Quotient of products

Average Error: 11.2 → 3.2

Time: 3.4s

Precision: binary64

\[ \begin{array}{c}[b1, b2] = \mathsf{sort}([b1, b2])\\ \end{array} \]

Math

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

↓

\[\begin{array}{l} t_0 := \frac{a1 \cdot a2}{b1 \cdot b2}\\ \mathbf{if}\;t_0 \leq -5 \cdot 10^{+282}:\\ \;\;\;\;\frac{a2}{\frac{b2}{\frac{a1}{b1}}}\\ \mathbf{elif}\;t_0 \leq -5 \cdot 10^{-302}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;t_0 \leq 0:\\ \;\;\;\;\frac{a1}{b1} \cdot \frac{a2}{b2}\\ \mathbf{elif}\;t_0 \leq 2 \cdot 10^{+283}:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;{\left(\frac{b1}{a1 \cdot \frac{a2}{b2}}\right)}^{-1}\\ \end{array} \]

FPCore

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

↓

(FPCore (a1 a2 b1 b2)
 :precision binary64
 (let* ((t_0 (/ (* a1 a2) (* b1 b2))))
   (if (<= t_0 -5e+282)
     (/ a2 (/ b2 (/ a1 b1)))
     (if (<= t_0 -5e-302)
       t_0
       (if (<= t_0 0.0)
         (* (/ a1 b1) (/ a2 b2))
         (if (<= t_0 2e+283) t_0 (pow (/ b1 (* a1 (/ a2 b2))) -1.0)))))))

C

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

↓

double code(double a1, double a2, double b1, double b2) {
	double t_0 = (a1 * a2) / (b1 * b2);
	double tmp;
	if (t_0 <= -5e+282) {
		tmp = a2 / (b2 / (a1 / b1));
	} else if (t_0 <= -5e-302) {
		tmp = t_0;
	} else if (t_0 <= 0.0) {
		tmp = (a1 / b1) * (a2 / b2);
	} else if (t_0 <= 2e+283) {
		tmp = t_0;
	} else {
		tmp = pow((b1 / (a1 * (a2 / b2))), -1.0);
	}
	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
    code = (a1 * a2) / (b1 * b2)
end 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) :: tmp
    t_0 = (a1 * a2) / (b1 * b2)
    if (t_0 <= (-5d+282)) then
        tmp = a2 / (b2 / (a1 / b1))
    else if (t_0 <= (-5d-302)) then
        tmp = t_0
    else if (t_0 <= 0.0d0) then
        tmp = (a1 / b1) * (a2 / b2)
    else if (t_0 <= 2d+283) then
        tmp = t_0
    else
        tmp = (b1 / (a1 * (a2 / b2))) ** (-1.0d0)
    end if
    code = tmp
end function

Java

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

↓

public static double code(double a1, double a2, double b1, double b2) {
	double t_0 = (a1 * a2) / (b1 * b2);
	double tmp;
	if (t_0 <= -5e+282) {
		tmp = a2 / (b2 / (a1 / b1));
	} else if (t_0 <= -5e-302) {
		tmp = t_0;
	} else if (t_0 <= 0.0) {
		tmp = (a1 / b1) * (a2 / b2);
	} else if (t_0 <= 2e+283) {
		tmp = t_0;
	} else {
		tmp = Math.pow((b1 / (a1 * (a2 / b2))), -1.0);
	}
	return tmp;
}

Python

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

↓

def code(a1, a2, b1, b2):
	t_0 = (a1 * a2) / (b1 * b2)
	tmp = 0
	if t_0 <= -5e+282:
		tmp = a2 / (b2 / (a1 / b1))
	elif t_0 <= -5e-302:
		tmp = t_0
	elif t_0 <= 0.0:
		tmp = (a1 / b1) * (a2 / b2)
	elif t_0 <= 2e+283:
		tmp = t_0
	else:
		tmp = math.pow((b1 / (a1 * (a2 / b2))), -1.0)
	return tmp

Julia

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

↓

function code(a1, a2, b1, b2)
	t_0 = Float64(Float64(a1 * a2) / Float64(b1 * b2))
	tmp = 0.0
	if (t_0 <= -5e+282)
		tmp = Float64(a2 / Float64(b2 / Float64(a1 / b1)));
	elseif (t_0 <= -5e-302)
		tmp = t_0;
	elseif (t_0 <= 0.0)
		tmp = Float64(Float64(a1 / b1) * Float64(a2 / b2));
	elseif (t_0 <= 2e+283)
		tmp = t_0;
	else
		tmp = Float64(b1 / Float64(a1 * Float64(a2 / b2))) ^ -1.0;
	end
	return tmp
end

