Average Error: 13.7 → 0.2
Time: 10.9s
Precision: 64
\[\left(x = 0.0 \lor 0.588414199999999998 \le x \le 505.590899999999976\right) \land \left(-1.79665800000000009 \cdot 10^{308} \le y \le -9.425585000000013 \cdot 10^{-310} \lor 1.284938 \cdot 10^{-309} \le y \le 1.7512240000000001 \cdot 10^{308}\right) \land \left(-1.7767070000000002 \cdot 10^{308} \le z \le -8.59979600000002 \cdot 10^{-310} \lor 3.29314499999998 \cdot 10^{-311} \le z \le 1.72515400000000009 \cdot 10^{308}\right) \land \left(-1.79665800000000009 \cdot 10^{308} \le a \le -9.425585000000013 \cdot 10^{-310} \lor 1.284938 \cdot 10^{-309} \le a \le 1.7512240000000001 \cdot 10^{308}\right)\]
\[x + \left(\tan \left(y + z\right) - \tan a\right)\]
↓
\[\left(\frac{\tan y + \tan z}{1 - \tan y \cdot \tan z} + x\right) - \tan a\]
x + \left(\tan \left(y + z\right) - \tan a\right)
↓
\left(\frac{\tan y + \tan z}{1 - \tan y \cdot \tan z} + x\right) - \tan a
double f(double x, double y, double z, double a) {
        double r127811 = x;
        double r127812 = y;
        double r127813 = z;
        double r127814 = r127812 + r127813;
        double r127815 = tan(r127814);
        double r127816 = a;
        double r127817 = tan(r127816);
        double r127818 = r127815 - r127817;
        double r127819 = r127811 + r127818;
        return r127819;
}
↓
double f(double x, double y, double z, double a) {
        double r127820 = y;
        double r127821 = tan(r127820);
        double r127822 = z;
        double r127823 = tan(r127822);
        double r127824 = r127821 + r127823;
        double r127825 = 1.0;
        double r127826 = r127821 * r127823;
        double r127827 = r127825 - r127826;
        double r127828 = r127824 / r127827;
        double r127829 = x;
        double r127830 = r127828 + r127829;
        double r127831 = a;
        double r127832 = tan(r127831);
        double r127833 = r127830 - r127832;
        return r127833;
}

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 13.7

    \[x + \left(\tan \left(y + z\right) - \tan a\right)\]
  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 associate-+r-0.2

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

  7. Applied +-commutative0.2

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

  8. Final simplification0.2

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

Reproduce

herbie shell --seed 2020083 
(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))))