ \mathbf{if}\;z \leq -4.15 \cdot 10^{+21}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -1.95 \cdot 10^{-185}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq 2.4 \cdot 10^{-279}:\\ \;\;\;\;t \cdot \frac{x}{z}\\ \mathbf{elif}\;z \leq 7 \cdot 10^{-11}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* x (/ t z))) (t_2 (* x (- t))))
   (if (<= z -4.15e+21)
     t_1
     (if (<= z -1.95e-185)
       t_2
       (if (<= z 2.4e-279) (* t (/ x z)) (if (<= z 7e-11) t_2 t_1))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x * (t / z);
	double t_2 = x * -t;
	double tmp;
	if (z <= -4.15e+21) {
		tmp = t_1;
	} else if (z <= -1.95e-185) {
		tmp = t_2;
	} else if (z <= 2.4e-279) {
		tmp = t * (x / z);
	} else if (z <= 7e-11) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = x * (t / z)
    t_2 = x * -t
    if (z <= (-4.15d+21)) then
        tmp = t_1
    else if (z <= (-1.95d-185)) then
        tmp = t_2
    else if (z <= 2.4d-279) then
        tmp = t * (x / z)
    else if (z <= 7d-11) then
        tmp = t_2
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = x * (t / z);
	double t_2 = x * -t;
	double tmp;
	if (z <= -4.15e+21) {
		tmp = t_1;
	} else if (z <= -1.95e-185) {
		tmp = t_2;
	} else if (z <= 2.4e-279) {
		tmp = t * (x / z);
	} else if (z <= 7e-11) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x * (t / z)
	t_2 = x * -t
	tmp = 0
	if z <= -4.15e+21:
		tmp = t_1
	elif z <= -1.95e-185:
		tmp = t_2
	elif z <= 2.4e-279:
		tmp = t * (x / z)
	elif z <= 7e-11:
		tmp = t_2
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x * Float64(t / z))
	t_2 = Float64(x * Float64(-t))
	tmp = 0.0
	if (z <= -4.15e+21)
		tmp = t_1;
	elseif (z <= -1.95e-185)
		tmp = t_2;
	elseif (z <= 2.4e-279)
		tmp = Float64(t * Float64(x / z));
	elseif (z <= 7e-11)
		tmp = t_2;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x * (t / z);
	t_2 = x * -t;
	tmp = 0.0;
	if (z <= -4.15e+21)
		tmp = t_1;
	elseif (z <= -1.95e-185)
		tmp = t_2;
	elseif (z <= 2.4e-279)
		tmp = t * (x / z);
	elseif (z <= 7e-11)
		tmp = t_2;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x * N[(t / z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x * (-t)), $MachinePrecision]}, If[LessEqual[z, -4.15e+21], t$95$1, If[LessEqual[z, -1.95e-185], t$95$2, If[LessEqual[z, 2.4e-279], N[(t * N[(x / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 7e-11], t$95$2, t$95$1]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -4.15e21 or 7.00000000000000038e-11 < z

   1. Initial program 93.8%

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

   2. Taylor expanded in y around 0 56.7%

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

      1. associate-*r/ 56.7%

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

      2. associate-*r* 56.7%

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

      3. mul-1-neg 56.7%

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

      4. associate-*l/ 59.3%

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

      5. *-commutative 59.3%

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

   4. Simplified 59.3%

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

   5. Taylor expanded in z around inf 58.2%

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

   if -4.15e21 < z < -1.95e-185 or 2.3999999999999999e-279 < z < 7.00000000000000038e-11

