Quotient of products

Percentage Accurate: 86.3% → 94.2%

Time: 2.7s

Alternatives: 5

Speedup: 0.3×

• 20.0% 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: 86.3% 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: 94.2% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{a1 \cdot a2}{b1 \cdot b2}\\ \mathbf{if}\;t_0 \leq -2 \cdot 10^{-274} \lor \neg \left(t_0 \leq 0\right) \land t_0 \leq 10^{+223}:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{a1}{b2}}{\frac{b1}{a2}}\\ \end{array} \end{array} \]

FPCore

(FPCore (a1 a2 b1 b2)
 :precision binary64
 (let* ((t_0 (/ (* a1 a2) (* b1 b2))))
   (if (or (<= t_0 -2e-274) (and (not (<= t_0 0.0)) (<= t_0 1e+223)))
     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-274) || (!(t_0 <= 0.0) && (t_0 <= 1e+223))) {
		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-274)) .or. (.not. (t_0 <= 0.0d0)) .and. (t_0 <= 1d+223)) 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-274) || (!(t_0 <= 0.0) && (t_0 <= 1e+223))) {
		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-274) or (not (t_0 <= 0.0) and (t_0 <= 1e+223)):
		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-274) || (!(t_0 <= 0.0) && (t_0 <= 1e+223)))
		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-274) || (~((t_0 <= 0.0)) && (t_0 <= 1e+223)))
		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-274], And[N[Not[LessEqual[t$95$0, 0.0]], $MachinePrecision], LessEqual[t$95$0, 1e+223]]], 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)) < -1.99999999999999993e-274 or 0.0 < (/.f64 (*.f64 a1 a2) (*.f64 b1 b2)) < 1.00000000000000005e223

   1. Initial program 95.3%

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

   if -1.99999999999999993e-274 < (/.f64 (*.f64 a1 a2) (*.f64 b1 b2)) < 0.0 or 1.00000000000000005e223 < (/.f64 (*.f64 a1 a2) (*.f64 b1 b2))

   1. Initial program 72.6%

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

      1. times-frac 94.0%

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

   3. Simplified 94.0%

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

      1. frac-times 72.6%

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

      2. *-commutative 72.6%

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

      3. frac-times 98.0%

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

      4. clear-num 98.0%

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

      5. un-div-inv 98.0%

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

   5. Applied egg-rr 98.0%

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

4. Final simplification 96.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{a1 \cdot a2}{b1 \cdot b2} \leq -2 \cdot 10^{-274} \lor \neg \left(\frac{a1 \cdot a2}{b1 \cdot b2} \leq 0\right) \land \frac{a1 \cdot a2}{b1 \cdot b2} \leq 10^{+223}:\\ \;\;\;\;\frac{a1 \cdot a2}{b1 \cdot b2}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{a1}{b2}}{\frac{b1}{a2}}\\ \end{array} \]

Alternative 2: 93.8% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{a1 \cdot a2}{b1 \cdot b2}\\ \mathbf{if}\;t_0 \leq -1 \cdot 10^{-274}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;t_0 \leq 0:\\ \;\;\;\;\frac{a1}{b1} \cdot \frac{a2}{b2}\\ \mathbf{elif}\;t_0 \leq 5 \cdot 10^{+262}:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;\frac{a1}{b1 \cdot \frac{b2}{a2}}\\ \end{array} \end{array} \]

FPCore

(FPCore (a1 a2 b1 b2)
 :precision binary64
 (let* ((t_0 (/ (* a1 a2) (* b1 b2))))
   (if (<= t_0 -1e-274)
     t_0
     (if (<= t_0 0.0)
       (* (/ a1 b1) (/ a2 b2))
       (if (<= t_0 5e+262) t_0 (/ a1 (* b1 (/ b2 a2))))))))

C

double code(double a1, double a2, double b1, double b2) {
	double t_0 = (a1 * a2) / (b1 * b2);
	double tmp;
	if (t_0 <= -1e-274) {
		tmp = t_0;
	} else if (t_0 <= 0.0) {
		tmp = (a1 / b1) * (a2 / b2);
	} else if (t_0 <= 5e+262) {
		tmp = t_0;
	} else {
		tmp = a1 / (b1 * (b2 / 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 <= (-1d-274)) then
        tmp = t_0
    else if (t_0 <= 0.0d0) then
        tmp = (a1 / b1) * (a2 / b2)
    else if (t_0 <= 5d+262) then
        tmp = t_0
    else
        tmp = a1 / (b1 * (b2 / 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 <= -1e-274) {
		tmp = t_0;
	} else if (t_0 <= 0.0) {
		tmp = (a1 / b1) * (a2 / b2);
	} else if (t_0 <= 5e+262) {
		tmp = t_0;
	} else {
		tmp = a1 / (b1 * (b2 / a2));
	}
	return tmp;
}

