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

Percentage Accurate: 94.8% → 98.3%

Time: 9.2s

Alternatives: 11

Speedup: 0.3×

• 21.2% 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: 94.8% 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: 98.3% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{y}{z} + \frac{t}{z + -1}\\ \mathbf{if}\;t\_1 \leq -\infty:\\ \;\;\;\;\frac{y \cdot x}{z}\\ \mathbf{elif}\;t\_1 \leq 2 \cdot 10^{+231}:\\ \;\;\;\;t\_1 \cdot x\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot \left(y \cdot \left(1 - z\right) - z \cdot t\right)}{z \cdot \left(1 - z\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (+ (/ y z) (/ t (+ z -1.0)))))
   (if (<= t_1 (- INFINITY))
     (/ (* y x) z)
     (if (<= t_1 2e+231)
       (* t_1 x)
       (/ (* x (- (* y (- 1.0 z)) (* z t))) (* z (- 1.0 z)))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (y / z) + (t / (z + -1.0));
	double tmp;
	if (t_1 <= -((double) INFINITY)) {
		tmp = (y * x) / z;
	} else if (t_1 <= 2e+231) {
		tmp = t_1 * x;
	} else {
		tmp = (x * ((y * (1.0 - z)) - (z * t))) / (z * (1.0 - z));
	}
	return tmp;
}

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = (y / z) + (t / (z + -1.0));
	double tmp;
	if (t_1 <= -Double.POSITIVE_INFINITY) {
		tmp = (y * x) / z;
	} else if (t_1 <= 2e+231) {
		tmp = t_1 * x;
	} else {
		tmp = (x * ((y * (1.0 - z)) - (z * t))) / (z * (1.0 - z));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (y / z) + (t / (z + -1.0))
	tmp = 0
	if t_1 <= -math.inf:
		tmp = (y * x) / z
	elif t_1 <= 2e+231:
		tmp = t_1 * x
	else:
		tmp = (x * ((y * (1.0 - z)) - (z * t))) / (z * (1.0 - z))
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(y / z) + Float64(t / Float64(z + -1.0)))
	tmp = 0.0
	if (t_1 <= Float64(-Inf))
		tmp = Float64(Float64(y * x) / z);
	elseif (t_1 <= 2e+231)
		tmp = Float64(t_1 * x);
	else
		tmp = Float64(Float64(x * Float64(Float64(y * Float64(1.0 - z)) - Float64(z * t))) / Float64(z * Float64(1.0 - z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (y / z) + (t / (z + -1.0));
	tmp = 0.0;
	if (t_1 <= -Inf)
		tmp = (y * x) / z;
	elseif (t_1 <= 2e+231)
		tmp = t_1 * x;
	else
		tmp = (x * ((y * (1.0 - z)) - (z * t))) / (z * (1.0 - z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(y / z), $MachinePrecision] + N[(t / N[(z + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, (-Infinity)], N[(N[(y * x), $MachinePrecision] / z), $MachinePrecision], If[LessEqual[t$95$1, 2e+231], N[(t$95$1 * x), $MachinePrecision], 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]]]]

Derivation

1. Split input into 3 regimes

2. if (-.f64 (/.f64 y z) (/.f64 t (-.f64 #s(literal 1 binary64) z))) < -inf.0

   1. Initial program 66.2%

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

   3. Taylor expanded in y around inf 99.9%

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

   if -inf.0 < (-.f64 (/.f64 y z) (/.f64 t (-.f64 #s(literal 1 binary64) z))) < 2.0000000000000001e231

   1. Initial program 97.9%

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

   if 2.0000000000000001e231 < (-.f64 (/.f64 y z) (/.f64 t (-.f64 #s(literal 1 binary64) z)))

