Quotient of products

Percentage Accurate: 86.3% → 93.4%

Time: 4.2s

Alternatives: 6

Speedup: 0.3×

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: 86.3% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 93.4% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{a2}{\frac{b1 \cdot b2}{a1}}\\ \mathbf{if}\;b1 \cdot b2 \leq -2 \cdot 10^{+131}:\\ \;\;\;\;\frac{\frac{a1}{\frac{b2}{a2}}}{b1}\\ \mathbf{elif}\;b1 \cdot b2 \leq -2 \cdot 10^{-177}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;b1 \cdot b2 \leq 5 \cdot 10^{-238}:\\ \;\;\;\;\frac{a1 \cdot \frac{a2}{b2}}{b1}\\ \mathbf{elif}\;b1 \cdot b2 \leq 4 \cdot 10^{+254}:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;\frac{a2}{b2} \cdot \frac{a1}{b1}\\ \end{array} \end{array} \]

FPCore

(FPCore (a1 a2 b1 b2)
 :precision binary64
 (let* ((t_0 (/ a2 (/ (* b1 b2) a1))))
   (if (<= (* b1 b2) -2e+131)
     (/ (/ a1 (/ b2 a2)) b1)
     (if (<= (* b1 b2) -2e-177)
       t_0
       (if (<= (* b1 b2) 5e-238)
         (/ (* a1 (/ a2 b2)) b1)
         (if (<= (* b1 b2) 4e+254) t_0 (* (/ a2 b2) (/ a1 b1))))))))

C

double code(double a1, double a2, double b1, double b2) {
	double t_0 = a2 / ((b1 * b2) / a1);
	double tmp;
	if ((b1 * b2) <= -2e+131) {
		tmp = (a1 / (b2 / a2)) / b1;
	} else if ((b1 * b2) <= -2e-177) {
		tmp = t_0;
	} else if ((b1 * b2) <= 5e-238) {
		tmp = (a1 * (a2 / b2)) / b1;
	} else if ((b1 * b2) <= 4e+254) {
		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 * b2) / a1)
    if ((b1 * b2) <= (-2d+131)) then
        tmp = (a1 / (b2 / a2)) / b1
    else if ((b1 * b2) <= (-2d-177)) then
        tmp = t_0
    else if ((b1 * b2) <= 5d-238) then
        tmp = (a1 * (a2 / b2)) / b1
    else if ((b1 * b2) <= 4d+254) 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 * b2) / a1);
	double tmp;
	if ((b1 * b2) <= -2e+131) {
		tmp = (a1 / (b2 / a2)) / b1;
	} else if ((b1 * b2) <= -2e-177) {
		tmp = t_0;
	} else if ((b1 * b2) <= 5e-238) {
		tmp = (a1 * (a2 / b2)) / b1;
	} else if ((b1 * b2) <= 4e+254) {
		tmp = t_0;
	} else {
		tmp = (a2 / b2) * (a1 / b1);
	}
	return tmp;
}

Python

def code(a1, a2, b1, b2):
	t_0 = a2 / ((b1 * b2) / a1)
	tmp = 0
	if (b1 * b2) <= -2e+131:
		tmp = (a1 / (b2 / a2)) / b1
	elif (b1 * b2) <= -2e-177:
		tmp = t_0
	elif (b1 * b2) <= 5e-238:
		tmp = (a1 * (a2 / b2)) / b1
	elif (b1 * b2) <= 4e+254:
		tmp = t_0
	else:
		tmp = (a2 / b2) * (a1 / b1)
	return tmp

