Quotient of products

Percentage Accurate: 86.1% → 94.5%

Time: 3.1s

Alternatives: 6

Speedup: 1.0×

• Unsound rule application detected in e-graph. Results may not be sound.

• 20.3% 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: 86.1% 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: 94.5% accurate, 0.2× speedup

Math

\[\begin{array}{l} [a1, a2] = \mathsf{sort}([a1, a2])\\ \\ \begin{array}{l} t_0 := \frac{a1 \cdot a2}{b1 \cdot b2}\\ \mathbf{if}\;t_0 \leq -1 \cdot 10^{-319}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;t_0 \leq 0:\\ \;\;\;\;\frac{a1}{\frac{b2}{\frac{a2}{b1}}}\\ \mathbf{elif}\;t_0 \leq 2 \cdot 10^{+264}:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;\frac{a1}{b1} \cdot \frac{a2}{b2}\\ \end{array} \end{array} \]

FPCore

NOTE: a1 and a2 should be sorted in increasing order before calling this function.
(FPCore (a1 a2 b1 b2)
 :precision binary64
 (let* ((t_0 (/ (* a1 a2) (* b1 b2))))
   (if (<= t_0 -1e-319)
     t_0
     (if (<= t_0 0.0)
       (/ a1 (/ b2 (/ a2 b1)))
       (if (<= t_0 2e+264) t_0 (* (/ a1 b1) (/ a2 b2)))))))

C

assert(a1 < a2);
double code(double a1, double a2, double b1, double b2) {
	double t_0 = (a1 * a2) / (b1 * b2);
	double tmp;
	if (t_0 <= -1e-319) {
		tmp = t_0;
	} else if (t_0 <= 0.0) {
		tmp = a1 / (b2 / (a2 / b1));
	} else if (t_0 <= 2e+264) {
		tmp = t_0;
	} else {
		tmp = (a1 / b1) * (a2 / b2);
	}
	return tmp;
}

Fortran

NOTE: a1 and a2 should be sorted in increasing order before calling this function.
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-319)) then
        tmp = t_0
    else if (t_0 <= 0.0d0) then
        tmp = a1 / (b2 / (a2 / b1))
    else if (t_0 <= 2d+264) then
        tmp = t_0
    else
        tmp = (a1 / b1) * (a2 / b2)
    end if
    code = tmp
end function

Java

assert a1 < a2;
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-319) {
		tmp = t_0;
	} else if (t_0 <= 0.0) {
		tmp = a1 / (b2 / (a2 / b1));
	} else if (t_0 <= 2e+264) {
		tmp = t_0;
	} else {
		tmp = (a1 / b1) * (a2 / b2);
	}
	return tmp;
}

Python

[a1, a2] = sort([a1, a2])
def code(a1, a2, b1, b2):
	t_0 = (a1 * a2) / (b1 * b2)
	tmp = 0
	if t_0 <= -1e-319:
		tmp = t_0
	elif t_0 <= 0.0:
		tmp = a1 / (b2 / (a2 / b1))
	elif t_0 <= 2e+264:
		tmp = t_0
	else:
		tmp = (a1 / b1) * (a2 / b2)
	return tmp

Julia

a1, a2 = sort([a1, a2])
function code(a1, a2, b1, b2)
	t_0 = Float64(Float64(a1 * a2) / Float64(b1 * b2))
	tmp = 0.0
	if (t_0 <= -1e-319)
		tmp = t_0;
	elseif (t_0 <= 0.0)
		tmp = Float64(a1 / Float64(b2 / Float64(a2 / b1)));
	elseif (t_0 <= 2e+264)
		tmp = t_0;
	else
		tmp = Float64(Float64(a1 / b1) * Float64(a2 / b2));
	end
	return tmp
end

MATLAB

a1, a2 = num2cell(sort([a1, a2])){:}
function tmp_2 = code(a1, a2, b1, b2)
	t_0 = (a1 * a2) / (b1 * b2);
	tmp = 0.0;
	if (t_0 <= -1e-319)
		tmp = t_0;
	elseif (t_0 <= 0.0)
		tmp = a1 / (b2 / (a2 / b1));
	elseif (t_0 <= 2e+264)
		tmp = t_0;
	else
		tmp = (a1 / b1) * (a2 / b2);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: a1 and a2 should be sorted in increasing order before calling this function.
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-319], t$95$0, If[LessEqual[t$95$0, 0.0], N[(a1 / N[(b2 / N[(a2 / b1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$0, 2e+264], 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)) < -9.99989e-320 or 0.0 < (/.f64 (*.f64 a1 a2) (*.f64 b1 b2)) < 2.00000000000000009e264

