Quotient of products

Percentage Accurate: 86.0% → 95.2%

Time: 3.6s

Alternatives: 6

Speedup: 1.0×

• 20.8% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

\[\begin{array}{l} \\ \frac{a1 \cdot a2}{b1 \cdot b2} \end{array} \]

FPCore

(FPCore (a1 a2 b1 b2) :precision binary64 (/ (* a1 a2) (* b1 b2)))

C

double code(double a1, double a2, double b1, double b2) {
	return (a1 * a2) / (b1 * b2);
}

Fortran

real(8) function code(a1, a2, b1, b2)
    real(8), intent (in) :: a1
    real(8), intent (in) :: a2
    real(8), intent (in) :: b1
    real(8), intent (in) :: b2
    code = (a1 * a2) / (b1 * b2)
end function

Java

public static double code(double a1, double a2, double b1, double b2) {
	return (a1 * a2) / (b1 * b2);
}

Python

def code(a1, a2, b1, b2):
	return (a1 * a2) / (b1 * b2)

Julia

function code(a1, a2, b1, b2)
	return Float64(Float64(a1 * a2) / Float64(b1 * b2))
end

MATLAB

function tmp = code(a1, a2, b1, b2)
	tmp = (a1 * a2) / (b1 * b2);
end

Wolfram

code[a1_, a2_, b1_, b2_] := N[(N[(a1 * a2), $MachinePrecision] / N[(b1 * b2), $MachinePrecision]), $MachinePrecision]

Initial Program: 86.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \frac{a1 \cdot a2}{b1 \cdot b2} \end{array} \]

FPCore

(FPCore (a1 a2 b1 b2) :precision binary64 (/ (* a1 a2) (* b1 b2)))

C

double code(double a1, double a2, double b1, double b2) {
	return (a1 * a2) / (b1 * b2);
}

Fortran

real(8) function code(a1, a2, b1, b2)
    real(8), intent (in) :: a1
    real(8), intent (in) :: a2
    real(8), intent (in) :: b1
    real(8), intent (in) :: b2
    code = (a1 * a2) / (b1 * b2)
end function

Java

public static double code(double a1, double a2, double b1, double b2) {
	return (a1 * a2) / (b1 * b2);
}

Python

def code(a1, a2, b1, b2):
	return (a1 * a2) / (b1 * b2)

Julia

function code(a1, a2, b1, b2)
	return Float64(Float64(a1 * a2) / Float64(b1 * b2))
end

MATLAB

function tmp = code(a1, a2, b1, b2)
	tmp = (a1 * a2) / (b1 * b2);
end

Wolfram

code[a1_, a2_, b1_, b2_] := N[(N[(a1 * a2), $MachinePrecision] / N[(b1 * b2), $MachinePrecision]), $MachinePrecision]

Alternative 1: 95.2% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{a1 \cdot a2}{b1 \cdot b2}\\ \mathbf{if}\;t_0 \leq -\infty:\\ \;\;\;\;a1 \cdot \left(\frac{1}{b1} \cdot \frac{a2}{b2}\right)\\ \mathbf{elif}\;t_0 \leq -2 \cdot 10^{-278} \lor \neg \left(t_0 \leq 4 \cdot 10^{-269}\right) \land t_0 \leq 2 \cdot 10^{+191}:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;\frac{a2}{b2} \cdot \frac{a1}{b1}\\ \end{array} \end{array} \]

FPCore

(FPCore (a1 a2 b1 b2)
 :precision binary64
 (let* ((t_0 (/ (* a1 a2) (* b1 b2))))
   (if (<= t_0 (- INFINITY))
     (* a1 (* (/ 1.0 b1) (/ a2 b2)))
     (if (or (<= t_0 -2e-278) (and (not (<= t_0 4e-269)) (<= t_0 2e+191)))
       t_0
       (* (/ a2 b2) (/ a1 b1))))))

C

double code(double a1, double a2, double b1, double b2) {
	double t_0 = (a1 * a2) / (b1 * b2);
	double tmp;
	if (t_0 <= -((double) INFINITY)) {
		tmp = a1 * ((1.0 / b1) * (a2 / b2));
	} else if ((t_0 <= -2e-278) || (!(t_0 <= 4e-269) && (t_0 <= 2e+191))) {
		tmp = t_0;
	} else {
		tmp = (a2 / b2) * (a1 / b1);
	}
	return tmp;
}

Java

public static double code(double a1, double a2, double b1, double b2) {
	double t_0 = (a1 * a2) / (b1 * b2);
	double tmp;
	if (t_0 <= -Double.POSITIVE_INFINITY) {
		tmp = a1 * ((1.0 / b1) * (a2 / b2));
	} else if ((t_0 <= -2e-278) || (!(t_0 <= 4e-269) && (t_0 <= 2e+191))) {
		tmp = t_0;
	} else {
		tmp = (a2 / b2) * (a1 / b1);
	}
	return tmp;
}

Python

def code(a1, a2, b1, b2):
	t_0 = (a1 * a2) / (b1 * b2)
	tmp = 0
	if t_0 <= -math.inf:
		tmp = a1 * ((1.0 / b1) * (a2 / b2))
	elif (t_0 <= -2e-278) or (not (t_0 <= 4e-269) and (t_0 <= 2e+191)):
		tmp = t_0
	else:
		tmp = (a2 / b2) * (a1 / b1)
	return tmp

Julia

function code(a1, a2, b1, b2)
	t_0 = Float64(Float64(a1 * a2) / Float64(b1 * b2))
	tmp = 0.0
	if (t_0 <= Float64(-Inf))
		tmp = Float64(a1 * Float64(Float64(1.0 / b1) * Float64(a2 / b2)));
	elseif ((t_0 <= -2e-278) || (!(t_0 <= 4e-269) && (t_0 <= 2e+191)))
		tmp = t_0;
	else
		tmp = Float64(Float64(a2 / b2) * Float64(a1 / b1));
	end
	return tmp
end

