Average Error: 13.5 → 0.2
Time: 12.4s
Precision: 64
\[\left(x = 0.0 \lor 0.5884141999999999983472775966220069676638 \le x \le 505.5908999999999764440872240811586380005\right) \land \left(-1.7966580000000000931214523812968299911 \cdot 10^{308} \le y \le -9.425585000000013069597555966781986720373 \cdot 10^{-310} \lor 1.284937999999999548796432976649400331091 \cdot 10^{-309} \le y \le 1.751224000000000127647232028319723370461 \cdot 10^{308}\right) \land \left(-1.776707000000000200843839711454021982841 \cdot 10^{308} \le z \le -8.599796000000016667475923823712126825539 \cdot 10^{-310} \lor 3.293144999999983071955117582595641261776 \cdot 10^{-311} \le z \le 1.725154000000000087891269878141591702413 \cdot 10^{308}\right) \land \left(-1.7966580000000000931214523812968299911 \cdot 10^{308} \le a \le -9.425585000000013069597555966781986720373 \cdot 10^{-310} \lor 1.284937999999999548796432976649400331091 \cdot 10^{-309} \le a \le 1.751224000000000127647232028319723370461 \cdot 10^{308}\right)\]
\[x + \left(\tan \left(y + z\right) - \tan a\right)\]
↓
\[x + \left(\frac{\sin y \cdot \cos z + \cos y \cdot \sin z}{\left(1 - \tan y \cdot \tan z\right) \cdot \left(\cos y \cdot \cos z\right)} - \tan a\right)\]
x + \left(\tan \left(y + z\right) - \tan a\right)
↓
x + \left(\frac{\sin y \cdot \cos z + \cos y \cdot \sin z}{\left(1 - \tan y \cdot \tan z\right) \cdot \left(\cos y \cdot \cos z\right)} - \tan a\right)
double f(double x, double y, double z, double a) {
        double r128385 = x;
        double r128386 = y;
        double r128387 = z;
        double r128388 = r128386 + r128387;
        double r128389 = tan(r128388);
        double r128390 = a;
        double r128391 = tan(r128390);
        double r128392 = r128389 - r128391;
        double r128393 = r128385 + r128392;
        return r128393;
}
↓
double f(double x, double y, double z, double a) {
        double r128394 = x;
        double r128395 = y;
        double r128396 = sin(r128395);
        double r128397 = z;
        double r128398 = cos(r128397);
        double r128399 = r128396 * r128398;
        double r128400 = cos(r128395);
        double r128401 = sin(r128397);
        double r128402 = r128400 * r128401;
        double r128403 = r128399 + r128402;
        double r128404 = 1.0;
        double r128405 = tan(r128395);
        double r128406 = tan(r128397);
        double r128407 = r128405 * r128406;
        double r128408 = r128404 - r128407;
        double r128409 = r128400 * r128398;
        double r128410 = r128408 * r128409;
        double r128411 = r128403 / r128410;
        double r128412 = a;
        double r128413 = tan(r128412);
        double r128414 = r128411 - r128413;
        double r128415 = r128394 + r128414;
        return r128415;
}

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 13.5

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

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

  6. Applied tan-quot0.2

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

  7. Applied frac-add0.2

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

  8. Applied associate-/l/0.2

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

  9. Final simplification0.2

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

Reproduce

herbie shell --seed 2019353 
(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))))