Average Error: 1.0 → 0.0
Time: 17.8s
Precision: 64
\[2 \cdot \cos \left(\frac{2 \cdot \pi}{3} + \frac{\cos^{-1} \left(\frac{-g}{h}\right)}{3}\right)\]
↓
\[\log \left(e^{\frac{\sqrt{3}}{\frac{2}{\sin \left(\frac{\cos^{-1} \left(\frac{g}{h}\right)}{3} - \frac{\pi}{\frac{3}{2}}\right)}} + \frac{1}{2} \cdot \cos \left(\frac{\frac{1}{27} \cdot \left(\cos^{-1} \left(\frac{g}{h}\right) \cdot \left(\cos^{-1} \left(\frac{g}{h}\right) \cdot \cos^{-1} \left(\frac{g}{h}\right)\right)\right) + \left(\pi \cdot \left(\frac{-8}{27} \cdot \pi\right)\right) \cdot \pi}{\left(\pi \cdot \frac{2}{3}\right) \cdot \left(\pi \cdot \frac{2}{3}\right) + \left(\pi \cdot \frac{2}{3} + \frac{1}{3} \cdot \cos^{-1} \left(\frac{g}{h}\right)\right) \cdot \left(\frac{1}{3} \cdot \cos^{-1} \left(\frac{g}{h}\right)\right)}\right)}\right) \cdot 2\]
2 \cdot \cos \left(\frac{2 \cdot \pi}{3} + \frac{\cos^{-1} \left(\frac{-g}{h}\right)}{3}\right)
↓
\log \left(e^{\frac{\sqrt{3}}{\frac{2}{\sin \left(\frac{\cos^{-1} \left(\frac{g}{h}\right)}{3} - \frac{\pi}{\frac{3}{2}}\right)}} + \frac{1}{2} \cdot \cos \left(\frac{\frac{1}{27} \cdot \left(\cos^{-1} \left(\frac{g}{h}\right) \cdot \left(\cos^{-1} \left(\frac{g}{h}\right) \cdot \cos^{-1} \left(\frac{g}{h}\right)\right)\right) + \left(\pi \cdot \left(\frac{-8}{27} \cdot \pi\right)\right) \cdot \pi}{\left(\pi \cdot \frac{2}{3}\right) \cdot \left(\pi \cdot \frac{2}{3}\right) + \left(\pi \cdot \frac{2}{3} + \frac{1}{3} \cdot \cos^{-1} \left(\frac{g}{h}\right)\right) \cdot \left(\frac{1}{3} \cdot \cos^{-1} \left(\frac{g}{h}\right)\right)}\right)}\right) \cdot 2
double f(double g, double h) {
        double r4850140 = 2.0;
        double r4850141 = atan2(1.0, 0.0);
        double r4850142 = r4850140 * r4850141;
        double r4850143 = 3.0;
        double r4850144 = r4850142 / r4850143;
        double r4850145 = g;
        double r4850146 = -r4850145;
        double r4850147 = h;
        double r4850148 = r4850146 / r4850147;
        double r4850149 = acos(r4850148);
        double r4850150 = r4850149 / r4850143;
        double r4850151 = r4850144 + r4850150;
        double r4850152 = cos(r4850151);
        double r4850153 = r4850140 * r4850152;
        return r4850153;
}
↓
double f(double g, double h) {
        double r4850154 = 3.0;
        double r4850155 = sqrt(r4850154);
        double r4850156 = 2.0;
        double r4850157 = g;
        double r4850158 = h;
        double r4850159 = r4850157 / r4850158;
        double r4850160 = acos(r4850159);
        double r4850161 = r4850160 / r4850154;
        double r4850162 = atan2(1.0, 0.0);
        double r4850163 = 1.5;
        double r4850164 = r4850162 / r4850163;
        double r4850165 = r4850161 - r4850164;
        double r4850166 = sin(r4850165);
        double r4850167 = r4850156 / r4850166;
        double r4850168 = r4850155 / r4850167;
        double r4850169 = 0.5;
        double r4850170 = 0.037037037037037035;
        double r4850171 = r4850160 * r4850160;
        double r4850172 = r4850160 * r4850171;
        double r4850173 = r4850170 * r4850172;
        double r4850174 = -0.2962962962962963;
        double r4850175 = r4850174 * r4850162;
        double r4850176 = r4850162 * r4850175;
        double r4850177 = r4850176 * r4850162;
        double r4850178 = r4850173 + r4850177;
        double r4850179 = 0.6666666666666666;
        double r4850180 = r4850162 * r4850179;
        double r4850181 = r4850180 * r4850180;
        double r4850182 = 0.3333333333333333;
        double r4850183 = r4850182 * r4850160;
        double r4850184 = r4850180 + r4850183;
        double r4850185 = r4850184 * r4850183;
        double r4850186 = r4850181 + r4850185;
        double r4850187 = r4850178 / r4850186;
        double r4850188 = cos(r4850187);
        double r4850189 = r4850169 * r4850188;
        double r4850190 = r4850168 + r4850189;
        double r4850191 = exp(r4850190);
        double r4850192 = log(r4850191);
        double r4850193 = r4850192 * r4850156;
        return r4850193;
}