MATLAB

function tmp_2 = code(a1, a2, b1, b2)
	t_0 = (a1 * a2) / (b1 * b2);
	tmp = 0.0;
	if (t_0 <= -Inf)
		tmp = a1 * ((1.0 / b1) * (a2 / b2));
	elseif ((t_0 <= -2e-278) || (~((t_0 <= 4e-269)) && (t_0 <= 2e+191)))
		tmp = t_0;
	else
		tmp = (a2 / b2) * (a1 / b1);
	end
	tmp_2 = tmp;
end

Wolfram

code[a1_, a2_, b1_, b2_] := Block[{t$95$0 = N[(N[(a1 * a2), $MachinePrecision] / N[(b1 * b2), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$0, (-Infinity)], N[(a1 * N[(N[(1.0 / b1), $MachinePrecision] * N[(a2 / b2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[t$95$0, -2e-278], And[N[Not[LessEqual[t$95$0, 4e-269]], $MachinePrecision], LessEqual[t$95$0, 2e+191]]], t$95$0, N[(N[(a2 / b2), $MachinePrecision] * N[(a1 / b1), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 (*.f64 a1 a2) (*.f64 b1 b2)) < -inf.0

   1. Initial program 84.2%

      \[\frac{a1 \cdot a2}{b1 \cdot b2} \]
   2. Step-by-step derivation

      1. associate-/l* 90.5%

         \[\leadsto \color{blue}{\frac{a1}{\frac{b1 \cdot b2}{a2}}} \]

      2. *-commutative 90.5%

         \[\leadsto \frac{a1}{\frac{\color{blue}{b2 \cdot b1}}{a2}} \]

      3. associate-/l* 96.8%

         \[\leadsto \frac{a1}{\color{blue}{\frac{b2}{\frac{a2}{b1}}}} \]

   3. Simplified 96.8%

      \[\leadsto \color{blue}{\frac{a1}{\frac{b2}{\frac{a2}{b1}}}} \]
   4. Step-by-step derivation

      1. associate-/r/ 96.8%

         \[\leadsto \color{blue}{\frac{a1}{b2} \cdot \frac{a2}{b1}} \]

      2. frac-times 84.2%

         \[\leadsto \color{blue}{\frac{a1 \cdot a2}{b2 \cdot b1}} \]

      3. *-commutative 84.2%

         \[\leadsto \frac{a1 \cdot a2}{\color{blue}{b1 \cdot b2}} \]

      4. frac-times 96.8%

         \[\leadsto \color{blue}{\frac{a1}{b1} \cdot \frac{a2}{b2}} \]

      5. div-inv 96.7%

         \[\leadsto \color{blue}{\left(a1 \cdot \frac{1}{b1}\right)} \cdot \frac{a2}{b2} \]

      6. associate-*l* 99.8%

         \[\leadsto \color{blue}{a1 \cdot \left(\frac{1}{b1} \cdot \frac{a2}{b2}\right)} \]

   5. Applied egg-rr 99.8%

      \[\leadsto \color{blue}{a1 \cdot \left(\frac{1}{b1} \cdot \frac{a2}{b2}\right)} \]

   if -inf.0 < (/.f64 (*.f64 a1 a2) (*.f64 b1 b2)) < -1.99999999999999988e-278 or 3.9999999999999998e-269 < (/.f64 (*.f64 a1 a2) (*.f64 b1 b2)) < 2.00000000000000015e191

   1. Initial program 99.0%

      \[\frac{a1 \cdot a2}{b1 \cdot b2} \]

   if -1.99999999999999988e-278 < (/.f64 (*.f64 a1 a2) (*.f64 b1 b2)) < 3.9999999999999998e-269 or 2.00000000000000015e191 < (/.f64 (*.f64 a1 a2) (*.f64 b1 b2))

   1. Initial program 72.6%

      \[\frac{a1 \cdot a2}{b1 \cdot b2} \]
   2. Step-by-step derivation

      1. times-frac 98.0%

         \[\leadsto \color{blue}{\frac{a1}{b1} \cdot \frac{a2}{b2}} \]

   3. Simplified 98.0%

      \[\leadsto \color{blue}{\frac{a1}{b1} \cdot \frac{a2}{b2}} \]
3. Recombined 3 regimes into one program.

4. Final simplification 98.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{a1 \cdot a2}{b1 \cdot b2} \leq -\infty:\\ \;\;\;\;a1 \cdot \left(\frac{1}{b1} \cdot \frac{a2}{b2}\right)\\ \mathbf{elif}\;\frac{a1 \cdot a2}{b1 \cdot b2} \leq -2 \cdot 10^{-278} \lor \neg \left(\frac{a1 \cdot a2}{b1 \cdot b2} \leq 4 \cdot 10^{-269}\right) \land \frac{a1 \cdot a2}{b1 \cdot b2} \leq 2 \cdot 10^{+191}:\\ \;\;\;\;\frac{a1 \cdot a2}{b1 \cdot b2}\\ \mathbf{else}:\\ \;\;\;\;\frac{a2}{b2} \cdot \frac{a1}{b1}\\ \end{array} \]

Alternative 2: 93.5% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{a1 \cdot a2}{b1 \cdot b2}\\ \mathbf{if}\;t_0 \leq -2 \cdot 10^{-278} \lor \neg \left(t_0 \leq 4 \cdot 10^{-269}\right) \land t_0 \leq 2 \cdot 10^{+191}:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;\frac{a2}{b2} \cdot \frac{a1}{b1}\\ \end{array} \end{array} \]

FPCore

(FPCore (a1 a2 b1 b2)
 :precision binary64
 (let* ((t_0 (/ (* a1 a2) (* b1 b2))))
   (if (or (<= t_0 -2e-278) (and (not (<= t_0 4e-269)) (<= t_0 2e+191)))
     t_0
     (* (/ a2 b2) (/ a1 b1)))))

C

double code(double a1, double a2, double b1, double b2) {
	double t_0 = (a1 * a2) / (b1 * b2);
	double tmp;
	if ((t_0 <= -2e-278) || (!(t_0 <= 4e-269) && (t_0 <= 2e+191))) {
		tmp = t_0;
	} else {
		tmp = (a2 / b2) * (a1 / b1);
	}
	return tmp;
}

