Quotient of products

Percentage Accurate: 85.8% → 96.7%

Time: 5.3s

Alternatives: 4

Speedup: 1.0×

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: 85.8% 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: 96.7% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{a1 \cdot a2}{b1 \cdot b2}\\ \mathbf{if}\;t_0 \leq -5 \cdot 10^{+250}:\\ \;\;\;\;\frac{a1}{b1 \cdot \frac{b2}{a2}}\\ \mathbf{elif}\;t_0 \leq -2 \cdot 10^{-304} \lor \neg \left(t_0 \leq 2 \cdot 10^{-317}\right) \land t_0 \leq 10^{+301}:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;\frac{a2}{b1} \cdot \frac{a1}{b2}\\ \end{array} \end{array} \]

FPCore

(FPCore (a1 a2 b1 b2)
 :precision binary64
 (let* ((t_0 (/ (* a1 a2) (* b1 b2))))
   (if (<= t_0 -5e+250)
     (/ a1 (* b1 (/ b2 a2)))
     (if (or (<= t_0 -2e-304) (and (not (<= t_0 2e-317)) (<= t_0 1e+301)))
       t_0
       (* (/ a2 b1) (/ a1 b2))))))

C

double code(double a1, double a2, double b1, double b2) {
	double t_0 = (a1 * a2) / (b1 * b2);
	double tmp;
	if (t_0 <= -5e+250) {
		tmp = a1 / (b1 * (b2 / a2));
	} else if ((t_0 <= -2e-304) || (!(t_0 <= 2e-317) && (t_0 <= 1e+301))) {
		tmp = t_0;
	} else {
		tmp = (a2 / b1) * (a1 / 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 = (a1 * a2) / (b1 * b2)
    if (t_0 <= (-5d+250)) then
        tmp = a1 / (b1 * (b2 / a2))
    else if ((t_0 <= (-2d-304)) .or. (.not. (t_0 <= 2d-317)) .and. (t_0 <= 1d+301)) then
        tmp = t_0
    else
        tmp = (a2 / b1) * (a1 / b2)
    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 tmp;
	if (t_0 <= -5e+250) {
		tmp = a1 / (b1 * (b2 / a2));
	} else if ((t_0 <= -2e-304) || (!(t_0 <= 2e-317) && (t_0 <= 1e+301))) {
		tmp = t_0;
	} else {
		tmp = (a2 / b1) * (a1 / b2);
	}
	return tmp;
}

Python

def code(a1, a2, b1, b2):
	t_0 = (a1 * a2) / (b1 * b2)
	tmp = 0
	if t_0 <= -5e+250:
		tmp = a1 / (b1 * (b2 / a2))
	elif (t_0 <= -2e-304) or (not (t_0 <= 2e-317) and (t_0 <= 1e+301)):
		tmp = t_0
	else:
		tmp = (a2 / b1) * (a1 / b2)
	return tmp

Julia

function code(a1, a2, b1, b2)
	t_0 = Float64(Float64(a1 * a2) / Float64(b1 * b2))
	tmp = 0.0
	if (t_0 <= -5e+250)
		tmp = Float64(a1 / Float64(b1 * Float64(b2 / a2)));
	elseif ((t_0 <= -2e-304) || (!(t_0 <= 2e-317) && (t_0 <= 1e+301)))
		tmp = t_0;
	else
		tmp = Float64(Float64(a2 / b1) * Float64(a1 / b2));
	end
	return tmp
end

MATLAB

function tmp_2 = code(a1, a2, b1, b2)
	t_0 = (a1 * a2) / (b1 * b2);
	tmp = 0.0;
	if (t_0 <= -5e+250)
		tmp = a1 / (b1 * (b2 / a2));
	elseif ((t_0 <= -2e-304) || (~((t_0 <= 2e-317)) && (t_0 <= 1e+301)))
		tmp = t_0;
	else
		tmp = (a2 / b1) * (a1 / 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]}, If[LessEqual[t$95$0, -5e+250], N[(a1 / N[(b1 * N[(b2 / a2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[t$95$0, -2e-304], And[N[Not[LessEqual[t$95$0, 2e-317]], $MachinePrecision], LessEqual[t$95$0, 1e+301]]], t$95$0, N[(N[(a2 / b1), $MachinePrecision] * N[(a1 / b2), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 (*.f64 a1 a2) (*.f64 b1 b2)) < -5.0000000000000002e250