MATLAB

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

↓

function tmp_2 = code(a1, a2, b1, b2)
	t_0 = (a1 * a2) / (b1 * b2);
	tmp = 0.0;
	if (t_0 <= -5e+282)
		tmp = a2 / (b2 / (a1 / b1));
	elseif (t_0 <= -5e-302)
		tmp = t_0;
	elseif (t_0 <= 0.0)
		tmp = (a1 / b1) * (a2 / b2);
	elseif (t_0 <= 2e+283)
		tmp = t_0;
	else
		tmp = (b1 / (a1 * (a2 / b2))) ^ -1.0;
	end
	tmp_2 = tmp;
end

Wolfram

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

↓

code[a1_, a2_, b1_, b2_] := Block[{t$95$0 = N[(N[(a1 * a2), $MachinePrecision] / N[(b1 * b2), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$0, -5e+282], N[(a2 / N[(b2 / N[(a1 / b1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$0, -5e-302], t$95$0, If[LessEqual[t$95$0, 0.0], N[(N[(a1 / b1), $MachinePrecision] * N[(a2 / b2), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$0, 2e+283], t$95$0, N[Power[N[(b1 / N[(a1 * N[(a2 / b2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], -1.0], $MachinePrecision]]]]]]

Target

Original	11.2
Target	11.2
Herbie	3.2

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

Derivation

1. Split input into 4 regimes

2. if (/.f64 (*.f64 a1 a2) (*.f64 b1 b2)) < -4.99999999999999978e282

   1. Initial program 50.0

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

   2. Applied egg-rr 13.8

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

   3. Taylor expanded in b1 around 0 50.0

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

   4. Simplified 17.1

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

   5. Applied egg-rr 17.2

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

   if -4.99999999999999978e282 < (/.f64 (*.f64 a1 a2) (*.f64 b1 b2)) < -5.00000000000000033e-302 or -0.0 < (/.f64 (*.f64 a1 a2) (*.f64 b1 b2)) < 1.99999999999999991e283

   1. Initial program 0.8

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

   2. Applied egg-rr 16.4

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

   3. Taylor expanded in b1 around 0 0.8

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

   4. Simplified 14.2

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

   5. Applied egg-rr 14.3

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

   6. Taylor expanded in a2 around 0 0.8

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

   if -5.00000000000000033e-302 < (/.f64 (*.f64 a1 a2) (*.f64 b1 b2)) < -0.0

   1. Initial program 13.2

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

   2. Applied egg-rr 3.2

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

   3. Applied egg-rr 2.5

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

   if 1.99999999999999991e283 < (/.f64 (*.f64 a1 a2) (*.f64 b1 b2))

   1. Initial program 58.9

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

   2. Applied egg-rr 7.3

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

   3. Applied egg-rr 16.7

      \[\leadsto {\color{blue}{\left(\frac{b1}{a1 \cdot \frac{a2}{b2}}\right)}}^{-1} \]
3. Recombined 4 regimes into one program.

4. Final simplification 3.2

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{a1 \cdot a2}{b1 \cdot b2} \leq -5 \cdot 10^{+282}:\\ \;\;\;\;\frac{a2}{\frac{b2}{\frac{a1}{b1}}}\\ \mathbf{elif}\;\frac{a1 \cdot a2}{b1 \cdot b2} \leq -5 \cdot 10^{-302}:\\ \;\;\;\;\frac{a1 \cdot a2}{b1 \cdot b2}\\ \mathbf{elif}\;\frac{a1 \cdot a2}{b1 \cdot b2} \leq 0:\\ \;\;\;\;\frac{a1}{b1} \cdot \frac{a2}{b2}\\ \mathbf{elif}\;\frac{a1 \cdot a2}{b1 \cdot b2} \leq 2 \cdot 10^{+283}:\\ \;\;\;\;\frac{a1 \cdot a2}{b1 \cdot b2}\\ \mathbf{else}:\\ \;\;\;\;{\left(\frac{b1}{a1 \cdot \frac{a2}{b2}}\right)}^{-1}\\ \end{array} \]

Reproduce

herbie shell --seed 2022210 
(FPCore (a1 a2 b1 b2)
  :name "Quotient of products"
  :precision binary64

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

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