Average Error: 0.0 → 0.0
Time: 1.2s
Precision: binary64
\[re \cdot re + im \cdot im \]
↓
\[{\left(\mathsf{hypot}\left(re, im\right)\right)}^{2} \]
(FPCore modulus_sqr (re im) :precision binary64 (+ (* re re) (* im im)))
↓
(FPCore modulus_sqr (re im) :precision binary64 (pow (hypot re im) 2.0))
double modulus_sqr(double re, double im) {
	return (re * re) + (im * im);
}
↓
double modulus_sqr(double re, double im) {
	return pow(hypot(re, im), 2.0);
}

public static double modulus_sqr(double re, double im) {
	return (re * re) + (im * im);
}
↓
public static double modulus_sqr(double re, double im) {
	return Math.pow(Math.hypot(re, im), 2.0);
}

def modulus_sqr(re, im):
	return (re * re) + (im * im)
↓
def modulus_sqr(re, im):
	return math.pow(math.hypot(re, im), 2.0)

function modulus_sqr(re, im)
	return Float64(Float64(re * re) + Float64(im * im))
end
↓
function modulus_sqr(re, im)
	return hypot(re, im) ^ 2.0
end

function tmp = modulus_sqr(re, im)
	tmp = (re * re) + (im * im);
end
↓
function tmp = modulus_sqr(re, im)
	tmp = hypot(re, im) ^ 2.0;
end

modulus$95$sqr[re_, im_] := N[(N[(re * re), $MachinePrecision] + N[(im * im), $MachinePrecision]), $MachinePrecision]
↓
modulus$95$sqr[re_, im_] := N[Power[N[Sqrt[re ^ 2 + im ^ 2], $MachinePrecision], 2.0], $MachinePrecision]

re \cdot re + im \cdot im
↓
{\left(\mathsf{hypot}\left(re, im\right)\right)}^{2}

Error

Bits error versus re

Bits error versus im

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 0.0

    \[re \cdot re + im \cdot im \]

  2. Applied egg-rr0.0

    \[\leadsto \color{blue}{{\left(\mathsf{hypot}\left(re, im\right)\right)}^{2}} \]

  3. Final simplification0.0

    \[\leadsto {\left(\mathsf{hypot}\left(re, im\right)\right)}^{2} \]

Reproduce

herbie shell --seed 2022150 
(FPCore modulus_sqr (re im)
  :name "math.abs on complex (squared)"
  :precision binary64
  (+ (* re re) (* im im)))