Average Error: 13.5 → 0.2
Time: 18.7s
Precision: 64
\[\left(x = 0.0 \lor 0.588414199999999998 \le x \le 505.590899999999976\right) \land \left(-1.79665800000000009 \cdot 10^{308} \le y \le -9.425585000000013 \cdot 10^{-310} \lor 1.284938 \cdot 10^{-309} \le y \le 1.7512240000000001 \cdot 10^{308}\right) \land \left(-1.7767070000000002 \cdot 10^{308} \le z \le -8.59979600000002 \cdot 10^{-310} \lor 3.29314499999998 \cdot 10^{-311} \le z \le 1.72515400000000009 \cdot 10^{308}\right) \land \left(-1.79665800000000009 \cdot 10^{308} \le a \le -9.425585000000013 \cdot 10^{-310} \lor 1.284938 \cdot 10^{-309} \le a \le 1.7512240000000001 \cdot 10^{308}\right)\]
\[x + \left(\tan \left(y + z\right) - \tan a\right)\]
↓
\[\left(\frac{\tan z + \tan y}{1 - \tan y \cdot \tan z} - \tan a\right) + x\]
x + \left(\tan \left(y + z\right) - \tan a\right)
↓
\left(\frac{\tan z + \tan y}{1 - \tan y \cdot \tan z} - \tan a\right) + x
double f(double x, double y, double z, double a) {
        double r168549 = x;
        double r168550 = y;
        double r168551 = z;
        double r168552 = r168550 + r168551;
        double r168553 = tan(r168552);
        double r168554 = a;
        double r168555 = tan(r168554);
        double r168556 = r168553 - r168555;
        double r168557 = r168549 + r168556;
        return r168557;
}
↓
double f(double x, double y, double z, double a) {
        double r168558 = z;
        double r168559 = tan(r168558);
        double r168560 = y;
        double r168561 = tan(r168560);
        double r168562 = r168559 + r168561;
        double r168563 = 1.0;
        double r168564 = r168561 * r168559;
        double r168565 = r168563 - r168564;
        double r168566 = r168562 / r168565;
        double r168567 = a;
        double r168568 = tan(r168567);
        double r168569 = r168566 - r168568;
        double r168570 = x;
        double r168571 = r168569 + r168570;
        return r168571;
}

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-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 clear-num0.2

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

  7. Applied *-un-lft-identity0.2

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

  8. Applied *-un-lft-identity0.2

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

  9. Applied times-frac0.2

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

  10. Applied add-cube-cbrt0.2

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

  11. Applied times-frac0.2

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

  12. Simplified0.2

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

  13. Simplified0.2

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

  14. Final simplification0.2

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

Reproduce

herbie shell --seed 2020046 +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))))