Average Error: 13.2 → 0.2
Time: 9.3s
Precision: 64
\[\left(x = 0.0 \lor 0.588414199999999998 \le x \le 505.590899999999976\right) \land \left(-1.79665800000000009 \cdot 10^{308} \le y \le -9.425585000000013 \cdot 10^{-310} \lor 1.284938 \cdot 10^{-309} \le y \le 1.7512240000000001 \cdot 10^{308}\right) \land \left(-1.7767070000000002 \cdot 10^{308} \le z \le -8.59979600000002 \cdot 10^{-310} \lor 3.29314499999998 \cdot 10^{-311} \le z \le 1.72515400000000009 \cdot 10^{308}\right) \land \left(-1.79665800000000009 \cdot 10^{308} \le a \le -9.425585000000013 \cdot 10^{-310} \lor 1.284938 \cdot 10^{-309} \le a \le 1.7512240000000001 \cdot 10^{308}\right)\]
\[x + \left(\tan \left(y + z\right) - \tan a\right)\]
↓
\[x + \left(\frac{\tan y + \tan z}{1 - \frac{\tan y \cdot \sin z}{\cos z}} - \tan a\right)\]
x + \left(\tan \left(y + z\right) - \tan a\right)
↓
x + \left(\frac{\tan y + \tan z}{1 - \frac{\tan y \cdot \sin z}{\cos z}} - \tan a\right)
double f(double x, double y, double z, double a) {
        double r140919 = x;
        double r140920 = y;
        double r140921 = z;
        double r140922 = r140920 + r140921;
        double r140923 = tan(r140922);
        double r140924 = a;
        double r140925 = tan(r140924);
        double r140926 = r140923 - r140925;
        double r140927 = r140919 + r140926;
        return r140927;
}
↓
double f(double x, double y, double z, double a) {
        double r140928 = x;
        double r140929 = y;
        double r140930 = tan(r140929);
        double r140931 = z;
        double r140932 = tan(r140931);
        double r140933 = r140930 + r140932;
        double r140934 = 1.0;
        double r140935 = sin(r140931);
        double r140936 = r140930 * r140935;
        double r140937 = cos(r140931);
        double r140938 = r140936 / r140937;
        double r140939 = r140934 - r140938;
        double r140940 = r140933 / r140939;
        double r140941 = a;
        double r140942 = tan(r140941);
        double r140943 = r140940 - r140942;
        double r140944 = r140928 + r140943;
        return r140944;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Bits error versus a

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 13.2

    \[x + \left(\tan \left(y + z\right) - \tan a\right)\]
  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 tan-quot0.2

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

  6. Applied associate-*r/0.2

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

  7. Final simplification0.2

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

Reproduce

herbie shell --seed 2020100 
(FPCore (x y z a)
  :name "(+ x (- (tan (+ y z)) (tan a)))"
  :precision binary64
  :pre (and (or (== x 0.0) (<= 0.5884142 x 505.5909)) (or (<= -1.796658e+308 y -9.425585e-310) (<= 1.284938e-309 y 1.7512240000000001e+308)) (or (<= -1.7767070000000002e+308 z -8.599796e-310) (<= 3.293145e-311 z 1.725154e+308)) (or (<= -1.796658e+308 a -9.425585e-310) (<= 1.284938e-309 a 1.7512240000000001e+308)))
  (+ x (- (tan (+ y z)) (tan a))))