Julia

function code(a1, a2, b1, b2)
	t_0 = Float64(a2 / Float64(Float64(b1 * b2) / a1))
	tmp = 0.0
	if (Float64(b1 * b2) <= -2e+131)
		tmp = Float64(Float64(a1 / Float64(b2 / a2)) / b1);
	elseif (Float64(b1 * b2) <= -2e-177)
		tmp = t_0;
	elseif (Float64(b1 * b2) <= 5e-238)
		tmp = Float64(Float64(a1 * Float64(a2 / b2)) / b1);
	elseif (Float64(b1 * b2) <= 4e+254)
		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 * b2) / a1);
	tmp = 0.0;
	if ((b1 * b2) <= -2e+131)
		tmp = (a1 / (b2 / a2)) / b1;
	elseif ((b1 * b2) <= -2e-177)
		tmp = t_0;
	elseif ((b1 * b2) <= 5e-238)
		tmp = (a1 * (a2 / b2)) / b1;
	elseif ((b1 * b2) <= 4e+254)
		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[(a2 / N[(N[(b1 * b2), $MachinePrecision] / a1), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(b1 * b2), $MachinePrecision], -2e+131], N[(N[(a1 / N[(b2 / a2), $MachinePrecision]), $MachinePrecision] / b1), $MachinePrecision], If[LessEqual[N[(b1 * b2), $MachinePrecision], -2e-177], t$95$0, If[LessEqual[N[(b1 * b2), $MachinePrecision], 5e-238], N[(N[(a1 * N[(a2 / b2), $MachinePrecision]), $MachinePrecision] / b1), $MachinePrecision], If[LessEqual[N[(b1 * b2), $MachinePrecision], 4e+254], t$95$0, N[(N[(a2 / b2), $MachinePrecision] * N[(a1 / b1), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if (*.f64 b1 b2) < -1.9999999999999998e131

   1. Initial program 76.8%

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

      1. times-frac 88.5%

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

      2. *-commutative 88.5%

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

   3. Simplified 88.5%

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

      1. associate-*r/ 95.9%

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

   5. Applied egg-rr 95.9%

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

      1. *-commutative 95.9%

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

      2. clear-num 95.9%

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

      3. un-div-inv 96.0%

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

   7. Applied egg-rr 96.0%

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

   if -1.9999999999999998e131 < (*.f64 b1 b2) < -1.9999999999999999e-177 or 5e-238 < (*.f64 b1 b2) < 3.9999999999999997e254

   1. Initial program 92.2%

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

      1. times-frac 78.0%

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

      2. *-commutative 78.0%

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

   3. Simplified 78.0%

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

      1. frac-times 92.2%

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

      2. *-commutative 92.2%

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

      3. associate-/l* 97.6%

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

      4. *-commutative 97.6%

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

   5. Applied egg-rr 97.6%

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

   if -1.9999999999999999e-177 < (*.f64 b1 b2) < 5e-238

   1. Initial program 68.6%

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

      1. times-frac 93.1%

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

      2. *-commutative 93.1%

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

   3. Simplified 93.1%

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

      1. associate-*r/ 95.6%

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

   5. Applied egg-rr 95.6%

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

   if 3.9999999999999997e254 < (*.f64 b1 b2)

   1. Initial program 59.3%

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

4. Final simplification 96.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b1 \cdot b2 \leq -2 \cdot 10^{+131}:\\ \;\;\;\;\frac{\frac{a1}{\frac{b2}{a2}}}{b1}\\ \mathbf{elif}\;b1 \cdot b2 \leq -2 \cdot 10^{-177}:\\ \;\;\;\;\frac{a2}{\frac{b1 \cdot b2}{a1}}\\ \mathbf{elif}\;b1 \cdot b2 \leq 5 \cdot 10^{-238}:\\ \;\;\;\;\frac{a1 \cdot \frac{a2}{b2}}{b1}\\ \mathbf{elif}\;b1 \cdot b2 \leq 4 \cdot 10^{+254}:\\ \;\;\;\;\frac{a2}{\frac{b1 \cdot b2}{a1}}\\ \mathbf{else}:\\ \;\;\;\;\frac{a2}{b2} \cdot \frac{a1}{b1}\\ \end{array} \]

Alternative 2: 96.2% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{a1 \cdot a2}{b1 \cdot b2}\\ \mathbf{if}\;t_0 \leq -\infty \lor \neg \left(t_0 \leq -2 \cdot 10^{-294}\right) \land \left(t_0 \leq 5 \cdot 10^{-186} \lor \neg \left(t_0 \leq 4 \cdot 10^{+292}\right)\right):\\ \;\;\;\;\frac{a2}{b2} \cdot \frac{a1}{b1}\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \end{array} \]

