Average Error: 0.0 → 0.0
Time: 2.0s
Precision: binary64
\[e^{-\left(1 - x \cdot x\right)} \]
↓
\[e^{-1} \cdot {\left({\left(e^{x}\right)}^{\left(\sqrt[3]{x \cdot x}\right)}\right)}^{\left(\sqrt[3]{x}\right)} \]
(FPCore (x) :precision binary64 (exp (- (- 1.0 (* x x)))))
↓
(FPCore (x)
 :precision binary64
 (* (exp -1.0) (pow (pow (exp x) (cbrt (* x x))) (cbrt x))))
double code(double x) {
	return exp(-(1.0 - (x * x)));
}
↓
double code(double x) {
	return exp(-1.0) * pow(pow(exp(x), cbrt((x * x))), cbrt(x));
}

public static double code(double x) {
	return Math.exp(-(1.0 - (x * x)));
}
↓
public static double code(double x) {
	return Math.exp(-1.0) * Math.pow(Math.pow(Math.exp(x), Math.cbrt((x * x))), Math.cbrt(x));
}

function code(x)
	return exp(Float64(-Float64(1.0 - Float64(x * x))))
end
↓
function code(x)
	return Float64(exp(-1.0) * ((exp(x) ^ cbrt(Float64(x * x))) ^ cbrt(x)))
end

code[x_] := N[Exp[(-N[(1.0 - N[(x * x), $MachinePrecision]), $MachinePrecision])], $MachinePrecision]
↓
code[x_] := N[(N[Exp[-1.0], $MachinePrecision] * N[Power[N[Power[N[Exp[x], $MachinePrecision], N[Power[N[(x * x), $MachinePrecision], 1/3], $MachinePrecision]], $MachinePrecision], N[Power[x, 1/3], $MachinePrecision]], $MachinePrecision]), $MachinePrecision]

e^{-\left(1 - x \cdot x\right)}
↓
e^{-1} \cdot {\left({\left(e^{x}\right)}^{\left(\sqrt[3]{x \cdot x}\right)}\right)}^{\left(\sqrt[3]{x}\right)}

Error

Bits error versus x

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 0.0

    \[e^{-\left(1 - x \cdot x\right)} \]

  2. Simplified0.0

    \[\leadsto \color{blue}{e^{\mathsf{fma}\left(x, x, -1\right)}} \]

  3. Applied egg-rr0.0

    \[\leadsto \color{blue}{e^{-1} \cdot {\left(e^{x}\right)}^{x}} \]

  4. Applied egg-rr0.0

    \[\leadsto e^{-1} \cdot \color{blue}{\left({\left({\left(\sqrt[3]{e^{x}}\right)}^{2}\right)}^{x} \cdot {\left(\sqrt[3]{e^{x}}\right)}^{x}\right)} \]

  5. Applied egg-rr0.0

    \[\leadsto e^{-1} \cdot \color{blue}{{\left({\left(e^{x}\right)}^{\left(\sqrt[3]{x \cdot x}\right)}\right)}^{\left(\sqrt[3]{x}\right)}} \]

  6. Final simplification0.0

    \[\leadsto e^{-1} \cdot {\left({\left(e^{x}\right)}^{\left(\sqrt[3]{x \cdot x}\right)}\right)}^{\left(\sqrt[3]{x}\right)} \]

Reproduce

herbie shell --seed 2022152 
(FPCore (x)
  :name "exp neg sub"
  :precision binary64
  (exp (- (- 1.0 (* x x)))))