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

Percentage Accurate: 94.6% → 98.3%

Time: 11.4s

Alternatives: 9

Speedup: 0.3×

• 20.7% 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: 98.3% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{y}{z} + \frac{t}{z + -1}\\ \mathbf{if}\;t\_1 \leq -\infty \lor \neg \left(t\_1 \leq 4 \cdot 10^{+296}\right):\\ \;\;\;\;y \cdot \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;t\_1 \cdot x\\ \end{array} \end{array} \]

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 4e+296)))
     (* 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 <= 4e+296)) {
		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 <= 4e+296)) {
		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 <= 4e+296):
		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 <= 4e+296))
		tmp = Float64(y * Float64(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 <= 4e+296)))
		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, 4e+296]], $MachinePrecision]], N[(y * N[(x / z), $MachinePrecision]), $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 3.99999999999999993e296 < (-.f64 (/.f64 y z) (/.f64 t (-.f64 #s(literal 1 binary64) z)))

   1. Initial program 63.7%

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

   3. Taylor expanded in z around 0 63.7%

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

   4. Taylor expanded in y around inf 95.1%

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

      1. +-commutative 95.1%

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

      2. mul-1-neg 95.1%

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

      3. unsub-neg 95.1%

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

      4. associate-/l* 99.8%

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

   6. Simplified 99.8%

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

   7. Taylor expanded in z around 0 99.8%

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

   if -inf.0 < (-.f64 (/.f64 y z) (/.f64 t (-.f64 #s(literal 1 binary64) z))) < 3.99999999999999993e296

   1. Initial program 98.7%

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

4. Final simplification 98.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{y}{z} + \frac{t}{z + -1} \leq -\infty \lor \neg \left(\frac{y}{z} + \frac{t}{z + -1} \leq 4 \cdot 10^{+296}\right):\\ \;\;\;\;y \cdot \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;\left(\frac{y}{z} + \frac{t}{z + -1}\right) \cdot x\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 93.7% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -165000 \lor \neg \left(z \leq 1\right):\\ \;\;\;\;x \cdot \frac{y + t}{z}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(\frac{y}{z} - t\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -165000.0) (not (<= z 1.0)))
   (* x (/ (+ y t) z))
   (* x (- (/ y z) t))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -165000.0) || !(z <= 1.0)) {
		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 <= (-165000.0d0)) .or. (.not. (z <= 1.0d0))) 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 <= -165000.0) || !(z <= 1.0)) {
		tmp = x * ((y + t) / z);
	} else {
		tmp = x * ((y / z) - t);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -165000.0) or not (z <= 1.0):
		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 <= -165000.0) || !(z <= 1.0))
		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 <= -165000.0) || ~((z <= 1.0)))
		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, -165000.0], N[Not[LessEqual[z, 1.0]], $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 < -165000 or 1 < z

   1. Initial program 97.9%

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

   3. Taylor expanded in z around inf 81.5%

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

      1. associate-/l* 96.5%

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

      2. cancel-sign-sub-inv 96.5%

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

      3. metadata-eval 96.5%

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

      4. *-lft-identity 96.5%

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

      5. +-commutative 96.5%

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

   5. Simplified 96.5%

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

   if -165000 < z < 1

   1. Initial program 87.9%

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

   3. Taylor expanded in z around 0 86.8%

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

4. Final simplification 91.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -165000 \lor \neg \left(z \leq 1\right):\\ \;\;\;\;x \cdot \frac{y + t}{z}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(\frac{y}{z} - t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 72.5% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -3.9 \cdot 10^{-46} \lor \neg \left(y \leq 5.2 \cdot 10^{-110}\right):\\ \;\;\;\;y \cdot \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{x}{z + -1}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= y -3.9e-46) (not (<= y 5.2e-110)))
   (* y (/ x z))
   (* t (/ x (+ z -1.0)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -3.9e-46) || !(y <= 5.2e-110)) {
		tmp = y * (x / z);
	} else {
		tmp = t * (x / (z + -1.0));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((y <= (-3.9d-46)) .or. (.not. (y <= 5.2d-110))) then
        tmp = y * (x / z)
    else
        tmp = t * (x / (z + (-1.0d0)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -3.9e-46) || !(y <= 5.2e-110)) {
		tmp = y * (x / z);
	} else {
		tmp = t * (x / (z + -1.0));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (y <= -3.9e-46) or not (y <= 5.2e-110):
		tmp = y * (x / z)
	else:
		tmp = t * (x / (z + -1.0))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((y <= -3.9e-46) || !(y <= 5.2e-110))
		tmp = Float64(y * Float64(x / z));
	else
		tmp = Float64(t * Float64(x / Float64(z + -1.0)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((y <= -3.9e-46) || ~((y <= 5.2e-110)))
		tmp = y * (x / z);
	else
		tmp = t * (x / (z + -1.0));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[y, -3.9e-46], N[Not[LessEqual[y, 5.2e-110]], $MachinePrecision]], N[(y * N[(x / z), $MachinePrecision]), $MachinePrecision], N[(t * N[(x / N[(z + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -3.9000000000000003e-46 or 5.19999999999999979e-110 < y

