Quotient of products

Percentage Accurate: 86.4% → 95.4%

Time: 4.2s

Alternatives: 6

Speedup: 0.8×

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: 86.4% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 95.4% accurate, 0.2× speedup

Math

\[\begin{array}{l} [a1, a2] = \mathsf{sort}([a1, a2])\\ [b1, b2] = \mathsf{sort}([b1, b2])\\ \\ \begin{array}{l} t_0 := \frac{a1 \cdot a2}{b1 \cdot b2}\\ t_1 := \frac{a1 \cdot \frac{-a2}{b2}}{-b1}\\ \mathbf{if}\;t_0 \leq -5 \cdot 10^{+291}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t_0 \leq -2 \cdot 10^{-265}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;t_0 \leq 4 \cdot 10^{-268}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t_0 \leq 5 \cdot 10^{+253}:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;\frac{a2}{b1} \cdot \frac{a1}{b2}\\ \end{array} \end{array} \]

FPCore

NOTE: a1 and a2 should be sorted in increasing order before calling this function.
NOTE: b1 and b2 should be sorted in increasing order before calling this function.
(FPCore (a1 a2 b1 b2)
 :precision binary64
 (let* ((t_0 (/ (* a1 a2) (* b1 b2))) (t_1 (/ (* a1 (/ (- a2) b2)) (- b1))))
   (if (<= t_0 -5e+291)
     t_1
     (if (<= t_0 -2e-265)
       t_0
       (if (<= t_0 4e-268)
         t_1
         (if (<= t_0 5e+253) t_0 (* (/ a2 b1) (/ a1 b2))))))))

C

assert(a1 < a2);
assert(b1 < b2);
double code(double a1, double a2, double b1, double b2) {
	double t_0 = (a1 * a2) / (b1 * b2);
	double t_1 = (a1 * (-a2 / b2)) / -b1;
	double tmp;
	if (t_0 <= -5e+291) {
		tmp = t_1;
	} else if (t_0 <= -2e-265) {
		tmp = t_0;
	} else if (t_0 <= 4e-268) {
		tmp = t_1;
	} else if (t_0 <= 5e+253) {
		tmp = t_0;
	} else {
		tmp = (a2 / b1) * (a1 / b2);
	}
	return tmp;
}

Fortran

NOTE: a1 and a2 should be sorted in increasing order before calling this function.
NOTE: b1 and b2 should be sorted in increasing order before calling this function.
real(8) function code(a1, a2, b1, b2)
    real(8), intent (in) :: a1
    real(8), intent (in) :: a2
    real(8), intent (in) :: b1
    real(8), intent (in) :: b2
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: tmp
    t_0 = (a1 * a2) / (b1 * b2)
    t_1 = (a1 * (-a2 / b2)) / -b1
    if (t_0 <= (-5d+291)) then
        tmp = t_1
    else if (t_0 <= (-2d-265)) then
        tmp = t_0
    else if (t_0 <= 4d-268) then
        tmp = t_1
    else if (t_0 <= 5d+253) then
        tmp = t_0
    else
        tmp = (a2 / b1) * (a1 / b2)
    end if
    code = tmp
end function

Java

assert a1 < a2;
assert b1 < b2;
public static double code(double a1, double a2, double b1, double b2) {
	double t_0 = (a1 * a2) / (b1 * b2);
	double t_1 = (a1 * (-a2 / b2)) / -b1;
	double tmp;
	if (t_0 <= -5e+291) {
		tmp = t_1;
	} else if (t_0 <= -2e-265) {
		tmp = t_0;
	} else if (t_0 <= 4e-268) {
		tmp = t_1;
	} else if (t_0 <= 5e+253) {
		tmp = t_0;
	} else {
		tmp = (a2 / b1) * (a1 / b2);
	}
	return tmp;
}

