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

Percentage Accurate: 94.8% → 94.8%

Time: 8.5s

Alternatives: 12

Speedup: 1.0×

• 20.6% 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: 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]

Derivation

1. Initial program 95.3%

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

3. Final simplification 95.3%

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

Alternative 2: 67.6% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{\frac{z}{t}}\\ \mathbf{if}\;t \leq -1.5 \cdot 10^{+153}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -1.7 \cdot 10^{+136}:\\ \;\;\;\;\frac{x \cdot y}{z}\\ \mathbf{elif}\;t \leq -1.7 \cdot 10^{+44}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 2.6 \cdot 10^{+118}:\\ \;\;\;\;\frac{x}{\frac{z}{y}}\\ \mathbf{elif}\;t \leq 3.4 \cdot 10^{+146} \lor \neg \left(t \leq 3.3 \cdot 10^{+253}\right):\\ \;\;\;\;x \cdot \frac{t}{z}\\ \mathbf{else}:\\ \;\;\;\;-x \cdot t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ x (/ z t))))
   (if (<= t -1.5e+153)
     t_1
     (if (<= t -1.7e+136)
       (/ (* x y) z)
       (if (<= t -1.7e+44)
         t_1
         (if (<= t 2.6e+118)
           (/ x (/ z y))
           (if (or (<= t 3.4e+146) (not (<= t 3.3e+253)))
             (* x (/ t z))
             (- (* x t)))))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x / (z / t);
	double tmp;
	if (t <= -1.5e+153) {
		tmp = t_1;
	} else if (t <= -1.7e+136) {
		tmp = (x * y) / z;
	} else if (t <= -1.7e+44) {
		tmp = t_1;
	} else if (t <= 2.6e+118) {
		tmp = x / (z / y);
	} else if ((t <= 3.4e+146) || !(t <= 3.3e+253)) {
		tmp = x * (t / z);
	} else {
		tmp = -(x * t);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x / (z / t)
    if (t <= (-1.5d+153)) then
        tmp = t_1
    else if (t <= (-1.7d+136)) then
        tmp = (x * y) / z
    else if (t <= (-1.7d+44)) then
        tmp = t_1
    else if (t <= 2.6d+118) then
        tmp = x / (z / y)
    else if ((t <= 3.4d+146) .or. (.not. (t <= 3.3d+253))) then
        tmp = x * (t / z)
    else
        tmp = -(x * t)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = x / (z / t);
	double tmp;
	if (t <= -1.5e+153) {
		tmp = t_1;
	} else if (t <= -1.7e+136) {
		tmp = (x * y) / z;
	} else if (t <= -1.7e+44) {
		tmp = t_1;
	} else if (t <= 2.6e+118) {
		tmp = x / (z / y);
	} else if ((t <= 3.4e+146) || !(t <= 3.3e+253)) {
		tmp = x * (t / z);
	} else {
		tmp = -(x * t);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x / (z / t)
	tmp = 0
	if t <= -1.5e+153:
		tmp = t_1
	elif t <= -1.7e+136:
		tmp = (x * y) / z
	elif t <= -1.7e+44:
		tmp = t_1
	elif t <= 2.6e+118:
		tmp = x / (z / y)
	elif (t <= 3.4e+146) or not (t <= 3.3e+253):
		tmp = x * (t / z)
	else:
		tmp = -(x * t)
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x / Float64(z / t))
	tmp = 0.0
	if (t <= -1.5e+153)
		tmp = t_1;
	elseif (t <= -1.7e+136)
		tmp = Float64(Float64(x * y) / z);
	elseif (t <= -1.7e+44)
		tmp = t_1;
	elseif (t <= 2.6e+118)
		tmp = Float64(x / Float64(z / y));
	elseif ((t <= 3.4e+146) || !(t <= 3.3e+253))
		tmp = Float64(x * Float64(t / z));
	else
		tmp = Float64(-Float64(x * t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x / (z / t);
	tmp = 0.0;
	if (t <= -1.5e+153)
		tmp = t_1;
	elseif (t <= -1.7e+136)
		tmp = (x * y) / z;
	elseif (t <= -1.7e+44)
		tmp = t_1;
	elseif (t <= 2.6e+118)
		tmp = x / (z / y);
	elseif ((t <= 3.4e+146) || ~((t <= 3.3e+253)))
		tmp = x * (t / z);
	else
		tmp = -(x * t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x / N[(z / t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -1.5e+153], t$95$1, If[LessEqual[t, -1.7e+136], N[(N[(x * y), $MachinePrecision] / z), $MachinePrecision], If[LessEqual[t, -1.7e+44], t$95$1, If[LessEqual[t, 2.6e+118], N[(x / N[(z / y), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[t, 3.4e+146], N[Not[LessEqual[t, 3.3e+253]], $MachinePrecision]], N[(x * N[(t / z), $MachinePrecision]), $MachinePrecision], (-N[(x * t), $MachinePrecision])]]]]]]

Derivation

1. Split input into 5 regimes

2. if t < -1.50000000000000009e153 or -1.69999999999999998e136 < t < -1.7e44

   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 76.4%

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

      1. cancel-sign-sub-inv 76.4%

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

      2. metadata-eval 76.4%

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

      3. *-lft-identity 76.4%

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

      4. +-commutative 76.4%

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

   5. Simplified 76.4%

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

      1. clear-num 76.3%

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

      2. un-div-inv 76.5%

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

      3. +-commutative 76.5%

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

   7. Applied egg-rr 76.5%

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

   8. Taylor expanded in y around 0 62.0%

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

   if -1.50000000000000009e153 < t < -1.69999999999999998e136

   1. Initial program 100.0%

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

   3. Taylor expanded in y around inf 75.7%

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

   if -1.7e44 < t < 2.60000000000000016e118

   1. Initial program 93.4%

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

   3. Taylor expanded in y around inf 79.6%

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

      1. associate-/l* 80.8%

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

   5. Simplified 80.8%

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

   if 2.60000000000000016e118 < t < 3.39999999999999991e146 or 3.2999999999999999e253 < t

