Quotient of products

Percentage Accurate: 86.7% → 95.7%

Time: 3.6s

Alternatives: 5

Speedup: 0.2×

• 20.1% 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: 86.7% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 95.7% accurate, 0.2× speedup

Math

\[\begin{array}{l} [a1, a2] = \mathsf{sort}([a1, a2])\\ [b1, b2] = \mathsf{sort}([b1, b2])\\ \\ \begin{array}{l} t_0 := \frac{a1 \cdot a2}{b1 \cdot b2}\\ t_1 := \frac{\frac{a1}{\frac{b1}{a2}}}{b2}\\ \mathbf{if}\;t_0 \leq -1 \cdot 10^{+294}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t_0 \leq -2 \cdot 10^{-268}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;t_0 \leq 0:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t_0 \leq 2 \cdot 10^{+244}:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;\frac{a1}{b1} \cdot \frac{a2}{b2}\\ \end{array} \end{array} \]

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
 (let* ((t_0 (/ (* a1 a2) (* b1 b2))) (t_1 (/ (/ a1 (/ b1 a2)) b2)))
   (if (<= t_0 -1e+294)
     t_1
     (if (<= t_0 -2e-268)
       t_0
       (if (<= t_0 0.0)
         t_1
         (if (<= t_0 2e+244) t_0 (* (/ a1 b1) (/ a2 b2))))))))

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 = (a1 / (b1 / a2)) / b2;
	double tmp;
	if (t_0 <= -1e+294) {
		tmp = t_1;
	} else if (t_0 <= -2e-268) {
		tmp = t_0;
	} else if (t_0 <= 0.0) {
		tmp = t_1;
	} else if (t_0 <= 2e+244) {
		tmp = t_0;
	} else {
		tmp = (a1 / b1) * (a2 / 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) :: t_0
    real(8) :: t_1
    real(8) :: tmp
    t_0 = (a1 * a2) / (b1 * b2)
    t_1 = (a1 / (b1 / a2)) / b2
    if (t_0 <= (-1d+294)) then
        tmp = t_1
    else if (t_0 <= (-2d-268)) then
        tmp = t_0
    else if (t_0 <= 0.0d0) then
        tmp = t_1
    else if (t_0 <= 2d+244) then
        tmp = t_0
    else
        tmp = (a1 / b1) * (a2 / 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 t_0 = (a1 * a2) / (b1 * b2);
	double t_1 = (a1 / (b1 / a2)) / b2;
	double tmp;
	if (t_0 <= -1e+294) {
		tmp = t_1;
	} else if (t_0 <= -2e-268) {
		tmp = t_0;
	} else if (t_0 <= 0.0) {
		tmp = t_1;
	} else if (t_0 <= 2e+244) {
		tmp = t_0;
	} else {
		tmp = (a1 / b1) * (a2 / b2);
	}
	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 = (a1 / (b1 / a2)) / b2
	tmp = 0
	if t_0 <= -1e+294:
		tmp = t_1
	elif t_0 <= -2e-268:
		tmp = t_0
	elif t_0 <= 0.0:
		tmp = t_1
	elif t_0 <= 2e+244:
		tmp = t_0
	else:
		tmp = (a1 / b1) * (a2 / b2)
	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(a1 / Float64(b1 / a2)) / b2)
	tmp = 0.0
	if (t_0 <= -1e+294)
		tmp = t_1;
	elseif (t_0 <= -2e-268)
		tmp = t_0;
	elseif (t_0 <= 0.0)
		tmp = t_1;
	elseif (t_0 <= 2e+244)
		tmp = t_0;
	else
		tmp = Float64(Float64(a1 / b1) * Float64(a2 / 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)
	t_0 = (a1 * a2) / (b1 * b2);
	t_1 = (a1 / (b1 / a2)) / b2;
	tmp = 0.0;
	if (t_0 <= -1e+294)
		tmp = t_1;
	elseif (t_0 <= -2e-268)
		tmp = t_0;
	elseif (t_0 <= 0.0)
		tmp = t_1;
	elseif (t_0 <= 2e+244)
		tmp = t_0;
	else
		tmp = (a1 / b1) * (a2 / 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_] := Block[{t$95$0 = N[(N[(a1 * a2), $MachinePrecision] / N[(b1 * b2), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(N[(a1 / N[(b1 / a2), $MachinePrecision]), $MachinePrecision] / b2), $MachinePrecision]}, If[LessEqual[t$95$0, -1e+294], t$95$1, If[LessEqual[t$95$0, -2e-268], t$95$0, If[LessEqual[t$95$0, 0.0], t$95$1, If[LessEqual[t$95$0, 2e+244], t$95$0, N[(N[(a1 / b1), $MachinePrecision] * N[(a2 / b2), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 (*.f64 a1 a2) (*.f64 b1 b2)) < -1.00000000000000007e294 or -1.99999999999999992e-268 < (/.f64 (*.f64 a1 a2) (*.f64 b1 b2)) < -0.0

