Average Error: 13.1 → 0.2
Time: 34.3s
Precision: 64
\[\left(x = 0 \lor 0.5884142 \le x \le 505.5909\right) \land \left(-1.796658 \cdot 10^{+308} \le y \le -9.425585 \cdot 10^{-310} \lor 1.284938 \cdot 10^{-309} \le y \le 1.751224 \cdot 10^{+308}\right) \land \left(-1.776707 \cdot 10^{+308} \le z \le -8.599796 \cdot 10^{-310} \lor 3.293145 \cdot 10^{-311} \le z \le 1.725154 \cdot 10^{+308}\right) \land \left(-1.796658 \cdot 10^{+308} \le a \le -9.425585 \cdot 10^{-310} \lor 1.284938 \cdot 10^{-309} \le a \le 1.751224 \cdot 10^{+308}\right)\]
\[x + \left(\tan \left(y + z\right) - \tan a\right)\]
↓
\[\left(\left(\tan y \cdot \tan z + 1\right) \cdot \frac{\tan z + \tan y}{1 - \frac{\left(\tan y \cdot \tan z\right) \cdot \left(\sin z \cdot \sin y\right)}{\cos z \cdot \cos y}} - \tan a\right) + x\]
x + \left(\tan \left(y + z\right) - \tan a\right)
↓
\left(\left(\tan y \cdot \tan z + 1\right) \cdot \frac{\tan z + \tan y}{1 - \frac{\left(\tan y \cdot \tan z\right) \cdot \left(\sin z \cdot \sin y\right)}{\cos z \cdot \cos y}} - \tan a\right) + x
double f(double x, double y, double z, double a) {
        double r6170271 = x;
        double r6170272 = y;
        double r6170273 = z;
        double r6170274 = r6170272 + r6170273;
        double r6170275 = tan(r6170274);
        double r6170276 = a;
        double r6170277 = tan(r6170276);
        double r6170278 = r6170275 - r6170277;
        double r6170279 = r6170271 + r6170278;
        return r6170279;
}
↓
double f(double x, double y, double z, double a) {
        double r6170280 = y;
        double r6170281 = tan(r6170280);
        double r6170282 = z;
        double r6170283 = tan(r6170282);
        double r6170284 = r6170281 * r6170283;
        double r6170285 = 1.0;
        double r6170286 = r6170284 + r6170285;
        double r6170287 = r6170283 + r6170281;
        double r6170288 = sin(r6170282);
        double r6170289 = sin(r6170280);
        double r6170290 = r6170288 * r6170289;
        double r6170291 = r6170284 * r6170290;
        double r6170292 = cos(r6170282);
        double r6170293 = cos(r6170280);
        double r6170294 = r6170292 * r6170293;
        double r6170295 = r6170291 / r6170294;
        double r6170296 = r6170285 - r6170295;
        double r6170297 = r6170287 / r6170296;
        double r6170298 = r6170286 * r6170297;
        double r6170299 = a;
        double r6170300 = tan(r6170299);
        double r6170301 = r6170298 - r6170300;
        double r6170302 = x;
        double r6170303 = r6170301 + r6170302;
        return r6170303;
}

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

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

  6. Applied associate-/r/0.2

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

  7. Simplified0.2

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

  9. Applied tan-quot0.2

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

  10. Applied tan-quot0.2

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

  11. Applied frac-times0.2

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

  12. Applied associate-*r/0.2

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

  13. Final simplification0.2

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

Reproduce

herbie shell --seed 2019142 
(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))))