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

Percentage Accurate: 94.3% → 96.3%

Time: 11.4s

Alternatives: 12

Speedup: 0.5×

• 21.4% 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: 94.3% 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: 96.3% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{y}{z} + \frac{t}{z + -1}\\ \mathbf{if}\;t\_1 \leq -\infty:\\ \;\;\;\;\frac{1}{z} \cdot \frac{x}{\frac{1}{y}}\\ \mathbf{else}:\\ \;\;\;\;t\_1 \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (+ (/ y z) (/ t (+ z -1.0)))))
   (if (<= t_1 (- INFINITY)) (* (/ 1.0 z) (/ x (/ 1.0 y))) (* 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)) {
		tmp = (1.0 / z) * (x / (1.0 / y));
	} 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) {
		tmp = (1.0 / z) * (x / (1.0 / y));
	} 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:
		tmp = (1.0 / z) * (x / (1.0 / y))
	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))
		tmp = Float64(Float64(1.0 / z) * Float64(x / Float64(1.0 / y)));
	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)
		tmp = (1.0 / z) * (x / (1.0 / y));
	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[LessEqual[t$95$1, (-Infinity)], N[(N[(1.0 / z), $MachinePrecision] * N[(x / N[(1.0 / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t$95$1 * x), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

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

   1. Initial program 58.7%

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

   3. Taylor expanded in y around inf 99.6%

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

      1. associate-*r/ 58.7%

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

   5. Simplified 58.7%

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

      1. clear-num 58.7%

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

      2. un-div-inv 64.3%

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

   7. Applied egg-rr 64.3%

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

      1. *-un-lft-identity 64.3%

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

      2. div-inv 64.3%

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

      3. times-frac 99.9%

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

   9. Applied egg-rr 99.9%

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

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

   1. Initial program 97.1%

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

4. Final simplification 97.3%

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

Alternative 2: 73.0% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(\frac{y}{z} - t\right)\\ \mathbf{if}\;z \leq -8.2 \cdot 10^{+77}:\\ \;\;\;\;\frac{y}{z} \cdot x\\ \mathbf{elif}\;z \leq -3.2 \cdot 10^{-269}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 5.8 \cdot 10^{-267}:\\ \;\;\;\;y \cdot \frac{x}{z}\\ \mathbf{elif}\;z \leq 6 \cdot 10^{+109}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 8 \cdot 10^{+224} \lor \neg \left(z \leq 1.2 \cdot 10^{+256}\right):\\ \;\;\;\;x \cdot \frac{t}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{y \cdot x}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* x (- (/ y z) t))))
   (if (<= z -8.2e+77)
     (* (/ y z) x)
     (if (<= z -3.2e-269)
       t_1
       (if (<= z 5.8e-267)
         (* y (/ x z))
         (if (<= z 6e+109)
           t_1
           (if (or (<= z 8e+224) (not (<= z 1.2e+256)))
             (* x (/ t z))
             (/ (* y x) z))))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x * ((y / z) - t);
	double tmp;
	if (z <= -8.2e+77) {
		tmp = (y / z) * x;
	} else if (z <= -3.2e-269) {
		tmp = t_1;
	} else if (z <= 5.8e-267) {
		tmp = y * (x / z);
	} else if (z <= 6e+109) {
		tmp = t_1;
	} else if ((z <= 8e+224) || !(z <= 1.2e+256)) {
		tmp = x * (t / z);
	} else {
		tmp = (y * x) / z;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x * ((y / z) - t)
    if (z <= (-8.2d+77)) then
        tmp = (y / z) * x
    else if (z <= (-3.2d-269)) then
        tmp = t_1
    else if (z <= 5.8d-267) then
        tmp = y * (x / z)
    else if (z <= 6d+109) then
        tmp = t_1
    else if ((z <= 8d+224) .or. (.not. (z <= 1.2d+256))) then
        tmp = x * (t / z)
    else
        tmp = (y * x) / z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = x * ((y / z) - t);
	double tmp;
	if (z <= -8.2e+77) {
		tmp = (y / z) * x;
	} else if (z <= -3.2e-269) {
		tmp = t_1;
	} else if (z <= 5.8e-267) {
		tmp = y * (x / z);
	} else if (z <= 6e+109) {
		tmp = t_1;
	} else if ((z <= 8e+224) || !(z <= 1.2e+256)) {
		tmp = x * (t / z);
	} else {
		tmp = (y * x) / z;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x * ((y / z) - t)
	tmp = 0
	if z <= -8.2e+77:
		tmp = (y / z) * x
	elif z <= -3.2e-269:
		tmp = t_1
	elif z <= 5.8e-267:
		tmp = y * (x / z)
	elif z <= 6e+109:
		tmp = t_1
	elif (z <= 8e+224) or not (z <= 1.2e+256):
		tmp = x * (t / z)
	else:
		tmp = (y * x) / z
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x * Float64(Float64(y / z) - t))
	tmp = 0.0
	if (z <= -8.2e+77)
		tmp = Float64(Float64(y / z) * x);
	elseif (z <= -3.2e-269)
		tmp = t_1;
	elseif (z <= 5.8e-267)
		tmp = Float64(y * Float64(x / z));
	elseif (z <= 6e+109)
		tmp = t_1;
	elseif ((z <= 8e+224) || !(z <= 1.2e+256))
		tmp = Float64(x * Float64(t / z));
	else
		tmp = Float64(Float64(y * x) / z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x * ((y / z) - t);
	tmp = 0.0;
	if (z <= -8.2e+77)
		tmp = (y / z) * x;
	elseif (z <= -3.2e-269)
		tmp = t_1;
	elseif (z <= 5.8e-267)
		tmp = y * (x / z);
	elseif (z <= 6e+109)
		tmp = t_1;
	elseif ((z <= 8e+224) || ~((z <= 1.2e+256)))
		tmp = x * (t / z);
	else
		tmp = (y * x) / z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x * N[(N[(y / z), $MachinePrecision] - t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -8.2e+77], N[(N[(y / z), $MachinePrecision] * x), $MachinePrecision], If[LessEqual[z, -3.2e-269], t$95$1, If[LessEqual[z, 5.8e-267], N[(y * N[(x / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 6e+109], t$95$1, If[Or[LessEqual[z, 8e+224], N[Not[LessEqual[z, 1.2e+256]], $MachinePrecision]], N[(x * N[(t / z), $MachinePrecision]), $MachinePrecision], N[(N[(y * x), $MachinePrecision] / z), $MachinePrecision]]]]]]]

