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

Percentage Accurate: 94.7% → 94.7%

Time: 7.7s

Alternatives: 16

Speedup: 1.0×

• 20.7% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 94.7% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 94.7% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 96.1%

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

2. Final simplification 96.1%

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

Alternative 2: 93.8% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2150000000 \lor \neg \left(z \leq 1\right):\\ \;\;\;\;\frac{x}{\frac{z}{y + t}}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(\frac{y}{z} - \left(t + z \cdot t\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -2150000000.0) (not (<= z 1.0)))
   (/ x (/ z (+ y t)))
   (* x (- (/ y z) (+ t (* z t))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -2150000000.0) || !(z <= 1.0)) {
		tmp = x / (z / (y + t));
	} else {
		tmp = x * ((y / z) - (t + (z * t)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((z <= (-2150000000.0d0)) .or. (.not. (z <= 1.0d0))) then
        tmp = x / (z / (y + t))
    else
        tmp = x * ((y / z) - (t + (z * t)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -2150000000.0) || !(z <= 1.0)) {
		tmp = x / (z / (y + t));
	} else {
		tmp = x * ((y / z) - (t + (z * t)));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -2150000000.0) or not (z <= 1.0):
		tmp = x / (z / (y + t))
	else:
		tmp = x * ((y / z) - (t + (z * t)))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -2150000000.0) || !(z <= 1.0))
		tmp = Float64(x / Float64(z / Float64(y + t)));
	else
		tmp = Float64(x * Float64(Float64(y / z) - Float64(t + Float64(z * t))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z <= -2150000000.0) || ~((z <= 1.0)))
		tmp = x / (z / (y + t));
	else
		tmp = x * ((y / z) - (t + (z * t)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -2150000000.0], N[Not[LessEqual[z, 1.0]], $MachinePrecision]], N[(x / N[(z / N[(y + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x * N[(N[(y / z), $MachinePrecision] - N[(t + N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -2.15e9 or 1 < z

   1. Initial program 97.8%

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

   2. Taylor expanded in z around inf 88.5%

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

      1. *-commutative 88.5%

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

      2. associate-/l* 96.7%

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

      3. neg-mul-1 96.7%

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

   4. Simplified 96.7%

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

   if -2.15e9 < z < 1

   1. Initial program 93.9%

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

   2. Taylor expanded in z around 0 93.5%

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

      1. *-commutative 93.5%

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

   4. Simplified 93.5%

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

4. Final simplification 95.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2150000000 \lor \neg \left(z \leq 1\right):\\ \;\;\;\;\frac{x}{\frac{z}{y + t}}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(\frac{y}{z} - \left(t + z \cdot t\right)\right)\\ \end{array} \]

Alternative 3: 42.8% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1 \lor \neg \left(z \leq -1.4 \cdot 10^{-270}\right) \land \left(z \leq 1.2 \cdot 10^{-254} \lor \neg \left(z \leq 1\right)\right):\\ \;\;\;\;t \cdot \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(-t\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -1.0)
         (and (not (<= z -1.4e-270)) (or (<= z 1.2e-254) (not (<= z 1.0)))))
   (* t (/ x z))
   (* x (- t))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -1.0) || (!(z <= -1.4e-270) && ((z <= 1.2e-254) || !(z <= 1.0)))) {
		tmp = t * (x / z);
	} else {
		tmp = x * -t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((z <= (-1.0d0)) .or. (.not. (z <= (-1.4d-270))) .and. (z <= 1.2d-254) .or. (.not. (z <= 1.0d0))) then
        tmp = t * (x / z)
    else
        tmp = x * -t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -1.0) || (!(z <= -1.4e-270) && ((z <= 1.2e-254) || !(z <= 1.0)))) {
		tmp = t * (x / z);
	} else {
		tmp = x * -t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -1.0) or (not (z <= -1.4e-270) and ((z <= 1.2e-254) or not (z <= 1.0))):
		tmp = t * (x / z)
	else:
		tmp = x * -t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -1.0) || (!(z <= -1.4e-270) && ((z <= 1.2e-254) || !(z <= 1.0))))
		tmp = Float64(t * Float64(x / z));
	else
		tmp = Float64(x * Float64(-t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z <= -1.0) || (~((z <= -1.4e-270)) && ((z <= 1.2e-254) || ~((z <= 1.0)))))
		tmp = t * (x / z);
	else
		tmp = x * -t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -1.0], And[N[Not[LessEqual[z, -1.4e-270]], $MachinePrecision], Or[LessEqual[z, 1.2e-254], N[Not[LessEqual[z, 1.0]], $MachinePrecision]]]], N[(t * N[(x / z), $MachinePrecision]), $MachinePrecision], N[(x * (-t)), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1 or -1.4e-270 < z < 1.20000000000000001e-254 or 1 < z

   1. Initial program 96.4%

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

   2. Taylor expanded in z around inf 85.2%

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

      1. *-commutative 85.2%

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

      2. associate-/l* 91.4%

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

      3. neg-mul-1 91.4%

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

   4. Simplified 91.4%

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

   5. Taylor expanded in y around 0 58.0%

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

      1. associate-*r/ 60.1%

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

   7. Simplified 60.1%

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

   if -1 < z < -1.4e-270 or 1.20000000000000001e-254 < z < 1

   1. Initial program 95.6%

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

   2. Taylor expanded in y around 0 40.0%

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

      1. associate-*r/ 40.0%

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

      2. associate-*r* 40.0%

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

      3. neg-mul-1 40.0%

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

      4. associate-*l/ 40.0%

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

      5. *-commutative 40.0%

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

      6. distribute-frac-neg 40.0%

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

      7. neg-mul-1 40.0%

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

      8. metadata-eval 40.0%

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

      9. times-frac 40.0%

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

      10. *-lft-identity 40.0%

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

      11. neg-mul-1 40.0%

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

      12. sub-neg 40.0%

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

      13. +-commutative 40.0%

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

      14. distribute-neg-in 40.0%

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

      15. remove-double-neg 40.0%

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

      16. metadata-eval 40.0%

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

   4. Simplified 40.0%

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

   5. Taylor expanded in z around 0 38.7%

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

      1. associate-*r* 38.7%

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

      2. mul-1-neg 38.7%

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

   7. Simplified 38.7%

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

4. Final simplification 52.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1 \lor \neg \left(z \leq -1.4 \cdot 10^{-270}\right) \land \left(z \leq 1.2 \cdot 10^{-254} \lor \neg \left(z \leq 1\right)\right):\\ \;\;\;\;t \cdot \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(-t\right)\\ \end{array} \]

