Quotient of products

Percentage Accurate: 86.7% → 93.3%

Time: 3.3s

Alternatives: 6

Speedup: 0.4×

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: 86.7% 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: 93.3% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := a2 \cdot \frac{a1}{b1 \cdot b2}\\ \mathbf{if}\;b1 \cdot b2 \leq -2 \cdot 10^{+94}:\\ \;\;\;\;\frac{\frac{a1}{b2}}{\frac{b1}{a2}}\\ \mathbf{elif}\;b1 \cdot b2 \leq -2 \cdot 10^{-197}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;b1 \cdot b2 \leq 5 \cdot 10^{-228}:\\ \;\;\;\;\frac{\frac{a2}{b2}}{\frac{b1}{a1}}\\ \mathbf{elif}\;b1 \cdot b2 \leq 2 \cdot 10^{+188}:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{b2} \cdot \left(a2 \cdot \frac{a1}{b1}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (a1 a2 b1 b2)
 :precision binary64
 (let* ((t_0 (* a2 (/ a1 (* b1 b2)))))
   (if (<= (* b1 b2) -2e+94)
     (/ (/ a1 b2) (/ b1 a2))
     (if (<= (* b1 b2) -2e-197)
       t_0
       (if (<= (* b1 b2) 5e-228)
         (/ (/ a2 b2) (/ b1 a1))
         (if (<= (* b1 b2) 2e+188) t_0 (* (/ 1.0 b2) (* a2 (/ a1 b1)))))))))

C

double code(double a1, double a2, double b1, double b2) {
	double t_0 = a2 * (a1 / (b1 * b2));
	double tmp;
	if ((b1 * b2) <= -2e+94) {
		tmp = (a1 / b2) / (b1 / a2);
	} else if ((b1 * b2) <= -2e-197) {
		tmp = t_0;
	} else if ((b1 * b2) <= 5e-228) {
		tmp = (a2 / b2) / (b1 / a1);
	} else if ((b1 * b2) <= 2e+188) {
		tmp = t_0;
	} else {
		tmp = (1.0 / b2) * (a2 * (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) :: t_0
    real(8) :: tmp
    t_0 = a2 * (a1 / (b1 * b2))
    if ((b1 * b2) <= (-2d+94)) then
        tmp = (a1 / b2) / (b1 / a2)
    else if ((b1 * b2) <= (-2d-197)) then
        tmp = t_0
    else if ((b1 * b2) <= 5d-228) then
        tmp = (a2 / b2) / (b1 / a1)
    else if ((b1 * b2) <= 2d+188) then
        tmp = t_0
    else
        tmp = (1.0d0 / b2) * (a2 * (a1 / b1))
    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) <= -2e+94) {
		tmp = (a1 / b2) / (b1 / a2);
	} else if ((b1 * b2) <= -2e-197) {
		tmp = t_0;
	} else if ((b1 * b2) <= 5e-228) {
		tmp = (a2 / b2) / (b1 / a1);
	} else if ((b1 * b2) <= 2e+188) {
		tmp = t_0;
	} else {
		tmp = (1.0 / b2) * (a2 * (a1 / b1));
	}
	return tmp;
}

Python

def code(a1, a2, b1, b2):
	t_0 = a2 * (a1 / (b1 * b2))
	tmp = 0
	if (b1 * b2) <= -2e+94:
		tmp = (a1 / b2) / (b1 / a2)
	elif (b1 * b2) <= -2e-197:
		tmp = t_0
	elif (b1 * b2) <= 5e-228:
		tmp = (a2 / b2) / (b1 / a1)
	elif (b1 * b2) <= 2e+188:
		tmp = t_0
	else:
		tmp = (1.0 / b2) * (a2 * (a1 / b1))
	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) <= -2e+94)
		tmp = Float64(Float64(a1 / b2) / Float64(b1 / a2));
	elseif (Float64(b1 * b2) <= -2e-197)
		tmp = t_0;
	elseif (Float64(b1 * b2) <= 5e-228)
		tmp = Float64(Float64(a2 / b2) / Float64(b1 / a1));
	elseif (Float64(b1 * b2) <= 2e+188)
		tmp = t_0;
	else
		tmp = Float64(Float64(1.0 / b2) * Float64(a2 * Float64(a1 / b1)));
	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) <= -2e+94)
		tmp = (a1 / b2) / (b1 / a2);
	elseif ((b1 * b2) <= -2e-197)
		tmp = t_0;
	elseif ((b1 * b2) <= 5e-228)
		tmp = (a2 / b2) / (b1 / a1);
	elseif ((b1 * b2) <= 2e+188)
		tmp = t_0;
	else
		tmp = (1.0 / b2) * (a2 * (a1 / b1));
	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], -2e+94], N[(N[(a1 / b2), $MachinePrecision] / N[(b1 / a2), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(b1 * b2), $MachinePrecision], -2e-197], t$95$0, If[LessEqual[N[(b1 * b2), $MachinePrecision], 5e-228], N[(N[(a2 / b2), $MachinePrecision] / N[(b1 / a1), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(b1 * b2), $MachinePrecision], 2e+188], t$95$0, N[(N[(1.0 / b2), $MachinePrecision] * N[(a2 * N[(a1 / b1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if (*.f64 b1 b2) < -2e94

