Quotient of products

Percentage Accurate: 86.4% → 94.8%

Time: 2.4s

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: 86.4% 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: 94.8% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{a1 \cdot a2}{b1 \cdot b2}\\ \mathbf{if}\;t_0 \leq -2 \cdot 10^{-295} \lor \neg \left(t_0 \leq 0\right) \land t_0 \leq 10^{+260}:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{a1}{b2}}{\frac{b1}{a2}}\\ \end{array} \end{array} \]

FPCore

(FPCore (a1 a2 b1 b2)
 :precision binary64
 (let* ((t_0 (/ (* a1 a2) (* b1 b2))))
   (if (or (<= t_0 -2e-295) (and (not (<= t_0 0.0)) (<= t_0 1e+260)))
     t_0
     (/ (/ a1 b2) (/ b1 a2)))))

C

double code(double a1, double a2, double b1, double b2) {
	double t_0 = (a1 * a2) / (b1 * b2);
	double tmp;
	if ((t_0 <= -2e-295) || (!(t_0 <= 0.0) && (t_0 <= 1e+260))) {
		tmp = t_0;
	} else {
		tmp = (a1 / b2) / (b1 / a2);
	}
	return tmp;
}

Fortran

real(8) function code(a1, a2, b1, b2)
    real(8), intent (in) :: a1
    real(8), intent (in) :: a2
    real(8), intent (in) :: b1
    real(8), intent (in) :: b2
    real(8) :: t_0
    real(8) :: tmp
    t_0 = (a1 * a2) / (b1 * b2)
    if ((t_0 <= (-2d-295)) .or. (.not. (t_0 <= 0.0d0)) .and. (t_0 <= 1d+260)) then
        tmp = t_0
    else
        tmp = (a1 / b2) / (b1 / a2)
    end if
    code = tmp
end function

Java

public static double code(double a1, double a2, double b1, double b2) {
	double t_0 = (a1 * a2) / (b1 * b2);
	double tmp;
	if ((t_0 <= -2e-295) || (!(t_0 <= 0.0) && (t_0 <= 1e+260))) {
		tmp = t_0;
	} else {
		tmp = (a1 / b2) / (b1 / a2);
	}
	return tmp;
}

Python

def code(a1, a2, b1, b2):
	t_0 = (a1 * a2) / (b1 * b2)
	tmp = 0
	if (t_0 <= -2e-295) or (not (t_0 <= 0.0) and (t_0 <= 1e+260)):
		tmp = t_0
	else:
		tmp = (a1 / b2) / (b1 / a2)
	return tmp

Julia

function code(a1, a2, b1, b2)
	t_0 = Float64(Float64(a1 * a2) / Float64(b1 * b2))
	tmp = 0.0
	if ((t_0 <= -2e-295) || (!(t_0 <= 0.0) && (t_0 <= 1e+260)))
		tmp = t_0;
	else
		tmp = Float64(Float64(a1 / b2) / Float64(b1 / a2));
	end
	return tmp
end

MATLAB

function tmp_2 = code(a1, a2, b1, b2)
	t_0 = (a1 * a2) / (b1 * b2);
	tmp = 0.0;
	if ((t_0 <= -2e-295) || (~((t_0 <= 0.0)) && (t_0 <= 1e+260)))
		tmp = t_0;
	else
		tmp = (a1 / b2) / (b1 / a2);
	end
	tmp_2 = tmp;
end

Wolfram

code[a1_, a2_, b1_, b2_] := Block[{t$95$0 = N[(N[(a1 * a2), $MachinePrecision] / N[(b1 * b2), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[t$95$0, -2e-295], And[N[Not[LessEqual[t$95$0, 0.0]], $MachinePrecision], LessEqual[t$95$0, 1e+260]]], t$95$0, N[(N[(a1 / b2), $MachinePrecision] / N[(b1 / a2), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (*.f64 a1 a2) (*.f64 b1 b2)) < -2.00000000000000012e-295 or 0.0 < (/.f64 (*.f64 a1 a2) (*.f64 b1 b2)) < 1.00000000000000007e260

   1. Initial program 95.7%

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

   if -2.00000000000000012e-295 < (/.f64 (*.f64 a1 a2) (*.f64 b1 b2)) < 0.0 or 1.00000000000000007e260 < (/.f64 (*.f64 a1 a2) (*.f64 b1 b2))

