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

Percentage Accurate: 94.4% → 96.3%

Time: 8.1s

Alternatives: 10

Speedup: 0.5×

• 21.1% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

(FPCore (x y z t) :precision binary64 (* x (- (/ y z) (/ t (- 1.0 z)))))

C

double code(double x, double y, double z, double t) {
	return x * ((y / z) - (t / (1.0 - z)));
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    code = x * ((y / z) - (t / (1.0d0 - z)))
end function

Java

public static double code(double x, double y, double z, double t) {
	return x * ((y / z) - (t / (1.0 - z)));
}

Python

def code(x, y, z, t):
	return x * ((y / z) - (t / (1.0 - z)))

Julia

function code(x, y, z, t)
	return Float64(x * Float64(Float64(y / z) - Float64(t / Float64(1.0 - z))))
end

MATLAB

function tmp = code(x, y, z, t)
	tmp = x * ((y / z) - (t / (1.0 - z)));
end

Wolfram

code[x_, y_, z_, t_] := N[(x * N[(N[(y / z), $MachinePrecision] - N[(t / N[(1.0 - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Initial Program: 94.4% 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

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{y}{z} + \frac{t}{z + -1}\\ \mathbf{if}\;t\_1 \leq 2 \cdot 10^{+301}:\\ \;\;\;\;t\_1 \cdot x\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{x}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (+ (/ y z) (/ t (+ z -1.0)))))
   (if (<= t_1 2e+301) (* t_1 x) (* y (/ x z)))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (y / z) + (t / (z + -1.0));
	double tmp;
	if (t_1 <= 2e+301) {
		tmp = t_1 * x;
	} 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 = (y / z) + (t / (z + (-1.0d0)))
    if (t_1 <= 2d+301) then
        tmp = t_1 * x
    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 = (y / z) + (t / (z + -1.0));
	double tmp;
	if (t_1 <= 2e+301) {
		tmp = t_1 * x;
	} else {
		tmp = y * (x / z);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (y / z) + (t / (z + -1.0))
	tmp = 0
	if t_1 <= 2e+301:
		tmp = t_1 * x
	else:
		tmp = y * (x / z)
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(y / z) + Float64(t / Float64(z + -1.0)))
	tmp = 0.0
	if (t_1 <= 2e+301)
		tmp = Float64(t_1 * x);
	else
		tmp = Float64(y * Float64(x / z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (y / z) + (t / (z + -1.0));
	tmp = 0.0;
	if (t_1 <= 2e+301)
		tmp = t_1 * x;
	else
		tmp = y * (x / z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(y / z), $MachinePrecision] + N[(t / N[(z + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, 2e+301], N[(t$95$1 * x), $MachinePrecision], N[(y * N[(x / z), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (-.f64 (/.f64 y z) (/.f64 t (-.f64 #s(literal 1 binary64) z))) < 2.00000000000000011e301

   1. Initial program 97.1%

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

   if 2.00000000000000011e301 < (-.f64 (/.f64 y z) (/.f64 t (-.f64 #s(literal 1 binary64) z)))

