Quotient of products

Percentage Accurate: 85.3% → 96.4%

Time: 2.5s

Alternatives: 5

Speedup: 1.0×

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 85.3% 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: 96.4% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{a1 \cdot a2}{b1 \cdot b2}\\ t_1 := \frac{a1}{b1} \cdot \frac{a2}{b2}\\ \mathbf{if}\;t_0 \leq -5 \cdot 10^{+226}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t_0 \leq -5 \cdot 10^{-322}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;t_0 \leq 0:\\ \;\;\;\;\frac{\frac{a2}{b2}}{\frac{b1}{a1}}\\ \mathbf{elif}\;t_0 \leq 2 \cdot 10^{+254}:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (a1 a2 b1 b2)
 :precision binary64
 (let* ((t_0 (/ (* a1 a2) (* b1 b2))) (t_1 (* (/ a1 b1) (/ a2 b2))))
   (if (<= t_0 -5e+226)
     t_1
     (if (<= t_0 -5e-322)
       t_0
       (if (<= t_0 0.0)
         (/ (/ a2 b2) (/ b1 a1))
         (if (<= t_0 2e+254) t_0 t_1))))))

C

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 <= -5e+226) {
		tmp = t_1;
	} else if (t_0 <= -5e-322) {
		tmp = t_0;
	} else if (t_0 <= 0.0) {
		tmp = (a2 / b2) / (b1 / a1);
	} else if (t_0 <= 2e+254) {
		tmp = t_0;
	} else {
		tmp = t_1;
	}
	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) :: t_1
    real(8) :: tmp
    t_0 = (a1 * a2) / (b1 * b2)
    t_1 = (a1 / b1) * (a2 / b2)
    if (t_0 <= (-5d+226)) then
        tmp = t_1
    else if (t_0 <= (-5d-322)) then
        tmp = t_0
    else if (t_0 <= 0.0d0) then
        tmp = (a2 / b2) / (b1 / a1)
    else if (t_0 <= 2d+254) then
        tmp = t_0
    else
        tmp = t_1
    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 t_1 = (a1 / b1) * (a2 / b2);
	double tmp;
	if (t_0 <= -5e+226) {
		tmp = t_1;
	} else if (t_0 <= -5e-322) {
		tmp = t_0;
	} else if (t_0 <= 0.0) {
		tmp = (a2 / b2) / (b1 / a1);
	} else if (t_0 <= 2e+254) {
		tmp = t_0;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(a1, a2, b1, b2):
	t_0 = (a1 * a2) / (b1 * b2)
	t_1 = (a1 / b1) * (a2 / b2)
	tmp = 0
	if t_0 <= -5e+226:
		tmp = t_1
	elif t_0 <= -5e-322:
		tmp = t_0
	elif t_0 <= 0.0:
		tmp = (a2 / b2) / (b1 / a1)
	elif t_0 <= 2e+254:
		tmp = t_0
	else:
		tmp = t_1
	return tmp

Julia

function code(a1, a2, b1, b2)
	t_0 = Float64(Float64(a1 * a2) / Float64(b1 * b2))
	t_1 = Float64(Float64(a1 / b1) * Float64(a2 / b2))
	tmp = 0.0
	if (t_0 <= -5e+226)
		tmp = t_1;
	elseif (t_0 <= -5e-322)
		tmp = t_0;
	elseif (t_0 <= 0.0)
		tmp = Float64(Float64(a2 / b2) / Float64(b1 / a1));
	elseif (t_0 <= 2e+254)
		tmp = t_0;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