   1. Initial program 86.0%

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

      1. *-commutative 86.0%

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

      2. frac-sub 86.0%

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

      3. associate-*l/ 99.9%

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

   4. Applied egg-rr 99.9%

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

4. Final simplification 98.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{y}{z} + \frac{t}{z + -1} \leq -\infty:\\ \;\;\;\;\frac{y \cdot x}{z}\\ \mathbf{elif}\;\frac{y}{z} + \frac{t}{z + -1} \leq 2 \cdot 10^{+231}:\\ \;\;\;\;\left(\frac{y}{z} + \frac{t}{z + -1}\right) \cdot x\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot \left(y \cdot \left(1 - z\right) - z \cdot t\right)}{z \cdot \left(1 - z\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 98.6% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{y}{z} + \frac{t}{z + -1}\\ \mathbf{if}\;t\_1 \leq -\infty \lor \neg \left(t\_1 \leq 10^{+308}\right):\\ \;\;\;\;\frac{y \cdot x}{z}\\ \mathbf{else}:\\ \;\;\;\;t\_1 \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (+ (/ y z) (/ t (+ z -1.0)))))
   (if (or (<= t_1 (- INFINITY)) (not (<= t_1 1e+308)))
     (/ (* y x) z)
     (* t_1 x))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (y / z) + (t / (z + -1.0));
	double tmp;
	if ((t_1 <= -((double) INFINITY)) || !(t_1 <= 1e+308)) {
		tmp = (y * x) / z;
	} else {
		tmp = t_1 * x;
	}
	return tmp;
}

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = (y / z) + (t / (z + -1.0));
	double tmp;
	if ((t_1 <= -Double.POSITIVE_INFINITY) || !(t_1 <= 1e+308)) {
		tmp = (y * x) / z;
	} else {
		tmp = t_1 * x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (y / z) + (t / (z + -1.0))
	tmp = 0
	if (t_1 <= -math.inf) or not (t_1 <= 1e+308):
		tmp = (y * x) / z
	else:
		tmp = t_1 * x
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(y / z) + Float64(t / Float64(z + -1.0)))
	tmp = 0.0
	if ((t_1 <= Float64(-Inf)) || !(t_1 <= 1e+308))
		tmp = Float64(Float64(y * x) / z);
	else
		tmp = Float64(t_1 * x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (y / z) + (t / (z + -1.0));
	tmp = 0.0;
	if ((t_1 <= -Inf) || ~((t_1 <= 1e+308)))
		tmp = (y * x) / z;
	else
		tmp = t_1 * x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(y / z), $MachinePrecision] + N[(t / N[(z + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[t$95$1, (-Infinity)], N[Not[LessEqual[t$95$1, 1e+308]], $MachinePrecision]], N[(N[(y * x), $MachinePrecision] / z), $MachinePrecision], N[(t$95$1 * x), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (-.f64 (/.f64 y z) (/.f64 t (-.f64 #s(literal 1 binary64) z))) < -inf.0 or 1e308 < (-.f64 (/.f64 y z) (/.f64 t (-.f64 #s(literal 1 binary64) z)))

   1. Initial program 66.3%

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

   3. Taylor expanded in y around inf 99.9%

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

   if -inf.0 < (-.f64 (/.f64 y z) (/.f64 t (-.f64 #s(literal 1 binary64) z))) < 1e308

   1. Initial program 98.1%

      \[x \cdot \left(\frac{y}{z} - \frac{t}{1 - z}\right) \]
   2. Add Preprocessing
3. Recombined 2 regimes into one program.

