Average Error: 12.9 → 0.2
Time: 39.2s
Precision: 64
\[\left(x = 0 \lor 0.5884142 \le x \le 505.5909\right) \land \left(-1.796658 \cdot 10^{+308} \le y \le -9.425585 \cdot 10^{-310} \lor 1.284938 \cdot 10^{-309} \le y \le 1.751224 \cdot 10^{+308}\right) \land \left(-1.776707 \cdot 10^{+308} \le z \le -8.599796 \cdot 10^{-310} \lor 3.293145 \cdot 10^{-311} \le z \le 1.725154 \cdot 10^{+308}\right) \land \left(-1.796658 \cdot 10^{+308} \le a \le -9.425585 \cdot 10^{-310} \lor 1.284938 \cdot 10^{-309} \le a \le 1.751224 \cdot 10^{+308}\right)\]
\[x + \left(\tan \left(y + z\right) - \tan a\right)\]
↓
\[\frac{\cos a \cdot \left(\tan y + \tan z\right) - \left(1 - \tan z \cdot \tan y\right) \cdot \sin a}{\left(1 - \tan z \cdot \tan y\right) \cdot \cos a} + x\]
x + \left(\tan \left(y + z\right) - \tan a\right)
↓
\frac{\cos a \cdot \left(\tan y + \tan z\right) - \left(1 - \tan z \cdot \tan y\right) \cdot \sin a}{\left(1 - \tan z \cdot \tan y\right) \cdot \cos a} + x
double f(double x, double y, double z, double a) {
        double r5806527 = x;
        double r5806528 = y;
        double r5806529 = z;
        double r5806530 = r5806528 + r5806529;
        double r5806531 = tan(r5806530);
        double r5806532 = a;
        double r5806533 = tan(r5806532);
        double r5806534 = r5806531 - r5806533;
        double r5806535 = r5806527 + r5806534;
        return r5806535;
}
↓
double f(double x, double y, double z, double a) {
        double r5806536 = a;
        double r5806537 = cos(r5806536);
        double r5806538 = y;
        double r5806539 = tan(r5806538);
        double r5806540 = z;
        double r5806541 = tan(r5806540);
        double r5806542 = r5806539 + r5806541;
        double r5806543 = r5806537 * r5806542;
        double r5806544 = 1.0;
        double r5806545 = r5806541 * r5806539;
        double r5806546 = r5806544 - r5806545;
        double r5806547 = sin(r5806536);
        double r5806548 = r5806546 * r5806547;
        double r5806549 = r5806543 - r5806548;
        double r5806550 = r5806546 * r5806537;
        double r5806551 = r5806549 / r5806550;
        double r5806552 = x;
        double r5806553 = r5806551 + r5806552;
        return r5806553;
}

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 12.9

    \[x + \left(\tan \left(y + z\right) - \tan a\right)\]
  2. Using strategy rm

  3. Applied tan-quot12.9

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

  4. Applied tan-sum0.2

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

  5. Applied frac-sub0.2

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

  6. Final simplification0.2

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

Reproduce

herbie shell --seed 2019163 
(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))))