   1. Initial program 62.5%

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

      1. clear-num 62.5%

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

      2. frac-sub 62.5%

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

      3. *-un-lft-identity 62.5%

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

   4. Applied egg-rr 62.5%

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

      1. div-sub 0.7%

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

      2. remove-double-neg 0.7%

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

      3. distribute-neg-frac 0.7%

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

      4. distribute-frac-neg2 0.7%

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

      5. distribute-rgt-neg-out 0.7%

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

      6. times-frac 0.7%

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

      7. *-inverses 62.5%

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

      8. cancel-sign-sub-inv 62.5%

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

      9. *-commutative 62.5%

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

      10. associate-/r* 62.5%

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

      11. *-inverses 62.5%

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

      12. metadata-eval 62.5%

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

      13. mul-1-neg 62.5%

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

      14. distribute-neg-frac2 62.5%

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

   6. Simplified 62.5%

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

   7. Taylor expanded in z around inf 99.9%

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

      1. +-commutative 99.9%

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

      2. associate-*l/ 99.9%

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

      3. +-commutative 99.9%

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

   9. Simplified 99.9%

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

   10. Taylor expanded in t around 0 99.9%

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

       1. associate-*l/ 99.9%

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

       2. *-commutative 99.9%

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

   12. Simplified 99.9%

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

4. Final simplification 97.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{y}{z} + \frac{t}{z + -1} \leq 2 \cdot 10^{+301}:\\ \;\;\;\;\left(\frac{y}{z} + \frac{t}{z + -1}\right) \cdot x\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{x}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 74.9% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{y}{z} \cdot x\\ \mathbf{if}\;z \leq -2.75 \cdot 10^{+78}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 4.6 \cdot 10^{+58}:\\ \;\;\;\;x \cdot \left(\frac{y}{z} - t\right)\\ \mathbf{elif}\;z \leq 3 \cdot 10^{+111}:\\ \;\;\;\;t \cdot \frac{x}{z}\\ \mathbf{elif}\;z \leq 9.6 \cdot 10^{+178}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 1.15 \cdot 10^{+206}:\\ \;\;\;\;x \cdot \frac{t}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\frac{z}{y}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* (/ y z) x)))
   (if (<= z -2.75e+78)
     t_1
     (if (<= z 4.6e+58)
       (* x (- (/ y z) t))
       (if (<= z 3e+111)
         (* t (/ x z))
         (if (<= z 9.6e+178)
           t_1
           (if (<= z 1.15e+206) (* x (/ t z)) (/ x (/ z y)))))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (y / z) * x;
	double tmp;
	if (z <= -2.75e+78) {
		tmp = t_1;
	} else if (z <= 4.6e+58) {
		tmp = x * ((y / z) - t);
	} else if (z <= 3e+111) {
		tmp = t * (x / z);
	} else if (z <= 9.6e+178) {
		tmp = t_1;
	} else if (z <= 1.15e+206) {
		tmp = x * (t / z);
	} else {
		tmp = x / (z / y);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (y / z) * x
    if (z <= (-2.75d+78)) then
        tmp = t_1
    else if (z <= 4.6d+58) then
        tmp = x * ((y / z) - t)
    else if (z <= 3d+111) then
        tmp = t * (x / z)
    else if (z <= 9.6d+178) then
        tmp = t_1
    else if (z <= 1.15d+206) then
        tmp = x * (t / z)
    else
        tmp = x / (z / y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = (y / z) * x;
	double tmp;
	if (z <= -2.75e+78) {
		tmp = t_1;
	} else if (z <= 4.6e+58) {
		tmp = x * ((y / z) - t);
	} else if (z <= 3e+111) {
		tmp = t * (x / z);
	} else if (z <= 9.6e+178) {
		tmp = t_1;
	} else if (z <= 1.15e+206) {
		tmp = x * (t / z);
	} else {
		tmp = x / (z / y);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (y / z) * x
	tmp = 0
	if z <= -2.75e+78:
		tmp = t_1
	elif z <= 4.6e+58:
		tmp = x * ((y / z) - t)
	elif z <= 3e+111:
		tmp = t * (x / z)
	elif z <= 9.6e+178:
		tmp = t_1
	elif z <= 1.15e+206:
		tmp = x * (t / z)
	else:
		tmp = x / (z / y)
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(y / z) * x)
	tmp = 0.0
	if (z <= -2.75e+78)
		tmp = t_1;
	elseif (z <= 4.6e+58)
		tmp = Float64(x * Float64(Float64(y / z) - t));
	elseif (z <= 3e+111)
		tmp = Float64(t * Float64(x / z));
	elseif (z <= 9.6e+178)
		tmp = t_1;
	elseif (z <= 1.15e+206)
		tmp = Float64(x * Float64(t / z));
	else
		tmp = Float64(x / Float64(z / y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (y / z) * x;
	tmp = 0.0;
	if (z <= -2.75e+78)
		tmp = t_1;
	elseif (z <= 4.6e+58)
		tmp = x * ((y / z) - t);
	elseif (z <= 3e+111)
		tmp = t * (x / z);
	elseif (z <= 9.6e+178)
		tmp = t_1;
	elseif (z <= 1.15e+206)
		tmp = x * (t / z);
	else
		tmp = x / (z / y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(y / z), $MachinePrecision] * x), $MachinePrecision]}, If[LessEqual[z, -2.75e+78], t$95$1, If[LessEqual[z, 4.6e+58], N[(x * N[(N[(y / z), $MachinePrecision] - t), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 3e+111], N[(t * N[(x / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 9.6e+178], t$95$1, If[LessEqual[z, 1.15e+206], N[(x * N[(t / z), $MachinePrecision]), $MachinePrecision], N[(x / N[(z / y), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 5 regimes

