Average Error: 29.8 → 0.0
Time: 1.3s
Precision: binary64
\[\sqrt{re \cdot re + im \cdot im} \]
↓
\[\mathsf{hypot}\left(re, im\right) \]
\sqrt{re \cdot re + im \cdot im}
↓
\mathsf{hypot}\left(re, im\right)

(FPCore modulus (re im) :precision binary64 (sqrt (+ (* re re) (* im im))))
↓
(FPCore modulus (re im) :precision binary64 (hypot re im))
double modulus(double re, double im) {
	return sqrt((re * re) + (im * im));
}
↓
double modulus(double re, double im) {
	return hypot(re, im);
}

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 29.8

    \[\sqrt{re \cdot re + im \cdot im} \]

  2. Simplified0.0

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

  3. Final simplification0.0

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

Reproduce

herbie shell --seed 2022067 
(FPCore modulus (re im)
  :name "math.abs on complex"
  :precision binary64
  (sqrt (+ (* re re) (* im im))))