Quotient of products

Percentage Accurate: 85.7% → 95.4%

Time: 3.1s

Alternatives: 5

Speedup: 1.0×

• 20.1% 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: 85.7% 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

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{a1 \cdot a2}{b1 \cdot b2}\\ \mathbf{if}\;t_0 \leq -2 \cdot 10^{+298}:\\ \;\;\;\;\frac{a2}{b2 \cdot \frac{b1}{a1}}\\ \mathbf{elif}\;t_0 \leq -5 \cdot 10^{-210}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;t_0 \leq 10^{-295}:\\ \;\;\;\;\frac{\frac{a1}{b1}}{\frac{b2}{a2}}\\ \mathbf{elif}\;t_0 \leq 5 \cdot 10^{+285}:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;\frac{a1}{b1 \cdot \frac{b2}{a2}}\\ \end{array} \end{array} \]

FPCore

(FPCore (a1 a2 b1 b2)
 :precision binary64
 (let* ((t_0 (/ (* a1 a2) (* b1 b2))))
   (if (<= t_0 -2e+298)
     (/ a2 (* b2 (/ b1 a1)))
     (if (<= t_0 -5e-210)
       t_0
       (if (<= t_0 1e-295)
         (/ (/ a1 b1) (/ b2 a2))
         (if (<= t_0 5e+285) t_0 (/ a1 (* b1 (/ b2 a2)))))))))

C

double code(double a1, double a2, double b1, double b2) {
	double t_0 = (a1 * a2) / (b1 * b2);
	double tmp;
	if (t_0 <= -2e+298) {
		tmp = a2 / (b2 * (b1 / a1));
	} else if (t_0 <= -5e-210) {
		tmp = t_0;
	} else if (t_0 <= 1e-295) {
		tmp = (a1 / b1) / (b2 / a2);
	} else if (t_0 <= 5e+285) {
		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 = (a1 * a2) / (b1 * b2)
    if (t_0 <= (-2d+298)) then
        tmp = a2 / (b2 * (b1 / a1))
    else if (t_0 <= (-5d-210)) then
        tmp = t_0
    else if (t_0 <= 1d-295) then
        tmp = (a1 / b1) / (b2 / a2)
    else if (t_0 <= 5d+285) 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 = (a1 * a2) / (b1 * b2);
	double tmp;
	if (t_0 <= -2e+298) {
		tmp = a2 / (b2 * (b1 / a1));
	} else if (t_0 <= -5e-210) {
		tmp = t_0;
	} else if (t_0 <= 1e-295) {
		tmp = (a1 / b1) / (b2 / a2);
	} else if (t_0 <= 5e+285) {
		tmp = t_0;
	} else {
		tmp = a1 / (b1 * (b2 / a2));
	}
	return tmp;
}

Python

def code(a1, a2, b1, b2):
	t_0 = (a1 * a2) / (b1 * b2)
	tmp = 0
	if t_0 <= -2e+298:
		tmp = a2 / (b2 * (b1 / a1))
	elif t_0 <= -5e-210:
		tmp = t_0
	elif t_0 <= 1e-295:
		tmp = (a1 / b1) / (b2 / a2)
	elif t_0 <= 5e+285:
		tmp = t_0
	else:
		tmp = a1 / (b1 * (b2 / a2))
	return tmp

Julia

function code(a1, a2, b1, b2)
	t_0 = Float64(Float64(a1 * a2) / Float64(b1 * b2))
	tmp = 0.0
	if (t_0 <= -2e+298)
		tmp = Float64(a2 / Float64(b2 * Float64(b1 / a1)));
	elseif (t_0 <= -5e-210)
		tmp = t_0;
	elseif (t_0 <= 1e-295)
		tmp = Float64(Float64(a1 / b1) / Float64(b2 / a2));
	elseif (t_0 <= 5e+285)
		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 = (a1 * a2) / (b1 * b2);
	tmp = 0.0;
	if (t_0 <= -2e+298)
		tmp = a2 / (b2 * (b1 / a1));
	elseif (t_0 <= -5e-210)
		tmp = t_0;
	elseif (t_0 <= 1e-295)
		tmp = (a1 / b1) / (b2 / a2);
	elseif (t_0 <= 5e+285)
		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[(a1 * a2), $MachinePrecision] / N[(b1 * b2), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$0, -2e+298], N[(a2 / N[(b2 * N[(b1 / a1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$0, -5e-210], t$95$0, If[LessEqual[t$95$0, 1e-295], N[(N[(a1 / b1), $MachinePrecision] / N[(b2 / a2), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$0, 5e+285], t$95$0, N[(a1 / N[(b1 * N[(b2 / a2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if (/.f64 (*.f64 a1 a2) (*.f64 b1 b2)) < -1.9999999999999999e298

