Average Error: 1.0 → 0.0
Time: 18.4s
Precision: 64
Internal Precision: 384
\[2 \cdot \cos \left(\frac{2 \cdot \pi}{3} + \frac{\cos^{-1} \left(\frac{-g}{h}\right)}{3}\right)\]
↓
\[2 \cdot \left(\cos \left(\frac{\cos^{-1} \left(-\frac{g}{h}\right)}{3}\right) \cdot \left(\left(\sqrt[3]{\cos \left(\frac{\pi}{\frac{3}{2}}\right)} \cdot \sqrt[3]{\cos \left(\frac{\pi}{\frac{3}{2}}\right)}\right) \cdot \sqrt[3]{\cos \left(\frac{\pi}{\frac{3}{2}}\right)}\right) - \sin \left(\frac{\cos^{-1} \left(-\frac{g}{h}\right)}{3}\right) \cdot \sin \left(\frac{\pi}{\frac{3}{2}}\right)\right)\]

Error

Bits error versus g

Bits error versus h

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 cos-sum1.0

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

  4. Applied simplify1.0

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

  5. Applied simplify1.0

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

  7. Applied add-cube-cbrt0.0

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

Runtime

Time bar (total: 18.4s)Debug logProfile

herbie shell --seed '#(1070991898 1055468627 4280279443 640792587 928206309 3646738750)' 
(FPCore (g h)
  :name "2-ancestry mixing, negative discriminant"
  (* 2 (cos (+ (/ (* 2 PI) 3) (/ (acos (/ (- g) h)) 3)))))