Average Error: 13.2 → 0.2
Time: 44.5s
Precision: 64
\[\left(x = 0 \lor 0.5884142 \le x \le 505.5909\right) \land \left(-1.796658 \cdot 10^{+308} \le y \le -9.425585 \cdot 10^{-310} \lor 1.284938 \cdot 10^{-309} \le y \le 1.751224 \cdot 10^{+308}\right) \land \left(-1.776707 \cdot 10^{+308} \le z \le -8.599796 \cdot 10^{-310} \lor 3.293145 \cdot 10^{-311} \le z \le 1.725154 \cdot 10^{+308}\right) \land \left(-1.796658 \cdot 10^{+308} \le a \le -9.425585 \cdot 10^{-310} \lor 1.284938 \cdot 10^{-309} \le a \le 1.751224 \cdot 10^{+308}\right)\]
\[x + \left(\tan \left(y + z\right) - \tan a\right)\]
↓
\[\frac{\left(\cos a \cdot \left(\cos z \cdot \sin y + \sin z \cdot \cos y\right)\right) \cdot \left(1 + \tan z \cdot \tan y\right) - \left(\sin a \cdot \left(1 - \left(\tan z \cdot \tan y\right) \cdot \left(\tan z \cdot \tan y\right)\right)\right) \cdot \left(\cos y \cdot \cos z\right)}{\left(\left(1 + \tan z \cdot \tan y\right) \cdot \left(\cos y \cdot \cos z\right)\right) \cdot \left(\left(1 - \tan z \cdot \tan y\right) \cdot \cos a\right)} + x\]
x + \left(\tan \left(y + z\right) - \tan a\right)
↓
\frac{\left(\cos a \cdot \left(\cos z \cdot \sin y + \sin z \cdot \cos y\right)\right) \cdot \left(1 + \tan z \cdot \tan y\right) - \left(\sin a \cdot \left(1 - \left(\tan z \cdot \tan y\right) \cdot \left(\tan z \cdot \tan y\right)\right)\right) \cdot \left(\cos y \cdot \cos z\right)}{\left(\left(1 + \tan z \cdot \tan y\right) \cdot \left(\cos y \cdot \cos z\right)\right) \cdot \left(\left(1 - \tan z \cdot \tan y\right) \cdot \cos a\right)} + x
double f(double x, double y, double z, double a) {
        double r4723948 = x;
        double r4723949 = y;
        double r4723950 = z;
        double r4723951 = r4723949 + r4723950;
        double r4723952 = tan(r4723951);
        double r4723953 = a;
        double r4723954 = tan(r4723953);
        double r4723955 = r4723952 - r4723954;
        double r4723956 = r4723948 + r4723955;
        return r4723956;
}
↓
double f(double x, double y, double z, double a) {
        double r4723957 = a;
        double r4723958 = cos(r4723957);
        double r4723959 = z;
        double r4723960 = cos(r4723959);
        double r4723961 = y;
        double r4723962 = sin(r4723961);
        double r4723963 = r4723960 * r4723962;
        double r4723964 = sin(r4723959);
        double r4723965 = cos(r4723961);
        double r4723966 = r4723964 * r4723965;
        double r4723967 = r4723963 + r4723966;
        double r4723968 = r4723958 * r4723967;
        double r4723969 = 1.0;
        double r4723970 = tan(r4723959);
        double r4723971 = tan(r4723961);
        double r4723972 = r4723970 * r4723971;
        double r4723973 = r4723969 + r4723972;
        double r4723974 = r4723968 * r4723973;
        double r4723975 = sin(r4723957);
        double r4723976 = r4723972 * r4723972;
        double r4723977 = r4723969 - r4723976;
        double r4723978 = r4723975 * r4723977;
        double r4723979 = r4723965 * r4723960;
        double r4723980 = r4723978 * r4723979;
        double r4723981 = r4723974 - r4723980;
        double r4723982 = r4723973 * r4723979;
        double r4723983 = r4723969 - r4723972;
        double r4723984 = r4723983 * r4723958;
        double r4723985 = r4723982 * r4723984;
        double r4723986 = r4723981 / r4723985;
        double r4723987 = x;
        double r4723988 = r4723986 + r4723987;
        return r4723988;
}

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-quot13.2

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

  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 flip--0.2

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

  8. Applied associate-*l/0.2

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

  9. Applied tan-quot0.2

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

  10. Applied tan-quot0.2

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

  11. Applied frac-add0.2

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

  12. Applied associate-*l/0.2

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

  13. Applied frac-sub0.3

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

  14. Applied associate-/l/0.2

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

  15. Final simplification0.2

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

Reproduce

herbie shell --seed 2019143 
(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))))