Quotient of products

Percentage Accurate: 86.6% → 95.7%

Time: 2.7s

Alternatives: 6

Speedup: 0.3×

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: 86.6% 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: 95.7% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{a1 \cdot a2}{b1 \cdot b2}\\ t_1 := \frac{a2 \cdot \frac{a1}{b2}}{b1}\\ \mathbf{if}\;t_0 \leq -\infty:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t_0 \leq -5 \cdot 10^{-294}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;t_0 \leq 0:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t_0 \leq 2 \cdot 10^{+264}:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;\frac{a2 \cdot \frac{a1}{b1}}{b2}\\ \end{array} \end{array} \]

FPCore

(FPCore (a1 a2 b1 b2)
 :precision binary64
 (let* ((t_0 (/ (* a1 a2) (* b1 b2))) (t_1 (/ (* a2 (/ a1 b2)) b1)))
   (if (<= t_0 (- INFINITY))
     t_1
     (if (<= t_0 -5e-294)
       t_0
       (if (<= t_0 0.0)
         t_1
         (if (<= t_0 2e+264) t_0 (/ (* a2 (/ a1 b1)) b2)))))))

C

double code(double a1, double a2, double b1, double b2) {
	double t_0 = (a1 * a2) / (b1 * b2);
	double t_1 = (a2 * (a1 / b2)) / b1;
	double tmp;
	if (t_0 <= -((double) INFINITY)) {
		tmp = t_1;
	} else if (t_0 <= -5e-294) {
		tmp = t_0;
	} else if (t_0 <= 0.0) {
		tmp = t_1;
	} else if (t_0 <= 2e+264) {
		tmp = t_0;
	} else {
		tmp = (a2 * (a1 / b1)) / b2;
	}
	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 * (a1 / b2)) / b1;
	double tmp;
	if (t_0 <= -Double.POSITIVE_INFINITY) {
		tmp = t_1;
	} else if (t_0 <= -5e-294) {
		tmp = t_0;
	} else if (t_0 <= 0.0) {
		tmp = t_1;
	} else if (t_0 <= 2e+264) {
		tmp = t_0;
	} else {
		tmp = (a2 * (a1 / b1)) / b2;
	}
	return tmp;
}

Python

def code(a1, a2, b1, b2):
	t_0 = (a1 * a2) / (b1 * b2)
	t_1 = (a2 * (a1 / b2)) / b1
	tmp = 0
	if t_0 <= -math.inf:
		tmp = t_1
	elif t_0 <= -5e-294:
		tmp = t_0
	elif t_0 <= 0.0:
		tmp = t_1
	elif t_0 <= 2e+264:
		tmp = t_0
	else:
		tmp = (a2 * (a1 / b1)) / b2
	return tmp

Julia

function code(a1, a2, b1, b2)
	t_0 = Float64(Float64(a1 * a2) / Float64(b1 * b2))
	t_1 = Float64(Float64(a2 * Float64(a1 / b2)) / b1)
	tmp = 0.0
	if (t_0 <= Float64(-Inf))
		tmp = t_1;
	elseif (t_0 <= -5e-294)
		tmp = t_0;
	elseif (t_0 <= 0.0)
		tmp = t_1;
	elseif (t_0 <= 2e+264)
		tmp = t_0;
	else
		tmp = Float64(Float64(a2 * Float64(a1 / b1)) / b2);
	end
	return tmp
end

MATLAB

function tmp_2 = code(a1, a2, b1, b2)
	t_0 = (a1 * a2) / (b1 * b2);
	t_1 = (a2 * (a1 / b2)) / b1;
	tmp = 0.0;
	if (t_0 <= -Inf)
		tmp = t_1;
	elseif (t_0 <= -5e-294)
		tmp = t_0;
	elseif (t_0 <= 0.0)
		tmp = t_1;
	elseif (t_0 <= 2e+264)
		tmp = t_0;
	else
		tmp = (a2 * (a1 / b1)) / b2;
	end
	tmp_2 = tmp;
end