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 <= -5e+226)
		tmp = t_1;
	elseif (t_0 <= -5e-322)
		tmp = t_0;
	elseif (t_0 <= 0.0)
		tmp = (a2 / b2) / (b1 / a1);
	elseif (t_0 <= 2e+254)
		tmp = t_0;
	else
		tmp = t_1;
	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]}, Block[{t$95$1 = N[(N[(a1 / b1), $MachinePrecision] * N[(a2 / b2), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$0, -5e+226], t$95$1, If[LessEqual[t$95$0, -5e-322], 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, 2e+254], t$95$0, t$95$1]]]]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 (*.f64 a1 a2) (*.f64 b1 b2)) < -5.0000000000000005e226 or 1.9999999999999999e254 < (/.f64 (*.f64 a1 a2) (*.f64 b1 b2))

   1. Initial program 77.9%

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

      1. times-frac 98.7%

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

   3. Simplified 98.7%

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

   if -5.0000000000000005e226 < (/.f64 (*.f64 a1 a2) (*.f64 b1 b2)) < -4.99006e-322 or -0.0 < (/.f64 (*.f64 a1 a2) (*.f64 b1 b2)) < 1.9999999999999999e254

   1. Initial program 99.3%

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

   if -4.99006e-322 < (/.f64 (*.f64 a1 a2) (*.f64 b1 b2)) < -0.0

   1. Initial program 74.6%

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

      1. times-frac 98.5%

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

   3. Simplified 98.5%

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

      1. *-commutative 98.5%

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

      2. clear-num 98.5%

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

      3. un-div-inv 98.6%

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

   5. Applied egg-rr 98.6%

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

4. Final simplification 99.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{a1 \cdot a2}{b1 \cdot b2} \leq -5 \cdot 10^{+226}:\\ \;\;\;\;\frac{a1}{b1} \cdot \frac{a2}{b2}\\ \mathbf{elif}\;\frac{a1 \cdot a2}{b1 \cdot b2} \leq -5 \cdot 10^{-322}:\\ \;\;\;\;\frac{a1 \cdot a2}{b1 \cdot b2}\\ \mathbf{elif}\;\frac{a1 \cdot a2}{b1 \cdot b2} \leq 0:\\ \;\;\;\;\frac{\frac{a2}{b2}}{\frac{b1}{a1}}\\ \mathbf{elif}\;\frac{a1 \cdot a2}{b1 \cdot b2} \leq 2 \cdot 10^{+254}:\\ \;\;\;\;\frac{a1 \cdot a2}{b1 \cdot b2}\\ \mathbf{else}:\\ \;\;\;\;\frac{a1}{b1} \cdot \frac{a2}{b2}\\ \end{array} \]

Alternative 2: 96.4% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{a1 \cdot a2}{b1 \cdot b2}\\ \mathbf{if}\;t_0 \leq -5 \cdot 10^{+226} \lor \neg \left(t_0 \leq -5 \cdot 10^{-322}\right) \land \left(t_0 \leq 0 \lor \neg \left(t_0 \leq 2 \cdot 10^{+254}\right)\right):\\ \;\;\;\;\frac{a1}{b1} \cdot \frac{a2}{b2}\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \end{array} \]

FPCore

(FPCore (a1 a2 b1 b2)
 :precision binary64
 (let* ((t_0 (/ (* a1 a2) (* b1 b2))))
   (if (or (<= t_0 -5e+226)
           (and (not (<= t_0 -5e-322))
                (or (<= t_0 0.0) (not (<= t_0 2e+254)))))
     (* (/ a1 b1) (/ a2 b2))
     t_0)))

