Quotient of products

Percentage Accurate: 85.9% → 97.1%

Time: 4.1s

Alternatives: 9

Speedup: 1.0×

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: 85.9% 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: 97.1% accurate, 0.2× speedup

Math

\[\begin{array}{l} [a1, a2] = \mathsf{sort}([a1, a2])\\ [b1, b2] = \mathsf{sort}([b1, b2])\\ \\ \begin{array}{l} t_0 := \frac{a2 \cdot a1}{b1 \cdot b2}\\ t_1 := \frac{a2}{b1} \cdot \frac{a1}{b2}\\ \mathbf{if}\;t_0 \leq -\infty:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t_0 \leq -1 \cdot 10^{-315}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;t_0 \leq 0:\\ \;\;\;\;a1 \cdot \frac{\frac{a2}{b2}}{b1}\\ \mathbf{elif}\;t_0 \leq 5 \cdot 10^{+303}:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

NOTE: a1 and a2 should be sorted in increasing order before calling this function.
NOTE: b1 and b2 should be sorted in increasing order before calling this function.
(FPCore (a1 a2 b1 b2)
 :precision binary64
 (let* ((t_0 (/ (* a2 a1) (* b1 b2))) (t_1 (* (/ a2 b1) (/ a1 b2))))
   (if (<= t_0 (- INFINITY))
     t_1
     (if (<= t_0 -1e-315)
       t_0
       (if (<= t_0 0.0)
         (* a1 (/ (/ a2 b2) b1))
         (if (<= t_0 5e+303) t_0 t_1))))))

C

assert(a1 < a2);
assert(b1 < b2);
double code(double a1, double a2, double b1, double b2) {
	double t_0 = (a2 * a1) / (b1 * b2);
	double t_1 = (a2 / b1) * (a1 / b2);
	double tmp;
	if (t_0 <= -((double) INFINITY)) {
		tmp = t_1;
	} else if (t_0 <= -1e-315) {
		tmp = t_0;
	} else if (t_0 <= 0.0) {
		tmp = a1 * ((a2 / b2) / b1);
	} else if (t_0 <= 5e+303) {
		tmp = t_0;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Java

assert a1 < a2;
assert b1 < b2;
public static double code(double a1, double a2, double b1, double b2) {
	double t_0 = (a2 * a1) / (b1 * b2);
	double t_1 = (a2 / b1) * (a1 / b2);
	double tmp;
	if (t_0 <= -Double.POSITIVE_INFINITY) {
		tmp = t_1;
	} else if (t_0 <= -1e-315) {
		tmp = t_0;
	} else if (t_0 <= 0.0) {
		tmp = a1 * ((a2 / b2) / b1);
	} else if (t_0 <= 5e+303) {
		tmp = t_0;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

[a1, a2] = sort([a1, a2])
[b1, b2] = sort([b1, b2])
def code(a1, a2, b1, b2):
	t_0 = (a2 * a1) / (b1 * b2)
	t_1 = (a2 / b1) * (a1 / b2)
	tmp = 0
	if t_0 <= -math.inf:
		tmp = t_1
	elif t_0 <= -1e-315:
		tmp = t_0
	elif t_0 <= 0.0:
		tmp = a1 * ((a2 / b2) / b1)
	elif t_0 <= 5e+303:
		tmp = t_0
	else:
		tmp = t_1
	return tmp

Julia

a1, a2 = sort([a1, a2])
b1, b2 = sort([b1, b2])
function code(a1, a2, b1, b2)
	t_0 = Float64(Float64(a2 * a1) / Float64(b1 * b2))
	t_1 = Float64(Float64(a2 / b1) * Float64(a1 / b2))
	tmp = 0.0
	if (t_0 <= Float64(-Inf))
		tmp = t_1;
	elseif (t_0 <= -1e-315)
		tmp = t_0;
	elseif (t_0 <= 0.0)
		tmp = Float64(a1 * Float64(Float64(a2 / b2) / b1));
	elseif (t_0 <= 5e+303)
		tmp = t_0;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

a1, a2 = num2cell(sort([a1, a2])){:}
b1, b2 = num2cell(sort([b1, b2])){:}
function tmp_2 = code(a1, a2, b1, b2)
	t_0 = (a2 * a1) / (b1 * b2);
	t_1 = (a2 / b1) * (a1 / b2);
	tmp = 0.0;
	if (t_0 <= -Inf)
		tmp = t_1;
	elseif (t_0 <= -1e-315)
		tmp = t_0;
	elseif (t_0 <= 0.0)
		tmp = a1 * ((a2 / b2) / b1);
	elseif (t_0 <= 5e+303)
		tmp = t_0;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: a1 and a2 should be sorted in increasing order before calling this function.
NOTE: b1 and b2 should be sorted in increasing order before calling this function.
code[a1_, a2_, b1_, b2_] := Block[{t$95$0 = N[(N[(a2 * a1), $MachinePrecision] / N[(b1 * b2), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(N[(a2 / b1), $MachinePrecision] * N[(a1 / b2), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$0, (-Infinity)], t$95$1, If[LessEqual[t$95$0, -1e-315], t$95$0, If[LessEqual[t$95$0, 0.0], N[(a1 * N[(N[(a2 / b2), $MachinePrecision] / b1), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$0, 5e+303], t$95$0, t$95$1]]]]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 (*.f64 a1 a2) (*.f64 b1 b2)) < -inf.0 or 4.9999999999999997e303 < (/.f64 (*.f64 a1 a2) (*.f64 b1 b2))

   1. Initial program 75.0%

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

      1. *-commutative 75.0%

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

      2. times-frac 96.2%

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

   3. Applied egg-rr 96.2%

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

   if -inf.0 < (/.f64 (*.f64 a1 a2) (*.f64 b1 b2)) < -9.999999985e-316 or -0.0 < (/.f64 (*.f64 a1 a2) (*.f64 b1 b2)) < 4.9999999999999997e303

   1. Initial program 99.4%

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

   if -9.999999985e-316 < (/.f64 (*.f64 a1 a2) (*.f64 b1 b2)) < -0.0

   1. Initial program 69.0%

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

      1. times-frac 94.9%

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

      2. associate-*l/ 90.3%

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

      3. associate-*r/ 93.2%

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

   3. Simplified 93.2%

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

4. Final simplification 96.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{a2 \cdot a1}{b1 \cdot b2} \leq -\infty:\\ \;\;\;\;\frac{a2}{b1} \cdot \frac{a1}{b2}\\ \mathbf{elif}\;\frac{a2 \cdot a1}{b1 \cdot b2} \leq -1 \cdot 10^{-315}:\\ \;\;\;\;\frac{a2 \cdot a1}{b1 \cdot b2}\\ \mathbf{elif}\;\frac{a2 \cdot a1}{b1 \cdot b2} \leq 0:\\ \;\;\;\;a1 \cdot \frac{\frac{a2}{b2}}{b1}\\ \mathbf{elif}\;\frac{a2 \cdot a1}{b1 \cdot b2} \leq 5 \cdot 10^{+303}:\\ \;\;\;\;\frac{a2 \cdot a1}{b1 \cdot b2}\\ \mathbf{else}:\\ \;\;\;\;\frac{a2}{b1} \cdot \frac{a1}{b2}\\ \end{array} \]