Wolfram

code[a1_, a2_, b1_, b2_] := Block[{t$95$0 = N[(N[(a1 * a2), $MachinePrecision] / N[(b1 * b2), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(N[(a2 * N[(a1 / b2), $MachinePrecision]), $MachinePrecision] / b1), $MachinePrecision]}, If[LessEqual[t$95$0, (-Infinity)], t$95$1, If[LessEqual[t$95$0, -5e-294], t$95$0, If[LessEqual[t$95$0, 0.0], t$95$1, If[LessEqual[t$95$0, 2e+264], t$95$0, N[(N[(a2 * N[(a1 / b1), $MachinePrecision]), $MachinePrecision] / b2), $MachinePrecision]]]]]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 (*.f64 a1 a2) (*.f64 b1 b2)) < -inf.0 or -5.0000000000000003e-294 < (/.f64 (*.f64 a1 a2) (*.f64 b1 b2)) < 0.0

   1. Initial program 75.0%

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

      1. times-frac 90.6%

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

   3. Simplified 90.6%

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

      1. frac-times 75.0%

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

      2. *-commutative 75.0%

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

      3. frac-times 90.7%

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

      4. associate-*r/ 96.1%

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

   5. Applied egg-rr 96.1%

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

   if -inf.0 < (/.f64 (*.f64 a1 a2) (*.f64 b1 b2)) < -5.0000000000000003e-294 or 0.0 < (/.f64 (*.f64 a1 a2) (*.f64 b1 b2)) < 2.00000000000000009e264

   1. Initial program 98.9%

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

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

   1. Initial program 51.7%

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

      1. times-frac 91.2%

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

   3. Simplified 91.2%

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

      1. associate-*r/ 95.5%

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

   5. Applied egg-rr 95.5%

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

4. Final simplification 97.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{a1 \cdot a2}{b1 \cdot b2} \leq -\infty:\\ \;\;\;\;\frac{a2 \cdot \frac{a1}{b2}}{b1}\\ \mathbf{elif}\;\frac{a1 \cdot a2}{b1 \cdot b2} \leq -5 \cdot 10^{-294}:\\ \;\;\;\;\frac{a1 \cdot a2}{b1 \cdot b2}\\ \mathbf{elif}\;\frac{a1 \cdot a2}{b1 \cdot b2} \leq 0:\\ \;\;\;\;\frac{a2 \cdot \frac{a1}{b2}}{b1}\\ \mathbf{elif}\;\frac{a1 \cdot a2}{b1 \cdot b2} \leq 2 \cdot 10^{+264}:\\ \;\;\;\;\frac{a1 \cdot a2}{b1 \cdot b2}\\ \mathbf{else}:\\ \;\;\;\;\frac{a2 \cdot \frac{a1}{b1}}{b2}\\ \end{array} \]