   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 90.2%

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

      1. cancel-sign-sub-inv 90.2%

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

      2. metadata-eval 90.2%

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

      3. *-lft-identity 90.2%

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

      4. +-commutative 90.2%

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

   5. Simplified 90.2%

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

   6. Taylor expanded in t around inf 83.2%

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

   if 3.39999999999999991e146 < t < 3.2999999999999999e253

   1. Initial program 94.0%

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

   3. Taylor expanded in y around 0 83.3%

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

      1. associate-*r/ 83.3%

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

      2. associate-*r* 83.3%

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

      3. neg-mul-1 83.3%

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

   5. Simplified 83.3%

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

   6. Taylor expanded in z around 0 72.0%

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

      1. associate-*r* 72.0%

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

      2. mul-1-neg 72.0%

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

   8. Simplified 72.0%

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

4. Final simplification 76.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.5 \cdot 10^{+153}:\\ \;\;\;\;\frac{x}{\frac{z}{t}}\\ \mathbf{elif}\;t \leq -1.7 \cdot 10^{+136}:\\ \;\;\;\;\frac{x \cdot y}{z}\\ \mathbf{elif}\;t \leq -1.7 \cdot 10^{+44}:\\ \;\;\;\;\frac{x}{\frac{z}{t}}\\ \mathbf{elif}\;t \leq 2.6 \cdot 10^{+118}:\\ \;\;\;\;\frac{x}{\frac{z}{y}}\\ \mathbf{elif}\;t \leq 3.4 \cdot 10^{+146} \lor \neg \left(t \leq 3.3 \cdot 10^{+253}\right):\\ \;\;\;\;x \cdot \frac{t}{z}\\ \mathbf{else}:\\ \;\;\;\;-x \cdot t\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 67.5% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{\frac{z}{t}}\\ \mathbf{if}\;t \leq -7.8 \cdot 10^{+153}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -2.4 \cdot 10^{+138}:\\ \;\;\;\;\frac{x \cdot y}{z}\\ \mathbf{elif}\;t \leq -1.05 \cdot 10^{+38}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 1.7 \cdot 10^{+119}:\\ \;\;\;\;\frac{x}{\frac{z}{y}}\\ \mathbf{elif}\;t \leq 3.2 \cdot 10^{+146}:\\ \;\;\;\;x \cdot \left(t \cdot \frac{1}{z}\right)\\ \mathbf{elif}\;t \leq 9.5 \cdot 10^{+253}:\\ \;\;\;\;-x \cdot t\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{t}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ x (/ z t))))
   (if (<= t -7.8e+153)
     t_1
     (if (<= t -2.4e+138)
       (/ (* x y) z)
       (if (<= t -1.05e+38)
         t_1
         (if (<= t 1.7e+119)
           (/ x (/ z y))
           (if (<= t 3.2e+146)
             (* x (* t (/ 1.0 z)))
             (if (<= t 9.5e+253) (- (* x t)) (* x (/ t z))))))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x / (z / t);
	double tmp;
	if (t <= -7.8e+153) {
		tmp = t_1;
	} else if (t <= -2.4e+138) {
		tmp = (x * y) / z;
	} else if (t <= -1.05e+38) {
		tmp = t_1;
	} else if (t <= 1.7e+119) {
		tmp = x / (z / y);
	} else if (t <= 3.2e+146) {
		tmp = x * (t * (1.0 / z));
	} else if (t <= 9.5e+253) {
		tmp = -(x * t);
	} else {
		tmp = x * (t / z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x / (z / t)
    if (t <= (-7.8d+153)) then
        tmp = t_1
    else if (t <= (-2.4d+138)) then
        tmp = (x * y) / z
    else if (t <= (-1.05d+38)) then
        tmp = t_1
    else if (t <= 1.7d+119) then
        tmp = x / (z / y)
    else if (t <= 3.2d+146) then
        tmp = x * (t * (1.0d0 / z))
    else if (t <= 9.5d+253) then
        tmp = -(x * t)
    else
        tmp = x * (t / z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = x / (z / t);
	double tmp;
	if (t <= -7.8e+153) {
		tmp = t_1;
	} else if (t <= -2.4e+138) {
		tmp = (x * y) / z;
	} else if (t <= -1.05e+38) {
		tmp = t_1;
	} else if (t <= 1.7e+119) {
		tmp = x / (z / y);
	} else if (t <= 3.2e+146) {
		tmp = x * (t * (1.0 / z));
	} else if (t <= 9.5e+253) {
		tmp = -(x * t);
	} else {
		tmp = x * (t / z);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x / (z / t)
	tmp = 0
	if t <= -7.8e+153:
		tmp = t_1
	elif t <= -2.4e+138:
		tmp = (x * y) / z
	elif t <= -1.05e+38:
		tmp = t_1
	elif t <= 1.7e+119:
		tmp = x / (z / y)
	elif t <= 3.2e+146:
		tmp = x * (t * (1.0 / z))
	elif t <= 9.5e+253:
		tmp = -(x * t)
	else:
		tmp = x * (t / z)
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x / Float64(z / t))
	tmp = 0.0
	if (t <= -7.8e+153)
		tmp = t_1;
	elseif (t <= -2.4e+138)
		tmp = Float64(Float64(x * y) / z);
	elseif (t <= -1.05e+38)
		tmp = t_1;
	elseif (t <= 1.7e+119)
		tmp = Float64(x / Float64(z / y));
	elseif (t <= 3.2e+146)
		tmp = Float64(x * Float64(t * Float64(1.0 / z)));
	elseif (t <= 9.5e+253)
		tmp = Float64(-Float64(x * t));
	else
		tmp = Float64(x * Float64(t / z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x / (z / t);
	tmp = 0.0;
	if (t <= -7.8e+153)
		tmp = t_1;
	elseif (t <= -2.4e+138)
		tmp = (x * y) / z;
	elseif (t <= -1.05e+38)
		tmp = t_1;
	elseif (t <= 1.7e+119)
		tmp = x / (z / y);
	elseif (t <= 3.2e+146)
		tmp = x * (t * (1.0 / z));
	elseif (t <= 9.5e+253)
		tmp = -(x * t);
	else
		tmp = x * (t / z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x / N[(z / t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -7.8e+153], t$95$1, If[LessEqual[t, -2.4e+138], N[(N[(x * y), $MachinePrecision] / z), $MachinePrecision], If[LessEqual[t, -1.05e+38], t$95$1, If[LessEqual[t, 1.7e+119], N[(x / N[(z / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 3.2e+146], N[(x * N[(t * N[(1.0 / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 9.5e+253], (-N[(x * t), $MachinePrecision]), N[(x * N[(t / z), $MachinePrecision]), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if t < -7.79999999999999966e153 or -2.4000000000000001e138 < t < -1.05e38