2. if z < -2.7499999999999999e78 or 3e111 < z < 9.599999999999999e178

   1. Initial program 96.0%

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

   3. Taylor expanded in y around inf 69.9%

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

      1. associate-*r/ 76.7%

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

   5. Simplified 76.7%

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

   if -2.7499999999999999e78 < z < 4.60000000000000005e58

   1. Initial program 94.8%

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

   3. Taylor expanded in z around 0 88.3%

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

      1. mul-1-neg 88.3%

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

      2. unsub-neg 88.3%

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

      3. div-sub 88.3%

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

      4. associate-/l* 88.3%

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

      5. *-inverses 88.3%

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

      6. *-rgt-identity 88.3%

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

   5. Simplified 88.3%

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

   if 4.60000000000000005e58 < z < 3e111

   1. Initial program 92.7%

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

   3. Taylor expanded in z around inf 87.8%

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

      1. *-commutative 87.8%

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

      2. sub-neg 87.8%

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

      3. remove-double-neg 87.8%

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

      4. neg-mul-1 87.8%

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

      5. distribute-neg-in 87.8%

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

      6. neg-mul-1 87.8%

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

      7. sub-neg 87.8%

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

      8. distribute-lft-neg-in 87.8%

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

      9. *-commutative 87.8%

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

      10. distribute-neg-frac 87.8%

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

      11. associate-/l* 92.7%

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

      12. distribute-rgt-neg-in 92.7%

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

      13. distribute-neg-frac 92.7%

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

   5. Simplified 92.7%

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

   6. Taylor expanded in t around inf 75.9%

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

      1. associate-/l* 87.8%

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

   8. Simplified 87.8%

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

   if 9.599999999999999e178 < z < 1.15000000000000008e206

   1. Initial program 100.0%

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

   3. Taylor expanded in z around inf 99.7%

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

      1. *-commutative 99.7%

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

      2. sub-neg 99.7%

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

      3. remove-double-neg 99.7%

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

      4. neg-mul-1 99.7%

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

      5. distribute-neg-in 99.7%

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

      6. neg-mul-1 99.7%

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

      7. sub-neg 99.7%

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

      8. distribute-lft-neg-in 99.7%

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

      9. *-commutative 99.7%

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

      10. distribute-neg-frac 99.7%

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

      11. associate-/l* 100.0%

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

      12. distribute-rgt-neg-in 100.0%

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

      13. distribute-neg-frac 100.0%

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

   5. Simplified 100.0%

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

   6. Taylor expanded in t around inf 100.0%

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

   if 1.15000000000000008e206 < z

   1. Initial program 95.1%

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

   3. Taylor expanded in y around inf 63.2%

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

      1. associate-*r/ 72.5%

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

   5. Simplified 72.5%

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

      1. clear-num 72.5%

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

      2. un-div-inv 72.8%

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

   7. Applied egg-rr 72.8%

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

4. Final simplification 84.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.75 \cdot 10^{+78}:\\ \;\;\;\;\frac{y}{z} \cdot x\\ \mathbf{elif}\;z \leq 4.6 \cdot 10^{+58}:\\ \;\;\;\;x \cdot \left(\frac{y}{z} - t\right)\\ \mathbf{elif}\;z \leq 3 \cdot 10^{+111}:\\ \;\;\;\;t \cdot \frac{x}{z}\\ \mathbf{elif}\;z \leq 9.6 \cdot 10^{+178}:\\ \;\;\;\;\frac{y}{z} \cdot x\\ \mathbf{elif}\;z \leq 1.15 \cdot 10^{+206}:\\ \;\;\;\;x \cdot \frac{t}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\frac{z}{y}}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 63.3% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{y}{z} \cdot x\\ \mathbf{if}\;y \leq -1.15 \cdot 10^{-106}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 8.8 \cdot 10^{-249}:\\ \;\;\;\;x \cdot \left(-t\right)\\ \mathbf{elif}\;y \leq 7.2 \cdot 10^{-187} \lor \neg \left(y \leq 2.3 \cdot 10^{-157}\right):\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{x}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* (/ y z) x)))
   (if (<= y -1.15e-106)
     t_1
     (if (<= y 8.8e-249)
       (* x (- t))
       (if (or (<= y 7.2e-187) (not (<= y 2.3e-157))) t_1 (* t (/ x z)))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (y / z) * x;
	double tmp;
	if (y <= -1.15e-106) {
		tmp = t_1;
	} else if (y <= 8.8e-249) {
		tmp = x * -t;
	} else if ((y <= 7.2e-187) || !(y <= 2.3e-157)) {
		tmp = t_1;
	} 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) :: t_1
    real(8) :: tmp
    t_1 = (y / z) * x
    if (y <= (-1.15d-106)) then
        tmp = t_1
    else if (y <= 8.8d-249) then
        tmp = x * -t
    else if ((y <= 7.2d-187) .or. (.not. (y <= 2.3d-157))) then
        tmp = t_1
    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 t_1 = (y / z) * x;
	double tmp;
	if (y <= -1.15e-106) {
		tmp = t_1;
	} else if (y <= 8.8e-249) {
		tmp = x * -t;
	} else if ((y <= 7.2e-187) || !(y <= 2.3e-157)) {
		tmp = t_1;
	} else {
		tmp = t * (x / z);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (y / z) * x
	tmp = 0
	if y <= -1.15e-106:
		tmp = t_1
	elif y <= 8.8e-249:
		tmp = x * -t
	elif (y <= 7.2e-187) or not (y <= 2.3e-157):
		tmp = t_1
	else:
		tmp = t * (x / z)
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(y / z) * x)
	tmp = 0.0
	if (y <= -1.15e-106)
		tmp = t_1;
	elseif (y <= 8.8e-249)
		tmp = Float64(x * Float64(-t));
	elseif ((y <= 7.2e-187) || !(y <= 2.3e-157))
		tmp = t_1;
	else
		tmp = Float64(t * Float64(x / z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (y / z) * x;
	tmp = 0.0;
	if (y <= -1.15e-106)
		tmp = t_1;
	elseif (y <= 8.8e-249)
		tmp = x * -t;
	elseif ((y <= 7.2e-187) || ~((y <= 2.3e-157)))
		tmp = t_1;
	else
		tmp = t * (x / z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(y / z), $MachinePrecision] * x), $MachinePrecision]}, If[LessEqual[y, -1.15e-106], t$95$1, If[LessEqual[y, 8.8e-249], N[(x * (-t)), $MachinePrecision], If[Or[LessEqual[y, 7.2e-187], N[Not[LessEqual[y, 2.3e-157]], $MachinePrecision]], t$95$1, N[(t * N[(x / z), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.15e-106 or 8.8e-249 < y < 7.19999999999999989e-187 or 2.29999999999999989e-157 < y