Alternative 4: 63.0% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.15 \cdot 10^{+25}:\\ \;\;\;\;\frac{y}{\frac{z}{x}}\\ \mathbf{elif}\;y \leq 1.5 \cdot 10^{-181} \lor \neg \left(y \leq 4.2 \cdot 10^{-134}\right) \land y \leq 2 \cdot 10^{-91}:\\ \;\;\;\;\frac{x}{\frac{z}{t}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot y}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -1.15e+25)
   (/ y (/ z x))
   (if (or (<= y 1.5e-181) (and (not (<= y 4.2e-134)) (<= y 2e-91)))
     (/ x (/ z t))
     (/ (* x y) z))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -1.15e+25) {
		tmp = y / (z / x);
	} else if ((y <= 1.5e-181) || (!(y <= 4.2e-134) && (y <= 2e-91))) {
		tmp = x / (z / t);
	} else {
		tmp = (x * y) / z;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (y <= (-1.15d+25)) then
        tmp = y / (z / x)
    else if ((y <= 1.5d-181) .or. (.not. (y <= 4.2d-134)) .and. (y <= 2d-91)) then
        tmp = x / (z / t)
    else
        tmp = (x * y) / z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -1.15e+25) {
		tmp = y / (z / x);
	} else if ((y <= 1.5e-181) || (!(y <= 4.2e-134) && (y <= 2e-91))) {
		tmp = x / (z / t);
	} else {
		tmp = (x * y) / z;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -1.15e+25:
		tmp = y / (z / x)
	elif (y <= 1.5e-181) or (not (y <= 4.2e-134) and (y <= 2e-91)):
		tmp = x / (z / t)
	else:
		tmp = (x * y) / z
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -1.15e+25)
		tmp = Float64(y / Float64(z / x));
	elseif ((y <= 1.5e-181) || (!(y <= 4.2e-134) && (y <= 2e-91)))
		tmp = Float64(x / Float64(z / t));
	else
		tmp = Float64(Float64(x * y) / z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= -1.15e+25)
		tmp = y / (z / x);
	elseif ((y <= 1.5e-181) || (~((y <= 4.2e-134)) && (y <= 2e-91)))
		tmp = x / (z / t);
	else
		tmp = (x * y) / z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -1.15e+25], N[(y / N[(z / x), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[y, 1.5e-181], And[N[Not[LessEqual[y, 4.2e-134]], $MachinePrecision], LessEqual[y, 2e-91]]], N[(x / N[(z / t), $MachinePrecision]), $MachinePrecision], N[(N[(x * y), $MachinePrecision] / z), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.1499999999999999e25

   1. Initial program 94.2%

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

   2. Taylor expanded in y around inf 80.5%

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

      1. associate-*l/ 84.4%

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

   4. Simplified 84.4%

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

      1. associate-/r/ 85.6%

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

   6. Applied egg-rr 85.6%

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

   if -1.1499999999999999e25 < y < 1.49999999999999987e-181 or 4.1999999999999998e-134 < y < 2.00000000000000004e-91

   1. Initial program 98.1%

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

   2. Taylor expanded in z around inf 66.0%

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

      1. *-commutative 66.0%

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

      2. associate-/l* 71.7%

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

      3. neg-mul-1 71.7%

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

   4. Simplified 71.7%

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

   5. Taylor expanded in y around 0 67.7%

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

   if 1.49999999999999987e-181 < y < 4.1999999999999998e-134 or 2.00000000000000004e-91 < y

   1. Initial program 94.7%

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

   2. Taylor expanded in y around inf 77.8%

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

4. Final simplification 74.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.15 \cdot 10^{+25}:\\ \;\;\;\;\frac{y}{\frac{z}{x}}\\ \mathbf{elif}\;y \leq 1.5 \cdot 10^{-181} \lor \neg \left(y \leq 4.2 \cdot 10^{-134}\right) \land y \leq 2 \cdot 10^{-91}:\\ \;\;\;\;\frac{x}{\frac{z}{t}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot y}{z}\\ \end{array} \]