FPCore

(FPCore (a1 a2 b1 b2)
 :precision binary64
 (let* ((t_0 (/ (* a1 a2) (* b1 b2))))
   (if (or (<= t_0 (- INFINITY))
           (and (not (<= t_0 -2e-294))
                (or (<= t_0 5e-186) (not (<= t_0 4e+292)))))
     (* (/ 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 <= -2e-294) && ((t_0 <= 5e-186) || !(t_0 <= 4e+292)))) {
		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 <= -2e-294) && ((t_0 <= 5e-186) || !(t_0 <= 4e+292)))) {
		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 <= -2e-294) and ((t_0 <= 5e-186) or not (t_0 <= 4e+292))):
		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 <= -2e-294) && ((t_0 <= 5e-186) || !(t_0 <= 4e+292))))
		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 <= -2e-294)) && ((t_0 <= 5e-186) || ~((t_0 <= 4e+292)))))
		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)], And[N[Not[LessEqual[t$95$0, -2e-294]], $MachinePrecision], Or[LessEqual[t$95$0, 5e-186], N[Not[LessEqual[t$95$0, 4e+292]], $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 -2.00000000000000003e-294 < (/.f64 (*.f64 a1 a2) (*.f64 b1 b2)) < 5e-186 or 4.0000000000000001e292 < (/.f64 (*.f64 a1 a2) (*.f64 b1 b2))

   1. Initial program 69.4%

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

      1. times-frac 95.9%

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

      2. *-commutative 95.9%

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

   3. Simplified 95.9%

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

   if -inf.0 < (/.f64 (*.f64 a1 a2) (*.f64 b1 b2)) < -2.00000000000000003e-294 or 5e-186 < (/.f64 (*.f64 a1 a2) (*.f64 b1 b2)) < 4.0000000000000001e292

   1. Initial program 98.3%

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

4. Final simplification 96.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{a1 \cdot a2}{b1 \cdot b2} \leq -\infty \lor \neg \left(\frac{a1 \cdot a2}{b1 \cdot b2} \leq -2 \cdot 10^{-294}\right) \land \left(\frac{a1 \cdot a2}{b1 \cdot b2} \leq 5 \cdot 10^{-186} \lor \neg \left(\frac{a1 \cdot a2}{b1 \cdot b2} \leq 4 \cdot 10^{+292}\right)\right):\\ \;\;\;\;\frac{a2}{b2} \cdot \frac{a1}{b1}\\ \mathbf{else}:\\ \;\;\;\;\frac{a1 \cdot a2}{b1 \cdot b2}\\ \end{array} \]

Alternative 3: 93.5% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{a2}{\frac{b1 \cdot b2}{a1}}\\ t_1 := \frac{a1 \cdot \frac{a2}{b2}}{b1}\\ \mathbf{if}\;b1 \cdot b2 \leq -2 \cdot 10^{+131}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b1 \cdot b2 \leq -2 \cdot 10^{-177}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;b1 \cdot b2 \leq 5 \cdot 10^{-238}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b1 \cdot b2 \leq 4 \cdot 10^{+254}:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;\frac{a2}{b2} \cdot \frac{a1}{b1}\\ \end{array} \end{array} \]

FPCore

(FPCore (a1 a2 b1 b2)
 :precision binary64
 (let* ((t_0 (/ a2 (/ (* b1 b2) a1))) (t_1 (/ (* a1 (/ a2 b2)) b1)))
   (if (<= (* b1 b2) -2e+131)
     t_1
     (if (<= (* b1 b2) -2e-177)
       t_0
       (if (<= (* b1 b2) 5e-238)
         t_1
         (if (<= (* b1 b2) 4e+254) t_0 (* (/ a2 b2) (/ a1 b1))))))))

C

double code(double a1, double a2, double b1, double b2) {
	double t_0 = a2 / ((b1 * b2) / a1);
	double t_1 = (a1 * (a2 / b2)) / b1;
	double tmp;
	if ((b1 * b2) <= -2e+131) {
		tmp = t_1;
	} else if ((b1 * b2) <= -2e-177) {
		tmp = t_0;
	} else if ((b1 * b2) <= 5e-238) {
		tmp = t_1;
	} else if ((b1 * b2) <= 4e+254) {
		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) :: t_1
    real(8) :: tmp
    t_0 = a2 / ((b1 * b2) / a1)
    t_1 = (a1 * (a2 / b2)) / b1
    if ((b1 * b2) <= (-2d+131)) then
        tmp = t_1
    else if ((b1 * b2) <= (-2d-177)) then
        tmp = t_0
    else if ((b1 * b2) <= 5d-238) then
        tmp = t_1
    else if ((b1 * b2) <= 4d+254) 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 * b2) / a1);
	double t_1 = (a1 * (a2 / b2)) / b1;
	double tmp;
	if ((b1 * b2) <= -2e+131) {
		tmp = t_1;
	} else if ((b1 * b2) <= -2e-177) {
		tmp = t_0;
	} else if ((b1 * b2) <= 5e-238) {
		tmp = t_1;
	} else if ((b1 * b2) <= 4e+254) {
		tmp = t_0;
	} else {
		tmp = (a2 / b2) * (a1 / b1);
	}
	return tmp;
}

