Average Error: 14.8 → 0.3
Time: 23.0s
Precision: 64
\[r \cdot \frac{\sin b}{\cos \left(a + b\right)}\]
↓
\[\frac{r \cdot \sin b}{\cos a \cdot \cos b - \sin b \cdot \sin a}\]
r \cdot \frac{\sin b}{\cos \left(a + b\right)}
↓
\frac{r \cdot \sin b}{\cos a \cdot \cos b - \sin b \cdot \sin a}
double f(double r, double a, double b) {
        double r1040147 = r;
        double r1040148 = b;
        double r1040149 = sin(r1040148);
        double r1040150 = a;
        double r1040151 = r1040150 + r1040148;
        double r1040152 = cos(r1040151);
        double r1040153 = r1040149 / r1040152;
        double r1040154 = r1040147 * r1040153;
        return r1040154;
}
↓
double f(double r, double a, double b) {
        double r1040155 = r;
        double r1040156 = b;
        double r1040157 = sin(r1040156);
        double r1040158 = r1040155 * r1040157;
        double r1040159 = a;
        double r1040160 = cos(r1040159);
        double r1040161 = cos(r1040156);
        double r1040162 = r1040160 * r1040161;
        double r1040163 = sin(r1040159);
        double r1040164 = r1040157 * r1040163;
        double r1040165 = r1040162 - r1040164;
        double r1040166 = r1040158 / r1040165;
        return r1040166;
}

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 associate-*r/0.3

    \[\leadsto \color{blue}{\frac{r \cdot \sin b}{\cos a \cdot \cos b - \sin a \cdot \sin b}}\]

  6. Final simplification0.3

    \[\leadsto \frac{r \cdot \sin b}{\cos a \cdot \cos b - \sin b \cdot \sin a}\]

Reproduce

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