Quotient of products

Percentage Accurate: 86.1% → 97.3%

Time: 4.7s

Alternatives: 6

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: 86.1% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 97.3% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{a1 \cdot a2}{b1 \cdot b2}\\ \mathbf{if}\;t_0 \leq -\infty \lor \neg \left(t_0 \leq -1 \cdot 10^{-313} \lor \neg \left(t_0 \leq 5 \cdot 10^{-309}\right) \land t_0 \leq 10^{+295}\right):\\ \;\;\;\;\frac{a2}{b2} \cdot \frac{a1}{b1}\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \end{array} \]

FPCore

(FPCore (a1 a2 b1 b2)
 :precision binary64
 (let* ((t_0 (/ (* a1 a2) (* b1 b2))))
   (if (or (<= t_0 (- INFINITY))
           (not
            (or (<= t_0 -1e-313) (and (not (<= t_0 5e-309)) (<= t_0 1e+295)))))
     (* (/ a2 b2) (/ a1 b1))
     t_0)))

C

double code(double a1, double a2, double b1, double b2) {
	double t_0 = (a1 * a2) / (b1 * b2);
	double tmp;
	if ((t_0 <= -((double) INFINITY)) || !((t_0 <= -1e-313) || (!(t_0 <= 5e-309) && (t_0 <= 1e+295)))) {
		tmp = (a2 / b2) * (a1 / b1);
	} else {
		tmp = t_0;
	}
	return tmp;
}

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 <= -Double.POSITIVE_INFINITY) || !((t_0 <= -1e-313) || (!(t_0 <= 5e-309) && (t_0 <= 1e+295)))) {
		tmp = (a2 / b2) * (a1 / b1);
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(a1, a2, b1, b2):
	t_0 = (a1 * a2) / (b1 * b2)
	tmp = 0
	if (t_0 <= -math.inf) or not ((t_0 <= -1e-313) or (not (t_0 <= 5e-309) and (t_0 <= 1e+295))):
		tmp = (a2 / b2) * (a1 / b1)
	else:
		tmp = t_0
	return tmp

Julia

function code(a1, a2, b1, b2)
	t_0 = Float64(Float64(a1 * a2) / Float64(b1 * b2))
	tmp = 0.0
	if ((t_0 <= Float64(-Inf)) || !((t_0 <= -1e-313) || (!(t_0 <= 5e-309) && (t_0 <= 1e+295))))
		tmp = Float64(Float64(a2 / b2) * Float64(a1 / b1));
	else
		tmp = t_0;
	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 <= -Inf) || ~(((t_0 <= -1e-313) || (~((t_0 <= 5e-309)) && (t_0 <= 1e+295)))))
		tmp = (a2 / b2) * (a1 / b1);
	else
		tmp = t_0;
	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[Or[LessEqual[t$95$0, (-Infinity)], N[Not[Or[LessEqual[t$95$0, -1e-313], And[N[Not[LessEqual[t$95$0, 5e-309]], $MachinePrecision], LessEqual[t$95$0, 1e+295]]]], $MachinePrecision]], N[(N[(a2 / b2), $MachinePrecision] * N[(a1 / b1), $MachinePrecision]), $MachinePrecision], t$95$0]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (*.f64 a1 a2) (*.f64 b1 b2)) < -inf.0 or -1.00000000001e-313 < (/.f64 (*.f64 a1 a2) (*.f64 b1 b2)) < 4.9999999999999995e-309 or 9.9999999999999998e294 < (/.f64 (*.f64 a1 a2) (*.f64 b1 b2))

   1. Initial program 76.1%

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

      1. times-frac 98.5%

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

      2. *-commutative 98.5%

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

   3. Simplified 98.5%

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

   if -inf.0 < (/.f64 (*.f64 a1 a2) (*.f64 b1 b2)) < -1.00000000001e-313 or 4.9999999999999995e-309 < (/.f64 (*.f64 a1 a2) (*.f64 b1 b2)) < 9.9999999999999998e294

