Quotient of products

Average Error: 11.6 → 3.0

Time: 12.5s

Precision: binary64

Cost: 2512

Math

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

↓

\[\begin{array}{l} t_0 := \frac{a1 \cdot a2}{b1 \cdot b2}\\ \mathbf{if}\;t_0 \leq -1 \cdot 10^{+259}:\\ \;\;\;\;\frac{\frac{a1}{b2} \cdot a2}{b1}\\ \mathbf{elif}\;t_0 \leq -1 \cdot 10^{-320}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;t_0 \leq 0:\\ \;\;\;\;\frac{a2}{b2} \cdot \frac{a1}{b1}\\ \mathbf{elif}\;t_0 \leq 5 \cdot 10^{+304}:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{a2}{b1}}{b2} \cdot a1\\ \end{array} \]

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 -1e+259)
     (/ (* (/ a1 b2) a2) b1)
     (if (<= t_0 -1e-320)
       t_0
       (if (<= t_0 0.0)
         (* (/ a2 b2) (/ a1 b1))
         (if (<= t_0 5e+304) t_0 (* (/ (/ a2 b1) b2) a1)))))))

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 <= -1e+259) {
		tmp = ((a1 / b2) * a2) / b1;
	} else if (t_0 <= -1e-320) {
		tmp = t_0;
	} else if (t_0 <= 0.0) {
		tmp = (a2 / b2) * (a1 / b1);
	} else if (t_0 <= 5e+304) {
		tmp = t_0;
	} else {
		tmp = ((a2 / b1) / b2) * 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
    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 <= (-1d+259)) then
        tmp = ((a1 / b2) * a2) / b1
    else if (t_0 <= (-1d-320)) then
        tmp = t_0
    else if (t_0 <= 0.0d0) then
        tmp = (a2 / b2) * (a1 / b1)
    else if (t_0 <= 5d+304) then
        tmp = t_0
    else
        tmp = ((a2 / b1) / b2) * a1
    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 <= -1e+259) {
		tmp = ((a1 / b2) * a2) / b1;
	} else if (t_0 <= -1e-320) {
		tmp = t_0;
	} else if (t_0 <= 0.0) {
		tmp = (a2 / b2) * (a1 / b1);
	} else if (t_0 <= 5e+304) {
		tmp = t_0;
	} else {
		tmp = ((a2 / b1) / b2) * a1;
	}
	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 <= -1e+259:
		tmp = ((a1 / b2) * a2) / b1
	elif t_0 <= -1e-320:
		tmp = t_0
	elif t_0 <= 0.0:
		tmp = (a2 / b2) * (a1 / b1)
	elif t_0 <= 5e+304:
		tmp = t_0
	else:
		tmp = ((a2 / b1) / b2) * a1
	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 <= -1e+259)
		tmp = Float64(Float64(Float64(a1 / b2) * a2) / b1);
	elseif (t_0 <= -1e-320)
		tmp = t_0;
	elseif (t_0 <= 0.0)
		tmp = Float64(Float64(a2 / b2) * Float64(a1 / b1));
	elseif (t_0 <= 5e+304)
		tmp = t_0;
	else
		tmp = Float64(Float64(Float64(a2 / b1) / b2) * a1);
	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 <= -1e+259)
		tmp = ((a1 / b2) * a2) / b1;
	elseif (t_0 <= -1e-320)
		tmp = t_0;
	elseif (t_0 <= 0.0)
		tmp = (a2 / b2) * (a1 / b1);
	elseif (t_0 <= 5e+304)
		tmp = t_0;
	else
		tmp = ((a2 / b1) / b2) * a1;
	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, -1e+259], N[(N[(N[(a1 / b2), $MachinePrecision] * a2), $MachinePrecision] / b1), $MachinePrecision], If[LessEqual[t$95$0, -1e-320], t$95$0, If[LessEqual[t$95$0, 0.0], N[(N[(a2 / b2), $MachinePrecision] * N[(a1 / b1), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$0, 5e+304], t$95$0, N[(N[(N[(a2 / b1), $MachinePrecision] / b2), $MachinePrecision] * a1), $MachinePrecision]]]]]]

