Quotient of products

Percentage Accurate: 85.7% → 95.5%

Time: 6.0s

Alternatives: 5

Speedup: 1.0×

• 20.2% 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: 85.7% 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: 95.5% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{a1 \cdot a2}{b1 \cdot b2}\\ \mathbf{if}\;t_0 \leq -4 \cdot 10^{+81}:\\ \;\;\;\;\frac{a2}{\frac{b2}{\frac{a1}{b1}}}\\ \mathbf{elif}\;t_0 \leq -5 \cdot 10^{-321}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;t_0 \leq 0:\\ \;\;\;\;\frac{\frac{a2}{b2}}{\frac{b1}{a1}}\\ \mathbf{elif}\;t_0 \leq 10^{+308}:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;\frac{a1}{b1} \cdot \frac{a2}{b2}\\ \end{array} \end{array} \]

FPCore

(FPCore (a1 a2 b1 b2)
 :precision binary64
 (let* ((t_0 (/ (* a1 a2) (* b1 b2))))
   (if (<= t_0 -4e+81)
     (/ a2 (/ b2 (/ a1 b1)))
     (if (<= t_0 -5e-321)
       t_0
       (if (<= t_0 0.0)
         (/ (/ a2 b2) (/ b1 a1))
         (if (<= t_0 1e+308) t_0 (* (/ a1 b1) (/ a2 b2))))))))

C

double code(double a1, double a2, double b1, double b2) {
	double t_0 = (a1 * a2) / (b1 * b2);
	double tmp;
	if (t_0 <= -4e+81) {
		tmp = a2 / (b2 / (a1 / b1));
	} else if (t_0 <= -5e-321) {
		tmp = t_0;
	} else if (t_0 <= 0.0) {
		tmp = (a2 / b2) / (b1 / a1);
	} else if (t_0 <= 1e+308) {
		tmp = t_0;
	} else {
		tmp = (a1 / b1) * (a2 / b2);
	}
	return tmp;
}

Fortran

real(8) function code(a1, a2, b1, b2)
    real(8), intent (in) :: a1
    real(8), intent (in) :: a2
    real(8), intent (in) :: b1
    real(8), intent (in) :: b2
    real(8) :: t_0
    real(8) :: tmp
    t_0 = (a1 * a2) / (b1 * b2)
    if (t_0 <= (-4d+81)) then
        tmp = a2 / (b2 / (a1 / b1))
    else if (t_0 <= (-5d-321)) then
        tmp = t_0
    else if (t_0 <= 0.0d0) then
        tmp = (a2 / b2) / (b1 / a1)
    else if (t_0 <= 1d+308) then
        tmp = t_0
    else
        tmp = (a1 / b1) * (a2 / b2)
    end if
    code = tmp
end function

Java

public static double code(double a1, double a2, double b1, double b2) {
	double t_0 = (a1 * a2) / (b1 * b2);
	double tmp;
	if (t_0 <= -4e+81) {
		tmp = a2 / (b2 / (a1 / b1));
	} else if (t_0 <= -5e-321) {
		tmp = t_0;
	} else if (t_0 <= 0.0) {
		tmp = (a2 / b2) / (b1 / a1);
	} else if (t_0 <= 1e+308) {
		tmp = t_0;
	} else {
		tmp = (a1 / b1) * (a2 / b2);
	}
	return tmp;
}

Python

def code(a1, a2, b1, b2):
	t_0 = (a1 * a2) / (b1 * b2)
	tmp = 0
	if t_0 <= -4e+81:
		tmp = a2 / (b2 / (a1 / b1))
	elif t_0 <= -5e-321:
		tmp = t_0
	elif t_0 <= 0.0:
		tmp = (a2 / b2) / (b1 / a1)
	elif t_0 <= 1e+308:
		tmp = t_0
	else:
		tmp = (a1 / b1) * (a2 / b2)
	return tmp