Alternative 5: 45.2% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \frac{t}{z}\\ t_2 := x \cdot \left(-t\right)\\ \mathbf{if}\;z \leq -1:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -1.35 \cdot 10^{-271}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq 2.4 \cdot 10^{-254}:\\ \;\;\;\;t \cdot \frac{x}{z}\\ \mathbf{elif}\;z \leq 0.78:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* x (/ t z))) (t_2 (* x (- t))))
   (if (<= z -1.0)
     t_1
     (if (<= z -1.35e-271)
       t_2
       (if (<= z 2.4e-254) (* t (/ x z)) (if (<= z 0.78) 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 <= -1.0) {
		tmp = t_1;
	} else if (z <= -1.35e-271) {
		tmp = t_2;
	} else if (z <= 2.4e-254) {
		tmp = t * (x / z);
	} else if (z <= 0.78) {
		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 <= (-1.0d0)) then
        tmp = t_1
    else if (z <= (-1.35d-271)) then
        tmp = t_2
    else if (z <= 2.4d-254) then
        tmp = t * (x / z)
    else if (z <= 0.78d0) 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 <= -1.0) {
		tmp = t_1;
	} else if (z <= -1.35e-271) {
		tmp = t_2;
	} else if (z <= 2.4e-254) {
		tmp = t * (x / z);
	} else if (z <= 0.78) {
		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 <= -1.0:
		tmp = t_1
	elif z <= -1.35e-271:
		tmp = t_2
	elif z <= 2.4e-254:
		tmp = t * (x / z)
	elif z <= 0.78:
		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 <= -1.0)
		tmp = t_1;
	elseif (z <= -1.35e-271)
		tmp = t_2;
	elseif (z <= 2.4e-254)
		tmp = Float64(t * Float64(x / z));
	elseif (z <= 0.78)
		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 <= -1.0)
		tmp = t_1;
	elseif (z <= -1.35e-271)
		tmp = t_2;
	elseif (z <= 2.4e-254)
		tmp = t * (x / z);
	elseif (z <= 0.78)
		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, -1.0], t$95$1, If[LessEqual[z, -1.35e-271], t$95$2, If[LessEqual[z, 2.4e-254], N[(t * N[(x / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 0.78], t$95$2, t$95$1]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -1 or 0.78000000000000003 < z

   1. Initial program 97.8%

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

   2. Taylor expanded in y around 0 64.1%

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

      1. associate-*r/ 64.1%

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

      2. associate-*r* 64.1%

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

      3. neg-mul-1 64.1%

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

      4. associate-*l/ 69.8%

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

      5. *-commutative 69.8%

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

      6. distribute-frac-neg 69.8%

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

      7. neg-mul-1 69.8%

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

      8. metadata-eval 69.8%

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

      9. times-frac 69.8%

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

      10. *-lft-identity 69.8%

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

      11. neg-mul-1 69.8%

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

      12. sub-neg 69.8%

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

      13. +-commutative 69.8%

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

      14. distribute-neg-in 69.8%

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

      15. remove-double-neg 69.8%

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

      16. metadata-eval 69.8%

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

   4. Simplified 69.8%

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

   5. Taylor expanded in z around inf 68.7%

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

   if -1 < z < -1.3499999999999999e-271 or 2.40000000000000002e-254 < z < 0.78000000000000003

   1. Initial program 95.6%

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

   2. Taylor expanded in y around 0 40.0%

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

      1. associate-*r/ 40.0%

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

      2. associate-*r* 40.0%

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

      3. neg-mul-1 40.0%

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

      4. associate-*l/ 40.0%

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

      5. *-commutative 40.0%

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

      6. distribute-frac-neg 40.0%

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

      7. neg-mul-1 40.0%

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

      8. metadata-eval 40.0%

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

      9. times-frac 40.0%

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

      10. *-lft-identity 40.0%

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

      11. neg-mul-1 40.0%

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

      12. sub-neg 40.0%

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

      13. +-commutative 40.0%

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

      14. distribute-neg-in 40.0%

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

      15. remove-double-neg 40.0%

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

      16. metadata-eval 40.0%

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

   4. Simplified 40.0%

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

   5. Taylor expanded in z around 0 38.7%

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

      1. associate-*r* 38.7%

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

      2. mul-1-neg 38.7%

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

   7. Simplified 38.7%

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

   if -1.3499999999999999e-271 < z < 2.40000000000000002e-254

   1. Initial program 85.4%

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

   2. Taylor expanded in z around inf 59.7%

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

      1. *-commutative 59.7%

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

      2. associate-/l* 50.1%

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

      3. neg-mul-1 50.1%

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

   4. Simplified 50.1%

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

   5. Taylor expanded in y around 0 19.0%

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

      1. associate-*r/ 24.2%

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

   7. Simplified 24.2%

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

4. Final simplification 54.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1:\\ \;\;\;\;x \cdot \frac{t}{z}\\ \mathbf{elif}\;z \leq -1.35 \cdot 10^{-271}:\\ \;\;\;\;x \cdot \left(-t\right)\\ \mathbf{elif}\;z \leq 2.4 \cdot 10^{-254}:\\ \;\;\;\;t \cdot \frac{x}{z}\\ \mathbf{elif}\;z \leq 0.78:\\ \;\;\;\;x \cdot \left(-t\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{t}{z}\\ \end{array} \]

Alternative 6: 74.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -6.2 \cdot 10^{+41} \lor \neg \left(z \leq 1.2 \cdot 10^{+22}\right):\\ \;\;\;\;\frac{x}{\frac{z}{t}}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(\frac{y}{z} - t\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -6.2e+41) (not (<= z 1.2e+22)))
   (/ x (/ z t))
   (* x (- (/ y z) t))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -6.2e+41) || !(z <= 1.2e+22)) {
		tmp = x / (z / t);
	} else {
		tmp = x * ((y / z) - t);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((z <= (-6.2d+41)) .or. (.not. (z <= 1.2d+22))) then
        tmp = x / (z / t)
    else
        tmp = x * ((y / z) - t)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -6.2e+41) || !(z <= 1.2e+22)) {
		tmp = x / (z / t);
	} else {
		tmp = x * ((y / z) - t);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -6.2e+41) or not (z <= 1.2e+22):
		tmp = x / (z / t)
	else:
		tmp = x * ((y / z) - t)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -6.2e+41) || !(z <= 1.2e+22))
		tmp = Float64(x / Float64(z / t));
	else
		tmp = Float64(x * Float64(Float64(y / z) - t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z <= -6.2e+41) || ~((z <= 1.2e+22)))
		tmp = x / (z / t);
	else
		tmp = x * ((y / z) - t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -6.2e+41], N[Not[LessEqual[z, 1.2e+22]], $MachinePrecision]], N[(x / N[(z / t), $MachinePrecision]), $MachinePrecision], N[(x * N[(N[(y / z), $MachinePrecision] - t), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -6.2e41 or 1.2e22 < z