   1. Initial program 80.4%

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

      1. times-frac 86.6%

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

   3. Simplified 86.6%

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

      1. frac-times 80.4%

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

      2. *-commutative 80.4%

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

      3. frac-times 99.7%

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

      4. clear-num 99.7%

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

      5. un-div-inv 99.8%

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

   5. Applied egg-rr 99.8%

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

   if -2e94 < (*.f64 b1 b2) < -2e-197 or 4.99999999999999972e-228 < (*.f64 b1 b2) < 2e188

   1. Initial program 86.9%

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

      1. associate-/l* 94.4%

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

      2. *-commutative 94.4%

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

      3. associate-/l* 87.3%

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

   3. Simplified 87.3%

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

      1. associate-/l* 94.4%

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

      2. *-commutative 94.4%

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

      3. associate-/r/ 97.4%

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

   5. Applied egg-rr 97.4%

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

   if -2e-197 < (*.f64 b1 b2) < 4.99999999999999972e-228

   1. Initial program 79.4%

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

      1. times-frac 96.2%

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

   3. Simplified 96.2%

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

      1. *-commutative 96.2%

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

      2. clear-num 96.2%

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

      3. un-div-inv 96.2%

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

   5. Applied egg-rr 96.2%

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

   if 2e188 < (*.f64 b1 b2)

   1. Initial program 87.2%

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

      1. associate-/l* 73.7%

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

      2. *-commutative 73.7%

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

      3. associate-/l* 83.3%

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

   3. Simplified 83.3%

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

      1. associate-/r/ 91.9%

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

      2. frac-times 87.2%

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

      3. *-un-lft-identity 87.2%

         \[\leadsto \frac{\color{blue}{1 \cdot \left(a1 \cdot a2\right)}}{b2 \cdot b1} \]

      4. times-frac 99.8%

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

      5. associate-*l/ 96.4%

         \[\leadsto \frac{1}{b2} \cdot \color{blue}{\left(\frac{a1}{b1} \cdot a2\right)} \]

   5. Applied egg-rr 96.4%

      \[\leadsto \color{blue}{\frac{1}{b2} \cdot \left(\frac{a1}{b1} \cdot a2\right)} \]
3. Recombined 4 regimes into one program.

4. Final simplification 97.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b1 \cdot b2 \leq -2 \cdot 10^{+94}:\\ \;\;\;\;\frac{\frac{a1}{b2}}{\frac{b1}{a2}}\\ \mathbf{elif}\;b1 \cdot b2 \leq -2 \cdot 10^{-197}:\\ \;\;\;\;a2 \cdot \frac{a1}{b1 \cdot b2}\\ \mathbf{elif}\;b1 \cdot b2 \leq 5 \cdot 10^{-228}:\\ \;\;\;\;\frac{\frac{a2}{b2}}{\frac{b1}{a1}}\\ \mathbf{elif}\;b1 \cdot b2 \leq 2 \cdot 10^{+188}:\\ \;\;\;\;a2 \cdot \frac{a1}{b1 \cdot b2}\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{b2} \cdot \left(a2 \cdot \frac{a1}{b1}\right)\\ \end{array} \]

