Quotient of products

Percentage Accurate: 86.2% → 94.7%

Time: 3.1s

Alternatives: 7

Speedup: 1.0×

• 20.3% 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: 86.2% 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: 94.7% accurate, 0.2× speedup

Math

\[\begin{array}{l} [a1, a2] = \mathsf{sort}([a1, a2])\\ [b1, b2] = \mathsf{sort}([b1, b2])\\ \\ \begin{array}{l} t_0 := \frac{a1 \cdot a2}{b1 \cdot b2}\\ t_1 := \frac{\frac{a2}{b2}}{\frac{b1}{a1}}\\ \mathbf{if}\;t_0 \leq -1 \cdot 10^{+276}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t_0 \leq -5 \cdot 10^{-58}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;t_0 \leq 0:\\ \;\;\;\;\frac{a2}{b1} \cdot \frac{a1}{b2}\\ \mathbf{elif}\;t_0 \leq 4 \cdot 10^{+292}:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

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 (/ (* a1 a2) (* b1 b2))) (t_1 (/ (/ a2 b2) (/ b1 a1))))
   (if (<= t_0 -1e+276)
     t_1
     (if (<= t_0 -5e-58)
       t_0
       (if (<= t_0 0.0)
         (* (/ a2 b1) (/ a1 b2))
         (if (<= t_0 4e+292) t_0 t_1))))))

C

assert(a1 < a2);
assert(b1 < b2);
double code(double a1, double a2, double b1, double b2) {
	double t_0 = (a1 * a2) / (b1 * b2);
	double t_1 = (a2 / b2) / (b1 / a1);
	double tmp;
	if (t_0 <= -1e+276) {
		tmp = t_1;
	} else if (t_0 <= -5e-58) {
		tmp = t_0;
	} else if (t_0 <= 0.0) {
		tmp = (a2 / b1) * (a1 / b2);
	} else if (t_0 <= 4e+292) {
		tmp = t_0;
	} else {
		tmp = t_1;
	}
	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) :: t_0
    real(8) :: t_1
    real(8) :: tmp
    t_0 = (a1 * a2) / (b1 * b2)
    t_1 = (a2 / b2) / (b1 / a1)
    if (t_0 <= (-1d+276)) then
        tmp = t_1
    else if (t_0 <= (-5d-58)) then
        tmp = t_0
    else if (t_0 <= 0.0d0) then
        tmp = (a2 / b1) * (a1 / b2)
    else if (t_0 <= 4d+292) then
        tmp = t_0
    else
        tmp = t_1
    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 t_0 = (a1 * a2) / (b1 * b2);
	double t_1 = (a2 / b2) / (b1 / a1);
	double tmp;
	if (t_0 <= -1e+276) {
		tmp = t_1;
	} else if (t_0 <= -5e-58) {
		tmp = t_0;
	} else if (t_0 <= 0.0) {
		tmp = (a2 / b1) * (a1 / b2);
	} else if (t_0 <= 4e+292) {
		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 = (a1 * a2) / (b1 * b2)
	t_1 = (a2 / b2) / (b1 / a1)
	tmp = 0
	if t_0 <= -1e+276:
		tmp = t_1
	elif t_0 <= -5e-58:
		tmp = t_0
	elif t_0 <= 0.0:
		tmp = (a2 / b1) * (a1 / b2)
	elif t_0 <= 4e+292:
		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(a1 * a2) / Float64(b1 * b2))
	t_1 = Float64(Float64(a2 / b2) / Float64(b1 / a1))
	tmp = 0.0
	if (t_0 <= -1e+276)
		tmp = t_1;
	elseif (t_0 <= -5e-58)
		tmp = t_0;
	elseif (t_0 <= 0.0)
		tmp = Float64(Float64(a2 / b1) * Float64(a1 / b2));
	elseif (t_0 <= 4e+292)
		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 = (a1 * a2) / (b1 * b2);
	t_1 = (a2 / b2) / (b1 / a1);
	tmp = 0.0;
	if (t_0 <= -1e+276)
		tmp = t_1;
	elseif (t_0 <= -5e-58)
		tmp = t_0;
	elseif (t_0 <= 0.0)
		tmp = (a2 / b1) * (a1 / b2);
	elseif (t_0 <= 4e+292)
		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[(a1 * a2), $MachinePrecision] / N[(b1 * b2), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(N[(a2 / b2), $MachinePrecision] / N[(b1 / a1), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$0, -1e+276], t$95$1, If[LessEqual[t$95$0, -5e-58], t$95$0, If[LessEqual[t$95$0, 0.0], N[(N[(a2 / b1), $MachinePrecision] * N[(a1 / b2), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$0, 4e+292], t$95$0, t$95$1]]]]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 (*.f64 a1 a2) (*.f64 b1 b2)) < -1.0000000000000001e276 or 4.0000000000000001e292 < (/.f64 (*.f64 a1 a2) (*.f64 b1 b2))