   1. Initial program 97.6%

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

   2. Taylor expanded in z around inf 89.2%

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

      1. *-commutative 89.2%

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

      2. associate-/l* 97.6%

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

      3. neg-mul-1 97.6%

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

   4. Simplified 97.6%

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

   5. Taylor expanded in y around 0 72.3%

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

   if -6.2e41 < z < 1.2e22

   1. Initial program 94.6%

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

   2. Taylor expanded in z around 0 86.6%

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

      1. mul-1-neg 86.6%

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

      2. unsub-neg 86.6%

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

      3. associate-*l/ 87.4%

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

      4. distribute-rgt-out-- 89.0%

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

   4. Simplified 89.0%

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

4. Final simplification 80.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -6.2 \cdot 10^{+41} \lor \neg \left(z \leq 1.2 \cdot 10^{+22}\right):\\ \;\;\;\;\frac{x}{\frac{z}{t}}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(\frac{y}{z} - t\right)\\ \end{array} \]

Alternative 7: 89.3% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2150000000 \lor \neg \left(z \leq 1\right):\\ \;\;\;\;\left(y + t\right) \cdot \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(\frac{y}{z} - t\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -2150000000.0) (not (<= z 1.0)))
   (* (+ y t) (/ x z))
   (* x (- (/ y z) t))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -2150000000.0) || !(z <= 1.0)) {
		tmp = (y + t) * (x / z);
	} else {
		tmp = x * ((y / z) - t);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((z <= (-2150000000.0d0)) .or. (.not. (z <= 1.0d0))) then
        tmp = (y + t) * (x / z)
    else
        tmp = x * ((y / z) - t)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -2150000000.0) || !(z <= 1.0)) {
		tmp = (y + t) * (x / z);
	} else {
		tmp = x * ((y / z) - t);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -2150000000.0) or not (z <= 1.0):
		tmp = (y + t) * (x / z)
	else:
		tmp = x * ((y / z) - t)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -2150000000.0) || !(z <= 1.0))
		tmp = Float64(Float64(y + t) * Float64(x / z));
	else
		tmp = Float64(x * Float64(Float64(y / z) - t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z <= -2150000000.0) || ~((z <= 1.0)))
		tmp = (y + t) * (x / z);
	else
		tmp = x * ((y / z) - t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -2150000000.0], N[Not[LessEqual[z, 1.0]], $MachinePrecision]], N[(N[(y + t), $MachinePrecision] * N[(x / z), $MachinePrecision]), $MachinePrecision], N[(x * N[(N[(y / z), $MachinePrecision] - t), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -2.15e9 or 1 < z

   1. Initial program 97.8%

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

   2. Taylor expanded in z around inf 88.5%

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

      1. *-commutative 88.5%

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

      2. associate-/l* 96.7%

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

      3. associate-/r/ 87.3%

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

      4. cancel-sign-sub-inv 87.3%

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

      5. metadata-eval 87.3%

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

      6. *-lft-identity 87.3%

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

   4. Simplified 87.3%

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

   if -2.15e9 < z < 1

   1. Initial program 93.9%

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

   2. Taylor expanded in z around 0 90.9%

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

      1. mul-1-neg 90.9%

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

      2. unsub-neg 90.9%

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

      3. associate-*l/ 91.0%

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

      4. distribute-rgt-out-- 92.8%

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

   4. Simplified 92.8%

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

4. Final simplification 89.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2150000000 \lor \neg \left(z \leq 1\right):\\ \;\;\;\;\left(y + t\right) \cdot \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(\frac{y}{z} - t\right)\\ \end{array} \]

Alternative 8: 93.7% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2150000000 \lor \neg \left(z \leq 1\right):\\ \;\;\;\;\frac{x}{\frac{z}{y + t}}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(\frac{y}{z} - t\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -2150000000.0) (not (<= z 1.0)))
   (/ x (/ z (+ y t)))
   (* x (- (/ y z) t))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -2150000000.0) || !(z <= 1.0)) {
		tmp = x / (z / (y + t));
	} else {
		tmp = x * ((y / z) - t);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((z <= (-2150000000.0d0)) .or. (.not. (z <= 1.0d0))) then
        tmp = x / (z / (y + t))
    else
        tmp = x * ((y / z) - t)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -2150000000.0) || !(z <= 1.0)) {
		tmp = x / (z / (y + t));
	} else {
		tmp = x * ((y / z) - t);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -2150000000.0) or not (z <= 1.0):
		tmp = x / (z / (y + t))
	else:
		tmp = x * ((y / z) - t)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -2150000000.0) || !(z <= 1.0))
		tmp = Float64(x / Float64(z / Float64(y + t)));
	else
		tmp = Float64(x * Float64(Float64(y / z) - t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z <= -2150000000.0) || ~((z <= 1.0)))
		tmp = x / (z / (y + t));
	else
		tmp = x * ((y / z) - t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -2150000000.0], N[Not[LessEqual[z, 1.0]], $MachinePrecision]], N[(x / N[(z / N[(y + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x * N[(N[(y / z), $MachinePrecision] - t), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -2.15e9 or 1 < z

   1. Initial program 97.8%

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

   2. Taylor expanded in z around inf 88.5%

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

      1. *-commutative 88.5%

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

      2. associate-/l* 96.7%

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

      3. neg-mul-1 96.7%

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

   4. Simplified 96.7%

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

   if -2.15e9 < z < 1

   1. Initial program 93.9%

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

   2. Taylor expanded in z around 0 90.9%

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

      1. mul-1-neg 90.9%

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

      2. unsub-neg 90.9%

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

      3. associate-*l/ 91.0%

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

      4. distribute-rgt-out-- 92.8%

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

   4. Simplified 92.8%

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

4. Final simplification 95.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2150000000 \lor \neg \left(z \leq 1\right):\\ \;\;\;\;\frac{x}{\frac{z}{y + t}}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(\frac{y}{z} - t\right)\\ \end{array} \]

