Average Error: 13.0 → 0.2
Time: 52.9s
Precision: 64
\[\left(x = 0 \lor 0.5884142 \le x \le 505.5909\right) \land \left(-1.796658 \cdot 10^{+308} \le y \le -9.425585 \cdot 10^{-310} \lor 1.284938 \cdot 10^{-309} \le y \le 1.751224 \cdot 10^{+308}\right) \land \left(-1.776707 \cdot 10^{+308} \le z \le -8.599796 \cdot 10^{-310} \lor 3.293145 \cdot 10^{-311} \le z \le 1.725154 \cdot 10^{+308}\right) \land \left(-1.796658 \cdot 10^{+308} \le a \le -9.425585 \cdot 10^{-310} \lor 1.284938 \cdot 10^{-309} \le a \le 1.751224 \cdot 10^{+308}\right)\]
\[x + \left(\tan \left(y + z\right) - \tan a\right)\]
↓
\[\left(1 + \left(\left(\tan z \cdot \tan y\right) \cdot \left(\tan z \cdot \tan y\right) + \tan z \cdot \tan y\right)\right) \cdot \frac{\cos a \cdot \left(\tan y + \tan z\right) - \left(1 - \tan z \cdot \tan y\right) \cdot \sin a}{\cos a \cdot \left(1 - {\left(\tan z \cdot \tan y\right)}^{3}\right)} + x\]
x + \left(\tan \left(y + z\right) - \tan a\right)
↓
\left(1 + \left(\left(\tan z \cdot \tan y\right) \cdot \left(\tan z \cdot \tan y\right) + \tan z \cdot \tan y\right)\right) \cdot \frac{\cos a \cdot \left(\tan y + \tan z\right) - \left(1 - \tan z \cdot \tan y\right) \cdot \sin a}{\cos a \cdot \left(1 - {\left(\tan z \cdot \tan y\right)}^{3}\right)} + x
double f(double x, double y, double z, double a) {
        double r16764015 = x;
        double r16764016 = y;
        double r16764017 = z;
        double r16764018 = r16764016 + r16764017;
        double r16764019 = tan(r16764018);
        double r16764020 = a;
        double r16764021 = tan(r16764020);
        double r16764022 = r16764019 - r16764021;
        double r16764023 = r16764015 + r16764022;
        return r16764023;
}
↓
double f(double x, double y, double z, double a) {
        double r16764024 = 1.0;
        double r16764025 = z;
        double r16764026 = tan(r16764025);
        double r16764027 = y;
        double r16764028 = tan(r16764027);
        double r16764029 = r16764026 * r16764028;
        double r16764030 = r16764029 * r16764029;
        double r16764031 = r16764030 + r16764029;
        double r16764032 = r16764024 + r16764031;
        double r16764033 = a;
        double r16764034 = cos(r16764033);
        double r16764035 = r16764028 + r16764026;
        double r16764036 = r16764034 * r16764035;
        double r16764037 = r16764024 - r16764029;
        double r16764038 = sin(r16764033);
        double r16764039 = r16764037 * r16764038;
        double r16764040 = r16764036 - r16764039;
        double r16764041 = 3.0;
        double r16764042 = pow(r16764029, r16764041);
        double r16764043 = r16764024 - r16764042;
        double r16764044 = r16764034 * r16764043;
        double r16764045 = r16764040 / r16764044;
        double r16764046 = r16764032 * r16764045;
        double r16764047 = x;
        double r16764048 = r16764046 + r16764047;
        return r16764048;
}

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 13.0

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

  3. Applied tan-quot13.0

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

  4. Applied tan-sum0.2

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

  5. Applied frac-sub0.2

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

  7. Applied flip3--0.2

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

  8. Applied associate-*l/0.2

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

  9. Applied associate-/r/0.2

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

  10. Simplified0.2

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

  11. Final simplification0.2

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

Reproduce

herbie shell --seed 2019112 
(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))))