Derivation

1. Split input into 5 regimes

2. if z < -8.2000000000000002e77

   1. Initial program 95.7%

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

   3. Taylor expanded in y around inf 59.2%

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

      1. associate-*r/ 65.0%

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

   5. Simplified 65.0%

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

   if -8.2000000000000002e77 < z < -3.2000000000000001e-269 or 5.80000000000000043e-267 < z < 6.00000000000000031e109

   1. Initial program 98.0%

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

   3. Taylor expanded in z around 0 82.1%

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

      1. +-commutative 82.1%

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

      2. associate-*r/ 81.7%

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

      3. *-commutative 81.7%

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

      4. associate-*r* 81.7%

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

      5. neg-mul-1 81.7%

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

      6. distribute-rgt-out 85.1%

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

      7. unsub-neg 85.1%

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

   5. Simplified 85.1%

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

   if -3.2000000000000001e-269 < z < 5.80000000000000043e-267

   1. Initial program 63.2%

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

   3. Taylor expanded in y around inf 94.5%

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

      1. *-commutative 94.5%

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

      2. associate-/l* 99.7%

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

   5. Simplified 99.7%

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

   if 6.00000000000000031e109 < z < 7.99999999999999976e224 or 1.20000000000000007e256 < z

   1. Initial program 97.1%

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

   3. Taylor expanded in y around 0 60.0%

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

      1. mul-1-neg 60.0%

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

      2. *-commutative 60.0%

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

      3. associate-/l* 73.4%

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

      4. distribute-rgt-neg-out 73.4%

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

      5. distribute-neg-frac2 73.4%

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

      6. neg-sub0 73.4%

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

      7. associate--r- 73.4%

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

      8. metadata-eval 73.4%

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

   5. Simplified 73.4%

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

   6. Taylor expanded in z around inf 73.4%

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

   if 7.99999999999999976e224 < z < 1.20000000000000007e256

   1. Initial program 88.8%

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

   3. Taylor expanded in y around inf 89.0%

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

4. Final simplification 80.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -8.2 \cdot 10^{+77}:\\ \;\;\;\;\frac{y}{z} \cdot x\\ \mathbf{elif}\;z \leq -3.2 \cdot 10^{-269}:\\ \;\;\;\;x \cdot \left(\frac{y}{z} - t\right)\\ \mathbf{elif}\;z \leq 5.8 \cdot 10^{-267}:\\ \;\;\;\;y \cdot \frac{x}{z}\\ \mathbf{elif}\;z \leq 6 \cdot 10^{+109}:\\ \;\;\;\;x \cdot \left(\frac{y}{z} - t\right)\\ \mathbf{elif}\;z \leq 8 \cdot 10^{+224} \lor \neg \left(z \leq 1.2 \cdot 10^{+256}\right):\\ \;\;\;\;x \cdot \frac{t}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{y \cdot x}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 65.8% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \frac{t}{z}\\ t_2 := \frac{y \cdot x}{z}\\ \mathbf{if}\;t \leq -3 \cdot 10^{+187}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq -3.6 \cdot 10^{+65}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t \leq -1.5 \cdot 10^{+32}:\\ \;\;\;\;\frac{t}{\frac{z}{x}}\\ \mathbf{elif}\;t \leq 2 \cdot 10^{-255}:\\ \;\;\;\;\frac{x}{\frac{z}{y}}\\ \mathbf{elif}\;t \leq 3.3 \cdot 10^{-10}:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* x (/ t z))) (t_2 (/ (* y x) z)))
   (if (<= t -3e+187)
     t_1
     (if (<= t -3.6e+65)
       t_2
       (if (<= t -1.5e+32)
         (/ t (/ z x))
         (if (<= t 2e-255) (/ x (/ z y)) (if (<= t 3.3e-10) t_2 t_1)))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x * (t / z);
	double t_2 = (y * x) / z;
	double tmp;
	if (t <= -3e+187) {
		tmp = t_1;
	} else if (t <= -3.6e+65) {
		tmp = t_2;
	} else if (t <= -1.5e+32) {
		tmp = t / (z / x);
	} else if (t <= 2e-255) {
		tmp = x / (z / y);
	} else if (t <= 3.3e-10) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = x * (t / z)
    t_2 = (y * x) / z
    if (t <= (-3d+187)) then
        tmp = t_1
    else if (t <= (-3.6d+65)) then
        tmp = t_2
    else if (t <= (-1.5d+32)) then
        tmp = t / (z / x)
    else if (t <= 2d-255) then
        tmp = x / (z / y)
    else if (t <= 3.3d-10) then
        tmp = t_2
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = x * (t / z);
	double t_2 = (y * x) / z;
	double tmp;
	if (t <= -3e+187) {
		tmp = t_1;
	} else if (t <= -3.6e+65) {
		tmp = t_2;
	} else if (t <= -1.5e+32) {
		tmp = t / (z / x);
	} else if (t <= 2e-255) {
		tmp = x / (z / y);
	} else if (t <= 3.3e-10) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x * (t / z)
	t_2 = (y * x) / z
	tmp = 0
	if t <= -3e+187:
		tmp = t_1
	elif t <= -3.6e+65:
		tmp = t_2
	elif t <= -1.5e+32:
		tmp = t / (z / x)
	elif t <= 2e-255:
		tmp = x / (z / y)
	elif t <= 3.3e-10:
		tmp = t_2
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x * Float64(t / z))
	t_2 = Float64(Float64(y * x) / z)
	tmp = 0.0
	if (t <= -3e+187)
		tmp = t_1;
	elseif (t <= -3.6e+65)
		tmp = t_2;
	elseif (t <= -1.5e+32)
		tmp = Float64(t / Float64(z / x));
	elseif (t <= 2e-255)
		tmp = Float64(x / Float64(z / y));
	elseif (t <= 3.3e-10)
		tmp = t_2;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x * (t / z);
	t_2 = (y * x) / z;
	tmp = 0.0;
	if (t <= -3e+187)
		tmp = t_1;
	elseif (t <= -3.6e+65)
		tmp = t_2;
	elseif (t <= -1.5e+32)
		tmp = t / (z / x);
	elseif (t <= 2e-255)
		tmp = x / (z / y);
	elseif (t <= 3.3e-10)
		tmp = t_2;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x * N[(t / z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(y * x), $MachinePrecision] / z), $MachinePrecision]}, If[LessEqual[t, -3e+187], t$95$1, If[LessEqual[t, -3.6e+65], t$95$2, If[LessEqual[t, -1.5e+32], N[(t / N[(z / x), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 2e-255], N[(x / N[(z / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 3.3e-10], t$95$2, t$95$1]]]]]]]