Alternative 2: 93.4% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := a2 \cdot \frac{a1}{b1 \cdot b2}\\ t_1 := \frac{a1}{b2} \cdot \frac{a2}{b1}\\ \mathbf{if}\;b1 \cdot b2 \leq -2 \cdot 10^{+94}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b1 \cdot b2 \leq -2 \cdot 10^{-197}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;b1 \cdot b2 \leq 5 \cdot 10^{-228}:\\ \;\;\;\;\frac{a2}{b2} \cdot \frac{a1}{b1}\\ \mathbf{elif}\;b1 \cdot b2 \leq 2 \cdot 10^{+251}:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (a1 a2 b1 b2)
 :precision binary64
 (let* ((t_0 (* a2 (/ a1 (* b1 b2)))) (t_1 (* (/ a1 b2) (/ a2 b1))))
   (if (<= (* b1 b2) -2e+94)
     t_1
     (if (<= (* b1 b2) -2e-197)
       t_0
       (if (<= (* b1 b2) 5e-228)
         (* (/ a2 b2) (/ a1 b1))
         (if (<= (* b1 b2) 2e+251) t_0 t_1))))))

C

double code(double a1, double a2, double b1, double b2) {
	double t_0 = a2 * (a1 / (b1 * b2));
	double t_1 = (a1 / b2) * (a2 / b1);
	double tmp;
	if ((b1 * b2) <= -2e+94) {
		tmp = t_1;
	} else if ((b1 * b2) <= -2e-197) {
		tmp = t_0;
	} else if ((b1 * b2) <= 5e-228) {
		tmp = (a2 / b2) * (a1 / b1);
	} else if ((b1 * b2) <= 2e+251) {
		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 = a2 * (a1 / (b1 * b2))
    t_1 = (a1 / b2) * (a2 / b1)
    if ((b1 * b2) <= (-2d+94)) then
        tmp = t_1
    else if ((b1 * b2) <= (-2d-197)) then
        tmp = t_0
    else if ((b1 * b2) <= 5d-228) then
        tmp = (a2 / b2) * (a1 / b1)
    else if ((b1 * b2) <= 2d+251) 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 = a2 * (a1 / (b1 * b2));
	double t_1 = (a1 / b2) * (a2 / b1);
	double tmp;
	if ((b1 * b2) <= -2e+94) {
		tmp = t_1;
	} else if ((b1 * b2) <= -2e-197) {
		tmp = t_0;
	} else if ((b1 * b2) <= 5e-228) {
		tmp = (a2 / b2) * (a1 / b1);
	} else if ((b1 * b2) <= 2e+251) {
		tmp = t_0;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(a1, a2, b1, b2):
	t_0 = a2 * (a1 / (b1 * b2))
	t_1 = (a1 / b2) * (a2 / b1)
	tmp = 0
	if (b1 * b2) <= -2e+94:
		tmp = t_1
	elif (b1 * b2) <= -2e-197:
		tmp = t_0
	elif (b1 * b2) <= 5e-228:
		tmp = (a2 / b2) * (a1 / b1)
	elif (b1 * b2) <= 2e+251:
		tmp = t_0
	else:
		tmp = t_1
	return tmp

Julia

function code(a1, a2, b1, b2)
	t_0 = Float64(a2 * Float64(a1 / Float64(b1 * b2)))
	t_1 = Float64(Float64(a1 / b2) * Float64(a2 / b1))
	tmp = 0.0
	if (Float64(b1 * b2) <= -2e+94)
		tmp = t_1;
	elseif (Float64(b1 * b2) <= -2e-197)
		tmp = t_0;
	elseif (Float64(b1 * b2) <= 5e-228)
		tmp = Float64(Float64(a2 / b2) * Float64(a1 / b1));
	elseif (Float64(b1 * b2) <= 2e+251)
		tmp = t_0;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(a1, a2, b1, b2)
	t_0 = a2 * (a1 / (b1 * b2));
	t_1 = (a1 / b2) * (a2 / b1);
	tmp = 0.0;
	if ((b1 * b2) <= -2e+94)
		tmp = t_1;
	elseif ((b1 * b2) <= -2e-197)
		tmp = t_0;
	elseif ((b1 * b2) <= 5e-228)
		tmp = (a2 / b2) * (a1 / b1);
	elseif ((b1 * b2) <= 2e+251)
		tmp = t_0;
	else
		tmp = t_1;
	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]}, Block[{t$95$1 = N[(N[(a1 / b2), $MachinePrecision] * N[(a2 / b1), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(b1 * b2), $MachinePrecision], -2e+94], t$95$1, If[LessEqual[N[(b1 * b2), $MachinePrecision], -2e-197], t$95$0, If[LessEqual[N[(b1 * b2), $MachinePrecision], 5e-228], N[(N[(a2 / b2), $MachinePrecision] * N[(a1 / b1), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(b1 * b2), $MachinePrecision], 2e+251], t$95$0, t$95$1]]]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 b1 b2) < -2e94 or 2.0000000000000001e251 < (*.f64 b1 b2)

