Average Error: 13.2 → 0.2
Time: 29.2s
Precision: 64
\[\left(x = 0 \lor 0.5884142 \le x \le 505.5909\right) \land \left(-1.796658 \cdot 10^{+308} \le y \le -9.425585 \cdot 10^{-310} \lor 1.284938 \cdot 10^{-309} \le y \le 1.751224 \cdot 10^{+308}\right) \land \left(-1.776707 \cdot 10^{+308} \le z \le -8.599796 \cdot 10^{-310} \lor 3.293145 \cdot 10^{-311} \le z \le 1.725154 \cdot 10^{+308}\right) \land \left(-1.796658 \cdot 10^{+308} \le a \le -9.425585 \cdot 10^{-310} \lor 1.284938 \cdot 10^{-309} \le a \le 1.751224 \cdot 10^{+308}\right)\]
\[x + \left(\tan \left(y + z\right) - \tan a\right)\]
↓
\[\left(\frac{\tan z + \tan y}{1 - \left(\tan y \cdot \tan z\right) \cdot \left(\tan y \cdot \tan z\right)} \cdot \left(\tan y \cdot \tan z + 1\right) - \tan a\right) + x\]
x + \left(\tan \left(y + z\right) - \tan a\right)
↓
\left(\frac{\tan z + \tan y}{1 - \left(\tan y \cdot \tan z\right) \cdot \left(\tan y \cdot \tan z\right)} \cdot \left(\tan y \cdot \tan z + 1\right) - \tan a\right) + x
double f(double x, double y, double z, double a) {
        double r3847164 = x;
        double r3847165 = y;
        double r3847166 = z;
        double r3847167 = r3847165 + r3847166;
        double r3847168 = tan(r3847167);
        double r3847169 = a;
        double r3847170 = tan(r3847169);
        double r3847171 = r3847168 - r3847170;
        double r3847172 = r3847164 + r3847171;
        return r3847172;
}
↓
double f(double x, double y, double z, double a) {
        double r3847173 = z;
        double r3847174 = tan(r3847173);
        double r3847175 = y;
        double r3847176 = tan(r3847175);
        double r3847177 = r3847174 + r3847176;
        double r3847178 = 1.0;
        double r3847179 = r3847176 * r3847174;
        double r3847180 = r3847179 * r3847179;
        double r3847181 = r3847178 - r3847180;
        double r3847182 = r3847177 / r3847181;
        double r3847183 = r3847179 + r3847178;
        double r3847184 = r3847182 * r3847183;
        double r3847185 = a;
        double r3847186 = tan(r3847185);
        double r3847187 = r3847184 - r3847186;
        double r3847188 = x;
        double r3847189 = r3847187 + r3847188;
        return r3847189;
}

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 flip--0.2

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

  6. Applied associate-/r/0.2

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

  7. Simplified0.2

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

  8. Final simplification0.2

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

Reproduce

herbie shell --seed 2019135 
(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))))