Python

[a1, a2] = sort([a1, a2])
[b1, b2] = sort([b1, b2])
def code(a1, a2, b1, b2):
	t_0 = (a1 * a2) / (b1 * b2)
	t_1 = (a1 * (-a2 / b2)) / -b1
	tmp = 0
	if t_0 <= -5e+291:
		tmp = t_1
	elif t_0 <= -2e-265:
		tmp = t_0
	elif t_0 <= 4e-268:
		tmp = t_1
	elif t_0 <= 5e+253:
		tmp = t_0
	else:
		tmp = (a2 / b1) * (a1 / b2)
	return tmp

Julia

a1, a2 = sort([a1, a2])
b1, b2 = sort([b1, b2])
function code(a1, a2, b1, b2)
	t_0 = Float64(Float64(a1 * a2) / Float64(b1 * b2))
	t_1 = Float64(Float64(a1 * Float64(Float64(-a2) / b2)) / Float64(-b1))
	tmp = 0.0
	if (t_0 <= -5e+291)
		tmp = t_1;
	elseif (t_0 <= -2e-265)
		tmp = t_0;
	elseif (t_0 <= 4e-268)
		tmp = t_1;
	elseif (t_0 <= 5e+253)
		tmp = t_0;
	else
		tmp = Float64(Float64(a2 / b1) * Float64(a1 / b2));
	end
	return tmp
end

MATLAB

a1, a2 = num2cell(sort([a1, a2])){:}
b1, b2 = num2cell(sort([b1, b2])){:}
function tmp_2 = code(a1, a2, b1, b2)
	t_0 = (a1 * a2) / (b1 * b2);
	t_1 = (a1 * (-a2 / b2)) / -b1;
	tmp = 0.0;
	if (t_0 <= -5e+291)
		tmp = t_1;
	elseif (t_0 <= -2e-265)
		tmp = t_0;
	elseif (t_0 <= 4e-268)
		tmp = t_1;
	elseif (t_0 <= 5e+253)
		tmp = t_0;
	else
		tmp = (a2 / b1) * (a1 / b2);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: a1 and a2 should be sorted in increasing order before calling this function.
NOTE: b1 and b2 should be sorted in increasing order before calling this function.
code[a1_, a2_, b1_, b2_] := Block[{t$95$0 = N[(N[(a1 * a2), $MachinePrecision] / N[(b1 * b2), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(N[(a1 * N[((-a2) / b2), $MachinePrecision]), $MachinePrecision] / (-b1)), $MachinePrecision]}, If[LessEqual[t$95$0, -5e+291], t$95$1, If[LessEqual[t$95$0, -2e-265], t$95$0, If[LessEqual[t$95$0, 4e-268], t$95$1, If[LessEqual[t$95$0, 5e+253], 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)) < -5.0000000000000001e291 or -1.99999999999999997e-265 < (/.f64 (*.f64 a1 a2) (*.f64 b1 b2)) < 3.99999999999999983e-268

   1. Initial program 79.6%

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

      1. times-frac 95.3%

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

      2. associate-*l/ 98.1%

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

      3. associate-*r/ 95.9%

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

   3. Simplified 95.9%

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

      1. *-commutative 95.9%

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

      2. frac-2neg 95.9%

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

      3. associate-*l/ 98.1%

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

      4. distribute-neg-frac 98.1%

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

   5. Applied egg-rr 98.1%

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

   if -5.0000000000000001e291 < (/.f64 (*.f64 a1 a2) (*.f64 b1 b2)) < -1.99999999999999997e-265 or 3.99999999999999983e-268 < (/.f64 (*.f64 a1 a2) (*.f64 b1 b2)) < 4.9999999999999997e253

   1. Initial program 98.7%

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

   if 4.9999999999999997e253 < (/.f64 (*.f64 a1 a2) (*.f64 b1 b2))