   1. Initial program 57.4%

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

      1. times-frac 93.7%

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

   3. Simplified 93.7%

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

      1. *-commutative 93.7%

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

      2. clear-num 93.7%

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

      3. un-div-inv 94.2%

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

   5. Applied egg-rr 94.2%

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

   if -1.0000000000000001e276 < (/.f64 (*.f64 a1 a2) (*.f64 b1 b2)) < -4.99999999999999977e-58 or 0.0 < (/.f64 (*.f64 a1 a2) (*.f64 b1 b2)) < 4.0000000000000001e292

   1. Initial program 98.7%

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

   if -4.99999999999999977e-58 < (/.f64 (*.f64 a1 a2) (*.f64 b1 b2)) < 0.0

   1. Initial program 86.2%

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

      1. associate-/l* 92.5%

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

      2. *-commutative 92.5%

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

      3. associate-/l* 90.4%

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

   3. Simplified 90.4%

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

      1. associate-/r/ 91.0%

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

      2. *-commutative 91.0%

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

   5. Applied egg-rr 91.0%

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

4. Final simplification 94.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{a1 \cdot a2}{b1 \cdot b2} \leq -1 \cdot 10^{+276}:\\ \;\;\;\;\frac{\frac{a2}{b2}}{\frac{b1}{a1}}\\ \mathbf{elif}\;\frac{a1 \cdot a2}{b1 \cdot b2} \leq -5 \cdot 10^{-58}:\\ \;\;\;\;\frac{a1 \cdot a2}{b1 \cdot b2}\\ \mathbf{elif}\;\frac{a1 \cdot a2}{b1 \cdot b2} \leq 0:\\ \;\;\;\;\frac{a2}{b1} \cdot \frac{a1}{b2}\\ \mathbf{elif}\;\frac{a1 \cdot a2}{b1 \cdot b2} \leq 4 \cdot 10^{+292}:\\ \;\;\;\;\frac{a1 \cdot a2}{b1 \cdot b2}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{a2}{b2}}{\frac{b1}{a1}}\\ \end{array} \]

Alternative 2: 95.0% accurate, 0.2× speedup

Math

\[\begin{array}{l} [a1, a2] = \mathsf{sort}([a1, a2])\\ [b1, b2] = \mathsf{sort}([b1, b2])\\ \\ \begin{array}{l} t_0 := \frac{a1 \cdot a2}{b1 \cdot b2}\\ t_1 := \frac{a2}{b2} \cdot \frac{a1}{b1}\\ \mathbf{if}\;t_0 \leq -1 \cdot 10^{+276}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t_0 \leq -2 \cdot 10^{-123}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;t_0 \leq 0:\\ \;\;\;\;\frac{a2}{b1} \cdot \frac{a1}{b2}\\ \mathbf{elif}\;t_0 \leq 5 \cdot 10^{+265}:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

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 (/ (* a1 a2) (* b1 b2))) (t_1 (* (/ a2 b2) (/ a1 b1))))
   (if (<= t_0 -1e+276)
     t_1
     (if (<= t_0 -2e-123)
       t_0
       (if (<= t_0 0.0)
         (* (/ a2 b1) (/ a1 b2))
         (if (<= t_0 5e+265) t_0 t_1))))))