Alternative 2: 91.3% accurate, 0.0× speedup

Math

\[\begin{array}{l} [a1, a2] = \mathsf{sort}([a1, a2])\\ [b1, b2] = \mathsf{sort}([b1, b2])\\ \\ \begin{array}{l} \mathbf{if}\;b1 \cdot b2 \leq -5 \cdot 10^{+214}:\\ \;\;\;\;\frac{\frac{a2 \cdot \frac{a1}{b1}}{\sqrt{b2}}}{\sqrt{b2}}\\ \mathbf{elif}\;b1 \cdot b2 \leq -5 \cdot 10^{-308} \lor \neg \left(b1 \cdot b2 \leq 5 \cdot 10^{-171}\right):\\ \;\;\;\;a1 \cdot \frac{a2}{b1 \cdot b2}\\ \mathbf{else}:\\ \;\;\;\;\frac{a2}{b1} \cdot \frac{a1}{b2}\\ \end{array} \end{array} \]

FPCore

NOTE: a1 and a2 should be sorted in increasing order before calling this function.
NOTE: b1 and b2 should be sorted in increasing order before calling this function.
(FPCore (a1 a2 b1 b2)
 :precision binary64
 (if (<= (* b1 b2) -5e+214)
   (/ (/ (* a2 (/ a1 b1)) (sqrt b2)) (sqrt b2))
   (if (or (<= (* b1 b2) -5e-308) (not (<= (* b1 b2) 5e-171)))
     (* a1 (/ a2 (* b1 b2)))
     (* (/ a2 b1) (/ a1 b2)))))

C

assert(a1 < a2);
assert(b1 < b2);
double code(double a1, double a2, double b1, double b2) {
	double tmp;
	if ((b1 * b2) <= -5e+214) {
		tmp = ((a2 * (a1 / b1)) / sqrt(b2)) / sqrt(b2);
	} else if (((b1 * b2) <= -5e-308) || !((b1 * b2) <= 5e-171)) {
		tmp = a1 * (a2 / (b1 * b2));
	} else {
		tmp = (a2 / b1) * (a1 / b2);
	}
	return tmp;
}

Fortran

NOTE: a1 and a2 should be sorted in increasing order before calling this function.
NOTE: b1 and b2 should be sorted in increasing order before calling this function.
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) <= (-5d+214)) then
        tmp = ((a2 * (a1 / b1)) / sqrt(b2)) / sqrt(b2)
    else if (((b1 * b2) <= (-5d-308)) .or. (.not. ((b1 * b2) <= 5d-171))) then
        tmp = a1 * (a2 / (b1 * b2))
    else
        tmp = (a2 / b1) * (a1 / b2)
    end if
    code = tmp
end function

Java

assert a1 < a2;
assert b1 < b2;
public static double code(double a1, double a2, double b1, double b2) {
	double tmp;
	if ((b1 * b2) <= -5e+214) {
		tmp = ((a2 * (a1 / b1)) / Math.sqrt(b2)) / Math.sqrt(b2);
	} else if (((b1 * b2) <= -5e-308) || !((b1 * b2) <= 5e-171)) {
		tmp = a1 * (a2 / (b1 * b2));
	} else {
		tmp = (a2 / b1) * (a1 / b2);
	}
	return tmp;
}

Python

[a1, a2] = sort([a1, a2])
[b1, b2] = sort([b1, b2])
def code(a1, a2, b1, b2):
	tmp = 0
	if (b1 * b2) <= -5e+214:
		tmp = ((a2 * (a1 / b1)) / math.sqrt(b2)) / math.sqrt(b2)
	elif ((b1 * b2) <= -5e-308) or not ((b1 * b2) <= 5e-171):
		tmp = a1 * (a2 / (b1 * b2))
	else:
		tmp = (a2 / b1) * (a1 / b2)
	return tmp

Julia

a1, a2 = sort([a1, a2])
b1, b2 = sort([b1, b2])
function code(a1, a2, b1, b2)
	tmp = 0.0
	if (Float64(b1 * b2) <= -5e+214)
		tmp = Float64(Float64(Float64(a2 * Float64(a1 / b1)) / sqrt(b2)) / sqrt(b2));
	elseif ((Float64(b1 * b2) <= -5e-308) || !(Float64(b1 * b2) <= 5e-171))
		tmp = Float64(a1 * Float64(a2 / Float64(b1 * b2)));
	else
		tmp = Float64(Float64(a2 / b1) * Float64(a1 / b2));
	end
	return tmp
end

MATLAB

a1, a2 = num2cell(sort([a1, a2])){:}
b1, b2 = num2cell(sort([b1, b2])){:}
function tmp_2 = code(a1, a2, b1, b2)
	tmp = 0.0;
	if ((b1 * b2) <= -5e+214)
		tmp = ((a2 * (a1 / b1)) / sqrt(b2)) / sqrt(b2);
	elseif (((b1 * b2) <= -5e-308) || ~(((b1 * b2) <= 5e-171)))
		tmp = a1 * (a2 / (b1 * b2));
	else
		tmp = (a2 / b1) * (a1 / b2);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: a1 and a2 should be sorted in increasing order before calling this function.
NOTE: b1 and b2 should be sorted in increasing order before calling this function.
code[a1_, a2_, b1_, b2_] := If[LessEqual[N[(b1 * b2), $MachinePrecision], -5e+214], N[(N[(N[(a2 * N[(a1 / b1), $MachinePrecision]), $MachinePrecision] / N[Sqrt[b2], $MachinePrecision]), $MachinePrecision] / N[Sqrt[b2], $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[N[(b1 * b2), $MachinePrecision], -5e-308], N[Not[LessEqual[N[(b1 * b2), $MachinePrecision], 5e-171]], $MachinePrecision]], N[(a1 * N[(a2 / N[(b1 * b2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(a2 / b1), $MachinePrecision] * N[(a1 / b2), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 b1 b2) < -4.99999999999999953e214

   1. Initial program 64.9%

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

      1. times-frac 81.0%

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

      2. associate-*l/ 92.9%

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

      3. associate-*r/ 83.8%

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

   3. Simplified 83.8%

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

      1. associate-/l/ 65.2%

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

      2. associate-*r/ 64.9%

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

      3. associate-/r* 92.5%

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

      4. add-sqr-sqrt 55.4%

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

      5. associate-/r* 55.4%

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

      6. associate-*l/ 50.2%

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

      7. *-commutative 50.2%

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

   5. Applied egg-rr 50.2%

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

   if -4.99999999999999953e214 < (*.f64 b1 b2) < -4.99999999999999955e-308 or 4.99999999999999992e-171 < (*.f64 b1 b2)