   1. Initial program 97.7%

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

   if -9.99989e-320 < (/.f64 (*.f64 a1 a2) (*.f64 b1 b2)) < 0.0

   1. Initial program 83.2%

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

      1. associate-/l* 91.8%

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

      2. *-commutative 91.8%

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

      3. associate-/l* 95.1%

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

   3. Simplified 95.1%

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

   if 2.00000000000000009e264 < (/.f64 (*.f64 a1 a2) (*.f64 b1 b2))

   1. Initial program 58.1%

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

      1. times-frac 99.8%

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

   3. Simplified 99.8%

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

4. Final simplification 97.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{a1 \cdot a2}{b1 \cdot b2} \leq -1 \cdot 10^{-319}:\\ \;\;\;\;\frac{a1 \cdot a2}{b1 \cdot b2}\\ \mathbf{elif}\;\frac{a1 \cdot a2}{b1 \cdot b2} \leq 0:\\ \;\;\;\;\frac{a1}{\frac{b2}{\frac{a2}{b1}}}\\ \mathbf{elif}\;\frac{a1 \cdot a2}{b1 \cdot b2} \leq 2 \cdot 10^{+264}:\\ \;\;\;\;\frac{a1 \cdot a2}{b1 \cdot b2}\\ \mathbf{else}:\\ \;\;\;\;\frac{a1}{b1} \cdot \frac{a2}{b2}\\ \end{array} \]

Alternative 2: 93.5% accurate, 0.3× speedup

Math

\[\begin{array}{l} [a1, a2] = \mathsf{sort}([a1, a2])\\ \\ \begin{array}{l} t_0 := a1 \cdot \frac{a2}{b1 \cdot b2}\\ t_1 := \frac{a1}{b1} \cdot \frac{a2}{b2}\\ \mathbf{if}\;b1 \cdot b2 \leq -5 \cdot 10^{+273}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b1 \cdot b2 \leq -5 \cdot 10^{-165}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;b1 \cdot b2 \leq 10^{-166}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b1 \cdot b2 \leq 10^{+268}:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;\frac{a1}{b1 \cdot \frac{b2}{a2}}\\ \end{array} \end{array} \]

FPCore

NOTE: a1 and a2 should be sorted in increasing order before calling this function.
(FPCore (a1 a2 b1 b2)
 :precision binary64
 (let* ((t_0 (* a1 (/ a2 (* b1 b2)))) (t_1 (* (/ a1 b1) (/ a2 b2))))
   (if (<= (* b1 b2) -5e+273)
     t_1
     (if (<= (* b1 b2) -5e-165)
       t_0
       (if (<= (* b1 b2) 1e-166)
         t_1
         (if (<= (* b1 b2) 1e+268) t_0 (/ a1 (* b1 (/ b2 a2)))))))))

C

assert(a1 < a2);
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 ((b1 * b2) <= -5e+273) {
		tmp = t_1;
	} else if ((b1 * b2) <= -5e-165) {
		tmp = t_0;
	} else if ((b1 * b2) <= 1e-166) {
		tmp = t_1;
	} else if ((b1 * b2) <= 1e+268) {
		tmp = t_0;
	} else {
		tmp = a1 / (b1 * (b2 / a2));
	}
	return tmp;
}

Fortran

NOTE: a1 and a2 should be sorted in increasing order before calling this function.
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 ((b1 * b2) <= (-5d+273)) then
        tmp = t_1
    else if ((b1 * b2) <= (-5d-165)) then
        tmp = t_0
    else if ((b1 * b2) <= 1d-166) then
        tmp = t_1
    else if ((b1 * b2) <= 1d+268) then
        tmp = t_0
    else
        tmp = a1 / (b1 * (b2 / a2))
    end if
    code = tmp
end function

Java

assert a1 < a2;
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 ((b1 * b2) <= -5e+273) {
		tmp = t_1;
	} else if ((b1 * b2) <= -5e-165) {
		tmp = t_0;
	} else if ((b1 * b2) <= 1e-166) {
		tmp = t_1;
	} else if ((b1 * b2) <= 1e+268) {
		tmp = t_0;
	} else {
		tmp = a1 / (b1 * (b2 / a2));
	}
	return tmp;
}

