Quotient of products

Percentage Accurate: 86.1% → 96.6%

Time: 3.4s

Alternatives: 4

Speedup: 0.6×

• 21.0% 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: 86.1% 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: 96.6% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{a1 \cdot a2}{b1 \cdot b2}\\ t_1 := \frac{a2}{b2} \cdot \frac{a1}{b1}\\ \mathbf{if}\;t_0 \leq -\infty:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t_0 \leq -1 \cdot 10^{-296}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;t_0 \leq 0:\\ \;\;\;\;\frac{a2}{b1} \cdot \frac{a1}{b2}\\ \mathbf{elif}\;t_0 \leq 5 \cdot 10^{+248}:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (a1 a2 b1 b2)
 :precision binary64
 (let* ((t_0 (/ (* a1 a2) (* b1 b2))) (t_1 (* (/ a2 b2) (/ a1 b1))))
   (if (<= t_0 (- INFINITY))
     t_1
     (if (<= t_0 -1e-296)
       t_0
       (if (<= t_0 0.0)
         (* (/ a2 b1) (/ a1 b2))
         (if (<= t_0 5e+248) t_0 t_1))))))

C

double code(double a1, double a2, double b1, double b2) {
	double t_0 = (a1 * a2) / (b1 * b2);
	double t_1 = (a2 / b2) * (a1 / b1);
	double tmp;
	if (t_0 <= -((double) INFINITY)) {
		tmp = t_1;
	} else if (t_0 <= -1e-296) {
		tmp = t_0;
	} else if (t_0 <= 0.0) {
		tmp = (a2 / b1) * (a1 / b2);
	} else if (t_0 <= 5e+248) {
		tmp = t_0;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Java

public static double code(double a1, double a2, double b1, double b2) {
	double t_0 = (a1 * a2) / (b1 * b2);
	double t_1 = (a2 / b2) * (a1 / b1);
	double tmp;
	if (t_0 <= -Double.POSITIVE_INFINITY) {
		tmp = t_1;
	} else if (t_0 <= -1e-296) {
		tmp = t_0;
	} else if (t_0 <= 0.0) {
		tmp = (a2 / b1) * (a1 / b2);
	} else if (t_0 <= 5e+248) {
		tmp = t_0;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(a1, a2, b1, b2):
	t_0 = (a1 * a2) / (b1 * b2)
	t_1 = (a2 / b2) * (a1 / b1)
	tmp = 0
	if t_0 <= -math.inf:
		tmp = t_1
	elif t_0 <= -1e-296:
		tmp = t_0
	elif t_0 <= 0.0:
		tmp = (a2 / b1) * (a1 / b2)
	elif t_0 <= 5e+248:
		tmp = t_0
	else:
		tmp = t_1
	return tmp

Julia

function code(a1, a2, b1, b2)
	t_0 = Float64(Float64(a1 * a2) / Float64(b1 * b2))
	t_1 = Float64(Float64(a2 / b2) * Float64(a1 / b1))
	tmp = 0.0
	if (t_0 <= Float64(-Inf))
		tmp = t_1;
	elseif (t_0 <= -1e-296)
		tmp = t_0;
	elseif (t_0 <= 0.0)
		tmp = Float64(Float64(a2 / b1) * Float64(a1 / b2));
	elseif (t_0 <= 5e+248)
		tmp = t_0;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(a1, a2, b1, b2)
	t_0 = (a1 * a2) / (b1 * b2);
	t_1 = (a2 / b2) * (a1 / b1);
	tmp = 0.0;
	if (t_0 <= -Inf)
		tmp = t_1;
	elseif (t_0 <= -1e-296)
		tmp = t_0;
	elseif (t_0 <= 0.0)
		tmp = (a2 / b1) * (a1 / b2);
	elseif (t_0 <= 5e+248)
		tmp = t_0;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[a1_, a2_, b1_, b2_] := Block[{t$95$0 = N[(N[(a1 * a2), $MachinePrecision] / N[(b1 * b2), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(N[(a2 / b2), $MachinePrecision] * N[(a1 / b1), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$0, (-Infinity)], t$95$1, If[LessEqual[t$95$0, -1e-296], 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, 5e+248], t$95$0, t$95$1]]]]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 (*.f64 a1 a2) (*.f64 b1 b2)) < -inf.0 or 4.9999999999999996e248 < (/.f64 (*.f64 a1 a2) (*.f64 b1 b2))

   1. Initial program 77.9%

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

      1. times-frac 98.7%

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

      2. *-commutative 98.7%

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

   3. Simplified 98.7%

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

   if -inf.0 < (/.f64 (*.f64 a1 a2) (*.f64 b1 b2)) < -1e-296 or -0.0 < (/.f64 (*.f64 a1 a2) (*.f64 b1 b2)) < 4.9999999999999996e248

