Average Error: 13.0 → 0.2
Time: 30.4s
Precision: 64
\[\left(x = 0 \lor 0.5884142 \le x \le 505.5909\right) \land \left(-1.796658 \cdot 10^{+308} \le y \le -9.425585 \cdot 10^{-310} \lor 1.284938 \cdot 10^{-309} \le y \le 1.751224 \cdot 10^{+308}\right) \land \left(-1.776707 \cdot 10^{+308} \le z \le -8.599796 \cdot 10^{-310} \lor 3.293145 \cdot 10^{-311} \le z \le 1.725154 \cdot 10^{+308}\right) \land \left(-1.796658 \cdot 10^{+308} \le a \le -9.425585 \cdot 10^{-310} \lor 1.284938 \cdot 10^{-309} \le a \le 1.751224 \cdot 10^{+308}\right)\]
\[x + \left(\tan \left(y + z\right) - \tan a\right)\]
↓
\[\left(\frac{\tan y + \tan z}{1 - \tan z \cdot \tan y} - \tan a\right) + x\]
x + \left(\tan \left(y + z\right) - \tan a\right)
↓
\left(\frac{\tan y + \tan z}{1 - \tan z \cdot \tan y} - \tan a\right) + x
double f(double x, double y, double z, double a) {
        double r3726191 = x;
        double r3726192 = y;
        double r3726193 = z;
        double r3726194 = r3726192 + r3726193;
        double r3726195 = tan(r3726194);
        double r3726196 = a;
        double r3726197 = tan(r3726196);
        double r3726198 = r3726195 - r3726197;
        double r3726199 = r3726191 + r3726198;
        return r3726199;
}
↓
double f(double x, double y, double z, double a) {
        double r3726200 = y;
        double r3726201 = tan(r3726200);
        double r3726202 = z;
        double r3726203 = tan(r3726202);
        double r3726204 = r3726201 + r3726203;
        double r3726205 = 1.0;
        double r3726206 = r3726203 * r3726201;
        double r3726207 = r3726205 - r3726206;
        double r3726208 = r3726204 / r3726207;
        double r3726209 = a;
        double r3726210 = tan(r3726209);
        double r3726211 = r3726208 - r3726210;
        double r3726212 = x;
        double r3726213 = r3726211 + r3726212;
        return r3726213;
}

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 13.0

    \[x + \left(\tan \left(y + z\right) - \tan a\right)\]
  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. Final simplification0.2

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

Reproduce

herbie shell --seed 2019132 +o rules:numerics
(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))))