Average Error: 15.3 → 0.4
Time: 51.1s
Precision: 64
\[\frac{r \cdot \sin b}{\cos \left(a + b\right)}\]
↓
\[\frac{r \cdot \sin b}{\cos a \cdot \cos b - \sqrt[3]{\left(\sin b \cdot \sin a\right) \cdot \left(\left(\sin b \cdot \sin a\right) \cdot \left(\sin b \cdot \sin a\right)\right)}}\]
\frac{r \cdot \sin b}{\cos \left(a + b\right)}
↓
\frac{r \cdot \sin b}{\cos a \cdot \cos b - \sqrt[3]{\left(\sin b \cdot \sin a\right) \cdot \left(\left(\sin b \cdot \sin a\right) \cdot \left(\sin b \cdot \sin a\right)\right)}}
double f(double r, double a, double b) {
        double r2135065 = r;
        double r2135066 = b;
        double r2135067 = sin(r2135066);
        double r2135068 = r2135065 * r2135067;
        double r2135069 = a;
        double r2135070 = r2135069 + r2135066;
        double r2135071 = cos(r2135070);
        double r2135072 = r2135068 / r2135071;
        return r2135072;
}
↓
double f(double r, double a, double b) {
        double r2135073 = r;
        double r2135074 = b;
        double r2135075 = sin(r2135074);
        double r2135076 = r2135073 * r2135075;
        double r2135077 = a;
        double r2135078 = cos(r2135077);
        double r2135079 = cos(r2135074);
        double r2135080 = r2135078 * r2135079;
        double r2135081 = sin(r2135077);
        double r2135082 = r2135075 * r2135081;
        double r2135083 = r2135082 * r2135082;
        double r2135084 = r2135082 * r2135083;
        double r2135085 = cbrt(r2135084);
        double r2135086 = r2135080 - r2135085;
        double r2135087 = r2135076 / r2135086;
        return r2135087;
}

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 15.3

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

  3. Applied cos-sum0.4

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

  5. Applied add-cbrt-cube0.4

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

  6. Final simplification0.4

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

Reproduce

herbie shell --seed 2019128 +o rules:numerics
(FPCore (r a b)
  :name "r*sin(b)/cos(a+b), A"
  (/ (* r (sin b)) (cos (+ a b))))