Derivation

1. Split input into 4 regimes

2. if t < -2.9999999999999999e187 or 3.3e-10 < t

   1. Initial program 98.5%

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

   3. Taylor expanded in y around 0 62.2%

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

      1. mul-1-neg 62.2%

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

      2. *-commutative 62.2%

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

      3. associate-/l* 70.5%

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

      4. distribute-rgt-neg-out 70.5%

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

      5. distribute-neg-frac2 70.5%

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

      6. neg-sub0 70.5%

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

      7. associate--r- 70.5%

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

      8. metadata-eval 70.5%

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

   5. Simplified 70.5%

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

   6. Taylor expanded in z around inf 64.9%

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

   if -2.9999999999999999e187 < t < -3.59999999999999978e65 or 2e-255 < t < 3.3e-10

   1. Initial program 91.9%

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

   3. Taylor expanded in y around inf 78.6%

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

   if -3.59999999999999978e65 < t < -1.5e32

   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 70.3%

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

      1. mul-1-neg 70.3%

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

      2. *-commutative 70.3%

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

      3. associate-/l* 70.6%

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

      4. distribute-rgt-neg-out 70.6%

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

      5. distribute-neg-frac2 70.6%

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

      6. neg-sub0 70.6%

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

      7. associate--r- 70.6%

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

      8. metadata-eval 70.6%

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

   5. Simplified 70.6%

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

   6. Taylor expanded in z around inf 55.5%

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

      1. associate-/l* 55.7%

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

   8. Simplified 55.7%

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

      1. clear-num 55.5%

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

      2. un-div-inv 55.8%

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

   10. Applied egg-rr 55.8%

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

   if -1.5e32 < t < 2e-255

   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 inf 81.0%

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

      1. associate-*r/ 83.9%

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

   5. Simplified 83.9%

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

      1. clear-num 83.8%

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

      2. un-div-inv 84.5%

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

   7. Applied egg-rr 84.5%

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

4. Final simplification 74.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -3 \cdot 10^{+187}:\\ \;\;\;\;x \cdot \frac{t}{z}\\ \mathbf{elif}\;t \leq -3.6 \cdot 10^{+65}:\\ \;\;\;\;\frac{y \cdot x}{z}\\ \mathbf{elif}\;t \leq -1.5 \cdot 10^{+32}:\\ \;\;\;\;\frac{t}{\frac{z}{x}}\\ \mathbf{elif}\;t \leq 2 \cdot 10^{-255}:\\ \;\;\;\;\frac{x}{\frac{z}{y}}\\ \mathbf{elif}\;t \leq 3.3 \cdot 10^{-10}:\\ \;\;\;\;\frac{y \cdot x}{z}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{t}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 93.0% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(\frac{y}{z} - t\right)\\ t_2 := x \cdot \frac{y + t}{z}\\ \mathbf{if}\;z \leq -1:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;z \leq -1.1 \cdot 10^{-269}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 1.6 \cdot 10^{-270}:\\ \;\;\;\;y \cdot \frac{x}{z}\\ \mathbf{elif}\;z \leq 1:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* x (- (/ y z) t))) (t_2 (* x (/ (+ y t) z))))
   (if (<= z -1.0)
     t_2
     (if (<= z -1.1e-269)
       t_1
       (if (<= z 1.6e-270) (* y (/ x z)) (if (<= z 1.0) t_1 t_2))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x * ((y / z) - t);
	double t_2 = x * ((y + t) / z);
	double tmp;
	if (z <= -1.0) {
		tmp = t_2;
	} else if (z <= -1.1e-269) {
		tmp = t_1;
	} else if (z <= 1.6e-270) {
		tmp = y * (x / z);
	} else if (z <= 1.0) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = x * ((y / z) - t)
    t_2 = x * ((y + t) / z)
    if (z <= (-1.0d0)) then
        tmp = t_2
    else if (z <= (-1.1d-269)) then
        tmp = t_1
    else if (z <= 1.6d-270) then
        tmp = y * (x / z)
    else if (z <= 1.0d0) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = x * ((y / z) - t);
	double t_2 = x * ((y + t) / z);
	double tmp;
	if (z <= -1.0) {
		tmp = t_2;
	} else if (z <= -1.1e-269) {
		tmp = t_1;
	} else if (z <= 1.6e-270) {
		tmp = y * (x / z);
	} else if (z <= 1.0) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x * ((y / z) - t)
	t_2 = x * ((y + t) / z)
	tmp = 0
	if z <= -1.0:
		tmp = t_2
	elif z <= -1.1e-269:
		tmp = t_1
	elif z <= 1.6e-270:
		tmp = y * (x / z)
	elif z <= 1.0:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x * Float64(Float64(y / z) - t))
	t_2 = Float64(x * Float64(Float64(y + t) / z))
	tmp = 0.0
	if (z <= -1.0)
		tmp = t_2;
	elseif (z <= -1.1e-269)
		tmp = t_1;
	elseif (z <= 1.6e-270)
		tmp = Float64(y * Float64(x / z));
	elseif (z <= 1.0)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x * ((y / z) - t);
	t_2 = x * ((y + t) / z);
	tmp = 0.0;
	if (z <= -1.0)
		tmp = t_2;
	elseif (z <= -1.1e-269)
		tmp = t_1;
	elseif (z <= 1.6e-270)
		tmp = y * (x / z);
	elseif (z <= 1.0)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x * N[(N[(y / z), $MachinePrecision] - t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x * N[(N[(y + t), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.0], t$95$2, If[LessEqual[z, -1.1e-269], t$95$1, If[LessEqual[z, 1.6e-270], N[(y * N[(x / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.0], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -1 or 1 < z