C

assert(a1 < a2);
assert(b1 < b2);
double code(double a1, double a2, double b1, double b2) {
	double t_0 = (a1 * a2) / (b1 * b2);
	double t_1 = (a2 / b2) * (a1 / b1);
	double tmp;
	if (t_0 <= -1e+276) {
		tmp = t_1;
	} else if (t_0 <= -2e-123) {
		tmp = t_0;
	} else if (t_0 <= 0.0) {
		tmp = (a2 / b1) * (a1 / b2);
	} else if (t_0 <= 5e+265) {
		tmp = t_0;
	} else {
		tmp = t_1;
	}
	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) :: t_0
    real(8) :: t_1
    real(8) :: tmp
    t_0 = (a1 * a2) / (b1 * b2)
    t_1 = (a2 / b2) * (a1 / b1)
    if (t_0 <= (-1d+276)) then
        tmp = t_1
    else if (t_0 <= (-2d-123)) then
        tmp = t_0
    else if (t_0 <= 0.0d0) then
        tmp = (a2 / b1) * (a1 / b2)
    else if (t_0 <= 5d+265) then
        tmp = t_0
    else
        tmp = t_1
    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 t_0 = (a1 * a2) / (b1 * b2);
	double t_1 = (a2 / b2) * (a1 / b1);
	double tmp;
	if (t_0 <= -1e+276) {
		tmp = t_1;
	} else if (t_0 <= -2e-123) {
		tmp = t_0;
	} else if (t_0 <= 0.0) {
		tmp = (a2 / b1) * (a1 / b2);
	} else if (t_0 <= 5e+265) {
		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 = (a1 * a2) / (b1 * b2)
	t_1 = (a2 / b2) * (a1 / b1)
	tmp = 0
	if t_0 <= -1e+276:
		tmp = t_1
	elif t_0 <= -2e-123:
		tmp = t_0
	elif t_0 <= 0.0:
		tmp = (a2 / b1) * (a1 / b2)
	elif t_0 <= 5e+265:
		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(a1 * a2) / Float64(b1 * b2))
	t_1 = Float64(Float64(a2 / b2) * Float64(a1 / b1))
	tmp = 0.0
	if (t_0 <= -1e+276)
		tmp = t_1;
	elseif (t_0 <= -2e-123)
		tmp = t_0;
	elseif (t_0 <= 0.0)
		tmp = Float64(Float64(a2 / b1) * Float64(a1 / b2));
	elseif (t_0 <= 5e+265)
		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 = (a1 * a2) / (b1 * b2);
	t_1 = (a2 / b2) * (a1 / b1);
	tmp = 0.0;
	if (t_0 <= -1e+276)
		tmp = t_1;
	elseif (t_0 <= -2e-123)
		tmp = t_0;
	elseif (t_0 <= 0.0)
		tmp = (a2 / b1) * (a1 / b2);
	elseif (t_0 <= 5e+265)
		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[(a1 * a2), $MachinePrecision] / N[(b1 * b2), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(N[(a2 / b2), $MachinePrecision] * N[(a1 / b1), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$0, -1e+276], t$95$1, If[LessEqual[t$95$0, -2e-123], t$95$0, If[LessEqual[t$95$0, 0.0], N[(N[(a2 / b1), $MachinePrecision] * N[(a1 / b2), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$0, 5e+265], t$95$0, t$95$1]]]]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 (*.f64 a1 a2) (*.f64 b1 b2)) < -1.0000000000000001e276 or 5.0000000000000002e265 < (/.f64 (*.f64 a1 a2) (*.f64 b1 b2))

   1. Initial program 57.9%

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

      1. times-frac 92.6%

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

   3. Simplified 92.6%

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

   if -1.0000000000000001e276 < (/.f64 (*.f64 a1 a2) (*.f64 b1 b2)) < -2.0000000000000001e-123 or 0.0 < (/.f64 (*.f64 a1 a2) (*.f64 b1 b2)) < 5.0000000000000002e265

   1. Initial program 98.7%

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

   if -2.0000000000000001e-123 < (/.f64 (*.f64 a1 a2) (*.f64 b1 b2)) < 0.0

   1. Initial program 84.9%

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

      1. associate-/l* 91.9%

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

      2. *-commutative 91.9%

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

      3. associate-/l* 90.7%

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

   3. Simplified 90.7%

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

      1. associate-/r/ 91.3%

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

      2. *-commutative 91.3%

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

   5. Applied egg-rr 91.3%

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

4. Final simplification 94.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{a1 \cdot a2}{b1 \cdot b2} \leq -1 \cdot 10^{+276}:\\ \;\;\;\;\frac{a2}{b2} \cdot \frac{a1}{b1}\\ \mathbf{elif}\;\frac{a1 \cdot a2}{b1 \cdot b2} \leq -2 \cdot 10^{-123}:\\ \;\;\;\;\frac{a1 \cdot a2}{b1 \cdot b2}\\ \mathbf{elif}\;\frac{a1 \cdot a2}{b1 \cdot b2} \leq 0:\\ \;\;\;\;\frac{a2}{b1} \cdot \frac{a1}{b2}\\ \mathbf{elif}\;\frac{a1 \cdot a2}{b1 \cdot b2} \leq 5 \cdot 10^{+265}:\\ \;\;\;\;\frac{a1 \cdot a2}{b1 \cdot b2}\\ \mathbf{else}:\\ \;\;\;\;\frac{a2}{b2} \cdot \frac{a1}{b1}\\ \end{array} \]

Alternative 3: 93.3% accurate, 0.3× speedup

Math

\[\begin{array}{l} [a1, a2] = \mathsf{sort}([a1, a2])\\ [b1, b2] = \mathsf{sort}([b1, b2])\\ \\ \begin{array}{l} \mathbf{if}\;b1 \cdot b2 \leq -5 \cdot 10^{+207} \lor \neg \left(b1 \cdot b2 \leq -5 \cdot 10^{-172}\right) \land \left(b1 \cdot b2 \leq 5 \cdot 10^{-132} \lor \neg \left(b1 \cdot b2 \leq 2 \cdot 10^{+158}\right)\right):\\ \;\;\;\;\frac{a2}{b2} \cdot \frac{a1}{b1}\\ \mathbf{else}:\\ \;\;\;\;a2 \cdot \frac{a1}{b1 \cdot b2}\\ \end{array} \end{array} \]

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 (or (<= (* b1 b2) -5e+207)
         (and (not (<= (* b1 b2) -5e-172))
              (or (<= (* b1 b2) 5e-132) (not (<= (* b1 b2) 2e+158)))))
   (* (/ a2 b2) (/ a1 b1))
   (* a2 (/ a1 (* b1 b2)))))