   1. Initial program 92.9%

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

   2. Taylor expanded in y around 0 34.3%

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

      1. associate-*r/ 34.3%

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

      2. associate-*r* 34.3%

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

      3. mul-1-neg 34.3%

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

      4. associate-*l/ 34.3%

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

      5. *-commutative 34.3%

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

   4. Simplified 34.3%

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

   5. Taylor expanded in z around 0 33.6%

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

      1. associate-*r* 33.6%

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

      2. mul-1-neg 33.6%

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

   7. Simplified 33.6%

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

   if -1.95e-185 < z < 2.3999999999999999e-279

   1. Initial program 88.2%

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

      1. flip-- 28.9%

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

      2. associate-*r/ 26.0%

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

      3. associate-/l* 28.7%

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

      4. *-un-lft-identity 28.7%

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

      5. associate-/l* 28.8%

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

      6. flip-- 87.9%

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

   3. Applied egg-rr 87.9%

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

   4. Taylor expanded in y around 0 8.7%

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

      1. associate-*r/ 8.7%

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

      2. neg-mul-1 8.7%

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

      3. neg-sub0 8.7%

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

      4. associate--r- 8.7%

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

      5. metadata-eval 8.7%

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

   6. Simplified 8.7%

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

   7. Taylor expanded in z around inf 21.8%

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

      1. associate-*r/ 27.7%

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

   9. Simplified 27.7%

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

4. Final simplification 44.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.15 \cdot 10^{+21}:\\ \;\;\;\;x \cdot \frac{t}{z}\\ \mathbf{elif}\;z \leq -1.95 \cdot 10^{-185}:\\ \;\;\;\;x \cdot \left(-t\right)\\ \mathbf{elif}\;z \leq 2.4 \cdot 10^{-279}:\\ \;\;\;\;t \cdot \frac{x}{z}\\ \mathbf{elif}\;z \leq 7 \cdot 10^{-11}:\\ \;\;\;\;x \cdot \left(-t\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{t}{z}\\ \end{array} \]

Alternative 9: 67.5% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \frac{t}{z}\\ \mathbf{if}\;t \leq -3.8 \cdot 10^{+154}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 1.62 \cdot 10^{+31}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \mathbf{elif}\;t \leq 5.4 \cdot 10^{+231}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(-t\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* x (/ t z))))
   (if (<= t -3.8e+154)
     t_1
     (if (<= t 1.62e+31) (* x (/ y z)) (if (<= t 5.4e+231) t_1 (* x (- t)))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x * (t / z);
	double tmp;
	if (t <= -3.8e+154) {
		tmp = t_1;
	} else if (t <= 1.62e+31) {
		tmp = x * (y / z);
	} else if (t <= 5.4e+231) {
		tmp = t_1;
	} 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) :: t_1
    real(8) :: tmp
    t_1 = x * (t / z)
    if (t <= (-3.8d+154)) then
        tmp = t_1
    else if (t <= 1.62d+31) then
        tmp = x * (y / z)
    else if (t <= 5.4d+231) then
        tmp = t_1
    else
        tmp = x * -t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = x * (t / z);
	double tmp;
	if (t <= -3.8e+154) {
		tmp = t_1;
	} else if (t <= 1.62e+31) {
		tmp = x * (y / z);
	} else if (t <= 5.4e+231) {
		tmp = t_1;
	} else {
		tmp = x * -t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x * (t / z)
	tmp = 0
	if t <= -3.8e+154:
		tmp = t_1
	elif t <= 1.62e+31:
		tmp = x * (y / z)
	elif t <= 5.4e+231:
		tmp = t_1
	else:
		tmp = x * -t
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x * Float64(t / z))
	tmp = 0.0
	if (t <= -3.8e+154)
		tmp = t_1;
	elseif (t <= 1.62e+31)
		tmp = Float64(x * Float64(y / z));
	elseif (t <= 5.4e+231)
		tmp = t_1;
	else
		tmp = Float64(x * Float64(-t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x * (t / z);
	tmp = 0.0;
	if (t <= -3.8e+154)
		tmp = t_1;
	elseif (t <= 1.62e+31)
		tmp = x * (y / z);
	elseif (t <= 5.4e+231)
		tmp = t_1;
	else
		tmp = x * -t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x * N[(t / z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -3.8e+154], t$95$1, If[LessEqual[t, 1.62e+31], N[(x * N[(y / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 5.4e+231], t$95$1, N[(x * (-t)), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if t < -3.7999999999999998e154 or 1.6199999999999999e31 < t < 5.3999999999999999e231

