Average Error: 1.0 → 0.0
Time: 15.4s
Precision: 64
\[2 \cdot \cos \left(\frac{2 \cdot \pi}{3} + \frac{\cos^{-1} \left(\frac{-g}{h}\right)}{3}\right)\]
↓
\[2 \cdot \left(\sin \left(\frac{\pi}{3}\right) \cdot \sin \left(\frac{\cos^{-1} \left(\frac{g}{h}\right)}{3} - \frac{\pi}{\frac{3}{2}}\right) + \frac{1}{2} \cdot \cos \left(\frac{\cos^{-1} \left(\frac{g}{h}\right) \cdot \frac{3}{2} - \pi \cdot 3}{\frac{9}{2}}\right)\right)\]
2 \cdot \cos \left(\frac{2 \cdot \pi}{3} + \frac{\cos^{-1} \left(\frac{-g}{h}\right)}{3}\right)
↓
2 \cdot \left(\sin \left(\frac{\pi}{3}\right) \cdot \sin \left(\frac{\cos^{-1} \left(\frac{g}{h}\right)}{3} - \frac{\pi}{\frac{3}{2}}\right) + \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)\right)
double f(double g, double h) {
        double r4607033 = 2.0;
        double r4607034 = atan2(1.0, 0.0);
        double r4607035 = r4607033 * r4607034;
        double r4607036 = 3.0;
        double r4607037 = r4607035 / r4607036;
        double r4607038 = g;
        double r4607039 = -r4607038;
        double r4607040 = h;
        double r4607041 = r4607039 / r4607040;
        double r4607042 = acos(r4607041);
        double r4607043 = r4607042 / r4607036;
        double r4607044 = r4607037 + r4607043;
        double r4607045 = cos(r4607044);
        double r4607046 = r4607033 * r4607045;
        return r4607046;
}
↓
double f(double g, double h) {
        double r4607047 = 2.0;
        double r4607048 = atan2(1.0, 0.0);
        double r4607049 = 3.0;
        double r4607050 = r4607048 / r4607049;
        double r4607051 = sin(r4607050);
        double r4607052 = g;
        double r4607053 = h;
        double r4607054 = r4607052 / r4607053;
        double r4607055 = acos(r4607054);
        double r4607056 = r4607055 / r4607049;
        double r4607057 = 1.5;
        double r4607058 = r4607048 / r4607057;
        double r4607059 = r4607056 - r4607058;
        double r4607060 = sin(r4607059);
        double r4607061 = r4607051 * r4607060;
        double r4607062 = 0.5;
        double r4607063 = r4607055 * r4607057;
        double r4607064 = r4607048 * r4607049;
        double r4607065 = r4607063 - r4607064;
        double r4607066 = 4.5;
        double r4607067 = r4607065 / r4607066;
        double r4607068 = cos(r4607067);
        double r4607069 = r4607062 * r4607068;
        double r4607070 = r4607061 + r4607069;
        double r4607071 = r4607047 * r4607070;
        return r4607071;
}

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. Using strategy rm

  11. Applied frac-sub0.0

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

  12. Simplified0.0

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

  13. Final simplification0.0

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

Reproduce

herbie shell --seed 2019120 
(FPCore (g h)
  :name "2-ancestry mixing, negative discriminant"
  (* 2 (cos (+ (/ (* 2 PI) 3) (/ (acos (/ (- g) h)) 3)))))