Average Error: 1.0 → 0.0
Time: 17.1s
Precision: 64
\[2 \cdot \cos \left(\frac{2 \cdot \pi}{3} + \frac{\cos^{-1} \left(\frac{-g}{h}\right)}{3}\right)\]
↓
\[\left(\left(\left(\sqrt[3]{\cos \left(\frac{\pi}{\frac{3}{2}}\right)} \cdot \sqrt[3]{\cos \left(\frac{\pi}{\frac{3}{2}}\right)}\right) \cdot \sqrt[3]{\cos \left(\frac{\pi}{\frac{3}{2}}\right)}\right) \cdot \cos \left(\frac{\cos^{-1} \left(\frac{-g}{h}\right)}{3}\right) - \sin \left(\frac{\cos^{-1} \left(\frac{-g}{h}\right)}{3}\right) \cdot \sin \left(\frac{\pi}{\frac{3}{2}}\right)\right) \cdot 2\]
2 \cdot \cos \left(\frac{2 \cdot \pi}{3} + \frac{\cos^{-1} \left(\frac{-g}{h}\right)}{3}\right)
↓
\left(\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) \cdot \cos \left(\frac{\cos^{-1} \left(\frac{-g}{h}\right)}{3}\right) - \sin \left(\frac{\cos^{-1} \left(\frac{-g}{h}\right)}{3}\right) \cdot \sin \left(\frac{\pi}{\frac{3}{2}}\right)\right) \cdot 2
double f(double g, double h) {
        double r5173183 = 2.0;
        double r5173184 = atan2(1.0, 0.0);
        double r5173185 = r5173183 * r5173184;
        double r5173186 = 3.0;
        double r5173187 = r5173185 / r5173186;
        double r5173188 = g;
        double r5173189 = -r5173188;
        double r5173190 = h;
        double r5173191 = r5173189 / r5173190;
        double r5173192 = acos(r5173191);
        double r5173193 = r5173192 / r5173186;
        double r5173194 = r5173187 + r5173193;
        double r5173195 = cos(r5173194);
        double r5173196 = r5173183 * r5173195;
        return r5173196;
}
↓
double f(double g, double h) {
        double r5173197 = atan2(1.0, 0.0);
        double r5173198 = 1.5;
        double r5173199 = r5173197 / r5173198;
        double r5173200 = cos(r5173199);
        double r5173201 = cbrt(r5173200);
        double r5173202 = r5173201 * r5173201;
        double r5173203 = r5173202 * r5173201;
        double r5173204 = g;
        double r5173205 = -r5173204;
        double r5173206 = h;
        double r5173207 = r5173205 / r5173206;
        double r5173208 = acos(r5173207);
        double r5173209 = 3.0;
        double r5173210 = r5173208 / r5173209;
        double r5173211 = cos(r5173210);
        double r5173212 = r5173203 * r5173211;
        double r5173213 = sin(r5173210);
        double r5173214 = sin(r5173199);
        double r5173215 = r5173213 * r5173214;
        double r5173216 = r5173212 - r5173215;
        double r5173217 = 2.0;
        double r5173218 = r5173216 * r5173217;
        return r5173218;
}

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 cos-sum1.0

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

  6. Applied add-cube-cbrt0.0

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

  7. Final simplification0.0

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

Reproduce

herbie shell --seed 2019141 
(FPCore (g h)
  :name "2-ancestry mixing, negative discriminant"
  (* 2 (cos (+ (/ (* 2 PI) 3) (/ (acos (/ (- g) h)) 3)))))