   1. Initial program 94.2%

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

   3. Taylor expanded in y around inf 76.0%

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

      1. associate-*r/ 75.6%

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

   5. Simplified 75.6%

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

   if -1.15e-106 < y < 8.8e-249

   1. Initial program 98.3%

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

   3. Taylor expanded in z around 0 73.6%

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

      1. mul-1-neg 73.6%

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

      2. unsub-neg 73.6%

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

      3. div-sub 73.6%

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

      4. associate-/l* 73.8%

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

      5. *-inverses 73.8%

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

      6. *-rgt-identity 73.8%

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

   5. Simplified 73.8%

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

   6. Taylor expanded in y around 0 62.8%

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

      1. associate-*r* 62.8%

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

      2. neg-mul-1 62.8%

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

      3. *-commutative 62.8%

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

   8. Simplified 62.8%

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

   if 7.19999999999999989e-187 < y < 2.29999999999999989e-157

   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 89.7%

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

      1. *-commutative 89.7%

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

      2. sub-neg 89.7%

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

      3. remove-double-neg 89.7%

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

      4. neg-mul-1 89.7%

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

      5. distribute-neg-in 89.7%

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

      6. neg-mul-1 89.7%

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

      7. sub-neg 89.7%

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

      8. distribute-lft-neg-in 89.7%

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

      9. *-commutative 89.7%

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

      10. distribute-neg-frac 89.7%

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

      11. associate-/l* 89.3%

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

      12. distribute-rgt-neg-in 89.3%

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

      13. distribute-neg-frac 89.3%

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

   5. Simplified 89.3%

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

   6. Taylor expanded in t around inf 89.7%

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

      1. associate-/l* 89.8%

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

   8. Simplified 89.8%

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

4. Final simplification 73.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.15 \cdot 10^{-106}:\\ \;\;\;\;\frac{y}{z} \cdot x\\ \mathbf{elif}\;y \leq 8.8 \cdot 10^{-249}:\\ \;\;\;\;x \cdot \left(-t\right)\\ \mathbf{elif}\;y \leq 7.2 \cdot 10^{-187} \lor \neg \left(y \leq 2.3 \cdot 10^{-157}\right):\\ \;\;\;\;\frac{y}{z} \cdot x\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{x}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 63.5% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.5 \cdot 10^{-106}:\\ \;\;\;\;y \cdot \frac{x}{z}\\ \mathbf{elif}\;y \leq 1.15 \cdot 10^{-248}:\\ \;\;\;\;x \cdot \left(-t\right)\\ \mathbf{elif}\;y \leq 1.7 \cdot 10^{-187} \lor \neg \left(y \leq 7.5 \cdot 10^{-158}\right):\\ \;\;\;\;\frac{y}{z} \cdot x\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{x}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -2.5e-106)
   (* y (/ x z))
   (if (<= y 1.15e-248)
     (* x (- t))
     (if (or (<= y 1.7e-187) (not (<= y 7.5e-158)))
       (* (/ y z) x)
       (* t (/ x z))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -2.5e-106) {
		tmp = y * (x / z);
	} else if (y <= 1.15e-248) {
		tmp = x * -t;
	} else if ((y <= 1.7e-187) || !(y <= 7.5e-158)) {
		tmp = (y / z) * x;
	} else {
		tmp = t * (x / z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (y <= (-2.5d-106)) then
        tmp = y * (x / z)
    else if (y <= 1.15d-248) then
        tmp = x * -t
    else if ((y <= 1.7d-187) .or. (.not. (y <= 7.5d-158))) then
        tmp = (y / z) * x
    else
        tmp = t * (x / z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -2.5e-106) {
		tmp = y * (x / z);
	} else if (y <= 1.15e-248) {
		tmp = x * -t;
	} else if ((y <= 1.7e-187) || !(y <= 7.5e-158)) {
		tmp = (y / z) * x;
	} else {
		tmp = t * (x / z);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -2.5e-106:
		tmp = y * (x / z)
	elif y <= 1.15e-248:
		tmp = x * -t
	elif (y <= 1.7e-187) or not (y <= 7.5e-158):
		tmp = (y / z) * x
	else:
		tmp = t * (x / z)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -2.5e-106)
		tmp = Float64(y * Float64(x / z));
	elseif (y <= 1.15e-248)
		tmp = Float64(x * Float64(-t));
	elseif ((y <= 1.7e-187) || !(y <= 7.5e-158))
		tmp = Float64(Float64(y / z) * x);
	else
		tmp = Float64(t * Float64(x / z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= -2.5e-106)
		tmp = y * (x / z);
	elseif (y <= 1.15e-248)
		tmp = x * -t;
	elseif ((y <= 1.7e-187) || ~((y <= 7.5e-158)))
		tmp = (y / z) * x;
	else
		tmp = t * (x / z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -2.5e-106], N[(y * N[(x / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.15e-248], N[(x * (-t)), $MachinePrecision], If[Or[LessEqual[y, 1.7e-187], N[Not[LessEqual[y, 7.5e-158]], $MachinePrecision]], N[(N[(y / z), $MachinePrecision] * x), $MachinePrecision], N[(t * N[(x / z), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if y < -2.49999999999999991e-106

