Quotient of products

Average Accuracy: 66.0% → 75.5%

Time: 30.0s

Precision: binary64

Cost: 2512

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

Math

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

↓

\[\begin{array}{l} t_0 := \frac{a1 \cdot a2}{b1 \cdot b2}\\ t_1 := \frac{a1 \cdot \frac{a2}{b2}}{b1}\\ \mathbf{if}\;t_0 \leq -4 \cdot 10^{+284}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t_0 \leq -5 \cdot 10^{-309}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;t_0 \leq 0:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t_0 \leq 10^{+305}:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;\frac{a1}{b2 \cdot \frac{b1}{a2}}\\ \end{array} \]

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))) (t_1 (/ (* a1 (/ a2 b2)) b1)))
   (if (<= t_0 -4e+284)
     t_1
     (if (<= t_0 -5e-309)
       t_0
       (if (<= t_0 0.0)
         t_1
         (if (<= t_0 1e+305) t_0 (/ a1 (* b2 (/ b1 a2)))))))))

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 t_1 = (a1 * (a2 / b2)) / b1;
	double tmp;
	if (t_0 <= -4e+284) {
		tmp = t_1;
	} else if (t_0 <= -5e-309) {
		tmp = t_0;
	} else if (t_0 <= 0.0) {
		tmp = t_1;
	} else if (t_0 <= 1e+305) {
		tmp = t_0;
	} else {
		tmp = a1 / (b2 * (b1 / 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
    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) :: t_1
    real(8) :: tmp
    t_0 = (a1 * a2) / (b1 * b2)
    t_1 = (a1 * (a2 / b2)) / b1
    if (t_0 <= (-4d+284)) then
        tmp = t_1
    else if (t_0 <= (-5d-309)) then
        tmp = t_0
    else if (t_0 <= 0.0d0) then
        tmp = t_1
    else if (t_0 <= 1d+305) then
        tmp = t_0
    else
        tmp = a1 / (b2 * (b1 / a2))
    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 t_1 = (a1 * (a2 / b2)) / b1;
	double tmp;
	if (t_0 <= -4e+284) {
		tmp = t_1;
	} else if (t_0 <= -5e-309) {
		tmp = t_0;
	} else if (t_0 <= 0.0) {
		tmp = t_1;
	} else if (t_0 <= 1e+305) {
		tmp = t_0;
	} else {
		tmp = a1 / (b2 * (b1 / a2));
	}
	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)
	t_1 = (a1 * (a2 / b2)) / b1
	tmp = 0
	if t_0 <= -4e+284:
		tmp = t_1
	elif t_0 <= -5e-309:
		tmp = t_0
	elif t_0 <= 0.0:
		tmp = t_1
	elif t_0 <= 1e+305:
		tmp = t_0
	else:
		tmp = a1 / (b2 * (b1 / a2))
	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))
	t_1 = Float64(Float64(a1 * Float64(a2 / b2)) / b1)
	tmp = 0.0
	if (t_0 <= -4e+284)
		tmp = t_1;
	elseif (t_0 <= -5e-309)
		tmp = t_0;
	elseif (t_0 <= 0.0)
		tmp = t_1;
	elseif (t_0 <= 1e+305)
		tmp = t_0;
	else
		tmp = Float64(a1 / Float64(b2 * Float64(b1 / a2)));
	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);
	t_1 = (a1 * (a2 / b2)) / b1;
	tmp = 0.0;
	if (t_0 <= -4e+284)
		tmp = t_1;
	elseif (t_0 <= -5e-309)
		tmp = t_0;
	elseif (t_0 <= 0.0)
		tmp = t_1;
	elseif (t_0 <= 1e+305)
		tmp = t_0;
	else
		tmp = a1 / (b2 * (b1 / a2));
	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]}, Block[{t$95$1 = N[(N[(a1 * N[(a2 / b2), $MachinePrecision]), $MachinePrecision] / b1), $MachinePrecision]}, If[LessEqual[t$95$0, -4e+284], t$95$1, If[LessEqual[t$95$0, -5e-309], t$95$0, If[LessEqual[t$95$0, 0.0], t$95$1, If[LessEqual[t$95$0, 1e+305], t$95$0, N[(a1 / N[(b2 * N[(b1 / a2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]

