Quotient of products

Percentage Accurate: 85.8% → 97.4%

Time: 3.5s

Alternatives: 6

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: 85.8% 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: 97.4% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{a1 \cdot a2}{b1 \cdot b2}\\ \mathbf{if}\;t_0 \leq -\infty \lor \neg \left(t_0 \leq -2 \cdot 10^{-313} \lor \neg \left(t_0 \leq 0\right) \land t_0 \leq 5 \cdot 10^{+298}\right):\\ \;\;\;\;\frac{\frac{a1}{b2}}{\frac{b1}{a2}}\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \end{array} \]

FPCore

(FPCore (a1 a2 b1 b2)
 :precision binary64
 (let* ((t_0 (/ (* a1 a2) (* b1 b2))))
   (if (or (<= t_0 (- INFINITY))
           (not
            (or (<= t_0 -2e-313) (and (not (<= t_0 0.0)) (<= t_0 5e+298)))))
     (/ (/ a1 b2) (/ b1 a2))
     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 <= -((double) INFINITY)) || !((t_0 <= -2e-313) || (!(t_0 <= 0.0) && (t_0 <= 5e+298)))) {
		tmp = (a1 / b2) / (b1 / a2);
	} else {
		tmp = t_0;
	}
	return tmp;
}

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 <= -Double.POSITIVE_INFINITY) || !((t_0 <= -2e-313) || (!(t_0 <= 0.0) && (t_0 <= 5e+298)))) {
		tmp = (a1 / b2) / (b1 / a2);
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(a1, a2, b1, b2):
	t_0 = (a1 * a2) / (b1 * b2)
	tmp = 0
	if (t_0 <= -math.inf) or not ((t_0 <= -2e-313) or (not (t_0 <= 0.0) and (t_0 <= 5e+298))):
		tmp = (a1 / b2) / (b1 / a2)
	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 <= Float64(-Inf)) || !((t_0 <= -2e-313) || (!(t_0 <= 0.0) && (t_0 <= 5e+298))))
		tmp = Float64(Float64(a1 / b2) / Float64(b1 / a2));
	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 <= -Inf) || ~(((t_0 <= -2e-313) || (~((t_0 <= 0.0)) && (t_0 <= 5e+298)))))
		tmp = (a1 / b2) / (b1 / a2);
	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, (-Infinity)], N[Not[Or[LessEqual[t$95$0, -2e-313], And[N[Not[LessEqual[t$95$0, 0.0]], $MachinePrecision], LessEqual[t$95$0, 5e+298]]]], $MachinePrecision]], N[(N[(a1 / b2), $MachinePrecision] / N[(b1 / a2), $MachinePrecision]), $MachinePrecision], t$95$0]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (*.f64 a1 a2) (*.f64 b1 b2)) < -inf.0 or -1.99999999998e-313 < (/.f64 (*.f64 a1 a2) (*.f64 b1 b2)) < -0.0 or 5.0000000000000003e298 < (/.f64 (*.f64 a1 a2) (*.f64 b1 b2))

   1. Initial program 77.6%

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

      1. times-frac 95.7%

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

   3. Simplified 95.7%

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

      1. frac-times 77.6%

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

      2. *-commutative 77.6%

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

      3. frac-times 97.6%

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

      4. clear-num 97.6%

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

      5. un-div-inv 97.6%

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

   5. Applied egg-rr 97.6%

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

   if -inf.0 < (/.f64 (*.f64 a1 a2) (*.f64 b1 b2)) < -1.99999999998e-313 or -0.0 < (/.f64 (*.f64 a1 a2) (*.f64 b1 b2)) < 5.0000000000000003e298

   1. Initial program 98.3%

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

4. Final simplification 97.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{a1 \cdot a2}{b1 \cdot b2} \leq -\infty \lor \neg \left(\frac{a1 \cdot a2}{b1 \cdot b2} \leq -2 \cdot 10^{-313} \lor \neg \left(\frac{a1 \cdot a2}{b1 \cdot b2} \leq 0\right) \land \frac{a1 \cdot a2}{b1 \cdot b2} \leq 5 \cdot 10^{+298}\right):\\ \;\;\;\;\frac{\frac{a1}{b2}}{\frac{b1}{a2}}\\ \mathbf{else}:\\ \;\;\;\;\frac{a1 \cdot a2}{b1 \cdot b2}\\ \end{array} \]