Alternative 9: 72.2% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -3.2 \cdot 10^{+28}:\\ \;\;\;\;\frac{y}{\frac{z}{x}}\\ \mathbf{elif}\;y \leq 2.1 \cdot 10^{-95}:\\ \;\;\;\;t \cdot \frac{x}{z + -1}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot y}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -3.2e+28)
   (/ y (/ z x))
   (if (<= y 2.1e-95) (* t (/ x (+ z -1.0))) (/ (* x y) z))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -3.2e+28) {
		tmp = y / (z / x);
	} else if (y <= 2.1e-95) {
		tmp = t * (x / (z + -1.0));
	} else {
		tmp = (x * y) / z;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (y <= (-3.2d+28)) then
        tmp = y / (z / x)
    else if (y <= 2.1d-95) then
        tmp = t * (x / (z + (-1.0d0)))
    else
        tmp = (x * y) / z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -3.2e+28) {
		tmp = y / (z / x);
	} else if (y <= 2.1e-95) {
		tmp = t * (x / (z + -1.0));
	} else {
		tmp = (x * y) / z;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -3.2e+28:
		tmp = y / (z / x)
	elif y <= 2.1e-95:
		tmp = t * (x / (z + -1.0))
	else:
		tmp = (x * y) / z
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -3.2e+28)
		tmp = Float64(y / Float64(z / x));
	elseif (y <= 2.1e-95)
		tmp = Float64(t * Float64(x / Float64(z + -1.0)));
	else
		tmp = Float64(Float64(x * y) / z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= -3.2e+28)
		tmp = y / (z / x);
	elseif (y <= 2.1e-95)
		tmp = t * (x / (z + -1.0));
	else
		tmp = (x * y) / z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -3.2e+28], N[(y / N[(z / x), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 2.1e-95], N[(t * N[(x / N[(z + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x * y), $MachinePrecision] / z), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -3.2e28

   1. Initial program 94.1%

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

   2. Taylor expanded in y around inf 82.1%

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

      1. associate-*l/ 86.1%

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

   4. Simplified 86.1%

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

      1. associate-/r/ 87.4%

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

   6. Applied egg-rr 87.4%

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

   if -3.2e28 < y < 2.1e-95

   1. Initial program 97.6%

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

   2. Taylor expanded in y around 0 75.2%

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

      1. associate-*r/ 75.2%

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

      2. associate-*r* 75.2%

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

      3. neg-mul-1 75.2%

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

      4. associate-*l/ 80.1%

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

      5. *-commutative 80.1%

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

      6. distribute-frac-neg 80.1%

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

      7. neg-mul-1 80.1%

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

      8. metadata-eval 80.1%

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

      9. times-frac 80.1%

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

      10. *-lft-identity 80.1%

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

      11. neg-mul-1 80.1%

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

      12. sub-neg 80.1%

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

      13. +-commutative 80.1%

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

      14. distribute-neg-in 80.1%

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

      15. remove-double-neg 80.1%

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

      16. metadata-eval 80.1%

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

   4. Simplified 80.1%

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

   5. Taylor expanded in x around 0 75.2%

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

      1. sub-neg 75.2%

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

      2. metadata-eval 75.2%

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

      3. associate-*r/ 78.6%

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

   7. Simplified 78.6%

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

   if 2.1e-95 < y

   1. Initial program 94.9%

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

   2. Taylor expanded in y around inf 79.9%

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

4. Final simplification 80.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.2 \cdot 10^{+28}:\\ \;\;\;\;\frac{y}{\frac{z}{x}}\\ \mathbf{elif}\;y \leq 2.1 \cdot 10^{-95}:\\ \;\;\;\;t \cdot \frac{x}{z + -1}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot y}{z}\\ \end{array} \]

Alternative 10: 74.6% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3.3 \cdot 10^{+43}:\\ \;\;\;\;\frac{x}{\frac{z}{t}}\\ \mathbf{elif}\;z \leq 1.65 \cdot 10^{-10}:\\ \;\;\;\;x \cdot \left(\frac{y}{z} - t\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{t}{z + -1}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -3.3e+43)
   (/ x (/ z t))
   (if (<= z 1.65e-10) (* x (- (/ y z) t)) (* x (/ t (+ z -1.0))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -3.3e+43) {
		tmp = x / (z / t);
	} else if (z <= 1.65e-10) {
		tmp = x * ((y / z) - t);
	} else {
		tmp = x * (t / (z + -1.0));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (z <= (-3.3d+43)) then
        tmp = x / (z / t)
    else if (z <= 1.65d-10) then
        tmp = x * ((y / z) - t)
    else
        tmp = x * (t / (z + (-1.0d0)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -3.3e+43) {
		tmp = x / (z / t);
	} else if (z <= 1.65e-10) {
		tmp = x * ((y / z) - t);
	} else {
		tmp = x * (t / (z + -1.0));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -3.3e+43:
		tmp = x / (z / t)
	elif z <= 1.65e-10:
		tmp = x * ((y / z) - t)
	else:
		tmp = x * (t / (z + -1.0))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -3.3e+43)
		tmp = Float64(x / Float64(z / t));
	elseif (z <= 1.65e-10)
		tmp = Float64(x * Float64(Float64(y / z) - t));
	else
		tmp = Float64(x * Float64(t / Float64(z + -1.0)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (z <= -3.3e+43)
		tmp = x / (z / t);
	elseif (z <= 1.65e-10)
		tmp = x * ((y / z) - t);
	else
		tmp = x * (t / (z + -1.0));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -3.3e+43], N[(x / N[(z / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.65e-10], N[(x * N[(N[(y / z), $MachinePrecision] - t), $MachinePrecision]), $MachinePrecision], N[(x * N[(t / N[(z + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -3.3000000000000001e43