   1. Initial program 89.6%

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

      1. *-commutative 89.6%

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

      2. associate-*l/ 96.8%

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

      3. *-commutative 96.8%

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

   3. Applied egg-rr 96.8%

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

   if -4.99999999999999955e-308 < (*.f64 b1 b2) < 4.99999999999999992e-171

   1. Initial program 76.2%

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

      1. *-commutative 76.2%

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

      2. times-frac 92.1%

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

   3. Applied egg-rr 92.1%

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

4. Final simplification 91.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b1 \cdot b2 \leq -5 \cdot 10^{+214}:\\ \;\;\;\;\frac{\frac{a2 \cdot \frac{a1}{b1}}{\sqrt{b2}}}{\sqrt{b2}}\\ \mathbf{elif}\;b1 \cdot b2 \leq -5 \cdot 10^{-308} \lor \neg \left(b1 \cdot b2 \leq 5 \cdot 10^{-171}\right):\\ \;\;\;\;a1 \cdot \frac{a2}{b1 \cdot b2}\\ \mathbf{else}:\\ \;\;\;\;\frac{a2}{b1} \cdot \frac{a1}{b2}\\ \end{array} \]

Alternative 3: 91.2% accurate, 0.4× speedup

Math

\[\begin{array}{l} [a1, a2] = \mathsf{sort}([a1, a2])\\ [b1, b2] = \mathsf{sort}([b1, b2])\\ \\ \begin{array}{l} \mathbf{if}\;b1 \cdot b2 \leq -1 \cdot 10^{+272}:\\ \;\;\;\;\frac{\frac{a1}{b1}}{\frac{b2}{a2}}\\ \mathbf{elif}\;b1 \cdot b2 \leq -5 \cdot 10^{-308} \lor \neg \left(b1 \cdot b2 \leq 5 \cdot 10^{-171}\right):\\ \;\;\;\;a1 \cdot \frac{a2}{b1 \cdot b2}\\ \mathbf{else}:\\ \;\;\;\;\frac{a2}{b1} \cdot \frac{a1}{b2}\\ \end{array} \end{array} \]

FPCore

NOTE: a1 and a2 should be sorted in increasing order before calling this function.
NOTE: b1 and b2 should be sorted in increasing order before calling this function.
(FPCore (a1 a2 b1 b2)
 :precision binary64
 (if (<= (* b1 b2) -1e+272)
   (/ (/ a1 b1) (/ b2 a2))
   (if (or (<= (* b1 b2) -5e-308) (not (<= (* b1 b2) 5e-171)))
     (* a1 (/ a2 (* b1 b2)))
     (* (/ a2 b1) (/ a1 b2)))))

C

assert(a1 < a2);
assert(b1 < b2);
double code(double a1, double a2, double b1, double b2) {
	double tmp;
	if ((b1 * b2) <= -1e+272) {
		tmp = (a1 / b1) / (b2 / a2);
	} else if (((b1 * b2) <= -5e-308) || !((b1 * b2) <= 5e-171)) {
		tmp = a1 * (a2 / (b1 * b2));
	} else {
		tmp = (a2 / b1) * (a1 / b2);
	}
	return tmp;
}

Fortran

NOTE: a1 and a2 should be sorted in increasing order before calling this function.
NOTE: b1 and b2 should be sorted in increasing order before calling this function.
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) <= (-1d+272)) then
        tmp = (a1 / b1) / (b2 / a2)
    else if (((b1 * b2) <= (-5d-308)) .or. (.not. ((b1 * b2) <= 5d-171))) then
        tmp = a1 * (a2 / (b1 * b2))
    else
        tmp = (a2 / b1) * (a1 / b2)
    end if
    code = tmp
end function

Java

assert a1 < a2;
assert b1 < b2;
public static double code(double a1, double a2, double b1, double b2) {
	double tmp;
	if ((b1 * b2) <= -1e+272) {
		tmp = (a1 / b1) / (b2 / a2);
	} else if (((b1 * b2) <= -5e-308) || !((b1 * b2) <= 5e-171)) {
		tmp = a1 * (a2 / (b1 * b2));
	} else {
		tmp = (a2 / b1) * (a1 / b2);
	}
	return tmp;
}

Python

[a1, a2] = sort([a1, a2])
[b1, b2] = sort([b1, b2])
def code(a1, a2, b1, b2):
	tmp = 0
	if (b1 * b2) <= -1e+272:
		tmp = (a1 / b1) / (b2 / a2)
	elif ((b1 * b2) <= -5e-308) or not ((b1 * b2) <= 5e-171):
		tmp = a1 * (a2 / (b1 * b2))
	else:
		tmp = (a2 / b1) * (a1 / b2)
	return tmp

Julia

a1, a2 = sort([a1, a2])
b1, b2 = sort([b1, b2])
function code(a1, a2, b1, b2)
	tmp = 0.0
	if (Float64(b1 * b2) <= -1e+272)
		tmp = Float64(Float64(a1 / b1) / Float64(b2 / a2));
	elseif ((Float64(b1 * b2) <= -5e-308) || !(Float64(b1 * b2) <= 5e-171))
		tmp = Float64(a1 * Float64(a2 / Float64(b1 * b2)));
	else
		tmp = Float64(Float64(a2 / b1) * Float64(a1 / b2));
	end
	return tmp
end

MATLAB

a1, a2 = num2cell(sort([a1, a2])){:}
b1, b2 = num2cell(sort([b1, b2])){:}
function tmp_2 = code(a1, a2, b1, b2)
	tmp = 0.0;
	if ((b1 * b2) <= -1e+272)
		tmp = (a1 / b1) / (b2 / a2);
	elseif (((b1 * b2) <= -5e-308) || ~(((b1 * b2) <= 5e-171)))
		tmp = a1 * (a2 / (b1 * b2));
	else
		tmp = (a2 / b1) * (a1 / b2);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: a1 and a2 should be sorted in increasing order before calling this function.
NOTE: b1 and b2 should be sorted in increasing order before calling this function.
code[a1_, a2_, b1_, b2_] := If[LessEqual[N[(b1 * b2), $MachinePrecision], -1e+272], N[(N[(a1 / b1), $MachinePrecision] / N[(b2 / a2), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[N[(b1 * b2), $MachinePrecision], -5e-308], N[Not[LessEqual[N[(b1 * b2), $MachinePrecision], 5e-171]], $MachinePrecision]], N[(a1 * N[(a2 / N[(b1 * b2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(a2 / b1), $MachinePrecision] * N[(a1 / b2), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 b1 b2) < -1.0000000000000001e272