Fortran

real(8) function code(a1, a2, b1, b2)
    real(8), intent (in) :: a1
    real(8), intent (in) :: a2
    real(8), intent (in) :: b1
    real(8), intent (in) :: b2
    real(8) :: t_0
    real(8) :: tmp
    t_0 = (a1 * a2) / (b1 * b2)
    if ((t_0 <= (-2d-278)) .or. (.not. (t_0 <= 4d-269)) .and. (t_0 <= 2d+191)) then
        tmp = t_0
    else
        tmp = (a2 / b2) * (a1 / b1)
    end if
    code = tmp
end function

Java

public static double code(double a1, double a2, double b1, double b2) {
	double t_0 = (a1 * a2) / (b1 * b2);
	double tmp;
	if ((t_0 <= -2e-278) || (!(t_0 <= 4e-269) && (t_0 <= 2e+191))) {
		tmp = t_0;
	} else {
		tmp = (a2 / b2) * (a1 / b1);
	}
	return tmp;
}

Python

def code(a1, a2, b1, b2):
	t_0 = (a1 * a2) / (b1 * b2)
	tmp = 0
	if (t_0 <= -2e-278) or (not (t_0 <= 4e-269) and (t_0 <= 2e+191)):
		tmp = t_0
	else:
		tmp = (a2 / b2) * (a1 / b1)
	return tmp

Julia

function code(a1, a2, b1, b2)
	t_0 = Float64(Float64(a1 * a2) / Float64(b1 * b2))
	tmp = 0.0
	if ((t_0 <= -2e-278) || (!(t_0 <= 4e-269) && (t_0 <= 2e+191)))
		tmp = t_0;
	else
		tmp = Float64(Float64(a2 / b2) * Float64(a1 / b1));
	end
	return tmp
end

MATLAB

function tmp_2 = code(a1, a2, b1, b2)
	t_0 = (a1 * a2) / (b1 * b2);
	tmp = 0.0;
	if ((t_0 <= -2e-278) || (~((t_0 <= 4e-269)) && (t_0 <= 2e+191)))
		tmp = t_0;
	else
		tmp = (a2 / b2) * (a1 / b1);
	end
	tmp_2 = tmp;
end

Wolfram

code[a1_, a2_, b1_, b2_] := Block[{t$95$0 = N[(N[(a1 * a2), $MachinePrecision] / N[(b1 * b2), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[t$95$0, -2e-278], And[N[Not[LessEqual[t$95$0, 4e-269]], $MachinePrecision], LessEqual[t$95$0, 2e+191]]], t$95$0, N[(N[(a2 / b2), $MachinePrecision] * N[(a1 / b1), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (*.f64 a1 a2) (*.f64 b1 b2)) < -1.99999999999999988e-278 or 3.9999999999999998e-269 < (/.f64 (*.f64 a1 a2) (*.f64 b1 b2)) < 2.00000000000000015e191

   1. Initial program 96.2%

      \[\frac{a1 \cdot a2}{b1 \cdot b2} \]

   if -1.99999999999999988e-278 < (/.f64 (*.f64 a1 a2) (*.f64 b1 b2)) < 3.9999999999999998e-269 or 2.00000000000000015e191 < (/.f64 (*.f64 a1 a2) (*.f64 b1 b2))

   1. Initial program 72.6%

      \[\frac{a1 \cdot a2}{b1 \cdot b2} \]
   2. Step-by-step derivation

      1. times-frac 98.0%

         \[\leadsto \color{blue}{\frac{a1}{b1} \cdot \frac{a2}{b2}} \]

   3. Simplified 98.0%

      \[\leadsto \color{blue}{\frac{a1}{b1} \cdot \frac{a2}{b2}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 96.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{a1 \cdot a2}{b1 \cdot b2} \leq -2 \cdot 10^{-278} \lor \neg \left(\frac{a1 \cdot a2}{b1 \cdot b2} \leq 4 \cdot 10^{-269}\right) \land \frac{a1 \cdot a2}{b1 \cdot b2} \leq 2 \cdot 10^{+191}:\\ \;\;\;\;\frac{a1 \cdot a2}{b1 \cdot b2}\\ \mathbf{else}:\\ \;\;\;\;\frac{a2}{b2} \cdot \frac{a1}{b1}\\ \end{array} \]

Alternative 3: 94.1% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b1 \cdot b2 \leq -4 \cdot 10^{+193} \lor \neg \left(b1 \cdot b2 \leq -2 \cdot 10^{-242}\right) \land \left(b1 \cdot b2 \leq 8 \cdot 10^{-265} \lor \neg \left(b1 \cdot b2 \leq 5 \cdot 10^{+194}\right)\right):\\ \;\;\;\;\frac{a2}{b2} \cdot \frac{a1}{b1}\\ \mathbf{else}:\\ \;\;\;\;a1 \cdot \frac{a2}{b1 \cdot b2}\\ \end{array} \end{array} \]

FPCore

(FPCore (a1 a2 b1 b2)
 :precision binary64
 (if (or (<= (* b1 b2) -4e+193)
         (and (not (<= (* b1 b2) -2e-242))
              (or (<= (* b1 b2) 8e-265) (not (<= (* b1 b2) 5e+194)))))
   (* (/ a2 b2) (/ a1 b1))
   (* a1 (/ a2 (* b1 b2)))))

C

double code(double a1, double a2, double b1, double b2) {
	double tmp;
	if (((b1 * b2) <= -4e+193) || (!((b1 * b2) <= -2e-242) && (((b1 * b2) <= 8e-265) || !((b1 * b2) <= 5e+194)))) {
		tmp = (a2 / b2) * (a1 / b1);
	} else {
		tmp = a1 * (a2 / (b1 * b2));
	}
	return tmp;
}