   1. Initial program 57.1%

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

      1. times-frac 97.6%

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

      2. associate-*l/ 89.0%

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

      3. associate-*r/ 88.9%

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

   3. Simplified 88.9%

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

   4. Taylor expanded in a1 around 0 57.1%

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

      1. *-commutative 57.1%

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

      2. times-frac 97.6%

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

   6. Simplified 97.6%

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

4. Final simplification 98.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{a1 \cdot a2}{b1 \cdot b2} \leq -5 \cdot 10^{+291}:\\ \;\;\;\;\frac{a1 \cdot \frac{-a2}{b2}}{-b1}\\ \mathbf{elif}\;\frac{a1 \cdot a2}{b1 \cdot b2} \leq -2 \cdot 10^{-265}:\\ \;\;\;\;\frac{a1 \cdot a2}{b1 \cdot b2}\\ \mathbf{elif}\;\frac{a1 \cdot a2}{b1 \cdot b2} \leq 4 \cdot 10^{-268}:\\ \;\;\;\;\frac{a1 \cdot \frac{-a2}{b2}}{-b1}\\ \mathbf{elif}\;\frac{a1 \cdot a2}{b1 \cdot b2} \leq 5 \cdot 10^{+253}:\\ \;\;\;\;\frac{a1 \cdot a2}{b1 \cdot b2}\\ \mathbf{else}:\\ \;\;\;\;\frac{a2}{b1} \cdot \frac{a1}{b2}\\ \end{array} \]

Alternative 2: 96.5% accurate, 0.2× speedup

Math

\[\begin{array}{l} [a1, a2] = \mathsf{sort}([a1, a2])\\ [b1, b2] = \mathsf{sort}([b1, b2])\\ \\ \begin{array}{l} t_0 := \frac{a1 \cdot a2}{b1 \cdot b2}\\ t_1 := \frac{a1}{b1} \cdot \frac{a2}{b2}\\ \mathbf{if}\;t_0 \leq -\infty:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t_0 \leq -2 \cdot 10^{-265}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;t_0 \leq 0:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t_0 \leq 5 \cdot 10^{+253}:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;\frac{a2}{b1} \cdot \frac{a1}{b2}\\ \end{array} \end{array} \]

FPCore

NOTE: a1 and a2 should be sorted in increasing order before calling this function.
NOTE: b1 and b2 should be sorted in increasing order before calling this function.
(FPCore (a1 a2 b1 b2)
 :precision binary64
 (let* ((t_0 (/ (* a1 a2) (* b1 b2))) (t_1 (* (/ a1 b1) (/ a2 b2))))
   (if (<= t_0 (- INFINITY))
     t_1
     (if (<= t_0 -2e-265)
       t_0
       (if (<= t_0 0.0)
         t_1
         (if (<= t_0 5e+253) t_0 (* (/ a2 b1) (/ a1 b2))))))))

C

assert(a1 < a2);
assert(b1 < b2);
double code(double a1, double a2, double b1, double b2) {
	double t_0 = (a1 * a2) / (b1 * b2);
	double t_1 = (a1 / b1) * (a2 / b2);
	double tmp;
	if (t_0 <= -((double) INFINITY)) {
		tmp = t_1;
	} else if (t_0 <= -2e-265) {
		tmp = t_0;
	} else if (t_0 <= 0.0) {
		tmp = t_1;
	} else if (t_0 <= 5e+253) {
		tmp = t_0;
	} else {
		tmp = (a2 / b1) * (a1 / b2);
	}
	return tmp;
}

Java

assert a1 < a2;
assert b1 < b2;
public static double code(double a1, double a2, double b1, double b2) {
	double t_0 = (a1 * a2) / (b1 * b2);
	double t_1 = (a1 / b1) * (a2 / b2);
	double tmp;
	if (t_0 <= -Double.POSITIVE_INFINITY) {
		tmp = t_1;
	} else if (t_0 <= -2e-265) {
		tmp = t_0;
	} else if (t_0 <= 0.0) {
		tmp = t_1;
	} else if (t_0 <= 5e+253) {
		tmp = t_0;
	} else {
		tmp = (a2 / b1) * (a1 / b2);
	}
	return tmp;
}

Python

[a1, a2] = sort([a1, a2])
[b1, b2] = sort([b1, b2])
def code(a1, a2, b1, b2):
	t_0 = (a1 * a2) / (b1 * b2)
	t_1 = (a1 / b1) * (a2 / b2)
	tmp = 0
	if t_0 <= -math.inf:
		tmp = t_1
	elif t_0 <= -2e-265:
		tmp = t_0
	elif t_0 <= 0.0:
		tmp = t_1
	elif t_0 <= 5e+253:
		tmp = t_0
	else:
		tmp = (a2 / b1) * (a1 / b2)
	return tmp