C

double code(double a1, double a2, double b1, double b2) {
	double t_0 = (a1 * a2) / (b1 * b2);
	double tmp;
	if ((t_0 <= -5e+226) || (!(t_0 <= -5e-322) && ((t_0 <= 0.0) || !(t_0 <= 2e+254)))) {
		tmp = (a1 / b1) * (a2 / b2);
	} else {
		tmp = t_0;
	}
	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 <= (-5d+226)) .or. (.not. (t_0 <= (-5d-322))) .and. (t_0 <= 0.0d0) .or. (.not. (t_0 <= 2d+254))) then
        tmp = (a1 / b1) * (a2 / b2)
    else
        tmp = t_0
    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 <= -5e+226) || (!(t_0 <= -5e-322) && ((t_0 <= 0.0) || !(t_0 <= 2e+254)))) {
		tmp = (a1 / b1) * (a2 / b2);
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(a1, a2, b1, b2):
	t_0 = (a1 * a2) / (b1 * b2)
	tmp = 0
	if (t_0 <= -5e+226) or (not (t_0 <= -5e-322) and ((t_0 <= 0.0) or not (t_0 <= 2e+254))):
		tmp = (a1 / b1) * (a2 / b2)
	else:
		tmp = t_0
	return tmp

Julia

function code(a1, a2, b1, b2)
	t_0 = Float64(Float64(a1 * a2) / Float64(b1 * b2))
	tmp = 0.0
	if ((t_0 <= -5e+226) || (!(t_0 <= -5e-322) && ((t_0 <= 0.0) || !(t_0 <= 2e+254))))
		tmp = Float64(Float64(a1 / b1) * Float64(a2 / b2));
	else
		tmp = t_0;
	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 <= -5e+226) || (~((t_0 <= -5e-322)) && ((t_0 <= 0.0) || ~((t_0 <= 2e+254)))))
		tmp = (a1 / b1) * (a2 / b2);
	else
		tmp = t_0;
	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, -5e+226], And[N[Not[LessEqual[t$95$0, -5e-322]], $MachinePrecision], Or[LessEqual[t$95$0, 0.0], N[Not[LessEqual[t$95$0, 2e+254]], $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)) < -5.0000000000000005e226 or -4.99006e-322 < (/.f64 (*.f64 a1 a2) (*.f64 b1 b2)) < -0.0 or 1.9999999999999999e254 < (/.f64 (*.f64 a1 a2) (*.f64 b1 b2))

   1. Initial program 76.6%

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

      1. times-frac 98.6%

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

   3. Simplified 98.6%

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

   if -5.0000000000000005e226 < (/.f64 (*.f64 a1 a2) (*.f64 b1 b2)) < -4.99006e-322 or -0.0 < (/.f64 (*.f64 a1 a2) (*.f64 b1 b2)) < 1.9999999999999999e254

   1. Initial program 99.3%

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

4. Final simplification 98.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{a1 \cdot a2}{b1 \cdot b2} \leq -5 \cdot 10^{+226} \lor \neg \left(\frac{a1 \cdot a2}{b1 \cdot b2} \leq -5 \cdot 10^{-322}\right) \land \left(\frac{a1 \cdot a2}{b1 \cdot b2} \leq 0 \lor \neg \left(\frac{a1 \cdot a2}{b1 \cdot b2} \leq 2 \cdot 10^{+254}\right)\right):\\ \;\;\;\;\frac{a1}{b1} \cdot \frac{a2}{b2}\\ \mathbf{else}:\\ \;\;\;\;\frac{a1 \cdot a2}{b1 \cdot b2}\\ \end{array} \]

Alternative 3: 86.8% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b1 \leq -1.05 \cdot 10^{-109} \lor \neg \left(b1 \leq 7.4 \cdot 10^{+123}\right):\\ \;\;\;\;\frac{a1}{b1} \cdot \frac{a2}{b2}\\ \mathbf{else}:\\ \;\;\;\;\frac{a2}{b1} \cdot \frac{a1}{b2}\\ \end{array} \end{array} \]

FPCore

(FPCore (a1 a2 b1 b2)
 :precision binary64
 (if (or (<= b1 -1.05e-109) (not (<= b1 7.4e+123)))
   (* (/ a1 b1) (/ a2 b2))
   (* (/ a2 b1) (/ a1 b2))))