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 add-log-exp1.0

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

  6. Applied distribute-frac-neg1.0

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

  7. Applied acos-neg1.0

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

  8. Applied div-sub1.0

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

  9. Applied associate-+l-1.0

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

  10. Applied cos-diff0.1

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

  11. Simplified0.1

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

  12. Simplified0.1

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

  13. Taylor expanded around -inf 0.1

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

  15. Applied flip3--1.0

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

  16. Simplified0.0

    \[\leadsto \log \left(e^{\cos \left(\frac{\color{blue}{\frac{1}{27} \cdot \left(\cos^{-1} \left(\frac{g}{h}\right) \cdot \left(\cos^{-1} \left(\frac{g}{h}\right) \cdot \cos^{-1} \left(\frac{g}{h}\right)\right)\right) + \pi \cdot \left(\pi \cdot \left(\frac{-8}{27} \cdot \pi\right)\right)}}{\left(\frac{1}{3} \cdot \cos^{-1} \left(\frac{g}{h}\right)\right) \cdot \left(\frac{1}{3} \cdot \cos^{-1} \left(\frac{g}{h}\right)\right) + \left(\left(\frac{2}{3} \cdot \pi\right) \cdot \left(\frac{2}{3} \cdot \pi\right) + \left(\frac{1}{3} \cdot \cos^{-1} \left(\frac{g}{h}\right)\right) \cdot \left(\frac{2}{3} \cdot \pi\right)\right)}\right) \cdot \frac{1}{2} + \frac{\sqrt{3}}{\frac{2}{\sin \left(\frac{\cos^{-1} \left(\frac{g}{h}\right)}{3} - \frac{\pi}{\frac{3}{2}}\right)}}}\right) \cdot 2\]

  17. Simplified0.0

    \[\leadsto \log \left(e^{\cos \left(\frac{\frac{1}{27} \cdot \left(\cos^{-1} \left(\frac{g}{h}\right) \cdot \left(\cos^{-1} \left(\frac{g}{h}\right) \cdot \cos^{-1} \left(\frac{g}{h}\right)\right)\right) + \pi \cdot \left(\pi \cdot \left(\frac{-8}{27} \cdot \pi\right)\right)}{\color{blue}{\left(\cos^{-1} \left(\frac{g}{h}\right) \cdot \frac{1}{3}\right) \cdot \left(\cos^{-1} \left(\frac{g}{h}\right) \cdot \frac{1}{3} + \frac{2}{3} \cdot \pi\right) + \left(\frac{2}{3} \cdot \pi\right) \cdot \left(\frac{2}{3} \cdot \pi\right)}}\right) \cdot \frac{1}{2} + \frac{\sqrt{3}}{\frac{2}{\sin \left(\frac{\cos^{-1} \left(\frac{g}{h}\right)}{3} - \frac{\pi}{\frac{3}{2}}\right)}}}\right) \cdot 2\]

  18. Final simplification0.0

    \[\leadsto \log \left(e^{\frac{\sqrt{3}}{\frac{2}{\sin \left(\frac{\cos^{-1} \left(\frac{g}{h}\right)}{3} - \frac{\pi}{\frac{3}{2}}\right)}} + \frac{1}{2} \cdot \cos \left(\frac{\frac{1}{27} \cdot \left(\cos^{-1} \left(\frac{g}{h}\right) \cdot \left(\cos^{-1} \left(\frac{g}{h}\right) \cdot \cos^{-1} \left(\frac{g}{h}\right)\right)\right) + \left(\pi \cdot \left(\frac{-8}{27} \cdot \pi\right)\right) \cdot \pi}{\left(\pi \cdot \frac{2}{3}\right) \cdot \left(\pi \cdot \frac{2}{3}\right) + \left(\pi \cdot \frac{2}{3} + \frac{1}{3} \cdot \cos^{-1} \left(\frac{g}{h}\right)\right) \cdot \left(\frac{1}{3} \cdot \cos^{-1} \left(\frac{g}{h}\right)\right)}\right)}\right) \cdot 2\]

Reproduce

herbie shell --seed 2019138 
(FPCore (g h)
  :name "2-ancestry mixing, negative discriminant"
  (* 2 (cos (+ (/ (* 2 PI) 3) (/ (acos (/ (- g) h)) 3)))))