Fortran

real(8) function code(a1, a2, b1, b2)
    real(8), intent (in) :: a1
    real(8), intent (in) :: a2
    real(8), intent (in) :: b1
    real(8), intent (in) :: b2
    real(8) :: tmp
    if (((b1 * b2) <= (-4d+193)) .or. (.not. ((b1 * b2) <= (-2d-242))) .and. ((b1 * b2) <= 8d-265) .or. (.not. ((b1 * b2) <= 5d+194))) then
        tmp = (a2 / b2) * (a1 / b1)
    else
        tmp = a1 * (a2 / (b1 * b2))
    end if
    code = tmp
end function

Java

public static double code(double a1, double a2, double b1, double b2) {
	double tmp;
	if (((b1 * b2) <= -4e+193) || (!((b1 * b2) <= -2e-242) && (((b1 * b2) <= 8e-265) || !((b1 * b2) <= 5e+194)))) {
		tmp = (a2 / b2) * (a1 / b1);
	} else {
		tmp = a1 * (a2 / (b1 * b2));
	}
	return tmp;
}

Python

def code(a1, a2, b1, b2):
	tmp = 0
	if ((b1 * b2) <= -4e+193) or (not ((b1 * b2) <= -2e-242) and (((b1 * b2) <= 8e-265) or not ((b1 * b2) <= 5e+194))):
		tmp = (a2 / b2) * (a1 / b1)
	else:
		tmp = a1 * (a2 / (b1 * b2))
	return tmp

Julia

function code(a1, a2, b1, b2)
	tmp = 0.0
	if ((Float64(b1 * b2) <= -4e+193) || (!(Float64(b1 * b2) <= -2e-242) && ((Float64(b1 * b2) <= 8e-265) || !(Float64(b1 * b2) <= 5e+194))))
		tmp = Float64(Float64(a2 / b2) * Float64(a1 / b1));
	else
		tmp = Float64(a1 * Float64(a2 / Float64(b1 * b2)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(a1, a2, b1, b2)
	tmp = 0.0;
	if (((b1 * b2) <= -4e+193) || (~(((b1 * b2) <= -2e-242)) && (((b1 * b2) <= 8e-265) || ~(((b1 * b2) <= 5e+194)))))
		tmp = (a2 / b2) * (a1 / b1);
	else
		tmp = a1 * (a2 / (b1 * b2));
	end
	tmp_2 = tmp;
end

Wolfram

code[a1_, a2_, b1_, b2_] := If[Or[LessEqual[N[(b1 * b2), $MachinePrecision], -4e+193], And[N[Not[LessEqual[N[(b1 * b2), $MachinePrecision], -2e-242]], $MachinePrecision], Or[LessEqual[N[(b1 * b2), $MachinePrecision], 8e-265], N[Not[LessEqual[N[(b1 * b2), $MachinePrecision], 5e+194]], $MachinePrecision]]]], N[(N[(a2 / b2), $MachinePrecision] * N[(a1 / b1), $MachinePrecision]), $MachinePrecision], N[(a1 * N[(a2 / N[(b1 * b2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 b1 b2) < -4.00000000000000026e193 or -2e-242 < (*.f64 b1 b2) < 7.99999999999999988e-265 or 4.99999999999999989e194 < (*.f64 b1 b2)

   1. Initial program 76.0%

      \[\frac{a1 \cdot a2}{b1 \cdot b2} \]
   2. Step-by-step derivation

      1. times-frac 95.9%

         \[\leadsto \color{blue}{\frac{a1}{b1} \cdot \frac{a2}{b2}} \]

   3. Simplified 95.9%

      \[\leadsto \color{blue}{\frac{a1}{b1} \cdot \frac{a2}{b2}} \]

   if -4.00000000000000026e193 < (*.f64 b1 b2) < -2e-242 or 7.99999999999999988e-265 < (*.f64 b1 b2) < 4.99999999999999989e194

   1. Initial program 93.9%

      \[\frac{a1 \cdot a2}{b1 \cdot b2} \]
   2. Step-by-step derivation

      1. associate-/l* 93.8%

         \[\leadsto \color{blue}{\frac{a1}{\frac{b1 \cdot b2}{a2}}} \]

      2. *-commutative 93.8%

         \[\leadsto \frac{a1}{\frac{\color{blue}{b2 \cdot b1}}{a2}} \]

      3. associate-/l* 82.4%

         \[\leadsto \frac{a1}{\color{blue}{\frac{b2}{\frac{a2}{b1}}}} \]

   3. Simplified 82.4%

      \[\leadsto \color{blue}{\frac{a1}{\frac{b2}{\frac{a2}{b1}}}} \]
   4. Step-by-step derivation

      1. clear-num 81.9%

         \[\leadsto \color{blue}{\frac{1}{\frac{\frac{b2}{\frac{a2}{b1}}}{a1}}} \]

      2. associate-/r/ 81.9%

         \[\leadsto \color{blue}{\frac{1}{\frac{b2}{\frac{a2}{b1}}} \cdot a1} \]

      3. clear-num 82.6%

         \[\leadsto \color{blue}{\frac{\frac{a2}{b1}}{b2}} \cdot a1 \]

      4. associate-/l/ 94.0%

         \[\leadsto \color{blue}{\frac{a2}{b2 \cdot b1}} \cdot a1 \]

      5. *-commutative 94.0%

         \[\leadsto \frac{a2}{\color{blue}{b1 \cdot b2}} \cdot a1 \]

   5. Applied egg-rr 94.0%

      \[\leadsto \color{blue}{\frac{a2}{b1 \cdot b2} \cdot a1} \]
3. Recombined 2 regimes into one program.