Alternative 2: 95.3% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{a1 \cdot a2}{b1 \cdot b2}\\ t_1 := \frac{a1}{b1} \cdot \frac{a2}{b2}\\ \mathbf{if}\;t_0 \leq -2 \cdot 10^{+214}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t_0 \leq -5 \cdot 10^{-302}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;t_0 \leq 0:\\ \;\;\;\;\frac{a1}{\frac{b2}{\frac{a2}{b1}}}\\ \mathbf{elif}\;t_0 \leq 5 \cdot 10^{+258}:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (a1 a2 b1 b2)
 :precision binary64
 (let* ((t_0 (/ (* a1 a2) (* b1 b2))) (t_1 (* (/ a1 b1) (/ a2 b2))))
   (if (<= t_0 -2e+214)
     t_1
     (if (<= t_0 -5e-302)
       t_0
       (if (<= t_0 0.0)
         (/ a1 (/ b2 (/ a2 b1)))
         (if (<= t_0 5e+258) 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 = (a1 / b1) * (a2 / b2);
	double tmp;
	if (t_0 <= -2e+214) {
		tmp = t_1;
	} else if (t_0 <= -5e-302) {
		tmp = t_0;
	} else if (t_0 <= 0.0) {
		tmp = a1 / (b2 / (a2 / b1));
	} else if (t_0 <= 5e+258) {
		tmp = t_0;
	} else {
		tmp = t_1;
	}
	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) :: t_1
    real(8) :: tmp
    t_0 = (a1 * a2) / (b1 * b2)
    t_1 = (a1 / b1) * (a2 / b2)
    if (t_0 <= (-2d+214)) then
        tmp = t_1
    else if (t_0 <= (-5d-302)) then
        tmp = t_0
    else if (t_0 <= 0.0d0) then
        tmp = a1 / (b2 / (a2 / b1))
    else if (t_0 <= 5d+258) then
        tmp = t_0
    else
        tmp = t_1
    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 t_1 = (a1 / b1) * (a2 / b2);
	double tmp;
	if (t_0 <= -2e+214) {
		tmp = t_1;
	} else if (t_0 <= -5e-302) {
		tmp = t_0;
	} else if (t_0 <= 0.0) {
		tmp = a1 / (b2 / (a2 / b1));
	} else if (t_0 <= 5e+258) {
		tmp = t_0;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(a1, a2, b1, b2):
	t_0 = (a1 * a2) / (b1 * b2)
	t_1 = (a1 / b1) * (a2 / b2)
	tmp = 0
	if t_0 <= -2e+214:
		tmp = t_1
	elif t_0 <= -5e-302:
		tmp = t_0
	elif t_0 <= 0.0:
		tmp = a1 / (b2 / (a2 / b1))
	elif t_0 <= 5e+258:
		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(a1 / b1) * Float64(a2 / b2))
	tmp = 0.0
	if (t_0 <= -2e+214)
		tmp = t_1;
	elseif (t_0 <= -5e-302)
		tmp = t_0;
	elseif (t_0 <= 0.0)
		tmp = Float64(a1 / Float64(b2 / Float64(a2 / b1)));
	elseif (t_0 <= 5e+258)
		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 = (a1 / b1) * (a2 / b2);
	tmp = 0.0;
	if (t_0 <= -2e+214)
		tmp = t_1;
	elseif (t_0 <= -5e-302)
		tmp = t_0;
	elseif (t_0 <= 0.0)
		tmp = a1 / (b2 / (a2 / b1));
	elseif (t_0 <= 5e+258)
		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[(a1 / b1), $MachinePrecision] * N[(a2 / b2), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$0, -2e+214], t$95$1, If[LessEqual[t$95$0, -5e-302], 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, 5e+258], t$95$0, t$95$1]]]]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 (*.f64 a1 a2) (*.f64 b1 b2)) < -1.9999999999999999e214 or 5e258 < (/.f64 (*.f64 a1 a2) (*.f64 b1 b2))

   1. Initial program 62.4%

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

      1. times-frac 91.5%

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

   3. Simplified 91.5%

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

   if -1.9999999999999999e214 < (/.f64 (*.f64 a1 a2) (*.f64 b1 b2)) < -5.00000000000000033e-302 or 0.0 < (/.f64 (*.f64 a1 a2) (*.f64 b1 b2)) < 5e258