   1. Initial program 83.5%

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

      1. times-frac 93.4%

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

      2. *-commutative 93.4%

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

   3. Simplified 93.4%

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

      1. clear-num 93.4%

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

      2. frac-times 99.9%

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

      3. *-un-lft-identity 99.9%

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

   5. Applied egg-rr 99.9%

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

   if -5.0000000000000002e250 < (/.f64 (*.f64 a1 a2) (*.f64 b1 b2)) < -1.99999999999999994e-304 or 1.99999997e-317 < (/.f64 (*.f64 a1 a2) (*.f64 b1 b2)) < 1.00000000000000005e301

   1. Initial program 99.4%

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

   if -1.99999999999999994e-304 < (/.f64 (*.f64 a1 a2) (*.f64 b1 b2)) < 1.99999997e-317 or 1.00000000000000005e301 < (/.f64 (*.f64 a1 a2) (*.f64 b1 b2))

   1. Initial program 74.2%

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

      1. *-commutative 74.2%

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

      2. times-frac 97.0%

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

   3. Applied egg-rr 97.0%

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

4. Final simplification 98.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{a1 \cdot a2}{b1 \cdot b2} \leq -5 \cdot 10^{+250}:\\ \;\;\;\;\frac{a1}{b1 \cdot \frac{b2}{a2}}\\ \mathbf{elif}\;\frac{a1 \cdot a2}{b1 \cdot b2} \leq -2 \cdot 10^{-304} \lor \neg \left(\frac{a1 \cdot a2}{b1 \cdot b2} \leq 2 \cdot 10^{-317}\right) \land \frac{a1 \cdot a2}{b1 \cdot b2} \leq 10^{+301}:\\ \;\;\;\;\frac{a1 \cdot a2}{b1 \cdot b2}\\ \mathbf{else}:\\ \;\;\;\;\frac{a2}{b1} \cdot \frac{a1}{b2}\\ \end{array} \]

Alternative 2: 91.3% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := a1 \cdot \frac{a2}{b1 \cdot b2}\\ \mathbf{if}\;b1 \cdot b2 \leq -1 \cdot 10^{-287}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;b1 \cdot b2 \leq 5 \cdot 10^{-251}:\\ \;\;\;\;\frac{a2}{b1} \cdot \frac{a1}{b2}\\ \mathbf{elif}\;b1 \cdot b2 \leq 5 \cdot 10^{+275}:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;\frac{a2}{b2} \cdot \frac{a1}{b1}\\ \end{array} \end{array} \]

FPCore

(FPCore (a1 a2 b1 b2)
 :precision binary64
 (let* ((t_0 (* a1 (/ a2 (* b1 b2)))))
   (if (<= (* b1 b2) -1e-287)
     t_0
     (if (<= (* b1 b2) 5e-251)
       (* (/ a2 b1) (/ a1 b2))
       (if (<= (* b1 b2) 5e+275) t_0 (* (/ a2 b2) (/ a1 b1)))))))

C

double code(double a1, double a2, double b1, double b2) {
	double t_0 = a1 * (a2 / (b1 * b2));
	double tmp;
	if ((b1 * b2) <= -1e-287) {
		tmp = t_0;
	} else if ((b1 * b2) <= 5e-251) {
		tmp = (a2 / b1) * (a1 / b2);
	} else if ((b1 * b2) <= 5e+275) {
		tmp = t_0;
	} 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) :: t_0
    real(8) :: tmp
    t_0 = a1 * (a2 / (b1 * b2))
    if ((b1 * b2) <= (-1d-287)) then
        tmp = t_0
    else if ((b1 * b2) <= 5d-251) then
        tmp = (a2 / b1) * (a1 / b2)
    else if ((b1 * b2) <= 5d+275) then
        tmp = t_0
    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 t_0 = a1 * (a2 / (b1 * b2));
	double tmp;
	if ((b1 * b2) <= -1e-287) {
		tmp = t_0;
	} else if ((b1 * b2) <= 5e-251) {
		tmp = (a2 / b1) * (a1 / b2);
	} else if ((b1 * b2) <= 5e+275) {
		tmp = t_0;
	} else {
		tmp = (a2 / b2) * (a1 / b1);
	}
	return tmp;
}