   1. Initial program 91.6%

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

      1. clear-num 91.6%

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

      2. frac-sub 71.7%

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

      3. *-un-lft-identity 71.7%

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

   4. Applied egg-rr 71.7%

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

      1. div-sub 62.7%

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

      2. remove-double-neg 62.7%

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

      3. distribute-neg-frac 62.7%

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

      4. distribute-frac-neg2 62.7%

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

      5. distribute-rgt-neg-out 62.7%

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

      6. times-frac 71.3%

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

      7. *-inverses 80.4%

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

      8. cancel-sign-sub-inv 80.4%

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

      9. *-commutative 80.4%

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

      10. associate-/r* 91.6%

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

      11. *-inverses 91.6%

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

      12. metadata-eval 91.6%

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

      13. mul-1-neg 91.6%

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

      14. distribute-neg-frac2 91.6%

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

   6. Simplified 91.6%

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

   7. Taylor expanded in z around inf 70.7%

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

      1. +-commutative 70.7%

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

      2. associate-*l/ 77.4%

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

      3. +-commutative 77.4%

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

   9. Simplified 77.4%

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

   10. Taylor expanded in t around 0 74.0%

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

       1. associate-*l/ 78.6%

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

       2. *-commutative 78.6%

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

   12. Simplified 78.6%

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

   if -2.49999999999999991e-106 < y < 1.15e-248

   1. Initial program 98.3%

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

   3. Taylor expanded in z around 0 73.6%

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

      1. mul-1-neg 73.6%

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

      2. unsub-neg 73.6%

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

      3. div-sub 73.6%

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

      4. associate-/l* 73.8%

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

      5. *-inverses 73.8%

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

      6. *-rgt-identity 73.8%

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

   5. Simplified 73.8%

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

   6. Taylor expanded in y around 0 62.8%

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

      1. associate-*r* 62.8%

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

      2. neg-mul-1 62.8%

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

      3. *-commutative 62.8%

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

   8. Simplified 62.8%

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

   if 1.15e-248 < y < 1.7000000000000001e-187 or 7.5e-158 < y

   1. Initial program 95.9%

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

   3. Taylor expanded in y around inf 77.2%

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

      1. associate-*r/ 77.3%

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

   5. Simplified 77.3%

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

   if 1.7000000000000001e-187 < y < 7.5e-158

   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 89.7%

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

      1. *-commutative 89.7%

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

      2. sub-neg 89.7%

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

      3. remove-double-neg 89.7%

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

      4. neg-mul-1 89.7%

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

      5. distribute-neg-in 89.7%

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

      6. neg-mul-1 89.7%

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

      7. sub-neg 89.7%

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

      8. distribute-lft-neg-in 89.7%

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

      9. *-commutative 89.7%

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

      10. distribute-neg-frac 89.7%

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

      11. associate-/l* 89.3%

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

      12. distribute-rgt-neg-in 89.3%

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

      13. distribute-neg-frac 89.3%

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

   5. Simplified 89.3%

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

   6. Taylor expanded in t around inf 89.7%

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

      1. associate-/l* 89.8%

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

   8. Simplified 89.8%

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

4. Final simplification 75.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.5 \cdot 10^{-106}:\\ \;\;\;\;y \cdot \frac{x}{z}\\ \mathbf{elif}\;y \leq 1.15 \cdot 10^{-248}:\\ \;\;\;\;x \cdot \left(-t\right)\\ \mathbf{elif}\;y \leq 1.7 \cdot 10^{-187} \lor \neg \left(y \leq 7.5 \cdot 10^{-158}\right):\\ \;\;\;\;\frac{y}{z} \cdot x\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{x}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 63.7% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.35 \cdot 10^{-106}:\\ \;\;\;\;y \cdot \frac{x}{z}\\ \mathbf{elif}\;y \leq 5.5 \cdot 10^{-251}:\\ \;\;\;\;x \cdot \left(-t\right)\\ \mathbf{elif}\;y \leq 8 \cdot 10^{-188}:\\ \;\;\;\;\frac{y}{z} \cdot x\\ \mathbf{elif}\;y \leq 8.6 \cdot 10^{-159}:\\ \;\;\;\;t \cdot \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\frac{z}{y}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -1.35e-106)
   (* y (/ x z))
   (if (<= y 5.5e-251)
     (* x (- t))
     (if (<= y 8e-188)
       (* (/ y z) x)
       (if (<= y 8.6e-159) (* t (/ x z)) (/ x (/ z y)))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -1.35e-106) {
		tmp = y * (x / z);
	} else if (y <= 5.5e-251) {
		tmp = x * -t;
	} else if (y <= 8e-188) {
		tmp = (y / z) * x;
	} else if (y <= 8.6e-159) {
		tmp = t * (x / z);
	} else {
		tmp = x / (z / y);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (y <= (-1.35d-106)) then
        tmp = y * (x / z)
    else if (y <= 5.5d-251) then
        tmp = x * -t
    else if (y <= 8d-188) then
        tmp = (y / z) * x
    else if (y <= 8.6d-159) then
        tmp = t * (x / z)
    else
        tmp = x / (z / y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -1.35e-106) {
		tmp = y * (x / z);
	} else if (y <= 5.5e-251) {
		tmp = x * -t;
	} else if (y <= 8e-188) {
		tmp = (y / z) * x;
	} else if (y <= 8.6e-159) {
		tmp = t * (x / z);
	} else {
		tmp = x / (z / y);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -1.35e-106:
		tmp = y * (x / z)
	elif y <= 5.5e-251:
		tmp = x * -t
	elif y <= 8e-188:
		tmp = (y / z) * x
	elif y <= 8.6e-159:
		tmp = t * (x / z)
	else:
		tmp = x / (z / y)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -1.35e-106)
		tmp = Float64(y * Float64(x / z));
	elseif (y <= 5.5e-251)
		tmp = Float64(x * Float64(-t));
	elseif (y <= 8e-188)
		tmp = Float64(Float64(y / z) * x);
	elseif (y <= 8.6e-159)
		tmp = Float64(t * Float64(x / z));
	else
		tmp = Float64(x / Float64(z / y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= -1.35e-106)
		tmp = y * (x / z);
	elseif (y <= 5.5e-251)
		tmp = x * -t;
	elseif (y <= 8e-188)
		tmp = (y / z) * x;
	elseif (y <= 8.6e-159)
		tmp = t * (x / z);
	else
		tmp = x / (z / y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -1.35e-106], N[(y * N[(x / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 5.5e-251], N[(x * (-t)), $MachinePrecision], If[LessEqual[y, 8e-188], N[(N[(y / z), $MachinePrecision] * x), $MachinePrecision], If[LessEqual[y, 8.6e-159], N[(t * N[(x / z), $MachinePrecision]), $MachinePrecision], N[(x / N[(z / y), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 5 regimes

