Quotient of products

Percentage Accurate: 85.9% → 95.4%

Time: 2.9s

Alternatives: 4

Speedup: 1.0×

• 20.2% 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: 85.9% 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: 95.4% accurate, 0.2× speedup

Math

\[\begin{array}{l} [a1, a2] = \mathsf{sort}([a1, a2])\\ [b1, b2] = \mathsf{sort}([b1, b2])\\ \\ \begin{array}{l} t_0 := \frac{a1 \cdot a2}{b1 \cdot b2}\\ \mathbf{if}\;t_0 \leq -1 \cdot 10^{-318}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;t_0 \leq 0:\\ \;\;\;\;\frac{a2}{b1} \cdot \frac{a1}{b2}\\ \mathbf{elif}\;t_0 \leq 2 \cdot 10^{+303}:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;\frac{a1}{b1} \cdot \frac{a2}{b2}\\ \end{array} \end{array} \]

FPCore

NOTE: a1 and a2 should be sorted in increasing order before calling this function.
NOTE: b1 and b2 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-318)
     t_0
     (if (<= t_0 0.0)
       (* (/ a2 b1) (/ a1 b2))
       (if (<= t_0 2e+303) t_0 (* (/ a1 b1) (/ a2 b2)))))))

C

assert(a1 < a2);
assert(b1 < b2);
double code(double a1, double a2, double b1, double b2) {
	double t_0 = (a1 * a2) / (b1 * b2);
	double tmp;
	if (t_0 <= -1e-318) {
		tmp = t_0;
	} else if (t_0 <= 0.0) {
		tmp = (a2 / b1) * (a1 / b2);
	} else if (t_0 <= 2e+303) {
		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.
NOTE: b1 and b2 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-318)) then
        tmp = t_0
    else if (t_0 <= 0.0d0) then
        tmp = (a2 / b1) * (a1 / b2)
    else if (t_0 <= 2d+303) then
        tmp = t_0
    else
        tmp = (a1 / b1) * (a2 / b2)
    end if
    code = tmp
end function

Java

assert a1 < a2;
assert b1 < b2;
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-318) {
		tmp = t_0;
	} else if (t_0 <= 0.0) {
		tmp = (a2 / b1) * (a1 / b2);
	} else if (t_0 <= 2e+303) {
		tmp = t_0;
	} else {
		tmp = (a1 / b1) * (a2 / b2);
	}
	return tmp;
}

Python

[a1, a2] = sort([a1, a2])
[b1, b2] = sort([b1, b2])
def code(a1, a2, b1, b2):
	t_0 = (a1 * a2) / (b1 * b2)
	tmp = 0
	if t_0 <= -1e-318:
		tmp = t_0
	elif t_0 <= 0.0:
		tmp = (a2 / b1) * (a1 / b2)
	elif t_0 <= 2e+303:
		tmp = t_0
	else:
		tmp = (a1 / b1) * (a2 / b2)
	return tmp

Julia

a1, a2 = sort([a1, a2])
b1, b2 = sort([b1, b2])
function code(a1, a2, b1, b2)
	t_0 = Float64(Float64(a1 * a2) / Float64(b1 * b2))
	tmp = 0.0
	if (t_0 <= -1e-318)
		tmp = t_0;
	elseif (t_0 <= 0.0)
		tmp = Float64(Float64(a2 / b1) * Float64(a1 / b2));
	elseif (t_0 <= 2e+303)
		tmp = t_0;
	else
		tmp = Float64(Float64(a1 / b1) * Float64(a2 / b2));
	end
	return tmp
end

MATLAB

a1, a2 = num2cell(sort([a1, a2])){:}
b1, b2 = num2cell(sort([b1, b2])){:}
function tmp_2 = code(a1, a2, b1, b2)
	t_0 = (a1 * a2) / (b1 * b2);
	tmp = 0.0;
	if (t_0 <= -1e-318)
		tmp = t_0;
	elseif (t_0 <= 0.0)
		tmp = (a2 / b1) * (a1 / b2);
	elseif (t_0 <= 2e+303)
		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.
NOTE: b1 and b2 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-318], t$95$0, If[LessEqual[t$95$0, 0.0], N[(N[(a2 / b1), $MachinePrecision] * N[(a1 / b2), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$0, 2e+303], 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)) < -9.9999875e-319 or -0.0 < (/.f64 (*.f64 a1 a2) (*.f64 b1 b2)) < 2e303

   1. Initial program 97.2%

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

   if -9.9999875e-319 < (/.f64 (*.f64 a1 a2) (*.f64 b1 b2)) < -0.0

   1. Initial program 69.7%

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

      1. *-commutative 69.7%

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

      2. times-frac 94.5%

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

   3. Applied egg-rr 94.5%

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

   if 2e303 < (/.f64 (*.f64 a1 a2) (*.f64 b1 b2))

