Radioactive exchange between two surfaces

Average Error: 0.0 → 0.0

Time: 4.2s

Precision: binary64

Cost: 13120

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 0.0

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

2. Final simplification 0.0

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

Alternatives

Alternative 1
Error	0.3
Cost	7232

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

Alternative 2
Error	5.3
Cost	968

\[\begin{array}{l} t_0 := \left(x \cdot x\right) \cdot \left(x \cdot x - y \cdot y\right)\\ \mathbf{if}\;x \leq -4.1352722338583584 \cdot 10^{-73}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;x \leq 2.3054401237413592 \cdot 10^{-77}:\\ \;\;\;\;\left(y \cdot y\right) \cdot \left(y \cdot \left(-y\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \]

Alternative 3
Error	0.3
Cost	960

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

Alternative 4
Error	5.5
Cost	776

\[\begin{array}{l} t_0 := \left(x \cdot x\right) \cdot \left(x \cdot x\right)\\ \mathbf{if}\;x \leq -4.1352722338583584 \cdot 10^{-73}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;x \leq 2.3054401237413592 \cdot 10^{-77}:\\ \;\;\;\;\left(y \cdot y\right) \cdot \left(y \cdot \left(-y\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \]

Alternative 5
Error	20.6
Cost	448

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

Reproduce

herbie shell --seed 2022291 
(FPCore (x y)
  :name "Radioactive exchange between two surfaces"
  :precision binary64
  (- (pow x 4.0) (pow y 4.0)))