   1. Initial program 97.8%

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

4. Final simplification 98.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{a1 \cdot a2}{b1 \cdot b2} \leq -\infty \lor \neg \left(\frac{a1 \cdot a2}{b1 \cdot b2} \leq -1 \cdot 10^{-313} \lor \neg \left(\frac{a1 \cdot a2}{b1 \cdot b2} \leq 5 \cdot 10^{-309}\right) \land \frac{a1 \cdot a2}{b1 \cdot b2} \leq 10^{+295}\right):\\ \;\;\;\;\frac{a2}{b2} \cdot \frac{a1}{b1}\\ \mathbf{else}:\\ \;\;\;\;\frac{a1 \cdot a2}{b1 \cdot b2}\\ \end{array} \]

Alternative 2: 86.4% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{a2}{b1} \cdot \frac{a1}{b2}\\ \mathbf{if}\;a1 \leq -4.7 \cdot 10^{-35}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;a1 \leq 7 \cdot 10^{-190}:\\ \;\;\;\;a2 \cdot \frac{a1}{b1 \cdot b2}\\ \mathbf{elif}\;a1 \leq 1.02 \cdot 10^{+144}:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;\frac{a2}{b2} \cdot \frac{a1}{b1}\\ \end{array} \end{array} \]

FPCore

(FPCore (a1 a2 b1 b2)
 :precision binary64
 (let* ((t_0 (* (/ a2 b1) (/ a1 b2))))
   (if (<= a1 -4.7e-35)
     t_0
     (if (<= a1 7e-190)
       (* a2 (/ a1 (* b1 b2)))
       (if (<= a1 1.02e+144) t_0 (* (/ a2 b2) (/ a1 b1)))))))

C

double code(double a1, double a2, double b1, double b2) {
	double t_0 = (a2 / b1) * (a1 / b2);
	double tmp;
	if (a1 <= -4.7e-35) {
		tmp = t_0;
	} else if (a1 <= 7e-190) {
		tmp = a2 * (a1 / (b1 * b2));
	} else if (a1 <= 1.02e+144) {
		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 = (a2 / b1) * (a1 / b2)
    if (a1 <= (-4.7d-35)) then
        tmp = t_0
    else if (a1 <= 7d-190) then
        tmp = a2 * (a1 / (b1 * b2))
    else if (a1 <= 1.02d+144) 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 = (a2 / b1) * (a1 / b2);
	double tmp;
	if (a1 <= -4.7e-35) {
		tmp = t_0;
	} else if (a1 <= 7e-190) {
		tmp = a2 * (a1 / (b1 * b2));
	} else if (a1 <= 1.02e+144) {
		tmp = t_0;
	} else {
		tmp = (a2 / b2) * (a1 / b1);
	}
	return tmp;
}

Python

def code(a1, a2, b1, b2):
	t_0 = (a2 / b1) * (a1 / b2)
	tmp = 0
	if a1 <= -4.7e-35:
		tmp = t_0
	elif a1 <= 7e-190:
		tmp = a2 * (a1 / (b1 * b2))
	elif a1 <= 1.02e+144:
		tmp = t_0
	else:
		tmp = (a2 / b2) * (a1 / b1)
	return tmp

Julia

function code(a1, a2, b1, b2)
	t_0 = Float64(Float64(a2 / b1) * Float64(a1 / b2))
	tmp = 0.0
	if (a1 <= -4.7e-35)
		tmp = t_0;
	elseif (a1 <= 7e-190)
		tmp = Float64(a2 * Float64(a1 / Float64(b1 * b2)));
	elseif (a1 <= 1.02e+144)
		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 = (a2 / b1) * (a1 / b2);
	tmp = 0.0;
	if (a1 <= -4.7e-35)
		tmp = t_0;
	elseif (a1 <= 7e-190)
		tmp = a2 * (a1 / (b1 * b2));
	elseif (a1 <= 1.02e+144)
		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[(N[(a2 / b1), $MachinePrecision] * N[(a1 / b2), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a1, -4.7e-35], t$95$0, If[LessEqual[a1, 7e-190], N[(a2 * N[(a1 / N[(b1 * b2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a1, 1.02e+144], t$95$0, N[(N[(a2 / b2), $MachinePrecision] * N[(a1 / b1), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if a1 < -4.7e-35 or 6.9999999999999999e-190 < a1 < 1.02000000000000008e144

