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

Percentage Accurate: 94.2% → 97.1%

Time: 12.3s

Alternatives: 13

Speedup: 0.2×

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: 94.2% 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: 97.1% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{y}{z} + \frac{t}{z + -1}\\ \mathbf{if}\;t\_1 \leq -\infty:\\ \;\;\;\;\frac{y \cdot x}{z}\\ \mathbf{elif}\;t\_1 \leq -4 \cdot 10^{-141} \lor \neg \left(t\_1 \leq 0\right):\\ \;\;\;\;t\_1 \cdot x\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(\frac{t}{y} \cdot \frac{x}{z + -1} + \frac{x}{z}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (+ (/ y z) (/ t (+ z -1.0)))))
   (if (<= t_1 (- INFINITY))
     (/ (* y x) z)
     (if (or (<= t_1 -4e-141) (not (<= t_1 0.0)))
       (* t_1 x)
       (* y (+ (* (/ t y) (/ x (+ z -1.0))) (/ 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 <= -((double) INFINITY)) {
		tmp = (y * x) / z;
	} else if ((t_1 <= -4e-141) || !(t_1 <= 0.0)) {
		tmp = t_1 * x;
	} else {
		tmp = y * (((t / y) * (x / (z + -1.0))) + (x / z));
	}
	return tmp;
}

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = (y / z) + (t / (z + -1.0));
	double tmp;
	if (t_1 <= -Double.POSITIVE_INFINITY) {
		tmp = (y * x) / z;
	} else if ((t_1 <= -4e-141) || !(t_1 <= 0.0)) {
		tmp = t_1 * x;
	} else {
		tmp = y * (((t / y) * (x / (z + -1.0))) + (x / z));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (y / z) + (t / (z + -1.0))
	tmp = 0
	if t_1 <= -math.inf:
		tmp = (y * x) / z
	elif (t_1 <= -4e-141) or not (t_1 <= 0.0):
		tmp = t_1 * x
	else:
		tmp = y * (((t / y) * (x / (z + -1.0))) + (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 <= Float64(-Inf))
		tmp = Float64(Float64(y * x) / z);
	elseif ((t_1 <= -4e-141) || !(t_1 <= 0.0))
		tmp = Float64(t_1 * x);
	else
		tmp = Float64(y * Float64(Float64(Float64(t / y) * Float64(x / Float64(z + -1.0))) + 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 <= -Inf)
		tmp = (y * x) / z;
	elseif ((t_1 <= -4e-141) || ~((t_1 <= 0.0)))
		tmp = t_1 * x;
	else
		tmp = y * (((t / y) * (x / (z + -1.0))) + (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, (-Infinity)], N[(N[(y * x), $MachinePrecision] / z), $MachinePrecision], If[Or[LessEqual[t$95$1, -4e-141], N[Not[LessEqual[t$95$1, 0.0]], $MachinePrecision]], N[(t$95$1 * x), $MachinePrecision], N[(y * N[(N[(N[(t / y), $MachinePrecision] * N[(x / N[(z + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(x / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

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

   1. Initial program 39.6%

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

   3. Taylor expanded in y around inf 100.0%

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

   if -inf.0 < (-.f64 (/.f64 y z) (/.f64 t (-.f64 #s(literal 1 binary64) z))) < -4.0000000000000002e-141 or 0.0 < (-.f64 (/.f64 y z) (/.f64 t (-.f64 #s(literal 1 binary64) z)))

   1. Initial program 97.9%

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

   if -4.0000000000000002e-141 < (-.f64 (/.f64 y z) (/.f64 t (-.f64 #s(literal 1 binary64) z))) < 0.0

   1. Initial program 83.4%

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

   3. Taylor expanded in y around inf 95.0%

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

      1. mul-1-neg 95.0%

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

      2. times-frac 97.8%

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

      3. distribute-rgt-neg-in 97.8%

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

      4. distribute-neg-frac2 97.8%

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

      5. neg-sub0 97.8%

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

      6. associate--r- 97.8%

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

      7. metadata-eval 97.8%

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

   5. Simplified 97.8%

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

4. Final simplification 98.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{y}{z} + \frac{t}{z + -1} \leq -\infty:\\ \;\;\;\;\frac{y \cdot x}{z}\\ \mathbf{elif}\;\frac{y}{z} + \frac{t}{z + -1} \leq -4 \cdot 10^{-141} \lor \neg \left(\frac{y}{z} + \frac{t}{z + -1} \leq 0\right):\\ \;\;\;\;\left(\frac{y}{z} + \frac{t}{z + -1}\right) \cdot x\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(\frac{t}{y} \cdot \frac{x}{z + -1} + \frac{x}{z}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 96.7% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(\frac{y}{z} + \frac{t}{z + -1}\right) \cdot x\\ \mathbf{if}\;t\_1 \leq -\infty:\\ \;\;\;\;\frac{x \cdot \left(y - z \cdot t\right)}{z}\\ \mathbf{elif}\;t\_1 \leq -5 \cdot 10^{-237} \lor \neg \left(t\_1 \leq 0\right):\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot \left(y + t\right)}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* (+ (/ y z) (/ t (+ z -1.0))) x)))
   (if (<= t_1 (- INFINITY))
     (/ (* x (- y (* z t))) z)
     (if (or (<= t_1 -5e-237) (not (<= t_1 0.0))) t_1 (/ (* x (+ y t)) z)))))

C

double code(double x, double y, double z, double t) {
	double t_1 = ((y / z) + (t / (z + -1.0))) * x;
	double tmp;
	if (t_1 <= -((double) INFINITY)) {
		tmp = (x * (y - (z * t))) / z;
	} else if ((t_1 <= -5e-237) || !(t_1 <= 0.0)) {
		tmp = t_1;
	} else {
		tmp = (x * (y + t)) / z;
	}
	return tmp;
}

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = ((y / z) + (t / (z + -1.0))) * x;
	double tmp;
	if (t_1 <= -Double.POSITIVE_INFINITY) {
		tmp = (x * (y - (z * t))) / z;
	} else if ((t_1 <= -5e-237) || !(t_1 <= 0.0)) {
		tmp = t_1;
	} else {
		tmp = (x * (y + t)) / z;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = ((y / z) + (t / (z + -1.0))) * x
	tmp = 0
	if t_1 <= -math.inf:
		tmp = (x * (y - (z * t))) / z
	elif (t_1 <= -5e-237) or not (t_1 <= 0.0):
		tmp = t_1
	else:
		tmp = (x * (y + t)) / z
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(Float64(y / z) + Float64(t / Float64(z + -1.0))) * x)
	tmp = 0.0
	if (t_1 <= Float64(-Inf))
		tmp = Float64(Float64(x * Float64(y - Float64(z * t))) / z);
	elseif ((t_1 <= -5e-237) || !(t_1 <= 0.0))
		tmp = t_1;
	else
		tmp = Float64(Float64(x * Float64(y + t)) / z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = ((y / z) + (t / (z + -1.0))) * x;
	tmp = 0.0;
	if (t_1 <= -Inf)
		tmp = (x * (y - (z * t))) / z;
	elseif ((t_1 <= -5e-237) || ~((t_1 <= 0.0)))
		tmp = t_1;
	else
		tmp = (x * (y + t)) / z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(N[(y / z), $MachinePrecision] + N[(t / N[(z + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * x), $MachinePrecision]}, If[LessEqual[t$95$1, (-Infinity)], N[(N[(x * N[(y - N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision], If[Or[LessEqual[t$95$1, -5e-237], N[Not[LessEqual[t$95$1, 0.0]], $MachinePrecision]], t$95$1, N[(N[(x * N[(y + t), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