   1. Initial program 90.4%

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

   3. Taylor expanded in z around 0 67.6%

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

   4. Taylor expanded in y around inf 71.0%

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

      1. +-commutative 71.0%

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

      2. mul-1-neg 71.0%

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

      3. unsub-neg 71.0%

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

      4. associate-/l* 72.2%

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

   6. Simplified 72.2%

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

   7. Taylor expanded in z around 0 78.9%

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

   if -3.9000000000000003e-46 < y < 5.19999999999999979e-110

   1. Initial program 97.4%

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

   3. Taylor expanded in y around 0 72.3%

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

      1. mul-1-neg 72.3%

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

      2. associate-/l* 70.6%

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

      3. distribute-rgt-neg-in 70.6%

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

      4. distribute-neg-frac2 70.6%

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

      5. neg-sub0 70.6%

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

      6. associate--r- 70.6%

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

      7. metadata-eval 70.6%

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

   5. Simplified 70.6%

      \[\leadsto \color{blue}{t \cdot \frac{x}{-1 + z}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 75.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.9 \cdot 10^{-46} \lor \neg \left(y \leq 5.2 \cdot 10^{-110}\right):\\ \;\;\;\;y \cdot \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{x}{z + -1}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 63.2% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.2 \cdot 10^{-10} \lor \neg \left(y \leq 1.55 \cdot 10^{-109}\right):\\ \;\;\;\;y \cdot \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{t \cdot x}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= y -1.2e-10) (not (<= y 1.55e-109))) (* y (/ x z)) (/ (* t x) z)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -1.2e-10) || !(y <= 1.55e-109)) {
		tmp = y * (x / z);
	} else {
		tmp = (t * x) / z;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((y <= (-1.2d-10)) .or. (.not. (y <= 1.55d-109))) then
        tmp = y * (x / z)
    else
        tmp = (t * x) / z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -1.2e-10) || !(y <= 1.55e-109)) {
		tmp = y * (x / z);
	} else {
		tmp = (t * x) / z;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (y <= -1.2e-10) or not (y <= 1.55e-109):
		tmp = y * (x / z)
	else:
		tmp = (t * x) / z
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((y <= -1.2e-10) || !(y <= 1.55e-109))
		tmp = Float64(y * Float64(x / z));
	else
		tmp = Float64(Float64(t * x) / z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((y <= -1.2e-10) || ~((y <= 1.55e-109)))
		tmp = y * (x / z);
	else
		tmp = (t * x) / z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[y, -1.2e-10], N[Not[LessEqual[y, 1.55e-109]], $MachinePrecision]], N[(y * N[(x / z), $MachinePrecision]), $MachinePrecision], N[(N[(t * x), $MachinePrecision] / z), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -1.2e-10 or 1.55e-109 < y