   1. Initial program 69.9%

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

      1. times-frac 96.1%

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

   3. Simplified 96.1%

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

      1. frac-times 69.9%

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

      2. *-commutative 69.9%

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

      3. frac-times 99.8%

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

      4. clear-num 99.8%

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

      5. un-div-inv 99.8%

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

   5. Applied egg-rr 99.8%

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

4. Final simplification 97.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{a1 \cdot a2}{b1 \cdot b2} \leq -2 \cdot 10^{-295} \lor \neg \left(\frac{a1 \cdot a2}{b1 \cdot b2} \leq 0\right) \land \frac{a1 \cdot a2}{b1 \cdot b2} \leq 10^{+260}:\\ \;\;\;\;\frac{a1 \cdot a2}{b1 \cdot b2}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{a1}{b2}}{\frac{b1}{a2}}\\ \end{array} \]

Alternative 2: 95.4% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{a1 \cdot a2}{b1 \cdot b2}\\ \mathbf{if}\;t_0 \leq -1 \cdot 10^{-315} \lor \neg \left(t_0 \leq 0\right) \land t_0 \leq 5 \cdot 10^{+306}:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;\frac{a1}{b1} \cdot \frac{a2}{b2}\\ \end{array} \end{array} \]

FPCore

(FPCore (a1 a2 b1 b2)
 :precision binary64
 (let* ((t_0 (/ (* a1 a2) (* b1 b2))))
   (if (or (<= t_0 -1e-315) (and (not (<= t_0 0.0)) (<= t_0 5e+306)))
     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 <= -1e-315) || (!(t_0 <= 0.0) && (t_0 <= 5e+306))) {
		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 <= (-1d-315)) .or. (.not. (t_0 <= 0.0d0)) .and. (t_0 <= 5d+306)) 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 <= -1e-315) || (!(t_0 <= 0.0) && (t_0 <= 5e+306))) {
		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 <= -1e-315) or (not (t_0 <= 0.0) and (t_0 <= 5e+306)):
		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 <= -1e-315) || (!(t_0 <= 0.0) && (t_0 <= 5e+306)))
		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 <= -1e-315) || (~((t_0 <= 0.0)) && (t_0 <= 5e+306)))
		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[Or[LessEqual[t$95$0, -1e-315], And[N[Not[LessEqual[t$95$0, 0.0]], $MachinePrecision], LessEqual[t$95$0, 5e+306]]], t$95$0, N[(N[(a1 / b1), $MachinePrecision] * N[(a2 / b2), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (*.f64 a1 a2) (*.f64 b1 b2)) < -9.999999985e-316 or 0.0 < (/.f64 (*.f64 a1 a2) (*.f64 b1 b2)) < 4.99999999999999993e306

   1. Initial program 95.7%

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

   if -9.999999985e-316 < (/.f64 (*.f64 a1 a2) (*.f64 b1 b2)) < 0.0 or 4.99999999999999993e306 < (/.f64 (*.f64 a1 a2) (*.f64 b1 b2))

   1. Initial program 68.6%

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

      1. times-frac 98.3%

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

   3. Simplified 98.3%

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

4. Final simplification 96.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{a1 \cdot a2}{b1 \cdot b2} \leq -1 \cdot 10^{-315} \lor \neg \left(\frac{a1 \cdot a2}{b1 \cdot b2} \leq 0\right) \land \frac{a1 \cdot a2}{b1 \cdot b2} \leq 5 \cdot 10^{+306}:\\ \;\;\;\;\frac{a1 \cdot a2}{b1 \cdot b2}\\ \mathbf{else}:\\ \;\;\;\;\frac{a1}{b1} \cdot \frac{a2}{b2}\\ \end{array} \]

Alternative 3: 86.0% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b2 \leq -7.6 \cdot 10^{+83}:\\ \;\;\;\;\frac{a1}{\frac{b1 \cdot b2}{a2}}\\ \mathbf{elif}\;b2 \leq -8.6 \cdot 10^{-267}:\\ \;\;\;\;\frac{a1}{b1} \cdot \frac{a2}{b2}\\ \mathbf{else}:\\ \;\;\;\;\frac{a1}{\frac{b2}{\frac{a2}{b1}}}\\ \end{array} \end{array} \]

FPCore

(FPCore (a1 a2 b1 b2)
 :precision binary64
 (if (<= b2 -7.6e+83)
   (/ a1 (/ (* b1 b2) a2))
   (if (<= b2 -8.6e-267) (* (/ a1 b1) (/ a2 b2)) (/ a1 (/ b2 (/ a2 b1))))))

C

double code(double a1, double a2, double b1, double b2) {
	double tmp;
	if (b2 <= -7.6e+83) {
		tmp = a1 / ((b1 * b2) / a2);
	} else if (b2 <= -8.6e-267) {
		tmp = (a1 / b1) * (a2 / b2);
	} else {
		tmp = a1 / (b2 / (a2 / b1));
	}
	return tmp;
}

