Average Error: 13.5 → 0.3
Time: 29.4s
Precision: 64
\[\left(x = 0.0 \lor 0.5884141999999999983472775966220069676638 \le x \le 505.5908999999999764440872240811586380005\right) \land \left(-1.7966580000000000931214523812968299911 \cdot 10^{308} \le y \le -9.425585000000013069597555966781986720373 \cdot 10^{-310} \lor 1.284937999999999548796432976649400331091 \cdot 10^{-309} \le y \le 1.751223999999999928063201074847742204824 \cdot 10^{308}\right) \land \left(-1.776707000000000001259808757982040817204 \cdot 10^{308} \le z \le -8.599796000000016667475923823712126825539 \cdot 10^{-310} \lor 3.293144999999983071955117582595641261776 \cdot 10^{-311} \le z \le 1.725154000000000087891269878141591702413 \cdot 10^{308}\right) \land \left(-1.7966580000000000931214523812968299911 \cdot 10^{308} \le a \le -9.425585000000013069597555966781986720373 \cdot 10^{-310} \lor 1.284937999999999548796432976649400331091 \cdot 10^{-309} \le a \le 1.751223999999999928063201074847742204824 \cdot 10^{308}\right)\]
\[x + \left(\tan \left(y + z\right) - \tan a\right)\]
↓
\[\frac{\left(x + \left(\frac{\tan y + \tan z}{1 - \tan y \cdot \tan z} - \tan a\right)\right) \cdot \left(x - \left(\frac{\tan y + \tan z}{1 - \tan y \cdot \tan z} - \tan a\right)\right)}{x - \left(\frac{\tan y + \tan z}{1 - \tan y \cdot \tan z} - \tan a\right)}\]
x + \left(\tan \left(y + z\right) - \tan a\right)
↓
\frac{\left(x + \left(\frac{\tan y + \tan z}{1 - \tan y \cdot \tan z} - \tan a\right)\right) \cdot \left(x - \left(\frac{\tan y + \tan z}{1 - \tan y \cdot \tan z} - \tan a\right)\right)}{x - \left(\frac{\tan y + \tan z}{1 - \tan y \cdot \tan z} - \tan a\right)}
double f(double x, double y, double z, double a) {
        double r128610 = x;
        double r128611 = y;
        double r128612 = z;
        double r128613 = r128611 + r128612;
        double r128614 = tan(r128613);
        double r128615 = a;
        double r128616 = tan(r128615);
        double r128617 = r128614 - r128616;
        double r128618 = r128610 + r128617;
        return r128618;
}
↓
double f(double x, double y, double z, double a) {
        double r128619 = x;
        double r128620 = y;
        double r128621 = tan(r128620);
        double r128622 = z;
        double r128623 = tan(r128622);
        double r128624 = r128621 + r128623;
        double r128625 = 1.0;
        double r128626 = r128621 * r128623;
        double r128627 = r128625 - r128626;
        double r128628 = r128624 / r128627;
        double r128629 = a;
        double r128630 = tan(r128629);
        double r128631 = r128628 - r128630;
        double r128632 = r128619 + r128631;
        double r128633 = r128619 - r128631;
        double r128634 = r128632 * r128633;
        double r128635 = r128634 / r128633;
        return r128635;
}

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 flip-+0.4

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

  7. Applied difference-of-squares0.3

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

  8. Final simplification0.3

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

Reproduce

herbie shell --seed 2019235 
(FPCore (x y z a)
  :name "(+ x (- (tan (+ y z)) (tan a)))"
  :precision binary64
  :pre (and (or (== x 0.0) (<= 0.588414199999999998 x 505.590899999999976)) (or (<= -1.79665800000000009e308 y -9.425585000000013e-310) (<= 1.284938e-309 y 1.75122399999999993e308)) (or (<= -1.776707e308 z -8.59979600000002e-310) (<= 3.29314499999998e-311 z 1.72515400000000009e308)) (or (<= -1.79665800000000009e308 a -9.425585000000013e-310) (<= 1.284938e-309 a 1.75122399999999993e308)))
  (+ x (- (tan (+ y z)) (tan a))))