C

assert(a1 < a2);
assert(b1 < b2);
double code(double a1, double a2, double b1, double b2) {
	double tmp;
	if (((b1 * b2) <= -5e+207) || (!((b1 * b2) <= -5e-172) && (((b1 * b2) <= 5e-132) || !((b1 * b2) <= 2e+158)))) {
		tmp = (a2 / b2) * (a1 / b1);
	} else {
		tmp = a2 * (a1 / (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 * b2) <= (-5d+207)) .or. (.not. ((b1 * b2) <= (-5d-172))) .and. ((b1 * b2) <= 5d-132) .or. (.not. ((b1 * b2) <= 2d+158))) then
        tmp = (a2 / b2) * (a1 / b1)
    else
        tmp = a2 * (a1 / (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 * b2) <= -5e+207) || (!((b1 * b2) <= -5e-172) && (((b1 * b2) <= 5e-132) || !((b1 * b2) <= 2e+158)))) {
		tmp = (a2 / b2) * (a1 / b1);
	} else {
		tmp = a2 * (a1 / (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 * b2) <= -5e+207) or (not ((b1 * b2) <= -5e-172) and (((b1 * b2) <= 5e-132) or not ((b1 * b2) <= 2e+158))):
		tmp = (a2 / b2) * (a1 / b1)
	else:
		tmp = a2 * (a1 / (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 ((Float64(b1 * b2) <= -5e+207) || (!(Float64(b1 * b2) <= -5e-172) && ((Float64(b1 * b2) <= 5e-132) || !(Float64(b1 * b2) <= 2e+158))))
		tmp = Float64(Float64(a2 / b2) * Float64(a1 / b1));
	else
		tmp = Float64(a2 * Float64(a1 / 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 * b2) <= -5e+207) || (~(((b1 * b2) <= -5e-172)) && (((b1 * b2) <= 5e-132) || ~(((b1 * b2) <= 2e+158)))))
		tmp = (a2 / b2) * (a1 / b1);
	else
		tmp = a2 * (a1 / (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[Or[LessEqual[N[(b1 * b2), $MachinePrecision], -5e+207], And[N[Not[LessEqual[N[(b1 * b2), $MachinePrecision], -5e-172]], $MachinePrecision], Or[LessEqual[N[(b1 * b2), $MachinePrecision], 5e-132], N[Not[LessEqual[N[(b1 * b2), $MachinePrecision], 2e+158]], $MachinePrecision]]]], N[(N[(a2 / b2), $MachinePrecision] * N[(a1 / b1), $MachinePrecision]), $MachinePrecision], N[(a2 * N[(a1 / N[(b1 * b2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 b1 b2) < -4.9999999999999999e207 or -4.9999999999999999e-172 < (*.f64 b1 b2) < 4.9999999999999999e-132 or 1.99999999999999991e158 < (*.f64 b1 b2)

   1. Initial program 73.5%

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

      1. times-frac 92.0%

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

   3. Simplified 92.0%

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

   if -4.9999999999999999e207 < (*.f64 b1 b2) < -4.9999999999999999e-172 or 4.9999999999999999e-132 < (*.f64 b1 b2) < 1.99999999999999991e158

   1. Initial program 90.2%

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

      1. associate-/l* 94.8%

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

      2. *-commutative 94.8%

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

      3. associate-/l* 82.6%

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

   3. Simplified 82.6%

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

      1. associate-/l* 94.8%

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

      2. *-commutative 94.8%

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

      3. associate-/r/ 94.2%

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

   5. Applied egg-rr 94.2%

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

4. Final simplification 93.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b1 \cdot b2 \leq -5 \cdot 10^{+207} \lor \neg \left(b1 \cdot b2 \leq -5 \cdot 10^{-172}\right) \land \left(b1 \cdot b2 \leq 5 \cdot 10^{-132} \lor \neg \left(b1 \cdot b2 \leq 2 \cdot 10^{+158}\right)\right):\\ \;\;\;\;\frac{a2}{b2} \cdot \frac{a1}{b1}\\ \mathbf{else}:\\ \;\;\;\;a2 \cdot \frac{a1}{b1 \cdot b2}\\ \end{array} \]

Alternative 4: 92.9% accurate, 0.3× speedup

Math

\[\begin{array}{l} [a1, a2] = \mathsf{sort}([a1, a2])\\ [b1, b2] = \mathsf{sort}([b1, b2])\\ \\ \begin{array}{l} \mathbf{if}\;b1 \cdot b2 \leq -5 \cdot 10^{+139}:\\ \;\;\;\;\frac{a2}{b1} \cdot \frac{a1}{b2}\\ \mathbf{elif}\;b1 \cdot b2 \leq -5 \cdot 10^{-172} \lor \neg \left(b1 \cdot b2 \leq 5 \cdot 10^{-132}\right) \land b1 \cdot b2 \leq 2 \cdot 10^{+158}:\\ \;\;\;\;a2 \cdot \frac{a1}{b1 \cdot b2}\\ \mathbf{else}:\\ \;\;\;\;\frac{a2}{b2} \cdot \frac{a1}{b1}\\ \end{array} \end{array} \]

