Radioactive exchange between two surfaces

Average Error: 100.0% → 100.0%

Time: 19.9s

Precision: binary64

Cost: 13120.00

Math

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

↓

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

FPCore

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

↓

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

C

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

↓

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

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 ** 4.0d0) - (y ** 4.0d0)
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 Math.pow(x, 4.0) - Math.pow(y, 4.0);
}

Python

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

↓

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

Julia

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

↓

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

MATLAB

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

↓

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

Wolfram

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

↓

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

Derivation

1. Initial program 100.0

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

2. Final simplification 100.0

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

Alternatives

Alternative 1
Error	99.6%
Cost	7936.00

\[\left(x \cdot x + y \cdot y\right) \cdot \left(\left(x \cdot x - y \cdot y\right) + 2 \cdot \mathsf{fma}\left(-y, y, y \cdot y\right)\right) \]

Alternative 2
Error	99.5%
Cost	1344.00

\[\left(x \cdot x + y \cdot y\right) \cdot \left(\frac{y}{\frac{1}{x - y}} + x \cdot \left(x - y\right)\right) \]

Alternative 3
Error	91.4%
Cost	969.00

\[\begin{array}{l} \mathbf{if}\;y \leq -1.4 \cdot 10^{-80} \lor \neg \left(y \leq 3 \cdot 10^{-80}\right):\\ \;\;\;\;\left(y \cdot y\right) \cdot \left(y \cdot \left(-y\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x \cdot x\right) \cdot \left(x \cdot x - y \cdot y\right)\\ \end{array} \]

Alternative 4
Error	99.5%
Cost	960.00

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

Alternative 5
Error	68.3%
Cost	512.00

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

Alternative 6
Error	37.4%
Cost	448.00

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

Reproduce

herbie shell --seed 2023093 
(FPCore (x y)
  :name "Radioactive exchange between two surfaces"
  :precision binary64
  (- (pow x 4.0) (pow y 4.0)))