Julia

a1, a2 = sort([a1, a2])
b1, b2 = sort([b1, b2])
function code(a1, a2, b1, b2)
	t_0 = Float64(Float64(a1 * a2) / Float64(b1 * b2))
	t_1 = Float64(Float64(a1 / b1) * Float64(a2 / b2))
	tmp = 0.0
	if (t_0 <= Float64(-Inf))
		tmp = t_1;
	elseif (t_0 <= -2e-265)
		tmp = t_0;
	elseif (t_0 <= 0.0)
		tmp = t_1;
	elseif (t_0 <= 5e+253)
		tmp = t_0;
	else
		tmp = Float64(Float64(a2 / b1) * Float64(a1 / b2));
	end
	return tmp
end

MATLAB

a1, a2 = num2cell(sort([a1, a2])){:}
b1, b2 = num2cell(sort([b1, b2])){:}
function tmp_2 = code(a1, a2, b1, b2)
	t_0 = (a1 * a2) / (b1 * b2);
	t_1 = (a1 / b1) * (a2 / b2);
	tmp = 0.0;
	if (t_0 <= -Inf)
		tmp = t_1;
	elseif (t_0 <= -2e-265)
		tmp = t_0;
	elseif (t_0 <= 0.0)
		tmp = t_1;
	elseif (t_0 <= 5e+253)
		tmp = t_0;
	else
		tmp = (a2 / b1) * (a1 / b2);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: a1 and a2 should be sorted in increasing order before calling this function.
NOTE: b1 and b2 should be sorted in increasing order before calling this function.
code[a1_, a2_, b1_, b2_] := Block[{t$95$0 = N[(N[(a1 * a2), $MachinePrecision] / N[(b1 * b2), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(N[(a1 / b1), $MachinePrecision] * N[(a2 / b2), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$0, (-Infinity)], t$95$1, If[LessEqual[t$95$0, -2e-265], t$95$0, If[LessEqual[t$95$0, 0.0], t$95$1, If[LessEqual[t$95$0, 5e+253], 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)) < -inf.0 or -1.99999999999999997e-265 < (/.f64 (*.f64 a1 a2) (*.f64 b1 b2)) < 0.0

   1. Initial program 77.9%

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

      1. times-frac 95.9%

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

   3. Simplified 95.9%

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

   if -inf.0 < (/.f64 (*.f64 a1 a2) (*.f64 b1 b2)) < -1.99999999999999997e-265 or 0.0 < (/.f64 (*.f64 a1 a2) (*.f64 b1 b2)) < 4.9999999999999997e253

   1. Initial program 98.7%

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

   if 4.9999999999999997e253 < (/.f64 (*.f64 a1 a2) (*.f64 b1 b2))

   1. Initial program 57.1%

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

      1. times-frac 97.6%

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

      2. associate-*l/ 89.0%

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

      3. associate-*r/ 88.9%

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

   3. Simplified 88.9%

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

   4. Taylor expanded in a1 around 0 57.1%

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

      1. *-commutative 57.1%

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

      2. times-frac 97.6%

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

   6. Simplified 97.6%

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

4. Final simplification 97.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{a1 \cdot a2}{b1 \cdot b2} \leq -\infty:\\ \;\;\;\;\frac{a1}{b1} \cdot \frac{a2}{b2}\\ \mathbf{elif}\;\frac{a1 \cdot a2}{b1 \cdot b2} \leq -2 \cdot 10^{-265}:\\ \;\;\;\;\frac{a1 \cdot a2}{b1 \cdot b2}\\ \mathbf{elif}\;\frac{a1 \cdot a2}{b1 \cdot b2} \leq 0:\\ \;\;\;\;\frac{a1}{b1} \cdot \frac{a2}{b2}\\ \mathbf{elif}\;\frac{a1 \cdot a2}{b1 \cdot b2} \leq 5 \cdot 10^{+253}:\\ \;\;\;\;\frac{a1 \cdot a2}{b1 \cdot b2}\\ \mathbf{else}:\\ \;\;\;\;\frac{a2}{b1} \cdot \frac{a1}{b2}\\ \end{array} \]