Alternative 2: 96.3% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{a1 \cdot a2}{b1 \cdot b2}\\ \mathbf{if}\;t_0 \leq -5 \cdot 10^{+291}:\\ \;\;\;\;\frac{a1}{\frac{b2}{\frac{a2}{b1}}}\\ \mathbf{elif}\;t_0 \leq -5 \cdot 10^{-222} \lor \neg \left(t_0 \leq 0\right) \land t_0 \leq 5 \cdot 10^{+298}:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;\frac{a1}{b1} \cdot \frac{a2}{b2}\\ \end{array} \end{array} \]

FPCore

(FPCore (a1 a2 b1 b2)
 :precision binary64
 (let* ((t_0 (/ (* a1 a2) (* b1 b2))))
   (if (<= t_0 -5e+291)
     (/ a1 (/ b2 (/ a2 b1)))
     (if (or (<= t_0 -5e-222) (and (not (<= t_0 0.0)) (<= t_0 5e+298)))
       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 <= -5e+291) {
		tmp = a1 / (b2 / (a2 / b1));
	} else if ((t_0 <= -5e-222) || (!(t_0 <= 0.0) && (t_0 <= 5e+298))) {
		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 <= (-5d+291)) then
        tmp = a1 / (b2 / (a2 / b1))
    else if ((t_0 <= (-5d-222)) .or. (.not. (t_0 <= 0.0d0)) .and. (t_0 <= 5d+298)) 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 <= -5e+291) {
		tmp = a1 / (b2 / (a2 / b1));
	} else if ((t_0 <= -5e-222) || (!(t_0 <= 0.0) && (t_0 <= 5e+298))) {
		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 <= -5e+291:
		tmp = a1 / (b2 / (a2 / b1))
	elif (t_0 <= -5e-222) or (not (t_0 <= 0.0) and (t_0 <= 5e+298)):
		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 <= -5e+291)
		tmp = Float64(a1 / Float64(b2 / Float64(a2 / b1)));
	elseif ((t_0 <= -5e-222) || (!(t_0 <= 0.0) && (t_0 <= 5e+298)))
		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 <= -5e+291)
		tmp = a1 / (b2 / (a2 / b1));
	elseif ((t_0 <= -5e-222) || (~((t_0 <= 0.0)) && (t_0 <= 5e+298)))
		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, -5e+291], N[(a1 / N[(b2 / N[(a2 / b1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[t$95$0, -5e-222], And[N[Not[LessEqual[t$95$0, 0.0]], $MachinePrecision], LessEqual[t$95$0, 5e+298]]], 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)) < -5.0000000000000001e291

   1. Initial program 74.4%

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

      1. associate-/l* 88.4%

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

      2. *-commutative 88.4%

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

      3. associate-/l* 96.0%

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

   3. Simplified 96.0%

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

   if -5.0000000000000001e291 < (/.f64 (*.f64 a1 a2) (*.f64 b1 b2)) < -5.00000000000000008e-222 or -0.0 < (/.f64 (*.f64 a1 a2) (*.f64 b1 b2)) < 5.0000000000000003e298

   1. Initial program 98.2%

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

   if -5.00000000000000008e-222 < (/.f64 (*.f64 a1 a2) (*.f64 b1 b2)) < -0.0 or 5.0000000000000003e298 < (/.f64 (*.f64 a1 a2) (*.f64 b1 b2))

   1. Initial program 80.0%

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

      1. times-frac 96.4%

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

   3. Simplified 96.4%

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

4. Final simplification 97.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{a1 \cdot a2}{b1 \cdot b2} \leq -5 \cdot 10^{+291}:\\ \;\;\;\;\frac{a1}{\frac{b2}{\frac{a2}{b1}}}\\ \mathbf{elif}\;\frac{a1 \cdot a2}{b1 \cdot b2} \leq -5 \cdot 10^{-222} \lor \neg \left(\frac{a1 \cdot a2}{b1 \cdot b2} \leq 0\right) \land \frac{a1 \cdot a2}{b1 \cdot b2} \leq 5 \cdot 10^{+298}:\\ \;\;\;\;\frac{a1 \cdot a2}{b1 \cdot b2}\\ \mathbf{else}:\\ \;\;\;\;\frac{a1}{b1} \cdot \frac{a2}{b2}\\ \end{array} \]

