Average Error: 13.3 → 0.2
Time: 10.1s
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 r152693 = x;
        double r152694 = y;
        double r152695 = z;
        double r152696 = r152694 + r152695;
        double r152697 = tan(r152696);
        double r152698 = a;
        double r152699 = tan(r152698);
        double r152700 = r152697 - r152699;
        double r152701 = r152693 + r152700;
        return r152701;
}
↓
double f(double x, double y, double z, double a) {
        double r152702 = x;
        double r152703 = y;
        double r152704 = tan(r152703);
        double r152705 = r152704 * r152704;
        double r152706 = z;
        double r152707 = tan(r152706);
        double r152708 = 6.0;
        double r152709 = pow(r152707, r152708);
        double r152710 = cbrt(r152709);
        double r152711 = r152705 - r152710;
        double r152712 = r152704 - r152707;
        double r152713 = r152711 / r152712;
        double r152714 = 1.0;
        double r152715 = r152704 * r152707;
        double r152716 = r152714 - r152715;
        double r152717 = r152713 / r152716;
        double r152718 = a;
        double r152719 = tan(r152718);
        double r152720 = r152717 - r152719;
        double r152721 = r152702 + r152720;
        return r152721;
}

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))))