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 b2) -5e+139)
   (* (/ a2 b1) (/ a1 b2))
   (if (or (<= (* b1 b2) -5e-172)
           (and (not (<= (* b1 b2) 5e-132)) (<= (* b1 b2) 2e+158)))
     (* a2 (/ a1 (* b1 b2)))
     (* (/ a2 b2) (/ a1 b1)))))

C

assert(a1 < a2);
assert(b1 < b2);
double code(double a1, double a2, double b1, double b2) {
	double tmp;
	if ((b1 * b2) <= -5e+139) {
		tmp = (a2 / b1) * (a1 / b2);
	} else if (((b1 * b2) <= -5e-172) || (!((b1 * b2) <= 5e-132) && ((b1 * b2) <= 2e+158))) {
		tmp = a2 * (a1 / (b1 * b2));
	} else {
		tmp = (a2 / b2) * (a1 / 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 * b2) <= (-5d+139)) then
        tmp = (a2 / b1) * (a1 / b2)
    else if (((b1 * b2) <= (-5d-172)) .or. (.not. ((b1 * b2) <= 5d-132)) .and. ((b1 * b2) <= 2d+158)) then
        tmp = a2 * (a1 / (b1 * b2))
    else
        tmp = (a2 / b2) * (a1 / 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 * b2) <= -5e+139) {
		tmp = (a2 / b1) * (a1 / b2);
	} else if (((b1 * b2) <= -5e-172) || (!((b1 * b2) <= 5e-132) && ((b1 * b2) <= 2e+158))) {
		tmp = a2 * (a1 / (b1 * b2));
	} else {
		tmp = (a2 / b2) * (a1 / b1);
	}
	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+139:
		tmp = (a2 / b1) * (a1 / b2)
	elif ((b1 * b2) <= -5e-172) or (not ((b1 * b2) <= 5e-132) and ((b1 * b2) <= 2e+158)):
		tmp = a2 * (a1 / (b1 * b2))
	else:
		tmp = (a2 / b2) * (a1 / b1)
	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+139)
		tmp = Float64(Float64(a2 / b1) * Float64(a1 / b2));
	elseif ((Float64(b1 * b2) <= -5e-172) || (!(Float64(b1 * b2) <= 5e-132) && (Float64(b1 * b2) <= 2e+158)))
		tmp = Float64(a2 * Float64(a1 / Float64(b1 * b2)));
	else
		tmp = Float64(Float64(a2 / b2) * Float64(a1 / 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 * b2) <= -5e+139)
		tmp = (a2 / b1) * (a1 / b2);
	elseif (((b1 * b2) <= -5e-172) || (~(((b1 * b2) <= 5e-132)) && ((b1 * b2) <= 2e+158)))
		tmp = a2 * (a1 / (b1 * b2));
	else
		tmp = (a2 / b2) * (a1 / 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[N[(b1 * b2), $MachinePrecision], -5e+139], N[(N[(a2 / b1), $MachinePrecision] * N[(a1 / b2), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[N[(b1 * b2), $MachinePrecision], -5e-172], And[N[Not[LessEqual[N[(b1 * b2), $MachinePrecision], 5e-132]], $MachinePrecision], LessEqual[N[(b1 * b2), $MachinePrecision], 2e+158]]], N[(a2 * N[(a1 / N[(b1 * b2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(a2 / b2), $MachinePrecision] * N[(a1 / b1), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 b1 b2) < -5.0000000000000003e139

   1. Initial program 75.8%

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

      1. associate-/l* 71.9%

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

      2. *-commutative 71.9%

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

      3. associate-/l* 84.3%

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

   3. Simplified 84.3%

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

      1. associate-/r/ 87.2%

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

      2. *-commutative 87.2%

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

   5. Applied egg-rr 87.2%

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

   if -5.0000000000000003e139 < (*.f64 b1 b2) < -4.9999999999999999e-172 or 4.9999999999999999e-132 < (*.f64 b1 b2) < 1.99999999999999991e158

   1. Initial program 91.1%

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

      1. associate-/l* 95.2%

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

      2. *-commutative 95.2%

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

      3. associate-/l* 82.9%

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

   3. Simplified 82.9%

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

      1. associate-/l* 95.2%

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

      2. *-commutative 95.2%

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

      3. associate-/r/ 96.2%

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

   5. Applied egg-rr 96.2%

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

   if -4.9999999999999999e-172 < (*.f64 b1 b2) < 4.9999999999999999e-132 or 1.99999999999999991e158 < (*.f64 b1 b2)