   1. Initial program 80.6%

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

      1. associate-/l* 81.7%

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

      2. *-commutative 81.7%

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

      3. associate-/l* 91.3%

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

   3. Simplified 91.3%

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

      1. associate-/r/ 99.0%

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

      2. *-commutative 99.0%

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

   5. Applied egg-rr 99.0%

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

   if -2e94 < (*.f64 b1 b2) < -2e-197 or 4.99999999999999972e-228 < (*.f64 b1 b2) < 2.0000000000000001e251

   1. Initial program 87.9%

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

      1. associate-/l* 92.7%

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

      2. *-commutative 92.7%

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

      3. associate-/l* 86.2%

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

   3. Simplified 86.2%

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

      1. associate-/l* 92.7%

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

      2. *-commutative 92.7%

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

      3. associate-/r/ 96.8%

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

   5. Applied egg-rr 96.8%

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

   if -2e-197 < (*.f64 b1 b2) < 4.99999999999999972e-228

   1. Initial program 79.4%

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

      1. times-frac 96.2%

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

   3. Simplified 96.2%

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

4. Final simplification 97.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b1 \cdot b2 \leq -2 \cdot 10^{+94}:\\ \;\;\;\;\frac{a1}{b2} \cdot \frac{a2}{b1}\\ \mathbf{elif}\;b1 \cdot b2 \leq -2 \cdot 10^{-197}:\\ \;\;\;\;a2 \cdot \frac{a1}{b1 \cdot b2}\\ \mathbf{elif}\;b1 \cdot b2 \leq 5 \cdot 10^{-228}:\\ \;\;\;\;\frac{a2}{b2} \cdot \frac{a1}{b1}\\ \mathbf{elif}\;b1 \cdot b2 \leq 2 \cdot 10^{+251}:\\ \;\;\;\;a2 \cdot \frac{a1}{b1 \cdot b2}\\ \mathbf{else}:\\ \;\;\;\;\frac{a1}{b2} \cdot \frac{a2}{b1}\\ \end{array} \]

Alternative 3: 93.4% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := a2 \cdot \frac{a1}{b1 \cdot b2}\\ t_1 := \frac{\frac{a1}{b2}}{\frac{b1}{a2}}\\ \mathbf{if}\;b1 \cdot b2 \leq -2 \cdot 10^{+94}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b1 \cdot b2 \leq -2 \cdot 10^{-197}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;b1 \cdot b2 \leq 5 \cdot 10^{-228}:\\ \;\;\;\;\frac{a2}{b2} \cdot \frac{a1}{b1}\\ \mathbf{elif}\;b1 \cdot b2 \leq 2 \cdot 10^{+251}:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (a1 a2 b1 b2)
 :precision binary64
 (let* ((t_0 (* a2 (/ a1 (* b1 b2)))) (t_1 (/ (/ a1 b2) (/ b1 a2))))
   (if (<= (* b1 b2) -2e+94)
     t_1
     (if (<= (* b1 b2) -2e-197)
       t_0
       (if (<= (* b1 b2) 5e-228)
         (* (/ a2 b2) (/ a1 b1))
         (if (<= (* b1 b2) 2e+251) t_0 t_1))))))