   1. Initial program 52.5%

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

      1. times-frac 97.5%

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

   3. Simplified 97.5%

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

4. Final simplification 96.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{a1 \cdot a2}{b1 \cdot b2} \leq -1 \cdot 10^{-318}:\\ \;\;\;\;\frac{a1 \cdot a2}{b1 \cdot b2}\\ \mathbf{elif}\;\frac{a1 \cdot a2}{b1 \cdot b2} \leq 0:\\ \;\;\;\;\frac{a2}{b1} \cdot \frac{a1}{b2}\\ \mathbf{elif}\;\frac{a1 \cdot a2}{b1 \cdot b2} \leq 2 \cdot 10^{+303}:\\ \;\;\;\;\frac{a1 \cdot a2}{b1 \cdot b2}\\ \mathbf{else}:\\ \;\;\;\;\frac{a1}{b1} \cdot \frac{a2}{b2}\\ \end{array} \]

Alternative 2: 86.5% accurate, 0.8× speedup

Math

\[\begin{array}{l} [a1, a2] = \mathsf{sort}([a1, a2])\\ [b1, b2] = \mathsf{sort}([b1, b2])\\ \\ \begin{array}{l} \mathbf{if}\;b2 \leq 9.5 \cdot 10^{-34}:\\ \;\;\;\;\frac{a1}{b1} \cdot \frac{a2}{b2}\\ \mathbf{else}:\\ \;\;\;\;a1 \cdot \frac{\frac{a2}{b2}}{b1}\\ \end{array} \end{array} \]

FPCore

NOTE: a1 and a2 should be sorted in increasing order before calling this function.
NOTE: b1 and b2 should be sorted in increasing order before calling this function.
(FPCore (a1 a2 b1 b2)
 :precision binary64
 (if (<= b2 9.5e-34) (* (/ a1 b1) (/ a2 b2)) (* a1 (/ (/ a2 b2) b1))))

C

assert(a1 < a2);
assert(b1 < b2);
double code(double a1, double a2, double b1, double b2) {
	double tmp;
	if (b2 <= 9.5e-34) {
		tmp = (a1 / b1) * (a2 / b2);
	} else {
		tmp = a1 * ((a2 / b2) / b1);
	}
	return tmp;
}

Fortran

NOTE: a1 and a2 should be sorted in increasing order before calling this function.
NOTE: b1 and b2 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 (b2 <= 9.5d-34) then
        tmp = (a1 / b1) * (a2 / b2)
    else
        tmp = a1 * ((a2 / b2) / b1)
    end if
    code = tmp
end function

Java

assert a1 < a2;
assert b1 < b2;
public static double code(double a1, double a2, double b1, double b2) {
	double tmp;
	if (b2 <= 9.5e-34) {
		tmp = (a1 / b1) * (a2 / b2);
	} else {
		tmp = a1 * ((a2 / b2) / b1);
	}
	return tmp;
}

Python

[a1, a2] = sort([a1, a2])
[b1, b2] = sort([b1, b2])
def code(a1, a2, b1, b2):
	tmp = 0
	if b2 <= 9.5e-34:
		tmp = (a1 / b1) * (a2 / b2)
	else:
		tmp = a1 * ((a2 / b2) / b1)
	return tmp

Julia

a1, a2 = sort([a1, a2])
b1, b2 = sort([b1, b2])
function code(a1, a2, b1, b2)
	tmp = 0.0
	if (b2 <= 9.5e-34)
		tmp = Float64(Float64(a1 / b1) * Float64(a2 / b2));
	else
		tmp = Float64(a1 * Float64(Float64(a2 / b2) / b1));
	end
	return tmp
end

MATLAB

a1, a2 = num2cell(sort([a1, a2])){:}
b1, b2 = num2cell(sort([b1, b2])){:}
function tmp_2 = code(a1, a2, b1, b2)
	tmp = 0.0;
	if (b2 <= 9.5e-34)
		tmp = (a1 / b1) * (a2 / b2);
	else
		tmp = a1 * ((a2 / b2) / b1);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: a1 and a2 should be sorted in increasing order before calling this function.
NOTE: b1 and b2 should be sorted in increasing order before calling this function.
code[a1_, a2_, b1_, b2_] := If[LessEqual[b2, 9.5e-34], N[(N[(a1 / b1), $MachinePrecision] * N[(a2 / b2), $MachinePrecision]), $MachinePrecision], N[(a1 * N[(N[(a2 / b2), $MachinePrecision] / b1), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b2 < 9.49999999999999985e-34

   1. Initial program 83.9%

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

      1. times-frac 83.8%

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

   3. Simplified 83.8%

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

   if 9.49999999999999985e-34 < b2

   1. Initial program 86.9%

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

      1. times-frac 88.1%

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

      2. associate-*l/ 87.2%

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

      3. associate-*r/ 90.3%

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

   3. Simplified 90.3%

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

4. Final simplification 85.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b2 \leq 9.5 \cdot 10^{-34}:\\ \;\;\;\;\frac{a1}{b1} \cdot \frac{a2}{b2}\\ \mathbf{else}:\\ \;\;\;\;a1 \cdot \frac{\frac{a2}{b2}}{b1}\\ \end{array} \]