   1. Initial program 96.9%

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

   2. Taylor expanded in z around inf 88.4%

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

      1. *-commutative 88.4%

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

      2. associate-/l* 96.9%

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

      3. neg-mul-1 96.9%

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

   4. Simplified 96.9%

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

   5. Taylor expanded in y around 0 67.8%

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

   if -3.3000000000000001e43 < z < 1.65e-10

   1. Initial program 94.3%

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

   2. Taylor expanded in z around 0 89.6%

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

      1. mul-1-neg 89.6%

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

      2. unsub-neg 89.6%

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

      3. associate-*l/ 89.7%

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

      4. distribute-rgt-out-- 91.4%

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

   4. Simplified 91.4%

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

   if 1.65e-10 < z

   1. Initial program 98.4%

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

   2. Taylor expanded in y around 0 69.8%

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

      1. associate-*r/ 69.8%

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

      2. associate-*r* 69.8%

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

      3. neg-mul-1 69.8%

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

      4. associate-*l/ 74.8%

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

      5. *-commutative 74.8%

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

      6. distribute-frac-neg 74.8%

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

      7. neg-mul-1 74.8%

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

      8. metadata-eval 74.8%

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

      9. times-frac 74.8%

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

      10. *-lft-identity 74.8%

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

      11. neg-mul-1 74.8%

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

      12. sub-neg 74.8%

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

      13. +-commutative 74.8%

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

      14. distribute-neg-in 74.8%

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

      15. remove-double-neg 74.8%

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

      16. metadata-eval 74.8%

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

   4. Simplified 74.8%

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

4. Final simplification 80.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.3 \cdot 10^{+43}:\\ \;\;\;\;\frac{x}{\frac{z}{t}}\\ \mathbf{elif}\;z \leq 1.65 \cdot 10^{-10}:\\ \;\;\;\;x \cdot \left(\frac{y}{z} - t\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{t}{z + -1}\\ \end{array} \]

Alternative 11: 88.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2150000000:\\ \;\;\;\;\frac{x \cdot \left(y + t\right)}{z}\\ \mathbf{elif}\;z \leq 1:\\ \;\;\;\;x \cdot \left(\frac{y}{z} - t\right)\\ \mathbf{else}:\\ \;\;\;\;\left(y + t\right) \cdot \frac{x}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -2150000000.0)
   (/ (* x (+ y t)) z)
   (if (<= z 1.0) (* x (- (/ y z) t)) (* (+ y t) (/ x z)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -2150000000.0) {
		tmp = (x * (y + t)) / z;
	} else if (z <= 1.0) {
		tmp = x * ((y / z) - t);
	} else {
		tmp = (y + t) * (x / z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (z <= (-2150000000.0d0)) then
        tmp = (x * (y + t)) / z
    else if (z <= 1.0d0) then
        tmp = x * ((y / z) - t)
    else
        tmp = (y + t) * (x / z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -2150000000.0) {
		tmp = (x * (y + t)) / z;
	} else if (z <= 1.0) {
		tmp = x * ((y / z) - t);
	} else {
		tmp = (y + t) * (x / z);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -2150000000.0:
		tmp = (x * (y + t)) / z
	elif z <= 1.0:
		tmp = x * ((y / z) - t)
	else:
		tmp = (y + t) * (x / z)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -2150000000.0)
		tmp = Float64(Float64(x * Float64(y + t)) / z);
	elseif (z <= 1.0)
		tmp = Float64(x * Float64(Float64(y / z) - t));
	else
		tmp = Float64(Float64(y + t) * Float64(x / z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (z <= -2150000000.0)
		tmp = (x * (y + t)) / z;
	elseif (z <= 1.0)
		tmp = x * ((y / z) - t);
	else
		tmp = (y + t) * (x / z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -2150000000.0], N[(N[(x * N[(y + t), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision], If[LessEqual[z, 1.0], N[(x * N[(N[(y / z), $MachinePrecision] - t), $MachinePrecision]), $MachinePrecision], N[(N[(y + t), $MachinePrecision] * N[(x / z), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -2.15e9

   1. Initial program 97.2%

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

   2. Taylor expanded in z around inf 89.5%

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

      1. *-commutative 89.5%

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

      2. associate-/l* 97.2%

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

      3. neg-mul-1 97.2%

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

   4. Simplified 97.2%

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

   5. Taylor expanded in x around 0 89.5%

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

   if -2.15e9 < z < 1

   1. Initial program 93.9%

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

   2. Taylor expanded in z around 0 90.9%

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

      1. mul-1-neg 90.9%

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

      2. unsub-neg 90.9%

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

      3. associate-*l/ 91.0%

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

      4. distribute-rgt-out-- 92.8%

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

   4. Simplified 92.8%

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

   if 1 < z

   1. Initial program 98.4%

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

   2. Taylor expanded in z around inf 87.3%

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

      1. *-commutative 87.3%

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

      2. associate-/l* 96.2%

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

      3. associate-/r/ 88.5%

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

      4. cancel-sign-sub-inv 88.5%

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

      5. metadata-eval 88.5%

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

      6. *-lft-identity 88.5%

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

   4. Simplified 88.5%

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

4. Final simplification 90.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2150000000:\\ \;\;\;\;\frac{x \cdot \left(y + t\right)}{z}\\ \mathbf{elif}\;z \leq 1:\\ \;\;\;\;x \cdot \left(\frac{y}{z} - t\right)\\ \mathbf{else}:\\ \;\;\;\;\left(y + t\right) \cdot \frac{x}{z}\\ \end{array} \]