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

   1. Initial program 78.0%

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

      1. clear-num 78.0%

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

      2. frac-sub 78.0%

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

      3. *-un-lft-identity 78.0%

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

   4. Applied egg-rr 78.0%

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

      1. div-sub 61.7%

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

      2. times-frac 61.7%

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

      3. *-inverses 78.0%

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

      4. *-lft-identity 78.0%

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

      5. remove-double-neg 78.0%

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

      6. distribute-frac-neg 78.0%

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

      7. *-rgt-identity 78.0%

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

      8. distribute-lft-neg-in 78.0%

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

      9. cancel-sign-sub 78.0%

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

      10. *-commutative 78.0%

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

      11. associate-/r* 78.0%

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

      12. *-inverses 78.0%

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

      13. *-rgt-identity 78.0%

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

      14. distribute-frac-neg 78.0%

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

      15. distribute-neg-frac2 78.0%

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

      16. neg-sub0 78.0%

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

      17. associate--r- 78.0%

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

      18. metadata-eval 78.0%

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

   6. Simplified 78.0%

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

      1. clear-num 78.0%

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

      2. inv-pow 78.0%

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

      3. +-commutative 78.0%

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

   8. Applied egg-rr 78.0%

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

      1. unpow-1 78.0%

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

   10. Simplified 78.0%

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

   11. Taylor expanded in z around 0 92.3%

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

       1. +-commutative 92.3%

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

       2. mul-1-neg 92.3%

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

       3. *-commutative 92.3%

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

       4. *-commutative 92.3%

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

       5. associate-*r* 84.6%

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

       6. *-commutative 84.6%

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

       7. distribute-rgt-neg-out 84.6%

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

       8. associate-*l* 92.3%

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

       9. distribute-rgt-neg-in 92.3%

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

       10. mul-1-neg 92.3%

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

       11. distribute-lft-out 96.2%

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

       12. mul-1-neg 96.2%

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

       13. unsub-neg 96.2%

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

   13. Simplified 96.2%

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

   if -inf.0 < (*.f64 x (-.f64 (/.f64 y z) (/.f64 t (-.f64 #s(literal 1 binary64) z)))) < -5.0000000000000002e-237 or -0.0 < (*.f64 x (-.f64 (/.f64 y z) (/.f64 t (-.f64 #s(literal 1 binary64) z))))

   1. Initial program 95.9%

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

   if -5.0000000000000002e-237 < (*.f64 x (-.f64 (/.f64 y z) (/.f64 t (-.f64 #s(literal 1 binary64) z)))) < -0.0

   1. Initial program 86.7%

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

      1. clear-num 86.7%

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

      2. frac-sub 49.0%

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

      3. *-un-lft-identity 49.0%

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

   4. Applied egg-rr 49.0%

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

      1. div-sub 49.0%

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

      2. times-frac 49.0%

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

      3. *-inverses 81.5%

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

      4. *-lft-identity 81.5%

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

      5. remove-double-neg 81.5%

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

      6. distribute-frac-neg 81.5%

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

      7. *-rgt-identity 81.5%

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

      8. distribute-lft-neg-in 81.5%

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

      9. cancel-sign-sub 81.5%

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

      10. *-commutative 81.5%

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

      11. associate-/r* 86.7%

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

      12. *-inverses 86.7%

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

      13. *-rgt-identity 86.7%

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

      14. distribute-frac-neg 86.7%

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

      15. distribute-neg-frac2 86.7%

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

      16. neg-sub0 86.7%

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

      17. associate--r- 86.7%

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

      18. metadata-eval 86.7%

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

   6. Simplified 86.7%

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

   7. Taylor expanded in z around inf 97.3%

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

4. Final simplification 96.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(\frac{y}{z} + \frac{t}{z + -1}\right) \cdot x \leq -\infty:\\ \;\;\;\;\frac{x \cdot \left(y - z \cdot t\right)}{z}\\ \mathbf{elif}\;\left(\frac{y}{z} + \frac{t}{z + -1}\right) \cdot x \leq -5 \cdot 10^{-237} \lor \neg \left(\left(\frac{y}{z} + \frac{t}{z + -1}\right) \cdot x \leq 0\right):\\ \;\;\;\;\left(\frac{y}{z} + \frac{t}{z + -1}\right) \cdot x\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot \left(y + t\right)}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 72.2% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \frac{x}{z}\\ t_2 := t \cdot \frac{x}{z + -1}\\ \mathbf{if}\;t \leq -1.45 \cdot 10^{+91}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t \leq -0.0016:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq -7.5 \cdot 10^{-9}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t \leq -1.5 \cdot 10^{-86}:\\ \;\;\;\;\frac{y}{z} \cdot x\\ \mathbf{elif}\;t \leq 8.8 \cdot 10^{+119}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* y (/ x z))) (t_2 (* t (/ x (+ z -1.0)))))
   (if (<= t -1.45e+91)
     t_2
     (if (<= t -0.0016)
       t_1
       (if (<= t -7.5e-9)
         t_2
         (if (<= t -1.5e-86) (* (/ y z) x) (if (<= t 8.8e+119) t_1 t_2)))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = y * (x / z);
	double t_2 = t * (x / (z + -1.0));
	double tmp;
	if (t <= -1.45e+91) {
		tmp = t_2;
	} else if (t <= -0.0016) {
		tmp = t_1;
	} else if (t <= -7.5e-9) {
		tmp = t_2;
	} else if (t <= -1.5e-86) {
		tmp = (y / z) * x;
	} else if (t <= 8.8e+119) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = y * (x / z)
    t_2 = t * (x / (z + (-1.0d0)))
    if (t <= (-1.45d+91)) then
        tmp = t_2
    else if (t <= (-0.0016d0)) then
        tmp = t_1
    else if (t <= (-7.5d-9)) then
        tmp = t_2
    else if (t <= (-1.5d-86)) then
        tmp = (y / z) * x
    else if (t <= 8.8d+119) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = y * (x / z);
	double t_2 = t * (x / (z + -1.0));
	double tmp;
	if (t <= -1.45e+91) {
		tmp = t_2;
	} else if (t <= -0.0016) {
		tmp = t_1;
	} else if (t <= -7.5e-9) {
		tmp = t_2;
	} else if (t <= -1.5e-86) {
		tmp = (y / z) * x;
	} else if (t <= 8.8e+119) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = y * (x / z)
	t_2 = t * (x / (z + -1.0))
	tmp = 0
	if t <= -1.45e+91:
		tmp = t_2
	elif t <= -0.0016:
		tmp = t_1
	elif t <= -7.5e-9:
		tmp = t_2
	elif t <= -1.5e-86:
		tmp = (y / z) * x
	elif t <= 8.8e+119:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(y * Float64(x / z))
	t_2 = Float64(t * Float64(x / Float64(z + -1.0)))
	tmp = 0.0
	if (t <= -1.45e+91)
		tmp = t_2;
	elseif (t <= -0.0016)
		tmp = t_1;
	elseif (t <= -7.5e-9)
		tmp = t_2;
	elseif (t <= -1.5e-86)
		tmp = Float64(Float64(y / z) * x);
	elseif (t <= 8.8e+119)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = y * (x / z);
	t_2 = t * (x / (z + -1.0));
	tmp = 0.0;
	if (t <= -1.45e+91)
		tmp = t_2;
	elseif (t <= -0.0016)
		tmp = t_1;
	elseif (t <= -7.5e-9)
		tmp = t_2;
	elseif (t <= -1.5e-86)
		tmp = (y / z) * x;
	elseif (t <= 8.8e+119)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(y * N[(x / z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t * N[(x / N[(z + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -1.45e+91], t$95$2, If[LessEqual[t, -0.0016], t$95$1, If[LessEqual[t, -7.5e-9], t$95$2, If[LessEqual[t, -1.5e-86], N[(N[(y / z), $MachinePrecision] * x), $MachinePrecision], If[LessEqual[t, 8.8e+119], t$95$1, t$95$2]]]]]]]

Derivation

1. Split input into 3 regimes

2. if t < -1.45000000000000007e91 or -0.00160000000000000008 < t < -7.49999999999999933e-9 or 8.8000000000000005e119 < t

   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 0 69.9%

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

      1. mul-1-neg 69.9%

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

      2. associate-/l* 70.0%

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

      3. distribute-rgt-neg-in 70.0%

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

      4. distribute-neg-frac2 70.0%

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

      5. neg-sub0 70.0%

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

      6. associate--r- 70.0%

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

      7. metadata-eval 70.0%

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

   5. Simplified 70.0%

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

   if -1.45000000000000007e91 < t < -0.00160000000000000008 or -1.5e-86 < t < 8.8000000000000005e119