Julia

function code(a1, a2, b1, b2)
	t_0 = Float64(Float64(a1 * a2) / Float64(b1 * b2))
	tmp = 0.0
	if (t_0 <= -4e+81)
		tmp = Float64(a2 / Float64(b2 / Float64(a1 / b1)));
	elseif (t_0 <= -5e-321)
		tmp = t_0;
	elseif (t_0 <= 0.0)
		tmp = Float64(Float64(a2 / b2) / Float64(b1 / a1));
	elseif (t_0 <= 1e+308)
		tmp = t_0;
	else
		tmp = Float64(Float64(a1 / b1) * Float64(a2 / b2));
	end
	return tmp
end

MATLAB

function tmp_2 = code(a1, a2, b1, b2)
	t_0 = (a1 * a2) / (b1 * b2);
	tmp = 0.0;
	if (t_0 <= -4e+81)
		tmp = a2 / (b2 / (a1 / b1));
	elseif (t_0 <= -5e-321)
		tmp = t_0;
	elseif (t_0 <= 0.0)
		tmp = (a2 / b2) / (b1 / a1);
	elseif (t_0 <= 1e+308)
		tmp = t_0;
	else
		tmp = (a1 / b1) * (a2 / b2);
	end
	tmp_2 = tmp;
end

Wolfram

code[a1_, a2_, b1_, b2_] := Block[{t$95$0 = N[(N[(a1 * a2), $MachinePrecision] / N[(b1 * b2), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$0, -4e+81], N[(a2 / N[(b2 / N[(a1 / b1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$0, -5e-321], t$95$0, If[LessEqual[t$95$0, 0.0], N[(N[(a2 / b2), $MachinePrecision] / N[(b1 / a1), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$0, 1e+308], t$95$0, N[(N[(a1 / b1), $MachinePrecision] * N[(a2 / b2), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if (/.f64 (*.f64 a1 a2) (*.f64 b1 b2)) < -3.99999999999999969e81

   1. Initial program 84.7%

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

      1. times-frac 97.6%

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

      2. *-commutative 97.6%

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

   3. Simplified 97.6%

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

      1. associate-*l/ 89.8%

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

      2. associate-/l* 99.2%

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

   5. Applied egg-rr 99.2%

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

   if -3.99999999999999969e81 < (/.f64 (*.f64 a1 a2) (*.f64 b1 b2)) < -4.99994e-321 or -0.0 < (/.f64 (*.f64 a1 a2) (*.f64 b1 b2)) < 1e308

   1. Initial program 99.0%

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

   if -4.99994e-321 < (/.f64 (*.f64 a1 a2) (*.f64 b1 b2)) < -0.0

   1. Initial program 78.4%

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

      1. times-frac 99.9%

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

      2. *-commutative 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in a2 around 0 78.4%

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

      1. *-commutative 78.4%

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

      2. associate-*r/ 88.4%

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

      3. *-commutative 88.4%

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

   6. Simplified 88.4%

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

      1. associate-*r/ 78.4%

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

      2. times-frac 99.9%

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

      3. *-commutative 99.9%

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

      4. clear-num 99.9%

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

      5. un-div-inv 99.9%

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

   8. Applied egg-rr 99.9%

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

   if 1e308 < (/.f64 (*.f64 a1 a2) (*.f64 b1 b2))

   1. Initial program 72.2%

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

      1. times-frac 99.8%

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

      2. *-commutative 99.8%

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

   3. Simplified 99.8%

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

4. Final simplification 99.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{a1 \cdot a2}{b1 \cdot b2} \leq -4 \cdot 10^{+81}:\\ \;\;\;\;\frac{a2}{\frac{b2}{\frac{a1}{b1}}}\\ \mathbf{elif}\;\frac{a1 \cdot a2}{b1 \cdot b2} \leq -5 \cdot 10^{-321}:\\ \;\;\;\;\frac{a1 \cdot a2}{b1 \cdot b2}\\ \mathbf{elif}\;\frac{a1 \cdot a2}{b1 \cdot b2} \leq 0:\\ \;\;\;\;\frac{\frac{a2}{b2}}{\frac{b1}{a1}}\\ \mathbf{elif}\;\frac{a1 \cdot a2}{b1 \cdot b2} \leq 10^{+308}:\\ \;\;\;\;\frac{a1 \cdot a2}{b1 \cdot b2}\\ \mathbf{else}:\\ \;\;\;\;\frac{a1}{b1} \cdot \frac{a2}{b2}\\ \end{array} \]