Target

Original	11.6
Target	11.3
Herbie	3.0

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

Derivation

1. Split input into 4 regimes

2. if (/.f64 (*.f64 a1 a2) (*.f64 b1 b2)) < -9.999999999999999e258

   1. Initial program 44.6

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

   2. Applied egg-rr 18.7

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

   if -9.999999999999999e258 < (/.f64 (*.f64 a1 a2) (*.f64 b1 b2)) < -9.99989e-321 or -0.0 < (/.f64 (*.f64 a1 a2) (*.f64 b1 b2)) < 4.9999999999999997e304

   1. Initial program 0.8

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

   if -9.99989e-321 < (/.f64 (*.f64 a1 a2) (*.f64 b1 b2)) < -0.0

   1. Initial program 13.4

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

   2. Applied egg-rr 2.0

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

   if 4.9999999999999997e304 < (/.f64 (*.f64 a1 a2) (*.f64 b1 b2))

   1. Initial program 62.9

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

   2. Applied egg-rr 45.9

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

   3. Applied egg-rr 13.2

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

Alternatives

Alternative 1
Error	2.4
Cost	2512

\[\begin{array}{l} t_0 := \frac{a1 \cdot a2}{b1 \cdot b2}\\ \mathbf{if}\;t_0 \leq -\infty:\\ \;\;\;\;\frac{a2}{b1} \cdot \frac{a1}{b2}\\ \mathbf{elif}\;t_0 \leq -1 \cdot 10^{-320}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;t_0 \leq 0:\\ \;\;\;\;\frac{a2}{b2} \cdot \frac{a1}{b1}\\ \mathbf{elif}\;t_0 \leq 5 \cdot 10^{+304}:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{a2}{b1}}{b2} \cdot a1\\ \end{array} \]

Alternative 2
Error	5.4
Cost	1488

\[\begin{array}{l} t_0 := \frac{a1}{b1 \cdot b2} \cdot a2\\ t_1 := \frac{a2}{b1} \cdot \frac{a1}{b2}\\ \mathbf{if}\;b1 \cdot b2 \leq -5 \cdot 10^{+276}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b1 \cdot b2 \leq -5 \cdot 10^{-273}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;b1 \cdot b2 \leq 5 \cdot 10^{-206}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b1 \cdot b2 \leq 10^{+147}:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 3
Error	5.3
Cost	1488

\[\begin{array}{l} t_0 := \frac{a1}{b1 \cdot b2} \cdot a2\\ t_1 := \frac{a2}{b1} \cdot \frac{a1}{b2}\\ \mathbf{if}\;b1 \cdot b2 \leq -2 \cdot 10^{+196}:\\ \;\;\;\;\frac{a2}{b2} \cdot \frac{a1}{b1}\\ \mathbf{elif}\;b1 \cdot b2 \leq -5 \cdot 10^{-273}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;b1 \cdot b2 \leq 5 \cdot 10^{-206}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b1 \cdot b2 \leq 10^{+147}:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 4
Error	5.8
Cost	1488

\[\begin{array}{l} t_0 := \frac{a1}{b1 \cdot b2} \cdot a2\\ \mathbf{if}\;b1 \cdot b2 \leq -2 \cdot 10^{+196}:\\ \;\;\;\;\frac{a2}{b2} \cdot \frac{a1}{b1}\\ \mathbf{elif}\;b1 \cdot b2 \leq -5 \cdot 10^{-273}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;b1 \cdot b2 \leq 5 \cdot 10^{-206}:\\ \;\;\;\;\frac{a2}{b1} \cdot \frac{a1}{b2}\\ \mathbf{elif}\;b1 \cdot b2 \leq 10^{+147}:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{a2}{b1}}{b2} \cdot a1\\ \end{array} \]

Alternative 5
Error	11.6
Cost	448

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

Reproduce

herbie shell --seed 2023010 
(FPCore (a1 a2 b1 b2)
  :name "Quotient of products"
  :precision binary64

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

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