   1. Initial program 96.3%

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

   3. Taylor expanded in z around inf 89.2%

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

      1. *-commutative 89.2%

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

      2. remove-double-neg 89.2%

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

      3. cancel-sign-sub-inv 89.2%

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

      4. metadata-eval 89.2%

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

      5. *-lft-identity 89.2%

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

      6. distribute-neg-out 89.2%

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

      7. neg-mul-1 89.2%

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

      8. sub-neg 89.2%

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

      9. mul-1-neg 89.2%

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

      10. associate-*r* 89.2%

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

      11. *-commutative 89.2%

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

      12. associate-*r/ 89.2%

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

      13. mul-1-neg 89.2%

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

      14. associate-/l* 95.0%

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

      15. distribute-rgt-neg-in 95.0%

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

      16. distribute-neg-frac 95.0%

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

   5. Simplified 95.0%

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

   if -1 < z < -1.09999999999999992e-269 or 1.59999999999999994e-270 < z < 1

   1. Initial program 98.0%

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

   3. Taylor expanded in z around 0 92.0%

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

      1. +-commutative 92.0%

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

      2. associate-*r/ 91.5%

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

      3. *-commutative 91.5%

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

      4. associate-*r* 91.5%

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

      5. neg-mul-1 91.5%

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

      6. distribute-rgt-out 96.2%

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

      7. unsub-neg 96.2%

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

   5. Simplified 96.2%

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

   if -1.09999999999999992e-269 < z < 1.59999999999999994e-270

   1. Initial program 63.2%

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

   3. Taylor expanded in y around inf 94.5%

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

      1. *-commutative 94.5%

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

      2. associate-/l* 99.7%

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

   5. Simplified 99.7%

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

4. Final simplification 95.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1:\\ \;\;\;\;x \cdot \frac{y + t}{z}\\ \mathbf{elif}\;z \leq -1.1 \cdot 10^{-269}:\\ \;\;\;\;x \cdot \left(\frac{y}{z} - t\right)\\ \mathbf{elif}\;z \leq 1.6 \cdot 10^{-270}:\\ \;\;\;\;y \cdot \frac{x}{z}\\ \mathbf{elif}\;z \leq 1:\\ \;\;\;\;x \cdot \left(\frac{y}{z} - t\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{y + t}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 66.8% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \frac{t}{z}\\ \mathbf{if}\;t \leq -4 \cdot 10^{+187}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq -3.95 \cdot 10^{+65}:\\ \;\;\;\;y \cdot \frac{x}{z}\\ \mathbf{elif}\;t \leq -1.5 \cdot 10^{+32} \lor \neg \left(t \leq 15000000000000\right):\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{z} \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* x (/ t z))))
   (if (<= t -4e+187)
     t_1
     (if (<= t -3.95e+65)
       (* y (/ x z))
       (if (or (<= t -1.5e+32) (not (<= t 15000000000000.0)))
         t_1
         (* (/ y z) x))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x * (t / z);
	double tmp;
	if (t <= -4e+187) {
		tmp = t_1;
	} else if (t <= -3.95e+65) {
		tmp = y * (x / z);
	} else if ((t <= -1.5e+32) || !(t <= 15000000000000.0)) {
		tmp = t_1;
	} 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) :: t_1
    real(8) :: tmp
    t_1 = x * (t / z)
    if (t <= (-4d+187)) then
        tmp = t_1
    else if (t <= (-3.95d+65)) then
        tmp = y * (x / z)
    else if ((t <= (-1.5d+32)) .or. (.not. (t <= 15000000000000.0d0))) then
        tmp = t_1
    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 t_1 = x * (t / z);
	double tmp;
	if (t <= -4e+187) {
		tmp = t_1;
	} else if (t <= -3.95e+65) {
		tmp = y * (x / z);
	} else if ((t <= -1.5e+32) || !(t <= 15000000000000.0)) {
		tmp = t_1;
	} else {
		tmp = (y / z) * x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x * (t / z)
	tmp = 0
	if t <= -4e+187:
		tmp = t_1
	elif t <= -3.95e+65:
		tmp = y * (x / z)
	elif (t <= -1.5e+32) or not (t <= 15000000000000.0):
		tmp = t_1
	else:
		tmp = (y / z) * x
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x * Float64(t / z))
	tmp = 0.0
	if (t <= -4e+187)
		tmp = t_1;
	elseif (t <= -3.95e+65)
		tmp = Float64(y * Float64(x / z));
	elseif ((t <= -1.5e+32) || !(t <= 15000000000000.0))
		tmp = t_1;
	else
		tmp = Float64(Float64(y / z) * x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x * (t / z);
	tmp = 0.0;
	if (t <= -4e+187)
		tmp = t_1;
	elseif (t <= -3.95e+65)
		tmp = y * (x / z);
	elseif ((t <= -1.5e+32) || ~((t <= 15000000000000.0)))
		tmp = t_1;
	else
		tmp = (y / z) * x;
	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, -4e+187], t$95$1, If[LessEqual[t, -3.95e+65], N[(y * N[(x / z), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[t, -1.5e+32], N[Not[LessEqual[t, 15000000000000.0]], $MachinePrecision]], t$95$1, N[(N[(y / z), $MachinePrecision] * x), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if t < -3.99999999999999963e187 or -3.9499999999999999e65 < t < -1.5e32 or 1.5e13 < t