Alternative 2: 95.6% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{a1 \cdot a2}{b1 \cdot b2}\\ \mathbf{if}\;t_0 \leq -4 \cdot 10^{+81}:\\ \;\;\;\;\frac{a2}{\frac{b2}{\frac{a1}{b1}}}\\ \mathbf{elif}\;t_0 \leq -5 \cdot 10^{-321} \lor \neg \left(t_0 \leq 0\right) \land t_0 \leq 10^{+308}:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;\frac{a1}{b1} \cdot \frac{a2}{b2}\\ \end{array} \end{array} \]

FPCore

(FPCore (a1 a2 b1 b2)
 :precision binary64
 (let* ((t_0 (/ (* a1 a2) (* b1 b2))))
   (if (<= t_0 -4e+81)
     (/ a2 (/ b2 (/ a1 b1)))
     (if (or (<= t_0 -5e-321) (and (not (<= t_0 0.0)) (<= t_0 1e+308)))
       t_0
       (* (/ a1 b1) (/ a2 b2))))))

C

double code(double a1, double a2, double b1, double b2) {
	double t_0 = (a1 * a2) / (b1 * b2);
	double tmp;
	if (t_0 <= -4e+81) {
		tmp = a2 / (b2 / (a1 / b1));
	} else if ((t_0 <= -5e-321) || (!(t_0 <= 0.0) && (t_0 <= 1e+308))) {
		tmp = t_0;
	} else {
		tmp = (a1 / b1) * (a2 / b2);
	}
	return tmp;
}

Fortran

real(8) function code(a1, a2, b1, b2)
    real(8), intent (in) :: a1
    real(8), intent (in) :: a2
    real(8), intent (in) :: b1
    real(8), intent (in) :: b2
    real(8) :: t_0
    real(8) :: tmp
    t_0 = (a1 * a2) / (b1 * b2)
    if (t_0 <= (-4d+81)) then
        tmp = a2 / (b2 / (a1 / b1))
    else if ((t_0 <= (-5d-321)) .or. (.not. (t_0 <= 0.0d0)) .and. (t_0 <= 1d+308)) then
        tmp = t_0
    else
        tmp = (a1 / b1) * (a2 / b2)
    end if
    code = tmp
end function

Java

public static double code(double a1, double a2, double b1, double b2) {
	double t_0 = (a1 * a2) / (b1 * b2);
	double tmp;
	if (t_0 <= -4e+81) {
		tmp = a2 / (b2 / (a1 / b1));
	} else if ((t_0 <= -5e-321) || (!(t_0 <= 0.0) && (t_0 <= 1e+308))) {
		tmp = t_0;
	} else {
		tmp = (a1 / b1) * (a2 / b2);
	}
	return tmp;
}

Python

def code(a1, a2, b1, b2):
	t_0 = (a1 * a2) / (b1 * b2)
	tmp = 0
	if t_0 <= -4e+81:
		tmp = a2 / (b2 / (a1 / b1))
	elif (t_0 <= -5e-321) or (not (t_0 <= 0.0) and (t_0 <= 1e+308)):
		tmp = t_0
	else:
		tmp = (a1 / b1) * (a2 / b2)
	return tmp

Julia

function code(a1, a2, b1, b2)
	t_0 = Float64(Float64(a1 * a2) / Float64(b1 * b2))
	tmp = 0.0
	if (t_0 <= -4e+81)
		tmp = Float64(a2 / Float64(b2 / Float64(a1 / b1)));
	elseif ((t_0 <= -5e-321) || (!(t_0 <= 0.0) && (t_0 <= 1e+308)))
		tmp = t_0;
	else
		tmp = Float64(Float64(a1 / b1) * Float64(a2 / b2));
	end
	return tmp
end