   1. Initial program 85.7%

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

      1. times-frac 91.8%

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

      2. *-commutative 91.8%

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

   3. Simplified 91.8%

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

      1. *-commutative 91.8%

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

      2. clear-num 91.7%

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

      3. frac-times 97.9%

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

      4. *-un-lft-identity 97.9%

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

   5. Applied egg-rr 97.9%

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

   if -1.9999999999999999e298 < (/.f64 (*.f64 a1 a2) (*.f64 b1 b2)) < -5.0000000000000002e-210 or 1.00000000000000006e-295 < (/.f64 (*.f64 a1 a2) (*.f64 b1 b2)) < 5.00000000000000016e285

   1. Initial program 98.7%

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

   if -5.0000000000000002e-210 < (/.f64 (*.f64 a1 a2) (*.f64 b1 b2)) < 1.00000000000000006e-295

   1. Initial program 75.1%

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

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

      1. *-commutative 95.9%

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

      2. clear-num 95.9%

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

      3. un-div-inv 96.0%

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

   5. Applied egg-rr 96.0%

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

   if 5.00000000000000016e285 < (/.f64 (*.f64 a1 a2) (*.f64 b1 b2))

   1. Initial program 72.7%

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

      1. times-frac 94.9%

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

      2. *-commutative 94.9%

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

   3. Simplified 94.9%

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

      1. clear-num 94.8%

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

      2. frac-times 97.4%

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

      3. *-un-lft-identity 97.4%

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

   5. Applied egg-rr 97.4%

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

4. Final simplification 97.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{a1 \cdot a2}{b1 \cdot b2} \leq -2 \cdot 10^{+298}:\\ \;\;\;\;\frac{a2}{b2 \cdot \frac{b1}{a1}}\\ \mathbf{elif}\;\frac{a1 \cdot a2}{b1 \cdot b2} \leq -5 \cdot 10^{-210}:\\ \;\;\;\;\frac{a1 \cdot a2}{b1 \cdot b2}\\ \mathbf{elif}\;\frac{a1 \cdot a2}{b1 \cdot b2} \leq 10^{-295}:\\ \;\;\;\;\frac{\frac{a1}{b1}}{\frac{b2}{a2}}\\ \mathbf{elif}\;\frac{a1 \cdot a2}{b1 \cdot b2} \leq 5 \cdot 10^{+285}:\\ \;\;\;\;\frac{a1 \cdot a2}{b1 \cdot b2}\\ \mathbf{else}:\\ \;\;\;\;\frac{a1}{b1 \cdot \frac{b2}{a2}}\\ \end{array} \]

Alternative 2: 95.8% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{a1 \cdot a2}{b1 \cdot b2}\\ \mathbf{if}\;t_0 \leq -2 \cdot 10^{+298}:\\ \;\;\;\;\frac{a2}{b2 \cdot \frac{b1}{a1}}\\ \mathbf{elif}\;t_0 \leq -2 \cdot 10^{-244}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;t_0 \leq 10^{-295}:\\ \;\;\;\;\frac{a1}{b1} \cdot \frac{a2}{b2}\\ \mathbf{elif}\;t_0 \leq 5 \cdot 10^{+285}:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;\frac{a1}{b1 \cdot \frac{b2}{a2}}\\ \end{array} \end{array} \]