Target

Original	66.0%
Target	65.5%
Herbie	75.5%

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

Derivation

1. Split input into 3 regimes

2. if (/.f64 (*.f64 a1 a2) (*.f64 b1 b2)) < -4.00000000000000032e284 or -4.9999999999999995e-309 < (/.f64 (*.f64 a1 a2) (*.f64 b1 b2)) < -0.0

   1. Initial program 55.7%

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

   2. Simplified 69.1%

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

      [Start] 55.7	\[ \frac{a1 \cdot a2}{b1 \cdot b2} \]
      times-frac [=>] 69.1	\[ \color{blue}{\frac{a1}{b1} \cdot \frac{a2}{b2}} \]

   3. Applied egg-rr 69.2%

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

      [Start] 69.1	\[ \frac{a1}{b1} \cdot \frac{a2}{b2} \]
      associate-*l/ [=>] 69.2	\[ \color{blue}{\frac{a1 \cdot \frac{a2}{b2}}{b1}} \]

   if -4.00000000000000032e284 < (/.f64 (*.f64 a1 a2) (*.f64 b1 b2)) < -4.9999999999999995e-309 or -0.0 < (/.f64 (*.f64 a1 a2) (*.f64 b1 b2)) < 9.9999999999999994e304

   1. Initial program 99.4%

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

   if 9.9999999999999994e304 < (/.f64 (*.f64 a1 a2) (*.f64 b1 b2))

   1. Initial program 0.0%

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

   2. Simplified 37.4%

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

      [Start] 0.0	\[ \frac{a1 \cdot a2}{b1 \cdot b2} \]
      associate-/l* [=>] 10.3	\[ \color{blue}{\frac{a1}{\frac{b1 \cdot b2}{a2}}} \]
      *-commutative [=>] 10.3	\[ \frac{a1}{\frac{\color{blue}{b2 \cdot b1}}{a2}} \]
      associate-/l* [=>] 37.4	\[ \frac{a1}{\color{blue}{\frac{b2}{\frac{a2}{b1}}}} \]

   3. Applied egg-rr 37.4%

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

      [Start] 37.4	\[ \frac{a1}{\frac{b2}{\frac{a2}{b1}}} \]
      clear-num [=>] 37.2	\[ \frac{a1}{\color{blue}{\frac{1}{\frac{\frac{a2}{b1}}{b2}}}} \]
      associate-/r/ [=>] 37.3	\[ \frac{a1}{\color{blue}{\frac{1}{\frac{a2}{b1}} \cdot b2}} \]
      clear-num [<=] 37.4	\[ \frac{a1}{\color{blue}{\frac{b1}{a2}} \cdot b2} \]

3. Recombined 3 regimes into one program.

4. Final simplification 78.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{a1 \cdot a2}{b1 \cdot b2} \leq -4 \cdot 10^{+284}:\\ \;\;\;\;\frac{a1 \cdot \frac{a2}{b2}}{b1}\\ \mathbf{elif}\;\frac{a1 \cdot a2}{b1 \cdot b2} \leq -5 \cdot 10^{-309}:\\ \;\;\;\;\frac{a1 \cdot a2}{b1 \cdot b2}\\ \mathbf{elif}\;\frac{a1 \cdot a2}{b1 \cdot b2} \leq 0:\\ \;\;\;\;\frac{a1 \cdot \frac{a2}{b2}}{b1}\\ \mathbf{elif}\;\frac{a1 \cdot a2}{b1 \cdot b2} \leq 10^{+305}:\\ \;\;\;\;\frac{a1 \cdot a2}{b1 \cdot b2}\\ \mathbf{else}:\\ \;\;\;\;\frac{a1}{b2 \cdot \frac{b1}{a2}}\\ \end{array} \]