MATLAB

function tmp_2 = code(a1, a2, b1, b2)
	t_0 = (a1 * a2) / (b1 * b2);
	tmp = 0.0;
	if (t_0 <= -4e+81)
		tmp = a2 / (b2 / (a1 / b1));
	elseif ((t_0 <= -5e-321) || (~((t_0 <= 0.0)) && (t_0 <= 1e+308)))
		tmp = t_0;
	else
		tmp = (a1 / b1) * (a2 / b2);
	end
	tmp_2 = tmp;
end

Wolfram

code[a1_, a2_, b1_, b2_] := Block[{t$95$0 = N[(N[(a1 * a2), $MachinePrecision] / N[(b1 * b2), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$0, -4e+81], N[(a2 / N[(b2 / N[(a1 / b1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[t$95$0, -5e-321], And[N[Not[LessEqual[t$95$0, 0.0]], $MachinePrecision], LessEqual[t$95$0, 1e+308]]], 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)) < -3.99999999999999969e81

   1. Initial program 84.7%

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

      1. times-frac 97.6%

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

      2. *-commutative 97.6%

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

   3. Simplified 97.6%

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

      1. associate-*l/ 89.8%

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

      2. associate-/l* 99.2%

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

   5. Applied egg-rr 99.2%

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

   if -3.99999999999999969e81 < (/.f64 (*.f64 a1 a2) (*.f64 b1 b2)) < -4.99994e-321 or -0.0 < (/.f64 (*.f64 a1 a2) (*.f64 b1 b2)) < 1e308

   1. Initial program 99.0%

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

   if -4.99994e-321 < (/.f64 (*.f64 a1 a2) (*.f64 b1 b2)) < -0.0 or 1e308 < (/.f64 (*.f64 a1 a2) (*.f64 b1 b2))

   1. Initial program 76.3%

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

      1. times-frac 99.9%

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

      2. *-commutative 99.9%

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

   3. Simplified 99.9%

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

4. Final simplification 99.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{a1 \cdot a2}{b1 \cdot b2} \leq -4 \cdot 10^{+81}:\\ \;\;\;\;\frac{a2}{\frac{b2}{\frac{a1}{b1}}}\\ \mathbf{elif}\;\frac{a1 \cdot a2}{b1 \cdot b2} \leq -5 \cdot 10^{-321} \lor \neg \left(\frac{a1 \cdot a2}{b1 \cdot b2} \leq 0\right) \land \frac{a1 \cdot a2}{b1 \cdot b2} \leq 10^{+308}:\\ \;\;\;\;\frac{a1 \cdot a2}{b1 \cdot b2}\\ \mathbf{else}:\\ \;\;\;\;\frac{a1}{b1} \cdot \frac{a2}{b2}\\ \end{array} \]

Alternative 3: 86.1% accurate, 1.0× speedup

Math

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

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(a1 * Float64(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[(a1 * N[(a2 / N[(b1 * b2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 87.2%

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

   1. times-frac 89.1%

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

   2. *-commutative 89.1%

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

3. Simplified 89.1%

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

4. Taylor expanded in a2 around 0 87.2%

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

   1. *-commutative 87.2%

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

   2. associate-*r/ 90.3%

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

   3. *-commutative 90.3%

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

6. Simplified 90.3%

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

7. Final simplification 90.3%

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

Alternative 4: 86.6% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 87.2%

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

   1. times-frac 89.1%

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

   2. *-commutative 89.1%

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

3. Simplified 89.1%

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

4. Taylor expanded in a2 around 0 87.2%

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

   1. times-frac 89.1%

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

   2. *-commutative 89.1%

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

   3. associate-*l/ 85.0%

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

   4. associate-*r/ 92.0%

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

6. Simplified 92.0%

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

7. Final simplification 92.0%

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

Alternative 5: 86.6% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 87.2%

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

   1. times-frac 89.1%

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

   2. *-commutative 89.1%

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

3. Simplified 89.1%

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

   1. associate-*l/ 85.0%

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

   2. associate-/l* 92.2%

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

5. Applied egg-rr 92.2%

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

6. Final simplification 92.2%

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

Developer target: 86.7% 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 2023277 
(FPCore (a1 a2 b1 b2)
  :name "Quotient of products"
  :precision binary64

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

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