   1. Initial program 72.9%

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

      1. times-frac 92.5%

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

   3. Simplified 92.5%

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

4. Final simplification 93.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b1 \cdot b2 \leq -5 \cdot 10^{+139}:\\ \;\;\;\;\frac{a2}{b1} \cdot \frac{a1}{b2}\\ \mathbf{elif}\;b1 \cdot b2 \leq -5 \cdot 10^{-172} \lor \neg \left(b1 \cdot b2 \leq 5 \cdot 10^{-132}\right) \land b1 \cdot b2 \leq 2 \cdot 10^{+158}:\\ \;\;\;\;a2 \cdot \frac{a1}{b1 \cdot b2}\\ \mathbf{else}:\\ \;\;\;\;\frac{a2}{b2} \cdot \frac{a1}{b1}\\ \end{array} \]

Alternative 5: 89.7% accurate, 0.4× speedup

Math

\[\begin{array}{l} [a1, a2] = \mathsf{sort}([a1, a2])\\ [b1, b2] = \mathsf{sort}([b1, b2])\\ \\ \begin{array}{l} t_0 := \frac{a1}{b2 \cdot \frac{b1}{a2}}\\ \mathbf{if}\;b1 \cdot b2 \leq -5 \cdot 10^{+207}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;b1 \cdot b2 \leq -5 \cdot 10^{-201}:\\ \;\;\;\;a2 \cdot \frac{a1}{b1 \cdot b2}\\ \mathbf{elif}\;b1 \cdot b2 \leq 10^{-249}:\\ \;\;\;\;\frac{a2}{b1} \cdot \frac{a1}{b2}\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \end{array} \]

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 (/ a1 (* b2 (/ b1 a2)))))
   (if (<= (* b1 b2) -5e+207)
     t_0
     (if (<= (* b1 b2) -5e-201)
       (* a2 (/ a1 (* b1 b2)))
       (if (<= (* b1 b2) 1e-249) (* (/ a2 b1) (/ a1 b2)) t_0)))))

C

assert(a1 < a2);
assert(b1 < b2);
double code(double a1, double a2, double b1, double b2) {
	double t_0 = a1 / (b2 * (b1 / a2));
	double tmp;
	if ((b1 * b2) <= -5e+207) {
		tmp = t_0;
	} else if ((b1 * b2) <= -5e-201) {
		tmp = a2 * (a1 / (b1 * b2));
	} else if ((b1 * b2) <= 1e-249) {
		tmp = (a2 / b1) * (a1 / b2);
	} else {
		tmp = t_0;
	}
	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) :: t_0
    real(8) :: tmp
    t_0 = a1 / (b2 * (b1 / a2))
    if ((b1 * b2) <= (-5d+207)) then
        tmp = t_0
    else if ((b1 * b2) <= (-5d-201)) then
        tmp = a2 * (a1 / (b1 * b2))
    else if ((b1 * b2) <= 1d-249) then
        tmp = (a2 / b1) * (a1 / b2)
    else
        tmp = t_0
    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 t_0 = a1 / (b2 * (b1 / a2));
	double tmp;
	if ((b1 * b2) <= -5e+207) {
		tmp = t_0;
	} else if ((b1 * b2) <= -5e-201) {
		tmp = a2 * (a1 / (b1 * b2));
	} else if ((b1 * b2) <= 1e-249) {
		tmp = (a2 / b1) * (a1 / b2);
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

[a1, a2] = sort([a1, a2])
[b1, b2] = sort([b1, b2])
def code(a1, a2, b1, b2):
	t_0 = a1 / (b2 * (b1 / a2))
	tmp = 0
	if (b1 * b2) <= -5e+207:
		tmp = t_0
	elif (b1 * b2) <= -5e-201:
		tmp = a2 * (a1 / (b1 * b2))
	elif (b1 * b2) <= 1e-249:
		tmp = (a2 / b1) * (a1 / b2)
	else:
		tmp = t_0
	return tmp

Julia

a1, a2 = sort([a1, a2])
b1, b2 = sort([b1, b2])
function code(a1, a2, b1, b2)
	t_0 = Float64(a1 / Float64(b2 * Float64(b1 / a2)))
	tmp = 0.0
	if (Float64(b1 * b2) <= -5e+207)
		tmp = t_0;
	elseif (Float64(b1 * b2) <= -5e-201)
		tmp = Float64(a2 * Float64(a1 / Float64(b1 * b2)));
	elseif (Float64(b1 * b2) <= 1e-249)
		tmp = Float64(Float64(a2 / b1) * Float64(a1 / b2));
	else
		tmp = t_0;
	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 = a1 / (b2 * (b1 / a2));
	tmp = 0.0;
	if ((b1 * b2) <= -5e+207)
		tmp = t_0;
	elseif ((b1 * b2) <= -5e-201)
		tmp = a2 * (a1 / (b1 * b2));
	elseif ((b1 * b2) <= 1e-249)
		tmp = (a2 / b1) * (a1 / b2);
	else
		tmp = t_0;
	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[(a1 / N[(b2 * N[(b1 / a2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(b1 * b2), $MachinePrecision], -5e+207], t$95$0, If[LessEqual[N[(b1 * b2), $MachinePrecision], -5e-201], N[(a2 * N[(a1 / N[(b1 * b2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(b1 * b2), $MachinePrecision], 1e-249], N[(N[(a2 / b1), $MachinePrecision] * N[(a1 / b2), $MachinePrecision]), $MachinePrecision], t$95$0]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 b1 b2) < -4.9999999999999999e207 or 1.00000000000000005e-249 < (*.f64 b1 b2)