Alternatives

Alternative 1
Accuracy	75.7%
Cost	2512

\[\begin{array}{l} t_0 := \frac{a1 \cdot a2}{b1 \cdot b2}\\ \mathbf{if}\;t_0 \leq -4 \cdot 10^{+284}:\\ \;\;\;\;\frac{a2}{b1} \cdot \frac{a1}{b2}\\ \mathbf{elif}\;t_0 \leq -2 \cdot 10^{-304}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;t_0 \leq 0:\\ \;\;\;\;\frac{a2}{b2 \cdot \frac{b1}{a1}}\\ \mathbf{elif}\;t_0 \leq 10^{+305}:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;\frac{a1}{b2 \cdot \frac{b1}{a2}}\\ \end{array} \]

Alternative 2
Accuracy	71.4%
Cost	1229

\[\begin{array}{l} \mathbf{if}\;b1 \cdot b2 \leq -1 \cdot 10^{-213} \lor \neg \left(b1 \cdot b2 \leq 5 \cdot 10^{-252}\right) \land b1 \cdot b2 \leq 10^{+201}:\\ \;\;\;\;a2 \cdot \frac{a1}{b1 \cdot b2}\\ \mathbf{else}:\\ \;\;\;\;\frac{a2}{b2} \cdot \frac{a1}{b1}\\ \end{array} \]

Alternative 3
Accuracy	70.9%
Cost	1228

\[\begin{array}{l} t_0 := a2 \cdot \frac{a1}{b1 \cdot b2}\\ \mathbf{if}\;b1 \cdot b2 \leq -1 \cdot 10^{-147}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;b1 \cdot b2 \leq 5 \cdot 10^{-163}:\\ \;\;\;\;\frac{a2}{b1} \cdot \frac{a1}{b2}\\ \mathbf{elif}\;b1 \cdot b2 \leq 10^{+201}:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;\frac{a2}{b2} \cdot \frac{a1}{b1}\\ \end{array} \]

Alternative 4
Accuracy	68.7%
Cost	1228

\[\begin{array}{l} \mathbf{if}\;b1 \cdot b2 \leq -5 \cdot 10^{+172}:\\ \;\;\;\;\frac{a2}{b2 \cdot \frac{b1}{a1}}\\ \mathbf{elif}\;b1 \cdot b2 \leq 5 \cdot 10^{-163}:\\ \;\;\;\;\frac{a1}{\frac{b2}{\frac{a2}{b1}}}\\ \mathbf{elif}\;b1 \cdot b2 \leq 10^{+201}:\\ \;\;\;\;a2 \cdot \frac{a1}{b1 \cdot b2}\\ \mathbf{else}:\\ \;\;\;\;\frac{a2}{b2} \cdot \frac{a1}{b1}\\ \end{array} \]

Alternative 5
Accuracy	68.9%
Cost	968

\[\begin{array}{l} \mathbf{if}\;b1 \cdot b2 \leq 5 \cdot 10^{-163}:\\ \;\;\;\;\frac{a1}{b2 \cdot \frac{b1}{a2}}\\ \mathbf{elif}\;b1 \cdot b2 \leq 10^{+201}:\\ \;\;\;\;a2 \cdot \frac{a1}{b1 \cdot b2}\\ \mathbf{else}:\\ \;\;\;\;\frac{a2}{b2} \cdot \frac{a1}{b1}\\ \end{array} \]

Alternative 6
Accuracy	68.8%
Cost	968

\[\begin{array}{l} \mathbf{if}\;b1 \cdot b2 \leq 5 \cdot 10^{-163}:\\ \;\;\;\;\frac{a1}{\frac{b2}{\frac{a2}{b1}}}\\ \mathbf{elif}\;b1 \cdot b2 \leq 10^{+201}:\\ \;\;\;\;a2 \cdot \frac{a1}{b1 \cdot b2}\\ \mathbf{else}:\\ \;\;\;\;\frac{a2}{b2} \cdot \frac{a1}{b1}\\ \end{array} \]

Alternative 7
Accuracy	65.5%
Cost	448

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

Alternative 8
Accuracy	22.3%
Cost	64

\[0 \]

Reproduce

herbie shell --seed 2023157 
(FPCore (a1 a2 b1 b2)
  :name "Quotient of products"
  :precision binary64

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

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