Python

[a1, a2] = sort([a1, a2])
def code(a1, a2, b1, b2):
	t_0 = a1 * (a2 / (b1 * b2))
	t_1 = (a1 / b1) * (a2 / b2)
	tmp = 0
	if (b1 * b2) <= -5e+273:
		tmp = t_1
	elif (b1 * b2) <= -5e-165:
		tmp = t_0
	elif (b1 * b2) <= 1e-166:
		tmp = t_1
	elif (b1 * b2) <= 1e+268:
		tmp = t_0
	else:
		tmp = a1 / (b1 * (b2 / a2))
	return tmp

Julia

a1, a2 = sort([a1, a2])
function code(a1, a2, b1, b2)
	t_0 = Float64(a1 * Float64(a2 / Float64(b1 * b2)))
	t_1 = Float64(Float64(a1 / b1) * Float64(a2 / b2))
	tmp = 0.0
	if (Float64(b1 * b2) <= -5e+273)
		tmp = t_1;
	elseif (Float64(b1 * b2) <= -5e-165)
		tmp = t_0;
	elseif (Float64(b1 * b2) <= 1e-166)
		tmp = t_1;
	elseif (Float64(b1 * b2) <= 1e+268)
		tmp = t_0;
	else
		tmp = Float64(a1 / Float64(b1 * Float64(b2 / a2)));
	end
	return tmp
end

MATLAB

a1, a2 = num2cell(sort([a1, a2])){:}
function tmp_2 = code(a1, a2, b1, b2)
	t_0 = a1 * (a2 / (b1 * b2));
	t_1 = (a1 / b1) * (a2 / b2);
	tmp = 0.0;
	if ((b1 * b2) <= -5e+273)
		tmp = t_1;
	elseif ((b1 * b2) <= -5e-165)
		tmp = t_0;
	elseif ((b1 * b2) <= 1e-166)
		tmp = t_1;
	elseif ((b1 * b2) <= 1e+268)
		tmp = t_0;
	else
		tmp = a1 / (b1 * (b2 / a2));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: a1 and a2 should be sorted in increasing order before calling this function.
code[a1_, a2_, b1_, b2_] := Block[{t$95$0 = N[(a1 * N[(a2 / N[(b1 * b2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(N[(a1 / b1), $MachinePrecision] * N[(a2 / b2), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(b1 * b2), $MachinePrecision], -5e+273], t$95$1, If[LessEqual[N[(b1 * b2), $MachinePrecision], -5e-165], t$95$0, If[LessEqual[N[(b1 * b2), $MachinePrecision], 1e-166], t$95$1, If[LessEqual[N[(b1 * b2), $MachinePrecision], 1e+268], t$95$0, N[(a1 / N[(b1 * N[(b2 / a2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 b1 b2) < -4.99999999999999961e273 or -4.99999999999999981e-165 < (*.f64 b1 b2) < 1.00000000000000004e-166

   1. Initial program 74.4%

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

      1. times-frac 88.8%

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

   3. Simplified 88.8%

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

   if -4.99999999999999961e273 < (*.f64 b1 b2) < -4.99999999999999981e-165 or 1.00000000000000004e-166 < (*.f64 b1 b2) < 9.9999999999999997e267

   1. Initial program 95.7%

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

      1. associate-/l* 95.1%

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

      2. *-commutative 95.1%

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

      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. Step-by-step derivation

      1. clear-num 85.1%

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

      2. associate-/r/ 85.0%

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

      3. clear-num 85.1%

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

      4. associate-/l/ 95.1%

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

      5. *-commutative 95.1%

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

   5. Applied egg-rr 95.1%

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

   if 9.9999999999999997e267 < (*.f64 b1 b2)

   1. Initial program 66.9%

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

      1. associate-/l* 67.4%

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

      2. *-commutative 67.4%

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

      3. associate-/l* 97.2%

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

   3. Simplified 97.2%

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

      1. associate-/r/ 97.1%

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

   5. Applied egg-rr 97.1%

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

4. Final simplification 93.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b1 \cdot b2 \leq -5 \cdot 10^{+273}:\\ \;\;\;\;\frac{a1}{b1} \cdot \frac{a2}{b2}\\ \mathbf{elif}\;b1 \cdot b2 \leq -5 \cdot 10^{-165}:\\ \;\;\;\;a1 \cdot \frac{a2}{b1 \cdot b2}\\ \mathbf{elif}\;b1 \cdot b2 \leq 10^{-166}:\\ \;\;\;\;\frac{a1}{b1} \cdot \frac{a2}{b2}\\ \mathbf{elif}\;b1 \cdot b2 \leq 10^{+268}:\\ \;\;\;\;a1 \cdot \frac{a2}{b1 \cdot b2}\\ \mathbf{else}:\\ \;\;\;\;\frac{a1}{b1 \cdot \frac{b2}{a2}}\\ \end{array} \]

