Average Error: 13.0 → 0.2
Time: 11.1s
Precision: 64
\[\left(x = 0.0 \lor 0.5884141999999999983472775966220069676638 \le x \le 505.5908999999999764440872240811586380005\right) \land \left(-1.7966580000000000931214523812968299911 \cdot 10^{308} \le y \le -9.425585000000013069597555966781986720373 \cdot 10^{-310} \lor 1.284937999999999548796432976649400331091 \cdot 10^{-309} \le y \le 1.751224000000000127647232028319723370461 \cdot 10^{308}\right) \land \left(-1.776707000000000200843839711454021982841 \cdot 10^{308} \le z \le -8.599796000000016667475923823712126825539 \cdot 10^{-310} \lor 3.293144999999983071955117582595641261776 \cdot 10^{-311} \le z \le 1.725154000000000087891269878141591702413 \cdot 10^{308}\right) \land \left(-1.7966580000000000931214523812968299911 \cdot 10^{308} \le a \le -9.425585000000013069597555966781986720373 \cdot 10^{-310} \lor 1.284937999999999548796432976649400331091 \cdot 10^{-309} \le a \le 1.751224000000000127647232028319723370461 \cdot 10^{308}\right)\]
\[x + \left(\tan \left(y + z\right) - \tan a\right)\]
↓
\[x + \left(\frac{\tan y + \tan z}{1 - \log \left(e^{\frac{\sin y \cdot \sin z}{\cos y \cdot \cos z}}\right)} - \tan a\right)\]
x + \left(\tan \left(y + z\right) - \tan a\right)
↓
x + \left(\frac{\tan y + \tan z}{1 - \log \left(e^{\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 r143397 = x;
        double r143398 = y;
        double r143399 = z;
        double r143400 = r143398 + r143399;
        double r143401 = tan(r143400);
        double r143402 = a;
        double r143403 = tan(r143402);
        double r143404 = r143401 - r143403;
        double r143405 = r143397 + r143404;
        return r143405;
}
↓
double f(double x, double y, double z, double a) {
        double r143406 = x;
        double r143407 = y;
        double r143408 = tan(r143407);
        double r143409 = z;
        double r143410 = tan(r143409);
        double r143411 = r143408 + r143410;
        double r143412 = 1.0;
        double r143413 = sin(r143407);
        double r143414 = sin(r143409);
        double r143415 = r143413 * r143414;
        double r143416 = cos(r143407);
        double r143417 = cos(r143409);
        double r143418 = r143416 * r143417;
        double r143419 = r143415 / r143418;
        double r143420 = exp(r143419);
        double r143421 = log(r143420);
        double r143422 = r143412 - r143421;
        double r143423 = r143411 / r143422;
        double r143424 = a;
        double r143425 = tan(r143424);
        double r143426 = r143423 - r143425;
        double r143427 = r143406 + r143426;
        return r143427;
}

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 13.0

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

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

  6. Applied tan-quot0.2

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

  7. Applied frac-times0.2

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

  9. Applied add-log-exp0.2

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

  10. Final simplification0.2

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

Reproduce

herbie shell --seed 2019362 
(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))))