Alternative 3: 96.1% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{a1 \cdot a2}{b1 \cdot b2}\\ \mathbf{if}\;t_0 \leq -\infty:\\ \;\;\;\;\frac{a2 \cdot \frac{a1}{b1}}{b2}\\ \mathbf{elif}\;t_0 \leq -5 \cdot 10^{-222} \lor \neg \left(t_0 \leq 0\right) \land t_0 \leq 5 \cdot 10^{+298}:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;\frac{a1}{b1} \cdot \frac{a2}{b2}\\ \end{array} \end{array} \]

FPCore

(FPCore (a1 a2 b1 b2)
 :precision binary64
 (let* ((t_0 (/ (* a1 a2) (* b1 b2))))
   (if (<= t_0 (- INFINITY))
     (/ (* a2 (/ a1 b1)) b2)
     (if (or (<= t_0 -5e-222) (and (not (<= t_0 0.0)) (<= t_0 5e+298)))
       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 <= -((double) INFINITY)) {
		tmp = (a2 * (a1 / b1)) / b2;
	} else if ((t_0 <= -5e-222) || (!(t_0 <= 0.0) && (t_0 <= 5e+298))) {
		tmp = t_0;
	} else {
		tmp = (a1 / b1) * (a2 / b2);
	}
	return tmp;
}

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 <= -Double.POSITIVE_INFINITY) {
		tmp = (a2 * (a1 / b1)) / b2;
	} else if ((t_0 <= -5e-222) || (!(t_0 <= 0.0) && (t_0 <= 5e+298))) {
		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 <= -math.inf:
		tmp = (a2 * (a1 / b1)) / b2
	elif (t_0 <= -5e-222) or (not (t_0 <= 0.0) and (t_0 <= 5e+298)):
		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 <= Float64(-Inf))
		tmp = Float64(Float64(a2 * Float64(a1 / b1)) / b2);
	elseif ((t_0 <= -5e-222) || (!(t_0 <= 0.0) && (t_0 <= 5e+298)))
		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 <= -Inf)
		tmp = (a2 * (a1 / b1)) / b2;
	elseif ((t_0 <= -5e-222) || (~((t_0 <= 0.0)) && (t_0 <= 5e+298)))
		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, (-Infinity)], N[(N[(a2 * N[(a1 / b1), $MachinePrecision]), $MachinePrecision] / b2), $MachinePrecision], If[Or[LessEqual[t$95$0, -5e-222], And[N[Not[LessEqual[t$95$0, 0.0]], $MachinePrecision], LessEqual[t$95$0, 5e+298]]], 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)) < -inf.0

   1. Initial program 73.6%

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

      1. times-frac 94.2%

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

   3. Simplified 94.2%

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

      1. associate-*r/ 96.9%

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

   5. Applied egg-rr 96.9%

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

   if -inf.0 < (/.f64 (*.f64 a1 a2) (*.f64 b1 b2)) < -5.00000000000000008e-222 or -0.0 < (/.f64 (*.f64 a1 a2) (*.f64 b1 b2)) < 5.0000000000000003e298

   1. Initial program 98.2%

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

   if -5.00000000000000008e-222 < (/.f64 (*.f64 a1 a2) (*.f64 b1 b2)) < -0.0 or 5.0000000000000003e298 < (/.f64 (*.f64 a1 a2) (*.f64 b1 b2))

   1. Initial program 80.0%

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

      1. times-frac 96.4%

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

   3. Simplified 96.4%

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

4. Final simplification 97.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{a1 \cdot a2}{b1 \cdot b2} \leq -\infty:\\ \;\;\;\;\frac{a2 \cdot \frac{a1}{b1}}{b2}\\ \mathbf{elif}\;\frac{a1 \cdot a2}{b1 \cdot b2} \leq -5 \cdot 10^{-222} \lor \neg \left(\frac{a1 \cdot a2}{b1 \cdot b2} \leq 0\right) \land \frac{a1 \cdot a2}{b1 \cdot b2} \leq 5 \cdot 10^{+298}:\\ \;\;\;\;\frac{a1 \cdot a2}{b1 \cdot b2}\\ \mathbf{else}:\\ \;\;\;\;\frac{a1}{b1} \cdot \frac{a2}{b2}\\ \end{array} \]