   1. Initial program 84.0%

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

      1. *-commutative 84.0%

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

      2. times-frac 92.4%

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

   3. Applied egg-rr 92.4%

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

   if -4.7e-35 < a1 < 6.9999999999999999e-190

   1. Initial program 89.9%

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

      1. associate-/l* 87.0%

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

      2. associate-/r/ 90.9%

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

      3. *-commutative 90.9%

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

   3. Applied egg-rr 90.9%

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

   if 1.02000000000000008e144 < a1

   1. Initial program 86.3%

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

      1. times-frac 83.9%

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

      2. *-commutative 83.9%

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

   3. Simplified 83.9%

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

4. Final simplification 90.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a1 \leq -4.7 \cdot 10^{-35}:\\ \;\;\;\;\frac{a2}{b1} \cdot \frac{a1}{b2}\\ \mathbf{elif}\;a1 \leq 7 \cdot 10^{-190}:\\ \;\;\;\;a2 \cdot \frac{a1}{b1 \cdot b2}\\ \mathbf{elif}\;a1 \leq 1.02 \cdot 10^{+144}:\\ \;\;\;\;\frac{a2}{b1} \cdot \frac{a1}{b2}\\ \mathbf{else}:\\ \;\;\;\;\frac{a2}{b2} \cdot \frac{a1}{b1}\\ \end{array} \]

Alternative 3: 86.4% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{a2}{b1} \cdot \frac{a1}{b2}\\ \mathbf{if}\;a1 \leq -3.4 \cdot 10^{-35}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;a1 \leq 1.95 \cdot 10^{-190}:\\ \;\;\;\;a2 \cdot \frac{a1}{b1 \cdot b2}\\ \mathbf{elif}\;a1 \leq 1.02 \cdot 10^{+144}:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;\frac{a1}{b1 \cdot \frac{b2}{a2}}\\ \end{array} \end{array} \]

FPCore

(FPCore (a1 a2 b1 b2)
 :precision binary64
 (let* ((t_0 (* (/ a2 b1) (/ a1 b2))))
   (if (<= a1 -3.4e-35)
     t_0
     (if (<= a1 1.95e-190)
       (* a2 (/ a1 (* b1 b2)))
       (if (<= a1 1.02e+144) t_0 (/ a1 (* b1 (/ b2 a2))))))))

C

double code(double a1, double a2, double b1, double b2) {
	double t_0 = (a2 / b1) * (a1 / b2);
	double tmp;
	if (a1 <= -3.4e-35) {
		tmp = t_0;
	} else if (a1 <= 1.95e-190) {
		tmp = a2 * (a1 / (b1 * b2));
	} else if (a1 <= 1.02e+144) {
		tmp = t_0;
	} else {
		tmp = a1 / (b1 * (b2 / a2));
	}
	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 / b1) * (a1 / b2)
    if (a1 <= (-3.4d-35)) then
        tmp = t_0
    else if (a1 <= 1.95d-190) then
        tmp = a2 * (a1 / (b1 * b2))
    else if (a1 <= 1.02d+144) then
        tmp = t_0
    else
        tmp = a1 / (b1 * (b2 / a2))
    end if
    code = tmp
end function

