Average Error: 12.9 → 0.2
Time: 34.5s
Precision: 64
\[\left(x = 0.0 \lor 0.5884141999999999983472775966220069676638 \le x \le 505.5908999999999764440872240811586380005\right) \land \left(-1.7966580000000000931214523812968299911 \cdot 10^{308} \le y \le -9.425585000000013069597555966781986720373 \cdot 10^{-310} \lor 1.284937999999999548796432976649400331091 \cdot 10^{-309} \le y \le 1.751223999999999928063201074847742204824 \cdot 10^{308}\right) \land \left(-1.776707000000000001259808757982040817204 \cdot 10^{308} \le z \le -8.599796000000016667475923823712126825539 \cdot 10^{-310} \lor 3.293144999999983071955117582595641261776 \cdot 10^{-311} \le z \le 1.725154000000000087891269878141591702413 \cdot 10^{308}\right) \land \left(-1.7966580000000000931214523812968299911 \cdot 10^{308} \le a \le -9.425585000000013069597555966781986720373 \cdot 10^{-310} \lor 1.284937999999999548796432976649400331091 \cdot 10^{-309} \le a \le 1.751223999999999928063201074847742204824 \cdot 10^{308}\right)\]
\[x + \left(\tan \left(y + z\right) - \tan a\right)\]
↓
\[x - \left(\tan a - \frac{\frac{\tan y \cdot \tan y - \tan z \cdot \tan z}{\tan y - \tan z}}{1 - \tan z \cdot \tan y}\right)\]
x + \left(\tan \left(y + z\right) - \tan a\right)
↓
x - \left(\tan a - \frac{\frac{\tan y \cdot \tan y - \tan z \cdot \tan z}{\tan y - \tan z}}{1 - \tan z \cdot \tan y}\right)
double f(double x, double y, double z, double a) {
        double r187336 = x;
        double r187337 = y;
        double r187338 = z;
        double r187339 = r187337 + r187338;
        double r187340 = tan(r187339);
        double r187341 = a;
        double r187342 = tan(r187341);
        double r187343 = r187340 - r187342;
        double r187344 = r187336 + r187343;
        return r187344;
}
↓
double f(double x, double y, double z, double a) {
        double r187345 = x;
        double r187346 = a;
        double r187347 = tan(r187346);
        double r187348 = y;
        double r187349 = tan(r187348);
        double r187350 = r187349 * r187349;
        double r187351 = z;
        double r187352 = tan(r187351);
        double r187353 = r187352 * r187352;
        double r187354 = r187350 - r187353;
        double r187355 = r187349 - r187352;
        double r187356 = r187354 / r187355;
        double r187357 = 1.0;
        double r187358 = r187352 * r187349;
        double r187359 = r187357 - r187358;
        double r187360 = r187356 / r187359;
        double r187361 = r187347 - r187360;
        double r187362 = r187345 - r187361;
        return r187362;
}

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 12.9

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

  2. Simplified12.9

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

  4. Applied tan-sum0.2

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

  5. Simplified0.2

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

  7. Applied flip-+0.2

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

  8. Final simplification0.2

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

Reproduce

herbie shell --seed 2019179 
(FPCore (x y z a)
  :name "(+ x (- (tan (+ y z)) (tan a)))"
  :pre (and (or (== x 0.0) (<= 0.5884142 x 505.5909)) (or (<= -1.796658e+308 y -9.425585e-310) (<= 1.284938e-309 y 1.751224e+308)) (or (<= -1.776707e+308 z -8.599796e-310) (<= 3.293145e-311 z 1.725154e+308)) (or (<= -1.796658e+308 a -9.425585e-310) (<= 1.284938e-309 a 1.751224e+308)))
  (+ x (- (tan (+ y z)) (tan a))))