   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 76.4%

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

      1. cancel-sign-sub-inv 76.4%

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

      2. metadata-eval 76.4%

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

      3. *-lft-identity 76.4%

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

      4. +-commutative 76.4%

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

   5. Simplified 76.4%

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

      1. clear-num 76.3%

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

      2. un-div-inv 76.5%

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

      3. +-commutative 76.5%

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

   7. Applied egg-rr 76.5%

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

   8. Taylor expanded in y around 0 62.0%

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

   if -7.79999999999999966e153 < t < -2.4000000000000001e138

   1. Initial program 100.0%

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

   3. Taylor expanded in y around inf 75.7%

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

   if -1.05e38 < t < 1.70000000000000007e119

   1. Initial program 93.4%

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

   3. Taylor expanded in y around inf 79.6%

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

      1. associate-/l* 80.8%

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

   5. Simplified 80.8%

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

   if 1.70000000000000007e119 < t < 3.2e146

   1. Initial program 99.5%

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

   3. Taylor expanded in z around inf 99.5%

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

      1. cancel-sign-sub-inv 99.5%

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

      2. metadata-eval 99.5%

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

      3. *-lft-identity 99.5%

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

      4. +-commutative 99.5%

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

   5. Simplified 99.5%

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

   6. Taylor expanded in t around inf 67.8%

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

      1. associate-/l* 85.0%

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

   8. Simplified 85.0%

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

      1. associate-/l* 67.8%

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

      2. *-commutative 67.8%

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

      3. associate-*l/ 84.7%

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

      4. div-inv 84.7%

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

      5. associate-*l* 99.7%

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

   10. Applied egg-rr 99.7%

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

   if 3.2e146 < t < 9.50000000000000005e253

   1. Initial program 94.0%

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

   3. Taylor expanded in y around 0 83.3%

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

      1. associate-*r/ 83.3%

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

      2. associate-*r* 83.3%

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

      3. neg-mul-1 83.3%

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

   5. Simplified 83.3%

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

   6. Taylor expanded in z around 0 72.0%

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

      1. associate-*r* 72.0%

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

      2. mul-1-neg 72.0%

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

   8. Simplified 72.0%

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

   if 9.50000000000000005e253 < t

   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 86.2%

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

      1. cancel-sign-sub-inv 86.2%

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

      2. metadata-eval 86.2%

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

      3. *-lft-identity 86.2%

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

      4. +-commutative 86.2%

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

   5. Simplified 86.2%

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

   6. Taylor expanded in t around inf 76.2%

      \[\leadsto x \cdot \color{blue}{\frac{t}{z}} \]
3. Recombined 6 regimes into one program.

4. Final simplification 76.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -7.8 \cdot 10^{+153}:\\ \;\;\;\;\frac{x}{\frac{z}{t}}\\ \mathbf{elif}\;t \leq -2.4 \cdot 10^{+138}:\\ \;\;\;\;\frac{x \cdot y}{z}\\ \mathbf{elif}\;t \leq -1.05 \cdot 10^{+38}:\\ \;\;\;\;\frac{x}{\frac{z}{t}}\\ \mathbf{elif}\;t \leq 1.7 \cdot 10^{+119}:\\ \;\;\;\;\frac{x}{\frac{z}{y}}\\ \mathbf{elif}\;t \leq 3.2 \cdot 10^{+146}:\\ \;\;\;\;x \cdot \left(t \cdot \frac{1}{z}\right)\\ \mathbf{elif}\;t \leq 9.5 \cdot 10^{+253}:\\ \;\;\;\;-x \cdot t\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{t}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 68.0% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \frac{t}{z}\\ \mathbf{if}\;t \leq -1.5 \cdot 10^{+153}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 2.2 \cdot 10^{+118}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \mathbf{elif}\;t \leq 3.4 \cdot 10^{+146} \lor \neg \left(t \leq 2.6 \cdot 10^{+253}\right):\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;-x \cdot t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* x (/ t z))))
   (if (<= t -1.5e+153)
     t_1
     (if (<= t 2.2e+118)
       (* x (/ y z))
       (if (or (<= t 3.4e+146) (not (<= t 2.6e+253))) t_1 (- (* x t)))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x * (t / z);
	double tmp;
	if (t <= -1.5e+153) {
		tmp = t_1;
	} else if (t <= 2.2e+118) {
		tmp = x * (y / z);
	} else if ((t <= 3.4e+146) || !(t <= 2.6e+253)) {
		tmp = t_1;
	} else {
		tmp = -(x * t);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x * (t / z)
    if (t <= (-1.5d+153)) then
        tmp = t_1
    else if (t <= 2.2d+118) then
        tmp = x * (y / z)
    else if ((t <= 3.4d+146) .or. (.not. (t <= 2.6d+253))) then
        tmp = t_1
    else
        tmp = -(x * t)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = x * (t / z);
	double tmp;
	if (t <= -1.5e+153) {
		tmp = t_1;
	} else if (t <= 2.2e+118) {
		tmp = x * (y / z);
	} else if ((t <= 3.4e+146) || !(t <= 2.6e+253)) {
		tmp = t_1;
	} else {
		tmp = -(x * t);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x * (t / z)
	tmp = 0
	if t <= -1.5e+153:
		tmp = t_1
	elif t <= 2.2e+118:
		tmp = x * (y / z)
	elif (t <= 3.4e+146) or not (t <= 2.6e+253):
		tmp = t_1
	else:
		tmp = -(x * t)
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x * Float64(t / z))
	tmp = 0.0
	if (t <= -1.5e+153)
		tmp = t_1;
	elseif (t <= 2.2e+118)
		tmp = Float64(x * Float64(y / z));
	elseif ((t <= 3.4e+146) || !(t <= 2.6e+253))
		tmp = t_1;
	else
		tmp = Float64(-Float64(x * t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x * (t / z);
	tmp = 0.0;
	if (t <= -1.5e+153)
		tmp = t_1;
	elseif (t <= 2.2e+118)
		tmp = x * (y / z);
	elseif ((t <= 3.4e+146) || ~((t <= 2.6e+253)))
		tmp = t_1;
	else
		tmp = -(x * t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x * N[(t / z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -1.5e+153], t$95$1, If[LessEqual[t, 2.2e+118], N[(x * N[(y / z), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[t, 3.4e+146], N[Not[LessEqual[t, 2.6e+253]], $MachinePrecision]], t$95$1, (-N[(x * t), $MachinePrecision])]]]]