Alternative 3: 93.5% accurate, 0.3× speedup

Math

\[\begin{array}{l} [a1, a2] = \mathsf{sort}([a1, a2])\\ \\ \begin{array}{l} t_0 := a1 \cdot \frac{a2}{b1 \cdot b2}\\ t_1 := \frac{a1}{b1} \cdot \frac{a2}{b2}\\ \mathbf{if}\;b1 \cdot b2 \leq -5 \cdot 10^{+273}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b1 \cdot b2 \leq -5 \cdot 10^{-165}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;b1 \cdot b2 \leq 10^{-166}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b1 \cdot b2 \leq 10^{+268}:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;\frac{a1}{\frac{b2}{\frac{a2}{b1}}}\\ \end{array} \end{array} \]

FPCore

NOTE: a1 and a2 should be sorted in increasing order before calling this function.
(FPCore (a1 a2 b1 b2)
 :precision binary64
 (let* ((t_0 (* a1 (/ a2 (* b1 b2)))) (t_1 (* (/ a1 b1) (/ a2 b2))))
   (if (<= (* b1 b2) -5e+273)
     t_1
     (if (<= (* b1 b2) -5e-165)
       t_0
       (if (<= (* b1 b2) 1e-166)
         t_1
         (if (<= (* b1 b2) 1e+268) t_0 (/ a1 (/ b2 (/ a2 b1)))))))))

C

assert(a1 < a2);
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 ((b1 * b2) <= -5e+273) {
		tmp = t_1;
	} else if ((b1 * b2) <= -5e-165) {
		tmp = t_0;
	} else if ((b1 * b2) <= 1e-166) {
		tmp = t_1;
	} else if ((b1 * b2) <= 1e+268) {
		tmp = t_0;
	} else {
		tmp = a1 / (b2 / (a2 / b1));
	}
	return tmp;
}

Fortran

NOTE: a1 and a2 should be sorted in increasing order before calling this function.
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 ((b1 * b2) <= (-5d+273)) then
        tmp = t_1
    else if ((b1 * b2) <= (-5d-165)) then
        tmp = t_0
    else if ((b1 * b2) <= 1d-166) then
        tmp = t_1
    else if ((b1 * b2) <= 1d+268) then
        tmp = t_0
    else
        tmp = a1 / (b2 / (a2 / b1))
    end if
    code = tmp
end function

Java

assert a1 < a2;
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 ((b1 * b2) <= -5e+273) {
		tmp = t_1;
	} else if ((b1 * b2) <= -5e-165) {
		tmp = t_0;
	} else if ((b1 * b2) <= 1e-166) {
		tmp = t_1;
	} else if ((b1 * b2) <= 1e+268) {
		tmp = t_0;
	} else {
		tmp = a1 / (b2 / (a2 / b1));
	}
	return tmp;
}

Python

[a1, a2] = sort([a1, a2])
def code(a1, a2, b1, b2):
	t_0 = a1 * (a2 / (b1 * b2))
	t_1 = (a1 / b1) * (a2 / b2)
	tmp = 0
	if (b1 * b2) <= -5e+273:
		tmp = t_1
	elif (b1 * b2) <= -5e-165:
		tmp = t_0
	elif (b1 * b2) <= 1e-166:
		tmp = t_1
	elif (b1 * b2) <= 1e+268:
		tmp = t_0
	else:
		tmp = a1 / (b2 / (a2 / b1))
	return tmp

Julia

a1, a2 = sort([a1, a2])
function code(a1, a2, b1, b2)
	t_0 = Float64(a1 * Float64(a2 / Float64(b1 * b2)))
	t_1 = Float64(Float64(a1 / b1) * Float64(a2 / b2))
	tmp = 0.0
	if (Float64(b1 * b2) <= -5e+273)
		tmp = t_1;
	elseif (Float64(b1 * b2) <= -5e-165)
		tmp = t_0;
	elseif (Float64(b1 * b2) <= 1e-166)
		tmp = t_1;
	elseif (Float64(b1 * b2) <= 1e+268)
		tmp = t_0;
	else
		tmp = Float64(a1 / Float64(b2 / Float64(a2 / b1)));
	end
	return tmp
end

