Average Error: 12.7 → 0.2
Time: 52.8s
Precision: 64
\[\left(x = 0.0 \lor 0.588414199999999998 \le x \le 505.590899999999976\right) \land \left(-1.79665800000000009 \cdot 10^{308} \le y \le -9.425585000000013 \cdot 10^{-310} \lor 1.284938 \cdot 10^{-309} \le y \le 1.75122399999999993 \cdot 10^{308}\right) \land \left(-1.776707 \cdot 10^{308} \le z \le -8.59979600000002 \cdot 10^{-310} \lor 3.29314499999998 \cdot 10^{-311} \le z \le 1.72515400000000009 \cdot 10^{308}\right) \land \left(-1.79665800000000009 \cdot 10^{308} \le a \le -9.425585000000013 \cdot 10^{-310} \lor 1.284938 \cdot 10^{-309} \le a \le 1.75122399999999993 \cdot 10^{308}\right)\]
\[x + \left(\tan \left(y + z\right) - \tan a\right)\]
↓
\[x + \left(\frac{\frac{\tan y \cdot \tan y - \tan z \cdot \tan z}{\tan y - \tan z}}{1 - \tan y \cdot \tan z} - \tan a\right)\]
x + \left(\tan \left(y + z\right) - \tan a\right)
↓
x + \left(\frac{\frac{\tan y \cdot \tan y - \tan z \cdot \tan z}{\tan y - \tan z}}{1 - \tan y \cdot \tan z} - \tan a\right)
double f(double x, double y, double z, double a) {
        double r96636 = x;
        double r96637 = y;
        double r96638 = z;
        double r96639 = r96637 + r96638;
        double r96640 = tan(r96639);
        double r96641 = a;
        double r96642 = tan(r96641);
        double r96643 = r96640 - r96642;
        double r96644 = r96636 + r96643;
        return r96644;
}
↓
double f(double x, double y, double z, double a) {
        double r96645 = x;
        double r96646 = y;
        double r96647 = tan(r96646);
        double r96648 = r96647 * r96647;
        double r96649 = z;
        double r96650 = tan(r96649);
        double r96651 = r96650 * r96650;
        double r96652 = r96648 - r96651;
        double r96653 = r96647 - r96650;
        double r96654 = r96652 / r96653;
        double r96655 = 1.0;
        double r96656 = r96647 * r96650;
        double r96657 = r96655 - r96656;
        double r96658 = r96654 / r96657;
        double r96659 = a;
        double r96660 = tan(r96659);
        double r96661 = r96658 - r96660;
        double r96662 = r96645 + r96661;
        return r96662;
}

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 flip-+0.2

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

  6. Final simplification0.2

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

Reproduce

herbie shell --seed 2019199 +o rules:numerics
(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))))