   1. Initial program 90.8%

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

      1. clear-num 90.5%

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

      2. frac-sub 75.4%

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

      3. *-un-lft-identity 75.4%

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

   4. Applied egg-rr 75.4%

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

      1. div-sub 68.4%

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

      2. times-frac 70.7%

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

      3. *-inverses 86.4%

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

      4. *-lft-identity 86.4%

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

      5. remove-double-neg 86.4%

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

      6. distribute-frac-neg 86.4%

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

      7. *-rgt-identity 86.4%

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

      8. distribute-lft-neg-in 86.4%

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

      9. cancel-sign-sub 86.4%

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

      10. *-commutative 86.4%

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

      11. associate-/r* 90.5%

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

      12. *-inverses 90.5%

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

      13. *-rgt-identity 90.5%

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

      14. distribute-frac-neg 90.5%

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

      15. distribute-neg-frac2 90.5%

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

      16. neg-sub0 90.5%

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

      17. associate--r- 90.5%

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

      18. metadata-eval 90.5%

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

   6. Simplified 90.5%

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

   7. Taylor expanded in z around 0 76.1%

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

      1. associate-*l/ 79.6%

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

      2. *-commutative 79.6%

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

   9. Simplified 79.6%

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

   if -7.49999999999999933e-9 < t < -1.5e-86

   1. Initial program 98.7%

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

   3. Taylor expanded in y around inf 87.4%

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

      1. associate-*r/ 92.5%

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

   5. Simplified 92.5%

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

4. Final simplification 77.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.45 \cdot 10^{+91}:\\ \;\;\;\;t \cdot \frac{x}{z + -1}\\ \mathbf{elif}\;t \leq -0.0016:\\ \;\;\;\;y \cdot \frac{x}{z}\\ \mathbf{elif}\;t \leq -7.5 \cdot 10^{-9}:\\ \;\;\;\;t \cdot \frac{x}{z + -1}\\ \mathbf{elif}\;t \leq -1.5 \cdot 10^{-86}:\\ \;\;\;\;\frac{y}{z} \cdot x\\ \mathbf{elif}\;t \leq 8.8 \cdot 10^{+119}:\\ \;\;\;\;y \cdot \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{x}{z + -1}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 89.8% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x \cdot \left(y - z \cdot t\right)}{z}\\ \mathbf{if}\;z \leq -1020000:\\ \;\;\;\;\frac{x \cdot \left(y + t\right)}{z}\\ \mathbf{elif}\;z \leq -3.8 \cdot 10^{-248}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 10^{-283}:\\ \;\;\;\;x \cdot \left(\frac{y}{z} - t\right)\\ \mathbf{elif}\;z \leq 8 \cdot 10^{-8}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{z} \cdot \left(y + t\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ (* x (- y (* z t))) z)))
   (if (<= z -1020000.0)
     (/ (* x (+ y t)) z)
     (if (<= z -3.8e-248)
       t_1
       (if (<= z 1e-283)
         (* x (- (/ y z) t))
         (if (<= z 8e-8) t_1 (* (/ x z) (+ y t))))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (x * (y - (z * t))) / z;
	double tmp;
	if (z <= -1020000.0) {
		tmp = (x * (y + t)) / z;
	} else if (z <= -3.8e-248) {
		tmp = t_1;
	} else if (z <= 1e-283) {
		tmp = x * ((y / z) - t);
	} else if (z <= 8e-8) {
		tmp = t_1;
	} else {
		tmp = (x / z) * (y + t);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (x * (y - (z * t))) / z
    if (z <= (-1020000.0d0)) then
        tmp = (x * (y + t)) / z
    else if (z <= (-3.8d-248)) then
        tmp = t_1
    else if (z <= 1d-283) then
        tmp = x * ((y / z) - t)
    else if (z <= 8d-8) then
        tmp = t_1
    else
        tmp = (x / z) * (y + t)
    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))) / z;
	double tmp;
	if (z <= -1020000.0) {
		tmp = (x * (y + t)) / z;
	} else if (z <= -3.8e-248) {
		tmp = t_1;
	} else if (z <= 1e-283) {
		tmp = x * ((y / z) - t);
	} else if (z <= 8e-8) {
		tmp = t_1;
	} else {
		tmp = (x / z) * (y + t);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (x * (y - (z * t))) / z
	tmp = 0
	if z <= -1020000.0:
		tmp = (x * (y + t)) / z
	elif z <= -3.8e-248:
		tmp = t_1
	elif z <= 1e-283:
		tmp = x * ((y / z) - t)
	elif z <= 8e-8:
		tmp = t_1
	else:
		tmp = (x / z) * (y + t)
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(x * Float64(y - Float64(z * t))) / z)
	tmp = 0.0
	if (z <= -1020000.0)
		tmp = Float64(Float64(x * Float64(y + t)) / z);
	elseif (z <= -3.8e-248)
		tmp = t_1;
	elseif (z <= 1e-283)
		tmp = Float64(x * Float64(Float64(y / z) - t));
	elseif (z <= 8e-8)
		tmp = t_1;
	else
		tmp = Float64(Float64(x / z) * Float64(y + t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (x * (y - (z * t))) / z;
	tmp = 0.0;
	if (z <= -1020000.0)
		tmp = (x * (y + t)) / z;
	elseif (z <= -3.8e-248)
		tmp = t_1;
	elseif (z <= 1e-283)
		tmp = x * ((y / z) - t);
	elseif (z <= 8e-8)
		tmp = t_1;
	else
		tmp = (x / z) * (y + t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(x * N[(y - N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]}, If[LessEqual[z, -1020000.0], N[(N[(x * N[(y + t), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision], If[LessEqual[z, -3.8e-248], t$95$1, If[LessEqual[z, 1e-283], N[(x * N[(N[(y / z), $MachinePrecision] - t), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 8e-8], t$95$1, N[(N[(x / z), $MachinePrecision] * N[(y + t), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -1.02e6

   1. Initial program 94.5%

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

      1. clear-num 92.7%

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

      2. frac-sub 52.5%

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

      3. *-un-lft-identity 52.5%

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

   4. Applied egg-rr 52.5%

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

      1. div-sub 52.5%

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

      2. times-frac 62.1%

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

      3. *-inverses 87.0%

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

      4. *-lft-identity 87.0%

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

      5. remove-double-neg 87.0%

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

      6. distribute-frac-neg 87.0%

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

      7. *-rgt-identity 87.0%

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

      8. distribute-lft-neg-in 87.0%

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

      9. cancel-sign-sub 87.0%

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

      10. *-commutative 87.0%

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

      11. associate-/r* 92.7%

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

      12. *-inverses 92.7%

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

      13. *-rgt-identity 92.7%

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

      14. distribute-frac-neg 92.7%

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

      15. distribute-neg-frac2 92.7%

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

      16. neg-sub0 92.7%

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

      17. associate--r- 92.7%

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

      18. metadata-eval 92.7%

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

   6. Simplified 92.7%

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

   7. Taylor expanded in z around inf 91.0%

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

   if -1.02e6 < z < -3.7999999999999999e-248 or 9.99999999999999947e-284 < z < 8.0000000000000002e-8