   1. Initial program 90.1%

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

   3. Taylor expanded in z around 0 67.8%

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

   4. Taylor expanded in y around inf 71.3%

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

      1. +-commutative 71.3%

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

      2. mul-1-neg 71.3%

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

      3. unsub-neg 71.3%

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

      4. associate-/l* 72.5%

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

   6. Simplified 72.5%

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

   7. Taylor expanded in z around 0 80.0%

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

   if -1.2e-10 < y < 1.55e-109

   1. Initial program 97.5%

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

      1. add-cube-cbrt 95.9%

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

      2. pow3 95.9%

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

   4. Applied egg-rr 95.9%

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

   5. Taylor expanded in z around inf 56.6%

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

      1. cancel-sign-sub-inv 56.6%

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

      2. metadata-eval 56.6%

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

      3. *-lft-identity 56.6%

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

   7. Simplified 56.6%

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

   8. Taylor expanded in y around 0 50.6%

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

4. Final simplification 68.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.2 \cdot 10^{-10} \lor \neg \left(y \leq 1.55 \cdot 10^{-109}\right):\\ \;\;\;\;y \cdot \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{t \cdot x}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 63.6% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.5 \cdot 10^{-45} \lor \neg \left(y \leq 1.4 \cdot 10^{-110}\right):\\ \;\;\;\;y \cdot \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{x}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= y -2.5e-45) (not (<= y 1.4e-110))) (* y (/ x z)) (* t (/ x z))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -2.5e-45) || !(y <= 1.4e-110)) {
		tmp = y * (x / z);
	} else {
		tmp = t * (x / z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((y <= (-2.5d-45)) .or. (.not. (y <= 1.4d-110))) then
        tmp = y * (x / z)
    else
        tmp = t * (x / z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -2.5e-45) || !(y <= 1.4e-110)) {
		tmp = y * (x / z);
	} else {
		tmp = t * (x / z);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (y <= -2.5e-45) or not (y <= 1.4e-110):
		tmp = y * (x / z)
	else:
		tmp = t * (x / z)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((y <= -2.5e-45) || !(y <= 1.4e-110))
		tmp = Float64(y * Float64(x / z));
	else
		tmp = Float64(t * Float64(x / z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((y <= -2.5e-45) || ~((y <= 1.4e-110)))
		tmp = y * (x / z);
	else
		tmp = t * (x / z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[y, -2.5e-45], N[Not[LessEqual[y, 1.4e-110]], $MachinePrecision]], N[(y * N[(x / z), $MachinePrecision]), $MachinePrecision], N[(t * N[(x / z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -2.49999999999999988e-45 or 1.4e-110 < y

   1. Initial program 90.4%

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

   3. Taylor expanded in z around 0 67.6%

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

   4. Taylor expanded in y around inf 71.0%

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

      1. +-commutative 71.0%

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

      2. mul-1-neg 71.0%

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

      3. unsub-neg 71.0%

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

      4. associate-/l* 72.2%

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

   6. Simplified 72.2%

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

   7. Taylor expanded in z around 0 78.9%

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

   if -2.49999999999999988e-45 < y < 1.4e-110

   1. Initial program 97.4%

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

   3. Taylor expanded in y around 0 72.3%

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

      1. mul-1-neg 72.3%

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

      2. associate-/l* 70.6%

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

      3. distribute-rgt-neg-in 70.6%

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

      4. distribute-neg-frac2 70.6%

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

      5. neg-sub0 70.6%

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

      6. associate--r- 70.6%

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

      7. metadata-eval 70.6%

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

   5. Simplified 70.6%

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

   6. Taylor expanded in z around inf 47.6%

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

4. Final simplification 67.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.5 \cdot 10^{-45} \lor \neg \left(y \leq 1.4 \cdot 10^{-110}\right):\\ \;\;\;\;y \cdot \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{x}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 65.3% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.35 \cdot 10^{+178} \lor \neg \left(t \leq 1.85 \cdot 10^{+54}\right):\\ \;\;\;\;t \cdot \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{z} \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= t -1.35e+178) (not (<= t 1.85e+54))) (* t (/ x z)) (* (/ y z) x)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((t <= -1.35e+178) || !(t <= 1.85e+54)) {
		tmp = t * (x / z);
	} else {
		tmp = (y / z) * x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((t <= (-1.35d+178)) .or. (.not. (t <= 1.85d+54))) then
        tmp = t * (x / z)
    else
        tmp = (y / z) * x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((t <= -1.35e+178) || !(t <= 1.85e+54)) {
		tmp = t * (x / z);
	} else {
		tmp = (y / z) * x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (t <= -1.35e+178) or not (t <= 1.85e+54):
		tmp = t * (x / z)
	else:
		tmp = (y / z) * x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((t <= -1.35e+178) || !(t <= 1.85e+54))
		tmp = Float64(t * Float64(x / z));
	else
		tmp = Float64(Float64(y / z) * x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((t <= -1.35e+178) || ~((t <= 1.85e+54)))
		tmp = t * (x / z);
	else
		tmp = (y / z) * x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[t, -1.35e+178], N[Not[LessEqual[t, 1.85e+54]], $MachinePrecision]], N[(t * N[(x / z), $MachinePrecision]), $MachinePrecision], N[(N[(y / z), $MachinePrecision] * x), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -1.35000000000000009e178 or 1.8500000000000001e54 < t