Java

public static double code(double a1, double a2, double b1, double b2) {
	double t_0 = (a2 / b1) * (a1 / b2);
	double tmp;
	if (a1 <= -3.4e-35) {
		tmp = t_0;
	} else if (a1 <= 1.95e-190) {
		tmp = a2 * (a1 / (b1 * b2));
	} else if (a1 <= 1.02e+144) {
		tmp = t_0;
	} else {
		tmp = a1 / (b1 * (b2 / a2));
	}
	return tmp;
}

Python

def code(a1, a2, b1, b2):
	t_0 = (a2 / b1) * (a1 / b2)
	tmp = 0
	if a1 <= -3.4e-35:
		tmp = t_0
	elif a1 <= 1.95e-190:
		tmp = a2 * (a1 / (b1 * b2))
	elif a1 <= 1.02e+144:
		tmp = t_0
	else:
		tmp = a1 / (b1 * (b2 / a2))
	return tmp

Julia

function code(a1, a2, b1, b2)
	t_0 = Float64(Float64(a2 / b1) * Float64(a1 / b2))
	tmp = 0.0
	if (a1 <= -3.4e-35)
		tmp = t_0;
	elseif (a1 <= 1.95e-190)
		tmp = Float64(a2 * Float64(a1 / Float64(b1 * b2)));
	elseif (a1 <= 1.02e+144)
		tmp = t_0;
	else
		tmp = Float64(a1 / Float64(b1 * Float64(b2 / a2)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(a1, a2, b1, b2)
	t_0 = (a2 / b1) * (a1 / b2);
	tmp = 0.0;
	if (a1 <= -3.4e-35)
		tmp = t_0;
	elseif (a1 <= 1.95e-190)
		tmp = a2 * (a1 / (b1 * b2));
	elseif (a1 <= 1.02e+144)
		tmp = t_0;
	else
		tmp = a1 / (b1 * (b2 / a2));
	end
	tmp_2 = tmp;
end

Wolfram

code[a1_, a2_, b1_, b2_] := Block[{t$95$0 = N[(N[(a2 / b1), $MachinePrecision] * N[(a1 / b2), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a1, -3.4e-35], t$95$0, If[LessEqual[a1, 1.95e-190], N[(a2 * N[(a1 / N[(b1 * b2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a1, 1.02e+144], t$95$0, N[(a1 / N[(b1 * N[(b2 / a2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if a1 < -3.4000000000000003e-35 or 1.94999999999999997e-190 < a1 < 1.02000000000000008e144

   1. Initial program 84.0%

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

      1. *-commutative 84.0%

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

      2. times-frac 92.4%

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

   3. Applied egg-rr 92.4%

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

   if -3.4000000000000003e-35 < a1 < 1.94999999999999997e-190

   1. Initial program 89.9%

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

      1. associate-/l* 87.0%

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

      2. associate-/r/ 90.9%

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

      3. *-commutative 90.9%

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

   3. Applied egg-rr 90.9%

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

   if 1.02000000000000008e144 < a1

   1. Initial program 86.3%

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

      1. times-frac 83.9%

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

      2. *-commutative 83.9%

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

   3. Simplified 83.9%

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

      1. clear-num 83.9%

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

      2. frac-times 84.6%

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

      3. *-un-lft-identity 84.6%

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

   5. Applied egg-rr 84.6%

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

4. Final simplification 90.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a1 \leq -3.4 \cdot 10^{-35}:\\ \;\;\;\;\frac{a2}{b1} \cdot \frac{a1}{b2}\\ \mathbf{elif}\;a1 \leq 1.95 \cdot 10^{-190}:\\ \;\;\;\;a2 \cdot \frac{a1}{b1 \cdot b2}\\ \mathbf{elif}\;a1 \leq 1.02 \cdot 10^{+144}:\\ \;\;\;\;\frac{a2}{b1} \cdot \frac{a1}{b2}\\ \mathbf{else}:\\ \;\;\;\;\frac{a1}{b1 \cdot \frac{b2}{a2}}\\ \end{array} \]