   1. Initial program 88.8%

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

      1. clear-num 88.7%

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

      2. frac-sub 86.9%

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

      3. *-un-lft-identity 86.9%

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

   4. Applied egg-rr 86.9%

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

      1. div-sub 74.7%

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

      2. times-frac 76.5%

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

      3. *-inverses 88.7%

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

      4. *-lft-identity 88.7%

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

      5. remove-double-neg 88.7%

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

      6. distribute-frac-neg 88.7%

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

      7. *-rgt-identity 88.7%

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

      8. distribute-lft-neg-in 88.7%

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

      9. cancel-sign-sub 88.7%

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

      10. *-commutative 88.7%

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

      11. associate-/r* 88.7%

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

      12. *-inverses 88.7%

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

      13. *-rgt-identity 88.7%

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

      14. distribute-frac-neg 88.7%

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

      15. distribute-neg-frac2 88.7%

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

      16. neg-sub0 88.7%

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

      17. associate--r- 88.7%

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

      18. metadata-eval 88.7%

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

   6. Simplified 88.7%

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

      1. clear-num 88.7%

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

      2. inv-pow 88.7%

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

      3. +-commutative 88.7%

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

   8. Applied egg-rr 88.7%

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

      1. unpow-1 88.7%

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

   10. Simplified 88.7%

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

   11. Taylor expanded in z around 0 90.9%

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

       1. +-commutative 90.9%

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

       2. mul-1-neg 90.9%

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

       3. *-commutative 90.9%

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

       4. *-commutative 90.9%

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

       5. associate-*r* 89.1%

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

       6. *-commutative 89.1%

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

       7. distribute-rgt-neg-out 89.1%

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

       8. associate-*l* 93.9%

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

       9. distribute-rgt-neg-in 93.9%

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

       10. mul-1-neg 93.9%

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

       11. distribute-lft-out 93.9%

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

       12. mul-1-neg 93.9%

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

       13. unsub-neg 93.9%

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

   13. Simplified 93.9%

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

   if -3.7999999999999999e-248 < z < 9.99999999999999947e-284

   1. Initial program 92.7%

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

   3. Taylor expanded in z around 0 92.5%

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

      1. mul-1-neg 92.5%

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

      2. unsub-neg 92.5%

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

      3. div-sub 92.5%

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

      4. associate-/l* 92.7%

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

      5. *-inverses 92.7%

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

      6. *-rgt-identity 92.7%

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

   5. Simplified 92.7%

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

   if 8.0000000000000002e-8 < z

   1. Initial program 97.1%

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

   3. Taylor expanded in z around inf 83.2%

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

      1. *-commutative 83.2%

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

      2. associate-/l* 86.4%

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

      3. cancel-sign-sub-inv 86.4%

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

      4. metadata-eval 86.4%

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

      5. *-lft-identity 86.4%

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

      6. +-commutative 86.4%

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

   5. Simplified 86.4%

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

4. Final simplification 91.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1020000:\\ \;\;\;\;\frac{x \cdot \left(y + t\right)}{z}\\ \mathbf{elif}\;z \leq -3.8 \cdot 10^{-248}:\\ \;\;\;\;\frac{x \cdot \left(y - z \cdot t\right)}{z}\\ \mathbf{elif}\;z \leq 10^{-283}:\\ \;\;\;\;x \cdot \left(\frac{y}{z} - t\right)\\ \mathbf{elif}\;z \leq 8 \cdot 10^{-8}:\\ \;\;\;\;\frac{x \cdot \left(y - z \cdot t\right)}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{z} \cdot \left(y + t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 87.1% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(\frac{y}{z} - t\right)\\ \mathbf{if}\;z \leq -1020000:\\ \;\;\;\;\frac{x \cdot \left(y + t\right)}{z}\\ \mathbf{elif}\;z \leq 3 \cdot 10^{-302}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 6.2 \cdot 10^{-149}:\\ \;\;\;\;y \cdot \frac{x}{z}\\ \mathbf{elif}\;z \leq 1.3 \cdot 10^{-7}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{z} \cdot \left(y + t\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* x (- (/ y z) t))))
   (if (<= z -1020000.0)
     (/ (* x (+ y t)) z)
     (if (<= z 3e-302)
       t_1
       (if (<= z 6.2e-149)
         (* y (/ x z))
         (if (<= z 1.3e-7) t_1 (* (/ x z) (+ y t))))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x * ((y / z) - t);
	double tmp;
	if (z <= -1020000.0) {
		tmp = (x * (y + t)) / z;
	} else if (z <= 3e-302) {
		tmp = t_1;
	} else if (z <= 6.2e-149) {
		tmp = y * (x / z);
	} else if (z <= 1.3e-7) {
		tmp = t_1;
	} else {
		tmp = (x / z) * (y + t);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x * ((y / z) - t)
    if (z <= (-1020000.0d0)) then
        tmp = (x * (y + t)) / z
    else if (z <= 3d-302) then
        tmp = t_1
    else if (z <= 6.2d-149) then
        tmp = y * (x / z)
    else if (z <= 1.3d-7) then
        tmp = t_1
    else
        tmp = (x / z) * (y + t)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = x * ((y / z) - t);
	double tmp;
	if (z <= -1020000.0) {
		tmp = (x * (y + t)) / z;
	} else if (z <= 3e-302) {
		tmp = t_1;
	} else if (z <= 6.2e-149) {
		tmp = y * (x / z);
	} else if (z <= 1.3e-7) {
		tmp = t_1;
	} else {
		tmp = (x / z) * (y + t);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x * ((y / z) - t)
	tmp = 0
	if z <= -1020000.0:
		tmp = (x * (y + t)) / z
	elif z <= 3e-302:
		tmp = t_1
	elif z <= 6.2e-149:
		tmp = y * (x / z)
	elif z <= 1.3e-7:
		tmp = t_1
	else:
		tmp = (x / z) * (y + t)
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x * Float64(Float64(y / z) - t))
	tmp = 0.0
	if (z <= -1020000.0)
		tmp = Float64(Float64(x * Float64(y + t)) / z);
	elseif (z <= 3e-302)
		tmp = t_1;
	elseif (z <= 6.2e-149)
		tmp = Float64(y * Float64(x / z));
	elseif (z <= 1.3e-7)
		tmp = t_1;
	else
		tmp = Float64(Float64(x / z) * Float64(y + t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x * ((y / z) - t);
	tmp = 0.0;
	if (z <= -1020000.0)
		tmp = (x * (y + t)) / z;
	elseif (z <= 3e-302)
		tmp = t_1;
	elseif (z <= 6.2e-149)
		tmp = y * (x / z);
	elseif (z <= 1.3e-7)
		tmp = t_1;
	else
		tmp = (x / z) * (y + t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x * N[(N[(y / z), $MachinePrecision] - t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1020000.0], N[(N[(x * N[(y + t), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision], If[LessEqual[z, 3e-302], t$95$1, If[LessEqual[z, 6.2e-149], N[(y * N[(x / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.3e-7], t$95$1, N[(N[(x / z), $MachinePrecision] * N[(y + t), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -1.02e6

   1. Initial program 94.5%

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

      1. clear-num 92.7%

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

      2. frac-sub 52.5%

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

      3. *-un-lft-identity 52.5%

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

   4. Applied egg-rr 52.5%

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

      1. div-sub 52.5%

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

      2. times-frac 62.1%

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

      3. *-inverses 87.0%

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

      4. *-lft-identity 87.0%

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

      5. remove-double-neg 87.0%

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

      6. distribute-frac-neg 87.0%

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

      7. *-rgt-identity 87.0%

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

      8. distribute-lft-neg-in 87.0%

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

      9. cancel-sign-sub 87.0%

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

      10. *-commutative 87.0%

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

      11. associate-/r* 92.7%

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

      12. *-inverses 92.7%

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

      13. *-rgt-identity 92.7%

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

      14. distribute-frac-neg 92.7%

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

      15. distribute-neg-frac2 92.7%

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

      16. neg-sub0 92.7%

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

      17. associate--r- 92.7%

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

      18. metadata-eval 92.7%

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

   6. Simplified 92.7%

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

   7. Taylor expanded in z around inf 91.0%

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

   if -1.02e6 < z < 2.99999999999999989e-302 or 6.19999999999999974e-149 < z < 1.29999999999999999e-7

