Average Error: 13.9 → 0.2
Time: 8.1s
Precision: 64
\[\left(x = 0.0 \lor 0.588414199999999998 \le x \le 505.590899999999976\right) \land \left(-1.79665800000000009 \cdot 10^{308} \le y \le -9.425585000000013 \cdot 10^{-310} \lor 1.284938 \cdot 10^{-309} \le y \le 1.7512240000000001 \cdot 10^{308}\right) \land \left(-1.7767070000000002 \cdot 10^{308} \le z \le -8.59979600000002 \cdot 10^{-310} \lor 3.29314499999998 \cdot 10^{-311} \le z \le 1.72515400000000009 \cdot 10^{308}\right) \land \left(-1.79665800000000009 \cdot 10^{308} \le a \le -9.425585000000013 \cdot 10^{-310} \lor 1.284938 \cdot 10^{-309} \le a \le 1.7512240000000001 \cdot 10^{308}\right)\]
\[x + \left(\tan \left(y + z\right) - \tan a\right)\]
↓
\[x + \left(\frac{\tan y + \tan z}{1 - \frac{\sqrt[3]{{\left(\sin y \cdot \tan z\right)}^{3}}}{\cos y}} - \tan a\right)\]
x + \left(\tan \left(y + z\right) - \tan a\right)
↓
x + \left(\frac{\tan y + \tan z}{1 - \frac{\sqrt[3]{{\left(\sin y \cdot \tan z\right)}^{3}}}{\cos y}} - \tan a\right)
double f(double x, double y, double z, double a) {
        double r169143 = x;
        double r169144 = y;
        double r169145 = z;
        double r169146 = r169144 + r169145;
        double r169147 = tan(r169146);
        double r169148 = a;
        double r169149 = tan(r169148);
        double r169150 = r169147 - r169149;
        double r169151 = r169143 + r169150;
        return r169151;
}
↓
double f(double x, double y, double z, double a) {
        double r169152 = x;
        double r169153 = y;
        double r169154 = tan(r169153);
        double r169155 = z;
        double r169156 = tan(r169155);
        double r169157 = r169154 + r169156;
        double r169158 = 1.0;
        double r169159 = sin(r169153);
        double r169160 = r169159 * r169156;
        double r169161 = 3.0;
        double r169162 = pow(r169160, r169161);
        double r169163 = cbrt(r169162);
        double r169164 = cos(r169153);
        double r169165 = r169163 / r169164;
        double r169166 = r169158 - r169165;
        double r169167 = r169157 / r169166;
        double r169168 = a;
        double r169169 = tan(r169168);
        double r169170 = r169167 - r169169;
        double r169171 = r169152 + r169170;
        return r169171;
}

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 13.9

    \[x + \left(\tan \left(y + z\right) - \tan a\right)\]
  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 tan-quot0.2

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

  6. Applied associate-*l/0.2

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

  8. Applied add-cbrt-cube0.2

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

  9. Applied add-cbrt-cube0.2

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

  10. Applied cbrt-unprod0.2

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

  11. Simplified0.2

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

  12. Final simplification0.2

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

Reproduce

herbie shell --seed 2020062 
(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))))