Average Error: 14.6 → 0.4
Time: 30.8s
Precision: 64
\[r \cdot \frac{\sin b}{\cos \left(a + b\right)}\]
↓
\[\frac{1}{\cos b \cdot \cos a - \sin b \cdot \sin a} \cdot \left(r \cdot \sin b\right)\]
r \cdot \frac{\sin b}{\cos \left(a + b\right)}
↓
\frac{1}{\cos b \cdot \cos a - \sin b \cdot \sin a} \cdot \left(r \cdot \sin b\right)
double f(double r, double a, double b) {
        double r847132 = r;
        double r847133 = b;
        double r847134 = sin(r847133);
        double r847135 = a;
        double r847136 = r847135 + r847133;
        double r847137 = cos(r847136);
        double r847138 = r847134 / r847137;
        double r847139 = r847132 * r847138;
        return r847139;
}
↓
double f(double r, double a, double b) {
        double r847140 = 1.0;
        double r847141 = b;
        double r847142 = cos(r847141);
        double r847143 = a;
        double r847144 = cos(r847143);
        double r847145 = r847142 * r847144;
        double r847146 = sin(r847141);
        double r847147 = sin(r847143);
        double r847148 = r847146 * r847147;
        double r847149 = r847145 - r847148;
        double r847150 = r847140 / r847149;
        double r847151 = r;
        double r847152 = r847151 * r847146;
        double r847153 = r847150 * r847152;
        return r847153;
}

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 14.6

    \[r \cdot \frac{\sin b}{\cos \left(a + b\right)}\]
  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 div-inv0.4

    \[\leadsto r \cdot \color{blue}{\left(\sin b \cdot \frac{1}{\cos a \cdot \cos b - \sin a \cdot \sin b}\right)}\]

  6. Applied associate-*r*0.4

    \[\leadsto \color{blue}{\left(r \cdot \sin b\right) \cdot \frac{1}{\cos a \cdot \cos b - \sin a \cdot \sin b}}\]

  7. Final simplification0.4

    \[\leadsto \frac{1}{\cos b \cdot \cos a - \sin b \cdot \sin a} \cdot \left(r \cdot \sin b\right)\]

Reproduce

herbie shell --seed 2019134 
(FPCore (r a b)
  :name "r*sin(b)/cos(a+b), B"
  (* r (/ (sin b) (cos (+ a b)))))