Average Error: 1.0 → 0.0
Time: 47.0s
Precision: 64
Internal Precision: 320
\[2 \cdot \cos \left(\frac{2 \cdot \pi}{3} + \frac{\cos^{-1} \left(\frac{-g}{h}\right)}{3}\right)\]
↓
\[2 \cdot \left(\cos \left(\frac{\cos^{-1} \left(\frac{g}{h}\right)}{3}\right) \cdot \cos \left(\left(2 + 1\right) \cdot \frac{\pi}{3}\right) + \sin \left(\frac{\cos^{-1} \left(\frac{g}{h}\right)}{3}\right) \cdot \sin \left(\left(2 + 1\right) \cdot \frac{\pi}{3}\right)\right)\]

Error

Bits error versus g

Bits error versus h

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Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 1.0

    \[2 \cdot \cos \left(\frac{2 \cdot \pi}{3} + \frac{\cos^{-1} \left(\frac{-g}{h}\right)}{3}\right)\]
  2. Using strategy rm

  3. Applied distribute-frac-neg1.0

    \[\leadsto 2 \cdot \cos \left(\frac{2 \cdot \pi}{3} + \frac{\cos^{-1} \color{blue}{\left(-\frac{g}{h}\right)}}{3}\right)\]

  4. Applied acos-neg1.0

    \[\leadsto 2 \cdot \cos \left(\frac{2 \cdot \pi}{3} + \frac{\color{blue}{\pi - \cos^{-1} \left(\frac{g}{h}\right)}}{3}\right)\]

  5. Applied div-sub1.0

    \[\leadsto 2 \cdot \cos \left(\frac{2 \cdot \pi}{3} + \color{blue}{\left(\frac{\pi}{3} - \frac{\cos^{-1} \left(\frac{g}{h}\right)}{3}\right)}\right)\]

  6. Applied associate-+r-1.0

    \[\leadsto 2 \cdot \cos \color{blue}{\left(\left(\frac{2 \cdot \pi}{3} + \frac{\pi}{3}\right) - \frac{\cos^{-1} \left(\frac{g}{h}\right)}{3}\right)}\]

  7. Applied cos-diff0.0

    \[\leadsto 2 \cdot \color{blue}{\left(\cos \left(\frac{2 \cdot \pi}{3} + \frac{\pi}{3}\right) \cdot \cos \left(\frac{\cos^{-1} \left(\frac{g}{h}\right)}{3}\right) + \sin \left(\frac{2 \cdot \pi}{3} + \frac{\pi}{3}\right) \cdot \sin \left(\frac{\cos^{-1} \left(\frac{g}{h}\right)}{3}\right)\right)}\]

  8. Applied simplify0.0

    \[\leadsto 2 \cdot \left(\color{blue}{\cos \left(\frac{\cos^{-1} \left(\frac{g}{h}\right)}{3}\right) \cdot \cos \left(\left(2 + 1\right) \cdot \frac{\pi}{3}\right)} + \sin \left(\frac{2 \cdot \pi}{3} + \frac{\pi}{3}\right) \cdot \sin \left(\frac{\cos^{-1} \left(\frac{g}{h}\right)}{3}\right)\right)\]

  9. Applied simplify0.0

    \[\leadsto 2 \cdot \left(\cos \left(\frac{\cos^{-1} \left(\frac{g}{h}\right)}{3}\right) \cdot \cos \left(\left(2 + 1\right) \cdot \frac{\pi}{3}\right) + \color{blue}{\sin \left(\frac{\cos^{-1} \left(\frac{g}{h}\right)}{3}\right) \cdot \sin \left(\left(2 + 1\right) \cdot \frac{\pi}{3}\right)}\right)\]

Runtime

Time bar (total: 47.0s)Debug logProfile

herbie shell --seed 2018198 
(FPCore (g h)
  :name "2-ancestry mixing, negative discriminant"
  (* 2 (cos (+ (/ (* 2 PI) 3) (/ (acos (/ (- g) h)) 3)))))