   1. Initial program 98.9%

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

   if -5.00000000000000033e-302 < (/.f64 (*.f64 a1 a2) (*.f64 b1 b2)) < 0.0

   1. Initial program 76.1%

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

      1. associate-/l* 87.4%

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

      2. *-commutative 87.4%

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

      3. associate-/l* 91.4%

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

   3. Simplified 91.4%

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

4. Final simplification 94.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{a1 \cdot a2}{b1 \cdot b2} \leq -2 \cdot 10^{+214}:\\ \;\;\;\;\frac{a1}{b1} \cdot \frac{a2}{b2}\\ \mathbf{elif}\;\frac{a1 \cdot a2}{b1 \cdot b2} \leq -5 \cdot 10^{-302}:\\ \;\;\;\;\frac{a1 \cdot a2}{b1 \cdot b2}\\ \mathbf{elif}\;\frac{a1 \cdot a2}{b1 \cdot b2} \leq 0:\\ \;\;\;\;\frac{a1}{\frac{b2}{\frac{a2}{b1}}}\\ \mathbf{elif}\;\frac{a1 \cdot a2}{b1 \cdot b2} \leq 5 \cdot 10^{+258}:\\ \;\;\;\;\frac{a1 \cdot a2}{b1 \cdot b2}\\ \mathbf{else}:\\ \;\;\;\;\frac{a1}{b1} \cdot \frac{a2}{b2}\\ \end{array} \]

Alternative 3: 93.5% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b1 \cdot b2 \leq -5 \cdot 10^{+292} \lor \neg \left(b1 \cdot b2 \leq -1 \cdot 10^{-234}\right) \land \left(b1 \cdot b2 \leq 10^{-299} \lor \neg \left(b1 \cdot b2 \leq 5 \cdot 10^{+118}\right)\right):\\ \;\;\;\;\frac{a1}{b1} \cdot \frac{a2}{b2}\\ \mathbf{else}:\\ \;\;\;\;a2 \cdot \frac{a1}{b1 \cdot b2}\\ \end{array} \end{array} \]

FPCore

(FPCore (a1 a2 b1 b2)
 :precision binary64
 (if (or (<= (* b1 b2) -5e+292)
         (and (not (<= (* b1 b2) -1e-234))
              (or (<= (* b1 b2) 1e-299) (not (<= (* b1 b2) 5e+118)))))
   (* (/ a1 b1) (/ a2 b2))
   (* a2 (/ a1 (* b1 b2)))))

C

double code(double a1, double a2, double b1, double b2) {
	double tmp;
	if (((b1 * b2) <= -5e+292) || (!((b1 * b2) <= -1e-234) && (((b1 * b2) <= 1e-299) || !((b1 * b2) <= 5e+118)))) {
		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) <= (-5d+292)) .or. (.not. ((b1 * b2) <= (-1d-234))) .and. ((b1 * b2) <= 1d-299) .or. (.not. ((b1 * b2) <= 5d+118))) 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) <= -5e+292) || (!((b1 * b2) <= -1e-234) && (((b1 * b2) <= 1e-299) || !((b1 * b2) <= 5e+118)))) {
		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) <= -5e+292) or (not ((b1 * b2) <= -1e-234) and (((b1 * b2) <= 1e-299) or not ((b1 * b2) <= 5e+118))):
		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) <= -5e+292) || (!(Float64(b1 * b2) <= -1e-234) && ((Float64(b1 * b2) <= 1e-299) || !(Float64(b1 * b2) <= 5e+118))))
		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) <= -5e+292) || (~(((b1 * b2) <= -1e-234)) && (((b1 * b2) <= 1e-299) || ~(((b1 * b2) <= 5e+118)))))
		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], -5e+292], And[N[Not[LessEqual[N[(b1 * b2), $MachinePrecision], -1e-234]], $MachinePrecision], Or[LessEqual[N[(b1 * b2), $MachinePrecision], 1e-299], N[Not[LessEqual[N[(b1 * b2), $MachinePrecision], 5e+118]], $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) < -4.9999999999999996e292 or -9.9999999999999996e-235 < (*.f64 b1 b2) < 9.99999999999999992e-300 or 4.99999999999999972e118 < (*.f64 b1 b2)