4. Final simplification 98.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{y}{z} + \frac{t}{z + -1} \leq -\infty \lor \neg \left(\frac{y}{z} + \frac{t}{z + -1} \leq 10^{+308}\right):\\ \;\;\;\;\frac{y \cdot x}{z}\\ \mathbf{else}:\\ \;\;\;\;\left(\frac{y}{z} + \frac{t}{z + -1}\right) \cdot x\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 93.8% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1:\\ \;\;\;\;x \cdot \frac{y + t}{z}\\ \mathbf{elif}\;z \leq 7.5 \cdot 10^{-11}:\\ \;\;\;\;x \cdot \left(\frac{y}{z} - t\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(\frac{y}{z} - t \cdot \frac{-1}{z}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -1.0)
   (* x (/ (+ y t) z))
   (if (<= z 7.5e-11) (* x (- (/ y z) t)) (* x (- (/ y z) (* t (/ -1.0 z)))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -1.0) {
		tmp = x * ((y + t) / z);
	} else if (z <= 7.5e-11) {
		tmp = x * ((y / z) - t);
	} else {
		tmp = x * ((y / z) - (t * (-1.0 / z)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (z <= (-1.0d0)) then
        tmp = x * ((y + t) / z)
    else if (z <= 7.5d-11) then
        tmp = x * ((y / z) - t)
    else
        tmp = x * ((y / z) - (t * ((-1.0d0) / z)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -1.0) {
		tmp = x * ((y + t) / z);
	} else if (z <= 7.5e-11) {
		tmp = x * ((y / z) - t);
	} else {
		tmp = x * ((y / z) - (t * (-1.0 / z)));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -1.0:
		tmp = x * ((y + t) / z)
	elif z <= 7.5e-11:
		tmp = x * ((y / z) - t)
	else:
		tmp = x * ((y / z) - (t * (-1.0 / z)))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -1.0)
		tmp = Float64(x * Float64(Float64(y + t) / z));
	elseif (z <= 7.5e-11)
		tmp = Float64(x * Float64(Float64(y / z) - t));
	else
		tmp = Float64(x * Float64(Float64(y / z) - Float64(t * Float64(-1.0 / z))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (z <= -1.0)
		tmp = x * ((y + t) / z);
	elseif (z <= 7.5e-11)
		tmp = x * ((y / z) - t);
	else
		tmp = x * ((y / z) - (t * (-1.0 / z)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -1.0], N[(x * N[(N[(y + t), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 7.5e-11], N[(x * N[(N[(y / z), $MachinePrecision] - t), $MachinePrecision]), $MachinePrecision], N[(x * N[(N[(y / z), $MachinePrecision] - N[(t * N[(-1.0 / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -1

