Average Error: 13.3 → 0.2
Time: 54.5s
Precision: 64
\[x + \left(\tan \left(y + z\right) - \tan a\right)\]
↓
\[\left(\frac{\tan y + \tan z}{1 - \left(\sqrt[3]{\tan z \cdot \tan y} \cdot \sqrt[3]{\tan z \cdot \tan y}\right) \cdot \sqrt[3]{\tan z \cdot \tan y}} - \tan a\right) + x\]
double f(double x, double y, double z, double a) {
        double r23621426 = x;
        double r23621427 = y;
        double r23621428 = z;
        double r23621429 = r23621427 + r23621428;
        double r23621430 = tan(r23621429);
        double r23621431 = a;
        double r23621432 = tan(r23621431);
        double r23621433 = r23621430 - r23621432;
        double r23621434 = r23621426 + r23621433;
        return r23621434;
}
↓
double f(double x, double y, double z, double a) {
        double r23621435 = y;
        double r23621436 = tan(r23621435);
        double r23621437 = z;
        double r23621438 = tan(r23621437);
        double r23621439 = r23621436 + r23621438;
        double r23621440 = 1.0;
        double r23621441 = r23621438 * r23621436;
        double r23621442 = cbrt(r23621441);
        double r23621443 = r23621442 * r23621442;
        double r23621444 = r23621443 * r23621442;
        double r23621445 = r23621440 - r23621444;
        double r23621446 = r23621439 / r23621445;
        double r23621447 = a;
        double r23621448 = tan(r23621447);
        double r23621449 = r23621446 - r23621448;
        double r23621450 = x;
        double r23621451 = r23621449 + r23621450;
        return r23621451;
}


x + \left(\tan \left(y + z\right) - \tan a\right)
↓
\left(\frac{\tan y + \tan z}{1 - \left(\sqrt[3]{\tan z \cdot \tan y} \cdot \sqrt[3]{\tan z \cdot \tan y}\right) \cdot \sqrt[3]{\tan z \cdot \tan y}} - \tan a\right) + x

Error

Bits error versus x

Bits error versus y

Bits error versus z

Bits error versus a

Derivation

  1. Initial program 13.3

    \[x + \left(\tan \left(y + z\right) - \tan a\right)\]
  2. Using strategy rm

  3. Applied tan-sum0.2

    \[\leadsto x + \left(\color{blue}{\frac{\tan y + \tan z}{1 - \tan y \cdot \tan z}} - \tan a\right)\]
  4. Using strategy rm

  5. Applied add-cube-cbrt0.2

    \[\leadsto x + \left(\frac{\tan y + \tan z}{1 - \color{blue}{\left(\sqrt[3]{\tan y \cdot \tan z} \cdot \sqrt[3]{\tan y \cdot \tan z}\right) \cdot \sqrt[3]{\tan y \cdot \tan z}}} - \tan a\right)\]

  6. Final simplification0.2

    \[\leadsto \left(\frac{\tan y + \tan z}{1 - \left(\sqrt[3]{\tan z \cdot \tan y} \cdot \sqrt[3]{\tan z \cdot \tan y}\right) \cdot \sqrt[3]{\tan z \cdot \tan y}} - \tan a\right) + x\]

Reproduce

herbie shell --seed 2019101 
(FPCore (x y z a)
  :name "(+ x (- (tan (+ y z)) (tan a)))"
  :pre (and (or (== x 0) (<= 0.5884142 x 505.5909)) (or (<= -1.796658e+308 y -9.425585e-310) (<= 1.284938e-309 y 1.751224e+308)) (or (<= -1.776707e+308 z -8.599796e-310) (<= 3.293145e-311 z 1.725154e+308)) (or (<= -1.796658e+308 a -9.425585e-310) (<= 1.284938e-309 a 1.751224e+308)))
  (+ x (- (tan (+ y z)) (tan a))))