Python

def code(a1, a2, b1, b2):
	t_0 = a1 * (a2 / (b1 * b2))
	tmp = 0
	if (b1 * b2) <= -1e-287:
		tmp = t_0
	elif (b1 * b2) <= 5e-251:
		tmp = (a2 / b1) * (a1 / b2)
	elif (b1 * b2) <= 5e+275:
		tmp = t_0
	else:
		tmp = (a2 / b2) * (a1 / b1)
	return tmp

Julia

function code(a1, a2, b1, b2)
	t_0 = Float64(a1 * Float64(a2 / Float64(b1 * b2)))
	tmp = 0.0
	if (Float64(b1 * b2) <= -1e-287)
		tmp = t_0;
	elseif (Float64(b1 * b2) <= 5e-251)
		tmp = Float64(Float64(a2 / b1) * Float64(a1 / b2));
	elseif (Float64(b1 * b2) <= 5e+275)
		tmp = t_0;
	else
		tmp = Float64(Float64(a2 / b2) * Float64(a1 / b1));
	end
	return tmp
end

MATLAB

function tmp_2 = code(a1, a2, b1, b2)
	t_0 = a1 * (a2 / (b1 * b2));
	tmp = 0.0;
	if ((b1 * b2) <= -1e-287)
		tmp = t_0;
	elseif ((b1 * b2) <= 5e-251)
		tmp = (a2 / b1) * (a1 / b2);
	elseif ((b1 * b2) <= 5e+275)
		tmp = t_0;
	else
		tmp = (a2 / b2) * (a1 / b1);
	end
	tmp_2 = tmp;
end

Wolfram

code[a1_, a2_, b1_, b2_] := Block[{t$95$0 = N[(a1 * N[(a2 / N[(b1 * b2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(b1 * b2), $MachinePrecision], -1e-287], t$95$0, If[LessEqual[N[(b1 * b2), $MachinePrecision], 5e-251], N[(N[(a2 / b1), $MachinePrecision] * N[(a1 / b2), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(b1 * b2), $MachinePrecision], 5e+275], t$95$0, N[(N[(a2 / b2), $MachinePrecision] * N[(a1 / b1), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 b1 b2) < -1.00000000000000002e-287 or 5.0000000000000003e-251 < (*.f64 b1 b2) < 5.0000000000000003e275

   1. Initial program 89.8%

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

      1. times-frac 82.0%

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

      2. *-commutative 82.0%

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

   3. Simplified 82.0%

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

   4. Taylor expanded in a2 around 0 89.8%

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

      1. *-commutative 89.8%

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

      2. associate-*r/ 94.1%

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

      3. *-commutative 94.1%

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

   6. Simplified 94.1%

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

   if -1.00000000000000002e-287 < (*.f64 b1 b2) < 5.0000000000000003e-251

   1. Initial program 76.2%

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

      1. *-commutative 76.2%

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

      2. times-frac 99.8%

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

   3. Applied egg-rr 99.8%

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

   if 5.0000000000000003e275 < (*.f64 b1 b2)

   1. Initial program 80.5%

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

      1. times-frac 99.8%

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

      2. *-commutative 99.8%

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

   3. Simplified 99.8%

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

4. Final simplification 95.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b1 \cdot b2 \leq -1 \cdot 10^{-287}:\\ \;\;\;\;a1 \cdot \frac{a2}{b1 \cdot b2}\\ \mathbf{elif}\;b1 \cdot b2 \leq 5 \cdot 10^{-251}:\\ \;\;\;\;\frac{a2}{b1} \cdot \frac{a1}{b2}\\ \mathbf{elif}\;b1 \cdot b2 \leq 5 \cdot 10^{+275}:\\ \;\;\;\;a1 \cdot \frac{a2}{b1 \cdot b2}\\ \mathbf{else}:\\ \;\;\;\;\frac{a2}{b2} \cdot \frac{a1}{b1}\\ \end{array} \]