   1. Initial program 99.7%

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

   3. Taylor expanded in z around inf 91.5%

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

      1. associate-/l* 98.2%

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

      2. sub-neg 98.2%

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

      3. remove-double-neg 98.2%

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

      4. neg-mul-1 98.2%

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

      5. distribute-rgt-neg-in 98.2%

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

      6. distribute-lft-in 98.2%

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

      7. neg-mul-1 98.2%

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

      8. sub-neg 98.2%

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

      9. *-commutative 98.2%

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

      10. associate-*l/ 98.2%

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

      11. *-commutative 98.2%

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

      12. associate-*r/ 98.2%

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

      13. sub-neg 98.2%

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

      14. neg-mul-1 98.2%

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

      15. distribute-lft-in 98.2%

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

      16. neg-mul-1 98.2%

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

      17. remove-double-neg 98.2%

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

      18. neg-mul-1 98.2%

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

      19. remove-double-neg 98.2%

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

      20. +-commutative 98.2%

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

   5. Simplified 98.2%

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

   if -1 < z < 7.5e-11

   1. Initial program 92.7%

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

   3. Taylor expanded in z around 0 92.6%

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

   if 7.5e-11 < z

   1. Initial program 94.2%

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

      1. clear-num 94.1%

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

      2. associate-/r/ 94.3%

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

   4. Applied egg-rr 94.3%

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

   5. Taylor expanded in z around inf 94.3%

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

4. Final simplification 94.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1:\\ \;\;\;\;x \cdot \frac{y + t}{z}\\ \mathbf{elif}\;z \leq 7.5 \cdot 10^{-11}:\\ \;\;\;\;x \cdot \left(\frac{y}{z} - t\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(\frac{y}{z} - t \cdot \frac{-1}{z}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 93.8% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1 \lor \neg \left(z \leq 7.5 \cdot 10^{-11}\right):\\ \;\;\;\;x \cdot \frac{y + t}{z}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(\frac{y}{z} - t\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -1.0) (not (<= z 7.5e-11)))
   (* x (/ (+ y t) z))
   (* x (- (/ y z) t))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -1.0) || !(z <= 7.5e-11)) {
		tmp = x * ((y + t) / z);
	} else {
		tmp = x * ((y / z) - t);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((z <= (-1.0d0)) .or. (.not. (z <= 7.5d-11))) then
        tmp = x * ((y + t) / z)
    else
        tmp = x * ((y / z) - t)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -1.0) || !(z <= 7.5e-11)) {
		tmp = x * ((y + t) / z);
	} else {
		tmp = x * ((y / z) - t);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -1.0) or not (z <= 7.5e-11):
		tmp = x * ((y + t) / z)
	else:
		tmp = x * ((y / z) - t)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -1.0) || !(z <= 7.5e-11))
		tmp = Float64(x * Float64(Float64(y + t) / z));
	else
		tmp = Float64(x * Float64(Float64(y / z) - t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z <= -1.0) || ~((z <= 7.5e-11)))
		tmp = x * ((y + t) / z);
	else
		tmp = x * ((y / z) - t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -1.0], N[Not[LessEqual[z, 7.5e-11]], $MachinePrecision]], N[(x * N[(N[(y + t), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], N[(x * N[(N[(y / z), $MachinePrecision] - t), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1 or 7.5e-11 < z

   1. Initial program 96.7%

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

   3. Taylor expanded in z around inf 88.5%

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

      1. associate-/l* 96.0%

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

      2. sub-neg 96.0%

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

      3. remove-double-neg 96.0%

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

      4. neg-mul-1 96.0%

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

      5. distribute-rgt-neg-in 96.0%

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

      6. distribute-lft-in 96.0%

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

      7. neg-mul-1 96.0%

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

      8. sub-neg 96.0%

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

      9. *-commutative 96.0%

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

      10. associate-*l/ 96.0%

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

      11. *-commutative 96.0%

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

      12. associate-*r/ 96.0%

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

      13. sub-neg 96.0%

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

      14. neg-mul-1 96.0%

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

      15. distribute-lft-in 96.0%

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

      16. neg-mul-1 96.0%

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

      17. remove-double-neg 96.0%

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

      18. neg-mul-1 96.0%

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

      19. remove-double-neg 96.0%

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

      20. +-commutative 96.0%

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

   5. Simplified 96.0%

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

   if -1 < z < 7.5e-11

   1. Initial program 92.7%

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

   3. Taylor expanded in z around 0 92.6%

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

4. Final simplification 94.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1 \lor \neg \left(z \leq 7.5 \cdot 10^{-11}\right):\\ \;\;\;\;x \cdot \frac{y + t}{z}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(\frac{y}{z} - t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 72.2% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -8 \cdot 10^{+144} \lor \neg \left(t \leq 270000000000\right):\\ \;\;\;\;t \cdot \frac{x}{z + -1}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\frac{z}{y}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= t -8e+144) (not (<= t 270000000000.0)))
   (* t (/ x (+ z -1.0)))
   (/ x (/ z y))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((t <= -8e+144) || !(t <= 270000000000.0)) {
		tmp = t * (x / (z + -1.0));
	} else {
		tmp = x / (z / y);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((t <= (-8d+144)) .or. (.not. (t <= 270000000000.0d0))) then
        tmp = t * (x / (z + (-1.0d0)))
    else
        tmp = x / (z / y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((t <= -8e+144) || !(t <= 270000000000.0)) {
		tmp = t * (x / (z + -1.0));
	} else {
		tmp = x / (z / y);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (t <= -8e+144) or not (t <= 270000000000.0):
		tmp = t * (x / (z + -1.0))
	else:
		tmp = x / (z / y)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((t <= -8e+144) || !(t <= 270000000000.0))
		tmp = Float64(t * Float64(x / Float64(z + -1.0)));
	else
		tmp = Float64(x / Float64(z / y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((t <= -8e+144) || ~((t <= 270000000000.0)))
		tmp = t * (x / (z + -1.0));
	else
		tmp = x / (z / y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[t, -8e+144], N[Not[LessEqual[t, 270000000000.0]], $MachinePrecision]], N[(t * N[(x / N[(z + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x / N[(z / y), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -8.00000000000000019e144 or 2.7e11 < t