   1. Initial program 92.2%

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

   3. Taylor expanded in z around 0 91.6%

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

      1. mul-1-neg 91.6%

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

      2. unsub-neg 91.6%

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

      3. div-sub 91.6%

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

      4. associate-/l* 91.6%

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

      5. *-inverses 91.6%

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

      6. *-rgt-identity 91.6%

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

   5. Simplified 91.6%

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

   if 2.99999999999999989e-302 < z < 6.19999999999999974e-149

   1. Initial program 81.9%

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

      1. clear-num 81.8%

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

      2. frac-sub 81.8%

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

      3. *-un-lft-identity 81.8%

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

   4. Applied egg-rr 81.8%

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

      1. div-sub 55.9%

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

      2. times-frac 55.9%

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

      3. *-inverses 81.8%

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

      4. *-lft-identity 81.8%

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

      5. remove-double-neg 81.8%

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

      6. distribute-frac-neg 81.8%

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

      7. *-rgt-identity 81.8%

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

      8. distribute-lft-neg-in 81.8%

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

      9. cancel-sign-sub 81.8%

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

      10. *-commutative 81.8%

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

      11. associate-/r* 81.8%

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

      12. *-inverses 81.8%

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

      13. *-rgt-identity 81.8%

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

      14. distribute-frac-neg 81.8%

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

      15. distribute-neg-frac2 81.8%

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

      16. neg-sub0 81.8%

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

      17. associate--r- 81.8%

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

      18. metadata-eval 81.8%

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

   6. Simplified 81.8%

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

   7. Taylor expanded in z around 0 79.6%

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

      1. associate-*l/ 94.4%

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

      2. *-commutative 94.4%

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

   9. Simplified 94.4%

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

   if 1.29999999999999999e-7 < z

   1. Initial program 97.0%

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

   3. Taylor expanded in z around inf 84.2%

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

      1. *-commutative 84.2%

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

      2. associate-/l* 87.5%

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

      3. cancel-sign-sub-inv 87.5%

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

      4. metadata-eval 87.5%

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

      5. *-lft-identity 87.5%

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

      6. +-commutative 87.5%

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

   5. Simplified 87.5%

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

4. Final simplification 90.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1020000:\\ \;\;\;\;\frac{x \cdot \left(y + t\right)}{z}\\ \mathbf{elif}\;z \leq 3 \cdot 10^{-302}:\\ \;\;\;\;x \cdot \left(\frac{y}{z} - t\right)\\ \mathbf{elif}\;z \leq 6.2 \cdot 10^{-149}:\\ \;\;\;\;y \cdot \frac{x}{z}\\ \mathbf{elif}\;z \leq 1.3 \cdot 10^{-7}:\\ \;\;\;\;x \cdot \left(\frac{y}{z} - t\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{z} \cdot \left(y + t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 87.2% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(\frac{y}{z} - t\right)\\ t_2 := \frac{x}{z} \cdot \left(y + t\right)\\ \mathbf{if}\;z \leq -1020000:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;z \leq 2.9 \cdot 10^{-296}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 6.2 \cdot 10^{-149}:\\ \;\;\;\;y \cdot \frac{x}{z}\\ \mathbf{elif}\;z \leq 1.3 \cdot 10^{-7}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* x (- (/ y z) t))) (t_2 (* (/ x z) (+ y t))))
   (if (<= z -1020000.0)
     t_2
     (if (<= z 2.9e-296)
       t_1
       (if (<= z 6.2e-149) (* y (/ x z)) (if (<= z 1.3e-7) t_1 t_2))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x * ((y / z) - t);
	double t_2 = (x / z) * (y + t);
	double tmp;
	if (z <= -1020000.0) {
		tmp = t_2;
	} else if (z <= 2.9e-296) {
		tmp = t_1;
	} else if (z <= 6.2e-149) {
		tmp = y * (x / z);
	} else if (z <= 1.3e-7) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = x * ((y / z) - t)
    t_2 = (x / z) * (y + t)
    if (z <= (-1020000.0d0)) then
        tmp = t_2
    else if (z <= 2.9d-296) then
        tmp = t_1
    else if (z <= 6.2d-149) then
        tmp = y * (x / z)
    else if (z <= 1.3d-7) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = x * ((y / z) - t);
	double t_2 = (x / z) * (y + t);
	double tmp;
	if (z <= -1020000.0) {
		tmp = t_2;
	} else if (z <= 2.9e-296) {
		tmp = t_1;
	} else if (z <= 6.2e-149) {
		tmp = y * (x / z);
	} else if (z <= 1.3e-7) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x * ((y / z) - t)
	t_2 = (x / z) * (y + t)
	tmp = 0
	if z <= -1020000.0:
		tmp = t_2
	elif z <= 2.9e-296:
		tmp = t_1
	elif z <= 6.2e-149:
		tmp = y * (x / z)
	elif z <= 1.3e-7:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x * Float64(Float64(y / z) - t))
	t_2 = Float64(Float64(x / z) * Float64(y + t))
	tmp = 0.0
	if (z <= -1020000.0)
		tmp = t_2;
	elseif (z <= 2.9e-296)
		tmp = t_1;
	elseif (z <= 6.2e-149)
		tmp = Float64(y * Float64(x / z));
	elseif (z <= 1.3e-7)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x * ((y / z) - t);
	t_2 = (x / z) * (y + t);
	tmp = 0.0;
	if (z <= -1020000.0)
		tmp = t_2;
	elseif (z <= 2.9e-296)
		tmp = t_1;
	elseif (z <= 6.2e-149)
		tmp = y * (x / z);
	elseif (z <= 1.3e-7)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x * N[(N[(y / z), $MachinePrecision] - t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x / z), $MachinePrecision] * N[(y + t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1020000.0], t$95$2, If[LessEqual[z, 2.9e-296], t$95$1, If[LessEqual[z, 6.2e-149], N[(y * N[(x / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.3e-7], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.02e6 or 1.29999999999999999e-7 < z

   1. Initial program 95.8%

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

   3. Taylor expanded in z around inf 87.6%

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

      1. *-commutative 87.6%

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

      2. associate-/l* 88.9%

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

      3. cancel-sign-sub-inv 88.9%

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

      4. metadata-eval 88.9%

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

      5. *-lft-identity 88.9%

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

      6. +-commutative 88.9%

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

   5. Simplified 88.9%

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

   if -1.02e6 < z < 2.89999999999999983e-296 or 6.19999999999999974e-149 < z < 1.29999999999999999e-7

   1. Initial program 92.3%

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

   3. Taylor expanded in z around 0 91.7%

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

      1. mul-1-neg 91.7%

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

      2. unsub-neg 91.7%

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

      3. div-sub 91.7%

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

      4. associate-/l* 91.7%

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

      5. *-inverses 91.7%

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

      6. *-rgt-identity 91.7%

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

   5. Simplified 91.7%

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

   if 2.89999999999999983e-296 < z < 6.19999999999999974e-149

   1. Initial program 81.3%

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

      1. clear-num 81.2%

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

      2. frac-sub 81.2%

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

      3. *-un-lft-identity 81.2%

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

   4. Applied egg-rr 81.2%

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

      1. div-sub 54.5%

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

      2. times-frac 54.5%

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

      3. *-inverses 81.2%

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

      4. *-lft-identity 81.2%

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

      5. remove-double-neg 81.2%

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

      6. distribute-frac-neg 81.2%

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

      7. *-rgt-identity 81.2%

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

      8. distribute-lft-neg-in 81.2%

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

      9. cancel-sign-sub 81.2%

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

      10. *-commutative 81.2%

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

      11. associate-/r* 81.2%

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

      12. *-inverses 81.2%

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

      13. *-rgt-identity 81.2%

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

      14. distribute-frac-neg 81.2%

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

      15. distribute-neg-frac2 81.2%

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

      16. neg-sub0 81.2%

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

      17. associate--r- 81.2%

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

      18. metadata-eval 81.2%

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

   6. Simplified 81.2%

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

   7. Taylor expanded in z around 0 82.1%

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

      1. associate-*l/ 94.3%

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

      2. *-commutative 94.3%

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

   9. Simplified 94.3%

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

4. Final simplification 90.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1020000:\\ \;\;\;\;\frac{x}{z} \cdot \left(y + t\right)\\ \mathbf{elif}\;z \leq 2.9 \cdot 10^{-296}:\\ \;\;\;\;x \cdot \left(\frac{y}{z} - t\right)\\ \mathbf{elif}\;z \leq 6.2 \cdot 10^{-149}:\\ \;\;\;\;y \cdot \frac{x}{z}\\ \mathbf{elif}\;z \leq 1.3 \cdot 10^{-7}:\\ \;\;\;\;x \cdot \left(\frac{y}{z} - t\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{z} \cdot \left(y + t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 74.9% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \frac{x}{z}\\ t_2 := x \cdot \frac{t}{z + -1}\\ \mathbf{if}\;t \leq -1.65 \cdot 10^{+92}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t \leq -4.6 \cdot 10^{+22}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq -4.8 \cdot 10^{-70}:\\ \;\;\;\;\frac{y \cdot x}{z}\\ \mathbf{elif}\;t \leq 1.85 \cdot 10^{+31}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* y (/ x z))) (t_2 (* x (/ t (+ z -1.0)))))
   (if (<= t -1.65e+92)
     t_2
     (if (<= t -4.6e+22)
       t_1
       (if (<= t -4.8e-70) (/ (* y x) z) (if (<= t 1.85e+31) t_1 t_2))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = y * (x / z);
	double t_2 = x * (t / (z + -1.0));
	double tmp;
	if (t <= -1.65e+92) {
		tmp = t_2;
	} else if (t <= -4.6e+22) {
		tmp = t_1;
	} else if (t <= -4.8e-70) {
		tmp = (y * x) / z;
	} else if (t <= 1.85e+31) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = y * (x / z)
    t_2 = x * (t / (z + (-1.0d0)))
    if (t <= (-1.65d+92)) then
        tmp = t_2
    else if (t <= (-4.6d+22)) then
        tmp = t_1
    else if (t <= (-4.8d-70)) then
        tmp = (y * x) / z
    else if (t <= 1.85d+31) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = y * (x / z);
	double t_2 = x * (t / (z + -1.0));
	double tmp;
	if (t <= -1.65e+92) {
		tmp = t_2;
	} else if (t <= -4.6e+22) {
		tmp = t_1;
	} else if (t <= -4.8e-70) {
		tmp = (y * x) / z;
	} else if (t <= 1.85e+31) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = y * (x / z)
	t_2 = x * (t / (z + -1.0))
	tmp = 0
	if t <= -1.65e+92:
		tmp = t_2
	elif t <= -4.6e+22:
		tmp = t_1
	elif t <= -4.8e-70:
		tmp = (y * x) / z
	elif t <= 1.85e+31:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(y * Float64(x / z))
	t_2 = Float64(x * Float64(t / Float64(z + -1.0)))
	tmp = 0.0
	if (t <= -1.65e+92)
		tmp = t_2;
	elseif (t <= -4.6e+22)
		tmp = t_1;
	elseif (t <= -4.8e-70)
		tmp = Float64(Float64(y * x) / z);
	elseif (t <= 1.85e+31)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = y * (x / z);
	t_2 = x * (t / (z + -1.0));
	tmp = 0.0;
	if (t <= -1.65e+92)
		tmp = t_2;
	elseif (t <= -4.6e+22)
		tmp = t_1;
	elseif (t <= -4.8e-70)
		tmp = (y * x) / z;
	elseif (t <= 1.85e+31)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(y * N[(x / z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x * N[(t / N[(z + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -1.65e+92], t$95$2, If[LessEqual[t, -4.6e+22], t$95$1, If[LessEqual[t, -4.8e-70], N[(N[(y * x), $MachinePrecision] / z), $MachinePrecision], If[LessEqual[t, 1.85e+31], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if t < -1.64999999999999987e92 or 1.8499999999999999e31 < t