   1. Initial program 85.6%

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

      1. frac-2neg 85.6%

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

      2. div-inv 84.9%

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

      3. *-commutative 84.9%

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

      4. distribute-rgt-neg-in 84.9%

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

      5. *-commutative 84.9%

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

   3. Applied egg-rr 84.9%

      \[\leadsto \color{blue}{\left(a2 \cdot \left(-a1\right)\right) \cdot \frac{1}{-b2 \cdot b1}} \]
   4. Step-by-step derivation

      1. un-div-inv 85.6%

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

      2. distribute-rgt-neg-out 85.6%

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

      3. frac-2neg 85.6%

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

      4. associate-/l/ 95.6%

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

      5. associate-*l/ 97.5%

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

      6. clear-num 97.5%

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

      7. associate-*l/ 97.5%

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

      8. *-un-lft-identity 97.5%

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

   5. Applied egg-rr 97.5%

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

   if -1.00000000000000007e294 < (/.f64 (*.f64 a1 a2) (*.f64 b1 b2)) < -1.99999999999999992e-268 or -0.0 < (/.f64 (*.f64 a1 a2) (*.f64 b1 b2)) < 2.00000000000000015e244

   1. Initial program 97.8%

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

   if 2.00000000000000015e244 < (/.f64 (*.f64 a1 a2) (*.f64 b1 b2))

   1. Initial program 64.1%

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

      1. times-frac 99.8%

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

   3. Simplified 99.8%

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

4. Final simplification 97.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{a1 \cdot a2}{b1 \cdot b2} \leq -1 \cdot 10^{+294}:\\ \;\;\;\;\frac{\frac{a1}{\frac{b1}{a2}}}{b2}\\ \mathbf{elif}\;\frac{a1 \cdot a2}{b1 \cdot b2} \leq -2 \cdot 10^{-268}:\\ \;\;\;\;\frac{a1 \cdot a2}{b1 \cdot b2}\\ \mathbf{elif}\;\frac{a1 \cdot a2}{b1 \cdot b2} \leq 0:\\ \;\;\;\;\frac{\frac{a1}{\frac{b1}{a2}}}{b2}\\ \mathbf{elif}\;\frac{a1 \cdot a2}{b1 \cdot b2} \leq 2 \cdot 10^{+244}:\\ \;\;\;\;\frac{a1 \cdot a2}{b1 \cdot b2}\\ \mathbf{else}:\\ \;\;\;\;\frac{a1}{b1} \cdot \frac{a2}{b2}\\ \end{array} \]

Alternative 2: 96.7% accurate, 0.2× speedup

Math

\[\begin{array}{l} [a1, a2] = \mathsf{sort}([a1, a2])\\ [b1, b2] = \mathsf{sort}([b1, b2])\\ \\ \begin{array}{l} t_0 := \frac{a1 \cdot a2}{b1 \cdot b2}\\ \mathbf{if}\;t_0 \leq -1 \cdot 10^{+294} \lor \neg \left(t_0 \leq -2 \cdot 10^{-323}\right) \land \left(t_0 \leq 0 \lor \neg \left(t_0 \leq 2 \cdot 10^{+244}\right)\right):\\ \;\;\;\;\frac{a1}{b1} \cdot \frac{a2}{b2}\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \end{array} \]