   1. Initial program 94.1%

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

   3. Taylor expanded in y around 0 70.9%

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

      1. mul-1-neg 70.9%

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

      2. associate-/l* 73.7%

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

      3. distribute-rgt-neg-in 73.7%

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

      4. distribute-neg-frac2 73.7%

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

      5. neg-sub0 73.7%

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

      6. associate--r- 73.7%

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

      7. metadata-eval 73.7%

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

   5. Simplified 73.7%

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

   if -8.00000000000000019e144 < t < 2.7e11

   1. Initial program 95.0%

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

   3. Taylor expanded in y around inf 78.2%

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

      1. associate-*r/ 80.5%

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

   5. Simplified 80.5%

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

      1. clear-num 80.4%

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

      2. un-div-inv 80.7%

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

   7. Applied egg-rr 80.7%

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

4. Final simplification 78.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -8 \cdot 10^{+144} \lor \neg \left(t \leq 270000000000\right):\\ \;\;\;\;t \cdot \frac{x}{z + -1}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\frac{z}{y}}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 72.3% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3.9 \cdot 10^{+107}:\\ \;\;\;\;\frac{t \cdot x}{z}\\ \mathbf{elif}\;z \leq 1.75 \cdot 10^{+48}:\\ \;\;\;\;x \cdot \left(\frac{y}{z} - t\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{x}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -3.9e+107)
   (/ (* t x) z)
   (if (<= z 1.75e+48) (* x (- (/ y z) t)) (* y (/ x z)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -3.9e+107) {
		tmp = (t * x) / z;
	} else if (z <= 1.75e+48) {
		tmp = x * ((y / 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 <= (-3.9d+107)) then
        tmp = (t * x) / z
    else if (z <= 1.75d+48) then
        tmp = x * ((y / 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 <= -3.9e+107) {
		tmp = (t * x) / z;
	} else if (z <= 1.75e+48) {
		tmp = x * ((y / z) - t);
	} else {
		tmp = y * (x / z);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -3.9e+107:
		tmp = (t * x) / z
	elif z <= 1.75e+48:
		tmp = x * ((y / z) - t)
	else:
		tmp = y * (x / z)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -3.9e+107)
		tmp = Float64(Float64(t * x) / z);
	elseif (z <= 1.75e+48)
		tmp = Float64(x * Float64(Float64(y / 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 <= -3.9e+107)
		tmp = (t * x) / z;
	elseif (z <= 1.75e+48)
		tmp = x * ((y / z) - t);
	else
		tmp = y * (x / z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -3.9e+107], N[(N[(t * x), $MachinePrecision] / z), $MachinePrecision], If[LessEqual[z, 1.75e+48], N[(x * N[(N[(y / z), $MachinePrecision] - t), $MachinePrecision]), $MachinePrecision], N[(y * N[(x / z), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -3.8999999999999998e107

