Average Error: 13.2 → 0.2
Time: 14.6s
Precision: 64
\[\left(x = 0.0 \lor 0.588414199999999998 \le x \le 505.590899999999976\right) \land \left(-1.79665800000000009 \cdot 10^{308} \le y \le -9.425585000000013 \cdot 10^{-310} \lor 1.284938 \cdot 10^{-309} \le y \le 1.7512240000000001 \cdot 10^{308}\right) \land \left(-1.7767070000000002 \cdot 10^{308} \le z \le -8.59979600000002 \cdot 10^{-310} \lor 3.29314499999998 \cdot 10^{-311} \le z \le 1.72515400000000009 \cdot 10^{308}\right) \land \left(-1.79665800000000009 \cdot 10^{308} \le a \le -9.425585000000013 \cdot 10^{-310} \lor 1.284938 \cdot 10^{-309} \le a \le 1.7512240000000001 \cdot 10^{308}\right)\]
\[x + \left(\tan \left(y + z\right) - \tan a\right)\]
↓
\[x + \left(\frac{\tan y + \tan z}{1 - \frac{\tan y \cdot \sin z}{\cos z} \cdot \left(\tan y \cdot \tan z\right)} \cdot \left(1 + \frac{\sin y \cdot \sin z}{\cos y \cdot \cos z}\right) - \tan a\right)\]
x + \left(\tan \left(y + z\right) - \tan a\right)
↓
x + \left(\frac{\tan y + \tan z}{1 - \frac{\tan y \cdot \sin z}{\cos z} \cdot \left(\tan y \cdot \tan z\right)} \cdot \left(1 + \frac{\sin y \cdot \sin z}{\cos y \cdot \cos z}\right) - \tan a\right)
double f(double x, double y, double z, double a) {
        double r140332 = x;
        double r140333 = y;
        double r140334 = z;
        double r140335 = r140333 + r140334;
        double r140336 = tan(r140335);
        double r140337 = a;
        double r140338 = tan(r140337);
        double r140339 = r140336 - r140338;
        double r140340 = r140332 + r140339;
        return r140340;
}
↓
double f(double x, double y, double z, double a) {
        double r140341 = x;
        double r140342 = y;
        double r140343 = tan(r140342);
        double r140344 = z;
        double r140345 = tan(r140344);
        double r140346 = r140343 + r140345;
        double r140347 = 1.0;
        double r140348 = sin(r140344);
        double r140349 = r140343 * r140348;
        double r140350 = cos(r140344);
        double r140351 = r140349 / r140350;
        double r140352 = r140343 * r140345;
        double r140353 = r140351 * r140352;
        double r140354 = r140347 - r140353;
        double r140355 = r140346 / r140354;
        double r140356 = sin(r140342);
        double r140357 = r140356 * r140348;
        double r140358 = cos(r140342);
        double r140359 = r140358 * r140350;
        double r140360 = r140357 / r140359;
        double r140361 = r140347 + r140360;
        double r140362 = r140355 * r140361;
        double r140363 = a;
        double r140364 = tan(r140363);
        double r140365 = r140362 - r140364;
        double r140366 = r140341 + r140365;
        return r140366;
}

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

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

  9. Applied tan-quot0.2

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

  10. Applied associate-*r/0.2

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

  12. Applied tan-quot0.2

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

  13. Applied tan-quot0.2

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

  14. Applied frac-times0.2

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

  15. Final simplification0.2

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

Reproduce

herbie shell --seed 2020043 
(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))))