FPCore

(FPCore (a1 a2 b1 b2)
 :precision binary64
 (let* ((t_0 (/ (* a1 a2) (* b1 b2))))
   (if (<= t_0 -2e+298)
     (/ a2 (* b2 (/ b1 a1)))
     (if (<= t_0 -2e-244)
       t_0
       (if (<= t_0 1e-295)
         (* (/ a1 b1) (/ a2 b2))
         (if (<= t_0 5e+285) t_0 (/ a1 (* b1 (/ b2 a2)))))))))

C

double code(double a1, double a2, double b1, double b2) {
	double t_0 = (a1 * a2) / (b1 * b2);
	double tmp;
	if (t_0 <= -2e+298) {
		tmp = a2 / (b2 * (b1 / a1));
	} else if (t_0 <= -2e-244) {
		tmp = t_0;
	} else if (t_0 <= 1e-295) {
		tmp = (a1 / b1) * (a2 / b2);
	} else if (t_0 <= 5e+285) {
		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 = (a1 * a2) / (b1 * b2)
    if (t_0 <= (-2d+298)) then
        tmp = a2 / (b2 * (b1 / a1))
    else if (t_0 <= (-2d-244)) then
        tmp = t_0
    else if (t_0 <= 1d-295) then
        tmp = (a1 / b1) * (a2 / b2)
    else if (t_0 <= 5d+285) 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 = (a1 * a2) / (b1 * b2);
	double tmp;
	if (t_0 <= -2e+298) {
		tmp = a2 / (b2 * (b1 / a1));
	} else if (t_0 <= -2e-244) {
		tmp = t_0;
	} else if (t_0 <= 1e-295) {
		tmp = (a1 / b1) * (a2 / b2);
	} else if (t_0 <= 5e+285) {
		tmp = t_0;
	} else {
		tmp = a1 / (b1 * (b2 / a2));
	}
	return tmp;
}

Python

def code(a1, a2, b1, b2):
	t_0 = (a1 * a2) / (b1 * b2)
	tmp = 0
	if t_0 <= -2e+298:
		tmp = a2 / (b2 * (b1 / a1))
	elif t_0 <= -2e-244:
		tmp = t_0
	elif t_0 <= 1e-295:
		tmp = (a1 / b1) * (a2 / b2)
	elif t_0 <= 5e+285:
		tmp = t_0
	else:
		tmp = a1 / (b1 * (b2 / a2))
	return tmp

Julia

function code(a1, a2, b1, b2)
	t_0 = Float64(Float64(a1 * a2) / Float64(b1 * b2))
	tmp = 0.0
	if (t_0 <= -2e+298)
		tmp = Float64(a2 / Float64(b2 * Float64(b1 / a1)));
	elseif (t_0 <= -2e-244)
		tmp = t_0;
	elseif (t_0 <= 1e-295)
		tmp = Float64(Float64(a1 / b1) * Float64(a2 / b2));
	elseif (t_0 <= 5e+285)
		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 = (a1 * a2) / (b1 * b2);
	tmp = 0.0;
	if (t_0 <= -2e+298)
		tmp = a2 / (b2 * (b1 / a1));
	elseif (t_0 <= -2e-244)
		tmp = t_0;
	elseif (t_0 <= 1e-295)
		tmp = (a1 / b1) * (a2 / b2);
	elseif (t_0 <= 5e+285)
		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[(a1 * a2), $MachinePrecision] / N[(b1 * b2), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$0, -2e+298], N[(a2 / N[(b2 * N[(b1 / a1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$0, -2e-244], t$95$0, If[LessEqual[t$95$0, 1e-295], N[(N[(a1 / b1), $MachinePrecision] * N[(a2 / b2), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$0, 5e+285], t$95$0, N[(a1 / N[(b1 * N[(b2 / a2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if (/.f64 (*.f64 a1 a2) (*.f64 b1 b2)) < -1.9999999999999999e298

   1. Initial program 85.7%

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

      1. times-frac 91.8%

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

      2. *-commutative 91.8%

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

   3. Simplified 91.8%

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

      1. *-commutative 91.8%

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

      2. clear-num 91.7%

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

      3. frac-times 97.9%

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

      4. *-un-lft-identity 97.9%

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

   5. Applied egg-rr 97.9%

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

   if -1.9999999999999999e298 < (/.f64 (*.f64 a1 a2) (*.f64 b1 b2)) < -1.9999999999999999e-244 or 1.00000000000000006e-295 < (/.f64 (*.f64 a1 a2) (*.f64 b1 b2)) < 5.00000000000000016e285