   1. Initial program 99.6%

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

   3. Taylor expanded in z around inf 90.4%

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

      1. neg-mul-1 90.4%

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

   5. Simplified 90.4%

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

   6. Taylor expanded in y around 0 66.8%

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

      1. *-commutative 66.8%

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

   8. Simplified 66.8%

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

   if -3.8999999999999998e107 < z < 1.7499999999999999e48

   1. Initial program 94.4%

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

   3. Taylor expanded in z around 0 86.4%

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

   if 1.7499999999999999e48 < z

   1. Initial program 92.5%

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

   3. Taylor expanded in y around inf 59.2%

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

      1. associate-/l* 61.0%

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

      2. *-un-lft-identity 61.0%

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

      3. associate-*l/ 61.1%

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

      4. associate-*r* 63.7%

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

      5. un-div-inv 63.8%

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

   5. Applied egg-rr 63.8%

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

4. Final simplification 79.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.9 \cdot 10^{+107}:\\ \;\;\;\;\frac{t \cdot x}{z}\\ \mathbf{elif}\;z \leq 1.75 \cdot 10^{+48}:\\ \;\;\;\;x \cdot \left(\frac{y}{z} - t\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{x}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 41.3% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -0.036 \lor \neg \left(z \leq 9.5 \cdot 10^{-13}\right):\\ \;\;\;\;t \cdot \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(-t\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -0.036) (not (<= z 9.5e-13))) (* t (/ x z)) (* x (- t))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -0.036) || !(z <= 9.5e-13)) {
		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 <= (-0.036d0)) .or. (.not. (z <= 9.5d-13))) 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 <= -0.036) || !(z <= 9.5e-13)) {
		tmp = t * (x / z);
	} else {
		tmp = x * -t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -0.036) or not (z <= 9.5e-13):
		tmp = t * (x / z)
	else:
		tmp = x * -t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -0.036) || !(z <= 9.5e-13))
		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 <= -0.036) || ~((z <= 9.5e-13)))
		tmp = t * (x / z);
	else
		tmp = x * -t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -0.036], N[Not[LessEqual[z, 9.5e-13]], $MachinePrecision]], N[(t * N[(x / z), $MachinePrecision]), $MachinePrecision], N[(x * (-t)), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -0.0359999999999999973 or 9.49999999999999991e-13 < z

   1. Initial program 96.8%

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

   3. Taylor expanded in z around inf 88.2%

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

      1. neg-mul-1 88.2%

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

   5. Simplified 88.2%

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

   6. Taylor expanded in y around 0 51.2%

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

      1. associate-/l* 51.1%

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

   8. Simplified 51.1%

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

   if -0.0359999999999999973 < z < 9.49999999999999991e-13

   1. Initial program 92.6%

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

   3. Taylor expanded in z around 0 92.5%

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

   4. Taylor expanded in y around 0 38.8%

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

      1. mul-1-neg 38.8%

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

      2. distribute-lft-neg-out 38.8%

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

      3. *-commutative 38.8%

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

   6. Simplified 38.8%

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

4. Final simplification 44.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -0.036 \lor \neg \left(z \leq 9.5 \cdot 10^{-13}\right):\\ \;\;\;\;t \cdot \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(-t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 65.4% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -6.5 \cdot 10^{+111}:\\ \;\;\;\;\frac{t \cdot x}{z}\\ \mathbf{elif}\;t \leq 3.9 \cdot 10^{+95}:\\ \;\;\;\;\frac{x}{\frac{z}{y}}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(-t\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= t -6.5e+111)
   (/ (* t x) z)
   (if (<= t 3.9e+95) (/ x (/ z y)) (* x (- t)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= -6.5e+111) {
		tmp = (t * x) / z;
	} else if (t <= 3.9e+95) {
		tmp = x / (z / y);
	} 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 <= (-6.5d+111)) then
        tmp = (t * x) / z
    else if (t <= 3.9d+95) then
        tmp = x / (z / y)
    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 <= -6.5e+111) {
		tmp = (t * x) / z;
	} else if (t <= 3.9e+95) {
		tmp = x / (z / y);
	} else {
		tmp = x * -t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if t <= -6.5e+111:
		tmp = (t * x) / z
	elif t <= 3.9e+95:
		tmp = x / (z / y)
	else:
		tmp = x * -t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (t <= -6.5e+111)
		tmp = Float64(Float64(t * x) / z);
	elseif (t <= 3.9e+95)
		tmp = Float64(x / Float64(z / y));
	else
		tmp = Float64(x * Float64(-t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (t <= -6.5e+111)
		tmp = (t * x) / z;
	elseif (t <= 3.9e+95)
		tmp = x / (z / y);
	else
		tmp = x * -t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[t, -6.5e+111], N[(N[(t * x), $MachinePrecision] / z), $MachinePrecision], If[LessEqual[t, 3.9e+95], N[(x / N[(z / y), $MachinePrecision]), $MachinePrecision], N[(x * (-t)), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -6.5000000000000002e111

