Average Error: 1.0 → 0.0
Time: 17.3s
Precision: 64
\[2 \cdot \cos \left(\frac{2 \cdot \pi}{3} + \frac{\cos^{-1} \left(\frac{-g}{h}\right)}{3}\right)\]
↓
\[2 \cdot \left(\cos \left(\frac{\sin^{-1} \left(-\frac{g}{h}\right)}{3} - \frac{\pi}{\frac{3}{2}}\right) \cdot \cos \left(\frac{\frac{\pi}{2}}{3}\right) + \sin \left(\frac{\frac{\pi}{2}}{3}\right) \cdot \sin \left(\frac{\sin^{-1} \left(-\frac{g}{h}\right)}{3} - \sqrt{\pi} \cdot \frac{\sqrt{\pi}}{\frac{3}{2}}\right)\right)\]
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{\sin^{-1} \left(-\frac{g}{h}\right)}{3} - \frac{\pi}{\frac{3}{2}}\right) \cdot \cos \left(\frac{\frac{\pi}{2}}{3}\right) + \sin \left(\frac{\frac{\pi}{2}}{3}\right) \cdot \sin \left(\frac{\sin^{-1} \left(-\frac{g}{h}\right)}{3} - \sqrt{\pi} \cdot \frac{\sqrt{\pi}}{\frac{3}{2}}\right)\right)
double f(double g, double h) {
        double r3917195 = 2.0;
        double r3917196 = atan2(1.0, 0.0);
        double r3917197 = r3917195 * r3917196;
        double r3917198 = 3.0;
        double r3917199 = r3917197 / r3917198;
        double r3917200 = g;
        double r3917201 = -r3917200;
        double r3917202 = h;
        double r3917203 = r3917201 / r3917202;
        double r3917204 = acos(r3917203);
        double r3917205 = r3917204 / r3917198;
        double r3917206 = r3917199 + r3917205;
        double r3917207 = cos(r3917206);
        double r3917208 = r3917195 * r3917207;
        return r3917208;
}
↓
double f(double g, double h) {
        double r3917209 = 2.0;
        double r3917210 = g;
        double r3917211 = h;
        double r3917212 = r3917210 / r3917211;
        double r3917213 = -r3917212;
        double r3917214 = asin(r3917213);
        double r3917215 = 3.0;
        double r3917216 = r3917214 / r3917215;
        double r3917217 = atan2(1.0, 0.0);
        double r3917218 = 1.5;
        double r3917219 = r3917217 / r3917218;
        double r3917220 = r3917216 - r3917219;
        double r3917221 = cos(r3917220);
        double r3917222 = r3917217 / r3917209;
        double r3917223 = r3917222 / r3917215;
        double r3917224 = cos(r3917223);
        double r3917225 = r3917221 * r3917224;
        double r3917226 = sin(r3917223);
        double r3917227 = sqrt(r3917217);
        double r3917228 = r3917227 / r3917218;
        double r3917229 = r3917227 * r3917228;
        double r3917230 = r3917216 - r3917229;
        double r3917231 = sin(r3917230);
        double r3917232 = r3917226 * r3917231;
        double r3917233 = r3917225 + r3917232;
        double r3917234 = r3917209 * r3917233;
        return r3917234;
}

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 acos-asin1.0

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

  5. Applied div-sub1.0

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

  6. Applied associate-+l-1.0

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

  7. Applied cos-diff1.0

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

  9. Applied *-un-lft-identity1.0

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

  10. Applied add-sqr-sqrt1.0

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

  11. Applied times-frac0.0

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

  12. Simplified0.0

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

  13. Final simplification0.0

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

Reproduce

herbie shell --seed 2019129 
(FPCore (g h)
  :name "2-ancestry mixing, negative discriminant"
  (* 2 (cos (+ (/ (* 2 PI) 3) (/ (acos (/ (- g) h)) 3)))))