ab-angle->ABCF D

Average Error: 16.2 → 0.3

Time: 23.8s

Precision: binary64

Cost: 900

Math

\[-\left(\left(a \cdot a\right) \cdot b\right) \cdot b \]

↓

\[-\left(\left(a \cdot b\right) \cdot 3\right) \cdot \begin{array}{l} \mathbf{if}\;b \ne 0:\\ \;\;\;\;\frac{a}{\frac{3}{b}}\\ \mathbf{else}:\\ \;\;\;\;\left(0.3333333333333333 \cdot b\right) \cdot a\\ \end{array} \]

FPCore

(FPCore (a b) :precision binary64 (- (* (* (* a a) b) b)))

↓

(FPCore (a b)
 :precision binary64
 (-
  (*
   (* (* a b) 3.0)
   (if (!= b 0.0) (/ a (/ 3.0 b)) (* (* 0.3333333333333333 b) a)))))

C

double code(double a, double b) {
	return -(((a * a) * b) * b);
}

↓

double code(double a, double b) {
	double tmp;
	if (b != 0.0) {
		tmp = a / (3.0 / b);
	} else {
		tmp = (0.3333333333333333 * b) * a;
	}
	return -(((a * b) * 3.0) * tmp);
}

Fortran

real(8) function code(a, b)
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    code = -(((a * a) * b) * b)
end function

↓

real(8) function code(a, b)
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (b /= 0.0d0) then
        tmp = a / (3.0d0 / b)
    else
        tmp = (0.3333333333333333d0 * b) * a
    end if
    code = -(((a * b) * 3.0d0) * tmp)
end function

Java

public static double code(double a, double b) {
	return -(((a * a) * b) * b);
}

↓

public static double code(double a, double b) {
	double tmp;
	if (b != 0.0) {
		tmp = a / (3.0 / b);
	} else {
		tmp = (0.3333333333333333 * b) * a;
	}
	return -(((a * b) * 3.0) * tmp);
}

Python

def code(a, b):
	return -(((a * a) * b) * b)

↓

def code(a, b):
	tmp = 0
	if b != 0.0:
		tmp = a / (3.0 / b)
	else:
		tmp = (0.3333333333333333 * b) * a
	return -(((a * b) * 3.0) * tmp)

Julia

function code(a, b)
	return Float64(-Float64(Float64(Float64(a * a) * b) * b))
end

↓

function code(a, b)
	tmp = 0.0
	if (b != 0.0)
		tmp = Float64(a / Float64(3.0 / b));
	else
		tmp = Float64(Float64(0.3333333333333333 * b) * a);
	end
	return Float64(-Float64(Float64(Float64(a * b) * 3.0) * tmp))
end

MATLAB

function tmp = code(a, b)
	tmp = -(((a * a) * b) * b);
end

↓

function tmp_2 = code(a, b)
	tmp = 0.0;
	if (b ~= 0.0)
		tmp = a / (3.0 / b);
	else
		tmp = (0.3333333333333333 * b) * a;
	end
	tmp_2 = -(((a * b) * 3.0) * tmp);
end

Wolfram

code[a_, b_] := (-N[(N[(N[(a * a), $MachinePrecision] * b), $MachinePrecision] * b), $MachinePrecision])

↓

code[a_, b_] := (-N[(N[(N[(a * b), $MachinePrecision] * 3.0), $MachinePrecision] * If[Unequal[b, 0.0], N[(a / N[(3.0 / b), $MachinePrecision]), $MachinePrecision], N[(N[(0.3333333333333333 * b), $MachinePrecision] * a), $MachinePrecision]]), $MachinePrecision])

Derivation

1. Initial program 16.2

   \[-\left(\left(a \cdot a\right) \cdot b\right) \cdot b \]

2. Applied egg-rr 0.8

   \[\leadsto -\color{blue}{{\left(\sqrt[3]{{\left(a \cdot b\right)}^{2}}\right)}^{3}} \]

3. Applied egg-rr 0.4

   \[\leadsto -\color{blue}{\frac{\frac{{\left(a \cdot b\right)}^{2}}{0.3333333333333333}}{3}} \]

4. Applied egg-rr 0.4

   \[\leadsto -\color{blue}{\left(\left(a \cdot b\right) \cdot 3\right) \cdot \left(0.3333333333333333 \cdot \left(a \cdot b\right)\right)} \]

5. Applied egg-rr 0.3

   \[\leadsto -\left(\left(a \cdot b\right) \cdot 3\right) \cdot \color{blue}{\begin{array}{l} \color{blue}{\mathbf{if}\;b \ne 0:\\ \;\;\;\;\frac{a}{\frac{3}{b}}\\ \mathbf{else}:\\ \;\;\;\;\left(0.3333333333333333 \cdot b\right) \cdot a\\ } \end{array}} \]

Alternatives

Alternative 1
Error	0.3
Cost	512

\[-\left(a \cdot b\right) \cdot \left(a \cdot b\right) \]

Reproduce

herbie shell --seed 2023010 
(FPCore (a b)
  :name "ab-angle->ABCF D"
  :precision binary64
  (- (* (* (* a a) b) b)))