4. Final simplification 94.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b1 \cdot b2 \leq -4 \cdot 10^{+193} \lor \neg \left(b1 \cdot b2 \leq -2 \cdot 10^{-242}\right) \land \left(b1 \cdot b2 \leq 8 \cdot 10^{-265} \lor \neg \left(b1 \cdot b2 \leq 5 \cdot 10^{+194}\right)\right):\\ \;\;\;\;\frac{a2}{b2} \cdot \frac{a1}{b1}\\ \mathbf{else}:\\ \;\;\;\;a1 \cdot \frac{a2}{b1 \cdot b2}\\ \end{array} \]

Alternative 4: 94.0% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{a2}{b2} \cdot \frac{a1}{b1}\\ \mathbf{if}\;b1 \cdot b2 \leq -4 \cdot 10^{+193}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;b1 \cdot b2 \leq -2 \cdot 10^{-242}:\\ \;\;\;\;a1 \cdot \frac{a2}{b1 \cdot b2}\\ \mathbf{elif}\;b1 \cdot b2 \leq 10^{-274} \lor \neg \left(b1 \cdot b2 \leq 10^{+155}\right):\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;\frac{a1}{\frac{b1 \cdot b2}{a2}}\\ \end{array} \end{array} \]

FPCore

(FPCore (a1 a2 b1 b2)
 :precision binary64
 (let* ((t_0 (* (/ a2 b2) (/ a1 b1))))
   (if (<= (* b1 b2) -4e+193)
     t_0
     (if (<= (* b1 b2) -2e-242)
       (* a1 (/ a2 (* b1 b2)))
       (if (or (<= (* b1 b2) 1e-274) (not (<= (* b1 b2) 1e+155)))
         t_0
         (/ a1 (/ (* b1 b2) a2)))))))

C

double code(double a1, double a2, double b1, double b2) {
	double t_0 = (a2 / b2) * (a1 / b1);
	double tmp;
	if ((b1 * b2) <= -4e+193) {
		tmp = t_0;
	} else if ((b1 * b2) <= -2e-242) {
		tmp = a1 * (a2 / (b1 * b2));
	} else if (((b1 * b2) <= 1e-274) || !((b1 * b2) <= 1e+155)) {
		tmp = t_0;
	} else {
		tmp = a1 / ((b1 * b2) / a2);
	}
	return tmp;
}

Fortran

real(8) function code(a1, a2, b1, b2)
    real(8), intent (in) :: a1
    real(8), intent (in) :: a2
    real(8), intent (in) :: b1
    real(8), intent (in) :: b2
    real(8) :: t_0
    real(8) :: tmp
    t_0 = (a2 / b2) * (a1 / b1)
    if ((b1 * b2) <= (-4d+193)) then
        tmp = t_0
    else if ((b1 * b2) <= (-2d-242)) then
        tmp = a1 * (a2 / (b1 * b2))
    else if (((b1 * b2) <= 1d-274) .or. (.not. ((b1 * b2) <= 1d+155))) then
        tmp = t_0
    else
        tmp = a1 / ((b1 * b2) / a2)
    end if
    code = tmp
end function

Java

public static double code(double a1, double a2, double b1, double b2) {
	double t_0 = (a2 / b2) * (a1 / b1);
	double tmp;
	if ((b1 * b2) <= -4e+193) {
		tmp = t_0;
	} else if ((b1 * b2) <= -2e-242) {
		tmp = a1 * (a2 / (b1 * b2));
	} else if (((b1 * b2) <= 1e-274) || !((b1 * b2) <= 1e+155)) {
		tmp = t_0;
	} else {
		tmp = a1 / ((b1 * b2) / a2);
	}
	return tmp;
}

Python

def code(a1, a2, b1, b2):
	t_0 = (a2 / b2) * (a1 / b1)
	tmp = 0
	if (b1 * b2) <= -4e+193:
		tmp = t_0
	elif (b1 * b2) <= -2e-242:
		tmp = a1 * (a2 / (b1 * b2))
	elif ((b1 * b2) <= 1e-274) or not ((b1 * b2) <= 1e+155):
		tmp = t_0
	else:
		tmp = a1 / ((b1 * b2) / a2)
	return tmp

Julia

function code(a1, a2, b1, b2)
	t_0 = Float64(Float64(a2 / b2) * Float64(a1 / b1))
	tmp = 0.0
	if (Float64(b1 * b2) <= -4e+193)
		tmp = t_0;
	elseif (Float64(b1 * b2) <= -2e-242)
		tmp = Float64(a1 * Float64(a2 / Float64(b1 * b2)));
	elseif ((Float64(b1 * b2) <= 1e-274) || !(Float64(b1 * b2) <= 1e+155))
		tmp = t_0;
	else
		tmp = Float64(a1 / Float64(Float64(b1 * b2) / a2));
	end
	return tmp
end

MATLAB

function tmp_2 = code(a1, a2, b1, b2)
	t_0 = (a2 / b2) * (a1 / b1);
	tmp = 0.0;
	if ((b1 * b2) <= -4e+193)
		tmp = t_0;
	elseif ((b1 * b2) <= -2e-242)
		tmp = a1 * (a2 / (b1 * b2));
	elseif (((b1 * b2) <= 1e-274) || ~(((b1 * b2) <= 1e+155)))
		tmp = t_0;
	else
		tmp = a1 / ((b1 * b2) / a2);
	end
	tmp_2 = tmp;
end

Wolfram

code[a1_, a2_, b1_, b2_] := Block[{t$95$0 = N[(N[(a2 / b2), $MachinePrecision] * N[(a1 / b1), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(b1 * b2), $MachinePrecision], -4e+193], t$95$0, If[LessEqual[N[(b1 * b2), $MachinePrecision], -2e-242], N[(a1 * N[(a2 / N[(b1 * b2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[N[(b1 * b2), $MachinePrecision], 1e-274], N[Not[LessEqual[N[(b1 * b2), $MachinePrecision], 1e+155]], $MachinePrecision]], t$95$0, N[(a1 / N[(N[(b1 * b2), $MachinePrecision] / a2), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 b1 b2) < -4.00000000000000026e193 or -2e-242 < (*.f64 b1 b2) < 9.99999999999999966e-275 or 1.00000000000000001e155 < (*.f64 b1 b2)

   1. Initial program 76.5%

      \[\frac{a1 \cdot a2}{b1 \cdot b2} \]
   2. Step-by-step derivation

      1. times-frac 95.2%

         \[\leadsto \color{blue}{\frac{a1}{b1} \cdot \frac{a2}{b2}} \]

