Average Error: 13.3 → 0.2
Time: 28.3s
Precision: 64
\[\left(x = 0.0 \lor 0.5884141999999999983472775966220069676638 \le x \le 505.5908999999999764440872240811586380005\right) \land \left(-1.7966580000000000931214523812968299911 \cdot 10^{308} \le y \le -9.425585000000013069597555966781986720373 \cdot 10^{-310} \lor 1.284937999999999548796432976649400331091 \cdot 10^{-309} \le y \le 1.751223999999999928063201074847742204824 \cdot 10^{308}\right) \land \left(-1.776707000000000001259808757982040817204 \cdot 10^{308} \le z \le -8.599796000000016667475923823712126825539 \cdot 10^{-310} \lor 3.293144999999983071955117582595641261776 \cdot 10^{-311} \le z \le 1.725154000000000087891269878141591702413 \cdot 10^{308}\right) \land \left(-1.7966580000000000931214523812968299911 \cdot 10^{308} \le a \le -9.425585000000013069597555966781986720373 \cdot 10^{-310} \lor 1.284937999999999548796432976649400331091 \cdot 10^{-309} \le a \le 1.751223999999999928063201074847742204824 \cdot 10^{308}\right)\]
\[x + \left(\tan \left(y + z\right) - \tan a\right)\]
↓
\[x + \left(\left(\left(\left(\tan z \cdot \tan y\right) \cdot \left(\tan z \cdot \tan y\right) + \tan z \cdot \tan y\right) + 1\right) \cdot \frac{\tan z + \tan y}{1 - {\left(\tan z \cdot \tan y\right)}^{3}} - \tan a\right)\]
x + \left(\tan \left(y + z\right) - \tan a\right)
↓
x + \left(\left(\left(\left(\tan z \cdot \tan y\right) \cdot \left(\tan z \cdot \tan y\right) + \tan z \cdot \tan y\right) + 1\right) \cdot \frac{\tan z + \tan y}{1 - {\left(\tan z \cdot \tan y\right)}^{3}} - \tan a\right)
double f(double x, double y, double z, double a) {
        double r104137 = x;
        double r104138 = y;
        double r104139 = z;
        double r104140 = r104138 + r104139;
        double r104141 = tan(r104140);
        double r104142 = a;
        double r104143 = tan(r104142);
        double r104144 = r104141 - r104143;
        double r104145 = r104137 + r104144;
        return r104145;
}
↓
double f(double x, double y, double z, double a) {
        double r104146 = x;
        double r104147 = z;
        double r104148 = tan(r104147);
        double r104149 = y;
        double r104150 = tan(r104149);
        double r104151 = r104148 * r104150;
        double r104152 = r104151 * r104151;
        double r104153 = r104152 + r104151;
        double r104154 = 1.0;
        double r104155 = r104153 + r104154;
        double r104156 = r104148 + r104150;
        double r104157 = 3.0;
        double r104158 = pow(r104151, r104157);
        double r104159 = r104154 - r104158;
        double r104160 = r104156 / r104159;
        double r104161 = r104155 * r104160;
        double r104162 = a;
        double r104163 = tan(r104162);
        double r104164 = r104161 - r104163;
        double r104165 = r104146 + r104164;
        return r104165;
}

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 13.3

    \[x + \left(\tan \left(y + z\right) - \tan a\right)\]
  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. Simplified0.2

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

  5. Simplified0.2

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

  7. Applied flip3--0.2

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

  8. Applied associate-/r/0.2

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

  9. Simplified0.2

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

  10. Final simplification0.2

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

Reproduce

herbie shell --seed 2019325 
(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 1.751224e+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))))