Alternative 3: 85.7% accurate, 0.8× speedup

Math

\[\begin{array}{l} [a1, a2] = \mathsf{sort}([a1, a2])\\ [b1, b2] = \mathsf{sort}([b1, b2])\\ \\ \begin{array}{l} \mathbf{if}\;a2 \leq 5.8 \cdot 10^{+42}:\\ \;\;\;\;\frac{a1}{b1} \cdot \frac{a2}{b2}\\ \mathbf{else}:\\ \;\;\;\;a1 \cdot \frac{\frac{a2}{b2}}{b1}\\ \end{array} \end{array} \]

FPCore

NOTE: a1 and a2 should be sorted in increasing order before calling this function.
NOTE: b1 and b2 should be sorted in increasing order before calling this function.
(FPCore (a1 a2 b1 b2)
 :precision binary64
 (if (<= a2 5.8e+42) (* (/ a1 b1) (/ a2 b2)) (* a1 (/ (/ a2 b2) b1))))

C

assert(a1 < a2);
assert(b1 < b2);
double code(double a1, double a2, double b1, double b2) {
	double tmp;
	if (a2 <= 5.8e+42) {
		tmp = (a1 / b1) * (a2 / b2);
	} else {
		tmp = a1 * ((a2 / b2) / b1);
	}
	return tmp;
}

Fortran

NOTE: a1 and a2 should be sorted in increasing order before calling this function.
NOTE: b1 and b2 should be sorted in increasing order before calling this function.
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 (a2 <= 5.8d+42) then
        tmp = (a1 / b1) * (a2 / b2)
    else
        tmp = a1 * ((a2 / b2) / b1)
    end if
    code = tmp
end function

Java

assert a1 < a2;
assert b1 < b2;
public static double code(double a1, double a2, double b1, double b2) {
	double tmp;
	if (a2 <= 5.8e+42) {
		tmp = (a1 / b1) * (a2 / b2);
	} else {
		tmp = a1 * ((a2 / b2) / b1);
	}
	return tmp;
}

Python

[a1, a2] = sort([a1, a2])
[b1, b2] = sort([b1, b2])
def code(a1, a2, b1, b2):
	tmp = 0
	if a2 <= 5.8e+42:
		tmp = (a1 / b1) * (a2 / b2)
	else:
		tmp = a1 * ((a2 / b2) / b1)
	return tmp

Julia

a1, a2 = sort([a1, a2])
b1, b2 = sort([b1, b2])
function code(a1, a2, b1, b2)
	tmp = 0.0
	if (a2 <= 5.8e+42)
		tmp = Float64(Float64(a1 / b1) * Float64(a2 / b2));
	else
		tmp = Float64(a1 * Float64(Float64(a2 / b2) / b1));
	end
	return tmp
end

MATLAB

a1, a2 = num2cell(sort([a1, a2])){:}
b1, b2 = num2cell(sort([b1, b2])){:}
function tmp_2 = code(a1, a2, b1, b2)
	tmp = 0.0;
	if (a2 <= 5.8e+42)
		tmp = (a1 / b1) * (a2 / b2);
	else
		tmp = a1 * ((a2 / b2) / b1);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: a1 and a2 should be sorted in increasing order before calling this function.
NOTE: b1 and b2 should be sorted in increasing order before calling this function.
code[a1_, a2_, b1_, b2_] := If[LessEqual[a2, 5.8e+42], N[(N[(a1 / b1), $MachinePrecision] * N[(a2 / b2), $MachinePrecision]), $MachinePrecision], N[(a1 * N[(N[(a2 / b2), $MachinePrecision] / b1), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a2 < 5.79999999999999961e42