   1. Initial program 97.7%

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

   3. Taylor expanded in y around 0 63.4%

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

      1. mul-1-neg 63.4%

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

      2. *-commutative 63.4%

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

      3. associate-/l* 71.0%

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

      4. distribute-rgt-neg-out 71.0%

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

      5. distribute-neg-frac2 71.0%

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

      6. neg-sub0 71.0%

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

      7. associate--r- 71.0%

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

      8. metadata-eval 71.0%

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

   5. Simplified 71.0%

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

   6. Taylor expanded in z around inf 64.8%

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

   if -3.99999999999999963e187 < t < -3.9499999999999999e65

   1. Initial program 92.3%

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

   3. Taylor expanded in y around inf 53.5%

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

      1. *-commutative 53.5%

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

      2. associate-/l* 53.4%

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

   5. Simplified 53.4%

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

   if -1.5e32 < t < 1.5e13

   1. Initial program 93.3%

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

   3. Taylor expanded in y around inf 82.4%

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

      1. associate-*r/ 82.6%

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

   5. Simplified 82.6%

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

4. Final simplification 73.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -4 \cdot 10^{+187}:\\ \;\;\;\;x \cdot \frac{t}{z}\\ \mathbf{elif}\;t \leq -3.95 \cdot 10^{+65}:\\ \;\;\;\;y \cdot \frac{x}{z}\\ \mathbf{elif}\;t \leq -1.5 \cdot 10^{+32} \lor \neg \left(t \leq 15000000000000\right):\\ \;\;\;\;x \cdot \frac{t}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{z} \cdot x\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 66.8% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \frac{t}{z}\\ \mathbf{if}\;t \leq -4.5 \cdot 10^{+187}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq -3 \cdot 10^{+65}:\\ \;\;\;\;y \cdot \frac{x}{z}\\ \mathbf{elif}\;t \leq -1.35 \cdot 10^{+32}:\\ \;\;\;\;\frac{t}{\frac{z}{x}}\\ \mathbf{elif}\;t \leq 1.02 \cdot 10^{+14}:\\ \;\;\;\;\frac{y}{z} \cdot x\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* x (/ t z))))
   (if (<= t -4.5e+187)
     t_1
     (if (<= t -3e+65)
       (* y (/ x z))
       (if (<= t -1.35e+32)
         (/ t (/ z x))
         (if (<= t 1.02e+14) (* (/ y z) x) t_1))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x * (t / z);
	double tmp;
	if (t <= -4.5e+187) {
		tmp = t_1;
	} else if (t <= -3e+65) {
		tmp = y * (x / z);
	} else if (t <= -1.35e+32) {
		tmp = t / (z / x);
	} else if (t <= 1.02e+14) {
		tmp = (y / z) * x;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x * (t / z)
    if (t <= (-4.5d+187)) then
        tmp = t_1
    else if (t <= (-3d+65)) then
        tmp = y * (x / z)
    else if (t <= (-1.35d+32)) then
        tmp = t / (z / x)
    else if (t <= 1.02d+14) then
        tmp = (y / z) * x
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = x * (t / z);
	double tmp;
	if (t <= -4.5e+187) {
		tmp = t_1;
	} else if (t <= -3e+65) {
		tmp = y * (x / z);
	} else if (t <= -1.35e+32) {
		tmp = t / (z / x);
	} else if (t <= 1.02e+14) {
		tmp = (y / z) * x;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x * (t / z)
	tmp = 0
	if t <= -4.5e+187:
		tmp = t_1
	elif t <= -3e+65:
		tmp = y * (x / z)
	elif t <= -1.35e+32:
		tmp = t / (z / x)
	elif t <= 1.02e+14:
		tmp = (y / z) * x
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x * Float64(t / z))
	tmp = 0.0
	if (t <= -4.5e+187)
		tmp = t_1;
	elseif (t <= -3e+65)
		tmp = Float64(y * Float64(x / z));
	elseif (t <= -1.35e+32)
		tmp = Float64(t / Float64(z / x));
	elseif (t <= 1.02e+14)
		tmp = Float64(Float64(y / z) * x);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x * (t / z);
	tmp = 0.0;
	if (t <= -4.5e+187)
		tmp = t_1;
	elseif (t <= -3e+65)
		tmp = y * (x / z);
	elseif (t <= -1.35e+32)
		tmp = t / (z / x);
	elseif (t <= 1.02e+14)
		tmp = (y / z) * x;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x * N[(t / z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -4.5e+187], t$95$1, If[LessEqual[t, -3e+65], N[(y * N[(x / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -1.35e+32], N[(t / N[(z / x), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.02e+14], N[(N[(y / z), $MachinePrecision] * x), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if t < -4.50000000000000026e187 or 1.02e14 < t