2. if y < -1.35000000000000011e-106

   1. Initial program 91.6%

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

      1. clear-num 91.6%

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

      2. frac-sub 71.7%

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

      3. *-un-lft-identity 71.7%

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

   4. Applied egg-rr 71.7%

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

      1. div-sub 62.7%

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

      2. remove-double-neg 62.7%

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

      3. distribute-neg-frac 62.7%

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

      4. distribute-frac-neg2 62.7%

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

      5. distribute-rgt-neg-out 62.7%

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

      6. times-frac 71.3%

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

      7. *-inverses 80.4%

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

      8. cancel-sign-sub-inv 80.4%

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

      9. *-commutative 80.4%

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

      10. associate-/r* 91.6%

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

      11. *-inverses 91.6%

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

      12. metadata-eval 91.6%

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

      13. mul-1-neg 91.6%

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

      14. distribute-neg-frac2 91.6%

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

   6. Simplified 91.6%

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

   7. Taylor expanded in z around inf 70.7%

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

      1. +-commutative 70.7%

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

      2. associate-*l/ 77.4%

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

      3. +-commutative 77.4%

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

   9. Simplified 77.4%

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

   10. Taylor expanded in t around 0 74.0%

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

       1. associate-*l/ 78.6%

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

       2. *-commutative 78.6%

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

   12. Simplified 78.6%

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

   if -1.35000000000000011e-106 < y < 5.5e-251

   1. Initial program 98.3%

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

   3. Taylor expanded in z around 0 73.6%

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

      1. mul-1-neg 73.6%

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

      2. unsub-neg 73.6%

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

      3. div-sub 73.6%

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

      4. associate-/l* 73.8%

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

      5. *-inverses 73.8%

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

      6. *-rgt-identity 73.8%

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

   5. Simplified 73.8%

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

   6. Taylor expanded in y around 0 62.8%

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

      1. associate-*r* 62.8%

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

      2. neg-mul-1 62.8%

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

      3. *-commutative 62.8%

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

   8. Simplified 62.8%

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

   if 5.5e-251 < y < 7.9999999999999996e-188

   1. Initial program 99.6%

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

   3. Taylor expanded in y around inf 71.9%

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

      1. associate-*r/ 78.6%

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

   5. Simplified 78.6%

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

   if 7.9999999999999996e-188 < y < 8.6e-159

   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 89.7%

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

      1. *-commutative 89.7%

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

      2. sub-neg 89.7%

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

      3. remove-double-neg 89.7%

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

      4. neg-mul-1 89.7%

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

      5. distribute-neg-in 89.7%

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

      6. neg-mul-1 89.7%

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

      7. sub-neg 89.7%

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

      8. distribute-lft-neg-in 89.7%

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

      9. *-commutative 89.7%

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

      10. distribute-neg-frac 89.7%

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

      11. associate-/l* 89.3%

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

      12. distribute-rgt-neg-in 89.3%

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

      13. distribute-neg-frac 89.3%

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

   5. Simplified 89.3%

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

   6. Taylor expanded in t around inf 89.7%

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

      1. associate-/l* 89.8%

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

   8. Simplified 89.8%

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

   if 8.6e-159 < y

   1. Initial program 95.5%

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

   3. Taylor expanded in y around inf 77.9%

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

      1. associate-*r/ 77.1%

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

   5. Simplified 77.1%

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

      1. clear-num 77.2%

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

      2. un-div-inv 77.2%

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

   7. Applied egg-rr 77.2%

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

4. Final simplification 75.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.35 \cdot 10^{-106}:\\ \;\;\;\;y \cdot \frac{x}{z}\\ \mathbf{elif}\;y \leq 5.5 \cdot 10^{-251}:\\ \;\;\;\;x \cdot \left(-t\right)\\ \mathbf{elif}\;y \leq 8 \cdot 10^{-188}:\\ \;\;\;\;\frac{y}{z} \cdot x\\ \mathbf{elif}\;y \leq 8.6 \cdot 10^{-159}:\\ \;\;\;\;t \cdot \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\frac{z}{y}}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 64.0% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -5.2 \cdot 10^{-106}:\\ \;\;\;\;y \cdot \frac{x}{z}\\ \mathbf{elif}\;y \leq 1.7 \cdot 10^{-250}:\\ \;\;\;\;x \cdot \left(-t\right)\\ \mathbf{elif}\;y \leq 1.4 \cdot 10^{-187}:\\ \;\;\;\;\frac{y}{z} \cdot x\\ \mathbf{elif}\;y \leq 2.7 \cdot 10^{-157}:\\ \;\;\;\;t \cdot \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{y \cdot x}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -5.2e-106)
   (* y (/ x z))
   (if (<= y 1.7e-250)
     (* x (- t))
     (if (<= y 1.4e-187)
       (* (/ y z) x)
       (if (<= y 2.7e-157) (* t (/ x z)) (/ (* y x) z))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -5.2e-106) {
		tmp = y * (x / z);
	} else if (y <= 1.7e-250) {
		tmp = x * -t;
	} else if (y <= 1.4e-187) {
		tmp = (y / z) * x;
	} else if (y <= 2.7e-157) {
		tmp = t * (x / 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) :: tmp
    if (y <= (-5.2d-106)) then
        tmp = y * (x / z)
    else if (y <= 1.7d-250) then
        tmp = x * -t
    else if (y <= 1.4d-187) then
        tmp = (y / z) * x
    else if (y <= 2.7d-157) then
        tmp = t * (x / 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 tmp;
	if (y <= -5.2e-106) {
		tmp = y * (x / z);
	} else if (y <= 1.7e-250) {
		tmp = x * -t;
	} else if (y <= 1.4e-187) {
		tmp = (y / z) * x;
	} else if (y <= 2.7e-157) {
		tmp = t * (x / z);
	} else {
		tmp = (y * x) / z;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -5.2e-106:
		tmp = y * (x / z)
	elif y <= 1.7e-250:
		tmp = x * -t
	elif y <= 1.4e-187:
		tmp = (y / z) * x
	elif y <= 2.7e-157:
		tmp = t * (x / z)
	else:
		tmp = (y * x) / z
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -5.2e-106)
		tmp = Float64(y * Float64(x / z));
	elseif (y <= 1.7e-250)
		tmp = Float64(x * Float64(-t));
	elseif (y <= 1.4e-187)
		tmp = Float64(Float64(y / z) * x);
	elseif (y <= 2.7e-157)
		tmp = Float64(t * Float64(x / z));
	else
		tmp = Float64(Float64(y * x) / z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= -5.2e-106)
		tmp = y * (x / z);
	elseif (y <= 1.7e-250)
		tmp = x * -t;
	elseif (y <= 1.4e-187)
		tmp = (y / z) * x;
	elseif (y <= 2.7e-157)
		tmp = t * (x / z);
	else
		tmp = (y * x) / z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -5.2e-106], N[(y * N[(x / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.7e-250], N[(x * (-t)), $MachinePrecision], If[LessEqual[y, 1.4e-187], N[(N[(y / z), $MachinePrecision] * x), $MachinePrecision], If[LessEqual[y, 2.7e-157], N[(t * N[(x / z), $MachinePrecision]), $MachinePrecision], N[(N[(y * x), $MachinePrecision] / z), $MachinePrecision]]]]]

