Quotient of products

Average Error: 11.1 → 6.3

Time: 3.1s

Precision: binary64

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

Math

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

↓

\[\begin{array}{l} t_0 := \frac{a2}{b1} \cdot a1\\ t_1 := \frac{t_0}{b2}\\ \mathbf{if}\;b1 \cdot b2 \leq -1 \cdot 10^{+254}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b1 \cdot b2 \leq -5 \cdot 10^{-124}:\\ \;\;\;\;a1 \cdot \frac{a2}{b1 \cdot b2}\\ \mathbf{elif}\;b1 \cdot b2 \leq 10^{-95}:\\ \;\;\;\;t_0 \cdot \frac{1}{b2}\\ \mathbf{elif}\;b1 \cdot b2 \leq 2 \cdot 10^{+140}:\\ \;\;\;\;\frac{1}{\frac{b1 \cdot b2}{a2 \cdot a1}}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

FPCore

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

↓

(FPCore (a1 a2 b1 b2)
 :precision binary64
 (let* ((t_0 (* (/ a2 b1) a1)) (t_1 (/ t_0 b2)))
   (if (<= (* b1 b2) -1e+254)
     t_1
     (if (<= (* b1 b2) -5e-124)
       (* a1 (/ a2 (* b1 b2)))
       (if (<= (* b1 b2) 1e-95)
         (* t_0 (/ 1.0 b2))
         (if (<= (* b1 b2) 2e+140) (/ 1.0 (/ (* b1 b2) (* a2 a1))) t_1))))))

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 = (a2 / b1) * a1;
	double t_1 = t_0 / b2;
	double tmp;
	if ((b1 * b2) <= -1e+254) {
		tmp = t_1;
	} else if ((b1 * b2) <= -5e-124) {
		tmp = a1 * (a2 / (b1 * b2));
	} else if ((b1 * b2) <= 1e-95) {
		tmp = t_0 * (1.0 / b2);
	} else if ((b1 * b2) <= 2e+140) {
		tmp = 1.0 / ((b1 * b2) / (a2 * a1));
	} else {
		tmp = t_1;
	}
	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 = (a2 / b1) * a1
    t_1 = t_0 / b2
    if ((b1 * b2) <= (-1d+254)) then
        tmp = t_1
    else if ((b1 * b2) <= (-5d-124)) then
        tmp = a1 * (a2 / (b1 * b2))
    else if ((b1 * b2) <= 1d-95) then
        tmp = t_0 * (1.0d0 / b2)
    else if ((b1 * b2) <= 2d+140) then
        tmp = 1.0d0 / ((b1 * b2) / (a2 * a1))
    else
        tmp = t_1
    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 = (a2 / b1) * a1;
	double t_1 = t_0 / b2;
	double tmp;
	if ((b1 * b2) <= -1e+254) {
		tmp = t_1;
	} else if ((b1 * b2) <= -5e-124) {
		tmp = a1 * (a2 / (b1 * b2));
	} else if ((b1 * b2) <= 1e-95) {
		tmp = t_0 * (1.0 / b2);
	} else if ((b1 * b2) <= 2e+140) {
		tmp = 1.0 / ((b1 * b2) / (a2 * a1));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