   1. Initial program 98.8%

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

   if -1.9999999999999999e-244 < (/.f64 (*.f64 a1 a2) (*.f64 b1 b2)) < 1.00000000000000006e-295

   1. Initial program 74.0%

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

      1. times-frac 95.7%

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

      2. *-commutative 95.7%

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

   3. Simplified 95.7%

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

   if 5.00000000000000016e285 < (/.f64 (*.f64 a1 a2) (*.f64 b1 b2))

   1. Initial program 72.7%

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

      1. times-frac 94.9%

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

      2. *-commutative 94.9%

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

   3. Simplified 94.9%

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

      1. clear-num 94.8%

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

      2. frac-times 97.4%

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

      3. *-un-lft-identity 97.4%

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

   5. Applied egg-rr 97.4%

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

4. Final simplification 97.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{a1 \cdot a2}{b1 \cdot b2} \leq -2 \cdot 10^{+298}:\\ \;\;\;\;\frac{a2}{b2 \cdot \frac{b1}{a1}}\\ \mathbf{elif}\;\frac{a1 \cdot a2}{b1 \cdot b2} \leq -2 \cdot 10^{-244}:\\ \;\;\;\;\frac{a1 \cdot a2}{b1 \cdot b2}\\ \mathbf{elif}\;\frac{a1 \cdot a2}{b1 \cdot b2} \leq 10^{-295}:\\ \;\;\;\;\frac{a1}{b1} \cdot \frac{a2}{b2}\\ \mathbf{elif}\;\frac{a1 \cdot a2}{b1 \cdot b2} \leq 5 \cdot 10^{+285}:\\ \;\;\;\;\frac{a1 \cdot a2}{b1 \cdot b2}\\ \mathbf{else}:\\ \;\;\;\;\frac{a1}{b1 \cdot \frac{b2}{a2}}\\ \end{array} \]

Alternative 3: 85.9% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b1 \leq -1.2 \cdot 10^{-233}:\\ \;\;\;\;a1 \cdot \frac{a2}{b1 \cdot b2}\\ \mathbf{else}:\\ \;\;\;\;\frac{a1}{b1} \cdot \frac{a2}{b2}\\ \end{array} \end{array} \]

FPCore

(FPCore (a1 a2 b1 b2)
 :precision binary64
 (if (<= b1 -1.2e-233) (* a1 (/ a2 (* b1 b2))) (* (/ a1 b1) (/ a2 b2))))

C

double code(double a1, double a2, double b1, double b2) {
	double tmp;
	if (b1 <= -1.2e-233) {
		tmp = a1 * (a2 / (b1 * b2));
	} 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 <= (-1.2d-233)) then
        tmp = a1 * (a2 / (b1 * b2))
    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 <= -1.2e-233) {
		tmp = a1 * (a2 / (b1 * b2));
	} else {
		tmp = (a1 / b1) * (a2 / b2);
	}
	return tmp;
}

Python

def code(a1, a2, b1, b2):
	tmp = 0
	if b1 <= -1.2e-233:
		tmp = a1 * (a2 / (b1 * b2))
	else:
		tmp = (a1 / b1) * (a2 / b2)
	return tmp

Julia

function code(a1, a2, b1, b2)
	tmp = 0.0
	if (b1 <= -1.2e-233)
		tmp = Float64(a1 * Float64(a2 / Float64(b1 * b2)));
	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 <= -1.2e-233)
		tmp = a1 * (a2 / (b1 * b2));
	else
		tmp = (a1 / b1) * (a2 / b2);
	end
	tmp_2 = tmp;
end

Wolfram

code[a1_, a2_, b1_, b2_] := If[LessEqual[b1, -1.2e-233], N[(a1 * N[(a2 / N[(b1 * b2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(a1 / b1), $MachinePrecision] * N[(a2 / b2), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b1 < -1.19999999999999995e-233