Python

def code(a1, a2, b1, b2):
	t_0 = a2 / ((b1 * b2) / a1)
	t_1 = (a1 * (a2 / b2)) / b1
	tmp = 0
	if (b1 * b2) <= -2e+131:
		tmp = t_1
	elif (b1 * b2) <= -2e-177:
		tmp = t_0
	elif (b1 * b2) <= 5e-238:
		tmp = t_1
	elif (b1 * b2) <= 4e+254:
		tmp = t_0
	else:
		tmp = (a2 / b2) * (a1 / b1)
	return tmp

Julia

function code(a1, a2, b1, b2)
	t_0 = Float64(a2 / Float64(Float64(b1 * b2) / a1))
	t_1 = Float64(Float64(a1 * Float64(a2 / b2)) / b1)
	tmp = 0.0
	if (Float64(b1 * b2) <= -2e+131)
		tmp = t_1;
	elseif (Float64(b1 * b2) <= -2e-177)
		tmp = t_0;
	elseif (Float64(b1 * b2) <= 5e-238)
		tmp = t_1;
	elseif (Float64(b1 * b2) <= 4e+254)
		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 * b2) / a1);
	t_1 = (a1 * (a2 / b2)) / b1;
	tmp = 0.0;
	if ((b1 * b2) <= -2e+131)
		tmp = t_1;
	elseif ((b1 * b2) <= -2e-177)
		tmp = t_0;
	elseif ((b1 * b2) <= 5e-238)
		tmp = t_1;
	elseif ((b1 * b2) <= 4e+254)
		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[(a2 / N[(N[(b1 * b2), $MachinePrecision] / a1), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(N[(a1 * N[(a2 / b2), $MachinePrecision]), $MachinePrecision] / b1), $MachinePrecision]}, If[LessEqual[N[(b1 * b2), $MachinePrecision], -2e+131], t$95$1, If[LessEqual[N[(b1 * b2), $MachinePrecision], -2e-177], t$95$0, If[LessEqual[N[(b1 * b2), $MachinePrecision], 5e-238], t$95$1, If[LessEqual[N[(b1 * b2), $MachinePrecision], 4e+254], 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) < -1.9999999999999998e131 or -1.9999999999999999e-177 < (*.f64 b1 b2) < 5e-238

   1. Initial program 72.0%

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

      1. times-frac 91.2%

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

      2. *-commutative 91.2%

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

   3. Simplified 91.2%

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

      1. associate-*r/ 95.8%

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

   5. Applied egg-rr 95.8%

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

   if -1.9999999999999998e131 < (*.f64 b1 b2) < -1.9999999999999999e-177 or 5e-238 < (*.f64 b1 b2) < 3.9999999999999997e254

   1. Initial program 92.2%

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

      1. times-frac 78.0%

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

      2. *-commutative 78.0%

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

   3. Simplified 78.0%

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

      1. frac-times 92.2%

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

      2. *-commutative 92.2%

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

      3. associate-/l* 97.6%

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

      4. *-commutative 97.6%

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

   5. Applied egg-rr 97.6%

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

   if 3.9999999999999997e254 < (*.f64 b1 b2)

   1. Initial program 59.3%

      \[\frac{a1 \cdot a2}{b1 \cdot b2} \]
   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 96.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b1 \cdot b2 \leq -2 \cdot 10^{+131}:\\ \;\;\;\;\frac{a1 \cdot \frac{a2}{b2}}{b1}\\ \mathbf{elif}\;b1 \cdot b2 \leq -2 \cdot 10^{-177}:\\ \;\;\;\;\frac{a2}{\frac{b1 \cdot b2}{a1}}\\ \mathbf{elif}\;b1 \cdot b2 \leq 5 \cdot 10^{-238}:\\ \;\;\;\;\frac{a1 \cdot \frac{a2}{b2}}{b1}\\ \mathbf{elif}\;b1 \cdot b2 \leq 4 \cdot 10^{+254}:\\ \;\;\;\;\frac{a2}{\frac{b1 \cdot b2}{a1}}\\ \mathbf{else}:\\ \;\;\;\;\frac{a2}{b2} \cdot \frac{a1}{b1}\\ \end{array} \]