   1. Initial program 98.5%

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

   3. Taylor expanded in y around 0 62.2%

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

      1. mul-1-neg 62.2%

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

      2. *-commutative 62.2%

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

      3. associate-/l* 71.1%

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

      4. distribute-rgt-neg-out 71.1%

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

      5. distribute-neg-frac2 71.1%

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

      6. neg-sub0 71.1%

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

      7. associate--r- 71.1%

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

      8. metadata-eval 71.1%

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

   5. Simplified 71.1%

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

   6. Taylor expanded in z around inf 66.4%

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

   if -4.50000000000000026e187 < t < -3.0000000000000002e65

   1. Initial program 92.3%

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

   3. Taylor expanded in y around inf 53.5%

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

      1. *-commutative 53.5%

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

      2. associate-/l* 53.4%

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

   5. Simplified 53.4%

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

   if -3.0000000000000002e65 < t < -1.35000000000000006e32

   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 70.3%

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

      1. mul-1-neg 70.3%

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

      2. *-commutative 70.3%

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

      3. associate-/l* 70.6%

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

      4. distribute-rgt-neg-out 70.6%

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

      5. distribute-neg-frac2 70.6%

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

      6. neg-sub0 70.6%

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

      7. associate--r- 70.6%

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

      8. metadata-eval 70.6%

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

   5. Simplified 70.6%

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

   6. Taylor expanded in z around inf 55.5%

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

      1. associate-/l* 55.7%

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

   8. Simplified 55.7%

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

      1. clear-num 55.5%

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

      2. un-div-inv 55.8%

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

   10. Applied egg-rr 55.8%

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

   if -1.35000000000000006e32 < t < 1.02e14

   1. Initial program 93.3%

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

   3. Taylor expanded in y around inf 82.4%

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

      1. associate-*r/ 82.6%

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

   5. Simplified 82.6%

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

4. Final simplification 73.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -4.5 \cdot 10^{+187}:\\ \;\;\;\;x \cdot \frac{t}{z}\\ \mathbf{elif}\;t \leq -3 \cdot 10^{+65}:\\ \;\;\;\;y \cdot \frac{x}{z}\\ \mathbf{elif}\;t \leq -1.35 \cdot 10^{+32}:\\ \;\;\;\;\frac{t}{\frac{z}{x}}\\ \mathbf{elif}\;t \leq 1.02 \cdot 10^{+14}:\\ \;\;\;\;\frac{y}{z} \cdot x\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{t}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 66.8% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \frac{t}{z}\\ \mathbf{if}\;t \leq -3 \cdot 10^{+187}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq -6.1 \cdot 10^{+65}:\\ \;\;\;\;y \cdot \frac{x}{z}\\ \mathbf{elif}\;t \leq -1.5 \cdot 10^{+32}:\\ \;\;\;\;\frac{t}{\frac{z}{x}}\\ \mathbf{elif}\;t \leq 1.02 \cdot 10^{+14}:\\ \;\;\;\;\frac{x}{\frac{z}{y}}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* x (/ t z))))
   (if (<= t -3e+187)
     t_1
     (if (<= t -6.1e+65)
       (* y (/ x z))
       (if (<= t -1.5e+32)
         (/ t (/ z x))
         (if (<= t 1.02e+14) (/ x (/ z y)) t_1))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x * (t / z);
	double tmp;
	if (t <= -3e+187) {
		tmp = t_1;
	} else if (t <= -6.1e+65) {
		tmp = y * (x / z);
	} else if (t <= -1.5e+32) {
		tmp = t / (z / x);
	} else if (t <= 1.02e+14) {
		tmp = x / (z / y);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x * (t / z)
    if (t <= (-3d+187)) then
        tmp = t_1
    else if (t <= (-6.1d+65)) then
        tmp = y * (x / z)
    else if (t <= (-1.5d+32)) then
        tmp = t / (z / x)
    else if (t <= 1.02d+14) then
        tmp = x / (z / y)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = x * (t / z);
	double tmp;
	if (t <= -3e+187) {
		tmp = t_1;
	} else if (t <= -6.1e+65) {
		tmp = y * (x / z);
	} else if (t <= -1.5e+32) {
		tmp = t / (z / x);
	} else if (t <= 1.02e+14) {
		tmp = x / (z / y);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x * (t / z)
	tmp = 0
	if t <= -3e+187:
		tmp = t_1
	elif t <= -6.1e+65:
		tmp = y * (x / z)
	elif t <= -1.5e+32:
		tmp = t / (z / x)
	elif t <= 1.02e+14:
		tmp = x / (z / y)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x * Float64(t / z))
	tmp = 0.0
	if (t <= -3e+187)
		tmp = t_1;
	elseif (t <= -6.1e+65)
		tmp = Float64(y * Float64(x / z));
	elseif (t <= -1.5e+32)
		tmp = Float64(t / Float64(z / x));
	elseif (t <= 1.02e+14)
		tmp = Float64(x / Float64(z / y));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x * (t / z);
	tmp = 0.0;
	if (t <= -3e+187)
		tmp = t_1;
	elseif (t <= -6.1e+65)
		tmp = y * (x / z);
	elseif (t <= -1.5e+32)
		tmp = t / (z / x);
	elseif (t <= 1.02e+14)
		tmp = x / (z / y);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x * N[(t / z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -3e+187], t$95$1, If[LessEqual[t, -6.1e+65], N[(y * N[(x / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -1.5e+32], N[(t / N[(z / x), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.02e+14], N[(x / N[(z / y), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if t < -2.9999999999999999e187 or 1.02e14 < t