   1. Initial program 85.0%

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

      1. times-frac 88.7%

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

   3. Simplified 88.7%

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

   if 5.79999999999999961e42 < a2

   1. Initial program 80.8%

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

      1. times-frac 86.4%

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

      2. associate-*l/ 89.1%

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

      3. associate-*r/ 88.1%

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

   3. Simplified 88.1%

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

4. Final simplification 88.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a2 \leq 5.8 \cdot 10^{+42}:\\ \;\;\;\;\frac{a1}{b1} \cdot \frac{a2}{b2}\\ \mathbf{else}:\\ \;\;\;\;a1 \cdot \frac{\frac{a2}{b2}}{b1}\\ \end{array} \]

Alternative 4: 86.1% accurate, 0.8× speedup

Math

\[\begin{array}{l} [a1, a2] = \mathsf{sort}([a1, a2])\\ [b1, b2] = \mathsf{sort}([b1, b2])\\ \\ \begin{array}{l} \mathbf{if}\;a2 \leq 8.2 \cdot 10^{+42}:\\ \;\;\;\;\frac{a1}{b1} \cdot \frac{a2}{b2}\\ \mathbf{else}:\\ \;\;\;\;\frac{a1}{b1 \cdot \frac{b2}{a2}}\\ \end{array} \end{array} \]

FPCore

NOTE: a1 and a2 should be sorted in increasing order before calling this function.
NOTE: b1 and b2 should be sorted in increasing order before calling this function.
(FPCore (a1 a2 b1 b2)
 :precision binary64
 (if (<= a2 8.2e+42) (* (/ a1 b1) (/ a2 b2)) (/ a1 (* b1 (/ b2 a2)))))

C

assert(a1 < a2);
assert(b1 < b2);
double code(double a1, double a2, double b1, double b2) {
	double tmp;
	if (a2 <= 8.2e+42) {
		tmp = (a1 / b1) * (a2 / b2);
	} else {
		tmp = a1 / (b1 * (b2 / a2));
	}
	return tmp;
}

Fortran

NOTE: a1 and a2 should be sorted in increasing order before calling this function.
NOTE: b1 and b2 should be sorted in increasing order before calling this function.
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 (a2 <= 8.2d+42) then
        tmp = (a1 / b1) * (a2 / b2)
    else
        tmp = a1 / (b1 * (b2 / a2))
    end if
    code = tmp
end function

Java

assert a1 < a2;
assert b1 < b2;
public static double code(double a1, double a2, double b1, double b2) {
	double tmp;
	if (a2 <= 8.2e+42) {
		tmp = (a1 / b1) * (a2 / b2);
	} else {
		tmp = a1 / (b1 * (b2 / a2));
	}
	return tmp;
}

Python

[a1, a2] = sort([a1, a2])
[b1, b2] = sort([b1, b2])
def code(a1, a2, b1, b2):
	tmp = 0
	if a2 <= 8.2e+42:
		tmp = (a1 / b1) * (a2 / b2)
	else:
		tmp = a1 / (b1 * (b2 / a2))
	return tmp

Julia

a1, a2 = sort([a1, a2])
b1, b2 = sort([b1, b2])
function code(a1, a2, b1, b2)
	tmp = 0.0
	if (a2 <= 8.2e+42)
		tmp = Float64(Float64(a1 / b1) * Float64(a2 / b2));
	else
		tmp = Float64(a1 / Float64(b1 * Float64(b2 / a2)));
	end
	return tmp
end

MATLAB

a1, a2 = num2cell(sort([a1, a2])){:}
b1, b2 = num2cell(sort([b1, b2])){:}
function tmp_2 = code(a1, a2, b1, b2)
	tmp = 0.0;
	if (a2 <= 8.2e+42)
		tmp = (a1 / b1) * (a2 / b2);
	else
		tmp = a1 / (b1 * (b2 / a2));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: a1 and a2 should be sorted in increasing order before calling this function.
NOTE: b1 and b2 should be sorted in increasing order before calling this function.
code[a1_, a2_, b1_, b2_] := If[LessEqual[a2, 8.2e+42], N[(N[(a1 / b1), $MachinePrecision] * N[(a2 / b2), $MachinePrecision]), $MachinePrecision], N[(a1 / N[(b1 * N[(b2 / a2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a2 < 8.2000000000000001e42