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

↓

def code(a1, a2, b1, b2):
	t_0 = (a2 / b1) * a1
	t_1 = t_0 / b2
	tmp = 0
	if (b1 * b2) <= -1e+254:
		tmp = t_1
	elif (b1 * b2) <= -5e-124:
		tmp = a1 * (a2 / (b1 * b2))
	elif (b1 * b2) <= 1e-95:
		tmp = t_0 * (1.0 / b2)
	elif (b1 * b2) <= 2e+140:
		tmp = 1.0 / ((b1 * b2) / (a2 * a1))
	else:
		tmp = t_1
	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(a2 / b1) * a1)
	t_1 = Float64(t_0 / b2)
	tmp = 0.0
	if (Float64(b1 * b2) <= -1e+254)
		tmp = t_1;
	elseif (Float64(b1 * b2) <= -5e-124)
		tmp = Float64(a1 * Float64(a2 / Float64(b1 * b2)));
	elseif (Float64(b1 * b2) <= 1e-95)
		tmp = Float64(t_0 * Float64(1.0 / b2));
	elseif (Float64(b1 * b2) <= 2e+140)
		tmp = Float64(1.0 / Float64(Float64(b1 * b2) / Float64(a2 * a1)));
	else
		tmp = t_1;
	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 = (a2 / b1) * a1;
	t_1 = t_0 / b2;
	tmp = 0.0;
	if ((b1 * b2) <= -1e+254)
		tmp = t_1;
	elseif ((b1 * b2) <= -5e-124)
		tmp = a1 * (a2 / (b1 * b2));
	elseif ((b1 * b2) <= 1e-95)
		tmp = t_0 * (1.0 / b2);
	elseif ((b1 * b2) <= 2e+140)
		tmp = 1.0 / ((b1 * b2) / (a2 * a1));
	else
		tmp = t_1;
	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[(a2 / b1), $MachinePrecision] * a1), $MachinePrecision]}, Block[{t$95$1 = N[(t$95$0 / b2), $MachinePrecision]}, If[LessEqual[N[(b1 * b2), $MachinePrecision], -1e+254], t$95$1, If[LessEqual[N[(b1 * b2), $MachinePrecision], -5e-124], N[(a1 * N[(a2 / N[(b1 * b2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(b1 * b2), $MachinePrecision], 1e-95], N[(t$95$0 * N[(1.0 / b2), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(b1 * b2), $MachinePrecision], 2e+140], N[(1.0 / N[(N[(b1 * b2), $MachinePrecision] / N[(a2 * a1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]

Target

Original	11.1
Target	11.4
Herbie	6.3

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

Derivation

1. Split input into 4 regimes

2. if (*.f64 b1 b2) < -9.9999999999999994e253 or 2.00000000000000012e140 < (*.f64 b1 b2)

   1. Initial program 16.0

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

   2. Simplified 15.3

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

   3. Applied egg-rr 5.6

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

   if -9.9999999999999994e253 < (*.f64 b1 b2) < -5.0000000000000003e-124

   1. Initial program 4.4

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

   2. Simplified 4.3

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

   if -5.0000000000000003e-124 < (*.f64 b1 b2) < 9.99999999999999989e-96

   1. Initial program 20.6

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

   2. Simplified 21.9

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

   3. Applied egg-rr 12.7

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

   4. Applied egg-rr 12.8

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

   if 9.99999999999999989e-96 < (*.f64 b1 b2) < 2.00000000000000012e140

   1. Initial program 2.9

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

   2. Simplified 2.7

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

   3. Applied egg-rr 3.2

      \[\leadsto \color{blue}{\frac{1}{\frac{b1 \cdot b2}{a1 \cdot a2}}} \]
3. Recombined 4 regimes into one program.

4. Final simplification 6.3

   \[\leadsto \begin{array}{l} \mathbf{if}\;b1 \cdot b2 \leq -1 \cdot 10^{+254}:\\ \;\;\;\;\frac{\frac{a2}{b1} \cdot a1}{b2}\\ \mathbf{elif}\;b1 \cdot b2 \leq -5 \cdot 10^{-124}:\\ \;\;\;\;a1 \cdot \frac{a2}{b1 \cdot b2}\\ \mathbf{elif}\;b1 \cdot b2 \leq 10^{-95}:\\ \;\;\;\;\left(\frac{a2}{b1} \cdot a1\right) \cdot \frac{1}{b2}\\ \mathbf{elif}\;b1 \cdot b2 \leq 2 \cdot 10^{+140}:\\ \;\;\;\;\frac{1}{\frac{b1 \cdot b2}{a2 \cdot a1}}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{a2}{b1} \cdot a1}{b2}\\ \end{array} \]

Reproduce

herbie shell --seed 2022197 
(FPCore (a1 a2 b1 b2)
  :name "Quotient of products"
  :precision binary64

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

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