   1. Initial program 98.5%

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

   3. Taylor expanded in y around 0 62.2%

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

      1. mul-1-neg 62.2%

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

      2. *-commutative 62.2%

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

      3. associate-/l* 71.1%

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

      4. distribute-rgt-neg-out 71.1%

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

      5. distribute-neg-frac2 71.1%

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

      6. neg-sub0 71.1%

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

      7. associate--r- 71.1%

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

      8. metadata-eval 71.1%

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

   5. Simplified 71.1%

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

   6. Taylor expanded in z around inf 66.4%

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

   if -2.9999999999999999e187 < t < -6.09999999999999965e65

   1. Initial program 92.3%

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

   3. Taylor expanded in y around inf 53.5%

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

      1. *-commutative 53.5%

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

      2. associate-/l* 53.4%

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

   5. Simplified 53.4%

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

   if -6.09999999999999965e65 < t < -1.5e32

   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 70.3%

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

      1. mul-1-neg 70.3%

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

      2. *-commutative 70.3%

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

      3. associate-/l* 70.6%

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

      4. distribute-rgt-neg-out 70.6%

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

      5. distribute-neg-frac2 70.6%

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

      6. neg-sub0 70.6%

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

      7. associate--r- 70.6%

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

      8. metadata-eval 70.6%

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

   5. Simplified 70.6%

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

   6. Taylor expanded in z around inf 55.5%

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

      1. associate-/l* 55.7%

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

   8. Simplified 55.7%

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

      1. clear-num 55.5%

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

      2. un-div-inv 55.8%

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

   10. Applied egg-rr 55.8%

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

   if -1.5e32 < t < 1.02e14

   1. Initial program 93.3%

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

   3. Taylor expanded in y around inf 82.4%

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

      1. associate-*r/ 82.6%

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

   5. Simplified 82.6%

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

      1. clear-num 82.5%

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

      2. un-div-inv 83.2%

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

   7. Applied egg-rr 83.2%

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

4. Final simplification 73.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -3 \cdot 10^{+187}:\\ \;\;\;\;x \cdot \frac{t}{z}\\ \mathbf{elif}\;t \leq -6.1 \cdot 10^{+65}:\\ \;\;\;\;y \cdot \frac{x}{z}\\ \mathbf{elif}\;t \leq -1.5 \cdot 10^{+32}:\\ \;\;\;\;\frac{t}{\frac{z}{x}}\\ \mathbf{elif}\;t \leq 1.02 \cdot 10^{+14}:\\ \;\;\;\;\frac{x}{\frac{z}{y}}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{t}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 75.9% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -8 \cdot 10^{+31} \lor \neg \left(t \leq 4.4 \cdot 10^{-11}\right):\\ \;\;\;\;x \cdot \frac{t}{z + -1}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\frac{z}{y}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= t -8e+31) (not (<= t 4.4e-11)))
   (* x (/ t (+ z -1.0)))
   (/ x (/ z y))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((t <= -8e+31) || !(t <= 4.4e-11)) {
		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 <= (-8d+31)) .or. (.not. (t <= 4.4d-11))) 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 <= -8e+31) || !(t <= 4.4e-11)) {
		tmp = x * (t / (z + -1.0));
	} else {
		tmp = x / (z / y);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (t <= -8e+31) or not (t <= 4.4e-11):
		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 <= -8e+31) || !(t <= 4.4e-11))
		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 <= -8e+31) || ~((t <= 4.4e-11)))
		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, -8e+31], N[Not[LessEqual[t, 4.4e-11]], $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 < -7.9999999999999997e31 or 4.4000000000000003e-11 < t

   1. Initial program 96.6%

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

   3. Taylor expanded in y around 0 59.7%

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

      1. mul-1-neg 59.7%

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

      2. *-commutative 59.7%

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

      3. associate-/l* 66.3%

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

      4. distribute-rgt-neg-out 66.3%

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

      5. distribute-neg-frac2 66.3%

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

      6. neg-sub0 66.3%

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

      7. associate--r- 66.3%

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

      8. metadata-eval 66.3%

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

   5. Simplified 66.3%

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

   if -7.9999999999999997e31 < t < 4.4000000000000003e-11

   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 inf 84.5%

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

      1. associate-*r/ 84.1%

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

   5. Simplified 84.1%

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

      1. clear-num 83.9%

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

      2. un-div-inv 84.7%

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

   7. Applied egg-rr 84.7%

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

4. Final simplification 76.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -8 \cdot 10^{+31} \lor \neg \left(t \leq 4.4 \cdot 10^{-11}\right):\\ \;\;\;\;x \cdot \frac{t}{z + -1}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\frac{z}{y}}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 67.1% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.25 \cdot 10^{+181} \lor \neg \left(t \leq 1.02 \cdot 10^{+14}\right):\\ \;\;\;\;x \cdot \frac{t}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{z} \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= t -1.25e+181) (not (<= t 1.02e+14))) (* x (/ t z)) (* (/ y z) x)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((t <= -1.25e+181) || !(t <= 1.02e+14)) {
		tmp = x * (t / 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 <= (-1.25d+181)) .or. (.not. (t <= 1.02d+14))) then
        tmp = x * (t / 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 <= -1.25e+181) || !(t <= 1.02e+14)) {
		tmp = x * (t / z);
	} else {
		tmp = (y / z) * x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (t <= -1.25e+181) or not (t <= 1.02e+14):
		tmp = x * (t / z)
	else:
		tmp = (y / z) * x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((t <= -1.25e+181) || !(t <= 1.02e+14))
		tmp = Float64(x * Float64(t / 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 <= -1.25e+181) || ~((t <= 1.02e+14)))
		tmp = x * (t / z);
	else
		tmp = (y / z) * x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[t, -1.25e+181], N[Not[LessEqual[t, 1.02e+14]], $MachinePrecision]], N[(x * N[(t / z), $MachinePrecision]), $MachinePrecision], N[(N[(y / z), $MachinePrecision] * x), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -1.2500000000000001e181 or 1.02e14 < t