Fortran

real(8) function code(a1, a2, b1, b2)
    real(8), intent (in) :: a1
    real(8), intent (in) :: a2
    real(8), intent (in) :: b1
    real(8), intent (in) :: b2
    real(8) :: tmp
    if (b2 <= (-7.6d+83)) then
        tmp = a1 / ((b1 * b2) / a2)
    else if (b2 <= (-8.6d-267)) then
        tmp = (a1 / b1) * (a2 / b2)
    else
        tmp = a1 / (b2 / (a2 / b1))
    end if
    code = tmp
end function

Java

public static double code(double a1, double a2, double b1, double b2) {
	double tmp;
	if (b2 <= -7.6e+83) {
		tmp = a1 / ((b1 * b2) / a2);
	} else if (b2 <= -8.6e-267) {
		tmp = (a1 / b1) * (a2 / b2);
	} else {
		tmp = a1 / (b2 / (a2 / b1));
	}
	return tmp;
}

Python

def code(a1, a2, b1, b2):
	tmp = 0
	if b2 <= -7.6e+83:
		tmp = a1 / ((b1 * b2) / a2)
	elif b2 <= -8.6e-267:
		tmp = (a1 / b1) * (a2 / b2)
	else:
		tmp = a1 / (b2 / (a2 / b1))
	return tmp

Julia

function code(a1, a2, b1, b2)
	tmp = 0.0
	if (b2 <= -7.6e+83)
		tmp = Float64(a1 / Float64(Float64(b1 * b2) / a2));
	elseif (b2 <= -8.6e-267)
		tmp = Float64(Float64(a1 / b1) * Float64(a2 / b2));
	else
		tmp = Float64(a1 / Float64(b2 / Float64(a2 / b1)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(a1, a2, b1, b2)
	tmp = 0.0;
	if (b2 <= -7.6e+83)
		tmp = a1 / ((b1 * b2) / a2);
	elseif (b2 <= -8.6e-267)
		tmp = (a1 / b1) * (a2 / b2);
	else
		tmp = a1 / (b2 / (a2 / b1));
	end
	tmp_2 = tmp;
end

Wolfram

code[a1_, a2_, b1_, b2_] := If[LessEqual[b2, -7.6e+83], N[(a1 / N[(N[(b1 * b2), $MachinePrecision] / a2), $MachinePrecision]), $MachinePrecision], If[LessEqual[b2, -8.6e-267], N[(N[(a1 / b1), $MachinePrecision] * N[(a2 / b2), $MachinePrecision]), $MachinePrecision], N[(a1 / N[(b2 / N[(a2 / b1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if b2 < -7.6000000000000004e83

   1. Initial program 90.2%

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

      1. associate-/l* 88.8%

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

      2. *-commutative 88.8%

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

      3. associate-/l* 85.1%

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

   3. Simplified 85.1%

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

   4. Taylor expanded in b2 around 0 88.8%

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

   if -7.6000000000000004e83 < b2 < -8.5999999999999992e-267

   1. Initial program 82.4%

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

      1. times-frac 91.3%

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

   3. Simplified 91.3%

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

   if -8.5999999999999992e-267 < b2

   1. Initial program 81.3%

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

      1. associate-/l* 84.5%

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

      2. *-commutative 84.5%

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

      3. associate-/l* 89.8%

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

   3. Simplified 89.8%

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

4. Final simplification 90.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b2 \leq -7.6 \cdot 10^{+83}:\\ \;\;\;\;\frac{a1}{\frac{b1 \cdot b2}{a2}}\\ \mathbf{elif}\;b2 \leq -8.6 \cdot 10^{-267}:\\ \;\;\;\;\frac{a1}{b1} \cdot \frac{a2}{b2}\\ \mathbf{else}:\\ \;\;\;\;\frac{a1}{\frac{b2}{\frac{a2}{b1}}}\\ \end{array} \]

Alternative 4: 86.4% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 83.4%

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

   1. times-frac 84.6%

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

3. Simplified 84.6%

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

4. Final simplification 84.6%

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

Alternative 5: 86.0% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 83.4%

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

   1. associate-/l* 85.5%

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

   2. *-commutative 85.5%

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

   3. associate-/l* 87.3%

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

3. Simplified 87.3%

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

4. Final simplification 87.3%

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

Developer target: 86.4% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Reproduce

herbie shell --seed 2023255 
(FPCore (a1 a2 b1 b2)
  :name "Quotient of products"
  :precision binary64

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

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