Average Error: 15.3 → 0.4
Time: 6.5s
Precision: 64
\[\frac{r \cdot \sin b}{\cos \left(a + b\right)}\]
↓
\[\frac{r \cdot \sin b}{\cos a \cdot \cos b - \sqrt[3]{{\left(\sin a \cdot \sin b\right)}^{3}}}\]
\frac{r \cdot \sin b}{\cos \left(a + b\right)}
↓
\frac{r \cdot \sin b}{\cos a \cdot \cos b - \sqrt[3]{{\left(\sin a \cdot \sin b\right)}^{3}}}
double f(double r, double a, double b) {
        double r17191 = r;
        double r17192 = b;
        double r17193 = sin(r17192);
        double r17194 = r17191 * r17193;
        double r17195 = a;
        double r17196 = r17195 + r17192;
        double r17197 = cos(r17196);
        double r17198 = r17194 / r17197;
        return r17198;
}
↓
double f(double r, double a, double b) {
        double r17199 = r;
        double r17200 = b;
        double r17201 = sin(r17200);
        double r17202 = r17199 * r17201;
        double r17203 = a;
        double r17204 = cos(r17203);
        double r17205 = cos(r17200);
        double r17206 = r17204 * r17205;
        double r17207 = sin(r17203);
        double r17208 = r17207 * r17201;
        double r17209 = 3.0;
        double r17210 = pow(r17208, r17209);
        double r17211 = cbrt(r17210);
        double r17212 = r17206 - r17211;
        double r17213 = r17202 / r17212;
        return r17213;
}

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-sum0.3

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

  5. Applied add-log-exp0.4

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

  7. Applied add-cbrt-cube0.4

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

  8. Simplified0.4

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

  9. Final simplification0.4

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

Reproduce

herbie shell --seed 2019352 
(FPCore (r a b)
  :name "r*sin(b)/cos(a+b), A"
  :precision binary64
  (/ (* r (sin b)) (cos (+ a b))))