   1. Initial program 95.6%

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

   3. Taylor expanded in y around 0 68.8%

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

      1. mul-1-neg 68.8%

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

      2. distribute-neg-frac2 68.8%

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

      3. neg-sub0 68.8%

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

      4. associate--r- 68.8%

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

      5. metadata-eval 68.8%

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

   5. Simplified 68.8%

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

   if -1.64999999999999987e92 < t < -4.6000000000000004e22 or -4.8000000000000002e-70 < t < 1.8499999999999999e31

   1. Initial program 90.8%

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

      1. clear-num 90.4%

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

      2. frac-sub 77.3%

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

      3. *-un-lft-identity 77.3%

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

   4. Applied egg-rr 77.3%

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

      1. div-sub 70.8%

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

      2. times-frac 70.7%

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

      3. *-inverses 85.8%

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

      4. *-lft-identity 85.8%

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

      5. remove-double-neg 85.8%

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

      6. distribute-frac-neg 85.8%

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

      7. *-rgt-identity 85.8%

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

      8. distribute-lft-neg-in 85.8%

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

      9. cancel-sign-sub 85.8%

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

      10. *-commutative 85.8%

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

      11. associate-/r* 90.4%

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

      12. *-inverses 90.4%

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

      13. *-rgt-identity 90.4%

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

      14. distribute-frac-neg 90.4%

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

      15. distribute-neg-frac2 90.4%

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

      16. neg-sub0 90.4%

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

      17. associate--r- 90.4%

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

      18. metadata-eval 90.4%

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

   6. Simplified 90.4%

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

   7. Taylor expanded in z around 0 80.4%

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

      1. associate-*l/ 83.7%

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

      2. *-commutative 83.7%

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

   9. Simplified 83.7%

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

   if -4.6000000000000004e22 < t < -4.8000000000000002e-70

   1. Initial program 94.3%

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

   3. Taylor expanded in y around inf 82.4%

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

4. Final simplification 78.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.65 \cdot 10^{+92}:\\ \;\;\;\;x \cdot \frac{t}{z + -1}\\ \mathbf{elif}\;t \leq -4.6 \cdot 10^{+22}:\\ \;\;\;\;y \cdot \frac{x}{z}\\ \mathbf{elif}\;t \leq -4.8 \cdot 10^{-70}:\\ \;\;\;\;\frac{y \cdot x}{z}\\ \mathbf{elif}\;t \leq 1.85 \cdot 10^{+31}:\\ \;\;\;\;y \cdot \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{t}{z + -1}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 41.2% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1020000 \lor \neg \left(z \leq -2.6 \cdot 10^{-122}\right) \land \left(z \leq -2.3 \cdot 10^{-261} \lor \neg \left(z \leq 0.033\right)\right):\\ \;\;\;\;t \cdot \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(-t\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -1020000.0)
         (and (not (<= z -2.6e-122)) (or (<= z -2.3e-261) (not (<= z 0.033)))))
   (* t (/ x z))
   (* x (- t))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -1020000.0) || (!(z <= -2.6e-122) && ((z <= -2.3e-261) || !(z <= 0.033)))) {
		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 <= (-1020000.0d0)) .or. (.not. (z <= (-2.6d-122))) .and. (z <= (-2.3d-261)) .or. (.not. (z <= 0.033d0))) 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 <= -1020000.0) || (!(z <= -2.6e-122) && ((z <= -2.3e-261) || !(z <= 0.033)))) {
		tmp = t * (x / z);
	} else {
		tmp = x * -t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -1020000.0) or (not (z <= -2.6e-122) and ((z <= -2.3e-261) or not (z <= 0.033))):
		tmp = t * (x / z)
	else:
		tmp = x * -t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -1020000.0) || (!(z <= -2.6e-122) && ((z <= -2.3e-261) || !(z <= 0.033))))
		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 <= -1020000.0) || (~((z <= -2.6e-122)) && ((z <= -2.3e-261) || ~((z <= 0.033)))))
		tmp = t * (x / z);
	else
		tmp = x * -t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -1020000.0], And[N[Not[LessEqual[z, -2.6e-122]], $MachinePrecision], Or[LessEqual[z, -2.3e-261], N[Not[LessEqual[z, 0.033]], $MachinePrecision]]]], N[(t * N[(x / z), $MachinePrecision]), $MachinePrecision], N[(x * (-t)), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.02e6 or -2.59999999999999975e-122 < z < -2.3e-261 or 0.033000000000000002 < z

   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 inf 84.1%

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

   4. Taylor expanded in y around 0 44.9%

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

      1. associate-/l* 45.8%

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

   6. Simplified 45.8%

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

   if -1.02e6 < z < -2.59999999999999975e-122 or -2.3e-261 < z < 0.033000000000000002

