Average Error: 1.0 → 0.0
Time: 32.9s
Precision: 64
\[2 \cdot \cos \left(\frac{2 \cdot \pi}{3} + \frac{\cos^{-1} \left(\frac{-g}{h}\right)}{3}\right)\]
↓
\[\left(\frac{1}{2} \cdot \cos \left(\frac{\cos^{-1} \left(\frac{g}{h}\right) \cdot \frac{3}{2} - \pi \cdot 3}{\frac{9}{2}}\right) + \sin \left(\frac{\cos^{-1} \left(\frac{g}{h}\right)}{3} - \frac{\pi}{\frac{3}{2}}\right) \cdot \frac{\sqrt{3}}{2}\right) \cdot 2\]
2 \cdot \cos \left(\frac{2 \cdot \pi}{3} + \frac{\cos^{-1} \left(\frac{-g}{h}\right)}{3}\right)
↓
\left(\frac{1}{2} \cdot \cos \left(\frac{\cos^{-1} \left(\frac{g}{h}\right) \cdot \frac{3}{2} - \pi \cdot 3}{\frac{9}{2}}\right) + \sin \left(\frac{\cos^{-1} \left(\frac{g}{h}\right)}{3} - \frac{\pi}{\frac{3}{2}}\right) \cdot \frac{\sqrt{3}}{2}\right) \cdot 2
double f(double g, double h) {
        double r6582983 = 2.0;
        double r6582984 = atan2(1.0, 0.0);
        double r6582985 = r6582983 * r6582984;
        double r6582986 = 3.0;
        double r6582987 = r6582985 / r6582986;
        double r6582988 = g;
        double r6582989 = -r6582988;
        double r6582990 = h;
        double r6582991 = r6582989 / r6582990;
        double r6582992 = acos(r6582991);
        double r6582993 = r6582992 / r6582986;
        double r6582994 = r6582987 + r6582993;
        double r6582995 = cos(r6582994);
        double r6582996 = r6582983 * r6582995;
        return r6582996;
}
↓
double f(double g, double h) {
        double r6582997 = 0.5;
        double r6582998 = g;
        double r6582999 = h;
        double r6583000 = r6582998 / r6582999;
        double r6583001 = acos(r6583000);
        double r6583002 = 1.5;
        double r6583003 = r6583001 * r6583002;
        double r6583004 = atan2(1.0, 0.0);
        double r6583005 = 3.0;
        double r6583006 = r6583004 * r6583005;
        double r6583007 = r6583003 - r6583006;
        double r6583008 = 4.5;
        double r6583009 = r6583007 / r6583008;
        double r6583010 = cos(r6583009);
        double r6583011 = r6582997 * r6583010;
        double r6583012 = r6583001 / r6583005;
        double r6583013 = r6583004 / r6583002;
        double r6583014 = r6583012 - r6583013;
        double r6583015 = sin(r6583014);
        double r6583016 = sqrt(r6583005);
        double r6583017 = 2.0;
        double r6583018 = r6583016 / r6583017;
        double r6583019 = r6583015 * r6583018;
        double r6583020 = r6583011 + r6583019;
        double r6583021 = r6583020 * r6583017;
        return r6583021;
}

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. Simplified1.0

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

  4. Applied distribute-frac-neg1.0

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

  5. Applied acos-neg1.0

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

  6. Applied div-sub1.0

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

  7. Applied associate-+l-1.0

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

  8. Applied cos-diff0.1

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

  9. Simplified0.1

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

  10. Simplified0.1

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

  12. Applied frac-sub0.0

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

  13. Simplified0.0

    \[\leadsto \left(\cos \left(\frac{\cos^{-1} \left(\frac{g}{h}\right) \cdot \frac{3}{2} - 3 \cdot \pi}{\color{blue}{\frac{9}{2}}}\right) \cdot \frac{1}{2} + \sin \left(\frac{\cos^{-1} \left(\frac{g}{h}\right)}{3} - \frac{\pi}{\frac{3}{2}}\right) \cdot \frac{\sqrt{3}}{2}\right) \cdot 2\]

  14. Final simplification0.0

    \[\leadsto \left(\frac{1}{2} \cdot \cos \left(\frac{\cos^{-1} \left(\frac{g}{h}\right) \cdot \frac{3}{2} - \pi \cdot 3}{\frac{9}{2}}\right) + \sin \left(\frac{\cos^{-1} \left(\frac{g}{h}\right)}{3} - \frac{\pi}{\frac{3}{2}}\right) \cdot \frac{\sqrt{3}}{2}\right) \cdot 2\]

Reproduce

herbie shell --seed 2019128 
(FPCore (g h)
  :name "2-ancestry mixing, negative discriminant"
  (* 2 (cos (+ (/ (* 2 PI) 3) (/ (acos (/ (- g) h)) 3)))))