   1. Initial program 86.3%

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

      1. associate-/l* 85.8%

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

      2. *-commutative 85.8%

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

      3. associate-/l* 86.1%

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

   3. Simplified 86.1%

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

      1. clear-num 86.1%

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

      2. associate-/r/ 85.8%

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

      3. clear-num 85.8%

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

   5. Applied egg-rr 85.8%

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

   if -4.9999999999999999e207 < (*.f64 b1 b2) < -4.9999999999999999e-201

   1. Initial program 87.6%

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

      1. associate-/l* 93.9%

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

      2. *-commutative 93.9%

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

      3. associate-/l* 83.5%

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

   3. Simplified 83.5%

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

      1. associate-/l* 93.9%

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

      2. *-commutative 93.9%

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

      3. associate-/r/ 90.6%

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

   5. Applied egg-rr 90.6%

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

   if -4.9999999999999999e-201 < (*.f64 b1 b2) < 1.00000000000000005e-249

   1. Initial program 59.7%

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

      1. associate-/l* 64.7%

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

      2. *-commutative 64.7%

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

      3. associate-/l* 86.5%

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

   3. Simplified 86.5%

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

      1. associate-/r/ 95.7%

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

      2. *-commutative 95.7%

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

   5. Applied egg-rr 95.7%

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

4. Final simplification 89.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b1 \cdot b2 \leq -5 \cdot 10^{+207}:\\ \;\;\;\;\frac{a1}{b2 \cdot \frac{b1}{a2}}\\ \mathbf{elif}\;b1 \cdot b2 \leq -5 \cdot 10^{-201}:\\ \;\;\;\;a2 \cdot \frac{a1}{b1 \cdot b2}\\ \mathbf{elif}\;b1 \cdot b2 \leq 10^{-249}:\\ \;\;\;\;\frac{a2}{b1} \cdot \frac{a1}{b2}\\ \mathbf{else}:\\ \;\;\;\;\frac{a1}{b2 \cdot \frac{b1}{a2}}\\ \end{array} \]

Alternative 6: 89.8% accurate, 0.4× speedup

Math

\[\begin{array}{l} [a1, a2] = \mathsf{sort}([a1, a2])\\ [b1, b2] = \mathsf{sort}([b1, b2])\\ \\ \begin{array}{l} \mathbf{if}\;b1 \cdot b2 \leq -5 \cdot 10^{+207}:\\ \;\;\;\;\frac{a1}{b2 \cdot \frac{b1}{a2}}\\ \mathbf{elif}\;b1 \cdot b2 \leq -5 \cdot 10^{-201}:\\ \;\;\;\;a2 \cdot \frac{a1}{b1 \cdot b2}\\ \mathbf{elif}\;b1 \cdot b2 \leq 10^{-249}:\\ \;\;\;\;\frac{a2}{b1} \cdot \frac{a1}{b2}\\ \mathbf{else}:\\ \;\;\;\;\frac{a1}{\frac{b2}{\frac{a2}{b1}}}\\ \end{array} \end{array} \]

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 b2) -5e+207)
   (/ a1 (* b2 (/ b1 a2)))
   (if (<= (* b1 b2) -5e-201)
     (* a2 (/ a1 (* b1 b2)))
     (if (<= (* b1 b2) 1e-249)
       (* (/ a2 b1) (/ a1 b2))
       (/ a1 (/ b2 (/ a2 b1)))))))