   1. Initial program 54.9%

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

      1. times-frac 84.2%

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

      2. associate-*l/ 95.3%

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

      3. associate-*r/ 83.6%

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

   3. Simplified 83.6%

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

      1. associate-*r/ 95.3%

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

      2. associate-*l/ 84.2%

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

      3. clear-num 84.2%

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

      4. un-div-inv 84.3%

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

   5. Applied egg-rr 84.3%

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

   if -1.0000000000000001e272 < (*.f64 b1 b2) < -4.99999999999999955e-308 or 4.99999999999999992e-171 < (*.f64 b1 b2)

   1. Initial program 89.9%

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

      1. *-commutative 89.9%

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

      2. associate-*l/ 96.4%

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

      3. *-commutative 96.4%

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

   3. Applied egg-rr 96.4%

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

   if -4.99999999999999955e-308 < (*.f64 b1 b2) < 4.99999999999999992e-171

   1. Initial program 76.2%

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

      1. *-commutative 76.2%

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

      2. times-frac 92.1%

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

   3. Applied egg-rr 92.1%

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

4. Final simplification 94.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b1 \cdot b2 \leq -1 \cdot 10^{+272}:\\ \;\;\;\;\frac{\frac{a1}{b1}}{\frac{b2}{a2}}\\ \mathbf{elif}\;b1 \cdot b2 \leq -5 \cdot 10^{-308} \lor \neg \left(b1 \cdot b2 \leq 5 \cdot 10^{-171}\right):\\ \;\;\;\;a1 \cdot \frac{a2}{b1 \cdot b2}\\ \mathbf{else}:\\ \;\;\;\;\frac{a2}{b1} \cdot \frac{a1}{b2}\\ \end{array} \]

Alternative 4: 86.6% accurate, 0.5× speedup

Math

\[\begin{array}{l} [a1, a2] = \mathsf{sort}([a1, a2])\\ [b1, b2] = \mathsf{sort}([b1, b2])\\ \\ \begin{array}{l} \mathbf{if}\;b1 \leq -2.7 \cdot 10^{+256}:\\ \;\;\;\;a2 \cdot \frac{a1}{b1 \cdot b2}\\ \mathbf{elif}\;b1 \leq -1.45 \cdot 10^{+63} \lor \neg \left(b1 \leq 1.6 \cdot 10^{-253}\right):\\ \;\;\;\;a1 \cdot \frac{\frac{a2}{b2}}{b1}\\ \mathbf{else}:\\ \;\;\;\;\frac{a2}{b1} \cdot \frac{a1}{b2}\\ \end{array} \end{array} \]

FPCore

NOTE: a1 and a2 should be sorted in increasing order before calling this function.
NOTE: b1 and b2 should be sorted in increasing order before calling this function.
(FPCore (a1 a2 b1 b2)
 :precision binary64
 (if (<= b1 -2.7e+256)
   (* a2 (/ a1 (* b1 b2)))
   (if (or (<= b1 -1.45e+63) (not (<= b1 1.6e-253)))
     (* a1 (/ (/ a2 b2) b1))
     (* (/ a2 b1) (/ a1 b2)))))

C

assert(a1 < a2);
assert(b1 < b2);
double code(double a1, double a2, double b1, double b2) {
	double tmp;
	if (b1 <= -2.7e+256) {
		tmp = a2 * (a1 / (b1 * b2));
	} else if ((b1 <= -1.45e+63) || !(b1 <= 1.6e-253)) {
		tmp = a1 * ((a2 / b2) / b1);
	} else {
		tmp = (a2 / b1) * (a1 / b2);
	}
	return tmp;
}

Fortran

NOTE: a1 and a2 should be sorted in increasing order before calling this function.
NOTE: b1 and b2 should be sorted in increasing order before calling this function.
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 <= (-2.7d+256)) then
        tmp = a2 * (a1 / (b1 * b2))
    else if ((b1 <= (-1.45d+63)) .or. (.not. (b1 <= 1.6d-253))) then
        tmp = a1 * ((a2 / b2) / b1)
    else
        tmp = (a2 / b1) * (a1 / b2)
    end if
    code = tmp
end function

Java

assert a1 < a2;
assert b1 < b2;
public static double code(double a1, double a2, double b1, double b2) {
	double tmp;
	if (b1 <= -2.7e+256) {
		tmp = a2 * (a1 / (b1 * b2));
	} else if ((b1 <= -1.45e+63) || !(b1 <= 1.6e-253)) {
		tmp = a1 * ((a2 / b2) / b1);
	} else {
		tmp = (a2 / b1) * (a1 / b2);
	}
	return tmp;
}

Python

[a1, a2] = sort([a1, a2])
[b1, b2] = sort([b1, b2])
def code(a1, a2, b1, b2):
	tmp = 0
	if b1 <= -2.7e+256:
		tmp = a2 * (a1 / (b1 * b2))
	elif (b1 <= -1.45e+63) or not (b1 <= 1.6e-253):
		tmp = a1 * ((a2 / b2) / b1)
	else:
		tmp = (a2 / b1) * (a1 / b2)
	return tmp

Julia

a1, a2 = sort([a1, a2])
b1, b2 = sort([b1, b2])
function code(a1, a2, b1, b2)
	tmp = 0.0
	if (b1 <= -2.7e+256)
		tmp = Float64(a2 * Float64(a1 / Float64(b1 * b2)));
	elseif ((b1 <= -1.45e+63) || !(b1 <= 1.6e-253))
		tmp = Float64(a1 * Float64(Float64(a2 / b2) / b1));
	else
		tmp = Float64(Float64(a2 / b1) * Float64(a1 / b2));
	end
	return tmp
end

MATLAB

a1, a2 = num2cell(sort([a1, a2])){:}
b1, b2 = num2cell(sort([b1, b2])){:}
function tmp_2 = code(a1, a2, b1, b2)
	tmp = 0.0;
	if (b1 <= -2.7e+256)
		tmp = a2 * (a1 / (b1 * b2));
	elseif ((b1 <= -1.45e+63) || ~((b1 <= 1.6e-253)))
		tmp = a1 * ((a2 / b2) / b1);
	else
		tmp = (a2 / b1) * (a1 / b2);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: a1 and a2 should be sorted in increasing order before calling this function.
NOTE: b1 and b2 should be sorted in increasing order before calling this function.
code[a1_, a2_, b1_, b2_] := If[LessEqual[b1, -2.7e+256], N[(a2 * N[(a1 / N[(b1 * b2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[b1, -1.45e+63], N[Not[LessEqual[b1, 1.6e-253]], $MachinePrecision]], N[(a1 * N[(N[(a2 / b2), $MachinePrecision] / b1), $MachinePrecision]), $MachinePrecision], N[(N[(a2 / b1), $MachinePrecision] * N[(a1 / b2), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if b1 < -2.69999999999999995e256

