Radioactive exchange between two surfaces

Percentage Accurate: 85.9% → 93.6%

Time: 3.7s

Precision: binary64

Cost: 960

• 60.6% of points produce a very large (infinite) output. You may want to add a precondition.

Math

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

↓

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

FPCore

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

↓

(FPCore (x y) :precision binary64 (* (+ (* x x) (* y y)) (- (* x x) (* y 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 * x) - (y * 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 * x) - (y * 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 * x) - (y * 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 * x) - (y * 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 * x) - Float64(y * 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 * x) - (y * 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 * x), $MachinePrecision] - N[(y * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 89.5%

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

2. Applied egg-rr 96.3%

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

   [Start] 89.5	\[ {x}^{4} - {y}^{4} \]
   sqr-pow [=>] 89.4	\[ \color{blue}{{x}^{\left(\frac{4}{2}\right)} \cdot {x}^{\left(\frac{4}{2}\right)}} - {y}^{4} \]
   sqr-pow [=>] 89.3	\[ {x}^{\left(\frac{4}{2}\right)} \cdot {x}^{\left(\frac{4}{2}\right)} - \color{blue}{{y}^{\left(\frac{4}{2}\right)} \cdot {y}^{\left(\frac{4}{2}\right)}} \]
   difference-of-squares [=>] 96.3	\[ \color{blue}{\left({x}^{\left(\frac{4}{2}\right)} + {y}^{\left(\frac{4}{2}\right)}\right) \cdot \left({x}^{\left(\frac{4}{2}\right)} - {y}^{\left(\frac{4}{2}\right)}\right)} \]
   metadata-eval [=>] 96.3	\[ \left({x}^{\color{blue}{2}} + {y}^{\left(\frac{4}{2}\right)}\right) \cdot \left({x}^{\left(\frac{4}{2}\right)} - {y}^{\left(\frac{4}{2}\right)}\right) \]
   pow2 [<=] 96.3	\[ \left(\color{blue}{x \cdot x} + {y}^{\left(\frac{4}{2}\right)}\right) \cdot \left({x}^{\left(\frac{4}{2}\right)} - {y}^{\left(\frac{4}{2}\right)}\right) \]
   metadata-eval [=>] 96.3	\[ \left(x \cdot x + {y}^{\color{blue}{2}}\right) \cdot \left({x}^{\left(\frac{4}{2}\right)} - {y}^{\left(\frac{4}{2}\right)}\right) \]
   pow2 [<=] 96.3	\[ \left(x \cdot x + \color{blue}{y \cdot y}\right) \cdot \left({x}^{\left(\frac{4}{2}\right)} - {y}^{\left(\frac{4}{2}\right)}\right) \]
   metadata-eval [=>] 96.3	\[ \left(x \cdot x + y \cdot y\right) \cdot \left({x}^{\color{blue}{2}} - {y}^{\left(\frac{4}{2}\right)}\right) \]
   pow2 [<=] 96.3	\[ \left(x \cdot x + y \cdot y\right) \cdot \left(\color{blue}{x \cdot x} - {y}^{\left(\frac{4}{2}\right)}\right) \]
   metadata-eval [=>] 96.3	\[ \left(x \cdot x + y \cdot y\right) \cdot \left(x \cdot x - {y}^{\color{blue}{2}}\right) \]
   pow2 [<=] 96.3	\[ \left(x \cdot x + y \cdot y\right) \cdot \left(x \cdot x - \color{blue}{y \cdot y}\right) \]

3. Final simplification 96.3%

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

Alternatives

Alternative 1
Accuracy	81.6%
Cost	1033

\[\begin{array}{l} \mathbf{if}\;y \leq -2.55 \cdot 10^{+62} \lor \neg \left(y \leq 4.4 \cdot 10^{+60}\right):\\ \;\;\;\;\left(y \cdot y\right) \cdot \left(\left(-y \cdot y\right) - x \cdot x\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x \cdot x\right) \cdot \left(x \cdot x + y \cdot y\right)\\ \end{array} \]

Alternative 2
Accuracy	70.1%
Cost	969

\[\begin{array}{l} \mathbf{if}\;y \leq -5 \cdot 10^{+109} \lor \neg \left(y \leq 6 \cdot 10^{+101}\right):\\ \;\;\;\;\left(x \cdot x\right) \cdot \left(-y \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x \cdot x\right) \cdot \left(x \cdot x + y \cdot y\right)\\ \end{array} \]

Alternative 3
Accuracy	45.0%
Cost	777

\[\begin{array}{l} \mathbf{if}\;y \leq -9 \cdot 10^{+110} \lor \neg \left(y \leq 1.2 \cdot 10^{+105}\right):\\ \;\;\;\;\left(x \cdot x\right) \cdot \left(-y \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x \cdot x\right) \cdot \left(y \cdot y\right)\\ \end{array} \]

Alternative 4
Accuracy	32.6%
Cost	448

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

Reproduce

herbie shell --seed 2023160 
(FPCore (x y)
  :name "Radioactive exchange between two surfaces"
  :precision binary64
  (- (pow x 4.0) (pow y 4.0)))