Alternative 4: 85.9% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b2 \leq -1.12 \cdot 10^{+62} \lor \neg \left(b2 \leq 1.08 \cdot 10^{+145}\right) \land b2 \leq 2.4 \cdot 10^{+208}:\\ \;\;\;\;\frac{a2}{b2} \cdot \frac{a1}{b1}\\ \mathbf{else}:\\ \;\;\;\;\frac{a2}{b1} \cdot \frac{a1}{b2}\\ \end{array} \end{array} \]

FPCore

(FPCore (a1 a2 b1 b2)
 :precision binary64
 (if (or (<= b2 -1.12e+62) (and (not (<= b2 1.08e+145)) (<= b2 2.4e+208)))
   (* (/ a2 b2) (/ a1 b1))
   (* (/ a2 b1) (/ a1 b2))))

C

double code(double a1, double a2, double b1, double b2) {
	double tmp;
	if ((b2 <= -1.12e+62) || (!(b2 <= 1.08e+145) && (b2 <= 2.4e+208))) {
		tmp = (a2 / b2) * (a1 / b1);
	} 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 ((b2 <= (-1.12d+62)) .or. (.not. (b2 <= 1.08d+145)) .and. (b2 <= 2.4d+208)) then
        tmp = (a2 / b2) * (a1 / b1)
    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 ((b2 <= -1.12e+62) || (!(b2 <= 1.08e+145) && (b2 <= 2.4e+208))) {
		tmp = (a2 / b2) * (a1 / b1);
	} else {
		tmp = (a2 / b1) * (a1 / b2);
	}
	return tmp;
}

Python

def code(a1, a2, b1, b2):
	tmp = 0
	if (b2 <= -1.12e+62) or (not (b2 <= 1.08e+145) and (b2 <= 2.4e+208)):
		tmp = (a2 / b2) * (a1 / b1)
	else:
		tmp = (a2 / b1) * (a1 / b2)
	return tmp

Julia

function code(a1, a2, b1, b2)
	tmp = 0.0
	if ((b2 <= -1.12e+62) || (!(b2 <= 1.08e+145) && (b2 <= 2.4e+208)))
		tmp = Float64(Float64(a2 / b2) * Float64(a1 / b1));
	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 ((b2 <= -1.12e+62) || (~((b2 <= 1.08e+145)) && (b2 <= 2.4e+208)))
		tmp = (a2 / b2) * (a1 / b1);
	else
		tmp = (a2 / b1) * (a1 / b2);
	end
	tmp_2 = tmp;
end

Wolfram

code[a1_, a2_, b1_, b2_] := If[Or[LessEqual[b2, -1.12e+62], And[N[Not[LessEqual[b2, 1.08e+145]], $MachinePrecision], LessEqual[b2, 2.4e+208]]], N[(N[(a2 / b2), $MachinePrecision] * N[(a1 / b1), $MachinePrecision]), $MachinePrecision], N[(N[(a2 / b1), $MachinePrecision] * N[(a1 / b2), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b2 < -1.1200000000000001e62 or 1.08000000000000006e145 < b2 < 2.39999999999999987e208

   1. Initial program 82.4%

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

      1. times-frac 97.0%

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

      2. *-commutative 97.0%

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

   3. Simplified 97.0%

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

   if -1.1200000000000001e62 < b2 < 1.08000000000000006e145 or 2.39999999999999987e208 < b2

   1. Initial program 79.7%

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

      1. *-commutative 79.7%

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

      2. times-frac 90.9%

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

   3. Applied egg-rr 90.9%

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

4. Final simplification 92.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b2 \leq -1.12 \cdot 10^{+62} \lor \neg \left(b2 \leq 1.08 \cdot 10^{+145}\right) \land b2 \leq 2.4 \cdot 10^{+208}:\\ \;\;\;\;\frac{a2}{b2} \cdot \frac{a1}{b1}\\ \mathbf{else}:\\ \;\;\;\;\frac{a2}{b1} \cdot \frac{a1}{b2}\\ \end{array} \]

