Average Error: 13.3 → 0.2
Time: 10.0s
Precision: 64
\[\left(x = 0.0 \lor 0.588414199999999998 \le x \le 505.590899999999976\right) \land \left(-1.79665800000000009 \cdot 10^{308} \le y \le -9.425585000000013 \cdot 10^{-310} \lor 1.284938 \cdot 10^{-309} \le y \le 1.7512240000000001 \cdot 10^{308}\right) \land \left(-1.7767070000000002 \cdot 10^{308} \le z \le -8.59979600000002 \cdot 10^{-310} \lor 3.29314499999998 \cdot 10^{-311} \le z \le 1.72515400000000009 \cdot 10^{308}\right) \land \left(-1.79665800000000009 \cdot 10^{308} \le a \le -9.425585000000013 \cdot 10^{-310} \lor 1.284938 \cdot 10^{-309} \le a \le 1.7512240000000001 \cdot 10^{308}\right)\]
\[x + \left(\tan \left(y + z\right) - \tan a\right)\]
↓
\[x + \left(\frac{\frac{\tan y \cdot \tan y - \sqrt[3]{{\left(\tan z\right)}^{6}}}{\tan y - \tan z}}{1 - \tan y \cdot \tan z} - \tan a\right)\]
x + \left(\tan \left(y + z\right) - \tan a\right)
↓
x + \left(\frac{\frac{\tan y \cdot \tan y - \sqrt[3]{{\left(\tan z\right)}^{6}}}{\tan y - \tan z}}{1 - \tan y \cdot \tan z} - \tan a\right)
double f(double x, double y, double z, double a) {
        double r166011 = x;
        double r166012 = y;
        double r166013 = z;
        double r166014 = r166012 + r166013;
        double r166015 = tan(r166014);
        double r166016 = a;
        double r166017 = tan(r166016);
        double r166018 = r166015 - r166017;
        double r166019 = r166011 + r166018;
        return r166019;
}
↓
double f(double x, double y, double z, double a) {
        double r166020 = x;
        double r166021 = y;
        double r166022 = tan(r166021);
        double r166023 = r166022 * r166022;
        double r166024 = z;
        double r166025 = tan(r166024);
        double r166026 = 6.0;
        double r166027 = pow(r166025, r166026);
        double r166028 = cbrt(r166027);
        double r166029 = r166023 - r166028;
        double r166030 = r166022 - r166025;
        double r166031 = r166029 / r166030;
        double r166032 = 1.0;
        double r166033 = r166022 * r166025;
        double r166034 = r166032 - r166033;
        double r166035 = r166031 / r166034;
        double r166036 = a;
        double r166037 = tan(r166036);
        double r166038 = r166035 - r166037;
        double r166039 = r166020 + r166038;
        return r166039;
}

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 13.3

    \[x + \left(\tan \left(y + z\right) - \tan a\right)\]
  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. Using strategy rm

  7. Applied add-cbrt-cube0.2

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

  8. Applied add-cbrt-cube0.3

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

  9. Applied cbrt-unprod0.2

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

  10. Simplified0.2

    \[\leadsto x + \left(\frac{\frac{\tan y \cdot \tan y - \sqrt[3]{\color{blue}{{\left(\tan z\right)}^{6}}}}{\tan y - \tan z}}{1 - \tan y \cdot \tan z} - \tan a\right)\]

  11. Final simplification0.2

    \[\leadsto x + \left(\frac{\frac{\tan y \cdot \tan y - \sqrt[3]{{\left(\tan z\right)}^{6}}}{\tan y - \tan z}}{1 - \tan y \cdot \tan z} - \tan a\right)\]

Reproduce

herbie shell --seed 2020056 
(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))))