Alternative 12: 62.7% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.25 \cdot 10^{+25} \lor \neg \left(y \leq 1.95 \cdot 10^{-78}\right):\\ \;\;\;\;x \cdot \frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{t}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= y -1.25e+25) (not (<= y 1.95e-78))) (* x (/ y z)) (* x (/ t z))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -1.25e+25) || !(y <= 1.95e-78)) {
		tmp = x * (y / z);
	} 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 ((y <= (-1.25d+25)) .or. (.not. (y <= 1.95d-78))) then
        tmp = x * (y / z)
    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 ((y <= -1.25e+25) || !(y <= 1.95e-78)) {
		tmp = x * (y / z);
	} else {
		tmp = x * (t / z);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (y <= -1.25e+25) or not (y <= 1.95e-78):
		tmp = x * (y / z)
	else:
		tmp = x * (t / z)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((y <= -1.25e+25) || !(y <= 1.95e-78))
		tmp = Float64(x * Float64(y / z));
	else
		tmp = Float64(x * Float64(t / z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((y <= -1.25e+25) || ~((y <= 1.95e-78)))
		tmp = x * (y / z);
	else
		tmp = x * (t / z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[y, -1.25e+25], N[Not[LessEqual[y, 1.95e-78]], $MachinePrecision]], N[(x * N[(y / z), $MachinePrecision]), $MachinePrecision], N[(x * N[(t / z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -1.25000000000000006e25 or 1.9500000000000001e-78 < y

   1. Initial program 94.6%

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

   2. Taylor expanded in y around inf 80.7%

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

      1. associate-*l/ 80.0%

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

   4. Simplified 80.0%

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

   if -1.25000000000000006e25 < y < 1.9500000000000001e-78

   1. Initial program 97.6%

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

   2. Taylor expanded in y around 0 75.2%

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

      1. associate-*r/ 75.2%

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

      2. associate-*r* 75.2%

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

      3. neg-mul-1 75.2%

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

      4. associate-*l/ 80.1%

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

      5. *-commutative 80.1%

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

      6. distribute-frac-neg 80.1%

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

      7. neg-mul-1 80.1%

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

      8. metadata-eval 80.1%

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

      9. times-frac 80.1%

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

      10. *-lft-identity 80.1%

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

      11. neg-mul-1 80.1%

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

      12. sub-neg 80.1%

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

      13. +-commutative 80.1%

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

      14. distribute-neg-in 80.1%

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

      15. remove-double-neg 80.1%

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

      16. metadata-eval 80.1%

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

   4. Simplified 80.1%

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

   5. Taylor expanded in z around inf 63.5%

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

4. Final simplification 71.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.25 \cdot 10^{+25} \lor \neg \left(y \leq 1.95 \cdot 10^{-78}\right):\\ \;\;\;\;x \cdot \frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{t}{z}\\ \end{array} \]

Alternative 13: 62.3% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.15 \cdot 10^{+25} \lor \neg \left(y \leq 3.1 \cdot 10^{-65}\right):\\ \;\;\;\;x \cdot \frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\frac{z}{t}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= y -1.15e+25) (not (<= y 3.1e-65))) (* x (/ y z)) (/ x (/ z t))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -1.15e+25) || !(y <= 3.1e-65)) {
		tmp = x * (y / z);
	} else {
		tmp = x / (z / t);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((y <= (-1.15d+25)) .or. (.not. (y <= 3.1d-65))) then
        tmp = x * (y / z)
    else
        tmp = x / (z / t)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -1.15e+25) || !(y <= 3.1e-65)) {
		tmp = x * (y / z);
	} else {
		tmp = x / (z / t);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (y <= -1.15e+25) or not (y <= 3.1e-65):
		tmp = x * (y / z)
	else:
		tmp = x / (z / t)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((y <= -1.15e+25) || !(y <= 3.1e-65))
		tmp = Float64(x * Float64(y / z));
	else
		tmp = Float64(x / Float64(z / t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((y <= -1.15e+25) || ~((y <= 3.1e-65)))
		tmp = x * (y / z);
	else
		tmp = x / (z / t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[y, -1.15e+25], N[Not[LessEqual[y, 3.1e-65]], $MachinePrecision]], N[(x * N[(y / z), $MachinePrecision]), $MachinePrecision], N[(x / N[(z / t), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -1.1499999999999999e25 or 3.10000000000000016e-65 < y

   1. Initial program 94.6%

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

   2. Taylor expanded in y around inf 80.7%

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

      1. associate-*l/ 80.0%

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

   4. Simplified 80.0%

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

   if -1.1499999999999999e25 < y < 3.10000000000000016e-65

   1. Initial program 97.6%

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

   2. Taylor expanded in z around inf 65.0%

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

      1. *-commutative 65.0%

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

      2. associate-/l* 70.0%

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

      3. neg-mul-1 70.0%

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

   4. Simplified 70.0%

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

   5. Taylor expanded in y around 0 63.6%

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

4. Final simplification 71.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.15 \cdot 10^{+25} \lor \neg \left(y \leq 3.1 \cdot 10^{-65}\right):\\ \;\;\;\;x \cdot \frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\frac{z}{t}}\\ \end{array} \]

Alternative 14: 62.5% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.6 \cdot 10^{+27} \lor \neg \left(y \leq 2.3 \cdot 10^{-62}\right):\\ \;\;\;\;\frac{x}{\frac{z}{y}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\frac{z}{t}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= y -1.6e+27) (not (<= y 2.3e-62))) (/ x (/ z y)) (/ x (/ z t))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -1.6e+27) || !(y <= 2.3e-62)) {
		tmp = x / (z / y);
	} else {
		tmp = x / (z / t);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((y <= (-1.6d+27)) .or. (.not. (y <= 2.3d-62))) then
        tmp = x / (z / y)
    else
        tmp = x / (z / t)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -1.6e+27) || !(y <= 2.3e-62)) {
		tmp = x / (z / y);
	} else {
		tmp = x / (z / t);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (y <= -1.6e+27) or not (y <= 2.3e-62):
		tmp = x / (z / y)
	else:
		tmp = x / (z / t)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((y <= -1.6e+27) || !(y <= 2.3e-62))
		tmp = Float64(x / Float64(z / y));
	else
		tmp = Float64(x / Float64(z / t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((y <= -1.6e+27) || ~((y <= 2.3e-62)))
		tmp = x / (z / y);
	else
		tmp = x / (z / t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[y, -1.6e+27], N[Not[LessEqual[y, 2.3e-62]], $MachinePrecision]], N[(x / N[(z / y), $MachinePrecision]), $MachinePrecision], N[(x / N[(z / t), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -1.60000000000000008e27 or 2.3e-62 < y