Derivation

1. Split input into 5 regimes

2. if y < -5.2000000000000001e-106

   1. Initial program 91.6%

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

      1. clear-num 91.6%

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

      2. frac-sub 71.7%

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

      3. *-un-lft-identity 71.7%

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

   4. Applied egg-rr 71.7%

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

      1. div-sub 62.7%

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

      2. remove-double-neg 62.7%

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

      3. distribute-neg-frac 62.7%

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

      4. distribute-frac-neg2 62.7%

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

      5. distribute-rgt-neg-out 62.7%

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

      6. times-frac 71.3%

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

      7. *-inverses 80.4%

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

      8. cancel-sign-sub-inv 80.4%

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

      9. *-commutative 80.4%

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

      10. associate-/r* 91.6%

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

      11. *-inverses 91.6%

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

      12. metadata-eval 91.6%

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

      13. mul-1-neg 91.6%

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

      14. distribute-neg-frac2 91.6%

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

   6. Simplified 91.6%

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

   7. Taylor expanded in z around inf 70.7%

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

      1. +-commutative 70.7%

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

      2. associate-*l/ 77.4%

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

      3. +-commutative 77.4%

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

   9. Simplified 77.4%

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

   10. Taylor expanded in t around 0 74.0%

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

       1. associate-*l/ 78.6%

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

       2. *-commutative 78.6%

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

   12. Simplified 78.6%

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

   if -5.2000000000000001e-106 < y < 1.69999999999999997e-250

   1. Initial program 98.3%

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

   3. Taylor expanded in z around 0 73.6%

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

      1. mul-1-neg 73.6%

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

      2. unsub-neg 73.6%

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

      3. div-sub 73.6%

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

      4. associate-/l* 73.8%

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

      5. *-inverses 73.8%

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

      6. *-rgt-identity 73.8%

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

   5. Simplified 73.8%

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

   6. Taylor expanded in y around 0 62.8%

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

      1. associate-*r* 62.8%

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

      2. neg-mul-1 62.8%

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

      3. *-commutative 62.8%

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

   8. Simplified 62.8%

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

   if 1.69999999999999997e-250 < y < 1.4e-187

   1. Initial program 99.6%

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

   3. Taylor expanded in y around inf 71.9%

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

      1. associate-*r/ 78.6%

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

   5. Simplified 78.6%

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

   if 1.4e-187 < y < 2.7e-157

   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 89.7%

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

      1. *-commutative 89.7%

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

      2. sub-neg 89.7%

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

      3. remove-double-neg 89.7%

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

      4. neg-mul-1 89.7%

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

      5. distribute-neg-in 89.7%

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

      6. neg-mul-1 89.7%

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

      7. sub-neg 89.7%

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

      8. distribute-lft-neg-in 89.7%

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

      9. *-commutative 89.7%

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

      10. distribute-neg-frac 89.7%

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

      11. associate-/l* 89.3%

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

      12. distribute-rgt-neg-in 89.3%

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

      13. distribute-neg-frac 89.3%

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

   5. Simplified 89.3%

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

   6. Taylor expanded in t around inf 89.7%

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

      1. associate-/l* 89.8%

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

   8. Simplified 89.8%

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

   if 2.7e-157 < y

   1. Initial program 95.5%

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

   3. Taylor expanded in y around inf 77.9%

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

4. Final simplification 76.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -5.2 \cdot 10^{-106}:\\ \;\;\;\;y \cdot \frac{x}{z}\\ \mathbf{elif}\;y \leq 1.7 \cdot 10^{-250}:\\ \;\;\;\;x \cdot \left(-t\right)\\ \mathbf{elif}\;y \leq 1.4 \cdot 10^{-187}:\\ \;\;\;\;\frac{y}{z} \cdot x\\ \mathbf{elif}\;y \leq 2.7 \cdot 10^{-157}:\\ \;\;\;\;t \cdot \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{y \cdot x}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 93.1% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -235000 \lor \neg \left(z \leq 8.8 \cdot 10^{-14}\right):\\ \;\;\;\;x \cdot \frac{y + t}{z}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(\frac{y}{z} - t\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -235000.0) (not (<= z 8.8e-14)))
   (* x (/ (+ y t) z))
   (* x (- (/ y z) t))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -235000.0) || !(z <= 8.8e-14)) {
		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 <= (-235000.0d0)) .or. (.not. (z <= 8.8d-14))) 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 <= -235000.0) || !(z <= 8.8e-14)) {
		tmp = x * ((y + t) / z);
	} else {
		tmp = x * ((y / z) - t);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -235000.0) or not (z <= 8.8e-14):
		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 <= -235000.0) || !(z <= 8.8e-14))
		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 <= -235000.0) || ~((z <= 8.8e-14)))
		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, -235000.0], N[Not[LessEqual[z, 8.8e-14]], $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 < -235000 or 8.8000000000000004e-14 < z

   1. Initial program 96.6%

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

   3. Taylor expanded in z around inf 90.1%

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

      1. *-commutative 90.1%

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

      2. sub-neg 90.1%

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

      3. remove-double-neg 90.1%

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

      4. neg-mul-1 90.1%

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

      5. distribute-neg-in 90.1%

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

      6. neg-mul-1 90.1%

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

      7. sub-neg 90.1%

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

      8. distribute-lft-neg-in 90.1%

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

      9. *-commutative 90.1%

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

      10. distribute-neg-frac 90.1%

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

      11. associate-/l* 96.2%

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

      12. distribute-rgt-neg-in 96.2%

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

      13. distribute-neg-frac 96.2%

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

   5. Simplified 96.2%

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

   if -235000 < z < 8.8000000000000004e-14

   1. Initial program 94.0%

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

   3. Taylor expanded in z around 0 93.6%

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

      1. mul-1-neg 93.6%

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

      2. unsub-neg 93.6%

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

      3. div-sub 93.6%

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

      4. associate-/l* 93.6%

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

      5. *-inverses 93.6%

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

      6. *-rgt-identity 93.6%

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

   5. Simplified 93.6%

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

4. Final simplification 94.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -235000 \lor \neg \left(z \leq 8.8 \cdot 10^{-14}\right):\\ \;\;\;\;x \cdot \frac{y + t}{z}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(\frac{y}{z} - t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 40.0% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.8 \cdot 10^{+35} \lor \neg \left(z \leq 8.8 \cdot 10^{-14}\right):\\ \;\;\;\;t \cdot \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(-t\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -2.8e+35) (not (<= z 8.8e-14))) (* t (/ x z)) (* x (- t))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -2.8e+35) || !(z <= 8.8e-14)) {
		tmp = t * (x / z);
	} else {
		tmp = x * -t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((z <= (-2.8d+35)) .or. (.not. (z <= 8.8d-14))) then
        tmp = t * (x / z)
    else
        tmp = x * -t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -2.8e+35) || !(z <= 8.8e-14)) {
		tmp = t * (x / z);
	} else {
		tmp = x * -t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -2.8e+35) or not (z <= 8.8e-14):
		tmp = t * (x / z)
	else:
		tmp = x * -t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -2.8e+35) || !(z <= 8.8e-14))
		tmp = Float64(t * Float64(x / z));
	else
		tmp = Float64(x * Float64(-t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z <= -2.8e+35) || ~((z <= 8.8e-14)))
		tmp = t * (x / z);
	else
		tmp = x * -t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -2.8e+35], N[Not[LessEqual[z, 8.8e-14]], $MachinePrecision]], N[(t * N[(x / z), $MachinePrecision]), $MachinePrecision], N[(x * (-t)), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -2.79999999999999999e35 or 8.8000000000000004e-14 < z

