Average Error: 13.2 → 0.2
Time: 1.3m
Precision: 64
\[\left(x = 0 \lor 0.5884142 \le x \le 505.5909\right) \land \left(-1.796658 \cdot 10^{+308} \le y \le -9.425585 \cdot 10^{-310} \lor 1.284938 \cdot 10^{-309} \le y \le 1.751224 \cdot 10^{+308}\right) \land \left(-1.776707 \cdot 10^{+308} \le z \le -8.599796 \cdot 10^{-310} \lor 3.293145 \cdot 10^{-311} \le z \le 1.725154 \cdot 10^{+308}\right) \land \left(-1.796658 \cdot 10^{+308} \le a \le -9.425585 \cdot 10^{-310} \lor 1.284938 \cdot 10^{-309} \le a \le 1.751224 \cdot 10^{+308}\right)\]
\[x + \left(\tan \left(y + z\right) - \tan a\right)\]
↓
\[x + \frac{\cos a \cdot \left(\tan z + \tan y\right) - \left(1 - \tan y \cdot \tan z\right) \cdot \sin a}{\left(1 - \frac{\sqrt[3]{\left(\sin y \cdot \tan z\right) \cdot \left(\left(\sin y \cdot \tan z\right) \cdot \left(\tan y \cdot \tan z\right)\right)}}{\sqrt[3]{\cos y \cdot \cos y}}\right) \cdot \cos a}\]
x + \left(\tan \left(y + z\right) - \tan a\right)
↓
x + \frac{\cos a \cdot \left(\tan z + \tan y\right) - \left(1 - \tan y \cdot \tan z\right) \cdot \sin a}{\left(1 - \frac{\sqrt[3]{\left(\sin y \cdot \tan z\right) \cdot \left(\left(\sin y \cdot \tan z\right) \cdot \left(\tan y \cdot \tan z\right)\right)}}{\sqrt[3]{\cos y \cdot \cos y}}\right) \cdot \cos a}
double f(double x, double y, double z, double a) {
        double r11779640 = x;
        double r11779641 = y;
        double r11779642 = z;
        double r11779643 = r11779641 + r11779642;
        double r11779644 = tan(r11779643);
        double r11779645 = a;
        double r11779646 = tan(r11779645);
        double r11779647 = r11779644 - r11779646;
        double r11779648 = r11779640 + r11779647;
        return r11779648;
}
↓
double f(double x, double y, double z, double a) {
        double r11779649 = x;
        double r11779650 = a;
        double r11779651 = cos(r11779650);
        double r11779652 = z;
        double r11779653 = tan(r11779652);
        double r11779654 = y;
        double r11779655 = tan(r11779654);
        double r11779656 = r11779653 + r11779655;
        double r11779657 = r11779651 * r11779656;
        double r11779658 = 1.0;
        double r11779659 = r11779655 * r11779653;
        double r11779660 = r11779658 - r11779659;
        double r11779661 = sin(r11779650);
        double r11779662 = r11779660 * r11779661;
        double r11779663 = r11779657 - r11779662;
        double r11779664 = sin(r11779654);
        double r11779665 = r11779664 * r11779653;
        double r11779666 = r11779665 * r11779659;
        double r11779667 = r11779665 * r11779666;
        double r11779668 = cbrt(r11779667);
        double r11779669 = cos(r11779654);
        double r11779670 = r11779669 * r11779669;
        double r11779671 = cbrt(r11779670);
        double r11779672 = r11779668 / r11779671;
        double r11779673 = r11779658 - r11779672;
        double r11779674 = r11779673 * r11779651;
        double r11779675 = r11779663 / r11779674;
        double r11779676 = r11779649 + r11779675;
        return r11779676;
}

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 13.2

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

  3. Applied tan-quot13.2

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

  4. Applied +-commutative13.2

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

  5. Applied tan-sum0.2

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

  6. Applied frac-sub0.2

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

  8. Applied add-cbrt-cube0.2

    \[\leadsto x + \frac{\left(\tan z + \tan y\right) \cdot \cos a - \left(1 - \tan z \cdot \tan y\right) \cdot \sin a}{\left(1 - \color{blue}{\sqrt[3]{\left(\left(\tan z \cdot \tan y\right) \cdot \left(\tan z \cdot \tan y\right)\right) \cdot \left(\tan z \cdot \tan y\right)}}\right) \cdot \cos a}\]
  9. Using strategy rm

  10. Applied tan-quot0.2

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

  11. Applied associate-*r/0.2

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

  12. Applied tan-quot0.2

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

  13. Applied associate-*r/0.2

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

  14. Applied associate-*l/0.2

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

  15. Applied frac-times0.2

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

  16. Applied cbrt-div0.2

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

  17. Final simplification0.2

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

Reproduce

herbie shell --seed 2019158 
(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))))