Average Error: 35.8 → 24.5
Time: 6.8s
Precision: 64
Internal Precision: 320
\[\sqrt{\left(a \cdot a + b \cdot b\right) + c \cdot c}\]
\[\begin{array}{l} \mathbf{if}\;a \le -5.77126452019715 \cdot 10^{+140}:\\ \;\;\;\;-a\\ \mathbf{elif}\;a \le 1.6019685912508635 \cdot 10^{+155}:\\ \;\;\;\;\sqrt{\left(a \cdot a + c \cdot c\right) + b \cdot b}\\ \mathbf{else}:\\ \;\;\;\;a\\ \end{array}\]

Error

Bits error versus a

Bits error versus b

Bits error versus c

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Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Split input into 3 regimes
  2. if a < -5.77126452019715e+140

    1. Initial program 56.3

      \[\sqrt{\left(a \cdot a + b \cdot b\right) + c \cdot c}\]
    2. Initial simplification56.3

      \[\leadsto \sqrt{\left(a \cdot a + c \cdot c\right) + b \cdot b}\]
    3. Taylor expanded around -inf 15.6

      \[\leadsto \color{blue}{-1 \cdot a}\]
    4. Simplified15.6

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

    if -5.77126452019715e+140 < a < 1.6019685912508635e+155

    1. Initial program 28.0

      \[\sqrt{\left(a \cdot a + b \cdot b\right) + c \cdot c}\]
    2. Initial simplification28.0

      \[\leadsto \sqrt{\left(a \cdot a + c \cdot c\right) + b \cdot b}\]

    if 1.6019685912508635e+155 < a

    1. Initial program 59.2

      \[\sqrt{\left(a \cdot a + b \cdot b\right) + c \cdot c}\]
    2. Initial simplification59.2

      \[\leadsto \sqrt{\left(a \cdot a + c \cdot c\right) + b \cdot b}\]
    3. Taylor expanded around inf 13.4

      \[\leadsto \color{blue}{a}\]
  3. Recombined 3 regimes into one program.
  4. Final simplification24.5

    \[\leadsto \begin{array}{l} \mathbf{if}\;a \le -5.77126452019715 \cdot 10^{+140}:\\ \;\;\;\;-a\\ \mathbf{elif}\;a \le 1.6019685912508635 \cdot 10^{+155}:\\ \;\;\;\;\sqrt{\left(a \cdot a + c \cdot c\right) + b \cdot b}\\ \mathbf{else}:\\ \;\;\;\;a\\ \end{array}\]

Runtime

Time bar (total: 6.8s)Debug log

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