Quotient of products

Percentage Accurate: 86.2% → 90.5%

Time: 3.5s

Alternatives: 5

Speedup: 1.0×

• 20.4% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

Fortran

real(8) function code(a1, a2, b1, b2)
    real(8), intent (in) :: a1
    real(8), intent (in) :: a2
    real(8), intent (in) :: b1
    real(8), intent (in) :: b2
    code = (a1 * a2) / (b1 * b2)
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 86.2% 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: 90.5% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a1 \cdot a2 \leq -4 \cdot 10^{-192}:\\ \;\;\;\;\frac{a2 \cdot \frac{a1}{b2}}{b1}\\ \mathbf{elif}\;a1 \cdot a2 \leq 2 \cdot 10^{-310}:\\ \;\;\;\;\frac{a2}{b2 \cdot \frac{b1}{a1}}\\ \mathbf{elif}\;a1 \cdot a2 \leq 5 \cdot 10^{+269}:\\ \;\;\;\;\frac{a1 \cdot a2}{b2} \cdot \frac{1}{b1}\\ \mathbf{else}:\\ \;\;\;\;a2 \cdot \frac{\frac{a1}{b2}}{b1}\\ \end{array} \end{array} \]

FPCore

(FPCore (a1 a2 b1 b2)
 :precision binary64
 (if (<= (* a1 a2) -4e-192)
   (/ (* a2 (/ a1 b2)) b1)
   (if (<= (* a1 a2) 2e-310)
     (/ a2 (* b2 (/ b1 a1)))
     (if (<= (* a1 a2) 5e+269)
       (* (/ (* a1 a2) b2) (/ 1.0 b1))
       (* a2 (/ (/ a1 b2) b1))))))

C

double code(double a1, double a2, double b1, double b2) {
	double tmp;
	if ((a1 * a2) <= -4e-192) {
		tmp = (a2 * (a1 / b2)) / b1;
	} else if ((a1 * a2) <= 2e-310) {
		tmp = a2 / (b2 * (b1 / a1));
	} else if ((a1 * a2) <= 5e+269) {
		tmp = ((a1 * a2) / b2) * (1.0 / b1);
	} else {
		tmp = a2 * ((a1 / b2) / b1);
	}
	return tmp;
}

Fortran

real(8) function code(a1, a2, b1, b2)
    real(8), intent (in) :: a1
    real(8), intent (in) :: a2
    real(8), intent (in) :: b1
    real(8), intent (in) :: b2
    real(8) :: tmp
    if ((a1 * a2) <= (-4d-192)) then
        tmp = (a2 * (a1 / b2)) / b1
    else if ((a1 * a2) <= 2d-310) then
        tmp = a2 / (b2 * (b1 / a1))
    else if ((a1 * a2) <= 5d+269) then
        tmp = ((a1 * a2) / b2) * (1.0d0 / b1)
    else
        tmp = a2 * ((a1 / b2) / b1)
    end if
    code = tmp
end function

Java

public static double code(double a1, double a2, double b1, double b2) {
	double tmp;
	if ((a1 * a2) <= -4e-192) {
		tmp = (a2 * (a1 / b2)) / b1;
	} else if ((a1 * a2) <= 2e-310) {
		tmp = a2 / (b2 * (b1 / a1));
	} else if ((a1 * a2) <= 5e+269) {
		tmp = ((a1 * a2) / b2) * (1.0 / b1);
	} else {
		tmp = a2 * ((a1 / b2) / b1);
	}
	return tmp;
}

Python

def code(a1, a2, b1, b2):
	tmp = 0
	if (a1 * a2) <= -4e-192:
		tmp = (a2 * (a1 / b2)) / b1
	elif (a1 * a2) <= 2e-310:
		tmp = a2 / (b2 * (b1 / a1))
	elif (a1 * a2) <= 5e+269:
		tmp = ((a1 * a2) / b2) * (1.0 / b1)
	else:
		tmp = a2 * ((a1 / b2) / b1)
	return tmp

