Average Error: 13.4 → 0.2
Time: 14.2s
Precision: 64
\[\left(x = 0.0 \lor 0.588414199999999998 \le x \le 505.590899999999976\right) \land \left(-1.79665800000000009 \cdot 10^{308} \le y \le -9.425585000000013 \cdot 10^{-310} \lor 1.284938 \cdot 10^{-309} \le y \le 1.7512240000000001 \cdot 10^{308}\right) \land \left(-1.7767070000000002 \cdot 10^{308} \le z \le -8.59979600000002 \cdot 10^{-310} \lor 3.29314499999998 \cdot 10^{-311} \le z \le 1.72515400000000009 \cdot 10^{308}\right) \land \left(-1.79665800000000009 \cdot 10^{308} \le a \le -9.425585000000013 \cdot 10^{-310} \lor 1.284938 \cdot 10^{-309} \le a \le 1.7512240000000001 \cdot 10^{308}\right)\]
\[x + \left(\tan \left(y + z\right) - \tan a\right)\]
↓
\[x + \frac{\frac{\tan y + \tan z}{1 - \tan y \cdot \tan z} \cdot \frac{\tan y + \tan z}{1 - \tan y \cdot \tan z} - \tan a \cdot \tan a}{\frac{\tan y + \tan z}{1 - \tan y \cdot \tan z} + \tan a}\]
x + \left(\tan \left(y + z\right) - \tan a\right)
↓
x + \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}
double f(double x, double y, double z, double a) {
        double r199281 = x;
        double r199282 = y;
        double r199283 = z;
        double r199284 = r199282 + r199283;
        double r199285 = tan(r199284);
        double r199286 = a;
        double r199287 = tan(r199286);
        double r199288 = r199285 - r199287;
        double r199289 = r199281 + r199288;
        return r199289;
}
↓
double f(double x, double y, double z, double a) {
        double r199290 = x;
        double r199291 = y;
        double r199292 = tan(r199291);
        double r199293 = z;
        double r199294 = tan(r199293);
        double r199295 = r199292 + r199294;
        double r199296 = 1.0;
        double r199297 = r199292 * r199294;
        double r199298 = r199296 - r199297;
        double r199299 = r199295 / r199298;
        double r199300 = r199299 * r199299;
        double r199301 = a;
        double r199302 = tan(r199301);
        double r199303 = r199302 * r199302;
        double r199304 = r199300 - r199303;
        double r199305 = r199299 + r199302;
        double r199306 = r199304 / r199305;
        double r199307 = r199290 + r199306;
        return r199307;
}

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 13.4

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

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

Reproduce

herbie shell --seed 2020047 +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))))