MATLAB

a1, a2 = num2cell(sort([a1, a2])){:}
function tmp_2 = code(a1, a2, b1, b2)
	t_0 = a1 * (a2 / (b1 * b2));
	t_1 = (a1 / b1) * (a2 / b2);
	tmp = 0.0;
	if ((b1 * b2) <= -5e+273)
		tmp = t_1;
	elseif ((b1 * b2) <= -5e-165)
		tmp = t_0;
	elseif ((b1 * b2) <= 1e-166)
		tmp = t_1;
	elseif ((b1 * b2) <= 1e+268)
		tmp = t_0;
	else
		tmp = a1 / (b2 / (a2 / b1));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: a1 and a2 should be sorted in increasing order before calling this function.
code[a1_, a2_, b1_, b2_] := Block[{t$95$0 = N[(a1 * N[(a2 / N[(b1 * b2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(N[(a1 / b1), $MachinePrecision] * N[(a2 / b2), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(b1 * b2), $MachinePrecision], -5e+273], t$95$1, If[LessEqual[N[(b1 * b2), $MachinePrecision], -5e-165], t$95$0, If[LessEqual[N[(b1 * b2), $MachinePrecision], 1e-166], t$95$1, If[LessEqual[N[(b1 * b2), $MachinePrecision], 1e+268], t$95$0, N[(a1 / N[(b2 / N[(a2 / b1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 b1 b2) < -4.99999999999999961e273 or -4.99999999999999981e-165 < (*.f64 b1 b2) < 1.00000000000000004e-166

   1. Initial program 74.4%

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

      1. times-frac 88.8%

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

   3. Simplified 88.8%

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

   if -4.99999999999999961e273 < (*.f64 b1 b2) < -4.99999999999999981e-165 or 1.00000000000000004e-166 < (*.f64 b1 b2) < 9.9999999999999997e267

   1. Initial program 95.7%

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

      1. associate-/l* 95.1%

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

      2. *-commutative 95.1%

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

      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. Step-by-step derivation

      1. clear-num 85.1%

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

      2. associate-/r/ 85.0%

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

      3. clear-num 85.1%

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

      4. associate-/l/ 95.1%

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

      5. *-commutative 95.1%

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

   5. Applied egg-rr 95.1%

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

   if 9.9999999999999997e267 < (*.f64 b1 b2)

   1. Initial program 66.9%

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

      1. associate-/l* 67.4%

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

      2. *-commutative 67.4%

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

      3. associate-/l* 97.2%

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

   3. Simplified 97.2%

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

4. Final simplification 93.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b1 \cdot b2 \leq -5 \cdot 10^{+273}:\\ \;\;\;\;\frac{a1}{b1} \cdot \frac{a2}{b2}\\ \mathbf{elif}\;b1 \cdot b2 \leq -5 \cdot 10^{-165}:\\ \;\;\;\;a1 \cdot \frac{a2}{b1 \cdot b2}\\ \mathbf{elif}\;b1 \cdot b2 \leq 10^{-166}:\\ \;\;\;\;\frac{a1}{b1} \cdot \frac{a2}{b2}\\ \mathbf{elif}\;b1 \cdot b2 \leq 10^{+268}:\\ \;\;\;\;a1 \cdot \frac{a2}{b1 \cdot b2}\\ \mathbf{else}:\\ \;\;\;\;\frac{a1}{\frac{b2}{\frac{a2}{b1}}}\\ \end{array} \]

Alternative 4: 86.5% accurate, 0.8× speedup

Math

\[\begin{array}{l} [a1, a2] = \mathsf{sort}([a1, a2])\\ \\ \begin{array}{l} \mathbf{if}\;b1 \leq -6.5 \cdot 10^{+164}:\\ \;\;\;\;a1 \cdot \frac{a2}{b1 \cdot b2}\\ \mathbf{else}:\\ \;\;\;\;\frac{a1}{b1} \cdot \frac{a2}{b2}\\ \end{array} \end{array} \]