C

double code(double a1, double a2, double b1, double b2) {
	double tmp;
	if ((b1 <= -1.05e-109) || !(b1 <= 7.4e+123)) {
		tmp = (a1 / b1) * (a2 / b2);
	} else {
		tmp = (a2 / b1) * (a1 / 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) :: tmp
    if ((b1 <= (-1.05d-109)) .or. (.not. (b1 <= 7.4d+123))) then
        tmp = (a1 / b1) * (a2 / b2)
    else
        tmp = (a2 / b1) * (a1 / b2)
    end if
    code = tmp
end function

Java

public static double code(double a1, double a2, double b1, double b2) {
	double tmp;
	if ((b1 <= -1.05e-109) || !(b1 <= 7.4e+123)) {
		tmp = (a1 / b1) * (a2 / b2);
	} else {
		tmp = (a2 / b1) * (a1 / b2);
	}
	return tmp;
}

Python

def code(a1, a2, b1, b2):
	tmp = 0
	if (b1 <= -1.05e-109) or not (b1 <= 7.4e+123):
		tmp = (a1 / b1) * (a2 / b2)
	else:
		tmp = (a2 / b1) * (a1 / b2)
	return tmp

Julia

function code(a1, a2, b1, b2)
	tmp = 0.0
	if ((b1 <= -1.05e-109) || !(b1 <= 7.4e+123))
		tmp = Float64(Float64(a1 / b1) * Float64(a2 / b2));
	else
		tmp = Float64(Float64(a2 / b1) * Float64(a1 / b2));
	end
	return tmp
end

MATLAB

function tmp_2 = code(a1, a2, b1, b2)
	tmp = 0.0;
	if ((b1 <= -1.05e-109) || ~((b1 <= 7.4e+123)))
		tmp = (a1 / b1) * (a2 / b2);
	else
		tmp = (a2 / b1) * (a1 / b2);
	end
	tmp_2 = tmp;
end

Wolfram

code[a1_, a2_, b1_, b2_] := If[Or[LessEqual[b1, -1.05e-109], N[Not[LessEqual[b1, 7.4e+123]], $MachinePrecision]], N[(N[(a1 / b1), $MachinePrecision] * N[(a2 / b2), $MachinePrecision]), $MachinePrecision], N[(N[(a2 / b1), $MachinePrecision] * N[(a1 / b2), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b1 < -1.04999999999999998e-109 or 7.39999999999999992e123 < b1

   1. Initial program 86.3%

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

      1. times-frac 88.9%

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

   3. Simplified 88.9%

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

   if -1.04999999999999998e-109 < b1 < 7.39999999999999992e123

   1. Initial program 88.8%

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

      1. associate-/l* 91.6%

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

      2. *-commutative 91.6%

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

      3. associate-/l* 93.0%

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

   3. Simplified 93.0%

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

      1. associate-/r/ 93.2%

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

      2. *-commutative 93.2%

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

   5. Applied egg-rr 93.2%

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

4. Final simplification 91.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b1 \leq -1.05 \cdot 10^{-109} \lor \neg \left(b1 \leq 7.4 \cdot 10^{+123}\right):\\ \;\;\;\;\frac{a1}{b1} \cdot \frac{a2}{b2}\\ \mathbf{else}:\\ \;\;\;\;\frac{a2}{b1} \cdot \frac{a1}{b2}\\ \end{array} \]

Alternative 4: 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]

Derivation

1. Initial program 87.6%

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

   1. times-frac 87.5%

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

3. Simplified 87.5%

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

4. Final simplification 87.5%

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

Alternative 5: 86.5% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

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 * (b2 / a2))
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 87.6%

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

   1. associate-/l* 89.3%

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

   2. *-commutative 89.3%

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

   3. associate-/l* 87.4%

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

3. Simplified 87.4%

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

   1. associate-/r/ 89.5%

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

5. Applied egg-rr 89.5%

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

6. Final simplification 89.5%

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

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 2023214 
(FPCore (a1 a2 b1 b2)
  :name "Quotient of products"
  :precision binary64

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

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