   1. Initial program 97.9%

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

   2. Taylor expanded in y around 0 71.3%

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

      1. associate-*r/ 71.3%

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

      2. associate-*r* 71.3%

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

      3. mul-1-neg 71.3%

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

      4. associate-*l/ 80.7%

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

      5. *-commutative 80.7%

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

   4. Simplified 80.7%

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

   5. Taylor expanded in z around inf 60.1%

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

   if -3.7999999999999998e154 < t < 1.6199999999999999e31

   1. Initial program 91.3%

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

   2. Taylor expanded in y around inf 77.2%

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

      1. associate-*r/ 76.4%

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

   4. Simplified 76.4%

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

   if 5.3999999999999999e231 < t

   1. Initial program 94.6%

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

   2. Taylor expanded in y around 0 75.9%

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

      1. associate-*r/ 75.9%

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

      2. associate-*r* 75.9%

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

      3. mul-1-neg 75.9%

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

      4. associate-*l/ 87.7%

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

      5. *-commutative 87.7%

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

   4. Simplified 87.7%

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

   5. Taylor expanded in z around 0 69.9%

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

      1. associate-*r* 69.9%

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

      2. mul-1-neg 69.9%

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

   7. Simplified 69.9%

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

4. Final simplification 72.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -3.8 \cdot 10^{+154}:\\ \;\;\;\;x \cdot \frac{t}{z}\\ \mathbf{elif}\;t \leq 1.62 \cdot 10^{+31}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \mathbf{elif}\;t \leq 5.4 \cdot 10^{+231}:\\ \;\;\;\;x \cdot \frac{t}{z}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(-t\right)\\ \end{array} \]

Alternative 10: 66.7% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \frac{t}{z}\\ \mathbf{if}\;t \leq -1.16 \cdot 10^{+159}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 1.62 \cdot 10^{+31}:\\ \;\;\;\;y \cdot \frac{x}{z}\\ \mathbf{elif}\;t \leq 8.5 \cdot 10^{+230}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(-t\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* x (/ t z))))
   (if (<= t -1.16e+159)
     t_1
     (if (<= t 1.62e+31) (* y (/ x z)) (if (<= t 8.5e+230) t_1 (* x (- t)))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x * (t / z);
	double tmp;
	if (t <= -1.16e+159) {
		tmp = t_1;
	} else if (t <= 1.62e+31) {
		tmp = y * (x / z);
	} else if (t <= 8.5e+230) {
		tmp = t_1;
	} 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) :: t_1
    real(8) :: tmp
    t_1 = x * (t / z)
    if (t <= (-1.16d+159)) then
        tmp = t_1
    else if (t <= 1.62d+31) then
        tmp = y * (x / z)
    else if (t <= 8.5d+230) then
        tmp = t_1
    else
        tmp = x * -t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = x * (t / z);
	double tmp;
	if (t <= -1.16e+159) {
		tmp = t_1;
	} else if (t <= 1.62e+31) {
		tmp = y * (x / z);
	} else if (t <= 8.5e+230) {
		tmp = t_1;
	} else {
		tmp = x * -t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x * (t / z)
	tmp = 0
	if t <= -1.16e+159:
		tmp = t_1
	elif t <= 1.62e+31:
		tmp = y * (x / z)
	elif t <= 8.5e+230:
		tmp = t_1
	else:
		tmp = x * -t
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x * Float64(t / z))
	tmp = 0.0
	if (t <= -1.16e+159)
		tmp = t_1;
	elseif (t <= 1.62e+31)
		tmp = Float64(y * Float64(x / z));
	elseif (t <= 8.5e+230)
		tmp = t_1;
	else
		tmp = Float64(x * Float64(-t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x * (t / z);
	tmp = 0.0;
	if (t <= -1.16e+159)
		tmp = t_1;
	elseif (t <= 1.62e+31)
		tmp = y * (x / z);
	elseif (t <= 8.5e+230)
		tmp = t_1;
	else
		tmp = x * -t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x * N[(t / z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -1.16e+159], t$95$1, If[LessEqual[t, 1.62e+31], N[(y * N[(x / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 8.5e+230], t$95$1, N[(x * (-t)), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if t < -1.1600000000000001e159 or 1.6199999999999999e31 < t < 8.499999999999999e230

