Average Error: 13.4 → 0.2
Time: 18.4s
Precision: 64
\[\left(x = 0.0 \lor 0.588414199999999998 \le x \le 505.590899999999976\right) \land \left(-1.79665800000000009 \cdot 10^{308} \le y \le -9.425585000000013 \cdot 10^{-310} \lor 1.284938 \cdot 10^{-309} \le y \le 1.7512240000000001 \cdot 10^{308}\right) \land \left(-1.7767070000000002 \cdot 10^{308} \le z \le -8.59979600000002 \cdot 10^{-310} \lor 3.29314499999998 \cdot 10^{-311} \le z \le 1.72515400000000009 \cdot 10^{308}\right) \land \left(-1.79665800000000009 \cdot 10^{308} \le a \le -9.425585000000013 \cdot 10^{-310} \lor 1.284938 \cdot 10^{-309} \le a \le 1.7512240000000001 \cdot 10^{308}\right)\]
\[x + \left(\tan \left(y + z\right) - \tan a\right)\]
↓
\[x + \frac{\left(\tan y + \tan z\right) \cdot \frac{\frac{\tan y + \tan z}{1 - \tan y \cdot \tan z}}{1 - \tan y \cdot \tan z} - \tan a \cdot \tan a}{\frac{\tan y + \tan z}{1 - \tan y \cdot \tan z} + \tan a}\]
x + \left(\tan \left(y + z\right) - \tan a\right)
↓
x + \frac{\left(\tan y + \tan z\right) \cdot \frac{\frac{\tan y + \tan z}{1 - \tan y \cdot \tan z}}{1 - \tan y \cdot \tan z} - \tan a \cdot \tan a}{\frac{\tan y + \tan z}{1 - \tan y \cdot \tan z} + \tan a}
double f(double x, double y, double z, double a) {
        double r201802 = x;
        double r201803 = y;
        double r201804 = z;
        double r201805 = r201803 + r201804;
        double r201806 = tan(r201805);
        double r201807 = a;
        double r201808 = tan(r201807);
        double r201809 = r201806 - r201808;
        double r201810 = r201802 + r201809;
        return r201810;
}
↓
double f(double x, double y, double z, double a) {
        double r201811 = x;
        double r201812 = y;
        double r201813 = tan(r201812);
        double r201814 = z;
        double r201815 = tan(r201814);
        double r201816 = r201813 + r201815;
        double r201817 = 1.0;
        double r201818 = r201813 * r201815;
        double r201819 = r201817 - r201818;
        double r201820 = r201816 / r201819;
        double r201821 = r201820 / r201819;
        double r201822 = r201816 * r201821;
        double r201823 = a;
        double r201824 = tan(r201823);
        double r201825 = r201824 * r201824;
        double r201826 = r201822 - r201825;
        double r201827 = r201820 + r201824;
        double r201828 = r201826 / r201827;
        double r201829 = r201811 + r201828;
        return r201829;
}

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 13.4

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

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

  7. Applied div-inv0.2

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

  8. Applied associate-*l*0.2

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

  9. Simplified0.2

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

  10. Final simplification0.2

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

Reproduce

herbie shell --seed 2020047 
(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))))