Average Error: 13.4 → 0.2
Time: 27.2s
Precision: 64
\[\left(x = 0 \lor 0.5884142 \le x \le 505.5909\right) \land \left(-1.796658 \cdot 10^{+308} \le y \le -9.425585 \cdot 10^{-310} \lor 1.284938 \cdot 10^{-309} \le y \le 1.751224 \cdot 10^{+308}\right) \land \left(-1.776707 \cdot 10^{+308} \le z \le -8.599796 \cdot 10^{-310} \lor 3.293145 \cdot 10^{-311} \le z \le 1.725154 \cdot 10^{+308}\right) \land \left(-1.796658 \cdot 10^{+308} \le a \le -9.425585 \cdot 10^{-310} \lor 1.284938 \cdot 10^{-309} \le a \le 1.751224 \cdot 10^{+308}\right)\]
\[x + \left(\tan \left(y + z\right) - \tan a\right)\]
↓
\[\left(\frac{\frac{\left(\tan z + \tan y\right) \cdot \left(\tan y - \tan z\right)}{\tan y - \tan z}}{1 - \sqrt[3]{\left(\tan y \cdot \left(\tan y \cdot \tan y\right)\right) \cdot \left(\tan z \cdot \left(\tan z \cdot \tan z\right)\right)}} - \tan a\right) + x\]
x + \left(\tan \left(y + z\right) - \tan a\right)
↓
\left(\frac{\frac{\left(\tan z + \tan y\right) \cdot \left(\tan y - \tan z\right)}{\tan y - \tan z}}{1 - \sqrt[3]{\left(\tan y \cdot \left(\tan y \cdot \tan y\right)\right) \cdot \left(\tan z \cdot \left(\tan z \cdot \tan z\right)\right)}} - \tan a\right) + x
double f(double x, double y, double z, double a) {
        double r3932078 = x;
        double r3932079 = y;
        double r3932080 = z;
        double r3932081 = r3932079 + r3932080;
        double r3932082 = tan(r3932081);
        double r3932083 = a;
        double r3932084 = tan(r3932083);
        double r3932085 = r3932082 - r3932084;
        double r3932086 = r3932078 + r3932085;
        return r3932086;
}
↓
double f(double x, double y, double z, double a) {
        double r3932087 = z;
        double r3932088 = tan(r3932087);
        double r3932089 = y;
        double r3932090 = tan(r3932089);
        double r3932091 = r3932088 + r3932090;
        double r3932092 = r3932090 - r3932088;
        double r3932093 = r3932091 * r3932092;
        double r3932094 = r3932093 / r3932092;
        double r3932095 = 1.0;
        double r3932096 = r3932090 * r3932090;
        double r3932097 = r3932090 * r3932096;
        double r3932098 = r3932088 * r3932088;
        double r3932099 = r3932088 * r3932098;
        double r3932100 = r3932097 * r3932099;
        double r3932101 = cbrt(r3932100);
        double r3932102 = r3932095 - r3932101;
        double r3932103 = r3932094 / r3932102;
        double r3932104 = a;
        double r3932105 = tan(r3932104);
        double r3932106 = r3932103 - r3932105;
        double r3932107 = x;
        double r3932108 = r3932106 + r3932107;
        return r3932108;
}

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

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

  6. Simplified0.2

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

  8. Applied add-cbrt-cube0.2

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

  9. Applied add-cbrt-cube0.2

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

  10. Applied cbrt-unprod0.2

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

  11. Final simplification0.2

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

Reproduce

herbie shell --seed 2019133 
(FPCore (x y z a)
  :name "(+ x (- (tan (+ y z)) (tan a)))"
  :pre (and (or (== x 0) (<= 0.5884142 x 505.5909)) (or (<= -1.796658e+308 y -9.425585e-310) (<= 1.284938e-309 y 1.751224e+308)) (or (<= -1.776707e+308 z -8.599796e-310) (<= 3.293145e-311 z 1.725154e+308)) (or (<= -1.796658e+308 a -9.425585e-310) (<= 1.284938e-309 a 1.751224e+308)))
  (+ x (- (tan (+ y z)) (tan a))))