Alternative 3: 85.9% accurate, 0.8× speedup

Math

\[\begin{array}{l} [a1, a2] = \mathsf{sort}([a1, a2])\\ [b1, b2] = \mathsf{sort}([b1, b2])\\ \\ \begin{array}{l} \mathbf{if}\;b2 \leq -3.8 \cdot 10^{-266}:\\ \;\;\;\;\frac{a2}{b1} \cdot \frac{a1}{b2}\\ \mathbf{else}:\\ \;\;\;\;a1 \cdot \frac{\frac{a2}{b2}}{b1}\\ \end{array} \end{array} \]

FPCore

NOTE: a1 and a2 should be sorted in increasing order before calling this function.
NOTE: b1 and b2 should be sorted in increasing order before calling this function.
(FPCore (a1 a2 b1 b2)
 :precision binary64
 (if (<= b2 -3.8e-266) (* (/ a2 b1) (/ a1 b2)) (* a1 (/ (/ a2 b2) b1))))

C

assert(a1 < a2);
assert(b1 < b2);
double code(double a1, double a2, double b1, double b2) {
	double tmp;
	if (b2 <= -3.8e-266) {
		tmp = (a2 / b1) * (a1 / b2);
	} else {
		tmp = a1 * ((a2 / b2) / b1);
	}
	return tmp;
}

Fortran

NOTE: a1 and a2 should be sorted in increasing order before calling this function.
NOTE: b1 and b2 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 (b2 <= (-3.8d-266)) then
        tmp = (a2 / b1) * (a1 / b2)
    else
        tmp = a1 * ((a2 / b2) / b1)
    end if
    code = tmp
end function

Java

assert a1 < a2;
assert b1 < b2;
public static double code(double a1, double a2, double b1, double b2) {
	double tmp;
	if (b2 <= -3.8e-266) {
		tmp = (a2 / b1) * (a1 / b2);
	} else {
		tmp = a1 * ((a2 / b2) / b1);
	}
	return tmp;
}

Python

[a1, a2] = sort([a1, a2])
[b1, b2] = sort([b1, b2])
def code(a1, a2, b1, b2):
	tmp = 0
	if b2 <= -3.8e-266:
		tmp = (a2 / b1) * (a1 / b2)
	else:
		tmp = a1 * ((a2 / b2) / b1)
	return tmp

Julia

a1, a2 = sort([a1, a2])
b1, b2 = sort([b1, b2])
function code(a1, a2, b1, b2)
	tmp = 0.0
	if (b2 <= -3.8e-266)
		tmp = Float64(Float64(a2 / b1) * Float64(a1 / b2));
	else
		tmp = Float64(a1 * Float64(Float64(a2 / b2) / b1));
	end
	return tmp
end

MATLAB

a1, a2 = num2cell(sort([a1, a2])){:}
b1, b2 = num2cell(sort([b1, b2])){:}
function tmp_2 = code(a1, a2, b1, b2)
	tmp = 0.0;
	if (b2 <= -3.8e-266)
		tmp = (a2 / b1) * (a1 / b2);
	else
		tmp = a1 * ((a2 / b2) / b1);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: a1 and a2 should be sorted in increasing order before calling this function.
NOTE: b1 and b2 should be sorted in increasing order before calling this function.
code[a1_, a2_, b1_, b2_] := If[LessEqual[b2, -3.8e-266], N[(N[(a2 / b1), $MachinePrecision] * N[(a1 / b2), $MachinePrecision]), $MachinePrecision], N[(a1 * N[(N[(a2 / b2), $MachinePrecision] / b1), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b2 < -3.79999999999999994e-266

   1. Initial program 83.8%

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

      1. *-commutative 83.8%

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

      2. times-frac 88.7%

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

   3. Applied egg-rr 88.7%

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

   if -3.79999999999999994e-266 < b2

   1. Initial program 85.5%

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

      1. times-frac 84.8%

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

      2. associate-*l/ 84.5%

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

      3. associate-*r/ 86.6%

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

   3. Simplified 86.6%

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

4. Final simplification 87.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b2 \leq -3.8 \cdot 10^{-266}:\\ \;\;\;\;\frac{a2}{b1} \cdot \frac{a1}{b2}\\ \mathbf{else}:\\ \;\;\;\;a1 \cdot \frac{\frac{a2}{b2}}{b1}\\ \end{array} \]

Alternative 4: 85.9% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 84.8%

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

   1. times-frac 85.1%

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

   2. associate-*l/ 83.9%

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

   3. associate-*r/ 85.5%

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

3. Simplified 85.5%

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

4. Final simplification 85.5%

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

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 2023332 
(FPCore (a1 a2 b1 b2)
  :name "Quotient of products"
  :precision binary64

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

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