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 a2) (* b1 b2))))
   (if (or (<= t_0 -1e+294)
           (and (not (<= t_0 -2e-323))
                (or (<= t_0 0.0) (not (<= t_0 2e+244)))))
     (* (/ a1 b1) (/ a2 b2))
     t_0)))

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 tmp;
	if ((t_0 <= -1e+294) || (!(t_0 <= -2e-323) && ((t_0 <= 0.0) || !(t_0 <= 2e+244)))) {
		tmp = (a1 / b1) * (a2 / 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 * a2) / (b1 * b2)
    if ((t_0 <= (-1d+294)) .or. (.not. (t_0 <= (-2d-323))) .and. (t_0 <= 0.0d0) .or. (.not. (t_0 <= 2d+244))) then
        tmp = (a1 / b1) * (a2 / 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 * a2) / (b1 * b2);
	double tmp;
	if ((t_0 <= -1e+294) || (!(t_0 <= -2e-323) && ((t_0 <= 0.0) || !(t_0 <= 2e+244)))) {
		tmp = (a1 / b1) * (a2 / 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 * a2) / (b1 * b2)
	tmp = 0
	if (t_0 <= -1e+294) or (not (t_0 <= -2e-323) and ((t_0 <= 0.0) or not (t_0 <= 2e+244))):
		tmp = (a1 / b1) * (a2 / 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(Float64(a1 * a2) / Float64(b1 * b2))
	tmp = 0.0
	if ((t_0 <= -1e+294) || (!(t_0 <= -2e-323) && ((t_0 <= 0.0) || !(t_0 <= 2e+244))))
		tmp = Float64(Float64(a1 / b1) * Float64(a2 / 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 * a2) / (b1 * b2);
	tmp = 0.0;
	if ((t_0 <= -1e+294) || (~((t_0 <= -2e-323)) && ((t_0 <= 0.0) || ~((t_0 <= 2e+244)))))
		tmp = (a1 / b1) * (a2 / 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[(N[(a1 * a2), $MachinePrecision] / N[(b1 * b2), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[t$95$0, -1e+294], And[N[Not[LessEqual[t$95$0, -2e-323]], $MachinePrecision], Or[LessEqual[t$95$0, 0.0], N[Not[LessEqual[t$95$0, 2e+244]], $MachinePrecision]]]], N[(N[(a1 / b1), $MachinePrecision] * N[(a2 / b2), $MachinePrecision]), $MachinePrecision], t$95$0]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (*.f64 a1 a2) (*.f64 b1 b2)) < -1.00000000000000007e294 or -1.97626e-323 < (/.f64 (*.f64 a1 a2) (*.f64 b1 b2)) < -0.0 or 2.00000000000000015e244 < (/.f64 (*.f64 a1 a2) (*.f64 b1 b2))

   1. Initial program 79.9%

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

      1. times-frac 96.7%

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

   3. Simplified 96.7%

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

   if -1.00000000000000007e294 < (/.f64 (*.f64 a1 a2) (*.f64 b1 b2)) < -1.97626e-323 or -0.0 < (/.f64 (*.f64 a1 a2) (*.f64 b1 b2)) < 2.00000000000000015e244

   1. Initial program 97.8%

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

4. Final simplification 97.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{a1 \cdot a2}{b1 \cdot b2} \leq -1 \cdot 10^{+294} \lor \neg \left(\frac{a1 \cdot a2}{b1 \cdot b2} \leq -2 \cdot 10^{-323}\right) \land \left(\frac{a1 \cdot a2}{b1 \cdot b2} \leq 0 \lor \neg \left(\frac{a1 \cdot a2}{b1 \cdot b2} \leq 2 \cdot 10^{+244}\right)\right):\\ \;\;\;\;\frac{a1}{b1} \cdot \frac{a2}{b2}\\ \mathbf{else}:\\ \;\;\;\;\frac{a1 \cdot a2}{b1 \cdot b2}\\ \end{array} \]