Derivation

1. Split input into 3 regimes

2. if t < -1.50000000000000009e153 or 2.19999999999999986e118 < t < 3.39999999999999991e146 or 2.6e253 < t

   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 82.7%

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

      1. cancel-sign-sub-inv 82.7%

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

      2. metadata-eval 82.7%

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

      3. *-lft-identity 82.7%

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

      4. +-commutative 82.7%

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

   5. Simplified 82.7%

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

   6. Taylor expanded in t around inf 75.7%

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

   if -1.50000000000000009e153 < t < 2.19999999999999986e118

   1. Initial program 94.4%

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

   3. Taylor expanded in y around inf 74.5%

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

      1. associate-*r/ 74.4%

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

   5. Simplified 74.4%

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

   if 3.39999999999999991e146 < t < 2.6e253

   1. Initial program 94.0%

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

   3. Taylor expanded in y around 0 83.3%

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

      1. associate-*r/ 83.3%

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

      2. associate-*r* 83.3%

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

      3. neg-mul-1 83.3%

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

   5. Simplified 83.3%

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

   6. Taylor expanded in z around 0 72.0%

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

      1. associate-*r* 72.0%

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

      2. mul-1-neg 72.0%

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

   8. Simplified 72.0%

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

4. Final simplification 74.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.5 \cdot 10^{+153}:\\ \;\;\;\;x \cdot \frac{t}{z}\\ \mathbf{elif}\;t \leq 2.2 \cdot 10^{+118}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \mathbf{elif}\;t \leq 3.4 \cdot 10^{+146} \lor \neg \left(t \leq 2.6 \cdot 10^{+253}\right):\\ \;\;\;\;x \cdot \frac{t}{z}\\ \mathbf{else}:\\ \;\;\;\;-x \cdot t\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 68.0% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.5 \cdot 10^{+152}:\\ \;\;\;\;\frac{x}{\frac{z}{t}}\\ \mathbf{elif}\;t \leq 3.2 \cdot 10^{+118}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \mathbf{elif}\;t \leq 1.15 \cdot 10^{+146} \lor \neg \left(t \leq 2.35 \cdot 10^{+253}\right):\\ \;\;\;\;x \cdot \frac{t}{z}\\ \mathbf{else}:\\ \;\;\;\;-x \cdot t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= t -1.5e+152)
   (/ x (/ z t))
   (if (<= t 3.2e+118)
     (* x (/ y z))
     (if (or (<= t 1.15e+146) (not (<= t 2.35e+253)))
       (* x (/ t z))
       (- (* x t))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= -1.5e+152) {
		tmp = x / (z / t);
	} else if (t <= 3.2e+118) {
		tmp = x * (y / z);
	} else if ((t <= 1.15e+146) || !(t <= 2.35e+253)) {
		tmp = x * (t / z);
	} else {
		tmp = -(x * t);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (t <= (-1.5d+152)) then
        tmp = x / (z / t)
    else if (t <= 3.2d+118) then
        tmp = x * (y / z)
    else if ((t <= 1.15d+146) .or. (.not. (t <= 2.35d+253))) then
        tmp = x * (t / z)
    else
        tmp = -(x * t)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= -1.5e+152) {
		tmp = x / (z / t);
	} else if (t <= 3.2e+118) {
		tmp = x * (y / z);
	} else if ((t <= 1.15e+146) || !(t <= 2.35e+253)) {
		tmp = x * (t / z);
	} else {
		tmp = -(x * t);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if t <= -1.5e+152:
		tmp = x / (z / t)
	elif t <= 3.2e+118:
		tmp = x * (y / z)
	elif (t <= 1.15e+146) or not (t <= 2.35e+253):
		tmp = x * (t / z)
	else:
		tmp = -(x * t)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (t <= -1.5e+152)
		tmp = Float64(x / Float64(z / t));
	elseif (t <= 3.2e+118)
		tmp = Float64(x * Float64(y / z));
	elseif ((t <= 1.15e+146) || !(t <= 2.35e+253))
		tmp = Float64(x * Float64(t / z));
	else
		tmp = Float64(-Float64(x * t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (t <= -1.5e+152)
		tmp = x / (z / t);
	elseif (t <= 3.2e+118)
		tmp = x * (y / z);
	elseif ((t <= 1.15e+146) || ~((t <= 2.35e+253)))
		tmp = x * (t / z);
	else
		tmp = -(x * t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[t, -1.5e+152], N[(x / N[(z / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 3.2e+118], N[(x * N[(y / z), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[t, 1.15e+146], N[Not[LessEqual[t, 2.35e+253]], $MachinePrecision]], N[(x * N[(t / z), $MachinePrecision]), $MachinePrecision], (-N[(x * t), $MachinePrecision])]]]