   1. Initial program 90.4%

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

   3. Taylor expanded in z around 0 89.4%

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

      1. mul-1-neg 89.4%

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

      2. unsub-neg 89.4%

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

      3. div-sub 89.4%

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

      4. associate-/l* 89.4%

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

      5. *-inverses 89.4%

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

      6. *-rgt-identity 89.4%

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

   5. Simplified 89.4%

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

   6. Taylor expanded in y around 0 30.5%

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

      1. mul-1-neg 30.5%

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

      2. *-commutative 30.5%

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

      3. distribute-rgt-neg-in 30.5%

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

   8. Simplified 30.5%

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

4. Final simplification 40.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1020000 \lor \neg \left(z \leq -2.6 \cdot 10^{-122}\right) \land \left(z \leq -2.3 \cdot 10^{-261} \lor \neg \left(z \leq 0.033\right)\right):\\ \;\;\;\;t \cdot \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(-t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 43.2% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \frac{t}{z}\\ t_2 := x \cdot \left(-t\right)\\ \mathbf{if}\;z \leq -1060000:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -3.5 \cdot 10^{-122}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;z \leq 3 \cdot 10^{-218}:\\ \;\;\;\;t \cdot \frac{x}{z}\\ \mathbf{elif}\;z \leq 8 \cdot 10^{-8}:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* x (/ t z))) (t_2 (* x (- t))))
   (if (<= z -1060000.0)
     t_1
     (if (<= z -3.5e-122)
       t_2
       (if (<= z 3e-218) (* t (/ x z)) (if (<= z 8e-8) t_2 t_1))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x * (t / z);
	double t_2 = x * -t;
	double tmp;
	if (z <= -1060000.0) {
		tmp = t_1;
	} else if (z <= -3.5e-122) {
		tmp = t_2;
	} else if (z <= 3e-218) {
		tmp = t * (x / z);
	} else if (z <= 8e-8) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = x * (t / z)
    t_2 = x * -t
    if (z <= (-1060000.0d0)) then
        tmp = t_1
    else if (z <= (-3.5d-122)) then
        tmp = t_2
    else if (z <= 3d-218) then
        tmp = t * (x / z)
    else if (z <= 8d-8) then
        tmp = t_2
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = x * (t / z);
	double t_2 = x * -t;
	double tmp;
	if (z <= -1060000.0) {
		tmp = t_1;
	} else if (z <= -3.5e-122) {
		tmp = t_2;
	} else if (z <= 3e-218) {
		tmp = t * (x / z);
	} else if (z <= 8e-8) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x * (t / z)
	t_2 = x * -t
	tmp = 0
	if z <= -1060000.0:
		tmp = t_1
	elif z <= -3.5e-122:
		tmp = t_2
	elif z <= 3e-218:
		tmp = t * (x / z)
	elif z <= 8e-8:
		tmp = t_2
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x * Float64(t / z))
	t_2 = Float64(x * Float64(-t))
	tmp = 0.0
	if (z <= -1060000.0)
		tmp = t_1;
	elseif (z <= -3.5e-122)
		tmp = t_2;
	elseif (z <= 3e-218)
		tmp = Float64(t * Float64(x / z));
	elseif (z <= 8e-8)
		tmp = t_2;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x * (t / z);
	t_2 = x * -t;
	tmp = 0.0;
	if (z <= -1060000.0)
		tmp = t_1;
	elseif (z <= -3.5e-122)
		tmp = t_2;
	elseif (z <= 3e-218)
		tmp = t * (x / z);
	elseif (z <= 8e-8)
		tmp = t_2;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x * N[(t / z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x * (-t)), $MachinePrecision]}, If[LessEqual[z, -1060000.0], t$95$1, If[LessEqual[z, -3.5e-122], t$95$2, If[LessEqual[z, 3e-218], N[(t * N[(x / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 8e-8], t$95$2, t$95$1]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.06e6 or 8.0000000000000002e-8 < z

   1. Initial program 95.8%

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

   3. Taylor expanded in z around inf 87.1%

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

   4. Taylor expanded in y around 0 48.7%

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

      1. *-commutative 48.7%

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

      2. *-lft-identity 48.7%

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

      3. times-frac 51.4%

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

      4. /-rgt-identity 51.4%

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

   6. Simplified 51.4%

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

   if -1.06e6 < z < -3.5000000000000001e-122 or 2.9999999999999998e-218 < z < 8.0000000000000002e-8

   1. Initial program 90.7%

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

   3. Taylor expanded in z around 0 89.9%

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

      1. mul-1-neg 89.9%

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

      2. unsub-neg 89.9%

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

      3. div-sub 89.9%

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

      4. associate-/l* 90.0%

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

      5. *-inverses 90.0%

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

      6. *-rgt-identity 90.0%

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

   5. Simplified 90.0%

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

   6. Taylor expanded in y around 0 34.3%

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

      1. mul-1-neg 34.3%

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

      2. *-commutative 34.3%

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

      3. distribute-rgt-neg-in 34.3%

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

   8. Simplified 34.3%

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

   if -3.5000000000000001e-122 < z < 2.9999999999999998e-218

   1. Initial program 87.4%

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

   3. Taylor expanded in z around inf 64.4%

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

   4. Taylor expanded in y around 0 19.7%

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

      1. associate-/l* 21.4%

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

   6. Simplified 21.4%

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

Alternative 10: 68.7% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -5.3 \cdot 10^{+155}:\\ \;\;\;\;\frac{x}{\frac{z}{t}}\\ \mathbf{elif}\;t \leq -2.6 \cdot 10^{-36}:\\ \;\;\;\;y \cdot \frac{x}{z}\\ \mathbf{elif}\;t \leq 1.3 \cdot 10^{+90}:\\ \;\;\;\;\frac{y}{z} \cdot x\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{t}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= t -5.3e+155)
   (/ x (/ z t))
   (if (<= t -2.6e-36)
     (* y (/ x z))
     (if (<= t 1.3e+90) (* (/ y z) x) (* x (/ t z))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= -5.3e+155) {
		tmp = x / (z / t);
	} else if (t <= -2.6e-36) {
		tmp = y * (x / z);
	} else if (t <= 1.3e+90) {
		tmp = (y / z) * x;
	} else {
		tmp = x * (t / z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (t <= (-5.3d+155)) then
        tmp = x / (z / t)
    else if (t <= (-2.6d-36)) then
        tmp = y * (x / z)
    else if (t <= 1.3d+90) then
        tmp = (y / z) * x
    else
        tmp = x * (t / z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= -5.3e+155) {
		tmp = x / (z / t);
	} else if (t <= -2.6e-36) {
		tmp = y * (x / z);
	} else if (t <= 1.3e+90) {
		tmp = (y / z) * x;
	} else {
		tmp = x * (t / z);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if t <= -5.3e+155:
		tmp = x / (z / t)
	elif t <= -2.6e-36:
		tmp = y * (x / z)
	elif t <= 1.3e+90:
		tmp = (y / z) * x
	else:
		tmp = x * (t / z)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (t <= -5.3e+155)
		tmp = Float64(x / Float64(z / t));
	elseif (t <= -2.6e-36)
		tmp = Float64(y * Float64(x / z));
	elseif (t <= 1.3e+90)
		tmp = Float64(Float64(y / z) * x);
	else
		tmp = Float64(x * Float64(t / z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (t <= -5.3e+155)
		tmp = x / (z / t);
	elseif (t <= -2.6e-36)
		tmp = y * (x / z);
	elseif (t <= 1.3e+90)
		tmp = (y / z) * x;
	else
		tmp = x * (t / z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[t, -5.3e+155], N[(x / N[(z / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -2.6e-36], N[(y * N[(x / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.3e+90], N[(N[(y / z), $MachinePrecision] * x), $MachinePrecision], N[(x * N[(t / z), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if t < -5.29999999999999965e155

