Average Error: 13.2 → 0.2
Time: 11.5s
Precision: 64
\[\left(x = 0.0 \lor 0.588414199999999998 \le x \le 505.590899999999976\right) \land \left(-1.79665800000000009 \cdot 10^{308} \le y \le -9.425585000000013 \cdot 10^{-310} \lor 1.284938 \cdot 10^{-309} \le y \le 1.7512240000000001 \cdot 10^{308}\right) \land \left(-1.7767070000000002 \cdot 10^{308} \le z \le -8.59979600000002 \cdot 10^{-310} \lor 3.29314499999998 \cdot 10^{-311} \le z \le 1.72515400000000009 \cdot 10^{308}\right) \land \left(-1.79665800000000009 \cdot 10^{308} \le a \le -9.425585000000013 \cdot 10^{-310} \lor 1.284938 \cdot 10^{-309} \le a \le 1.7512240000000001 \cdot 10^{308}\right)\]
\[x + \left(\tan \left(y + z\right) - \tan a\right)\]
↓
\[x + \left(\frac{1}{\frac{1 - \frac{\tan y \cdot \sin z}{\cos z}}{\tan y + \tan z}} - \tan a\right)\]
x + \left(\tan \left(y + z\right) - \tan a\right)
↓
x + \left(\frac{1}{\frac{1 - \frac{\tan y \cdot \sin z}{\cos z}}{\tan y + \tan z}} - \tan a\right)
double f(double x, double y, double z, double a) {
        double r133392 = x;
        double r133393 = y;
        double r133394 = z;
        double r133395 = r133393 + r133394;
        double r133396 = tan(r133395);
        double r133397 = a;
        double r133398 = tan(r133397);
        double r133399 = r133396 - r133398;
        double r133400 = r133392 + r133399;
        return r133400;
}
↓
double f(double x, double y, double z, double a) {
        double r133401 = x;
        double r133402 = 1.0;
        double r133403 = y;
        double r133404 = tan(r133403);
        double r133405 = z;
        double r133406 = sin(r133405);
        double r133407 = r133404 * r133406;
        double r133408 = cos(r133405);
        double r133409 = r133407 / r133408;
        double r133410 = r133402 - r133409;
        double r133411 = tan(r133405);
        double r133412 = r133404 + r133411;
        double r133413 = r133410 / r133412;
        double r133414 = r133402 / r133413;
        double r133415 = a;
        double r133416 = tan(r133415);
        double r133417 = r133414 - r133416;
        double r133418 = r133401 + r133417;
        return r133418;
}

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 13.2

    \[x + \left(\tan \left(y + z\right) - \tan a\right)\]
  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 tan-quot0.2

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

  6. Applied associate-*r/0.2

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

  8. Applied clear-num0.2

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

  9. Final simplification0.2

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

Reproduce

herbie shell --seed 2020100 +o rules:numerics
(FPCore (x y z a)
  :name "(+ x (- (tan (+ y z)) (tan a)))"
  :precision binary64
  :pre (and (or (== x 0.0) (<= 0.5884142 x 505.5909)) (or (<= -1.796658e+308 y -9.425585e-310) (<= 1.284938e-309 y 1.7512240000000001e+308)) (or (<= -1.7767070000000002e+308 z -8.599796e-310) (<= 3.293145e-311 z 1.725154e+308)) (or (<= -1.796658e+308 a -9.425585e-310) (<= 1.284938e-309 a 1.7512240000000001e+308)))
  (+ x (- (tan (+ y z)) (tan a))))