   1. Initial program 63.5%

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

      1. times-frac 90.3%

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

   3. Simplified 90.3%

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

   if -4.9999999999999996e292 < (*.f64 b1 b2) < -9.9999999999999996e-235 or 9.99999999999999992e-300 < (*.f64 b1 b2) < 4.99999999999999972e118

   1. Initial program 94.0%

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

      1. associate-/l* 93.5%

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

      2. *-commutative 93.5%

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

      3. associate-/l* 88.2%

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

   3. Simplified 88.2%

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

      1. associate-/l* 93.5%

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

      2. *-commutative 93.5%

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

      3. associate-/r/ 95.0%

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

   5. Applied egg-rr 95.0%

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

4. Final simplification 93.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b1 \cdot b2 \leq -5 \cdot 10^{+292} \lor \neg \left(b1 \cdot b2 \leq -1 \cdot 10^{-234}\right) \land \left(b1 \cdot b2 \leq 10^{-299} \lor \neg \left(b1 \cdot b2 \leq 5 \cdot 10^{+118}\right)\right):\\ \;\;\;\;\frac{a1}{b1} \cdot \frac{a2}{b2}\\ \mathbf{else}:\\ \;\;\;\;a2 \cdot \frac{a1}{b1 \cdot b2}\\ \end{array} \]

Alternative 4: 92.6% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b1 \cdot b2 \leq -5 \cdot 10^{+142}:\\ \;\;\;\;\frac{a1}{\frac{b2}{\frac{a2}{b1}}}\\ \mathbf{elif}\;b1 \cdot b2 \leq -1 \cdot 10^{-234} \lor \neg \left(b1 \cdot b2 \leq 10^{-299}\right) \land b1 \cdot b2 \leq 5 \cdot 10^{+118}:\\ \;\;\;\;a2 \cdot \frac{a1}{b1 \cdot b2}\\ \mathbf{else}:\\ \;\;\;\;\frac{a1}{b1} \cdot \frac{a2}{b2}\\ \end{array} \end{array} \]

FPCore

(FPCore (a1 a2 b1 b2)
 :precision binary64
 (if (<= (* b1 b2) -5e+142)
   (/ a1 (/ b2 (/ a2 b1)))
   (if (or (<= (* b1 b2) -1e-234)
           (and (not (<= (* b1 b2) 1e-299)) (<= (* b1 b2) 5e+118)))
     (* a2 (/ a1 (* b1 b2)))
     (* (/ a1 b1) (/ a2 b2)))))

C

double code(double a1, double a2, double b1, double b2) {
	double tmp;
	if ((b1 * b2) <= -5e+142) {
		tmp = a1 / (b2 / (a2 / b1));
	} else if (((b1 * b2) <= -1e-234) || (!((b1 * b2) <= 1e-299) && ((b1 * b2) <= 5e+118))) {
		tmp = a2 * (a1 / (b1 * b2));
	} 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) :: tmp
    if ((b1 * b2) <= (-5d+142)) then
        tmp = a1 / (b2 / (a2 / b1))
    else if (((b1 * b2) <= (-1d-234)) .or. (.not. ((b1 * b2) <= 1d-299)) .and. ((b1 * b2) <= 5d+118)) then
        tmp = a2 * (a1 / (b1 * b2))
    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 tmp;
	if ((b1 * b2) <= -5e+142) {
		tmp = a1 / (b2 / (a2 / b1));
	} else if (((b1 * b2) <= -1e-234) || (!((b1 * b2) <= 1e-299) && ((b1 * b2) <= 5e+118))) {
		tmp = a2 * (a1 / (b1 * b2));
	} else {
		tmp = (a1 / b1) * (a2 / b2);
	}
	return tmp;
}

Python

def code(a1, a2, b1, b2):
	tmp = 0
	if (b1 * b2) <= -5e+142:
		tmp = a1 / (b2 / (a2 / b1))
	elif ((b1 * b2) <= -1e-234) or (not ((b1 * b2) <= 1e-299) and ((b1 * b2) <= 5e+118)):
		tmp = a2 * (a1 / (b1 * b2))
	else:
		tmp = (a1 / b1) * (a2 / b2)
	return tmp