   1. Initial program 93.1%

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

   3. Taylor expanded in y around 0 63.8%

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

      1. mul-1-neg 63.8%

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

      2. associate-/l* 63.6%

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

      3. distribute-rgt-neg-in 63.6%

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

      4. distribute-neg-frac2 63.6%

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

      5. neg-sub0 63.6%

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

      6. associate--r- 63.6%

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

      7. metadata-eval 63.6%

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

   5. Simplified 63.6%

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

   6. Taylor expanded in z around inf 43.4%

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

   if -1.35000000000000009e178 < t < 1.8500000000000001e54

   1. Initial program 92.9%

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

   3. Taylor expanded in y around inf 75.8%

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

      1. associate-*r/ 78.0%

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

   5. Simplified 78.0%

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

4. Final simplification 66.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.35 \cdot 10^{+178} \lor \neg \left(t \leq 1.85 \cdot 10^{+54}\right):\\ \;\;\;\;t \cdot \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{z} \cdot x\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 42.4% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -165000 \lor \neg \left(z \leq 1\right):\\ \;\;\;\;t \cdot \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(-t\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -165000.0) (not (<= z 1.0))) (* t (/ x z)) (* x (- t))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -165000.0) || !(z <= 1.0)) {
		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 <= (-165000.0d0)) .or. (.not. (z <= 1.0d0))) 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 <= -165000.0) || !(z <= 1.0)) {
		tmp = t * (x / z);
	} else {
		tmp = x * -t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -165000.0) or not (z <= 1.0):
		tmp = t * (x / z)
	else:
		tmp = x * -t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -165000.0) || !(z <= 1.0))
		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 <= -165000.0) || ~((z <= 1.0)))
		tmp = t * (x / z);
	else
		tmp = x * -t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -165000.0], N[Not[LessEqual[z, 1.0]], $MachinePrecision]], N[(t * N[(x / z), $MachinePrecision]), $MachinePrecision], N[(x * (-t)), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -165000 or 1 < z

   1. Initial program 97.9%

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

   3. Taylor expanded in y around 0 53.0%

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

      1. mul-1-neg 53.0%

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

      2. associate-/l* 51.1%

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

      3. distribute-rgt-neg-in 51.1%

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

      4. distribute-neg-frac2 51.1%

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

      5. neg-sub0 51.1%

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

      6. associate--r- 51.1%

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

      7. metadata-eval 51.1%

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

   5. Simplified 51.1%

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

   6. Taylor expanded in z around inf 50.0%

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

   if -165000 < z < 1

   1. Initial program 87.9%

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

   3. Taylor expanded in z around 0 86.8%

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

   4. Taylor expanded in y around 0 25.7%

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

      1. associate-*r* 25.7%

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

      2. neg-mul-1 25.7%

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

   6. Simplified 25.7%

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

4. Final simplification 38.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -165000 \lor \neg \left(z \leq 1\right):\\ \;\;\;\;t \cdot \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(-t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 23.2% 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 92.9%

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

3. Taylor expanded in z around 0 62.4%

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

4. Taylor expanded in y around 0 19.4%

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

   1. associate-*r* 19.4%

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

   2. neg-mul-1 19.4%

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

6. Simplified 19.4%

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

7. Final simplification 19.4%

   \[\leadsto x \cdot \left(-t\right) \]
8. Add Preprocessing

Alternative 9: 9.8% accurate, 3.7× speedup

Math

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

FPCore

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

C

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

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 = t * x
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

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 0 62.4%

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

4. Taylor expanded in y around 0 19.4%

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

   1. associate-*r* 19.4%

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

   2. neg-mul-1 19.4%

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

6. Simplified 19.4%

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

   1. *-commutative 19.4%

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

   2. add-sqr-sqrt 9.2%

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

   3. sqrt-unprod 12.3%

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

   4. sqr-neg 12.3%

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

   5. sqrt-unprod 3.3%

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

   6. add-sqr-sqrt 7.8%

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

   7. pow1 7.8%

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

8. Applied egg-rr 7.8%

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

   1. unpow1 7.8%

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

10. Simplified 7.8%

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

11. Final simplification 7.8%

    \[\leadsto t \cdot x \]
12. Add Preprocessing

Developer Target 1: 94.7% 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 2024185 
(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)))))