Average Error: 1.0 → 0.1
Time: 4.9s
Precision: 64
\[2 \cdot \cos \left(\frac{2 \cdot \pi}{3} + \frac{\cos^{-1} \left(\frac{-g}{h}\right)}{3}\right)\]
↓
\[2 \cdot \left(\cos \left(\frac{2 \cdot \pi}{3} + \frac{\pi}{3}\right) \cdot \cos \left(\frac{\cos^{-1} \left(\frac{g}{h}\right)}{3}\right) + \sin \left(\frac{2 \cdot \pi}{3} + \frac{\pi}{3}\right) \cdot \sin \left(\frac{\cos^{-1} \left(\frac{g}{h}\right)}{3}\right)\right)\]
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{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)
double f(double g, double h) {
        double r144024 = 2.0;
        double r144025 = atan2(1.0, 0.0);
        double r144026 = r144024 * r144025;
        double r144027 = 3.0;
        double r144028 = r144026 / r144027;
        double r144029 = g;
        double r144030 = -r144029;
        double r144031 = h;
        double r144032 = r144030 / r144031;
        double r144033 = acos(r144032);
        double r144034 = r144033 / r144027;
        double r144035 = r144028 + r144034;
        double r144036 = cos(r144035);
        double r144037 = r144024 * r144036;
        return r144037;
}
↓
double f(double g, double h) {
        double r144038 = 2.0;
        double r144039 = atan2(1.0, 0.0);
        double r144040 = r144038 * r144039;
        double r144041 = 3.0;
        double r144042 = r144040 / r144041;
        double r144043 = r144039 / r144041;
        double r144044 = r144042 + r144043;
        double r144045 = cos(r144044);
        double r144046 = g;
        double r144047 = h;
        double r144048 = r144046 / r144047;
        double r144049 = acos(r144048);
        double r144050 = r144049 / r144041;
        double r144051 = cos(r144050);
        double r144052 = r144045 * r144051;
        double r144053 = sin(r144044);
        double r144054 = sin(r144050);
        double r144055 = r144053 * r144054;
        double r144056 = r144052 + r144055;
        double r144057 = r144038 * r144056;
        return r144057;
}

Error

Bits error versus g

Bits error versus h

Try it out

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-diff0.1

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

  8. Final simplification0.1

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

Reproduce

herbie shell --seed 2020056 
(FPCore (g h)
  :name "2-ancestry mixing, negative discriminant"
  :precision binary64
  (* 2 (cos (+ (/ (* 2 PI) 3) (/ (acos (/ (- g) h)) 3)))))