   1. Initial program 92.9%

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

   3. Taylor expanded in z around inf 61.0%

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

      1. neg-mul-1 61.0%

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

   5. Simplified 61.0%

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

   6. Taylor expanded in y around 0 51.6%

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

      1. *-commutative 51.6%

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

   8. Simplified 51.6%

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

   if -6.5000000000000002e111 < t < 3.8999999999999997e95

   1. Initial program 94.7%

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

   3. Taylor expanded in y around inf 77.1%

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

      1. associate-*r/ 78.7%

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

   5. Simplified 78.7%

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

      1. clear-num 78.7%

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

      2. un-div-inv 78.9%

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

   7. Applied egg-rr 78.9%

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

   if 3.8999999999999997e95 < t

   1. Initial program 95.8%

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

   3. Taylor expanded in z around 0 60.0%

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

   4. Taylor expanded in y around 0 48.1%

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

      1. mul-1-neg 48.1%

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

      2. distribute-lft-neg-out 48.1%

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

      3. *-commutative 48.1%

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

   6. Simplified 48.1%

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

4. Final simplification 69.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -6.5 \cdot 10^{+111}:\\ \;\;\;\;\frac{t \cdot x}{z}\\ \mathbf{elif}\;t \leq 3.9 \cdot 10^{+95}:\\ \;\;\;\;\frac{x}{\frac{z}{y}}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(-t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 65.3% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -3.8 \cdot 10^{+147}:\\ \;\;\;\;t \cdot \frac{x}{z}\\ \mathbf{elif}\;t \leq 5.1 \cdot 10^{+95}:\\ \;\;\;\;\frac{x}{\frac{z}{y}}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(-t\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= t -3.8e+147)
   (* t (/ x z))
   (if (<= t 5.1e+95) (/ x (/ z y)) (* x (- t)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= -3.8e+147) {
		tmp = t * (x / z);
	} else if (t <= 5.1e+95) {
		tmp = x / (z / y);
	} 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 <= (-3.8d+147)) then
        tmp = t * (x / z)
    else if (t <= 5.1d+95) then
        tmp = x / (z / y)
    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 <= -3.8e+147) {
		tmp = t * (x / z);
	} else if (t <= 5.1e+95) {
		tmp = x / (z / y);
	} else {
		tmp = x * -t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if t <= -3.8e+147:
		tmp = t * (x / z)
	elif t <= 5.1e+95:
		tmp = x / (z / y)
	else:
		tmp = x * -t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (t <= -3.8e+147)
		tmp = Float64(t * Float64(x / z));
	elseif (t <= 5.1e+95)
		tmp = Float64(x / Float64(z / y));
	else
		tmp = Float64(x * Float64(-t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (t <= -3.8e+147)
		tmp = t * (x / z);
	elseif (t <= 5.1e+95)
		tmp = x / (z / y);
	else
		tmp = x * -t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[t, -3.8e+147], N[(t * N[(x / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 5.1e+95], N[(x / N[(z / y), $MachinePrecision]), $MachinePrecision], N[(x * (-t)), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -3.7999999999999997e147