   1. Initial program 97.9%

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

   2. Taylor expanded in y around 0 71.3%

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

      1. associate-*r/ 71.3%

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

      2. associate-*r* 71.3%

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

      3. mul-1-neg 71.3%

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

      4. associate-*l/ 80.7%

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

      5. *-commutative 80.7%

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

   4. Simplified 80.7%

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

   5. Taylor expanded in z around inf 60.1%

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

   if -1.1600000000000001e159 < t < 1.6199999999999999e31

   1. Initial program 91.3%

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

      1. add-cube-cbrt 90.3%

         \[\leadsto x \cdot \color{blue}{\left(\left(\sqrt[3]{\frac{y}{z} - \frac{t}{1 - z}} \cdot \sqrt[3]{\frac{y}{z} - \frac{t}{1 - z}}\right) \cdot \sqrt[3]{\frac{y}{z} - \frac{t}{1 - z}}\right)} \]

      2. pow3 90.3%

         \[\leadsto x \cdot \color{blue}{{\left(\sqrt[3]{\frac{y}{z} - \frac{t}{1 - z}}\right)}^{3}} \]

   3. Applied egg-rr 90.3%

      \[\leadsto x \cdot \color{blue}{{\left(\sqrt[3]{\frac{y}{z} - \frac{t}{1 - z}}\right)}^{3}} \]

   4. Taylor expanded in y around inf 77.2%

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

      1. associate-/l* 76.2%

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

      2. associate-/r/ 78.5%

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

   6. Simplified 78.5%

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

   if 8.499999999999999e230 < t

   1. Initial program 94.6%

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

   2. Taylor expanded in y around 0 75.9%

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

      1. associate-*r/ 75.9%

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

      2. associate-*r* 75.9%

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

      3. mul-1-neg 75.9%

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

      4. associate-*l/ 87.7%

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

      5. *-commutative 87.7%

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

   4. Simplified 87.7%

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

   5. Taylor expanded in z around 0 69.9%

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

      1. associate-*r* 69.9%

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

      2. mul-1-neg 69.9%

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

   7. Simplified 69.9%

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

4. Final simplification 74.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.16 \cdot 10^{+159}:\\ \;\;\;\;x \cdot \frac{t}{z}\\ \mathbf{elif}\;t \leq 1.62 \cdot 10^{+31}:\\ \;\;\;\;y \cdot \frac{x}{z}\\ \mathbf{elif}\;t \leq 8.5 \cdot 10^{+230}:\\ \;\;\;\;x \cdot \frac{t}{z}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(-t\right)\\ \end{array} \]

Alternative 11: 66.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -5.1 \cdot 10^{+157}:\\ \;\;\;\;\frac{x}{\frac{z}{t}}\\ \mathbf{elif}\;t \leq 4.3 \cdot 10^{+30}:\\ \;\;\;\;y \cdot \frac{x}{z}\\ \mathbf{elif}\;t \leq 7.2 \cdot 10^{+230}:\\ \;\;\;\;x \cdot \frac{t}{z}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(-t\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= t -5.1e+157)
   (/ x (/ z t))
   (if (<= t 4.3e+30)
     (* y (/ x z))
     (if (<= t 7.2e+230) (* x (/ t z)) (* x (- t))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= -5.1e+157) {
		tmp = x / (z / t);
	} else if (t <= 4.3e+30) {
		tmp = y * (x / z);
	} else if (t <= 7.2e+230) {
		tmp = x * (t / 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 <= (-5.1d+157)) then
        tmp = x / (z / t)
    else if (t <= 4.3d+30) then
        tmp = y * (x / z)
    else if (t <= 7.2d+230) then
        tmp = x * (t / 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 <= -5.1e+157) {
		tmp = x / (z / t);
	} else if (t <= 4.3e+30) {
		tmp = y * (x / z);
	} else if (t <= 7.2e+230) {
		tmp = x * (t / z);
	} else {
		tmp = x * -t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if t <= -5.1e+157:
		tmp = x / (z / t)
	elif t <= 4.3e+30:
		tmp = y * (x / z)
	elif t <= 7.2e+230:
		tmp = x * (t / z)
	else:
		tmp = x * -t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (t <= -5.1e+157)
		tmp = Float64(x / Float64(z / t));
	elseif (t <= 4.3e+30)
		tmp = Float64(y * Float64(x / z));
	elseif (t <= 7.2e+230)
		tmp = Float64(x * Float64(t / 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 <= -5.1e+157)
		tmp = x / (z / t);
	elseif (t <= 4.3e+30)
		tmp = y * (x / z);
	elseif (t <= 7.2e+230)
		tmp = x * (t / z);
	else
		tmp = x * -t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[t, -5.1e+157], N[(x / N[(z / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 4.3e+30], N[(y * N[(x / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 7.2e+230], N[(x * N[(t / z), $MachinePrecision]), $MachinePrecision], N[(x * (-t)), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if t < -5.09999999999999999e157

