Average Error: 13.9 → 0.2
Time: 8.4s
Precision: 64
\[\left(x = 0.0 \lor 0.588414199999999998 \le x \le 505.590899999999976\right) \land \left(-1.79665800000000009 \cdot 10^{308} \le y \le -9.425585000000013 \cdot 10^{-310} \lor 1.284938 \cdot 10^{-309} \le y \le 1.7512240000000001 \cdot 10^{308}\right) \land \left(-1.7767070000000002 \cdot 10^{308} \le z \le -8.59979600000002 \cdot 10^{-310} \lor 3.29314499999998 \cdot 10^{-311} \le z \le 1.72515400000000009 \cdot 10^{308}\right) \land \left(-1.79665800000000009 \cdot 10^{308} \le a \le -9.425585000000013 \cdot 10^{-310} \lor 1.284938 \cdot 10^{-309} \le a \le 1.7512240000000001 \cdot 10^{308}\right)\]
\[x + \left(\tan \left(y + z\right) - \tan a\right)\]
↓
\[x + \left(\frac{\tan y + \tan z}{1 - \frac{\sqrt[3]{{\left(\sin y \cdot \tan z\right)}^{3}}}{\cos y}} - \tan a\right)\]
x + \left(\tan \left(y + z\right) - \tan a\right)
↓
x + \left(\frac{\tan y + \tan z}{1 - \frac{\sqrt[3]{{\left(\sin y \cdot \tan z\right)}^{3}}}{\cos y}} - \tan a\right)
double f(double x, double y, double z, double a) {
        double r137321 = x;
        double r137322 = y;
        double r137323 = z;
        double r137324 = r137322 + r137323;
        double r137325 = tan(r137324);
        double r137326 = a;
        double r137327 = tan(r137326);
        double r137328 = r137325 - r137327;
        double r137329 = r137321 + r137328;
        return r137329;
}
↓
double f(double x, double y, double z, double a) {
        double r137330 = x;
        double r137331 = y;
        double r137332 = tan(r137331);
        double r137333 = z;
        double r137334 = tan(r137333);
        double r137335 = r137332 + r137334;
        double r137336 = 1.0;
        double r137337 = sin(r137331);
        double r137338 = r137337 * r137334;
        double r137339 = 3.0;
        double r137340 = pow(r137338, r137339);
        double r137341 = cbrt(r137340);
        double r137342 = cos(r137331);
        double r137343 = r137341 / r137342;
        double r137344 = r137336 - r137343;
        double r137345 = r137335 / r137344;
        double r137346 = a;
        double r137347 = tan(r137346);
        double r137348 = r137345 - r137347;
        double r137349 = r137330 + r137348;
        return r137349;
}

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 13.9

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

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

  6. Applied associate-*l/0.2

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

  8. Applied add-cbrt-cube0.2

    \[\leadsto x + \left(\frac{\tan y + \tan z}{1 - \frac{\sin y \cdot \color{blue}{\sqrt[3]{\left(\tan z \cdot \tan z\right) \cdot \tan z}}}{\cos y}} - \tan a\right)\]

  9. Applied add-cbrt-cube0.2

    \[\leadsto x + \left(\frac{\tan y + \tan z}{1 - \frac{\color{blue}{\sqrt[3]{\left(\sin y \cdot \sin y\right) \cdot \sin y}} \cdot \sqrt[3]{\left(\tan z \cdot \tan z\right) \cdot \tan z}}{\cos y}} - \tan a\right)\]

  10. Applied cbrt-unprod0.2

    \[\leadsto x + \left(\frac{\tan y + \tan z}{1 - \frac{\color{blue}{\sqrt[3]{\left(\left(\sin y \cdot \sin y\right) \cdot \sin y\right) \cdot \left(\left(\tan z \cdot \tan z\right) \cdot \tan z\right)}}}{\cos y}} - \tan a\right)\]

  11. Simplified0.2

    \[\leadsto x + \left(\frac{\tan y + \tan z}{1 - \frac{\sqrt[3]{\color{blue}{{\left(\sin y \cdot \tan z\right)}^{3}}}}{\cos y}} - \tan a\right)\]

  12. Final simplification0.2

    \[\leadsto x + \left(\frac{\tan y + \tan z}{1 - \frac{\sqrt[3]{{\left(\sin y \cdot \tan z\right)}^{3}}}{\cos y}} - \tan a\right)\]

Reproduce

herbie shell --seed 2020062 
(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))))