Derivation

1. Split input into 4 regimes

2. if t < -1.49999999999999995e152

   1. Initial program 99.8%

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

   3. Taylor expanded in z around inf 76.9%

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

      1. cancel-sign-sub-inv 76.9%

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

      2. metadata-eval 76.9%

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

      3. *-lft-identity 76.9%

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

      4. +-commutative 76.9%

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

   5. Simplified 76.9%

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

      1. clear-num 76.9%

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

      2. un-div-inv 77.0%

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

      3. +-commutative 77.0%

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

   7. Applied egg-rr 77.0%

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

   8. Taylor expanded in y around 0 70.0%

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

   if -1.49999999999999995e152 < t < 3.20000000000000016e118

   1. Initial program 94.4%

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

   3. Taylor expanded in y around inf 74.5%

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

      1. associate-*r/ 74.4%

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

   5. Simplified 74.4%

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

   if 3.20000000000000016e118 < t < 1.15e146 or 2.35000000000000011e253 < t

   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 90.2%

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

      1. cancel-sign-sub-inv 90.2%

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

      2. metadata-eval 90.2%

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

      3. *-lft-identity 90.2%

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

      4. +-commutative 90.2%

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

   5. Simplified 90.2%

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

   6. Taylor expanded in t around inf 83.2%

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

   if 1.15e146 < t < 2.35000000000000011e253

   1. Initial program 94.0%

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

   3. Taylor expanded in y around 0 83.3%

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

      1. associate-*r/ 83.3%

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

      2. associate-*r* 83.3%

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

      3. neg-mul-1 83.3%

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

   5. Simplified 83.3%

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

   6. Taylor expanded in z around 0 72.0%

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

      1. associate-*r* 72.0%

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

      2. mul-1-neg 72.0%

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

   8. Simplified 72.0%

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

4. Final simplification 74.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.5 \cdot 10^{+152}:\\ \;\;\;\;\frac{x}{\frac{z}{t}}\\ \mathbf{elif}\;t \leq 3.2 \cdot 10^{+118}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \mathbf{elif}\;t \leq 1.15 \cdot 10^{+146} \lor \neg \left(t \leq 2.35 \cdot 10^{+253}\right):\\ \;\;\;\;x \cdot \frac{t}{z}\\ \mathbf{else}:\\ \;\;\;\;-x \cdot t\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 68.1% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.45 \cdot 10^{+152}:\\ \;\;\;\;\frac{x}{\frac{z}{t}}\\ \mathbf{elif}\;t \leq 6.8 \cdot 10^{+118}:\\ \;\;\;\;\frac{x}{\frac{z}{y}}\\ \mathbf{elif}\;t \leq 3.4 \cdot 10^{+146} \lor \neg \left(t \leq 3 \cdot 10^{+253}\right):\\ \;\;\;\;x \cdot \frac{t}{z}\\ \mathbf{else}:\\ \;\;\;\;-x \cdot t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= t -1.45e+152)
   (/ x (/ z t))
   (if (<= t 6.8e+118)
     (/ x (/ z y))
     (if (or (<= t 3.4e+146) (not (<= t 3e+253))) (* x (/ t z)) (- (* x t))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= -1.45e+152) {
		tmp = x / (z / t);
	} else if (t <= 6.8e+118) {
		tmp = x / (z / y);
	} else if ((t <= 3.4e+146) || !(t <= 3e+253)) {
		tmp = x * (t / z);
	} else {
		tmp = -(x * t);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (t <= (-1.45d+152)) then
        tmp = x / (z / t)
    else if (t <= 6.8d+118) then
        tmp = x / (z / y)
    else if ((t <= 3.4d+146) .or. (.not. (t <= 3d+253))) then
        tmp = x * (t / z)
    else
        tmp = -(x * t)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= -1.45e+152) {
		tmp = x / (z / t);
	} else if (t <= 6.8e+118) {
		tmp = x / (z / y);
	} else if ((t <= 3.4e+146) || !(t <= 3e+253)) {
		tmp = x * (t / z);
	} else {
		tmp = -(x * t);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if t <= -1.45e+152:
		tmp = x / (z / t)
	elif t <= 6.8e+118:
		tmp = x / (z / y)
	elif (t <= 3.4e+146) or not (t <= 3e+253):
		tmp = x * (t / z)
	else:
		tmp = -(x * t)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (t <= -1.45e+152)
		tmp = Float64(x / Float64(z / t));
	elseif (t <= 6.8e+118)
		tmp = Float64(x / Float64(z / y));
	elseif ((t <= 3.4e+146) || !(t <= 3e+253))
		tmp = Float64(x * Float64(t / z));
	else
		tmp = Float64(-Float64(x * t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (t <= -1.45e+152)
		tmp = x / (z / t);
	elseif (t <= 6.8e+118)
		tmp = x / (z / y);
	elseif ((t <= 3.4e+146) || ~((t <= 3e+253)))
		tmp = x * (t / z);
	else
		tmp = -(x * t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[t, -1.45e+152], N[(x / N[(z / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 6.8e+118], N[(x / N[(z / y), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[t, 3.4e+146], N[Not[LessEqual[t, 3e+253]], $MachinePrecision]], N[(x * N[(t / z), $MachinePrecision]), $MachinePrecision], (-N[(x * t), $MachinePrecision])]]]

Derivation

1. Split input into 4 regimes

2. if t < -1.4499999999999999e152

   1. Initial program 99.8%

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

   3. Taylor expanded in z around inf 76.9%

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

      1. cancel-sign-sub-inv 76.9%

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

      2. metadata-eval 76.9%

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

      3. *-lft-identity 76.9%

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

      4. +-commutative 76.9%

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

   5. Simplified 76.9%

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

      1. clear-num 76.9%

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

      2. un-div-inv 77.0%

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

      3. +-commutative 77.0%

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

   7. Applied egg-rr 77.0%

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

   8. Taylor expanded in y around 0 70.0%

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

   if -1.4499999999999999e152 < t < 6.79999999999999973e118

   1. Initial program 94.4%

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

   3. Taylor expanded in y around inf 74.5%

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

      1. associate-/l* 75.1%

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

   5. Simplified 75.1%

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

   if 6.79999999999999973e118 < t < 3.39999999999999991e146 or 2.9999999999999998e253 < t