   1. Initial program 90.2%

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

   3. Taylor expanded in z around inf 75.0%

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

   4. Taylor expanded in y around 0 75.0%

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

      1. *-commutative 75.0%

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

      2. *-lft-identity 75.0%

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

      3. times-frac 74.9%

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

      4. /-rgt-identity 74.9%

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

   6. Simplified 74.9%

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

      1. clear-num 74.9%

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

      2. un-div-inv 75.1%

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

   8. Applied egg-rr 75.1%

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

   if -5.29999999999999965e155 < t < -2.6e-36

   1. Initial program 89.5%

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

      1. clear-num 89.5%

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

      2. frac-sub 65.6%

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

      3. *-un-lft-identity 65.6%

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

   4. Applied egg-rr 65.6%

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

      1. div-sub 59.7%

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

      2. times-frac 67.2%

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

      3. *-inverses 86.5%

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

      4. *-lft-identity 86.5%

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

      5. remove-double-neg 86.5%

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

      6. distribute-frac-neg 86.5%

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

      7. *-rgt-identity 86.5%

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

      8. distribute-lft-neg-in 86.5%

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

      9. cancel-sign-sub 86.5%

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

      10. *-commutative 86.5%

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

      11. associate-/r* 89.5%

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

      12. *-inverses 89.5%

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

      13. *-rgt-identity 89.5%

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

      14. distribute-frac-neg 89.5%

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

      15. distribute-neg-frac2 89.5%

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

      16. neg-sub0 89.5%

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

      17. associate--r- 89.5%

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

      18. metadata-eval 89.5%

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

   6. Simplified 89.5%

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

   7. Taylor expanded in z around 0 54.2%

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

      1. associate-*l/ 59.8%

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

      2. *-commutative 59.8%

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

   9. Simplified 59.8%

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

   if -2.6e-36 < t < 1.2999999999999999e90

   1. Initial program 92.6%

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

   3. Taylor expanded in y around inf 80.0%

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

      1. associate-*r/ 82.1%

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

   5. Simplified 82.1%

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

   if 1.2999999999999999e90 < t

   1. Initial program 97.6%

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

   3. Taylor expanded in z around inf 53.8%

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

   4. Taylor expanded in y around 0 40.4%

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

      1. *-commutative 40.4%

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

      2. *-lft-identity 40.4%

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

      3. times-frac 48.9%

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

      4. /-rgt-identity 48.9%

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

   6. Simplified 48.9%

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

4. Final simplification 72.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -5.3 \cdot 10^{+155}:\\ \;\;\;\;\frac{x}{\frac{z}{t}}\\ \mathbf{elif}\;t \leq -2.6 \cdot 10^{-36}:\\ \;\;\;\;y \cdot \frac{x}{z}\\ \mathbf{elif}\;t \leq 1.3 \cdot 10^{+90}:\\ \;\;\;\;\frac{y}{z} \cdot x\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{t}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 68.7% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \frac{t}{z}\\ \mathbf{if}\;t \leq -3.6 \cdot 10^{+156}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq -1.55 \cdot 10^{-37}:\\ \;\;\;\;y \cdot \frac{x}{z}\\ \mathbf{elif}\;t \leq 1.06 \cdot 10^{+88}:\\ \;\;\;\;\frac{y}{z} \cdot x\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* x (/ t z))))
   (if (<= t -3.6e+156)
     t_1
     (if (<= t -1.55e-37)
       (* y (/ x z))
       (if (<= t 1.06e+88) (* (/ y z) x) t_1)))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x * (t / z);
	double tmp;
	if (t <= -3.6e+156) {
		tmp = t_1;
	} else if (t <= -1.55e-37) {
		tmp = y * (x / z);
	} else if (t <= 1.06e+88) {
		tmp = (y / z) * x;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x * (t / z)
    if (t <= (-3.6d+156)) then
        tmp = t_1
    else if (t <= (-1.55d-37)) then
        tmp = y * (x / z)
    else if (t <= 1.06d+88) then
        tmp = (y / z) * x
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = x * (t / z);
	double tmp;
	if (t <= -3.6e+156) {
		tmp = t_1;
	} else if (t <= -1.55e-37) {
		tmp = y * (x / z);
	} else if (t <= 1.06e+88) {
		tmp = (y / z) * x;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x * (t / z)
	tmp = 0
	if t <= -3.6e+156:
		tmp = t_1
	elif t <= -1.55e-37:
		tmp = y * (x / z)
	elif t <= 1.06e+88:
		tmp = (y / z) * x
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x * Float64(t / z))
	tmp = 0.0
	if (t <= -3.6e+156)
		tmp = t_1;
	elseif (t <= -1.55e-37)
		tmp = Float64(y * Float64(x / z));
	elseif (t <= 1.06e+88)
		tmp = Float64(Float64(y / z) * x);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x * (t / z);
	tmp = 0.0;
	if (t <= -3.6e+156)
		tmp = t_1;
	elseif (t <= -1.55e-37)
		tmp = y * (x / z);
	elseif (t <= 1.06e+88)
		tmp = (y / z) * x;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x * N[(t / z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -3.6e+156], t$95$1, If[LessEqual[t, -1.55e-37], N[(y * N[(x / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.06e+88], N[(N[(y / z), $MachinePrecision] * x), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if t < -3.59999999999999979e156 or 1.06000000000000001e88 < t

   1. Initial program 95.3%

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

   3. Taylor expanded in z around inf 60.4%

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

   4. Taylor expanded in y around 0 51.2%

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

      1. *-commutative 51.2%

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

      2. *-lft-identity 51.2%

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

      3. times-frac 57.0%

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

      4. /-rgt-identity 57.0%

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

   6. Simplified 57.0%

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

   if -3.59999999999999979e156 < t < -1.54999999999999997e-37

   1. Initial program 89.5%

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

      1. clear-num 89.5%

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

      2. frac-sub 65.6%

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

      3. *-un-lft-identity 65.6%

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

   4. Applied egg-rr 65.6%

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

      1. div-sub 59.7%

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

      2. times-frac 67.2%

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

      3. *-inverses 86.5%

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

      4. *-lft-identity 86.5%

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

      5. remove-double-neg 86.5%

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

      6. distribute-frac-neg 86.5%

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

      7. *-rgt-identity 86.5%

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

      8. distribute-lft-neg-in 86.5%

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

      9. cancel-sign-sub 86.5%

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

      10. *-commutative 86.5%

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

      11. associate-/r* 89.5%

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

      12. *-inverses 89.5%

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

      13. *-rgt-identity 89.5%

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

      14. distribute-frac-neg 89.5%

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

      15. distribute-neg-frac2 89.5%

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

      16. neg-sub0 89.5%

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

      17. associate--r- 89.5%

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

      18. metadata-eval 89.5%

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

   6. Simplified 89.5%

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

   7. Taylor expanded in z around 0 54.2%

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

      1. associate-*l/ 59.8%

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

      2. *-commutative 59.8%

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

   9. Simplified 59.8%

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

   if -1.54999999999999997e-37 < t < 1.06000000000000001e88

   1. Initial program 92.6%

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

   3. Taylor expanded in y around inf 80.0%

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

      1. associate-*r/ 82.1%

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

   5. Simplified 82.1%

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

4. Final simplification 72.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -3.6 \cdot 10^{+156}:\\ \;\;\;\;x \cdot \frac{t}{z}\\ \mathbf{elif}\;t \leq -1.55 \cdot 10^{-37}:\\ \;\;\;\;y \cdot \frac{x}{z}\\ \mathbf{elif}\;t \leq 1.06 \cdot 10^{+88}:\\ \;\;\;\;\frac{y}{z} \cdot x\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{t}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 68.6% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -2.95 \cdot 10^{+153} \lor \neg \left(t \leq 2.2 \cdot 10^{+148}\right):\\ \;\;\;\;x \cdot \frac{t}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{z} \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= t -2.95e+153) (not (<= t 2.2e+148))) (* x (/ t z)) (* (/ y z) x)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((t <= -2.95e+153) || !(t <= 2.2e+148)) {
		tmp = x * (t / z);
	} else {
		tmp = (y / z) * x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((t <= (-2.95d+153)) .or. (.not. (t <= 2.2d+148))) then
        tmp = x * (t / z)
    else
        tmp = (y / z) * x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((t <= -2.95e+153) || !(t <= 2.2e+148)) {
		tmp = x * (t / z);
	} else {
		tmp = (y / z) * x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (t <= -2.95e+153) or not (t <= 2.2e+148):
		tmp = x * (t / z)
	else:
		tmp = (y / z) * x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((t <= -2.95e+153) || !(t <= 2.2e+148))
		tmp = Float64(x * Float64(t / z));
	else
		tmp = Float64(Float64(y / z) * x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((t <= -2.95e+153) || ~((t <= 2.2e+148)))
		tmp = x * (t / z);
	else
		tmp = (y / z) * x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[t, -2.95e+153], N[Not[LessEqual[t, 2.2e+148]], $MachinePrecision]], N[(x * N[(t / z), $MachinePrecision]), $MachinePrecision], N[(N[(y / z), $MachinePrecision] * x), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -2.9500000000000001e153 or 2.1999999999999999e148 < t

   1. Initial program 95.9%

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

   3. Taylor expanded in z around inf 64.2%

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

   4. Taylor expanded in y around 0 58.2%

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

      1. *-commutative 58.2%

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

      2. *-lft-identity 58.2%

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

      3. times-frac 65.9%

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

      4. /-rgt-identity 65.9%

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

   6. Simplified 65.9%

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

   if -2.9500000000000001e153 < t < 2.1999999999999999e148

   1. Initial program 92.1%

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

   3. Taylor expanded in y around inf 73.0%

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

      1. associate-*r/ 73.8%

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

   5. Simplified 73.8%

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

4. Final simplification 72.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.95 \cdot 10^{+153} \lor \neg \left(t \leq 2.2 \cdot 10^{+148}\right):\\ \;\;\;\;x \cdot \frac{t}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{z} \cdot x\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 22.4% accurate, 2.8× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 92.8%

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

3. Taylor expanded in z around 0 64.6%

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

   1. mul-1-neg 64.6%

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

   2. unsub-neg 64.6%

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

   3. div-sub 64.6%

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

   4. associate-/l* 64.7%

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

   5. *-inverses 64.7%

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

   6. *-rgt-identity 64.7%

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

5. Simplified 64.7%

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

6. Taylor expanded in y around 0 20.9%

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

   1. mul-1-neg 20.9%

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

   2. *-commutative 20.9%

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

   3. distribute-rgt-neg-in 20.9%

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

8. Simplified 20.9%

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

Developer target: 94.7% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(\frac{y}{z} - t \cdot \frac{1}{1 - z}\right)\\ t_2 := x \cdot \left(\frac{y}{z} - \frac{t}{1 - z}\right)\\ \mathbf{if}\;t\_2 < -7.623226303312042 \cdot 10^{-196}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_2 < 1.4133944927702302 \cdot 10^{-211}:\\ \;\;\;\;\frac{y \cdot x}{z} + \left(-\frac{t \cdot x}{1 - z}\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Reproduce

herbie shell --seed 2024107 
(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)))))