   1. Initial program 83.9%

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

      1. associate-/l* 99.2%

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

      2. associate-/r/ 84.3%

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

      3. *-commutative 84.3%

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

   3. Applied egg-rr 84.3%

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

   if -2.69999999999999995e256 < b1 < -1.45e63 or 1.5999999999999999e-253 < b1

   1. Initial program 85.5%

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

      1. times-frac 85.1%

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

      2. associate-*l/ 88.2%

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

      3. associate-*r/ 89.2%

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

   3. Simplified 89.2%

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

   if -1.45e63 < b1 < 1.5999999999999999e-253

   1. Initial program 82.0%

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

      1. *-commutative 82.0%

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

      2. times-frac 91.6%

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

   3. Applied egg-rr 91.6%

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

4. Final simplification 89.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b1 \leq -2.7 \cdot 10^{+256}:\\ \;\;\;\;a2 \cdot \frac{a1}{b1 \cdot b2}\\ \mathbf{elif}\;b1 \leq -1.45 \cdot 10^{+63} \lor \neg \left(b1 \leq 1.6 \cdot 10^{-253}\right):\\ \;\;\;\;a1 \cdot \frac{\frac{a2}{b2}}{b1}\\ \mathbf{else}:\\ \;\;\;\;\frac{a2}{b1} \cdot \frac{a1}{b2}\\ \end{array} \]

Alternative 5: 86.3% accurate, 0.5× speedup

Math

\[\begin{array}{l} [a1, a2] = \mathsf{sort}([a1, a2])\\ [b1, b2] = \mathsf{sort}([b1, b2])\\ \\ \begin{array}{l} \mathbf{if}\;b1 \leq -4 \cdot 10^{+256}:\\ \;\;\;\;a2 \cdot \frac{a1}{b1 \cdot b2}\\ \mathbf{elif}\;b1 \leq -5 \cdot 10^{+60}:\\ \;\;\;\;a1 \cdot \frac{\frac{a2}{b2}}{b1}\\ \mathbf{elif}\;b1 \leq -1.52 \cdot 10^{-290}:\\ \;\;\;\;\frac{a2}{b1} \cdot \frac{a1}{b2}\\ \mathbf{else}:\\ \;\;\;\;a1 \cdot \frac{a2}{b1 \cdot b2}\\ \end{array} \end{array} \]

FPCore

NOTE: a1 and a2 should be sorted in increasing order before calling this function.
NOTE: b1 and b2 should be sorted in increasing order before calling this function.
(FPCore (a1 a2 b1 b2)
 :precision binary64
 (if (<= b1 -4e+256)
   (* a2 (/ a1 (* b1 b2)))
   (if (<= b1 -5e+60)
     (* a1 (/ (/ a2 b2) b1))
     (if (<= b1 -1.52e-290) (* (/ a2 b1) (/ a1 b2)) (* a1 (/ a2 (* b1 b2)))))))

C

assert(a1 < a2);
assert(b1 < b2);
double code(double a1, double a2, double b1, double b2) {
	double tmp;
	if (b1 <= -4e+256) {
		tmp = a2 * (a1 / (b1 * b2));
	} else if (b1 <= -5e+60) {
		tmp = a1 * ((a2 / b2) / b1);
	} else if (b1 <= -1.52e-290) {
		tmp = (a2 / b1) * (a1 / b2);
	} else {
		tmp = a1 * (a2 / (b1 * b2));
	}
	return tmp;
}

Fortran

NOTE: a1 and a2 should be sorted in increasing order before calling this function.
NOTE: b1 and b2 should be sorted in increasing order before calling this function.
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 <= (-4d+256)) then
        tmp = a2 * (a1 / (b1 * b2))
    else if (b1 <= (-5d+60)) then
        tmp = a1 * ((a2 / b2) / b1)
    else if (b1 <= (-1.52d-290)) then
        tmp = (a2 / b1) * (a1 / b2)
    else
        tmp = a1 * (a2 / (b1 * b2))
    end if
    code = tmp
end function

Java

assert a1 < a2;
assert b1 < b2;
public static double code(double a1, double a2, double b1, double b2) {
	double tmp;
	if (b1 <= -4e+256) {
		tmp = a2 * (a1 / (b1 * b2));
	} else if (b1 <= -5e+60) {
		tmp = a1 * ((a2 / b2) / b1);
	} else if (b1 <= -1.52e-290) {
		tmp = (a2 / b1) * (a1 / b2);
	} else {
		tmp = a1 * (a2 / (b1 * b2));
	}
	return tmp;
}

Python

[a1, a2] = sort([a1, a2])
[b1, b2] = sort([b1, b2])
def code(a1, a2, b1, b2):
	tmp = 0
	if b1 <= -4e+256:
		tmp = a2 * (a1 / (b1 * b2))
	elif b1 <= -5e+60:
		tmp = a1 * ((a2 / b2) / b1)
	elif b1 <= -1.52e-290:
		tmp = (a2 / b1) * (a1 / b2)
	else:
		tmp = a1 * (a2 / (b1 * b2))
	return tmp

Julia

a1, a2 = sort([a1, a2])
b1, b2 = sort([b1, b2])
function code(a1, a2, b1, b2)
	tmp = 0.0
	if (b1 <= -4e+256)
		tmp = Float64(a2 * Float64(a1 / Float64(b1 * b2)));
	elseif (b1 <= -5e+60)
		tmp = Float64(a1 * Float64(Float64(a2 / b2) / b1));
	elseif (b1 <= -1.52e-290)
		tmp = Float64(Float64(a2 / b1) * Float64(a1 / b2));
	else
		tmp = Float64(a1 * Float64(a2 / Float64(b1 * b2)));
	end
	return tmp
end

MATLAB

a1, a2 = num2cell(sort([a1, a2])){:}
b1, b2 = num2cell(sort([b1, b2])){:}
function tmp_2 = code(a1, a2, b1, b2)
	tmp = 0.0;
	if (b1 <= -4e+256)
		tmp = a2 * (a1 / (b1 * b2));
	elseif (b1 <= -5e+60)
		tmp = a1 * ((a2 / b2) / b1);
	elseif (b1 <= -1.52e-290)
		tmp = (a2 / b1) * (a1 / b2);
	else
		tmp = a1 * (a2 / (b1 * b2));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: a1 and a2 should be sorted in increasing order before calling this function.
NOTE: b1 and b2 should be sorted in increasing order before calling this function.
code[a1_, a2_, b1_, b2_] := If[LessEqual[b1, -4e+256], N[(a2 * N[(a1 / N[(b1 * b2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b1, -5e+60], N[(a1 * N[(N[(a2 / b2), $MachinePrecision] / b1), $MachinePrecision]), $MachinePrecision], If[LessEqual[b1, -1.52e-290], N[(N[(a2 / b1), $MachinePrecision] * N[(a1 / b2), $MachinePrecision]), $MachinePrecision], N[(a1 * N[(a2 / N[(b1 * b2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if b1 < -4.0000000000000001e256