C

double code(double a1, double a2, double b1, double b2) {
	double t_0 = a2 * (a1 / (b1 * b2));
	double t_1 = (a1 / b2) / (b1 / a2);
	double tmp;
	if ((b1 * b2) <= -2e+94) {
		tmp = t_1;
	} else if ((b1 * b2) <= -2e-197) {
		tmp = t_0;
	} else if ((b1 * b2) <= 5e-228) {
		tmp = (a2 / b2) * (a1 / b1);
	} else if ((b1 * b2) <= 2e+251) {
		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 = a2 * (a1 / (b1 * b2))
    t_1 = (a1 / b2) / (b1 / a2)
    if ((b1 * b2) <= (-2d+94)) then
        tmp = t_1
    else if ((b1 * b2) <= (-2d-197)) then
        tmp = t_0
    else if ((b1 * b2) <= 5d-228) then
        tmp = (a2 / b2) * (a1 / b1)
    else if ((b1 * b2) <= 2d+251) 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 = a2 * (a1 / (b1 * b2));
	double t_1 = (a1 / b2) / (b1 / a2);
	double tmp;
	if ((b1 * b2) <= -2e+94) {
		tmp = t_1;
	} else if ((b1 * b2) <= -2e-197) {
		tmp = t_0;
	} else if ((b1 * b2) <= 5e-228) {
		tmp = (a2 / b2) * (a1 / b1);
	} else if ((b1 * b2) <= 2e+251) {
		tmp = t_0;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(a1, a2, b1, b2):
	t_0 = a2 * (a1 / (b1 * b2))
	t_1 = (a1 / b2) / (b1 / a2)
	tmp = 0
	if (b1 * b2) <= -2e+94:
		tmp = t_1
	elif (b1 * b2) <= -2e-197:
		tmp = t_0
	elif (b1 * b2) <= 5e-228:
		tmp = (a2 / b2) * (a1 / b1)
	elif (b1 * b2) <= 2e+251:
		tmp = t_0
	else:
		tmp = t_1
	return tmp

Julia

function code(a1, a2, b1, b2)
	t_0 = Float64(a2 * Float64(a1 / Float64(b1 * b2)))
	t_1 = Float64(Float64(a1 / b2) / Float64(b1 / a2))
	tmp = 0.0
	if (Float64(b1 * b2) <= -2e+94)
		tmp = t_1;
	elseif (Float64(b1 * b2) <= -2e-197)
		tmp = t_0;
	elseif (Float64(b1 * b2) <= 5e-228)
		tmp = Float64(Float64(a2 / b2) * Float64(a1 / b1));
	elseif (Float64(b1 * b2) <= 2e+251)
		tmp = t_0;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(a1, a2, b1, b2)
	t_0 = a2 * (a1 / (b1 * b2));
	t_1 = (a1 / b2) / (b1 / a2);
	tmp = 0.0;
	if ((b1 * b2) <= -2e+94)
		tmp = t_1;
	elseif ((b1 * b2) <= -2e-197)
		tmp = t_0;
	elseif ((b1 * b2) <= 5e-228)
		tmp = (a2 / b2) * (a1 / b1);
	elseif ((b1 * b2) <= 2e+251)
		tmp = t_0;
	else
		tmp = t_1;
	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]}, Block[{t$95$1 = N[(N[(a1 / b2), $MachinePrecision] / N[(b1 / a2), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(b1 * b2), $MachinePrecision], -2e+94], t$95$1, If[LessEqual[N[(b1 * b2), $MachinePrecision], -2e-197], t$95$0, If[LessEqual[N[(b1 * b2), $MachinePrecision], 5e-228], N[(N[(a2 / b2), $MachinePrecision] * N[(a1 / b1), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(b1 * b2), $MachinePrecision], 2e+251], t$95$0, t$95$1]]]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 b1 b2) < -2e94 or 2.0000000000000001e251 < (*.f64 b1 b2)

   1. Initial program 80.6%

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

      1. times-frac 87.1%

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

   3. Simplified 87.1%

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

      1. frac-times 80.6%

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

      2. *-commutative 80.6%

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

      3. frac-times 99.0%

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

      4. clear-num 99.0%

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

      5. un-div-inv 99.1%

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

   5. Applied egg-rr 99.1%

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

   if -2e94 < (*.f64 b1 b2) < -2e-197 or 4.99999999999999972e-228 < (*.f64 b1 b2) < 2.0000000000000001e251