Julia

function code(a1, a2, b1, b2)
	tmp = 0.0
	if (Float64(b1 * b2) <= -5e+142)
		tmp = Float64(a1 / Float64(b2 / Float64(a2 / b1)));
	elseif ((Float64(b1 * b2) <= -1e-234) || (!(Float64(b1 * b2) <= 1e-299) && (Float64(b1 * b2) <= 5e+118)))
		tmp = Float64(a2 * Float64(a1 / Float64(b1 * b2)));
	else
		tmp = Float64(Float64(a1 / b1) * Float64(a2 / b2));
	end
	return tmp
end

MATLAB

function tmp_2 = code(a1, a2, b1, b2)
	tmp = 0.0;
	if ((b1 * b2) <= -5e+142)
		tmp = a1 / (b2 / (a2 / b1));
	elseif (((b1 * b2) <= -1e-234) || (~(((b1 * b2) <= 1e-299)) && ((b1 * b2) <= 5e+118)))
		tmp = a2 * (a1 / (b1 * b2));
	else
		tmp = (a1 / b1) * (a2 / b2);
	end
	tmp_2 = tmp;
end

Wolfram

code[a1_, a2_, b1_, b2_] := If[LessEqual[N[(b1 * b2), $MachinePrecision], -5e+142], N[(a1 / N[(b2 / N[(a2 / b1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[N[(b1 * b2), $MachinePrecision], -1e-234], And[N[Not[LessEqual[N[(b1 * b2), $MachinePrecision], 1e-299]], $MachinePrecision], LessEqual[N[(b1 * b2), $MachinePrecision], 5e+118]]], N[(a2 * N[(a1 / N[(b1 * b2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(a1 / b1), $MachinePrecision] * N[(a2 / b2), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 b1 b2) < -5.0000000000000001e142

   1. Initial program 77.3%

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

      1. associate-/l* 77.6%

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

      2. *-commutative 77.6%

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

      3. associate-/l* 94.4%

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

   3. Simplified 94.4%

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

   if -5.0000000000000001e142 < (*.f64 b1 b2) < -9.9999999999999996e-235 or 9.99999999999999992e-300 < (*.f64 b1 b2) < 4.99999999999999972e118

   1. Initial program 93.6%

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

      1. associate-/l* 93.8%

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

      2. *-commutative 93.8%

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

      3. associate-/l* 87.6%

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

   3. Simplified 87.6%

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

      1. associate-/l* 93.8%

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

      2. *-commutative 93.8%

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

      3. associate-/r/ 96.2%

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

   5. Applied egg-rr 96.2%

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

   if -9.9999999999999996e-235 < (*.f64 b1 b2) < 9.99999999999999992e-300 or 4.99999999999999972e118 < (*.f64 b1 b2)

   1. Initial program 65.5%

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

      1. times-frac 91.5%

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

   3. Simplified 91.5%

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

4. Final simplification 94.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b1 \cdot b2 \leq -5 \cdot 10^{+142}:\\ \;\;\;\;\frac{a1}{\frac{b2}{\frac{a2}{b1}}}\\ \mathbf{elif}\;b1 \cdot b2 \leq -1 \cdot 10^{-234} \lor \neg \left(b1 \cdot b2 \leq 10^{-299}\right) \land b1 \cdot b2 \leq 5 \cdot 10^{+118}:\\ \;\;\;\;a2 \cdot \frac{a1}{b1 \cdot b2}\\ \mathbf{else}:\\ \;\;\;\;\frac{a1}{b1} \cdot \frac{a2}{b2}\\ \end{array} \]

