Average Error: 1.0 → 0.0
Time: 20.1s
Precision: 64
\[2 \cdot \cos \left(\frac{2 \cdot \pi}{3} + \frac{\cos^{-1} \left(\frac{-g}{h}\right)}{3}\right)\]
↓
\[2 \cdot \left(\cos \left(\frac{\cos^{-1} \left(\frac{g}{h}\right) \cdot \frac{3}{2} - 3 \cdot \pi}{\frac{9}{2}}\right) \cdot \frac{1}{2} + \frac{\sqrt{3}}{2} \cdot \sin \left(\frac{\cos^{-1} \left(\frac{g}{h}\right)}{3} - \frac{\pi}{\frac{3}{2}}\right)\right)\]
2 \cdot \cos \left(\frac{2 \cdot \pi}{3} + \frac{\cos^{-1} \left(\frac{-g}{h}\right)}{3}\right)
↓
2 \cdot \left(\cos \left(\frac{\cos^{-1} \left(\frac{g}{h}\right) \cdot \frac{3}{2} - 3 \cdot \pi}{\frac{9}{2}}\right) \cdot \frac{1}{2} + \frac{\sqrt{3}}{2} \cdot \sin \left(\frac{\cos^{-1} \left(\frac{g}{h}\right)}{3} - \frac{\pi}{\frac{3}{2}}\right)\right)
double f(double g, double h) {
        double r4289227 = 2.0;
        double r4289228 = atan2(1.0, 0.0);
        double r4289229 = r4289227 * r4289228;
        double r4289230 = 3.0;
        double r4289231 = r4289229 / r4289230;
        double r4289232 = g;
        double r4289233 = -r4289232;
        double r4289234 = h;
        double r4289235 = r4289233 / r4289234;
        double r4289236 = acos(r4289235);
        double r4289237 = r4289236 / r4289230;
        double r4289238 = r4289231 + r4289237;
        double r4289239 = cos(r4289238);
        double r4289240 = r4289227 * r4289239;
        return r4289240;
}
↓
double f(double g, double h) {
        double r4289241 = 2.0;
        double r4289242 = g;
        double r4289243 = h;
        double r4289244 = r4289242 / r4289243;
        double r4289245 = acos(r4289244);
        double r4289246 = 1.5;
        double r4289247 = r4289245 * r4289246;
        double r4289248 = 3.0;
        double r4289249 = atan2(1.0, 0.0);
        double r4289250 = r4289248 * r4289249;
        double r4289251 = r4289247 - r4289250;
        double r4289252 = 4.5;
        double r4289253 = r4289251 / r4289252;
        double r4289254 = cos(r4289253);
        double r4289255 = 0.5;
        double r4289256 = r4289254 * r4289255;
        double r4289257 = sqrt(r4289248);
        double r4289258 = r4289257 / r4289241;
        double r4289259 = r4289245 / r4289248;
        double r4289260 = r4289249 / r4289246;
        double r4289261 = r4289259 - r4289260;
        double r4289262 = sin(r4289261);
        double r4289263 = r4289258 * r4289262;
        double r4289264 = r4289256 + r4289263;
        double r4289265 = r4289241 * r4289264;
        return r4289265;
}

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

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

  10. Simplified0.1

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

  12. Applied frac-sub0.0

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

  13. Simplified0.0

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

  14. Final simplification0.0

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

Reproduce

herbie shell --seed 2019163 
(FPCore (g h)
  :name "2-ancestry mixing, negative discriminant"
  (* 2 (cos (+ (/ (* 2 PI) 3) (/ (acos (/ (- g) h)) 3)))))