Alternative 3: 86.6% accurate, 0.6× speedup

Math

\[\begin{array}{l} [a1, a2] = \mathsf{sort}([a1, a2])\\ [b1, b2] = \mathsf{sort}([b1, b2])\\ \\ \begin{array}{l} \mathbf{if}\;a2 \leq 3.05 \cdot 10^{+136}:\\ \;\;\;\;\frac{a1}{b1} \cdot \frac{a2}{b2}\\ \mathbf{elif}\;a2 \leq 1.9 \cdot 10^{+273}:\\ \;\;\;\;\frac{a2}{b1} \cdot \frac{a1}{b2}\\ \mathbf{else}:\\ \;\;\;\;a1 \cdot \frac{\frac{a2}{b2}}{b1}\\ \end{array} \end{array} \]

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 (<= a2 3.05e+136)
   (* (/ a1 b1) (/ a2 b2))
   (if (<= a2 1.9e+273) (* (/ a2 b1) (/ a1 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 (a2 <= 3.05e+136) {
		tmp = (a1 / b1) * (a2 / b2);
	} else if (a2 <= 1.9e+273) {
		tmp = (a2 / b1) * (a1 / 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 (a2 <= 3.05d+136) then
        tmp = (a1 / b1) * (a2 / b2)
    else if (a2 <= 1.9d+273) then
        tmp = (a2 / b1) * (a1 / 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 (a2 <= 3.05e+136) {
		tmp = (a1 / b1) * (a2 / b2);
	} else if (a2 <= 1.9e+273) {
		tmp = (a2 / b1) * (a1 / 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 a2 <= 3.05e+136:
		tmp = (a1 / b1) * (a2 / b2)
	elif a2 <= 1.9e+273:
		tmp = (a2 / b1) * (a1 / 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 (a2 <= 3.05e+136)
		tmp = Float64(Float64(a1 / b1) * Float64(a2 / b2));
	elseif (a2 <= 1.9e+273)
		tmp = Float64(Float64(a2 / b1) * Float64(a1 / 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 (a2 <= 3.05e+136)
		tmp = (a1 / b1) * (a2 / b2);
	elseif (a2 <= 1.9e+273)
		tmp = (a2 / b1) * (a1 / 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[a2, 3.05e+136], N[(N[(a1 / b1), $MachinePrecision] * N[(a2 / b2), $MachinePrecision]), $MachinePrecision], If[LessEqual[a2, 1.9e+273], N[(N[(a2 / b1), $MachinePrecision] * N[(a1 / b2), $MachinePrecision]), $MachinePrecision], N[(a1 * N[(N[(a2 / b2), $MachinePrecision] / b1), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if a2 < 3.0499999999999998e136

   1. Initial program 87.1%

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

      1. times-frac 89.0%

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

   3. Simplified 89.0%

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

   if 3.0499999999999998e136 < a2 < 1.9e273

   1. Initial program 93.2%

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

      1. *-commutative 93.2%

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

      2. times-frac 90.1%

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

   3. Applied egg-rr 90.1%

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

   if 1.9e273 < a2

   1. Initial program 78.4%

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

      1. times-frac 88.7%

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

      2. associate-*l/ 68.1%

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

      3. associate-*r/ 89.0%

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

   3. Simplified 89.0%

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

4. Final simplification 89.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a2 \leq 3.05 \cdot 10^{+136}:\\ \;\;\;\;\frac{a1}{b1} \cdot \frac{a2}{b2}\\ \mathbf{elif}\;a2 \leq 1.9 \cdot 10^{+273}:\\ \;\;\;\;\frac{a2}{b1} \cdot \frac{a1}{b2}\\ \mathbf{else}:\\ \;\;\;\;a1 \cdot \frac{\frac{a2}{b2}}{b1}\\ \end{array} \]