   1. Initial program 87.9%

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

      1. associate-/l* 92.7%

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

      2. *-commutative 92.7%

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

      3. associate-/l* 86.2%

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

   3. Simplified 86.2%

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

      1. associate-/l* 92.7%

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

      2. *-commutative 92.7%

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

      3. associate-/r/ 96.8%

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

   5. Applied egg-rr 96.8%

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

   if -2e-197 < (*.f64 b1 b2) < 4.99999999999999972e-228

   1. Initial program 79.4%

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

      1. times-frac 96.2%

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

   3. Simplified 96.2%

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

4. Final simplification 97.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b1 \cdot b2 \leq -2 \cdot 10^{+94}:\\ \;\;\;\;\frac{\frac{a1}{b2}}{\frac{b1}{a2}}\\ \mathbf{elif}\;b1 \cdot b2 \leq -2 \cdot 10^{-197}:\\ \;\;\;\;a2 \cdot \frac{a1}{b1 \cdot b2}\\ \mathbf{elif}\;b1 \cdot b2 \leq 5 \cdot 10^{-228}:\\ \;\;\;\;\frac{a2}{b2} \cdot \frac{a1}{b1}\\ \mathbf{elif}\;b1 \cdot b2 \leq 2 \cdot 10^{+251}:\\ \;\;\;\;a2 \cdot \frac{a1}{b1 \cdot b2}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{a1}{b2}}{\frac{b1}{a2}}\\ \end{array} \]

Alternative 4: 93.5% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := a2 \cdot \frac{a1}{b1 \cdot b2}\\ t_1 := \frac{\frac{a1}{b2}}{\frac{b1}{a2}}\\ \mathbf{if}\;b1 \cdot b2 \leq -2 \cdot 10^{+94}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b1 \cdot b2 \leq -2 \cdot 10^{-197}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;b1 \cdot b2 \leq 5 \cdot 10^{-228}:\\ \;\;\;\;\frac{\frac{a2}{b2}}{\frac{b1}{a1}}\\ \mathbf{elif}\;b1 \cdot b2 \leq 2 \cdot 10^{+251}:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (a1 a2 b1 b2)
 :precision binary64
 (let* ((t_0 (* a2 (/ a1 (* b1 b2)))) (t_1 (/ (/ a1 b2) (/ b1 a2))))
   (if (<= (* b1 b2) -2e+94)
     t_1
     (if (<= (* b1 b2) -2e-197)
       t_0
       (if (<= (* b1 b2) 5e-228)
         (/ (/ a2 b2) (/ b1 a1))
         (if (<= (* b1 b2) 2e+251) t_0 t_1))))))

C

double code(double a1, double a2, double b1, double b2) {
	double t_0 = a2 * (a1 / (b1 * b2));
	double t_1 = (a1 / b2) / (b1 / a2);
	double tmp;
	if ((b1 * b2) <= -2e+94) {
		tmp = t_1;
	} else if ((b1 * b2) <= -2e-197) {
		tmp = t_0;
	} else if ((b1 * b2) <= 5e-228) {
		tmp = (a2 / b2) / (b1 / a1);
	} else if ((b1 * b2) <= 2e+251) {
		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 = a2 * (a1 / (b1 * b2))
    t_1 = (a1 / b2) / (b1 / a2)
    if ((b1 * b2) <= (-2d+94)) then
        tmp = t_1
    else if ((b1 * b2) <= (-2d-197)) then
        tmp = t_0
    else if ((b1 * b2) <= 5d-228) then
        tmp = (a2 / b2) / (b1 / a1)
    else if ((b1 * b2) <= 2d+251) 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 = a2 * (a1 / (b1 * b2));
	double t_1 = (a1 / b2) / (b1 / a2);
	double tmp;
	if ((b1 * b2) <= -2e+94) {
		tmp = t_1;
	} else if ((b1 * b2) <= -2e-197) {
		tmp = t_0;
	} else if ((b1 * b2) <= 5e-228) {
		tmp = (a2 / b2) / (b1 / a1);
	} else if ((b1 * b2) <= 2e+251) {
		tmp = t_0;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(a1, a2, b1, b2):
	t_0 = a2 * (a1 / (b1 * b2))
	t_1 = (a1 / b2) / (b1 / a2)
	tmp = 0
	if (b1 * b2) <= -2e+94:
		tmp = t_1
	elif (b1 * b2) <= -2e-197:
		tmp = t_0
	elif (b1 * b2) <= 5e-228:
		tmp = (a2 / b2) / (b1 / a1)
	elif (b1 * b2) <= 2e+251:
		tmp = t_0
	else:
		tmp = t_1
	return tmp