Alternative 4: 86.6% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a1 \leq -3 \cdot 10^{-35} \lor \neg \left(a1 \leq 7.5 \cdot 10^{-190}\right):\\ \;\;\;\;\frac{a2}{b1} \cdot \frac{a1}{b2}\\ \mathbf{else}:\\ \;\;\;\;a2 \cdot \frac{a1}{b1 \cdot b2}\\ \end{array} \end{array} \]

FPCore

(FPCore (a1 a2 b1 b2)
 :precision binary64
 (if (or (<= a1 -3e-35) (not (<= a1 7.5e-190)))
   (* (/ a2 b1) (/ a1 b2))
   (* a2 (/ a1 (* b1 b2)))))

C

double code(double a1, double a2, double b1, double b2) {
	double tmp;
	if ((a1 <= -3e-35) || !(a1 <= 7.5e-190)) {
		tmp = (a2 / b1) * (a1 / b2);
	} else {
		tmp = a2 * (a1 / (b1 * b2));
	}
	return tmp;
}

Fortran

real(8) function code(a1, a2, b1, b2)
    real(8), intent (in) :: a1
    real(8), intent (in) :: a2
    real(8), intent (in) :: b1
    real(8), intent (in) :: b2
    real(8) :: tmp
    if ((a1 <= (-3d-35)) .or. (.not. (a1 <= 7.5d-190))) then
        tmp = (a2 / b1) * (a1 / b2)
    else
        tmp = a2 * (a1 / (b1 * b2))
    end if
    code = tmp
end function

Java

public static double code(double a1, double a2, double b1, double b2) {
	double tmp;
	if ((a1 <= -3e-35) || !(a1 <= 7.5e-190)) {
		tmp = (a2 / b1) * (a1 / b2);
	} else {
		tmp = a2 * (a1 / (b1 * b2));
	}
	return tmp;
}

Python

def code(a1, a2, b1, b2):
	tmp = 0
	if (a1 <= -3e-35) or not (a1 <= 7.5e-190):
		tmp = (a2 / b1) * (a1 / b2)
	else:
		tmp = a2 * (a1 / (b1 * b2))
	return tmp

Julia

function code(a1, a2, b1, b2)
	tmp = 0.0
	if ((a1 <= -3e-35) || !(a1 <= 7.5e-190))
		tmp = Float64(Float64(a2 / b1) * Float64(a1 / 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 ((a1 <= -3e-35) || ~((a1 <= 7.5e-190)))
		tmp = (a2 / b1) * (a1 / b2);
	else
		tmp = a2 * (a1 / (b1 * b2));
	end
	tmp_2 = tmp;
end

Wolfram

code[a1_, a2_, b1_, b2_] := If[Or[LessEqual[a1, -3e-35], N[Not[LessEqual[a1, 7.5e-190]], $MachinePrecision]], N[(N[(a2 / b1), $MachinePrecision] * N[(a1 / b2), $MachinePrecision]), $MachinePrecision], N[(a2 * N[(a1 / N[(b1 * b2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a1 < -2.99999999999999989e-35 or 7.5e-190 < a1

   1. Initial program 84.5%

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

      1. *-commutative 84.5%

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

      2. times-frac 87.7%

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

   3. Applied egg-rr 87.7%

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

   if -2.99999999999999989e-35 < a1 < 7.5e-190

   1. Initial program 89.9%

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

      1. associate-/l* 87.0%

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

      2. associate-/r/ 90.9%

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

      3. *-commutative 90.9%

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

   3. Applied egg-rr 90.9%

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

4. Final simplification 88.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a1 \leq -3 \cdot 10^{-35} \lor \neg \left(a1 \leq 7.5 \cdot 10^{-190}\right):\\ \;\;\;\;\frac{a2}{b1} \cdot \frac{a1}{b2}\\ \mathbf{else}:\\ \;\;\;\;a2 \cdot \frac{a1}{b1 \cdot b2}\\ \end{array} \]

