Radioactive exchange between two surfaces

Average Error: 0.0 → 0.0

Time: 13.1s

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	5.8
Cost	1097

\[\begin{array}{l} \mathbf{if}\;x \leq -1.16 \cdot 10^{-70} \lor \neg \left(x \leq 1.05 \cdot 10^{-67}\right):\\ \;\;\;\;\left(x \cdot x\right) \cdot \frac{x + y}{\frac{1}{x - y}}\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(y \cdot \left(x \cdot x - y \cdot y\right)\right)\\ \end{array} \]

Alternative 2
Error	0.3
Cost	1088

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

Alternative 3
Error	5.8
Cost	969

\[\begin{array}{l} \mathbf{if}\;x \leq -3.5 \cdot 10^{-71} \lor \neg \left(x \leq 7.4 \cdot 10^{-68}\right):\\ \;\;\;\;\left(x \cdot x\right) \cdot \left(\left(x - y\right) \cdot \left(x + y\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(y \cdot \left(x \cdot x - y \cdot y\right)\right)\\ \end{array} \]

Alternative 4
Error	5.8
Cost	968

\[\begin{array}{l} t_0 := x \cdot x - y \cdot y\\ \mathbf{if}\;x \leq -6.5 \cdot 10^{-71}:\\ \;\;\;\;\left(x \cdot x\right) \cdot \frac{x + y}{\frac{1}{x - y}}\\ \mathbf{elif}\;x \leq 8.2 \cdot 10^{-68}:\\ \;\;\;\;y \cdot \left(y \cdot t_0\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(x \cdot t_0\right)\\ \end{array} \]

Alternative 5
Error	0.3
Cost	960

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

Alternative 6
Error	19.9
Cost	704

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

Alternative 7
Error	20.1
Cost	512

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

Alternative 8
Error	39.8
Cost	448

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

Reproduce

herbie shell --seed 2023073 
(FPCore (x y)
  :name "Radioactive exchange between two surfaces"
  :precision binary64
  (- (pow x 4.0) (pow y 4.0)))