Average Error: 14.7 → 0.4
Time: 24.7s
Precision: 64
\[r \cdot \frac{\sin b}{\cos \left(a + b\right)}\]
↓
\[\frac{\sin b}{\frac{\cos a \cdot \cos b}{r} - \frac{\sin a \cdot \sin b}{r}}\]
r \cdot \frac{\sin b}{\cos \left(a + b\right)}
↓
\frac{\sin b}{\frac{\cos a \cdot \cos b}{r} - \frac{\sin a \cdot \sin b}{r}}
double f(double r, double a, double b) {
        double r738129 = r;
        double r738130 = b;
        double r738131 = sin(r738130);
        double r738132 = a;
        double r738133 = r738132 + r738130;
        double r738134 = cos(r738133);
        double r738135 = r738131 / r738134;
        double r738136 = r738129 * r738135;
        return r738136;
}
↓
double f(double r, double a, double b) {
        double r738137 = b;
        double r738138 = sin(r738137);
        double r738139 = a;
        double r738140 = cos(r738139);
        double r738141 = cos(r738137);
        double r738142 = r738140 * r738141;
        double r738143 = r;
        double r738144 = r738142 / r738143;
        double r738145 = sin(r738139);
        double r738146 = r738145 * r738138;
        double r738147 = r738146 / r738143;
        double r738148 = r738144 - r738147;
        double r738149 = r738138 / r738148;
        return r738149;
}

Error

Bits error versus r

Bits error versus a

Bits error versus b

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Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 14.7

    \[r \cdot \frac{\sin b}{\cos \left(a + b\right)}\]
  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. Taylor expanded around -inf 0.3

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

  6. Applied associate-/l*0.4

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

  8. Applied div-sub0.4

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

  9. Final simplification0.4

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

Reproduce

herbie shell --seed 2019132 
(FPCore (r a b)
  :name "r*sin(b)/cos(a+b), B"
  (* r (/ (sin b) (cos (+ a b)))))