   1. Initial program 96.5%

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

   3. Taylor expanded in z around inf 89.9%

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

      1. *-commutative 89.9%

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

      2. sub-neg 89.9%

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

      3. remove-double-neg 89.9%

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

      4. neg-mul-1 89.9%

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

      5. distribute-neg-in 89.9%

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

      6. neg-mul-1 89.9%

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

      7. sub-neg 89.9%

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

      8. distribute-lft-neg-in 89.9%

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

      9. *-commutative 89.9%

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

      10. distribute-neg-frac 89.9%

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

      11. associate-/l* 96.1%

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

      12. distribute-rgt-neg-in 96.1%

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

      13. distribute-neg-frac 96.1%

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

   5. Simplified 96.1%

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

   6. Taylor expanded in t around inf 50.6%

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

      1. associate-/l* 50.1%

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

   8. Simplified 50.1%

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

   if -2.79999999999999999e35 < z < 8.8000000000000004e-14

   1. Initial program 94.1%

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

   3. Taylor expanded in z around 0 93.1%

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

      1. mul-1-neg 93.1%

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

      2. unsub-neg 93.1%

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

      3. div-sub 93.1%

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

      4. associate-/l* 93.2%

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

      5. *-inverses 93.2%

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

      6. *-rgt-identity 93.2%

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

   5. Simplified 93.2%

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

   6. Taylor expanded in y around 0 31.7%

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

      1. associate-*r* 31.7%

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

      2. neg-mul-1 31.7%

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

      3. *-commutative 31.7%

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

   8. Simplified 31.7%

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

4. Final simplification 39.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.8 \cdot 10^{+35} \lor \neg \left(z \leq 8.8 \cdot 10^{-14}\right):\\ \;\;\;\;t \cdot \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(-t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 42.4% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.8 \cdot 10^{+35} \lor \neg \left(z \leq 8.8 \cdot 10^{-14}\right):\\ \;\;\;\;x \cdot \frac{t}{z}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(-t\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -2.8e+35) (not (<= z 8.8e-14))) (* x (/ t z)) (* x (- t))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -2.8e+35) || !(z <= 8.8e-14)) {
		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 <= (-2.8d+35)) .or. (.not. (z <= 8.8d-14))) 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 <= -2.8e+35) || !(z <= 8.8e-14)) {
		tmp = x * (t / z);
	} else {
		tmp = x * -t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -2.8e+35) or not (z <= 8.8e-14):
		tmp = x * (t / z)
	else:
		tmp = x * -t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -2.8e+35) || !(z <= 8.8e-14))
		tmp = Float64(x * Float64(t / z));
	else
		tmp = Float64(x * Float64(-t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z <= -2.8e+35) || ~((z <= 8.8e-14)))
		tmp = x * (t / z);
	else
		tmp = x * -t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -2.8e+35], N[Not[LessEqual[z, 8.8e-14]], $MachinePrecision]], N[(x * N[(t / z), $MachinePrecision]), $MachinePrecision], N[(x * (-t)), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -2.79999999999999999e35 or 8.8000000000000004e-14 < z

   1. Initial program 96.5%

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

   3. Taylor expanded in z around inf 89.9%

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

      1. *-commutative 89.9%

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

      2. sub-neg 89.9%

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

      3. remove-double-neg 89.9%

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

      4. neg-mul-1 89.9%

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

      5. distribute-neg-in 89.9%

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

      6. neg-mul-1 89.9%

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

      7. sub-neg 89.9%

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

      8. distribute-lft-neg-in 89.9%

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

      9. *-commutative 89.9%

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

      10. distribute-neg-frac 89.9%

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

      11. associate-/l* 96.1%

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

      12. distribute-rgt-neg-in 96.1%

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

      13. distribute-neg-frac 96.1%

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

   5. Simplified 96.1%

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

   6. Taylor expanded in t around inf 51.6%

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

   if -2.79999999999999999e35 < z < 8.8000000000000004e-14

   1. Initial program 94.1%

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

   3. Taylor expanded in z around 0 93.1%

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

      1. mul-1-neg 93.1%

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

      2. unsub-neg 93.1%

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

      3. div-sub 93.1%

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

      4. associate-/l* 93.2%

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

      5. *-inverses 93.2%

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

      6. *-rgt-identity 93.2%

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

   5. Simplified 93.2%

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

   6. Taylor expanded in y around 0 31.7%

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

      1. associate-*r* 31.7%

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

      2. neg-mul-1 31.7%

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

      3. *-commutative 31.7%

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

   8. Simplified 31.7%

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

4. Final simplification 40.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.8 \cdot 10^{+35} \lor \neg \left(z \leq 8.8 \cdot 10^{-14}\right):\\ \;\;\;\;x \cdot \frac{t}{z}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(-t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 23.0% accurate, 2.8× speedup

Math

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

FPCore

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

C

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

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    code = x * -t
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 95.1%

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

3. Taylor expanded in z around 0 68.1%

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

   1. mul-1-neg 68.1%

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

   2. unsub-neg 68.1%

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

   3. div-sub 68.1%

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

   4. associate-/l* 68.2%

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

   5. *-inverses 68.2%

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

   6. *-rgt-identity 68.2%

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

5. Simplified 68.2%

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

6. Taylor expanded in y around 0 23.5%

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

   1. associate-*r* 23.5%

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

   2. neg-mul-1 23.5%

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

   3. *-commutative 23.5%

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

8. Simplified 23.5%

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

9. Final simplification 23.5%

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

Developer target: 94.9% 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 2024072 
(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)))))