   1. Initial program 89.5%

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

      1. times-frac 85.7%

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

      2. *-commutative 85.7%

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

   3. Simplified 85.7%

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

   4. Taylor expanded in a2 around 0 89.5%

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

      1. *-commutative 89.5%

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

      2. associate-*r/ 90.9%

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

      3. *-commutative 90.9%

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

   6. Simplified 90.9%

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

   if -1.19999999999999995e-233 < b1

   1. Initial program 84.6%

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

      1. times-frac 89.2%

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

      2. *-commutative 89.2%

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

   3. Simplified 89.2%

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

4. Final simplification 89.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b1 \leq -1.2 \cdot 10^{-233}:\\ \;\;\;\;a1 \cdot \frac{a2}{b1 \cdot b2}\\ \mathbf{else}:\\ \;\;\;\;\frac{a1}{b1} \cdot \frac{a2}{b2}\\ \end{array} \]

Alternative 4: 86.3% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b1 \leq 2 \cdot 10^{+81}:\\ \;\;\;\;\frac{a1}{b1 \cdot \frac{b2}{a2}}\\ \mathbf{else}:\\ \;\;\;\;\frac{a1}{b1} \cdot \frac{a2}{b2}\\ \end{array} \end{array} \]

FPCore

(FPCore (a1 a2 b1 b2)
 :precision binary64
 (if (<= b1 2e+81) (/ a1 (* b1 (/ b2 a2))) (* (/ a1 b1) (/ a2 b2))))

C

double code(double a1, double a2, double b1, double b2) {
	double tmp;
	if (b1 <= 2e+81) {
		tmp = a1 / (b1 * (b2 / a2));
	} 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 <= 2d+81) then
        tmp = a1 / (b1 * (b2 / a2))
    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 <= 2e+81) {
		tmp = a1 / (b1 * (b2 / a2));
	} else {
		tmp = (a1 / b1) * (a2 / b2);
	}
	return tmp;
}

Python

def code(a1, a2, b1, b2):
	tmp = 0
	if b1 <= 2e+81:
		tmp = a1 / (b1 * (b2 / a2))
	else:
		tmp = (a1 / b1) * (a2 / b2)
	return tmp

Julia

function code(a1, a2, b1, b2)
	tmp = 0.0
	if (b1 <= 2e+81)
		tmp = Float64(a1 / Float64(b1 * Float64(b2 / a2)));
	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 <= 2e+81)
		tmp = a1 / (b1 * (b2 / a2));
	else
		tmp = (a1 / b1) * (a2 / b2);
	end
	tmp_2 = tmp;
end

Wolfram

code[a1_, a2_, b1_, b2_] := If[LessEqual[b1, 2e+81], N[(a1 / N[(b1 * N[(b2 / a2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(a1 / b1), $MachinePrecision] * N[(a2 / b2), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b1 < 1.99999999999999984e81

   1. Initial program 88.3%

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

      1. times-frac 86.3%

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

      2. *-commutative 86.3%

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

   3. Simplified 86.3%

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

      1. clear-num 86.2%

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

      2. frac-times 91.4%

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

      3. *-un-lft-identity 91.4%

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

   5. Applied egg-rr 91.4%

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

   if 1.99999999999999984e81 < b1

   1. Initial program 80.2%

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

      1. times-frac 93.3%

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

      2. *-commutative 93.3%

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

   3. Simplified 93.3%

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

4. Final simplification 91.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b1 \leq 2 \cdot 10^{+81}:\\ \;\;\;\;\frac{a1}{b1 \cdot \frac{b2}{a2}}\\ \mathbf{else}:\\ \;\;\;\;\frac{a1}{b1} \cdot \frac{a2}{b2}\\ \end{array} \]

Alternative 5: 86.0% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 86.7%

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

   1. times-frac 87.7%

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

   2. *-commutative 87.7%

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

3. Simplified 87.7%

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

4. Taylor expanded in a2 around 0 86.7%

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

   1. *-commutative 86.7%

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

   2. associate-*r/ 86.9%

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

   3. *-commutative 86.9%

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

6. Simplified 86.9%

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

7. Final simplification 86.9%

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

Developer target: 85.9% 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 2023292 
(FPCore (a1 a2 b1 b2)
  :name "Quotient of products"
  :precision binary64

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

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