   1. Initial program 91.2%

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

   3. Taylor expanded in z around inf 60.7%

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

      1. neg-mul-1 60.7%

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

   5. Simplified 60.7%

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

   6. Taylor expanded in y around 0 51.7%

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

      1. associate-/l* 54.1%

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

   8. Simplified 54.1%

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

   if -3.7999999999999997e147 < t < 5.10000000000000003e95

   1. Initial program 94.9%

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

   3. Taylor expanded in y around inf 75.5%

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

      1. associate-*r/ 77.0%

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

   5. Simplified 77.0%

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

      1. clear-num 77.0%

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

      2. un-div-inv 77.2%

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

   7. Applied egg-rr 77.2%

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

   if 5.10000000000000003e95 < t

   1. Initial program 95.8%

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

   3. Taylor expanded in z around 0 60.0%

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

   4. Taylor expanded in y around 0 48.1%

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

      1. mul-1-neg 48.1%

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

      2. distribute-lft-neg-out 48.1%

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

      3. *-commutative 48.1%

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

   6. Simplified 48.1%

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

Alternative 10: 65.1% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.55 \cdot 10^{+148}:\\ \;\;\;\;t \cdot \frac{x}{z}\\ \mathbf{elif}\;t \leq 2.3 \cdot 10^{+95}:\\ \;\;\;\;\frac{y}{z} \cdot x\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(-t\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= t -1.55e+148)
   (* t (/ x z))
   (if (<= t 2.3e+95) (* (/ y z) x) (* x (- t)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= -1.55e+148) {
		tmp = t * (x / z);
	} else if (t <= 2.3e+95) {
		tmp = (y / z) * x;
	} 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 <= (-1.55d+148)) then
        tmp = t * (x / z)
    else if (t <= 2.3d+95) then
        tmp = (y / z) * x
    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 <= -1.55e+148) {
		tmp = t * (x / z);
	} else if (t <= 2.3e+95) {
		tmp = (y / z) * x;
	} else {
		tmp = x * -t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if t <= -1.55e+148:
		tmp = t * (x / z)
	elif t <= 2.3e+95:
		tmp = (y / z) * x
	else:
		tmp = x * -t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (t <= -1.55e+148)
		tmp = Float64(t * Float64(x / z));
	elseif (t <= 2.3e+95)
		tmp = Float64(Float64(y / z) * x);
	else
		tmp = Float64(x * Float64(-t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (t <= -1.55e+148)
		tmp = t * (x / z);
	elseif (t <= 2.3e+95)
		tmp = (y / z) * x;
	else
		tmp = x * -t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[t, -1.55e+148], N[(t * N[(x / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 2.3e+95], N[(N[(y / z), $MachinePrecision] * x), $MachinePrecision], N[(x * (-t)), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -1.54999999999999988e148

   1. Initial program 91.2%

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

   3. Taylor expanded in z around inf 60.7%

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

      1. neg-mul-1 60.7%

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

   5. Simplified 60.7%

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

   6. Taylor expanded in y around 0 51.7%

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

      1. associate-/l* 54.1%

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

   8. Simplified 54.1%

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

   if -1.54999999999999988e148 < t < 2.29999999999999997e95

   1. Initial program 94.9%

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

   3. Taylor expanded in y around inf 75.5%

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

      1. associate-*r/ 77.0%

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

   5. Simplified 77.0%

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

   if 2.29999999999999997e95 < t

   1. Initial program 95.8%

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

   3. Taylor expanded in z around 0 60.0%

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

   4. Taylor expanded in y around 0 48.1%

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

      1. mul-1-neg 48.1%

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

      2. distribute-lft-neg-out 48.1%

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

      3. *-commutative 48.1%

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

   6. Simplified 48.1%

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

4. Final simplification 68.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.55 \cdot 10^{+148}:\\ \;\;\;\;t \cdot \frac{x}{z}\\ \mathbf{elif}\;t \leq 2.3 \cdot 10^{+95}:\\ \;\;\;\;\frac{y}{z} \cdot x\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(-t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 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 94.6%

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

3. Taylor expanded in z around 0 67.7%

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

4. Taylor expanded in y around 0 28.0%

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

   1. mul-1-neg 28.0%

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

   2. distribute-lft-neg-out 28.0%

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

   3. *-commutative 28.0%

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

6. Simplified 28.0%

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

Developer Target 1: 95.1% accurate, 0.2× 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 2024181 
(FPCore (x y z t)
  :name "Numeric.SpecFunctions:invIncompleteBetaWorker from math-functions-0.1.5.2, C"
  :precision binary64

  :alt
  (! :herbie-platform default (if (< (* x (- (/ y z) (/ t (- 1 z)))) -3811613151656021/5000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000) (* x (- (/ y z) (* t (/ 1 (- 1 z))))) (if (< (* x (- (/ y z) (/ t (- 1 z)))) 7066972463851151/50000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000) (+ (/ (* y x) z) (- (/ (* t x) (- 1 z)))) (* x (- (/ y z) (* t (/ 1 (- 1 z))))))))

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