Average Error: 13.3 → 0.3
Time: 1.3m
Precision: 64
Internal Precision: 1408
\[x + \left(\tan \left(y + z\right) - \tan a\right)\]
↓
\[\frac{\tan y + \tan z}{1 - \tan y \cdot \tan z} - \left(\frac{\sin a}{\cos a} - x\right)\]

Error

Bits error versus x

Bits error versus y

Bits error versus z

Bits error versus a

Derivation

  1. Initial program 13.3

    \[x + \left(\tan \left(y + z\right) - \tan a\right)\]
  2. Using strategy rm

  3. Applied tan-quot13.3

    \[\leadsto x + \left(\tan \left(y + z\right) - \color{blue}{\frac{\sin a}{\cos a}}\right)\]

  4. Applied tan-sum0.2

    \[\leadsto x + \left(\color{blue}{\frac{\tan y + \tan z}{1 - \tan y \cdot \tan z}} - \frac{\sin a}{\cos a}\right)\]

  5. Applied frac-sub0.2

    \[\leadsto x + \color{blue}{\frac{\left(\tan y + \tan z\right) \cdot \cos a - \left(1 - \tan y \cdot \tan z\right) \cdot \sin a}{\left(1 - \tan y \cdot \tan z\right) \cdot \cos a}}\]
  6. Using strategy rm

  7. Applied add-log-exp0.3

    \[\leadsto x + \frac{\left(\tan y + \tan z\right) \cdot \cos a - \left(1 - \tan y \cdot \tan z\right) \cdot \sin a}{\left(1 - \color{blue}{\log \left(e^{\tan y \cdot \tan z}\right)}\right) \cdot \cos a}\]
  8. Removed slow pow expressions.

  9. Applied simplify0.3

    \[\leadsto \color{blue}{\frac{\tan y + \tan z}{1 - \tan y \cdot \tan z} - \left(\frac{\sin a}{\cos a} - x\right)}\]

Runtime

Time bar (total: 1.3m)Debug log

herbie shell --seed '#(3283474051 1289610787 1499701197 2084134920 230624152 3245116961)' 
(FPCore (x y z a)
  :name "(+ x (- (tan (+ y z)) (tan a)))"
  :pre (and (or (== x 0) (<= 0.5884142 x 505.5909)) (or (<= -1.796658e+308 y -9.425585e-310) (<= 1.284938e-309 y 1.751224e+308)) (or (<= -1.776707e+308 z -8.599796e-310) (<= 3.293145e-311 z 1.725154e+308)) (or (<= -1.796658e+308 a -9.425585e-310) (<= 1.284938e-309 a 1.751224e+308)))
  (+ x (- (tan (+ y z)) (tan a))))