Alternative 5: 92.6% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := a2 \cdot \frac{a1}{b1 \cdot b2}\\ \mathbf{if}\;b1 \cdot b2 \leq -5 \cdot 10^{+142}:\\ \;\;\;\;\frac{a1}{\frac{b2}{\frac{a2}{b1}}}\\ \mathbf{elif}\;b1 \cdot b2 \leq -5 \cdot 10^{-170}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;b1 \cdot b2 \leq 5 \cdot 10^{-217}:\\ \;\;\;\;\frac{a2 \cdot \frac{a1}{b1}}{b2}\\ \mathbf{elif}\;b1 \cdot b2 \leq 5 \cdot 10^{+118}:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;\frac{a1}{b1} \cdot \frac{a2}{b2}\\ \end{array} \end{array} \]

FPCore

(FPCore (a1 a2 b1 b2)
 :precision binary64
 (let* ((t_0 (* a2 (/ a1 (* b1 b2)))))
   (if (<= (* b1 b2) -5e+142)
     (/ a1 (/ b2 (/ a2 b1)))
     (if (<= (* b1 b2) -5e-170)
       t_0
       (if (<= (* b1 b2) 5e-217)
         (/ (* a2 (/ a1 b1)) b2)
         (if (<= (* b1 b2) 5e+118) t_0 (* (/ a1 b1) (/ a2 b2))))))))

C

double code(double a1, double a2, double b1, double b2) {
	double t_0 = a2 * (a1 / (b1 * b2));
	double tmp;
	if ((b1 * b2) <= -5e+142) {
		tmp = a1 / (b2 / (a2 / b1));
	} else if ((b1 * b2) <= -5e-170) {
		tmp = t_0;
	} else if ((b1 * b2) <= 5e-217) {
		tmp = (a2 * (a1 / b1)) / b2;
	} else if ((b1 * b2) <= 5e+118) {
		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 = a2 * (a1 / (b1 * b2))
    if ((b1 * b2) <= (-5d+142)) then
        tmp = a1 / (b2 / (a2 / b1))
    else if ((b1 * b2) <= (-5d-170)) then
        tmp = t_0
    else if ((b1 * b2) <= 5d-217) then
        tmp = (a2 * (a1 / b1)) / b2
    else if ((b1 * b2) <= 5d+118) 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 = a2 * (a1 / (b1 * b2));
	double tmp;
	if ((b1 * b2) <= -5e+142) {
		tmp = a1 / (b2 / (a2 / b1));
	} else if ((b1 * b2) <= -5e-170) {
		tmp = t_0;
	} else if ((b1 * b2) <= 5e-217) {
		tmp = (a2 * (a1 / b1)) / b2;
	} else if ((b1 * b2) <= 5e+118) {
		tmp = t_0;
	} else {
		tmp = (a1 / b1) * (a2 / b2);
	}
	return tmp;
}

Python

def code(a1, a2, b1, b2):
	t_0 = a2 * (a1 / (b1 * b2))
	tmp = 0
	if (b1 * b2) <= -5e+142:
		tmp = a1 / (b2 / (a2 / b1))
	elif (b1 * b2) <= -5e-170:
		tmp = t_0
	elif (b1 * b2) <= 5e-217:
		tmp = (a2 * (a1 / b1)) / b2
	elif (b1 * b2) <= 5e+118:
		tmp = t_0
	else:
		tmp = (a1 / b1) * (a2 / b2)
	return tmp

