Average Error: 13.5 → 0.2
Time: 19.1s
Precision: 64
\[\left(x = 0.0 \lor 0.588414199999999998 \le x \le 505.590899999999976\right) \land \left(-1.79665800000000009 \cdot 10^{308} \le y \le -9.425585000000013 \cdot 10^{-310} \lor 1.284938 \cdot 10^{-309} \le y \le 1.7512240000000001 \cdot 10^{308}\right) \land \left(-1.7767070000000002 \cdot 10^{308} \le z \le -8.59979600000002 \cdot 10^{-310} \lor 3.29314499999998 \cdot 10^{-311} \le z \le 1.72515400000000009 \cdot 10^{308}\right) \land \left(-1.79665800000000009 \cdot 10^{308} \le a \le -9.425585000000013 \cdot 10^{-310} \lor 1.284938 \cdot 10^{-309} \le a \le 1.7512240000000001 \cdot 10^{308}\right)\]
\[x + \left(\tan \left(y + z\right) - \tan a\right)\]
↓
\[x + \frac{\left(\tan y + \tan z\right) \cdot \cos a - \left(1 - \tan y \cdot \tan z\right) \cdot \sin a}{\left(1 - \sqrt[3]{{\left(\tan y \cdot \tan z\right)}^{3}}\right) \cdot \cos a}\]
x + \left(\tan \left(y + z\right) - \tan a\right)
↓
x + \frac{\left(\tan y + \tan z\right) \cdot \cos a - \left(1 - \tan y \cdot \tan z\right) \cdot \sin a}{\left(1 - \sqrt[3]{{\left(\tan y \cdot \tan z\right)}^{3}}\right) \cdot \cos a}
double f(double x, double y, double z, double a) {
        double r650 = x;
        double r651 = y;
        double r652 = z;
        double r653 = r651 + r652;
        double r654 = tan(r653);
        double r655 = a;
        double r656 = tan(r655);
        double r657 = r654 - r656;
        double r658 = r650 + r657;
        return r658;
}
↓
double f(double x, double y, double z, double a) {
        double r659 = x;
        double r660 = y;
        double r661 = tan(r660);
        double r662 = z;
        double r663 = tan(r662);
        double r664 = r661 + r663;
        double r665 = a;
        double r666 = cos(r665);
        double r667 = r664 * r666;
        double r668 = 1.0;
        double r669 = r661 * r663;
        double r670 = r668 - r669;
        double r671 = sin(r665);
        double r672 = r670 * r671;
        double r673 = r667 - r672;
        double r674 = 3.0;
        double r675 = pow(r669, r674);
        double r676 = cbrt(r675);
        double r677 = r668 - r676;
        double r678 = r677 * r666;
        double r679 = r673 / r678;
        double r680 = r659 + r679;
        return r680;
}

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 13.5

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

  3. Applied tan-quot13.5

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

  4. Applied tan-sum0.2

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

  5. Applied frac-sub0.2

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

  7. Applied add-cbrt-cube0.2

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

  8. Applied add-cbrt-cube0.2

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

  9. Applied cbrt-unprod0.2

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

  10. Simplified0.2

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

  11. Final simplification0.2

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

Reproduce

herbie shell --seed 2020025 +o rules:numerics
(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))))