   3. Simplified 95.2%

      \[\leadsto \color{blue}{\frac{a1}{b1} \cdot \frac{a2}{b2}} \]

   if -4.00000000000000026e193 < (*.f64 b1 b2) < -2e-242

   1. Initial program 93.4%

      \[\frac{a1 \cdot a2}{b1 \cdot b2} \]
   2. Step-by-step derivation

      1. associate-/l* 95.3%

         \[\leadsto \color{blue}{\frac{a1}{\frac{b1 \cdot b2}{a2}}} \]

      2. *-commutative 95.3%

         \[\leadsto \frac{a1}{\frac{\color{blue}{b2 \cdot b1}}{a2}} \]

      3. associate-/l* 82.4%

         \[\leadsto \frac{a1}{\color{blue}{\frac{b2}{\frac{a2}{b1}}}} \]

   3. Simplified 82.4%

      \[\leadsto \color{blue}{\frac{a1}{\frac{b2}{\frac{a2}{b1}}}} \]
   4. Step-by-step derivation

      1. clear-num 82.3%

         \[\leadsto \color{blue}{\frac{1}{\frac{\frac{b2}{\frac{a2}{b1}}}{a1}}} \]

      2. associate-/r/ 82.4%

         \[\leadsto \color{blue}{\frac{1}{\frac{b2}{\frac{a2}{b1}}} \cdot a1} \]

      3. clear-num 82.5%

         \[\leadsto \color{blue}{\frac{\frac{a2}{b1}}{b2}} \cdot a1 \]

      4. associate-/l/ 95.3%

         \[\leadsto \color{blue}{\frac{a2}{b2 \cdot b1}} \cdot a1 \]

      5. *-commutative 95.3%

         \[\leadsto \frac{a2}{\color{blue}{b1 \cdot b2}} \cdot a1 \]

   5. Applied egg-rr 95.3%

      \[\leadsto \color{blue}{\frac{a2}{b1 \cdot b2} \cdot a1} \]

   if 9.99999999999999966e-275 < (*.f64 b1 b2) < 1.00000000000000001e155

   1. Initial program 95.3%

      \[\frac{a1 \cdot a2}{b1 \cdot b2} \]
   2. Step-by-step derivation

      1. associate-/l* 94.3%

         \[\leadsto \color{blue}{\frac{a1}{\frac{b1 \cdot b2}{a2}}} \]

      2. *-commutative 94.3%

         \[\leadsto \frac{a1}{\frac{\color{blue}{b2 \cdot b1}}{a2}} \]

      3. associate-/l* 83.4%

         \[\leadsto \frac{a1}{\color{blue}{\frac{b2}{\frac{a2}{b1}}}} \]

   3. Simplified 83.4%

      \[\leadsto \color{blue}{\frac{a1}{\frac{b2}{\frac{a2}{b1}}}} \]

   4. Taylor expanded in b2 around 0 94.3%

      \[\leadsto \frac{a1}{\color{blue}{\frac{b2 \cdot b1}{a2}}} \]
3. Recombined 3 regimes into one program.

4. Final simplification 95.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b1 \cdot b2 \leq -4 \cdot 10^{+193}:\\ \;\;\;\;\frac{a2}{b2} \cdot \frac{a1}{b1}\\ \mathbf{elif}\;b1 \cdot b2 \leq -2 \cdot 10^{-242}:\\ \;\;\;\;a1 \cdot \frac{a2}{b1 \cdot b2}\\ \mathbf{elif}\;b1 \cdot b2 \leq 10^{-274} \lor \neg \left(b1 \cdot b2 \leq 10^{+155}\right):\\ \;\;\;\;\frac{a2}{b2} \cdot \frac{a1}{b1}\\ \mathbf{else}:\\ \;\;\;\;\frac{a1}{\frac{b1 \cdot b2}{a2}}\\ \end{array} \]

Alternative 5: 92.8% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{a2}{b2} \cdot \frac{a1}{b1}\\ \mathbf{if}\;b1 \cdot b2 \leq -4 \cdot 10^{+193}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;b1 \cdot b2 \leq -1 \cdot 10^{-175}:\\ \;\;\;\;a1 \cdot \frac{a2}{b1 \cdot b2}\\ \mathbf{elif}\;b1 \cdot b2 \leq 10^{-218}:\\ \;\;\;\;\frac{a1}{\frac{b2}{\frac{a2}{b1}}}\\ \mathbf{elif}\;b1 \cdot b2 \leq 10^{+155}:\\ \;\;\;\;\frac{a2}{\frac{b1 \cdot b2}{a1}}\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \end{array} \]

FPCore

(FPCore (a1 a2 b1 b2)
 :precision binary64
 (let* ((t_0 (* (/ a2 b2) (/ a1 b1))))
   (if (<= (* b1 b2) -4e+193)
     t_0
     (if (<= (* b1 b2) -1e-175)
       (* a1 (/ a2 (* b1 b2)))
       (if (<= (* b1 b2) 1e-218)
         (/ a1 (/ b2 (/ a2 b1)))
         (if (<= (* b1 b2) 1e+155) (/ a2 (/ (* b1 b2) a1)) t_0))))))

C

double code(double a1, double a2, double b1, double b2) {
	double t_0 = (a2 / b2) * (a1 / b1);
	double tmp;
	if ((b1 * b2) <= -4e+193) {
		tmp = t_0;
	} else if ((b1 * b2) <= -1e-175) {
		tmp = a1 * (a2 / (b1 * b2));
	} else if ((b1 * b2) <= 1e-218) {
		tmp = a1 / (b2 / (a2 / b1));
	} else if ((b1 * b2) <= 1e+155) {
		tmp = a2 / ((b1 * b2) / a1);
	} else {
		tmp = t_0;
	}
	return tmp;
}

