Radioactive exchange between two surfaces

Percentage Accurate: 86.6% → 99.8%

Time: 4.7s

Precision: binary64

Cost: 960

• 60.1% of points produce a very large (infinite) output. You may want to add a precondition.

Math

\[{x}^{4} - {y}^{4} \]

↓

\[\left(x \cdot x + y \cdot y\right) \cdot \left(\left(x - y\right) \cdot \left(x + y\right)\right) \]

FPCore

(FPCore (x y) :precision binary64 (- (pow x 4.0) (pow y 4.0)))

↓

(FPCore (x y) :precision binary64 (* (+ (* x x) (* y y)) (* (- x y) (+ x y))))

C

double code(double x, double y) {
	return pow(x, 4.0) - pow(y, 4.0);
}

↓

double code(double x, double y) {
	return ((x * x) + (y * y)) * ((x - y) * (x + y));
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    code = (x ** 4.0d0) - (y ** 4.0d0)
end function

↓

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    code = ((x * x) + (y * y)) * ((x - y) * (x + y))
end function

Java

public static double code(double x, double y) {
	return Math.pow(x, 4.0) - Math.pow(y, 4.0);
}

↓

public static double code(double x, double y) {
	return ((x * x) + (y * y)) * ((x - y) * (x + y));
}

Python

def code(x, y):
	return math.pow(x, 4.0) - math.pow(y, 4.0)

↓

def code(x, y):
	return ((x * x) + (y * y)) * ((x - y) * (x + y))

Julia

function code(x, y)
	return Float64((x ^ 4.0) - (y ^ 4.0))
end

↓

function code(x, y)
	return Float64(Float64(Float64(x * x) + Float64(y * y)) * Float64(Float64(x - y) * Float64(x + y)))
end

MATLAB

function tmp = code(x, y)
	tmp = (x ^ 4.0) - (y ^ 4.0);
end

↓

function tmp = code(x, y)
	tmp = ((x * x) + (y * y)) * ((x - y) * (x + y));
end

Wolfram

code[x_, y_] := N[(N[Power[x, 4.0], $MachinePrecision] - N[Power[y, 4.0], $MachinePrecision]), $MachinePrecision]

↓

code[x_, y_] := N[(N[(N[(x * x), $MachinePrecision] + N[(y * y), $MachinePrecision]), $MachinePrecision] * N[(N[(x - y), $MachinePrecision] * N[(x + y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 82.0%

   \[{x}^{4} - {y}^{4} \]

2. Applied egg-rr 91.2%

   \[\leadsto \color{blue}{\left(x \cdot x + y \cdot y\right) \cdot \left(x \cdot x - y \cdot y\right)} \]
   Step-by-step derivation

   [Start] 82.0	\[ {x}^{4} - {y}^{4} \]
   sqr-pow [=>] 81.9	\[ \color{blue}{{x}^{\left(\frac{4}{2}\right)} \cdot {x}^{\left(\frac{4}{2}\right)}} - {y}^{4} \]
   sqr-pow [=>] 81.8	\[ {x}^{\left(\frac{4}{2}\right)} \cdot {x}^{\left(\frac{4}{2}\right)} - \color{blue}{{y}^{\left(\frac{4}{2}\right)} \cdot {y}^{\left(\frac{4}{2}\right)}} \]
   difference-of-squares [=>] 91.2	\[ \color{blue}{\left({x}^{\left(\frac{4}{2}\right)} + {y}^{\left(\frac{4}{2}\right)}\right) \cdot \left({x}^{\left(\frac{4}{2}\right)} - {y}^{\left(\frac{4}{2}\right)}\right)} \]
   metadata-eval [=>] 91.2	\[ \left({x}^{\color{blue}{2}} + {y}^{\left(\frac{4}{2}\right)}\right) \cdot \left({x}^{\left(\frac{4}{2}\right)} - {y}^{\left(\frac{4}{2}\right)}\right) \]
   pow2 [<=] 91.2	\[ \left(\color{blue}{x \cdot x} + {y}^{\left(\frac{4}{2}\right)}\right) \cdot \left({x}^{\left(\frac{4}{2}\right)} - {y}^{\left(\frac{4}{2}\right)}\right) \]
   metadata-eval [=>] 91.2	\[ \left(x \cdot x + {y}^{\color{blue}{2}}\right) \cdot \left({x}^{\left(\frac{4}{2}\right)} - {y}^{\left(\frac{4}{2}\right)}\right) \]
   pow2 [<=] 91.2	\[ \left(x \cdot x + \color{blue}{y \cdot y}\right) \cdot \left({x}^{\left(\frac{4}{2}\right)} - {y}^{\left(\frac{4}{2}\right)}\right) \]
   metadata-eval [=>] 91.2	\[ \left(x \cdot x + y \cdot y\right) \cdot \left({x}^{\color{blue}{2}} - {y}^{\left(\frac{4}{2}\right)}\right) \]
   pow2 [<=] 91.2	\[ \left(x \cdot x + y \cdot y\right) \cdot \left(\color{blue}{x \cdot x} - {y}^{\left(\frac{4}{2}\right)}\right) \]
   metadata-eval [=>] 91.2	\[ \left(x \cdot x + y \cdot y\right) \cdot \left(x \cdot x - {y}^{\color{blue}{2}}\right) \]
   pow2 [<=] 91.2	\[ \left(x \cdot x + y \cdot y\right) \cdot \left(x \cdot x - \color{blue}{y \cdot y}\right) \]

