Average Error: 12.7 → 0.2
Time: 43.8s
Precision: 64
\[\left(x = 0.0 \lor 0.588414199999999998 \le x \le 505.590899999999976\right) \land \left(-1.79665800000000009 \cdot 10^{308} \le y \le -9.425585000000013 \cdot 10^{-310} \lor 1.284938 \cdot 10^{-309} \le y \le 1.75122399999999993 \cdot 10^{308}\right) \land \left(-1.776707 \cdot 10^{308} \le z \le -8.59979600000002 \cdot 10^{-310} \lor 3.29314499999998 \cdot 10^{-311} \le z \le 1.72515400000000009 \cdot 10^{308}\right) \land \left(-1.79665800000000009 \cdot 10^{308} \le a \le -9.425585000000013 \cdot 10^{-310} \lor 1.284938 \cdot 10^{-309} \le a \le 1.75122399999999993 \cdot 10^{308}\right)\]
\[x + \left(\tan \left(y + z\right) - \tan a\right)\]
↓
\[\left(x + \frac{\tan y + \tan z}{1 - \tan y \cdot \tan z}\right) - \tan a\]
x + \left(\tan \left(y + z\right) - \tan a\right)
↓
\left(x + \frac{\tan y + \tan z}{1 - \tan y \cdot \tan z}\right) - \tan a
double f(double x, double y, double z, double a) {
        double r110505 = x;
        double r110506 = y;
        double r110507 = z;
        double r110508 = r110506 + r110507;
        double r110509 = tan(r110508);
        double r110510 = a;
        double r110511 = tan(r110510);
        double r110512 = r110509 - r110511;
        double r110513 = r110505 + r110512;
        return r110513;
}
↓
double f(double x, double y, double z, double a) {
        double r110514 = x;
        double r110515 = y;
        double r110516 = tan(r110515);
        double r110517 = z;
        double r110518 = tan(r110517);
        double r110519 = r110516 + r110518;
        double r110520 = 1.0;
        double r110521 = r110516 * r110518;
        double r110522 = r110520 - r110521;
        double r110523 = r110519 / r110522;
        double r110524 = r110514 + r110523;
        double r110525 = a;
        double r110526 = tan(r110525);
        double r110527 = r110524 - r110526;
        return r110527;
}

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 12.7

    \[x + \left(\tan \left(y + z\right) - \tan a\right)\]
  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 associate-+r-0.2

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

  6. Final simplification0.2

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

Reproduce

herbie shell --seed 2019199 
(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))))