Julia

function code(a1, a2, b1, b2)
	t_0 = Float64(a2 * Float64(a1 / Float64(b1 * b2)))
	tmp = 0.0
	if (Float64(b1 * b2) <= -5e+142)
		tmp = Float64(a1 / Float64(b2 / Float64(a2 / b1)));
	elseif (Float64(b1 * b2) <= -5e-170)
		tmp = t_0;
	elseif (Float64(b1 * b2) <= 5e-217)
		tmp = Float64(Float64(a2 * Float64(a1 / b1)) / b2);
	elseif (Float64(b1 * b2) <= 5e+118)
		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 = a2 * (a1 / (b1 * b2));
	tmp = 0.0;
	if ((b1 * b2) <= -5e+142)
		tmp = a1 / (b2 / (a2 / b1));
	elseif ((b1 * b2) <= -5e-170)
		tmp = t_0;
	elseif ((b1 * b2) <= 5e-217)
		tmp = (a2 * (a1 / b1)) / b2;
	elseif ((b1 * b2) <= 5e+118)
		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[(a2 * N[(a1 / N[(b1 * b2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(b1 * b2), $MachinePrecision], -5e+142], N[(a1 / N[(b2 / N[(a2 / b1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(b1 * b2), $MachinePrecision], -5e-170], t$95$0, If[LessEqual[N[(b1 * b2), $MachinePrecision], 5e-217], N[(N[(a2 * N[(a1 / b1), $MachinePrecision]), $MachinePrecision] / b2), $MachinePrecision], If[LessEqual[N[(b1 * b2), $MachinePrecision], 5e+118], t$95$0, N[(N[(a1 / b1), $MachinePrecision] * N[(a2 / b2), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if (*.f64 b1 b2) < -5.0000000000000001e142

   1. Initial program 77.3%

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

      1. associate-/l* 77.6%

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

      2. *-commutative 77.6%

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

      3. associate-/l* 94.4%

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

   3. Simplified 94.4%

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

   if -5.0000000000000001e142 < (*.f64 b1 b2) < -5.0000000000000001e-170 or 5.0000000000000002e-217 < (*.f64 b1 b2) < 4.99999999999999972e118

   1. Initial program 94.6%

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

      1. associate-/l* 96.1%

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

      2. *-commutative 96.1%

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

      3. associate-/l* 89.7%

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

   3. Simplified 89.7%

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

      1. associate-/l* 96.1%

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

      2. *-commutative 96.1%

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

      3. associate-/r/ 96.5%

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

   5. Applied egg-rr 96.5%

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

   if -5.0000000000000001e-170 < (*.f64 b1 b2) < 5.0000000000000002e-217

   1. Initial program 64.9%

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

      1. times-frac 88.6%

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

   3. Simplified 88.6%

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

      1. associate-*r/ 98.2%

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

   5. Applied egg-rr 98.2%

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

   if 4.99999999999999972e118 < (*.f64 b1 b2)

   1. Initial program 76.8%

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

      1. times-frac 92.4%

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

   3. Simplified 92.4%

      \[\leadsto \color{blue}{\frac{a1}{b1} \cdot \frac{a2}{b2}} \]
3. Recombined 4 regimes into one program.

4. Final simplification 95.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b1 \cdot b2 \leq -5 \cdot 10^{+142}:\\ \;\;\;\;\frac{a1}{\frac{b2}{\frac{a2}{b1}}}\\ \mathbf{elif}\;b1 \cdot b2 \leq -5 \cdot 10^{-170}:\\ \;\;\;\;a2 \cdot \frac{a1}{b1 \cdot b2}\\ \mathbf{elif}\;b1 \cdot b2 \leq 5 \cdot 10^{-217}:\\ \;\;\;\;\frac{a2 \cdot \frac{a1}{b1}}{b2}\\ \mathbf{elif}\;b1 \cdot b2 \leq 5 \cdot 10^{+118}:\\ \;\;\;\;a2 \cdot \frac{a1}{b1 \cdot b2}\\ \mathbf{else}:\\ \;\;\;\;\frac{a1}{b1} \cdot \frac{a2}{b2}\\ \end{array} \]

Alternative 6: 85.0% 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 82.3%

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

   1. times-frac 84.0%

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

3. Simplified 84.0%

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

4. Final simplification 84.0%

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

Developer target: 85.0% 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 2023227 
(FPCore (a1 a2 b1 b2)
  :name "Quotient of products"
  :precision binary64

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

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