Julia

function code(a1, a2, b1, b2)
	tmp = 0.0
	if (Float64(a1 * a2) <= -4e-192)
		tmp = Float64(Float64(a2 * Float64(a1 / b2)) / b1);
	elseif (Float64(a1 * a2) <= 2e-310)
		tmp = Float64(a2 / Float64(b2 * Float64(b1 / a1)));
	elseif (Float64(a1 * a2) <= 5e+269)
		tmp = Float64(Float64(Float64(a1 * a2) / b2) * Float64(1.0 / b1));
	else
		tmp = Float64(a2 * Float64(Float64(a1 / b2) / b1));
	end
	return tmp
end

MATLAB

function tmp_2 = code(a1, a2, b1, b2)
	tmp = 0.0;
	if ((a1 * a2) <= -4e-192)
		tmp = (a2 * (a1 / b2)) / b1;
	elseif ((a1 * a2) <= 2e-310)
		tmp = a2 / (b2 * (b1 / a1));
	elseif ((a1 * a2) <= 5e+269)
		tmp = ((a1 * a2) / b2) * (1.0 / b1);
	else
		tmp = a2 * ((a1 / b2) / b1);
	end
	tmp_2 = tmp;
end

Wolfram

code[a1_, a2_, b1_, b2_] := If[LessEqual[N[(a1 * a2), $MachinePrecision], -4e-192], N[(N[(a2 * N[(a1 / b2), $MachinePrecision]), $MachinePrecision] / b1), $MachinePrecision], If[LessEqual[N[(a1 * a2), $MachinePrecision], 2e-310], N[(a2 / N[(b2 * N[(b1 / a1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(a1 * a2), $MachinePrecision], 5e+269], N[(N[(N[(a1 * a2), $MachinePrecision] / b2), $MachinePrecision] * N[(1.0 / b1), $MachinePrecision]), $MachinePrecision], N[(a2 * N[(N[(a1 / b2), $MachinePrecision] / b1), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if (*.f64 a1 a2) < -4.0000000000000004e-192

   1. Initial program 86.1%

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

      1. times-frac 82.8%

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

   3. Simplified 82.8%

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

      1. frac-times 86.1%

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

      2. *-commutative 86.1%

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

      3. frac-times 84.9%

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

      4. associate-*r/ 95.2%

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

   5. Applied egg-rr 95.2%

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

   if -4.0000000000000004e-192 < (*.f64 a1 a2) < 1.999999999999994e-310

   1. Initial program 71.5%

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

      1. times-frac 93.2%

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

   3. Simplified 93.2%

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

      1. clear-num 93.0%

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

      2. frac-times 99.8%

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

      3. *-un-lft-identity 99.8%

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

   5. Applied egg-rr 99.8%

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

   if 1.999999999999994e-310 < (*.f64 a1 a2) < 5.0000000000000002e269

   1. Initial program 89.4%

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

      1. associate-/l* 82.7%

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

      2. *-commutative 82.7%

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

      3. associate-/l* 83.8%

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

   3. Simplified 83.8%

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

      1. associate-/r/ 85.7%

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

      2. frac-times 89.4%

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

      3. associate-/r* 98.7%

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

      4. associate-*r/ 91.5%

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

      5. div-inv 91.4%

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

      6. associate-*r/ 98.6%

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

   5. Applied egg-rr 98.6%

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

   if 5.0000000000000002e269 < (*.f64 a1 a2)

   1. Initial program 69.6%

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

      1. times-frac 88.7%

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

   3. Simplified 88.7%

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

      1. frac-times 69.6%

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

      2. *-commutative 69.6%

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

      3. frac-times 95.7%

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

      4. associate-*r/ 88.4%

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

   5. Applied egg-rr 88.4%

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

      1. associate-*l/ 99.9%

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

   7. Applied egg-rr 99.9%

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

4. Final simplification 97.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a1 \cdot a2 \leq -4 \cdot 10^{-192}:\\ \;\;\;\;\frac{a2 \cdot \frac{a1}{b2}}{b1}\\ \mathbf{elif}\;a1 \cdot a2 \leq 2 \cdot 10^{-310}:\\ \;\;\;\;\frac{a2}{b2 \cdot \frac{b1}{a1}}\\ \mathbf{elif}\;a1 \cdot a2 \leq 5 \cdot 10^{+269}:\\ \;\;\;\;\frac{a1 \cdot a2}{b2} \cdot \frac{1}{b1}\\ \mathbf{else}:\\ \;\;\;\;a2 \cdot \frac{\frac{a1}{b2}}{b1}\\ \end{array} \]