   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 90.2%

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

      1. cancel-sign-sub-inv 90.2%

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

      2. metadata-eval 90.2%

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

      3. *-lft-identity 90.2%

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

      4. +-commutative 90.2%

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

   5. Simplified 90.2%

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

   6. Taylor expanded in t around inf 83.2%

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

   if 3.39999999999999991e146 < t < 2.9999999999999998e253

   1. Initial program 94.0%

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

   3. Taylor expanded in y around 0 83.3%

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

      1. associate-*r/ 83.3%

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

      2. associate-*r* 83.3%

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

      3. neg-mul-1 83.3%

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

   5. Simplified 83.3%

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

   6. Taylor expanded in z around 0 72.0%

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

      1. associate-*r* 72.0%

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

      2. mul-1-neg 72.0%

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

   8. Simplified 72.0%

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

4. Final simplification 75.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.45 \cdot 10^{+152}:\\ \;\;\;\;\frac{x}{\frac{z}{t}}\\ \mathbf{elif}\;t \leq 6.8 \cdot 10^{+118}:\\ \;\;\;\;\frac{x}{\frac{z}{y}}\\ \mathbf{elif}\;t \leq 3.4 \cdot 10^{+146} \lor \neg \left(t \leq 3 \cdot 10^{+253}\right):\\ \;\;\;\;x \cdot \frac{t}{z}\\ \mathbf{else}:\\ \;\;\;\;-x \cdot t\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 75.0% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.1 \cdot 10^{+242}:\\ \;\;\;\;\frac{x}{\frac{z}{y}}\\ \mathbf{elif}\;z \leq -1.58 \cdot 10^{+91} \lor \neg \left(z \leq 2.35 \cdot 10^{+29}\right):\\ \;\;\;\;\frac{x}{\frac{z}{t}}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(\frac{y}{z} - t\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -1.1e+242)
   (/ x (/ z y))
   (if (or (<= z -1.58e+91) (not (<= z 2.35e+29)))
     (/ x (/ z t))
     (* x (- (/ y z) t)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -1.1e+242) {
		tmp = x / (z / y);
	} else if ((z <= -1.58e+91) || !(z <= 2.35e+29)) {
		tmp = x / (z / t);
	} else {
		tmp = x * ((y / z) - t);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (z <= (-1.1d+242)) then
        tmp = x / (z / y)
    else if ((z <= (-1.58d+91)) .or. (.not. (z <= 2.35d+29))) then
        tmp = x / (z / t)
    else
        tmp = x * ((y / z) - t)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -1.1e+242) {
		tmp = x / (z / y);
	} else if ((z <= -1.58e+91) || !(z <= 2.35e+29)) {
		tmp = x / (z / t);
	} else {
		tmp = x * ((y / z) - t);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -1.1e+242:
		tmp = x / (z / y)
	elif (z <= -1.58e+91) or not (z <= 2.35e+29):
		tmp = x / (z / t)
	else:
		tmp = x * ((y / z) - t)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -1.1e+242)
		tmp = Float64(x / Float64(z / y));
	elseif ((z <= -1.58e+91) || !(z <= 2.35e+29))
		tmp = Float64(x / Float64(z / t));
	else
		tmp = Float64(x * Float64(Float64(y / z) - t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (z <= -1.1e+242)
		tmp = x / (z / y);
	elseif ((z <= -1.58e+91) || ~((z <= 2.35e+29)))
		tmp = x / (z / t);
	else
		tmp = x * ((y / z) - t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -1.1e+242], N[(x / N[(z / y), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[z, -1.58e+91], N[Not[LessEqual[z, 2.35e+29]], $MachinePrecision]], N[(x / N[(z / t), $MachinePrecision]), $MachinePrecision], N[(x * N[(N[(y / z), $MachinePrecision] - t), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.1e242