FPCore

NOTE: a1 and a2 should be sorted in increasing order before calling this function.
(FPCore (a1 a2 b1 b2)
 :precision binary64
 (if (<= b1 -6.5e+164) (* a1 (/ a2 (* b1 b2))) (* (/ a1 b1) (/ a2 b2))))

C

assert(a1 < a2);
double code(double a1, double a2, double b1, double b2) {
	double tmp;
	if (b1 <= -6.5e+164) {
		tmp = a1 * (a2 / (b1 * b2));
	} else {
		tmp = (a1 / b1) * (a2 / b2);
	}
	return tmp;
}

Fortran

NOTE: a1 and a2 should be sorted in increasing order before calling this function.
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 <= (-6.5d+164)) then
        tmp = a1 * (a2 / (b1 * b2))
    else
        tmp = (a1 / b1) * (a2 / b2)
    end if
    code = tmp
end function

Java

assert a1 < a2;
public static double code(double a1, double a2, double b1, double b2) {
	double tmp;
	if (b1 <= -6.5e+164) {
		tmp = a1 * (a2 / (b1 * b2));
	} else {
		tmp = (a1 / b1) * (a2 / b2);
	}
	return tmp;
}

Python

[a1, a2] = sort([a1, a2])
def code(a1, a2, b1, b2):
	tmp = 0
	if b1 <= -6.5e+164:
		tmp = a1 * (a2 / (b1 * b2))
	else:
		tmp = (a1 / b1) * (a2 / b2)
	return tmp

Julia

a1, a2 = sort([a1, a2])
function code(a1, a2, b1, b2)
	tmp = 0.0
	if (b1 <= -6.5e+164)
		tmp = Float64(a1 * Float64(a2 / Float64(b1 * b2)));
	else
		tmp = Float64(Float64(a1 / b1) * Float64(a2 / b2));
	end
	return tmp
end

MATLAB

a1, a2 = num2cell(sort([a1, a2])){:}
function tmp_2 = code(a1, a2, b1, b2)
	tmp = 0.0;
	if (b1 <= -6.5e+164)
		tmp = a1 * (a2 / (b1 * b2));
	else
		tmp = (a1 / b1) * (a2 / b2);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: a1 and a2 should be sorted in increasing order before calling this function.
code[a1_, a2_, b1_, b2_] := If[LessEqual[b1, -6.5e+164], N[(a1 * N[(a2 / N[(b1 * b2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(a1 / b1), $MachinePrecision] * N[(a2 / b2), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b1 < -6.5000000000000003e164

   1. Initial program 92.5%

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

      1. associate-/l* 92.5%

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

      2. *-commutative 92.5%

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

      3. associate-/l* 83.2%

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

   3. Simplified 83.2%

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

      1. clear-num 83.1%

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

      2. associate-/r/ 83.1%

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

      3. clear-num 83.2%

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

      4. associate-/l/ 92.5%

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

      5. *-commutative 92.5%

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

   5. Applied egg-rr 92.5%

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

   if -6.5000000000000003e164 < b1

   1. Initial program 86.8%

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

      1. times-frac 82.3%

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

   3. Simplified 82.3%

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

4. Final simplification 83.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b1 \leq -6.5 \cdot 10^{+164}:\\ \;\;\;\;a1 \cdot \frac{a2}{b1 \cdot b2}\\ \mathbf{else}:\\ \;\;\;\;\frac{a1}{b1} \cdot \frac{a2}{b2}\\ \end{array} \]

Alternative 5: 86.2% accurate, 0.8× speedup

Math

\[\begin{array}{l} [a1, a2] = \mathsf{sort}([a1, a2])\\ \\ \begin{array}{l} \mathbf{if}\;b1 \leq -8 \cdot 10^{+200}:\\ \;\;\;\;\frac{a1}{\frac{b1 \cdot b2}{a2}}\\ \mathbf{else}:\\ \;\;\;\;\frac{a2}{b2 \cdot \frac{b1}{a1}}\\ \end{array} \end{array} \]

FPCore

NOTE: a1 and a2 should be sorted in increasing order before calling this function.
(FPCore (a1 a2 b1 b2)
 :precision binary64
 (if (<= b1 -8e+200) (/ a1 (/ (* b1 b2) a2)) (/ a2 (* b2 (/ b1 a1)))))

C

assert(a1 < a2);
double code(double a1, double a2, double b1, double b2) {
	double tmp;
	if (b1 <= -8e+200) {
		tmp = a1 / ((b1 * b2) / a2);
	} else {
		tmp = a2 / (b2 * (b1 / a1));
	}
	return tmp;
}