Alternative 2: 95.3% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{a1 \cdot a2}{b2 \cdot b1}\\ \mathbf{if}\;t_0 \leq -2 \cdot 10^{-279} \lor \neg \left(t_0 \leq 0\right) \land t_0 \leq 2 \cdot 10^{+293}:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;\frac{a1}{b1} \cdot \frac{a2}{b2}\\ \end{array} \end{array} \]

FPCore

(FPCore (a1 a2 b1 b2)
 :precision binary64
 (let* ((t_0 (/ (* a1 a2) (* b2 b1))))
   (if (or (<= t_0 -2e-279) (and (not (<= t_0 0.0)) (<= t_0 2e+293)))
     t_0
     (* (/ a1 b1) (/ a2 b2)))))

C

double code(double a1, double a2, double b1, double b2) {
	double t_0 = (a1 * a2) / (b2 * b1);
	double tmp;
	if ((t_0 <= -2e-279) || (!(t_0 <= 0.0) && (t_0 <= 2e+293))) {
		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 = (a1 * a2) / (b2 * b1)
    if ((t_0 <= (-2d-279)) .or. (.not. (t_0 <= 0.0d0)) .and. (t_0 <= 2d+293)) 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 = (a1 * a2) / (b2 * b1);
	double tmp;
	if ((t_0 <= -2e-279) || (!(t_0 <= 0.0) && (t_0 <= 2e+293))) {
		tmp = t_0;
	} else {
		tmp = (a1 / b1) * (a2 / b2);
	}
	return tmp;
}

Python

def code(a1, a2, b1, b2):
	t_0 = (a1 * a2) / (b2 * b1)
	tmp = 0
	if (t_0 <= -2e-279) or (not (t_0 <= 0.0) and (t_0 <= 2e+293)):
		tmp = t_0
	else:
		tmp = (a1 / b1) * (a2 / b2)
	return tmp

Julia

function code(a1, a2, b1, b2)
	t_0 = Float64(Float64(a1 * a2) / Float64(b2 * b1))
	tmp = 0.0
	if ((t_0 <= -2e-279) || (!(t_0 <= 0.0) && (t_0 <= 2e+293)))
		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 = (a1 * a2) / (b2 * b1);
	tmp = 0.0;
	if ((t_0 <= -2e-279) || (~((t_0 <= 0.0)) && (t_0 <= 2e+293)))
		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[(N[(a1 * a2), $MachinePrecision] / N[(b2 * b1), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[t$95$0, -2e-279], And[N[Not[LessEqual[t$95$0, 0.0]], $MachinePrecision], LessEqual[t$95$0, 2e+293]]], t$95$0, N[(N[(a1 / b1), $MachinePrecision] * N[(a2 / b2), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (*.f64 a1 a2) (*.f64 b1 b2)) < -2.00000000000000011e-279 or -0.0 < (/.f64 (*.f64 a1 a2) (*.f64 b1 b2)) < 1.9999999999999998e293

   1. Initial program 95.3%

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

   if -2.00000000000000011e-279 < (/.f64 (*.f64 a1 a2) (*.f64 b1 b2)) < -0.0 or 1.9999999999999998e293 < (/.f64 (*.f64 a1 a2) (*.f64 b1 b2))

