Radioactive exchange between two surfaces

Average Accuracy: 100.0% → 100.0%

Time: 7.7s

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 100.0%

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

2. Final simplification 100.0%

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

Alternatives

Alternative 1
Accuracy	99.5%
Cost	7232

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

Alternative 2
Accuracy	90.6%
Cost	1096

\[\begin{array}{l} t_0 := x \cdot x - y \cdot y\\ \mathbf{if}\;y \leq -1.85 \cdot 10^{-71}:\\ \;\;\;\;\frac{y}{\frac{\frac{-1}{y \cdot y}}{y}}\\ \mathbf{elif}\;y \leq 1.15 \cdot 10^{-56}:\\ \;\;\;\;x \cdot \frac{x}{\frac{1}{t_0}}\\ \mathbf{else}:\\ \;\;\;\;\left(y \cdot y\right) \cdot t_0\\ \end{array} \]

Alternative 3
Accuracy	90.7%
Cost	1096

\[\begin{array}{l} t_0 := x \cdot x - y \cdot y\\ \mathbf{if}\;y \leq -1.85 \cdot 10^{-71}:\\ \;\;\;\;\frac{y}{\frac{\frac{-1}{y \cdot y}}{y}}\\ \mathbf{elif}\;y \leq 6.8 \cdot 10^{-58}:\\ \;\;\;\;x \cdot \frac{x}{\frac{1}{t_0}}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{\frac{\frac{1}{y}}{t_0}}\\ \end{array} \]

Alternative 4
Accuracy	90.7%
Cost	1096

\[\begin{array}{l} t_0 := \frac{1}{x \cdot x - y \cdot y}\\ \mathbf{if}\;y \leq -1.85 \cdot 10^{-71}:\\ \;\;\;\;\frac{y}{\frac{\frac{-1}{y \cdot y}}{y}}\\ \mathbf{elif}\;y \leq 7 \cdot 10^{-58}:\\ \;\;\;\;x \cdot \frac{x}{t_0}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{\frac{t_0}{y}}\\ \end{array} \]

Alternative 5
Accuracy	90.6%
Cost	968

\[\begin{array}{l} \mathbf{if}\;y \leq -1.85 \cdot 10^{-71}:\\ \;\;\;\;\frac{y}{\frac{\frac{-1}{y \cdot y}}{y}}\\ \mathbf{elif}\;y \leq 6 \cdot 10^{-57}:\\ \;\;\;\;\left(x \cdot x\right) \cdot \left(x \cdot x\right)\\ \mathbf{else}:\\ \;\;\;\;\left(y \cdot y\right) \cdot \left(x \cdot x - y \cdot y\right)\\ \end{array} \]

Alternative 6
Accuracy	99.5%
Cost	960

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

Alternative 7
Accuracy	90.6%
Cost	841

\[\begin{array}{l} \mathbf{if}\;y \leq -1.85 \cdot 10^{-71} \lor \neg \left(y \leq 6.8 \cdot 10^{-58}\right):\\ \;\;\;\;\frac{y}{\frac{\frac{-1}{y \cdot y}}{y}}\\ \mathbf{else}:\\ \;\;\;\;\left(x \cdot x\right) \cdot \left(x \cdot x\right)\\ \end{array} \]

Alternative 8
Accuracy	90.5%
Cost	777

\[\begin{array}{l} \mathbf{if}\;y \leq -1.85 \cdot 10^{-71} \lor \neg \left(y \leq 1.35 \cdot 10^{-57}\right):\\ \;\;\;\;\left(y \cdot y\right) \cdot \left(y \cdot \left(-y\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x \cdot x\right) \cdot \left(x \cdot x\right)\\ \end{array} \]

Alternative 9
Accuracy	68.7%
Cost	448

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

Reproduce

herbie shell --seed 2023150 
(FPCore (x y)
  :name "Radioactive exchange between two surfaces"
  :precision binary64
  (- (pow x 4.0) (pow y 4.0)))