   1. Initial program 83.9%

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

      1. associate-/l* 99.2%

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

      2. associate-/r/ 84.3%

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

      3. *-commutative 84.3%

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

   3. Applied egg-rr 84.3%

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

   if -4.0000000000000001e256 < b1 < -4.99999999999999975e60

   1. Initial program 80.1%

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

      1. times-frac 78.6%

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

      2. associate-*l/ 83.8%

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

      3. associate-*r/ 82.5%

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

   3. Simplified 82.5%

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

   if -4.99999999999999975e60 < b1 < -1.5199999999999999e-290

   1. Initial program 82.7%

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

      1. *-commutative 82.7%

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

      2. times-frac 91.9%

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

   3. Applied egg-rr 91.9%

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

   if -1.5199999999999999e-290 < b1

   1. Initial program 86.6%

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

      1. *-commutative 86.6%

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

      2. associate-*l/ 91.6%

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

      3. *-commutative 91.6%

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

   3. Applied egg-rr 91.6%

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

4. Final simplification 89.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b1 \leq -4 \cdot 10^{+256}:\\ \;\;\;\;a2 \cdot \frac{a1}{b1 \cdot b2}\\ \mathbf{elif}\;b1 \leq -5 \cdot 10^{+60}:\\ \;\;\;\;a1 \cdot \frac{\frac{a2}{b2}}{b1}\\ \mathbf{elif}\;b1 \leq -1.52 \cdot 10^{-290}:\\ \;\;\;\;\frac{a2}{b1} \cdot \frac{a1}{b2}\\ \mathbf{else}:\\ \;\;\;\;a1 \cdot \frac{a2}{b1 \cdot b2}\\ \end{array} \]

Alternative 6: 85.9% accurate, 0.5× speedup

Math

\[\begin{array}{l} [a1, a2] = \mathsf{sort}([a1, a2])\\ [b1, b2] = \mathsf{sort}([b1, b2])\\ \\ \begin{array}{l} \mathbf{if}\;b1 \leq -9.4 \cdot 10^{+257}:\\ \;\;\;\;a2 \cdot \frac{a1}{b1 \cdot b2}\\ \mathbf{elif}\;b1 \leq -1.28 \cdot 10^{+51}:\\ \;\;\;\;a1 \cdot \frac{\frac{a2}{b2}}{b1}\\ \mathbf{elif}\;b1 \leq -1.15 \cdot 10^{-159}:\\ \;\;\;\;\frac{a2}{b1 \cdot \frac{b2}{a1}}\\ \mathbf{else}:\\ \;\;\;\;a1 \cdot \frac{a2}{b1 \cdot b2}\\ \end{array} \end{array} \]

FPCore

NOTE: a1 and a2 should be sorted in increasing order before calling this function.
NOTE: b1 and b2 should be sorted in increasing order before calling this function.
(FPCore (a1 a2 b1 b2)
 :precision binary64
 (if (<= b1 -9.4e+257)
   (* a2 (/ a1 (* b1 b2)))
   (if (<= b1 -1.28e+51)
     (* a1 (/ (/ a2 b2) b1))
     (if (<= b1 -1.15e-159) (/ a2 (* b1 (/ b2 a1))) (* a1 (/ a2 (* b1 b2)))))))

C

assert(a1 < a2);
assert(b1 < b2);
double code(double a1, double a2, double b1, double b2) {
	double tmp;
	if (b1 <= -9.4e+257) {
		tmp = a2 * (a1 / (b1 * b2));
	} else if (b1 <= -1.28e+51) {
		tmp = a1 * ((a2 / b2) / b1);
	} else if (b1 <= -1.15e-159) {
		tmp = a2 / (b1 * (b2 / a1));
	} else {
		tmp = a1 * (a2 / (b1 * b2));
	}
	return tmp;
}

Fortran

NOTE: a1 and a2 should be sorted in increasing order before calling this function.
NOTE: b1 and b2 should be sorted in increasing order before calling this function.
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 <= (-9.4d+257)) then
        tmp = a2 * (a1 / (b1 * b2))
    else if (b1 <= (-1.28d+51)) then
        tmp = a1 * ((a2 / b2) / b1)
    else if (b1 <= (-1.15d-159)) then
        tmp = a2 / (b1 * (b2 / a1))
    else
        tmp = a1 * (a2 / (b1 * b2))
    end if
    code = tmp
end function

Java

assert a1 < a2;
assert b1 < b2;
public static double code(double a1, double a2, double b1, double b2) {
	double tmp;
	if (b1 <= -9.4e+257) {
		tmp = a2 * (a1 / (b1 * b2));
	} else if (b1 <= -1.28e+51) {
		tmp = a1 * ((a2 / b2) / b1);
	} else if (b1 <= -1.15e-159) {
		tmp = a2 / (b1 * (b2 / a1));
	} else {
		tmp = a1 * (a2 / (b1 * b2));
	}
	return tmp;
}

Python

[a1, a2] = sort([a1, a2])
[b1, b2] = sort([b1, b2])
def code(a1, a2, b1, b2):
	tmp = 0
	if b1 <= -9.4e+257:
		tmp = a2 * (a1 / (b1 * b2))
	elif b1 <= -1.28e+51:
		tmp = a1 * ((a2 / b2) / b1)
	elif b1 <= -1.15e-159:
		tmp = a2 / (b1 * (b2 / a1))
	else:
		tmp = a1 * (a2 / (b1 * b2))
	return tmp

Julia

a1, a2 = sort([a1, a2])
b1, b2 = sort([b1, b2])
function code(a1, a2, b1, b2)
	tmp = 0.0
	if (b1 <= -9.4e+257)
		tmp = Float64(a2 * Float64(a1 / Float64(b1 * b2)));
	elseif (b1 <= -1.28e+51)
		tmp = Float64(a1 * Float64(Float64(a2 / b2) / b1));
	elseif (b1 <= -1.15e-159)
		tmp = Float64(a2 / Float64(b1 * Float64(b2 / a1)));
	else
		tmp = Float64(a1 * Float64(a2 / Float64(b1 * b2)));
	end
	return tmp
end

MATLAB

a1, a2 = num2cell(sort([a1, a2])){:}
b1, b2 = num2cell(sort([b1, b2])){:}
function tmp_2 = code(a1, a2, b1, b2)
	tmp = 0.0;
	if (b1 <= -9.4e+257)
		tmp = a2 * (a1 / (b1 * b2));
	elseif (b1 <= -1.28e+51)
		tmp = a1 * ((a2 / b2) / b1);
	elseif (b1 <= -1.15e-159)
		tmp = a2 / (b1 * (b2 / a1));
	else
		tmp = a1 * (a2 / (b1 * b2));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: a1 and a2 should be sorted in increasing order before calling this function.
NOTE: b1 and b2 should be sorted in increasing order before calling this function.
code[a1_, a2_, b1_, b2_] := If[LessEqual[b1, -9.4e+257], N[(a2 * N[(a1 / N[(b1 * b2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b1, -1.28e+51], N[(a1 * N[(N[(a2 / b2), $MachinePrecision] / b1), $MachinePrecision]), $MachinePrecision], If[LessEqual[b1, -1.15e-159], N[(a2 / N[(b1 * N[(b2 / a1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(a1 * N[(a2 / N[(b1 * b2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if b1 < -9.4e257

