Average Error: 13.4 → 0.2
Time: 14.7s
Precision: 64
\[\left(x = 0.0 \lor 0.588414199999999998 \le x \le 505.590899999999976\right) \land \left(-1.79665800000000009 \cdot 10^{308} \le y \le -9.425585000000013 \cdot 10^{-310} \lor 1.284938 \cdot 10^{-309} \le y \le 1.7512240000000001 \cdot 10^{308}\right) \land \left(-1.7767070000000002 \cdot 10^{308} \le z \le -8.59979600000002 \cdot 10^{-310} \lor 3.29314499999998 \cdot 10^{-311} \le z \le 1.72515400000000009 \cdot 10^{308}\right) \land \left(-1.79665800000000009 \cdot 10^{308} \le a \le -9.425585000000013 \cdot 10^{-310} \lor 1.284938 \cdot 10^{-309} \le a \le 1.7512240000000001 \cdot 10^{308}\right)\]
\[x + \left(\tan \left(y + z\right) - \tan a\right)\]
↓
\[x + \left(\frac{\tan y + \tan z}{1 - \sqrt[3]{{\left(\tan y \cdot \tan z\right)}^{3}}} - \tan a\right)\]
x + \left(\tan \left(y + z\right) - \tan a\right)
↓
x + \left(\frac{\tan y + \tan z}{1 - \sqrt[3]{{\left(\tan y \cdot \tan z\right)}^{3}}} - \tan a\right)
double f(double x, double y, double z, double a) {
        double r138132 = x;
        double r138133 = y;
        double r138134 = z;
        double r138135 = r138133 + r138134;
        double r138136 = tan(r138135);
        double r138137 = a;
        double r138138 = tan(r138137);
        double r138139 = r138136 - r138138;
        double r138140 = r138132 + r138139;
        return r138140;
}
↓
double f(double x, double y, double z, double a) {
        double r138141 = x;
        double r138142 = y;
        double r138143 = tan(r138142);
        double r138144 = z;
        double r138145 = tan(r138144);
        double r138146 = r138143 + r138145;
        double r138147 = 1.0;
        double r138148 = r138143 * r138145;
        double r138149 = 3.0;
        double r138150 = pow(r138148, r138149);
        double r138151 = cbrt(r138150);
        double r138152 = r138147 - r138151;
        double r138153 = r138146 / r138152;
        double r138154 = a;
        double r138155 = tan(r138154);
        double r138156 = r138153 - r138155;
        double r138157 = r138141 + r138156;
        return r138157;
}

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 13.4

    \[x + \left(\tan \left(y + z\right) - \tan a\right)\]
  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 add-cbrt-cube0.2

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

  6. Applied add-cbrt-cube0.2

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

  7. Applied cbrt-unprod0.2

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

  8. Simplified0.2

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

  9. Final simplification0.2

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

Reproduce

herbie shell --seed 2020034 +o rules:numerics
(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))))