Average Error: 14.8 → 0.4
Time: 22.5s
Precision: 64
\[r \cdot \frac{\sin b}{\cos \left(a + b\right)}\]
↓
\[\frac{\sin b}{\cos a \cdot \cos b - \sqrt[3]{\left(\left(\sin a \cdot \sin b\right) \cdot \left(\sin a \cdot \sin b\right)\right) \cdot \left(\sin a \cdot \sin b\right)}} \cdot r\]
r \cdot \frac{\sin b}{\cos \left(a + b\right)}
↓
\frac{\sin b}{\cos a \cdot \cos b - \sqrt[3]{\left(\left(\sin a \cdot \sin b\right) \cdot \left(\sin a \cdot \sin b\right)\right) \cdot \left(\sin a \cdot \sin b\right)}} \cdot r
double f(double r, double a, double b) {
        double r944180 = r;
        double r944181 = b;
        double r944182 = sin(r944181);
        double r944183 = a;
        double r944184 = r944183 + r944181;
        double r944185 = cos(r944184);
        double r944186 = r944182 / r944185;
        double r944187 = r944180 * r944186;
        return r944187;
}
↓
double f(double r, double a, double b) {
        double r944188 = b;
        double r944189 = sin(r944188);
        double r944190 = a;
        double r944191 = cos(r944190);
        double r944192 = cos(r944188);
        double r944193 = r944191 * r944192;
        double r944194 = sin(r944190);
        double r944195 = r944194 * r944189;
        double r944196 = r944195 * r944195;
        double r944197 = r944196 * r944195;
        double r944198 = cbrt(r944197);
        double r944199 = r944193 - r944198;
        double r944200 = r944189 / r944199;
        double r944201 = r;
        double r944202 = r944200 * r944201;
        return r944202;
}

Error

Bits error versus r

Bits error versus a

Bits error versus b

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 14.8

    \[r \cdot \frac{\sin b}{\cos \left(a + b\right)}\]
  2. Using strategy rm

  3. Applied cos-sum0.3

    \[\leadsto r \cdot \frac{\sin b}{\color{blue}{\cos a \cdot \cos b - \sin a \cdot \sin b}}\]
  4. Using strategy rm

  5. Applied add-cbrt-cube0.4

    \[\leadsto r \cdot \frac{\sin b}{\cos a \cdot \cos b - \color{blue}{\sqrt[3]{\left(\left(\sin a \cdot \sin b\right) \cdot \left(\sin a \cdot \sin b\right)\right) \cdot \left(\sin a \cdot \sin b\right)}}}\]

  6. Final simplification0.4

    \[\leadsto \frac{\sin b}{\cos a \cdot \cos b - \sqrt[3]{\left(\left(\sin a \cdot \sin b\right) \cdot \left(\sin a \cdot \sin b\right)\right) \cdot \left(\sin a \cdot \sin b\right)}} \cdot r\]

Reproduce

herbie shell --seed 2019168 +o rules:numerics
(FPCore (r a b)
  :name "r*sin(b)/cos(a+b), B"
  (* r (/ (sin b) (cos (+ a b)))))