   1. Initial program 97.3%

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

   3. Taylor expanded in y around 0 61.9%

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

      1. mul-1-neg 61.9%

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

      2. *-commutative 61.9%

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

      3. associate-/l* 70.6%

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

      4. distribute-rgt-neg-out 70.6%

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

      5. distribute-neg-frac2 70.6%

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

      6. neg-sub0 70.6%

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

      7. associate--r- 70.6%

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

      8. metadata-eval 70.6%

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

   5. Simplified 70.6%

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

   6. Taylor expanded in z around inf 65.9%

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

   if -1.2500000000000001e181 < t < 1.02e14

   1. Initial program 93.6%

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

   3. Taylor expanded in y around inf 75.0%

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

      1. associate-*r/ 74.2%

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

   5. Simplified 74.2%

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

4. Final simplification 71.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.25 \cdot 10^{+181} \lor \neg \left(t \leq 1.02 \cdot 10^{+14}\right):\\ \;\;\;\;x \cdot \frac{t}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{z} \cdot x\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 36.3% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq 0.00035:\\ \;\;\;\;x \cdot \frac{t}{z}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{x}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= x 0.00035) (* x (/ t z)) (* t (/ x z))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= 0.00035) {
		tmp = x * (t / 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 (x <= 0.00035d0) then
        tmp = x * (t / 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 (x <= 0.00035) {
		tmp = x * (t / z);
	} else {
		tmp = t * (x / z);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if x <= 0.00035:
		tmp = x * (t / z)
	else:
		tmp = t * (x / z)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (x <= 0.00035)
		tmp = Float64(x * Float64(t / 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 (x <= 0.00035)
		tmp = x * (t / z);
	else
		tmp = t * (x / z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[x, 0.00035], N[(x * N[(t / z), $MachinePrecision]), $MachinePrecision], N[(t * N[(x / z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < 3.49999999999999996e-4

   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 40.5%

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

      1. mul-1-neg 40.5%

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

      2. *-commutative 40.5%

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

      3. associate-/l* 41.7%

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

      4. distribute-rgt-neg-out 41.7%

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

      5. distribute-neg-frac2 41.7%

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

      6. neg-sub0 41.7%

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

      7. associate--r- 41.7%

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

      8. metadata-eval 41.7%

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

   5. Simplified 41.7%

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

   6. Taylor expanded in z around inf 38.4%

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

   if 3.49999999999999996e-4 < x

   1. Initial program 93.8%

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

   3. Taylor expanded in y around 0 48.7%

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

      1. mul-1-neg 48.7%

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

      2. *-commutative 48.7%

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

      3. associate-/l* 50.2%

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

      4. distribute-rgt-neg-out 50.2%

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

      5. distribute-neg-frac2 50.2%

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

      6. neg-sub0 50.2%

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

      7. associate--r- 50.2%

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

      8. metadata-eval 50.2%

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

   5. Simplified 50.2%

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

   6. Taylor expanded in z around inf 38.1%

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

      1. associate-/l* 48.6%

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

   8. Simplified 48.6%

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

4. Final simplification 40.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq 0.00035:\\ \;\;\;\;x \cdot \frac{t}{z}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{x}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 34.2% accurate, 2.2× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 94.7%

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

3. Taylor expanded in y around 0 42.5%

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

   1. mul-1-neg 42.5%

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

   2. *-commutative 42.5%

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

   3. associate-/l* 43.8%

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

   4. distribute-rgt-neg-out 43.8%

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

   5. distribute-neg-frac2 43.8%

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

   6. neg-sub0 43.8%

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

   7. associate--r- 43.8%

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

   8. metadata-eval 43.8%

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

5. Simplified 43.8%

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

6. Taylor expanded in z around inf 37.4%

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

   1. associate-/l* 40.2%

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

8. Simplified 40.2%

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

9. Final simplification 40.2%

   \[\leadsto t \cdot \frac{x}{z} \]
10. Add Preprocessing

Alternative 12: 23.4% accurate, 2.8× speedup

Math

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

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 * Float64(-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 94.7%

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

3. Taylor expanded in y around 0 42.5%

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

   1. mul-1-neg 42.5%

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

   2. *-commutative 42.5%

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

   3. associate-/l* 43.8%

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

   4. distribute-rgt-neg-out 43.8%

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

   5. distribute-neg-frac2 43.8%

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

   6. neg-sub0 43.8%

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

   7. associate--r- 43.8%

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

   8. metadata-eval 43.8%

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

5. Simplified 43.8%

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

6. Taylor expanded in z around 0 19.7%

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

   1. associate-*r* 19.7%

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

   2. neg-mul-1 19.7%

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

8. Simplified 19.7%

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

9. Final simplification 19.7%

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

Developer target: 95.0% 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 2024053 
(FPCore (x y z t)
  :name "Numeric.SpecFunctions:invIncompleteBetaWorker from math-functions-0.1.5.2, C"
  :precision binary64

  :alt
  (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)))))