Julia

function code(a1, a2, b1, b2)
	t_0 = Float64(a2 * Float64(a1 / Float64(b1 * b2)))
	t_1 = Float64(Float64(a1 / b2) / Float64(b1 / a2))
	tmp = 0.0
	if (Float64(b1 * b2) <= -2e+94)
		tmp = t_1;
	elseif (Float64(b1 * b2) <= -2e-197)
		tmp = t_0;
	elseif (Float64(b1 * b2) <= 5e-228)
		tmp = Float64(Float64(a2 / b2) / Float64(b1 / a1));
	elseif (Float64(b1 * b2) <= 2e+251)
		tmp = t_0;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(a1, a2, b1, b2)
	t_0 = a2 * (a1 / (b1 * b2));
	t_1 = (a1 / b2) / (b1 / a2);
	tmp = 0.0;
	if ((b1 * b2) <= -2e+94)
		tmp = t_1;
	elseif ((b1 * b2) <= -2e-197)
		tmp = t_0;
	elseif ((b1 * b2) <= 5e-228)
		tmp = (a2 / b2) / (b1 / a1);
	elseif ((b1 * b2) <= 2e+251)
		tmp = t_0;
	else
		tmp = t_1;
	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]}, Block[{t$95$1 = N[(N[(a1 / b2), $MachinePrecision] / N[(b1 / a2), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(b1 * b2), $MachinePrecision], -2e+94], t$95$1, If[LessEqual[N[(b1 * b2), $MachinePrecision], -2e-197], t$95$0, If[LessEqual[N[(b1 * b2), $MachinePrecision], 5e-228], N[(N[(a2 / b2), $MachinePrecision] / N[(b1 / a1), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(b1 * b2), $MachinePrecision], 2e+251], t$95$0, t$95$1]]]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 b1 b2) < -2e94 or 2.0000000000000001e251 < (*.f64 b1 b2)

   1. Initial program 80.6%

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

      1. times-frac 87.1%

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

   3. Simplified 87.1%

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

      1. frac-times 80.6%

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

      2. *-commutative 80.6%

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

      3. frac-times 99.0%

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

      4. clear-num 99.0%

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

      5. un-div-inv 99.1%

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

   5. Applied egg-rr 99.1%

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

   if -2e94 < (*.f64 b1 b2) < -2e-197 or 4.99999999999999972e-228 < (*.f64 b1 b2) < 2.0000000000000001e251

   1. Initial program 87.9%

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

      1. associate-/l* 92.7%

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

      2. *-commutative 92.7%

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

      3. associate-/l* 86.2%

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

   3. Simplified 86.2%

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

      1. associate-/l* 92.7%

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

      2. *-commutative 92.7%

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

      3. associate-/r/ 96.8%

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

   5. Applied egg-rr 96.8%

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

   if -2e-197 < (*.f64 b1 b2) < 4.99999999999999972e-228

   1. Initial program 79.4%

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

      1. times-frac 96.2%

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

   3. Simplified 96.2%

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

      1. *-commutative 96.2%

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

      2. clear-num 96.2%

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

      3. un-div-inv 96.2%

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

   5. Applied egg-rr 96.2%

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

4. Final simplification 97.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b1 \cdot b2 \leq -2 \cdot 10^{+94}:\\ \;\;\;\;\frac{\frac{a1}{b2}}{\frac{b1}{a2}}\\ \mathbf{elif}\;b1 \cdot b2 \leq -2 \cdot 10^{-197}:\\ \;\;\;\;a2 \cdot \frac{a1}{b1 \cdot b2}\\ \mathbf{elif}\;b1 \cdot b2 \leq 5 \cdot 10^{-228}:\\ \;\;\;\;\frac{\frac{a2}{b2}}{\frac{b1}{a1}}\\ \mathbf{elif}\;b1 \cdot b2 \leq 2 \cdot 10^{+251}:\\ \;\;\;\;a2 \cdot \frac{a1}{b1 \cdot b2}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{a1}{b2}}{\frac{b1}{a2}}\\ \end{array} \]

Alternative 5: 91.9% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b1 \cdot b2 \leq -4 \cdot 10^{+218} \lor \neg \left(b1 \cdot b2 \leq -2 \cdot 10^{-197}\right) \land b1 \cdot b2 \leq 5 \cdot 10^{-228}:\\ \;\;\;\;\frac{a2}{b2} \cdot \frac{a1}{b1}\\ \mathbf{else}:\\ \;\;\;\;a2 \cdot \frac{a1}{b1 \cdot b2}\\ \end{array} \end{array} \]