   1. Initial program 83.9%

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

      1. associate-/l* 99.2%

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

      2. associate-/r/ 84.3%

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

      3. *-commutative 84.3%

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

   3. Applied egg-rr 84.3%

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

   if -9.4e257 < b1 < -1.27999999999999993e51

   1. Initial program 80.4%

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

      1. times-frac 79.1%

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

      2. associate-*l/ 84.1%

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

      3. associate-*r/ 82.8%

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

   3. Simplified 82.8%

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

   if -1.27999999999999993e51 < b1 < -1.14999999999999989e-159

   1. Initial program 78.7%

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

      1. *-commutative 78.7%

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

      2. associate-*l/ 93.1%

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

      3. *-commutative 93.1%

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

   3. Applied egg-rr 93.1%

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

      1. associate-*l/ 78.7%

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

      2. *-commutative 78.7%

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

      3. frac-times 97.0%

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

      4. clear-num 97.1%

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

      5. frac-times 96.1%

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

      6. *-commutative 96.1%

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

      7. *-un-lft-identity 96.1%

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

   5. Applied egg-rr 96.1%

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

   if -1.14999999999999989e-159 < b1

   1. Initial program 86.8%

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

      1. *-commutative 86.8%

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

      2. associate-*l/ 91.6%

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

      3. *-commutative 91.6%

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

   3. Applied egg-rr 91.6%

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

4. Final simplification 90.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b1 \leq -9.4 \cdot 10^{+257}:\\ \;\;\;\;a2 \cdot \frac{a1}{b1 \cdot b2}\\ \mathbf{elif}\;b1 \leq -1.28 \cdot 10^{+51}:\\ \;\;\;\;a1 \cdot \frac{\frac{a2}{b2}}{b1}\\ \mathbf{elif}\;b1 \leq -1.15 \cdot 10^{-159}:\\ \;\;\;\;\frac{a2}{b1 \cdot \frac{b2}{a1}}\\ \mathbf{else}:\\ \;\;\;\;a1 \cdot \frac{a2}{b1 \cdot b2}\\ \end{array} \]

Alternative 7: 86.8% accurate, 0.8× speedup

Math

\[\begin{array}{l} [a1, a2] = \mathsf{sort}([a1, a2])\\ [b1, b2] = \mathsf{sort}([b1, b2])\\ \\ \begin{array}{l} \mathbf{if}\;b2 \leq 2.2 \cdot 10^{-157}:\\ \;\;\;\;a2 \cdot \frac{\frac{a1}{b1}}{b2}\\ \mathbf{else}:\\ \;\;\;\;a1 \cdot \frac{\frac{a2}{b2}}{b1}\\ \end{array} \end{array} \]

FPCore

NOTE: a1 and a2 should be sorted in increasing order before calling this function.
NOTE: b1 and b2 should be sorted in increasing order before calling this function.
(FPCore (a1 a2 b1 b2)
 :precision binary64
 (if (<= b2 2.2e-157) (* a2 (/ (/ a1 b1) b2)) (* a1 (/ (/ a2 b2) b1))))

C

assert(a1 < a2);
assert(b1 < b2);
double code(double a1, double a2, double b1, double b2) {
	double tmp;
	if (b2 <= 2.2e-157) {
		tmp = a2 * ((a1 / b1) / b2);
	} else {
		tmp = a1 * ((a2 / b2) / b1);
	}
	return tmp;
}

Fortran

NOTE: a1 and a2 should be sorted in increasing order before calling this function.
NOTE: b1 and b2 should be sorted in increasing order before calling this function.
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 (b2 <= 2.2d-157) then
        tmp = a2 * ((a1 / b1) / b2)
    else
        tmp = a1 * ((a2 / b2) / b1)
    end if
    code = tmp
end function

Java

assert a1 < a2;
assert b1 < b2;
public static double code(double a1, double a2, double b1, double b2) {
	double tmp;
	if (b2 <= 2.2e-157) {
		tmp = a2 * ((a1 / b1) / b2);
	} else {
		tmp = a1 * ((a2 / b2) / b1);
	}
	return tmp;
}

Python

[a1, a2] = sort([a1, a2])
[b1, b2] = sort([b1, b2])
def code(a1, a2, b1, b2):
	tmp = 0
	if b2 <= 2.2e-157:
		tmp = a2 * ((a1 / b1) / b2)
	else:
		tmp = a1 * ((a2 / b2) / b1)
	return tmp

Julia

a1, a2 = sort([a1, a2])
b1, b2 = sort([b1, b2])
function code(a1, a2, b1, b2)
	tmp = 0.0
	if (b2 <= 2.2e-157)
		tmp = Float64(a2 * Float64(Float64(a1 / b1) / b2));
	else
		tmp = Float64(a1 * Float64(Float64(a2 / b2) / b1));
	end
	return tmp
end

MATLAB

a1, a2 = num2cell(sort([a1, a2])){:}
b1, b2 = num2cell(sort([b1, b2])){:}
function tmp_2 = code(a1, a2, b1, b2)
	tmp = 0.0;
	if (b2 <= 2.2e-157)
		tmp = a2 * ((a1 / b1) / b2);
	else
		tmp = a1 * ((a2 / b2) / b1);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: a1 and a2 should be sorted in increasing order before calling this function.
NOTE: b1 and b2 should be sorted in increasing order before calling this function.
code[a1_, a2_, b1_, b2_] := If[LessEqual[b2, 2.2e-157], N[(a2 * N[(N[(a1 / b1), $MachinePrecision] / b2), $MachinePrecision]), $MachinePrecision], N[(a1 * N[(N[(a2 / b2), $MachinePrecision] / b1), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b2 < 2.2000000000000001e-157

   1. Initial program 84.3%

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

      1. times-frac 84.9%

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

      2. associate-*l/ 86.0%

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

      3. associate-*r/ 89.0%

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

   3. Simplified 89.0%

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

   4. Taylor expanded in a1 around 0 84.3%

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

      1. times-frac 84.9%

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

      2. *-commutative 84.9%

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

      3. associate-*l/ 81.6%

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

      4. associate-*r/ 85.4%

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

   6. Simplified 85.4%

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

   if 2.2000000000000001e-157 < b2

   1. Initial program 84.6%

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

      1. times-frac 88.1%

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

      2. associate-*l/ 90.6%

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

      3. associate-*r/ 91.7%

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

   3. Simplified 91.7%

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

4. Final simplification 87.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b2 \leq 2.2 \cdot 10^{-157}:\\ \;\;\;\;a2 \cdot \frac{\frac{a1}{b1}}{b2}\\ \mathbf{else}:\\ \;\;\;\;a1 \cdot \frac{\frac{a2}{b2}}{b1}\\ \end{array} \]