Python

def code(a1, a2, b1, b2):
	t_0 = (a1 * a2) / (b1 * b2)
	tmp = 0
	if t_0 <= -1e-274:
		tmp = t_0
	elif t_0 <= 0.0:
		tmp = (a1 / b1) * (a2 / b2)
	elif t_0 <= 5e+262:
		tmp = t_0
	else:
		tmp = a1 / (b1 * (b2 / 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 <= -1e-274)
		tmp = t_0;
	elseif (t_0 <= 0.0)
		tmp = Float64(Float64(a1 / b1) * Float64(a2 / b2));
	elseif (t_0 <= 5e+262)
		tmp = t_0;
	else
		tmp = Float64(a1 / Float64(b1 * Float64(b2 / 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 <= -1e-274)
		tmp = t_0;
	elseif (t_0 <= 0.0)
		tmp = (a1 / b1) * (a2 / b2);
	elseif (t_0 <= 5e+262)
		tmp = t_0;
	else
		tmp = a1 / (b1 * (b2 / 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[LessEqual[t$95$0, -1e-274], t$95$0, If[LessEqual[t$95$0, 0.0], N[(N[(a1 / b1), $MachinePrecision] * N[(a2 / b2), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$0, 5e+262], t$95$0, N[(a1 / N[(b1 * N[(b2 / a2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 (*.f64 a1 a2) (*.f64 b1 b2)) < -9.99999999999999966e-275 or 0.0 < (/.f64 (*.f64 a1 a2) (*.f64 b1 b2)) < 5.00000000000000008e262

   1. Initial program 95.3%

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

   if -9.99999999999999966e-275 < (/.f64 (*.f64 a1 a2) (*.f64 b1 b2)) < 0.0

   1. Initial program 78.8%

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

      1. times-frac 95.8%

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

   3. Simplified 95.8%

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

   if 5.00000000000000008e262 < (/.f64 (*.f64 a1 a2) (*.f64 b1 b2))

   1. Initial program 61.6%

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

      1. associate-/l* 67.2%

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

      2. *-commutative 67.2%

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

      3. associate-/l* 95.3%

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

   3. Simplified 95.3%

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

      1. associate-/r/ 95.4%

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

   5. Applied egg-rr 95.4%

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

4. Final simplification 95.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{a1 \cdot a2}{b1 \cdot b2} \leq -1 \cdot 10^{-274}:\\ \;\;\;\;\frac{a1 \cdot a2}{b1 \cdot b2}\\ \mathbf{elif}\;\frac{a1 \cdot a2}{b1 \cdot b2} \leq 0:\\ \;\;\;\;\frac{a1}{b1} \cdot \frac{a2}{b2}\\ \mathbf{elif}\;\frac{a1 \cdot a2}{b1 \cdot b2} \leq 5 \cdot 10^{+262}:\\ \;\;\;\;\frac{a1 \cdot a2}{b1 \cdot b2}\\ \mathbf{else}:\\ \;\;\;\;\frac{a1}{b1 \cdot \frac{b2}{a2}}\\ \end{array} \]

Alternative 3: 93.8% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{a1 \cdot a2}{b1 \cdot b2}\\ \mathbf{if}\;t_0 \leq -1 \cdot 10^{-274}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;t_0 \leq 0:\\ \;\;\;\;\frac{a1}{b1} \cdot \frac{a2}{b2}\\ \mathbf{elif}\;t_0 \leq 5 \cdot 10^{+262}:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;\frac{a2 \cdot \frac{a1}{b1}}{b2}\\ \end{array} \end{array} \]

FPCore

(FPCore (a1 a2 b1 b2)
 :precision binary64
 (let* ((t_0 (/ (* a1 a2) (* b1 b2))))
   (if (<= t_0 -1e-274)
     t_0
     (if (<= t_0 0.0)
       (* (/ a1 b1) (/ a2 b2))
       (if (<= t_0 5e+262) t_0 (/ (* a2 (/ a1 b1)) 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-274) {
		tmp = t_0;
	} else if (t_0 <= 0.0) {
		tmp = (a1 / b1) * (a2 / b2);
	} else if (t_0 <= 5e+262) {
		tmp = t_0;
	} else {
		tmp = (a2 * (a1 / b1)) / 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-274)) then
        tmp = t_0
    else if (t_0 <= 0.0d0) then
        tmp = (a1 / b1) * (a2 / b2)
    else if (t_0 <= 5d+262) then
        tmp = t_0
    else
        tmp = (a2 * (a1 / b1)) / 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-274) {
		tmp = t_0;
	} else if (t_0 <= 0.0) {
		tmp = (a1 / b1) * (a2 / b2);
	} else if (t_0 <= 5e+262) {
		tmp = t_0;
	} else {
		tmp = (a2 * (a1 / b1)) / b2;
	}
	return tmp;
}

