Average Error: 15.2 → 0.4
Time: 1.4m
Precision: 64
\[r \cdot \frac{\sin b}{\cos \left(a + b\right)}\]
↓
\[r \cdot \frac{\sin b}{\frac{{\left(\cos b\right)}^{3} \cdot \left(\cos a \cdot \left(\cos a \cdot \cos a\right)\right) - {\left(\sin a \cdot \sin b\right)}^{3}}{\left(\cos b \cdot \cos a\right) \cdot \left(\cos b \cdot \cos a\right) + \left(\left(\sin a \cdot \sin b\right) \cdot \left(\sin a \cdot \sin b\right) + \left(\cos b \cdot \cos a\right) \cdot \left(\sin a \cdot \sin b\right)\right)}}\]
r \cdot \frac{\sin b}{\cos \left(a + b\right)}
↓
r \cdot \frac{\sin b}{\frac{{\left(\cos b\right)}^{3} \cdot \left(\cos a \cdot \left(\cos a \cdot \cos a\right)\right) - {\left(\sin a \cdot \sin b\right)}^{3}}{\left(\cos b \cdot \cos a\right) \cdot \left(\cos b \cdot \cos a\right) + \left(\left(\sin a \cdot \sin b\right) \cdot \left(\sin a \cdot \sin b\right) + \left(\cos b \cdot \cos a\right) \cdot \left(\sin a \cdot \sin b\right)\right)}}
double f(double r, double a, double b) {
        double r5209168 = r;
        double r5209169 = b;
        double r5209170 = sin(r5209169);
        double r5209171 = a;
        double r5209172 = r5209171 + r5209169;
        double r5209173 = cos(r5209172);
        double r5209174 = r5209170 / r5209173;
        double r5209175 = r5209168 * r5209174;
        return r5209175;
}
↓
double f(double r, double a, double b) {
        double r5209176 = r;
        double r5209177 = b;
        double r5209178 = sin(r5209177);
        double r5209179 = cos(r5209177);
        double r5209180 = 3.0;
        double r5209181 = pow(r5209179, r5209180);
        double r5209182 = a;
        double r5209183 = cos(r5209182);
        double r5209184 = r5209183 * r5209183;
        double r5209185 = r5209183 * r5209184;
        double r5209186 = r5209181 * r5209185;
        double r5209187 = sin(r5209182);
        double r5209188 = r5209187 * r5209178;
        double r5209189 = pow(r5209188, r5209180);
        double r5209190 = r5209186 - r5209189;
        double r5209191 = r5209179 * r5209183;
        double r5209192 = r5209191 * r5209191;
        double r5209193 = r5209188 * r5209188;
        double r5209194 = r5209191 * r5209188;
        double r5209195 = r5209193 + r5209194;
        double r5209196 = r5209192 + r5209195;
        double r5209197 = r5209190 / r5209196;
        double r5209198 = r5209178 / r5209197;
        double r5209199 = r5209176 * r5209198;
        return r5209199;
}

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 15.2

    \[r \cdot \frac{\sin b}{\cos \left(a + b\right)}\]
  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 flip3--0.4

    \[\leadsto r \cdot \frac{\sin b}{\color{blue}{\frac{{\left(\cos a \cdot \cos b\right)}^{3} - {\left(\sin a \cdot \sin b\right)}^{3}}{\left(\cos a \cdot \cos b\right) \cdot \left(\cos a \cdot \cos b\right) + \left(\left(\sin a \cdot \sin b\right) \cdot \left(\sin a \cdot \sin b\right) + \left(\cos a \cdot \cos b\right) \cdot \left(\sin a \cdot \sin b\right)\right)}}}\]
  6. Using strategy rm

  7. Applied cube-prod0.4

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

  8. Simplified0.4

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

  9. Final simplification0.4

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

Reproduce

herbie shell --seed 2019104 
(FPCore (r a b)
  :name "r*sin(b)/cos(a+b), B"
  (* r (/ (sin b) (cos (+ a b)))))