Alternative 4: 85.9% accurate, 0.8× speedup

Math

\[\begin{array}{l} [a1, a2] = \mathsf{sort}([a1, a2])\\ [b1, b2] = \mathsf{sort}([b1, b2])\\ \\ \begin{array}{l} \mathbf{if}\;b2 \leq 20500:\\ \;\;\;\;a1 \cdot \frac{\frac{a2}{b2}}{b1}\\ \mathbf{else}:\\ \;\;\;\;\frac{a2}{b2 \cdot \frac{b1}{a1}}\\ \end{array} \end{array} \]

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 20500.0) (* a1 (/ (/ a2 b2) b1)) (/ a2 (* b2 (/ b1 a1)))))

C

assert(a1 < a2);
assert(b1 < b2);
double code(double a1, double a2, double b1, double b2) {
	double tmp;
	if (b2 <= 20500.0) {
		tmp = a1 * ((a2 / b2) / b1);
	} else {
		tmp = a2 / (b2 * (b1 / a1));
	}
	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 <= 20500.0d0) then
        tmp = a1 * ((a2 / b2) / b1)
    else
        tmp = a2 / (b2 * (b1 / a1))
    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 <= 20500.0) {
		tmp = a1 * ((a2 / b2) / b1);
	} else {
		tmp = a2 / (b2 * (b1 / a1));
	}
	return tmp;
}

Python

[a1, a2] = sort([a1, a2])
[b1, b2] = sort([b1, b2])
def code(a1, a2, b1, b2):
	tmp = 0
	if b2 <= 20500.0:
		tmp = a1 * ((a2 / b2) / b1)
	else:
		tmp = a2 / (b2 * (b1 / a1))
	return tmp

Julia

a1, a2 = sort([a1, a2])
b1, b2 = sort([b1, b2])
function code(a1, a2, b1, b2)
	tmp = 0.0
	if (b2 <= 20500.0)
		tmp = Float64(a1 * Float64(Float64(a2 / b2) / b1));
	else
		tmp = Float64(a2 / Float64(b2 * Float64(b1 / a1)));
	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 <= 20500.0)
		tmp = a1 * ((a2 / b2) / b1);
	else
		tmp = a2 / (b2 * (b1 / a1));
	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, 20500.0], N[(a1 * N[(N[(a2 / b2), $MachinePrecision] / b1), $MachinePrecision]), $MachinePrecision], N[(a2 / N[(b2 * N[(b1 / a1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b2 < 20500

   1. Initial program 87.6%

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

      1. times-frac 90.8%

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

      2. associate-*l/ 88.4%

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

      3. associate-*r/ 89.6%

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

   3. Simplified 89.6%

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

   if 20500 < b2

   1. Initial program 87.0%

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

      1. times-frac 85.0%

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

      2. associate-*l/ 81.5%

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

      3. associate-*r/ 88.1%

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

   3. Simplified 88.1%

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

      1. associate-*r/ 81.5%

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

      2. associate-*l/ 85.0%

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

      3. clear-num 84.9%

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

      4. frac-times 91.7%

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

      5. *-un-lft-identity 91.7%

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

   5. Applied egg-rr 91.7%

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

4. Final simplification 90.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b2 \leq 20500:\\ \;\;\;\;a1 \cdot \frac{\frac{a2}{b2}}{b1}\\ \mathbf{else}:\\ \;\;\;\;\frac{a2}{b2 \cdot \frac{b1}{a1}}\\ \end{array} \]

Alternative 5: 86.2% 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 87.5%

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

   1. times-frac 89.4%

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

   2. associate-*l/ 86.8%

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

   3. associate-*r/ 89.3%

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

3. Simplified 89.3%

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

4. Final simplification 89.3%

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

Developer target: 86.2% 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 2023312 
(FPCore (a1 a2 b1 b2)
  :name "Quotient of products"
  :precision binary64

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

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