Average Error: 14.7 → 0.5
Time: 33.0s
Precision: 64
Internal Precision: 1344
\[r \cdot \frac{\sin b}{\cos \left(a + b\right)}\]
↓
\[\frac{\sin b}{\cos a \cdot \cos b - \left(\sqrt[3]{\sin a} \cdot \sqrt[3]{\sin a}\right) \cdot \left(\sin b \cdot \sqrt[3]{\sin a}\right)} \cdot r\]

Error

Bits error versus r

Bits error versus a

Bits error versus b

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Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 14.7

    \[r \cdot \frac{\sin b}{\cos \left(a + b\right)}\]
  2. Using strategy rm

  3. Applied cos-sum0.3

    \[\leadsto r \cdot \frac{\sin b}{\color{blue}{\cos a \cdot \cos b - \sin a \cdot \sin b}}\]
  4. Using strategy rm

  5. Applied add-cube-cbrt0.5

    \[\leadsto r \cdot \frac{\sin b}{\cos a \cdot \cos b - \color{blue}{\left(\left(\sqrt[3]{\sin a} \cdot \sqrt[3]{\sin a}\right) \cdot \sqrt[3]{\sin a}\right)} \cdot \sin b}\]

  6. Applied associate-*l*0.5

    \[\leadsto r \cdot \frac{\sin b}{\cos a \cdot \cos b - \color{blue}{\left(\sqrt[3]{\sin a} \cdot \sqrt[3]{\sin a}\right) \cdot \left(\sqrt[3]{\sin a} \cdot \sin b\right)}}\]

  7. Final simplification0.5

    \[\leadsto \frac{\sin b}{\cos a \cdot \cos b - \left(\sqrt[3]{\sin a} \cdot \sqrt[3]{\sin a}\right) \cdot \left(\sin b \cdot \sqrt[3]{\sin a}\right)} \cdot r\]

Runtime

Time bar (total: 33.0s)Debug logProfile

herbie shell --seed 2018216 
(FPCore (r a b)
  :name "r*sin(b)/cos(a+b), B"
  (* r (/ (sin b) (cos (+ a b)))))