Fortran

real(8) function code(a1, a2, b1, b2)
    real(8), intent (in) :: a1
    real(8), intent (in) :: a2
    real(8), intent (in) :: b1
    real(8), intent (in) :: b2
    real(8) :: t_0
    real(8) :: tmp
    t_0 = (a2 / b2) * (a1 / b1)
    if ((b1 * b2) <= (-4d+193)) then
        tmp = t_0
    else if ((b1 * b2) <= (-1d-175)) then
        tmp = a1 * (a2 / (b1 * b2))
    else if ((b1 * b2) <= 1d-218) then
        tmp = a1 / (b2 / (a2 / b1))
    else if ((b1 * b2) <= 1d+155) then
        tmp = a2 / ((b1 * b2) / a1)
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double a1, double a2, double b1, double b2) {
	double t_0 = (a2 / b2) * (a1 / b1);
	double tmp;
	if ((b1 * b2) <= -4e+193) {
		tmp = t_0;
	} else if ((b1 * b2) <= -1e-175) {
		tmp = a1 * (a2 / (b1 * b2));
	} else if ((b1 * b2) <= 1e-218) {
		tmp = a1 / (b2 / (a2 / b1));
	} else if ((b1 * b2) <= 1e+155) {
		tmp = a2 / ((b1 * b2) / a1);
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(a1, a2, b1, b2):
	t_0 = (a2 / b2) * (a1 / b1)
	tmp = 0
	if (b1 * b2) <= -4e+193:
		tmp = t_0
	elif (b1 * b2) <= -1e-175:
		tmp = a1 * (a2 / (b1 * b2))
	elif (b1 * b2) <= 1e-218:
		tmp = a1 / (b2 / (a2 / b1))
	elif (b1 * b2) <= 1e+155:
		tmp = a2 / ((b1 * b2) / a1)
	else:
		tmp = t_0
	return tmp

Julia

function code(a1, a2, b1, b2)
	t_0 = Float64(Float64(a2 / b2) * Float64(a1 / b1))
	tmp = 0.0
	if (Float64(b1 * b2) <= -4e+193)
		tmp = t_0;
	elseif (Float64(b1 * b2) <= -1e-175)
		tmp = Float64(a1 * Float64(a2 / Float64(b1 * b2)));
	elseif (Float64(b1 * b2) <= 1e-218)
		tmp = Float64(a1 / Float64(b2 / Float64(a2 / b1)));
	elseif (Float64(b1 * b2) <= 1e+155)
		tmp = Float64(a2 / Float64(Float64(b1 * b2) / a1));
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(a1, a2, b1, b2)
	t_0 = (a2 / b2) * (a1 / b1);
	tmp = 0.0;
	if ((b1 * b2) <= -4e+193)
		tmp = t_0;
	elseif ((b1 * b2) <= -1e-175)
		tmp = a1 * (a2 / (b1 * b2));
	elseif ((b1 * b2) <= 1e-218)
		tmp = a1 / (b2 / (a2 / b1));
	elseif ((b1 * b2) <= 1e+155)
		tmp = a2 / ((b1 * b2) / a1);
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[a1_, a2_, b1_, b2_] := Block[{t$95$0 = N[(N[(a2 / b2), $MachinePrecision] * N[(a1 / b1), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(b1 * b2), $MachinePrecision], -4e+193], t$95$0, If[LessEqual[N[(b1 * b2), $MachinePrecision], -1e-175], N[(a1 * N[(a2 / N[(b1 * b2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(b1 * b2), $MachinePrecision], 1e-218], N[(a1 / N[(b2 / N[(a2 / b1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(b1 * b2), $MachinePrecision], 1e+155], N[(a2 / N[(N[(b1 * b2), $MachinePrecision] / a1), $MachinePrecision]), $MachinePrecision], t$95$0]]]]]

Derivation

1. Split input into 4 regimes

2. if (*.f64 b1 b2) < -4.00000000000000026e193 or 1.00000000000000001e155 < (*.f64 b1 b2)

   1. Initial program 75.3%

      \[\frac{a1 \cdot a2}{b1 \cdot b2} \]
   2. Step-by-step derivation

      1. times-frac 95.4%

         \[\leadsto \color{blue}{\frac{a1}{b1} \cdot \frac{a2}{b2}} \]

   3. Simplified 95.4%

      \[\leadsto \color{blue}{\frac{a1}{b1} \cdot \frac{a2}{b2}} \]

   if -4.00000000000000026e193 < (*.f64 b1 b2) < -1e-175

   1. Initial program 94.0%

      \[\frac{a1 \cdot a2}{b1 \cdot b2} \]
   2. Step-by-step derivation

      1. associate-/l* 94.6%

         \[\leadsto \color{blue}{\frac{a1}{\frac{b1 \cdot b2}{a2}}} \]

      2. *-commutative 94.6%

         \[\leadsto \frac{a1}{\frac{\color{blue}{b2 \cdot b1}}{a2}} \]

      3. associate-/l* 79.8%

         \[\leadsto \frac{a1}{\color{blue}{\frac{b2}{\frac{a2}{b1}}}} \]

   3. Simplified 79.8%

      \[\leadsto \color{blue}{\frac{a1}{\frac{b2}{\frac{a2}{b1}}}} \]
   4. Step-by-step derivation

      1. clear-num 79.6%

         \[\leadsto \color{blue}{\frac{1}{\frac{\frac{b2}{\frac{a2}{b1}}}{a1}}} \]

      2. associate-/r/ 79.8%

         \[\leadsto \color{blue}{\frac{1}{\frac{b2}{\frac{a2}{b1}}} \cdot a1} \]

      3. clear-num 80.0%

         \[\leadsto \color{blue}{\frac{\frac{a2}{b1}}{b2}} \cdot a1 \]

      4. associate-/l/ 94.7%

         \[\leadsto \color{blue}{\frac{a2}{b2 \cdot b1}} \cdot a1 \]

      5. *-commutative 94.7%

         \[\leadsto \frac{a2}{\color{blue}{b1 \cdot b2}} \cdot a1 \]

   5. Applied egg-rr 94.7%

      \[\leadsto \color{blue}{\frac{a2}{b1 \cdot b2} \cdot a1} \]

   if -1e-175 < (*.f64 b1 b2) < 1e-218

   1. Initial program 84.1%

      \[\frac{a1 \cdot a2}{b1 \cdot b2} \]
   2. Step-by-step derivation

      1. associate-/l* 86.3%

         \[\leadsto \color{blue}{\frac{a1}{\frac{b1 \cdot b2}{a2}}} \]