C

assert(a1 < a2);
assert(b1 < b2);
double code(double a1, double a2, double b1, double b2) {
	double tmp;
	if ((b1 * b2) <= -5e+207) {
		tmp = a1 / (b2 * (b1 / a2));
	} else if ((b1 * b2) <= -5e-201) {
		tmp = a2 * (a1 / (b1 * b2));
	} else if ((b1 * b2) <= 1e-249) {
		tmp = (a2 / b1) * (a1 / b2);
	} else {
		tmp = a1 / (b2 / (a2 / 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 * b2) <= (-5d+207)) then
        tmp = a1 / (b2 * (b1 / a2))
    else if ((b1 * b2) <= (-5d-201)) then
        tmp = a2 * (a1 / (b1 * b2))
    else if ((b1 * b2) <= 1d-249) then
        tmp = (a2 / b1) * (a1 / b2)
    else
        tmp = a1 / (b2 / (a2 / 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 * b2) <= -5e+207) {
		tmp = a1 / (b2 * (b1 / a2));
	} else if ((b1 * b2) <= -5e-201) {
		tmp = a2 * (a1 / (b1 * b2));
	} else if ((b1 * b2) <= 1e-249) {
		tmp = (a2 / b1) * (a1 / b2);
	} else {
		tmp = a1 / (b2 / (a2 / b1));
	}
	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+207:
		tmp = a1 / (b2 * (b1 / a2))
	elif (b1 * b2) <= -5e-201:
		tmp = a2 * (a1 / (b1 * b2))
	elif (b1 * b2) <= 1e-249:
		tmp = (a2 / b1) * (a1 / b2)
	else:
		tmp = a1 / (b2 / (a2 / b1))
	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+207)
		tmp = Float64(a1 / Float64(b2 * Float64(b1 / a2)));
	elseif (Float64(b1 * b2) <= -5e-201)
		tmp = Float64(a2 * Float64(a1 / Float64(b1 * b2)));
	elseif (Float64(b1 * b2) <= 1e-249)
		tmp = Float64(Float64(a2 / b1) * Float64(a1 / b2));
	else
		tmp = Float64(a1 / Float64(b2 / Float64(a2 / 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 * b2) <= -5e+207)
		tmp = a1 / (b2 * (b1 / a2));
	elseif ((b1 * b2) <= -5e-201)
		tmp = a2 * (a1 / (b1 * b2));
	elseif ((b1 * b2) <= 1e-249)
		tmp = (a2 / b1) * (a1 / b2);
	else
		tmp = a1 / (b2 / (a2 / 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[N[(b1 * b2), $MachinePrecision], -5e+207], N[(a1 / N[(b2 * N[(b1 / a2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(b1 * b2), $MachinePrecision], -5e-201], N[(a2 * N[(a1 / N[(b1 * b2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(b1 * b2), $MachinePrecision], 1e-249], N[(N[(a2 / b1), $MachinePrecision] * N[(a1 / b2), $MachinePrecision]), $MachinePrecision], N[(a1 / N[(b2 / N[(a2 / b1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if (*.f64 b1 b2) < -4.9999999999999999e207

   1. Initial program 75.0%

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

      1. associate-/l* 67.5%

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

      2. *-commutative 67.5%

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

      3. associate-/l* 85.7%

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

   3. Simplified 85.7%

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

      1. clear-num 85.6%

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

      2. associate-/r/ 85.7%

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

      3. clear-num 85.6%

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

   5. Applied egg-rr 85.6%

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

   if -4.9999999999999999e207 < (*.f64 b1 b2) < -4.9999999999999999e-201

   1. Initial program 87.6%

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

      1. associate-/l* 93.9%

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

      2. *-commutative 93.9%

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

      3. associate-/l* 83.5%

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

   3. Simplified 83.5%

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

      1. associate-/l* 93.9%

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

      2. *-commutative 93.9%

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

      3. associate-/r/ 90.6%

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

   5. Applied egg-rr 90.6%

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

   if -4.9999999999999999e-201 < (*.f64 b1 b2) < 1.00000000000000005e-249

   1. Initial program 59.7%

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

      1. associate-/l* 64.7%

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

      2. *-commutative 64.7%

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

      3. associate-/l* 86.5%

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

   3. Simplified 86.5%

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

      1. associate-/r/ 95.7%

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

      2. *-commutative 95.7%

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

   5. Applied egg-rr 95.7%

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

   if 1.00000000000000005e-249 < (*.f64 b1 b2)

   1. Initial program 90.5%

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

      1. associate-/l* 92.6%

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

      2. *-commutative 92.6%

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

      3. associate-/l* 86.3%

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

   3. Simplified 86.3%

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

4. Final simplification 89.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b1 \cdot b2 \leq -5 \cdot 10^{+207}:\\ \;\;\;\;\frac{a1}{b2 \cdot \frac{b1}{a2}}\\ \mathbf{elif}\;b1 \cdot b2 \leq -5 \cdot 10^{-201}:\\ \;\;\;\;a2 \cdot \frac{a1}{b1 \cdot b2}\\ \mathbf{elif}\;b1 \cdot b2 \leq 10^{-249}:\\ \;\;\;\;\frac{a2}{b1} \cdot \frac{a1}{b2}\\ \mathbf{else}:\\ \;\;\;\;\frac{a1}{\frac{b2}{\frac{a2}{b1}}}\\ \end{array} \]

Alternative 7: 86.6% accurate, 1.0× speedup

Math

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

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Derivation

1. Initial program 81.8%

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

   1. times-frac 87.6%

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

3. Simplified 87.6%

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

4. Final simplification 87.6%

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

Developer target: 86.6% 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 2023189 
(FPCore (a1 a2 b1 b2)
  :name "Quotient of products"
  :precision binary64

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

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