Alternative 5: 86.2% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b2 \leq -6.1 \cdot 10^{+62}:\\ \;\;\;\;\frac{a2}{b2} \cdot \frac{a1}{b1}\\ \mathbf{elif}\;b2 \leq 3.2 \cdot 10^{-61} \lor \neg \left(b2 \leq 5.2 \cdot 10^{+232}\right):\\ \;\;\;\;\frac{a2}{b1} \cdot \frac{a1}{b2}\\ \mathbf{else}:\\ \;\;\;\;\frac{a2}{b2 \cdot \frac{b1}{a1}}\\ \end{array} \end{array} \]

FPCore

(FPCore (a1 a2 b1 b2)
 :precision binary64
 (if (<= b2 -6.1e+62)
   (* (/ a2 b2) (/ a1 b1))
   (if (or (<= b2 3.2e-61) (not (<= b2 5.2e+232)))
     (* (/ a2 b1) (/ a1 b2))
     (/ a2 (* b2 (/ b1 a1))))))

C

double code(double a1, double a2, double b1, double b2) {
	double tmp;
	if (b2 <= -6.1e+62) {
		tmp = (a2 / b2) * (a1 / b1);
	} else if ((b2 <= 3.2e-61) || !(b2 <= 5.2e+232)) {
		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 <= (-6.1d+62)) then
        tmp = (a2 / b2) * (a1 / b1)
    else if ((b2 <= 3.2d-61) .or. (.not. (b2 <= 5.2d+232))) 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 <= -6.1e+62) {
		tmp = (a2 / b2) * (a1 / b1);
	} else if ((b2 <= 3.2e-61) || !(b2 <= 5.2e+232)) {
		tmp = (a2 / b1) * (a1 / b2);
	} else {
		tmp = a2 / (b2 * (b1 / a1));
	}
	return tmp;
}

Python

def code(a1, a2, b1, b2):
	tmp = 0
	if b2 <= -6.1e+62:
		tmp = (a2 / b2) * (a1 / b1)
	elif (b2 <= 3.2e-61) or not (b2 <= 5.2e+232):
		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 <= -6.1e+62)
		tmp = Float64(Float64(a2 / b2) * Float64(a1 / b1));
	elseif ((b2 <= 3.2e-61) || !(b2 <= 5.2e+232))
		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 <= -6.1e+62)
		tmp = (a2 / b2) * (a1 / b1);
	elseif ((b2 <= 3.2e-61) || ~((b2 <= 5.2e+232)))
		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, -6.1e+62], N[(N[(a2 / b2), $MachinePrecision] * N[(a1 / b1), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[b2, 3.2e-61], N[Not[LessEqual[b2, 5.2e+232]], $MachinePrecision]], 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 3 regimes

2. if b2 < -6.0999999999999997e62

   1. Initial program 83.3%

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

      1. times-frac 96.4%

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

      2. *-commutative 96.4%

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

   3. Simplified 96.4%

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

   if -6.0999999999999997e62 < b2 < 3.2000000000000001e-61 or 5.19999999999999947e232 < b2

   1. Initial program 78.6%

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

      1. *-commutative 78.6%

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

      2. times-frac 91.8%

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

   3. Applied egg-rr 91.8%

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

   if 3.2000000000000001e-61 < b2 < 5.19999999999999947e232

   1. Initial program 82.6%

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

      1. times-frac 85.2%

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

      2. *-commutative 85.2%

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

   3. Simplified 85.2%

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

      1. *-commutative 85.2%

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

      2. clear-num 85.2%

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

      3. frac-times 92.6%

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

      4. *-un-lft-identity 92.6%

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

   5. Applied egg-rr 92.6%

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

4. Final simplification 93.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b2 \leq -6.1 \cdot 10^{+62}:\\ \;\;\;\;\frac{a2}{b2} \cdot \frac{a1}{b1}\\ \mathbf{elif}\;b2 \leq 3.2 \cdot 10^{-61} \lor \neg \left(b2 \leq 5.2 \cdot 10^{+232}\right):\\ \;\;\;\;\frac{a2}{b1} \cdot \frac{a1}{b2}\\ \mathbf{else}:\\ \;\;\;\;\frac{a2}{b2 \cdot \frac{b1}{a1}}\\ \end{array} \]

Alternative 6: 85.8% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 80.4%

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

   1. *-commutative 80.4%

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

   2. times-frac 86.6%

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

3. Applied egg-rr 86.6%

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

4. Final simplification 86.6%

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

Developer target: 86.7% 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 2023287 
(FPCore (a1 a2 b1 b2)
  :name "Quotient of products"
  :precision binary64

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

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