   1. Initial program 88.5%

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

   3. Taylor expanded in y around inf 68.8%

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

      1. associate-/l* 68.8%

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

   5. Simplified 68.8%

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

   if -1.1e242 < z < -1.5799999999999999e91 or 2.3500000000000001e29 < z

   1. Initial program 95.4%

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

   3. Taylor expanded in z around inf 95.4%

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

      1. cancel-sign-sub-inv 95.4%

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

      2. metadata-eval 95.4%

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

      3. *-lft-identity 95.4%

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

      4. +-commutative 95.4%

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

   5. Simplified 95.4%

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

      1. clear-num 95.4%

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

      2. un-div-inv 95.6%

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

      3. +-commutative 95.6%

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

   7. Applied egg-rr 95.6%

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

   8. Taylor expanded in y around 0 64.8%

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

   if -1.5799999999999999e91 < z < 2.3500000000000001e29

   1. Initial program 96.0%

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

   3. Taylor expanded in z around 0 87.3%

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

      1. +-commutative 87.3%

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

      2. associate-*r/ 86.0%

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

      3. *-commutative 86.0%

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

      4. associate-*r* 86.0%

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

      5. neg-mul-1 86.0%

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

      6. distribute-rgt-out 88.7%

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

      7. unsub-neg 88.7%

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

   5. Simplified 88.7%

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

4. Final simplification 79.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.1 \cdot 10^{+242}:\\ \;\;\;\;\frac{x}{\frac{z}{y}}\\ \mathbf{elif}\;z \leq -1.58 \cdot 10^{+91} \lor \neg \left(z \leq 2.35 \cdot 10^{+29}\right):\\ \;\;\;\;\frac{x}{\frac{z}{t}}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(\frac{y}{z} - t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 76.7% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.25 \cdot 10^{+44} \lor \neg \left(t \leq 7.5 \cdot 10^{+108}\right):\\ \;\;\;\;x \cdot \frac{t}{z + -1}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\frac{z}{y}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= t -1.25e+44) (not (<= t 7.5e+108)))
   (* x (/ t (+ z -1.0)))
   (/ x (/ z y))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((t <= -1.25e+44) || !(t <= 7.5e+108)) {
		tmp = x * (t / (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 <= (-1.25d+44)) .or. (.not. (t <= 7.5d+108))) then
        tmp = x * (t / (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 <= -1.25e+44) || !(t <= 7.5e+108)) {
		tmp = x * (t / (z + -1.0));
	} else {
		tmp = x / (z / y);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (t <= -1.25e+44) or not (t <= 7.5e+108):
		tmp = x * (t / (z + -1.0))
	else:
		tmp = x / (z / y)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((t <= -1.25e+44) || !(t <= 7.5e+108))
		tmp = Float64(x * Float64(t / 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 <= -1.25e+44) || ~((t <= 7.5e+108)))
		tmp = x * (t / (z + -1.0));
	else
		tmp = x / (z / y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[t, -1.25e+44], N[Not[LessEqual[t, 7.5e+108]], $MachinePrecision]], N[(x * N[(t / N[(z + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x / N[(z / y), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -1.2499999999999999e44 or 7.50000000000000039e108 < t

   1. Initial program 98.8%

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

   3. Taylor expanded in y around 0 69.6%

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

      1. associate-*r/ 69.6%

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

      2. mul-1-neg 69.6%

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

      3. *-commutative 69.6%

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

      4. distribute-rgt-neg-in 69.6%

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

      5. associate-*r/ 78.8%

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

      6. neg-mul-1 78.8%

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

      7. *-commutative 78.8%

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

      8. associate-*r/ 78.7%

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

      9. metadata-eval 78.7%

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

      10. associate-/r* 78.7%

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

      11. neg-mul-1 78.7%

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

      12. associate-*r/ 78.8%

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

      13. *-rgt-identity 78.8%

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

      14. neg-sub0 78.8%

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

      15. associate--r- 78.8%

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

      16. metadata-eval 78.8%

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

   5. Simplified 78.8%

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

   if -1.2499999999999999e44 < t < 7.50000000000000039e108

   1. Initial program 93.4%

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

   3. Taylor expanded in y around inf 80.1%

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

      1. associate-/l* 81.3%

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

   5. Simplified 81.3%

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

4. Final simplification 80.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.25 \cdot 10^{+44} \lor \neg \left(t \leq 7.5 \cdot 10^{+108}\right):\\ \;\;\;\;x \cdot \frac{t}{z + -1}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\frac{z}{y}}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 94.1% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1 \lor \neg \left(z \leq 0.0038\right):\\ \;\;\;\;x \cdot \frac{y + t}{z}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(\frac{y}{z} - t\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -1.0) (not (<= z 0.0038)))
   (* 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 <= 0.0038)) {
		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 <= 0.0038d0))) 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 <= 0.0038)) {
		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 <= 0.0038):
		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 <= 0.0038))
		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 <= 0.0038)))
		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, 0.0038]], $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 0.00379999999999999999 < z

   1. Initial program 95.6%

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

   3. Taylor expanded in z around inf 94.5%

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

      1. cancel-sign-sub-inv 94.5%

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

      2. metadata-eval 94.5%

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

      3. *-lft-identity 94.5%

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

      4. +-commutative 94.5%

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

   5. Simplified 94.5%

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

   if -1 < z < 0.00379999999999999999

   1. Initial program 95.0%

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

   3. Taylor expanded in z around 0 92.5%

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

      1. +-commutative 92.5%

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

      2. associate-*r/ 90.8%

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

      3. *-commutative 90.8%

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

      4. associate-*r* 90.8%

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

      5. neg-mul-1 90.8%

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

      6. distribute-rgt-out 93.3%

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

      7. unsub-neg 93.3%

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

   5. Simplified 93.3%

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

4. Final simplification 94.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1 \lor \neg \left(z \leq 0.0038\right):\\ \;\;\;\;x \cdot \frac{y + t}{z}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(\frac{y}{z} - t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 93.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.1 \lor \neg \left(z \leq 1550000\right):\\ \;\;\;\;\frac{x}{\frac{z}{y + t}}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(\frac{y}{z} - t\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -1.1) (not (<= z 1550000.0)))
   (/ x (/ z (+ y t)))
   (* x (- (/ y z) t))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -1.1) || !(z <= 1550000.0)) {
		tmp = x / (z / (y + t));
	} else {
		tmp = x * ((y / z) - t);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((z <= (-1.1d0)) .or. (.not. (z <= 1550000.0d0))) then
        tmp = x / (z / (y + t))
    else
        tmp = x * ((y / z) - t)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -1.1) || !(z <= 1550000.0)) {
		tmp = x / (z / (y + t));
	} else {
		tmp = x * ((y / z) - t);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -1.1) or not (z <= 1550000.0):
		tmp = x / (z / (y + t))
	else:
		tmp = x * ((y / z) - t)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -1.1) || !(z <= 1550000.0))
		tmp = Float64(x / Float64(z / Float64(y + t)));
	else
		tmp = Float64(x * Float64(Float64(y / z) - t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z <= -1.1) || ~((z <= 1550000.0)))
		tmp = x / (z / (y + t));
	else
		tmp = x * ((y / z) - t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -1.1], N[Not[LessEqual[z, 1550000.0]], $MachinePrecision]], N[(x / N[(z / N[(y + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x * N[(N[(y / z), $MachinePrecision] - t), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.1000000000000001 or 1.55e6 < z