   1. Initial program 99.9%

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

      1. flip-- 64.5%

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

      2. associate-*r/ 56.4%

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

      3. associate-/l* 64.5%

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

      4. *-un-lft-identity 64.5%

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

      5. associate-/l* 64.5%

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

      6. flip-- 99.8%

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

   3. Applied egg-rr 99.8%

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

   4. Taylor expanded in y around 0 92.0%

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

      1. associate-*r/ 92.0%

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

      2. neg-mul-1 92.0%

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

      3. neg-sub0 92.0%

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

      4. associate--r- 92.0%

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

      5. metadata-eval 92.0%

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

   6. Simplified 92.0%

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

   7. Taylor expanded in z around inf 60.7%

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

   if -5.09999999999999999e157 < t < 4.3e30

   1. Initial program 91.3%

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

      1. add-cube-cbrt 90.3%

         \[\leadsto x \cdot \color{blue}{\left(\left(\sqrt[3]{\frac{y}{z} - \frac{t}{1 - z}} \cdot \sqrt[3]{\frac{y}{z} - \frac{t}{1 - z}}\right) \cdot \sqrt[3]{\frac{y}{z} - \frac{t}{1 - z}}\right)} \]

      2. pow3 90.3%

         \[\leadsto x \cdot \color{blue}{{\left(\sqrt[3]{\frac{y}{z} - \frac{t}{1 - z}}\right)}^{3}} \]

   3. Applied egg-rr 90.3%

      \[\leadsto x \cdot \color{blue}{{\left(\sqrt[3]{\frac{y}{z} - \frac{t}{1 - z}}\right)}^{3}} \]

   4. Taylor expanded in y around inf 77.2%

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

      1. associate-/l* 76.2%

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

      2. associate-/r/ 78.5%

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

   6. Simplified 78.5%

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

   if 4.3e30 < t < 7.20000000000000037e230

   1. Initial program 96.3%

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

   2. Taylor expanded in y around 0 61.0%

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

      1. associate-*r/ 61.0%

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

      2. associate-*r* 61.0%

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

      3. mul-1-neg 61.0%

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

      4. associate-*l/ 71.5%

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

      5. *-commutative 71.5%

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

   4. Simplified 71.5%

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

   5. Taylor expanded in z around inf 59.7%

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

   if 7.20000000000000037e230 < t

   1. Initial program 94.6%

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

   2. Taylor expanded in y around 0 75.9%

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

      1. associate-*r/ 75.9%

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

      2. associate-*r* 75.9%

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

      3. mul-1-neg 75.9%

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

      4. associate-*l/ 87.7%

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

      5. *-commutative 87.7%

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

   4. Simplified 87.7%

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

   5. Taylor expanded in z around 0 69.9%

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

      1. associate-*r* 69.9%

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

      2. mul-1-neg 69.9%

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

   7. Simplified 69.9%

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

4. Final simplification 74.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -5.1 \cdot 10^{+157}:\\ \;\;\;\;\frac{x}{\frac{z}{t}}\\ \mathbf{elif}\;t \leq 4.3 \cdot 10^{+30}:\\ \;\;\;\;y \cdot \frac{x}{z}\\ \mathbf{elif}\;t \leq 7.2 \cdot 10^{+230}:\\ \;\;\;\;x \cdot \frac{t}{z}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(-t\right)\\ \end{array} \]

Alternative 12: 22.8% 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 92.7%

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

2. Taylor expanded in y around 0 41.3%

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

   1. associate-*r/ 41.3%

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

   2. associate-*r* 41.3%

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

   3. mul-1-neg 41.3%

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

   4. associate-*l/ 42.5%

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

   5. *-commutative 42.5%

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

4. Simplified 42.5%

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

5. Taylor expanded in z around 0 23.0%

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

   1. associate-*r* 23.0%

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

   2. mul-1-neg 23.0%

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

7. Simplified 23.0%

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

8. Final simplification 23.0%

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

Developer target: 95.0% 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 2023301 
(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)))))