   1. Initial program 69.7%

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

      1. times-frac 95.7%

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

   3. Simplified 95.7%

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

4. Final simplification 95.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{a1 \cdot a2}{b2 \cdot b1} \leq -2 \cdot 10^{-279} \lor \neg \left(\frac{a1 \cdot a2}{b2 \cdot b1} \leq 0\right) \land \frac{a1 \cdot a2}{b2 \cdot b1} \leq 2 \cdot 10^{+293}:\\ \;\;\;\;\frac{a1 \cdot a2}{b2 \cdot b1}\\ \mathbf{else}:\\ \;\;\;\;\frac{a1}{b1} \cdot \frac{a2}{b2}\\ \end{array} \]

Alternative 3: 86.6% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b1 \leq 1.25 \cdot 10^{+97}:\\ \;\;\;\;a2 \cdot \frac{\frac{a1}{b2}}{b1}\\ \mathbf{else}:\\ \;\;\;\;\frac{a1}{b1} \cdot \frac{a2}{b2}\\ \end{array} \end{array} \]

FPCore

(FPCore (a1 a2 b1 b2)
 :precision binary64
 (if (<= b1 1.25e+97) (* a2 (/ (/ a1 b2) b1)) (* (/ a1 b1) (/ a2 b2))))

C

double code(double a1, double a2, double b1, double b2) {
	double tmp;
	if (b1 <= 1.25e+97) {
		tmp = a2 * ((a1 / b2) / b1);
	} 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 <= 1.25d+97) then
        tmp = a2 * ((a1 / b2) / b1)
    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 <= 1.25e+97) {
		tmp = a2 * ((a1 / b2) / b1);
	} else {
		tmp = (a1 / b1) * (a2 / b2);
	}
	return tmp;
}

Python

def code(a1, a2, b1, b2):
	tmp = 0
	if b1 <= 1.25e+97:
		tmp = a2 * ((a1 / b2) / b1)
	else:
		tmp = (a1 / b1) * (a2 / b2)
	return tmp

Julia

function code(a1, a2, b1, b2)
	tmp = 0.0
	if (b1 <= 1.25e+97)
		tmp = Float64(a2 * Float64(Float64(a1 / b2) / b1));
	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 <= 1.25e+97)
		tmp = a2 * ((a1 / b2) / b1);
	else
		tmp = (a1 / b1) * (a2 / b2);
	end
	tmp_2 = tmp;
end

Wolfram

code[a1_, a2_, b1_, b2_] := If[LessEqual[b1, 1.25e+97], N[(a2 * N[(N[(a1 / b2), $MachinePrecision] / b1), $MachinePrecision]), $MachinePrecision], N[(N[(a1 / b1), $MachinePrecision] * N[(a2 / b2), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b1 < 1.25e97

   1. Initial program 83.0%

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

      1. times-frac 84.5%

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

   3. Simplified 84.5%

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

      1. frac-times 83.0%

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

      2. *-commutative 83.0%

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

      3. frac-times 87.6%

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

      4. associate-*r/ 92.1%

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

   5. Applied egg-rr 92.1%

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

      1. associate-*l/ 91.6%

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

   7. Applied egg-rr 91.6%

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

   if 1.25e97 < b1

   1. Initial program 82.8%

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

      1. times-frac 92.6%

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

   3. Simplified 92.6%

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

4. Final simplification 91.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b1 \leq 1.25 \cdot 10^{+97}:\\ \;\;\;\;a2 \cdot \frac{\frac{a1}{b2}}{b1}\\ \mathbf{else}:\\ \;\;\;\;\frac{a1}{b1} \cdot \frac{a2}{b2}\\ \end{array} \]

Alternative 4: 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]

Derivation

1. Initial program 82.9%

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

   1. times-frac 86.0%

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

3. Simplified 86.0%

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

4. Final simplification 86.0%

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

Alternative 5: 86.1% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 82.9%

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

   1. times-frac 86.0%

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

3. Simplified 86.0%

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

   1. frac-times 82.9%

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

   2. *-commutative 82.9%

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

   3. frac-times 87.6%

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

   4. associate-*r/ 92.0%

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

5. Applied egg-rr 92.0%

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

6. Final simplification 92.0%

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

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 2023252 
(FPCore (a1 a2 b1 b2)
  :name "Quotient of products"
  :precision binary64

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

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