3. Applied egg-rr 99.8%

   \[\leadsto \left(x \cdot x + y \cdot y\right) \cdot \color{blue}{\left(\left(x - y\right) \cdot \left(x + y\right)\right)} \]
   Step-by-step derivation

   [Start] 91.2	\[ \left(x \cdot x + y \cdot y\right) \cdot \left(x \cdot x - y \cdot y\right) \]
   difference-of-squares [=>] 99.8	\[ \left(x \cdot x + y \cdot y\right) \cdot \color{blue}{\left(\left(x + y\right) \cdot \left(x - y\right)\right)} \]
   *-commutative [=>] 99.8	\[ \left(x \cdot x + y \cdot y\right) \cdot \color{blue}{\left(\left(x - y\right) \cdot \left(x + y\right)\right)} \]

4. Final simplification 99.8%

   \[\leadsto \left(x \cdot x + y \cdot y\right) \cdot \left(\left(x - y\right) \cdot \left(x + y\right)\right) \]

Alternatives

Alternative 1
Accuracy	81.6%
Cost	1298

\[\begin{array}{l} t_0 := x \cdot x + y \cdot y\\ \mathbf{if}\;x \leq -2.1 \cdot 10^{+26} \lor \neg \left(x \leq -1.7 \cdot 10^{-32} \lor \neg \left(x \leq -8.5 \cdot 10^{-49}\right) \land x \leq 1250000000000\right):\\ \;\;\;\;\left(x \cdot x\right) \cdot t_0\\ \mathbf{else}:\\ \;\;\;\;t_0 \cdot \left(y \cdot \left(-y\right)\right)\\ \end{array} \]

Alternative 2
Accuracy	69.4%
Cost	969

\[\begin{array}{l} \mathbf{if}\;y \leq -6.5 \cdot 10^{+175} \lor \neg \left(y \leq 4.5 \cdot 10^{+131}\right):\\ \;\;\;\;\left(x \cdot x\right) \cdot \left(y \cdot \left(-y\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x \cdot x\right) \cdot \left(x \cdot x + y \cdot y\right)\\ \end{array} \]

Alternative 3
Accuracy	44.5%
Cost	777

\[\begin{array}{l} \mathbf{if}\;y \leq -6.5 \cdot 10^{+175} \lor \neg \left(y \leq 1.3 \cdot 10^{+131}\right):\\ \;\;\;\;\left(x \cdot x\right) \cdot \left(y \cdot \left(-y\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x \cdot x\right) \cdot \left(y \cdot y\right)\\ \end{array} \]

Alternative 4
Accuracy	32.2%
Cost	448

\[\left(x \cdot x\right) \cdot \left(y \cdot y\right) \]

Reproduce

herbie shell --seed 2023161 
(FPCore (x y)
  :name "Radioactive exchange between two surfaces"
  :precision binary64
  (- (pow x 4.0) (pow y 4.0)))