Alternative 8: 86.1% accurate, 0.8× speedup

Math

\[\begin{array}{l} [a1, a2] = \mathsf{sort}([a1, a2])\\ [b1, b2] = \mathsf{sort}([b1, b2])\\ \\ \begin{array}{l} \mathbf{if}\;b1 \leq -4.8 \cdot 10^{+256}:\\ \;\;\;\;a2 \cdot \frac{a1}{b1 \cdot b2}\\ \mathbf{else}:\\ \;\;\;\;a1 \cdot \frac{\frac{a2}{b2}}{b1}\\ \end{array} \end{array} \]

FPCore

NOTE: a1 and a2 should be sorted in increasing order before calling this function.
NOTE: b1 and b2 should be sorted in increasing order before calling this function.
(FPCore (a1 a2 b1 b2)
 :precision binary64
 (if (<= b1 -4.8e+256) (* a2 (/ a1 (* b1 b2))) (* a1 (/ (/ a2 b2) b1))))

C

assert(a1 < a2);
assert(b1 < b2);
double code(double a1, double a2, double b1, double b2) {
	double tmp;
	if (b1 <= -4.8e+256) {
		tmp = a2 * (a1 / (b1 * b2));
	} else {
		tmp = a1 * ((a2 / b2) / b1);
	}
	return tmp;
}

Fortran

NOTE: a1 and a2 should be sorted in increasing order before calling this function.
NOTE: b1 and b2 should be sorted in increasing order before calling this function.
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 <= (-4.8d+256)) then
        tmp = a2 * (a1 / (b1 * b2))
    else
        tmp = a1 * ((a2 / b2) / b1)
    end if
    code = tmp
end function

Java

assert a1 < a2;
assert b1 < b2;
public static double code(double a1, double a2, double b1, double b2) {
	double tmp;
	if (b1 <= -4.8e+256) {
		tmp = a2 * (a1 / (b1 * b2));
	} else {
		tmp = a1 * ((a2 / b2) / b1);
	}
	return tmp;
}

Python

[a1, a2] = sort([a1, a2])
[b1, b2] = sort([b1, b2])
def code(a1, a2, b1, b2):
	tmp = 0
	if b1 <= -4.8e+256:
		tmp = a2 * (a1 / (b1 * b2))
	else:
		tmp = a1 * ((a2 / b2) / b1)
	return tmp

Julia

a1, a2 = sort([a1, a2])
b1, b2 = sort([b1, b2])
function code(a1, a2, b1, b2)
	tmp = 0.0
	if (b1 <= -4.8e+256)
		tmp = Float64(a2 * Float64(a1 / Float64(b1 * b2)));
	else
		tmp = Float64(a1 * Float64(Float64(a2 / b2) / b1));
	end
	return tmp
end

MATLAB

a1, a2 = num2cell(sort([a1, a2])){:}
b1, b2 = num2cell(sort([b1, b2])){:}
function tmp_2 = code(a1, a2, b1, b2)
	tmp = 0.0;
	if (b1 <= -4.8e+256)
		tmp = a2 * (a1 / (b1 * b2));
	else
		tmp = a1 * ((a2 / b2) / b1);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: a1 and a2 should be sorted in increasing order before calling this function.
NOTE: b1 and b2 should be sorted in increasing order before calling this function.
code[a1_, a2_, b1_, b2_] := If[LessEqual[b1, -4.8e+256], N[(a2 * N[(a1 / N[(b1 * b2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(a1 * N[(N[(a2 / b2), $MachinePrecision] / b1), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b1 < -4.80000000000000028e256

   1. Initial program 83.9%

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

      1. associate-/l* 99.2%

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

      2. associate-/r/ 84.3%

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

      3. *-commutative 84.3%

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

   3. Applied egg-rr 84.3%

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

   if -4.80000000000000028e256 < b1

   1. Initial program 84.4%

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

      1. times-frac 86.6%

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

      2. associate-*l/ 87.9%

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

      3. associate-*r/ 89.8%

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

   3. Simplified 89.8%

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

4. Final simplification 89.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b1 \leq -4.8 \cdot 10^{+256}:\\ \;\;\;\;a2 \cdot \frac{a1}{b1 \cdot b2}\\ \mathbf{else}:\\ \;\;\;\;a1 \cdot \frac{\frac{a2}{b2}}{b1}\\ \end{array} \]

Alternative 9: 86.3% accurate, 1.0× speedup

Math

\[\begin{array}{l} [a1, a2] = \mathsf{sort}([a1, a2])\\ [b1, b2] = \mathsf{sort}([b1, b2])\\ \\ a1 \cdot \frac{\frac{a2}{b2}}{b1} \end{array} \]

FPCore

NOTE: a1 and a2 should be sorted in increasing order before calling this function.
NOTE: b1 and b2 should be sorted in increasing order before calling this function.
(FPCore (a1 a2 b1 b2) :precision binary64 (* a1 (/ (/ a2 b2) b1)))

C

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

Fortran

NOTE: a1 and a2 should be sorted in increasing order before calling this function.
NOTE: b1 and b2 should be sorted in increasing order before calling this function.
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 / b2) / b1)
end function

Java

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

Python

[a1, a2] = sort([a1, a2])
[b1, b2] = sort([b1, b2])
def code(a1, a2, b1, b2):
	return a1 * ((a2 / b2) / b1)

Julia

a1, a2 = sort([a1, a2])
b1, b2 = sort([b1, b2])
function code(a1, a2, b1, b2)
	return Float64(a1 * Float64(Float64(a2 / b2) / b1))
end

MATLAB

a1, a2 = num2cell(sort([a1, a2])){:}
b1, b2 = num2cell(sort([b1, b2])){:}
function tmp = code(a1, a2, b1, b2)
	tmp = a1 * ((a2 / b2) / b1);
end

Wolfram

NOTE: a1 and a2 should be sorted in increasing order before calling this function.
NOTE: b1 and b2 should be sorted in increasing order before calling this function.
code[a1_, a2_, b1_, b2_] := N[(a1 * N[(N[(a2 / b2), $MachinePrecision] / b1), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 84.4%

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

   1. times-frac 86.2%

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

   2. associate-*l/ 87.8%

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

   3. associate-*r/ 90.1%

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

3. Simplified 90.1%

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

4. Final simplification 90.1%

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

Developer target: 86.5% 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 2023307 
(FPCore (a1 a2 b1 b2)
  :name "Quotient of products"
  :precision binary64

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

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