   1. Initial program 98.3%

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

   if -1e-296 < (/.f64 (*.f64 a1 a2) (*.f64 b1 b2)) < -0.0

   1. Initial program 83.1%

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

      1. *-commutative 83.1%

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

      2. times-frac 99.9%

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

   3. Applied egg-rr 99.9%

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

4. Final simplification 98.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{a1 \cdot a2}{b1 \cdot b2} \leq -\infty:\\ \;\;\;\;\frac{a2}{b2} \cdot \frac{a1}{b1}\\ \mathbf{elif}\;\frac{a1 \cdot a2}{b1 \cdot b2} \leq -1 \cdot 10^{-296}:\\ \;\;\;\;\frac{a1 \cdot a2}{b1 \cdot b2}\\ \mathbf{elif}\;\frac{a1 \cdot a2}{b1 \cdot b2} \leq 0:\\ \;\;\;\;\frac{a2}{b1} \cdot \frac{a1}{b2}\\ \mathbf{elif}\;\frac{a1 \cdot a2}{b1 \cdot b2} \leq 5 \cdot 10^{+248}:\\ \;\;\;\;\frac{a1 \cdot a2}{b1 \cdot b2}\\ \mathbf{else}:\\ \;\;\;\;\frac{a2}{b2} \cdot \frac{a1}{b1}\\ \end{array} \]

Alternative 2: 86.3% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b1 \leq -3.4 \cdot 10^{+84} \lor \neg \left(b1 \leq -2.3 \cdot 10^{-282}\right):\\ \;\;\;\;\frac{a2}{b1} \cdot \frac{a1}{b2}\\ \mathbf{else}:\\ \;\;\;\;a2 \cdot \frac{\frac{a1}{b1}}{b2}\\ \end{array} \end{array} \]

FPCore

(FPCore (a1 a2 b1 b2)
 :precision binary64
 (if (or (<= b1 -3.4e+84) (not (<= b1 -2.3e-282)))
   (* (/ a2 b1) (/ a1 b2))
   (* a2 (/ (/ a1 b1) b2))))

C

double code(double a1, double a2, double b1, double b2) {
	double tmp;
	if ((b1 <= -3.4e+84) || !(b1 <= -2.3e-282)) {
		tmp = (a2 / b1) * (a1 / 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 <= (-3.4d+84)) .or. (.not. (b1 <= (-2.3d-282)))) then
        tmp = (a2 / b1) * (a1 / 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 <= -3.4e+84) || !(b1 <= -2.3e-282)) {
		tmp = (a2 / b1) * (a1 / b2);
	} else {
		tmp = a2 * ((a1 / b1) / b2);
	}
	return tmp;
}

Python

def code(a1, a2, b1, b2):
	tmp = 0
	if (b1 <= -3.4e+84) or not (b1 <= -2.3e-282):
		tmp = (a2 / b1) * (a1 / b2)
	else:
		tmp = a2 * ((a1 / b1) / b2)
	return tmp

Julia

function code(a1, a2, b1, b2)
	tmp = 0.0
	if ((b1 <= -3.4e+84) || !(b1 <= -2.3e-282))
		tmp = Float64(Float64(a2 / b1) * Float64(a1 / b2));
	else
		tmp = Float64(a2 * Float64(Float64(a1 / b1) / b2));
	end
	return tmp
end

MATLAB

function tmp_2 = code(a1, a2, b1, b2)
	tmp = 0.0;
	if ((b1 <= -3.4e+84) || ~((b1 <= -2.3e-282)))
		tmp = (a2 / b1) * (a1 / b2);
	else
		tmp = a2 * ((a1 / b1) / b2);
	end
	tmp_2 = tmp;
end

Wolfram

code[a1_, a2_, b1_, b2_] := If[Or[LessEqual[b1, -3.4e+84], N[Not[LessEqual[b1, -2.3e-282]], $MachinePrecision]], N[(N[(a2 / b1), $MachinePrecision] * N[(a1 / b2), $MachinePrecision]), $MachinePrecision], N[(a2 * N[(N[(a1 / b1), $MachinePrecision] / b2), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b1 < -3.3999999999999998e84 or -2.2999999999999999e-282 < b1

   1. Initial program 88.8%

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

      1. *-commutative 88.8%

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

      2. times-frac 89.4%

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

   3. Applied egg-rr 89.4%

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

   if -3.3999999999999998e84 < b1 < -2.2999999999999999e-282

   1. Initial program 88.8%

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

      1. times-frac 90.9%

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

      2. *-commutative 90.9%

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

   3. Simplified 90.9%

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

   4. Taylor expanded in a2 around 0 88.8%

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

      1. times-frac 90.9%

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

      2. *-commutative 90.9%

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

      3. associate-*l/ 95.4%

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

      4. associate-*r/ 93.9%

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

   6. Simplified 93.9%

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

4. Final simplification 90.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b1 \leq -3.4 \cdot 10^{+84} \lor \neg \left(b1 \leq -2.3 \cdot 10^{-282}\right):\\ \;\;\;\;\frac{a2}{b1} \cdot \frac{a1}{b2}\\ \mathbf{else}:\\ \;\;\;\;a2 \cdot \frac{\frac{a1}{b1}}{b2}\\ \end{array} \]