   1. Initial program 94.6%

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

   2. Taylor expanded in y around inf 80.7%

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

      1. *-commutative 80.7%

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

      2. associate-/l* 80.2%

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

   4. Simplified 80.2%

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

   if -1.60000000000000008e27 < y < 2.3e-62

   1. Initial program 97.6%

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

   2. Taylor expanded in z around inf 65.0%

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

      1. *-commutative 65.0%

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

      2. associate-/l* 70.0%

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

      3. neg-mul-1 70.0%

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

   4. Simplified 70.0%

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

   5. Taylor expanded in y around 0 63.6%

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

4. Final simplification 71.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.6 \cdot 10^{+27} \lor \neg \left(y \leq 2.3 \cdot 10^{-62}\right):\\ \;\;\;\;\frac{x}{\frac{z}{y}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\frac{z}{t}}\\ \end{array} \]

Alternative 15: 62.9% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.1 \cdot 10^{+25}:\\ \;\;\;\;\frac{y}{\frac{z}{x}}\\ \mathbf{elif}\;y \leq 6.6 \cdot 10^{-69}:\\ \;\;\;\;\frac{x}{\frac{z}{t}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\frac{z}{y}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -1.1e+25)
   (/ y (/ z x))
   (if (<= y 6.6e-69) (/ x (/ z t)) (/ x (/ z y)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -1.1e+25) {
		tmp = y / (z / x);
	} else if (y <= 6.6e-69) {
		tmp = x / (z / t);
	} else {
		tmp = x / (z / y);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (y <= (-1.1d+25)) then
        tmp = y / (z / x)
    else if (y <= 6.6d-69) then
        tmp = x / (z / t)
    else
        tmp = x / (z / y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -1.1e+25) {
		tmp = y / (z / x);
	} else if (y <= 6.6e-69) {
		tmp = x / (z / t);
	} else {
		tmp = x / (z / y);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -1.1e+25:
		tmp = y / (z / x)
	elif y <= 6.6e-69:
		tmp = x / (z / t)
	else:
		tmp = x / (z / y)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -1.1e+25)
		tmp = Float64(y / Float64(z / x));
	elseif (y <= 6.6e-69)
		tmp = Float64(x / Float64(z / t));
	else
		tmp = Float64(x / Float64(z / y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= -1.1e+25)
		tmp = y / (z / x);
	elseif (y <= 6.6e-69)
		tmp = x / (z / t);
	else
		tmp = x / (z / y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -1.1e+25], N[(y / N[(z / x), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 6.6e-69], N[(x / N[(z / t), $MachinePrecision]), $MachinePrecision], N[(x / N[(z / y), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.1e25

   1. Initial program 94.2%

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

   2. Taylor expanded in y around inf 80.5%

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

      1. associate-*l/ 84.4%

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

   4. Simplified 84.4%

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

      1. associate-/r/ 85.6%

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

   6. Applied egg-rr 85.6%

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

   if -1.1e25 < y < 6.6000000000000001e-69

   1. Initial program 97.6%

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

   2. Taylor expanded in z around inf 65.0%

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

      1. *-commutative 65.0%

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

      2. associate-/l* 70.0%

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

      3. neg-mul-1 70.0%

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

   4. Simplified 70.0%

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

   5. Taylor expanded in y around 0 63.6%

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

   if 6.6000000000000001e-69 < y

   1. Initial program 94.8%

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

   2. Taylor expanded in y around inf 80.9%

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

      1. *-commutative 80.9%

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

      2. associate-/l* 77.4%

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

   4. Simplified 77.4%

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

4. Final simplification 71.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.1 \cdot 10^{+25}:\\ \;\;\;\;\frac{y}{\frac{z}{x}}\\ \mathbf{elif}\;y \leq 6.6 \cdot 10^{-69}:\\ \;\;\;\;\frac{x}{\frac{z}{t}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\frac{z}{y}}\\ \end{array} \]

Alternative 16: 23.8% 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 96.1%

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

2. Taylor expanded in y around 0 51.2%

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

   1. associate-*r/ 51.2%

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

   2. associate-*r* 51.2%

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

   3. neg-mul-1 51.2%

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

   4. associate-*l/ 54.5%

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

   5. *-commutative 54.5%

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

   6. distribute-frac-neg 54.5%

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

   7. neg-mul-1 54.5%

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

   8. metadata-eval 54.5%

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

   9. times-frac 54.5%

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

   10. *-lft-identity 54.5%

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

   11. neg-mul-1 54.5%

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

   12. sub-neg 54.5%

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

   13. +-commutative 54.5%

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

   14. distribute-neg-in 54.5%

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

   15. remove-double-neg 54.5%

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

   16. metadata-eval 54.5%

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

4. Simplified 54.5%

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

5. Taylor expanded in z around 0 21.5%

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

   1. associate-*r* 21.5%

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

   2. mul-1-neg 21.5%

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

7. Simplified 21.5%

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

8. Final simplification 21.5%

   \[\leadsto x \cdot \left(-t\right) \]

Developer target: 95.2% accurate, 0.3× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Reproduce

herbie shell --seed 2023238 
(FPCore (x y z t)
  :name "Numeric.SpecFunctions:invIncompleteBetaWorker from math-functions-0.1.5.2, C"
  :precision binary64

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

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