Alternative 5: 86.4% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b2 \leq 2.6 \cdot 10^{-94}:\\ \;\;\;\;\frac{a2}{b1} \cdot \frac{a1}{b2}\\ \mathbf{else}:\\ \;\;\;\;\frac{a2}{b2 \cdot \frac{b1}{a1}}\\ \end{array} \end{array} \]

FPCore

(FPCore (a1 a2 b1 b2)
 :precision binary64
 (if (<= b2 2.6e-94) (* (/ a2 b1) (/ a1 b2)) (/ a2 (* b2 (/ b1 a1)))))

C

double code(double a1, double a2, double b1, double b2) {
	double tmp;
	if (b2 <= 2.6e-94) {
		tmp = (a2 / b1) * (a1 / b2);
	} else {
		tmp = a2 / (b2 * (b1 / a1));
	}
	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 (b2 <= 2.6d-94) then
        tmp = (a2 / b1) * (a1 / b2)
    else
        tmp = a2 / (b2 * (b1 / a1))
    end if
    code = tmp
end function

Java

public static double code(double a1, double a2, double b1, double b2) {
	double tmp;
	if (b2 <= 2.6e-94) {
		tmp = (a2 / b1) * (a1 / b2);
	} else {
		tmp = a2 / (b2 * (b1 / a1));
	}
	return tmp;
}

Python

def code(a1, a2, b1, b2):
	tmp = 0
	if b2 <= 2.6e-94:
		tmp = (a2 / b1) * (a1 / b2)
	else:
		tmp = a2 / (b2 * (b1 / a1))
	return tmp

Julia

function code(a1, a2, b1, b2)
	tmp = 0.0
	if (b2 <= 2.6e-94)
		tmp = Float64(Float64(a2 / b1) * Float64(a1 / b2));
	else
		tmp = Float64(a2 / Float64(b2 * Float64(b1 / a1)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(a1, a2, b1, b2)
	tmp = 0.0;
	if (b2 <= 2.6e-94)
		tmp = (a2 / b1) * (a1 / b2);
	else
		tmp = a2 / (b2 * (b1 / a1));
	end
	tmp_2 = tmp;
end

Wolfram

code[a1_, a2_, b1_, b2_] := If[LessEqual[b2, 2.6e-94], N[(N[(a2 / b1), $MachinePrecision] * N[(a1 / b2), $MachinePrecision]), $MachinePrecision], N[(a2 / N[(b2 * N[(b1 / a1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b2 < 2.59999999999999994e-94

   1. Initial program 85.0%

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

      1. *-commutative 85.0%

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

      2. times-frac 87.9%

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

   3. Applied egg-rr 87.9%

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

   if 2.59999999999999994e-94 < b2

   1. Initial program 89.1%

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

      1. times-frac 83.7%

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

      2. *-commutative 83.7%

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

   3. Simplified 83.7%

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

      1. *-commutative 83.7%

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

      2. clear-num 83.4%

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

      3. frac-times 87.6%

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

      4. *-un-lft-identity 87.6%

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

   5. Applied egg-rr 87.6%

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

4. Final simplification 87.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b2 \leq 2.6 \cdot 10^{-94}:\\ \;\;\;\;\frac{a2}{b1} \cdot \frac{a1}{b2}\\ \mathbf{else}:\\ \;\;\;\;\frac{a2}{b2 \cdot \frac{b1}{a1}}\\ \end{array} \]

Alternative 6: 86.5% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 86.4%

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

   1. associate-/l* 85.9%

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

   2. associate-/r/ 84.7%

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

   3. *-commutative 84.7%

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

3. Applied egg-rr 84.7%

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

4. Final simplification 84.7%

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

Developer target: 86.4% 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 2023285 
(FPCore (a1 a2 b1 b2)
  :name "Quotient of products"
  :precision binary64

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

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