Fortran

NOTE: a1 and a2 should be sorted in increasing order before calling this function.
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 <= (-8d+200)) then
        tmp = a1 / ((b1 * b2) / a2)
    else
        tmp = a2 / (b2 * (b1 / a1))
    end if
    code = tmp
end function

Java

assert a1 < a2;
public static double code(double a1, double a2, double b1, double b2) {
	double tmp;
	if (b1 <= -8e+200) {
		tmp = a1 / ((b1 * b2) / a2);
	} else {
		tmp = a2 / (b2 * (b1 / a1));
	}
	return tmp;
}

Python

[a1, a2] = sort([a1, a2])
def code(a1, a2, b1, b2):
	tmp = 0
	if b1 <= -8e+200:
		tmp = a1 / ((b1 * b2) / a2)
	else:
		tmp = a2 / (b2 * (b1 / a1))
	return tmp

Julia

a1, a2 = sort([a1, a2])
function code(a1, a2, b1, b2)
	tmp = 0.0
	if (b1 <= -8e+200)
		tmp = Float64(a1 / Float64(Float64(b1 * b2) / a2));
	else
		tmp = Float64(a2 / Float64(b2 * Float64(b1 / a1)));
	end
	return tmp
end

MATLAB

a1, a2 = num2cell(sort([a1, a2])){:}
function tmp_2 = code(a1, a2, b1, b2)
	tmp = 0.0;
	if (b1 <= -8e+200)
		tmp = a1 / ((b1 * b2) / a2);
	else
		tmp = a2 / (b2 * (b1 / a1));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: a1 and a2 should be sorted in increasing order before calling this function.
code[a1_, a2_, b1_, b2_] := If[LessEqual[b1, -8e+200], N[(a1 / N[(N[(b1 * b2), $MachinePrecision] / a2), $MachinePrecision]), $MachinePrecision], N[(a2 / N[(b2 * N[(b1 / a1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b1 < -7.9999999999999998e200

   1. Initial program 89.6%

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

      1. associate-/l* 93.6%

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

      2. *-commutative 93.6%

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

      3. associate-/l* 80.9%

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

   3. Simplified 80.9%

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

   4. Taylor expanded in b2 around 0 93.6%

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

   if -7.9999999999999998e200 < b1

   1. Initial program 87.3%

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

      1. times-frac 82.2%

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

   3. Simplified 82.2%

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

      1. clear-num 82.2%

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

      2. frac-times 84.2%

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

      3. *-un-lft-identity 84.2%

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

   5. Applied egg-rr 84.2%

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

4. Final simplification 85.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b1 \leq -8 \cdot 10^{+200}:\\ \;\;\;\;\frac{a1}{\frac{b1 \cdot b2}{a2}}\\ \mathbf{else}:\\ \;\;\;\;\frac{a2}{b2 \cdot \frac{b1}{a1}}\\ \end{array} \]

Alternative 6: 86.4% accurate, 1.0× speedup

Math

\[\begin{array}{l} [a1, a2] = \mathsf{sort}([a1, a2])\\ \\ \frac{a1}{b1} \cdot \frac{a2}{b2} \end{array} \]

FPCore

NOTE: a1 and a2 should be sorted in increasing order before calling this function.
(FPCore (a1 a2 b1 b2) :precision binary64 (* (/ a1 b1) (/ a2 b2)))

C

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

Fortran

NOTE: a1 and a2 should be sorted in increasing order before calling this function.
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

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

Python

[a1, a2] = sort([a1, a2])
def code(a1, a2, b1, b2):
	return (a1 / b1) * (a2 / b2)

Julia

a1, a2 = sort([a1, a2])
function code(a1, a2, b1, b2)
	return Float64(Float64(a1 / b1) * Float64(a2 / b2))
end

MATLAB

a1, a2 = num2cell(sort([a1, a2])){:}
function tmp = code(a1, a2, b1, b2)
	tmp = (a1 / b1) * (a2 / b2);
end

Wolfram

NOTE: a1 and a2 should be sorted in increasing order before calling this function.
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 80.9%

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

3. Simplified 80.9%

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

4. Final simplification 80.9%

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

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 2023187 
(FPCore (a1 a2 b1 b2)
  :name "Quotient of products"
  :precision binary64

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

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