   1. Initial program 85.0%

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

      1. times-frac 88.7%

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

   3. Simplified 88.7%

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

   if 8.2000000000000001e42 < a2

   1. Initial program 80.8%

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

      1. times-frac 86.4%

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

      2. associate-*l/ 89.1%

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

      3. associate-*r/ 88.1%

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

   3. Simplified 88.1%

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

      1. associate-*r/ 89.1%

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

      2. associate-*l/ 86.4%

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

      3. *-commutative 86.4%

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

      4. clear-num 86.2%

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

      5. frac-times 88.0%

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

      6. *-un-lft-identity 88.0%

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

   5. Applied egg-rr 88.0%

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

4. Final simplification 88.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a2 \leq 8.2 \cdot 10^{+42}:\\ \;\;\;\;\frac{a1}{b1} \cdot \frac{a2}{b2}\\ \mathbf{else}:\\ \;\;\;\;\frac{a1}{b1 \cdot \frac{b2}{a2}}\\ \end{array} \]

Alternative 5: 86.6% accurate, 0.8× speedup

Math

\[\begin{array}{l} [a1, a2] = \mathsf{sort}([a1, a2])\\ [b1, b2] = \mathsf{sort}([b1, b2])\\ \\ \begin{array}{l} \mathbf{if}\;a2 \leq 23:\\ \;\;\;\;\frac{a2}{b2 \cdot \frac{b1}{a1}}\\ \mathbf{else}:\\ \;\;\;\;\frac{a1}{b1 \cdot \frac{b2}{a2}}\\ \end{array} \end{array} \]

FPCore

NOTE: a1 and a2 should be sorted in increasing order before calling this function.
NOTE: b1 and b2 should be sorted in increasing order before calling this function.
(FPCore (a1 a2 b1 b2)
 :precision binary64
 (if (<= a2 23.0) (/ a2 (* b2 (/ b1 a1))) (/ a1 (* b1 (/ b2 a2)))))

C

assert(a1 < a2);
assert(b1 < b2);
double code(double a1, double a2, double b1, double b2) {
	double tmp;
	if (a2 <= 23.0) {
		tmp = a2 / (b2 * (b1 / a1));
	} else {
		tmp = a1 / (b1 * (b2 / a2));
	}
	return tmp;
}

Fortran

NOTE: a1 and a2 should be sorted in increasing order before calling this function.
NOTE: b1 and b2 should be sorted in increasing order before calling this function.
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 (a2 <= 23.0d0) then
        tmp = a2 / (b2 * (b1 / a1))
    else
        tmp = a1 / (b1 * (b2 / a2))
    end if
    code = tmp
end function

Java

assert a1 < a2;
assert b1 < b2;
public static double code(double a1, double a2, double b1, double b2) {
	double tmp;
	if (a2 <= 23.0) {
		tmp = a2 / (b2 * (b1 / a1));
	} else {
		tmp = a1 / (b1 * (b2 / a2));
	}
	return tmp;
}

Python

[a1, a2] = sort([a1, a2])
[b1, b2] = sort([b1, b2])
def code(a1, a2, b1, b2):
	tmp = 0
	if a2 <= 23.0:
		tmp = a2 / (b2 * (b1 / a1))
	else:
		tmp = a1 / (b1 * (b2 / a2))
	return tmp

Julia

a1, a2 = sort([a1, a2])
b1, b2 = sort([b1, b2])
function code(a1, a2, b1, b2)
	tmp = 0.0
	if (a2 <= 23.0)
		tmp = Float64(a2 / Float64(b2 * Float64(b1 / a1)));
	else
		tmp = Float64(a1 / Float64(b1 * Float64(b2 / a2)));
	end
	return tmp
end