      2. *-commutative 86.3%

         \[\leadsto \frac{a1}{\frac{\color{blue}{b2 \cdot b1}}{a2}} \]

      3. associate-/l* 96.4%

         \[\leadsto \frac{a1}{\color{blue}{\frac{b2}{\frac{a2}{b1}}}} \]

   3. Simplified 96.4%

      \[\leadsto \color{blue}{\frac{a1}{\frac{b2}{\frac{a2}{b1}}}} \]

   if 1e-218 < (*.f64 b1 b2) < 1.00000000000000001e155

   1. Initial program 94.8%

      \[\frac{a1 \cdot a2}{b1 \cdot b2} \]
   2. Step-by-step derivation

      1. times-frac 79.7%

         \[\leadsto \color{blue}{\frac{a1}{b1} \cdot \frac{a2}{b2}} \]

   3. Simplified 79.7%

      \[\leadsto \color{blue}{\frac{a1}{b1} \cdot \frac{a2}{b2}} \]
   4. Step-by-step derivation

      1. frac-times 94.8%

         \[\leadsto \color{blue}{\frac{a1 \cdot a2}{b1 \cdot b2}} \]

      2. *-commutative 94.8%

         \[\leadsto \frac{\color{blue}{a2 \cdot a1}}{b1 \cdot b2} \]

      3. associate-/l* 95.3%

         \[\leadsto \color{blue}{\frac{a2}{\frac{b1 \cdot b2}{a1}}} \]

   5. Applied egg-rr 95.3%

      \[\leadsto \color{blue}{\frac{a2}{\frac{b1 \cdot b2}{a1}}} \]
3. Recombined 4 regimes into one program.

4. Final simplification 95.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b1 \cdot b2 \leq -4 \cdot 10^{+193}:\\ \;\;\;\;\frac{a2}{b2} \cdot \frac{a1}{b1}\\ \mathbf{elif}\;b1 \cdot b2 \leq -1 \cdot 10^{-175}:\\ \;\;\;\;a1 \cdot \frac{a2}{b1 \cdot b2}\\ \mathbf{elif}\;b1 \cdot b2 \leq 10^{-218}:\\ \;\;\;\;\frac{a1}{\frac{b2}{\frac{a2}{b1}}}\\ \mathbf{elif}\;b1 \cdot b2 \leq 10^{+155}:\\ \;\;\;\;\frac{a2}{\frac{b1 \cdot b2}{a1}}\\ \mathbf{else}:\\ \;\;\;\;\frac{a2}{b2} \cdot \frac{a1}{b1}\\ \end{array} \]

Alternative 6: 86.4% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \frac{a2}{b2} \cdot \frac{a1}{b1} \end{array} \]

FPCore

(FPCore (a1 a2 b1 b2) :precision binary64 (* (/ a2 b2) (/ a1 b1)))

C

double code(double a1, double a2, double b1, double b2) {
	return (a2 / b2) * (a1 / b1);
}

Fortran

real(8) function code(a1, a2, b1, b2)
    real(8), intent (in) :: a1
    real(8), intent (in) :: a2
    real(8), intent (in) :: b1
    real(8), intent (in) :: b2
    code = (a2 / b2) * (a1 / b1)
end function

Java

public static double code(double a1, double a2, double b1, double b2) {
	return (a2 / b2) * (a1 / b1);
}

Python

def code(a1, a2, b1, b2):
	return (a2 / b2) * (a1 / b1)

Julia

function code(a1, a2, b1, b2)
	return Float64(Float64(a2 / b2) * Float64(a1 / b1))
end

MATLAB

function tmp = code(a1, a2, b1, b2)
	tmp = (a2 / b2) * (a1 / b1);
end

Wolfram

code[a1_, a2_, b1_, b2_] := N[(N[(a2 / b2), $MachinePrecision] * N[(a1 / b1), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 87.2%

   \[\frac{a1 \cdot a2}{b1 \cdot b2} \]
2. Step-by-step derivation

   1. times-frac 85.6%

      \[\leadsto \color{blue}{\frac{a1}{b1} \cdot \frac{a2}{b2}} \]

3. Simplified 85.6%

   \[\leadsto \color{blue}{\frac{a1}{b1} \cdot \frac{a2}{b2}} \]

4. Final simplification 85.6%

   \[\leadsto \frac{a2}{b2} \cdot \frac{a1}{b1} \]

Developer target: 86.4% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \frac{a1}{b1} \cdot \frac{a2}{b2} \end{array} \]

FPCore

(FPCore (a1 a2 b1 b2) :precision binary64 (* (/ a1 b1) (/ a2 b2)))

C

double code(double a1, double a2, double b1, double b2) {
	return (a1 / b1) * (a2 / b2);
}

Fortran

real(8) function code(a1, a2, b1, b2)
    real(8), intent (in) :: a1
    real(8), intent (in) :: a2
    real(8), intent (in) :: b1
    real(8), intent (in) :: b2
    code = (a1 / b1) * (a2 / b2)
end function

Java

public static double code(double a1, double a2, double b1, double b2) {
	return (a1 / b1) * (a2 / b2);
}

Python

def code(a1, a2, b1, b2):
	return (a1 / b1) * (a2 / b2)

Julia

function code(a1, a2, b1, b2)
	return Float64(Float64(a1 / b1) * Float64(a2 / b2))
end

MATLAB

function tmp = code(a1, a2, b1, b2)
	tmp = (a1 / b1) * (a2 / b2);
end

Wolfram

code[a1_, a2_, b1_, b2_] := N[(N[(a1 / b1), $MachinePrecision] * N[(a2 / b2), $MachinePrecision]), $MachinePrecision]

Reproduce

herbie shell --seed 2023207 
(FPCore (a1 a2 b1 b2)
  :name "Quotient of products"
  :precision binary64

  :herbie-target
  (* (/ a1 b1) (/ a2 b2))

  (/ (* a1 a2) (* b1 b2)))