Alternative 4: 93.2% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b1 \cdot b2 \leq -8 \cdot 10^{+222} \lor \neg \left(b1 \cdot b2 \leq -1 \cdot 10^{-241}\right) \land \left(b1 \cdot b2 \leq 2 \cdot 10^{-96} \lor \neg \left(b1 \cdot b2 \leq 2 \cdot 10^{+122}\right)\right):\\ \;\;\;\;\frac{a1}{b1} \cdot \frac{a2}{b2}\\ \mathbf{else}:\\ \;\;\;\;a2 \cdot \frac{a1}{b1 \cdot b2}\\ \end{array} \end{array} \]

FPCore

(FPCore (a1 a2 b1 b2)
 :precision binary64
 (if (or (<= (* b1 b2) -8e+222)
         (and (not (<= (* b1 b2) -1e-241))
              (or (<= (* b1 b2) 2e-96) (not (<= (* b1 b2) 2e+122)))))
   (* (/ a1 b1) (/ a2 b2))
   (* a2 (/ a1 (* b1 b2)))))

C

double code(double a1, double a2, double b1, double b2) {
	double tmp;
	if (((b1 * b2) <= -8e+222) || (!((b1 * b2) <= -1e-241) && (((b1 * b2) <= 2e-96) || !((b1 * b2) <= 2e+122)))) {
		tmp = (a1 / b1) * (a2 / b2);
	} 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) :: tmp
    if (((b1 * b2) <= (-8d+222)) .or. (.not. ((b1 * b2) <= (-1d-241))) .and. ((b1 * b2) <= 2d-96) .or. (.not. ((b1 * b2) <= 2d+122))) then
        tmp = (a1 / b1) * (a2 / b2)
    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 tmp;
	if (((b1 * b2) <= -8e+222) || (!((b1 * b2) <= -1e-241) && (((b1 * b2) <= 2e-96) || !((b1 * b2) <= 2e+122)))) {
		tmp = (a1 / b1) * (a2 / b2);
	} else {
		tmp = a2 * (a1 / (b1 * b2));
	}
	return tmp;
}

Python

def code(a1, a2, b1, b2):
	tmp = 0
	if ((b1 * b2) <= -8e+222) or (not ((b1 * b2) <= -1e-241) and (((b1 * b2) <= 2e-96) or not ((b1 * b2) <= 2e+122))):
		tmp = (a1 / b1) * (a2 / b2)
	else:
		tmp = a2 * (a1 / (b1 * b2))
	return tmp

Julia

function code(a1, a2, b1, b2)
	tmp = 0.0
	if ((Float64(b1 * b2) <= -8e+222) || (!(Float64(b1 * b2) <= -1e-241) && ((Float64(b1 * b2) <= 2e-96) || !(Float64(b1 * b2) <= 2e+122))))
		tmp = Float64(Float64(a1 / b1) * Float64(a2 / b2));
	else
		tmp = Float64(a2 * Float64(a1 / Float64(b1 * b2)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(a1, a2, b1, b2)
	tmp = 0.0;
	if (((b1 * b2) <= -8e+222) || (~(((b1 * b2) <= -1e-241)) && (((b1 * b2) <= 2e-96) || ~(((b1 * b2) <= 2e+122)))))
		tmp = (a1 / b1) * (a2 / b2);
	else
		tmp = a2 * (a1 / (b1 * b2));
	end
	tmp_2 = tmp;
end

Wolfram

code[a1_, a2_, b1_, b2_] := If[Or[LessEqual[N[(b1 * b2), $MachinePrecision], -8e+222], And[N[Not[LessEqual[N[(b1 * b2), $MachinePrecision], -1e-241]], $MachinePrecision], Or[LessEqual[N[(b1 * b2), $MachinePrecision], 2e-96], N[Not[LessEqual[N[(b1 * b2), $MachinePrecision], 2e+122]], $MachinePrecision]]]], N[(N[(a1 / b1), $MachinePrecision] * N[(a2 / b2), $MachinePrecision]), $MachinePrecision], N[(a2 * N[(a1 / N[(b1 * b2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 b1 b2) < -8.0000000000000004e222 or -9.9999999999999997e-242 < (*.f64 b1 b2) < 1.9999999999999998e-96 or 2.00000000000000003e122 < (*.f64 b1 b2)

   1. Initial program 81.0%

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

      1. times-frac 92.9%

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

   3. Simplified 92.9%

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

   if -8.0000000000000004e222 < (*.f64 b1 b2) < -9.9999999999999997e-242 or 1.9999999999999998e-96 < (*.f64 b1 b2) < 2.00000000000000003e122

