Average Error: 30.1 → 17.0
Time: 4.2s
Precision: 64
Internal Precision: 320
\[\sqrt{vect0 \cdot vect0 + vect1 \cdot vect1}\]
\[\begin{array}{l} \mathbf{if}\;vect0 \le -5.147403001023096 \cdot 10^{+84}:\\ \;\;\;\;-vect0\\ \mathbf{elif}\;vect0 \le 1.7967825844854412 \cdot 10^{+130}:\\ \;\;\;\;\sqrt{vect0 \cdot vect0 + vect1 \cdot vect1}\\ \mathbf{else}:\\ \;\;\;\;vect0\\ \end{array}\]

Error

Bits error versus vect0

Bits error versus vect1

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Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Split input into 3 regimes
  2. if vect0 < -5.147403001023096e+84

    1. Initial program 45.3

      \[\sqrt{vect0 \cdot vect0 + vect1 \cdot vect1}\]
    2. Taylor expanded around -inf 10.5

      \[\leadsto \color{blue}{-1 \cdot vect0}\]
    3. Simplified10.5

      \[\leadsto \color{blue}{-vect0}\]

    if -5.147403001023096e+84 < vect0 < 1.7967825844854412e+130

    1. Initial program 20.5

      \[\sqrt{vect0 \cdot vect0 + vect1 \cdot vect1}\]

    if 1.7967825844854412e+130 < vect0

    1. Initial program 53.8

      \[\sqrt{vect0 \cdot vect0 + vect1 \cdot vect1}\]
    2. Taylor expanded around inf 9.7

      \[\leadsto \color{blue}{vect0}\]
  3. Recombined 3 regimes into one program.
  4. Final simplification17.0

    \[\leadsto \begin{array}{l} \mathbf{if}\;vect0 \le -5.147403001023096 \cdot 10^{+84}:\\ \;\;\;\;-vect0\\ \mathbf{elif}\;vect0 \le 1.7967825844854412 \cdot 10^{+130}:\\ \;\;\;\;\sqrt{vect0 \cdot vect0 + vect1 \cdot vect1}\\ \mathbf{else}:\\ \;\;\;\;vect0\\ \end{array}\]

Runtime

Time bar (total: 4.2s)Debug log

herbie shell --seed '#(2775764126 3555076145 3898259844 1891440260 2599947619 1948460636)' 
(FPCore (vect0 vect1)
  :name "sqrt(vect0 * vect0 + vect1 * vect1)"
  (sqrt (+ (* vect0 vect0) (* vect1 vect1))))