Average Error: 1.0 → 0.0
Time: 15.2s
Precision: 64
\[2 \cdot \cos \left(\frac{2 \cdot \pi}{3} + \frac{\cos^{-1} \left(\frac{-g}{h}\right)}{3}\right)\]
↓
\[2 \cdot \left(\cos \left(\frac{2 \cdot \pi}{3}\right) \cdot \cos \left(\left(\sqrt{\frac{1}{\sqrt{3}}} \cdot \sqrt{\frac{1}{\sqrt{3}}}\right) \cdot \frac{\cos^{-1} \left(\frac{-g}{h}\right)}{\sqrt{3}}\right) - \sin \left(\frac{2 \cdot \pi}{3}\right) \cdot \sin \left(\left(\sqrt{\frac{1}{\sqrt{3}}} \cdot \sqrt{\frac{1}{\sqrt{3}}}\right) \cdot \frac{\cos^{-1} \left(\frac{-g}{h}\right)}{\sqrt{3}}\right)\right)\]
2 \cdot \cos \left(\frac{2 \cdot \pi}{3} + \frac{\cos^{-1} \left(\frac{-g}{h}\right)}{3}\right)
↓
2 \cdot \left(\cos \left(\frac{2 \cdot \pi}{3}\right) \cdot \cos \left(\left(\sqrt{\frac{1}{\sqrt{3}}} \cdot \sqrt{\frac{1}{\sqrt{3}}}\right) \cdot \frac{\cos^{-1} \left(\frac{-g}{h}\right)}{\sqrt{3}}\right) - \sin \left(\frac{2 \cdot \pi}{3}\right) \cdot \sin \left(\left(\sqrt{\frac{1}{\sqrt{3}}} \cdot \sqrt{\frac{1}{\sqrt{3}}}\right) \cdot \frac{\cos^{-1} \left(\frac{-g}{h}\right)}{\sqrt{3}}\right)\right)
double f(double g, double h) {
        double r9332065 = 2.0;
        double r9332066 = atan2(1.0, 0.0);
        double r9332067 = r9332065 * r9332066;
        double r9332068 = 3.0;
        double r9332069 = r9332067 / r9332068;
        double r9332070 = g;
        double r9332071 = -r9332070;
        double r9332072 = h;
        double r9332073 = r9332071 / r9332072;
        double r9332074 = acos(r9332073);
        double r9332075 = r9332074 / r9332068;
        double r9332076 = r9332069 + r9332075;
        double r9332077 = cos(r9332076);
        double r9332078 = r9332065 * r9332077;
        return r9332078;
}
↓
double f(double g, double h) {
        double r9332079 = 2.0;
        double r9332080 = atan2(1.0, 0.0);
        double r9332081 = r9332079 * r9332080;
        double r9332082 = 3.0;
        double r9332083 = r9332081 / r9332082;
        double r9332084 = cos(r9332083);
        double r9332085 = 1.0;
        double r9332086 = sqrt(r9332082);
        double r9332087 = r9332085 / r9332086;
        double r9332088 = sqrt(r9332087);
        double r9332089 = r9332088 * r9332088;
        double r9332090 = g;
        double r9332091 = -r9332090;
        double r9332092 = h;
        double r9332093 = r9332091 / r9332092;
        double r9332094 = acos(r9332093);
        double r9332095 = r9332094 / r9332086;
        double r9332096 = r9332089 * r9332095;
        double r9332097 = cos(r9332096);
        double r9332098 = r9332084 * r9332097;
        double r9332099 = sin(r9332083);
        double r9332100 = sin(r9332096);
        double r9332101 = r9332099 * r9332100;
        double r9332102 = r9332098 - r9332101;
        double r9332103 = r9332079 * r9332102;
        return r9332103;
}

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 *-un-lft-identity1.0

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

  5. Applied times-frac1.0

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

  7. Applied add-sqr-sqrt1.0

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

  9. Applied cos-sum0.0

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

  10. Final simplification0.0

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

Reproduce

herbie shell --seed 2019174 
(FPCore (g h)
  :name "2-ancestry mixing, negative discriminant"
  (* 2.0 (cos (+ (/ (* 2.0 PI) 3.0) (/ (acos (/ (- g) h)) 3.0)))))