Python

def code(a1, a2, b1, b2):
	t_0 = (a1 * a2) / (b1 * b2)
	tmp = 0
	if t_0 <= -1e-274:
		tmp = t_0
	elif t_0 <= 0.0:
		tmp = (a1 / b1) * (a2 / b2)
	elif t_0 <= 5e+262:
		tmp = t_0
	else:
		tmp = (a2 * (a1 / b1)) / 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-274)
		tmp = t_0;
	elseif (t_0 <= 0.0)
		tmp = Float64(Float64(a1 / b1) * Float64(a2 / b2));
	elseif (t_0 <= 5e+262)
		tmp = t_0;
	else
		tmp = Float64(Float64(a2 * Float64(a1 / b1)) / 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-274)
		tmp = t_0;
	elseif (t_0 <= 0.0)
		tmp = (a1 / b1) * (a2 / b2);
	elseif (t_0 <= 5e+262)
		tmp = t_0;
	else
		tmp = (a2 * (a1 / b1)) / 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, -1e-274], t$95$0, If[LessEqual[t$95$0, 0.0], N[(N[(a1 / b1), $MachinePrecision] * N[(a2 / b2), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$0, 5e+262], t$95$0, N[(N[(a2 * N[(a1 / b1), $MachinePrecision]), $MachinePrecision] / b2), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 (*.f64 a1 a2) (*.f64 b1 b2)) < -9.99999999999999966e-275 or 0.0 < (/.f64 (*.f64 a1 a2) (*.f64 b1 b2)) < 5.00000000000000008e262

   1. Initial program 95.3%

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

   if -9.99999999999999966e-275 < (/.f64 (*.f64 a1 a2) (*.f64 b1 b2)) < 0.0

   1. Initial program 78.8%

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

      1. times-frac 95.8%

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

   3. Simplified 95.8%

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

   if 5.00000000000000008e262 < (/.f64 (*.f64 a1 a2) (*.f64 b1 b2))

   1. Initial program 61.6%

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

      1. times-frac 95.4%

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

   3. Simplified 95.4%

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

      1. associate-*r/ 95.8%

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

   5. Applied egg-rr 95.8%

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

4. Final simplification 95.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{a1 \cdot a2}{b1 \cdot b2} \leq -1 \cdot 10^{-274}:\\ \;\;\;\;\frac{a1 \cdot a2}{b1 \cdot b2}\\ \mathbf{elif}\;\frac{a1 \cdot a2}{b1 \cdot b2} \leq 0:\\ \;\;\;\;\frac{a1}{b1} \cdot \frac{a2}{b2}\\ \mathbf{elif}\;\frac{a1 \cdot a2}{b1 \cdot b2} \leq 5 \cdot 10^{+262}:\\ \;\;\;\;\frac{a1 \cdot a2}{b1 \cdot b2}\\ \mathbf{else}:\\ \;\;\;\;\frac{a2 \cdot \frac{a1}{b1}}{b2}\\ \end{array} \]

Alternative 4: 93.6% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b1 \cdot b2 \leq -1 \cdot 10^{+278} \lor \neg \left(b1 \cdot b2 \leq -2 \cdot 10^{-180} \lor \neg \left(b1 \cdot b2 \leq 2 \cdot 10^{-219}\right) \land b1 \cdot b2 \leq 2 \cdot 10^{+172}\right):\\ \;\;\;\;\frac{a1}{b1} \cdot \frac{a2}{b2}\\ \mathbf{else}:\\ \;\;\;\;a1 \cdot \frac{a2}{b1 \cdot b2}\\ \end{array} \end{array} \]

FPCore

(FPCore (a1 a2 b1 b2)
 :precision binary64
 (if (or (<= (* b1 b2) -1e+278)
         (not
          (or (<= (* b1 b2) -2e-180)
              (and (not (<= (* b1 b2) 2e-219)) (<= (* b1 b2) 2e+172)))))
   (* (/ a1 b1) (/ a2 b2))
   (* a1 (/ a2 (* b1 b2)))))

C

double code(double a1, double a2, double b1, double b2) {
	double tmp;
	if (((b1 * b2) <= -1e+278) || !(((b1 * b2) <= -2e-180) || (!((b1 * b2) <= 2e-219) && ((b1 * b2) <= 2e+172)))) {
		tmp = (a1 / b1) * (a2 / b2);
	} else {
		tmp = a1 * (a2 / (b1 * 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 * b2) <= (-1d+278)) .or. (.not. ((b1 * b2) <= (-2d-180)) .or. (.not. ((b1 * b2) <= 2d-219)) .and. ((b1 * b2) <= 2d+172))) then
        tmp = (a1 / b1) * (a2 / b2)
    else
        tmp = a1 * (a2 / (b1 * b2))
    end if
    code = tmp
end function

