Average Error: 33.6 → 21.7
Time: 20.5s
Precision: 64
Internal Precision: 1344
\[\sin \left(\sqrt{x \cdot x + y \cdot y}\right)\]
\[\begin{array}{l} \mathbf{if}\;x \le -2.0167639031292305 \cdot 10^{+81}:\\ \;\;\;\;\sin \left(-x\right)\\ \mathbf{if}\;x \le 9.121103776106908 \cdot 10^{+58}:\\ \;\;\;\;\sin \left(\sqrt{x \cdot x + y \cdot y}\right)\\ \mathbf{else}:\\ \;\;\;\;\sin x\\ \end{array}\]

Error

Bits error versus x

Bits error versus y

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Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Split input into 3 regimes
  2. if x < -2.0167639031292305e+81

    1. Initial program 50.9

      \[\sin \left(\sqrt{x \cdot x + y \cdot y}\right)\]
    2. Taylor expanded around -inf 18.7

      \[\leadsto \sin \color{blue}{\left(-1 \cdot x\right)}\]
    3. Applied simplify18.7

      \[\leadsto \color{blue}{\sin \left(-x\right)}\]

    if -2.0167639031292305e+81 < x < 9.121103776106908e+58

    1. Initial program 23.2

      \[\sin \left(\sqrt{x \cdot x + y \cdot y}\right)\]

    if 9.121103776106908e+58 < x

    1. Initial program 48.5

      \[\sin \left(\sqrt{x \cdot x + y \cdot y}\right)\]
    2. Taylor expanded around inf 19.8

      \[\leadsto \sin \color{blue}{x}\]
  3. Recombined 3 regimes into one program.

Runtime

Time bar (total: 20.5s)Debug log

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