   1. Initial program 95.4%

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

   3. Taylor expanded in z around inf 88.9%

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

      1. associate-/l* 94.4%

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

      2. cancel-sign-sub-inv 94.4%

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

      3. metadata-eval 94.4%

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

      4. *-lft-identity 94.4%

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

      5. +-commutative 94.4%

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

   5. Simplified 94.4%

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

   if -1.1000000000000001 < z < 1.55e6

   1. Initial program 95.2%

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

   3. Taylor expanded in z around 0 92.7%

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

      1. +-commutative 92.7%

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

      2. associate-*r/ 91.1%

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

      3. *-commutative 91.1%

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

      4. associate-*r* 91.1%

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

      5. neg-mul-1 91.1%

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

      6. distribute-rgt-out 93.6%

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

      7. unsub-neg 93.6%

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

   5. Simplified 93.6%

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

4. Final simplification 94.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.1 \lor \neg \left(z \leq 1550000\right):\\ \;\;\;\;\frac{x}{\frac{z}{y + t}}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(\frac{y}{z} - t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 44.4% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1 \lor \neg \left(z \leq 0.0038\right):\\ \;\;\;\;x \cdot \frac{t}{z}\\ \mathbf{else}:\\ \;\;\;\;-x \cdot t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -1.0) (not (<= z 0.0038))) (* x (/ t z)) (- (* x t))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -1.0) || !(z <= 0.0038)) {
		tmp = x * (t / z);
	} else {
		tmp = -(x * t);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((z <= (-1.0d0)) .or. (.not. (z <= 0.0038d0))) then
        tmp = x * (t / z)
    else
        tmp = -(x * t)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -1.0) || !(z <= 0.0038)) {
		tmp = x * (t / z);
	} else {
		tmp = -(x * t);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -1.0) or not (z <= 0.0038):
		tmp = x * (t / z)
	else:
		tmp = -(x * t)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -1.0) || !(z <= 0.0038))
		tmp = Float64(x * Float64(t / z));
	else
		tmp = Float64(-Float64(x * t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z <= -1.0) || ~((z <= 0.0038)))
		tmp = x * (t / z);
	else
		tmp = -(x * t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -1.0], N[Not[LessEqual[z, 0.0038]], $MachinePrecision]], N[(x * N[(t / z), $MachinePrecision]), $MachinePrecision], (-N[(x * t), $MachinePrecision])]

Derivation

1. Split input into 2 regimes

2. if z < -1 or 0.00379999999999999999 < z

   1. Initial program 95.6%

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

   3. Taylor expanded in z around inf 94.5%

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

      1. cancel-sign-sub-inv 94.5%

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

      2. metadata-eval 94.5%

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

      3. *-lft-identity 94.5%

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

      4. +-commutative 94.5%

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

   5. Simplified 94.5%

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

   6. Taylor expanded in t around inf 57.1%

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

   if -1 < z < 0.00379999999999999999

   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 0 37.3%

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

      1. associate-*r/ 37.3%

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

      2. associate-*r* 37.3%

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

      3. neg-mul-1 37.3%

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

   5. Simplified 37.3%

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

   6. Taylor expanded in z around 0 35.6%

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

      1. associate-*r* 35.6%

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

      2. mul-1-neg 35.6%

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

   8. Simplified 35.6%

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

4. Final simplification 47.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1 \lor \neg \left(z \leq 0.0038\right):\\ \;\;\;\;x \cdot \frac{t}{z}\\ \mathbf{else}:\\ \;\;\;\;-x \cdot t\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 22.6% accurate, 2.8× speedup

Math

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

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(-Float64(x * 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 95.3%

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

3. Taylor expanded in y around 0 46.6%

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

   1. associate-*r/ 46.6%

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

   2. associate-*r* 46.6%

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

   3. neg-mul-1 46.6%

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

5. Simplified 46.6%

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

6. Taylor expanded in z around 0 24.8%

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

   1. associate-*r* 24.8%

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

   2. mul-1-neg 24.8%

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

8. Simplified 24.8%

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

9. Final simplification 24.8%

   \[\leadsto -x \cdot t \]
10. Add Preprocessing

Developer target: 95.1% accurate, 0.3× speedup

Math

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

FPCore

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

C

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

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = x * ((y / z) - (t * (1.0d0 / (1.0d0 - z))))
    t_2 = x * ((y / z) - (t / (1.0d0 - z)))
    if (t_2 < (-7.623226303312042d-196)) then
        tmp = t_1
    else if (t_2 < 1.4133944927702302d-211) then
        tmp = ((y * x) / z) + -((t * x) / (1.0d0 - z))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = x * ((y / z) - (t * (1.0 / (1.0 - z))));
	double t_2 = x * ((y / z) - (t / (1.0 - z)));
	double tmp;
	if (t_2 < -7.623226303312042e-196) {
		tmp = t_1;
	} else if (t_2 < 1.4133944927702302e-211) {
		tmp = ((y * x) / z) + -((t * x) / (1.0 - z));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

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

Julia

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

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x * ((y / z) - (t * (1.0 / (1.0 - z))));
	t_2 = x * ((y / z) - (t / (1.0 - z)));
	tmp = 0.0;
	if (t_2 < -7.623226303312042e-196)
		tmp = t_1;
	elseif (t_2 < 1.4133944927702302e-211)
		tmp = ((y * x) / z) + -((t * x) / (1.0 - z));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x * N[(N[(y / z), $MachinePrecision] - N[(t * N[(1.0 / N[(1.0 - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x * N[(N[(y / z), $MachinePrecision] - N[(t / N[(1.0 - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[Less[t$95$2, -7.623226303312042e-196], t$95$1, If[Less[t$95$2, 1.4133944927702302e-211], N[(N[(N[(y * x), $MachinePrecision] / z), $MachinePrecision] + (-N[(N[(t * x), $MachinePrecision] / N[(1.0 - z), $MachinePrecision]), $MachinePrecision])), $MachinePrecision], t$95$1]]]]

Reproduce

herbie shell --seed 2024010 
(FPCore (x y z t)
  :name "Numeric.SpecFunctions:invIncompleteBetaWorker from math-functions-0.1.5.2, C"
  :precision binary64

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

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