   1. Initial program 95.0%

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

      1. associate-/l* 94.2%

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

      2. *-commutative 94.2%

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

      3. associate-/l* 85.7%

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

   3. Simplified 85.7%

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

      1. associate-/l* 94.2%

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

      2. *-commutative 94.2%

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

      3. associate-/r/ 94.2%

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

   5. Applied egg-rr 94.2%

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

4. Final simplification 93.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b1 \cdot b2 \leq -8 \cdot 10^{+222} \lor \neg \left(b1 \cdot b2 \leq -1 \cdot 10^{-241}\right) \land \left(b1 \cdot b2 \leq 2 \cdot 10^{-96} \lor \neg \left(b1 \cdot b2 \leq 2 \cdot 10^{+122}\right)\right):\\ \;\;\;\;\frac{a1}{b1} \cdot \frac{a2}{b2}\\ \mathbf{else}:\\ \;\;\;\;a2 \cdot \frac{a1}{b1 \cdot b2}\\ \end{array} \]

Alternative 5: 85.7% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a2 \leq -2.4 \cdot 10^{-236}:\\ \;\;\;\;\frac{a1}{b1} \cdot \frac{a2}{b2}\\ \mathbf{else}:\\ \;\;\;\;\frac{a1}{b2 \cdot \frac{b1}{a2}}\\ \end{array} \end{array} \]

FPCore

(FPCore (a1 a2 b1 b2)
 :precision binary64
 (if (<= a2 -2.4e-236) (* (/ a1 b1) (/ a2 b2)) (/ a1 (* b2 (/ b1 a2)))))

C

double code(double a1, double a2, double b1, double b2) {
	double tmp;
	if (a2 <= -2.4e-236) {
		tmp = (a1 / b1) * (a2 / b2);
	} 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) :: tmp
    if (a2 <= (-2.4d-236)) then
        tmp = (a1 / b1) * (a2 / b2)
    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 tmp;
	if (a2 <= -2.4e-236) {
		tmp = (a1 / b1) * (a2 / b2);
	} else {
		tmp = a1 / (b2 * (b1 / a2));
	}
	return tmp;
}

Python

def code(a1, a2, b1, b2):
	tmp = 0
	if a2 <= -2.4e-236:
		tmp = (a1 / b1) * (a2 / b2)
	else:
		tmp = a1 / (b2 * (b1 / a2))
	return tmp

Julia

function code(a1, a2, b1, b2)
	tmp = 0.0
	if (a2 <= -2.4e-236)
		tmp = Float64(Float64(a1 / b1) * Float64(a2 / b2));
	else
		tmp = Float64(a1 / Float64(b2 * Float64(b1 / a2)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(a1, a2, b1, b2)
	tmp = 0.0;
	if (a2 <= -2.4e-236)
		tmp = (a1 / b1) * (a2 / b2);
	else
		tmp = a1 / (b2 * (b1 / a2));
	end
	tmp_2 = tmp;
end

Wolfram

code[a1_, a2_, b1_, b2_] := If[LessEqual[a2, -2.4e-236], N[(N[(a1 / b1), $MachinePrecision] * N[(a2 / b2), $MachinePrecision]), $MachinePrecision], N[(a1 / N[(b2 * N[(b1 / a2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a2 < -2.4000000000000002e-236

   1. Initial program 86.2%

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

      1. times-frac 90.9%

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

   3. Simplified 90.9%

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

   if -2.4000000000000002e-236 < a2

   1. Initial program 88.7%

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

      1. associate-/l* 87.3%

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

      2. *-commutative 87.3%

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

      3. associate-/l* 89.1%

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

   3. Simplified 89.1%

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

      1. clear-num 89.1%

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

      2. associate-/r/ 89.1%

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

      3. clear-num 89.1%

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

   5. Applied egg-rr 89.1%

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

4. Final simplification 89.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a2 \leq -2.4 \cdot 10^{-236}:\\ \;\;\;\;\frac{a1}{b1} \cdot \frac{a2}{b2}\\ \mathbf{else}:\\ \;\;\;\;\frac{a1}{b2 \cdot \frac{b1}{a2}}\\ \end{array} \]

Alternative 6: 86.1% 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 85.3%

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

3. Simplified 85.3%

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

4. Final simplification 85.3%

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

Developer target: 86.1% 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 2023228 
(FPCore (a1 a2 b1 b2)
  :name "Quotient of products"
  :precision binary64

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

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