Alternative 3: 85.5% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a1 \leq 7.8 \cdot 10^{-109}:\\ \;\;\;\;a1 \cdot \frac{a2}{b1 \cdot b2}\\ \mathbf{else}:\\ \;\;\;\;\frac{a2}{b1} \cdot \frac{a1}{b2}\\ \end{array} \end{array} \]

FPCore

(FPCore (a1 a2 b1 b2)
 :precision binary64
 (if (<= a1 7.8e-109) (* a1 (/ a2 (* b1 b2))) (* (/ a2 b1) (/ a1 b2))))

C

double code(double a1, double a2, double b1, double b2) {
	double tmp;
	if (a1 <= 7.8e-109) {
		tmp = a1 * (a2 / (b1 * b2));
	} else {
		tmp = (a2 / b1) * (a1 / 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 (a1 <= 7.8d-109) then
        tmp = a1 * (a2 / (b1 * b2))
    else
        tmp = (a2 / b1) * (a1 / b2)
    end if
    code = tmp
end function

Java

public static double code(double a1, double a2, double b1, double b2) {
	double tmp;
	if (a1 <= 7.8e-109) {
		tmp = a1 * (a2 / (b1 * b2));
	} else {
		tmp = (a2 / b1) * (a1 / b2);
	}
	return tmp;
}

Python

def code(a1, a2, b1, b2):
	tmp = 0
	if a1 <= 7.8e-109:
		tmp = a1 * (a2 / (b1 * b2))
	else:
		tmp = (a2 / b1) * (a1 / b2)
	return tmp

Julia

function code(a1, a2, b1, b2)
	tmp = 0.0
	if (a1 <= 7.8e-109)
		tmp = Float64(a1 * Float64(a2 / Float64(b1 * b2)));
	else
		tmp = Float64(Float64(a2 / b1) * Float64(a1 / b2));
	end
	return tmp
end

MATLAB

function tmp_2 = code(a1, a2, b1, b2)
	tmp = 0.0;
	if (a1 <= 7.8e-109)
		tmp = a1 * (a2 / (b1 * b2));
	else
		tmp = (a2 / b1) * (a1 / b2);
	end
	tmp_2 = tmp;
end

Wolfram

code[a1_, a2_, b1_, b2_] := If[LessEqual[a1, 7.8e-109], N[(a1 * N[(a2 / N[(b1 * b2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(a2 / b1), $MachinePrecision] * N[(a1 / b2), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a1 < 7.80000000000000046e-109

   1. Initial program 88.1%

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

      1. times-frac 84.2%

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

      2. *-commutative 84.2%

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

   3. Simplified 84.2%

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

   4. Taylor expanded in a2 around 0 88.1%

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

      1. *-commutative 88.1%

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

      2. associate-*r/ 90.8%

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

      3. *-commutative 90.8%

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

   6. Simplified 90.8%

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

   if 7.80000000000000046e-109 < a1

   1. Initial program 84.6%

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

      1. *-commutative 84.6%

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

      2. times-frac 94.8%

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

   3. Applied egg-rr 94.8%

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

4. Final simplification 92.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a1 \leq 7.8 \cdot 10^{-109}:\\ \;\;\;\;a1 \cdot \frac{a2}{b1 \cdot b2}\\ \mathbf{else}:\\ \;\;\;\;\frac{a2}{b1} \cdot \frac{a1}{b2}\\ \end{array} \]

Alternative 4: 85.8% accurate, 1.0× speedup

Math

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

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(a1 * Float64(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[(a1 * N[(a2 / N[(b1 * b2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 86.9%

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

   1. times-frac 85.1%

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

   2. *-commutative 85.1%

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

3. Simplified 85.1%

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

4. Taylor expanded in a2 around 0 86.9%

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

   1. *-commutative 86.9%

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

   2. associate-*r/ 90.1%

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

   3. *-commutative 90.1%

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

6. Simplified 90.1%

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

7. Final simplification 90.1%

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

Developer target: 85.6% 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 2023283 
(FPCore (a1 a2 b1 b2)
  :name "Quotient of products"
  :precision binary64

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

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