Alternative 3: 86.1% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b1 \leq -2.4 \cdot 10^{-11} \lor \neg \left(b1 \leq 8.5 \cdot 10^{-110}\right):\\ \;\;\;\;\frac{a2}{b1} \cdot \frac{a1}{b2}\\ \mathbf{else}:\\ \;\;\;\;\frac{a2}{b2} \cdot \frac{a1}{b1}\\ \end{array} \end{array} \]

FPCore

(FPCore (a1 a2 b1 b2)
 :precision binary64
 (if (or (<= b1 -2.4e-11) (not (<= b1 8.5e-110)))
   (* (/ a2 b1) (/ a1 b2))
   (* (/ a2 b2) (/ a1 b1))))

C

double code(double a1, double a2, double b1, double b2) {
	double tmp;
	if ((b1 <= -2.4e-11) || !(b1 <= 8.5e-110)) {
		tmp = (a2 / b1) * (a1 / b2);
	} else {
		tmp = (a2 / b2) * (a1 / b1);
	}
	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 <= (-2.4d-11)) .or. (.not. (b1 <= 8.5d-110))) then
        tmp = (a2 / b1) * (a1 / b2)
    else
        tmp = (a2 / b2) * (a1 / b1)
    end if
    code = tmp
end function

Java

public static double code(double a1, double a2, double b1, double b2) {
	double tmp;
	if ((b1 <= -2.4e-11) || !(b1 <= 8.5e-110)) {
		tmp = (a2 / b1) * (a1 / b2);
	} else {
		tmp = (a2 / b2) * (a1 / b1);
	}
	return tmp;
}

Python

def code(a1, a2, b1, b2):
	tmp = 0
	if (b1 <= -2.4e-11) or not (b1 <= 8.5e-110):
		tmp = (a2 / b1) * (a1 / b2)
	else:
		tmp = (a2 / b2) * (a1 / b1)
	return tmp

Julia

function code(a1, a2, b1, b2)
	tmp = 0.0
	if ((b1 <= -2.4e-11) || !(b1 <= 8.5e-110))
		tmp = Float64(Float64(a2 / b1) * Float64(a1 / b2));
	else
		tmp = Float64(Float64(a2 / b2) * Float64(a1 / b1));
	end
	return tmp
end

MATLAB

function tmp_2 = code(a1, a2, b1, b2)
	tmp = 0.0;
	if ((b1 <= -2.4e-11) || ~((b1 <= 8.5e-110)))
		tmp = (a2 / b1) * (a1 / b2);
	else
		tmp = (a2 / b2) * (a1 / b1);
	end
	tmp_2 = tmp;
end

Wolfram

code[a1_, a2_, b1_, b2_] := If[Or[LessEqual[b1, -2.4e-11], N[Not[LessEqual[b1, 8.5e-110]], $MachinePrecision]], N[(N[(a2 / b1), $MachinePrecision] * N[(a1 / b2), $MachinePrecision]), $MachinePrecision], N[(N[(a2 / b2), $MachinePrecision] * N[(a1 / b1), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b1 < -2.4000000000000001e-11 or 8.50000000000000029e-110 < b1

   1. Initial program 90.0%

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

      1. *-commutative 90.0%

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

      2. times-frac 90.6%

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

   3. Applied egg-rr 90.6%

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

   if -2.4000000000000001e-11 < b1 < 8.50000000000000029e-110

   1. Initial program 86.9%

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

      1. times-frac 91.3%

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

      2. *-commutative 91.3%

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

   3. Simplified 91.3%

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

4. Final simplification 90.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b1 \leq -2.4 \cdot 10^{-11} \lor \neg \left(b1 \leq 8.5 \cdot 10^{-110}\right):\\ \;\;\;\;\frac{a2}{b1} \cdot \frac{a1}{b2}\\ \mathbf{else}:\\ \;\;\;\;\frac{a2}{b2} \cdot \frac{a1}{b1}\\ \end{array} \]

Alternative 4: 86.1% accurate, 1.0× speedup

Math

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

FPCore

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

C

double code(double a1, double a2, double b1, double b2) {
	return a2 * ((a1 / 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 = a2 * ((a1 / b1) / b2)
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 88.8%

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

   1. times-frac 85.7%

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

   2. *-commutative 85.7%

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

3. Simplified 85.7%

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

4. Taylor expanded in a2 around 0 88.8%

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

   1. times-frac 85.7%

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

   2. *-commutative 85.7%

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

   3. associate-*l/ 85.0%

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

   4. associate-*r/ 84.2%

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

6. Simplified 84.2%

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

7. Final simplification 84.2%

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

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 2023279 
(FPCore (a1 a2 b1 b2)
  :name "Quotient of products"
  :precision binary64

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

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