Average Error: 13.1 → 0.2
Time: 55.2s
Precision: 64
\[\left(x = 0 \lor 0.5884142 \le x \le 505.5909\right) \land \left(-1.796658 \cdot 10^{+308} \le y \le -9.425585 \cdot 10^{-310} \lor 1.284938 \cdot 10^{-309} \le y \le 1.751224 \cdot 10^{+308}\right) \land \left(-1.776707 \cdot 10^{+308} \le z \le -8.599796 \cdot 10^{-310} \lor 3.293145 \cdot 10^{-311} \le z \le 1.725154 \cdot 10^{+308}\right) \land \left(-1.796658 \cdot 10^{+308} \le a \le -9.425585 \cdot 10^{-310} \lor 1.284938 \cdot 10^{-309} \le a \le 1.751224 \cdot 10^{+308}\right)\]
\[x + \left(\tan \left(y + z\right) - \tan a\right)\]
↓
\[\frac{\frac{\tan y + \tan z}{1 - \tan z \cdot \tan y} \cdot \frac{\tan y + \tan z}{1 - \tan z \cdot \tan y} - \tan a \cdot \tan a}{\tan a + \frac{\tan y + \tan z}{1 - \tan z \cdot \tan y}} + x\]
x + \left(\tan \left(y + z\right) - \tan a\right)
↓
\frac{\frac{\tan y + \tan z}{1 - \tan z \cdot \tan y} \cdot \frac{\tan y + \tan z}{1 - \tan z \cdot \tan y} - \tan a \cdot \tan a}{\tan a + \frac{\tan y + \tan z}{1 - \tan z \cdot \tan y}} + x
double f(double x, double y, double z, double a) {
        double r39471613 = x;
        double r39471614 = y;
        double r39471615 = z;
        double r39471616 = r39471614 + r39471615;
        double r39471617 = tan(r39471616);
        double r39471618 = a;
        double r39471619 = tan(r39471618);
        double r39471620 = r39471617 - r39471619;
        double r39471621 = r39471613 + r39471620;
        return r39471621;
}
↓
double f(double x, double y, double z, double a) {
        double r39471622 = y;
        double r39471623 = tan(r39471622);
        double r39471624 = z;
        double r39471625 = tan(r39471624);
        double r39471626 = r39471623 + r39471625;
        double r39471627 = 1.0;
        double r39471628 = r39471625 * r39471623;
        double r39471629 = r39471627 - r39471628;
        double r39471630 = r39471626 / r39471629;
        double r39471631 = r39471630 * r39471630;
        double r39471632 = a;
        double r39471633 = tan(r39471632);
        double r39471634 = r39471633 * r39471633;
        double r39471635 = r39471631 - r39471634;
        double r39471636 = r39471633 + r39471630;
        double r39471637 = r39471635 / r39471636;
        double r39471638 = x;
        double r39471639 = r39471637 + r39471638;
        return r39471639;
}

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 13.1

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

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

  6. Final simplification0.2

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

Reproduce

herbie shell --seed 2019120 
(FPCore (x y z a)
  :name "(+ x (- (tan (+ y z)) (tan a)))"
  :pre (and (or (== x 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))))