MATLAB

a1, a2 = num2cell(sort([a1, a2])){:}
b1, b2 = num2cell(sort([b1, b2])){:}
function tmp_2 = code(a1, a2, b1, b2)
	tmp = 0.0;
	if (a2 <= 23.0)
		tmp = a2 / (b2 * (b1 / a1));
	else
		tmp = a1 / (b1 * (b2 / a2));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: a1 and a2 should be sorted in increasing order before calling this function.
NOTE: b1 and b2 should be sorted in increasing order before calling this function.
code[a1_, a2_, b1_, b2_] := If[LessEqual[a2, 23.0], N[(a2 / N[(b2 * N[(b1 / a1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(a1 / N[(b1 * N[(b2 / a2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a2 < 23

   1. Initial program 84.9%

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

      1. times-frac 87.9%

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

      2. associate-*l/ 90.1%

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

      3. associate-*r/ 84.7%

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

   3. Simplified 84.7%

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

      1. associate-*r/ 90.1%

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

      2. associate-*l/ 87.9%

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

      3. clear-num 87.6%

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

      4. frac-times 87.9%

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

      5. *-un-lft-identity 87.9%

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

   5. Applied egg-rr 87.9%

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

   if 23 < a2

   1. Initial program 82.0%

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

      1. times-frac 89.3%

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

      2. associate-*l/ 87.0%

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

      3. associate-*r/ 89.1%

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

   3. Simplified 89.1%

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

      1. associate-*r/ 87.0%

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

      2. associate-*l/ 89.3%

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

      3. *-commutative 89.3%

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

      4. clear-num 89.1%

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

      5. frac-times 89.1%

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

      6. *-un-lft-identity 89.1%

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

   5. Applied egg-rr 89.1%

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

4. Final simplification 88.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a2 \leq 23:\\ \;\;\;\;\frac{a2}{b2 \cdot \frac{b1}{a1}}\\ \mathbf{else}:\\ \;\;\;\;\frac{a1}{b1 \cdot \frac{b2}{a2}}\\ \end{array} \]

Alternative 6: 86.2% accurate, 1.0× speedup

Math

\[\begin{array}{l} [a1, a2] = \mathsf{sort}([a1, a2])\\ [b1, b2] = \mathsf{sort}([b1, b2])\\ \\ a1 \cdot \frac{\frac{a2}{b2}}{b1} \end{array} \]

FPCore

NOTE: a1 and a2 should be sorted in increasing order before calling this function.
NOTE: b1 and b2 should be sorted in increasing order before calling this function.
(FPCore (a1 a2 b1 b2) :precision binary64 (* a1 (/ (/ a2 b2) b1)))

C

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

Fortran

NOTE: a1 and a2 should be sorted in increasing order before calling this function.
NOTE: b1 and b2 should be sorted in increasing order before calling this function.
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 / b2) / b1)
end function

Java

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

Python

[a1, a2] = sort([a1, a2])
[b1, b2] = sort([b1, b2])
def code(a1, a2, b1, b2):
	return a1 * ((a2 / b2) / b1)

Julia

a1, a2 = sort([a1, a2])
b1, b2 = sort([b1, b2])
function code(a1, a2, b1, b2)
	return Float64(a1 * Float64(Float64(a2 / b2) / b1))
end

MATLAB

a1, a2 = num2cell(sort([a1, a2])){:}
b1, b2 = num2cell(sort([b1, b2])){:}
function tmp = code(a1, a2, b1, b2)
	tmp = a1 * ((a2 / b2) / b1);
end

Wolfram

NOTE: a1 and a2 should be sorted in increasing order before calling this function.
NOTE: b1 and b2 should be sorted in increasing order before calling this function.
code[a1_, a2_, b1_, b2_] := N[(a1 * N[(N[(a2 / b2), $MachinePrecision] / b1), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 84.2%

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

   1. times-frac 88.2%

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

   2. associate-*l/ 89.4%

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

   3. associate-*r/ 85.8%

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

3. Simplified 85.8%

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

4. Final simplification 85.8%

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

Developer target: 85.7% 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 2023310 
(FPCore (a1 a2 b1 b2)
  :name "Quotient of products"
  :precision binary64

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

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