Average Error: 1.0 → 0.0
Time: 3.7s
Precision: 64
\[2 \cdot \cos \left(\frac{2 \cdot \pi}{3} + \frac{\cos^{-1} \left(\frac{-g}{h}\right)}{3}\right)\]
↓
\[2 \cdot \left(\left(\left(\sqrt[3]{\cos \left(\frac{2 \cdot \pi}{3}\right)} \cdot \sqrt[3]{\cos \left(\frac{2 \cdot \pi}{3}\right)}\right) \cdot \sqrt[3]{\cos \left(\frac{2 \cdot \pi}{3}\right)}\right) \cdot \cos \left(\frac{\sqrt{\cos^{-1} \left(\frac{-g}{h}\right)}}{\sqrt{3}} \cdot \frac{\sqrt{\cos^{-1} \left(\frac{-g}{h}\right)}}{\sqrt{3}}\right) - \sin \left(\frac{2 \cdot \pi}{3}\right) \cdot \sin \left(\frac{\sqrt{\cos^{-1} \left(\frac{-g}{h}\right)}}{\sqrt{3}} \cdot \frac{\sqrt{\cos^{-1} \left(\frac{-g}{h}\right)}}{\sqrt{3}}\right)\right)\]
2 \cdot \cos \left(\frac{2 \cdot \pi}{3} + \frac{\cos^{-1} \left(\frac{-g}{h}\right)}{3}\right)
↓
2 \cdot \left(\left(\left(\sqrt[3]{\cos \left(\frac{2 \cdot \pi}{3}\right)} \cdot \sqrt[3]{\cos \left(\frac{2 \cdot \pi}{3}\right)}\right) \cdot \sqrt[3]{\cos \left(\frac{2 \cdot \pi}{3}\right)}\right) \cdot \cos \left(\frac{\sqrt{\cos^{-1} \left(\frac{-g}{h}\right)}}{\sqrt{3}} \cdot \frac{\sqrt{\cos^{-1} \left(\frac{-g}{h}\right)}}{\sqrt{3}}\right) - \sin \left(\frac{2 \cdot \pi}{3}\right) \cdot \sin \left(\frac{\sqrt{\cos^{-1} \left(\frac{-g}{h}\right)}}{\sqrt{3}} \cdot \frac{\sqrt{\cos^{-1} \left(\frac{-g}{h}\right)}}{\sqrt{3}}\right)\right)
double f(double g, double h) {
        double r137224 = 2.0;
        double r137225 = atan2(1.0, 0.0);
        double r137226 = r137224 * r137225;
        double r137227 = 3.0;
        double r137228 = r137226 / r137227;
        double r137229 = g;
        double r137230 = -r137229;
        double r137231 = h;
        double r137232 = r137230 / r137231;
        double r137233 = acos(r137232);
        double r137234 = r137233 / r137227;
        double r137235 = r137228 + r137234;
        double r137236 = cos(r137235);
        double r137237 = r137224 * r137236;
        return r137237;
}
↓
double f(double g, double h) {
        double r137238 = 2.0;
        double r137239 = atan2(1.0, 0.0);
        double r137240 = r137238 * r137239;
        double r137241 = 3.0;
        double r137242 = r137240 / r137241;
        double r137243 = cos(r137242);
        double r137244 = cbrt(r137243);
        double r137245 = r137244 * r137244;
        double r137246 = r137245 * r137244;
        double r137247 = g;
        double r137248 = -r137247;
        double r137249 = h;
        double r137250 = r137248 / r137249;
        double r137251 = acos(r137250);
        double r137252 = sqrt(r137251);
        double r137253 = sqrt(r137241);
        double r137254 = r137252 / r137253;
        double r137255 = r137254 * r137254;
        double r137256 = cos(r137255);
        double r137257 = r137246 * r137256;
        double r137258 = sin(r137242);
        double r137259 = sin(r137255);
        double r137260 = r137258 * r137259;
        double r137261 = r137257 - r137260;
        double r137262 = r137238 * r137261;
        return r137262;
}

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. Using strategy rm

  3. Applied add-sqr-sqrt1.0

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

  4. Applied add-sqr-sqrt1.0

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

  5. Applied times-frac1.0

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

  7. Applied cos-sum1.0

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

  9. Applied add-cube-cbrt0.0

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

  10. Final simplification0.0

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

Reproduce

herbie shell --seed 2020001 
(FPCore (g h)
  :name "2-ancestry mixing, negative discriminant"
  :precision binary64
  (* 2 (cos (+ (/ (* 2 PI) 3) (/ (acos (/ (- g) h)) 3)))))