FPCore

(FPCore (a1 a2 b1 b2)
 :precision binary64
 (if (or (<= (* b1 b2) -4e+218)
         (and (not (<= (* b1 b2) -2e-197)) (<= (* b1 b2) 5e-228)))
   (* (/ a2 b2) (/ a1 b1))
   (* a2 (/ a1 (* b1 b2)))))

C

double code(double a1, double a2, double b1, double b2) {
	double tmp;
	if (((b1 * b2) <= -4e+218) || (!((b1 * b2) <= -2e-197) && ((b1 * b2) <= 5e-228))) {
		tmp = (a2 / b2) * (a1 / b1);
	} 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) <= (-4d+218)) .or. (.not. ((b1 * b2) <= (-2d-197))) .and. ((b1 * b2) <= 5d-228)) then
        tmp = (a2 / b2) * (a1 / b1)
    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) <= -4e+218) || (!((b1 * b2) <= -2e-197) && ((b1 * b2) <= 5e-228))) {
		tmp = (a2 / b2) * (a1 / b1);
	} else {
		tmp = a2 * (a1 / (b1 * b2));
	}
	return tmp;
}

Python

def code(a1, a2, b1, b2):
	tmp = 0
	if ((b1 * b2) <= -4e+218) or (not ((b1 * b2) <= -2e-197) and ((b1 * b2) <= 5e-228)):
		tmp = (a2 / b2) * (a1 / b1)
	else:
		tmp = a2 * (a1 / (b1 * b2))
	return tmp

Julia

function code(a1, a2, b1, b2)
	tmp = 0.0
	if ((Float64(b1 * b2) <= -4e+218) || (!(Float64(b1 * b2) <= -2e-197) && (Float64(b1 * b2) <= 5e-228)))
		tmp = Float64(Float64(a2 / b2) * Float64(a1 / b1));
	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) <= -4e+218) || (~(((b1 * b2) <= -2e-197)) && ((b1 * b2) <= 5e-228)))
		tmp = (a2 / b2) * (a1 / b1);
	else
		tmp = a2 * (a1 / (b1 * b2));
	end
	tmp_2 = tmp;
end

Wolfram

code[a1_, a2_, b1_, b2_] := If[Or[LessEqual[N[(b1 * b2), $MachinePrecision], -4e+218], And[N[Not[LessEqual[N[(b1 * b2), $MachinePrecision], -2e-197]], $MachinePrecision], LessEqual[N[(b1 * b2), $MachinePrecision], 5e-228]]], N[(N[(a2 / b2), $MachinePrecision] * N[(a1 / b1), $MachinePrecision]), $MachinePrecision], N[(a2 * N[(a1 / N[(b1 * b2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 b1 b2) < -4.00000000000000033e218 or -2e-197 < (*.f64 b1 b2) < 4.99999999999999972e-228

   1. Initial program 75.3%

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

      1. times-frac 94.2%

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

   3. Simplified 94.2%

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

   if -4.00000000000000033e218 < (*.f64 b1 b2) < -2e-197 or 4.99999999999999972e-228 < (*.f64 b1 b2)

   1. Initial program 88.4%

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

      1. associate-/l* 91.4%

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

      2. *-commutative 91.4%

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

      3. associate-/l* 88.0%

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

   3. Simplified 88.0%

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

      1. associate-/l* 91.4%

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

      2. *-commutative 91.4%

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

      3. associate-/r/ 93.1%

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

   5. Applied egg-rr 93.1%

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

4. Final simplification 93.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b1 \cdot b2 \leq -4 \cdot 10^{+218} \lor \neg \left(b1 \cdot b2 \leq -2 \cdot 10^{-197}\right) \land b1 \cdot b2 \leq 5 \cdot 10^{-228}:\\ \;\;\;\;\frac{a2}{b2} \cdot \frac{a1}{b1}\\ \mathbf{else}:\\ \;\;\;\;a2 \cdot \frac{a1}{b1 \cdot b2}\\ \end{array} \]

Alternative 6: 86.5% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

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 / b2) * (a1 / b1)
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 84.1%

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

   1. times-frac 83.7%

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

3. Simplified 83.7%

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

4. Final simplification 83.7%

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

Developer target: 86.5% 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 2023215 
(FPCore (a1 a2 b1 b2)
  :name "Quotient of products"
  :precision binary64

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

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