Java

public static double code(double a1, double a2, double b1, double b2) {
	double tmp;
	if (((b1 * b2) <= -1e+278) || !(((b1 * b2) <= -2e-180) || (!((b1 * b2) <= 2e-219) && ((b1 * b2) <= 2e+172)))) {
		tmp = (a1 / b1) * (a2 / b2);
	} else {
		tmp = a1 * (a2 / (b1 * b2));
	}
	return tmp;
}

Python

def code(a1, a2, b1, b2):
	tmp = 0
	if ((b1 * b2) <= -1e+278) or not (((b1 * b2) <= -2e-180) or (not ((b1 * b2) <= 2e-219) and ((b1 * b2) <= 2e+172))):
		tmp = (a1 / b1) * (a2 / b2)
	else:
		tmp = a1 * (a2 / (b1 * b2))
	return tmp

Julia

function code(a1, a2, b1, b2)
	tmp = 0.0
	if ((Float64(b1 * b2) <= -1e+278) || !((Float64(b1 * b2) <= -2e-180) || (!(Float64(b1 * b2) <= 2e-219) && (Float64(b1 * b2) <= 2e+172))))
		tmp = Float64(Float64(a1 / b1) * Float64(a2 / b2));
	else
		tmp = Float64(a1 * Float64(a2 / Float64(b1 * b2)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(a1, a2, b1, b2)
	tmp = 0.0;
	if (((b1 * b2) <= -1e+278) || ~((((b1 * b2) <= -2e-180) || (~(((b1 * b2) <= 2e-219)) && ((b1 * b2) <= 2e+172)))))
		tmp = (a1 / b1) * (a2 / b2);
	else
		tmp = a1 * (a2 / (b1 * b2));
	end
	tmp_2 = tmp;
end

Wolfram

code[a1_, a2_, b1_, b2_] := If[Or[LessEqual[N[(b1 * b2), $MachinePrecision], -1e+278], N[Not[Or[LessEqual[N[(b1 * b2), $MachinePrecision], -2e-180], And[N[Not[LessEqual[N[(b1 * b2), $MachinePrecision], 2e-219]], $MachinePrecision], LessEqual[N[(b1 * b2), $MachinePrecision], 2e+172]]]], $MachinePrecision]], N[(N[(a1 / b1), $MachinePrecision] * N[(a2 / b2), $MachinePrecision]), $MachinePrecision], N[(a1 * N[(a2 / N[(b1 * b2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 b1 b2) < -9.99999999999999964e277 or -2e-180 < (*.f64 b1 b2) < 2.0000000000000001e-219 or 2.0000000000000002e172 < (*.f64 b1 b2)

   1. Initial program 73.4%

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

      1. times-frac 93.6%

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

   3. Simplified 93.6%

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

   if -9.99999999999999964e277 < (*.f64 b1 b2) < -2e-180 or 2.0000000000000001e-219 < (*.f64 b1 b2) < 2.0000000000000002e172

   1. Initial program 95.0%

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

      1. associate-/l* 96.4%

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

      2. *-commutative 96.4%

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

      3. associate-/l* 87.0%

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

   3. Simplified 87.0%

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

      1. clear-num 87.0%

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

      2. associate-/r/ 86.9%

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

      3. clear-num 87.1%

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

      4. associate-/l/ 96.3%

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

      5. *-commutative 96.3%

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

   5. Applied egg-rr 96.3%

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

4. Final simplification 95.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b1 \cdot b2 \leq -1 \cdot 10^{+278} \lor \neg \left(b1 \cdot b2 \leq -2 \cdot 10^{-180} \lor \neg \left(b1 \cdot b2 \leq 2 \cdot 10^{-219}\right) \land b1 \cdot b2 \leq 2 \cdot 10^{+172}\right):\\ \;\;\;\;\frac{a1}{b1} \cdot \frac{a2}{b2}\\ \mathbf{else}:\\ \;\;\;\;a1 \cdot \frac{a2}{b1 \cdot b2}\\ \end{array} \]

Alternative 5: 85.7% 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]

Derivation

1. Initial program 85.7%

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

   1. times-frac 85.8%

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

3. Simplified 85.8%

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

4. Final simplification 85.8%

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

Developer target: 85.7% 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 2023238 
(FPCore (a1 a2 b1 b2)
  :name "Quotient of products"
  :precision binary64

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

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