Average Error: 13.0 → 0.3
Time: 26.1s
Precision: 64
\[\left(x = 0.0 \lor 0.5884141999999999983472775966220069676638 \le x \le 505.5908999999999764440872240811586380005\right) \land \left(-1.7966580000000000931214523812968299911 \cdot 10^{308} \le y \le -9.425585000000013069597555966781986720373 \cdot 10^{-310} \lor 1.284937999999999548796432976649400331091 \cdot 10^{-309} \le y \le 1.751223999999999928063201074847742204824 \cdot 10^{308}\right) \land \left(-1.776707000000000001259808757982040817204 \cdot 10^{308} \le z \le -8.599796000000016667475923823712126825539 \cdot 10^{-310} \lor 3.293144999999983071955117582595641261776 \cdot 10^{-311} \le z \le 1.725154000000000087891269878141591702413 \cdot 10^{308}\right) \land \left(-1.7966580000000000931214523812968299911 \cdot 10^{308} \le a \le -9.425585000000013069597555966781986720373 \cdot 10^{-310} \lor 1.284937999999999548796432976649400331091 \cdot 10^{-309} \le a \le 1.751223999999999928063201074847742204824 \cdot 10^{308}\right)\]
\[x + \left(\tan \left(y + z\right) - \tan a\right)\]
↓
\[x + \left(\frac{\tan z + \tan y}{1 - \left(\sqrt[3]{\tan z} \cdot \sqrt[3]{\tan z}\right) \cdot \left(\sqrt[3]{\tan z} \cdot \tan y\right)} - \tan a\right)\]
x + \left(\tan \left(y + z\right) - \tan a\right)
↓
x + \left(\frac{\tan z + \tan y}{1 - \left(\sqrt[3]{\tan z} \cdot \sqrt[3]{\tan z}\right) \cdot \left(\sqrt[3]{\tan z} \cdot \tan y\right)} - \tan a\right)
double f(double x, double y, double z, double a) {
        double r116738 = x;
        double r116739 = y;
        double r116740 = z;
        double r116741 = r116739 + r116740;
        double r116742 = tan(r116741);
        double r116743 = a;
        double r116744 = tan(r116743);
        double r116745 = r116742 - r116744;
        double r116746 = r116738 + r116745;
        return r116746;
}
↓
double f(double x, double y, double z, double a) {
        double r116747 = x;
        double r116748 = z;
        double r116749 = tan(r116748);
        double r116750 = y;
        double r116751 = tan(r116750);
        double r116752 = r116749 + r116751;
        double r116753 = 1.0;
        double r116754 = cbrt(r116749);
        double r116755 = r116754 * r116754;
        double r116756 = r116754 * r116751;
        double r116757 = r116755 * r116756;
        double r116758 = r116753 - r116757;
        double r116759 = r116752 / r116758;
        double r116760 = a;
        double r116761 = tan(r116760);
        double r116762 = r116759 - r116761;
        double r116763 = r116747 + r116762;
        return r116763;
}

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 13.0

    \[x + \left(\tan \left(y + z\right) - \tan a\right)\]
  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. Simplified0.2

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

  5. Simplified0.2

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

  7. Applied add-cube-cbrt0.3

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

  8. Applied associate-*l*0.3

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

  9. Final simplification0.3

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

Reproduce

herbie shell --seed 2019306 
(FPCore (x y z a)
  :name "(+ x (- (tan (+ y z)) (tan a)))"
  :precision binary64
  :pre (and (or (== x 0.0) (<= 0.588414199999999998 x 505.590899999999976)) (or (<= -1.79665800000000009e308 y -9.425585000000013e-310) (<= 1.284938e-309 y 1.75122399999999993e308)) (or (<= -1.776707e308 z -8.59979600000002e-310) (<= 3.29314499999998e-311 z 1.72515400000000009e308)) (or (<= -1.79665800000000009e308 a -9.425585000000013e-310) (<= 1.284938e-309 a 1.75122399999999993e308)))
  (+ x (- (tan (+ y z)) (tan a))))